Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 48 x^{13} + 44 x^{12} + 872 x^{11} - 707 x^{10} - 7580 x^{9} + 5112 x^{8} + 33191 x^{7} - 16428 x^{6} - 71361 x^{5} + 21747 x^{4} + 65434 x^{3} - 11840 x^{2} + \cdots + 2048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(-3.01123\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.01123 | 1.34666 | 0.673332 | − | 0.739341i | \(-0.264863\pi\) | ||||
0.673332 | + | 0.739341i | \(0.264863\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.871929 | −0.329558 | −0.164779 | − | 0.986331i | \(-0.552691\pi\) | ||||
−0.164779 | + | 0.986331i | \(0.552691\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.01123 | 0.952235 | ||||||||
\(11\) | −3.54795 | −1.06975 | −0.534874 | − | 0.844932i | \(-0.679641\pi\) | ||||
−0.534874 | + | 0.844932i | \(0.679641\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −0.871929 | −0.233033 | ||||||||
\(15\) | −3.01123 | −0.777496 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.08800 | −0.263879 | −0.131939 | − | 0.991258i | \(-0.542120\pi\) | ||||
−0.131939 | + | 0.991258i | \(0.542120\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −2.36288 | −0.542083 | −0.271041 | − | 0.962568i | \(-0.587368\pi\) | ||||
−0.271041 | + | 0.962568i | \(0.587368\pi\) | |||||||
\(20\) | 3.01123 | 0.673332 | ||||||||
\(21\) | 0.871929 | 0.190270 | ||||||||
\(22\) | −3.54795 | −0.756426 | ||||||||
\(23\) | 6.14753 | 1.28185 | 0.640924 | − | 0.767604i | \(-0.278551\pi\) | ||||
0.640924 | + | 0.767604i | \(0.278551\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 4.06751 | 0.813501 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.871929 | −0.164779 | ||||||||
\(29\) | −2.17058 | −0.403066 | −0.201533 | − | 0.979482i | \(-0.564592\pi\) | ||||
−0.201533 | + | 0.979482i | \(0.564592\pi\) | |||||||
\(30\) | −3.01123 | −0.549773 | ||||||||
\(31\) | 0.257032 | 0.0461643 | 0.0230822 | − | 0.999734i | \(-0.492652\pi\) | ||||
0.0230822 | + | 0.999734i | \(0.492652\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.54795 | 0.617619 | ||||||||
\(34\) | −1.08800 | −0.186591 | ||||||||
\(35\) | −2.62558 | −0.443804 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.01359 | −0.331032 | −0.165516 | − | 0.986207i | \(-0.552929\pi\) | ||||
−0.165516 | + | 0.986207i | \(0.552929\pi\) | |||||||
\(38\) | −2.36288 | −0.383311 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 3.01123 | 0.476117 | ||||||||
\(41\) | 8.60323 | 1.34360 | 0.671800 | − | 0.740733i | \(-0.265522\pi\) | ||||
0.671800 | + | 0.740733i | \(0.265522\pi\) | |||||||
\(42\) | 0.871929 | 0.134542 | ||||||||
\(43\) | −1.44174 | −0.219863 | −0.109932 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109932 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(44\) | −3.54795 | −0.534874 | ||||||||
\(45\) | 3.01123 | 0.448888 | ||||||||
\(46\) | 6.14753 | 0.906404 | ||||||||
\(47\) | 8.61755 | 1.25700 | 0.628500 | − | 0.777810i | \(-0.283669\pi\) | ||||
0.628500 | + | 0.777810i | \(0.283669\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.23974 | −0.891391 | ||||||||
\(50\) | 4.06751 | 0.575232 | ||||||||
\(51\) | 1.08800 | 0.152351 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 8.32354 | 1.14333 | 0.571663 | − | 0.820488i | \(-0.306298\pi\) | ||||
0.571663 | + | 0.820488i | \(0.306298\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −10.6837 | −1.44059 | ||||||||
\(56\) | −0.871929 | −0.116516 | ||||||||
\(57\) | 2.36288 | 0.312972 | ||||||||
\(58\) | −2.17058 | −0.285011 | ||||||||
\(59\) | 6.35243 | 0.827016 | 0.413508 | − | 0.910501i | \(-0.364303\pi\) | ||||
0.413508 | + | 0.910501i | \(0.364303\pi\) | |||||||
\(60\) | −3.01123 | −0.388748 | ||||||||
\(61\) | 15.0315 | 1.92458 | 0.962290 | − | 0.272026i | \(-0.0876935\pi\) | ||||
0.962290 | + | 0.272026i | \(0.0876935\pi\) | |||||||
\(62\) | 0.257032 | 0.0326431 | ||||||||
\(63\) | −0.871929 | −0.109853 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.01123 | −0.373497 | ||||||||
\(66\) | 3.54795 | 0.436723 | ||||||||
\(67\) | −4.89108 | −0.597541 | −0.298770 | − | 0.954325i | \(-0.596576\pi\) | ||||
−0.298770 | + | 0.954325i | \(0.596576\pi\) | |||||||
\(68\) | −1.08800 | −0.131939 | ||||||||
\(69\) | −6.14753 | −0.740075 | ||||||||
\(70\) | −2.62558 | −0.313817 | ||||||||
\(71\) | −6.82395 | −0.809853 | −0.404927 | − | 0.914349i | \(-0.632703\pi\) | ||||
−0.404927 | + | 0.914349i | \(0.632703\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 15.2479 | 1.78463 | 0.892315 | − | 0.451414i | \(-0.149080\pi\) | ||||
0.892315 | + | 0.451414i | \(0.149080\pi\) | |||||||
\(74\) | −2.01359 | −0.234075 | ||||||||
\(75\) | −4.06751 | −0.469675 | ||||||||
\(76\) | −2.36288 | −0.271041 | ||||||||
\(77\) | 3.09356 | 0.352544 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −5.43391 | −0.611362 | −0.305681 | − | 0.952134i | \(-0.598884\pi\) | ||||
−0.305681 | + | 0.952134i | \(0.598884\pi\) | |||||||
\(80\) | 3.01123 | 0.336666 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.60323 | 0.950068 | ||||||||
\(83\) | −6.99737 | −0.768062 | −0.384031 | − | 0.923320i | \(-0.625464\pi\) | ||||
−0.384031 | + | 0.923320i | \(0.625464\pi\) | |||||||
\(84\) | 0.871929 | 0.0951352 | ||||||||
\(85\) | −3.27622 | −0.355356 | ||||||||
\(86\) | −1.44174 | −0.155467 | ||||||||
\(87\) | 2.17058 | 0.232710 | ||||||||
\(88\) | −3.54795 | −0.378213 | ||||||||
\(89\) | 13.7319 | 1.45557 | 0.727787 | − | 0.685803i | \(-0.240549\pi\) | ||||
0.727787 | + | 0.685803i | \(0.240549\pi\) | |||||||
\(90\) | 3.01123 | 0.317412 | ||||||||
\(91\) | 0.871929 | 0.0914030 | ||||||||
\(92\) | 6.14753 | 0.640924 | ||||||||
\(93\) | −0.257032 | −0.0266530 | ||||||||
\(94\) | 8.61755 | 0.888833 | ||||||||
\(95\) | −7.11519 | −0.730003 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 14.3069 | 1.45264 | 0.726322 | − | 0.687355i | \(-0.241228\pi\) | ||||
0.726322 | + | 0.687355i | \(0.241228\pi\) | |||||||
\(98\) | −6.23974 | −0.630309 | ||||||||
\(99\) | −3.54795 | −0.356583 | ||||||||
\(100\) | 4.06751 | 0.406751 | ||||||||
\(101\) | 12.5408 | 1.24786 | 0.623929 | − | 0.781481i | \(-0.285535\pi\) | ||||
0.623929 | + | 0.781481i | \(0.285535\pi\) | |||||||
\(102\) | 1.08800 | 0.107728 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 2.62558 | 0.256230 | ||||||||
\(106\) | 8.32354 | 0.808454 | ||||||||
\(107\) | 6.50708 | 0.629063 | 0.314531 | − | 0.949247i | \(-0.398153\pi\) | ||||
0.314531 | + | 0.949247i | \(0.398153\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 11.0157 | 1.05511 | 0.527557 | − | 0.849520i | \(-0.323108\pi\) | ||||
0.527557 | + | 0.849520i | \(0.323108\pi\) | |||||||
\(110\) | −10.6837 | −1.01865 | ||||||||
\(111\) | 2.01359 | 0.191121 | ||||||||
\(112\) | −0.871929 | −0.0823895 | ||||||||
\(113\) | 8.84167 | 0.831754 | 0.415877 | − | 0.909421i | \(-0.363475\pi\) | ||||
0.415877 | + | 0.909421i | \(0.363475\pi\) | |||||||
\(114\) | 2.36288 | 0.221304 | ||||||||
\(115\) | 18.5116 | 1.72622 | ||||||||
\(116\) | −2.17058 | −0.201533 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 6.35243 | 0.584789 | ||||||||
\(119\) | 0.948659 | 0.0869634 | ||||||||
\(120\) | −3.01123 | −0.274886 | ||||||||
\(121\) | 1.58796 | 0.144360 | ||||||||
\(122\) | 15.0315 | 1.36088 | ||||||||
\(123\) | −8.60323 | −0.775728 | ||||||||
\(124\) | 0.257032 | 0.0230822 | ||||||||
\(125\) | −2.80795 | −0.251151 | ||||||||
\(126\) | −0.871929 | −0.0776776 | ||||||||
\(127\) | 6.76430 | 0.600234 | 0.300117 | − | 0.953902i | \(-0.402974\pi\) | ||||
0.300117 | + | 0.953902i | \(0.402974\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.44174 | 0.126938 | ||||||||
\(130\) | −3.01123 | −0.264102 | ||||||||
\(131\) | 19.9488 | 1.74293 | 0.871466 | − | 0.490456i | \(-0.163170\pi\) | ||||
0.871466 | + | 0.490456i | \(0.163170\pi\) | |||||||
\(132\) | 3.54795 | 0.308810 | ||||||||
\(133\) | 2.06027 | 0.178648 | ||||||||
\(134\) | −4.89108 | −0.422525 | ||||||||
\(135\) | −3.01123 | −0.259165 | ||||||||
\(136\) | −1.08800 | −0.0932953 | ||||||||
\(137\) | −21.0698 | −1.80011 | −0.900055 | − | 0.435775i | \(-0.856474\pi\) | ||||
−0.900055 | + | 0.435775i | \(0.856474\pi\) | |||||||
\(138\) | −6.14753 | −0.523312 | ||||||||
\(139\) | 11.4453 | 0.970777 | 0.485389 | − | 0.874299i | \(-0.338678\pi\) | ||||
0.485389 | + | 0.874299i | \(0.338678\pi\) | |||||||
\(140\) | −2.62558 | −0.221902 | ||||||||
\(141\) | −8.61755 | −0.725729 | ||||||||
\(142\) | −6.82395 | −0.572653 | ||||||||
\(143\) | 3.54795 | 0.296695 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −6.53610 | −0.542794 | ||||||||
\(146\) | 15.2479 | 1.26192 | ||||||||
\(147\) | 6.23974 | 0.514645 | ||||||||
\(148\) | −2.01359 | −0.165516 | ||||||||
\(149\) | −16.5724 | −1.35766 | −0.678830 | − | 0.734295i | \(-0.737513\pi\) | ||||
−0.678830 | + | 0.734295i | \(0.737513\pi\) | |||||||
\(150\) | −4.06751 | −0.332111 | ||||||||
\(151\) | 1.15504 | 0.0939960 | 0.0469980 | − | 0.998895i | \(-0.485035\pi\) | ||||
0.0469980 | + | 0.998895i | \(0.485035\pi\) | |||||||
\(152\) | −2.36288 | −0.191655 | ||||||||
\(153\) | −1.08800 | −0.0879596 | ||||||||
\(154\) | 3.09356 | 0.249286 | ||||||||
\(155\) | 0.773983 | 0.0621678 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 3.32560 | 0.265412 | 0.132706 | − | 0.991155i | \(-0.457633\pi\) | ||||
0.132706 | + | 0.991155i | \(0.457633\pi\) | |||||||
\(158\) | −5.43391 | −0.432298 | ||||||||
\(159\) | −8.32354 | −0.660100 | ||||||||
\(160\) | 3.01123 | 0.238059 | ||||||||
\(161\) | −5.36021 | −0.422443 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −10.0530 | −0.787409 | −0.393704 | − | 0.919237i | \(-0.628807\pi\) | ||||
−0.393704 | + | 0.919237i | \(0.628807\pi\) | |||||||
\(164\) | 8.60323 | 0.671800 | ||||||||
\(165\) | 10.6837 | 0.831725 | ||||||||
\(166\) | −6.99737 | −0.543102 | ||||||||
\(167\) | 9.56882 | 0.740458 | 0.370229 | − | 0.928941i | \(-0.379279\pi\) | ||||
0.370229 | + | 0.928941i | \(0.379279\pi\) | |||||||
\(168\) | 0.871929 | 0.0672708 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −3.27622 | −0.251275 | ||||||||
\(171\) | −2.36288 | −0.180694 | ||||||||
\(172\) | −1.44174 | −0.109932 | ||||||||
\(173\) | −7.30957 | −0.555737 | −0.277868 | − | 0.960619i | \(-0.589628\pi\) | ||||
−0.277868 | + | 0.960619i | \(0.589628\pi\) | |||||||
\(174\) | 2.17058 | 0.164551 | ||||||||
\(175\) | −3.54658 | −0.268096 | ||||||||
\(176\) | −3.54795 | −0.267437 | ||||||||
\(177\) | −6.35243 | −0.477478 | ||||||||
\(178\) | 13.7319 | 1.02925 | ||||||||
\(179\) | 11.1967 | 0.836882 | 0.418441 | − | 0.908244i | \(-0.362577\pi\) | ||||
0.418441 | + | 0.908244i | \(0.362577\pi\) | |||||||
\(180\) | 3.01123 | 0.224444 | ||||||||
\(181\) | 1.94900 | 0.144868 | 0.0724340 | − | 0.997373i | \(-0.476923\pi\) | ||||
0.0724340 | + | 0.997373i | \(0.476923\pi\) | |||||||
\(182\) | 0.871929 | 0.0646317 | ||||||||
\(183\) | −15.0315 | −1.11116 | ||||||||
\(184\) | 6.14753 | 0.453202 | ||||||||
\(185\) | −6.06337 | −0.445788 | ||||||||
\(186\) | −0.257032 | −0.0188465 | ||||||||
\(187\) | 3.86017 | 0.282284 | ||||||||
\(188\) | 8.61755 | 0.628500 | ||||||||
\(189\) | 0.871929 | 0.0634235 | ||||||||
\(190\) | −7.11519 | −0.516190 | ||||||||
\(191\) | −10.9502 | −0.792330 | −0.396165 | − | 0.918179i | \(-0.629659\pi\) | ||||
−0.396165 | + | 0.918179i | \(0.629659\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −5.43921 | −0.391523 | −0.195761 | − | 0.980652i | \(-0.562718\pi\) | ||||
−0.195761 | + | 0.980652i | \(0.562718\pi\) | |||||||
\(194\) | 14.3069 | 1.02717 | ||||||||
\(195\) | 3.01123 | 0.215639 | ||||||||
\(196\) | −6.23974 | −0.445696 | ||||||||
\(197\) | 21.7761 | 1.55148 | 0.775740 | − | 0.631052i | \(-0.217377\pi\) | ||||
0.775740 | + | 0.631052i | \(0.217377\pi\) | |||||||
\(198\) | −3.54795 | −0.252142 | ||||||||
\(199\) | −13.6495 | −0.967586 | −0.483793 | − | 0.875182i | \(-0.660741\pi\) | ||||
−0.483793 | + | 0.875182i | \(0.660741\pi\) | |||||||
\(200\) | 4.06751 | 0.287616 | ||||||||
\(201\) | 4.89108 | 0.344990 | ||||||||
\(202\) | 12.5408 | 0.882369 | ||||||||
\(203\) | 1.89259 | 0.132834 | ||||||||
\(204\) | 1.08800 | 0.0761753 | ||||||||
\(205\) | 25.9063 | 1.80938 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | 6.14753 | 0.427283 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 8.38340 | 0.579892 | ||||||||
\(210\) | 2.62558 | 0.181182 | ||||||||
\(211\) | −19.2055 | −1.32216 | −0.661081 | − | 0.750315i | \(-0.729902\pi\) | ||||
−0.661081 | + | 0.750315i | \(0.729902\pi\) | |||||||
\(212\) | 8.32354 | 0.571663 | ||||||||
\(213\) | 6.82395 | 0.467569 | ||||||||
\(214\) | 6.50708 | 0.444815 | ||||||||
\(215\) | −4.34141 | −0.296081 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −0.224114 | −0.0152138 | ||||||||
\(218\) | 11.0157 | 0.746078 | ||||||||
\(219\) | −15.2479 | −1.03036 | ||||||||
\(220\) | −10.6837 | −0.720295 | ||||||||
\(221\) | 1.08800 | 0.0731868 | ||||||||
\(222\) | 2.01359 | 0.135143 | ||||||||
\(223\) | 7.76423 | 0.519931 | 0.259966 | − | 0.965618i | \(-0.416289\pi\) | ||||
0.259966 | + | 0.965618i | \(0.416289\pi\) | |||||||
\(224\) | −0.871929 | −0.0582582 | ||||||||
\(225\) | 4.06751 | 0.271167 | ||||||||
\(226\) | 8.84167 | 0.588139 | ||||||||
\(227\) | −9.20208 | −0.610764 | −0.305382 | − | 0.952230i | \(-0.598784\pi\) | ||||
−0.305382 | + | 0.952230i | \(0.598784\pi\) | |||||||
\(228\) | 2.36288 | 0.156486 | ||||||||
\(229\) | −22.1657 | −1.46475 | −0.732375 | − | 0.680902i | \(-0.761588\pi\) | ||||
−0.732375 | + | 0.680902i | \(0.761588\pi\) | |||||||
\(230\) | 18.5116 | 1.22062 | ||||||||
\(231\) | −3.09356 | −0.203541 | ||||||||
\(232\) | −2.17058 | −0.142505 | ||||||||
\(233\) | −16.5704 | −1.08556 | −0.542780 | − | 0.839875i | \(-0.682628\pi\) | ||||
−0.542780 | + | 0.839875i | \(0.682628\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 25.9494 | 1.69275 | ||||||||
\(236\) | 6.35243 | 0.413508 | ||||||||
\(237\) | 5.43391 | 0.352970 | ||||||||
\(238\) | 0.948659 | 0.0614924 | ||||||||
\(239\) | 21.6746 | 1.40201 | 0.701007 | − | 0.713155i | \(-0.252734\pi\) | ||||
0.701007 | + | 0.713155i | \(0.252734\pi\) | |||||||
\(240\) | −3.01123 | −0.194374 | ||||||||
\(241\) | −16.7333 | −1.07789 | −0.538943 | − | 0.842342i | \(-0.681176\pi\) | ||||
−0.538943 | + | 0.842342i | \(0.681176\pi\) | |||||||
\(242\) | 1.58796 | 0.102078 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 15.0315 | 0.962290 | ||||||||
\(245\) | −18.7893 | −1.20040 | ||||||||
\(246\) | −8.60323 | −0.548522 | ||||||||
\(247\) | 2.36288 | 0.150347 | ||||||||
\(248\) | 0.257032 | 0.0163216 | ||||||||
\(249\) | 6.99737 | 0.443441 | ||||||||
\(250\) | −2.80795 | −0.177590 | ||||||||
\(251\) | 23.0103 | 1.45240 | 0.726200 | − | 0.687483i | \(-0.241285\pi\) | ||||
0.726200 | + | 0.687483i | \(0.241285\pi\) | |||||||
\(252\) | −0.871929 | −0.0549263 | ||||||||
\(253\) | −21.8111 | −1.37125 | ||||||||
\(254\) | 6.76430 | 0.424430 | ||||||||
\(255\) | 3.27622 | 0.205165 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.89130 | −0.305111 | −0.152556 | − | 0.988295i | \(-0.548750\pi\) | ||||
−0.152556 | + | 0.988295i | \(0.548750\pi\) | |||||||
\(258\) | 1.44174 | 0.0897587 | ||||||||
\(259\) | 1.75570 | 0.109094 | ||||||||
\(260\) | −3.01123 | −0.186749 | ||||||||
\(261\) | −2.17058 | −0.134355 | ||||||||
\(262\) | 19.9488 | 1.23244 | ||||||||
\(263\) | −5.62766 | −0.347016 | −0.173508 | − | 0.984832i | \(-0.555510\pi\) | ||||
−0.173508 | + | 0.984832i | \(0.555510\pi\) | |||||||
\(264\) | 3.54795 | 0.218361 | ||||||||
\(265\) | 25.0641 | 1.53968 | ||||||||
\(266\) | 2.06027 | 0.126323 | ||||||||
\(267\) | −13.7319 | −0.840377 | ||||||||
\(268\) | −4.89108 | −0.298770 | ||||||||
\(269\) | −9.72299 | −0.592821 | −0.296411 | − | 0.955061i | \(-0.595790\pi\) | ||||
−0.296411 | + | 0.955061i | \(0.595790\pi\) | |||||||
\(270\) | −3.01123 | −0.183258 | ||||||||
\(271\) | −0.275577 | −0.0167401 | −0.00837007 | − | 0.999965i | \(-0.502664\pi\) | ||||
−0.00837007 | + | 0.999965i | \(0.502664\pi\) | |||||||
\(272\) | −1.08800 | −0.0659697 | ||||||||
\(273\) | −0.871929 | −0.0527715 | ||||||||
\(274\) | −21.0698 | −1.27287 | ||||||||
\(275\) | −14.4313 | −0.870241 | ||||||||
\(276\) | −6.14753 | −0.370038 | ||||||||
\(277\) | 9.98438 | 0.599903 | 0.299951 | − | 0.953954i | \(-0.403030\pi\) | ||||
0.299951 | + | 0.953954i | \(0.403030\pi\) | |||||||
\(278\) | 11.4453 | 0.686443 | ||||||||
\(279\) | 0.257032 | 0.0153881 | ||||||||
\(280\) | −2.62558 | −0.156908 | ||||||||
\(281\) | 10.8011 | 0.644338 | 0.322169 | − | 0.946682i | \(-0.395588\pi\) | ||||
0.322169 | + | 0.946682i | \(0.395588\pi\) | |||||||
\(282\) | −8.61755 | −0.513168 | ||||||||
\(283\) | −6.93304 | −0.412126 | −0.206063 | − | 0.978539i | \(-0.566065\pi\) | ||||
−0.206063 | + | 0.978539i | \(0.566065\pi\) | |||||||
\(284\) | −6.82395 | −0.404927 | ||||||||
\(285\) | 7.11519 | 0.421467 | ||||||||
\(286\) | 3.54795 | 0.209795 | ||||||||
\(287\) | −7.50141 | −0.442794 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −15.8163 | −0.930368 | ||||||||
\(290\) | −6.53610 | −0.383813 | ||||||||
\(291\) | −14.3069 | −0.838684 | ||||||||
\(292\) | 15.2479 | 0.892315 | ||||||||
\(293\) | −0.802976 | −0.0469104 | −0.0234552 | − | 0.999725i | \(-0.507467\pi\) | ||||
−0.0234552 | + | 0.999725i | \(0.507467\pi\) | |||||||
\(294\) | 6.23974 | 0.363909 | ||||||||
\(295\) | 19.1286 | 1.11371 | ||||||||
\(296\) | −2.01359 | −0.117037 | ||||||||
\(297\) | 3.54795 | 0.205873 | ||||||||
\(298\) | −16.5724 | −0.960011 | ||||||||
\(299\) | −6.14753 | −0.355521 | ||||||||
\(300\) | −4.06751 | −0.234838 | ||||||||
\(301\) | 1.25709 | 0.0724577 | ||||||||
\(302\) | 1.15504 | 0.0664652 | ||||||||
\(303\) | −12.5408 | −0.720451 | ||||||||
\(304\) | −2.36288 | −0.135521 | ||||||||
\(305\) | 45.2632 | 2.59176 | ||||||||
\(306\) | −1.08800 | −0.0621968 | ||||||||
\(307\) | 0.918828 | 0.0524403 | 0.0262201 | − | 0.999656i | \(-0.491653\pi\) | ||||
0.0262201 | + | 0.999656i | \(0.491653\pi\) | |||||||
\(308\) | 3.09356 | 0.176272 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 0.773983 | 0.0439593 | ||||||||
\(311\) | −22.0719 | −1.25158 | −0.625792 | − | 0.779990i | \(-0.715224\pi\) | ||||
−0.625792 | + | 0.779990i | \(0.715224\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −15.5057 | −0.876436 | −0.438218 | − | 0.898869i | \(-0.644390\pi\) | ||||
−0.438218 | + | 0.898869i | \(0.644390\pi\) | |||||||
\(314\) | 3.32560 | 0.187674 | ||||||||
\(315\) | −2.62558 | −0.147935 | ||||||||
\(316\) | −5.43391 | −0.305681 | ||||||||
\(317\) | 26.8110 | 1.50585 | 0.752927 | − | 0.658104i | \(-0.228641\pi\) | ||||
0.752927 | + | 0.658104i | \(0.228641\pi\) | |||||||
\(318\) | −8.32354 | −0.466761 | ||||||||
\(319\) | 7.70110 | 0.431179 | ||||||||
\(320\) | 3.01123 | 0.168333 | ||||||||
\(321\) | −6.50708 | −0.363190 | ||||||||
\(322\) | −5.36021 | −0.298713 | ||||||||
\(323\) | 2.57082 | 0.143044 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.06751 | −0.225625 | ||||||||
\(326\) | −10.0530 | −0.556782 | ||||||||
\(327\) | −11.0157 | −0.609170 | ||||||||
\(328\) | 8.60323 | 0.475034 | ||||||||
\(329\) | −7.51389 | −0.414254 | ||||||||
\(330\) | 10.6837 | 0.588118 | ||||||||
\(331\) | 3.71332 | 0.204102 | 0.102051 | − | 0.994779i | \(-0.467459\pi\) | ||||
0.102051 | + | 0.994779i | \(0.467459\pi\) | |||||||
\(332\) | −6.99737 | −0.384031 | ||||||||
\(333\) | −2.01359 | −0.110344 | ||||||||
\(334\) | 9.56882 | 0.523583 | ||||||||
\(335\) | −14.7282 | −0.804686 | ||||||||
\(336\) | 0.871929 | 0.0475676 | ||||||||
\(337\) | 8.97722 | 0.489021 | 0.244510 | − | 0.969647i | \(-0.421373\pi\) | ||||
0.244510 | + | 0.969647i | \(0.421373\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −8.84167 | −0.480214 | ||||||||
\(340\) | −3.27622 | −0.177678 | ||||||||
\(341\) | −0.911938 | −0.0493842 | ||||||||
\(342\) | −2.36288 | −0.127770 | ||||||||
\(343\) | 11.5441 | 0.623323 | ||||||||
\(344\) | −1.44174 | −0.0777333 | ||||||||
\(345\) | −18.5116 | −0.996632 | ||||||||
\(346\) | −7.30957 | −0.392965 | ||||||||
\(347\) | −11.5432 | −0.619672 | −0.309836 | − | 0.950790i | \(-0.600274\pi\) | ||||
−0.309836 | + | 0.950790i | \(0.600274\pi\) | |||||||
\(348\) | 2.17058 | 0.116355 | ||||||||
\(349\) | 0.844753 | 0.0452186 | 0.0226093 | − | 0.999744i | \(-0.492803\pi\) | ||||
0.0226093 | + | 0.999744i | \(0.492803\pi\) | |||||||
\(350\) | −3.54658 | −0.189572 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −3.54795 | −0.189106 | ||||||||
\(353\) | 19.3423 | 1.02949 | 0.514744 | − | 0.857344i | \(-0.327887\pi\) | ||||
0.514744 | + | 0.857344i | \(0.327887\pi\) | |||||||
\(354\) | −6.35243 | −0.337628 | ||||||||
\(355\) | −20.5485 | −1.09060 | ||||||||
\(356\) | 13.7319 | 0.727787 | ||||||||
\(357\) | −0.948659 | −0.0502083 | ||||||||
\(358\) | 11.1967 | 0.591765 | ||||||||
\(359\) | 10.1494 | 0.535663 | 0.267831 | − | 0.963466i | \(-0.413693\pi\) | ||||
0.267831 | + | 0.963466i | \(0.413693\pi\) | |||||||
\(360\) | 3.01123 | 0.158706 | ||||||||
\(361\) | −13.4168 | −0.706146 | ||||||||
\(362\) | 1.94900 | 0.102437 | ||||||||
\(363\) | −1.58796 | −0.0833463 | ||||||||
\(364\) | 0.871929 | 0.0457015 | ||||||||
\(365\) | 45.9149 | 2.40330 | ||||||||
\(366\) | −15.0315 | −0.785707 | ||||||||
\(367\) | −7.35480 | −0.383917 | −0.191959 | − | 0.981403i | \(-0.561484\pi\) | ||||
−0.191959 | + | 0.981403i | \(0.561484\pi\) | |||||||
\(368\) | 6.14753 | 0.320462 | ||||||||
\(369\) | 8.60323 | 0.447867 | ||||||||
\(370\) | −6.06337 | −0.315220 | ||||||||
\(371\) | −7.25753 | −0.376792 | ||||||||
\(372\) | −0.257032 | −0.0133265 | ||||||||
\(373\) | −0.00733682 | −0.000379886 0 | −0.000189943 | − | 1.00000i | \(-0.500060\pi\) | ||||
−0.000189943 | 1.00000i | \(0.500060\pi\) | ||||||||
\(374\) | 3.86017 | 0.199605 | ||||||||
\(375\) | 2.80795 | 0.145002 | ||||||||
\(376\) | 8.61755 | 0.444416 | ||||||||
\(377\) | 2.17058 | 0.111790 | ||||||||
\(378\) | 0.871929 | 0.0448472 | ||||||||
\(379\) | −17.2292 | −0.885004 | −0.442502 | − | 0.896768i | \(-0.645909\pi\) | ||||
−0.442502 | + | 0.896768i | \(0.645909\pi\) | |||||||
\(380\) | −7.11519 | −0.365002 | ||||||||
\(381\) | −6.76430 | −0.346545 | ||||||||
\(382\) | −10.9502 | −0.560262 | ||||||||
\(383\) | −37.0826 | −1.89483 | −0.947417 | − | 0.320003i | \(-0.896316\pi\) | ||||
−0.947417 | + | 0.320003i | \(0.896316\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 9.31542 | 0.474758 | ||||||||
\(386\) | −5.43921 | −0.276849 | ||||||||
\(387\) | −1.44174 | −0.0732877 | ||||||||
\(388\) | 14.3069 | 0.726322 | ||||||||
\(389\) | 16.4678 | 0.834949 | 0.417474 | − | 0.908689i | \(-0.362915\pi\) | ||||
0.417474 | + | 0.908689i | \(0.362915\pi\) | |||||||
\(390\) | 3.01123 | 0.152480 | ||||||||
\(391\) | −6.68851 | −0.338253 | ||||||||
\(392\) | −6.23974 | −0.315154 | ||||||||
\(393\) | −19.9488 | −1.00628 | ||||||||
\(394\) | 21.7761 | 1.09706 | ||||||||
\(395\) | −16.3627 | −0.823299 | ||||||||
\(396\) | −3.54795 | −0.178291 | ||||||||
\(397\) | 33.6723 | 1.68996 | 0.844982 | − | 0.534795i | \(-0.179611\pi\) | ||||
0.844982 | + | 0.534795i | \(0.179611\pi\) | |||||||
\(398\) | −13.6495 | −0.684187 | ||||||||
\(399\) | −2.06027 | −0.103142 | ||||||||
\(400\) | 4.06751 | 0.203375 | ||||||||
\(401\) | −18.2404 | −0.910882 | −0.455441 | − | 0.890266i | \(-0.650518\pi\) | ||||
−0.455441 | + | 0.890266i | \(0.650518\pi\) | |||||||
\(402\) | 4.89108 | 0.243945 | ||||||||
\(403\) | −0.257032 | −0.0128037 | ||||||||
\(404\) | 12.5408 | 0.623929 | ||||||||
\(405\) | 3.01123 | 0.149629 | ||||||||
\(406\) | 1.89259 | 0.0939275 | ||||||||
\(407\) | 7.14411 | 0.354120 | ||||||||
\(408\) | 1.08800 | 0.0538640 | ||||||||
\(409\) | −24.8804 | −1.23025 | −0.615127 | − | 0.788428i | \(-0.710895\pi\) | ||||
−0.615127 | + | 0.788428i | \(0.710895\pi\) | |||||||
\(410\) | 25.9063 | 1.27942 | ||||||||
\(411\) | 21.0698 | 1.03929 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | −5.53887 | −0.272550 | ||||||||
\(414\) | 6.14753 | 0.302135 | ||||||||
\(415\) | −21.0707 | −1.03432 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −11.4453 | −0.560478 | ||||||||
\(418\) | 8.38340 | 0.410046 | ||||||||
\(419\) | 1.72810 | 0.0844232 | 0.0422116 | − | 0.999109i | \(-0.486560\pi\) | ||||
0.0422116 | + | 0.999109i | \(0.486560\pi\) | |||||||
\(420\) | 2.62558 | 0.128115 | ||||||||
\(421\) | 40.5952 | 1.97849 | 0.989245 | − | 0.146266i | \(-0.0467255\pi\) | ||||
0.989245 | + | 0.146266i | \(0.0467255\pi\) | |||||||
\(422\) | −19.2055 | −0.934909 | ||||||||
\(423\) | 8.61755 | 0.419000 | ||||||||
\(424\) | 8.32354 | 0.404227 | ||||||||
\(425\) | −4.42545 | −0.214666 | ||||||||
\(426\) | 6.82395 | 0.330621 | ||||||||
\(427\) | −13.1064 | −0.634261 | ||||||||
\(428\) | 6.50708 | 0.314531 | ||||||||
\(429\) | −3.54795 | −0.171297 | ||||||||
\(430\) | −4.34141 | −0.209361 | ||||||||
\(431\) | −21.6324 | −1.04199 | −0.520997 | − | 0.853559i | \(-0.674440\pi\) | ||||
−0.520997 | + | 0.853559i | \(0.674440\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 2.23507 | 0.107411 | 0.0537054 | − | 0.998557i | \(-0.482897\pi\) | ||||
0.0537054 | + | 0.998557i | \(0.482897\pi\) | |||||||
\(434\) | −0.224114 | −0.0107578 | ||||||||
\(435\) | 6.53610 | 0.313382 | ||||||||
\(436\) | 11.0157 | 0.527557 | ||||||||
\(437\) | −14.5259 | −0.694868 | ||||||||
\(438\) | −15.2479 | −0.728572 | ||||||||
\(439\) | −28.8935 | −1.37901 | −0.689505 | − | 0.724281i | \(-0.742172\pi\) | ||||
−0.689505 | + | 0.724281i | \(0.742172\pi\) | |||||||
\(440\) | −10.6837 | −0.509325 | ||||||||
\(441\) | −6.23974 | −0.297130 | ||||||||
\(442\) | 1.08800 | 0.0517509 | ||||||||
\(443\) | 18.5915 | 0.883308 | 0.441654 | − | 0.897186i | \(-0.354392\pi\) | ||||
0.441654 | + | 0.897186i | \(0.354392\pi\) | |||||||
\(444\) | 2.01359 | 0.0955606 | ||||||||
\(445\) | 41.3498 | 1.96017 | ||||||||
\(446\) | 7.76423 | 0.367647 | ||||||||
\(447\) | 16.5724 | 0.783846 | ||||||||
\(448\) | −0.871929 | −0.0411948 | ||||||||
\(449\) | −0.663272 | −0.0313018 | −0.0156509 | − | 0.999878i | \(-0.504982\pi\) | ||||
−0.0156509 | + | 0.999878i | \(0.504982\pi\) | |||||||
\(450\) | 4.06751 | 0.191744 | ||||||||
\(451\) | −30.5239 | −1.43731 | ||||||||
\(452\) | 8.84167 | 0.415877 | ||||||||
\(453\) | −1.15504 | −0.0542686 | ||||||||
\(454\) | −9.20208 | −0.431875 | ||||||||
\(455\) | 2.62558 | 0.123089 | ||||||||
\(456\) | 2.36288 | 0.110652 | ||||||||
\(457\) | 5.01979 | 0.234816 | 0.117408 | − | 0.993084i | \(-0.462542\pi\) | ||||
0.117408 | + | 0.993084i | \(0.462542\pi\) | |||||||
\(458\) | −22.1657 | −1.03573 | ||||||||
\(459\) | 1.08800 | 0.0507835 | ||||||||
\(460\) | 18.5116 | 0.863109 | ||||||||
\(461\) | 38.2064 | 1.77945 | 0.889725 | − | 0.456497i | \(-0.150896\pi\) | ||||
0.889725 | + | 0.456497i | \(0.150896\pi\) | |||||||
\(462\) | −3.09356 | −0.143925 | ||||||||
\(463\) | 14.6836 | 0.682403 | 0.341201 | − | 0.939990i | \(-0.389166\pi\) | ||||
0.341201 | + | 0.939990i | \(0.389166\pi\) | |||||||
\(464\) | −2.17058 | −0.100766 | ||||||||
\(465\) | −0.773983 | −0.0358926 | ||||||||
\(466\) | −16.5704 | −0.767607 | ||||||||
\(467\) | −0.537681 | −0.0248809 | −0.0124405 | − | 0.999923i | \(-0.503960\pi\) | ||||
−0.0124405 | + | 0.999923i | \(0.503960\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 4.26468 | 0.196924 | ||||||||
\(470\) | 25.9494 | 1.19696 | ||||||||
\(471\) | −3.32560 | −0.153235 | ||||||||
\(472\) | 6.35243 | 0.292394 | ||||||||
\(473\) | 5.11522 | 0.235198 | ||||||||
\(474\) | 5.43391 | 0.249588 | ||||||||
\(475\) | −9.61105 | −0.440985 | ||||||||
\(476\) | 0.948659 | 0.0434817 | ||||||||
\(477\) | 8.32354 | 0.381109 | ||||||||
\(478\) | 21.6746 | 0.991373 | ||||||||
\(479\) | −35.3522 | −1.61528 | −0.807642 | − | 0.589673i | \(-0.799257\pi\) | ||||
−0.807642 | + | 0.589673i | \(0.799257\pi\) | |||||||
\(480\) | −3.01123 | −0.137443 | ||||||||
\(481\) | 2.01359 | 0.0918116 | ||||||||
\(482\) | −16.7333 | −0.762181 | ||||||||
\(483\) | 5.36021 | 0.243898 | ||||||||
\(484\) | 1.58796 | 0.0721800 | ||||||||
\(485\) | 43.0813 | 1.95622 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 5.58605 | 0.253128 | 0.126564 | − | 0.991958i | \(-0.459605\pi\) | ||||
0.126564 | + | 0.991958i | \(0.459605\pi\) | |||||||
\(488\) | 15.0315 | 0.680442 | ||||||||
\(489\) | 10.0530 | 0.454611 | ||||||||
\(490\) | −18.7893 | −0.848814 | ||||||||
\(491\) | 8.79074 | 0.396721 | 0.198360 | − | 0.980129i | \(-0.436438\pi\) | ||||
0.198360 | + | 0.980129i | \(0.436438\pi\) | |||||||
\(492\) | −8.60323 | −0.387864 | ||||||||
\(493\) | 2.36159 | 0.106361 | ||||||||
\(494\) | 2.36288 | 0.106311 | ||||||||
\(495\) | −10.6837 | −0.480197 | ||||||||
\(496\) | 0.257032 | 0.0115411 | ||||||||
\(497\) | 5.94999 | 0.266894 | ||||||||
\(498\) | 6.99737 | 0.313560 | ||||||||
\(499\) | −5.15866 | −0.230933 | −0.115467 | − | 0.993311i | \(-0.536836\pi\) | ||||
−0.115467 | + | 0.993311i | \(0.536836\pi\) | |||||||
\(500\) | −2.80795 | −0.125575 | ||||||||
\(501\) | −9.56882 | −0.427503 | ||||||||
\(502\) | 23.0103 | 1.02700 | ||||||||
\(503\) | −5.12429 | −0.228481 | −0.114240 | − | 0.993453i | \(-0.536443\pi\) | ||||
−0.114240 | + | 0.993453i | \(0.536443\pi\) | |||||||
\(504\) | −0.871929 | −0.0388388 | ||||||||
\(505\) | 37.7633 | 1.68044 | ||||||||
\(506\) | −21.8111 | −0.969623 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 6.76430 | 0.300117 | ||||||||
\(509\) | 10.2395 | 0.453858 | 0.226929 | − | 0.973911i | \(-0.427132\pi\) | ||||
0.226929 | + | 0.973911i | \(0.427132\pi\) | |||||||
\(510\) | 3.27622 | 0.145073 | ||||||||
\(511\) | −13.2951 | −0.588139 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.36288 | 0.104324 | ||||||||
\(514\) | −4.89130 | −0.215746 | ||||||||
\(515\) | −3.01123 | −0.132691 | ||||||||
\(516\) | 1.44174 | 0.0634690 | ||||||||
\(517\) | −30.5747 | −1.34467 | ||||||||
\(518\) | 1.75570 | 0.0771412 | ||||||||
\(519\) | 7.30957 | 0.320855 | ||||||||
\(520\) | −3.01123 | −0.132051 | ||||||||
\(521\) | −28.3680 | −1.24282 | −0.621412 | − | 0.783484i | \(-0.713441\pi\) | ||||
−0.621412 | + | 0.783484i | \(0.713441\pi\) | |||||||
\(522\) | −2.17058 | −0.0950035 | ||||||||
\(523\) | 7.52975 | 0.329253 | 0.164627 | − | 0.986356i | \(-0.447358\pi\) | ||||
0.164627 | + | 0.986356i | \(0.447358\pi\) | |||||||
\(524\) | 19.9488 | 0.871466 | ||||||||
\(525\) | 3.54658 | 0.154785 | ||||||||
\(526\) | −5.62766 | −0.245377 | ||||||||
\(527\) | −0.279651 | −0.0121818 | ||||||||
\(528\) | 3.54795 | 0.154405 | ||||||||
\(529\) | 14.7921 | 0.643135 | ||||||||
\(530\) | 25.0641 | 1.08871 | ||||||||
\(531\) | 6.35243 | 0.275672 | ||||||||
\(532\) | 2.06027 | 0.0893239 | ||||||||
\(533\) | −8.60323 | −0.372647 | ||||||||
\(534\) | −13.7319 | −0.594236 | ||||||||
\(535\) | 19.5943 | 0.847136 | ||||||||
\(536\) | −4.89108 | −0.211263 | ||||||||
\(537\) | −11.1967 | −0.483174 | ||||||||
\(538\) | −9.72299 | −0.419188 | ||||||||
\(539\) | 22.1383 | 0.953564 | ||||||||
\(540\) | −3.01123 | −0.129583 | ||||||||
\(541\) | 34.4659 | 1.48181 | 0.740903 | − | 0.671613i | \(-0.234398\pi\) | ||||
0.740903 | + | 0.671613i | \(0.234398\pi\) | |||||||
\(542\) | −0.275577 | −0.0118371 | ||||||||
\(543\) | −1.94900 | −0.0836396 | ||||||||
\(544\) | −1.08800 | −0.0466476 | ||||||||
\(545\) | 33.1708 | 1.42088 | ||||||||
\(546\) | −0.871929 | −0.0373151 | ||||||||
\(547\) | −18.3243 | −0.783490 | −0.391745 | − | 0.920074i | \(-0.628128\pi\) | ||||
−0.391745 | + | 0.920074i | \(0.628128\pi\) | |||||||
\(548\) | −21.0698 | −0.900055 | ||||||||
\(549\) | 15.0315 | 0.641527 | ||||||||
\(550\) | −14.4313 | −0.615354 | ||||||||
\(551\) | 5.12882 | 0.218495 | ||||||||
\(552\) | −6.14753 | −0.261656 | ||||||||
\(553\) | 4.73798 | 0.201479 | ||||||||
\(554\) | 9.98438 | 0.424195 | ||||||||
\(555\) | 6.06337 | 0.257376 | ||||||||
\(556\) | 11.4453 | 0.485389 | ||||||||
\(557\) | 6.68277 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(558\) | 0.257032 | 0.0108810 | ||||||||
\(559\) | 1.44174 | 0.0609790 | ||||||||
\(560\) | −2.62558 | −0.110951 | ||||||||
\(561\) | −3.86017 | −0.162977 | ||||||||
\(562\) | 10.8011 | 0.455615 | ||||||||
\(563\) | 24.3222 | 1.02506 | 0.512528 | − | 0.858670i | \(-0.328709\pi\) | ||||
0.512528 | + | 0.858670i | \(0.328709\pi\) | |||||||
\(564\) | −8.61755 | −0.362864 | ||||||||
\(565\) | 26.6243 | 1.12009 | ||||||||
\(566\) | −6.93304 | −0.291417 | ||||||||
\(567\) | −0.871929 | −0.0366176 | ||||||||
\(568\) | −6.82395 | −0.286326 | ||||||||
\(569\) | 12.3646 | 0.518353 | 0.259176 | − | 0.965830i | \(-0.416549\pi\) | ||||
0.259176 | + | 0.965830i | \(0.416549\pi\) | |||||||
\(570\) | 7.11519 | 0.298023 | ||||||||
\(571\) | −32.7042 | −1.36863 | −0.684314 | − | 0.729187i | \(-0.739898\pi\) | ||||
−0.684314 | + | 0.729187i | \(0.739898\pi\) | |||||||
\(572\) | 3.54795 | 0.148347 | ||||||||
\(573\) | 10.9502 | 0.457452 | ||||||||
\(574\) | −7.50141 | −0.313103 | ||||||||
\(575\) | 25.0051 | 1.04279 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 40.8430 | 1.70032 | 0.850159 | − | 0.526527i | \(-0.176506\pi\) | ||||
0.850159 | + | 0.526527i | \(0.176506\pi\) | |||||||
\(578\) | −15.8163 | −0.657869 | ||||||||
\(579\) | 5.43921 | 0.226046 | ||||||||
\(580\) | −6.53610 | −0.271397 | ||||||||
\(581\) | 6.10121 | 0.253121 | ||||||||
\(582\) | −14.3069 | −0.593039 | ||||||||
\(583\) | −29.5315 | −1.22307 | ||||||||
\(584\) | 15.2479 | 0.630962 | ||||||||
\(585\) | −3.01123 | −0.124499 | ||||||||
\(586\) | −0.802976 | −0.0331706 | ||||||||
\(587\) | −4.37148 | −0.180430 | −0.0902151 | − | 0.995922i | \(-0.528755\pi\) | ||||
−0.0902151 | + | 0.995922i | \(0.528755\pi\) | |||||||
\(588\) | 6.23974 | 0.257323 | ||||||||
\(589\) | −0.607337 | −0.0250249 | ||||||||
\(590\) | 19.1286 | 0.787513 | ||||||||
\(591\) | −21.7761 | −0.895748 | ||||||||
\(592\) | −2.01359 | −0.0827579 | ||||||||
\(593\) | −1.68463 | −0.0691793 | −0.0345897 | − | 0.999402i | \(-0.511012\pi\) | ||||
−0.0345897 | + | 0.999402i | \(0.511012\pi\) | |||||||
\(594\) | 3.54795 | 0.145574 | ||||||||
\(595\) | 2.85663 | 0.117110 | ||||||||
\(596\) | −16.5724 | −0.678830 | ||||||||
\(597\) | 13.6495 | 0.558636 | ||||||||
\(598\) | −6.14753 | −0.251391 | ||||||||
\(599\) | 23.8658 | 0.975132 | 0.487566 | − | 0.873086i | \(-0.337885\pi\) | ||||
0.487566 | + | 0.873086i | \(0.337885\pi\) | |||||||
\(600\) | −4.06751 | −0.166055 | ||||||||
\(601\) | −5.07650 | −0.207075 | −0.103537 | − | 0.994626i | \(-0.533016\pi\) | ||||
−0.103537 | + | 0.994626i | \(0.533016\pi\) | |||||||
\(602\) | 1.25709 | 0.0512353 | ||||||||
\(603\) | −4.89108 | −0.199180 | ||||||||
\(604\) | 1.15504 | 0.0469980 | ||||||||
\(605\) | 4.78172 | 0.194404 | ||||||||
\(606\) | −12.5408 | −0.509436 | ||||||||
\(607\) | −9.89991 | −0.401825 | −0.200912 | − | 0.979609i | \(-0.564391\pi\) | ||||
−0.200912 | + | 0.979609i | \(0.564391\pi\) | |||||||
\(608\) | −2.36288 | −0.0958276 | ||||||||
\(609\) | −1.89259 | −0.0766915 | ||||||||
\(610\) | 45.2632 | 1.83265 | ||||||||
\(611\) | −8.61755 | −0.348629 | ||||||||
\(612\) | −1.08800 | −0.0439798 | ||||||||
\(613\) | 9.11675 | 0.368222 | 0.184111 | − | 0.982905i | \(-0.441059\pi\) | ||||
0.184111 | + | 0.982905i | \(0.441059\pi\) | |||||||
\(614\) | 0.918828 | 0.0370809 | ||||||||
\(615\) | −25.9063 | −1.04464 | ||||||||
\(616\) | 3.09356 | 0.124643 | ||||||||
\(617\) | −23.4627 | −0.944575 | −0.472287 | − | 0.881445i | \(-0.656572\pi\) | ||||
−0.472287 | + | 0.881445i | \(0.656572\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | 10.6859 | 0.429503 | 0.214751 | − | 0.976669i | \(-0.431106\pi\) | ||||
0.214751 | + | 0.976669i | \(0.431106\pi\) | |||||||
\(620\) | 0.773983 | 0.0310839 | ||||||||
\(621\) | −6.14753 | −0.246692 | ||||||||
\(622\) | −22.0719 | −0.885004 | ||||||||
\(623\) | −11.9732 | −0.479696 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −28.7929 | −1.15172 | ||||||||
\(626\) | −15.5057 | −0.619734 | ||||||||
\(627\) | −8.38340 | −0.334801 | ||||||||
\(628\) | 3.32560 | 0.132706 | ||||||||
\(629\) | 2.19078 | 0.0873522 | ||||||||
\(630\) | −2.62558 | −0.104606 | ||||||||
\(631\) | 2.34265 | 0.0932596 | 0.0466298 | − | 0.998912i | \(-0.485152\pi\) | ||||
0.0466298 | + | 0.998912i | \(0.485152\pi\) | |||||||
\(632\) | −5.43391 | −0.216149 | ||||||||
\(633\) | 19.2055 | 0.763350 | ||||||||
\(634\) | 26.8110 | 1.06480 | ||||||||
\(635\) | 20.3689 | 0.808313 | ||||||||
\(636\) | −8.32354 | −0.330050 | ||||||||
\(637\) | 6.23974 | 0.247228 | ||||||||
\(638\) | 7.70110 | 0.304889 | ||||||||
\(639\) | −6.82395 | −0.269951 | ||||||||
\(640\) | 3.01123 | 0.119029 | ||||||||
\(641\) | 8.44115 | 0.333405 | 0.166703 | − | 0.986007i | \(-0.446688\pi\) | ||||
0.166703 | + | 0.986007i | \(0.446688\pi\) | |||||||
\(642\) | −6.50708 | −0.256814 | ||||||||
\(643\) | 29.9959 | 1.18292 | 0.591462 | − | 0.806333i | \(-0.298551\pi\) | ||||
0.591462 | + | 0.806333i | \(0.298551\pi\) | |||||||
\(644\) | −5.36021 | −0.211222 | ||||||||
\(645\) | 4.34141 | 0.170943 | ||||||||
\(646\) | 2.57082 | 0.101148 | ||||||||
\(647\) | 19.8516 | 0.780446 | 0.390223 | − | 0.920720i | \(-0.372398\pi\) | ||||
0.390223 | + | 0.920720i | \(0.372398\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −22.5381 | −0.884698 | ||||||||
\(650\) | −4.06751 | −0.159541 | ||||||||
\(651\) | 0.224114 | 0.00878371 | ||||||||
\(652\) | −10.0530 | −0.393704 | ||||||||
\(653\) | −12.4747 | −0.488173 | −0.244087 | − | 0.969753i | \(-0.578488\pi\) | ||||
−0.244087 | + | 0.969753i | \(0.578488\pi\) | |||||||
\(654\) | −11.0157 | −0.430748 | ||||||||
\(655\) | 60.0703 | 2.34714 | ||||||||
\(656\) | 8.60323 | 0.335900 | ||||||||
\(657\) | 15.2479 | 0.594877 | ||||||||
\(658\) | −7.51389 | −0.292922 | ||||||||
\(659\) | 28.5645 | 1.11271 | 0.556357 | − | 0.830944i | \(-0.312199\pi\) | ||||
0.556357 | + | 0.830944i | \(0.312199\pi\) | |||||||
\(660\) | 10.6837 | 0.415862 | ||||||||
\(661\) | 1.94352 | 0.0755942 | 0.0377971 | − | 0.999285i | \(-0.487966\pi\) | ||||
0.0377971 | + | 0.999285i | \(0.487966\pi\) | |||||||
\(662\) | 3.71332 | 0.144322 | ||||||||
\(663\) | −1.08800 | −0.0422544 | ||||||||
\(664\) | −6.99737 | −0.271551 | ||||||||
\(665\) | 6.20394 | 0.240578 | ||||||||
\(666\) | −2.01359 | −0.0780249 | ||||||||
\(667\) | −13.3437 | −0.516669 | ||||||||
\(668\) | 9.56882 | 0.370229 | ||||||||
\(669\) | −7.76423 | −0.300183 | ||||||||
\(670\) | −14.7282 | −0.568999 | ||||||||
\(671\) | −53.3309 | −2.05881 | ||||||||
\(672\) | 0.871929 | 0.0336354 | ||||||||
\(673\) | 29.4988 | 1.13709 | 0.568547 | − | 0.822650i | \(-0.307506\pi\) | ||||
0.568547 | + | 0.822650i | \(0.307506\pi\) | |||||||
\(674\) | 8.97722 | 0.345790 | ||||||||
\(675\) | −4.06751 | −0.156558 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −35.1531 | −1.35104 | −0.675522 | − | 0.737340i | \(-0.736082\pi\) | ||||
−0.675522 | + | 0.737340i | \(0.736082\pi\) | |||||||
\(678\) | −8.84167 | −0.339562 | ||||||||
\(679\) | −12.4746 | −0.478730 | ||||||||
\(680\) | −3.27622 | −0.125637 | ||||||||
\(681\) | 9.20208 | 0.352625 | ||||||||
\(682\) | −0.911938 | −0.0349199 | ||||||||
\(683\) | 11.0341 | 0.422207 | 0.211103 | − | 0.977464i | \(-0.432294\pi\) | ||||
0.211103 | + | 0.977464i | \(0.432294\pi\) | |||||||
\(684\) | −2.36288 | −0.0903472 | ||||||||
\(685\) | −63.4459 | −2.42414 | ||||||||
\(686\) | 11.5441 | 0.440756 | ||||||||
\(687\) | 22.1657 | 0.845674 | ||||||||
\(688\) | −1.44174 | −0.0549658 | ||||||||
\(689\) | −8.32354 | −0.317102 | ||||||||
\(690\) | −18.5116 | −0.704725 | ||||||||
\(691\) | 16.5485 | 0.629536 | 0.314768 | − | 0.949169i | \(-0.398073\pi\) | ||||
0.314768 | + | 0.949169i | \(0.398073\pi\) | |||||||
\(692\) | −7.30957 | −0.277868 | ||||||||
\(693\) | 3.09356 | 0.117515 | ||||||||
\(694\) | −11.5432 | −0.438174 | ||||||||
\(695\) | 34.4644 | 1.30731 | ||||||||
\(696\) | 2.17058 | 0.0822755 | ||||||||
\(697\) | −9.36032 | −0.354547 | ||||||||
\(698\) | 0.844753 | 0.0319744 | ||||||||
\(699\) | 16.5704 | 0.626748 | ||||||||
\(700\) | −3.54658 | −0.134048 | ||||||||
\(701\) | 43.0980 | 1.62779 | 0.813894 | − | 0.581013i | \(-0.197343\pi\) | ||||
0.813894 | + | 0.581013i | \(0.197343\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 4.75787 | 0.179447 | ||||||||
\(704\) | −3.54795 | −0.133718 | ||||||||
\(705\) | −25.9494 | −0.977312 | ||||||||
\(706\) | 19.3423 | 0.727958 | ||||||||
\(707\) | −10.9347 | −0.411242 | ||||||||
\(708\) | −6.35243 | −0.238739 | ||||||||
\(709\) | −14.8018 | −0.555892 | −0.277946 | − | 0.960597i | \(-0.589654\pi\) | ||||
−0.277946 | + | 0.960597i | \(0.589654\pi\) | |||||||
\(710\) | −20.5485 | −0.771170 | ||||||||
\(711\) | −5.43391 | −0.203787 | ||||||||
\(712\) | 13.7319 | 0.514623 | ||||||||
\(713\) | 1.58011 | 0.0591757 | ||||||||
\(714\) | −0.948659 | −0.0355027 | ||||||||
\(715\) | 10.6837 | 0.399548 | ||||||||
\(716\) | 11.1967 | 0.418441 | ||||||||
\(717\) | −21.6746 | −0.809453 | ||||||||
\(718\) | 10.1494 | 0.378771 | ||||||||
\(719\) | 6.56249 | 0.244740 | 0.122370 | − | 0.992485i | \(-0.460951\pi\) | ||||
0.122370 | + | 0.992485i | \(0.460951\pi\) | |||||||
\(720\) | 3.01123 | 0.112222 | ||||||||
\(721\) | 0.871929 | 0.0324723 | ||||||||
\(722\) | −13.4168 | −0.499321 | ||||||||
\(723\) | 16.7333 | 0.622318 | ||||||||
\(724\) | 1.94900 | 0.0724340 | ||||||||
\(725\) | −8.82883 | −0.327895 | ||||||||
\(726\) | −1.58796 | −0.0589348 | ||||||||
\(727\) | 16.4538 | 0.610239 | 0.305120 | − | 0.952314i | \(-0.401304\pi\) | ||||
0.305120 | + | 0.952314i | \(0.401304\pi\) | |||||||
\(728\) | 0.871929 | 0.0323158 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 45.9149 | 1.69939 | ||||||||
\(731\) | 1.56861 | 0.0580172 | ||||||||
\(732\) | −15.0315 | −0.555578 | ||||||||
\(733\) | −24.6565 | −0.910707 | −0.455354 | − | 0.890311i | \(-0.650487\pi\) | ||||
−0.455354 | + | 0.890311i | \(0.650487\pi\) | |||||||
\(734\) | −7.35480 | −0.271471 | ||||||||
\(735\) | 18.7893 | 0.693054 | ||||||||
\(736\) | 6.14753 | 0.226601 | ||||||||
\(737\) | 17.3533 | 0.639218 | ||||||||
\(738\) | 8.60323 | 0.316689 | ||||||||
\(739\) | −37.4776 | −1.37864 | −0.689318 | − | 0.724459i | \(-0.742090\pi\) | ||||
−0.689318 | + | 0.724459i | \(0.742090\pi\) | |||||||
\(740\) | −6.06337 | −0.222894 | ||||||||
\(741\) | −2.36288 | −0.0868027 | ||||||||
\(742\) | −7.25753 | −0.266432 | ||||||||
\(743\) | 18.1213 | 0.664807 | 0.332404 | − | 0.943137i | \(-0.392140\pi\) | ||||
0.332404 | + | 0.943137i | \(0.392140\pi\) | |||||||
\(744\) | −0.257032 | −0.00942325 | ||||||||
\(745\) | −49.9032 | −1.82831 | ||||||||
\(746\) | −0.00733682 | −0.000268620 0 | ||||||||
\(747\) | −6.99737 | −0.256021 | ||||||||
\(748\) | 3.86017 | 0.141142 | ||||||||
\(749\) | −5.67371 | −0.207313 | ||||||||
\(750\) | 2.80795 | 0.102532 | ||||||||
\(751\) | 27.8326 | 1.01563 | 0.507813 | − | 0.861468i | \(-0.330454\pi\) | ||||
0.507813 | + | 0.861468i | \(0.330454\pi\) | |||||||
\(752\) | 8.61755 | 0.314250 | ||||||||
\(753\) | −23.0103 | −0.838544 | ||||||||
\(754\) | 2.17058 | 0.0790477 | ||||||||
\(755\) | 3.47810 | 0.126581 | ||||||||
\(756\) | 0.871929 | 0.0317117 | ||||||||
\(757\) | 14.3010 | 0.519778 | 0.259889 | − | 0.965638i | \(-0.416314\pi\) | ||||
0.259889 | + | 0.965638i | \(0.416314\pi\) | |||||||
\(758\) | −17.2292 | −0.625792 | ||||||||
\(759\) | 21.8111 | 0.791694 | ||||||||
\(760\) | −7.11519 | −0.258095 | ||||||||
\(761\) | −12.3610 | −0.448085 | −0.224042 | − | 0.974579i | \(-0.571925\pi\) | ||||
−0.224042 | + | 0.974579i | \(0.571925\pi\) | |||||||
\(762\) | −6.76430 | −0.245045 | ||||||||
\(763\) | −9.60491 | −0.347721 | ||||||||
\(764\) | −10.9502 | −0.396165 | ||||||||
\(765\) | −3.27622 | −0.118452 | ||||||||
\(766\) | −37.0826 | −1.33985 | ||||||||
\(767\) | −6.35243 | −0.229373 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −9.39885 | −0.338931 | −0.169466 | − | 0.985536i | \(-0.554204\pi\) | ||||
−0.169466 | + | 0.985536i | \(0.554204\pi\) | |||||||
\(770\) | 9.31542 | 0.335705 | ||||||||
\(771\) | 4.89130 | 0.176156 | ||||||||
\(772\) | −5.43921 | −0.195761 | ||||||||
\(773\) | −31.8392 | −1.14518 | −0.572589 | − | 0.819843i | \(-0.694061\pi\) | ||||
−0.572589 | + | 0.819843i | \(0.694061\pi\) | |||||||
\(774\) | −1.44174 | −0.0518222 | ||||||||
\(775\) | 1.04548 | 0.0375548 | ||||||||
\(776\) | 14.3069 | 0.513587 | ||||||||
\(777\) | −1.75570 | −0.0629855 | ||||||||
\(778\) | 16.4678 | 0.590398 | ||||||||
\(779\) | −20.3285 | −0.728342 | ||||||||
\(780\) | 3.01123 | 0.107819 | ||||||||
\(781\) | 24.2110 | 0.866339 | ||||||||
\(782\) | −6.68851 | −0.239181 | ||||||||
\(783\) | 2.17058 | 0.0775700 | ||||||||
\(784\) | −6.23974 | −0.222848 | ||||||||
\(785\) | 10.0141 | 0.357420 | ||||||||
\(786\) | −19.9488 | −0.711549 | ||||||||
\(787\) | −0.192285 | −0.00685421 | −0.00342711 | − | 0.999994i | \(-0.501091\pi\) | ||||
−0.00342711 | + | 0.999994i | \(0.501091\pi\) | |||||||
\(788\) | 21.7761 | 0.775740 | ||||||||
\(789\) | 5.62766 | 0.200350 | ||||||||
\(790\) | −16.3627 | −0.582160 | ||||||||
\(791\) | −7.70931 | −0.274111 | ||||||||
\(792\) | −3.54795 | −0.126071 | ||||||||
\(793\) | −15.0315 | −0.533782 | ||||||||
\(794\) | 33.6723 | 1.19498 | ||||||||
\(795\) | −25.0641 | −0.888932 | ||||||||
\(796\) | −13.6495 | −0.483793 | ||||||||
\(797\) | −43.0459 | −1.52477 | −0.762383 | − | 0.647126i | \(-0.775971\pi\) | ||||
−0.762383 | + | 0.647126i | \(0.775971\pi\) | |||||||
\(798\) | −2.06027 | −0.0729327 | ||||||||
\(799\) | −9.37590 | −0.331696 | ||||||||
\(800\) | 4.06751 | 0.143808 | ||||||||
\(801\) | 13.7319 | 0.485192 | ||||||||
\(802\) | −18.2404 | −0.644091 | ||||||||
\(803\) | −54.0988 | −1.90910 | ||||||||
\(804\) | 4.89108 | 0.172495 | ||||||||
\(805\) | −16.1408 | −0.568889 | ||||||||
\(806\) | −0.257032 | −0.00905357 | ||||||||
\(807\) | 9.72299 | 0.342265 | ||||||||
\(808\) | 12.5408 | 0.441184 | ||||||||
\(809\) | −18.9263 | −0.665415 | −0.332707 | − | 0.943030i | \(-0.607962\pi\) | ||||
−0.332707 | + | 0.943030i | \(0.607962\pi\) | |||||||
\(810\) | 3.01123 | 0.105804 | ||||||||
\(811\) | −4.82654 | −0.169483 | −0.0847414 | − | 0.996403i | \(-0.527006\pi\) | ||||
−0.0847414 | + | 0.996403i | \(0.527006\pi\) | |||||||
\(812\) | 1.89259 | 0.0664168 | ||||||||
\(813\) | 0.275577 | 0.00966492 | ||||||||
\(814\) | 7.14411 | 0.250401 | ||||||||
\(815\) | −30.2718 | −1.06037 | ||||||||
\(816\) | 1.08800 | 0.0380876 | ||||||||
\(817\) | 3.40666 | 0.119184 | ||||||||
\(818\) | −24.8804 | −0.869921 | ||||||||
\(819\) | 0.871929 | 0.0304677 | ||||||||
\(820\) | 25.9063 | 0.904688 | ||||||||
\(821\) | 5.60454 | 0.195600 | 0.0977999 | − | 0.995206i | \(-0.468819\pi\) | ||||
0.0977999 | + | 0.995206i | \(0.468819\pi\) | |||||||
\(822\) | 21.0698 | 0.734892 | ||||||||
\(823\) | −52.8892 | −1.84360 | −0.921801 | − | 0.387664i | \(-0.873282\pi\) | ||||
−0.921801 | + | 0.387664i | \(0.873282\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 14.4313 | 0.502434 | ||||||||
\(826\) | −5.53887 | −0.192722 | ||||||||
\(827\) | −55.8331 | −1.94151 | −0.970753 | − | 0.240079i | \(-0.922827\pi\) | ||||
−0.970753 | + | 0.240079i | \(0.922827\pi\) | |||||||
\(828\) | 6.14753 | 0.213641 | ||||||||
\(829\) | 53.0679 | 1.84313 | 0.921563 | − | 0.388229i | \(-0.126913\pi\) | ||||
0.921563 | + | 0.388229i | \(0.126913\pi\) | |||||||
\(830\) | −21.0707 | −0.731375 | ||||||||
\(831\) | −9.98438 | −0.346354 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 6.78884 | 0.235219 | ||||||||
\(834\) | −11.4453 | −0.396318 | ||||||||
\(835\) | 28.8139 | 0.997147 | ||||||||
\(836\) | 8.38340 | 0.289946 | ||||||||
\(837\) | −0.257032 | −0.00888433 | ||||||||
\(838\) | 1.72810 | 0.0596962 | ||||||||
\(839\) | 31.5211 | 1.08823 | 0.544114 | − | 0.839011i | \(-0.316866\pi\) | ||||
0.544114 | + | 0.839011i | \(0.316866\pi\) | |||||||
\(840\) | 2.62558 | 0.0905911 | ||||||||
\(841\) | −24.2886 | −0.837538 | ||||||||
\(842\) | 40.5952 | 1.39900 | ||||||||
\(843\) | −10.8011 | −0.372008 | ||||||||
\(844\) | −19.2055 | −0.661081 | ||||||||
\(845\) | 3.01123 | 0.103589 | ||||||||
\(846\) | 8.61755 | 0.296278 | ||||||||
\(847\) | −1.38459 | −0.0475750 | ||||||||
\(848\) | 8.32354 | 0.285832 | ||||||||
\(849\) | 6.93304 | 0.237941 | ||||||||
\(850\) | −4.42545 | −0.151792 | ||||||||
\(851\) | −12.3786 | −0.424332 | ||||||||
\(852\) | 6.82395 | 0.233785 | ||||||||
\(853\) | 31.3549 | 1.07357 | 0.536787 | − | 0.843718i | \(-0.319638\pi\) | ||||
0.536787 | + | 0.843718i | \(0.319638\pi\) | |||||||
\(854\) | −13.1064 | −0.448490 | ||||||||
\(855\) | −7.11519 | −0.243334 | ||||||||
\(856\) | 6.50708 | 0.222407 | ||||||||
\(857\) | 39.4533 | 1.34770 | 0.673849 | − | 0.738869i | \(-0.264640\pi\) | ||||
0.673849 | + | 0.738869i | \(0.264640\pi\) | |||||||
\(858\) | −3.54795 | −0.121125 | ||||||||
\(859\) | 17.7902 | 0.606994 | 0.303497 | − | 0.952832i | \(-0.401846\pi\) | ||||
0.303497 | + | 0.952832i | \(0.401846\pi\) | |||||||
\(860\) | −4.34141 | −0.148041 | ||||||||
\(861\) | 7.50141 | 0.255647 | ||||||||
\(862\) | −21.6324 | −0.736801 | ||||||||
\(863\) | −10.7348 | −0.365418 | −0.182709 | − | 0.983167i | \(-0.558487\pi\) | ||||
−0.182709 | + | 0.983167i | \(0.558487\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −22.0108 | −0.748390 | ||||||||
\(866\) | 2.23507 | 0.0759509 | ||||||||
\(867\) | 15.8163 | 0.537148 | ||||||||
\(868\) | −0.224114 | −0.00760691 | ||||||||
\(869\) | 19.2792 | 0.654003 | ||||||||
\(870\) | 6.53610 | 0.221595 | ||||||||
\(871\) | 4.89108 | 0.165728 | ||||||||
\(872\) | 11.0157 | 0.373039 | ||||||||
\(873\) | 14.3069 | 0.484215 | ||||||||
\(874\) | −14.5259 | −0.491346 | ||||||||
\(875\) | 2.44833 | 0.0827687 | ||||||||
\(876\) | −15.2479 | −0.515178 | ||||||||
\(877\) | 26.3710 | 0.890486 | 0.445243 | − | 0.895410i | \(-0.353117\pi\) | ||||
0.445243 | + | 0.895410i | \(0.353117\pi\) | |||||||
\(878\) | −28.8935 | −0.975107 | ||||||||
\(879\) | 0.802976 | 0.0270837 | ||||||||
\(880\) | −10.6837 | −0.360147 | ||||||||
\(881\) | −7.45488 | −0.251161 | −0.125581 | − | 0.992083i | \(-0.540079\pi\) | ||||
−0.125581 | + | 0.992083i | \(0.540079\pi\) | |||||||
\(882\) | −6.23974 | −0.210103 | ||||||||
\(883\) | 58.9504 | 1.98384 | 0.991919 | − | 0.126871i | \(-0.0404935\pi\) | ||||
0.991919 | + | 0.126871i | \(0.0404935\pi\) | |||||||
\(884\) | 1.08800 | 0.0365934 | ||||||||
\(885\) | −19.1286 | −0.643002 | ||||||||
\(886\) | 18.5915 | 0.624593 | ||||||||
\(887\) | −43.4323 | −1.45831 | −0.729157 | − | 0.684347i | \(-0.760087\pi\) | ||||
−0.729157 | + | 0.684347i | \(0.760087\pi\) | |||||||
\(888\) | 2.01359 | 0.0675715 | ||||||||
\(889\) | −5.89798 | −0.197812 | ||||||||
\(890\) | 41.3498 | 1.38605 | ||||||||
\(891\) | −3.54795 | −0.118861 | ||||||||
\(892\) | 7.76423 | 0.259966 | ||||||||
\(893\) | −20.3623 | −0.681398 | ||||||||
\(894\) | 16.5724 | 0.554263 | ||||||||
\(895\) | 33.7159 | 1.12700 | ||||||||
\(896\) | −0.871929 | −0.0291291 | ||||||||
\(897\) | 6.14753 | 0.205260 | ||||||||
\(898\) | −0.663272 | −0.0221337 | ||||||||
\(899\) | −0.557908 | −0.0186073 | ||||||||
\(900\) | 4.06751 | 0.135584 | ||||||||
\(901\) | −9.05601 | −0.301700 | ||||||||
\(902\) | −30.5239 | −1.01633 | ||||||||
\(903\) | −1.25709 | −0.0418334 | ||||||||
\(904\) | 8.84167 | 0.294070 | ||||||||
\(905\) | 5.86888 | 0.195088 | ||||||||
\(906\) | −1.15504 | −0.0383737 | ||||||||
\(907\) | −31.4571 | −1.04452 | −0.522258 | − | 0.852787i | \(-0.674910\pi\) | ||||
−0.522258 | + | 0.852787i | \(0.674910\pi\) | |||||||
\(908\) | −9.20208 | −0.305382 | ||||||||
\(909\) | 12.5408 | 0.415953 | ||||||||
\(910\) | 2.62558 | 0.0870371 | ||||||||
\(911\) | −23.6402 | −0.783236 | −0.391618 | − | 0.920128i | \(-0.628084\pi\) | ||||
−0.391618 | + | 0.920128i | \(0.628084\pi\) | |||||||
\(912\) | 2.36288 | 0.0782429 | ||||||||
\(913\) | 24.8263 | 0.821632 | ||||||||
\(914\) | 5.01979 | 0.166040 | ||||||||
\(915\) | −45.2632 | −1.49635 | ||||||||
\(916\) | −22.1657 | −0.732375 | ||||||||
\(917\) | −17.3939 | −0.574397 | ||||||||
\(918\) | 1.08800 | 0.0359094 | ||||||||
\(919\) | 20.1374 | 0.664273 | 0.332136 | − | 0.943231i | \(-0.392231\pi\) | ||||
0.332136 | + | 0.943231i | \(0.392231\pi\) | |||||||
\(920\) | 18.5116 | 0.610310 | ||||||||
\(921\) | −0.918828 | −0.0302764 | ||||||||
\(922\) | 38.2064 | 1.25826 | ||||||||
\(923\) | 6.82395 | 0.224613 | ||||||||
\(924\) | −3.09356 | −0.101771 | ||||||||
\(925\) | −8.19028 | −0.269295 | ||||||||
\(926\) | 14.6836 | 0.482532 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −2.17058 | −0.0712526 | ||||||||
\(929\) | −30.8944 | −1.01361 | −0.506807 | − | 0.862060i | \(-0.669174\pi\) | ||||
−0.506807 | + | 0.862060i | \(0.669174\pi\) | |||||||
\(930\) | −0.773983 | −0.0253799 | ||||||||
\(931\) | 14.7438 | 0.483208 | ||||||||
\(932\) | −16.5704 | −0.542780 | ||||||||
\(933\) | 22.0719 | 0.722603 | ||||||||
\(934\) | −0.537681 | −0.0175935 | ||||||||
\(935\) | 11.6239 | 0.380141 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −41.1730 | −1.34506 | −0.672532 | − | 0.740068i | \(-0.734793\pi\) | ||||
−0.672532 | + | 0.740068i | \(0.734793\pi\) | |||||||
\(938\) | 4.26468 | 0.139247 | ||||||||
\(939\) | 15.5057 | 0.506011 | ||||||||
\(940\) | 25.9494 | 0.846377 | ||||||||
\(941\) | 23.8092 | 0.776158 | 0.388079 | − | 0.921626i | \(-0.373139\pi\) | ||||
0.388079 | + | 0.921626i | \(0.373139\pi\) | |||||||
\(942\) | −3.32560 | −0.108354 | ||||||||
\(943\) | 52.8886 | 1.72229 | ||||||||
\(944\) | 6.35243 | 0.206754 | ||||||||
\(945\) | 2.62558 | 0.0854101 | ||||||||
\(946\) | 5.11522 | 0.166310 | ||||||||
\(947\) | −43.1387 | −1.40182 | −0.700910 | − | 0.713250i | \(-0.747223\pi\) | ||||
−0.700910 | + | 0.713250i | \(0.747223\pi\) | |||||||
\(948\) | 5.43391 | 0.176485 | ||||||||
\(949\) | −15.2479 | −0.494967 | ||||||||
\(950\) | −9.61105 | −0.311824 | ||||||||
\(951\) | −26.8110 | −0.869405 | ||||||||
\(952\) | 0.948659 | 0.0307462 | ||||||||
\(953\) | 8.71067 | 0.282166 | 0.141083 | − | 0.989998i | \(-0.454942\pi\) | ||||
0.141083 | + | 0.989998i | \(0.454942\pi\) | |||||||
\(954\) | 8.32354 | 0.269485 | ||||||||
\(955\) | −32.9736 | −1.06700 | ||||||||
\(956\) | 21.6746 | 0.701007 | ||||||||
\(957\) | −7.70110 | −0.248941 | ||||||||
\(958\) | −35.3522 | −1.14218 | ||||||||
\(959\) | 18.3713 | 0.593241 | ||||||||
\(960\) | −3.01123 | −0.0971870 | ||||||||
\(961\) | −30.9339 | −0.997869 | ||||||||
\(962\) | 2.01359 | 0.0649206 | ||||||||
\(963\) | 6.50708 | 0.209688 | ||||||||
\(964\) | −16.7333 | −0.538943 | ||||||||
\(965\) | −16.3787 | −0.527249 | ||||||||
\(966\) | 5.36021 | 0.172462 | ||||||||
\(967\) | −5.99975 | −0.192939 | −0.0964694 | − | 0.995336i | \(-0.530755\pi\) | ||||
−0.0964694 | + | 0.995336i | \(0.530755\pi\) | |||||||
\(968\) | 1.58796 | 0.0510390 | ||||||||
\(969\) | −2.57082 | −0.0825866 | ||||||||
\(970\) | 43.0813 | 1.38326 | ||||||||
\(971\) | −56.2319 | −1.80457 | −0.902283 | − | 0.431144i | \(-0.858110\pi\) | ||||
−0.902283 | + | 0.431144i | \(0.858110\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −9.97948 | −0.319927 | ||||||||
\(974\) | 5.58605 | 0.178989 | ||||||||
\(975\) | 4.06751 | 0.130264 | ||||||||
\(976\) | 15.0315 | 0.481145 | ||||||||
\(977\) | 15.8848 | 0.508198 | 0.254099 | − | 0.967178i | \(-0.418221\pi\) | ||||
0.254099 | + | 0.967178i | \(0.418221\pi\) | |||||||
\(978\) | 10.0530 | 0.321458 | ||||||||
\(979\) | −48.7200 | −1.55710 | ||||||||
\(980\) | −18.7893 | −0.600202 | ||||||||
\(981\) | 11.0157 | 0.351704 | ||||||||
\(982\) | 8.79074 | 0.280524 | ||||||||
\(983\) | −33.7501 | −1.07646 | −0.538230 | − | 0.842798i | \(-0.680907\pi\) | ||||
−0.538230 | + | 0.842798i | \(0.680907\pi\) | |||||||
\(984\) | −8.60323 | −0.274261 | ||||||||
\(985\) | 65.5727 | 2.08932 | ||||||||
\(986\) | 2.36159 | 0.0752082 | ||||||||
\(987\) | 7.51389 | 0.239170 | ||||||||
\(988\) | 2.36288 | 0.0751734 | ||||||||
\(989\) | −8.86313 | −0.281831 | ||||||||
\(990\) | −10.6837 | −0.339550 | ||||||||
\(991\) | 50.6049 | 1.60752 | 0.803759 | − | 0.594954i | \(-0.202830\pi\) | ||||
0.803759 | + | 0.594954i | \(0.202830\pi\) | |||||||
\(992\) | 0.257032 | 0.00816078 | ||||||||
\(993\) | −3.71332 | −0.117839 | ||||||||
\(994\) | 5.94999 | 0.188722 | ||||||||
\(995\) | −41.1017 | −1.30301 | ||||||||
\(996\) | 6.99737 | 0.221720 | ||||||||
\(997\) | 53.0623 | 1.68050 | 0.840250 | − | 0.542199i | \(-0.182408\pi\) | ||||
0.840250 | + | 0.542199i | \(0.182408\pi\) | |||||||
\(998\) | −5.15866 | −0.163294 | ||||||||
\(999\) | 2.01359 | 0.0637070 |
(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 | 8034.2.a.bc.1.13 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.bc.1.13 | ✓ | 15 | 1.1 | even | 1 | trivial |