Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3360,2,Mod(1009,3360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3360.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3360.j (of order \(2\), degree \(1\), not 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: | \(26.8297350792\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1009.2 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3360.1009 |
Dual form | 3360.2.j.c.1009.1 |
$q$-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 \(\left(\mathbb{Z}/3360\mathbb{Z}\right)^\times\).
\(n\) | \(421\) | \(1121\) | \(1471\) | \(1921\) | \(2017\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.00000 | + | 1.00000i | −0.894427 | + | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.00000i | − | 1.20605i | −0.797724 | − | 0.603023i | \(-0.793963\pi\) | ||
0.797724 | − | 0.603023i | \(-0.206037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | + | 1.00000i | −0.516398 | + | 0.258199i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000i | 0.485071i | 0.970143 | + | 0.242536i | \(0.0779791\pi\) | ||||
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.00000i | 1.83533i | 0.397360 | + | 0.917663i | \(0.369927\pi\) | ||||
−0.397360 | + | 0.917663i | \(0.630073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000i | 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.00000i | − | 0.834058i | −0.908893 | − | 0.417029i | \(-0.863071\pi\) | ||
0.908893 | − | 0.417029i | \(-0.136929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000i | 0.371391i | 0.982607 | + | 0.185695i | \(0.0594537\pi\) | ||||
−0.982607 | + | 0.185695i | \(0.940546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 4.00000i | − | 0.696311i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | − | 2.00000i | −0.169031 | − | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0000 | 1.52499 | 0.762493 | − | 0.646997i | \(-0.223975\pi\) | ||||
0.762493 | + | 0.646997i | \(0.223975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.00000 | + | 1.00000i | −0.298142 | + | 0.149071i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.00000i | 0.875190i | 0.899172 | + | 0.437595i | \(0.144170\pi\) | ||||
−0.899172 | + | 0.437595i | \(0.855830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000i | 0.280056i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −14.0000 | −1.92305 | −0.961524 | − | 0.274721i | \(-0.911414\pi\) | ||||
−0.961524 | + | 0.274721i | \(0.911414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | + | 8.00000i | 0.539360 | + | 1.07872i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.00000i | 1.05963i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000i | 0.781133i | 0.920575 | + | 0.390567i | \(0.127721\pi\) | ||||
−0.920575 | + | 0.390567i | \(0.872279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000i | 0.256074i | 0.991769 | + | 0.128037i | \(0.0408676\pi\) | ||||
−0.991769 | + | 0.128037i | \(0.959132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.00000 | + | 2.00000i | −0.496139 | + | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.0000 | −1.22169 | −0.610847 | − | 0.791748i | \(-0.709171\pi\) | ||||
−0.610847 | + | 0.791748i | \(0.709171\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 4.00000i | − | 0.481543i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000i | 0.702247i | 0.936329 | + | 0.351123i | \(0.114200\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.00000 | − | 4.00000i | 0.346410 | − | 0.461880i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.0000 | 1.57512 | 0.787562 | − | 0.616236i | \(-0.211343\pi\) | ||||
0.787562 | + | 0.616236i | \(0.211343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | − | 4.00000i | −0.216930 | − | 0.433861i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.00000i | 0.214423i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.00000 | 0.847998 | 0.423999 | − | 0.905663i | \(-0.360626\pi\) | ||||
0.423999 | + | 0.905663i | \(0.360626\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000i | 0.209657i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.00000 | 0.414781 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.00000 | − | 16.0000i | −0.820783 | − | 1.64157i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000i | 0.609208i | 0.952479 | + | 0.304604i | \(0.0985241\pi\) | ||||
−0.952479 | + | 0.304604i | \(0.901476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.00000i | − | 0.402015i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 6.00000i | − | 0.597022i | −0.954406 | − | 0.298511i | \(-0.903510\pi\) | ||
0.954406 | − | 0.298511i | \(-0.0964900\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000i | 0.788263i | 0.919054 | + | 0.394132i | \(0.128955\pi\) | ||||
−0.919054 | + | 0.394132i | \(0.871045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00000 | − | 2.00000i | −0.0975900 | − | 0.195180i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.0000i | 1.53252i | 0.642529 | + | 0.766261i | \(0.277885\pi\) | ||||
−0.642529 | + | 0.766261i | \(0.722115\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | −0.569495 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | + | 8.00000i | 0.373002 | + | 0.746004i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.00000 | + | 11.0000i | −0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000i | 1.41977i | 0.704317 | + | 0.709885i | \(0.251253\pi\) | ||||
−0.704317 | + | 0.709885i | \(0.748747\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.0000 | 0.880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.0000i | 1.57267i | 0.617802 | + | 0.786334i | \(0.288023\pi\) | ||||
−0.617802 | + | 0.786334i | \(0.711977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | −0.693688 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.00000 | + | 1.00000i | −0.172133 | + | 0.0860663i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 6.00000i | − | 0.512615i | −0.966595 | − | 0.256307i | \(-0.917494\pi\) | ||
0.966595 | − | 0.256307i | \(-0.0825059\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000i | 1.01783i | 0.860818 | + | 0.508913i | \(0.169953\pi\) | ||||
−0.860818 | + | 0.508913i | \(0.830047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000i | 0.505291i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 8.00000i | − | 0.668994i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | − | 4.00000i | −0.166091 | − | 0.332182i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 10.0000i | − | 0.819232i | −0.912258 | − | 0.409616i | \(-0.865663\pi\) | ||
0.912258 | − | 0.409616i | \(-0.134337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.00000 | −0.162758 | −0.0813788 | − | 0.996683i | \(-0.525932\pi\) | ||||
−0.0813788 | + | 0.996683i | \(0.525932\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000i | 0.161690i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | + | 4.00000i | −0.642575 | + | 0.321288i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.0000 | −1.11027 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.0000 | −1.72317 | −0.861586 | − | 0.507611i | \(-0.830529\pi\) | ||||
−0.861586 | + | 0.507611i | \(0.830529\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.00000 | + | 8.00000i | 0.311400 | + | 0.622799i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 6.00000i | − | 0.464294i | −0.972681 | − | 0.232147i | \(-0.925425\pi\) | ||
0.972681 | − | 0.232147i | \(-0.0745750\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.00000i | 0.611775i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.0000 | −1.82469 | −0.912343 | − | 0.409426i | \(-0.865729\pi\) | ||||
−0.912343 | + | 0.409426i | \(0.865729\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.00000 | + | 3.00000i | 0.302372 | + | 0.226779i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.00000i | 0.450988i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.0000i | 1.49487i | 0.664335 | + | 0.747435i | \(0.268715\pi\) | ||||
−0.664335 | + | 0.747435i | \(0.731285\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.00000i | − | 0.148659i | −0.997234 | − | 0.0743294i | \(-0.976318\pi\) | ||
0.997234 | − | 0.0743294i | \(-0.0236816\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000i | 0.147844i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.0000 | − | 6.00000i | 0.882258 | − | 0.441129i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.00000 | 0.585018 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.0000 | 1.44715 | 0.723575 | − | 0.690246i | \(-0.242498\pi\) | ||||
0.723575 | + | 0.690246i | \(0.242498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.0000i | 1.15171i | 0.817554 | + | 0.575853i | \(0.195330\pi\) | ||||
−0.817554 | + | 0.575853i | \(0.804670\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.00000 | + | 2.00000i | −0.286446 | + | 0.143223i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.0000 | −0.705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.00000 | −0.140372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 4.00000i | − | 0.278019i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 32.0000 | 2.21349 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4.00000i | − | 0.275371i | −0.990476 | − | 0.137686i | \(-0.956034\pi\) | ||
0.990476 | − | 0.137686i | \(-0.0439664\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.0000 | 0.822226 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.0000 | + | 10.0000i | −1.36399 | + | 0.681994i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000i | 0.271538i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.00000i | 0.405442i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.00000i | 0.269069i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4.00000i | − | 0.267860i | −0.990991 | − | 0.133930i | \(-0.957240\pi\) | ||
0.990991 | − | 0.133930i | \(-0.0427597\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | − | 4.00000i | 0.200000 | − | 0.266667i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.0000 | −1.32745 | −0.663723 | − | 0.747978i | \(-0.731025\pi\) | ||||
−0.663723 | + | 0.747978i | \(0.731025\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0000i | 0.925146i | 0.886581 | + | 0.462573i | \(0.153074\pi\) | ||||
−0.886581 | + | 0.462573i | \(0.846926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.00000 | 0.263181 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.00000i | 0.393073i | 0.980497 | + | 0.196537i | \(0.0629694\pi\) | ||||
−0.980497 | + | 0.196537i | \(0.937031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | − | 12.0000i | −0.391397 | − | 0.782794i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.0000 | 0.909398 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.00000 | − | 1.00000i | 0.127775 | − | 0.0638877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.0000i | 1.01806i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0000 | 0.760469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 26.0000i | − | 1.64111i | −0.571571 | − | 0.820553i | \(-0.693666\pi\) | ||
0.571571 | − | 0.820553i | \(-0.306334\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.0000 | −1.00591 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.00000 | − | 4.00000i | −0.125245 | − | 0.250490i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 10.0000i | − | 0.623783i | −0.950118 | − | 0.311891i | \(-0.899037\pi\) | ||
0.950118 | − | 0.311891i | \(-0.100963\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 6.00000i | − | 0.372822i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000i | 0.123797i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 16.0000i | − | 0.986602i | −0.869859 | − | 0.493301i | \(-0.835790\pi\) | ||
0.869859 | − | 0.493301i | \(-0.164210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.0000 | − | 14.0000i | 1.72003 | − | 0.860013i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.00000 | 0.489592 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 18.0000i | − | 1.09748i | −0.835993 | − | 0.548740i | \(-0.815108\pi\) | ||
0.835993 | − | 0.548740i | \(-0.184892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.0000 | 0.971931 | 0.485965 | − | 0.873978i | \(-0.338468\pi\) | ||||
0.485965 | + | 0.873978i | \(0.338468\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.00000i | 0.121046i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.0000 | − | 12.0000i | −0.964836 | − | 0.723627i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.0000 | 1.32185 | 0.660926 | − | 0.750451i | \(-0.270164\pi\) | ||||
0.660926 | + | 0.750451i | \(0.270164\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.00000 | 0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.00000 | − | 16.0000i | −0.473879 | − | 0.947758i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00000i | 0.351726i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.00000 | − | 12.0000i | −0.349334 | − | 0.698667i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 4.00000i | − | 0.232104i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 8.00000i | − | 0.462652i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0000i | 0.576390i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 6.00000i | − | 0.344691i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.00000 | − | 4.00000i | −0.114520 | − | 0.229039i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0000 | 1.59804 | 0.799022 | − | 0.601302i | \(-0.205351\pi\) | ||||
0.799022 | + | 0.601302i | \(0.205351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000i | 0.455104i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.00000 | 0.453638 | 0.226819 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 14.0000i | − | 0.791327i | −0.918396 | − | 0.395663i | \(-0.870515\pi\) | ||
0.918396 | − | 0.395663i | \(-0.129485\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.00000 | − | 2.00000i | −0.0563436 | − | 0.112687i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.00000 | 0.112331 | 0.0561656 | − | 0.998421i | \(-0.482113\pi\) | ||||
0.0561656 | + | 0.998421i | \(0.482113\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.00000 | 0.447914 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.00000 | 0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.0000 | −0.890264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.00000 | − | 8.00000i | 0.332820 | − | 0.443760i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.0000i | 0.884802i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.00000 | −0.330791 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000i | 0.219860i | 0.993939 | + | 0.109930i | \(0.0350627\pi\) | ||||
−0.993939 | + | 0.109930i | \(0.964937\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.00000 | −0.328798 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20.0000 | − | 10.0000i | 1.09272 | − | 0.546358i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8.00000i | − | 0.435788i | −0.975972 | − | 0.217894i | \(-0.930081\pi\) | ||
0.975972 | − | 0.217894i | \(-0.0699187\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000i | 0.325875i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 16.0000i | − | 0.866449i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.00000 | + | 8.00000i | 0.215353 | + | 0.430706i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.0000 | 0.644194 | 0.322097 | − | 0.946707i | \(-0.395612\pi\) | ||||
0.322097 | + | 0.946707i | \(0.395612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0000i | 0.535288i | 0.963518 | + | 0.267644i | \(0.0862451\pi\) | ||||
−0.963518 | + | 0.267644i | \(0.913755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.00000 | 0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 2.00000i | − | 0.106449i | −0.998583 | − | 0.0532246i | \(-0.983050\pi\) | ||
0.998583 | − | 0.0532246i | \(-0.0169499\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.0000 | + | 12.0000i | −1.27379 | + | 0.636894i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.00000 | −0.105851 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.0000 | −1.26667 | −0.633336 | − | 0.773877i | \(-0.718315\pi\) | ||||
−0.633336 | + | 0.773877i | \(0.718315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −45.0000 | −2.36842 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.00000 | −0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | − | 12.0000i | −0.314054 | − | 0.628109i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 12.0000i | − | 0.626395i | −0.949688 | − | 0.313197i | \(-0.898600\pi\) | ||
0.949688 | − | 0.313197i | \(-0.101400\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 14.0000i | − | 0.726844i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.0000 | 1.34623 | 0.673114 | − | 0.739538i | \(-0.264956\pi\) | ||||
0.673114 | + | 0.739538i | \(0.264956\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.00000 | + | 11.0000i | −0.103280 | + | 0.568038i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.00000i | 0.206010i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 36.0000i | − | 1.84920i | −0.380945 | − | 0.924598i | \(-0.624401\pi\) | ||
0.380945 | − | 0.924598i | \(-0.375599\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.0000i | 0.819705i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 22.0000i | − | 1.12415i | −0.827087 | − | 0.562074i | \(-0.810004\pi\) | ||
0.827087 | − | 0.562074i | \(-0.189996\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | + | 4.00000i | −0.407718 | + | 0.203859i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.0000 | 0.508329 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 38.0000i | 1.92668i | 0.268290 | + | 0.963338i | \(0.413542\pi\) | ||||
−0.268290 | + | 0.963338i | \(0.586458\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.0000i | 0.907980i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −28.0000 | + | 14.0000i | −1.40883 | + | 0.704416i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.00000 | 0.301131 | 0.150566 | − | 0.988600i | \(-0.451890\pi\) | ||||
0.150566 | + | 0.988600i | \(0.451890\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.00000 | −0.400501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.00000 | −0.299626 | −0.149813 | − | 0.988714i | \(-0.547867\pi\) | ||||
−0.149813 | + | 0.988714i | \(0.547867\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.00000 | 0.398508 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.00000 | + | 1.00000i | −0.0993808 | + | 0.0496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0000i | 1.18964i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.0000 | −1.48340 | −0.741702 | − | 0.670729i | \(-0.765981\pi\) | ||||
−0.741702 | + | 0.670729i | \(0.765981\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 6.00000i | − | 0.295958i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.00000 | −0.295241 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.0000 | + | 12.0000i | −1.17811 | + | 0.589057i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.0000i | 0.587643i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 26.0000i | − | 1.27018i | −0.772437 | − | 0.635092i | \(-0.780962\pi\) | ||
0.772437 | − | 0.635092i | \(-0.219038\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.00000i | 0.194948i | 0.995238 | + | 0.0974740i | \(0.0310763\pi\) | ||||
−0.995238 | + | 0.0974740i | \(0.968924\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.00000i | 0.291730i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.00000 | + | 6.00000i | 0.388057 | + | 0.291043i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.00000 | −0.0967868 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 8.00000i | − | 0.386244i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 34.0000i | − | 1.63394i | −0.576683 | − | 0.816968i | \(-0.695653\pi\) | ||
0.576683 | − | 0.816968i | \(-0.304347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.00000 | − | 4.00000i | −0.0958927 | − | 0.191785i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 32.0000 | 1.53077 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.0000 | 0.572729 | 0.286364 | − | 0.958121i | \(-0.407553\pi\) | ||||
0.286364 | + | 0.958121i | \(0.407553\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.0000 | −1.33032 | −0.665160 | − | 0.746701i | \(-0.731637\pi\) | ||||
−0.665160 | + | 0.746701i | \(0.731637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.0000 | + | 8.00000i | −0.758473 | + | 0.379236i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 10.0000i | − | 0.472984i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.00000 | −0.0939682 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.00000 | − | 4.00000i | −0.0937614 | − | 0.187523i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.0000i | 0.935561i | 0.883845 | + | 0.467780i | \(0.154946\pi\) | ||||
−0.883845 | + | 0.467780i | \(0.845054\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.00000i | 0.0933520i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.0000i | 0.838344i | 0.907907 | + | 0.419172i | \(0.137680\pi\) | ||||
−0.907907 | + | 0.419172i | \(0.862320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.00000i | − | 0.371792i | −0.982569 | − | 0.185896i | \(-0.940481\pi\) | ||
0.982569 | − | 0.185896i | \(-0.0595187\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.00000 | + | 4.00000i | −0.370991 | + | 0.185496i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.0000 | −1.66588 | −0.832941 | − | 0.553362i | \(-0.813345\pi\) | ||||
−0.832941 | + | 0.553362i | \(0.813345\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 10.0000i | − | 0.461757i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.0000 | 0.460776 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 40.0000i | − | 1.83920i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 32.0000 | + | 24.0000i | 1.46826 | + | 1.10120i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.0000 | −0.641016 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0000 | −0.547153 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.00000 | 0.182006 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.00000 | − | 12.0000i | −0.272446 | − | 0.544892i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8.00000i | − | 0.362515i | −0.983436 | − | 0.181257i | \(-0.941983\pi\) | ||
0.983436 | − | 0.181257i | \(-0.0580167\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22.0000 | −0.994874 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 8.00000i | − | 0.361035i | −0.983572 | − | 0.180517i | \(-0.942223\pi\) | ||
0.983572 | − | 0.180517i | \(-0.0577772\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.00000 | −0.180151 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.00000 | + | 8.00000i | 0.179787 | + | 0.359573i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.0000i | 0.538274i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 20.0000i | − | 0.895323i | −0.894203 | − | 0.447661i | \(-0.852257\pi\) | ||
0.894203 | − | 0.447661i | \(-0.147743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 6.00000i | − | 0.268060i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 10.0000i | − | 0.445878i | −0.974832 | − | 0.222939i | \(-0.928435\pi\) | ||
0.974832 | − | 0.222939i | \(-0.0715651\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | + | 12.0000i | 0.266996 | + | 0.533993i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.00000 | −0.399704 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.00000i | 0.0886484i | 0.999017 | + | 0.0443242i | \(0.0141135\pi\) | ||||
−0.999017 | + | 0.0443242i | \(0.985887\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00000 | −0.265424 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.00000i | 0.353209i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.00000 | − | 16.0000i | −0.352522 | − | 0.705044i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.0000 | 1.05552 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.0000 | −1.05348 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.0000 | 0.525730 | 0.262865 | − | 0.964833i | \(-0.415333\pi\) | ||||
0.262865 | + | 0.964833i | \(0.415333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0000 | 0.699631 | 0.349816 | − | 0.936819i | \(-0.386244\pi\) | ||||
0.349816 | + | 0.936819i | \(0.386244\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.00000 | + | 3.00000i | 0.174574 | + | 0.130931i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.00000i | 0.348485i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.00000i | 0.260378i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.00000 | + | 4.00000i | −0.345870 | + | 0.172935i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.0000i | 0.863064i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.00000i | 0.172292i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 28.0000i | − | 1.20381i | −0.798566 | − | 0.601907i | \(-0.794408\pi\) | ||
0.798566 | − | 0.601907i | \(-0.205592\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 2.00000i | − | 0.0858282i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.0000 | − | 32.0000i | −0.685365 | − | 1.37073i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.0000 | 1.62476 | 0.812381 | − | 0.583127i | \(-0.198171\pi\) | ||||
0.812381 | + | 0.583127i | \(0.198171\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.00000i | 0.0853579i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.0000 | −0.681623 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.0000i | 0.595341i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.0000 | − | 6.00000i | 0.509372 | − | 0.254686i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.0000 | 0.593199 | 0.296600 | − | 0.955002i | \(-0.404147\pi\) | ||||
0.296600 | + | 0.955002i | \(0.404147\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.0000 | 0.845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.0000 | 1.51722 | 0.758610 | − | 0.651546i | \(-0.225879\pi\) | ||||
0.758610 | + | 0.651546i | \(0.225879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.00000 | − | 12.0000i | −0.252422 | − | 0.504844i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.0000 | 1.08998 | 0.544988 | − | 0.838444i | \(-0.316534\pi\) | ||||
0.544988 | + | 0.838444i | \(0.316534\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 20.0000i | − | 0.836974i | −0.908223 | − | 0.418487i | \(-0.862561\pi\) | ||
0.908223 | − | 0.418487i | \(-0.137439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.0000 | 0.835512 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.0000 | − | 12.0000i | −0.667246 | − | 0.500435i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.0000i | 0.915872i | 0.888985 | + | 0.457936i | \(0.151411\pi\) | ||||
−0.888985 | + | 0.457936i | \(0.848589\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.0000i | 0.664937i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000i | 0.497844i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 56.0000i | 2.31928i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.00000 | + | 2.00000i | −0.165380 | + | 0.0826898i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.0000 | 1.48588 | 0.742940 | − | 0.669359i | \(-0.233431\pi\) | ||||
0.742940 | + | 0.669359i | \(0.233431\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.0000i | 1.31854i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.00000 | −0.246807 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 18.0000i | − | 0.739171i | −0.929197 | − | 0.369586i | \(-0.879500\pi\) | ||
0.929197 | − | 0.369586i | \(-0.120500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.00000 | − | 2.00000i | 0.163984 | − | 0.0819920i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.00000 | 0.163436 | 0.0817178 | − | 0.996656i | \(-0.473959\pi\) | ||||
0.0817178 | + | 0.996656i | \(0.473959\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.0000 | −1.22373 | −0.611863 | − | 0.790964i | \(-0.709580\pi\) | ||||
−0.611863 | + | 0.790964i | \(0.709580\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.0000 | −0.407231 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.0000 | − | 5.00000i | 0.406558 | − | 0.203279i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 16.0000i | − | 0.649420i | −0.945814 | − | 0.324710i | \(-0.894733\pi\) | ||
0.945814 | − | 0.324710i | \(-0.105267\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.00000 | −0.0810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.0000i | 0.485468i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.0000 | 1.37325 | 0.686624 | − | 0.727013i | \(-0.259092\pi\) | ||||
0.686624 | + | 0.727013i | \(0.259092\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 22.0000i | − | 0.885687i | −0.896599 | − | 0.442843i | \(-0.853970\pi\) | ||
0.896599 | − | 0.442843i | \(-0.146030\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.0000i | 1.60774i | 0.594808 | + | 0.803868i | \(0.297228\pi\) | ||||
−0.594808 | + | 0.803868i | \(0.702772\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 4.00000i | − | 0.160514i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.00000i | 0.320513i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 32.0000 | 1.27796 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 12.0000i | − | 0.478471i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.0000 | −1.51276 | −0.756378 | − | 0.654135i | \(-0.773033\pi\) | ||||
−0.756378 | + | 0.654135i | \(0.773033\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 4.00000i | − | 0.158986i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.0000 | − | 32.0000i | −0.634941 | − | 1.26988i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.00000 | −0.0792429 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000 | 0.474713 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.0000 | −1.02694 | −0.513469 | − | 0.858108i | \(-0.671640\pi\) | ||||
−0.513469 | + | 0.858108i | \(0.671640\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.0000 | −0.630978 | −0.315489 | − | 0.948929i | \(-0.602169\pi\) | ||||
−0.315489 | + | 0.948929i | \(0.602169\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20.0000 | + | 10.0000i | −0.787499 | + | 0.393750i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.0000i | 1.49393i | 0.664861 | + | 0.746967i | \(0.268491\pi\) | ||||
−0.664861 | + | 0.746967i | \(0.731509\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.0000 | 0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.00000i | 0.156772i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.0000 | −0.704394 | −0.352197 | − | 0.935926i | \(-0.614565\pi\) | ||||
−0.352197 | + | 0.935926i | \(0.614565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.0000 | − | 36.0000i | −0.703318 | − | 1.40664i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.00000i | 0.234082i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 24.0000i | − | 0.934907i | −0.884018 | − | 0.467454i | \(-0.845171\pi\) | ||
0.884018 | − | 0.467454i | \(-0.154829\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 42.0000i | − | 1.63361i | −0.576913 | − | 0.816805i | \(-0.695743\pi\) | ||
0.576913 | − | 0.816805i | \(-0.304257\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.00000i | 0.155347i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.0000 | − | 8.00000i | 0.620453 | − | 0.310227i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.00000 | 0.309761 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 4.00000i | − | 0.154649i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.00000 | 0.308837 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.00000i | 0.154189i | 0.997024 | + | 0.0770943i | \(0.0245643\pi\) | ||||
−0.997024 | + | 0.0770943i | \(0.975436\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.00000 | − | 4.00000i | 0.115470 | − | 0.153960i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.0000 | −1.22986 | −0.614930 | − | 0.788582i | \(-0.710816\pi\) | ||||
−0.614930 | + | 0.788582i | \(0.710816\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.00000 | −0.230259 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.0000 | −0.766402 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.00000 | −0.153056 | −0.0765279 | − | 0.997067i | \(-0.524383\pi\) | ||||
−0.0765279 | + | 0.997067i | \(0.524383\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.00000 | + | 12.0000i | 0.229248 | + | 0.458496i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.0000i | 0.534133i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.0000 | −1.06672 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000i | 0.760836i | 0.924815 | + | 0.380418i | \(0.124220\pi\) | ||||
−0.924815 | + | 0.380418i | \(0.875780\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.00000 | 0.151947 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.0000 | − | 24.0000i | −0.455186 | − | 0.910372i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.00000i | 0.226941i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 18.0000i | − | 0.679851i | −0.940452 | − | 0.339925i | \(-0.889598\pi\) | ||
0.940452 | − | 0.339925i | \(-0.110402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 48.0000i | − | 1.81035i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.00000 | − | 12.0000i | −0.225973 | − | 0.451946i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00000 | 0.225653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 48.0000i | − | 1.80268i | −0.433114 | − | 0.901339i | \(-0.642585\pi\) | ||
0.433114 | − | 0.901339i | \(-0.357415\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.0000 | 0.525041 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 16.0000i | − | 0.599205i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.00000 | + | 16.0000i | 0.299183 | + | 0.598366i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.0000 | 0.448148 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.0000 | −1.49175 | −0.745874 | − | 0.666087i | \(-0.767968\pi\) | ||||
−0.745874 | + | 0.666087i | \(0.767968\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.0000 | −0.371904 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.00000 | + | 6.00000i | 0.297113 | + | 0.222834i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.0000i | 1.03846i | 0.854634 | + | 0.519231i | \(0.173782\pi\) | ||||
−0.854634 | + | 0.519231i | \(0.826218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.0000i | 0.739727i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.0000 | 0.517102 | 0.258551 | − | 0.965998i | \(-0.416755\pi\) | ||||
0.258551 | + | 0.965998i | \(0.416755\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.00000 | − | 1.00000i | 0.0737711 | − | 0.0368856i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 40.0000i | 1.47342i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 20.0000i | − | 0.735712i | −0.929883 | − | 0.367856i | \(-0.880092\pi\) | ||
0.929883 | − | 0.367856i | \(-0.119908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.0000i | 0.587775i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.0000i | 0.880475i | 0.897881 | + | 0.440237i | \(0.145106\pi\) | ||||
−0.897881 | + | 0.440237i | \(0.854894\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.0000 | + | 20.0000i | 0.366372 | + | 0.732743i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.0000 | 0.439057 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.00000i | 0.146157i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −50.0000 | −1.82453 | −0.912263 | − | 0.409605i | \(-0.865667\pi\) | ||||
−0.912263 | + | 0.409605i | \(0.865667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 26.0000i | − | 0.947493i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.00000 | − | 2.00000i | 0.145575 | − | 0.0727875i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.0000 | −0.580763 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.0000 | −1.16000 | −0.580000 | − | 0.814617i | \(-0.696947\pi\) | ||||
−0.580000 | + | 0.814617i | \(0.696947\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.0000 | −0.579239 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.00000 | − | 4.00000i | −0.0723102 | − | 0.144620i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.0000i | 0.433295i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.00000 | −0.0721218 | −0.0360609 | − | 0.999350i | \(-0.511481\pi\) | ||||
−0.0360609 | + | 0.999350i | \(0.511481\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 10.0000i | − | 0.360141i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.0000 | −0.863220 | −0.431610 | − | 0.902060i | \(-0.642054\pi\) | ||||
−0.431610 | + | 0.902060i | \(0.642054\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.0000 | − | 16.0000i | 0.431053 | − | 0.574737i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 6.00000i | − | 0.215249i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 48.0000i | − | 1.71758i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.00000i | 0.0714742i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.0000 | + | 10.0000i | −0.713831 | + | 0.356915i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.0000 | 0.998092 | 0.499046 | − | 0.866575i | \(-0.333684\pi\) | ||||
0.499046 | + | 0.866575i | \(0.333684\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 16.0000i | − | 0.569615i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.00000 | −0.213335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.00000i | 0.142044i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 28.0000 | − | 14.0000i | 0.993058 | − | 0.496529i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.0000 | 0.850124 | 0.425062 | − | 0.905164i | \(-0.360252\pi\) | ||||
0.425062 | + | 0.905164i | \(0.360252\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.0000 | −0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.00000 | 0.282666 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.0000 | 0.846942 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.00000 | + | 4.00000i | −0.281963 | + | 0.140981i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 18.0000i | − | 0.633630i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.0000 | 0.914111 | 0.457056 | − | 0.889438i | \(-0.348904\pi\) | ||||
0.457056 | + | 0.889438i | \(0.348904\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.00000i | 0.280918i | 0.990086 | + | 0.140459i | \(0.0448578\pi\) | ||||
−0.990086 | + | 0.140459i | \(0.955142\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.0000 | 0.561144 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 44.0000 | − | 22.0000i | 1.54125 | − | 0.770626i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 80.0000i | 2.79885i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.00000i | 0.0698857i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.0000i | 0.628204i | 0.949389 | + | 0.314102i | \(0.101703\pi\) | ||||
−0.949389 | + | 0.314102i | \(0.898297\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0000i | 0.836587i | 0.908312 | + | 0.418294i | \(0.137372\pi\) | ||||
−0.908312 | + | 0.418294i | \(0.862628\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −16.0000 | − | 12.0000i | −0.557048 | − | 0.417786i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.00000i | 0.0694629i | 0.999397 | + | 0.0347314i | \(0.0110576\pi\) | ||||
−0.999397 | + | 0.0347314i | \(0.988942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.0000 | 0.763172 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 2.00000i | − | 0.0692959i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.00000 | + | 12.0000i | 0.207639 | + | 0.415277i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.00000 | 0.138260 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.0000 | −0.552381 | −0.276191 | − | 0.961103i | \(-0.589072\pi\) | ||||
−0.276191 | + | 0.961103i | \(0.589072\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.00000 | 0.206651 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.0000 | − | 9.00000i | 0.619219 | − | 0.309609i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 5.00000i | − | 0.171802i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.00000 | −0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.0000i | 0.822709i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.00000 | 0.205436 | 0.102718 | − | 0.994711i | \(-0.467246\pi\) | ||||
0.102718 | + | 0.994711i | \(0.467246\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.00000 | − | 16.0000i | −0.273594 | − | 0.547188i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 42.0000i | − | 1.43469i | −0.696717 | − | 0.717346i | \(-0.745357\pi\) | ||
0.696717 | − | 0.717346i | \(-0.254643\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 8.00000i | − | 0.272956i | −0.990643 | − | 0.136478i | \(-0.956422\pi\) | ||
0.990643 | − | 0.136478i | \(-0.0435784\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 36.0000i | − | 1.22545i | −0.790295 | − | 0.612727i | \(-0.790072\pi\) | ||
0.790295 | − | 0.612727i | \(-0.209928\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 48.0000 | − | 24.0000i | 1.63205 | − | 0.816024i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000 | 0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 56.0000i | − | 1.89967i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.0000 | −0.677674 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.00000i | 0.203069i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.0000 | − | 2.00000i | −0.371868 | − | 0.0676123i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.0000 | −0.877958 | −0.438979 | − | 0.898497i | \(-0.644660\pi\) | ||||
−0.438979 | + | 0.898497i | \(0.644660\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.0000 | 1.48240 | 0.741199 | − | 0.671286i | \(-0.234258\pi\) | ||||
0.741199 | + | 0.671286i | \(0.234258\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −50.0000 | −1.68263 | −0.841317 | − | 0.540542i | \(-0.818219\pi\) | ||||
−0.841317 | + | 0.540542i | \(0.818219\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.00000 | − | 12.0000i | −0.201688 | − | 0.403376i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 18.0000i | − | 0.604381i | −0.953248 | − | 0.302190i | \(-0.902282\pi\) | ||
0.953248 | − | 0.302190i | \(-0.0977178\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.0000 | −0.536623 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 4.00000i | − | 0.134005i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −48.0000 | −1.60626 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.0000 | − | 40.0000i | −0.668526 | − | 1.33705i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 8.00000i | − | 0.267112i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.00000i | 0.266815i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 28.0000i | − | 0.932815i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.0000i | 0.332779i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.00000 | + | 4.00000i | 0.0664822 | + | 0.132964i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.0000 | 0.863316 | 0.431658 | − | 0.902037i | \(-0.357929\pi\) | ||||
0.431658 | + | 0.902037i | \(0.357929\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 6.00000i | − | 0.199007i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.00000 | 0.265052 | 0.132526 | − | 0.991180i | \(-0.457691\pi\) | ||||
0.132526 | + | 0.991180i | \(0.457691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 48.0000i | − | 1.58857i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.00000 | − | 4.00000i | −0.0661180 | − | 0.132236i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.0000 | −0.594412 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.0000 | −0.329870 | −0.164935 | − | 0.986304i | \(-0.552741\pi\) | ||||
−0.164935 | + | 0.986304i | \(0.552741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.0000 | 0.922631 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.0000 | 0.789970 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.0000 | + | 24.0000i | −0.591836 | + | 0.789115i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.00000i | 0.262754i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −56.0000 | −1.83730 | −0.918650 | − | 0.395072i | \(-0.870720\pi\) | ||||
−0.918650 | + | 0.395072i | \(0.870720\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 8.00000i | − | 0.262189i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.00000 | 0.261908 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.0000 | + | 8.00000i | −0.523256 | + | 0.261628i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 18.0000i | − | 0.588034i | −0.955800 | − | 0.294017i | \(-0.905008\pi\) | ||
0.955800 | − | 0.294017i | \(-0.0949923\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 14.0000i | − | 0.456873i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 18.0000i | − | 0.586783i | −0.955992 | − | 0.293392i | \(-0.905216\pi\) | ||
0.955992 | − | 0.293392i | \(-0.0947840\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.00000 | − | 2.00000i | −0.0325300 | − | 0.0650600i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.0000 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.0000i | 0.389536i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.00000 | 0.0648544 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.00000i | 0.194359i | 0.995267 | + | 0.0971795i | \(0.0309821\pi\) | ||||
−0.995267 | + | 0.0971795i | \(0.969018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.0000 | + | 20.0000i | −1.29437 | + | 0.647185i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.00000 | 0.258603 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.00000 | 0.193750 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.00000 | 0.128898 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.0000 | − | 32.0000i | −0.515058 | − | 1.03012i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.0000i | 1.80084i | 0.435023 | + | 0.900419i | \(0.356740\pi\) | ||||
−0.435023 | + | 0.900419i | \(0.643260\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.0000 | −0.513994 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 26.0000i | − | 0.834380i | −0.908819 | − | 0.417190i | \(-0.863015\pi\) | ||
0.908819 | − | 0.417190i | \(-0.136985\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0000 | −0.384702 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.00000 | − | 8.00000i | 0.192154 | − | 0.256205i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.00000i | 0.0639857i | 0.999488 | + | 0.0319928i | \(0.0101854\pi\) | ||||
−0.999488 | + | 0.0319928i | \(0.989815\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 32.0000i | − | 1.02272i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.0000i | 0.510841i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 6.00000i | − | 0.191370i | −0.995412 | − | 0.0956851i | \(-0.969496\pi\) | ||
0.995412 | − | 0.0956851i | \(-0.0305042\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.0000 | − | 6.00000i | 0.382352 | − | 0.191176i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.00000 | −0.190982 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 40.0000i | − | 1.27193i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.0000 | 1.58830 | 0.794151 | − | 0.607720i | \(-0.207916\pi\) | ||||
0.794151 | + | 0.607720i | \(0.207916\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.00000i | 0.126936i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.0000 | −1.07679 | −0.538395 | − | 0.842692i | \(-0.680969\pi\) | ||||
−0.538395 | + | 0.842692i | \(0.680969\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.00000 | −0.189832 |
(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 | 3360.2.j.c.1009.2 | 2 | ||
4.3 | odd | 2 | 840.2.j.a.589.1 | ✓ | 2 | ||
5.4 | even | 2 | 3360.2.j.b.1009.2 | 2 | |||
8.3 | odd | 2 | 840.2.j.d.589.1 | yes | 2 | ||
8.5 | even | 2 | 3360.2.j.b.1009.1 | 2 | |||
20.19 | odd | 2 | 840.2.j.d.589.2 | yes | 2 | ||
40.19 | odd | 2 | 840.2.j.a.589.2 | yes | 2 | ||
40.29 | even | 2 | inner | 3360.2.j.c.1009.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.j.a.589.1 | ✓ | 2 | 4.3 | odd | 2 | ||
840.2.j.a.589.2 | yes | 2 | 40.19 | odd | 2 | ||
840.2.j.d.589.1 | yes | 2 | 8.3 | odd | 2 | ||
840.2.j.d.589.2 | yes | 2 | 20.19 | odd | 2 | ||
3360.2.j.b.1009.1 | 2 | 8.5 | even | 2 | |||
3360.2.j.b.1009.2 | 2 | 5.4 | even | 2 | |||
3360.2.j.c.1009.1 | 2 | 40.29 | even | 2 | inner | ||
3360.2.j.c.1009.2 | 2 | 1.1 | even | 1 | trivial |