Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [124,4,Mod(123,124)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(124, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("124.123");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 124 = 2^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 124.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.31623684071\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 123.6 | ||
Character | \(\chi\) | \(=\) | 124.123 |
Dual form | 124.4.d.c.123.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).
\(n\) | \(63\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59794 | − | 1.11835i | −0.918511 | − | 0.395397i | ||||
\(3\) | 8.21784 | 1.58152 | 0.790762 | − | 0.612124i | \(-0.209685\pi\) | ||||
0.790762 | + | 0.612124i | \(0.209685\pi\) | |||||||
\(4\) | 5.49858 | + | 5.81081i | 0.687323 | + | 0.726352i | ||||
\(5\) | 6.37189 | 0.569919 | 0.284960 | − | 0.958540i | \(-0.408020\pi\) | ||||
0.284960 | + | 0.958540i | \(0.408020\pi\) | |||||||
\(6\) | −21.3495 | − | 9.19042i | −1.45265 | − | 0.625329i | ||||
\(7\) | − | 24.3788i | − | 1.31633i | −0.752873 | − | 0.658166i | \(-0.771333\pi\) | ||
0.752873 | − | 0.658166i | \(-0.228667\pi\) | |||||||
\(8\) | −7.78647 | − | 21.2455i | −0.344117 | − | 0.938927i | ||||
\(9\) | 40.5329 | 1.50122 | ||||||||
\(10\) | −16.5538 | − | 7.12601i | −0.523477 | − | 0.225344i | ||||
\(11\) | 4.11924 | 0.112909 | 0.0564544 | − | 0.998405i | \(-0.482020\pi\) | ||||
0.0564544 | + | 0.998405i | \(0.482020\pi\) | |||||||
\(12\) | 45.1865 | + | 47.7523i | 1.08702 | + | 1.14874i | ||||
\(13\) | 3.21970i | 0.0686911i | 0.999410 | + | 0.0343455i | \(0.0109347\pi\) | ||||
−0.999410 | + | 0.0343455i | \(0.989065\pi\) | |||||||
\(14\) | −27.2640 | + | 63.3346i | −0.520473 | + | 1.20906i | ||||
\(15\) | 52.3632 | 0.901341 | ||||||||
\(16\) | −3.53113 | + | 63.9025i | −0.0551738 | + | 0.998477i | ||||
\(17\) | − | 7.66134i | − | 0.109303i | −0.998505 | − | 0.0546514i | \(-0.982595\pi\) | ||
0.998505 | − | 0.0546514i | \(-0.0174047\pi\) | |||||||
\(18\) | −105.302 | − | 45.3300i | −1.37888 | − | 0.593576i | ||||
\(19\) | 53.5148i | 0.646166i | 0.946371 | + | 0.323083i | \(0.104719\pi\) | ||||
−0.946371 | + | 0.323083i | \(0.895281\pi\) | |||||||
\(20\) | 35.0364 | + | 37.0259i | 0.391719 | + | 0.413962i | ||||
\(21\) | − | 200.341i | − | 2.08181i | ||||||
\(22\) | −10.7015 | − | 4.60675i | −0.103708 | − | 0.0446437i | ||||
\(23\) | 134.680 | 1.22099 | 0.610493 | − | 0.792021i | \(-0.290971\pi\) | ||||
0.610493 | + | 0.792021i | \(0.290971\pi\) | |||||||
\(24\) | −63.9879 | − | 174.592i | −0.544228 | − | 1.48494i | ||||
\(25\) | −84.3990 | −0.675192 | ||||||||
\(26\) | 3.60075 | − | 8.36459i | 0.0271602 | − | 0.0630935i | ||||
\(27\) | 111.211 | 0.792688 | ||||||||
\(28\) | 141.661 | − | 134.049i | 0.956119 | − | 0.904745i | ||||
\(29\) | − | 191.200i | − | 1.22431i | −0.790738 | − | 0.612155i | \(-0.790303\pi\) | ||
0.790738 | − | 0.612155i | \(-0.209697\pi\) | |||||||
\(30\) | −136.036 | − | 58.5604i | −0.827891 | − | 0.356387i | ||||
\(31\) | 172.600 | + | 0.266751i | 0.999999 | + | 0.00154548i | ||||
\(32\) | 80.6391 | − | 162.066i | 0.445472 | − | 0.895296i | ||||
\(33\) | 33.8512 | 0.178568 | ||||||||
\(34\) | −8.56806 | + | 19.9037i | −0.0432179 | + | 0.100396i | ||||
\(35\) | − | 155.339i | − | 0.750202i | ||||||
\(36\) | 222.874 | + | 235.529i | 1.03182 | + | 1.09041i | ||||
\(37\) | 342.585i | 1.52218i | 0.648646 | + | 0.761090i | \(0.275335\pi\) | ||||
−0.648646 | + | 0.761090i | \(0.724665\pi\) | |||||||
\(38\) | 59.8483 | − | 139.028i | 0.255492 | − | 0.593510i | ||||
\(39\) | 26.4590i | 0.108637i | ||||||||
\(40\) | −49.6145 | − | 135.374i | −0.196119 | − | 0.535112i | ||||
\(41\) | −368.673 | −1.40432 | −0.702158 | − | 0.712021i | \(-0.747780\pi\) | ||||
−0.702158 | + | 0.712021i | \(0.747780\pi\) | |||||||
\(42\) | −224.051 | + | 520.474i | −0.823140 | + | 1.91216i | ||||
\(43\) | 0.524399 | 0.00185977 | 0.000929886 | − | 1.00000i | \(-0.499704\pi\) | ||||
0.000929886 | 1.00000i | \(0.499704\pi\) | ||||||||
\(44\) | 22.6500 | + | 23.9361i | 0.0776048 | + | 0.0820115i | ||||
\(45\) | 258.271 | 0.855573 | ||||||||
\(46\) | −349.890 | − | 150.619i | −1.12149 | − | 0.482774i | ||||
\(47\) | 521.551i | 1.61864i | 0.587368 | + | 0.809320i | \(0.300164\pi\) | ||||
−0.587368 | + | 0.809320i | \(0.699836\pi\) | |||||||
\(48\) | −29.0182 | + | 525.141i | −0.0872588 | + | 1.57911i | ||||
\(49\) | −251.326 | −0.732727 | ||||||||
\(50\) | 219.264 | + | 94.3877i | 0.620171 | + | 0.266969i | ||||
\(51\) | − | 62.9596i | − | 0.172865i | ||||||
\(52\) | −18.7091 | + | 17.7038i | −0.0498939 | + | 0.0472130i | ||||
\(53\) | − | 679.302i | − | 1.76055i | −0.474461 | − | 0.880276i | \(-0.657357\pi\) | ||
0.474461 | − | 0.880276i | \(-0.342643\pi\) | |||||||
\(54\) | −288.920 | − | 124.373i | −0.728092 | − | 0.313426i | ||||
\(55\) | 26.2473 | 0.0643489 | ||||||||
\(56\) | −517.939 | + | 189.825i | −1.23594 | + | 0.452971i | ||||
\(57\) | 439.776i | 1.02193i | ||||||||
\(58\) | −213.829 | + | 496.727i | −0.484088 | + | 1.12454i | ||||
\(59\) | − | 151.118i | − | 0.333455i | −0.986003 | − | 0.166728i | \(-0.946680\pi\) | ||
0.986003 | − | 0.166728i | \(-0.0533201\pi\) | |||||||
\(60\) | 287.923 | + | 304.273i | 0.619512 | + | 0.654691i | ||||
\(61\) | 622.927i | 1.30750i | 0.756710 | + | 0.653751i | \(0.226806\pi\) | ||||
−0.756710 | + | 0.653751i | \(0.773194\pi\) | |||||||
\(62\) | −448.107 | − | 193.721i | −0.917898 | − | 0.396816i | ||||
\(63\) | − | 988.143i | − | 1.97610i | ||||||
\(64\) | −390.742 | + | 330.855i | −0.763168 | + | 0.646201i | ||||
\(65\) | 20.5156i | 0.0391484i | ||||||||
\(66\) | −87.9435 | − | 37.8575i | −0.164017 | − | 0.0706052i | ||||
\(67\) | 639.069i | 1.16529i | 0.812726 | + | 0.582647i | \(0.197983\pi\) | ||||
−0.812726 | + | 0.582647i | \(0.802017\pi\) | |||||||
\(68\) | 44.5186 | − | 42.1265i | 0.0793923 | − | 0.0751263i | ||||
\(69\) | 1106.78 | 1.93102 | ||||||||
\(70\) | −173.723 | + | 403.561i | −0.296627 | + | 0.689069i | ||||
\(71\) | 406.107i | 0.678817i | 0.940639 | + | 0.339409i | \(0.110227\pi\) | ||||
−0.940639 | + | 0.339409i | \(0.889773\pi\) | |||||||
\(72\) | −315.608 | − | 861.141i | −0.516594 | − | 1.40953i | ||||
\(73\) | 424.285i | 0.680257i | 0.940379 | + | 0.340128i | \(0.110471\pi\) | ||||
−0.940379 | + | 0.340128i | \(0.889529\pi\) | |||||||
\(74\) | 383.130 | − | 890.016i | 0.601865 | − | 1.39814i | ||||
\(75\) | −693.578 | −1.06783 | ||||||||
\(76\) | −310.965 | + | 294.256i | −0.469343 | + | 0.444125i | ||||
\(77\) | − | 100.422i | − | 0.148625i | ||||||
\(78\) | 29.5904 | − | 68.7388i | 0.0429545 | − | 0.0997838i | ||||
\(79\) | −985.028 | −1.40284 | −0.701419 | − | 0.712749i | \(-0.747450\pi\) | ||||
−0.701419 | + | 0.712749i | \(0.747450\pi\) | |||||||
\(80\) | −22.4999 | + | 407.180i | −0.0314446 | + | 0.569051i | ||||
\(81\) | −180.473 | −0.247563 | ||||||||
\(82\) | 957.789 | + | 412.305i | 1.28988 | + | 0.555262i | ||||
\(83\) | 811.239 | 1.07283 | 0.536416 | − | 0.843954i | \(-0.319778\pi\) | ||||
0.536416 | + | 0.843954i | \(0.319778\pi\) | |||||||
\(84\) | 1164.14 | − | 1101.59i | 1.51213 | − | 1.43088i | ||||
\(85\) | − | 48.8172i | − | 0.0622938i | ||||||
\(86\) | −1.36236 | − | 0.586462i | −0.00170822 | − | 0.000735347i | ||||
\(87\) | − | 1571.25i | − | 1.93628i | ||||||
\(88\) | −32.0743 | − | 87.5152i | −0.0388538 | − | 0.106013i | ||||
\(89\) | − | 729.206i | − | 0.868491i | −0.900794 | − | 0.434246i | \(-0.857015\pi\) | ||
0.900794 | − | 0.434246i | \(-0.142985\pi\) | |||||||
\(90\) | −670.973 | − | 288.838i | −0.785853 | − | 0.338291i | ||||
\(91\) | 78.4924 | 0.0904202 | ||||||||
\(92\) | 740.549 | + | 782.600i | 0.839213 | + | 0.886866i | ||||
\(93\) | 1418.40 | + | 2.19212i | 1.58152 | + | 0.00244421i | ||||
\(94\) | 583.277 | − | 1354.96i | 0.640004 | − | 1.48674i | ||||
\(95\) | 340.991i | 0.368262i | ||||||||
\(96\) | 662.679 | − | 1331.83i | 0.704525 | − | 1.41593i | ||||
\(97\) | −453.812 | −0.475027 | −0.237513 | − | 0.971384i | \(-0.576332\pi\) | ||||
−0.237513 | + | 0.971384i | \(0.576332\pi\) | |||||||
\(98\) | 652.929 | + | 281.070i | 0.673018 | + | 0.289718i | ||||
\(99\) | 166.965 | 0.169501 | ||||||||
\(100\) | −464.075 | − | 490.427i | −0.464075 | − | 0.490427i | ||||
\(101\) | −91.5450 | −0.0901888 | −0.0450944 | − | 0.998983i | \(-0.514359\pi\) | ||||
−0.0450944 | + | 0.998983i | \(0.514359\pi\) | |||||||
\(102\) | −70.4109 | + | 163.565i | −0.0683502 | + | 0.158778i | ||||
\(103\) | 150.428i | 0.143904i | 0.997408 | + | 0.0719519i | \(0.0229228\pi\) | ||||
−0.997408 | + | 0.0719519i | \(0.977077\pi\) | |||||||
\(104\) | 68.4041 | − | 25.0701i | 0.0644959 | − | 0.0236377i | ||||
\(105\) | − | 1276.55i | − | 1.18646i | ||||||
\(106\) | −759.697 | + | 1764.79i | −0.696116 | + | 1.61709i | ||||
\(107\) | − | 822.621i | − | 0.743232i | −0.928387 | − | 0.371616i | \(-0.878804\pi\) | ||
0.928387 | − | 0.371616i | \(-0.121196\pi\) | |||||||
\(108\) | 611.503 | + | 646.227i | 0.544833 | + | 0.575770i | ||||
\(109\) | −1101.11 | −0.967588 | −0.483794 | − | 0.875182i | \(-0.660742\pi\) | ||||
−0.483794 | + | 0.875182i | \(0.660742\pi\) | |||||||
\(110\) | −68.1890 | − | 29.3537i | −0.0591051 | − | 0.0254433i | ||||
\(111\) | 2815.31i | 2.40736i | ||||||||
\(112\) | 1557.87 | + | 86.0846i | 1.31433 | + | 0.0726271i | ||||
\(113\) | −1626.67 | −1.35420 | −0.677100 | − | 0.735891i | \(-0.736763\pi\) | ||||
−0.677100 | + | 0.735891i | \(0.736763\pi\) | |||||||
\(114\) | 491.824 | − | 1142.51i | 0.404066 | − | 0.938650i | ||||
\(115\) | 858.166 | 0.695864 | ||||||||
\(116\) | 1111.03 | − | 1051.33i | 0.889280 | − | 0.841497i | ||||
\(117\) | 130.504i | 0.103120i | ||||||||
\(118\) | −169.003 | + | 392.595i | −0.131847 | + | 0.306282i | ||||
\(119\) | −186.774 | −0.143879 | ||||||||
\(120\) | −407.724 | − | 1112.48i | −0.310166 | − | 0.846293i | ||||
\(121\) | −1314.03 | −0.987252 | ||||||||
\(122\) | 696.651 | − | 1618.33i | 0.516982 | − | 1.20095i | ||||
\(123\) | −3029.69 | −2.22096 | ||||||||
\(124\) | 947.508 | + | 1004.42i | 0.686200 | + | 0.727413i | ||||
\(125\) | −1334.27 | −0.954724 | ||||||||
\(126\) | −1105.09 | + | 2567.14i | −0.781343 | + | 1.81507i | ||||
\(127\) | 8.22941 | 0.00574994 | 0.00287497 | − | 0.999996i | \(-0.499085\pi\) | ||||
0.00287497 | + | 0.999996i | \(0.499085\pi\) | |||||||
\(128\) | 1385.14 | − | 422.554i | 0.956483 | − | 0.291788i | ||||
\(129\) | 4.30943 | 0.00294127 | ||||||||
\(130\) | 22.9436 | − | 53.2982i | 0.0154791 | − | 0.0359582i | ||||
\(131\) | 897.000i | 0.598254i | 0.954213 | + | 0.299127i | \(0.0966954\pi\) | ||||
−0.954213 | + | 0.299127i | \(0.903305\pi\) | |||||||
\(132\) | 186.134 | + | 196.703i | 0.122734 | + | 0.129703i | ||||
\(133\) | 1304.63 | 0.850568 | ||||||||
\(134\) | 714.703 | − | 1660.26i | 0.460753 | − | 1.07033i | ||||
\(135\) | 708.625 | 0.451768 | ||||||||
\(136\) | −162.769 | + | 59.6548i | −0.102627 | + | 0.0376129i | ||||
\(137\) | 3027.12i | 1.88777i | 0.330280 | + | 0.943883i | \(0.392857\pi\) | ||||
−0.330280 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(138\) | −2875.34 | − | 1237.77i | −1.77366 | − | 0.763519i | ||||
\(139\) | −1864.92 | −1.13799 | −0.568994 | − | 0.822342i | \(-0.692667\pi\) | ||||
−0.568994 | + | 0.822342i | \(0.692667\pi\) | |||||||
\(140\) | 902.646 | − | 854.145i | 0.544911 | − | 0.515631i | ||||
\(141\) | 4286.02i | 2.55992i | ||||||||
\(142\) | 454.170 | − | 1055.04i | 0.268402 | − | 0.623501i | ||||
\(143\) | 13.2627i | 0.00775583i | ||||||||
\(144\) | −143.127 | + | 2590.15i | −0.0828280 | + | 1.49893i | ||||
\(145\) | − | 1218.31i | − | 0.697758i | ||||||
\(146\) | 474.499 | − | 1102.27i | 0.268971 | − | 0.624823i | ||||
\(147\) | −2065.35 | −1.15883 | ||||||||
\(148\) | −1990.70 | + | 1883.73i | −1.10564 | + | 1.04623i | ||||
\(149\) | 2717.97 | 1.49440 | 0.747199 | − | 0.664601i | \(-0.231398\pi\) | ||||
0.747199 | + | 0.664601i | \(0.231398\pi\) | |||||||
\(150\) | 1801.87 | + | 775.663i | 0.980815 | + | 0.422217i | ||||
\(151\) | 843.042 | 0.454343 | 0.227172 | − | 0.973855i | \(-0.427052\pi\) | ||||
0.227172 | + | 0.973855i | \(0.427052\pi\) | |||||||
\(152\) | 1136.95 | − | 416.692i | 0.606702 | − | 0.222356i | ||||
\(153\) | − | 310.536i | − | 0.164087i | ||||||
\(154\) | −112.307 | + | 260.890i | −0.0587660 | + | 0.136514i | ||||
\(155\) | 1099.79 | + | 1.69971i | 0.569918 | + | 0.000880799i | ||||
\(156\) | −153.748 | + | 145.487i | −0.0789084 | + | 0.0746684i | ||||
\(157\) | 674.043 | 0.342640 | 0.171320 | − | 0.985215i | \(-0.445197\pi\) | ||||
0.171320 | + | 0.985215i | \(0.445197\pi\) | |||||||
\(158\) | 2559.04 | + | 1101.61i | 1.28852 | + | 0.554678i | ||||
\(159\) | − | 5582.39i | − | 2.78436i | ||||||
\(160\) | 513.823 | − | 1032.67i | 0.253883 | − | 0.510246i | ||||
\(161\) | − | 3283.33i | − | 1.60722i | ||||||
\(162\) | 468.859 | + | 201.832i | 0.227389 | + | 0.0978855i | ||||
\(163\) | − | 2780.43i | − | 1.33608i | −0.744127 | − | 0.668038i | \(-0.767134\pi\) | ||
0.744127 | − | 0.668038i | \(-0.232866\pi\) | |||||||
\(164\) | −2027.18 | − | 2142.29i | −0.965219 | − | 1.02003i | ||||
\(165\) | 215.696 | 0.101769 | ||||||||
\(166\) | −2107.55 | − | 907.249i | −0.985407 | − | 0.424194i | ||||
\(167\) | 2616.11 | 1.21222 | 0.606110 | − | 0.795381i | \(-0.292729\pi\) | ||||
0.606110 | + | 0.795381i | \(0.292729\pi\) | |||||||
\(168\) | −4256.34 | + | 1559.95i | −1.95467 | + | 0.716385i | ||||
\(169\) | 2186.63 | 0.995282 | ||||||||
\(170\) | −54.5947 | + | 126.824i | −0.0246307 | + | 0.0572175i | ||||
\(171\) | 2169.11i | 0.970035i | ||||||||
\(172\) | 2.88345 | + | 3.04719i | 0.00127826 | + | 0.00135085i | ||||
\(173\) | 597.428 | 0.262553 | 0.131276 | − | 0.991346i | \(-0.458092\pi\) | ||||
0.131276 | + | 0.991346i | \(0.458092\pi\) | |||||||
\(174\) | −1757.21 | + | 4082.02i | −0.765597 | + | 1.77849i | ||||
\(175\) | 2057.55i | 0.888776i | ||||||||
\(176\) | −14.5455 | + | 263.230i | −0.00622961 | + | 0.112737i | ||||
\(177\) | − | 1241.86i | − | 0.527367i | ||||||
\(178\) | −815.508 | + | 1894.43i | −0.343399 | + | 0.797718i | ||||
\(179\) | −1741.04 | −0.726991 | −0.363496 | − | 0.931596i | \(-0.618417\pi\) | ||||
−0.363496 | + | 0.931596i | \(0.618417\pi\) | |||||||
\(180\) | 1420.13 | + | 1500.77i | 0.588055 | + | 0.621447i | ||||
\(181\) | − | 2109.76i | − | 0.866395i | −0.901299 | − | 0.433197i | \(-0.857385\pi\) | ||
0.901299 | − | 0.433197i | \(-0.142615\pi\) | |||||||
\(182\) | −203.918 | − | 87.7820i | −0.0830519 | − | 0.0357518i | ||||
\(183\) | 5119.12i | 2.06785i | ||||||||
\(184\) | −1048.68 | − | 2861.34i | −0.420162 | − | 1.14642i | ||||
\(185\) | 2182.91i | 0.867519i | ||||||||
\(186\) | −3682.47 | − | 1591.97i | −1.45168 | − | 0.627573i | ||||
\(187\) | − | 31.5589i | − | 0.0123412i | ||||||
\(188\) | −3030.64 | + | 2867.79i | −1.17570 | + | 1.11253i | ||||
\(189\) | − | 2711.19i | − | 1.04344i | ||||||
\(190\) | 381.347 | − | 885.873i | 0.145610 | − | 0.338253i | ||||
\(191\) | − | 3518.47i | − | 1.33292i | −0.745541 | − | 0.666460i | \(-0.767809\pi\) | ||
0.745541 | − | 0.666460i | \(-0.232191\pi\) | |||||||
\(192\) | −3211.05 | + | 2718.91i | −1.20697 | + | 1.02198i | ||||
\(193\) | −208.681 | −0.0778301 | −0.0389150 | − | 0.999243i | \(-0.512390\pi\) | ||||
−0.0389150 | + | 0.999243i | \(0.512390\pi\) | |||||||
\(194\) | 1178.98 | + | 507.521i | 0.436317 | + | 0.187824i | ||||
\(195\) | 168.594i | 0.0619141i | ||||||||
\(196\) | −1381.93 | − | 1460.41i | −0.503621 | − | 0.532218i | ||||
\(197\) | − | 1942.13i | − | 0.702392i | −0.936302 | − | 0.351196i | \(-0.885775\pi\) | ||
0.936302 | − | 0.351196i | \(-0.114225\pi\) | |||||||
\(198\) | −433.764 | − | 186.725i | −0.155688 | − | 0.0670200i | ||||
\(199\) | 3686.68 | 1.31328 | 0.656638 | − | 0.754206i | \(-0.271978\pi\) | ||||
0.656638 | + | 0.754206i | \(0.271978\pi\) | |||||||
\(200\) | 657.170 | + | 1793.10i | 0.232345 | + | 0.633956i | ||||
\(201\) | 5251.76i | 1.84294i | ||||||||
\(202\) | 237.828 | + | 102.379i | 0.0828393 | + | 0.0356603i | ||||
\(203\) | −4661.23 | −1.61160 | ||||||||
\(204\) | 365.847 | − | 346.189i | 0.125561 | − | 0.118814i | ||||
\(205\) | −2349.14 | −0.800347 | ||||||||
\(206\) | 168.231 | − | 390.802i | 0.0568991 | − | 0.132177i | ||||
\(207\) | 5458.96 | 1.83297 | ||||||||
\(208\) | −205.747 | − | 11.3692i | −0.0685864 | − | 0.00378995i | ||||
\(209\) | 220.440i | 0.0729578i | ||||||||
\(210\) | −1427.63 | + | 3316.40i | −0.469123 | + | 1.08978i | ||||
\(211\) | − | 2817.07i | − | 0.919123i | −0.888146 | − | 0.459562i | \(-0.848007\pi\) | ||
0.888146 | − | 0.459562i | \(-0.151993\pi\) | |||||||
\(212\) | 3947.30 | − | 3735.20i | 1.27878 | − | 1.21007i | ||||
\(213\) | 3337.32i | 1.07357i | ||||||||
\(214\) | −919.979 | + | 2137.12i | −0.293871 | + | 0.682666i | ||||
\(215\) | 3.34142 | 0.00105992 | ||||||||
\(216\) | −865.941 | − | 2362.73i | −0.272777 | − | 0.744276i | ||||
\(217\) | 6.50307 | − | 4207.79i | 0.00203436 | − | 1.31633i | ||||
\(218\) | 2860.62 | + | 1231.43i | 0.888740 | + | 0.382581i | ||||
\(219\) | 3486.70i | 1.07584i | ||||||||
\(220\) | 144.323 | + | 152.518i | 0.0442285 | + | 0.0467399i | ||||
\(221\) | 24.6672 | 0.00750813 | ||||||||
\(222\) | 3148.50 | − | 7314.01i | 0.951863 | − | 2.21119i | ||||
\(223\) | 6236.78 | 1.87285 | 0.936425 | − | 0.350868i | \(-0.114113\pi\) | ||||
0.936425 | + | 0.350868i | \(0.114113\pi\) | |||||||
\(224\) | −3950.97 | − | 1965.88i | −1.17851 | − | 0.586389i | ||||
\(225\) | −3420.94 | −1.01361 | ||||||||
\(226\) | 4226.00 | + | 1819.19i | 1.24385 | + | 0.535446i | ||||
\(227\) | 492.860i | 0.144107i | 0.997401 | + | 0.0720534i | \(0.0229552\pi\) | ||||
−0.997401 | + | 0.0720534i | \(0.977045\pi\) | |||||||
\(228\) | −2555.46 | + | 2418.15i | −0.742278 | + | 0.702394i | ||||
\(229\) | − | 495.691i | − | 0.143040i | −0.997439 | − | 0.0715201i | \(-0.977215\pi\) | ||
0.997439 | − | 0.0715201i | \(-0.0227850\pi\) | |||||||
\(230\) | −2229.46 | − | 959.730i | −0.639158 | − | 0.275142i | ||||
\(231\) | − | 825.252i | − | 0.235055i | ||||||
\(232\) | −4062.14 | + | 1488.77i | −1.14954 | + | 0.421305i | ||||
\(233\) | 3120.86 | 0.877486 | 0.438743 | − | 0.898612i | \(-0.355424\pi\) | ||||
0.438743 | + | 0.898612i | \(0.355424\pi\) | |||||||
\(234\) | 145.949 | − | 339.041i | 0.0407734 | − | 0.0947170i | ||||
\(235\) | 3323.27i | 0.922494i | ||||||||
\(236\) | 878.117 | − | 830.934i | 0.242206 | − | 0.229191i | ||||
\(237\) | −8094.80 | −2.21862 | ||||||||
\(238\) | 485.228 | + | 208.879i | 0.132154 | + | 0.0568891i | ||||
\(239\) | 4611.23 | 1.24802 | 0.624008 | − | 0.781418i | \(-0.285503\pi\) | ||||
0.624008 | + | 0.781418i | \(0.285503\pi\) | |||||||
\(240\) | −184.901 | + | 3346.14i | −0.0497304 | + | 0.899968i | ||||
\(241\) | 3920.07i | 1.04778i | 0.851787 | + | 0.523888i | \(0.175519\pi\) | ||||
−0.851787 | + | 0.523888i | \(0.824481\pi\) | |||||||
\(242\) | 3413.78 | + | 1469.55i | 0.906801 | + | 0.390356i | ||||
\(243\) | −4485.80 | −1.18421 | ||||||||
\(244\) | −3619.71 | + | 3425.22i | −0.949707 | + | 0.898677i | ||||
\(245\) | −1601.42 | −0.417595 | ||||||||
\(246\) | 7870.96 | + | 3388.26i | 2.03998 | + | 0.878160i | ||||
\(247\) | −172.302 | −0.0443858 | ||||||||
\(248\) | −1338.28 | − | 3669.06i | −0.342665 | − | 0.939458i | ||||
\(249\) | 6666.63 | 1.69671 | ||||||||
\(250\) | 3466.35 | + | 1492.18i | 0.876924 | + | 0.377495i | ||||
\(251\) | −932.359 | −0.234462 | −0.117231 | − | 0.993105i | \(-0.537402\pi\) | ||||
−0.117231 | + | 0.993105i | \(0.537402\pi\) | |||||||
\(252\) | 5741.91 | − | 5433.39i | 1.43534 | − | 1.35822i | ||||
\(253\) | 554.778 | 0.137860 | ||||||||
\(254\) | −21.3795 | − | 9.20336i | −0.00528138 | − | 0.00227351i | ||||
\(255\) | − | 401.172i | − | 0.0985191i | ||||||
\(256\) | −4071.06 | − | 451.296i | −0.993912 | − | 0.110180i | ||||
\(257\) | −2870.10 | −0.696621 | −0.348311 | − | 0.937379i | \(-0.613245\pi\) | ||||
−0.348311 | + | 0.937379i | \(0.613245\pi\) | |||||||
\(258\) | −11.1956 | − | 4.81945i | −0.00270159 | − | 0.00116297i | ||||
\(259\) | 8351.81 | 2.00369 | ||||||||
\(260\) | −119.212 | + | 112.807i | −0.0284355 | + | 0.0269076i | ||||
\(261\) | − | 7749.90i | − | 1.83796i | ||||||
\(262\) | 1003.16 | − | 2330.35i | 0.236548 | − | 0.549503i | ||||
\(263\) | −7122.00 | −1.66982 | −0.834908 | − | 0.550390i | \(-0.814479\pi\) | ||||
−0.834908 | + | 0.550390i | \(0.814479\pi\) | |||||||
\(264\) | −263.582 | − | 719.186i | −0.0614482 | − | 0.167662i | ||||
\(265\) | − | 4328.44i | − | 1.00337i | ||||||
\(266\) | −3389.34 | − | 1459.03i | −0.781255 | − | 0.336312i | ||||
\(267\) | − | 5992.50i | − | 1.37354i | ||||||
\(268\) | −3713.51 | + | 3513.97i | −0.846413 | + | 0.800933i | ||||
\(269\) | − | 8156.73i | − | 1.84879i | −0.381435 | − | 0.924396i | \(-0.624570\pi\) | ||
0.381435 | − | 0.924396i | \(-0.375430\pi\) | |||||||
\(270\) | −1840.96 | − | 792.491i | −0.414954 | − | 0.178628i | ||||
\(271\) | −156.738 | −0.0351334 | −0.0175667 | − | 0.999846i | \(-0.505592\pi\) | ||||
−0.0175667 | + | 0.999846i | \(0.505592\pi\) | |||||||
\(272\) | 489.579 | + | 27.0532i | 0.109136 | + | 0.00603066i | ||||
\(273\) | 645.038 | 0.143002 | ||||||||
\(274\) | 3385.38 | − | 7864.27i | 0.746416 | − | 1.73393i | ||||
\(275\) | −347.660 | −0.0762351 | ||||||||
\(276\) | 6085.71 | + | 6431.28i | 1.32723 | + | 1.40260i | ||||
\(277\) | 2551.02i | 0.553343i | 0.960965 | + | 0.276671i | \(0.0892314\pi\) | ||||
−0.960965 | + | 0.276671i | \(0.910769\pi\) | |||||||
\(278\) | 4844.95 | + | 2085.63i | 1.04525 | + | 0.449957i | ||||
\(279\) | 6996.00 | + | 10.8122i | 1.50122 | + | 0.00232010i | ||||
\(280\) | −3300.25 | + | 1209.54i | −0.704385 | + | 0.258157i | ||||
\(281\) | 1291.63 | 0.274207 | 0.137104 | − | 0.990557i | \(-0.456221\pi\) | ||||
0.137104 | + | 0.990557i | \(0.456221\pi\) | |||||||
\(282\) | 4793.28 | − | 11134.8i | 1.01218 | − | 2.35131i | ||||
\(283\) | − | 3764.73i | − | 0.790778i | −0.918514 | − | 0.395389i | \(-0.870610\pi\) | ||
0.918514 | − | 0.395389i | \(-0.129390\pi\) | |||||||
\(284\) | −2359.81 | + | 2233.01i | −0.493060 | + | 0.466567i | ||||
\(285\) | 2802.21i | 0.582415i | ||||||||
\(286\) | 14.8324 | − | 34.4557i | 0.00306663 | − | 0.00712381i | ||||
\(287\) | 8987.79i | 1.84855i | ||||||||
\(288\) | 3268.53 | − | 6569.00i | 0.668751 | − | 1.34403i | ||||
\(289\) | 4854.30 | 0.988053 | ||||||||
\(290\) | −1362.49 | + | 3165.09i | −0.275891 | + | 0.640898i | ||||
\(291\) | −3729.35 | −0.751266 | ||||||||
\(292\) | −2465.44 | + | 2332.96i | −0.494106 | + | 0.467556i | ||||
\(293\) | −3704.15 | −0.738562 | −0.369281 | − | 0.929318i | \(-0.620396\pi\) | ||||
−0.369281 | + | 0.929318i | \(0.620396\pi\) | |||||||
\(294\) | 5365.66 | + | 2309.79i | 1.06439 | + | 0.458196i | ||||
\(295\) | − | 962.906i | − | 0.190043i | ||||||
\(296\) | 7278.39 | − | 2667.53i | 1.42922 | − | 0.523807i | ||||
\(297\) | 458.105 | 0.0895015 | ||||||||
\(298\) | −7061.13 | − | 3039.65i | −1.37262 | − | 0.590879i | ||||
\(299\) | 433.629i | 0.0838709i | ||||||||
\(300\) | −3813.70 | − | 4030.25i | −0.733946 | − | 0.775622i | ||||
\(301\) | − | 12.7842i | − | 0.00244807i | ||||||
\(302\) | −2190.17 | − | 942.817i | −0.417319 | − | 0.179646i | ||||
\(303\) | −752.302 | −0.142636 | ||||||||
\(304\) | −3419.73 | − | 188.968i | −0.645181 | − | 0.0356514i | ||||
\(305\) | 3969.22i | 0.745171i | ||||||||
\(306\) | −347.288 | + | 806.754i | −0.0648796 | + | 0.150716i | ||||
\(307\) | 8943.10i | 1.66257i | 0.555845 | + | 0.831286i | \(0.312395\pi\) | ||||
−0.555845 | + | 0.831286i | \(0.687605\pi\) | |||||||
\(308\) | 583.534 | − | 552.179i | 0.107954 | − | 0.102154i | ||||
\(309\) | 1236.19i | 0.227587i | ||||||||
\(310\) | −2855.29 | − | 1234.37i | −0.523128 | − | 0.226153i | ||||
\(311\) | − | 6079.45i | − | 1.10847i | −0.832360 | − | 0.554235i | \(-0.813011\pi\) | ||
0.832360 | − | 0.554235i | \(-0.186989\pi\) | |||||||
\(312\) | 562.134 | − | 206.022i | 0.102002 | − | 0.0373836i | ||||
\(313\) | 5292.00i | 0.955660i | 0.878452 | + | 0.477830i | \(0.158577\pi\) | ||||
−0.878452 | + | 0.477830i | \(0.841423\pi\) | |||||||
\(314\) | −1751.12 | − | 753.816i | −0.314718 | − | 0.135479i | ||||
\(315\) | − | 6296.34i | − | 1.12622i | ||||||
\(316\) | −5416.26 | − | 5723.81i | −0.964204 | − | 1.01895i | ||||
\(317\) | −2198.06 | −0.389450 | −0.194725 | − | 0.980858i | \(-0.562381\pi\) | ||||
−0.194725 | + | 0.980858i | \(0.562381\pi\) | |||||||
\(318\) | −6243.07 | + | 14502.7i | −1.10092 | + | 2.55746i | ||||
\(319\) | − | 787.599i | − | 0.138235i | ||||||
\(320\) | −2489.76 | + | 2108.17i | −0.434944 | + | 0.368282i | ||||
\(321\) | − | 6760.17i | − | 1.17544i | ||||||
\(322\) | −3671.92 | + | 8529.90i | −0.635490 | + | 1.47625i | ||||
\(323\) | 409.995 | 0.0706277 | ||||||||
\(324\) | −992.347 | − | 1048.70i | −0.170156 | − | 0.179818i | ||||
\(325\) | − | 271.739i | − | 0.0463797i | ||||||
\(326\) | −3109.50 | + | 7223.40i | −0.528280 | + | 1.22720i | ||||
\(327\) | −9048.74 | −1.53026 | ||||||||
\(328\) | 2870.66 | + | 7832.63i | 0.483249 | + | 1.31855i | ||||
\(329\) | 12714.8 | 2.13067 | ||||||||
\(330\) | −560.366 | − | 241.224i | −0.0934762 | − | 0.0402392i | ||||
\(331\) | 5474.89 | 0.909145 | 0.454572 | − | 0.890710i | \(-0.349792\pi\) | ||||
0.454572 | + | 0.890710i | \(0.349792\pi\) | |||||||
\(332\) | 4460.67 | + | 4713.96i | 0.737382 | + | 0.779253i | ||||
\(333\) | 13886.0i | 2.28512i | ||||||||
\(334\) | −6796.49 | − | 2925.73i | −1.11344 | − | 0.479307i | ||||
\(335\) | 4072.08i | 0.664123i | ||||||||
\(336\) | 12802.3 | + | 707.429i | 2.07864 | + | 0.114861i | ||||
\(337\) | − | 6373.90i | − | 1.03029i | −0.857102 | − | 0.515146i | \(-0.827738\pi\) | ||
0.857102 | − | 0.515146i | \(-0.172262\pi\) | |||||||
\(338\) | −5680.74 | − | 2445.42i | −0.914177 | − | 0.393531i | ||||
\(339\) | −13367.7 | −2.14170 | ||||||||
\(340\) | 283.668 | − | 268.426i | 0.0452472 | − | 0.0428159i | ||||
\(341\) | 710.982 | + | 1.09881i | 0.112909 | + | 0.000174498i | ||||
\(342\) | 2425.83 | − | 5635.22i | 0.383549 | − | 0.890988i | ||||
\(343\) | − | 2234.91i | − | 0.351819i | ||||||
\(344\) | −4.08322 | − | 11.1411i | −0.000639978 | − | 0.00174619i | ||||
\(345\) | 7052.27 | 1.10053 | ||||||||
\(346\) | −1552.08 | − | 668.134i | −0.241158 | − | 0.103812i | ||||
\(347\) | 5249.23 | 0.812085 | 0.406043 | − | 0.913854i | \(-0.366908\pi\) | ||||
0.406043 | + | 0.913854i | \(0.366908\pi\) | |||||||
\(348\) | 9130.26 | − | 8639.67i | 1.40642 | − | 1.33085i | ||||
\(349\) | −6385.22 | −0.979350 | −0.489675 | − | 0.871905i | \(-0.662884\pi\) | ||||
−0.489675 | + | 0.871905i | \(0.662884\pi\) | |||||||
\(350\) | 2301.06 | − | 5345.38i | 0.351419 | − | 0.816350i | ||||
\(351\) | 358.066i | 0.0544506i | ||||||||
\(352\) | 332.171 | − | 667.588i | 0.0502977 | − | 0.101087i | ||||
\(353\) | 11832.1i | 1.78403i | 0.452008 | + | 0.892014i | \(0.350708\pi\) | ||||
−0.452008 | + | 0.892014i | \(0.649292\pi\) | |||||||
\(354\) | −1388.84 | + | 3226.28i | −0.208519 | + | 0.484392i | ||||
\(355\) | 2587.67i | 0.386871i | ||||||||
\(356\) | 4237.28 | − | 4009.60i | 0.630830 | − | 0.596934i | ||||
\(357\) | −1534.88 | −0.227548 | ||||||||
\(358\) | 4523.12 | + | 1947.09i | 0.667749 | + | 0.287450i | ||||
\(359\) | − | 7973.37i | − | 1.17220i | −0.810240 | − | 0.586098i | \(-0.800663\pi\) | ||
0.810240 | − | 0.586098i | \(-0.199337\pi\) | |||||||
\(360\) | −2011.02 | − | 5487.10i | −0.294417 | − | 0.803320i | ||||
\(361\) | 3995.16 | 0.582470 | ||||||||
\(362\) | −2359.45 | + | 5481.04i | −0.342569 | + | 0.795793i | ||||
\(363\) | −10798.5 | −1.56136 | ||||||||
\(364\) | 431.597 | + | 456.105i | 0.0621479 | + | 0.0656769i | ||||
\(365\) | 2703.49i | 0.387691i | ||||||||
\(366\) | 5724.96 | − | 13299.2i | 0.817619 | − | 1.89934i | ||||
\(367\) | −7390.19 | −1.05113 | −0.525565 | − | 0.850753i | \(-0.676146\pi\) | ||||
−0.525565 | + | 0.850753i | \(0.676146\pi\) | |||||||
\(368\) | −475.572 | + | 8606.38i | −0.0673666 | + | 1.21913i | ||||
\(369\) | −14943.4 | −2.10819 | ||||||||
\(370\) | 2441.26 | − | 5671.08i | 0.343014 | − | 0.796826i | ||||
\(371\) | −16560.6 | −2.31747 | ||||||||
\(372\) | 7786.47 | + | 8254.13i | 1.08524 | + | 1.15042i | ||||
\(373\) | 10312.0 | 1.43147 | 0.715734 | − | 0.698373i | \(-0.246092\pi\) | ||||
0.715734 | + | 0.698373i | \(0.246092\pi\) | |||||||
\(374\) | −35.2939 | + | 81.9880i | −0.00487969 | + | 0.0113356i | ||||
\(375\) | −10964.8 | −1.50992 | ||||||||
\(376\) | 11080.6 | − | 4061.04i | 1.51978 | − | 0.557001i | ||||
\(377\) | 615.607 | 0.0840992 | ||||||||
\(378\) | −3032.06 | + | 7043.51i | −0.412573 | + | 0.958411i | ||||
\(379\) | − | 6741.72i | − | 0.913718i | −0.889539 | − | 0.456859i | \(-0.848974\pi\) | ||
0.889539 | − | 0.456859i | \(-0.151026\pi\) | |||||||
\(380\) | −1981.43 | + | 1874.97i | −0.267488 | + | 0.253115i | ||||
\(381\) | 67.6280 | 0.00909366 | ||||||||
\(382\) | −3934.89 | + | 9140.78i | −0.527032 | + | 1.22430i | ||||
\(383\) | 4966.24 | 0.662567 | 0.331284 | − | 0.943531i | \(-0.392518\pi\) | ||||
0.331284 | + | 0.943531i | \(0.392518\pi\) | |||||||
\(384\) | 11382.8 | − | 3472.48i | 1.51270 | − | 0.461470i | ||||
\(385\) | − | 639.878i | − | 0.0847044i | ||||||
\(386\) | 542.141 | + | 233.379i | 0.0714877 | + | 0.0307737i | ||||
\(387\) | 21.2554 | 0.00279192 | ||||||||
\(388\) | −2495.32 | − | 2637.02i | −0.326497 | − | 0.345037i | ||||
\(389\) | 7562.25i | 0.985659i | 0.870126 | + | 0.492829i | \(0.164037\pi\) | ||||
−0.870126 | + | 0.492829i | \(0.835963\pi\) | |||||||
\(390\) | 188.547 | − | 437.996i | 0.0244806 | − | 0.0568687i | ||||
\(391\) | − | 1031.83i | − | 0.133457i | ||||||
\(392\) | 1956.94 | + | 5339.53i | 0.252144 | + | 0.687978i | ||||
\(393\) | 7371.41i | 0.946153i | ||||||||
\(394\) | −2171.99 | + | 5045.55i | −0.277723 | + | 0.645155i | ||||
\(395\) | −6276.49 | −0.799505 | ||||||||
\(396\) | 918.069 | + | 970.200i | 0.116502 | + | 0.123117i | ||||
\(397\) | −15118.7 | −1.91130 | −0.955652 | − | 0.294500i | \(-0.904847\pi\) | ||||
−0.955652 | + | 0.294500i | \(0.904847\pi\) | |||||||
\(398\) | −9577.78 | − | 4123.00i | −1.20626 | − | 0.519265i | ||||
\(399\) | 10721.2 | 1.34519 | ||||||||
\(400\) | 298.024 | − | 5393.31i | 0.0372529 | − | 0.674164i | ||||
\(401\) | − | 2660.11i | − | 0.331271i | −0.986187 | − | 0.165635i | \(-0.947032\pi\) | ||
0.986187 | − | 0.165635i | \(-0.0529675\pi\) | |||||||
\(402\) | 5873.31 | − | 13643.8i | 0.728692 | − | 1.69276i | ||||
\(403\) | −0.858858 | + | 555.722i | −0.000106161 | + | 0.0686910i | ||||
\(404\) | −503.368 | − | 531.951i | −0.0619888 | − | 0.0655088i | ||||
\(405\) | −1149.96 | −0.141091 | ||||||||
\(406\) | 12109.6 | + | 5212.89i | 1.48027 | + | 0.637220i | ||||
\(407\) | 1411.19i | 0.171867i | ||||||||
\(408\) | −1337.61 | + | 490.233i | −0.162308 | + | 0.0594857i | ||||
\(409\) | − | 10763.0i | − | 1.30121i | −0.759417 | − | 0.650604i | \(-0.774516\pi\) | ||
0.759417 | − | 0.650604i | \(-0.225484\pi\) | |||||||
\(410\) | 6102.93 | + | 2627.16i | 0.735127 | + | 0.316454i | ||||
\(411\) | 24876.4i | 2.98555i | ||||||||
\(412\) | −874.108 | + | 827.140i | −0.104525 | + | 0.0989084i | ||||
\(413\) | −3684.07 | −0.438937 | ||||||||
\(414\) | −14182.1 | − | 6105.04i | −1.68360 | − | 0.724749i | ||||
\(415\) | 5169.13 | 0.611427 | ||||||||
\(416\) | 521.803 | + | 259.633i | 0.0614988 | + | 0.0306000i | ||||
\(417\) | −15325.6 | −1.79976 | ||||||||
\(418\) | 246.529 | − | 572.691i | 0.0288473 | − | 0.0670125i | ||||
\(419\) | 6632.28i | 0.773289i | 0.922229 | + | 0.386645i | \(0.126366\pi\) | ||||
−0.922229 | + | 0.386645i | \(0.873634\pi\) | |||||||
\(420\) | 7417.80 | − | 7019.22i | 0.861789 | − | 0.815483i | ||||
\(421\) | 6926.28 | 0.801820 | 0.400910 | − | 0.916117i | \(-0.368694\pi\) | ||||
0.400910 | + | 0.916117i | \(0.368694\pi\) | |||||||
\(422\) | −3150.47 | + | 7318.58i | −0.363418 | + | 0.844224i | ||||
\(423\) | 21140.0i | 2.42993i | ||||||||
\(424\) | −14432.1 | + | 5289.36i | −1.65303 | + | 0.605835i | ||||
\(425\) | 646.609i | 0.0738004i | ||||||||
\(426\) | 3732.29 | − | 8670.16i | 0.424484 | − | 0.986081i | ||||
\(427\) | 15186.2 | 1.72111 | ||||||||
\(428\) | 4780.10 | − | 4523.25i | 0.539848 | − | 0.510840i | ||||
\(429\) | 108.991i | 0.0122660i | ||||||||
\(430\) | −8.68080 | − | 3.73687i | −0.000973547 | − | 0.000419088i | ||||
\(431\) | − | 13596.8i | − | 1.51957i | −0.650173 | − | 0.759786i | \(-0.725304\pi\) | ||
0.650173 | − | 0.759786i | \(-0.274696\pi\) | |||||||
\(432\) | −392.700 | + | 7106.67i | −0.0437357 | + | 0.791481i | ||||
\(433\) | 4322.71i | 0.479760i | 0.970803 | + | 0.239880i | \(0.0771081\pi\) | ||||
−0.970803 | + | 0.239880i | \(0.922892\pi\) | |||||||
\(434\) | −4722.68 | + | 10924.3i | −0.522341 | + | 1.20826i | ||||
\(435\) | − | 10011.9i | − | 1.10352i | ||||||
\(436\) | −6054.54 | − | 6398.34i | −0.665046 | − | 0.702810i | ||||
\(437\) | 7207.37i | 0.788960i | ||||||||
\(438\) | 3899.35 | − | 9058.24i | 0.425384 | − | 0.988173i | ||||
\(439\) | − | 3573.81i | − | 0.388539i | −0.980948 | − | 0.194269i | \(-0.937766\pi\) | ||
0.980948 | − | 0.194269i | \(-0.0622336\pi\) | |||||||
\(440\) | −204.374 | − | 557.637i | −0.0221435 | − | 0.0604189i | ||||
\(441\) | −10186.9 | −1.09998 | ||||||||
\(442\) | −64.0839 | − | 27.5866i | −0.00689629 | − | 0.00296869i | ||||
\(443\) | − | 9881.07i | − | 1.05974i | −0.848080 | − | 0.529869i | \(-0.822241\pi\) | ||
0.848080 | − | 0.529869i | \(-0.177759\pi\) | |||||||
\(444\) | −16359.2 | + | 15480.2i | −1.74859 | + | 1.65464i | ||||
\(445\) | − | 4646.42i | − | 0.494970i | ||||||
\(446\) | −16202.8 | − | 6974.90i | −1.72023 | − | 0.740519i | ||||
\(447\) | 22335.9 | 2.36342 | ||||||||
\(448\) | 8065.84 | + | 9525.81i | 0.850614 | + | 1.00458i | ||||
\(449\) | 3376.75i | 0.354920i | 0.984128 | + | 0.177460i | \(0.0567880\pi\) | ||||
−0.984128 | + | 0.177460i | \(0.943212\pi\) | |||||||
\(450\) | 8887.39 | + | 3825.80i | 0.931012 | + | 0.400778i | ||||
\(451\) | −1518.65 | −0.158560 | ||||||||
\(452\) | −8944.40 | − | 9452.29i | −0.930772 | − | 0.983625i | ||||
\(453\) | 6927.99 | 0.718555 | ||||||||
\(454\) | 551.190 | − | 1280.42i | 0.0569794 | − | 0.132364i | ||||
\(455\) | 500.145 | 0.0515322 | ||||||||
\(456\) | 9343.26 | − | 3424.30i | 0.959514 | − | 0.351662i | ||||
\(457\) | − | 18986.2i | − | 1.94341i | −0.236199 | − | 0.971705i | \(-0.575902\pi\) | ||
0.236199 | − | 0.971705i | \(-0.424098\pi\) | |||||||
\(458\) | −554.357 | + | 1287.78i | −0.0565576 | + | 0.131384i | ||||
\(459\) | − | 852.025i | − | 0.0866430i | ||||||
\(460\) | 4718.70 | + | 4986.64i | 0.478283 | + | 0.505442i | ||||
\(461\) | − | 4730.38i | − | 0.477908i | −0.971031 | − | 0.238954i | \(-0.923195\pi\) | ||
0.971031 | − | 0.238954i | \(-0.0768045\pi\) | |||||||
\(462\) | −922.921 | + | 2143.96i | −0.0929398 | + | 0.215900i | ||||
\(463\) | 5068.16 | 0.508720 | 0.254360 | − | 0.967110i | \(-0.418135\pi\) | ||||
0.254360 | + | 0.967110i | \(0.418135\pi\) | |||||||
\(464\) | 12218.2 | + | 675.152i | 1.22245 | + | 0.0675499i | ||||
\(465\) | 9037.91 | + | 13.9679i | 0.901340 | + | 0.00139300i | ||||
\(466\) | −8107.81 | − | 3490.21i | −0.805980 | − | 0.346955i | ||||
\(467\) | 3333.36i | 0.330298i | 0.986269 | + | 0.165149i | \(0.0528106\pi\) | ||||
−0.986269 | + | 0.165149i | \(0.947189\pi\) | |||||||
\(468\) | −758.333 | + | 717.586i | −0.0749016 | + | 0.0708769i | ||||
\(469\) | 15579.7 | 1.53391 | ||||||||
\(470\) | 3716.58 | − | 8633.65i | 0.364751 | − | 0.847320i | ||||
\(471\) | 5539.18 | 0.541893 | ||||||||
\(472\) | −3210.57 | + | 1176.67i | −0.313090 | + | 0.114747i | ||||
\(473\) | 2.16013 | 0.000209985 | ||||||||
\(474\) | 21029.8 | + | 9052.82i | 2.03783 | + | 0.877236i | ||||
\(475\) | − | 4516.60i | − | 0.436286i | ||||||
\(476\) | −1026.99 | − | 1085.31i | −0.0988911 | − | 0.104507i | ||||
\(477\) | − | 27534.1i | − | 2.64297i | ||||||
\(478\) | −11979.7 | − | 5156.98i | −1.14632 | − | 0.493461i | ||||
\(479\) | 12341.2i | 1.17721i | 0.808422 | + | 0.588604i | \(0.200322\pi\) | ||||
−0.808422 | + | 0.588604i | \(0.799678\pi\) | |||||||
\(480\) | 4222.52 | − | 8486.28i | 0.401522 | − | 0.806967i | ||||
\(481\) | −1103.02 | −0.104560 | ||||||||
\(482\) | 4384.02 | − | 10184.1i | 0.414287 | − | 0.962394i | ||||
\(483\) | − | 26981.9i | − | 2.54186i | ||||||
\(484\) | −7225.32 | − | 7635.60i | −0.678561 | − | 0.717092i | ||||
\(485\) | −2891.64 | −0.270727 | ||||||||
\(486\) | 11653.8 | + | 5016.69i | 1.08771 | + | 0.468234i | ||||
\(487\) | 1383.56 | 0.128737 | 0.0643687 | − | 0.997926i | \(-0.479497\pi\) | ||||
0.0643687 | + | 0.997926i | \(0.479497\pi\) | |||||||
\(488\) | 13234.4 | − | 4850.40i | 1.22765 | − | 0.449933i | ||||
\(489\) | − | 22849.2i | − | 2.11304i | ||||||
\(490\) | 4160.39 | + | 1790.95i | 0.383566 | + | 0.165116i | ||||
\(491\) | −11694.5 | −1.07488 | −0.537440 | − | 0.843302i | \(-0.680609\pi\) | ||||
−0.537440 | + | 0.843302i | \(0.680609\pi\) | |||||||
\(492\) | −16659.0 | − | 17605.0i | −1.52652 | − | 1.61320i | ||||
\(493\) | −1464.85 | −0.133821 | ||||||||
\(494\) | 447.629 | + | 192.694i | 0.0407688 | + | 0.0175500i | ||||
\(495\) | 1063.88 | 0.0966017 | ||||||||
\(496\) | −626.520 | + | 11028.7i | −0.0567169 | + | 0.998390i | ||||
\(497\) | 9900.39 | 0.893548 | ||||||||
\(498\) | −17319.5 | − | 7455.63i | −1.55845 | − | 0.670873i | ||||
\(499\) | −12374.0 | −1.11009 | −0.555045 | − | 0.831821i | \(-0.687299\pi\) | ||||
−0.555045 | + | 0.831821i | \(0.687299\pi\) | |||||||
\(500\) | −7336.58 | − | 7753.18i | −0.656204 | − | 0.693466i | ||||
\(501\) | 21498.8 | 1.91715 | ||||||||
\(502\) | 2422.21 | + | 1042.70i | 0.215356 | + | 0.0927055i | ||||
\(503\) | 2691.77i | 0.238608i | 0.992858 | + | 0.119304i | \(0.0380663\pi\) | ||||
−0.992858 | + | 0.119304i | \(0.961934\pi\) | |||||||
\(504\) | −20993.6 | + | 7694.14i | −1.85541 | + | 0.680009i | ||||
\(505\) | −583.315 | −0.0514003 | ||||||||
\(506\) | −1441.28 | − | 620.437i | −0.126626 | − | 0.0545094i | ||||
\(507\) | 17969.4 | 1.57406 | ||||||||
\(508\) | 45.2501 | + | 47.8196i | 0.00395206 | + | 0.00417648i | ||||
\(509\) | − | 448.742i | − | 0.0390769i | −0.999809 | − | 0.0195385i | \(-0.993780\pi\) | ||
0.999809 | − | 0.0195385i | \(-0.00621968\pi\) | |||||||
\(510\) | −448.651 | + | 1042.22i | −0.0389541 | + | 0.0904908i | ||||
\(511\) | 10343.5 | 0.895443 | ||||||||
\(512\) | 10071.7 | + | 5725.31i | 0.869354 | + | 0.494190i | ||||
\(513\) | 5951.44i | 0.512208i | ||||||||
\(514\) | 7456.34 | + | 3209.77i | 0.639854 | + | 0.275442i | ||||
\(515\) | 958.510i | 0.0820135i | ||||||||
\(516\) | 23.6958 | + | 25.0413i | 0.00202160 | + | 0.00213640i | ||||
\(517\) | 2148.39i | 0.182759i | ||||||||
\(518\) | −21697.5 | − | 9340.25i | −1.84041 | − | 0.792253i | ||||
\(519\) | 4909.57 | 0.415234 | ||||||||
\(520\) | 435.863 | − | 159.744i | 0.0367574 | − | 0.0134716i | ||||
\(521\) | 11857.0 | 0.997057 | 0.498528 | − | 0.866873i | \(-0.333874\pi\) | ||||
0.498528 | + | 0.866873i | \(0.333874\pi\) | |||||||
\(522\) | −8667.10 | + | 20133.8i | −0.726722 | + | 1.68818i | ||||
\(523\) | 7735.42 | 0.646743 | 0.323371 | − | 0.946272i | \(-0.395184\pi\) | ||||
0.323371 | + | 0.946272i | \(0.395184\pi\) | |||||||
\(524\) | −5212.30 | + | 4932.23i | −0.434543 | + | 0.411194i | ||||
\(525\) | 16908.6i | 1.40562i | ||||||||
\(526\) | 18502.5 | + | 7964.89i | 1.53374 | + | 0.660239i | ||||
\(527\) | 2.04367 | − | 1322.35i | 0.000168925 | − | 0.109303i | ||||
\(528\) | −119.533 | + | 2163.18i | −0.00985228 | + | 0.178296i | ||||
\(529\) | 5971.68 | 0.490809 | ||||||||
\(530\) | −4840.71 | + | 11245.0i | −0.396730 | + | 0.921608i | ||||
\(531\) | − | 6125.24i | − | 0.500589i | ||||||
\(532\) | 7173.60 | + | 7580.95i | 0.584615 | + | 0.617811i | ||||
\(533\) | − | 1187.02i | − | 0.0964640i | ||||||
\(534\) | −6701.72 | + | 15568.2i | −0.543093 | + | 1.26161i | ||||
\(535\) | − | 5241.65i | − | 0.423582i | ||||||
\(536\) | 13577.3 | − | 4976.09i | 1.09413 | − | 0.400997i | ||||
\(537\) | −14307.6 | −1.14975 | ||||||||
\(538\) | −9122.09 | + | 21190.7i | −0.731006 | + | 1.69813i | ||||
\(539\) | −1035.27 | −0.0827314 | ||||||||
\(540\) | 3896.43 | + | 4117.69i | 0.310511 | + | 0.328143i | ||||
\(541\) | −12026.7 | −0.955766 | −0.477883 | − | 0.878423i | \(-0.658596\pi\) | ||||
−0.477883 | + | 0.878423i | \(0.658596\pi\) | |||||||
\(542\) | 407.196 | + | 175.288i | 0.0322704 | + | 0.0138916i | ||||
\(543\) | − | 17337.7i | − | 1.37022i | ||||||
\(544\) | −1241.64 | − | 617.803i | −0.0978583 | − | 0.0486913i | ||||
\(545\) | −7016.15 | −0.551447 | ||||||||
\(546\) | −1675.77 | − | 721.378i | −0.131349 | − | 0.0565424i | ||||
\(547\) | 23953.9i | 1.87238i | 0.351488 | + | 0.936192i | \(0.385676\pi\) | ||||
−0.351488 | + | 0.936192i | \(0.614324\pi\) | |||||||
\(548\) | −17590.0 | + | 16644.9i | −1.37118 | + | 1.29751i | ||||
\(549\) | 25249.0i | 1.96285i | ||||||||
\(550\) | 903.199 | + | 388.805i | 0.0700228 | + | 0.0301431i | ||||
\(551\) | 10232.1 | 0.791107 | ||||||||
\(552\) | −8617.89 | − | 23514.0i | −0.664496 | − | 1.81309i | ||||
\(553\) | 24013.8i | 1.84660i | ||||||||
\(554\) | 2852.94 | − | 6627.40i | 0.218790 | − | 0.508251i | ||||
\(555\) | 17938.8i | 1.37200i | ||||||||
\(556\) | −10254.4 | − | 10836.7i | −0.782165 | − | 0.826580i | ||||
\(557\) | − | 3287.46i | − | 0.250079i | −0.992152 | − | 0.125040i | \(-0.960094\pi\) | ||
0.992152 | − | 0.125040i | \(-0.0399058\pi\) | |||||||
\(558\) | −18163.1 | − | 7852.06i | −1.37797 | − | 0.595707i | ||||
\(559\) | 1.68841i | 0.000127750i | ||||||||
\(560\) | 9926.55 | + | 548.522i | 0.749060 | + | 0.0413915i | ||||
\(561\) | − | 259.346i | − | 0.0195180i | ||||||
\(562\) | −3355.58 | − | 1444.50i | −0.251862 | − | 0.108421i | ||||
\(563\) | − | 1480.42i | − | 0.110821i | −0.998464 | − | 0.0554104i | \(-0.982353\pi\) | ||
0.998464 | − | 0.0554104i | \(-0.0176467\pi\) | |||||||
\(564\) | −24905.3 | + | 23567.1i | −1.85940 | + | 1.75949i | ||||
\(565\) | −10365.0 | −0.771784 | ||||||||
\(566\) | −4210.29 | + | 9780.55i | −0.312671 | + | 0.726338i | ||||
\(567\) | 4399.72i | 0.325875i | ||||||||
\(568\) | 8627.94 | − | 3162.14i | 0.637360 | − | 0.233592i | ||||
\(569\) | 14217.7i | 1.04752i | 0.851866 | + | 0.523760i | \(0.175471\pi\) | ||||
−0.851866 | + | 0.523760i | \(0.824529\pi\) | |||||||
\(570\) | 3133.85 | − | 7279.96i | 0.230285 | − | 0.534955i | ||||
\(571\) | 13527.4 | 0.991426 | 0.495713 | − | 0.868486i | \(-0.334907\pi\) | ||||
0.495713 | + | 0.868486i | \(0.334907\pi\) | |||||||
\(572\) | −77.0671 | + | 72.9261i | −0.00563346 | + | 0.00533076i | ||||
\(573\) | − | 28914.2i | − | 2.10805i | ||||||
\(574\) | 10051.5 | − | 23349.7i | 0.730909 | − | 1.69791i | ||||
\(575\) | −11366.9 | −0.824401 | ||||||||
\(576\) | −15837.9 | + | 13410.5i | −1.14568 | + | 0.970088i | ||||
\(577\) | −5347.07 | −0.385791 | −0.192895 | − | 0.981219i | \(-0.561788\pi\) | ||||
−0.192895 | + | 0.981219i | \(0.561788\pi\) | |||||||
\(578\) | −12611.2 | − | 5428.81i | −0.907537 | − | 0.390673i | ||||
\(579\) | −1714.91 | −0.123090 | ||||||||
\(580\) | 7079.36 | − | 6698.96i | 0.506818 | − | 0.479585i | ||||
\(581\) | − | 19777.0i | − | 1.41220i | ||||||
\(582\) | 9688.63 | + | 4170.72i | 0.690046 | + | 0.297048i | ||||
\(583\) | − | 2798.21i | − | 0.198782i | ||||||
\(584\) | 9014.13 | − | 3303.68i | 0.638711 | − | 0.234088i | ||||
\(585\) | 831.555i | 0.0587702i | ||||||||
\(586\) | 9623.16 | + | 4142.54i | 0.678377 | + | 0.292025i | ||||
\(587\) | −617.638 | −0.0434287 | −0.0217144 | − | 0.999764i | \(-0.506912\pi\) | ||||
−0.0217144 | + | 0.999764i | \(0.506912\pi\) | |||||||
\(588\) | −11356.5 | − | 12001.4i | −0.796488 | − | 0.841715i | ||||
\(589\) | −14.2751 | + | 9236.69i | −0.000998636 | + | 0.646165i | ||||
\(590\) | −1076.87 | + | 2501.57i | −0.0751422 | + | 0.174556i | ||||
\(591\) | − | 15960.1i | − | 1.11085i | ||||||
\(592\) | −21892.1 | − | 1209.71i | −1.51986 | − | 0.0839845i | ||||
\(593\) | −14345.5 | −0.993419 | −0.496710 | − | 0.867917i | \(-0.665459\pi\) | ||||
−0.496710 | + | 0.867917i | \(0.665459\pi\) | |||||||
\(594\) | −1190.13 | − | 512.322i | −0.0822080 | − | 0.0353886i | ||||
\(595\) | −1190.10 | −0.0819992 | ||||||||
\(596\) | 14945.0 | + | 15793.6i | 1.02713 | + | 1.08546i | ||||
\(597\) | 30296.6 | 2.07698 | ||||||||
\(598\) | 484.949 | − | 1126.54i | 0.0331623 | − | 0.0770363i | ||||
\(599\) | 4714.45i | 0.321581i | 0.986989 | + | 0.160791i | \(0.0514044\pi\) | ||||
−0.986989 | + | 0.160791i | \(0.948596\pi\) | |||||||
\(600\) | 5400.52 | + | 14735.4i | 0.367459 | + | 1.00262i | ||||
\(601\) | 17139.6i | 1.16329i | 0.813443 | + | 0.581645i | \(0.197591\pi\) | ||||
−0.813443 | + | 0.581645i | \(0.802409\pi\) | |||||||
\(602\) | −14.2972 | + | 33.2126i | −0.000967960 | + | 0.00224858i | ||||
\(603\) | 25903.3i | 1.74936i | ||||||||
\(604\) | 4635.54 | + | 4898.76i | 0.312281 | + | 0.330013i | ||||
\(605\) | −8372.87 | −0.562654 | ||||||||
\(606\) | 1954.44 | + | 841.337i | 0.131012 | + | 0.0563977i | ||||
\(607\) | 5484.88i | 0.366762i | 0.983042 | + | 0.183381i | \(0.0587041\pi\) | ||||
−0.983042 | + | 0.183381i | \(0.941296\pi\) | |||||||
\(608\) | 8672.93 | + | 4315.39i | 0.578509 | + | 0.287849i | ||||
\(609\) | −38305.3 | −2.54878 | ||||||||
\(610\) | 4438.98 | − | 10311.8i | 0.294638 | − | 0.684447i | ||||
\(611\) | −1679.24 | −0.111186 | ||||||||
\(612\) | 1804.47 | − | 1707.51i | 0.119185 | − | 0.112781i | ||||
\(613\) | − | 17217.3i | − | 1.13442i | −0.823572 | − | 0.567212i | \(-0.808022\pi\) | ||
0.823572 | − | 0.567212i | \(-0.191978\pi\) | |||||||
\(614\) | 10001.5 | − | 23233.6i | 0.657375 | − | 1.52709i | ||||
\(615\) | −19304.9 | −1.26577 | ||||||||
\(616\) | −2133.52 | + | 781.933i | −0.139548 | + | 0.0511444i | ||||
\(617\) | −24689.5 | −1.61096 | −0.805480 | − | 0.592623i | \(-0.798092\pi\) | ||||
−0.805480 | + | 0.592623i | \(0.798092\pi\) | |||||||
\(618\) | 1382.50 | − | 3211.55i | 0.0899872 | − | 0.209041i | ||||
\(619\) | −1617.84 | −0.105051 | −0.0525255 | − | 0.998620i | \(-0.516727\pi\) | ||||
−0.0525255 | + | 0.998620i | \(0.516727\pi\) | |||||||
\(620\) | 6037.42 | + | 6400.03i | 0.391078 | + | 0.414567i | ||||
\(621\) | 14977.9 | 0.967862 | ||||||||
\(622\) | −6798.96 | + | 15794.1i | −0.438285 | + | 1.01814i | ||||
\(623\) | −17777.2 | −1.14322 | ||||||||
\(624\) | −1690.79 | − | 93.4300i | −0.108471 | − | 0.00599390i | ||||
\(625\) | 2048.07 | 0.131077 | ||||||||
\(626\) | 5918.31 | − | 13748.3i | 0.377865 | − | 0.877784i | ||||
\(627\) | 1811.54i | 0.115384i | ||||||||
\(628\) | 3706.28 | + | 3916.74i | 0.235504 | + | 0.248877i | ||||
\(629\) | 2624.66 | 0.166378 | ||||||||
\(630\) | −7041.51 | + | 16357.5i | −0.445302 | + | 1.03444i | ||||
\(631\) | −15779.9 | −0.995542 | −0.497771 | − | 0.867309i | \(-0.665848\pi\) | ||||
−0.497771 | + | 0.867309i | \(0.665848\pi\) | |||||||
\(632\) | 7669.89 | + | 20927.4i | 0.482740 | + | 1.31716i | ||||
\(633\) | − | 23150.2i | − | 1.45362i | ||||||
\(634\) | 5710.44 | + | 2458.21i | 0.357714 | + | 0.153987i | ||||
\(635\) | 52.4369 | 0.00327700 | ||||||||
\(636\) | 32438.3 | − | 30695.3i | 2.02242 | − | 1.91375i | ||||
\(637\) | − | 809.193i | − | 0.0503318i | ||||||
\(638\) | −880.812 | + | 2046.14i | −0.0546578 | + | 0.126971i | ||||
\(639\) | 16460.7i | 1.01905i | ||||||||
\(640\) | 8825.93 | − | 2692.47i | 0.545118 | − | 0.166296i | ||||
\(641\) | 7025.46i | 0.432900i | 0.976294 | + | 0.216450i | \(0.0694478\pi\) | ||||
−0.976294 | + | 0.216450i | \(0.930552\pi\) | |||||||
\(642\) | −7560.24 | + | 17562.5i | −0.464765 | + | 1.07965i | ||||
\(643\) | 9969.78 | 0.611461 | 0.305731 | − | 0.952118i | \(-0.401099\pi\) | ||||
0.305731 | + | 0.952118i | \(0.401099\pi\) | |||||||
\(644\) | 19078.8 | − | 18053.7i | 1.16741 | − | 1.10468i | ||||
\(645\) | 27.4592 | 0.00167629 | ||||||||
\(646\) | −1065.14 | − | 458.518i | −0.0648723 | − | 0.0279259i | ||||
\(647\) | 5450.08 | 0.331167 | 0.165583 | − | 0.986196i | \(-0.447049\pi\) | ||||
0.165583 | + | 0.986196i | \(0.447049\pi\) | |||||||
\(648\) | 1405.25 | + | 3834.24i | 0.0851904 | + | 0.232443i | ||||
\(649\) | − | 622.490i | − | 0.0376500i | ||||||
\(650\) | −303.900 | + | 705.963i | −0.0183384 | + | 0.0426002i | ||||
\(651\) | 53.4411 | − | 34579.0i | 0.00321739 | − | 2.08181i | ||||
\(652\) | 16156.6 | − | 15288.5i | 0.970461 | − | 0.918316i | ||||
\(653\) | 10249.9 | 0.614255 | 0.307127 | − | 0.951668i | \(-0.400632\pi\) | ||||
0.307127 | + | 0.951668i | \(0.400632\pi\) | |||||||
\(654\) | 23508.1 | + | 10119.7i | 1.40556 | + | 0.605061i | ||||
\(655\) | 5715.59i | 0.340956i | ||||||||
\(656\) | 1301.83 | − | 23559.1i | 0.0774816 | − | 1.40218i | ||||
\(657\) | 17197.5i | 1.02121i | ||||||||
\(658\) | −33032.3 | − | 14219.6i | −1.95704 | − | 0.842458i | ||||
\(659\) | − | 15288.1i | − | 0.903701i | −0.892094 | − | 0.451850i | \(-0.850764\pi\) | ||
0.892094 | − | 0.451850i | \(-0.149236\pi\) | |||||||
\(660\) | 1186.02 | + | 1253.37i | 0.0699484 | + | 0.0739203i | ||||
\(661\) | −18036.6 | −1.06133 | −0.530667 | − | 0.847581i | \(-0.678058\pi\) | ||||
−0.530667 | + | 0.847581i | \(0.678058\pi\) | |||||||
\(662\) | −14223.4 | − | 6122.84i | −0.835059 | − | 0.359473i | ||||
\(663\) | 202.711 | 0.0118743 | ||||||||
\(664\) | −6316.69 | − | 17235.2i | −0.369179 | − | 1.00731i | ||||
\(665\) | 8312.94 | 0.484755 | ||||||||
\(666\) | 15529.4 | − | 36074.9i | 0.903530 | − | 2.09891i | ||||
\(667\) | − | 25750.8i | − | 1.49487i | ||||||
\(668\) | 14384.9 | + | 15201.7i | 0.833186 | + | 0.880498i | ||||
\(669\) | 51252.8 | 2.96196 | ||||||||
\(670\) | 4554.01 | − | 10579.0i | 0.262592 | − | 0.610004i | ||||
\(671\) | 2565.98i | 0.147629i | ||||||||
\(672\) | −32468.4 | − | 16155.3i | −1.86384 | − | 0.927388i | ||||
\(673\) | − | 28021.3i | − | 1.60497i | −0.596675 | − | 0.802483i | \(-0.703512\pi\) | ||
0.596675 | − | 0.802483i | \(-0.296488\pi\) | |||||||
\(674\) | −7128.25 | + | 16559.0i | −0.407374 | + | 0.946334i | ||||
\(675\) | −9386.10 | −0.535217 | ||||||||
\(676\) | 12023.4 | + | 12706.1i | 0.684080 | + | 0.722925i | ||||
\(677\) | 15621.1i | 0.886808i | 0.896322 | + | 0.443404i | \(0.146229\pi\) | ||||
−0.896322 | + | 0.443404i | \(0.853771\pi\) | |||||||
\(678\) | 34728.6 | + | 14949.8i | 1.96717 | + | 0.846820i | ||||
\(679\) | 11063.4i | 0.625293i | ||||||||
\(680\) | −1037.15 | + | 380.114i | −0.0584893 | + | 0.0214363i | ||||
\(681\) | 4050.24i | 0.227908i | ||||||||
\(682\) | −1845.86 | − | 797.982i | −0.103639 | − | 0.0448040i | ||||
\(683\) | 11709.8i | 0.656023i | 0.944674 | + | 0.328012i | \(0.106379\pi\) | ||||
−0.944674 | + | 0.328012i | \(0.893621\pi\) | |||||||
\(684\) | −12604.3 | + | 11927.0i | −0.704587 | + | 0.666728i | ||||
\(685\) | 19288.5i | 1.07587i | ||||||||
\(686\) | −2499.42 | + | 5806.17i | −0.139108 | + | 0.323150i | ||||
\(687\) | − | 4073.51i | − | 0.226222i | ||||||
\(688\) | −1.85172 | + | 33.5104i | −0.000102611 | + | 0.00185694i | ||||
\(689\) | 2187.15 | 0.120934 | ||||||||
\(690\) | −18321.4 | − | 7886.90i | −1.01084 | − | 0.435144i | ||||
\(691\) | − | 14082.3i | − | 0.775277i | −0.921811 | − | 0.387639i | \(-0.873291\pi\) | ||
0.921811 | − | 0.387639i | \(-0.126709\pi\) | |||||||
\(692\) | 3285.01 | + | 3471.55i | 0.180459 | + | 0.190706i | ||||
\(693\) | − | 4070.39i | − | 0.223119i | ||||||
\(694\) | −13637.2 | − | 5870.48i | −0.745909 | − | 0.321096i | ||||
\(695\) | −11883.1 | −0.648561 | ||||||||
\(696\) | −33382.0 | + | 12234.5i | −1.81802 | + | 0.666305i | ||||
\(697\) | 2824.53i | 0.153496i | ||||||||
\(698\) | 16588.4 | + | 7140.91i | 0.899543 | + | 0.387231i | ||||
\(699\) | 25646.7 | 1.38777 | ||||||||
\(700\) | −11956.0 | + | 11313.6i | −0.645564 | + | 0.610877i | ||||
\(701\) | −23267.1 | −1.25362 | −0.626810 | − | 0.779172i | \(-0.715640\pi\) | ||||
−0.626810 | + | 0.779172i | \(0.715640\pi\) | |||||||
\(702\) | 400.443 | − | 930.234i | 0.0215296 | − | 0.0500134i | ||||
\(703\) | −18333.4 | −0.983580 | ||||||||
\(704\) | −1609.56 | + | 1362.87i | −0.0861683 | + | 0.0729617i | ||||
\(705\) | 27310.1i | 1.45895i | ||||||||
\(706\) | 13232.5 | − | 30739.2i | 0.705398 | − | 1.63865i | ||||
\(707\) | 2231.76i | 0.118718i | ||||||||
\(708\) | 7216.23 | − | 6828.48i | 0.383054 | − | 0.362472i | ||||
\(709\) | − | 2172.74i | − | 0.115090i | −0.998343 | − | 0.0575451i | \(-0.981673\pi\) | ||
0.998343 | − | 0.0575451i | \(-0.0183273\pi\) | |||||||
\(710\) | 2893.92 | − | 6722.61i | 0.152967 | − | 0.355345i | ||||
\(711\) | −39926.0 | −2.10597 | ||||||||
\(712\) | −15492.4 | + | 5677.94i | −0.815450 | + | 0.298862i | ||||
\(713\) | 23245.8 | + | 35.9260i | 1.22099 | + | 0.00188701i | ||||
\(714\) | 3987.53 | + | 1716.53i | 0.209005 | + | 0.0899715i | ||||
\(715\) | 84.5085i | 0.00442019i | ||||||||
\(716\) | −9573.26 | − | 10116.9i | −0.499678 | − | 0.528051i | ||||
\(717\) | 37894.4 | 1.97377 | ||||||||
\(718\) | −8917.02 | + | 20714.3i | −0.463482 | + | 1.07667i | ||||
\(719\) | −756.839 | −0.0392564 | −0.0196282 | − | 0.999807i | \(-0.506248\pi\) | ||||
−0.0196282 | + | 0.999807i | \(0.506248\pi\) | |||||||
\(720\) | −911.988 | + | 16504.2i | −0.0472052 | + | 0.854270i | ||||
\(721\) | 3667.25 | 0.189425 | ||||||||
\(722\) | −10379.2 | − | 4467.99i | −0.535005 | − | 0.230307i | ||||
\(723\) | 32214.5i | 1.65708i | ||||||||
\(724\) | 12259.4 | − | 11600.7i | 0.629307 | − | 0.595493i | ||||
\(725\) | 16137.1i | 0.826645i | ||||||||
\(726\) | 28053.9 | + | 12076.5i | 1.43413 | + | 0.617357i | ||||
\(727\) | − | 19408.3i | − | 0.990113i | −0.868861 | − | 0.495057i | \(-0.835147\pi\) | ||
0.868861 | − | 0.495057i | \(-0.164853\pi\) | |||||||
\(728\) | −611.178 | − | 1667.61i | −0.0311151 | − | 0.0848980i | ||||
\(729\) | −31990.8 | −1.62530 | ||||||||
\(730\) | 3023.45 | − | 7023.52i | 0.153292 | − | 0.356099i | ||||
\(731\) | − | 4.01760i | − | 0.000203278i | ||||||
\(732\) | −29746.2 | + | 28147.9i | −1.50198 | + | 1.42128i | ||||
\(733\) | −20136.0 | −1.01465 | −0.507325 | − | 0.861755i | \(-0.669366\pi\) | ||||
−0.507325 | + | 0.861755i | \(0.669366\pi\) | |||||||
\(734\) | 19199.3 | + | 8264.82i | 0.965474 | + | 0.415613i | ||||
\(735\) | −13160.2 | −0.660437 | ||||||||
\(736\) | 10860.5 | − | 21827.0i | 0.543916 | − | 1.09314i | ||||
\(737\) | 2632.48i | 0.131572i | ||||||||
\(738\) | 38822.0 | + | 16711.9i | 1.93639 | + | 0.833569i | ||||
\(739\) | −4767.83 | −0.237331 | −0.118665 | − | 0.992934i | \(-0.537862\pi\) | ||||
−0.118665 | + | 0.992934i | \(0.537862\pi\) | |||||||
\(740\) | −12684.5 | + | 12002.9i | −0.630124 | + | 0.596266i | ||||
\(741\) | −1415.95 | −0.0701972 | ||||||||
\(742\) | 43023.3 | + | 18520.5i | 2.12862 | + | 0.916320i | ||||
\(743\) | 12976.0 | 0.640707 | 0.320353 | − | 0.947298i | \(-0.396198\pi\) | ||||
0.320353 | + | 0.947298i | \(0.396198\pi\) | |||||||
\(744\) | −10997.8 | − | 30151.7i | −0.541933 | − | 1.48577i | ||||
\(745\) | 17318.6 | 0.851686 | ||||||||
\(746\) | −26790.1 | − | 11532.5i | −1.31482 | − | 0.565997i | ||||
\(747\) | 32881.9 | 1.61055 | ||||||||
\(748\) | 183.383 | − | 173.529i | 0.00896409 | − | 0.00848242i | ||||
\(749\) | −20054.5 | −0.978339 | ||||||||
\(750\) | 28485.9 | + | 12262.5i | 1.38688 | + | 0.597017i | ||||
\(751\) | 17680.1i | 0.859061i | 0.903052 | + | 0.429530i | \(0.141321\pi\) | ||||
−0.903052 | + | 0.429530i | \(0.858679\pi\) | |||||||
\(752\) | −33328.4 | − | 1841.66i | −1.61617 | − | 0.0893066i | ||||
\(753\) | −7661.98 | −0.370807 | ||||||||
\(754\) | −1599.31 | − | 688.465i | −0.0772460 | − | 0.0332525i | ||||
\(755\) | 5371.77 | 0.258939 | ||||||||
\(756\) | 15754.2 | − | 14907.7i | 0.757904 | − | 0.717180i | ||||
\(757\) | 6029.84i | 0.289509i | 0.989468 | + | 0.144754i | \(0.0462392\pi\) | ||||
−0.989468 | + | 0.144754i | \(0.953761\pi\) | |||||||
\(758\) | −7539.61 | + | 17514.6i | −0.361281 | + | 0.839259i | ||||
\(759\) | 4559.08 | 0.218029 | ||||||||
\(760\) | 7244.51 | − | 2655.11i | 0.345771 | − | 0.126725i | ||||
\(761\) | − | 31328.1i | − | 1.49230i | −0.665777 | − | 0.746151i | \(-0.731900\pi\) | ||
0.665777 | − | 0.746151i | \(-0.268100\pi\) | |||||||
\(762\) | −175.693 | − | 75.6318i | −0.00835263 | − | 0.00359560i | ||||
\(763\) | 26843.7i | 1.27367i | ||||||||
\(764\) | 20445.2 | − | 19346.6i | 0.968169 | − | 0.916147i | ||||
\(765\) | − | 1978.70i | − | 0.0935165i | ||||||
\(766\) | −12902.0 | − | 5554.00i | −0.608575 | − | 0.261977i | ||||
\(767\) | 486.554 | 0.0229054 | ||||||||
\(768\) | −33455.3 | − | 3708.68i | −1.57190 | − | 0.174252i | ||||
\(769\) | 15877.3 | 0.744539 | 0.372269 | − | 0.928125i | \(-0.378580\pi\) | ||||
0.372269 | + | 0.928125i | \(0.378580\pi\) | |||||||
\(770\) | −715.608 | + | 1662.37i | −0.0334918 | + | 0.0778019i | ||||
\(771\) | −23586.0 | −1.10172 | ||||||||
\(772\) | −1147.45 | − | 1212.61i | −0.0534944 | − | 0.0565320i | ||||
\(773\) | − | 7719.60i | − | 0.359191i | −0.983741 | − | 0.179596i | \(-0.942521\pi\) | ||
0.983741 | − | 0.179596i | \(-0.0574789\pi\) | |||||||
\(774\) | −55.2203 | − | 23.7710i | −0.00256441 | − | 0.00110392i | ||||
\(775\) | −14567.3 | − | 22.5135i | −0.675191 | − | 0.00104350i | ||||
\(776\) | 3533.59 | + | 9641.46i | 0.163465 | + | 0.446016i | ||||
\(777\) | 68633.9 | 3.16889 | ||||||||
\(778\) | 8457.24 | − | 19646.3i | 0.389726 | − | 0.905338i | ||||
\(779\) | − | 19729.5i | − | 0.907421i | ||||||
\(780\) | −979.666 | + | 927.027i | −0.0449714 | + | 0.0425550i | ||||
\(781\) | 1672.85i | 0.0766444i | ||||||||
\(782\) | −1153.95 | + | 2680.63i | −0.0527685 | + | 0.122582i | ||||
\(783\) | − | 21263.6i | − | 0.970496i | ||||||
\(784\) | 887.462 | − | 16060.3i | 0.0404274 | − | 0.731611i | ||||
\(785\) | 4294.93 | 0.195277 | ||||||||
\(786\) | 8243.81 | − | 19150.5i | 0.374106 | − | 0.869052i | ||||
\(787\) | −8739.04 | −0.395824 | −0.197912 | − | 0.980220i | \(-0.563416\pi\) | ||||
−0.197912 | + | 0.980220i | \(0.563416\pi\) | |||||||
\(788\) | 11285.4 | − | 10679.0i | 0.510184 | − | 0.482770i | ||||
\(789\) | −58527.5 | −2.64085 | ||||||||
\(790\) | 16305.9 | + | 7019.31i | 0.734354 | + | 0.316121i | ||||
\(791\) | 39656.3i | 1.78257i | ||||||||
\(792\) | −1300.06 | − | 3547.24i | −0.0583280 | − | 0.159149i | ||||
\(793\) | −2005.64 | −0.0898137 | ||||||||
\(794\) | 39277.6 | + | 16908.0i | 1.75555 | + | 0.755723i | ||||
\(795\) | − | 35570.4i | − | 1.58686i | ||||||
\(796\) | 20271.5 | + | 21422.6i | 0.902646 | + | 0.953901i | ||||
\(797\) | − | 22427.4i | − | 0.996762i | −0.866958 | − | 0.498381i | \(-0.833928\pi\) | ||
0.866958 | − | 0.498381i | \(-0.166072\pi\) | |||||||
\(798\) | −27853.1 | − | 11990.1i | −1.23557 | − | 0.531885i | ||||
\(799\) | 3995.78 | 0.176922 | ||||||||
\(800\) | −6805.86 | + | 13678.2i | −0.300779 | + | 0.604497i | ||||
\(801\) | − | 29556.8i | − | 1.30379i | ||||||
\(802\) | −2974.94 | + | 6910.81i | −0.130983 | + | 0.304276i | ||||
\(803\) | 1747.73i | 0.0768070i | ||||||||
\(804\) | −30517.0 | + | 28877.3i | −1.33862 | + | 1.26669i | ||||
\(805\) | − | 20921.0i | − | 0.915987i | ||||||
\(806\) | 623.723 | − | 1442.77i | 0.0272577 | − | 0.0630514i | ||||
\(807\) | − | 67030.7i | − | 2.92391i | ||||||
\(808\) | 712.812 | + | 1944.92i | 0.0310354 | + | 0.0846807i | ||||
\(809\) | 1481.51i | 0.0643847i | 0.999482 | + | 0.0321924i | \(0.0102489\pi\) | ||||
−0.999482 | + | 0.0321924i | \(0.989751\pi\) | |||||||
\(810\) | 2987.52 | + | 1286.05i | 0.129593 | + | 0.0557868i | ||||
\(811\) | 15631.4i | 0.676808i | 0.941001 | + | 0.338404i | \(0.109887\pi\) | ||||
−0.941001 | + | 0.338404i | \(0.890113\pi\) | |||||||
\(812\) | −25630.2 | − | 27085.5i | −1.10769 | − | 1.17059i | ||||
\(813\) | −1288.05 | −0.0555643 | ||||||||
\(814\) | 1578.20 | − | 3666.19i | 0.0679558 | − | 0.157862i | ||||
\(815\) | − | 17716.6i | − | 0.761456i | ||||||
\(816\) | 4023.28 | + | 222.318i | 0.172602 | + | 0.00953763i | ||||
\(817\) | 28.0631i | 0.00120172i | ||||||||
\(818\) | −12036.8 | + | 27961.5i | −0.514494 | + | 1.19517i | ||||
\(819\) | 3181.52 | 0.135740 | ||||||||
\(820\) | −12917.0 | − | 13650.4i | −0.550097 | − | 0.581334i | ||||
\(821\) | 29286.0i | 1.24493i | 0.782647 | + | 0.622466i | \(0.213869\pi\) | ||||
−0.782647 | + | 0.622466i | \(0.786131\pi\) | |||||||
\(822\) | 27820.5 | − | 64627.3i | 1.18048 | − | 2.74226i | ||||
\(823\) | −3469.07 | −0.146931 | −0.0734654 | − | 0.997298i | \(-0.523406\pi\) | ||||
−0.0734654 | + | 0.997298i | \(0.523406\pi\) | |||||||
\(824\) | 3195.91 | − | 1171.30i | 0.135115 | − | 0.0495197i | ||||
\(825\) | −2857.01 | −0.120568 | ||||||||
\(826\) | 9570.99 | + | 4120.08i | 0.403169 | + | 0.173554i | ||||
\(827\) | 11410.0 | 0.479764 | 0.239882 | − | 0.970802i | \(-0.422891\pi\) | ||||
0.239882 | + | 0.970802i | \(0.422891\pi\) | |||||||
\(828\) | 30016.6 | + | 31721.0i | 1.25984 | + | 1.33138i | ||||
\(829\) | 12401.3i | 0.519559i | 0.965668 | + | 0.259779i | \(0.0836498\pi\) | ||||
−0.965668 | + | 0.259779i | \(0.916350\pi\) | |||||||
\(830\) | −13429.1 | − | 5780.89i | −0.561603 | − | 0.241756i | ||||
\(831\) | 20963.9i | 0.875125i | ||||||||
\(832\) | −1065.25 | − | 1258.07i | −0.0443882 | − | 0.0524228i | ||||
\(833\) | 1925.49i | 0.0800892i | ||||||||
\(834\) | 39815.0 | + | 17139.4i | 1.65309 | + | 0.711617i | ||||
\(835\) | 16669.6 | 0.690867 | ||||||||
\(836\) | −1280.94 | + | 1212.11i | −0.0529930 | + | 0.0501456i | ||||
\(837\) | 19195.1 | + | 29.6657i | 0.792687 | + | 0.00122508i | ||||
\(838\) | 7417.22 | − | 17230.3i | 0.305756 | − | 0.710274i | ||||
\(839\) | − | 16120.0i | − | 0.663320i | −0.943399 | − | 0.331660i | \(-0.892391\pi\) | ||
0.943399 | − | 0.331660i | \(-0.107609\pi\) | |||||||
\(840\) | −27120.9 | + | 9939.82i | −1.11400 | + | 0.408281i | ||||
\(841\) | −12168.5 | −0.498935 | ||||||||
\(842\) | −17994.1 | − | 7746.01i | −0.736480 | − | 0.317037i | ||||
\(843\) | 10614.4 | 0.433665 | ||||||||
\(844\) | 16369.5 | − | 15489.9i | 0.667607 | − | 0.631735i | ||||
\(845\) | 13933.0 | 0.567230 | ||||||||
\(846\) | 23641.9 | − | 54920.4i | 0.960786 | − | 2.23192i | ||||
\(847\) | 32034.5i | 1.29955i | ||||||||
\(848\) | 43409.1 | + | 2398.70i | 1.75787 | + | 0.0971365i | ||||
\(849\) | − | 30938.0i | − | 1.25063i | ||||||
\(850\) | 723.136 | − | 1679.85i | 0.0291804 | − | 0.0677864i | ||||
\(851\) | 46139.3i | 1.85856i | ||||||||
\(852\) | −19392.6 | + | 18350.5i | −0.779786 | + | 0.737886i | ||||
\(853\) | −41657.7 | −1.67214 | −0.836068 | − | 0.548625i | \(-0.815151\pi\) | ||||
−0.836068 | + | 0.548625i | \(0.815151\pi\) | |||||||
\(854\) | −39452.9 | − | 16983.5i | −1.58085 | − | 0.680519i | ||||
\(855\) | 13821.3i | 0.552842i | ||||||||
\(856\) | −17477.0 | + | 6405.31i | −0.697840 | + | 0.255758i | ||||
\(857\) | −21081.2 | −0.840280 | −0.420140 | − | 0.907459i | \(-0.638019\pi\) | ||||
−0.420140 | + | 0.907459i | \(0.638019\pi\) | |||||||
\(858\) | 121.890 | − | 283.152i | 0.00484994 | − | 0.0112665i | ||||
\(859\) | 3810.49 | 0.151353 | 0.0756765 | − | 0.997132i | \(-0.475888\pi\) | ||||
0.0756765 | + | 0.997132i | \(0.475888\pi\) | |||||||
\(860\) | 18.3731 | + | 19.4163i | 0.000728507 | + | 0.000769874i | ||||
\(861\) | 73860.2i | 2.92352i | ||||||||
\(862\) | −15206.0 | + | 35323.7i | −0.600834 | + | 1.39574i | ||||
\(863\) | 30169.9 | 1.19003 | 0.595014 | − | 0.803715i | \(-0.297146\pi\) | ||||
0.595014 | + | 0.803715i | \(0.297146\pi\) | |||||||
\(864\) | 8967.95 | − | 18023.5i | 0.353120 | − | 0.709690i | ||||
\(865\) | 3806.75 | 0.149634 | ||||||||
\(866\) | 4834.30 | − | 11230.1i | 0.189695 | − | 0.440665i | ||||
\(867\) | 39891.9 | 1.56263 | ||||||||
\(868\) | 24486.5 | − | 23099.1i | 0.957517 | − | 0.903266i | ||||
\(869\) | −4057.56 | −0.158393 | ||||||||
\(870\) | −11196.8 | + | 26010.2i | −0.436328 | + | 1.01360i | ||||
\(871\) | −2057.61 | −0.0800453 | ||||||||
\(872\) | 8573.75 | + | 23393.6i | 0.332963 | + | 0.908495i | ||||
\(873\) | −18394.3 | −0.713119 | ||||||||
\(874\) | 8060.37 | − | 18724.3i | 0.311952 | − | 0.724668i | ||||
\(875\) | 32527.8i | 1.25673i | ||||||||
\(876\) | −20260.6 | + | 19171.9i | −0.781440 | + | 0.739451i | ||||
\(877\) | −5489.99 | −0.211384 | −0.105692 | − | 0.994399i | \(-0.533706\pi\) | ||||
−0.105692 | + | 0.994399i | \(0.533706\pi\) | |||||||
\(878\) | −3996.77 | + | 9284.54i | −0.153627 | + | 0.356877i | ||||
\(879\) | −30440.1 | −1.16805 | ||||||||
\(880\) | −92.6826 | + | 1677.27i | −0.00355038 | + | 0.0642509i | ||||
\(881\) | 261.977i | 0.0100184i | 0.999987 | + | 0.00500921i | \(0.00159449\pi\) | ||||
−0.999987 | + | 0.00500921i | \(0.998406\pi\) | |||||||
\(882\) | 26465.1 | + | 11392.6i | 1.01035 | + | 0.434930i | ||||
\(883\) | −25733.9 | −0.980765 | −0.490383 | − | 0.871507i | \(-0.663143\pi\) | ||||
−0.490383 | + | 0.871507i | \(0.663143\pi\) | |||||||
\(884\) | 135.635 | + | 143.337i | 0.00516051 | + | 0.00545354i | ||||
\(885\) | − | 7913.00i | − | 0.300557i | ||||||
\(886\) | −11050.5 | + | 25670.4i | −0.419016 | + | 0.973380i | ||||
\(887\) | − | 14312.8i | − | 0.541800i | −0.962608 | − | 0.270900i | \(-0.912679\pi\) | ||
0.962608 | − | 0.270900i | \(-0.0873212\pi\) | |||||||
\(888\) | 59812.6 | − | 21921.3i | 2.26034 | − | 0.828414i | ||||
\(889\) | − | 200.623i | − | 0.00756882i | ||||||
\(890\) | −5196.33 | + | 12071.1i | −0.195709 | + | 0.454635i | ||||
\(891\) | −743.412 | −0.0279520 | ||||||||
\(892\) | 34293.5 | + | 36240.8i | 1.28725 | + | 1.36035i | ||||
\(893\) | −27910.7 | −1.04591 | ||||||||
\(894\) | −58027.3 | − | 24979.3i | −2.17083 | − | 0.934490i | ||||
\(895\) | −11093.7 | −0.414326 | ||||||||
\(896\) | −10301.4 | − | 33767.9i | −0.384090 | − | 1.25905i | ||||
\(897\) | 3563.49i | 0.132644i | ||||||||
\(898\) | 3776.39 | − | 8772.60i | 0.140334 | − | 0.325997i | ||||
\(899\) | 51.0028 | − | 33001.3i | 0.00189215 | − | 1.22431i | ||||
\(900\) | −18810.3 | − | 19878.4i | −0.696678 | − | 0.736238i | ||||
\(901\) | −5204.36 | −0.192433 | ||||||||
\(902\) | 3945.36 | + | 1698.38i | 0.145639 | + | 0.0626940i | ||||
\(903\) | − | 105.059i | − | 0.00387169i | ||||||
\(904\) | 12666.0 | + | 34559.5i | 0.466002 | + | 1.27149i | ||||
\(905\) | − | 13443.2i | − | 0.493775i | ||||||
\(906\) | −17998.5 | − | 7747.92i | −0.660000 | − | 0.284114i | ||||
\(907\) | − | 45682.4i | − | 1.67239i | −0.548430 | − | 0.836196i | \(-0.684774\pi\) | ||
0.548430 | − | 0.836196i | \(-0.315226\pi\) | |||||||
\(908\) | −2863.92 | + | 2710.03i | −0.104672 | + | 0.0990480i | ||||
\(909\) | −3710.58 | −0.135393 | ||||||||
\(910\) | −1299.35 | − | 559.337i | −0.0473329 | − | 0.0203757i | ||||
\(911\) | −7089.18 | −0.257821 | −0.128911 | − | 0.991656i | \(-0.541148\pi\) | ||||
−0.128911 | + | 0.991656i | \(0.541148\pi\) | |||||||
\(912\) | −28102.8 | − | 1552.91i | −1.02037 | − | 0.0563836i | ||||
\(913\) | 3341.69 | 0.121132 | ||||||||
\(914\) | −21233.2 | + | 49325.1i | −0.768417 | + | 1.78504i | ||||
\(915\) | 32618.4i | 1.17851i | ||||||||
\(916\) | 2880.37 | − | 2725.60i | 0.103898 | − | 0.0983148i | ||||
\(917\) | 21867.8 | 0.787500 | ||||||||
\(918\) | −952.863 | + | 2213.51i | −0.0342584 | + | 0.0795825i | ||||
\(919\) | 18233.4i | 0.654478i | 0.944942 | + | 0.327239i | \(0.106118\pi\) | ||||
−0.944942 | + | 0.327239i | \(0.893882\pi\) | |||||||
\(920\) | −6682.08 | − | 18232.1i | −0.239458 | − | 0.653365i | ||||
\(921\) | 73492.9i | 2.62940i | ||||||||
\(922\) | −5290.22 | + | 12289.2i | −0.188963 | + | 0.438964i | ||||
\(923\) | −1307.54 | −0.0466287 | ||||||||
\(924\) | 4795.39 | − | 4537.72i | 0.170732 | − | 0.161558i | ||||
\(925\) | − | 28913.8i | − | 1.02776i | ||||||
\(926\) | −13166.8 | − | 5667.97i | −0.467264 | − | 0.201146i | ||||
\(927\) | 6097.27i | 0.216031i | ||||||||
\(928\) | −30987.0 | − | 15418.2i | −1.09612 | − | 0.545396i | ||||
\(929\) | − | 2119.94i | − | 0.0748686i | −0.999299 | − | 0.0374343i | \(-0.988082\pi\) | ||
0.999299 | − | 0.0374343i | \(-0.0119185\pi\) | |||||||
\(930\) | −23464.3 | − | 10143.8i | −0.827339 | − | 0.357666i | ||||
\(931\) | − | 13449.6i | − | 0.473463i | ||||||
\(932\) | 17160.3 | + | 18134.7i | 0.603117 | + | 0.637364i | ||||
\(933\) | − | 49960.0i | − | 1.75307i | ||||||
\(934\) | 3727.86 | − | 8659.86i | 0.130599 | − | 0.303383i | ||||
\(935\) | − | 201.090i | − | 0.00703351i | ||||||
\(936\) | 2772.62 | − | 1016.16i | 0.0968224 | − | 0.0354854i | ||||
\(937\) | 21580.4 | 0.752402 | 0.376201 | − | 0.926538i | \(-0.377230\pi\) | ||||
0.376201 | + | 0.926538i | \(0.377230\pi\) | |||||||
\(938\) | −40475.2 | − | 17423.6i | −1.40891 | − | 0.606504i | ||||
\(939\) | 43488.8i | 1.51140i | ||||||||
\(940\) | −19310.9 | + | 18273.3i | −0.670055 | + | 0.634051i | ||||
\(941\) | − | 27530.2i | − | 0.953727i | −0.878977 | − | 0.476864i | \(-0.841774\pi\) | ||
0.878977 | − | 0.476864i | \(-0.158226\pi\) | |||||||
\(942\) | −14390.4 | − | 6194.74i | −0.497735 | − | 0.214263i | ||||
\(943\) | −49652.8 | −1.71465 | ||||||||
\(944\) | 9656.80 | + | 533.616i | 0.332947 | + | 0.0183980i | ||||
\(945\) | − | 17275.4i | − | 0.594676i | ||||||
\(946\) | −5.61188 | − | 2.41578i | −0.000192873 | − | 8.30272e-5i | ||||
\(947\) | 34068.2 | 1.16903 | 0.584513 | − | 0.811384i | \(-0.301286\pi\) | ||||
0.584513 | + | 0.811384i | \(0.301286\pi\) | |||||||
\(948\) | −44509.9 | − | 47037.4i | −1.52491 | − | 1.61150i | ||||
\(949\) | −1366.07 | −0.0467276 | ||||||||
\(950\) | −5051.14 | + | 11733.9i | −0.172506 | + | 0.400733i | ||||
\(951\) | −18063.3 | −0.615924 | ||||||||
\(952\) | 1454.31 | + | 3968.11i | 0.0495110 | + | 0.135092i | ||||
\(953\) | 8468.47i | 0.287850i | 0.989589 | + | 0.143925i | \(0.0459724\pi\) | ||||
−0.989589 | + | 0.143925i | \(0.954028\pi\) | |||||||
\(954\) | −30792.7 | + | 71531.8i | −1.04502 | + | 2.42760i | ||||
\(955\) | − | 22419.3i | − | 0.759657i | ||||||
\(956\) | 25355.3 | + | 26795.0i | 0.857791 | + | 0.906499i | ||||
\(957\) | − | 6472.36i | − | 0.218623i | ||||||
\(958\) | 13801.8 | − | 32061.6i | 0.465464 | − | 1.08128i | ||||
\(959\) | 73797.4 | 2.48493 | ||||||||
\(960\) | −20460.5 | + | 17324.6i | −0.687874 | + | 0.582447i | ||||
\(961\) | 29790.9 | + | 92.0827i | 0.999995 | + | 0.00309096i | ||||
\(962\) | 2865.58 | + | 1233.56i | 0.0960396 | + | 0.0413427i | ||||
\(963\) | − | 33343.2i | − | 1.11575i | ||||||
\(964\) | −22778.8 | + | 21554.9i | −0.761055 | + | 0.720161i | ||||
\(965\) | −1329.69 | −0.0443568 | ||||||||
\(966\) | −30175.2 | + | 70097.4i | −1.00504 | + | 2.33473i | ||||
\(967\) | −41759.5 | −1.38872 | −0.694361 | − | 0.719627i | \(-0.744313\pi\) | ||||
−0.694361 | + | 0.719627i | \(0.744313\pi\) | |||||||
\(968\) | 10231.7 | + | 27917.3i | 0.339730 | + | 0.926957i | ||||
\(969\) | 3369.27 | 0.111699 | ||||||||
\(970\) | 7512.30 | + | 3233.87i | 0.248666 | + | 0.107045i | ||||
\(971\) | − | 7146.50i | − | 0.236192i | −0.993002 | − | 0.118096i | \(-0.962321\pi\) | ||
0.993002 | − | 0.118096i | \(-0.0376790\pi\) | |||||||
\(972\) | −24665.5 | − | 26066.1i | −0.813938 | − | 0.860156i | ||||
\(973\) | 45464.5i | 1.49797i | ||||||||
\(974\) | −3594.41 | − | 1547.30i | −0.118247 | − | 0.0509023i | ||||
\(975\) | − | 2233.11i | − | 0.0733506i | ||||||
\(976\) | −39806.6 | − | 2199.63i | −1.30551 | − | 0.0721399i | ||||
\(977\) | 47479.2 | 1.55475 | 0.777377 | − | 0.629035i | \(-0.216550\pi\) | ||||
0.777377 | + | 0.629035i | \(0.216550\pi\) | |||||||
\(978\) | −25553.4 | + | 59360.8i | −0.835487 | + | 1.94085i | ||||
\(979\) | − | 3003.77i | − | 0.0980603i | ||||||
\(980\) | −8805.54 | − | 9305.55i | −0.287023 | − | 0.303321i | ||||
\(981\) | −44631.1 | −1.45256 | ||||||||
\(982\) | 30381.7 | + | 13078.6i | 0.987289 | + | 0.425004i | ||||
\(983\) | 39884.1 | 1.29411 | 0.647053 | − | 0.762445i | \(-0.276001\pi\) | ||||
0.647053 | + | 0.762445i | \(0.276001\pi\) | |||||||
\(984\) | 23590.6 | + | 64367.3i | 0.764269 | + | 2.08532i | ||||
\(985\) | − | 12375.1i | − | 0.400307i | ||||||
\(986\) | 3805.59 | + | 1638.22i | 0.122916 | + | 0.0529122i | ||||
\(987\) | 104488. | 3.36970 | ||||||||
\(988\) | −947.415 | − | 1001.21i | −0.0305074 | − | 0.0322397i | ||||
\(989\) | 70.6261 | 0.00227076 | ||||||||
\(990\) | −2763.90 | − | 1189.79i | −0.0887297 | − | 0.0381960i | ||||
\(991\) | −33296.6 | −1.06731 | −0.533654 | − | 0.845703i | \(-0.679182\pi\) | ||||
−0.533654 | + | 0.845703i | \(0.679182\pi\) | |||||||
\(992\) | 13961.6 | − | 27951.1i | 0.446855 | − | 0.894606i | ||||
\(993\) | 44991.7 | 1.43783 | ||||||||
\(994\) | −25720.6 | − | 11072.1i | −0.820733 | − | 0.353306i | ||||
\(995\) | 23491.1 | 0.748462 | ||||||||
\(996\) | 36657.0 | + | 38738.6i | 1.16619 | + | 1.23241i | ||||
\(997\) | 35975.1 | 1.14277 | 0.571385 | − | 0.820682i | \(-0.306406\pi\) | ||||
0.571385 | + | 0.820682i | \(0.306406\pi\) | |||||||
\(998\) | 32146.8 | + | 13838.4i | 1.01963 | + | 0.438926i | ||||
\(999\) | 38099.3i | 1.20661i |
(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 | 124.4.d.c.123.6 | yes | 40 | |
4.3 | odd | 2 | inner | 124.4.d.c.123.7 | yes | 40 | |
31.30 | odd | 2 | inner | 124.4.d.c.123.5 | ✓ | 40 | |
124.123 | even | 2 | inner | 124.4.d.c.123.8 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
124.4.d.c.123.5 | ✓ | 40 | 31.30 | odd | 2 | inner | |
124.4.d.c.123.6 | yes | 40 | 1.1 | even | 1 | trivial | |
124.4.d.c.123.7 | yes | 40 | 4.3 | odd | 2 | inner | |
124.4.d.c.123.8 | yes | 40 | 124.123 | even | 2 | inner |