Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(107,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.107");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{10} - 14x^{8} - 512x^{6} + 3889x^{4} + 126224x^{2} + 506944 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 107.2 | ||
Root | \(-0.347140 - 2.27426i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.107 |
Dual form | 225.4.f.c.143.2 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62140 | + | 2.62140i | −0.926806 | + | 0.926806i | −0.997498 | − | 0.0706924i | \(-0.977479\pi\) |
0.0706924 | + | 0.997498i | \(0.477479\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 5.74350i | − | 0.717938i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.8652 | + | 10.8652i | 0.586664 | + | 0.586664i | 0.936726 | − | 0.350062i | \(-0.113840\pi\) |
−0.350062 | + | 0.936726i | \(0.613840\pi\) | |||||||
\(8\) | −5.91519 | − | 5.91519i | −0.261417 | − | 0.261417i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 37.8905i | 1.03858i | 0.854597 | + | 0.519291i | \(0.173804\pi\) | ||||
−0.854597 | + | 0.519291i | \(0.826196\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 48.1085 | − | 48.1085i | 1.02638 | − | 1.02638i | 0.0267344 | − | 0.999643i | \(-0.491489\pi\) |
0.999643 | − | 0.0267344i | \(-0.00851083\pi\) | |||||||
\(14\) | −56.9640 | −1.08745 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 76.9602 | 1.20250 | ||||||||
\(17\) | −60.3458 | + | 60.3458i | −0.860942 | + | 0.860942i | −0.991448 | − | 0.130506i | \(-0.958340\pi\) |
0.130506 | + | 0.991448i | \(0.458340\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 109.678i | 1.32430i | 0.749369 | + | 0.662152i | \(0.230357\pi\) | ||||
−0.749369 | + | 0.662152i | \(0.769643\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −99.3262 | − | 99.3262i | −0.962564 | − | 0.962564i | ||||
\(23\) | 39.7660 | + | 39.7660i | 0.360512 | + | 0.360512i | 0.864002 | − | 0.503489i | \(-0.167951\pi\) |
−0.503489 | + | 0.864002i | \(0.667951\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 252.224i | 1.90250i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 62.4042 | − | 62.4042i | 0.421188 | − | 0.421188i | ||||
\(29\) | −90.3553 | −0.578571 | −0.289285 | − | 0.957243i | \(-0.593418\pi\) | ||||
−0.289285 | + | 0.957243i | \(0.593418\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −233.678 | −1.35386 | −0.676932 | − | 0.736046i | \(-0.736691\pi\) | ||||
−0.676932 | + | 0.736046i | \(0.736691\pi\) | |||||||
\(32\) | −154.422 | + | 154.422i | −0.853070 | + | 0.853070i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 316.381i | − | 1.59585i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 19.0042 | + | 19.0042i | 0.0844399 | + | 0.0844399i | 0.748065 | − | 0.663625i | \(-0.230983\pi\) |
−0.663625 | + | 0.748065i | \(0.730983\pi\) | |||||||
\(38\) | −287.509 | − | 287.509i | −1.22737 | − | 1.22737i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 260.783i | − | 0.993354i | −0.867935 | − | 0.496677i | \(-0.834553\pi\) | ||
0.867935 | − | 0.496677i | \(-0.165447\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −176.216 | + | 176.216i | −0.624948 | + | 0.624948i | −0.946792 | − | 0.321845i | \(-0.895697\pi\) |
0.321845 | + | 0.946792i | \(0.395697\pi\) | |||||||
\(44\) | 217.624 | 0.745638 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −208.485 | −0.668250 | ||||||||
\(47\) | −145.788 | + | 145.788i | −0.452456 | + | 0.452456i | −0.896169 | − | 0.443713i | \(-0.853661\pi\) |
0.443713 | + | 0.896169i | \(0.353661\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 106.896i | − | 0.311650i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −276.311 | − | 276.311i | −0.736875 | − | 0.736875i | ||||
\(53\) | −183.285 | − | 183.285i | −0.475022 | − | 0.475022i | 0.428513 | − | 0.903535i | \(-0.359038\pi\) |
−0.903535 | + | 0.428513i | \(0.859038\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 128.539i | − | 0.306728i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 236.858 | − | 236.858i | 0.536223 | − | 0.536223i | ||||
\(59\) | −279.564 | −0.616883 | −0.308441 | − | 0.951243i | \(-0.599807\pi\) | ||||
−0.308441 | + | 0.951243i | \(0.599807\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −390.267 | −0.819157 | −0.409578 | − | 0.912275i | \(-0.634324\pi\) | ||||
−0.409578 | + | 0.912275i | \(0.634324\pi\) | |||||||
\(62\) | 612.563 | − | 612.563i | 1.25477 | − | 1.25477i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 193.924i | − | 0.378757i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −150.444 | − | 150.444i | −0.274324 | − | 0.274324i | 0.556514 | − | 0.830838i | \(-0.312139\pi\) |
−0.830838 | + | 0.556514i | \(0.812139\pi\) | |||||||
\(68\) | 346.596 | + | 346.596i | 0.618103 | + | 0.618103i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 470.042i | 0.785686i | 0.919605 | + | 0.392843i | \(0.128508\pi\) | ||||
−0.919605 | + | 0.392843i | \(0.871492\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −480.765 | + | 480.765i | −0.770812 | + | 0.770812i | −0.978249 | − | 0.207436i | \(-0.933488\pi\) |
0.207436 | + | 0.978249i | \(0.433488\pi\) | |||||||
\(74\) | −99.6355 | −0.156519 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 629.934 | 0.950769 | ||||||||
\(77\) | −411.687 | + | 411.687i | −0.609299 | + | 0.609299i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1322.44i | 1.88337i | 0.336497 | + | 0.941685i | \(0.390758\pi\) | ||||
−0.336497 | + | 0.941685i | \(0.609242\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 683.618 | + | 683.618i | 0.920646 | + | 0.920646i | ||||
\(83\) | 456.192 | + | 456.192i | 0.603296 | + | 0.603296i | 0.941186 | − | 0.337890i | \(-0.109713\pi\) |
−0.337890 | + | 0.941186i | \(0.609713\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 923.868i | − | 1.15841i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 224.129 | − | 224.129i | 0.271503 | − | 0.271503i | ||||
\(89\) | 1364.85 | 1.62555 | 0.812774 | − | 0.582580i | \(-0.197957\pi\) | ||||
0.812774 | + | 0.582580i | \(0.197957\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1045.41 | 1.20428 | ||||||||
\(92\) | 228.396 | − | 228.396i | 0.258825 | − | 0.258825i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 764.340i | − | 0.838677i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 785.308 | + | 785.308i | 0.822020 | + | 0.822020i | 0.986398 | − | 0.164377i | \(-0.0525614\pi\) |
−0.164377 | + | 0.986398i | \(0.552561\pi\) | |||||||
\(98\) | 280.218 | + | 280.218i | 0.288839 | + | 0.288839i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 111.555i | 0.109902i | 0.998489 | + | 0.0549510i | \(0.0175003\pi\) | ||||
−0.998489 | + | 0.0549510i | \(0.982500\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.8820 | + | 13.8820i | −0.0132800 | + | 0.0132800i | −0.713716 | − | 0.700436i | \(-0.752989\pi\) |
0.700436 | + | 0.713716i | \(0.252989\pi\) | |||||||
\(104\) | −569.142 | −0.536624 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 960.929 | 0.880507 | ||||||||
\(107\) | 776.165 | − | 776.165i | 0.701259 | − | 0.701259i | −0.263422 | − | 0.964681i | \(-0.584851\pi\) |
0.964681 | + | 0.263422i | \(0.0848510\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 410.579i | 0.360792i | 0.983594 | + | 0.180396i | \(0.0577379\pi\) | ||||
−0.983594 | + | 0.180396i | \(0.942262\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 836.186 | + | 836.186i | 0.705465 | + | 0.705465i | ||||
\(113\) | 521.328 | + | 521.328i | 0.434004 | + | 0.434004i | 0.889988 | − | 0.455984i | \(-0.150713\pi\) |
−0.455984 | + | 0.889988i | \(0.650713\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 518.956i | 0.415378i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 732.849 | − | 732.849i | 0.571730 | − | 0.571730i | ||||
\(119\) | −1311.34 | −1.01017 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −104.688 | −0.0786538 | ||||||||
\(122\) | 1023.05 | − | 1023.05i | 0.759199 | − | 0.759199i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1342.13i | 0.971990i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −786.555 | − | 786.555i | −0.549571 | − | 0.549571i | 0.376746 | − | 0.926317i | \(-0.377043\pi\) |
−0.926317 | + | 0.376746i | \(0.877043\pi\) | |||||||
\(128\) | −727.025 | − | 727.025i | −0.502036 | − | 0.502036i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 448.364i | − | 0.299036i | −0.988759 | − | 0.149518i | \(-0.952228\pi\) | ||
0.988759 | − | 0.149518i | \(-0.0477722\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1191.67 | + | 1191.67i | −0.776922 | + | 0.776922i | ||||
\(134\) | 788.751 | 0.508490 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 713.914 | 0.450129 | ||||||||
\(137\) | −950.120 | + | 950.120i | −0.592512 | + | 0.592512i | −0.938309 | − | 0.345797i | \(-0.887609\pi\) |
0.345797 | + | 0.938309i | \(0.387609\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 112.735i | 0.0687918i | 0.999408 | + | 0.0343959i | \(0.0109507\pi\) | ||||
−0.999408 | + | 0.0343959i | \(0.989049\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1232.17 | − | 1232.17i | −0.728179 | − | 0.728179i | ||||
\(143\) | 1822.85 | + | 1822.85i | 1.06598 | + | 1.06598i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 2520.56i | − | 1.42879i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 109.151 | − | 109.151i | 0.0606226 | − | 0.0606226i | ||||
\(149\) | 1492.95 | 0.820852 | 0.410426 | − | 0.911894i | \(-0.365380\pi\) | ||||
0.410426 | + | 0.911894i | \(0.365380\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2939.54 | −1.58422 | −0.792108 | − | 0.610381i | \(-0.791016\pi\) | ||||
−0.792108 | + | 0.610381i | \(0.791016\pi\) | |||||||
\(152\) | 648.764 | − | 648.764i | 0.346196 | − | 0.346196i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 2158.39i | − | 1.12940i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −156.386 | − | 156.386i | −0.0794967 | − | 0.0794967i | 0.666240 | − | 0.745737i | \(-0.267902\pi\) |
−0.745737 | + | 0.666240i | \(0.767902\pi\) | |||||||
\(158\) | −3466.65 | − | 3466.65i | −1.74552 | − | 1.74552i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 864.129i | 0.422999i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 239.292 | − | 239.292i | 0.114986 | − | 0.114986i | −0.647272 | − | 0.762259i | \(-0.724090\pi\) |
0.762259 | + | 0.647272i | \(0.224090\pi\) | |||||||
\(164\) | −1497.81 | −0.713167 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2391.72 | −1.11828 | ||||||||
\(167\) | −677.159 | + | 677.159i | −0.313773 | + | 0.313773i | −0.846369 | − | 0.532596i | \(-0.821216\pi\) |
0.532596 | + | 0.846369i | \(0.321216\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 2431.86i | − | 1.10690i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1012.10 | + | 1012.10i | 0.448674 | + | 0.448674i | ||||
\(173\) | −441.523 | − | 441.523i | −0.194037 | − | 0.194037i | 0.603401 | − | 0.797438i | \(-0.293812\pi\) |
−0.797438 | + | 0.603401i | \(0.793812\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2916.06i | 1.24890i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3577.82 | + | 3577.82i | −1.50657 | + | 1.50657i | ||||
\(179\) | 4724.27 | 1.97267 | 0.986337 | − | 0.164737i | \(-0.0526776\pi\) | ||||
0.986337 | + | 0.164737i | \(0.0526776\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1548.35 | −0.635847 | −0.317923 | − | 0.948116i | \(-0.602985\pi\) | ||||
−0.317923 | + | 0.948116i | \(0.602985\pi\) | |||||||
\(182\) | −2740.45 | + | 2740.45i | −1.11613 | + | 1.11613i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 470.447i | − | 0.188488i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2286.53 | − | 2286.53i | −0.894159 | − | 0.894159i | ||||
\(188\) | 837.336 | + | 837.336i | 0.324835 | + | 0.324835i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1090.71i | − | 0.413200i | −0.978426 | − | 0.206600i | \(-0.933760\pi\) | ||
0.978426 | − | 0.206600i | \(-0.0662398\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2825.69 | − | 2825.69i | 1.05387 | − | 1.05387i | 0.0554112 | − | 0.998464i | \(-0.482353\pi\) |
0.998464 | − | 0.0554112i | \(-0.0176470\pi\) | |||||||
\(194\) | −4117.22 | −1.52371 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −613.958 | −0.223746 | ||||||||
\(197\) | −1163.99 | + | 1163.99i | −0.420969 | + | 0.420969i | −0.885537 | − | 0.464569i | \(-0.846209\pi\) |
0.464569 | + | 0.885537i | \(0.346209\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 520.257i | − | 0.185327i | −0.995697 | − | 0.0926633i | \(-0.970462\pi\) | ||
0.995697 | − | 0.0926633i | \(-0.0295380\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −292.430 | − | 292.430i | −0.101858 | − | 0.101858i | ||||
\(203\) | −981.726 | − | 981.726i | −0.339427 | − | 0.339427i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 72.7808i | − | 0.0246159i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3702.44 | − | 3702.44i | 1.23422 | − | 1.23422i | ||||
\(209\) | −4155.74 | −1.37540 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5524.38 | 1.80244 | 0.901219 | − | 0.433365i | \(-0.142674\pi\) | ||||
0.901219 | + | 0.433365i | \(0.142674\pi\) | |||||||
\(212\) | −1052.70 | + | 1052.70i | −0.341036 | + | 0.341036i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4069.28i | 1.29986i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2538.95 | − | 2538.95i | −0.794263 | − | 0.794263i | ||||
\(218\) | −1076.29 | − | 1076.29i | −0.334384 | − | 0.334384i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5806.30i | 1.76730i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −323.198 | + | 323.198i | −0.0970537 | + | 0.0970537i | −0.753967 | − | 0.656913i | \(-0.771862\pi\) |
0.656913 | + | 0.753967i | \(0.271862\pi\) | |||||||
\(224\) | −3355.65 | −1.00093 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2733.22 | −0.804474 | ||||||||
\(227\) | 2739.76 | − | 2739.76i | 0.801077 | − | 0.801077i | −0.182187 | − | 0.983264i | \(-0.558318\pi\) |
0.983264 | + | 0.182187i | \(0.0583177\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 230.334i | 0.0664667i | 0.999448 | + | 0.0332333i | \(0.0105804\pi\) | ||||
−0.999448 | + | 0.0332333i | \(0.989420\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 534.468 | + | 534.468i | 0.151248 | + | 0.151248i | ||||
\(233\) | 350.156 | + | 350.156i | 0.0984526 | + | 0.0984526i | 0.754618 | − | 0.656165i | \(-0.227822\pi\) |
−0.656165 | + | 0.754618i | \(0.727822\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1605.67i | 0.442883i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3437.54 | − | 3437.54i | 0.936229 | − | 0.936229i | ||||
\(239\) | 1013.20 | 0.274218 | 0.137109 | − | 0.990556i | \(-0.456219\pi\) | ||||
0.137109 | + | 0.990556i | \(0.456219\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2584.30 | 0.690744 | 0.345372 | − | 0.938466i | \(-0.387753\pi\) | ||||
0.345372 | + | 0.938466i | \(0.387753\pi\) | |||||||
\(242\) | 274.430 | − | 274.430i | 0.0728968 | − | 0.0728968i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2241.50i | 0.588104i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5276.43 | + | 5276.43i | 1.35924 | + | 1.35924i | ||||
\(248\) | 1382.25 | + | 1382.25i | 0.353923 | + | 0.353923i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1708.34i | 0.429599i | 0.976658 | + | 0.214800i | \(0.0689099\pi\) | ||||
−0.976658 | + | 0.214800i | \(0.931090\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1506.75 | + | 1506.75i | −0.374422 | + | 0.374422i | ||||
\(254\) | 4123.76 | 1.01869 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5363.04 | 1.30934 | ||||||||
\(257\) | −2659.48 | + | 2659.48i | −0.645500 | + | 0.645500i | −0.951902 | − | 0.306402i | \(-0.900875\pi\) |
0.306402 | + | 0.951902i | \(0.400875\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 412.969i | 0.0990757i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1175.34 | + | 1175.34i | 0.277148 | + | 0.277148i | ||||
\(263\) | 2307.03 | + | 2307.03i | 0.540903 | + | 0.540903i | 0.923794 | − | 0.382891i | \(-0.125071\pi\) |
−0.382891 | + | 0.923794i | \(0.625071\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 6247.68i | − | 1.44011i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −864.078 | + | 864.078i | −0.196948 | + | 0.196948i | ||||
\(269\) | −447.584 | −0.101449 | −0.0507243 | − | 0.998713i | \(-0.516153\pi\) | ||||
−0.0507243 | + | 0.998713i | \(0.516153\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1573.15 | 0.352627 | 0.176314 | − | 0.984334i | \(-0.443583\pi\) | ||||
0.176314 | + | 0.984334i | \(0.443583\pi\) | |||||||
\(272\) | −4644.23 | + | 4644.23i | −1.03529 | + | 1.03529i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 4981.29i | − | 1.09829i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5816.91 | − | 5816.91i | −1.26175 | − | 1.26175i | −0.950245 | − | 0.311504i | \(-0.899167\pi\) |
−0.311504 | − | 0.950245i | \(-0.600833\pi\) | |||||||
\(278\) | −295.524 | − | 295.524i | −0.0637566 | − | 0.0637566i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 140.032i | − | 0.0297281i | −0.999890 | − | 0.0148640i | \(-0.995268\pi\) | ||
0.999890 | − | 0.0148640i | \(-0.00473155\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4431.85 | + | 4431.85i | −0.930905 | + | 0.930905i | −0.997763 | − | 0.0668572i | \(-0.978703\pi\) |
0.0668572 | + | 0.997763i | \(0.478703\pi\) | |||||||
\(284\) | 2699.69 | 0.564074 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9556.87 | −1.97591 | ||||||||
\(287\) | 2833.46 | − | 2833.46i | 0.582765 | − | 0.582765i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 2370.24i | − | 0.482442i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2761.28 | + | 2761.28i | 0.553395 | + | 0.553395i | ||||
\(293\) | 1244.45 | + | 1244.45i | 0.248127 | + | 0.248127i | 0.820202 | − | 0.572074i | \(-0.193861\pi\) |
−0.572074 | + | 0.820202i | \(0.693861\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 224.827i | − | 0.0441480i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3913.61 | + | 3913.61i | −0.760771 | + | 0.760771i | ||||
\(299\) | 3826.17 | 0.740043 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3829.24 | −0.733269 | ||||||||
\(302\) | 7705.73 | − | 7705.73i | 1.46826 | − | 1.46826i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8440.82i | 1.59248i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7327.60 | + | 7327.60i | 1.36224 | + | 1.36224i | 0.871053 | + | 0.491189i | \(0.163437\pi\) |
0.491189 | + | 0.871053i | \(0.336563\pi\) | |||||||
\(308\) | 2364.52 | + | 2364.52i | 0.437439 | + | 0.437439i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 7489.38i | − | 1.36554i | −0.730632 | − | 0.682771i | \(-0.760775\pi\) | ||
0.730632 | − | 0.682771i | \(-0.239225\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2456.04 | − | 2456.04i | 0.443525 | − | 0.443525i | −0.449670 | − | 0.893195i | \(-0.648458\pi\) |
0.893195 | + | 0.449670i | \(0.148458\pi\) | |||||||
\(314\) | 819.903 | 0.147356 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7595.44 | 1.35214 | ||||||||
\(317\) | 6724.30 | − | 6724.30i | 1.19140 | − | 1.19140i | 0.214728 | − | 0.976674i | \(-0.431113\pi\) |
0.976674 | − | 0.214728i | \(-0.0688866\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3423.60i | − | 0.600894i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2265.23 | − | 2265.23i | −0.392038 | − | 0.392038i | ||||
\(323\) | −6618.59 | − | 6618.59i | −1.14015 | − | 1.14015i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1254.56i | 0.213140i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1542.58 | + | 1542.58i | −0.259679 | + | 0.259679i | ||||
\(329\) | −3168.03 | −0.530879 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −199.080 | −0.0330586 | −0.0165293 | − | 0.999863i | \(-0.505262\pi\) | ||||
−0.0165293 | + | 0.999863i | \(0.505262\pi\) | |||||||
\(332\) | 2620.14 | − | 2620.14i | 0.433129 | − | 0.433129i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 3550.21i | − | 0.581614i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3308.77 | − | 3308.77i | −0.534838 | − | 0.534838i | 0.387170 | − | 0.922008i | \(-0.373453\pi\) |
−0.922008 | + | 0.387170i | \(0.873453\pi\) | |||||||
\(338\) | 6374.88 | + | 6374.88i | 1.02588 | + | 1.02588i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 8854.16i | − | 1.40610i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4888.20 | − | 4888.20i | 0.769498 | − | 0.769498i | ||||
\(344\) | 2084.71 | 0.326744 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2314.82 | 0.359669 | ||||||||
\(347\) | −2371.68 | + | 2371.68i | −0.366912 | + | 0.366912i | −0.866350 | − | 0.499438i | \(-0.833540\pi\) |
0.499438 | + | 0.866350i | \(0.333540\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8208.92i | 1.25906i | 0.776975 | + | 0.629532i | \(0.216753\pi\) | ||||
−0.776975 | + | 0.629532i | \(0.783247\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5851.13 | − | 5851.13i | −0.885984 | − | 0.885984i | ||||
\(353\) | −6800.98 | − | 6800.98i | −1.02544 | − | 1.02544i | −0.999668 | − | 0.0257707i | \(-0.991796\pi\) |
−0.0257707 | − | 0.999668i | \(-0.508204\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 7839.01i | − | 1.16704i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12384.2 | + | 12384.2i | −1.82829 | + | 1.82829i | ||||
\(359\) | −1778.14 | −0.261411 | −0.130705 | − | 0.991421i | \(-0.541724\pi\) | ||||
−0.130705 | + | 0.991421i | \(0.541724\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5170.20 | −0.753783 | ||||||||
\(362\) | 4058.86 | − | 4058.86i | 0.589306 | − | 0.589306i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 6004.34i | − | 0.864596i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4673.56 | + | 4673.56i | 0.664735 | + | 0.664735i | 0.956492 | − | 0.291757i | \(-0.0942400\pi\) |
−0.291757 | + | 0.956492i | \(0.594240\pi\) | |||||||
\(368\) | 3060.40 | + | 3060.40i | 0.433517 | + | 0.433517i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 3982.85i | − | 0.557357i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5729.37 | − | 5729.37i | 0.795323 | − | 0.795323i | −0.187031 | − | 0.982354i | \(-0.559886\pi\) |
0.982354 | + | 0.187031i | \(0.0598865\pi\) | |||||||
\(374\) | 11987.8 | 1.65742 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1724.73 | 0.236559 | ||||||||
\(377\) | −4346.86 | + | 4346.86i | −0.593832 | + | 0.593832i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 153.883i | 0.0208561i | 0.999946 | + | 0.0104280i | \(0.00331941\pi\) | ||||
−0.999946 | + | 0.0104280i | \(0.996681\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2859.19 | + | 2859.19i | 0.382956 | + | 0.382956i | ||||
\(383\) | 4297.76 | + | 4297.76i | 0.573382 | + | 0.573382i | 0.933072 | − | 0.359690i | \(-0.117118\pi\) |
−0.359690 | + | 0.933072i | \(0.617118\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14814.6i | 1.95347i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4510.42 | − | 4510.42i | 0.590160 | − | 0.590160i | ||||
\(389\) | −7833.00 | −1.02095 | −0.510474 | − | 0.859893i | \(-0.670530\pi\) | ||||
−0.510474 | + | 0.859893i | \(0.670530\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4799.42 | −0.620760 | ||||||||
\(392\) | −632.310 | + | 632.310i | −0.0814706 | + | 0.0814706i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 6102.57i | − | 0.780312i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10195.4 | + | 10195.4i | 1.28889 | + | 1.28889i | 0.935459 | + | 0.353435i | \(0.114987\pi\) |
0.353435 | + | 0.935459i | \(0.385013\pi\) | |||||||
\(398\) | 1363.80 | + | 1363.80i | 0.171762 | + | 0.171762i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10778.3i | 1.34226i | 0.741341 | + | 0.671128i | \(0.234190\pi\) | ||||
−0.741341 | + | 0.671128i | \(0.765810\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11241.9 | + | 11241.9i | −1.38957 | + | 1.38957i | ||||
\(404\) | 640.714 | 0.0789028 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5147.00 | 0.629165 | ||||||||
\(407\) | −720.079 | + | 720.079i | −0.0876978 | + | 0.0876978i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4629.92i | 0.559743i | 0.960037 | + | 0.279872i | \(0.0902919\pi\) | ||||
−0.960037 | + | 0.279872i | \(0.909708\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 79.7315 | + | 79.7315i | 0.00953420 | + | 0.00953420i | ||||
\(413\) | −3037.51 | − | 3037.51i | −0.361903 | − | 0.361903i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 14858.0i | 1.75114i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10893.9 | − | 10893.9i | 1.27473 | − | 1.27473i | ||||
\(419\) | −11276.5 | −1.31478 | −0.657389 | − | 0.753551i | \(-0.728339\pi\) | ||||
−0.657389 | + | 0.753551i | \(0.728339\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3387.58 | 0.392163 | 0.196082 | − | 0.980588i | \(-0.437178\pi\) | ||||
0.196082 | + | 0.980588i | \(0.437178\pi\) | |||||||
\(422\) | −14481.6 | + | 14481.6i | −1.67051 | + | 1.67051i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2168.33i | 0.248358i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4240.32 | − | 4240.32i | −0.480570 | − | 0.480570i | ||||
\(428\) | −4457.91 | − | 4457.91i | −0.503461 | − | 0.503461i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 16161.7i | − | 1.80623i | −0.429402 | − | 0.903113i | \(-0.641276\pi\) | ||
0.429402 | − | 0.903113i | \(-0.358724\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3808.79 | − | 3808.79i | 0.422722 | − | 0.422722i | −0.463418 | − | 0.886140i | \(-0.653377\pi\) |
0.886140 | + | 0.463418i | \(0.153377\pi\) | |||||||
\(434\) | 13311.2 | 1.47226 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2358.16 | 0.259026 | ||||||||
\(437\) | −4361.44 | + | 4361.44i | −0.477428 | + | 0.477428i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1607.30i | 0.174744i | 0.996176 | + | 0.0873718i | \(0.0278468\pi\) | ||||
−0.996176 | + | 0.0873718i | \(0.972153\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −15220.6 | − | 15220.6i | −1.63795 | − | 1.63795i | ||||
\(443\) | 8296.60 | + | 8296.60i | 0.889805 | + | 0.889805i | 0.994504 | − | 0.104699i | \(-0.0333880\pi\) |
−0.104699 | + | 0.994504i | \(0.533388\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 1694.47i | − | 0.179900i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2107.02 | − | 2107.02i | 0.222203 | − | 0.222203i | ||||
\(449\) | −15061.8 | −1.58309 | −0.791547 | − | 0.611108i | \(-0.790724\pi\) | ||||
−0.791547 | + | 0.611108i | \(0.790724\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9881.20 | 1.03168 | ||||||||
\(452\) | 2994.25 | − | 2994.25i | 0.311588 | − | 0.311588i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14364.0i | 1.48489i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2671.27 | − | 2671.27i | −0.273428 | − | 0.273428i | 0.557050 | − | 0.830479i | \(-0.311933\pi\) |
−0.830479 | + | 0.557050i | \(0.811933\pi\) | |||||||
\(458\) | −603.797 | − | 603.797i | −0.0616017 | − | 0.0616017i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12809.1i | 1.29410i | 0.762449 | + | 0.647049i | \(0.223997\pi\) | ||||
−0.762449 | + | 0.647049i | \(0.776003\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11154.1 | − | 11154.1i | 1.11960 | − | 1.11960i | 0.127804 | − | 0.991799i | \(-0.459207\pi\) |
0.991799 | − | 0.127804i | \(-0.0407927\pi\) | |||||||
\(464\) | −6953.76 | −0.695733 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1835.80 | −0.182493 | ||||||||
\(467\) | 7905.44 | − | 7905.44i | 0.783341 | − | 0.783341i | −0.197052 | − | 0.980393i | \(-0.563137\pi\) |
0.980393 | + | 0.197052i | \(0.0631368\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 3269.21i | − | 0.321872i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1653.67 | + | 1653.67i | 0.161263 | + | 0.161263i | ||||
\(473\) | −6676.92 | − | 6676.92i | −0.649060 | − | 0.649060i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7531.66i | 0.725238i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2655.99 | + | 2655.99i | −0.254147 | + | 0.254147i | ||||
\(479\) | 10715.8 | 1.02217 | 0.511085 | − | 0.859530i | \(-0.329244\pi\) | ||||
0.511085 | + | 0.859530i | \(0.329244\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1828.53 | 0.173334 | ||||||||
\(482\) | −6774.48 | + | 6774.48i | −0.640185 | + | 0.640185i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 601.277i | 0.0564685i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4489.84 | + | 4489.84i | 0.417770 | + | 0.417770i | 0.884435 | − | 0.466664i | \(-0.154544\pi\) |
−0.466664 | + | 0.884435i | \(0.654544\pi\) | |||||||
\(488\) | 2308.50 | + | 2308.50i | 0.214141 | + | 0.214141i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15174.1i | 1.39470i | 0.716729 | + | 0.697352i | \(0.245638\pi\) | ||||
−0.716729 | + | 0.697352i | \(0.754362\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5452.56 | − | 5452.56i | 0.498116 | − | 0.498116i | ||||
\(494\) | −27663.3 | −2.51950 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17983.9 | −1.62802 | ||||||||
\(497\) | −5107.09 | + | 5107.09i | −0.460934 | + | 0.460934i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 8887.20i | − | 0.797286i | −0.917106 | − | 0.398643i | \(-0.869481\pi\) | ||
0.917106 | − | 0.398643i | \(-0.130519\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4478.25 | − | 4478.25i | −0.398155 | − | 0.398155i | ||||
\(503\) | −12740.5 | − | 12740.5i | −1.12936 | − | 1.12936i | −0.990281 | − | 0.139084i | \(-0.955584\pi\) |
−0.139084 | − | 0.990281i | \(-0.544416\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 7899.61i | − | 0.694033i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4517.58 | + | 4517.58i | −0.394558 | + | 0.394558i | ||||
\(509\) | 9257.00 | 0.806108 | 0.403054 | − | 0.915176i | \(-0.367949\pi\) | ||||
0.403054 | + | 0.915176i | \(0.367949\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10447.2 | −0.904416 | ||||||||
\(512\) | −8242.49 | + | 8242.49i | −0.711465 | + | 0.711465i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 13943.1i | − | 1.19651i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5523.99 | − | 5523.99i | −0.469913 | − | 0.469913i | ||||
\(518\) | −1082.56 | − | 1082.56i | −0.0918240 | − | 0.0918240i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 13563.3i | − | 1.14054i | −0.821458 | − | 0.570268i | \(-0.806839\pi\) | ||
0.821458 | − | 0.570268i | \(-0.193161\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11193.8 | + | 11193.8i | −0.935894 | + | 0.935894i | −0.998065 | − | 0.0621714i | \(-0.980197\pi\) |
0.0621714 | + | 0.998065i | \(0.480197\pi\) | |||||||
\(524\) | −2575.18 | −0.214689 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12095.3 | −1.00262 | ||||||||
\(527\) | 14101.5 | − | 14101.5i | 1.16560 | − | 1.16560i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 9004.33i | − | 0.740062i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6844.34 | + | 6844.34i | 0.557782 | + | 0.557782i | ||||
\(533\) | −12545.9 | − | 12545.9i | −1.01956 | − | 1.01956i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1779.81i | 0.143426i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1173.30 | − | 1173.30i | 0.0940231 | − | 0.0940231i | ||||
\(539\) | 4050.34 | 0.323675 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1383.33 | 0.109934 | 0.0549668 | − | 0.998488i | \(-0.482495\pi\) | ||||
0.0549668 | + | 0.998488i | \(0.482495\pi\) | |||||||
\(542\) | −4123.86 | + | 4123.86i | −0.326817 | + | 0.326817i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 18637.5i | − | 1.46889i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2181.76 | − | 2181.76i | −0.170540 | − | 0.170540i | 0.616677 | − | 0.787217i | \(-0.288479\pi\) |
−0.787217 | + | 0.616677i | \(0.788479\pi\) | |||||||
\(548\) | 5457.01 | + | 5457.01i | 0.425387 | + | 0.425387i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 9909.96i | − | 0.766204i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14368.5 | + | 14368.5i | −1.10491 | + | 1.10491i | ||||
\(554\) | 30496.9 | 2.33879 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 647.494 | 0.0493882 | ||||||||
\(557\) | −15674.9 | + | 15674.9i | −1.19240 | + | 1.19240i | −0.216007 | + | 0.976392i | \(0.569303\pi\) |
−0.976392 | + | 0.216007i | \(0.930697\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16955.0i | 1.28286i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 367.080 | + | 367.080i | 0.0275522 | + | 0.0275522i | ||||
\(563\) | 8213.60 | + | 8213.60i | 0.614852 | + | 0.614852i | 0.944206 | − | 0.329354i | \(-0.106831\pi\) |
−0.329354 | + | 0.944206i | \(0.606831\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 23235.3i | − | 1.72554i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2780.39 | − | 2780.39i | 0.205392 | − | 0.205392i | ||||
\(569\) | 16902.1 | 1.24530 | 0.622648 | − | 0.782502i | \(-0.286057\pi\) | ||||
0.622648 | + | 0.782502i | \(0.286057\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6507.12 | 0.476908 | 0.238454 | − | 0.971154i | \(-0.423359\pi\) | ||||
0.238454 | + | 0.971154i | \(0.423359\pi\) | |||||||
\(572\) | 10469.6 | − | 10469.6i | 0.765305 | − | 0.765305i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14855.3i | 1.08022i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7884.54 | − | 7884.54i | −0.568870 | − | 0.568870i | 0.362942 | − | 0.931812i | \(-0.381772\pi\) |
−0.931812 | + | 0.362942i | \(0.881772\pi\) | |||||||
\(578\) | 6213.35 | + | 6213.35i | 0.447130 | + | 0.447130i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9913.20i | 0.707864i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6944.77 | − | 6944.77i | 0.493350 | − | 0.493350i | ||||
\(584\) | 5687.63 | 0.403007 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6524.39 | −0.459932 | ||||||||
\(587\) | 9548.44 | − | 9548.44i | 0.671390 | − | 0.671390i | −0.286646 | − | 0.958037i | \(-0.592540\pi\) |
0.958037 | + | 0.286646i | \(0.0925404\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 25629.2i | − | 1.79293i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1462.57 | + | 1462.57i | 0.101539 | + | 0.101539i | ||||
\(593\) | 3491.97 | + | 3491.97i | 0.241818 | + | 0.241818i | 0.817602 | − | 0.575784i | \(-0.195303\pi\) |
−0.575784 | + | 0.817602i | \(0.695303\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 8574.75i | − | 0.589321i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10029.9 | + | 10029.9i | −0.685876 | + | 0.685876i | ||||
\(599\) | −11203.0 | −0.764175 | −0.382087 | − | 0.924126i | \(-0.624795\pi\) | ||||
−0.382087 | + | 0.924126i | \(0.624795\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13953.5 | −0.947048 | −0.473524 | − | 0.880781i | \(-0.657018\pi\) | ||||
−0.473524 | + | 0.880781i | \(0.657018\pi\) | |||||||
\(602\) | 10038.0 | − | 10038.0i | 0.679598 | − | 0.679598i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 16883.3i | 1.13737i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1292.54 | + | 1292.54i | 0.0864293 | + | 0.0864293i | 0.749000 | − | 0.662570i | \(-0.230534\pi\) |
−0.662570 | + | 0.749000i | \(0.730534\pi\) | |||||||
\(608\) | −16936.7 | − | 16936.7i | −1.12972 | − | 1.12972i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14027.3i | 0.928780i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −225.964 | + | 225.964i | −0.0148884 | + | 0.0148884i | −0.714512 | − | 0.699623i | \(-0.753351\pi\) |
0.699623 | + | 0.714512i | \(0.253351\pi\) | |||||||
\(614\) | −38417.2 | −2.52507 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4870.41 | 0.318562 | ||||||||
\(617\) | 2717.41 | − | 2717.41i | 0.177308 | − | 0.177308i | −0.612873 | − | 0.790181i | \(-0.709986\pi\) |
0.790181 | + | 0.612873i | \(0.209986\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8870.55i | 0.575989i | 0.957632 | + | 0.287995i | \(0.0929886\pi\) | ||||
−0.957632 | + | 0.287995i | \(0.907011\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19632.7 | + | 19632.7i | 1.26559 | + | 1.26559i | ||||
\(623\) | 14829.3 | + | 14829.3i | 0.953650 | + | 0.953650i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12876.5i | 0.822123i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −898.205 | + | 898.205i | −0.0570737 | + | 0.0570737i | ||||
\(629\) | −2293.65 | −0.145396 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29762.7 | 1.87771 | 0.938853 | − | 0.344318i | \(-0.111890\pi\) | ||||
0.938853 | + | 0.344318i | \(0.111890\pi\) | |||||||
\(632\) | 7822.48 | − | 7822.48i | 0.492344 | − | 0.492344i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 35254.2i | 2.20840i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5142.61 | − | 5142.61i | −0.319871 | − | 0.319871i | ||||
\(638\) | 8974.65 | + | 8974.65i | 0.556912 | + | 0.556912i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 5168.75i | − | 0.318492i | −0.987239 | − | 0.159246i | \(-0.949094\pi\) | ||
0.987239 | − | 0.159246i | \(-0.0509063\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2078.46 | − | 2078.46i | 0.127475 | − | 0.127475i | −0.640491 | − | 0.767966i | \(-0.721269\pi\) |
0.767966 | + | 0.640491i | \(0.221269\pi\) | |||||||
\(644\) | 4963.13 | 0.303687 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 34700.0 | 2.11339 | ||||||||
\(647\) | 10765.7 | − | 10765.7i | 0.654164 | − | 0.654164i | −0.299829 | − | 0.953993i | \(-0.596930\pi\) |
0.953993 | + | 0.299829i | \(0.0969297\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 10592.8i | − | 0.640684i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1374.37 | − | 1374.37i | −0.0825530 | − | 0.0825530i | ||||
\(653\) | 12815.1 | + | 12815.1i | 0.767984 | + | 0.767984i | 0.977751 | − | 0.209767i | \(-0.0672707\pi\) |
−0.209767 | + | 0.977751i | \(0.567271\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 20069.9i | − | 1.19451i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8304.68 | − | 8304.68i | 0.492022 | − | 0.492022i | ||||
\(659\) | 16634.8 | 0.983307 | 0.491654 | − | 0.870791i | \(-0.336393\pi\) | ||||
0.491654 | + | 0.870791i | \(0.336393\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10835.6 | −0.637601 | −0.318800 | − | 0.947822i | \(-0.603280\pi\) | ||||
−0.318800 | + | 0.947822i | \(0.603280\pi\) | |||||||
\(662\) | 521.868 | − | 521.868i | 0.0306389 | − | 0.0306389i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 5396.92i | − | 0.315423i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3593.07 | − | 3593.07i | −0.208582 | − | 0.208582i | ||||
\(668\) | 3889.27 | + | 3889.27i | 0.225270 | + | 0.225270i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 14787.4i | − | 0.850762i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16220.3 | − | 16220.3i | 0.929045 | − | 0.929045i | −0.0685992 | − | 0.997644i | \(-0.521853\pi\) |
0.997644 | + | 0.0685992i | \(0.0218530\pi\) | |||||||
\(674\) | 17347.3 | 0.991382 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13967.4 | −0.794685 | ||||||||
\(677\) | −11196.6 | + | 11196.6i | −0.635626 | + | 0.635626i | −0.949473 | − | 0.313847i | \(-0.898382\pi\) |
0.313847 | + | 0.949473i | \(0.398382\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17065.0i | 0.964500i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 23210.3 | + | 23210.3i | 1.30318 | + | 1.30318i | ||||
\(683\) | 15428.1 | + | 15428.1i | 0.864331 | + | 0.864331i | 0.991838 | − | 0.127507i | \(-0.0406975\pi\) |
−0.127507 | + | 0.991838i | \(0.540697\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 25627.9i | 1.42635i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −13561.6 | + | 13561.6i | −0.751501 | + | 0.751501i | ||||
\(689\) | −17635.2 | −0.975104 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21858.6 | 1.20339 | 0.601693 | − | 0.798728i | \(-0.294493\pi\) | ||||
0.601693 | + | 0.798728i | \(0.294493\pi\) | |||||||
\(692\) | −2535.89 | + | 2535.89i | −0.139307 | + | 0.139307i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 12434.2i | − | 0.680112i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15737.2 | + | 15737.2i | 0.855220 | + | 0.855220i | ||||
\(698\) | −21518.9 | − | 21518.9i | −1.16691 | − | 1.16691i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8846.82i | 0.476662i | 0.971184 | + | 0.238331i | \(0.0766002\pi\) | ||||
−0.971184 | + | 0.238331i | \(0.923400\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2084.34 | + | 2084.34i | −0.111824 | + | 0.111824i | ||||
\(704\) | 7347.86 | 0.393371 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 35656.2 | 1.90076 | ||||||||
\(707\) | −1212.06 | + | 1212.06i | −0.0644755 | + | 0.0644755i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 23189.8i | − | 1.22837i | −0.789163 | − | 0.614184i | \(-0.789485\pi\) | ||
0.789163 | − | 0.614184i | \(-0.210515\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8073.34 | − | 8073.34i | −0.424945 | − | 0.424945i | ||||
\(713\) | −9292.43 | − | 9292.43i | −0.488084 | − | 0.488084i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 27133.9i | − | 1.41626i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4661.21 | − | 4661.21i | 0.242277 | − | 0.242277i | ||||
\(719\) | 7005.29 | 0.363356 | 0.181678 | − | 0.983358i | \(-0.441847\pi\) | ||||
0.181678 | + | 0.983358i | \(0.441847\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −301.661 | −0.0155818 | ||||||||
\(722\) | 13553.2 | − | 13553.2i | 0.698611 | − | 0.698611i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8892.98i | 0.456498i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16025.7 | + | 16025.7i | 0.817553 | + | 0.817553i | 0.985753 | − | 0.168200i | \(-0.0537954\pi\) |
−0.168200 | + | 0.985753i | \(0.553795\pi\) | |||||||
\(728\) | −6183.82 | − | 6183.82i | −0.314818 | − | 0.314818i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 21267.8i | − | 1.07609i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3319.43 | − | 3319.43i | 0.167266 | − | 0.167266i | −0.618511 | − | 0.785777i | \(-0.712264\pi\) |
0.785777 | + | 0.618511i | \(0.212264\pi\) | |||||||
\(734\) | −24502.5 | −1.23216 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12281.5 | −0.615084 | ||||||||
\(737\) | 5700.41 | − | 5700.41i | 0.284908 | − | 0.284908i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19979.4i | 0.994526i | 0.867600 | + | 0.497263i | \(0.165662\pi\) | ||||
−0.867600 | + | 0.497263i | \(0.834338\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10440.7 | + | 10440.7i | 0.516562 | + | 0.516562i | ||||
\(743\) | 14574.6 | + | 14574.6i | 0.719637 | + | 0.719637i | 0.968531 | − | 0.248894i | \(-0.0800670\pi\) |
−0.248894 | + | 0.968531i | \(0.580067\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 30038.0i | 1.47422i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −13132.7 | + | 13132.7i | −0.641951 | + | 0.641951i | ||||
\(749\) | 16866.3 | 0.822807 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11620.1 | −0.564612 | −0.282306 | − | 0.959324i | \(-0.591099\pi\) | ||||
−0.282306 | + | 0.959324i | \(0.591099\pi\) | |||||||
\(752\) | −11219.9 | + | 11219.9i | −0.544079 | + | 0.544079i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 22789.7i | − | 1.10073i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10502.0 | − | 10502.0i | −0.504229 | − | 0.504229i | 0.408520 | − | 0.912749i | \(-0.366045\pi\) |
−0.912749 | + | 0.408520i | \(0.866045\pi\) | |||||||
\(758\) | −403.390 | − | 403.390i | −0.0193296 | − | 0.0193296i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36489.6i | 1.73817i | 0.494664 | + | 0.869085i | \(0.335291\pi\) | ||||
−0.494664 | + | 0.869085i | \(0.664709\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4461.01 | + | 4461.01i | −0.211664 | + | 0.211664i | ||||
\(764\) | −6264.50 | −0.296652 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22532.3 | −1.06283 | ||||||||
\(767\) | −13449.4 | + | 13449.4i | −0.633154 | + | 0.633154i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30323.9i | 1.42199i | 0.703198 | + | 0.710994i | \(0.251755\pi\) | ||||
−0.703198 | + | 0.710994i | \(0.748245\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16229.4 | − | 16229.4i | −0.756617 | − | 0.756617i | ||||
\(773\) | 10327.2 | + | 10327.2i | 0.480522 | + | 0.480522i | 0.905298 | − | 0.424777i | \(-0.139647\pi\) |
−0.424777 | + | 0.905298i | \(0.639647\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 9290.49i | − | 0.429780i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20533.4 | − | 20533.4i | 0.946220 | − | 0.946220i | ||||
\(779\) | 28602.1 | 1.31550 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17810.1 | −0.816000 | ||||||||
\(782\) | 12581.2 | − | 12581.2i | 0.575324 | − | 0.575324i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 8226.74i | − | 0.374760i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21521.8 | − | 21521.8i | −0.974802 | − | 0.974802i | 0.0248882 | − | 0.999690i | \(-0.492077\pi\) |
−0.999690 | + | 0.0248882i | \(0.992077\pi\) | |||||||
\(788\) | 6685.38 | + | 6685.38i | 0.302229 | + | 0.302229i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11328.6i | 0.509229i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18775.2 | + | 18775.2i | −0.840764 | + | 0.840764i | ||||
\(794\) | −53452.3 | −2.38911 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2988.10 | −0.133053 | ||||||||
\(797\) | −17277.8 | + | 17277.8i | −0.767895 | + | 0.767895i | −0.977736 | − | 0.209841i | \(-0.932706\pi\) |
0.209841 | + | 0.977736i | \(0.432706\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 17595.4i | − | 0.779076i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −28254.4 | − | 28254.4i | −1.24401 | − | 1.24401i | ||||
\(803\) | −18216.4 | − | 18216.4i | −0.800552 | − | 0.800552i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 58939.0i | − | 2.57573i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 659.866 | − | 659.866i | 0.0287302 | − | 0.0287302i | ||||
\(809\) | 41260.2 | 1.79312 | 0.896558 | − | 0.442926i | \(-0.146059\pi\) | ||||
0.896558 | + | 0.442926i | \(0.146059\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23357.1 | −1.01132 | −0.505659 | − | 0.862733i | \(-0.668751\pi\) | ||||
−0.505659 | + | 0.862733i | \(0.668751\pi\) | |||||||
\(812\) | −5638.54 | + | 5638.54i | −0.243687 | + | 0.243687i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 3775.24i | − | 0.162558i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19327.0 | − | 19327.0i | −0.827621 | − | 0.827621i | ||||
\(818\) | −12136.9 | − | 12136.9i | −0.518773 | − | 0.518773i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8296.46i | 0.352678i | 0.984330 | + | 0.176339i | \(0.0564254\pi\) | ||||
−0.984330 | + | 0.176339i | \(0.943575\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17980.5 | + | 17980.5i | −0.761555 | + | 0.761555i | −0.976603 | − | 0.215048i | \(-0.931009\pi\) |
0.215048 | + | 0.976603i | \(0.431009\pi\) | |||||||
\(824\) | 164.230 | 0.00694322 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15925.1 | 0.670827 | ||||||||
\(827\) | 9128.21 | − | 9128.21i | 0.383820 | − | 0.383820i | −0.488656 | − | 0.872476i | \(-0.662513\pi\) |
0.872476 | + | 0.488656i | \(0.162513\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24401.3i | 1.02231i | 0.859489 | + | 0.511154i | \(0.170782\pi\) | ||||
−0.859489 | + | 0.511154i | \(0.829218\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9329.38 | − | 9329.38i | −0.388748 | − | 0.388748i | ||||
\(833\) | 6450.73 | + | 6450.73i | 0.268313 | + | 0.268313i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 23868.5i | 0.987452i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 29560.2 | − | 29560.2i | 1.21854 | − | 1.21854i | ||||
\(839\) | −38174.8 | −1.57084 | −0.785422 | − | 0.618960i | \(-0.787554\pi\) | ||||
−0.785422 | + | 0.618960i | \(0.787554\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16224.9 | −0.665256 | ||||||||
\(842\) | −8880.22 | + | 8880.22i | −0.363459 | + | 0.363459i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 31729.3i | − | 1.29404i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1137.45 | − | 1137.45i | −0.0461433 | − | 0.0461433i | ||||
\(848\) | −14105.7 | − | 14105.7i | −0.571216 | − | 0.571216i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1511.44i | 0.0608833i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1757.73 | + | 1757.73i | −0.0705550 | + | 0.0705550i | −0.741504 | − | 0.670949i | \(-0.765887\pi\) |
0.670949 | + | 0.741504i | \(0.265887\pi\) | |||||||
\(854\) | 22231.2 | 0.890790 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9182.33 | −0.366642 | ||||||||
\(857\) | −7091.77 | + | 7091.77i | −0.282672 | + | 0.282672i | −0.834174 | − | 0.551501i | \(-0.814055\pi\) |
0.551501 | + | 0.834174i | \(0.314055\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 16842.4i | − | 0.668982i | −0.942399 | − | 0.334491i | \(-0.891436\pi\) | ||
0.942399 | − | 0.334491i | \(-0.108564\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 42366.4 | + | 42366.4i | 1.67402 | + | 1.67402i | ||||
\(863\) | −33056.1 | − | 33056.1i | −1.30387 | − | 1.30387i | −0.925759 | − | 0.378114i | \(-0.876573\pi\) |
−0.378114 | − | 0.925759i | \(-0.623427\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19968.7i | 0.783562i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −14582.5 | + | 14582.5i | −0.570231 | + | 0.570231i | ||||
\(869\) | −50107.9 | −1.95603 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14475.3 | −0.563120 | ||||||||
\(872\) | 2428.65 | − | 2428.65i | 0.0943171 | − | 0.0943171i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 22866.2i | − | 0.884966i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1780.97 | − | 1780.97i | −0.0685738 | − | 0.0685738i | 0.671988 | − | 0.740562i | \(-0.265441\pi\) |
−0.740562 | + | 0.671988i | \(0.765441\pi\) | |||||||
\(878\) | −4213.39 | − | 4213.39i | −0.161953 | − | 0.161953i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2698.82i | − | 0.103207i | −0.998668 | − | 0.0516036i | \(-0.983567\pi\) | ||
0.998668 | − | 0.0516036i | \(-0.0164332\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6744.66 | + | 6744.66i | −0.257051 | + | 0.257051i | −0.823854 | − | 0.566803i | \(-0.808180\pi\) |
0.566803 | + | 0.823854i | \(0.308180\pi\) | |||||||
\(884\) | 33348.5 | 1.26881 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −43497.5 | −1.64935 | ||||||||
\(887\) | 1302.99 | − | 1302.99i | 0.0493238 | − | 0.0493238i | −0.682015 | − | 0.731338i | \(-0.738896\pi\) |
0.731338 | + | 0.682015i | \(0.238896\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 17092.1i | − | 0.644827i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1856.29 | + | 1856.29i | 0.0696785 | + | 0.0696785i | ||||
\(893\) | −15989.7 | − | 15989.7i | −0.599189 | − | 0.599189i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 15798.5i | − | 0.589052i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 39483.0 | − | 39483.0i | 1.46722 | − | 1.46722i | ||||
\(899\) | 21114.0 | 0.783306 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22121.0 | 0.817933 | ||||||||
\(902\) | −25902.6 | + | 25902.6i | −0.956167 | + | 0.956167i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 6167.50i | − | 0.226912i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3070.33 | + | 3070.33i | 0.112402 | + | 0.112402i | 0.761071 | − | 0.648669i | \(-0.224674\pi\) |
−0.648669 | + | 0.761071i | \(0.724674\pi\) | |||||||
\(908\) | −15735.8 | − | 15735.8i | −0.575123 | − | 0.575123i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 19102.6i | − | 0.694727i | −0.937731 | − | 0.347364i | \(-0.887077\pi\) | ||
0.937731 | − | 0.347364i | \(-0.112923\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17285.3 | + | 17285.3i | −0.626572 | + | 0.626572i | ||||
\(914\) | 14004.9 | 0.506830 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1322.92 | 0.0477189 | ||||||||
\(917\) | 4871.55 | − | 4871.55i | 0.175434 | − | 0.175434i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 29786.7i | − | 1.06917i | −0.845113 | − | 0.534587i | \(-0.820467\pi\) | ||
0.845113 | − | 0.534587i | \(-0.179533\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −33577.8 | − | 33577.8i | −1.19938 | − | 1.19938i | ||||
\(923\) | 22613.0 | + | 22613.0i | 0.806410 | + | 0.806410i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 58478.9i | 2.07531i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13952.9 | − | 13952.9i | 0.493561 | − | 0.493561i | ||||
\(929\) | −7724.87 | −0.272815 | −0.136407 | − | 0.990653i | \(-0.543556\pi\) | ||||
−0.136407 | + | 0.990653i | \(0.543556\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11724.1 | 0.412720 | ||||||||
\(932\) | 2011.12 | − | 2011.12i | 0.0706829 | − | 0.0706829i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 41446.7i | 1.45201i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20722.5 | + | 20722.5i | 0.722492 | + | 0.722492i | 0.969112 | − | 0.246620i | \(-0.0793199\pi\) |
−0.246620 | + | 0.969112i | \(0.579320\pi\) | |||||||
\(938\) | 8569.92 | + | 8569.92i | 0.298313 | + | 0.298313i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 21780.7i | − | 0.754548i | −0.926102 | − | 0.377274i | \(-0.876862\pi\) | ||
0.926102 | − | 0.377274i | \(-0.123138\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10370.3 | − | 10370.3i | 0.358116 | − | 0.358116i | ||||
\(944\) | −21515.3 | −0.741803 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35005.8 | 1.20310 | ||||||||
\(947\) | −29938.4 | + | 29938.4i | −1.02731 | + | 1.02731i | −0.0276975 | + | 0.999616i | \(0.508818\pi\) |
−0.999616 | + | 0.0276975i | \(0.991182\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 46257.8i | 1.58229i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7756.79 | + | 7756.79i | 0.264075 | + | 0.264075i | ||||
\(953\) | 29572.1 | + | 29572.1i | 1.00518 | + | 1.00518i | 0.999987 | + | 0.00519163i | \(0.00165255\pi\) |
0.00519163 | + | 0.999987i | \(0.498347\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 5819.29i | − | 0.196872i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −28090.5 | + | 28090.5i | −0.947353 | + | 0.947353i | ||||
\(959\) | −20646.4 | −0.695212 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24814.3 | 0.832945 | ||||||||
\(962\) | −4793.32 | + | 4793.32i | −0.160647 | + | 0.160647i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 14842.9i | − | 0.495911i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9478.37 | + | 9478.37i | 0.315206 | + | 0.315206i | 0.846922 | − | 0.531717i | \(-0.178453\pi\) |
−0.531717 | + | 0.846922i | \(0.678453\pi\) | |||||||
\(968\) | 619.250 | + | 619.250i | 0.0205614 | + | 0.0205614i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8382.79i | 0.277051i | 0.990359 | + | 0.138525i | \(0.0442363\pi\) | ||||
−0.990359 | + | 0.138525i | \(0.955764\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1224.89 | + | 1224.89i | −0.0403577 | + | 0.0403577i | ||||
\(974\) | −23539.4 | −0.774384 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −30035.0 | −0.985039 | ||||||||
\(977\) | −24277.3 | + | 24277.3i | −0.794986 | + | 0.794986i | −0.982300 | − | 0.187314i | \(-0.940022\pi\) |
0.187314 | + | 0.982300i | \(0.440022\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 51714.8i | 1.68826i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −39777.5 | − | 39777.5i | −1.29262 | − | 1.29262i | ||||
\(983\) | 14666.4 | + | 14666.4i | 0.475876 | + | 0.475876i | 0.903810 | − | 0.427934i | \(-0.140758\pi\) |
−0.427934 | + | 0.903810i | \(0.640758\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 28586.7i | 0.923313i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 30305.2 | − | 30305.2i | 0.975847 | − | 0.975847i | ||||
\(989\) | −14014.8 | −0.450603 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17192.0 | 0.551080 | 0.275540 | − | 0.961290i | \(-0.411143\pi\) | ||||
0.275540 | + | 0.961290i | \(0.411143\pi\) | |||||||
\(992\) | 36085.0 | − | 36085.0i | 1.15494 | − | 1.15494i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 26775.5i | − | 0.854393i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13617.4 | − | 13617.4i | −0.432566 | − | 0.432566i | 0.456935 | − | 0.889500i | \(-0.348947\pi\) |
−0.889500 | + | 0.456935i | \(0.848947\pi\) | |||||||
\(998\) | 23296.9 | + | 23296.9i | 0.738929 | + | 0.738929i | ||||
\(999\) | 0 | 0 |
(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.f.c.107.2 | 12 | ||
3.2 | odd | 2 | inner | 225.4.f.c.107.5 | 12 | ||
5.2 | odd | 4 | 45.4.f.a.8.2 | ✓ | 12 | ||
5.3 | odd | 4 | inner | 225.4.f.c.143.5 | 12 | ||
5.4 | even | 2 | 45.4.f.a.17.5 | yes | 12 | ||
15.2 | even | 4 | 45.4.f.a.8.5 | yes | 12 | ||
15.8 | even | 4 | inner | 225.4.f.c.143.2 | 12 | ||
15.14 | odd | 2 | 45.4.f.a.17.2 | yes | 12 | ||
20.7 | even | 4 | 720.4.w.d.593.2 | 12 | |||
20.19 | odd | 2 | 720.4.w.d.17.5 | 12 | |||
60.47 | odd | 4 | 720.4.w.d.593.5 | 12 | |||
60.59 | even | 2 | 720.4.w.d.17.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.f.a.8.2 | ✓ | 12 | 5.2 | odd | 4 | ||
45.4.f.a.8.5 | yes | 12 | 15.2 | even | 4 | ||
45.4.f.a.17.2 | yes | 12 | 15.14 | odd | 2 | ||
45.4.f.a.17.5 | yes | 12 | 5.4 | even | 2 | ||
225.4.f.c.107.2 | 12 | 1.1 | even | 1 | trivial | ||
225.4.f.c.107.5 | 12 | 3.2 | odd | 2 | inner | ||
225.4.f.c.143.2 | 12 | 15.8 | even | 4 | inner | ||
225.4.f.c.143.5 | 12 | 5.3 | odd | 4 | inner | ||
720.4.w.d.17.2 | 12 | 60.59 | even | 2 | |||
720.4.w.d.17.5 | 12 | 20.19 | odd | 2 | |||
720.4.w.d.593.2 | 12 | 20.7 | even | 4 | |||
720.4.w.d.593.5 | 12 | 60.47 | odd | 4 |