Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.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: | \(64.0959177025\) |
Analytic rank: | \(1\) |
Dimension: | \(149\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.37150 | −1.67690 | −0.838452 | − | 0.544975i | \(-0.816539\pi\) | ||||
−0.838452 | + | 0.544975i | \(0.816539\pi\) | |||||||
\(3\) | 0.0708005 | 0.0408767 | 0.0204383 | − | 0.999791i | \(-0.493494\pi\) | ||||
0.0204383 | + | 0.999791i | \(0.493494\pi\) | |||||||
\(4\) | 3.62401 | 1.81201 | ||||||||
\(5\) | 3.28290 | 1.46816 | 0.734078 | − | 0.679065i | \(-0.237615\pi\) | ||||
0.734078 | + | 0.679065i | \(0.237615\pi\) | |||||||
\(6\) | −0.167903 | −0.0685463 | ||||||||
\(7\) | −0.427363 | −0.161528 | −0.0807640 | − | 0.996733i | \(-0.525736\pi\) | ||||
−0.0807640 | + | 0.996733i | \(0.525736\pi\) | |||||||
\(8\) | −3.85135 | −1.36166 | ||||||||
\(9\) | −2.99499 | −0.998329 | ||||||||
\(10\) | −7.78539 | −2.46196 | ||||||||
\(11\) | −1.35871 | −0.409666 | −0.204833 | − | 0.978797i | \(-0.565665\pi\) | ||||
−0.204833 | + | 0.978797i | \(0.565665\pi\) | |||||||
\(12\) | 0.256582 | 0.0740688 | ||||||||
\(13\) | 0.448163 | 0.124298 | 0.0621490 | − | 0.998067i | \(-0.480205\pi\) | ||||
0.0621490 | + | 0.998067i | \(0.480205\pi\) | |||||||
\(14\) | 1.01349 | 0.270867 | ||||||||
\(15\) | 0.232431 | 0.0600133 | ||||||||
\(16\) | 1.88545 | 0.471363 | ||||||||
\(17\) | 2.46900 | 0.598820 | 0.299410 | − | 0.954125i | \(-0.403210\pi\) | ||||
0.299410 | + | 0.954125i | \(0.403210\pi\) | |||||||
\(18\) | 7.10261 | 1.67410 | ||||||||
\(19\) | −2.99998 | −0.688242 | −0.344121 | − | 0.938925i | \(-0.611823\pi\) | ||||
−0.344121 | + | 0.938925i | \(0.611823\pi\) | |||||||
\(20\) | 11.8973 | 2.66031 | ||||||||
\(21\) | −0.0302575 | −0.00660273 | ||||||||
\(22\) | 3.22218 | 0.686971 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −0.272678 | −0.0556601 | ||||||||
\(25\) | 5.77741 | 1.15548 | ||||||||
\(26\) | −1.06282 | −0.208436 | ||||||||
\(27\) | −0.424448 | −0.0816850 | ||||||||
\(28\) | −1.54877 | −0.292690 | ||||||||
\(29\) | −4.84023 | −0.898808 | −0.449404 | − | 0.893329i | \(-0.648364\pi\) | ||||
−0.449404 | + | 0.893329i | \(0.648364\pi\) | |||||||
\(30\) | −0.551209 | −0.100637 | ||||||||
\(31\) | 3.26639 | 0.586661 | 0.293330 | − | 0.956011i | \(-0.405236\pi\) | ||||
0.293330 | + | 0.956011i | \(0.405236\pi\) | |||||||
\(32\) | 3.23135 | 0.571227 | ||||||||
\(33\) | −0.0961972 | −0.0167458 | ||||||||
\(34\) | −5.85523 | −1.00416 | ||||||||
\(35\) | −1.40299 | −0.237148 | ||||||||
\(36\) | −10.8539 | −1.80898 | ||||||||
\(37\) | −3.58915 | −0.590052 | −0.295026 | − | 0.955489i | \(-0.595328\pi\) | ||||
−0.295026 | + | 0.955489i | \(0.595328\pi\) | |||||||
\(38\) | 7.11445 | 1.15412 | ||||||||
\(39\) | 0.0317301 | 0.00508089 | ||||||||
\(40\) | −12.6436 | −1.99913 | ||||||||
\(41\) | −0.627600 | −0.0980147 | −0.0490073 | − | 0.998798i | \(-0.515606\pi\) | ||||
−0.0490073 | + | 0.998798i | \(0.515606\pi\) | |||||||
\(42\) | 0.0717557 | 0.0110721 | ||||||||
\(43\) | 4.02417 | 0.613681 | 0.306840 | − | 0.951761i | \(-0.400728\pi\) | ||||
0.306840 | + | 0.951761i | \(0.400728\pi\) | |||||||
\(44\) | −4.92398 | −0.742318 | ||||||||
\(45\) | −9.83223 | −1.46570 | ||||||||
\(46\) | 2.37150 | 0.349659 | ||||||||
\(47\) | 1.73579 | 0.253191 | 0.126595 | − | 0.991954i | \(-0.459595\pi\) | ||||
0.126595 | + | 0.991954i | \(0.459595\pi\) | |||||||
\(48\) | 0.133491 | 0.0192678 | ||||||||
\(49\) | −6.81736 | −0.973909 | ||||||||
\(50\) | −13.7011 | −1.93763 | ||||||||
\(51\) | 0.174806 | 0.0244778 | ||||||||
\(52\) | 1.62415 | 0.225229 | ||||||||
\(53\) | −0.795557 | −0.109278 | −0.0546390 | − | 0.998506i | \(-0.517401\pi\) | ||||
−0.0546390 | + | 0.998506i | \(0.517401\pi\) | |||||||
\(54\) | 1.00658 | 0.136978 | ||||||||
\(55\) | −4.46050 | −0.601454 | ||||||||
\(56\) | 1.64593 | 0.219946 | ||||||||
\(57\) | −0.212400 | −0.0281331 | ||||||||
\(58\) | 11.4786 | 1.50722 | ||||||||
\(59\) | −8.98326 | −1.16952 | −0.584761 | − | 0.811206i | \(-0.698812\pi\) | ||||
−0.584761 | + | 0.811206i | \(0.698812\pi\) | |||||||
\(60\) | 0.842332 | 0.108745 | ||||||||
\(61\) | 1.00698 | 0.128931 | 0.0644656 | − | 0.997920i | \(-0.479466\pi\) | ||||
0.0644656 | + | 0.997920i | \(0.479466\pi\) | |||||||
\(62\) | −7.74624 | −0.983774 | ||||||||
\(63\) | 1.27995 | 0.161258 | ||||||||
\(64\) | −11.4341 | −1.42926 | ||||||||
\(65\) | 1.47127 | 0.182489 | ||||||||
\(66\) | 0.228132 | 0.0280811 | ||||||||
\(67\) | 11.1909 | 1.36719 | 0.683594 | − | 0.729862i | \(-0.260416\pi\) | ||||
0.683594 | + | 0.729862i | \(0.260416\pi\) | |||||||
\(68\) | 8.94768 | 1.08507 | ||||||||
\(69\) | −0.0708005 | −0.00852338 | ||||||||
\(70\) | 3.32719 | 0.397675 | ||||||||
\(71\) | 15.5165 | 1.84147 | 0.920736 | − | 0.390186i | \(-0.127589\pi\) | ||||
0.920736 | + | 0.390186i | \(0.127589\pi\) | |||||||
\(72\) | 11.5347 | 1.35938 | ||||||||
\(73\) | 6.40922 | 0.750142 | 0.375071 | − | 0.926996i | \(-0.377618\pi\) | ||||
0.375071 | + | 0.926996i | \(0.377618\pi\) | |||||||
\(74\) | 8.51166 | 0.989461 | ||||||||
\(75\) | 0.409043 | 0.0472322 | ||||||||
\(76\) | −10.8720 | −1.24710 | ||||||||
\(77\) | 0.580662 | 0.0661726 | ||||||||
\(78\) | −0.0752480 | −0.00852016 | ||||||||
\(79\) | 10.7771 | 1.21252 | 0.606259 | − | 0.795267i | \(-0.292669\pi\) | ||||
0.606259 | + | 0.795267i | \(0.292669\pi\) | |||||||
\(80\) | 6.18975 | 0.692035 | ||||||||
\(81\) | 8.95491 | 0.994990 | ||||||||
\(82\) | 1.48835 | 0.164361 | ||||||||
\(83\) | 0.837580 | 0.0919364 | 0.0459682 | − | 0.998943i | \(-0.485363\pi\) | ||||
0.0459682 | + | 0.998943i | \(0.485363\pi\) | |||||||
\(84\) | −0.109654 | −0.0119642 | ||||||||
\(85\) | 8.10546 | 0.879160 | ||||||||
\(86\) | −9.54333 | −1.02908 | ||||||||
\(87\) | −0.342691 | −0.0367403 | ||||||||
\(88\) | 5.23287 | 0.557825 | ||||||||
\(89\) | 5.96724 | 0.632526 | 0.316263 | − | 0.948672i | \(-0.397572\pi\) | ||||
0.316263 | + | 0.948672i | \(0.397572\pi\) | |||||||
\(90\) | 23.3171 | 2.45784 | ||||||||
\(91\) | −0.191528 | −0.0200776 | ||||||||
\(92\) | −3.62401 | −0.377830 | ||||||||
\(93\) | 0.231262 | 0.0239807 | ||||||||
\(94\) | −4.11643 | −0.424577 | ||||||||
\(95\) | −9.84862 | −1.01045 | ||||||||
\(96\) | 0.228781 | 0.0233499 | ||||||||
\(97\) | −11.5225 | −1.16994 | −0.584968 | − | 0.811056i | \(-0.698893\pi\) | ||||
−0.584968 | + | 0.811056i | \(0.698893\pi\) | |||||||
\(98\) | 16.1674 | 1.63315 | ||||||||
\(99\) | 4.06932 | 0.408982 | ||||||||
\(100\) | 20.9374 | 2.09374 | ||||||||
\(101\) | −11.1059 | −1.10508 | −0.552539 | − | 0.833487i | \(-0.686341\pi\) | ||||
−0.552539 | + | 0.833487i | \(0.686341\pi\) | |||||||
\(102\) | −0.414553 | −0.0410468 | ||||||||
\(103\) | 5.32715 | 0.524900 | 0.262450 | − | 0.964946i | \(-0.415470\pi\) | ||||
0.262450 | + | 0.964946i | \(0.415470\pi\) | |||||||
\(104\) | −1.72603 | −0.169251 | ||||||||
\(105\) | −0.0993323 | −0.00969384 | ||||||||
\(106\) | 1.88666 | 0.183249 | ||||||||
\(107\) | −20.5489 | −1.98654 | −0.993269 | − | 0.115830i | \(-0.963047\pi\) | ||||
−0.993269 | + | 0.115830i | \(0.963047\pi\) | |||||||
\(108\) | −1.53821 | −0.148014 | ||||||||
\(109\) | 12.8758 | 1.23328 | 0.616640 | − | 0.787245i | \(-0.288493\pi\) | ||||
0.616640 | + | 0.787245i | \(0.288493\pi\) | |||||||
\(110\) | 10.5781 | 1.00858 | ||||||||
\(111\) | −0.254113 | −0.0241194 | ||||||||
\(112\) | −0.805773 | −0.0761384 | ||||||||
\(113\) | 8.14394 | 0.766117 | 0.383059 | − | 0.923724i | \(-0.374871\pi\) | ||||
0.383059 | + | 0.923724i | \(0.374871\pi\) | |||||||
\(114\) | 0.503706 | 0.0471764 | ||||||||
\(115\) | −3.28290 | −0.306132 | ||||||||
\(116\) | −17.5411 | −1.62865 | ||||||||
\(117\) | −1.34224 | −0.124090 | ||||||||
\(118\) | 21.3038 | 1.96118 | ||||||||
\(119\) | −1.05516 | −0.0967262 | ||||||||
\(120\) | −0.895172 | −0.0817176 | ||||||||
\(121\) | −9.15391 | −0.832174 | ||||||||
\(122\) | −2.38806 | −0.216205 | ||||||||
\(123\) | −0.0444344 | −0.00400651 | ||||||||
\(124\) | 11.8374 | 1.06303 | ||||||||
\(125\) | 2.55214 | 0.228271 | ||||||||
\(126\) | −3.03540 | −0.270415 | ||||||||
\(127\) | −12.3627 | −1.09702 | −0.548508 | − | 0.836145i | \(-0.684804\pi\) | ||||
−0.548508 | + | 0.836145i | \(0.684804\pi\) | |||||||
\(128\) | 20.6532 | 1.82550 | ||||||||
\(129\) | 0.284913 | 0.0250852 | ||||||||
\(130\) | −3.48912 | −0.306016 | ||||||||
\(131\) | −15.5315 | −1.35699 | −0.678495 | − | 0.734605i | \(-0.737367\pi\) | ||||
−0.678495 | + | 0.734605i | \(0.737367\pi\) | |||||||
\(132\) | −0.348620 | −0.0303435 | ||||||||
\(133\) | 1.28208 | 0.111170 | ||||||||
\(134\) | −26.5393 | −2.29264 | ||||||||
\(135\) | −1.39342 | −0.119926 | ||||||||
\(136\) | −9.50897 | −0.815388 | ||||||||
\(137\) | −11.8098 | −1.00898 | −0.504490 | − | 0.863417i | \(-0.668320\pi\) | ||||
−0.504490 | + | 0.863417i | \(0.668320\pi\) | |||||||
\(138\) | 0.167903 | 0.0142929 | ||||||||
\(139\) | −14.9424 | −1.26739 | −0.633697 | − | 0.773581i | \(-0.718464\pi\) | ||||
−0.633697 | + | 0.773581i | \(0.718464\pi\) | |||||||
\(140\) | −5.08445 | −0.429715 | ||||||||
\(141\) | 0.122895 | 0.0103496 | ||||||||
\(142\) | −36.7974 | −3.08797 | ||||||||
\(143\) | −0.608923 | −0.0509207 | ||||||||
\(144\) | −5.64691 | −0.470576 | ||||||||
\(145\) | −15.8900 | −1.31959 | ||||||||
\(146\) | −15.1995 | −1.25792 | ||||||||
\(147\) | −0.482672 | −0.0398101 | ||||||||
\(148\) | −13.0071 | −1.06918 | ||||||||
\(149\) | 20.4166 | 1.67259 | 0.836297 | − | 0.548276i | \(-0.184716\pi\) | ||||
0.836297 | + | 0.548276i | \(0.184716\pi\) | |||||||
\(150\) | −0.970046 | −0.0792039 | ||||||||
\(151\) | 4.48504 | 0.364987 | 0.182494 | − | 0.983207i | \(-0.441583\pi\) | ||||
0.182494 | + | 0.983207i | \(0.441583\pi\) | |||||||
\(152\) | 11.5540 | 0.937151 | ||||||||
\(153\) | −7.39461 | −0.597819 | ||||||||
\(154\) | −1.37704 | −0.110965 | ||||||||
\(155\) | 10.7232 | 0.861309 | ||||||||
\(156\) | 0.114990 | 0.00920660 | ||||||||
\(157\) | 11.0909 | 0.885149 | 0.442574 | − | 0.896732i | \(-0.354065\pi\) | ||||
0.442574 | + | 0.896732i | \(0.354065\pi\) | |||||||
\(158\) | −25.5579 | −2.03328 | ||||||||
\(159\) | −0.0563258 | −0.00446692 | ||||||||
\(160\) | 10.6082 | 0.838651 | ||||||||
\(161\) | 0.427363 | 0.0336809 | ||||||||
\(162\) | −21.2366 | −1.66850 | ||||||||
\(163\) | −4.63888 | −0.363345 | −0.181673 | − | 0.983359i | \(-0.558151\pi\) | ||||
−0.181673 | + | 0.983359i | \(0.558151\pi\) | |||||||
\(164\) | −2.27443 | −0.177603 | ||||||||
\(165\) | −0.315806 | −0.0245854 | ||||||||
\(166\) | −1.98632 | −0.154168 | ||||||||
\(167\) | 14.2776 | 1.10484 | 0.552418 | − | 0.833567i | \(-0.313705\pi\) | ||||
0.552418 | + | 0.833567i | \(0.313705\pi\) | |||||||
\(168\) | 0.116532 | 0.00899066 | ||||||||
\(169\) | −12.7992 | −0.984550 | ||||||||
\(170\) | −19.2221 | −1.47427 | ||||||||
\(171\) | 8.98490 | 0.687092 | ||||||||
\(172\) | 14.5837 | 1.11199 | ||||||||
\(173\) | 2.25904 | 0.171752 | 0.0858759 | − | 0.996306i | \(-0.472631\pi\) | ||||
0.0858759 | + | 0.996306i | \(0.472631\pi\) | |||||||
\(174\) | 0.812691 | 0.0616099 | ||||||||
\(175\) | −2.46905 | −0.186643 | ||||||||
\(176\) | −2.56178 | −0.193102 | ||||||||
\(177\) | −0.636019 | −0.0478061 | ||||||||
\(178\) | −14.1513 | −1.06069 | ||||||||
\(179\) | −17.2344 | −1.28816 | −0.644078 | − | 0.764960i | \(-0.722759\pi\) | ||||
−0.644078 | + | 0.764960i | \(0.722759\pi\) | |||||||
\(180\) | −35.6322 | −2.65586 | ||||||||
\(181\) | −14.5030 | −1.07800 | −0.539000 | − | 0.842306i | \(-0.681198\pi\) | ||||
−0.539000 | + | 0.842306i | \(0.681198\pi\) | |||||||
\(182\) | 0.454209 | 0.0336682 | ||||||||
\(183\) | 0.0712950 | 0.00527028 | ||||||||
\(184\) | 3.85135 | 0.283925 | ||||||||
\(185\) | −11.7828 | −0.866288 | ||||||||
\(186\) | −0.548438 | −0.0402134 | ||||||||
\(187\) | −3.35465 | −0.245316 | ||||||||
\(188\) | 6.29053 | 0.458784 | ||||||||
\(189\) | 0.181393 | 0.0131944 | ||||||||
\(190\) | 23.3560 | 1.69442 | ||||||||
\(191\) | −3.71005 | −0.268450 | −0.134225 | − | 0.990951i | \(-0.542855\pi\) | ||||
−0.134225 | + | 0.990951i | \(0.542855\pi\) | |||||||
\(192\) | −0.809537 | −0.0584233 | ||||||||
\(193\) | −9.17138 | −0.660171 | −0.330085 | − | 0.943951i | \(-0.607078\pi\) | ||||
−0.330085 | + | 0.943951i | \(0.607078\pi\) | |||||||
\(194\) | 27.3257 | 1.96187 | ||||||||
\(195\) | 0.104167 | 0.00745953 | ||||||||
\(196\) | −24.7062 | −1.76473 | ||||||||
\(197\) | −4.71946 | −0.336247 | −0.168124 | − | 0.985766i | \(-0.553771\pi\) | ||||
−0.168124 | + | 0.985766i | \(0.553771\pi\) | |||||||
\(198\) | −9.65039 | −0.685823 | ||||||||
\(199\) | −21.5208 | −1.52557 | −0.762783 | − | 0.646654i | \(-0.776168\pi\) | ||||
−0.762783 | + | 0.646654i | \(0.776168\pi\) | |||||||
\(200\) | −22.2508 | −1.57337 | ||||||||
\(201\) | 0.792322 | 0.0558861 | ||||||||
\(202\) | 26.3376 | 1.85311 | ||||||||
\(203\) | 2.06854 | 0.145183 | ||||||||
\(204\) | 0.633500 | 0.0443539 | ||||||||
\(205\) | −2.06035 | −0.143901 | ||||||||
\(206\) | −12.6333 | −0.880206 | ||||||||
\(207\) | 2.99499 | 0.208166 | ||||||||
\(208\) | 0.844990 | 0.0585895 | ||||||||
\(209\) | 4.07610 | 0.281950 | ||||||||
\(210\) | 0.235567 | 0.0162556 | ||||||||
\(211\) | −21.8699 | −1.50559 | −0.752794 | − | 0.658256i | \(-0.771295\pi\) | ||||
−0.752794 | + | 0.658256i | \(0.771295\pi\) | |||||||
\(212\) | −2.88311 | −0.198013 | ||||||||
\(213\) | 1.09858 | 0.0752733 | ||||||||
\(214\) | 48.7318 | 3.33123 | ||||||||
\(215\) | 13.2109 | 0.900979 | ||||||||
\(216\) | 1.63470 | 0.111227 | ||||||||
\(217\) | −1.39593 | −0.0947622 | ||||||||
\(218\) | −30.5350 | −2.06809 | ||||||||
\(219\) | 0.453776 | 0.0306633 | ||||||||
\(220\) | −16.1649 | −1.08984 | ||||||||
\(221\) | 1.10651 | 0.0744320 | ||||||||
\(222\) | 0.602630 | 0.0404459 | ||||||||
\(223\) | −8.55830 | −0.573106 | −0.286553 | − | 0.958064i | \(-0.592509\pi\) | ||||
−0.286553 | + | 0.958064i | \(0.592509\pi\) | |||||||
\(224\) | −1.38096 | −0.0922693 | ||||||||
\(225\) | −17.3033 | −1.15355 | ||||||||
\(226\) | −19.3133 | −1.28470 | ||||||||
\(227\) | −8.33166 | −0.552992 | −0.276496 | − | 0.961015i | \(-0.589173\pi\) | ||||
−0.276496 | + | 0.961015i | \(0.589173\pi\) | |||||||
\(228\) | −0.769740 | −0.0509773 | ||||||||
\(229\) | −7.47362 | −0.493871 | −0.246935 | − | 0.969032i | \(-0.579424\pi\) | ||||
−0.246935 | + | 0.969032i | \(0.579424\pi\) | |||||||
\(230\) | 7.78539 | 0.513353 | ||||||||
\(231\) | 0.0411112 | 0.00270492 | ||||||||
\(232\) | 18.6414 | 1.22387 | ||||||||
\(233\) | −4.98420 | −0.326526 | −0.163263 | − | 0.986583i | \(-0.552202\pi\) | ||||
−0.163263 | + | 0.986583i | \(0.552202\pi\) | |||||||
\(234\) | 3.18313 | 0.208087 | ||||||||
\(235\) | 5.69842 | 0.371724 | ||||||||
\(236\) | −32.5555 | −2.11918 | ||||||||
\(237\) | 0.763024 | 0.0495637 | ||||||||
\(238\) | 2.50231 | 0.162201 | ||||||||
\(239\) | −1.14546 | −0.0740934 | −0.0370467 | − | 0.999314i | \(-0.511795\pi\) | ||||
−0.0370467 | + | 0.999314i | \(0.511795\pi\) | |||||||
\(240\) | 0.438237 | 0.0282881 | ||||||||
\(241\) | 5.66505 | 0.364918 | 0.182459 | − | 0.983213i | \(-0.441594\pi\) | ||||
0.182459 | + | 0.983213i | \(0.441594\pi\) | |||||||
\(242\) | 21.7085 | 1.39548 | ||||||||
\(243\) | 1.90736 | 0.122357 | ||||||||
\(244\) | 3.64933 | 0.233624 | ||||||||
\(245\) | −22.3807 | −1.42985 | ||||||||
\(246\) | 0.105376 | 0.00671854 | ||||||||
\(247\) | −1.34448 | −0.0855471 | ||||||||
\(248\) | −12.5800 | −0.798831 | ||||||||
\(249\) | 0.0593011 | 0.00375805 | ||||||||
\(250\) | −6.05241 | −0.382788 | ||||||||
\(251\) | −16.2542 | −1.02595 | −0.512977 | − | 0.858402i | \(-0.671457\pi\) | ||||
−0.512977 | + | 0.858402i | \(0.671457\pi\) | |||||||
\(252\) | 4.63855 | 0.292201 | ||||||||
\(253\) | 1.35871 | 0.0854213 | ||||||||
\(254\) | 29.3183 | 1.83959 | ||||||||
\(255\) | 0.573870 | 0.0359371 | ||||||||
\(256\) | −26.1109 | −1.63193 | ||||||||
\(257\) | 16.0377 | 1.00041 | 0.500203 | − | 0.865908i | \(-0.333259\pi\) | ||||
0.500203 | + | 0.865908i | \(0.333259\pi\) | |||||||
\(258\) | −0.675672 | −0.0420655 | ||||||||
\(259\) | 1.53387 | 0.0953100 | ||||||||
\(260\) | 5.33191 | 0.330671 | ||||||||
\(261\) | 14.4964 | 0.897306 | ||||||||
\(262\) | 36.8328 | 2.27554 | ||||||||
\(263\) | 0.228052 | 0.0140623 | 0.00703115 | − | 0.999975i | \(-0.497762\pi\) | ||||
0.00703115 | + | 0.999975i | \(0.497762\pi\) | |||||||
\(264\) | 0.370489 | 0.0228020 | ||||||||
\(265\) | −2.61173 | −0.160437 | ||||||||
\(266\) | −3.04045 | −0.186422 | ||||||||
\(267\) | 0.422483 | 0.0258556 | ||||||||
\(268\) | 40.5561 | 2.47736 | ||||||||
\(269\) | −19.5438 | −1.19161 | −0.595803 | − | 0.803131i | \(-0.703166\pi\) | ||||
−0.595803 | + | 0.803131i | \(0.703166\pi\) | |||||||
\(270\) | 3.30449 | 0.201105 | ||||||||
\(271\) | −3.59548 | −0.218410 | −0.109205 | − | 0.994019i | \(-0.534830\pi\) | ||||
−0.109205 | + | 0.994019i | \(0.534830\pi\) | |||||||
\(272\) | 4.65518 | 0.282262 | ||||||||
\(273\) | −0.0135603 | −0.000820706 0 | ||||||||
\(274\) | 28.0070 | 1.69196 | ||||||||
\(275\) | −7.84981 | −0.473362 | ||||||||
\(276\) | −0.256582 | −0.0154444 | ||||||||
\(277\) | −17.6664 | −1.06147 | −0.530736 | − | 0.847537i | \(-0.678085\pi\) | ||||
−0.530736 | + | 0.847537i | \(0.678085\pi\) | |||||||
\(278\) | 35.4358 | 2.12530 | ||||||||
\(279\) | −9.78279 | −0.585680 | ||||||||
\(280\) | 5.40340 | 0.322915 | ||||||||
\(281\) | −0.521324 | −0.0310996 | −0.0155498 | − | 0.999879i | \(-0.504950\pi\) | ||||
−0.0155498 | + | 0.999879i | \(0.504950\pi\) | |||||||
\(282\) | −0.291445 | −0.0173553 | ||||||||
\(283\) | 3.94745 | 0.234652 | 0.117326 | − | 0.993093i | \(-0.462568\pi\) | ||||
0.117326 | + | 0.993093i | \(0.462568\pi\) | |||||||
\(284\) | 56.2321 | 3.33676 | ||||||||
\(285\) | −0.697287 | −0.0413037 | ||||||||
\(286\) | 1.44406 | 0.0853891 | ||||||||
\(287\) | 0.268213 | 0.0158321 | ||||||||
\(288\) | −9.67785 | −0.570273 | ||||||||
\(289\) | −10.9041 | −0.641415 | ||||||||
\(290\) | 37.6831 | 2.21283 | ||||||||
\(291\) | −0.815801 | −0.0478231 | ||||||||
\(292\) | 23.2271 | 1.35926 | ||||||||
\(293\) | −27.8062 | −1.62445 | −0.812227 | − | 0.583341i | \(-0.801745\pi\) | ||||
−0.812227 | + | 0.583341i | \(0.801745\pi\) | |||||||
\(294\) | 1.14466 | 0.0667578 | ||||||||
\(295\) | −29.4911 | −1.71704 | ||||||||
\(296\) | 13.8231 | 0.803449 | ||||||||
\(297\) | 0.576701 | 0.0334636 | ||||||||
\(298\) | −48.4180 | −2.80478 | ||||||||
\(299\) | −0.448163 | −0.0259179 | ||||||||
\(300\) | 1.48238 | 0.0855851 | ||||||||
\(301\) | −1.71978 | −0.0991267 | ||||||||
\(302\) | −10.6363 | −0.612049 | ||||||||
\(303\) | −0.786302 | −0.0451719 | ||||||||
\(304\) | −5.65632 | −0.324412 | ||||||||
\(305\) | 3.30583 | 0.189291 | ||||||||
\(306\) | 17.5363 | 1.00249 | ||||||||
\(307\) | 15.1753 | 0.866103 | 0.433051 | − | 0.901369i | \(-0.357437\pi\) | ||||
0.433051 | + | 0.901369i | \(0.357437\pi\) | |||||||
\(308\) | 2.10433 | 0.119905 | ||||||||
\(309\) | 0.377165 | 0.0214561 | ||||||||
\(310\) | −25.4301 | −1.44433 | ||||||||
\(311\) | −8.00813 | −0.454099 | −0.227050 | − | 0.973883i | \(-0.572908\pi\) | ||||
−0.227050 | + | 0.973883i | \(0.572908\pi\) | |||||||
\(312\) | −0.122204 | −0.00691843 | ||||||||
\(313\) | 32.1945 | 1.81974 | 0.909871 | − | 0.414890i | \(-0.136180\pi\) | ||||
0.909871 | + | 0.414890i | \(0.136180\pi\) | |||||||
\(314\) | −26.3020 | −1.48431 | ||||||||
\(315\) | 4.20193 | 0.236752 | ||||||||
\(316\) | 39.0564 | 2.19709 | ||||||||
\(317\) | 1.53520 | 0.0862256 | 0.0431128 | − | 0.999070i | \(-0.486273\pi\) | ||||
0.0431128 | + | 0.999070i | \(0.486273\pi\) | |||||||
\(318\) | 0.133577 | 0.00749060 | ||||||||
\(319\) | 6.57647 | 0.368211 | ||||||||
\(320\) | −37.5368 | −2.09837 | ||||||||
\(321\) | −1.45487 | −0.0812031 | ||||||||
\(322\) | −1.01349 | −0.0564797 | ||||||||
\(323\) | −7.40694 | −0.412133 | ||||||||
\(324\) | 32.4527 | 1.80293 | ||||||||
\(325\) | 2.58922 | 0.143624 | ||||||||
\(326\) | 11.0011 | 0.609295 | ||||||||
\(327\) | 0.911615 | 0.0504124 | ||||||||
\(328\) | 2.41711 | 0.133463 | ||||||||
\(329\) | −0.741813 | −0.0408974 | ||||||||
\(330\) | 0.748933 | 0.0412274 | ||||||||
\(331\) | −20.1527 | −1.10769 | −0.553846 | − | 0.832619i | \(-0.686840\pi\) | ||||
−0.553846 | + | 0.832619i | \(0.686840\pi\) | |||||||
\(332\) | 3.03540 | 0.166589 | ||||||||
\(333\) | 10.7494 | 0.589066 | ||||||||
\(334\) | −33.8594 | −1.85271 | ||||||||
\(335\) | 36.7386 | 2.00725 | ||||||||
\(336\) | −0.0570491 | −0.00311228 | ||||||||
\(337\) | −26.1121 | −1.42242 | −0.711208 | − | 0.702982i | \(-0.751851\pi\) | ||||
−0.711208 | + | 0.702982i | \(0.751851\pi\) | |||||||
\(338\) | 30.3532 | 1.65100 | ||||||||
\(339\) | 0.576595 | 0.0313163 | ||||||||
\(340\) | 29.3743 | 1.59305 | ||||||||
\(341\) | −4.43807 | −0.240335 | ||||||||
\(342\) | −21.3077 | −1.15219 | ||||||||
\(343\) | 5.90503 | 0.318842 | ||||||||
\(344\) | −15.4985 | −0.835624 | ||||||||
\(345\) | −0.232431 | −0.0125136 | ||||||||
\(346\) | −5.35732 | −0.288011 | ||||||||
\(347\) | 1.81219 | 0.0972835 | 0.0486417 | − | 0.998816i | \(-0.484511\pi\) | ||||
0.0486417 | + | 0.998816i | \(0.484511\pi\) | |||||||
\(348\) | −1.24192 | −0.0665737 | ||||||||
\(349\) | −1.00000 | −0.0535288 | ||||||||
\(350\) | 5.85535 | 0.312982 | ||||||||
\(351\) | −0.190222 | −0.0101533 | ||||||||
\(352\) | −4.39047 | −0.234013 | ||||||||
\(353\) | −6.41239 | −0.341297 | −0.170649 | − | 0.985332i | \(-0.554586\pi\) | ||||
−0.170649 | + | 0.985332i | \(0.554586\pi\) | |||||||
\(354\) | 1.50832 | 0.0801663 | ||||||||
\(355\) | 50.9391 | 2.70357 | ||||||||
\(356\) | 21.6254 | 1.14614 | ||||||||
\(357\) | −0.0747057 | −0.00395384 | ||||||||
\(358\) | 40.8713 | 2.16012 | ||||||||
\(359\) | 12.1824 | 0.642961 | 0.321481 | − | 0.946916i | \(-0.395820\pi\) | ||||
0.321481 | + | 0.946916i | \(0.395820\pi\) | |||||||
\(360\) | 37.8674 | 1.99579 | ||||||||
\(361\) | −10.0001 | −0.526323 | ||||||||
\(362\) | 34.3939 | 1.80770 | ||||||||
\(363\) | −0.648101 | −0.0340165 | ||||||||
\(364\) | −0.694101 | −0.0363808 | ||||||||
\(365\) | 21.0408 | 1.10133 | ||||||||
\(366\) | −0.169076 | −0.00883775 | ||||||||
\(367\) | 10.7597 | 0.561650 | 0.280825 | − | 0.959759i | \(-0.409392\pi\) | ||||
0.280825 | + | 0.959759i | \(0.409392\pi\) | |||||||
\(368\) | −1.88545 | −0.0982860 | ||||||||
\(369\) | 1.87965 | 0.0978509 | ||||||||
\(370\) | 27.9429 | 1.45268 | ||||||||
\(371\) | 0.339992 | 0.0176515 | ||||||||
\(372\) | 0.838096 | 0.0434533 | ||||||||
\(373\) | −27.2837 | −1.41269 | −0.706347 | − | 0.707865i | \(-0.749658\pi\) | ||||
−0.706347 | + | 0.707865i | \(0.749658\pi\) | |||||||
\(374\) | 7.95555 | 0.411372 | ||||||||
\(375\) | 0.180693 | 0.00933094 | ||||||||
\(376\) | −6.68514 | −0.344760 | ||||||||
\(377\) | −2.16921 | −0.111720 | ||||||||
\(378\) | −0.430175 | −0.0221258 | ||||||||
\(379\) | −27.0044 | −1.38712 | −0.693562 | − | 0.720397i | \(-0.743960\pi\) | ||||
−0.693562 | + | 0.720397i | \(0.743960\pi\) | |||||||
\(380\) | −35.6915 | −1.83094 | ||||||||
\(381\) | −0.875288 | −0.0448424 | ||||||||
\(382\) | 8.79840 | 0.450165 | ||||||||
\(383\) | 4.44985 | 0.227377 | 0.113688 | − | 0.993516i | \(-0.463733\pi\) | ||||
0.113688 | + | 0.993516i | \(0.463733\pi\) | |||||||
\(384\) | 1.46225 | 0.0746203 | ||||||||
\(385\) | 1.90625 | 0.0971517 | ||||||||
\(386\) | 21.7499 | 1.10704 | ||||||||
\(387\) | −12.0524 | −0.612656 | ||||||||
\(388\) | −41.7578 | −2.11993 | ||||||||
\(389\) | −9.66647 | −0.490109 | −0.245055 | − | 0.969509i | \(-0.578806\pi\) | ||||
−0.245055 | + | 0.969509i | \(0.578806\pi\) | |||||||
\(390\) | −0.247031 | −0.0125089 | ||||||||
\(391\) | −2.46900 | −0.124863 | ||||||||
\(392\) | 26.2561 | 1.32613 | ||||||||
\(393\) | −1.09963 | −0.0554692 | ||||||||
\(394\) | 11.1922 | 0.563855 | ||||||||
\(395\) | 35.3801 | 1.78017 | ||||||||
\(396\) | 14.7473 | 0.741078 | ||||||||
\(397\) | −14.1734 | −0.711342 | −0.355671 | − | 0.934611i | \(-0.615748\pi\) | ||||
−0.355671 | + | 0.934611i | \(0.615748\pi\) | |||||||
\(398\) | 51.0365 | 2.55823 | ||||||||
\(399\) | 0.0907719 | 0.00454428 | ||||||||
\(400\) | 10.8930 | 0.544651 | ||||||||
\(401\) | 29.4412 | 1.47022 | 0.735111 | − | 0.677947i | \(-0.237130\pi\) | ||||
0.735111 | + | 0.677947i | \(0.237130\pi\) | |||||||
\(402\) | −1.87899 | −0.0937156 | ||||||||
\(403\) | 1.46387 | 0.0729207 | ||||||||
\(404\) | −40.2479 | −2.00241 | ||||||||
\(405\) | 29.3980 | 1.46080 | ||||||||
\(406\) | −4.90553 | −0.243458 | ||||||||
\(407\) | 4.87661 | 0.241724 | ||||||||
\(408\) | −0.673240 | −0.0333303 | ||||||||
\(409\) | 8.84877 | 0.437544 | 0.218772 | − | 0.975776i | \(-0.429795\pi\) | ||||
0.218772 | + | 0.975776i | \(0.429795\pi\) | |||||||
\(410\) | 4.88611 | 0.241308 | ||||||||
\(411\) | −0.836140 | −0.0412438 | ||||||||
\(412\) | 19.3057 | 0.951122 | ||||||||
\(413\) | 3.83912 | 0.188911 | ||||||||
\(414\) | −7.10261 | −0.349074 | ||||||||
\(415\) | 2.74969 | 0.134977 | ||||||||
\(416\) | 1.44817 | 0.0710024 | ||||||||
\(417\) | −1.05793 | −0.0518069 | ||||||||
\(418\) | −9.66647 | −0.472802 | ||||||||
\(419\) | 1.89585 | 0.0926185 | 0.0463092 | − | 0.998927i | \(-0.485254\pi\) | ||||
0.0463092 | + | 0.998927i | \(0.485254\pi\) | |||||||
\(420\) | −0.359982 | −0.0175653 | ||||||||
\(421\) | 7.76042 | 0.378220 | 0.189110 | − | 0.981956i | \(-0.439440\pi\) | ||||
0.189110 | + | 0.981956i | \(0.439440\pi\) | |||||||
\(422\) | 51.8646 | 2.52473 | ||||||||
\(423\) | −5.19867 | −0.252768 | ||||||||
\(424\) | 3.06397 | 0.148799 | ||||||||
\(425\) | 14.2644 | 0.691925 | ||||||||
\(426\) | −2.60528 | −0.126226 | ||||||||
\(427\) | −0.430348 | −0.0208260 | ||||||||
\(428\) | −74.4696 | −3.59962 | ||||||||
\(429\) | −0.0431120 | −0.00208147 | ||||||||
\(430\) | −31.3298 | −1.51086 | ||||||||
\(431\) | 35.5311 | 1.71147 | 0.855737 | − | 0.517411i | \(-0.173104\pi\) | ||||
0.855737 | + | 0.517411i | \(0.173104\pi\) | |||||||
\(432\) | −0.800277 | −0.0385033 | ||||||||
\(433\) | −1.94044 | −0.0932517 | −0.0466258 | − | 0.998912i | \(-0.514847\pi\) | ||||
−0.0466258 | + | 0.998912i | \(0.514847\pi\) | |||||||
\(434\) | 3.31046 | 0.158907 | ||||||||
\(435\) | −1.12502 | −0.0539405 | ||||||||
\(436\) | 46.6622 | 2.23471 | ||||||||
\(437\) | 2.99998 | 0.143508 | ||||||||
\(438\) | −1.07613 | −0.0514194 | ||||||||
\(439\) | 38.8947 | 1.85635 | 0.928173 | − | 0.372150i | \(-0.121379\pi\) | ||||
0.928173 | + | 0.372150i | \(0.121379\pi\) | |||||||
\(440\) | 17.1790 | 0.818975 | ||||||||
\(441\) | 20.4179 | 0.972281 | ||||||||
\(442\) | −2.62409 | −0.124815 | ||||||||
\(443\) | 25.9508 | 1.23296 | 0.616479 | − | 0.787371i | \(-0.288559\pi\) | ||||
0.616479 | + | 0.787371i | \(0.288559\pi\) | |||||||
\(444\) | −0.920910 | −0.0437045 | ||||||||
\(445\) | 19.5898 | 0.928647 | ||||||||
\(446\) | 20.2960 | 0.961044 | ||||||||
\(447\) | 1.44551 | 0.0683701 | ||||||||
\(448\) | 4.88649 | 0.230865 | ||||||||
\(449\) | 9.62968 | 0.454453 | 0.227226 | − | 0.973842i | \(-0.427034\pi\) | ||||
0.227226 | + | 0.973842i | \(0.427034\pi\) | |||||||
\(450\) | 41.0347 | 1.93439 | ||||||||
\(451\) | 0.852726 | 0.0401533 | ||||||||
\(452\) | 29.5137 | 1.38821 | ||||||||
\(453\) | 0.317543 | 0.0149195 | ||||||||
\(454\) | 19.7585 | 0.927314 | ||||||||
\(455\) | −0.628767 | −0.0294771 | ||||||||
\(456\) | 0.818027 | 0.0383076 | ||||||||
\(457\) | −5.82946 | −0.272691 | −0.136345 | − | 0.990661i | \(-0.543536\pi\) | ||||
−0.136345 | + | 0.990661i | \(0.543536\pi\) | |||||||
\(458\) | 17.7237 | 0.828174 | ||||||||
\(459\) | −1.04796 | −0.0489146 | ||||||||
\(460\) | −11.8973 | −0.554713 | ||||||||
\(461\) | −11.5466 | −0.537780 | −0.268890 | − | 0.963171i | \(-0.586657\pi\) | ||||
−0.268890 | + | 0.963171i | \(0.586657\pi\) | |||||||
\(462\) | −0.0974951 | −0.00453588 | ||||||||
\(463\) | −14.7008 | −0.683203 | −0.341602 | − | 0.939845i | \(-0.610969\pi\) | ||||
−0.341602 | + | 0.939845i | \(0.610969\pi\) | |||||||
\(464\) | −9.12603 | −0.423665 | ||||||||
\(465\) | 0.759209 | 0.0352075 | ||||||||
\(466\) | 11.8200 | 0.547553 | ||||||||
\(467\) | 5.68488 | 0.263065 | 0.131533 | − | 0.991312i | \(-0.458010\pi\) | ||||
0.131533 | + | 0.991312i | \(0.458010\pi\) | |||||||
\(468\) | −4.86430 | −0.224852 | ||||||||
\(469\) | −4.78259 | −0.220839 | ||||||||
\(470\) | −13.5138 | −0.623345 | ||||||||
\(471\) | 0.785240 | 0.0361819 | ||||||||
\(472\) | 34.5977 | 1.59249 | ||||||||
\(473\) | −5.46768 | −0.251404 | ||||||||
\(474\) | −1.80951 | −0.0831136 | ||||||||
\(475\) | −17.3321 | −0.795251 | ||||||||
\(476\) | −3.82391 | −0.175269 | ||||||||
\(477\) | 2.38268 | 0.109095 | ||||||||
\(478\) | 2.71645 | 0.124247 | ||||||||
\(479\) | 25.5967 | 1.16954 | 0.584772 | − | 0.811198i | \(-0.301184\pi\) | ||||
0.584772 | + | 0.811198i | \(0.301184\pi\) | |||||||
\(480\) | 0.751065 | 0.0342813 | ||||||||
\(481\) | −1.60852 | −0.0733423 | ||||||||
\(482\) | −13.4347 | −0.611933 | ||||||||
\(483\) | 0.0302575 | 0.00137676 | ||||||||
\(484\) | −33.1739 | −1.50790 | ||||||||
\(485\) | −37.8273 | −1.71765 | ||||||||
\(486\) | −4.52330 | −0.205181 | ||||||||
\(487\) | −16.9416 | −0.767698 | −0.383849 | − | 0.923396i | \(-0.625402\pi\) | ||||
−0.383849 | + | 0.923396i | \(0.625402\pi\) | |||||||
\(488\) | −3.87825 | −0.175560 | ||||||||
\(489\) | −0.328435 | −0.0148523 | ||||||||
\(490\) | 53.0758 | 2.39772 | ||||||||
\(491\) | 34.5459 | 1.55903 | 0.779517 | − | 0.626382i | \(-0.215465\pi\) | ||||
0.779517 | + | 0.626382i | \(0.215465\pi\) | |||||||
\(492\) | −0.161031 | −0.00725983 | ||||||||
\(493\) | −11.9505 | −0.538224 | ||||||||
\(494\) | 3.18843 | 0.143454 | ||||||||
\(495\) | 13.3591 | 0.600449 | ||||||||
\(496\) | 6.15862 | 0.276530 | ||||||||
\(497\) | −6.63119 | −0.297449 | ||||||||
\(498\) | −0.140633 | −0.00630190 | ||||||||
\(499\) | −28.7286 | −1.28607 | −0.643034 | − | 0.765837i | \(-0.722325\pi\) | ||||
−0.643034 | + | 0.765837i | \(0.722325\pi\) | |||||||
\(500\) | 9.24901 | 0.413628 | ||||||||
\(501\) | 1.01086 | 0.0451620 | ||||||||
\(502\) | 38.5468 | 1.72043 | ||||||||
\(503\) | 25.7974 | 1.15025 | 0.575125 | − | 0.818065i | \(-0.304953\pi\) | ||||
0.575125 | + | 0.818065i | \(0.304953\pi\) | |||||||
\(504\) | −4.92953 | −0.219579 | ||||||||
\(505\) | −36.4595 | −1.62243 | ||||||||
\(506\) | −3.22218 | −0.143243 | ||||||||
\(507\) | −0.906186 | −0.0402451 | ||||||||
\(508\) | −44.8028 | −1.98780 | ||||||||
\(509\) | −38.7204 | −1.71625 | −0.858126 | − | 0.513439i | \(-0.828371\pi\) | ||||
−0.858126 | + | 0.513439i | \(0.828371\pi\) | |||||||
\(510\) | −1.36093 | −0.0602632 | ||||||||
\(511\) | −2.73906 | −0.121169 | ||||||||
\(512\) | 20.6156 | 0.911091 | ||||||||
\(513\) | 1.27333 | 0.0562191 | ||||||||
\(514\) | −38.0335 | −1.67759 | ||||||||
\(515\) | 17.4885 | 0.770634 | ||||||||
\(516\) | 1.03253 | 0.0454546 | ||||||||
\(517\) | −2.35843 | −0.103724 | ||||||||
\(518\) | −3.63757 | −0.159826 | ||||||||
\(519\) | 0.159941 | 0.00702064 | ||||||||
\(520\) | −5.66638 | −0.248487 | ||||||||
\(521\) | −23.6813 | −1.03750 | −0.518749 | − | 0.854926i | \(-0.673602\pi\) | ||||
−0.518749 | + | 0.854926i | \(0.673602\pi\) | |||||||
\(522\) | −34.3783 | −1.50470 | ||||||||
\(523\) | −7.47918 | −0.327042 | −0.163521 | − | 0.986540i | \(-0.552285\pi\) | ||||
−0.163521 | + | 0.986540i | \(0.552285\pi\) | |||||||
\(524\) | −56.2862 | −2.45887 | ||||||||
\(525\) | −0.174810 | −0.00762933 | ||||||||
\(526\) | −0.540826 | −0.0235811 | ||||||||
\(527\) | 8.06470 | 0.351304 | ||||||||
\(528\) | −0.181375 | −0.00789335 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 6.19372 | 0.269038 | ||||||||
\(531\) | 26.9048 | 1.16757 | ||||||||
\(532\) | 4.64628 | 0.201442 | ||||||||
\(533\) | −0.281267 | −0.0121830 | ||||||||
\(534\) | −1.00192 | −0.0433573 | ||||||||
\(535\) | −67.4599 | −2.91655 | ||||||||
\(536\) | −43.1002 | −1.86164 | ||||||||
\(537\) | −1.22020 | −0.0526556 | ||||||||
\(538\) | 46.3481 | 1.99821 | ||||||||
\(539\) | 9.26281 | 0.398977 | ||||||||
\(540\) | −5.04977 | −0.217307 | ||||||||
\(541\) | −10.6869 | −0.459464 | −0.229732 | − | 0.973254i | \(-0.573785\pi\) | ||||
−0.229732 | + | 0.973254i | \(0.573785\pi\) | |||||||
\(542\) | 8.52668 | 0.366252 | ||||||||
\(543\) | −1.02682 | −0.0440650 | ||||||||
\(544\) | 7.97819 | 0.342062 | ||||||||
\(545\) | 42.2700 | 1.81065 | ||||||||
\(546\) | 0.0321582 | 0.00137625 | ||||||||
\(547\) | −21.0523 | −0.900129 | −0.450065 | − | 0.892996i | \(-0.648599\pi\) | ||||
−0.450065 | + | 0.892996i | \(0.648599\pi\) | |||||||
\(548\) | −42.7989 | −1.82828 | ||||||||
\(549\) | −3.01591 | −0.128716 | ||||||||
\(550\) | 18.6158 | 0.793782 | ||||||||
\(551\) | 14.5206 | 0.618598 | ||||||||
\(552\) | 0.272678 | 0.0116059 | ||||||||
\(553\) | −4.60573 | −0.195856 | ||||||||
\(554\) | 41.8959 | 1.77999 | ||||||||
\(555\) | −0.834227 | −0.0354110 | ||||||||
\(556\) | −54.1514 | −2.29653 | ||||||||
\(557\) | −26.6241 | −1.12810 | −0.564049 | − | 0.825741i | \(-0.690757\pi\) | ||||
−0.564049 | + | 0.825741i | \(0.690757\pi\) | |||||||
\(558\) | 23.1999 | 0.982130 | ||||||||
\(559\) | 1.80348 | 0.0762793 | ||||||||
\(560\) | −2.64527 | −0.111783 | ||||||||
\(561\) | −0.237511 | −0.0100277 | ||||||||
\(562\) | 1.23632 | 0.0521511 | ||||||||
\(563\) | −12.9520 | −0.545863 | −0.272932 | − | 0.962033i | \(-0.587993\pi\) | ||||
−0.272932 | + | 0.962033i | \(0.587993\pi\) | |||||||
\(564\) | 0.445372 | 0.0187536 | ||||||||
\(565\) | 26.7357 | 1.12478 | ||||||||
\(566\) | −9.36139 | −0.393488 | ||||||||
\(567\) | −3.82700 | −0.160719 | ||||||||
\(568\) | −59.7596 | −2.50746 | ||||||||
\(569\) | 1.54625 | 0.0648223 | 0.0324111 | − | 0.999475i | \(-0.489681\pi\) | ||||
0.0324111 | + | 0.999475i | \(0.489681\pi\) | |||||||
\(570\) | 1.65362 | 0.0692623 | ||||||||
\(571\) | 9.90623 | 0.414563 | 0.207281 | − | 0.978281i | \(-0.433538\pi\) | ||||
0.207281 | + | 0.978281i | \(0.433538\pi\) | |||||||
\(572\) | −2.20674 | −0.0922686 | ||||||||
\(573\) | −0.262674 | −0.0109733 | ||||||||
\(574\) | −0.636068 | −0.0265489 | ||||||||
\(575\) | −5.77741 | −0.240934 | ||||||||
\(576\) | 34.2449 | 1.42687 | ||||||||
\(577\) | −38.2024 | −1.59039 | −0.795193 | − | 0.606356i | \(-0.792631\pi\) | ||||
−0.795193 | + | 0.606356i | \(0.792631\pi\) | |||||||
\(578\) | 25.8590 | 1.07559 | ||||||||
\(579\) | −0.649338 | −0.0269856 | ||||||||
\(580\) | −57.5855 | −2.39111 | ||||||||
\(581\) | −0.357951 | −0.0148503 | ||||||||
\(582\) | 1.93467 | 0.0801947 | ||||||||
\(583\) | 1.08093 | 0.0447675 | ||||||||
\(584\) | −24.6842 | −1.02144 | ||||||||
\(585\) | −4.40644 | −0.182184 | ||||||||
\(586\) | 65.9424 | 2.72406 | ||||||||
\(587\) | −15.5300 | −0.640991 | −0.320496 | − | 0.947250i | \(-0.603849\pi\) | ||||
−0.320496 | + | 0.947250i | \(0.603849\pi\) | |||||||
\(588\) | −1.74921 | −0.0721363 | ||||||||
\(589\) | −9.79909 | −0.403765 | ||||||||
\(590\) | 69.9382 | 2.87931 | ||||||||
\(591\) | −0.334140 | −0.0137447 | ||||||||
\(592\) | −6.76717 | −0.278129 | ||||||||
\(593\) | 18.0864 | 0.742719 | 0.371360 | − | 0.928489i | \(-0.378892\pi\) | ||||
0.371360 | + | 0.928489i | \(0.378892\pi\) | |||||||
\(594\) | −1.36765 | −0.0561153 | ||||||||
\(595\) | −3.46397 | −0.142009 | ||||||||
\(596\) | 73.9901 | 3.03075 | ||||||||
\(597\) | −1.52368 | −0.0623601 | ||||||||
\(598\) | 1.06282 | 0.0434619 | ||||||||
\(599\) | 41.4872 | 1.69512 | 0.847561 | − | 0.530698i | \(-0.178070\pi\) | ||||
0.847561 | + | 0.530698i | \(0.178070\pi\) | |||||||
\(600\) | −1.57537 | −0.0643142 | ||||||||
\(601\) | 5.38795 | 0.219779 | 0.109889 | − | 0.993944i | \(-0.464950\pi\) | ||||
0.109889 | + | 0.993944i | \(0.464950\pi\) | |||||||
\(602\) | 4.07847 | 0.166226 | ||||||||
\(603\) | −33.5167 | −1.36490 | ||||||||
\(604\) | 16.2538 | 0.661360 | ||||||||
\(605\) | −30.0513 | −1.22176 | ||||||||
\(606\) | 1.86472 | 0.0757489 | ||||||||
\(607\) | 35.2111 | 1.42917 | 0.714587 | − | 0.699546i | \(-0.246614\pi\) | ||||
0.714587 | + | 0.699546i | \(0.246614\pi\) | |||||||
\(608\) | −9.69398 | −0.393143 | ||||||||
\(609\) | 0.146453 | 0.00593459 | ||||||||
\(610\) | −7.83977 | −0.317423 | ||||||||
\(611\) | 0.777916 | 0.0314711 | ||||||||
\(612\) | −26.7982 | −1.08325 | ||||||||
\(613\) | −24.5858 | −0.993010 | −0.496505 | − | 0.868034i | \(-0.665384\pi\) | ||||
−0.496505 | + | 0.868034i | \(0.665384\pi\) | |||||||
\(614\) | −35.9883 | −1.45237 | ||||||||
\(615\) | −0.145873 | −0.00588219 | ||||||||
\(616\) | −2.23633 | −0.0901045 | ||||||||
\(617\) | −24.0060 | −0.966447 | −0.483223 | − | 0.875497i | \(-0.660534\pi\) | ||||
−0.483223 | + | 0.875497i | \(0.660534\pi\) | |||||||
\(618\) | −0.894446 | −0.0359799 | ||||||||
\(619\) | −6.83191 | −0.274598 | −0.137299 | − | 0.990530i | \(-0.543842\pi\) | ||||
−0.137299 | + | 0.990530i | \(0.543842\pi\) | |||||||
\(620\) | 38.8611 | 1.56070 | ||||||||
\(621\) | 0.424448 | 0.0170325 | ||||||||
\(622\) | 18.9913 | 0.761481 | ||||||||
\(623\) | −2.55018 | −0.102171 | ||||||||
\(624\) | 0.0598257 | 0.00239494 | ||||||||
\(625\) | −20.5086 | −0.820344 | ||||||||
\(626\) | −76.3494 | −3.05153 | ||||||||
\(627\) | 0.288590 | 0.0115252 | ||||||||
\(628\) | 40.1935 | 1.60390 | ||||||||
\(629\) | −8.86159 | −0.353335 | ||||||||
\(630\) | −9.96489 | −0.397011 | ||||||||
\(631\) | 17.4275 | 0.693779 | 0.346890 | − | 0.937906i | \(-0.387238\pi\) | ||||
0.346890 | + | 0.937906i | \(0.387238\pi\) | |||||||
\(632\) | −41.5064 | −1.65104 | ||||||||
\(633\) | −1.54840 | −0.0615435 | ||||||||
\(634\) | −3.64074 | −0.144592 | ||||||||
\(635\) | −40.5856 | −1.61059 | ||||||||
\(636\) | −0.204125 | −0.00809410 | ||||||||
\(637\) | −3.05529 | −0.121055 | ||||||||
\(638\) | −15.5961 | −0.617455 | ||||||||
\(639\) | −46.4718 | −1.83840 | ||||||||
\(640\) | 67.8022 | 2.68012 | ||||||||
\(641\) | −40.2322 | −1.58907 | −0.794537 | − | 0.607215i | \(-0.792287\pi\) | ||||
−0.794537 | + | 0.607215i | \(0.792287\pi\) | |||||||
\(642\) | 3.45023 | 0.136170 | ||||||||
\(643\) | 30.0436 | 1.18480 | 0.592402 | − | 0.805642i | \(-0.298180\pi\) | ||||
0.592402 | + | 0.805642i | \(0.298180\pi\) | |||||||
\(644\) | 1.54877 | 0.0610301 | ||||||||
\(645\) | 0.935341 | 0.0368290 | ||||||||
\(646\) | 17.5656 | 0.691107 | ||||||||
\(647\) | 30.3655 | 1.19379 | 0.596895 | − | 0.802320i | \(-0.296401\pi\) | ||||
0.596895 | + | 0.802320i | \(0.296401\pi\) | |||||||
\(648\) | −34.4885 | −1.35484 | ||||||||
\(649\) | 12.2056 | 0.479113 | ||||||||
\(650\) | −6.14033 | −0.240844 | ||||||||
\(651\) | −0.0988328 | −0.00387356 | ||||||||
\(652\) | −16.8114 | −0.658384 | ||||||||
\(653\) | −49.1340 | −1.92276 | −0.961382 | − | 0.275218i | \(-0.911250\pi\) | ||||
−0.961382 | + | 0.275218i | \(0.911250\pi\) | |||||||
\(654\) | −2.16189 | −0.0845368 | ||||||||
\(655\) | −50.9881 | −1.99227 | ||||||||
\(656\) | −1.18331 | −0.0462005 | ||||||||
\(657\) | −19.1955 | −0.748889 | ||||||||
\(658\) | 1.75921 | 0.0685811 | ||||||||
\(659\) | 42.0950 | 1.63979 | 0.819894 | − | 0.572516i | \(-0.194032\pi\) | ||||
0.819894 | + | 0.572516i | \(0.194032\pi\) | |||||||
\(660\) | −1.14448 | −0.0445490 | ||||||||
\(661\) | 16.7546 | 0.651679 | 0.325840 | − | 0.945425i | \(-0.394353\pi\) | ||||
0.325840 | + | 0.945425i | \(0.394353\pi\) | |||||||
\(662\) | 47.7921 | 1.85749 | ||||||||
\(663\) | 0.0783416 | 0.00304253 | ||||||||
\(664\) | −3.22582 | −0.125186 | ||||||||
\(665\) | 4.20894 | 0.163216 | ||||||||
\(666\) | −25.4923 | −0.987807 | ||||||||
\(667\) | 4.84023 | 0.187414 | ||||||||
\(668\) | 51.7424 | 2.00197 | ||||||||
\(669\) | −0.605931 | −0.0234267 | ||||||||
\(670\) | −87.1257 | −3.36596 | ||||||||
\(671\) | −1.36820 | −0.0528187 | ||||||||
\(672\) | −0.0977726 | −0.00377166 | ||||||||
\(673\) | −42.0184 | −1.61969 | −0.809845 | − | 0.586644i | \(-0.800449\pi\) | ||||
−0.809845 | + | 0.586644i | \(0.800449\pi\) | |||||||
\(674\) | 61.9248 | 2.38525 | ||||||||
\(675\) | −2.45221 | −0.0943855 | ||||||||
\(676\) | −46.3843 | −1.78401 | ||||||||
\(677\) | −10.7287 | −0.412339 | −0.206169 | − | 0.978516i | \(-0.566100\pi\) | ||||
−0.206169 | + | 0.978516i | \(0.566100\pi\) | |||||||
\(678\) | −1.36739 | −0.0525145 | ||||||||
\(679\) | 4.92431 | 0.188977 | ||||||||
\(680\) | −31.2170 | −1.19712 | ||||||||
\(681\) | −0.589886 | −0.0226045 | ||||||||
\(682\) | 10.5249 | 0.403019 | ||||||||
\(683\) | −41.2719 | −1.57922 | −0.789612 | − | 0.613606i | \(-0.789718\pi\) | ||||
−0.789612 | + | 0.613606i | \(0.789718\pi\) | |||||||
\(684\) | 32.5614 | 1.24502 | ||||||||
\(685\) | −38.7704 | −1.48134 | ||||||||
\(686\) | −14.0038 | −0.534667 | ||||||||
\(687\) | −0.529136 | −0.0201878 | ||||||||
\(688\) | 7.58739 | 0.289267 | ||||||||
\(689\) | −0.356539 | −0.0135830 | ||||||||
\(690\) | 0.551209 | 0.0209842 | ||||||||
\(691\) | 9.22467 | 0.350923 | 0.175462 | − | 0.984486i | \(-0.443858\pi\) | ||||
0.175462 | + | 0.984486i | \(0.443858\pi\) | |||||||
\(692\) | 8.18681 | 0.311216 | ||||||||
\(693\) | −1.73908 | −0.0660620 | ||||||||
\(694\) | −4.29761 | −0.163135 | ||||||||
\(695\) | −49.0542 | −1.86073 | ||||||||
\(696\) | 1.31982 | 0.0500277 | ||||||||
\(697\) | −1.54954 | −0.0586931 | ||||||||
\(698\) | 2.37150 | 0.0897626 | ||||||||
\(699\) | −0.352884 | −0.0133473 | ||||||||
\(700\) | −8.94787 | −0.338198 | ||||||||
\(701\) | −18.5219 | −0.699564 | −0.349782 | − | 0.936831i | \(-0.613744\pi\) | ||||
−0.349782 | + | 0.936831i | \(0.613744\pi\) | |||||||
\(702\) | 0.451111 | 0.0170261 | ||||||||
\(703\) | 10.7674 | 0.406099 | ||||||||
\(704\) | 15.5356 | 0.585518 | ||||||||
\(705\) | 0.403451 | 0.0151948 | ||||||||
\(706\) | 15.2070 | 0.572323 | ||||||||
\(707\) | 4.74625 | 0.178501 | ||||||||
\(708\) | −2.30494 | −0.0866251 | ||||||||
\(709\) | 28.7336 | 1.07911 | 0.539556 | − | 0.841950i | \(-0.318592\pi\) | ||||
0.539556 | + | 0.841950i | \(0.318592\pi\) | |||||||
\(710\) | −120.802 | −4.53362 | ||||||||
\(711\) | −32.2773 | −1.21049 | ||||||||
\(712\) | −22.9819 | −0.861285 | ||||||||
\(713\) | −3.26639 | −0.122327 | ||||||||
\(714\) | 0.177165 | 0.00663022 | ||||||||
\(715\) | −1.99903 | −0.0747595 | ||||||||
\(716\) | −62.4576 | −2.33415 | ||||||||
\(717\) | −0.0810988 | −0.00302869 | ||||||||
\(718\) | −28.8905 | −1.07818 | ||||||||
\(719\) | 45.3951 | 1.69295 | 0.846476 | − | 0.532427i | \(-0.178720\pi\) | ||||
0.846476 | + | 0.532427i | \(0.178720\pi\) | |||||||
\(720\) | −18.5382 | −0.690878 | ||||||||
\(721\) | −2.27663 | −0.0847860 | ||||||||
\(722\) | 23.7153 | 0.882593 | ||||||||
\(723\) | 0.401088 | 0.0149166 | ||||||||
\(724\) | −52.5591 | −1.95334 | ||||||||
\(725\) | −27.9640 | −1.03856 | ||||||||
\(726\) | 1.53697 | 0.0570424 | ||||||||
\(727\) | −25.2832 | −0.937701 | −0.468851 | − | 0.883277i | \(-0.655332\pi\) | ||||
−0.468851 | + | 0.883277i | \(0.655332\pi\) | |||||||
\(728\) | 0.737642 | 0.0273388 | ||||||||
\(729\) | −26.7297 | −0.989989 | ||||||||
\(730\) | −49.8983 | −1.84682 | ||||||||
\(731\) | 9.93567 | 0.367484 | ||||||||
\(732\) | 0.258374 | 0.00954978 | ||||||||
\(733\) | −1.59212 | −0.0588064 | −0.0294032 | − | 0.999568i | \(-0.509361\pi\) | ||||
−0.0294032 | + | 0.999568i | \(0.509361\pi\) | |||||||
\(734\) | −25.5166 | −0.941833 | ||||||||
\(735\) | −1.58456 | −0.0584475 | ||||||||
\(736\) | −3.23135 | −0.119109 | ||||||||
\(737\) | −15.2052 | −0.560091 | ||||||||
\(738\) | −4.45760 | −0.164087 | ||||||||
\(739\) | 9.43878 | 0.347211 | 0.173606 | − | 0.984815i | \(-0.444458\pi\) | ||||
0.173606 | + | 0.984815i | \(0.444458\pi\) | |||||||
\(740\) | −42.7010 | −1.56972 | ||||||||
\(741\) | −0.0951897 | −0.00349688 | ||||||||
\(742\) | −0.806290 | −0.0295998 | ||||||||
\(743\) | −50.9796 | −1.87026 | −0.935131 | − | 0.354302i | \(-0.884718\pi\) | ||||
−0.935131 | + | 0.354302i | \(0.884718\pi\) | |||||||
\(744\) | −0.890671 | −0.0326536 | ||||||||
\(745\) | 67.0256 | 2.45563 | ||||||||
\(746\) | 64.7032 | 2.36895 | ||||||||
\(747\) | −2.50854 | −0.0917828 | ||||||||
\(748\) | −12.1573 | −0.444515 | ||||||||
\(749\) | 8.78185 | 0.320882 | ||||||||
\(750\) | −0.428513 | −0.0156471 | ||||||||
\(751\) | 12.3512 | 0.450701 | 0.225350 | − | 0.974278i | \(-0.427647\pi\) | ||||
0.225350 | + | 0.974278i | \(0.427647\pi\) | |||||||
\(752\) | 3.27275 | 0.119345 | ||||||||
\(753\) | −1.15080 | −0.0419376 | ||||||||
\(754\) | 5.14428 | 0.187344 | ||||||||
\(755\) | 14.7239 | 0.535858 | ||||||||
\(756\) | 0.657372 | 0.0239084 | ||||||||
\(757\) | −36.7649 | −1.33624 | −0.668121 | − | 0.744053i | \(-0.732901\pi\) | ||||
−0.668121 | + | 0.744053i | \(0.732901\pi\) | |||||||
\(758\) | 64.0410 | 2.32608 | ||||||||
\(759\) | 0.0961972 | 0.00349174 | ||||||||
\(760\) | 37.9305 | 1.37588 | ||||||||
\(761\) | 20.7152 | 0.750926 | 0.375463 | − | 0.926837i | \(-0.377484\pi\) | ||||
0.375463 | + | 0.926837i | \(0.377484\pi\) | |||||||
\(762\) | 2.07575 | 0.0751964 | ||||||||
\(763\) | −5.50265 | −0.199209 | ||||||||
\(764\) | −13.4453 | −0.486434 | ||||||||
\(765\) | −24.2757 | −0.877691 | ||||||||
\(766\) | −10.5528 | −0.381289 | ||||||||
\(767\) | −4.02596 | −0.145369 | ||||||||
\(768\) | −1.84866 | −0.0667079 | ||||||||
\(769\) | 35.8345 | 1.29222 | 0.646112 | − | 0.763243i | \(-0.276394\pi\) | ||||
0.646112 | + | 0.763243i | \(0.276394\pi\) | |||||||
\(770\) | −4.52068 | −0.162914 | ||||||||
\(771\) | 1.13548 | 0.0408933 | ||||||||
\(772\) | −33.2372 | −1.19623 | ||||||||
\(773\) | −12.5653 | −0.451942 | −0.225971 | − | 0.974134i | \(-0.572556\pi\) | ||||
−0.225971 | + | 0.974134i | \(0.572556\pi\) | |||||||
\(774\) | 28.5822 | 1.02736 | ||||||||
\(775\) | 18.8713 | 0.677875 | ||||||||
\(776\) | 44.3773 | 1.59305 | ||||||||
\(777\) | 0.108599 | 0.00389595 | ||||||||
\(778\) | 22.9240 | 0.821867 | ||||||||
\(779\) | 1.88279 | 0.0674578 | ||||||||
\(780\) | 0.377502 | 0.0135167 | ||||||||
\(781\) | −21.0824 | −0.754389 | ||||||||
\(782\) | 5.85523 | 0.209382 | ||||||||
\(783\) | 2.05443 | 0.0734192 | ||||||||
\(784\) | −12.8538 | −0.459065 | ||||||||
\(785\) | 36.4102 | 1.29954 | ||||||||
\(786\) | 2.60778 | 0.0930165 | ||||||||
\(787\) | −43.6081 | −1.55446 | −0.777231 | − | 0.629216i | \(-0.783376\pi\) | ||||
−0.777231 | + | 0.629216i | \(0.783376\pi\) | |||||||
\(788\) | −17.1034 | −0.609283 | ||||||||
\(789\) | 0.0161462 | 0.000574820 0 | ||||||||
\(790\) | −83.9039 | −2.98517 | ||||||||
\(791\) | −3.48042 | −0.123749 | ||||||||
\(792\) | −15.6724 | −0.556893 | ||||||||
\(793\) | 0.451293 | 0.0160259 | ||||||||
\(794\) | 33.6122 | 1.19285 | ||||||||
\(795\) | −0.184912 | −0.00655814 | ||||||||
\(796\) | −77.9916 | −2.76434 | ||||||||
\(797\) | −22.1270 | −0.783779 | −0.391889 | − | 0.920012i | \(-0.628178\pi\) | ||||
−0.391889 | + | 0.920012i | \(0.628178\pi\) | |||||||
\(798\) | −0.215266 | −0.00762032 | ||||||||
\(799\) | 4.28566 | 0.151616 | ||||||||
\(800\) | 18.6688 | 0.660043 | ||||||||
\(801\) | −17.8718 | −0.631469 | ||||||||
\(802\) | −69.8198 | −2.46542 | ||||||||
\(803\) | −8.70826 | −0.307308 | ||||||||
\(804\) | 2.87139 | 0.101266 | ||||||||
\(805\) | 1.40299 | 0.0494489 | ||||||||
\(806\) | −3.47158 | −0.122281 | ||||||||
\(807\) | −1.38371 | −0.0487089 | ||||||||
\(808\) | 42.7727 | 1.50474 | ||||||||
\(809\) | −1.43560 | −0.0504731 | −0.0252366 | − | 0.999682i | \(-0.508034\pi\) | ||||
−0.0252366 | + | 0.999682i | \(0.508034\pi\) | |||||||
\(810\) | −69.7175 | −2.44962 | ||||||||
\(811\) | −22.2219 | −0.780318 | −0.390159 | − | 0.920748i | \(-0.627580\pi\) | ||||
−0.390159 | + | 0.920748i | \(0.627580\pi\) | |||||||
\(812\) | 7.49640 | 0.263072 | ||||||||
\(813\) | −0.254562 | −0.00892787 | ||||||||
\(814\) | −11.5649 | −0.405349 | ||||||||
\(815\) | −15.2290 | −0.533448 | ||||||||
\(816\) | 0.329589 | 0.0115379 | ||||||||
\(817\) | −12.0724 | −0.422361 | ||||||||
\(818\) | −20.9849 | −0.733719 | ||||||||
\(819\) | 0.573624 | 0.0200441 | ||||||||
\(820\) | −7.46672 | −0.260749 | ||||||||
\(821\) | 20.9555 | 0.731351 | 0.365675 | − | 0.930742i | \(-0.380838\pi\) | ||||
0.365675 | + | 0.930742i | \(0.380838\pi\) | |||||||
\(822\) | 1.98291 | 0.0691618 | ||||||||
\(823\) | 26.3829 | 0.919649 | 0.459824 | − | 0.888010i | \(-0.347912\pi\) | ||||
0.459824 | + | 0.888010i | \(0.347912\pi\) | |||||||
\(824\) | −20.5167 | −0.714734 | ||||||||
\(825\) | −0.555771 | −0.0193494 | ||||||||
\(826\) | −9.10446 | −0.316785 | ||||||||
\(827\) | 36.4958 | 1.26908 | 0.634542 | − | 0.772888i | \(-0.281189\pi\) | ||||
0.634542 | + | 0.772888i | \(0.281189\pi\) | |||||||
\(828\) | 10.8539 | 0.377198 | ||||||||
\(829\) | −36.8024 | −1.27820 | −0.639100 | − | 0.769124i | \(-0.720693\pi\) | ||||
−0.639100 | + | 0.769124i | \(0.720693\pi\) | |||||||
\(830\) | −6.52089 | −0.226343 | ||||||||
\(831\) | −1.25079 | −0.0433895 | ||||||||
\(832\) | −5.12432 | −0.177654 | ||||||||
\(833\) | −16.8320 | −0.583196 | ||||||||
\(834\) | 2.50887 | 0.0868752 | ||||||||
\(835\) | 46.8720 | 1.62207 | ||||||||
\(836\) | 14.7718 | 0.510895 | ||||||||
\(837\) | −1.38641 | −0.0479214 | ||||||||
\(838\) | −4.49602 | −0.155312 | ||||||||
\(839\) | 8.80000 | 0.303810 | 0.151905 | − | 0.988395i | \(-0.451459\pi\) | ||||
0.151905 | + | 0.988395i | \(0.451459\pi\) | |||||||
\(840\) | 0.382563 | 0.0131997 | ||||||||
\(841\) | −5.57217 | −0.192144 | ||||||||
\(842\) | −18.4038 | −0.634238 | ||||||||
\(843\) | −0.0369100 | −0.00127125 | ||||||||
\(844\) | −79.2570 | −2.72814 | ||||||||
\(845\) | −42.0183 | −1.44547 | ||||||||
\(846\) | 12.3286 | 0.423868 | ||||||||
\(847\) | 3.91204 | 0.134419 | ||||||||
\(848\) | −1.49998 | −0.0515097 | ||||||||
\(849\) | 0.279482 | 0.00959178 | ||||||||
\(850\) | −33.8280 | −1.16029 | ||||||||
\(851\) | 3.58915 | 0.123034 | ||||||||
\(852\) | 3.98126 | 0.136396 | ||||||||
\(853\) | 36.2770 | 1.24210 | 0.621051 | − | 0.783770i | \(-0.286706\pi\) | ||||
0.621051 | + | 0.783770i | \(0.286706\pi\) | |||||||
\(854\) | 1.02057 | 0.0349232 | ||||||||
\(855\) | 29.4965 | 1.00876 | ||||||||
\(856\) | 79.1411 | 2.70499 | ||||||||
\(857\) | 10.2509 | 0.350165 | 0.175082 | − | 0.984554i | \(-0.443981\pi\) | ||||
0.175082 | + | 0.984554i | \(0.443981\pi\) | |||||||
\(858\) | 0.102240 | 0.00349042 | ||||||||
\(859\) | 35.5395 | 1.21259 | 0.606295 | − | 0.795239i | \(-0.292655\pi\) | ||||
0.606295 | + | 0.795239i | \(0.292655\pi\) | |||||||
\(860\) | 47.8767 | 1.63258 | ||||||||
\(861\) | 0.0189896 | 0.000647164 0 | ||||||||
\(862\) | −84.2621 | −2.86998 | ||||||||
\(863\) | 38.5309 | 1.31161 | 0.655804 | − | 0.754931i | \(-0.272330\pi\) | ||||
0.655804 | + | 0.754931i | \(0.272330\pi\) | |||||||
\(864\) | −1.37154 | −0.0466607 | ||||||||
\(865\) | 7.41620 | 0.252158 | ||||||||
\(866\) | 4.60176 | 0.156374 | ||||||||
\(867\) | −0.772012 | −0.0262189 | ||||||||
\(868\) | −5.05889 | −0.171710 | ||||||||
\(869\) | −14.6429 | −0.496728 | ||||||||
\(870\) | 2.66798 | 0.0904530 | ||||||||
\(871\) | 5.01535 | 0.169939 | ||||||||
\(872\) | −49.5893 | −1.67931 | ||||||||
\(873\) | 34.5098 | 1.16798 | ||||||||
\(874\) | −7.11445 | −0.240650 | ||||||||
\(875\) | −1.09069 | −0.0368721 | ||||||||
\(876\) | 1.64449 | 0.0555622 | ||||||||
\(877\) | −13.1817 | −0.445116 | −0.222558 | − | 0.974919i | \(-0.571441\pi\) | ||||
−0.222558 | + | 0.974919i | \(0.571441\pi\) | |||||||
\(878\) | −92.2389 | −3.11291 | ||||||||
\(879\) | −1.96869 | −0.0664023 | ||||||||
\(880\) | −8.41006 | −0.283503 | ||||||||
\(881\) | 52.2107 | 1.75902 | 0.879511 | − | 0.475878i | \(-0.157870\pi\) | ||||
0.879511 | + | 0.475878i | \(0.157870\pi\) | |||||||
\(882\) | −48.4211 | −1.63042 | ||||||||
\(883\) | 1.13890 | 0.0383269 | 0.0191635 | − | 0.999816i | \(-0.493900\pi\) | ||||
0.0191635 | + | 0.999816i | \(0.493900\pi\) | |||||||
\(884\) | 4.01002 | 0.134871 | ||||||||
\(885\) | −2.08799 | −0.0701869 | ||||||||
\(886\) | −61.5422 | −2.06755 | ||||||||
\(887\) | −39.3793 | −1.32223 | −0.661113 | − | 0.750286i | \(-0.729916\pi\) | ||||
−0.661113 | + | 0.750286i | \(0.729916\pi\) | |||||||
\(888\) | 0.978679 | 0.0328423 | ||||||||
\(889\) | 5.28338 | 0.177199 | ||||||||
\(890\) | −46.4573 | −1.55725 | ||||||||
\(891\) | −12.1671 | −0.407614 | ||||||||
\(892\) | −31.0154 | −1.03847 | ||||||||
\(893\) | −5.20733 | −0.174257 | ||||||||
\(894\) | −3.42802 | −0.114650 | ||||||||
\(895\) | −56.5786 | −1.89121 | ||||||||
\(896\) | −8.82640 | −0.294869 | ||||||||
\(897\) | −0.0317301 | −0.00105944 | ||||||||
\(898\) | −22.8368 | −0.762073 | ||||||||
\(899\) | −15.8101 | −0.527295 | ||||||||
\(900\) | −62.7073 | −2.09024 | ||||||||
\(901\) | −1.96423 | −0.0654379 | ||||||||
\(902\) | −2.02224 | −0.0673332 | ||||||||
\(903\) | −0.121762 | −0.00405197 | ||||||||
\(904\) | −31.3652 | −1.04319 | ||||||||
\(905\) | −47.6118 | −1.58267 | ||||||||
\(906\) | −0.753053 | −0.0250185 | ||||||||
\(907\) | 23.4040 | 0.777115 | 0.388558 | − | 0.921424i | \(-0.372973\pi\) | ||||
0.388558 | + | 0.921424i | \(0.372973\pi\) | |||||||
\(908\) | −30.1941 | −1.00203 | ||||||||
\(909\) | 33.2620 | 1.10323 | ||||||||
\(910\) | 1.49112 | 0.0494302 | ||||||||
\(911\) | 43.5934 | 1.44431 | 0.722157 | − | 0.691729i | \(-0.243151\pi\) | ||||
0.722157 | + | 0.691729i | \(0.243151\pi\) | |||||||
\(912\) | −0.400470 | −0.0132609 | ||||||||
\(913\) | −1.13803 | −0.0376632 | ||||||||
\(914\) | 13.8246 | 0.457276 | ||||||||
\(915\) | 0.234054 | 0.00773759 | ||||||||
\(916\) | −27.0845 | −0.894898 | ||||||||
\(917\) | 6.63757 | 0.219192 | ||||||||
\(918\) | 2.48524 | 0.0820251 | ||||||||
\(919\) | 9.27019 | 0.305795 | 0.152898 | − | 0.988242i | \(-0.451140\pi\) | ||||
0.152898 | + | 0.988242i | \(0.451140\pi\) | |||||||
\(920\) | 12.6436 | 0.416847 | ||||||||
\(921\) | 1.07442 | 0.0354034 | ||||||||
\(922\) | 27.3828 | 0.901805 | ||||||||
\(923\) | 6.95393 | 0.228891 | ||||||||
\(924\) | 0.148987 | 0.00490133 | ||||||||
\(925\) | −20.7360 | −0.681794 | ||||||||
\(926\) | 34.8629 | 1.14567 | ||||||||
\(927\) | −15.9547 | −0.524023 | ||||||||
\(928\) | −15.6405 | −0.513424 | ||||||||
\(929\) | 37.3546 | 1.22557 | 0.612783 | − | 0.790251i | \(-0.290050\pi\) | ||||
0.612783 | + | 0.790251i | \(0.290050\pi\) | |||||||
\(930\) | −1.80046 | −0.0590395 | ||||||||
\(931\) | 20.4519 | 0.670285 | ||||||||
\(932\) | −18.0628 | −0.591667 | ||||||||
\(933\) | −0.566979 | −0.0185621 | ||||||||
\(934\) | −13.4817 | −0.441135 | ||||||||
\(935\) | −11.0130 | −0.360162 | ||||||||
\(936\) | 5.16944 | 0.168969 | ||||||||
\(937\) | −34.9379 | −1.14137 | −0.570686 | − | 0.821168i | \(-0.693323\pi\) | ||||
−0.570686 | + | 0.821168i | \(0.693323\pi\) | |||||||
\(938\) | 11.3419 | 0.370326 | ||||||||
\(939\) | 2.27939 | 0.0743850 | ||||||||
\(940\) | 20.6511 | 0.673566 | ||||||||
\(941\) | 32.4318 | 1.05724 | 0.528622 | − | 0.848857i | \(-0.322709\pi\) | ||||
0.528622 | + | 0.848857i | \(0.322709\pi\) | |||||||
\(942\) | −1.86220 | −0.0606736 | ||||||||
\(943\) | 0.627600 | 0.0204375 | ||||||||
\(944\) | −16.9375 | −0.551269 | ||||||||
\(945\) | 0.595496 | 0.0193715 | ||||||||
\(946\) | 12.9666 | 0.421581 | ||||||||
\(947\) | −43.1450 | −1.40202 | −0.701012 | − | 0.713150i | \(-0.747268\pi\) | ||||
−0.701012 | + | 0.713150i | \(0.747268\pi\) | |||||||
\(948\) | 2.76521 | 0.0898098 | ||||||||
\(949\) | 2.87237 | 0.0932411 | ||||||||
\(950\) | 41.1031 | 1.33356 | ||||||||
\(951\) | 0.108693 | 0.00352462 | ||||||||
\(952\) | 4.06378 | 0.131708 | ||||||||
\(953\) | 52.6746 | 1.70630 | 0.853148 | − | 0.521669i | \(-0.174690\pi\) | ||||
0.853148 | + | 0.521669i | \(0.174690\pi\) | |||||||
\(954\) | −5.65053 | −0.182943 | ||||||||
\(955\) | −12.1797 | −0.394127 | ||||||||
\(956\) | −4.15115 | −0.134258 | ||||||||
\(957\) | 0.465617 | 0.0150513 | ||||||||
\(958\) | −60.7027 | −1.96121 | ||||||||
\(959\) | 5.04708 | 0.162979 | ||||||||
\(960\) | −2.65762 | −0.0857745 | ||||||||
\(961\) | −20.3307 | −0.655829 | ||||||||
\(962\) | 3.81461 | 0.122988 | ||||||||
\(963\) | 61.5437 | 1.98322 | ||||||||
\(964\) | 20.5302 | 0.661234 | ||||||||
\(965\) | −30.1087 | −0.969233 | ||||||||
\(966\) | −0.0717557 | −0.00230870 | ||||||||
\(967\) | −2.45234 | −0.0788620 | −0.0394310 | − | 0.999222i | \(-0.512555\pi\) | ||||
−0.0394310 | + | 0.999222i | \(0.512555\pi\) | |||||||
\(968\) | 35.2549 | 1.13314 | ||||||||
\(969\) | −0.524415 | −0.0168466 | ||||||||
\(970\) | 89.7074 | 2.88033 | ||||||||
\(971\) | −32.5981 | −1.04612 | −0.523062 | − | 0.852295i | \(-0.675210\pi\) | ||||
−0.523062 | + | 0.852295i | \(0.675210\pi\) | |||||||
\(972\) | 6.91229 | 0.221712 | ||||||||
\(973\) | 6.38582 | 0.204720 | ||||||||
\(974\) | 40.1770 | 1.28736 | ||||||||
\(975\) | 0.183318 | 0.00587087 | ||||||||
\(976\) | 1.89862 | 0.0607734 | ||||||||
\(977\) | 18.3561 | 0.587263 | 0.293632 | − | 0.955919i | \(-0.405136\pi\) | ||||
0.293632 | + | 0.955919i | \(0.405136\pi\) | |||||||
\(978\) | 0.778884 | 0.0249060 | ||||||||
\(979\) | −8.10774 | −0.259125 | ||||||||
\(980\) | −81.1079 | −2.59090 | ||||||||
\(981\) | −38.5629 | −1.23122 | ||||||||
\(982\) | −81.9255 | −2.61435 | ||||||||
\(983\) | −20.6927 | −0.659994 | −0.329997 | − | 0.943982i | \(-0.607048\pi\) | ||||
−0.329997 | + | 0.943982i | \(0.607048\pi\) | |||||||
\(984\) | 0.171132 | 0.00545550 | ||||||||
\(985\) | −15.4935 | −0.493663 | ||||||||
\(986\) | 28.3406 | 0.902550 | ||||||||
\(987\) | −0.0525207 | −0.00167175 | ||||||||
\(988\) | −4.87241 | −0.155012 | ||||||||
\(989\) | −4.02417 | −0.127961 | ||||||||
\(990\) | −31.6812 | −1.00690 | ||||||||
\(991\) | −3.84181 | −0.122039 | −0.0610196 | − | 0.998137i | \(-0.519435\pi\) | ||||
−0.0610196 | + | 0.998137i | \(0.519435\pi\) | |||||||
\(992\) | 10.5548 | 0.335117 | ||||||||
\(993\) | −1.42682 | −0.0452787 | ||||||||
\(994\) | 15.7259 | 0.498794 | ||||||||
\(995\) | −70.6504 | −2.23977 | ||||||||
\(996\) | 0.214908 | 0.00680962 | ||||||||
\(997\) | −8.35678 | −0.264662 | −0.132331 | − | 0.991206i | \(-0.542246\pi\) | ||||
−0.132331 | + | 0.991206i | \(0.542246\pi\) | |||||||
\(998\) | 68.1299 | 2.15661 | ||||||||
\(999\) | 1.52341 | 0.0481984 |
(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 | 8027.2.a.d.1.12 | ✓ | 149 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.d.1.12 | ✓ | 149 | 1.1 | even | 1 | trivial |