Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,10,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(1.54510750849\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 3.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 18.0000 | 0.795495 | 0.397748 | − | 0.917495i | \(-0.369792\pi\) | ||||
0.397748 | + | 0.917495i | \(0.369792\pi\) | |||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | −188.000 | −0.367188 | ||||||||
\(5\) | −1530.00 | −1.09478 | −0.547389 | − | 0.836878i | \(-0.684378\pi\) | ||||
−0.547389 | + | 0.836878i | \(0.684378\pi\) | |||||||
\(6\) | 1458.00 | 0.459279 | ||||||||
\(7\) | 9128.00 | 1.43693 | 0.718463 | − | 0.695565i | \(-0.244846\pi\) | ||||
0.718463 | + | 0.695565i | \(0.244846\pi\) | |||||||
\(8\) | −12600.0 | −1.08759 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −27540.0 | −0.870891 | ||||||||
\(11\) | 21132.0 | 0.435185 | 0.217592 | − | 0.976040i | \(-0.430180\pi\) | ||||
0.217592 | + | 0.976040i | \(0.430180\pi\) | |||||||
\(12\) | −15228.0 | −0.211996 | ||||||||
\(13\) | 31214.0 | 0.303113 | 0.151556 | − | 0.988449i | \(-0.451571\pi\) | ||||
0.151556 | + | 0.988449i | \(0.451571\pi\) | |||||||
\(14\) | 164304. | 1.14307 | ||||||||
\(15\) | −123930. | −0.632071 | ||||||||
\(16\) | −130544. | −0.497986 | ||||||||
\(17\) | −279342. | −0.811178 | −0.405589 | − | 0.914056i | \(-0.632934\pi\) | ||||
−0.405589 | + | 0.914056i | \(0.632934\pi\) | |||||||
\(18\) | 118098. | 0.265165 | ||||||||
\(19\) | 144020. | 0.253531 | 0.126766 | − | 0.991933i | \(-0.459540\pi\) | ||||
0.126766 | + | 0.991933i | \(0.459540\pi\) | |||||||
\(20\) | 287640. | 0.401989 | ||||||||
\(21\) | 739368. | 0.829610 | ||||||||
\(22\) | 380376. | 0.346187 | ||||||||
\(23\) | −1.76350e6 | −1.31401 | −0.657006 | − | 0.753885i | \(-0.728177\pi\) | ||||
−0.657006 | + | 0.753885i | \(0.728177\pi\) | |||||||
\(24\) | −1.02060e6 | −0.627921 | ||||||||
\(25\) | 387775. | 0.198541 | ||||||||
\(26\) | 561852. | 0.241125 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | −1.71606e6 | −0.527621 | ||||||||
\(29\) | 4.69251e6 | 1.23201 | 0.616005 | − | 0.787742i | \(-0.288750\pi\) | ||||
0.616005 | + | 0.787742i | \(0.288750\pi\) | |||||||
\(30\) | −2.23074e6 | −0.502809 | ||||||||
\(31\) | −369088. | −0.0717798 | −0.0358899 | − | 0.999356i | \(-0.511427\pi\) | ||||
−0.0358899 | + | 0.999356i | \(0.511427\pi\) | |||||||
\(32\) | 4.10141e6 | 0.691446 | ||||||||
\(33\) | 1.71169e6 | 0.251254 | ||||||||
\(34\) | −5.02816e6 | −0.645288 | ||||||||
\(35\) | −1.39658e7 | −1.57312 | ||||||||
\(36\) | −1.23347e6 | −0.122396 | ||||||||
\(37\) | 9.34708e6 | 0.819914 | 0.409957 | − | 0.912105i | \(-0.365544\pi\) | ||||
0.409957 | + | 0.912105i | \(0.365544\pi\) | |||||||
\(38\) | 2.59236e6 | 0.201683 | ||||||||
\(39\) | 2.52833e6 | 0.175002 | ||||||||
\(40\) | 1.92780e7 | 1.19067 | ||||||||
\(41\) | −7.22684e6 | −0.399412 | −0.199706 | − | 0.979856i | \(-0.563999\pi\) | ||||
−0.199706 | + | 0.979856i | \(0.563999\pi\) | |||||||
\(42\) | 1.33086e7 | 0.659950 | ||||||||
\(43\) | −2.31475e7 | −1.03251 | −0.516257 | − | 0.856434i | \(-0.672675\pi\) | ||||
−0.516257 | + | 0.856434i | \(0.672675\pi\) | |||||||
\(44\) | −3.97282e6 | −0.159794 | ||||||||
\(45\) | −1.00383e7 | −0.364926 | ||||||||
\(46\) | −3.17429e7 | −1.04529 | ||||||||
\(47\) | 2.29719e7 | 0.686683 | 0.343342 | − | 0.939211i | \(-0.388441\pi\) | ||||
0.343342 | + | 0.939211i | \(0.388441\pi\) | |||||||
\(48\) | −1.05741e7 | −0.287512 | ||||||||
\(49\) | 4.29668e7 | 1.06476 | ||||||||
\(50\) | 6.97995e6 | 0.157938 | ||||||||
\(51\) | −2.26267e7 | −0.468334 | ||||||||
\(52\) | −5.86823e6 | −0.111299 | ||||||||
\(53\) | 7.84772e7 | 1.36616 | 0.683081 | − | 0.730343i | \(-0.260640\pi\) | ||||
0.683081 | + | 0.730343i | \(0.260640\pi\) | |||||||
\(54\) | 9.56594e6 | 0.153093 | ||||||||
\(55\) | −3.23320e7 | −0.476431 | ||||||||
\(56\) | −1.15013e8 | −1.56279 | ||||||||
\(57\) | 1.16656e7 | 0.146376 | ||||||||
\(58\) | 8.44652e7 | 0.980058 | ||||||||
\(59\) | −2.03107e7 | −0.218218 | −0.109109 | − | 0.994030i | \(-0.534800\pi\) | ||||
−0.109109 | + | 0.994030i | \(0.534800\pi\) | |||||||
\(60\) | 2.32988e7 | 0.232089 | ||||||||
\(61\) | −1.79340e8 | −1.65841 | −0.829207 | − | 0.558942i | \(-0.811207\pi\) | ||||
−0.829207 | + | 0.558942i | \(0.811207\pi\) | |||||||
\(62\) | −6.64358e6 | −0.0571005 | ||||||||
\(63\) | 5.98888e7 | 0.478975 | ||||||||
\(64\) | 1.40664e8 | 1.04803 | ||||||||
\(65\) | −4.77574e7 | −0.331842 | ||||||||
\(66\) | 3.08105e7 | 0.199871 | ||||||||
\(67\) | 2.74528e8 | 1.66437 | 0.832186 | − | 0.554496i | \(-0.187089\pi\) | ||||
0.832186 | + | 0.554496i | \(0.187089\pi\) | |||||||
\(68\) | 5.25163e7 | 0.297854 | ||||||||
\(69\) | −1.42843e8 | −0.758645 | ||||||||
\(70\) | −2.51385e8 | −1.25141 | ||||||||
\(71\) | −3.63426e7 | −0.169728 | −0.0848641 | − | 0.996393i | \(-0.527046\pi\) | ||||
−0.0848641 | + | 0.996393i | \(0.527046\pi\) | |||||||
\(72\) | −8.26686e7 | −0.362530 | ||||||||
\(73\) | −2.47090e8 | −1.01836 | −0.509180 | − | 0.860660i | \(-0.670051\pi\) | ||||
−0.509180 | + | 0.860660i | \(0.670051\pi\) | |||||||
\(74\) | 1.68247e8 | 0.652237 | ||||||||
\(75\) | 3.14098e7 | 0.114628 | ||||||||
\(76\) | −2.70758e7 | −0.0930935 | ||||||||
\(77\) | 1.92893e8 | 0.625328 | ||||||||
\(78\) | 4.55100e7 | 0.139213 | ||||||||
\(79\) | 1.91875e8 | 0.554238 | 0.277119 | − | 0.960836i | \(-0.410620\pi\) | ||||
0.277119 | + | 0.960836i | \(0.410620\pi\) | |||||||
\(80\) | 1.99732e8 | 0.545184 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −1.30083e8 | −0.317730 | ||||||||
\(83\) | −2.76159e8 | −0.638717 | −0.319358 | − | 0.947634i | \(-0.603467\pi\) | ||||
−0.319358 | + | 0.947634i | \(0.603467\pi\) | |||||||
\(84\) | −1.39001e8 | −0.304622 | ||||||||
\(85\) | 4.27393e8 | 0.888060 | ||||||||
\(86\) | −4.16655e8 | −0.821359 | ||||||||
\(87\) | 3.80093e8 | 0.711301 | ||||||||
\(88\) | −2.66263e8 | −0.473303 | ||||||||
\(89\) | −6.78997e8 | −1.14713 | −0.573566 | − | 0.819160i | \(-0.694440\pi\) | ||||
−0.573566 | + | 0.819160i | \(0.694440\pi\) | |||||||
\(90\) | −1.80690e8 | −0.290297 | ||||||||
\(91\) | 2.84921e8 | 0.435551 | ||||||||
\(92\) | 3.31537e8 | 0.482489 | ||||||||
\(93\) | −2.98961e7 | −0.0414421 | ||||||||
\(94\) | 4.13494e8 | 0.546253 | ||||||||
\(95\) | −2.20351e8 | −0.277561 | ||||||||
\(96\) | 3.32214e8 | 0.399206 | ||||||||
\(97\) | −5.67658e8 | −0.651049 | −0.325524 | − | 0.945534i | \(-0.605541\pi\) | ||||
−0.325524 | + | 0.945534i | \(0.605541\pi\) | |||||||
\(98\) | 7.73402e8 | 0.847009 | ||||||||
\(99\) | 1.38647e8 | 0.145062 | ||||||||
\(100\) | −7.29017e7 | −0.0729017 | ||||||||
\(101\) | 1.62282e9 | 1.55176 | 0.775881 | − | 0.630879i | \(-0.217306\pi\) | ||||
0.775881 | + | 0.630879i | \(0.217306\pi\) | |||||||
\(102\) | −4.07281e8 | −0.372557 | ||||||||
\(103\) | −1.75103e9 | −1.53294 | −0.766470 | − | 0.642280i | \(-0.777989\pi\) | ||||
−0.766470 | + | 0.642280i | \(0.777989\pi\) | |||||||
\(104\) | −3.93296e8 | −0.329663 | ||||||||
\(105\) | −1.13123e9 | −0.908239 | ||||||||
\(106\) | 1.41259e9 | 1.08677 | ||||||||
\(107\) | −1.54296e9 | −1.13796 | −0.568980 | − | 0.822352i | \(-0.692662\pi\) | ||||
−0.568980 | + | 0.822352i | \(0.692662\pi\) | |||||||
\(108\) | −9.99109e7 | −0.0706653 | ||||||||
\(109\) | 4.57665e8 | 0.310548 | 0.155274 | − | 0.987871i | \(-0.450374\pi\) | ||||
0.155274 | + | 0.987871i | \(0.450374\pi\) | |||||||
\(110\) | −5.81975e8 | −0.378998 | ||||||||
\(111\) | 7.57113e8 | 0.473377 | ||||||||
\(112\) | −1.19161e9 | −0.715569 | ||||||||
\(113\) | 3.26794e9 | 1.88548 | 0.942739 | − | 0.333531i | \(-0.108240\pi\) | ||||
0.942739 | + | 0.333531i | \(0.108240\pi\) | |||||||
\(114\) | 2.09981e8 | 0.116442 | ||||||||
\(115\) | 2.69815e9 | 1.43855 | ||||||||
\(116\) | −8.82192e8 | −0.452379 | ||||||||
\(117\) | 2.04795e8 | 0.101038 | ||||||||
\(118\) | −3.65592e8 | −0.173591 | ||||||||
\(119\) | −2.54983e9 | −1.16560 | ||||||||
\(120\) | 1.56152e9 | 0.687435 | ||||||||
\(121\) | −1.91139e9 | −0.810614 | ||||||||
\(122\) | −3.22812e9 | −1.31926 | ||||||||
\(123\) | −5.85374e8 | −0.230601 | ||||||||
\(124\) | 6.93885e7 | 0.0263566 | ||||||||
\(125\) | 2.39499e9 | 0.877421 | ||||||||
\(126\) | 1.07800e9 | 0.381023 | ||||||||
\(127\) | 9.28879e8 | 0.316842 | 0.158421 | − | 0.987372i | \(-0.449360\pi\) | ||||
0.158421 | + | 0.987372i | \(0.449360\pi\) | |||||||
\(128\) | 4.32029e8 | 0.142255 | ||||||||
\(129\) | −1.87495e9 | −0.596122 | ||||||||
\(130\) | −8.59634e8 | −0.263978 | ||||||||
\(131\) | −9.88659e8 | −0.293309 | −0.146655 | − | 0.989188i | \(-0.546851\pi\) | ||||
−0.146655 | + | 0.989188i | \(0.546851\pi\) | |||||||
\(132\) | −3.21798e8 | −0.0922573 | ||||||||
\(133\) | 1.31461e9 | 0.364306 | ||||||||
\(134\) | 4.94151e9 | 1.32400 | ||||||||
\(135\) | −8.13105e8 | −0.210690 | ||||||||
\(136\) | 3.51971e9 | 0.882230 | ||||||||
\(137\) | −5.73253e7 | −0.0139028 | −0.00695142 | − | 0.999976i | \(-0.502213\pi\) | ||||
−0.00695142 | + | 0.999976i | \(0.502213\pi\) | |||||||
\(138\) | −2.57118e9 | −0.603498 | ||||||||
\(139\) | −4.65052e9 | −1.05666 | −0.528330 | − | 0.849039i | \(-0.677182\pi\) | ||||
−0.528330 | + | 0.849039i | \(0.677182\pi\) | |||||||
\(140\) | 2.62558e9 | 0.577629 | ||||||||
\(141\) | 1.86072e9 | 0.396457 | ||||||||
\(142\) | −6.54168e8 | −0.135018 | ||||||||
\(143\) | 6.59614e8 | 0.131910 | ||||||||
\(144\) | −8.56499e8 | −0.165995 | ||||||||
\(145\) | −7.17954e9 | −1.34878 | ||||||||
\(146\) | −4.44761e9 | −0.810101 | ||||||||
\(147\) | 3.48031e9 | 0.614738 | ||||||||
\(148\) | −1.75725e9 | −0.301062 | ||||||||
\(149\) | −1.40236e9 | −0.233089 | −0.116545 | − | 0.993185i | \(-0.537182\pi\) | ||||
−0.116545 | + | 0.993185i | \(0.537182\pi\) | |||||||
\(150\) | 5.65376e8 | 0.0911857 | ||||||||
\(151\) | 1.01548e10 | 1.58955 | 0.794773 | − | 0.606907i | \(-0.207590\pi\) | ||||
0.794773 | + | 0.606907i | \(0.207590\pi\) | |||||||
\(152\) | −1.81465e9 | −0.275738 | ||||||||
\(153\) | −1.83276e9 | −0.270393 | ||||||||
\(154\) | 3.47207e9 | 0.497445 | ||||||||
\(155\) | 5.64705e8 | 0.0785830 | ||||||||
\(156\) | −4.75327e8 | −0.0642587 | ||||||||
\(157\) | 9.36605e9 | 1.23029 | 0.615146 | − | 0.788413i | \(-0.289097\pi\) | ||||
0.615146 | + | 0.788413i | \(0.289097\pi\) | |||||||
\(158\) | 3.45375e9 | 0.440893 | ||||||||
\(159\) | 6.35665e9 | 0.788754 | ||||||||
\(160\) | −6.27515e9 | −0.756980 | ||||||||
\(161\) | −1.60972e10 | −1.88814 | ||||||||
\(162\) | 7.74841e8 | 0.0883883 | ||||||||
\(163\) | −7.34780e8 | −0.0815292 | −0.0407646 | − | 0.999169i | \(-0.512979\pi\) | ||||
−0.0407646 | + | 0.999169i | \(0.512979\pi\) | |||||||
\(164\) | 1.35865e9 | 0.146659 | ||||||||
\(165\) | −2.61889e9 | −0.275068 | ||||||||
\(166\) | −4.97087e9 | −0.508096 | ||||||||
\(167\) | 1.55584e9 | 0.154789 | 0.0773947 | − | 0.997001i | \(-0.475340\pi\) | ||||
0.0773947 | + | 0.997001i | \(0.475340\pi\) | |||||||
\(168\) | −9.31604e9 | −0.902276 | ||||||||
\(169\) | −9.63019e9 | −0.908123 | ||||||||
\(170\) | 7.69308e9 | 0.706448 | ||||||||
\(171\) | 9.44915e8 | 0.0845104 | ||||||||
\(172\) | 4.35173e9 | 0.379126 | ||||||||
\(173\) | 1.90448e10 | 1.61648 | 0.808238 | − | 0.588856i | \(-0.200421\pi\) | ||||
0.808238 | + | 0.588856i | \(0.200421\pi\) | |||||||
\(174\) | 6.84168e9 | 0.565837 | ||||||||
\(175\) | 3.53961e9 | 0.285288 | ||||||||
\(176\) | −2.75866e9 | −0.216716 | ||||||||
\(177\) | −1.64516e9 | −0.125988 | ||||||||
\(178\) | −1.22220e10 | −0.912537 | ||||||||
\(179\) | 4.32852e9 | 0.315138 | 0.157569 | − | 0.987508i | \(-0.449634\pi\) | ||||
0.157569 | + | 0.987508i | \(0.449634\pi\) | |||||||
\(180\) | 1.88721e9 | 0.133996 | ||||||||
\(181\) | −9.56757e8 | −0.0662595 | −0.0331298 | − | 0.999451i | \(-0.510547\pi\) | ||||
−0.0331298 | + | 0.999451i | \(0.510547\pi\) | |||||||
\(182\) | 5.12859e9 | 0.346479 | ||||||||
\(183\) | −1.45265e10 | −0.957485 | ||||||||
\(184\) | 2.22200e10 | 1.42911 | ||||||||
\(185\) | −1.43010e10 | −0.897624 | ||||||||
\(186\) | −5.38130e8 | −0.0329670 | ||||||||
\(187\) | −5.90306e9 | −0.353012 | ||||||||
\(188\) | −4.31871e9 | −0.252141 | ||||||||
\(189\) | 4.85099e9 | 0.276537 | ||||||||
\(190\) | −3.96631e9 | −0.220798 | ||||||||
\(191\) | −1.76438e10 | −0.959274 | −0.479637 | − | 0.877467i | \(-0.659232\pi\) | ||||
−0.479637 | + | 0.877467i | \(0.659232\pi\) | |||||||
\(192\) | 1.13938e10 | 0.605079 | ||||||||
\(193\) | 1.30993e10 | 0.679581 | 0.339790 | − | 0.940501i | \(-0.389644\pi\) | ||||
0.339790 | + | 0.940501i | \(0.389644\pi\) | |||||||
\(194\) | −1.02178e10 | −0.517906 | ||||||||
\(195\) | −3.86835e9 | −0.191589 | ||||||||
\(196\) | −8.07775e9 | −0.390965 | ||||||||
\(197\) | 4.74589e9 | 0.224502 | 0.112251 | − | 0.993680i | \(-0.464194\pi\) | ||||
0.112251 | + | 0.993680i | \(0.464194\pi\) | |||||||
\(198\) | 2.49565e9 | 0.115396 | ||||||||
\(199\) | −1.92102e10 | −0.868348 | −0.434174 | − | 0.900829i | \(-0.642960\pi\) | ||||
−0.434174 | + | 0.900829i | \(0.642960\pi\) | |||||||
\(200\) | −4.88596e9 | −0.215931 | ||||||||
\(201\) | 2.22368e10 | 0.960926 | ||||||||
\(202\) | 2.92108e10 | 1.23442 | ||||||||
\(203\) | 4.28332e10 | 1.77031 | ||||||||
\(204\) | 4.25382e9 | 0.171966 | ||||||||
\(205\) | 1.10571e10 | 0.437268 | ||||||||
\(206\) | −3.15185e10 | −1.21945 | ||||||||
\(207\) | −1.15703e10 | −0.438004 | ||||||||
\(208\) | −4.07480e9 | −0.150946 | ||||||||
\(209\) | 3.04343e9 | 0.110333 | ||||||||
\(210\) | −2.03622e10 | −0.722500 | ||||||||
\(211\) | −1.81273e10 | −0.629597 | −0.314798 | − | 0.949159i | \(-0.601937\pi\) | ||||
−0.314798 | + | 0.949159i | \(0.601937\pi\) | |||||||
\(212\) | −1.47537e10 | −0.501637 | ||||||||
\(213\) | −2.94375e9 | −0.0979926 | ||||||||
\(214\) | −2.77732e10 | −0.905241 | ||||||||
\(215\) | 3.54156e10 | 1.13037 | ||||||||
\(216\) | −6.69616e9 | −0.209307 | ||||||||
\(217\) | −3.36904e9 | −0.103142 | ||||||||
\(218\) | 8.23797e9 | 0.247039 | ||||||||
\(219\) | −2.00143e10 | −0.587951 | ||||||||
\(220\) | 6.07841e9 | 0.174939 | ||||||||
\(221\) | −8.71938e9 | −0.245878 | ||||||||
\(222\) | 1.36280e10 | 0.376569 | ||||||||
\(223\) | 3.91081e9 | 0.105900 | 0.0529499 | − | 0.998597i | \(-0.483138\pi\) | ||||
0.0529499 | + | 0.998597i | \(0.483138\pi\) | |||||||
\(224\) | 3.74377e10 | 0.993556 | ||||||||
\(225\) | 2.54419e9 | 0.0661803 | ||||||||
\(226\) | 5.88230e10 | 1.49989 | ||||||||
\(227\) | −3.58126e10 | −0.895199 | −0.447599 | − | 0.894234i | \(-0.647721\pi\) | ||||
−0.447599 | + | 0.894234i | \(0.647721\pi\) | |||||||
\(228\) | −2.19314e9 | −0.0537476 | ||||||||
\(229\) | 5.30445e9 | 0.127462 | 0.0637310 | − | 0.997967i | \(-0.479700\pi\) | ||||
0.0637310 | + | 0.997967i | \(0.479700\pi\) | |||||||
\(230\) | 4.85667e10 | 1.14436 | ||||||||
\(231\) | 1.56243e10 | 0.361033 | ||||||||
\(232\) | −5.91256e10 | −1.33992 | ||||||||
\(233\) | −2.54172e10 | −0.564970 | −0.282485 | − | 0.959272i | \(-0.591159\pi\) | ||||
−0.282485 | + | 0.959272i | \(0.591159\pi\) | |||||||
\(234\) | 3.68631e9 | 0.0803749 | ||||||||
\(235\) | −3.51470e10 | −0.751766 | ||||||||
\(236\) | 3.81840e9 | 0.0801268 | ||||||||
\(237\) | 1.55419e10 | 0.319989 | ||||||||
\(238\) | −4.58970e10 | −0.927231 | ||||||||
\(239\) | −6.33494e10 | −1.25589 | −0.627946 | − | 0.778257i | \(-0.716104\pi\) | ||||
−0.627946 | + | 0.778257i | \(0.716104\pi\) | |||||||
\(240\) | 1.61783e10 | 0.314762 | ||||||||
\(241\) | 1.01929e11 | 1.94635 | 0.973173 | − | 0.230073i | \(-0.0738965\pi\) | ||||
0.973173 | + | 0.230073i | \(0.0738965\pi\) | |||||||
\(242\) | −3.44050e10 | −0.644840 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | 3.37159e10 | 0.608949 | ||||||||
\(245\) | −6.57392e10 | −1.16567 | ||||||||
\(246\) | −1.05367e10 | −0.183442 | ||||||||
\(247\) | 4.49544e9 | 0.0768486 | ||||||||
\(248\) | 4.65051e9 | 0.0780671 | ||||||||
\(249\) | −2.23689e10 | −0.368763 | ||||||||
\(250\) | 4.31097e10 | 0.697984 | ||||||||
\(251\) | 9.64745e10 | 1.53420 | 0.767098 | − | 0.641530i | \(-0.221700\pi\) | ||||
0.767098 | + | 0.641530i | \(0.221700\pi\) | |||||||
\(252\) | −1.12591e10 | −0.175874 | ||||||||
\(253\) | −3.72662e10 | −0.571838 | ||||||||
\(254\) | 1.67198e10 | 0.252046 | ||||||||
\(255\) | 3.46189e10 | 0.512722 | ||||||||
\(256\) | −6.42434e10 | −0.934864 | ||||||||
\(257\) | −7.99591e9 | −0.114332 | −0.0571661 | − | 0.998365i | \(-0.518206\pi\) | ||||
−0.0571661 | + | 0.998365i | \(0.518206\pi\) | |||||||
\(258\) | −3.37490e10 | −0.474212 | ||||||||
\(259\) | 8.53201e10 | 1.17816 | ||||||||
\(260\) | 8.97839e9 | 0.121848 | ||||||||
\(261\) | 3.07876e10 | 0.410670 | ||||||||
\(262\) | −1.77959e10 | −0.233326 | ||||||||
\(263\) | 1.06269e11 | 1.36964 | 0.684821 | − | 0.728712i | \(-0.259881\pi\) | ||||
0.684821 | + | 0.728712i | \(0.259881\pi\) | |||||||
\(264\) | −2.15673e10 | −0.273262 | ||||||||
\(265\) | −1.20070e11 | −1.49564 | ||||||||
\(266\) | 2.36631e10 | 0.289803 | ||||||||
\(267\) | −5.49988e10 | −0.662296 | ||||||||
\(268\) | −5.16113e10 | −0.611137 | ||||||||
\(269\) | −1.00886e11 | −1.17475 | −0.587377 | − | 0.809313i | \(-0.699840\pi\) | ||||
−0.587377 | + | 0.809313i | \(0.699840\pi\) | |||||||
\(270\) | −1.46359e10 | −0.167603 | ||||||||
\(271\) | −2.86345e10 | −0.322498 | −0.161249 | − | 0.986914i | \(-0.551552\pi\) | ||||
−0.161249 | + | 0.986914i | \(0.551552\pi\) | |||||||
\(272\) | 3.64664e10 | 0.403955 | ||||||||
\(273\) | 2.30786e10 | 0.251465 | ||||||||
\(274\) | −1.03186e9 | −0.0110596 | ||||||||
\(275\) | 8.19446e9 | 0.0864019 | ||||||||
\(276\) | 2.68545e10 | 0.278565 | ||||||||
\(277\) | 4.12251e10 | 0.420729 | 0.210365 | − | 0.977623i | \(-0.432535\pi\) | ||||
0.210365 | + | 0.977623i | \(0.432535\pi\) | |||||||
\(278\) | −8.37094e10 | −0.840568 | ||||||||
\(279\) | −2.42159e9 | −0.0239266 | ||||||||
\(280\) | 1.75970e11 | 1.71091 | ||||||||
\(281\) | 1.21800e11 | 1.16538 | 0.582692 | − | 0.812693i | \(-0.301999\pi\) | ||||
0.582692 | + | 0.812693i | \(0.301999\pi\) | |||||||
\(282\) | 3.34930e10 | 0.315379 | ||||||||
\(283\) | 2.32820e10 | 0.215765 | 0.107883 | − | 0.994164i | \(-0.465593\pi\) | ||||
0.107883 | + | 0.994164i | \(0.465593\pi\) | |||||||
\(284\) | 6.83242e9 | 0.0623221 | ||||||||
\(285\) | −1.78484e10 | −0.160250 | ||||||||
\(286\) | 1.18731e10 | 0.104934 | ||||||||
\(287\) | −6.59666e10 | −0.573925 | ||||||||
\(288\) | 2.69093e10 | 0.230482 | ||||||||
\(289\) | −4.05559e10 | −0.341990 | ||||||||
\(290\) | −1.29232e11 | −1.07295 | ||||||||
\(291\) | −4.59803e10 | −0.375883 | ||||||||
\(292\) | 4.64528e10 | 0.373929 | ||||||||
\(293\) | −9.12801e10 | −0.723555 | −0.361778 | − | 0.932264i | \(-0.617830\pi\) | ||||
−0.361778 | + | 0.932264i | \(0.617830\pi\) | |||||||
\(294\) | 6.26456e10 | 0.489021 | ||||||||
\(295\) | 3.10753e10 | 0.238900 | ||||||||
\(296\) | −1.17773e11 | −0.891731 | ||||||||
\(297\) | 1.12304e10 | 0.0837513 | ||||||||
\(298\) | −2.52425e10 | −0.185421 | ||||||||
\(299\) | −5.50458e10 | −0.398294 | ||||||||
\(300\) | −5.90504e9 | −0.0420898 | ||||||||
\(301\) | −2.11290e11 | −1.48365 | ||||||||
\(302\) | 1.82786e11 | 1.26448 | ||||||||
\(303\) | 1.31449e11 | 0.895910 | ||||||||
\(304\) | −1.88009e10 | −0.126255 | ||||||||
\(305\) | 2.74390e11 | 1.81560 | ||||||||
\(306\) | −3.29897e10 | −0.215096 | ||||||||
\(307\) | −4.39070e10 | −0.282105 | −0.141053 | − | 0.990002i | \(-0.545049\pi\) | ||||
−0.141053 | + | 0.990002i | \(0.545049\pi\) | |||||||
\(308\) | −3.62639e10 | −0.229613 | ||||||||
\(309\) | −1.41833e11 | −0.885043 | ||||||||
\(310\) | 1.01647e10 | 0.0625124 | ||||||||
\(311\) | −7.64835e10 | −0.463603 | −0.231801 | − | 0.972763i | \(-0.574462\pi\) | ||||
−0.231801 | + | 0.972763i | \(0.574462\pi\) | |||||||
\(312\) | −3.18570e10 | −0.190331 | ||||||||
\(313\) | 2.68488e11 | 1.58116 | 0.790580 | − | 0.612359i | \(-0.209779\pi\) | ||||
0.790580 | + | 0.612359i | \(0.209779\pi\) | |||||||
\(314\) | 1.68589e11 | 0.978691 | ||||||||
\(315\) | −9.16299e10 | −0.524372 | ||||||||
\(316\) | −3.60725e10 | −0.203509 | ||||||||
\(317\) | 1.52056e11 | 0.845738 | 0.422869 | − | 0.906191i | \(-0.361023\pi\) | ||||
0.422869 | + | 0.906191i | \(0.361023\pi\) | |||||||
\(318\) | 1.14420e11 | 0.627450 | ||||||||
\(319\) | 9.91621e10 | 0.536152 | ||||||||
\(320\) | −2.15216e11 | −1.14736 | ||||||||
\(321\) | −1.24980e11 | −0.657001 | ||||||||
\(322\) | −2.89749e11 | −1.50200 | ||||||||
\(323\) | −4.02308e10 | −0.205659 | ||||||||
\(324\) | −8.09278e9 | −0.0407986 | ||||||||
\(325\) | 1.21040e10 | 0.0601803 | ||||||||
\(326\) | −1.32260e10 | −0.0648561 | ||||||||
\(327\) | 3.70709e10 | 0.179295 | ||||||||
\(328\) | 9.10582e10 | 0.434397 | ||||||||
\(329\) | 2.09687e11 | 0.986713 | ||||||||
\(330\) | −4.71400e10 | −0.218815 | ||||||||
\(331\) | −2.63057e11 | −1.20455 | −0.602274 | − | 0.798289i | \(-0.705739\pi\) | ||||
−0.602274 | + | 0.798289i | \(0.705739\pi\) | |||||||
\(332\) | 5.19179e10 | 0.234529 | ||||||||
\(333\) | 6.13262e10 | 0.273305 | ||||||||
\(334\) | 2.80051e10 | 0.123134 | ||||||||
\(335\) | −4.20028e11 | −1.82212 | ||||||||
\(336\) | −9.65201e10 | −0.413134 | ||||||||
\(337\) | 2.97183e11 | 1.25513 | 0.627566 | − | 0.778564i | \(-0.284051\pi\) | ||||
0.627566 | + | 0.778564i | \(0.284051\pi\) | |||||||
\(338\) | −1.73343e11 | −0.722407 | ||||||||
\(339\) | 2.64703e11 | 1.08858 | ||||||||
\(340\) | −8.03499e10 | −0.326085 | ||||||||
\(341\) | −7.79957e9 | −0.0312375 | ||||||||
\(342\) | 1.70085e10 | 0.0672276 | ||||||||
\(343\) | 2.38530e10 | 0.0930507 | ||||||||
\(344\) | 2.91658e11 | 1.12295 | ||||||||
\(345\) | 2.18550e11 | 0.830549 | ||||||||
\(346\) | 3.42807e11 | 1.28590 | ||||||||
\(347\) | 1.40219e11 | 0.519186 | 0.259593 | − | 0.965718i | \(-0.416412\pi\) | ||||
0.259593 | + | 0.965718i | \(0.416412\pi\) | |||||||
\(348\) | −7.14575e10 | −0.261181 | ||||||||
\(349\) | −3.14891e11 | −1.13618 | −0.568088 | − | 0.822968i | \(-0.692317\pi\) | ||||
−0.568088 | + | 0.822968i | \(0.692317\pi\) | |||||||
\(350\) | 6.37130e10 | 0.226946 | ||||||||
\(351\) | 1.65884e10 | 0.0583341 | ||||||||
\(352\) | 8.66710e10 | 0.300907 | ||||||||
\(353\) | −5.31195e11 | −1.82082 | −0.910411 | − | 0.413704i | \(-0.864235\pi\) | ||||
−0.910411 | + | 0.413704i | \(0.864235\pi\) | |||||||
\(354\) | −2.96129e10 | −0.100223 | ||||||||
\(355\) | 5.56043e10 | 0.185815 | ||||||||
\(356\) | 1.27652e11 | 0.421212 | ||||||||
\(357\) | −2.06537e11 | −0.672961 | ||||||||
\(358\) | 7.79133e10 | 0.250691 | ||||||||
\(359\) | −4.97684e11 | −1.58135 | −0.790676 | − | 0.612235i | \(-0.790271\pi\) | ||||
−0.790676 | + | 0.612235i | \(0.790271\pi\) | |||||||
\(360\) | 1.26483e11 | 0.396891 | ||||||||
\(361\) | −3.01946e11 | −0.935722 | ||||||||
\(362\) | −1.72216e10 | −0.0527091 | ||||||||
\(363\) | −1.54822e11 | −0.468008 | ||||||||
\(364\) | −5.35652e10 | −0.159929 | ||||||||
\(365\) | 3.78047e11 | 1.11488 | ||||||||
\(366\) | −2.61478e11 | −0.761675 | ||||||||
\(367\) | 2.77743e11 | 0.799183 | 0.399591 | − | 0.916693i | \(-0.369152\pi\) | ||||
0.399591 | + | 0.916693i | \(0.369152\pi\) | |||||||
\(368\) | 2.30214e11 | 0.654359 | ||||||||
\(369\) | −4.74153e10 | −0.133137 | ||||||||
\(370\) | −2.57419e11 | −0.714056 | ||||||||
\(371\) | 7.16340e11 | 1.96307 | ||||||||
\(372\) | 5.62047e9 | 0.0152170 | ||||||||
\(373\) | 2.55319e11 | 0.682957 | 0.341478 | − | 0.939890i | \(-0.389072\pi\) | ||||
0.341478 | + | 0.939890i | \(0.389072\pi\) | |||||||
\(374\) | −1.06255e11 | −0.280819 | ||||||||
\(375\) | 1.93994e11 | 0.506579 | ||||||||
\(376\) | −2.89446e11 | −0.746830 | ||||||||
\(377\) | 1.46472e11 | 0.373438 | ||||||||
\(378\) | 8.73179e10 | 0.219983 | ||||||||
\(379\) | 8.12103e10 | 0.202178 | 0.101089 | − | 0.994877i | \(-0.467767\pi\) | ||||
0.101089 | + | 0.994877i | \(0.467767\pi\) | |||||||
\(380\) | 4.14259e10 | 0.101917 | ||||||||
\(381\) | 7.52392e10 | 0.182929 | ||||||||
\(382\) | −3.17589e11 | −0.763097 | ||||||||
\(383\) | −4.13123e11 | −0.981036 | −0.490518 | − | 0.871431i | \(-0.663192\pi\) | ||||
−0.490518 | + | 0.871431i | \(0.663192\pi\) | |||||||
\(384\) | 3.49943e10 | 0.0821310 | ||||||||
\(385\) | −2.95126e11 | −0.684596 | ||||||||
\(386\) | 2.35788e11 | 0.540603 | ||||||||
\(387\) | −1.51871e11 | −0.344171 | ||||||||
\(388\) | 1.06720e11 | 0.239057 | ||||||||
\(389\) | 2.53052e11 | 0.560321 | 0.280160 | − | 0.959953i | \(-0.409612\pi\) | ||||
0.280160 | + | 0.959953i | \(0.409612\pi\) | |||||||
\(390\) | −6.96303e10 | −0.152408 | ||||||||
\(391\) | 4.92618e11 | 1.06590 | ||||||||
\(392\) | −5.41381e11 | −1.15802 | ||||||||
\(393\) | −8.00814e10 | −0.169342 | ||||||||
\(394\) | 8.54259e10 | 0.178590 | ||||||||
\(395\) | −2.93568e11 | −0.606768 | ||||||||
\(396\) | −2.60656e10 | −0.0532648 | ||||||||
\(397\) | −6.53562e10 | −0.132047 | −0.0660236 | − | 0.997818i | \(-0.521031\pi\) | ||||
−0.0660236 | + | 0.997818i | \(0.521031\pi\) | |||||||
\(398\) | −3.45784e11 | −0.690766 | ||||||||
\(399\) | 1.06484e11 | 0.210332 | ||||||||
\(400\) | −5.06217e10 | −0.0988705 | ||||||||
\(401\) | −2.40886e11 | −0.465225 | −0.232612 | − | 0.972570i | \(-0.574727\pi\) | ||||
−0.232612 | + | 0.972570i | \(0.574727\pi\) | |||||||
\(402\) | 4.00262e11 | 0.764412 | ||||||||
\(403\) | −1.15207e10 | −0.0217574 | ||||||||
\(404\) | −3.05091e11 | −0.569788 | ||||||||
\(405\) | −6.58615e10 | −0.121642 | ||||||||
\(406\) | 7.70998e11 | 1.40827 | ||||||||
\(407\) | 1.97522e11 | 0.356814 | ||||||||
\(408\) | 2.85096e11 | 0.509356 | ||||||||
\(409\) | −3.78340e11 | −0.668540 | −0.334270 | − | 0.942477i | \(-0.608490\pi\) | ||||
−0.334270 | + | 0.942477i | \(0.608490\pi\) | |||||||
\(410\) | 1.99027e11 | 0.347844 | ||||||||
\(411\) | −4.64335e9 | −0.00802681 | ||||||||
\(412\) | 3.29193e11 | 0.562876 | ||||||||
\(413\) | −1.85396e11 | −0.313563 | ||||||||
\(414\) | −2.08265e11 | −0.348430 | ||||||||
\(415\) | 4.22524e11 | 0.699253 | ||||||||
\(416\) | 1.28021e11 | 0.209586 | ||||||||
\(417\) | −3.76693e11 | −0.610063 | ||||||||
\(418\) | 5.47818e10 | 0.0877693 | ||||||||
\(419\) | 9.68766e11 | 1.53552 | 0.767760 | − | 0.640737i | \(-0.221371\pi\) | ||||
0.767760 | + | 0.640737i | \(0.221371\pi\) | |||||||
\(420\) | 2.12672e11 | 0.333494 | ||||||||
\(421\) | −1.43789e11 | −0.223077 | −0.111539 | − | 0.993760i | \(-0.535578\pi\) | ||||
−0.111539 | + | 0.993760i | \(0.535578\pi\) | |||||||
\(422\) | −3.26292e11 | −0.500841 | ||||||||
\(423\) | 1.50719e11 | 0.228894 | ||||||||
\(424\) | −9.88812e11 | −1.48582 | ||||||||
\(425\) | −1.08322e11 | −0.161052 | ||||||||
\(426\) | −5.29876e10 | −0.0779527 | ||||||||
\(427\) | −1.63701e12 | −2.38302 | ||||||||
\(428\) | 2.90076e11 | 0.417845 | ||||||||
\(429\) | 5.34288e10 | 0.0761583 | ||||||||
\(430\) | 6.37481e11 | 0.899207 | ||||||||
\(431\) | 2.06890e11 | 0.288796 | 0.144398 | − | 0.989520i | \(-0.453875\pi\) | ||||
0.144398 | + | 0.989520i | \(0.453875\pi\) | |||||||
\(432\) | −6.93764e10 | −0.0958374 | ||||||||
\(433\) | −4.81883e10 | −0.0658789 | −0.0329394 | − | 0.999457i | \(-0.510487\pi\) | ||||
−0.0329394 | + | 0.999457i | \(0.510487\pi\) | |||||||
\(434\) | −6.06426e10 | −0.0820492 | ||||||||
\(435\) | −5.81543e11 | −0.778718 | ||||||||
\(436\) | −8.60411e10 | −0.114029 | ||||||||
\(437\) | −2.53979e11 | −0.333143 | ||||||||
\(438\) | −3.60257e11 | −0.467712 | ||||||||
\(439\) | 4.37941e11 | 0.562763 | 0.281381 | − | 0.959596i | \(-0.409207\pi\) | ||||
0.281381 | + | 0.959596i | \(0.409207\pi\) | |||||||
\(440\) | 4.07383e11 | 0.518162 | ||||||||
\(441\) | 2.81905e11 | 0.354919 | ||||||||
\(442\) | −1.56949e11 | −0.195595 | ||||||||
\(443\) | 7.58665e11 | 0.935908 | 0.467954 | − | 0.883753i | \(-0.344991\pi\) | ||||
0.467954 | + | 0.883753i | \(0.344991\pi\) | |||||||
\(444\) | −1.42337e11 | −0.173818 | ||||||||
\(445\) | 1.03887e12 | 1.25585 | ||||||||
\(446\) | 7.03946e10 | 0.0842427 | ||||||||
\(447\) | −1.13591e11 | −0.134574 | ||||||||
\(448\) | 1.28398e12 | 1.50594 | ||||||||
\(449\) | −1.37280e11 | −0.159403 | −0.0797017 | − | 0.996819i | \(-0.525397\pi\) | ||||
−0.0797017 | + | 0.996819i | \(0.525397\pi\) | |||||||
\(450\) | 4.57955e10 | 0.0526461 | ||||||||
\(451\) | −1.52718e11 | −0.173818 | ||||||||
\(452\) | −6.14373e11 | −0.692324 | ||||||||
\(453\) | 8.22535e11 | 0.917725 | ||||||||
\(454\) | −6.44627e11 | −0.712126 | ||||||||
\(455\) | −4.35930e11 | −0.476832 | ||||||||
\(456\) | −1.46987e11 | −0.159198 | ||||||||
\(457\) | 1.31091e11 | 0.140589 | 0.0702944 | − | 0.997526i | \(-0.477606\pi\) | ||||
0.0702944 | + | 0.997526i | \(0.477606\pi\) | |||||||
\(458\) | 9.54800e10 | 0.101395 | ||||||||
\(459\) | −1.48454e11 | −0.156111 | ||||||||
\(460\) | −5.07252e11 | −0.528218 | ||||||||
\(461\) | −8.03508e11 | −0.828583 | −0.414291 | − | 0.910144i | \(-0.635971\pi\) | ||||
−0.414291 | + | 0.910144i | \(0.635971\pi\) | |||||||
\(462\) | 2.81238e11 | 0.287200 | ||||||||
\(463\) | −1.78582e12 | −1.80602 | −0.903009 | − | 0.429621i | \(-0.858647\pi\) | ||||
−0.903009 | + | 0.429621i | \(0.858647\pi\) | |||||||
\(464\) | −6.12579e11 | −0.613524 | ||||||||
\(465\) | 4.57411e10 | 0.0453699 | ||||||||
\(466\) | −4.57509e11 | −0.449431 | ||||||||
\(467\) | 6.44366e11 | 0.626912 | 0.313456 | − | 0.949603i | \(-0.398513\pi\) | ||||
0.313456 | + | 0.949603i | \(0.398513\pi\) | |||||||
\(468\) | −3.85015e10 | −0.0370997 | ||||||||
\(469\) | 2.50590e12 | 2.39158 | ||||||||
\(470\) | −6.32646e11 | −0.598026 | ||||||||
\(471\) | 7.58650e11 | 0.710309 | ||||||||
\(472\) | 2.55914e11 | 0.237332 | ||||||||
\(473\) | −4.89152e11 | −0.449334 | ||||||||
\(474\) | 2.79753e11 | 0.254550 | ||||||||
\(475\) | 5.58474e10 | 0.0503363 | ||||||||
\(476\) | 4.79369e11 | 0.427995 | ||||||||
\(477\) | 5.14889e11 | 0.455387 | ||||||||
\(478\) | −1.14029e12 | −0.999056 | ||||||||
\(479\) | −1.87701e12 | −1.62913 | −0.814565 | − | 0.580073i | \(-0.803024\pi\) | ||||
−0.814565 | + | 0.580073i | \(0.803024\pi\) | |||||||
\(480\) | −5.08287e11 | −0.437043 | ||||||||
\(481\) | 2.91760e11 | 0.248526 | ||||||||
\(482\) | 1.83472e12 | 1.54831 | ||||||||
\(483\) | −1.30387e12 | −1.09012 | ||||||||
\(484\) | 3.59341e11 | 0.297647 | ||||||||
\(485\) | 8.68516e11 | 0.712755 | ||||||||
\(486\) | 6.27621e10 | 0.0510310 | ||||||||
\(487\) | 1.49355e12 | 1.20321 | 0.601603 | − | 0.798795i | \(-0.294529\pi\) | ||||
0.601603 | + | 0.798795i | \(0.294529\pi\) | |||||||
\(488\) | 2.25968e12 | 1.80368 | ||||||||
\(489\) | −5.95172e10 | −0.0470709 | ||||||||
\(490\) | −1.18331e12 | −0.927287 | ||||||||
\(491\) | −7.47313e11 | −0.580278 | −0.290139 | − | 0.956985i | \(-0.593702\pi\) | ||||
−0.290139 | + | 0.956985i | \(0.593702\pi\) | |||||||
\(492\) | 1.10050e11 | 0.0846736 | ||||||||
\(493\) | −1.31082e12 | −0.999379 | ||||||||
\(494\) | 8.09179e10 | 0.0611327 | ||||||||
\(495\) | −2.12130e11 | −0.158810 | ||||||||
\(496\) | 4.81822e10 | 0.0357453 | ||||||||
\(497\) | −3.31736e11 | −0.243887 | ||||||||
\(498\) | −4.02640e11 | −0.293349 | ||||||||
\(499\) | 1.01300e12 | 0.731402 | 0.365701 | − | 0.930732i | \(-0.380829\pi\) | ||||
0.365701 | + | 0.930732i | \(0.380829\pi\) | |||||||
\(500\) | −4.50257e11 | −0.322178 | ||||||||
\(501\) | 1.26023e11 | 0.0893677 | ||||||||
\(502\) | 1.73654e12 | 1.22044 | ||||||||
\(503\) | 2.03399e11 | 0.141675 | 0.0708373 | − | 0.997488i | \(-0.477433\pi\) | ||||
0.0708373 | + | 0.997488i | \(0.477433\pi\) | |||||||
\(504\) | −7.54599e11 | −0.520929 | ||||||||
\(505\) | −2.48292e12 | −1.69884 | ||||||||
\(506\) | −6.70792e11 | −0.454894 | ||||||||
\(507\) | −7.80045e11 | −0.524305 | ||||||||
\(508\) | −1.74629e11 | −0.116340 | ||||||||
\(509\) | 5.93699e11 | 0.392045 | 0.196023 | − | 0.980599i | \(-0.437197\pi\) | ||||
0.196023 | + | 0.980599i | \(0.437197\pi\) | |||||||
\(510\) | 6.23139e11 | 0.407868 | ||||||||
\(511\) | −2.25543e12 | −1.46331 | ||||||||
\(512\) | −1.37758e12 | −0.885935 | ||||||||
\(513\) | 7.65381e10 | 0.0487921 | ||||||||
\(514\) | −1.43926e11 | −0.0909508 | ||||||||
\(515\) | 2.67907e12 | 1.67823 | ||||||||
\(516\) | 3.52490e11 | 0.218888 | ||||||||
\(517\) | 4.85442e11 | 0.298834 | ||||||||
\(518\) | 1.53576e12 | 0.937217 | ||||||||
\(519\) | 1.54263e12 | 0.933273 | ||||||||
\(520\) | 6.01743e11 | 0.360908 | ||||||||
\(521\) | −1.74950e12 | −1.04027 | −0.520133 | − | 0.854085i | \(-0.674118\pi\) | ||||
−0.520133 | + | 0.854085i | \(0.674118\pi\) | |||||||
\(522\) | 5.54176e11 | 0.326686 | ||||||||
\(523\) | 3.20555e11 | 0.187346 | 0.0936731 | − | 0.995603i | \(-0.470139\pi\) | ||||
0.0936731 | + | 0.995603i | \(0.470139\pi\) | |||||||
\(524\) | 1.85868e11 | 0.107699 | ||||||||
\(525\) | 2.86708e11 | 0.164711 | ||||||||
\(526\) | 1.91285e12 | 1.08954 | ||||||||
\(527\) | 1.03102e11 | 0.0582262 | ||||||||
\(528\) | −2.23451e11 | −0.125121 | ||||||||
\(529\) | 1.30877e12 | 0.726627 | ||||||||
\(530\) | −2.16126e12 | −1.18978 | ||||||||
\(531\) | −1.33258e11 | −0.0727392 | ||||||||
\(532\) | −2.47148e11 | −0.133769 | ||||||||
\(533\) | −2.25579e11 | −0.121067 | ||||||||
\(534\) | −9.89978e11 | −0.526854 | ||||||||
\(535\) | 2.36072e12 | 1.24581 | ||||||||
\(536\) | −3.45906e12 | −1.81016 | ||||||||
\(537\) | 3.50610e11 | 0.181945 | ||||||||
\(538\) | −1.81595e12 | −0.934512 | ||||||||
\(539\) | 9.07974e11 | 0.463366 | ||||||||
\(540\) | 1.52864e11 | 0.0773628 | ||||||||
\(541\) | 3.50229e11 | 0.175778 | 0.0878889 | − | 0.996130i | \(-0.471988\pi\) | ||||
0.0878889 | + | 0.996130i | \(0.471988\pi\) | |||||||
\(542\) | −5.15421e11 | −0.256546 | ||||||||
\(543\) | −7.74974e10 | −0.0382549 | ||||||||
\(544\) | −1.14570e12 | −0.560885 | ||||||||
\(545\) | −7.00228e11 | −0.339981 | ||||||||
\(546\) | 4.15415e11 | 0.200039 | ||||||||
\(547\) | −2.46037e12 | −1.17505 | −0.587527 | − | 0.809205i | \(-0.699898\pi\) | ||||
−0.587527 | + | 0.809205i | \(0.699898\pi\) | |||||||
\(548\) | 1.07772e10 | 0.00510495 | ||||||||
\(549\) | −1.17665e12 | −0.552804 | ||||||||
\(550\) | 1.47500e11 | 0.0687323 | ||||||||
\(551\) | 6.75815e11 | 0.312353 | ||||||||
\(552\) | 1.79982e12 | 0.825095 | ||||||||
\(553\) | 1.75143e12 | 0.796399 | ||||||||
\(554\) | 7.42051e11 | 0.334688 | ||||||||
\(555\) | −1.15838e12 | −0.518244 | ||||||||
\(556\) | 8.74299e11 | 0.387992 | ||||||||
\(557\) | 1.04356e12 | 0.459376 | 0.229688 | − | 0.973264i | \(-0.426229\pi\) | ||||
0.229688 | + | 0.973264i | \(0.426229\pi\) | |||||||
\(558\) | −4.35886e10 | −0.0190335 | ||||||||
\(559\) | −7.22525e11 | −0.312968 | ||||||||
\(560\) | 1.82316e12 | 0.783390 | ||||||||
\(561\) | −4.78147e11 | −0.203812 | ||||||||
\(562\) | 2.19240e12 | 0.927057 | ||||||||
\(563\) | 3.81849e12 | 1.60179 | 0.800893 | − | 0.598808i | \(-0.204359\pi\) | ||||
0.800893 | + | 0.598808i | \(0.204359\pi\) | |||||||
\(564\) | −3.49816e11 | −0.145574 | ||||||||
\(565\) | −4.99995e12 | −2.06418 | ||||||||
\(566\) | 4.19076e11 | 0.171640 | ||||||||
\(567\) | 3.92930e11 | 0.159658 | ||||||||
\(568\) | 4.57917e11 | 0.184595 | ||||||||
\(569\) | 4.84062e11 | 0.193596 | 0.0967979 | − | 0.995304i | \(-0.469140\pi\) | ||||
0.0967979 | + | 0.995304i | \(0.469140\pi\) | |||||||
\(570\) | −3.21271e11 | −0.127478 | ||||||||
\(571\) | 1.77044e10 | 0.00696978 | 0.00348489 | − | 0.999994i | \(-0.498891\pi\) | ||||
0.00348489 | + | 0.999994i | \(0.498891\pi\) | |||||||
\(572\) | −1.24007e11 | −0.0484357 | ||||||||
\(573\) | −1.42915e12 | −0.553837 | ||||||||
\(574\) | −1.18740e12 | −0.456555 | ||||||||
\(575\) | −6.83840e11 | −0.260885 | ||||||||
\(576\) | 9.22896e11 | 0.349343 | ||||||||
\(577\) | −7.46985e11 | −0.280557 | −0.140278 | − | 0.990112i | \(-0.544800\pi\) | ||||
−0.140278 | + | 0.990112i | \(0.544800\pi\) | |||||||
\(578\) | −7.30007e11 | −0.272052 | ||||||||
\(579\) | 1.06105e12 | 0.392356 | ||||||||
\(580\) | 1.34975e12 | 0.495255 | ||||||||
\(581\) | −2.52078e12 | −0.917789 | ||||||||
\(582\) | −8.27645e11 | −0.299013 | ||||||||
\(583\) | 1.65838e12 | 0.594532 | ||||||||
\(584\) | 3.11333e12 | 1.10756 | ||||||||
\(585\) | −3.13336e11 | −0.110614 | ||||||||
\(586\) | −1.64304e12 | −0.575585 | ||||||||
\(587\) | −4.33948e12 | −1.50857 | −0.754286 | − | 0.656546i | \(-0.772017\pi\) | ||||
−0.754286 | + | 0.656546i | \(0.772017\pi\) | |||||||
\(588\) | −6.54298e11 | −0.225724 | ||||||||
\(589\) | −5.31561e10 | −0.0181984 | ||||||||
\(590\) | 5.59356e11 | 0.190044 | ||||||||
\(591\) | 3.84417e11 | 0.129616 | ||||||||
\(592\) | −1.22020e12 | −0.408305 | ||||||||
\(593\) | 1.90120e12 | 0.631366 | 0.315683 | − | 0.948865i | \(-0.397766\pi\) | ||||
0.315683 | + | 0.948865i | \(0.397766\pi\) | |||||||
\(594\) | 2.02147e11 | 0.0666238 | ||||||||
\(595\) | 3.90125e12 | 1.27608 | ||||||||
\(596\) | 2.63644e11 | 0.0855874 | ||||||||
\(597\) | −1.55603e12 | −0.501341 | ||||||||
\(598\) | −9.90824e11 | −0.316841 | ||||||||
\(599\) | −5.49649e12 | −1.74447 | −0.872237 | − | 0.489083i | \(-0.837332\pi\) | ||||
−0.872237 | + | 0.489083i | \(0.837332\pi\) | |||||||
\(600\) | −3.95763e11 | −0.124668 | ||||||||
\(601\) | 4.77698e12 | 1.49355 | 0.746773 | − | 0.665079i | \(-0.231602\pi\) | ||||
0.746773 | + | 0.665079i | \(0.231602\pi\) | |||||||
\(602\) | −3.80322e12 | −1.18023 | ||||||||
\(603\) | 1.80118e12 | 0.554791 | ||||||||
\(604\) | −1.90909e12 | −0.583661 | ||||||||
\(605\) | 2.92442e12 | 0.887443 | ||||||||
\(606\) | 2.36608e12 | 0.712692 | ||||||||
\(607\) | 8.25000e11 | 0.246663 | 0.123332 | − | 0.992366i | \(-0.460642\pi\) | ||||
0.123332 | + | 0.992366i | \(0.460642\pi\) | |||||||
\(608\) | 5.90685e11 | 0.175303 | ||||||||
\(609\) | 3.46949e12 | 1.02209 | ||||||||
\(610\) | 4.93902e12 | 1.44430 | ||||||||
\(611\) | 7.17045e11 | 0.208142 | ||||||||
\(612\) | 3.44559e11 | 0.0992848 | ||||||||
\(613\) | −1.46985e12 | −0.420438 | −0.210219 | − | 0.977654i | \(-0.567418\pi\) | ||||
−0.210219 | + | 0.977654i | \(0.567418\pi\) | |||||||
\(614\) | −7.90326e11 | −0.224413 | ||||||||
\(615\) | 8.95622e11 | 0.252457 | ||||||||
\(616\) | −2.43045e12 | −0.680101 | ||||||||
\(617\) | 5.17373e12 | 1.43721 | 0.718606 | − | 0.695418i | \(-0.244781\pi\) | ||||
0.718606 | + | 0.695418i | \(0.244781\pi\) | |||||||
\(618\) | −2.55300e12 | −0.704048 | ||||||||
\(619\) | −4.80274e12 | −1.31487 | −0.657433 | − | 0.753513i | \(-0.728358\pi\) | ||||
−0.657433 | + | 0.753513i | \(0.728358\pi\) | |||||||
\(620\) | −1.06164e11 | −0.0288547 | ||||||||
\(621\) | −9.37194e11 | −0.252882 | ||||||||
\(622\) | −1.37670e12 | −0.368794 | ||||||||
\(623\) | −6.19789e12 | −1.64834 | ||||||||
\(624\) | −3.30059e11 | −0.0871487 | ||||||||
\(625\) | −4.42170e12 | −1.15912 | ||||||||
\(626\) | 4.83279e12 | 1.25780 | ||||||||
\(627\) | 2.46518e11 | 0.0637007 | ||||||||
\(628\) | −1.76082e12 | −0.451748 | ||||||||
\(629\) | −2.61103e12 | −0.665096 | ||||||||
\(630\) | −1.64934e12 | −0.417135 | ||||||||
\(631\) | 5.93992e12 | 1.49159 | 0.745794 | − | 0.666177i | \(-0.232071\pi\) | ||||
0.745794 | + | 0.666177i | \(0.232071\pi\) | |||||||
\(632\) | −2.41762e12 | −0.602784 | ||||||||
\(633\) | −1.46831e12 | −0.363498 | ||||||||
\(634\) | 2.73700e12 | 0.672780 | ||||||||
\(635\) | −1.42119e12 | −0.346872 | ||||||||
\(636\) | −1.19505e12 | −0.289620 | ||||||||
\(637\) | 1.34116e12 | 0.322741 | ||||||||
\(638\) | 1.78492e12 | 0.426506 | ||||||||
\(639\) | −2.38444e11 | −0.0565761 | ||||||||
\(640\) | −6.61004e11 | −0.155738 | ||||||||
\(641\) | 6.47738e12 | 1.51544 | 0.757720 | − | 0.652580i | \(-0.226313\pi\) | ||||
0.757720 | + | 0.652580i | \(0.226313\pi\) | |||||||
\(642\) | −2.24963e12 | −0.522641 | ||||||||
\(643\) | −1.74519e12 | −0.402619 | −0.201309 | − | 0.979528i | \(-0.564520\pi\) | ||||
−0.201309 | + | 0.979528i | \(0.564520\pi\) | |||||||
\(644\) | 3.02627e12 | 0.693301 | ||||||||
\(645\) | 2.86867e12 | 0.652621 | ||||||||
\(646\) | −7.24155e11 | −0.163601 | ||||||||
\(647\) | 4.97244e12 | 1.11558 | 0.557790 | − | 0.829982i | \(-0.311650\pi\) | ||||
0.557790 | + | 0.829982i | \(0.311650\pi\) | |||||||
\(648\) | −5.42389e11 | −0.120843 | ||||||||
\(649\) | −4.29205e11 | −0.0949650 | ||||||||
\(650\) | 2.17872e11 | 0.0478731 | ||||||||
\(651\) | −2.72892e11 | −0.0595492 | ||||||||
\(652\) | 1.38139e11 | 0.0299365 | ||||||||
\(653\) | −1.45057e12 | −0.312198 | −0.156099 | − | 0.987741i | \(-0.549892\pi\) | ||||
−0.156099 | + | 0.987741i | \(0.549892\pi\) | |||||||
\(654\) | 6.67276e11 | 0.142628 | ||||||||
\(655\) | 1.51265e12 | 0.321109 | ||||||||
\(656\) | 9.43420e11 | 0.198901 | ||||||||
\(657\) | −1.62115e12 | −0.339453 | ||||||||
\(658\) | 3.77437e12 | 0.784925 | ||||||||
\(659\) | −3.05175e12 | −0.630325 | −0.315162 | − | 0.949038i | \(-0.602059\pi\) | ||||
−0.315162 | + | 0.949038i | \(0.602059\pi\) | |||||||
\(660\) | 4.92351e11 | 0.101001 | ||||||||
\(661\) | −1.88315e12 | −0.383688 | −0.191844 | − | 0.981425i | \(-0.561447\pi\) | ||||
−0.191844 | + | 0.981425i | \(0.561447\pi\) | |||||||
\(662\) | −4.73503e12 | −0.958213 | ||||||||
\(663\) | −7.06270e11 | −0.141958 | ||||||||
\(664\) | 3.47961e12 | 0.694662 | ||||||||
\(665\) | −2.01136e12 | −0.398834 | ||||||||
\(666\) | 1.10387e12 | 0.217412 | ||||||||
\(667\) | −8.27522e12 | −1.61888 | ||||||||
\(668\) | −2.92498e11 | −0.0568367 | ||||||||
\(669\) | 3.16776e11 | 0.0611412 | ||||||||
\(670\) | −7.56051e12 | −1.44949 | ||||||||
\(671\) | −3.78981e12 | −0.721716 | ||||||||
\(672\) | 3.03245e12 | 0.573630 | ||||||||
\(673\) | 7.84359e12 | 1.47383 | 0.736914 | − | 0.675986i | \(-0.236282\pi\) | ||||
0.736914 | + | 0.675986i | \(0.236282\pi\) | |||||||
\(674\) | 5.34929e12 | 0.998451 | ||||||||
\(675\) | 2.06080e11 | 0.0382092 | ||||||||
\(676\) | 1.81047e12 | 0.333451 | ||||||||
\(677\) | 2.32420e12 | 0.425230 | 0.212615 | − | 0.977136i | \(-0.431802\pi\) | ||||
0.212615 | + | 0.977136i | \(0.431802\pi\) | |||||||
\(678\) | 4.76466e12 | 0.865961 | ||||||||
\(679\) | −5.18158e12 | −0.935509 | ||||||||
\(680\) | −5.38516e12 | −0.965846 | ||||||||
\(681\) | −2.90082e12 | −0.516843 | ||||||||
\(682\) | −1.40392e11 | −0.0248493 | ||||||||
\(683\) | −6.89265e12 | −1.21197 | −0.605986 | − | 0.795475i | \(-0.707221\pi\) | ||||
−0.605986 | + | 0.795475i | \(0.707221\pi\) | |||||||
\(684\) | −1.77644e11 | −0.0310312 | ||||||||
\(685\) | 8.77077e10 | 0.0152205 | ||||||||
\(686\) | 4.29354e11 | 0.0740214 | ||||||||
\(687\) | 4.29660e11 | 0.0735902 | ||||||||
\(688\) | 3.02176e12 | 0.514177 | ||||||||
\(689\) | 2.44959e12 | 0.414101 | ||||||||
\(690\) | 3.93390e12 | 0.660697 | ||||||||
\(691\) | 1.11430e13 | 1.85931 | 0.929654 | − | 0.368434i | \(-0.120106\pi\) | ||||
0.929654 | + | 0.368434i | \(0.120106\pi\) | |||||||
\(692\) | −3.58043e12 | −0.593550 | ||||||||
\(693\) | 1.26557e12 | 0.208443 | ||||||||
\(694\) | 2.52393e12 | 0.413010 | ||||||||
\(695\) | 7.11530e12 | 1.15681 | ||||||||
\(696\) | −4.78918e12 | −0.773605 | ||||||||
\(697\) | 2.01876e12 | 0.323994 | ||||||||
\(698\) | −5.66803e12 | −0.903822 | ||||||||
\(699\) | −2.05879e12 | −0.326186 | ||||||||
\(700\) | −6.65447e11 | −0.104754 | ||||||||
\(701\) | −5.78015e12 | −0.904082 | −0.452041 | − | 0.891997i | \(-0.649304\pi\) | ||||
−0.452041 | + | 0.891997i | \(0.649304\pi\) | |||||||
\(702\) | 2.98591e11 | 0.0464045 | ||||||||
\(703\) | 1.34617e12 | 0.207874 | ||||||||
\(704\) | 2.97251e12 | 0.456085 | ||||||||
\(705\) | −2.84691e12 | −0.434032 | ||||||||
\(706\) | −9.56151e12 | −1.44846 | ||||||||
\(707\) | 1.48131e13 | 2.22977 | ||||||||
\(708\) | 3.09291e11 | 0.0462612 | ||||||||
\(709\) | −3.39902e12 | −0.505180 | −0.252590 | − | 0.967573i | \(-0.581282\pi\) | ||||
−0.252590 | + | 0.967573i | \(0.581282\pi\) | |||||||
\(710\) | 1.00088e12 | 0.147815 | ||||||||
\(711\) | 1.25889e12 | 0.184746 | ||||||||
\(712\) | 8.55537e12 | 1.24761 | ||||||||
\(713\) | 6.50885e11 | 0.0943195 | ||||||||
\(714\) | −3.71766e12 | −0.535337 | ||||||||
\(715\) | −1.00921e12 | −0.144412 | ||||||||
\(716\) | −8.13761e11 | −0.115715 | ||||||||
\(717\) | −5.13130e12 | −0.725089 | ||||||||
\(718\) | −8.95831e12 | −1.25796 | ||||||||
\(719\) | 2.71272e11 | 0.0378551 | 0.0189276 | − | 0.999821i | \(-0.493975\pi\) | ||||
0.0189276 | + | 0.999821i | \(0.493975\pi\) | |||||||
\(720\) | 1.31044e12 | 0.181728 | ||||||||
\(721\) | −1.59834e13 | −2.20272 | ||||||||
\(722\) | −5.43503e12 | −0.744362 | ||||||||
\(723\) | 8.25623e12 | 1.12372 | ||||||||
\(724\) | 1.79870e11 | 0.0243297 | ||||||||
\(725\) | 1.81964e12 | 0.244604 | ||||||||
\(726\) | −2.78680e12 | −0.372298 | ||||||||
\(727\) | −2.13863e12 | −0.283943 | −0.141972 | − | 0.989871i | \(-0.545344\pi\) | ||||
−0.141972 | + | 0.989871i | \(0.545344\pi\) | |||||||
\(728\) | −3.59001e12 | −0.473701 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 6.80485e12 | 0.886881 | ||||||||
\(731\) | 6.46606e12 | 0.837552 | ||||||||
\(732\) | 2.73099e12 | 0.351577 | ||||||||
\(733\) | 4.60033e12 | 0.588601 | 0.294301 | − | 0.955713i | \(-0.404913\pi\) | ||||
0.294301 | + | 0.955713i | \(0.404913\pi\) | |||||||
\(734\) | 4.99938e12 | 0.635746 | ||||||||
\(735\) | −5.32487e12 | −0.673002 | ||||||||
\(736\) | −7.23282e12 | −0.908568 | ||||||||
\(737\) | 5.80133e12 | 0.724309 | ||||||||
\(738\) | −8.53475e11 | −0.105910 | ||||||||
\(739\) | 8.60245e12 | 1.06102 | 0.530508 | − | 0.847680i | \(-0.322001\pi\) | ||||
0.530508 | + | 0.847680i | \(0.322001\pi\) | |||||||
\(740\) | 2.68859e12 | 0.329596 | ||||||||
\(741\) | 3.64131e11 | 0.0443686 | ||||||||
\(742\) | 1.28941e13 | 1.56161 | ||||||||
\(743\) | 1.31407e12 | 0.158187 | 0.0790934 | − | 0.996867i | \(-0.474797\pi\) | ||||
0.0790934 | + | 0.996867i | \(0.474797\pi\) | |||||||
\(744\) | 3.76691e11 | 0.0450720 | ||||||||
\(745\) | 2.14561e12 | 0.255181 | ||||||||
\(746\) | 4.59574e12 | 0.543289 | ||||||||
\(747\) | −1.81188e12 | −0.212906 | ||||||||
\(748\) | 1.10977e12 | 0.129622 | ||||||||
\(749\) | −1.40841e13 | −1.63516 | ||||||||
\(750\) | 3.49189e12 | 0.402981 | ||||||||
\(751\) | −7.95810e12 | −0.912913 | −0.456457 | − | 0.889746i | \(-0.650882\pi\) | ||||
−0.456457 | + | 0.889746i | \(0.650882\pi\) | |||||||
\(752\) | −2.99884e12 | −0.341958 | ||||||||
\(753\) | 7.81443e12 | 0.885768 | ||||||||
\(754\) | 2.63650e12 | 0.297068 | ||||||||
\(755\) | −1.55368e13 | −1.74020 | ||||||||
\(756\) | −9.11987e11 | −0.101541 | ||||||||
\(757\) | −6.95936e12 | −0.770261 | −0.385131 | − | 0.922862i | \(-0.625844\pi\) | ||||
−0.385131 | + | 0.922862i | \(0.625844\pi\) | |||||||
\(758\) | 1.46179e12 | 0.160832 | ||||||||
\(759\) | −3.01856e12 | −0.330151 | ||||||||
\(760\) | 2.77642e12 | 0.301873 | ||||||||
\(761\) | −1.38632e13 | −1.49841 | −0.749207 | − | 0.662336i | \(-0.769565\pi\) | ||||
−0.749207 | + | 0.662336i | \(0.769565\pi\) | |||||||
\(762\) | 1.35431e12 | 0.145519 | ||||||||
\(763\) | 4.17757e12 | 0.446234 | ||||||||
\(764\) | 3.31704e12 | 0.352233 | ||||||||
\(765\) | 2.80413e12 | 0.296020 | ||||||||
\(766\) | −7.43621e12 | −0.780409 | ||||||||
\(767\) | −6.33977e11 | −0.0661446 | ||||||||
\(768\) | −5.20371e12 | −0.539744 | ||||||||
\(769\) | 1.35604e13 | 1.39832 | 0.699158 | − | 0.714967i | \(-0.253558\pi\) | ||||
0.699158 | + | 0.714967i | \(0.253558\pi\) | |||||||
\(770\) | −5.31227e12 | −0.544593 | ||||||||
\(771\) | −6.47669e11 | −0.0660098 | ||||||||
\(772\) | −2.46267e12 | −0.249534 | ||||||||
\(773\) | 4.96740e12 | 0.500405 | 0.250203 | − | 0.968194i | \(-0.419503\pi\) | ||||
0.250203 | + | 0.968194i | \(0.419503\pi\) | |||||||
\(774\) | −2.73367e12 | −0.273786 | ||||||||
\(775\) | −1.43123e11 | −0.0142512 | ||||||||
\(776\) | 7.15248e12 | 0.708075 | ||||||||
\(777\) | 6.91093e12 | 0.680208 | ||||||||
\(778\) | 4.55494e12 | 0.445732 | ||||||||
\(779\) | −1.04081e12 | −0.101263 | ||||||||
\(780\) | 7.27250e11 | 0.0703490 | ||||||||
\(781\) | −7.67993e11 | −0.0738631 | ||||||||
\(782\) | 8.86713e12 | 0.847916 | ||||||||
\(783\) | 2.49379e12 | 0.237100 | ||||||||
\(784\) | −5.60905e12 | −0.530234 | ||||||||
\(785\) | −1.43301e13 | −1.34690 | ||||||||
\(786\) | −1.44146e12 | −0.134711 | ||||||||
\(787\) | −5.25809e12 | −0.488587 | −0.244293 | − | 0.969701i | \(-0.578556\pi\) | ||||
−0.244293 | + | 0.969701i | \(0.578556\pi\) | |||||||
\(788\) | −8.92227e11 | −0.0824342 | ||||||||
\(789\) | 8.60781e12 | 0.790763 | ||||||||
\(790\) | −5.28423e12 | −0.482681 | ||||||||
\(791\) | 2.98298e13 | 2.70929 | ||||||||
\(792\) | −1.74695e12 | −0.157768 | ||||||||
\(793\) | −5.59792e12 | −0.502686 | ||||||||
\(794\) | −1.17641e12 | −0.105043 | ||||||||
\(795\) | −9.72568e12 | −0.863511 | ||||||||
\(796\) | 3.61152e12 | 0.318846 | ||||||||
\(797\) | 1.61816e13 | 1.42056 | 0.710281 | − | 0.703918i | \(-0.248568\pi\) | ||||
0.710281 | + | 0.703918i | \(0.248568\pi\) | |||||||
\(798\) | 1.91671e12 | 0.167318 | ||||||||
\(799\) | −6.41701e12 | −0.557022 | ||||||||
\(800\) | 1.59042e12 | 0.137280 | ||||||||
\(801\) | −4.45490e12 | −0.382377 | ||||||||
\(802\) | −4.33596e12 | −0.370084 | ||||||||
\(803\) | −5.22150e12 | −0.443175 | ||||||||
\(804\) | −4.18052e12 | −0.352840 | ||||||||
\(805\) | 2.46287e13 | 2.06709 | ||||||||
\(806\) | −2.07373e11 | −0.0173079 | ||||||||
\(807\) | −8.17180e12 | −0.678245 | ||||||||
\(808\) | −2.04476e13 | −1.68768 | ||||||||
\(809\) | −1.39276e13 | −1.14317 | −0.571583 | − | 0.820544i | \(-0.693671\pi\) | ||||
−0.571583 | + | 0.820544i | \(0.693671\pi\) | |||||||
\(810\) | −1.18551e12 | −0.0967657 | ||||||||
\(811\) | 1.38190e13 | 1.12171 | 0.560857 | − | 0.827913i | \(-0.310472\pi\) | ||||
0.560857 | + | 0.827913i | \(0.310472\pi\) | |||||||
\(812\) | −8.05265e12 | −0.650035 | ||||||||
\(813\) | −2.31939e12 | −0.186194 | ||||||||
\(814\) | 3.55540e12 | 0.283844 | ||||||||
\(815\) | 1.12421e12 | 0.0892564 | ||||||||
\(816\) | 2.95378e12 | 0.233224 | ||||||||
\(817\) | −3.33370e12 | −0.261774 | ||||||||
\(818\) | −6.81012e12 | −0.531820 | ||||||||
\(819\) | 1.86937e12 | 0.145184 | ||||||||
\(820\) | −2.07873e12 | −0.160559 | ||||||||
\(821\) | 3.48578e12 | 0.267766 | 0.133883 | − | 0.990997i | \(-0.457255\pi\) | ||||
0.133883 | + | 0.990997i | \(0.457255\pi\) | |||||||
\(822\) | −8.35803e10 | −0.00638529 | ||||||||
\(823\) | −1.21472e13 | −0.922948 | −0.461474 | − | 0.887154i | \(-0.652679\pi\) | ||||
−0.461474 | + | 0.887154i | \(0.652679\pi\) | |||||||
\(824\) | 2.20629e13 | 1.66721 | ||||||||
\(825\) | 6.63751e11 | 0.0498842 | ||||||||
\(826\) | −3.33712e12 | −0.249438 | ||||||||
\(827\) | −1.70702e13 | −1.26901 | −0.634504 | − | 0.772919i | \(-0.718796\pi\) | ||||
−0.634504 | + | 0.772919i | \(0.718796\pi\) | |||||||
\(828\) | 2.17522e12 | 0.160830 | ||||||||
\(829\) | 5.58071e12 | 0.410387 | 0.205194 | − | 0.978721i | \(-0.434218\pi\) | ||||
0.205194 | + | 0.978721i | \(0.434218\pi\) | |||||||
\(830\) | 7.60543e12 | 0.556253 | ||||||||
\(831\) | 3.33923e12 | 0.242908 | ||||||||
\(832\) | 4.39068e12 | 0.317671 | ||||||||
\(833\) | −1.20024e13 | −0.863707 | ||||||||
\(834\) | −6.78047e12 | −0.485302 | ||||||||
\(835\) | −2.38044e12 | −0.169460 | ||||||||
\(836\) | −5.72165e11 | −0.0405129 | ||||||||
\(837\) | −1.96148e11 | −0.0138140 | ||||||||
\(838\) | 1.74378e13 | 1.22150 | ||||||||
\(839\) | 1.28642e13 | 0.896304 | 0.448152 | − | 0.893957i | \(-0.352082\pi\) | ||||
0.448152 | + | 0.893957i | \(0.352082\pi\) | |||||||
\(840\) | 1.42535e13 | 0.987793 | ||||||||
\(841\) | 7.51250e12 | 0.517849 | ||||||||
\(842\) | −2.58819e12 | −0.177457 | ||||||||
\(843\) | 9.86580e12 | 0.672835 | ||||||||
\(844\) | 3.40793e12 | 0.231180 | ||||||||
\(845\) | 1.47342e13 | 0.994193 | ||||||||
\(846\) | 2.71293e12 | 0.182084 | ||||||||
\(847\) | −1.74471e13 | −1.16479 | ||||||||
\(848\) | −1.02447e13 | −0.680329 | ||||||||
\(849\) | 1.88584e12 | 0.124572 | ||||||||
\(850\) | −1.94979e12 | −0.128116 | ||||||||
\(851\) | −1.64835e13 | −1.07738 | ||||||||
\(852\) | 5.53426e11 | 0.0359817 | ||||||||
\(853\) | 1.03465e13 | 0.669147 | 0.334574 | − | 0.942370i | \(-0.391408\pi\) | ||||
0.334574 | + | 0.942370i | \(0.391408\pi\) | |||||||
\(854\) | −2.94663e13 | −1.89568 | ||||||||
\(855\) | −1.44572e12 | −0.0925202 | ||||||||
\(856\) | 1.94413e13 | 1.23763 | ||||||||
\(857\) | 5.63216e12 | 0.356666 | 0.178333 | − | 0.983970i | \(-0.442930\pi\) | ||||
0.178333 | + | 0.983970i | \(0.442930\pi\) | |||||||
\(858\) | 9.61718e11 | 0.0605836 | ||||||||
\(859\) | −2.28289e13 | −1.43059 | −0.715295 | − | 0.698822i | \(-0.753708\pi\) | ||||
−0.715295 | + | 0.698822i | \(0.753708\pi\) | |||||||
\(860\) | −6.65814e12 | −0.415059 | ||||||||
\(861\) | −5.34329e12 | −0.331356 | ||||||||
\(862\) | 3.72401e12 | 0.229736 | ||||||||
\(863\) | 4.62918e12 | 0.284090 | 0.142045 | − | 0.989860i | \(-0.454632\pi\) | ||||
0.142045 | + | 0.989860i | \(0.454632\pi\) | |||||||
\(864\) | 2.17966e12 | 0.133069 | ||||||||
\(865\) | −2.91386e13 | −1.76968 | ||||||||
\(866\) | −8.67389e11 | −0.0524063 | ||||||||
\(867\) | −3.28503e12 | −0.197448 | ||||||||
\(868\) | 6.33379e11 | 0.0378726 | ||||||||
\(869\) | 4.05470e12 | 0.241196 | ||||||||
\(870\) | −1.04678e13 | −0.619466 | ||||||||
\(871\) | 8.56913e12 | 0.504493 | ||||||||
\(872\) | −5.76658e12 | −0.337749 | ||||||||
\(873\) | −3.72440e12 | −0.217016 | ||||||||
\(874\) | −4.57162e12 | −0.265014 | ||||||||
\(875\) | 2.18614e13 | 1.26079 | ||||||||
\(876\) | 3.76268e12 | 0.215888 | ||||||||
\(877\) | 5.33611e12 | 0.304598 | 0.152299 | − | 0.988334i | \(-0.451332\pi\) | ||||
0.152299 | + | 0.988334i | \(0.451332\pi\) | |||||||
\(878\) | 7.88294e12 | 0.447675 | ||||||||
\(879\) | −7.39369e12 | −0.417745 | ||||||||
\(880\) | 4.22074e12 | 0.237256 | ||||||||
\(881\) | 7.87890e12 | 0.440630 | 0.220315 | − | 0.975429i | \(-0.429291\pi\) | ||||
0.220315 | + | 0.975429i | \(0.429291\pi\) | |||||||
\(882\) | 5.07429e12 | 0.282336 | ||||||||
\(883\) | 1.38973e13 | 0.769320 | 0.384660 | − | 0.923058i | \(-0.374319\pi\) | ||||
0.384660 | + | 0.923058i | \(0.374319\pi\) | |||||||
\(884\) | 1.63924e12 | 0.0902835 | ||||||||
\(885\) | 2.51710e12 | 0.137929 | ||||||||
\(886\) | 1.36560e13 | 0.744510 | ||||||||
\(887\) | −5.86607e12 | −0.318193 | −0.159097 | − | 0.987263i | \(-0.550858\pi\) | ||||
−0.159097 | + | 0.987263i | \(0.550858\pi\) | |||||||
\(888\) | −9.53963e12 | −0.514841 | ||||||||
\(889\) | 8.47881e12 | 0.455278 | ||||||||
\(890\) | 1.86996e13 | 0.999026 | ||||||||
\(891\) | 9.09663e11 | 0.0483538 | ||||||||
\(892\) | −7.35232e11 | −0.0388851 | ||||||||
\(893\) | 3.30841e12 | 0.174096 | ||||||||
\(894\) | −2.04464e12 | −0.107053 | ||||||||
\(895\) | −6.62263e12 | −0.345006 | ||||||||
\(896\) | 3.94356e12 | 0.204410 | ||||||||
\(897\) | −4.45871e12 | −0.229955 | ||||||||
\(898\) | −2.47103e12 | −0.126805 | ||||||||
\(899\) | −1.73195e12 | −0.0884334 | ||||||||
\(900\) | −4.78308e11 | −0.0243006 | ||||||||
\(901\) | −2.19220e13 | −1.10820 | ||||||||
\(902\) | −2.74892e12 | −0.138271 | ||||||||
\(903\) | −1.71145e13 | −0.856583 | ||||||||
\(904\) | −4.11761e13 | −2.05063 | ||||||||
\(905\) | 1.46384e12 | 0.0725395 | ||||||||
\(906\) | 1.48056e13 | 0.730045 | ||||||||
\(907\) | 8.52250e12 | 0.418152 | 0.209076 | − | 0.977899i | \(-0.432954\pi\) | ||||
0.209076 | + | 0.977899i | \(0.432954\pi\) | |||||||
\(908\) | 6.73277e12 | 0.328706 | ||||||||
\(909\) | 1.06473e13 | 0.517254 | ||||||||
\(910\) | −7.84674e12 | −0.379317 | ||||||||
\(911\) | 1.63369e13 | 0.785843 | 0.392921 | − | 0.919572i | \(-0.371464\pi\) | ||||
0.392921 | + | 0.919572i | \(0.371464\pi\) | |||||||
\(912\) | −1.52288e12 | −0.0728934 | ||||||||
\(913\) | −5.83580e12 | −0.277960 | ||||||||
\(914\) | 2.35964e12 | 0.111838 | ||||||||
\(915\) | 2.22256e13 | 1.04823 | ||||||||
\(916\) | −9.97236e11 | −0.0468024 | ||||||||
\(917\) | −9.02448e12 | −0.421464 | ||||||||
\(918\) | −2.67217e12 | −0.124186 | ||||||||
\(919\) | 3.24712e13 | 1.50169 | 0.750843 | − | 0.660481i | \(-0.229648\pi\) | ||||
0.750843 | + | 0.660481i | \(0.229648\pi\) | |||||||
\(920\) | −3.39967e13 | −1.56456 | ||||||||
\(921\) | −3.55647e12 | −0.162873 | ||||||||
\(922\) | −1.44631e13 | −0.659134 | ||||||||
\(923\) | −1.13440e12 | −0.0514468 | ||||||||
\(924\) | −2.93737e12 | −0.132567 | ||||||||
\(925\) | 3.62456e12 | 0.162786 | ||||||||
\(926\) | −3.21447e13 | −1.43668 | ||||||||
\(927\) | −1.14885e13 | −0.510980 | ||||||||
\(928\) | 1.92459e13 | 0.851868 | ||||||||
\(929\) | −1.24571e13 | −0.548716 | −0.274358 | − | 0.961628i | \(-0.588465\pi\) | ||||
−0.274358 | + | 0.961628i | \(0.588465\pi\) | |||||||
\(930\) | 8.23339e11 | 0.0360916 | ||||||||
\(931\) | 6.18808e12 | 0.269949 | ||||||||
\(932\) | 4.77843e12 | 0.207450 | ||||||||
\(933\) | −6.19516e12 | −0.267661 | ||||||||
\(934\) | 1.15986e13 | 0.498706 | ||||||||
\(935\) | 9.03167e12 | 0.386470 | ||||||||
\(936\) | −2.58042e12 | −0.109888 | ||||||||
\(937\) | 9.29012e12 | 0.393725 | 0.196863 | − | 0.980431i | \(-0.436925\pi\) | ||||
0.196863 | + | 0.980431i | \(0.436925\pi\) | |||||||
\(938\) | 4.51061e13 | 1.90249 | ||||||||
\(939\) | 2.17475e13 | 0.912883 | ||||||||
\(940\) | 6.60763e12 | 0.276039 | ||||||||
\(941\) | −3.24831e13 | −1.35053 | −0.675265 | − | 0.737575i | \(-0.735971\pi\) | ||||
−0.675265 | + | 0.737575i | \(0.735971\pi\) | |||||||
\(942\) | 1.36557e13 | 0.565048 | ||||||||
\(943\) | 1.27445e13 | 0.524832 | ||||||||
\(944\) | 2.65143e12 | 0.108669 | ||||||||
\(945\) | −7.42202e12 | −0.302746 | ||||||||
\(946\) | −8.80474e12 | −0.357443 | ||||||||
\(947\) | −4.16258e13 | −1.68185 | −0.840926 | − | 0.541151i | \(-0.817989\pi\) | ||||
−0.840926 | + | 0.541151i | \(0.817989\pi\) | |||||||
\(948\) | −2.92187e12 | −0.117496 | ||||||||
\(949\) | −7.71265e12 | −0.308678 | ||||||||
\(950\) | 1.00525e12 | 0.0400423 | ||||||||
\(951\) | 1.23165e13 | 0.488287 | ||||||||
\(952\) | 3.21279e13 | 1.26770 | ||||||||
\(953\) | 1.86479e13 | 0.732339 | 0.366169 | − | 0.930548i | \(-0.380669\pi\) | ||||
0.366169 | + | 0.930548i | \(0.380669\pi\) | |||||||
\(954\) | 9.26800e12 | 0.362258 | ||||||||
\(955\) | 2.69950e13 | 1.05019 | ||||||||
\(956\) | 1.19097e13 | 0.461148 | ||||||||
\(957\) | 8.03213e12 | 0.309547 | ||||||||
\(958\) | −3.37861e13 | −1.29596 | ||||||||
\(959\) | −5.23265e11 | −0.0199774 | ||||||||
\(960\) | −1.74325e13 | −0.662428 | ||||||||
\(961\) | −2.63034e13 | −0.994848 | ||||||||
\(962\) | 5.25167e12 | 0.197702 | ||||||||
\(963\) | −1.01233e13 | −0.379320 | ||||||||
\(964\) | −1.91626e13 | −0.714674 | ||||||||
\(965\) | −2.00420e13 | −0.743991 | ||||||||
\(966\) | −2.34697e13 | −0.867183 | ||||||||
\(967\) | −2.32990e13 | −0.856875 | −0.428437 | − | 0.903572i | \(-0.640936\pi\) | ||||
−0.428437 | + | 0.903572i | \(0.640936\pi\) | |||||||
\(968\) | 2.40835e13 | 0.881617 | ||||||||
\(969\) | −3.25870e12 | −0.118737 | ||||||||
\(970\) | 1.56333e13 | 0.566993 | ||||||||
\(971\) | −3.63628e13 | −1.31272 | −0.656358 | − | 0.754450i | \(-0.727904\pi\) | ||||
−0.656358 | + | 0.754450i | \(0.727904\pi\) | |||||||
\(972\) | −6.55515e11 | −0.0235551 | ||||||||
\(973\) | −4.24500e13 | −1.51834 | ||||||||
\(974\) | 2.68839e13 | 0.957145 | ||||||||
\(975\) | 9.80425e11 | 0.0347451 | ||||||||
\(976\) | 2.34118e13 | 0.825866 | ||||||||
\(977\) | 5.18141e13 | 1.81938 | 0.909688 | − | 0.415291i | \(-0.136320\pi\) | ||||
0.909688 | + | 0.415291i | \(0.136320\pi\) | |||||||
\(978\) | −1.07131e12 | −0.0374447 | ||||||||
\(979\) | −1.43486e13 | −0.499214 | ||||||||
\(980\) | 1.23590e13 | 0.428021 | ||||||||
\(981\) | 3.00274e12 | 0.103516 | ||||||||
\(982\) | −1.34516e13 | −0.461608 | ||||||||
\(983\) | −2.54862e13 | −0.870592 | −0.435296 | − | 0.900287i | \(-0.643356\pi\) | ||||
−0.435296 | + | 0.900287i | \(0.643356\pi\) | |||||||
\(984\) | 7.37571e12 | 0.250799 | ||||||||
\(985\) | −7.26121e12 | −0.245780 | ||||||||
\(986\) | −2.35947e13 | −0.795001 | ||||||||
\(987\) | 1.69847e13 | 0.569679 | ||||||||
\(988\) | −8.45143e11 | −0.0282178 | ||||||||
\(989\) | 4.08205e13 | 1.35673 | ||||||||
\(990\) | −3.81834e12 | −0.126333 | ||||||||
\(991\) | 3.92830e13 | 1.29382 | 0.646910 | − | 0.762567i | \(-0.276061\pi\) | ||||
0.646910 | + | 0.762567i | \(0.276061\pi\) | |||||||
\(992\) | −1.51378e12 | −0.0496318 | ||||||||
\(993\) | −2.13076e13 | −0.695447 | ||||||||
\(994\) | −5.97124e12 | −0.194011 | ||||||||
\(995\) | 2.93917e13 | 0.950649 | ||||||||
\(996\) | 4.20535e12 | 0.135405 | ||||||||
\(997\) | 4.98389e13 | 1.59750 | 0.798748 | − | 0.601665i | \(-0.205496\pi\) | ||||
0.798748 | + | 0.601665i | \(0.205496\pi\) | |||||||
\(998\) | 1.82340e13 | 0.581827 | ||||||||
\(999\) | 4.96742e12 | 0.157792 |
(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 | 3.10.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 9.10.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 48.10.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 75.10.b.c.49.2 | 2 | |||
5.3 | odd | 4 | 75.10.b.c.49.1 | 2 | |||
5.4 | even | 2 | 75.10.a.b.1.1 | 1 | |||
7.6 | odd | 2 | 147.10.a.c.1.1 | 1 | |||
8.3 | odd | 2 | 192.10.a.n.1.1 | 1 | |||
8.5 | even | 2 | 192.10.a.g.1.1 | 1 | |||
9.2 | odd | 6 | 81.10.c.d.28.1 | 2 | |||
9.4 | even | 3 | 81.10.c.b.55.1 | 2 | |||
9.5 | odd | 6 | 81.10.c.d.55.1 | 2 | |||
9.7 | even | 3 | 81.10.c.b.28.1 | 2 | |||
11.10 | odd | 2 | 363.10.a.a.1.1 | 1 | |||
12.11 | even | 2 | 144.10.a.m.1.1 | 1 | |||
15.2 | even | 4 | 225.10.b.c.199.1 | 2 | |||
15.8 | even | 4 | 225.10.b.c.199.2 | 2 | |||
15.14 | odd | 2 | 225.10.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.10.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
9.10.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
48.10.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
75.10.a.b.1.1 | 1 | 5.4 | even | 2 | |||
75.10.b.c.49.1 | 2 | 5.3 | odd | 4 | |||
75.10.b.c.49.2 | 2 | 5.2 | odd | 4 | |||
81.10.c.b.28.1 | 2 | 9.7 | even | 3 | |||
81.10.c.b.55.1 | 2 | 9.4 | even | 3 | |||
81.10.c.d.28.1 | 2 | 9.2 | odd | 6 | |||
81.10.c.d.55.1 | 2 | 9.5 | odd | 6 | |||
144.10.a.m.1.1 | 1 | 12.11 | even | 2 | |||
147.10.a.c.1.1 | 1 | 7.6 | odd | 2 | |||
192.10.a.g.1.1 | 1 | 8.5 | even | 2 | |||
192.10.a.n.1.1 | 1 | 8.3 | odd | 2 | |||
225.10.a.e.1.1 | 1 | 15.14 | odd | 2 | |||
225.10.b.c.199.1 | 2 | 15.2 | even | 4 | |||
225.10.b.c.199.2 | 2 | 15.8 | even | 4 | |||
363.10.a.a.1.1 | 1 | 11.10 | odd | 2 |