Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,4,Mod(1,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, 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("43.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(2.53708213025\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 32x^{4} - 16x^{3} + 251x^{2} + 276x + 60 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.15653\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.15653 | −1.11600 | −0.558001 | − | 0.829840i | \(-0.688431\pi\) | ||||
−0.558001 | + | 0.829840i | \(0.688431\pi\) | |||||||
\(3\) | 7.20925 | 1.38742 | 0.693710 | − | 0.720254i | \(-0.255975\pi\) | ||||
0.693710 | + | 0.720254i | \(0.255975\pi\) | |||||||
\(4\) | 1.96369 | 0.245461 | ||||||||
\(5\) | 1.36370 | 0.121973 | 0.0609864 | − | 0.998139i | \(-0.480575\pi\) | ||||
0.0609864 | + | 0.998139i | \(0.480575\pi\) | |||||||
\(6\) | −22.7562 | −1.54836 | ||||||||
\(7\) | 13.0131 | 0.702643 | 0.351321 | − | 0.936255i | \(-0.385732\pi\) | ||||
0.351321 | + | 0.936255i | \(0.385732\pi\) | |||||||
\(8\) | 19.0538 | 0.842067 | ||||||||
\(9\) | 24.9733 | 0.924936 | ||||||||
\(10\) | −4.30455 | −0.136122 | ||||||||
\(11\) | 64.7677 | 1.77529 | 0.887646 | − | 0.460527i | \(-0.152339\pi\) | ||||
0.887646 | + | 0.460527i | \(0.152339\pi\) | |||||||
\(12\) | 14.1567 | 0.340557 | ||||||||
\(13\) | −19.2944 | −0.411638 | −0.205819 | − | 0.978590i | \(-0.565986\pi\) | ||||
−0.205819 | + | 0.978590i | \(0.565986\pi\) | |||||||
\(14\) | −41.0763 | −0.784151 | ||||||||
\(15\) | 9.83123 | 0.169227 | ||||||||
\(16\) | −75.8534 | −1.18521 | ||||||||
\(17\) | −54.1213 | −0.772138 | −0.386069 | − | 0.922470i | \(-0.626167\pi\) | ||||
−0.386069 | + | 0.922470i | \(0.626167\pi\) | |||||||
\(18\) | −78.8289 | −1.03223 | ||||||||
\(19\) | −69.0659 | −0.833938 | −0.416969 | − | 0.908921i | \(-0.636908\pi\) | ||||
−0.416969 | + | 0.908921i | \(0.636908\pi\) | |||||||
\(20\) | 2.67787 | 0.0299395 | ||||||||
\(21\) | 93.8149 | 0.974861 | ||||||||
\(22\) | −204.441 | −1.98123 | ||||||||
\(23\) | 29.6031 | 0.268377 | 0.134189 | − | 0.990956i | \(-0.457157\pi\) | ||||
0.134189 | + | 0.990956i | \(0.457157\pi\) | |||||||
\(24\) | 137.364 | 1.16830 | ||||||||
\(25\) | −123.140 | −0.985123 | ||||||||
\(26\) | 60.9032 | 0.459389 | ||||||||
\(27\) | −14.6112 | −0.104145 | ||||||||
\(28\) | 25.5537 | 0.172471 | ||||||||
\(29\) | 13.1279 | 0.0840614 | 0.0420307 | − | 0.999116i | \(-0.486617\pi\) | ||||
0.0420307 | + | 0.999116i | \(0.486617\pi\) | |||||||
\(30\) | −31.0326 | −0.188858 | ||||||||
\(31\) | 185.439 | 1.07438 | 0.537191 | − | 0.843461i | \(-0.319486\pi\) | ||||
0.537191 | + | 0.843461i | \(0.319486\pi\) | |||||||
\(32\) | 87.0032 | 0.480629 | ||||||||
\(33\) | 466.927 | 2.46308 | ||||||||
\(34\) | 170.836 | 0.861707 | ||||||||
\(35\) | 17.7460 | 0.0857032 | ||||||||
\(36\) | 49.0397 | 0.227035 | ||||||||
\(37\) | −369.949 | −1.64376 | −0.821881 | − | 0.569659i | \(-0.807075\pi\) | ||||
−0.821881 | + | 0.569659i | \(0.807075\pi\) | |||||||
\(38\) | 218.009 | 0.930676 | ||||||||
\(39\) | −139.098 | −0.571115 | ||||||||
\(40\) | 25.9836 | 0.102709 | ||||||||
\(41\) | −294.860 | −1.12315 | −0.561577 | − | 0.827424i | \(-0.689805\pi\) | ||||
−0.561577 | + | 0.827424i | \(0.689805\pi\) | |||||||
\(42\) | −296.129 | −1.08795 | ||||||||
\(43\) | −43.0000 | −0.152499 | ||||||||
\(44\) | 127.183 | 0.435764 | ||||||||
\(45\) | 34.0560 | 0.112817 | ||||||||
\(46\) | −93.4431 | −0.299509 | ||||||||
\(47\) | 367.319 | 1.13998 | 0.569989 | − | 0.821652i | \(-0.306947\pi\) | ||||
0.569989 | + | 0.821652i | \(0.306947\pi\) | |||||||
\(48\) | −546.846 | −1.64438 | ||||||||
\(49\) | −173.659 | −0.506293 | ||||||||
\(50\) | 388.696 | 1.09940 | ||||||||
\(51\) | −390.174 | −1.07128 | ||||||||
\(52\) | −37.8881 | −0.101041 | ||||||||
\(53\) | 708.046 | 1.83505 | 0.917524 | − | 0.397680i | \(-0.130185\pi\) | ||||
0.917524 | + | 0.397680i | \(0.130185\pi\) | |||||||
\(54\) | 46.1207 | 0.116226 | ||||||||
\(55\) | 88.3236 | 0.216537 | ||||||||
\(56\) | 247.950 | 0.591672 | ||||||||
\(57\) | −497.914 | −1.15702 | ||||||||
\(58\) | −41.4385 | −0.0938127 | ||||||||
\(59\) | 116.159 | 0.256316 | 0.128158 | − | 0.991754i | \(-0.459094\pi\) | ||||
0.128158 | + | 0.991754i | \(0.459094\pi\) | |||||||
\(60\) | 19.3054 | 0.0415387 | ||||||||
\(61\) | 218.910 | 0.459484 | 0.229742 | − | 0.973252i | \(-0.426212\pi\) | ||||
0.229742 | + | 0.973252i | \(0.426212\pi\) | |||||||
\(62\) | −585.344 | −1.19901 | ||||||||
\(63\) | 324.980 | 0.649899 | ||||||||
\(64\) | 332.199 | 0.648827 | ||||||||
\(65\) | −26.3116 | −0.0502086 | ||||||||
\(66\) | −1473.87 | −2.74880 | ||||||||
\(67\) | −133.114 | −0.242723 | −0.121361 | − | 0.992608i | \(-0.538726\pi\) | ||||
−0.121361 | + | 0.992608i | \(0.538726\pi\) | |||||||
\(68\) | −106.277 | −0.189529 | ||||||||
\(69\) | 213.416 | 0.372352 | ||||||||
\(70\) | −56.0156 | −0.0956450 | ||||||||
\(71\) | −926.738 | −1.54906 | −0.774532 | − | 0.632535i | \(-0.782015\pi\) | ||||
−0.774532 | + | 0.632535i | \(0.782015\pi\) | |||||||
\(72\) | 475.836 | 0.778858 | ||||||||
\(73\) | 455.867 | 0.730893 | 0.365446 | − | 0.930832i | \(-0.380916\pi\) | ||||
0.365446 | + | 0.930832i | \(0.380916\pi\) | |||||||
\(74\) | 1167.75 | 1.83444 | ||||||||
\(75\) | −887.749 | −1.36678 | ||||||||
\(76\) | −135.624 | −0.204699 | ||||||||
\(77\) | 842.831 | 1.24740 | ||||||||
\(78\) | 439.067 | 0.637365 | ||||||||
\(79\) | −620.178 | −0.883234 | −0.441617 | − | 0.897204i | \(-0.645595\pi\) | ||||
−0.441617 | + | 0.897204i | \(0.645595\pi\) | |||||||
\(80\) | −103.441 | −0.144563 | ||||||||
\(81\) | −779.614 | −1.06943 | ||||||||
\(82\) | 930.734 | 1.25344 | ||||||||
\(83\) | −1317.85 | −1.74281 | −0.871405 | − | 0.490564i | \(-0.836791\pi\) | ||||
−0.871405 | + | 0.490564i | \(0.836791\pi\) | |||||||
\(84\) | 184.223 | 0.239290 | ||||||||
\(85\) | −73.8050 | −0.0941797 | ||||||||
\(86\) | 135.731 | 0.170189 | ||||||||
\(87\) | 94.6419 | 0.116629 | ||||||||
\(88\) | 1234.07 | 1.49492 | ||||||||
\(89\) | 509.295 | 0.606575 | 0.303287 | − | 0.952899i | \(-0.401916\pi\) | ||||
0.303287 | + | 0.952899i | \(0.401916\pi\) | |||||||
\(90\) | −107.499 | −0.125904 | ||||||||
\(91\) | −251.080 | −0.289234 | ||||||||
\(92\) | 58.1312 | 0.0658760 | ||||||||
\(93\) | 1336.88 | 1.49062 | ||||||||
\(94\) | −1159.45 | −1.27222 | ||||||||
\(95\) | −94.1850 | −0.101718 | ||||||||
\(96\) | 627.228 | 0.666835 | ||||||||
\(97\) | 965.870 | 1.01102 | 0.505511 | − | 0.862820i | \(-0.331304\pi\) | ||||
0.505511 | + | 0.862820i | \(0.331304\pi\) | |||||||
\(98\) | 548.159 | 0.565024 | ||||||||
\(99\) | 1617.46 | 1.64203 | ||||||||
\(100\) | −241.809 | −0.241809 | ||||||||
\(101\) | −1501.80 | −1.47955 | −0.739776 | − | 0.672853i | \(-0.765068\pi\) | ||||
−0.739776 | + | 0.672853i | \(0.765068\pi\) | |||||||
\(102\) | 1231.60 | 1.19555 | ||||||||
\(103\) | 1312.60 | 1.25567 | 0.627837 | − | 0.778345i | \(-0.283940\pi\) | ||||
0.627837 | + | 0.778345i | \(0.283940\pi\) | |||||||
\(104\) | −367.631 | −0.346627 | ||||||||
\(105\) | 127.935 | 0.118906 | ||||||||
\(106\) | −2234.97 | −2.04792 | ||||||||
\(107\) | −611.656 | −0.552627 | −0.276313 | − | 0.961068i | \(-0.589113\pi\) | ||||
−0.276313 | + | 0.961068i | \(0.589113\pi\) | |||||||
\(108\) | −28.6918 | −0.0255636 | ||||||||
\(109\) | −946.664 | −0.831871 | −0.415935 | − | 0.909394i | \(-0.636546\pi\) | ||||
−0.415935 | + | 0.909394i | \(0.636546\pi\) | |||||||
\(110\) | −278.796 | −0.241656 | ||||||||
\(111\) | −2667.05 | −2.28059 | ||||||||
\(112\) | −987.090 | −0.832779 | ||||||||
\(113\) | 2109.50 | 1.75615 | 0.878076 | − | 0.478521i | \(-0.158827\pi\) | ||||
0.878076 | + | 0.478521i | \(0.158827\pi\) | |||||||
\(114\) | 1571.68 | 1.29124 | ||||||||
\(115\) | 40.3696 | 0.0327347 | ||||||||
\(116\) | 25.7790 | 0.0206338 | ||||||||
\(117\) | −481.843 | −0.380739 | ||||||||
\(118\) | −366.660 | −0.286049 | ||||||||
\(119\) | −704.287 | −0.542537 | ||||||||
\(120\) | 187.322 | 0.142501 | ||||||||
\(121\) | 2863.86 | 2.15166 | ||||||||
\(122\) | −690.996 | −0.512785 | ||||||||
\(123\) | −2125.72 | −1.55829 | ||||||||
\(124\) | 364.144 | 0.263718 | ||||||||
\(125\) | −338.388 | −0.242131 | ||||||||
\(126\) | −1025.81 | −0.725289 | ||||||||
\(127\) | 788.583 | 0.550988 | 0.275494 | − | 0.961303i | \(-0.411159\pi\) | ||||
0.275494 | + | 0.961303i | \(0.411159\pi\) | |||||||
\(128\) | −1744.62 | −1.20472 | ||||||||
\(129\) | −309.998 | −0.211580 | ||||||||
\(130\) | 83.0535 | 0.0560329 | ||||||||
\(131\) | 1873.57 | 1.24957 | 0.624787 | − | 0.780795i | \(-0.285186\pi\) | ||||
0.624787 | + | 0.780795i | \(0.285186\pi\) | |||||||
\(132\) | 916.897 | 0.604588 | ||||||||
\(133\) | −898.764 | −0.585960 | ||||||||
\(134\) | 420.177 | 0.270879 | ||||||||
\(135\) | −19.9252 | −0.0127029 | ||||||||
\(136\) | −1031.22 | −0.650192 | ||||||||
\(137\) | −1860.27 | −1.16010 | −0.580050 | − | 0.814581i | \(-0.696967\pi\) | ||||
−0.580050 | + | 0.814581i | \(0.696967\pi\) | |||||||
\(138\) | −673.654 | −0.415545 | ||||||||
\(139\) | −2822.52 | −1.72232 | −0.861161 | − | 0.508333i | \(-0.830262\pi\) | ||||
−0.861161 | + | 0.508333i | \(0.830262\pi\) | |||||||
\(140\) | 34.8475 | 0.0210368 | ||||||||
\(141\) | 2648.09 | 1.58163 | ||||||||
\(142\) | 2925.28 | 1.72876 | ||||||||
\(143\) | −1249.65 | −0.730777 | ||||||||
\(144\) | −1894.31 | −1.09624 | ||||||||
\(145\) | 17.9024 | 0.0102532 | ||||||||
\(146\) | −1438.96 | −0.815678 | ||||||||
\(147\) | −1251.95 | −0.702442 | ||||||||
\(148\) | −726.463 | −0.403479 | ||||||||
\(149\) | 1615.30 | 0.888126 | 0.444063 | − | 0.895996i | \(-0.353537\pi\) | ||||
0.444063 | + | 0.895996i | \(0.353537\pi\) | |||||||
\(150\) | 2802.21 | 1.52533 | ||||||||
\(151\) | 1399.96 | 0.754483 | 0.377241 | − | 0.926115i | \(-0.376873\pi\) | ||||
0.377241 | + | 0.926115i | \(0.376873\pi\) | |||||||
\(152\) | −1315.97 | −0.702232 | ||||||||
\(153\) | −1351.59 | −0.714178 | ||||||||
\(154\) | −2660.42 | −1.39210 | ||||||||
\(155\) | 252.882 | 0.131045 | ||||||||
\(156\) | −273.144 | −0.140186 | ||||||||
\(157\) | 2933.25 | 1.49108 | 0.745539 | − | 0.666462i | \(-0.232192\pi\) | ||||
0.745539 | + | 0.666462i | \(0.232192\pi\) | |||||||
\(158\) | 1957.61 | 0.985691 | ||||||||
\(159\) | 5104.48 | 2.54598 | ||||||||
\(160\) | 118.646 | 0.0586237 | ||||||||
\(161\) | 385.229 | 0.188573 | ||||||||
\(162\) | 2460.88 | 1.19349 | ||||||||
\(163\) | −166.212 | −0.0798695 | −0.0399347 | − | 0.999202i | \(-0.512715\pi\) | ||||
−0.0399347 | + | 0.999202i | \(0.512715\pi\) | |||||||
\(164\) | −579.012 | −0.275690 | ||||||||
\(165\) | 636.746 | 0.300428 | ||||||||
\(166\) | 4159.85 | 1.94498 | ||||||||
\(167\) | 2143.42 | 0.993191 | 0.496595 | − | 0.867982i | \(-0.334583\pi\) | ||||
0.496595 | + | 0.867982i | \(0.334583\pi\) | |||||||
\(168\) | 1787.53 | 0.820899 | ||||||||
\(169\) | −1824.73 | −0.830554 | ||||||||
\(170\) | 232.968 | 0.105105 | ||||||||
\(171\) | −1724.80 | −0.771339 | ||||||||
\(172\) | −84.4385 | −0.0374324 | ||||||||
\(173\) | −119.018 | −0.0523050 | −0.0261525 | − | 0.999658i | \(-0.508326\pi\) | ||||
−0.0261525 | + | 0.999658i | \(0.508326\pi\) | |||||||
\(174\) | −298.740 | −0.130158 | ||||||||
\(175\) | −1602.44 | −0.692189 | ||||||||
\(176\) | −4912.85 | −2.10409 | ||||||||
\(177\) | 837.420 | 0.355618 | ||||||||
\(178\) | −1607.61 | −0.676939 | ||||||||
\(179\) | 2572.05 | 1.07399 | 0.536995 | − | 0.843585i | \(-0.319559\pi\) | ||||
0.536995 | + | 0.843585i | \(0.319559\pi\) | |||||||
\(180\) | 66.8752 | 0.0276921 | ||||||||
\(181\) | 1429.30 | 0.586956 | 0.293478 | − | 0.955966i | \(-0.405187\pi\) | ||||
0.293478 | + | 0.955966i | \(0.405187\pi\) | |||||||
\(182\) | 792.541 | 0.322786 | ||||||||
\(183\) | 1578.18 | 0.637498 | ||||||||
\(184\) | 564.052 | 0.225992 | ||||||||
\(185\) | −504.498 | −0.200494 | ||||||||
\(186\) | −4219.89 | −1.66353 | ||||||||
\(187\) | −3505.31 | −1.37077 | ||||||||
\(188\) | 721.299 | 0.279820 | ||||||||
\(189\) | −190.137 | −0.0731769 | ||||||||
\(190\) | 297.298 | 0.113517 | ||||||||
\(191\) | 411.149 | 0.155758 | 0.0778788 | − | 0.996963i | \(-0.475185\pi\) | ||||
0.0778788 | + | 0.996963i | \(0.475185\pi\) | |||||||
\(192\) | 2394.91 | 0.900195 | ||||||||
\(193\) | −3108.57 | −1.15938 | −0.579689 | − | 0.814838i | \(-0.696826\pi\) | ||||
−0.579689 | + | 0.814838i | \(0.696826\pi\) | |||||||
\(194\) | −3048.80 | −1.12830 | ||||||||
\(195\) | −189.687 | −0.0696604 | ||||||||
\(196\) | −341.011 | −0.124275 | ||||||||
\(197\) | 1960.75 | 0.709125 | 0.354563 | − | 0.935032i | \(-0.384630\pi\) | ||||
0.354563 | + | 0.935032i | \(0.384630\pi\) | |||||||
\(198\) | −5105.57 | −1.83251 | ||||||||
\(199\) | 456.187 | 0.162504 | 0.0812519 | − | 0.996694i | \(-0.474108\pi\) | ||||
0.0812519 | + | 0.996694i | \(0.474108\pi\) | |||||||
\(200\) | −2346.29 | −0.829540 | ||||||||
\(201\) | −959.650 | −0.336759 | ||||||||
\(202\) | 4740.48 | 1.65118 | ||||||||
\(203\) | 170.834 | 0.0590651 | ||||||||
\(204\) | −766.179 | −0.262957 | ||||||||
\(205\) | −402.099 | −0.136994 | ||||||||
\(206\) | −4143.27 | −1.40133 | ||||||||
\(207\) | 739.286 | 0.248232 | ||||||||
\(208\) | 1463.54 | 0.487877 | ||||||||
\(209\) | −4473.24 | −1.48048 | ||||||||
\(210\) | −403.831 | −0.132700 | ||||||||
\(211\) | −1742.50 | −0.568524 | −0.284262 | − | 0.958747i | \(-0.591749\pi\) | ||||
−0.284262 | + | 0.958747i | \(0.591749\pi\) | |||||||
\(212\) | 1390.38 | 0.450432 | ||||||||
\(213\) | −6681.08 | −2.14920 | ||||||||
\(214\) | 1930.71 | 0.616732 | ||||||||
\(215\) | −58.6390 | −0.0186007 | ||||||||
\(216\) | −278.399 | −0.0876974 | ||||||||
\(217\) | 2413.14 | 0.754906 | ||||||||
\(218\) | 2988.17 | 0.928370 | ||||||||
\(219\) | 3286.46 | 1.01406 | ||||||||
\(220\) | 173.440 | 0.0531514 | ||||||||
\(221\) | 1044.24 | 0.317841 | ||||||||
\(222\) | 8418.63 | 2.54514 | ||||||||
\(223\) | 3149.26 | 0.945697 | 0.472848 | − | 0.881144i | \(-0.343226\pi\) | ||||
0.472848 | + | 0.881144i | \(0.343226\pi\) | |||||||
\(224\) | 1132.18 | 0.337711 | ||||||||
\(225\) | −3075.22 | −0.911175 | ||||||||
\(226\) | −6658.71 | −1.95987 | ||||||||
\(227\) | 2108.03 | 0.616365 | 0.308182 | − | 0.951327i | \(-0.400279\pi\) | ||||
0.308182 | + | 0.951327i | \(0.400279\pi\) | |||||||
\(228\) | −977.746 | −0.284003 | ||||||||
\(229\) | 1529.66 | 0.441409 | 0.220704 | − | 0.975341i | \(-0.429164\pi\) | ||||
0.220704 | + | 0.975341i | \(0.429164\pi\) | |||||||
\(230\) | −127.428 | −0.0365320 | ||||||||
\(231\) | 6076.18 | 1.73066 | ||||||||
\(232\) | 250.136 | 0.0707854 | ||||||||
\(233\) | 2999.86 | 0.843466 | 0.421733 | − | 0.906720i | \(-0.361422\pi\) | ||||
0.421733 | + | 0.906720i | \(0.361422\pi\) | |||||||
\(234\) | 1520.95 | 0.424905 | ||||||||
\(235\) | 500.912 | 0.139046 | ||||||||
\(236\) | 228.100 | 0.0629154 | ||||||||
\(237\) | −4471.02 | −1.22542 | ||||||||
\(238\) | 2223.10 | 0.605472 | ||||||||
\(239\) | 3421.34 | 0.925976 | 0.462988 | − | 0.886364i | \(-0.346777\pi\) | ||||
0.462988 | + | 0.886364i | \(0.346777\pi\) | |||||||
\(240\) | −745.732 | −0.200570 | ||||||||
\(241\) | −4496.86 | −1.20194 | −0.600971 | − | 0.799271i | \(-0.705219\pi\) | ||||
−0.600971 | + | 0.799271i | \(0.705219\pi\) | |||||||
\(242\) | −9039.86 | −2.40126 | ||||||||
\(243\) | −5225.93 | −1.37960 | ||||||||
\(244\) | 429.870 | 0.112785 | ||||||||
\(245\) | −236.818 | −0.0617540 | ||||||||
\(246\) | 6709.89 | 1.73905 | ||||||||
\(247\) | 1332.58 | 0.343280 | ||||||||
\(248\) | 3533.32 | 0.904701 | ||||||||
\(249\) | −9500.74 | −2.41801 | ||||||||
\(250\) | 1068.13 | 0.270219 | ||||||||
\(251\) | 1478.05 | 0.371688 | 0.185844 | − | 0.982579i | \(-0.440498\pi\) | ||||
0.185844 | + | 0.982579i | \(0.440498\pi\) | |||||||
\(252\) | 638.159 | 0.159525 | ||||||||
\(253\) | 1917.33 | 0.476448 | ||||||||
\(254\) | −2489.19 | −0.614904 | ||||||||
\(255\) | −532.079 | −0.130667 | ||||||||
\(256\) | 2849.36 | 0.695645 | ||||||||
\(257\) | 677.467 | 0.164433 | 0.0822164 | − | 0.996614i | \(-0.473800\pi\) | ||||
0.0822164 | + | 0.996614i | \(0.473800\pi\) | |||||||
\(258\) | 978.517 | 0.236123 | ||||||||
\(259\) | −4814.19 | −1.15498 | ||||||||
\(260\) | −51.6678 | −0.0123242 | ||||||||
\(261\) | 327.845 | 0.0777514 | ||||||||
\(262\) | −5913.97 | −1.39453 | ||||||||
\(263\) | −7753.56 | −1.81789 | −0.908944 | − | 0.416917i | \(-0.863110\pi\) | ||||
−0.908944 | + | 0.416917i | \(0.863110\pi\) | |||||||
\(264\) | 8896.73 | 2.07408 | ||||||||
\(265\) | 965.560 | 0.223826 | ||||||||
\(266\) | 2836.97 | 0.653933 | ||||||||
\(267\) | 3671.63 | 0.841574 | ||||||||
\(268\) | −261.393 | −0.0595789 | ||||||||
\(269\) | −300.965 | −0.0682161 | −0.0341081 | − | 0.999418i | \(-0.510859\pi\) | ||||
−0.0341081 | + | 0.999418i | \(0.510859\pi\) | |||||||
\(270\) | 62.8946 | 0.0141765 | ||||||||
\(271\) | −2176.33 | −0.487833 | −0.243917 | − | 0.969796i | \(-0.578432\pi\) | ||||
−0.243917 | + | 0.969796i | \(0.578432\pi\) | |||||||
\(272\) | 4105.28 | 0.915145 | ||||||||
\(273\) | −1810.10 | −0.401290 | ||||||||
\(274\) | 5872.00 | 1.29467 | ||||||||
\(275\) | −7975.52 | −1.74888 | ||||||||
\(276\) | 419.082 | 0.0913978 | ||||||||
\(277\) | 2947.64 | 0.639373 | 0.319687 | − | 0.947523i | \(-0.396422\pi\) | ||||
0.319687 | + | 0.947523i | \(0.396422\pi\) | |||||||
\(278\) | 8909.36 | 1.92211 | ||||||||
\(279\) | 4631.02 | 0.993734 | ||||||||
\(280\) | 338.128 | 0.0721679 | ||||||||
\(281\) | 459.209 | 0.0974879 | 0.0487440 | − | 0.998811i | \(-0.484478\pi\) | ||||
0.0487440 | + | 0.998811i | \(0.484478\pi\) | |||||||
\(282\) | −8358.79 | −1.76510 | ||||||||
\(283\) | 6190.86 | 1.30038 | 0.650192 | − | 0.759770i | \(-0.274688\pi\) | ||||
0.650192 | + | 0.759770i | \(0.274688\pi\) | |||||||
\(284\) | −1819.82 | −0.380234 | ||||||||
\(285\) | −679.003 | −0.141125 | ||||||||
\(286\) | 3944.56 | 0.815549 | ||||||||
\(287\) | −3837.05 | −0.789176 | ||||||||
\(288\) | 2172.75 | 0.444551 | ||||||||
\(289\) | −1983.89 | −0.403803 | ||||||||
\(290\) | −56.5095 | −0.0114426 | ||||||||
\(291\) | 6963.20 | 1.40271 | ||||||||
\(292\) | 895.179 | 0.179405 | ||||||||
\(293\) | 5693.95 | 1.13530 | 0.567652 | − | 0.823269i | \(-0.307852\pi\) | ||||
0.567652 | + | 0.823269i | \(0.307852\pi\) | |||||||
\(294\) | 3951.81 | 0.783927 | ||||||||
\(295\) | 158.406 | 0.0312635 | ||||||||
\(296\) | −7048.93 | −1.38416 | ||||||||
\(297\) | −946.333 | −0.184888 | ||||||||
\(298\) | −5098.75 | −0.991150 | ||||||||
\(299\) | −571.173 | −0.110474 | ||||||||
\(300\) | −1743.26 | −0.335491 | ||||||||
\(301\) | −559.564 | −0.107152 | ||||||||
\(302\) | −4419.01 | −0.842005 | ||||||||
\(303\) | −10826.9 | −2.05276 | ||||||||
\(304\) | 5238.89 | 0.988391 | ||||||||
\(305\) | 298.527 | 0.0560446 | ||||||||
\(306\) | 4266.32 | 0.797024 | ||||||||
\(307\) | −5108.18 | −0.949639 | −0.474819 | − | 0.880083i | \(-0.657487\pi\) | ||||
−0.474819 | + | 0.880083i | \(0.657487\pi\) | |||||||
\(308\) | 1655.05 | 0.306187 | ||||||||
\(309\) | 9462.87 | 1.74215 | ||||||||
\(310\) | −798.231 | −0.146247 | ||||||||
\(311\) | −1048.11 | −0.191102 | −0.0955511 | − | 0.995425i | \(-0.530461\pi\) | ||||
−0.0955511 | + | 0.995425i | \(0.530461\pi\) | |||||||
\(312\) | −2650.34 | −0.480917 | ||||||||
\(313\) | 4279.92 | 0.772893 | 0.386446 | − | 0.922312i | \(-0.373702\pi\) | ||||
0.386446 | + | 0.922312i | \(0.373702\pi\) | |||||||
\(314\) | −9258.91 | −1.66405 | ||||||||
\(315\) | 443.175 | 0.0792700 | ||||||||
\(316\) | −1217.83 | −0.216799 | ||||||||
\(317\) | 5929.95 | 1.05066 | 0.525330 | − | 0.850899i | \(-0.323942\pi\) | ||||
0.525330 | + | 0.850899i | \(0.323942\pi\) | |||||||
\(318\) | −16112.4 | −2.84132 | ||||||||
\(319\) | 850.261 | 0.149234 | ||||||||
\(320\) | 453.019 | 0.0791392 | ||||||||
\(321\) | −4409.58 | −0.766725 | ||||||||
\(322\) | −1215.99 | −0.210448 | ||||||||
\(323\) | 3737.94 | 0.643915 | ||||||||
\(324\) | −1530.92 | −0.262503 | ||||||||
\(325\) | 2375.91 | 0.405514 | ||||||||
\(326\) | 524.653 | 0.0891345 | ||||||||
\(327\) | −6824.73 | −1.15415 | ||||||||
\(328\) | −5618.20 | −0.945772 | ||||||||
\(329\) | 4779.97 | 0.800997 | ||||||||
\(330\) | −2009.91 | −0.335278 | ||||||||
\(331\) | 509.174 | 0.0845521 | 0.0422761 | − | 0.999106i | \(-0.486539\pi\) | ||||
0.0422761 | + | 0.999106i | \(0.486539\pi\) | |||||||
\(332\) | −2587.85 | −0.427792 | ||||||||
\(333\) | −9238.83 | −1.52037 | ||||||||
\(334\) | −6765.77 | −1.10840 | ||||||||
\(335\) | −181.527 | −0.0296056 | ||||||||
\(336\) | −7116.18 | −1.15541 | ||||||||
\(337\) | −10856.3 | −1.75484 | −0.877419 | − | 0.479724i | \(-0.840737\pi\) | ||||
−0.877419 | + | 0.479724i | \(0.840737\pi\) | |||||||
\(338\) | 5759.81 | 0.926900 | ||||||||
\(339\) | 15207.9 | 2.43652 | ||||||||
\(340\) | −144.930 | −0.0231174 | ||||||||
\(341\) | 12010.5 | 1.90734 | ||||||||
\(342\) | 5444.39 | 0.860816 | ||||||||
\(343\) | −6723.34 | −1.05839 | ||||||||
\(344\) | −819.314 | −0.128414 | ||||||||
\(345\) | 291.035 | 0.0454168 | ||||||||
\(346\) | 375.684 | 0.0583725 | ||||||||
\(347\) | 8973.74 | 1.38829 | 0.694143 | − | 0.719837i | \(-0.255783\pi\) | ||||
0.694143 | + | 0.719837i | \(0.255783\pi\) | |||||||
\(348\) | 185.847 | 0.0286277 | ||||||||
\(349\) | −5.70408 | −0.000874877 0 | −0.000437439 | − | 1.00000i | \(-0.500139\pi\) | ||||
−0.000437439 | 1.00000i | \(0.500139\pi\) | ||||||||
\(350\) | 5058.15 | 0.772485 | ||||||||
\(351\) | 281.913 | 0.0428702 | ||||||||
\(352\) | 5635.00 | 0.853257 | ||||||||
\(353\) | −1504.40 | −0.226830 | −0.113415 | − | 0.993548i | \(-0.536179\pi\) | ||||
−0.113415 | + | 0.993548i | \(0.536179\pi\) | |||||||
\(354\) | −2643.34 | −0.396870 | ||||||||
\(355\) | −1263.79 | −0.188944 | ||||||||
\(356\) | 1000.10 | 0.148890 | ||||||||
\(357\) | −5077.38 | −0.752727 | ||||||||
\(358\) | −8118.76 | −1.19857 | ||||||||
\(359\) | −1296.86 | −0.190657 | −0.0953285 | − | 0.995446i | \(-0.530390\pi\) | ||||
−0.0953285 | + | 0.995446i | \(0.530390\pi\) | |||||||
\(360\) | 648.896 | 0.0949995 | ||||||||
\(361\) | −2088.90 | −0.304548 | ||||||||
\(362\) | −4511.63 | −0.655044 | ||||||||
\(363\) | 20646.3 | 2.98526 | ||||||||
\(364\) | −493.042 | −0.0709957 | ||||||||
\(365\) | 621.664 | 0.0891490 | ||||||||
\(366\) | −4981.56 | −0.711449 | ||||||||
\(367\) | 12908.3 | 1.83599 | 0.917995 | − | 0.396592i | \(-0.129807\pi\) | ||||
0.917995 | + | 0.396592i | \(0.129807\pi\) | |||||||
\(368\) | −2245.50 | −0.318083 | ||||||||
\(369\) | −7363.61 | −1.03885 | ||||||||
\(370\) | 1592.46 | 0.223752 | ||||||||
\(371\) | 9213.89 | 1.28938 | ||||||||
\(372\) | 2625.20 | 0.365888 | ||||||||
\(373\) | −1371.48 | −0.190382 | −0.0951908 | − | 0.995459i | \(-0.530346\pi\) | ||||
−0.0951908 | + | 0.995459i | \(0.530346\pi\) | |||||||
\(374\) | 11064.6 | 1.52978 | ||||||||
\(375\) | −2439.52 | −0.335937 | ||||||||
\(376\) | 6998.83 | 0.959939 | ||||||||
\(377\) | −253.293 | −0.0346029 | ||||||||
\(378\) | 600.174 | 0.0816656 | ||||||||
\(379\) | −458.768 | −0.0621776 | −0.0310888 | − | 0.999517i | \(-0.509897\pi\) | ||||
−0.0310888 | + | 0.999517i | \(0.509897\pi\) | |||||||
\(380\) | −184.950 | −0.0249677 | ||||||||
\(381\) | 5685.09 | 0.764452 | ||||||||
\(382\) | −1297.80 | −0.173826 | ||||||||
\(383\) | 9513.45 | 1.26923 | 0.634614 | − | 0.772829i | \(-0.281159\pi\) | ||||
0.634614 | + | 0.772829i | \(0.281159\pi\) | |||||||
\(384\) | −12577.4 | −1.67145 | ||||||||
\(385\) | 1149.37 | 0.152148 | ||||||||
\(386\) | 9812.31 | 1.29387 | ||||||||
\(387\) | −1073.85 | −0.141051 | ||||||||
\(388\) | 1896.66 | 0.248166 | ||||||||
\(389\) | 5643.25 | 0.735538 | 0.367769 | − | 0.929917i | \(-0.380122\pi\) | ||||
0.367769 | + | 0.929917i | \(0.380122\pi\) | |||||||
\(390\) | 598.754 | 0.0777412 | ||||||||
\(391\) | −1602.16 | −0.207224 | ||||||||
\(392\) | −3308.86 | −0.426333 | ||||||||
\(393\) | 13507.0 | 1.73369 | ||||||||
\(394\) | −6189.17 | −0.791385 | ||||||||
\(395\) | −845.735 | −0.107730 | ||||||||
\(396\) | 3176.19 | 0.403054 | ||||||||
\(397\) | −13816.5 | −1.74668 | −0.873340 | − | 0.487110i | \(-0.838051\pi\) | ||||
−0.873340 | + | 0.487110i | \(0.838051\pi\) | |||||||
\(398\) | −1439.97 | −0.181355 | ||||||||
\(399\) | −6479.41 | −0.812973 | ||||||||
\(400\) | 9340.62 | 1.16758 | ||||||||
\(401\) | 3544.45 | 0.441400 | 0.220700 | − | 0.975342i | \(-0.429166\pi\) | ||||
0.220700 | + | 0.975342i | \(0.429166\pi\) | |||||||
\(402\) | 3029.16 | 0.375823 | ||||||||
\(403\) | −3577.93 | −0.442256 | ||||||||
\(404\) | −2949.06 | −0.363172 | ||||||||
\(405\) | −1063.16 | −0.130441 | ||||||||
\(406\) | −539.244 | −0.0659168 | ||||||||
\(407\) | −23960.7 | −2.91816 | ||||||||
\(408\) | −7434.30 | −0.902090 | ||||||||
\(409\) | −2736.88 | −0.330880 | −0.165440 | − | 0.986220i | \(-0.552904\pi\) | ||||
−0.165440 | + | 0.986220i | \(0.552904\pi\) | |||||||
\(410\) | 1269.24 | 0.152886 | ||||||||
\(411\) | −13411.2 | −1.60955 | ||||||||
\(412\) | 2577.54 | 0.308219 | ||||||||
\(413\) | 1511.59 | 0.180098 | ||||||||
\(414\) | −2333.58 | −0.277027 | ||||||||
\(415\) | −1797.15 | −0.212575 | ||||||||
\(416\) | −1678.67 | −0.197845 | ||||||||
\(417\) | −20348.2 | −2.38958 | ||||||||
\(418\) | 14119.9 | 1.65222 | ||||||||
\(419\) | 9280.65 | 1.08208 | 0.541038 | − | 0.840998i | \(-0.318032\pi\) | ||||
0.541038 | + | 0.840998i | \(0.318032\pi\) | |||||||
\(420\) | 251.224 | 0.0291869 | ||||||||
\(421\) | −7308.00 | −0.846010 | −0.423005 | − | 0.906127i | \(-0.639025\pi\) | ||||
−0.423005 | + | 0.906127i | \(0.639025\pi\) | |||||||
\(422\) | 5500.26 | 0.634475 | ||||||||
\(423\) | 9173.16 | 1.05441 | ||||||||
\(424\) | 13491.0 | 1.54523 | ||||||||
\(425\) | 6664.51 | 0.760650 | ||||||||
\(426\) | 21089.0 | 2.39852 | ||||||||
\(427\) | 2848.70 | 0.322853 | ||||||||
\(428\) | −1201.10 | −0.135648 | ||||||||
\(429\) | −9009.05 | −1.01390 | ||||||||
\(430\) | 185.096 | 0.0207584 | ||||||||
\(431\) | −953.510 | −0.106564 | −0.0532818 | − | 0.998580i | \(-0.516968\pi\) | ||||
−0.0532818 | + | 0.998580i | \(0.516968\pi\) | |||||||
\(432\) | 1108.31 | 0.123434 | ||||||||
\(433\) | 3447.00 | 0.382569 | 0.191284 | − | 0.981535i | \(-0.438735\pi\) | ||||
0.191284 | + | 0.981535i | \(0.438735\pi\) | |||||||
\(434\) | −7617.15 | −0.842477 | ||||||||
\(435\) | 129.063 | 0.0142255 | ||||||||
\(436\) | −1858.95 | −0.204192 | ||||||||
\(437\) | −2044.57 | −0.223810 | ||||||||
\(438\) | −10373.8 | −1.13169 | ||||||||
\(439\) | −9245.65 | −1.00517 | −0.502586 | − | 0.864527i | \(-0.667618\pi\) | ||||
−0.502586 | + | 0.864527i | \(0.667618\pi\) | |||||||
\(440\) | 1682.90 | 0.182339 | ||||||||
\(441\) | −4336.82 | −0.468289 | ||||||||
\(442\) | −3296.16 | −0.354711 | ||||||||
\(443\) | −3885.76 | −0.416745 | −0.208372 | − | 0.978050i | \(-0.566817\pi\) | ||||
−0.208372 | + | 0.978050i | \(0.566817\pi\) | |||||||
\(444\) | −5237.25 | −0.559795 | ||||||||
\(445\) | 694.524 | 0.0739856 | ||||||||
\(446\) | −9940.75 | −1.05540 | ||||||||
\(447\) | 11645.1 | 1.23220 | ||||||||
\(448\) | 4322.95 | 0.455893 | ||||||||
\(449\) | −14413.1 | −1.51491 | −0.757455 | − | 0.652887i | \(-0.773557\pi\) | ||||
−0.757455 | + | 0.652887i | \(0.773557\pi\) | |||||||
\(450\) | 9707.02 | 1.01687 | ||||||||
\(451\) | −19097.4 | −1.99393 | ||||||||
\(452\) | 4142.40 | 0.431066 | ||||||||
\(453\) | 10092.6 | 1.04679 | ||||||||
\(454\) | −6654.06 | −0.687864 | ||||||||
\(455\) | −342.397 | −0.0352787 | ||||||||
\(456\) | −9487.15 | −0.974291 | ||||||||
\(457\) | −1765.21 | −0.180685 | −0.0903424 | − | 0.995911i | \(-0.528796\pi\) | ||||
−0.0903424 | + | 0.995911i | \(0.528796\pi\) | |||||||
\(458\) | −4828.41 | −0.492613 | ||||||||
\(459\) | 790.776 | 0.0804145 | ||||||||
\(460\) | 79.2733 | 0.00803508 | ||||||||
\(461\) | 7626.64 | 0.770517 | 0.385258 | − | 0.922809i | \(-0.374112\pi\) | ||||
0.385258 | + | 0.922809i | \(0.374112\pi\) | |||||||
\(462\) | −19179.6 | −1.93142 | ||||||||
\(463\) | −5954.18 | −0.597655 | −0.298827 | − | 0.954307i | \(-0.596595\pi\) | ||||
−0.298827 | + | 0.954307i | \(0.596595\pi\) | |||||||
\(464\) | −995.792 | −0.0996304 | ||||||||
\(465\) | 1823.09 | 0.181815 | ||||||||
\(466\) | −9469.16 | −0.941310 | ||||||||
\(467\) | 153.388 | 0.0151991 | 0.00759954 | − | 0.999971i | \(-0.497581\pi\) | ||||
0.00759954 | + | 0.999971i | \(0.497581\pi\) | |||||||
\(468\) | −946.189 | −0.0934564 | ||||||||
\(469\) | −1732.22 | −0.170547 | ||||||||
\(470\) | −1581.14 | −0.155176 | ||||||||
\(471\) | 21146.6 | 2.06875 | ||||||||
\(472\) | 2213.27 | 0.215835 | ||||||||
\(473\) | −2785.01 | −0.270729 | ||||||||
\(474\) | 14112.9 | 1.36757 | ||||||||
\(475\) | 8504.80 | 0.821531 | ||||||||
\(476\) | −1383.00 | −0.133171 | ||||||||
\(477\) | 17682.2 | 1.69730 | ||||||||
\(478\) | −10799.6 | −1.03339 | ||||||||
\(479\) | −11334.3 | −1.08117 | −0.540584 | − | 0.841290i | \(-0.681797\pi\) | ||||
−0.540584 | + | 0.841290i | \(0.681797\pi\) | |||||||
\(480\) | 855.348 | 0.0813357 | ||||||||
\(481\) | 7137.92 | 0.676635 | ||||||||
\(482\) | 14194.5 | 1.34137 | ||||||||
\(483\) | 2777.21 | 0.261630 | ||||||||
\(484\) | 5623.72 | 0.528148 | ||||||||
\(485\) | 1317.15 | 0.123317 | ||||||||
\(486\) | 16495.8 | 1.53964 | ||||||||
\(487\) | −2845.89 | −0.264804 | −0.132402 | − | 0.991196i | \(-0.542269\pi\) | ||||
−0.132402 | + | 0.991196i | \(0.542269\pi\) | |||||||
\(488\) | 4171.07 | 0.386917 | ||||||||
\(489\) | −1198.26 | −0.110813 | ||||||||
\(490\) | 747.522 | 0.0689176 | ||||||||
\(491\) | −8345.94 | −0.767102 | −0.383551 | − | 0.923520i | \(-0.625299\pi\) | ||||
−0.383551 | + | 0.923520i | \(0.625299\pi\) | |||||||
\(492\) | −4174.24 | −0.382499 | ||||||||
\(493\) | −710.496 | −0.0649070 | ||||||||
\(494\) | −4206.34 | −0.383101 | ||||||||
\(495\) | 2205.73 | 0.200283 | ||||||||
\(496\) | −14066.2 | −1.27337 | ||||||||
\(497\) | −12059.8 | −1.08844 | ||||||||
\(498\) | 29989.4 | 2.69851 | ||||||||
\(499\) | 17591.1 | 1.57813 | 0.789064 | − | 0.614311i | \(-0.210566\pi\) | ||||
0.789064 | + | 0.614311i | \(0.210566\pi\) | |||||||
\(500\) | −664.488 | −0.0594336 | ||||||||
\(501\) | 15452.5 | 1.37797 | ||||||||
\(502\) | −4665.51 | −0.414805 | ||||||||
\(503\) | −7975.83 | −0.707008 | −0.353504 | − | 0.935433i | \(-0.615010\pi\) | ||||
−0.353504 | + | 0.935433i | \(0.615010\pi\) | |||||||
\(504\) | 6192.11 | 0.547259 | ||||||||
\(505\) | −2048.00 | −0.180465 | ||||||||
\(506\) | −6052.10 | −0.531717 | ||||||||
\(507\) | −13154.9 | −1.15233 | ||||||||
\(508\) | 1548.53 | 0.135246 | ||||||||
\(509\) | −9016.94 | −0.785204 | −0.392602 | − | 0.919708i | \(-0.628425\pi\) | ||||
−0.392602 | + | 0.919708i | \(0.628425\pi\) | |||||||
\(510\) | 1679.52 | 0.145825 | ||||||||
\(511\) | 5932.25 | 0.513556 | ||||||||
\(512\) | 4962.89 | 0.428380 | ||||||||
\(513\) | 1009.14 | 0.0868507 | ||||||||
\(514\) | −2138.45 | −0.183507 | ||||||||
\(515\) | 1789.99 | 0.153158 | ||||||||
\(516\) | −608.738 | −0.0519345 | ||||||||
\(517\) | 23790.4 | 2.02379 | ||||||||
\(518\) | 15196.1 | 1.28896 | ||||||||
\(519\) | −858.030 | −0.0725691 | ||||||||
\(520\) | −501.337 | −0.0422790 | ||||||||
\(521\) | −3086.13 | −0.259512 | −0.129756 | − | 0.991546i | \(-0.541419\pi\) | ||||
−0.129756 | + | 0.991546i | \(0.541419\pi\) | |||||||
\(522\) | −1034.85 | −0.0867707 | ||||||||
\(523\) | 8338.32 | 0.697149 | 0.348575 | − | 0.937281i | \(-0.386666\pi\) | ||||
0.348575 | + | 0.937281i | \(0.386666\pi\) | |||||||
\(524\) | 3679.10 | 0.306722 | ||||||||
\(525\) | −11552.4 | −0.960358 | ||||||||
\(526\) | 24474.3 | 2.02877 | ||||||||
\(527\) | −10036.2 | −0.829570 | ||||||||
\(528\) | −35418.0 | −2.91926 | ||||||||
\(529\) | −11290.7 | −0.927974 | ||||||||
\(530\) | −3047.82 | −0.249790 | ||||||||
\(531\) | 2900.87 | 0.237076 | ||||||||
\(532\) | −1764.89 | −0.143830 | ||||||||
\(533\) | 5689.13 | 0.462333 | ||||||||
\(534\) | −11589.6 | −0.939199 | ||||||||
\(535\) | −834.114 | −0.0674054 | ||||||||
\(536\) | −2536.32 | −0.204389 | ||||||||
\(537\) | 18542.6 | 1.49008 | ||||||||
\(538\) | 950.004 | 0.0761293 | ||||||||
\(539\) | −11247.5 | −0.898818 | ||||||||
\(540\) | −39.1269 | −0.00311806 | ||||||||
\(541\) | −14924.6 | −1.18606 | −0.593029 | − | 0.805181i | \(-0.702068\pi\) | ||||
−0.593029 | + | 0.805181i | \(0.702068\pi\) | |||||||
\(542\) | 6869.66 | 0.544423 | ||||||||
\(543\) | 10304.2 | 0.814355 | ||||||||
\(544\) | −4708.72 | −0.371112 | ||||||||
\(545\) | −1290.96 | −0.101466 | ||||||||
\(546\) | 5713.63 | 0.447840 | ||||||||
\(547\) | 10658.3 | 0.833120 | 0.416560 | − | 0.909108i | \(-0.363236\pi\) | ||||
0.416560 | + | 0.909108i | \(0.363236\pi\) | |||||||
\(548\) | −3652.99 | −0.284759 | ||||||||
\(549\) | 5466.90 | 0.424994 | ||||||||
\(550\) | 25175.0 | 1.95175 | ||||||||
\(551\) | −906.687 | −0.0701020 | ||||||||
\(552\) | 4066.39 | 0.313545 | ||||||||
\(553\) | −8070.45 | −0.620598 | ||||||||
\(554\) | −9304.31 | −0.713542 | ||||||||
\(555\) | −3637.05 | −0.278170 | ||||||||
\(556\) | −5542.53 | −0.422762 | ||||||||
\(557\) | 4303.28 | 0.327354 | 0.163677 | − | 0.986514i | \(-0.447665\pi\) | ||||
0.163677 | + | 0.986514i | \(0.447665\pi\) | |||||||
\(558\) | −14617.9 | −1.10901 | ||||||||
\(559\) | 829.657 | 0.0627742 | ||||||||
\(560\) | −1346.09 | −0.101576 | ||||||||
\(561\) | −25270.7 | −1.90183 | ||||||||
\(562\) | −1449.51 | −0.108797 | ||||||||
\(563\) | −13280.8 | −0.994173 | −0.497086 | − | 0.867701i | \(-0.665597\pi\) | ||||
−0.497086 | + | 0.867701i | \(0.665597\pi\) | |||||||
\(564\) | 5200.02 | 0.388228 | ||||||||
\(565\) | 2876.72 | 0.214203 | ||||||||
\(566\) | −19541.7 | −1.45123 | ||||||||
\(567\) | −10145.2 | −0.751427 | ||||||||
\(568\) | −17657.9 | −1.30442 | ||||||||
\(569\) | 11641.6 | 0.857720 | 0.428860 | − | 0.903371i | \(-0.358915\pi\) | ||||
0.428860 | + | 0.903371i | \(0.358915\pi\) | |||||||
\(570\) | 2143.29 | 0.157496 | ||||||||
\(571\) | 21799.0 | 1.59765 | 0.798825 | − | 0.601563i | \(-0.205455\pi\) | ||||
0.798825 | + | 0.601563i | \(0.205455\pi\) | |||||||
\(572\) | −2453.92 | −0.179377 | ||||||||
\(573\) | 2964.07 | 0.216101 | ||||||||
\(574\) | 12111.8 | 0.880723 | ||||||||
\(575\) | −3645.34 | −0.264384 | ||||||||
\(576\) | 8296.10 | 0.600123 | ||||||||
\(577\) | 6854.44 | 0.494548 | 0.247274 | − | 0.968946i | \(-0.420465\pi\) | ||||
0.247274 | + | 0.968946i | \(0.420465\pi\) | |||||||
\(578\) | 6262.20 | 0.450645 | ||||||||
\(579\) | −22410.5 | −1.60855 | ||||||||
\(580\) | 35.1547 | 0.00251676 | ||||||||
\(581\) | −17149.4 | −1.22457 | ||||||||
\(582\) | −21979.5 | −1.56543 | ||||||||
\(583\) | 45858.5 | 3.25775 | ||||||||
\(584\) | 8686.00 | 0.615461 | ||||||||
\(585\) | −657.088 | −0.0464397 | ||||||||
\(586\) | −17973.1 | −1.26700 | ||||||||
\(587\) | −16741.7 | −1.17718 | −0.588589 | − | 0.808433i | \(-0.700316\pi\) | ||||
−0.588589 | + | 0.808433i | \(0.700316\pi\) | |||||||
\(588\) | −2458.43 | −0.172422 | ||||||||
\(589\) | −12807.5 | −0.895967 | ||||||||
\(590\) | −500.012 | −0.0348902 | ||||||||
\(591\) | 14135.5 | 0.983855 | ||||||||
\(592\) | 28061.9 | 1.94820 | ||||||||
\(593\) | 21885.0 | 1.51553 | 0.757764 | − | 0.652529i | \(-0.226292\pi\) | ||||
0.757764 | + | 0.652529i | \(0.226292\pi\) | |||||||
\(594\) | 2987.13 | 0.206336 | ||||||||
\(595\) | −960.434 | −0.0661747 | ||||||||
\(596\) | 3171.95 | 0.218000 | ||||||||
\(597\) | 3288.77 | 0.225461 | ||||||||
\(598\) | 1802.92 | 0.123289 | ||||||||
\(599\) | −14440.9 | −0.985039 | −0.492519 | − | 0.870301i | \(-0.663924\pi\) | ||||
−0.492519 | + | 0.870301i | \(0.663924\pi\) | |||||||
\(600\) | −16915.0 | −1.15092 | ||||||||
\(601\) | 2570.21 | 0.174444 | 0.0872221 | − | 0.996189i | \(-0.472201\pi\) | ||||
0.0872221 | + | 0.996189i | \(0.472201\pi\) | |||||||
\(602\) | 1766.28 | 0.119582 | ||||||||
\(603\) | −3324.28 | −0.224503 | ||||||||
\(604\) | 2749.08 | 0.185196 | ||||||||
\(605\) | 3905.44 | 0.262444 | ||||||||
\(606\) | 34175.3 | 2.29089 | ||||||||
\(607\) | −11683.5 | −0.781249 | −0.390624 | − | 0.920550i | \(-0.627741\pi\) | ||||
−0.390624 | + | 0.920550i | \(0.627741\pi\) | |||||||
\(608\) | −6008.96 | −0.400815 | ||||||||
\(609\) | 1231.59 | 0.0819482 | ||||||||
\(610\) | −942.309 | −0.0625458 | ||||||||
\(611\) | −7087.18 | −0.469258 | ||||||||
\(612\) | −2654.09 | −0.175303 | ||||||||
\(613\) | 12739.0 | 0.839356 | 0.419678 | − | 0.907673i | \(-0.362143\pi\) | ||||
0.419678 | + | 0.907673i | \(0.362143\pi\) | |||||||
\(614\) | 16124.1 | 1.05980 | ||||||||
\(615\) | −2898.83 | −0.190069 | ||||||||
\(616\) | 16059.1 | 1.05039 | ||||||||
\(617\) | 4380.70 | 0.285835 | 0.142918 | − | 0.989735i | \(-0.454352\pi\) | ||||
0.142918 | + | 0.989735i | \(0.454352\pi\) | |||||||
\(618\) | −29869.8 | −1.94424 | ||||||||
\(619\) | −5157.68 | −0.334902 | −0.167451 | − | 0.985880i | \(-0.553554\pi\) | ||||
−0.167451 | + | 0.985880i | \(0.553554\pi\) | |||||||
\(620\) | 496.582 | 0.0321665 | ||||||||
\(621\) | −432.536 | −0.0279502 | ||||||||
\(622\) | 3308.39 | 0.213270 | ||||||||
\(623\) | 6627.52 | 0.426205 | ||||||||
\(624\) | 10551.0 | 0.676891 | ||||||||
\(625\) | 14931.1 | 0.955589 | ||||||||
\(626\) | −13509.7 | −0.862550 | ||||||||
\(627\) | −32248.7 | −2.05405 | ||||||||
\(628\) | 5759.99 | 0.366001 | ||||||||
\(629\) | 20022.1 | 1.26921 | ||||||||
\(630\) | −1398.89 | −0.0884655 | ||||||||
\(631\) | −27679.9 | −1.74631 | −0.873154 | − | 0.487444i | \(-0.837929\pi\) | ||||
−0.873154 | + | 0.487444i | \(0.837929\pi\) | |||||||
\(632\) | −11816.8 | −0.743743 | ||||||||
\(633\) | −12562.1 | −0.788783 | ||||||||
\(634\) | −18718.1 | −1.17254 | ||||||||
\(635\) | 1075.39 | 0.0672055 | ||||||||
\(636\) | 10023.6 | 0.624939 | ||||||||
\(637\) | 3350.63 | 0.208409 | ||||||||
\(638\) | −2683.88 | −0.166545 | ||||||||
\(639\) | −23143.7 | −1.43278 | ||||||||
\(640\) | −2379.14 | −0.146943 | ||||||||
\(641\) | −16453.5 | −1.01384 | −0.506921 | − | 0.861992i | \(-0.669217\pi\) | ||||
−0.506921 | + | 0.861992i | \(0.669217\pi\) | |||||||
\(642\) | 13919.0 | 0.855667 | ||||||||
\(643\) | −29203.6 | −1.79110 | −0.895551 | − | 0.444958i | \(-0.853219\pi\) | ||||
−0.895551 | + | 0.444958i | \(0.853219\pi\) | |||||||
\(644\) | 756.468 | 0.0462873 | ||||||||
\(645\) | −422.743 | −0.0258070 | ||||||||
\(646\) | −11798.9 | −0.718610 | ||||||||
\(647\) | −16835.6 | −1.02299 | −0.511495 | − | 0.859286i | \(-0.670908\pi\) | ||||
−0.511495 | + | 0.859286i | \(0.670908\pi\) | |||||||
\(648\) | −14854.6 | −0.900532 | ||||||||
\(649\) | 7523.36 | 0.455035 | ||||||||
\(650\) | −7499.64 | −0.452554 | ||||||||
\(651\) | 17396.9 | 1.04737 | ||||||||
\(652\) | −326.388 | −0.0196048 | ||||||||
\(653\) | −13735.1 | −0.823117 | −0.411558 | − | 0.911383i | \(-0.635015\pi\) | ||||
−0.411558 | + | 0.911383i | \(0.635015\pi\) | |||||||
\(654\) | 21542.5 | 1.28804 | ||||||||
\(655\) | 2554.98 | 0.152414 | ||||||||
\(656\) | 22366.1 | 1.33117 | ||||||||
\(657\) | 11384.5 | 0.676029 | ||||||||
\(658\) | −15088.1 | −0.893915 | ||||||||
\(659\) | −5708.76 | −0.337453 | −0.168727 | − | 0.985663i | \(-0.553966\pi\) | ||||
−0.168727 | + | 0.985663i | \(0.553966\pi\) | |||||||
\(660\) | 1250.37 | 0.0737433 | ||||||||
\(661\) | 18339.5 | 1.07916 | 0.539578 | − | 0.841936i | \(-0.318584\pi\) | ||||
0.539578 | + | 0.841936i | \(0.318584\pi\) | |||||||
\(662\) | −1607.22 | −0.0943604 | ||||||||
\(663\) | 7528.15 | 0.440979 | ||||||||
\(664\) | −25110.1 | −1.46756 | ||||||||
\(665\) | −1225.64 | −0.0714712 | ||||||||
\(666\) | 29162.7 | 1.69674 | ||||||||
\(667\) | 388.625 | 0.0225602 | ||||||||
\(668\) | 4209.00 | 0.243789 | ||||||||
\(669\) | 22703.8 | 1.31208 | ||||||||
\(670\) | 572.995 | 0.0330399 | ||||||||
\(671\) | 14178.3 | 0.815719 | ||||||||
\(672\) | 8162.19 | 0.468547 | ||||||||
\(673\) | −482.234 | −0.0276207 | −0.0138104 | − | 0.999905i | \(-0.504396\pi\) | ||||
−0.0138104 | + | 0.999905i | \(0.504396\pi\) | |||||||
\(674\) | 34268.3 | 1.95840 | ||||||||
\(675\) | 1799.23 | 0.102596 | ||||||||
\(676\) | −3583.19 | −0.203868 | ||||||||
\(677\) | 31086.0 | 1.76474 | 0.882372 | − | 0.470553i | \(-0.155945\pi\) | ||||
0.882372 | + | 0.470553i | \(0.155945\pi\) | |||||||
\(678\) | −48004.3 | −2.71916 | ||||||||
\(679\) | 12569.0 | 0.710388 | ||||||||
\(680\) | −1406.27 | −0.0793057 | ||||||||
\(681\) | 15197.3 | 0.855157 | ||||||||
\(682\) | −37911.4 | −2.12860 | ||||||||
\(683\) | 31381.0 | 1.75807 | 0.879034 | − | 0.476758i | \(-0.158188\pi\) | ||||
0.879034 | + | 0.476758i | \(0.158188\pi\) | |||||||
\(684\) | −3386.97 | −0.189333 | ||||||||
\(685\) | −2536.85 | −0.141501 | ||||||||
\(686\) | 21222.4 | 1.18116 | ||||||||
\(687\) | 11027.7 | 0.612420 | ||||||||
\(688\) | 3261.70 | 0.180743 | ||||||||
\(689\) | −13661.3 | −0.755375 | ||||||||
\(690\) | −918.660 | −0.0506852 | ||||||||
\(691\) | 19856.9 | 1.09319 | 0.546593 | − | 0.837398i | \(-0.315924\pi\) | ||||
0.546593 | + | 0.837398i | \(0.315924\pi\) | |||||||
\(692\) | −233.714 | −0.0128388 | ||||||||
\(693\) | 21048.2 | 1.15376 | ||||||||
\(694\) | −28325.9 | −1.54933 | ||||||||
\(695\) | −3849.06 | −0.210076 | ||||||||
\(696\) | 1803.29 | 0.0982091 | ||||||||
\(697\) | 15958.2 | 0.867230 | ||||||||
\(698\) | 18.0051 | 0.000976365 0 | ||||||||
\(699\) | 21626.8 | 1.17024 | ||||||||
\(700\) | −3146.69 | −0.169905 | ||||||||
\(701\) | 2722.80 | 0.146703 | 0.0733514 | − | 0.997306i | \(-0.476631\pi\) | ||||
0.0733514 | + | 0.997306i | \(0.476631\pi\) | |||||||
\(702\) | −889.868 | −0.0478432 | ||||||||
\(703\) | 25550.9 | 1.37079 | ||||||||
\(704\) | 21515.8 | 1.15186 | ||||||||
\(705\) | 3611.20 | 0.192916 | ||||||||
\(706\) | 4748.67 | 0.253143 | ||||||||
\(707\) | −19543.1 | −1.03960 | ||||||||
\(708\) | 1644.43 | 0.0872901 | ||||||||
\(709\) | −1225.30 | −0.0649043 | −0.0324521 | − | 0.999473i | \(-0.510332\pi\) | ||||
−0.0324521 | + | 0.999473i | \(0.510332\pi\) | |||||||
\(710\) | 3989.19 | 0.210861 | ||||||||
\(711\) | −15487.9 | −0.816935 | ||||||||
\(712\) | 9704.01 | 0.510777 | ||||||||
\(713\) | 5489.57 | 0.288339 | ||||||||
\(714\) | 16026.9 | 0.840045 | ||||||||
\(715\) | −1704.15 | −0.0891349 | ||||||||
\(716\) | 5050.70 | 0.263622 | ||||||||
\(717\) | 24665.3 | 1.28472 | ||||||||
\(718\) | 4093.59 | 0.212774 | ||||||||
\(719\) | −28875.1 | −1.49772 | −0.748858 | − | 0.662730i | \(-0.769398\pi\) | ||||
−0.748858 | + | 0.662730i | \(0.769398\pi\) | |||||||
\(720\) | −2583.26 | −0.133712 | ||||||||
\(721\) | 17081.0 | 0.882290 | ||||||||
\(722\) | 6593.67 | 0.339876 | ||||||||
\(723\) | −32419.0 | −1.66760 | ||||||||
\(724\) | 2806.70 | 0.144075 | ||||||||
\(725\) | −1616.57 | −0.0828108 | ||||||||
\(726\) | −65170.6 | −3.33155 | ||||||||
\(727\) | −25072.0 | −1.27905 | −0.639525 | − | 0.768770i | \(-0.720869\pi\) | ||||
−0.639525 | + | 0.768770i | \(0.720869\pi\) | |||||||
\(728\) | −4784.03 | −0.243555 | ||||||||
\(729\) | −16625.5 | −0.844660 | ||||||||
\(730\) | −1962.30 | −0.0994905 | ||||||||
\(731\) | 2327.22 | 0.117750 | ||||||||
\(732\) | 3099.04 | 0.156481 | ||||||||
\(733\) | 1017.07 | 0.0512503 | 0.0256251 | − | 0.999672i | \(-0.491842\pi\) | ||||
0.0256251 | + | 0.999672i | \(0.491842\pi\) | |||||||
\(734\) | −40745.5 | −2.04897 | ||||||||
\(735\) | −1707.28 | −0.0856787 | ||||||||
\(736\) | 2575.56 | 0.128990 | ||||||||
\(737\) | −8621.47 | −0.430904 | ||||||||
\(738\) | 23243.5 | 1.15935 | ||||||||
\(739\) | −1001.77 | −0.0498658 | −0.0249329 | − | 0.999689i | \(-0.507937\pi\) | ||||
−0.0249329 | + | 0.999689i | \(0.507937\pi\) | |||||||
\(740\) | −990.675 | −0.0492134 | ||||||||
\(741\) | 9606.92 | 0.476274 | ||||||||
\(742\) | −29083.9 | −1.43895 | ||||||||
\(743\) | −2115.35 | −0.104448 | −0.0522238 | − | 0.998635i | \(-0.516631\pi\) | ||||
−0.0522238 | + | 0.998635i | \(0.516631\pi\) | |||||||
\(744\) | 25472.6 | 1.25520 | ||||||||
\(745\) | 2202.78 | 0.108327 | ||||||||
\(746\) | 4329.11 | 0.212466 | ||||||||
\(747\) | −32911.1 | −1.61199 | ||||||||
\(748\) | −6883.33 | −0.336470 | ||||||||
\(749\) | −7959.56 | −0.388299 | ||||||||
\(750\) | 7700.43 | 0.374907 | ||||||||
\(751\) | 39172.1 | 1.90334 | 0.951671 | − | 0.307119i | \(-0.0993649\pi\) | ||||
0.951671 | + | 0.307119i | \(0.0993649\pi\) | |||||||
\(752\) | −27862.4 | −1.35111 | ||||||||
\(753\) | 10655.6 | 0.515688 | ||||||||
\(754\) | 799.528 | 0.0386169 | ||||||||
\(755\) | 1909.12 | 0.0920263 | ||||||||
\(756\) | −373.370 | −0.0179621 | ||||||||
\(757\) | 5944.10 | 0.285392 | 0.142696 | − | 0.989767i | \(-0.454423\pi\) | ||||
0.142696 | + | 0.989767i | \(0.454423\pi\) | |||||||
\(758\) | 1448.12 | 0.0693904 | ||||||||
\(759\) | 13822.5 | 0.661033 | ||||||||
\(760\) | −1794.58 | −0.0856531 | ||||||||
\(761\) | −1954.89 | −0.0931205 | −0.0465603 | − | 0.998915i | \(-0.514826\pi\) | ||||
−0.0465603 | + | 0.998915i | \(0.514826\pi\) | |||||||
\(762\) | −17945.2 | −0.853130 | ||||||||
\(763\) | −12319.1 | −0.584508 | ||||||||
\(764\) | 807.367 | 0.0382324 | ||||||||
\(765\) | −1843.15 | −0.0871102 | ||||||||
\(766\) | −30029.5 | −1.41646 | ||||||||
\(767\) | −2241.21 | −0.105509 | ||||||||
\(768\) | 20541.7 | 0.965152 | ||||||||
\(769\) | −39312.9 | −1.84351 | −0.921756 | − | 0.387770i | \(-0.873245\pi\) | ||||
−0.921756 | + | 0.387770i | \(0.873245\pi\) | |||||||
\(770\) | −3628.01 | −0.169798 | ||||||||
\(771\) | 4884.03 | 0.228138 | ||||||||
\(772\) | −6104.26 | −0.284582 | ||||||||
\(773\) | −5102.38 | −0.237413 | −0.118706 | − | 0.992929i | \(-0.537875\pi\) | ||||
−0.118706 | + | 0.992929i | \(0.537875\pi\) | |||||||
\(774\) | 3389.64 | 0.157414 | ||||||||
\(775\) | −22835.0 | −1.05840 | ||||||||
\(776\) | 18403.5 | 0.851349 | ||||||||
\(777\) | −34706.7 | −1.60244 | ||||||||
\(778\) | −17813.1 | −0.820862 | ||||||||
\(779\) | 20364.8 | 0.936641 | ||||||||
\(780\) | −372.486 | −0.0170989 | ||||||||
\(781\) | −60022.7 | −2.75004 | ||||||||
\(782\) | 5057.26 | 0.231262 | ||||||||
\(783\) | −191.813 | −0.00875460 | ||||||||
\(784\) | 13172.6 | 0.600064 | ||||||||
\(785\) | 4000.07 | 0.181871 | ||||||||
\(786\) | −42635.3 | −1.93480 | ||||||||
\(787\) | 21898.3 | 0.991855 | 0.495928 | − | 0.868364i | \(-0.334828\pi\) | ||||
0.495928 | + | 0.868364i | \(0.334828\pi\) | |||||||
\(788\) | 3850.30 | 0.174062 | ||||||||
\(789\) | −55897.3 | −2.52218 | ||||||||
\(790\) | 2669.59 | 0.120227 | ||||||||
\(791\) | 27451.2 | 1.23395 | ||||||||
\(792\) | 30818.8 | 1.38270 | ||||||||
\(793\) | −4223.73 | −0.189141 | ||||||||
\(794\) | 43612.3 | 1.94930 | ||||||||
\(795\) | 6960.96 | 0.310541 | ||||||||
\(796\) | 895.809 | 0.0398883 | ||||||||
\(797\) | 18262.4 | 0.811652 | 0.405826 | − | 0.913950i | \(-0.366984\pi\) | ||||
0.405826 | + | 0.913950i | \(0.366984\pi\) | |||||||
\(798\) | 20452.5 | 0.907280 | ||||||||
\(799\) | −19879.8 | −0.880220 | ||||||||
\(800\) | −10713.6 | −0.473479 | ||||||||
\(801\) | 12718.8 | 0.561043 | ||||||||
\(802\) | −11188.2 | −0.492604 | ||||||||
\(803\) | 29525.5 | 1.29755 | ||||||||
\(804\) | −1884.45 | −0.0826610 | ||||||||
\(805\) | 525.335 | 0.0230008 | ||||||||
\(806\) | 11293.8 | 0.493559 | ||||||||
\(807\) | −2169.73 | −0.0946444 | ||||||||
\(808\) | −28615.0 | −1.24588 | ||||||||
\(809\) | 26097.8 | 1.13418 | 0.567089 | − | 0.823656i | \(-0.308069\pi\) | ||||
0.567089 | + | 0.823656i | \(0.308069\pi\) | |||||||
\(810\) | 3355.89 | 0.145573 | ||||||||
\(811\) | 1067.58 | 0.0462243 | 0.0231122 | − | 0.999733i | \(-0.492643\pi\) | ||||
0.0231122 | + | 0.999733i | \(0.492643\pi\) | |||||||
\(812\) | 335.465 | 0.0144982 | ||||||||
\(813\) | −15689.7 | −0.676830 | ||||||||
\(814\) | 75632.8 | 3.25667 | ||||||||
\(815\) | −226.663 | −0.00974190 | ||||||||
\(816\) | 29596.0 | 1.26969 | ||||||||
\(817\) | 2969.84 | 0.127174 | ||||||||
\(818\) | 8639.05 | 0.369263 | ||||||||
\(819\) | −6270.29 | −0.267523 | ||||||||
\(820\) | −789.596 | −0.0336267 | ||||||||
\(821\) | −20127.0 | −0.855585 | −0.427793 | − | 0.903877i | \(-0.640709\pi\) | ||||
−0.427793 | + | 0.903877i | \(0.640709\pi\) | |||||||
\(822\) | 42332.7 | 1.79626 | ||||||||
\(823\) | −3011.70 | −0.127559 | −0.0637797 | − | 0.997964i | \(-0.520315\pi\) | ||||
−0.0637797 | + | 0.997964i | \(0.520315\pi\) | |||||||
\(824\) | 25010.1 | 1.05736 | ||||||||
\(825\) | −57497.5 | −2.42643 | ||||||||
\(826\) | −4771.39 | −0.200990 | ||||||||
\(827\) | −13138.4 | −0.552437 | −0.276219 | − | 0.961095i | \(-0.589081\pi\) | ||||
−0.276219 | + | 0.961095i | \(0.589081\pi\) | |||||||
\(828\) | 1451.73 | 0.0609311 | ||||||||
\(829\) | 19550.4 | 0.819075 | 0.409538 | − | 0.912293i | \(-0.365690\pi\) | ||||
0.409538 | + | 0.912293i | \(0.365690\pi\) | |||||||
\(830\) | 5672.77 | 0.237235 | ||||||||
\(831\) | 21250.2 | 0.887079 | ||||||||
\(832\) | −6409.57 | −0.267082 | ||||||||
\(833\) | 9398.63 | 0.390928 | ||||||||
\(834\) | 64229.8 | 2.66678 | ||||||||
\(835\) | 2922.98 | 0.121142 | ||||||||
\(836\) | −8784.05 | −0.363400 | ||||||||
\(837\) | −2709.48 | −0.111892 | ||||||||
\(838\) | −29294.7 | −1.20760 | ||||||||
\(839\) | 3227.69 | 0.132816 | 0.0664078 | − | 0.997793i | \(-0.478846\pi\) | ||||
0.0664078 | + | 0.997793i | \(0.478846\pi\) | |||||||
\(840\) | 2437.65 | 0.100127 | ||||||||
\(841\) | −24216.7 | −0.992934 | ||||||||
\(842\) | 23067.9 | 0.944149 | ||||||||
\(843\) | 3310.55 | 0.135257 | ||||||||
\(844\) | −3421.72 | −0.139550 | ||||||||
\(845\) | −2488.38 | −0.101305 | ||||||||
\(846\) | −28955.4 | −1.17672 | ||||||||
\(847\) | 37267.8 | 1.51185 | ||||||||
\(848\) | −53707.7 | −2.17492 | ||||||||
\(849\) | 44631.5 | 1.80418 | ||||||||
\(850\) | −21036.7 | −0.848887 | ||||||||
\(851\) | −10951.6 | −0.441148 | ||||||||
\(852\) | −13119.5 | −0.527545 | ||||||||
\(853\) | 12419.8 | 0.498530 | 0.249265 | − | 0.968435i | \(-0.419811\pi\) | ||||
0.249265 | + | 0.968435i | \(0.419811\pi\) | |||||||
\(854\) | −8992.01 | −0.360305 | ||||||||
\(855\) | −2352.11 | −0.0940823 | ||||||||
\(856\) | −11654.4 | −0.465349 | ||||||||
\(857\) | 18592.3 | 0.741075 | 0.370537 | − | 0.928818i | \(-0.379174\pi\) | ||||
0.370537 | + | 0.928818i | \(0.379174\pi\) | |||||||
\(858\) | 28437.3 | 1.13151 | ||||||||
\(859\) | 6443.09 | 0.255920 | 0.127960 | − | 0.991779i | \(-0.459157\pi\) | ||||
0.127960 | + | 0.991779i | \(0.459157\pi\) | |||||||
\(860\) | −115.148 | −0.00456573 | ||||||||
\(861\) | −27662.2 | −1.09492 | ||||||||
\(862\) | 3009.78 | 0.118925 | ||||||||
\(863\) | −22085.1 | −0.871132 | −0.435566 | − | 0.900157i | \(-0.643452\pi\) | ||||
−0.435566 | + | 0.900157i | \(0.643452\pi\) | |||||||
\(864\) | −1271.22 | −0.0500553 | ||||||||
\(865\) | −162.304 | −0.00637979 | ||||||||
\(866\) | −10880.6 | −0.426948 | ||||||||
\(867\) | −14302.3 | −0.560245 | ||||||||
\(868\) | 4738.65 | 0.185300 | ||||||||
\(869\) | −40167.5 | −1.56800 | ||||||||
\(870\) | −407.391 | −0.0158757 | ||||||||
\(871\) | 2568.34 | 0.0999139 | ||||||||
\(872\) | −18037.5 | −0.700491 | ||||||||
\(873\) | 24120.9 | 0.935131 | ||||||||
\(874\) | 6453.73 | 0.249772 | ||||||||
\(875\) | −4403.49 | −0.170131 | ||||||||
\(876\) | 6453.57 | 0.248911 | ||||||||
\(877\) | 39786.3 | 1.53191 | 0.765956 | − | 0.642893i | \(-0.222266\pi\) | ||||
0.765956 | + | 0.642893i | \(0.222266\pi\) | |||||||
\(878\) | 29184.2 | 1.12177 | ||||||||
\(879\) | 41049.1 | 1.57514 | ||||||||
\(880\) | −6699.64 | −0.256642 | ||||||||
\(881\) | 38834.0 | 1.48508 | 0.742538 | − | 0.669804i | \(-0.233622\pi\) | ||||
0.742538 | + | 0.669804i | \(0.233622\pi\) | |||||||
\(882\) | 13689.3 | 0.522611 | ||||||||
\(883\) | −5483.65 | −0.208992 | −0.104496 | − | 0.994525i | \(-0.533323\pi\) | ||||
−0.104496 | + | 0.994525i | \(0.533323\pi\) | |||||||
\(884\) | 2050.55 | 0.0780175 | ||||||||
\(885\) | 1141.99 | 0.0433756 | ||||||||
\(886\) | 12265.5 | 0.465088 | ||||||||
\(887\) | 21289.7 | 0.805905 | 0.402953 | − | 0.915221i | \(-0.367984\pi\) | ||||
0.402953 | + | 0.915221i | \(0.367984\pi\) | |||||||
\(888\) | −50817.5 | −1.92041 | ||||||||
\(889\) | 10261.9 | 0.387148 | ||||||||
\(890\) | −2192.29 | −0.0825681 | ||||||||
\(891\) | −50493.8 | −1.89855 | ||||||||
\(892\) | 6184.17 | 0.232131 | ||||||||
\(893\) | −25369.2 | −0.950671 | ||||||||
\(894\) | −36758.2 | −1.37514 | ||||||||
\(895\) | 3507.50 | 0.130997 | ||||||||
\(896\) | −22703.0 | −0.846488 | ||||||||
\(897\) | −4117.73 | −0.153274 | ||||||||
\(898\) | 45495.3 | 1.69064 | ||||||||
\(899\) | 2434.41 | 0.0903140 | ||||||||
\(900\) | −6038.76 | −0.223658 | ||||||||
\(901\) | −38320.4 | −1.41691 | ||||||||
\(902\) | 60281.5 | 2.22523 | ||||||||
\(903\) | −4034.04 | −0.148665 | ||||||||
\(904\) | 40194.0 | 1.47880 | ||||||||
\(905\) | 1949.13 | 0.0715927 | ||||||||
\(906\) | −31857.7 | −1.16821 | ||||||||
\(907\) | 16875.4 | 0.617794 | 0.308897 | − | 0.951095i | \(-0.400040\pi\) | ||||
0.308897 | + | 0.951095i | \(0.400040\pi\) | |||||||
\(908\) | 4139.51 | 0.151293 | ||||||||
\(909\) | −37504.9 | −1.36849 | ||||||||
\(910\) | 1080.79 | 0.0393711 | ||||||||
\(911\) | 17586.7 | 0.639597 | 0.319799 | − | 0.947486i | \(-0.396385\pi\) | ||||
0.319799 | + | 0.947486i | \(0.396385\pi\) | |||||||
\(912\) | 37768.4 | 1.37131 | ||||||||
\(913\) | −85354.4 | −3.09400 | ||||||||
\(914\) | 5571.94 | 0.201645 | ||||||||
\(915\) | 2152.15 | 0.0777574 | ||||||||
\(916\) | 3003.77 | 0.108349 | ||||||||
\(917\) | 24381.0 | 0.878005 | ||||||||
\(918\) | −2496.11 | −0.0897428 | ||||||||
\(919\) | −43891.7 | −1.57547 | −0.787733 | − | 0.616017i | \(-0.788745\pi\) | ||||
−0.787733 | + | 0.616017i | \(0.788745\pi\) | |||||||
\(920\) | 769.196 | 0.0275648 | ||||||||
\(921\) | −36826.1 | −1.31755 | ||||||||
\(922\) | −24073.7 | −0.859898 | ||||||||
\(923\) | 17880.8 | 0.637653 | ||||||||
\(924\) | 11931.7 | 0.424810 | ||||||||
\(925\) | 45555.6 | 1.61931 | ||||||||
\(926\) | 18794.5 | 0.666984 | ||||||||
\(927\) | 32779.9 | 1.16142 | ||||||||
\(928\) | 1142.16 | 0.0404024 | ||||||||
\(929\) | −41161.8 | −1.45369 | −0.726844 | − | 0.686803i | \(-0.759013\pi\) | ||||
−0.726844 | + | 0.686803i | \(0.759013\pi\) | |||||||
\(930\) | −5754.65 | −0.202906 | ||||||||
\(931\) | 11993.9 | 0.422217 | ||||||||
\(932\) | 5890.79 | 0.207038 | ||||||||
\(933\) | −7556.08 | −0.265139 | ||||||||
\(934\) | −484.175 | −0.0169622 | ||||||||
\(935\) | −4780.18 | −0.167197 | ||||||||
\(936\) | −9180.95 | −0.320608 | ||||||||
\(937\) | 41754.1 | 1.45576 | 0.727880 | − | 0.685705i | \(-0.240506\pi\) | ||||
0.727880 | + | 0.685705i | \(0.240506\pi\) | |||||||
\(938\) | 5467.82 | 0.190331 | ||||||||
\(939\) | 30855.0 | 1.07233 | ||||||||
\(940\) | 983.633 | 0.0341304 | ||||||||
\(941\) | −37587.5 | −1.30214 | −0.651071 | − | 0.759016i | \(-0.725680\pi\) | ||||
−0.651071 | + | 0.759016i | \(0.725680\pi\) | |||||||
\(942\) | −66749.8 | −2.30873 | ||||||||
\(943\) | −8728.76 | −0.301429 | ||||||||
\(944\) | −8811.06 | −0.303788 | ||||||||
\(945\) | −259.289 | −0.00892559 | ||||||||
\(946\) | 8790.98 | 0.302135 | ||||||||
\(947\) | −25689.0 | −0.881500 | −0.440750 | − | 0.897630i | \(-0.645287\pi\) | ||||
−0.440750 | + | 0.897630i | \(0.645287\pi\) | |||||||
\(948\) | −8779.67 | −0.300792 | ||||||||
\(949\) | −8795.66 | −0.300863 | ||||||||
\(950\) | −26845.7 | −0.916830 | ||||||||
\(951\) | 42750.5 | 1.45771 | ||||||||
\(952\) | −13419.4 | −0.456853 | ||||||||
\(953\) | −10527.3 | −0.357831 | −0.178916 | − | 0.983864i | \(-0.557259\pi\) | ||||
−0.178916 | + | 0.983864i | \(0.557259\pi\) | |||||||
\(954\) | −55814.5 | −1.89419 | ||||||||
\(955\) | 560.682 | 0.0189982 | ||||||||
\(956\) | 6718.44 | 0.227291 | ||||||||
\(957\) | 6129.75 | 0.207050 | ||||||||
\(958\) | 35777.2 | 1.20659 | ||||||||
\(959\) | −24207.9 | −0.815136 | ||||||||
\(960\) | 3265.93 | 0.109799 | ||||||||
\(961\) | 4596.60 | 0.154295 | ||||||||
\(962\) | −22531.1 | −0.755126 | ||||||||
\(963\) | −15275.1 | −0.511144 | ||||||||
\(964\) | −8830.41 | −0.295029 | ||||||||
\(965\) | −4239.15 | −0.141413 | ||||||||
\(966\) | −8766.35 | −0.291980 | ||||||||
\(967\) | 4292.71 | 0.142755 | 0.0713776 | − | 0.997449i | \(-0.477260\pi\) | ||||
0.0713776 | + | 0.997449i | \(0.477260\pi\) | |||||||
\(968\) | 54567.5 | 1.81184 | ||||||||
\(969\) | 26947.7 | 0.893380 | ||||||||
\(970\) | −4157.63 | −0.137622 | ||||||||
\(971\) | −41459.8 | −1.37025 | −0.685123 | − | 0.728427i | \(-0.740252\pi\) | ||||
−0.685123 | + | 0.728427i | \(0.740252\pi\) | |||||||
\(972\) | −10262.1 | −0.338638 | ||||||||
\(973\) | −36729.8 | −1.21018 | ||||||||
\(974\) | 8983.13 | 0.295522 | ||||||||
\(975\) | 17128.6 | 0.562618 | ||||||||
\(976\) | −16605.1 | −0.544585 | ||||||||
\(977\) | 3577.72 | 0.117156 | 0.0585779 | − | 0.998283i | \(-0.481343\pi\) | ||||
0.0585779 | + | 0.998283i | \(0.481343\pi\) | |||||||
\(978\) | 3782.36 | 0.123667 | ||||||||
\(979\) | 32985.9 | 1.07685 | ||||||||
\(980\) | −465.035 | −0.0151582 | ||||||||
\(981\) | −23641.3 | −0.769427 | ||||||||
\(982\) | 26344.2 | 0.856088 | ||||||||
\(983\) | 50532.3 | 1.63960 | 0.819802 | − | 0.572647i | \(-0.194083\pi\) | ||||
0.819802 | + | 0.572647i | \(0.194083\pi\) | |||||||
\(984\) | −40503.0 | −1.31218 | ||||||||
\(985\) | 2673.87 | 0.0864939 | ||||||||
\(986\) | 2242.70 | 0.0724363 | ||||||||
\(987\) | 34460.0 | 1.11132 | ||||||||
\(988\) | 2616.77 | 0.0842618 | ||||||||
\(989\) | −1272.93 | −0.0409271 | ||||||||
\(990\) | −6962.45 | −0.223516 | ||||||||
\(991\) | 46280.6 | 1.48350 | 0.741752 | − | 0.670674i | \(-0.233995\pi\) | ||||
0.741752 | + | 0.670674i | \(0.233995\pi\) | |||||||
\(992\) | 16133.8 | 0.516379 | ||||||||
\(993\) | 3670.76 | 0.117309 | ||||||||
\(994\) | 38067.0 | 1.21470 | ||||||||
\(995\) | 622.101 | 0.0198210 | ||||||||
\(996\) | −18656.5 | −0.593527 | ||||||||
\(997\) | 53334.8 | 1.69421 | 0.847107 | − | 0.531423i | \(-0.178342\pi\) | ||||
0.847107 | + | 0.531423i | \(0.178342\pi\) | |||||||
\(998\) | −55526.9 | −1.76119 | ||||||||
\(999\) | 5405.39 | 0.171190 |
(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 | 43.4.a.b.1.2 | ✓ | 6 | |
3.2 | odd | 2 | 387.4.a.h.1.5 | 6 | |||
4.3 | odd | 2 | 688.4.a.i.1.2 | 6 | |||
5.4 | even | 2 | 1075.4.a.b.1.5 | 6 | |||
7.6 | odd | 2 | 2107.4.a.c.1.2 | 6 | |||
43.42 | odd | 2 | 1849.4.a.c.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.a.b.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
387.4.a.h.1.5 | 6 | 3.2 | odd | 2 | |||
688.4.a.i.1.2 | 6 | 4.3 | odd | 2 | |||
1075.4.a.b.1.5 | 6 | 5.4 | even | 2 | |||
1849.4.a.c.1.5 | 6 | 43.42 | odd | 2 | |||
2107.4.a.c.1.2 | 6 | 7.6 | odd | 2 |