Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,8,Mod(1,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.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: | \(23.1164918858\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 2x^{3} - 2177x^{2} - 14018x + 634476 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(14.6748\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | −82.6714 | −1.76779 | −0.883896 | − | 0.467684i | \(-0.845088\pi\) | ||||
−0.883896 | + | 0.467684i | \(0.845088\pi\) | |||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | 114.337 | 0.409064 | 0.204532 | − | 0.978860i | \(-0.434433\pi\) | ||||
0.204532 | + | 0.978860i | \(0.434433\pi\) | |||||||
\(6\) | −661.371 | −1.25002 | ||||||||
\(7\) | 130.721 | 0.144046 | 0.0720230 | − | 0.997403i | \(-0.477055\pi\) | ||||
0.0720230 | + | 0.997403i | \(0.477055\pi\) | |||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 4647.56 | 2.12509 | ||||||||
\(10\) | 914.695 | 0.289252 | ||||||||
\(11\) | 2344.52 | 0.531104 | 0.265552 | − | 0.964097i | \(-0.414446\pi\) | ||||
0.265552 | + | 0.964097i | \(0.414446\pi\) | |||||||
\(12\) | −5290.97 | −0.883896 | ||||||||
\(13\) | −5974.20 | −0.754185 | −0.377092 | − | 0.926176i | \(-0.623076\pi\) | ||||
−0.377092 | + | 0.926176i | \(0.623076\pi\) | |||||||
\(14\) | 1045.76 | 0.101856 | ||||||||
\(15\) | −9452.39 | −0.723139 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | −19882.8 | −0.981535 | −0.490767 | − | 0.871291i | \(-0.663284\pi\) | ||||
−0.490767 | + | 0.871291i | \(0.663284\pi\) | |||||||
\(18\) | 37180.5 | 1.50266 | ||||||||
\(19\) | −7787.29 | −0.260465 | −0.130232 | − | 0.991484i | \(-0.541572\pi\) | ||||
−0.130232 | + | 0.991484i | \(0.541572\pi\) | |||||||
\(20\) | 7317.56 | 0.204532 | ||||||||
\(21\) | −10806.9 | −0.254643 | ||||||||
\(22\) | 18756.2 | 0.375547 | ||||||||
\(23\) | 4821.07 | 0.0826221 | 0.0413111 | − | 0.999146i | \(-0.486847\pi\) | ||||
0.0413111 | + | 0.999146i | \(0.486847\pi\) | |||||||
\(24\) | −42327.8 | −0.625009 | ||||||||
\(25\) | −65052.1 | −0.832667 | ||||||||
\(26\) | −47793.6 | −0.533289 | ||||||||
\(27\) | −203418. | −1.98892 | ||||||||
\(28\) | 8366.12 | 0.0720230 | ||||||||
\(29\) | −246156. | −1.87421 | −0.937105 | − | 0.349048i | \(-0.886505\pi\) | ||||
−0.937105 | + | 0.349048i | \(0.886505\pi\) | |||||||
\(30\) | −75619.1 | −0.511337 | ||||||||
\(31\) | −67628.9 | −0.407724 | −0.203862 | − | 0.979000i | \(-0.565349\pi\) | ||||
−0.203862 | + | 0.979000i | \(0.565349\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | −193825. | −0.938881 | ||||||||
\(34\) | −159062. | −0.694050 | ||||||||
\(35\) | 14946.2 | 0.0589240 | ||||||||
\(36\) | 297444. | 1.06254 | ||||||||
\(37\) | −50653.0 | −0.164399 | ||||||||
\(38\) | −62298.3 | −0.184176 | ||||||||
\(39\) | 493895. | 1.33324 | ||||||||
\(40\) | 58540.4 | 0.144626 | ||||||||
\(41\) | −242383. | −0.549236 | −0.274618 | − | 0.961553i | \(-0.588551\pi\) | ||||
−0.274618 | + | 0.961553i | \(0.588551\pi\) | |||||||
\(42\) | −86454.9 | −0.180060 | ||||||||
\(43\) | 660296. | 1.26648 | 0.633241 | − | 0.773955i | \(-0.281724\pi\) | ||||
0.633241 | + | 0.773955i | \(0.281724\pi\) | |||||||
\(44\) | 150049. | 0.265552 | ||||||||
\(45\) | 531388. | 0.869296 | ||||||||
\(46\) | 38568.6 | 0.0584227 | ||||||||
\(47\) | −310360. | −0.436037 | −0.218019 | − | 0.975945i | \(-0.569959\pi\) | ||||
−0.218019 | + | 0.975945i | \(0.569959\pi\) | |||||||
\(48\) | −338622. | −0.441948 | ||||||||
\(49\) | −806455. | −0.979251 | ||||||||
\(50\) | −520417. | −0.588784 | ||||||||
\(51\) | 1.64374e6 | 1.73515 | ||||||||
\(52\) | −382349. | −0.377092 | ||||||||
\(53\) | 859068. | 0.792614 | 0.396307 | − | 0.918118i | \(-0.370292\pi\) | ||||
0.396307 | + | 0.918118i | \(0.370292\pi\) | |||||||
\(54\) | −1.62735e6 | −1.40638 | ||||||||
\(55\) | 268065. | 0.217255 | ||||||||
\(56\) | 66929.0 | 0.0509279 | ||||||||
\(57\) | 643786. | 0.460447 | ||||||||
\(58\) | −1.96925e6 | −1.32527 | ||||||||
\(59\) | −1.22165e6 | −0.774396 | −0.387198 | − | 0.921996i | \(-0.626557\pi\) | ||||
−0.387198 | + | 0.921996i | \(0.626557\pi\) | |||||||
\(60\) | −604953. | −0.361570 | ||||||||
\(61\) | −1.70926e6 | −0.964170 | −0.482085 | − | 0.876124i | \(-0.660120\pi\) | ||||
−0.482085 | + | 0.876124i | \(0.660120\pi\) | |||||||
\(62\) | −541031. | −0.288305 | ||||||||
\(63\) | 607532. | 0.306110 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −683071. | −0.308510 | ||||||||
\(66\) | −1.55060e6 | −0.663889 | ||||||||
\(67\) | 1.29584e6 | 0.526367 | 0.263184 | − | 0.964746i | \(-0.415227\pi\) | ||||
0.263184 | + | 0.964746i | \(0.415227\pi\) | |||||||
\(68\) | −1.27250e6 | −0.490767 | ||||||||
\(69\) | −398565. | −0.146059 | ||||||||
\(70\) | 119569. | 0.0416655 | ||||||||
\(71\) | −518524. | −0.171935 | −0.0859675 | − | 0.996298i | \(-0.527398\pi\) | ||||
−0.0859675 | + | 0.996298i | \(0.527398\pi\) | |||||||
\(72\) | 2.37955e6 | 0.751331 | ||||||||
\(73\) | 872444. | 0.262487 | 0.131243 | − | 0.991350i | \(-0.458103\pi\) | ||||
0.131243 | + | 0.991350i | \(0.458103\pi\) | |||||||
\(74\) | −405224. | −0.116248 | ||||||||
\(75\) | 5.37795e6 | 1.47198 | ||||||||
\(76\) | −498387. | −0.130232 | ||||||||
\(77\) | 306477. | 0.0765033 | ||||||||
\(78\) | 3.95116e6 | 0.942744 | ||||||||
\(79\) | −4.72622e6 | −1.07850 | −0.539249 | − | 0.842147i | \(-0.681292\pi\) | ||||
−0.539249 | + | 0.842147i | \(0.681292\pi\) | |||||||
\(80\) | 468324. | 0.102266 | ||||||||
\(81\) | 6.65266e6 | 1.39091 | ||||||||
\(82\) | −1.93906e6 | −0.388368 | ||||||||
\(83\) | 1.69885e6 | 0.326124 | 0.163062 | − | 0.986616i | \(-0.447863\pi\) | ||||
0.163062 | + | 0.986616i | \(0.447863\pi\) | |||||||
\(84\) | −691639. | −0.127322 | ||||||||
\(85\) | −2.27333e6 | −0.401510 | ||||||||
\(86\) | 5.28237e6 | 0.895538 | ||||||||
\(87\) | 2.03501e7 | 3.31321 | ||||||||
\(88\) | 1.20039e6 | 0.187774 | ||||||||
\(89\) | −4.21199e6 | −0.633318 | −0.316659 | − | 0.948539i | \(-0.602561\pi\) | ||||
−0.316659 | + | 0.948539i | \(0.602561\pi\) | |||||||
\(90\) | 4.25110e6 | 0.614685 | ||||||||
\(91\) | −780951. | −0.108637 | ||||||||
\(92\) | 308549. | 0.0413111 | ||||||||
\(93\) | 5.59098e6 | 0.720771 | ||||||||
\(94\) | −2.48288e6 | −0.308325 | ||||||||
\(95\) | −890374. | −0.106547 | ||||||||
\(96\) | −2.70898e6 | −0.312504 | ||||||||
\(97\) | 1.31862e7 | 1.46697 | 0.733483 | − | 0.679708i | \(-0.237894\pi\) | ||||
0.733483 | + | 0.679708i | \(0.237894\pi\) | |||||||
\(98\) | −6.45164e6 | −0.692435 | ||||||||
\(99\) | 1.08963e7 | 1.12864 | ||||||||
\(100\) | −4.16333e6 | −0.416333 | ||||||||
\(101\) | −1.96105e7 | −1.89393 | −0.946965 | − | 0.321336i | \(-0.895868\pi\) | ||||
−0.946965 | + | 0.321336i | \(0.895868\pi\) | |||||||
\(102\) | 1.31499e7 | 1.22694 | ||||||||
\(103\) | −7.59111e6 | −0.684502 | −0.342251 | − | 0.939609i | \(-0.611189\pi\) | ||||
−0.342251 | + | 0.939609i | \(0.611189\pi\) | |||||||
\(104\) | −3.05879e6 | −0.266645 | ||||||||
\(105\) | −1.23562e6 | −0.104165 | ||||||||
\(106\) | 6.87254e6 | 0.560463 | ||||||||
\(107\) | 1.56821e7 | 1.23755 | 0.618773 | − | 0.785570i | \(-0.287630\pi\) | ||||
0.618773 | + | 0.785570i | \(0.287630\pi\) | |||||||
\(108\) | −1.30188e7 | −0.994459 | ||||||||
\(109\) | −533820. | −0.0394823 | −0.0197411 | − | 0.999805i | \(-0.506284\pi\) | ||||
−0.0197411 | + | 0.999805i | \(0.506284\pi\) | |||||||
\(110\) | 2.14452e6 | 0.153623 | ||||||||
\(111\) | 4.18756e6 | 0.290623 | ||||||||
\(112\) | 535432. | 0.0360115 | ||||||||
\(113\) | −1.42250e7 | −0.927420 | −0.463710 | − | 0.885987i | \(-0.653482\pi\) | ||||
−0.463710 | + | 0.885987i | \(0.653482\pi\) | |||||||
\(114\) | 5.15029e6 | 0.325585 | ||||||||
\(115\) | 551226. | 0.0337977 | ||||||||
\(116\) | −1.57540e7 | −0.937105 | ||||||||
\(117\) | −2.77655e7 | −1.60271 | ||||||||
\(118\) | −9.77317e6 | −0.547581 | ||||||||
\(119\) | −2.59909e6 | −0.141386 | ||||||||
\(120\) | −4.83962e6 | −0.255668 | ||||||||
\(121\) | −1.39904e7 | −0.717929 | ||||||||
\(122\) | −1.36741e7 | −0.681771 | ||||||||
\(123\) | 2.00381e7 | 0.970934 | ||||||||
\(124\) | −4.32825e6 | −0.203862 | ||||||||
\(125\) | −1.63704e7 | −0.749678 | ||||||||
\(126\) | 4.86026e6 | 0.216452 | ||||||||
\(127\) | −2.12729e7 | −0.921537 | −0.460768 | − | 0.887520i | \(-0.652426\pi\) | ||||
−0.460768 | + | 0.887520i | \(0.652426\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | −5.45876e7 | −2.23888 | ||||||||
\(130\) | −5.46457e6 | −0.218149 | ||||||||
\(131\) | 1.89968e7 | 0.738297 | 0.369148 | − | 0.929370i | \(-0.379649\pi\) | ||||
0.369148 | + | 0.929370i | \(0.379649\pi\) | |||||||
\(132\) | −1.24048e7 | −0.469440 | ||||||||
\(133\) | −1.01796e6 | −0.0375189 | ||||||||
\(134\) | 1.03667e7 | 0.372198 | ||||||||
\(135\) | −2.32582e7 | −0.813594 | ||||||||
\(136\) | −1.01800e7 | −0.347025 | ||||||||
\(137\) | 5.66328e7 | 1.88168 | 0.940841 | − | 0.338848i | \(-0.110037\pi\) | ||||
0.940841 | + | 0.338848i | \(0.110037\pi\) | |||||||
\(138\) | −3.18852e6 | −0.103279 | ||||||||
\(139\) | 3.15115e7 | 0.995215 | 0.497607 | − | 0.867402i | \(-0.334212\pi\) | ||||
0.497607 | + | 0.867402i | \(0.334212\pi\) | |||||||
\(140\) | 956555. | 0.0294620 | ||||||||
\(141\) | 2.56579e7 | 0.770823 | ||||||||
\(142\) | −4.14819e6 | −0.121576 | ||||||||
\(143\) | −1.40066e7 | −0.400551 | ||||||||
\(144\) | 1.90364e7 | 0.531272 | ||||||||
\(145\) | −2.81447e7 | −0.766671 | ||||||||
\(146\) | 6.97955e6 | 0.185606 | ||||||||
\(147\) | 6.66708e7 | 1.73111 | ||||||||
\(148\) | −3.24179e6 | −0.0821995 | ||||||||
\(149\) | 206567. | 0.00511575 | 0.00255787 | − | 0.999997i | \(-0.499186\pi\) | ||||
0.00255787 | + | 0.999997i | \(0.499186\pi\) | |||||||
\(150\) | 4.30236e7 | 1.04085 | ||||||||
\(151\) | 3.08004e7 | 0.728009 | 0.364005 | − | 0.931397i | \(-0.381409\pi\) | ||||
0.364005 | + | 0.931397i | \(0.381409\pi\) | |||||||
\(152\) | −3.98709e6 | −0.0920882 | ||||||||
\(153\) | −9.24064e7 | −2.08585 | ||||||||
\(154\) | 2.45182e6 | 0.0540960 | ||||||||
\(155\) | −7.73248e6 | −0.166785 | ||||||||
\(156\) | 3.16093e7 | 0.666621 | ||||||||
\(157\) | 5.53862e7 | 1.14223 | 0.571114 | − | 0.820871i | \(-0.306511\pi\) | ||||
0.571114 | + | 0.820871i | \(0.306511\pi\) | |||||||
\(158\) | −3.78097e7 | −0.762613 | ||||||||
\(159\) | −7.10204e7 | −1.40118 | ||||||||
\(160\) | 3.74659e6 | 0.0723130 | ||||||||
\(161\) | 630214. | 0.0119014 | ||||||||
\(162\) | 5.32213e7 | 0.983519 | ||||||||
\(163\) | −1.01371e8 | −1.83340 | −0.916701 | − | 0.399574i | \(-0.869158\pi\) | ||||
−0.916701 | + | 0.399574i | \(0.869158\pi\) | |||||||
\(164\) | −1.55125e7 | −0.274618 | ||||||||
\(165\) | −2.21613e7 | −0.384062 | ||||||||
\(166\) | 1.35908e7 | 0.230605 | ||||||||
\(167\) | −1.14227e8 | −1.89785 | −0.948926 | − | 0.315498i | \(-0.897829\pi\) | ||||
−0.948926 | + | 0.315498i | \(0.897829\pi\) | |||||||
\(168\) | −5.53311e6 | −0.0900299 | ||||||||
\(169\) | −2.70575e7 | −0.431205 | ||||||||
\(170\) | −1.81867e7 | −0.283911 | ||||||||
\(171\) | −3.61919e7 | −0.553510 | ||||||||
\(172\) | 4.22589e7 | 0.633241 | ||||||||
\(173\) | −4.78631e7 | −0.702813 | −0.351407 | − | 0.936223i | \(-0.614297\pi\) | ||||
−0.351407 | + | 0.936223i | \(0.614297\pi\) | |||||||
\(174\) | 1.62801e8 | 2.34279 | ||||||||
\(175\) | −8.50365e6 | −0.119942 | ||||||||
\(176\) | 9.60315e6 | 0.132776 | ||||||||
\(177\) | 1.00995e8 | 1.36897 | ||||||||
\(178\) | −3.36959e7 | −0.447824 | ||||||||
\(179\) | 1.97413e7 | 0.257271 | 0.128635 | − | 0.991692i | \(-0.458940\pi\) | ||||
0.128635 | + | 0.991692i | \(0.458940\pi\) | |||||||
\(180\) | 3.40088e7 | 0.434648 | ||||||||
\(181\) | 6.57898e7 | 0.824676 | 0.412338 | − | 0.911031i | \(-0.364712\pi\) | ||||
0.412338 | + | 0.911031i | \(0.364712\pi\) | |||||||
\(182\) | −6.24761e6 | −0.0768181 | ||||||||
\(183\) | 1.41307e8 | 1.70445 | ||||||||
\(184\) | 2.46839e6 | 0.0292113 | ||||||||
\(185\) | −5.79150e6 | −0.0672497 | ||||||||
\(186\) | 4.47278e7 | 0.509662 | ||||||||
\(187\) | −4.66155e7 | −0.521297 | ||||||||
\(188\) | −1.98631e7 | −0.218019 | ||||||||
\(189\) | −2.65910e7 | −0.286495 | ||||||||
\(190\) | −7.12299e6 | −0.0753399 | ||||||||
\(191\) | −6.84589e7 | −0.710907 | −0.355454 | − | 0.934694i | \(-0.615674\pi\) | ||||
−0.355454 | + | 0.934694i | \(0.615674\pi\) | |||||||
\(192\) | −2.16718e7 | −0.220974 | ||||||||
\(193\) | 9.33194e7 | 0.934375 | 0.467187 | − | 0.884158i | \(-0.345267\pi\) | ||||
0.467187 | + | 0.884158i | \(0.345267\pi\) | |||||||
\(194\) | 1.05490e8 | 1.03730 | ||||||||
\(195\) | 5.64704e7 | 0.545381 | ||||||||
\(196\) | −5.16131e7 | −0.489625 | ||||||||
\(197\) | 1.41425e8 | 1.31794 | 0.658970 | − | 0.752169i | \(-0.270992\pi\) | ||||
0.658970 | + | 0.752169i | \(0.270992\pi\) | |||||||
\(198\) | 8.71704e7 | 0.798070 | ||||||||
\(199\) | 1.09895e8 | 0.988531 | 0.494265 | − | 0.869311i | \(-0.335437\pi\) | ||||
0.494265 | + | 0.869311i | \(0.335437\pi\) | |||||||
\(200\) | −3.33067e7 | −0.294392 | ||||||||
\(201\) | −1.07129e8 | −0.930508 | ||||||||
\(202\) | −1.56884e8 | −1.33921 | ||||||||
\(203\) | −3.21777e7 | −0.269972 | ||||||||
\(204\) | 1.05199e8 | 0.867574 | ||||||||
\(205\) | −2.77133e7 | −0.224672 | ||||||||
\(206\) | −6.07288e7 | −0.484016 | ||||||||
\(207\) | 2.24062e7 | 0.175579 | ||||||||
\(208\) | −2.44703e7 | −0.188546 | ||||||||
\(209\) | −1.82575e7 | −0.138334 | ||||||||
\(210\) | −9.88497e6 | −0.0736560 | ||||||||
\(211\) | 1.70421e8 | 1.24892 | 0.624458 | − | 0.781058i | \(-0.285320\pi\) | ||||
0.624458 | + | 0.781058i | \(0.285320\pi\) | |||||||
\(212\) | 5.49804e7 | 0.396307 | ||||||||
\(213\) | 4.28671e7 | 0.303945 | ||||||||
\(214\) | 1.25457e8 | 0.875078 | ||||||||
\(215\) | 7.54961e7 | 0.518072 | ||||||||
\(216\) | −1.04150e8 | −0.703189 | ||||||||
\(217\) | −8.84049e6 | −0.0587310 | ||||||||
\(218\) | −4.27056e6 | −0.0279182 | ||||||||
\(219\) | −7.21262e7 | −0.464022 | ||||||||
\(220\) | 1.71562e7 | 0.108628 | ||||||||
\(221\) | 1.18784e8 | 0.740259 | ||||||||
\(222\) | 3.35004e7 | 0.205502 | ||||||||
\(223\) | 5.64211e7 | 0.340702 | 0.170351 | − | 0.985383i | \(-0.445510\pi\) | ||||
0.170351 | + | 0.985383i | \(0.445510\pi\) | |||||||
\(224\) | 4.28345e6 | 0.0254640 | ||||||||
\(225\) | −3.02334e8 | −1.76949 | ||||||||
\(226\) | −1.13800e8 | −0.655785 | ||||||||
\(227\) | −1.82878e8 | −1.03770 | −0.518848 | − | 0.854866i | \(-0.673639\pi\) | ||||
−0.518848 | + | 0.854866i | \(0.673639\pi\) | |||||||
\(228\) | 4.12023e7 | 0.230224 | ||||||||
\(229\) | 1.93904e7 | 0.106700 | 0.0533498 | − | 0.998576i | \(-0.483010\pi\) | ||||
0.0533498 | + | 0.998576i | \(0.483010\pi\) | |||||||
\(230\) | 4.40981e6 | 0.0238986 | ||||||||
\(231\) | −2.53369e7 | −0.135242 | ||||||||
\(232\) | −1.26032e8 | −0.662633 | ||||||||
\(233\) | −7.65219e7 | −0.396314 | −0.198157 | − | 0.980170i | \(-0.563496\pi\) | ||||
−0.198157 | + | 0.980170i | \(0.563496\pi\) | |||||||
\(234\) | −2.22124e8 | −1.13329 | ||||||||
\(235\) | −3.54856e7 | −0.178367 | ||||||||
\(236\) | −7.81853e7 | −0.387198 | ||||||||
\(237\) | 3.90723e8 | 1.90656 | ||||||||
\(238\) | −2.07927e7 | −0.0999750 | ||||||||
\(239\) | 3.45231e8 | 1.63575 | 0.817875 | − | 0.575396i | \(-0.195152\pi\) | ||||
0.817875 | + | 0.575396i | \(0.195152\pi\) | |||||||
\(240\) | −3.87170e7 | −0.180785 | ||||||||
\(241\) | −2.61103e8 | −1.20158 | −0.600789 | − | 0.799408i | \(-0.705147\pi\) | ||||
−0.600789 | + | 0.799408i | \(0.705147\pi\) | |||||||
\(242\) | −1.11923e8 | −0.507652 | ||||||||
\(243\) | −1.05109e8 | −0.469913 | ||||||||
\(244\) | −1.09393e8 | −0.482085 | ||||||||
\(245\) | −9.22075e7 | −0.400576 | ||||||||
\(246\) | 1.60305e8 | 0.686554 | ||||||||
\(247\) | 4.65228e7 | 0.196439 | ||||||||
\(248\) | −3.46260e7 | −0.144152 | ||||||||
\(249\) | −1.40447e8 | −0.576519 | ||||||||
\(250\) | −1.30963e8 | −0.530102 | ||||||||
\(251\) | 1.56531e8 | 0.624804 | 0.312402 | − | 0.949950i | \(-0.398866\pi\) | ||||
0.312402 | + | 0.949950i | \(0.398866\pi\) | |||||||
\(252\) | 3.88821e7 | 0.153055 | ||||||||
\(253\) | 1.13031e7 | 0.0438809 | ||||||||
\(254\) | −1.70183e8 | −0.651625 | ||||||||
\(255\) | 1.87940e8 | 0.709787 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | 1.85640e8 | 0.682191 | 0.341095 | − | 0.940029i | \(-0.389202\pi\) | ||||
0.341095 | + | 0.940029i | \(0.389202\pi\) | |||||||
\(258\) | −4.36701e8 | −1.58312 | ||||||||
\(259\) | −6.62139e6 | −0.0236810 | ||||||||
\(260\) | −4.37165e7 | −0.154255 | ||||||||
\(261\) | −1.14403e9 | −3.98286 | ||||||||
\(262\) | 1.51974e8 | 0.522055 | ||||||||
\(263\) | 5.09760e8 | 1.72791 | 0.863953 | − | 0.503572i | \(-0.167981\pi\) | ||||
0.863953 | + | 0.503572i | \(0.167981\pi\) | |||||||
\(264\) | −9.92383e7 | −0.331945 | ||||||||
\(265\) | 9.82231e7 | 0.324230 | ||||||||
\(266\) | −8.14368e6 | −0.0265298 | ||||||||
\(267\) | 3.48211e8 | 1.11957 | ||||||||
\(268\) | 8.29336e7 | 0.263184 | ||||||||
\(269\) | 3.92417e8 | 1.22918 | 0.614589 | − | 0.788848i | \(-0.289322\pi\) | ||||
0.614589 | + | 0.788848i | \(0.289322\pi\) | |||||||
\(270\) | −1.86066e8 | −0.575298 | ||||||||
\(271\) | −4.63684e8 | −1.41524 | −0.707619 | − | 0.706594i | \(-0.750231\pi\) | ||||
−0.707619 | + | 0.706594i | \(0.750231\pi\) | |||||||
\(272\) | −8.14398e7 | −0.245384 | ||||||||
\(273\) | 6.45623e7 | 0.192048 | ||||||||
\(274\) | 4.53063e8 | 1.33055 | ||||||||
\(275\) | −1.52516e8 | −0.442233 | ||||||||
\(276\) | −2.55082e7 | −0.0730293 | ||||||||
\(277\) | 1.93073e8 | 0.545811 | 0.272906 | − | 0.962041i | \(-0.412015\pi\) | ||||
0.272906 | + | 0.962041i | \(0.412015\pi\) | |||||||
\(278\) | 2.52092e8 | 0.703723 | ||||||||
\(279\) | −3.14310e8 | −0.866449 | ||||||||
\(280\) | 7.65244e6 | 0.0208328 | ||||||||
\(281\) | 3.95956e8 | 1.06457 | 0.532285 | − | 0.846565i | \(-0.321333\pi\) | ||||
0.532285 | + | 0.846565i | \(0.321333\pi\) | |||||||
\(282\) | 2.05263e8 | 0.545054 | ||||||||
\(283\) | −5.52836e8 | −1.44992 | −0.724959 | − | 0.688792i | \(-0.758142\pi\) | ||||
−0.724959 | + | 0.688792i | \(0.758142\pi\) | |||||||
\(284\) | −3.31855e7 | −0.0859675 | ||||||||
\(285\) | 7.36085e7 | 0.188352 | ||||||||
\(286\) | −1.12053e8 | −0.283232 | ||||||||
\(287\) | −3.16845e7 | −0.0791151 | ||||||||
\(288\) | 1.52291e8 | 0.375666 | ||||||||
\(289\) | −1.50141e7 | −0.0365895 | ||||||||
\(290\) | −2.25158e8 | −0.542119 | ||||||||
\(291\) | −1.09013e9 | −2.59329 | ||||||||
\(292\) | 5.58364e7 | 0.131243 | ||||||||
\(293\) | −8.34151e7 | −0.193735 | −0.0968675 | − | 0.995297i | \(-0.530882\pi\) | ||||
−0.0968675 | + | 0.995297i | \(0.530882\pi\) | |||||||
\(294\) | 5.33366e8 | 1.22408 | ||||||||
\(295\) | −1.39679e8 | −0.316778 | ||||||||
\(296\) | −2.59343e7 | −0.0581238 | ||||||||
\(297\) | −4.76918e8 | −1.05632 | ||||||||
\(298\) | 1.65254e6 | 0.00361738 | ||||||||
\(299\) | −2.88020e7 | −0.0623123 | ||||||||
\(300\) | 3.44189e8 | 0.735991 | ||||||||
\(301\) | 8.63143e7 | 0.182432 | ||||||||
\(302\) | 2.46403e8 | 0.514780 | ||||||||
\(303\) | 1.62123e9 | 3.34807 | ||||||||
\(304\) | −3.18967e7 | −0.0651162 | ||||||||
\(305\) | −1.95431e8 | −0.394407 | ||||||||
\(306\) | −7.39252e8 | −1.47492 | ||||||||
\(307\) | 8.49160e8 | 1.67496 | 0.837482 | − | 0.546466i | \(-0.184027\pi\) | ||||
0.837482 | + | 0.546466i | \(0.184027\pi\) | |||||||
\(308\) | 1.96145e7 | 0.0382517 | ||||||||
\(309\) | 6.27567e8 | 1.21006 | ||||||||
\(310\) | −6.18598e7 | −0.117935 | ||||||||
\(311\) | 3.12972e8 | 0.589990 | 0.294995 | − | 0.955499i | \(-0.404682\pi\) | ||||
0.294995 | + | 0.955499i | \(0.404682\pi\) | |||||||
\(312\) | 2.52874e8 | 0.471372 | ||||||||
\(313\) | −3.68233e8 | −0.678763 | −0.339381 | − | 0.940649i | \(-0.610218\pi\) | ||||
−0.339381 | + | 0.940649i | \(0.610218\pi\) | |||||||
\(314\) | 4.43090e8 | 0.807677 | ||||||||
\(315\) | 6.94633e7 | 0.125219 | ||||||||
\(316\) | −3.02478e8 | −0.539249 | ||||||||
\(317\) | 8.20621e8 | 1.44689 | 0.723445 | − | 0.690382i | \(-0.242558\pi\) | ||||
0.723445 | + | 0.690382i | \(0.242558\pi\) | |||||||
\(318\) | −5.68163e8 | −0.990782 | ||||||||
\(319\) | −5.77119e8 | −0.995400 | ||||||||
\(320\) | 2.99727e7 | 0.0511330 | ||||||||
\(321\) | −1.29646e9 | −2.18772 | ||||||||
\(322\) | 5.04171e6 | 0.00841554 | ||||||||
\(323\) | 1.54833e8 | 0.255655 | ||||||||
\(324\) | 4.25770e8 | 0.695453 | ||||||||
\(325\) | 3.88634e8 | 0.627985 | ||||||||
\(326\) | −8.10969e8 | −1.29641 | ||||||||
\(327\) | 4.41317e7 | 0.0697964 | ||||||||
\(328\) | −1.24100e8 | −0.194184 | ||||||||
\(329\) | −4.05705e7 | −0.0628094 | ||||||||
\(330\) | −1.77290e8 | −0.271573 | ||||||||
\(331\) | 3.11691e7 | 0.0472418 | 0.0236209 | − | 0.999721i | \(-0.492481\pi\) | ||||
0.0236209 | + | 0.999721i | \(0.492481\pi\) | |||||||
\(332\) | 1.08727e8 | 0.163062 | ||||||||
\(333\) | −2.35413e8 | −0.349362 | ||||||||
\(334\) | −9.13819e8 | −1.34198 | ||||||||
\(335\) | 1.48162e8 | 0.215318 | ||||||||
\(336\) | −4.42649e7 | −0.0636608 | ||||||||
\(337\) | −1.31728e9 | −1.87487 | −0.937437 | − | 0.348155i | \(-0.886808\pi\) | ||||
−0.937437 | + | 0.348155i | \(0.886808\pi\) | |||||||
\(338\) | −2.16460e8 | −0.304908 | ||||||||
\(339\) | 1.17600e9 | 1.63949 | ||||||||
\(340\) | −1.45493e8 | −0.200755 | ||||||||
\(341\) | −1.58557e8 | −0.216544 | ||||||||
\(342\) | −2.89535e8 | −0.391391 | ||||||||
\(343\) | −2.13074e8 | −0.285103 | ||||||||
\(344\) | 3.38071e8 | 0.447769 | ||||||||
\(345\) | −4.55706e7 | −0.0597473 | ||||||||
\(346\) | −3.82905e8 | −0.496964 | ||||||||
\(347\) | 1.01825e9 | 1.30829 | 0.654144 | − | 0.756370i | \(-0.273029\pi\) | ||||
0.654144 | + | 0.756370i | \(0.273029\pi\) | |||||||
\(348\) | 1.30241e9 | 1.65661 | ||||||||
\(349\) | −1.02153e9 | −1.28636 | −0.643182 | − | 0.765713i | \(-0.722386\pi\) | ||||
−0.643182 | + | 0.765713i | \(0.722386\pi\) | |||||||
\(350\) | −6.80292e7 | −0.0848120 | ||||||||
\(351\) | 1.21526e9 | 1.50001 | ||||||||
\(352\) | 7.68252e7 | 0.0938868 | ||||||||
\(353\) | 1.14845e8 | 0.138964 | 0.0694818 | − | 0.997583i | \(-0.477865\pi\) | ||||
0.0694818 | + | 0.997583i | \(0.477865\pi\) | |||||||
\(354\) | 8.07962e8 | 0.968009 | ||||||||
\(355\) | −5.92863e7 | −0.0703324 | ||||||||
\(356\) | −2.69567e8 | −0.316659 | ||||||||
\(357\) | 2.14870e8 | 0.249941 | ||||||||
\(358\) | 1.57931e8 | 0.181918 | ||||||||
\(359\) | 1.15379e9 | 1.31612 | 0.658061 | − | 0.752965i | \(-0.271377\pi\) | ||||
0.658061 | + | 0.752965i | \(0.271377\pi\) | |||||||
\(360\) | 2.72070e8 | 0.307343 | ||||||||
\(361\) | −8.33230e8 | −0.932158 | ||||||||
\(362\) | 5.26318e8 | 0.583134 | ||||||||
\(363\) | 1.15661e9 | 1.26915 | ||||||||
\(364\) | −4.99808e7 | −0.0543186 | ||||||||
\(365\) | 9.97525e7 | 0.107374 | ||||||||
\(366\) | 1.13046e9 | 1.20523 | ||||||||
\(367\) | −7.43776e7 | −0.0785436 | −0.0392718 | − | 0.999229i | \(-0.512504\pi\) | ||||
−0.0392718 | + | 0.999229i | \(0.512504\pi\) | |||||||
\(368\) | 1.97471e7 | 0.0206555 | ||||||||
\(369\) | −1.12649e9 | −1.16717 | ||||||||
\(370\) | −4.63320e7 | −0.0475527 | ||||||||
\(371\) | 1.12298e8 | 0.114173 | ||||||||
\(372\) | 3.57823e8 | 0.360386 | ||||||||
\(373\) | −1.22089e9 | −1.21814 | −0.609070 | − | 0.793117i | \(-0.708457\pi\) | ||||
−0.609070 | + | 0.793117i | \(0.708457\pi\) | |||||||
\(374\) | −3.72924e8 | −0.368613 | ||||||||
\(375\) | 1.35337e9 | 1.32527 | ||||||||
\(376\) | −1.58904e8 | −0.154162 | ||||||||
\(377\) | 1.47059e9 | 1.41350 | ||||||||
\(378\) | −2.12728e8 | −0.202583 | ||||||||
\(379\) | −1.09902e9 | −1.03698 | −0.518490 | − | 0.855084i | \(-0.673506\pi\) | ||||
−0.518490 | + | 0.855084i | \(0.673506\pi\) | |||||||
\(380\) | −5.69839e7 | −0.0532733 | ||||||||
\(381\) | 1.75866e9 | 1.62908 | ||||||||
\(382\) | −5.47671e8 | −0.502687 | ||||||||
\(383\) | −5.67152e8 | −0.515827 | −0.257913 | − | 0.966168i | \(-0.583035\pi\) | ||||
−0.257913 | + | 0.966168i | \(0.583035\pi\) | |||||||
\(384\) | −1.73375e8 | −0.156252 | ||||||||
\(385\) | 3.50416e7 | 0.0312947 | ||||||||
\(386\) | 7.46555e8 | 0.660703 | ||||||||
\(387\) | 3.06877e9 | 2.69138 | ||||||||
\(388\) | 8.43919e8 | 0.733483 | ||||||||
\(389\) | −7.90877e8 | −0.681217 | −0.340608 | − | 0.940205i | \(-0.610633\pi\) | ||||
−0.340608 | + | 0.940205i | \(0.610633\pi\) | |||||||
\(390\) | 4.51763e8 | 0.385643 | ||||||||
\(391\) | −9.58563e7 | −0.0810965 | ||||||||
\(392\) | −4.12905e8 | −0.346217 | ||||||||
\(393\) | −1.57049e9 | −1.30515 | ||||||||
\(394\) | 1.13140e9 | 0.931925 | ||||||||
\(395\) | −5.40381e8 | −0.441174 | ||||||||
\(396\) | 6.97363e8 | 0.564321 | ||||||||
\(397\) | −1.40683e9 | −1.12843 | −0.564217 | − | 0.825626i | \(-0.690822\pi\) | ||||
−0.564217 | + | 0.825626i | \(0.690822\pi\) | |||||||
\(398\) | 8.79156e8 | 0.698997 | ||||||||
\(399\) | 8.41562e7 | 0.0663255 | ||||||||
\(400\) | −2.66453e8 | −0.208167 | ||||||||
\(401\) | −2.07896e9 | −1.61005 | −0.805027 | − | 0.593238i | \(-0.797849\pi\) | ||||
−0.805027 | + | 0.593238i | \(0.797849\pi\) | |||||||
\(402\) | −8.57030e8 | −0.657968 | ||||||||
\(403\) | 4.04029e8 | 0.307499 | ||||||||
\(404\) | −1.25507e9 | −0.946965 | ||||||||
\(405\) | 7.60644e8 | 0.568969 | ||||||||
\(406\) | −2.57422e8 | −0.190899 | ||||||||
\(407\) | −1.18757e8 | −0.0873129 | ||||||||
\(408\) | 8.41593e8 | 0.613468 | ||||||||
\(409\) | −1.36197e8 | −0.0984319 | −0.0492160 | − | 0.998788i | \(-0.515672\pi\) | ||||
−0.0492160 | + | 0.998788i | \(0.515672\pi\) | |||||||
\(410\) | −2.21706e8 | −0.158867 | ||||||||
\(411\) | −4.68192e9 | −3.32642 | ||||||||
\(412\) | −4.85831e8 | −0.342251 | ||||||||
\(413\) | −1.59694e8 | −0.111549 | ||||||||
\(414\) | 1.79250e8 | 0.124153 | ||||||||
\(415\) | 1.94242e8 | 0.133406 | ||||||||
\(416\) | −1.95763e8 | −0.133322 | ||||||||
\(417\) | −2.60510e9 | −1.75933 | ||||||||
\(418\) | −1.46060e8 | −0.0978168 | ||||||||
\(419\) | 8.70749e8 | 0.578287 | 0.289144 | − | 0.957286i | \(-0.406629\pi\) | ||||
0.289144 | + | 0.957286i | \(0.406629\pi\) | |||||||
\(420\) | −7.90798e7 | −0.0520826 | ||||||||
\(421\) | −1.78983e9 | −1.16903 | −0.584514 | − | 0.811384i | \(-0.698715\pi\) | ||||
−0.584514 | + | 0.811384i | \(0.698715\pi\) | |||||||
\(422\) | 1.36336e9 | 0.883118 | ||||||||
\(423\) | −1.44242e9 | −0.926617 | ||||||||
\(424\) | 4.39843e8 | 0.280232 | ||||||||
\(425\) | 1.29342e9 | 0.817291 | ||||||||
\(426\) | 3.42937e8 | 0.214922 | ||||||||
\(427\) | −2.23435e8 | −0.138885 | ||||||||
\(428\) | 1.00366e9 | 0.618773 | ||||||||
\(429\) | 1.15795e9 | 0.708090 | ||||||||
\(430\) | 6.03969e8 | 0.366332 | ||||||||
\(431\) | −2.43619e9 | −1.46568 | −0.732842 | − | 0.680399i | \(-0.761807\pi\) | ||||
−0.732842 | + | 0.680399i | \(0.761807\pi\) | |||||||
\(432\) | −8.33201e8 | −0.497229 | ||||||||
\(433\) | 1.60081e8 | 0.0947614 | 0.0473807 | − | 0.998877i | \(-0.484913\pi\) | ||||
0.0473807 | + | 0.998877i | \(0.484913\pi\) | |||||||
\(434\) | −7.07240e7 | −0.0415291 | ||||||||
\(435\) | 2.32677e9 | 1.35532 | ||||||||
\(436\) | −3.41645e7 | −0.0197411 | ||||||||
\(437\) | −3.75431e7 | −0.0215201 | ||||||||
\(438\) | −5.77009e8 | −0.328113 | ||||||||
\(439\) | −2.78349e9 | −1.57023 | −0.785115 | − | 0.619350i | \(-0.787396\pi\) | ||||
−0.785115 | + | 0.619350i | \(0.787396\pi\) | |||||||
\(440\) | 1.37249e8 | 0.0768114 | ||||||||
\(441\) | −3.74805e9 | −2.08099 | ||||||||
\(442\) | 9.50269e8 | 0.523442 | ||||||||
\(443\) | −2.30211e9 | −1.25809 | −0.629046 | − | 0.777368i | \(-0.716554\pi\) | ||||
−0.629046 | + | 0.777368i | \(0.716554\pi\) | |||||||
\(444\) | 2.68004e8 | 0.145312 | ||||||||
\(445\) | −4.81585e8 | −0.259068 | ||||||||
\(446\) | 4.51369e8 | 0.240913 | ||||||||
\(447\) | −1.70772e7 | −0.00904357 | ||||||||
\(448\) | 3.42676e7 | 0.0180057 | ||||||||
\(449\) | −1.65040e9 | −0.860451 | −0.430225 | − | 0.902721i | \(-0.641566\pi\) | ||||
−0.430225 | + | 0.902721i | \(0.641566\pi\) | |||||||
\(450\) | −2.41867e9 | −1.25122 | ||||||||
\(451\) | −5.68272e8 | −0.291701 | ||||||||
\(452\) | −9.10398e8 | −0.463710 | ||||||||
\(453\) | −2.54631e9 | −1.28697 | ||||||||
\(454\) | −1.46302e9 | −0.733763 | ||||||||
\(455\) | −8.92914e7 | −0.0444396 | ||||||||
\(456\) | 3.29619e8 | 0.162793 | ||||||||
\(457\) | 2.78651e8 | 0.136569 | 0.0682847 | − | 0.997666i | \(-0.478247\pi\) | ||||
0.0682847 | + | 0.997666i | \(0.478247\pi\) | |||||||
\(458\) | 1.55123e8 | 0.0754479 | ||||||||
\(459\) | 4.04452e9 | 1.95219 | ||||||||
\(460\) | 3.52785e7 | 0.0168989 | ||||||||
\(461\) | 3.50867e9 | 1.66798 | 0.833988 | − | 0.551783i | \(-0.186052\pi\) | ||||
0.833988 | + | 0.551783i | \(0.186052\pi\) | |||||||
\(462\) | −2.02695e8 | −0.0956305 | ||||||||
\(463\) | −9.72895e8 | −0.455546 | −0.227773 | − | 0.973714i | \(-0.573144\pi\) | ||||
−0.227773 | + | 0.973714i | \(0.573144\pi\) | |||||||
\(464\) | −1.00826e9 | −0.468552 | ||||||||
\(465\) | 6.39255e8 | 0.294842 | ||||||||
\(466\) | −6.12175e8 | −0.280237 | ||||||||
\(467\) | 1.32759e9 | 0.603191 | 0.301596 | − | 0.953436i | \(-0.402481\pi\) | ||||
0.301596 | + | 0.953436i | \(0.402481\pi\) | |||||||
\(468\) | −1.77699e9 | −0.801354 | ||||||||
\(469\) | 1.69393e8 | 0.0758211 | ||||||||
\(470\) | −2.83885e8 | −0.126125 | ||||||||
\(471\) | −4.57886e9 | −2.01922 | ||||||||
\(472\) | −6.25483e8 | −0.273790 | ||||||||
\(473\) | 1.54808e9 | 0.672633 | ||||||||
\(474\) | 3.12579e9 | 1.34814 | ||||||||
\(475\) | 5.06580e8 | 0.216880 | ||||||||
\(476\) | −1.66342e8 | −0.0706930 | ||||||||
\(477\) | 3.99257e9 | 1.68437 | ||||||||
\(478\) | 2.76185e9 | 1.15665 | ||||||||
\(479\) | 4.21765e9 | 1.75346 | 0.876730 | − | 0.480983i | \(-0.159720\pi\) | ||||
0.876730 | + | 0.480983i | \(0.159720\pi\) | |||||||
\(480\) | −3.09736e8 | −0.127834 | ||||||||
\(481\) | 3.02611e8 | 0.123987 | ||||||||
\(482\) | −2.08882e9 | −0.849644 | ||||||||
\(483\) | −5.21006e7 | −0.0210391 | ||||||||
\(484\) | −8.95386e8 | −0.358964 | ||||||||
\(485\) | 1.50767e9 | 0.600082 | ||||||||
\(486\) | −8.40870e8 | −0.332278 | ||||||||
\(487\) | −1.37133e9 | −0.538012 | −0.269006 | − | 0.963139i | \(-0.586695\pi\) | ||||
−0.269006 | + | 0.963139i | \(0.586695\pi\) | |||||||
\(488\) | −8.75141e8 | −0.340886 | ||||||||
\(489\) | 8.38049e9 | 3.24107 | ||||||||
\(490\) | −7.37660e8 | −0.283250 | ||||||||
\(491\) | 8.25588e8 | 0.314759 | 0.157379 | − | 0.987538i | \(-0.449695\pi\) | ||||
0.157379 | + | 0.987538i | \(0.449695\pi\) | |||||||
\(492\) | 1.28244e9 | 0.485467 | ||||||||
\(493\) | 4.89427e9 | 1.83960 | ||||||||
\(494\) | 3.72183e8 | 0.138903 | ||||||||
\(495\) | 1.24585e9 | 0.461686 | ||||||||
\(496\) | −2.77008e8 | −0.101931 | ||||||||
\(497\) | −6.77817e7 | −0.0247665 | ||||||||
\(498\) | −1.12357e9 | −0.407661 | ||||||||
\(499\) | 4.64880e9 | 1.67490 | 0.837450 | − | 0.546514i | \(-0.184045\pi\) | ||||
0.837450 | + | 0.546514i | \(0.184045\pi\) | |||||||
\(500\) | −1.04771e9 | −0.374839 | ||||||||
\(501\) | 9.44334e9 | 3.35501 | ||||||||
\(502\) | 1.25225e9 | 0.441803 | ||||||||
\(503\) | −5.35012e9 | −1.87446 | −0.937228 | − | 0.348716i | \(-0.886618\pi\) | ||||
−0.937228 | + | 0.348716i | \(0.886618\pi\) | |||||||
\(504\) | 3.11057e8 | 0.108226 | ||||||||
\(505\) | −2.24220e9 | −0.774738 | ||||||||
\(506\) | 9.04248e7 | 0.0310285 | ||||||||
\(507\) | 2.23688e9 | 0.762281 | ||||||||
\(508\) | −1.36146e9 | −0.460768 | ||||||||
\(509\) | 2.75912e9 | 0.927383 | 0.463691 | − | 0.885997i | \(-0.346525\pi\) | ||||
0.463691 | + | 0.885997i | \(0.346525\pi\) | |||||||
\(510\) | 1.50352e9 | 0.501895 | ||||||||
\(511\) | 1.14046e8 | 0.0378102 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | 1.58408e9 | 0.518043 | ||||||||
\(514\) | 1.48512e9 | 0.482382 | ||||||||
\(515\) | −8.67943e8 | −0.280005 | ||||||||
\(516\) | −3.49361e9 | −1.11944 | ||||||||
\(517\) | −7.27646e8 | −0.231581 | ||||||||
\(518\) | −5.29711e7 | −0.0167450 | ||||||||
\(519\) | 3.95691e9 | 1.24243 | ||||||||
\(520\) | −3.49732e8 | −0.109075 | ||||||||
\(521\) | −4.81094e9 | −1.49038 | −0.745191 | − | 0.666851i | \(-0.767642\pi\) | ||||
−0.745191 | + | 0.666851i | \(0.767642\pi\) | |||||||
\(522\) | −9.15222e9 | −2.81631 | ||||||||
\(523\) | −1.61447e9 | −0.493486 | −0.246743 | − | 0.969081i | \(-0.579360\pi\) | ||||
−0.246743 | + | 0.969081i | \(0.579360\pi\) | |||||||
\(524\) | 1.21580e9 | 0.369148 | ||||||||
\(525\) | 7.03009e8 | 0.212033 | ||||||||
\(526\) | 4.07808e9 | 1.22181 | ||||||||
\(527\) | 1.34465e9 | 0.400196 | ||||||||
\(528\) | −7.93906e8 | −0.234720 | ||||||||
\(529\) | −3.38158e9 | −0.993174 | ||||||||
\(530\) | 7.85785e8 | 0.229265 | ||||||||
\(531\) | −5.67768e9 | −1.64566 | ||||||||
\(532\) | −6.51494e7 | −0.0187594 | ||||||||
\(533\) | 1.44804e9 | 0.414225 | ||||||||
\(534\) | 2.78569e9 | 0.791659 | ||||||||
\(535\) | 1.79304e9 | 0.506236 | ||||||||
\(536\) | 6.63469e8 | 0.186099 | ||||||||
\(537\) | −1.63204e9 | −0.454801 | ||||||||
\(538\) | 3.13933e9 | 0.869159 | ||||||||
\(539\) | −1.89075e9 | −0.520084 | ||||||||
\(540\) | −1.48852e9 | −0.406797 | ||||||||
\(541\) | 6.90904e9 | 1.87598 | 0.937988 | − | 0.346667i | \(-0.112687\pi\) | ||||
0.937988 | + | 0.346667i | \(0.112687\pi\) | |||||||
\(542\) | −3.70947e9 | −1.00072 | ||||||||
\(543\) | −5.43893e9 | −1.45785 | ||||||||
\(544\) | −6.51519e8 | −0.173512 | ||||||||
\(545\) | −6.10353e7 | −0.0161508 | ||||||||
\(546\) | 5.16498e8 | 0.135798 | ||||||||
\(547\) | −4.45727e9 | −1.16443 | −0.582215 | − | 0.813035i | \(-0.697814\pi\) | ||||
−0.582215 | + | 0.813035i | \(0.697814\pi\) | |||||||
\(548\) | 3.62450e9 | 0.940841 | ||||||||
\(549\) | −7.94389e9 | −2.04894 | ||||||||
\(550\) | −1.22013e9 | −0.312706 | ||||||||
\(551\) | 1.91689e9 | 0.488165 | ||||||||
\(552\) | −2.04065e8 | −0.0516395 | ||||||||
\(553\) | −6.17814e8 | −0.155353 | ||||||||
\(554\) | 1.54458e9 | 0.385947 | ||||||||
\(555\) | 4.78792e8 | 0.118883 | ||||||||
\(556\) | 2.01673e9 | 0.497607 | ||||||||
\(557\) | −1.21053e9 | −0.296813 | −0.148406 | − | 0.988926i | \(-0.547414\pi\) | ||||
−0.148406 | + | 0.988926i | \(0.547414\pi\) | |||||||
\(558\) | −2.51448e9 | −0.612672 | ||||||||
\(559\) | −3.94474e9 | −0.955162 | ||||||||
\(560\) | 6.12195e7 | 0.0147310 | ||||||||
\(561\) | 3.85377e9 | 0.921544 | ||||||||
\(562\) | 3.16764e9 | 0.752765 | ||||||||
\(563\) | 3.68621e9 | 0.870565 | 0.435282 | − | 0.900294i | \(-0.356649\pi\) | ||||
0.435282 | + | 0.900294i | \(0.356649\pi\) | |||||||
\(564\) | 1.64211e9 | 0.385411 | ||||||||
\(565\) | −1.62644e9 | −0.379374 | ||||||||
\(566\) | −4.42269e9 | −1.02525 | ||||||||
\(567\) | 8.69639e8 | 0.200354 | ||||||||
\(568\) | −2.65484e8 | −0.0607882 | ||||||||
\(569\) | 4.78409e9 | 1.08869 | 0.544347 | − | 0.838860i | \(-0.316777\pi\) | ||||
0.544347 | + | 0.838860i | \(0.316777\pi\) | |||||||
\(570\) | 5.88868e8 | 0.133185 | ||||||||
\(571\) | 4.52250e9 | 1.01661 | 0.508303 | − | 0.861178i | \(-0.330273\pi\) | ||||
0.508303 | + | 0.861178i | \(0.330273\pi\) | |||||||
\(572\) | −8.96424e8 | −0.200275 | ||||||||
\(573\) | 5.65959e9 | 1.25674 | ||||||||
\(574\) | −2.53476e8 | −0.0559429 | ||||||||
\(575\) | −3.13621e8 | −0.0687967 | ||||||||
\(576\) | 1.21833e9 | 0.265636 | ||||||||
\(577\) | −3.92270e9 | −0.850100 | −0.425050 | − | 0.905170i | \(-0.639743\pi\) | ||||
−0.425050 | + | 0.905170i | \(0.639743\pi\) | |||||||
\(578\) | −1.20113e8 | −0.0258727 | ||||||||
\(579\) | −7.71484e9 | −1.65178 | ||||||||
\(580\) | −1.80126e9 | −0.383336 | ||||||||
\(581\) | 2.22075e8 | 0.0469768 | ||||||||
\(582\) | −8.72100e9 | −1.83373 | ||||||||
\(583\) | 2.01410e9 | 0.420961 | ||||||||
\(584\) | 4.46691e8 | 0.0928031 | ||||||||
\(585\) | −3.17461e9 | −0.655610 | ||||||||
\(586\) | −6.67321e8 | −0.136991 | ||||||||
\(587\) | 4.45656e9 | 0.909424 | 0.454712 | − | 0.890638i | \(-0.349742\pi\) | ||||
0.454712 | + | 0.890638i | \(0.349742\pi\) | |||||||
\(588\) | 4.26693e9 | 0.865556 | ||||||||
\(589\) | 5.26646e8 | 0.106198 | ||||||||
\(590\) | −1.11743e9 | −0.223996 | ||||||||
\(591\) | −1.16918e10 | −2.32984 | ||||||||
\(592\) | −2.07475e8 | −0.0410997 | ||||||||
\(593\) | 3.49353e9 | 0.687976 | 0.343988 | − | 0.938974i | \(-0.388222\pi\) | ||||
0.343988 | + | 0.938974i | \(0.388222\pi\) | |||||||
\(594\) | −3.81535e9 | −0.746932 | ||||||||
\(595\) | −2.97171e8 | −0.0578359 | ||||||||
\(596\) | 1.32203e7 | 0.00255787 | ||||||||
\(597\) | −9.08513e9 | −1.74752 | ||||||||
\(598\) | −2.30416e8 | −0.0440615 | ||||||||
\(599\) | −2.49362e9 | −0.474063 | −0.237032 | − | 0.971502i | \(-0.576175\pi\) | ||||
−0.237032 | + | 0.971502i | \(0.576175\pi\) | |||||||
\(600\) | 2.75351e9 | 0.520424 | ||||||||
\(601\) | 1.04034e10 | 1.95486 | 0.977429 | − | 0.211262i | \(-0.0677574\pi\) | ||||
0.977429 | + | 0.211262i | \(0.0677574\pi\) | |||||||
\(602\) | 6.90514e8 | 0.128999 | ||||||||
\(603\) | 6.02249e9 | 1.11858 | ||||||||
\(604\) | 1.97123e9 | 0.364005 | ||||||||
\(605\) | −1.59962e9 | −0.293679 | ||||||||
\(606\) | 1.29698e10 | 2.36745 | ||||||||
\(607\) | 3.56887e9 | 0.647694 | 0.323847 | − | 0.946110i | \(-0.395024\pi\) | ||||
0.323847 | + | 0.946110i | \(0.395024\pi\) | |||||||
\(608\) | −2.55174e8 | −0.0460441 | ||||||||
\(609\) | 2.66018e9 | 0.477255 | ||||||||
\(610\) | −1.56345e9 | −0.278888 | ||||||||
\(611\) | 1.85415e9 | 0.328853 | ||||||||
\(612\) | −5.91401e9 | −1.04292 | ||||||||
\(613\) | −5.03005e8 | −0.0881984 | −0.0440992 | − | 0.999027i | \(-0.514042\pi\) | ||||
−0.0440992 | + | 0.999027i | \(0.514042\pi\) | |||||||
\(614\) | 6.79328e9 | 1.18438 | ||||||||
\(615\) | 2.29110e9 | 0.397174 | ||||||||
\(616\) | 1.56916e8 | 0.0270480 | ||||||||
\(617\) | −1.25403e9 | −0.214936 | −0.107468 | − | 0.994209i | \(-0.534274\pi\) | ||||
−0.107468 | + | 0.994209i | \(0.534274\pi\) | |||||||
\(618\) | 5.02054e9 | 0.855639 | ||||||||
\(619\) | −9.27046e9 | −1.57103 | −0.785514 | − | 0.618843i | \(-0.787602\pi\) | ||||
−0.785514 | + | 0.618843i | \(0.787602\pi\) | |||||||
\(620\) | −4.94878e8 | −0.0833926 | ||||||||
\(621\) | −9.80694e8 | −0.164329 | ||||||||
\(622\) | 2.50378e9 | 0.417186 | ||||||||
\(623\) | −5.50593e8 | −0.0912269 | ||||||||
\(624\) | 2.02300e9 | 0.333310 | ||||||||
\(625\) | 3.21045e9 | 0.526001 | ||||||||
\(626\) | −2.94587e9 | −0.479958 | ||||||||
\(627\) | 1.50937e9 | 0.244545 | ||||||||
\(628\) | 3.54472e9 | 0.571114 | ||||||||
\(629\) | 1.00712e9 | 0.161363 | ||||||||
\(630\) | 5.55706e8 | 0.0885429 | ||||||||
\(631\) | 1.19395e9 | 0.189184 | 0.0945918 | − | 0.995516i | \(-0.469845\pi\) | ||||
0.0945918 | + | 0.995516i | \(0.469845\pi\) | |||||||
\(632\) | −2.41982e9 | −0.381306 | ||||||||
\(633\) | −1.40889e10 | −2.20782 | ||||||||
\(634\) | 6.56497e9 | 1.02311 | ||||||||
\(635\) | −2.43227e9 | −0.376967 | ||||||||
\(636\) | −4.54530e9 | −0.700589 | ||||||||
\(637\) | 4.81792e9 | 0.738536 | ||||||||
\(638\) | −4.61695e9 | −0.703854 | ||||||||
\(639\) | −2.40987e9 | −0.365377 | ||||||||
\(640\) | 2.39782e8 | 0.0361565 | ||||||||
\(641\) | −6.01299e9 | −0.901752 | −0.450876 | − | 0.892587i | \(-0.648888\pi\) | ||||
−0.450876 | + | 0.892587i | \(0.648888\pi\) | |||||||
\(642\) | −1.03717e10 | −1.54695 | ||||||||
\(643\) | −8.03723e9 | −1.19225 | −0.596126 | − | 0.802891i | \(-0.703294\pi\) | ||||
−0.596126 | + | 0.802891i | \(0.703294\pi\) | |||||||
\(644\) | 4.03337e7 | 0.00595069 | ||||||||
\(645\) | −6.24137e9 | −0.915843 | ||||||||
\(646\) | 1.23866e9 | 0.180775 | ||||||||
\(647\) | −2.66241e9 | −0.386465 | −0.193233 | − | 0.981153i | \(-0.561897\pi\) | ||||
−0.193233 | + | 0.981153i | \(0.561897\pi\) | |||||||
\(648\) | 3.40616e9 | 0.491759 | ||||||||
\(649\) | −2.86417e9 | −0.411285 | ||||||||
\(650\) | 3.10907e9 | 0.444052 | ||||||||
\(651\) | 7.30856e8 | 0.103824 | ||||||||
\(652\) | −6.48775e9 | −0.916701 | ||||||||
\(653\) | 2.98529e9 | 0.419557 | 0.209779 | − | 0.977749i | \(-0.432726\pi\) | ||||
0.209779 | + | 0.977749i | \(0.432726\pi\) | |||||||
\(654\) | 3.53053e8 | 0.0493535 | ||||||||
\(655\) | 2.17203e9 | 0.302010 | ||||||||
\(656\) | −9.92801e8 | −0.137309 | ||||||||
\(657\) | 4.05474e9 | 0.557807 | ||||||||
\(658\) | −3.24564e8 | −0.0444129 | ||||||||
\(659\) | −6.82535e9 | −0.929022 | −0.464511 | − | 0.885567i | \(-0.653770\pi\) | ||||
−0.464511 | + | 0.885567i | \(0.653770\pi\) | |||||||
\(660\) | −1.41832e9 | −0.192031 | ||||||||
\(661\) | −5.93750e9 | −0.799648 | −0.399824 | − | 0.916592i | \(-0.630929\pi\) | ||||
−0.399824 | + | 0.916592i | \(0.630929\pi\) | |||||||
\(662\) | 2.49353e8 | 0.0334050 | ||||||||
\(663\) | −9.82001e9 | −1.30862 | ||||||||
\(664\) | 8.69813e8 | 0.115302 | ||||||||
\(665\) | −1.16390e8 | −0.0153476 | ||||||||
\(666\) | −1.88330e9 | −0.247036 | ||||||||
\(667\) | −1.18674e9 | −0.154851 | ||||||||
\(668\) | −7.31055e9 | −0.948926 | ||||||||
\(669\) | −4.66442e9 | −0.602290 | ||||||||
\(670\) | 1.18530e9 | 0.152253 | ||||||||
\(671\) | −4.00739e9 | −0.512074 | ||||||||
\(672\) | −3.54119e8 | −0.0450150 | ||||||||
\(673\) | 2.34747e9 | 0.296857 | 0.148428 | − | 0.988923i | \(-0.452579\pi\) | ||||
0.148428 | + | 0.988923i | \(0.452579\pi\) | |||||||
\(674\) | −1.05382e10 | −1.32574 | ||||||||
\(675\) | 1.32328e10 | 1.65611 | ||||||||
\(676\) | −1.73168e9 | −0.215603 | ||||||||
\(677\) | 2.16956e9 | 0.268727 | 0.134363 | − | 0.990932i | \(-0.457101\pi\) | ||||
0.134363 | + | 0.990932i | \(0.457101\pi\) | |||||||
\(678\) | 9.40798e9 | 1.15929 | ||||||||
\(679\) | 1.72371e9 | 0.211310 | ||||||||
\(680\) | −1.16395e9 | −0.141955 | ||||||||
\(681\) | 1.51188e10 | 1.83443 | ||||||||
\(682\) | −1.26846e9 | −0.153120 | ||||||||
\(683\) | 2.03106e9 | 0.243922 | 0.121961 | − | 0.992535i | \(-0.461082\pi\) | ||||
0.121961 | + | 0.992535i | \(0.461082\pi\) | |||||||
\(684\) | −2.31628e9 | −0.276755 | ||||||||
\(685\) | 6.47522e9 | 0.769728 | ||||||||
\(686\) | −1.70459e9 | −0.201598 | ||||||||
\(687\) | −1.60303e9 | −0.188622 | ||||||||
\(688\) | 2.70457e9 | 0.316620 | ||||||||
\(689\) | −5.13224e9 | −0.597778 | ||||||||
\(690\) | −3.64565e8 | −0.0422477 | ||||||||
\(691\) | 1.81275e9 | 0.209009 | 0.104504 | − | 0.994524i | \(-0.466674\pi\) | ||||
0.104504 | + | 0.994524i | \(0.466674\pi\) | |||||||
\(692\) | −3.06324e9 | −0.351407 | ||||||||
\(693\) | 1.42437e9 | 0.162576 | ||||||||
\(694\) | 8.14604e9 | 0.925099 | ||||||||
\(695\) | 3.60292e9 | 0.407106 | ||||||||
\(696\) | 1.04193e10 | 1.17140 | ||||||||
\(697\) | 4.81925e9 | 0.539094 | ||||||||
\(698\) | −8.17227e9 | −0.909597 | ||||||||
\(699\) | 6.32617e9 | 0.700601 | ||||||||
\(700\) | −5.44234e8 | −0.0599711 | ||||||||
\(701\) | 1.39158e10 | 1.52580 | 0.762898 | − | 0.646519i | \(-0.223776\pi\) | ||||
0.762898 | + | 0.646519i | \(0.223776\pi\) | |||||||
\(702\) | 9.72209e9 | 1.06067 | ||||||||
\(703\) | 3.94450e8 | 0.0428201 | ||||||||
\(704\) | 6.14602e8 | 0.0663880 | ||||||||
\(705\) | 2.93364e9 | 0.315316 | ||||||||
\(706\) | 9.18761e8 | 0.0982621 | ||||||||
\(707\) | −2.56350e9 | −0.272813 | ||||||||
\(708\) | 6.46369e9 | 0.684486 | ||||||||
\(709\) | 7.10889e9 | 0.749100 | 0.374550 | − | 0.927207i | \(-0.377797\pi\) | ||||
0.374550 | + | 0.927207i | \(0.377797\pi\) | |||||||
\(710\) | −4.74291e8 | −0.0497325 | ||||||||
\(711\) | −2.19654e10 | −2.29190 | ||||||||
\(712\) | −2.15654e9 | −0.223912 | ||||||||
\(713\) | −3.26044e8 | −0.0336870 | ||||||||
\(714\) | 1.71896e9 | 0.176735 | ||||||||
\(715\) | −1.60147e9 | −0.163851 | ||||||||
\(716\) | 1.26345e9 | 0.128635 | ||||||||
\(717\) | −2.85407e10 | −2.89166 | ||||||||
\(718\) | 9.23032e9 | 0.930639 | ||||||||
\(719\) | −1.34368e10 | −1.34818 | −0.674088 | − | 0.738651i | \(-0.735463\pi\) | ||||
−0.674088 | + | 0.738651i | \(0.735463\pi\) | |||||||
\(720\) | 2.17656e9 | 0.217324 | ||||||||
\(721\) | −9.92314e8 | −0.0985997 | ||||||||
\(722\) | −6.66584e9 | −0.659135 | ||||||||
\(723\) | 2.15857e10 | 2.12414 | ||||||||
\(724\) | 4.21054e9 | 0.412338 | ||||||||
\(725\) | 1.60130e10 | 1.56059 | ||||||||
\(726\) | 9.25285e9 | 0.897423 | ||||||||
\(727\) | 1.28066e10 | 1.23612 | 0.618062 | − | 0.786129i | \(-0.287918\pi\) | ||||
0.618062 | + | 0.786129i | \(0.287918\pi\) | |||||||
\(728\) | −3.99847e8 | −0.0384091 | ||||||||
\(729\) | −5.85987e9 | −0.560198 | ||||||||
\(730\) | 7.98020e8 | 0.0759248 | ||||||||
\(731\) | −1.31285e10 | −1.24310 | ||||||||
\(732\) | 9.04364e9 | 0.852226 | ||||||||
\(733\) | −1.30841e10 | −1.22710 | −0.613549 | − | 0.789657i | \(-0.710259\pi\) | ||||
−0.613549 | + | 0.789657i | \(0.710259\pi\) | |||||||
\(734\) | −5.95021e8 | −0.0555387 | ||||||||
\(735\) | 7.62293e9 | 0.708135 | ||||||||
\(736\) | 1.57977e8 | 0.0146057 | ||||||||
\(737\) | 3.03812e9 | 0.279556 | ||||||||
\(738\) | −9.01192e9 | −0.825316 | ||||||||
\(739\) | −1.06618e10 | −0.971800 | −0.485900 | − | 0.874014i | \(-0.661508\pi\) | ||||
−0.485900 | + | 0.874014i | \(0.661508\pi\) | |||||||
\(740\) | −3.70656e8 | −0.0336248 | ||||||||
\(741\) | −3.84611e9 | −0.347262 | ||||||||
\(742\) | 8.98383e8 | 0.0807324 | ||||||||
\(743\) | 4.71447e9 | 0.421670 | 0.210835 | − | 0.977522i | \(-0.432382\pi\) | ||||
0.210835 | + | 0.977522i | \(0.432382\pi\) | |||||||
\(744\) | 2.86258e9 | 0.254831 | ||||||||
\(745\) | 2.36182e7 | 0.00209267 | ||||||||
\(746\) | −9.76715e9 | −0.861354 | ||||||||
\(747\) | 7.89553e9 | 0.693042 | ||||||||
\(748\) | −2.98340e9 | −0.260648 | ||||||||
\(749\) | 2.04998e9 | 0.178264 | ||||||||
\(750\) | 1.08269e10 | 0.937110 | ||||||||
\(751\) | 1.44861e10 | 1.24799 | 0.623996 | − | 0.781427i | \(-0.285508\pi\) | ||||
0.623996 | + | 0.781427i | \(0.285508\pi\) | |||||||
\(752\) | −1.27124e9 | −0.109009 | ||||||||
\(753\) | −1.29407e10 | −1.10452 | ||||||||
\(754\) | 1.17647e10 | 0.999496 | ||||||||
\(755\) | 3.52162e9 | 0.297802 | ||||||||
\(756\) | −1.70182e9 | −0.143248 | ||||||||
\(757\) | 1.05477e10 | 0.883737 | 0.441869 | − | 0.897080i | \(-0.354316\pi\) | ||||
0.441869 | + | 0.897080i | \(0.354316\pi\) | |||||||
\(758\) | −8.79220e9 | −0.733255 | ||||||||
\(759\) | −9.34443e8 | −0.0775723 | ||||||||
\(760\) | −4.55872e8 | −0.0376699 | ||||||||
\(761\) | 1.75003e9 | 0.143946 | 0.0719730 | − | 0.997407i | \(-0.477070\pi\) | ||||
0.0719730 | + | 0.997407i | \(0.477070\pi\) | |||||||
\(762\) | 1.40693e10 | 1.15194 | ||||||||
\(763\) | −6.97813e7 | −0.00568726 | ||||||||
\(764\) | −4.38137e9 | −0.355454 | ||||||||
\(765\) | −1.05655e10 | −0.853244 | ||||||||
\(766\) | −4.53722e9 | −0.364745 | ||||||||
\(767\) | 7.29835e9 | 0.584038 | ||||||||
\(768\) | −1.38700e9 | −0.110487 | ||||||||
\(769\) | 9.57155e8 | 0.0758997 | 0.0379498 | − | 0.999280i | \(-0.487917\pi\) | ||||
0.0379498 | + | 0.999280i | \(0.487917\pi\) | |||||||
\(770\) | 2.80333e8 | 0.0221287 | ||||||||
\(771\) | −1.53471e10 | −1.20597 | ||||||||
\(772\) | 5.97244e9 | 0.467187 | ||||||||
\(773\) | 6.52807e9 | 0.508343 | 0.254171 | − | 0.967159i | \(-0.418197\pi\) | ||||
0.254171 | + | 0.967159i | \(0.418197\pi\) | |||||||
\(774\) | 2.45501e10 | 1.90310 | ||||||||
\(775\) | 4.39940e9 | 0.339498 | ||||||||
\(776\) | 6.75135e9 | 0.518651 | ||||||||
\(777\) | 5.47400e8 | 0.0418631 | ||||||||
\(778\) | −6.32701e9 | −0.481693 | ||||||||
\(779\) | 1.88751e9 | 0.143056 | ||||||||
\(780\) | 3.61411e9 | 0.272690 | ||||||||
\(781\) | −1.21569e9 | −0.0913154 | ||||||||
\(782\) | −7.66850e8 | −0.0573439 | ||||||||
\(783\) | 5.00727e10 | 3.72765 | ||||||||
\(784\) | −3.30324e9 | −0.244813 | ||||||||
\(785\) | 6.33268e9 | 0.467244 | ||||||||
\(786\) | −1.25639e10 | −0.922884 | ||||||||
\(787\) | 1.10475e10 | 0.807889 | 0.403944 | − | 0.914784i | \(-0.367639\pi\) | ||||
0.403944 | + | 0.914784i | \(0.367639\pi\) | |||||||
\(788\) | 9.05123e9 | 0.658970 | ||||||||
\(789\) | −4.21426e10 | −3.05458 | ||||||||
\(790\) | −4.32305e9 | −0.311957 | ||||||||
\(791\) | −1.85950e9 | −0.133591 | ||||||||
\(792\) | 5.57891e9 | 0.399035 | ||||||||
\(793\) | 1.02115e10 | 0.727162 | ||||||||
\(794\) | −1.12547e10 | −0.797924 | ||||||||
\(795\) | −8.12024e9 | −0.573171 | ||||||||
\(796\) | 7.03325e9 | 0.494265 | ||||||||
\(797\) | −1.85828e10 | −1.30019 | −0.650095 | − | 0.759853i | \(-0.725271\pi\) | ||||
−0.650095 | + | 0.759853i | \(0.725271\pi\) | |||||||
\(798\) | 6.73249e8 | 0.0468992 | ||||||||
\(799\) | 6.17082e9 | 0.427986 | ||||||||
\(800\) | −2.13163e9 | −0.147196 | ||||||||
\(801\) | −1.95755e10 | −1.34586 | ||||||||
\(802\) | −1.66317e10 | −1.13848 | ||||||||
\(803\) | 2.04546e9 | 0.139408 | ||||||||
\(804\) | −6.85624e9 | −0.465254 | ||||||||
\(805\) | 7.20566e7 | 0.00486842 | ||||||||
\(806\) | 3.23223e9 | 0.217435 | ||||||||
\(807\) | −3.24416e10 | −2.17293 | ||||||||
\(808\) | −1.00406e10 | −0.669606 | ||||||||
\(809\) | −9.21373e9 | −0.611809 | −0.305904 | − | 0.952062i | \(-0.598959\pi\) | ||||
−0.305904 | + | 0.952062i | \(0.598959\pi\) | |||||||
\(810\) | 6.08515e9 | 0.402322 | ||||||||
\(811\) | −5.90313e8 | −0.0388606 | −0.0194303 | − | 0.999811i | \(-0.506185\pi\) | ||||
−0.0194303 | + | 0.999811i | \(0.506185\pi\) | |||||||
\(812\) | −2.05937e9 | −0.134986 | ||||||||
\(813\) | 3.83334e10 | 2.50185 | ||||||||
\(814\) | −9.50056e8 | −0.0617396 | ||||||||
\(815\) | −1.15904e10 | −0.749978 | ||||||||
\(816\) | 6.73275e9 | 0.433787 | ||||||||
\(817\) | −5.14192e9 | −0.329874 | ||||||||
\(818\) | −1.08958e9 | −0.0696019 | ||||||||
\(819\) | −3.62952e9 | −0.230864 | ||||||||
\(820\) | −1.77365e9 | −0.112336 | ||||||||
\(821\) | 4.22037e9 | 0.266164 | 0.133082 | − | 0.991105i | \(-0.457513\pi\) | ||||
0.133082 | + | 0.991105i | \(0.457513\pi\) | |||||||
\(822\) | −3.74553e10 | −2.35214 | ||||||||
\(823\) | 3.49867e8 | 0.0218778 | 0.0109389 | − | 0.999940i | \(-0.496518\pi\) | ||||
0.0109389 | + | 0.999940i | \(0.496518\pi\) | |||||||
\(824\) | −3.88665e9 | −0.242008 | ||||||||
\(825\) | 1.26087e10 | 0.781775 | ||||||||
\(826\) | −1.27755e9 | −0.0788768 | ||||||||
\(827\) | 2.50807e10 | 1.54195 | 0.770976 | − | 0.636864i | \(-0.219769\pi\) | ||||
0.770976 | + | 0.636864i | \(0.219769\pi\) | |||||||
\(828\) | 1.43400e9 | 0.0877896 | ||||||||
\(829\) | −1.89801e10 | −1.15706 | −0.578532 | − | 0.815660i | \(-0.696374\pi\) | ||||
−0.578532 | + | 0.815660i | \(0.696374\pi\) | |||||||
\(830\) | 1.55393e9 | 0.0943320 | ||||||||
\(831\) | −1.59616e10 | −0.964880 | ||||||||
\(832\) | −1.56610e9 | −0.0942731 | ||||||||
\(833\) | 1.60346e10 | 0.961169 | ||||||||
\(834\) | −2.08408e10 | −1.24404 | ||||||||
\(835\) | −1.30604e10 | −0.776343 | ||||||||
\(836\) | −1.16848e9 | −0.0691669 | ||||||||
\(837\) | 1.37570e10 | 0.810930 | ||||||||
\(838\) | 6.96599e9 | 0.408911 | ||||||||
\(839\) | −8.08351e9 | −0.472534 | −0.236267 | − | 0.971688i | \(-0.575924\pi\) | ||||
−0.236267 | + | 0.971688i | \(0.575924\pi\) | |||||||
\(840\) | −6.32638e8 | −0.0368280 | ||||||||
\(841\) | 4.33431e10 | 2.51266 | ||||||||
\(842\) | −1.43186e10 | −0.826627 | ||||||||
\(843\) | −3.27342e10 | −1.88194 | ||||||||
\(844\) | 1.09069e10 | 0.624458 | ||||||||
\(845\) | −3.09367e9 | −0.176390 | ||||||||
\(846\) | −1.15394e10 | −0.655217 | ||||||||
\(847\) | −1.82883e9 | −0.103415 | ||||||||
\(848\) | 3.51874e9 | 0.198154 | ||||||||
\(849\) | 4.57037e10 | 2.56315 | ||||||||
\(850\) | 1.03473e10 | 0.577912 | ||||||||
\(851\) | −2.44202e8 | −0.0135830 | ||||||||
\(852\) | 2.74349e9 | 0.151973 | ||||||||
\(853\) | 7.31648e9 | 0.403627 | 0.201814 | − | 0.979424i | \(-0.435316\pi\) | ||||
0.201814 | + | 0.979424i | \(0.435316\pi\) | |||||||
\(854\) | −1.78748e9 | −0.0982063 | ||||||||
\(855\) | −4.13807e9 | −0.226421 | ||||||||
\(856\) | 8.02925e9 | 0.437539 | ||||||||
\(857\) | 1.69375e10 | 0.919214 | 0.459607 | − | 0.888122i | \(-0.347990\pi\) | ||||
0.459607 | + | 0.888122i | \(0.347990\pi\) | |||||||
\(858\) | 9.26358e9 | 0.500695 | ||||||||
\(859\) | −3.12574e10 | −1.68258 | −0.841292 | − | 0.540581i | \(-0.818204\pi\) | ||||
−0.841292 | + | 0.540581i | \(0.818204\pi\) | |||||||
\(860\) | 4.83175e9 | 0.259036 | ||||||||
\(861\) | 2.61940e9 | 0.139859 | ||||||||
\(862\) | −1.94895e10 | −1.03640 | ||||||||
\(863\) | −1.82116e10 | −0.964517 | −0.482258 | − | 0.876029i | \(-0.660183\pi\) | ||||
−0.482258 | + | 0.876029i | \(0.660183\pi\) | |||||||
\(864\) | −6.66561e9 | −0.351594 | ||||||||
\(865\) | −5.47252e9 | −0.287495 | ||||||||
\(866\) | 1.28065e9 | 0.0670065 | ||||||||
\(867\) | 1.24124e9 | 0.0646827 | ||||||||
\(868\) | −5.65792e8 | −0.0293655 | ||||||||
\(869\) | −1.10807e10 | −0.572794 | ||||||||
\(870\) | 1.86141e10 | 0.958353 | ||||||||
\(871\) | −7.74159e9 | −0.396978 | ||||||||
\(872\) | −2.73316e8 | −0.0139591 | ||||||||
\(873\) | 6.12839e10 | 3.11743 | ||||||||
\(874\) | −3.00345e8 | −0.0152170 | ||||||||
\(875\) | −2.13995e9 | −0.107988 | ||||||||
\(876\) | −4.61608e9 | −0.232011 | ||||||||
\(877\) | −4.59540e9 | −0.230051 | −0.115026 | − | 0.993363i | \(-0.536695\pi\) | ||||
−0.115026 | + | 0.993363i | \(0.536695\pi\) | |||||||
\(878\) | −2.22679e10 | −1.11032 | ||||||||
\(879\) | 6.89604e9 | 0.342483 | ||||||||
\(880\) | 1.09799e9 | 0.0543138 | ||||||||
\(881\) | 2.03239e10 | 1.00136 | 0.500680 | − | 0.865632i | \(-0.333083\pi\) | ||||
0.500680 | + | 0.865632i | \(0.333083\pi\) | |||||||
\(882\) | −2.99844e10 | −1.47148 | ||||||||
\(883\) | 3.32637e10 | 1.62595 | 0.812976 | − | 0.582297i | \(-0.197846\pi\) | ||||
0.812976 | + | 0.582297i | \(0.197846\pi\) | |||||||
\(884\) | 7.60215e9 | 0.370129 | ||||||||
\(885\) | 1.15475e10 | 0.559997 | ||||||||
\(886\) | −1.84168e10 | −0.889605 | ||||||||
\(887\) | −8.51025e8 | −0.0409458 | −0.0204729 | − | 0.999790i | \(-0.506517\pi\) | ||||
−0.0204729 | + | 0.999790i | \(0.506517\pi\) | |||||||
\(888\) | 2.14403e9 | 0.102751 | ||||||||
\(889\) | −2.78080e9 | −0.132744 | ||||||||
\(890\) | −3.85268e9 | −0.183188 | ||||||||
\(891\) | 1.55973e10 | 0.738715 | ||||||||
\(892\) | 3.61095e9 | 0.170351 | ||||||||
\(893\) | 2.41687e9 | 0.113572 | ||||||||
\(894\) | −1.36617e8 | −0.00639477 | ||||||||
\(895\) | 2.25716e9 | 0.105240 | ||||||||
\(896\) | 2.74141e8 | 0.0127320 | ||||||||
\(897\) | 2.38111e9 | 0.110155 | ||||||||
\(898\) | −1.32032e10 | −0.608431 | ||||||||
\(899\) | 1.66473e10 | 0.764161 | ||||||||
\(900\) | −1.93494e10 | −0.884744 | ||||||||
\(901\) | −1.70807e10 | −0.777979 | ||||||||
\(902\) | −4.54617e9 | −0.206264 | ||||||||
\(903\) | −7.13572e9 | −0.322501 | ||||||||
\(904\) | −7.28318e9 | −0.327893 | ||||||||
\(905\) | 7.52219e9 | 0.337345 | ||||||||
\(906\) | −2.03705e10 | −0.910024 | ||||||||
\(907\) | −2.88263e10 | −1.28282 | −0.641408 | − | 0.767200i | \(-0.721649\pi\) | ||||
−0.641408 | + | 0.767200i | \(0.721649\pi\) | |||||||
\(908\) | −1.17042e10 | −0.518848 | ||||||||
\(909\) | −9.11411e10 | −4.02477 | ||||||||
\(910\) | −7.14331e8 | −0.0314235 | ||||||||
\(911\) | −1.58607e10 | −0.695039 | −0.347519 | − | 0.937673i | \(-0.612976\pi\) | ||||
−0.347519 | + | 0.937673i | \(0.612976\pi\) | |||||||
\(912\) | 2.63695e9 | 0.115112 | ||||||||
\(913\) | 3.98300e9 | 0.173206 | ||||||||
\(914\) | 2.22920e9 | 0.0965691 | ||||||||
\(915\) | 1.61566e10 | 0.697229 | ||||||||
\(916\) | 1.24099e9 | 0.0533498 | ||||||||
\(917\) | 2.48327e9 | 0.106349 | ||||||||
\(918\) | 3.23562e10 | 1.38041 | ||||||||
\(919\) | 2.56364e9 | 0.108956 | 0.0544782 | − | 0.998515i | \(-0.482650\pi\) | ||||
0.0544782 | + | 0.998515i | \(0.482650\pi\) | |||||||
\(920\) | 2.82228e8 | 0.0119493 | ||||||||
\(921\) | −7.02013e10 | −2.96099 | ||||||||
\(922\) | 2.80694e10 | 1.17944 | ||||||||
\(923\) | 3.09776e9 | 0.129671 | ||||||||
\(924\) | −1.62156e9 | −0.0676210 | ||||||||
\(925\) | 3.29508e9 | 0.136890 | ||||||||
\(926\) | −7.78316e9 | −0.322120 | ||||||||
\(927\) | −3.52801e10 | −1.45463 | ||||||||
\(928\) | −8.06605e9 | −0.331317 | ||||||||
\(929\) | 3.94497e10 | 1.61431 | 0.807157 | − | 0.590336i | \(-0.201005\pi\) | ||||
0.807157 | + | 0.590336i | \(0.201005\pi\) | |||||||
\(930\) | 5.11404e9 | 0.208484 | ||||||||
\(931\) | 6.28010e9 | 0.255060 | ||||||||
\(932\) | −4.89740e9 | −0.198157 | ||||||||
\(933\) | −2.58739e10 | −1.04298 | ||||||||
\(934\) | 1.06207e10 | 0.426520 | ||||||||
\(935\) | −5.32987e9 | −0.213244 | ||||||||
\(936\) | −1.42159e10 | −0.566643 | ||||||||
\(937\) | 3.28786e9 | 0.130564 | 0.0652822 | − | 0.997867i | \(-0.479205\pi\) | ||||
0.0652822 | + | 0.997867i | \(0.479205\pi\) | |||||||
\(938\) | 1.35514e9 | 0.0536136 | ||||||||
\(939\) | 3.04424e10 | 1.19991 | ||||||||
\(940\) | −2.27108e9 | −0.0891835 | ||||||||
\(941\) | 1.85752e9 | 0.0726724 | 0.0363362 | − | 0.999340i | \(-0.488431\pi\) | ||||
0.0363362 | + | 0.999340i | \(0.488431\pi\) | |||||||
\(942\) | −3.66308e10 | −1.42780 | ||||||||
\(943\) | −1.16855e9 | −0.0453790 | ||||||||
\(944\) | −5.00386e9 | −0.193599 | ||||||||
\(945\) | −3.04033e9 | −0.117195 | ||||||||
\(946\) | 1.23846e10 | 0.475624 | ||||||||
\(947\) | 1.06515e10 | 0.407556 | 0.203778 | − | 0.979017i | \(-0.434678\pi\) | ||||
0.203778 | + | 0.979017i | \(0.434678\pi\) | |||||||
\(948\) | 2.50063e10 | 0.953279 | ||||||||
\(949\) | −5.21215e9 | −0.197964 | ||||||||
\(950\) | 4.05264e9 | 0.153358 | ||||||||
\(951\) | −6.78419e10 | −2.55780 | ||||||||
\(952\) | −1.33073e9 | −0.0499875 | ||||||||
\(953\) | −5.95593e9 | −0.222907 | −0.111454 | − | 0.993770i | \(-0.535551\pi\) | ||||
−0.111454 | + | 0.993770i | \(0.535551\pi\) | |||||||
\(954\) | 3.19406e10 | 1.19103 | ||||||||
\(955\) | −7.82737e9 | −0.290807 | ||||||||
\(956\) | 2.20948e10 | 0.817875 | ||||||||
\(957\) | 4.77112e10 | 1.75966 | ||||||||
\(958\) | 3.37412e10 | 1.23988 | ||||||||
\(959\) | 7.40308e9 | 0.271049 | ||||||||
\(960\) | −2.47789e9 | −0.0903924 | ||||||||
\(961\) | −2.29389e10 | −0.833761 | ||||||||
\(962\) | 2.42089e9 | 0.0876722 | ||||||||
\(963\) | 7.28837e10 | 2.62989 | ||||||||
\(964\) | −1.67106e10 | −0.600789 | ||||||||
\(965\) | 1.06698e10 | 0.382219 | ||||||||
\(966\) | −4.16805e8 | −0.0148769 | ||||||||
\(967\) | −1.98986e10 | −0.707669 | −0.353834 | − | 0.935308i | \(-0.615122\pi\) | ||||
−0.353834 | + | 0.935308i | \(0.615122\pi\) | |||||||
\(968\) | −7.16308e9 | −0.253826 | ||||||||
\(969\) | −1.28003e10 | −0.451945 | ||||||||
\(970\) | 1.20614e10 | 0.424322 | ||||||||
\(971\) | 4.28048e10 | 1.50046 | 0.750231 | − | 0.661176i | \(-0.229942\pi\) | ||||
0.750231 | + | 0.661176i | \(0.229942\pi\) | |||||||
\(972\) | −6.72696e9 | −0.234956 | ||||||||
\(973\) | 4.11920e9 | 0.143357 | ||||||||
\(974\) | −1.09707e10 | −0.380432 | ||||||||
\(975\) | −3.21289e10 | −1.11015 | ||||||||
\(976\) | −7.00113e9 | −0.241042 | ||||||||
\(977\) | −3.09752e10 | −1.06263 | −0.531316 | − | 0.847174i | \(-0.678302\pi\) | ||||
−0.531316 | + | 0.847174i | \(0.678302\pi\) | |||||||
\(978\) | 6.70439e10 | 2.29178 | ||||||||
\(979\) | −9.87509e9 | −0.336358 | ||||||||
\(980\) | −5.90128e9 | −0.200288 | ||||||||
\(981\) | −2.48096e9 | −0.0839032 | ||||||||
\(982\) | 6.60470e9 | 0.222568 | ||||||||
\(983\) | −1.77744e10 | −0.596839 | −0.298420 | − | 0.954435i | \(-0.596459\pi\) | ||||
−0.298420 | + | 0.954435i | \(0.596459\pi\) | |||||||
\(984\) | 1.02595e10 | 0.343277 | ||||||||
\(985\) | 1.61701e10 | 0.539122 | ||||||||
\(986\) | 3.91542e10 | 1.30080 | ||||||||
\(987\) | 3.35402e9 | 0.111034 | ||||||||
\(988\) | 2.97746e9 | 0.0982193 | ||||||||
\(989\) | 3.18333e9 | 0.104639 | ||||||||
\(990\) | 9.96679e9 | 0.326462 | ||||||||
\(991\) | −5.34227e10 | −1.74369 | −0.871843 | − | 0.489786i | \(-0.837075\pi\) | ||||
−0.871843 | + | 0.489786i | \(0.837075\pi\) | |||||||
\(992\) | −2.21606e9 | −0.0720761 | ||||||||
\(993\) | −2.57679e9 | −0.0835136 | ||||||||
\(994\) | −5.42254e8 | −0.0175126 | ||||||||
\(995\) | 1.25650e10 | 0.404372 | ||||||||
\(996\) | −8.98859e9 | −0.288260 | ||||||||
\(997\) | 1.20062e10 | 0.383682 | 0.191841 | − | 0.981426i | \(-0.438554\pi\) | ||||
0.191841 | + | 0.981426i | \(0.438554\pi\) | |||||||
\(998\) | 3.71904e10 | 1.18433 | ||||||||
\(999\) | 1.03037e10 | 0.326976 |
(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 | 74.8.a.b.1.1 | ✓ | 4 | |
4.3 | odd | 2 | 592.8.a.a.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.8.a.b.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
592.8.a.a.1.4 | 4 | 4.3 | odd | 2 |