Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,4,Mod(361,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.i (of order \(3\), 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: | \(34.6931230834\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 27x^{6} + 10x^{5} + 446x^{4} + 62x^{3} + 3061x^{2} + 2142x + 14161 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.3 | ||
Root | \(2.46576 - 4.27083i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.361 |
Dual form | 588.4.i.k.373.3 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0 | ||||||||
\(3\) | −1.50000 | + | 2.59808i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.32752 | + | 9.22754i | 0.476508 | + | 0.825336i | 0.999638 | − | 0.0269168i | \(-0.00856891\pi\) |
−0.523129 | + | 0.852253i | \(0.675236\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.32699 | − | 5.76252i | 0.0911933 | − | 0.157951i | −0.816820 | − | 0.576892i | \(-0.804265\pi\) |
0.908014 | + | 0.418941i | \(0.137599\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 75.9335 | 1.62001 | 0.810006 | − | 0.586422i | \(-0.199464\pi\) | ||||
0.810006 | + | 0.586422i | \(0.199464\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −31.9651 | −0.550224 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 52.1435 | − | 90.3152i | 0.743921 | − | 1.28851i | −0.206776 | − | 0.978388i | \(-0.566297\pi\) |
0.950697 | − | 0.310121i | \(-0.100369\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −42.7472 | − | 74.0402i | −0.516151 | − | 0.894000i | −0.999824 | − | 0.0187511i | \(-0.994031\pi\) |
0.483673 | − | 0.875249i | \(-0.339302\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 34.3366 | + | 59.4728i | 0.311291 | + | 0.539171i | 0.978642 | − | 0.205572i | \(-0.0659054\pi\) |
−0.667351 | + | 0.744743i | \(0.732572\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.73498 | − | 9.93327i | 0.0458798 | − | 0.0794662i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 87.7843 | 0.562108 | 0.281054 | − | 0.959692i | \(-0.409316\pi\) | ||||
0.281054 | + | 0.959692i | \(0.409316\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −31.3841 | + | 54.3589i | −0.181831 | + | 0.314940i | −0.942504 | − | 0.334195i | \(-0.891536\pi\) |
0.760673 | + | 0.649135i | \(0.224869\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.98098 | + | 17.2876i | 0.0526505 | + | 0.0911933i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −21.1047 | − | 36.5544i | −0.0937726 | − | 0.162419i | 0.815323 | − | 0.579006i | \(-0.196559\pi\) |
−0.909096 | + | 0.416587i | \(0.863226\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −113.900 | + | 197.281i | −0.467657 | + | 0.810006i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 313.904 | 1.19570 | 0.597848 | − | 0.801609i | \(-0.296023\pi\) | ||||
0.597848 | + | 0.801609i | \(0.296023\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 306.591 | 1.08732 | 0.543659 | − | 0.839306i | \(-0.317038\pi\) | ||||
0.543659 | + | 0.839306i | \(0.317038\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 47.9477 | − | 83.0479i | 0.158836 | − | 0.275112i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −107.541 | − | 186.266i | −0.333754 | − | 0.578079i | 0.649491 | − | 0.760369i | \(-0.274982\pi\) |
−0.983245 | + | 0.182291i | \(0.941649\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 156.430 | + | 270.946i | 0.429503 | + | 0.743921i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −262.512 | + | 454.684i | −0.680354 | + | 1.17841i | 0.294519 | + | 0.955646i | \(0.404841\pi\) |
−0.974873 | + | 0.222762i | \(0.928493\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 70.8986 | 0.173818 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 256.483 | 0.596000 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −180.246 | + | 312.195i | −0.397729 | + | 0.688886i | −0.993445 | − | 0.114308i | \(-0.963535\pi\) |
0.595717 | + | 0.803195i | \(0.296868\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −400.363 | − | 693.449i | −0.840348 | − | 1.45553i | −0.889601 | − | 0.456739i | \(-0.849017\pi\) |
0.0492530 | − | 0.998786i | \(-0.484316\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 404.537 | + | 700.679i | 0.771949 | + | 1.33705i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 20.1143 | − | 34.8390i | 0.0366769 | − | 0.0635262i | −0.847104 | − | 0.531427i | \(-0.821656\pi\) |
0.883781 | + | 0.467900i | \(0.154989\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −206.020 | −0.359447 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −298.781 | −0.499419 | −0.249709 | − | 0.968321i | \(-0.580335\pi\) | ||||
−0.249709 | + | 0.968321i | \(0.580335\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −258.563 | + | 447.844i | −0.414555 | + | 0.718030i | −0.995382 | − | 0.0959971i | \(-0.969396\pi\) |
0.580827 | + | 0.814027i | \(0.302729\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 17.2049 | + | 29.7998i | 0.0264887 | + | 0.0458798i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 611.233 | + | 1058.69i | 0.870494 | + | 1.50774i | 0.861486 | + | 0.507781i | \(0.169534\pi\) |
0.00900832 | + | 0.999959i | \(0.497133\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1328.55 | 1.75696 | 0.878479 | − | 0.477782i | \(-0.158559\pi\) | ||||
0.878479 | + | 0.477782i | \(0.158559\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1111.18 | 1.41794 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −131.676 | + | 228.070i | −0.162267 | + | 0.281054i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 319.969 | + | 554.203i | 0.381086 | + | 0.660060i | 0.991218 | − | 0.132240i | \(-0.0422169\pi\) |
−0.610132 | + | 0.792300i | \(0.708884\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −94.1524 | − | 163.077i | −0.104980 | − | 0.181831i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 455.473 | − | 788.902i | 0.491900 | − | 0.851996i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1425.65 | 1.49230 | 0.746149 | − | 0.665779i | \(-0.231901\pi\) | ||||
0.746149 | + | 0.665779i | \(0.231901\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −59.8859 | −0.0607956 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 496.085 | − | 859.244i | 0.488736 | − | 0.846515i | −0.511180 | − | 0.859473i | \(-0.670792\pi\) |
0.999916 | + | 0.0129585i | \(0.00412493\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −133.786 | − | 231.724i | −0.127984 | − | 0.221674i | 0.794912 | − | 0.606725i | \(-0.207517\pi\) |
−0.922895 | + | 0.385051i | \(0.874184\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 768.312 | + | 1330.76i | 0.694164 | + | 1.20233i | 0.970462 | + | 0.241255i | \(0.0775591\pi\) |
−0.276298 | + | 0.961072i | \(0.589108\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −499.410 | + | 865.004i | −0.438852 | + | 0.760113i | −0.997601 | − | 0.0692232i | \(-0.977948\pi\) |
0.558750 | + | 0.829336i | \(0.311281\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 126.628 | 0.108279 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 939.006 | 0.781719 | 0.390860 | − | 0.920450i | \(-0.372178\pi\) | ||||
0.390860 | + | 0.920450i | \(0.372178\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −365.858 | + | 633.685i | −0.296665 | + | 0.513839i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −341.701 | − | 591.843i | −0.270002 | − | 0.467657i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 643.362 | + | 1114.34i | 0.483368 | + | 0.837217i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −470.856 | + | 815.546i | −0.345168 | + | 0.597848i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1454.09 | 1.04046 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1621.27 | −1.13279 | −0.566397 | − | 0.824133i | \(-0.691663\pi\) | ||||
−0.566397 | + | 0.824133i | \(0.691663\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −459.887 | + | 796.547i | −0.313882 | + | 0.543659i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −759.214 | − | 1315.00i | −0.506357 | − | 0.877037i | −0.999973 | − | 0.00735640i | \(-0.997658\pi\) |
0.493616 | − | 0.869680i | \(-0.335675\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 143.843 | + | 249.144i | 0.0917041 | + | 0.158836i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1242.50 | − | 2152.07i | 0.774844 | − | 1.34207i | −0.160038 | − | 0.987111i | \(-0.551162\pi\) |
0.934882 | − | 0.354958i | \(-0.115505\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1655.36 | −1.01011 | −0.505057 | − | 0.863086i | \(-0.668529\pi\) | ||||
−0.505057 | + | 0.863086i | \(0.668529\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 645.244 | 0.385386 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 252.630 | − | 437.568i | 0.147734 | − | 0.255883i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 467.673 | + | 810.033i | 0.267849 | + | 0.463928i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −175.095 | − | 303.274i | −0.0962709 | − | 0.166746i | 0.813867 | − | 0.581051i | \(-0.197358\pi\) |
−0.910138 | + | 0.414305i | \(0.864025\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1669.07 | + | 2890.91i | −0.899516 | + | 1.55801i | −0.0714022 | + | 0.997448i | \(0.522747\pi\) |
−0.828114 | + | 0.560560i | \(0.810586\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −938.583 | −0.495947 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −668.799 | −0.346576 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 871.836 | − | 1510.06i | 0.443185 | − | 0.767620i | −0.554738 | − | 0.832025i | \(-0.687182\pi\) |
0.997924 | + | 0.0644052i | \(0.0205150\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −787.535 | − | 1364.05i | −0.392803 | − | 0.680354i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1715.78 | − | 2971.82i | −0.824480 | − | 1.42804i | −0.902316 | − | 0.431076i | \(-0.858134\pi\) |
0.0778354 | − | 0.996966i | \(-0.475199\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −106.348 | + | 184.200i | −0.0501768 | + | 0.0869088i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3381.05 | 1.56667 | 0.783335 | − | 0.621600i | \(-0.213517\pi\) | ||||
0.783335 | + | 0.621600i | \(0.213517\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3568.89 | 1.62444 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −384.724 | + | 666.362i | −0.172050 | + | 0.298000i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 670.501 | + | 1161.34i | 0.294666 | + | 0.510377i | 0.974907 | − | 0.222612i | \(-0.0714583\pi\) |
−0.680241 | + | 0.732988i | \(0.738125\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −540.737 | − | 936.584i | −0.229629 | − | 0.397729i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −562.574 | + | 974.407i | −0.234909 | + | 0.406875i | −0.959246 | − | 0.282571i | \(-0.908813\pi\) |
0.724337 | + | 0.689446i | \(0.242146\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3535.04 | −1.45170 | −0.725848 | − | 0.687855i | \(-0.758553\pi\) | ||||
−0.725848 | + | 0.687855i | \(0.758553\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2402.18 | 0.970350 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 224.871 | − | 389.488i | 0.0893668 | − | 0.154788i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −346.962 | − | 600.956i | −0.135681 | − | 0.235007i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1319.95 | − | 2286.21i | −0.500041 | − | 0.866097i | −1.00000 | 4.78599e-5i | \(-0.999985\pi\) | |
0.499959 | − | 0.866049i | \(-0.333349\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −523.526 | + | 906.774i | −0.195255 | + | 0.338192i | −0.946984 | − | 0.321280i | \(-0.895887\pi\) |
0.751729 | + | 0.659472i | \(0.229220\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2427.22 | −0.891370 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4585.45 | −1.65837 | −0.829187 | − | 0.558972i | \(-0.811196\pi\) | ||||
−0.829187 | + | 0.558972i | \(0.811196\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −415.371 | + | 719.444i | −0.147964 | + | 0.256282i | −0.930475 | − | 0.366356i | \(-0.880605\pi\) |
0.782511 | + | 0.622637i | \(0.213939\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 60.3429 | + | 104.517i | 0.0211754 | + | 0.0366769i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1672.33 | + | 2896.56i | 0.569759 | + | 0.986852i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 309.030 | − | 535.255i | 0.103764 | − | 0.179724i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −568.878 | −0.188278 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2630.08 | −0.858114 | −0.429057 | − | 0.903277i | \(-0.641154\pi\) | ||||
−0.429057 | + | 0.903277i | \(0.641154\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 448.171 | − | 776.255i | 0.144170 | − | 0.249709i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1633.37 | + | 2829.08i | 0.518116 | + | 0.897404i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −775.689 | − | 1343.53i | −0.239343 | − | 0.414555i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3959.44 | − | 6857.94i | 1.20516 | − | 2.08740i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −863.988 | −0.259448 | −0.129724 | − | 0.991550i | \(-0.541409\pi\) | ||||
−0.129724 | + | 0.991550i | \(0.541409\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −103.230 | −0.0305865 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2080.18 | − | 3602.97i | 0.608221 | − | 1.05347i | −0.383312 | − | 0.923619i | \(-0.625217\pi\) |
0.991533 | − | 0.129851i | \(-0.0414500\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 90.6052 | + | 156.933i | 0.0261457 | + | 0.0452856i | 0.878802 | − | 0.477186i | \(-0.158343\pi\) |
−0.852657 | + | 0.522472i | \(0.825010\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1075.22 | − | 1862.34i | −0.302319 | − | 0.523631i | 0.674342 | − | 0.738419i | \(-0.264427\pi\) |
−0.976661 | + | 0.214788i | \(0.931094\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1145.85 | − | 1984.67i | 0.318073 | − | 0.550918i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3667.40 | −1.00516 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6939.47 | −1.87815 | −0.939073 | − | 0.343719i | \(-0.888313\pi\) | ||||
−0.939073 | + | 0.343719i | \(0.888313\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 103.085 | − | 178.548i | 0.0275530 | − | 0.0477232i | −0.851920 | − | 0.523672i | \(-0.824562\pi\) |
0.879473 | + | 0.475949i | \(0.157895\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −121.500 | − | 210.444i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3245.94 | − | 5622.13i | −0.836171 | − | 1.44829i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1992.83 | + | 3451.68i | −0.507190 | + | 0.878479i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5011.93 | 1.26036 | 0.630180 | − | 0.776449i | \(-0.282981\pi\) | ||||
0.630180 | + | 0.776449i | \(0.282981\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 456.951 | 0.113551 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1666.77 | + | 2886.94i | −0.409323 | + | 0.708969i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2931.54 | + | 5077.58i | 0.711535 | + | 1.23241i | 0.964281 | + | 0.264882i | \(0.0853329\pi\) |
−0.252746 | + | 0.967533i | \(0.581334\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −395.029 | − | 684.211i | −0.0936847 | − | 0.162267i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2819.78 | − | 4884.00i | 0.661122 | − | 1.14510i | −0.319200 | − | 0.947688i | \(-0.603414\pi\) |
0.980321 | − | 0.197409i | \(-0.0632526\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5594.15 | −1.29678 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1919.81 | −0.440040 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1488.32 | − | 2577.84i | 0.337339 | − | 0.584289i | −0.646592 | − | 0.762836i | \(-0.723806\pi\) |
0.983931 | + | 0.178547i | \(0.0571397\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1403.67 | + | 2431.22i | 0.314637 | + | 0.544968i | 0.979360 | − | 0.202122i | \(-0.0647838\pi\) |
−0.664723 | + | 0.747090i | \(0.731450\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −38.1605 | − | 66.0959i | −0.00836787 | − | 0.0144936i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 959.194 | − | 1661.37i | 0.208059 | − | 0.360369i | −0.743044 | − | 0.669243i | \(-0.766619\pi\) |
0.951103 | + | 0.308874i | \(0.0999520\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 564.915 | 0.121221 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5209.50 | 1.10595 | 0.552977 | − | 0.833197i | \(-0.313492\pi\) | ||||
0.552977 | + | 0.833197i | \(0.313492\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3748.35 | + | 6492.33i | −0.787337 | + | 1.36371i | 0.140256 | + | 0.990115i | \(0.455207\pi\) |
−0.927593 | + | 0.373592i | \(0.878126\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1366.42 | + | 2366.71i | 0.283999 | + | 0.491900i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2981.39 | − | 5163.92i | −0.606837 | − | 1.05107i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2138.48 | + | 3703.95i | −0.430789 | + | 0.746149i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3358.94 | −0.669732 | −0.334866 | − | 0.942266i | \(-0.608691\pi\) | ||||
−0.334866 | + | 0.942266i | \(0.608691\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3841.05 | −0.758084 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 89.8289 | − | 155.588i | 0.0175502 | − | 0.0303978i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2607.30 | + | 4515.98i | 0.504294 | + | 0.873463i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1488.25 | + | 2577.73i | 0.282172 | + | 0.488736i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4265.89 | − | 7388.73i | 0.800865 | − | 1.38714i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7330.92 | −1.36286 | −0.681429 | − | 0.731884i | \(-0.738641\pi\) | ||||
−0.681429 | + | 0.731884i | \(0.738641\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 802.716 | 0.147783 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1019.27 | − | 1765.42i | 0.185843 | − | 0.321890i | −0.758017 | − | 0.652235i | \(-0.773832\pi\) |
0.943860 | + | 0.330345i | \(0.107165\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2069.44 | − | 3584.37i | −0.373711 | − | 0.647286i | 0.616423 | − | 0.787416i | \(-0.288581\pi\) |
−0.990133 | + | 0.140130i | \(0.955248\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3776.13 | + | 6540.44i | 0.669049 | + | 1.15883i | 0.978171 | + | 0.207804i | \(0.0666316\pi\) |
−0.309122 | + | 0.951022i | \(0.600035\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 292.058 | − | 505.859i | 0.0512605 | − | 0.0887858i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4609.87 | −0.801552 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8915.94 | −1.53590 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 435.477 | − | 754.268i | 0.0743258 | − | 0.128736i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1498.23 | − | 2595.01i | −0.253371 | − | 0.438852i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2788.85 | − | 4830.43i | −0.463109 | − | 0.802128i | 0.536005 | − | 0.844215i | \(-0.319933\pi\) |
−0.999114 | + | 0.0420865i | \(0.986599\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −189.942 | + | 328.989i | −0.0312575 | + | 0.0541396i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 428.637 | 0.0699073 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4467.16 | 0.722083 | 0.361041 | − | 0.932550i | \(-0.382421\pi\) | ||||
0.361041 | + | 0.932550i | \(0.382421\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1408.51 | + | 2439.61i | −0.225663 | + | 0.390860i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 208.830 | + | 361.704i | 0.0331635 | + | 0.0574409i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1097.58 | − | 1901.06i | −0.171280 | − | 0.296665i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4894.21 | + | 8477.01i | −0.757161 | + | 1.31144i | 0.187132 | + | 0.982335i | \(0.440081\pi\) |
−0.944293 | + | 0.329106i | \(0.893253\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4746.95 | −0.728075 | −0.364038 | − | 0.931384i | \(-0.618602\pi\) | ||||
−0.364038 | + | 0.931384i | \(0.618602\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2050.20 | 0.311771 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4717.33 | − | 8170.65i | 0.711269 | − | 1.23195i | −0.253112 | − | 0.967437i | \(-0.581454\pi\) |
0.964381 | − | 0.264517i | \(-0.0852127\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1591.76 | − | 2757.01i | −0.237977 | − | 0.412189i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5653.77 | − | 9792.62i | −0.831183 | − | 1.43965i | −0.897101 | − | 0.441826i | \(-0.854331\pi\) |
0.0659178 | − | 0.997825i | \(-0.479002\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −225.138 | + | 389.950i | −0.0328237 | + | 0.0568523i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3860.17 | −0.558145 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5510.00 | −0.790155 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3044.80 | + | 5273.76i | −0.433072 | + | 0.750103i | −0.997136 | − | 0.0756282i | \(-0.975904\pi\) |
0.564064 | + | 0.825731i | \(0.309237\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1412.57 | − | 2446.64i | −0.199283 | − | 0.345168i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1300.92 | + | 2253.26i | 0.180588 | + | 0.312787i | 0.942081 | − | 0.335386i | \(-0.108867\pi\) |
−0.761493 | + | 0.648173i | \(0.775533\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2181.14 | + | 3777.85i | −0.300356 | + | 0.520232i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6665.77 | 0.910622 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10416.2 | 1.41173 | 0.705865 | − | 0.708347i | \(-0.250559\pi\) | ||||
0.705865 | + | 0.708347i | \(0.250559\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2431.91 | − | 4212.19i | 0.327009 | − | 0.566397i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 832.230 | + | 1441.47i | 0.111031 | + | 0.192312i | 0.916186 | − | 0.400753i | \(-0.131251\pi\) |
−0.805155 | + | 0.593064i | \(0.797918\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1379.66 | − | 2389.64i | −0.181220 | − | 0.313882i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 667.078 | − | 1155.41i | 0.0869465 | − | 0.150596i | −0.819272 | − | 0.573404i | \(-0.805622\pi\) |
0.906219 | + | 0.422809i | \(0.138956\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7161.73 | 0.926302 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4555.28 | 0.584691 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6512.71 | + | 11280.4i | −0.829596 | + | 1.43690i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2222.44 | − | 3849.38i | −0.280960 | − | 0.486637i | 0.690662 | − | 0.723178i | \(-0.257319\pi\) |
−0.971621 | + | 0.236541i | \(0.923986\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1324.91 | + | 2294.81i | 0.164995 | + | 0.285779i | 0.936653 | − | 0.350258i | \(-0.113906\pi\) |
−0.771659 | + | 0.636037i | \(0.780573\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2383.11 | + | 4127.66i | −0.294568 | + | 0.510207i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −863.059 | −0.105891 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −280.860 | −0.0342057 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4796.33 | − | 8307.49i | 0.579862 | − | 1.00435i | −0.415633 | − | 0.909532i | \(-0.636440\pi\) |
0.995495 | − | 0.0948173i | \(-0.0302267\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3727.49 | + | 6456.20i | 0.447356 | + | 0.774844i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7077.89 | + | 12259.3i | 0.837205 | + | 1.45008i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2483.04 | − | 4300.76i | 0.291595 | − | 0.505057i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16850.1 | 1.96463 | 0.982317 | − | 0.187224i | \(-0.0599491\pi\) | ||||
0.982317 | + | 0.187224i | \(0.0599491\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1691.10 | 0.195770 | 0.0978849 | − | 0.995198i | \(-0.468792\pi\) | ||||
0.0978849 | + | 0.995198i | \(0.468792\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −967.867 | + | 1676.39i | −0.111251 | + | 0.192693i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −598.084 | − | 1035.91i | −0.0682619 | − | 0.118233i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 757.891 | + | 1312.71i | 0.0852944 | + | 0.147734i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3394.67 | − | 5879.74i | 0.379386 | − | 0.657117i | −0.611587 | − | 0.791177i | \(-0.709468\pi\) |
0.990973 | + | 0.134061i | \(0.0428018\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10386.6 | 1.15276 | 0.576382 | − | 0.817180i | \(-0.304464\pi\) | ||||
0.576382 | + | 0.817180i | \(0.304464\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2806.04 | −0.309286 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2935.59 | − | 5084.58i | 0.321346 | − | 0.556587i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2106.13 | + | 3647.92i | 0.228975 | + | 0.396596i | 0.957505 | − | 0.288418i | \(-0.0931292\pi\) |
−0.728530 | + | 0.685014i | \(0.759796\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 904.980 | + | 1567.47i | 0.0970585 | + | 0.168110i | 0.910466 | − | 0.413584i | \(-0.135723\pi\) |
−0.813407 | + | 0.581694i | \(0.802390\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3409.28 | + | 5905.05i | −0.363181 | + | 0.629048i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1050.57 | 0.111164 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1768.29 | 0.185859 | 0.0929297 | − | 0.995673i | \(-0.470377\pi\) | ||||
0.0929297 | + | 0.995673i | \(0.470377\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1044.36 | − | 1808.88i | 0.109040 | − | 0.188862i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5007.21 | − | 8672.74i | −0.519336 | − | 0.899516i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2186.30 | − | 3786.79i | −0.223788 | − | 0.387611i | 0.732167 | − | 0.681125i | \(-0.238509\pi\) |
−0.955955 | + | 0.293513i | \(0.905176\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1407.87 | − | 2438.51i | 0.143168 | − | 0.247974i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1164.34 | −0.117633 | −0.0588165 | − | 0.998269i | \(-0.518733\pi\) | ||||
−0.0588165 | + | 0.998269i | \(0.518733\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14893.9 | −1.49498 | −0.747491 | − | 0.664272i | \(-0.768742\pi\) | ||||
−0.747491 | + | 0.664272i | \(0.768742\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1003.20 | − | 1737.59i | 0.100048 | − | 0.173288i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9580.14 | − | 16593.3i | −0.949285 | − | 1.64421i | −0.746936 | − | 0.664896i | \(-0.768476\pi\) |
−0.202349 | − | 0.979314i | \(-0.564857\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2615.51 | + | 4530.19i | 0.255873 | + | 0.443185i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1020.03 | − | 1766.74i | 0.0991562 | − | 0.171744i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −980.616 | −0.0947237 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4725.21 | 0.453569 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4703.14 | − | 8146.08i | 0.448626 | − | 0.777043i | −0.549671 | − | 0.835381i | \(-0.685247\pi\) |
0.998297 | + | 0.0583380i | \(0.0185801\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1602.55 | − | 2775.70i | −0.151913 | − | 0.263121i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7595.19 | + | 13155.3i | 0.711092 | + | 1.23165i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6230.39 | + | 10791.4i | −0.579725 | + | 1.00411i | 0.415786 | + | 0.909463i | \(0.363507\pi\) |
−0.995511 | + | 0.0946505i | \(0.969827\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10294.7 | 0.952028 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12868.0 | 1.18274 | 0.591369 | − | 0.806401i | \(-0.298588\pi\) | ||||
0.591369 | + | 0.806401i | \(0.298588\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4577.38 | − | 7928.26i | 0.418164 | − | 0.724281i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −319.044 | − | 552.600i | −0.0289696 | − | 0.0501768i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6852.50 | + | 11868.9i | 0.614750 | + | 1.06478i | 0.990428 | + | 0.138028i | \(0.0440763\pi\) |
−0.375679 | + | 0.926750i | \(0.622590\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5071.58 | + | 8784.23i | −0.452258 | + | 0.783335i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10126.1 | 0.897616 | 0.448808 | − | 0.893628i | \(-0.351849\pi\) | ||||
0.448808 | + | 0.893628i | \(0.351849\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10571.6 | 0.931546 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5353.34 | + | 9272.25i | −0.468935 | + | 0.812219i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3118.03 | + | 5400.59i | 0.271521 | + | 0.470288i | 0.969252 | − | 0.246072i | \(-0.0791400\pi\) |
−0.697730 | + | 0.716360i | \(0.745807\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1154.17 | − | 1999.09i | −0.0993333 | − | 0.172050i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1425.50 | − | 2469.03i | 0.121971 | − | 0.211259i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1431.15 | −0.121744 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4023.00 | −0.340251 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8508.38 | + | 14737.0i | −0.715468 | + | 1.23923i | 0.247310 | + | 0.968936i | \(0.420453\pi\) |
−0.962779 | + | 0.270291i | \(0.912880\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2907.31 | + | 5035.61i | 0.243074 | + | 0.421017i | 0.961588 | − | 0.274496i | \(-0.0885109\pi\) |
−0.718514 | + | 0.695512i | \(0.755178\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3272.96 | + | 5668.93i | 0.270536 | + | 0.468582i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3725.49 | − | 6452.74i | 0.306196 | − | 0.530348i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3244.42 | 0.265152 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23835.8 | 1.93704 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8186.41 | + | 14179.3i | −0.661550 | + | 1.14584i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1687.72 | − | 2923.22i | −0.135625 | − | 0.234909i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5034.59 | + | 8720.17i | 0.400100 | + | 0.692993i | 0.993738 | − | 0.111739i | \(-0.0356421\pi\) |
−0.593638 | + | 0.804732i | \(0.702309\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5302.55 | − | 9184.29i | 0.419069 | − | 0.725848i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10642.5 | −0.836466 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7437.51 | −0.581362 | −0.290681 | − | 0.956820i | \(-0.593882\pi\) | ||||
−0.290681 | + | 0.956820i | \(0.593882\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3603.27 | + | 6241.04i | −0.280116 | + | 0.485175i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3752.53 | − | 6499.57i | −0.290133 | − | 0.502525i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 674.614 | + | 1168.47i | 0.0515960 | + | 0.0893668i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10893.6 | + | 18868.2i | −0.828680 | + | 1.43532i | 0.0703944 | + | 0.997519i | \(0.477574\pi\) |
−0.899074 | + | 0.437796i | \(0.855759\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23280.5 | 1.76147 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2081.77 | 0.156671 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1286.24 | + | 2227.83i | −0.0962851 | + | 0.166771i | −0.910144 | − | 0.414292i | \(-0.864029\pi\) |
0.813859 | + | 0.581062i | \(0.197363\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5002.58 | + | 8664.72i | 0.372496 | + | 0.645181i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8790.29 | + | 15225.2i | 0.647642 | + | 1.12175i | 0.983685 | + | 0.179902i | \(0.0575780\pi\) |
−0.336043 | + | 0.941847i | \(0.609089\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3610.37 | + | 6253.35i | −0.264605 | + | 0.458309i | −0.967460 | − | 0.253024i | \(-0.918575\pi\) |
0.702855 | + | 0.711333i | \(0.251908\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7919.67 | 0.577398 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 787.679 | 0.0571278 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5577.54 | + | 9660.58i | −0.402419 | + | 0.697011i | −0.994017 | − | 0.109222i | \(-0.965164\pi\) |
0.591598 | + | 0.806233i | \(0.298497\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1570.58 | − | 2720.32i | −0.112731 | − | 0.195255i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1746.75 | + | 3025.46i | 0.124088 | + | 0.214926i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3640.84 | − | 6306.11i | 0.257316 | − | 0.445685i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15216.2 | −1.06992 | −0.534958 | − | 0.844879i | \(-0.679673\pi\) | ||||
−0.534958 | + | 0.844879i | \(0.679673\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5366.33 | 0.375409 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6878.17 | − | 11913.3i | 0.478731 | − | 0.829187i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1921.95 | − | 3328.91i | −0.133094 | − | 0.230526i | 0.791774 | − | 0.610815i | \(-0.209158\pi\) |
−0.924868 | + | 0.380289i | \(0.875825\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1246.11 | − | 2158.33i | −0.0854272 | − | 0.147964i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9373.48 | + | 16235.3i | −0.639382 | + | 1.10744i | 0.346186 | + | 0.938166i | \(0.387476\pi\) |
−0.985569 | + | 0.169277i | \(0.945857\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9864.63 | −0.669529 | −0.334764 | − | 0.942302i | \(-0.608657\pi\) | ||||
−0.334764 | + | 0.942302i | \(0.608657\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −362.057 | −0.0244513 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6855.06 | + | 11873.3i | −0.460657 | + | 0.797882i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11146.4 | − | 19306.2i | −0.745336 | − | 1.29096i | −0.950038 | − | 0.312136i | \(-0.898956\pi\) |
0.204701 | − | 0.978824i | \(-0.434378\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8165.94 | − | 14143.8i | −0.540685 | − | 0.936494i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3023.39 | + | 5236.67i | −0.199206 | + | 0.345036i | −0.948271 | − | 0.317461i | \(-0.897170\pi\) |
0.749065 | + | 0.662497i | \(0.230503\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10034.0 | −0.657901 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9383.68 | −0.612273 | −0.306137 | − | 0.951988i | \(-0.599036\pi\) | ||||
−0.306137 | + | 0.951988i | \(0.599036\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1994.75 | − | 3455.00i | 0.129525 | − | 0.224343i | −0.793968 | − | 0.607960i | \(-0.791988\pi\) |
0.923492 | + | 0.383617i | \(0.125322\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 927.089 | + | 1605.77i | 0.0599079 | + | 0.103764i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7029.85 | + | 12176.1i | 0.449910 | + | 0.779267i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 853.317 | − | 1477.99i | 0.0543512 | − | 0.0941391i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4401.88 | −0.279038 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11434.0 | 0.721363 | 0.360681 | − | 0.932689i | \(-0.382544\pi\) | ||||
0.360681 | + | 0.932689i | \(0.382544\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3945.12 | − | 6833.14i | 0.247716 | − | 0.429057i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8637.37 | − | 14960.4i | −0.539785 | − | 0.934935i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1344.51 | + | 2328.76i | 0.0832365 | + | 0.144170i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7548.63 | − | 13074.6i | 0.465137 | − | 0.805641i | −0.534071 | − | 0.845440i | \(-0.679338\pi\) |
0.999208 | + | 0.0397989i | \(0.0126717\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4170.19 | 0.255764 | 0.127882 | − | 0.991789i | \(-0.459182\pi\) | ||||
0.127882 | + | 0.991789i | \(0.459182\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9800.23 | −0.598269 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2281.94 | − | 3952.44i | 0.138659 | − | 0.240164i | −0.788330 | − | 0.615252i | \(-0.789054\pi\) |
0.926989 | + | 0.375088i | \(0.122387\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1199.35 | + | 2077.34i | 0.0725404 | + | 0.125644i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1909.52 | − | 3307.39i | −0.114434 | − | 0.198205i | 0.803119 | − | 0.595818i | \(-0.203172\pi\) |
−0.917553 | + | 0.397613i | \(0.869839\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8089.46 | − | 14011.4i | 0.482567 | − | 0.835830i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4654.13 | 0.276370 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4326.02 | −0.255717 | −0.127859 | − | 0.991792i | \(-0.540810\pi\) | ||||
−0.127859 | + | 0.991792i | \(0.540810\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14658.9 | − | 25389.9i | 0.862579 | − | 1.49403i | −0.00685243 | − | 0.999977i | \(-0.502181\pi\) |
0.869431 | − | 0.494054i | \(-0.164485\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11878.3 | + | 20573.8i | 0.695800 | + | 1.20516i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3014.22 | + | 5220.78i | 0.174979 | + | 0.303072i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1295.98 | − | 2244.71i | 0.0748962 | − | 0.129724i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5328.02 | −0.306536 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5483.56 | −0.314080 | −0.157040 | − | 0.987592i | \(-0.550195\pi\) | ||||
−0.157040 | + | 0.987592i | \(0.550195\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 154.844 | − | 268.198i | 0.00882957 | − | 0.0152933i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6034.67 | + | 10452.4i | 0.342587 | + | 0.593378i | 0.984912 | − | 0.173054i | \(-0.0553635\pi\) |
−0.642325 | + | 0.766432i | \(0.722030\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6240.53 | + | 10808.9i | 0.351157 | + | 0.608221i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15398.4 | + | 26670.7i | −0.862667 | + | 1.49418i | 0.00667825 | + | 0.999978i | \(0.497874\pi\) |
−0.869345 | + | 0.494205i | \(0.835459\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26477.7 | 1.47688 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −543.631 | −0.0301904 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19933.4 | + | 34525.7i | −1.10218 | + | 1.90903i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3250.98 | + | 5630.87i | 0.178977 | + | 0.309997i | 0.941530 | − | 0.336928i | \(-0.109388\pi\) |
−0.762553 | + | 0.646925i | \(0.776055\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8818.98 | − | 15274.9i | −0.481328 | − | 0.833685i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16368.0 | − | 28350.3i | 0.889504 | − | 1.54067i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6451.34 | 0.349088 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2235.98 | −0.120473 | −0.0602367 | − | 0.998184i | \(-0.519186\pi\) | ||||
−0.0602367 | + | 0.998184i | \(0.519186\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1804.33 | + | 3125.19i | −0.0968016 | + | 0.167665i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3437.56 | + | 5954.02i | 0.183639 | + | 0.318073i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17782.2 | − | 30799.7i | −0.941926 | − | 1.63146i | −0.761792 | − | 0.647822i | \(-0.775680\pi\) |
−0.180134 | − | 0.983642i | \(-0.557653\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5501.09 | − | 9528.18i | 0.290165 | − | 0.502580i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4310.50 | −0.226409 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5383.57 | 0.281586 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10409.2 | − | 18029.3i | 0.542174 | − | 0.939073i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4962.07 | + | 8594.56i | 0.257377 | + | 0.445790i | 0.965538 | − | 0.260260i | \(-0.0838084\pi\) |
−0.708161 | + | 0.706051i | \(0.750475\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 309.254 | + | 535.644i | 0.0159077 | + | 0.0275530i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 503.441 | − | 871.985i | 0.0257894 | − | 0.0446686i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 880.081 | 0.0448974 | 0.0224487 | − | 0.999748i | \(-0.492854\pi\) | ||||
0.0224487 | + | 0.999748i | \(0.492854\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15986.7 | − | 27689.8i | 0.808879 | − | 1.40102i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8668.08 | + | 15013.5i | 0.436784 | + | 0.756532i | 0.997439 | − | 0.0715172i | \(-0.0227841\pi\) |
−0.560655 | + | 0.828049i | \(0.689451\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −133.840 | − | 231.818i | −0.00668937 | − | 0.0115863i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12293.2 | − | 21292.4i | 0.611924 | − | 1.05988i | −0.378992 | − | 0.925400i | \(-0.623729\pi\) |
0.990916 | − | 0.134483i | \(-0.0429375\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19475.6 | 0.965527 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14579.3 | 0.719870 | 0.359935 | − | 0.932977i | \(-0.382799\pi\) | ||||
0.359935 | + | 0.932977i | \(0.382799\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1865.65 | − | 3231.40i | 0.0917478 | − | 0.158912i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5978.48 | − | 10355.0i | −0.292826 | − | 0.507190i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8042.98 | − | 13930.8i | −0.390802 | − | 0.676889i | 0.601753 | − | 0.798682i | \(-0.294469\pi\) |
−0.992556 | + | 0.121793i | \(0.961136\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7517.90 | + | 13021.4i | −0.363834 | + | 0.630180i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −35568.0 | −1.71451 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37017.3 | −1.77730 | −0.888651 | − | 0.458584i | \(-0.848357\pi\) | ||||
−0.888651 | + | 0.458584i | \(0.848357\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −685.427 | + | 1187.19i | −0.0327792 | + | 0.0567753i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12303.2 | − | 21309.8i | −0.586060 | − | 1.01509i | −0.994742 | − | 0.102410i | \(-0.967345\pi\) |
0.408682 | − | 0.912677i | \(-0.365989\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5000.32 | − | 8660.81i | −0.236323 | − | 0.409323i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13686.7 | + | 23706.0i | −0.644325 | + | 1.11600i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12715.6 | −0.596275 | −0.298137 | − | 0.954523i | \(-0.596365\pi\) | ||||
−0.298137 | + | 0.954523i | \(0.596365\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17589.2 | −0.821610 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1587.11 | + | 2748.96i | −0.0738480 | + | 0.127908i | −0.900585 | − | 0.434681i | \(-0.856861\pi\) |
0.826737 | + | 0.562589i | \(0.190195\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 359.975 | + | 623.495i | 0.0166847 | + | 0.0288988i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13418.5 | − | 23241.5i | −0.617160 | − | 1.06895i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −994.042 | + | 1721.73i | −0.0455437 | + | 0.0788840i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2370.18 | 0.108178 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18578.9 | 0.844726 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7784.94 | − | 13483.9i | 0.352609 | − | 0.610736i | −0.634097 | − | 0.773254i | \(-0.718628\pi\) |
0.986706 | + | 0.162517i | \(0.0519613\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8459.34 | + | 14652.0i | 0.381699 | + | 0.661122i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30400.9 | − | 52656.0i | −1.36137 | − | 2.35797i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8391.23 | − | 14534.0i | 0.374347 | − | 0.648389i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31514.5 | −1.40063 | −0.700314 | − | 0.713835i | \(-0.746957\pi\) | ||||
−0.700314 | + | 0.713835i | \(0.746957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22430.2 | −0.993146 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2879.72 | − | 4987.82i | 0.127029 | − | 0.220020i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1720.48 | + | 2979.95i | 0.0756093 | + | 0.130959i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4464.95 | + | 7733.52i | 0.194763 | + | 0.337339i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5514.54 | + | 9551.47i | −0.239655 | + | 0.415095i | −0.960615 | − | 0.277882i | \(-0.910368\pi\) |
0.720960 | + | 0.692976i | \(0.243701\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20830.5 | −0.901920 | −0.450960 | − | 0.892544i | \(-0.648918\pi\) | ||||
−0.450960 | + | 0.892544i | \(0.648918\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8422.00 | −0.363312 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18281.7 | − | 31664.9i | 0.785743 | − | 1.36095i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13105.9 | − | 22700.1i | −0.561221 | − | 0.972063i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4674.53 | + | 8096.53i | 0.198712 | + | 0.344179i | 0.948111 | − | 0.317940i | \(-0.102991\pi\) |
−0.749399 | + | 0.662118i | \(0.769658\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16445.3 | − | 28484.1i | 0.696533 | − | 1.20643i | −0.273129 | − | 0.961978i | \(-0.588058\pi\) |
0.969661 | − | 0.244452i | \(-0.0786082\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 228.963 | 0.00966238 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13081.2 | −0.550033 | −0.275016 | − | 0.961440i | \(-0.588683\pi\) | ||||
−0.275016 | + | 0.961440i | \(0.588683\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14395.6 | + | 24933.9i | −0.603112 | + | 1.04462i | 0.389235 | + | 0.921138i | \(0.372739\pi\) |
−0.992347 | + | 0.123482i | \(0.960594\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2877.58 | + | 4984.12i | 0.120123 | + | 0.208059i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18012.6 | + | 31198.8i | 0.746531 | + | 1.29303i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −847.372 | + | 1467.69i | −0.0349934 | + | 0.0606103i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36766.8 | −1.51291 | −0.756455 | − | 0.654046i | \(-0.773070\pi\) | ||||
−0.756455 | + | 0.654046i | \(0.773070\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16682.9 | −0.684034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7814.25 | + | 13534.7i | −0.319261 | + | 0.552977i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19013.4 | + | 32932.1i | 0.774058 | + | 1.34071i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11245.1 | − | 19477.0i | −0.454569 | − | 0.787337i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1449.33 | − | 2510.31i | 0.0583810 | − | 0.101119i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5899.55 | 0.236808 | 0.118404 | − | 0.992966i | \(-0.462222\pi\) | ||||
0.118404 | + | 0.992966i | \(0.462222\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8198.51 | −0.327934 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21138.5 | + | 36613.0i | −0.842564 | + | 1.45936i | 0.0451553 | + | 0.998980i | \(0.485622\pi\) |
−0.887720 | + | 0.460384i | \(0.847712\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3171.73 | + | 5493.59i | 0.125981 | + | 0.218206i | 0.922116 | − | 0.386913i | \(-0.126459\pi\) |
−0.796135 | + | 0.605119i | \(0.793125\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3464.89 | − | 6001.36i | −0.136670 | − | 0.236719i | 0.789564 | − | 0.613668i | \(-0.210307\pi\) |
−0.926234 | + | 0.376949i | \(0.876973\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7144.22 | + | 12374.1i | −0.280822 | + | 0.486397i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17888.3 | 0.700715 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8134.27 | 0.317533 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1527.35 | − | 2645.44i | 0.0594170 | − | 0.102913i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6415.43 | − | 11111.8i | −0.248716 | − | 0.430789i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1643.94 | − | 2847.39i | −0.0632976 | − | 0.109635i | 0.832640 | − | 0.553815i | \(-0.186828\pi\) |
−0.895938 | + | 0.444180i | \(0.853495\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5038.41 | − | 8726.79i | 0.193335 | − | 0.334866i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46875.9 | −1.79261 | −0.896304 | − | 0.443439i | \(-0.853758\pi\) | ||||
−0.896304 | + | 0.443439i | \(0.853758\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42479.4 | 1.61897 | 0.809483 | − | 0.587144i | \(-0.199748\pi\) | ||||
0.809483 | + | 0.587144i | \(0.199748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5761.58 | − | 9979.35i | 0.218840 | − | 0.379042i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1840.08 | − | 3187.11i | −0.0696547 | − | 0.120645i | 0.829095 | − | 0.559108i | \(-0.188856\pi\) |
−0.898749 | + | 0.438463i | \(0.855523\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 269.487 | + | 466.764i | 0.0101326 | + | 0.0175502i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9194.12 | + | 15924.7i | −0.344535 | + | 0.596752i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11988.5 | −0.447745 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15643.8 | −0.582309 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2755.04 | + | 4771.86i | −0.102209 | + | 0.177031i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27376.6 | + | 47417.6i | 1.01226 | + | 1.75328i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18833.0 | − | 32619.7i | −0.691745 | − | 1.19814i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3551.09 | − | 6150.67i | 0.130002 | − | 0.225171i | −0.793675 | − | 0.608342i | \(-0.791835\pi\) |
0.923677 | + | 0.383172i | \(0.125168\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8929.53 | −0.325824 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38119.0 | 1.38632 | 0.693161 | − | 0.720783i | \(-0.256218\pi\) | ||||
0.693161 | + | 0.720783i | \(0.256218\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4420.08 | − | 7655.81i | 0.160223 | − | 0.277514i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12797.7 | + | 22166.2i | 0.462380 | + | 0.800865i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8595.28 | − | 14887.5i | −0.308522 | − | 0.534377i | 0.669517 | − | 0.742797i | \(-0.266501\pi\) |
−0.978039 | + | 0.208420i | \(0.933168\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10996.4 | − | 19046.3i | 0.393423 | − | 0.681429i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22687.5 | −0.809065 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −484.139 | −0.0172091 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1204.07 | + | 2085.52i | −0.0426612 | + | 0.0738914i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16128.2 | − | 27934.9i | −0.569591 | − | 0.986561i | −0.996606 | − | 0.0823167i | \(-0.973768\pi\) |
0.427015 | − | 0.904245i | \(-0.359565\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3057.80 | + | 5296.26i | 0.107297 | + | 0.185843i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3696.90 | − | 6403.22i | 0.129306 | − | 0.223965i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26213.6 | 0.913940 | 0.456970 | − | 0.889482i | \(-0.348935\pi\) | ||||
0.456970 | + | 0.889482i | \(0.348935\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12416.6 | 0.431524 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17120.0 | + | 29652.8i | −0.593089 | + | 1.02726i | 0.400724 | + | 0.916199i | \(0.368759\pi\) |
−0.993813 | + | 0.111062i | \(0.964575\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10778.4 | + | 18668.7i | 0.372209 | + | 0.644685i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18002.3 | − | 31180.8i | −0.617735 | − | 1.06995i | −0.989898 | − | 0.141781i | \(-0.954717\pi\) |
0.372163 | − | 0.928167i | \(-0.378616\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19633.6 | + | 34006.4i | −0.671584 | + | 1.16322i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22656.8 | −0.772551 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29488.1 | −1.00232 | −0.501161 | − | 0.865354i | \(-0.667093\pi\) | ||||
−0.501161 | + | 0.865354i | \(0.667093\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14064.1 | − | 24359.7i | 0.476548 | − | 0.825405i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 876.174 | + | 1517.58i | 0.0295953 | + | 0.0512605i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12925.6 | + | 22387.7i | 0.433875 | + | 0.751494i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6914.81 | − | 11976.8i | 0.231388 | − | 0.400776i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11156.4 | −0.372163 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −56009.0 | −1.86260 | −0.931298 | − | 0.364259i | \(-0.881322\pi\) | ||||
−0.931298 | + | 0.364259i | \(0.881322\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13373.9 | − | 23164.3i | 0.443377 | − | 0.767951i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6788.44 | − | 11757.9i | −0.224358 | − | 0.388599i | 0.731769 | − | 0.681553i | \(-0.238695\pi\) |
−0.956127 | + | 0.292954i | \(0.905362\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1306.43 | + | 2262.80i | 0.0429120 | + | 0.0743258i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15887.6 | − | 27518.1i | 0.520254 | − | 0.901107i | −0.479468 | − | 0.877559i | \(-0.659171\pi\) |
0.999723 | − | 0.0235477i | \(-0.00749615\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4258.14 | 0.139010 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8989.38 | 0.292568 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16377.7 | + | 28367.0i | −0.531401 | + | 0.920414i | 0.467927 | + | 0.883767i | \(0.345001\pi\) |
−0.999328 | + | 0.0366471i | \(0.988332\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24429.1 | − | 42312.4i | −0.790228 | − | 1.36872i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10527.3 | + | 18233.8i | 0.338472 | + | 0.586251i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20398.5 | − | 35331.3i | 0.653865 | − | 1.13253i | −0.328312 | − | 0.944569i | \(-0.606480\pi\) |
0.982177 | − | 0.187958i | \(-0.0601869\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16733.1 | 0.534752 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8851.60 | −0.282025 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8685.25 | − | 15043.3i | 0.275892 | − | 0.477859i | −0.694468 | − | 0.719524i | \(-0.744360\pi\) |
0.970360 | + | 0.241665i | \(0.0776934\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −569.826 | − | 986.968i | −0.0180465 | − | 0.0312575i |
(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 | 588.4.i.k.361.3 | 8 | ||
3.2 | odd | 2 | 1764.4.k.bd.361.2 | 8 | |||
7.2 | even | 3 | inner | 588.4.i.k.373.3 | 8 | ||
7.3 | odd | 6 | 588.4.a.j.1.3 | ✓ | 4 | ||
7.4 | even | 3 | 588.4.a.k.1.2 | yes | 4 | ||
7.5 | odd | 6 | 588.4.i.l.373.2 | 8 | |||
7.6 | odd | 2 | 588.4.i.l.361.2 | 8 | |||
21.2 | odd | 6 | 1764.4.k.bd.1549.2 | 8 | |||
21.5 | even | 6 | 1764.4.k.bb.1549.3 | 8 | |||
21.11 | odd | 6 | 1764.4.a.ba.1.3 | 4 | |||
21.17 | even | 6 | 1764.4.a.bc.1.2 | 4 | |||
21.20 | even | 2 | 1764.4.k.bb.361.3 | 8 | |||
28.3 | even | 6 | 2352.4.a.cq.1.3 | 4 | |||
28.11 | odd | 6 | 2352.4.a.cl.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.4.a.j.1.3 | ✓ | 4 | 7.3 | odd | 6 | ||
588.4.a.k.1.2 | yes | 4 | 7.4 | even | 3 | ||
588.4.i.k.361.3 | 8 | 1.1 | even | 1 | trivial | ||
588.4.i.k.373.3 | 8 | 7.2 | even | 3 | inner | ||
588.4.i.l.361.2 | 8 | 7.6 | odd | 2 | |||
588.4.i.l.373.2 | 8 | 7.5 | odd | 6 | |||
1764.4.a.ba.1.3 | 4 | 21.11 | odd | 6 | |||
1764.4.a.bc.1.2 | 4 | 21.17 | even | 6 | |||
1764.4.k.bb.361.3 | 8 | 21.20 | even | 2 | |||
1764.4.k.bb.1549.3 | 8 | 21.5 | even | 6 | |||
1764.4.k.bd.361.2 | 8 | 3.2 | odd | 2 | |||
1764.4.k.bd.1549.2 | 8 | 21.2 | odd | 6 | |||
2352.4.a.cl.1.2 | 4 | 28.11 | odd | 6 | |||
2352.4.a.cq.1.3 | 4 | 28.3 | even | 6 |