Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(221,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 221.6 | ||
Root | \(0.264658 + 1.38923i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.221 |
Dual form | 370.2.d.c.221.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 2.24914 | 1.29854 | 0.649271 | − | 0.760557i | \(-0.275074\pi\) | ||||
0.649271 | + | 0.760557i | \(0.275074\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 2.24914i | 0.918208i | ||||||||
\(7\) | 1.52932 | 0.578027 | 0.289014 | − | 0.957325i | \(-0.406673\pi\) | ||||
0.289014 | + | 0.957325i | \(0.406673\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 2.05863 | 0.686211 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 2.71982 | 0.820058 | 0.410029 | − | 0.912073i | \(-0.365519\pi\) | ||||
0.410029 | + | 0.912073i | \(0.365519\pi\) | |||||||
\(12\) | −2.24914 | −0.649271 | ||||||||
\(13\) | − | 0.941367i | − | 0.261088i | −0.991443 | − | 0.130544i | \(-0.958328\pi\) | ||
0.991443 | − | 0.130544i | \(-0.0416724\pi\) | |||||||
\(14\) | 1.52932i | 0.408727i | ||||||||
\(15\) | − | 2.24914i | − | 0.580726i | ||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.83709i | 1.17317i | 0.809889 | + | 0.586583i | \(0.199527\pi\) | ||||
−0.809889 | + | 0.586583i | \(0.800473\pi\) | |||||||
\(18\) | 2.05863i | 0.485224i | ||||||||
\(19\) | 0.249141i | 0.0571568i | 0.999592 | + | 0.0285784i | \(0.00909802\pi\) | ||||
−0.999592 | + | 0.0285784i | \(0.990902\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | 3.43965 | 0.750593 | ||||||||
\(22\) | 2.71982i | 0.579868i | ||||||||
\(23\) | − | 0.941367i | − | 0.196289i | −0.995172 | − | 0.0981443i | \(-0.968709\pi\) | ||
0.995172 | − | 0.0981443i | \(-0.0312907\pi\) | |||||||
\(24\) | − | 2.24914i | − | 0.459104i | ||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0.941367 | 0.184617 | ||||||||
\(27\) | −2.11727 | −0.407468 | ||||||||
\(28\) | −1.52932 | −0.289014 | ||||||||
\(29\) | − | 0.719824i | − | 0.133668i | −0.997764 | − | 0.0668340i | \(-0.978710\pi\) | ||
0.997764 | − | 0.0668340i | \(-0.0212898\pi\) | |||||||
\(30\) | 2.24914 | 0.410635 | ||||||||
\(31\) | − | 4.02760i | − | 0.723378i | −0.932299 | − | 0.361689i | \(-0.882200\pi\) | ||
0.932299 | − | 0.361689i | \(-0.117800\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 6.11727 | 1.06488 | ||||||||
\(34\) | −4.83709 | −0.829554 | ||||||||
\(35\) | − | 1.52932i | − | 0.258502i | ||||||
\(36\) | −2.05863 | −0.343106 | ||||||||
\(37\) | −4.71982 | + | 3.83709i | −0.775934 | + | 0.630814i | ||||
\(38\) | −0.249141 | −0.0404159 | ||||||||
\(39\) | − | 2.11727i | − | 0.339034i | ||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −8.27674 | −1.29261 | −0.646305 | − | 0.763079i | \(-0.723686\pi\) | ||||
−0.646305 | + | 0.763079i | \(0.723686\pi\) | |||||||
\(42\) | 3.43965i | 0.530749i | ||||||||
\(43\) | − | 2.71982i | − | 0.414769i | −0.978259 | − | 0.207385i | \(-0.933505\pi\) | ||
0.978259 | − | 0.207385i | \(-0.0664952\pi\) | |||||||
\(44\) | −2.71982 | −0.410029 | ||||||||
\(45\) | − | 2.05863i | − | 0.306883i | ||||||
\(46\) | 0.941367 | 0.138797 | ||||||||
\(47\) | −3.30777 | −0.482488 | −0.241244 | − | 0.970464i | \(-0.577555\pi\) | ||||
−0.241244 | + | 0.970464i | \(0.577555\pi\) | |||||||
\(48\) | 2.24914 | 0.324635 | ||||||||
\(49\) | −4.66119 | −0.665884 | ||||||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | 10.8793i | 1.52341i | ||||||||
\(52\) | 0.941367i | 0.130544i | ||||||||
\(53\) | 8.39400 | 1.15301 | 0.576503 | − | 0.817095i | \(-0.304417\pi\) | ||||
0.576503 | + | 0.817095i | \(0.304417\pi\) | |||||||
\(54\) | − | 2.11727i | − | 0.288123i | ||||||
\(55\) | − | 2.71982i | − | 0.366741i | ||||||
\(56\) | − | 1.52932i | − | 0.204364i | ||||||
\(57\) | 0.560352i | 0.0742204i | ||||||||
\(58\) | 0.719824 | 0.0945175 | ||||||||
\(59\) | 7.30777i | 0.951391i | 0.879610 | + | 0.475696i | \(0.157804\pi\) | ||||
−0.879610 | + | 0.475696i | \(0.842196\pi\) | |||||||
\(60\) | 2.24914i | 0.290363i | ||||||||
\(61\) | − | 6.83709i | − | 0.875400i | −0.899121 | − | 0.437700i | \(-0.855793\pi\) | ||
0.899121 | − | 0.437700i | \(-0.144207\pi\) | |||||||
\(62\) | 4.02760 | 0.511505 | ||||||||
\(63\) | 3.14830 | 0.396649 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −0.941367 | −0.116762 | ||||||||
\(66\) | 6.11727i | 0.752983i | ||||||||
\(67\) | −7.68879 | −0.939335 | −0.469668 | − | 0.882843i | \(-0.655626\pi\) | ||||
−0.469668 | + | 0.882843i | \(0.655626\pi\) | |||||||
\(68\) | − | 4.83709i | − | 0.586583i | ||||||
\(69\) | − | 2.11727i | − | 0.254889i | ||||||
\(70\) | 1.52932 | 0.182788 | ||||||||
\(71\) | −3.05863 | −0.362993 | −0.181496 | − | 0.983392i | \(-0.558094\pi\) | ||||
−0.181496 | + | 0.983392i | \(0.558094\pi\) | |||||||
\(72\) | − | 2.05863i | − | 0.242612i | ||||||
\(73\) | 9.11383 | 1.06669 | 0.533346 | − | 0.845897i | \(-0.320934\pi\) | ||||
0.533346 | + | 0.845897i | \(0.320934\pi\) | |||||||
\(74\) | −3.83709 | − | 4.71982i | −0.446053 | − | 0.548668i | ||||
\(75\) | −2.24914 | −0.259708 | ||||||||
\(76\) | − | 0.249141i | − | 0.0285784i | ||||||
\(77\) | 4.15947 | 0.474016 | ||||||||
\(78\) | 2.11727 | 0.239733 | ||||||||
\(79\) | 1.75086i | 0.196987i | 0.995138 | + | 0.0984935i | \(0.0314024\pi\) | ||||
−0.995138 | + | 0.0984935i | \(0.968598\pi\) | |||||||
\(80\) | − | 1.00000i | − | 0.111803i | ||||||
\(81\) | −10.9379 | −1.21533 | ||||||||
\(82\) | − | 8.27674i | − | 0.914013i | ||||||
\(83\) | 0.131874 | 0.0144751 | 0.00723754 | − | 0.999974i | \(-0.497696\pi\) | ||||
0.00723754 | + | 0.999974i | \(0.497696\pi\) | |||||||
\(84\) | −3.43965 | −0.375296 | ||||||||
\(85\) | 4.83709 | 0.524656 | ||||||||
\(86\) | 2.71982 | 0.293286 | ||||||||
\(87\) | − | 1.61899i | − | 0.173573i | ||||||
\(88\) | − | 2.71982i | − | 0.289934i | ||||||
\(89\) | 8.99656i | 0.953634i | 0.879003 | + | 0.476817i | \(0.158210\pi\) | ||||
−0.879003 | + | 0.476817i | \(0.841790\pi\) | |||||||
\(90\) | 2.05863 | 0.216999 | ||||||||
\(91\) | − | 1.43965i | − | 0.150916i | ||||||
\(92\) | 0.941367i | 0.0981443i | ||||||||
\(93\) | − | 9.05863i | − | 0.939337i | ||||||
\(94\) | − | 3.30777i | − | 0.341171i | ||||||
\(95\) | 0.249141 | 0.0255613 | ||||||||
\(96\) | 2.24914i | 0.229552i | ||||||||
\(97\) | − | 16.2767i | − | 1.65265i | −0.563192 | − | 0.826326i | \(-0.690427\pi\) | ||
0.563192 | − | 0.826326i | \(-0.309573\pi\) | |||||||
\(98\) | − | 4.66119i | − | 0.470851i | ||||||
\(99\) | 5.59912 | 0.562733 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −11.1138 | −1.10587 | −0.552934 | − | 0.833225i | \(-0.686492\pi\) | ||||
−0.552934 | + | 0.833225i | \(0.686492\pi\) | |||||||
\(102\) | −10.8793 | −1.07721 | ||||||||
\(103\) | − | 14.1725i | − | 1.39645i | −0.715876 | − | 0.698227i | \(-0.753973\pi\) | ||
0.715876 | − | 0.698227i | \(-0.246027\pi\) | |||||||
\(104\) | −0.941367 | −0.0923086 | ||||||||
\(105\) | − | 3.43965i | − | 0.335675i | ||||||
\(106\) | 8.39400i | 0.815298i | ||||||||
\(107\) | 10.6922 | 1.03366 | 0.516828 | − | 0.856089i | \(-0.327113\pi\) | ||||
0.516828 | + | 0.856089i | \(0.327113\pi\) | |||||||
\(108\) | 2.11727 | 0.203734 | ||||||||
\(109\) | − | 12.2767i | − | 1.17590i | −0.808898 | − | 0.587949i | \(-0.799936\pi\) | ||
0.808898 | − | 0.587949i | \(-0.200064\pi\) | |||||||
\(110\) | 2.71982 | 0.259325 | ||||||||
\(111\) | −10.6155 | + | 8.63016i | −1.00758 | + | 0.819138i | ||||
\(112\) | 1.52932 | 0.144507 | ||||||||
\(113\) | 2.95436i | 0.277922i | 0.990298 | + | 0.138961i | \(0.0443763\pi\) | ||||
−0.990298 | + | 0.138961i | \(0.955624\pi\) | |||||||
\(114\) | −0.560352 | −0.0524818 | ||||||||
\(115\) | −0.941367 | −0.0877829 | ||||||||
\(116\) | 0.719824i | 0.0668340i | ||||||||
\(117\) | − | 1.93793i | − | 0.179162i | ||||||
\(118\) | −7.30777 | −0.672735 | ||||||||
\(119\) | 7.39744i | 0.678122i | ||||||||
\(120\) | −2.24914 | −0.205318 | ||||||||
\(121\) | −3.60256 | −0.327505 | ||||||||
\(122\) | 6.83709 | 0.619001 | ||||||||
\(123\) | −18.6155 | −1.67851 | ||||||||
\(124\) | 4.02760i | 0.361689i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 3.14830i | 0.280473i | ||||||||
\(127\) | 8.30434 | 0.736891 | 0.368445 | − | 0.929649i | \(-0.379890\pi\) | ||||
0.368445 | + | 0.929649i | \(0.379890\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | − | 6.11727i | − | 0.538595i | ||||||
\(130\) | − | 0.941367i | − | 0.0825633i | ||||||
\(131\) | 11.0732i | 0.967474i | 0.875214 | + | 0.483737i | \(0.160721\pi\) | ||||
−0.875214 | + | 0.483737i | \(0.839279\pi\) | |||||||
\(132\) | −6.11727 | −0.532440 | ||||||||
\(133\) | 0.381015i | 0.0330382i | ||||||||
\(134\) | − | 7.68879i | − | 0.664210i | ||||||
\(135\) | 2.11727i | 0.182225i | ||||||||
\(136\) | 4.83709 | 0.414777 | ||||||||
\(137\) | 0.325819 | 0.0278366 | 0.0139183 | − | 0.999903i | \(-0.495570\pi\) | ||||
0.0139183 | + | 0.999903i | \(0.495570\pi\) | |||||||
\(138\) | 2.11727 | 0.180234 | ||||||||
\(139\) | −13.3906 | −1.13577 | −0.567887 | − | 0.823107i | \(-0.692239\pi\) | ||||
−0.567887 | + | 0.823107i | \(0.692239\pi\) | |||||||
\(140\) | 1.52932i | 0.129251i | ||||||||
\(141\) | −7.43965 | −0.626531 | ||||||||
\(142\) | − | 3.05863i | − | 0.256675i | ||||||
\(143\) | − | 2.56035i | − | 0.214107i | ||||||
\(144\) | 2.05863 | 0.171553 | ||||||||
\(145\) | −0.719824 | −0.0597781 | ||||||||
\(146\) | 9.11383i | 0.754266i | ||||||||
\(147\) | −10.4837 | −0.864679 | ||||||||
\(148\) | 4.71982 | − | 3.83709i | 0.387967 | − | 0.315407i | ||||
\(149\) | 8.44309 | 0.691685 | 0.345842 | − | 0.938293i | \(-0.387593\pi\) | ||||
0.345842 | + | 0.938293i | \(0.387593\pi\) | |||||||
\(150\) | − | 2.24914i | − | 0.183642i | ||||||
\(151\) | −4.94137 | −0.402123 | −0.201061 | − | 0.979579i | \(-0.564439\pi\) | ||||
−0.201061 | + | 0.979579i | \(0.564439\pi\) | |||||||
\(152\) | 0.249141 | 0.0202080 | ||||||||
\(153\) | 9.95779i | 0.805040i | ||||||||
\(154\) | 4.15947i | 0.335180i | ||||||||
\(155\) | −4.02760 | −0.323504 | ||||||||
\(156\) | 2.11727i | 0.169517i | ||||||||
\(157\) | 19.2733 | 1.53818 | 0.769088 | − | 0.639142i | \(-0.220711\pi\) | ||||
0.769088 | + | 0.639142i | \(0.220711\pi\) | |||||||
\(158\) | −1.75086 | −0.139291 | ||||||||
\(159\) | 18.8793 | 1.49723 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | − | 1.43965i | − | 0.113460i | ||||||
\(162\) | − | 10.9379i | − | 0.859365i | ||||||
\(163\) | 17.3354i | 1.35781i | 0.734226 | + | 0.678906i | \(0.237545\pi\) | ||||
−0.734226 | + | 0.678906i | \(0.762455\pi\) | |||||||
\(164\) | 8.27674 | 0.646305 | ||||||||
\(165\) | − | 6.11727i | − | 0.476229i | ||||||
\(166\) | 0.131874i | 0.0102354i | ||||||||
\(167\) | 17.0518i | 1.31950i | 0.751483 | + | 0.659752i | \(0.229339\pi\) | ||||
−0.751483 | + | 0.659752i | \(0.770661\pi\) | |||||||
\(168\) | − | 3.43965i | − | 0.265375i | ||||||
\(169\) | 12.1138 | 0.931833 | ||||||||
\(170\) | 4.83709i | 0.370988i | ||||||||
\(171\) | 0.512889i | 0.0392216i | ||||||||
\(172\) | 2.71982i | 0.207385i | ||||||||
\(173\) | 10.7198 | 0.815013 | 0.407507 | − | 0.913202i | \(-0.366398\pi\) | ||||
0.407507 | + | 0.913202i | \(0.366398\pi\) | |||||||
\(174\) | 1.61899 | 0.122735 | ||||||||
\(175\) | −1.52932 | −0.115605 | ||||||||
\(176\) | 2.71982 | 0.205014 | ||||||||
\(177\) | 16.4362i | 1.23542i | ||||||||
\(178\) | −8.99656 | −0.674321 | ||||||||
\(179\) | 9.48024i | 0.708586i | 0.935134 | + | 0.354293i | \(0.115278\pi\) | ||||
−0.935134 | + | 0.354293i | \(0.884722\pi\) | |||||||
\(180\) | 2.05863i | 0.153441i | ||||||||
\(181\) | 20.9966 | 1.56066 | 0.780331 | − | 0.625367i | \(-0.215051\pi\) | ||||
0.780331 | + | 0.625367i | \(0.215051\pi\) | |||||||
\(182\) | 1.43965 | 0.106714 | ||||||||
\(183\) | − | 15.3776i | − | 1.13674i | ||||||
\(184\) | −0.941367 | −0.0693985 | ||||||||
\(185\) | 3.83709 | + | 4.71982i | 0.282108 | + | 0.347008i | ||||
\(186\) | 9.05863 | 0.664211 | ||||||||
\(187\) | 13.1560i | 0.962064i | ||||||||
\(188\) | 3.30777 | 0.241244 | ||||||||
\(189\) | −3.23797 | −0.235528 | ||||||||
\(190\) | 0.249141i | 0.0180746i | ||||||||
\(191\) | 11.0862i | 0.802172i | 0.916041 | + | 0.401086i | \(0.131367\pi\) | ||||
−0.916041 | + | 0.401086i | \(0.868633\pi\) | |||||||
\(192\) | −2.24914 | −0.162318 | ||||||||
\(193\) | − | 2.23453i | − | 0.160845i | −0.996761 | − | 0.0804226i | \(-0.974373\pi\) | ||
0.996761 | − | 0.0804226i | \(-0.0256270\pi\) | |||||||
\(194\) | 16.2767 | 1.16860 | ||||||||
\(195\) | −2.11727 | −0.151621 | ||||||||
\(196\) | 4.66119 | 0.332942 | ||||||||
\(197\) | 13.4396 | 0.957535 | 0.478768 | − | 0.877942i | \(-0.341084\pi\) | ||||
0.478768 | + | 0.877942i | \(0.341084\pi\) | |||||||
\(198\) | 5.59912i | 0.397912i | ||||||||
\(199\) | 23.4802i | 1.66447i | 0.554423 | + | 0.832235i | \(0.312939\pi\) | ||||
−0.554423 | + | 0.832235i | \(0.687061\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | −17.2932 | −1.21977 | ||||||||
\(202\) | − | 11.1138i | − | 0.781966i | ||||||
\(203\) | − | 1.10084i | − | 0.0772637i | ||||||
\(204\) | − | 10.8793i | − | 0.761703i | ||||||
\(205\) | 8.27674i | 0.578072i | ||||||||
\(206\) | 14.1725 | 0.987442 | ||||||||
\(207\) | − | 1.93793i | − | 0.134695i | ||||||
\(208\) | − | 0.941367i | − | 0.0652720i | ||||||
\(209\) | 0.677618i | 0.0468718i | ||||||||
\(210\) | 3.43965 | 0.237358 | ||||||||
\(211\) | −19.7716 | −1.36113 | −0.680566 | − | 0.732687i | \(-0.738266\pi\) | ||||
−0.680566 | + | 0.732687i | \(0.738266\pi\) | |||||||
\(212\) | −8.39400 | −0.576503 | ||||||||
\(213\) | −6.87930 | −0.471362 | ||||||||
\(214\) | 10.6922i | 0.730906i | ||||||||
\(215\) | −2.71982 | −0.185490 | ||||||||
\(216\) | 2.11727i | 0.144062i | ||||||||
\(217\) | − | 6.15947i | − | 0.418132i | ||||||
\(218\) | 12.2767 | 0.831486 | ||||||||
\(219\) | 20.4983 | 1.38515 | ||||||||
\(220\) | 2.71982i | 0.183370i | ||||||||
\(221\) | 4.55348 | 0.306300 | ||||||||
\(222\) | −8.63016 | − | 10.6155i | −0.579218 | − | 0.712469i | ||||
\(223\) | −9.14143 | −0.612155 | −0.306078 | − | 0.952007i | \(-0.599017\pi\) | ||||
−0.306078 | + | 0.952007i | \(0.599017\pi\) | |||||||
\(224\) | 1.52932i | 0.102182i | ||||||||
\(225\) | −2.05863 | −0.137242 | ||||||||
\(226\) | −2.95436 | −0.196521 | ||||||||
\(227\) | 18.7198i | 1.24248i | 0.783621 | + | 0.621239i | \(0.213370\pi\) | ||||
−0.783621 | + | 0.621239i | \(0.786630\pi\) | |||||||
\(228\) | − | 0.560352i | − | 0.0371102i | ||||||
\(229\) | −25.1138 | −1.65957 | −0.829784 | − | 0.558084i | \(-0.811537\pi\) | ||||
−0.829784 | + | 0.558084i | \(0.811537\pi\) | |||||||
\(230\) | − | 0.941367i | − | 0.0620719i | ||||||
\(231\) | 9.35524 | 0.615529 | ||||||||
\(232\) | −0.719824 | −0.0472588 | ||||||||
\(233\) | 20.4362 | 1.33882 | 0.669410 | − | 0.742893i | \(-0.266547\pi\) | ||||
0.669410 | + | 0.742893i | \(0.266547\pi\) | |||||||
\(234\) | 1.93793 | 0.126686 | ||||||||
\(235\) | 3.30777i | 0.215775i | ||||||||
\(236\) | − | 7.30777i | − | 0.475696i | ||||||
\(237\) | 3.93793i | 0.255796i | ||||||||
\(238\) | −7.39744 | −0.479505 | ||||||||
\(239\) | − | 8.91377i | − | 0.576584i | −0.957543 | − | 0.288292i | \(-0.906913\pi\) | ||
0.957543 | − | 0.288292i | \(-0.0930873\pi\) | |||||||
\(240\) | − | 2.24914i | − | 0.145181i | ||||||
\(241\) | − | 13.8827i | − | 0.894265i | −0.894468 | − | 0.447133i | \(-0.852445\pi\) | ||
0.894468 | − | 0.447133i | \(-0.147555\pi\) | |||||||
\(242\) | − | 3.60256i | − | 0.231581i | ||||||
\(243\) | −18.2491 | −1.17068 | ||||||||
\(244\) | 6.83709i | 0.437700i | ||||||||
\(245\) | 4.66119i | 0.297793i | ||||||||
\(246\) | − | 18.6155i | − | 1.18688i | ||||||
\(247\) | 0.234533 | 0.0149230 | ||||||||
\(248\) | −4.02760 | −0.255753 | ||||||||
\(249\) | 0.296604 | 0.0187965 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | − | 3.80605i | − | 0.240236i | −0.992760 | − | 0.120118i | \(-0.961673\pi\) | ||
0.992760 | − | 0.120118i | \(-0.0383273\pi\) | |||||||
\(252\) | −3.14830 | −0.198324 | ||||||||
\(253\) | − | 2.56035i | − | 0.160968i | ||||||
\(254\) | 8.30434i | 0.521060i | ||||||||
\(255\) | 10.8793 | 0.681288 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.78801i | 0.548181i | 0.961704 | + | 0.274090i | \(0.0883768\pi\) | ||||
−0.961704 | + | 0.274090i | \(0.911623\pi\) | |||||||
\(258\) | 6.11727 | 0.380844 | ||||||||
\(259\) | −7.21811 | + | 5.86813i | −0.448511 | + | 0.364628i | ||||
\(260\) | 0.941367 | 0.0583811 | ||||||||
\(261\) | − | 1.48185i | − | 0.0917244i | ||||||
\(262\) | −11.0732 | −0.684107 | ||||||||
\(263\) | −10.4707 | −0.645650 | −0.322825 | − | 0.946459i | \(-0.604633\pi\) | ||||
−0.322825 | + | 0.946459i | \(0.604633\pi\) | |||||||
\(264\) | − | 6.11727i | − | 0.376492i | ||||||
\(265\) | − | 8.39400i | − | 0.515640i | ||||||
\(266\) | −0.381015 | −0.0233615 | ||||||||
\(267\) | 20.2345i | 1.23833i | ||||||||
\(268\) | 7.68879 | 0.469668 | ||||||||
\(269\) | −5.88273 | −0.358677 | −0.179338 | − | 0.983787i | \(-0.557396\pi\) | ||||
−0.179338 | + | 0.983787i | \(0.557396\pi\) | |||||||
\(270\) | −2.11727 | −0.128853 | ||||||||
\(271\) | 7.61211 | 0.462403 | 0.231201 | − | 0.972906i | \(-0.425734\pi\) | ||||
0.231201 | + | 0.972906i | \(0.425734\pi\) | |||||||
\(272\) | 4.83709i | 0.293292i | ||||||||
\(273\) | − | 3.23797i | − | 0.195971i | ||||||
\(274\) | 0.325819i | 0.0196835i | ||||||||
\(275\) | −2.71982 | −0.164012 | ||||||||
\(276\) | 2.11727i | 0.127444i | ||||||||
\(277\) | − | 26.4914i | − | 1.59171i | −0.605484 | − | 0.795857i | \(-0.707021\pi\) | ||
0.605484 | − | 0.795857i | \(-0.292979\pi\) | |||||||
\(278\) | − | 13.3906i | − | 0.803113i | ||||||
\(279\) | − | 8.29135i | − | 0.496390i | ||||||
\(280\) | −1.52932 | −0.0913941 | ||||||||
\(281\) | − | 26.6707i | − | 1.59104i | −0.605925 | − | 0.795522i | \(-0.707197\pi\) | ||
0.605925 | − | 0.795522i | \(-0.292803\pi\) | |||||||
\(282\) | − | 7.43965i | − | 0.443025i | ||||||
\(283\) | − | 8.73281i | − | 0.519112i | −0.965728 | − | 0.259556i | \(-0.916424\pi\) | ||
0.965728 | − | 0.259556i | \(-0.0835762\pi\) | |||||||
\(284\) | 3.05863 | 0.181496 | ||||||||
\(285\) | 0.560352 | 0.0331924 | ||||||||
\(286\) | 2.56035 | 0.151397 | ||||||||
\(287\) | −12.6578 | −0.747164 | ||||||||
\(288\) | 2.05863i | 0.121306i | ||||||||
\(289\) | −6.39744 | −0.376320 | ||||||||
\(290\) | − | 0.719824i | − | 0.0422695i | ||||||
\(291\) | − | 36.6087i | − | 2.14604i | ||||||
\(292\) | −9.11383 | −0.533346 | ||||||||
\(293\) | 23.4819 | 1.37182 | 0.685912 | − | 0.727684i | \(-0.259403\pi\) | ||||
0.685912 | + | 0.727684i | \(0.259403\pi\) | |||||||
\(294\) | − | 10.4837i | − | 0.611420i | ||||||
\(295\) | 7.30777 | 0.425475 | ||||||||
\(296\) | 3.83709 | + | 4.71982i | 0.223026 | + | 0.274334i | ||||
\(297\) | −5.75859 | −0.334147 | ||||||||
\(298\) | 8.44309i | 0.489095i | ||||||||
\(299\) | −0.886172 | −0.0512486 | ||||||||
\(300\) | 2.24914 | 0.129854 | ||||||||
\(301\) | − | 4.15947i | − | 0.239748i | ||||||
\(302\) | − | 4.94137i | − | 0.284344i | ||||||
\(303\) | −24.9966 | −1.43601 | ||||||||
\(304\) | 0.249141i | 0.0142892i | ||||||||
\(305\) | −6.83709 | −0.391491 | ||||||||
\(306\) | −9.95779 | −0.569249 | ||||||||
\(307\) | 27.2457 | 1.55499 | 0.777497 | − | 0.628886i | \(-0.216489\pi\) | ||||
0.777497 | + | 0.628886i | \(0.216489\pi\) | |||||||
\(308\) | −4.15947 | −0.237008 | ||||||||
\(309\) | − | 31.8759i | − | 1.81335i | ||||||
\(310\) | − | 4.02760i | − | 0.228752i | ||||||
\(311\) | − | 17.7018i | − | 1.00378i | −0.864933 | − | 0.501888i | \(-0.832639\pi\) | ||
0.864933 | − | 0.501888i | \(-0.167361\pi\) | |||||||
\(312\) | −2.11727 | −0.119867 | ||||||||
\(313\) | 23.9931i | 1.35617i | 0.734983 | + | 0.678086i | \(0.237190\pi\) | ||||
−0.734983 | + | 0.678086i | \(0.762810\pi\) | |||||||
\(314\) | 19.2733i | 1.08766i | ||||||||
\(315\) | − | 3.14830i | − | 0.177387i | ||||||
\(316\) | − | 1.75086i | − | 0.0984935i | ||||||
\(317\) | −3.16291 | −0.177647 | −0.0888234 | − | 0.996047i | \(-0.528311\pi\) | ||||
−0.0888234 | + | 0.996047i | \(0.528311\pi\) | |||||||
\(318\) | 18.8793i | 1.05870i | ||||||||
\(319\) | − | 1.95779i | − | 0.109615i | ||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | 24.0483 | 1.34225 | ||||||||
\(322\) | 1.43965 | 0.0802284 | ||||||||
\(323\) | −1.20512 | −0.0670544 | ||||||||
\(324\) | 10.9379 | 0.607663 | ||||||||
\(325\) | 0.941367i | 0.0522176i | ||||||||
\(326\) | −17.3354 | −0.960117 | ||||||||
\(327\) | − | 27.6121i | − | 1.52695i | ||||||
\(328\) | 8.27674i | 0.457006i | ||||||||
\(329\) | −5.05863 | −0.278891 | ||||||||
\(330\) | 6.11727 | 0.336744 | ||||||||
\(331\) | − | 4.48367i | − | 0.246445i | −0.992379 | − | 0.123222i | \(-0.960677\pi\) | ||
0.992379 | − | 0.123222i | \(-0.0393229\pi\) | |||||||
\(332\) | −0.131874 | −0.00723754 | ||||||||
\(333\) | −9.71639 | + | 7.89916i | −0.532455 | + | 0.432871i | ||||
\(334\) | −17.0518 | −0.933031 | ||||||||
\(335\) | 7.68879i | 0.420083i | ||||||||
\(336\) | 3.43965 | 0.187648 | ||||||||
\(337\) | −11.2051 | −0.610382 | −0.305191 | − | 0.952291i | \(-0.598720\pi\) | ||||
−0.305191 | + | 0.952291i | \(0.598720\pi\) | |||||||
\(338\) | 12.1138i | 0.658905i | ||||||||
\(339\) | 6.64476i | 0.360894i | ||||||||
\(340\) | −4.83709 | −0.262328 | ||||||||
\(341\) | − | 10.9544i | − | 0.593212i | ||||||
\(342\) | −0.512889 | −0.0277339 | ||||||||
\(343\) | −17.8337 | −0.962927 | ||||||||
\(344\) | −2.71982 | −0.146643 | ||||||||
\(345\) | −2.11727 | −0.113990 | ||||||||
\(346\) | 10.7198i | 0.576301i | ||||||||
\(347\) | − | 13.9931i | − | 0.751190i | −0.926784 | − | 0.375595i | \(-0.877438\pi\) | ||
0.926784 | − | 0.375595i | \(-0.122562\pi\) | |||||||
\(348\) | 1.61899i | 0.0867867i | ||||||||
\(349\) | −6.56035 | −0.351168 | −0.175584 | − | 0.984464i | \(-0.556181\pi\) | ||||
−0.175584 | + | 0.984464i | \(0.556181\pi\) | |||||||
\(350\) | − | 1.52932i | − | 0.0817454i | ||||||
\(351\) | 1.99312i | 0.106385i | ||||||||
\(352\) | 2.71982i | 0.144967i | ||||||||
\(353\) | 36.5957i | 1.94779i | 0.226995 | + | 0.973896i | \(0.427110\pi\) | ||||
−0.226995 | + | 0.973896i | \(0.572890\pi\) | |||||||
\(354\) | −16.4362 | −0.873575 | ||||||||
\(355\) | 3.05863i | 0.162335i | ||||||||
\(356\) | − | 8.99656i | − | 0.476817i | ||||||
\(357\) | 16.6379i | 0.880570i | ||||||||
\(358\) | −9.48024 | −0.501046 | ||||||||
\(359\) | 21.2311 | 1.12053 | 0.560267 | − | 0.828312i | \(-0.310698\pi\) | ||||
0.560267 | + | 0.828312i | \(0.310698\pi\) | |||||||
\(360\) | −2.05863 | −0.108499 | ||||||||
\(361\) | 18.9379 | 0.996733 | ||||||||
\(362\) | 20.9966i | 1.10355i | ||||||||
\(363\) | −8.10266 | −0.425279 | ||||||||
\(364\) | 1.43965i | 0.0754581i | ||||||||
\(365\) | − | 9.11383i | − | 0.477040i | ||||||
\(366\) | 15.3776 | 0.803799 | ||||||||
\(367\) | 23.4932 | 1.22634 | 0.613168 | − | 0.789952i | \(-0.289895\pi\) | ||||
0.613168 | + | 0.789952i | \(0.289895\pi\) | |||||||
\(368\) | − | 0.941367i | − | 0.0490721i | ||||||
\(369\) | −17.0388 | −0.887003 | ||||||||
\(370\) | −4.71982 | + | 3.83709i | −0.245372 | + | 0.199481i | ||||
\(371\) | 12.8371 | 0.666469 | ||||||||
\(372\) | 9.05863i | 0.469668i | ||||||||
\(373\) | −7.55691 | −0.391282 | −0.195641 | − | 0.980676i | \(-0.562679\pi\) | ||||
−0.195641 | + | 0.980676i | \(0.562679\pi\) | |||||||
\(374\) | −13.1560 | −0.680282 | ||||||||
\(375\) | 2.24914i | 0.116145i | ||||||||
\(376\) | 3.30777i | 0.170585i | ||||||||
\(377\) | −0.677618 | −0.0348991 | ||||||||
\(378\) | − | 3.23797i | − | 0.166543i | ||||||
\(379\) | 12.2637 | 0.629946 | 0.314973 | − | 0.949101i | \(-0.398004\pi\) | ||||
0.314973 | + | 0.949101i | \(0.398004\pi\) | |||||||
\(380\) | −0.249141 | −0.0127806 | ||||||||
\(381\) | 18.6776 | 0.956883 | ||||||||
\(382\) | −11.0862 | −0.567221 | ||||||||
\(383\) | − | 33.5208i | − | 1.71283i | −0.516285 | − | 0.856417i | \(-0.672685\pi\) | ||
0.516285 | − | 0.856417i | \(-0.327315\pi\) | |||||||
\(384\) | − | 2.24914i | − | 0.114776i | ||||||
\(385\) | − | 4.15947i | − | 0.211986i | ||||||
\(386\) | 2.23453 | 0.113735 | ||||||||
\(387\) | − | 5.59912i | − | 0.284619i | ||||||
\(388\) | 16.2767i | 0.826326i | ||||||||
\(389\) | − | 9.95092i | − | 0.504532i | −0.967658 | − | 0.252266i | \(-0.918824\pi\) | ||
0.967658 | − | 0.252266i | \(-0.0811757\pi\) | |||||||
\(390\) | − | 2.11727i | − | 0.107212i | ||||||
\(391\) | 4.55348 | 0.230279 | ||||||||
\(392\) | 4.66119i | 0.235426i | ||||||||
\(393\) | 24.9053i | 1.25630i | ||||||||
\(394\) | 13.4396i | 0.677080i | ||||||||
\(395\) | 1.75086 | 0.0880953 | ||||||||
\(396\) | −5.59912 | −0.281366 | ||||||||
\(397\) | 8.67762 | 0.435517 | 0.217759 | − | 0.976003i | \(-0.430125\pi\) | ||||
0.217759 | + | 0.976003i | \(0.430125\pi\) | |||||||
\(398\) | −23.4802 | −1.17696 | ||||||||
\(399\) | 0.856956i | 0.0429014i | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 11.5569i | 0.577125i | 0.957461 | + | 0.288562i | \(0.0931773\pi\) | ||||
−0.957461 | + | 0.288562i | \(0.906823\pi\) | |||||||
\(402\) | − | 17.2932i | − | 0.862505i | ||||||
\(403\) | −3.79145 | −0.188865 | ||||||||
\(404\) | 11.1138 | 0.552934 | ||||||||
\(405\) | 10.9379i | 0.543510i | ||||||||
\(406\) | 1.10084 | 0.0546337 | ||||||||
\(407\) | −12.8371 | + | 10.4362i | −0.636311 | + | 0.517304i | ||||
\(408\) | 10.8793 | 0.538605 | ||||||||
\(409\) | − | 3.34836i | − | 0.165566i | −0.996568 | − | 0.0827829i | \(-0.973619\pi\) | ||
0.996568 | − | 0.0827829i | \(-0.0263808\pi\) | |||||||
\(410\) | −8.27674 | −0.408759 | ||||||||
\(411\) | 0.732814 | 0.0361470 | ||||||||
\(412\) | 14.1725i | 0.698227i | ||||||||
\(413\) | 11.1759i | 0.549930i | ||||||||
\(414\) | 1.93793 | 0.0952440 | ||||||||
\(415\) | − | 0.131874i | − | 0.00647345i | ||||||
\(416\) | 0.941367 | 0.0461543 | ||||||||
\(417\) | −30.1173 | −1.47485 | ||||||||
\(418\) | −0.677618 | −0.0331434 | ||||||||
\(419\) | −11.3776 | −0.555831 | −0.277916 | − | 0.960606i | \(-0.589644\pi\) | ||||
−0.277916 | + | 0.960606i | \(0.589644\pi\) | |||||||
\(420\) | 3.43965i | 0.167838i | ||||||||
\(421\) | 3.23109i | 0.157474i | 0.996895 | + | 0.0787370i | \(0.0250887\pi\) | ||||
−0.996895 | + | 0.0787370i | \(0.974911\pi\) | |||||||
\(422\) | − | 19.7716i | − | 0.962466i | ||||||
\(423\) | −6.80949 | −0.331089 | ||||||||
\(424\) | − | 8.39400i | − | 0.407649i | ||||||
\(425\) | − | 4.83709i | − | 0.234633i | ||||||
\(426\) | − | 6.87930i | − | 0.333303i | ||||||
\(427\) | − | 10.4561i | − | 0.506005i | ||||||
\(428\) | −10.6922 | −0.516828 | ||||||||
\(429\) | − | 5.75859i | − | 0.278027i | ||||||
\(430\) | − | 2.71982i | − | 0.131162i | ||||||
\(431\) | − | 29.2327i | − | 1.40809i | −0.710155 | − | 0.704045i | \(-0.751375\pi\) | ||
0.710155 | − | 0.704045i | \(-0.248625\pi\) | |||||||
\(432\) | −2.11727 | −0.101867 | ||||||||
\(433\) | 17.7655 | 0.853754 | 0.426877 | − | 0.904310i | \(-0.359614\pi\) | ||||
0.426877 | + | 0.904310i | \(0.359614\pi\) | |||||||
\(434\) | 6.15947 | 0.295664 | ||||||||
\(435\) | −1.61899 | −0.0776244 | ||||||||
\(436\) | 12.2767i | 0.587949i | ||||||||
\(437\) | 0.234533 | 0.0112192 | ||||||||
\(438\) | 20.4983i | 0.979446i | ||||||||
\(439\) | 32.7604i | 1.56357i | 0.623549 | + | 0.781785i | \(0.285690\pi\) | ||||
−0.623549 | + | 0.781785i | \(0.714310\pi\) | |||||||
\(440\) | −2.71982 | −0.129663 | ||||||||
\(441\) | −9.59568 | −0.456937 | ||||||||
\(442\) | 4.55348i | 0.216587i | ||||||||
\(443\) | −0.600939 | −0.0285515 | −0.0142757 | − | 0.999898i | \(-0.504544\pi\) | ||||
−0.0142757 | + | 0.999898i | \(0.504544\pi\) | |||||||
\(444\) | 10.6155 | − | 8.63016i | 0.503792 | − | 0.409569i | ||||
\(445\) | 8.99656 | 0.426478 | ||||||||
\(446\) | − | 9.14143i | − | 0.432859i | ||||||
\(447\) | 18.9897 | 0.898181 | ||||||||
\(448\) | −1.52932 | −0.0722534 | ||||||||
\(449\) | − | 34.0191i | − | 1.60546i | −0.596342 | − | 0.802730i | \(-0.703380\pi\) | ||
0.596342 | − | 0.802730i | \(-0.296620\pi\) | |||||||
\(450\) | − | 2.05863i | − | 0.0970449i | ||||||
\(451\) | −22.5113 | −1.06001 | ||||||||
\(452\) | − | 2.95436i | − | 0.138961i | ||||||
\(453\) | −11.1138 | −0.522173 | ||||||||
\(454\) | −18.7198 | −0.878565 | ||||||||
\(455\) | −1.43965 | −0.0674917 | ||||||||
\(456\) | 0.560352 | 0.0262409 | ||||||||
\(457\) | − | 30.9215i | − | 1.44645i | −0.690614 | − | 0.723223i | \(-0.742660\pi\) | ||
0.690614 | − | 0.723223i | \(-0.257340\pi\) | |||||||
\(458\) | − | 25.1138i | − | 1.17349i | ||||||
\(459\) | − | 10.2414i | − | 0.478028i | ||||||
\(460\) | 0.941367 | 0.0438915 | ||||||||
\(461\) | 1.27330i | 0.0593035i | 0.999560 | + | 0.0296518i | \(0.00943983\pi\) | ||||
−0.999560 | + | 0.0296518i | \(0.990560\pi\) | |||||||
\(462\) | 9.35524i | 0.435245i | ||||||||
\(463\) | 2.61555i | 0.121555i | 0.998151 | + | 0.0607774i | \(0.0193580\pi\) | ||||
−0.998151 | + | 0.0607774i | \(0.980642\pi\) | |||||||
\(464\) | − | 0.719824i | − | 0.0334170i | ||||||
\(465\) | −9.05863 | −0.420084 | ||||||||
\(466\) | 20.4362i | 0.946689i | ||||||||
\(467\) | 19.0096i | 0.879657i | 0.898082 | + | 0.439829i | \(0.144961\pi\) | ||||
−0.898082 | + | 0.439829i | \(0.855039\pi\) | |||||||
\(468\) | 1.93793i | 0.0895808i | ||||||||
\(469\) | −11.7586 | −0.542961 | ||||||||
\(470\) | −3.30777 | −0.152576 | ||||||||
\(471\) | 43.3484 | 1.99739 | ||||||||
\(472\) | 7.30777 | 0.336368 | ||||||||
\(473\) | − | 7.39744i | − | 0.340135i | ||||||
\(474\) | −3.93793 | −0.180875 | ||||||||
\(475\) | − | 0.249141i | − | 0.0114314i | ||||||
\(476\) | − | 7.39744i | − | 0.339061i | ||||||
\(477\) | 17.2802 | 0.791205 | ||||||||
\(478\) | 8.91377 | 0.407706 | ||||||||
\(479\) | − | 38.8578i | − | 1.77546i | −0.460366 | − | 0.887729i | \(-0.652282\pi\) | ||
0.460366 | − | 0.887729i | \(-0.347718\pi\) | |||||||
\(480\) | 2.24914 | 0.102659 | ||||||||
\(481\) | 3.61211 | + | 4.44309i | 0.164698 | + | 0.202587i | ||||
\(482\) | 13.8827 | 0.632341 | ||||||||
\(483\) | − | 3.23797i | − | 0.147333i | ||||||
\(484\) | 3.60256 | 0.163753 | ||||||||
\(485\) | −16.2767 | −0.739089 | ||||||||
\(486\) | − | 18.2491i | − | 0.827798i | ||||||
\(487\) | − | 38.4914i | − | 1.74421i | −0.489317 | − | 0.872106i | \(-0.662754\pi\) | ||
0.489317 | − | 0.872106i | \(-0.337246\pi\) | |||||||
\(488\) | −6.83709 | −0.309501 | ||||||||
\(489\) | 38.9897i | 1.76317i | ||||||||
\(490\) | −4.66119 | −0.210571 | ||||||||
\(491\) | −11.2672 | −0.508481 | −0.254240 | − | 0.967141i | \(-0.581825\pi\) | ||||
−0.254240 | + | 0.967141i | \(0.581825\pi\) | |||||||
\(492\) | 18.6155 | 0.839254 | ||||||||
\(493\) | 3.48185 | 0.156815 | ||||||||
\(494\) | 0.234533i | 0.0105521i | ||||||||
\(495\) | − | 5.59912i | − | 0.251662i | ||||||
\(496\) | − | 4.02760i | − | 0.180844i | ||||||
\(497\) | −4.67762 | −0.209820 | ||||||||
\(498\) | 0.296604i | 0.0132911i | ||||||||
\(499\) | 20.8578i | 0.933724i | 0.884330 | + | 0.466862i | \(0.154616\pi\) | ||||
−0.884330 | + | 0.466862i | \(0.845384\pi\) | |||||||
\(500\) | − | 1.00000i | − | 0.0447214i | ||||||
\(501\) | 38.3518i | 1.71343i | ||||||||
\(502\) | 3.80605 | 0.169873 | ||||||||
\(503\) | − | 6.64476i | − | 0.296275i | −0.988967 | − | 0.148138i | \(-0.952672\pi\) | ||
0.988967 | − | 0.148138i | \(-0.0473279\pi\) | |||||||
\(504\) | − | 3.14830i | − | 0.140237i | ||||||
\(505\) | 11.1138i | 0.494559i | ||||||||
\(506\) | 2.56035 | 0.113822 | ||||||||
\(507\) | 27.2457 | 1.21002 | ||||||||
\(508\) | −8.30434 | −0.368445 | ||||||||
\(509\) | −18.5535 | −0.822368 | −0.411184 | − | 0.911552i | \(-0.634885\pi\) | ||||
−0.411184 | + | 0.911552i | \(0.634885\pi\) | |||||||
\(510\) | 10.8793i | 0.481743i | ||||||||
\(511\) | 13.9379 | 0.616578 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 0.527497i | − | 0.0232896i | ||||||
\(514\) | −8.78801 | −0.387622 | ||||||||
\(515\) | −14.1725 | −0.624513 | ||||||||
\(516\) | 6.11727i | 0.269298i | ||||||||
\(517\) | −8.99656 | −0.395668 | ||||||||
\(518\) | −5.86813 | − | 7.21811i | −0.257831 | − | 0.317145i | ||||
\(519\) | 24.1104 | 1.05833 | ||||||||
\(520\) | 0.941367i | 0.0412817i | ||||||||
\(521\) | −42.6509 | −1.86857 | −0.934284 | − | 0.356529i | \(-0.883960\pi\) | ||||
−0.934284 | + | 0.356529i | \(0.883960\pi\) | |||||||
\(522\) | 1.48185 | 0.0648590 | ||||||||
\(523\) | 12.3879i | 0.541685i | 0.962624 | + | 0.270842i | \(0.0873022\pi\) | ||||
−0.962624 | + | 0.270842i | \(0.912698\pi\) | |||||||
\(524\) | − | 11.0732i | − | 0.483737i | ||||||
\(525\) | −3.43965 | −0.150119 | ||||||||
\(526\) | − | 10.4707i | − | 0.456543i | ||||||
\(527\) | 19.4819 | 0.848643 | ||||||||
\(528\) | 6.11727 | 0.266220 | ||||||||
\(529\) | 22.1138 | 0.961471 | ||||||||
\(530\) | 8.39400 | 0.364612 | ||||||||
\(531\) | 15.0440i | 0.652855i | ||||||||
\(532\) | − | 0.381015i | − | 0.0165191i | ||||||
\(533\) | 7.79145i | 0.337485i | ||||||||
\(534\) | −20.2345 | −0.875634 | ||||||||
\(535\) | − | 10.6922i | − | 0.462265i | ||||||
\(536\) | 7.68879i | 0.332105i | ||||||||
\(537\) | 21.3224i | 0.920129i | ||||||||
\(538\) | − | 5.88273i | − | 0.253623i | ||||||
\(539\) | −12.6776 | −0.546064 | ||||||||
\(540\) | − | 2.11727i | − | 0.0911126i | ||||||
\(541\) | − | 7.64820i | − | 0.328822i | −0.986392 | − | 0.164411i | \(-0.947428\pi\) | ||
0.986392 | − | 0.164411i | \(-0.0525723\pi\) | |||||||
\(542\) | 7.61211i | 0.326968i | ||||||||
\(543\) | 47.2242 | 2.02659 | ||||||||
\(544\) | −4.83709 | −0.207389 | ||||||||
\(545\) | −12.2767 | −0.525878 | ||||||||
\(546\) | 3.23797 | 0.138572 | ||||||||
\(547\) | 12.6837i | 0.542317i | 0.962535 | + | 0.271159i | \(0.0874068\pi\) | ||||
−0.962535 | + | 0.271159i | \(0.912593\pi\) | |||||||
\(548\) | −0.325819 | −0.0139183 | ||||||||
\(549\) | − | 14.0751i | − | 0.600709i | ||||||
\(550\) | − | 2.71982i | − | 0.115974i | ||||||
\(551\) | 0.179337 | 0.00764003 | ||||||||
\(552\) | −2.11727 | −0.0901168 | ||||||||
\(553\) | 2.67762i | 0.113864i | ||||||||
\(554\) | 26.4914 | 1.12551 | ||||||||
\(555\) | 8.63016 | + | 10.6155i | 0.366330 | + | 0.450605i | ||||
\(556\) | 13.3906 | 0.567887 | ||||||||
\(557\) | 2.61555i | 0.110824i | 0.998464 | + | 0.0554121i | \(0.0176473\pi\) | ||||
−0.998464 | + | 0.0554121i | \(0.982353\pi\) | |||||||
\(558\) | 8.29135 | 0.351001 | ||||||||
\(559\) | −2.56035 | −0.108291 | ||||||||
\(560\) | − | 1.52932i | − | 0.0646254i | ||||||
\(561\) | 29.5898i | 1.24928i | ||||||||
\(562\) | 26.6707 | 1.12504 | ||||||||
\(563\) | 35.3285i | 1.48892i | 0.667668 | + | 0.744459i | \(0.267293\pi\) | ||||
−0.667668 | + | 0.744459i | \(0.732707\pi\) | |||||||
\(564\) | 7.43965 | 0.313266 | ||||||||
\(565\) | 2.95436 | 0.124291 | ||||||||
\(566\) | 8.73281 | 0.367068 | ||||||||
\(567\) | −16.7276 | −0.702491 | ||||||||
\(568\) | 3.05863i | 0.128337i | ||||||||
\(569\) | 28.8724i | 1.21039i | 0.796075 | + | 0.605197i | \(0.206906\pi\) | ||||
−0.796075 | + | 0.605197i | \(0.793094\pi\) | |||||||
\(570\) | 0.560352i | 0.0234706i | ||||||||
\(571\) | −8.15947 | −0.341463 | −0.170732 | − | 0.985318i | \(-0.554613\pi\) | ||||
−0.170732 | + | 0.985318i | \(0.554613\pi\) | |||||||
\(572\) | 2.56035i | 0.107054i | ||||||||
\(573\) | 24.9345i | 1.04165i | ||||||||
\(574\) | − | 12.6578i | − | 0.528324i | ||||||
\(575\) | 0.941367i | 0.0392577i | ||||||||
\(576\) | −2.05863 | −0.0857764 | ||||||||
\(577\) | − | 37.5500i | − | 1.56323i | −0.623762 | − | 0.781614i | \(-0.714397\pi\) | ||
0.623762 | − | 0.781614i | \(-0.285603\pi\) | |||||||
\(578\) | − | 6.39744i | − | 0.266099i | ||||||
\(579\) | − | 5.02578i | − | 0.208864i | ||||||
\(580\) | 0.719824 | 0.0298891 | ||||||||
\(581\) | 0.201677 | 0.00836699 | ||||||||
\(582\) | 36.6087 | 1.51748 | ||||||||
\(583\) | 22.8302 | 0.945531 | ||||||||
\(584\) | − | 9.11383i | − | 0.377133i | ||||||
\(585\) | −1.93793 | −0.0801235 | ||||||||
\(586\) | 23.4819i | 0.970026i | ||||||||
\(587\) | − | 19.5078i | − | 0.805174i | −0.915382 | − | 0.402587i | \(-0.868111\pi\) | ||
0.915382 | − | 0.402587i | \(-0.131889\pi\) | |||||||
\(588\) | 10.4837 | 0.432339 | ||||||||
\(589\) | 1.00344 | 0.0413459 | ||||||||
\(590\) | 7.30777i | 0.300856i | ||||||||
\(591\) | 30.2277 | 1.24340 | ||||||||
\(592\) | −4.71982 | + | 3.83709i | −0.193984 | + | 0.157703i | ||||
\(593\) | 41.5569 | 1.70654 | 0.853269 | − | 0.521471i | \(-0.174617\pi\) | ||||
0.853269 | + | 0.521471i | \(0.174617\pi\) | |||||||
\(594\) | − | 5.75859i | − | 0.236278i | ||||||
\(595\) | 7.39744 | 0.303266 | ||||||||
\(596\) | −8.44309 | −0.345842 | ||||||||
\(597\) | 52.8103i | 2.16138i | ||||||||
\(598\) | − | 0.886172i | − | 0.0362382i | ||||||
\(599\) | 27.6381 | 1.12926 | 0.564631 | − | 0.825344i | \(-0.309019\pi\) | ||||
0.564631 | + | 0.825344i | \(0.309019\pi\) | |||||||
\(600\) | 2.24914i | 0.0918208i | ||||||||
\(601\) | 14.4301 | 0.588616 | 0.294308 | − | 0.955711i | \(-0.404911\pi\) | ||||
0.294308 | + | 0.955711i | \(0.404911\pi\) | |||||||
\(602\) | 4.15947 | 0.169527 | ||||||||
\(603\) | −15.8284 | −0.644582 | ||||||||
\(604\) | 4.94137 | 0.201061 | ||||||||
\(605\) | 3.60256i | 0.146465i | ||||||||
\(606\) | − | 24.9966i | − | 1.01542i | ||||||
\(607\) | − | 47.4880i | − | 1.92748i | −0.266848 | − | 0.963739i | \(-0.585982\pi\) | ||
0.266848 | − | 0.963739i | \(-0.414018\pi\) | |||||||
\(608\) | −0.249141 | −0.0101040 | ||||||||
\(609\) | − | 2.47594i | − | 0.100330i | ||||||
\(610\) | − | 6.83709i | − | 0.276826i | ||||||
\(611\) | 3.11383i | 0.125972i | ||||||||
\(612\) | − | 9.95779i | − | 0.402520i | ||||||
\(613\) | −18.7198 | −0.756087 | −0.378043 | − | 0.925788i | \(-0.623403\pi\) | ||||
−0.378043 | + | 0.925788i | \(0.623403\pi\) | |||||||
\(614\) | 27.2457i | 1.09955i | ||||||||
\(615\) | 18.6155i | 0.750651i | ||||||||
\(616\) | − | 4.15947i | − | 0.167590i | ||||||
\(617\) | −15.0225 | −0.604785 | −0.302392 | − | 0.953184i | \(-0.597785\pi\) | ||||
−0.302392 | + | 0.953184i | \(0.597785\pi\) | |||||||
\(618\) | 31.8759 | 1.28224 | ||||||||
\(619\) | 16.6318 | 0.668487 | 0.334244 | − | 0.942487i | \(-0.391519\pi\) | ||||
0.334244 | + | 0.942487i | \(0.391519\pi\) | |||||||
\(620\) | 4.02760 | 0.161752 | ||||||||
\(621\) | 1.99312i | 0.0799813i | ||||||||
\(622\) | 17.7018 | 0.709777 | ||||||||
\(623\) | 13.7586i | 0.551226i | ||||||||
\(624\) | − | 2.11727i | − | 0.0847585i | ||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −23.9931 | −0.958958 | ||||||||
\(627\) | 1.52406i | 0.0608651i | ||||||||
\(628\) | −19.2733 | −0.769088 | ||||||||
\(629\) | −18.5604 | − | 22.8302i | −0.740050 | − | 0.910300i | ||||
\(630\) | 3.14830 | 0.125431 | ||||||||
\(631\) | 35.9294i | 1.43033i | 0.698957 | + | 0.715164i | \(0.253648\pi\) | ||||
−0.698957 | + | 0.715164i | \(0.746352\pi\) | |||||||
\(632\) | 1.75086 | 0.0696454 | ||||||||
\(633\) | −44.4691 | −1.76749 | ||||||||
\(634\) | − | 3.16291i | − | 0.125615i | ||||||
\(635\) | − | 8.30434i | − | 0.329548i | ||||||
\(636\) | −18.8793 | −0.748613 | ||||||||
\(637\) | 4.38789i | 0.173855i | ||||||||
\(638\) | 1.95779 | 0.0775098 | ||||||||
\(639\) | −6.29660 | −0.249090 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 29.3354 | 1.15868 | 0.579339 | − | 0.815087i | \(-0.303311\pi\) | ||||
0.579339 | + | 0.815087i | \(0.303311\pi\) | |||||||
\(642\) | 24.0483i | 0.949111i | ||||||||
\(643\) | 0.368025i | 0.0145135i | 0.999974 | + | 0.00725674i | \(0.00230991\pi\) | ||||
−0.999974 | + | 0.00725674i | \(0.997690\pi\) | |||||||
\(644\) | 1.43965i | 0.0567301i | ||||||||
\(645\) | −6.11727 | −0.240867 | ||||||||
\(646\) | − | 1.20512i | − | 0.0474146i | ||||||
\(647\) | − | 26.7811i | − | 1.05287i | −0.850214 | − | 0.526437i | \(-0.823527\pi\) | ||
0.850214 | − | 0.526437i | \(-0.176473\pi\) | |||||||
\(648\) | 10.9379i | 0.429682i | ||||||||
\(649\) | 19.8759i | 0.780196i | ||||||||
\(650\) | −0.941367 | −0.0369234 | ||||||||
\(651\) | − | 13.8535i | − | 0.542962i | ||||||
\(652\) | − | 17.3354i | − | 0.678906i | ||||||
\(653\) | − | 2.00000i | − | 0.0782660i | −0.999234 | − | 0.0391330i | \(-0.987540\pi\) | ||
0.999234 | − | 0.0391330i | \(-0.0124596\pi\) | |||||||
\(654\) | 27.6121 | 1.07972 | ||||||||
\(655\) | 11.0732 | 0.432667 | ||||||||
\(656\) | −8.27674 | −0.323152 | ||||||||
\(657\) | 18.7620 | 0.731976 | ||||||||
\(658\) | − | 5.05863i | − | 0.197206i | ||||||
\(659\) | −12.9966 | −0.506274 | −0.253137 | − | 0.967430i | \(-0.581462\pi\) | ||||
−0.253137 | + | 0.967430i | \(0.581462\pi\) | |||||||
\(660\) | 6.11727i | 0.238114i | ||||||||
\(661\) | 18.6026i | 0.723556i | 0.932264 | + | 0.361778i | \(0.117830\pi\) | ||||
−0.932264 | + | 0.361778i | \(0.882170\pi\) | |||||||
\(662\) | 4.48367 | 0.174263 | ||||||||
\(663\) | 10.2414 | 0.397743 | ||||||||
\(664\) | − | 0.131874i | − | 0.00511771i | ||||||
\(665\) | 0.381015 | 0.0147751 | ||||||||
\(666\) | −7.89916 | − | 9.71639i | −0.306086 | − | 0.376502i | ||||
\(667\) | −0.677618 | −0.0262375 | ||||||||
\(668\) | − | 17.0518i | − | 0.659752i | ||||||
\(669\) | −20.5604 | −0.794909 | ||||||||
\(670\) | −7.68879 | −0.297044 | ||||||||
\(671\) | − | 18.5957i | − | 0.717878i | ||||||
\(672\) | 3.43965i | 0.132687i | ||||||||
\(673\) | 20.4622 | 0.788759 | 0.394380 | − | 0.918948i | \(-0.370959\pi\) | ||||
0.394380 | + | 0.918948i | \(0.370959\pi\) | |||||||
\(674\) | − | 11.2051i | − | 0.431605i | ||||||
\(675\) | 2.11727 | 0.0814936 | ||||||||
\(676\) | −12.1138 | −0.465916 | ||||||||
\(677\) | −39.9018 | −1.53355 | −0.766776 | − | 0.641915i | \(-0.778140\pi\) | ||||
−0.766776 | + | 0.641915i | \(0.778140\pi\) | |||||||
\(678\) | −6.64476 | −0.255191 | ||||||||
\(679\) | − | 24.8923i | − | 0.955278i | ||||||
\(680\) | − | 4.83709i | − | 0.185494i | ||||||
\(681\) | 42.1035i | 1.61341i | ||||||||
\(682\) | 10.9544 | 0.419464 | ||||||||
\(683\) | − | 12.3940i | − | 0.474243i | −0.971480 | − | 0.237122i | \(-0.923796\pi\) | ||
0.971480 | − | 0.237122i | \(-0.0762040\pi\) | |||||||
\(684\) | − | 0.512889i | − | 0.0196108i | ||||||
\(685\) | − | 0.325819i | − | 0.0124489i | ||||||
\(686\) | − | 17.8337i | − | 0.680892i | ||||||
\(687\) | −56.4845 | −2.15502 | ||||||||
\(688\) | − | 2.71982i | − | 0.103692i | ||||||
\(689\) | − | 7.90184i | − | 0.301036i | ||||||
\(690\) | − | 2.11727i | − | 0.0806030i | ||||||
\(691\) | −51.5630 | −1.96155 | −0.980775 | − | 0.195142i | \(-0.937483\pi\) | ||||
−0.980775 | + | 0.195142i | \(0.937483\pi\) | |||||||
\(692\) | −10.7198 | −0.407507 | ||||||||
\(693\) | 8.56283 | 0.325275 | ||||||||
\(694\) | 13.9931 | 0.531172 | ||||||||
\(695\) | 13.3906i | 0.507933i | ||||||||
\(696\) | −1.61899 | −0.0613675 | ||||||||
\(697\) | − | 40.0353i | − | 1.51645i | ||||||
\(698\) | − | 6.56035i | − | 0.248313i | ||||||
\(699\) | 45.9639 | 1.73851 | ||||||||
\(700\) | 1.52932 | 0.0578027 | ||||||||
\(701\) | 9.76547i | 0.368837i | 0.982848 | + | 0.184418i | \(0.0590401\pi\) | ||||
−0.982848 | + | 0.184418i | \(0.940960\pi\) | |||||||
\(702\) | −1.99312 | −0.0752256 | ||||||||
\(703\) | −0.955975 | − | 1.17590i | −0.0360553 | − | 0.0443499i | ||||
\(704\) | −2.71982 | −0.102507 | ||||||||
\(705\) | 7.43965i | 0.280193i | ||||||||
\(706\) | −36.5957 | −1.37730 | ||||||||
\(707\) | −16.9966 | −0.639222 | ||||||||
\(708\) | − | 16.4362i | − | 0.617711i | ||||||
\(709\) | 49.8268i | 1.87128i | 0.352951 | + | 0.935642i | \(0.385178\pi\) | ||||
−0.352951 | + | 0.935642i | \(0.614822\pi\) | |||||||
\(710\) | −3.05863 | −0.114788 | ||||||||
\(711\) | 3.60438i | 0.135175i | ||||||||
\(712\) | 8.99656 | 0.337160 | ||||||||
\(713\) | −3.79145 | −0.141991 | ||||||||
\(714\) | −16.6379 | −0.622657 | ||||||||
\(715\) | −2.56035 | −0.0957517 | ||||||||
\(716\) | − | 9.48024i | − | 0.354293i | ||||||
\(717\) | − | 20.0483i | − | 0.748718i | ||||||
\(718\) | 21.2311i | 0.792337i | ||||||||
\(719\) | −4.26375 | −0.159011 | −0.0795055 | − | 0.996834i | \(-0.525334\pi\) | ||||
−0.0795055 | + | 0.996834i | \(0.525334\pi\) | |||||||
\(720\) | − | 2.05863i | − | 0.0767207i | ||||||
\(721\) | − | 21.6742i | − | 0.807189i | ||||||
\(722\) | 18.9379i | 0.704797i | ||||||||
\(723\) | − | 31.2242i | − | 1.16124i | ||||||
\(724\) | −20.9966 | −0.780331 | ||||||||
\(725\) | 0.719824i | 0.0267336i | ||||||||
\(726\) | − | 8.10266i | − | 0.300718i | ||||||
\(727\) | 13.1759i | 0.488667i | 0.969691 | + | 0.244334i | \(0.0785692\pi\) | ||||
−0.969691 | + | 0.244334i | \(0.921431\pi\) | |||||||
\(728\) | −1.43965 | −0.0533569 | ||||||||
\(729\) | −8.23109 | −0.304855 | ||||||||
\(730\) | 9.11383 | 0.337318 | ||||||||
\(731\) | 13.1560 | 0.486593 | ||||||||
\(732\) | 15.3776i | 0.568372i | ||||||||
\(733\) | 9.39057 | 0.346848 | 0.173424 | − | 0.984847i | \(-0.444517\pi\) | ||||
0.173424 | + | 0.984847i | \(0.444517\pi\) | |||||||
\(734\) | 23.4932i | 0.867151i | ||||||||
\(735\) | 10.4837i | 0.386696i | ||||||||
\(736\) | 0.941367 | 0.0346992 | ||||||||
\(737\) | −20.9122 | −0.770309 | ||||||||
\(738\) | − | 17.0388i | − | 0.627206i | ||||||
\(739\) | −9.62510 | −0.354065 | −0.177033 | − | 0.984205i | \(-0.556650\pi\) | ||||
−0.177033 | + | 0.984205i | \(0.556650\pi\) | |||||||
\(740\) | −3.83709 | − | 4.71982i | −0.141054 | − | 0.173504i | ||||
\(741\) | 0.527497 | 0.0193781 | ||||||||
\(742\) | 12.8371i | 0.471264i | ||||||||
\(743\) | −25.6137 | −0.939677 | −0.469838 | − | 0.882753i | \(-0.655688\pi\) | ||||
−0.469838 | + | 0.882753i | \(0.655688\pi\) | |||||||
\(744\) | −9.05863 | −0.332106 | ||||||||
\(745\) | − | 8.44309i | − | 0.309331i | ||||||
\(746\) | − | 7.55691i | − | 0.276678i | ||||||
\(747\) | 0.271481 | 0.00993296 | ||||||||
\(748\) | − | 13.1560i | − | 0.481032i | ||||||
\(749\) | 16.3518 | 0.597482 | ||||||||
\(750\) | −2.24914 | −0.0821270 | ||||||||
\(751\) | 11.9740 | 0.436938 | 0.218469 | − | 0.975844i | \(-0.429894\pi\) | ||||
0.218469 | + | 0.975844i | \(0.429894\pi\) | |||||||
\(752\) | −3.30777 | −0.120622 | ||||||||
\(753\) | − | 8.56035i | − | 0.311957i | ||||||
\(754\) | − | 0.677618i | − | 0.0246774i | ||||||
\(755\) | 4.94137i | 0.179835i | ||||||||
\(756\) | 3.23797 | 0.117764 | ||||||||
\(757\) | 19.2051i | 0.698022i | 0.937119 | + | 0.349011i | \(0.113482\pi\) | ||||
−0.937119 | + | 0.349011i | \(0.886518\pi\) | |||||||
\(758\) | 12.2637i | 0.445439i | ||||||||
\(759\) | − | 5.75859i | − | 0.209024i | ||||||
\(760\) | − | 0.249141i | − | 0.00903728i | ||||||
\(761\) | −31.8596 | −1.15491 | −0.577455 | − | 0.816422i | \(-0.695954\pi\) | ||||
−0.577455 | + | 0.816422i | \(0.695954\pi\) | |||||||
\(762\) | 18.6776i | 0.676619i | ||||||||
\(763\) | − | 18.7750i | − | 0.679701i | ||||||
\(764\) | − | 11.0862i | − | 0.401086i | ||||||
\(765\) | 9.95779 | 0.360025 | ||||||||
\(766\) | 33.5208 | 1.21116 | ||||||||
\(767\) | 6.87930 | 0.248397 | ||||||||
\(768\) | 2.24914 | 0.0811589 | ||||||||
\(769\) | − | 35.2242i | − | 1.27022i | −0.772423 | − | 0.635109i | \(-0.780955\pi\) | ||
0.772423 | − | 0.635109i | \(-0.219045\pi\) | |||||||
\(770\) | 4.15947 | 0.149897 | ||||||||
\(771\) | 19.7655i | 0.711836i | ||||||||
\(772\) | 2.23453i | 0.0804226i | ||||||||
\(773\) | −50.2630 | −1.80783 | −0.903917 | − | 0.427708i | \(-0.859321\pi\) | ||||
−0.903917 | + | 0.427708i | \(0.859321\pi\) | |||||||
\(774\) | 5.59912 | 0.201256 | ||||||||
\(775\) | 4.02760i | 0.144676i | ||||||||
\(776\) | −16.2767 | −0.584301 | ||||||||
\(777\) | −16.2345 | + | 13.1982i | −0.582411 | + | 0.473484i | ||||
\(778\) | 9.95092 | 0.356758 | ||||||||
\(779\) | − | 2.06207i | − | 0.0738814i | ||||||
\(780\) | 2.11727 | 0.0758103 | ||||||||
\(781\) | −8.31894 | −0.297675 | ||||||||
\(782\) | 4.55348i | 0.162832i | ||||||||
\(783\) | 1.52406i | 0.0544654i | ||||||||
\(784\) | −4.66119 | −0.166471 | ||||||||
\(785\) | − | 19.2733i | − | 0.687894i | ||||||
\(786\) | −24.9053 | −0.888342 | ||||||||
\(787\) | −51.9525 | −1.85191 | −0.925954 | − | 0.377636i | \(-0.876737\pi\) | ||||
−0.925954 | + | 0.377636i | \(0.876737\pi\) | |||||||
\(788\) | −13.4396 | −0.478768 | ||||||||
\(789\) | −23.5500 | −0.838404 | ||||||||
\(790\) | 1.75086i | 0.0622928i | ||||||||
\(791\) | 4.51815i | 0.160647i | ||||||||
\(792\) | − | 5.59912i | − | 0.198956i | ||||||
\(793\) | −6.43621 | −0.228557 | ||||||||
\(794\) | 8.67762i | 0.307957i | ||||||||
\(795\) | − | 18.8793i | − | 0.669580i | ||||||
\(796\) | − | 23.4802i | − | 0.832235i | ||||||
\(797\) | 35.4880i | 1.25705i | 0.777790 | + | 0.628524i | \(0.216341\pi\) | ||||
−0.777790 | + | 0.628524i | \(0.783659\pi\) | |||||||
\(798\) | −0.856956 | −0.0303359 | ||||||||
\(799\) | − | 16.0000i | − | 0.566039i | ||||||
\(800\) | − | 1.00000i | − | 0.0353553i | ||||||
\(801\) | 18.5206i | 0.654394i | ||||||||
\(802\) | −11.5569 | −0.408089 | ||||||||
\(803\) | 24.7880 | 0.874750 | ||||||||
\(804\) | 17.2932 | 0.609883 | ||||||||
\(805\) | −1.43965 | −0.0507409 | ||||||||
\(806\) | − | 3.79145i | − | 0.133548i | ||||||
\(807\) | −13.2311 | −0.465757 | ||||||||
\(808\) | 11.1138i | 0.390983i | ||||||||
\(809\) | 13.2051i | 0.464267i | 0.972684 | + | 0.232134i | \(0.0745706\pi\) | ||||
−0.972684 | + | 0.232134i | \(0.925429\pi\) | |||||||
\(810\) | −10.9379 | −0.384320 | ||||||||
\(811\) | −10.1173 | −0.355265 | −0.177633 | − | 0.984097i | \(-0.556844\pi\) | ||||
−0.177633 | + | 0.984097i | \(0.556844\pi\) | |||||||
\(812\) | 1.10084i | 0.0386319i | ||||||||
\(813\) | 17.1207 | 0.600449 | ||||||||
\(814\) | −10.4362 | − | 12.8371i | −0.365789 | − | 0.449940i | ||||
\(815\) | 17.3354 | 0.607232 | ||||||||
\(816\) | 10.8793i | 0.380852i | ||||||||
\(817\) | 0.677618 | 0.0237069 | ||||||||
\(818\) | 3.34836 | 0.117073 | ||||||||
\(819\) | − | 2.96371i | − | 0.103560i | ||||||
\(820\) | − | 8.27674i | − | 0.289036i | ||||||
\(821\) | 5.68106 | 0.198270 | 0.0991351 | − | 0.995074i | \(-0.468392\pi\) | ||||
0.0991351 | + | 0.995074i | \(0.468392\pi\) | |||||||
\(822\) | 0.732814i | 0.0255598i | ||||||||
\(823\) | −22.3404 | −0.778738 | −0.389369 | − | 0.921082i | \(-0.627307\pi\) | ||||
−0.389369 | + | 0.921082i | \(0.627307\pi\) | |||||||
\(824\) | −14.1725 | −0.493721 | ||||||||
\(825\) | −6.11727 | −0.212976 | ||||||||
\(826\) | −11.1759 | −0.388859 | ||||||||
\(827\) | 3.71639i | 0.129231i | 0.997910 | + | 0.0646157i | \(0.0205822\pi\) | ||||
−0.997910 | + | 0.0646157i | \(0.979418\pi\) | |||||||
\(828\) | 1.93793i | 0.0673477i | ||||||||
\(829\) | 15.8596i | 0.550828i | 0.961326 | + | 0.275414i | \(0.0888149\pi\) | ||||
−0.961326 | + | 0.275414i | \(0.911185\pi\) | |||||||
\(830\) | 0.131874 | 0.00457742 | ||||||||
\(831\) | − | 59.5829i | − | 2.06691i | ||||||
\(832\) | 0.941367i | 0.0326360i | ||||||||
\(833\) | − | 22.5466i | − | 0.781193i | ||||||
\(834\) | − | 30.1173i | − | 1.04288i | ||||||
\(835\) | 17.0518 | 0.590100 | ||||||||
\(836\) | − | 0.677618i | − | 0.0234359i | ||||||
\(837\) | 8.52750i | 0.294753i | ||||||||
\(838\) | − | 11.3776i | − | 0.393032i | ||||||
\(839\) | −33.8950 | −1.17018 | −0.585092 | − | 0.810967i | \(-0.698942\pi\) | ||||
−0.585092 | + | 0.810967i | \(0.698942\pi\) | |||||||
\(840\) | −3.43965 | −0.118679 | ||||||||
\(841\) | 28.4819 | 0.982133 | ||||||||
\(842\) | −3.23109 | −0.111351 | ||||||||
\(843\) | − | 59.9862i | − | 2.06604i | ||||||
\(844\) | 19.7716 | 0.680566 | ||||||||
\(845\) | − | 12.1138i | − | 0.416728i | ||||||
\(846\) | − | 6.80949i | − | 0.234115i | ||||||
\(847\) | −5.50945 | −0.189307 | ||||||||
\(848\) | 8.39400 | 0.288251 | ||||||||
\(849\) | − | 19.6413i | − | 0.674089i | ||||||
\(850\) | 4.83709 | 0.165911 | ||||||||
\(851\) | 3.61211 | + | 4.44309i | 0.123822 | + | 0.152307i | ||||
\(852\) | 6.87930 | 0.235681 | ||||||||
\(853\) | − | 35.7586i | − | 1.22435i | −0.790722 | − | 0.612175i | \(-0.790295\pi\) | ||
0.790722 | − | 0.612175i | \(-0.209705\pi\) | |||||||
\(854\) | 10.4561 | 0.357800 | ||||||||
\(855\) | 0.512889 | 0.0175404 | ||||||||
\(856\) | − | 10.6922i | − | 0.365453i | ||||||
\(857\) | − | 17.3837i | − | 0.593816i | −0.954906 | − | 0.296908i | \(-0.904045\pi\) | ||
0.954906 | − | 0.296908i | \(-0.0959554\pi\) | |||||||
\(858\) | 5.75859 | 0.196595 | ||||||||
\(859\) | 43.3922i | 1.48052i | 0.672319 | + | 0.740261i | \(0.265298\pi\) | ||||
−0.672319 | + | 0.740261i | \(0.734702\pi\) | |||||||
\(860\) | 2.71982 | 0.0927452 | ||||||||
\(861\) | −28.4691 | −0.970223 | ||||||||
\(862\) | 29.2327 | 0.995670 | ||||||||
\(863\) | 34.8708 | 1.18702 | 0.593508 | − | 0.804828i | \(-0.297743\pi\) | ||||
0.593508 | + | 0.804828i | \(0.297743\pi\) | |||||||
\(864\) | − | 2.11727i | − | 0.0720309i | ||||||
\(865\) | − | 10.7198i | − | 0.364485i | ||||||
\(866\) | 17.7655i | 0.603695i | ||||||||
\(867\) | −14.3887 | −0.488667 | ||||||||
\(868\) | 6.15947i | 0.209066i | ||||||||
\(869\) | 4.76203i | 0.161541i | ||||||||
\(870\) | − | 1.61899i | − | 0.0548887i | ||||||
\(871\) | 7.23797i | 0.245249i | ||||||||
\(872\) | −12.2767 | −0.415743 | ||||||||
\(873\) | − | 33.5078i | − | 1.13407i | ||||||
\(874\) | 0.234533i | 0.00793318i | ||||||||
\(875\) | 1.52932i | 0.0517003i | ||||||||
\(876\) | −20.4983 | −0.692573 | ||||||||
\(877\) | 47.0907 | 1.59014 | 0.795070 | − | 0.606517i | \(-0.207434\pi\) | ||||
0.795070 | + | 0.606517i | \(0.207434\pi\) | |||||||
\(878\) | −32.7604 | −1.10561 | ||||||||
\(879\) | 52.8140 | 1.78137 | ||||||||
\(880\) | − | 2.71982i | − | 0.0916852i | ||||||
\(881\) | 29.0027 | 0.977125 | 0.488562 | − | 0.872529i | \(-0.337521\pi\) | ||||
0.488562 | + | 0.872529i | \(0.337521\pi\) | |||||||
\(882\) | − | 9.59568i | − | 0.323103i | ||||||
\(883\) | 11.0388i | 0.371484i | 0.982599 | + | 0.185742i | \(0.0594689\pi\) | ||||
−0.982599 | + | 0.185742i | \(0.940531\pi\) | |||||||
\(884\) | −4.55348 | −0.153150 | ||||||||
\(885\) | 16.4362 | 0.552497 | ||||||||
\(886\) | − | 0.600939i | − | 0.0201890i | ||||||
\(887\) | −5.76709 | −0.193640 | −0.0968199 | − | 0.995302i | \(-0.530867\pi\) | ||||
−0.0968199 | + | 0.995302i | \(0.530867\pi\) | |||||||
\(888\) | 8.63016 | + | 10.6155i | 0.289609 | + | 0.356234i | ||||
\(889\) | 12.7000 | 0.425943 | ||||||||
\(890\) | 8.99656i | 0.301565i | ||||||||
\(891\) | −29.7492 | −0.996637 | ||||||||
\(892\) | 9.14143 | 0.306078 | ||||||||
\(893\) | − | 0.824101i | − | 0.0275775i | ||||||
\(894\) | 18.9897i | 0.635110i | ||||||||
\(895\) | 9.48024 | 0.316889 | ||||||||
\(896\) | − | 1.52932i | − | 0.0510909i | ||||||
\(897\) | −1.99312 | −0.0665485 | ||||||||
\(898\) | 34.0191 | 1.13523 | ||||||||
\(899\) | −2.89916 | −0.0966924 | ||||||||
\(900\) | 2.05863 | 0.0686211 | ||||||||
\(901\) | 40.6026i | 1.35267i | ||||||||
\(902\) | − | 22.5113i | − | 0.749543i | ||||||
\(903\) | − | 9.35524i | − | 0.311323i | ||||||
\(904\) | 2.95436 | 0.0982604 | ||||||||
\(905\) | − | 20.9966i | − | 0.697949i | ||||||
\(906\) | − | 11.1138i | − | 0.369232i | ||||||
\(907\) | 54.2139i | 1.80014i | 0.435742 | + | 0.900072i | \(0.356486\pi\) | ||||
−0.435742 | + | 0.900072i | \(0.643514\pi\) | |||||||
\(908\) | − | 18.7198i | − | 0.621239i | ||||||
\(909\) | −22.8793 | −0.758858 | ||||||||
\(910\) | − | 1.43965i | − | 0.0477239i | ||||||
\(911\) | 37.1284i | 1.23012i | 0.788480 | + | 0.615060i | \(0.210868\pi\) | ||||
−0.788480 | + | 0.615060i | \(0.789132\pi\) | |||||||
\(912\) | 0.560352i | 0.0185551i | ||||||||
\(913\) | 0.358675 | 0.0118704 | ||||||||
\(914\) | 30.9215 | 1.02279 | ||||||||
\(915\) | −15.3776 | −0.508367 | ||||||||
\(916\) | 25.1138 | 0.829784 | ||||||||
\(917\) | 16.9345i | 0.559226i | ||||||||
\(918\) | 10.2414 | 0.338017 | ||||||||
\(919\) | 20.0889i | 0.662672i | 0.943513 | + | 0.331336i | \(0.107499\pi\) | ||||
−0.943513 | + | 0.331336i | \(0.892501\pi\) | |||||||
\(920\) | 0.941367i | 0.0310359i | ||||||||
\(921\) | 61.2794 | 2.01923 | ||||||||
\(922\) | −1.27330 | −0.0419339 | ||||||||
\(923\) | 2.87930i | 0.0947732i | ||||||||
\(924\) | −9.35524 | −0.307765 | ||||||||
\(925\) | 4.71982 | − | 3.83709i | 0.155187 | − | 0.126163i | ||||
\(926\) | −2.61555 | −0.0859522 | ||||||||
\(927\) | − | 29.1759i | − | 0.958262i | ||||||
\(928\) | 0.719824 | 0.0236294 | ||||||||
\(929\) | 12.9803 | 0.425871 | 0.212936 | − | 0.977066i | \(-0.431698\pi\) | ||||
0.212936 | + | 0.977066i | \(0.431698\pi\) | |||||||
\(930\) | − | 9.05863i | − | 0.297044i | ||||||
\(931\) | − | 1.16129i | − | 0.0380598i | ||||||
\(932\) | −20.4362 | −0.669410 | ||||||||
\(933\) | − | 39.8138i | − | 1.30344i | ||||||
\(934\) | −19.0096 | −0.622012 | ||||||||
\(935\) | 13.1560 | 0.430248 | ||||||||
\(936\) | −1.93793 | −0.0633432 | ||||||||
\(937\) | −9.32238 | −0.304549 | −0.152274 | − | 0.988338i | \(-0.548660\pi\) | ||||
−0.152274 | + | 0.988338i | \(0.548660\pi\) | |||||||
\(938\) | − | 11.7586i | − | 0.383932i | ||||||
\(939\) | 53.9639i | 1.76105i | ||||||||
\(940\) | − | 3.30777i | − | 0.107888i | ||||||
\(941\) | −17.7586 | −0.578914 | −0.289457 | − | 0.957191i | \(-0.593475\pi\) | ||||
−0.289457 | + | 0.957191i | \(0.593475\pi\) | |||||||
\(942\) | 43.3484i | 1.41237i | ||||||||
\(943\) | 7.79145i | 0.253724i | ||||||||
\(944\) | 7.30777i | 0.237848i | ||||||||
\(945\) | 3.23797i | 0.105331i | ||||||||
\(946\) | 7.39744 | 0.240512 | ||||||||
\(947\) | 17.3354i | 0.563324i | 0.959514 | + | 0.281662i | \(0.0908857\pi\) | ||||
−0.959514 | + | 0.281662i | \(0.909114\pi\) | |||||||
\(948\) | − | 3.93793i | − | 0.127898i | ||||||
\(949\) | − | 8.57946i | − | 0.278501i | ||||||
\(950\) | 0.249141 | 0.00808319 | ||||||||
\(951\) | −7.11383 | −0.230682 | ||||||||
\(952\) | 7.39744 | 0.239752 | ||||||||
\(953\) | −5.88961 | −0.190783 | −0.0953916 | − | 0.995440i | \(-0.530410\pi\) | ||||
−0.0953916 | + | 0.995440i | \(0.530410\pi\) | |||||||
\(954\) | 17.2802i | 0.559466i | ||||||||
\(955\) | 11.0862 | 0.358742 | ||||||||
\(956\) | 8.91377i | 0.288292i | ||||||||
\(957\) | − | 4.40335i | − | 0.142340i | ||||||
\(958\) | 38.8578 | 1.25544 | ||||||||
\(959\) | 0.498281 | 0.0160903 | ||||||||
\(960\) | 2.24914i | 0.0725907i | ||||||||
\(961\) | 14.7785 | 0.476724 | ||||||||
\(962\) | −4.44309 | + | 3.61211i | −0.143251 | + | 0.116459i | ||||
\(963\) | 22.0114 | 0.709307 | ||||||||
\(964\) | 13.8827i | 0.447133i | ||||||||
\(965\) | −2.23453 | −0.0719322 | ||||||||
\(966\) | 3.23797 | 0.104180 | ||||||||
\(967\) | 32.3189i | 1.03931i | 0.854377 | + | 0.519654i | \(0.173939\pi\) | ||||
−0.854377 | + | 0.519654i | \(0.826061\pi\) | |||||||
\(968\) | 3.60256i | 0.115791i | ||||||||
\(969\) | −2.71047 | −0.0870730 | ||||||||
\(970\) | − | 16.2767i | − | 0.522615i | ||||||
\(971\) | 6.11115 | 0.196116 | 0.0980581 | − | 0.995181i | \(-0.468737\pi\) | ||||
0.0980581 | + | 0.995181i | \(0.468737\pi\) | |||||||
\(972\) | 18.2491 | 0.585341 | ||||||||
\(973\) | −20.4784 | −0.656508 | ||||||||
\(974\) | 38.4914 | 1.23334 | ||||||||
\(975\) | 2.11727i | 0.0678068i | ||||||||
\(976\) | − | 6.83709i | − | 0.218850i | ||||||
\(977\) | − | 47.3906i | − | 1.51616i | −0.652162 | − | 0.758079i | \(-0.726138\pi\) | ||
0.652162 | − | 0.758079i | \(-0.273862\pi\) | |||||||
\(978\) | −38.9897 | −1.24675 | ||||||||
\(979\) | 24.4691i | 0.782035i | ||||||||
\(980\) | − | 4.66119i | − | 0.148896i | ||||||
\(981\) | − | 25.2733i | − | 0.806914i | ||||||
\(982\) | − | 11.2672i | − | 0.359550i | ||||||
\(983\) | −55.7862 | −1.77930 | −0.889652 | − | 0.456640i | \(-0.849053\pi\) | ||||
−0.889652 | + | 0.456640i | \(0.849053\pi\) | |||||||
\(984\) | 18.6155i | 0.593442i | ||||||||
\(985\) | − | 13.4396i | − | 0.428223i | ||||||
\(986\) | 3.48185i | 0.110885i | ||||||||
\(987\) | −11.3776 | −0.362152 | ||||||||
\(988\) | −0.234533 | −0.00746148 | ||||||||
\(989\) | −2.56035 | −0.0814145 | ||||||||
\(990\) | 5.59912 | 0.177952 | ||||||||
\(991\) | − | 29.9655i | − | 0.951886i | −0.879476 | − | 0.475943i | \(-0.842107\pi\) | ||
0.879476 | − | 0.475943i | \(-0.157893\pi\) | |||||||
\(992\) | 4.02760 | 0.127876 | ||||||||
\(993\) | − | 10.0844i | − | 0.320019i | ||||||
\(994\) | − | 4.67762i | − | 0.148365i | ||||||
\(995\) | 23.4802 | 0.744374 | ||||||||
\(996\) | −0.296604 | −0.00939825 | ||||||||
\(997\) | 20.7811i | 0.658145i | 0.944305 | + | 0.329073i | \(0.106736\pi\) | ||||
−0.944305 | + | 0.329073i | \(0.893264\pi\) | |||||||
\(998\) | −20.8578 | −0.660243 | ||||||||
\(999\) | 9.99312 | − | 8.12414i | 0.316168 | − | 0.257036i |
(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 | 370.2.d.c.221.6 | yes | 6 | |
3.2 | odd | 2 | 3330.2.h.n.2071.2 | 6 | |||
4.3 | odd | 2 | 2960.2.p.g.961.1 | 6 | |||
5.2 | odd | 4 | 1850.2.c.i.1849.2 | 6 | |||
5.3 | odd | 4 | 1850.2.c.j.1849.5 | 6 | |||
5.4 | even | 2 | 1850.2.d.f.1701.1 | 6 | |||
37.36 | even | 2 | inner | 370.2.d.c.221.3 | ✓ | 6 | |
111.110 | odd | 2 | 3330.2.h.n.2071.5 | 6 | |||
148.147 | odd | 2 | 2960.2.p.g.961.2 | 6 | |||
185.73 | odd | 4 | 1850.2.c.i.1849.5 | 6 | |||
185.147 | odd | 4 | 1850.2.c.j.1849.2 | 6 | |||
185.184 | even | 2 | 1850.2.d.f.1701.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.d.c.221.3 | ✓ | 6 | 37.36 | even | 2 | inner | |
370.2.d.c.221.6 | yes | 6 | 1.1 | even | 1 | trivial | |
1850.2.c.i.1849.2 | 6 | 5.2 | odd | 4 | |||
1850.2.c.i.1849.5 | 6 | 185.73 | odd | 4 | |||
1850.2.c.j.1849.2 | 6 | 185.147 | odd | 4 | |||
1850.2.c.j.1849.5 | 6 | 5.3 | odd | 4 | |||
1850.2.d.f.1701.1 | 6 | 5.4 | even | 2 | |||
1850.2.d.f.1701.4 | 6 | 185.184 | even | 2 | |||
2960.2.p.g.961.1 | 6 | 4.3 | odd | 2 | |||
2960.2.p.g.961.2 | 6 | 148.147 | odd | 2 | |||
3330.2.h.n.2071.2 | 6 | 3.2 | odd | 2 | |||
3330.2.h.n.2071.5 | 6 | 111.110 | odd | 2 |