Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(26,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.e (of order \(3\), degree \(2\), 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: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 6x^{10} + 29x^{8} + 40x^{6} + 43x^{4} + 7x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 201.4 | ||
Root | \(-1.05958 + 1.83525i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.201 |
Dual form | 475.2.e.g.26.4 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.235942 | − | 0.408663i | 0.166836 | − | 0.288969i | −0.770470 | − | 0.637477i | \(-0.779978\pi\) |
0.937306 | + | 0.348508i | \(0.113312\pi\) | |||||||
\(3\) | −0.520111 | + | 0.900858i | −0.300286 | + | 0.520111i | −0.976201 | − | 0.216869i | \(-0.930415\pi\) |
0.675915 | + | 0.736980i | \(0.263749\pi\) | |||||||
\(4\) | 0.888663 | + | 1.53921i | 0.444331 | + | 0.769605i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.245432 | + | 0.425100i | 0.100197 | + | 0.173546i | ||||
\(7\) | 1.17540 | 0.444259 | 0.222129 | − | 0.975017i | \(-0.428699\pi\) | ||||
0.222129 | + | 0.975017i | \(0.428699\pi\) | |||||||
\(8\) | 1.78246 | 0.630194 | ||||||||
\(9\) | 0.958970 | + | 1.66098i | 0.319657 | + | 0.553661i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.713538 | 0.215140 | 0.107570 | − | 0.994198i | \(-0.465693\pi\) | ||||
0.107570 | + | 0.994198i | \(0.465693\pi\) | |||||||
\(12\) | −1.84881 | −0.533706 | ||||||||
\(13\) | −2.05158 | − | 3.55344i | −0.569005 | − | 0.985546i | −0.996665 | − | 0.0816060i | \(-0.973995\pi\) |
0.427659 | − | 0.903940i | \(-0.359338\pi\) | |||||||
\(14\) | 0.277326 | − | 0.480342i | 0.0741184 | − | 0.128377i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.35677 | + | 2.34999i | −0.339192 | + | 0.587498i | ||||
\(17\) | −1.27616 | + | 2.21038i | −0.309515 | + | 0.536096i | −0.978256 | − | 0.207399i | \(-0.933500\pi\) |
0.668741 | + | 0.743495i | \(0.266833\pi\) | |||||||
\(18\) | 0.905045 | 0.213321 | ||||||||
\(19\) | 1.57031 | + | 4.06622i | 0.360253 | + | 0.932855i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.611337 | + | 1.05887i | −0.133405 | + | 0.231064i | ||||
\(22\) | 0.168353 | − | 0.291597i | 0.0358931 | − | 0.0621686i | ||||
\(23\) | 0.303530 | + | 0.525730i | 0.0632904 | + | 0.109622i | 0.895934 | − | 0.444186i | \(-0.146507\pi\) |
−0.832644 | + | 0.553809i | \(0.813174\pi\) | |||||||
\(24\) | −0.927076 | + | 1.60574i | −0.189239 | + | 0.327771i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.93621 | −0.379722 | ||||||||
\(27\) | −5.11575 | −0.984526 | ||||||||
\(28\) | 1.04453 | + | 1.80918i | 0.197398 | + | 0.341904i | ||||
\(29\) | 0.429693 | + | 0.744250i | 0.0797920 | + | 0.138204i | 0.903160 | − | 0.429304i | \(-0.141241\pi\) |
−0.823368 | + | 0.567508i | \(0.807908\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.50914 | 0.450654 | 0.225327 | − | 0.974283i | \(-0.427655\pi\) | ||||
0.225327 | + | 0.974283i | \(0.427655\pi\) | |||||||
\(32\) | 2.42270 | + | 4.19623i | 0.428276 | + | 0.741796i | ||||
\(33\) | −0.371119 | + | 0.642796i | −0.0646035 | + | 0.111897i | ||||
\(34\) | 0.602201 | + | 1.04304i | 0.103277 | + | 0.178880i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.70440 | + | 2.95211i | −0.284067 | + | 0.492018i | ||||
\(37\) | 9.38171 | 1.54234 | 0.771172 | − | 0.636627i | \(-0.219671\pi\) | ||||
0.771172 | + | 0.636627i | \(0.219671\pi\) | |||||||
\(38\) | 2.03222 | + | 0.317665i | 0.329669 | + | 0.0515320i | ||||
\(39\) | 4.26819 | 0.683457 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.06117 | − | 3.57005i | 0.321901 | − | 0.557548i | −0.658979 | − | 0.752161i | \(-0.729012\pi\) |
0.980880 | + | 0.194612i | \(0.0623449\pi\) | |||||||
\(42\) | 0.288480 | + | 0.499662i | 0.0445134 | + | 0.0770996i | ||||
\(43\) | −5.06197 | + | 8.76759i | −0.771944 | + | 1.33705i | 0.164553 | + | 0.986368i | \(0.447382\pi\) |
−0.936496 | + | 0.350677i | \(0.885951\pi\) | |||||||
\(44\) | 0.634095 | + | 1.09828i | 0.0955934 | + | 0.165573i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.286462 | 0.0422365 | ||||||||
\(47\) | −5.25919 | − | 9.10919i | −0.767132 | − | 1.32871i | −0.939112 | − | 0.343611i | \(-0.888350\pi\) |
0.171980 | − | 0.985100i | \(-0.444984\pi\) | |||||||
\(48\) | −1.41134 | − | 2.44451i | −0.203709 | − | 0.352835i | ||||
\(49\) | −5.61844 | −0.802634 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.32749 | − | 2.29928i | −0.185886 | − | 0.321964i | ||||
\(52\) | 3.64632 | − | 6.31561i | 0.505654 | − | 0.875818i | ||||
\(53\) | −2.49028 | − | 4.31330i | −0.342067 | − | 0.592477i | 0.642750 | − | 0.766076i | \(-0.277794\pi\) |
−0.984816 | + | 0.173599i | \(0.944460\pi\) | |||||||
\(54\) | −1.20702 | + | 2.09062i | −0.164254 | + | 0.284497i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.09510 | 0.279969 | ||||||||
\(57\) | −4.47982 | − | 0.700260i | −0.593367 | − | 0.0927517i | ||||
\(58\) | 0.405530 | 0.0532488 | ||||||||
\(59\) | 3.12496 | − | 5.41259i | 0.406835 | − | 0.704659i | −0.587698 | − | 0.809080i | \(-0.699966\pi\) |
0.994533 | + | 0.104421i | \(0.0332991\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.27733 | + | 3.94444i | 0.291582 | + | 0.505034i | 0.974184 | − | 0.225756i | \(-0.0724852\pi\) |
−0.682602 | + | 0.730790i | \(0.739152\pi\) | |||||||
\(62\) | 0.592010 | − | 1.02539i | 0.0751854 | − | 0.130225i | ||||
\(63\) | 1.12717 | + | 1.95232i | 0.142010 | + | 0.245969i | ||||
\(64\) | −3.14061 | −0.392577 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.175125 | + | 0.303325i | 0.0215564 | + | 0.0373368i | ||||
\(67\) | 2.59105 | + | 4.48783i | 0.316547 | + | 0.548276i | 0.979765 | − | 0.200151i | \(-0.0641431\pi\) |
−0.663218 | + | 0.748426i | \(0.730810\pi\) | |||||||
\(68\) | −4.53632 | −0.550109 | ||||||||
\(69\) | −0.631477 | −0.0760209 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.58393 | − | 11.4037i | 0.781368 | − | 1.35337i | −0.149776 | − | 0.988720i | \(-0.547855\pi\) |
0.931145 | − | 0.364650i | \(-0.118811\pi\) | |||||||
\(72\) | 1.70932 | + | 2.96064i | 0.201446 | + | 0.348914i | ||||
\(73\) | 6.18914 | − | 10.7199i | 0.724384 | − | 1.25467i | −0.234842 | − | 0.972033i | \(-0.575457\pi\) |
0.959227 | − | 0.282637i | \(-0.0912093\pi\) | |||||||
\(74\) | 2.21354 | − | 3.83396i | 0.257319 | − | 0.445689i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.86329 | + | 6.03053i | −0.557857 | + | 0.691749i | ||||
\(77\) | 0.838691 | 0.0955777 | ||||||||
\(78\) | 1.00704 | − | 1.74425i | 0.114025 | − | 0.197498i | ||||
\(79\) | 2.98173 | − | 5.16450i | 0.335471 | − | 0.581052i | −0.648105 | − | 0.761551i | \(-0.724438\pi\) |
0.983575 | + | 0.180499i | \(0.0577714\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.216155 | + | 0.374392i | −0.0240172 | + | 0.0415991i | ||||
\(82\) | −0.972633 | − | 1.68465i | −0.107409 | − | 0.186038i | ||||
\(83\) | 13.8603 | 1.52136 | 0.760682 | − | 0.649124i | \(-0.224864\pi\) | ||||
0.760682 | + | 0.649124i | \(0.224864\pi\) | |||||||
\(84\) | −2.17309 | −0.237104 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.38866 | + | 4.13729i | 0.257576 | + | 0.446135i | ||||
\(87\) | −0.893952 | −0.0958417 | ||||||||
\(88\) | 1.27185 | 0.135580 | ||||||||
\(89\) | −7.98173 | − | 13.8248i | −0.846061 | − | 1.46542i | −0.884696 | − | 0.466168i | \(-0.845634\pi\) |
0.0386349 | − | 0.999253i | \(-0.487699\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.41142 | − | 4.17670i | −0.252786 | − | 0.437837i | ||||
\(92\) | −0.539472 | + | 0.934393i | −0.0562439 | + | 0.0974172i | ||||
\(93\) | −1.30503 | + | 2.26038i | −0.135325 | + | 0.234390i | ||||
\(94\) | −4.96345 | −0.511941 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.04028 | −0.514421 | ||||||||
\(97\) | −8.35099 | + | 14.4643i | −0.847915 | + | 1.46863i | 0.0351512 | + | 0.999382i | \(0.488809\pi\) |
−0.883066 | + | 0.469249i | \(0.844525\pi\) | |||||||
\(98\) | −1.32563 | + | 2.29605i | −0.133908 | + | 0.231936i | ||||
\(99\) | 0.684261 | + | 1.18518i | 0.0687708 | + | 0.119115i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.01362 | − | 12.1479i | −0.697881 | − | 1.20877i | −0.969200 | − | 0.246276i | \(-0.920793\pi\) |
0.271318 | − | 0.962490i | \(-0.412540\pi\) | |||||||
\(102\) | −1.25284 | −0.124050 | ||||||||
\(103\) | 3.55382 | 0.350169 | 0.175084 | − | 0.984553i | \(-0.443980\pi\) | ||||
0.175084 | + | 0.984553i | \(0.443980\pi\) | |||||||
\(104\) | −3.65685 | − | 6.33385i | −0.358584 | − | 0.621085i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.35025 | −0.228276 | ||||||||
\(107\) | 3.63127 | 0.351048 | 0.175524 | − | 0.984475i | \(-0.443838\pi\) | ||||
0.175524 | + | 0.984475i | \(0.443838\pi\) | |||||||
\(108\) | −4.54617 | − | 7.87420i | −0.437456 | − | 0.757696i | ||||
\(109\) | 3.11134 | − | 5.38899i | 0.298012 | − | 0.516172i | −0.677669 | − | 0.735367i | \(-0.737010\pi\) |
0.975681 | + | 0.219195i | \(0.0703431\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.87953 | + | 8.45159i | −0.463144 | + | 0.802189i | ||||
\(112\) | −1.59474 | + | 2.76218i | −0.150689 | + | 0.261001i | ||||
\(113\) | −12.2707 | −1.15433 | −0.577167 | − | 0.816626i | \(-0.695842\pi\) | ||||
−0.577167 | + | 0.816626i | \(0.695842\pi\) | |||||||
\(114\) | −1.34315 | + | 1.66552i | −0.125797 | + | 0.155990i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.763705 | + | 1.32278i | −0.0709082 | + | 0.122817i | ||||
\(117\) | 3.93480 | − | 6.81528i | 0.363773 | − | 0.630072i | ||||
\(118\) | −1.47462 | − | 2.55411i | −0.135750 | − | 0.235125i | ||||
\(119\) | −1.50000 | + | 2.59808i | −0.137505 | + | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4909 | −0.953715 | ||||||||
\(122\) | 2.14927 | 0.194585 | ||||||||
\(123\) | 2.14407 | + | 3.71364i | 0.193325 | + | 0.334848i | ||||
\(124\) | 2.22978 | + | 3.86209i | 0.200240 | + | 0.346826i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.06379 | 0.0947697 | ||||||||
\(127\) | −1.07894 | − | 1.86879i | −0.0957408 | − | 0.165828i | 0.814177 | − | 0.580617i | \(-0.197189\pi\) |
−0.909918 | + | 0.414789i | \(0.863855\pi\) | |||||||
\(128\) | −5.58639 | + | 9.67592i | −0.493772 | + | 0.855239i | ||||
\(129\) | −5.26557 | − | 9.12024i | −0.463608 | − | 0.802992i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.77471 | − | 15.1982i | 0.766650 | − | 1.32788i | −0.172720 | − | 0.984971i | \(-0.555256\pi\) |
0.939370 | − | 0.342906i | \(-0.111411\pi\) | |||||||
\(132\) | −1.31920 | −0.114821 | ||||||||
\(133\) | 1.84574 | + | 4.77943i | 0.160046 | + | 0.414429i | ||||
\(134\) | 2.44535 | 0.211246 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.27471 | + | 3.93991i | −0.195055 | + | 0.337845i | ||||
\(137\) | −2.53728 | − | 4.39469i | −0.216774 | − | 0.375464i | 0.737046 | − | 0.675843i | \(-0.236220\pi\) |
−0.953820 | + | 0.300379i | \(0.902887\pi\) | |||||||
\(138\) | −0.148992 | + | 0.258062i | −0.0126830 | + | 0.0219677i | ||||
\(139\) | −2.99086 | − | 5.18033i | −0.253682 | − | 0.439390i | 0.710855 | − | 0.703339i | \(-0.248308\pi\) |
−0.964537 | + | 0.263949i | \(0.914975\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.9414 | 0.921436 | ||||||||
\(142\) | −3.10685 | − | 5.38122i | −0.260721 | − | 0.451582i | ||||
\(143\) | −1.46388 | − | 2.53551i | −0.122416 | − | 0.212030i | ||||
\(144\) | −5.20440 | −0.433700 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.92056 | − | 5.05855i | −0.241707 | − | 0.418649i | ||||
\(147\) | 2.92221 | − | 5.06142i | 0.241020 | − | 0.417459i | ||||
\(148\) | 8.33718 | + | 14.4404i | 0.685312 | + | 1.18699i | ||||
\(149\) | −4.80008 | + | 8.31399i | −0.393238 | + | 0.681108i | −0.992875 | − | 0.119164i | \(-0.961979\pi\) |
0.599636 | + | 0.800273i | \(0.295312\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.53638 | 0.613302 | 0.306651 | − | 0.951822i | \(-0.400792\pi\) | ||||
0.306651 | + | 0.951822i | \(0.400792\pi\) | |||||||
\(152\) | 2.79901 | + | 7.24787i | 0.227029 | + | 0.587880i | ||||
\(153\) | −4.89521 | −0.395754 | ||||||||
\(154\) | 0.197882 | − | 0.342742i | 0.0159458 | − | 0.0276190i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.79298 | + | 6.56964i | 0.303682 | + | 0.525992i | ||||
\(157\) | 4.92803 | − | 8.53560i | 0.393300 | − | 0.681215i | −0.599583 | − | 0.800313i | \(-0.704667\pi\) |
0.992883 | + | 0.119098i | \(0.0380002\pi\) | |||||||
\(158\) | −1.40703 | − | 2.43705i | −0.111937 | − | 0.193881i | ||||
\(159\) | 5.18089 | 0.410872 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.356769 | + | 0.617942i | 0.0281173 | + | 0.0487007i | ||||
\(162\) | 0.102000 | + | 0.176669i | 0.00801389 | + | 0.0138805i | ||||
\(163\) | −0.0688234 | −0.00539067 | −0.00269533 | − | 0.999996i | \(-0.500858\pi\) | ||||
−0.00269533 | + | 0.999996i | \(0.500858\pi\) | |||||||
\(164\) | 7.32674 | 0.572122 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.27022 | − | 5.66419i | 0.253819 | − | 0.439627i | ||||
\(167\) | 8.32212 | + | 14.4143i | 0.643985 | + | 1.11542i | 0.984535 | + | 0.175189i | \(0.0560536\pi\) |
−0.340550 | + | 0.940227i | \(0.610613\pi\) | |||||||
\(168\) | −1.08968 | + | 1.88739i | −0.0840709 | + | 0.145615i | ||||
\(169\) | −1.91794 | + | 3.32197i | −0.147534 | + | 0.255536i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.24805 | + | 6.50764i | −0.401328 | + | 0.497651i | ||||
\(172\) | −17.9935 | −1.37200 | ||||||||
\(173\) | −6.06778 | + | 10.5097i | −0.461325 | + | 0.799038i | −0.999027 | − | 0.0440965i | \(-0.985959\pi\) |
0.537702 | + | 0.843135i | \(0.319292\pi\) | |||||||
\(174\) | −0.210921 | + | 0.365325i | −0.0159899 | + | 0.0276952i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.968106 | + | 1.67681i | −0.0729737 | + | 0.126394i | ||||
\(177\) | 3.25065 | + | 5.63029i | 0.244334 | + | 0.423198i | ||||
\(178\) | −7.53290 | −0.564614 | ||||||||
\(179\) | 11.7538 | 0.878522 | 0.439261 | − | 0.898360i | \(-0.355240\pi\) | ||||
0.439261 | + | 0.898360i | \(0.355240\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.41794 | + | 7.65210i | 0.328383 | + | 0.568776i | 0.982191 | − | 0.187884i | \(-0.0601631\pi\) |
−0.653808 | + | 0.756660i | \(0.726830\pi\) | |||||||
\(182\) | −2.27582 | −0.168695 | ||||||||
\(183\) | −4.73785 | −0.350232 | ||||||||
\(184\) | 0.541030 | + | 0.937092i | 0.0398853 | + | 0.0690833i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.615822 | + | 1.06663i | 0.0451543 | + | 0.0782095i | ||||
\(187\) | −0.910591 | + | 1.57719i | −0.0665890 | + | 0.115336i | ||||
\(188\) | 9.34730 | − | 16.1900i | 0.681722 | − | 1.18078i | ||||
\(189\) | −6.01304 | −0.437384 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.2447 | 1.03071 | 0.515355 | − | 0.856977i | \(-0.327660\pi\) | ||||
0.515355 | + | 0.856977i | \(0.327660\pi\) | |||||||
\(192\) | 1.63347 | − | 2.82925i | 0.117885 | − | 0.204183i | ||||
\(193\) | 9.75283 | − | 16.8924i | 0.702024 | − | 1.21594i | −0.265731 | − | 0.964047i | \(-0.585613\pi\) |
0.967755 | − | 0.251894i | \(-0.0810533\pi\) | |||||||
\(194\) | 3.94070 | + | 6.82549i | 0.282926 | + | 0.490041i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.99290 | − | 8.64795i | −0.356636 | − | 0.617711i | ||||
\(197\) | 4.33232 | 0.308665 | 0.154332 | − | 0.988019i | \(-0.450677\pi\) | ||||
0.154332 | + | 0.988019i | \(0.450677\pi\) | |||||||
\(198\) | 0.645784 | 0.0458938 | ||||||||
\(199\) | 6.31574 | + | 10.9392i | 0.447711 | + | 0.775458i | 0.998237 | − | 0.0593602i | \(-0.0189061\pi\) |
−0.550526 | + | 0.834818i | \(0.685573\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.39053 | −0.380219 | ||||||||
\(202\) | −6.61923 | −0.465727 | ||||||||
\(203\) | 0.505060 | + | 0.874790i | 0.0354483 | + | 0.0613983i | ||||
\(204\) | 2.35939 | − | 4.08658i | 0.165190 | − | 0.286118i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.838496 | − | 1.45232i | 0.0584208 | − | 0.101188i | ||||
\(207\) | −0.582153 | + | 1.00832i | −0.0404624 | + | 0.0700830i | ||||
\(208\) | 11.1341 | 0.772009 | ||||||||
\(209\) | 1.12047 | + | 2.90140i | 0.0775048 | + | 0.200694i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.1223 | + | 19.2645i | −0.765694 | + | 1.32622i | 0.174186 | + | 0.984713i | \(0.444271\pi\) |
−0.939879 | + | 0.341507i | \(0.889063\pi\) | |||||||
\(212\) | 4.42605 | − | 7.66614i | 0.303982 | − | 0.526512i | ||||
\(213\) | 6.84874 | + | 11.8624i | 0.469268 | + | 0.812796i | ||||
\(214\) | 0.856769 | − | 1.48397i | 0.0585675 | − | 0.101442i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −9.11861 | −0.620443 | ||||||||
\(217\) | 2.94923 | 0.200207 | ||||||||
\(218\) | −1.46819 | − | 2.54298i | −0.0994383 | − | 0.172232i | ||||
\(219\) | 6.43808 | + | 11.1511i | 0.435045 | + | 0.753520i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.4726 | 0.704463 | ||||||||
\(222\) | 2.30257 | + | 3.98817i | 0.154538 | + | 0.267668i | ||||
\(223\) | 6.81125 | − | 11.7974i | 0.456115 | − | 0.790015i | −0.542636 | − | 0.839968i | \(-0.682574\pi\) |
0.998752 | + | 0.0499529i | \(0.0159071\pi\) | |||||||
\(224\) | 2.84763 | + | 4.93224i | 0.190265 | + | 0.329549i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.89518 | + | 5.01460i | −0.192585 | + | 0.333566i | ||||
\(227\) | −6.58913 | −0.437336 | −0.218668 | − | 0.975799i | \(-0.570171\pi\) | ||||
−0.218668 | + | 0.975799i | \(0.570171\pi\) | |||||||
\(228\) | −2.90320 | − | 7.51768i | −0.192269 | − | 0.497870i | ||||
\(229\) | −0.585962 | −0.0387215 | −0.0193607 | − | 0.999813i | \(-0.506163\pi\) | ||||
−0.0193607 | + | 0.999813i | \(0.506163\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.436212 | + | 0.755542i | −0.0287007 | + | 0.0497110i | ||||
\(232\) | 0.765910 | + | 1.32660i | 0.0502845 | + | 0.0870953i | ||||
\(233\) | 3.57873 | − | 6.19855i | 0.234451 | − | 0.406080i | −0.724662 | − | 0.689104i | \(-0.758004\pi\) |
0.959113 | + | 0.283024i | \(0.0913376\pi\) | |||||||
\(234\) | −1.85677 | − | 3.21602i | −0.121381 | − | 0.210238i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 11.1081 | 0.723078 | ||||||||
\(237\) | 3.10166 | + | 5.37223i | 0.201474 | + | 0.348964i | ||||
\(238\) | 0.707826 | + | 1.22599i | 0.0458815 | + | 0.0794691i | ||||
\(239\) | 3.65498 | 0.236421 | 0.118211 | − | 0.992989i | \(-0.462284\pi\) | ||||
0.118211 | + | 0.992989i | \(0.462284\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.63148 | − | 14.9502i | −0.556002 | − | 0.963024i | −0.997825 | − | 0.0659218i | \(-0.979001\pi\) |
0.441822 | − | 0.897103i | \(-0.354332\pi\) | |||||||
\(242\) | −2.47523 | + | 4.28723i | −0.159114 | + | 0.275594i | ||||
\(243\) | −7.89847 | − | 13.6805i | −0.506687 | − | 0.877608i | ||||
\(244\) | −4.04755 | + | 7.01056i | −0.259118 | + | 0.448805i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.02351 | 0.129014 | ||||||||
\(247\) | 11.2274 | − | 13.9221i | 0.714385 | − | 0.885845i | ||||
\(248\) | 4.47243 | 0.284000 | ||||||||
\(249\) | −7.20889 | + | 12.4862i | −0.456845 | + | 0.791278i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.70702 | + | 16.8130i | 0.612702 | + | 1.06123i | 0.990783 | + | 0.135458i | \(0.0432506\pi\) |
−0.378082 | + | 0.925772i | \(0.623416\pi\) | |||||||
\(252\) | −2.00335 | + | 3.46990i | −0.126199 | + | 0.218583i | ||||
\(253\) | 0.216580 | + | 0.375128i | 0.0136163 | + | 0.0235841i | ||||
\(254\) | −1.01827 | −0.0638921 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.504485 | − | 0.873793i | −0.0315303 | − | 0.0546121i | ||||
\(257\) | −6.94643 | − | 12.0316i | −0.433306 | − | 0.750509i | 0.563849 | − | 0.825878i | \(-0.309320\pi\) |
−0.997156 | + | 0.0753689i | \(0.975987\pi\) | |||||||
\(258\) | −4.96948 | −0.309386 | ||||||||
\(259\) | 11.0272 | 0.685199 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.824125 | + | 1.42743i | −0.0510121 | + | 0.0883555i | ||||
\(262\) | −4.14064 | − | 7.17180i | −0.255810 | − | 0.443076i | ||||
\(263\) | −7.49417 | + | 12.9803i | −0.462110 | + | 0.800399i | −0.999066 | − | 0.0432118i | \(-0.986241\pi\) |
0.536955 | + | 0.843611i | \(0.319574\pi\) | |||||||
\(264\) | −0.661504 | + | 1.14576i | −0.0407127 | + | 0.0705165i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.38866 | + | 0.373382i | 0.146458 | + | 0.0228935i | ||||
\(267\) | 16.6055 | 1.01624 | ||||||||
\(268\) | −4.60514 | + | 7.97633i | −0.281304 | + | 0.487232i | ||||
\(269\) | −9.68613 | + | 16.7769i | −0.590574 | + | 1.02290i | 0.403582 | + | 0.914944i | \(0.367765\pi\) |
−0.994155 | + | 0.107960i | \(0.965568\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.95897 | + | 10.3212i | −0.361982 | + | 0.626971i | −0.988287 | − | 0.152607i | \(-0.951233\pi\) |
0.626305 | + | 0.779578i | \(0.284566\pi\) | |||||||
\(272\) | −3.46292 | − | 5.99795i | −0.209970 | − | 0.363679i | ||||
\(273\) | 5.01682 | 0.303632 | ||||||||
\(274\) | −2.39460 | −0.144663 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.561171 | − | 0.971976i | −0.0337785 | − | 0.0585061i | ||||
\(277\) | −10.9824 | −0.659866 | −0.329933 | − | 0.944004i | \(-0.607026\pi\) | ||||
−0.329933 | + | 0.944004i | \(0.607026\pi\) | |||||||
\(278\) | −2.82268 | −0.169293 | ||||||||
\(279\) | 2.40619 | + | 4.16764i | 0.144055 | + | 0.249510i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.32488 | − | 12.6871i | −0.436965 | − | 0.756846i | 0.560488 | − | 0.828162i | \(-0.310613\pi\) |
−0.997454 | + | 0.0713160i | \(0.977280\pi\) | |||||||
\(282\) | 2.58155 | − | 4.47137i | 0.153729 | − | 0.266266i | ||||
\(283\) | −9.46435 | + | 16.3927i | −0.562597 | + | 0.974447i | 0.434672 | + | 0.900589i | \(0.356864\pi\) |
−0.997269 | + | 0.0738576i | \(0.976469\pi\) | |||||||
\(284\) | 23.4036 | 1.38875 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.38156 | −0.0816934 | ||||||||
\(287\) | 2.42270 | − | 4.19623i | 0.143007 | − | 0.247696i | ||||
\(288\) | −4.64658 | + | 8.04812i | −0.273803 | + | 0.474240i | ||||
\(289\) | 5.24281 | + | 9.08082i | 0.308401 | + | 0.534166i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.68688 | − | 15.0461i | −0.509234 | − | 0.882019i | ||||
\(292\) | 22.0002 | 1.28747 | ||||||||
\(293\) | −5.59625 | −0.326937 | −0.163468 | − | 0.986549i | \(-0.552268\pi\) | ||||
−0.163468 | + | 0.986549i | \(0.552268\pi\) | |||||||
\(294\) | −1.37894 | − | 2.38840i | −0.0804216 | − | 0.139294i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 16.7225 | 0.971976 | ||||||||
\(297\) | −3.65028 | −0.211811 | ||||||||
\(298\) | 2.26508 | + | 3.92324i | 0.131213 | + | 0.227267i | ||||
\(299\) | 1.24543 | − | 2.15715i | 0.0720252 | − | 0.124751i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.94983 | + | 10.3054i | −0.342943 | + | 0.593994i | ||||
\(302\) | 1.77815 | − | 3.07984i | 0.102321 | − | 0.177225i | ||||
\(303\) | 14.5914 | 0.838256 | ||||||||
\(304\) | −11.6861 | − | 1.82671i | −0.670245 | − | 0.104769i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.15498 | + | 2.00049i | −0.0660261 | + | 0.114361i | ||||
\(307\) | −10.3160 | + | 17.8678i | −0.588764 | + | 1.01977i | 0.405631 | + | 0.914037i | \(0.367052\pi\) |
−0.994395 | + | 0.105732i | \(0.966282\pi\) | |||||||
\(308\) | 0.745314 | + | 1.29092i | 0.0424682 | + | 0.0735571i | ||||
\(309\) | −1.84838 | + | 3.20149i | −0.105151 | + | 0.182127i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.6587 | −1.39827 | −0.699134 | − | 0.714991i | \(-0.746431\pi\) | ||||
−0.699134 | + | 0.714991i | \(0.746431\pi\) | |||||||
\(312\) | 7.60787 | 0.430711 | ||||||||
\(313\) | −1.74928 | − | 3.02985i | −0.0988753 | − | 0.171257i | 0.812344 | − | 0.583178i | \(-0.198191\pi\) |
−0.911219 | + | 0.411921i | \(0.864858\pi\) | |||||||
\(314\) | −2.32546 | − | 4.02781i | −0.131233 | − | 0.227303i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.5990 | 0.596240 | ||||||||
\(317\) | −15.6854 | − | 27.1680i | −0.880982 | − | 1.52590i | −0.850251 | − | 0.526377i | \(-0.823550\pi\) |
−0.0307305 | − | 0.999528i | \(-0.509783\pi\) | |||||||
\(318\) | 1.22239 | − | 2.11724i | 0.0685482 | − | 0.118729i | ||||
\(319\) | 0.306602 | + | 0.531051i | 0.0171664 | + | 0.0297331i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.88866 | + | 3.27126i | −0.105415 | + | 0.182584i | ||||
\(322\) | 0.336707 | 0.0187639 | ||||||||
\(323\) | −10.9919 | − | 1.71818i | −0.611603 | − | 0.0956024i | ||||
\(324\) | −0.768356 | −0.0426865 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.0162383 | + | 0.0281256i | −0.000899358 | + | 0.00155773i | ||||
\(327\) | 3.23648 | + | 5.60575i | 0.178978 | + | 0.309999i | ||||
\(328\) | 3.67395 | − | 6.36347i | 0.202860 | − | 0.351364i | ||||
\(329\) | −6.18164 | − | 10.7069i | −0.340805 | − | 0.590292i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.7497 | 1.96498 | 0.982492 | − | 0.186305i | \(-0.0596512\pi\) | ||||
0.982492 | + | 0.186305i | \(0.0596512\pi\) | |||||||
\(332\) | 12.3171 | + | 21.3339i | 0.675990 | + | 1.17085i | ||||
\(333\) | 8.99677 | + | 15.5829i | 0.493020 | + | 0.853936i | ||||
\(334\) | 7.85415 | 0.429760 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.65889 | − | 2.87328i | −0.0904997 | − | 0.156750i | ||||
\(337\) | −13.2446 | + | 22.9403i | −0.721480 | + | 1.24964i | 0.238927 | + | 0.971038i | \(0.423204\pi\) |
−0.960407 | + | 0.278602i | \(0.910129\pi\) | |||||||
\(338\) | 0.905045 | + | 1.56758i | 0.0492279 | + | 0.0852653i | ||||
\(339\) | 6.38214 | − | 11.0542i | 0.346630 | − | 0.600382i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.79036 | 0.0969536 | ||||||||
\(342\) | 1.42120 | + | 3.68011i | 0.0768496 | + | 0.198998i | ||||
\(343\) | −14.8317 | −0.800836 | ||||||||
\(344\) | −9.02276 | + | 15.6279i | −0.486474 | + | 0.842599i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.86329 | + | 4.95936i | 0.153931 | + | 0.266617i | ||||
\(347\) | −17.1699 | + | 29.7392i | −0.921729 | + | 1.59648i | −0.124990 | + | 0.992158i | \(0.539890\pi\) |
−0.796739 | + | 0.604323i | \(0.793444\pi\) | |||||||
\(348\) | −0.794422 | − | 1.37598i | −0.0425855 | − | 0.0737602i | ||||
\(349\) | −21.4308 | −1.14717 | −0.573583 | − | 0.819148i | \(-0.694447\pi\) | ||||
−0.573583 | + | 0.819148i | \(0.694447\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.4953 | + | 18.1785i | 0.560200 | + | 0.970295i | ||||
\(352\) | 1.72869 | + | 2.99417i | 0.0921393 | + | 0.159590i | ||||
\(353\) | 19.5659 | 1.04139 | 0.520693 | − | 0.853744i | \(-0.325674\pi\) | ||||
0.520693 | + | 0.853744i | \(0.325674\pi\) | |||||||
\(354\) | 3.06786 | 0.163055 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.1861 | − | 24.5711i | 0.751863 | − | 1.30227i | ||||
\(357\) | −1.56033 | − | 2.70257i | −0.0825815 | − | 0.143035i | ||||
\(358\) | 2.77322 | − | 4.80335i | 0.146569 | − | 0.253865i | ||||
\(359\) | 8.23630 | − | 14.2657i | 0.434695 | − | 0.752914i | −0.562576 | − | 0.826746i | \(-0.690189\pi\) |
0.997271 | + | 0.0738319i | \(0.0235228\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.0683 | + | 12.7704i | −0.740435 | + | 0.672128i | ||||
\(362\) | 4.16951 | 0.219144 | ||||||||
\(363\) | 5.45641 | − | 9.45078i | 0.286387 | − | 0.496037i | ||||
\(364\) | 4.28588 | − | 7.42336i | 0.224641 | − | 0.389090i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.11786 | + | 1.93618i | −0.0584313 | + | 0.101206i | ||||
\(367\) | −6.36735 | − | 11.0286i | −0.332373 | − | 0.575687i | 0.650603 | − | 0.759418i | \(-0.274516\pi\) |
−0.982977 | + | 0.183730i | \(0.941183\pi\) | |||||||
\(368\) | −1.64728 | −0.0858705 | ||||||||
\(369\) | 7.90640 | 0.411591 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.92708 | − | 5.06984i | −0.151966 | − | 0.263213i | ||||
\(372\) | −4.63892 | −0.240517 | ||||||||
\(373\) | −19.3342 | −1.00109 | −0.500544 | − | 0.865711i | \(-0.666867\pi\) | ||||
−0.500544 | + | 0.865711i | \(0.666867\pi\) | |||||||
\(374\) | 0.429693 | + | 0.744250i | 0.0222189 | + | 0.0384843i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.37429 | − | 16.2368i | −0.483442 | − | 0.837346i | ||||
\(377\) | 1.76310 | − | 3.05377i | 0.0908041 | − | 0.157277i | ||||
\(378\) | −1.41873 | + | 2.45731i | −0.0729715 | + | 0.126390i | ||||
\(379\) | 9.85789 | 0.506366 | 0.253183 | − | 0.967418i | \(-0.418523\pi\) | ||||
0.253183 | + | 0.967418i | \(0.418523\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.24468 | 0.114999 | ||||||||
\(382\) | 3.36092 | − | 5.82128i | 0.171959 | − | 0.297843i | ||||
\(383\) | 10.1666 | − | 17.6091i | 0.519490 | − | 0.899784i | −0.480253 | − | 0.877130i | \(-0.659455\pi\) |
0.999743 | − | 0.0226536i | \(-0.00721149\pi\) | |||||||
\(384\) | −5.81109 | − | 10.0651i | −0.296546 | − | 0.513632i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.60220 | − | 7.97125i | −0.234246 | − | 0.405726i | ||||
\(387\) | −19.4171 | −0.987027 | ||||||||
\(388\) | −29.6849 | −1.50702 | ||||||||
\(389\) | 0.502617 | + | 0.870559i | 0.0254837 | + | 0.0441391i | 0.878486 | − | 0.477768i | \(-0.158554\pi\) |
−0.853002 | + | 0.521907i | \(0.825221\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.54942 | −0.0783574 | ||||||||
\(392\) | −10.0146 | −0.505816 | ||||||||
\(393\) | 9.12764 | + | 15.8095i | 0.460428 | + | 0.797486i | ||||
\(394\) | 1.02217 | − | 1.77046i | 0.0514964 | − | 0.0891944i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.21616 | + | 2.10644i | −0.0611141 | + | 0.105853i | ||||
\(397\) | 4.93111 | − | 8.54093i | 0.247485 | − | 0.428657i | −0.715342 | − | 0.698774i | \(-0.753729\pi\) |
0.962827 | + | 0.270117i | \(0.0870625\pi\) | |||||||
\(398\) | 5.96059 | 0.298777 | ||||||||
\(399\) | −5.26557 | − | 0.823085i | −0.263608 | − | 0.0412058i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.9159 | + | 25.8351i | −0.744865 | + | 1.29014i | 0.205393 | + | 0.978680i | \(0.434153\pi\) |
−0.950258 | + | 0.311464i | \(0.899181\pi\) | |||||||
\(402\) | −1.27185 | + | 2.20291i | −0.0634342 | + | 0.109871i | ||||
\(403\) | −5.14769 | − | 8.91606i | −0.256425 | − | 0.444140i | ||||
\(404\) | 12.4655 | − | 21.5909i | 0.620181 | − | 1.07419i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.476660 | 0.0236562 | ||||||||
\(407\) | 6.69420 | 0.331819 | ||||||||
\(408\) | −2.36620 | − | 4.09838i | −0.117144 | − | 0.202900i | ||||
\(409\) | −13.8221 | − | 23.9406i | −0.683458 | − | 1.18378i | −0.973919 | − | 0.226898i | \(-0.927142\pi\) |
0.290460 | − | 0.956887i | \(-0.406192\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.27866 | 0.260377 | ||||||||
\(412\) | 3.15815 | + | 5.47008i | 0.155591 | + | 0.269491i | ||||
\(413\) | 3.67307 | − | 6.36194i | 0.180740 | − | 0.313051i | ||||
\(414\) | 0.274708 | + | 0.475809i | 0.0135012 | + | 0.0233847i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 9.94070 | − | 17.2178i | 0.487383 | − | 0.844172i | ||||
\(417\) | 6.22232 | 0.304708 | ||||||||
\(418\) | 1.45006 | + | 0.226666i | 0.0709249 | + | 0.0110866i | ||||
\(419\) | −11.2902 | −0.551562 | −0.275781 | − | 0.961220i | \(-0.588936\pi\) | ||||
−0.275781 | + | 0.961220i | \(0.588936\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.27471 | + | 3.93991i | −0.110863 | + | 0.192019i | −0.916118 | − | 0.400908i | \(-0.868695\pi\) |
0.805256 | + | 0.592928i | \(0.202028\pi\) | |||||||
\(422\) | 5.24845 | + | 9.09059i | 0.255491 | + | 0.442523i | ||||
\(423\) | 10.0868 | − | 17.4709i | 0.490438 | − | 0.849463i | ||||
\(424\) | −4.43883 | − | 7.68828i | −0.215569 | − | 0.373376i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.46362 | 0.313163 | ||||||||
\(427\) | 2.67676 | + | 4.63629i | 0.129538 | + | 0.224366i | ||||
\(428\) | 3.22698 | + | 5.58929i | 0.155982 | + | 0.270168i | ||||
\(429\) | 3.04551 | 0.147039 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.4517 | − | 28.4952i | −0.792451 | − | 1.37256i | −0.924445 | − | 0.381314i | \(-0.875472\pi\) |
0.131995 | − | 0.991250i | \(-0.457862\pi\) | |||||||
\(432\) | 6.94089 | − | 12.0220i | 0.333943 | − | 0.578407i | ||||
\(433\) | 11.1547 | + | 19.3204i | 0.536059 | + | 0.928481i | 0.999111 | + | 0.0421503i | \(0.0134208\pi\) |
−0.463052 | + | 0.886331i | \(0.653246\pi\) | |||||||
\(434\) | 0.695848 | − | 1.20524i | 0.0334018 | − | 0.0578536i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.0597 | 0.529664 | ||||||||
\(437\) | −1.66110 | + | 2.05978i | −0.0794611 | + | 0.0985325i | ||||
\(438\) | 6.07605 | 0.290325 | ||||||||
\(439\) | −2.85287 | + | 4.94131i | −0.136160 | + | 0.235836i | −0.926040 | − | 0.377425i | \(-0.876809\pi\) |
0.789880 | + | 0.613261i | \(0.210143\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.38791 | − | 9.33214i | −0.256567 | − | 0.444388i | ||||
\(442\) | 2.47092 | − | 4.27976i | 0.117530 | − | 0.203568i | ||||
\(443\) | 5.78881 | + | 10.0265i | 0.275034 | + | 0.476374i | 0.970144 | − | 0.242530i | \(-0.0779774\pi\) |
−0.695109 | + | 0.718904i | \(0.744644\pi\) | |||||||
\(444\) | −17.3450 | −0.823158 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.21412 | − | 5.56702i | −0.152193 | − | 0.263606i | ||||
\(447\) | −4.99315 | − | 8.64839i | −0.236168 | − | 0.409055i | ||||
\(448\) | −3.69147 | −0.174406 | ||||||||
\(449\) | −25.4726 | −1.20213 | −0.601063 | − | 0.799202i | \(-0.705256\pi\) | ||||
−0.601063 | + | 0.799202i | \(0.705256\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.47072 | − | 2.54737i | 0.0692537 | − | 0.119951i | ||||
\(452\) | −10.9046 | − | 18.8872i | −0.512907 | − | 0.888381i | ||||
\(453\) | −3.91975 | + | 6.78921i | −0.184166 | + | 0.318985i | ||||
\(454\) | −1.55465 | + | 2.69274i | −0.0729634 | + | 0.126376i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.98509 | − | 1.24818i | −0.373936 | − | 0.0584516i | ||||
\(457\) | 6.92830 | 0.324092 | 0.162046 | − | 0.986783i | \(-0.448191\pi\) | ||||
0.162046 | + | 0.986783i | \(0.448191\pi\) | |||||||
\(458\) | −0.138253 | + | 0.239461i | −0.00646014 | + | 0.0111893i | ||||
\(459\) | 6.52853 | − | 11.3077i | 0.304726 | − | 0.527800i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.2473 | + | 28.1411i | −0.756712 | + | 1.31066i | 0.187806 | + | 0.982206i | \(0.439862\pi\) |
−0.944519 | + | 0.328458i | \(0.893471\pi\) | |||||||
\(462\) | 0.205841 | + | 0.356528i | 0.00957661 | + | 0.0165872i | ||||
\(463\) | −21.5062 | −0.999477 | −0.499738 | − | 0.866176i | \(-0.666571\pi\) | ||||
−0.499738 | + | 0.866176i | \(0.666571\pi\) | |||||||
\(464\) | −2.33198 | −0.108259 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.68875 | − | 2.92499i | −0.0782296 | − | 0.135498i | ||||
\(467\) | 16.9509 | 0.784392 | 0.392196 | − | 0.919882i | \(-0.371715\pi\) | ||||
0.392196 | + | 0.919882i | \(0.371715\pi\) | |||||||
\(468\) | 13.9868 | 0.646542 | ||||||||
\(469\) | 3.04551 | + | 5.27499i | 0.140629 | + | 0.243576i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.12624 | + | 8.87891i | 0.236205 | + | 0.409119i | ||||
\(472\) | 5.57011 | − | 9.64771i | 0.256385 | − | 0.444072i | ||||
\(473\) | −3.61191 | + | 6.25601i | −0.166076 | + | 0.287652i | ||||
\(474\) | 2.92724 | 0.134453 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.33198 | −0.244391 | ||||||||
\(477\) | 4.77621 | − | 8.27265i | 0.218688 | − | 0.378778i | ||||
\(478\) | 0.862364 | − | 1.49366i | 0.0394436 | − | 0.0683183i | ||||
\(479\) | −4.42894 | − | 7.67115i | −0.202364 | − | 0.350504i | 0.746926 | − | 0.664907i | \(-0.231529\pi\) |
−0.949290 | + | 0.314403i | \(0.898196\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.2473 | − | 33.3373i | −0.877601 | − | 1.52005i | ||||
\(482\) | −8.14611 | −0.371045 | ||||||||
\(483\) | −0.742237 | −0.0337730 | ||||||||
\(484\) | −9.32284 | − | 16.1476i | −0.423765 | − | 0.733983i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7.45432 | −0.338135 | ||||||||
\(487\) | 30.0628 | 1.36227 | 0.681137 | − | 0.732156i | \(-0.261486\pi\) | ||||
0.681137 | + | 0.732156i | \(0.261486\pi\) | |||||||
\(488\) | 4.05924 | + | 7.03081i | 0.183753 | + | 0.318270i | ||||
\(489\) | 0.0357958 | − | 0.0620001i | 0.00161874 | − | 0.00280374i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.55017 | + | 2.68497i | −0.0699580 | + | 0.121171i | −0.898883 | − | 0.438190i | \(-0.855620\pi\) |
0.828925 | + | 0.559360i | \(0.188953\pi\) | |||||||
\(492\) | −3.81072 | + | 6.60036i | −0.171800 | + | 0.297567i | ||||
\(493\) | −2.19343 | −0.0987873 | ||||||||
\(494\) | −3.04045 | − | 7.87306i | −0.136796 | − | 0.354226i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.40432 | + | 5.89645i | −0.152858 | + | 0.264759i | ||||
\(497\) | 7.73874 | − | 13.4039i | 0.347130 | − | 0.601246i | ||||
\(498\) | 3.40176 | + | 5.89202i | 0.152436 | + | 0.264028i | ||||
\(499\) | −16.0696 | + | 27.8333i | −0.719372 | + | 1.24599i | 0.241877 | + | 0.970307i | \(0.422237\pi\) |
−0.961249 | + | 0.275682i | \(0.911096\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.3137 | −0.773519 | ||||||||
\(502\) | 9.16117 | 0.408883 | ||||||||
\(503\) | −4.20911 | − | 7.29040i | −0.187675 | − | 0.325063i | 0.756800 | − | 0.653647i | \(-0.226762\pi\) |
−0.944475 | + | 0.328584i | \(0.893429\pi\) | |||||||
\(504\) | 2.00914 | + | 3.47993i | 0.0894940 | + | 0.155008i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.204402 | 0.00908676 | ||||||||
\(507\) | −1.99508 | − | 3.45558i | −0.0886047 | − | 0.153468i | ||||
\(508\) | 1.91764 | − | 3.32144i | 0.0850813 | − | 0.147365i | ||||
\(509\) | −10.1725 | − | 17.6193i | −0.450888 | − | 0.780962i | 0.547553 | − | 0.836771i | \(-0.315559\pi\) |
−0.998441 | + | 0.0558093i | \(0.982226\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.27471 | − | 12.6002i | 0.321814 | − | 0.557398i | ||||
\(512\) | −22.8217 | −1.00859 | ||||||||
\(513\) | −8.03329 | − | 20.8017i | −0.354678 | − | 0.918419i | ||||
\(514\) | −6.55582 | −0.289165 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.35864 | − | 16.2096i | 0.411991 | − | 0.713589i | ||||
\(517\) | −3.75263 | − | 6.49975i | −0.165041 | − | 0.285859i | ||||
\(518\) | 2.60179 | − | 4.50643i | 0.114316 | − | 0.198001i | ||||
\(519\) | −6.31184 | − | 10.9324i | −0.277059 | − | 0.479880i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.3502 | 0.672507 | 0.336253 | − | 0.941772i | \(-0.390840\pi\) | ||||
0.336253 | + | 0.941772i | \(0.390840\pi\) | |||||||
\(522\) | 0.388891 | + | 0.673580i | 0.0170213 | + | 0.0294818i | ||||
\(523\) | −6.61835 | − | 11.4633i | −0.289400 | − | 0.501256i | 0.684267 | − | 0.729232i | \(-0.260122\pi\) |
−0.973667 | + | 0.227976i | \(0.926789\pi\) | |||||||
\(524\) | 31.1910 | 1.36259 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.53638 | + | 6.12519i | 0.154193 | + | 0.267071i | ||||
\(527\) | −3.20207 | + | 5.54614i | −0.139484 | + | 0.241594i | ||||
\(528\) | −1.00704 | − | 1.74425i | −0.0438260 | − | 0.0759088i | ||||
\(529\) | 11.3157 | − | 19.5994i | 0.491989 | − | 0.852149i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.9870 | 0.520190 | ||||||||
\(532\) | −5.71630 | + | 7.08827i | −0.247833 | + | 0.307316i | ||||
\(533\) | −16.9146 | −0.732653 | ||||||||
\(534\) | 3.91794 | − | 6.78607i | 0.169546 | − | 0.293662i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.61844 | + | 7.99937i | 0.199486 | + | 0.345520i | ||||
\(537\) | −6.11329 | + | 10.5885i | −0.263808 | + | 0.456928i | ||||
\(538\) | 4.57073 | + | 7.91673i | 0.197058 | + | 0.341315i | ||||
\(539\) | −4.00897 | −0.172679 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.8704 | + | 24.0242i | 0.596335 | + | 1.03288i | 0.993357 | + | 0.115073i | \(0.0367102\pi\) |
−0.397022 | + | 0.917809i | \(0.629956\pi\) | |||||||
\(542\) | 2.81194 | + | 4.87043i | 0.120783 | + | 0.209203i | ||||
\(543\) | −9.19127 | −0.394435 | ||||||||
\(544\) | −12.3670 | −0.530232 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.18368 | − | 2.05019i | 0.0506568 | − | 0.0877401i | ||||
\(547\) | −8.53008 | − | 14.7745i | −0.364720 | − | 0.631714i | 0.624011 | − | 0.781415i | \(-0.285502\pi\) |
−0.988731 | + | 0.149702i | \(0.952169\pi\) | |||||||
\(548\) | 4.50957 | − | 7.81080i | 0.192639 | − | 0.333661i | ||||
\(549\) | −4.36777 | + | 7.56520i | −0.186412 | + | 0.322875i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.35153 | + | 2.91593i | −0.100179 | + | 0.124223i | ||||
\(552\) | −1.12558 | −0.0479080 | ||||||||
\(553\) | 3.50472 | − | 6.07035i | 0.149036 | − | 0.258137i | ||||
\(554\) | −2.59120 | + | 4.48808i | −0.110089 | + | 0.190680i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.31574 | − | 9.20713i | 0.225438 | − | 0.390469i | ||||
\(557\) | 13.2708 | + | 22.9856i | 0.562300 | + | 0.973932i | 0.997295 | + | 0.0734992i | \(0.0234166\pi\) |
−0.434995 | + | 0.900433i | \(0.643250\pi\) | |||||||
\(558\) | 2.27088 | 0.0961340 | ||||||||
\(559\) | 41.5401 | 1.75696 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.947216 | − | 1.64063i | −0.0399915 | − | 0.0692673i | ||||
\(562\) | −6.91298 | −0.291606 | ||||||||
\(563\) | 35.5594 | 1.49865 | 0.749325 | − | 0.662203i | \(-0.230378\pi\) | ||||
0.749325 | + | 0.662203i | \(0.230378\pi\) | |||||||
\(564\) | 9.72326 | + | 16.8412i | 0.409423 | + | 0.709141i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.46607 | + | 7.73546i | 0.187723 | + | 0.325146i | ||||
\(567\) | −0.254068 | + | 0.440059i | −0.0106699 | + | 0.0184808i | ||||
\(568\) | 11.7356 | − | 20.3266i | 0.492414 | − | 0.852886i | ||||
\(569\) | −14.9713 | −0.627628 | −0.313814 | − | 0.949485i | \(-0.601607\pi\) | ||||
−0.313814 | + | 0.949485i | \(0.601607\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.92724 | 0.248047 | 0.124024 | − | 0.992279i | \(-0.460420\pi\) | ||||
0.124024 | + | 0.992279i | \(0.460420\pi\) | |||||||
\(572\) | 2.60179 | − | 4.50643i | 0.108786 | − | 0.188423i | ||||
\(573\) | −7.40881 | + | 12.8324i | −0.309508 | + | 0.536083i | ||||
\(574\) | −1.14323 | − | 1.98013i | −0.0477175 | − | 0.0826492i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.01175 | − | 5.21651i | −0.125490 | − | 0.217355i | ||||
\(577\) | 14.5559 | 0.605970 | 0.302985 | − | 0.952995i | \(-0.402017\pi\) | ||||
0.302985 | + | 0.952995i | \(0.402017\pi\) | |||||||
\(578\) | 4.94800 | 0.205810 | ||||||||
\(579\) | 10.1451 | + | 17.5718i | 0.421616 | + | 0.730260i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.2914 | 0.675880 | ||||||||
\(582\) | −8.19839 | −0.339834 | ||||||||
\(583\) | −1.77691 | − | 3.07770i | −0.0735922 | − | 0.127465i | ||||
\(584\) | 11.0319 | − | 19.1078i | 0.456503 | − | 0.790686i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.32039 | + | 2.28698i | −0.0545448 | + | 0.0944744i | ||||
\(587\) | 10.2919 | − | 17.8262i | 0.424794 | − | 0.735765i | −0.571607 | − | 0.820527i | \(-0.693680\pi\) |
0.996401 | + | 0.0847626i | \(0.0270132\pi\) | |||||||
\(588\) | 10.3874 | 0.428371 | ||||||||
\(589\) | 3.94011 | + | 10.2027i | 0.162350 | + | 0.420395i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.25328 | + | 3.90280i | −0.0926877 | + | 0.160540i | ||||
\(592\) | −12.7288 | + | 22.0469i | −0.523151 | + | 0.906124i | ||||
\(593\) | 7.16609 | + | 12.4120i | 0.294276 | + | 0.509701i | 0.974816 | − | 0.223010i | \(-0.0715882\pi\) |
−0.680540 | + | 0.732711i | \(0.738255\pi\) | |||||||
\(594\) | −0.861254 | + | 1.49174i | −0.0353377 | + | 0.0612066i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17.0626 | −0.698912 | ||||||||
\(597\) | −13.1395 | −0.537765 | ||||||||
\(598\) | −0.587699 | − | 1.01792i | −0.0240328 | − | 0.0416260i | ||||
\(599\) | −1.25008 | − | 2.16521i | −0.0510770 | − | 0.0884680i | 0.839356 | − | 0.543581i | \(-0.182932\pi\) |
−0.890434 | + | 0.455113i | \(0.849599\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.5259 | 0.592524 | 0.296262 | − | 0.955107i | \(-0.404260\pi\) | ||||
0.296262 | + | 0.955107i | \(0.404260\pi\) | |||||||
\(602\) | 2.80763 | + | 4.86296i | 0.114430 | + | 0.198199i | ||||
\(603\) | −4.96948 | + | 8.60739i | −0.202373 | + | 0.350520i | ||||
\(604\) | 6.69730 | + | 11.6001i | 0.272509 | + | 0.472000i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.44273 | − | 5.96299i | 0.139851 | − | 0.242230i | ||||
\(607\) | −31.8704 | −1.29358 | −0.646789 | − | 0.762669i | \(-0.723889\pi\) | ||||
−0.646789 | + | 0.762669i | \(0.723889\pi\) | |||||||
\(608\) | −13.2584 | + | 16.4406i | −0.537700 | + | 0.666754i | ||||
\(609\) | −1.05075 | −0.0425785 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.5793 | + | 37.3764i | −0.873004 | + | 1.51209i | ||||
\(612\) | −4.35019 | − | 7.53475i | −0.175846 | − | 0.304574i | ||||
\(613\) | −10.0244 | + | 17.3628i | −0.404882 | + | 0.701277i | −0.994308 | − | 0.106546i | \(-0.966021\pi\) |
0.589425 | + | 0.807823i | \(0.299354\pi\) | |||||||
\(614\) | 4.86794 | + | 8.43152i | 0.196454 | + | 0.340268i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.49493 | 0.0602325 | ||||||||
\(617\) | 10.0410 | + | 17.3914i | 0.404234 | + | 0.700153i | 0.994232 | − | 0.107251i | \(-0.0342050\pi\) |
−0.589998 | + | 0.807404i | \(0.700872\pi\) | |||||||
\(618\) | 0.872222 | + | 1.51073i | 0.0350859 | + | 0.0607706i | ||||
\(619\) | 5.62217 | 0.225974 | 0.112987 | − | 0.993596i | \(-0.463958\pi\) | ||||
0.112987 | + | 0.993596i | \(0.463958\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.55278 | − | 2.68950i | −0.0623111 | − | 0.107926i | ||||
\(622\) | −5.81803 | + | 10.0771i | −0.233282 | + | 0.404056i | ||||
\(623\) | −9.38171 | − | 16.2496i | −0.375870 | − | 0.651026i | ||||
\(624\) | −5.79095 | + | 10.0302i | −0.231823 | + | 0.401530i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.65092 | −0.0659839 | ||||||||
\(627\) | −3.19652 | − | 0.499662i | −0.127657 | − | 0.0199546i | ||||
\(628\) | 17.5174 | 0.699022 | ||||||||
\(629\) | −11.9726 | + | 20.7371i | −0.477378 | + | 0.826844i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.42184 | + | 4.19475i | 0.0964120 | + | 0.166990i | 0.910197 | − | 0.414176i | \(-0.135930\pi\) |
−0.813785 | + | 0.581166i | \(0.802597\pi\) | |||||||
\(632\) | 5.31481 | − | 9.20551i | 0.211412 | − | 0.366176i | ||||
\(633\) | −11.5697 | − | 20.0393i | −0.459854 | − | 0.796491i | ||||
\(634\) | −14.8034 | −0.587918 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.60407 | + | 7.97448i | 0.182563 | + | 0.316209i | ||||
\(637\) | 11.5267 | + | 19.9648i | 0.456703 | + | 0.791033i | ||||
\(638\) | 0.289361 | 0.0114559 | ||||||||
\(639\) | 25.2552 | 0.999078 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.6503 | − | 21.9110i | 0.499658 | − | 0.865433i | −0.500342 | − | 0.865828i | \(-0.666792\pi\) |
1.00000 | 0.000394734i | \(0.000125648\pi\) | ||||||||
\(642\) | 0.891229 | + | 1.54365i | 0.0351740 | + | 0.0609232i | ||||
\(643\) | −6.97283 | + | 12.0773i | −0.274981 | + | 0.476282i | −0.970130 | − | 0.242584i | \(-0.922005\pi\) |
0.695149 | + | 0.718866i | \(0.255338\pi\) | |||||||
\(644\) | −0.634095 | + | 1.09828i | −0.0249868 | + | 0.0432785i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.29560 | + | 4.08658i | −0.129664 | + | 0.160784i | ||||
\(647\) | −2.51360 | −0.0988200 | −0.0494100 | − | 0.998779i | \(-0.515734\pi\) | ||||
−0.0494100 | + | 0.998779i | \(0.515734\pi\) | |||||||
\(648\) | −0.385288 | + | 0.667338i | −0.0151355 | + | 0.0262155i | ||||
\(649\) | 2.22978 | − | 3.86209i | 0.0875264 | − | 0.151600i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.53393 | + | 2.65684i | −0.0601194 | + | 0.104130i | ||||
\(652\) | −0.0611608 | − | 0.105934i | −0.00239524 | − | 0.00414868i | ||||
\(653\) | 1.92873 | 0.0754770 | 0.0377385 | − | 0.999288i | \(-0.487985\pi\) | ||||
0.0377385 | + | 0.999288i | \(0.487985\pi\) | |||||||
\(654\) | 3.05448 | 0.119440 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.59306 | + | 9.68747i | 0.218372 | + | 0.378232i | ||||
\(657\) | 23.7408 | 0.926217 | ||||||||
\(658\) | −5.83404 | −0.227434 | ||||||||
\(659\) | −7.90042 | − | 13.6839i | −0.307757 | − | 0.533050i | 0.670115 | − | 0.742258i | \(-0.266245\pi\) |
−0.977871 | + | 0.209208i | \(0.932912\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.20178 | − | 14.2059i | −0.319012 | − | 0.552546i | 0.661270 | − | 0.750148i | \(-0.270018\pi\) |
−0.980282 | + | 0.197602i | \(0.936685\pi\) | |||||||
\(662\) | 8.43486 | − | 14.6096i | 0.327830 | − | 0.567819i | ||||
\(663\) | −5.44691 | + | 9.43432i | −0.211540 | + | 0.366399i | ||||
\(664\) | 24.7054 | 0.958755 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.49086 | 0.329014 | ||||||||
\(667\) | −0.260850 | + | 0.451805i | −0.0101001 | + | 0.0174940i | ||||
\(668\) | −14.7911 | + | 25.6190i | −0.572286 | + | 0.991228i | ||||
\(669\) | 7.08521 | + | 12.2719i | 0.273930 | + | 0.474461i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.62496 | + | 2.81451i | 0.0627308 | + | 0.108653i | ||||
\(672\) | −5.92434 | −0.228536 | ||||||||
\(673\) | 17.0878 | 0.658686 | 0.329343 | − | 0.944210i | \(-0.393173\pi\) | ||||
0.329343 | + | 0.944210i | \(0.393173\pi\) | |||||||
\(674\) | 6.24992 | + | 10.8252i | 0.240738 | + | 0.416970i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.81761 | −0.262216 | ||||||||
\(677\) | −4.57680 | −0.175901 | −0.0879504 | − | 0.996125i | \(-0.528032\pi\) | ||||
−0.0879504 | + | 0.996125i | \(0.528032\pi\) | |||||||
\(678\) | −3.01163 | − | 5.21630i | −0.115661 | − | 0.200331i | ||||
\(679\) | −9.81574 | + | 17.0014i | −0.376693 | + | 0.652452i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.42708 | − | 5.93587i | 0.131326 | − | 0.227463i | ||||
\(682\) | 0.422422 | − | 0.731656i | 0.0161754 | − | 0.0280166i | ||||
\(683\) | −29.0692 | −1.11230 | −0.556151 | − | 0.831082i | \(-0.687722\pi\) | ||||
−0.556151 | + | 0.831082i | \(0.687722\pi\) | |||||||
\(684\) | −14.6804 | − | 2.29475i | −0.561318 | − | 0.0877420i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.49942 | + | 6.06117i | −0.133608 | + | 0.231416i | ||||
\(687\) | 0.304765 | − | 0.527869i | 0.0116275 | − | 0.0201395i | ||||
\(688\) | −13.7359 | − | 23.7912i | −0.523675 | − | 0.907031i | ||||
\(689\) | −10.2180 | + | 17.6981i | −0.389276 | + | 0.674245i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.07833 | −0.231230 | −0.115615 | − | 0.993294i | \(-0.536884\pi\) | ||||
−0.115615 | + | 0.993294i | \(0.536884\pi\) | |||||||
\(692\) | −21.5689 | −0.819925 | ||||||||
\(693\) | 0.804279 | + | 1.39305i | 0.0305521 | + | 0.0529177i | ||||
\(694\) | 8.10220 | + | 14.0334i | 0.307555 | + | 0.532701i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.59343 | −0.0603989 | ||||||||
\(697\) | 5.26078 | + | 9.11194i | 0.199266 | + | 0.345139i | ||||
\(698\) | −5.05643 | + | 8.75799i | −0.191389 | + | 0.331495i | ||||
\(699\) | 3.72267 | + | 6.44786i | 0.140804 | + | 0.243881i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.20569 | + | 9.01651i | −0.196616 | + | 0.340549i | −0.947429 | − | 0.319966i | \(-0.896329\pi\) |
0.750813 | + | 0.660515i | \(0.229662\pi\) | |||||||
\(702\) | 9.90517 | 0.373847 | ||||||||
\(703\) | 14.7322 | + | 38.1481i | 0.555634 | + | 1.43878i | ||||
\(704\) | −2.24095 | −0.0844589 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.61640 | − | 7.99585i | 0.173741 | − | 0.300928i | ||||
\(707\) | −8.24380 | − | 14.2787i | −0.310040 | − | 0.537005i | ||||
\(708\) | −5.77746 | + | 10.0069i | −0.217130 | + | 0.376081i | ||||
\(709\) | 0.265572 | + | 0.459984i | 0.00997377 | + | 0.0172751i | 0.870969 | − | 0.491338i | \(-0.163492\pi\) |
−0.860995 | + | 0.508613i | \(0.830159\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.4375 | 0.428941 | ||||||||
\(712\) | −14.2271 | − | 24.6421i | −0.533183 | − | 0.923500i | ||||
\(713\) | 0.761599 | + | 1.31913i | 0.0285221 | + | 0.0494017i | ||||
\(714\) | −1.47259 | −0.0551103 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.4452 | + | 18.0916i | 0.390355 | + | 0.676114i | ||||
\(717\) | −1.90100 | + | 3.29262i | −0.0709940 | + | 0.122965i | ||||
\(718\) | −3.88657 | − | 6.73174i | −0.145046 | − | 0.251226i | ||||
\(719\) | −11.2135 | + | 19.4224i | −0.418194 | + | 0.724334i | −0.995758 | − | 0.0920118i | \(-0.970670\pi\) |
0.577564 | + | 0.816346i | \(0.304004\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.17716 | 0.155566 | ||||||||
\(722\) | 1.89951 | + | 8.76227i | 0.0706924 | + | 0.326098i | ||||
\(723\) | 17.9573 | 0.667839 | ||||||||
\(724\) | −7.85212 | + | 13.6003i | −0.291822 | + | 0.505450i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.57479 | − | 4.45967i | −0.0955595 | − | 0.165514i | ||||
\(727\) | 22.9867 | − | 39.8141i | 0.852529 | − | 1.47662i | −0.0263888 | − | 0.999652i | \(-0.508401\pi\) |
0.878918 | − | 0.476972i | \(-0.158266\pi\) | |||||||
\(728\) | −4.29826 | − | 7.44480i | −0.159304 | − | 0.275923i | ||||
\(729\) | 15.1354 | 0.560570 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.9198 | − | 22.3778i | −0.477856 | − | 0.827671i | ||||
\(732\) | −4.21035 | − | 7.29254i | −0.155619 | − | 0.269540i | ||||
\(733\) | 42.5178 | 1.57043 | 0.785215 | − | 0.619223i | \(-0.212552\pi\) | ||||
0.785215 | + | 0.619223i | \(0.212552\pi\) | |||||||
\(734\) | −6.00930 | −0.221807 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.47072 | + | 2.54737i | −0.0542116 | + | 0.0938972i | ||||
\(737\) | 1.84881 | + | 3.20224i | 0.0681019 | + | 0.117956i | ||||
\(738\) | 1.86545 | − | 3.23106i | 0.0686682 | − | 0.118937i | ||||
\(739\) | 1.70889 | − | 2.95988i | 0.0628624 | − | 0.108881i | −0.832881 | − | 0.553452i | \(-0.813310\pi\) |
0.895744 | + | 0.444571i | \(0.146644\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.70237 | + | 17.3554i | 0.246218 | + | 0.637566i | ||||
\(742\) | −2.76248 | −0.101414 | ||||||||
\(743\) | 4.86044 | − | 8.41853i | 0.178312 | − | 0.308846i | −0.762990 | − | 0.646410i | \(-0.776270\pi\) |
0.941303 | + | 0.337564i | \(0.109603\pi\) | |||||||
\(744\) | −2.32616 | + | 4.02903i | −0.0852812 | + | 0.147711i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.56175 | + | 7.90119i | −0.167018 | + | 0.289283i | ||||
\(747\) | 13.2916 | + | 23.0217i | 0.486314 | + | 0.842321i | ||||
\(748\) | −3.23683 | −0.118350 | ||||||||
\(749\) | 4.26819 | 0.155956 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.69265 | + | 9.85996i | 0.207728 | + | 0.359795i | 0.950998 | − | 0.309196i | \(-0.100060\pi\) |
−0.743271 | + | 0.668991i | \(0.766727\pi\) | |||||||
\(752\) | 28.5420 | 1.04082 | ||||||||
\(753\) | −20.1949 | −0.735943 | ||||||||
\(754\) | −0.831977 | − | 1.44103i | −0.0302988 | − | 0.0524791i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.34356 | − | 9.25532i | −0.194344 | − | 0.336613i | ||||
\(757\) | −11.3921 | + | 19.7317i | −0.414053 | + | 0.717160i | −0.995328 | − | 0.0965464i | \(-0.969220\pi\) |
0.581276 | + | 0.813707i | \(0.302554\pi\) | |||||||
\(758\) | 2.32589 | − | 4.02856i | 0.0844801 | − | 0.146324i | ||||
\(759\) | −0.450583 | −0.0163551 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.7665 | −1.33279 | −0.666393 | − | 0.745601i | \(-0.732163\pi\) | ||||
−0.666393 | + | 0.745601i | \(0.732163\pi\) | |||||||
\(762\) | 0.529615 | − | 0.917319i | 0.0191859 | − | 0.0332310i | ||||
\(763\) | 3.65706 | − | 6.33421i | 0.132394 | − | 0.229314i | ||||
\(764\) | 12.6587 | + | 21.9255i | 0.457976 | + | 0.793238i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.79747 | − | 8.30945i | −0.173339 | − | 0.300233i | ||||
\(767\) | −25.6444 | −0.925965 | ||||||||
\(768\) | 1.04955 | 0.0378724 | ||||||||
\(769\) | 10.4004 | + | 18.0140i | 0.375049 | + | 0.649603i | 0.990334 | − | 0.138701i | \(-0.0442927\pi\) |
−0.615286 | + | 0.788304i | \(0.710959\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.4517 | 0.520464 | ||||||||
\(772\) | 34.6679 | 1.24772 | ||||||||
\(773\) | −10.5046 | − | 18.1944i | −0.377823 | − | 0.654409i | 0.612922 | − | 0.790143i | \(-0.289994\pi\) |
−0.990745 | + | 0.135735i | \(0.956661\pi\) | |||||||
\(774\) | −4.58131 | + | 7.93506i | −0.164672 | + | 0.285220i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.8853 | + | 25.7821i | −0.534351 | + | 0.925523i | ||||
\(777\) | −5.73539 | + | 9.93398i | −0.205756 | + | 0.356380i | ||||
\(778\) | 0.474354 | 0.0170064 | ||||||||
\(779\) | 17.7533 | + | 2.77509i | 0.636077 | + | 0.0994280i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.69788 | − | 8.13697i | 0.168103 | − | 0.291164i | ||||
\(782\) | −0.365572 | + | 0.633190i | −0.0130728 | + | 0.0226428i | ||||
\(783\) | −2.19820 | − | 3.80740i | −0.0785573 | − | 0.136065i | ||||
\(784\) | 7.62292 | − | 13.2033i | 0.272247 | − | 0.471546i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.61437 | 0.307264 | ||||||||
\(787\) | −18.0606 | −0.643791 | −0.321896 | − | 0.946775i | \(-0.604320\pi\) | ||||
−0.321896 | + | 0.946775i | \(0.604320\pi\) | |||||||
\(788\) | 3.84997 | + | 6.66834i | 0.137149 | + | 0.237550i | ||||
\(789\) | −7.79560 | − | 13.5024i | −0.277531 | − | 0.480697i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.4230 | −0.512823 | ||||||||
\(792\) | 1.21967 | + | 2.11253i | 0.0433390 | + | 0.0750653i | ||||
\(793\) | 9.34422 | − | 16.1847i | 0.331823 | − | 0.574734i | ||||
\(794\) | −2.32691 | − | 4.03033i | −0.0825789 | − | 0.143031i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.2251 | + | 19.4425i | −0.397864 | + | 0.689121i | ||||
\(797\) | 24.2571 | 0.859229 | 0.429615 | − | 0.903012i | \(-0.358649\pi\) | ||||
0.429615 | + | 0.903012i | \(0.358649\pi\) | |||||||
\(798\) | −1.57873 | + | 1.95765i | −0.0558866 | + | 0.0692999i | ||||
\(799\) | 26.8463 | 0.949756 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.3085 | − | 26.5150i | 0.540898 | − | 0.936863i | ||||
\(802\) | 7.03857 | + | 12.1912i | 0.248541 | + | 0.430485i | ||||
\(803\) | 4.41619 | − | 7.64906i | 0.155844 | − | 0.269930i | ||||
\(804\) | −4.79036 | − | 8.29715i | −0.168943 | − | 0.292618i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.85822 | −0.171124 | ||||||||
\(807\) | −10.0757 | − | 17.4517i | −0.354682 | − | 0.614327i | ||||
\(808\) | −12.5015 | − | 21.6532i | −0.439801 | − | 0.761758i | ||||
\(809\) | −4.27192 | −0.150193 | −0.0750964 | − | 0.997176i | \(-0.523926\pi\) | ||||
−0.0750964 | + | 0.997176i | \(0.523926\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.09120 | − | 8.81821i | −0.178776 | − | 0.309649i | 0.762685 | − | 0.646770i | \(-0.223880\pi\) |
−0.941462 | + | 0.337120i | \(0.890547\pi\) | |||||||
\(812\) | −0.897657 | + | 1.55479i | −0.0315016 | + | 0.0545623i | ||||
\(813\) | −6.19865 | − | 10.7364i | −0.217396 | − | 0.376541i | ||||
\(814\) | 1.57944 | − | 2.73568i | 0.0553595 | − | 0.0958854i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.20440 | 0.252205 | ||||||||
\(817\) | −43.5998 | − | 6.81528i | −1.52536 | − | 0.238436i | ||||
\(818\) | −13.0448 | −0.456102 | ||||||||
\(819\) | 4.62496 | − | 8.01066i | 0.161609 | − | 0.279915i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.0108 | + | 48.5162i | 0.977585 | + | 1.69323i | 0.671127 | + | 0.741343i | \(0.265811\pi\) |
0.306458 | + | 0.951884i | \(0.400856\pi\) | |||||||
\(822\) | 1.24546 | − | 2.15719i | 0.0434403 | − | 0.0752408i | ||||
\(823\) | 16.7708 | + | 29.0479i | 0.584593 | + | 1.01255i | 0.994926 | + | 0.100610i | \(0.0320793\pi\) |
−0.410333 | + | 0.911936i | \(0.634587\pi\) | |||||||
\(824\) | 6.33455 | 0.220674 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.73326 | − | 3.00210i | −0.0603079 | − | 0.104456i | ||||
\(827\) | −0.0181265 | − | 0.0313960i | −0.000630320 | − | 0.00109175i | 0.865710 | − | 0.500546i | \(-0.166867\pi\) |
−0.866340 | + | 0.499454i | \(0.833534\pi\) | |||||||
\(828\) | −2.06935 | −0.0719149 | ||||||||
\(829\) | 39.5662 | 1.37419 | 0.687095 | − | 0.726567i | \(-0.258885\pi\) | ||||
0.687095 | + | 0.726567i | \(0.258885\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.71204 | − | 9.89354i | 0.198148 | − | 0.343203i | ||||
\(832\) | 6.44321 | + | 11.1600i | 0.223378 | + | 0.386902i | ||||
\(833\) | 7.17005 | − | 12.4189i | 0.248427 | − | 0.430289i | ||||
\(834\) | 1.46811 | − | 2.54283i | 0.0508364 | − | 0.0880512i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.47014 | + | 4.30301i | −0.120017 | + | 0.148823i | ||||
\(837\) | −12.8361 | −0.443681 | ||||||||
\(838\) | −2.66383 | + | 4.61389i | −0.0920205 | + | 0.159384i | ||||
\(839\) | −20.0811 | + | 34.7816i | −0.693278 | + | 1.20079i | 0.277480 | + | 0.960732i | \(0.410501\pi\) |
−0.970758 | + | 0.240061i | \(0.922832\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.1307 | − | 24.4751i | 0.487266 | − | 0.843970i | ||||
\(842\) | 1.07340 | + | 1.85918i | 0.0369917 | + | 0.0640716i | ||||
\(843\) | 15.2390 | 0.524858 | ||||||||
\(844\) | −39.5360 | −1.36089 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.75980 | − | 8.24422i | −0.163645 | − | 0.283442i | ||||
\(847\) | −12.3309 | −0.423696 | ||||||||
\(848\) | 13.5150 | 0.464106 | ||||||||
\(849\) | −9.84502 | − | 17.0521i | −0.337880 | − | 0.585225i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.84763 | + | 4.93224i | 0.0976156 | + | 0.169075i | ||||
\(852\) | −12.1724 | + | 21.0833i | −0.417021 | + | 0.722302i | ||||
\(853\) | 8.23086 | − | 14.2563i | 0.281819 | − | 0.488126i | −0.690014 | − | 0.723796i | \(-0.742395\pi\) |
0.971833 | + | 0.235671i | \(0.0757288\pi\) | |||||||
\(854\) | 2.52624 | 0.0864463 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.47259 | 0.221229 | ||||||||
\(857\) | 2.80332 | − | 4.85549i | 0.0957595 | − | 0.165860i | −0.814166 | − | 0.580632i | \(-0.802805\pi\) |
0.909925 | + | 0.414772i | \(0.136139\pi\) | |||||||
\(858\) | 0.718565 | − | 1.24459i | 0.0245314 | − | 0.0424896i | ||||
\(859\) | −12.5149 | − | 21.6765i | −0.427003 | − | 0.739591i | 0.569602 | − | 0.821921i | \(-0.307097\pi\) |
−0.996605 | + | 0.0823296i | \(0.973764\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.52014 | + | 4.36501i | 0.0858862 | + | 0.148759i | ||||
\(862\) | −15.5266 | −0.528837 | ||||||||
\(863\) | 42.4307 | 1.44436 | 0.722178 | − | 0.691707i | \(-0.243141\pi\) | ||||
0.722178 | + | 0.691707i | \(0.243141\pi\) | |||||||
\(864\) | −12.3939 | − | 21.4669i | −0.421649 | − | 0.730317i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.5274 | 0.357736 | ||||||||
\(867\) | −10.9074 | −0.370434 | ||||||||
\(868\) | 2.62087 | + | 4.53949i | 0.0889583 | + | 0.154080i | ||||
\(869\) | 2.12758 | − | 3.68507i | 0.0721731 | − | 0.125007i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.6315 | − | 18.4143i | 0.360234 | − | 0.623943i | ||||
\(872\) | 5.54583 | − | 9.60566i | 0.187806 | − | 0.325289i | ||||
\(873\) | −32.0334 | −1.08417 | ||||||||
\(874\) | 0.449833 | + | 1.16482i | 0.0152158 | + | 0.0394005i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.4426 | + | 19.8191i | −0.386608 | + | 0.669625i | ||||
\(877\) | 0.278622 | − | 0.482588i | 0.00940841 | − | 0.0162958i | −0.861283 | − | 0.508126i | \(-0.830338\pi\) |
0.870691 | + | 0.491830i | \(0.163672\pi\) | |||||||
\(878\) | 1.34622 | + | 2.33172i | 0.0454328 | + | 0.0786919i | ||||
\(879\) | 2.91067 | − | 5.04143i | 0.0981745 | − | 0.170043i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.35432 | 0.281464 | 0.140732 | − | 0.990048i | \(-0.455054\pi\) | ||||
0.140732 | + | 0.990048i | \(0.455054\pi\) | |||||||
\(882\) | −5.08494 | −0.171219 | ||||||||
\(883\) | 9.74209 | + | 16.8738i | 0.327847 | + | 0.567848i | 0.982084 | − | 0.188441i | \(-0.0603435\pi\) |
−0.654237 | + | 0.756289i | \(0.727010\pi\) | |||||||
\(884\) | 9.30660 | + | 16.1195i | 0.313015 | + | 0.542158i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.46329 | 0.183543 | ||||||||
\(887\) | 17.9686 | + | 31.1226i | 0.603328 | + | 1.04499i | 0.992313 | + | 0.123751i | \(0.0394923\pi\) |
−0.388985 | + | 0.921244i | \(0.627174\pi\) | |||||||
\(888\) | −8.69755 | + | 15.0646i | −0.291871 | + | 0.505535i | ||||
\(889\) | −1.26819 | − | 2.19657i | −0.0425337 | − | 0.0736705i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.154235 | + | 0.267143i | −0.00516706 | + | 0.00894962i | ||||
\(892\) | 24.2116 | 0.810666 | ||||||||
\(893\) | 28.7814 | − | 35.6892i | 0.963133 | − | 1.19429i | ||||
\(894\) | −4.71237 | −0.157605 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6.56624 | + | 11.3731i | −0.219363 | + | 0.379947i | ||||
\(897\) | 1.29552 | + | 2.24391i | 0.0432563 | + | 0.0749221i | ||||
\(898\) | −6.01005 | + | 10.4097i | −0.200558 | + | 0.347377i | ||||
\(899\) | 1.07816 | + | 1.86743i | 0.0359586 | + | 0.0622821i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.7120 | 0.423499 | ||||||||
\(902\) | −0.694011 | − | 1.20206i | −0.0231080 | − | 0.0400243i | ||||
\(903\) | −6.18914 | − | 10.7199i | −0.205962 | − | 0.356736i | ||||
\(904\) | −21.8721 | −0.727455 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.84967 | + | 3.20372i | 0.0614511 | + | 0.106436i | ||||
\(907\) | 24.4751 | − | 42.3922i | 0.812683 | − | 1.40761i | −0.0982962 | − | 0.995157i | \(-0.531339\pi\) |
0.910980 | − | 0.412452i | \(-0.135327\pi\) | |||||||
\(908\) | −5.85551 | − | 10.1420i | −0.194322 | − | 0.336576i | ||||
\(909\) | 13.4517 | − | 23.2990i | 0.446165 | − | 0.772780i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.7811 | −0.655376 | −0.327688 | − | 0.944786i | \(-0.606269\pi\) | ||||
−0.327688 | + | 0.944786i | \(0.606269\pi\) | |||||||
\(912\) | 7.72369 | − | 9.57745i | 0.255757 | − | 0.317141i | ||||
\(913\) | 9.88984 | 0.327306 | ||||||||
\(914\) | 1.63468 | − | 2.83134i | 0.0540703 | − | 0.0936525i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.520723 | − | 0.901919i | −0.0172052 | − | 0.0298002i | ||||
\(917\) | 10.3138 | − | 17.8640i | 0.340591 | − | 0.589921i | ||||
\(918\) | −3.08071 | − | 5.33594i | −0.101678 | − | 0.176112i | ||||
\(919\) | 26.0582 | 0.859581 | 0.429791 | − | 0.902929i | \(-0.358587\pi\) | ||||
0.429791 | + | 0.902929i | \(0.358587\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.7309 | − | 18.5865i | −0.353595 | − | 0.612444i | ||||
\(922\) | 7.66684 | + | 13.2794i | 0.252494 | + | 0.437332i | ||||
\(923\) | −54.0298 | −1.77841 | ||||||||
\(924\) | −1.55058 | −0.0510104 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.07421 | + | 8.78879i | −0.166749 | + | 0.288817i | ||||
\(927\) | 3.40801 | + | 5.90285i | 0.111934 | + | 0.193875i | ||||
\(928\) | −2.08203 | + | 3.60618i | −0.0683460 | + | 0.118379i | ||||
\(929\) | 3.98900 | − | 6.90914i | 0.130875 | − | 0.226682i | −0.793139 | − | 0.609040i | \(-0.791555\pi\) |
0.924014 | + | 0.382359i | \(0.124888\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.82267 | − | 22.8458i | −0.289151 | − | 0.748741i | ||||
\(932\) | 12.7211 | 0.416695 | ||||||||
\(933\) | 12.8253 | − | 22.2140i | 0.419880 | − | 0.727254i | ||||
\(934\) | 3.99942 | − | 6.92719i | 0.130865 | − | 0.226665i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.01362 | − | 12.1479i | 0.229247 | − | 0.397068i | ||||
\(937\) | −23.3271 | − | 40.4037i | −0.762063 | − | 1.31993i | −0.941785 | − | 0.336215i | \(-0.890853\pi\) |
0.179722 | − | 0.983717i | \(-0.442480\pi\) | |||||||
\(938\) | 2.87426 | 0.0938479 | ||||||||
\(939\) | 3.63928 | 0.118763 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.700500 | + | 1.21330i | 0.0228356 | + | 0.0395525i | 0.877217 | − | 0.480093i | \(-0.159397\pi\) |
−0.854382 | + | 0.519646i | \(0.826064\pi\) | |||||||
\(942\) | 4.83798 | 0.157630 | ||||||||
\(943\) | 2.50251 | 0.0814930 | ||||||||
\(944\) | 8.47969 | + | 14.6873i | 0.275990 | + | 0.478030i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.70440 | + | 2.95211i | 0.0554149 | + | 0.0959814i | ||||
\(947\) | −19.1250 | + | 33.1255i | −0.621480 | + | 1.07643i | 0.367730 | + | 0.929932i | \(0.380135\pi\) |
−0.989210 | + | 0.146502i | \(0.953198\pi\) | |||||||
\(948\) | −5.51265 | + | 9.54820i | −0.179043 | + | 0.310111i | ||||
\(949\) | −50.7900 | −1.64871 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.6326 | 1.05819 | ||||||||
\(952\) | −2.67369 | + | 4.63096i | −0.0866547 | + | 0.150090i | ||||
\(953\) | −27.2195 | + | 47.1455i | −0.881726 | + | 1.52719i | −0.0323042 | + | 0.999478i | \(0.510285\pi\) |
−0.849421 | + | 0.527715i | \(0.823049\pi\) | |||||||
\(954\) | −2.25382 | − | 3.90373i | −0.0729701 | − | 0.126388i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.24805 | + | 5.62579i | 0.105049 | + | 0.181951i | ||||
\(957\) | −0.637869 | −0.0206194 | ||||||||
\(958\) | −4.17989 | −0.135046 | ||||||||
\(959\) | −2.98231 | − | 5.16551i | −0.0963038 | − | 0.166803i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.7042 | −0.796911 | ||||||||
\(962\) | −18.1650 | −0.585662 | ||||||||
\(963\) | 3.48228 | + | 6.03148i | 0.112215 | + | 0.194362i | ||||
\(964\) | 15.3409 | − | 26.5713i | 0.494099 | − | 0.855804i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.175125 | + | 0.303325i | −0.00563455 | + | 0.00975933i | ||||
\(967\) | −2.49460 | + | 4.32077i | −0.0802208 | + | 0.138946i | −0.903345 | − | 0.428915i | \(-0.858896\pi\) |
0.823124 | + | 0.567862i | \(0.192229\pi\) | |||||||
\(968\) | −18.6995 | −0.601026 | ||||||||
\(969\) | 7.26482 | − | 9.00846i | 0.233380 | − | 0.289393i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.27006 | − | 12.5921i | 0.233307 | − | 0.404100i | −0.725472 | − | 0.688252i | \(-0.758379\pi\) |
0.958779 | + | 0.284152i | \(0.0917119\pi\) | |||||||
\(972\) | 14.0381 | − | 24.3148i | 0.450274 | − | 0.779897i | ||||
\(973\) | −3.51546 | − | 6.08895i | −0.112700 | − | 0.195203i | ||||
\(974\) | 7.09306 | − | 12.2855i | 0.227276 | − | 0.393654i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.3592 | −0.395609 | ||||||||
\(977\) | 26.1353 | 0.836141 | 0.418071 | − | 0.908415i | \(-0.362706\pi\) | ||||
0.418071 | + | 0.908415i | \(0.362706\pi\) | |||||||
\(978\) | −0.0168915 | − | 0.0292569i | −0.000540129 | − | 0.000935531i | ||||
\(979\) | −5.69527 | − | 9.86449i | −0.182021 | − | 0.315270i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.9347 | 0.381046 | ||||||||
\(982\) | 0.731499 | + | 1.26699i | 0.0233431 | + | 0.0404314i | ||||
\(983\) | −23.0580 | + | 39.9376i | −0.735436 | + | 1.27381i | 0.219096 | + | 0.975703i | \(0.429689\pi\) |
−0.954532 | + | 0.298109i | \(0.903644\pi\) | |||||||
\(984\) | 3.82172 | + | 6.61942i | 0.121832 | + | 0.211019i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.517523 | + | 0.896376i | −0.0164813 | + | 0.0285464i | ||||
\(987\) | 12.8606 | 0.409356 | ||||||||
\(988\) | 31.4065 | + | 4.90929i | 0.999174 | + | 0.156185i | ||||
\(989\) | −6.14585 | −0.195427 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.6640 | − | 27.1308i | 0.497582 | − | 0.861837i | −0.502414 | − | 0.864627i | \(-0.667555\pi\) |
0.999996 | + | 0.00278993i | \(0.000888065\pi\) | |||||||
\(992\) | 6.07887 | + | 10.5289i | 0.193004 | + | 0.334294i | ||||
\(993\) | −18.5938 | + | 32.2055i | −0.590057 | + | 1.02201i | ||||
\(994\) | −3.65178 | − | 6.32508i | −0.115828 | − | 0.200619i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −25.6251 | −0.811962 | ||||||||
\(997\) | 10.8072 | + | 18.7186i | 0.342268 | + | 0.592826i | 0.984854 | − | 0.173388i | \(-0.0554716\pi\) |
−0.642586 | + | 0.766214i | \(0.722138\pi\) | |||||||
\(998\) | 7.58296 | + | 13.1341i | 0.240035 | + | 0.415752i | ||||
\(999\) | −47.9944 | −1.51848 |
(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 | 475.2.e.g.201.4 | 12 | ||
5.2 | odd | 4 | 95.2.i.b.49.4 | yes | 12 | ||
5.3 | odd | 4 | 95.2.i.b.49.3 | ✓ | 12 | ||
5.4 | even | 2 | inner | 475.2.e.g.201.3 | 12 | ||
15.2 | even | 4 | 855.2.be.d.334.3 | 12 | |||
15.8 | even | 4 | 855.2.be.d.334.4 | 12 | |||
19.7 | even | 3 | inner | 475.2.e.g.26.4 | 12 | ||
19.8 | odd | 6 | 9025.2.a.bt.1.4 | 6 | |||
19.11 | even | 3 | 9025.2.a.bu.1.3 | 6 | |||
95.7 | odd | 12 | 95.2.i.b.64.3 | yes | 12 | ||
95.8 | even | 12 | 1805.2.b.g.1084.3 | 6 | |||
95.27 | even | 12 | 1805.2.b.g.1084.4 | 6 | |||
95.49 | even | 6 | 9025.2.a.bu.1.4 | 6 | |||
95.64 | even | 6 | inner | 475.2.e.g.26.3 | 12 | ||
95.68 | odd | 12 | 1805.2.b.f.1084.4 | 6 | |||
95.83 | odd | 12 | 95.2.i.b.64.4 | yes | 12 | ||
95.84 | odd | 6 | 9025.2.a.bt.1.3 | 6 | |||
95.87 | odd | 12 | 1805.2.b.f.1084.3 | 6 | |||
285.83 | even | 12 | 855.2.be.d.64.3 | 12 | |||
285.197 | even | 12 | 855.2.be.d.64.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.i.b.49.3 | ✓ | 12 | 5.3 | odd | 4 | ||
95.2.i.b.49.4 | yes | 12 | 5.2 | odd | 4 | ||
95.2.i.b.64.3 | yes | 12 | 95.7 | odd | 12 | ||
95.2.i.b.64.4 | yes | 12 | 95.83 | odd | 12 | ||
475.2.e.g.26.3 | 12 | 95.64 | even | 6 | inner | ||
475.2.e.g.26.4 | 12 | 19.7 | even | 3 | inner | ||
475.2.e.g.201.3 | 12 | 5.4 | even | 2 | inner | ||
475.2.e.g.201.4 | 12 | 1.1 | even | 1 | trivial | ||
855.2.be.d.64.3 | 12 | 285.83 | even | 12 | |||
855.2.be.d.64.4 | 12 | 285.197 | even | 12 | |||
855.2.be.d.334.3 | 12 | 15.2 | even | 4 | |||
855.2.be.d.334.4 | 12 | 15.8 | even | 4 | |||
1805.2.b.f.1084.3 | 6 | 95.87 | odd | 12 | |||
1805.2.b.f.1084.4 | 6 | 95.68 | odd | 12 | |||
1805.2.b.g.1084.3 | 6 | 95.8 | even | 12 | |||
1805.2.b.g.1084.4 | 6 | 95.27 | even | 12 | |||
9025.2.a.bt.1.3 | 6 | 95.84 | odd | 6 | |||
9025.2.a.bt.1.4 | 6 | 19.8 | odd | 6 | |||
9025.2.a.bu.1.3 | 6 | 19.11 | even | 3 | |||
9025.2.a.bu.1.4 | 6 | 95.49 | even | 6 |