Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5290,2,Mod(1,5290)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5290, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5290.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5290 = 2 \cdot 5 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5290.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: | \(42.2408626693\) |
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: | \( x^{15} - 5 x^{14} - 24 x^{13} + 142 x^{12} + 184 x^{11} - 1488 x^{10} - 426 x^{9} + 7165 x^{8} - 206 x^{7} - 16453 x^{6} + 637 x^{5} + 16290 x^{4} + 1068 x^{3} - 4992 x^{2} + \cdots - 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.53931\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5290.1 |
$q$-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 | ||||||||
\(3\) | −1.53931 | −0.888720 | −0.444360 | − | 0.895848i | \(-0.646569\pi\) | ||||
−0.444360 | + | 0.895848i | \(0.646569\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.53931 | −0.628420 | ||||||||
\(7\) | −3.71769 | −1.40515 | −0.702577 | − | 0.711608i | \(-0.747967\pi\) | ||||
−0.702577 | + | 0.711608i | \(0.747967\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.630528 | −0.210176 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −5.52957 | −1.66723 | −0.833614 | − | 0.552347i | \(-0.813732\pi\) | ||||
−0.833614 | + | 0.552347i | \(0.813732\pi\) | |||||||
\(12\) | −1.53931 | −0.444360 | ||||||||
\(13\) | 2.56268 | 0.710758 | 0.355379 | − | 0.934722i | \(-0.384352\pi\) | ||||
0.355379 | + | 0.934722i | \(0.384352\pi\) | |||||||
\(14\) | −3.71769 | −0.993593 | ||||||||
\(15\) | 1.53931 | 0.397448 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.76605 | −1.39847 | −0.699237 | − | 0.714890i | \(-0.746477\pi\) | ||||
−0.699237 | + | 0.714890i | \(0.746477\pi\) | |||||||
\(18\) | −0.630528 | −0.148617 | ||||||||
\(19\) | −3.65701 | −0.838975 | −0.419487 | − | 0.907761i | \(-0.637790\pi\) | ||||
−0.419487 | + | 0.907761i | \(0.637790\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 5.72267 | 1.24879 | ||||||||
\(22\) | −5.52957 | −1.17891 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | −1.53931 | −0.314210 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.56268 | 0.502582 | ||||||||
\(27\) | 5.58850 | 1.07551 | ||||||||
\(28\) | −3.71769 | −0.702577 | ||||||||
\(29\) | 8.55120 | 1.58792 | 0.793959 | − | 0.607971i | \(-0.208016\pi\) | ||||
0.793959 | + | 0.607971i | \(0.208016\pi\) | |||||||
\(30\) | 1.53931 | 0.281038 | ||||||||
\(31\) | −9.24402 | −1.66028 | −0.830138 | − | 0.557559i | \(-0.811738\pi\) | ||||
−0.830138 | + | 0.557559i | \(0.811738\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 8.51172 | 1.48170 | ||||||||
\(34\) | −5.76605 | −0.988870 | ||||||||
\(35\) | 3.71769 | 0.628404 | ||||||||
\(36\) | −0.630528 | −0.105088 | ||||||||
\(37\) | 0.490152 | 0.0805805 | 0.0402903 | − | 0.999188i | \(-0.487172\pi\) | ||||
0.0402903 | + | 0.999188i | \(0.487172\pi\) | |||||||
\(38\) | −3.65701 | −0.593245 | ||||||||
\(39\) | −3.94475 | −0.631665 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −11.3942 | −1.77947 | −0.889735 | − | 0.456478i | \(-0.849111\pi\) | ||||
−0.889735 | + | 0.456478i | \(0.849111\pi\) | |||||||
\(42\) | 5.72267 | 0.883027 | ||||||||
\(43\) | −9.04149 | −1.37881 | −0.689407 | − | 0.724374i | \(-0.742129\pi\) | ||||
−0.689407 | + | 0.724374i | \(0.742129\pi\) | |||||||
\(44\) | −5.52957 | −0.833614 | ||||||||
\(45\) | 0.630528 | 0.0939935 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.73542 | −1.42006 | −0.710028 | − | 0.704173i | \(-0.751318\pi\) | ||||
−0.710028 | + | 0.704173i | \(0.751318\pi\) | |||||||
\(48\) | −1.53931 | −0.222180 | ||||||||
\(49\) | 6.82119 | 0.974456 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 8.87574 | 1.24285 | ||||||||
\(52\) | 2.56268 | 0.355379 | ||||||||
\(53\) | 0.824873 | 0.113305 | 0.0566525 | − | 0.998394i | \(-0.481957\pi\) | ||||
0.0566525 | + | 0.998394i | \(0.481957\pi\) | |||||||
\(54\) | 5.58850 | 0.760499 | ||||||||
\(55\) | 5.52957 | 0.745607 | ||||||||
\(56\) | −3.71769 | −0.496797 | ||||||||
\(57\) | 5.62926 | 0.745614 | ||||||||
\(58\) | 8.55120 | 1.12283 | ||||||||
\(59\) | 2.08710 | 0.271718 | 0.135859 | − | 0.990728i | \(-0.456621\pi\) | ||||
0.135859 | + | 0.990728i | \(0.456621\pi\) | |||||||
\(60\) | 1.53931 | 0.198724 | ||||||||
\(61\) | 9.46716 | 1.21215 | 0.606073 | − | 0.795409i | \(-0.292744\pi\) | ||||
0.606073 | + | 0.795409i | \(0.292744\pi\) | |||||||
\(62\) | −9.24402 | −1.17399 | ||||||||
\(63\) | 2.34410 | 0.295329 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.56268 | −0.317861 | ||||||||
\(66\) | 8.51172 | 1.04772 | ||||||||
\(67\) | −1.14674 | −0.140096 | −0.0700482 | − | 0.997544i | \(-0.522315\pi\) | ||||
−0.0700482 | + | 0.997544i | \(0.522315\pi\) | |||||||
\(68\) | −5.76605 | −0.699237 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.71769 | 0.444349 | ||||||||
\(71\) | 2.86767 | 0.340330 | 0.170165 | − | 0.985416i | \(-0.445570\pi\) | ||||
0.170165 | + | 0.985416i | \(0.445570\pi\) | |||||||
\(72\) | −0.630528 | −0.0743084 | ||||||||
\(73\) | −3.21969 | −0.376836 | −0.188418 | − | 0.982089i | \(-0.560336\pi\) | ||||
−0.188418 | + | 0.982089i | \(0.560336\pi\) | |||||||
\(74\) | 0.490152 | 0.0569790 | ||||||||
\(75\) | −1.53931 | −0.177744 | ||||||||
\(76\) | −3.65701 | −0.419487 | ||||||||
\(77\) | 20.5572 | 2.34271 | ||||||||
\(78\) | −3.94475 | −0.446655 | ||||||||
\(79\) | 6.94974 | 0.781907 | 0.390954 | − | 0.920410i | \(-0.372145\pi\) | ||||
0.390954 | + | 0.920410i | \(0.372145\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −6.71085 | −0.745650 | ||||||||
\(82\) | −11.3942 | −1.25827 | ||||||||
\(83\) | 9.86488 | 1.08281 | 0.541406 | − | 0.840762i | \(-0.317892\pi\) | ||||
0.541406 | + | 0.840762i | \(0.317892\pi\) | |||||||
\(84\) | 5.72267 | 0.624394 | ||||||||
\(85\) | 5.76605 | 0.625416 | ||||||||
\(86\) | −9.04149 | −0.974969 | ||||||||
\(87\) | −13.1629 | −1.41122 | ||||||||
\(88\) | −5.52957 | −0.589454 | ||||||||
\(89\) | 3.58473 | 0.379981 | 0.189990 | − | 0.981786i | \(-0.439154\pi\) | ||||
0.189990 | + | 0.981786i | \(0.439154\pi\) | |||||||
\(90\) | 0.630528 | 0.0664635 | ||||||||
\(91\) | −9.52722 | −0.998724 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.2294 | 1.47552 | ||||||||
\(94\) | −9.73542 | −1.00413 | ||||||||
\(95\) | 3.65701 | 0.375201 | ||||||||
\(96\) | −1.53931 | −0.157105 | ||||||||
\(97\) | 2.55727 | 0.259651 | 0.129826 | − | 0.991537i | \(-0.458558\pi\) | ||||
0.129826 | + | 0.991537i | \(0.458558\pi\) | |||||||
\(98\) | 6.82119 | 0.689044 | ||||||||
\(99\) | 3.48655 | 0.350411 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −6.99569 | −0.696097 | −0.348048 | − | 0.937477i | \(-0.613156\pi\) | ||||
−0.348048 | + | 0.937477i | \(0.613156\pi\) | |||||||
\(102\) | 8.87574 | 0.878829 | ||||||||
\(103\) | −1.74044 | −0.171491 | −0.0857455 | − | 0.996317i | \(-0.527327\pi\) | ||||
−0.0857455 | + | 0.996317i | \(0.527327\pi\) | |||||||
\(104\) | 2.56268 | 0.251291 | ||||||||
\(105\) | −5.72267 | −0.558475 | ||||||||
\(106\) | 0.824873 | 0.0801187 | ||||||||
\(107\) | 1.08182 | 0.104584 | 0.0522919 | − | 0.998632i | \(-0.483347\pi\) | ||||
0.0522919 | + | 0.998632i | \(0.483347\pi\) | |||||||
\(108\) | 5.58850 | 0.537754 | ||||||||
\(109\) | 2.33737 | 0.223880 | 0.111940 | − | 0.993715i | \(-0.464294\pi\) | ||||
0.111940 | + | 0.993715i | \(0.464294\pi\) | |||||||
\(110\) | 5.52957 | 0.527224 | ||||||||
\(111\) | −0.754496 | −0.0716136 | ||||||||
\(112\) | −3.71769 | −0.351288 | ||||||||
\(113\) | 16.0040 | 1.50553 | 0.752766 | − | 0.658288i | \(-0.228719\pi\) | ||||
0.752766 | + | 0.658288i | \(0.228719\pi\) | |||||||
\(114\) | 5.62926 | 0.527229 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.55120 | 0.793959 | ||||||||
\(117\) | −1.61584 | −0.149384 | ||||||||
\(118\) | 2.08710 | 0.192133 | ||||||||
\(119\) | 21.4364 | 1.96507 | ||||||||
\(120\) | 1.53931 | 0.140519 | ||||||||
\(121\) | 19.5762 | 1.77965 | ||||||||
\(122\) | 9.46716 | 0.857117 | ||||||||
\(123\) | 17.5391 | 1.58145 | ||||||||
\(124\) | −9.24402 | −0.830138 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.34410 | 0.208829 | ||||||||
\(127\) | −2.46423 | −0.218665 | −0.109332 | − | 0.994005i | \(-0.534871\pi\) | ||||
−0.109332 | + | 0.994005i | \(0.534871\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 13.9176 | 1.22538 | ||||||||
\(130\) | −2.56268 | −0.224762 | ||||||||
\(131\) | 21.8887 | 1.91243 | 0.956214 | − | 0.292669i | \(-0.0945433\pi\) | ||||
0.956214 | + | 0.292669i | \(0.0945433\pi\) | |||||||
\(132\) | 8.51172 | 0.740850 | ||||||||
\(133\) | 13.5956 | 1.17889 | ||||||||
\(134\) | −1.14674 | −0.0990631 | ||||||||
\(135\) | −5.58850 | −0.480982 | ||||||||
\(136\) | −5.76605 | −0.494435 | ||||||||
\(137\) | 3.01304 | 0.257421 | 0.128711 | − | 0.991682i | \(-0.458916\pi\) | ||||
0.128711 | + | 0.991682i | \(0.458916\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.93581 | −0.503469 | −0.251734 | − | 0.967796i | \(-0.581001\pi\) | ||||
−0.251734 | + | 0.967796i | \(0.581001\pi\) | |||||||
\(140\) | 3.71769 | 0.314202 | ||||||||
\(141\) | 14.9858 | 1.26203 | ||||||||
\(142\) | 2.86767 | 0.240650 | ||||||||
\(143\) | −14.1705 | −1.18500 | ||||||||
\(144\) | −0.630528 | −0.0525440 | ||||||||
\(145\) | −8.55120 | −0.710139 | ||||||||
\(146\) | −3.21969 | −0.266463 | ||||||||
\(147\) | −10.4999 | −0.866019 | ||||||||
\(148\) | 0.490152 | 0.0402903 | ||||||||
\(149\) | 1.49328 | 0.122334 | 0.0611671 | − | 0.998128i | \(-0.480518\pi\) | ||||
0.0611671 | + | 0.998128i | \(0.480518\pi\) | |||||||
\(150\) | −1.53931 | −0.125684 | ||||||||
\(151\) | −15.6386 | −1.27265 | −0.636326 | − | 0.771420i | \(-0.719547\pi\) | ||||
−0.636326 | + | 0.771420i | \(0.719547\pi\) | |||||||
\(152\) | −3.65701 | −0.296622 | ||||||||
\(153\) | 3.63566 | 0.293925 | ||||||||
\(154\) | 20.5572 | 1.65655 | ||||||||
\(155\) | 9.24402 | 0.742498 | ||||||||
\(156\) | −3.94475 | −0.315833 | ||||||||
\(157\) | 6.10683 | 0.487378 | 0.243689 | − | 0.969853i | \(-0.421642\pi\) | ||||
0.243689 | + | 0.969853i | \(0.421642\pi\) | |||||||
\(158\) | 6.94974 | 0.552892 | ||||||||
\(159\) | −1.26973 | −0.100696 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −6.71085 | −0.527254 | ||||||||
\(163\) | 16.4053 | 1.28496 | 0.642479 | − | 0.766303i | \(-0.277906\pi\) | ||||
0.642479 | + | 0.766303i | \(0.277906\pi\) | |||||||
\(164\) | −11.3942 | −0.889735 | ||||||||
\(165\) | −8.51172 | −0.662637 | ||||||||
\(166\) | 9.86488 | 0.765663 | ||||||||
\(167\) | −14.3536 | −1.11071 | −0.555357 | − | 0.831612i | \(-0.687418\pi\) | ||||
−0.555357 | + | 0.831612i | \(0.687418\pi\) | |||||||
\(168\) | 5.72267 | 0.441513 | ||||||||
\(169\) | −6.43269 | −0.494823 | ||||||||
\(170\) | 5.76605 | 0.442236 | ||||||||
\(171\) | 2.30584 | 0.176332 | ||||||||
\(172\) | −9.04149 | −0.689407 | ||||||||
\(173\) | −10.4022 | −0.790863 | −0.395432 | − | 0.918495i | \(-0.629405\pi\) | ||||
−0.395432 | + | 0.918495i | \(0.629405\pi\) | |||||||
\(174\) | −13.1629 | −0.997880 | ||||||||
\(175\) | −3.71769 | −0.281031 | ||||||||
\(176\) | −5.52957 | −0.416807 | ||||||||
\(177\) | −3.21270 | −0.241481 | ||||||||
\(178\) | 3.58473 | 0.268687 | ||||||||
\(179\) | −12.6474 | −0.945310 | −0.472655 | − | 0.881248i | \(-0.656704\pi\) | ||||
−0.472655 | + | 0.881248i | \(0.656704\pi\) | |||||||
\(180\) | 0.630528 | 0.0469968 | ||||||||
\(181\) | −4.07323 | −0.302761 | −0.151380 | − | 0.988476i | \(-0.548372\pi\) | ||||
−0.151380 | + | 0.988476i | \(0.548372\pi\) | |||||||
\(182\) | −9.52722 | −0.706205 | ||||||||
\(183\) | −14.5729 | −1.07726 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.490152 | −0.0360367 | ||||||||
\(186\) | 14.2294 | 1.04335 | ||||||||
\(187\) | 31.8838 | 2.33157 | ||||||||
\(188\) | −9.73542 | −0.710028 | ||||||||
\(189\) | −20.7763 | −1.51125 | ||||||||
\(190\) | 3.65701 | 0.265307 | ||||||||
\(191\) | −6.14225 | −0.444438 | −0.222219 | − | 0.974997i | \(-0.571330\pi\) | ||||
−0.222219 | + | 0.974997i | \(0.571330\pi\) | |||||||
\(192\) | −1.53931 | −0.111090 | ||||||||
\(193\) | 6.53510 | 0.470406 | 0.235203 | − | 0.971946i | \(-0.424424\pi\) | ||||
0.235203 | + | 0.971946i | \(0.424424\pi\) | |||||||
\(194\) | 2.55727 | 0.183601 | ||||||||
\(195\) | 3.94475 | 0.282489 | ||||||||
\(196\) | 6.82119 | 0.487228 | ||||||||
\(197\) | 4.45551 | 0.317442 | 0.158721 | − | 0.987323i | \(-0.449263\pi\) | ||||
0.158721 | + | 0.987323i | \(0.449263\pi\) | |||||||
\(198\) | 3.48655 | 0.247778 | ||||||||
\(199\) | −15.1131 | −1.07134 | −0.535671 | − | 0.844427i | \(-0.679941\pi\) | ||||
−0.535671 | + | 0.844427i | \(0.679941\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 1.76518 | 0.124507 | ||||||||
\(202\) | −6.99569 | −0.492215 | ||||||||
\(203\) | −31.7907 | −2.23127 | ||||||||
\(204\) | 8.87574 | 0.621426 | ||||||||
\(205\) | 11.3942 | 0.795803 | ||||||||
\(206\) | −1.74044 | −0.121262 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.56268 | 0.177690 | ||||||||
\(209\) | 20.2217 | 1.39876 | ||||||||
\(210\) | −5.72267 | −0.394902 | ||||||||
\(211\) | −8.59548 | −0.591737 | −0.295868 | − | 0.955229i | \(-0.595609\pi\) | ||||
−0.295868 | + | 0.955229i | \(0.595609\pi\) | |||||||
\(212\) | 0.824873 | 0.0566525 | ||||||||
\(213\) | −4.41424 | −0.302459 | ||||||||
\(214\) | 1.08182 | 0.0739520 | ||||||||
\(215\) | 9.04149 | 0.616624 | ||||||||
\(216\) | 5.58850 | 0.380250 | ||||||||
\(217\) | 34.3664 | 2.33294 | ||||||||
\(218\) | 2.33737 | 0.158307 | ||||||||
\(219\) | 4.95609 | 0.334902 | ||||||||
\(220\) | 5.52957 | 0.372804 | ||||||||
\(221\) | −14.7765 | −0.993976 | ||||||||
\(222\) | −0.754496 | −0.0506384 | ||||||||
\(223\) | 1.23633 | 0.0827906 | 0.0413953 | − | 0.999143i | \(-0.486820\pi\) | ||||
0.0413953 | + | 0.999143i | \(0.486820\pi\) | |||||||
\(224\) | −3.71769 | −0.248398 | ||||||||
\(225\) | −0.630528 | −0.0420352 | ||||||||
\(226\) | 16.0040 | 1.06457 | ||||||||
\(227\) | 21.1727 | 1.40528 | 0.702640 | − | 0.711545i | \(-0.252004\pi\) | ||||
0.702640 | + | 0.711545i | \(0.252004\pi\) | |||||||
\(228\) | 5.62926 | 0.372807 | ||||||||
\(229\) | −11.2218 | −0.741557 | −0.370779 | − | 0.928721i | \(-0.620909\pi\) | ||||
−0.370779 | + | 0.928721i | \(0.620909\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −31.6439 | −2.08202 | ||||||||
\(232\) | 8.55120 | 0.561414 | ||||||||
\(233\) | 1.43374 | 0.0939276 | 0.0469638 | − | 0.998897i | \(-0.485045\pi\) | ||||
0.0469638 | + | 0.998897i | \(0.485045\pi\) | |||||||
\(234\) | −1.61584 | −0.105631 | ||||||||
\(235\) | 9.73542 | 0.635068 | ||||||||
\(236\) | 2.08710 | 0.135859 | ||||||||
\(237\) | −10.6978 | −0.694897 | ||||||||
\(238\) | 21.4364 | 1.38951 | ||||||||
\(239\) | −6.91805 | −0.447491 | −0.223746 | − | 0.974648i | \(-0.571828\pi\) | ||||
−0.223746 | + | 0.974648i | \(0.571828\pi\) | |||||||
\(240\) | 1.53931 | 0.0993620 | ||||||||
\(241\) | −16.4852 | −1.06191 | −0.530953 | − | 0.847401i | \(-0.678166\pi\) | ||||
−0.530953 | + | 0.847401i | \(0.678166\pi\) | |||||||
\(242\) | 19.5762 | 1.25840 | ||||||||
\(243\) | −6.43544 | −0.412834 | ||||||||
\(244\) | 9.46716 | 0.606073 | ||||||||
\(245\) | −6.82119 | −0.435790 | ||||||||
\(246\) | 17.5391 | 1.11825 | ||||||||
\(247\) | −9.37172 | −0.596308 | ||||||||
\(248\) | −9.24402 | −0.586996 | ||||||||
\(249\) | −15.1851 | −0.962316 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 21.1825 | 1.33703 | 0.668513 | − | 0.743701i | \(-0.266931\pi\) | ||||
0.668513 | + | 0.743701i | \(0.266931\pi\) | |||||||
\(252\) | 2.34410 | 0.147665 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2.46423 | −0.154619 | ||||||||
\(255\) | −8.87574 | −0.555820 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.629630 | 0.0392752 | 0.0196376 | − | 0.999807i | \(-0.493749\pi\) | ||||
0.0196376 | + | 0.999807i | \(0.493749\pi\) | |||||||
\(258\) | 13.9176 | 0.866475 | ||||||||
\(259\) | −1.82223 | −0.113228 | ||||||||
\(260\) | −2.56268 | −0.158930 | ||||||||
\(261\) | −5.39177 | −0.333742 | ||||||||
\(262\) | 21.8887 | 1.35229 | ||||||||
\(263\) | 26.2962 | 1.62149 | 0.810747 | − | 0.585397i | \(-0.199061\pi\) | ||||
0.810747 | + | 0.585397i | \(0.199061\pi\) | |||||||
\(264\) | 8.51172 | 0.523860 | ||||||||
\(265\) | −0.824873 | −0.0506715 | ||||||||
\(266\) | 13.5956 | 0.833600 | ||||||||
\(267\) | −5.51801 | −0.337697 | ||||||||
\(268\) | −1.14674 | −0.0700482 | ||||||||
\(269\) | 26.6135 | 1.62266 | 0.811328 | − | 0.584591i | \(-0.198745\pi\) | ||||
0.811328 | + | 0.584591i | \(0.198745\pi\) | |||||||
\(270\) | −5.58850 | −0.340106 | ||||||||
\(271\) | 9.82645 | 0.596914 | 0.298457 | − | 0.954423i | \(-0.403528\pi\) | ||||
0.298457 | + | 0.954423i | \(0.403528\pi\) | |||||||
\(272\) | −5.76605 | −0.349618 | ||||||||
\(273\) | 14.6653 | 0.887587 | ||||||||
\(274\) | 3.01304 | 0.182024 | ||||||||
\(275\) | −5.52957 | −0.333446 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.7531 | 0.706178 | 0.353089 | − | 0.935590i | \(-0.385131\pi\) | ||||
0.353089 | + | 0.935590i | \(0.385131\pi\) | |||||||
\(278\) | −5.93581 | −0.356006 | ||||||||
\(279\) | 5.82861 | 0.348950 | ||||||||
\(280\) | 3.71769 | 0.222174 | ||||||||
\(281\) | −14.7365 | −0.879103 | −0.439552 | − | 0.898217i | \(-0.644863\pi\) | ||||
−0.439552 | + | 0.898217i | \(0.644863\pi\) | |||||||
\(282\) | 14.9858 | 0.892392 | ||||||||
\(283\) | −2.06989 | −0.123042 | −0.0615211 | − | 0.998106i | \(-0.519595\pi\) | ||||
−0.0615211 | + | 0.998106i | \(0.519595\pi\) | |||||||
\(284\) | 2.86767 | 0.170165 | ||||||||
\(285\) | −5.62926 | −0.333449 | ||||||||
\(286\) | −14.1705 | −0.837919 | ||||||||
\(287\) | 42.3599 | 2.50043 | ||||||||
\(288\) | −0.630528 | −0.0371542 | ||||||||
\(289\) | 16.2474 | 0.955727 | ||||||||
\(290\) | −8.55120 | −0.502144 | ||||||||
\(291\) | −3.93642 | −0.230757 | ||||||||
\(292\) | −3.21969 | −0.188418 | ||||||||
\(293\) | −20.4438 | −1.19434 | −0.597169 | − | 0.802115i | \(-0.703708\pi\) | ||||
−0.597169 | + | 0.802115i | \(0.703708\pi\) | |||||||
\(294\) | −10.4999 | −0.612368 | ||||||||
\(295\) | −2.08710 | −0.121516 | ||||||||
\(296\) | 0.490152 | 0.0284895 | ||||||||
\(297\) | −30.9020 | −1.79312 | ||||||||
\(298\) | 1.49328 | 0.0865033 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.53931 | −0.0888720 | ||||||||
\(301\) | 33.6134 | 1.93745 | ||||||||
\(302\) | −15.6386 | −0.899901 | ||||||||
\(303\) | 10.7685 | 0.618636 | ||||||||
\(304\) | −3.65701 | −0.209744 | ||||||||
\(305\) | −9.46716 | −0.542088 | ||||||||
\(306\) | 3.63566 | 0.207837 | ||||||||
\(307\) | −9.37242 | −0.534912 | −0.267456 | − | 0.963570i | \(-0.586183\pi\) | ||||
−0.267456 | + | 0.963570i | \(0.586183\pi\) | |||||||
\(308\) | 20.5572 | 1.17136 | ||||||||
\(309\) | 2.67908 | 0.152408 | ||||||||
\(310\) | 9.24402 | 0.525025 | ||||||||
\(311\) | 7.48356 | 0.424354 | 0.212177 | − | 0.977231i | \(-0.431945\pi\) | ||||
0.212177 | + | 0.977231i | \(0.431945\pi\) | |||||||
\(312\) | −3.94475 | −0.223327 | ||||||||
\(313\) | −2.78633 | −0.157492 | −0.0787462 | − | 0.996895i | \(-0.525092\pi\) | ||||
−0.0787462 | + | 0.996895i | \(0.525092\pi\) | |||||||
\(314\) | 6.10683 | 0.344628 | ||||||||
\(315\) | −2.34410 | −0.132075 | ||||||||
\(316\) | 6.94974 | 0.390954 | ||||||||
\(317\) | 15.8539 | 0.890442 | 0.445221 | − | 0.895421i | \(-0.353125\pi\) | ||||
0.445221 | + | 0.895421i | \(0.353125\pi\) | |||||||
\(318\) | −1.26973 | −0.0712032 | ||||||||
\(319\) | −47.2845 | −2.64742 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −1.66526 | −0.0929458 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.0865 | 1.17328 | ||||||||
\(324\) | −6.71085 | −0.372825 | ||||||||
\(325\) | 2.56268 | 0.142152 | ||||||||
\(326\) | 16.4053 | 0.908603 | ||||||||
\(327\) | −3.59794 | −0.198967 | ||||||||
\(328\) | −11.3942 | −0.629137 | ||||||||
\(329\) | 36.1932 | 1.99540 | ||||||||
\(330\) | −8.51172 | −0.468555 | ||||||||
\(331\) | −10.9915 | −0.604149 | −0.302074 | − | 0.953284i | \(-0.597679\pi\) | ||||
−0.302074 | + | 0.953284i | \(0.597679\pi\) | |||||||
\(332\) | 9.86488 | 0.541406 | ||||||||
\(333\) | −0.309055 | −0.0169361 | ||||||||
\(334\) | −14.3536 | −0.785394 | ||||||||
\(335\) | 1.14674 | 0.0626530 | ||||||||
\(336\) | 5.72267 | 0.312197 | ||||||||
\(337\) | 24.4167 | 1.33006 | 0.665030 | − | 0.746817i | \(-0.268419\pi\) | ||||
0.665030 | + | 0.746817i | \(0.268419\pi\) | |||||||
\(338\) | −6.43269 | −0.349892 | ||||||||
\(339\) | −24.6351 | −1.33800 | ||||||||
\(340\) | 5.76605 | 0.312708 | ||||||||
\(341\) | 51.1155 | 2.76806 | ||||||||
\(342\) | 2.30584 | 0.124686 | ||||||||
\(343\) | 0.664752 | 0.0358932 | ||||||||
\(344\) | −9.04149 | −0.487484 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.4022 | −0.559225 | ||||||||
\(347\) | 23.9579 | 1.28613 | 0.643063 | − | 0.765813i | \(-0.277663\pi\) | ||||
0.643063 | + | 0.765813i | \(0.277663\pi\) | |||||||
\(348\) | −13.1629 | −0.705608 | ||||||||
\(349\) | −5.85393 | −0.313354 | −0.156677 | − | 0.987650i | \(-0.550078\pi\) | ||||
−0.156677 | + | 0.987650i | \(0.550078\pi\) | |||||||
\(350\) | −3.71769 | −0.198719 | ||||||||
\(351\) | 14.3215 | 0.764426 | ||||||||
\(352\) | −5.52957 | −0.294727 | ||||||||
\(353\) | −13.8742 | −0.738452 | −0.369226 | − | 0.929340i | \(-0.620377\pi\) | ||||
−0.369226 | + | 0.929340i | \(0.620377\pi\) | |||||||
\(354\) | −3.21270 | −0.170753 | ||||||||
\(355\) | −2.86767 | −0.152200 | ||||||||
\(356\) | 3.58473 | 0.189990 | ||||||||
\(357\) | −32.9972 | −1.74640 | ||||||||
\(358\) | −12.6474 | −0.668435 | ||||||||
\(359\) | −19.9793 | −1.05447 | −0.527234 | − | 0.849720i | \(-0.676771\pi\) | ||||
−0.527234 | + | 0.849720i | \(0.676771\pi\) | |||||||
\(360\) | 0.630528 | 0.0332317 | ||||||||
\(361\) | −5.62631 | −0.296121 | ||||||||
\(362\) | −4.07323 | −0.214084 | ||||||||
\(363\) | −30.1338 | −1.58161 | ||||||||
\(364\) | −9.52722 | −0.499362 | ||||||||
\(365\) | 3.21969 | 0.168526 | ||||||||
\(366\) | −14.5729 | −0.761737 | ||||||||
\(367\) | 5.43074 | 0.283482 | 0.141741 | − | 0.989904i | \(-0.454730\pi\) | ||||
0.141741 | + | 0.989904i | \(0.454730\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.18434 | 0.374002 | ||||||||
\(370\) | −0.490152 | −0.0254818 | ||||||||
\(371\) | −3.06662 | −0.159211 | ||||||||
\(372\) | 14.2294 | 0.737760 | ||||||||
\(373\) | −30.6865 | −1.58889 | −0.794444 | − | 0.607337i | \(-0.792238\pi\) | ||||
−0.794444 | + | 0.607337i | \(0.792238\pi\) | |||||||
\(374\) | 31.8838 | 1.64867 | ||||||||
\(375\) | 1.53931 | 0.0794896 | ||||||||
\(376\) | −9.73542 | −0.502066 | ||||||||
\(377\) | 21.9140 | 1.12863 | ||||||||
\(378\) | −20.7763 | −1.06862 | ||||||||
\(379\) | 11.4897 | 0.590188 | 0.295094 | − | 0.955468i | \(-0.404649\pi\) | ||||
0.295094 | + | 0.955468i | \(0.404649\pi\) | |||||||
\(380\) | 3.65701 | 0.187600 | ||||||||
\(381\) | 3.79321 | 0.194332 | ||||||||
\(382\) | −6.14225 | −0.314265 | ||||||||
\(383\) | −10.6061 | −0.541944 | −0.270972 | − | 0.962587i | \(-0.587345\pi\) | ||||
−0.270972 | + | 0.962587i | \(0.587345\pi\) | |||||||
\(384\) | −1.53931 | −0.0785525 | ||||||||
\(385\) | −20.5572 | −1.04769 | ||||||||
\(386\) | 6.53510 | 0.332628 | ||||||||
\(387\) | 5.70091 | 0.289794 | ||||||||
\(388\) | 2.55727 | 0.129826 | ||||||||
\(389\) | −36.6757 | −1.85953 | −0.929766 | − | 0.368152i | \(-0.879991\pi\) | ||||
−0.929766 | + | 0.368152i | \(0.879991\pi\) | |||||||
\(390\) | 3.94475 | 0.199750 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 6.82119 | 0.344522 | ||||||||
\(393\) | −33.6935 | −1.69961 | ||||||||
\(394\) | 4.45551 | 0.224466 | ||||||||
\(395\) | −6.94974 | −0.349680 | ||||||||
\(396\) | 3.48655 | 0.175206 | ||||||||
\(397\) | −4.28172 | −0.214893 | −0.107447 | − | 0.994211i | \(-0.534268\pi\) | ||||
−0.107447 | + | 0.994211i | \(0.534268\pi\) | |||||||
\(398\) | −15.1131 | −0.757553 | ||||||||
\(399\) | −20.9278 | −1.04770 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 27.0327 | 1.34995 | 0.674975 | − | 0.737840i | \(-0.264154\pi\) | ||||
0.674975 | + | 0.737840i | \(0.264154\pi\) | |||||||
\(402\) | 1.76518 | 0.0880394 | ||||||||
\(403\) | −23.6894 | −1.18005 | ||||||||
\(404\) | −6.99569 | −0.348048 | ||||||||
\(405\) | 6.71085 | 0.333465 | ||||||||
\(406\) | −31.7907 | −1.57775 | ||||||||
\(407\) | −2.71033 | −0.134346 | ||||||||
\(408\) | 8.87574 | 0.439414 | ||||||||
\(409\) | −26.7573 | −1.32306 | −0.661532 | − | 0.749917i | \(-0.730094\pi\) | ||||
−0.661532 | + | 0.749917i | \(0.730094\pi\) | |||||||
\(410\) | 11.3942 | 0.562718 | ||||||||
\(411\) | −4.63800 | −0.228776 | ||||||||
\(412\) | −1.74044 | −0.0857455 | ||||||||
\(413\) | −7.75919 | −0.381805 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.86488 | −0.484248 | ||||||||
\(416\) | 2.56268 | 0.125646 | ||||||||
\(417\) | 9.13705 | 0.447443 | ||||||||
\(418\) | 20.2217 | 0.989075 | ||||||||
\(419\) | −4.58163 | −0.223827 | −0.111914 | − | 0.993718i | \(-0.535698\pi\) | ||||
−0.111914 | + | 0.993718i | \(0.535698\pi\) | |||||||
\(420\) | −5.72267 | −0.279238 | ||||||||
\(421\) | −14.5615 | −0.709686 | −0.354843 | − | 0.934926i | \(-0.615466\pi\) | ||||
−0.354843 | + | 0.934926i | \(0.615466\pi\) | |||||||
\(422\) | −8.59548 | −0.418421 | ||||||||
\(423\) | 6.13845 | 0.298462 | ||||||||
\(424\) | 0.824873 | 0.0400594 | ||||||||
\(425\) | −5.76605 | −0.279695 | ||||||||
\(426\) | −4.41424 | −0.213870 | ||||||||
\(427\) | −35.1959 | −1.70325 | ||||||||
\(428\) | 1.08182 | 0.0522919 | ||||||||
\(429\) | 21.8128 | 1.05313 | ||||||||
\(430\) | 9.04149 | 0.436019 | ||||||||
\(431\) | −8.19202 | −0.394596 | −0.197298 | − | 0.980344i | \(-0.563217\pi\) | ||||
−0.197298 | + | 0.980344i | \(0.563217\pi\) | |||||||
\(432\) | 5.58850 | 0.268877 | ||||||||
\(433\) | 4.11382 | 0.197697 | 0.0988487 | − | 0.995102i | \(-0.468484\pi\) | ||||
0.0988487 | + | 0.995102i | \(0.468484\pi\) | |||||||
\(434\) | 34.3664 | 1.64964 | ||||||||
\(435\) | 13.1629 | 0.631115 | ||||||||
\(436\) | 2.33737 | 0.111940 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 4.95609 | 0.236811 | ||||||||
\(439\) | −7.79137 | −0.371862 | −0.185931 | − | 0.982563i | \(-0.559530\pi\) | ||||
−0.185931 | + | 0.982563i | \(0.559530\pi\) | |||||||
\(440\) | 5.52957 | 0.263612 | ||||||||
\(441\) | −4.30095 | −0.204807 | ||||||||
\(442\) | −14.7765 | −0.702847 | ||||||||
\(443\) | 36.6224 | 1.73998 | 0.869991 | − | 0.493068i | \(-0.164124\pi\) | ||||
0.869991 | + | 0.493068i | \(0.164124\pi\) | |||||||
\(444\) | −0.754496 | −0.0358068 | ||||||||
\(445\) | −3.58473 | −0.169932 | ||||||||
\(446\) | 1.23633 | 0.0585418 | ||||||||
\(447\) | −2.29862 | −0.108721 | ||||||||
\(448\) | −3.71769 | −0.175644 | ||||||||
\(449\) | 3.52535 | 0.166371 | 0.0831857 | − | 0.996534i | \(-0.473491\pi\) | ||||
0.0831857 | + | 0.996534i | \(0.473491\pi\) | |||||||
\(450\) | −0.630528 | −0.0297234 | ||||||||
\(451\) | 63.0048 | 2.96678 | ||||||||
\(452\) | 16.0040 | 0.752766 | ||||||||
\(453\) | 24.0727 | 1.13103 | ||||||||
\(454\) | 21.1727 | 0.993683 | ||||||||
\(455\) | 9.52722 | 0.446643 | ||||||||
\(456\) | 5.62926 | 0.263614 | ||||||||
\(457\) | 30.5111 | 1.42725 | 0.713624 | − | 0.700529i | \(-0.247052\pi\) | ||||
0.713624 | + | 0.700529i | \(0.247052\pi\) | |||||||
\(458\) | −11.2218 | −0.524360 | ||||||||
\(459\) | −32.2236 | −1.50407 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.50868 | −0.303139 | −0.151570 | − | 0.988447i | \(-0.548433\pi\) | ||||
−0.151570 | + | 0.988447i | \(0.548433\pi\) | |||||||
\(462\) | −31.6439 | −1.47221 | ||||||||
\(463\) | 4.72959 | 0.219803 | 0.109901 | − | 0.993942i | \(-0.464946\pi\) | ||||
0.109901 | + | 0.993942i | \(0.464946\pi\) | |||||||
\(464\) | 8.55120 | 0.396980 | ||||||||
\(465\) | −14.2294 | −0.659873 | ||||||||
\(466\) | 1.43374 | 0.0664169 | ||||||||
\(467\) | 26.7107 | 1.23602 | 0.618011 | − | 0.786169i | \(-0.287939\pi\) | ||||
0.618011 | + | 0.786169i | \(0.287939\pi\) | |||||||
\(468\) | −1.61584 | −0.0746921 | ||||||||
\(469\) | 4.26321 | 0.196857 | ||||||||
\(470\) | 9.73542 | 0.449061 | ||||||||
\(471\) | −9.40030 | −0.433143 | ||||||||
\(472\) | 2.08710 | 0.0960667 | ||||||||
\(473\) | 49.9956 | 2.29880 | ||||||||
\(474\) | −10.6978 | −0.491366 | ||||||||
\(475\) | −3.65701 | −0.167795 | ||||||||
\(476\) | 21.4364 | 0.982535 | ||||||||
\(477\) | −0.520105 | −0.0238140 | ||||||||
\(478\) | −6.91805 | −0.316424 | ||||||||
\(479\) | −8.12800 | −0.371378 | −0.185689 | − | 0.982609i | \(-0.559452\pi\) | ||||
−0.185689 | + | 0.982609i | \(0.559452\pi\) | |||||||
\(480\) | 1.53931 | 0.0702595 | ||||||||
\(481\) | 1.25610 | 0.0572733 | ||||||||
\(482\) | −16.4852 | −0.750881 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.5762 | 0.889826 | ||||||||
\(485\) | −2.55727 | −0.116120 | ||||||||
\(486\) | −6.43544 | −0.291917 | ||||||||
\(487\) | −7.40083 | −0.335364 | −0.167682 | − | 0.985841i | \(-0.553628\pi\) | ||||
−0.167682 | + | 0.985841i | \(0.553628\pi\) | |||||||
\(488\) | 9.46716 | 0.428558 | ||||||||
\(489\) | −25.2527 | −1.14197 | ||||||||
\(490\) | −6.82119 | −0.308150 | ||||||||
\(491\) | −25.9839 | −1.17264 | −0.586318 | − | 0.810081i | \(-0.699423\pi\) | ||||
−0.586318 | + | 0.810081i | \(0.699423\pi\) | |||||||
\(492\) | 17.5391 | 0.790725 | ||||||||
\(493\) | −49.3067 | −2.22066 | ||||||||
\(494\) | −9.37172 | −0.421654 | ||||||||
\(495\) | −3.48655 | −0.156709 | ||||||||
\(496\) | −9.24402 | −0.415069 | ||||||||
\(497\) | −10.6611 | −0.478216 | ||||||||
\(498\) | −15.1851 | −0.680460 | ||||||||
\(499\) | −34.5272 | −1.54565 | −0.772824 | − | 0.634620i | \(-0.781157\pi\) | ||||
−0.772824 | + | 0.634620i | \(0.781157\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 22.0946 | 0.987115 | ||||||||
\(502\) | 21.1825 | 0.945420 | ||||||||
\(503\) | −6.49298 | −0.289508 | −0.144754 | − | 0.989468i | \(-0.546239\pi\) | ||||
−0.144754 | + | 0.989468i | \(0.546239\pi\) | |||||||
\(504\) | 2.34410 | 0.104415 | ||||||||
\(505\) | 6.99569 | 0.311304 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.90190 | 0.439759 | ||||||||
\(508\) | −2.46423 | −0.109332 | ||||||||
\(509\) | 29.0414 | 1.28724 | 0.643620 | − | 0.765345i | \(-0.277432\pi\) | ||||
0.643620 | + | 0.765345i | \(0.277432\pi\) | |||||||
\(510\) | −8.87574 | −0.393024 | ||||||||
\(511\) | 11.9698 | 0.529512 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −20.4372 | −0.902324 | ||||||||
\(514\) | 0.629630 | 0.0277718 | ||||||||
\(515\) | 1.74044 | 0.0766931 | ||||||||
\(516\) | 13.9176 | 0.612690 | ||||||||
\(517\) | 53.8327 | 2.36756 | ||||||||
\(518\) | −1.82223 | −0.0800643 | ||||||||
\(519\) | 16.0122 | 0.702857 | ||||||||
\(520\) | −2.56268 | −0.112381 | ||||||||
\(521\) | −30.2264 | −1.32424 | −0.662121 | − | 0.749397i | \(-0.730343\pi\) | ||||
−0.662121 | + | 0.749397i | \(0.730343\pi\) | |||||||
\(522\) | −5.39177 | −0.235991 | ||||||||
\(523\) | −15.3474 | −0.671094 | −0.335547 | − | 0.942024i | \(-0.608921\pi\) | ||||
−0.335547 | + | 0.942024i | \(0.608921\pi\) | |||||||
\(524\) | 21.8887 | 0.956214 | ||||||||
\(525\) | 5.72267 | 0.249758 | ||||||||
\(526\) | 26.2962 | 1.14657 | ||||||||
\(527\) | 53.3015 | 2.32185 | ||||||||
\(528\) | 8.51172 | 0.370425 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | −0.824873 | −0.0358302 | ||||||||
\(531\) | −1.31598 | −0.0571085 | ||||||||
\(532\) | 13.5956 | 0.589444 | ||||||||
\(533\) | −29.1995 | −1.26477 | ||||||||
\(534\) | −5.51801 | −0.238788 | ||||||||
\(535\) | −1.08182 | −0.0467713 | ||||||||
\(536\) | −1.14674 | −0.0495316 | ||||||||
\(537\) | 19.4682 | 0.840116 | ||||||||
\(538\) | 26.6135 | 1.14739 | ||||||||
\(539\) | −37.7183 | −1.62464 | ||||||||
\(540\) | −5.58850 | −0.240491 | ||||||||
\(541\) | 12.3830 | 0.532386 | 0.266193 | − | 0.963920i | \(-0.414234\pi\) | ||||
0.266193 | + | 0.963920i | \(0.414234\pi\) | |||||||
\(542\) | 9.82645 | 0.422082 | ||||||||
\(543\) | 6.26995 | 0.269070 | ||||||||
\(544\) | −5.76605 | −0.247217 | ||||||||
\(545\) | −2.33737 | −0.100122 | ||||||||
\(546\) | 14.6653 | 0.627619 | ||||||||
\(547\) | −13.3181 | −0.569439 | −0.284720 | − | 0.958611i | \(-0.591901\pi\) | ||||
−0.284720 | + | 0.958611i | \(0.591901\pi\) | |||||||
\(548\) | 3.01304 | 0.128711 | ||||||||
\(549\) | −5.96931 | −0.254764 | ||||||||
\(550\) | −5.52957 | −0.235782 | ||||||||
\(551\) | −31.2718 | −1.33222 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.8370 | −1.09870 | ||||||||
\(554\) | 11.7531 | 0.499343 | ||||||||
\(555\) | 0.754496 | 0.0320266 | ||||||||
\(556\) | −5.93581 | −0.251734 | ||||||||
\(557\) | 20.8720 | 0.884375 | 0.442188 | − | 0.896923i | \(-0.354203\pi\) | ||||
0.442188 | + | 0.896923i | \(0.354203\pi\) | |||||||
\(558\) | 5.82861 | 0.246745 | ||||||||
\(559\) | −23.1704 | −0.980004 | ||||||||
\(560\) | 3.71769 | 0.157101 | ||||||||
\(561\) | −49.0790 | −2.07212 | ||||||||
\(562\) | −14.7365 | −0.621620 | ||||||||
\(563\) | 2.67269 | 0.112641 | 0.0563203 | − | 0.998413i | \(-0.482063\pi\) | ||||
0.0563203 | + | 0.998413i | \(0.482063\pi\) | |||||||
\(564\) | 14.9858 | 0.631017 | ||||||||
\(565\) | −16.0040 | −0.673294 | ||||||||
\(566\) | −2.06989 | −0.0870040 | ||||||||
\(567\) | 24.9488 | 1.04775 | ||||||||
\(568\) | 2.86767 | 0.120325 | ||||||||
\(569\) | −17.1915 | −0.720704 | −0.360352 | − | 0.932816i | \(-0.617343\pi\) | ||||
−0.360352 | + | 0.932816i | \(0.617343\pi\) | |||||||
\(570\) | −5.62926 | −0.235784 | ||||||||
\(571\) | −26.3607 | −1.10316 | −0.551581 | − | 0.834121i | \(-0.685975\pi\) | ||||
−0.551581 | + | 0.834121i | \(0.685975\pi\) | |||||||
\(572\) | −14.1705 | −0.592498 | ||||||||
\(573\) | 9.45483 | 0.394981 | ||||||||
\(574\) | 42.3599 | 1.76807 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.630528 | −0.0262720 | ||||||||
\(577\) | 14.4867 | 0.603087 | 0.301544 | − | 0.953452i | \(-0.402498\pi\) | ||||
0.301544 | + | 0.953452i | \(0.402498\pi\) | |||||||
\(578\) | 16.2474 | 0.675801 | ||||||||
\(579\) | −10.0595 | −0.418060 | ||||||||
\(580\) | −8.55120 | −0.355069 | ||||||||
\(581\) | −36.6745 | −1.52152 | ||||||||
\(582\) | −3.93642 | −0.163170 | ||||||||
\(583\) | −4.56119 | −0.188905 | ||||||||
\(584\) | −3.21969 | −0.133232 | ||||||||
\(585\) | 1.61584 | 0.0668067 | ||||||||
\(586\) | −20.4438 | −0.844525 | ||||||||
\(587\) | 9.94004 | 0.410269 | 0.205135 | − | 0.978734i | \(-0.434237\pi\) | ||||
0.205135 | + | 0.978734i | \(0.434237\pi\) | |||||||
\(588\) | −10.4999 | −0.433010 | ||||||||
\(589\) | 33.8054 | 1.39293 | ||||||||
\(590\) | −2.08710 | −0.0859246 | ||||||||
\(591\) | −6.85841 | −0.282117 | ||||||||
\(592\) | 0.490152 | 0.0201451 | ||||||||
\(593\) | 17.2518 | 0.708445 | 0.354222 | − | 0.935161i | \(-0.384746\pi\) | ||||
0.354222 | + | 0.935161i | \(0.384746\pi\) | |||||||
\(594\) | −30.9020 | −1.26793 | ||||||||
\(595\) | −21.4364 | −0.878806 | ||||||||
\(596\) | 1.49328 | 0.0611671 | ||||||||
\(597\) | 23.2638 | 0.952123 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.22276 | −0.295114 | −0.147557 | − | 0.989054i | \(-0.547141\pi\) | ||||
−0.147557 | + | 0.989054i | \(0.547141\pi\) | |||||||
\(600\) | −1.53931 | −0.0628420 | ||||||||
\(601\) | −23.4338 | −0.955886 | −0.477943 | − | 0.878391i | \(-0.658618\pi\) | ||||
−0.477943 | + | 0.878391i | \(0.658618\pi\) | |||||||
\(602\) | 33.6134 | 1.36998 | ||||||||
\(603\) | 0.723050 | 0.0294449 | ||||||||
\(604\) | −15.6386 | −0.636326 | ||||||||
\(605\) | −19.5762 | −0.795884 | ||||||||
\(606\) | 10.7685 | 0.437441 | ||||||||
\(607\) | 32.4537 | 1.31726 | 0.658628 | − | 0.752468i | \(-0.271137\pi\) | ||||
0.658628 | + | 0.752468i | \(0.271137\pi\) | |||||||
\(608\) | −3.65701 | −0.148311 | ||||||||
\(609\) | 48.9357 | 1.98297 | ||||||||
\(610\) | −9.46716 | −0.383314 | ||||||||
\(611\) | −24.9487 | −1.00932 | ||||||||
\(612\) | 3.63566 | 0.146963 | ||||||||
\(613\) | −5.76585 | −0.232881 | −0.116440 | − | 0.993198i | \(-0.537148\pi\) | ||||
−0.116440 | + | 0.993198i | \(0.537148\pi\) | |||||||
\(614\) | −9.37242 | −0.378240 | ||||||||
\(615\) | −17.5391 | −0.707246 | ||||||||
\(616\) | 20.5572 | 0.828274 | ||||||||
\(617\) | −1.34969 | −0.0543365 | −0.0271682 | − | 0.999631i | \(-0.508649\pi\) | ||||
−0.0271682 | + | 0.999631i | \(0.508649\pi\) | |||||||
\(618\) | 2.67908 | 0.107768 | ||||||||
\(619\) | 14.7990 | 0.594822 | 0.297411 | − | 0.954750i | \(-0.403877\pi\) | ||||
0.297411 | + | 0.954750i | \(0.403877\pi\) | |||||||
\(620\) | 9.24402 | 0.371249 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.48356 | 0.300064 | ||||||||
\(623\) | −13.3269 | −0.533931 | ||||||||
\(624\) | −3.94475 | −0.157916 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −2.78633 | −0.111364 | ||||||||
\(627\) | −31.1274 | −1.24311 | ||||||||
\(628\) | 6.10683 | 0.243689 | ||||||||
\(629\) | −2.82624 | −0.112690 | ||||||||
\(630\) | −2.34410 | −0.0933914 | ||||||||
\(631\) | −15.8874 | −0.632469 | −0.316235 | − | 0.948681i | \(-0.602419\pi\) | ||||
−0.316235 | + | 0.948681i | \(0.602419\pi\) | |||||||
\(632\) | 6.94974 | 0.276446 | ||||||||
\(633\) | 13.2311 | 0.525889 | ||||||||
\(634\) | 15.8539 | 0.629637 | ||||||||
\(635\) | 2.46423 | 0.0977899 | ||||||||
\(636\) | −1.26973 | −0.0503482 | ||||||||
\(637\) | 17.4805 | 0.692603 | ||||||||
\(638\) | −47.2845 | −1.87201 | ||||||||
\(639\) | −1.80815 | −0.0715292 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −17.0653 | −0.674040 | −0.337020 | − | 0.941498i | \(-0.609419\pi\) | ||||
−0.337020 | + | 0.941498i | \(0.609419\pi\) | |||||||
\(642\) | −1.66526 | −0.0657226 | ||||||||
\(643\) | 40.2129 | 1.58584 | 0.792920 | − | 0.609326i | \(-0.208560\pi\) | ||||
0.792920 | + | 0.609326i | \(0.208560\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13.9176 | −0.548007 | ||||||||
\(646\) | 21.0865 | 0.829637 | ||||||||
\(647\) | −44.6393 | −1.75495 | −0.877475 | − | 0.479622i | \(-0.840774\pi\) | ||||
−0.877475 | + | 0.479622i | \(0.840774\pi\) | |||||||
\(648\) | −6.71085 | −0.263627 | ||||||||
\(649\) | −11.5408 | −0.453015 | ||||||||
\(650\) | 2.56268 | 0.100516 | ||||||||
\(651\) | −52.9005 | −2.07333 | ||||||||
\(652\) | 16.4053 | 0.642479 | ||||||||
\(653\) | −21.1084 | −0.826034 | −0.413017 | − | 0.910723i | \(-0.635525\pi\) | ||||
−0.413017 | + | 0.910723i | \(0.635525\pi\) | |||||||
\(654\) | −3.59794 | −0.140691 | ||||||||
\(655\) | −21.8887 | −0.855264 | ||||||||
\(656\) | −11.3942 | −0.444867 | ||||||||
\(657\) | 2.03010 | 0.0792018 | ||||||||
\(658\) | 36.1932 | 1.41096 | ||||||||
\(659\) | −15.9775 | −0.622394 | −0.311197 | − | 0.950345i | \(-0.600730\pi\) | ||||
−0.311197 | + | 0.950345i | \(0.600730\pi\) | |||||||
\(660\) | −8.51172 | −0.331318 | ||||||||
\(661\) | 13.4394 | 0.522734 | 0.261367 | − | 0.965240i | \(-0.415827\pi\) | ||||
0.261367 | + | 0.965240i | \(0.415827\pi\) | |||||||
\(662\) | −10.9915 | −0.427198 | ||||||||
\(663\) | 22.7456 | 0.883367 | ||||||||
\(664\) | 9.86488 | 0.382832 | ||||||||
\(665\) | −13.5956 | −0.527215 | ||||||||
\(666\) | −0.309055 | −0.0119756 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −14.3536 | −0.555357 | ||||||||
\(669\) | −1.90309 | −0.0735777 | ||||||||
\(670\) | 1.14674 | 0.0443024 | ||||||||
\(671\) | −52.3494 | −2.02092 | ||||||||
\(672\) | 5.72267 | 0.220757 | ||||||||
\(673\) | 33.0607 | 1.27440 | 0.637198 | − | 0.770700i | \(-0.280093\pi\) | ||||
0.637198 | + | 0.770700i | \(0.280093\pi\) | |||||||
\(674\) | 24.4167 | 0.940495 | ||||||||
\(675\) | 5.58850 | 0.215102 | ||||||||
\(676\) | −6.43269 | −0.247411 | ||||||||
\(677\) | 30.4215 | 1.16919 | 0.584596 | − | 0.811324i | \(-0.301253\pi\) | ||||
0.584596 | + | 0.811324i | \(0.301253\pi\) | |||||||
\(678\) | −24.6351 | −0.946107 | ||||||||
\(679\) | −9.50712 | −0.364850 | ||||||||
\(680\) | 5.76605 | 0.221118 | ||||||||
\(681\) | −32.5913 | −1.24890 | ||||||||
\(682\) | 51.1155 | 1.95731 | ||||||||
\(683\) | −47.2669 | −1.80862 | −0.904309 | − | 0.426879i | \(-0.859613\pi\) | ||||
−0.904309 | + | 0.426879i | \(0.859613\pi\) | |||||||
\(684\) | 2.30584 | 0.0881661 | ||||||||
\(685\) | −3.01304 | −0.115122 | ||||||||
\(686\) | 0.664752 | 0.0253803 | ||||||||
\(687\) | 17.2738 | 0.659037 | ||||||||
\(688\) | −9.04149 | −0.344704 | ||||||||
\(689\) | 2.11388 | 0.0805325 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.7843 | −0.638507 | −0.319253 | − | 0.947669i | \(-0.603432\pi\) | ||||
−0.319253 | + | 0.947669i | \(0.603432\pi\) | |||||||
\(692\) | −10.4022 | −0.395432 | ||||||||
\(693\) | −12.9619 | −0.492382 | ||||||||
\(694\) | 23.9579 | 0.909428 | ||||||||
\(695\) | 5.93581 | 0.225158 | ||||||||
\(696\) | −13.1629 | −0.498940 | ||||||||
\(697\) | 65.6993 | 2.48854 | ||||||||
\(698\) | −5.85393 | −0.221575 | ||||||||
\(699\) | −2.20697 | −0.0834754 | ||||||||
\(700\) | −3.71769 | −0.140515 | ||||||||
\(701\) | −12.8024 | −0.483540 | −0.241770 | − | 0.970334i | \(-0.577728\pi\) | ||||
−0.241770 | + | 0.970334i | \(0.577728\pi\) | |||||||
\(702\) | 14.3215 | 0.540531 | ||||||||
\(703\) | −1.79249 | −0.0676050 | ||||||||
\(704\) | −5.52957 | −0.208404 | ||||||||
\(705\) | −14.9858 | −0.564398 | ||||||||
\(706\) | −13.8742 | −0.522164 | ||||||||
\(707\) | 26.0078 | 0.978123 | ||||||||
\(708\) | −3.21270 | −0.120740 | ||||||||
\(709\) | −25.6434 | −0.963060 | −0.481530 | − | 0.876430i | \(-0.659919\pi\) | ||||
−0.481530 | + | 0.876430i | \(0.659919\pi\) | |||||||
\(710\) | −2.86767 | −0.107622 | ||||||||
\(711\) | −4.38201 | −0.164338 | ||||||||
\(712\) | 3.58473 | 0.134343 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −32.9972 | −1.23489 | ||||||||
\(715\) | 14.1705 | 0.529947 | ||||||||
\(716\) | −12.6474 | −0.472655 | ||||||||
\(717\) | 10.6490 | 0.397695 | ||||||||
\(718\) | −19.9793 | −0.745622 | ||||||||
\(719\) | 38.7793 | 1.44622 | 0.723112 | − | 0.690730i | \(-0.242711\pi\) | ||||
0.723112 | + | 0.690730i | \(0.242711\pi\) | |||||||
\(720\) | 0.630528 | 0.0234984 | ||||||||
\(721\) | 6.47042 | 0.240971 | ||||||||
\(722\) | −5.62631 | −0.209389 | ||||||||
\(723\) | 25.3758 | 0.943737 | ||||||||
\(724\) | −4.07323 | −0.151380 | ||||||||
\(725\) | 8.55120 | 0.317584 | ||||||||
\(726\) | −30.1338 | −1.11837 | ||||||||
\(727\) | −22.2487 | −0.825159 | −0.412579 | − | 0.910922i | \(-0.635372\pi\) | ||||
−0.412579 | + | 0.910922i | \(0.635372\pi\) | |||||||
\(728\) | −9.52722 | −0.353102 | ||||||||
\(729\) | 30.0387 | 1.11254 | ||||||||
\(730\) | 3.21969 | 0.119166 | ||||||||
\(731\) | 52.1337 | 1.92823 | ||||||||
\(732\) | −14.5729 | −0.538629 | ||||||||
\(733\) | 3.98219 | 0.147086 | 0.0735428 | − | 0.997292i | \(-0.476569\pi\) | ||||
0.0735428 | + | 0.997292i | \(0.476569\pi\) | |||||||
\(734\) | 5.43074 | 0.200452 | ||||||||
\(735\) | 10.4999 | 0.387295 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.34097 | 0.233573 | ||||||||
\(738\) | 7.18434 | 0.264459 | ||||||||
\(739\) | −46.1521 | −1.69773 | −0.848867 | − | 0.528606i | \(-0.822715\pi\) | ||||
−0.848867 | + | 0.528606i | \(0.822715\pi\) | |||||||
\(740\) | −0.490152 | −0.0180184 | ||||||||
\(741\) | 14.4260 | 0.529951 | ||||||||
\(742\) | −3.06662 | −0.112579 | ||||||||
\(743\) | 46.1168 | 1.69186 | 0.845931 | − | 0.533292i | \(-0.179045\pi\) | ||||
0.845931 | + | 0.533292i | \(0.179045\pi\) | |||||||
\(744\) | 14.2294 | 0.521675 | ||||||||
\(745\) | −1.49328 | −0.0547095 | ||||||||
\(746\) | −30.6865 | −1.12351 | ||||||||
\(747\) | −6.22008 | −0.227581 | ||||||||
\(748\) | 31.8838 | 1.16579 | ||||||||
\(749\) | −4.02188 | −0.146956 | ||||||||
\(750\) | 1.53931 | 0.0562076 | ||||||||
\(751\) | 48.1341 | 1.75644 | 0.878219 | − | 0.478259i | \(-0.158732\pi\) | ||||
0.878219 | + | 0.478259i | \(0.158732\pi\) | |||||||
\(752\) | −9.73542 | −0.355014 | ||||||||
\(753\) | −32.6064 | −1.18824 | ||||||||
\(754\) | 21.9140 | 0.798059 | ||||||||
\(755\) | 15.6386 | 0.569147 | ||||||||
\(756\) | −20.7763 | −0.755627 | ||||||||
\(757\) | 16.9349 | 0.615511 | 0.307755 | − | 0.951466i | \(-0.400422\pi\) | ||||
0.307755 | + | 0.951466i | \(0.400422\pi\) | |||||||
\(758\) | 11.4897 | 0.417326 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.65701 | 0.132654 | ||||||||
\(761\) | 19.3763 | 0.702390 | 0.351195 | − | 0.936302i | \(-0.385775\pi\) | ||||
0.351195 | + | 0.936302i | \(0.385775\pi\) | |||||||
\(762\) | 3.79321 | 0.137413 | ||||||||
\(763\) | −8.68962 | −0.314585 | ||||||||
\(764\) | −6.14225 | −0.222219 | ||||||||
\(765\) | −3.63566 | −0.131447 | ||||||||
\(766\) | −10.6061 | −0.383213 | ||||||||
\(767\) | 5.34857 | 0.193126 | ||||||||
\(768\) | −1.53931 | −0.0555450 | ||||||||
\(769\) | 35.5736 | 1.28282 | 0.641408 | − | 0.767200i | \(-0.278351\pi\) | ||||
0.641408 | + | 0.767200i | \(0.278351\pi\) | |||||||
\(770\) | −20.5572 | −0.740831 | ||||||||
\(771\) | −0.969195 | −0.0349047 | ||||||||
\(772\) | 6.53510 | 0.235203 | ||||||||
\(773\) | −10.4461 | −0.375721 | −0.187860 | − | 0.982196i | \(-0.560155\pi\) | ||||
−0.187860 | + | 0.982196i | \(0.560155\pi\) | |||||||
\(774\) | 5.70091 | 0.204915 | ||||||||
\(775\) | −9.24402 | −0.332055 | ||||||||
\(776\) | 2.55727 | 0.0918005 | ||||||||
\(777\) | 2.80498 | 0.100628 | ||||||||
\(778\) | −36.6757 | −1.31489 | ||||||||
\(779\) | 41.6685 | 1.49293 | ||||||||
\(780\) | 3.94475 | 0.141245 | ||||||||
\(781\) | −15.8570 | −0.567408 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 47.7884 | 1.70782 | ||||||||
\(784\) | 6.82119 | 0.243614 | ||||||||
\(785\) | −6.10683 | −0.217962 | ||||||||
\(786\) | −33.6935 | −1.20181 | ||||||||
\(787\) | 7.02667 | 0.250474 | 0.125237 | − | 0.992127i | \(-0.460031\pi\) | ||||
0.125237 | + | 0.992127i | \(0.460031\pi\) | |||||||
\(788\) | 4.45551 | 0.158721 | ||||||||
\(789\) | −40.4780 | −1.44105 | ||||||||
\(790\) | −6.94974 | −0.247261 | ||||||||
\(791\) | −59.4979 | −2.11550 | ||||||||
\(792\) | 3.48655 | 0.123889 | ||||||||
\(793\) | 24.2613 | 0.861543 | ||||||||
\(794\) | −4.28172 | −0.151953 | ||||||||
\(795\) | 1.26973 | 0.0450328 | ||||||||
\(796\) | −15.1131 | −0.535671 | ||||||||
\(797\) | −47.1489 | −1.67010 | −0.835049 | − | 0.550175i | \(-0.814561\pi\) | ||||
−0.835049 | + | 0.550175i | \(0.814561\pi\) | |||||||
\(798\) | −20.9278 | −0.740837 | ||||||||
\(799\) | 56.1349 | 1.98591 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −2.26027 | −0.0798628 | ||||||||
\(802\) | 27.0327 | 0.954559 | ||||||||
\(803\) | 17.8035 | 0.628271 | ||||||||
\(804\) | 1.76518 | 0.0622533 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −23.6894 | −0.834424 | ||||||||
\(807\) | −40.9664 | −1.44209 | ||||||||
\(808\) | −6.99569 | −0.246107 | ||||||||
\(809\) | 24.3207 | 0.855070 | 0.427535 | − | 0.903999i | \(-0.359382\pi\) | ||||
0.427535 | + | 0.903999i | \(0.359382\pi\) | |||||||
\(810\) | 6.71085 | 0.235795 | ||||||||
\(811\) | −47.9783 | −1.68475 | −0.842373 | − | 0.538894i | \(-0.818842\pi\) | ||||
−0.842373 | + | 0.538894i | \(0.818842\pi\) | |||||||
\(812\) | −31.7907 | −1.11563 | ||||||||
\(813\) | −15.1259 | −0.530490 | ||||||||
\(814\) | −2.71033 | −0.0949971 | ||||||||
\(815\) | −16.4053 | −0.574651 | ||||||||
\(816\) | 8.87574 | 0.310713 | ||||||||
\(817\) | 33.0648 | 1.15679 | ||||||||
\(818\) | −26.7573 | −0.935548 | ||||||||
\(819\) | 6.00718 | 0.209908 | ||||||||
\(820\) | 11.3942 | 0.397901 | ||||||||
\(821\) | 35.9961 | 1.25627 | 0.628137 | − | 0.778103i | \(-0.283818\pi\) | ||||
0.628137 | + | 0.778103i | \(0.283818\pi\) | |||||||
\(822\) | −4.63800 | −0.161769 | ||||||||
\(823\) | −26.6789 | −0.929967 | −0.464984 | − | 0.885319i | \(-0.653940\pi\) | ||||
−0.464984 | + | 0.885319i | \(0.653940\pi\) | |||||||
\(824\) | −1.74044 | −0.0606312 | ||||||||
\(825\) | 8.51172 | 0.296340 | ||||||||
\(826\) | −7.75919 | −0.269977 | ||||||||
\(827\) | −1.18494 | −0.0412043 | −0.0206021 | − | 0.999788i | \(-0.506558\pi\) | ||||
−0.0206021 | + | 0.999788i | \(0.506558\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.1131 | 0.385974 | 0.192987 | − | 0.981201i | \(-0.438182\pi\) | ||||
0.192987 | + | 0.981201i | \(0.438182\pi\) | |||||||
\(830\) | −9.86488 | −0.342415 | ||||||||
\(831\) | −18.0917 | −0.627595 | ||||||||
\(832\) | 2.56268 | 0.0888448 | ||||||||
\(833\) | −39.3314 | −1.36275 | ||||||||
\(834\) | 9.13705 | 0.316390 | ||||||||
\(835\) | 14.3536 | 0.496727 | ||||||||
\(836\) | 20.2217 | 0.699381 | ||||||||
\(837\) | −51.6603 | −1.78564 | ||||||||
\(838\) | −4.58163 | −0.158270 | ||||||||
\(839\) | −24.1312 | −0.833103 | −0.416552 | − | 0.909112i | \(-0.636761\pi\) | ||||
−0.416552 | + | 0.909112i | \(0.636761\pi\) | |||||||
\(840\) | −5.72267 | −0.197451 | ||||||||
\(841\) | 44.1231 | 1.52149 | ||||||||
\(842\) | −14.5615 | −0.501824 | ||||||||
\(843\) | 22.6840 | 0.781277 | ||||||||
\(844\) | −8.59548 | −0.295868 | ||||||||
\(845\) | 6.43269 | 0.221291 | ||||||||
\(846\) | 6.13845 | 0.211044 | ||||||||
\(847\) | −72.7781 | −2.50068 | ||||||||
\(848\) | 0.824873 | 0.0283263 | ||||||||
\(849\) | 3.18620 | 0.109350 | ||||||||
\(850\) | −5.76605 | −0.197774 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −4.41424 | −0.151229 | ||||||||
\(853\) | −48.2825 | −1.65316 | −0.826581 | − | 0.562818i | \(-0.809717\pi\) | ||||
−0.826581 | + | 0.562818i | \(0.809717\pi\) | |||||||
\(854\) | −35.1959 | −1.20438 | ||||||||
\(855\) | −2.30584 | −0.0788582 | ||||||||
\(856\) | 1.08182 | 0.0369760 | ||||||||
\(857\) | −21.2639 | −0.726362 | −0.363181 | − | 0.931719i | \(-0.618309\pi\) | ||||
−0.363181 | + | 0.931719i | \(0.618309\pi\) | |||||||
\(858\) | 21.8128 | 0.744676 | ||||||||
\(859\) | 5.40004 | 0.184247 | 0.0921236 | − | 0.995748i | \(-0.470635\pi\) | ||||
0.0921236 | + | 0.995748i | \(0.470635\pi\) | |||||||
\(860\) | 9.04149 | 0.308312 | ||||||||
\(861\) | −65.2050 | −2.22218 | ||||||||
\(862\) | −8.19202 | −0.279021 | ||||||||
\(863\) | −42.7775 | −1.45616 | −0.728082 | − | 0.685490i | \(-0.759588\pi\) | ||||
−0.728082 | + | 0.685490i | \(0.759588\pi\) | |||||||
\(864\) | 5.58850 | 0.190125 | ||||||||
\(865\) | 10.4022 | 0.353685 | ||||||||
\(866\) | 4.11382 | 0.139793 | ||||||||
\(867\) | −25.0097 | −0.849374 | ||||||||
\(868\) | 34.3664 | 1.16647 | ||||||||
\(869\) | −38.4291 | −1.30362 | ||||||||
\(870\) | 13.1629 | 0.446266 | ||||||||
\(871\) | −2.93872 | −0.0995747 | ||||||||
\(872\) | 2.33737 | 0.0791535 | ||||||||
\(873\) | −1.61243 | −0.0545724 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.71769 | 0.125681 | ||||||||
\(876\) | 4.95609 | 0.167451 | ||||||||
\(877\) | 15.4981 | 0.523334 | 0.261667 | − | 0.965158i | \(-0.415728\pi\) | ||||
0.261667 | + | 0.965158i | \(0.415728\pi\) | |||||||
\(878\) | −7.79137 | −0.262946 | ||||||||
\(879\) | 31.4693 | 1.06143 | ||||||||
\(880\) | 5.52957 | 0.186402 | ||||||||
\(881\) | −6.24048 | −0.210247 | −0.105124 | − | 0.994459i | \(-0.533524\pi\) | ||||
−0.105124 | + | 0.994459i | \(0.533524\pi\) | |||||||
\(882\) | −4.30095 | −0.144821 | ||||||||
\(883\) | 14.4886 | 0.487582 | 0.243791 | − | 0.969828i | \(-0.421609\pi\) | ||||
0.243791 | + | 0.969828i | \(0.421609\pi\) | |||||||
\(884\) | −14.7765 | −0.496988 | ||||||||
\(885\) | 3.21270 | 0.107994 | ||||||||
\(886\) | 36.6224 | 1.23035 | ||||||||
\(887\) | −1.33272 | −0.0447483 | −0.0223741 | − | 0.999750i | \(-0.507123\pi\) | ||||
−0.0223741 | + | 0.999750i | \(0.507123\pi\) | |||||||
\(888\) | −0.754496 | −0.0253192 | ||||||||
\(889\) | 9.16122 | 0.307258 | ||||||||
\(890\) | −3.58473 | −0.120160 | ||||||||
\(891\) | 37.1081 | 1.24317 | ||||||||
\(892\) | 1.23633 | 0.0413953 | ||||||||
\(893\) | 35.6025 | 1.19139 | ||||||||
\(894\) | −2.29862 | −0.0768772 | ||||||||
\(895\) | 12.6474 | 0.422755 | ||||||||
\(896\) | −3.71769 | −0.124199 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.52535 | 0.117642 | ||||||||
\(899\) | −79.0475 | −2.63638 | ||||||||
\(900\) | −0.630528 | −0.0210176 | ||||||||
\(901\) | −4.75626 | −0.158454 | ||||||||
\(902\) | 63.0048 | 2.09783 | ||||||||
\(903\) | −51.7414 | −1.72185 | ||||||||
\(904\) | 16.0040 | 0.532286 | ||||||||
\(905\) | 4.07323 | 0.135399 | ||||||||
\(906\) | 24.0727 | 0.799761 | ||||||||
\(907\) | 26.5828 | 0.882667 | 0.441334 | − | 0.897343i | \(-0.354506\pi\) | ||||
0.441334 | + | 0.897343i | \(0.354506\pi\) | |||||||
\(908\) | 21.1727 | 0.702640 | ||||||||
\(909\) | 4.41097 | 0.146303 | ||||||||
\(910\) | 9.52722 | 0.315824 | ||||||||
\(911\) | −10.9950 | −0.364282 | −0.182141 | − | 0.983272i | \(-0.558303\pi\) | ||||
−0.182141 | + | 0.983272i | \(0.558303\pi\) | |||||||
\(912\) | 5.62926 | 0.186404 | ||||||||
\(913\) | −54.5486 | −1.80529 | ||||||||
\(914\) | 30.5111 | 1.00922 | ||||||||
\(915\) | 14.5729 | 0.481765 | ||||||||
\(916\) | −11.2218 | −0.370779 | ||||||||
\(917\) | −81.3755 | −2.68725 | ||||||||
\(918\) | −32.2236 | −1.06354 | ||||||||
\(919\) | −29.3494 | −0.968148 | −0.484074 | − | 0.875027i | \(-0.660844\pi\) | ||||
−0.484074 | + | 0.875027i | \(0.660844\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.4271 | 0.475388 | ||||||||
\(922\) | −6.50868 | −0.214352 | ||||||||
\(923\) | 7.34892 | 0.241893 | ||||||||
\(924\) | −31.6439 | −1.04101 | ||||||||
\(925\) | 0.490152 | 0.0161161 | ||||||||
\(926\) | 4.72959 | 0.155424 | ||||||||
\(927\) | 1.09740 | 0.0360433 | ||||||||
\(928\) | 8.55120 | 0.280707 | ||||||||
\(929\) | 51.1379 | 1.67778 | 0.838889 | − | 0.544302i | \(-0.183205\pi\) | ||||
0.838889 | + | 0.544302i | \(0.183205\pi\) | |||||||
\(930\) | −14.2294 | −0.466601 | ||||||||
\(931\) | −24.9451 | −0.817544 | ||||||||
\(932\) | 1.43374 | 0.0469638 | ||||||||
\(933\) | −11.5195 | −0.377132 | ||||||||
\(934\) | 26.7107 | 0.874000 | ||||||||
\(935\) | −31.8838 | −1.04271 | ||||||||
\(936\) | −1.61584 | −0.0528153 | ||||||||
\(937\) | 49.6173 | 1.62093 | 0.810464 | − | 0.585788i | \(-0.199215\pi\) | ||||
0.810464 | + | 0.585788i | \(0.199215\pi\) | |||||||
\(938\) | 4.26321 | 0.139199 | ||||||||
\(939\) | 4.28902 | 0.139967 | ||||||||
\(940\) | 9.73542 | 0.317534 | ||||||||
\(941\) | 19.5044 | 0.635824 | 0.317912 | − | 0.948120i | \(-0.397018\pi\) | ||||
0.317912 | + | 0.948120i | \(0.397018\pi\) | |||||||
\(942\) | −9.40030 | −0.306278 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 2.08710 | 0.0679294 | ||||||||
\(945\) | 20.7763 | 0.675853 | ||||||||
\(946\) | 49.9956 | 1.62550 | ||||||||
\(947\) | 39.8475 | 1.29487 | 0.647435 | − | 0.762121i | \(-0.275842\pi\) | ||||
0.647435 | + | 0.762121i | \(0.275842\pi\) | |||||||
\(948\) | −10.6978 | −0.347449 | ||||||||
\(949\) | −8.25101 | −0.267839 | ||||||||
\(950\) | −3.65701 | −0.118649 | ||||||||
\(951\) | −24.4040 | −0.791354 | ||||||||
\(952\) | 21.4364 | 0.694757 | ||||||||
\(953\) | −33.7408 | −1.09297 | −0.546486 | − | 0.837469i | \(-0.684035\pi\) | ||||
−0.546486 | + | 0.837469i | \(0.684035\pi\) | |||||||
\(954\) | −0.520105 | −0.0168390 | ||||||||
\(955\) | 6.14225 | 0.198759 | ||||||||
\(956\) | −6.91805 | −0.223746 | ||||||||
\(957\) | 72.7854 | 2.35282 | ||||||||
\(958\) | −8.12800 | −0.262604 | ||||||||
\(959\) | −11.2015 | −0.361717 | ||||||||
\(960\) | 1.53931 | 0.0496810 | ||||||||
\(961\) | 54.4519 | 1.75651 | ||||||||
\(962\) | 1.25610 | 0.0404983 | ||||||||
\(963\) | −0.682120 | −0.0219810 | ||||||||
\(964\) | −16.4852 | −0.530953 | ||||||||
\(965\) | −6.53510 | −0.210372 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.3031 | 0.395642 | 0.197821 | − | 0.980238i | \(-0.436614\pi\) | ||||
0.197821 | + | 0.980238i | \(0.436614\pi\) | |||||||
\(968\) | 19.5762 | 0.629202 | ||||||||
\(969\) | −32.4586 | −1.04272 | ||||||||
\(970\) | −2.55727 | −0.0821089 | ||||||||
\(971\) | −18.1012 | −0.580896 | −0.290448 | − | 0.956891i | \(-0.593804\pi\) | ||||
−0.290448 | + | 0.956891i | \(0.593804\pi\) | |||||||
\(972\) | −6.43544 | −0.206417 | ||||||||
\(973\) | 22.0675 | 0.707451 | ||||||||
\(974\) | −7.40083 | −0.237138 | ||||||||
\(975\) | −3.94475 | −0.126333 | ||||||||
\(976\) | 9.46716 | 0.303036 | ||||||||
\(977\) | 40.8441 | 1.30672 | 0.653359 | − | 0.757048i | \(-0.273359\pi\) | ||||
0.653359 | + | 0.757048i | \(0.273359\pi\) | |||||||
\(978\) | −25.2527 | −0.807494 | ||||||||
\(979\) | −19.8220 | −0.633515 | ||||||||
\(980\) | −6.82119 | −0.217895 | ||||||||
\(981\) | −1.47378 | −0.0470541 | ||||||||
\(982\) | −25.9839 | −0.829179 | ||||||||
\(983\) | 7.99453 | 0.254986 | 0.127493 | − | 0.991839i | \(-0.459307\pi\) | ||||
0.127493 | + | 0.991839i | \(0.459307\pi\) | |||||||
\(984\) | 17.5391 | 0.559127 | ||||||||
\(985\) | −4.45551 | −0.141965 | ||||||||
\(986\) | −49.3067 | −1.57024 | ||||||||
\(987\) | −55.7126 | −1.77335 | ||||||||
\(988\) | −9.37172 | −0.298154 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −3.48655 | −0.110810 | ||||||||
\(991\) | 6.88475 | 0.218701 | 0.109351 | − | 0.994003i | \(-0.465123\pi\) | ||||
0.109351 | + | 0.994003i | \(0.465123\pi\) | |||||||
\(992\) | −9.24402 | −0.293498 | ||||||||
\(993\) | 16.9194 | 0.536919 | ||||||||
\(994\) | −10.6611 | −0.338150 | ||||||||
\(995\) | 15.1131 | 0.479118 | ||||||||
\(996\) | −15.1851 | −0.481158 | ||||||||
\(997\) | −26.7299 | −0.846544 | −0.423272 | − | 0.906003i | \(-0.639119\pi\) | ||||
−0.423272 | + | 0.906003i | \(0.639119\pi\) | |||||||
\(998\) | −34.5272 | −1.09294 | ||||||||
\(999\) | 2.73922 | 0.0866650 |
(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 | 5290.2.a.bk.1.4 | 15 | ||
23.9 | even | 11 | 230.2.g.d.81.3 | yes | 30 | ||
23.18 | even | 11 | 230.2.g.d.71.3 | ✓ | 30 | ||
23.22 | odd | 2 | 5290.2.a.bl.1.4 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.g.d.71.3 | ✓ | 30 | 23.18 | even | 11 | ||
230.2.g.d.81.3 | yes | 30 | 23.9 | even | 11 | ||
5290.2.a.bk.1.4 | 15 | 1.1 | even | 1 | trivial | ||
5290.2.a.bl.1.4 | 15 | 23.22 | odd | 2 |