Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,4,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.a (trivial) |
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: | yes |
Analytic conductor: | \(61.6569959560\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} - 82 x^{18} + 700 x^{17} + 2826 x^{16} - 25467 x^{15} - 53768 x^{14} + 498499 x^{13} + 623613 x^{12} - 5673747 x^{11} - 4539454 x^{10} + 37893109 x^{9} + \cdots + 17756160 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3}\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Root | \(4.30367\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.30367 | 1.16802 | 0.584012 | − | 0.811745i | \(-0.301482\pi\) | ||||
0.584012 | + | 0.811745i | \(0.301482\pi\) | |||||||
\(3\) | −7.25904 | −1.39700 | −0.698501 | − | 0.715609i | \(-0.746149\pi\) | ||||
−0.698501 | + | 0.715609i | \(0.746149\pi\) | |||||||
\(4\) | 2.91425 | 0.364282 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −23.9815 | −1.63173 | ||||||||
\(7\) | −9.92986 | −0.536162 | −0.268081 | − | 0.963396i | \(-0.586390\pi\) | ||||
−0.268081 | + | 0.963396i | \(0.586390\pi\) | |||||||
\(8\) | −16.8016 | −0.742535 | ||||||||
\(9\) | 25.6936 | 0.951616 | ||||||||
\(10\) | 16.5184 | 0.522357 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | −21.1547 | −0.508902 | ||||||||
\(13\) | 57.0738 | 1.21765 | 0.608824 | − | 0.793305i | \(-0.291642\pi\) | ||||
0.608824 | + | 0.793305i | \(0.291642\pi\) | |||||||
\(14\) | −32.8050 | −0.626251 | ||||||||
\(15\) | −36.2952 | −0.624758 | ||||||||
\(16\) | −78.8212 | −1.23158 | ||||||||
\(17\) | 50.0959 | 0.714708 | 0.357354 | − | 0.933969i | \(-0.383679\pi\) | ||||
0.357354 | + | 0.933969i | \(0.383679\pi\) | |||||||
\(18\) | 84.8833 | 1.11151 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | 14.5713 | 0.162912 | ||||||||
\(21\) | 72.0813 | 0.749020 | ||||||||
\(22\) | 36.3404 | 0.352173 | ||||||||
\(23\) | −40.7075 | −0.369048 | −0.184524 | − | 0.982828i | \(-0.559074\pi\) | ||||
−0.184524 | + | 0.982828i | \(0.559074\pi\) | |||||||
\(24\) | 121.964 | 1.03732 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 188.553 | 1.42224 | ||||||||
\(27\) | 9.48305 | 0.0675931 | ||||||||
\(28\) | −28.9381 | −0.195314 | ||||||||
\(29\) | 99.7381 | 0.638652 | 0.319326 | − | 0.947645i | \(-0.396544\pi\) | ||||
0.319326 | + | 0.947645i | \(0.396544\pi\) | |||||||
\(30\) | −119.907 | −0.729733 | ||||||||
\(31\) | −61.4620 | −0.356093 | −0.178047 | − | 0.984022i | \(-0.556978\pi\) | ||||
−0.178047 | + | 0.984022i | \(0.556978\pi\) | |||||||
\(32\) | −125.986 | −0.695982 | ||||||||
\(33\) | −79.8494 | −0.421212 | ||||||||
\(34\) | 165.500 | 0.834797 | ||||||||
\(35\) | −49.6493 | −0.239779 | ||||||||
\(36\) | 74.8777 | 0.346656 | ||||||||
\(37\) | −107.743 | −0.478724 | −0.239362 | − | 0.970930i | \(-0.576938\pi\) | ||||
−0.239362 | + | 0.970930i | \(0.576938\pi\) | |||||||
\(38\) | 62.7698 | 0.267963 | ||||||||
\(39\) | −414.301 | −1.70106 | ||||||||
\(40\) | −84.0082 | −0.332072 | ||||||||
\(41\) | 95.4636 | 0.363632 | 0.181816 | − | 0.983333i | \(-0.441803\pi\) | ||||
0.181816 | + | 0.983333i | \(0.441803\pi\) | |||||||
\(42\) | 238.133 | 0.874874 | ||||||||
\(43\) | −480.111 | −1.70270 | −0.851351 | − | 0.524596i | \(-0.824216\pi\) | ||||
−0.851351 | + | 0.524596i | \(0.824216\pi\) | |||||||
\(44\) | 32.0568 | 0.109835 | ||||||||
\(45\) | 128.468 | 0.425575 | ||||||||
\(46\) | −134.484 | −0.431057 | ||||||||
\(47\) | −311.050 | −0.965346 | −0.482673 | − | 0.875801i | \(-0.660334\pi\) | ||||
−0.482673 | + | 0.875801i | \(0.660334\pi\) | |||||||
\(48\) | 572.166 | 1.72052 | ||||||||
\(49\) | −244.398 | −0.712530 | ||||||||
\(50\) | 82.5918 | 0.233605 | ||||||||
\(51\) | −363.648 | −0.998449 | ||||||||
\(52\) | 166.328 | 0.443567 | ||||||||
\(53\) | 193.574 | 0.501688 | 0.250844 | − | 0.968028i | \(-0.419292\pi\) | ||||
0.250844 | + | 0.968028i | \(0.419292\pi\) | |||||||
\(54\) | 31.3289 | 0.0789504 | ||||||||
\(55\) | 55.0000 | 0.134840 | ||||||||
\(56\) | 166.838 | 0.398119 | ||||||||
\(57\) | −137.922 | −0.320494 | ||||||||
\(58\) | 329.502 | 0.745961 | ||||||||
\(59\) | 341.118 | 0.752707 | 0.376354 | − | 0.926476i | \(-0.377178\pi\) | ||||
0.376354 | + | 0.926476i | \(0.377178\pi\) | |||||||
\(60\) | −105.773 | −0.227588 | ||||||||
\(61\) | −408.667 | −0.857777 | −0.428889 | − | 0.903357i | \(-0.641095\pi\) | ||||
−0.428889 | + | 0.903357i | \(0.641095\pi\) | |||||||
\(62\) | −203.050 | −0.415926 | ||||||||
\(63\) | −255.134 | −0.510220 | ||||||||
\(64\) | 214.352 | 0.418656 | ||||||||
\(65\) | 285.369 | 0.544549 | ||||||||
\(66\) | −263.796 | −0.491986 | ||||||||
\(67\) | −520.416 | −0.948940 | −0.474470 | − | 0.880272i | \(-0.657360\pi\) | ||||
−0.474470 | + | 0.880272i | \(0.657360\pi\) | |||||||
\(68\) | 145.992 | 0.260355 | ||||||||
\(69\) | 295.497 | 0.515561 | ||||||||
\(70\) | −164.025 | −0.280068 | ||||||||
\(71\) | −881.595 | −1.47361 | −0.736804 | − | 0.676107i | \(-0.763666\pi\) | ||||
−0.736804 | + | 0.676107i | \(0.763666\pi\) | |||||||
\(72\) | −431.695 | −0.706608 | ||||||||
\(73\) | 1023.02 | 1.64022 | 0.820110 | − | 0.572206i | \(-0.193912\pi\) | ||||
0.820110 | + | 0.572206i | \(0.193912\pi\) | |||||||
\(74\) | −355.947 | −0.559162 | ||||||||
\(75\) | −181.476 | −0.279400 | ||||||||
\(76\) | 55.3708 | 0.0835720 | ||||||||
\(77\) | −109.229 | −0.161659 | ||||||||
\(78\) | −1368.71 | −1.98688 | ||||||||
\(79\) | −78.3320 | −0.111557 | −0.0557787 | − | 0.998443i | \(-0.517764\pi\) | ||||
−0.0557787 | + | 0.998443i | \(0.517764\pi\) | |||||||
\(80\) | −394.106 | −0.550780 | ||||||||
\(81\) | −762.566 | −1.04604 | ||||||||
\(82\) | 315.380 | 0.424731 | ||||||||
\(83\) | 902.858 | 1.19399 | 0.596997 | − | 0.802243i | \(-0.296360\pi\) | ||||
0.596997 | + | 0.802243i | \(0.296360\pi\) | |||||||
\(84\) | 210.063 | 0.272854 | ||||||||
\(85\) | 250.479 | 0.319627 | ||||||||
\(86\) | −1586.13 | −1.98880 | ||||||||
\(87\) | −724.003 | −0.892198 | ||||||||
\(88\) | −184.818 | −0.223883 | ||||||||
\(89\) | −995.340 | −1.18546 | −0.592729 | − | 0.805402i | \(-0.701950\pi\) | ||||
−0.592729 | + | 0.805402i | \(0.701950\pi\) | |||||||
\(90\) | 424.417 | 0.497083 | ||||||||
\(91\) | −566.735 | −0.652857 | ||||||||
\(92\) | −118.632 | −0.134437 | ||||||||
\(93\) | 446.155 | 0.497463 | ||||||||
\(94\) | −1027.61 | −1.12755 | ||||||||
\(95\) | 95.0000 | 0.102598 | ||||||||
\(96\) | 914.538 | 0.972288 | ||||||||
\(97\) | −410.183 | −0.429358 | −0.214679 | − | 0.976685i | \(-0.568871\pi\) | ||||
−0.214679 | + | 0.976685i | \(0.568871\pi\) | |||||||
\(98\) | −807.410 | −0.832253 | ||||||||
\(99\) | 282.630 | 0.286923 | ||||||||
\(100\) | 72.8564 | 0.0728564 | ||||||||
\(101\) | 775.920 | 0.764425 | 0.382213 | − | 0.924074i | \(-0.375162\pi\) | ||||
0.382213 | + | 0.924074i | \(0.375162\pi\) | |||||||
\(102\) | −1201.37 | −1.16621 | ||||||||
\(103\) | −1437.83 | −1.37547 | −0.687737 | − | 0.725960i | \(-0.741396\pi\) | ||||
−0.687737 | + | 0.725960i | \(0.741396\pi\) | |||||||
\(104\) | −958.934 | −0.904146 | ||||||||
\(105\) | 360.406 | 0.334972 | ||||||||
\(106\) | 639.505 | 0.585983 | ||||||||
\(107\) | −1562.36 | −1.41158 | −0.705789 | − | 0.708422i | \(-0.749407\pi\) | ||||
−0.705789 | + | 0.708422i | \(0.749407\pi\) | |||||||
\(108\) | 27.6360 | 0.0246229 | ||||||||
\(109\) | −1203.46 | −1.05752 | −0.528762 | − | 0.848770i | \(-0.677344\pi\) | ||||
−0.528762 | + | 0.848770i | \(0.677344\pi\) | |||||||
\(110\) | 181.702 | 0.157496 | ||||||||
\(111\) | 782.109 | 0.668779 | ||||||||
\(112\) | 782.683 | 0.660327 | ||||||||
\(113\) | −1652.95 | −1.37608 | −0.688038 | − | 0.725675i | \(-0.741528\pi\) | ||||
−0.688038 | + | 0.725675i | \(0.741528\pi\) | |||||||
\(114\) | −455.648 | −0.374345 | ||||||||
\(115\) | −203.538 | −0.165043 | ||||||||
\(116\) | 290.662 | 0.232649 | ||||||||
\(117\) | 1466.43 | 1.15873 | ||||||||
\(118\) | 1126.94 | 0.879181 | ||||||||
\(119\) | −497.445 | −0.383200 | ||||||||
\(120\) | 609.819 | 0.463905 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −1350.10 | −1.00191 | ||||||||
\(123\) | −692.974 | −0.507995 | ||||||||
\(124\) | −179.116 | −0.129718 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −842.880 | −0.595950 | ||||||||
\(127\) | −820.257 | −0.573119 | −0.286559 | − | 0.958062i | \(-0.592512\pi\) | ||||
−0.286559 | + | 0.958062i | \(0.592512\pi\) | |||||||
\(128\) | 1716.04 | 1.18498 | ||||||||
\(129\) | 3485.14 | 2.37868 | ||||||||
\(130\) | 942.766 | 0.636046 | ||||||||
\(131\) | −224.528 | −0.149749 | −0.0748744 | − | 0.997193i | \(-0.523856\pi\) | ||||
−0.0748744 | + | 0.997193i | \(0.523856\pi\) | |||||||
\(132\) | −232.701 | −0.153440 | ||||||||
\(133\) | −188.667 | −0.123004 | ||||||||
\(134\) | −1719.29 | −1.10839 | ||||||||
\(135\) | 47.4152 | 0.0302285 | ||||||||
\(136\) | −841.693 | −0.530696 | ||||||||
\(137\) | −2474.25 | −1.54299 | −0.771493 | − | 0.636237i | \(-0.780490\pi\) | ||||
−0.771493 | + | 0.636237i | \(0.780490\pi\) | |||||||
\(138\) | 976.227 | 0.602188 | ||||||||
\(139\) | 697.199 | 0.425437 | 0.212718 | − | 0.977114i | \(-0.431768\pi\) | ||||
0.212718 | + | 0.977114i | \(0.431768\pi\) | |||||||
\(140\) | −144.691 | −0.0873471 | ||||||||
\(141\) | 2257.92 | 1.34859 | ||||||||
\(142\) | −2912.50 | −1.72121 | ||||||||
\(143\) | 627.812 | 0.367135 | ||||||||
\(144\) | −2025.20 | −1.17199 | ||||||||
\(145\) | 498.691 | 0.285614 | ||||||||
\(146\) | 3379.74 | 1.91582 | ||||||||
\(147\) | 1774.09 | 0.995406 | ||||||||
\(148\) | −313.990 | −0.174391 | ||||||||
\(149\) | 3320.36 | 1.82560 | 0.912801 | − | 0.408405i | \(-0.133915\pi\) | ||||
0.912801 | + | 0.408405i | \(0.133915\pi\) | |||||||
\(150\) | −599.537 | −0.326347 | ||||||||
\(151\) | −480.979 | −0.259215 | −0.129608 | − | 0.991565i | \(-0.541372\pi\) | ||||
−0.129608 | + | 0.991565i | \(0.541372\pi\) | |||||||
\(152\) | −319.231 | −0.170349 | ||||||||
\(153\) | 1287.14 | 0.680127 | ||||||||
\(154\) | −360.855 | −0.188822 | ||||||||
\(155\) | −307.310 | −0.159250 | ||||||||
\(156\) | −1207.38 | −0.619664 | ||||||||
\(157\) | −1113.11 | −0.565832 | −0.282916 | − | 0.959145i | \(-0.591302\pi\) | ||||
−0.282916 | + | 0.959145i | \(0.591302\pi\) | |||||||
\(158\) | −258.783 | −0.130302 | ||||||||
\(159\) | −1405.16 | −0.700859 | ||||||||
\(160\) | −629.931 | −0.311253 | ||||||||
\(161\) | 404.220 | 0.197870 | ||||||||
\(162\) | −2519.27 | −1.22180 | ||||||||
\(163\) | 1089.57 | 0.523568 | 0.261784 | − | 0.965127i | \(-0.415689\pi\) | ||||
0.261784 | + | 0.965127i | \(0.415689\pi\) | |||||||
\(164\) | 278.205 | 0.132464 | ||||||||
\(165\) | −399.247 | −0.188372 | ||||||||
\(166\) | 2982.75 | 1.39461 | ||||||||
\(167\) | −1285.41 | −0.595616 | −0.297808 | − | 0.954626i | \(-0.596256\pi\) | ||||
−0.297808 | + | 0.954626i | \(0.596256\pi\) | |||||||
\(168\) | −1211.08 | −0.556173 | ||||||||
\(169\) | 1060.42 | 0.482667 | ||||||||
\(170\) | 827.502 | 0.373332 | ||||||||
\(171\) | 488.179 | 0.218316 | ||||||||
\(172\) | −1399.17 | −0.620264 | ||||||||
\(173\) | −1399.78 | −0.615163 | −0.307581 | − | 0.951522i | \(-0.599520\pi\) | ||||
−0.307581 | + | 0.951522i | \(0.599520\pi\) | |||||||
\(174\) | −2391.87 | −1.04211 | ||||||||
\(175\) | −248.247 | −0.107232 | ||||||||
\(176\) | −867.033 | −0.371336 | ||||||||
\(177\) | −2476.19 | −1.05153 | ||||||||
\(178\) | −3288.28 | −1.38464 | ||||||||
\(179\) | 225.412 | 0.0941234 | 0.0470617 | − | 0.998892i | \(-0.485014\pi\) | ||||
0.0470617 | + | 0.998892i | \(0.485014\pi\) | |||||||
\(180\) | 374.389 | 0.155029 | ||||||||
\(181\) | 243.788 | 0.100114 | 0.0500571 | − | 0.998746i | \(-0.484060\pi\) | ||||
0.0500571 | + | 0.998746i | \(0.484060\pi\) | |||||||
\(182\) | −1872.31 | −0.762553 | ||||||||
\(183\) | 2966.53 | 1.19832 | ||||||||
\(184\) | 683.953 | 0.274031 | ||||||||
\(185\) | −538.714 | −0.214092 | ||||||||
\(186\) | 1473.95 | 0.581049 | ||||||||
\(187\) | 551.055 | 0.215493 | ||||||||
\(188\) | −906.478 | −0.351658 | ||||||||
\(189\) | −94.1654 | −0.0362409 | ||||||||
\(190\) | 313.849 | 0.119837 | ||||||||
\(191\) | 2583.89 | 0.978868 | 0.489434 | − | 0.872040i | \(-0.337203\pi\) | ||||
0.489434 | + | 0.872040i | \(0.337203\pi\) | |||||||
\(192\) | −1555.99 | −0.584864 | ||||||||
\(193\) | −324.276 | −0.120943 | −0.0604713 | − | 0.998170i | \(-0.519260\pi\) | ||||
−0.0604713 | + | 0.998170i | \(0.519260\pi\) | |||||||
\(194\) | −1355.11 | −0.501501 | ||||||||
\(195\) | −2071.50 | −0.760736 | ||||||||
\(196\) | −712.237 | −0.259562 | ||||||||
\(197\) | −2961.19 | −1.07094 | −0.535472 | − | 0.844553i | \(-0.679866\pi\) | ||||
−0.535472 | + | 0.844553i | \(0.679866\pi\) | |||||||
\(198\) | 933.717 | 0.335133 | ||||||||
\(199\) | −1551.15 | −0.552555 | −0.276278 | − | 0.961078i | \(-0.589101\pi\) | ||||
−0.276278 | + | 0.961078i | \(0.589101\pi\) | |||||||
\(200\) | −420.041 | −0.148507 | ||||||||
\(201\) | 3777.72 | 1.32567 | ||||||||
\(202\) | 2563.39 | 0.892868 | ||||||||
\(203\) | −990.386 | −0.342421 | ||||||||
\(204\) | −1059.76 | −0.363717 | ||||||||
\(205\) | 477.318 | 0.162621 | ||||||||
\(206\) | −4750.12 | −1.60659 | ||||||||
\(207\) | −1045.92 | −0.351192 | ||||||||
\(208\) | −4498.62 | −1.49963 | ||||||||
\(209\) | 209.000 | 0.0691714 | ||||||||
\(210\) | 1190.66 | 0.391255 | ||||||||
\(211\) | 2329.33 | 0.759989 | 0.379994 | − | 0.924989i | \(-0.375926\pi\) | ||||
0.379994 | + | 0.924989i | \(0.375926\pi\) | |||||||
\(212\) | 564.124 | 0.182756 | ||||||||
\(213\) | 6399.53 | 2.05863 | ||||||||
\(214\) | −5161.52 | −1.64876 | ||||||||
\(215\) | −2400.55 | −0.761472 | ||||||||
\(216\) | −159.331 | −0.0501902 | ||||||||
\(217\) | 610.309 | 0.190924 | ||||||||
\(218\) | −3975.82 | −1.23521 | ||||||||
\(219\) | −7426.18 | −2.29139 | ||||||||
\(220\) | 160.284 | 0.0491197 | ||||||||
\(221\) | 2859.16 | 0.870263 | ||||||||
\(222\) | 2583.83 | 0.781151 | ||||||||
\(223\) | 192.527 | 0.0578141 | 0.0289070 | − | 0.999582i | \(-0.490797\pi\) | ||||
0.0289070 | + | 0.999582i | \(0.490797\pi\) | |||||||
\(224\) | 1251.03 | 0.373159 | ||||||||
\(225\) | 642.341 | 0.190323 | ||||||||
\(226\) | −5460.81 | −1.60729 | ||||||||
\(227\) | 189.492 | 0.0554053 | 0.0277026 | − | 0.999616i | \(-0.491181\pi\) | ||||
0.0277026 | + | 0.999616i | \(0.491181\pi\) | |||||||
\(228\) | −401.939 | −0.116750 | ||||||||
\(229\) | −3616.47 | −1.04360 | −0.521798 | − | 0.853069i | \(-0.674738\pi\) | ||||
−0.521798 | + | 0.853069i | \(0.674738\pi\) | |||||||
\(230\) | −672.422 | −0.192775 | ||||||||
\(231\) | 792.894 | 0.225838 | ||||||||
\(232\) | −1675.76 | −0.474221 | ||||||||
\(233\) | 3665.01 | 1.03048 | 0.515242 | − | 0.857045i | \(-0.327702\pi\) | ||||
0.515242 | + | 0.857045i | \(0.327702\pi\) | |||||||
\(234\) | 4844.61 | 1.35343 | ||||||||
\(235\) | −1555.25 | −0.431716 | ||||||||
\(236\) | 994.103 | 0.274198 | ||||||||
\(237\) | 568.615 | 0.155846 | ||||||||
\(238\) | −1643.40 | −0.447587 | ||||||||
\(239\) | −191.701 | −0.0518833 | −0.0259416 | − | 0.999663i | \(-0.508258\pi\) | ||||
−0.0259416 | + | 0.999663i | \(0.508258\pi\) | |||||||
\(240\) | 2860.83 | 0.769440 | ||||||||
\(241\) | −130.956 | −0.0350025 | −0.0175012 | − | 0.999847i | \(-0.505571\pi\) | ||||
−0.0175012 | + | 0.999847i | \(0.505571\pi\) | |||||||
\(242\) | 399.744 | 0.106184 | ||||||||
\(243\) | 5279.45 | 1.39373 | ||||||||
\(244\) | −1190.96 | −0.312473 | ||||||||
\(245\) | −1221.99 | −0.318653 | ||||||||
\(246\) | −2289.36 | −0.593350 | ||||||||
\(247\) | 1084.40 | 0.279348 | ||||||||
\(248\) | 1032.66 | 0.264412 | ||||||||
\(249\) | −6553.88 | −1.66801 | ||||||||
\(250\) | 412.959 | 0.104471 | ||||||||
\(251\) | −3751.83 | −0.943481 | −0.471740 | − | 0.881737i | \(-0.656374\pi\) | ||||
−0.471740 | + | 0.881737i | \(0.656374\pi\) | |||||||
\(252\) | −743.526 | −0.185864 | ||||||||
\(253\) | −447.783 | −0.111272 | ||||||||
\(254\) | −2709.86 | −0.669417 | ||||||||
\(255\) | −1818.24 | −0.446520 | ||||||||
\(256\) | 3954.41 | 0.965433 | ||||||||
\(257\) | −793.367 | −0.192564 | −0.0962818 | − | 0.995354i | \(-0.530695\pi\) | ||||
−0.0962818 | + | 0.995354i | \(0.530695\pi\) | |||||||
\(258\) | 11513.8 | 2.77836 | ||||||||
\(259\) | 1069.87 | 0.256674 | ||||||||
\(260\) | 831.638 | 0.198369 | ||||||||
\(261\) | 2562.63 | 0.607751 | ||||||||
\(262\) | −741.767 | −0.174910 | ||||||||
\(263\) | −4848.74 | −1.13683 | −0.568414 | − | 0.822742i | \(-0.692443\pi\) | ||||
−0.568414 | + | 0.822742i | \(0.692443\pi\) | |||||||
\(264\) | 1341.60 | 0.312765 | ||||||||
\(265\) | 967.870 | 0.224361 | ||||||||
\(266\) | −623.295 | −0.143672 | ||||||||
\(267\) | 7225.21 | 1.65609 | ||||||||
\(268\) | −1516.63 | −0.345681 | ||||||||
\(269\) | 3140.99 | 0.711930 | 0.355965 | − | 0.934499i | \(-0.384152\pi\) | ||||
0.355965 | + | 0.934499i | \(0.384152\pi\) | |||||||
\(270\) | 156.644 | 0.0353077 | ||||||||
\(271\) | 3402.74 | 0.762738 | 0.381369 | − | 0.924423i | \(-0.375453\pi\) | ||||
0.381369 | + | 0.924423i | \(0.375453\pi\) | |||||||
\(272\) | −3948.62 | −0.880221 | ||||||||
\(273\) | 4113.95 | 0.912043 | ||||||||
\(274\) | −8174.10 | −1.80225 | ||||||||
\(275\) | 275.000 | 0.0603023 | ||||||||
\(276\) | 861.154 | 0.187809 | ||||||||
\(277\) | 7059.57 | 1.53130 | 0.765648 | − | 0.643260i | \(-0.222419\pi\) | ||||
0.765648 | + | 0.643260i | \(0.222419\pi\) | |||||||
\(278\) | 2303.32 | 0.496920 | ||||||||
\(279\) | −1579.18 | −0.338864 | ||||||||
\(280\) | 834.190 | 0.178044 | ||||||||
\(281\) | 7065.36 | 1.49994 | 0.749971 | − | 0.661470i | \(-0.230067\pi\) | ||||
0.749971 | + | 0.661470i | \(0.230067\pi\) | |||||||
\(282\) | 7459.44 | 1.57519 | ||||||||
\(283\) | −5348.00 | −1.12334 | −0.561671 | − | 0.827361i | \(-0.689841\pi\) | ||||
−0.561671 | + | 0.827361i | \(0.689841\pi\) | |||||||
\(284\) | −2569.19 | −0.536808 | ||||||||
\(285\) | −689.609 | −0.143329 | ||||||||
\(286\) | 2074.09 | 0.428822 | ||||||||
\(287\) | −947.940 | −0.194966 | ||||||||
\(288\) | −3237.04 | −0.662307 | ||||||||
\(289\) | −2403.40 | −0.489192 | ||||||||
\(290\) | 1647.51 | 0.333604 | ||||||||
\(291\) | 2977.53 | 0.599815 | ||||||||
\(292\) | 2981.35 | 0.597502 | ||||||||
\(293\) | 5155.07 | 1.02786 | 0.513929 | − | 0.857833i | \(-0.328189\pi\) | ||||
0.513929 | + | 0.857833i | \(0.328189\pi\) | |||||||
\(294\) | 5861.02 | 1.16266 | ||||||||
\(295\) | 1705.59 | 0.336621 | ||||||||
\(296\) | 1810.26 | 0.355469 | ||||||||
\(297\) | 104.314 | 0.0203801 | ||||||||
\(298\) | 10969.4 | 2.13235 | ||||||||
\(299\) | −2323.33 | −0.449371 | ||||||||
\(300\) | −528.867 | −0.101780 | ||||||||
\(301\) | 4767.44 | 0.912925 | ||||||||
\(302\) | −1589.00 | −0.302770 | ||||||||
\(303\) | −5632.44 | −1.06790 | ||||||||
\(304\) | −1497.60 | −0.282544 | ||||||||
\(305\) | −2043.33 | −0.383610 | ||||||||
\(306\) | 4252.31 | 0.794406 | ||||||||
\(307\) | 343.562 | 0.0638701 | 0.0319351 | − | 0.999490i | \(-0.489833\pi\) | ||||
0.0319351 | + | 0.999490i | \(0.489833\pi\) | |||||||
\(308\) | −318.320 | −0.0588894 | ||||||||
\(309\) | 10437.3 | 1.92154 | ||||||||
\(310\) | −1015.25 | −0.186008 | ||||||||
\(311\) | −2132.90 | −0.388893 | −0.194447 | − | 0.980913i | \(-0.562291\pi\) | ||||
−0.194447 | + | 0.980913i | \(0.562291\pi\) | |||||||
\(312\) | 6960.93 | 1.26309 | ||||||||
\(313\) | −2932.08 | −0.529492 | −0.264746 | − | 0.964318i | \(-0.585288\pi\) | ||||
−0.264746 | + | 0.964318i | \(0.585288\pi\) | |||||||
\(314\) | −3677.34 | −0.660906 | ||||||||
\(315\) | −1275.67 | −0.228178 | ||||||||
\(316\) | −228.279 | −0.0406383 | ||||||||
\(317\) | −521.450 | −0.0923898 | −0.0461949 | − | 0.998932i | \(-0.514710\pi\) | ||||
−0.0461949 | + | 0.998932i | \(0.514710\pi\) | |||||||
\(318\) | −4642.19 | −0.818620 | ||||||||
\(319\) | 1097.12 | 0.192561 | ||||||||
\(320\) | 1071.76 | 0.187229 | ||||||||
\(321\) | 11341.2 | 1.97198 | ||||||||
\(322\) | 1335.41 | 0.231117 | ||||||||
\(323\) | 951.822 | 0.163965 | ||||||||
\(324\) | −2222.31 | −0.381054 | ||||||||
\(325\) | 1426.85 | 0.243530 | ||||||||
\(326\) | 3599.58 | 0.611540 | ||||||||
\(327\) | 8735.93 | 1.47736 | ||||||||
\(328\) | −1603.94 | −0.270009 | ||||||||
\(329\) | 3088.68 | 0.517582 | ||||||||
\(330\) | −1318.98 | −0.220023 | ||||||||
\(331\) | −1301.60 | −0.216141 | −0.108070 | − | 0.994143i | \(-0.534467\pi\) | ||||
−0.108070 | + | 0.994143i | \(0.534467\pi\) | |||||||
\(332\) | 2631.16 | 0.434950 | ||||||||
\(333\) | −2768.30 | −0.455562 | ||||||||
\(334\) | −4246.57 | −0.695694 | ||||||||
\(335\) | −2602.08 | −0.424379 | ||||||||
\(336\) | −5681.53 | −0.922478 | ||||||||
\(337\) | −3908.83 | −0.631832 | −0.315916 | − | 0.948787i | \(-0.602312\pi\) | ||||
−0.315916 | + | 0.948787i | \(0.602312\pi\) | |||||||
\(338\) | 3503.28 | 0.563767 | ||||||||
\(339\) | 11998.8 | 1.92238 | ||||||||
\(340\) | 729.961 | 0.116434 | ||||||||
\(341\) | −676.082 | −0.107366 | ||||||||
\(342\) | 1612.78 | 0.254998 | ||||||||
\(343\) | 5832.78 | 0.918194 | ||||||||
\(344\) | 8066.65 | 1.26432 | ||||||||
\(345\) | 1477.49 | 0.230566 | ||||||||
\(346\) | −4624.41 | −0.718525 | ||||||||
\(347\) | −7032.79 | −1.08801 | −0.544006 | − | 0.839081i | \(-0.683093\pi\) | ||||
−0.544006 | + | 0.839081i | \(0.683093\pi\) | |||||||
\(348\) | −2109.93 | −0.325011 | ||||||||
\(349\) | −7182.01 | −1.10156 | −0.550780 | − | 0.834651i | \(-0.685670\pi\) | ||||
−0.550780 | + | 0.834651i | \(0.685670\pi\) | |||||||
\(350\) | −820.126 | −0.125250 | ||||||||
\(351\) | 541.234 | 0.0823046 | ||||||||
\(352\) | −1385.85 | −0.209846 | ||||||||
\(353\) | 110.537 | 0.0166666 | 0.00833330 | − | 0.999965i | \(-0.497347\pi\) | ||||
0.00833330 | + | 0.999965i | \(0.497347\pi\) | |||||||
\(354\) | −8180.51 | −1.22822 | ||||||||
\(355\) | −4407.98 | −0.659017 | ||||||||
\(356\) | −2900.67 | −0.431841 | ||||||||
\(357\) | 3610.97 | 0.535331 | ||||||||
\(358\) | 744.688 | 0.109938 | ||||||||
\(359\) | 9563.33 | 1.40594 | 0.702971 | − | 0.711218i | \(-0.251856\pi\) | ||||
0.702971 | + | 0.711218i | \(0.251856\pi\) | |||||||
\(360\) | −2158.48 | −0.316005 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 805.397 | 0.116936 | ||||||||
\(363\) | −878.344 | −0.127000 | ||||||||
\(364\) | −1651.61 | −0.237824 | ||||||||
\(365\) | 5115.12 | 0.733528 | ||||||||
\(366\) | 9800.43 | 1.39966 | ||||||||
\(367\) | −6333.20 | −0.900791 | −0.450396 | − | 0.892829i | \(-0.648717\pi\) | ||||
−0.450396 | + | 0.892829i | \(0.648717\pi\) | |||||||
\(368\) | 3208.61 | 0.454512 | ||||||||
\(369\) | 2452.80 | 0.346038 | ||||||||
\(370\) | −1779.73 | −0.250065 | ||||||||
\(371\) | −1922.16 | −0.268986 | ||||||||
\(372\) | 1300.21 | 0.181217 | ||||||||
\(373\) | −7815.40 | −1.08490 | −0.542448 | − | 0.840089i | \(-0.682502\pi\) | ||||
−0.542448 | + | 0.840089i | \(0.682502\pi\) | |||||||
\(374\) | 1820.50 | 0.251701 | ||||||||
\(375\) | −907.380 | −0.124952 | ||||||||
\(376\) | 5226.15 | 0.716803 | ||||||||
\(377\) | 5692.43 | 0.777653 | ||||||||
\(378\) | −311.092 | −0.0423302 | ||||||||
\(379\) | −3004.64 | −0.407224 | −0.203612 | − | 0.979052i | \(-0.565268\pi\) | ||||
−0.203612 | + | 0.979052i | \(0.565268\pi\) | |||||||
\(380\) | 276.854 | 0.0373745 | ||||||||
\(381\) | 5954.28 | 0.800648 | ||||||||
\(382\) | 8536.33 | 1.14334 | ||||||||
\(383\) | 13591.9 | 1.81335 | 0.906677 | − | 0.421826i | \(-0.138611\pi\) | ||||
0.906677 | + | 0.421826i | \(0.138611\pi\) | |||||||
\(384\) | −12456.8 | −1.65542 | ||||||||
\(385\) | −546.143 | −0.0722961 | ||||||||
\(386\) | −1071.30 | −0.141264 | ||||||||
\(387\) | −12335.8 | −1.62032 | ||||||||
\(388\) | −1195.38 | −0.156407 | ||||||||
\(389\) | −5797.55 | −0.755648 | −0.377824 | − | 0.925877i | \(-0.623328\pi\) | ||||
−0.377824 | + | 0.925877i | \(0.623328\pi\) | |||||||
\(390\) | −6843.57 | −0.888558 | ||||||||
\(391\) | −2039.28 | −0.263762 | ||||||||
\(392\) | 4106.28 | 0.529078 | ||||||||
\(393\) | 1629.86 | 0.209200 | ||||||||
\(394\) | −9782.80 | −1.25089 | ||||||||
\(395\) | −391.660 | −0.0498900 | ||||||||
\(396\) | 823.655 | 0.104521 | ||||||||
\(397\) | 4511.41 | 0.570331 | 0.285165 | − | 0.958478i | \(-0.407951\pi\) | ||||
0.285165 | + | 0.958478i | \(0.407951\pi\) | |||||||
\(398\) | −5124.51 | −0.645398 | ||||||||
\(399\) | 1369.54 | 0.171837 | ||||||||
\(400\) | −1970.53 | −0.246316 | ||||||||
\(401\) | 5389.27 | 0.671140 | 0.335570 | − | 0.942015i | \(-0.391071\pi\) | ||||
0.335570 | + | 0.942015i | \(0.391071\pi\) | |||||||
\(402\) | 12480.4 | 1.54842 | ||||||||
\(403\) | −3507.87 | −0.433596 | ||||||||
\(404\) | 2261.23 | 0.278466 | ||||||||
\(405\) | −3812.83 | −0.467805 | ||||||||
\(406\) | −3271.91 | −0.399956 | ||||||||
\(407\) | −1185.17 | −0.144341 | ||||||||
\(408\) | 6109.88 | 0.741383 | ||||||||
\(409\) | 9962.17 | 1.20440 | 0.602198 | − | 0.798347i | \(-0.294292\pi\) | ||||
0.602198 | + | 0.798347i | \(0.294292\pi\) | |||||||
\(410\) | 1576.90 | 0.189945 | ||||||||
\(411\) | 17960.7 | 2.15556 | ||||||||
\(412\) | −4190.21 | −0.501060 | ||||||||
\(413\) | −3387.25 | −0.403573 | ||||||||
\(414\) | −3455.39 | −0.410201 | ||||||||
\(415\) | 4514.29 | 0.533970 | ||||||||
\(416\) | −7190.51 | −0.847461 | ||||||||
\(417\) | −5061.00 | −0.594336 | ||||||||
\(418\) | 690.468 | 0.0807940 | ||||||||
\(419\) | 16460.3 | 1.91919 | 0.959594 | − | 0.281387i | \(-0.0907946\pi\) | ||||
0.959594 | + | 0.281387i | \(0.0907946\pi\) | |||||||
\(420\) | 1050.32 | 0.122024 | ||||||||
\(421\) | 15275.0 | 1.76830 | 0.884151 | − | 0.467200i | \(-0.154737\pi\) | ||||
0.884151 | + | 0.467200i | \(0.154737\pi\) | |||||||
\(422\) | 7695.34 | 0.887686 | ||||||||
\(423\) | −7992.00 | −0.918639 | ||||||||
\(424\) | −3252.36 | −0.372520 | ||||||||
\(425\) | 1252.40 | 0.142942 | ||||||||
\(426\) | 21142.0 | 2.40453 | ||||||||
\(427\) | 4058.01 | 0.459908 | ||||||||
\(428\) | −4553.11 | −0.514212 | ||||||||
\(429\) | −4557.31 | −0.512888 | ||||||||
\(430\) | −7930.65 | −0.889418 | ||||||||
\(431\) | 5924.25 | 0.662090 | 0.331045 | − | 0.943615i | \(-0.392599\pi\) | ||||
0.331045 | + | 0.943615i | \(0.392599\pi\) | |||||||
\(432\) | −747.465 | −0.0832463 | ||||||||
\(433\) | 1296.43 | 0.143886 | 0.0719429 | − | 0.997409i | \(-0.477080\pi\) | ||||
0.0719429 | + | 0.997409i | \(0.477080\pi\) | |||||||
\(434\) | 2016.26 | 0.223004 | ||||||||
\(435\) | −3620.01 | −0.399003 | ||||||||
\(436\) | −3507.18 | −0.385237 | ||||||||
\(437\) | −773.443 | −0.0846654 | ||||||||
\(438\) | −24533.7 | −2.67640 | ||||||||
\(439\) | −10400.8 | −1.13076 | −0.565379 | − | 0.824831i | \(-0.691270\pi\) | ||||
−0.565379 | + | 0.824831i | \(0.691270\pi\) | |||||||
\(440\) | −924.090 | −0.100123 | ||||||||
\(441\) | −6279.46 | −0.678055 | ||||||||
\(442\) | 9445.74 | 1.01649 | ||||||||
\(443\) | −11481.8 | −1.23142 | −0.615709 | − | 0.787973i | \(-0.711130\pi\) | ||||
−0.615709 | + | 0.787973i | \(0.711130\pi\) | |||||||
\(444\) | 2279.26 | 0.243624 | ||||||||
\(445\) | −4976.70 | −0.530153 | ||||||||
\(446\) | 636.045 | 0.0675282 | ||||||||
\(447\) | −24102.6 | −2.55037 | ||||||||
\(448\) | −2128.49 | −0.224468 | ||||||||
\(449\) | −8437.38 | −0.886825 | −0.443412 | − | 0.896318i | \(-0.646232\pi\) | ||||
−0.443412 | + | 0.896318i | \(0.646232\pi\) | |||||||
\(450\) | 2122.08 | 0.222302 | ||||||||
\(451\) | 1050.10 | 0.109639 | ||||||||
\(452\) | −4817.12 | −0.501279 | ||||||||
\(453\) | 3491.44 | 0.362124 | ||||||||
\(454\) | 626.018 | 0.0647147 | ||||||||
\(455\) | −2833.68 | −0.291967 | ||||||||
\(456\) | 2317.31 | 0.237978 | ||||||||
\(457\) | −8733.81 | −0.893983 | −0.446992 | − | 0.894538i | \(-0.647505\pi\) | ||||
−0.446992 | + | 0.894538i | \(0.647505\pi\) | |||||||
\(458\) | −11947.6 | −1.21895 | ||||||||
\(459\) | 475.062 | 0.0483093 | ||||||||
\(460\) | −593.160 | −0.0601223 | ||||||||
\(461\) | −6012.15 | −0.607406 | −0.303703 | − | 0.952767i | \(-0.598223\pi\) | ||||
−0.303703 | + | 0.952767i | \(0.598223\pi\) | |||||||
\(462\) | 2619.46 | 0.263784 | ||||||||
\(463\) | −19497.3 | −1.95705 | −0.978527 | − | 0.206119i | \(-0.933917\pi\) | ||||
−0.978527 | + | 0.206119i | \(0.933917\pi\) | |||||||
\(464\) | −7861.47 | −0.786551 | ||||||||
\(465\) | 2230.77 | 0.222472 | ||||||||
\(466\) | 12108.0 | 1.20363 | ||||||||
\(467\) | −2105.61 | −0.208643 | −0.104321 | − | 0.994544i | \(-0.533267\pi\) | ||||
−0.104321 | + | 0.994544i | \(0.533267\pi\) | |||||||
\(468\) | 4273.56 | 0.422105 | ||||||||
\(469\) | 5167.66 | 0.508786 | ||||||||
\(470\) | −5138.03 | −0.504255 | ||||||||
\(471\) | 8080.09 | 0.790469 | ||||||||
\(472\) | −5731.34 | −0.558911 | ||||||||
\(473\) | −5281.22 | −0.513384 | ||||||||
\(474\) | 1878.52 | 0.182032 | ||||||||
\(475\) | 475.000 | 0.0458831 | ||||||||
\(476\) | −1449.68 | −0.139593 | ||||||||
\(477\) | 4973.62 | 0.477414 | ||||||||
\(478\) | −633.317 | −0.0606009 | ||||||||
\(479\) | −10637.9 | −1.01473 | −0.507367 | − | 0.861730i | \(-0.669381\pi\) | ||||
−0.507367 | + | 0.861730i | \(0.669381\pi\) | |||||||
\(480\) | 4572.69 | 0.434821 | ||||||||
\(481\) | −6149.29 | −0.582918 | ||||||||
\(482\) | −432.635 | −0.0408838 | ||||||||
\(483\) | −2934.25 | −0.276424 | ||||||||
\(484\) | 352.625 | 0.0331165 | ||||||||
\(485\) | −2050.91 | −0.192015 | ||||||||
\(486\) | 17441.6 | 1.62791 | ||||||||
\(487\) | −6695.45 | −0.622997 | −0.311499 | − | 0.950247i | \(-0.600831\pi\) | ||||
−0.311499 | + | 0.950247i | \(0.600831\pi\) | |||||||
\(488\) | 6866.27 | 0.636929 | ||||||||
\(489\) | −7909.22 | −0.731426 | ||||||||
\(490\) | −4037.05 | −0.372195 | ||||||||
\(491\) | −5573.36 | −0.512265 | −0.256133 | − | 0.966642i | \(-0.582448\pi\) | ||||
−0.256133 | + | 0.966642i | \(0.582448\pi\) | |||||||
\(492\) | −2019.50 | −0.185053 | ||||||||
\(493\) | 4996.47 | 0.456450 | ||||||||
\(494\) | 3582.51 | 0.326285 | ||||||||
\(495\) | 1413.15 | 0.128316 | ||||||||
\(496\) | 4844.50 | 0.438558 | ||||||||
\(497\) | 8754.12 | 0.790093 | ||||||||
\(498\) | −21651.9 | −1.94828 | ||||||||
\(499\) | −18791.5 | −1.68581 | −0.842907 | − | 0.538059i | \(-0.819158\pi\) | ||||
−0.842907 | + | 0.538059i | \(0.819158\pi\) | |||||||
\(500\) | 364.282 | 0.0325824 | ||||||||
\(501\) | 9330.83 | 0.832077 | ||||||||
\(502\) | −12394.8 | −1.10201 | ||||||||
\(503\) | −13598.0 | −1.20538 | −0.602690 | − | 0.797976i | \(-0.705904\pi\) | ||||
−0.602690 | + | 0.797976i | \(0.705904\pi\) | |||||||
\(504\) | 4286.67 | 0.378856 | ||||||||
\(505\) | 3879.60 | 0.341861 | ||||||||
\(506\) | −1479.33 | −0.129969 | ||||||||
\(507\) | −7697.62 | −0.674287 | ||||||||
\(508\) | −2390.44 | −0.208777 | ||||||||
\(509\) | −9983.72 | −0.869392 | −0.434696 | − | 0.900577i | \(-0.643144\pi\) | ||||
−0.434696 | + | 0.900577i | \(0.643144\pi\) | |||||||
\(510\) | −6006.87 | −0.521546 | ||||||||
\(511\) | −10158.5 | −0.879424 | ||||||||
\(512\) | −664.221 | −0.0573334 | ||||||||
\(513\) | 180.178 | 0.0155069 | ||||||||
\(514\) | −2621.02 | −0.224919 | ||||||||
\(515\) | −7189.16 | −0.615130 | ||||||||
\(516\) | 10156.6 | 0.866510 | ||||||||
\(517\) | −3421.55 | −0.291063 | ||||||||
\(518\) | 3534.50 | 0.299802 | ||||||||
\(519\) | 10161.0 | 0.859384 | ||||||||
\(520\) | −4794.67 | −0.404346 | ||||||||
\(521\) | −13869.7 | −1.16630 | −0.583151 | − | 0.812364i | \(-0.698180\pi\) | ||||
−0.583151 | + | 0.812364i | \(0.698180\pi\) | |||||||
\(522\) | 8466.10 | 0.709868 | ||||||||
\(523\) | 13770.6 | 1.15133 | 0.575667 | − | 0.817684i | \(-0.304743\pi\) | ||||
0.575667 | + | 0.817684i | \(0.304743\pi\) | |||||||
\(524\) | −654.332 | −0.0545508 | ||||||||
\(525\) | 1802.03 | 0.149804 | ||||||||
\(526\) | −16018.6 | −1.32784 | ||||||||
\(527\) | −3078.99 | −0.254503 | ||||||||
\(528\) | 6293.82 | 0.518757 | ||||||||
\(529\) | −10509.9 | −0.863804 | ||||||||
\(530\) | 3197.53 | 0.262060 | ||||||||
\(531\) | 8764.55 | 0.716288 | ||||||||
\(532\) | −549.825 | −0.0448081 | ||||||||
\(533\) | 5448.47 | 0.442776 | ||||||||
\(534\) | 23869.7 | 1.93435 | ||||||||
\(535\) | −7811.79 | −0.631277 | ||||||||
\(536\) | 8743.85 | 0.704621 | ||||||||
\(537\) | −1636.28 | −0.131491 | ||||||||
\(538\) | 10376.8 | 0.831552 | ||||||||
\(539\) | −2688.38 | −0.214836 | ||||||||
\(540\) | 138.180 | 0.0110117 | ||||||||
\(541\) | 17008.9 | 1.35170 | 0.675848 | − | 0.737041i | \(-0.263777\pi\) | ||||
0.675848 | + | 0.737041i | \(0.263777\pi\) | |||||||
\(542\) | 11241.6 | 0.890897 | ||||||||
\(543\) | −1769.67 | −0.139860 | ||||||||
\(544\) | −6311.39 | −0.497424 | ||||||||
\(545\) | −6017.28 | −0.472939 | ||||||||
\(546\) | 13591.2 | 1.06529 | ||||||||
\(547\) | −5652.22 | −0.441812 | −0.220906 | − | 0.975295i | \(-0.570901\pi\) | ||||
−0.220906 | + | 0.975295i | \(0.570901\pi\) | |||||||
\(548\) | −7210.58 | −0.562082 | ||||||||
\(549\) | −10500.1 | −0.816274 | ||||||||
\(550\) | 908.510 | 0.0704345 | ||||||||
\(551\) | 1895.02 | 0.146517 | ||||||||
\(552\) | −4964.84 | −0.382822 | ||||||||
\(553\) | 777.826 | 0.0598129 | ||||||||
\(554\) | 23322.5 | 1.78859 | ||||||||
\(555\) | 3910.54 | 0.299087 | ||||||||
\(556\) | 2031.82 | 0.154979 | ||||||||
\(557\) | 5392.78 | 0.410232 | 0.205116 | − | 0.978738i | \(-0.434243\pi\) | ||||
0.205116 | + | 0.978738i | \(0.434243\pi\) | |||||||
\(558\) | −5217.10 | −0.395802 | ||||||||
\(559\) | −27401.8 | −2.07329 | ||||||||
\(560\) | 3913.42 | 0.295307 | ||||||||
\(561\) | −4000.13 | −0.301044 | ||||||||
\(562\) | 23341.6 | 1.75197 | ||||||||
\(563\) | 21450.9 | 1.60577 | 0.802883 | − | 0.596137i | \(-0.203298\pi\) | ||||
0.802883 | + | 0.596137i | \(0.203298\pi\) | |||||||
\(564\) | 6580.16 | 0.491267 | ||||||||
\(565\) | −8264.76 | −0.615400 | ||||||||
\(566\) | −17668.0 | −1.31209 | ||||||||
\(567\) | 7572.17 | 0.560849 | ||||||||
\(568\) | 14812.2 | 1.09420 | ||||||||
\(569\) | 1495.70 | 0.110199 | 0.0550994 | − | 0.998481i | \(-0.482452\pi\) | ||||
0.0550994 | + | 0.998481i | \(0.482452\pi\) | |||||||
\(570\) | −2278.24 | −0.167412 | ||||||||
\(571\) | 15375.5 | 1.12688 | 0.563438 | − | 0.826159i | \(-0.309479\pi\) | ||||
0.563438 | + | 0.826159i | \(0.309479\pi\) | |||||||
\(572\) | 1829.60 | 0.133740 | ||||||||
\(573\) | −18756.6 | −1.36748 | ||||||||
\(574\) | −3131.68 | −0.227725 | ||||||||
\(575\) | −1017.69 | −0.0738096 | ||||||||
\(576\) | 5507.48 | 0.398400 | ||||||||
\(577\) | −16691.0 | −1.20425 | −0.602127 | − | 0.798401i | \(-0.705680\pi\) | ||||
−0.602127 | + | 0.798401i | \(0.705680\pi\) | |||||||
\(578\) | −7940.05 | −0.571389 | ||||||||
\(579\) | 2353.93 | 0.168957 | ||||||||
\(580\) | 1453.31 | 0.104044 | ||||||||
\(581\) | −8965.26 | −0.640175 | ||||||||
\(582\) | 9836.79 | 0.700598 | ||||||||
\(583\) | 2129.31 | 0.151264 | ||||||||
\(584\) | −17188.5 | −1.21792 | ||||||||
\(585\) | 7332.16 | 0.518201 | ||||||||
\(586\) | 17030.7 | 1.20056 | ||||||||
\(587\) | −13097.7 | −0.920957 | −0.460478 | − | 0.887671i | \(-0.652322\pi\) | ||||
−0.460478 | + | 0.887671i | \(0.652322\pi\) | |||||||
\(588\) | 5170.16 | 0.362608 | ||||||||
\(589\) | −1167.78 | −0.0816934 | ||||||||
\(590\) | 5634.71 | 0.393182 | ||||||||
\(591\) | 21495.4 | 1.49611 | ||||||||
\(592\) | 8492.41 | 0.589588 | ||||||||
\(593\) | 7213.10 | 0.499505 | 0.249752 | − | 0.968310i | \(-0.419651\pi\) | ||||
0.249752 | + | 0.968310i | \(0.419651\pi\) | |||||||
\(594\) | 344.618 | 0.0238044 | ||||||||
\(595\) | −2487.23 | −0.171372 | ||||||||
\(596\) | 9676.38 | 0.665033 | ||||||||
\(597\) | 11259.9 | 0.771921 | ||||||||
\(598\) | −7675.53 | −0.524876 | ||||||||
\(599\) | 26706.6 | 1.82171 | 0.910855 | − | 0.412727i | \(-0.135424\pi\) | ||||
0.910855 | + | 0.412727i | \(0.135424\pi\) | |||||||
\(600\) | 3049.09 | 0.207465 | ||||||||
\(601\) | 5806.31 | 0.394084 | 0.197042 | − | 0.980395i | \(-0.436867\pi\) | ||||
0.197042 | + | 0.980395i | \(0.436867\pi\) | |||||||
\(602\) | 15750.0 | 1.06632 | ||||||||
\(603\) | −13371.4 | −0.903026 | ||||||||
\(604\) | −1401.69 | −0.0944274 | ||||||||
\(605\) | 605.000 | 0.0406558 | ||||||||
\(606\) | −18607.7 | −1.24734 | ||||||||
\(607\) | 3285.76 | 0.219712 | 0.109856 | − | 0.993948i | \(-0.464961\pi\) | ||||
0.109856 | + | 0.993948i | \(0.464961\pi\) | |||||||
\(608\) | −2393.74 | −0.159669 | ||||||||
\(609\) | 7189.25 | 0.478363 | ||||||||
\(610\) | −6750.51 | −0.448066 | ||||||||
\(611\) | −17752.8 | −1.17545 | ||||||||
\(612\) | 3751.07 | 0.247758 | ||||||||
\(613\) | −12836.7 | −0.845790 | −0.422895 | − | 0.906179i | \(-0.638986\pi\) | ||||
−0.422895 | + | 0.906179i | \(0.638986\pi\) | |||||||
\(614\) | 1135.02 | 0.0746019 | ||||||||
\(615\) | −3464.87 | −0.227182 | ||||||||
\(616\) | 1835.22 | 0.120037 | ||||||||
\(617\) | −9678.22 | −0.631492 | −0.315746 | − | 0.948844i | \(-0.602255\pi\) | ||||
−0.315746 | + | 0.948844i | \(0.602255\pi\) | |||||||
\(618\) | 34481.3 | 2.24441 | ||||||||
\(619\) | 23000.6 | 1.49349 | 0.746747 | − | 0.665108i | \(-0.231614\pi\) | ||||
0.746747 | + | 0.665108i | \(0.231614\pi\) | |||||||
\(620\) | −895.579 | −0.0580118 | ||||||||
\(621\) | −386.031 | −0.0249451 | ||||||||
\(622\) | −7046.41 | −0.454237 | ||||||||
\(623\) | 9883.59 | 0.635598 | ||||||||
\(624\) | 32655.7 | 2.09499 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −9686.63 | −0.618460 | ||||||||
\(627\) | −1517.14 | −0.0966327 | ||||||||
\(628\) | −3243.88 | −0.206122 | ||||||||
\(629\) | −5397.47 | −0.342148 | ||||||||
\(630\) | −4214.40 | −0.266517 | ||||||||
\(631\) | −25171.9 | −1.58808 | −0.794039 | − | 0.607866i | \(-0.792026\pi\) | ||||
−0.794039 | + | 0.607866i | \(0.792026\pi\) | |||||||
\(632\) | 1316.11 | 0.0828352 | ||||||||
\(633\) | −16908.7 | −1.06171 | ||||||||
\(634\) | −1722.70 | −0.107914 | ||||||||
\(635\) | −4101.29 | −0.256306 | ||||||||
\(636\) | −4095.00 | −0.255310 | ||||||||
\(637\) | −13948.7 | −0.867611 | ||||||||
\(638\) | 3624.52 | 0.224916 | ||||||||
\(639\) | −22651.4 | −1.40231 | ||||||||
\(640\) | 8580.19 | 0.529941 | ||||||||
\(641\) | −23772.4 | −1.46483 | −0.732414 | − | 0.680860i | \(-0.761606\pi\) | ||||
−0.732414 | + | 0.680860i | \(0.761606\pi\) | |||||||
\(642\) | 37467.7 | 2.30332 | ||||||||
\(643\) | 13205.3 | 0.809898 | 0.404949 | − | 0.914339i | \(-0.367289\pi\) | ||||
0.404949 | + | 0.914339i | \(0.367289\pi\) | |||||||
\(644\) | 1178.00 | 0.0720803 | ||||||||
\(645\) | 17425.7 | 1.06378 | ||||||||
\(646\) | 3144.51 | 0.191516 | ||||||||
\(647\) | −2137.65 | −0.129891 | −0.0649456 | − | 0.997889i | \(-0.520687\pi\) | ||||
−0.0649456 | + | 0.997889i | \(0.520687\pi\) | |||||||
\(648\) | 12812.4 | 0.776723 | ||||||||
\(649\) | 3752.29 | 0.226950 | ||||||||
\(650\) | 4713.83 | 0.284449 | ||||||||
\(651\) | −4430.26 | −0.266721 | ||||||||
\(652\) | 3175.28 | 0.190726 | ||||||||
\(653\) | 28100.5 | 1.68401 | 0.842003 | − | 0.539472i | \(-0.181376\pi\) | ||||
0.842003 | + | 0.539472i | \(0.181376\pi\) | |||||||
\(654\) | 28860.7 | 1.72560 | ||||||||
\(655\) | −1122.64 | −0.0669697 | ||||||||
\(656\) | −7524.55 | −0.447842 | ||||||||
\(657\) | 26285.2 | 1.56086 | ||||||||
\(658\) | 10204.0 | 0.604549 | ||||||||
\(659\) | 10173.2 | 0.601355 | 0.300677 | − | 0.953726i | \(-0.402787\pi\) | ||||
0.300677 | + | 0.953726i | \(0.402787\pi\) | |||||||
\(660\) | −1163.51 | −0.0686204 | ||||||||
\(661\) | 17788.8 | 1.04675 | 0.523377 | − | 0.852101i | \(-0.324672\pi\) | ||||
0.523377 | + | 0.852101i | \(0.324672\pi\) | |||||||
\(662\) | −4300.07 | −0.252458 | ||||||||
\(663\) | −20754.8 | −1.21576 | ||||||||
\(664\) | −15169.5 | −0.886582 | ||||||||
\(665\) | −943.337 | −0.0550091 | ||||||||
\(666\) | −9145.56 | −0.532107 | ||||||||
\(667\) | −4060.09 | −0.235693 | ||||||||
\(668\) | −3746.01 | −0.216972 | ||||||||
\(669\) | −1397.56 | −0.0807664 | ||||||||
\(670\) | −8596.43 | −0.495685 | ||||||||
\(671\) | −4495.33 | −0.258630 | ||||||||
\(672\) | −9081.24 | −0.521304 | ||||||||
\(673\) | 1731.14 | 0.0991541 | 0.0495771 | − | 0.998770i | \(-0.484213\pi\) | ||||
0.0495771 | + | 0.998770i | \(0.484213\pi\) | |||||||
\(674\) | −12913.5 | −0.737996 | ||||||||
\(675\) | 237.076 | 0.0135186 | ||||||||
\(676\) | 3090.33 | 0.175827 | ||||||||
\(677\) | −8414.86 | −0.477710 | −0.238855 | − | 0.971055i | \(-0.576772\pi\) | ||||
−0.238855 | + | 0.971055i | \(0.576772\pi\) | |||||||
\(678\) | 39640.2 | 2.24539 | ||||||||
\(679\) | 4073.06 | 0.230206 | ||||||||
\(680\) | −4208.47 | −0.237334 | ||||||||
\(681\) | −1375.53 | −0.0774013 | ||||||||
\(682\) | −2233.55 | −0.125406 | ||||||||
\(683\) | −23096.7 | −1.29396 | −0.646978 | − | 0.762508i | \(-0.723968\pi\) | ||||
−0.646978 | + | 0.762508i | \(0.723968\pi\) | |||||||
\(684\) | 1422.68 | 0.0795284 | ||||||||
\(685\) | −12371.2 | −0.690045 | ||||||||
\(686\) | 19269.6 | 1.07247 | ||||||||
\(687\) | 26252.1 | 1.45791 | ||||||||
\(688\) | 37842.9 | 2.09702 | ||||||||
\(689\) | 11048.0 | 0.610879 | ||||||||
\(690\) | 4881.13 | 0.269307 | ||||||||
\(691\) | −34725.8 | −1.91177 | −0.955884 | − | 0.293745i | \(-0.905098\pi\) | ||||
−0.955884 | + | 0.293745i | \(0.905098\pi\) | |||||||
\(692\) | −4079.31 | −0.224093 | ||||||||
\(693\) | −2806.48 | −0.153837 | ||||||||
\(694\) | −23234.0 | −1.27082 | ||||||||
\(695\) | 3486.00 | 0.190261 | ||||||||
\(696\) | 12164.4 | 0.662488 | ||||||||
\(697\) | 4782.33 | 0.259891 | ||||||||
\(698\) | −23727.0 | −1.28665 | ||||||||
\(699\) | −26604.4 | −1.43959 | ||||||||
\(700\) | −723.454 | −0.0390628 | ||||||||
\(701\) | −8117.51 | −0.437367 | −0.218683 | − | 0.975796i | \(-0.570176\pi\) | ||||
−0.218683 | + | 0.975796i | \(0.570176\pi\) | |||||||
\(702\) | 1788.06 | 0.0961338 | ||||||||
\(703\) | −2047.11 | −0.109827 | ||||||||
\(704\) | 2357.87 | 0.126230 | ||||||||
\(705\) | 11289.6 | 0.603108 | ||||||||
\(706\) | 365.179 | 0.0194670 | ||||||||
\(707\) | −7704.78 | −0.409856 | ||||||||
\(708\) | −7216.23 | −0.383055 | ||||||||
\(709\) | 35388.5 | 1.87453 | 0.937265 | − | 0.348618i | \(-0.113349\pi\) | ||||
0.937265 | + | 0.348618i | \(0.113349\pi\) | |||||||
\(710\) | −14562.5 | −0.769748 | ||||||||
\(711\) | −2012.63 | −0.106160 | ||||||||
\(712\) | 16723.3 | 0.880244 | ||||||||
\(713\) | 2501.96 | 0.131416 | ||||||||
\(714\) | 11929.5 | 0.625279 | ||||||||
\(715\) | 3139.06 | 0.164188 | ||||||||
\(716\) | 656.908 | 0.0342874 | ||||||||
\(717\) | 1391.56 | 0.0724811 | ||||||||
\(718\) | 31594.1 | 1.64218 | ||||||||
\(719\) | 1660.90 | 0.0861490 | 0.0430745 | − | 0.999072i | \(-0.486285\pi\) | ||||
0.0430745 | + | 0.999072i | \(0.486285\pi\) | |||||||
\(720\) | −10126.0 | −0.524130 | ||||||||
\(721\) | 14277.5 | 0.737477 | ||||||||
\(722\) | 1192.63 | 0.0614750 | ||||||||
\(723\) | 950.612 | 0.0488986 | ||||||||
\(724\) | 710.462 | 0.0364697 | ||||||||
\(725\) | 2493.45 | 0.127730 | ||||||||
\(726\) | −2901.76 | −0.148339 | ||||||||
\(727\) | 211.015 | 0.0107650 | 0.00538248 | − | 0.999986i | \(-0.498287\pi\) | ||||
0.00538248 | + | 0.999986i | \(0.498287\pi\) | |||||||
\(728\) | 9522.08 | 0.484769 | ||||||||
\(729\) | −17734.5 | −0.901003 | ||||||||
\(730\) | 16898.7 | 0.856779 | ||||||||
\(731\) | −24051.6 | −1.21694 | ||||||||
\(732\) | 8645.21 | 0.436525 | ||||||||
\(733\) | −37127.2 | −1.87084 | −0.935420 | − | 0.353539i | \(-0.884978\pi\) | ||||
−0.935420 | + | 0.353539i | \(0.884978\pi\) | |||||||
\(734\) | −20922.8 | −1.05215 | ||||||||
\(735\) | 8870.46 | 0.445159 | ||||||||
\(736\) | 5128.58 | 0.256851 | ||||||||
\(737\) | −5724.58 | −0.286116 | ||||||||
\(738\) | 8103.26 | 0.404181 | ||||||||
\(739\) | −7152.21 | −0.356019 | −0.178010 | − | 0.984029i | \(-0.556966\pi\) | ||||
−0.178010 | + | 0.984029i | \(0.556966\pi\) | |||||||
\(740\) | −1569.95 | −0.0779898 | ||||||||
\(741\) | −7871.72 | −0.390249 | ||||||||
\(742\) | −6350.20 | −0.314182 | ||||||||
\(743\) | −3028.15 | −0.149518 | −0.0747590 | − | 0.997202i | \(-0.523819\pi\) | ||||
−0.0747590 | + | 0.997202i | \(0.523819\pi\) | |||||||
\(744\) | −7496.13 | −0.369384 | ||||||||
\(745\) | 16601.8 | 0.816434 | ||||||||
\(746\) | −25819.5 | −1.26719 | ||||||||
\(747\) | 23197.7 | 1.13622 | ||||||||
\(748\) | 1605.91 | 0.0785000 | ||||||||
\(749\) | 15514.0 | 0.756835 | ||||||||
\(750\) | −2997.69 | −0.145947 | ||||||||
\(751\) | −10125.2 | −0.491975 | −0.245987 | − | 0.969273i | \(-0.579112\pi\) | ||||
−0.245987 | + | 0.969273i | \(0.579112\pi\) | |||||||
\(752\) | 24517.3 | 1.18890 | ||||||||
\(753\) | 27234.7 | 1.31804 | ||||||||
\(754\) | 18805.9 | 0.908318 | ||||||||
\(755\) | −2404.89 | −0.115925 | ||||||||
\(756\) | −274.422 | −0.0132019 | ||||||||
\(757\) | −11000.4 | −0.528160 | −0.264080 | − | 0.964501i | \(-0.585068\pi\) | ||||
−0.264080 | + | 0.964501i | \(0.585068\pi\) | |||||||
\(758\) | −9926.34 | −0.475647 | ||||||||
\(759\) | 3250.47 | 0.155447 | ||||||||
\(760\) | −1596.16 | −0.0761824 | ||||||||
\(761\) | 29465.0 | 1.40356 | 0.701778 | − | 0.712396i | \(-0.252390\pi\) | ||||
0.701778 | + | 0.712396i | \(0.252390\pi\) | |||||||
\(762\) | 19671.0 | 0.935177 | ||||||||
\(763\) | 11950.2 | 0.567005 | ||||||||
\(764\) | 7530.11 | 0.356584 | ||||||||
\(765\) | 6435.72 | 0.304162 | ||||||||
\(766\) | 44903.2 | 2.11804 | ||||||||
\(767\) | 19468.9 | 0.916533 | ||||||||
\(768\) | −28705.2 | −1.34871 | ||||||||
\(769\) | −26711.0 | −1.25257 | −0.626284 | − | 0.779595i | \(-0.715425\pi\) | ||||
−0.626284 | + | 0.779595i | \(0.715425\pi\) | |||||||
\(770\) | −1804.28 | −0.0844436 | ||||||||
\(771\) | 5759.08 | 0.269012 | ||||||||
\(772\) | −945.023 | −0.0440572 | ||||||||
\(773\) | −11057.2 | −0.514488 | −0.257244 | − | 0.966346i | \(-0.582814\pi\) | ||||
−0.257244 | + | 0.966346i | \(0.582814\pi\) | |||||||
\(774\) | −40753.4 | −1.89257 | ||||||||
\(775\) | −1536.55 | −0.0712187 | ||||||||
\(776\) | 6891.74 | 0.318813 | ||||||||
\(777\) | −7766.23 | −0.358574 | ||||||||
\(778\) | −19153.2 | −0.882616 | ||||||||
\(779\) | 1813.81 | 0.0834229 | ||||||||
\(780\) | −6036.89 | −0.277122 | ||||||||
\(781\) | −9697.55 | −0.444309 | ||||||||
\(782\) | −6737.11 | −0.308080 | ||||||||
\(783\) | 945.821 | 0.0431684 | ||||||||
\(784\) | 19263.7 | 0.877538 | ||||||||
\(785\) | −5565.54 | −0.253048 | ||||||||
\(786\) | 5384.51 | 0.244350 | ||||||||
\(787\) | 5963.94 | 0.270129 | 0.135064 | − | 0.990837i | \(-0.456876\pi\) | ||||
0.135064 | + | 0.990837i | \(0.456876\pi\) | |||||||
\(788\) | −8629.65 | −0.390125 | ||||||||
\(789\) | 35197.2 | 1.58815 | ||||||||
\(790\) | −1293.92 | −0.0582727 | ||||||||
\(791\) | 16413.6 | 0.737800 | ||||||||
\(792\) | −4748.65 | −0.213050 | ||||||||
\(793\) | −23324.2 | −1.04447 | ||||||||
\(794\) | 14904.2 | 0.666161 | ||||||||
\(795\) | −7025.81 | −0.313434 | ||||||||
\(796\) | −4520.46 | −0.201286 | ||||||||
\(797\) | −2716.54 | −0.120734 | −0.0603668 | − | 0.998176i | \(-0.519227\pi\) | ||||
−0.0603668 | + | 0.998176i | \(0.519227\pi\) | |||||||
\(798\) | 4524.52 | 0.200710 | ||||||||
\(799\) | −15582.3 | −0.689941 | ||||||||
\(800\) | −3149.65 | −0.139196 | ||||||||
\(801\) | −25573.9 | −1.12810 | ||||||||
\(802\) | 17804.4 | 0.783909 | ||||||||
\(803\) | 11253.3 | 0.494545 | ||||||||
\(804\) | 11009.2 | 0.482918 | ||||||||
\(805\) | 2021.10 | 0.0884900 | ||||||||
\(806\) | −11588.8 | −0.506451 | ||||||||
\(807\) | −22800.5 | −0.994568 | ||||||||
\(808\) | −13036.7 | −0.567612 | ||||||||
\(809\) | 21072.5 | 0.915784 | 0.457892 | − | 0.889008i | \(-0.348605\pi\) | ||||
0.457892 | + | 0.889008i | \(0.348605\pi\) | |||||||
\(810\) | −12596.3 | −0.546408 | ||||||||
\(811\) | 19349.8 | 0.837810 | 0.418905 | − | 0.908030i | \(-0.362414\pi\) | ||||
0.418905 | + | 0.908030i | \(0.362414\pi\) | |||||||
\(812\) | −2886.24 | −0.124738 | ||||||||
\(813\) | −24700.7 | −1.06555 | ||||||||
\(814\) | −3915.42 | −0.168594 | ||||||||
\(815\) | 5447.84 | 0.234147 | ||||||||
\(816\) | 28663.1 | 1.22967 | ||||||||
\(817\) | −9122.11 | −0.390627 | ||||||||
\(818\) | 32911.7 | 1.40676 | ||||||||
\(819\) | −14561.5 | −0.621269 | ||||||||
\(820\) | 1391.03 | 0.0592399 | ||||||||
\(821\) | 27124.6 | 1.15305 | 0.576526 | − | 0.817079i | \(-0.304408\pi\) | ||||
0.576526 | + | 0.817079i | \(0.304408\pi\) | |||||||
\(822\) | 59336.1 | 2.51774 | ||||||||
\(823\) | 12546.0 | 0.531379 | 0.265690 | − | 0.964059i | \(-0.414400\pi\) | ||||
0.265690 | + | 0.964059i | \(0.414400\pi\) | |||||||
\(824\) | 24157.9 | 1.02134 | ||||||||
\(825\) | −1996.24 | −0.0842424 | ||||||||
\(826\) | −11190.4 | −0.471384 | ||||||||
\(827\) | −8121.61 | −0.341495 | −0.170747 | − | 0.985315i | \(-0.554618\pi\) | ||||
−0.170747 | + | 0.985315i | \(0.554618\pi\) | |||||||
\(828\) | −3048.09 | −0.127933 | ||||||||
\(829\) | 17848.9 | 0.747792 | 0.373896 | − | 0.927471i | \(-0.378022\pi\) | ||||
0.373896 | + | 0.927471i | \(0.378022\pi\) | |||||||
\(830\) | 14913.7 | 0.623691 | ||||||||
\(831\) | −51245.7 | −2.13922 | ||||||||
\(832\) | 12233.9 | 0.509776 | ||||||||
\(833\) | −12243.3 | −0.509251 | ||||||||
\(834\) | −16719.9 | −0.694199 | ||||||||
\(835\) | −6427.04 | −0.266368 | ||||||||
\(836\) | 609.079 | 0.0251979 | ||||||||
\(837\) | −582.847 | −0.0240695 | ||||||||
\(838\) | 54379.6 | 2.24166 | ||||||||
\(839\) | 1723.99 | 0.0709402 | 0.0354701 | − | 0.999371i | \(-0.488707\pi\) | ||||
0.0354701 | + | 0.999371i | \(0.488707\pi\) | |||||||
\(840\) | −6055.42 | −0.248728 | ||||||||
\(841\) | −14441.3 | −0.592124 | ||||||||
\(842\) | 50463.4 | 2.06542 | ||||||||
\(843\) | −51287.7 | −2.09542 | ||||||||
\(844\) | 6788.26 | 0.276850 | ||||||||
\(845\) | 5302.10 | 0.215855 | ||||||||
\(846\) | −26402.9 | −1.07299 | ||||||||
\(847\) | −1201.51 | −0.0487420 | ||||||||
\(848\) | −15257.7 | −0.617869 | ||||||||
\(849\) | 38821.3 | 1.56931 | ||||||||
\(850\) | 4137.51 | 0.166959 | ||||||||
\(851\) | 4385.94 | 0.176672 | ||||||||
\(852\) | 18649.9 | 0.749922 | ||||||||
\(853\) | −5910.96 | −0.237266 | −0.118633 | − | 0.992938i | \(-0.537851\pi\) | ||||
−0.118633 | + | 0.992938i | \(0.537851\pi\) | |||||||
\(854\) | 13406.3 | 0.537184 | ||||||||
\(855\) | 2440.89 | 0.0976337 | ||||||||
\(856\) | 26250.2 | 1.04815 | ||||||||
\(857\) | −20640.8 | −0.822728 | −0.411364 | − | 0.911471i | \(-0.634948\pi\) | ||||
−0.411364 | + | 0.911471i | \(0.634948\pi\) | |||||||
\(858\) | −15055.9 | −0.599066 | ||||||||
\(859\) | −27701.0 | −1.10029 | −0.550144 | − | 0.835070i | \(-0.685427\pi\) | ||||
−0.550144 | + | 0.835070i | \(0.685427\pi\) | |||||||
\(860\) | −6995.83 | −0.277390 | ||||||||
\(861\) | 6881.13 | 0.272368 | ||||||||
\(862\) | 19571.8 | 0.773338 | ||||||||
\(863\) | 23833.0 | 0.940073 | 0.470037 | − | 0.882647i | \(-0.344241\pi\) | ||||
0.470037 | + | 0.882647i | \(0.344241\pi\) | |||||||
\(864\) | −1194.73 | −0.0470436 | ||||||||
\(865\) | −6998.89 | −0.275109 | ||||||||
\(866\) | 4282.99 | 0.168062 | ||||||||
\(867\) | 17446.4 | 0.683403 | ||||||||
\(868\) | 1778.60 | 0.0695501 | ||||||||
\(869\) | −861.652 | −0.0336358 | ||||||||
\(870\) | −11959.3 | −0.466045 | ||||||||
\(871\) | −29702.1 | −1.15547 | ||||||||
\(872\) | 20220.0 | 0.785248 | ||||||||
\(873\) | −10539.1 | −0.408584 | ||||||||
\(874\) | −2555.20 | −0.0988913 | ||||||||
\(875\) | −1241.23 | −0.0479558 | ||||||||
\(876\) | −21641.8 | −0.834712 | ||||||||
\(877\) | 46313.1 | 1.78322 | 0.891609 | − | 0.452806i | \(-0.149577\pi\) | ||||
0.891609 | + | 0.452806i | \(0.149577\pi\) | |||||||
\(878\) | −34360.8 | −1.32075 | ||||||||
\(879\) | −37420.9 | −1.43592 | ||||||||
\(880\) | −4335.16 | −0.166066 | ||||||||
\(881\) | −21314.0 | −0.815080 | −0.407540 | − | 0.913187i | \(-0.633613\pi\) | ||||
−0.407540 | + | 0.913187i | \(0.633613\pi\) | |||||||
\(882\) | −20745.3 | −0.791985 | ||||||||
\(883\) | −38824.9 | −1.47968 | −0.739842 | − | 0.672781i | \(-0.765100\pi\) | ||||
−0.739842 | + | 0.672781i | \(0.765100\pi\) | |||||||
\(884\) | 8332.33 | 0.317021 | ||||||||
\(885\) | −12380.9 | −0.470260 | ||||||||
\(886\) | −37932.2 | −1.43833 | ||||||||
\(887\) | −49927.7 | −1.88997 | −0.944987 | − | 0.327108i | \(-0.893926\pi\) | ||||
−0.944987 | + | 0.327108i | \(0.893926\pi\) | |||||||
\(888\) | −13140.7 | −0.496592 | ||||||||
\(889\) | 8145.05 | 0.307285 | ||||||||
\(890\) | −16441.4 | −0.619232 | ||||||||
\(891\) | −8388.22 | −0.315394 | ||||||||
\(892\) | 561.071 | 0.0210606 | ||||||||
\(893\) | −5909.95 | −0.221466 | ||||||||
\(894\) | −79627.2 | −2.97889 | ||||||||
\(895\) | 1127.06 | 0.0420933 | ||||||||
\(896\) | −17040.0 | −0.635343 | ||||||||
\(897\) | 16865.2 | 0.627772 | ||||||||
\(898\) | −27874.3 | −1.03583 | ||||||||
\(899\) | −6130.10 | −0.227420 | ||||||||
\(900\) | 1871.94 | 0.0693312 | ||||||||
\(901\) | 9697.26 | 0.358560 | ||||||||
\(902\) | 3469.18 | 0.128061 | ||||||||
\(903\) | −34607.0 | −1.27536 | ||||||||
\(904\) | 27772.3 | 1.02178 | ||||||||
\(905\) | 1218.94 | 0.0447724 | ||||||||
\(906\) | 11534.6 | 0.422970 | ||||||||
\(907\) | −9529.34 | −0.348860 | −0.174430 | − | 0.984670i | \(-0.555808\pi\) | ||||
−0.174430 | + | 0.984670i | \(0.555808\pi\) | |||||||
\(908\) | 552.227 | 0.0201831 | ||||||||
\(909\) | 19936.2 | 0.727439 | ||||||||
\(910\) | −9361.54 | −0.341024 | ||||||||
\(911\) | 107.105 | 0.00389523 | 0.00194762 | − | 0.999998i | \(-0.499380\pi\) | ||||
0.00194762 | + | 0.999998i | \(0.499380\pi\) | |||||||
\(912\) | 10871.1 | 0.394715 | ||||||||
\(913\) | 9931.44 | 0.360003 | ||||||||
\(914\) | −28853.6 | −1.04419 | ||||||||
\(915\) | 14832.6 | 0.535904 | ||||||||
\(916\) | −10539.3 | −0.380163 | ||||||||
\(917\) | 2229.53 | 0.0802897 | ||||||||
\(918\) | 1569.45 | 0.0564265 | ||||||||
\(919\) | 32125.5 | 1.15313 | 0.576563 | − | 0.817053i | \(-0.304394\pi\) | ||||
0.576563 | + | 0.817053i | \(0.304394\pi\) | |||||||
\(920\) | 3419.77 | 0.122550 | ||||||||
\(921\) | −2493.93 | −0.0892267 | ||||||||
\(922\) | −19862.2 | −0.709465 | ||||||||
\(923\) | −50316.0 | −1.79434 | ||||||||
\(924\) | 2310.69 | 0.0822687 | ||||||||
\(925\) | −2693.57 | −0.0957449 | ||||||||
\(926\) | −64412.7 | −2.28589 | ||||||||
\(927\) | −36943.1 | −1.30892 | ||||||||
\(928\) | −12565.6 | −0.444490 | ||||||||
\(929\) | 8705.07 | 0.307432 | 0.153716 | − | 0.988115i | \(-0.450876\pi\) | ||||
0.153716 | + | 0.988115i | \(0.450876\pi\) | |||||||
\(930\) | 7369.75 | 0.259853 | ||||||||
\(931\) | −4643.56 | −0.163466 | ||||||||
\(932\) | 10680.8 | 0.375386 | ||||||||
\(933\) | 15482.8 | 0.543285 | ||||||||
\(934\) | −6956.26 | −0.243700 | ||||||||
\(935\) | 2755.27 | 0.0963712 | ||||||||
\(936\) | −24638.5 | −0.860399 | ||||||||
\(937\) | −13023.4 | −0.454063 | −0.227031 | − | 0.973887i | \(-0.572902\pi\) | ||||
−0.227031 | + | 0.973887i | \(0.572902\pi\) | |||||||
\(938\) | 17072.3 | 0.594274 | ||||||||
\(939\) | 21284.1 | 0.739701 | ||||||||
\(940\) | −4532.39 | −0.157266 | ||||||||
\(941\) | 12077.7 | 0.418407 | 0.209203 | − | 0.977872i | \(-0.432913\pi\) | ||||
0.209203 | + | 0.977872i | \(0.432913\pi\) | |||||||
\(942\) | 26694.0 | 0.923288 | ||||||||
\(943\) | −3886.09 | −0.134198 | ||||||||
\(944\) | −26887.3 | −0.927020 | ||||||||
\(945\) | −470.827 | −0.0162074 | ||||||||
\(946\) | −17447.4 | −0.599645 | ||||||||
\(947\) | −10883.2 | −0.373448 | −0.186724 | − | 0.982412i | \(-0.559787\pi\) | ||||
−0.186724 | + | 0.982412i | \(0.559787\pi\) | |||||||
\(948\) | 1657.09 | 0.0567718 | ||||||||
\(949\) | 58387.9 | 1.99721 | ||||||||
\(950\) | 1569.24 | 0.0535926 | ||||||||
\(951\) | 3785.23 | 0.129069 | ||||||||
\(952\) | 8357.90 | 0.284539 | ||||||||
\(953\) | 1403.82 | 0.0477170 | 0.0238585 | − | 0.999715i | \(-0.492405\pi\) | ||||
0.0238585 | + | 0.999715i | \(0.492405\pi\) | |||||||
\(954\) | 16431.2 | 0.557631 | ||||||||
\(955\) | 12919.5 | 0.437763 | ||||||||
\(956\) | −558.665 | −0.0189001 | ||||||||
\(957\) | −7964.03 | −0.269008 | ||||||||
\(958\) | −35144.1 | −1.18524 | ||||||||
\(959\) | 24568.9 | 0.827291 | ||||||||
\(960\) | −7779.95 | −0.261559 | ||||||||
\(961\) | −26013.4 | −0.873197 | ||||||||
\(962\) | −20315.2 | −0.680862 | ||||||||
\(963\) | −40142.6 | −1.34328 | ||||||||
\(964\) | −381.638 | −0.0127508 | ||||||||
\(965\) | −1621.38 | −0.0540872 | ||||||||
\(966\) | −9693.80 | −0.322870 | ||||||||
\(967\) | −29281.0 | −0.973748 | −0.486874 | − | 0.873472i | \(-0.661863\pi\) | ||||
−0.486874 | + | 0.873472i | \(0.661863\pi\) | |||||||
\(968\) | −2033.00 | −0.0675031 | ||||||||
\(969\) | −6909.31 | −0.229060 | ||||||||
\(970\) | −6775.55 | −0.224278 | ||||||||
\(971\) | −26579.6 | −0.878454 | −0.439227 | − | 0.898376i | \(-0.644748\pi\) | ||||
−0.439227 | + | 0.898376i | \(0.644748\pi\) | |||||||
\(972\) | 15385.7 | 0.507711 | ||||||||
\(973\) | −6923.10 | −0.228103 | ||||||||
\(974\) | −22119.6 | −0.727676 | ||||||||
\(975\) | −10357.5 | −0.340211 | ||||||||
\(976\) | 32211.6 | 1.05642 | ||||||||
\(977\) | 7065.14 | 0.231355 | 0.115678 | − | 0.993287i | \(-0.463096\pi\) | ||||
0.115678 | + | 0.993287i | \(0.463096\pi\) | |||||||
\(978\) | −26129.5 | −0.854323 | ||||||||
\(979\) | −10948.7 | −0.357429 | ||||||||
\(980\) | −3561.19 | −0.116080 | ||||||||
\(981\) | −30921.1 | −1.00636 | ||||||||
\(982\) | −18412.6 | −0.598338 | ||||||||
\(983\) | 19667.6 | 0.638146 | 0.319073 | − | 0.947730i | \(-0.396628\pi\) | ||||
0.319073 | + | 0.947730i | \(0.396628\pi\) | |||||||
\(984\) | 11643.1 | 0.377204 | ||||||||
\(985\) | −14805.9 | −0.478941 | ||||||||
\(986\) | 16506.7 | 0.533144 | ||||||||
\(987\) | −22420.9 | −0.723064 | ||||||||
\(988\) | 3160.22 | 0.101761 | ||||||||
\(989\) | 19544.1 | 0.628379 | ||||||||
\(990\) | 4668.58 | 0.149876 | ||||||||
\(991\) | −36972.3 | −1.18513 | −0.592565 | − | 0.805523i | \(-0.701885\pi\) | ||||
−0.592565 | + | 0.805523i | \(0.701885\pi\) | |||||||
\(992\) | 7743.36 | 0.247835 | ||||||||
\(993\) | 9448.38 | 0.301949 | ||||||||
\(994\) | 28920.8 | 0.922848 | ||||||||
\(995\) | −7755.77 | −0.247110 | ||||||||
\(996\) | −19099.7 | −0.607627 | ||||||||
\(997\) | −24394.5 | −0.774905 | −0.387453 | − | 0.921890i | \(-0.626645\pi\) | ||||
−0.387453 | + | 0.921890i | \(0.626645\pi\) | |||||||
\(998\) | −62080.8 | −1.96907 | ||||||||
\(999\) | −1021.73 | −0.0323585 |
(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 | 1045.4.a.b.1.18 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.4.a.b.1.18 | ✓ | 20 | 1.1 | even | 1 | trivial |