Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(961,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1110.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.h (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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.279290944.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 26x^{4} + 169x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{37}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 961.2 | ||
Root | \(-0.309984i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.961 |
Dual form | 1110.2.h.f.961.5 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | −1.30998 | −0.495127 | −0.247564 | − | 0.968872i | \(-0.579630\pi\) | ||||
−0.247564 | + | 0.968872i | \(0.579630\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0.690016 | 0.208048 | 0.104024 | − | 0.994575i | \(-0.466828\pi\) | ||||
0.104024 | + | 0.994575i | \(0.466828\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 2.69002i | 0.746076i | 0.927816 | + | 0.373038i | \(0.121684\pi\) | ||||
−0.927816 | + | 0.373038i | \(0.878316\pi\) | |||||||
\(14\) | 1.30998i | 0.350108i | ||||||||
\(15\) | − | 1.00000i | − | 0.258199i | ||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 6.90391i | − | 1.67444i | −0.546863 | − | 0.837222i | \(-0.684178\pi\) | ||
0.546863 | − | 0.837222i | \(-0.315822\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | − | 2.69002i | − | 0.617132i | −0.951203 | − | 0.308566i | \(-0.900151\pi\) | ||
0.951203 | − | 0.308566i | \(-0.0998491\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | −1.30998 | −0.285862 | ||||||||
\(22\) | − | 0.690016i | − | 0.147112i | ||||||
\(23\) | − | 8.90391i | − | 1.85659i | −0.371840 | − | 0.928297i | \(-0.621273\pi\) | ||
0.371840 | − | 0.928297i | \(-0.378727\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 2.69002 | 0.527556 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.30998 | 0.247564 | ||||||||
\(29\) | 2.00000i | 0.371391i | 0.982607 | + | 0.185695i | \(0.0594537\pi\) | ||||
−0.982607 | + | 0.185695i | \(0.940546\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | − | 9.59393i | − | 1.72312i | −0.507656 | − | 0.861560i | \(-0.669488\pi\) | ||
0.507656 | − | 0.861560i | \(-0.330512\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0.690016 | 0.120116 | ||||||||
\(34\) | −6.90391 | −1.18401 | ||||||||
\(35\) | 1.30998i | 0.221428i | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 4.10695 | − | 4.48698i | 0.675178 | − | 0.737655i | ||||
\(38\) | −2.69002 | −0.436378 | ||||||||
\(39\) | 2.69002i | 0.430747i | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 1.30998i | 0.202135i | ||||||||
\(43\) | 8.21389i | 1.25261i | 0.779579 | + | 0.626304i | \(0.215433\pi\) | ||||
−0.779579 | + | 0.626304i | \(0.784567\pi\) | |||||||
\(44\) | −0.690016 | −0.104024 | ||||||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | −8.90391 | −1.31281 | ||||||||
\(47\) | −4.61997 | −0.673891 | −0.336946 | − | 0.941524i | \(-0.609394\pi\) | ||||
−0.336946 | + | 0.941524i | \(0.609394\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −5.28394 | −0.754849 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | − | 6.90391i | − | 0.966741i | ||||||
\(52\) | − | 2.69002i | − | 0.373038i | ||||||
\(53\) | 0.690016 | 0.0947810 | 0.0473905 | − | 0.998876i | \(-0.484909\pi\) | ||||
0.0473905 | + | 0.998876i | \(0.484909\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | − | 0.690016i | − | 0.0930418i | ||||||
\(56\) | − | 1.30998i | − | 0.175054i | ||||||
\(57\) | − | 2.69002i | − | 0.356301i | ||||||
\(58\) | 2.00000 | 0.262613 | ||||||||
\(59\) | 6.21389i | 0.808980i | 0.914542 | + | 0.404490i | \(0.132551\pi\) | ||||
−0.914542 | + | 0.404490i | \(0.867449\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | 2.00000i | 0.256074i | 0.991769 | + | 0.128037i | \(0.0408676\pi\) | ||||
−0.991769 | + | 0.128037i | \(0.959132\pi\) | |||||||
\(62\) | −9.59393 | −1.21843 | ||||||||
\(63\) | −1.30998 | −0.165042 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.69002 | 0.333655 | ||||||||
\(66\) | − | 0.690016i | − | 0.0849352i | ||||||
\(67\) | −1.23993 | −0.151482 | −0.0757410 | − | 0.997128i | \(-0.524132\pi\) | ||||
−0.0757410 | + | 0.997128i | \(0.524132\pi\) | |||||||
\(68\) | 6.90391i | 0.837222i | ||||||||
\(69\) | − | 8.90391i | − | 1.07190i | ||||||
\(70\) | 1.30998 | 0.156573 | ||||||||
\(71\) | 13.8078 | 1.63869 | 0.819343 | − | 0.573303i | \(-0.194338\pi\) | ||||
0.819343 | + | 0.573303i | \(0.194338\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | −12.2839 | −1.43773 | −0.718863 | − | 0.695151i | \(-0.755337\pi\) | ||||
−0.718863 | + | 0.695151i | \(0.755337\pi\) | |||||||
\(74\) | −4.48698 | − | 4.10695i | −0.521601 | − | 0.477423i | ||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 2.69002i | 0.308566i | ||||||||
\(77\) | −0.903910 | −0.103010 | ||||||||
\(78\) | 2.69002 | 0.304584 | ||||||||
\(79\) | 1.59393i | 0.179331i | 0.995972 | + | 0.0896654i | \(0.0285798\pi\) | ||||
−0.995972 | + | 0.0896654i | \(0.971420\pi\) | |||||||
\(80\) | − | 1.00000i | − | 0.111803i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.00000i | 0.220863i | ||||||||
\(83\) | 10.2839 | 1.12881 | 0.564405 | − | 0.825498i | \(-0.309106\pi\) | ||||
0.564405 | + | 0.825498i | \(0.309106\pi\) | |||||||
\(84\) | 1.30998 | 0.142931 | ||||||||
\(85\) | −6.90391 | −0.748834 | ||||||||
\(86\) | 8.21389 | 0.885727 | ||||||||
\(87\) | 2.00000i | 0.214423i | ||||||||
\(88\) | 0.690016i | 0.0735560i | ||||||||
\(89\) | − | 5.92995i | − | 0.628574i | −0.949328 | − | 0.314287i | \(-0.898235\pi\) | ||
0.949328 | − | 0.314287i | \(-0.101765\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | − | 3.52388i | − | 0.369403i | ||||||
\(92\) | 8.90391i | 0.928297i | ||||||||
\(93\) | − | 9.59393i | − | 0.994844i | ||||||
\(94\) | 4.61997i | 0.476513i | ||||||||
\(95\) | −2.69002 | −0.275990 | ||||||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | − | 3.38003i | − | 0.343190i | −0.985168 | − | 0.171595i | \(-0.945108\pi\) | ||
0.985168 | − | 0.171595i | \(-0.0548921\pi\) | |||||||
\(98\) | 5.28394i | 0.533759i | ||||||||
\(99\) | 0.690016 | 0.0693493 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 8.97396 | 0.892942 | 0.446471 | − | 0.894798i | \(-0.352681\pi\) | ||||
0.446471 | + | 0.894798i | \(0.352681\pi\) | |||||||
\(102\) | −6.90391 | −0.683589 | ||||||||
\(103\) | − | 19.1879i | − | 1.89064i | −0.326151 | − | 0.945318i | \(-0.605752\pi\) | ||
0.326151 | − | 0.945318i | \(-0.394248\pi\) | |||||||
\(104\) | −2.69002 | −0.263778 | ||||||||
\(105\) | 1.30998i | 0.127841i | ||||||||
\(106\) | − | 0.690016i | − | 0.0670203i | ||||||
\(107\) | 18.1438 | 1.75403 | 0.877016 | − | 0.480461i | \(-0.159531\pi\) | ||||
0.877016 | + | 0.480461i | \(0.159531\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 17.5239i | 1.67848i | 0.543759 | + | 0.839242i | \(0.317001\pi\) | ||||
−0.543759 | + | 0.839242i | \(0.682999\pi\) | |||||||
\(110\) | −0.690016 | −0.0657905 | ||||||||
\(111\) | 4.10695 | − | 4.48698i | 0.389814 | − | 0.425885i | ||||
\(112\) | −1.30998 | −0.123782 | ||||||||
\(113\) | − | 2.00000i | − | 0.188144i | −0.995565 | − | 0.0940721i | \(-0.970012\pi\) | ||
0.995565 | − | 0.0940721i | \(-0.0299884\pi\) | |||||||
\(114\) | −2.69002 | −0.251943 | ||||||||
\(115\) | −8.90391 | −0.830294 | ||||||||
\(116\) | − | 2.00000i | − | 0.185695i | ||||||
\(117\) | 2.69002i | 0.248692i | ||||||||
\(118\) | 6.21389 | 0.572035 | ||||||||
\(119\) | 9.04401i | 0.829063i | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −10.5239 | −0.956716 | ||||||||
\(122\) | 2.00000 | 0.181071 | ||||||||
\(123\) | −2.00000 | −0.180334 | ||||||||
\(124\) | 9.59393i | 0.861560i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 1.30998i | 0.116703i | ||||||||
\(127\) | −10.6900 | −0.948586 | −0.474293 | − | 0.880367i | \(-0.657296\pi\) | ||||
−0.474293 | + | 0.880367i | \(0.657296\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 8.21389i | 0.723193i | ||||||||
\(130\) | − | 2.69002i | − | 0.235930i | ||||||
\(131\) | 8.97396i | 0.784058i | 0.919953 | + | 0.392029i | \(0.128227\pi\) | ||||
−0.919953 | + | 0.392029i | \(0.871773\pi\) | |||||||
\(132\) | −0.690016 | −0.0600582 | ||||||||
\(133\) | 3.52388i | 0.305559i | ||||||||
\(134\) | 1.23993i | 0.107114i | ||||||||
\(135\) | − | 1.00000i | − | 0.0860663i | ||||||
\(136\) | 6.90391 | 0.592005 | ||||||||
\(137\) | −11.5939 | −0.990536 | −0.495268 | − | 0.868740i | \(-0.664930\pi\) | ||||
−0.495268 | + | 0.868740i | \(0.664930\pi\) | |||||||
\(138\) | −8.90391 | −0.757951 | ||||||||
\(139\) | −6.76007 | −0.573381 | −0.286691 | − | 0.958023i | \(-0.592555\pi\) | ||||
−0.286691 | + | 0.958023i | \(0.592555\pi\) | |||||||
\(140\) | − | 1.30998i | − | 0.110714i | ||||||
\(141\) | −4.61997 | −0.389071 | ||||||||
\(142\) | − | 13.8078i | − | 1.15873i | ||||||
\(143\) | 1.85616i | 0.155220i | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | 12.2839i | 1.01663i | ||||||||
\(147\) | −5.28394 | −0.435812 | ||||||||
\(148\) | −4.10695 | + | 4.48698i | −0.337589 | + | 0.368827i | ||||
\(149\) | 10.2139 | 0.836755 | 0.418377 | − | 0.908273i | \(-0.362599\pi\) | ||||
0.418377 | + | 0.908273i | \(0.362599\pi\) | |||||||
\(150\) | 1.00000i | 0.0816497i | ||||||||
\(151\) | 22.2839 | 1.81344 | 0.906721 | − | 0.421731i | \(-0.138577\pi\) | ||||
0.906721 | + | 0.421731i | \(0.138577\pi\) | |||||||
\(152\) | 2.69002 | 0.218189 | ||||||||
\(153\) | − | 6.90391i | − | 0.558148i | ||||||
\(154\) | 0.903910i | 0.0728392i | ||||||||
\(155\) | −9.59393 | −0.770603 | ||||||||
\(156\) | − | 2.69002i | − | 0.215374i | ||||||
\(157\) | 12.2139 | 0.974775 | 0.487387 | − | 0.873186i | \(-0.337950\pi\) | ||||
0.487387 | + | 0.873186i | \(0.337950\pi\) | |||||||
\(158\) | 1.59393 | 0.126806 | ||||||||
\(159\) | 0.690016 | 0.0547219 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 11.6640i | 0.919250i | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | − | 6.07005i | − | 0.475443i | −0.971333 | − | 0.237721i | \(-0.923599\pi\) | ||
0.971333 | − | 0.237721i | \(-0.0764006\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | − | 0.690016i | − | 0.0537177i | ||||||
\(166\) | − | 10.2839i | − | 0.798189i | ||||||
\(167\) | 8.90391i | 0.689005i | 0.938785 | + | 0.344503i | \(0.111952\pi\) | ||||
−0.938785 | + | 0.344503i | \(0.888048\pi\) | |||||||
\(168\) | − | 1.30998i | − | 0.101067i | ||||||
\(169\) | 5.76381 | 0.443370 | ||||||||
\(170\) | 6.90391i | 0.529506i | ||||||||
\(171\) | − | 2.69002i | − | 0.205711i | ||||||
\(172\) | − | 8.21389i | − | 0.626304i | ||||||
\(173\) | 19.8779 | 1.51129 | 0.755643 | − | 0.654983i | \(-0.227324\pi\) | ||||
0.755643 | + | 0.654983i | \(0.227324\pi\) | |||||||
\(174\) | 2.00000 | 0.151620 | ||||||||
\(175\) | 1.30998 | 0.0990254 | ||||||||
\(176\) | 0.690016 | 0.0520119 | ||||||||
\(177\) | 6.21389i | 0.467065i | ||||||||
\(178\) | −5.92995 | −0.444469 | ||||||||
\(179\) | 19.5939i | 1.46452i | 0.681026 | + | 0.732259i | \(0.261534\pi\) | ||||
−0.681026 | + | 0.732259i | \(0.738466\pi\) | |||||||
\(180\) | 1.00000i | 0.0745356i | ||||||||
\(181\) | −9.18785 | −0.682928 | −0.341464 | − | 0.939895i | \(-0.610923\pi\) | ||||
−0.341464 | + | 0.939895i | \(0.610923\pi\) | |||||||
\(182\) | −3.52388 | −0.261207 | ||||||||
\(183\) | 2.00000i | 0.147844i | ||||||||
\(184\) | 8.90391 | 0.656405 | ||||||||
\(185\) | −4.48698 | − | 4.10695i | −0.329889 | − | 0.301949i | ||||
\(186\) | −9.59393 | −0.703461 | ||||||||
\(187\) | − | 4.76381i | − | 0.348364i | ||||||
\(188\) | 4.61997 | 0.336946 | ||||||||
\(189\) | −1.30998 | −0.0952873 | ||||||||
\(190\) | 2.69002i | 0.195154i | ||||||||
\(191\) | − | 20.9039i | − | 1.51255i | −0.654252 | − | 0.756277i | \(-0.727016\pi\) | ||
0.654252 | − | 0.756277i | \(-0.272984\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 8.61997i | 0.620479i | 0.950658 | + | 0.310239i | \(0.100409\pi\) | ||||
−0.950658 | + | 0.310239i | \(0.899591\pi\) | |||||||
\(194\) | −3.38003 | −0.242672 | ||||||||
\(195\) | 2.69002 | 0.192636 | ||||||||
\(196\) | 5.28394 | 0.377425 | ||||||||
\(197\) | −12.6900 | −0.904126 | −0.452063 | − | 0.891986i | \(-0.649312\pi\) | ||||
−0.452063 | + | 0.891986i | \(0.649312\pi\) | |||||||
\(198\) | − | 0.690016i | − | 0.0490373i | ||||||
\(199\) | 22.8339i | 1.61865i | 0.587361 | + | 0.809325i | \(0.300167\pi\) | ||||
−0.587361 | + | 0.809325i | \(0.699833\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | −1.23993 | −0.0874582 | ||||||||
\(202\) | − | 8.97396i | − | 0.631406i | ||||||
\(203\) | − | 2.61997i | − | 0.183886i | ||||||
\(204\) | 6.90391i | 0.483370i | ||||||||
\(205\) | 2.00000i | 0.139686i | ||||||||
\(206\) | −19.1879 | −1.33688 | ||||||||
\(207\) | − | 8.90391i | − | 0.618865i | ||||||
\(208\) | 2.69002i | 0.186519i | ||||||||
\(209\) | − | 1.85616i | − | 0.128393i | ||||||
\(210\) | 1.30998 | 0.0903975 | ||||||||
\(211\) | −5.38003 | −0.370377 | −0.185188 | − | 0.982703i | \(-0.559290\pi\) | ||||
−0.185188 | + | 0.982703i | \(0.559290\pi\) | |||||||
\(212\) | −0.690016 | −0.0473905 | ||||||||
\(213\) | 13.8078 | 0.946096 | ||||||||
\(214\) | − | 18.1438i | − | 1.24029i | ||||||
\(215\) | 8.21389 | 0.560183 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 12.5679i | 0.853164i | ||||||||
\(218\) | 17.5239 | 1.18687 | ||||||||
\(219\) | −12.2839 | −0.830072 | ||||||||
\(220\) | 0.690016i | 0.0465209i | ||||||||
\(221\) | 18.5716 | 1.24926 | ||||||||
\(222\) | −4.48698 | − | 4.10695i | −0.301146 | − | 0.275640i | ||||
\(223\) | −0.833861 | −0.0558395 | −0.0279197 | − | 0.999610i | \(-0.508888\pi\) | ||||
−0.0279197 | + | 0.999610i | \(0.508888\pi\) | |||||||
\(224\) | 1.30998i | 0.0875270i | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | −2.00000 | −0.133038 | ||||||||
\(227\) | − | 15.1879i | − | 1.00805i | −0.863688 | − | 0.504027i | \(-0.831851\pi\) | ||
0.863688 | − | 0.504027i | \(-0.168149\pi\) | |||||||
\(228\) | 2.69002i | 0.178151i | ||||||||
\(229\) | −7.80782 | −0.515955 | −0.257978 | − | 0.966151i | \(-0.583056\pi\) | ||||
−0.257978 | + | 0.966151i | \(0.583056\pi\) | |||||||
\(230\) | 8.90391i | 0.587106i | ||||||||
\(231\) | −0.903910 | −0.0594729 | ||||||||
\(232\) | −2.00000 | −0.131306 | ||||||||
\(233\) | 3.59393 | 0.235446 | 0.117723 | − | 0.993046i | \(-0.462441\pi\) | ||||
0.117723 | + | 0.993046i | \(0.462441\pi\) | |||||||
\(234\) | 2.69002 | 0.175852 | ||||||||
\(235\) | 4.61997i | 0.301373i | ||||||||
\(236\) | − | 6.21389i | − | 0.404490i | ||||||
\(237\) | 1.59393i | 0.103537i | ||||||||
\(238\) | 9.04401 | 0.586236 | ||||||||
\(239\) | 7.18785i | 0.464944i | 0.972603 | + | 0.232472i | \(0.0746813\pi\) | ||||
−0.972603 | + | 0.232472i | \(0.925319\pi\) | |||||||
\(240\) | − | 1.00000i | − | 0.0645497i | ||||||
\(241\) | 3.18785i | 0.205348i | 0.994715 | + | 0.102674i | \(0.0327398\pi\) | ||||
−0.994715 | + | 0.102674i | \(0.967260\pi\) | |||||||
\(242\) | 10.5239i | 0.676500i | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | − | 2.00000i | − | 0.128037i | ||||||
\(245\) | 5.28394i | 0.337579i | ||||||||
\(246\) | 2.00000i | 0.127515i | ||||||||
\(247\) | 7.23619 | 0.460428 | ||||||||
\(248\) | 9.59393 | 0.609215 | ||||||||
\(249\) | 10.2839 | 0.651718 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 11.5939i | 0.731802i | 0.930654 | + | 0.365901i | \(0.119239\pi\) | ||||
−0.930654 | + | 0.365901i | \(0.880761\pi\) | |||||||
\(252\) | 1.30998 | 0.0825212 | ||||||||
\(253\) | − | 6.14384i | − | 0.386260i | ||||||
\(254\) | 10.6900i | 0.670751i | ||||||||
\(255\) | −6.90391 | −0.432340 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 25.5239i | 1.59214i | 0.605207 | + | 0.796068i | \(0.293090\pi\) | ||||
−0.605207 | + | 0.796068i | \(0.706910\pi\) | |||||||
\(258\) | 8.21389 | 0.511375 | ||||||||
\(259\) | −5.38003 | + | 5.87787i | −0.334299 | + | 0.365233i | ||||
\(260\) | −2.69002 | −0.166828 | ||||||||
\(261\) | 2.00000i | 0.123797i | ||||||||
\(262\) | 8.97396 | 0.554413 | ||||||||
\(263\) | 18.5679 | 1.14494 | 0.572472 | − | 0.819924i | \(-0.305984\pi\) | ||||
0.572472 | + | 0.819924i | \(0.305984\pi\) | |||||||
\(264\) | 0.690016i | 0.0424676i | ||||||||
\(265\) | − | 0.690016i | − | 0.0423874i | ||||||
\(266\) | 3.52388 | 0.216063 | ||||||||
\(267\) | − | 5.92995i | − | 0.362907i | ||||||
\(268\) | 1.23993 | 0.0757410 | ||||||||
\(269\) | −13.3100 | −0.811524 | −0.405762 | − | 0.913979i | \(-0.632994\pi\) | ||||
−0.405762 | + | 0.913979i | \(0.632994\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 17.9479 | 1.09026 | 0.545129 | − | 0.838352i | \(-0.316481\pi\) | ||||
0.545129 | + | 0.838352i | \(0.316481\pi\) | |||||||
\(272\) | − | 6.90391i | − | 0.418611i | ||||||
\(273\) | − | 3.52388i | − | 0.213275i | ||||||
\(274\) | 11.5939i | 0.700415i | ||||||||
\(275\) | −0.690016 | −0.0416096 | ||||||||
\(276\) | 8.90391i | 0.535952i | ||||||||
\(277\) | − | 13.7378i | − | 0.825423i | −0.910862 | − | 0.412711i | \(-0.864582\pi\) | ||
0.910862 | − | 0.412711i | \(-0.135418\pi\) | |||||||
\(278\) | 6.76007i | 0.405442i | ||||||||
\(279\) | − | 9.59393i | − | 0.574373i | ||||||
\(280\) | −1.30998 | −0.0782865 | ||||||||
\(281\) | − | 4.54992i | − | 0.271425i | −0.990748 | − | 0.135713i | \(-0.956668\pi\) | ||
0.990748 | − | 0.135713i | \(-0.0433324\pi\) | |||||||
\(282\) | 4.61997i | 0.275115i | ||||||||
\(283\) | − | 27.7378i | − | 1.64884i | −0.565979 | − | 0.824420i | \(-0.691502\pi\) | ||
0.565979 | − | 0.824420i | \(-0.308498\pi\) | |||||||
\(284\) | −13.8078 | −0.819343 | ||||||||
\(285\) | −2.69002 | −0.159343 | ||||||||
\(286\) | 1.85616 | 0.109757 | ||||||||
\(287\) | 2.61997 | 0.154652 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −30.6640 | −1.80376 | ||||||||
\(290\) | − | 2.00000i | − | 0.117444i | ||||||
\(291\) | − | 3.38003i | − | 0.198141i | ||||||
\(292\) | 12.2839 | 0.718863 | ||||||||
\(293\) | −3.30998 | −0.193371 | −0.0966857 | − | 0.995315i | \(-0.530824\pi\) | ||||
−0.0966857 | + | 0.995315i | \(0.530824\pi\) | |||||||
\(294\) | 5.28394i | 0.308166i | ||||||||
\(295\) | 6.21389 | 0.361787 | ||||||||
\(296\) | 4.48698 | + | 4.10695i | 0.260800 | + | 0.238711i | ||||
\(297\) | 0.690016 | 0.0400388 | ||||||||
\(298\) | − | 10.2139i | − | 0.591675i | ||||||
\(299\) | 23.9517 | 1.38516 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | − | 10.7601i | − | 0.620200i | ||||||
\(302\) | − | 22.2839i | − | 1.28230i | ||||||
\(303\) | 8.97396 | 0.515541 | ||||||||
\(304\) | − | 2.69002i | − | 0.154283i | ||||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | −6.90391 | −0.394670 | ||||||||
\(307\) | 21.9479 | 1.25263 | 0.626317 | − | 0.779569i | \(-0.284562\pi\) | ||||
0.626317 | + | 0.779569i | \(0.284562\pi\) | |||||||
\(308\) | 0.903910 | 0.0515051 | ||||||||
\(309\) | − | 19.1879i | − | 1.09156i | ||||||
\(310\) | 9.59393i | 0.544898i | ||||||||
\(311\) | 18.7601i | 1.06379i | 0.846812 | + | 0.531893i | \(0.178519\pi\) | ||||
−0.846812 | + | 0.531893i | \(0.821481\pi\) | |||||||
\(312\) | −2.69002 | −0.152292 | ||||||||
\(313\) | 21.1879i | 1.19761i | 0.800896 | + | 0.598804i | \(0.204357\pi\) | ||||
−0.800896 | + | 0.598804i | \(0.795643\pi\) | |||||||
\(314\) | − | 12.2139i | − | 0.689270i | ||||||
\(315\) | 1.30998i | 0.0738092i | ||||||||
\(316\) | − | 1.59393i | − | 0.0896654i | ||||||
\(317\) | 23.5418 | 1.32224 | 0.661121 | − | 0.750279i | \(-0.270081\pi\) | ||||
0.661121 | + | 0.750279i | \(0.270081\pi\) | |||||||
\(318\) | − | 0.690016i | − | 0.0386942i | ||||||
\(319\) | 1.38003i | 0.0772670i | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | 18.1438 | 1.01269 | ||||||||
\(322\) | 11.6640 | 0.650008 | ||||||||
\(323\) | −18.5716 | −1.03335 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | − | 2.69002i | − | 0.149215i | ||||||
\(326\) | −6.07005 | −0.336189 | ||||||||
\(327\) | 17.5239i | 0.969073i | ||||||||
\(328\) | − | 2.00000i | − | 0.110432i | ||||||
\(329\) | 6.05208 | 0.333662 | ||||||||
\(330\) | −0.690016 | −0.0379842 | ||||||||
\(331\) | 16.4061i | 0.901759i | 0.892585 | + | 0.450880i | \(0.148890\pi\) | ||||
−0.892585 | + | 0.450880i | \(0.851110\pi\) | |||||||
\(332\) | −10.2839 | −0.564405 | ||||||||
\(333\) | 4.10695 | − | 4.48698i | 0.225059 | − | 0.245885i | ||||
\(334\) | 8.90391 | 0.487200 | ||||||||
\(335\) | 1.23993i | 0.0677448i | ||||||||
\(336\) | −1.30998 | −0.0714655 | ||||||||
\(337\) | 23.3317 | 1.27096 | 0.635479 | − | 0.772118i | \(-0.280803\pi\) | ||||
0.635479 | + | 0.772118i | \(0.280803\pi\) | |||||||
\(338\) | − | 5.76381i | − | 0.313510i | ||||||
\(339\) | − | 2.00000i | − | 0.108625i | ||||||
\(340\) | 6.90391 | 0.374417 | ||||||||
\(341\) | − | 6.61997i | − | 0.358491i | ||||||
\(342\) | −2.69002 | −0.145459 | ||||||||
\(343\) | 16.0918 | 0.868874 | ||||||||
\(344\) | −8.21389 | −0.442863 | ||||||||
\(345\) | −8.90391 | −0.479370 | ||||||||
\(346\) | − | 19.8779i | − | 1.06864i | ||||||
\(347\) | − | 5.38003i | − | 0.288815i | −0.989518 | − | 0.144408i | \(-0.953872\pi\) | ||
0.989518 | − | 0.144408i | \(-0.0461277\pi\) | |||||||
\(348\) | − | 2.00000i | − | 0.107211i | ||||||
\(349\) | −29.1879 | −1.56239 | −0.781195 | − | 0.624287i | \(-0.785390\pi\) | ||||
−0.781195 | + | 0.624287i | \(0.785390\pi\) | |||||||
\(350\) | − | 1.30998i | − | 0.0700216i | ||||||
\(351\) | 2.69002i | 0.143582i | ||||||||
\(352\) | − | 0.690016i | − | 0.0367780i | ||||||
\(353\) | − | 22.4278i | − | 1.19371i | −0.802349 | − | 0.596855i | \(-0.796417\pi\) | ||
0.802349 | − | 0.596855i | \(-0.203583\pi\) | |||||||
\(354\) | 6.21389 | 0.330265 | ||||||||
\(355\) | − | 13.8078i | − | 0.732843i | ||||||
\(356\) | 5.92995i | 0.314287i | ||||||||
\(357\) | 9.04401i | 0.478660i | ||||||||
\(358\) | 19.5939 | 1.03557 | ||||||||
\(359\) | 20.5679 | 1.08553 | 0.542766 | − | 0.839884i | \(-0.317377\pi\) | ||||
0.542766 | + | 0.839884i | \(0.317377\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 11.7638 | 0.619148 | ||||||||
\(362\) | 9.18785i | 0.482903i | ||||||||
\(363\) | −10.5239 | −0.552360 | ||||||||
\(364\) | 3.52388i | 0.184701i | ||||||||
\(365\) | 12.2839i | 0.642971i | ||||||||
\(366\) | 2.00000 | 0.104542 | ||||||||
\(367\) | 17.8779 | 0.933217 | 0.466609 | − | 0.884464i | \(-0.345476\pi\) | ||||
0.466609 | + | 0.884464i | \(0.345476\pi\) | |||||||
\(368\) | − | 8.90391i | − | 0.464148i | ||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | −4.10695 | + | 4.48698i | −0.213510 | + | 0.233267i | ||||
\(371\) | −0.903910 | −0.0469287 | ||||||||
\(372\) | 9.59393i | 0.497422i | ||||||||
\(373\) | −34.5896 | −1.79098 | −0.895491 | − | 0.445080i | \(-0.853175\pi\) | ||||
−0.895491 | + | 0.445080i | \(0.853175\pi\) | |||||||
\(374\) | −4.76381 | −0.246331 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | − | 4.61997i | − | 0.238257i | ||||||
\(377\) | −5.38003 | −0.277086 | ||||||||
\(378\) | 1.30998i | 0.0673783i | ||||||||
\(379\) | 15.8599 | 0.814668 | 0.407334 | − | 0.913279i | \(-0.366458\pi\) | ||||
0.407334 | + | 0.913279i | \(0.366458\pi\) | |||||||
\(380\) | 2.69002 | 0.137995 | ||||||||
\(381\) | −10.6900 | −0.547666 | ||||||||
\(382\) | −20.9039 | −1.06954 | ||||||||
\(383\) | − | 26.7117i | − | 1.36491i | −0.730930 | − | 0.682453i | \(-0.760913\pi\) | ||
0.730930 | − | 0.682453i | \(-0.239087\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 0.903910i | 0.0460675i | ||||||||
\(386\) | 8.61997 | 0.438745 | ||||||||
\(387\) | 8.21389i | 0.417536i | ||||||||
\(388\) | 3.38003i | 0.171595i | ||||||||
\(389\) | 4.19218i | 0.212552i | 0.994337 | + | 0.106276i | \(0.0338927\pi\) | ||||
−0.994337 | + | 0.106276i | \(0.966107\pi\) | |||||||
\(390\) | − | 2.69002i | − | 0.136214i | ||||||
\(391\) | −61.4718 | −3.10876 | ||||||||
\(392\) | − | 5.28394i | − | 0.266879i | ||||||
\(393\) | 8.97396i | 0.452676i | ||||||||
\(394\) | 12.6900i | 0.639314i | ||||||||
\(395\) | 1.59393 | 0.0801992 | ||||||||
\(396\) | −0.690016 | −0.0346746 | ||||||||
\(397\) | 5.45383 | 0.273720 | 0.136860 | − | 0.990590i | \(-0.456299\pi\) | ||||
0.136860 | + | 0.990590i | \(0.456299\pi\) | |||||||
\(398\) | 22.8339 | 1.14456 | ||||||||
\(399\) | 3.52388i | 0.176415i | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 34.4978i | 1.72274i | 0.507978 | + | 0.861370i | \(0.330393\pi\) | ||||
−0.507978 | + | 0.861370i | \(0.669607\pi\) | |||||||
\(402\) | 1.23993i | 0.0618423i | ||||||||
\(403\) | 25.8078 | 1.28558 | ||||||||
\(404\) | −8.97396 | −0.446471 | ||||||||
\(405\) | − | 1.00000i | − | 0.0496904i | ||||||
\(406\) | −2.61997 | −0.130027 | ||||||||
\(407\) | 2.83386 | − | 3.09609i | 0.140469 | − | 0.153467i | ||||
\(408\) | 6.90391 | 0.341794 | ||||||||
\(409\) | 30.9077i | 1.52829i | 0.645047 | + | 0.764143i | \(0.276838\pi\) | ||||
−0.645047 | + | 0.764143i | \(0.723162\pi\) | |||||||
\(410\) | 2.00000 | 0.0987730 | ||||||||
\(411\) | −11.5939 | −0.571886 | ||||||||
\(412\) | 19.1879i | 0.945318i | ||||||||
\(413\) | − | 8.14010i | − | 0.400548i | ||||||
\(414\) | −8.90391 | −0.437603 | ||||||||
\(415\) | − | 10.2839i | − | 0.504819i | ||||||
\(416\) | 2.69002 | 0.131889 | ||||||||
\(417\) | −6.76007 | −0.331042 | ||||||||
\(418\) | −1.85616 | −0.0907875 | ||||||||
\(419\) | −21.6857 | −1.05942 | −0.529708 | − | 0.848180i | \(-0.677698\pi\) | ||||
−0.529708 | + | 0.848180i | \(0.677698\pi\) | |||||||
\(420\) | − | 1.30998i | − | 0.0639207i | ||||||
\(421\) | 36.3757i | 1.77284i | 0.462879 | + | 0.886422i | \(0.346817\pi\) | ||||
−0.462879 | + | 0.886422i | \(0.653183\pi\) | |||||||
\(422\) | 5.38003i | 0.261896i | ||||||||
\(423\) | −4.61997 | −0.224630 | ||||||||
\(424\) | 0.690016i | 0.0335102i | ||||||||
\(425\) | 6.90391i | 0.334889i | ||||||||
\(426\) | − | 13.8078i | − | 0.668991i | ||||||
\(427\) | − | 2.61997i | − | 0.126789i | ||||||
\(428\) | −18.1438 | −0.877016 | ||||||||
\(429\) | 1.85616i | 0.0896160i | ||||||||
\(430\) | − | 8.21389i | − | 0.396109i | ||||||
\(431\) | − | 4.47612i | − | 0.215607i | −0.994172 | − | 0.107804i | \(-0.965618\pi\) | ||
0.994172 | − | 0.107804i | \(-0.0343818\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −13.5239 | −0.649916 | −0.324958 | − | 0.945728i | \(-0.605350\pi\) | ||||
−0.324958 | + | 0.945728i | \(0.605350\pi\) | |||||||
\(434\) | 12.5679 | 0.603278 | ||||||||
\(435\) | 2.00000 | 0.0958927 | ||||||||
\(436\) | − | 17.5239i | − | 0.839242i | ||||||
\(437\) | −23.9517 | −1.14576 | ||||||||
\(438\) | 12.2839i | 0.586950i | ||||||||
\(439\) | 1.59393i | 0.0760740i | 0.999276 | + | 0.0380370i | \(0.0121105\pi\) | ||||
−0.999276 | + | 0.0380370i | \(0.987890\pi\) | |||||||
\(440\) | 0.690016 | 0.0328952 | ||||||||
\(441\) | −5.28394 | −0.251616 | ||||||||
\(442\) | − | 18.5716i | − | 0.883362i | ||||||
\(443\) | −36.8556 | −1.75106 | −0.875531 | − | 0.483163i | \(-0.839488\pi\) | ||||
−0.875531 | + | 0.483163i | \(0.839488\pi\) | |||||||
\(444\) | −4.10695 | + | 4.48698i | −0.194907 | + | 0.212943i | ||||
\(445\) | −5.92995 | −0.281107 | ||||||||
\(446\) | 0.833861i | 0.0394845i | ||||||||
\(447\) | 10.2139 | 0.483101 | ||||||||
\(448\) | 1.30998 | 0.0618909 | ||||||||
\(449\) | 12.0738i | 0.569798i | 0.958558 | + | 0.284899i | \(0.0919600\pi\) | ||||
−0.958558 | + | 0.284899i | \(0.908040\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | −1.38003 | −0.0649832 | ||||||||
\(452\) | 2.00000i | 0.0940721i | ||||||||
\(453\) | 22.2839 | 1.04699 | ||||||||
\(454\) | −15.1879 | −0.712801 | ||||||||
\(455\) | −3.52388 | −0.165202 | ||||||||
\(456\) | 2.69002 | 0.125972 | ||||||||
\(457\) | 9.18785i | 0.429790i | 0.976637 | + | 0.214895i | \(0.0689409\pi\) | ||||
−0.976637 | + | 0.214895i | \(0.931059\pi\) | |||||||
\(458\) | 7.80782i | 0.364835i | ||||||||
\(459\) | − | 6.90391i | − | 0.322247i | ||||||
\(460\) | 8.90391 | 0.415147 | ||||||||
\(461\) | − | 6.14010i | − | 0.285973i | −0.989725 | − | 0.142986i | \(-0.954329\pi\) | ||
0.989725 | − | 0.142986i | \(-0.0456705\pi\) | |||||||
\(462\) | 0.903910i | 0.0420537i | ||||||||
\(463\) | 1.09984i | 0.0511137i | 0.999673 | + | 0.0255568i | \(0.00813588\pi\) | ||||
−0.999673 | + | 0.0255568i | \(0.991864\pi\) | |||||||
\(464\) | 2.00000i | 0.0928477i | ||||||||
\(465\) | −9.59393 | −0.444908 | ||||||||
\(466\) | − | 3.59393i | − | 0.166485i | ||||||
\(467\) | 3.18785i | 0.147516i | 0.997276 | + | 0.0737581i | \(0.0234993\pi\) | ||||
−0.997276 | + | 0.0737581i | \(0.976501\pi\) | |||||||
\(468\) | − | 2.69002i | − | 0.124346i | ||||||
\(469\) | 1.62429 | 0.0750029 | ||||||||
\(470\) | 4.61997 | 0.213103 | ||||||||
\(471\) | 12.2139 | 0.562787 | ||||||||
\(472\) | −6.21389 | −0.286018 | ||||||||
\(473\) | 5.66772i | 0.260602i | ||||||||
\(474\) | 1.59393 | 0.0732115 | ||||||||
\(475\) | 2.69002i | 0.123426i | ||||||||
\(476\) | − | 9.04401i | − | 0.414531i | ||||||
\(477\) | 0.690016 | 0.0315937 | ||||||||
\(478\) | 7.18785 | 0.328765 | ||||||||
\(479\) | − | 41.1916i | − | 1.88209i | −0.338278 | − | 0.941046i | \(-0.609845\pi\) | ||
0.338278 | − | 0.941046i | \(-0.390155\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 12.0700 | + | 11.0478i | 0.550347 | + | 0.503734i | ||||
\(482\) | 3.18785 | 0.145203 | ||||||||
\(483\) | 11.6640i | 0.530729i | ||||||||
\(484\) | 10.5239 | 0.478358 | ||||||||
\(485\) | −3.38003 | −0.153479 | ||||||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | − | 24.4278i | − | 1.10693i | −0.832873 | − | 0.553464i | \(-0.813306\pi\) | ||
0.832873 | − | 0.553464i | \(-0.186694\pi\) | |||||||
\(488\) | −2.00000 | −0.0905357 | ||||||||
\(489\) | − | 6.07005i | − | 0.274497i | ||||||
\(490\) | 5.28394 | 0.238704 | ||||||||
\(491\) | −0.690016 | −0.0311400 | −0.0155700 | − | 0.999879i | \(-0.504956\pi\) | ||||
−0.0155700 | + | 0.999879i | \(0.504956\pi\) | |||||||
\(492\) | 2.00000 | 0.0901670 | ||||||||
\(493\) | 13.8078 | 0.621873 | ||||||||
\(494\) | − | 7.23619i | − | 0.325572i | ||||||
\(495\) | − | 0.690016i | − | 0.0310139i | ||||||
\(496\) | − | 9.59393i | − | 0.430780i | ||||||
\(497\) | −18.0880 | −0.811358 | ||||||||
\(498\) | − | 10.2839i | − | 0.460835i | ||||||
\(499\) | − | 8.63794i | − | 0.386687i | −0.981131 | − | 0.193344i | \(-0.938067\pi\) | ||
0.981131 | − | 0.193344i | \(-0.0619332\pi\) | |||||||
\(500\) | − | 1.00000i | − | 0.0447214i | ||||||
\(501\) | 8.90391i | 0.397797i | ||||||||
\(502\) | 11.5939 | 0.517462 | ||||||||
\(503\) | − | 30.3757i | − | 1.35439i | −0.735806 | − | 0.677193i | \(-0.763196\pi\) | ||
0.735806 | − | 0.677193i | \(-0.236804\pi\) | |||||||
\(504\) | − | 1.30998i | − | 0.0583513i | ||||||
\(505\) | − | 8.97396i | − | 0.399336i | ||||||
\(506\) | −6.14384 | −0.273127 | ||||||||
\(507\) | 5.76381 | 0.255980 | ||||||||
\(508\) | 10.6900 | 0.474293 | ||||||||
\(509\) | −36.9256 | −1.63670 | −0.818350 | − | 0.574721i | \(-0.805111\pi\) | ||||
−0.818350 | + | 0.574721i | \(0.805111\pi\) | |||||||
\(510\) | 6.90391i | 0.305710i | ||||||||
\(511\) | 16.0918 | 0.711858 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 2.69002i | − | 0.118767i | ||||||
\(514\) | 25.5239 | 1.12581 | ||||||||
\(515\) | −19.1879 | −0.845518 | ||||||||
\(516\) | − | 8.21389i | − | 0.361597i | ||||||
\(517\) | −3.18785 | −0.140202 | ||||||||
\(518\) | 5.87787 | + | 5.38003i | 0.258259 | + | 0.236385i | ||||
\(519\) | 19.8779 | 0.872542 | ||||||||
\(520\) | 2.69002i | 0.117965i | ||||||||
\(521\) | 10.8121 | 0.473689 | 0.236844 | − | 0.971548i | \(-0.423887\pi\) | ||||
0.236844 | + | 0.971548i | \(0.423887\pi\) | |||||||
\(522\) | 2.00000 | 0.0875376 | ||||||||
\(523\) | 20.9219i | 0.914850i | 0.889248 | + | 0.457425i | \(0.151228\pi\) | ||||
−0.889248 | + | 0.457425i | \(0.848772\pi\) | |||||||
\(524\) | − | 8.97396i | − | 0.392029i | ||||||
\(525\) | 1.30998 | 0.0571724 | ||||||||
\(526\) | − | 18.5679i | − | 0.809598i | ||||||
\(527\) | −66.2356 | −2.88527 | ||||||||
\(528\) | 0.690016 | 0.0300291 | ||||||||
\(529\) | −56.2796 | −2.44694 | ||||||||
\(530\) | −0.690016 | −0.0299724 | ||||||||
\(531\) | 6.21389i | 0.269660i | ||||||||
\(532\) | − | 3.52388i | − | 0.152779i | ||||||
\(533\) | − | 5.38003i | − | 0.233035i | ||||||
\(534\) | −5.92995 | −0.256614 | ||||||||
\(535\) | − | 18.1438i | − | 0.784427i | ||||||
\(536\) | − | 1.23993i | − | 0.0535570i | ||||||
\(537\) | 19.5939i | 0.845540i | ||||||||
\(538\) | 13.3100i | 0.573834i | ||||||||
\(539\) | −3.64601 | −0.157045 | ||||||||
\(540\) | 1.00000i | 0.0430331i | ||||||||
\(541\) | − | 25.5239i | − | 1.09736i | −0.836033 | − | 0.548679i | \(-0.815131\pi\) | ||
0.836033 | − | 0.548679i | \(-0.184869\pi\) | |||||||
\(542\) | − | 17.9479i | − | 0.770929i | ||||||
\(543\) | −9.18785 | −0.394289 | ||||||||
\(544\) | −6.90391 | −0.296003 | ||||||||
\(545\) | 17.5239 | 0.750640 | ||||||||
\(546\) | −3.52388 | −0.150808 | ||||||||
\(547\) | − | 6.49784i | − | 0.277827i | −0.990304 | − | 0.138914i | \(-0.955639\pi\) | ||
0.990304 | − | 0.138914i | \(-0.0443611\pi\) | |||||||
\(548\) | 11.5939 | 0.495268 | ||||||||
\(549\) | 2.00000i | 0.0853579i | ||||||||
\(550\) | 0.690016i | 0.0294224i | ||||||||
\(551\) | 5.38003 | 0.229197 | ||||||||
\(552\) | 8.90391 | 0.378976 | ||||||||
\(553\) | − | 2.08802i | − | 0.0887915i | ||||||
\(554\) | −13.7378 | −0.583662 | ||||||||
\(555\) | −4.48698 | − | 4.10695i | −0.190462 | − | 0.174330i | ||||
\(556\) | 6.76007 | 0.286691 | ||||||||
\(557\) | − | 0.760066i | − | 0.0322050i | −0.999870 | − | 0.0161025i | \(-0.994874\pi\) | ||
0.999870 | − | 0.0161025i | \(-0.00512581\pi\) | |||||||
\(558\) | −9.59393 | −0.406143 | ||||||||
\(559\) | −22.0955 | −0.934540 | ||||||||
\(560\) | 1.30998i | 0.0553569i | ||||||||
\(561\) | − | 4.76381i | − | 0.201128i | ||||||
\(562\) | −4.54992 | −0.191927 | ||||||||
\(563\) | − | 18.0880i | − | 0.762319i | −0.924509 | − | 0.381160i | \(-0.875525\pi\) | ||
0.924509 | − | 0.381160i | \(-0.124475\pi\) | |||||||
\(564\) | 4.61997 | 0.194536 | ||||||||
\(565\) | −2.00000 | −0.0841406 | ||||||||
\(566\) | −27.7378 | −1.16591 | ||||||||
\(567\) | −1.30998 | −0.0550141 | ||||||||
\(568\) | 13.8078i | 0.579363i | ||||||||
\(569\) | 2.74210i | 0.114955i | 0.998347 | + | 0.0574774i | \(0.0183057\pi\) | ||||
−0.998347 | + | 0.0574774i | \(0.981694\pi\) | |||||||
\(570\) | 2.69002i | 0.112672i | ||||||||
\(571\) | −25.2399 | −1.05626 | −0.528129 | − | 0.849164i | \(-0.677106\pi\) | ||||
−0.528129 | + | 0.849164i | \(0.677106\pi\) | |||||||
\(572\) | − | 1.85616i | − | 0.0776098i | ||||||
\(573\) | − | 20.9039i | − | 0.873273i | ||||||
\(574\) | − | 2.61997i | − | 0.109355i | ||||||
\(575\) | 8.90391i | 0.371319i | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 38.5679i | 1.60560i | 0.596247 | + | 0.802801i | \(0.296658\pi\) | ||||
−0.596247 | + | 0.802801i | \(0.703342\pi\) | |||||||
\(578\) | 30.6640i | 1.27545i | ||||||||
\(579\) | 8.61997i | 0.358234i | ||||||||
\(580\) | −2.00000 | −0.0830455 | ||||||||
\(581\) | −13.4718 | −0.558904 | ||||||||
\(582\) | −3.38003 | −0.140107 | ||||||||
\(583\) | 0.476123 | 0.0197190 | ||||||||
\(584\) | − | 12.2839i | − | 0.508313i | ||||||
\(585\) | 2.69002 | 0.111218 | ||||||||
\(586\) | 3.30998i | 0.136734i | ||||||||
\(587\) | − | 3.32795i | − | 0.137359i | −0.997639 | − | 0.0686796i | \(-0.978121\pi\) | ||
0.997639 | − | 0.0686796i | \(-0.0218786\pi\) | |||||||
\(588\) | 5.28394 | 0.217906 | ||||||||
\(589\) | −25.8078 | −1.06339 | ||||||||
\(590\) | − | 6.21389i | − | 0.255822i | ||||||
\(591\) | −12.6900 | −0.521998 | ||||||||
\(592\) | 4.10695 | − | 4.48698i | 0.168794 | − | 0.184414i | ||||
\(593\) | −24.5896 | −1.00977 | −0.504887 | − | 0.863185i | \(-0.668466\pi\) | ||||
−0.504887 | + | 0.863185i | \(0.668466\pi\) | |||||||
\(594\) | − | 0.690016i | − | 0.0283117i | ||||||
\(595\) | 9.04401 | 0.370768 | ||||||||
\(596\) | −10.2139 | −0.418377 | ||||||||
\(597\) | 22.8339i | 0.934528i | ||||||||
\(598\) | − | 23.9517i | − | 0.979456i | ||||||
\(599\) | 7.85990 | 0.321147 | 0.160573 | − | 0.987024i | \(-0.448666\pi\) | ||||
0.160573 | + | 0.987024i | \(0.448666\pi\) | |||||||
\(600\) | − | 1.00000i | − | 0.0408248i | ||||||
\(601\) | 0.143844 | 0.00586754 | 0.00293377 | − | 0.999996i | \(-0.499066\pi\) | ||||
0.00293377 | + | 0.999996i | \(0.499066\pi\) | |||||||
\(602\) | −10.7601 | −0.438548 | ||||||||
\(603\) | −1.23993 | −0.0504940 | ||||||||
\(604\) | −22.2839 | −0.906721 | ||||||||
\(605\) | 10.5239i | 0.427856i | ||||||||
\(606\) | − | 8.97396i | − | 0.364542i | ||||||
\(607\) | − | 27.1879i | − | 1.10352i | −0.834003 | − | 0.551760i | \(-0.813956\pi\) | ||
0.834003 | − | 0.551760i | \(-0.186044\pi\) | |||||||
\(608\) | −2.69002 | −0.109095 | ||||||||
\(609\) | − | 2.61997i | − | 0.106166i | ||||||
\(610\) | − | 2.00000i | − | 0.0809776i | ||||||
\(611\) | − | 12.4278i | − | 0.502774i | ||||||
\(612\) | 6.90391i | 0.279074i | ||||||||
\(613\) | −10.9740 | −0.443234 | −0.221617 | − | 0.975134i | \(-0.571133\pi\) | ||||
−0.221617 | + | 0.975134i | \(0.571133\pi\) | |||||||
\(614\) | − | 21.9479i | − | 0.885746i | ||||||
\(615\) | 2.00000i | 0.0806478i | ||||||||
\(616\) | − | 0.903910i | − | 0.0364196i | ||||||
\(617\) | 8.97396 | 0.361278 | 0.180639 | − | 0.983549i | \(-0.442183\pi\) | ||||
0.180639 | + | 0.983549i | \(0.442183\pi\) | |||||||
\(618\) | −19.1879 | −0.771849 | ||||||||
\(619\) | −1.52013 | −0.0610992 | −0.0305496 | − | 0.999533i | \(-0.509726\pi\) | ||||
−0.0305496 | + | 0.999533i | \(0.509726\pi\) | |||||||
\(620\) | 9.59393 | 0.385301 | ||||||||
\(621\) | − | 8.90391i | − | 0.357302i | ||||||
\(622\) | 18.7601 | 0.752210 | ||||||||
\(623\) | 7.76814i | 0.311224i | ||||||||
\(624\) | 2.69002i | 0.107687i | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 21.1879 | 0.846837 | ||||||||
\(627\) | − | 1.85616i | − | 0.0741277i | ||||||
\(628\) | −12.2139 | −0.487387 | ||||||||
\(629\) | −30.9777 | − | 28.3540i | −1.23516 | − | 1.13055i | ||||
\(630\) | 1.30998 | 0.0521910 | ||||||||
\(631\) | − | 12.2139i | − | 0.486227i | −0.969998 | − | 0.243114i | \(-0.921831\pi\) | ||
0.969998 | − | 0.243114i | \(-0.0781688\pi\) | |||||||
\(632\) | −1.59393 | −0.0634030 | ||||||||
\(633\) | −5.38003 | −0.213837 | ||||||||
\(634\) | − | 23.5418i | − | 0.934966i | ||||||
\(635\) | 10.6900i | 0.424220i | ||||||||
\(636\) | −0.690016 | −0.0273609 | ||||||||
\(637\) | − | 14.2139i | − | 0.563175i | ||||||
\(638\) | 1.38003 | 0.0546360 | ||||||||
\(639\) | 13.8078 | 0.546229 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −1.43211 | −0.0565651 | −0.0282825 | − | 0.999600i | \(-0.509004\pi\) | ||||
−0.0282825 | + | 0.999600i | \(0.509004\pi\) | |||||||
\(642\) | − | 18.1438i | − | 0.716080i | ||||||
\(643\) | 10.0700i | 0.397124i | 0.980088 | + | 0.198562i | \(0.0636271\pi\) | ||||
−0.980088 | + | 0.198562i | \(0.936373\pi\) | |||||||
\(644\) | − | 11.6640i | − | 0.459625i | ||||||
\(645\) | 8.21389 | 0.323422 | ||||||||
\(646\) | 18.5716i | 0.730691i | ||||||||
\(647\) | 6.14384i | 0.241539i | 0.992681 | + | 0.120770i | \(0.0385363\pi\) | ||||
−0.992681 | + | 0.120770i | \(0.961464\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 4.28769i | 0.168307i | ||||||||
\(650\) | −2.69002 | −0.105511 | ||||||||
\(651\) | 12.5679i | 0.492574i | ||||||||
\(652\) | 6.07005i | 0.237721i | ||||||||
\(653\) | − | 45.1879i | − | 1.76834i | −0.467168 | − | 0.884169i | \(-0.654726\pi\) | ||
0.467168 | − | 0.884169i | \(-0.345274\pi\) | |||||||
\(654\) | 17.5239 | 0.685238 | ||||||||
\(655\) | 8.97396 | 0.350642 | ||||||||
\(656\) | −2.00000 | −0.0780869 | ||||||||
\(657\) | −12.2839 | −0.479242 | ||||||||
\(658\) | − | 6.05208i | − | 0.235935i | ||||||
\(659\) | 19.4017 | 0.755785 | 0.377892 | − | 0.925850i | \(-0.376649\pi\) | ||||
0.377892 | + | 0.925850i | \(0.376649\pi\) | |||||||
\(660\) | 0.690016i | 0.0268589i | ||||||||
\(661\) | − | 0.424042i | − | 0.0164933i | −0.999966 | − | 0.00824666i | \(-0.997375\pi\) | ||
0.999966 | − | 0.00824666i | \(-0.00262502\pi\) | |||||||
\(662\) | 16.4061 | 0.637640 | ||||||||
\(663\) | 18.5716 | 0.721262 | ||||||||
\(664\) | 10.2839i | 0.399094i | ||||||||
\(665\) | 3.52388 | 0.136650 | ||||||||
\(666\) | −4.48698 | − | 4.10695i | −0.173867 | − | 0.159141i | ||||
\(667\) | 17.8078 | 0.689522 | ||||||||
\(668\) | − | 8.90391i | − | 0.344503i | ||||||
\(669\) | −0.833861 | −0.0322389 | ||||||||
\(670\) | 1.23993 | 0.0479028 | ||||||||
\(671\) | 1.38003i | 0.0532756i | ||||||||
\(672\) | 1.30998i | 0.0505337i | ||||||||
\(673\) | 2.76381 | 0.106537 | 0.0532686 | − | 0.998580i | \(-0.483036\pi\) | ||||
0.0532686 | + | 0.998580i | \(0.483036\pi\) | |||||||
\(674\) | − | 23.3317i | − | 0.898703i | ||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −5.76381 | −0.221685 | ||||||||
\(677\) | 23.5977 | 0.906932 | 0.453466 | − | 0.891274i | \(-0.350187\pi\) | ||||
0.453466 | + | 0.891274i | \(0.350187\pi\) | |||||||
\(678\) | −2.00000 | −0.0768095 | ||||||||
\(679\) | 4.42779i | 0.169923i | ||||||||
\(680\) | − | 6.90391i | − | 0.264753i | ||||||
\(681\) | − | 15.1879i | − | 0.582000i | ||||||
\(682\) | −6.61997 | −0.253492 | ||||||||
\(683\) | − | 17.9479i | − | 0.686758i | −0.939197 | − | 0.343379i | \(-0.888428\pi\) | ||
0.939197 | − | 0.343379i | \(-0.111572\pi\) | |||||||
\(684\) | 2.69002i | 0.102855i | ||||||||
\(685\) | 11.5939i | 0.442981i | ||||||||
\(686\) | − | 16.0918i | − | 0.614386i | ||||||
\(687\) | −7.80782 | −0.297887 | ||||||||
\(688\) | 8.21389i | 0.313152i | ||||||||
\(689\) | 1.85616i | 0.0707139i | ||||||||
\(690\) | 8.90391i | 0.338966i | ||||||||
\(691\) | 46.2356 | 1.75889 | 0.879443 | − | 0.476005i | \(-0.157915\pi\) | ||||
0.879443 | + | 0.476005i | \(0.157915\pi\) | |||||||
\(692\) | −19.8779 | −0.755643 | ||||||||
\(693\) | −0.903910 | −0.0343367 | ||||||||
\(694\) | −5.38003 | −0.204223 | ||||||||
\(695\) | 6.76007i | 0.256424i | ||||||||
\(696\) | −2.00000 | −0.0758098 | ||||||||
\(697\) | 13.8078i | 0.523008i | ||||||||
\(698\) | 29.1879i | 1.10478i | ||||||||
\(699\) | 3.59393 | 0.135935 | ||||||||
\(700\) | −1.30998 | −0.0495127 | ||||||||
\(701\) | 0.192180i | 0.00725852i | 0.999993 | + | 0.00362926i | \(0.00115523\pi\) | ||||
−0.999993 | + | 0.00362926i | \(0.998845\pi\) | |||||||
\(702\) | 2.69002 | 0.101528 | ||||||||
\(703\) | −12.0700 | − | 11.0478i | −0.455231 | − | 0.416674i | ||||
\(704\) | −0.690016 | −0.0260060 | ||||||||
\(705\) | 4.61997i | 0.173998i | ||||||||
\(706\) | −22.4278 | −0.844081 | ||||||||
\(707\) | −11.7557 | −0.442120 | ||||||||
\(708\) | − | 6.21389i | − | 0.233532i | ||||||
\(709\) | − | 3.85616i | − | 0.144821i | −0.997375 | − | 0.0724105i | \(-0.976931\pi\) | ||
0.997375 | − | 0.0724105i | \(-0.0230692\pi\) | |||||||
\(710\) | −13.8078 | −0.518198 | ||||||||
\(711\) | 1.59393i | 0.0597769i | ||||||||
\(712\) | 5.92995 | 0.222234 | ||||||||
\(713\) | −85.4235 | −3.19913 | ||||||||
\(714\) | 9.04401 | 0.338464 | ||||||||
\(715\) | 1.85616 | 0.0694163 | ||||||||
\(716\) | − | 19.5939i | − | 0.732259i | ||||||
\(717\) | 7.18785i | 0.268435i | ||||||||
\(718\) | − | 20.5679i | − | 0.767587i | ||||||
\(719\) | 15.6156 | 0.582365 | 0.291183 | − | 0.956668i | \(-0.405951\pi\) | ||||
0.291183 | + | 0.956668i | \(0.405951\pi\) | |||||||
\(720\) | − | 1.00000i | − | 0.0372678i | ||||||
\(721\) | 25.1358i | 0.936105i | ||||||||
\(722\) | − | 11.7638i | − | 0.437804i | ||||||
\(723\) | 3.18785i | 0.118558i | ||||||||
\(724\) | 9.18785 | 0.341464 | ||||||||
\(725\) | − | 2.00000i | − | 0.0742781i | ||||||
\(726\) | 10.5239i | 0.390578i | ||||||||
\(727\) | 31.0478i | 1.15150i | 0.817627 | + | 0.575749i | \(0.195289\pi\) | ||||
−0.817627 | + | 0.575749i | \(0.804711\pi\) | |||||||
\(728\) | 3.52388 | 0.130604 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.2839 | 0.454649 | ||||||||
\(731\) | 56.7080 | 2.09742 | ||||||||
\(732\) | − | 2.00000i | − | 0.0739221i | ||||||
\(733\) | −36.7818 | −1.35857 | −0.679283 | − | 0.733876i | \(-0.737709\pi\) | ||||
−0.679283 | + | 0.733876i | \(0.737709\pi\) | |||||||
\(734\) | − | 17.8779i | − | 0.659884i | ||||||
\(735\) | 5.28394i | 0.194901i | ||||||||
\(736\) | −8.90391 | −0.328202 | ||||||||
\(737\) | −0.855575 | −0.0315155 | ||||||||
\(738\) | 2.00000i | 0.0736210i | ||||||||
\(739\) | 31.8958 | 1.17331 | 0.586654 | − | 0.809838i | \(-0.300445\pi\) | ||||
0.586654 | + | 0.809838i | \(0.300445\pi\) | |||||||
\(740\) | 4.48698 | + | 4.10695i | 0.164945 | + | 0.150974i | ||||
\(741\) | 7.23619 | 0.265828 | ||||||||
\(742\) | 0.903910i | 0.0331836i | ||||||||
\(743\) | 21.1879 | 0.777307 | 0.388653 | − | 0.921384i | \(-0.372940\pi\) | ||||
0.388653 | + | 0.921384i | \(0.372940\pi\) | |||||||
\(744\) | 9.59393 | 0.351730 | ||||||||
\(745\) | − | 10.2139i | − | 0.374208i | ||||||
\(746\) | 34.5896i | 1.26642i | ||||||||
\(747\) | 10.2839 | 0.376270 | ||||||||
\(748\) | 4.76381i | 0.174182i | ||||||||
\(749\) | −23.7681 | −0.868469 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 16.0000 | 0.583848 | 0.291924 | − | 0.956441i | \(-0.405705\pi\) | ||||
0.291924 | + | 0.956441i | \(0.405705\pi\) | |||||||
\(752\) | −4.61997 | −0.168473 | ||||||||
\(753\) | 11.5939i | 0.422506i | ||||||||
\(754\) | 5.38003i | 0.195929i | ||||||||
\(755\) | − | 22.2839i | − | 0.810996i | ||||||
\(756\) | 1.30998 | 0.0476436 | ||||||||
\(757\) | 24.7780i | 0.900573i | 0.892884 | + | 0.450286i | \(0.148678\pi\) | ||||
−0.892884 | + | 0.450286i | \(0.851322\pi\) | |||||||
\(758\) | − | 15.8599i | − | 0.576058i | ||||||
\(759\) | − | 6.14384i | − | 0.223007i | ||||||
\(760\) | − | 2.69002i | − | 0.0975772i | ||||||
\(761\) | −10.8121 | −0.391940 | −0.195970 | − | 0.980610i | \(-0.562786\pi\) | ||||
−0.195970 | + | 0.980610i | \(0.562786\pi\) | |||||||
\(762\) | 10.6900i | 0.387258i | ||||||||
\(763\) | − | 22.9560i | − | 0.831063i | ||||||
\(764\) | 20.9039i | 0.756277i | ||||||||
\(765\) | −6.90391 | −0.249611 | ||||||||
\(766\) | −26.7117 | −0.965134 | ||||||||
\(767\) | −16.7155 | −0.603561 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 15.0478i | 0.542636i | 0.962490 | + | 0.271318i | \(0.0874595\pi\) | ||||
−0.962490 | + | 0.271318i | \(0.912541\pi\) | |||||||
\(770\) | 0.903910 | 0.0325747 | ||||||||
\(771\) | 25.5239i | 0.919220i | ||||||||
\(772\) | − | 8.61997i | − | 0.310239i | ||||||
\(773\) | 34.0700 | 1.22541 | 0.612707 | − | 0.790310i | \(-0.290080\pi\) | ||||
0.612707 | + | 0.790310i | \(0.290080\pi\) | |||||||
\(774\) | 8.21389 | 0.295242 | ||||||||
\(775\) | 9.59393i | 0.344624i | ||||||||
\(776\) | 3.38003 | 0.121336 | ||||||||
\(777\) | −5.38003 | + | 5.87787i | −0.193008 | + | 0.210867i | ||||
\(778\) | 4.19218 | 0.150297 | ||||||||
\(779\) | 5.38003i | 0.192760i | ||||||||
\(780\) | −2.69002 | −0.0963180 | ||||||||
\(781\) | 9.52762 | 0.340925 | ||||||||
\(782\) | 61.4718i | 2.19823i | ||||||||
\(783\) | 2.00000i | 0.0714742i | ||||||||
\(784\) | −5.28394 | −0.188712 | ||||||||
\(785\) | − | 12.2139i | − | 0.435933i | ||||||
\(786\) | 8.97396 | 0.320091 | ||||||||
\(787\) | 11.3280 | 0.403798 | 0.201899 | − | 0.979406i | \(-0.435289\pi\) | ||||
0.201899 | + | 0.979406i | \(0.435289\pi\) | |||||||
\(788\) | 12.6900 | 0.452063 | ||||||||
\(789\) | 18.5679 | 0.661034 | ||||||||
\(790\) | − | 1.59393i | − | 0.0567094i | ||||||
\(791\) | 2.61997i | 0.0931553i | ||||||||
\(792\) | 0.690016i | 0.0245187i | ||||||||
\(793\) | −5.38003 | −0.191051 | ||||||||
\(794\) | − | 5.45383i | − | 0.193549i | ||||||
\(795\) | − | 0.690016i | − | 0.0244724i | ||||||
\(796\) | − | 22.8339i | − | 0.809325i | ||||||
\(797\) | − | 14.2877i | − | 0.506096i | −0.967454 | − | 0.253048i | \(-0.918567\pi\) | ||
0.967454 | − | 0.253048i | \(-0.0814330\pi\) | |||||||
\(798\) | 3.52388 | 0.124744 | ||||||||
\(799\) | 31.8958i | 1.12839i | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | − | 5.92995i | − | 0.209525i | ||||||
\(802\) | 34.4978 | 1.21816 | ||||||||
\(803\) | −8.47612 | −0.299116 | ||||||||
\(804\) | 1.23993 | 0.0437291 | ||||||||
\(805\) | 11.6640 | 0.411101 | ||||||||
\(806\) | − | 25.8078i | − | 0.909042i | ||||||
\(807\) | −13.3100 | −0.468534 | ||||||||
\(808\) | 8.97396i | 0.315703i | ||||||||
\(809\) | − | 31.1699i | − | 1.09587i | −0.836519 | − | 0.547937i | \(-0.815413\pi\) | ||
0.836519 | − | 0.547937i | \(-0.184587\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 7.85990 | 0.275998 | 0.137999 | − | 0.990432i | \(-0.455933\pi\) | ||||
0.137999 | + | 0.990432i | \(0.455933\pi\) | |||||||
\(812\) | 2.61997i | 0.0919428i | ||||||||
\(813\) | 17.9479 | 0.629461 | ||||||||
\(814\) | −3.09609 | − | 2.83386i | −0.108518 | − | 0.0993268i | ||||
\(815\) | −6.07005 | −0.212625 | ||||||||
\(816\) | − | 6.90391i | − | 0.241685i | ||||||
\(817\) | 22.0955 | 0.773024 | ||||||||
\(818\) | 30.9077 | 1.08066 | ||||||||
\(819\) | − | 3.52388i | − | 0.123134i | ||||||
\(820\) | − | 2.00000i | − | 0.0698430i | ||||||
\(821\) | 20.9256 | 0.730309 | 0.365155 | − | 0.930947i | \(-0.381016\pi\) | ||||
0.365155 | + | 0.930947i | \(0.381016\pi\) | |||||||
\(822\) | 11.5939i | 0.404385i | ||||||||
\(823\) | −52.2536 | −1.82145 | −0.910723 | − | 0.413019i | \(-0.864474\pi\) | ||||
−0.910723 | + | 0.413019i | \(0.864474\pi\) | |||||||
\(824\) | 19.1879 | 0.668441 | ||||||||
\(825\) | −0.690016 | −0.0240233 | ||||||||
\(826\) | −8.14010 | −0.283230 | ||||||||
\(827\) | 13.8078i | 0.480145i | 0.970755 | + | 0.240072i | \(0.0771712\pi\) | ||||
−0.970755 | + | 0.240072i | \(0.922829\pi\) | |||||||
\(828\) | 8.90391i | 0.309432i | ||||||||
\(829\) | − | 17.5239i | − | 0.608629i | −0.952572 | − | 0.304315i | \(-0.901573\pi\) | ||
0.952572 | − | 0.304315i | \(-0.0984274\pi\) | |||||||
\(830\) | −10.2839 | −0.356961 | ||||||||
\(831\) | − | 13.7378i | − | 0.476558i | ||||||
\(832\) | − | 2.69002i | − | 0.0932595i | ||||||
\(833\) | 36.4799i | 1.26395i | ||||||||
\(834\) | 6.76007i | 0.234082i | ||||||||
\(835\) | 8.90391 | 0.308133 | ||||||||
\(836\) | 1.85616i | 0.0641965i | ||||||||
\(837\) | − | 9.59393i | − | 0.331615i | ||||||
\(838\) | 21.6857i | 0.749120i | ||||||||
\(839\) | 45.9479 | 1.58630 | 0.793149 | − | 0.609027i | \(-0.208440\pi\) | ||||
0.793149 | + | 0.609027i | \(0.208440\pi\) | |||||||
\(840\) | −1.30998 | −0.0451987 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 36.3757 | 1.25359 | ||||||||
\(843\) | − | 4.54992i | − | 0.156707i | ||||||
\(844\) | 5.38003 | 0.185188 | ||||||||
\(845\) | − | 5.76381i | − | 0.198281i | ||||||
\(846\) | 4.61997i | 0.158838i | ||||||||
\(847\) | 13.7861 | 0.473696 | ||||||||
\(848\) | 0.690016 | 0.0236953 | ||||||||
\(849\) | − | 27.7378i | − | 0.951958i | ||||||
\(850\) | 6.90391 | 0.236802 | ||||||||
\(851\) | −39.9517 | − | 36.5679i | −1.36953 | − | 1.25353i | ||||
\(852\) | −13.8078 | −0.473048 | ||||||||
\(853\) | 44.4978i | 1.52358i | 0.647826 | + | 0.761788i | \(0.275678\pi\) | ||||
−0.647826 | + | 0.761788i | \(0.724322\pi\) | |||||||
\(854\) | −2.61997 | −0.0896534 | ||||||||
\(855\) | −2.69002 | −0.0919966 | ||||||||
\(856\) | 18.1438i | 0.620144i | ||||||||
\(857\) | 20.8518i | 0.712285i | 0.934432 | + | 0.356142i | \(0.115908\pi\) | ||||
−0.934432 | + | 0.356142i | \(0.884092\pi\) | |||||||
\(858\) | 1.85616 | 0.0633681 | ||||||||
\(859\) | − | 14.9777i | − | 0.511033i | −0.966805 | − | 0.255516i | \(-0.917755\pi\) | ||
0.966805 | − | 0.255516i | \(-0.0822455\pi\) | |||||||
\(860\) | −8.21389 | −0.280091 | ||||||||
\(861\) | 2.61997 | 0.0892882 | ||||||||
\(862\) | −4.47612 | −0.152457 | ||||||||
\(863\) | −22.1401 | −0.753658 | −0.376829 | − | 0.926283i | \(-0.622986\pi\) | ||||
−0.376829 | + | 0.926283i | \(0.622986\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | − | 19.8779i | − | 0.675868i | ||||||
\(866\) | 13.5239i | 0.459560i | ||||||||
\(867\) | −30.6640 | −1.04140 | ||||||||
\(868\) | − | 12.5679i | − | 0.426582i | ||||||
\(869\) | 1.09984i | 0.0373094i | ||||||||
\(870\) | − | 2.00000i | − | 0.0678064i | ||||||
\(871\) | − | 3.33544i | − | 0.113017i | ||||||
\(872\) | −17.5239 | −0.593433 | ||||||||
\(873\) | − | 3.38003i | − | 0.114397i | ||||||
\(874\) | 23.9517i | 0.810177i | ||||||||
\(875\) | − | 1.30998i | − | 0.0442855i | ||||||
\(876\) | 12.2839 | 0.415036 | ||||||||
\(877\) | 23.4017 | 0.790221 | 0.395110 | − | 0.918634i | \(-0.370706\pi\) | ||||
0.395110 | + | 0.918634i | \(0.370706\pi\) | |||||||
\(878\) | 1.59393 | 0.0537924 | ||||||||
\(879\) | −3.30998 | −0.111643 | ||||||||
\(880\) | − | 0.690016i | − | 0.0232604i | ||||||
\(881\) | −29.8958 | −1.00722 | −0.503608 | − | 0.863932i | \(-0.667994\pi\) | ||||
−0.503608 | + | 0.863932i | \(0.667994\pi\) | |||||||
\(882\) | 5.28394i | 0.177920i | ||||||||
\(883\) | 32.8376i | 1.10507i | 0.833489 | + | 0.552537i | \(0.186340\pi\) | ||||
−0.833489 | + | 0.552537i | \(0.813660\pi\) | |||||||
\(884\) | −18.5716 | −0.624632 | ||||||||
\(885\) | 6.21389 | 0.208878 | ||||||||
\(886\) | 36.8556i | 1.23819i | ||||||||
\(887\) | 43.4235 | 1.45802 | 0.729009 | − | 0.684505i | \(-0.239981\pi\) | ||||
0.729009 | + | 0.684505i | \(0.239981\pi\) | |||||||
\(888\) | 4.48698 | + | 4.10695i | 0.150573 | + | 0.137820i | ||||
\(889\) | 14.0037 | 0.469671 | ||||||||
\(890\) | 5.92995i | 0.198772i | ||||||||
\(891\) | 0.690016 | 0.0231164 | ||||||||
\(892\) | 0.833861 | 0.0279197 | ||||||||
\(893\) | 12.4278i | 0.415880i | ||||||||
\(894\) | − | 10.2139i | − | 0.341604i | ||||||
\(895\) | 19.5939 | 0.654953 | ||||||||
\(896\) | − | 1.30998i | − | 0.0437635i | ||||||
\(897\) | 23.9517 | 0.799723 | ||||||||
\(898\) | 12.0738 | 0.402908 | ||||||||
\(899\) | 19.1879 | 0.639951 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | − | 4.76381i | − | 0.158706i | ||||||
\(902\) | 1.38003i | 0.0459501i | ||||||||
\(903\) | − | 10.7601i | − | 0.358073i | ||||||
\(904\) | 2.00000 | 0.0665190 | ||||||||
\(905\) | 9.18785i | 0.305415i | ||||||||
\(906\) | − | 22.2839i | − | 0.740334i | ||||||
\(907\) | − | 25.5456i | − | 0.848227i | −0.905609 | − | 0.424114i | \(-0.860586\pi\) | ||
0.905609 | − | 0.424114i | \(-0.139414\pi\) | |||||||
\(908\) | 15.1879i | 0.504027i | ||||||||
\(909\) | 8.97396 | 0.297647 | ||||||||
\(910\) | 3.52388i | 0.116815i | ||||||||
\(911\) | − | 24.0000i | − | 0.795155i | −0.917568 | − | 0.397578i | \(-0.869851\pi\) | ||
0.917568 | − | 0.397578i | \(-0.130149\pi\) | |||||||
\(912\) | − | 2.69002i | − | 0.0890753i | ||||||
\(913\) | 7.09609 | 0.234846 | ||||||||
\(914\) | 9.18785 | 0.303907 | ||||||||
\(915\) | 2.00000 | 0.0661180 | ||||||||
\(916\) | 7.80782 | 0.257978 | ||||||||
\(917\) | − | 11.7557i | − | 0.388209i | ||||||
\(918\) | −6.90391 | −0.227863 | ||||||||
\(919\) | − | 6.69376i | − | 0.220807i | −0.993887 | − | 0.110403i | \(-0.964786\pi\) | ||
0.993887 | − | 0.110403i | \(-0.0352143\pi\) | |||||||
\(920\) | − | 8.90391i | − | 0.293553i | ||||||
\(921\) | 21.9479 | 0.723209 | ||||||||
\(922\) | −6.14010 | −0.202213 | ||||||||
\(923\) | 37.1433i | 1.22259i | ||||||||
\(924\) | 0.903910 | 0.0297365 | ||||||||
\(925\) | −4.10695 | + | 4.48698i | −0.135036 | + | 0.147531i | ||||
\(926\) | 1.09984 | 0.0361428 | ||||||||
\(927\) | − | 19.1879i | − | 0.630212i | ||||||
\(928\) | 2.00000 | 0.0656532 | ||||||||
\(929\) | 35.8078 | 1.17482 | 0.587408 | − | 0.809291i | \(-0.300148\pi\) | ||||
0.587408 | + | 0.809291i | \(0.300148\pi\) | |||||||
\(930\) | 9.59393i | 0.314597i | ||||||||
\(931\) | 14.2139i | 0.465842i | ||||||||
\(932\) | −3.59393 | −0.117723 | ||||||||
\(933\) | 18.7601i | 0.614177i | ||||||||
\(934\) | 3.18785 | 0.104310 | ||||||||
\(935\) | −4.76381 | −0.155793 | ||||||||
\(936\) | −2.69002 | −0.0879259 | ||||||||
\(937\) | −36.7601 | −1.20090 | −0.600450 | − | 0.799663i | \(-0.705012\pi\) | ||||
−0.600450 | + | 0.799663i | \(0.705012\pi\) | |||||||
\(938\) | − | 1.62429i | − | 0.0530351i | ||||||
\(939\) | 21.1879i | 0.691439i | ||||||||
\(940\) | − | 4.61997i | − | 0.150687i | ||||||
\(941\) | 33.6819 | 1.09800 | 0.549000 | − | 0.835822i | \(-0.315009\pi\) | ||||
0.549000 | + | 0.835822i | \(0.315009\pi\) | |||||||
\(942\) | − | 12.2139i | − | 0.397950i | ||||||
\(943\) | 17.8078i | 0.579902i | ||||||||
\(944\) | 6.21389i | 0.202245i | ||||||||
\(945\) | 1.30998i | 0.0426138i | ||||||||
\(946\) | 5.66772 | 0.184274 | ||||||||
\(947\) | 13.5201i | 0.439345i | 0.975574 | + | 0.219673i | \(0.0704989\pi\) | ||||
−0.975574 | + | 0.219673i | \(0.929501\pi\) | |||||||
\(948\) | − | 1.59393i | − | 0.0517683i | ||||||
\(949\) | − | 33.0440i | − | 1.07265i | ||||||
\(950\) | 2.69002 | 0.0872757 | ||||||||
\(951\) | 23.5418 | 0.763397 | ||||||||
\(952\) | −9.04401 | −0.293118 | ||||||||
\(953\) | −13.2616 | −0.429587 | −0.214793 | − | 0.976659i | \(-0.568908\pi\) | ||||
−0.214793 | + | 0.976659i | \(0.568908\pi\) | |||||||
\(954\) | − | 0.690016i | − | 0.0223401i | ||||||
\(955\) | −20.9039 | −0.676435 | ||||||||
\(956\) | − | 7.18785i | − | 0.232472i | ||||||
\(957\) | 1.38003i | 0.0446101i | ||||||||
\(958\) | −41.1916 | −1.33084 | ||||||||
\(959\) | 15.1879 | 0.490441 | ||||||||
\(960\) | 1.00000i | 0.0322749i | ||||||||
\(961\) | −61.0434 | −1.96914 | ||||||||
\(962\) | 11.0478 | − | 12.0700i | 0.356194 | − | 0.389154i | ||||
\(963\) | 18.1438 | 0.584677 | ||||||||
\(964\) | − | 3.18785i | − | 0.102674i | ||||||
\(965\) | 8.61997 | 0.277487 | ||||||||
\(966\) | 11.6640 | 0.375282 | ||||||||
\(967\) | − | 48.8556i | − | 1.57109i | −0.618805 | − | 0.785545i | \(-0.712383\pi\) | ||
0.618805 | − | 0.785545i | \(-0.287617\pi\) | |||||||
\(968\) | − | 10.5239i | − | 0.338250i | ||||||
\(969\) | −18.5716 | −0.596607 | ||||||||
\(970\) | 3.38003i | 0.108526i | ||||||||
\(971\) | −39.7861 | −1.27680 | −0.638398 | − | 0.769706i | \(-0.720403\pi\) | ||||
−0.638398 | + | 0.769706i | \(0.720403\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 8.85558 | 0.283897 | ||||||||
\(974\) | −24.4278 | −0.782717 | ||||||||
\(975\) | − | 2.69002i | − | 0.0861495i | ||||||
\(976\) | 2.00000i | 0.0640184i | ||||||||
\(977\) | − | 49.5239i | − | 1.58441i | −0.610256 | − | 0.792205i | \(-0.708933\pi\) | ||
0.610256 | − | 0.792205i | \(-0.291067\pi\) | |||||||
\(978\) | −6.07005 | −0.194099 | ||||||||
\(979\) | − | 4.09176i | − | 0.130773i | ||||||
\(980\) | − | 5.28394i | − | 0.168789i | ||||||
\(981\) | 17.5239i | 0.559494i | ||||||||
\(982\) | 0.690016i | 0.0220193i | ||||||||
\(983\) | −40.2356 | −1.28332 | −0.641658 | − | 0.766991i | \(-0.721753\pi\) | ||||
−0.641658 | + | 0.766991i | \(0.721753\pi\) | |||||||
\(984\) | − | 2.00000i | − | 0.0637577i | ||||||
\(985\) | 12.6900i | 0.404338i | ||||||||
\(986\) | − | 13.8078i | − | 0.439731i | ||||||
\(987\) | 6.05208 | 0.192640 | ||||||||
\(988\) | −7.23619 | −0.230214 | ||||||||
\(989\) | 73.1358 | 2.32558 | ||||||||
\(990\) | −0.690016 | −0.0219302 | ||||||||
\(991\) | 54.4495i | 1.72965i | 0.502077 | + | 0.864823i | \(0.332569\pi\) | ||||
−0.502077 | + | 0.864823i | \(0.667431\pi\) | |||||||
\(992\) | −9.59393 | −0.304607 | ||||||||
\(993\) | 16.4061i | 0.520631i | ||||||||
\(994\) | 18.0880i | 0.573717i | ||||||||
\(995\) | 22.8339 | 0.723882 | ||||||||
\(996\) | −10.2839 | −0.325859 | ||||||||
\(997\) | 51.2579i | 1.62335i | 0.584106 | + | 0.811677i | \(0.301445\pi\) | ||||
−0.584106 | + | 0.811677i | \(0.698555\pi\) | |||||||
\(998\) | −8.63794 | −0.273429 | ||||||||
\(999\) | 4.10695 | − | 4.48698i | 0.129938 | − | 0.141962i |
(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 | 1110.2.h.f.961.2 | ✓ | 6 | |
3.2 | odd | 2 | 3330.2.h.m.2071.5 | 6 | |||
37.36 | even | 2 | inner | 1110.2.h.f.961.5 | yes | 6 | |
111.110 | odd | 2 | 3330.2.h.m.2071.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.h.f.961.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1110.2.h.f.961.5 | yes | 6 | 37.36 | even | 2 | inner | |
3330.2.h.m.2071.2 | 6 | 111.110 | odd | 2 | |||
3330.2.h.m.2071.5 | 6 | 3.2 | odd | 2 |