Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,6,Mod(1,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(5.61343369345\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{65}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 16 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.53113\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 35.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.53113 | −0.624221 | −0.312111 | − | 0.950046i | \(-0.601036\pi\) | ||||
−0.312111 | + | 0.950046i | \(0.601036\pi\) | |||||||
\(3\) | 13.5934 | 0.872016 | 0.436008 | − | 0.899943i | \(-0.356392\pi\) | ||||
0.436008 | + | 0.899943i | \(0.356392\pi\) | |||||||
\(4\) | −19.5311 | −0.610348 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | −48.0000 | −0.544331 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 181.963 | 1.00521 | ||||||||
\(9\) | −58.2198 | −0.239588 | ||||||||
\(10\) | 88.2782 | 0.279160 | ||||||||
\(11\) | −691.520 | −1.72315 | −0.861574 | − | 0.507632i | \(-0.830521\pi\) | ||||
−0.861574 | + | 0.507632i | \(0.830521\pi\) | |||||||
\(12\) | −265.494 | −0.532233 | ||||||||
\(13\) | −502.150 | −0.824091 | −0.412045 | − | 0.911163i | \(-0.635185\pi\) | ||||
−0.412045 | + | 0.911163i | \(0.635185\pi\) | |||||||
\(14\) | 173.025 | 0.235933 | ||||||||
\(15\) | −339.835 | −0.389977 | ||||||||
\(16\) | −17.5389 | −0.0171278 | ||||||||
\(17\) | −991.313 | −0.831934 | −0.415967 | − | 0.909380i | \(-0.636557\pi\) | ||||
−0.415967 | + | 0.909380i | \(0.636557\pi\) | |||||||
\(18\) | 205.582 | 0.149556 | ||||||||
\(19\) | 661.677 | 0.420496 | 0.210248 | − | 0.977648i | \(-0.432573\pi\) | ||||
0.210248 | + | 0.977648i | \(0.432573\pi\) | |||||||
\(20\) | 488.278 | 0.272956 | ||||||||
\(21\) | −666.076 | −0.329591 | ||||||||
\(22\) | 2441.84 | 1.07563 | ||||||||
\(23\) | 3415.08 | 1.34611 | 0.673056 | − | 0.739592i | \(-0.264981\pi\) | ||||
0.673056 | + | 0.739592i | \(0.264981\pi\) | |||||||
\(24\) | 2473.49 | 0.876562 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 1773.16 | 0.514415 | ||||||||
\(27\) | −4094.60 | −1.08094 | ||||||||
\(28\) | 957.025 | 0.230690 | ||||||||
\(29\) | 6751.92 | 1.49084 | 0.745422 | − | 0.666593i | \(-0.232248\pi\) | ||||
0.745422 | + | 0.666593i | \(0.232248\pi\) | |||||||
\(30\) | 1200.00 | 0.243432 | ||||||||
\(31\) | −3922.76 | −0.733142 | −0.366571 | − | 0.930390i | \(-0.619468\pi\) | ||||
−0.366571 | + | 0.930390i | \(0.619468\pi\) | |||||||
\(32\) | −5760.89 | −0.994522 | ||||||||
\(33\) | −9400.09 | −1.50261 | ||||||||
\(34\) | 3500.46 | 0.519311 | ||||||||
\(35\) | 1225.00 | 0.169031 | ||||||||
\(36\) | 1137.10 | 0.146232 | ||||||||
\(37\) | 627.222 | 0.0753212 | 0.0376606 | − | 0.999291i | \(-0.488009\pi\) | ||||
0.0376606 | + | 0.999291i | \(0.488009\pi\) | |||||||
\(38\) | −2336.47 | −0.262483 | ||||||||
\(39\) | −6825.92 | −0.718620 | ||||||||
\(40\) | −4549.08 | −0.449545 | ||||||||
\(41\) | 16277.9 | 1.51230 | 0.756149 | − | 0.654399i | \(-0.227078\pi\) | ||||
0.756149 | + | 0.654399i | \(0.227078\pi\) | |||||||
\(42\) | 2352.00 | 0.205738 | ||||||||
\(43\) | −17277.7 | −1.42500 | −0.712500 | − | 0.701672i | \(-0.752437\pi\) | ||||
−0.712500 | + | 0.701672i | \(0.752437\pi\) | |||||||
\(44\) | 13506.2 | 1.05172 | ||||||||
\(45\) | 1455.50 | 0.107147 | ||||||||
\(46\) | −12059.1 | −0.840272 | ||||||||
\(47\) | −4295.47 | −0.283639 | −0.141820 | − | 0.989893i | \(-0.545295\pi\) | ||||
−0.141820 | + | 0.989893i | \(0.545295\pi\) | |||||||
\(48\) | −238.413 | −0.0149357 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | −2206.96 | −0.124844 | ||||||||
\(51\) | −13475.3 | −0.725460 | ||||||||
\(52\) | 9807.55 | 0.502982 | ||||||||
\(53\) | −25960.9 | −1.26949 | −0.634745 | − | 0.772721i | \(-0.718895\pi\) | ||||
−0.634745 | + | 0.772721i | \(0.718895\pi\) | |||||||
\(54\) | 14458.6 | 0.674746 | ||||||||
\(55\) | 17288.0 | 0.770615 | ||||||||
\(56\) | −8916.19 | −0.379935 | ||||||||
\(57\) | 8994.43 | 0.366679 | ||||||||
\(58\) | −23841.9 | −0.930616 | ||||||||
\(59\) | 8902.63 | 0.332957 | 0.166479 | − | 0.986045i | \(-0.446760\pi\) | ||||
0.166479 | + | 0.986045i | \(0.446760\pi\) | |||||||
\(60\) | 6637.35 | 0.238022 | ||||||||
\(61\) | −48924.6 | −1.68346 | −0.841730 | − | 0.539898i | \(-0.818463\pi\) | ||||
−0.841730 | + | 0.539898i | \(0.818463\pi\) | |||||||
\(62\) | 13851.8 | 0.457643 | ||||||||
\(63\) | 2852.77 | 0.0905557 | ||||||||
\(64\) | 20903.7 | 0.637930 | ||||||||
\(65\) | 12553.7 | 0.368545 | ||||||||
\(66\) | 33192.9 | 0.937963 | ||||||||
\(67\) | −4257.80 | −0.115877 | −0.0579387 | − | 0.998320i | \(-0.518453\pi\) | ||||
−0.0579387 | + | 0.998320i | \(0.518453\pi\) | |||||||
\(68\) | 19361.5 | 0.507769 | ||||||||
\(69\) | 46422.5 | 1.17383 | ||||||||
\(70\) | −4325.63 | −0.105513 | ||||||||
\(71\) | 18990.9 | 0.447095 | 0.223547 | − | 0.974693i | \(-0.428236\pi\) | ||||
0.223547 | + | 0.974693i | \(0.428236\pi\) | |||||||
\(72\) | −10593.9 | −0.240837 | ||||||||
\(73\) | 10132.5 | 0.222541 | 0.111270 | − | 0.993790i | \(-0.464508\pi\) | ||||
0.111270 | + | 0.993790i | \(0.464508\pi\) | |||||||
\(74\) | −2214.80 | −0.0470171 | ||||||||
\(75\) | 8495.87 | 0.174403 | ||||||||
\(76\) | −12923.3 | −0.256649 | ||||||||
\(77\) | 33884.5 | 0.651289 | ||||||||
\(78\) | 24103.2 | 0.448578 | ||||||||
\(79\) | −96986.5 | −1.74841 | −0.874205 | − | 0.485557i | \(-0.838617\pi\) | ||||
−0.874205 | + | 0.485557i | \(0.838617\pi\) | |||||||
\(80\) | 438.472 | 0.00765979 | ||||||||
\(81\) | −41512.0 | −0.703010 | ||||||||
\(82\) | −57479.2 | −0.944009 | ||||||||
\(83\) | 70732.1 | 1.12699 | 0.563497 | − | 0.826118i | \(-0.309456\pi\) | ||||
0.563497 | + | 0.826118i | \(0.309456\pi\) | |||||||
\(84\) | 13009.2 | 0.201165 | ||||||||
\(85\) | 24782.8 | 0.372052 | ||||||||
\(86\) | 61009.8 | 0.889515 | ||||||||
\(87\) | 91781.4 | 1.30004 | ||||||||
\(88\) | −125831. | −1.73213 | ||||||||
\(89\) | 4241.12 | 0.0567552 | 0.0283776 | − | 0.999597i | \(-0.490966\pi\) | ||||
0.0283776 | + | 0.999597i | \(0.490966\pi\) | |||||||
\(90\) | −5139.54 | −0.0668834 | ||||||||
\(91\) | 24605.3 | 0.311477 | ||||||||
\(92\) | −66700.3 | −0.821596 | ||||||||
\(93\) | −53323.6 | −0.639311 | ||||||||
\(94\) | 15167.9 | 0.177054 | ||||||||
\(95\) | −16541.9 | −0.188052 | ||||||||
\(96\) | −78309.9 | −0.867239 | ||||||||
\(97\) | −104376. | −1.12634 | −0.563170 | − | 0.826341i | \(-0.690418\pi\) | ||||
−0.563170 | + | 0.826341i | \(0.690418\pi\) | |||||||
\(98\) | −8478.24 | −0.0891745 | ||||||||
\(99\) | 40260.2 | 0.412845 | ||||||||
\(100\) | −12207.0 | −0.122070 | ||||||||
\(101\) | −45715.1 | −0.445919 | −0.222959 | − | 0.974828i | \(-0.571572\pi\) | ||||
−0.222959 | + | 0.974828i | \(0.571572\pi\) | |||||||
\(102\) | 47583.0 | 0.452847 | ||||||||
\(103\) | 89278.1 | 0.829186 | 0.414593 | − | 0.910007i | \(-0.363924\pi\) | ||||
0.414593 | + | 0.910007i | \(0.363924\pi\) | |||||||
\(104\) | −91372.7 | −0.828387 | ||||||||
\(105\) | 16651.9 | 0.147398 | ||||||||
\(106\) | 91671.2 | 0.792443 | ||||||||
\(107\) | −106330. | −0.897834 | −0.448917 | − | 0.893573i | \(-0.648190\pi\) | ||||
−0.448917 | + | 0.893573i | \(0.648190\pi\) | |||||||
\(108\) | 79972.1 | 0.659750 | ||||||||
\(109\) | −49816.5 | −0.401613 | −0.200806 | − | 0.979631i | \(-0.564356\pi\) | ||||
−0.200806 | + | 0.979631i | \(0.564356\pi\) | |||||||
\(110\) | −61046.1 | −0.481035 | ||||||||
\(111\) | 8526.08 | 0.0656813 | ||||||||
\(112\) | 859.405 | 0.00647370 | ||||||||
\(113\) | −37160.7 | −0.273771 | −0.136886 | − | 0.990587i | \(-0.543709\pi\) | ||||
−0.136886 | + | 0.990587i | \(0.543709\pi\) | |||||||
\(114\) | −31760.5 | −0.228889 | ||||||||
\(115\) | −85377.0 | −0.601999 | ||||||||
\(116\) | −131873. | −0.909933 | ||||||||
\(117\) | 29235.1 | 0.197442 | ||||||||
\(118\) | −31436.3 | −0.207839 | ||||||||
\(119\) | 48574.4 | 0.314441 | ||||||||
\(120\) | −61837.4 | −0.392011 | ||||||||
\(121\) | 317148. | 1.96924 | ||||||||
\(122\) | 172759. | 1.05085 | ||||||||
\(123\) | 221271. | 1.31875 | ||||||||
\(124\) | 76616.0 | 0.447471 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | −10073.5 | −0.0565268 | ||||||||
\(127\) | −46510.2 | −0.255882 | −0.127941 | − | 0.991782i | \(-0.540837\pi\) | ||||
−0.127941 | + | 0.991782i | \(0.540837\pi\) | |||||||
\(128\) | 110535. | 0.596313 | ||||||||
\(129\) | −234862. | −1.24262 | ||||||||
\(130\) | −44328.9 | −0.230053 | ||||||||
\(131\) | 381771. | 1.94368 | 0.971839 | − | 0.235646i | \(-0.0757206\pi\) | ||||
0.971839 | + | 0.235646i | \(0.0757206\pi\) | |||||||
\(132\) | 183594. | 0.917117 | ||||||||
\(133\) | −32422.2 | −0.158933 | ||||||||
\(134\) | 15034.9 | 0.0723331 | ||||||||
\(135\) | 102365. | 0.483411 | ||||||||
\(136\) | −180382. | −0.836271 | ||||||||
\(137\) | −1894.54 | −0.00862389 | −0.00431194 | − | 0.999991i | \(-0.501373\pi\) | ||||
−0.00431194 | + | 0.999991i | \(0.501373\pi\) | |||||||
\(138\) | −163924. | −0.732730 | ||||||||
\(139\) | 201798. | 0.885889 | 0.442944 | − | 0.896549i | \(-0.353934\pi\) | ||||
0.442944 | + | 0.896549i | \(0.353934\pi\) | |||||||
\(140\) | −23925.6 | −0.103168 | ||||||||
\(141\) | −58390.0 | −0.247338 | ||||||||
\(142\) | −67059.3 | −0.279086 | ||||||||
\(143\) | 347246. | 1.42003 | ||||||||
\(144\) | 1021.11 | 0.00410362 | ||||||||
\(145\) | −168798. | −0.666726 | ||||||||
\(146\) | −35779.1 | −0.138915 | ||||||||
\(147\) | 32637.7 | 0.124574 | ||||||||
\(148\) | −12250.4 | −0.0459721 | ||||||||
\(149\) | −466237. | −1.72045 | −0.860224 | − | 0.509917i | \(-0.829676\pi\) | ||||
−0.860224 | + | 0.509917i | \(0.829676\pi\) | |||||||
\(150\) | −30000.0 | −0.108866 | ||||||||
\(151\) | −122212. | −0.436185 | −0.218093 | − | 0.975928i | \(-0.569983\pi\) | ||||
−0.218093 | + | 0.975928i | \(0.569983\pi\) | |||||||
\(152\) | 120401. | 0.422688 | ||||||||
\(153\) | 57714.1 | 0.199321 | ||||||||
\(154\) | −119650. | −0.406548 | ||||||||
\(155\) | 98069.1 | 0.327871 | ||||||||
\(156\) | 133318. | 0.438608 | ||||||||
\(157\) | −410638. | −1.32957 | −0.664784 | − | 0.747036i | \(-0.731476\pi\) | ||||
−0.664784 | + | 0.747036i | \(0.731476\pi\) | |||||||
\(158\) | 342472. | 1.09139 | ||||||||
\(159\) | −352896. | −1.10702 | ||||||||
\(160\) | 144022. | 0.444764 | ||||||||
\(161\) | −167339. | −0.508782 | ||||||||
\(162\) | 146584. | 0.438834 | ||||||||
\(163\) | 78525.4 | 0.231495 | 0.115747 | − | 0.993279i | \(-0.463074\pi\) | ||||
0.115747 | + | 0.993279i | \(0.463074\pi\) | |||||||
\(164\) | −317925. | −0.923028 | ||||||||
\(165\) | 235002. | 0.671989 | ||||||||
\(166\) | −249764. | −0.703494 | ||||||||
\(167\) | −597714. | −1.65845 | −0.829224 | − | 0.558916i | \(-0.811217\pi\) | ||||
−0.829224 | + | 0.558916i | \(0.811217\pi\) | |||||||
\(168\) | −121201. | −0.331309 | ||||||||
\(169\) | −119139. | −0.320875 | ||||||||
\(170\) | −87511.4 | −0.232243 | ||||||||
\(171\) | −38522.7 | −0.100746 | ||||||||
\(172\) | 337453. | 0.869745 | ||||||||
\(173\) | −59874.0 | −0.152098 | −0.0760490 | − | 0.997104i | \(-0.524231\pi\) | ||||
−0.0760490 | + | 0.997104i | \(0.524231\pi\) | |||||||
\(174\) | −324092. | −0.811512 | ||||||||
\(175\) | −30625.0 | −0.0755929 | ||||||||
\(176\) | 12128.5 | 0.0295138 | ||||||||
\(177\) | 121017. | 0.290344 | ||||||||
\(178\) | −14975.9 | −0.0354278 | ||||||||
\(179\) | 616812. | 1.43887 | 0.719433 | − | 0.694562i | \(-0.244402\pi\) | ||||
0.719433 | + | 0.694562i | \(0.244402\pi\) | |||||||
\(180\) | −28427.5 | −0.0653969 | ||||||||
\(181\) | −37287.0 | −0.0845981 | −0.0422990 | − | 0.999105i | \(-0.513468\pi\) | ||||
−0.0422990 | + | 0.999105i | \(0.513468\pi\) | |||||||
\(182\) | −86884.6 | −0.194431 | ||||||||
\(183\) | −665051. | −1.46800 | ||||||||
\(184\) | 621418. | 1.35313 | ||||||||
\(185\) | −15680.6 | −0.0336847 | ||||||||
\(186\) | 188293. | 0.399072 | ||||||||
\(187\) | 685513. | 1.43355 | ||||||||
\(188\) | 83895.4 | 0.173119 | ||||||||
\(189\) | 200635. | 0.408557 | ||||||||
\(190\) | 58411.7 | 0.117386 | ||||||||
\(191\) | 326760. | 0.648106 | 0.324053 | − | 0.946039i | \(-0.394954\pi\) | ||||
0.324053 | + | 0.946039i | \(0.394954\pi\) | |||||||
\(192\) | 284152. | 0.556285 | ||||||||
\(193\) | −265735. | −0.513518 | −0.256759 | − | 0.966475i | \(-0.582655\pi\) | ||||
−0.256759 | + | 0.966475i | \(0.582655\pi\) | |||||||
\(194\) | 368563. | 0.703085 | ||||||||
\(195\) | 170648. | 0.321377 | ||||||||
\(196\) | −46894.2 | −0.0871925 | ||||||||
\(197\) | −517865. | −0.950716 | −0.475358 | − | 0.879792i | \(-0.657682\pi\) | ||||
−0.475358 | + | 0.879792i | \(0.657682\pi\) | |||||||
\(198\) | −142164. | −0.257707 | ||||||||
\(199\) | −148687. | −0.266158 | −0.133079 | − | 0.991105i | \(-0.542486\pi\) | ||||
−0.133079 | + | 0.991105i | \(0.542486\pi\) | |||||||
\(200\) | 113727. | 0.201043 | ||||||||
\(201\) | −57878.0 | −0.101047 | ||||||||
\(202\) | 161426. | 0.278352 | ||||||||
\(203\) | −330844. | −0.563486 | ||||||||
\(204\) | 263188. | 0.442783 | ||||||||
\(205\) | −406946. | −0.676320 | ||||||||
\(206\) | −315252. | −0.517595 | ||||||||
\(207\) | −198825. | −0.322512 | ||||||||
\(208\) | 8807.15 | 0.0141149 | ||||||||
\(209\) | −457563. | −0.724577 | ||||||||
\(210\) | −58800.0 | −0.0920087 | ||||||||
\(211\) | 7443.09 | 0.0115093 | 0.00575463 | − | 0.999983i | \(-0.498168\pi\) | ||||
0.00575463 | + | 0.999983i | \(0.498168\pi\) | |||||||
\(212\) | 507045. | 0.774831 | ||||||||
\(213\) | 258151. | 0.389874 | ||||||||
\(214\) | 375465. | 0.560447 | ||||||||
\(215\) | 431943. | 0.637279 | ||||||||
\(216\) | −745066. | −1.08658 | ||||||||
\(217\) | 192215. | 0.277101 | ||||||||
\(218\) | 175909. | 0.250695 | ||||||||
\(219\) | 137735. | 0.194059 | ||||||||
\(220\) | −337654. | −0.470343 | ||||||||
\(221\) | 497788. | 0.685589 | ||||||||
\(222\) | −30106.7 | −0.0409997 | ||||||||
\(223\) | 119157. | 0.160456 | 0.0802280 | − | 0.996777i | \(-0.474435\pi\) | ||||
0.0802280 | + | 0.996777i | \(0.474435\pi\) | |||||||
\(224\) | 282283. | 0.375894 | ||||||||
\(225\) | −36387.4 | −0.0479176 | ||||||||
\(226\) | 131219. | 0.170894 | ||||||||
\(227\) | −388843. | −0.500852 | −0.250426 | − | 0.968136i | \(-0.580571\pi\) | ||||
−0.250426 | + | 0.968136i | \(0.580571\pi\) | |||||||
\(228\) | −175671. | −0.223802 | ||||||||
\(229\) | 732622. | 0.923191 | 0.461595 | − | 0.887091i | \(-0.347277\pi\) | ||||
0.461595 | + | 0.887091i | \(0.347277\pi\) | |||||||
\(230\) | 301477. | 0.375781 | ||||||||
\(231\) | 460605. | 0.567934 | ||||||||
\(232\) | 1.22860e6 | 1.49862 | ||||||||
\(233\) | −1.12639e6 | −1.35925 | −0.679626 | − | 0.733559i | \(-0.737858\pi\) | ||||
−0.679626 | + | 0.733559i | \(0.737858\pi\) | |||||||
\(234\) | −103233. | −0.123248 | ||||||||
\(235\) | 107387. | 0.126847 | ||||||||
\(236\) | −173878. | −0.203220 | ||||||||
\(237\) | −1.31837e6 | −1.52464 | ||||||||
\(238\) | −171522. | −0.196281 | ||||||||
\(239\) | 772317. | 0.874583 | 0.437292 | − | 0.899320i | \(-0.355938\pi\) | ||||
0.437292 | + | 0.899320i | \(0.355938\pi\) | |||||||
\(240\) | 5960.32 | 0.00667946 | ||||||||
\(241\) | 1.40297e6 | 1.55598 | 0.777991 | − | 0.628275i | \(-0.216239\pi\) | ||||
0.777991 | + | 0.628275i | \(0.216239\pi\) | |||||||
\(242\) | −1.11989e6 | −1.22924 | ||||||||
\(243\) | 430698. | 0.467905 | ||||||||
\(244\) | 955553. | 1.02750 | ||||||||
\(245\) | −60025.0 | −0.0638877 | ||||||||
\(246\) | −781337. | −0.823191 | ||||||||
\(247\) | −332261. | −0.346527 | ||||||||
\(248\) | −713798. | −0.736964 | ||||||||
\(249\) | 961489. | 0.982757 | ||||||||
\(250\) | 55173.9 | 0.0558320 | ||||||||
\(251\) | −1.63922e6 | −1.64230 | −0.821151 | − | 0.570712i | \(-0.806667\pi\) | ||||
−0.821151 | + | 0.570712i | \(0.806667\pi\) | |||||||
\(252\) | −55717.9 | −0.0552705 | ||||||||
\(253\) | −2.36159e6 | −2.31955 | ||||||||
\(254\) | 164234. | 0.159727 | ||||||||
\(255\) | 336883. | 0.324435 | ||||||||
\(256\) | −1.05923e6 | −1.01016 | ||||||||
\(257\) | −223664. | −0.211234 | −0.105617 | − | 0.994407i | \(-0.533682\pi\) | ||||
−0.105617 | + | 0.994407i | \(0.533682\pi\) | |||||||
\(258\) | 829330. | 0.775672 | ||||||||
\(259\) | −30733.9 | −0.0284687 | ||||||||
\(260\) | −245189. | −0.224940 | ||||||||
\(261\) | −393096. | −0.357188 | ||||||||
\(262\) | −1.34808e6 | −1.21329 | ||||||||
\(263\) | 299519. | 0.267014 | 0.133507 | − | 0.991048i | \(-0.457376\pi\) | ||||
0.133507 | + | 0.991048i | \(0.457376\pi\) | |||||||
\(264\) | −1.71047e6 | −1.51045 | ||||||||
\(265\) | 649022. | 0.567734 | ||||||||
\(266\) | 114487. | 0.0992091 | ||||||||
\(267\) | 57651.2 | 0.0494914 | ||||||||
\(268\) | 83159.7 | 0.0707255 | ||||||||
\(269\) | 134341. | 0.113195 | 0.0565974 | − | 0.998397i | \(-0.481975\pi\) | ||||
0.0565974 | + | 0.998397i | \(0.481975\pi\) | |||||||
\(270\) | −361464. | −0.301756 | ||||||||
\(271\) | 1.93414e6 | 1.59980 | 0.799898 | − | 0.600136i | \(-0.204887\pi\) | ||||
0.799898 | + | 0.600136i | \(0.204887\pi\) | |||||||
\(272\) | 17386.5 | 0.0142492 | ||||||||
\(273\) | 334470. | 0.271613 | ||||||||
\(274\) | 6689.88 | 0.00538321 | ||||||||
\(275\) | −432200. | −0.344630 | ||||||||
\(276\) | −906683. | −0.716445 | ||||||||
\(277\) | 177599. | 0.139072 | 0.0695362 | − | 0.997579i | \(-0.477848\pi\) | ||||
0.0695362 | + | 0.997579i | \(0.477848\pi\) | |||||||
\(278\) | −712574. | −0.552991 | ||||||||
\(279\) | 228383. | 0.175652 | ||||||||
\(280\) | 222905. | 0.169912 | ||||||||
\(281\) | 1.85131e6 | 1.39867 | 0.699333 | − | 0.714796i | \(-0.253481\pi\) | ||||
0.699333 | + | 0.714796i | \(0.253481\pi\) | |||||||
\(282\) | 206183. | 0.154394 | ||||||||
\(283\) | 2.39851e6 | 1.78023 | 0.890114 | − | 0.455737i | \(-0.150624\pi\) | ||||
0.890114 | + | 0.455737i | \(0.150624\pi\) | |||||||
\(284\) | −370914. | −0.272883 | ||||||||
\(285\) | −224861. | −0.163984 | ||||||||
\(286\) | −1.22617e6 | −0.886413 | ||||||||
\(287\) | −797615. | −0.571595 | ||||||||
\(288\) | 335398. | 0.238275 | ||||||||
\(289\) | −437155. | −0.307887 | ||||||||
\(290\) | 596047. | 0.416184 | ||||||||
\(291\) | −1.41882e6 | −0.982186 | ||||||||
\(292\) | −197899. | −0.135827 | ||||||||
\(293\) | 2.49922e6 | 1.70073 | 0.850364 | − | 0.526196i | \(-0.176382\pi\) | ||||
0.850364 | + | 0.526196i | \(0.176382\pi\) | |||||||
\(294\) | −115248. | −0.0777616 | ||||||||
\(295\) | −222566. | −0.148903 | ||||||||
\(296\) | 114131. | 0.0757139 | ||||||||
\(297\) | 2.83149e6 | 1.86262 | ||||||||
\(298\) | 1.64634e6 | 1.07394 | ||||||||
\(299\) | −1.71488e6 | −1.10932 | ||||||||
\(300\) | −165934. | −0.106447 | ||||||||
\(301\) | 846607. | 0.538599 | ||||||||
\(302\) | 431546. | 0.272276 | ||||||||
\(303\) | −621422. | −0.388848 | ||||||||
\(304\) | −11605.1 | −0.00720218 | ||||||||
\(305\) | 1.22312e6 | 0.752866 | ||||||||
\(306\) | −203796. | −0.124421 | ||||||||
\(307\) | 3.07195e6 | 1.86024 | 0.930119 | − | 0.367258i | \(-0.119703\pi\) | ||||
0.930119 | + | 0.367258i | \(0.119703\pi\) | |||||||
\(308\) | −661802. | −0.397513 | ||||||||
\(309\) | 1.21359e6 | 0.723063 | ||||||||
\(310\) | −346295. | −0.204664 | ||||||||
\(311\) | 661233. | 0.387662 | 0.193831 | − | 0.981035i | \(-0.437909\pi\) | ||||
0.193831 | + | 0.981035i | \(0.437909\pi\) | |||||||
\(312\) | −1.24206e6 | −0.722367 | ||||||||
\(313\) | −3.29393e6 | −1.90043 | −0.950217 | − | 0.311588i | \(-0.899139\pi\) | ||||
−0.950217 | + | 0.311588i | \(0.899139\pi\) | |||||||
\(314\) | 1.45002e6 | 0.829944 | ||||||||
\(315\) | −71319.3 | −0.0404977 | ||||||||
\(316\) | 1.89426e6 | 1.06714 | ||||||||
\(317\) | 639724. | 0.357556 | 0.178778 | − | 0.983889i | \(-0.442786\pi\) | ||||
0.178778 | + | 0.983889i | \(0.442786\pi\) | |||||||
\(318\) | 1.24612e6 | 0.691023 | ||||||||
\(319\) | −4.66908e6 | −2.56894 | ||||||||
\(320\) | −522592. | −0.285291 | ||||||||
\(321\) | −1.44538e6 | −0.782926 | ||||||||
\(322\) | 590895. | 0.317593 | ||||||||
\(323\) | −655929. | −0.349825 | ||||||||
\(324\) | 810777. | 0.429081 | ||||||||
\(325\) | −313844. | −0.164818 | ||||||||
\(326\) | −277283. | −0.144504 | ||||||||
\(327\) | −677175. | −0.350213 | ||||||||
\(328\) | 2.96197e6 | 1.52018 | ||||||||
\(329\) | 210478. | 0.107206 | ||||||||
\(330\) | −829823. | −0.419470 | ||||||||
\(331\) | −1.13876e6 | −0.571298 | −0.285649 | − | 0.958334i | \(-0.592209\pi\) | ||||
−0.285649 | + | 0.958334i | \(0.592209\pi\) | |||||||
\(332\) | −1.38148e6 | −0.687858 | ||||||||
\(333\) | −36516.8 | −0.0180460 | ||||||||
\(334\) | 2.11060e6 | 1.03524 | ||||||||
\(335\) | 106445. | 0.0518219 | ||||||||
\(336\) | 11682.2 | 0.00564518 | ||||||||
\(337\) | 685493. | 0.328797 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(338\) | 420694. | 0.200297 | ||||||||
\(339\) | −505140. | −0.238733 | ||||||||
\(340\) | −484037. | −0.227081 | ||||||||
\(341\) | 2.71267e6 | 1.26331 | ||||||||
\(342\) | 136029. | 0.0628877 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | −3.14390e6 | −1.43243 | ||||||||
\(345\) | −1.16056e6 | −0.524953 | ||||||||
\(346\) | 211423. | 0.0949428 | ||||||||
\(347\) | −1.25151e6 | −0.557970 | −0.278985 | − | 0.960295i | \(-0.589998\pi\) | ||||
−0.278985 | + | 0.960295i | \(0.589998\pi\) | |||||||
\(348\) | −1.79259e6 | −0.793476 | ||||||||
\(349\) | −3.16606e6 | −1.39141 | −0.695706 | − | 0.718327i | \(-0.744908\pi\) | ||||
−0.695706 | + | 0.718327i | \(0.744908\pi\) | |||||||
\(350\) | 108141. | 0.0471867 | ||||||||
\(351\) | 2.05610e6 | 0.890793 | ||||||||
\(352\) | 3.98376e6 | 1.71371 | ||||||||
\(353\) | −2.43368e6 | −1.03951 | −0.519754 | − | 0.854316i | \(-0.673976\pi\) | ||||
−0.519754 | + | 0.854316i | \(0.673976\pi\) | |||||||
\(354\) | −427326. | −0.181239 | ||||||||
\(355\) | −474772. | −0.199947 | ||||||||
\(356\) | −82833.8 | −0.0346404 | ||||||||
\(357\) | 660290. | 0.274198 | ||||||||
\(358\) | −2.17804e6 | −0.898171 | ||||||||
\(359\) | −2.13021e6 | −0.872341 | −0.436170 | − | 0.899864i | \(-0.643665\pi\) | ||||
−0.436170 | + | 0.899864i | \(0.643665\pi\) | |||||||
\(360\) | 264847. | 0.107706 | ||||||||
\(361\) | −2.03828e6 | −0.823183 | ||||||||
\(362\) | 131665. | 0.0528079 | ||||||||
\(363\) | 4.31112e6 | 1.71721 | ||||||||
\(364\) | −480570. | −0.190109 | ||||||||
\(365\) | −253312. | −0.0995232 | ||||||||
\(366\) | 2.34838e6 | 0.916360 | ||||||||
\(367\) | −3.10976e6 | −1.20521 | −0.602604 | − | 0.798041i | \(-0.705870\pi\) | ||||
−0.602604 | + | 0.798041i | \(0.705870\pi\) | |||||||
\(368\) | −59896.7 | −0.0230559 | ||||||||
\(369\) | −947694. | −0.362328 | ||||||||
\(370\) | 55370.1 | 0.0210267 | ||||||||
\(371\) | 1.27208e6 | 0.479822 | ||||||||
\(372\) | 1.04147e6 | 0.390202 | ||||||||
\(373\) | −3.15189e6 | −1.17300 | −0.586502 | − | 0.809948i | \(-0.699495\pi\) | ||||
−0.586502 | + | 0.809948i | \(0.699495\pi\) | |||||||
\(374\) | −2.42063e6 | −0.894849 | ||||||||
\(375\) | −212397. | −0.0779955 | ||||||||
\(376\) | −781617. | −0.285118 | ||||||||
\(377\) | −3.39047e6 | −1.22859 | ||||||||
\(378\) | −708469. | −0.255030 | ||||||||
\(379\) | 342350. | 0.122426 | 0.0612129 | − | 0.998125i | \(-0.480503\pi\) | ||||
0.0612129 | + | 0.998125i | \(0.480503\pi\) | |||||||
\(380\) | 323083. | 0.114777 | ||||||||
\(381\) | −632231. | −0.223133 | ||||||||
\(382\) | −1.15383e6 | −0.404562 | ||||||||
\(383\) | 3.69387e6 | 1.28672 | 0.643361 | − | 0.765563i | \(-0.277539\pi\) | ||||
0.643361 | + | 0.765563i | \(0.277539\pi\) | |||||||
\(384\) | 1.50254e6 | 0.519994 | ||||||||
\(385\) | −847111. | −0.291265 | ||||||||
\(386\) | 938345. | 0.320549 | ||||||||
\(387\) | 1.00590e6 | 0.341413 | ||||||||
\(388\) | 2.03857e6 | 0.687459 | ||||||||
\(389\) | 2.05313e6 | 0.687928 | 0.343964 | − | 0.938983i | \(-0.388230\pi\) | ||||
0.343964 | + | 0.938983i | \(0.388230\pi\) | |||||||
\(390\) | −602580. | −0.200610 | ||||||||
\(391\) | −3.38541e6 | −1.11988 | ||||||||
\(392\) | 436893. | 0.143602 | ||||||||
\(393\) | 5.18956e6 | 1.69492 | ||||||||
\(394\) | 1.82865e6 | 0.593457 | ||||||||
\(395\) | 2.42466e6 | 0.781913 | ||||||||
\(396\) | −786326. | −0.251979 | ||||||||
\(397\) | −2.28107e6 | −0.726377 | −0.363189 | − | 0.931716i | \(-0.618312\pi\) | ||||
−0.363189 | + | 0.931716i | \(0.618312\pi\) | |||||||
\(398\) | 525031. | 0.166141 | ||||||||
\(399\) | −440727. | −0.138592 | ||||||||
\(400\) | −10961.8 | −0.00342556 | ||||||||
\(401\) | 3.32082e6 | 1.03130 | 0.515649 | − | 0.856800i | \(-0.327551\pi\) | ||||
0.515649 | + | 0.856800i | \(0.327551\pi\) | |||||||
\(402\) | 204375. | 0.0630756 | ||||||||
\(403\) | 1.96981e6 | 0.604175 | ||||||||
\(404\) | 892867. | 0.272166 | ||||||||
\(405\) | 1.03780e6 | 0.314396 | ||||||||
\(406\) | 1.16825e6 | 0.351740 | ||||||||
\(407\) | −433737. | −0.129790 | ||||||||
\(408\) | −2.45201e6 | −0.729242 | ||||||||
\(409\) | 5.15938e6 | 1.52507 | 0.762534 | − | 0.646948i | \(-0.223955\pi\) | ||||
0.762534 | + | 0.646948i | \(0.223955\pi\) | |||||||
\(410\) | 1.43698e6 | 0.422174 | ||||||||
\(411\) | −25753.3 | −0.00752017 | ||||||||
\(412\) | −1.74370e6 | −0.506092 | ||||||||
\(413\) | −436229. | −0.125846 | ||||||||
\(414\) | 702078. | 0.201319 | ||||||||
\(415\) | −1.76830e6 | −0.504007 | ||||||||
\(416\) | 2.89283e6 | 0.819576 | ||||||||
\(417\) | 2.74311e6 | 0.772509 | ||||||||
\(418\) | 1.61571e6 | 0.452297 | ||||||||
\(419\) | −4.85187e6 | −1.35012 | −0.675062 | − | 0.737761i | \(-0.735883\pi\) | ||||
−0.675062 | + | 0.737761i | \(0.735883\pi\) | |||||||
\(420\) | −325230. | −0.0899638 | ||||||||
\(421\) | −6.14767e6 | −1.69046 | −0.845231 | − | 0.534401i | \(-0.820537\pi\) | ||||
−0.845231 | + | 0.534401i | \(0.820537\pi\) | |||||||
\(422\) | −26282.5 | −0.00718432 | ||||||||
\(423\) | 250082. | 0.0679565 | ||||||||
\(424\) | −4.72392e6 | −1.27611 | ||||||||
\(425\) | −619571. | −0.166387 | ||||||||
\(426\) | −911563. | −0.243368 | ||||||||
\(427\) | 2.39731e6 | 0.636288 | ||||||||
\(428\) | 2.07674e6 | 0.547991 | ||||||||
\(429\) | 4.72025e6 | 1.23829 | ||||||||
\(430\) | −1.52524e6 | −0.397803 | ||||||||
\(431\) | 3.55411e6 | 0.921590 | 0.460795 | − | 0.887507i | \(-0.347564\pi\) | ||||
0.460795 | + | 0.887507i | \(0.347564\pi\) | |||||||
\(432\) | 71814.7 | 0.0185141 | ||||||||
\(433\) | 2.82650e6 | 0.724485 | 0.362243 | − | 0.932084i | \(-0.382011\pi\) | ||||
0.362243 | + | 0.932084i | \(0.382011\pi\) | |||||||
\(434\) | −678737. | −0.172973 | ||||||||
\(435\) | −2.29454e6 | −0.581395 | ||||||||
\(436\) | 972973. | 0.245123 | ||||||||
\(437\) | 2.25968e6 | 0.566035 | ||||||||
\(438\) | −486360. | −0.121136 | ||||||||
\(439\) | 4.64410e6 | 1.15011 | 0.575056 | − | 0.818114i | \(-0.304980\pi\) | ||||
0.575056 | + | 0.818114i | \(0.304980\pi\) | |||||||
\(440\) | 3.14578e6 | 0.774633 | ||||||||
\(441\) | −139786. | −0.0342268 | ||||||||
\(442\) | −1.75775e6 | −0.427959 | ||||||||
\(443\) | −6.15534e6 | −1.49019 | −0.745097 | − | 0.666957i | \(-0.767597\pi\) | ||||
−0.745097 | + | 0.666957i | \(0.767597\pi\) | |||||||
\(444\) | −166524. | −0.0400884 | ||||||||
\(445\) | −106028. | −0.0253817 | ||||||||
\(446\) | −420757. | −0.100160 | ||||||||
\(447\) | −6.33774e6 | −1.50026 | ||||||||
\(448\) | −1.02428e6 | −0.241115 | ||||||||
\(449\) | 3.67035e6 | 0.859196 | 0.429598 | − | 0.903020i | \(-0.358655\pi\) | ||||
0.429598 | + | 0.903020i | \(0.358655\pi\) | |||||||
\(450\) | 128489. | 0.0299112 | ||||||||
\(451\) | −1.12565e7 | −2.60591 | ||||||||
\(452\) | 725791. | 0.167096 | ||||||||
\(453\) | −1.66127e6 | −0.380360 | ||||||||
\(454\) | 1.37305e6 | 0.312642 | ||||||||
\(455\) | −615134. | −0.139297 | ||||||||
\(456\) | 1.63665e6 | 0.368591 | ||||||||
\(457\) | −866327. | −0.194040 | −0.0970201 | − | 0.995282i | \(-0.530931\pi\) | ||||
−0.0970201 | + | 0.995282i | \(0.530931\pi\) | |||||||
\(458\) | −2.58698e6 | −0.576275 | ||||||||
\(459\) | 4.05903e6 | 0.899271 | ||||||||
\(460\) | 1.66751e6 | 0.367429 | ||||||||
\(461\) | −1.88572e6 | −0.413261 | −0.206631 | − | 0.978419i | \(-0.566250\pi\) | ||||
−0.206631 | + | 0.978419i | \(0.566250\pi\) | |||||||
\(462\) | −1.62645e6 | −0.354517 | ||||||||
\(463\) | −8.49017e6 | −1.84062 | −0.920309 | − | 0.391192i | \(-0.872063\pi\) | ||||
−0.920309 | + | 0.391192i | \(0.872063\pi\) | |||||||
\(464\) | −118421. | −0.0255349 | ||||||||
\(465\) | 1.33309e6 | 0.285909 | ||||||||
\(466\) | 3.97744e6 | 0.848474 | ||||||||
\(467\) | 1.82738e6 | 0.387737 | 0.193868 | − | 0.981028i | \(-0.437896\pi\) | ||||
0.193868 | + | 0.981028i | \(0.437896\pi\) | |||||||
\(468\) | −570994. | −0.120508 | ||||||||
\(469\) | 208632. | 0.0437975 | ||||||||
\(470\) | −379197. | −0.0791808 | ||||||||
\(471\) | −5.58197e6 | −1.15940 | ||||||||
\(472\) | 1.61995e6 | 0.334693 | ||||||||
\(473\) | 1.19479e7 | 2.45549 | ||||||||
\(474\) | 4.65535e6 | 0.951714 | ||||||||
\(475\) | 413548. | 0.0840992 | ||||||||
\(476\) | −948712. | −0.191919 | ||||||||
\(477\) | 1.51144e6 | 0.304155 | ||||||||
\(478\) | −2.72715e6 | −0.545933 | ||||||||
\(479\) | 4.68744e6 | 0.933463 | 0.466731 | − | 0.884399i | \(-0.345432\pi\) | ||||
0.466731 | + | 0.884399i | \(0.345432\pi\) | |||||||
\(480\) | 1.95775e6 | 0.387841 | ||||||||
\(481\) | −314960. | −0.0620715 | ||||||||
\(482\) | −4.95405e6 | −0.971277 | ||||||||
\(483\) | −2.27470e6 | −0.443666 | ||||||||
\(484\) | −6.19426e6 | −1.20192 | ||||||||
\(485\) | 2.60939e6 | 0.503714 | ||||||||
\(486\) | −1.52085e6 | −0.292076 | ||||||||
\(487\) | 4.59651e6 | 0.878225 | 0.439112 | − | 0.898432i | \(-0.355293\pi\) | ||||
0.439112 | + | 0.898432i | \(0.355293\pi\) | |||||||
\(488\) | −8.90247e6 | −1.69224 | ||||||||
\(489\) | 1.06743e6 | 0.201867 | ||||||||
\(490\) | 211956. | 0.0398800 | ||||||||
\(491\) | 6.62099e6 | 1.23942 | 0.619711 | − | 0.784830i | \(-0.287250\pi\) | ||||
0.619711 | + | 0.784830i | \(0.287250\pi\) | |||||||
\(492\) | −4.32167e6 | −0.804895 | ||||||||
\(493\) | −6.69327e6 | −1.24028 | ||||||||
\(494\) | 1.17326e6 | 0.216310 | ||||||||
\(495\) | −1.00650e6 | −0.184630 | ||||||||
\(496\) | 68800.9 | 0.0125571 | ||||||||
\(497\) | −930554. | −0.168986 | ||||||||
\(498\) | −3.39514e6 | −0.613458 | ||||||||
\(499\) | −4.52632e6 | −0.813756 | −0.406878 | − | 0.913482i | \(-0.633383\pi\) | ||||
−0.406878 | + | 0.913482i | \(0.633383\pi\) | |||||||
\(500\) | 305174. | 0.0545912 | ||||||||
\(501\) | −8.12495e6 | −1.44619 | ||||||||
\(502\) | 5.78829e6 | 1.02516 | ||||||||
\(503\) | 3.83316e6 | 0.675518 | 0.337759 | − | 0.941233i | \(-0.390331\pi\) | ||||
0.337759 | + | 0.941233i | \(0.390331\pi\) | |||||||
\(504\) | 519099. | 0.0910278 | ||||||||
\(505\) | 1.14288e6 | 0.199421 | ||||||||
\(506\) | 8.33909e6 | 1.44791 | ||||||||
\(507\) | −1.61950e6 | −0.279808 | ||||||||
\(508\) | 908397. | 0.156177 | ||||||||
\(509\) | −3.25460e6 | −0.556806 | −0.278403 | − | 0.960464i | \(-0.589805\pi\) | ||||
−0.278403 | + | 0.960464i | \(0.589805\pi\) | |||||||
\(510\) | −1.18958e6 | −0.202519 | ||||||||
\(511\) | −496492. | −0.0841124 | ||||||||
\(512\) | 203165. | 0.0342511 | ||||||||
\(513\) | −2.70930e6 | −0.454531 | ||||||||
\(514\) | 789788. | 0.131857 | ||||||||
\(515\) | −2.23195e6 | −0.370823 | ||||||||
\(516\) | 4.58713e6 | 0.758432 | ||||||||
\(517\) | 2.97040e6 | 0.488752 | ||||||||
\(518\) | 108525. | 0.0177708 | ||||||||
\(519\) | −813891. | −0.132632 | ||||||||
\(520\) | 2.28432e6 | 0.370466 | ||||||||
\(521\) | −1.07842e6 | −0.174057 | −0.0870287 | − | 0.996206i | \(-0.527737\pi\) | ||||
−0.0870287 | + | 0.996206i | \(0.527737\pi\) | |||||||
\(522\) | 1.38807e6 | 0.222964 | ||||||||
\(523\) | 408626. | 0.0653238 | 0.0326619 | − | 0.999466i | \(-0.489602\pi\) | ||||
0.0326619 | + | 0.999466i | \(0.489602\pi\) | |||||||
\(524\) | −7.45641e6 | −1.18632 | ||||||||
\(525\) | −416297. | −0.0659182 | ||||||||
\(526\) | −1.05764e6 | −0.166676 | ||||||||
\(527\) | 3.88869e6 | 0.609925 | ||||||||
\(528\) | 164867. | 0.0257365 | ||||||||
\(529\) | 5.22642e6 | 0.812016 | ||||||||
\(530\) | −2.29178e6 | −0.354391 | ||||||||
\(531\) | −518310. | −0.0797724 | ||||||||
\(532\) | 633242. | 0.0970042 | ||||||||
\(533\) | −8.17392e6 | −1.24627 | ||||||||
\(534\) | −203574. | −0.0308936 | ||||||||
\(535\) | 2.65825e6 | 0.401524 | ||||||||
\(536\) | −774763. | −0.116481 | ||||||||
\(537\) | 8.38456e6 | 1.25471 | ||||||||
\(538\) | −474374. | −0.0706586 | ||||||||
\(539\) | −1.66034e6 | −0.246164 | ||||||||
\(540\) | −1.99930e6 | −0.295049 | ||||||||
\(541\) | 1.13918e7 | 1.67340 | 0.836701 | − | 0.547659i | \(-0.184481\pi\) | ||||
0.836701 | + | 0.547659i | \(0.184481\pi\) | |||||||
\(542\) | −6.82970e6 | −0.998627 | ||||||||
\(543\) | −506856. | −0.0737709 | ||||||||
\(544\) | 5.71084e6 | 0.827376 | ||||||||
\(545\) | 1.24541e6 | 0.179607 | ||||||||
\(546\) | −1.18106e6 | −0.169547 | ||||||||
\(547\) | −3.44866e6 | −0.492813 | −0.246406 | − | 0.969167i | \(-0.579250\pi\) | ||||
−0.246406 | + | 0.969167i | \(0.579250\pi\) | |||||||
\(548\) | 37002.6 | 0.00526357 | ||||||||
\(549\) | 2.84838e6 | 0.403337 | ||||||||
\(550\) | 1.52615e6 | 0.215125 | ||||||||
\(551\) | 4.46759e6 | 0.626894 | ||||||||
\(552\) | 8.44718e6 | 1.17995 | ||||||||
\(553\) | 4.75234e6 | 0.660837 | ||||||||
\(554\) | −627124. | −0.0868119 | ||||||||
\(555\) | −213152. | −0.0293736 | ||||||||
\(556\) | −3.94134e6 | −0.540700 | ||||||||
\(557\) | −4.69772e6 | −0.641577 | −0.320789 | − | 0.947151i | \(-0.603948\pi\) | ||||
−0.320789 | + | 0.947151i | \(0.603948\pi\) | |||||||
\(558\) | −806449. | −0.109646 | ||||||||
\(559\) | 8.67599e6 | 1.17433 | ||||||||
\(560\) | −21485.1 | −0.00289513 | ||||||||
\(561\) | 9.31844e6 | 1.25007 | ||||||||
\(562\) | −6.53722e6 | −0.873077 | ||||||||
\(563\) | −561642. | −0.0746772 | −0.0373386 | − | 0.999303i | \(-0.511888\pi\) | ||||
−0.0373386 | + | 0.999303i | \(0.511888\pi\) | |||||||
\(564\) | 1.14042e6 | 0.150962 | ||||||||
\(565\) | 929018. | 0.122434 | ||||||||
\(566\) | −8.46945e6 | −1.11126 | ||||||||
\(567\) | 2.03409e6 | 0.265713 | ||||||||
\(568\) | 3.45564e6 | 0.449426 | ||||||||
\(569\) | 5.19019e6 | 0.672051 | 0.336026 | − | 0.941853i | \(-0.390917\pi\) | ||||
0.336026 | + | 0.941853i | \(0.390917\pi\) | |||||||
\(570\) | 794012. | 0.102362 | ||||||||
\(571\) | −5.20274e6 | −0.667793 | −0.333897 | − | 0.942610i | \(-0.608364\pi\) | ||||
−0.333897 | + | 0.942610i | \(0.608364\pi\) | |||||||
\(572\) | −6.78211e6 | −0.866712 | ||||||||
\(573\) | 4.44178e6 | 0.565159 | ||||||||
\(574\) | 2.81648e6 | 0.356802 | ||||||||
\(575\) | 2.13442e6 | 0.269222 | ||||||||
\(576\) | −1.21701e6 | −0.152840 | ||||||||
\(577\) | 8.70662e6 | 1.08870 | 0.544352 | − | 0.838857i | \(-0.316775\pi\) | ||||
0.544352 | + | 0.838857i | \(0.316775\pi\) | |||||||
\(578\) | 1.54365e6 | 0.192189 | ||||||||
\(579\) | −3.61224e6 | −0.447796 | ||||||||
\(580\) | 3.29681e6 | 0.406934 | ||||||||
\(581\) | −3.46588e6 | −0.425964 | ||||||||
\(582\) | 5.01003e6 | 0.613102 | ||||||||
\(583\) | 1.79524e7 | 2.18752 | ||||||||
\(584\) | 1.84374e6 | 0.223701 | ||||||||
\(585\) | −730877. | −0.0882988 | ||||||||
\(586\) | −8.82505e6 | −1.06163 | ||||||||
\(587\) | −4.35717e6 | −0.521926 | −0.260963 | − | 0.965349i | \(-0.584040\pi\) | ||||
−0.260963 | + | 0.965349i | \(0.584040\pi\) | |||||||
\(588\) | −637452. | −0.0760333 | ||||||||
\(589\) | −2.59560e6 | −0.308283 | ||||||||
\(590\) | 785908. | 0.0929484 | ||||||||
\(591\) | −7.03954e6 | −0.829040 | ||||||||
\(592\) | −11000.8 | −0.00129009 | ||||||||
\(593\) | −3.22991e6 | −0.377184 | −0.188592 | − | 0.982055i | \(-0.560392\pi\) | ||||
−0.188592 | + | 0.982055i | \(0.560392\pi\) | |||||||
\(594\) | −9.99837e6 | −1.16269 | ||||||||
\(595\) | −1.21436e6 | −0.140622 | ||||||||
\(596\) | 9.10614e6 | 1.05007 | ||||||||
\(597\) | −2.02115e6 | −0.232094 | ||||||||
\(598\) | 6.05547e6 | 0.692460 | ||||||||
\(599\) | −7.23988e6 | −0.824450 | −0.412225 | − | 0.911082i | \(-0.635248\pi\) | ||||
−0.412225 | + | 0.911082i | \(0.635248\pi\) | |||||||
\(600\) | 1.54593e6 | 0.175312 | ||||||||
\(601\) | −1.06837e7 | −1.20652 | −0.603262 | − | 0.797543i | \(-0.706133\pi\) | ||||
−0.603262 | + | 0.797543i | \(0.706133\pi\) | |||||||
\(602\) | −2.98948e6 | −0.336205 | ||||||||
\(603\) | 247889. | 0.0277628 | ||||||||
\(604\) | 2.38693e6 | 0.266225 | ||||||||
\(605\) | −7.92871e6 | −0.880671 | ||||||||
\(606\) | 2.19432e6 | 0.242727 | ||||||||
\(607\) | 2.51528e6 | 0.277086 | 0.138543 | − | 0.990356i | \(-0.455758\pi\) | ||||
0.138543 | + | 0.990356i | \(0.455758\pi\) | |||||||
\(608\) | −3.81185e6 | −0.418193 | ||||||||
\(609\) | −4.49729e6 | −0.491369 | ||||||||
\(610\) | −4.31898e6 | −0.469955 | ||||||||
\(611\) | 2.15697e6 | 0.233744 | ||||||||
\(612\) | −1.12722e6 | −0.121655 | ||||||||
\(613\) | 213999. | 0.0230017 | 0.0115009 | − | 0.999934i | \(-0.496339\pi\) | ||||
0.0115009 | + | 0.999934i | \(0.496339\pi\) | |||||||
\(614\) | −1.08475e7 | −1.16120 | ||||||||
\(615\) | −5.53178e6 | −0.589762 | ||||||||
\(616\) | 6.16572e6 | 0.654684 | ||||||||
\(617\) | −127951. | −0.0135310 | −0.00676552 | − | 0.999977i | \(-0.502154\pi\) | ||||
−0.00676552 | + | 0.999977i | \(0.502154\pi\) | |||||||
\(618\) | −4.28535e6 | −0.451352 | ||||||||
\(619\) | −1.23980e7 | −1.30054 | −0.650272 | − | 0.759701i | \(-0.725345\pi\) | ||||
−0.650272 | + | 0.759701i | \(0.725345\pi\) | |||||||
\(620\) | −1.91540e6 | −0.200115 | ||||||||
\(621\) | −1.39834e7 | −1.45507 | ||||||||
\(622\) | −2.33490e6 | −0.241987 | ||||||||
\(623\) | −207815. | −0.0214514 | ||||||||
\(624\) | 119719. | 0.0123084 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 1.16313e7 | 1.18629 | ||||||||
\(627\) | −6.21983e6 | −0.631843 | ||||||||
\(628\) | 8.02023e6 | 0.811499 | ||||||||
\(629\) | −621774. | −0.0626622 | ||||||||
\(630\) | 251838. | 0.0252795 | ||||||||
\(631\) | −5.87683e6 | −0.587584 | −0.293792 | − | 0.955869i | \(-0.594917\pi\) | ||||
−0.293792 | + | 0.955869i | \(0.594917\pi\) | |||||||
\(632\) | −1.76480e7 | −1.75753 | ||||||||
\(633\) | 101177. | 0.0100363 | ||||||||
\(634\) | −2.25895e6 | −0.223194 | ||||||||
\(635\) | 1.16275e6 | 0.114434 | ||||||||
\(636\) | 6.89246e6 | 0.675665 | ||||||||
\(637\) | −1.20566e6 | −0.117727 | ||||||||
\(638\) | 1.64871e7 | 1.60359 | ||||||||
\(639\) | −1.10565e6 | −0.107118 | ||||||||
\(640\) | −2.76337e6 | −0.266679 | ||||||||
\(641\) | −2.60122e6 | −0.250053 | −0.125026 | − | 0.992153i | \(-0.539902\pi\) | ||||
−0.125026 | + | 0.992153i | \(0.539902\pi\) | |||||||
\(642\) | 5.10384e6 | 0.488719 | ||||||||
\(643\) | 1.31345e7 | 1.25282 | 0.626408 | − | 0.779495i | \(-0.284524\pi\) | ||||
0.626408 | + | 0.779495i | \(0.284524\pi\) | |||||||
\(644\) | 3.26832e6 | 0.310534 | ||||||||
\(645\) | 5.87156e6 | 0.555718 | ||||||||
\(646\) | 2.31617e6 | 0.218368 | ||||||||
\(647\) | 5.54662e6 | 0.520916 | 0.260458 | − | 0.965485i | \(-0.416126\pi\) | ||||
0.260458 | + | 0.965485i | \(0.416126\pi\) | |||||||
\(648\) | −7.55366e6 | −0.706675 | ||||||||
\(649\) | −6.15634e6 | −0.573734 | ||||||||
\(650\) | 1.10822e6 | 0.102883 | ||||||||
\(651\) | 2.61286e6 | 0.241637 | ||||||||
\(652\) | −1.53369e6 | −0.141292 | ||||||||
\(653\) | −1.54993e7 | −1.42242 | −0.711212 | − | 0.702978i | \(-0.751853\pi\) | ||||
−0.711212 | + | 0.702978i | \(0.751853\pi\) | |||||||
\(654\) | 2.39119e6 | 0.218610 | ||||||||
\(655\) | −9.54427e6 | −0.869239 | ||||||||
\(656\) | −285495. | −0.0259024 | ||||||||
\(657\) | −589912. | −0.0533180 | ||||||||
\(658\) | −743225. | −0.0669200 | ||||||||
\(659\) | −4.30145e6 | −0.385835 | −0.192917 | − | 0.981215i | \(-0.561795\pi\) | ||||
−0.192917 | + | 0.981215i | \(0.561795\pi\) | |||||||
\(660\) | −4.58986e6 | −0.410147 | ||||||||
\(661\) | 861980. | 0.0767350 | 0.0383675 | − | 0.999264i | \(-0.487784\pi\) | ||||
0.0383675 | + | 0.999264i | \(0.487784\pi\) | |||||||
\(662\) | 4.02111e6 | 0.356616 | ||||||||
\(663\) | 6.76662e6 | 0.597844 | ||||||||
\(664\) | 1.28706e7 | 1.13287 | ||||||||
\(665\) | 810554. | 0.0710768 | ||||||||
\(666\) | 128945. | 0.0112647 | ||||||||
\(667\) | 2.30583e7 | 2.00684 | ||||||||
\(668\) | 1.16740e7 | 1.01223 | ||||||||
\(669\) | 1.61974e6 | 0.139920 | ||||||||
\(670\) | −375871. | −0.0323484 | ||||||||
\(671\) | 3.38323e7 | 2.90085 | ||||||||
\(672\) | 3.83719e6 | 0.327786 | ||||||||
\(673\) | −953818. | −0.0811760 | −0.0405880 | − | 0.999176i | \(-0.512923\pi\) | ||||
−0.0405880 | + | 0.999176i | \(0.512923\pi\) | |||||||
\(674\) | −2.42056e6 | −0.205242 | ||||||||
\(675\) | −2.55912e6 | −0.216188 | ||||||||
\(676\) | 2.32691e6 | 0.195845 | ||||||||
\(677\) | −1.48606e7 | −1.24613 | −0.623065 | − | 0.782170i | \(-0.714113\pi\) | ||||
−0.623065 | + | 0.782170i | \(0.714113\pi\) | |||||||
\(678\) | 1.78371e6 | 0.149022 | ||||||||
\(679\) | 5.11440e6 | 0.425716 | ||||||||
\(680\) | 4.50956e6 | 0.373992 | ||||||||
\(681\) | −5.28569e6 | −0.436751 | ||||||||
\(682\) | −9.57878e6 | −0.788586 | ||||||||
\(683\) | −1.57605e7 | −1.29276 | −0.646381 | − | 0.763015i | \(-0.723718\pi\) | ||||
−0.646381 | + | 0.763015i | \(0.723718\pi\) | |||||||
\(684\) | 752392. | 0.0614900 | ||||||||
\(685\) | 47363.6 | 0.00385672 | ||||||||
\(686\) | 415434. | 0.0337048 | ||||||||
\(687\) | 9.95882e6 | 0.805037 | ||||||||
\(688\) | 303032. | 0.0244071 | ||||||||
\(689\) | 1.30362e7 | 1.04618 | ||||||||
\(690\) | 4.09809e6 | 0.327687 | ||||||||
\(691\) | 1.59740e7 | 1.27267 | 0.636337 | − | 0.771411i | \(-0.280449\pi\) | ||||
0.636337 | + | 0.771411i | \(0.280449\pi\) | |||||||
\(692\) | 1.16941e6 | 0.0928326 | ||||||||
\(693\) | −1.97275e6 | −0.156041 | ||||||||
\(694\) | 4.41925e6 | 0.348297 | ||||||||
\(695\) | −5.04494e6 | −0.396182 | ||||||||
\(696\) | 1.67008e7 | 1.30682 | ||||||||
\(697\) | −1.61365e7 | −1.25813 | ||||||||
\(698\) | 1.11798e7 | 0.868549 | ||||||||
\(699\) | −1.53115e7 | −1.18529 | ||||||||
\(700\) | 598141. | 0.0461380 | ||||||||
\(701\) | −1.85736e7 | −1.42758 | −0.713790 | − | 0.700360i | \(-0.753023\pi\) | ||||
−0.713790 | + | 0.700360i | \(0.753023\pi\) | |||||||
\(702\) | −7.26036e6 | −0.556052 | ||||||||
\(703\) | 415019. | 0.0316723 | ||||||||
\(704\) | −1.44553e7 | −1.09925 | ||||||||
\(705\) | 1.45975e6 | 0.110613 | ||||||||
\(706\) | 8.59365e6 | 0.648883 | ||||||||
\(707\) | 2.24004e6 | 0.168541 | ||||||||
\(708\) | −2.36360e6 | −0.177211 | ||||||||
\(709\) | −1.71029e7 | −1.27778 | −0.638888 | − | 0.769300i | \(-0.720605\pi\) | ||||
−0.638888 | + | 0.769300i | \(0.720605\pi\) | |||||||
\(710\) | 1.67648e6 | 0.124811 | ||||||||
\(711\) | 5.64654e6 | 0.418898 | ||||||||
\(712\) | 771727. | 0.0570511 | ||||||||
\(713\) | −1.33965e7 | −0.986890 | ||||||||
\(714\) | −2.33157e6 | −0.171160 | ||||||||
\(715\) | −8.68116e6 | −0.635057 | ||||||||
\(716\) | −1.20470e7 | −0.878208 | ||||||||
\(717\) | 1.04984e7 | 0.762651 | ||||||||
\(718\) | 7.52204e6 | 0.544534 | ||||||||
\(719\) | −1.40945e7 | −1.01678 | −0.508390 | − | 0.861127i | \(-0.669759\pi\) | ||||
−0.508390 | + | 0.861127i | \(0.669759\pi\) | |||||||
\(720\) | −25527.8 | −0.00183519 | ||||||||
\(721\) | −4.37463e6 | −0.313403 | ||||||||
\(722\) | 7.19744e6 | 0.513848 | ||||||||
\(723\) | 1.90711e7 | 1.35684 | ||||||||
\(724\) | 728256. | 0.0516343 | ||||||||
\(725\) | 4.21995e6 | 0.298169 | ||||||||
\(726\) | −1.52231e7 | −1.07192 | ||||||||
\(727\) | 2.24196e7 | 1.57323 | 0.786616 | − | 0.617443i | \(-0.211831\pi\) | ||||
0.786616 | + | 0.617443i | \(0.211831\pi\) | |||||||
\(728\) | 4.47726e6 | 0.313101 | ||||||||
\(729\) | 1.59421e7 | 1.11103 | ||||||||
\(730\) | 894478. | 0.0621245 | ||||||||
\(731\) | 1.71276e7 | 1.18551 | ||||||||
\(732\) | 1.29892e7 | 0.895993 | ||||||||
\(733\) | −8.02464e6 | −0.551653 | −0.275826 | − | 0.961208i | \(-0.588951\pi\) | ||||
−0.275826 | + | 0.961208i | \(0.588951\pi\) | |||||||
\(734\) | 1.09810e7 | 0.752316 | ||||||||
\(735\) | −815943. | −0.0557111 | ||||||||
\(736\) | −1.96739e7 | −1.33874 | ||||||||
\(737\) | 2.94435e6 | 0.199674 | ||||||||
\(738\) | 3.34643e6 | 0.226173 | ||||||||
\(739\) | 1.15678e7 | 0.779181 | 0.389591 | − | 0.920988i | \(-0.372616\pi\) | ||||
0.389591 | + | 0.920988i | \(0.372616\pi\) | |||||||
\(740\) | 306259. | 0.0205594 | ||||||||
\(741\) | −4.51655e6 | −0.302177 | ||||||||
\(742\) | −4.49189e6 | −0.299515 | ||||||||
\(743\) | 3.79387e6 | 0.252122 | 0.126061 | − | 0.992023i | \(-0.459767\pi\) | ||||
0.126061 | + | 0.992023i | \(0.459767\pi\) | |||||||
\(744\) | −9.70293e6 | −0.642644 | ||||||||
\(745\) | 1.16559e7 | 0.769407 | ||||||||
\(746\) | 1.11297e7 | 0.732214 | ||||||||
\(747\) | −4.11801e6 | −0.270014 | ||||||||
\(748\) | −1.33888e7 | −0.874961 | ||||||||
\(749\) | 5.21017e6 | 0.339349 | ||||||||
\(750\) | 750000. | 0.0486864 | ||||||||
\(751\) | −9.07884e6 | −0.587395 | −0.293698 | − | 0.955898i | \(-0.594886\pi\) | ||||
−0.293698 | + | 0.955898i | \(0.594886\pi\) | |||||||
\(752\) | 75337.8 | 0.00485812 | ||||||||
\(753\) | −2.22825e7 | −1.43211 | ||||||||
\(754\) | 1.19722e7 | 0.766912 | ||||||||
\(755\) | 3.05530e6 | 0.195068 | ||||||||
\(756\) | −3.91863e6 | −0.249362 | ||||||||
\(757\) | −2.33210e7 | −1.47913 | −0.739565 | − | 0.673085i | \(-0.764969\pi\) | ||||
−0.739565 | + | 0.673085i | \(0.764969\pi\) | |||||||
\(758\) | −1.20888e6 | −0.0764208 | ||||||||
\(759\) | −3.21020e7 | −2.02269 | ||||||||
\(760\) | −3.01002e6 | −0.189032 | ||||||||
\(761\) | 1.44859e7 | 0.906745 | 0.453373 | − | 0.891321i | \(-0.350221\pi\) | ||||
0.453373 | + | 0.891321i | \(0.350221\pi\) | |||||||
\(762\) | 2.23249e6 | 0.139284 | ||||||||
\(763\) | 2.44101e6 | 0.151795 | ||||||||
\(764\) | −6.38200e6 | −0.395570 | ||||||||
\(765\) | −1.44285e6 | −0.0891391 | ||||||||
\(766\) | −1.30435e7 | −0.803200 | ||||||||
\(767\) | −4.47045e6 | −0.274387 | ||||||||
\(768\) | −1.43985e7 | −0.880876 | ||||||||
\(769\) | 1.59424e7 | 0.972162 | 0.486081 | − | 0.873914i | \(-0.338426\pi\) | ||||
0.486081 | + | 0.873914i | \(0.338426\pi\) | |||||||
\(770\) | 2.99126e6 | 0.181814 | ||||||||
\(771\) | −3.04036e6 | −0.184200 | ||||||||
\(772\) | 5.19011e6 | 0.313425 | ||||||||
\(773\) | −3.36066e6 | −0.202290 | −0.101145 | − | 0.994872i | \(-0.532251\pi\) | ||||
−0.101145 | + | 0.994872i | \(0.532251\pi\) | |||||||
\(774\) | −3.55198e6 | −0.213117 | ||||||||
\(775\) | −2.45173e6 | −0.146628 | ||||||||
\(776\) | −1.89925e7 | −1.13221 | ||||||||
\(777\) | −417778. | −0.0248252 | ||||||||
\(778\) | −7.24988e6 | −0.429419 | ||||||||
\(779\) | 1.07707e7 | 0.635916 | ||||||||
\(780\) | −3.33295e6 | −0.196152 | ||||||||
\(781\) | −1.31326e7 | −0.770411 | ||||||||
\(782\) | 1.19543e7 | 0.699050 | ||||||||
\(783\) | −2.76464e7 | −1.61151 | ||||||||
\(784\) | −42110.9 | −0.00244683 | ||||||||
\(785\) | 1.02660e7 | 0.594601 | ||||||||
\(786\) | −1.83250e7 | −1.05800 | ||||||||
\(787\) | −3.28918e6 | −0.189300 | −0.0946500 | − | 0.995511i | \(-0.530173\pi\) | ||||
−0.0946500 | + | 0.995511i | \(0.530173\pi\) | |||||||
\(788\) | 1.01145e7 | 0.580268 | ||||||||
\(789\) | 4.07147e6 | 0.232841 | ||||||||
\(790\) | −8.56179e6 | −0.488087 | ||||||||
\(791\) | 1.82088e6 | 0.103476 | ||||||||
\(792\) | 7.32586e6 | 0.414998 | ||||||||
\(793\) | 2.45675e7 | 1.38732 | ||||||||
\(794\) | 8.05475e6 | 0.453420 | ||||||||
\(795\) | 8.82240e6 | 0.495073 | ||||||||
\(796\) | 2.90402e6 | 0.162449 | ||||||||
\(797\) | −2.51939e6 | −0.140492 | −0.0702458 | − | 0.997530i | \(-0.522378\pi\) | ||||
−0.0702458 | + | 0.997530i | \(0.522378\pi\) | |||||||
\(798\) | 1.55626e6 | 0.0865120 | ||||||||
\(799\) | 4.25816e6 | 0.235969 | ||||||||
\(800\) | −3.60055e6 | −0.198904 | ||||||||
\(801\) | −246917. | −0.0135978 | ||||||||
\(802\) | −1.17262e7 | −0.643758 | ||||||||
\(803\) | −7.00682e6 | −0.383470 | ||||||||
\(804\) | 1.13042e6 | 0.0616738 | ||||||||
\(805\) | 4.18347e6 | 0.227534 | ||||||||
\(806\) | −6.95567e6 | −0.377139 | ||||||||
\(807\) | 1.82614e6 | 0.0987077 | ||||||||
\(808\) | −8.31845e6 | −0.448244 | ||||||||
\(809\) | 8.93808e6 | 0.480146 | 0.240073 | − | 0.970755i | \(-0.422829\pi\) | ||||
0.240073 | + | 0.970755i | \(0.422829\pi\) | |||||||
\(810\) | −3.66461e6 | −0.196252 | ||||||||
\(811\) | 3.01341e7 | 1.60881 | 0.804406 | − | 0.594080i | \(-0.202484\pi\) | ||||
0.804406 | + | 0.594080i | \(0.202484\pi\) | |||||||
\(812\) | 6.46176e6 | 0.343922 | ||||||||
\(813\) | 2.62915e7 | 1.39505 | ||||||||
\(814\) | 1.53158e6 | 0.0810174 | ||||||||
\(815\) | −1.96313e6 | −0.103528 | ||||||||
\(816\) | 236342. | 0.0124255 | ||||||||
\(817\) | −1.14323e7 | −0.599207 | ||||||||
\(818\) | −1.82184e7 | −0.951980 | ||||||||
\(819\) | −1.43252e6 | −0.0746261 | ||||||||
\(820\) | 7.94812e6 | 0.412791 | ||||||||
\(821\) | −3.25440e7 | −1.68505 | −0.842524 | − | 0.538658i | \(-0.818931\pi\) | ||||
−0.842524 | + | 0.538658i | \(0.818931\pi\) | |||||||
\(822\) | 90938.1 | 0.00469425 | ||||||||
\(823\) | −499640. | −0.0257133 | −0.0128566 | − | 0.999917i | \(-0.504093\pi\) | ||||
−0.0128566 | + | 0.999917i | \(0.504093\pi\) | |||||||
\(824\) | 1.62453e7 | 0.833509 | ||||||||
\(825\) | −5.87506e6 | −0.300523 | ||||||||
\(826\) | 1.54038e6 | 0.0785557 | ||||||||
\(827\) | −4.64084e6 | −0.235957 | −0.117978 | − | 0.993016i | \(-0.537641\pi\) | ||||
−0.117978 | + | 0.993016i | \(0.537641\pi\) | |||||||
\(828\) | 3.88328e6 | 0.196844 | ||||||||
\(829\) | −3.08794e7 | −1.56057 | −0.780283 | − | 0.625427i | \(-0.784925\pi\) | ||||
−0.780283 | + | 0.625427i | \(0.784925\pi\) | |||||||
\(830\) | 6.24411e6 | 0.314612 | ||||||||
\(831\) | 2.41417e6 | 0.121273 | ||||||||
\(832\) | −1.04968e7 | −0.525712 | ||||||||
\(833\) | −2.38014e6 | −0.118848 | ||||||||
\(834\) | −9.68629e6 | −0.482217 | ||||||||
\(835\) | 1.49428e7 | 0.741681 | ||||||||
\(836\) | 8.93671e6 | 0.442244 | ||||||||
\(837\) | 1.60621e7 | 0.792482 | ||||||||
\(838\) | 1.71326e7 | 0.842777 | ||||||||
\(839\) | 1.93485e7 | 0.948948 | 0.474474 | − | 0.880269i | \(-0.342638\pi\) | ||||
0.474474 | + | 0.880269i | \(0.342638\pi\) | |||||||
\(840\) | 3.03003e6 | 0.148166 | ||||||||
\(841\) | 2.50772e7 | 1.22261 | ||||||||
\(842\) | 2.17082e7 | 1.05522 | ||||||||
\(843\) | 2.51656e7 | 1.21966 | ||||||||
\(844\) | −145372. | −0.00702465 | ||||||||
\(845\) | 2.97846e6 | 0.143500 | ||||||||
\(846\) | −883071. | −0.0424199 | ||||||||
\(847\) | −1.55403e7 | −0.744303 | ||||||||
\(848\) | 455325. | 0.0217436 | ||||||||
\(849\) | 3.26039e7 | 1.55239 | ||||||||
\(850\) | 2.18778e6 | 0.103862 | ||||||||
\(851\) | 2.14201e6 | 0.101391 | ||||||||
\(852\) | −5.04197e6 | −0.237959 | ||||||||
\(853\) | −3.05998e7 | −1.43994 | −0.719972 | − | 0.694003i | \(-0.755845\pi\) | ||||
−0.719972 | + | 0.694003i | \(0.755845\pi\) | |||||||
\(854\) | −8.46520e6 | −0.397185 | ||||||||
\(855\) | 963068. | 0.0450549 | ||||||||
\(856\) | −1.93481e7 | −0.902515 | ||||||||
\(857\) | −1.33039e7 | −0.618766 | −0.309383 | − | 0.950937i | \(-0.600123\pi\) | ||||
−0.309383 | + | 0.950937i | \(0.600123\pi\) | |||||||
\(858\) | −1.66678e7 | −0.772967 | ||||||||
\(859\) | −1.27708e7 | −0.590520 | −0.295260 | − | 0.955417i | \(-0.595406\pi\) | ||||
−0.295260 | + | 0.955417i | \(0.595406\pi\) | |||||||
\(860\) | −8.43633e6 | −0.388962 | ||||||||
\(861\) | −1.08423e7 | −0.498440 | ||||||||
\(862\) | −1.25500e7 | −0.575276 | ||||||||
\(863\) | 1.37987e7 | 0.630684 | 0.315342 | − | 0.948978i | \(-0.397881\pi\) | ||||
0.315342 | + | 0.948978i | \(0.397881\pi\) | |||||||
\(864\) | 2.35885e7 | 1.07502 | ||||||||
\(865\) | 1.49685e6 | 0.0680203 | ||||||||
\(866\) | −9.98074e6 | −0.452239 | ||||||||
\(867\) | −5.94241e6 | −0.268482 | ||||||||
\(868\) | −3.75418e6 | −0.169128 | ||||||||
\(869\) | 6.70680e7 | 3.01277 | ||||||||
\(870\) | 8.10230e6 | 0.362919 | ||||||||
\(871\) | 2.13806e6 | 0.0954934 | ||||||||
\(872\) | −9.06477e6 | −0.403706 | ||||||||
\(873\) | 6.07673e6 | 0.269857 | ||||||||
\(874\) | −7.97922e6 | −0.353331 | ||||||||
\(875\) | 765625. | 0.0338062 | ||||||||
\(876\) | −2.69012e6 | −0.118443 | ||||||||
\(877\) | 6.68992e6 | 0.293712 | 0.146856 | − | 0.989158i | \(-0.453085\pi\) | ||||
0.146856 | + | 0.989158i | \(0.453085\pi\) | |||||||
\(878\) | −1.63989e7 | −0.717924 | ||||||||
\(879\) | 3.39728e7 | 1.48306 | ||||||||
\(880\) | −303212. | −0.0131990 | ||||||||
\(881\) | −7.25051e6 | −0.314723 | −0.157362 | − | 0.987541i | \(-0.550299\pi\) | ||||
−0.157362 | + | 0.987541i | \(0.550299\pi\) | |||||||
\(882\) | 493602. | 0.0213651 | ||||||||
\(883\) | −2.55944e7 | −1.10470 | −0.552348 | − | 0.833613i | \(-0.686268\pi\) | ||||
−0.552348 | + | 0.833613i | \(0.686268\pi\) | |||||||
\(884\) | −9.72236e6 | −0.418447 | ||||||||
\(885\) | −3.02542e6 | −0.129846 | ||||||||
\(886\) | 2.17353e7 | 0.930210 | ||||||||
\(887\) | −2.33204e7 | −0.995240 | −0.497620 | − | 0.867395i | \(-0.665793\pi\) | ||||
−0.497620 | + | 0.867395i | \(0.665793\pi\) | |||||||
\(888\) | 1.55143e6 | 0.0660237 | ||||||||
\(889\) | 2.27900e6 | 0.0967141 | ||||||||
\(890\) | 374398. | 0.0158438 | ||||||||
\(891\) | 2.87064e7 | 1.21139 | ||||||||
\(892\) | −2.32726e6 | −0.0979340 | ||||||||
\(893\) | −2.84222e6 | −0.119269 | ||||||||
\(894\) | 2.23794e7 | 0.936493 | ||||||||
\(895\) | −1.54203e7 | −0.643480 | ||||||||
\(896\) | −5.41620e6 | −0.225385 | ||||||||
\(897\) | −2.33110e7 | −0.967343 | ||||||||
\(898\) | −1.29605e7 | −0.536328 | ||||||||
\(899\) | −2.64862e7 | −1.09300 | ||||||||
\(900\) | 710687. | 0.0292464 | ||||||||
\(901\) | 2.57354e7 | 1.05613 | ||||||||
\(902\) | 3.97480e7 | 1.62667 | ||||||||
\(903\) | 1.15083e7 | 0.469667 | ||||||||
\(904\) | −6.76188e6 | −0.275199 | ||||||||
\(905\) | 932174. | 0.0378334 | ||||||||
\(906\) | 5.86617e6 | 0.237429 | ||||||||
\(907\) | 3.71721e7 | 1.50037 | 0.750187 | − | 0.661226i | \(-0.229964\pi\) | ||||
0.750187 | + | 0.661226i | \(0.229964\pi\) | |||||||
\(908\) | 7.59453e6 | 0.305694 | ||||||||
\(909\) | 2.66152e6 | 0.106837 | ||||||||
\(910\) | 2.17212e6 | 0.0869520 | ||||||||
\(911\) | −2.89923e7 | −1.15741 | −0.578704 | − | 0.815537i | \(-0.696441\pi\) | ||||
−0.578704 | + | 0.815537i | \(0.696441\pi\) | |||||||
\(912\) | −157752. | −0.00628042 | ||||||||
\(913\) | −4.89127e7 | −1.94198 | ||||||||
\(914\) | 3.05911e6 | 0.121124 | ||||||||
\(915\) | 1.66263e7 | 0.656512 | ||||||||
\(916\) | −1.43089e7 | −0.563468 | ||||||||
\(917\) | −1.87068e7 | −0.734641 | ||||||||
\(918\) | −1.43330e7 | −0.561344 | ||||||||
\(919\) | −1.25020e6 | −0.0488306 | −0.0244153 | − | 0.999702i | \(-0.507772\pi\) | ||||
−0.0244153 | + | 0.999702i | \(0.507772\pi\) | |||||||
\(920\) | −1.55355e7 | −0.605138 | ||||||||
\(921\) | 4.17582e7 | 1.62216 | ||||||||
\(922\) | 6.65872e6 | 0.257966 | ||||||||
\(923\) | −9.53627e6 | −0.368447 | ||||||||
\(924\) | −8.99613e6 | −0.346638 | ||||||||
\(925\) | 392014. | 0.0150642 | ||||||||
\(926\) | 2.99799e7 | 1.14895 | ||||||||
\(927\) | −5.19776e6 | −0.198663 | ||||||||
\(928\) | −3.88970e7 | −1.48268 | ||||||||
\(929\) | 6.87875e6 | 0.261499 | 0.130749 | − | 0.991415i | \(-0.458262\pi\) | ||||
0.130749 | + | 0.991415i | \(0.458262\pi\) | |||||||
\(930\) | −4.70732e6 | −0.178470 | ||||||||
\(931\) | 1.58869e6 | 0.0600709 | ||||||||
\(932\) | 2.19997e7 | 0.829616 | ||||||||
\(933\) | 8.98840e6 | 0.338048 | ||||||||
\(934\) | −6.45272e6 | −0.242034 | ||||||||
\(935\) | −1.71378e7 | −0.641101 | ||||||||
\(936\) | 5.31971e6 | 0.198471 | ||||||||
\(937\) | 2.18600e7 | 0.813396 | 0.406698 | − | 0.913563i | \(-0.366680\pi\) | ||||
0.406698 | + | 0.913563i | \(0.366680\pi\) | |||||||
\(938\) | −736708. | −0.0273393 | ||||||||
\(939\) | −4.47756e7 | −1.65721 | ||||||||
\(940\) | −2.09739e6 | −0.0774210 | ||||||||
\(941\) | 2.26450e6 | 0.0833679 | 0.0416840 | − | 0.999131i | \(-0.486728\pi\) | ||||
0.0416840 | + | 0.999131i | \(0.486728\pi\) | |||||||
\(942\) | 1.97106e7 | 0.723725 | ||||||||
\(943\) | 5.55901e7 | 2.03572 | ||||||||
\(944\) | −156142. | −0.00570283 | ||||||||
\(945\) | −5.01588e6 | −0.182712 | ||||||||
\(946\) | −4.21895e7 | −1.53277 | ||||||||
\(947\) | −2.45846e7 | −0.890815 | −0.445408 | − | 0.895328i | \(-0.646941\pi\) | ||||
−0.445408 | + | 0.895328i | \(0.646941\pi\) | |||||||
\(948\) | 2.57493e7 | 0.930562 | ||||||||
\(949\) | −5.08803e6 | −0.183394 | ||||||||
\(950\) | −1.46029e6 | −0.0524965 | ||||||||
\(951\) | 8.69601e6 | 0.311795 | ||||||||
\(952\) | 8.83874e6 | 0.316081 | ||||||||
\(953\) | 4.59681e7 | 1.63955 | 0.819774 | − | 0.572687i | \(-0.194099\pi\) | ||||
0.819774 | + | 0.572687i | \(0.194099\pi\) | |||||||
\(954\) | −5.33708e6 | −0.189860 | ||||||||
\(955\) | −8.16901e6 | −0.289842 | ||||||||
\(956\) | −1.50842e7 | −0.533800 | ||||||||
\(957\) | −6.34686e7 | −2.24016 | ||||||||
\(958\) | −1.65520e7 | −0.582687 | ||||||||
\(959\) | 92832.6 | 0.00325952 | ||||||||
\(960\) | −7.10379e6 | −0.248778 | ||||||||
\(961\) | −1.32411e7 | −0.462503 | ||||||||
\(962\) | 1.11216e6 | 0.0387463 | ||||||||
\(963\) | 6.19051e6 | 0.215110 | ||||||||
\(964\) | −2.74015e7 | −0.949690 | ||||||||
\(965\) | 6.64338e6 | 0.229652 | ||||||||
\(966\) | 8.03226e6 | 0.276946 | ||||||||
\(967\) | −5.30202e7 | −1.82337 | −0.911686 | − | 0.410888i | \(-0.865219\pi\) | ||||
−0.911686 | + | 0.410888i | \(0.865219\pi\) | |||||||
\(968\) | 5.77093e7 | 1.97951 | ||||||||
\(969\) | −8.91630e6 | −0.305053 | ||||||||
\(970\) | −9.21409e6 | −0.314429 | ||||||||
\(971\) | −5.43523e7 | −1.84999 | −0.924996 | − | 0.379976i | \(-0.875932\pi\) | ||||
−0.924996 | + | 0.379976i | \(0.875932\pi\) | |||||||
\(972\) | −8.41202e6 | −0.285585 | ||||||||
\(973\) | −9.88809e6 | −0.334835 | ||||||||
\(974\) | −1.62309e7 | −0.548207 | ||||||||
\(975\) | −4.26620e6 | −0.143724 | ||||||||
\(976\) | 858083. | 0.0288340 | ||||||||
\(977\) | 1.08929e7 | 0.365097 | 0.182549 | − | 0.983197i | \(-0.441565\pi\) | ||||
0.182549 | + | 0.983197i | \(0.441565\pi\) | |||||||
\(978\) | −3.76922e6 | −0.126010 | ||||||||
\(979\) | −2.93282e6 | −0.0977976 | ||||||||
\(980\) | 1.17236e6 | 0.0389937 | ||||||||
\(981\) | 2.90031e6 | 0.0962215 | ||||||||
\(982\) | −2.33796e7 | −0.773674 | ||||||||
\(983\) | −3.42136e7 | −1.12932 | −0.564658 | − | 0.825325i | \(-0.690992\pi\) | ||||
−0.564658 | + | 0.825325i | \(0.690992\pi\) | |||||||
\(984\) | 4.02632e7 | 1.32562 | ||||||||
\(985\) | 1.29466e7 | 0.425173 | ||||||||
\(986\) | 2.36348e7 | 0.774211 | ||||||||
\(987\) | 2.86111e6 | 0.0934850 | ||||||||
\(988\) | 6.48943e6 | 0.211502 | ||||||||
\(989\) | −5.90047e7 | −1.91821 | ||||||||
\(990\) | 3.55409e6 | 0.115250 | ||||||||
\(991\) | 4.22117e6 | 0.136537 | 0.0682683 | − | 0.997667i | \(-0.478253\pi\) | ||||
0.0682683 | + | 0.997667i | \(0.478253\pi\) | |||||||
\(992\) | 2.25986e7 | 0.729125 | ||||||||
\(993\) | −1.54796e7 | −0.498181 | ||||||||
\(994\) | 3.28591e6 | 0.105485 | ||||||||
\(995\) | 3.71716e6 | 0.119029 | ||||||||
\(996\) | −1.87790e7 | −0.599824 | ||||||||
\(997\) | 4.30323e7 | 1.37106 | 0.685530 | − | 0.728044i | \(-0.259571\pi\) | ||||
0.685530 | + | 0.728044i | \(0.259571\pi\) | |||||||
\(998\) | 1.59830e7 | 0.507964 | ||||||||
\(999\) | −2.56822e6 | −0.0814177 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 35.6.a.b.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 315.6.a.c.1.2 | 2 | |||
4.3 | odd | 2 | 560.6.a.l.1.1 | 2 | |||
5.2 | odd | 4 | 175.6.b.d.99.2 | 4 | |||
5.3 | odd | 4 | 175.6.b.d.99.3 | 4 | |||
5.4 | even | 2 | 175.6.a.d.1.2 | 2 | |||
7.6 | odd | 2 | 245.6.a.c.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.6.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
175.6.a.d.1.2 | 2 | 5.4 | even | 2 | |||
175.6.b.d.99.2 | 4 | 5.2 | odd | 4 | |||
175.6.b.d.99.3 | 4 | 5.3 | odd | 4 | |||
245.6.a.c.1.1 | 2 | 7.6 | odd | 2 | |||
315.6.a.c.1.2 | 2 | 3.2 | odd | 2 | |||
560.6.a.l.1.1 | 2 | 4.3 | odd | 2 |