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: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 34 x^{10} + 124 x^{9} + 671 x^{8} - 1984 x^{7} - 5452 x^{6} + 8264 x^{5} + \cdots + 300356 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 17) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 288.8 | ||
Root | \(-0.705468 + 1.84776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.288 |
Dual form | 289.4.b.e.288.7 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.70547 | 0.602974 | 0.301487 | − | 0.953470i | \(-0.402517\pi\) | ||||
0.301487 | + | 0.953470i | \(0.402517\pi\) | |||||||
\(3\) | 4.44379i | 0.855209i | 0.903966 | + | 0.427604i | \(0.140642\pi\) | ||||
−0.903966 | + | 0.427604i | \(0.859358\pi\) | |||||||
\(4\) | −5.09138 | −0.636422 | ||||||||
\(5\) | − 6.80983i | − 0.609090i | −0.952498 | − | 0.304545i | \(-0.901496\pi\) | ||||
0.952498 | − | 0.304545i | \(-0.0985044\pi\) | |||||||
\(6\) | 7.57875i | 0.515668i | ||||||||
\(7\) | − 13.8760i | − 0.749235i | −0.927179 | − | 0.374618i | \(-0.877774\pi\) | ||||
0.927179 | − | 0.374618i | \(-0.122226\pi\) | |||||||
\(8\) | −22.3269 | −0.986720 | ||||||||
\(9\) | 7.25269 | 0.268618 | ||||||||
\(10\) | − 11.6140i | − 0.367265i | ||||||||
\(11\) | 30.8361i | 0.845221i | 0.906311 | + | 0.422610i | \(0.138886\pi\) | ||||
−0.906311 | + | 0.422610i | \(0.861114\pi\) | |||||||
\(12\) | − 22.6250i | − 0.544274i | ||||||||
\(13\) | 66.0130 | 1.40836 | 0.704181 | − | 0.710021i | \(-0.251314\pi\) | ||||
0.704181 | + | 0.710021i | \(0.251314\pi\) | |||||||
\(14\) | − 23.6651i | − 0.451769i | ||||||||
\(15\) | 30.2615 | 0.520899 | ||||||||
\(16\) | 2.65318 | 0.0414559 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 12.3692 | 0.161970 | ||||||||
\(19\) | 79.7150 | 0.962520 | 0.481260 | − | 0.876578i | \(-0.340179\pi\) | ||||
0.481260 | + | 0.876578i | \(0.340179\pi\) | |||||||
\(20\) | 34.6714i | 0.387639i | ||||||||
\(21\) | 61.6622 | 0.640752 | ||||||||
\(22\) | 52.5899i | 0.509646i | ||||||||
\(23\) | 28.8986i | 0.261990i | 0.991383 | + | 0.130995i | \(0.0418173\pi\) | ||||
−0.991383 | + | 0.130995i | \(0.958183\pi\) | |||||||
\(24\) | − 99.2163i | − 0.843851i | ||||||||
\(25\) | 78.6262 | 0.629009 | ||||||||
\(26\) | 112.583 | 0.849205 | ||||||||
\(27\) | 152.212i | 1.08493i | ||||||||
\(28\) | 70.6481i | 0.476830i | ||||||||
\(29\) | − 266.201i | − 1.70456i | −0.523084 | − | 0.852281i | \(-0.675219\pi\) | ||||
0.523084 | − | 0.852281i | \(-0.324781\pi\) | |||||||
\(30\) | 51.6100 | 0.314089 | ||||||||
\(31\) | 35.7906i | 0.207361i | 0.994611 | + | 0.103680i | \(0.0330619\pi\) | ||||
−0.994611 | + | 0.103680i | \(0.966938\pi\) | |||||||
\(32\) | 183.140 | 1.01172 | ||||||||
\(33\) | −137.029 | −0.722840 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −94.4935 | −0.456352 | ||||||||
\(36\) | −36.9262 | −0.170955 | ||||||||
\(37\) | 357.875i | 1.59011i | 0.606535 | + | 0.795057i | \(0.292559\pi\) | ||||
−0.606535 | + | 0.795057i | \(0.707441\pi\) | |||||||
\(38\) | 135.951 | 0.580374 | ||||||||
\(39\) | 293.348i | 1.20444i | ||||||||
\(40\) | 152.043i | 0.601001i | ||||||||
\(41\) | 32.7452i | 0.124730i | 0.998053 | + | 0.0623652i | \(0.0198644\pi\) | ||||
−0.998053 | + | 0.0623652i | \(0.980136\pi\) | |||||||
\(42\) | 105.163 | 0.386357 | ||||||||
\(43\) | 516.157 | 1.83054 | 0.915270 | − | 0.402841i | \(-0.131977\pi\) | ||||
0.915270 | + | 0.402841i | \(0.131977\pi\) | |||||||
\(44\) | − 156.998i | − 0.537917i | ||||||||
\(45\) | − 49.3896i | − 0.163613i | ||||||||
\(46\) | 49.2857i | 0.157973i | ||||||||
\(47\) | −210.602 | −0.653606 | −0.326803 | − | 0.945093i | \(-0.605971\pi\) | ||||
−0.326803 | + | 0.945093i | \(0.605971\pi\) | |||||||
\(48\) | 11.7902i | 0.0354534i | ||||||||
\(49\) | 150.456 | 0.438647 | ||||||||
\(50\) | 134.094 | 0.379276 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −336.097 | −0.896313 | ||||||||
\(53\) | −87.2324 | −0.226081 | −0.113040 | − | 0.993590i | \(-0.536059\pi\) | ||||
−0.113040 | + | 0.993590i | \(0.536059\pi\) | |||||||
\(54\) | 259.593i | 0.654186i | ||||||||
\(55\) | 209.989 | 0.514815 | ||||||||
\(56\) | 309.809i | 0.739285i | ||||||||
\(57\) | 354.237i | 0.823155i | ||||||||
\(58\) | − 453.997i | − 1.02781i | ||||||||
\(59\) | 310.728 | 0.685651 | 0.342825 | − | 0.939399i | \(-0.388616\pi\) | ||||
0.342825 | + | 0.939399i | \(0.388616\pi\) | |||||||
\(60\) | −154.073 | −0.331512 | ||||||||
\(61\) | − 365.247i | − 0.766641i | −0.923615 | − | 0.383321i | \(-0.874780\pi\) | ||||
0.923615 | − | 0.383321i | \(-0.125220\pi\) | |||||||
\(62\) | 61.0397i | 0.125033i | ||||||||
\(63\) | − 100.639i | − 0.201258i | ||||||||
\(64\) | 291.115 | 0.568583 | ||||||||
\(65\) | − 449.537i | − 0.857819i | ||||||||
\(66\) | −233.699 | −0.435854 | ||||||||
\(67\) | −660.131 | −1.20370 | −0.601850 | − | 0.798609i | \(-0.705569\pi\) | ||||
−0.601850 | + | 0.798609i | \(0.705569\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −128.420 | −0.224056 | ||||||||
\(70\) | −161.156 | −0.275168 | ||||||||
\(71\) | − 398.030i | − 0.665316i | −0.943047 | − | 0.332658i | \(-0.892054\pi\) | ||||
0.943047 | − | 0.332658i | \(-0.107946\pi\) | |||||||
\(72\) | −161.930 | −0.265051 | ||||||||
\(73\) | − 643.443i | − 1.03163i | −0.856699 | − | 0.515817i | \(-0.827489\pi\) | ||||
0.856699 | − | 0.515817i | \(-0.172511\pi\) | |||||||
\(74\) | 610.344i | 0.958797i | ||||||||
\(75\) | 349.399i | 0.537934i | ||||||||
\(76\) | −405.859 | −0.612569 | ||||||||
\(77\) | 427.882 | 0.633269 | ||||||||
\(78\) | 500.296i | 0.726248i | ||||||||
\(79\) | − 384.511i | − 0.547605i | −0.961786 | − | 0.273803i | \(-0.911718\pi\) | ||||
0.961786 | − | 0.273803i | \(-0.0882815\pi\) | |||||||
\(80\) | − 18.0677i | − 0.0252504i | ||||||||
\(81\) | −480.576 | −0.659226 | ||||||||
\(82\) | 55.8460i | 0.0752092i | ||||||||
\(83\) | 153.488 | 0.202983 | 0.101491 | − | 0.994836i | \(-0.467639\pi\) | ||||
0.101491 | + | 0.994836i | \(0.467639\pi\) | |||||||
\(84\) | −313.946 | −0.407789 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 880.289 | 1.10377 | ||||||||
\(87\) | 1182.94 | 1.45776 | ||||||||
\(88\) | − 688.475i | − 0.833996i | ||||||||
\(89\) | −599.053 | −0.713477 | −0.356738 | − | 0.934204i | \(-0.616111\pi\) | ||||
−0.356738 | + | 0.934204i | \(0.616111\pi\) | |||||||
\(90\) | − 84.2324i | − 0.0986542i | ||||||||
\(91\) | − 915.998i | − 1.05519i | ||||||||
\(92\) | − 147.134i | − 0.166737i | ||||||||
\(93\) | −159.046 | −0.177336 | ||||||||
\(94\) | −359.175 | −0.394107 | ||||||||
\(95\) | − 542.846i | − 0.586261i | ||||||||
\(96\) | 813.838i | 0.865229i | ||||||||
\(97\) | − 44.5693i | − 0.0466529i | −0.999728 | − | 0.0233265i | \(-0.992574\pi\) | ||||
0.999728 | − | 0.0233265i | \(-0.00742571\pi\) | |||||||
\(98\) | 256.598 | 0.264492 | ||||||||
\(99\) | 223.645i | 0.227042i | ||||||||
\(100\) | −400.316 | −0.400316 | ||||||||
\(101\) | 1478.33 | 1.45643 | 0.728215 | − | 0.685348i | \(-0.240350\pi\) | ||||
0.728215 | + | 0.685348i | \(0.240350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 618.133 | 0.591325 | 0.295662 | − | 0.955293i | \(-0.404460\pi\) | ||||
0.295662 | + | 0.955293i | \(0.404460\pi\) | |||||||
\(104\) | −1473.87 | −1.38966 | ||||||||
\(105\) | − 419.909i | − 0.390276i | ||||||||
\(106\) | −148.772 | −0.136321 | ||||||||
\(107\) | − 138.979i | − 0.125567i | −0.998027 | − | 0.0627833i | \(-0.980002\pi\) | ||||
0.998027 | − | 0.0627833i | \(-0.0199977\pi\) | |||||||
\(108\) | − 774.969i | − 0.690476i | ||||||||
\(109\) | 823.466i | 0.723612i | 0.932253 | + | 0.361806i | \(0.117840\pi\) | ||||
−0.932253 | + | 0.361806i | \(0.882160\pi\) | |||||||
\(110\) | 358.129 | 0.310420 | ||||||||
\(111\) | −1590.32 | −1.35988 | ||||||||
\(112\) | − 36.8156i | − 0.0310602i | ||||||||
\(113\) | − 602.474i | − 0.501558i | −0.968044 | − | 0.250779i | \(-0.919313\pi\) | ||||
0.968044 | − | 0.250779i | \(-0.0806867\pi\) | |||||||
\(114\) | 604.140i | 0.496341i | ||||||||
\(115\) | 196.795 | 0.159576 | ||||||||
\(116\) | 1355.33i | 1.08482i | ||||||||
\(117\) | 478.772 | 0.378312 | ||||||||
\(118\) | 529.937 | 0.413430 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −675.646 | −0.513982 | ||||||||
\(121\) | 380.136 | 0.285602 | ||||||||
\(122\) | − 622.917i | − 0.462265i | ||||||||
\(123\) | −145.513 | −0.106671 | ||||||||
\(124\) | − 182.223i | − 0.131969i | ||||||||
\(125\) | − 1386.66i | − 0.992213i | ||||||||
\(126\) | − 171.636i | − 0.121354i | ||||||||
\(127\) | −1506.98 | −1.05294 | −0.526468 | − | 0.850195i | \(-0.676484\pi\) | ||||
−0.526468 | + | 0.850195i | \(0.676484\pi\) | |||||||
\(128\) | −968.636 | −0.668876 | ||||||||
\(129\) | 2293.70i | 1.56549i | ||||||||
\(130\) | − 766.671i | − 0.517243i | ||||||||
\(131\) | 2783.58i | 1.85651i | 0.371946 | + | 0.928254i | \(0.378691\pi\) | ||||
−0.371946 | + | 0.928254i | \(0.621309\pi\) | |||||||
\(132\) | 697.667 | 0.460032 | ||||||||
\(133\) | − 1106.13i | − 0.721154i | ||||||||
\(134\) | −1125.83 | −0.725799 | ||||||||
\(135\) | 1036.54 | 0.660822 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −629.783 | −0.392744 | −0.196372 | − | 0.980529i | \(-0.562916\pi\) | ||||
−0.196372 | + | 0.980529i | \(0.562916\pi\) | |||||||
\(138\) | −219.015 | −0.135100 | ||||||||
\(139\) | 2654.10i | 1.61955i | 0.586740 | + | 0.809775i | \(0.300411\pi\) | ||||
−0.586740 | + | 0.809775i | \(0.699589\pi\) | |||||||
\(140\) | 481.102 | 0.290432 | ||||||||
\(141\) | − 935.872i | − 0.558969i | ||||||||
\(142\) | − 678.827i | − 0.401168i | ||||||||
\(143\) | 2035.58i | 1.19038i | ||||||||
\(144\) | 19.2427 | 0.0111358 | ||||||||
\(145\) | −1812.78 | −1.03823 | ||||||||
\(146\) | − 1097.37i | − 0.622048i | ||||||||
\(147\) | 668.595i | 0.375134i | ||||||||
\(148\) | − 1822.08i | − 1.01198i | ||||||||
\(149\) | −2216.30 | −1.21857 | −0.609283 | − | 0.792953i | \(-0.708543\pi\) | ||||
−0.609283 | + | 0.792953i | \(0.708543\pi\) | |||||||
\(150\) | 595.888i | 0.324360i | ||||||||
\(151\) | −2133.15 | −1.14963 | −0.574813 | − | 0.818285i | \(-0.694925\pi\) | ||||
−0.574813 | + | 0.818285i | \(0.694925\pi\) | |||||||
\(152\) | −1779.79 | −0.949737 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 729.740 | 0.381845 | ||||||||
\(155\) | 243.728 | 0.126301 | ||||||||
\(156\) | − 1493.55i | − 0.766534i | ||||||||
\(157\) | −345.107 | −0.175430 | −0.0877152 | − | 0.996146i | \(-0.527957\pi\) | ||||
−0.0877152 | + | 0.996146i | \(0.527957\pi\) | |||||||
\(158\) | − 655.770i | − 0.330192i | ||||||||
\(159\) | − 387.643i | − 0.193346i | ||||||||
\(160\) | − 1247.16i | − 0.616227i | ||||||||
\(161\) | 400.998 | 0.196292 | ||||||||
\(162\) | −819.606 | −0.397496 | ||||||||
\(163\) | − 678.526i | − 0.326050i | −0.986622 | − | 0.163025i | \(-0.947875\pi\) | ||||
0.986622 | − | 0.163025i | \(-0.0521252\pi\) | |||||||
\(164\) | − 166.718i | − 0.0793812i | ||||||||
\(165\) | 933.146i | 0.440275i | ||||||||
\(166\) | 261.770 | 0.122393 | ||||||||
\(167\) | 799.790i | 0.370596i | 0.982682 | + | 0.185298i | \(0.0593251\pi\) | ||||
−0.982682 | + | 0.185298i | \(0.940675\pi\) | |||||||
\(168\) | −1376.73 | −0.632243 | ||||||||
\(169\) | 2160.71 | 0.983483 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 578.148 | 0.258550 | ||||||||
\(172\) | −2627.95 | −1.16500 | ||||||||
\(173\) | − 1885.48i | − 0.828615i | −0.910137 | − | 0.414307i | \(-0.864024\pi\) | ||||
0.910137 | − | 0.414307i | \(-0.135976\pi\) | |||||||
\(174\) | 2017.47 | 0.878989 | ||||||||
\(175\) | − 1091.02i | − 0.471276i | ||||||||
\(176\) | 81.8136i | 0.0350394i | ||||||||
\(177\) | 1380.81i | 0.586374i | ||||||||
\(178\) | −1021.66 | −0.430208 | ||||||||
\(179\) | 3588.86 | 1.49857 | 0.749286 | − | 0.662247i | \(-0.230397\pi\) | ||||
0.749286 | + | 0.662247i | \(0.230397\pi\) | |||||||
\(180\) | 251.461i | 0.104127i | ||||||||
\(181\) | − 461.347i | − 0.189457i | −0.995503 | − | 0.0947284i | \(-0.969802\pi\) | ||||
0.995503 | − | 0.0947284i | \(-0.0301983\pi\) | |||||||
\(182\) | − 1562.20i | − 0.636255i | ||||||||
\(183\) | 1623.08 | 0.655638 | ||||||||
\(184\) | − 645.218i | − 0.258511i | ||||||||
\(185\) | 2437.07 | 0.968522 | ||||||||
\(186\) | −271.248 | −0.106929 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1072.26 | 0.415969 | ||||||||
\(189\) | 2112.10 | 0.812870 | ||||||||
\(190\) | − 925.806i | − 0.353500i | ||||||||
\(191\) | −4519.91 | −1.71230 | −0.856149 | − | 0.516728i | \(-0.827150\pi\) | ||||
−0.856149 | + | 0.516728i | \(0.827150\pi\) | |||||||
\(192\) | 1293.65i | 0.486257i | ||||||||
\(193\) | 2928.92i | 1.09238i | 0.837663 | + | 0.546188i | \(0.183922\pi\) | ||||
−0.837663 | + | 0.546188i | \(0.816078\pi\) | |||||||
\(194\) | − 76.0116i | − 0.0281305i | ||||||||
\(195\) | 1997.65 | 0.733614 | ||||||||
\(196\) | −766.027 | −0.279165 | ||||||||
\(197\) | − 1926.13i | − 0.696606i | −0.937382 | − | 0.348303i | \(-0.886758\pi\) | ||||
0.937382 | − | 0.348303i | \(-0.113242\pi\) | |||||||
\(198\) | 381.419i | 0.136900i | ||||||||
\(199\) | 3086.61i | 1.09952i | 0.835323 | + | 0.549759i | \(0.185280\pi\) | ||||
−0.835323 | + | 0.549759i | \(0.814720\pi\) | |||||||
\(200\) | −1755.48 | −0.620656 | ||||||||
\(201\) | − 2933.49i | − 1.02941i | ||||||||
\(202\) | 2521.25 | 0.878190 | ||||||||
\(203\) | −3693.81 | −1.27712 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 222.990 | 0.0759721 | ||||||||
\(206\) | 1054.21 | 0.356553 | ||||||||
\(207\) | 209.593i | 0.0703754i | ||||||||
\(208\) | 175.144 | 0.0583849 | ||||||||
\(209\) | 2458.10i | 0.813541i | ||||||||
\(210\) | − 716.142i | − 0.235326i | ||||||||
\(211\) | − 3602.40i | − 1.17535i | −0.809097 | − | 0.587676i | \(-0.800043\pi\) | ||||
0.809097 | − | 0.587676i | \(-0.199957\pi\) | |||||||
\(212\) | 444.133 | 0.143883 | ||||||||
\(213\) | 1768.76 | 0.568984 | ||||||||
\(214\) | − 237.024i | − 0.0757133i | ||||||||
\(215\) | − 3514.94i | − 1.11496i | ||||||||
\(216\) | − 3398.42i | − 1.07053i | ||||||||
\(217\) | 496.631 | 0.155362 | ||||||||
\(218\) | 1404.39i | 0.436319i | ||||||||
\(219\) | 2859.33 | 0.882262 | ||||||||
\(220\) | −1069.13 | −0.327640 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2712.24 | −0.819972 | ||||||||
\(223\) | 1577.43 | 0.473688 | 0.236844 | − | 0.971548i | \(-0.423887\pi\) | ||||
0.236844 | + | 0.971548i | \(0.423887\pi\) | |||||||
\(224\) | − 2541.26i | − 0.758014i | ||||||||
\(225\) | 570.252 | 0.168963 | ||||||||
\(226\) | − 1027.50i | − 0.302426i | ||||||||
\(227\) | 4292.90i | 1.25520i | 0.778537 | + | 0.627599i | \(0.215962\pi\) | ||||
−0.778537 | + | 0.627599i | \(0.784038\pi\) | |||||||
\(228\) | − 1803.55i | − 0.523874i | ||||||||
\(229\) | −580.893 | −0.167627 | −0.0838133 | − | 0.996481i | \(-0.526710\pi\) | ||||
−0.0838133 | + | 0.996481i | \(0.526710\pi\) | |||||||
\(230\) | 335.627 | 0.0962200 | ||||||||
\(231\) | 1901.42i | 0.541577i | ||||||||
\(232\) | 5943.45i | 1.68193i | ||||||||
\(233\) | − 671.778i | − 0.188883i | −0.995530 | − | 0.0944413i | \(-0.969894\pi\) | ||||
0.995530 | − | 0.0944413i | \(-0.0301065\pi\) | |||||||
\(234\) | 816.530 | 0.228112 | ||||||||
\(235\) | 1434.16i | 0.398105i | ||||||||
\(236\) | −1582.04 | −0.436363 | ||||||||
\(237\) | 1708.69 | 0.468317 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −273.635 | −0.0740584 | −0.0370292 | − | 0.999314i | \(-0.511789\pi\) | ||||
−0.0370292 | + | 0.999314i | \(0.511789\pi\) | |||||||
\(240\) | 80.2891 | 0.0215943 | ||||||||
\(241\) | 6486.56i | 1.73376i | 0.498518 | + | 0.866879i | \(0.333878\pi\) | ||||
−0.498518 | + | 0.866879i | \(0.666122\pi\) | |||||||
\(242\) | 648.310 | 0.172211 | ||||||||
\(243\) | 1974.14i | 0.521158i | ||||||||
\(244\) | 1859.61i | 0.487908i | ||||||||
\(245\) | − 1024.58i | − 0.267175i | ||||||||
\(246\) | −248.168 | −0.0643195 | ||||||||
\(247\) | 5262.22 | 1.35558 | ||||||||
\(248\) | − 799.093i | − 0.204607i | ||||||||
\(249\) | 682.071i | 0.173592i | ||||||||
\(250\) | − 2364.90i | − 0.598279i | ||||||||
\(251\) | −2527.58 | −0.635615 | −0.317808 | − | 0.948155i | \(-0.602947\pi\) | ||||
−0.317808 | + | 0.948155i | \(0.602947\pi\) | |||||||
\(252\) | 512.389i | 0.128085i | ||||||||
\(253\) | −891.120 | −0.221440 | ||||||||
\(254\) | −2570.11 | −0.634893 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3980.89 | −0.971898 | ||||||||
\(257\) | −1702.44 | −0.413211 | −0.206605 | − | 0.978424i | \(-0.566242\pi\) | ||||
−0.206605 | + | 0.978424i | \(0.566242\pi\) | |||||||
\(258\) | 3911.82i | 0.943952i | ||||||||
\(259\) | 4965.88 | 1.19137 | ||||||||
\(260\) | 2288.76i | 0.545935i | ||||||||
\(261\) | − 1930.67i | − 0.457877i | ||||||||
\(262\) | 4747.31i | 1.11943i | ||||||||
\(263\) | 4274.40 | 1.00217 | 0.501085 | − | 0.865398i | \(-0.332934\pi\) | ||||
0.501085 | + | 0.865398i | \(0.332934\pi\) | |||||||
\(264\) | 3059.44 | 0.713241 | ||||||||
\(265\) | 594.038i | 0.137704i | ||||||||
\(266\) | − 1886.46i | − 0.434837i | ||||||||
\(267\) | − 2662.07i | − 0.610172i | ||||||||
\(268\) | 3360.98 | 0.766061 | ||||||||
\(269\) | − 7996.34i | − 1.81244i | −0.422810 | − | 0.906218i | \(-0.638956\pi\) | ||||
0.422810 | − | 0.906218i | \(-0.361044\pi\) | |||||||
\(270\) | 1767.78 | 0.398458 | ||||||||
\(271\) | 474.268 | 0.106309 | 0.0531545 | − | 0.998586i | \(-0.483072\pi\) | ||||
0.0531545 | + | 0.998586i | \(0.483072\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4070.51 | 0.902411 | ||||||||
\(274\) | −1074.07 | −0.236815 | ||||||||
\(275\) | 2424.52i | 0.531652i | ||||||||
\(276\) | 653.833 | 0.142595 | ||||||||
\(277\) | 2826.25i | 0.613043i | 0.951864 | + | 0.306521i | \(0.0991651\pi\) | ||||
−0.951864 | + | 0.306521i | \(0.900835\pi\) | |||||||
\(278\) | 4526.48i | 0.976547i | ||||||||
\(279\) | 259.578i | 0.0557008i | ||||||||
\(280\) | 2109.75 | 0.450291 | ||||||||
\(281\) | 2498.15 | 0.530346 | 0.265173 | − | 0.964201i | \(-0.414571\pi\) | ||||
0.265173 | + | 0.964201i | \(0.414571\pi\) | |||||||
\(282\) | − 1596.10i | − 0.337044i | ||||||||
\(283\) | 2417.07i | 0.507704i | 0.967243 | + | 0.253852i | \(0.0816976\pi\) | ||||
−0.967243 | + | 0.253852i | \(0.918302\pi\) | |||||||
\(284\) | 2026.52i | 0.423422i | ||||||||
\(285\) | 2412.29 | 0.501375 | ||||||||
\(286\) | 3471.62i | 0.717766i | ||||||||
\(287\) | 454.374 | 0.0934524 | ||||||||
\(288\) | 1328.26 | 0.271766 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −3091.65 | −0.626027 | ||||||||
\(291\) | 198.057 | 0.0398980 | ||||||||
\(292\) | 3276.01i | 0.656555i | ||||||||
\(293\) | 6652.17 | 1.32636 | 0.663181 | − | 0.748459i | \(-0.269206\pi\) | ||||
0.663181 | + | 0.748459i | \(0.269206\pi\) | |||||||
\(294\) | 1140.27i | 0.226196i | ||||||||
\(295\) | − 2116.01i | − 0.417623i | ||||||||
\(296\) | − 7990.24i | − 1.56900i | ||||||||
\(297\) | −4693.62 | −0.917008 | ||||||||
\(298\) | −3779.83 | −0.734764 | ||||||||
\(299\) | 1907.68i | 0.368977i | ||||||||
\(300\) | − 1778.92i | − 0.342353i | ||||||||
\(301\) | − 7162.21i | − 1.37150i | ||||||||
\(302\) | −3638.02 | −0.693194 | ||||||||
\(303\) | 6569.40i | 1.24555i | ||||||||
\(304\) | 211.498 | 0.0399021 | ||||||||
\(305\) | −2487.27 | −0.466954 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2511.18 | −0.466842 | −0.233421 | − | 0.972376i | \(-0.574992\pi\) | ||||
−0.233421 | + | 0.972376i | \(0.574992\pi\) | |||||||
\(308\) | −2178.51 | −0.403027 | ||||||||
\(309\) | 2746.85i | 0.505706i | ||||||||
\(310\) | 415.670 | 0.0761563 | ||||||||
\(311\) | − 3585.10i | − 0.653674i | −0.945081 | − | 0.326837i | \(-0.894017\pi\) | ||||
0.945081 | − | 0.326837i | \(-0.105983\pi\) | |||||||
\(312\) | − 6549.56i | − 1.18845i | ||||||||
\(313\) | − 2612.32i | − 0.471747i | −0.971784 | − | 0.235874i | \(-0.924205\pi\) | ||||
0.971784 | − | 0.235874i | \(-0.0757952\pi\) | |||||||
\(314\) | −588.570 | −0.105780 | ||||||||
\(315\) | −685.332 | −0.122584 | ||||||||
\(316\) | 1957.69i | 0.348508i | ||||||||
\(317\) | − 3903.80i | − 0.691669i | −0.938296 | − | 0.345834i | \(-0.887596\pi\) | ||||
0.938296 | − | 0.345834i | \(-0.112404\pi\) | |||||||
\(318\) | − 661.112i | − 0.116583i | ||||||||
\(319\) | 8208.60 | 1.44073 | ||||||||
\(320\) | − 1982.44i | − 0.346318i | ||||||||
\(321\) | 617.594 | 0.107386 | ||||||||
\(322\) | 683.890 | 0.118359 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 2446.79 | 0.419546 | ||||||||
\(325\) | 5190.35 | 0.885873 | ||||||||
\(326\) | − 1157.20i | − 0.196600i | ||||||||
\(327\) | −3659.31 | −0.618839 | ||||||||
\(328\) | − 731.101i | − 0.123074i | ||||||||
\(329\) | 2922.32i | 0.489704i | ||||||||
\(330\) | 1591.45i | 0.265474i | ||||||||
\(331\) | 6236.03 | 1.03554 | 0.517769 | − | 0.855520i | \(-0.326763\pi\) | ||||
0.517769 | + | 0.855520i | \(0.326763\pi\) | |||||||
\(332\) | −781.468 | −0.129183 | ||||||||
\(333\) | 2595.55i | 0.427134i | ||||||||
\(334\) | 1364.02i | 0.223460i | ||||||||
\(335\) | 4495.38i | 0.733161i | ||||||||
\(336\) | 163.601 | 0.0265630 | ||||||||
\(337\) | − 3842.08i | − 0.621043i | −0.950566 | − | 0.310521i | \(-0.899496\pi\) | ||||
0.950566 | − | 0.310521i | \(-0.100504\pi\) | |||||||
\(338\) | 3685.02 | 0.593014 | ||||||||
\(339\) | 2677.27 | 0.428936 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1103.64 | −0.175265 | ||||||||
\(342\) | 986.014 | 0.155899 | ||||||||
\(343\) | − 6847.21i | − 1.07788i | ||||||||
\(344\) | −11524.2 | −1.80623 | ||||||||
\(345\) | 874.516i | 0.136471i | ||||||||
\(346\) | − 3215.62i | − 0.499633i | ||||||||
\(347\) | 8301.86i | 1.28434i | 0.766561 | + | 0.642172i | \(0.221966\pi\) | ||||
−0.766561 | + | 0.642172i | \(0.778034\pi\) | |||||||
\(348\) | −6022.81 | −0.927748 | ||||||||
\(349\) | −4929.17 | −0.756024 | −0.378012 | − | 0.925801i | \(-0.623392\pi\) | ||||
−0.378012 | + | 0.925801i | \(0.623392\pi\) | |||||||
\(350\) | − 1860.70i | − 0.284167i | ||||||||
\(351\) | 10048.0i | 1.52798i | ||||||||
\(352\) | 5647.33i | 0.855124i | ||||||||
\(353\) | −9607.54 | −1.44861 | −0.724303 | − | 0.689482i | \(-0.757838\pi\) | ||||
−0.724303 | + | 0.689482i | \(0.757838\pi\) | |||||||
\(354\) | 2354.93i | 0.353568i | ||||||||
\(355\) | −2710.52 | −0.405237 | ||||||||
\(356\) | 3050.00 | 0.454073 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6120.69 | 0.903600 | ||||||||
\(359\) | 1962.76 | 0.288553 | 0.144277 | − | 0.989537i | \(-0.453915\pi\) | ||||
0.144277 | + | 0.989537i | \(0.453915\pi\) | |||||||
\(360\) | 1102.72i | 0.161440i | ||||||||
\(361\) | −504.522 | −0.0735561 | ||||||||
\(362\) | − 786.813i | − 0.114238i | ||||||||
\(363\) | 1689.25i | 0.244249i | ||||||||
\(364\) | 4663.69i | 0.671549i | ||||||||
\(365\) | −4381.74 | −0.628358 | ||||||||
\(366\) | 2768.12 | 0.395333 | ||||||||
\(367\) | 3458.29i | 0.491883i | 0.969285 | + | 0.245941i | \(0.0790971\pi\) | ||||
−0.969285 | + | 0.245941i | \(0.920903\pi\) | |||||||
\(368\) | 76.6732i | 0.0108610i | ||||||||
\(369\) | 237.491i | 0.0335049i | ||||||||
\(370\) | 4156.34 | 0.583994 | ||||||||
\(371\) | 1210.44i | 0.169388i | ||||||||
\(372\) | 809.763 | 0.112861 | ||||||||
\(373\) | 2661.22 | 0.369418 | 0.184709 | − | 0.982793i | \(-0.440866\pi\) | ||||
0.184709 | + | 0.982793i | \(0.440866\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6162.03 | 0.848549 | ||||||||
\(376\) | 4702.10 | 0.644926 | ||||||||
\(377\) | − 17572.7i | − 2.40064i | ||||||||
\(378\) | 3602.11 | 0.490140 | ||||||||
\(379\) | − 5583.03i | − 0.756677i | −0.925667 | − | 0.378339i | \(-0.876495\pi\) | ||||
0.925667 | − | 0.378339i | \(-0.123505\pi\) | |||||||
\(380\) | 2763.83i | 0.373110i | ||||||||
\(381\) | − 6696.71i | − 0.900480i | ||||||||
\(382\) | −7708.56 | −1.03247 | ||||||||
\(383\) | −7832.13 | −1.04492 | −0.522459 | − | 0.852665i | \(-0.674985\pi\) | ||||
−0.522459 | + | 0.852665i | \(0.674985\pi\) | |||||||
\(384\) | − 4304.42i | − 0.572029i | ||||||||
\(385\) | − 2913.81i | − 0.385718i | ||||||||
\(386\) | 4995.18i | 0.658674i | ||||||||
\(387\) | 3743.53 | 0.491717 | ||||||||
\(388\) | 226.919i | 0.0296910i | ||||||||
\(389\) | −7432.95 | −0.968807 | −0.484403 | − | 0.874845i | \(-0.660963\pi\) | ||||
−0.484403 | + | 0.874845i | \(0.660963\pi\) | |||||||
\(390\) | 3406.93 | 0.442350 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −3359.22 | −0.432821 | ||||||||
\(393\) | −12369.7 | −1.58770 | ||||||||
\(394\) | − 3284.96i | − 0.420035i | ||||||||
\(395\) | −2618.45 | −0.333541 | ||||||||
\(396\) | − 1138.66i | − 0.144494i | ||||||||
\(397\) | − 9540.26i | − 1.20608i | −0.797713 | − | 0.603038i | \(-0.793957\pi\) | ||||
0.797713 | − | 0.603038i | \(-0.206043\pi\) | |||||||
\(398\) | 5264.12i | 0.662981i | ||||||||
\(399\) | 4915.40 | 0.616737 | ||||||||
\(400\) | 208.609 | 0.0260761 | ||||||||
\(401\) | − 8663.30i | − 1.07886i | −0.842029 | − | 0.539432i | \(-0.818639\pi\) | ||||
0.842029 | − | 0.539432i | \(-0.181361\pi\) | |||||||
\(402\) | − 5002.97i | − 0.620710i | ||||||||
\(403\) | 2362.64i | 0.292039i | ||||||||
\(404\) | −7526.75 | −0.926905 | ||||||||
\(405\) | 3272.64i | 0.401528i | ||||||||
\(406\) | −6299.68 | −0.770069 | ||||||||
\(407\) | −11035.4 | −1.34400 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5279.17 | 0.638235 | 0.319117 | − | 0.947715i | \(-0.396614\pi\) | ||||
0.319117 | + | 0.947715i | \(0.396614\pi\) | |||||||
\(410\) | 380.302 | 0.0458092 | ||||||||
\(411\) | − 2798.62i | − 0.335878i | ||||||||
\(412\) | −3147.15 | −0.376332 | ||||||||
\(413\) | − 4311.68i | − 0.513714i | ||||||||
\(414\) | 357.454i | 0.0424346i | ||||||||
\(415\) | − 1045.23i | − 0.123635i | ||||||||
\(416\) | 12089.6 | 1.42486 | ||||||||
\(417\) | −11794.3 | −1.38505 | ||||||||
\(418\) | 4192.21i | 0.490544i | ||||||||
\(419\) | − 9408.24i | − 1.09695i | −0.836166 | − | 0.548476i | \(-0.815208\pi\) | ||||
0.836166 | − | 0.548476i | \(-0.184792\pi\) | |||||||
\(420\) | 2137.92i | 0.248380i | ||||||||
\(421\) | −8191.97 | −0.948343 | −0.474171 | − | 0.880433i | \(-0.657252\pi\) | ||||
−0.474171 | + | 0.880433i | \(0.657252\pi\) | |||||||
\(422\) | − 6143.77i | − 0.708706i | ||||||||
\(423\) | −1527.43 | −0.175570 | ||||||||
\(424\) | 1947.63 | 0.223079 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3016.57 | 0.343083 | ||||||||
\(427\) | −5068.18 | −0.574395 | ||||||||
\(428\) | 707.595i | 0.0799133i | ||||||||
\(429\) | −9045.70 | −1.01802 | ||||||||
\(430\) | − 5994.62i | − 0.672294i | ||||||||
\(431\) | − 1950.29i | − 0.217964i | −0.994044 | − | 0.108982i | \(-0.965241\pi\) | ||||
0.994044 | − | 0.108982i | \(-0.0347590\pi\) | |||||||
\(432\) | 403.845i | 0.0449769i | ||||||||
\(433\) | −11152.3 | −1.23775 | −0.618876 | − | 0.785489i | \(-0.712412\pi\) | ||||
−0.618876 | + | 0.785489i | \(0.712412\pi\) | |||||||
\(434\) | 846.988 | 0.0936791 | ||||||||
\(435\) | − 8055.64i | − 0.887905i | ||||||||
\(436\) | − 4192.58i | − 0.460523i | ||||||||
\(437\) | 2303.65i | 0.252171i | ||||||||
\(438\) | 4876.49 | 0.531981 | ||||||||
\(439\) | 470.158i | 0.0511149i | 0.999673 | + | 0.0255574i | \(0.00813607\pi\) | ||||
−0.999673 | + | 0.0255574i | \(0.991864\pi\) | |||||||
\(440\) | −4688.40 | −0.507979 | ||||||||
\(441\) | 1091.21 | 0.117829 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13132.9 | −1.40849 | −0.704246 | − | 0.709956i | \(-0.748715\pi\) | ||||
−0.704246 | + | 0.709956i | \(0.748715\pi\) | |||||||
\(444\) | 8096.93 | 0.865457 | ||||||||
\(445\) | 4079.45i | 0.434572i | ||||||||
\(446\) | 2690.25 | 0.285621 | ||||||||
\(447\) | − 9848.78i | − 1.04213i | ||||||||
\(448\) | − 4039.51i | − 0.426002i | ||||||||
\(449\) | 10433.0i | 1.09658i | 0.836288 | + | 0.548291i | \(0.184721\pi\) | ||||
−0.836288 | + | 0.548291i | \(0.815279\pi\) | |||||||
\(450\) | 972.546 | 0.101881 | ||||||||
\(451\) | −1009.73 | −0.105425 | ||||||||
\(452\) | 3067.43i | 0.319203i | ||||||||
\(453\) | − 9479.28i | − 0.983169i | ||||||||
\(454\) | 7321.40i | 0.756851i | ||||||||
\(455\) | −6237.79 | −0.642708 | ||||||||
\(456\) | − 7909.02i | − 0.812224i | ||||||||
\(457\) | 253.385 | 0.0259362 | 0.0129681 | − | 0.999916i | \(-0.495872\pi\) | ||||
0.0129681 | + | 0.999916i | \(0.495872\pi\) | |||||||
\(458\) | −990.694 | −0.101074 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1001.96 | −0.101558 | ||||||||
\(461\) | −15560.2 | −1.57204 | −0.786019 | − | 0.618202i | \(-0.787861\pi\) | ||||
−0.786019 | + | 0.618202i | \(0.787861\pi\) | |||||||
\(462\) | 3242.81i | 0.326557i | ||||||||
\(463\) | 10727.9 | 1.07682 | 0.538409 | − | 0.842684i | \(-0.319026\pi\) | ||||
0.538409 | + | 0.842684i | \(0.319026\pi\) | |||||||
\(464\) | − 706.279i | − 0.0706641i | ||||||||
\(465\) | 1083.08i | 0.108014i | ||||||||
\(466\) | − 1145.70i | − 0.113891i | ||||||||
\(467\) | 1960.48 | 0.194262 | 0.0971308 | − | 0.995272i | \(-0.469033\pi\) | ||||
0.0971308 | + | 0.995272i | \(0.469033\pi\) | |||||||
\(468\) | −2437.61 | −0.240766 | ||||||||
\(469\) | 9160.00i | 0.901854i | ||||||||
\(470\) | 2445.92i | 0.240047i | ||||||||
\(471\) | − 1533.59i | − 0.150030i | ||||||||
\(472\) | −6937.61 | −0.676545 | ||||||||
\(473\) | 15916.3i | 1.54721i | ||||||||
\(474\) | 2914.11 | 0.282383 | ||||||||
\(475\) | 6267.68 | 0.605434 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −632.670 | −0.0607295 | ||||||||
\(478\) | −466.675 | −0.0446553 | ||||||||
\(479\) | − 4294.19i | − 0.409617i | −0.978802 | − | 0.204808i | \(-0.934343\pi\) | ||||
0.978802 | − | 0.204808i | \(-0.0656571\pi\) | |||||||
\(480\) | 5542.10 | 0.527002 | ||||||||
\(481\) | 23624.4i | 2.23946i | ||||||||
\(482\) | 11062.6i | 1.04541i | ||||||||
\(483\) | 1781.95i | 0.167871i | ||||||||
\(484\) | −1935.42 | −0.181764 | ||||||||
\(485\) | −303.510 | −0.0284158 | ||||||||
\(486\) | 3366.84i | 0.314244i | ||||||||
\(487\) | 18013.5i | 1.67612i | 0.545578 | + | 0.838060i | \(0.316310\pi\) | ||||
−0.545578 | + | 0.838060i | \(0.683690\pi\) | |||||||
\(488\) | 8154.85i | 0.756460i | ||||||||
\(489\) | 3015.23 | 0.278841 | ||||||||
\(490\) | − 1747.39i | − 0.161100i | ||||||||
\(491\) | −13733.2 | −1.26226 | −0.631129 | − | 0.775678i | \(-0.717408\pi\) | ||||
−0.631129 | + | 0.775678i | \(0.717408\pi\) | |||||||
\(492\) | 740.862 | 0.0678875 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 8974.55 | 0.817377 | ||||||||
\(495\) | 1522.98 | 0.138289 | ||||||||
\(496\) | 94.9587i | 0.00859632i | ||||||||
\(497\) | −5523.07 | −0.498478 | ||||||||
\(498\) | 1163.25i | 0.104672i | ||||||||
\(499\) | − 7747.71i | − 0.695060i | −0.937669 | − | 0.347530i | \(-0.887020\pi\) | ||||
0.937669 | − | 0.347530i | \(-0.112980\pi\) | |||||||
\(500\) | 7060.01i | 0.631467i | ||||||||
\(501\) | −3554.10 | −0.316937 | ||||||||
\(502\) | −4310.71 | −0.383259 | ||||||||
\(503\) | − 19203.7i | − 1.70229i | −0.524934 | − | 0.851143i | \(-0.675910\pi\) | ||||
0.524934 | − | 0.851143i | \(-0.324090\pi\) | |||||||
\(504\) | 2246.95i | 0.198586i | ||||||||
\(505\) | − 10067.2i | − 0.887098i | ||||||||
\(506\) | −1519.78 | −0.133522 | ||||||||
\(507\) | 9601.76i | 0.841083i | ||||||||
\(508\) | 7672.61 | 0.670112 | ||||||||
\(509\) | 151.325 | 0.0131775 | 0.00658876 | − | 0.999978i | \(-0.497903\pi\) | ||||
0.00658876 | + | 0.999978i | \(0.497903\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8928.43 | −0.772936 | ||||||||
\(512\) | 959.802 | 0.0828470 | ||||||||
\(513\) | 12133.6i | 1.04427i | ||||||||
\(514\) | −2903.45 | −0.249155 | ||||||||
\(515\) | − 4209.38i | − 0.360170i | ||||||||
\(516\) | − 11678.1i | − 0.996315i | ||||||||
\(517\) | − 6494.14i | − 0.552441i | ||||||||
\(518\) | 8469.15 | 0.718365 | ||||||||
\(519\) | 8378.68 | 0.708638 | ||||||||
\(520\) | 10036.8i | 0.846427i | ||||||||
\(521\) | 8548.62i | 0.718852i | 0.933174 | + | 0.359426i | \(0.117027\pi\) | ||||
−0.933174 | + | 0.359426i | \(0.882973\pi\) | |||||||
\(522\) | − 3292.70i | − 0.276088i | ||||||||
\(523\) | 17874.0 | 1.49441 | 0.747205 | − | 0.664593i | \(-0.231395\pi\) | ||||
0.747205 | + | 0.664593i | \(0.231395\pi\) | |||||||
\(524\) | − 14172.3i | − 1.18152i | ||||||||
\(525\) | 4848.26 | 0.403039 | ||||||||
\(526\) | 7289.85 | 0.604283 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −363.563 | −0.0299660 | ||||||||
\(529\) | 11331.9 | 0.931361 | ||||||||
\(530\) | 1013.11i | 0.0830317i | ||||||||
\(531\) | 2253.62 | 0.184178 | ||||||||
\(532\) | 5631.71i | 0.458958i | ||||||||
\(533\) | 2161.61i | 0.175666i | ||||||||
\(534\) | − 4540.07i | − 0.367918i | ||||||||
\(535\) | −946.425 | −0.0764813 | ||||||||
\(536\) | 14738.7 | 1.18771 | ||||||||
\(537\) | 15948.2i | 1.28159i | ||||||||
\(538\) | − 13637.5i | − 1.09285i | ||||||||
\(539\) | 4639.47i | 0.370753i | ||||||||
\(540\) | −5277.41 | −0.420562 | ||||||||
\(541\) | 2122.24i | 0.168655i | 0.996438 | + | 0.0843273i | \(0.0268741\pi\) | ||||
−0.996438 | + | 0.0843273i | \(0.973126\pi\) | |||||||
\(542\) | 808.849 | 0.0641015 | ||||||||
\(543\) | 2050.13 | 0.162025 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5607.67 | 0.440745 | ||||||||
\(546\) | 6942.12 | 0.544130 | ||||||||
\(547\) | 284.066i | 0.0222044i | 0.999938 | + | 0.0111022i | \(0.00353401\pi\) | ||||
−0.999938 | + | 0.0111022i | \(0.996466\pi\) | |||||||
\(548\) | 3206.46 | 0.249951 | ||||||||
\(549\) | − 2649.03i | − 0.205934i | ||||||||
\(550\) | 4134.95i | 0.320572i | ||||||||
\(551\) | − 21220.2i | − 1.64067i | ||||||||
\(552\) | 2867.21 | 0.221081 | ||||||||
\(553\) | −5335.48 | −0.410285 | ||||||||
\(554\) | 4820.08i | 0.369649i | ||||||||
\(555\) | 10829.8i | 0.828289i | ||||||||
\(556\) | − 13513.0i | − 1.03072i | ||||||||
\(557\) | 9915.36 | 0.754268 | 0.377134 | − | 0.926159i | \(-0.376910\pi\) | ||||
0.377134 | + | 0.926159i | \(0.376910\pi\) | |||||||
\(558\) | 442.702i | 0.0335862i | ||||||||
\(559\) | 34073.1 | 2.57806 | ||||||||
\(560\) | −250.708 | −0.0189185 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4260.52 | 0.319785 | ||||||||
\(563\) | 5048.52 | 0.377922 | 0.188961 | − | 0.981985i | \(-0.439488\pi\) | ||||
0.188961 | + | 0.981985i | \(0.439488\pi\) | |||||||
\(564\) | 4764.88i | 0.355741i | ||||||||
\(565\) | −4102.75 | −0.305494 | ||||||||
\(566\) | 4122.24i | 0.306132i | ||||||||
\(567\) | 6668.48i | 0.493915i | ||||||||
\(568\) | 8886.78i | 0.656481i | ||||||||
\(569\) | −10964.5 | −0.807828 | −0.403914 | − | 0.914797i | \(-0.632350\pi\) | ||||
−0.403914 | + | 0.914797i | \(0.632350\pi\) | |||||||
\(570\) | 4114.09 | 0.302316 | ||||||||
\(571\) | − 6757.57i | − 0.495263i | −0.968854 | − | 0.247632i | \(-0.920348\pi\) | ||||
0.968854 | − | 0.247632i | \(-0.0796523\pi\) | |||||||
\(572\) | − 10363.9i | − 0.757582i | ||||||||
\(573\) | − 20085.5i | − 1.46437i | ||||||||
\(574\) | 774.920 | 0.0563494 | ||||||||
\(575\) | 2272.19i | 0.164794i | ||||||||
\(576\) | 2111.36 | 0.152732 | ||||||||
\(577\) | −18050.9 | −1.30237 | −0.651187 | − | 0.758917i | \(-0.725729\pi\) | ||||
−0.651187 | + | 0.758917i | \(0.725729\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13015.5 | −0.934209 | ||||||||
\(580\) | 9229.57 | 0.660754 | ||||||||
\(581\) | − 2129.81i | − 0.152082i | ||||||||
\(582\) | 337.780 | 0.0240574 | ||||||||
\(583\) | − 2689.90i | − 0.191088i | ||||||||
\(584\) | 14366.1i | 1.01793i | ||||||||
\(585\) | − 3260.36i | − 0.230426i | ||||||||
\(586\) | 11345.1 | 0.799762 | ||||||||
\(587\) | 7447.06 | 0.523634 | 0.261817 | − | 0.965118i | \(-0.415678\pi\) | ||||
0.261817 | + | 0.965118i | \(0.415678\pi\) | |||||||
\(588\) | − 3404.07i | − 0.238744i | ||||||||
\(589\) | 2853.04i | 0.199589i | ||||||||
\(590\) | − 3608.78i | − 0.251816i | ||||||||
\(591\) | 8559.34 | 0.595743 | ||||||||
\(592\) | 949.505i | 0.0659196i | ||||||||
\(593\) | 1229.32 | 0.0851298 | 0.0425649 | − | 0.999094i | \(-0.486447\pi\) | ||||
0.0425649 | + | 0.999094i | \(0.486447\pi\) | |||||||
\(594\) | −8004.82 | −0.552932 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11284.0 | 0.775523 | ||||||||
\(597\) | −13716.3 | −0.940317 | ||||||||
\(598\) | 3253.49i | 0.222484i | ||||||||
\(599\) | 10655.6 | 0.726840 | 0.363420 | − | 0.931625i | \(-0.381609\pi\) | ||||
0.363420 | + | 0.931625i | \(0.381609\pi\) | |||||||
\(600\) | − 7800.99i | − 0.530790i | ||||||||
\(601\) | − 2134.49i | − 0.144871i | −0.997373 | − | 0.0724356i | \(-0.976923\pi\) | ||||
0.997373 | − | 0.0724356i | \(-0.0230772\pi\) | |||||||
\(602\) | − 12214.9i | − 0.826982i | ||||||||
\(603\) | −4787.73 | −0.323336 | ||||||||
\(604\) | 10860.7 | 0.731647 | ||||||||
\(605\) | − 2588.67i | − 0.173957i | ||||||||
\(606\) | 11203.9i | 0.751036i | ||||||||
\(607\) | − 12364.9i | − 0.826812i | −0.910547 | − | 0.413406i | \(-0.864339\pi\) | ||||
0.910547 | − | 0.413406i | \(-0.135661\pi\) | |||||||
\(608\) | 14599.0 | 0.973797 | ||||||||
\(609\) | − 16414.5i | − 1.09220i | ||||||||
\(610\) | −4241.96 | −0.281561 | ||||||||
\(611\) | −13902.5 | −0.920513 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4888.87 | 0.322120 | 0.161060 | − | 0.986945i | \(-0.448509\pi\) | ||||
0.161060 | + | 0.986945i | \(0.448509\pi\) | |||||||
\(614\) | −4282.73 | −0.281493 | ||||||||
\(615\) | 990.920i | 0.0649720i | ||||||||
\(616\) | −9553.30 | −0.624859 | ||||||||
\(617\) | 24750.0i | 1.61491i | 0.589932 | + | 0.807453i | \(0.299155\pi\) | ||||
−0.589932 | + | 0.807453i | \(0.700845\pi\) | |||||||
\(618\) | 4684.67i | 0.304927i | ||||||||
\(619\) | − 10794.8i | − 0.700937i | −0.936574 | − | 0.350469i | \(-0.886022\pi\) | ||||
0.936574 | − | 0.350469i | \(-0.113978\pi\) | |||||||
\(620\) | −1240.91 | −0.0803809 | ||||||||
\(621\) | −4398.72 | −0.284242 | ||||||||
\(622\) | − 6114.28i | − 0.394148i | ||||||||
\(623\) | 8312.47i | 0.534562i | ||||||||
\(624\) | 778.304i | 0.0499313i | ||||||||
\(625\) | 385.346 | 0.0246621 | ||||||||
\(626\) | − 4455.22i | − 0.284451i | ||||||||
\(627\) | −10923.3 | −0.695748 | ||||||||
\(628\) | 1757.07 | 0.111648 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −1168.81 | −0.0739152 | ||||||||
\(631\) | 7579.90 | 0.478211 | 0.239106 | − | 0.970994i | \(-0.423146\pi\) | ||||
0.239106 | + | 0.970994i | \(0.423146\pi\) | |||||||
\(632\) | 8584.94i | 0.540333i | ||||||||
\(633\) | 16008.3 | 1.00517 | ||||||||
\(634\) | − 6657.80i | − 0.417058i | ||||||||
\(635\) | 10262.3i | 0.641333i | ||||||||
\(636\) | 1973.64i | 0.123050i | ||||||||
\(637\) | 9932.03 | 0.617773 | ||||||||
\(638\) | 13999.5 | 0.868723 | ||||||||
\(639\) | − 2886.79i | − 0.178716i | ||||||||
\(640\) | 6596.25i | 0.407406i | ||||||||
\(641\) | − 3181.53i | − 0.196042i | −0.995184 | − | 0.0980208i | \(-0.968749\pi\) | ||||
0.995184 | − | 0.0980208i | \(-0.0312512\pi\) | |||||||
\(642\) | 1053.29 | 0.0647507 | ||||||||
\(643\) | 10552.8i | 0.647219i | 0.946191 | + | 0.323609i | \(0.104896\pi\) | ||||
−0.946191 | + | 0.323609i | \(0.895104\pi\) | |||||||
\(644\) | −2041.63 | −0.124925 | ||||||||
\(645\) | 15619.7 | 0.953526 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10952.0 | −0.665483 | −0.332742 | − | 0.943018i | \(-0.607974\pi\) | ||||
−0.332742 | + | 0.943018i | \(0.607974\pi\) | |||||||
\(648\) | 10729.8 | 0.650471 | ||||||||
\(649\) | 9581.64i | 0.579526i | ||||||||
\(650\) | 8851.97 | 0.534158 | ||||||||
\(651\) | 2206.93i | 0.132867i | ||||||||
\(652\) | 3454.63i | 0.207506i | ||||||||
\(653\) | 6526.76i | 0.391136i | 0.980690 | + | 0.195568i | \(0.0626550\pi\) | ||||
−0.980690 | + | 0.195568i | \(0.937345\pi\) | |||||||
\(654\) | −6240.84 | −0.373144 | ||||||||
\(655\) | 18955.7 | 1.13078 | ||||||||
\(656\) | 86.8789i | 0.00517081i | ||||||||
\(657\) | − 4666.69i | − 0.277116i | ||||||||
\(658\) | 4983.92i | 0.295279i | ||||||||
\(659\) | −25717.9 | −1.52022 | −0.760111 | − | 0.649793i | \(-0.774855\pi\) | ||||
−0.760111 | + | 0.649793i | \(0.774855\pi\) | |||||||
\(660\) | − 4751.00i | − 0.280201i | ||||||||
\(661\) | −11808.9 | −0.694878 | −0.347439 | − | 0.937703i | \(-0.612949\pi\) | ||||
−0.347439 | + | 0.937703i | \(0.612949\pi\) | |||||||
\(662\) | 10635.3 | 0.624403 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3426.93 | −0.200287 | ||||||||
\(665\) | −7532.54 | −0.439247 | ||||||||
\(666\) | 4426.64i | 0.257550i | ||||||||
\(667\) | 7692.85 | 0.446579 | ||||||||
\(668\) | − 4072.03i | − 0.235856i | ||||||||
\(669\) | 7009.76i | 0.405102i | ||||||||
\(670\) | 7666.73i | 0.442077i | ||||||||
\(671\) | 11262.8 | 0.647981 | ||||||||
\(672\) | 11292.8 | 0.648260 | ||||||||
\(673\) | 6282.85i | 0.359860i | 0.983679 | + | 0.179930i | \(0.0575872\pi\) | ||||
−0.983679 | + | 0.179930i | \(0.942413\pi\) | |||||||
\(674\) | − 6552.54i | − 0.374472i | ||||||||
\(675\) | 11967.8i | 0.682433i | ||||||||
\(676\) | −11001.0 | −0.625910 | ||||||||
\(677\) | − 18502.8i | − 1.05040i | −0.850979 | − | 0.525200i | \(-0.823991\pi\) | ||||
0.850979 | − | 0.525200i | \(-0.176009\pi\) | |||||||
\(678\) | 4566.00 | 0.258638 | ||||||||
\(679\) | −618.446 | −0.0349540 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19076.8 | −1.07346 | ||||||||
\(682\) | −1882.22 | −0.105680 | ||||||||
\(683\) | 137.518i | 0.00770424i | 0.999993 | + | 0.00385212i | \(0.00122617\pi\) | ||||
−0.999993 | + | 0.00385212i | \(0.998774\pi\) | |||||||
\(684\) | −2943.57 | −0.164547 | ||||||||
\(685\) | 4288.71i | 0.239217i | ||||||||
\(686\) | − 11677.7i | − 0.649936i | ||||||||
\(687\) | − 2581.37i | − 0.143356i | ||||||||
\(688\) | 1369.46 | 0.0758867 | ||||||||
\(689\) | −5758.47 | −0.318404 | ||||||||
\(690\) | 1491.46i | 0.0822882i | ||||||||
\(691\) | − 303.235i | − 0.0166940i | −0.999965 | − | 0.00834702i | \(-0.997343\pi\) | ||||
0.999965 | − | 0.00834702i | \(-0.00265697\pi\) | |||||||
\(692\) | 9599.69i | 0.527349i | ||||||||
\(693\) | 3103.30 | 0.170108 | ||||||||
\(694\) | 14158.6i | 0.774426i | ||||||||
\(695\) | 18074.0 | 0.986452 | ||||||||
\(696\) | −26411.5 | −1.43840 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −8406.54 | −0.455863 | ||||||||
\(699\) | 2985.24 | 0.161534 | ||||||||
\(700\) | 5554.79i | 0.299931i | ||||||||
\(701\) | −23434.3 | −1.26263 | −0.631313 | − | 0.775528i | \(-0.717484\pi\) | ||||
−0.631313 | + | 0.775528i | \(0.717484\pi\) | |||||||
\(702\) | 17136.5i | 0.921331i | ||||||||
\(703\) | 28528.0i | 1.53052i | ||||||||
\(704\) | 8976.83i | 0.480578i | ||||||||
\(705\) | −6373.13 | −0.340463 | ||||||||
\(706\) | −16385.4 | −0.873472 | ||||||||
\(707\) | − 20513.4i | − 1.09121i | ||||||||
\(708\) | − 7030.24i | − 0.373182i | ||||||||
\(709\) | 52.1860i | 0.00276430i | 0.999999 | + | 0.00138215i | \(0.000439952\pi\) | ||||
−0.999999 | + | 0.00138215i | \(0.999560\pi\) | |||||||
\(710\) | −4622.70 | −0.244348 | ||||||||
\(711\) | − 2788.74i | − 0.147097i | ||||||||
\(712\) | 13375.0 | 0.704002 | ||||||||
\(713\) | −1034.30 | −0.0543265 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13862.0 | 0.725046 | ||||||||
\(716\) | −18272.3 | −0.953725 | ||||||||
\(717\) | − 1215.98i | − 0.0633354i | ||||||||
\(718\) | 3347.43 | 0.173990 | ||||||||
\(719\) | 2244.80i | 0.116435i | 0.998304 | + | 0.0582175i | \(0.0185417\pi\) | ||||
−0.998304 | + | 0.0582175i | \(0.981458\pi\) | |||||||
\(720\) | − 131.039i | − 0.00678271i | ||||||||
\(721\) | − 8577.23i | − 0.443041i | ||||||||
\(722\) | −860.445 | −0.0443524 | ||||||||
\(723\) | −28824.9 | −1.48272 | ||||||||
\(724\) | 2348.89i | 0.120575i | ||||||||
\(725\) | − 20930.4i | − 1.07219i | ||||||||
\(726\) | 2880.96i | 0.147276i | ||||||||
\(727\) | −2971.90 | −0.151612 | −0.0758059 | − | 0.997123i | \(-0.524153\pi\) | ||||
−0.0758059 | + | 0.997123i | \(0.524153\pi\) | |||||||
\(728\) | 20451.4i | 1.04118i | ||||||||
\(729\) | −21748.2 | −1.10492 | ||||||||
\(730\) | −7472.91 | −0.378883 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −8263.73 | −0.417263 | ||||||||
\(733\) | −31704.8 | −1.59760 | −0.798802 | − | 0.601594i | \(-0.794532\pi\) | ||||
−0.798802 | + | 0.601594i | \(0.794532\pi\) | |||||||
\(734\) | 5898.00i | 0.296593i | ||||||||
\(735\) | 4553.02 | 0.228491 | ||||||||
\(736\) | 5292.50i | 0.265060i | ||||||||
\(737\) | − 20355.9i | − 1.01739i | ||||||||
\(738\) | 405.034i | 0.0202026i | ||||||||
\(739\) | 36985.6 | 1.84105 | 0.920526 | − | 0.390681i | \(-0.127760\pi\) | ||||
0.920526 | + | 0.390681i | \(0.127760\pi\) | |||||||
\(740\) | −12408.0 | −0.616389 | ||||||||
\(741\) | 23384.2i | 1.15930i | ||||||||
\(742\) | 2064.36i | 0.102136i | ||||||||
\(743\) | − 10601.9i | − 0.523481i | −0.965138 | − | 0.261741i | \(-0.915704\pi\) | ||||
0.965138 | − | 0.261741i | \(-0.0842965\pi\) | |||||||
\(744\) | 3551.01 | 0.174981 | ||||||||
\(745\) | 15092.6i | 0.742217i | ||||||||
\(746\) | 4538.63 | 0.222750 | ||||||||
\(747\) | 1113.21 | 0.0545248 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1928.48 | −0.0940789 | ||||||||
\(750\) | 10509.1 | 0.511653 | ||||||||
\(751\) | − 29161.5i | − 1.41694i | −0.705743 | − | 0.708468i | \(-0.749387\pi\) | ||||
0.705743 | − | 0.708468i | \(-0.250613\pi\) | |||||||
\(752\) | −558.765 | −0.0270958 | ||||||||
\(753\) | − 11232.0i | − 0.543583i | ||||||||
\(754\) | − 29969.7i | − 1.44752i | ||||||||
\(755\) | 14526.4i | 0.700225i | ||||||||
\(756\) | −10753.5 | −0.517329 | ||||||||
\(757\) | 34447.9 | 1.65394 | 0.826969 | − | 0.562248i | \(-0.190063\pi\) | ||||
0.826969 | + | 0.562248i | \(0.190063\pi\) | |||||||
\(758\) | − 9521.67i | − 0.456257i | ||||||||
\(759\) | − 3959.96i | − 0.189377i | ||||||||
\(760\) | 12120.1i | 0.578476i | ||||||||
\(761\) | −14414.5 | −0.686632 | −0.343316 | − | 0.939220i | \(-0.611550\pi\) | ||||
−0.343316 | + | 0.939220i | \(0.611550\pi\) | |||||||
\(762\) | − 11421.0i | − 0.542966i | ||||||||
\(763\) | 11426.4 | 0.542156 | ||||||||
\(764\) | 23012.6 | 1.08975 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13357.5 | −0.630058 | ||||||||
\(767\) | 20512.1 | 0.965644 | ||||||||
\(768\) | − 17690.3i | − 0.831175i | ||||||||
\(769\) | −7049.33 | −0.330566 | −0.165283 | − | 0.986246i | \(-0.552854\pi\) | ||||
−0.165283 | + | 0.986246i | \(0.552854\pi\) | |||||||
\(770\) | − 4969.40i | − 0.232578i | ||||||||
\(771\) | − 7565.28i | − 0.353381i | ||||||||
\(772\) | − 14912.3i | − 0.695212i | ||||||||
\(773\) | −26768.3 | −1.24552 | −0.622760 | − | 0.782413i | \(-0.713989\pi\) | ||||
−0.622760 | + | 0.782413i | \(0.713989\pi\) | |||||||
\(774\) | 6384.47 | 0.296492 | ||||||||
\(775\) | 2814.08i | 0.130432i | ||||||||
\(776\) | 995.097i | 0.0460334i | ||||||||
\(777\) | 22067.3i | 1.01887i | ||||||||
\(778\) | −12676.7 | −0.584165 | ||||||||
\(779\) | 2610.29i | 0.120055i | ||||||||
\(780\) | −10170.8 | −0.466889 | ||||||||
\(781\) | 12273.7 | 0.562339 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 40519.0 | 1.84934 | ||||||||
\(784\) | 399.186 | 0.0181845 | ||||||||
\(785\) | 2350.12i | 0.106853i | ||||||||
\(786\) | −21096.1 | −0.957343 | ||||||||
\(787\) | − 26085.5i | − 1.18151i | −0.806851 | − | 0.590755i | \(-0.798830\pi\) | ||||
0.806851 | − | 0.590755i | \(-0.201170\pi\) | |||||||
\(788\) | 9806.68i | 0.443336i | ||||||||
\(789\) | 18994.6i | 0.857065i | ||||||||
\(790\) | −4465.69 | −0.201116 | ||||||||
\(791\) | −8359.95 | −0.375785 | ||||||||
\(792\) | − 4993.30i | − 0.224027i | ||||||||
\(793\) | − 24111.1i | − 1.07971i | ||||||||
\(794\) | − 16270.6i | − 0.727232i | ||||||||
\(795\) | −2639.78 | −0.117765 | ||||||||
\(796\) | − 15715.1i | − 0.699758i | ||||||||
\(797\) | −18108.6 | −0.804818 | −0.402409 | − | 0.915460i | \(-0.631827\pi\) | ||||
−0.402409 | + | 0.915460i | \(0.631827\pi\) | |||||||
\(798\) | 8383.06 | 0.371876 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 14399.6 | 0.636379 | ||||||||
\(801\) | −4344.75 | −0.191653 | ||||||||
\(802\) | − 14775.0i | − 0.650527i | ||||||||
\(803\) | 19841.2 | 0.871958 | ||||||||
\(804\) | 14935.5i | 0.655142i | ||||||||
\(805\) | − 2730.73i | − 0.119560i | ||||||||
\(806\) | 4029.41i | 0.176092i | ||||||||
\(807\) | 35534.1 | 1.55001 | ||||||||
\(808\) | −33006.6 | −1.43709 | ||||||||
\(809\) | − 7304.62i | − 0.317450i | −0.987323 | − | 0.158725i | \(-0.949262\pi\) | ||||
0.987323 | − | 0.158725i | \(-0.0507383\pi\) | |||||||
\(810\) | 5581.38i | 0.242111i | ||||||||
\(811\) | 19511.7i | 0.844817i | 0.906405 | + | 0.422409i | \(0.138815\pi\) | ||||
−0.906405 | + | 0.422409i | \(0.861185\pi\) | |||||||
\(812\) | 18806.6 | 0.812786 | ||||||||
\(813\) | 2107.55i | 0.0909163i | ||||||||
\(814\) | −18820.6 | −0.810395 | ||||||||
\(815\) | −4620.65 | −0.198594 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 41145.5 | 1.76193 | ||||||||
\(818\) | 9003.45 | 0.384839 | ||||||||
\(819\) | − 6643.45i | − 0.283444i | ||||||||
\(820\) | −1135.32 | −0.0483503 | ||||||||
\(821\) | − 29364.3i | − 1.24826i | −0.781320 | − | 0.624131i | \(-0.785453\pi\) | ||||
0.781320 | − | 0.624131i | \(-0.214547\pi\) | |||||||
\(822\) | − 4772.96i | − 0.202526i | ||||||||
\(823\) | 28112.4i | 1.19069i | 0.803470 | + | 0.595345i | \(0.202985\pi\) | ||||
−0.803470 | + | 0.595345i | \(0.797015\pi\) | |||||||
\(824\) | −13801.0 | −0.583472 | ||||||||
\(825\) | −10774.1 | −0.454673 | ||||||||
\(826\) | − 7353.43i | − 0.309756i | ||||||||
\(827\) | 39360.5i | 1.65502i | 0.561453 | + | 0.827509i | \(0.310243\pi\) | ||||
−0.561453 | + | 0.827509i | \(0.689757\pi\) | |||||||
\(828\) | − 1067.12i | − 0.0447885i | ||||||||
\(829\) | 15525.3 | 0.650443 | 0.325221 | − | 0.945638i | \(-0.394561\pi\) | ||||
0.325221 | + | 0.945638i | \(0.394561\pi\) | |||||||
\(830\) | − 1782.61i | − 0.0745485i | ||||||||
\(831\) | −12559.3 | −0.524280 | ||||||||
\(832\) | 19217.3 | 0.800771 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −20114.7 | −0.835151 | ||||||||
\(835\) | 5446.44 | 0.225727 | ||||||||
\(836\) | − 12515.1i | − 0.517756i | ||||||||
\(837\) | −5447.75 | −0.224972 | ||||||||
\(838\) | − 16045.5i | − 0.661433i | ||||||||
\(839\) | − 30007.9i | − 1.23479i | −0.786654 | − | 0.617394i | \(-0.788189\pi\) | ||||
0.786654 | − | 0.617394i | \(-0.211811\pi\) | |||||||
\(840\) | 9375.29i | 0.385093i | ||||||||
\(841\) | −46474.0 | −1.90553 | ||||||||
\(842\) | −13971.1 | −0.571826 | ||||||||
\(843\) | 11101.3i | 0.453556i | ||||||||
\(844\) | 18341.2i | 0.748020i | ||||||||
\(845\) | − 14714.1i | − 0.599029i | ||||||||
\(846\) | −2604.99 | −0.105864 | ||||||||
\(847\) | − 5274.78i | − 0.213983i | ||||||||
\(848\) | −231.443 | −0.00937239 | ||||||||
\(849\) | −10741.0 | −0.434193 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10342.1 | −0.416595 | ||||||||
\(852\) | −9005.44 | −0.362114 | ||||||||
\(853\) | − 4351.43i | − 0.174666i | −0.996179 | − | 0.0873331i | \(-0.972166\pi\) | ||||
0.996179 | − | 0.0873331i | \(-0.0278344\pi\) | |||||||
\(854\) | −8643.62 | −0.346345 | ||||||||
\(855\) | − 3937.09i | − 0.157480i | ||||||||
\(856\) | 3102.98i | 0.123899i | ||||||||
\(857\) | − 25861.5i | − 1.03082i | −0.856944 | − | 0.515410i | \(-0.827640\pi\) | ||||
0.856944 | − | 0.515410i | \(-0.172360\pi\) | |||||||
\(858\) | −15427.2 | −0.613840 | ||||||||
\(859\) | −19084.0 | −0.758017 | −0.379009 | − | 0.925393i | \(-0.623735\pi\) | ||||
−0.379009 | + | 0.925393i | \(0.623735\pi\) | |||||||
\(860\) | 17895.9i | 0.709588i | ||||||||
\(861\) | 2019.14i | 0.0799213i | ||||||||
\(862\) | − 3326.16i | − 0.131426i | ||||||||
\(863\) | 24790.2 | 0.977831 | 0.488916 | − | 0.872331i | \(-0.337393\pi\) | ||||
0.488916 | + | 0.872331i | \(0.337393\pi\) | |||||||
\(864\) | 27876.1i | 1.09765i | ||||||||
\(865\) | −12839.8 | −0.504701 | ||||||||
\(866\) | −19019.9 | −0.746332 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2528.54 | −0.0988757 | ||||||||
\(869\) | 11856.8 | 0.462847 | ||||||||
\(870\) | − 13738.6i | − 0.535383i | ||||||||
\(871\) | −43577.2 | −1.69524 | ||||||||
\(872\) | − 18385.5i | − 0.714003i | ||||||||
\(873\) | − 323.248i | − 0.0125318i | ||||||||
\(874\) | 3928.81i | 0.152053i | ||||||||
\(875\) | −19241.3 | −0.743401 | ||||||||
\(876\) | −14557.9 | −0.561491 | ||||||||
\(877\) | 14394.0i | 0.554219i | 0.960838 | + | 0.277109i | \(0.0893764\pi\) | ||||
−0.960838 | + | 0.277109i | \(0.910624\pi\) | |||||||
\(878\) | 801.839i | 0.0308209i | ||||||||
\(879\) | 29560.9i | 1.13432i | ||||||||
\(880\) | 557.137 | 0.0213421 | ||||||||
\(881\) | − 15328.6i | − 0.586190i | −0.956083 | − | 0.293095i | \(-0.905315\pi\) | ||||
0.956083 | − | 0.293095i | \(-0.0946853\pi\) | |||||||
\(882\) | 1861.02 | 0.0710475 | ||||||||
\(883\) | 8385.90 | 0.319602 | 0.159801 | − | 0.987149i | \(-0.448915\pi\) | ||||
0.159801 | + | 0.987149i | \(0.448915\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9403.11 | 0.357155 | ||||||||
\(886\) | −22397.7 | −0.849283 | ||||||||
\(887\) | 9215.90i | 0.348861i | 0.984669 | + | 0.174430i | \(0.0558084\pi\) | ||||
−0.984669 | + | 0.174430i | \(0.944192\pi\) | |||||||
\(888\) | 35507.0 | 1.34182 | ||||||||
\(889\) | 20910.9i | 0.788897i | ||||||||
\(890\) | 6957.37i | 0.262035i | ||||||||
\(891\) | − 14819.1i | − 0.557191i | ||||||||
\(892\) | −8031.28 | −0.301465 | ||||||||
\(893\) | −16788.1 | −0.629108 | ||||||||
\(894\) | − 16796.8i | − 0.628376i | ||||||||
\(895\) | − 24439.6i | − 0.912765i | ||||||||
\(896\) | 13440.8i | 0.501146i | ||||||||
\(897\) | −8477.36 | −0.315553 | ||||||||
\(898\) | 17793.2i | 0.661211i | ||||||||
\(899\) | 9527.49 | 0.353459 | ||||||||
\(900\) | −2903.37 | −0.107532 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −1722.07 | −0.0635684 | ||||||||
\(903\) | 31827.4 | 1.17292 | ||||||||
\(904\) | 13451.4i | 0.494897i | ||||||||
\(905\) | −3141.70 | −0.115396 | ||||||||
\(906\) | − 16166.6i | − 0.592825i | ||||||||
\(907\) | 7468.98i | 0.273433i | 0.990610 | + | 0.136716i | \(0.0436549\pi\) | ||||
−0.990610 | + | 0.136716i | \(0.956345\pi\) | |||||||
\(908\) | − 21856.8i | − 0.798836i | ||||||||
\(909\) | 10721.9 | 0.391224 | ||||||||
\(910\) | −10638.4 | −0.387536 | ||||||||
\(911\) | 30698.3i | 1.11644i | 0.829692 | + | 0.558222i | \(0.188516\pi\) | ||||
−0.829692 | + | 0.558222i | \(0.811484\pi\) | |||||||
\(912\) | 939.854i | 0.0341246i | ||||||||
\(913\) | 4732.98i | 0.171565i | ||||||||
\(914\) | 432.140 | 0.0156389 | ||||||||
\(915\) | − 11052.9i | − 0.399343i | ||||||||
\(916\) | 2957.55 | 0.106681 | ||||||||
\(917\) | 38625.1 | 1.39096 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24550.8 | −0.881237 | −0.440619 | − | 0.897694i | \(-0.645241\pi\) | ||||
−0.440619 | + | 0.897694i | \(0.645241\pi\) | |||||||
\(920\) | −4393.82 | −0.157457 | ||||||||
\(921\) | − 11159.2i | − 0.399247i | ||||||||
\(922\) | −26537.4 | −0.947898 | ||||||||
\(923\) | − 26275.1i | − 0.937006i | ||||||||
\(924\) | − 9680.86i | − 0.344672i | ||||||||
\(925\) | 28138.3i | 1.00020i | ||||||||
\(926\) | 18296.0 | 0.649293 | ||||||||
\(927\) | 4483.13 | 0.158841 | ||||||||
\(928\) | − 48752.1i | − 1.72453i | ||||||||
\(929\) | − 41655.0i | − 1.47110i | −0.677468 | − | 0.735552i | \(-0.736923\pi\) | ||||
0.677468 | − | 0.735552i | \(-0.263077\pi\) | |||||||
\(930\) | 1847.15i | 0.0651296i | ||||||||
\(931\) | 11993.6 | 0.422206 | ||||||||
\(932\) | 3420.28i | 0.120209i | ||||||||
\(933\) | 15931.5 | 0.559027 | ||||||||
\(934\) | 3343.54 | 0.117135 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10689.5 | −0.373288 | ||||||||
\(937\) | −83.7368 | −0.00291949 | −0.00145975 | − | 0.999999i | \(-0.500465\pi\) | ||||
−0.00145975 | + | 0.999999i | \(0.500465\pi\) | |||||||
\(938\) | 15622.1i | 0.543795i | ||||||||
\(939\) | 11608.6 | 0.403442 | ||||||||
\(940\) | − 7301.88i | − 0.253363i | ||||||||
\(941\) | − 49294.1i | − 1.70770i | −0.520523 | − | 0.853848i | \(-0.674263\pi\) | ||||
0.520523 | − | 0.853848i | \(-0.325737\pi\) | |||||||
\(942\) | − 2615.48i | − 0.0904639i | ||||||||
\(943\) | −946.293 | −0.0326782 | ||||||||
\(944\) | 824.418 | 0.0284243 | ||||||||
\(945\) | − 14383.0i | − 0.495111i | ||||||||
\(946\) | 27144.7i | 0.932927i | ||||||||
\(947\) | 9445.27i | 0.324108i | 0.986782 | + | 0.162054i | \(0.0518118\pi\) | ||||
−0.986782 | + | 0.162054i | \(0.948188\pi\) | |||||||
\(948\) | −8699.57 | −0.298047 | ||||||||
\(949\) | − 42475.5i | − 1.45291i | ||||||||
\(950\) | 10689.3 | 0.365061 | ||||||||
\(951\) | 17347.7 | 0.591521 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41693.4 | 1.41719 | 0.708595 | − | 0.705616i | \(-0.249329\pi\) | ||||
0.708595 | + | 0.705616i | \(0.249329\pi\) | |||||||
\(954\) | −1079.00 | −0.0366183 | ||||||||
\(955\) | 30779.8i | 1.04294i | ||||||||
\(956\) | 1393.18 | 0.0471324 | ||||||||
\(957\) | 36477.3i | 1.23213i | ||||||||
\(958\) | − 7323.60i | − 0.246988i | ||||||||
\(959\) | 8738.88i | 0.294258i | ||||||||
\(960\) | 8809.56 | 0.296174 | ||||||||
\(961\) | 28510.0 | 0.957002 | ||||||||
\(962\) | 40290.6i | 1.35033i | ||||||||
\(963\) | − 1007.97i | − 0.0337295i | ||||||||
\(964\) | − 33025.5i | − 1.10340i | ||||||||
\(965\) | 19945.5 | 0.665355 | ||||||||
\(966\) | 3039.06i | 0.101222i | ||||||||
\(967\) | −32380.0 | −1.07681 | −0.538403 | − | 0.842688i | \(-0.680972\pi\) | ||||
−0.538403 | + | 0.842688i | \(0.680972\pi\) | |||||||
\(968\) | −8487.28 | −0.281809 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −517.626 | −0.0171340 | ||||||||
\(971\) | −5401.25 | −0.178511 | −0.0892556 | − | 0.996009i | \(-0.528449\pi\) | ||||
−0.0892556 | + | 0.996009i | \(0.528449\pi\) | |||||||
\(972\) | − 10051.1i | − 0.331676i | ||||||||
\(973\) | 36828.3 | 1.21342 | ||||||||
\(974\) | 30721.5i | 1.01066i | ||||||||
\(975\) | 23064.8i | 0.757606i | ||||||||
\(976\) | − 969.066i | − 0.0317818i | ||||||||
\(977\) | 25086.2 | 0.821473 | 0.410737 | − | 0.911754i | \(-0.365272\pi\) | ||||
0.410737 | + | 0.911754i | \(0.365272\pi\) | |||||||
\(978\) | 5142.37 | 0.168134 | ||||||||
\(979\) | − 18472.4i | − 0.603045i | ||||||||
\(980\) | 5216.52i | 0.170036i | ||||||||
\(981\) | 5972.35i | 0.194375i | ||||||||
\(982\) | −23421.4 | −0.761108 | ||||||||
\(983\) | 59631.6i | 1.93485i | 0.253166 | + | 0.967423i | \(0.418528\pi\) | ||||
−0.253166 | + | 0.967423i | \(0.581472\pi\) | |||||||
\(984\) | 3248.86 | 0.105254 | ||||||||
\(985\) | −13116.7 | −0.424296 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12986.2 | −0.418799 | ||||||||
\(988\) | −26792.0 | −0.862719 | ||||||||
\(989\) | 14916.2i | 0.479584i | ||||||||
\(990\) | 2597.40 | 0.0833846 | ||||||||
\(991\) | 40063.8i | 1.28423i | 0.766609 | + | 0.642114i | \(0.221942\pi\) | ||||
−0.766609 | + | 0.642114i | \(0.778058\pi\) | |||||||
\(992\) | 6554.70i | 0.209790i | ||||||||
\(993\) | 27711.6i | 0.885601i | ||||||||
\(994\) | −9419.43 | −0.300569 | ||||||||
\(995\) | 21019.3 | 0.669706 | ||||||||
\(996\) | − 3472.68i | − 0.110478i | ||||||||
\(997\) | − 10818.4i | − 0.343652i | −0.985127 | − | 0.171826i | \(-0.945033\pi\) | ||||
0.985127 | − | 0.171826i | \(-0.0549667\pi\) | |||||||
\(998\) | − 13213.5i | − 0.419103i | ||||||||
\(999\) | −54472.8 | −1.72517 |
(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.e.288.8 | 12 | ||
17.4 | even | 4 | 289.4.a.g.1.6 | 12 | |||
17.7 | odd | 16 | 17.4.d.a.2.2 | ✓ | 12 | ||
17.12 | odd | 16 | 17.4.d.a.9.2 | yes | 12 | ||
17.13 | even | 4 | 289.4.a.g.1.5 | 12 | |||
17.16 | even | 2 | inner | 289.4.b.e.288.7 | 12 | ||
51.29 | even | 16 | 153.4.l.a.145.2 | 12 | |||
51.41 | even | 16 | 153.4.l.a.19.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.d.a.2.2 | ✓ | 12 | 17.7 | odd | 16 | ||
17.4.d.a.9.2 | yes | 12 | 17.12 | odd | 16 | ||
153.4.l.a.19.2 | 12 | 51.41 | even | 16 | |||
153.4.l.a.145.2 | 12 | 51.29 | even | 16 | |||
289.4.a.g.1.5 | 12 | 17.13 | even | 4 | |||
289.4.a.g.1.6 | 12 | 17.4 | even | 4 | |||
289.4.b.e.288.7 | 12 | 17.16 | even | 2 | inner | ||
289.4.b.e.288.8 | 12 | 1.1 | even | 1 | trivial |