Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [145,4,Mod(86,145)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(145, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("145.86");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 145 = 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 145.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.55527695083\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 95 x^{14} + 3576 x^{12} + 68256 x^{10} + 700479 x^{8} + 3754089 x^{6} + 9373424 x^{4} + \cdots + 2560000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 86.9 | ||
Root | \(0.702546i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 145.86 |
Dual form | 145.4.c.b.86.8 |
$q$-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 \(\left(\mathbb{Z}/145\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(117\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.702546i | 0.248387i | 0.992258 | + | 0.124194i | \(0.0396344\pi\) | ||||
−0.992258 | + | 0.124194i | \(0.960366\pi\) | |||||||
\(3\) | 0.260656i | 0.0501632i | 0.999685 | + | 0.0250816i | \(0.00798456\pi\) | ||||
−0.999685 | + | 0.0250816i | \(0.992015\pi\) | |||||||
\(4\) | 7.50643 | 0.938304 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | −0.183122 | −0.0124599 | ||||||||
\(7\) | 0.749935 | 0.0404927 | 0.0202463 | − | 0.999795i | \(-0.493555\pi\) | ||||
0.0202463 | + | 0.999795i | \(0.493555\pi\) | |||||||
\(8\) | 10.8940i | 0.481450i | ||||||||
\(9\) | 26.9321 | 0.997484 | ||||||||
\(10\) | − | 3.51273i | − | 0.111082i | ||||||
\(11\) | 20.4233i | 0.559804i | 0.960029 | + | 0.279902i | \(0.0903020\pi\) | ||||
−0.960029 | + | 0.279902i | \(0.909698\pi\) | |||||||
\(12\) | 1.95659i | 0.0470683i | ||||||||
\(13\) | 28.8903 | 0.616363 | 0.308181 | − | 0.951328i | \(-0.400280\pi\) | ||||
0.308181 | + | 0.951328i | \(0.400280\pi\) | |||||||
\(14\) | 0.526863i | 0.0100579i | ||||||||
\(15\) | − | 1.30328i | − | 0.0224337i | ||||||
\(16\) | 52.3979 | 0.818718 | ||||||||
\(17\) | − | 85.6406i | − | 1.22182i | −0.791701 | − | 0.610908i | \(-0.790804\pi\) | ||
0.791701 | − | 0.610908i | \(-0.209196\pi\) | |||||||
\(18\) | 18.9210i | 0.247762i | ||||||||
\(19\) | 157.803i | 1.90540i | 0.303919 | + | 0.952698i | \(0.401705\pi\) | ||||
−0.303919 | + | 0.952698i | \(0.598295\pi\) | |||||||
\(20\) | −37.5321 | −0.419622 | ||||||||
\(21\) | 0.195475i | 0.00203124i | ||||||||
\(22\) | −14.3483 | −0.139048 | ||||||||
\(23\) | 67.9963 | 0.616444 | 0.308222 | − | 0.951314i | \(-0.400266\pi\) | ||||
0.308222 | + | 0.951314i | \(0.400266\pi\) | |||||||
\(24\) | −2.83958 | −0.0241511 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 20.2967i | 0.153097i | ||||||||
\(27\) | 14.0577i | 0.100200i | ||||||||
\(28\) | 5.62933 | 0.0379944 | ||||||||
\(29\) | 121.277 | − | 98.3910i | 0.776574 | − | 0.630026i | ||||
\(30\) | 0.915612 | 0.00557224 | ||||||||
\(31\) | 184.356i | 1.06811i | 0.845450 | + | 0.534054i | \(0.179332\pi\) | ||||
−0.845450 | + | 0.534054i | \(0.820668\pi\) | |||||||
\(32\) | 123.964i | 0.684809i | ||||||||
\(33\) | −5.32344 | −0.0280816 | ||||||||
\(34\) | 60.1664 | 0.303484 | ||||||||
\(35\) | −3.74967 | −0.0181089 | ||||||||
\(36\) | 202.164 | 0.935943 | ||||||||
\(37\) | 286.331i | 1.27223i | 0.771593 | + | 0.636116i | \(0.219460\pi\) | ||||
−0.771593 | + | 0.636116i | \(0.780540\pi\) | |||||||
\(38\) | −110.864 | −0.473276 | ||||||||
\(39\) | 7.53041i | 0.0309187i | ||||||||
\(40\) | − | 54.4699i | − | 0.215311i | ||||||
\(41\) | − | 108.517i | − | 0.413355i | −0.978409 | − | 0.206677i | \(-0.933735\pi\) | ||
0.978409 | − | 0.206677i | \(-0.0662650\pi\) | |||||||
\(42\) | −0.137330 | −0.000504535 | ||||||||
\(43\) | − | 352.237i | − | 1.24920i | −0.780944 | − | 0.624600i | \(-0.785262\pi\) | ||
0.780944 | − | 0.624600i | \(-0.214738\pi\) | |||||||
\(44\) | 153.306i | 0.525266i | ||||||||
\(45\) | −134.660 | −0.446088 | ||||||||
\(46\) | 47.7705i | 0.153117i | ||||||||
\(47\) | − | 508.650i | − | 1.57860i | −0.614008 | − | 0.789300i | \(-0.710444\pi\) | ||
0.614008 | − | 0.789300i | \(-0.289556\pi\) | |||||||
\(48\) | 13.6578i | 0.0410695i | ||||||||
\(49\) | −342.438 | −0.998360 | ||||||||
\(50\) | 17.5636i | 0.0496775i | ||||||||
\(51\) | 22.3227 | 0.0612902 | ||||||||
\(52\) | 216.863 | 0.578336 | ||||||||
\(53\) | −667.231 | −1.72927 | −0.864634 | − | 0.502402i | \(-0.832450\pi\) | ||||
−0.864634 | + | 0.502402i | \(0.832450\pi\) | |||||||
\(54\) | −9.87617 | −0.0248885 | ||||||||
\(55\) | − | 102.116i | − | 0.250352i | ||||||
\(56\) | 8.16977i | 0.0194952i | ||||||||
\(57\) | −41.1323 | −0.0955808 | ||||||||
\(58\) | 69.1241 | + | 85.2029i | 0.156490 | + | 0.192891i | ||||
\(59\) | −367.954 | −0.811924 | −0.405962 | − | 0.913890i | \(-0.633064\pi\) | ||||
−0.405962 | + | 0.913890i | \(0.633064\pi\) | |||||||
\(60\) | − | 9.78297i | − | 0.0210496i | ||||||
\(61\) | − | 513.500i | − | 1.07782i | −0.842364 | − | 0.538909i | \(-0.818837\pi\) | ||
0.842364 | − | 0.538909i | \(-0.181163\pi\) | |||||||
\(62\) | −129.519 | −0.265305 | ||||||||
\(63\) | 20.1973 | 0.0403908 | ||||||||
\(64\) | 332.093 | 0.648620 | ||||||||
\(65\) | −144.451 | −0.275646 | ||||||||
\(66\) | − | 3.73996i | − | 0.00697510i | ||||||
\(67\) | 94.0371 | 0.171469 | 0.0857347 | − | 0.996318i | \(-0.472676\pi\) | ||||
0.0857347 | + | 0.996318i | \(0.472676\pi\) | |||||||
\(68\) | − | 642.855i | − | 1.14644i | ||||||
\(69\) | 17.7236i | 0.0309228i | ||||||||
\(70\) | − | 2.63432i | − | 0.00449802i | ||||||
\(71\) | −38.3555 | −0.0641121 | −0.0320560 | − | 0.999486i | \(-0.510206\pi\) | ||||
−0.0320560 | + | 0.999486i | \(0.510206\pi\) | |||||||
\(72\) | 293.397i | 0.480239i | ||||||||
\(73\) | − | 721.153i | − | 1.15623i | −0.815956 | − | 0.578114i | \(-0.803789\pi\) | ||
0.815956 | − | 0.578114i | \(-0.196211\pi\) | |||||||
\(74\) | −201.161 | −0.316006 | ||||||||
\(75\) | 6.51639i | 0.0100326i | ||||||||
\(76\) | 1184.54i | 1.78784i | ||||||||
\(77\) | 15.3161i | 0.0226680i | ||||||||
\(78\) | −5.29046 | −0.00767982 | ||||||||
\(79\) | − | 365.512i | − | 0.520548i | −0.965535 | − | 0.260274i | \(-0.916187\pi\) | ||
0.965535 | − | 0.260274i | \(-0.0838129\pi\) | |||||||
\(80\) | −261.990 | −0.366142 | ||||||||
\(81\) | 723.501 | 0.992457 | ||||||||
\(82\) | 76.2383 | 0.102672 | ||||||||
\(83\) | −1030.81 | −1.36321 | −0.681605 | − | 0.731720i | \(-0.738718\pi\) | ||||
−0.681605 | + | 0.731720i | \(0.738718\pi\) | |||||||
\(84\) | 1.46732i | 0.00190592i | ||||||||
\(85\) | 428.203i | 0.546413i | ||||||||
\(86\) | 247.463 | 0.310286 | ||||||||
\(87\) | 25.6462 | + | 31.6117i | 0.0316041 | + | 0.0389555i | ||||
\(88\) | −222.490 | −0.269518 | ||||||||
\(89\) | − | 796.188i | − | 0.948267i | −0.880453 | − | 0.474133i | \(-0.842761\pi\) | ||
0.880453 | − | 0.474133i | \(-0.157239\pi\) | |||||||
\(90\) | − | 94.6050i | − | 0.110803i | ||||||
\(91\) | 21.6658 | 0.0249582 | ||||||||
\(92\) | 510.410 | 0.578412 | ||||||||
\(93\) | −48.0535 | −0.0535797 | ||||||||
\(94\) | 357.350 | 0.392104 | ||||||||
\(95\) | − | 789.016i | − | 0.852119i | ||||||
\(96\) | −32.3118 | −0.0343522 | ||||||||
\(97\) | 1026.88i | 1.07489i | 0.843300 | + | 0.537444i | \(0.180610\pi\) | ||||
−0.843300 | + | 0.537444i | \(0.819390\pi\) | |||||||
\(98\) | − | 240.578i | − | 0.247980i | ||||||
\(99\) | 550.040i | 0.558395i | ||||||||
\(100\) | 187.661 | 0.187661 | ||||||||
\(101\) | 1592.50i | 1.56891i | 0.620185 | + | 0.784456i | \(0.287058\pi\) | ||||
−0.620185 | + | 0.784456i | \(0.712942\pi\) | |||||||
\(102\) | 15.6827i | 0.0152237i | ||||||||
\(103\) | −1192.20 | −1.14049 | −0.570245 | − | 0.821474i | \(-0.693152\pi\) | ||||
−0.570245 | + | 0.821474i | \(0.693152\pi\) | |||||||
\(104\) | 314.730i | 0.296748i | ||||||||
\(105\) | − | 0.977374i | − | 0.000908399i | ||||||
\(106\) | − | 468.760i | − | 0.429528i | ||||||
\(107\) | 1074.70 | 0.970983 | 0.485492 | − | 0.874241i | \(-0.338641\pi\) | ||||
0.485492 | + | 0.874241i | \(0.338641\pi\) | |||||||
\(108\) | 105.523i | 0.0940182i | ||||||||
\(109\) | −1132.08 | −0.994807 | −0.497403 | − | 0.867519i | \(-0.665713\pi\) | ||||
−0.497403 | + | 0.867519i | \(0.665713\pi\) | |||||||
\(110\) | 71.7413 | 0.0621842 | ||||||||
\(111\) | −74.6339 | −0.0638192 | ||||||||
\(112\) | 39.2950 | 0.0331521 | ||||||||
\(113\) | − | 1750.93i | − | 1.45764i | −0.684704 | − | 0.728822i | \(-0.740068\pi\) | ||
0.684704 | − | 0.728822i | \(-0.259932\pi\) | |||||||
\(114\) | − | 28.8973i | − | 0.0237411i | ||||||
\(115\) | −339.982 | −0.275682 | ||||||||
\(116\) | 910.361 | − | 738.565i | 0.728663 | − | 0.591155i | ||||
\(117\) | 778.074 | 0.614812 | ||||||||
\(118\) | − | 258.504i | − | 0.201672i | ||||||
\(119\) | − | 64.2248i | − | 0.0494746i | ||||||
\(120\) | 14.1979 | 0.0108007 | ||||||||
\(121\) | 913.891 | 0.686620 | ||||||||
\(122\) | 360.757 | 0.267717 | ||||||||
\(123\) | 28.2856 | 0.0207352 | ||||||||
\(124\) | 1383.86i | 1.00221i | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 14.1895i | 0.0100326i | ||||||||
\(127\) | 1306.97i | 0.913187i | 0.889675 | + | 0.456594i | \(0.150931\pi\) | ||||
−0.889675 | + | 0.456594i | \(0.849069\pi\) | |||||||
\(128\) | 1225.02i | 0.845918i | ||||||||
\(129\) | 91.8126 | 0.0626639 | ||||||||
\(130\) | − | 101.484i | − | 0.0684669i | ||||||
\(131\) | 1486.65i | 0.991520i | 0.868460 | + | 0.495760i | \(0.165110\pi\) | ||||
−0.868460 | + | 0.495760i | \(0.834890\pi\) | |||||||
\(132\) | −39.9600 | −0.0263490 | ||||||||
\(133\) | 118.342i | 0.0771546i | ||||||||
\(134\) | 66.0653i | 0.0425908i | ||||||||
\(135\) | − | 70.2885i | − | 0.0448109i | ||||||
\(136\) | 932.966 | 0.588244 | ||||||||
\(137\) | 1086.03i | 0.677270i | 0.940918 | + | 0.338635i | \(0.109965\pi\) | ||||
−0.940918 | + | 0.338635i | \(0.890035\pi\) | |||||||
\(138\) | −12.4517 | −0.00768084 | ||||||||
\(139\) | 2548.45 | 1.55509 | 0.777543 | − | 0.628829i | \(-0.216466\pi\) | ||||
0.777543 | + | 0.628829i | \(0.216466\pi\) | |||||||
\(140\) | −28.1467 | −0.0169916 | ||||||||
\(141\) | 132.582 | 0.0791876 | ||||||||
\(142\) | − | 26.9465i | − | 0.0159246i | ||||||
\(143\) | 590.033i | 0.345042i | ||||||||
\(144\) | 1411.18 | 0.816657 | ||||||||
\(145\) | −606.387 | + | 491.955i | −0.347295 | + | 0.281756i | ||||
\(146\) | 506.643 | 0.287192 | ||||||||
\(147\) | − | 89.2583i | − | 0.0500810i | ||||||
\(148\) | 2149.33i | 1.19374i | ||||||||
\(149\) | 909.758 | 0.500203 | 0.250101 | − | 0.968220i | \(-0.419536\pi\) | ||||
0.250101 | + | 0.968220i | \(0.419536\pi\) | |||||||
\(150\) | −4.57806 | −0.00249198 | ||||||||
\(151\) | 1531.36 | 0.825299 | 0.412649 | − | 0.910890i | \(-0.364603\pi\) | ||||
0.412649 | + | 0.910890i | \(0.364603\pi\) | |||||||
\(152\) | −1719.10 | −0.917353 | ||||||||
\(153\) | − | 2306.48i | − | 1.21874i | ||||||
\(154\) | −10.7603 | −0.00563043 | ||||||||
\(155\) | − | 921.781i | − | 0.477673i | ||||||
\(156\) | 56.5265i | 0.0290112i | ||||||||
\(157\) | − | 2764.09i | − | 1.40509i | −0.711641 | − | 0.702543i | \(-0.752048\pi\) | ||
0.711641 | − | 0.702543i | \(-0.247952\pi\) | |||||||
\(158\) | 256.789 | 0.129298 | ||||||||
\(159\) | − | 173.918i | − | 0.0867456i | ||||||
\(160\) | − | 619.819i | − | 0.306256i | ||||||
\(161\) | 50.9928 | 0.0249615 | ||||||||
\(162\) | 508.293i | 0.246514i | ||||||||
\(163\) | − | 761.250i | − | 0.365802i | −0.983131 | − | 0.182901i | \(-0.941451\pi\) | ||
0.983131 | − | 0.182901i | \(-0.0585488\pi\) | |||||||
\(164\) | − | 814.577i | − | 0.387852i | ||||||
\(165\) | 26.6172 | 0.0125585 | ||||||||
\(166\) | − | 724.193i | − | 0.338604i | ||||||
\(167\) | −2607.55 | −1.20825 | −0.604126 | − | 0.796889i | \(-0.706478\pi\) | ||||
−0.604126 | + | 0.796889i | \(0.706478\pi\) | |||||||
\(168\) | −2.12950 | −0.000977942 | ||||||||
\(169\) | −1362.35 | −0.620097 | ||||||||
\(170\) | −300.832 | −0.135722 | ||||||||
\(171\) | 4249.96i | 1.90060i | ||||||||
\(172\) | − | 2644.04i | − | 1.17213i | ||||||
\(173\) | −3985.94 | −1.75171 | −0.875854 | − | 0.482576i | \(-0.839701\pi\) | ||||
−0.875854 | + | 0.482576i | \(0.839701\pi\) | |||||||
\(174\) | −22.2086 | + | 18.0176i | −0.00967604 | + | 0.00785006i | ||||
\(175\) | 18.7484 | 0.00809853 | ||||||||
\(176\) | 1070.14i | 0.458321i | ||||||||
\(177\) | − | 95.9093i | − | 0.0407287i | ||||||
\(178\) | 559.358 | 0.235537 | ||||||||
\(179\) | 1515.40 | 0.632772 | 0.316386 | − | 0.948631i | \(-0.397531\pi\) | ||||
0.316386 | + | 0.948631i | \(0.397531\pi\) | |||||||
\(180\) | −1010.82 | −0.418566 | ||||||||
\(181\) | −2305.13 | −0.946624 | −0.473312 | − | 0.880895i | \(-0.656942\pi\) | ||||
−0.473312 | + | 0.880895i | \(0.656942\pi\) | |||||||
\(182\) | 15.2212i | 0.00619930i | ||||||||
\(183\) | 133.847 | 0.0540668 | ||||||||
\(184\) | 740.750i | 0.296787i | ||||||||
\(185\) | − | 1431.66i | − | 0.568960i | ||||||
\(186\) | − | 33.7598i | − | 0.0133085i | ||||||
\(187\) | 1749.06 | 0.683978 | ||||||||
\(188\) | − | 3818.14i | − | 1.48121i | ||||||
\(189\) | 10.5424i | 0.00405737i | ||||||||
\(190\) | 554.319 | 0.211656 | ||||||||
\(191\) | − | 4595.21i | − | 1.74083i | −0.492321 | − | 0.870414i | \(-0.663851\pi\) | ||
0.492321 | − | 0.870414i | \(-0.336149\pi\) | |||||||
\(192\) | 86.5620i | 0.0325368i | ||||||||
\(193\) | 3552.85i | 1.32508i | 0.749029 | + | 0.662538i | \(0.230520\pi\) | ||||
−0.749029 | + | 0.662538i | \(0.769480\pi\) | |||||||
\(194\) | −721.431 | −0.266988 | ||||||||
\(195\) | − | 37.6521i | − | 0.0138273i | ||||||
\(196\) | −2570.48 | −0.936765 | ||||||||
\(197\) | 838.413 | 0.303221 | 0.151610 | − | 0.988440i | \(-0.451554\pi\) | ||||
0.151610 | + | 0.988440i | \(0.451554\pi\) | |||||||
\(198\) | −386.428 | −0.138698 | ||||||||
\(199\) | −378.636 | −0.134878 | −0.0674391 | − | 0.997723i | \(-0.521483\pi\) | ||||
−0.0674391 | + | 0.997723i | \(0.521483\pi\) | |||||||
\(200\) | 272.349i | 0.0962900i | ||||||||
\(201\) | 24.5113i | 0.00860146i | ||||||||
\(202\) | −1118.81 | −0.389698 | ||||||||
\(203\) | 90.9502 | − | 73.7868i | 0.0314456 | − | 0.0255114i | ||||
\(204\) | 167.564 | 0.0575089 | ||||||||
\(205\) | 542.586i | 0.184858i | ||||||||
\(206\) | − | 837.572i | − | 0.283283i | ||||||
\(207\) | 1831.28 | 0.614893 | ||||||||
\(208\) | 1513.79 | 0.504627 | ||||||||
\(209\) | −3222.85 | −1.06665 | ||||||||
\(210\) | 0.686650 | 0.000225635 | ||||||||
\(211\) | 1823.72i | 0.595024i | 0.954718 | + | 0.297512i | \(0.0961568\pi\) | ||||
−0.954718 | + | 0.297512i | \(0.903843\pi\) | |||||||
\(212\) | −5008.52 | −1.62258 | ||||||||
\(213\) | − | 9.99757i | − | 0.00321607i | ||||||
\(214\) | 755.026i | 0.241180i | ||||||||
\(215\) | 1761.19i | 0.558660i | ||||||||
\(216\) | −153.144 | −0.0482414 | ||||||||
\(217\) | 138.255i | 0.0432506i | ||||||||
\(218\) | − | 795.340i | − | 0.247097i | ||||||
\(219\) | 187.973 | 0.0580001 | ||||||||
\(220\) | − | 766.529i | − | 0.234906i | ||||||
\(221\) | − | 2474.18i | − | 0.753083i | ||||||
\(222\) | − | 52.4337i | − | 0.0158519i | ||||||
\(223\) | 3024.91 | 0.908354 | 0.454177 | − | 0.890911i | \(-0.349933\pi\) | ||||
0.454177 | + | 0.890911i | \(0.349933\pi\) | |||||||
\(224\) | 92.9647i | 0.0277298i | ||||||||
\(225\) | 673.301 | 0.199497 | ||||||||
\(226\) | 1230.11 | 0.362060 | ||||||||
\(227\) | 3464.13 | 1.01288 | 0.506438 | − | 0.862277i | \(-0.330962\pi\) | ||||
0.506438 | + | 0.862277i | \(0.330962\pi\) | |||||||
\(228\) | −308.757 | −0.0896838 | ||||||||
\(229\) | − | 4857.40i | − | 1.40169i | −0.713316 | − | 0.700843i | \(-0.752808\pi\) | ||
0.713316 | − | 0.700843i | \(-0.247192\pi\) | |||||||
\(230\) | − | 238.853i | − | 0.0684760i | ||||||
\(231\) | −3.99223 | −0.00113710 | ||||||||
\(232\) | 1071.87 | + | 1321.19i | 0.303326 | + | 0.373882i | ||||
\(233\) | −1518.33 | −0.426907 | −0.213453 | − | 0.976953i | \(-0.568471\pi\) | ||||
−0.213453 | + | 0.976953i | \(0.568471\pi\) | |||||||
\(234\) | 546.633i | 0.152712i | ||||||||
\(235\) | 2543.25i | 0.705971i | ||||||||
\(236\) | −2762.02 | −0.761832 | ||||||||
\(237\) | 95.2728 | 0.0261124 | ||||||||
\(238\) | 45.1209 | 0.0122889 | ||||||||
\(239\) | −2424.17 | −0.656096 | −0.328048 | − | 0.944661i | \(-0.606391\pi\) | ||||
−0.328048 | + | 0.944661i | \(0.606391\pi\) | |||||||
\(240\) | − | 68.2891i | − | 0.0183668i | ||||||
\(241\) | −4370.91 | −1.16828 | −0.584139 | − | 0.811654i | \(-0.698568\pi\) | ||||
−0.584139 | + | 0.811654i | \(0.698568\pi\) | |||||||
\(242\) | 642.050i | 0.170548i | ||||||||
\(243\) | 568.143i | 0.149985i | ||||||||
\(244\) | − | 3854.55i | − | 1.01132i | ||||||
\(245\) | 1712.19 | 0.446480 | ||||||||
\(246\) | 19.8719i | 0.00515036i | ||||||||
\(247\) | 4558.97i | 1.17442i | ||||||||
\(248\) | −2008.37 | −0.514241 | ||||||||
\(249\) | − | 268.687i | − | 0.0683830i | ||||||
\(250\) | − | 87.8182i | − | 0.0222164i | ||||||
\(251\) | − | 1066.96i | − | 0.268310i | −0.990960 | − | 0.134155i | \(-0.957168\pi\) | ||
0.990960 | − | 0.134155i | \(-0.0428320\pi\) | |||||||
\(252\) | 151.610 | 0.0378988 | ||||||||
\(253\) | 1388.71i | 0.345088i | ||||||||
\(254\) | −918.205 | −0.226824 | ||||||||
\(255\) | −111.613 | −0.0274098 | ||||||||
\(256\) | 1796.11 | 0.438504 | ||||||||
\(257\) | −1243.55 | −0.301830 | −0.150915 | − | 0.988547i | \(-0.548222\pi\) | ||||
−0.150915 | + | 0.988547i | \(0.548222\pi\) | |||||||
\(258\) | 64.5025i | 0.0155649i | ||||||||
\(259\) | 214.730i | 0.0515161i | ||||||||
\(260\) | −1084.31 | −0.258640 | ||||||||
\(261\) | 3266.25 | − | 2649.87i | 0.774620 | − | 0.628440i | ||||
\(262\) | −1044.44 | −0.246281 | ||||||||
\(263\) | 1285.68i | 0.301440i | 0.988576 | + | 0.150720i | \(0.0481592\pi\) | ||||
−0.988576 | + | 0.150720i | \(0.951841\pi\) | |||||||
\(264\) | − | 57.9934i | − | 0.0135199i | ||||||
\(265\) | 3336.15 | 0.773352 | ||||||||
\(266\) | −83.1407 | −0.0191642 | ||||||||
\(267\) | 207.531 | 0.0475681 | ||||||||
\(268\) | 705.883 | 0.160890 | ||||||||
\(269\) | − | 1663.13i | − | 0.376961i | −0.982077 | − | 0.188481i | \(-0.939644\pi\) | ||
0.982077 | − | 0.188481i | \(-0.0603563\pi\) | |||||||
\(270\) | 49.3809 | 0.0111305 | ||||||||
\(271\) | − | 2409.91i | − | 0.540190i | −0.962834 | − | 0.270095i | \(-0.912945\pi\) | ||
0.962834 | − | 0.270095i | \(-0.0870551\pi\) | |||||||
\(272\) | − | 4487.39i | − | 1.00032i | ||||||
\(273\) | 5.64732i | 0.00125198i | ||||||||
\(274\) | −762.987 | −0.168225 | ||||||||
\(275\) | 510.581i | 0.111961i | ||||||||
\(276\) | 133.041i | 0.0290150i | ||||||||
\(277\) | 4668.95 | 1.01274 | 0.506372 | − | 0.862315i | \(-0.330986\pi\) | ||||
0.506372 | + | 0.862315i | \(0.330986\pi\) | |||||||
\(278\) | 1790.40i | 0.386264i | ||||||||
\(279\) | 4965.09i | 1.06542i | ||||||||
\(280\) | − | 40.8488i | − | 0.00871852i | ||||||
\(281\) | −482.466 | −0.102425 | −0.0512126 | − | 0.998688i | \(-0.516309\pi\) | ||||
−0.0512126 | + | 0.998688i | \(0.516309\pi\) | |||||||
\(282\) | 93.1452i | 0.0196692i | ||||||||
\(283\) | 7419.37 | 1.55843 | 0.779215 | − | 0.626756i | \(-0.215618\pi\) | ||||
0.779215 | + | 0.626756i | \(0.215618\pi\) | |||||||
\(284\) | −287.913 | −0.0601566 | ||||||||
\(285\) | 205.661 | 0.0427450 | ||||||||
\(286\) | −414.525 | −0.0857042 | ||||||||
\(287\) | − | 81.3808i | − | 0.0167378i | ||||||
\(288\) | 3338.60i | 0.683086i | ||||||||
\(289\) | −2421.30 | −0.492836 | ||||||||
\(290\) | −345.621 | − | 426.015i | −0.0699846 | − | 0.0862636i | ||||
\(291\) | −267.663 | −0.0539198 | ||||||||
\(292\) | − | 5413.29i | − | 1.08489i | ||||||
\(293\) | 283.298i | 0.0564861i | 0.999601 | + | 0.0282431i | \(0.00899124\pi\) | ||||
−0.999601 | + | 0.0282431i | \(0.991009\pi\) | |||||||
\(294\) | 62.7080 | 0.0124395 | ||||||||
\(295\) | 1839.77 | 0.363104 | ||||||||
\(296\) | −3119.29 | −0.612516 | ||||||||
\(297\) | −287.104 | −0.0560925 | ||||||||
\(298\) | 639.146i | 0.124244i | ||||||||
\(299\) | 1964.43 | 0.379953 | ||||||||
\(300\) | 48.9148i | 0.00941366i | ||||||||
\(301\) | − | 264.155i | − | 0.0505835i | ||||||
\(302\) | 1075.85i | 0.204994i | ||||||||
\(303\) | −415.095 | −0.0787016 | ||||||||
\(304\) | 8268.56i | 1.55998i | ||||||||
\(305\) | 2567.50i | 0.482015i | ||||||||
\(306\) | 1620.40 | 0.302720 | ||||||||
\(307\) | 6778.63i | 1.26018i | 0.776520 | + | 0.630092i | \(0.216983\pi\) | ||||
−0.776520 | + | 0.630092i | \(0.783017\pi\) | |||||||
\(308\) | 114.969i | 0.0212694i | ||||||||
\(309\) | − | 310.753i | − | 0.0572107i | ||||||
\(310\) | 647.593 | 0.118648 | ||||||||
\(311\) | 3553.89i | 0.647982i | 0.946060 | + | 0.323991i | \(0.105025\pi\) | ||||
−0.946060 | + | 0.323991i | \(0.894975\pi\) | |||||||
\(312\) | −82.0361 | −0.0148858 | ||||||||
\(313\) | 8669.94 | 1.56567 | 0.782833 | − | 0.622231i | \(-0.213774\pi\) | ||||
0.782833 | + | 0.622231i | \(0.213774\pi\) | |||||||
\(314\) | 1941.90 | 0.349006 | ||||||||
\(315\) | −100.986 | −0.0180633 | ||||||||
\(316\) | − | 2743.69i | − | 0.488432i | ||||||
\(317\) | − | 2287.04i | − | 0.405215i | −0.979260 | − | 0.202608i | \(-0.935058\pi\) | ||
0.979260 | − | 0.202608i | \(-0.0649416\pi\) | |||||||
\(318\) | 122.185 | 0.0215465 | ||||||||
\(319\) | 2009.46 | + | 2476.88i | 0.352691 | + | 0.434729i | ||||
\(320\) | −1660.47 | −0.290072 | ||||||||
\(321\) | 280.127i | 0.0487076i | ||||||||
\(322\) | 35.8248i | 0.00620012i | ||||||||
\(323\) | 13514.3 | 2.32804 | ||||||||
\(324\) | 5430.91 | 0.931226 | ||||||||
\(325\) | 722.257 | 0.123273 | ||||||||
\(326\) | 534.813 | 0.0908605 | ||||||||
\(327\) | − | 295.084i | − | 0.0499027i | ||||||
\(328\) | 1182.18 | 0.199010 | ||||||||
\(329\) | − | 381.454i | − | 0.0639217i | ||||||
\(330\) | 18.6998i | 0.00311936i | ||||||||
\(331\) | 480.145i | 0.0797315i | 0.999205 | + | 0.0398658i | \(0.0126930\pi\) | ||||
−0.999205 | + | 0.0398658i | \(0.987307\pi\) | |||||||
\(332\) | −7737.72 | −1.27910 | ||||||||
\(333\) | 7711.49i | 1.26903i | ||||||||
\(334\) | − | 1831.92i | − | 0.300114i | ||||||
\(335\) | −470.185 | −0.0766835 | ||||||||
\(336\) | 10.2425i | 0.00166301i | ||||||||
\(337\) | 371.348i | 0.0600256i | 0.999550 | + | 0.0300128i | \(0.00955480\pi\) | ||||
−0.999550 | + | 0.0300128i | \(0.990445\pi\) | |||||||
\(338\) | − | 957.115i | − | 0.154024i | ||||||
\(339\) | 456.390 | 0.0731201 | ||||||||
\(340\) | 3214.27i | 0.512701i | ||||||||
\(341\) | −3765.15 | −0.597931 | ||||||||
\(342\) | −2985.79 | −0.472085 | ||||||||
\(343\) | −514.034 | −0.0809190 | ||||||||
\(344\) | 3837.26 | 0.601428 | ||||||||
\(345\) | − | 88.6182i | − | 0.0138291i | ||||||
\(346\) | − | 2800.30i | − | 0.435102i | ||||||
\(347\) | −329.969 | −0.0510480 | −0.0255240 | − | 0.999674i | \(-0.508125\pi\) | ||||
−0.0255240 | + | 0.999674i | \(0.508125\pi\) | |||||||
\(348\) | 192.511 | + | 237.291i | 0.0296543 | + | 0.0365521i | ||||
\(349\) | −9179.88 | −1.40799 | −0.703993 | − | 0.710206i | \(-0.748602\pi\) | ||||
−0.703993 | + | 0.710206i | \(0.748602\pi\) | |||||||
\(350\) | 13.1716i | 0.00201157i | ||||||||
\(351\) | 406.131i | 0.0617597i | ||||||||
\(352\) | −2531.74 | −0.383359 | ||||||||
\(353\) | 469.239 | 0.0707509 | 0.0353755 | − | 0.999374i | \(-0.488737\pi\) | ||||
0.0353755 | + | 0.999374i | \(0.488737\pi\) | |||||||
\(354\) | 67.3806 | 0.0101165 | ||||||||
\(355\) | 191.777 | 0.0286718 | ||||||||
\(356\) | − | 5976.53i | − | 0.889762i | ||||||
\(357\) | 16.7406 | 0.00248181 | ||||||||
\(358\) | 1064.64i | 0.157172i | ||||||||
\(359\) | − | 1666.06i | − | 0.244933i | −0.992473 | − | 0.122467i | \(-0.960920\pi\) | ||
0.992473 | − | 0.122467i | \(-0.0390805\pi\) | |||||||
\(360\) | − | 1466.99i | − | 0.214769i | ||||||
\(361\) | −18042.8 | −2.63053 | ||||||||
\(362\) | − | 1619.46i | − | 0.235129i | ||||||
\(363\) | 238.211i | 0.0344430i | ||||||||
\(364\) | 162.633 | 0.0234184 | ||||||||
\(365\) | 3605.77i | 0.517081i | ||||||||
\(366\) | 94.0334i | 0.0134295i | ||||||||
\(367\) | − | 1626.59i | − | 0.231354i | −0.993287 | − | 0.115677i | \(-0.963096\pi\) | ||
0.993287 | − | 0.115677i | \(-0.0369038\pi\) | |||||||
\(368\) | 3562.87 | 0.504694 | ||||||||
\(369\) | − | 2922.59i | − | 0.412315i | ||||||
\(370\) | 1005.80 | 0.141322 | ||||||||
\(371\) | −500.380 | −0.0700227 | ||||||||
\(372\) | −360.710 | −0.0502741 | ||||||||
\(373\) | −3223.36 | −0.447452 | −0.223726 | − | 0.974652i | \(-0.571822\pi\) | ||||
−0.223726 | + | 0.974652i | \(0.571822\pi\) | |||||||
\(374\) | 1228.79i | 0.169891i | ||||||||
\(375\) | − | 32.5820i | − | 0.00448673i | ||||||
\(376\) | 5541.22 | 0.760017 | ||||||||
\(377\) | 3503.74 | − | 2842.54i | 0.478652 | − | 0.388324i | ||||
\(378\) | −7.40649 | −0.00100780 | ||||||||
\(379\) | − | 8682.97i | − | 1.17682i | −0.808563 | − | 0.588409i | \(-0.799754\pi\) | ||
0.808563 | − | 0.588409i | \(-0.200246\pi\) | |||||||
\(380\) | − | 5922.69i | − | 0.799546i | ||||||
\(381\) | −340.669 | −0.0458084 | ||||||||
\(382\) | 3228.35 | 0.432400 | ||||||||
\(383\) | −9051.26 | −1.20757 | −0.603783 | − | 0.797149i | \(-0.706341\pi\) | ||||
−0.603783 | + | 0.797149i | \(0.706341\pi\) | |||||||
\(384\) | −319.308 | −0.0424340 | ||||||||
\(385\) | − | 76.5805i | − | 0.0101374i | ||||||
\(386\) | −2496.04 | −0.329132 | ||||||||
\(387\) | − | 9486.47i | − | 1.24606i | ||||||
\(388\) | 7708.22i | 1.00857i | ||||||||
\(389\) | 7273.00i | 0.947959i | 0.880536 | + | 0.473979i | \(0.157183\pi\) | ||||
−0.880536 | + | 0.473979i | \(0.842817\pi\) | |||||||
\(390\) | 26.4523 | 0.00343452 | ||||||||
\(391\) | − | 5823.24i | − | 0.753182i | ||||||
\(392\) | − | 3730.51i | − | 0.480661i | ||||||
\(393\) | −387.503 | −0.0497378 | ||||||||
\(394\) | 589.023i | 0.0753161i | ||||||||
\(395\) | 1827.56i | 0.232796i | ||||||||
\(396\) | 4128.84i | 0.523944i | ||||||||
\(397\) | −153.154 | −0.0193617 | −0.00968084 | − | 0.999953i | \(-0.503082\pi\) | ||||
−0.00968084 | + | 0.999953i | \(0.503082\pi\) | |||||||
\(398\) | − | 266.009i | − | 0.0335020i | ||||||
\(399\) | −30.8465 | −0.00387032 | ||||||||
\(400\) | 1309.95 | 0.163744 | ||||||||
\(401\) | 7559.20 | 0.941368 | 0.470684 | − | 0.882302i | \(-0.344007\pi\) | ||||
0.470684 | + | 0.882302i | \(0.344007\pi\) | |||||||
\(402\) | −17.2203 | −0.00213649 | ||||||||
\(403\) | 5326.10i | 0.658342i | ||||||||
\(404\) | 11954.0i | 1.47212i | ||||||||
\(405\) | −3617.51 | −0.443840 | ||||||||
\(406\) | 51.8386 | + | 63.8966i | 0.00633671 | + | 0.00781068i | ||||
\(407\) | −5847.82 | −0.712200 | ||||||||
\(408\) | 243.183i | 0.0295082i | ||||||||
\(409\) | − | 5240.16i | − | 0.633518i | −0.948506 | − | 0.316759i | \(-0.897405\pi\) | ||
0.948506 | − | 0.316759i | \(-0.102595\pi\) | |||||||
\(410\) | −381.191 | −0.0459163 | ||||||||
\(411\) | −283.080 | −0.0339740 | ||||||||
\(412\) | −8949.13 | −1.07013 | ||||||||
\(413\) | −275.942 | −0.0328770 | ||||||||
\(414\) | 1286.56i | 0.152732i | ||||||||
\(415\) | 5154.06 | 0.609646 | ||||||||
\(416\) | 3581.34i | 0.422091i | ||||||||
\(417\) | 664.269i | 0.0780081i | ||||||||
\(418\) | − | 2264.20i | − | 0.264942i | ||||||
\(419\) | −11062.2 | −1.28980 | −0.644899 | − | 0.764268i | \(-0.723101\pi\) | ||||
−0.644899 | + | 0.764268i | \(0.723101\pi\) | |||||||
\(420\) | − | 7.33659i | − | 0.000852354i | ||||||
\(421\) | − | 9553.19i | − | 1.10592i | −0.833206 | − | 0.552962i | \(-0.813497\pi\) | ||
0.833206 | − | 0.552962i | \(-0.186503\pi\) | |||||||
\(422\) | −1281.25 | −0.147796 | ||||||||
\(423\) | − | 13699.0i | − | 1.57463i | ||||||
\(424\) | − | 7268.80i | − | 0.832556i | ||||||
\(425\) | − | 2141.01i | − | 0.244363i | ||||||
\(426\) | 7.02375 | 0.000798830 | ||||||||
\(427\) | − | 385.092i | − | 0.0436438i | ||||||
\(428\) | 8067.16 | 0.911077 | ||||||||
\(429\) | −153.795 | −0.0173084 | ||||||||
\(430\) | −1237.31 | −0.138764 | ||||||||
\(431\) | 9579.11 | 1.07056 | 0.535278 | − | 0.844676i | \(-0.320207\pi\) | ||||
0.535278 | + | 0.844676i | \(0.320207\pi\) | |||||||
\(432\) | 736.594i | 0.0820357i | ||||||||
\(433\) | − | 11966.1i | − | 1.32807i | −0.747702 | − | 0.664035i | \(-0.768843\pi\) | ||
0.747702 | − | 0.664035i | \(-0.231157\pi\) | |||||||
\(434\) | −97.1306 | −0.0107429 | ||||||||
\(435\) | −128.231 | − | 158.058i | −0.0141338 | − | 0.0174214i | ||||
\(436\) | −8497.91 | −0.933431 | ||||||||
\(437\) | 10730.0i | 1.17457i | ||||||||
\(438\) | 132.059i | 0.0144065i | ||||||||
\(439\) | 2419.37 | 0.263030 | 0.131515 | − | 0.991314i | \(-0.458016\pi\) | ||||
0.131515 | + | 0.991314i | \(0.458016\pi\) | |||||||
\(440\) | 1112.45 | 0.120532 | ||||||||
\(441\) | −9222.55 | −0.995848 | ||||||||
\(442\) | 1738.22 | 0.187056 | ||||||||
\(443\) | 16518.9i | 1.77164i | 0.464033 | + | 0.885818i | \(0.346402\pi\) | ||||
−0.464033 | + | 0.885818i | \(0.653598\pi\) | |||||||
\(444\) | −560.234 | −0.0598818 | ||||||||
\(445\) | 3980.94i | 0.424078i | ||||||||
\(446\) | 2125.14i | 0.225624i | ||||||||
\(447\) | 237.133i | 0.0250918i | ||||||||
\(448\) | 249.048 | 0.0262643 | ||||||||
\(449\) | − | 10498.5i | − | 1.10346i | −0.834022 | − | 0.551732i | \(-0.813967\pi\) | ||
0.834022 | − | 0.551732i | \(-0.186033\pi\) | |||||||
\(450\) | 473.025i | 0.0495525i | ||||||||
\(451\) | 2216.27 | 0.231398 | ||||||||
\(452\) | − | 13143.2i | − | 1.36771i | ||||||
\(453\) | 399.157i | 0.0413996i | ||||||||
\(454\) | 2433.71i | 0.251585i | ||||||||
\(455\) | −108.329 | −0.0111616 | ||||||||
\(456\) | − | 448.094i | − | 0.0460174i | ||||||
\(457\) | 56.5857 | 0.00579205 | 0.00289603 | − | 0.999996i | \(-0.499078\pi\) | ||||
0.00289603 | + | 0.999996i | \(0.499078\pi\) | |||||||
\(458\) | 3412.54 | 0.348161 | ||||||||
\(459\) | 1203.91 | 0.122426 | ||||||||
\(460\) | −2552.05 | −0.258674 | ||||||||
\(461\) | − | 16324.7i | − | 1.64928i | −0.565658 | − | 0.824640i | \(-0.691378\pi\) | ||
0.565658 | − | 0.824640i | \(-0.308622\pi\) | |||||||
\(462\) | − | 2.80472i | − | 0.000282441i | ||||||
\(463\) | −18047.4 | −1.81152 | −0.905761 | − | 0.423790i | \(-0.860700\pi\) | ||||
−0.905761 | + | 0.423790i | \(0.860700\pi\) | |||||||
\(464\) | 6354.69 | − | 5155.48i | 0.635795 | − | 0.515813i | ||||
\(465\) | 240.268 | 0.0239616 | ||||||||
\(466\) | − | 1066.70i | − | 0.106038i | ||||||
\(467\) | 14536.6i | 1.44042i | 0.693757 | + | 0.720209i | \(0.255954\pi\) | ||||
−0.693757 | + | 0.720209i | \(0.744046\pi\) | |||||||
\(468\) | 5840.56 | 0.576880 | ||||||||
\(469\) | 70.5217 | 0.00694326 | ||||||||
\(470\) | −1786.75 | −0.175354 | ||||||||
\(471\) | 720.476 | 0.0704836 | ||||||||
\(472\) | − | 4008.48i | − | 0.390901i | ||||||
\(473\) | 7193.83 | 0.699308 | ||||||||
\(474\) | 66.9334i | 0.00648598i | ||||||||
\(475\) | 3945.08i | 0.381079i | ||||||||
\(476\) | − | 482.099i | − | 0.0464222i | ||||||
\(477\) | −17969.9 | −1.72492 | ||||||||
\(478\) | − | 1703.09i | − | 0.162966i | ||||||
\(479\) | 6578.64i | 0.627528i | 0.949501 | + | 0.313764i | \(0.101590\pi\) | ||||
−0.949501 | + | 0.313764i | \(0.898410\pi\) | |||||||
\(480\) | 161.559 | 0.0153628 | ||||||||
\(481\) | 8272.19i | 0.784157i | ||||||||
\(482\) | − | 3070.76i | − | 0.290186i | ||||||
\(483\) | 13.2916i | 0.00125215i | ||||||||
\(484\) | 6860.06 | 0.644258 | ||||||||
\(485\) | − | 5134.41i | − | 0.480704i | ||||||
\(486\) | −399.146 | −0.0372544 | ||||||||
\(487\) | 14087.6 | 1.31082 | 0.655409 | − | 0.755274i | \(-0.272496\pi\) | ||||
0.655409 | + | 0.755274i | \(0.272496\pi\) | |||||||
\(488\) | 5594.05 | 0.518916 | ||||||||
\(489\) | 198.424 | 0.0183498 | ||||||||
\(490\) | 1202.89i | 0.110900i | ||||||||
\(491\) | 9408.56i | 0.864771i | 0.901689 | + | 0.432385i | \(0.142328\pi\) | ||||
−0.901689 | + | 0.432385i | \(0.857672\pi\) | |||||||
\(492\) | 212.324 | 0.0194559 | ||||||||
\(493\) | −8426.26 | − | 10386.3i | −0.769776 | − | 0.948832i | ||||
\(494\) | −3202.89 | −0.291710 | ||||||||
\(495\) | − | 2750.20i | − | 0.249722i | ||||||
\(496\) | 9659.89i | 0.874479i | ||||||||
\(497\) | −28.7641 | −0.00259607 | ||||||||
\(498\) | 188.765 | 0.0169855 | ||||||||
\(499\) | −13042.9 | −1.17010 | −0.585052 | − | 0.810996i | \(-0.698926\pi\) | ||||
−0.585052 | + | 0.810996i | \(0.698926\pi\) | |||||||
\(500\) | −938.304 | −0.0839244 | ||||||||
\(501\) | − | 679.672i | − | 0.0606098i | ||||||
\(502\) | 749.587 | 0.0666448 | ||||||||
\(503\) | − | 1051.24i | − | 0.0931861i | −0.998914 | − | 0.0465930i | \(-0.985164\pi\) | ||
0.998914 | − | 0.0465930i | \(-0.0148364\pi\) | |||||||
\(504\) | 220.029i | 0.0194461i | ||||||||
\(505\) | − | 7962.52i | − | 0.701638i | ||||||
\(506\) | −975.630 | −0.0857155 | ||||||||
\(507\) | − | 355.105i | − | 0.0311060i | ||||||
\(508\) | 9810.67i | 0.856847i | ||||||||
\(509\) | 15303.4 | 1.33264 | 0.666319 | − | 0.745667i | \(-0.267869\pi\) | ||||
0.666319 | + | 0.745667i | \(0.267869\pi\) | |||||||
\(510\) | − | 78.4135i | − | 0.00680826i | ||||||
\(511\) | − | 540.818i | − | 0.0468187i | ||||||
\(512\) | 11062.0i | 0.954837i | ||||||||
\(513\) | −2218.35 | −0.190921 | ||||||||
\(514\) | − | 873.648i | − | 0.0749708i | ||||||
\(515\) | 5960.98 | 0.510043 | ||||||||
\(516\) | 689.185 | 0.0587978 | ||||||||
\(517\) | 10388.3 | 0.883706 | ||||||||
\(518\) | −150.858 | −0.0127959 | ||||||||
\(519\) | − | 1038.96i | − | 0.0878713i | ||||||
\(520\) | − | 1573.65i | − | 0.132710i | ||||||
\(521\) | 1164.47 | 0.0979197 | 0.0489598 | − | 0.998801i | \(-0.484409\pi\) | ||||
0.0489598 | + | 0.998801i | \(0.484409\pi\) | |||||||
\(522\) | 1861.66 | + | 2294.69i | 0.156097 | + | 0.192406i | ||||
\(523\) | −23530.9 | −1.96737 | −0.983683 | − | 0.179908i | \(-0.942420\pi\) | ||||
−0.983683 | + | 0.179908i | \(0.942420\pi\) | |||||||
\(524\) | 11159.4i | 0.930347i | ||||||||
\(525\) | 4.88687i | 0.000406248i | ||||||||
\(526\) | −903.252 | −0.0748739 | ||||||||
\(527\) | 15788.4 | 1.30503 | ||||||||
\(528\) | −278.937 | −0.0229909 | ||||||||
\(529\) | −7543.50 | −0.619996 | ||||||||
\(530\) | 2343.80i | 0.192091i | ||||||||
\(531\) | −9909.76 | −0.809881 | ||||||||
\(532\) | 888.326i | 0.0723944i | ||||||||
\(533\) | − | 3135.09i | − | 0.254776i | ||||||
\(534\) | 145.800i | 0.0118153i | ||||||||
\(535\) | −5373.50 | −0.434237 | ||||||||
\(536\) | 1024.44i | 0.0825540i | ||||||||
\(537\) | 394.997i | 0.0317419i | ||||||||
\(538\) | 1168.42 | 0.0936324 | ||||||||
\(539\) | − | 6993.69i | − | 0.558886i | ||||||
\(540\) | − | 527.616i | − | 0.0420462i | ||||||
\(541\) | 8712.72i | 0.692401i | 0.938160 | + | 0.346201i | \(0.112528\pi\) | ||||
−0.938160 | + | 0.346201i | \(0.887472\pi\) | |||||||
\(542\) | 1693.07 | 0.134176 | ||||||||
\(543\) | − | 600.845i | − | 0.0474857i | ||||||
\(544\) | 10616.3 | 0.836711 | ||||||||
\(545\) | 5660.42 | 0.444891 | ||||||||
\(546\) | −3.96750 | −0.000310977 | ||||||||
\(547\) | 20255.7 | 1.58331 | 0.791656 | − | 0.610967i | \(-0.209219\pi\) | ||||
0.791656 | + | 0.610967i | \(0.209219\pi\) | |||||||
\(548\) | 8152.22i | 0.635485i | ||||||||
\(549\) | − | 13829.6i | − | 1.07511i | ||||||
\(550\) | −358.707 | −0.0278096 | ||||||||
\(551\) | 15526.4 | + | 19138.0i | 1.20045 | + | 1.47968i | ||||
\(552\) | −193.081 | −0.0148878 | ||||||||
\(553\) | − | 274.110i | − | 0.0210784i | ||||||
\(554\) | 3280.15i | 0.251553i | ||||||||
\(555\) | 373.169 | 0.0285408 | ||||||||
\(556\) | 19129.8 | 1.45914 | ||||||||
\(557\) | −7354.79 | −0.559484 | −0.279742 | − | 0.960075i | \(-0.590249\pi\) | ||||
−0.279742 | + | 0.960075i | \(0.590249\pi\) | |||||||
\(558\) | −3488.20 | −0.264637 | ||||||||
\(559\) | − | 10176.2i | − | 0.769961i | ||||||
\(560\) | −196.475 | −0.0148261 | ||||||||
\(561\) | 455.902i | 0.0343105i | ||||||||
\(562\) | − | 338.954i | − | 0.0254411i | ||||||
\(563\) | − | 8899.97i | − | 0.666233i | −0.942886 | − | 0.333116i | \(-0.891900\pi\) | ||
0.942886 | − | 0.333116i | \(-0.108100\pi\) | |||||||
\(564\) | 995.221 | 0.0743020 | ||||||||
\(565\) | 8754.65i | 0.651878i | ||||||||
\(566\) | 5212.45i | 0.387094i | ||||||||
\(567\) | 542.579 | 0.0401873 | ||||||||
\(568\) | − | 417.843i | − | 0.0308668i | ||||||
\(569\) | 22986.8i | 1.69360i | 0.531913 | + | 0.846799i | \(0.321473\pi\) | ||||
−0.531913 | + | 0.846799i | \(0.678527\pi\) | |||||||
\(570\) | 144.487i | 0.0106173i | ||||||||
\(571\) | 15897.1 | 1.16510 | 0.582551 | − | 0.812794i | \(-0.302055\pi\) | ||||
0.582551 | + | 0.812794i | \(0.302055\pi\) | |||||||
\(572\) | 4429.04i | 0.323755i | ||||||||
\(573\) | 1197.77 | 0.0873255 | ||||||||
\(574\) | 57.1737 | 0.00415747 | ||||||||
\(575\) | 1699.91 | 0.123289 | ||||||||
\(576\) | 8943.96 | 0.646988 | ||||||||
\(577\) | 9121.19i | 0.658094i | 0.944314 | + | 0.329047i | \(0.106727\pi\) | ||||
−0.944314 | + | 0.329047i | \(0.893273\pi\) | |||||||
\(578\) | − | 1701.08i | − | 0.122414i | ||||||
\(579\) | −926.070 | −0.0664700 | ||||||||
\(580\) | −4551.80 | + | 3692.82i | −0.325868 | + | 0.264373i | ||||
\(581\) | −773.042 | −0.0552000 | ||||||||
\(582\) | − | 188.045i | − | 0.0133930i | ||||||
\(583\) | − | 13627.0i | − | 0.968051i | ||||||
\(584\) | 7856.22 | 0.556666 | ||||||||
\(585\) | −3890.37 | −0.274952 | ||||||||
\(586\) | −199.030 | −0.0140304 | ||||||||
\(587\) | 13244.0 | 0.931243 | 0.465622 | − | 0.884984i | \(-0.345831\pi\) | ||||
0.465622 | + | 0.884984i | \(0.345831\pi\) | |||||||
\(588\) | − | 670.011i | − | 0.0469911i | ||||||
\(589\) | −29092.0 | −2.03517 | ||||||||
\(590\) | 1292.52i | 0.0901903i | ||||||||
\(591\) | 218.537i | 0.0152105i | ||||||||
\(592\) | 15003.2i | 1.04160i | ||||||||
\(593\) | −9343.12 | −0.647008 | −0.323504 | − | 0.946227i | \(-0.604861\pi\) | ||||
−0.323504 | + | 0.946227i | \(0.604861\pi\) | |||||||
\(594\) | − | 201.704i | − | 0.0139327i | ||||||
\(595\) | 321.124i | 0.0221257i | ||||||||
\(596\) | 6829.03 | 0.469342 | ||||||||
\(597\) | − | 98.6935i | − | 0.00676592i | ||||||
\(598\) | 1380.10i | 0.0943756i | ||||||||
\(599\) | − | 9177.01i | − | 0.625981i | −0.949756 | − | 0.312991i | \(-0.898669\pi\) | ||
0.949756 | − | 0.312991i | \(-0.101331\pi\) | |||||||
\(600\) | −70.9894 | −0.00483022 | ||||||||
\(601\) | 957.868i | 0.0650121i | 0.999472 | + | 0.0325060i | \(0.0103488\pi\) | ||||
−0.999472 | + | 0.0325060i | \(0.989651\pi\) | |||||||
\(602\) | 185.581 | 0.0125643 | ||||||||
\(603\) | 2532.61 | 0.171038 | ||||||||
\(604\) | 11495.0 | 0.774381 | ||||||||
\(605\) | −4569.45 | −0.307066 | ||||||||
\(606\) | − | 291.623i | − | 0.0195485i | ||||||
\(607\) | 27135.2i | 1.81447i | 0.420626 | + | 0.907234i | \(0.361811\pi\) | ||||
−0.420626 | + | 0.907234i | \(0.638189\pi\) | |||||||
\(608\) | −19561.9 | −1.30483 | ||||||||
\(609\) | 19.2330 | + | 23.7067i | 0.00127973 | + | 0.00157741i | ||||
\(610\) | −1803.79 | −0.119726 | ||||||||
\(611\) | − | 14695.0i | − | 0.972990i | ||||||
\(612\) | − | 17313.4i | − | 1.14355i | ||||||
\(613\) | 12116.5 | 0.798338 | 0.399169 | − | 0.916877i | \(-0.369299\pi\) | ||||
0.399169 | + | 0.916877i | \(0.369299\pi\) | |||||||
\(614\) | −4762.29 | −0.313014 | ||||||||
\(615\) | −141.428 | −0.00927306 | ||||||||
\(616\) | −166.853 | −0.0109135 | ||||||||
\(617\) | − | 7220.67i | − | 0.471140i | −0.971857 | − | 0.235570i | \(-0.924304\pi\) | ||
0.971857 | − | 0.235570i | \(-0.0756957\pi\) | |||||||
\(618\) | 218.318 | 0.0142104 | ||||||||
\(619\) | 1237.39i | 0.0803472i | 0.999193 | + | 0.0401736i | \(0.0127911\pi\) | ||||
−0.999193 | + | 0.0401736i | \(0.987209\pi\) | |||||||
\(620\) | − | 6919.29i | − | 0.448202i | ||||||
\(621\) | 955.872i | 0.0617678i | ||||||||
\(622\) | −2496.77 | −0.160951 | ||||||||
\(623\) | − | 597.089i | − | 0.0383979i | ||||||
\(624\) | 394.578i | 0.0253137i | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 6091.02i | 0.388892i | ||||||||
\(627\) | − | 840.055i | − | 0.0535065i | ||||||
\(628\) | − | 20748.5i | − | 1.31840i | ||||||
\(629\) | 24521.6 | 1.55443 | ||||||||
\(630\) | − | 70.9476i | − | 0.00448670i | ||||||
\(631\) | −15074.3 | −0.951026 | −0.475513 | − | 0.879709i | \(-0.657737\pi\) | ||||
−0.475513 | + | 0.879709i | \(0.657737\pi\) | |||||||
\(632\) | 3981.88 | 0.250618 | ||||||||
\(633\) | −475.363 | −0.0298483 | ||||||||
\(634\) | 1606.75 | 0.100650 | ||||||||
\(635\) | − | 6534.85i | − | 0.408390i | ||||||
\(636\) | − | 1305.50i | − | 0.0813938i | ||||||
\(637\) | −9893.11 | −0.615352 | ||||||||
\(638\) | −1740.12 | + | 1411.74i | −0.107981 | + | 0.0876039i | ||||
\(639\) | −1032.99 | −0.0639507 | ||||||||
\(640\) | − | 6125.10i | − | 0.378306i | ||||||
\(641\) | 7258.04i | 0.447232i | 0.974677 | + | 0.223616i | \(0.0717861\pi\) | ||||
−0.974677 | + | 0.223616i | \(0.928214\pi\) | |||||||
\(642\) | −196.802 | −0.0120984 | ||||||||
\(643\) | −10177.0 | −0.624173 | −0.312086 | − | 0.950054i | \(-0.601028\pi\) | ||||
−0.312086 | + | 0.950054i | \(0.601028\pi\) | |||||||
\(644\) | 382.774 | 0.0234214 | ||||||||
\(645\) | −459.063 | −0.0280242 | ||||||||
\(646\) | 9494.44i | 0.578257i | ||||||||
\(647\) | −9522.88 | −0.578645 | −0.289322 | − | 0.957232i | \(-0.593430\pi\) | ||||
−0.289322 | + | 0.957232i | \(0.593430\pi\) | |||||||
\(648\) | 7881.80i | 0.477819i | ||||||||
\(649\) | − | 7514.82i | − | 0.454518i | ||||||
\(650\) | 507.418i | 0.0306193i | ||||||||
\(651\) | −36.0370 | −0.00216959 | ||||||||
\(652\) | − | 5714.27i | − | 0.343233i | ||||||
\(653\) | − | 5253.00i | − | 0.314802i | −0.987535 | − | 0.157401i | \(-0.949688\pi\) | ||
0.987535 | − | 0.157401i | \(-0.0503115\pi\) | |||||||
\(654\) | 207.310 | 0.0123952 | ||||||||
\(655\) | − | 7433.24i | − | 0.443421i | ||||||
\(656\) | − | 5686.08i | − | 0.338421i | ||||||
\(657\) | − | 19422.1i | − | 1.15332i | ||||||
\(658\) | 267.989 | 0.0158773 | ||||||||
\(659\) | 9643.61i | 0.570048i | 0.958520 | + | 0.285024i | \(0.0920016\pi\) | ||||
−0.958520 | + | 0.285024i | \(0.907998\pi\) | |||||||
\(660\) | 199.800 | 0.0117836 | ||||||||
\(661\) | 2006.02 | 0.118041 | 0.0590204 | − | 0.998257i | \(-0.481202\pi\) | ||||
0.0590204 | + | 0.998257i | \(0.481202\pi\) | |||||||
\(662\) | −337.323 | −0.0198043 | ||||||||
\(663\) | 644.909 | 0.0377770 | ||||||||
\(664\) | − | 11229.6i | − | 0.656317i | ||||||
\(665\) | − | 591.710i | − | 0.0345046i | ||||||
\(666\) | −5417.68 | −0.315211 | ||||||||
\(667\) | 8246.42 | − | 6690.23i | 0.478715 | − | 0.388376i | ||||
\(668\) | −19573.4 | −1.13371 | ||||||||
\(669\) | 788.460i | 0.0455659i | ||||||||
\(670\) | − | 330.327i | − | 0.0190472i | ||||||
\(671\) | 10487.3 | 0.603367 | ||||||||
\(672\) | −24.2318 | −0.00139101 | ||||||||
\(673\) | −2029.01 | −0.116215 | −0.0581075 | − | 0.998310i | \(-0.518507\pi\) | ||||
−0.0581075 | + | 0.998310i | \(0.518507\pi\) | |||||||
\(674\) | −260.889 | −0.0149096 | ||||||||
\(675\) | 351.442i | 0.0200400i | ||||||||
\(676\) | −10226.4 | −0.581839 | ||||||||
\(677\) | 6459.49i | 0.366703i | 0.983047 | + | 0.183352i | \(0.0586947\pi\) | ||||
−0.983047 | + | 0.183352i | \(0.941305\pi\) | |||||||
\(678\) | 320.635i | 0.0181621i | ||||||||
\(679\) | 770.094i | 0.0435251i | ||||||||
\(680\) | −4664.83 | −0.263071 | ||||||||
\(681\) | 902.946i | 0.0508091i | ||||||||
\(682\) | − | 2645.19i | − | 0.148519i | ||||||
\(683\) | 20758.5 | 1.16296 | 0.581481 | − | 0.813560i | \(-0.302474\pi\) | ||||
0.581481 | + | 0.813560i | \(0.302474\pi\) | |||||||
\(684\) | 31902.1i | 1.78334i | ||||||||
\(685\) | − | 5430.16i | − | 0.302884i | ||||||
\(686\) | − | 361.132i | − | 0.0200992i | ||||||
\(687\) | 1266.11 | 0.0703130 | ||||||||
\(688\) | − | 18456.5i | − | 1.02274i | ||||||
\(689\) | −19276.5 | −1.06586 | ||||||||
\(690\) | 62.2583 | 0.00343498 | ||||||||
\(691\) | 19700.4 | 1.08457 | 0.542286 | − | 0.840194i | \(-0.317559\pi\) | ||||
0.542286 | + | 0.840194i | \(0.317559\pi\) | |||||||
\(692\) | −29920.2 | −1.64363 | ||||||||
\(693\) | 412.494i | 0.0226109i | ||||||||
\(694\) | − | 231.818i | − | 0.0126797i | ||||||
\(695\) | −12742.3 | −0.695456 | ||||||||
\(696\) | −344.376 | + | 279.389i | −0.0187551 | + | 0.0152158i | ||||
\(697\) | −9293.47 | −0.505044 | ||||||||
\(698\) | − | 6449.28i | − | 0.349726i | ||||||
\(699\) | − | 395.762i | − | 0.0214150i | ||||||
\(700\) | 140.733 | 0.00759889 | ||||||||
\(701\) | 21184.3 | 1.14140 | 0.570699 | − | 0.821159i | \(-0.306672\pi\) | ||||
0.570699 | + | 0.821159i | \(0.306672\pi\) | |||||||
\(702\) | −285.325 | −0.0153403 | ||||||||
\(703\) | −45184.0 | −2.42411 | ||||||||
\(704\) | 6782.42i | 0.363100i | ||||||||
\(705\) | −662.912 | −0.0354138 | ||||||||
\(706\) | 329.662i | 0.0175736i | ||||||||
\(707\) | 1194.27i | 0.0635294i | ||||||||
\(708\) | − | 719.936i | − | 0.0382159i | ||||||
\(709\) | −3620.22 | −0.191763 | −0.0958817 | − | 0.995393i | \(-0.530567\pi\) | ||||
−0.0958817 | + | 0.995393i | \(0.530567\pi\) | |||||||
\(710\) | 134.732i | 0.00712171i | ||||||||
\(711\) | − | 9843.99i | − | 0.519238i | ||||||
\(712\) | 8673.65 | 0.456543 | ||||||||
\(713\) | 12535.6i | 0.658429i | ||||||||
\(714\) | 11.7610i | 0.000616449i | ||||||||
\(715\) | − | 2950.17i | − | 0.154308i | ||||||
\(716\) | 11375.2 | 0.593732 | ||||||||
\(717\) | − | 631.875i | − | 0.0329119i | ||||||
\(718\) | 1170.48 | 0.0608383 | ||||||||
\(719\) | 18796.0 | 0.974927 | 0.487463 | − | 0.873143i | \(-0.337922\pi\) | ||||
0.487463 | + | 0.873143i | \(0.337922\pi\) | |||||||
\(720\) | −7055.92 | −0.365220 | ||||||||
\(721\) | −894.069 | −0.0461815 | ||||||||
\(722\) | − | 12675.9i | − | 0.653391i | ||||||
\(723\) | − | 1139.30i | − | 0.0586046i | ||||||
\(724\) | −17303.3 | −0.888220 | ||||||||
\(725\) | 3031.94 | − | 2459.77i | 0.155315 | − | 0.126005i | ||||
\(726\) | −167.354 | −0.00855522 | ||||||||
\(727\) | 6712.96i | 0.342462i | 0.985231 | + | 0.171231i | \(0.0547745\pi\) | ||||
−0.985231 | + | 0.171231i | \(0.945226\pi\) | |||||||
\(728\) | 236.027i | 0.0120161i | ||||||||
\(729\) | 19386.4 | 0.984934 | ||||||||
\(730\) | −2533.21 | −0.128436 | ||||||||
\(731\) | −30165.8 | −1.52629 | ||||||||
\(732\) | 1004.71 | 0.0507311 | ||||||||
\(733\) | − | 23783.9i | − | 1.19847i | −0.800574 | − | 0.599234i | \(-0.795472\pi\) | ||
0.800574 | − | 0.599234i | \(-0.204528\pi\) | |||||||
\(734\) | 1142.75 | 0.0574655 | ||||||||
\(735\) | 446.292i | 0.0223969i | ||||||||
\(736\) | 8429.08i | 0.422147i | ||||||||
\(737\) | 1920.54i | 0.0959893i | ||||||||
\(738\) | 2053.25 | 0.102414 | ||||||||
\(739\) | 15926.7i | 0.792792i | 0.918080 | + | 0.396396i | \(0.129739\pi\) | ||||
−0.918080 | + | 0.396396i | \(0.870261\pi\) | |||||||
\(740\) | − | 10746.6i | − | 0.533857i | ||||||
\(741\) | −1188.32 | −0.0589124 | ||||||||
\(742\) | − | 351.540i | − | 0.0173928i | ||||||
\(743\) | − | 18447.5i | − | 0.910867i | −0.890270 | − | 0.455434i | \(-0.849484\pi\) | ||
0.890270 | − | 0.455434i | \(-0.150516\pi\) | |||||||
\(744\) | − | 523.494i | − | 0.0257960i | ||||||
\(745\) | −4548.79 | −0.223698 | ||||||||
\(746\) | − | 2264.56i | − | 0.111141i | ||||||
\(747\) | −27761.9 | −1.35978 | ||||||||
\(748\) | 13129.2 | 0.641779 | ||||||||
\(749\) | 805.955 | 0.0393177 | ||||||||
\(750\) | 22.8903 | 0.00111445 | ||||||||
\(751\) | 25690.4i | 1.24828i | 0.781314 | + | 0.624138i | \(0.214550\pi\) | ||||
−0.781314 | + | 0.624138i | \(0.785450\pi\) | |||||||
\(752\) | − | 26652.2i | − | 1.29243i | ||||||
\(753\) | 278.109 | 0.0134593 | ||||||||
\(754\) | 1997.01 | + | 2461.53i | 0.0964549 | + | 0.118891i | ||||
\(755\) | −7656.79 | −0.369085 | ||||||||
\(756\) | 79.1355i | 0.00380705i | ||||||||
\(757\) | − | 5216.53i | − | 0.250460i | −0.992128 | − | 0.125230i | \(-0.960033\pi\) | ||
0.992128 | − | 0.125230i | \(-0.0399669\pi\) | |||||||
\(758\) | 6100.18 | 0.292307 | ||||||||
\(759\) | −361.974 | −0.0173107 | ||||||||
\(760\) | 8595.52 | 0.410253 | ||||||||
\(761\) | 22366.9 | 1.06544 | 0.532719 | − | 0.846292i | \(-0.321170\pi\) | ||||
0.532719 | + | 0.846292i | \(0.321170\pi\) | |||||||
\(762\) | − | 239.335i | − | 0.0113782i | ||||||
\(763\) | −848.989 | −0.0402824 | ||||||||
\(764\) | − | 34493.7i | − | 1.63343i | ||||||
\(765\) | 11532.4i | 0.545038i | ||||||||
\(766\) | − | 6358.92i | − | 0.299944i | ||||||
\(767\) | −10630.3 | −0.500440 | ||||||||
\(768\) | 468.167i | 0.0219968i | ||||||||
\(769\) | − | 2100.89i | − | 0.0985178i | −0.998786 | − | 0.0492589i | \(-0.984314\pi\) | ||
0.998786 | − | 0.0492589i | \(-0.0156859\pi\) | |||||||
\(770\) | 53.8013 | 0.00251801 | ||||||||
\(771\) | − | 324.138i | − | 0.0151408i | ||||||
\(772\) | 26669.2i | 1.24332i | ||||||||
\(773\) | 29744.0i | 1.38398i | 0.721907 | + | 0.691990i | \(0.243266\pi\) | ||||
−0.721907 | + | 0.691990i | \(0.756734\pi\) | |||||||
\(774\) | 6664.68 | 0.309505 | ||||||||
\(775\) | 4608.91i | 0.213622i | ||||||||
\(776\) | −11186.8 | −0.517505 | ||||||||
\(777\) | −55.9706 | −0.00258421 | ||||||||
\(778\) | −5109.62 | −0.235461 | ||||||||
\(779\) | 17124.4 | 0.787604 | ||||||||
\(780\) | − | 282.633i | − | 0.0129742i | ||||||
\(781\) | − | 783.343i | − | 0.0358902i | ||||||
\(782\) | 4091.09 | 0.187081 | ||||||||
\(783\) | 1383.15 | + | 1704.88i | 0.0631287 | + | 0.0778129i | ||||
\(784\) | −17943.0 | −0.817375 | ||||||||
\(785\) | 13820.5i | 0.628373i | ||||||||
\(786\) | − | 272.239i | − | 0.0123542i | ||||||
\(787\) | 15934.9 | 0.721751 | 0.360875 | − | 0.932614i | \(-0.382478\pi\) | ||||
0.360875 | + | 0.932614i | \(0.382478\pi\) | |||||||
\(788\) | 6293.49 | 0.284513 | ||||||||
\(789\) | −335.121 | −0.0151212 | ||||||||
\(790\) | −1283.94 | −0.0578236 | ||||||||
\(791\) | − | 1313.08i | − | 0.0590239i | ||||||
\(792\) | −5992.12 | −0.268839 | ||||||||
\(793\) | − | 14835.1i | − | 0.664327i | ||||||
\(794\) | − | 107.598i | − | 0.00480919i | ||||||
\(795\) | 869.588i | 0.0387938i | ||||||||
\(796\) | −2842.20 | −0.126557 | ||||||||
\(797\) | 6928.06i | 0.307910i | 0.988078 | + | 0.153955i | \(0.0492011\pi\) | ||||
−0.988078 | + | 0.153955i | \(0.950799\pi\) | |||||||
\(798\) | − | 21.6711i | − | 0.000961339i | ||||||
\(799\) | −43561.0 | −1.92876 | ||||||||
\(800\) | 3099.09i | 0.136962i | ||||||||
\(801\) | − | 21443.0i | − | 0.945881i | ||||||
\(802\) | 5310.68i | 0.233824i | ||||||||
\(803\) | 14728.3 | 0.647261 | ||||||||
\(804\) | 183.992i | 0.00807078i | ||||||||
\(805\) | −254.964 | −0.0111631 | ||||||||
\(806\) | −3741.83 | −0.163524 | ||||||||
\(807\) | 433.503 | 0.0189096 | ||||||||
\(808\) | −17348.7 | −0.755353 | ||||||||
\(809\) | 43601.8i | 1.89488i | 0.319933 | + | 0.947440i | \(0.396340\pi\) | ||||
−0.319933 | + | 0.947440i | \(0.603660\pi\) | |||||||
\(810\) | − | 2541.46i | − | 0.110244i | ||||||
\(811\) | 18082.8 | 0.782950 | 0.391475 | − | 0.920189i | \(-0.371965\pi\) | ||||
0.391475 | + | 0.920189i | \(0.371965\pi\) | |||||||
\(812\) | 682.711 | − | 553.876i | 0.0295055 | − | 0.0239375i | ||||
\(813\) | 628.156 | 0.0270977 | ||||||||
\(814\) | − | 4108.36i | − | 0.176902i | ||||||
\(815\) | 3806.25i | 0.163592i | ||||||||
\(816\) | 1169.66 | 0.0501794 | ||||||||
\(817\) | 55584.1 | 2.38022 | ||||||||
\(818\) | 3681.45 | 0.157358 | ||||||||
\(819\) | 583.505 | 0.0248954 | ||||||||
\(820\) | 4072.88i | 0.173453i | ||||||||
\(821\) | −18056.9 | −0.767590 | −0.383795 | − | 0.923418i | \(-0.625383\pi\) | ||||
−0.383795 | + | 0.923418i | \(0.625383\pi\) | |||||||
\(822\) | − | 198.877i | − | 0.00843872i | ||||||
\(823\) | − | 24106.9i | − | 1.02104i | −0.859866 | − | 0.510519i | \(-0.829453\pi\) | ||
0.859866 | − | 0.510519i | \(-0.170547\pi\) | |||||||
\(824\) | − | 12987.7i | − | 0.549089i | ||||||
\(825\) | −133.086 | −0.00561631 | ||||||||
\(826\) | − | 193.861i | − | 0.00816623i | ||||||
\(827\) | 4471.24i | 0.188005i | 0.995572 | + | 0.0940026i | \(0.0299662\pi\) | ||||
−0.995572 | + | 0.0940026i | \(0.970034\pi\) | |||||||
\(828\) | 13746.4 | 0.576956 | ||||||||
\(829\) | − | 25414.5i | − | 1.06475i | −0.846508 | − | 0.532377i | \(-0.821299\pi\) | ||
0.846508 | − | 0.532377i | \(-0.178701\pi\) | |||||||
\(830\) | 3620.96i | 0.151428i | ||||||||
\(831\) | 1216.99i | 0.0508025i | ||||||||
\(832\) | 9594.26 | 0.399785 | ||||||||
\(833\) | 29326.5i | 1.21981i | ||||||||
\(834\) | −466.679 | −0.0193762 | ||||||||
\(835\) | 13037.7 | 0.540346 | ||||||||
\(836\) | −24192.1 | −1.00084 | ||||||||
\(837\) | −2591.62 | −0.107025 | ||||||||
\(838\) | − | 7771.72i | − | 0.320369i | ||||||
\(839\) | − | 2810.55i | − | 0.115651i | −0.998327 | − | 0.0578254i | \(-0.981583\pi\) | ||
0.998327 | − | 0.0578254i | \(-0.0184167\pi\) | |||||||
\(840\) | 10.6475 | 0.000437349 | ||||||||
\(841\) | 5027.44 | − | 23865.2i | 0.206135 | − | 0.978523i | ||||
\(842\) | 6711.55 | 0.274698 | ||||||||
\(843\) | − | 125.757i | − | 0.00513798i | ||||||
\(844\) | 13689.6i | 0.558313i | ||||||||
\(845\) | 6811.76 | 0.277316 | ||||||||
\(846\) | 9624.16 | 0.391117 | ||||||||
\(847\) | 685.358 | 0.0278031 | ||||||||
\(848\) | −34961.5 | −1.41578 | ||||||||
\(849\) | 1933.90i | 0.0781759i | ||||||||
\(850\) | 1504.16 | 0.0606968 | ||||||||
\(851\) | 19469.5i | 0.784260i | ||||||||
\(852\) | − | 75.0461i | − | 0.00301765i | ||||||
\(853\) | 28705.4i | 1.15223i | 0.817368 | + | 0.576116i | \(0.195432\pi\) | ||||
−0.817368 | + | 0.576116i | \(0.804568\pi\) | |||||||
\(854\) | 270.544 | 0.0108406 | ||||||||
\(855\) | − | 21249.8i | − | 0.849975i | ||||||
\(856\) | 11707.8i | 0.467480i | ||||||||
\(857\) | 878.580 | 0.0350195 | 0.0175098 | − | 0.999847i | \(-0.494426\pi\) | ||||
0.0175098 | + | 0.999847i | \(0.494426\pi\) | |||||||
\(858\) | − | 108.048i | − | 0.00429920i | ||||||
\(859\) | − | 32796.6i | − | 1.30269i | −0.758784 | − | 0.651343i | \(-0.774206\pi\) | ||
0.758784 | − | 0.651343i | \(-0.225794\pi\) | |||||||
\(860\) | 13220.2i | 0.524192i | ||||||||
\(861\) | 21.2124 | 0.000839624 | ||||||||
\(862\) | 6729.76i | 0.265912i | ||||||||
\(863\) | −11086.6 | −0.437303 | −0.218652 | − | 0.975803i | \(-0.570166\pi\) | ||||
−0.218652 | + | 0.975803i | \(0.570166\pi\) | |||||||
\(864\) | −1742.64 | −0.0686180 | ||||||||
\(865\) | 19929.7 | 0.783388 | ||||||||
\(866\) | 8406.73 | 0.329876 | ||||||||
\(867\) | − | 631.127i | − | 0.0247222i | ||||||
\(868\) | 1037.80i | 0.0405822i | ||||||||
\(869\) | 7464.94 | 0.291405 | ||||||||
\(870\) | 111.043 | − | 90.0880i | 0.00432726 | − | 0.00351065i | ||||
\(871\) | 2716.76 | 0.105687 | ||||||||
\(872\) | − | 12332.9i | − | 0.478950i | ||||||
\(873\) | 27656.0i | 1.07218i | ||||||||
\(874\) | −7538.34 | −0.291748 | ||||||||
\(875\) | −93.7419 | −0.00362177 | ||||||||
\(876\) | 1411.00 | 0.0544217 | ||||||||
\(877\) | 27008.6 | 1.03993 | 0.519964 | − | 0.854188i | \(-0.325945\pi\) | ||||
0.519964 | + | 0.854188i | \(0.325945\pi\) | |||||||
\(878\) | 1699.71i | 0.0653332i | ||||||||
\(879\) | −73.8432 | −0.00283353 | ||||||||
\(880\) | − | 5350.68i | − | 0.204968i | ||||||
\(881\) | − | 2049.80i | − | 0.0783876i | −0.999232 | − | 0.0391938i | \(-0.987521\pi\) | ||
0.999232 | − | 0.0391938i | \(-0.0124790\pi\) | |||||||
\(882\) | − | 6479.26i | − | 0.247356i | ||||||
\(883\) | −4525.79 | −0.172486 | −0.0862429 | − | 0.996274i | \(-0.527486\pi\) | ||||
−0.0862429 | + | 0.996274i | \(0.527486\pi\) | |||||||
\(884\) | − | 18572.2i | − | 0.706620i | ||||||
\(885\) | 479.546i | 0.0182144i | ||||||||
\(886\) | −11605.3 | −0.440052 | ||||||||
\(887\) | 19358.9i | 0.732816i | 0.930454 | + | 0.366408i | \(0.119413\pi\) | ||||
−0.930454 | + | 0.366408i | \(0.880587\pi\) | |||||||
\(888\) | − | 813.060i | − | 0.0307258i | ||||||
\(889\) | 980.142i | 0.0369774i | ||||||||
\(890\) | −2796.79 | −0.105336 | ||||||||
\(891\) | 14776.3i | 0.555581i | ||||||||
\(892\) | 22706.3 | 0.852312 | ||||||||
\(893\) | 80266.5 | 3.00786 | ||||||||
\(894\) | −166.597 | −0.00623248 | ||||||||
\(895\) | −7576.99 | −0.282984 | ||||||||
\(896\) | 918.685i | 0.0342535i | ||||||||
\(897\) | 512.040i | 0.0190597i | ||||||||
\(898\) | 7375.68 | 0.274086 | ||||||||
\(899\) | 18139.0 | + | 22358.3i | 0.672936 | + | 0.829466i | ||||
\(900\) | 5054.09 | 0.187189 | ||||||||
\(901\) | 57142.0i | 2.11285i | ||||||||
\(902\) | 1557.03i | 0.0574762i | ||||||||
\(903\) | 68.8534 | 0.00253743 | ||||||||
\(904\) | 19074.6 | 0.701783 | ||||||||
\(905\) | 11525.6 | 0.423343 | ||||||||
\(906\) | −280.426 | −0.0102831 | ||||||||
\(907\) | 46378.0i | 1.69786i | 0.528507 | + | 0.848929i | \(0.322752\pi\) | ||||
−0.528507 | + | 0.848929i | \(0.677248\pi\) | |||||||
\(908\) | 26003.3 | 0.950385 | ||||||||
\(909\) | 42889.4i | 1.56496i | ||||||||
\(910\) | − | 76.1061i | − | 0.00277241i | ||||||
\(911\) | − | 19248.7i | − | 0.700040i | −0.936742 | − | 0.350020i | \(-0.886175\pi\) | ||
0.936742 | − | 0.350020i | \(-0.113825\pi\) | |||||||
\(912\) | −2155.25 | −0.0782537 | ||||||||
\(913\) | − | 21052.6i | − | 0.763130i | ||||||
\(914\) | 39.7540i | 0.00143867i | ||||||||
\(915\) | −669.233 | −0.0241794 | ||||||||
\(916\) | − | 36461.7i | − | 1.31521i | ||||||
\(917\) | 1114.89i | 0.0401493i | ||||||||
\(918\) | 845.801i | 0.0304091i | ||||||||
\(919\) | 4695.28 | 0.168534 | 0.0842672 | − | 0.996443i | \(-0.473145\pi\) | ||||
0.0842672 | + | 0.996443i | \(0.473145\pi\) | |||||||
\(920\) | − | 3703.75i | − | 0.132727i | ||||||
\(921\) | −1766.89 | −0.0632149 | ||||||||
\(922\) | 11468.9 | 0.409660 | ||||||||
\(923\) | −1108.10 | −0.0395163 | ||||||||
\(924\) | −29.9674 | −0.00106694 | ||||||||
\(925\) | 7158.28i | 0.254446i | ||||||||
\(926\) | − | 12679.1i | − | 0.449959i | ||||||
\(927\) | −32108.3 | −1.13762 | ||||||||
\(928\) | 12196.9 | + | 15034.0i | 0.431447 | + | 0.531805i | ||||
\(929\) | 3528.94 | 0.124629 | 0.0623147 | − | 0.998057i | \(-0.480152\pi\) | ||||
0.0623147 | + | 0.998057i | \(0.480152\pi\) | |||||||
\(930\) | 168.799i | 0.00595176i | ||||||||
\(931\) | − | 54037.7i | − | 1.90227i | ||||||
\(932\) | −11397.3 | −0.400568 | ||||||||
\(933\) | −926.341 | −0.0325049 | ||||||||
\(934\) | −10212.6 | −0.357781 | ||||||||
\(935\) | −8745.29 | −0.305884 | ||||||||
\(936\) | 8476.32i | 0.296001i | ||||||||
\(937\) | −23907.6 | −0.833541 | −0.416770 | − | 0.909012i | \(-0.636838\pi\) | ||||
−0.416770 | + | 0.909012i | \(0.636838\pi\) | |||||||
\(938\) | 49.5447i | 0.00172462i | ||||||||
\(939\) | 2259.87i | 0.0785389i | ||||||||
\(940\) | 19090.7i | 0.662415i | ||||||||
\(941\) | 4265.50 | 0.147770 | 0.0738848 | − | 0.997267i | \(-0.476460\pi\) | ||||
0.0738848 | + | 0.997267i | \(0.476460\pi\) | |||||||
\(942\) | 506.167i | 0.0175072i | ||||||||
\(943\) | − | 7378.77i | − | 0.254810i | ||||||
\(944\) | −19280.0 | −0.664737 | ||||||||
\(945\) | − | 52.7118i | − | 0.00181451i | ||||||
\(946\) | 5053.99i | 0.173699i | ||||||||
\(947\) | 8485.96i | 0.291190i | 0.989344 | + | 0.145595i | \(0.0465096\pi\) | ||||
−0.989344 | + | 0.145595i | \(0.953490\pi\) | |||||||
\(948\) | 715.158 | 0.0245013 | ||||||||
\(949\) | − | 20834.3i | − | 0.712656i | ||||||
\(950\) | −2771.60 | −0.0946553 | ||||||||
\(951\) | 596.131 | 0.0203269 | ||||||||
\(952\) | 699.664 | 0.0238196 | ||||||||
\(953\) | −9378.00 | −0.318765 | −0.159383 | − | 0.987217i | \(-0.550950\pi\) | ||||
−0.159383 | + | 0.987217i | \(0.550950\pi\) | |||||||
\(954\) | − | 12624.7i | − | 0.428447i | ||||||
\(955\) | 22976.1i | 0.778522i | ||||||||
\(956\) | −18196.9 | −0.615617 | ||||||||
\(957\) | −645.613 | + | 523.778i | −0.0218074 | + | 0.0176921i | ||||
\(958\) | −4621.79 | −0.155870 | ||||||||
\(959\) | 814.453i | 0.0274245i | ||||||||
\(960\) | − | 432.810i | − | 0.0145509i | ||||||
\(961\) | −4196.23 | −0.140856 | ||||||||
\(962\) | −5811.59 | −0.194775 | ||||||||
\(963\) | 28943.9 | 0.968540 | ||||||||
\(964\) | −32809.9 | −1.09620 | ||||||||
\(965\) | − | 17764.2i | − | 0.592592i | ||||||
\(966\) | −9.33793 | −0.000311018 | ||||||||
\(967\) | − | 17477.3i | − | 0.581213i | −0.956843 | − | 0.290607i | \(-0.906143\pi\) | ||
0.956843 | − | 0.290607i | \(-0.0938571\pi\) | |||||||
\(968\) | 9955.90i | 0.330573i | ||||||||
\(969\) | 3522.59i | 0.116782i | ||||||||
\(970\) | 3607.16 | 0.119401 | ||||||||
\(971\) | 14368.0i | 0.474863i | 0.971404 | + | 0.237432i | \(0.0763055\pi\) | ||||
−0.971404 | + | 0.237432i | \(0.923694\pi\) | |||||||
\(972\) | 4264.72i | 0.140732i | ||||||||
\(973\) | 1911.17 | 0.0629696 | ||||||||
\(974\) | 9897.15i | 0.325591i | ||||||||
\(975\) | 188.260i | 0.00618375i | ||||||||
\(976\) | − | 26906.3i | − | 0.882429i | ||||||
\(977\) | −22544.5 | −0.738242 | −0.369121 | − | 0.929381i | \(-0.620341\pi\) | ||||
−0.369121 | + | 0.929381i | \(0.620341\pi\) | |||||||
\(978\) | 139.402i | 0.00455786i | ||||||||
\(979\) | 16260.7 | 0.530843 | ||||||||
\(980\) | 12852.4 | 0.418934 | ||||||||
\(981\) | −30489.3 | −0.992304 | ||||||||
\(982\) | −6609.94 | −0.214798 | ||||||||
\(983\) | − | 32899.0i | − | 1.06746i | −0.845654 | − | 0.533732i | \(-0.820789\pi\) | ||
0.845654 | − | 0.533732i | \(-0.179211\pi\) | |||||||
\(984\) | 308.143i | 0.00998296i | ||||||||
\(985\) | −4192.06 | −0.135604 | ||||||||
\(986\) | 7296.83 | − | 5919.83i | 0.235678 | − | 0.191203i | ||||
\(987\) | 99.4282 | 0.00320652 | ||||||||
\(988\) | 34221.6i | 1.10196i | ||||||||
\(989\) | − | 23950.8i | − | 0.770063i | ||||||
\(990\) | 1932.14 | 0.0620278 | ||||||||
\(991\) | 23125.7 | 0.741284 | 0.370642 | − | 0.928776i | \(-0.379138\pi\) | ||||
0.370642 | + | 0.928776i | \(0.379138\pi\) | |||||||
\(992\) | −22853.5 | −0.731451 | ||||||||
\(993\) | −125.152 | −0.00399959 | ||||||||
\(994\) | − | 20.2081i | − | 0.000644831i | ||||||
\(995\) | 1893.18 | 0.0603194 | ||||||||
\(996\) | − | 2016.88i | − | 0.0641640i | ||||||
\(997\) | 8970.92i | 0.284967i | 0.989797 | + | 0.142483i | \(0.0455088\pi\) | ||||
−0.989797 | + | 0.142483i | \(0.954491\pi\) | |||||||
\(998\) | − | 9163.25i | − | 0.290639i | ||||||
\(999\) | −4025.16 | −0.127478 |
(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 | 145.4.c.b.86.9 | yes | 16 | |
29.28 | even | 2 | inner | 145.4.c.b.86.8 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
145.4.c.b.86.8 | ✓ | 16 | 29.28 | even | 2 | inner | |
145.4.c.b.86.9 | yes | 16 | 1.1 | even | 1 | trivial |