Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(49,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 23x^{10} + 198x^{8} - 719x^{6} + 886x^{4} + 585x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 124.2 | ||
Root | \(-0.0378788 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.124 |
Dual form | 225.4.k.c.49.2 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.24635 | − | 1.87428i | −1.14776 | − | 0.662659i | −0.199419 | − | 0.979914i | \(-0.563905\pi\) |
−0.948340 | + | 0.317255i | \(0.897239\pi\) | |||||||
\(3\) | −3.24635 | + | 4.05724i | −0.624761 | + | 0.780816i | ||||
\(4\) | 3.02587 | + | 5.24096i | 0.378234 | + | 0.655120i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 18.1432 | − | 7.08665i | 1.23449 | − | 0.482185i | ||||
\(7\) | 27.1492 | + | 15.6746i | 1.46592 | + | 0.846348i | 0.999274 | − | 0.0380969i | \(-0.0121296\pi\) |
0.466644 | + | 0.884445i | \(0.345463\pi\) | |||||||
\(8\) | 7.30318i | 0.322758i | ||||||||
\(9\) | −5.92239 | − | 26.3425i | −0.219348 | − | 0.975647i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.4166 | − | 18.0422i | 0.285522 | − | 0.494538i | −0.687214 | − | 0.726455i | \(-0.741166\pi\) |
0.972736 | + | 0.231917i | \(0.0744998\pi\) | |||||||
\(12\) | −31.0869 | − | 4.73733i | −0.747834 | − | 0.113962i | ||||
\(13\) | −51.9018 | + | 29.9655i | −1.10731 | + | 0.639303i | −0.938130 | − | 0.346283i | \(-0.887444\pi\) |
−0.169175 | + | 0.985586i | \(0.554110\pi\) | |||||||
\(14\) | −58.7572 | − | 101.770i | −1.12168 | − | 1.94281i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 37.8952 | − | 65.6364i | 0.592112 | − | 1.02557i | ||||
\(17\) | − | 74.0460i | − | 1.05640i | −0.849120 | − | 0.528200i | \(-0.822867\pi\) | ||
0.849120 | − | 0.528200i | \(-0.177133\pi\) | |||||||
\(18\) | −30.1471 | + | 96.6172i | −0.394763 | + | 1.26516i | ||||
\(19\) | 63.8390 | 0.770825 | 0.385413 | − | 0.922744i | \(-0.374059\pi\) | ||||
0.385413 | + | 0.922744i | \(0.374059\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −151.731 | + | 59.2655i | −1.57669 | + | 0.615847i | ||||
\(22\) | −67.6322 | + | 39.0475i | −0.655420 | + | 0.378407i | ||||
\(23\) | 28.4484 | − | 16.4247i | 0.257909 | − | 0.148904i | −0.365472 | − | 0.930823i | \(-0.619092\pi\) |
0.623380 | + | 0.781919i | \(0.285759\pi\) | |||||||
\(24\) | −29.6307 | − | 23.7087i | −0.252015 | − | 0.201646i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 224.655 | 1.69456 | ||||||||
\(27\) | 126.104 | + | 61.4884i | 0.898841 | + | 0.438276i | ||||
\(28\) | 189.717i | 1.28047i | ||||||||
\(29\) | −80.0044 | + | 138.572i | −0.512291 | + | 0.887314i | 0.487607 | + | 0.873063i | \(0.337870\pi\) |
−0.999898 | + | 0.0142513i | \(0.995464\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 127.187 | + | 220.294i | 0.736884 | + | 1.27632i | 0.953892 | + | 0.300151i | \(0.0970371\pi\) |
−0.217007 | + | 0.976170i | \(0.569630\pi\) | |||||||
\(32\) | −195.444 | + | 112.840i | −1.07969 | + | 0.623358i | ||||
\(33\) | 39.3853 | + | 100.834i | 0.207760 | + | 0.531908i | ||||
\(34\) | −138.783 | + | 240.379i | −0.700033 | + | 1.21249i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 120.139 | − | 110.748i | 0.556201 | − | 0.512722i | ||||
\(37\) | 215.365i | 0.956914i | 0.878111 | + | 0.478457i | \(0.158804\pi\) | ||||
−0.878111 | + | 0.478457i | \(0.841196\pi\) | |||||||
\(38\) | −207.244 | − | 119.652i | −0.884722 | − | 0.510794i | ||||
\(39\) | 46.9143 | − | 307.857i | 0.192623 | − | 1.26401i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −70.8407 | − | 122.700i | −0.269841 | − | 0.467377i | 0.698980 | − | 0.715141i | \(-0.253638\pi\) |
−0.968820 | + | 0.247764i | \(0.920304\pi\) | |||||||
\(42\) | 603.654 | + | 91.9908i | 2.21776 | + | 0.337964i | ||||
\(43\) | 119.430 | + | 68.9529i | 0.423556 | + | 0.244540i | 0.696597 | − | 0.717462i | \(-0.254696\pi\) |
−0.273042 | + | 0.962002i | \(0.588030\pi\) | |||||||
\(44\) | 126.078 | 0.431976 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −123.138 | −0.394689 | ||||||||
\(47\) | −29.0803 | − | 16.7895i | −0.0902509 | − | 0.0521064i | 0.454195 | − | 0.890902i | \(-0.349927\pi\) |
−0.544446 | + | 0.838796i | \(0.683260\pi\) | |||||||
\(48\) | 143.281 | + | 366.829i | 0.430852 | + | 1.10307i | ||||
\(49\) | 319.885 | + | 554.058i | 0.932611 | + | 1.61533i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 300.422 | + | 240.379i | 0.824854 | + | 0.659997i | ||||
\(52\) | −314.096 | − | 181.344i | −0.837641 | − | 0.483612i | ||||
\(53\) | 41.9914i | 0.108829i | 0.998518 | + | 0.0544147i | \(0.0173293\pi\) | ||||
−0.998518 | + | 0.0544147i | \(0.982671\pi\) | |||||||
\(54\) | −294.131 | − | 435.967i | −0.741225 | − | 1.09866i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −114.474 | + | 198.275i | −0.273166 | + | 0.473137i | ||||
\(57\) | −207.244 | + | 259.010i | −0.481581 | + | 0.601873i | ||||
\(58\) | 519.445 | − | 299.902i | 1.17597 | − | 0.678949i | ||||
\(59\) | 307.571 | + | 532.728i | 0.678683 | + | 1.17551i | 0.975378 | + | 0.220541i | \(0.0707824\pi\) |
−0.296694 | + | 0.954973i | \(0.595884\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 67.1535 | − | 116.313i | 0.140953 | − | 0.244137i | −0.786903 | − | 0.617077i | \(-0.788317\pi\) |
0.927856 | + | 0.372939i | \(0.121650\pi\) | |||||||
\(62\) | − | 953.535i | − | 1.95321i | ||||||
\(63\) | 252.119 | − | 808.007i | 0.504191 | − | 1.61586i | ||||
\(64\) | 239.652 | 0.468071 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 61.1331 | − | 401.162i | 0.114015 | − | 0.748176i | ||||
\(67\) | −742.646 | + | 428.767i | −1.35416 | + | 0.781824i | −0.988829 | − | 0.149055i | \(-0.952377\pi\) |
−0.365329 | + | 0.930878i | \(0.619044\pi\) | |||||||
\(68\) | 388.072 | − | 224.054i | 0.692069 | − | 0.399566i | ||||
\(69\) | −25.7146 | + | 168.742i | −0.0448649 | + | 0.294408i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 588.665 | 0.983968 | 0.491984 | − | 0.870604i | \(-0.336272\pi\) | ||||
0.491984 | + | 0.870604i | \(0.336272\pi\) | |||||||
\(72\) | 192.384 | − | 43.2522i | 0.314898 | − | 0.0707962i | ||||
\(73\) | 618.191i | 0.991148i | 0.868566 | + | 0.495574i | \(0.165042\pi\) | ||||
−0.868566 | + | 0.495574i | \(0.834958\pi\) | |||||||
\(74\) | 403.655 | − | 699.152i | 0.634108 | − | 1.09831i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 193.169 | + | 334.578i | 0.291552 | + | 0.504983i | ||||
\(77\) | 565.607 | − | 326.553i | 0.837103 | − | 0.483301i | ||||
\(78\) | −729.311 | + | 911.481i | −1.05869 | + | 1.32314i | ||||
\(79\) | −172.644 | + | 299.029i | −0.245873 | + | 0.425865i | −0.962377 | − | 0.271718i | \(-0.912408\pi\) |
0.716503 | + | 0.697584i | \(0.245741\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −658.851 | + | 312.021i | −0.903773 | + | 0.428012i | ||||
\(82\) | 531.102i | 0.715249i | ||||||||
\(83\) | −946.711 | − | 546.584i | −1.25199 | − | 0.722836i | −0.280484 | − | 0.959859i | \(-0.590495\pi\) |
−0.971504 | + | 0.237023i | \(0.923828\pi\) | |||||||
\(84\) | −769.728 | − | 615.889i | −0.999812 | − | 0.799988i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −258.474 | − | 447.691i | −0.324093 | − | 0.561346i | ||||
\(87\) | −302.496 | − | 774.450i | −0.372770 | − | 0.954365i | ||||
\(88\) | 131.765 | + | 76.0746i | 0.159616 | + | 0.0921543i | ||||
\(89\) | −414.849 | −0.494089 | −0.247045 | − | 0.969004i | \(-0.579459\pi\) | ||||
−0.247045 | + | 0.969004i | \(0.579459\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1878.79 | −2.16429 | ||||||||
\(92\) | 172.162 | + | 99.3979i | 0.195100 | + | 0.112641i | ||||
\(93\) | −1306.68 | − | 199.125i | −1.45695 | − | 0.222024i | ||||
\(94\) | 62.9366 | + | 109.009i | 0.0690576 | + | 0.119611i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 176.663 | − | 1159.28i | 0.187819 | − | 1.23249i | ||||
\(97\) | 174.427 | + | 100.705i | 0.182581 | + | 0.105413i | 0.588505 | − | 0.808494i | \(-0.299717\pi\) |
−0.405924 | + | 0.913907i | \(0.633050\pi\) | |||||||
\(98\) | − | 2398.22i | − | 2.47201i | ||||||
\(99\) | −536.967 | − | 167.547i | −0.545123 | − | 0.170092i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −132.691 | + | 229.828i | −0.130726 | + | 0.226424i | −0.923957 | − | 0.382498i | \(-0.875064\pi\) |
0.793231 | + | 0.608921i | \(0.208397\pi\) | |||||||
\(102\) | −524.738 | − | 1343.43i | −0.509380 | − | 1.30411i | ||||
\(103\) | 456.931 | − | 263.809i | 0.437114 | − | 0.252368i | −0.265259 | − | 0.964177i | \(-0.585457\pi\) |
0.702373 | + | 0.711810i | \(0.252124\pi\) | |||||||
\(104\) | −218.843 | − | 379.048i | −0.206340 | − | 0.357391i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 78.7038 | − | 136.319i | 0.0721168 | − | 0.124910i | ||||
\(107\) | 2084.24i | 1.88310i | 0.336877 | + | 0.941549i | \(0.390629\pi\) | ||||
−0.336877 | + | 0.941549i | \(0.609371\pi\) | |||||||
\(108\) | 59.3157 | + | 846.961i | 0.0528487 | + | 0.754619i | ||||
\(109\) | −925.651 | −0.813406 | −0.406703 | − | 0.913560i | \(-0.633322\pi\) | ||||
−0.406703 | + | 0.913560i | \(0.633322\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −873.788 | − | 699.152i | −0.747174 | − | 0.597843i | ||||
\(112\) | 2057.65 | − | 1187.98i | 1.73598 | − | 1.00227i | ||||
\(113\) | −472.866 | + | 273.009i | −0.393659 | + | 0.227279i | −0.683745 | − | 0.729721i | \(-0.739650\pi\) |
0.290085 | + | 0.957001i | \(0.406316\pi\) | |||||||
\(114\) | 1158.25 | − | 452.405i | 0.951576 | − | 0.371681i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −968.332 | −0.775063 | ||||||||
\(117\) | 1096.75 | + | 1189.75i | 0.866619 | + | 0.940109i | ||||
\(118\) | − | 2305.90i | − | 1.79894i | ||||||
\(119\) | 1160.64 | − | 2010.29i | 0.894082 | − | 1.54860i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 448.487 | + | 776.802i | 0.336955 | + | 0.583623i | ||||
\(122\) | −436.008 | + | 251.729i | −0.323560 | + | 0.186807i | ||||
\(123\) | 727.796 | + | 110.909i | 0.533522 | + | 0.0813033i | ||||
\(124\) | −769.701 | + | 1333.16i | −0.557429 | + | 0.965495i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2332.90 | + | 2150.53i | −1.64946 | + | 1.52051i | ||||
\(127\) | − | 975.972i | − | 0.681918i | −0.940078 | − | 0.340959i | \(-0.889248\pi\) | ||
0.940078 | − | 0.340959i | \(-0.110752\pi\) | |||||||
\(128\) | 785.559 | + | 453.543i | 0.542455 | + | 0.313187i | ||||
\(129\) | −667.470 | + | 260.710i | −0.455562 | + | 0.177940i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 814.614 | + | 1410.95i | 0.543307 | + | 0.941035i | 0.998711 | + | 0.0507502i | \(0.0161612\pi\) |
−0.455405 | + | 0.890285i | \(0.650505\pi\) | |||||||
\(132\) | −409.293 | + | 511.528i | −0.269882 | + | 0.337294i | ||||
\(133\) | 1733.18 | + | 1000.65i | 1.12997 | + | 0.652387i | ||||
\(134\) | 3214.52 | 2.07233 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 540.771 | 0.340961 | ||||||||
\(137\) | −572.833 | − | 330.725i | −0.357229 | − | 0.206246i | 0.310635 | − | 0.950529i | \(-0.399458\pi\) |
−0.667865 | + | 0.744283i | \(0.732792\pi\) | |||||||
\(138\) | 399.749 | − | 499.600i | 0.246586 | − | 0.308180i | ||||
\(139\) | 691.495 | + | 1197.70i | 0.421955 | + | 0.730848i | 0.996131 | − | 0.0878842i | \(-0.0280105\pi\) |
−0.574175 | + | 0.818732i | \(0.694677\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 162.524 | − | 63.4810i | 0.0970708 | − | 0.0379153i | ||||
\(142\) | −1911.02 | − | 1103.33i | −1.12936 | − | 0.652035i | ||||
\(143\) | 1248.56i | 0.730139i | ||||||||
\(144\) | −1953.45 | − | 609.528i | −1.13047 | − | 0.352736i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1158.66 | − | 2006.87i | 0.656793 | − | 1.13760i | ||||
\(147\) | −3286.41 | − | 500.815i | −1.84393 | − | 0.280997i | ||||
\(148\) | −1128.72 | + | 651.667i | −0.626894 | + | 0.361937i | ||||
\(149\) | 1581.75 | + | 2739.66i | 0.869676 | + | 1.50632i | 0.862328 | + | 0.506349i | \(0.169005\pi\) |
0.00734719 | + | 0.999973i | \(0.497661\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1279.40 | − | 2215.98i | 0.689509 | − | 1.19427i | −0.282488 | − | 0.959271i | \(-0.591160\pi\) |
0.971997 | − | 0.234994i | \(-0.0755071\pi\) | |||||||
\(152\) | 466.228i | 0.248790i | ||||||||
\(153\) | −1950.55 | + | 438.529i | −1.03067 | + | 0.231719i | ||||
\(154\) | −2448.21 | −1.28106 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1755.42 | − | 685.659i | 0.900937 | − | 0.351901i | ||||
\(157\) | 3031.92 | − | 1750.48i | 1.54123 | − | 0.889832i | 0.542474 | − | 0.840073i | \(-0.317488\pi\) |
0.998761 | − | 0.0497594i | \(-0.0158454\pi\) | |||||||
\(158\) | 1120.93 | − | 647.168i | 0.564407 | − | 0.325860i | ||||
\(159\) | −170.369 | − | 136.319i | −0.0849758 | − | 0.0679924i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1029.80 | 0.504097 | ||||||||
\(162\) | 2723.68 | + | 221.943i | 1.32094 | + | 0.107639i | ||||
\(163\) | − | 263.950i | − | 0.126835i | −0.997987 | − | 0.0634176i | \(-0.979800\pi\) | ||
0.997987 | − | 0.0634176i | \(-0.0202000\pi\) | |||||||
\(164\) | 428.710 | − | 742.547i | 0.204126 | − | 0.353556i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2048.90 | + | 3548.81i | 0.957987 | + | 1.65928i | ||||
\(167\) | −3108.21 | + | 1794.53i | −1.44024 | + | 0.831524i | −0.997865 | − | 0.0653054i | \(-0.979198\pi\) |
−0.442377 | + | 0.896829i | \(0.645865\pi\) | |||||||
\(168\) | −432.826 | − | 1108.12i | −0.198770 | − | 0.508889i | ||||
\(169\) | 697.365 | − | 1207.87i | 0.317417 | − | 0.549782i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −378.080 | − | 1681.68i | −0.169079 | − | 0.752053i | ||||
\(172\) | 834.570i | 0.369973i | ||||||||
\(173\) | 320.824 | + | 185.228i | 0.140993 | + | 0.0814024i | 0.568837 | − | 0.822450i | \(-0.307393\pi\) |
−0.427844 | + | 0.903853i | \(0.640727\pi\) | |||||||
\(174\) | −469.529 | + | 3081.10i | −0.204568 | + | 1.34240i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −789.482 | − | 1367.42i | −0.338122 | − | 0.585644i | ||||
\(177\) | −3159.89 | − | 481.535i | −1.34188 | − | 0.204488i | ||||
\(178\) | 1346.75 | + | 777.545i | 0.567095 | + | 0.327413i | ||||
\(179\) | −446.898 | −0.186607 | −0.0933036 | − | 0.995638i | \(-0.529743\pi\) | ||||
−0.0933036 | + | 0.995638i | \(0.529743\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −904.046 | −0.371255 | −0.185628 | − | 0.982620i | \(-0.559432\pi\) | ||||
−0.185628 | + | 0.982620i | \(0.559432\pi\) | |||||||
\(182\) | 6099.21 | + | 3521.38i | 2.48409 | + | 1.43419i | ||||
\(183\) | 253.907 | + | 650.051i | 0.102565 | + | 0.262586i | ||||
\(184\) | 119.952 | + | 207.764i | 0.0480598 | + | 0.0832420i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3868.72 | + | 3095.51i | 1.52510 | + | 1.22029i | ||||
\(187\) | −1335.95 | − | 771.311i | −0.522430 | − | 0.301625i | ||||
\(188\) | − | 203.211i | − | 0.0788336i | ||||||
\(189\) | 2459.81 | + | 3645.99i | 0.946693 | + | 1.40321i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 299.793 | − | 519.257i | 0.113572 | − | 0.196713i | −0.803636 | − | 0.595121i | \(-0.797104\pi\) |
0.917208 | + | 0.398409i | \(0.130437\pi\) | |||||||
\(192\) | −777.995 | + | 972.326i | −0.292432 | + | 0.365477i | ||||
\(193\) | 3822.40 | − | 2206.87i | 1.42561 | − | 0.823076i | 0.428839 | − | 0.903381i | \(-0.358923\pi\) |
0.996770 | + | 0.0803048i | \(0.0255894\pi\) | |||||||
\(194\) | −377.500 | − | 653.850i | −0.139706 | − | 0.241978i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1935.86 | + | 3353.01i | −0.705490 | + | 1.22194i | ||||
\(197\) | − | 4807.15i | − | 1.73855i | −0.494325 | − | 0.869277i | \(-0.664585\pi\) | ||
0.494325 | − | 0.869277i | \(-0.335415\pi\) | |||||||
\(198\) | 1429.15 | + | 1550.35i | 0.512956 | + | 0.556456i | ||||
\(199\) | −313.833 | −0.111794 | −0.0558970 | − | 0.998437i | \(-0.517802\pi\) | ||||
−0.0558970 | + | 0.998437i | \(0.517802\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 671.281 | − | 4405.02i | 0.235565 | − | 1.54580i | ||||
\(202\) | 861.527 | − | 497.403i | 0.300083 | − | 0.173253i | ||||
\(203\) | −4344.11 | + | 2508.07i | −1.50195 | + | 0.867153i | ||||
\(204\) | −350.780 | + | 2301.86i | −0.120390 | + | 0.790012i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1977.81 | −0.668935 | ||||||||
\(207\) | −601.149 | − | 652.127i | −0.201849 | − | 0.218966i | ||||
\(208\) | 4542.20i | 1.51416i | ||||||||
\(209\) | 664.989 | − | 1151.79i | 0.220087 | − | 0.381202i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1219.41 | − | 2112.08i | −0.397856 | − | 0.689106i | 0.595605 | − | 0.803277i | \(-0.296912\pi\) |
−0.993461 | + | 0.114171i | \(0.963579\pi\) | |||||||
\(212\) | −220.075 | + | 127.061i | −0.0712964 | + | 0.0411630i | ||||
\(213\) | −1911.02 | + | 2388.36i | −0.614745 | + | 0.768298i | ||||
\(214\) | 3906.46 | − | 6766.19i | 1.24785 | − | 2.16134i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −449.060 | + | 920.959i | −0.141457 | + | 0.290108i | ||||
\(217\) | 7974.40i | 2.49464i | ||||||||
\(218\) | 3004.99 | + | 1734.93i | 0.933594 | + | 0.539011i | ||||
\(219\) | −2508.15 | − | 2006.87i | −0.773904 | − | 0.619230i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2218.83 | + | 3843.12i | 0.675360 | + | 1.16976i | ||||
\(222\) | 1526.22 | + | 3907.42i | 0.461410 | + | 1.18130i | ||||
\(223\) | −2020.79 | − | 1166.71i | −0.606827 | − | 0.350352i | 0.164896 | − | 0.986311i | \(-0.447271\pi\) |
−0.771722 | + | 0.635959i | \(0.780605\pi\) | |||||||
\(224\) | −7074.87 | −2.11031 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2046.79 | 0.602435 | ||||||||
\(227\) | 2358.79 | + | 1361.85i | 0.689684 | + | 0.398189i | 0.803494 | − | 0.595313i | \(-0.202972\pi\) |
−0.113810 | + | 0.993503i | \(0.536305\pi\) | |||||||
\(228\) | −1984.56 | − | 302.426i | −0.576449 | − | 0.0878451i | ||||
\(229\) | −1657.08 | − | 2870.15i | −0.478179 | − | 0.828230i | 0.521508 | − | 0.853246i | \(-0.325370\pi\) |
−0.999687 | + | 0.0250162i | \(0.992036\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −511.255 | + | 3354.91i | −0.145619 | + | 0.955571i | ||||
\(232\) | −1012.01 | − | 584.286i | −0.286388 | − | 0.165346i | ||||
\(233\) | 3175.44i | 0.892833i | 0.894825 | + | 0.446416i | \(0.147300\pi\) | ||||
−0.894825 | + | 0.446416i | \(0.852700\pi\) | |||||||
\(234\) | −1330.50 | − | 5917.98i | −0.371698 | − | 1.65329i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1861.34 | + | 3223.93i | −0.513402 | + | 0.889238i | ||||
\(237\) | −652.767 | − | 1671.21i | −0.178910 | − | 0.458046i | ||||
\(238\) | −7535.70 | + | 4350.74i | −2.05238 | + | 1.18494i | ||||
\(239\) | −123.062 | − | 213.150i | −0.0333064 | − | 0.0576884i | 0.848892 | − | 0.528567i | \(-0.177270\pi\) |
−0.882198 | + | 0.470878i | \(0.843937\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2643.87 | − | 4579.31i | 0.706666 | − | 1.22398i | −0.259421 | − | 0.965764i | \(-0.583532\pi\) |
0.966087 | − | 0.258217i | \(-0.0831349\pi\) | |||||||
\(242\) | − | 3362.36i | − | 0.893144i | ||||||
\(243\) | 872.919 | − | 3686.04i | 0.230444 | − | 0.973086i | ||||
\(244\) | 812.791 | 0.213252 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2154.81 | − | 1724.14i | −0.558478 | − | 0.446860i | ||||
\(247\) | −3313.36 | + | 1912.97i | −0.853539 | + | 0.492791i | ||||
\(248\) | −1608.84 | + | 928.867i | −0.411943 | + | 0.237835i | ||||
\(249\) | 5290.98 | − | 2066.63i | 1.34659 | − | 0.525973i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2821.23 | 0.709459 | 0.354730 | − | 0.934969i | \(-0.384573\pi\) | ||||
0.354730 | + | 0.934969i | \(0.384573\pi\) | |||||||
\(252\) | 4997.62 | − | 1123.58i | 1.24929 | − | 0.280868i | ||||
\(253\) | − | 684.361i | − | 0.170061i | ||||||
\(254\) | −1829.25 | + | 3168.35i | −0.451879 | + | 0.782677i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2658.74 | − | 4605.08i | −0.649107 | − | 1.12429i | ||||
\(257\) | −1631.76 | + | 942.096i | −0.396056 | + | 0.228663i | −0.684781 | − | 0.728749i | \(-0.740102\pi\) |
0.288725 | + | 0.957412i | \(0.406769\pi\) | |||||||
\(258\) | 2655.49 | + | 404.670i | 0.640789 | + | 0.0976497i | ||||
\(259\) | −3375.76 | + | 5846.99i | −0.809883 | + | 1.40276i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4124.14 | + | 1286.84i | 0.978075 | + | 0.305185i | ||||
\(262\) | − | 6107.27i | − | 1.44011i | ||||||
\(263\) | 478.922 | + | 276.506i | 0.112287 | + | 0.0648292i | 0.555092 | − | 0.831789i | \(-0.312683\pi\) |
−0.442804 | + | 0.896618i | \(0.646016\pi\) | |||||||
\(264\) | −736.409 | + | 287.638i | −0.171677 | + | 0.0670563i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3751.00 | − | 6496.93i | −0.864620 | − | 1.49757i | ||||
\(267\) | 1346.75 | − | 1683.14i | 0.308688 | − | 0.385793i | ||||
\(268\) | −4494.30 | − | 2594.78i | −1.02438 | − | 0.591424i | ||||
\(269\) | −3363.48 | −0.762361 | −0.381180 | − | 0.924501i | \(-0.624482\pi\) | ||||
−0.381180 | + | 0.924501i | \(0.624482\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3333.85 | −0.747295 | −0.373648 | − | 0.927571i | \(-0.621893\pi\) | ||||
−0.373648 | + | 0.927571i | \(0.621893\pi\) | |||||||
\(272\) | −4860.11 | − | 2805.99i | −1.08341 | − | 0.625507i | ||||
\(273\) | 6099.21 | − | 7622.70i | 1.35217 | − | 1.68991i | ||||
\(274\) | 1239.75 | + | 2147.30i | 0.273342 | + | 0.473443i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −962.181 | + | 375.823i | −0.209842 | + | 0.0819633i | ||||
\(277\) | 4665.50 | + | 2693.63i | 1.01199 | + | 0.584275i | 0.911775 | − | 0.410690i | \(-0.134712\pi\) |
0.100220 | + | 0.994965i | \(0.468045\pi\) | |||||||
\(278\) | − | 5184.23i | − | 1.11845i | ||||||
\(279\) | 5049.83 | − | 4655.08i | 1.08360 | − | 0.998897i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1858.35 | + | 3218.76i | −0.394519 | + | 0.683327i | −0.993040 | − | 0.117781i | \(-0.962422\pi\) |
0.598521 | + | 0.801107i | \(0.295755\pi\) | |||||||
\(282\) | −646.591 | − | 98.5340i | −0.136539 | − | 0.0208071i | ||||
\(283\) | −2397.81 | + | 1384.38i | −0.503658 | + | 0.290787i | −0.730223 | − | 0.683209i | \(-0.760584\pi\) |
0.226565 | + | 0.973996i | \(0.427250\pi\) | |||||||
\(284\) | 1781.23 | + | 3085.17i | 0.372170 | + | 0.644617i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2340.16 | − | 4053.27i | 0.483833 | − | 0.838024i | ||||
\(287\) | − | 4441.60i | − | 0.913516i | ||||||
\(288\) | 4129.98 | + | 4480.20i | 0.845004 | + | 0.916662i | ||||
\(289\) | −569.810 | −0.115980 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −974.836 | + | 380.766i | −0.196378 | + | 0.0767041i | ||||
\(292\) | −3239.91 | + | 1870.57i | −0.649321 | + | 0.374886i | ||||
\(293\) | 3013.76 | − | 1740.00i | 0.600907 | − | 0.346934i | −0.168491 | − | 0.985703i | \(-0.553890\pi\) |
0.769398 | + | 0.638769i | \(0.220556\pi\) | |||||||
\(294\) | 9730.17 | + | 7785.48i | 1.93019 | + | 1.54442i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1572.85 | −0.308852 | ||||||||
\(297\) | 2422.96 | − | 1634.68i | 0.473382 | − | 0.319374i | ||||
\(298\) | − | 11858.6i | − | 2.30519i | ||||||
\(299\) | −984.348 | + | 1704.94i | −0.190389 | + | 0.329764i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2161.62 | + | 3744.03i | 0.413932 | + | 0.716951i | ||||
\(302\) | −8306.75 | + | 4795.91i | −1.58278 | + | 0.913819i | ||||
\(303\) | −501.705 | − | 1284.47i | −0.0951229 | − | 0.243533i | ||||
\(304\) | 2419.19 | − | 4190.16i | 0.456415 | − | 0.790534i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 7154.11 | + | 2232.27i | 1.33651 | + | 0.417027i | ||||
\(307\) | − | 1810.36i | − | 0.336555i | −0.985740 | − | 0.168278i | \(-0.946179\pi\) | ||
0.985740 | − | 0.168278i | \(-0.0538205\pi\) | |||||||
\(308\) | 3422.91 | + | 1976.22i | 0.633241 | + | 0.365602i | ||||
\(309\) | −413.021 | + | 2710.29i | −0.0760387 | + | 0.498975i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 443.649 | + | 768.422i | 0.0808907 | + | 0.140107i | 0.903633 | − | 0.428308i | \(-0.140890\pi\) |
−0.822742 | + | 0.568415i | \(0.807557\pi\) | |||||||
\(312\) | 2248.33 | + | 342.623i | 0.407970 | + | 0.0621706i | ||||
\(313\) | −1918.36 | − | 1107.57i | −0.346429 | − | 0.200011i | 0.316682 | − | 0.948532i | \(-0.397431\pi\) |
−0.663111 | + | 0.748521i | \(0.730764\pi\) | |||||||
\(314\) | −13123.6 | −2.35862 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2089.60 | −0.371990 | ||||||||
\(317\) | 569.884 | + | 329.023i | 0.100971 | + | 0.0582958i | 0.549635 | − | 0.835405i | \(-0.314767\pi\) |
−0.448664 | + | 0.893700i | \(0.648100\pi\) | |||||||
\(318\) | 297.578 | + | 761.859i | 0.0524760 | + | 0.134349i | ||||
\(319\) | 1666.76 | + | 2886.91i | 0.292540 | + | 0.506695i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8456.28 | − | 6766.19i | −1.47035 | − | 1.17649i | ||||
\(322\) | −3343.10 | − | 1930.14i | −0.578582 | − | 0.334045i | ||||
\(323\) | − | 4727.03i | − | 0.814299i | ||||||
\(324\) | −3628.88 | − | 2508.88i | −0.622237 | − | 0.430192i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −494.717 | + | 856.875i | −0.0840485 | + | 0.145576i | ||||
\(327\) | 3004.99 | − | 3755.59i | 0.508184 | − | 0.635121i | ||||
\(328\) | 896.098 | − | 517.362i | 0.150850 | − | 0.0870931i | ||||
\(329\) | −526.337 | − | 911.643i | −0.0882003 | − | 0.152767i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2638.22 | + | 4569.53i | −0.438096 | + | 0.758804i | −0.997543 | − | 0.0700619i | \(-0.977680\pi\) |
0.559447 | + | 0.828866i | \(0.311014\pi\) | |||||||
\(332\) | − | 6615.57i | − | 1.09360i | ||||||
\(333\) | 5673.25 | − | 1275.48i | 0.933610 | − | 0.209897i | ||||
\(334\) | 13453.8 | 2.20407 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1859.92 | + | 12205.0i | −0.301984 | + | 1.98165i | ||||
\(337\) | −2910.95 | + | 1680.64i | −0.470532 | + | 0.271662i | −0.716462 | − | 0.697626i | \(-0.754240\pi\) |
0.245930 | + | 0.969288i | \(0.420907\pi\) | |||||||
\(338\) | −4527.78 | + | 2614.12i | −0.728636 | + | 0.420678i | ||||
\(339\) | 427.426 | − | 2804.82i | 0.0684796 | − | 0.449371i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5299.44 | 0.841586 | ||||||||
\(342\) | −1924.56 | + | 6167.95i | −0.304293 | + | 0.975217i | ||||
\(343\) | 9303.52i | 1.46456i | ||||||||
\(344\) | −503.575 | + | 872.218i | −0.0789272 | + | 0.136706i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −694.339 | − | 1202.63i | −0.107884 | − | 0.186861i | ||||
\(347\) | 8102.13 | − | 4677.77i | 1.25344 | − | 0.723677i | 0.281653 | − | 0.959516i | \(-0.409117\pi\) |
0.971792 | + | 0.235840i | \(0.0757841\pi\) | |||||||
\(348\) | 3143.55 | − | 3928.75i | 0.484229 | − | 0.605182i | ||||
\(349\) | 3519.65 | − | 6096.22i | 0.539836 | − | 0.935023i | −0.459077 | − | 0.888397i | \(-0.651820\pi\) |
0.998912 | − | 0.0466263i | \(-0.0148470\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8387.55 | + | 587.410i | −1.27548 | + | 0.0893266i | ||||
\(352\) | 4701.65i | 0.711929i | ||||||||
\(353\) | 3639.19 | + | 2101.09i | 0.548710 | + | 0.316798i | 0.748602 | − | 0.663020i | \(-0.230726\pi\) |
−0.199891 | + | 0.979818i | \(0.564059\pi\) | |||||||
\(354\) | 9355.58 | + | 7485.76i | 1.40464 | + | 1.12391i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1255.28 | − | 2174.21i | −0.186881 | − | 0.323688i | ||||
\(357\) | 4388.37 | + | 11235.1i | 0.650581 | + | 1.66562i | ||||
\(358\) | 1450.79 | + | 837.612i | 0.214180 | + | 0.123657i | ||||
\(359\) | −588.013 | −0.0864461 | −0.0432230 | − | 0.999065i | \(-0.513763\pi\) | ||||
−0.0432230 | + | 0.999065i | \(0.513763\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2783.58 | −0.405828 | ||||||||
\(362\) | 2934.85 | + | 1694.44i | 0.426112 | + | 0.246016i | ||||
\(363\) | −4607.62 | − | 702.155i | −0.666218 | − | 0.101525i | ||||
\(364\) | −5684.97 | − | 9846.66i | −0.818608 | − | 1.41787i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 394.109 | − | 2586.19i | 0.0562853 | − | 0.369350i | ||||
\(367\) | 6742.10 | + | 3892.55i | 0.958950 | + | 0.553650i | 0.895850 | − | 0.444357i | \(-0.146568\pi\) |
0.0631004 | + | 0.998007i | \(0.479901\pi\) | |||||||
\(368\) | − | 2489.67i | − | 0.352671i | ||||||
\(369\) | −2812.67 | + | 2592.79i | −0.396806 | + | 0.365787i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −658.198 | + | 1140.03i | −0.0921077 | + | 0.159535i | ||||
\(372\) | −2910.23 | − | 7450.77i | −0.405615 | − | 1.03845i | ||||
\(373\) | 6775.81 | − | 3912.02i | 0.940585 | − | 0.543047i | 0.0504412 | − | 0.998727i | \(-0.483937\pi\) |
0.890144 | + | 0.455680i | \(0.150604\pi\) | |||||||
\(374\) | 2891.31 | + | 5007.90i | 0.399749 | + | 0.692385i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 122.617 | − | 212.378i | 0.0168177 | − | 0.0291292i | ||||
\(377\) | − | 9589.49i | − | 1.31004i | ||||||
\(378\) | −1151.81 | − | 16446.5i | −0.156727 | − | 2.23788i | ||||
\(379\) | 4679.90 | 0.634275 | 0.317138 | − | 0.948379i | \(-0.397278\pi\) | ||||
0.317138 | + | 0.948379i | \(0.397278\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3959.75 | + | 3168.35i | 0.532452 | + | 0.426036i | ||||
\(382\) | −1946.47 | + | 1123.79i | −0.260707 | + | 0.150519i | ||||
\(383\) | 5826.31 | − | 3363.82i | 0.777313 | − | 0.448782i | −0.0581644 | − | 0.998307i | \(-0.518525\pi\) |
0.835477 | + | 0.549525i | \(0.185191\pi\) | |||||||
\(384\) | −4390.33 | + | 1714.84i | −0.583446 | + | 0.227891i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16545.2 | −2.18167 | ||||||||
\(387\) | 1109.08 | − | 3554.44i | 0.145679 | − | 0.466880i | ||||
\(388\) | 1218.89i | 0.159483i | ||||||||
\(389\) | −2386.44 | + | 4133.43i | −0.311047 | + | 0.538749i | −0.978589 | − | 0.205823i | \(-0.934013\pi\) |
0.667542 | + | 0.744572i | \(0.267346\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1216.18 | − | 2106.49i | −0.157302 | − | 0.272455i | ||||
\(392\) | −4046.38 | + | 2336.18i | −0.521360 | + | 0.301007i | ||||
\(393\) | −8369.10 | − | 1275.37i | −1.07421 | − | 0.163699i | ||||
\(394\) | −9009.95 | + | 15605.7i | −1.15207 | + | 1.99544i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −746.681 | − | 3321.20i | −0.0947529 | − | 0.421456i | ||||
\(397\) | − | 4688.95i | − | 0.592775i | −0.955068 | − | 0.296388i | \(-0.904218\pi\) | ||
0.955068 | − | 0.296388i | \(-0.0957820\pi\) | |||||||
\(398\) | 1018.81 | + | 588.211i | 0.128313 | + | 0.0740813i | ||||
\(399\) | −9686.39 | + | 3783.45i | −1.21535 | + | 0.474711i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −766.916 | − | 1328.34i | −0.0955061 | − | 0.165421i | 0.814314 | − | 0.580425i | \(-0.197114\pi\) |
−0.909820 | + | 0.415004i | \(0.863780\pi\) | |||||||
\(402\) | −10435.5 | + | 13042.1i | −1.29471 | + | 1.61811i | ||||
\(403\) | −13202.4 | − | 7622.43i | −1.63191 | − | 0.942185i | ||||
\(404\) | −1606.03 | −0.197780 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18803.3 | 2.29851 | ||||||||
\(407\) | 3885.66 | + | 2243.38i | 0.473230 | + | 0.273220i | ||||
\(408\) | −1755.53 | + | 2194.04i | −0.213019 | + | 0.266228i | ||||
\(409\) | −4389.41 | − | 7602.68i | −0.530666 | − | 0.919140i | −0.999360 | − | 0.0357796i | \(-0.988609\pi\) |
0.468694 | − | 0.883361i | \(-0.344725\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3201.45 | − | 1250.47i | 0.384224 | − | 0.150076i | ||||
\(412\) | 2765.23 | + | 1596.50i | 0.330662 | + | 0.190908i | ||||
\(413\) | 19284.2i | 2.29761i | ||||||||
\(414\) | 729.271 | + | 3243.76i | 0.0865742 | + | 0.385077i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6762.61 | − | 11713.2i | 0.797029 | − | 1.38050i | ||||
\(417\) | −7104.21 | − | 1082.61i | −0.834279 | − | 0.127136i | ||||
\(418\) | −4317.58 | + | 2492.75i | −0.505214 | + | 0.291686i | ||||
\(419\) | −2138.02 | − | 3703.17i | −0.249282 | − | 0.431770i | 0.714044 | − | 0.700100i | \(-0.246861\pi\) |
−0.963327 | + | 0.268330i | \(0.913528\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7231.64 | + | 12525.6i | −0.837169 | + | 1.45002i | 0.0550823 | + | 0.998482i | \(0.482458\pi\) |
−0.892252 | + | 0.451538i | \(0.850875\pi\) | |||||||
\(422\) | 9142.07i | 1.05457i | ||||||||
\(423\) | −270.052 | + | 865.480i | −0.0310411 | + | 0.0994825i | ||||
\(424\) | −306.671 | −0.0351256 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10680.3 | − | 4171.66i | 1.21470 | − | 0.474455i | ||||
\(427\) | 3646.32 | − | 2105.21i | 0.413250 | − | 0.238590i | ||||
\(428\) | −10923.4 | + | 6306.65i | −1.23366 | + | 0.712251i | ||||
\(429\) | −5065.71 | − | 4053.27i | −0.570105 | − | 0.456163i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2208.11 | −0.246777 | −0.123389 | − | 0.992358i | \(-0.539376\pi\) | ||||
−0.123389 | + | 0.992358i | \(0.539376\pi\) | |||||||
\(432\) | 8814.60 | − | 5946.89i | 0.981696 | − | 0.662314i | ||||
\(433\) | 10062.3i | 1.11677i | 0.829581 | + | 0.558386i | \(0.188579\pi\) | ||||
−0.829581 | + | 0.558386i | \(0.811421\pi\) | |||||||
\(434\) | 14946.3 | − | 25887.7i | 1.65310 | − | 2.86325i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2800.90 | − | 4851.30i | −0.307658 | − | 0.532879i | ||||
\(437\) | 1816.12 | − | 1048.54i | 0.198803 | − | 0.114779i | ||||
\(438\) | 4380.90 | + | 11216.0i | 0.477917 | + | 1.22356i | ||||
\(439\) | 6658.62 | − | 11533.1i | 0.723915 | − | 1.25386i | −0.235504 | − | 0.971873i | \(-0.575674\pi\) |
0.959419 | − | 0.281984i | \(-0.0909925\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12700.8 | − | 11707.9i | 1.37142 | − | 1.26422i | ||||
\(442\) | − | 16634.8i | − | 1.79013i | ||||||
\(443\) | −12362.6 | − | 7137.55i | −1.32588 | − | 0.765497i | −0.341220 | − | 0.939983i | \(-0.610840\pi\) |
−0.984660 | + | 0.174486i | \(0.944174\pi\) | |||||||
\(444\) | 1020.26 | − | 6695.03i | 0.109052 | − | 0.715613i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4373.47 | + | 7575.08i | 0.464327 | + | 0.804238i | ||||
\(447\) | −16250.4 | − | 2476.39i | −1.71950 | − | 0.262034i | ||||
\(448\) | 6506.36 | + | 3756.45i | 0.686153 | + | 0.396151i | ||||
\(449\) | 1690.02 | 0.177632 | 0.0888162 | − | 0.996048i | \(-0.471692\pi\) | ||||
0.0888162 | + | 0.996048i | \(0.471692\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2951.69 | −0.308181 | ||||||||
\(452\) | −2861.66 | − | 1652.18i | −0.297791 | − | 0.171929i | ||||
\(453\) | 4837.39 | + | 12384.7i | 0.501723 | + | 1.28451i | ||||
\(454\) | −5104.97 | − | 8842.07i | −0.527727 | − | 0.914051i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1891.60 | − | 1513.54i | −0.194259 | − | 0.155434i | ||||
\(457\) | 5771.53 | + | 3332.19i | 0.590767 | + | 0.341080i | 0.765401 | − | 0.643554i | \(-0.222541\pi\) |
−0.174633 | + | 0.984634i | \(0.555874\pi\) | |||||||
\(458\) | 12423.3i | 1.26748i | ||||||||
\(459\) | 4552.97 | − | 9337.49i | 0.462994 | − | 0.949535i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −833.712 | + | 1444.03i | −0.0842295 | + | 0.145890i | −0.905063 | − | 0.425278i | \(-0.860176\pi\) |
0.820833 | + | 0.571168i | \(0.193510\pi\) | |||||||
\(462\) | 7947.76 | − | 9932.99i | 0.800354 | − | 1.00027i | ||||
\(463\) | 5050.68 | − | 2916.01i | 0.506966 | − | 0.292697i | −0.224620 | − | 0.974446i | \(-0.572114\pi\) |
0.731585 | + | 0.681750i | \(0.238781\pi\) | |||||||
\(464\) | 6063.56 | + | 10502.4i | 0.606668 | + | 1.05078i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5951.67 | − | 10308.6i | 0.591644 | − | 1.02476i | ||||
\(467\) | 17410.6i | 1.72519i | 0.505892 | + | 0.862597i | \(0.331163\pi\) | ||||
−0.505892 | + | 0.862597i | \(0.668837\pi\) | |||||||
\(468\) | −2916.84 | + | 9348.06i | −0.288100 | + | 0.923321i | ||||
\(469\) | −26883.0 | −2.64678 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2740.57 | + | 17983.9i | −0.268108 | + | 1.75935i | ||||
\(472\) | −3890.61 | + | 2246.24i | −0.379406 | + | 0.219050i | ||||
\(473\) | 2488.12 | − | 1436.52i | 0.241869 | − | 0.139643i | ||||
\(474\) | −1013.21 | + | 6648.81i | −0.0981822 | + | 0.644283i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 14047.8 | 1.35269 | ||||||||
\(477\) | 1106.16 | − | 248.689i | 0.106179 | − | 0.0238715i | ||||
\(478\) | 922.614i | 0.0882832i | ||||||||
\(479\) | −1639.67 | + | 2839.99i | −0.156406 | + | 0.270903i | −0.933570 | − | 0.358395i | \(-0.883324\pi\) |
0.777164 | + | 0.629298i | \(0.216657\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6453.53 | − | 11177.8i | −0.611758 | − | 1.05960i | ||||
\(482\) | −17165.9 | + | 9910.71i | −1.62216 | + | 0.936557i | ||||
\(483\) | −3343.10 | + | 4178.15i | −0.314940 | + | 0.393607i | ||||
\(484\) | −2714.13 | + | 4701.00i | −0.254895 | + | 0.441492i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9742.49 | + | 10330.1i | −0.909318 | + | 0.964162i | ||||
\(487\) | − | 10506.7i | − | 0.977624i | −0.872389 | − | 0.488812i | \(-0.837430\pi\) | ||
0.872389 | − | 0.488812i | \(-0.162570\pi\) | |||||||
\(488\) | 849.456 | + | 490.433i | 0.0787972 | + | 0.0454936i | ||||
\(489\) | 1070.91 | + | 856.875i | 0.0990350 | + | 0.0792417i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7132.25 | + | 12353.4i | 0.655548 | + | 1.13544i | 0.981756 | + | 0.190144i | \(0.0608956\pi\) |
−0.326208 | + | 0.945298i | \(0.605771\pi\) | |||||||
\(492\) | 1620.95 | + | 4149.95i | 0.148532 | + | 0.380272i | ||||
\(493\) | 10260.7 | + | 5924.01i | 0.937359 | + | 0.541184i | ||||
\(494\) | 14341.8 | 1.30621 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 19279.1 | 1.74527 | ||||||||
\(497\) | 15981.8 | + | 9227.09i | 1.44242 | + | 0.832780i | ||||
\(498\) | −21049.8 | − | 3207.78i | −1.89411 | − | 0.288643i | ||||
\(499\) | 4723.70 | + | 8181.68i | 0.423771 | + | 0.733993i | 0.996305 | − | 0.0858882i | \(-0.0273728\pi\) |
−0.572534 | + | 0.819881i | \(0.694039\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2809.52 | − | 18436.4i | 0.250539 | − | 1.64407i | ||||
\(502\) | −9158.70 | − | 5287.78i | −0.814288 | − | 0.470130i | ||||
\(503\) | − | 14579.2i | − | 1.29235i | −0.763188 | − | 0.646177i | \(-0.776367\pi\) | ||
0.763188 | − | 0.646177i | \(-0.223633\pi\) | |||||||
\(504\) | 5901.02 | + | 1841.27i | 0.521532 | + | 0.162732i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1282.69 | + | 2221.68i | −0.112692 | + | 0.195189i | ||||
\(507\) | 2636.73 | + | 6750.55i | 0.230969 | + | 0.591327i | ||||
\(508\) | 5115.03 | − | 2953.17i | 0.446738 | − | 0.257924i | ||||
\(509\) | 4205.32 | + | 7283.83i | 0.366204 | + | 0.634283i | 0.988969 | − | 0.148126i | \(-0.0473240\pi\) |
−0.622765 | + | 0.782409i | \(0.713991\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9689.89 | + | 16783.4i | −0.838856 | + | 1.45294i | ||||
\(512\) | 12676.3i | 1.09417i | ||||||||
\(513\) | 8050.35 | + | 3925.36i | 0.692849 | + | 0.337834i | ||||
\(514\) | 7063.02 | 0.606102 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3386.05 | − | 2709.31i | −0.288881 | − | 0.231145i | ||||
\(517\) | −605.838 | + | 349.781i | −0.0515372 | + | 0.0297550i | ||||
\(518\) | 21917.8 | − | 12654.3i | 1.85910 | − | 1.07335i | ||||
\(519\) | −1793.02 | + | 700.345i | −0.151647 | + | 0.0592327i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10058.1 | 0.845781 | 0.422890 | − | 0.906181i | \(-0.361016\pi\) | ||||
0.422890 | + | 0.906181i | \(0.361016\pi\) | |||||||
\(522\) | −10976.5 | − | 11907.3i | −0.920361 | − | 0.998409i | ||||
\(523\) | − | 20006.3i | − | 1.67269i | −0.548205 | − | 0.836344i | \(-0.684688\pi\) | ||
0.548205 | − | 0.836344i | \(-0.315312\pi\) | |||||||
\(524\) | −4929.83 | + | 8538.72i | −0.410994 | + | 0.711862i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1036.50 | − | 1795.27i | −0.0859192 | − | 0.148817i | ||||
\(527\) | 16311.9 | − | 9417.67i | 1.34830 | − | 0.778444i | ||||
\(528\) | 8110.90 | + | 1236.02i | 0.668525 | + | 0.101877i | ||||
\(529\) | −5543.96 | + | 9602.42i | −0.455655 | + | 0.789218i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12211.8 | − | 11257.2i | 0.998019 | − | 0.920001i | ||||
\(532\) | 12111.4i | 0.987019i | ||||||||
\(533\) | 7353.52 | + | 4245.56i | 0.597592 | + | 0.345020i | ||||
\(534\) | −7526.70 | + | 2939.89i | −0.609948 | + | 0.238243i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3131.36 | − | 5423.67i | −0.252340 | − | 0.437065i | ||||
\(537\) | 1450.79 | − | 1813.17i | 0.116585 | − | 0.145706i | ||||
\(538\) | 10919.0 | + | 6304.11i | 0.875006 | + | 0.505185i | ||||
\(539\) | 13328.5 | 1.06512 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1884.15 | −0.149734 | −0.0748668 | − | 0.997194i | \(-0.523853\pi\) | ||||
−0.0748668 | + | 0.997194i | \(0.523853\pi\) | |||||||
\(542\) | 10822.9 | + | 6248.58i | 0.857715 | + | 0.495202i | ||||
\(543\) | 2934.85 | − | 3667.93i | 0.231946 | − | 0.289882i | ||||
\(544\) | 8355.34 | + | 14471.9i | 0.658515 | + | 1.14058i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −34087.3 | + | 13314.3i | −2.67180 | + | 1.04359i | ||||
\(547\) | 15585.4 | + | 8998.24i | 1.21825 | + | 0.703358i | 0.964544 | − | 0.263922i | \(-0.0850163\pi\) |
0.253708 | + | 0.967281i | \(0.418350\pi\) | |||||||
\(548\) | − | 4002.93i | − | 0.312038i | ||||||
\(549\) | −3461.68 | − | 1080.14i | −0.269109 | − | 0.0839691i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5107.40 | + | 8846.28i | −0.394887 | + | 0.683964i | ||||
\(552\) | −1232.35 | − | 187.798i | −0.0950226 | − | 0.0144805i | ||||
\(553\) | −9374.30 | + | 5412.25i | −0.720860 | + | 0.416189i | ||||
\(554\) | −10097.2 | − | 17488.9i | −0.774351 | − | 1.34121i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4184.75 | + | 7248.19i | −0.319196 | + | 0.552863i | ||||
\(557\) | − | 3615.76i | − | 0.275054i | −0.990498 | − | 0.137527i | \(-0.956085\pi\) | ||
0.990498 | − | 0.137527i | \(-0.0439153\pi\) | |||||||
\(558\) | −25118.5 | + | 5647.21i | −1.90564 | + | 0.428433i | ||||
\(559\) | −8264.84 | −0.625341 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7466.36 | − | 2916.32i | 0.561907 | − | 0.219478i | ||||
\(562\) | 12065.7 | − | 6966.14i | 0.905625 | − | 0.522863i | ||||
\(563\) | −12836.1 | + | 7410.91i | −0.960881 | + | 0.554765i | −0.896444 | − | 0.443157i | \(-0.853858\pi\) |
−0.0644370 | + | 0.997922i | \(0.520525\pi\) | |||||||
\(564\) | 824.478 | + | 659.696i | 0.0615546 | + | 0.0492522i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10378.9 | 0.770771 | ||||||||
\(567\) | −22778.1 | − | 1856.11i | −1.68710 | − | 0.137477i | ||||
\(568\) | 4299.13i | 0.317583i | ||||||||
\(569\) | 11224.7 | − | 19441.8i | 0.827005 | − | 1.43241i | −0.0733726 | − | 0.997305i | \(-0.523376\pi\) |
0.900377 | − | 0.435110i | \(-0.143290\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8006.75 | + | 13868.1i | 0.586817 | + | 1.01640i | 0.994646 | + | 0.103338i | \(0.0329523\pi\) |
−0.407830 | + | 0.913058i | \(0.633714\pi\) | |||||||
\(572\) | −6543.66 | + | 3777.98i | −0.478329 | + | 0.276163i | ||||
\(573\) | 1133.52 | + | 2902.03i | 0.0826410 | + | 0.211577i | ||||
\(574\) | −8324.81 | + | 14419.0i | −0.605350 | + | 1.04850i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1419.31 | − | 6313.03i | −0.102670 | − | 0.456672i | ||||
\(577\) | 3096.97i | 0.223446i | 0.993739 | + | 0.111723i | \(0.0356370\pi\) | ||||
−0.993739 | + | 0.111723i | \(0.964363\pi\) | |||||||
\(578\) | 1849.81 | + | 1067.99i | 0.133117 | + | 0.0768553i | ||||
\(579\) | −3455.09 | + | 22672.7i | −0.247994 | + | 1.62736i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17135.0 | − | 29678.6i | −1.22354 | − | 2.11924i | ||||
\(582\) | 3878.33 | + | 591.018i | 0.276223 | + | 0.0420936i | ||||
\(583\) | 757.616 | + | 437.410i | 0.0538203 | + | 0.0310732i | ||||
\(584\) | −4514.76 | −0.319901 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13045.0 | −0.919595 | ||||||||
\(587\) | −21325.7 | − | 12312.4i | −1.49950 | − | 0.865734i | −0.499496 | − | 0.866316i | \(-0.666481\pi\) |
−1.00000 | 0.000582275i | \(0.999815\pi\) | ||||||||
\(588\) | −7319.49 | − | 18739.3i | −0.513351 | − | 1.31428i | ||||
\(589\) | 8119.48 | + | 14063.3i | 0.568009 | + | 0.983820i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19503.8 | + | 15605.7i | 1.35749 | + | 1.08618i | ||||
\(592\) | 14135.8 | + | 8161.30i | 0.981381 | + | 0.566601i | ||||
\(593\) | − | 27128.8i | − | 1.87866i | −0.343014 | − | 0.939330i | \(-0.611448\pi\) | ||
0.343014 | − | 0.939330i | \(-0.388552\pi\) | |||||||
\(594\) | −10929.7 | + | 765.442i | −0.754965 | + | 0.0528729i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9572.32 | + | 16579.7i | −0.657881 | + | 1.13948i | ||||
\(597\) | 1018.81 | − | 1273.29i | 0.0698445 | − | 0.0872906i | ||||
\(598\) | 6391.08 | − | 3689.89i | 0.437042 | − | 0.252326i | ||||
\(599\) | 2815.87 | + | 4877.24i | 0.192076 | + | 0.332685i | 0.945938 | − | 0.324347i | \(-0.105145\pi\) |
−0.753862 | + | 0.657033i | \(0.771811\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7375.88 | − | 12775.4i | 0.500613 | − | 0.867087i | −0.499387 | − | 0.866379i | \(-0.666441\pi\) |
1.00000 | 0.000707853i | \(-0.000225317\pi\) | ||||||||
\(602\) | − | 16205.9i | − | 1.09718i | ||||||
\(603\) | 15693.0 | + | 17023.8i | 1.05982 | + | 1.14969i | ||||
\(604\) | 15485.2 | 1.04318 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −778.738 | + | 5110.16i | −0.0522014 | + | 0.342552i | ||||
\(607\) | −12801.7 | + | 7391.04i | −0.856018 | + | 0.494222i | −0.862677 | − | 0.505756i | \(-0.831214\pi\) |
0.00665872 | + | 0.999978i | \(0.497880\pi\) | |||||||
\(608\) | −12477.0 | + | 7203.59i | −0.832251 | + | 0.480500i | ||||
\(609\) | 3926.66 | − | 25767.2i | 0.261275 | − | 1.71451i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2012.43 | 0.133247 | ||||||||
\(612\) | −8200.44 | − | 8895.85i | −0.541639 | − | 0.587571i | ||||
\(613\) | − | 4947.28i | − | 0.325969i | −0.986629 | − | 0.162984i | \(-0.947888\pi\) | ||
0.986629 | − | 0.162984i | \(-0.0521120\pi\) | |||||||
\(614\) | −3393.12 | + | 5877.06i | −0.223021 | + | 0.386284i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2384.88 | + | 4130.73i | 0.155989 | + | 0.270181i | ||||
\(617\) | −3242.09 | + | 1871.82i | −0.211543 | + | 0.122134i | −0.602028 | − | 0.798475i | \(-0.705640\pi\) |
0.390485 | + | 0.920609i | \(0.372307\pi\) | |||||||
\(618\) | 6420.67 | − | 8024.45i | 0.417924 | − | 0.522315i | ||||
\(619\) | 3069.37 | − | 5316.30i | 0.199303 | − | 0.345202i | −0.749000 | − | 0.662570i | \(-0.769466\pi\) |
0.948303 | + | 0.317368i | \(0.102799\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4597.38 | − | 321.971i | 0.297080 | − | 0.0208055i | ||||
\(622\) | − | 3326.09i | − | 0.214412i | ||||||
\(623\) | −11262.8 | − | 6502.59i | −0.724294 | − | 0.418171i | ||||
\(624\) | −18428.8 | − | 14745.6i | −1.18228 | − | 0.945986i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4151.79 | + | 7191.11i | 0.265078 | + | 0.459128i | ||||
\(627\) | 2514.32 | + | 6437.15i | 0.160147 | + | 0.410008i | ||||
\(628\) | 18348.4 | + | 10593.5i | 1.16589 | + | 0.673129i | ||||
\(629\) | 15946.9 | 1.01088 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5548.00 | −0.350019 | −0.175010 | − | 0.984567i | \(-0.555996\pi\) | ||||
−0.175010 | + | 0.984567i | \(0.555996\pi\) | |||||||
\(632\) | −2183.86 | − | 1260.85i | −0.137451 | − | 0.0793575i | ||||
\(633\) | 12527.8 | + | 1909.12i | 0.786630 | + | 0.119874i | ||||
\(634\) | −1233.36 | − | 2136.25i | −0.0772605 | − | 0.133819i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 198.927 | − | 1305.38i | 0.0124025 | − | 0.0813864i | ||||
\(637\) | −33205.3 | − | 19171.1i | −2.06537 | − | 1.19244i | ||||
\(638\) | − | 12495.9i | − | 0.775418i | ||||||
\(639\) | −3486.31 | − | 15506.9i | −0.215831 | − | 0.960005i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5804.05 | − | 10052.9i | 0.357639 | − | 0.619448i | −0.629927 | − | 0.776654i | \(-0.716915\pi\) |
0.987566 | + | 0.157206i | \(0.0502487\pi\) | |||||||
\(642\) | 14770.3 | + | 37814.9i | 0.908002 | + | 2.32466i | ||||
\(643\) | 11017.3 | − | 6360.85i | 0.675708 | − | 0.390120i | −0.122528 | − | 0.992465i | \(-0.539100\pi\) |
0.798236 | + | 0.602345i | \(0.205767\pi\) | |||||||
\(644\) | 3116.04 | + | 5397.15i | 0.190667 | + | 0.330244i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8859.78 | + | 15345.6i | −0.539603 | + | 0.934620i | ||||
\(647\) | − | 28203.7i | − | 1.71376i | −0.515518 | − | 0.856879i | \(-0.672400\pi\) | ||
0.515518 | − | 0.856879i | \(-0.327600\pi\) | |||||||
\(648\) | −2278.74 | − | 4811.70i | −0.138144 | − | 0.291700i | ||||
\(649\) | 12815.4 | 0.775115 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −32354.0 | − | 25887.7i | −1.94786 | − | 1.55856i | ||||
\(652\) | 1383.35 | − | 798.678i | 0.0830924 | − | 0.0479734i | ||||
\(653\) | 19652.5 | − | 11346.4i | 1.17774 | − | 0.679966i | 0.222247 | − | 0.974991i | \(-0.428661\pi\) |
0.955490 | + | 0.295024i | \(0.0953277\pi\) | |||||||
\(654\) | −16794.3 | + | 6559.76i | −1.00414 | + | 0.392213i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −10738.1 | −0.639103 | ||||||||
\(657\) | 16284.7 | − | 3661.17i | 0.967010 | − | 0.217406i | ||||
\(658\) | 3946.02i | 0.233787i | ||||||||
\(659\) | 3002.00 | − | 5199.61i | 0.177453 | − | 0.307357i | −0.763555 | − | 0.645743i | \(-0.776548\pi\) |
0.941007 | + | 0.338386i | \(0.109881\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5958.18 | − | 10319.9i | −0.350600 | − | 0.607256i | 0.635755 | − | 0.771891i | \(-0.280689\pi\) |
−0.986355 | + | 0.164635i | \(0.947356\pi\) | |||||||
\(662\) | 17129.2 | − | 9889.54i | 1.00566 | − | 0.580616i | ||||
\(663\) | −22795.6 | − | 3473.81i | −1.33530 | − | 0.203487i | ||||
\(664\) | 3991.80 | − | 6914.00i | 0.233301 | − | 0.404089i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −20808.0 | − | 6492.63i | −1.21065 | − | 0.377754i | ||||
\(667\) | 5256.19i | 0.305128i | ||||||||
\(668\) | −18810.1 | − | 10860.0i | −1.08950 | − | 0.629021i | ||||
\(669\) | 11293.8 | − | 4411.31i | 0.652682 | − | 0.254934i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1399.03 | − | 2423.19i | −0.0804901 | − | 0.139413i | ||||
\(672\) | 22967.5 | − | 28704.5i | 1.31844 | − | 1.64777i | ||||
\(673\) | −13885.6 | − | 8016.85i | −0.795319 | − | 0.459178i | 0.0465125 | − | 0.998918i | \(-0.485189\pi\) |
−0.841832 | + | 0.539740i | \(0.818523\pi\) | |||||||
\(674\) | 12599.9 | 0.720077 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8440.54 | 0.480231 | ||||||||
\(677\) | −9796.38 | − | 5655.94i | −0.556138 | − | 0.321086i | 0.195456 | − | 0.980712i | \(-0.437381\pi\) |
−0.751594 | + | 0.659626i | \(0.770715\pi\) | |||||||
\(678\) | −6644.59 | + | 8304.31i | −0.376378 | + | 0.470391i | ||||
\(679\) | 3157.03 | + | 5468.14i | 0.178432 | + | 0.309054i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13182.8 | + | 5149.13i | −0.741800 | + | 0.289743i | ||||
\(682\) | −17203.8 | − | 9932.64i | −0.965937 | − | 0.557684i | ||||
\(683\) | 652.395i | 0.0365493i | 0.999833 | + | 0.0182747i | \(0.00581733\pi\) | ||||
−0.999833 | + | 0.0182747i | \(0.994183\pi\) | |||||||
\(684\) | 7669.59 | − | 7070.04i | 0.428734 | − | 0.395219i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17437.4 | − | 30202.5i | 0.970502 | − | 1.68096i | ||||
\(687\) | 17024.3 | + | 2594.34i | 0.945443 | + | 0.144076i | ||||
\(688\) | 9051.64 | − | 5225.96i | 0.501585 | − | 0.289590i | ||||
\(689\) | −1258.29 | − | 2179.43i | −0.0695750 | − | 0.120507i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6268.93 | + | 10858.1i | −0.345125 | + | 0.597774i | −0.985376 | − | 0.170392i | \(-0.945497\pi\) |
0.640252 | + | 0.768165i | \(0.278830\pi\) | |||||||
\(692\) | 2241.90i | 0.123157i | ||||||||
\(693\) | −11952.0 | − | 12965.5i | −0.655148 | − | 0.710705i | ||||
\(694\) | −35069.8 | −1.91820 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5655.94 | − | 2209.18i | 0.308029 | − | 0.120314i | ||||
\(697\) | −9085.42 | + | 5245.47i | −0.493737 | + | 0.285059i | ||||
\(698\) | −22852.1 | + | 13193.6i | −1.23920 | + | 0.715454i | ||||
\(699\) | −12883.5 | − | 10308.6i | −0.697138 | − | 0.557807i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5880.60 | 0.316844 | 0.158422 | − | 0.987372i | \(-0.449359\pi\) | ||||
0.158422 | + | 0.987372i | \(0.449359\pi\) | |||||||
\(702\) | 28329.9 | + | 13813.7i | 1.52314 | + | 0.742684i | ||||
\(703\) | 13748.7i | 0.737614i | ||||||||
\(704\) | 2496.37 | − | 4323.84i | 0.133644 | − | 0.231479i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7876.07 | − | 13641.8i | −0.419858 | − | 0.727216i | ||||
\(707\) | −7204.93 | + | 4159.77i | −0.383266 | + | 0.221279i | ||||
\(708\) | −7037.71 | − | 18017.9i | −0.373578 | − | 0.956434i | ||||
\(709\) | 3203.33 | − | 5548.33i | 0.169681 | − | 0.293895i | −0.768627 | − | 0.639697i | \(-0.779060\pi\) |
0.938308 | + | 0.345802i | \(0.112393\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8899.62 | + | 2776.91i | 0.469426 | + | 0.146473i | ||||
\(712\) | − | 3029.72i | − | 0.159471i | ||||||
\(713\) | 7236.52 | + | 4178.00i | 0.380098 | + | 0.219449i | ||||
\(714\) | 6811.55 | − | 44698.2i | 0.357025 | − | 2.34284i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1352.25 | − | 2342.17i | −0.0705812 | − | 0.122250i | ||||
\(717\) | 1264.30 | + | 192.667i | 0.0658526 | + | 0.0100353i | ||||
\(718\) | 1908.90 | + | 1102.10i | 0.0992193 | + | 0.0572843i | ||||
\(719\) | −21907.0 | −1.13629 | −0.568144 | − | 0.822929i | \(-0.692338\pi\) | ||||
−0.568144 | + | 0.822929i | \(0.692338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16540.4 | 0.854364 | ||||||||
\(722\) | 9036.47 | + | 5217.21i | 0.465793 | + | 0.268926i | ||||
\(723\) | 9996.44 | + | 25592.9i | 0.514207 | + | 1.31647i | ||||
\(724\) | −2735.53 | − | 4738.07i | −0.140421 | − | 0.243217i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 13641.9 | + | 10915.4i | 0.697382 | + | 0.558002i | ||||
\(727\) | −11579.6 | − | 6685.46i | −0.590732 | − | 0.341059i | 0.174655 | − | 0.984630i | \(-0.444119\pi\) |
−0.765387 | + | 0.643571i | \(0.777452\pi\) | |||||||
\(728\) | − | 13721.1i | − | 0.698542i | ||||||
\(729\) | 12121.4 | + | 15507.8i | 0.615829 | + | 0.787880i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5105.69 | − | 8843.31i | 0.258332 | − | 0.447444i | ||||
\(732\) | −2638.61 | + | 3297.69i | −0.133232 | + | 0.166511i | ||||
\(733\) | −26146.2 | + | 15095.5i | −1.31751 | + | 0.760663i | −0.983327 | − | 0.181846i | \(-0.941793\pi\) |
−0.334181 | + | 0.942509i | \(0.608460\pi\) | |||||||
\(734\) | −14591.5 | − | 25273.2i | −0.733762 | − | 1.27091i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3706.72 | + | 6420.22i | −0.185641 | + | 0.321539i | ||||
\(737\) | 17865.2i | 0.892910i | ||||||||
\(738\) | 13990.5 | − | 3145.39i | 0.697830 | − | 0.156888i | ||||
\(739\) | 11624.7 | 0.578650 | 0.289325 | − | 0.957231i | \(-0.406569\pi\) | ||||
0.289325 | + | 0.957231i | \(0.406569\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2994.96 | − | 19653.3i | 0.148479 | − | 0.974334i | ||||
\(742\) | 4273.49 | − | 2467.30i | 0.211435 | − | 0.122072i | ||||
\(743\) | 4550.42 | − | 2627.19i | 0.224682 | − | 0.129720i | −0.383434 | − | 0.923568i | \(-0.625259\pi\) |
0.608116 | + | 0.793848i | \(0.291925\pi\) | |||||||
\(744\) | 1454.24 | − | 9542.90i | 0.0716601 | − | 0.470241i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −29328.9 | −1.43942 | ||||||||
\(747\) | −8791.57 | + | 28175.8i | −0.430612 | + | 1.38005i | ||||
\(748\) | − | 9335.55i | − | 0.456339i | ||||||
\(749\) | −32669.7 | + | 56585.5i | −1.59376 | + | 2.76047i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14614.4 | + | 25312.9i | 0.710102 | + | 1.22993i | 0.964819 | + | 0.262917i | \(0.0846844\pi\) |
−0.254717 | + | 0.967016i | \(0.581982\pi\) | |||||||
\(752\) | −2204.00 | + | 1272.48i | −0.106877 | + | 0.0617057i | ||||
\(753\) | −9158.70 | + | 11446.4i | −0.443242 | + | 0.553957i | ||||
\(754\) | −17973.4 | + | 31130.9i | −0.868108 | + | 1.50361i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −11665.4 | + | 23924.1i | −0.561199 | + | 1.15094i | ||||
\(757\) | 32885.9i | 1.57894i | 0.613789 | + | 0.789470i | \(0.289645\pi\) | ||||
−0.613789 | + | 0.789470i | \(0.710355\pi\) | |||||||
\(758\) | −15192.6 | − | 8771.46i | −0.727995 | − | 0.420308i | ||||
\(759\) | 2776.62 | + | 2221.68i | 0.132786 | + | 0.106247i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6634.11 | + | 11490.6i | 0.316014 | + | 0.547352i | 0.979652 | − | 0.200702i | \(-0.0643221\pi\) |
−0.663639 | + | 0.748053i | \(0.730989\pi\) | |||||||
\(762\) | −6916.37 | − | 17707.3i | −0.328811 | − | 0.841820i | ||||
\(763\) | −25130.7 | − | 14509.2i | −1.19239 | − | 0.688425i | ||||
\(764\) | 3628.54 | 0.171827 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25219.0 | −1.18956 | ||||||||
\(767\) | −31927.0 | − | 18433.0i | −1.50302 | − | 0.867769i | ||||
\(768\) | 27315.1 | + | 4162.55i | 1.28340 | + | 0.195577i | ||||
\(769\) | 17142.9 | + | 29692.4i | 0.803887 | + | 1.39237i | 0.917040 | + | 0.398796i | \(0.130572\pi\) |
−0.113153 | + | 0.993578i | \(0.536095\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1474.95 | − | 9678.81i | 0.0688964 | − | 0.452106i | ||||
\(772\) | 23132.2 | + | 13355.4i | 1.07843 | + | 0.622630i | ||||
\(773\) | 27987.1i | 1.30223i | 0.758978 | + | 0.651117i | \(0.225699\pi\) | ||||
−0.758978 | + | 0.651117i | \(0.774301\pi\) | |||||||
\(774\) | −10262.5 | + | 9460.25i | −0.476586 | + | 0.439330i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −735.469 | + | 1273.87i | −0.0340229 | + | 0.0589294i | ||||
\(777\) | −12763.7 | − | 32677.7i | −0.589313 | − | 1.50876i | ||||
\(778\) | 15494.4 | − | 8945.72i | 0.714014 | − | 0.412236i | ||||
\(779\) | −4522.40 | − | 7833.03i | −0.208000 | − | 0.360266i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6131.92 | − | 10620.8i | 0.280944 | − | 0.486610i | ||||
\(782\) | 9117.88i | 0.416950i | ||||||||
\(783\) | −18609.4 | + | 12555.1i | −0.849356 | + | 0.573029i | ||||
\(784\) | 48488.5 | 2.20884 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 24778.7 | + | 19826.3i | 1.12446 | + | 0.899723i | ||||
\(787\) | 307.265 | − | 177.400i | 0.0139172 | − | 0.00803509i | −0.493025 | − | 0.870015i | \(-0.664109\pi\) |
0.506942 | + | 0.861980i | \(0.330776\pi\) | |||||||
\(788\) | 25194.1 | − | 14545.8i | 1.13896 | − | 0.657580i | ||||
\(789\) | −2676.60 | + | 1045.47i | −0.120772 | + | 0.0471731i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17117.2 | −0.769430 | ||||||||
\(792\) | 1223.63 | − | 3921.56i | 0.0548987 | − | 0.175943i | ||||
\(793\) | 8049.15i | 0.360446i | ||||||||
\(794\) | −8788.42 | + | 15222.0i | −0.392808 | + | 0.680363i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −949.617 | − | 1644.78i | −0.0422843 | − | 0.0732385i | ||||
\(797\) | 11086.2 | − | 6400.65i | 0.492717 | − | 0.284470i | −0.232984 | − | 0.972481i | \(-0.574849\pi\) |
0.725701 | + | 0.688011i | \(0.241516\pi\) | |||||||
\(798\) | 38536.7 | + | 5872.60i | 1.70950 | + | 0.260511i | ||||
\(799\) | −1243.20 | + | 2153.28i | −0.0550452 | + | 0.0953411i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2456.90 | + | 10928.2i | 0.108377 | + | 0.482056i | ||||
\(802\) | 5749.67i | 0.253152i | ||||||||
\(803\) | 11153.5 | + | 6439.48i | 0.490160 | + | 0.282994i | ||||
\(804\) | 25117.7 | − | 9810.86i | 1.10178 | − | 0.430351i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 28573.2 | + | 49490.2i | 1.24869 | + | 2.16280i | ||||
\(807\) | 10919.0 | − | 13646.4i | 0.476293 | − | 0.595264i | ||||
\(808\) | −1678.48 | − | 969.069i | −0.0730800 | − | 0.0421927i | ||||
\(809\) | 16374.9 | 0.711632 | 0.355816 | − | 0.934556i | \(-0.384203\pi\) | ||||
0.355816 | + | 0.934556i | \(0.384203\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35518.2 | −1.53787 | −0.768936 | − | 0.639326i | \(-0.779214\pi\) | ||||
−0.768936 | + | 0.639326i | \(0.779214\pi\) | |||||||
\(812\) | −26289.4 | − | 15178.2i | −1.13618 | − | 0.655974i | ||||
\(813\) | 10822.9 | − | 13526.2i | 0.466881 | − | 0.583500i | ||||
\(814\) | −8409.47 | − | 14565.6i | −0.362103 | − | 0.627181i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 27162.2 | − | 10609.4i | 1.16528 | − | 0.455152i | ||||
\(817\) | 7624.29 | + | 4401.89i | 0.326487 | + | 0.188498i | ||||
\(818\) | 32908.0i | 1.40660i | ||||||||
\(819\) | 11126.9 | + | 49491.9i | 0.474733 | + | 2.11158i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21471.9 | + | 37190.5i | −0.912760 | + | 1.58095i | −0.102612 | + | 0.994721i | \(0.532720\pi\) |
−0.810148 | + | 0.586226i | \(0.800613\pi\) | |||||||
\(822\) | −12736.8 | − | 1940.96i | −0.540445 | − | 0.0823584i | ||||
\(823\) | 6856.26 | − | 3958.46i | 0.290394 | − | 0.167659i | −0.347726 | − | 0.937596i | \(-0.613046\pi\) |
0.638119 | + | 0.769937i | \(0.279713\pi\) | |||||||
\(824\) | 1926.64 | + | 3337.04i | 0.0814536 | + | 0.141082i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 36144.0 | − | 62603.3i | 1.52253 | − | 2.63710i | ||||
\(827\) | 18774.4i | 0.789421i | 0.918806 | + | 0.394710i | \(0.129155\pi\) | ||||
−0.918806 | + | 0.394710i | \(0.870845\pi\) | |||||||
\(828\) | 1598.77 | − | 5123.85i | 0.0671030 | − | 0.215056i | ||||
\(829\) | −22166.1 | −0.928661 | −0.464330 | − | 0.885662i | \(-0.653705\pi\) | ||||
−0.464330 | + | 0.885662i | \(0.653705\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26074.5 | + | 10184.6i | −1.08847 | + | 0.425149i | ||||
\(832\) | −12438.4 | + | 7181.30i | −0.518297 | + | 0.299239i | ||||
\(833\) | 41025.8 | − | 23686.2i | 1.70643 | − | 0.985210i | ||||
\(834\) | 21033.6 | + | 16829.8i | 0.873304 | + | 0.698764i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8048.68 | 0.332978 | ||||||||
\(837\) | 2493.22 | + | 35600.4i | 0.102961 | + | 1.47017i | ||||
\(838\) | 16029.1i | 0.660757i | ||||||||
\(839\) | 21295.4 | − | 36884.7i | 0.876279 | − | 1.51776i | 0.0208849 | − | 0.999782i | \(-0.493352\pi\) |
0.855394 | − | 0.517978i | \(-0.173315\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −606.908 | − | 1051.20i | −0.0248845 | − | 0.0431012i | ||||
\(842\) | 46952.9 | − | 27108.3i | 1.92174 | − | 1.10952i | ||||
\(843\) | −7026.40 | − | 17989.0i | −0.287073 | − | 0.734963i | ||||
\(844\) | 7379.55 | − | 12781.7i | 0.300965 | − | 0.521287i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2498.84 | − | 2303.50i | 0.101551 | − | 0.0936122i | ||||
\(847\) | 28119.4i | 1.14072i | ||||||||
\(848\) | 2756.16 | + | 1591.27i | 0.111612 | + | 0.0644393i | ||||
\(849\) | 2167.39 | − | 14222.7i | 0.0876145 | − | 0.574937i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3537.31 | + | 6126.79i | 0.142488 | + | 0.246796i | ||||
\(852\) | −18299.8 | − | 2788.70i | −0.735845 | − | 0.112135i | ||||
\(853\) | 22916.0 | + | 13230.6i | 0.919847 | + | 0.531074i | 0.883586 | − | 0.468269i | \(-0.155122\pi\) |
0.0362605 | + | 0.999342i | \(0.488455\pi\) | |||||||
\(854\) | −15783.0 | −0.632416 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15221.6 | −0.607784 | ||||||||
\(857\) | 17328.3 | + | 10004.5i | 0.690693 | + | 0.398772i | 0.803871 | − | 0.594803i | \(-0.202770\pi\) |
−0.113179 | + | 0.993575i | \(0.536103\pi\) | |||||||
\(858\) | 8848.12 | + | 22652.9i | 0.352063 | + | 0.901350i | ||||
\(859\) | −8909.03 | − | 15430.9i | −0.353868 | − | 0.612917i | 0.633056 | − | 0.774106i | \(-0.281800\pi\) |
−0.986923 | + | 0.161189i | \(0.948467\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18020.6 | + | 14419.0i | 0.713288 | + | 0.570729i | ||||
\(862\) | 7168.31 | + | 4138.63i | 0.283241 | + | 0.163529i | ||||
\(863\) | − | 12769.5i | − | 0.503683i | −0.967769 | − | 0.251841i | \(-0.918964\pi\) | ||
0.967769 | − | 0.251841i | \(-0.0810361\pi\) | |||||||
\(864\) | −31584.6 | + | 2211.98i | −1.24367 | + | 0.0870986i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 18859.6 | − | 32665.7i | 0.740039 | − | 1.28179i | ||||
\(867\) | 1849.81 | − | 2311.86i | 0.0724598 | − | 0.0905592i | ||||
\(868\) | −41793.5 | + | 24129.5i | −1.63429 | + | 0.943558i | ||||
\(869\) | 3596.75 | + | 6229.75i | 0.140404 | + | 0.243187i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25696.4 | − | 44507.5i | 0.999644 | − | 1.73144i | ||||
\(872\) | − | 6760.19i | − | 0.262533i | ||||||
\(873\) | 1619.80 | − | 5191.25i | 0.0627973 | − | 0.201257i | ||||
\(874\) | −7861.01 | −0.304236 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2928.57 | − | 19217.6i | 0.112954 | − | 0.741214i | ||||
\(877\) | 23796.0 | − | 13738.6i | 0.916231 | − | 0.528986i | 0.0338003 | − | 0.999429i | \(-0.489239\pi\) |
0.882431 | + | 0.470442i | \(0.155906\pi\) | |||||||
\(878\) | −43232.5 | + | 24960.3i | −1.66176 | + | 0.959417i | ||||
\(879\) | −2724.15 | + | 17876.2i | −0.104532 | + | 0.685948i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31509.1 | 1.20496 | 0.602480 | − | 0.798134i | \(-0.294179\pi\) | ||||
0.602480 | + | 0.798134i | \(0.294179\pi\) | |||||||
\(882\) | −63175.1 | + | 14203.2i | −2.41181 | + | 0.542230i | ||||
\(883\) | − | 5271.46i | − | 0.200905i | −0.994942 | − | 0.100452i | \(-0.967971\pi\) | ||
0.994942 | − | 0.100452i | \(-0.0320290\pi\) | |||||||
\(884\) | −13427.8 | + | 23257.6i | −0.510888 | + | 0.884883i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 26755.6 | + | 46342.0i | 1.01453 | + | 1.75721i | ||||
\(887\) | 9035.91 | − | 5216.89i | 0.342048 | − | 0.197481i | −0.319130 | − | 0.947711i | \(-0.603391\pi\) |
0.661177 | + | 0.750230i | \(0.270057\pi\) | |||||||
\(888\) | 5106.03 | − | 6381.43i | 0.192958 | − | 0.241156i | ||||
\(889\) | 15298.0 | − | 26496.9i | 0.577140 | − | 0.999636i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1233.49 | + | 15137.3i | −0.0463787 | + | 0.569157i | ||||
\(892\) | − | 14121.2i | − | 0.530059i | ||||||
\(893\) | −1856.46 | − | 1071.83i | −0.0695677 | − | 0.0401649i | ||||
\(894\) | 48113.0 | + | 38497.1i | 1.79993 | + | 1.44019i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 14218.2 | + | 24626.6i | 0.530130 | + | 0.918212i | ||||
\(897\) | −3721.81 | − | 9528.58i | −0.138537 | − | 0.354682i | ||||
\(898\) | −5486.40 | − | 3167.57i | −0.203879 | − | 0.117710i | ||||
\(899\) | −40702.0 | −1.51000 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3109.30 | 0.114967 | ||||||||
\(902\) | 9582.23 | + | 5532.30i | 0.353718 | + | 0.204219i | ||||
\(903\) | −22207.8 | − | 3384.24i | −0.818415 | − | 0.124718i | ||||
\(904\) | −1993.84 | − | 3453.43i | −0.0733562 | − | 0.127057i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7508.51 | − | 49271.7i | 0.275335 | − | 1.80678i | ||||
\(907\) | −17915.1 | − | 10343.3i | −0.655856 | − | 0.378659i | 0.134840 | − | 0.990867i | \(-0.456948\pi\) |
−0.790696 | + | 0.612209i | \(0.790281\pi\) | |||||||
\(908\) | 16483.1i | 0.602434i | ||||||||
\(909\) | 6840.10 | + | 2134.29i | 0.249584 | + | 0.0778766i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11820.0 | − | 20472.9i | 0.429874 | − | 0.744563i | −0.566988 | − | 0.823726i | \(-0.691891\pi\) |
0.996862 | + | 0.0791627i | \(0.0252247\pi\) | |||||||
\(912\) | 9146.95 | + | 23418.0i | 0.332111 | + | 0.850271i | ||||
\(913\) | −19723.1 | + | 11387.1i | −0.714939 | + | 0.412770i | ||||
\(914\) | −12490.9 | − | 21635.0i | −0.452039 | − | 0.782955i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10028.2 | − | 17369.4i | 0.361727 | − | 0.626529i | ||||
\(917\) | 51075.0i | 1.83931i | ||||||||
\(918\) | −32281.6 | + | 21779.2i | −1.16062 | + | 0.783030i | ||||
\(919\) | −27335.2 | −0.981180 | −0.490590 | − | 0.871390i | \(-0.663219\pi\) | ||||
−0.490590 | + | 0.871390i | \(0.663219\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7345.05 | + | 5877.06i | 0.262788 | + | 0.210267i | ||||
\(922\) | 5413.04 | − | 3125.22i | 0.193350 | − | 0.111631i | ||||
\(923\) | −30552.8 | + | 17639.7i | −1.08955 | + | 0.629054i | ||||
\(924\) | −19129.9 | + | 7472.06i | −0.681092 | + | 0.266031i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −21861.7 | −0.775832 | ||||||||
\(927\) | −9655.50 | − | 10474.3i | −0.342102 | − | 0.371112i | ||||
\(928\) | − | 36110.7i | − | 1.27736i | ||||||
\(929\) | −6614.28 | + | 11456.3i | −0.233593 | + | 0.404594i | −0.958863 | − | 0.283870i | \(-0.908382\pi\) |
0.725270 | + | 0.688464i | \(0.241715\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20421.2 | + | 35370.5i | 0.718880 | + | 1.24514i | ||||
\(932\) | −16642.4 | + | 9608.47i | −0.584913 | + | 0.337700i | ||||
\(933\) | −4557.91 | − | 694.580i | −0.159935 | − | 0.0243725i | ||||
\(934\) | 32632.3 | − | 56520.9i | 1.14321 | − | 1.98011i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8688.98 | + | 8009.75i | −0.303428 | + | 0.279708i | ||||
\(937\) | − | 18740.4i | − | 0.653387i | −0.945130 | − | 0.326693i | \(-0.894066\pi\) | ||
0.945130 | − | 0.326693i | \(-0.105934\pi\) | |||||||
\(938\) | 87271.6 | + | 50386.3i | 3.03787 | + | 1.75391i | ||||
\(939\) | 10721.3 | − | 4187.70i | 0.372607 | − | 0.145538i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27244.5 | − | 47188.9i | −0.943832 | − | 1.63476i | −0.758074 | − | 0.652169i | \(-0.773859\pi\) |
−0.185758 | − | 0.982596i | \(-0.559474\pi\) | |||||||
\(942\) | 42603.8 | − | 53245.6i | 1.47357 | − | 1.84165i | ||||
\(943\) | −4030.61 | − | 2327.07i | −0.139188 | − | 0.0803605i | ||||
\(944\) | 46621.8 | 1.60743 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10769.7 | −0.370142 | ||||||||
\(947\) | 9771.11 | + | 5641.35i | 0.335289 | + | 0.193579i | 0.658187 | − | 0.752855i | \(-0.271324\pi\) |
−0.322898 | + | 0.946434i | \(0.604657\pi\) | |||||||
\(948\) | 6783.57 | − | 8477.99i | 0.232405 | − | 0.290456i | ||||
\(949\) | −18524.4 | − | 32085.2i | −0.633644 | − | 1.09750i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3184.97 | + | 1244.03i | −0.108601 | + | 0.0424191i | ||||
\(952\) | 14681.5 | + | 8476.36i | 0.499821 | + | 0.288572i | ||||
\(953\) | 51190.0i | 1.73999i | 0.493063 | + | 0.869994i | \(0.335877\pi\) | ||||
−0.493063 | + | 0.869994i | \(0.664123\pi\) | |||||||
\(954\) | −4057.09 | − | 1265.92i | −0.137687 | − | 0.0429618i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 744.741 | − | 1289.93i | 0.0251952 | − | 0.0436394i | ||||
\(957\) | −17123.7 | − | 2609.49i | −0.578403 | − | 0.0881428i | ||||
\(958\) | 10645.9 | − | 6146.41i | 0.359033 | − | 0.207288i | ||||
\(959\) | −10368.0 | − | 17957.8i | −0.349113 | − | 0.604681i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17457.4 | + | 30237.2i | −0.585997 | + | 1.01498i | ||||
\(962\) | 48383.0i | 1.62155i | ||||||||
\(963\) | 54904.1 | − | 12343.7i | 1.83724 | − | 0.413053i | ||||
\(964\) | 32000.0 | 1.06914 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 18683.9 | − | 7297.84i | 0.622303 | − | 0.243068i | ||||
\(967\) | 20042.9 | − | 11571.8i | 0.666530 | − | 0.384822i | −0.128230 | − | 0.991744i | \(-0.540930\pi\) |
0.794761 | + | 0.606923i | \(0.207596\pi\) | |||||||
\(968\) | −5673.12 | + | 3275.38i | −0.188369 | + | 0.108755i | ||||
\(969\) | 19178.7 | + | 15345.6i | 0.635818 | + | 0.508742i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34124.5 | −1.12782 | −0.563908 | − | 0.825838i | \(-0.690703\pi\) | ||||
−0.563908 | + | 0.825838i | \(0.690703\pi\) | |||||||
\(972\) | 21959.8 | − | 6578.56i | 0.724650 | − | 0.217086i | ||||
\(973\) | 43355.6i | 1.42848i | ||||||||
\(974\) | −19692.5 | + | 34108.4i | −0.647831 | + | 1.12208i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5089.58 | − | 8815.42i | −0.166920 | − | 0.289113i | ||||
\(977\) | −31578.5 | + | 18231.8i | −1.03407 | + | 0.597020i | −0.918148 | − | 0.396239i | \(-0.870315\pi\) |
−0.115921 | + | 0.993258i | \(0.536982\pi\) | |||||||
\(978\) | −1870.52 | − | 4788.90i | −0.0611581 | − | 0.156577i | ||||
\(979\) | −4321.34 | + | 7484.78i | −0.141073 | + | 0.244346i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5482.06 | + | 24383.9i | 0.178419 | + | 0.793597i | ||||
\(982\) | − | 53471.4i | − | 1.73762i | ||||||
\(983\) | −44636.3 | − | 25770.8i | −1.44830 | − | 0.836176i | −0.449918 | − | 0.893070i | \(-0.648547\pi\) |
−0.998380 | + | 0.0568941i | \(0.981880\pi\) | |||||||
\(984\) | −809.986 | + | 5315.22i | −0.0262413 | + | 0.172198i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −22206.5 | − | 38462.8i | −0.717241 | − | 1.24230i | ||||
\(987\) | 5407.43 | + | 824.038i | 0.174387 | + | 0.0265749i | ||||
\(988\) | −20051.6 | − | 11576.8i | −0.645675 | − | 0.372780i | ||||
\(989\) | 4530.12 | 0.145652 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34299.1 | 1.09944 | 0.549721 | − | 0.835348i | \(-0.314734\pi\) | ||||
0.549721 | + | 0.835348i | \(0.314734\pi\) | |||||||
\(992\) | −49715.9 | − | 28703.5i | −1.59121 | − | 0.918685i | ||||
\(993\) | −9975.10 | − | 25538.2i | −0.318782 | − | 0.816144i | ||||
\(994\) | −34588.3 | − | 59908.8i | −1.10370 | − | 1.91166i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 26840.9 | + | 21476.5i | 0.853903 | + | 0.683241i | ||||
\(997\) | −18443.7 | − | 10648.5i | −0.585877 | − | 0.338256i | 0.177589 | − | 0.984105i | \(-0.443170\pi\) |
−0.763465 | + | 0.645849i | \(0.776504\pi\) | |||||||
\(998\) | − | 35414.2i | − | 1.12326i | ||||||
\(999\) | −13242.5 | + | 27158.4i | −0.419392 | + | 0.860113i |
(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 | 225.4.k.c.124.2 | 12 | ||
5.2 | odd | 4 | 225.4.e.c.151.3 | 6 | |||
5.3 | odd | 4 | 45.4.e.b.16.1 | ✓ | 6 | ||
5.4 | even | 2 | inner | 225.4.k.c.124.5 | 12 | ||
9.4 | even | 3 | inner | 225.4.k.c.49.5 | 12 | ||
15.8 | even | 4 | 135.4.e.b.46.3 | 6 | |||
45.2 | even | 12 | 2025.4.a.q.1.3 | 3 | |||
45.4 | even | 6 | inner | 225.4.k.c.49.2 | 12 | ||
45.7 | odd | 12 | 2025.4.a.s.1.1 | 3 | |||
45.13 | odd | 12 | 45.4.e.b.31.1 | yes | 6 | ||
45.22 | odd | 12 | 225.4.e.c.76.3 | 6 | |||
45.23 | even | 12 | 135.4.e.b.91.3 | 6 | |||
45.38 | even | 12 | 405.4.a.j.1.1 | 3 | |||
45.43 | odd | 12 | 405.4.a.h.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.b.16.1 | ✓ | 6 | 5.3 | odd | 4 | ||
45.4.e.b.31.1 | yes | 6 | 45.13 | odd | 12 | ||
135.4.e.b.46.3 | 6 | 15.8 | even | 4 | |||
135.4.e.b.91.3 | 6 | 45.23 | even | 12 | |||
225.4.e.c.76.3 | 6 | 45.22 | odd | 12 | |||
225.4.e.c.151.3 | 6 | 5.2 | odd | 4 | |||
225.4.k.c.49.2 | 12 | 45.4 | even | 6 | inner | ||
225.4.k.c.49.5 | 12 | 9.4 | even | 3 | inner | ||
225.4.k.c.124.2 | 12 | 1.1 | even | 1 | trivial | ||
225.4.k.c.124.5 | 12 | 5.4 | even | 2 | inner | ||
405.4.a.h.1.3 | 3 | 45.43 | odd | 12 | |||
405.4.a.j.1.1 | 3 | 45.38 | even | 12 | |||
2025.4.a.q.1.3 | 3 | 45.2 | even | 12 | |||
2025.4.a.s.1.1 | 3 | 45.7 | odd | 12 |