Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(288,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.288");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.0515519917\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 288.12 | ||
Character | \(\chi\) | \(=\) | 289.288 |
Dual form | 289.4.b.f.288.11 |
$q$-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 \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.447590 | −0.158247 | −0.0791235 | − | 0.996865i | \(-0.525212\pi\) | ||||
−0.0791235 | + | 0.996865i | \(0.525212\pi\) | |||||||
\(3\) | − 9.51519i | − 1.83120i | −0.402092 | − | 0.915599i | \(-0.631717\pi\) | ||||
0.402092 | − | 0.915599i | \(-0.368283\pi\) | |||||||
\(4\) | −7.79966 | −0.974958 | ||||||||
\(5\) | 11.7425i | 1.05028i | 0.851015 | + | 0.525142i | \(0.175988\pi\) | ||||
−0.851015 | + | 0.525142i | \(0.824012\pi\) | |||||||
\(6\) | 4.25890i | 0.289782i | ||||||||
\(7\) | 2.27797i | 0.122999i | 0.998107 | + | 0.0614994i | \(0.0195882\pi\) | ||||
−0.998107 | + | 0.0614994i | \(0.980412\pi\) | |||||||
\(8\) | 7.07177 | 0.312531 | ||||||||
\(9\) | −63.5388 | −2.35329 | ||||||||
\(10\) | − 5.25584i | − 0.166204i | ||||||||
\(11\) | 22.6868i | 0.621848i | 0.950435 | + | 0.310924i | \(0.100638\pi\) | ||||
−0.950435 | + | 0.310924i | \(0.899362\pi\) | |||||||
\(12\) | 74.2152i | 1.78534i | ||||||||
\(13\) | 67.4022 | 1.43800 | 0.719001 | − | 0.695009i | \(-0.244600\pi\) | ||||
0.719001 | + | 0.695009i | \(0.244600\pi\) | |||||||
\(14\) | − 1.01960i | − 0.0194642i | ||||||||
\(15\) | 111.732 | 1.92328 | ||||||||
\(16\) | 59.2321 | 0.925501 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 28.4393 | 0.372400 | ||||||||
\(19\) | −42.9965 | −0.519161 | −0.259581 | − | 0.965721i | \(-0.583584\pi\) | ||||
−0.259581 | + | 0.965721i | \(0.583584\pi\) | |||||||
\(20\) | − 91.5878i | − 1.02398i | ||||||||
\(21\) | 21.6753 | 0.225235 | ||||||||
\(22\) | − 10.1544i | − 0.0984055i | ||||||||
\(23\) | 117.444i | 1.06473i | 0.846516 | + | 0.532364i | \(0.178696\pi\) | ||||
−0.846516 | + | 0.532364i | \(0.821304\pi\) | |||||||
\(24\) | − 67.2892i | − 0.572306i | ||||||||
\(25\) | −12.8870 | −0.103096 | ||||||||
\(26\) | −30.1686 | −0.227559 | ||||||||
\(27\) | 347.673i | 2.47814i | ||||||||
\(28\) | − 17.7674i | − 0.119919i | ||||||||
\(29\) | − 226.336i | − 1.44930i | −0.689120 | − | 0.724648i | \(-0.742003\pi\) | ||||
0.689120 | − | 0.724648i | \(-0.257997\pi\) | |||||||
\(30\) | −50.0103 | −0.304353 | ||||||||
\(31\) | 0.673139i | 0.00389998i | 0.999998 | + | 0.00194999i | \(0.000620702\pi\) | ||||
−0.999998 | + | 0.00194999i | \(0.999379\pi\) | |||||||
\(32\) | −83.0858 | −0.458989 | ||||||||
\(33\) | 215.869 | 1.13873 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −26.7491 | −0.129184 | ||||||||
\(36\) | 495.581 | 2.29436 | ||||||||
\(37\) | 99.9003i | 0.443878i | 0.975060 | + | 0.221939i | \(0.0712387\pi\) | ||||
−0.975060 | + | 0.221939i | \(0.928761\pi\) | |||||||
\(38\) | 19.2448 | 0.0821557 | ||||||||
\(39\) | − 641.345i | − 2.63327i | ||||||||
\(40\) | 83.0405i | 0.328246i | ||||||||
\(41\) | − 154.092i | − 0.586956i | −0.955966 | − | 0.293478i | \(-0.905187\pi\) | ||||
0.955966 | − | 0.293478i | \(-0.0948128\pi\) | |||||||
\(42\) | −9.70165 | −0.0356428 | ||||||||
\(43\) | 321.792 | 1.14123 | 0.570615 | − | 0.821218i | \(-0.306705\pi\) | ||||
0.570615 | + | 0.821218i | \(0.306705\pi\) | |||||||
\(44\) | − 176.949i | − 0.606275i | ||||||||
\(45\) | − 746.106i | − 2.47162i | ||||||||
\(46\) | − 52.5667i | − 0.168490i | ||||||||
\(47\) | −30.4214 | −0.0944132 | −0.0472066 | − | 0.998885i | \(-0.515032\pi\) | ||||
−0.0472066 | + | 0.998885i | \(0.515032\pi\) | |||||||
\(48\) | − 563.604i | − 1.69478i | ||||||||
\(49\) | 337.811 | 0.984871 | ||||||||
\(50\) | 5.76808 | 0.0163146 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −525.715 | −1.40199 | ||||||||
\(53\) | 361.595 | 0.937148 | 0.468574 | − | 0.883424i | \(-0.344768\pi\) | ||||
0.468574 | + | 0.883424i | \(0.344768\pi\) | |||||||
\(54\) | − 155.615i | − 0.392158i | ||||||||
\(55\) | −266.400 | −0.653116 | ||||||||
\(56\) | 16.1093i | 0.0384410i | ||||||||
\(57\) | 409.119i | 0.950687i | ||||||||
\(58\) | 101.306i | 0.229347i | ||||||||
\(59\) | −147.417 | −0.325289 | −0.162645 | − | 0.986685i | \(-0.552002\pi\) | ||||
−0.162645 | + | 0.986685i | \(0.552002\pi\) | |||||||
\(60\) | −871.475 | −1.87511 | ||||||||
\(61\) | 321.075i | 0.673925i | 0.941518 | + | 0.336963i | \(0.109400\pi\) | ||||
−0.941518 | + | 0.336963i | \(0.890600\pi\) | |||||||
\(62\) | − 0.301290i | 0 0.000617160i | ||||||||
\(63\) | − 144.739i | − 0.289452i | ||||||||
\(64\) | −436.668 | −0.852867 | ||||||||
\(65\) | 791.473i | 1.51031i | ||||||||
\(66\) | −96.6208 | −0.180200 | ||||||||
\(67\) | 612.509 | 1.11686 | 0.558432 | − | 0.829550i | \(-0.311403\pi\) | ||||
0.558432 | + | 0.829550i | \(0.311403\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1117.50 | 1.94973 | ||||||||
\(70\) | 11.9726 | 0.0204429 | ||||||||
\(71\) | − 248.823i | − 0.415913i | −0.978138 | − | 0.207956i | \(-0.933319\pi\) | ||||
0.978138 | − | 0.207956i | \(-0.0666812\pi\) | |||||||
\(72\) | −449.331 | −0.735475 | ||||||||
\(73\) | 701.031i | 1.12397i | 0.827149 | + | 0.561983i | \(0.189961\pi\) | ||||
−0.827149 | + | 0.561983i | \(0.810039\pi\) | |||||||
\(74\) | − 44.7144i | − 0.0702424i | ||||||||
\(75\) | 122.622i | 0.188789i | ||||||||
\(76\) | 335.358 | 0.506160 | ||||||||
\(77\) | −51.6798 | −0.0764865 | ||||||||
\(78\) | 287.059i | 0.416706i | ||||||||
\(79\) | 773.040i | 1.10093i | 0.834857 | + | 0.550467i | \(0.185550\pi\) | ||||
−0.834857 | + | 0.550467i | \(0.814450\pi\) | |||||||
\(80\) | 695.534i | 0.972038i | ||||||||
\(81\) | 1592.63 | 2.18467 | ||||||||
\(82\) | 68.9702i | 0.0928840i | ||||||||
\(83\) | 1005.91 | 1.33028 | 0.665139 | − | 0.746720i | \(-0.268372\pi\) | ||||
0.665139 | + | 0.746720i | \(0.268372\pi\) | |||||||
\(84\) | −169.060 | −0.219595 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −144.031 | −0.180596 | ||||||||
\(87\) | −2153.63 | −2.65395 | ||||||||
\(88\) | 160.436i | 0.194347i | ||||||||
\(89\) | 1641.08 | 1.95454 | 0.977271 | − | 0.211994i | \(-0.0679958\pi\) | ||||
0.977271 | + | 0.211994i | \(0.0679958\pi\) | |||||||
\(90\) | 333.949i | 0.391126i | ||||||||
\(91\) | 153.540i | 0.176872i | ||||||||
\(92\) | − 916.023i | − 1.03806i | ||||||||
\(93\) | 6.40505 | 0.00714164 | ||||||||
\(94\) | 13.6163 | 0.0149406 | ||||||||
\(95\) | − 504.887i | − 0.545267i | ||||||||
\(96\) | 790.577i | 0.840499i | ||||||||
\(97\) | 479.663i | 0.502087i | 0.967976 | + | 0.251043i | \(0.0807737\pi\) | ||||
−0.967976 | + | 0.251043i | \(0.919226\pi\) | |||||||
\(98\) | −151.201 | −0.155853 | ||||||||
\(99\) | − 1441.49i | − 1.46339i | ||||||||
\(100\) | 100.514 | 0.100514 | ||||||||
\(101\) | −814.043 | −0.801984 | −0.400992 | − | 0.916082i | \(-0.631334\pi\) | ||||
−0.400992 | + | 0.916082i | \(0.631334\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −543.806 | −0.520222 | −0.260111 | − | 0.965579i | \(-0.583759\pi\) | ||||
−0.260111 | + | 0.965579i | \(0.583759\pi\) | |||||||
\(104\) | 476.653 | 0.449420 | ||||||||
\(105\) | 254.523i | 0.236561i | ||||||||
\(106\) | −161.846 | −0.148301 | ||||||||
\(107\) | 171.706i | 0.155135i | 0.996987 | + | 0.0775673i | \(0.0247153\pi\) | ||||
−0.996987 | + | 0.0775673i | \(0.975285\pi\) | |||||||
\(108\) | − 2711.73i | − 2.41608i | ||||||||
\(109\) | 1310.16i | 1.15129i | 0.817700 | + | 0.575644i | \(0.195249\pi\) | ||||
−0.817700 | + | 0.575644i | \(0.804751\pi\) | |||||||
\(110\) | 119.238 | 0.103354 | ||||||||
\(111\) | 950.570 | 0.812830 | ||||||||
\(112\) | 134.929i | 0.113836i | ||||||||
\(113\) | 879.939i | 0.732546i | 0.930507 | + | 0.366273i | \(0.119366\pi\) | ||||
−0.930507 | + | 0.366273i | \(0.880634\pi\) | |||||||
\(114\) | − 183.118i | − 0.150443i | ||||||||
\(115\) | −1379.09 | −1.11827 | ||||||||
\(116\) | 1765.35i | 1.41300i | ||||||||
\(117\) | −4282.65 | −3.38403 | ||||||||
\(118\) | 65.9824 | 0.0514760 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 790.145 | 0.601084 | ||||||||
\(121\) | 816.310 | 0.613306 | ||||||||
\(122\) | − 143.710i | − 0.106647i | ||||||||
\(123\) | −1466.22 | −1.07483 | ||||||||
\(124\) | − 5.25026i | − 0.00380232i | ||||||||
\(125\) | 1316.49i | 0.942004i | ||||||||
\(126\) | 64.7839i | 0.0458048i | ||||||||
\(127\) | 1303.39 | 0.910684 | 0.455342 | − | 0.890317i | \(-0.349517\pi\) | ||||
0.455342 | + | 0.890317i | \(0.349517\pi\) | |||||||
\(128\) | 860.135 | 0.593952 | ||||||||
\(129\) | − 3061.91i | − 2.08982i | ||||||||
\(130\) | − 354.255i | − 0.239002i | ||||||||
\(131\) | − 1523.87i | − 1.01634i | −0.861256 | − | 0.508171i | \(-0.830322\pi\) | ||||
0.861256 | − | 0.508171i | \(-0.169678\pi\) | |||||||
\(132\) | −1683.71 | −1.11021 | ||||||||
\(133\) | − 97.9447i | − 0.0638562i | ||||||||
\(134\) | −274.153 | −0.176740 | ||||||||
\(135\) | −4082.56 | −2.60275 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2617.59 | −1.63238 | −0.816189 | − | 0.577785i | \(-0.803917\pi\) | ||||
−0.816189 | + | 0.577785i | \(0.803917\pi\) | |||||||
\(138\) | −500.182 | −0.308538 | ||||||||
\(139\) | 232.950i | 0.142148i | 0.997471 | + | 0.0710741i | \(0.0226427\pi\) | ||||
−0.997471 | + | 0.0710741i | \(0.977357\pi\) | |||||||
\(140\) | 208.634 | 0.125949 | ||||||||
\(141\) | 289.466i | 0.172889i | ||||||||
\(142\) | 111.370i | 0.0658169i | ||||||||
\(143\) | 1529.14i | 0.894218i | ||||||||
\(144\) | −3763.53 | −2.17797 | ||||||||
\(145\) | 2657.76 | 1.52217 | ||||||||
\(146\) | − 313.774i | − 0.177864i | ||||||||
\(147\) | − 3214.33i | − 1.80349i | ||||||||
\(148\) | − 779.189i | − 0.432763i | ||||||||
\(149\) | 429.754 | 0.236287 | 0.118144 | − | 0.992997i | \(-0.462306\pi\) | ||||
0.118144 | + | 0.992997i | \(0.462306\pi\) | |||||||
\(150\) | − 54.8844i | − 0.0298753i | ||||||||
\(151\) | 1373.00 | 0.739953 | 0.369976 | − | 0.929041i | \(-0.379366\pi\) | ||||
0.369976 | + | 0.929041i | \(0.379366\pi\) | |||||||
\(152\) | −304.061 | −0.162254 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 23.1314 | 0.0121038 | ||||||||
\(155\) | −7.90436 | −0.00409609 | ||||||||
\(156\) | 5002.27i | 2.56732i | ||||||||
\(157\) | 616.059 | 0.313165 | 0.156582 | − | 0.987665i | \(-0.449952\pi\) | ||||
0.156582 | + | 0.987665i | \(0.449952\pi\) | |||||||
\(158\) | − 346.005i | − 0.174220i | ||||||||
\(159\) | − 3440.64i | − 1.71610i | ||||||||
\(160\) | − 975.638i | − 0.482068i | ||||||||
\(161\) | −267.534 | −0.130960 | ||||||||
\(162\) | −712.844 | −0.345718 | ||||||||
\(163\) | − 3460.81i | − 1.66301i | −0.555515 | − | 0.831507i | \(-0.687479\pi\) | ||||
0.555515 | − | 0.831507i | \(-0.312521\pi\) | |||||||
\(164\) | 1201.87i | 0.572257i | ||||||||
\(165\) | 2534.85i | 1.19599i | ||||||||
\(166\) | −450.235 | −0.210512 | ||||||||
\(167\) | 2424.76i | 1.12355i | 0.827288 | + | 0.561777i | \(0.189882\pi\) | ||||
−0.827288 | + | 0.561777i | \(0.810118\pi\) | |||||||
\(168\) | 153.283 | 0.0703930 | ||||||||
\(169\) | 2346.06 | 1.06785 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2731.94 | 1.22174 | ||||||||
\(172\) | −2509.87 | −1.11265 | ||||||||
\(173\) | − 2853.14i | − 1.25388i | −0.779069 | − | 0.626938i | \(-0.784308\pi\) | ||||
0.779069 | − | 0.626938i | \(-0.215692\pi\) | |||||||
\(174\) | 963.943 | 0.419979 | ||||||||
\(175\) | − 29.3562i | − 0.0126807i | ||||||||
\(176\) | 1343.79i | 0.575521i | ||||||||
\(177\) | 1402.70i | 0.595669i | ||||||||
\(178\) | −734.531 | −0.309300 | ||||||||
\(179\) | −1195.13 | −0.499040 | −0.249520 | − | 0.968370i | \(-0.580273\pi\) | ||||
−0.249520 | + | 0.968370i | \(0.580273\pi\) | |||||||
\(180\) | 5819.37i | 2.40972i | ||||||||
\(181\) | 2669.80i | 1.09638i | 0.836354 | + | 0.548190i | \(0.184683\pi\) | ||||
−0.836354 | + | 0.548190i | \(0.815317\pi\) | |||||||
\(182\) | − 68.7231i | − 0.0279895i | ||||||||
\(183\) | 3055.09 | 1.23409 | ||||||||
\(184\) | 830.536i | 0.332760i | ||||||||
\(185\) | −1173.08 | −0.466198 | ||||||||
\(186\) | −2.86683 | −0.00113014 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 237.277 | 0.0920489 | ||||||||
\(189\) | −791.989 | −0.304808 | ||||||||
\(190\) | 225.982i | 0.0862868i | ||||||||
\(191\) | −3394.56 | −1.28598 | −0.642988 | − | 0.765876i | \(-0.722306\pi\) | ||||
−0.642988 | + | 0.765876i | \(0.722306\pi\) | |||||||
\(192\) | 4154.98i | 1.56177i | ||||||||
\(193\) | 3003.88i | 1.12033i | 0.828381 | + | 0.560165i | \(0.189262\pi\) | ||||
−0.828381 | + | 0.560165i | \(0.810738\pi\) | |||||||
\(194\) | − 214.692i | − 0.0794537i | ||||||||
\(195\) | 7531.01 | 2.76568 | ||||||||
\(196\) | −2634.81 | −0.960208 | ||||||||
\(197\) | 1636.63i | 0.591902i | 0.955203 | + | 0.295951i | \(0.0956365\pi\) | ||||
−0.955203 | + | 0.295951i | \(0.904363\pi\) | |||||||
\(198\) | 645.197i | 0.231576i | ||||||||
\(199\) | − 1600.54i | − 0.570146i | −0.958506 | − | 0.285073i | \(-0.907982\pi\) | ||||
0.958506 | − | 0.285073i | \(-0.0920179\pi\) | |||||||
\(200\) | −91.1337 | −0.0322206 | ||||||||
\(201\) | − 5828.14i | − 2.04520i | ||||||||
\(202\) | 364.358 | 0.126911 | ||||||||
\(203\) | 515.587 | 0.178262 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1809.44 | 0.616470 | ||||||||
\(206\) | 243.402 | 0.0823235 | ||||||||
\(207\) | − 7462.24i | − 2.50561i | ||||||||
\(208\) | 3992.37 | 1.33087 | ||||||||
\(209\) | − 975.452i | − 0.322839i | ||||||||
\(210\) | − 113.922i | − 0.0374350i | ||||||||
\(211\) | − 4282.36i | − 1.39720i | −0.715510 | − | 0.698602i | \(-0.753806\pi\) | ||||
0.715510 | − | 0.698602i | \(-0.246194\pi\) | |||||||
\(212\) | −2820.32 | −0.913680 | ||||||||
\(213\) | −2367.59 | −0.761619 | ||||||||
\(214\) | − 76.8537i | − 0.0245496i | ||||||||
\(215\) | 3778.65i | 1.19861i | ||||||||
\(216\) | 2458.66i | 0.774495i | ||||||||
\(217\) | −1.53339 | −0.000479693 0 | ||||||||
\(218\) | − 586.414i | − 0.182188i | ||||||||
\(219\) | 6670.44 | 2.05820 | ||||||||
\(220\) | 2077.83 | 0.636761 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −425.465 | −0.128628 | ||||||||
\(223\) | 1396.84 | 0.419460 | 0.209730 | − | 0.977759i | \(-0.432742\pi\) | ||||
0.209730 | + | 0.977759i | \(0.432742\pi\) | |||||||
\(224\) | − 189.267i | − 0.0564551i | ||||||||
\(225\) | 818.822 | 0.242614 | ||||||||
\(226\) | − 393.852i | − 0.115923i | ||||||||
\(227\) | − 1612.43i | − 0.471458i | −0.971819 | − | 0.235729i | \(-0.924252\pi\) | ||||
0.971819 | − | 0.235729i | \(-0.0757477\pi\) | |||||||
\(228\) | − 3190.99i | − 0.926880i | ||||||||
\(229\) | 2530.45 | 0.730204 | 0.365102 | − | 0.930968i | \(-0.381034\pi\) | ||||
0.365102 | + | 0.930968i | \(0.381034\pi\) | |||||||
\(230\) | 617.266 | 0.176962 | ||||||||
\(231\) | 491.743i | 0.140062i | ||||||||
\(232\) | − 1600.60i | − 0.452950i | ||||||||
\(233\) | 4689.59i | 1.31856i | 0.751896 | + | 0.659282i | \(0.229140\pi\) | ||||
−0.751896 | + | 0.659282i | \(0.770860\pi\) | |||||||
\(234\) | 1916.87 | 0.535512 | ||||||||
\(235\) | − 357.225i | − 0.0991607i | ||||||||
\(236\) | 1149.80 | 0.317143 | ||||||||
\(237\) | 7355.62 | 2.01603 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6332.33 | −1.71383 | −0.856913 | − | 0.515462i | \(-0.827620\pi\) | ||||
−0.856913 | + | 0.515462i | \(0.827620\pi\) | |||||||
\(240\) | 6618.14 | 1.78000 | ||||||||
\(241\) | 4438.39i | 1.18631i | 0.805087 | + | 0.593157i | \(0.202119\pi\) | ||||
−0.805087 | + | 0.593157i | \(0.797881\pi\) | |||||||
\(242\) | −365.372 | −0.0970537 | ||||||||
\(243\) | − 5766.97i | − 1.52243i | ||||||||
\(244\) | − 2504.28i | − 0.657049i | ||||||||
\(245\) | 3966.75i | 1.03439i | ||||||||
\(246\) | 656.265 | 0.170089 | ||||||||
\(247\) | −2898.06 | −0.746555 | ||||||||
\(248\) | 4.76029i | 0.00121886i | ||||||||
\(249\) | − 9571.43i | − 2.43600i | ||||||||
\(250\) | − 589.248i | − 0.149069i | ||||||||
\(251\) | 2085.26 | 0.524385 | 0.262193 | − | 0.965016i | \(-0.415554\pi\) | ||||
0.262193 | + | 0.965016i | \(0.415554\pi\) | |||||||
\(252\) | 1128.92i | 0.282203i | ||||||||
\(253\) | −2664.42 | −0.662098 | ||||||||
\(254\) | −583.383 | −0.144113 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3108.36 | 0.758876 | ||||||||
\(257\) | 537.124 | 0.130369 | 0.0651846 | − | 0.997873i | \(-0.479236\pi\) | ||||
0.0651846 | + | 0.997873i | \(0.479236\pi\) | |||||||
\(258\) | 1370.48i | 0.330707i | ||||||||
\(259\) | −227.570 | −0.0545965 | ||||||||
\(260\) | − 6173.22i | − 1.47249i | ||||||||
\(261\) | 14381.1i | 3.41061i | ||||||||
\(262\) | 682.068i | 0.160833i | ||||||||
\(263\) | −6617.18 | −1.55146 | −0.775728 | − | 0.631068i | \(-0.782617\pi\) | ||||
−0.775728 | + | 0.631068i | \(0.782617\pi\) | |||||||
\(264\) | 1526.58 | 0.355887 | ||||||||
\(265\) | 4246.03i | 0.984271i | ||||||||
\(266\) | 43.8390i | 0.0101051i | ||||||||
\(267\) | − 15615.2i | − 3.57915i | ||||||||
\(268\) | −4777.36 | −1.08890 | ||||||||
\(269\) | 617.429i | 0.139945i | 0.997549 | + | 0.0699726i | \(0.0222912\pi\) | ||||
−0.997549 | + | 0.0699726i | \(0.977709\pi\) | |||||||
\(270\) | 1827.31 | 0.411877 | ||||||||
\(271\) | −5332.00 | −1.19519 | −0.597594 | − | 0.801799i | \(-0.703877\pi\) | ||||
−0.597594 | + | 0.801799i | \(0.703877\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1460.96 | 0.323889 | ||||||||
\(274\) | 1171.61 | 0.258319 | ||||||||
\(275\) | − 292.364i | − 0.0641099i | ||||||||
\(276\) | −8716.12 | −1.90090 | ||||||||
\(277\) | 2486.63i | 0.539376i | 0.962948 | + | 0.269688i | \(0.0869205\pi\) | ||||
−0.962948 | + | 0.269688i | \(0.913079\pi\) | |||||||
\(278\) | − 104.266i | − 0.0224945i | ||||||||
\(279\) | − 42.7704i | − 0.00917777i | ||||||||
\(280\) | −189.164 | −0.0403739 | ||||||||
\(281\) | 4951.96 | 1.05128 | 0.525639 | − | 0.850708i | \(-0.323826\pi\) | ||||
0.525639 | + | 0.850708i | \(0.323826\pi\) | |||||||
\(282\) | − 129.562i | − 0.0273592i | ||||||||
\(283\) | − 8216.86i | − 1.72594i | −0.505253 | − | 0.862971i | \(-0.668601\pi\) | ||||
0.505253 | − | 0.862971i | \(-0.331399\pi\) | |||||||
\(284\) | 1940.73i | 0.405498i | ||||||||
\(285\) | −4804.10 | −0.998491 | ||||||||
\(286\) | − 684.428i | − 0.141507i | ||||||||
\(287\) | 351.018 | 0.0721949 | ||||||||
\(288\) | 5279.17 | 1.08013 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −1189.59 | −0.240879 | ||||||||
\(291\) | 4564.08 | 0.919420 | ||||||||
\(292\) | − 5467.81i | − 1.09582i | ||||||||
\(293\) | −737.775 | −0.147103 | −0.0735516 | − | 0.997291i | \(-0.523433\pi\) | ||||
−0.0735516 | + | 0.997291i | \(0.523433\pi\) | |||||||
\(294\) | 1438.70i | 0.285397i | ||||||||
\(295\) | − 1731.05i | − 0.341646i | ||||||||
\(296\) | 706.472i | 0.138726i | ||||||||
\(297\) | −7887.59 | −1.54102 | ||||||||
\(298\) | −192.354 | −0.0373917 | ||||||||
\(299\) | 7915.98i | 1.53108i | ||||||||
\(300\) | − 956.410i | − 0.184061i | ||||||||
\(301\) | 733.033i | 0.140370i | ||||||||
\(302\) | −614.539 | −0.117095 | ||||||||
\(303\) | 7745.77i | 1.46859i | ||||||||
\(304\) | −2546.77 | −0.480484 | ||||||||
\(305\) | −3770.23 | −0.707813 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5994.47 | 1.11441 | 0.557203 | − | 0.830377i | \(-0.311875\pi\) | ||||
0.557203 | + | 0.830377i | \(0.311875\pi\) | |||||||
\(308\) | 403.085 | 0.0745712 | ||||||||
\(309\) | 5174.42i | 0.952629i | ||||||||
\(310\) | 3.53791 | 0.000648193 0 | ||||||||
\(311\) | − 9460.76i | − 1.72498i | −0.506070 | − | 0.862492i | \(-0.668902\pi\) | ||||
0.506070 | − | 0.862492i | \(-0.331098\pi\) | |||||||
\(312\) | − 4535.44i | − 0.822977i | ||||||||
\(313\) | − 4674.92i | − 0.844225i | −0.906544 | − | 0.422112i | \(-0.861289\pi\) | ||||
0.906544 | − | 0.422112i | \(-0.138711\pi\) | |||||||
\(314\) | −275.742 | −0.0495574 | ||||||||
\(315\) | 1699.61 | 0.304006 | ||||||||
\(316\) | − 6029.45i | − 1.07336i | ||||||||
\(317\) | 692.929i | 0.122772i | 0.998114 | + | 0.0613861i | \(0.0195521\pi\) | ||||
−0.998114 | + | 0.0613861i | \(0.980448\pi\) | |||||||
\(318\) | 1540.00i | 0.271568i | ||||||||
\(319\) | 5134.84 | 0.901241 | ||||||||
\(320\) | − 5127.59i | − 0.895753i | ||||||||
\(321\) | 1633.81 | 0.284082 | ||||||||
\(322\) | 119.745 | 0.0207241 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −12422.0 | −2.12997 | ||||||||
\(325\) | −868.611 | −0.148252 | ||||||||
\(326\) | 1549.02i | 0.263167i | ||||||||
\(327\) | 12466.4 | 2.10824 | ||||||||
\(328\) | − 1089.71i | − 0.183442i | ||||||||
\(329\) | − 69.2991i | − 0.0116127i | ||||||||
\(330\) | − 1134.57i | − 0.189261i | ||||||||
\(331\) | 7067.34 | 1.17358 | 0.586792 | − | 0.809738i | \(-0.300391\pi\) | ||||
0.586792 | + | 0.809738i | \(0.300391\pi\) | |||||||
\(332\) | −7845.76 | −1.29696 | ||||||||
\(333\) | − 6347.54i | − 1.04457i | ||||||||
\(334\) | − 1085.30i | − 0.177799i | ||||||||
\(335\) | 7192.40i | 1.17302i | ||||||||
\(336\) | 1283.87 | 0.208455 | ||||||||
\(337\) | − 5897.11i | − 0.953223i | −0.879114 | − | 0.476611i | \(-0.841865\pi\) | ||||
0.879114 | − | 0.476611i | \(-0.158135\pi\) | |||||||
\(338\) | −1050.07 | −0.168984 | ||||||||
\(339\) | 8372.78 | 1.34144 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.2714 | −0.00242519 | ||||||||
\(342\) | −1222.79 | −0.193336 | ||||||||
\(343\) | 1550.87i | 0.244137i | ||||||||
\(344\) | 2275.64 | 0.356669 | ||||||||
\(345\) | 13122.3i | 2.04777i | ||||||||
\(346\) | 1277.04i | 0.198422i | ||||||||
\(347\) | 9529.27i | 1.47423i | 0.675767 | + | 0.737115i | \(0.263812\pi\) | ||||
−0.675767 | + | 0.737115i | \(0.736188\pi\) | |||||||
\(348\) | 16797.6 | 2.58749 | ||||||||
\(349\) | 2516.87 | 0.386031 | 0.193016 | − | 0.981196i | \(-0.438173\pi\) | ||||
0.193016 | + | 0.981196i | \(0.438173\pi\) | |||||||
\(350\) | 13.1395i | 0.00200668i | ||||||||
\(351\) | 23433.9i | 3.56356i | ||||||||
\(352\) | − 1884.95i | − 0.285421i | ||||||||
\(353\) | 9296.21 | 1.40166 | 0.700832 | − | 0.713327i | \(-0.252812\pi\) | ||||
0.700832 | + | 0.713327i | \(0.252812\pi\) | |||||||
\(354\) | − 627.834i | − 0.0942628i | ||||||||
\(355\) | 2921.81 | 0.436826 | ||||||||
\(356\) | −12799.9 | −1.90560 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 534.928 | 0.0789716 | ||||||||
\(359\) | −10477.8 | −1.54038 | −0.770192 | − | 0.637812i | \(-0.779840\pi\) | ||||
−0.770192 | + | 0.637812i | \(0.779840\pi\) | |||||||
\(360\) | − 5276.29i | − 0.772458i | ||||||||
\(361\) | −5010.30 | −0.730472 | ||||||||
\(362\) | − 1194.98i | − 0.173499i | ||||||||
\(363\) | − 7767.34i | − 1.12308i | ||||||||
\(364\) | − 1197.56i | − 0.172443i | ||||||||
\(365\) | −8231.88 | −1.18048 | ||||||||
\(366\) | −1367.43 | −0.195291 | ||||||||
\(367\) | 2779.47i | 0.395332i | 0.980269 | + | 0.197666i | \(0.0633362\pi\) | ||||
−0.980269 | + | 0.197666i | \(0.936664\pi\) | |||||||
\(368\) | 6956.44i | 0.985406i | ||||||||
\(369\) | 9790.84i | 1.38128i | ||||||||
\(370\) | 525.060 | 0.0737745 | ||||||||
\(371\) | 823.702i | 0.115268i | ||||||||
\(372\) | −49.9572 | −0.00696280 | ||||||||
\(373\) | 2548.58 | 0.353782 | 0.176891 | − | 0.984230i | \(-0.443396\pi\) | ||||
0.176891 | + | 0.984230i | \(0.443396\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12526.7 | 1.72500 | ||||||||
\(376\) | −215.133 | −0.0295071 | ||||||||
\(377\) | − 15255.6i | − 2.08409i | ||||||||
\(378\) | 354.486 | 0.0482349 | ||||||||
\(379\) | 11378.4i | 1.54213i | 0.636754 | + | 0.771067i | \(0.280277\pi\) | ||||
−0.636754 | + | 0.771067i | \(0.719723\pi\) | |||||||
\(380\) | 3937.95i | 0.531612i | ||||||||
\(381\) | − 12402.0i | − 1.66764i | ||||||||
\(382\) | 1519.37 | 0.203502 | ||||||||
\(383\) | 633.266 | 0.0844867 | 0.0422433 | − | 0.999107i | \(-0.486550\pi\) | ||||
0.0422433 | + | 0.999107i | \(0.486550\pi\) | |||||||
\(384\) | − 8184.34i | − 1.08764i | ||||||||
\(385\) | − 606.852i | − 0.0803326i | ||||||||
\(386\) | − 1344.50i | − 0.177289i | ||||||||
\(387\) | −20446.3 | −2.68564 | ||||||||
\(388\) | − 3741.21i | − 0.489513i | ||||||||
\(389\) | −12163.4 | −1.58537 | −0.792685 | − | 0.609632i | \(-0.791317\pi\) | ||||
−0.792685 | + | 0.609632i | \(0.791317\pi\) | |||||||
\(390\) | −3370.80 | −0.437660 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 2388.92 | 0.307803 | ||||||||
\(393\) | −14499.9 | −1.86113 | ||||||||
\(394\) | − 732.537i | − 0.0936667i | ||||||||
\(395\) | −9077.45 | −1.15629 | ||||||||
\(396\) | 11243.1i | 1.42674i | ||||||||
\(397\) | − 11911.8i | − 1.50589i | −0.658084 | − | 0.752944i | \(-0.728633\pi\) | ||||
0.658084 | − | 0.752944i | \(-0.271367\pi\) | |||||||
\(398\) | 716.384i | 0.0902239i | ||||||||
\(399\) | −931.962 | −0.116933 | ||||||||
\(400\) | −763.322 | −0.0954153 | ||||||||
\(401\) | 7875.79i | 0.980793i | 0.871499 | + | 0.490396i | \(0.163148\pi\) | ||||
−0.871499 | + | 0.490396i | \(0.836852\pi\) | |||||||
\(402\) | 2608.62i | 0.323647i | ||||||||
\(403\) | 45.3711i | 0.00560818i | ||||||||
\(404\) | 6349.26 | 0.781900 | ||||||||
\(405\) | 18701.5i | 2.29453i | ||||||||
\(406\) | −230.772 | −0.0282094 | ||||||||
\(407\) | −2266.42 | −0.276025 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4351.34 | −0.526064 | −0.263032 | − | 0.964787i | \(-0.584722\pi\) | ||||
−0.263032 | + | 0.964787i | \(0.584722\pi\) | |||||||
\(410\) | −809.885 | −0.0975545 | ||||||||
\(411\) | 24906.9i | 2.98921i | ||||||||
\(412\) | 4241.51 | 0.507194 | ||||||||
\(413\) | − 335.812i | − 0.0400102i | ||||||||
\(414\) | 3340.02i | 0.396505i | ||||||||
\(415\) | 11811.9i | 1.39717i | ||||||||
\(416\) | −5600.17 | −0.660026 | ||||||||
\(417\) | 2216.57 | 0.260301 | ||||||||
\(418\) | 436.602i | 0.0510883i | ||||||||
\(419\) | − 2066.20i | − 0.240908i | −0.992719 | − | 0.120454i | \(-0.961565\pi\) | ||||
0.992719 | − | 0.120454i | \(-0.0384351\pi\) | |||||||
\(420\) | − 1985.19i | − 0.230637i | ||||||||
\(421\) | 10563.5 | 1.22289 | 0.611443 | − | 0.791289i | \(-0.290589\pi\) | ||||
0.611443 | + | 0.791289i | \(0.290589\pi\) | |||||||
\(422\) | 1916.74i | 0.221103i | ||||||||
\(423\) | 1932.94 | 0.222181 | ||||||||
\(424\) | 2557.11 | 0.292888 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1059.71 | 0.120524 | ||||||||
\(427\) | −731.399 | −0.0828920 | ||||||||
\(428\) | − 1339.25i | − 0.151250i | ||||||||
\(429\) | 14550.1 | 1.63749 | ||||||||
\(430\) | − 1691.29i | − 0.189677i | ||||||||
\(431\) | − 4347.98i | − 0.485928i | −0.970035 | − | 0.242964i | \(-0.921880\pi\) | ||||
0.970035 | − | 0.242964i | \(-0.0781197\pi\) | |||||||
\(432\) | 20593.4i | 2.29352i | ||||||||
\(433\) | −949.003 | −0.105326 | −0.0526630 | − | 0.998612i | \(-0.516771\pi\) | ||||
−0.0526630 | + | 0.998612i | \(0.516771\pi\) | |||||||
\(434\) | 0.686331 | 7.59100e−5 0 | ||||||||
\(435\) | − 25289.1i | − 2.78740i | ||||||||
\(436\) | − 10218.8i | − 1.12246i | ||||||||
\(437\) | − 5049.67i | − 0.552765i | ||||||||
\(438\) | −2985.62 | −0.325704 | ||||||||
\(439\) | − 7256.78i | − 0.788946i | −0.918908 | − | 0.394473i | \(-0.870927\pi\) | ||||
0.918908 | − | 0.394473i | \(-0.129073\pi\) | |||||||
\(440\) | −1883.92 | −0.204119 | ||||||||
\(441\) | −21464.1 | −2.31769 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3674.08 | −0.394043 | −0.197021 | − | 0.980399i | \(-0.563127\pi\) | ||||
−0.197021 | + | 0.980399i | \(0.563127\pi\) | |||||||
\(444\) | −7414.12 | −0.792475 | ||||||||
\(445\) | 19270.4i | 2.05282i | ||||||||
\(446\) | −625.213 | −0.0663782 | ||||||||
\(447\) | − 4089.19i | − 0.432689i | ||||||||
\(448\) | − 994.717i | − 0.104902i | ||||||||
\(449\) | − 13012.3i | − 1.36769i | −0.729630 | − | 0.683843i | \(-0.760307\pi\) | ||||
0.729630 | − | 0.683843i | \(-0.239693\pi\) | |||||||
\(450\) | −366.497 | −0.0383929 | ||||||||
\(451\) | 3495.86 | 0.364997 | ||||||||
\(452\) | − 6863.23i | − 0.714201i | ||||||||
\(453\) | − 13064.3i | − 1.35500i | ||||||||
\(454\) | 721.708i | 0.0746067i | ||||||||
\(455\) | −1802.95 | −0.185766 | ||||||||
\(456\) | 2893.20i | 0.297119i | ||||||||
\(457\) | 13.1283 | 0.00134380 | 0.000671900 | − | 1.00000i | \(-0.499786\pi\) | ||||
0.000671900 | 1.00000i | \(0.499786\pi\) | ||||||||
\(458\) | −1132.60 | −0.115553 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10756.4 | 1.09026 | ||||||||
\(461\) | 14382.6 | 1.45307 | 0.726537 | − | 0.687128i | \(-0.241129\pi\) | ||||
0.726537 | + | 0.687128i | \(0.241129\pi\) | |||||||
\(462\) | − 220.099i | − 0.0221644i | ||||||||
\(463\) | −13264.3 | −1.33141 | −0.665705 | − | 0.746215i | \(-0.731869\pi\) | ||||
−0.665705 | + | 0.746215i | \(0.731869\pi\) | |||||||
\(464\) | − 13406.4i | − 1.34132i | ||||||||
\(465\) | 75.2114i | 0.00750075i | ||||||||
\(466\) | − 2099.01i | − 0.208659i | ||||||||
\(467\) | −12992.0 | −1.28736 | −0.643681 | − | 0.765294i | \(-0.722594\pi\) | ||||
−0.643681 | + | 0.765294i | \(0.722594\pi\) | |||||||
\(468\) | 33403.3 | 3.29929 | ||||||||
\(469\) | 1395.28i | 0.137373i | ||||||||
\(470\) | 159.890i | 0.0156919i | ||||||||
\(471\) | − 5861.92i | − 0.573467i | ||||||||
\(472\) | −1042.50 | −0.101663 | ||||||||
\(473\) | 7300.43i | 0.709671i | ||||||||
\(474\) | −3292.30 | −0.319030 | ||||||||
\(475\) | 554.094 | 0.0535234 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22975.3 | −2.20538 | ||||||||
\(478\) | 2834.29 | 0.271208 | ||||||||
\(479\) | − 8697.74i | − 0.829665i | −0.909898 | − | 0.414833i | \(-0.863840\pi\) | ||||
0.909898 | − | 0.414833i | \(-0.136160\pi\) | |||||||
\(480\) | −9283.37 | −0.882763 | ||||||||
\(481\) | 6733.50i | 0.638298i | ||||||||
\(482\) | − 1986.58i | − 0.187730i | ||||||||
\(483\) | 2545.63i | 0.239814i | ||||||||
\(484\) | −6366.94 | −0.597947 | ||||||||
\(485\) | −5632.46 | −0.527333 | ||||||||
\(486\) | 2581.24i | 0.240920i | ||||||||
\(487\) | 1219.66i | 0.113487i | 0.998389 | + | 0.0567435i | \(0.0180717\pi\) | ||||
−0.998389 | + | 0.0567435i | \(0.981928\pi\) | |||||||
\(488\) | 2270.57i | 0.210623i | ||||||||
\(489\) | −32930.2 | −3.04531 | ||||||||
\(490\) | − 1775.48i | − 0.163690i | ||||||||
\(491\) | −11340.1 | −1.04231 | −0.521154 | − | 0.853463i | \(-0.674498\pi\) | ||||
−0.521154 | + | 0.853463i | \(0.674498\pi\) | |||||||
\(492\) | 11436.0 | 1.04792 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 1297.14 | 0.118140 | ||||||||
\(495\) | 16926.7 | 1.53697 | ||||||||
\(496\) | 39.8714i | 0.00360944i | ||||||||
\(497\) | 566.811 | 0.0511568 | ||||||||
\(498\) | 4284.07i | 0.385490i | ||||||||
\(499\) | − 7357.73i | − 0.660074i | −0.943968 | − | 0.330037i | \(-0.892939\pi\) | ||||
0.943968 | − | 0.330037i | \(-0.107061\pi\) | |||||||
\(500\) | − 10268.2i | − 0.918414i | ||||||||
\(501\) | 23072.1 | 2.05745 | ||||||||
\(502\) | −933.343 | −0.0829824 | ||||||||
\(503\) | 4549.92i | 0.403321i | 0.979455 | + | 0.201661i | \(0.0646338\pi\) | ||||
−0.979455 | + | 0.201661i | \(0.935366\pi\) | |||||||
\(504\) | − 1023.56i | − 0.0904626i | ||||||||
\(505\) | − 9558.93i | − 0.842310i | ||||||||
\(506\) | 1192.57 | 0.104775 | ||||||||
\(507\) | − 22323.2i | − 1.95544i | ||||||||
\(508\) | −10166.0 | −0.887879 | ||||||||
\(509\) | −13630.1 | −1.18692 | −0.593461 | − | 0.804863i | \(-0.702239\pi\) | ||||
−0.593461 | + | 0.804863i | \(0.702239\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1596.93 | −0.138246 | ||||||||
\(512\) | −8272.35 | −0.714042 | ||||||||
\(513\) | − 14948.7i | − 1.28655i | ||||||||
\(514\) | −240.411 | −0.0206305 | ||||||||
\(515\) | − 6385.66i | − 0.546380i | ||||||||
\(516\) | 23881.9i | 2.03748i | ||||||||
\(517\) | − 690.165i | − 0.0587106i | ||||||||
\(518\) | 101.858 | 0.00863974 | ||||||||
\(519\) | −27148.2 | −2.29609 | ||||||||
\(520\) | 5597.11i | 0.472018i | ||||||||
\(521\) | 14004.2i | 1.17761i | 0.808275 | + | 0.588805i | \(0.200402\pi\) | ||||
−0.808275 | + | 0.588805i | \(0.799598\pi\) | |||||||
\(522\) | − 6436.84i | − 0.539718i | ||||||||
\(523\) | −5652.21 | −0.472570 | −0.236285 | − | 0.971684i | \(-0.575930\pi\) | ||||
−0.236285 | + | 0.971684i | \(0.575930\pi\) | |||||||
\(524\) | 11885.7i | 0.990891i | ||||||||
\(525\) | −279.329 | −0.0232208 | ||||||||
\(526\) | 2961.78 | 0.245513 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 12786.4 | 1.05389 | ||||||||
\(529\) | −1626.06 | −0.133645 | ||||||||
\(530\) | − 1900.48i | − 0.155758i | ||||||||
\(531\) | 9366.69 | 0.765499 | ||||||||
\(532\) | 763.935i | 0.0622571i | ||||||||
\(533\) | − 10386.2i | − 0.844044i | ||||||||
\(534\) | 6989.20i | 0.566390i | ||||||||
\(535\) | −2016.26 | −0.162935 | ||||||||
\(536\) | 4331.52 | 0.349055 | ||||||||
\(537\) | 11371.9i | 0.913842i | ||||||||
\(538\) | − 276.355i | − 0.0221459i | ||||||||
\(539\) | 7663.84i | 0.612440i | ||||||||
\(540\) | 31842.6 | 2.53757 | ||||||||
\(541\) | − 8809.75i | − 0.700112i | −0.936729 | − | 0.350056i | \(-0.886163\pi\) | ||||
0.936729 | − | 0.350056i | \(-0.113837\pi\) | |||||||
\(542\) | 2386.55 | 0.189135 | ||||||||
\(543\) | 25403.7 | 2.00769 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15384.6 | −1.20918 | ||||||||
\(546\) | −653.913 | −0.0512544 | ||||||||
\(547\) | − 2198.83i | − 0.171874i | −0.996301 | − | 0.0859372i | \(-0.972612\pi\) | ||||
0.996301 | − | 0.0859372i | \(-0.0273884\pi\) | |||||||
\(548\) | 20416.3 | 1.59150 | ||||||||
\(549\) | − 20400.7i | − 1.58594i | ||||||||
\(550\) | 130.859i | 0.0101452i | ||||||||
\(551\) | 9731.65i | 0.752418i | ||||||||
\(552\) | 7902.70 | 0.609350 | ||||||||
\(553\) | −1760.96 | −0.135414 | ||||||||
\(554\) | − 1112.99i | − 0.0853546i | ||||||||
\(555\) | 11162.1i | 0.853702i | ||||||||
\(556\) | − 1816.93i | − 0.138588i | ||||||||
\(557\) | 19799.3 | 1.50614 | 0.753072 | − | 0.657938i | \(-0.228571\pi\) | ||||
0.753072 | + | 0.657938i | \(0.228571\pi\) | |||||||
\(558\) | 19.1436i | 0.00145235i | ||||||||
\(559\) | 21689.5 | 1.64109 | ||||||||
\(560\) | −1584.41 | −0.119560 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2216.45 | −0.166362 | ||||||||
\(563\) | 20671.9 | 1.54745 | 0.773726 | − | 0.633521i | \(-0.218391\pi\) | ||||
0.773726 | + | 0.633521i | \(0.218391\pi\) | |||||||
\(564\) | − 2257.73i | − 0.168560i | ||||||||
\(565\) | −10332.7 | −0.769381 | ||||||||
\(566\) | 3677.78i | 0.273125i | ||||||||
\(567\) | 3627.96i | 0.268712i | ||||||||
\(568\) | − 1759.62i | − 0.129986i | ||||||||
\(569\) | 10735.1 | 0.790928 | 0.395464 | − | 0.918481i | \(-0.370584\pi\) | ||||
0.395464 | + | 0.918481i | \(0.370584\pi\) | |||||||
\(570\) | 2150.26 | 0.158008 | ||||||||
\(571\) | 1413.36i | 0.103586i | 0.998658 | + | 0.0517929i | \(0.0164936\pi\) | ||||
−0.998658 | + | 0.0517929i | \(0.983506\pi\) | |||||||
\(572\) | − 11926.8i | − 0.871825i | ||||||||
\(573\) | 32299.8i | 2.35488i | ||||||||
\(574\) | −157.112 | −0.0114246 | ||||||||
\(575\) | − 1513.50i | − 0.109769i | ||||||||
\(576\) | 27745.3 | 2.00704 | ||||||||
\(577\) | 13903.6 | 1.00314 | 0.501572 | − | 0.865116i | \(-0.332755\pi\) | ||||
0.501572 | + | 0.865116i | \(0.332755\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 28582.4 | 2.05155 | ||||||||
\(580\) | −20729.6 | −1.48405 | ||||||||
\(581\) | 2291.43i | 0.163623i | ||||||||
\(582\) | −2042.84 | −0.145495 | ||||||||
\(583\) | 8203.42i | 0.582763i | ||||||||
\(584\) | 4957.53i | 0.351274i | ||||||||
\(585\) | − 50289.2i | − 3.55419i | ||||||||
\(586\) | 330.220 | 0.0232786 | ||||||||
\(587\) | −7153.64 | −0.503002 | −0.251501 | − | 0.967857i | \(-0.580924\pi\) | ||||
−0.251501 | + | 0.967857i | \(0.580924\pi\) | |||||||
\(588\) | 25070.7i | 1.75833i | ||||||||
\(589\) | − 28.9426i | − 0.00202472i | ||||||||
\(590\) | 774.800i | 0.0540644i | ||||||||
\(591\) | 15572.8 | 1.08389 | ||||||||
\(592\) | 5917.30i | 0.410810i | ||||||||
\(593\) | 22686.9 | 1.57106 | 0.785530 | − | 0.618824i | \(-0.212390\pi\) | ||||
0.785530 | + | 0.618824i | \(0.212390\pi\) | |||||||
\(594\) | 3530.40 | 0.243862 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3351.94 | −0.230370 | ||||||||
\(597\) | −15229.4 | −1.04405 | ||||||||
\(598\) | − 3543.11i | − 0.242289i | ||||||||
\(599\) | 9190.22 | 0.626882 | 0.313441 | − | 0.949608i | \(-0.398518\pi\) | ||||
0.313441 | + | 0.949608i | \(0.398518\pi\) | |||||||
\(600\) | 867.154i | 0.0590024i | ||||||||
\(601\) | 12350.7i | 0.838260i | 0.907926 | + | 0.419130i | \(0.137665\pi\) | ||||
−0.907926 | + | 0.419130i | \(0.862335\pi\) | |||||||
\(602\) | − 328.098i | − 0.0222131i | ||||||||
\(603\) | −38918.1 | −2.62830 | ||||||||
\(604\) | −10708.9 | −0.721423 | ||||||||
\(605\) | 9585.54i | 0.644145i | ||||||||
\(606\) | − 3466.93i | − 0.232400i | ||||||||
\(607\) | 22662.6i | 1.51540i | 0.652606 | + | 0.757698i | \(0.273676\pi\) | ||||
−0.652606 | + | 0.757698i | \(0.726324\pi\) | |||||||
\(608\) | 3572.40 | 0.238289 | ||||||||
\(609\) | − 4905.91i | − 0.326432i | ||||||||
\(610\) | 1687.52 | 0.112009 | ||||||||
\(611\) | −2050.47 | −0.135766 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5314.94 | 0.350193 | 0.175097 | − | 0.984551i | \(-0.443976\pi\) | ||||
0.175097 | + | 0.984551i | \(0.443976\pi\) | |||||||
\(614\) | −2683.06 | −0.176351 | ||||||||
\(615\) | − 17217.1i | − 1.12888i | ||||||||
\(616\) | −365.468 | −0.0239044 | ||||||||
\(617\) | 7956.05i | 0.519122i | 0.965727 | + | 0.259561i | \(0.0835779\pi\) | ||||
−0.965727 | + | 0.259561i | \(0.916422\pi\) | |||||||
\(618\) | − 2316.02i | − 0.150751i | ||||||||
\(619\) | 13874.9i | 0.900933i | 0.892793 | + | 0.450467i | \(0.148742\pi\) | ||||
−0.892793 | + | 0.450467i | \(0.851258\pi\) | |||||||
\(620\) | 61.6513 | 0.00399351 | ||||||||
\(621\) | −40832.1 | −2.63854 | ||||||||
\(622\) | 4234.54i | 0.272974i | ||||||||
\(623\) | 3738.33i | 0.240406i | ||||||||
\(624\) | − 37988.2i | − 2.43709i | ||||||||
\(625\) | −17069.8 | −1.09247 | ||||||||
\(626\) | 2092.45i | 0.133596i | ||||||||
\(627\) | −9281.60 | −0.591183 | ||||||||
\(628\) | −4805.06 | −0.305323 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −760.727 | −0.0481081 | ||||||||
\(631\) | 23668.0 | 1.49320 | 0.746598 | − | 0.665276i | \(-0.231686\pi\) | ||||
0.746598 | + | 0.665276i | \(0.231686\pi\) | |||||||
\(632\) | 5466.76i | 0.344076i | ||||||||
\(633\) | −40747.5 | −2.55856 | ||||||||
\(634\) | − 310.148i | − 0.0194283i | ||||||||
\(635\) | 15305.1i | 0.956477i | ||||||||
\(636\) | 26835.8i | 1.67313i | ||||||||
\(637\) | 22769.2 | 1.41625 | ||||||||
\(638\) | −2298.30 | −0.142619 | ||||||||
\(639\) | 15809.9i | 0.978762i | ||||||||
\(640\) | 10100.2i | 0.623818i | ||||||||
\(641\) | − 18274.3i | − 1.12604i | −0.826442 | − | 0.563021i | \(-0.809639\pi\) | ||||
0.826442 | − | 0.563021i | \(-0.190361\pi\) | |||||||
\(642\) | −731.277 | −0.0449552 | ||||||||
\(643\) | 19527.2i | 1.19763i | 0.800887 | + | 0.598815i | \(0.204361\pi\) | ||||
−0.800887 | + | 0.598815i | \(0.795639\pi\) | |||||||
\(644\) | 2086.67 | 0.127681 | ||||||||
\(645\) | 35954.6 | 2.19490 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4471.27 | −0.271690 | −0.135845 | − | 0.990730i | \(-0.543375\pi\) | ||||
−0.135845 | + | 0.990730i | \(0.543375\pi\) | |||||||
\(648\) | 11262.7 | 0.682778 | ||||||||
\(649\) | − 3344.42i | − 0.202280i | ||||||||
\(650\) | 388.781 | 0.0234604 | ||||||||
\(651\) | 14.5905i | 0 0.000878413i | ||||||||
\(652\) | 26993.1i | 1.62137i | ||||||||
\(653\) | 10869.7i | 0.651399i | 0.945473 | + | 0.325699i | \(0.105600\pi\) | ||||
−0.945473 | + | 0.325699i | \(0.894400\pi\) | |||||||
\(654\) | −5579.84 | −0.333622 | ||||||||
\(655\) | 17894.1 | 1.06745 | ||||||||
\(656\) | − 9127.21i | − 0.543228i | ||||||||
\(657\) | − 44542.6i | − 2.64501i | ||||||||
\(658\) | 31.0176i | 0.00183768i | ||||||||
\(659\) | −3827.54 | −0.226252 | −0.113126 | − | 0.993581i | \(-0.536086\pi\) | ||||
−0.113126 | + | 0.993581i | \(0.536086\pi\) | |||||||
\(660\) | − 19771.0i | − 1.16604i | ||||||||
\(661\) | −15347.3 | −0.903087 | −0.451543 | − | 0.892249i | \(-0.649126\pi\) | ||||
−0.451543 | + | 0.892249i | \(0.649126\pi\) | |||||||
\(662\) | −3163.27 | −0.185716 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7113.57 | 0.415753 | ||||||||
\(665\) | 1150.12 | 0.0670672 | ||||||||
\(666\) | 2841.09i | 0.165301i | ||||||||
\(667\) | 26581.8 | 1.54310 | ||||||||
\(668\) | − 18912.3i | − 1.09542i | ||||||||
\(669\) | − 13291.2i | − 0.768114i | ||||||||
\(670\) | − 3219.25i | − 0.185627i | ||||||||
\(671\) | −7284.16 | −0.419079 | ||||||||
\(672\) | −1800.91 | −0.103380 | ||||||||
\(673\) | − 26133.5i | − 1.49684i | −0.663227 | − | 0.748418i | \(-0.730814\pi\) | ||||
0.663227 | − | 0.748418i | \(-0.269186\pi\) | |||||||
\(674\) | 2639.49i | 0.150845i | ||||||||
\(675\) | − 4480.45i | − 0.255486i | ||||||||
\(676\) | −18298.5 | −1.04111 | ||||||||
\(677\) | 19539.0i | 1.10922i | 0.832109 | + | 0.554612i | \(0.187133\pi\) | ||||
−0.832109 | + | 0.554612i | \(0.812867\pi\) | |||||||
\(678\) | −3747.57 | −0.212278 | ||||||||
\(679\) | −1092.66 | −0.0617561 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15342.6 | −0.863332 | ||||||||
\(682\) | 6.83531 | 0.000383779 0 | ||||||||
\(683\) | − 16057.8i | − 0.899612i | −0.893126 | − | 0.449806i | \(-0.851493\pi\) | ||||
0.893126 | − | 0.449806i | \(-0.148507\pi\) | |||||||
\(684\) | −21308.2 | −1.19114 | ||||||||
\(685\) | − 30737.1i | − 1.71446i | ||||||||
\(686\) | − 694.152i | − 0.0386339i | ||||||||
\(687\) | − 24077.7i | − 1.33715i | ||||||||
\(688\) | 19060.4 | 1.05621 | ||||||||
\(689\) | 24372.3 | 1.34762 | ||||||||
\(690\) | − 5873.40i | − 0.324053i | ||||||||
\(691\) | − 14698.6i | − 0.809206i | −0.914493 | − | 0.404603i | \(-0.867410\pi\) | ||||
0.914493 | − | 0.404603i | \(-0.132590\pi\) | |||||||
\(692\) | 22253.6i | 1.22248i | ||||||||
\(693\) | 3283.67 | 0.179995 | ||||||||
\(694\) | − 4265.20i | − 0.233292i | ||||||||
\(695\) | −2735.43 | −0.149296 | ||||||||
\(696\) | −15230.0 | −0.829441 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −1126.53 | −0.0610883 | ||||||||
\(699\) | 44622.3 | 2.41455 | ||||||||
\(700\) | 228.968i | 0.0123631i | ||||||||
\(701\) | −7042.75 | −0.379459 | −0.189730 | − | 0.981836i | \(-0.560761\pi\) | ||||
−0.189730 | + | 0.981836i | \(0.560761\pi\) | |||||||
\(702\) | − 10488.8i | − 0.563923i | ||||||||
\(703\) | − 4295.36i | − 0.230445i | ||||||||
\(704\) | − 9906.60i | − 0.530354i | ||||||||
\(705\) | −3399.06 | −0.181583 | ||||||||
\(706\) | −4160.89 | −0.221809 | ||||||||
\(707\) | − 1854.37i | − 0.0986431i | ||||||||
\(708\) | − 10940.6i | − 0.580752i | ||||||||
\(709\) | − 5951.66i | − 0.315260i | −0.987498 | − | 0.157630i | \(-0.949615\pi\) | ||||
0.987498 | − | 0.157630i | \(-0.0503853\pi\) | |||||||
\(710\) | −1307.77 | −0.0691265 | ||||||||
\(711\) | − 49118.0i | − 2.59082i | ||||||||
\(712\) | 11605.3 | 0.610855 | ||||||||
\(713\) | −79.0561 | −0.00415242 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17956.0 | −0.939182 | ||||||||
\(716\) | 9321.61 | 0.486543 | ||||||||
\(717\) | 60253.3i | 3.13835i | ||||||||
\(718\) | 4689.76 | 0.243761 | ||||||||
\(719\) | 34823.3i | 1.80625i | 0.429381 | + | 0.903123i | \(0.358732\pi\) | ||||
−0.429381 | + | 0.903123i | \(0.641268\pi\) | |||||||
\(720\) | − 44193.4i | − 2.28749i | ||||||||
\(721\) | − 1238.77i | − 0.0639866i | ||||||||
\(722\) | 2242.56 | 0.115595 | ||||||||
\(723\) | 42232.1 | 2.17238 | ||||||||
\(724\) | − 20823.6i | − 1.06892i | ||||||||
\(725\) | 2916.79i | 0.149416i | ||||||||
\(726\) | 3476.58i | 0.177725i | ||||||||
\(727\) | −3241.15 | −0.165348 | −0.0826738 | − | 0.996577i | \(-0.526346\pi\) | ||||
−0.0826738 | + | 0.996577i | \(0.526346\pi\) | |||||||
\(728\) | 1085.80i | 0.0552781i | ||||||||
\(729\) | −11872.9 | −0.603204 | ||||||||
\(730\) | 3684.51 | 0.186808 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −23828.7 | −1.20319 | ||||||||
\(733\) | −18578.8 | −0.936185 | −0.468093 | − | 0.883679i | \(-0.655059\pi\) | ||||
−0.468093 | + | 0.883679i | \(0.655059\pi\) | |||||||
\(734\) | − 1244.06i | − 0.0625601i | ||||||||
\(735\) | 37744.4 | 1.89418 | ||||||||
\(736\) | − 9757.92i | − 0.488698i | ||||||||
\(737\) | 13895.9i | 0.694519i | ||||||||
\(738\) | − 4382.28i | − 0.218583i | ||||||||
\(739\) | −30393.0 | −1.51289 | −0.756444 | − | 0.654058i | \(-0.773065\pi\) | ||||
−0.756444 | + | 0.654058i | \(0.773065\pi\) | |||||||
\(740\) | 9149.64 | 0.454524 | ||||||||
\(741\) | 27575.6i | 1.36709i | ||||||||
\(742\) | − 368.681i | − 0.0182408i | ||||||||
\(743\) | − 37449.0i | − 1.84908i | −0.381081 | − | 0.924542i | \(-0.624448\pi\) | ||||
0.381081 | − | 0.924542i | \(-0.375552\pi\) | |||||||
\(744\) | 45.2950 | 0.00223198 | ||||||||
\(745\) | 5046.40i | 0.248169i | ||||||||
\(746\) | −1140.72 | −0.0559849 | ||||||||
\(747\) | −63914.3 | −3.13052 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −391.140 | −0.0190814 | ||||||||
\(750\) | −5606.80 | −0.272975 | ||||||||
\(751\) | 5541.28i | 0.269247i | 0.990897 | + | 0.134623i | \(0.0429825\pi\) | ||||
−0.990897 | + | 0.134623i | \(0.957018\pi\) | |||||||
\(752\) | −1801.92 | −0.0873795 | ||||||||
\(753\) | − 19841.7i | − 0.960253i | ||||||||
\(754\) | 6828.23i | 0.329801i | ||||||||
\(755\) | 16122.5i | 0.777160i | ||||||||
\(756\) | 6177.25 | 0.297175 | ||||||||
\(757\) | −13531.4 | −0.649680 | −0.324840 | − | 0.945769i | \(-0.605310\pi\) | ||||
−0.324840 | + | 0.945769i | \(0.605310\pi\) | |||||||
\(758\) | − 5092.85i | − 0.244038i | ||||||||
\(759\) | 25352.5i | 1.21243i | ||||||||
\(760\) | − 3570.45i | − 0.170413i | ||||||||
\(761\) | −37110.8 | −1.76776 | −0.883879 | − | 0.467715i | \(-0.845077\pi\) | ||||
−0.883879 | + | 0.467715i | \(0.845077\pi\) | |||||||
\(762\) | 5551.00i | 0.263899i | ||||||||
\(763\) | −2984.50 | −0.141607 | ||||||||
\(764\) | 26476.4 | 1.25377 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −283.444 | −0.0133698 | ||||||||
\(767\) | −9936.24 | −0.467766 | ||||||||
\(768\) | − 29576.6i | − 1.38965i | ||||||||
\(769\) | −820.351 | −0.0384689 | −0.0192345 | − | 0.999815i | \(-0.506123\pi\) | ||||
−0.0192345 | + | 0.999815i | \(0.506123\pi\) | |||||||
\(770\) | 271.621i | 0.0127124i | ||||||||
\(771\) | − 5110.84i | − 0.238732i | ||||||||
\(772\) | − 23429.2i | − 1.09227i | ||||||||
\(773\) | 25113.2 | 1.16851 | 0.584255 | − | 0.811570i | \(-0.301387\pi\) | ||||
0.584255 | + | 0.811570i | \(0.301387\pi\) | |||||||
\(774\) | 9151.55 | 0.424994 | ||||||||
\(775\) | − 8.67473i | 0 0.000402072i | ||||||||
\(776\) | 3392.07i | 0.156918i | ||||||||
\(777\) | 2165.37i | 0.0999771i | ||||||||
\(778\) | 5444.21 | 0.250880 | ||||||||
\(779\) | 6625.43i | 0.304725i | ||||||||
\(780\) | −58739.3 | −2.69642 | ||||||||
\(781\) | 5644.99 | 0.258634 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 78691.0 | 3.59155 | ||||||||
\(784\) | 20009.2 | 0.911499 | ||||||||
\(785\) | 7234.10i | 0.328912i | ||||||||
\(786\) | 6490.00 | 0.294517 | ||||||||
\(787\) | 20784.0i | 0.941384i | 0.882298 | + | 0.470692i | \(0.155996\pi\) | ||||
−0.882298 | + | 0.470692i | \(0.844004\pi\) | |||||||
\(788\) | − 12765.1i | − 0.577080i | ||||||||
\(789\) | 62963.7i | 2.84102i | ||||||||
\(790\) | 4062.97 | 0.182980 | ||||||||
\(791\) | −2004.47 | −0.0901023 | ||||||||
\(792\) | − 10193.9i | − 0.457354i | ||||||||
\(793\) | 21641.2i | 0.969105i | ||||||||
\(794\) | 5331.62i | 0.238302i | ||||||||
\(795\) | 40401.8 | 1.80240 | ||||||||
\(796\) | 12483.7i | 0.555868i | ||||||||
\(797\) | −4974.23 | −0.221074 | −0.110537 | − | 0.993872i | \(-0.535257\pi\) | ||||
−0.110537 | + | 0.993872i | \(0.535257\pi\) | |||||||
\(798\) | 417.137 | 0.0185044 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 1070.73 | 0.0473198 | ||||||||
\(801\) | −104272. | −4.59960 | ||||||||
\(802\) | − 3525.12i | − 0.155207i | ||||||||
\(803\) | −15904.1 | −0.698935 | ||||||||
\(804\) | 45457.5i | 1.99398i | ||||||||
\(805\) | − 3141.52i | − 0.137545i | ||||||||
\(806\) | − 20.3076i | 0 0.000887477i | ||||||||
\(807\) | 5874.95 | 0.256268 | ||||||||
\(808\) | −5756.73 | −0.250645 | ||||||||
\(809\) | 27460.1i | 1.19338i | 0.802471 | + | 0.596692i | \(0.203519\pi\) | ||||
−0.802471 | + | 0.596692i | \(0.796481\pi\) | |||||||
\(810\) | − 8370.59i | − 0.363102i | ||||||||
\(811\) | − 14356.6i | − 0.621612i | −0.950473 | − | 0.310806i | \(-0.899401\pi\) | ||||
0.950473 | − | 0.310806i | \(-0.100599\pi\) | |||||||
\(812\) | −4021.40 | −0.173798 | ||||||||
\(813\) | 50735.0i | 2.18863i | ||||||||
\(814\) | 1014.43 | 0.0436801 | ||||||||
\(815\) | 40638.6 | 1.74664 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13835.9 | −0.592482 | ||||||||
\(818\) | 1947.62 | 0.0832480 | ||||||||
\(819\) | − 9755.76i | − 0.416232i | ||||||||
\(820\) | −14113.0 | −0.601033 | ||||||||
\(821\) | 15953.0i | 0.678155i | 0.940758 | + | 0.339077i | \(0.110115\pi\) | ||||
−0.940758 | + | 0.339077i | \(0.889885\pi\) | |||||||
\(822\) | − 11148.1i | − 0.473033i | ||||||||
\(823\) | − 17581.1i | − 0.744641i | −0.928104 | − | 0.372321i | \(-0.878562\pi\) | ||||
0.928104 | − | 0.372321i | \(-0.121438\pi\) | |||||||
\(824\) | −3845.67 | −0.162585 | ||||||||
\(825\) | −2781.90 | −0.117398 | ||||||||
\(826\) | 150.306i | 0.00633149i | ||||||||
\(827\) | 39492.2i | 1.66056i | 0.557349 | + | 0.830278i | \(0.311818\pi\) | ||||
−0.557349 | + | 0.830278i | \(0.688182\pi\) | |||||||
\(828\) | 58202.9i | 2.44286i | ||||||||
\(829\) | 15789.1 | 0.661494 | 0.330747 | − | 0.943720i | \(-0.392699\pi\) | ||||
0.330747 | + | 0.943720i | \(0.392699\pi\) | |||||||
\(830\) | − 5286.90i | − 0.221098i | ||||||||
\(831\) | 23660.7 | 0.987704 | ||||||||
\(832\) | −29432.4 | −1.22642 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −992.112 | −0.0411919 | ||||||||
\(835\) | −28472.8 | −1.18005 | ||||||||
\(836\) | 7608.19i | 0.314755i | ||||||||
\(837\) | −234.032 | −0.00966469 | ||||||||
\(838\) | 924.812i | 0.0381230i | ||||||||
\(839\) | 9439.37i | 0.388419i | 0.980960 | + | 0.194209i | \(0.0622141\pi\) | ||||
−0.980960 | + | 0.194209i | \(0.937786\pi\) | |||||||
\(840\) | 1799.93i | 0.0739326i | ||||||||
\(841\) | −26839.0 | −1.10046 | ||||||||
\(842\) | −4728.13 | −0.193518 | ||||||||
\(843\) | − 47118.8i | − 1.92510i | ||||||||
\(844\) | 33401.0i | 1.36222i | ||||||||
\(845\) | 27548.7i | 1.12154i | ||||||||
\(846\) | −865.164 | −0.0351595 | ||||||||
\(847\) | 1859.53i | 0.0754359i | ||||||||
\(848\) | 21418.0 | 0.867331 | ||||||||
\(849\) | −78185.0 | −3.16054 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11732.7 | −0.472610 | ||||||||
\(852\) | 18466.4 | 0.742546 | ||||||||
\(853\) | − 2324.12i | − 0.0932898i | −0.998912 | − | 0.0466449i | \(-0.985147\pi\) | ||||
0.998912 | − | 0.0466449i | \(-0.0148529\pi\) | |||||||
\(854\) | 327.367 | 0.0131174 | ||||||||
\(855\) | 32079.9i | 1.28317i | ||||||||
\(856\) | 1214.26i | 0.0484844i | ||||||||
\(857\) | − 22464.0i | − 0.895399i | −0.894184 | − | 0.447699i | \(-0.852244\pi\) | ||||
0.894184 | − | 0.447699i | \(-0.147756\pi\) | |||||||
\(858\) | −6512.46 | −0.259128 | ||||||||
\(859\) | 1314.36 | 0.0522064 | 0.0261032 | − | 0.999659i | \(-0.491690\pi\) | ||||
0.0261032 | + | 0.999659i | \(0.491690\pi\) | |||||||
\(860\) | − 29472.2i | − 1.16860i | ||||||||
\(861\) | − 3340.00i | − 0.132203i | ||||||||
\(862\) | 1946.11i | 0.0768966i | ||||||||
\(863\) | −15380.5 | −0.606674 | −0.303337 | − | 0.952883i | \(-0.598101\pi\) | ||||
−0.303337 | + | 0.952883i | \(0.598101\pi\) | |||||||
\(864\) | − 28886.7i | − 1.13744i | ||||||||
\(865\) | 33503.1 | 1.31693 | ||||||||
\(866\) | 424.764 | 0.0166675 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11.9599 | 0.000467681 0 | ||||||||
\(869\) | −17537.8 | −0.684614 | ||||||||
\(870\) | 11319.1i | 0.441097i | ||||||||
\(871\) | 41284.5 | 1.60605 | ||||||||
\(872\) | 9265.14i | 0.359813i | ||||||||
\(873\) | − 30477.2i | − 1.18155i | ||||||||
\(874\) | 2260.18i | 0.0874734i | ||||||||
\(875\) | −2998.93 | −0.115865 | ||||||||
\(876\) | −52027.2 | −2.00666 | ||||||||
\(877\) | − 14688.9i | − 0.565574i | −0.959183 | − | 0.282787i | \(-0.908741\pi\) | ||||
0.959183 | − | 0.282787i | \(-0.0912590\pi\) | |||||||
\(878\) | 3248.06i | 0.124848i | ||||||||
\(879\) | 7020.06i | 0.269375i | ||||||||
\(880\) | −15779.4 | −0.604460 | ||||||||
\(881\) | − 9512.25i | − 0.363764i | −0.983320 | − | 0.181882i | \(-0.941781\pi\) | ||||
0.983320 | − | 0.181882i | \(-0.0582189\pi\) | |||||||
\(882\) | 9607.11 | 0.366767 | ||||||||
\(883\) | 14662.1 | 0.558798 | 0.279399 | − | 0.960175i | \(-0.409865\pi\) | ||||
0.279399 | + | 0.960175i | \(0.409865\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16471.2 | −0.625621 | ||||||||
\(886\) | 1644.48 | 0.0623561 | ||||||||
\(887\) | 27847.1i | 1.05413i | 0.849825 | + | 0.527065i | \(0.176708\pi\) | ||||
−0.849825 | + | 0.527065i | \(0.823292\pi\) | |||||||
\(888\) | 6722.21 | 0.254034 | ||||||||
\(889\) | 2969.08i | 0.112013i | ||||||||
\(890\) | − 8625.25i | − 0.324853i | ||||||||
\(891\) | 36131.6i | 1.35853i | ||||||||
\(892\) | −10894.9 | −0.408956 | ||||||||
\(893\) | 1308.01 | 0.0490157 | ||||||||
\(894\) | 1830.28i | 0.0684717i | ||||||||
\(895\) | − 14033.8i | − 0.524134i | ||||||||
\(896\) | 1959.36i | 0.0730554i | ||||||||
\(897\) | 75322.0 | 2.80371 | ||||||||
\(898\) | 5824.20i | 0.216432i | ||||||||
\(899\) | 152.356 | 0.00565222 | ||||||||
\(900\) | −6386.54 | −0.236538 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −1564.71 | −0.0577597 | ||||||||
\(903\) | 6974.95 | 0.257045 | ||||||||
\(904\) | 6222.72i | 0.228943i | ||||||||
\(905\) | −31350.2 | −1.15151 | ||||||||
\(906\) | 5847.46i | 0.214425i | ||||||||
\(907\) | − 141.986i | − 0.00519799i | −0.999997 | − | 0.00259899i | \(-0.999173\pi\) | ||||
0.999997 | − | 0.00259899i | \(-0.000827286\pi\) | |||||||
\(908\) | 12576.4i | 0.459651i | ||||||||
\(909\) | 51723.3 | 1.88730 | ||||||||
\(910\) | 806.983 | 0.0293969 | ||||||||
\(911\) | − 32439.3i | − 1.17976i | −0.807490 | − | 0.589881i | \(-0.799175\pi\) | ||||
0.807490 | − | 0.589881i | \(-0.200825\pi\) | |||||||
\(912\) | 24233.0i | 0.879862i | ||||||||
\(913\) | 22820.9i | 0.827230i | ||||||||
\(914\) | −5.87610 | −0.000212652 0 | ||||||||
\(915\) | 35874.5i | 1.29615i | ||||||||
\(916\) | −19736.6 | −0.711918 | ||||||||
\(917\) | 3471.32 | 0.125009 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11802.3 | 0.423638 | 0.211819 | − | 0.977309i | \(-0.432061\pi\) | ||||
0.211819 | + | 0.977309i | \(0.432061\pi\) | |||||||
\(920\) | −9752.59 | −0.349493 | ||||||||
\(921\) | − 57038.5i | − 2.04070i | ||||||||
\(922\) | −6437.53 | −0.229944 | ||||||||
\(923\) | − 16771.2i | − 0.598083i | ||||||||
\(924\) | − 3835.43i | − 0.136555i | ||||||||
\(925\) | − 1287.41i | − 0.0457620i | ||||||||
\(926\) | 5936.95 | 0.210691 | ||||||||
\(927\) | 34552.8 | 1.22423 | ||||||||
\(928\) | 18805.3i | 0.665210i | ||||||||
\(929\) | − 30089.9i | − 1.06267i | −0.847163 | − | 0.531334i | \(-0.821691\pi\) | ||||
0.847163 | − | 0.531334i | \(-0.178309\pi\) | |||||||
\(930\) | − 33.6639i | − 0.00118697i | ||||||||
\(931\) | −14524.7 | −0.511307 | ||||||||
\(932\) | − 36577.2i | − 1.28554i | ||||||||
\(933\) | −90020.9 | −3.15879 | ||||||||
\(934\) | 5815.09 | 0.203721 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −30285.9 | −1.05761 | ||||||||
\(937\) | 34961.5 | 1.21894 | 0.609468 | − | 0.792810i | \(-0.291383\pi\) | ||||
0.609468 | + | 0.792810i | \(0.291383\pi\) | |||||||
\(938\) | − 624.512i | − 0.0217389i | ||||||||
\(939\) | −44482.8 | −1.54594 | ||||||||
\(940\) | 2786.23i | 0.0966775i | ||||||||
\(941\) | 8933.80i | 0.309494i | 0.987954 | + | 0.154747i | \(0.0494562\pi\) | ||||
−0.987954 | + | 0.154747i | \(0.950544\pi\) | |||||||
\(942\) | 2623.74i | 0.0907494i | ||||||||
\(943\) | 18097.2 | 0.624948 | ||||||||
\(944\) | −8731.81 | −0.301055 | ||||||||
\(945\) | − 9299.95i | − 0.320135i | ||||||||
\(946\) | − 3267.60i | − 0.112303i | ||||||||
\(947\) | − 17816.2i | − 0.611350i | −0.952136 | − | 0.305675i | \(-0.901118\pi\) | ||||
0.952136 | − | 0.305675i | \(-0.0988822\pi\) | |||||||
\(948\) | −57371.4 | −1.96554 | ||||||||
\(949\) | 47251.1i | 1.61626i | ||||||||
\(950\) | −248.007 | −0.00846991 | ||||||||
\(951\) | 6593.35 | 0.224820 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36249.3 | 1.23214 | 0.616070 | − | 0.787691i | \(-0.288724\pi\) | ||||
0.616070 | + | 0.787691i | \(0.288724\pi\) | |||||||
\(954\) | 10283.5 | 0.348994 | ||||||||
\(955\) | − 39860.7i | − 1.35064i | ||||||||
\(956\) | 49390.0 | 1.67091 | ||||||||
\(957\) | − 48858.9i | − 1.65035i | ||||||||
\(958\) | 3893.02i | 0.131292i | ||||||||
\(959\) | − 5962.79i | − 0.200781i | ||||||||
\(960\) | −48789.9 | −1.64030 | ||||||||
\(961\) | 29790.5 | 0.999985 | ||||||||
\(962\) | − 3013.85i | − 0.101009i | ||||||||
\(963\) | − 10910.0i | − 0.365076i | ||||||||
\(964\) | − 34617.9i | − 1.15661i | ||||||||
\(965\) | −35273.1 | −1.17666 | ||||||||
\(966\) | − 1139.40i | − 0.0379499i | ||||||||
\(967\) | −10020.3 | −0.333227 | −0.166613 | − | 0.986022i | \(-0.553283\pi\) | ||||
−0.166613 | + | 0.986022i | \(0.553283\pi\) | |||||||
\(968\) | 5772.75 | 0.191677 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2521.03 | 0.0834489 | ||||||||
\(971\) | −24562.5 | −0.811789 | −0.405894 | − | 0.913920i | \(-0.633040\pi\) | ||||
−0.405894 | + | 0.913920i | \(0.633040\pi\) | |||||||
\(972\) | 44980.4i | 1.48431i | ||||||||
\(973\) | −530.654 | −0.0174841 | ||||||||
\(974\) | − 545.908i | − 0.0179590i | ||||||||
\(975\) | 8264.99i | 0.271479i | ||||||||
\(976\) | 19017.9i | 0.623718i | ||||||||
\(977\) | 17102.8 | 0.560048 | 0.280024 | − | 0.959993i | \(-0.409658\pi\) | ||||
0.280024 | + | 0.959993i | \(0.409658\pi\) | |||||||
\(978\) | 14739.2 | 0.481911 | ||||||||
\(979\) | 37230.9i | 1.21543i | ||||||||
\(980\) | − 30939.3i | − 1.00849i | ||||||||
\(981\) | − 83245.8i | − 2.70931i | ||||||||
\(982\) | 5075.73 | 0.164942 | ||||||||
\(983\) | − 51204.2i | − 1.66140i | −0.556718 | − | 0.830702i | \(-0.687939\pi\) | ||||
0.556718 | − | 0.830702i | \(-0.312061\pi\) | |||||||
\(984\) | −10368.8 | −0.335919 | ||||||||
\(985\) | −19218.1 | −0.621665 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −659.394 | −0.0212652 | ||||||||
\(988\) | 22603.9 | 0.727859 | ||||||||
\(989\) | 37792.5i | 1.21510i | ||||||||
\(990\) | −7576.24 | −0.243221 | ||||||||
\(991\) | − 19176.3i | − 0.614686i | −0.951599 | − | 0.307343i | \(-0.900560\pi\) | ||||
0.951599 | − | 0.307343i | \(-0.0994399\pi\) | |||||||
\(992\) | − 55.9283i | − 0.00179005i | ||||||||
\(993\) | − 67247.0i | − 2.14906i | ||||||||
\(994\) | −253.699 | −0.00809541 | ||||||||
\(995\) | 18794.4 | 0.598815 | ||||||||
\(996\) | 74653.9i | 2.37500i | ||||||||
\(997\) | 18251.7i | 0.579775i | 0.957061 | + | 0.289888i | \(0.0936179\pi\) | ||||
−0.957061 | + | 0.289888i | \(0.906382\pi\) | |||||||
\(998\) | 3293.24i | 0.104455i | ||||||||
\(999\) | −34732.6 | −1.09999 |
(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 | 289.4.b.f.288.12 | 24 | ||
17.4 | even | 4 | 289.4.a.h.1.7 | ✓ | 12 | ||
17.13 | even | 4 | 289.4.a.i.1.7 | yes | 12 | ||
17.16 | even | 2 | inner | 289.4.b.f.288.11 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.4.a.h.1.7 | ✓ | 12 | 17.4 | even | 4 | ||
289.4.a.i.1.7 | yes | 12 | 17.13 | even | 4 | ||
289.4.b.f.288.11 | 24 | 17.16 | even | 2 | inner | ||
289.4.b.f.288.12 | 24 | 1.1 | even | 1 | trivial |