Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(311,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("403.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.c (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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 311.11 | ||
Character | \(\chi\) | \(=\) | 403.311 |
Dual form | 403.2.c.b.311.22 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.40506i | − | 0.993528i | −0.867886 | − | 0.496764i | \(-0.834521\pi\) | ||
0.867886 | − | 0.496764i | \(-0.165479\pi\) | |||||||
\(3\) | 1.52886 | 0.882687 | 0.441344 | − | 0.897338i | \(-0.354502\pi\) | ||||
0.441344 | + | 0.897338i | \(0.354502\pi\) | |||||||
\(4\) | 0.0258025 | 0.0129013 | ||||||||
\(5\) | − | 1.01618i | − | 0.454448i | −0.973843 | − | 0.227224i | \(-0.927035\pi\) | ||
0.973843 | − | 0.227224i | \(-0.0729649\pi\) | |||||||
\(6\) | − | 2.14814i | − | 0.876975i | ||||||
\(7\) | − | 2.90958i | − | 1.09972i | −0.835258 | − | 0.549858i | \(-0.814682\pi\) | ||
0.835258 | − | 0.549858i | \(-0.185318\pi\) | |||||||
\(8\) | − | 2.84638i | − | 1.00635i | ||||||
\(9\) | −0.662589 | −0.220863 | ||||||||
\(10\) | −1.42779 | −0.451507 | ||||||||
\(11\) | 2.94134i | 0.886848i | 0.896312 | + | 0.443424i | \(0.146236\pi\) | ||||
−0.896312 | + | 0.443424i | \(0.853764\pi\) | |||||||
\(12\) | 0.0394484 | 0.0113878 | ||||||||
\(13\) | 3.36248 | + | 1.30143i | 0.932585 | + | 0.360951i | ||||
\(14\) | −4.08813 | −1.09260 | ||||||||
\(15\) | − | 1.55359i | − | 0.401135i | ||||||
\(16\) | −3.94773 | −0.986932 | ||||||||
\(17\) | −5.52858 | −1.34088 | −0.670438 | − | 0.741965i | \(-0.733894\pi\) | ||||
−0.670438 | + | 0.741965i | \(0.733894\pi\) | |||||||
\(18\) | 0.930978i | 0.219434i | ||||||||
\(19\) | 3.13639i | 0.719537i | 0.933042 | + | 0.359768i | \(0.117144\pi\) | ||||
−0.933042 | + | 0.359768i | \(0.882856\pi\) | |||||||
\(20\) | − | 0.0262199i | − | 0.00586295i | ||||||
\(21\) | − | 4.44833i | − | 0.970706i | ||||||
\(22\) | 4.13277 | 0.881109 | ||||||||
\(23\) | 3.87847 | 0.808717 | 0.404358 | − | 0.914601i | \(-0.367495\pi\) | ||||
0.404358 | + | 0.914601i | \(0.367495\pi\) | |||||||
\(24\) | − | 4.35171i | − | 0.888289i | ||||||
\(25\) | 3.96739 | 0.793477 | ||||||||
\(26\) | 1.82859 | − | 4.72449i | 0.358615 | − | 0.926549i | ||||
\(27\) | −5.59958 | −1.07764 | ||||||||
\(28\) | − | 0.0750744i | − | 0.0141877i | ||||||
\(29\) | 5.59296 | 1.03859 | 0.519294 | − | 0.854596i | \(-0.326195\pi\) | ||||
0.519294 | + | 0.854596i | \(0.326195\pi\) | |||||||
\(30\) | −2.18289 | −0.398539 | ||||||||
\(31\) | − | 1.00000i | − | 0.179605i | ||||||
\(32\) | − | 0.145952i | − | 0.0258009i | ||||||
\(33\) | 4.49690i | 0.782810i | ||||||||
\(34\) | 7.76799i | 1.33220i | ||||||||
\(35\) | −2.95664 | −0.499764 | ||||||||
\(36\) | −0.0170965 | −0.00284941 | ||||||||
\(37\) | − | 3.92962i | − | 0.646025i | −0.946395 | − | 0.323013i | \(-0.895304\pi\) | ||
0.946395 | − | 0.323013i | \(-0.104696\pi\) | |||||||
\(38\) | 4.40682 | 0.714880 | ||||||||
\(39\) | 5.14076 | + | 1.98970i | 0.823181 | + | 0.318607i | ||||
\(40\) | −2.89242 | −0.457332 | ||||||||
\(41\) | 12.1899i | 1.90374i | 0.306509 | + | 0.951868i | \(0.400839\pi\) | ||||
−0.306509 | + | 0.951868i | \(0.599161\pi\) | |||||||
\(42\) | −6.25018 | −0.964424 | ||||||||
\(43\) | 3.52296 | 0.537246 | 0.268623 | − | 0.963245i | \(-0.413431\pi\) | ||||
0.268623 | + | 0.963245i | \(0.413431\pi\) | |||||||
\(44\) | 0.0758940i | 0.0114415i | ||||||||
\(45\) | 0.673307i | 0.100371i | ||||||||
\(46\) | − | 5.44949i | − | 0.803483i | ||||||
\(47\) | − | 9.64114i | − | 1.40630i | −0.711040 | − | 0.703152i | \(-0.751775\pi\) | ||
0.711040 | − | 0.703152i | \(-0.248225\pi\) | |||||||
\(48\) | −6.03552 | −0.871153 | ||||||||
\(49\) | −1.46564 | −0.209377 | ||||||||
\(50\) | − | 5.57442i | − | 0.788342i | ||||||
\(51\) | −8.45242 | −1.18358 | ||||||||
\(52\) | 0.0867605 | + | 0.0335801i | 0.0120315 | + | 0.00465672i | ||||
\(53\) | −11.3388 | −1.55751 | −0.778753 | − | 0.627330i | \(-0.784148\pi\) | ||||
−0.778753 | + | 0.627330i | \(0.784148\pi\) | |||||||
\(54\) | 7.86776i | 1.07067i | ||||||||
\(55\) | 2.98892 | 0.403026 | ||||||||
\(56\) | −8.28175 | −1.10670 | ||||||||
\(57\) | 4.79510i | 0.635126i | ||||||||
\(58\) | − | 7.85846i | − | 1.03187i | ||||||
\(59\) | 12.4904i | 1.62611i | 0.582190 | + | 0.813053i | \(0.302196\pi\) | ||||
−0.582190 | + | 0.813053i | \(0.697804\pi\) | |||||||
\(60\) | − | 0.0400865i | − | 0.00517515i | ||||||
\(61\) | 5.57570 | 0.713895 | 0.356947 | − | 0.934125i | \(-0.383818\pi\) | ||||
0.356947 | + | 0.934125i | \(0.383818\pi\) | |||||||
\(62\) | −1.40506 | −0.178443 | ||||||||
\(63\) | 1.92785i | 0.242887i | ||||||||
\(64\) | −8.10053 | −1.01257 | ||||||||
\(65\) | 1.32248 | − | 3.41687i | 0.164033 | − | 0.423811i | ||||
\(66\) | 6.31842 | 0.777744 | ||||||||
\(67\) | 4.26478i | 0.521026i | 0.965470 | + | 0.260513i | \(0.0838916\pi\) | ||||
−0.965470 | + | 0.260513i | \(0.916108\pi\) | |||||||
\(68\) | −0.142651 | −0.0172990 | ||||||||
\(69\) | 5.92963 | 0.713844 | ||||||||
\(70\) | 4.15426i | 0.496530i | ||||||||
\(71\) | 9.44757i | 1.12122i | 0.828080 | + | 0.560610i | \(0.189433\pi\) | ||||
−0.828080 | + | 0.560610i | \(0.810567\pi\) | |||||||
\(72\) | 1.88598i | 0.222265i | ||||||||
\(73\) | 0.784520i | 0.0918211i | 0.998946 | + | 0.0459106i | \(0.0146189\pi\) | ||||
−0.998946 | + | 0.0459106i | \(0.985381\pi\) | |||||||
\(74\) | −5.52136 | −0.641845 | ||||||||
\(75\) | 6.06558 | 0.700392 | ||||||||
\(76\) | 0.0809267i | 0.00928293i | ||||||||
\(77\) | 8.55806 | 0.975282 | ||||||||
\(78\) | 2.79565 | − | 7.22309i | 0.316545 | − | 0.817854i | ||||
\(79\) | 6.11817 | 0.688348 | 0.344174 | − | 0.938906i | \(-0.388159\pi\) | ||||
0.344174 | + | 0.938906i | \(0.388159\pi\) | |||||||
\(80\) | 4.01159i | 0.448509i | ||||||||
\(81\) | −6.57321 | −0.730357 | ||||||||
\(82\) | 17.1275 | 1.89142 | ||||||||
\(83\) | − | 8.81342i | − | 0.967399i | −0.875234 | − | 0.483699i | \(-0.839293\pi\) | ||
0.875234 | − | 0.483699i | \(-0.160707\pi\) | |||||||
\(84\) | − | 0.114778i | − | 0.0125233i | ||||||
\(85\) | 5.61801i | 0.609358i | ||||||||
\(86\) | − | 4.94997i | − | 0.533769i | ||||||
\(87\) | 8.55086 | 0.916748 | ||||||||
\(88\) | 8.37217 | 0.892476 | ||||||||
\(89\) | − | 6.58407i | − | 0.697910i | −0.937140 | − | 0.348955i | \(-0.886537\pi\) | ||
0.937140 | − | 0.348955i | \(-0.113463\pi\) | |||||||
\(90\) | 0.946037 | 0.0997211 | ||||||||
\(91\) | 3.78660 | − | 9.78340i | 0.396944 | − | 1.02558i | ||||
\(92\) | 0.100074 | 0.0104335 | ||||||||
\(93\) | − | 1.52886i | − | 0.158535i | ||||||
\(94\) | −13.5464 | −1.39720 | ||||||||
\(95\) | 3.18712 | 0.326992 | ||||||||
\(96\) | − | 0.223140i | − | 0.0227741i | ||||||
\(97\) | 6.44332i | 0.654220i | 0.944986 | + | 0.327110i | \(0.106075\pi\) | ||||
−0.944986 | + | 0.327110i | \(0.893925\pi\) | |||||||
\(98\) | 2.05931i | 0.208022i | ||||||||
\(99\) | − | 1.94890i | − | 0.195872i | ||||||
\(100\) | 0.102369 | 0.0102369 | ||||||||
\(101\) | −18.1325 | −1.80425 | −0.902123 | − | 0.431478i | \(-0.857992\pi\) | ||||
−0.902123 | + | 0.431478i | \(0.857992\pi\) | |||||||
\(102\) | 11.8762i | 1.17592i | ||||||||
\(103\) | 17.3257 | 1.70715 | 0.853575 | − | 0.520970i | \(-0.174430\pi\) | ||||
0.853575 | + | 0.520970i | \(0.174430\pi\) | |||||||
\(104\) | 3.70435 | − | 9.57089i | 0.363242 | − | 0.938503i | ||||
\(105\) | −4.52029 | −0.441135 | ||||||||
\(106\) | 15.9317i | 1.54743i | ||||||||
\(107\) | −7.73734 | −0.747997 | −0.373998 | − | 0.927429i | \(-0.622013\pi\) | ||||
−0.373998 | + | 0.927429i | \(0.622013\pi\) | |||||||
\(108\) | −0.144483 | −0.0139029 | ||||||||
\(109\) | 11.1918i | 1.07198i | 0.844224 | + | 0.535991i | \(0.180062\pi\) | ||||
−0.844224 | + | 0.535991i | \(0.819938\pi\) | |||||||
\(110\) | − | 4.19962i | − | 0.400418i | ||||||
\(111\) | − | 6.00784i | − | 0.570238i | ||||||
\(112\) | 11.4862i | 1.08535i | ||||||||
\(113\) | 14.3095 | 1.34612 | 0.673061 | − | 0.739587i | \(-0.264979\pi\) | ||||
0.673061 | + | 0.739587i | \(0.264979\pi\) | |||||||
\(114\) | 6.73741 | 0.631016 | ||||||||
\(115\) | − | 3.94121i | − | 0.367519i | ||||||
\(116\) | 0.144313 | 0.0133991 | ||||||||
\(117\) | −2.22794 | − | 0.862311i | −0.205973 | − | 0.0797207i | ||||
\(118\) | 17.5497 | 1.61558 | ||||||||
\(119\) | 16.0858i | 1.47458i | ||||||||
\(120\) | −4.42210 | −0.403681 | ||||||||
\(121\) | 2.34851 | 0.213501 | ||||||||
\(122\) | − | 7.83419i | − | 0.709275i | ||||||
\(123\) | 18.6366i | 1.68040i | ||||||||
\(124\) | − | 0.0258025i | − | 0.00231713i | ||||||
\(125\) | − | 9.11244i | − | 0.815042i | ||||||
\(126\) | 2.70875 | 0.241315 | ||||||||
\(127\) | −17.9788 | −1.59536 | −0.797682 | − | 0.603079i | \(-0.793940\pi\) | ||||
−0.797682 | + | 0.603079i | \(0.793940\pi\) | |||||||
\(128\) | 11.0898i | 0.980212i | ||||||||
\(129\) | 5.38611 | 0.474220 | ||||||||
\(130\) | −4.80092 | − | 1.85816i | −0.421068 | − | 0.162972i | ||||
\(131\) | −8.60202 | −0.751562 | −0.375781 | − | 0.926708i | \(-0.622626\pi\) | ||||
−0.375781 | + | 0.926708i | \(0.622626\pi\) | |||||||
\(132\) | 0.116031i | 0.0100992i | ||||||||
\(133\) | 9.12556 | 0.791287 | ||||||||
\(134\) | 5.99228 | 0.517654 | ||||||||
\(135\) | 5.69016i | 0.489731i | ||||||||
\(136\) | 15.7364i | 1.34939i | ||||||||
\(137\) | − | 13.4868i | − | 1.15226i | −0.817360 | − | 0.576128i | \(-0.804563\pi\) | ||
0.817360 | − | 0.576128i | \(-0.195437\pi\) | |||||||
\(138\) | − | 8.33150i | − | 0.709224i | ||||||
\(139\) | −8.93572 | −0.757918 | −0.378959 | − | 0.925414i | \(-0.623718\pi\) | ||||
−0.378959 | + | 0.925414i | \(0.623718\pi\) | |||||||
\(140\) | −0.0762888 | −0.00644758 | ||||||||
\(141\) | − | 14.7399i | − | 1.24133i | ||||||
\(142\) | 13.2744 | 1.11396 | ||||||||
\(143\) | −3.82794 | + | 9.89021i | −0.320109 | + | 0.827061i | ||||
\(144\) | 2.61572 | 0.217977 | ||||||||
\(145\) | − | 5.68344i | − | 0.471984i | ||||||
\(146\) | 1.10230 | 0.0912269 | ||||||||
\(147\) | −2.24076 | −0.184814 | ||||||||
\(148\) | − | 0.101394i | − | 0.00833454i | ||||||
\(149\) | − | 2.58006i | − | 0.211367i | −0.994400 | − | 0.105683i | \(-0.966297\pi\) | ||
0.994400 | − | 0.105683i | \(-0.0337030\pi\) | |||||||
\(150\) | − | 8.52251i | − | 0.695860i | ||||||
\(151\) | 1.75601i | 0.142902i | 0.997444 | + | 0.0714510i | \(0.0227629\pi\) | ||||
−0.997444 | + | 0.0714510i | \(0.977237\pi\) | |||||||
\(152\) | 8.92734 | 0.724103 | ||||||||
\(153\) | 3.66317 | 0.296150 | ||||||||
\(154\) | − | 12.0246i | − | 0.968970i | ||||||
\(155\) | −1.01618 | −0.0816212 | ||||||||
\(156\) | 0.132645 | + | 0.0513393i | 0.0106201 | + | 0.00411043i | ||||
\(157\) | −19.0327 | −1.51898 | −0.759489 | − | 0.650520i | \(-0.774551\pi\) | ||||
−0.759489 | + | 0.650520i | \(0.774551\pi\) | |||||||
\(158\) | − | 8.59640i | − | 0.683893i | ||||||
\(159\) | −17.3355 | −1.37479 | ||||||||
\(160\) | −0.148313 | −0.0117252 | ||||||||
\(161\) | − | 11.2847i | − | 0.889359i | ||||||
\(162\) | 9.23576i | 0.725630i | ||||||||
\(163\) | 7.89713i | 0.618551i | 0.950973 | + | 0.309275i | \(0.100086\pi\) | ||||
−0.950973 | + | 0.309275i | \(0.899914\pi\) | |||||||
\(164\) | 0.314529i | 0.0245606i | ||||||||
\(165\) | 4.56964 | 0.355746 | ||||||||
\(166\) | −12.3834 | −0.961138 | ||||||||
\(167\) | 6.55351i | 0.507126i | 0.967319 | + | 0.253563i | \(0.0816025\pi\) | ||||
−0.967319 | + | 0.253563i | \(0.918398\pi\) | |||||||
\(168\) | −12.6616 | −0.976866 | ||||||||
\(169\) | 9.61257 | + | 8.75205i | 0.739429 | + | 0.673235i | ||||
\(170\) | 7.89364 | 0.605415 | ||||||||
\(171\) | − | 2.07814i | − | 0.158919i | ||||||
\(172\) | 0.0909012 | 0.00693115 | ||||||||
\(173\) | −21.5664 | −1.63966 | −0.819832 | − | 0.572604i | \(-0.805933\pi\) | ||||
−0.819832 | + | 0.572604i | \(0.805933\pi\) | |||||||
\(174\) | − | 12.0145i | − | 0.910815i | ||||||
\(175\) | − | 11.5434i | − | 0.872600i | ||||||
\(176\) | − | 11.6116i | − | 0.875259i | ||||||
\(177\) | 19.0960i | 1.43534i | ||||||||
\(178\) | −9.25102 | −0.693393 | ||||||||
\(179\) | −5.03686 | −0.376472 | −0.188236 | − | 0.982124i | \(-0.560277\pi\) | ||||
−0.188236 | + | 0.982124i | \(0.560277\pi\) | |||||||
\(180\) | 0.0173730i | 0.00129491i | ||||||||
\(181\) | 9.32320 | 0.692988 | 0.346494 | − | 0.938052i | \(-0.387372\pi\) | ||||
0.346494 | + | 0.938052i | \(0.387372\pi\) | |||||||
\(182\) | −13.7463 | − | 5.32041i | −1.01894 | − | 0.394375i | ||||
\(183\) | 8.52445 | 0.630146 | ||||||||
\(184\) | − | 11.0396i | − | 0.813849i | ||||||
\(185\) | −3.99318 | −0.293585 | ||||||||
\(186\) | −2.14814 | −0.157509 | ||||||||
\(187\) | − | 16.2614i | − | 1.18915i | ||||||
\(188\) | − | 0.248766i | − | 0.0181431i | ||||||
\(189\) | 16.2924i | 1.18510i | ||||||||
\(190\) | − | 4.47810i | − | 0.324876i | ||||||
\(191\) | 10.5572 | 0.763892 | 0.381946 | − | 0.924185i | \(-0.375254\pi\) | ||||
0.381946 | + | 0.924185i | \(0.375254\pi\) | |||||||
\(192\) | −12.3846 | −0.893779 | ||||||||
\(193\) | − | 16.1267i | − | 1.16082i | −0.814324 | − | 0.580411i | \(-0.802892\pi\) | ||
0.814324 | − | 0.580411i | \(-0.197108\pi\) | |||||||
\(194\) | 9.05326 | 0.649986 | ||||||||
\(195\) | 2.02189 | − | 5.22392i | 0.144790 | − | 0.374093i | ||||
\(196\) | −0.0378172 | −0.00270123 | ||||||||
\(197\) | 4.22408i | 0.300953i | 0.988614 | + | 0.150477i | \(0.0480808\pi\) | ||||
−0.988614 | + | 0.150477i | \(0.951919\pi\) | |||||||
\(198\) | −2.73832 | −0.194604 | ||||||||
\(199\) | 2.01987 | 0.143185 | 0.0715923 | − | 0.997434i | \(-0.477192\pi\) | ||||
0.0715923 | + | 0.997434i | \(0.477192\pi\) | |||||||
\(200\) | − | 11.2927i | − | 0.798513i | ||||||
\(201\) | 6.52025i | 0.459903i | ||||||||
\(202\) | 25.4772i | 1.79257i | ||||||||
\(203\) | − | 16.2732i | − | 1.14215i | ||||||
\(204\) | −0.218094 | −0.0152696 | ||||||||
\(205\) | 12.3870 | 0.865148 | ||||||||
\(206\) | − | 24.3436i | − | 1.69610i | ||||||
\(207\) | −2.56983 | −0.178615 | ||||||||
\(208\) | −13.2742 | − | 5.13768i | −0.920398 | − | 0.356234i | ||||
\(209\) | −9.22519 | −0.638120 | ||||||||
\(210\) | 6.35129i | 0.438280i | ||||||||
\(211\) | −24.2401 | −1.66876 | −0.834379 | − | 0.551191i | \(-0.814174\pi\) | ||||
−0.834379 | + | 0.551191i | \(0.814174\pi\) | |||||||
\(212\) | −0.292570 | −0.0200938 | ||||||||
\(213\) | 14.4440i | 0.989687i | ||||||||
\(214\) | 10.8714i | 0.743156i | ||||||||
\(215\) | − | 3.57995i | − | 0.244150i | ||||||
\(216\) | 15.9385i | 1.08448i | ||||||||
\(217\) | −2.90958 | −0.197515 | ||||||||
\(218\) | 15.7252 | 1.06504 | ||||||||
\(219\) | 1.19942i | 0.0810494i | ||||||||
\(220\) | 0.0771217 | 0.00519954 | ||||||||
\(221\) | −18.5897 | − | 7.19504i | −1.25048 | − | 0.483991i | ||||
\(222\) | −8.44138 | −0.566548 | ||||||||
\(223\) | 5.61510i | 0.376015i | 0.982168 | + | 0.188008i | \(0.0602029\pi\) | ||||
−0.982168 | + | 0.188008i | \(0.939797\pi\) | |||||||
\(224\) | −0.424658 | −0.0283737 | ||||||||
\(225\) | −2.62875 | −0.175250 | ||||||||
\(226\) | − | 20.1057i | − | 1.33741i | ||||||
\(227\) | − | 8.69104i | − | 0.576845i | −0.957503 | − | 0.288422i | \(-0.906869\pi\) | ||
0.957503 | − | 0.288422i | \(-0.0931307\pi\) | |||||||
\(228\) | 0.123726i | 0.00819393i | ||||||||
\(229\) | − | 27.5444i | − | 1.82018i | −0.414407 | − | 0.910092i | \(-0.636011\pi\) | ||
0.414407 | − | 0.910092i | \(-0.363989\pi\) | |||||||
\(230\) | −5.53764 | −0.365141 | ||||||||
\(231\) | 13.0841 | 0.860869 | ||||||||
\(232\) | − | 15.9197i | − | 1.04518i | ||||||
\(233\) | −13.7931 | −0.903615 | −0.451808 | − | 0.892115i | \(-0.649221\pi\) | ||||
−0.451808 | + | 0.892115i | \(0.649221\pi\) | |||||||
\(234\) | −1.21160 | + | 3.13040i | −0.0792048 | + | 0.204640i | ||||
\(235\) | −9.79709 | −0.639092 | ||||||||
\(236\) | 0.322283i | 0.0209788i | ||||||||
\(237\) | 9.35382 | 0.607596 | ||||||||
\(238\) | 22.6016 | 1.46504 | ||||||||
\(239\) | − | 1.37922i | − | 0.0892146i | −0.999005 | − | 0.0446073i | \(-0.985796\pi\) | ||
0.999005 | − | 0.0446073i | \(-0.0142037\pi\) | |||||||
\(240\) | 6.13315i | 0.395893i | ||||||||
\(241\) | − | 27.8626i | − | 1.79479i | −0.441231 | − | 0.897394i | \(-0.645458\pi\) | ||
0.441231 | − | 0.897394i | \(-0.354542\pi\) | |||||||
\(242\) | − | 3.29980i | − | 0.212119i | ||||||
\(243\) | 6.74924 | 0.432964 | ||||||||
\(244\) | 0.143867 | 0.00921014 | ||||||||
\(245\) | 1.48935i | 0.0951509i | ||||||||
\(246\) | 26.1855 | 1.66953 | ||||||||
\(247\) | −4.08178 | + | 10.5461i | −0.259718 | + | 0.671029i | ||||
\(248\) | −2.84638 | −0.180745 | ||||||||
\(249\) | − | 13.4745i | − | 0.853911i | ||||||
\(250\) | −12.8035 | −0.809767 | ||||||||
\(251\) | 5.04891 | 0.318685 | 0.159342 | − | 0.987223i | \(-0.449063\pi\) | ||||
0.159342 | + | 0.987223i | \(0.449063\pi\) | |||||||
\(252\) | 0.0497435i | 0.00313354i | ||||||||
\(253\) | 11.4079i | 0.717209i | ||||||||
\(254\) | 25.2614i | 1.58504i | ||||||||
\(255\) | 8.58914i | 0.537873i | ||||||||
\(256\) | −0.619157 | −0.0386973 | ||||||||
\(257\) | −21.7141 | −1.35449 | −0.677243 | − | 0.735759i | \(-0.736825\pi\) | ||||
−0.677243 | + | 0.735759i | \(0.736825\pi\) | |||||||
\(258\) | − | 7.56781i | − | 0.471151i | ||||||
\(259\) | −11.4335 | −0.710445 | ||||||||
\(260\) | 0.0341233 | − | 0.0881640i | 0.00211624 | − | 0.00546770i | ||||
\(261\) | −3.70584 | −0.229385 | ||||||||
\(262\) | 12.0864i | 0.746698i | ||||||||
\(263\) | 21.0672 | 1.29906 | 0.649529 | − | 0.760337i | \(-0.274966\pi\) | ||||
0.649529 | + | 0.760337i | \(0.274966\pi\) | |||||||
\(264\) | 12.7999 | 0.787777 | ||||||||
\(265\) | 11.5222i | 0.707805i | ||||||||
\(266\) | − | 12.8220i | − | 0.786166i | ||||||
\(267\) | − | 10.0661i | − | 0.616036i | ||||||
\(268\) | 0.110042i | 0.00672189i | ||||||||
\(269\) | 11.1314 | 0.678696 | 0.339348 | − | 0.940661i | \(-0.389794\pi\) | ||||
0.339348 | + | 0.940661i | \(0.389794\pi\) | |||||||
\(270\) | 7.99503 | 0.486562 | ||||||||
\(271\) | 17.2105i | 1.04546i | 0.852498 | + | 0.522731i | \(0.175087\pi\) | ||||
−0.852498 | + | 0.522731i | \(0.824913\pi\) | |||||||
\(272\) | 21.8253 | 1.32335 | ||||||||
\(273\) | 5.78918 | − | 14.9574i | 0.350377 | − | 0.905266i | ||||
\(274\) | −18.9498 | −1.14480 | ||||||||
\(275\) | 11.6694i | 0.703694i | ||||||||
\(276\) | 0.152999 | 0.00920949 | ||||||||
\(277\) | 1.64549 | 0.0988681 | 0.0494340 | − | 0.998777i | \(-0.484258\pi\) | ||||
0.0494340 | + | 0.998777i | \(0.484258\pi\) | |||||||
\(278\) | 12.5552i | 0.753013i | ||||||||
\(279\) | 0.662589i | 0.0396681i | ||||||||
\(280\) | 8.41572i | 0.502935i | ||||||||
\(281\) | − | 21.4692i | − | 1.28075i | −0.768064 | − | 0.640374i | \(-0.778780\pi\) | ||
0.768064 | − | 0.640374i | \(-0.221220\pi\) | |||||||
\(282\) | −20.7105 | −1.23329 | ||||||||
\(283\) | −2.52897 | −0.150332 | −0.0751660 | − | 0.997171i | \(-0.523949\pi\) | ||||
−0.0751660 | + | 0.997171i | \(0.523949\pi\) | |||||||
\(284\) | 0.243771i | 0.0144652i | ||||||||
\(285\) | 4.87266 | 0.288632 | ||||||||
\(286\) | 13.8964 | + | 5.37849i | 0.821709 | + | 0.318037i | ||||
\(287\) | 35.4673 | 2.09357 | ||||||||
\(288\) | 0.0967061i | 0.00569846i | ||||||||
\(289\) | 13.5652 | 0.797950 | ||||||||
\(290\) | −7.98558 | −0.468929 | ||||||||
\(291\) | 9.85093i | 0.577472i | ||||||||
\(292\) | 0.0202426i | 0.00118461i | ||||||||
\(293\) | 8.49502i | 0.496284i | 0.968724 | + | 0.248142i | \(0.0798200\pi\) | ||||
−0.968724 | + | 0.248142i | \(0.920180\pi\) | |||||||
\(294\) | 3.14840i | 0.183618i | ||||||||
\(295\) | 12.6924 | 0.738980 | ||||||||
\(296\) | −11.1852 | −0.650125 | ||||||||
\(297\) | − | 16.4703i | − | 0.955703i | ||||||
\(298\) | −3.62514 | −0.209999 | ||||||||
\(299\) | 13.0413 | + | 5.04754i | 0.754197 | + | 0.291907i | ||||
\(300\) | 0.156507 | 0.00903594 | ||||||||
\(301\) | − | 10.2503i | − | 0.590819i | ||||||
\(302\) | 2.46730 | 0.141977 | ||||||||
\(303\) | −27.7220 | −1.59259 | ||||||||
\(304\) | − | 12.3816i | − | 0.710134i | ||||||
\(305\) | − | 5.66589i | − | 0.324428i | ||||||
\(306\) | − | 5.14698i | − | 0.294233i | ||||||
\(307\) | 24.6040i | 1.40423i | 0.712065 | + | 0.702113i | \(0.247760\pi\) | ||||
−0.712065 | + | 0.702113i | \(0.752240\pi\) | |||||||
\(308\) | 0.220820 | 0.0125824 | ||||||||
\(309\) | 26.4885 | 1.50688 | ||||||||
\(310\) | 1.42779i | 0.0810930i | ||||||||
\(311\) | −8.07331 | −0.457795 | −0.228898 | − | 0.973451i | \(-0.573512\pi\) | ||||
−0.228898 | + | 0.973451i | \(0.573512\pi\) | |||||||
\(312\) | 5.66343 | − | 14.6325i | 0.320629 | − | 0.828405i | ||||
\(313\) | −14.6297 | −0.826922 | −0.413461 | − | 0.910522i | \(-0.635680\pi\) | ||||
−0.413461 | + | 0.910522i | \(0.635680\pi\) | |||||||
\(314\) | 26.7422i | 1.50915i | ||||||||
\(315\) | 1.95904 | 0.110379 | ||||||||
\(316\) | 0.157864 | 0.00888055 | ||||||||
\(317\) | − | 6.32778i | − | 0.355403i | −0.984084 | − | 0.177702i | \(-0.943134\pi\) | ||
0.984084 | − | 0.177702i | \(-0.0568662\pi\) | |||||||
\(318\) | 24.3574i | 1.36589i | ||||||||
\(319\) | 16.4508i | 0.921069i | ||||||||
\(320\) | 8.23156i | 0.460158i | ||||||||
\(321\) | −11.8293 | −0.660247 | ||||||||
\(322\) | −15.8557 | −0.883604 | ||||||||
\(323\) | − | 17.3398i | − | 0.964810i | ||||||
\(324\) | −0.169605 | −0.00942252 | ||||||||
\(325\) | 13.3403 | + | 5.16326i | 0.739985 | + | 0.286406i | ||||
\(326\) | 11.0959 | 0.614548 | ||||||||
\(327\) | 17.1107i | 0.946224i | ||||||||
\(328\) | 34.6969 | 1.91582 | ||||||||
\(329\) | −28.0516 | −1.54654 | ||||||||
\(330\) | − | 6.42063i | − | 0.353444i | ||||||
\(331\) | 8.95949i | 0.492458i | 0.969212 | + | 0.246229i | \(0.0791915\pi\) | ||||
−0.969212 | + | 0.246229i | \(0.920808\pi\) | |||||||
\(332\) | − | 0.227408i | − | 0.0124807i | ||||||
\(333\) | 2.60372i | 0.142683i | ||||||||
\(334\) | 9.20808 | 0.503844 | ||||||||
\(335\) | 4.33377 | 0.236779 | ||||||||
\(336\) | 17.5608i | 0.958021i | ||||||||
\(337\) | −19.7375 | −1.07517 | −0.537586 | − | 0.843209i | \(-0.680664\pi\) | ||||
−0.537586 | + | 0.843209i | \(0.680664\pi\) | |||||||
\(338\) | 12.2972 | − | 13.5063i | 0.668878 | − | 0.734644i | ||||
\(339\) | 21.8772 | 1.18820 | ||||||||
\(340\) | 0.144959i | 0.00786149i | ||||||||
\(341\) | 2.94134 | 0.159283 | ||||||||
\(342\) | −2.91991 | −0.157891 | ||||||||
\(343\) | − | 16.1027i | − | 0.869461i | ||||||
\(344\) | − | 10.0277i | − | 0.540656i | ||||||
\(345\) | − | 6.02555i | − | 0.324405i | ||||||
\(346\) | 30.3021i | 1.62905i | ||||||||
\(347\) | 13.0978 | 0.703127 | 0.351563 | − | 0.936164i | \(-0.385650\pi\) | ||||
0.351563 | + | 0.936164i | \(0.385650\pi\) | |||||||
\(348\) | 0.220634 | 0.0118272 | ||||||||
\(349\) | − | 7.30002i | − | 0.390761i | −0.980728 | − | 0.195381i | \(-0.937406\pi\) | ||
0.980728 | − | 0.195381i | \(-0.0625942\pi\) | |||||||
\(350\) | −16.2192 | −0.866953 | ||||||||
\(351\) | −18.8285 | − | 7.28745i | −1.00499 | − | 0.388975i | ||||
\(352\) | 0.429295 | 0.0228815 | ||||||||
\(353\) | − | 34.9174i | − | 1.85846i | −0.369497 | − | 0.929232i | \(-0.620470\pi\) | ||
0.369497 | − | 0.929232i | \(-0.379530\pi\) | |||||||
\(354\) | 26.8310 | 1.42605 | ||||||||
\(355\) | 9.60039 | 0.509536 | ||||||||
\(356\) | − | 0.169885i | − | 0.00900391i | ||||||
\(357\) | 24.5930i | 1.30160i | ||||||||
\(358\) | 7.07709i | 0.374036i | ||||||||
\(359\) | 11.6905i | 0.617002i | 0.951224 | + | 0.308501i | \(0.0998273\pi\) | ||||
−0.951224 | + | 0.308501i | \(0.900173\pi\) | |||||||
\(360\) | 1.91648 | 0.101008 | ||||||||
\(361\) | 9.16307 | 0.482267 | ||||||||
\(362\) | − | 13.0997i | − | 0.688503i | ||||||
\(363\) | 3.59054 | 0.188454 | ||||||||
\(364\) | 0.0977039 | − | 0.252436i | 0.00512108 | − | 0.0132313i | ||||
\(365\) | 0.797211 | 0.0417279 | ||||||||
\(366\) | − | 11.9774i | − | 0.626068i | ||||||
\(367\) | 19.0286 | 0.993286 | 0.496643 | − | 0.867955i | \(-0.334566\pi\) | ||||
0.496643 | + | 0.867955i | \(0.334566\pi\) | |||||||
\(368\) | −15.3111 | −0.798149 | ||||||||
\(369\) | − | 8.07686i | − | 0.420465i | ||||||
\(370\) | 5.61067i | 0.291685i | ||||||||
\(371\) | 32.9912i | 1.71282i | ||||||||
\(372\) | − | 0.0394484i | − | 0.00204531i | ||||||
\(373\) | 8.09393 | 0.419088 | 0.209544 | − | 0.977799i | \(-0.432802\pi\) | ||||
0.209544 | + | 0.977799i | \(0.432802\pi\) | |||||||
\(374\) | −22.8483 | −1.18146 | ||||||||
\(375\) | − | 13.9316i | − | 0.719427i | ||||||
\(376\) | −27.4423 | −1.41523 | ||||||||
\(377\) | 18.8062 | + | 7.27884i | 0.968571 | + | 0.374879i | ||||
\(378\) | 22.8918 | 1.17743 | ||||||||
\(379\) | 8.82330i | 0.453222i | 0.973985 | + | 0.226611i | \(0.0727647\pi\) | ||||
−0.973985 | + | 0.226611i | \(0.927235\pi\) | |||||||
\(380\) | 0.0822358 | 0.00421861 | ||||||||
\(381\) | −27.4871 | −1.40821 | ||||||||
\(382\) | − | 14.8335i | − | 0.758948i | ||||||
\(383\) | 36.6362i | 1.87202i | 0.351973 | + | 0.936010i | \(0.385511\pi\) | ||||
−0.351973 | + | 0.936010i | \(0.614489\pi\) | |||||||
\(384\) | 16.9548i | 0.865221i | ||||||||
\(385\) | − | 8.69650i | − | 0.443215i | ||||||
\(386\) | −22.6589 | −1.15331 | ||||||||
\(387\) | −2.33427 | −0.118658 | ||||||||
\(388\) | 0.166254i | 0.00844026i | ||||||||
\(389\) | −7.70656 | −0.390738 | −0.195369 | − | 0.980730i | \(-0.562590\pi\) | ||||
−0.195369 | + | 0.980730i | \(0.562590\pi\) | |||||||
\(390\) | −7.33993 | − | 2.84087i | −0.371672 | − | 0.143853i | ||||
\(391\) | −21.4424 | −1.08439 | ||||||||
\(392\) | 4.17176i | 0.210706i | ||||||||
\(393\) | −13.1513 | −0.663394 | ||||||||
\(394\) | 5.93509 | 0.299006 | ||||||||
\(395\) | − | 6.21714i | − | 0.312818i | ||||||
\(396\) | − | 0.0502865i | − | 0.00252699i | ||||||
\(397\) | − | 8.55515i | − | 0.429371i | −0.976683 | − | 0.214685i | \(-0.931127\pi\) | ||
0.976683 | − | 0.214685i | \(-0.0688726\pi\) | |||||||
\(398\) | − | 2.83804i | − | 0.142258i | ||||||
\(399\) | 13.9517 | 0.698459 | ||||||||
\(400\) | −15.6622 | −0.783108 | ||||||||
\(401\) | − | 2.11758i | − | 0.105747i | −0.998601 | − | 0.0528734i | \(-0.983162\pi\) | ||
0.998601 | − | 0.0528734i | \(-0.0168380\pi\) | |||||||
\(402\) | 9.16135 | 0.456926 | ||||||||
\(403\) | 1.30143 | − | 3.36248i | 0.0648287 | − | 0.167497i | ||||
\(404\) | −0.467863 | −0.0232771 | ||||||||
\(405\) | 6.67954i | 0.331909i | ||||||||
\(406\) | −22.8648 | −1.13476 | ||||||||
\(407\) | 11.5584 | 0.572926 | ||||||||
\(408\) | 24.0588i | 1.19109i | ||||||||
\(409\) | 4.47719i | 0.221383i | 0.993855 | + | 0.110691i | \(0.0353065\pi\) | ||||
−0.993855 | + | 0.110691i | \(0.964694\pi\) | |||||||
\(410\) | − | 17.4046i | − | 0.859550i | ||||||
\(411\) | − | 20.6194i | − | 1.01708i | ||||||
\(412\) | 0.447046 | 0.0220244 | ||||||||
\(413\) | 36.3416 | 1.78826 | ||||||||
\(414\) | 3.61077i | 0.177460i | ||||||||
\(415\) | −8.95599 | −0.439632 | ||||||||
\(416\) | 0.189946 | − | 0.490761i | 0.00931286 | − | 0.0240615i | ||||
\(417\) | −13.6615 | −0.669004 | ||||||||
\(418\) | 12.9620i | 0.633990i | ||||||||
\(419\) | 34.4369 | 1.68235 | 0.841176 | − | 0.540761i | \(-0.181864\pi\) | ||||
0.841176 | + | 0.540761i | \(0.181864\pi\) | |||||||
\(420\) | −0.116635 | −0.00569120 | ||||||||
\(421\) | − | 33.7742i | − | 1.64605i | −0.568002 | − | 0.823027i | \(-0.692283\pi\) | ||
0.568002 | − | 0.823027i | \(-0.307717\pi\) | |||||||
\(422\) | 34.0589i | 1.65796i | ||||||||
\(423\) | 6.38811i | 0.310600i | ||||||||
\(424\) | 32.2745i | 1.56739i | ||||||||
\(425\) | −21.9340 | −1.06396 | ||||||||
\(426\) | 20.2947 | 0.983282 | ||||||||
\(427\) | − | 16.2229i | − | 0.785082i | ||||||
\(428\) | −0.199643 | −0.00965010 | ||||||||
\(429\) | −5.85239 | + | 15.1207i | −0.282556 | + | 0.730036i | ||||
\(430\) | −5.03004 | −0.242570 | ||||||||
\(431\) | − | 17.7153i | − | 0.853318i | −0.904413 | − | 0.426659i | \(-0.859690\pi\) | ||
0.904413 | − | 0.426659i | \(-0.140310\pi\) | |||||||
\(432\) | 22.1056 | 1.06356 | ||||||||
\(433\) | −4.59958 | −0.221042 | −0.110521 | − | 0.993874i | \(-0.535252\pi\) | ||||
−0.110521 | + | 0.993874i | \(0.535252\pi\) | |||||||
\(434\) | 4.08813i | 0.196237i | ||||||||
\(435\) | − | 8.68918i | − | 0.416614i | ||||||
\(436\) | 0.288777i | 0.0138299i | ||||||||
\(437\) | 12.1644i | 0.581901i | ||||||||
\(438\) | 1.68526 | 0.0805249 | ||||||||
\(439\) | −25.5577 | −1.21980 | −0.609900 | − | 0.792478i | \(-0.708791\pi\) | ||||
−0.609900 | + | 0.792478i | \(0.708791\pi\) | |||||||
\(440\) | − | 8.50760i | − | 0.405584i | ||||||
\(441\) | 0.971115 | 0.0462436 | ||||||||
\(442\) | −10.1095 | + | 26.1197i | −0.480859 | + | 1.24239i | ||||
\(443\) | 24.7736 | 1.17703 | 0.588515 | − | 0.808486i | \(-0.299713\pi\) | ||||
0.588515 | + | 0.808486i | \(0.299713\pi\) | |||||||
\(444\) | − | 0.155017i | − | 0.00735679i | ||||||
\(445\) | −6.69057 | −0.317163 | ||||||||
\(446\) | 7.88956 | 0.373582 | ||||||||
\(447\) | − | 3.94455i | − | 0.186571i | ||||||
\(448\) | 23.5691i | 1.11354i | ||||||||
\(449\) | − | 38.0058i | − | 1.79360i | −0.442433 | − | 0.896801i | \(-0.645885\pi\) | ||
0.442433 | − | 0.896801i | \(-0.354115\pi\) | |||||||
\(450\) | 3.69355i | 0.174116i | ||||||||
\(451\) | −35.8545 | −1.68832 | ||||||||
\(452\) | 0.369220 | 0.0173667 | ||||||||
\(453\) | 2.68469i | 0.126138i | ||||||||
\(454\) | −12.2114 | −0.573111 | ||||||||
\(455\) | −9.94166 | − | 3.84786i | −0.466072 | − | 0.180390i | ||||
\(456\) | 13.6487 | 0.639157 | ||||||||
\(457\) | − | 0.690146i | − | 0.0322837i | −0.999870 | − | 0.0161418i | \(-0.994862\pi\) | ||
0.999870 | − | 0.0161418i | \(-0.00513833\pi\) | |||||||
\(458\) | −38.7015 | −1.80840 | ||||||||
\(459\) | 30.9577 | 1.44498 | ||||||||
\(460\) | − | 0.101693i | − | 0.00474146i | ||||||
\(461\) | 3.50495i | 0.163242i | 0.996663 | + | 0.0816210i | \(0.0260097\pi\) | ||||
−0.996663 | + | 0.0816210i | \(0.973990\pi\) | |||||||
\(462\) | − | 18.3839i | − | 0.855298i | ||||||
\(463\) | − | 11.0533i | − | 0.513691i | −0.966453 | − | 0.256845i | \(-0.917317\pi\) | ||
0.966453 | − | 0.256845i | \(-0.0826831\pi\) | |||||||
\(464\) | −22.0795 | −1.02502 | ||||||||
\(465\) | −1.55359 | −0.0720460 | ||||||||
\(466\) | 19.3801i | 0.897768i | ||||||||
\(467\) | −13.4125 | −0.620655 | −0.310328 | − | 0.950630i | \(-0.600439\pi\) | ||||
−0.310328 | + | 0.950630i | \(0.600439\pi\) | |||||||
\(468\) | −0.0574865 | − | 0.0222498i | −0.00265732 | − | 0.00102850i | ||||
\(469\) | 12.4087 | 0.572981 | ||||||||
\(470\) | 13.7655i | 0.634956i | ||||||||
\(471\) | −29.0984 | −1.34078 | ||||||||
\(472\) | 35.5523 | 1.63643 | ||||||||
\(473\) | 10.3622i | 0.476456i | ||||||||
\(474\) | − | 13.1427i | − | 0.603664i | ||||||
\(475\) | 12.4433i | 0.570936i | ||||||||
\(476\) | 0.415055i | 0.0190240i | ||||||||
\(477\) | 7.51297 | 0.343995 | ||||||||
\(478\) | −1.93790 | −0.0886373 | ||||||||
\(479\) | 9.11526i | 0.416487i | 0.978077 | + | 0.208243i | \(0.0667746\pi\) | ||||
−0.978077 | + | 0.208243i | \(0.933225\pi\) | |||||||
\(480\) | −0.226750 | −0.0103497 | ||||||||
\(481\) | 5.11411 | − | 13.2133i | 0.233183 | − | 0.602473i | ||||
\(482\) | −39.1487 | −1.78317 | ||||||||
\(483\) | − | 17.2527i | − | 0.785026i | ||||||
\(484\) | 0.0605974 | 0.00275443 | ||||||||
\(485\) | 6.54755 | 0.297309 | ||||||||
\(486\) | − | 9.48309i | − | 0.430162i | ||||||
\(487\) | 7.68894i | 0.348419i | 0.984709 | + | 0.174210i | \(0.0557370\pi\) | ||||
−0.984709 | + | 0.174210i | \(0.944263\pi\) | |||||||
\(488\) | − | 15.8705i | − | 0.718425i | ||||||
\(489\) | 12.0736i | 0.545987i | ||||||||
\(490\) | 2.09262 | 0.0945351 | ||||||||
\(491\) | 2.30951 | 0.104227 | 0.0521134 | − | 0.998641i | \(-0.483404\pi\) | ||||
0.0521134 | + | 0.998641i | \(0.483404\pi\) | |||||||
\(492\) | 0.480871i | 0.0216793i | ||||||||
\(493\) | −30.9211 | −1.39262 | ||||||||
\(494\) | 14.8179 | + | 5.73515i | 0.666687 | + | 0.258037i | ||||
\(495\) | −1.98043 | −0.0890135 | ||||||||
\(496\) | 3.94773i | 0.177258i | ||||||||
\(497\) | 27.4884 | 1.23302 | ||||||||
\(498\) | −18.9325 | −0.848384 | ||||||||
\(499\) | − | 16.9769i | − | 0.759992i | −0.924988 | − | 0.379996i | \(-0.875925\pi\) | ||
0.924988 | − | 0.379996i | \(-0.124075\pi\) | |||||||
\(500\) | − | 0.235124i | − | 0.0105151i | ||||||
\(501\) | 10.0194i | 0.447633i | ||||||||
\(502\) | − | 7.09403i | − | 0.316622i | ||||||
\(503\) | 9.24502 | 0.412215 | 0.206108 | − | 0.978529i | \(-0.433920\pi\) | ||||
0.206108 | + | 0.978529i | \(0.433920\pi\) | |||||||
\(504\) | 5.48740 | 0.244428 | ||||||||
\(505\) | 18.4258i | 0.819936i | ||||||||
\(506\) | 16.0288 | 0.712567 | ||||||||
\(507\) | 14.6963 | + | 13.3807i | 0.652684 | + | 0.594256i | ||||
\(508\) | −0.463899 | −0.0205822 | ||||||||
\(509\) | 1.38544i | 0.0614086i | 0.999529 | + | 0.0307043i | \(0.00977501\pi\) | ||||
−0.999529 | + | 0.0307043i | \(0.990225\pi\) | |||||||
\(510\) | 12.0683 | 0.534392 | ||||||||
\(511\) | 2.28262 | 0.100977 | ||||||||
\(512\) | 23.0496i | 1.01866i | ||||||||
\(513\) | − | 17.5625i | − | 0.775402i | ||||||
\(514\) | 30.5096i | 1.34572i | ||||||||
\(515\) | − | 17.6059i | − | 0.775810i | ||||||
\(516\) | 0.138975 | 0.00611804 | ||||||||
\(517\) | 28.3579 | 1.24718 | ||||||||
\(518\) | 16.0648i | 0.705847i | ||||||||
\(519\) | −32.9720 | −1.44731 | ||||||||
\(520\) | −9.72571 | − | 3.76427i | −0.426501 | − | 0.165074i | ||||
\(521\) | 5.80992 | 0.254537 | 0.127268 | − | 0.991868i | \(-0.459379\pi\) | ||||
0.127268 | + | 0.991868i | \(0.459379\pi\) | |||||||
\(522\) | 5.20693i | 0.227901i | ||||||||
\(523\) | −2.01451 | −0.0880885 | −0.0440443 | − | 0.999030i | \(-0.514024\pi\) | ||||
−0.0440443 | + | 0.999030i | \(0.514024\pi\) | |||||||
\(524\) | −0.221954 | −0.00969610 | ||||||||
\(525\) | − | 17.6483i | − | 0.770233i | ||||||
\(526\) | − | 29.6007i | − | 1.29065i | ||||||
\(527\) | 5.52858i | 0.240829i | ||||||||
\(528\) | − | 17.7525i | − | 0.772580i | ||||||
\(529\) | −7.95748 | −0.345977 | ||||||||
\(530\) | 16.1894 | 0.703225 | ||||||||
\(531\) | − | 8.27597i | − | 0.359146i | ||||||
\(532\) | 0.235463 | 0.0102086 | ||||||||
\(533\) | −15.8642 | + | 40.9882i | −0.687155 | + | 1.77540i | ||||
\(534\) | −14.1435 | −0.612049 | ||||||||
\(535\) | 7.86250i | 0.339926i | ||||||||
\(536\) | 12.1392 | 0.524332 | ||||||||
\(537\) | −7.70065 | −0.332307 | ||||||||
\(538\) | − | 15.6404i | − | 0.674304i | ||||||
\(539\) | − | 4.31094i | − | 0.185685i | ||||||
\(540\) | 0.146821i | 0.00631815i | ||||||||
\(541\) | − | 21.4836i | − | 0.923652i | −0.886971 | − | 0.461826i | \(-0.847194\pi\) | ||
0.886971 | − | 0.461826i | \(-0.152806\pi\) | |||||||
\(542\) | 24.1818 | 1.03870 | ||||||||
\(543\) | 14.2539 | 0.611692 | ||||||||
\(544\) | 0.806906i | 0.0345958i | ||||||||
\(545\) | 11.3729 | 0.487160 | ||||||||
\(546\) | −21.0161 | − | 8.13416i | −0.899407 | − | 0.348110i | ||||
\(547\) | 7.77420 | 0.332401 | 0.166200 | − | 0.986092i | \(-0.446850\pi\) | ||||
0.166200 | + | 0.986092i | \(0.446850\pi\) | |||||||
\(548\) | − | 0.347993i | − | 0.0148655i | ||||||
\(549\) | −3.69439 | −0.157673 | ||||||||
\(550\) | 16.3963 | 0.699140 | ||||||||
\(551\) | 17.5417i | 0.747302i | ||||||||
\(552\) | − | 16.8780i | − | 0.718374i | ||||||
\(553\) | − | 17.8013i | − | 0.756987i | ||||||
\(554\) | − | 2.31202i | − | 0.0982282i | ||||||
\(555\) | −6.10502 | −0.259144 | ||||||||
\(556\) | −0.230564 | −0.00977809 | ||||||||
\(557\) | 8.44764i | 0.357938i | 0.983855 | + | 0.178969i | \(0.0572762\pi\) | ||||
−0.983855 | + | 0.178969i | \(0.942724\pi\) | |||||||
\(558\) | 0.930978 | 0.0394114 | ||||||||
\(559\) | 11.8459 | + | 4.58487i | 0.501028 | + | 0.193920i | ||||
\(560\) | 11.6720 | 0.493233 | ||||||||
\(561\) | − | 24.8614i | − | 1.04965i | ||||||
\(562\) | −30.1656 | −1.27246 | ||||||||
\(563\) | −35.3836 | −1.49124 | −0.745620 | − | 0.666371i | \(-0.767847\pi\) | ||||
−0.745620 | + | 0.666371i | \(0.767847\pi\) | |||||||
\(564\) | − | 0.380328i | − | 0.0160147i | ||||||
\(565\) | − | 14.5409i | − | 0.611742i | ||||||
\(566\) | 3.55336i | 0.149359i | ||||||||
\(567\) | 19.1253i | 0.803185i | ||||||||
\(568\) | 26.8913 | 1.12834 | ||||||||
\(569\) | −20.3682 | −0.853881 | −0.426940 | − | 0.904280i | \(-0.640409\pi\) | ||||
−0.426940 | + | 0.904280i | \(0.640409\pi\) | |||||||
\(570\) | − | 6.84639i | − | 0.286764i | ||||||
\(571\) | 18.7808 | 0.785951 | 0.392976 | − | 0.919549i | \(-0.371446\pi\) | ||||
0.392976 | + | 0.919549i | \(0.371446\pi\) | |||||||
\(572\) | −0.0987706 | + | 0.255192i | −0.00412980 | + | 0.0106701i | ||||
\(573\) | 16.1405 | 0.674278 | ||||||||
\(574\) | − | 49.8338i | − | 2.08002i | ||||||
\(575\) | 15.3874 | 0.641698 | ||||||||
\(576\) | 5.36732 | 0.223638 | ||||||||
\(577\) | 33.7171i | 1.40366i | 0.712345 | + | 0.701830i | \(0.247633\pi\) | ||||
−0.712345 | + | 0.701830i | \(0.752367\pi\) | |||||||
\(578\) | − | 19.0599i | − | 0.792786i | ||||||
\(579\) | − | 24.6554i | − | 1.02464i | ||||||
\(580\) | − | 0.146647i | − | 0.00608918i | ||||||
\(581\) | −25.6433 | −1.06386 | ||||||||
\(582\) | 13.8412 | 0.573735 | ||||||||
\(583\) | − | 33.3513i | − | 1.38127i | ||||||
\(584\) | 2.23304 | 0.0924039 | ||||||||
\(585\) | −0.876260 | + | 2.26398i | −0.0362289 | + | 0.0936041i | ||||
\(586\) | 11.9360 | 0.493072 | ||||||||
\(587\) | 33.1106i | 1.36662i | 0.730129 | + | 0.683310i | \(0.239460\pi\) | ||||
−0.730129 | + | 0.683310i | \(0.760540\pi\) | |||||||
\(588\) | −0.0578171 | −0.00238434 | ||||||||
\(589\) | 3.13639 | 0.129233 | ||||||||
\(590\) | − | 17.8336i | − | 0.734198i | ||||||
\(591\) | 6.45803i | 0.265648i | ||||||||
\(592\) | 15.5131i | 0.637583i | ||||||||
\(593\) | 30.7925i | 1.26449i | 0.774767 | + | 0.632247i | \(0.217867\pi\) | ||||
−0.774767 | + | 0.632247i | \(0.782133\pi\) | |||||||
\(594\) | −23.1418 | −0.949518 | ||||||||
\(595\) | 16.3460 | 0.670122 | ||||||||
\(596\) | − | 0.0665721i | − | 0.00272690i | ||||||
\(597\) | 3.08809 | 0.126387 | ||||||||
\(598\) | 7.09211 | − | 18.3238i | 0.290018 | − | 0.749316i | ||||
\(599\) | 3.80719 | 0.155558 | 0.0777788 | − | 0.996971i | \(-0.475217\pi\) | ||||
0.0777788 | + | 0.996971i | \(0.475217\pi\) | |||||||
\(600\) | − | 17.2649i | − | 0.704837i | ||||||
\(601\) | 7.77021 | 0.316954 | 0.158477 | − | 0.987363i | \(-0.449342\pi\) | ||||
0.158477 | + | 0.987363i | \(0.449342\pi\) | |||||||
\(602\) | −14.4023 | −0.586995 | ||||||||
\(603\) | − | 2.82579i | − | 0.115075i | ||||||
\(604\) | 0.0453094i | 0.00184361i | ||||||||
\(605\) | − | 2.38650i | − | 0.0970249i | ||||||
\(606\) | 38.9511i | 1.58228i | ||||||||
\(607\) | −15.3747 | −0.624042 | −0.312021 | − | 0.950075i | \(-0.601006\pi\) | ||||
−0.312021 | + | 0.950075i | \(0.601006\pi\) | |||||||
\(608\) | 0.457762 | 0.0185647 | ||||||||
\(609\) | − | 24.8794i | − | 1.00816i | ||||||
\(610\) | −7.96092 | −0.322328 | ||||||||
\(611\) | 12.5472 | − | 32.4181i | 0.507607 | − | 1.31150i | ||||
\(612\) | 0.0945191 | 0.00382071 | ||||||||
\(613\) | − | 37.2449i | − | 1.50431i | −0.658987 | − | 0.752154i | \(-0.729015\pi\) | ||
0.658987 | − | 0.752154i | \(-0.270985\pi\) | |||||||
\(614\) | 34.5702 | 1.39514 | ||||||||
\(615\) | 18.9380 | 0.763656 | ||||||||
\(616\) | − | 24.3595i | − | 0.981471i | ||||||
\(617\) | − | 12.2249i | − | 0.492154i | −0.969250 | − | 0.246077i | \(-0.920858\pi\) | ||
0.969250 | − | 0.246077i | \(-0.0791417\pi\) | |||||||
\(618\) | − | 37.2180i | − | 1.49713i | ||||||
\(619\) | − | 35.0566i | − | 1.40904i | −0.709683 | − | 0.704521i | \(-0.751162\pi\) | ||
0.709683 | − | 0.704521i | \(-0.248838\pi\) | |||||||
\(620\) | −0.0262199 | −0.00105302 | ||||||||
\(621\) | −21.7178 | −0.871506 | ||||||||
\(622\) | 11.3435i | 0.454832i | ||||||||
\(623\) | −19.1568 | −0.767503 | ||||||||
\(624\) | −20.2943 | − | 7.85479i | −0.812424 | − | 0.314443i | ||||
\(625\) | 10.5771 | 0.423083 | ||||||||
\(626\) | 20.5557i | 0.821571i | ||||||||
\(627\) | −14.1040 | −0.563260 | ||||||||
\(628\) | −0.491093 | −0.0195967 | ||||||||
\(629\) | 21.7252i | 0.866240i | ||||||||
\(630\) | − | 2.75257i | − | 0.109665i | ||||||
\(631\) | − | 7.46467i | − | 0.297164i | −0.988900 | − | 0.148582i | \(-0.952529\pi\) | ||
0.988900 | − | 0.148582i | \(-0.0474708\pi\) | |||||||
\(632\) | − | 17.4146i | − | 0.692716i | ||||||
\(633\) | −37.0597 | −1.47299 | ||||||||
\(634\) | −8.89092 | −0.353103 | ||||||||
\(635\) | 18.2697i | 0.725009i | ||||||||
\(636\) | −0.447298 | −0.0177365 | ||||||||
\(637\) | −4.92818 | − | 1.90742i | −0.195262 | − | 0.0755748i | ||||
\(638\) | 23.1144 | 0.915108 | ||||||||
\(639\) | − | 6.25985i | − | 0.247636i | ||||||
\(640\) | 11.2692 | 0.445455 | ||||||||
\(641\) | 35.1991 | 1.39028 | 0.695141 | − | 0.718873i | \(-0.255342\pi\) | ||||
0.695141 | + | 0.718873i | \(0.255342\pi\) | |||||||
\(642\) | 16.6209i | 0.655975i | ||||||||
\(643\) | 20.9264i | 0.825257i | 0.910899 | + | 0.412628i | \(0.135389\pi\) | ||||
−0.910899 | + | 0.412628i | \(0.864611\pi\) | |||||||
\(644\) | − | 0.291174i | − | 0.0114739i | ||||||
\(645\) | − | 5.47323i | − | 0.215508i | ||||||
\(646\) | −24.3634 | −0.958567 | ||||||||
\(647\) | 48.3523 | 1.90092 | 0.950462 | − | 0.310841i | \(-0.100611\pi\) | ||||
0.950462 | + | 0.310841i | \(0.100611\pi\) | |||||||
\(648\) | 18.7098i | 0.734992i | ||||||||
\(649\) | −36.7384 | −1.44211 | ||||||||
\(650\) | 7.25470 | − | 18.7439i | 0.284553 | − | 0.735196i | ||||
\(651\) | −4.44833 | −0.174344 | ||||||||
\(652\) | 0.203766i | 0.00798008i | ||||||||
\(653\) | −13.8535 | −0.542127 | −0.271064 | − | 0.962561i | \(-0.587375\pi\) | ||||
−0.271064 | + | 0.962561i | \(0.587375\pi\) | |||||||
\(654\) | 24.0416 | 0.940101 | ||||||||
\(655\) | 8.74117i | 0.341546i | ||||||||
\(656\) | − | 48.1223i | − | 1.87886i | ||||||
\(657\) | − | 0.519814i | − | 0.0202799i | ||||||
\(658\) | 39.4143i | 1.53653i | ||||||||
\(659\) | 24.2242 | 0.943639 | 0.471820 | − | 0.881695i | \(-0.343597\pi\) | ||||
0.471820 | + | 0.881695i | \(0.343597\pi\) | |||||||
\(660\) | 0.117908 | 0.00458957 | ||||||||
\(661\) | 22.2852i | 0.866795i | 0.901203 | + | 0.433397i | \(0.142685\pi\) | ||||
−0.901203 | + | 0.433397i | \(0.857315\pi\) | |||||||
\(662\) | 12.5886 | 0.489271 | ||||||||
\(663\) | −28.4211 | − | 11.0002i | −1.10378 | − | 0.427213i | ||||
\(664\) | −25.0863 | −0.973538 | ||||||||
\(665\) | − | 9.27318i | − | 0.359599i | ||||||
\(666\) | 3.65839 | 0.141760 | ||||||||
\(667\) | 21.6921 | 0.839923 | ||||||||
\(668\) | 0.169097i | 0.00654256i | ||||||||
\(669\) | 8.58470i | 0.331904i | ||||||||
\(670\) | − | 6.08921i | − | 0.235247i | ||||||
\(671\) | 16.4000i | 0.633116i | ||||||||
\(672\) | −0.649243 | −0.0250451 | ||||||||
\(673\) | 20.4711 | 0.789103 | 0.394552 | − | 0.918874i | \(-0.370900\pi\) | ||||
0.394552 | + | 0.918874i | \(0.370900\pi\) | |||||||
\(674\) | 27.7325i | 1.06821i | ||||||||
\(675\) | −22.2157 | −0.855083 | ||||||||
\(676\) | 0.248029 | + | 0.225825i | 0.00953956 | + | 0.00868558i | ||||
\(677\) | −2.15024 | −0.0826404 | −0.0413202 | − | 0.999146i | \(-0.513156\pi\) | ||||
−0.0413202 | + | 0.999146i | \(0.513156\pi\) | |||||||
\(678\) | − | 30.7388i | − | 1.18052i | ||||||
\(679\) | 18.7473 | 0.719457 | ||||||||
\(680\) | 15.9910 | 0.613226 | ||||||||
\(681\) | − | 13.2874i | − | 0.509173i | ||||||
\(682\) | − | 4.13277i | − | 0.158252i | ||||||
\(683\) | 38.4682i | 1.47194i | 0.677013 | + | 0.735971i | \(0.263274\pi\) | ||||
−0.677013 | + | 0.735971i | \(0.736726\pi\) | |||||||
\(684\) | − | 0.0536211i | − | 0.00205026i | ||||||
\(685\) | −13.7050 | −0.523640 | ||||||||
\(686\) | −22.6252 | −0.863835 | ||||||||
\(687\) | − | 42.1115i | − | 1.60665i | ||||||
\(688\) | −13.9077 | −0.530226 | ||||||||
\(689\) | −38.1266 | − | 14.7566i | −1.45251 | − | 0.562183i | ||||
\(690\) | −8.46627 | −0.322305 | ||||||||
\(691\) | 17.9832i | 0.684112i | 0.939679 | + | 0.342056i | \(0.111123\pi\) | ||||
−0.939679 | + | 0.342056i | \(0.888877\pi\) | |||||||
\(692\) | −0.556468 | −0.0211537 | ||||||||
\(693\) | −5.67047 | −0.215404 | ||||||||
\(694\) | − | 18.4032i | − | 0.698576i | ||||||
\(695\) | 9.08026i | 0.344434i | ||||||||
\(696\) | − | 24.3390i | − | 0.922566i | ||||||
\(697\) | − | 67.3926i | − | 2.55267i | ||||||
\(698\) | −10.2570 | −0.388232 | ||||||||
\(699\) | −21.0877 | −0.797610 | ||||||||
\(700\) | − | 0.297849i | − | 0.0112576i | ||||||
\(701\) | 23.3608 | 0.882327 | 0.441164 | − | 0.897427i | \(-0.354566\pi\) | ||||
0.441164 | + | 0.897427i | \(0.354566\pi\) | |||||||
\(702\) | −10.2393 | + | 26.4552i | −0.386458 | + | 0.998487i | ||||
\(703\) | 12.3248 | 0.464839 | ||||||||
\(704\) | − | 23.8264i | − | 0.897992i | ||||||
\(705\) | −14.9784 | −0.564118 | ||||||||
\(706\) | −49.0610 | −1.84644 | ||||||||
\(707\) | 52.7578i | 1.98416i | ||||||||
\(708\) | 0.492725i | 0.0185177i | ||||||||
\(709\) | 33.1442i | 1.24476i | 0.782717 | + | 0.622378i | \(0.213833\pi\) | ||||
−0.782717 | + | 0.622378i | \(0.786167\pi\) | |||||||
\(710\) | − | 13.4891i | − | 0.506239i | ||||||
\(711\) | −4.05383 | −0.152030 | ||||||||
\(712\) | −18.7407 | −0.702339 | ||||||||
\(713\) | − | 3.87847i | − | 0.145250i | ||||||
\(714\) | 34.5546 | 1.29317 | ||||||||
\(715\) | 10.0502 | + | 3.88986i | 0.375856 | + | 0.145473i | ||||
\(716\) | −0.129964 | −0.00485697 | ||||||||
\(717\) | − | 2.10864i | − | 0.0787486i | ||||||
\(718\) | 16.4259 | 0.613009 | ||||||||
\(719\) | −16.8313 | −0.627700 | −0.313850 | − | 0.949473i | \(-0.601619\pi\) | ||||
−0.313850 | + | 0.949473i | \(0.601619\pi\) | |||||||
\(720\) | − | 2.65803i | − | 0.0990590i | ||||||
\(721\) | − | 50.4104i | − | 1.87738i | ||||||
\(722\) | − | 12.8747i | − | 0.479146i | ||||||
\(723\) | − | 42.5980i | − | 1.58424i | ||||||
\(724\) | 0.240562 | 0.00894042 | ||||||||
\(725\) | 22.1895 | 0.824096 | ||||||||
\(726\) | − | 5.04493i | − | 0.187235i | ||||||
\(727\) | 14.8322 | 0.550095 | 0.275047 | − | 0.961431i | \(-0.411306\pi\) | ||||
0.275047 | + | 0.961431i | \(0.411306\pi\) | |||||||
\(728\) | −27.8472 | − | 10.7781i | −1.03209 | − | 0.399463i | ||||
\(729\) | 30.0383 | 1.11253 | ||||||||
\(730\) | − | 1.12013i | − | 0.0414579i | ||||||
\(731\) | −19.4769 | −0.720381 | ||||||||
\(732\) | 0.219952 | 0.00812967 | ||||||||
\(733\) | 31.6000i | 1.16717i | 0.812050 | + | 0.583587i | \(0.198351\pi\) | ||||
−0.812050 | + | 0.583587i | \(0.801649\pi\) | |||||||
\(734\) | − | 26.7364i | − | 0.986858i | ||||||
\(735\) | 2.27700i | 0.0839885i | ||||||||
\(736\) | − | 0.566070i | − | 0.0208656i | ||||||
\(737\) | −12.5442 | −0.462070 | ||||||||
\(738\) | −11.3485 | −0.417744 | ||||||||
\(739\) | 18.2260i | 0.670453i | 0.942138 | + | 0.335226i | \(0.108813\pi\) | ||||
−0.942138 | + | 0.335226i | \(0.891187\pi\) | |||||||
\(740\) | −0.103034 | −0.00378761 | ||||||||
\(741\) | −6.24047 | + | 16.1234i | −0.229249 | + | 0.592309i | ||||
\(742\) | 46.3546 | 1.70173 | ||||||||
\(743\) | 36.3278i | 1.33274i | 0.745622 | + | 0.666369i | \(0.232152\pi\) | ||||
−0.745622 | + | 0.666369i | \(0.767848\pi\) | |||||||
\(744\) | −4.35171 | −0.159541 | ||||||||
\(745\) | −2.62180 | −0.0960552 | ||||||||
\(746\) | − | 11.3725i | − | 0.416375i | ||||||
\(747\) | 5.83967i | 0.213662i | ||||||||
\(748\) | − | 0.419586i | − | 0.0153416i | ||||||
\(749\) | 22.5124i | 0.822585i | ||||||||
\(750\) | −19.5748 | −0.714771 | ||||||||
\(751\) | 14.5974 | 0.532667 | 0.266333 | − | 0.963881i | \(-0.414188\pi\) | ||||
0.266333 | + | 0.963881i | \(0.414188\pi\) | |||||||
\(752\) | 38.0606i | 1.38793i | ||||||||
\(753\) | 7.71908 | 0.281299 | ||||||||
\(754\) | 10.2272 | − | 26.4239i | 0.372453 | − | 0.962303i | ||||
\(755\) | 1.78441 | 0.0649415 | ||||||||
\(756\) | 0.420385i | 0.0152893i | ||||||||
\(757\) | 21.1706 | 0.769457 | 0.384728 | − | 0.923030i | \(-0.374295\pi\) | ||||
0.384728 | + | 0.923030i | \(0.374295\pi\) | |||||||
\(758\) | 12.3973 | 0.450289 | ||||||||
\(759\) | 17.4411i | 0.633071i | ||||||||
\(760\) | − | 9.07175i | − | 0.329067i | ||||||
\(761\) | 11.2052i | 0.406188i | 0.979159 | + | 0.203094i | \(0.0650997\pi\) | ||||
−0.979159 | + | 0.203094i | \(0.934900\pi\) | |||||||
\(762\) | 38.6211i | 1.39909i | ||||||||
\(763\) | 32.5634 | 1.17888 | ||||||||
\(764\) | 0.272402 | 0.00985516 | ||||||||
\(765\) | − | 3.72243i | − | 0.134585i | ||||||
\(766\) | 51.4760 | 1.85991 | ||||||||
\(767\) | −16.2553 | + | 41.9986i | −0.586944 | + | 1.51648i | ||||
\(768\) | −0.946604 | −0.0341576 | ||||||||
\(769\) | 31.9705i | 1.15289i | 0.817137 | + | 0.576444i | \(0.195560\pi\) | ||||
−0.817137 | + | 0.576444i | \(0.804440\pi\) | |||||||
\(770\) | −12.2191 | −0.440346 | ||||||||
\(771\) | −33.1978 | −1.19559 | ||||||||
\(772\) | − | 0.416108i | − | 0.0149761i | ||||||
\(773\) | 11.6707i | 0.419767i | 0.977726 | + | 0.209884i | \(0.0673085\pi\) | ||||
−0.977726 | + | 0.209884i | \(0.932691\pi\) | |||||||
\(774\) | 3.27980i | 0.117890i | ||||||||
\(775\) | − | 3.96739i | − | 0.142513i | ||||||
\(776\) | 18.3401 | 0.658372 | ||||||||
\(777\) | −17.4803 | −0.627101 | ||||||||
\(778\) | 10.8282i | 0.388210i | ||||||||
\(779\) | −38.2321 | −1.36981 | ||||||||
\(780\) | 0.0521697 | − | 0.134790i | 0.00186798 | − | 0.00482627i | ||||
\(781\) | −27.7885 | −0.994352 | ||||||||
\(782\) | 30.1279i | 1.07737i | ||||||||
\(783\) | −31.3183 | −1.11922 | ||||||||
\(784\) | 5.78594 | 0.206641 | ||||||||
\(785\) | 19.3406i | 0.690296i | ||||||||
\(786\) | 18.4784i | 0.659101i | ||||||||
\(787\) | − | 9.35234i | − | 0.333375i | −0.986010 | − | 0.166687i | \(-0.946693\pi\) | ||
0.986010 | − | 0.166687i | \(-0.0533071\pi\) | |||||||
\(788\) | 0.108992i | 0.00388268i | ||||||||
\(789\) | 32.2088 | 1.14666 | ||||||||
\(790\) | −8.73546 | −0.310794 | ||||||||
\(791\) | − | 41.6345i | − | 1.48035i | ||||||
\(792\) | −5.54730 | −0.197115 | ||||||||
\(793\) | 18.7482 | + | 7.25636i | 0.665767 | + | 0.257681i | ||||
\(794\) | −12.0205 | −0.426592 | ||||||||
\(795\) | 17.6159i | 0.624771i | ||||||||
\(796\) | 0.0521177 | 0.00184726 | ||||||||
\(797\) | −3.91090 | −0.138531 | −0.0692656 | − | 0.997598i | \(-0.522066\pi\) | ||||
−0.0692656 | + | 0.997598i | \(0.522066\pi\) | |||||||
\(798\) | − | 19.6030i | − | 0.693939i | ||||||
\(799\) | 53.3018i | 1.88568i | ||||||||
\(800\) | − | 0.579048i | − | 0.0204724i | ||||||
\(801\) | 4.36253i | 0.154142i | ||||||||
\(802\) | −2.97533 | −0.105063 | ||||||||
\(803\) | −2.30754 | −0.0814314 | ||||||||
\(804\) | 0.168239i | 0.00593332i | ||||||||
\(805\) | −11.4672 | −0.404167 | ||||||||
\(806\) | −4.72449 | − | 1.82859i | −0.166413 | − | 0.0644092i | ||||
\(807\) | 17.0184 | 0.599077 | ||||||||
\(808\) | 51.6118i | 1.81570i | ||||||||
\(809\) | −23.7735 | −0.835833 | −0.417917 | − | 0.908485i | \(-0.637240\pi\) | ||||
−0.417917 | + | 0.908485i | \(0.637240\pi\) | |||||||
\(810\) | 9.38516 | 0.329761 | ||||||||
\(811\) | 42.9117i | 1.50683i | 0.657543 | + | 0.753417i | \(0.271596\pi\) | ||||
−0.657543 | + | 0.753417i | \(0.728404\pi\) | |||||||
\(812\) | − | 0.419889i | − | 0.0147352i | ||||||
\(813\) | 26.3124i | 0.922816i | ||||||||
\(814\) | − | 16.2402i | − | 0.569219i | ||||||
\(815\) | 8.02487 | 0.281099 | ||||||||
\(816\) | 33.3679 | 1.16811 | ||||||||
\(817\) | 11.0494i | 0.386568i | ||||||||
\(818\) | 6.29072 | 0.219950 | ||||||||
\(819\) | −2.50896 | + | 6.48237i | −0.0876702 | + | 0.226512i | ||||
\(820\) | 0.319617 | 0.0111615 | ||||||||
\(821\) | 26.4026i | 0.921455i | 0.887542 | + | 0.460728i | \(0.152412\pi\) | ||||
−0.887542 | + | 0.460728i | \(0.847588\pi\) | |||||||
\(822\) | −28.9716 | −1.01050 | ||||||||
\(823\) | −40.1436 | −1.39932 | −0.699660 | − | 0.714476i | \(-0.746665\pi\) | ||||
−0.699660 | + | 0.714476i | \(0.746665\pi\) | |||||||
\(824\) | − | 49.3154i | − | 1.71798i | ||||||
\(825\) | 17.8409i | 0.621142i | ||||||||
\(826\) | − | 51.0622i | − | 1.77668i | ||||||
\(827\) | − | 3.59807i | − | 0.125117i | −0.998041 | − | 0.0625585i | \(-0.980074\pi\) | ||
0.998041 | − | 0.0625585i | \(-0.0199260\pi\) | |||||||
\(828\) | −0.0663081 | −0.00230436 | ||||||||
\(829\) | −37.0408 | −1.28648 | −0.643240 | − | 0.765665i | \(-0.722410\pi\) | ||||
−0.643240 | + | 0.765665i | \(0.722410\pi\) | |||||||
\(830\) | 12.5837i | 0.436787i | ||||||||
\(831\) | 2.51573 | 0.0872696 | ||||||||
\(832\) | −27.2379 | − | 10.5423i | −0.944304 | − | 0.365487i | ||||
\(833\) | 8.10289 | 0.280749 | ||||||||
\(834\) | 19.1952i | 0.664675i | ||||||||
\(835\) | 6.65952 | 0.230462 | ||||||||
\(836\) | −0.238033 | −0.00823255 | ||||||||
\(837\) | 5.59958i | 0.193550i | ||||||||
\(838\) | − | 48.3860i | − | 1.67146i | ||||||
\(839\) | − | 5.11651i | − | 0.176641i | −0.996092 | − | 0.0883207i | \(-0.971850\pi\) | ||
0.996092 | − | 0.0883207i | \(-0.0281500\pi\) | |||||||
\(840\) | 12.8665i | 0.443935i | ||||||||
\(841\) | 2.28125 | 0.0786639 | ||||||||
\(842\) | −47.4549 | −1.63540 | ||||||||
\(843\) | − | 32.8234i | − | 1.13050i | ||||||
\(844\) | −0.625456 | −0.0215291 | ||||||||
\(845\) | 8.89363 | − | 9.76807i | 0.305950 | − | 0.336032i | ||||
\(846\) | 8.97568 | 0.308590 | ||||||||
\(847\) | − | 6.83316i | − | 0.234790i | ||||||
\(848\) | 44.7626 | 1.53715 | ||||||||
\(849\) | −3.86645 | −0.132696 | ||||||||
\(850\) | 30.8186i | 1.05707i | ||||||||
\(851\) | − | 15.2409i | − | 0.522451i | ||||||
\(852\) | 0.372692i | 0.0127682i | ||||||||
\(853\) | − | 18.5310i | − | 0.634489i | −0.948344 | − | 0.317244i | \(-0.897242\pi\) | ||
0.948344 | − | 0.317244i | \(-0.102758\pi\) | |||||||
\(854\) | −22.7942 | −0.780001 | ||||||||
\(855\) | −2.11175 | −0.0722204 | ||||||||
\(856\) | 22.0234i | 0.752744i | ||||||||
\(857\) | 29.0052 | 0.990799 | 0.495399 | − | 0.868665i | \(-0.335022\pi\) | ||||
0.495399 | + | 0.868665i | \(0.335022\pi\) | |||||||
\(858\) | 21.2456 | + | 8.22296i | 0.725312 | + | 0.280727i | ||||
\(859\) | −37.6122 | −1.28331 | −0.641656 | − | 0.766993i | \(-0.721752\pi\) | ||||
−0.641656 | + | 0.766993i | \(0.721752\pi\) | |||||||
\(860\) | − | 0.0923716i | − | 0.00314985i | ||||||
\(861\) | 54.2246 | 1.84797 | ||||||||
\(862\) | −24.8911 | −0.847796 | ||||||||
\(863\) | 6.95953i | 0.236905i | 0.992960 | + | 0.118453i | \(0.0377934\pi\) | ||||
−0.992960 | + | 0.118453i | \(0.962207\pi\) | |||||||
\(864\) | 0.817270i | 0.0278041i | ||||||||
\(865\) | 21.9153i | 0.745142i | ||||||||
\(866\) | 6.46269i | 0.219611i | ||||||||
\(867\) | 20.7392 | 0.704341 | ||||||||
\(868\) | −0.0750744 | −0.00254819 | ||||||||
\(869\) | 17.9956i | 0.610460i | ||||||||
\(870\) | −12.2088 | −0.413918 | ||||||||
\(871\) | −5.55030 | + | 14.3402i | −0.188065 | + | 0.485901i | ||||
\(872\) | 31.8561 | 1.07878 | ||||||||
\(873\) | − | 4.26927i | − | 0.144493i | ||||||
\(874\) | 17.0917 | 0.578136 | ||||||||
\(875\) | −26.5134 | −0.896315 | ||||||||
\(876\) | 0.0309481i | 0.00104564i | ||||||||
\(877\) | − | 16.1474i | − | 0.545259i | −0.962119 | − | 0.272629i | \(-0.912107\pi\) | ||
0.962119 | − | 0.272629i | \(-0.0878933\pi\) | |||||||
\(878\) | 35.9101i | 1.21191i | ||||||||
\(879\) | 12.9877i | 0.438064i | ||||||||
\(880\) | −11.7995 | −0.397759 | ||||||||
\(881\) | 57.8312 | 1.94838 | 0.974191 | − | 0.225723i | \(-0.0724745\pi\) | ||||
0.974191 | + | 0.225723i | \(0.0724745\pi\) | |||||||
\(882\) | − | 1.36448i | − | 0.0459443i | ||||||
\(883\) | 35.2033 | 1.18468 | 0.592342 | − | 0.805686i | \(-0.298203\pi\) | ||||
0.592342 | + | 0.805686i | \(0.298203\pi\) | |||||||
\(884\) | −0.479662 | − | 0.185650i | −0.0161328 | − | 0.00624409i | ||||
\(885\) | 19.4049 | 0.652288 | ||||||||
\(886\) | − | 34.8085i | − | 1.16941i | ||||||
\(887\) | −9.93969 | −0.333742 | −0.166871 | − | 0.985979i | \(-0.553366\pi\) | ||||
−0.166871 | + | 0.985979i | \(0.553366\pi\) | |||||||
\(888\) | −17.1006 | −0.573857 | ||||||||
\(889\) | 52.3108i | 1.75445i | ||||||||
\(890\) | 9.40066i | 0.315111i | ||||||||
\(891\) | − | 19.3341i | − | 0.647715i | ||||||
\(892\) | 0.144884i | 0.00485107i | ||||||||
\(893\) | 30.2383 | 1.01189 | ||||||||
\(894\) | −5.54233 | −0.185363 | ||||||||
\(895\) | 5.11833i | 0.171087i | ||||||||
\(896\) | 32.2667 | 1.07796 | ||||||||
\(897\) | 19.9383 | + | 7.71699i | 0.665720 | + | 0.257663i | ||||
\(898\) | −53.4004 | −1.78200 | ||||||||
\(899\) | − | 5.59296i | − | 0.186536i | ||||||
\(900\) | −0.0678282 | −0.00226094 | ||||||||
\(901\) | 62.6875 | 2.08842 | ||||||||
\(902\) | 50.3778i | 1.67740i | ||||||||
\(903\) | − | 15.6713i | − | 0.521508i | ||||||
\(904\) | − | 40.7302i | − | 1.35466i | ||||||
\(905\) | − | 9.47401i | − | 0.314927i | ||||||
\(906\) | 3.77215 | 0.125321 | ||||||||
\(907\) | 38.5077 | 1.27863 | 0.639314 | − | 0.768946i | \(-0.279218\pi\) | ||||
0.639314 | + | 0.768946i | \(0.279218\pi\) | |||||||
\(908\) | − | 0.224251i | − | 0.00744202i | ||||||
\(909\) | 12.0144 | 0.398491 | ||||||||
\(910\) | −5.40647 | + | 13.9686i | −0.179223 | + | 0.463056i | ||||
\(911\) | 26.1703 | 0.867061 | 0.433531 | − | 0.901139i | \(-0.357268\pi\) | ||||
0.433531 | + | 0.901139i | \(0.357268\pi\) | |||||||
\(912\) | − | 18.9297i | − | 0.626827i | ||||||
\(913\) | 25.9233 | 0.857935 | ||||||||
\(914\) | −0.969697 | −0.0320747 | ||||||||
\(915\) | − | 8.66235i | − | 0.286368i | ||||||
\(916\) | − | 0.710714i | − | 0.0234827i | ||||||
\(917\) | 25.0282i | 0.826505i | ||||||||
\(918\) | − | 43.4975i | − | 1.43563i | ||||||
\(919\) | −41.2705 | −1.36139 | −0.680694 | − | 0.732568i | \(-0.738321\pi\) | ||||
−0.680694 | + | 0.732568i | \(0.738321\pi\) | |||||||
\(920\) | −11.2182 | −0.369852 | ||||||||
\(921\) | 37.6161i | 1.23949i | ||||||||
\(922\) | 4.92467 | 0.162185 | ||||||||
\(923\) | −12.2953 | + | 31.7673i | −0.404706 | + | 1.04563i | ||||
\(924\) | 0.337602 | 0.0111063 | ||||||||
\(925\) | − | 15.5903i | − | 0.512606i | ||||||
\(926\) | −15.5306 | −0.510366 | ||||||||
\(927\) | −11.4798 | −0.377046 | ||||||||
\(928\) | − | 0.816304i | − | 0.0267965i | ||||||
\(929\) | − | 8.54363i | − | 0.280307i | −0.990130 | − | 0.140154i | \(-0.955240\pi\) | ||
0.990130 | − | 0.140154i | \(-0.0447597\pi\) | |||||||
\(930\) | 2.18289i | 0.0715798i | ||||||||
\(931\) | − | 4.59681i | − | 0.150654i | ||||||
\(932\) | −0.355896 | −0.0116578 | ||||||||
\(933\) | −12.3429 | −0.404090 | ||||||||
\(934\) | 18.8454i | 0.616639i | ||||||||
\(935\) | −16.5245 | −0.540408 | ||||||||
\(936\) | −2.45446 | + | 6.34156i | −0.0802266 | + | 0.207281i | ||||
\(937\) | −9.82051 | −0.320822 | −0.160411 | − | 0.987050i | \(-0.551282\pi\) | ||||
−0.160411 | + | 0.987050i | \(0.551282\pi\) | |||||||
\(938\) | − | 17.4350i | − | 0.569272i | ||||||
\(939\) | −22.3668 | −0.729914 | ||||||||
\(940\) | −0.252790 | −0.00824509 | ||||||||
\(941\) | 6.99443i | 0.228012i | 0.993480 | + | 0.114006i | \(0.0363683\pi\) | ||||
−0.993480 | + | 0.114006i | \(0.963632\pi\) | |||||||
\(942\) | 40.8850i | 1.33211i | ||||||||
\(943\) | 47.2780i | 1.53958i | ||||||||
\(944\) | − | 49.3085i | − | 1.60486i | ||||||
\(945\) | 16.5560 | 0.538566 | ||||||||
\(946\) | 14.5596 | 0.473372 | ||||||||
\(947\) | − | 2.07373i | − | 0.0673872i | −0.999432 | − | 0.0336936i | \(-0.989273\pi\) | ||
0.999432 | − | 0.0336936i | \(-0.0107270\pi\) | |||||||
\(948\) | 0.241352 | 0.00783875 | ||||||||
\(949\) | −1.02100 | + | 2.63794i | −0.0331429 | + | 0.0856310i | ||||
\(950\) | 17.4836 | 0.567241 | ||||||||
\(951\) | − | 9.67428i | − | 0.313710i | ||||||
\(952\) | 45.7863 | 1.48394 | ||||||||
\(953\) | 5.68472 | 0.184146 | 0.0920730 | − | 0.995752i | \(-0.470651\pi\) | ||||
0.0920730 | + | 0.995752i | \(0.470651\pi\) | |||||||
\(954\) | − | 10.5562i | − | 0.341769i | ||||||
\(955\) | − | 10.7280i | − | 0.347149i | ||||||
\(956\) | − | 0.0355875i | − | 0.00115098i | ||||||
\(957\) | 25.1510i | 0.813016i | ||||||||
\(958\) | 12.8075 | 0.413791 | ||||||||
\(959\) | −39.2409 | −1.26715 | ||||||||
\(960\) | 12.5849i | 0.406176i | ||||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | −18.5655 | − | 7.18564i | −0.598574 | − | 0.231674i | ||||
\(963\) | 5.12667 | 0.165205 | ||||||||
\(964\) | − | 0.718925i | − | 0.0231550i | ||||||
\(965\) | −16.3875 | −0.527533 | ||||||||
\(966\) | −24.2411 | −0.779946 | ||||||||
\(967\) | − | 60.0678i | − | 1.93165i | −0.259193 | − | 0.965826i | \(-0.583457\pi\) | ||
0.259193 | − | 0.965826i | \(-0.416543\pi\) | |||||||
\(968\) | − | 6.68474i | − | 0.214856i | ||||||
\(969\) | − | 26.5101i | − | 0.851626i | ||||||
\(970\) | − | 9.19971i | − | 0.295385i | ||||||
\(971\) | 15.2770 | 0.490263 | 0.245132 | − | 0.969490i | \(-0.421169\pi\) | ||||
0.245132 | + | 0.969490i | \(0.421169\pi\) | |||||||
\(972\) | 0.174147 | 0.00558578 | ||||||||
\(973\) | 25.9992i | 0.833495i | ||||||||
\(974\) | 10.8034 | 0.346164 | ||||||||
\(975\) | 20.3954 | + | 7.89391i | 0.653175 | + | 0.252807i | ||||
\(976\) | −22.0113 | −0.704566 | ||||||||
\(977\) | − | 18.3389i | − | 0.586715i | −0.956003 | − | 0.293357i | \(-0.905227\pi\) | ||
0.956003 | − | 0.293357i | \(-0.0947726\pi\) | |||||||
\(978\) | 16.9641 | 0.542454 | ||||||||
\(979\) | 19.3660 | 0.618940 | ||||||||
\(980\) | 0.0384289i | 0.00122757i | ||||||||
\(981\) | − | 7.41557i | − | 0.236761i | ||||||
\(982\) | − | 3.24501i | − | 0.103552i | ||||||
\(983\) | − | 11.3039i | − | 0.360538i | −0.983617 | − | 0.180269i | \(-0.942303\pi\) | ||
0.983617 | − | 0.180269i | \(-0.0576968\pi\) | |||||||
\(984\) | 53.0467 | 1.69107 | ||||||||
\(985\) | 4.29241 | 0.136768 | ||||||||
\(986\) | 43.4461i | 1.38361i | ||||||||
\(987\) | −42.8870 | −1.36511 | ||||||||
\(988\) | −0.105320 | + | 0.272115i | −0.00335068 | + | 0.00865712i | ||||
\(989\) | 13.6637 | 0.434480 | ||||||||
\(990\) | 2.78262i | 0.0884375i | ||||||||
\(991\) | −9.29869 | −0.295383 | −0.147691 | − | 0.989033i | \(-0.547184\pi\) | ||||
−0.147691 | + | 0.989033i | \(0.547184\pi\) | |||||||
\(992\) | −0.145952 | −0.00463398 | ||||||||
\(993\) | 13.6978i | 0.434686i | ||||||||
\(994\) | − | 38.6229i | − | 1.22505i | ||||||
\(995\) | − | 2.05254i | − | 0.0650699i | ||||||
\(996\) | − | 0.347676i | − | 0.0110165i | ||||||
\(997\) | −14.4171 | −0.456594 | −0.228297 | − | 0.973592i | \(-0.573316\pi\) | ||||
−0.228297 | + | 0.973592i | \(0.573316\pi\) | |||||||
\(998\) | −23.8536 | −0.755073 | ||||||||
\(999\) | 22.0042i | 0.696183i |
(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 | 403.2.c.b.311.11 | ✓ | 32 | |
13.5 | odd | 4 | 5239.2.a.l.1.5 | 16 | |||
13.8 | odd | 4 | 5239.2.a.k.1.12 | 16 | |||
13.12 | even | 2 | inner | 403.2.c.b.311.22 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.c.b.311.11 | ✓ | 32 | 1.1 | even | 1 | trivial | |
403.2.c.b.311.22 | yes | 32 | 13.12 | even | 2 | inner | |
5239.2.a.k.1.12 | 16 | 13.8 | odd | 4 | |||
5239.2.a.l.1.5 | 16 | 13.5 | odd | 4 |