Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,4,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("177.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(10.4433380710\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 49x^{6} + 89x^{5} + 648x^{4} - 1023x^{3} - 1476x^{2} + 1940x - 384 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-4.21744\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.21744 | −1.49109 | −0.745546 | − | 0.666454i | \(-0.767811\pi\) | ||||
−0.745546 | + | 0.666454i | \(0.767811\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 9.78684 | 1.22335 | ||||||||
\(5\) | 17.5635 | 1.57093 | 0.785464 | − | 0.618907i | \(-0.212424\pi\) | ||||
0.785464 | + | 0.618907i | \(0.212424\pi\) | |||||||
\(6\) | 12.6523 | 0.860882 | ||||||||
\(7\) | 14.8996 | 0.804501 | 0.402251 | − | 0.915530i | \(-0.368228\pi\) | ||||
0.402251 | + | 0.915530i | \(0.368228\pi\) | |||||||
\(8\) | −7.53588 | −0.333042 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −74.0731 | −2.34240 | ||||||||
\(11\) | −18.9001 | −0.518054 | −0.259027 | − | 0.965870i | \(-0.583402\pi\) | ||||
−0.259027 | + | 0.965870i | \(0.583402\pi\) | |||||||
\(12\) | −29.3605 | −0.706304 | ||||||||
\(13\) | 31.7591 | 0.677569 | 0.338784 | − | 0.940864i | \(-0.389984\pi\) | ||||
0.338784 | + | 0.940864i | \(0.389984\pi\) | |||||||
\(14\) | −62.8381 | −1.19958 | ||||||||
\(15\) | −52.6905 | −0.906976 | ||||||||
\(16\) | −46.5125 | −0.726758 | ||||||||
\(17\) | −84.1910 | −1.20114 | −0.600568 | − | 0.799574i | \(-0.705059\pi\) | ||||
−0.600568 | + | 0.799574i | \(0.705059\pi\) | |||||||
\(18\) | −37.9570 | −0.497031 | ||||||||
\(19\) | 126.537 | 1.52787 | 0.763934 | − | 0.645294i | \(-0.223265\pi\) | ||||
0.763934 | + | 0.645294i | \(0.223265\pi\) | |||||||
\(20\) | 171.891 | 1.92180 | ||||||||
\(21\) | −44.6987 | −0.464479 | ||||||||
\(22\) | 79.7102 | 0.772467 | ||||||||
\(23\) | −21.1777 | −0.191993 | −0.0959967 | − | 0.995382i | \(-0.530604\pi\) | ||||
−0.0959967 | + | 0.995382i | \(0.530604\pi\) | |||||||
\(24\) | 22.6076 | 0.192282 | ||||||||
\(25\) | 183.477 | 1.46782 | ||||||||
\(26\) | −133.942 | −1.01032 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 145.820 | 0.984190 | ||||||||
\(29\) | −12.6033 | −0.0807025 | −0.0403512 | − | 0.999186i | \(-0.512848\pi\) | ||||
−0.0403512 | + | 0.999186i | \(0.512848\pi\) | |||||||
\(30\) | 222.219 | 1.35238 | ||||||||
\(31\) | 215.817 | 1.25038 | 0.625191 | − | 0.780472i | \(-0.285021\pi\) | ||||
0.625191 | + | 0.780472i | \(0.285021\pi\) | |||||||
\(32\) | 256.451 | 1.41671 | ||||||||
\(33\) | 56.7003 | 0.299099 | ||||||||
\(34\) | 355.071 | 1.79100 | ||||||||
\(35\) | 261.689 | 1.26381 | ||||||||
\(36\) | 88.0815 | 0.407785 | ||||||||
\(37\) | −3.62282 | −0.0160970 | −0.00804848 | − | 0.999968i | \(-0.502562\pi\) | ||||
−0.00804848 | + | 0.999968i | \(0.502562\pi\) | |||||||
\(38\) | −533.661 | −2.27819 | ||||||||
\(39\) | −95.2774 | −0.391195 | ||||||||
\(40\) | −132.357 | −0.523185 | ||||||||
\(41\) | −381.728 | −1.45405 | −0.727023 | − | 0.686613i | \(-0.759097\pi\) | ||||
−0.727023 | + | 0.686613i | \(0.759097\pi\) | |||||||
\(42\) | 188.514 | 0.692581 | ||||||||
\(43\) | 168.813 | 0.598692 | 0.299346 | − | 0.954145i | \(-0.403231\pi\) | ||||
0.299346 | + | 0.954145i | \(0.403231\pi\) | |||||||
\(44\) | −184.972 | −0.633764 | ||||||||
\(45\) | 158.072 | 0.523643 | ||||||||
\(46\) | 89.3156 | 0.286280 | ||||||||
\(47\) | 613.793 | 1.90491 | 0.952457 | − | 0.304674i | \(-0.0985475\pi\) | ||||
0.952457 | + | 0.304674i | \(0.0985475\pi\) | |||||||
\(48\) | 139.538 | 0.419594 | ||||||||
\(49\) | −121.003 | −0.352778 | ||||||||
\(50\) | −773.804 | −2.18865 | ||||||||
\(51\) | 252.573 | 0.693476 | ||||||||
\(52\) | 310.821 | 0.828907 | ||||||||
\(53\) | 270.545 | 0.701173 | 0.350587 | − | 0.936530i | \(-0.385982\pi\) | ||||
0.350587 | + | 0.936530i | \(0.385982\pi\) | |||||||
\(54\) | 113.871 | 0.286961 | ||||||||
\(55\) | −331.952 | −0.813826 | ||||||||
\(56\) | −112.281 | −0.267933 | ||||||||
\(57\) | −379.610 | −0.882115 | ||||||||
\(58\) | 53.1537 | 0.120335 | ||||||||
\(59\) | −59.0000 | −0.130189 | ||||||||
\(60\) | −515.674 | −1.10955 | ||||||||
\(61\) | 311.206 | 0.653211 | 0.326605 | − | 0.945161i | \(-0.394095\pi\) | ||||
0.326605 | + | 0.945161i | \(0.394095\pi\) | |||||||
\(62\) | −910.195 | −1.86443 | ||||||||
\(63\) | 134.096 | 0.268167 | ||||||||
\(64\) | −709.468 | −1.38568 | ||||||||
\(65\) | 557.802 | 1.06441 | ||||||||
\(66\) | −239.130 | −0.445984 | ||||||||
\(67\) | 375.157 | 0.684071 | 0.342035 | − | 0.939687i | \(-0.388884\pi\) | ||||
0.342035 | + | 0.939687i | \(0.388884\pi\) | |||||||
\(68\) | −823.963 | −1.46942 | ||||||||
\(69\) | 63.5330 | 0.110847 | ||||||||
\(70\) | −1103.66 | −1.88446 | ||||||||
\(71\) | −987.919 | −1.65133 | −0.825665 | − | 0.564160i | \(-0.809200\pi\) | ||||
−0.825665 | + | 0.564160i | \(0.809200\pi\) | |||||||
\(72\) | −67.8229 | −0.111014 | ||||||||
\(73\) | −359.475 | −0.576348 | −0.288174 | − | 0.957578i | \(-0.593048\pi\) | ||||
−0.288174 | + | 0.957578i | \(0.593048\pi\) | |||||||
\(74\) | 15.2790 | 0.0240020 | ||||||||
\(75\) | −550.431 | −0.847444 | ||||||||
\(76\) | 1238.39 | 1.86912 | ||||||||
\(77\) | −281.604 | −0.416775 | ||||||||
\(78\) | 401.827 | 0.583307 | ||||||||
\(79\) | 933.998 | 1.33016 | 0.665082 | − | 0.746770i | \(-0.268397\pi\) | ||||
0.665082 | + | 0.746770i | \(0.268397\pi\) | |||||||
\(80\) | −816.923 | −1.14169 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1609.92 | 2.16811 | ||||||||
\(83\) | 1262.64 | 1.66979 | 0.834893 | − | 0.550412i | \(-0.185529\pi\) | ||||
0.834893 | + | 0.550412i | \(0.185529\pi\) | |||||||
\(84\) | −437.459 | −0.568222 | ||||||||
\(85\) | −1478.69 | −1.88690 | ||||||||
\(86\) | −711.960 | −0.892705 | ||||||||
\(87\) | 37.8099 | 0.0465936 | ||||||||
\(88\) | 142.429 | 0.172534 | ||||||||
\(89\) | 273.294 | 0.325496 | 0.162748 | − | 0.986668i | \(-0.447964\pi\) | ||||
0.162748 | + | 0.986668i | \(0.447964\pi\) | |||||||
\(90\) | −666.658 | −0.780799 | ||||||||
\(91\) | 473.197 | 0.545105 | ||||||||
\(92\) | −207.262 | −0.234876 | ||||||||
\(93\) | −647.450 | −0.721908 | ||||||||
\(94\) | −2588.64 | −2.84040 | ||||||||
\(95\) | 2222.43 | 2.40017 | ||||||||
\(96\) | −769.353 | −0.817935 | ||||||||
\(97\) | −897.200 | −0.939143 | −0.469571 | − | 0.882895i | \(-0.655592\pi\) | ||||
−0.469571 | + | 0.882895i | \(0.655592\pi\) | |||||||
\(98\) | 510.323 | 0.526024 | ||||||||
\(99\) | −170.101 | −0.172685 | ||||||||
\(100\) | 1795.66 | 1.79566 | ||||||||
\(101\) | 296.784 | 0.292387 | 0.146194 | − | 0.989256i | \(-0.453298\pi\) | ||||
0.146194 | + | 0.989256i | \(0.453298\pi\) | |||||||
\(102\) | −1065.21 | −1.03404 | ||||||||
\(103\) | −36.8226 | −0.0352257 | −0.0176128 | − | 0.999845i | \(-0.505607\pi\) | ||||
−0.0176128 | + | 0.999845i | \(0.505607\pi\) | |||||||
\(104\) | −239.333 | −0.225659 | ||||||||
\(105\) | −785.066 | −0.729663 | ||||||||
\(106\) | −1141.01 | −1.04551 | ||||||||
\(107\) | −479.349 | −0.433088 | −0.216544 | − | 0.976273i | \(-0.569479\pi\) | ||||
−0.216544 | + | 0.976273i | \(0.569479\pi\) | |||||||
\(108\) | −264.245 | −0.235435 | ||||||||
\(109\) | 946.780 | 0.831973 | 0.415987 | − | 0.909371i | \(-0.363436\pi\) | ||||
0.415987 | + | 0.909371i | \(0.363436\pi\) | |||||||
\(110\) | 1399.99 | 1.21349 | ||||||||
\(111\) | 10.8684 | 0.00929358 | ||||||||
\(112\) | −693.017 | −0.584678 | ||||||||
\(113\) | 2131.61 | 1.77456 | 0.887279 | − | 0.461234i | \(-0.152593\pi\) | ||||
0.887279 | + | 0.461234i | \(0.152593\pi\) | |||||||
\(114\) | 1600.98 | 1.31531 | ||||||||
\(115\) | −371.954 | −0.301608 | ||||||||
\(116\) | −123.346 | −0.0987277 | ||||||||
\(117\) | 285.832 | 0.225856 | ||||||||
\(118\) | 248.829 | 0.194124 | ||||||||
\(119\) | −1254.41 | −0.966315 | ||||||||
\(120\) | 397.070 | 0.302061 | ||||||||
\(121\) | −973.786 | −0.731620 | ||||||||
\(122\) | −1312.49 | −0.973997 | ||||||||
\(123\) | 1145.18 | 0.839493 | ||||||||
\(124\) | 2112.16 | 1.52966 | ||||||||
\(125\) | 1027.06 | 0.734904 | ||||||||
\(126\) | −565.543 | −0.399862 | ||||||||
\(127\) | 2054.51 | 1.43550 | 0.717751 | − | 0.696300i | \(-0.245172\pi\) | ||||
0.717751 | + | 0.696300i | \(0.245172\pi\) | |||||||
\(128\) | 940.532 | 0.649469 | ||||||||
\(129\) | −506.440 | −0.345655 | ||||||||
\(130\) | −2352.50 | −1.58714 | ||||||||
\(131\) | −602.309 | −0.401710 | −0.200855 | − | 0.979621i | \(-0.564372\pi\) | ||||
−0.200855 | + | 0.979621i | \(0.564372\pi\) | |||||||
\(132\) | 554.917 | 0.365904 | ||||||||
\(133\) | 1885.34 | 1.22917 | ||||||||
\(134\) | −1582.20 | −1.02001 | ||||||||
\(135\) | −474.215 | −0.302325 | ||||||||
\(136\) | 634.453 | 0.400029 | ||||||||
\(137\) | 1919.26 | 1.19689 | 0.598444 | − | 0.801164i | \(-0.295786\pi\) | ||||
0.598444 | + | 0.801164i | \(0.295786\pi\) | |||||||
\(138\) | −267.947 | −0.165284 | ||||||||
\(139\) | −448.518 | −0.273689 | −0.136845 | − | 0.990593i | \(-0.543696\pi\) | ||||
−0.136845 | + | 0.990593i | \(0.543696\pi\) | |||||||
\(140\) | 2561.10 | 1.54609 | ||||||||
\(141\) | −1841.38 | −1.09980 | ||||||||
\(142\) | 4166.49 | 2.46228 | ||||||||
\(143\) | −600.251 | −0.351017 | ||||||||
\(144\) | −418.613 | −0.242253 | ||||||||
\(145\) | −221.358 | −0.126778 | ||||||||
\(146\) | 1516.07 | 0.859388 | ||||||||
\(147\) | 363.009 | 0.203676 | ||||||||
\(148\) | −35.4559 | −0.0196923 | ||||||||
\(149\) | −1613.45 | −0.887105 | −0.443553 | − | 0.896248i | \(-0.646282\pi\) | ||||
−0.443553 | + | 0.896248i | \(0.646282\pi\) | |||||||
\(150\) | 2321.41 | 1.26362 | ||||||||
\(151\) | −1522.22 | −0.820374 | −0.410187 | − | 0.912002i | \(-0.634537\pi\) | ||||
−0.410187 | + | 0.912002i | \(0.634537\pi\) | |||||||
\(152\) | −953.565 | −0.508844 | ||||||||
\(153\) | −757.719 | −0.400379 | ||||||||
\(154\) | 1187.65 | 0.621450 | ||||||||
\(155\) | 3790.50 | 1.96426 | ||||||||
\(156\) | −932.464 | −0.478570 | ||||||||
\(157\) | −79.4233 | −0.0403737 | −0.0201868 | − | 0.999796i | \(-0.506426\pi\) | ||||
−0.0201868 | + | 0.999796i | \(0.506426\pi\) | |||||||
\(158\) | −3939.08 | −1.98340 | ||||||||
\(159\) | −811.634 | −0.404823 | ||||||||
\(160\) | 4504.18 | 2.22554 | ||||||||
\(161\) | −315.538 | −0.154459 | ||||||||
\(162\) | −341.613 | −0.165677 | ||||||||
\(163\) | 2254.35 | 1.08328 | 0.541639 | − | 0.840611i | \(-0.317804\pi\) | ||||
0.541639 | + | 0.840611i | \(0.317804\pi\) | |||||||
\(164\) | −3735.91 | −1.77881 | ||||||||
\(165\) | 995.857 | 0.469863 | ||||||||
\(166\) | −5325.10 | −2.48981 | ||||||||
\(167\) | −382.224 | −0.177110 | −0.0885550 | − | 0.996071i | \(-0.528225\pi\) | ||||
−0.0885550 | + | 0.996071i | \(0.528225\pi\) | |||||||
\(168\) | 336.844 | 0.154691 | ||||||||
\(169\) | −1188.36 | −0.540901 | ||||||||
\(170\) | 6236.29 | 2.81354 | ||||||||
\(171\) | 1138.83 | 0.509289 | ||||||||
\(172\) | 1652.15 | 0.732413 | ||||||||
\(173\) | −929.824 | −0.408631 | −0.204316 | − | 0.978905i | \(-0.565497\pi\) | ||||
−0.204316 | + | 0.978905i | \(0.565497\pi\) | |||||||
\(174\) | −159.461 | −0.0694753 | ||||||||
\(175\) | 2733.73 | 1.18086 | ||||||||
\(176\) | 879.092 | 0.376500 | ||||||||
\(177\) | 177.000 | 0.0751646 | ||||||||
\(178\) | −1152.60 | −0.485344 | ||||||||
\(179\) | −509.106 | −0.212583 | −0.106291 | − | 0.994335i | \(-0.533898\pi\) | ||||
−0.106291 | + | 0.994335i | \(0.533898\pi\) | |||||||
\(180\) | 1547.02 | 0.640601 | ||||||||
\(181\) | 824.865 | 0.338739 | 0.169369 | − | 0.985553i | \(-0.445827\pi\) | ||||
0.169369 | + | 0.985553i | \(0.445827\pi\) | |||||||
\(182\) | −1995.68 | −0.812801 | ||||||||
\(183\) | −933.618 | −0.377131 | ||||||||
\(184\) | 159.592 | 0.0639419 | ||||||||
\(185\) | −63.6294 | −0.0252872 | ||||||||
\(186\) | 2730.58 | 1.07643 | ||||||||
\(187\) | 1591.22 | 0.622254 | ||||||||
\(188\) | 6007.09 | 2.33038 | ||||||||
\(189\) | −402.288 | −0.154826 | ||||||||
\(190\) | −9372.97 | −3.57888 | ||||||||
\(191\) | −3681.09 | −1.39453 | −0.697263 | − | 0.716815i | \(-0.745599\pi\) | ||||
−0.697263 | + | 0.716815i | \(0.745599\pi\) | |||||||
\(192\) | 2128.40 | 0.800022 | ||||||||
\(193\) | −3051.17 | −1.13797 | −0.568985 | − | 0.822348i | \(-0.692664\pi\) | ||||
−0.568985 | + | 0.822348i | \(0.692664\pi\) | |||||||
\(194\) | 3783.89 | 1.40035 | ||||||||
\(195\) | −1673.40 | −0.614538 | ||||||||
\(196\) | −1184.23 | −0.431573 | ||||||||
\(197\) | −5332.57 | −1.92858 | −0.964290 | − | 0.264849i | \(-0.914678\pi\) | ||||
−0.964290 | + | 0.264849i | \(0.914678\pi\) | |||||||
\(198\) | 717.391 | 0.257489 | ||||||||
\(199\) | −5371.72 | −1.91352 | −0.956761 | − | 0.290874i | \(-0.906054\pi\) | ||||
−0.956761 | + | 0.290874i | \(0.906054\pi\) | |||||||
\(200\) | −1382.66 | −0.488844 | ||||||||
\(201\) | −1125.47 | −0.394949 | ||||||||
\(202\) | −1251.67 | −0.435976 | ||||||||
\(203\) | −187.784 | −0.0649252 | ||||||||
\(204\) | 2471.89 | 0.848367 | ||||||||
\(205\) | −6704.48 | −2.28420 | ||||||||
\(206\) | 155.297 | 0.0525247 | ||||||||
\(207\) | −190.599 | −0.0639978 | ||||||||
\(208\) | −1477.20 | −0.492429 | ||||||||
\(209\) | −2391.56 | −0.791519 | ||||||||
\(210\) | 3310.97 | 1.08799 | ||||||||
\(211\) | 1896.92 | 0.618907 | 0.309454 | − | 0.950915i | \(-0.399854\pi\) | ||||
0.309454 | + | 0.950915i | \(0.399854\pi\) | |||||||
\(212\) | 2647.78 | 0.857784 | ||||||||
\(213\) | 2963.76 | 0.953396 | ||||||||
\(214\) | 2021.63 | 0.645775 | ||||||||
\(215\) | 2964.95 | 0.940503 | ||||||||
\(216\) | 203.469 | 0.0640940 | ||||||||
\(217\) | 3215.57 | 1.00593 | ||||||||
\(218\) | −3992.99 | −1.24055 | ||||||||
\(219\) | 1078.43 | 0.332755 | ||||||||
\(220\) | −3248.76 | −0.995598 | ||||||||
\(221\) | −2673.83 | −0.813852 | ||||||||
\(222\) | −45.8371 | −0.0138576 | ||||||||
\(223\) | −2808.85 | −0.843472 | −0.421736 | − | 0.906719i | \(-0.638579\pi\) | ||||
−0.421736 | + | 0.906719i | \(0.638579\pi\) | |||||||
\(224\) | 3821.01 | 1.13974 | ||||||||
\(225\) | 1651.29 | 0.489272 | ||||||||
\(226\) | −8989.95 | −2.64603 | ||||||||
\(227\) | 3302.83 | 0.965711 | 0.482856 | − | 0.875700i | \(-0.339600\pi\) | ||||
0.482856 | + | 0.875700i | \(0.339600\pi\) | |||||||
\(228\) | −3715.18 | −1.07914 | ||||||||
\(229\) | −5780.19 | −1.66797 | −0.833987 | − | 0.551785i | \(-0.813947\pi\) | ||||
−0.833987 | + | 0.551785i | \(0.813947\pi\) | |||||||
\(230\) | 1568.70 | 0.449725 | ||||||||
\(231\) | 844.811 | 0.240625 | ||||||||
\(232\) | 94.9769 | 0.0268773 | ||||||||
\(233\) | 4892.84 | 1.37571 | 0.687856 | − | 0.725847i | \(-0.258552\pi\) | ||||
0.687856 | + | 0.725847i | \(0.258552\pi\) | |||||||
\(234\) | −1205.48 | −0.336772 | ||||||||
\(235\) | 10780.4 | 2.99248 | ||||||||
\(236\) | −577.423 | −0.159267 | ||||||||
\(237\) | −2801.99 | −0.767970 | ||||||||
\(238\) | 5290.40 | 1.44086 | ||||||||
\(239\) | −6461.39 | −1.74876 | −0.874378 | − | 0.485246i | \(-0.838730\pi\) | ||||
−0.874378 | + | 0.485246i | \(0.838730\pi\) | |||||||
\(240\) | 2450.77 | 0.659152 | ||||||||
\(241\) | −60.7729 | −0.0162437 | −0.00812184 | − | 0.999967i | \(-0.502585\pi\) | ||||
−0.00812184 | + | 0.999967i | \(0.502585\pi\) | |||||||
\(242\) | 4106.89 | 1.09091 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 3045.72 | 0.799108 | ||||||||
\(245\) | −2125.23 | −0.554189 | ||||||||
\(246\) | −4829.75 | −1.25176 | ||||||||
\(247\) | 4018.69 | 1.03524 | ||||||||
\(248\) | −1626.37 | −0.416429 | ||||||||
\(249\) | −3787.91 | −0.964052 | ||||||||
\(250\) | −4331.57 | −1.09581 | ||||||||
\(251\) | −3782.13 | −0.951100 | −0.475550 | − | 0.879689i | \(-0.657751\pi\) | ||||
−0.475550 | + | 0.879689i | \(0.657751\pi\) | |||||||
\(252\) | 1312.38 | 0.328063 | ||||||||
\(253\) | 400.260 | 0.0994630 | ||||||||
\(254\) | −8664.80 | −2.14046 | ||||||||
\(255\) | 4436.07 | 1.08940 | ||||||||
\(256\) | 1709.10 | 0.417261 | ||||||||
\(257\) | −72.7427 | −0.0176559 | −0.00882795 | − | 0.999961i | \(-0.502810\pi\) | ||||
−0.00882795 | + | 0.999961i | \(0.502810\pi\) | |||||||
\(258\) | 2135.88 | 0.515404 | ||||||||
\(259\) | −53.9784 | −0.0129500 | ||||||||
\(260\) | 5459.11 | 1.30215 | ||||||||
\(261\) | −113.430 | −0.0269008 | ||||||||
\(262\) | 2540.20 | 0.598986 | ||||||||
\(263\) | −4787.49 | −1.12247 | −0.561235 | − | 0.827657i | \(-0.689673\pi\) | ||||
−0.561235 | + | 0.827657i | \(0.689673\pi\) | |||||||
\(264\) | −427.287 | −0.0996125 | ||||||||
\(265\) | 4751.72 | 1.10149 | ||||||||
\(266\) | −7951.32 | −1.83281 | ||||||||
\(267\) | −819.883 | −0.187925 | ||||||||
\(268\) | 3671.60 | 0.836861 | ||||||||
\(269\) | 3320.18 | 0.752546 | 0.376273 | − | 0.926509i | \(-0.377205\pi\) | ||||
0.376273 | + | 0.926509i | \(0.377205\pi\) | |||||||
\(270\) | 1999.97 | 0.450795 | ||||||||
\(271\) | 7147.95 | 1.60224 | 0.801120 | − | 0.598504i | \(-0.204238\pi\) | ||||
0.801120 | + | 0.598504i | \(0.204238\pi\) | |||||||
\(272\) | 3915.94 | 0.872936 | ||||||||
\(273\) | −1419.59 | −0.314716 | ||||||||
\(274\) | −8094.39 | −1.78467 | ||||||||
\(275\) | −3467.73 | −0.760408 | ||||||||
\(276\) | 621.787 | 0.135606 | ||||||||
\(277\) | 4611.19 | 1.00021 | 0.500107 | − | 0.865963i | \(-0.333294\pi\) | ||||
0.500107 | + | 0.865963i | \(0.333294\pi\) | |||||||
\(278\) | 1891.60 | 0.408096 | ||||||||
\(279\) | 1942.35 | 0.416794 | ||||||||
\(280\) | −1972.05 | −0.420903 | ||||||||
\(281\) | 8307.67 | 1.76368 | 0.881840 | − | 0.471548i | \(-0.156305\pi\) | ||||
0.881840 | + | 0.471548i | \(0.156305\pi\) | |||||||
\(282\) | 7765.91 | 1.63991 | ||||||||
\(283\) | −8181.70 | −1.71856 | −0.859279 | − | 0.511507i | \(-0.829087\pi\) | ||||
−0.859279 | + | 0.511507i | \(0.829087\pi\) | |||||||
\(284\) | −9668.60 | −2.02016 | ||||||||
\(285\) | −6667.28 | −1.38574 | ||||||||
\(286\) | 2531.52 | 0.523399 | ||||||||
\(287\) | −5687.58 | −1.16978 | ||||||||
\(288\) | 2308.06 | 0.472235 | ||||||||
\(289\) | 2175.12 | 0.442728 | ||||||||
\(290\) | 933.565 | 0.189037 | ||||||||
\(291\) | 2691.60 | 0.542214 | ||||||||
\(292\) | −3518.13 | −0.705078 | ||||||||
\(293\) | −264.862 | −0.0528102 | −0.0264051 | − | 0.999651i | \(-0.508406\pi\) | ||||
−0.0264051 | + | 0.999651i | \(0.508406\pi\) | |||||||
\(294\) | −1530.97 | −0.303700 | ||||||||
\(295\) | −1036.25 | −0.204517 | ||||||||
\(296\) | 27.3011 | 0.00536096 | ||||||||
\(297\) | 510.303 | 0.0996996 | ||||||||
\(298\) | 6804.62 | 1.32276 | ||||||||
\(299\) | −672.584 | −0.130089 | ||||||||
\(300\) | −5386.98 | −1.03672 | ||||||||
\(301\) | 2515.24 | 0.481649 | ||||||||
\(302\) | 6419.87 | 1.22325 | ||||||||
\(303\) | −890.351 | −0.168810 | ||||||||
\(304\) | −5885.54 | −1.11039 | ||||||||
\(305\) | 5465.87 | 1.02615 | ||||||||
\(306\) | 3195.64 | 0.597001 | ||||||||
\(307\) | 4379.69 | 0.814209 | 0.407104 | − | 0.913382i | \(-0.366539\pi\) | ||||
0.407104 | + | 0.913382i | \(0.366539\pi\) | |||||||
\(308\) | −2756.01 | −0.509864 | ||||||||
\(309\) | 110.468 | 0.0203375 | ||||||||
\(310\) | −15986.2 | −2.92889 | ||||||||
\(311\) | 10544.6 | 1.92261 | 0.961303 | − | 0.275494i | \(-0.0888413\pi\) | ||||
0.961303 | + | 0.275494i | \(0.0888413\pi\) | |||||||
\(312\) | 717.999 | 0.130284 | ||||||||
\(313\) | −6496.71 | −1.17321 | −0.586607 | − | 0.809872i | \(-0.699537\pi\) | ||||
−0.586607 | + | 0.809872i | \(0.699537\pi\) | |||||||
\(314\) | 334.963 | 0.0602009 | ||||||||
\(315\) | 2355.20 | 0.421271 | ||||||||
\(316\) | 9140.88 | 1.62726 | ||||||||
\(317\) | 2628.81 | 0.465769 | 0.232884 | − | 0.972504i | \(-0.425184\pi\) | ||||
0.232884 | + | 0.972504i | \(0.425184\pi\) | |||||||
\(318\) | 3423.02 | 0.603628 | ||||||||
\(319\) | 238.204 | 0.0418083 | ||||||||
\(320\) | −12460.7 | −2.17680 | ||||||||
\(321\) | 1438.05 | 0.250044 | ||||||||
\(322\) | 1330.76 | 0.230312 | ||||||||
\(323\) | −10653.2 | −1.83518 | ||||||||
\(324\) | 792.734 | 0.135928 | ||||||||
\(325\) | 5827.06 | 0.994546 | ||||||||
\(326\) | −9507.59 | −1.61527 | ||||||||
\(327\) | −2840.34 | −0.480340 | ||||||||
\(328\) | 2876.65 | 0.484258 | ||||||||
\(329\) | 9145.25 | 1.53250 | ||||||||
\(330\) | −4199.97 | −0.700608 | ||||||||
\(331\) | −3679.05 | −0.610933 | −0.305466 | − | 0.952203i | \(-0.598812\pi\) | ||||
−0.305466 | + | 0.952203i | \(0.598812\pi\) | |||||||
\(332\) | 12357.2 | 2.04274 | ||||||||
\(333\) | −32.6053 | −0.00536565 | ||||||||
\(334\) | 1612.01 | 0.264087 | ||||||||
\(335\) | 6589.08 | 1.07463 | ||||||||
\(336\) | 2079.05 | 0.337564 | ||||||||
\(337\) | 1323.74 | 0.213972 | 0.106986 | − | 0.994261i | \(-0.465880\pi\) | ||||
0.106986 | + | 0.994261i | \(0.465880\pi\) | |||||||
\(338\) | 5011.84 | 0.806532 | ||||||||
\(339\) | −6394.83 | −1.02454 | ||||||||
\(340\) | −14471.7 | −2.30835 | ||||||||
\(341\) | −4078.96 | −0.647765 | ||||||||
\(342\) | −4802.95 | −0.759397 | ||||||||
\(343\) | −6913.44 | −1.08831 | ||||||||
\(344\) | −1272.16 | −0.199390 | ||||||||
\(345\) | 1115.86 | 0.174133 | ||||||||
\(346\) | 3921.48 | 0.609307 | ||||||||
\(347\) | 5541.30 | 0.857270 | 0.428635 | − | 0.903478i | \(-0.358995\pi\) | ||||
0.428635 | + | 0.903478i | \(0.358995\pi\) | |||||||
\(348\) | 370.039 | 0.0570005 | ||||||||
\(349\) | −6590.45 | −1.01083 | −0.505414 | − | 0.862877i | \(-0.668660\pi\) | ||||
−0.505414 | + | 0.862877i | \(0.668660\pi\) | |||||||
\(350\) | −11529.3 | −1.76077 | ||||||||
\(351\) | −857.496 | −0.130398 | ||||||||
\(352\) | −4846.95 | −0.733930 | ||||||||
\(353\) | −5633.11 | −0.849349 | −0.424674 | − | 0.905346i | \(-0.639611\pi\) | ||||
−0.424674 | + | 0.905346i | \(0.639611\pi\) | |||||||
\(354\) | −746.488 | −0.112077 | ||||||||
\(355\) | −17351.3 | −2.59412 | ||||||||
\(356\) | 2674.69 | 0.398197 | ||||||||
\(357\) | 3763.23 | 0.557902 | ||||||||
\(358\) | 2147.13 | 0.316981 | ||||||||
\(359\) | 2672.65 | 0.392916 | 0.196458 | − | 0.980512i | \(-0.437056\pi\) | ||||
0.196458 | + | 0.980512i | \(0.437056\pi\) | |||||||
\(360\) | −1191.21 | −0.174395 | ||||||||
\(361\) | 9152.52 | 1.33438 | ||||||||
\(362\) | −3478.82 | −0.505091 | ||||||||
\(363\) | 2921.36 | 0.422401 | ||||||||
\(364\) | 4631.10 | 0.666856 | ||||||||
\(365\) | −6313.65 | −0.905402 | ||||||||
\(366\) | 3937.48 | 0.562337 | ||||||||
\(367\) | −2881.92 | −0.409904 | −0.204952 | − | 0.978772i | \(-0.565704\pi\) | ||||
−0.204952 | + | 0.978772i | \(0.565704\pi\) | |||||||
\(368\) | 985.027 | 0.139533 | ||||||||
\(369\) | −3435.55 | −0.484682 | ||||||||
\(370\) | 268.353 | 0.0377055 | ||||||||
\(371\) | 4031.00 | 0.564095 | ||||||||
\(372\) | −6336.49 | −0.883149 | ||||||||
\(373\) | 7349.59 | 1.02023 | 0.510117 | − | 0.860105i | \(-0.329602\pi\) | ||||
0.510117 | + | 0.860105i | \(0.329602\pi\) | |||||||
\(374\) | −6710.88 | −0.927837 | ||||||||
\(375\) | −3081.18 | −0.424297 | ||||||||
\(376\) | −4625.47 | −0.634416 | ||||||||
\(377\) | −400.269 | −0.0546815 | ||||||||
\(378\) | 1696.63 | 0.230860 | ||||||||
\(379\) | 6001.29 | 0.813366 | 0.406683 | − | 0.913569i | \(-0.366685\pi\) | ||||
0.406683 | + | 0.913569i | \(0.366685\pi\) | |||||||
\(380\) | 21750.5 | 2.93626 | ||||||||
\(381\) | −6163.54 | −0.828787 | ||||||||
\(382\) | 15524.8 | 2.07937 | ||||||||
\(383\) | −7844.21 | −1.04653 | −0.523264 | − | 0.852171i | \(-0.675286\pi\) | ||||
−0.523264 | + | 0.852171i | \(0.675286\pi\) | |||||||
\(384\) | −2821.60 | −0.374971 | ||||||||
\(385\) | −4945.95 | −0.654724 | ||||||||
\(386\) | 12868.2 | 1.69682 | ||||||||
\(387\) | 1519.32 | 0.199564 | ||||||||
\(388\) | −8780.75 | −1.14890 | ||||||||
\(389\) | −574.603 | −0.0748934 | −0.0374467 | − | 0.999299i | \(-0.511922\pi\) | ||||
−0.0374467 | + | 0.999299i | \(0.511922\pi\) | |||||||
\(390\) | 7057.49 | 0.916333 | ||||||||
\(391\) | 1782.97 | 0.230610 | ||||||||
\(392\) | 911.863 | 0.117490 | ||||||||
\(393\) | 1806.93 | 0.231927 | ||||||||
\(394\) | 22489.8 | 2.87569 | ||||||||
\(395\) | 16404.3 | 2.08959 | ||||||||
\(396\) | −1664.75 | −0.211255 | ||||||||
\(397\) | −14329.0 | −1.81147 | −0.905735 | − | 0.423844i | \(-0.860680\pi\) | ||||
−0.905735 | + | 0.423844i | \(0.860680\pi\) | |||||||
\(398\) | 22654.9 | 2.85324 | ||||||||
\(399\) | −5656.02 | −0.709663 | ||||||||
\(400\) | −8533.98 | −1.06675 | ||||||||
\(401\) | 8440.51 | 1.05112 | 0.525560 | − | 0.850757i | \(-0.323856\pi\) | ||||
0.525560 | + | 0.850757i | \(0.323856\pi\) | |||||||
\(402\) | 4746.61 | 0.588904 | ||||||||
\(403\) | 6854.15 | 0.847219 | ||||||||
\(404\) | 2904.57 | 0.357693 | ||||||||
\(405\) | 1422.64 | 0.174548 | ||||||||
\(406\) | 791.967 | 0.0968095 | ||||||||
\(407\) | 68.4716 | 0.00833910 | ||||||||
\(408\) | −1903.36 | −0.230957 | ||||||||
\(409\) | −3995.02 | −0.482985 | −0.241492 | − | 0.970403i | \(-0.577637\pi\) | ||||
−0.241492 | + | 0.970403i | \(0.577637\pi\) | |||||||
\(410\) | 28275.8 | 3.40595 | ||||||||
\(411\) | −5757.79 | −0.691024 | ||||||||
\(412\) | −360.377 | −0.0430935 | ||||||||
\(413\) | −879.075 | −0.104737 | ||||||||
\(414\) | 803.840 | 0.0954266 | ||||||||
\(415\) | 22176.3 | 2.62312 | ||||||||
\(416\) | 8144.66 | 0.959915 | ||||||||
\(417\) | 1345.56 | 0.158015 | ||||||||
\(418\) | 10086.3 | 1.18023 | ||||||||
\(419\) | −1885.71 | −0.219864 | −0.109932 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109932 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(420\) | −7683.31 | −0.892637 | ||||||||
\(421\) | −9268.38 | −1.07295 | −0.536477 | − | 0.843915i | \(-0.680245\pi\) | ||||
−0.536477 | + | 0.843915i | \(0.680245\pi\) | |||||||
\(422\) | −8000.16 | −0.922848 | ||||||||
\(423\) | 5524.14 | 0.634971 | ||||||||
\(424\) | −2038.79 | −0.233520 | ||||||||
\(425\) | −15447.1 | −1.76305 | ||||||||
\(426\) | −12499.5 | −1.42160 | ||||||||
\(427\) | 4636.84 | 0.525509 | ||||||||
\(428\) | −4691.31 | −0.529821 | ||||||||
\(429\) | 1800.75 | 0.202660 | ||||||||
\(430\) | −12504.5 | −1.40238 | ||||||||
\(431\) | −3346.11 | −0.373959 | −0.186980 | − | 0.982364i | \(-0.559870\pi\) | ||||
−0.186980 | + | 0.982364i | \(0.559870\pi\) | |||||||
\(432\) | 1255.84 | 0.139865 | ||||||||
\(433\) | −927.848 | −0.102978 | −0.0514891 | − | 0.998674i | \(-0.516397\pi\) | ||||
−0.0514891 | + | 0.998674i | \(0.516397\pi\) | |||||||
\(434\) | −13561.5 | −1.49994 | ||||||||
\(435\) | 664.074 | 0.0731952 | ||||||||
\(436\) | 9265.98 | 1.01780 | ||||||||
\(437\) | −2679.75 | −0.293341 | ||||||||
\(438\) | −4548.20 | −0.496168 | ||||||||
\(439\) | 10124.5 | 1.10072 | 0.550361 | − | 0.834927i | \(-0.314490\pi\) | ||||
0.550361 | + | 0.834927i | \(0.314490\pi\) | |||||||
\(440\) | 2501.55 | 0.271038 | ||||||||
\(441\) | −1089.03 | −0.117593 | ||||||||
\(442\) | 11276.7 | 1.21353 | ||||||||
\(443\) | −6492.44 | −0.696310 | −0.348155 | − | 0.937437i | \(-0.613192\pi\) | ||||
−0.348155 | + | 0.937437i | \(0.613192\pi\) | |||||||
\(444\) | 106.368 | 0.0113693 | ||||||||
\(445\) | 4800.01 | 0.511331 | ||||||||
\(446\) | 11846.2 | 1.25769 | ||||||||
\(447\) | 4840.34 | 0.512170 | ||||||||
\(448\) | −10570.8 | −1.11478 | ||||||||
\(449\) | −17708.0 | −1.86123 | −0.930614 | − | 0.366003i | \(-0.880726\pi\) | ||||
−0.930614 | + | 0.366003i | \(0.880726\pi\) | |||||||
\(450\) | −6964.23 | −0.729549 | ||||||||
\(451\) | 7214.70 | 0.753275 | ||||||||
\(452\) | 20861.7 | 2.17091 | ||||||||
\(453\) | 4566.66 | 0.473643 | ||||||||
\(454\) | −13929.5 | −1.43996 | ||||||||
\(455\) | 8311.00 | 0.856321 | ||||||||
\(456\) | 2860.70 | 0.293781 | ||||||||
\(457\) | 10785.3 | 1.10397 | 0.551984 | − | 0.833855i | \(-0.313871\pi\) | ||||
0.551984 | + | 0.833855i | \(0.313871\pi\) | |||||||
\(458\) | 24377.6 | 2.48710 | ||||||||
\(459\) | 2273.16 | 0.231159 | ||||||||
\(460\) | −3640.25 | −0.368973 | ||||||||
\(461\) | −14512.5 | −1.46619 | −0.733097 | − | 0.680124i | \(-0.761926\pi\) | ||||
−0.733097 | + | 0.680124i | \(0.761926\pi\) | |||||||
\(462\) | −3562.94 | −0.358794 | ||||||||
\(463\) | −9637.81 | −0.967402 | −0.483701 | − | 0.875233i | \(-0.660708\pi\) | ||||
−0.483701 | + | 0.875233i | \(0.660708\pi\) | |||||||
\(464\) | 586.211 | 0.0586512 | ||||||||
\(465\) | −11371.5 | −1.13407 | ||||||||
\(466\) | −20635.3 | −2.05131 | ||||||||
\(467\) | −7260.33 | −0.719417 | −0.359709 | − | 0.933065i | \(-0.617124\pi\) | ||||
−0.359709 | + | 0.933065i | \(0.617124\pi\) | |||||||
\(468\) | 2797.39 | 0.276302 | ||||||||
\(469\) | 5589.68 | 0.550336 | ||||||||
\(470\) | −45465.6 | −4.46207 | ||||||||
\(471\) | 238.270 | 0.0233098 | ||||||||
\(472\) | 444.617 | 0.0433584 | ||||||||
\(473\) | −3190.59 | −0.310155 | ||||||||
\(474\) | 11817.2 | 1.14511 | ||||||||
\(475\) | 23216.6 | 2.24263 | ||||||||
\(476\) | −12276.7 | −1.18215 | ||||||||
\(477\) | 2434.90 | 0.233724 | ||||||||
\(478\) | 27250.6 | 2.60756 | ||||||||
\(479\) | 12069.4 | 1.15128 | 0.575641 | − | 0.817703i | \(-0.304753\pi\) | ||||
0.575641 | + | 0.817703i | \(0.304753\pi\) | |||||||
\(480\) | −13512.5 | −1.28492 | ||||||||
\(481\) | −115.057 | −0.0109068 | ||||||||
\(482\) | 256.306 | 0.0242208 | ||||||||
\(483\) | 946.614 | 0.0891769 | ||||||||
\(484\) | −9530.28 | −0.895030 | ||||||||
\(485\) | −15758.0 | −1.47533 | ||||||||
\(486\) | 1024.84 | 0.0956536 | ||||||||
\(487\) | −6015.96 | −0.559773 | −0.279886 | − | 0.960033i | \(-0.590297\pi\) | ||||
−0.279886 | + | 0.960033i | \(0.590297\pi\) | |||||||
\(488\) | −2345.21 | −0.217547 | ||||||||
\(489\) | −6763.05 | −0.625430 | ||||||||
\(490\) | 8963.06 | 0.826346 | ||||||||
\(491\) | 4022.81 | 0.369749 | 0.184875 | − | 0.982762i | \(-0.440812\pi\) | ||||
0.184875 | + | 0.982762i | \(0.440812\pi\) | |||||||
\(492\) | 11207.7 | 1.02700 | ||||||||
\(493\) | 1061.08 | 0.0969347 | ||||||||
\(494\) | −16948.6 | −1.54363 | ||||||||
\(495\) | −2987.57 | −0.271275 | ||||||||
\(496\) | −10038.2 | −0.908725 | ||||||||
\(497\) | −14719.6 | −1.32850 | ||||||||
\(498\) | 15975.3 | 1.43749 | ||||||||
\(499\) | −14112.8 | −1.26608 | −0.633042 | − | 0.774117i | \(-0.718194\pi\) | ||||
−0.633042 | + | 0.774117i | \(0.718194\pi\) | |||||||
\(500\) | 10051.7 | 0.899048 | ||||||||
\(501\) | 1146.67 | 0.102255 | ||||||||
\(502\) | 15950.9 | 1.41818 | ||||||||
\(503\) | 689.493 | 0.0611192 | 0.0305596 | − | 0.999533i | \(-0.490271\pi\) | ||||
0.0305596 | + | 0.999533i | \(0.490271\pi\) | |||||||
\(504\) | −1010.53 | −0.0893109 | ||||||||
\(505\) | 5212.56 | 0.459319 | ||||||||
\(506\) | −1688.07 | −0.148308 | ||||||||
\(507\) | 3565.08 | 0.312289 | ||||||||
\(508\) | 20107.2 | 1.75613 | ||||||||
\(509\) | −12620.3 | −1.09899 | −0.549495 | − | 0.835497i | \(-0.685180\pi\) | ||||
−0.549495 | + | 0.835497i | \(0.685180\pi\) | |||||||
\(510\) | −18708.9 | −1.62440 | ||||||||
\(511\) | −5356.03 | −0.463673 | ||||||||
\(512\) | −14732.3 | −1.27164 | ||||||||
\(513\) | −3416.49 | −0.294038 | ||||||||
\(514\) | 306.788 | 0.0263266 | ||||||||
\(515\) | −646.735 | −0.0553370 | ||||||||
\(516\) | −4956.44 | −0.422859 | ||||||||
\(517\) | −11600.8 | −0.986849 | ||||||||
\(518\) | 227.651 | 0.0193097 | ||||||||
\(519\) | 2789.47 | 0.235923 | ||||||||
\(520\) | −4203.53 | −0.354494 | ||||||||
\(521\) | 2186.17 | 0.183835 | 0.0919174 | − | 0.995767i | \(-0.470700\pi\) | ||||
0.0919174 | + | 0.995767i | \(0.470700\pi\) | |||||||
\(522\) | 478.383 | 0.0401116 | ||||||||
\(523\) | −18639.4 | −1.55840 | −0.779202 | − | 0.626773i | \(-0.784375\pi\) | ||||
−0.779202 | + | 0.626773i | \(0.784375\pi\) | |||||||
\(524\) | −5894.70 | −0.491433 | ||||||||
\(525\) | −8201.18 | −0.681769 | ||||||||
\(526\) | 20191.0 | 1.67370 | ||||||||
\(527\) | −18169.8 | −1.50188 | ||||||||
\(528\) | −2637.28 | −0.217373 | ||||||||
\(529\) | −11718.5 | −0.963139 | ||||||||
\(530\) | −20040.1 | −1.64243 | ||||||||
\(531\) | −531.000 | −0.0433963 | ||||||||
\(532\) | 18451.5 | 1.50371 | ||||||||
\(533\) | −12123.3 | −0.985216 | ||||||||
\(534\) | 3457.81 | 0.280214 | ||||||||
\(535\) | −8419.06 | −0.680351 | ||||||||
\(536\) | −2827.14 | −0.227824 | ||||||||
\(537\) | 1527.32 | 0.122735 | ||||||||
\(538\) | −14002.7 | −1.12211 | ||||||||
\(539\) | 2286.97 | 0.182758 | ||||||||
\(540\) | −4641.06 | −0.369851 | ||||||||
\(541\) | −6609.92 | −0.525291 | −0.262646 | − | 0.964892i | \(-0.584595\pi\) | ||||
−0.262646 | + | 0.964892i | \(0.584595\pi\) | |||||||
\(542\) | −30146.1 | −2.38909 | ||||||||
\(543\) | −2474.59 | −0.195571 | ||||||||
\(544\) | −21590.9 | −1.70166 | ||||||||
\(545\) | 16628.8 | 1.30697 | ||||||||
\(546\) | 5987.05 | 0.469271 | ||||||||
\(547\) | 8883.37 | 0.694379 | 0.347190 | − | 0.937795i | \(-0.387136\pi\) | ||||
0.347190 | + | 0.937795i | \(0.387136\pi\) | |||||||
\(548\) | 18783.5 | 1.46422 | ||||||||
\(549\) | 2800.85 | 0.217737 | ||||||||
\(550\) | 14625.0 | 1.13384 | ||||||||
\(551\) | −1594.78 | −0.123303 | ||||||||
\(552\) | −478.777 | −0.0369168 | ||||||||
\(553\) | 13916.2 | 1.07012 | ||||||||
\(554\) | −19447.4 | −1.49141 | ||||||||
\(555\) | 190.888 | 0.0145995 | ||||||||
\(556\) | −4389.58 | −0.334819 | ||||||||
\(557\) | 13797.8 | 1.04961 | 0.524805 | − | 0.851222i | \(-0.324138\pi\) | ||||
0.524805 | + | 0.851222i | \(0.324138\pi\) | |||||||
\(558\) | −8191.75 | −0.621478 | ||||||||
\(559\) | 5361.36 | 0.405655 | ||||||||
\(560\) | −12171.8 | −0.918487 | ||||||||
\(561\) | −4773.66 | −0.359258 | ||||||||
\(562\) | −35037.1 | −2.62981 | ||||||||
\(563\) | −666.036 | −0.0498581 | −0.0249290 | − | 0.999689i | \(-0.507936\pi\) | ||||
−0.0249290 | + | 0.999689i | \(0.507936\pi\) | |||||||
\(564\) | −18021.3 | −1.34545 | ||||||||
\(565\) | 37438.6 | 2.78770 | ||||||||
\(566\) | 34505.9 | 2.56253 | ||||||||
\(567\) | 1206.87 | 0.0893890 | ||||||||
\(568\) | 7444.84 | 0.549962 | ||||||||
\(569\) | −18945.7 | −1.39586 | −0.697932 | − | 0.716164i | \(-0.745896\pi\) | ||||
−0.697932 | + | 0.716164i | \(0.745896\pi\) | |||||||
\(570\) | 28118.9 | 2.06626 | ||||||||
\(571\) | 23781.4 | 1.74295 | 0.871473 | − | 0.490443i | \(-0.163165\pi\) | ||||
0.871473 | + | 0.490443i | \(0.163165\pi\) | |||||||
\(572\) | −5874.56 | −0.429419 | ||||||||
\(573\) | 11043.3 | 0.805130 | ||||||||
\(574\) | 23987.0 | 1.74425 | ||||||||
\(575\) | −3885.61 | −0.281811 | ||||||||
\(576\) | −6385.21 | −0.461893 | ||||||||
\(577\) | 12773.4 | 0.921601 | 0.460800 | − | 0.887504i | \(-0.347562\pi\) | ||||
0.460800 | + | 0.887504i | \(0.347562\pi\) | |||||||
\(578\) | −9173.45 | −0.660148 | ||||||||
\(579\) | 9153.52 | 0.657007 | ||||||||
\(580\) | −2166.39 | −0.155094 | ||||||||
\(581\) | 18812.7 | 1.34335 | ||||||||
\(582\) | −11351.7 | −0.808491 | ||||||||
\(583\) | −5113.33 | −0.363246 | ||||||||
\(584\) | 2708.96 | 0.191948 | ||||||||
\(585\) | 5020.21 | 0.354804 | ||||||||
\(586\) | 1117.04 | 0.0787448 | ||||||||
\(587\) | 11287.3 | 0.793658 | 0.396829 | − | 0.917893i | \(-0.370111\pi\) | ||||
0.396829 | + | 0.917893i | \(0.370111\pi\) | |||||||
\(588\) | 3552.70 | 0.249169 | ||||||||
\(589\) | 27308.7 | 1.91042 | ||||||||
\(590\) | 4370.31 | 0.304954 | ||||||||
\(591\) | 15997.7 | 1.11347 | ||||||||
\(592\) | 168.506 | 0.0116986 | ||||||||
\(593\) | −23122.5 | −1.60123 | −0.800614 | − | 0.599181i | \(-0.795493\pi\) | ||||
−0.800614 | + | 0.599181i | \(0.795493\pi\) | |||||||
\(594\) | −2152.17 | −0.148661 | ||||||||
\(595\) | −22031.8 | −1.51801 | ||||||||
\(596\) | −15790.5 | −1.08524 | ||||||||
\(597\) | 16115.2 | 1.10477 | ||||||||
\(598\) | 2836.58 | 0.193974 | ||||||||
\(599\) | −28372.3 | −1.93533 | −0.967665 | − | 0.252239i | \(-0.918833\pi\) | ||||
−0.967665 | + | 0.252239i | \(0.918833\pi\) | |||||||
\(600\) | 4147.98 | 0.282234 | ||||||||
\(601\) | −15958.6 | −1.08314 | −0.541569 | − | 0.840656i | \(-0.682170\pi\) | ||||
−0.541569 | + | 0.840656i | \(0.682170\pi\) | |||||||
\(602\) | −10607.9 | −0.718182 | ||||||||
\(603\) | 3376.42 | 0.228024 | ||||||||
\(604\) | −14897.7 | −1.00361 | ||||||||
\(605\) | −17103.1 | −1.14932 | ||||||||
\(606\) | 3755.01 | 0.251711 | ||||||||
\(607\) | 12001.9 | 0.802540 | 0.401270 | − | 0.915960i | \(-0.368569\pi\) | ||||
0.401270 | + | 0.915960i | \(0.368569\pi\) | |||||||
\(608\) | 32450.5 | 2.16454 | ||||||||
\(609\) | 563.351 | 0.0374846 | ||||||||
\(610\) | −23052.0 | −1.53008 | ||||||||
\(611\) | 19493.5 | 1.29071 | ||||||||
\(612\) | −7415.67 | −0.489805 | ||||||||
\(613\) | −17040.5 | −1.12277 | −0.561384 | − | 0.827555i | \(-0.689731\pi\) | ||||
−0.561384 | + | 0.827555i | \(0.689731\pi\) | |||||||
\(614\) | −18471.1 | −1.21406 | ||||||||
\(615\) | 20113.4 | 1.31878 | ||||||||
\(616\) | 2122.13 | 0.138804 | ||||||||
\(617\) | −23366.1 | −1.52461 | −0.762304 | − | 0.647219i | \(-0.775932\pi\) | ||||
−0.762304 | + | 0.647219i | \(0.775932\pi\) | |||||||
\(618\) | −465.892 | −0.0303251 | ||||||||
\(619\) | 3475.30 | 0.225661 | 0.112831 | − | 0.993614i | \(-0.464008\pi\) | ||||
0.112831 | + | 0.993614i | \(0.464008\pi\) | |||||||
\(620\) | 37097.0 | 2.40298 | ||||||||
\(621\) | 571.797 | 0.0369491 | ||||||||
\(622\) | −44471.3 | −2.86678 | ||||||||
\(623\) | 4071.97 | 0.261862 | ||||||||
\(624\) | 4431.59 | 0.284304 | ||||||||
\(625\) | −4895.84 | −0.313334 | ||||||||
\(626\) | 27399.5 | 1.74937 | ||||||||
\(627\) | 7174.67 | 0.456984 | ||||||||
\(628\) | −777.303 | −0.0493913 | ||||||||
\(629\) | 305.008 | 0.0193346 | ||||||||
\(630\) | −9932.92 | −0.628154 | ||||||||
\(631\) | 16882.7 | 1.06512 | 0.532561 | − | 0.846392i | \(-0.321230\pi\) | ||||
0.532561 | + | 0.846392i | \(0.321230\pi\) | |||||||
\(632\) | −7038.49 | −0.443000 | ||||||||
\(633\) | −5690.77 | −0.357326 | ||||||||
\(634\) | −11086.9 | −0.694504 | ||||||||
\(635\) | 36084.5 | 2.25507 | ||||||||
\(636\) | −7943.33 | −0.495242 | ||||||||
\(637\) | −3842.94 | −0.239031 | ||||||||
\(638\) | −1004.61 | −0.0623400 | ||||||||
\(639\) | −8891.27 | −0.550443 | ||||||||
\(640\) | 16519.0 | 1.02027 | ||||||||
\(641\) | 19928.1 | 1.22794 | 0.613971 | − | 0.789328i | \(-0.289571\pi\) | ||||
0.613971 | + | 0.789328i | \(0.289571\pi\) | |||||||
\(642\) | −6064.89 | −0.372838 | ||||||||
\(643\) | −27843.0 | −1.70765 | −0.853827 | − | 0.520556i | \(-0.825725\pi\) | ||||
−0.853827 | + | 0.520556i | \(0.825725\pi\) | |||||||
\(644\) | −3088.12 | −0.188958 | ||||||||
\(645\) | −8894.86 | −0.543000 | ||||||||
\(646\) | 44929.5 | 2.73642 | ||||||||
\(647\) | 28838.3 | 1.75232 | 0.876160 | − | 0.482021i | \(-0.160097\pi\) | ||||
0.876160 | + | 0.482021i | \(0.160097\pi\) | |||||||
\(648\) | −610.406 | −0.0370047 | ||||||||
\(649\) | 1115.11 | 0.0674449 | ||||||||
\(650\) | −24575.3 | −1.48296 | ||||||||
\(651\) | −9646.72 | −0.580776 | ||||||||
\(652\) | 22062.9 | 1.32523 | ||||||||
\(653\) | 17697.2 | 1.06056 | 0.530280 | − | 0.847823i | \(-0.322087\pi\) | ||||
0.530280 | + | 0.847823i | \(0.322087\pi\) | |||||||
\(654\) | 11979.0 | 0.716231 | ||||||||
\(655\) | −10578.7 | −0.631057 | ||||||||
\(656\) | 17755.1 | 1.05674 | ||||||||
\(657\) | −3235.28 | −0.192116 | ||||||||
\(658\) | −38569.6 | −2.28511 | ||||||||
\(659\) | 21288.4 | 1.25839 | 0.629196 | − | 0.777247i | \(-0.283384\pi\) | ||||
0.629196 | + | 0.777247i | \(0.283384\pi\) | |||||||
\(660\) | 9746.29 | 0.574809 | ||||||||
\(661\) | −3564.16 | −0.209727 | −0.104864 | − | 0.994487i | \(-0.533441\pi\) | ||||
−0.104864 | + | 0.994487i | \(0.533441\pi\) | |||||||
\(662\) | 15516.2 | 0.910957 | ||||||||
\(663\) | 8021.49 | 0.469878 | ||||||||
\(664\) | −9515.07 | −0.556109 | ||||||||
\(665\) | 33113.2 | 1.93094 | ||||||||
\(666\) | 137.511 | 0.00800068 | ||||||||
\(667\) | 266.908 | 0.0154943 | ||||||||
\(668\) | −3740.76 | −0.216668 | ||||||||
\(669\) | 8426.54 | 0.486979 | ||||||||
\(670\) | −27789.1 | −1.60237 | ||||||||
\(671\) | −5881.83 | −0.338399 | ||||||||
\(672\) | −11463.0 | −0.658030 | ||||||||
\(673\) | 803.878 | 0.0460434 | 0.0230217 | − | 0.999735i | \(-0.492671\pi\) | ||||
0.0230217 | + | 0.999735i | \(0.492671\pi\) | |||||||
\(674\) | −5582.80 | −0.319053 | ||||||||
\(675\) | −4953.88 | −0.282481 | ||||||||
\(676\) | −11630.3 | −0.661713 | ||||||||
\(677\) | −14587.1 | −0.828106 | −0.414053 | − | 0.910253i | \(-0.635887\pi\) | ||||
−0.414053 | + | 0.910253i | \(0.635887\pi\) | |||||||
\(678\) | 26969.8 | 1.52768 | ||||||||
\(679\) | −13367.9 | −0.755541 | ||||||||
\(680\) | 11143.2 | 0.628416 | ||||||||
\(681\) | −9908.48 | −0.557554 | ||||||||
\(682\) | 17202.8 | 0.965878 | ||||||||
\(683\) | 19187.3 | 1.07494 | 0.537469 | − | 0.843284i | \(-0.319381\pi\) | ||||
0.537469 | + | 0.843284i | \(0.319381\pi\) | |||||||
\(684\) | 11145.5 | 0.623042 | ||||||||
\(685\) | 33709.0 | 1.88023 | ||||||||
\(686\) | 29157.1 | 1.62277 | ||||||||
\(687\) | 17340.6 | 0.963005 | ||||||||
\(688\) | −7851.93 | −0.435105 | ||||||||
\(689\) | 8592.26 | 0.475093 | ||||||||
\(690\) | −4706.09 | −0.259649 | ||||||||
\(691\) | 19785.3 | 1.08924 | 0.544622 | − | 0.838682i | \(-0.316673\pi\) | ||||
0.544622 | + | 0.838682i | \(0.316673\pi\) | |||||||
\(692\) | −9100.03 | −0.499901 | ||||||||
\(693\) | −2534.43 | −0.138925 | ||||||||
\(694\) | −23370.1 | −1.27827 | ||||||||
\(695\) | −7877.56 | −0.429946 | ||||||||
\(696\) | −284.931 | −0.0155176 | ||||||||
\(697\) | 32138.0 | 1.74651 | ||||||||
\(698\) | 27794.9 | 1.50724 | ||||||||
\(699\) | −14678.5 | −0.794267 | ||||||||
\(700\) | 26754.5 | 1.44461 | ||||||||
\(701\) | −14311.7 | −0.771104 | −0.385552 | − | 0.922686i | \(-0.625989\pi\) | ||||
−0.385552 | + | 0.922686i | \(0.625989\pi\) | |||||||
\(702\) | 3616.44 | 0.194436 | ||||||||
\(703\) | −458.419 | −0.0245940 | ||||||||
\(704\) | 13409.0 | 0.717857 | ||||||||
\(705\) | −32341.1 | −1.72771 | ||||||||
\(706\) | 23757.3 | 1.26646 | ||||||||
\(707\) | 4421.95 | 0.235226 | ||||||||
\(708\) | 1732.27 | 0.0919530 | ||||||||
\(709\) | −11747.7 | −0.622277 | −0.311139 | − | 0.950365i | \(-0.600710\pi\) | ||||
−0.311139 | + | 0.950365i | \(0.600710\pi\) | |||||||
\(710\) | 73178.3 | 3.86807 | ||||||||
\(711\) | 8405.98 | 0.443388 | ||||||||
\(712\) | −2059.51 | −0.108404 | ||||||||
\(713\) | −4570.49 | −0.240065 | ||||||||
\(714\) | −15871.2 | −0.831884 | ||||||||
\(715\) | −10542.5 | −0.551423 | ||||||||
\(716\) | −4982.53 | −0.260064 | ||||||||
\(717\) | 19384.2 | 1.00964 | ||||||||
\(718\) | −11271.7 | −0.585874 | ||||||||
\(719\) | 1263.52 | 0.0655374 | 0.0327687 | − | 0.999463i | \(-0.489568\pi\) | ||||
0.0327687 | + | 0.999463i | \(0.489568\pi\) | |||||||
\(720\) | −7352.31 | −0.380562 | ||||||||
\(721\) | −548.642 | −0.0283391 | ||||||||
\(722\) | −38600.3 | −1.98969 | ||||||||
\(723\) | 182.319 | 0.00937829 | ||||||||
\(724\) | 8072.82 | 0.414398 | ||||||||
\(725\) | −2312.41 | −0.118456 | ||||||||
\(726\) | −12320.7 | −0.629838 | ||||||||
\(727\) | −15608.6 | −0.796275 | −0.398138 | − | 0.917326i | \(-0.630343\pi\) | ||||
−0.398138 | + | 0.917326i | \(0.630343\pi\) | |||||||
\(728\) | −3565.96 | −0.181543 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 26627.5 | 1.35004 | ||||||||
\(731\) | −14212.6 | −0.719111 | ||||||||
\(732\) | −9137.17 | −0.461365 | ||||||||
\(733\) | 5555.30 | 0.279931 | 0.139966 | − | 0.990156i | \(-0.455301\pi\) | ||||
0.139966 | + | 0.990156i | \(0.455301\pi\) | |||||||
\(734\) | 12154.3 | 0.611205 | ||||||||
\(735\) | 6375.70 | 0.319961 | ||||||||
\(736\) | −5431.03 | −0.271998 | ||||||||
\(737\) | −7090.51 | −0.354386 | ||||||||
\(738\) | 14489.2 | 0.722705 | ||||||||
\(739\) | −6833.98 | −0.340179 | −0.170089 | − | 0.985429i | \(-0.554406\pi\) | ||||
−0.170089 | + | 0.985429i | \(0.554406\pi\) | |||||||
\(740\) | −622.730 | −0.0309352 | ||||||||
\(741\) | −12056.1 | −0.597694 | ||||||||
\(742\) | −17000.5 | −0.841117 | ||||||||
\(743\) | 35475.6 | 1.75165 | 0.875823 | − | 0.482633i | \(-0.160319\pi\) | ||||
0.875823 | + | 0.482633i | \(0.160319\pi\) | |||||||
\(744\) | 4879.11 | 0.240426 | ||||||||
\(745\) | −28337.8 | −1.39358 | ||||||||
\(746\) | −30996.5 | −1.52126 | ||||||||
\(747\) | 11363.7 | 0.556596 | ||||||||
\(748\) | 15573.0 | 0.761237 | ||||||||
\(749\) | −7142.10 | −0.348420 | ||||||||
\(750\) | 12994.7 | 0.632666 | ||||||||
\(751\) | −33087.6 | −1.60770 | −0.803850 | − | 0.594832i | \(-0.797218\pi\) | ||||
−0.803850 | + | 0.594832i | \(0.797218\pi\) | |||||||
\(752\) | −28549.1 | −1.38441 | ||||||||
\(753\) | 11346.4 | 0.549118 | ||||||||
\(754\) | 1688.11 | 0.0815351 | ||||||||
\(755\) | −26735.5 | −1.28875 | ||||||||
\(756\) | −3937.13 | −0.189407 | ||||||||
\(757\) | −11497.2 | −0.552013 | −0.276007 | − | 0.961156i | \(-0.589011\pi\) | ||||
−0.276007 | + | 0.961156i | \(0.589011\pi\) | |||||||
\(758\) | −25310.1 | −1.21280 | ||||||||
\(759\) | −1200.78 | −0.0574250 | ||||||||
\(760\) | −16747.9 | −0.799358 | ||||||||
\(761\) | 7865.73 | 0.374681 | 0.187341 | − | 0.982295i | \(-0.440013\pi\) | ||||
0.187341 | + | 0.982295i | \(0.440013\pi\) | |||||||
\(762\) | 25994.4 | 1.23580 | ||||||||
\(763\) | 14106.6 | 0.669323 | ||||||||
\(764\) | −36026.3 | −1.70600 | ||||||||
\(765\) | −13308.2 | −0.628966 | ||||||||
\(766\) | 33082.5 | 1.56047 | ||||||||
\(767\) | −1873.79 | −0.0882119 | ||||||||
\(768\) | −5127.30 | −0.240906 | ||||||||
\(769\) | 8020.94 | 0.376128 | 0.188064 | − | 0.982157i | \(-0.439779\pi\) | ||||
0.188064 | + | 0.982157i | \(0.439779\pi\) | |||||||
\(770\) | 20859.3 | 0.976254 | ||||||||
\(771\) | 218.228 | 0.0101936 | ||||||||
\(772\) | −29861.3 | −1.39214 | ||||||||
\(773\) | −17731.7 | −0.825053 | −0.412526 | − | 0.910946i | \(-0.635354\pi\) | ||||
−0.412526 | + | 0.910946i | \(0.635354\pi\) | |||||||
\(774\) | −6407.64 | −0.297568 | ||||||||
\(775\) | 39597.4 | 1.83533 | ||||||||
\(776\) | 6761.19 | 0.312774 | ||||||||
\(777\) | 161.935 | 0.00747670 | ||||||||
\(778\) | 2423.36 | 0.111673 | ||||||||
\(779\) | −48302.5 | −2.22159 | ||||||||
\(780\) | −16377.3 | −0.751798 | ||||||||
\(781\) | 18671.8 | 0.855479 | ||||||||
\(782\) | −7519.57 | −0.343861 | ||||||||
\(783\) | 340.289 | 0.0155312 | ||||||||
\(784\) | 5628.15 | 0.256384 | ||||||||
\(785\) | −1394.95 | −0.0634242 | ||||||||
\(786\) | −7620.61 | −0.345825 | ||||||||
\(787\) | −10866.2 | −0.492170 | −0.246085 | − | 0.969248i | \(-0.579144\pi\) | ||||
−0.246085 | + | 0.969248i | \(0.579144\pi\) | |||||||
\(788\) | −52189.0 | −2.35934 | ||||||||
\(789\) | 14362.5 | 0.648058 | ||||||||
\(790\) | −69184.1 | −3.11577 | ||||||||
\(791\) | 31760.1 | 1.42763 | ||||||||
\(792\) | 1281.86 | 0.0575113 | ||||||||
\(793\) | 9883.63 | 0.442595 | ||||||||
\(794\) | 60431.9 | 2.70107 | ||||||||
\(795\) | −14255.2 | −0.635947 | ||||||||
\(796\) | −52572.1 | −2.34092 | ||||||||
\(797\) | −36334.0 | −1.61483 | −0.807414 | − | 0.589985i | \(-0.799134\pi\) | ||||
−0.807414 | + | 0.589985i | \(0.799134\pi\) | |||||||
\(798\) | 23854.0 | 1.05817 | ||||||||
\(799\) | −51675.8 | −2.28806 | ||||||||
\(800\) | 47052.8 | 2.07946 | ||||||||
\(801\) | 2459.65 | 0.108499 | ||||||||
\(802\) | −35597.4 | −1.56731 | ||||||||
\(803\) | 6794.13 | 0.298580 | ||||||||
\(804\) | −11014.8 | −0.483162 | ||||||||
\(805\) | −5541.96 | −0.242644 | ||||||||
\(806\) | −28907.0 | −1.26328 | ||||||||
\(807\) | −9960.53 | −0.434483 | ||||||||
\(808\) | −2236.53 | −0.0973772 | ||||||||
\(809\) | 29433.4 | 1.27914 | 0.639569 | − | 0.768734i | \(-0.279113\pi\) | ||||
0.639569 | + | 0.768734i | \(0.279113\pi\) | |||||||
\(810\) | −5999.92 | −0.260266 | ||||||||
\(811\) | −6295.17 | −0.272569 | −0.136284 | − | 0.990670i | \(-0.543516\pi\) | ||||
−0.136284 | + | 0.990670i | \(0.543516\pi\) | |||||||
\(812\) | −1837.81 | −0.0794266 | ||||||||
\(813\) | −21443.8 | −0.925053 | ||||||||
\(814\) | −288.775 | −0.0124344 | ||||||||
\(815\) | 39594.3 | 1.70175 | ||||||||
\(816\) | −11747.8 | −0.503990 | ||||||||
\(817\) | 21361.1 | 0.914723 | ||||||||
\(818\) | 16848.8 | 0.720175 | ||||||||
\(819\) | 4258.77 | 0.181702 | ||||||||
\(820\) | −65615.6 | −2.79439 | ||||||||
\(821\) | 39899.7 | 1.69611 | 0.848057 | − | 0.529905i | \(-0.177772\pi\) | ||||
0.848057 | + | 0.529905i | \(0.177772\pi\) | |||||||
\(822\) | 24283.2 | 1.03038 | ||||||||
\(823\) | −1122.81 | −0.0475560 | −0.0237780 | − | 0.999717i | \(-0.507569\pi\) | ||||
−0.0237780 | + | 0.999717i | \(0.507569\pi\) | |||||||
\(824\) | 277.491 | 0.0117316 | ||||||||
\(825\) | 10403.2 | 0.439022 | ||||||||
\(826\) | 3707.45 | 0.156173 | ||||||||
\(827\) | −11050.5 | −0.464649 | −0.232325 | − | 0.972638i | \(-0.574633\pi\) | ||||
−0.232325 | + | 0.972638i | \(0.574633\pi\) | |||||||
\(828\) | −1865.36 | −0.0782920 | ||||||||
\(829\) | 28472.9 | 1.19289 | 0.596444 | − | 0.802654i | \(-0.296580\pi\) | ||||
0.596444 | + | 0.802654i | \(0.296580\pi\) | |||||||
\(830\) | −93527.4 | −3.91131 | ||||||||
\(831\) | −13833.6 | −0.577474 | ||||||||
\(832\) | −22532.1 | −0.938893 | ||||||||
\(833\) | 10187.3 | 0.423734 | ||||||||
\(834\) | −5674.80 | −0.235614 | ||||||||
\(835\) | −6713.19 | −0.278227 | ||||||||
\(836\) | −23405.8 | −0.968308 | ||||||||
\(837\) | −5827.05 | −0.240636 | ||||||||
\(838\) | 7952.88 | 0.327837 | ||||||||
\(839\) | 6906.38 | 0.284189 | 0.142095 | − | 0.989853i | \(-0.454616\pi\) | ||||
0.142095 | + | 0.989853i | \(0.454616\pi\) | |||||||
\(840\) | 5916.16 | 0.243008 | ||||||||
\(841\) | −24230.2 | −0.993487 | ||||||||
\(842\) | 39088.9 | 1.59987 | ||||||||
\(843\) | −24923.0 | −1.01826 | ||||||||
\(844\) | 18564.9 | 0.757143 | ||||||||
\(845\) | −20871.7 | −0.849716 | ||||||||
\(846\) | −23297.7 | −0.946800 | ||||||||
\(847\) | −14509.0 | −0.588589 | ||||||||
\(848\) | −12583.7 | −0.509584 | ||||||||
\(849\) | 24545.1 | 0.992210 | ||||||||
\(850\) | 65147.3 | 2.62886 | ||||||||
\(851\) | 76.7228 | 0.00309051 | ||||||||
\(852\) | 29005.8 | 1.16634 | ||||||||
\(853\) | −22035.5 | −0.884504 | −0.442252 | − | 0.896891i | \(-0.645820\pi\) | ||||
−0.442252 | + | 0.896891i | \(0.645820\pi\) | |||||||
\(854\) | −19555.6 | −0.783582 | ||||||||
\(855\) | 20001.9 | 0.800057 | ||||||||
\(856\) | 3612.32 | 0.144237 | ||||||||
\(857\) | 39983.9 | 1.59373 | 0.796864 | − | 0.604159i | \(-0.206491\pi\) | ||||
0.796864 | + | 0.604159i | \(0.206491\pi\) | |||||||
\(858\) | −7594.57 | −0.302185 | ||||||||
\(859\) | −17967.4 | −0.713668 | −0.356834 | − | 0.934168i | \(-0.616144\pi\) | ||||
−0.356834 | + | 0.934168i | \(0.616144\pi\) | |||||||
\(860\) | 29017.5 | 1.15057 | ||||||||
\(861\) | 17062.7 | 0.675373 | ||||||||
\(862\) | 14112.0 | 0.557608 | ||||||||
\(863\) | 42533.4 | 1.67770 | 0.838850 | − | 0.544363i | \(-0.183229\pi\) | ||||
0.838850 | + | 0.544363i | \(0.183229\pi\) | |||||||
\(864\) | −6924.18 | −0.272645 | ||||||||
\(865\) | −16331.0 | −0.641930 | ||||||||
\(866\) | 3913.15 | 0.153550 | ||||||||
\(867\) | −6525.36 | −0.255609 | ||||||||
\(868\) | 31470.3 | 1.23061 | ||||||||
\(869\) | −17652.7 | −0.689097 | ||||||||
\(870\) | −2800.69 | −0.109141 | ||||||||
\(871\) | 11914.7 | 0.463505 | ||||||||
\(872\) | −7134.82 | −0.277082 | ||||||||
\(873\) | −8074.80 | −0.313048 | ||||||||
\(874\) | 11301.7 | 0.437398 | ||||||||
\(875\) | 15302.8 | 0.591231 | ||||||||
\(876\) | 10554.4 | 0.407077 | ||||||||
\(877\) | 48368.0 | 1.86234 | 0.931169 | − | 0.364589i | \(-0.118791\pi\) | ||||
0.931169 | + | 0.364589i | \(0.118791\pi\) | |||||||
\(878\) | −42699.6 | −1.64128 | ||||||||
\(879\) | 794.585 | 0.0304900 | ||||||||
\(880\) | 15439.9 | 0.591455 | ||||||||
\(881\) | 29172.9 | 1.11562 | 0.557810 | − | 0.829969i | \(-0.311642\pi\) | ||||
0.557810 | + | 0.829969i | \(0.311642\pi\) | |||||||
\(882\) | 4592.90 | 0.175341 | ||||||||
\(883\) | −17067.5 | −0.650471 | −0.325235 | − | 0.945633i | \(-0.605444\pi\) | ||||
−0.325235 | + | 0.945633i | \(0.605444\pi\) | |||||||
\(884\) | −26168.3 | −0.995630 | ||||||||
\(885\) | 3108.74 | 0.118078 | ||||||||
\(886\) | 27381.5 | 1.03826 | ||||||||
\(887\) | 19672.0 | 0.744671 | 0.372335 | − | 0.928098i | \(-0.378557\pi\) | ||||
0.372335 | + | 0.928098i | \(0.378557\pi\) | |||||||
\(888\) | −81.9033 | −0.00309515 | ||||||||
\(889\) | 30611.4 | 1.15486 | ||||||||
\(890\) | −20243.8 | −0.762441 | ||||||||
\(891\) | −1530.91 | −0.0575616 | ||||||||
\(892\) | −27489.7 | −1.03187 | ||||||||
\(893\) | 77667.3 | 2.91046 | ||||||||
\(894\) | −20413.9 | −0.763693 | ||||||||
\(895\) | −8941.68 | −0.333953 | ||||||||
\(896\) | 14013.5 | 0.522499 | ||||||||
\(897\) | 2017.75 | 0.0751067 | ||||||||
\(898\) | 74682.4 | 2.77526 | ||||||||
\(899\) | −2720.00 | −0.100909 | ||||||||
\(900\) | 16160.9 | 0.598553 | ||||||||
\(901\) | −22777.4 | −0.842205 | ||||||||
\(902\) | −30427.6 | −1.12320 | ||||||||
\(903\) | −7545.73 | −0.278080 | ||||||||
\(904\) | −16063.6 | −0.591002 | ||||||||
\(905\) | 14487.5 | 0.532134 | ||||||||
\(906\) | −19259.6 | −0.706245 | ||||||||
\(907\) | −6730.37 | −0.246393 | −0.123196 | − | 0.992382i | \(-0.539315\pi\) | ||||
−0.123196 | + | 0.992382i | \(0.539315\pi\) | |||||||
\(908\) | 32324.2 | 1.18141 | ||||||||
\(909\) | 2671.05 | 0.0974623 | ||||||||
\(910\) | −35051.2 | −1.27685 | ||||||||
\(911\) | 5094.05 | 0.185262 | 0.0926308 | − | 0.995701i | \(-0.470472\pi\) | ||||
0.0926308 | + | 0.995701i | \(0.470472\pi\) | |||||||
\(912\) | 17656.6 | 0.641085 | ||||||||
\(913\) | −23864.0 | −0.865040 | ||||||||
\(914\) | −45486.2 | −1.64612 | ||||||||
\(915\) | −16397.6 | −0.592446 | ||||||||
\(916\) | −56569.8 | −2.04052 | ||||||||
\(917\) | −8974.14 | −0.323176 | ||||||||
\(918\) | −9586.91 | −0.344679 | ||||||||
\(919\) | −18873.8 | −0.677464 | −0.338732 | − | 0.940883i | \(-0.609998\pi\) | ||||
−0.338732 | + | 0.940883i | \(0.609998\pi\) | |||||||
\(920\) | 2803.00 | 0.100448 | ||||||||
\(921\) | −13139.1 | −0.470084 | ||||||||
\(922\) | 61205.7 | 2.18623 | ||||||||
\(923\) | −31375.4 | −1.11889 | ||||||||
\(924\) | 8268.02 | 0.294370 | ||||||||
\(925\) | −664.703 | −0.0236274 | ||||||||
\(926\) | 40646.9 | 1.44248 | ||||||||
\(927\) | −331.404 | −0.0117419 | ||||||||
\(928\) | −3232.13 | −0.114332 | ||||||||
\(929\) | 42077.8 | 1.48603 | 0.743017 | − | 0.669272i | \(-0.233394\pi\) | ||||
0.743017 | + | 0.669272i | \(0.233394\pi\) | |||||||
\(930\) | 47958.6 | 1.69100 | ||||||||
\(931\) | −15311.3 | −0.538998 | ||||||||
\(932\) | 47885.4 | 1.68298 | ||||||||
\(933\) | −31633.9 | −1.11002 | ||||||||
\(934\) | 30620.0 | 1.07272 | ||||||||
\(935\) | 27947.4 | 0.977516 | ||||||||
\(936\) | −2154.00 | −0.0752196 | ||||||||
\(937\) | −16791.9 | −0.585452 | −0.292726 | − | 0.956196i | \(-0.594562\pi\) | ||||
−0.292726 | + | 0.956196i | \(0.594562\pi\) | |||||||
\(938\) | −23574.2 | −0.820601 | ||||||||
\(939\) | 19490.1 | 0.677355 | ||||||||
\(940\) | 105506. | 3.66087 | ||||||||
\(941\) | −21099.3 | −0.730943 | −0.365472 | − | 0.930822i | \(-0.619092\pi\) | ||||
−0.365472 | + | 0.930822i | \(0.619092\pi\) | |||||||
\(942\) | −1004.89 | −0.0347570 | ||||||||
\(943\) | 8084.10 | 0.279167 | ||||||||
\(944\) | 2744.24 | 0.0946159 | ||||||||
\(945\) | −7065.60 | −0.243221 | ||||||||
\(946\) | 13456.1 | 0.462470 | ||||||||
\(947\) | −13159.7 | −0.451567 | −0.225783 | − | 0.974178i | \(-0.572494\pi\) | ||||
−0.225783 | + | 0.974178i | \(0.572494\pi\) | |||||||
\(948\) | −27422.6 | −0.939500 | ||||||||
\(949\) | −11416.6 | −0.390516 | ||||||||
\(950\) | −97914.5 | −3.34396 | ||||||||
\(951\) | −7886.43 | −0.268912 | ||||||||
\(952\) | 9453.08 | 0.321824 | ||||||||
\(953\) | −14229.9 | −0.483685 | −0.241843 | − | 0.970315i | \(-0.577752\pi\) | ||||
−0.241843 | + | 0.970315i | \(0.577752\pi\) | |||||||
\(954\) | −10269.1 | −0.348505 | ||||||||
\(955\) | −64652.9 | −2.19070 | ||||||||
\(956\) | −63236.6 | −2.13935 | ||||||||
\(957\) | −714.611 | −0.0241380 | ||||||||
\(958\) | −50901.9 | −1.71667 | ||||||||
\(959\) | 28596.2 | 0.962898 | ||||||||
\(960\) | 37382.2 | 1.25678 | ||||||||
\(961\) | 16785.8 | 0.563453 | ||||||||
\(962\) | 485.248 | 0.0162630 | ||||||||
\(963\) | −4314.15 | −0.144363 | ||||||||
\(964\) | −594.774 | −0.0198718 | ||||||||
\(965\) | −53589.3 | −1.78767 | ||||||||
\(966\) | −3992.29 | −0.132971 | ||||||||
\(967\) | −43103.2 | −1.43341 | −0.716704 | − | 0.697377i | \(-0.754350\pi\) | ||||
−0.716704 | + | 0.697377i | \(0.754350\pi\) | |||||||
\(968\) | 7338.33 | 0.243660 | ||||||||
\(969\) | 31959.7 | 1.05954 | ||||||||
\(970\) | 66458.4 | 2.19985 | ||||||||
\(971\) | −24953.4 | −0.824710 | −0.412355 | − | 0.911023i | \(-0.635294\pi\) | ||||
−0.412355 | + | 0.911023i | \(0.635294\pi\) | |||||||
\(972\) | −2378.20 | −0.0784782 | ||||||||
\(973\) | −6682.73 | −0.220183 | ||||||||
\(974\) | 25372.0 | 0.834673 | ||||||||
\(975\) | −17481.2 | −0.574201 | ||||||||
\(976\) | −14475.0 | −0.474726 | ||||||||
\(977\) | −7739.34 | −0.253432 | −0.126716 | − | 0.991939i | \(-0.540444\pi\) | ||||
−0.126716 | + | 0.991939i | \(0.540444\pi\) | |||||||
\(978\) | 28522.8 | 0.932574 | ||||||||
\(979\) | −5165.29 | −0.168625 | ||||||||
\(980\) | −20799.3 | −0.677969 | ||||||||
\(981\) | 8521.02 | 0.277324 | ||||||||
\(982\) | −16966.0 | −0.551330 | ||||||||
\(983\) | 19799.0 | 0.642410 | 0.321205 | − | 0.947010i | \(-0.395912\pi\) | ||||
0.321205 | + | 0.947010i | \(0.395912\pi\) | |||||||
\(984\) | −8629.96 | −0.279587 | ||||||||
\(985\) | −93658.7 | −3.02966 | ||||||||
\(986\) | −4475.06 | −0.144538 | ||||||||
\(987\) | −27435.8 | −0.884792 | ||||||||
\(988\) | 39330.3 | 1.26646 | ||||||||
\(989\) | −3575.07 | −0.114945 | ||||||||
\(990\) | 12599.9 | 0.404497 | ||||||||
\(991\) | 10262.8 | 0.328968 | 0.164484 | − | 0.986380i | \(-0.447404\pi\) | ||||
0.164484 | + | 0.986380i | \(0.447404\pi\) | |||||||
\(992\) | 55346.4 | 1.77142 | ||||||||
\(993\) | 11037.1 | 0.352722 | ||||||||
\(994\) | 62079.0 | 1.98091 | ||||||||
\(995\) | −94346.2 | −3.00601 | ||||||||
\(996\) | −37071.6 | −1.17938 | ||||||||
\(997\) | −18748.2 | −0.595549 | −0.297774 | − | 0.954636i | \(-0.596244\pi\) | ||||
−0.297774 | + | 0.954636i | \(0.596244\pi\) | |||||||
\(998\) | 59520.0 | 1.88785 | ||||||||
\(999\) | 97.8160 | 0.00309786 |
(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 | 177.4.a.c.1.2 | ✓ | 8 | |
3.2 | odd | 2 | 531.4.a.f.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.a.c.1.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
531.4.a.f.1.7 | 8 | 3.2 | odd | 2 |