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E-008 — Li coefficients n<=2000 from zero table with tail bounds

08-17-2026 · 2000 rows · script research/numerics/scripts/E-008-li-coefficients.py

Metadata

Li coefficients lambda_n (n<=2000) from E-002 zeros with explicit tail bound; validation vs lambda_1 literature value; leading-asymptotic ratio trend

Validation checks

lambda_1_within_tail_bound PASS
all_positive_in_range PASS
usable_range_at_least_n100 PASS

Key values

lambda_10.022961009776646203
lambda_100117.25678701049617
lambda_10002191.3892531979554
lambda_20004813.526935739563

Parameters

n_max2000
zeros_used10000
H9877.782654005501
precisionfloat64

Caveats

Chart

Data preview (2000 rows total)

nlambda_n_trunctail_boundlambda_over_half_n_log_n
10.022961009780.00053881
20.091806938470.002155240.13244941485069064
30.20642662790.004849290.12526507606054607
40.36663529250.008620960.13223572956501617
50.57217523470.01347020.1422049848148852
60.82271684150.01939720.15305567062901207
71.1178598570.02640170.16413323648684855
81.4571349290.03448380.17518344468412358
91.8400054140.04364360.18609390058540218
102.2658694450.0538810.19681091930016117
112.7340622370.0651960.20730772962145133
123.2438586380.07758860.21757079139798177
133.7944758960.09105890.2275933911665634
144.3850766390.1056070.23737245599476084
155.0147720560.1212320.24690689776885238
165.6826252590.1379350.25619672749715683
176.3876548090.1557160.2652425743617933
187.1288384050.1745740.2740454247458607
197.9051166910.194510.2826064837346345
208.7153972020.2155240.290927105832316
219.5585583870.2376150.2990087649745957
2210.433453740.2607840.3068530466490012
2311.338915950.285030.31446165208036386
2412.273761170.3103550.3218364085460194
2513.236793230.3367560.328979282293977