Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2209,4,Mod(1,2209)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2209, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2209.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2209 = 47^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2209.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: | \(130.335219203\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1101.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 9x + 12 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 47) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.68740\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2209.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.90952 | −1.73578 | −0.867888 | − | 0.496760i | \(-0.834523\pi\) | ||||
−0.867888 | + | 0.496760i | \(0.834523\pi\) | |||||||
\(3\) | −0.777884 | −0.149704 | −0.0748519 | − | 0.997195i | \(-0.523848\pi\) | ||||
−0.0748519 | + | 0.997195i | \(0.523848\pi\) | |||||||
\(4\) | 16.1033 | 2.01292 | ||||||||
\(5\) | −9.19383 | −0.822321 | −0.411161 | − | 0.911563i | \(-0.634876\pi\) | ||||
−0.411161 | + | 0.911563i | \(0.634876\pi\) | |||||||
\(6\) | 3.81903 | 0.259852 | ||||||||
\(7\) | −30.3255 | −1.63742 | −0.818711 | − | 0.574206i | \(-0.805311\pi\) | ||||
−0.818711 | + | 0.574206i | \(0.805311\pi\) | |||||||
\(8\) | −39.7835 | −1.75820 | ||||||||
\(9\) | −26.3949 | −0.977589 | ||||||||
\(10\) | 45.1373 | 1.42737 | ||||||||
\(11\) | −22.4298 | −0.614803 | −0.307401 | − | 0.951580i | \(-0.599459\pi\) | ||||
−0.307401 | + | 0.951580i | \(0.599459\pi\) | |||||||
\(12\) | −12.5265 | −0.301341 | ||||||||
\(13\) | 62.0257 | 1.32330 | 0.661648 | − | 0.749815i | \(-0.269857\pi\) | ||||
0.661648 | + | 0.749815i | \(0.269857\pi\) | |||||||
\(14\) | 148.883 | 2.84220 | ||||||||
\(15\) | 7.15173 | 0.123105 | ||||||||
\(16\) | 66.4910 | 1.03892 | ||||||||
\(17\) | −72.1639 | −1.02955 | −0.514774 | − | 0.857326i | \(-0.672124\pi\) | ||||
−0.514774 | + | 0.857326i | \(0.672124\pi\) | |||||||
\(18\) | 129.586 | 1.69688 | ||||||||
\(19\) | 25.0550 | 0.302526 | 0.151263 | − | 0.988494i | \(-0.451666\pi\) | ||||
0.151263 | + | 0.988494i | \(0.451666\pi\) | |||||||
\(20\) | −148.051 | −1.65527 | ||||||||
\(21\) | 23.5897 | 0.245128 | ||||||||
\(22\) | 110.119 | 1.06716 | ||||||||
\(23\) | −103.176 | −0.935373 | −0.467687 | − | 0.883894i | \(-0.654912\pi\) | ||||
−0.467687 | + | 0.883894i | \(0.654912\pi\) | |||||||
\(24\) | 30.9469 | 0.263209 | ||||||||
\(25\) | −40.4735 | −0.323788 | ||||||||
\(26\) | −304.516 | −2.29694 | ||||||||
\(27\) | 41.5350 | 0.296052 | ||||||||
\(28\) | −488.341 | −3.29600 | ||||||||
\(29\) | 234.381 | 1.50081 | 0.750405 | − | 0.660978i | \(-0.229858\pi\) | ||||
0.750405 | + | 0.660978i | \(0.229858\pi\) | |||||||
\(30\) | −35.1115 | −0.213682 | ||||||||
\(31\) | −198.714 | −1.15129 | −0.575647 | − | 0.817698i | \(-0.695250\pi\) | ||||
−0.575647 | + | 0.817698i | \(0.695250\pi\) | |||||||
\(32\) | −8.17058 | −0.0451365 | ||||||||
\(33\) | 17.4477 | 0.0920383 | ||||||||
\(34\) | 354.290 | 1.78707 | ||||||||
\(35\) | 278.807 | 1.34649 | ||||||||
\(36\) | −425.046 | −1.96781 | ||||||||
\(37\) | −203.083 | −0.902343 | −0.451171 | − | 0.892437i | \(-0.648994\pi\) | ||||
−0.451171 | + | 0.892437i | \(0.648994\pi\) | |||||||
\(38\) | −123.008 | −0.525118 | ||||||||
\(39\) | −48.2488 | −0.198102 | ||||||||
\(40\) | 365.763 | 1.44580 | ||||||||
\(41\) | −210.889 | −0.803303 | −0.401651 | − | 0.915793i | \(-0.631564\pi\) | ||||
−0.401651 | + | 0.915793i | \(0.631564\pi\) | |||||||
\(42\) | −115.814 | −0.425487 | ||||||||
\(43\) | −111.430 | −0.395184 | −0.197592 | − | 0.980284i | \(-0.563312\pi\) | ||||
−0.197592 | + | 0.980284i | \(0.563312\pi\) | |||||||
\(44\) | −361.194 | −1.23755 | ||||||||
\(45\) | 242.670 | 0.803892 | ||||||||
\(46\) | 506.542 | 1.62360 | ||||||||
\(47\) | 0 | 0 | ||||||||
\(48\) | −51.7223 | −0.155531 | ||||||||
\(49\) | 576.634 | 1.68115 | ||||||||
\(50\) | 198.705 | 0.562023 | ||||||||
\(51\) | 56.1351 | 0.154127 | ||||||||
\(52\) | 998.822 | 2.66369 | ||||||||
\(53\) | 499.576 | 1.29476 | 0.647378 | − | 0.762169i | \(-0.275866\pi\) | ||||
0.647378 | + | 0.762169i | \(0.275866\pi\) | |||||||
\(54\) | −203.917 | −0.513881 | ||||||||
\(55\) | 206.215 | 0.505565 | ||||||||
\(56\) | 1206.45 | 2.87891 | ||||||||
\(57\) | −19.4898 | −0.0452894 | ||||||||
\(58\) | −1150.70 | −2.60507 | ||||||||
\(59\) | −562.752 | −1.24176 | −0.620882 | − | 0.783904i | \(-0.713225\pi\) | ||||
−0.620882 | + | 0.783904i | \(0.713225\pi\) | |||||||
\(60\) | 115.167 | 0.247799 | ||||||||
\(61\) | 548.091 | 1.15042 | 0.575212 | − | 0.818004i | \(-0.304919\pi\) | ||||
0.575212 | + | 0.818004i | \(0.304919\pi\) | |||||||
\(62\) | 975.591 | 1.99839 | ||||||||
\(63\) | 800.437 | 1.60072 | ||||||||
\(64\) | −491.814 | −0.960575 | ||||||||
\(65\) | −570.254 | −1.08817 | ||||||||
\(66\) | −85.6600 | −0.159758 | ||||||||
\(67\) | 760.831 | 1.38732 | 0.693659 | − | 0.720304i | \(-0.255998\pi\) | ||||
0.693659 | + | 0.720304i | \(0.255998\pi\) | |||||||
\(68\) | −1162.08 | −2.07240 | ||||||||
\(69\) | 80.2586 | 0.140029 | ||||||||
\(70\) | −1368.81 | −2.33720 | ||||||||
\(71\) | −668.059 | −1.11668 | −0.558338 | − | 0.829613i | \(-0.688561\pi\) | ||||
−0.558338 | + | 0.829613i | \(0.688561\pi\) | |||||||
\(72\) | 1050.08 | 1.71880 | ||||||||
\(73\) | 1145.92 | 1.83726 | 0.918629 | − | 0.395121i | \(-0.129297\pi\) | ||||
0.918629 | + | 0.395121i | \(0.129297\pi\) | |||||||
\(74\) | 997.040 | 1.56626 | ||||||||
\(75\) | 31.4836 | 0.0484722 | ||||||||
\(76\) | 403.469 | 0.608961 | ||||||||
\(77\) | 680.193 | 1.00669 | ||||||||
\(78\) | 236.878 | 0.343861 | ||||||||
\(79\) | 975.010 | 1.38857 | 0.694286 | − | 0.719699i | \(-0.255720\pi\) | ||||
0.694286 | + | 0.719699i | \(0.255720\pi\) | |||||||
\(80\) | −611.307 | −0.854328 | ||||||||
\(81\) | 680.353 | 0.933269 | ||||||||
\(82\) | 1035.37 | 1.39435 | ||||||||
\(83\) | 698.827 | 0.924171 | 0.462086 | − | 0.886835i | \(-0.347101\pi\) | ||||
0.462086 | + | 0.886835i | \(0.347101\pi\) | |||||||
\(84\) | 379.873 | 0.493423 | ||||||||
\(85\) | 663.463 | 0.846620 | ||||||||
\(86\) | 547.067 | 0.685950 | ||||||||
\(87\) | −182.321 | −0.224677 | ||||||||
\(88\) | 892.335 | 1.08095 | ||||||||
\(89\) | 451.477 | 0.537713 | 0.268857 | − | 0.963180i | \(-0.413354\pi\) | ||||
0.268857 | + | 0.963180i | \(0.413354\pi\) | |||||||
\(90\) | −1191.39 | −1.39538 | ||||||||
\(91\) | −1880.96 | −2.16679 | ||||||||
\(92\) | −1661.47 | −1.88283 | ||||||||
\(93\) | 154.577 | 0.172353 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −230.351 | −0.248774 | ||||||||
\(96\) | 6.35576 | 0.00675710 | ||||||||
\(97\) | −390.906 | −0.409180 | −0.204590 | − | 0.978848i | \(-0.565586\pi\) | ||||
−0.204590 | + | 0.978848i | \(0.565586\pi\) | |||||||
\(98\) | −2830.99 | −2.91810 | ||||||||
\(99\) | 592.031 | 0.601024 | ||||||||
\(100\) | −651.758 | −0.651758 | ||||||||
\(101\) | −1112.66 | −1.09618 | −0.548089 | − | 0.836420i | \(-0.684644\pi\) | ||||
−0.548089 | + | 0.836420i | \(0.684644\pi\) | |||||||
\(102\) | −275.596 | −0.267530 | ||||||||
\(103\) | −882.574 | −0.844298 | −0.422149 | − | 0.906527i | \(-0.638724\pi\) | ||||
−0.422149 | + | 0.906527i | \(0.638724\pi\) | |||||||
\(104\) | −2467.60 | −2.32662 | ||||||||
\(105\) | −216.880 | −0.201574 | ||||||||
\(106\) | −2452.68 | −2.24741 | ||||||||
\(107\) | −840.742 | −0.759604 | −0.379802 | − | 0.925068i | \(-0.624008\pi\) | ||||
−0.379802 | + | 0.925068i | \(0.624008\pi\) | |||||||
\(108\) | 668.853 | 0.595930 | ||||||||
\(109\) | 1321.06 | 1.16086 | 0.580432 | − | 0.814309i | \(-0.302884\pi\) | ||||
0.580432 | + | 0.814309i | \(0.302884\pi\) | |||||||
\(110\) | −1012.42 | −0.877548 | ||||||||
\(111\) | 157.975 | 0.135084 | ||||||||
\(112\) | −2016.37 | −1.70115 | ||||||||
\(113\) | −701.293 | −0.583824 | −0.291912 | − | 0.956445i | \(-0.594291\pi\) | ||||
−0.291912 | + | 0.956445i | \(0.594291\pi\) | |||||||
\(114\) | 95.6857 | 0.0786122 | ||||||||
\(115\) | 948.579 | 0.769177 | ||||||||
\(116\) | 3774.32 | 3.02101 | ||||||||
\(117\) | −1637.16 | −1.29364 | ||||||||
\(118\) | 2762.84 | 2.15542 | ||||||||
\(119\) | 2188.40 | 1.68580 | ||||||||
\(120\) | −284.521 | −0.216442 | ||||||||
\(121\) | −827.906 | −0.622018 | ||||||||
\(122\) | −2690.86 | −1.99688 | ||||||||
\(123\) | 164.047 | 0.120257 | ||||||||
\(124\) | −3199.96 | −2.31746 | ||||||||
\(125\) | 1521.34 | 1.08858 | ||||||||
\(126\) | −3929.76 | −2.77850 | ||||||||
\(127\) | −1142.65 | −0.798374 | −0.399187 | − | 0.916869i | \(-0.630708\pi\) | ||||
−0.399187 | + | 0.916869i | \(0.630708\pi\) | |||||||
\(128\) | 2479.94 | 1.71248 | ||||||||
\(129\) | 86.6795 | 0.0591605 | ||||||||
\(130\) | 2799.67 | 1.88883 | ||||||||
\(131\) | 104.451 | 0.0696639 | 0.0348319 | − | 0.999393i | \(-0.488910\pi\) | ||||
0.0348319 | + | 0.999393i | \(0.488910\pi\) | |||||||
\(132\) | 280.967 | 0.185265 | ||||||||
\(133\) | −759.803 | −0.495363 | ||||||||
\(134\) | −3735.31 | −2.40807 | ||||||||
\(135\) | −381.866 | −0.243450 | ||||||||
\(136\) | 2870.93 | 1.81015 | ||||||||
\(137\) | 543.914 | 0.339195 | 0.169598 | − | 0.985513i | \(-0.445753\pi\) | ||||
0.169598 | + | 0.985513i | \(0.445753\pi\) | |||||||
\(138\) | −394.031 | −0.243059 | ||||||||
\(139\) | 41.8374 | 0.0255295 | 0.0127647 | − | 0.999919i | \(-0.495937\pi\) | ||||
0.0127647 | + | 0.999919i | \(0.495937\pi\) | |||||||
\(140\) | 4489.73 | 2.71037 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3279.85 | 1.93830 | ||||||||
\(143\) | −1391.22 | −0.813565 | ||||||||
\(144\) | −1755.02 | −1.01564 | ||||||||
\(145\) | −2154.86 | −1.23415 | ||||||||
\(146\) | −5625.91 | −3.18907 | ||||||||
\(147\) | −448.554 | −0.251674 | ||||||||
\(148\) | −3270.32 | −1.81634 | ||||||||
\(149\) | 790.139 | 0.434435 | 0.217217 | − | 0.976123i | \(-0.430302\pi\) | ||||
0.217217 | + | 0.976123i | \(0.430302\pi\) | |||||||
\(150\) | −154.569 | −0.0841370 | ||||||||
\(151\) | 2073.79 | 1.11763 | 0.558816 | − | 0.829292i | \(-0.311256\pi\) | ||||
0.558816 | + | 0.829292i | \(0.311256\pi\) | |||||||
\(152\) | −996.774 | −0.531902 | ||||||||
\(153\) | 1904.76 | 1.00648 | ||||||||
\(154\) | −3339.42 | −1.74739 | ||||||||
\(155\) | 1826.95 | 0.946734 | ||||||||
\(156\) | −776.967 | −0.398764 | ||||||||
\(157\) | 2501.12 | 1.27141 | 0.635704 | − | 0.771933i | \(-0.280710\pi\) | ||||
0.635704 | + | 0.771933i | \(0.280710\pi\) | |||||||
\(158\) | −4786.83 | −2.41025 | ||||||||
\(159\) | −388.612 | −0.193830 | ||||||||
\(160\) | 75.1189 | 0.0371167 | ||||||||
\(161\) | 3128.85 | 1.53160 | ||||||||
\(162\) | −3340.20 | −1.61995 | ||||||||
\(163\) | 97.0569 | 0.0466386 | 0.0233193 | − | 0.999728i | \(-0.492577\pi\) | ||||
0.0233193 | + | 0.999728i | \(0.492577\pi\) | |||||||
\(164\) | −3396.03 | −1.61698 | ||||||||
\(165\) | −160.412 | −0.0756850 | ||||||||
\(166\) | −3430.90 | −1.60415 | ||||||||
\(167\) | 1826.71 | 0.846437 | 0.423218 | − | 0.906028i | \(-0.360900\pi\) | ||||
0.423218 | + | 0.906028i | \(0.360900\pi\) | |||||||
\(168\) | −938.480 | −0.430984 | ||||||||
\(169\) | 1650.19 | 0.751111 | ||||||||
\(170\) | −3257.28 | −1.46954 | ||||||||
\(171\) | −661.323 | −0.295746 | ||||||||
\(172\) | −1794.39 | −0.795473 | ||||||||
\(173\) | −1843.63 | −0.810223 | −0.405111 | − | 0.914267i | \(-0.632767\pi\) | ||||
−0.405111 | + | 0.914267i | \(0.632767\pi\) | |||||||
\(174\) | 895.109 | 0.389989 | ||||||||
\(175\) | 1227.38 | 0.530177 | ||||||||
\(176\) | −1491.38 | −0.638732 | ||||||||
\(177\) | 437.756 | 0.185897 | ||||||||
\(178\) | −2216.53 | −0.933350 | ||||||||
\(179\) | 370.515 | 0.154713 | 0.0773565 | − | 0.997003i | \(-0.475352\pi\) | ||||
0.0773565 | + | 0.997003i | \(0.475352\pi\) | |||||||
\(180\) | 3907.80 | 1.61817 | ||||||||
\(181\) | 866.586 | 0.355872 | 0.177936 | − | 0.984042i | \(-0.443058\pi\) | ||||
0.177936 | + | 0.984042i | \(0.443058\pi\) | |||||||
\(182\) | 9234.60 | 3.76107 | ||||||||
\(183\) | −426.351 | −0.172223 | ||||||||
\(184\) | 4104.69 | 1.64457 | ||||||||
\(185\) | 1867.11 | 0.742016 | ||||||||
\(186\) | −758.896 | −0.299166 | ||||||||
\(187\) | 1618.62 | 0.632969 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1259.57 | −0.484763 | ||||||||
\(190\) | 1130.91 | 0.431816 | ||||||||
\(191\) | −3667.49 | −1.38937 | −0.694687 | − | 0.719312i | \(-0.744457\pi\) | ||||
−0.694687 | + | 0.719312i | \(0.744457\pi\) | |||||||
\(192\) | 382.574 | 0.143802 | ||||||||
\(193\) | 4676.91 | 1.74431 | 0.872154 | − | 0.489231i | \(-0.162723\pi\) | ||||
0.872154 | + | 0.489231i | \(0.162723\pi\) | |||||||
\(194\) | 1919.16 | 0.710245 | ||||||||
\(195\) | 443.591 | 0.162904 | ||||||||
\(196\) | 9285.73 | 3.38401 | ||||||||
\(197\) | 3700.99 | 1.33850 | 0.669251 | − | 0.743037i | \(-0.266615\pi\) | ||||
0.669251 | + | 0.743037i | \(0.266615\pi\) | |||||||
\(198\) | −2906.59 | −1.04324 | ||||||||
\(199\) | 1361.63 | 0.485042 | 0.242521 | − | 0.970146i | \(-0.422026\pi\) | ||||
0.242521 | + | 0.970146i | \(0.422026\pi\) | |||||||
\(200\) | 1610.18 | 0.569283 | ||||||||
\(201\) | −591.838 | −0.207687 | ||||||||
\(202\) | 5462.63 | 1.90272 | ||||||||
\(203\) | −7107.72 | −2.45746 | ||||||||
\(204\) | 903.964 | 0.310246 | ||||||||
\(205\) | 1938.88 | 0.660573 | ||||||||
\(206\) | 4333.01 | 1.46551 | ||||||||
\(207\) | 2723.31 | 0.914411 | ||||||||
\(208\) | 4124.15 | 1.37480 | ||||||||
\(209\) | −561.977 | −0.185994 | ||||||||
\(210\) | 1064.77 | 0.349887 | ||||||||
\(211\) | 2873.21 | 0.937442 | 0.468721 | − | 0.883346i | \(-0.344715\pi\) | ||||
0.468721 | + | 0.883346i | \(0.344715\pi\) | |||||||
\(212\) | 8044.85 | 2.60624 | ||||||||
\(213\) | 519.672 | 0.167171 | ||||||||
\(214\) | 4127.64 | 1.31850 | ||||||||
\(215\) | 1024.47 | 0.324968 | ||||||||
\(216\) | −1652.41 | −0.520519 | ||||||||
\(217\) | 6026.10 | 1.88515 | ||||||||
\(218\) | −6485.74 | −2.01500 | ||||||||
\(219\) | −891.393 | −0.275044 | ||||||||
\(220\) | 3320.76 | 1.01766 | ||||||||
\(221\) | −4476.02 | −1.36240 | ||||||||
\(222\) | −775.581 | −0.234476 | ||||||||
\(223\) | −3356.14 | −1.00782 | −0.503909 | − | 0.863757i | \(-0.668105\pi\) | ||||
−0.503909 | + | 0.863757i | \(0.668105\pi\) | |||||||
\(224\) | 247.777 | 0.0739074 | ||||||||
\(225\) | 1068.29 | 0.316531 | ||||||||
\(226\) | 3443.01 | 1.01339 | ||||||||
\(227\) | 3991.01 | 1.16693 | 0.583464 | − | 0.812139i | \(-0.301697\pi\) | ||||
0.583464 | + | 0.812139i | \(0.301697\pi\) | |||||||
\(228\) | −313.852 | −0.0911638 | ||||||||
\(229\) | 968.028 | 0.279341 | 0.139670 | − | 0.990198i | \(-0.455396\pi\) | ||||
0.139670 | + | 0.990198i | \(0.455396\pi\) | |||||||
\(230\) | −4657.06 | −1.33512 | ||||||||
\(231\) | −529.111 | −0.150705 | ||||||||
\(232\) | −9324.51 | −2.63872 | ||||||||
\(233\) | 1227.70 | 0.345189 | 0.172595 | − | 0.984993i | \(-0.444785\pi\) | ||||
0.172595 | + | 0.984993i | \(0.444785\pi\) | |||||||
\(234\) | 8037.68 | 2.24547 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9062.19 | −2.49957 | ||||||||
\(237\) | −758.444 | −0.207875 | ||||||||
\(238\) | −10744.0 | −2.92618 | ||||||||
\(239\) | 647.534 | 0.175253 | 0.0876265 | − | 0.996153i | \(-0.472072\pi\) | ||||
0.0876265 | + | 0.996153i | \(0.472072\pi\) | |||||||
\(240\) | 475.526 | 0.127896 | ||||||||
\(241\) | −4174.42 | −1.11576 | −0.557880 | − | 0.829922i | \(-0.688385\pi\) | ||||
−0.557880 | + | 0.829922i | \(0.688385\pi\) | |||||||
\(242\) | 4064.62 | 1.07968 | ||||||||
\(243\) | −1650.68 | −0.435766 | ||||||||
\(244\) | 8826.10 | 2.31571 | ||||||||
\(245\) | −5301.47 | −1.38244 | ||||||||
\(246\) | −805.394 | −0.208740 | ||||||||
\(247\) | 1554.05 | 0.400332 | ||||||||
\(248\) | 7905.55 | 2.02421 | ||||||||
\(249\) | −543.606 | −0.138352 | ||||||||
\(250\) | −7469.02 | −1.88953 | ||||||||
\(251\) | −1368.39 | −0.344112 | −0.172056 | − | 0.985087i | \(-0.555041\pi\) | ||||
−0.172056 | + | 0.985087i | \(0.555041\pi\) | |||||||
\(252\) | 12889.7 | 3.22213 | ||||||||
\(253\) | 2314.20 | 0.575070 | ||||||||
\(254\) | 5609.84 | 1.38580 | ||||||||
\(255\) | −516.097 | −0.126742 | ||||||||
\(256\) | −8240.77 | −2.01191 | ||||||||
\(257\) | −1709.94 | −0.415031 | −0.207515 | − | 0.978232i | \(-0.566538\pi\) | ||||
−0.207515 | + | 0.978232i | \(0.566538\pi\) | |||||||
\(258\) | −425.554 | −0.102689 | ||||||||
\(259\) | 6158.59 | 1.47752 | ||||||||
\(260\) | −9183.00 | −2.19041 | ||||||||
\(261\) | −6186.47 | −1.46718 | ||||||||
\(262\) | −512.806 | −0.120921 | ||||||||
\(263\) | 5368.95 | 1.25880 | 0.629399 | − | 0.777082i | \(-0.283301\pi\) | ||||
0.629399 | + | 0.777082i | \(0.283301\pi\) | |||||||
\(264\) | −694.133 | −0.161822 | ||||||||
\(265\) | −4593.02 | −1.06471 | ||||||||
\(266\) | 3730.27 | 0.859840 | ||||||||
\(267\) | −351.197 | −0.0804977 | ||||||||
\(268\) | 12251.9 | 2.79256 | ||||||||
\(269\) | −4213.70 | −0.955070 | −0.477535 | − | 0.878613i | \(-0.658470\pi\) | ||||
−0.477535 | + | 0.878613i | \(0.658470\pi\) | |||||||
\(270\) | 1874.78 | 0.422575 | ||||||||
\(271\) | 4769.83 | 1.06918 | 0.534588 | − | 0.845113i | \(-0.320467\pi\) | ||||
0.534588 | + | 0.845113i | \(0.320467\pi\) | |||||||
\(272\) | −4798.25 | −1.06962 | ||||||||
\(273\) | 1463.17 | 0.324377 | ||||||||
\(274\) | −2670.36 | −0.588767 | ||||||||
\(275\) | 907.810 | 0.199066 | ||||||||
\(276\) | 1292.43 | 0.281867 | ||||||||
\(277\) | 5651.38 | 1.22584 | 0.612922 | − | 0.790144i | \(-0.289994\pi\) | ||||
0.612922 | + | 0.790144i | \(0.289994\pi\) | |||||||
\(278\) | −205.401 | −0.0443135 | ||||||||
\(279\) | 5245.04 | 1.12549 | ||||||||
\(280\) | −11091.9 | −2.36739 | ||||||||
\(281\) | −3264.83 | −0.693109 | −0.346554 | − | 0.938030i | \(-0.612648\pi\) | ||||
−0.346554 | + | 0.938030i | \(0.612648\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2019.38 | 0.424169 | 0.212084 | − | 0.977251i | \(-0.431975\pi\) | ||||
0.212084 | + | 0.977251i | \(0.431975\pi\) | |||||||
\(284\) | −10758.0 | −2.24778 | ||||||||
\(285\) | 179.186 | 0.0372424 | ||||||||
\(286\) | 6830.23 | 1.41217 | ||||||||
\(287\) | 6395.32 | 1.31534 | ||||||||
\(288\) | 215.662 | 0.0441249 | ||||||||
\(289\) | 294.634 | 0.0599703 | ||||||||
\(290\) | 10579.3 | 2.14221 | ||||||||
\(291\) | 304.079 | 0.0612558 | ||||||||
\(292\) | 18453.2 | 3.69825 | ||||||||
\(293\) | −3432.28 | −0.684354 | −0.342177 | − | 0.939636i | \(-0.611164\pi\) | ||||
−0.342177 | + | 0.939636i | \(0.611164\pi\) | |||||||
\(294\) | 2202.18 | 0.436850 | ||||||||
\(295\) | 5173.85 | 1.02113 | ||||||||
\(296\) | 8079.36 | 1.58650 | ||||||||
\(297\) | −931.621 | −0.182014 | ||||||||
\(298\) | −3879.20 | −0.754081 | ||||||||
\(299\) | −6399.54 | −1.23778 | ||||||||
\(300\) | 506.992 | 0.0975707 | ||||||||
\(301\) | 3379.16 | 0.647082 | ||||||||
\(302\) | −10181.3 | −1.93996 | ||||||||
\(303\) | 865.521 | 0.164102 | ||||||||
\(304\) | 1665.93 | 0.314301 | ||||||||
\(305\) | −5039.06 | −0.946019 | ||||||||
\(306\) | −9351.45 | −1.74702 | ||||||||
\(307\) | −6327.92 | −1.17640 | −0.588198 | − | 0.808717i | \(-0.700162\pi\) | ||||
−0.588198 | + | 0.808717i | \(0.700162\pi\) | |||||||
\(308\) | 10953.4 | 2.02639 | ||||||||
\(309\) | 686.540 | 0.126395 | ||||||||
\(310\) | −8969.42 | −1.64332 | ||||||||
\(311\) | −9118.69 | −1.66262 | −0.831308 | − | 0.555812i | \(-0.812408\pi\) | ||||
−0.831308 | + | 0.555812i | \(0.812408\pi\) | |||||||
\(312\) | 1919.51 | 0.348303 | ||||||||
\(313\) | −4611.70 | −0.832808 | −0.416404 | − | 0.909180i | \(-0.636710\pi\) | ||||
−0.416404 | + | 0.909180i | \(0.636710\pi\) | |||||||
\(314\) | −12279.3 | −2.20688 | ||||||||
\(315\) | −7359.09 | −1.31631 | ||||||||
\(316\) | 15700.9 | 2.79508 | ||||||||
\(317\) | 4243.78 | 0.751907 | 0.375954 | − | 0.926638i | \(-0.377315\pi\) | ||||
0.375954 | + | 0.926638i | \(0.377315\pi\) | |||||||
\(318\) | 1907.90 | 0.336445 | ||||||||
\(319\) | −5257.12 | −0.922702 | ||||||||
\(320\) | 4521.66 | 0.789901 | ||||||||
\(321\) | 654.000 | 0.113716 | ||||||||
\(322\) | −15361.1 | −2.65851 | ||||||||
\(323\) | −1808.06 | −0.311466 | ||||||||
\(324\) | 10956.0 | 1.87859 | ||||||||
\(325\) | −2510.40 | −0.428467 | ||||||||
\(326\) | −476.502 | −0.0809541 | ||||||||
\(327\) | −1027.63 | −0.173786 | ||||||||
\(328\) | 8389.92 | 1.41237 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 787.543 | 0.131372 | ||||||||
\(331\) | −3803.59 | −0.631613 | −0.315807 | − | 0.948824i | \(-0.602275\pi\) | ||||
−0.315807 | + | 0.948824i | \(0.602275\pi\) | |||||||
\(332\) | 11253.5 | 1.86028 | ||||||||
\(333\) | 5360.36 | 0.882120 | ||||||||
\(334\) | −8968.25 | −1.46922 | ||||||||
\(335\) | −6994.95 | −1.14082 | ||||||||
\(336\) | 1568.50 | 0.254669 | ||||||||
\(337\) | −6419.12 | −1.03760 | −0.518801 | − | 0.854895i | \(-0.673621\pi\) | ||||
−0.518801 | + | 0.854895i | \(0.673621\pi\) | |||||||
\(338\) | −8101.64 | −1.30376 | ||||||||
\(339\) | 545.524 | 0.0874006 | ||||||||
\(340\) | 10684.0 | 1.70418 | ||||||||
\(341\) | 4457.11 | 0.707819 | ||||||||
\(342\) | 3246.78 | 0.513350 | ||||||||
\(343\) | −7085.05 | −1.11533 | ||||||||
\(344\) | 4433.07 | 0.694812 | ||||||||
\(345\) | −737.884 | −0.115149 | ||||||||
\(346\) | 9051.33 | 1.40637 | ||||||||
\(347\) | −3495.57 | −0.540783 | −0.270392 | − | 0.962750i | \(-0.587153\pi\) | ||||
−0.270392 | + | 0.962750i | \(0.587153\pi\) | |||||||
\(348\) | −2935.98 | −0.452256 | ||||||||
\(349\) | 435.838 | 0.0668477 | 0.0334239 | − | 0.999441i | \(-0.489359\pi\) | ||||
0.0334239 | + | 0.999441i | \(0.489359\pi\) | |||||||
\(350\) | −6025.83 | −0.920268 | ||||||||
\(351\) | 2576.24 | 0.391765 | ||||||||
\(352\) | 183.264 | 0.0277500 | ||||||||
\(353\) | 1941.73 | 0.292771 | 0.146385 | − | 0.989228i | \(-0.453236\pi\) | ||||
0.146385 | + | 0.989228i | \(0.453236\pi\) | |||||||
\(354\) | −2149.17 | −0.322675 | ||||||||
\(355\) | 6142.03 | 0.918267 | ||||||||
\(356\) | 7270.29 | 1.08237 | ||||||||
\(357\) | −1702.32 | −0.252371 | ||||||||
\(358\) | −1819.05 | −0.268547 | ||||||||
\(359\) | −7188.88 | −1.05687 | −0.528433 | − | 0.848975i | \(-0.677220\pi\) | ||||
−0.528433 | + | 0.848975i | \(0.677220\pi\) | |||||||
\(360\) | −9654.27 | −1.41340 | ||||||||
\(361\) | −6231.25 | −0.908478 | ||||||||
\(362\) | −4254.52 | −0.617714 | ||||||||
\(363\) | 644.014 | 0.0931184 | ||||||||
\(364\) | −30289.7 | −4.36158 | ||||||||
\(365\) | −10535.4 | −1.51082 | ||||||||
\(366\) | 2093.18 | 0.298940 | ||||||||
\(367\) | −1674.78 | −0.238209 | −0.119105 | − | 0.992882i | \(-0.538002\pi\) | ||||
−0.119105 | + | 0.992882i | \(0.538002\pi\) | |||||||
\(368\) | −6860.25 | −0.971780 | ||||||||
\(369\) | 5566.41 | 0.785300 | ||||||||
\(370\) | −9166.62 | −1.28797 | ||||||||
\(371\) | −15149.9 | −2.12006 | ||||||||
\(372\) | 2489.20 | 0.346933 | ||||||||
\(373\) | −6028.31 | −0.836820 | −0.418410 | − | 0.908258i | \(-0.637412\pi\) | ||||
−0.418410 | + | 0.908258i | \(0.637412\pi\) | |||||||
\(374\) | −7946.64 | −1.09869 | ||||||||
\(375\) | −1183.42 | −0.162964 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14537.7 | 1.98602 | ||||||||
\(378\) | 6183.87 | 0.841439 | ||||||||
\(379\) | −2065.63 | −0.279959 | −0.139979 | − | 0.990154i | \(-0.544704\pi\) | ||||
−0.139979 | + | 0.990154i | \(0.544704\pi\) | |||||||
\(380\) | −3709.42 | −0.500762 | ||||||||
\(381\) | 888.846 | 0.119520 | ||||||||
\(382\) | 18005.6 | 2.41164 | ||||||||
\(383\) | 7634.28 | 1.01852 | 0.509260 | − | 0.860613i | \(-0.329919\pi\) | ||||
0.509260 | + | 0.860613i | \(0.329919\pi\) | |||||||
\(384\) | −1929.10 | −0.256365 | ||||||||
\(385\) | −6253.58 | −0.827823 | ||||||||
\(386\) | −22961.4 | −3.02773 | ||||||||
\(387\) | 2941.18 | 0.386327 | ||||||||
\(388\) | −6294.89 | −0.823646 | ||||||||
\(389\) | 2814.13 | 0.366792 | 0.183396 | − | 0.983039i | \(-0.441291\pi\) | ||||
0.183396 | + | 0.983039i | \(0.441291\pi\) | |||||||
\(390\) | −2177.82 | −0.282764 | ||||||||
\(391\) | 7445.55 | 0.963012 | ||||||||
\(392\) | −22940.5 | −2.95579 | ||||||||
\(393\) | −81.2511 | −0.0104289 | ||||||||
\(394\) | −18170.1 | −2.32334 | ||||||||
\(395\) | −8964.08 | −1.14185 | ||||||||
\(396\) | 9533.69 | 1.20981 | ||||||||
\(397\) | 8990.52 | 1.13658 | 0.568288 | − | 0.822829i | \(-0.307606\pi\) | ||||
0.568288 | + | 0.822829i | \(0.307606\pi\) | |||||||
\(398\) | −6684.94 | −0.841924 | ||||||||
\(399\) | 591.039 | 0.0741577 | ||||||||
\(400\) | −2691.12 | −0.336390 | ||||||||
\(401\) | −4829.93 | −0.601484 | −0.300742 | − | 0.953706i | \(-0.597234\pi\) | ||||
−0.300742 | + | 0.953706i | \(0.597234\pi\) | |||||||
\(402\) | 2905.64 | 0.360497 | ||||||||
\(403\) | −12325.4 | −1.52350 | ||||||||
\(404\) | −17917.6 | −2.20652 | ||||||||
\(405\) | −6255.05 | −0.767447 | ||||||||
\(406\) | 34895.5 | 4.26560 | ||||||||
\(407\) | 4555.11 | 0.554763 | ||||||||
\(408\) | −2233.25 | −0.270987 | ||||||||
\(409\) | 6551.78 | 0.792089 | 0.396045 | − | 0.918231i | \(-0.370383\pi\) | ||||
0.396045 | + | 0.918231i | \(0.370383\pi\) | |||||||
\(410\) | −9518.97 | −1.14661 | ||||||||
\(411\) | −423.102 | −0.0507788 | ||||||||
\(412\) | −14212.4 | −1.69950 | ||||||||
\(413\) | 17065.7 | 2.03329 | ||||||||
\(414\) | −13370.1 | −1.58721 | ||||||||
\(415\) | −6424.90 | −0.759966 | ||||||||
\(416\) | −506.786 | −0.0597289 | ||||||||
\(417\) | −32.5446 | −0.00382186 | ||||||||
\(418\) | 2759.03 | 0.322844 | ||||||||
\(419\) | −10660.5 | −1.24296 | −0.621481 | − | 0.783429i | \(-0.713469\pi\) | ||||
−0.621481 | + | 0.783429i | \(0.713469\pi\) | |||||||
\(420\) | −3492.49 | −0.405752 | ||||||||
\(421\) | 8654.47 | 1.00188 | 0.500942 | − | 0.865481i | \(-0.332987\pi\) | ||||
0.500942 | + | 0.865481i | \(0.332987\pi\) | |||||||
\(422\) | −14106.1 | −1.62719 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −19874.9 | −2.27644 | ||||||||
\(425\) | 2920.73 | 0.333355 | ||||||||
\(426\) | −2551.34 | −0.290171 | ||||||||
\(427\) | −16621.1 | −1.88373 | ||||||||
\(428\) | −13538.8 | −1.52902 | ||||||||
\(429\) | 1082.21 | 0.121794 | ||||||||
\(430\) | −5029.64 | −0.564072 | ||||||||
\(431\) | 4990.22 | 0.557703 | 0.278852 | − | 0.960334i | \(-0.410046\pi\) | ||||
0.278852 | + | 0.960334i | \(0.410046\pi\) | |||||||
\(432\) | 2761.71 | 0.307575 | ||||||||
\(433\) | 7921.49 | 0.879174 | 0.439587 | − | 0.898200i | \(-0.355125\pi\) | ||||
0.439587 | + | 0.898200i | \(0.355125\pi\) | |||||||
\(434\) | −29585.2 | −3.27220 | ||||||||
\(435\) | 1676.23 | 0.184757 | ||||||||
\(436\) | 21273.4 | 2.33673 | ||||||||
\(437\) | −2585.06 | −0.282975 | ||||||||
\(438\) | 4376.31 | 0.477416 | ||||||||
\(439\) | 11034.1 | 1.19961 | 0.599807 | − | 0.800145i | \(-0.295244\pi\) | ||||
0.599807 | + | 0.800145i | \(0.295244\pi\) | |||||||
\(440\) | −8203.97 | −0.888884 | ||||||||
\(441\) | −15220.2 | −1.64347 | ||||||||
\(442\) | 21975.1 | 2.36482 | ||||||||
\(443\) | −9160.66 | −0.982474 | −0.491237 | − | 0.871026i | \(-0.663455\pi\) | ||||
−0.491237 | + | 0.871026i | \(0.663455\pi\) | |||||||
\(444\) | 2543.93 | 0.271913 | ||||||||
\(445\) | −4150.80 | −0.442173 | ||||||||
\(446\) | 16477.0 | 1.74935 | ||||||||
\(447\) | −614.636 | −0.0650365 | ||||||||
\(448\) | 14914.5 | 1.57287 | ||||||||
\(449\) | 10071.1 | 1.05854 | 0.529271 | − | 0.848453i | \(-0.322465\pi\) | ||||
0.529271 | + | 0.848453i | \(0.322465\pi\) | |||||||
\(450\) | −5244.80 | −0.549427 | ||||||||
\(451\) | 4730.20 | 0.493872 | ||||||||
\(452\) | −11293.2 | −1.17519 | ||||||||
\(453\) | −1613.16 | −0.167314 | ||||||||
\(454\) | −19593.9 | −2.02553 | ||||||||
\(455\) | 17293.2 | 1.78180 | ||||||||
\(456\) | 775.374 | 0.0796277 | ||||||||
\(457\) | −2988.54 | −0.305904 | −0.152952 | − | 0.988234i | \(-0.548878\pi\) | ||||
−0.152952 | + | 0.988234i | \(0.548878\pi\) | |||||||
\(458\) | −4752.55 | −0.484873 | ||||||||
\(459\) | −2997.33 | −0.304800 | ||||||||
\(460\) | 15275.3 | 1.54829 | ||||||||
\(461\) | −956.638 | −0.0966487 | −0.0483244 | − | 0.998832i | \(-0.515388\pi\) | ||||
−0.0483244 | + | 0.998832i | \(0.515388\pi\) | |||||||
\(462\) | 2597.68 | 0.261591 | ||||||||
\(463\) | 4352.75 | 0.436910 | 0.218455 | − | 0.975847i | \(-0.429898\pi\) | ||||
0.218455 | + | 0.975847i | \(0.429898\pi\) | |||||||
\(464\) | 15584.2 | 1.55923 | ||||||||
\(465\) | −1421.15 | −0.141730 | ||||||||
\(466\) | −6027.40 | −0.599171 | ||||||||
\(467\) | −8131.35 | −0.805725 | −0.402863 | − | 0.915260i | \(-0.631985\pi\) | ||||
−0.402863 | + | 0.915260i | \(0.631985\pi\) | |||||||
\(468\) | −26363.8 | −2.60399 | ||||||||
\(469\) | −23072.5 | −2.27162 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1945.58 | −0.190335 | ||||||||
\(472\) | 22388.2 | 2.18327 | ||||||||
\(473\) | 2499.35 | 0.242960 | ||||||||
\(474\) | 3723.60 | 0.360824 | ||||||||
\(475\) | −1014.06 | −0.0979544 | ||||||||
\(476\) | 35240.6 | 3.39339 | ||||||||
\(477\) | −13186.3 | −1.26574 | ||||||||
\(478\) | −3179.08 | −0.304200 | ||||||||
\(479\) | −12912.4 | −1.23170 | −0.615849 | − | 0.787864i | \(-0.711187\pi\) | ||||
−0.615849 | + | 0.787864i | \(0.711187\pi\) | |||||||
\(480\) | −58.4338 | −0.00555651 | ||||||||
\(481\) | −12596.4 | −1.19407 | ||||||||
\(482\) | 20494.4 | 1.93671 | ||||||||
\(483\) | −2433.88 | −0.229286 | ||||||||
\(484\) | −13332.1 | −1.25207 | ||||||||
\(485\) | 3593.92 | 0.336477 | ||||||||
\(486\) | 8104.04 | 0.756393 | ||||||||
\(487\) | −11010.0 | −1.02446 | −0.512228 | − | 0.858850i | \(-0.671180\pi\) | ||||
−0.512228 | + | 0.858850i | \(0.671180\pi\) | |||||||
\(488\) | −21805.0 | −2.02268 | ||||||||
\(489\) | −75.4990 | −0.00698197 | ||||||||
\(490\) | 26027.7 | 2.39961 | ||||||||
\(491\) | −14636.7 | −1.34531 | −0.672655 | − | 0.739956i | \(-0.734846\pi\) | ||||
−0.672655 | + | 0.739956i | \(0.734846\pi\) | |||||||
\(492\) | 2641.71 | 0.242068 | ||||||||
\(493\) | −16913.9 | −1.54516 | ||||||||
\(494\) | −7629.64 | −0.694887 | ||||||||
\(495\) | −5443.04 | −0.494235 | ||||||||
\(496\) | −13212.7 | −1.19611 | ||||||||
\(497\) | 20259.2 | 1.82847 | ||||||||
\(498\) | 2668.84 | 0.240148 | ||||||||
\(499\) | 7549.78 | 0.677304 | 0.338652 | − | 0.940912i | \(-0.390029\pi\) | ||||
0.338652 | + | 0.940912i | \(0.390029\pi\) | |||||||
\(500\) | 24498.6 | 2.19122 | ||||||||
\(501\) | −1420.97 | −0.126715 | ||||||||
\(502\) | 6718.14 | 0.597301 | ||||||||
\(503\) | 16150.9 | 1.43167 | 0.715837 | − | 0.698267i | \(-0.246045\pi\) | ||||
0.715837 | + | 0.698267i | \(0.246045\pi\) | |||||||
\(504\) | −31844.2 | −2.81439 | ||||||||
\(505\) | 10229.6 | 0.901410 | ||||||||
\(506\) | −11361.6 | −0.998193 | ||||||||
\(507\) | −1283.66 | −0.112444 | ||||||||
\(508\) | −18400.4 | −1.60706 | ||||||||
\(509\) | −19183.7 | −1.67053 | −0.835266 | − | 0.549846i | \(-0.814686\pi\) | ||||
−0.835266 | + | 0.549846i | \(0.814686\pi\) | |||||||
\(510\) | 2533.79 | 0.219996 | ||||||||
\(511\) | −34750.6 | −3.00836 | ||||||||
\(512\) | 20618.7 | 1.77974 | ||||||||
\(513\) | 1040.66 | 0.0895637 | ||||||||
\(514\) | 8394.96 | 0.720400 | ||||||||
\(515\) | 8114.24 | 0.694284 | ||||||||
\(516\) | 1395.83 | 0.119085 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −30235.7 | −2.56464 | ||||||||
\(519\) | 1434.13 | 0.121293 | ||||||||
\(520\) | 22686.7 | 1.91323 | ||||||||
\(521\) | 6867.69 | 0.577503 | 0.288751 | − | 0.957404i | \(-0.406760\pi\) | ||||
0.288751 | + | 0.957404i | \(0.406760\pi\) | |||||||
\(522\) | 30372.6 | 2.54669 | ||||||||
\(523\) | 11205.2 | 0.936841 | 0.468420 | − | 0.883506i | \(-0.344823\pi\) | ||||
0.468420 | + | 0.883506i | \(0.344823\pi\) | |||||||
\(524\) | 1682.02 | 0.140228 | ||||||||
\(525\) | −954.756 | −0.0793695 | ||||||||
\(526\) | −26359.0 | −2.18499 | ||||||||
\(527\) | 14340.0 | 1.18531 | ||||||||
\(528\) | 1160.12 | 0.0956206 | ||||||||
\(529\) | −1521.81 | −0.125076 | ||||||||
\(530\) | 22549.5 | 1.84809 | ||||||||
\(531\) | 14853.8 | 1.21393 | ||||||||
\(532\) | −12235.4 | −0.997126 | ||||||||
\(533\) | −13080.6 | −1.06301 | ||||||||
\(534\) | 1724.21 | 0.139726 | ||||||||
\(535\) | 7729.64 | 0.624639 | ||||||||
\(536\) | −30268.5 | −2.43918 | ||||||||
\(537\) | −288.218 | −0.0231611 | ||||||||
\(538\) | 20687.2 | 1.65779 | ||||||||
\(539\) | −12933.8 | −1.03357 | ||||||||
\(540\) | −6149.32 | −0.490045 | ||||||||
\(541\) | 14471.4 | 1.15004 | 0.575021 | − | 0.818139i | \(-0.304994\pi\) | ||||
0.575021 | + | 0.818139i | \(0.304994\pi\) | |||||||
\(542\) | −23417.6 | −1.85585 | ||||||||
\(543\) | −674.103 | −0.0532754 | ||||||||
\(544\) | 589.621 | 0.0464702 | ||||||||
\(545\) | −12145.6 | −0.954603 | ||||||||
\(546\) | −7183.44 | −0.563046 | ||||||||
\(547\) | 13482.7 | 1.05389 | 0.526946 | − | 0.849899i | \(-0.323337\pi\) | ||||
0.526946 | + | 0.849899i | \(0.323337\pi\) | |||||||
\(548\) | 8758.84 | 0.682772 | ||||||||
\(549\) | −14466.8 | −1.12464 | ||||||||
\(550\) | −4456.91 | −0.345533 | ||||||||
\(551\) | 5872.41 | 0.454035 | ||||||||
\(552\) | −3192.97 | −0.246199 | ||||||||
\(553\) | −29567.6 | −2.27368 | ||||||||
\(554\) | −27745.6 | −2.12779 | ||||||||
\(555\) | −1452.40 | −0.111083 | ||||||||
\(556\) | 673.722 | 0.0513888 | ||||||||
\(557\) | −10194.0 | −0.775466 | −0.387733 | − | 0.921772i | \(-0.626742\pi\) | ||||
−0.387733 | + | 0.921772i | \(0.626742\pi\) | |||||||
\(558\) | −25750.6 | −1.95360 | ||||||||
\(559\) | −6911.52 | −0.522945 | ||||||||
\(560\) | 18538.2 | 1.39889 | ||||||||
\(561\) | −1259.10 | −0.0947579 | ||||||||
\(562\) | 16028.7 | 1.20308 | ||||||||
\(563\) | −3725.21 | −0.278862 | −0.139431 | − | 0.990232i | \(-0.544527\pi\) | ||||
−0.139431 | + | 0.990232i | \(0.544527\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6447.57 | 0.480091 | ||||||||
\(566\) | −9914.18 | −0.736262 | ||||||||
\(567\) | −20632.0 | −1.52815 | ||||||||
\(568\) | 26577.7 | 1.96334 | ||||||||
\(569\) | 6274.57 | 0.462291 | 0.231145 | − | 0.972919i | \(-0.425753\pi\) | ||||
0.231145 | + | 0.972919i | \(0.425753\pi\) | |||||||
\(570\) | −879.718 | −0.0646445 | ||||||||
\(571\) | 20390.6 | 1.49443 | 0.747214 | − | 0.664584i | \(-0.231391\pi\) | ||||
0.747214 | + | 0.664584i | \(0.231391\pi\) | |||||||
\(572\) | −22403.3 | −1.63764 | ||||||||
\(573\) | 2852.88 | 0.207995 | ||||||||
\(574\) | −31397.9 | −2.28314 | ||||||||
\(575\) | 4175.87 | 0.302862 | ||||||||
\(576\) | 12981.4 | 0.939048 | ||||||||
\(577\) | −675.385 | −0.0487290 | −0.0243645 | − | 0.999703i | \(-0.507756\pi\) | ||||
−0.0243645 | + | 0.999703i | \(0.507756\pi\) | |||||||
\(578\) | −1446.51 | −0.104095 | ||||||||
\(579\) | −3638.09 | −0.261130 | ||||||||
\(580\) | −34700.5 | −2.48424 | ||||||||
\(581\) | −21192.3 | −1.51326 | ||||||||
\(582\) | −1492.88 | −0.106326 | ||||||||
\(583\) | −11205.4 | −0.796019 | ||||||||
\(584\) | −45588.7 | −3.23027 | ||||||||
\(585\) | 15051.8 | 1.06379 | ||||||||
\(586\) | 16850.8 | 1.18788 | ||||||||
\(587\) | 5949.63 | 0.418343 | 0.209172 | − | 0.977879i | \(-0.432923\pi\) | ||||
0.209172 | + | 0.977879i | \(0.432923\pi\) | |||||||
\(588\) | −7223.22 | −0.506600 | ||||||||
\(589\) | −4978.78 | −0.348297 | ||||||||
\(590\) | −25401.1 | −1.77245 | ||||||||
\(591\) | −2878.94 | −0.200379 | ||||||||
\(592\) | −13503.2 | −0.937464 | ||||||||
\(593\) | 22071.9 | 1.52847 | 0.764235 | − | 0.644937i | \(-0.223117\pi\) | ||||
0.764235 | + | 0.644937i | \(0.223117\pi\) | |||||||
\(594\) | 4573.81 | 0.315935 | ||||||||
\(595\) | −20119.8 | −1.38627 | ||||||||
\(596\) | 12723.9 | 0.874481 | ||||||||
\(597\) | −1059.19 | −0.0726126 | ||||||||
\(598\) | 31418.6 | 2.14850 | ||||||||
\(599\) | 9547.79 | 0.651272 | 0.325636 | − | 0.945495i | \(-0.394422\pi\) | ||||
0.325636 | + | 0.945495i | \(0.394422\pi\) | |||||||
\(600\) | −1252.53 | −0.0852239 | ||||||||
\(601\) | −12303.7 | −0.835076 | −0.417538 | − | 0.908660i | \(-0.637107\pi\) | ||||
−0.417538 | + | 0.908660i | \(0.637107\pi\) | |||||||
\(602\) | −16590.1 | −1.12319 | ||||||||
\(603\) | −20082.0 | −1.35623 | ||||||||
\(604\) | 33394.9 | 2.24970 | ||||||||
\(605\) | 7611.63 | 0.511498 | ||||||||
\(606\) | −4249.29 | −0.284844 | ||||||||
\(607\) | −18252.2 | −1.22049 | −0.610243 | − | 0.792214i | \(-0.708928\pi\) | ||||
−0.610243 | + | 0.792214i | \(0.708928\pi\) | |||||||
\(608\) | −204.714 | −0.0136550 | ||||||||
\(609\) | 5528.98 | 0.367891 | ||||||||
\(610\) | 24739.3 | 1.64208 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 30673.0 | 2.02595 | ||||||||
\(613\) | −13990.5 | −0.921809 | −0.460905 | − | 0.887450i | \(-0.652475\pi\) | ||||
−0.460905 | + | 0.887450i | \(0.652475\pi\) | |||||||
\(614\) | 31067.0 | 2.04196 | ||||||||
\(615\) | −1508.22 | −0.0988902 | ||||||||
\(616\) | −27060.5 | −1.76996 | ||||||||
\(617\) | −5747.16 | −0.374995 | −0.187498 | − | 0.982265i | \(-0.560038\pi\) | ||||
−0.187498 | + | 0.982265i | \(0.560038\pi\) | |||||||
\(618\) | −3370.58 | −0.219393 | ||||||||
\(619\) | −3913.70 | −0.254127 | −0.127064 | − | 0.991895i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991895i | \(0.540555\pi\) | |||||||
\(620\) | 29419.9 | 1.90570 | ||||||||
\(621\) | −4285.40 | −0.276920 | ||||||||
\(622\) | 44768.4 | 2.88593 | ||||||||
\(623\) | −13691.3 | −0.880463 | ||||||||
\(624\) | −3208.11 | −0.205813 | ||||||||
\(625\) | −8927.71 | −0.571374 | ||||||||
\(626\) | 22641.2 | 1.44557 | ||||||||
\(627\) | 437.153 | 0.0278440 | ||||||||
\(628\) | 40276.4 | 2.55924 | ||||||||
\(629\) | 14655.3 | 0.929006 | ||||||||
\(630\) | 36129.6 | 2.28482 | ||||||||
\(631\) | −26311.5 | −1.65998 | −0.829988 | − | 0.557781i | \(-0.811653\pi\) | ||||
−0.829988 | + | 0.557781i | \(0.811653\pi\) | |||||||
\(632\) | −38789.3 | −2.44139 | ||||||||
\(633\) | −2235.03 | −0.140339 | ||||||||
\(634\) | −20834.9 | −1.30514 | ||||||||
\(635\) | 10505.3 | 0.656520 | ||||||||
\(636\) | −6257.96 | −0.390164 | ||||||||
\(637\) | 35766.1 | 2.22466 | ||||||||
\(638\) | 25809.9 | 1.60160 | ||||||||
\(639\) | 17633.4 | 1.09165 | ||||||||
\(640\) | −22800.1 | −1.40821 | ||||||||
\(641\) | −15538.7 | −0.957476 | −0.478738 | − | 0.877958i | \(-0.658906\pi\) | ||||
−0.478738 | + | 0.877958i | \(0.658906\pi\) | |||||||
\(642\) | −3210.82 | −0.197385 | ||||||||
\(643\) | 6125.10 | 0.375661 | 0.187831 | − | 0.982201i | \(-0.439854\pi\) | ||||
0.187831 | + | 0.982201i | \(0.439854\pi\) | |||||||
\(644\) | 50384.9 | 3.08299 | ||||||||
\(645\) | −796.917 | −0.0486489 | ||||||||
\(646\) | 8876.72 | 0.540635 | ||||||||
\(647\) | 4635.86 | 0.281692 | 0.140846 | − | 0.990032i | \(-0.455018\pi\) | ||||
0.140846 | + | 0.990032i | \(0.455018\pi\) | |||||||
\(648\) | −27066.8 | −1.64087 | ||||||||
\(649\) | 12622.4 | 0.763440 | ||||||||
\(650\) | 12324.8 | 0.743723 | ||||||||
\(651\) | −4687.61 | −0.282215 | ||||||||
\(652\) | 1562.94 | 0.0938796 | ||||||||
\(653\) | −11926.6 | −0.714740 | −0.357370 | − | 0.933963i | \(-0.616326\pi\) | ||||
−0.357370 | + | 0.933963i | \(0.616326\pi\) | |||||||
\(654\) | 5045.15 | 0.301653 | ||||||||
\(655\) | −960.309 | −0.0572861 | ||||||||
\(656\) | −14022.3 | −0.834569 | ||||||||
\(657\) | −30246.4 | −1.79608 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 881.384 | 0.0520999 | 0.0260500 | − | 0.999661i | \(-0.491707\pi\) | ||||
0.0260500 | + | 0.999661i | \(0.491707\pi\) | |||||||
\(660\) | −2583.16 | −0.152348 | ||||||||
\(661\) | −19161.6 | −1.12753 | −0.563766 | − | 0.825935i | \(-0.690648\pi\) | ||||
−0.563766 | + | 0.825935i | \(0.690648\pi\) | |||||||
\(662\) | 18673.8 | 1.09634 | ||||||||
\(663\) | 3481.82 | 0.203956 | ||||||||
\(664\) | −27801.8 | −1.62488 | ||||||||
\(665\) | 6985.50 | 0.407348 | ||||||||
\(666\) | −26316.8 | −1.53116 | ||||||||
\(667\) | −24182.4 | −1.40382 | ||||||||
\(668\) | 29416.1 | 1.70381 | ||||||||
\(669\) | 2610.68 | 0.150874 | ||||||||
\(670\) | 34341.8 | 1.98021 | ||||||||
\(671\) | −12293.6 | −0.707284 | ||||||||
\(672\) | −192.741 | −0.0110642 | ||||||||
\(673\) | −20156.0 | −1.15447 | −0.577235 | − | 0.816578i | \(-0.695868\pi\) | ||||
−0.577235 | + | 0.816578i | \(0.695868\pi\) | |||||||
\(674\) | 31514.8 | 1.80104 | ||||||||
\(675\) | −1681.07 | −0.0958582 | ||||||||
\(676\) | 26573.6 | 1.51192 | ||||||||
\(677\) | −5567.34 | −0.316056 | −0.158028 | − | 0.987435i | \(-0.550514\pi\) | ||||
−0.158028 | + | 0.987435i | \(0.550514\pi\) | |||||||
\(678\) | −2678.26 | −0.151708 | ||||||||
\(679\) | 11854.4 | 0.670000 | ||||||||
\(680\) | −26394.9 | −1.48853 | ||||||||
\(681\) | −3104.54 | −0.174694 | ||||||||
\(682\) | −21882.3 | −1.22861 | ||||||||
\(683\) | −27835.8 | −1.55946 | −0.779728 | − | 0.626118i | \(-0.784643\pi\) | ||||
−0.779728 | + | 0.626118i | \(0.784643\pi\) | |||||||
\(684\) | −10649.5 | −0.595314 | ||||||||
\(685\) | −5000.66 | −0.278927 | ||||||||
\(686\) | 34784.2 | 1.93596 | ||||||||
\(687\) | −753.013 | −0.0418184 | ||||||||
\(688\) | −7409.09 | −0.410565 | ||||||||
\(689\) | 30986.6 | 1.71334 | ||||||||
\(690\) | 3622.65 | 0.199872 | ||||||||
\(691\) | −17125.7 | −0.942824 | −0.471412 | − | 0.881913i | \(-0.656255\pi\) | ||||
−0.471412 | + | 0.881913i | \(0.656255\pi\) | |||||||
\(692\) | −29688.6 | −1.63091 | ||||||||
\(693\) | −17953.6 | −0.984129 | ||||||||
\(694\) | 17161.5 | 0.938679 | ||||||||
\(695\) | −384.646 | −0.0209934 | ||||||||
\(696\) | 7253.38 | 0.395027 | ||||||||
\(697\) | 15218.6 | 0.827039 | ||||||||
\(698\) | −2139.75 | −0.116033 | ||||||||
\(699\) | −955.005 | −0.0516761 | ||||||||
\(700\) | 19764.9 | 1.06720 | ||||||||
\(701\) | −5107.63 | −0.275196 | −0.137598 | − | 0.990488i | \(-0.543938\pi\) | ||||
−0.137598 | + | 0.990488i | \(0.543938\pi\) | |||||||
\(702\) | −12648.1 | −0.680016 | ||||||||
\(703\) | −5088.24 | −0.272983 | ||||||||
\(704\) | 11031.3 | 0.590564 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9532.97 | −0.508184 | ||||||||
\(707\) | 33742.0 | 1.79490 | ||||||||
\(708\) | 7049.33 | 0.374195 | ||||||||
\(709\) | 11258.0 | 0.596335 | 0.298167 | − | 0.954514i | \(-0.403625\pi\) | ||||
0.298167 | + | 0.954514i | \(0.403625\pi\) | |||||||
\(710\) | −30154.4 | −1.59391 | ||||||||
\(711\) | −25735.3 | −1.35745 | ||||||||
\(712\) | −17961.3 | −0.945407 | ||||||||
\(713\) | 20502.5 | 1.07689 | ||||||||
\(714\) | 8357.59 | 0.438060 | ||||||||
\(715\) | 12790.7 | 0.669012 | ||||||||
\(716\) | 5966.54 | 0.311425 | ||||||||
\(717\) | −503.706 | −0.0262360 | ||||||||
\(718\) | 35293.9 | 1.83448 | ||||||||
\(719\) | −13735.6 | −0.712448 | −0.356224 | − | 0.934401i | \(-0.615936\pi\) | ||||
−0.356224 | + | 0.934401i | \(0.615936\pi\) | |||||||
\(720\) | 16135.4 | 0.835181 | ||||||||
\(721\) | 26764.5 | 1.38247 | ||||||||
\(722\) | 30592.4 | 1.57691 | ||||||||
\(723\) | 3247.21 | 0.167033 | ||||||||
\(724\) | 13954.9 | 0.716341 | ||||||||
\(725\) | −9486.22 | −0.485944 | ||||||||
\(726\) | −3161.80 | −0.161633 | ||||||||
\(727\) | −14515.4 | −0.740502 | −0.370251 | − | 0.928932i | \(-0.620728\pi\) | ||||
−0.370251 | + | 0.928932i | \(0.620728\pi\) | |||||||
\(728\) | 74831.1 | 3.80965 | ||||||||
\(729\) | −17085.5 | −0.868033 | ||||||||
\(730\) | 51723.7 | 2.62244 | ||||||||
\(731\) | 8041.22 | 0.406861 | ||||||||
\(732\) | −6865.68 | −0.346671 | ||||||||
\(733\) | 14218.5 | 0.716471 | 0.358236 | − | 0.933631i | \(-0.383378\pi\) | ||||
0.358236 | + | 0.933631i | \(0.383378\pi\) | |||||||
\(734\) | 8222.36 | 0.413478 | ||||||||
\(735\) | 4123.93 | 0.206957 | ||||||||
\(736\) | 843.004 | 0.0422195 | ||||||||
\(737\) | −17065.3 | −0.852926 | ||||||||
\(738\) | −27328.4 | −1.36310 | ||||||||
\(739\) | 8651.36 | 0.430643 | 0.215322 | − | 0.976543i | \(-0.430920\pi\) | ||||
0.215322 | + | 0.976543i | \(0.430920\pi\) | |||||||
\(740\) | 30066.8 | 1.49362 | ||||||||
\(741\) | −1208.87 | −0.0599312 | ||||||||
\(742\) | 74378.6 | 3.67995 | ||||||||
\(743\) | 37263.7 | 1.83993 | 0.919967 | − | 0.391996i | \(-0.128215\pi\) | ||||
0.919967 | + | 0.391996i | \(0.128215\pi\) | |||||||
\(744\) | −6149.60 | −0.303031 | ||||||||
\(745\) | −7264.41 | −0.357245 | ||||||||
\(746\) | 29596.1 | 1.45253 | ||||||||
\(747\) | −18445.5 | −0.903460 | ||||||||
\(748\) | 26065.2 | 1.27412 | ||||||||
\(749\) | 25495.9 | 1.24379 | ||||||||
\(750\) | 5810.03 | 0.282870 | ||||||||
\(751\) | 33980.7 | 1.65110 | 0.825548 | − | 0.564331i | \(-0.190866\pi\) | ||||
0.825548 | + | 0.564331i | \(0.190866\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1064.45 | 0.0515148 | ||||||||
\(754\) | −71372.9 | −3.44728 | ||||||||
\(755\) | −19066.0 | −0.919052 | ||||||||
\(756\) | −20283.3 | −0.975788 | ||||||||
\(757\) | 33247.9 | 1.59632 | 0.798161 | − | 0.602445i | \(-0.205807\pi\) | ||||
0.798161 | + | 0.602445i | \(0.205807\pi\) | |||||||
\(758\) | 10141.2 | 0.485945 | ||||||||
\(759\) | −1800.18 | −0.0860901 | ||||||||
\(760\) | 9164.18 | 0.437394 | ||||||||
\(761\) | −13023.6 | −0.620376 | −0.310188 | − | 0.950675i | \(-0.600392\pi\) | ||||
−0.310188 | + | 0.950675i | \(0.600392\pi\) | |||||||
\(762\) | −4363.81 | −0.207459 | ||||||||
\(763\) | −40061.6 | −1.90082 | ||||||||
\(764\) | −59058.9 | −2.79670 | ||||||||
\(765\) | −17512.0 | −0.827646 | ||||||||
\(766\) | −37480.6 | −1.76792 | ||||||||
\(767\) | −34905.1 | −1.64322 | ||||||||
\(768\) | 6410.36 | 0.301190 | ||||||||
\(769\) | 26526.2 | 1.24390 | 0.621949 | − | 0.783057i | \(-0.286341\pi\) | ||||
0.621949 | + | 0.783057i | \(0.286341\pi\) | |||||||
\(770\) | 30702.0 | 1.43692 | ||||||||
\(771\) | 1330.13 | 0.0621316 | ||||||||
\(772\) | 75313.9 | 3.51115 | ||||||||
\(773\) | 1143.17 | 0.0531914 | 0.0265957 | − | 0.999646i | \(-0.491533\pi\) | ||||
0.0265957 | + | 0.999646i | \(0.491533\pi\) | |||||||
\(774\) | −14439.8 | −0.670577 | ||||||||
\(775\) | 8042.65 | 0.372775 | ||||||||
\(776\) | 15551.6 | 0.719420 | ||||||||
\(777\) | −4790.67 | −0.221190 | ||||||||
\(778\) | −13816.0 | −0.636668 | ||||||||
\(779\) | −5283.83 | −0.243020 | ||||||||
\(780\) | 7143.30 | 0.327912 | ||||||||
\(781\) | 14984.4 | 0.686536 | ||||||||
\(782\) | −36554.1 | −1.67157 | ||||||||
\(783\) | 9735.03 | 0.444319 | ||||||||
\(784\) | 38341.0 | 1.74658 | ||||||||
\(785\) | −22994.9 | −1.04551 | ||||||||
\(786\) | 398.904 | 0.0181023 | ||||||||
\(787\) | −41354.8 | −1.87311 | −0.936556 | − | 0.350519i | \(-0.886005\pi\) | ||||
−0.936556 | + | 0.350519i | \(0.886005\pi\) | |||||||
\(788\) | 59598.4 | 2.69429 | ||||||||
\(789\) | −4176.42 | −0.188447 | ||||||||
\(790\) | 44009.3 | 1.98200 | ||||||||
\(791\) | 21267.0 | 0.955965 | ||||||||
\(792\) | −23553.1 | −1.05672 | ||||||||
\(793\) | 33995.8 | 1.52235 | ||||||||
\(794\) | −44139.1 | −1.97284 | ||||||||
\(795\) | 3572.83 | 0.159390 | ||||||||
\(796\) | 21926.8 | 0.976349 | ||||||||
\(797\) | −8795.77 | −0.390918 | −0.195459 | − | 0.980712i | \(-0.562620\pi\) | ||||
−0.195459 | + | 0.980712i | \(0.562620\pi\) | |||||||
\(798\) | −2901.71 | −0.128721 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 330.692 | 0.0146146 | ||||||||
\(801\) | −11916.7 | −0.525662 | ||||||||
\(802\) | 23712.6 | 1.04404 | ||||||||
\(803\) | −25702.7 | −1.12955 | ||||||||
\(804\) | −9530.57 | −0.418056 | ||||||||
\(805\) | −28766.1 | −1.25947 | ||||||||
\(806\) | 60511.7 | 2.64446 | ||||||||
\(807\) | 3277.77 | 0.142978 | ||||||||
\(808\) | 44265.6 | 1.92730 | ||||||||
\(809\) | −2152.09 | −0.0935272 | −0.0467636 | − | 0.998906i | \(-0.514891\pi\) | ||||
−0.0467636 | + | 0.998906i | \(0.514891\pi\) | |||||||
\(810\) | 30709.3 | 1.33212 | ||||||||
\(811\) | 24307.1 | 1.05245 | 0.526225 | − | 0.850346i | \(-0.323607\pi\) | ||||
0.526225 | + | 0.850346i | \(0.323607\pi\) | |||||||
\(812\) | −114458. | −4.94666 | ||||||||
\(813\) | −3710.38 | −0.160060 | ||||||||
\(814\) | −22363.4 | −0.962944 | ||||||||
\(815\) | −892.325 | −0.0383519 | ||||||||
\(816\) | 3732.48 | 0.160126 | ||||||||
\(817\) | −2791.87 | −0.119554 | ||||||||
\(818\) | −32166.0 | −1.37489 | ||||||||
\(819\) | 49647.7 | 2.11823 | ||||||||
\(820\) | 31222.5 | 1.32968 | ||||||||
\(821\) | −45118.9 | −1.91798 | −0.958988 | − | 0.283446i | \(-0.908522\pi\) | ||||
−0.958988 | + | 0.283446i | \(0.908522\pi\) | |||||||
\(822\) | 2077.23 | 0.0881406 | ||||||||
\(823\) | 38608.9 | 1.63526 | 0.817631 | − | 0.575742i | \(-0.195287\pi\) | ||||
0.817631 | + | 0.575742i | \(0.195287\pi\) | |||||||
\(824\) | 35111.9 | 1.48444 | ||||||||
\(825\) | −706.171 | −0.0298009 | ||||||||
\(826\) | −83784.4 | −3.52934 | ||||||||
\(827\) | −17908.8 | −0.753023 | −0.376512 | − | 0.926412i | \(-0.622876\pi\) | ||||
−0.376512 | + | 0.926412i | \(0.622876\pi\) | |||||||
\(828\) | 43854.4 | 1.84063 | ||||||||
\(829\) | −42616.2 | −1.78543 | −0.892716 | − | 0.450620i | \(-0.851203\pi\) | ||||
−0.892716 | + | 0.450620i | \(0.851203\pi\) | |||||||
\(830\) | 31543.1 | 1.31913 | ||||||||
\(831\) | −4396.12 | −0.183513 | ||||||||
\(832\) | −30505.2 | −1.27112 | ||||||||
\(833\) | −41612.2 | −1.73082 | ||||||||
\(834\) | 159.778 | 0.00663389 | ||||||||
\(835\) | −16794.4 | −0.696043 | ||||||||
\(836\) | −9049.71 | −0.374391 | ||||||||
\(837\) | −8253.60 | −0.340844 | ||||||||
\(838\) | 52338.1 | 2.15750 | ||||||||
\(839\) | −9077.30 | −0.373520 | −0.186760 | − | 0.982406i | \(-0.559799\pi\) | ||||
−0.186760 | + | 0.982406i | \(0.559799\pi\) | |||||||
\(840\) | 8628.23 | 0.354407 | ||||||||
\(841\) | 30545.6 | 1.25243 | ||||||||
\(842\) | −42489.2 | −1.73905 | ||||||||
\(843\) | 2539.66 | 0.103761 | ||||||||
\(844\) | 46268.4 | 1.88699 | ||||||||
\(845\) | −15171.6 | −0.617654 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25106.6 | 1.01851 | ||||||||
\(848\) | 33217.3 | 1.34515 | ||||||||
\(849\) | −1570.84 | −0.0634997 | ||||||||
\(850\) | −14339.3 | −0.578630 | ||||||||
\(851\) | 20953.2 | 0.844027 | ||||||||
\(852\) | 8368.47 | 0.336501 | ||||||||
\(853\) | −18315.0 | −0.735163 | −0.367581 | − | 0.929991i | \(-0.619814\pi\) | ||||
−0.367581 | + | 0.929991i | \(0.619814\pi\) | |||||||
\(854\) | 81601.7 | 3.26973 | ||||||||
\(855\) | 6080.09 | 0.243199 | ||||||||
\(856\) | 33447.7 | 1.33554 | ||||||||
\(857\) | 13738.7 | 0.547615 | 0.273807 | − | 0.961785i | \(-0.411717\pi\) | ||||
0.273807 | + | 0.961785i | \(0.411717\pi\) | |||||||
\(858\) | −5313.12 | −0.211407 | ||||||||
\(859\) | −9424.20 | −0.374330 | −0.187165 | − | 0.982328i | \(-0.559930\pi\) | ||||
−0.187165 | + | 0.982328i | \(0.559930\pi\) | |||||||
\(860\) | 16497.4 | 0.654134 | ||||||||
\(861\) | −4974.82 | −0.196912 | ||||||||
\(862\) | −24499.5 | −0.968048 | ||||||||
\(863\) | −40557.8 | −1.59977 | −0.799887 | − | 0.600151i | \(-0.795107\pi\) | ||||
−0.799887 | + | 0.600151i | \(0.795107\pi\) | |||||||
\(864\) | −339.365 | −0.0133628 | ||||||||
\(865\) | 16950.0 | 0.666263 | ||||||||
\(866\) | −38890.7 | −1.52605 | ||||||||
\(867\) | −229.191 | −0.00897778 | ||||||||
\(868\) | 97040.4 | 3.79466 | ||||||||
\(869\) | −21869.2 | −0.853698 | ||||||||
\(870\) | −8229.48 | −0.320696 | ||||||||
\(871\) | 47191.1 | 1.83583 | ||||||||
\(872\) | −52556.2 | −2.04103 | ||||||||
\(873\) | 10317.9 | 0.400010 | ||||||||
\(874\) | 12691.4 | 0.491182 | ||||||||
\(875\) | −46135.2 | −1.78246 | ||||||||
\(876\) | −14354.4 | −0.553642 | ||||||||
\(877\) | 12966.5 | 0.499258 | 0.249629 | − | 0.968342i | \(-0.419691\pi\) | ||||
0.249629 | + | 0.968342i | \(0.419691\pi\) | |||||||
\(878\) | −54172.2 | −2.08226 | ||||||||
\(879\) | 2669.91 | 0.102450 | ||||||||
\(880\) | 13711.5 | 0.525243 | ||||||||
\(881\) | 15640.0 | 0.598098 | 0.299049 | − | 0.954238i | \(-0.403331\pi\) | ||||
0.299049 | + | 0.954238i | \(0.403331\pi\) | |||||||
\(882\) | 74723.8 | 2.85270 | ||||||||
\(883\) | −10326.2 | −0.393548 | −0.196774 | − | 0.980449i | \(-0.563047\pi\) | ||||
−0.196774 | + | 0.980449i | \(0.563047\pi\) | |||||||
\(884\) | −72078.9 | −2.74239 | ||||||||
\(885\) | −4024.65 | −0.152867 | ||||||||
\(886\) | 44974.4 | 1.70535 | ||||||||
\(887\) | 2173.72 | 0.0822846 | 0.0411423 | − | 0.999153i | \(-0.486900\pi\) | ||||
0.0411423 | + | 0.999153i | \(0.486900\pi\) | |||||||
\(888\) | −6284.81 | −0.237505 | ||||||||
\(889\) | 34651.3 | 1.30727 | ||||||||
\(890\) | 20378.4 | 0.767513 | ||||||||
\(891\) | −15260.2 | −0.573776 | ||||||||
\(892\) | −54045.0 | −2.02866 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 3017.57 | 0.112889 | ||||||||
\(895\) | −3406.46 | −0.127224 | ||||||||
\(896\) | −75205.2 | −2.80405 | ||||||||
\(897\) | 4978.10 | 0.185300 | ||||||||
\(898\) | −49444.3 | −1.83739 | ||||||||
\(899\) | −46574.9 | −1.72787 | ||||||||
\(900\) | 17203.1 | 0.637152 | ||||||||
\(901\) | −36051.4 | −1.33301 | ||||||||
\(902\) | −23223.0 | −0.857252 | ||||||||
\(903\) | −2628.60 | −0.0968706 | ||||||||
\(904\) | 27899.9 | 1.02648 | ||||||||
\(905\) | −7967.24 | −0.292641 | ||||||||
\(906\) | 7919.85 | 0.290419 | ||||||||
\(907\) | 29981.6 | 1.09760 | 0.548800 | − | 0.835954i | \(-0.315085\pi\) | ||||
0.548800 | + | 0.835954i | \(0.315085\pi\) | |||||||
\(908\) | 64268.7 | 2.34893 | ||||||||
\(909\) | 29368.6 | 1.07161 | ||||||||
\(910\) | −84901.3 | −3.09280 | ||||||||
\(911\) | −725.040 | −0.0263684 | −0.0131842 | − | 0.999913i | \(-0.504197\pi\) | ||||
−0.0131842 | + | 0.999913i | \(0.504197\pi\) | |||||||
\(912\) | −1295.90 | −0.0470521 | ||||||||
\(913\) | −15674.5 | −0.568183 | ||||||||
\(914\) | 14672.3 | 0.530980 | ||||||||
\(915\) | 3919.80 | 0.141623 | ||||||||
\(916\) | 15588.5 | 0.562291 | ||||||||
\(917\) | −3167.54 | −0.114069 | ||||||||
\(918\) | 14715.4 | 0.529065 | ||||||||
\(919\) | 1750.94 | 0.0628488 | 0.0314244 | − | 0.999506i | \(-0.489996\pi\) | ||||
0.0314244 | + | 0.999506i | \(0.489996\pi\) | |||||||
\(920\) | −37737.8 | −1.35237 | ||||||||
\(921\) | 4922.39 | 0.176111 | ||||||||
\(922\) | 4696.63 | 0.167761 | ||||||||
\(923\) | −41436.9 | −1.47769 | ||||||||
\(924\) | −8520.46 | −0.303358 | ||||||||
\(925\) | 8219.48 | 0.292168 | ||||||||
\(926\) | −21369.9 | −0.758378 | ||||||||
\(927\) | 23295.5 | 0.825376 | ||||||||
\(928\) | −1915.03 | −0.0677413 | ||||||||
\(929\) | 5500.62 | 0.194262 | 0.0971311 | − | 0.995272i | \(-0.469033\pi\) | ||||
0.0971311 | + | 0.995272i | \(0.469033\pi\) | |||||||
\(930\) | 6977.16 | 0.246011 | ||||||||
\(931\) | 14447.5 | 0.508592 | ||||||||
\(932\) | 19770.0 | 0.694838 | ||||||||
\(933\) | 7093.28 | 0.248900 | ||||||||
\(934\) | 39921.0 | 1.39856 | ||||||||
\(935\) | −14881.3 | −0.520504 | ||||||||
\(936\) | 65132.1 | 2.27448 | ||||||||
\(937\) | 55288.1 | 1.92762 | 0.963811 | − | 0.266586i | \(-0.0858956\pi\) | ||||
0.963811 | + | 0.266586i | \(0.0858956\pi\) | |||||||
\(938\) | 113275. | 3.94303 | ||||||||
\(939\) | 3587.37 | 0.124675 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47729.6 | 1.65350 | 0.826748 | − | 0.562573i | \(-0.190188\pi\) | ||||
0.826748 | + | 0.562573i | \(0.190188\pi\) | |||||||
\(942\) | 9551.86 | 0.330378 | ||||||||
\(943\) | 21758.6 | 0.751388 | ||||||||
\(944\) | −37417.9 | −1.29010 | ||||||||
\(945\) | 11580.3 | 0.398631 | ||||||||
\(946\) | −12270.6 | −0.421724 | ||||||||
\(947\) | −27191.6 | −0.933061 | −0.466530 | − | 0.884505i | \(-0.654496\pi\) | ||||
−0.466530 | + | 0.884505i | \(0.654496\pi\) | |||||||
\(948\) | −12213.5 | −0.418434 | ||||||||
\(949\) | 71076.5 | 2.43124 | ||||||||
\(950\) | 4978.55 | 0.170027 | ||||||||
\(951\) | −3301.17 | −0.112563 | ||||||||
\(952\) | −87062.4 | −2.96398 | ||||||||
\(953\) | −2941.45 | −0.0999822 | −0.0499911 | − | 0.998750i | \(-0.515919\pi\) | ||||
−0.0499911 | + | 0.998750i | \(0.515919\pi\) | |||||||
\(954\) | 64738.2 | 2.19704 | ||||||||
\(955\) | 33718.3 | 1.14251 | ||||||||
\(956\) | 10427.5 | 0.352770 | ||||||||
\(957\) | 4089.42 | 0.138132 | ||||||||
\(958\) | 63393.8 | 2.13795 | ||||||||
\(959\) | −16494.5 | −0.555405 | ||||||||
\(960\) | −3517.32 | −0.118251 | ||||||||
\(961\) | 9696.35 | 0.325479 | ||||||||
\(962\) | 61842.2 | 2.07263 | ||||||||
\(963\) | 22191.3 | 0.742580 | ||||||||
\(964\) | −67222.1 | −2.24593 | ||||||||
\(965\) | −42998.7 | −1.43438 | ||||||||
\(966\) | 11949.2 | 0.397990 | ||||||||
\(967\) | 45733.8 | 1.52089 | 0.760445 | − | 0.649402i | \(-0.224981\pi\) | ||||
0.760445 | + | 0.649402i | \(0.224981\pi\) | |||||||
\(968\) | 32937.0 | 1.09363 | ||||||||
\(969\) | 1406.46 | 0.0466276 | ||||||||
\(970\) | −17644.4 | −0.584050 | ||||||||
\(971\) | −57658.9 | −1.90562 | −0.952812 | − | 0.303561i | \(-0.901824\pi\) | ||||
−0.952812 | + | 0.303561i | \(0.901824\pi\) | |||||||
\(972\) | −26581.5 | −0.877162 | ||||||||
\(973\) | −1268.74 | −0.0418025 | ||||||||
\(974\) | 54053.7 | 1.77823 | ||||||||
\(975\) | 1952.80 | 0.0641431 | ||||||||
\(976\) | 36443.1 | 1.19520 | ||||||||
\(977\) | 46156.4 | 1.51144 | 0.755718 | − | 0.654897i | \(-0.227288\pi\) | ||||
0.755718 | + | 0.654897i | \(0.227288\pi\) | |||||||
\(978\) | 370.663 | 0.0121191 | ||||||||
\(979\) | −10126.5 | −0.330587 | ||||||||
\(980\) | −85371.5 | −2.78275 | ||||||||
\(981\) | −34869.1 | −1.13485 | ||||||||
\(982\) | 71859.3 | 2.33516 | ||||||||
\(983\) | −10931.6 | −0.354694 | −0.177347 | − | 0.984148i | \(-0.556752\pi\) | ||||
−0.177347 | + | 0.984148i | \(0.556752\pi\) | |||||||
\(984\) | −6526.38 | −0.211437 | ||||||||
\(985\) | −34026.3 | −1.10068 | ||||||||
\(986\) | 83038.9 | 2.68205 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 25025.4 | 0.805835 | ||||||||
\(989\) | 11496.8 | 0.369644 | ||||||||
\(990\) | 26722.7 | 0.857881 | ||||||||
\(991\) | −15279.8 | −0.489788 | −0.244894 | − | 0.969550i | \(-0.578753\pi\) | ||||
−0.244894 | + | 0.969550i | \(0.578753\pi\) | |||||||
\(992\) | 1623.61 | 0.0519654 | ||||||||
\(993\) | 2958.75 | 0.0945549 | ||||||||
\(994\) | −99462.9 | −3.17382 | ||||||||
\(995\) | −12518.6 | −0.398860 | ||||||||
\(996\) | −8753.88 | −0.278491 | ||||||||
\(997\) | 7648.81 | 0.242969 | 0.121485 | − | 0.992593i | \(-0.461234\pi\) | ||||
0.121485 | + | 0.992593i | \(0.461234\pi\) | |||||||
\(998\) | −37065.8 | −1.17565 | ||||||||
\(999\) | −8435.07 | −0.267141 |
(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 | 2209.4.a.a.1.1 | 3 | ||
47.46 | odd | 2 | 47.4.a.a.1.1 | ✓ | 3 | ||
141.140 | even | 2 | 423.4.a.b.1.3 | 3 | |||
188.187 | even | 2 | 752.4.a.c.1.2 | 3 | |||
235.234 | odd | 2 | 1175.4.a.a.1.3 | 3 | |||
329.328 | even | 2 | 2303.4.a.a.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
47.4.a.a.1.1 | ✓ | 3 | 47.46 | odd | 2 | ||
423.4.a.b.1.3 | 3 | 141.140 | even | 2 | |||
752.4.a.c.1.2 | 3 | 188.187 | even | 2 | |||
1175.4.a.a.1.3 | 3 | 235.234 | odd | 2 | |||
2209.4.a.a.1.1 | 3 | 1.1 | even | 1 | trivial | ||
2303.4.a.a.1.1 | 3 | 329.328 | even | 2 |