Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, 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("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{10} + 88x^{8} - 197x^{6} + 172x^{4} - 36x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.34523\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.34523 | −0.951219 | −0.475609 | − | 0.879657i | \(-0.657772\pi\) | ||||
−0.475609 | + | 0.879657i | \(0.657772\pi\) | |||||||
\(3\) | 2.05010 | 1.18363 | 0.591814 | − | 0.806075i | \(-0.298412\pi\) | ||||
0.591814 | + | 0.806075i | \(0.298412\pi\) | |||||||
\(4\) | −0.190366 | −0.0951832 | ||||||||
\(5\) | −3.56778 | −1.59556 | −0.797779 | − | 0.602950i | \(-0.793992\pi\) | ||||
−0.797779 | + | 0.602950i | \(0.793992\pi\) | |||||||
\(6\) | −2.75785 | −1.12589 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.94654 | 1.04176 | ||||||||
\(9\) | 1.20292 | 0.400975 | ||||||||
\(10\) | 4.79947 | 1.51772 | ||||||||
\(11\) | −1.27867 | −0.385534 | −0.192767 | − | 0.981245i | \(-0.561746\pi\) | ||||
−0.192767 | + | 0.981245i | \(0.561746\pi\) | |||||||
\(12\) | −0.390271 | −0.112661 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.31431 | −1.88855 | ||||||||
\(16\) | −3.58303 | −0.895757 | ||||||||
\(17\) | 7.73920 | 1.87703 | 0.938515 | − | 0.345238i | \(-0.112202\pi\) | ||||
0.938515 | + | 0.345238i | \(0.112202\pi\) | |||||||
\(18\) | −1.61821 | −0.381415 | ||||||||
\(19\) | 0.943878 | 0.216540 | 0.108270 | − | 0.994121i | \(-0.465469\pi\) | ||||
0.108270 | + | 0.994121i | \(0.465469\pi\) | |||||||
\(20\) | 0.679185 | 0.151870 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.72010 | 0.366727 | ||||||||
\(23\) | 1.64727 | 0.343481 | 0.171740 | − | 0.985142i | \(-0.445061\pi\) | ||||
0.171740 | + | 0.985142i | \(0.445061\pi\) | |||||||
\(24\) | 6.04071 | 1.23305 | ||||||||
\(25\) | 7.72903 | 1.54581 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.68419 | −0.709023 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.04484 | 0.751107 | 0.375554 | − | 0.926801i | \(-0.377453\pi\) | ||||
0.375554 | + | 0.926801i | \(0.377453\pi\) | |||||||
\(30\) | 9.83940 | 1.79642 | ||||||||
\(31\) | 5.15220 | 0.925362 | 0.462681 | − | 0.886525i | \(-0.346888\pi\) | ||||
0.462681 | + | 0.886525i | \(0.346888\pi\) | |||||||
\(32\) | −1.07309 | −0.189698 | ||||||||
\(33\) | −2.62141 | −0.456329 | ||||||||
\(34\) | −10.4110 | −1.78547 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.228996 | −0.0381661 | ||||||||
\(37\) | 1.05608 | 0.173619 | 0.0868094 | − | 0.996225i | \(-0.472333\pi\) | ||||
0.0868094 | + | 0.996225i | \(0.472333\pi\) | |||||||
\(38\) | −1.26973 | −0.205977 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.5126 | −1.66219 | ||||||||
\(41\) | −4.19882 | −0.655746 | −0.327873 | − | 0.944722i | \(-0.606332\pi\) | ||||
−0.327873 | + | 0.944722i | \(0.606332\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.83065 | 0.584168 | 0.292084 | − | 0.956393i | \(-0.405651\pi\) | ||||
0.292084 | + | 0.956393i | \(0.405651\pi\) | |||||||
\(44\) | 0.243416 | 0.0366964 | ||||||||
\(45\) | −4.29176 | −0.639778 | ||||||||
\(46\) | −2.21596 | −0.326725 | ||||||||
\(47\) | 0.894217 | 0.130435 | 0.0652175 | − | 0.997871i | \(-0.479226\pi\) | ||||
0.0652175 | + | 0.997871i | \(0.479226\pi\) | |||||||
\(48\) | −7.34558 | −1.06024 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −10.3973 | −1.47040 | ||||||||
\(51\) | 15.8662 | 2.22171 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.0799923 | −0.0109878 | −0.00549389 | − | 0.999985i | \(-0.501749\pi\) | ||||
−0.00549389 | + | 0.999985i | \(0.501749\pi\) | |||||||
\(54\) | 4.95607 | 0.674436 | ||||||||
\(55\) | 4.56202 | 0.615142 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.93505 | 0.256303 | ||||||||
\(58\) | −5.44122 | −0.714467 | ||||||||
\(59\) | −11.1847 | −1.45613 | −0.728064 | − | 0.685509i | \(-0.759580\pi\) | ||||
−0.728064 | + | 0.685509i | \(0.759580\pi\) | |||||||
\(60\) | 1.39240 | 0.179758 | ||||||||
\(61\) | −7.62392 | −0.976143 | −0.488072 | − | 0.872804i | \(-0.662299\pi\) | ||||
−0.488072 | + | 0.872804i | \(0.662299\pi\) | |||||||
\(62\) | −6.93087 | −0.880221 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.60961 | 1.07620 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.52639 | 0.434069 | ||||||||
\(67\) | −6.32103 | −0.772237 | −0.386119 | − | 0.922449i | \(-0.626184\pi\) | ||||
−0.386119 | + | 0.922449i | \(0.626184\pi\) | |||||||
\(68\) | −1.47328 | −0.178662 | ||||||||
\(69\) | 3.37708 | 0.406553 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.4240 | −1.35578 | −0.677889 | − | 0.735165i | \(-0.737105\pi\) | ||||
−0.677889 | + | 0.735165i | \(0.737105\pi\) | |||||||
\(72\) | 3.54446 | 0.417719 | ||||||||
\(73\) | −0.760506 | −0.0890105 | −0.0445052 | − | 0.999009i | \(-0.514171\pi\) | ||||
−0.0445052 | + | 0.999009i | \(0.514171\pi\) | |||||||
\(74\) | −1.42067 | −0.165149 | ||||||||
\(75\) | 15.8453 | 1.82966 | ||||||||
\(76\) | −0.179683 | −0.0206110 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.85531 | −0.321247 | −0.160624 | − | 0.987016i | \(-0.551351\pi\) | ||||
−0.160624 | + | 0.987016i | \(0.551351\pi\) | |||||||
\(80\) | 12.7834 | 1.42923 | ||||||||
\(81\) | −11.1617 | −1.24019 | ||||||||
\(82\) | 5.64837 | 0.623758 | ||||||||
\(83\) | 2.32483 | 0.255183 | 0.127591 | − | 0.991827i | \(-0.459275\pi\) | ||||
0.127591 | + | 0.991827i | \(0.459275\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −27.6117 | −2.99491 | ||||||||
\(86\) | −5.15308 | −0.555671 | ||||||||
\(87\) | 8.29233 | 0.889032 | ||||||||
\(88\) | −3.76766 | −0.401634 | ||||||||
\(89\) | 7.57626 | 0.803082 | 0.401541 | − | 0.915841i | \(-0.368475\pi\) | ||||
0.401541 | + | 0.915841i | \(0.368475\pi\) | |||||||
\(90\) | 5.77339 | 0.608569 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.313586 | −0.0326936 | ||||||||
\(93\) | 10.5625 | 1.09528 | ||||||||
\(94\) | −1.20292 | −0.124072 | ||||||||
\(95\) | −3.36755 | −0.345503 | ||||||||
\(96\) | −2.19995 | −0.224532 | ||||||||
\(97\) | 0.478557 | 0.0485901 | 0.0242951 | − | 0.999705i | \(-0.492266\pi\) | ||||
0.0242951 | + | 0.999705i | \(0.492266\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.53815 | −0.154589 | ||||||||
\(100\) | −1.47135 | −0.147135 | ||||||||
\(101\) | 2.87836 | 0.286407 | 0.143204 | − | 0.989693i | \(-0.454260\pi\) | ||||
0.143204 | + | 0.989693i | \(0.454260\pi\) | |||||||
\(102\) | −21.3436 | −2.11333 | ||||||||
\(103\) | −11.3351 | −1.11688 | −0.558441 | − | 0.829544i | \(-0.688600\pi\) | ||||
−0.558441 | + | 0.829544i | \(0.688600\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.107608 | 0.0104518 | ||||||||
\(107\) | −6.57206 | −0.635345 | −0.317673 | − | 0.948200i | \(-0.602901\pi\) | ||||
−0.317673 | + | 0.948200i | \(0.602901\pi\) | |||||||
\(108\) | 0.701346 | 0.0674871 | ||||||||
\(109\) | −5.83914 | −0.559288 | −0.279644 | − | 0.960104i | \(-0.590216\pi\) | ||||
−0.279644 | + | 0.960104i | \(0.590216\pi\) | |||||||
\(110\) | −6.13694 | −0.585135 | ||||||||
\(111\) | 2.16508 | 0.205500 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.53233 | 0.614510 | 0.307255 | − | 0.951627i | \(-0.400590\pi\) | ||||
0.307255 | + | 0.951627i | \(0.400590\pi\) | |||||||
\(114\) | −2.60308 | −0.243800 | ||||||||
\(115\) | −5.87711 | −0.548043 | ||||||||
\(116\) | −0.770001 | −0.0714928 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.0460 | 1.38510 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −21.5519 | −1.96741 | ||||||||
\(121\) | −9.36500 | −0.851363 | ||||||||
\(122\) | 10.2559 | 0.928525 | ||||||||
\(123\) | −8.60802 | −0.776159 | ||||||||
\(124\) | −0.980805 | −0.0880789 | ||||||||
\(125\) | −9.73656 | −0.870865 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.7164 | 1.30586 | 0.652932 | − | 0.757416i | \(-0.273539\pi\) | ||||
0.652932 | + | 0.757416i | \(0.273539\pi\) | |||||||
\(128\) | −9.43568 | −0.834005 | ||||||||
\(129\) | 7.85322 | 0.691437 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.1867 | 0.977386 | 0.488693 | − | 0.872456i | \(-0.337474\pi\) | ||||
0.488693 | + | 0.872456i | \(0.337474\pi\) | |||||||
\(132\) | 0.499028 | 0.0434349 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.50322 | 0.734566 | ||||||||
\(135\) | 13.1444 | 1.13129 | ||||||||
\(136\) | 22.8038 | 1.95541 | ||||||||
\(137\) | 17.6308 | 1.50630 | 0.753151 | − | 0.657848i | \(-0.228533\pi\) | ||||
0.753151 | + | 0.657848i | \(0.228533\pi\) | |||||||
\(138\) | −4.54294 | −0.386721 | ||||||||
\(139\) | −5.85710 | −0.496793 | −0.248396 | − | 0.968658i | \(-0.579904\pi\) | ||||
−0.248396 | + | 0.968658i | \(0.579904\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.83324 | 0.154386 | ||||||||
\(142\) | 15.3678 | 1.28964 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.31011 | −0.359176 | ||||||||
\(145\) | −14.4311 | −1.19844 | ||||||||
\(146\) | 1.02305 | 0.0846684 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.201043 | −0.0165256 | ||||||||
\(149\) | 10.4790 | 0.858470 | 0.429235 | − | 0.903193i | \(-0.358783\pi\) | ||||
0.429235 | + | 0.903193i | \(0.358783\pi\) | |||||||
\(150\) | −21.3155 | −1.74041 | ||||||||
\(151\) | 4.71406 | 0.383625 | 0.191812 | − | 0.981432i | \(-0.438564\pi\) | ||||
0.191812 | + | 0.981432i | \(0.438564\pi\) | |||||||
\(152\) | 2.78117 | 0.225583 | ||||||||
\(153\) | 9.30967 | 0.752642 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.3819 | −1.47647 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00210 | 0.718445 | 0.359223 | − | 0.933252i | \(-0.383042\pi\) | ||||
0.359223 | + | 0.933252i | \(0.383042\pi\) | |||||||
\(158\) | 3.84103 | 0.305576 | ||||||||
\(159\) | −0.163992 | −0.0130054 | ||||||||
\(160\) | 3.82856 | 0.302674 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 15.0151 | 1.17970 | ||||||||
\(163\) | −12.0324 | −0.942449 | −0.471224 | − | 0.882013i | \(-0.656188\pi\) | ||||
−0.471224 | + | 0.882013i | \(0.656188\pi\) | |||||||
\(164\) | 0.799315 | 0.0624160 | ||||||||
\(165\) | 9.35261 | 0.728099 | ||||||||
\(166\) | −3.12742 | −0.242735 | ||||||||
\(167\) | 19.4220 | 1.50292 | 0.751459 | − | 0.659780i | \(-0.229350\pi\) | ||||
0.751459 | + | 0.659780i | \(0.229350\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 37.1440 | 2.84882 | ||||||||
\(171\) | 1.13541 | 0.0868273 | ||||||||
\(172\) | −0.729226 | −0.0556030 | ||||||||
\(173\) | 14.3795 | 1.09325 | 0.546627 | − | 0.837376i | \(-0.315912\pi\) | ||||
0.546627 | + | 0.837376i | \(0.315912\pi\) | |||||||
\(174\) | −11.1551 | −0.845663 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.58152 | 0.345345 | ||||||||
\(177\) | −22.9299 | −1.72351 | ||||||||
\(178\) | −10.1918 | −0.763907 | ||||||||
\(179\) | 5.42606 | 0.405563 | 0.202781 | − | 0.979224i | \(-0.435002\pi\) | ||||
0.202781 | + | 0.979224i | \(0.435002\pi\) | |||||||
\(180\) | 0.817008 | 0.0608962 | ||||||||
\(181\) | 15.4902 | 1.15138 | 0.575688 | − | 0.817669i | \(-0.304734\pi\) | ||||
0.575688 | + | 0.817669i | \(0.304734\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.6298 | −1.15539 | ||||||||
\(184\) | 4.85376 | 0.357824 | ||||||||
\(185\) | −3.76786 | −0.277019 | ||||||||
\(186\) | −14.2090 | −1.04185 | ||||||||
\(187\) | −9.89589 | −0.723659 | ||||||||
\(188\) | −0.170229 | −0.0124152 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.53011 | 0.328649 | ||||||||
\(191\) | 4.74622 | 0.343425 | 0.171712 | − | 0.985147i | \(-0.445070\pi\) | ||||
0.171712 | + | 0.985147i | \(0.445070\pi\) | |||||||
\(192\) | 17.6506 | 1.27382 | ||||||||
\(193\) | 21.0391 | 1.51443 | 0.757215 | − | 0.653166i | \(-0.226559\pi\) | ||||
0.757215 | + | 0.653166i | \(0.226559\pi\) | |||||||
\(194\) | −0.643768 | −0.0462198 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.81209 | 0.414094 | 0.207047 | − | 0.978331i | \(-0.433615\pi\) | ||||
0.207047 | + | 0.978331i | \(0.433615\pi\) | |||||||
\(198\) | 2.06915 | 0.147048 | ||||||||
\(199\) | 10.6182 | 0.752703 | 0.376352 | − | 0.926477i | \(-0.377179\pi\) | ||||
0.376352 | + | 0.926477i | \(0.377179\pi\) | |||||||
\(200\) | 22.7739 | 1.61036 | ||||||||
\(201\) | −12.9588 | −0.914041 | ||||||||
\(202\) | −3.87204 | −0.272436 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.02038 | −0.211469 | ||||||||
\(205\) | 14.9805 | 1.04628 | ||||||||
\(206\) | 15.2483 | 1.06240 | ||||||||
\(207\) | 1.98155 | 0.137727 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.20691 | −0.0834837 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.66549 | −0.321186 | −0.160593 | − | 0.987021i | \(-0.551341\pi\) | ||||
−0.160593 | + | 0.987021i | \(0.551341\pi\) | |||||||
\(212\) | 0.0152278 | 0.00104585 | ||||||||
\(213\) | −23.4203 | −1.60474 | ||||||||
\(214\) | 8.84091 | 0.604352 | ||||||||
\(215\) | −13.6669 | −0.932074 | ||||||||
\(216\) | −10.8556 | −0.738631 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.85497 | 0.532005 | ||||||||
\(219\) | −1.55912 | −0.105355 | ||||||||
\(220\) | −0.868455 | −0.0585512 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2.91252 | −0.195475 | ||||||||
\(223\) | 24.2254 | 1.62225 | 0.811126 | − | 0.584871i | \(-0.198855\pi\) | ||||
0.811126 | + | 0.584871i | \(0.198855\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.29744 | 0.619829 | ||||||||
\(226\) | −8.78747 | −0.584534 | ||||||||
\(227\) | −15.3753 | −1.02049 | −0.510247 | − | 0.860028i | \(-0.670446\pi\) | ||||
−0.510247 | + | 0.860028i | \(0.670446\pi\) | |||||||
\(228\) | −0.368368 | −0.0243958 | ||||||||
\(229\) | −16.3515 | −1.08054 | −0.540268 | − | 0.841493i | \(-0.681677\pi\) | ||||
−0.540268 | + | 0.841493i | \(0.681677\pi\) | |||||||
\(230\) | 7.90604 | 0.521309 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.9183 | 0.782473 | ||||||||
\(233\) | −29.1107 | −1.90711 | −0.953554 | − | 0.301223i | \(-0.902605\pi\) | ||||
−0.953554 | + | 0.301223i | \(0.902605\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.19037 | −0.208117 | ||||||||
\(236\) | 2.12920 | 0.138599 | ||||||||
\(237\) | −5.85368 | −0.380237 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.65409 | −0.559787 | −0.279893 | − | 0.960031i | \(-0.590299\pi\) | ||||
−0.279893 | + | 0.960031i | \(0.590299\pi\) | |||||||
\(240\) | 26.2074 | 1.69168 | ||||||||
\(241\) | −18.1982 | −1.17225 | −0.586124 | − | 0.810222i | \(-0.699347\pi\) | ||||
−0.586124 | + | 0.810222i | \(0.699347\pi\) | |||||||
\(242\) | 12.5980 | 0.809833 | ||||||||
\(243\) | −11.8302 | −0.758905 | ||||||||
\(244\) | 1.45134 | 0.0929124 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.5797 | 0.738297 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 15.1811 | 0.964003 | ||||||||
\(249\) | 4.76614 | 0.302042 | ||||||||
\(250\) | 13.0979 | 0.828383 | ||||||||
\(251\) | 15.8720 | 1.00183 | 0.500915 | − | 0.865497i | \(-0.332997\pi\) | ||||
0.500915 | + | 0.865497i | \(0.332997\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.10632 | −0.132423 | ||||||||
\(254\) | −19.7968 | −1.24216 | ||||||||
\(255\) | −56.6069 | −3.54486 | ||||||||
\(256\) | −4.52609 | −0.282880 | ||||||||
\(257\) | −24.3267 | −1.51746 | −0.758730 | − | 0.651406i | \(-0.774180\pi\) | ||||
−0.758730 | + | 0.651406i | \(0.774180\pi\) | |||||||
\(258\) | −10.5644 | −0.657708 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.86563 | 0.301175 | ||||||||
\(262\) | −15.0486 | −0.929708 | ||||||||
\(263\) | 15.4345 | 0.951734 | 0.475867 | − | 0.879517i | \(-0.342134\pi\) | ||||
0.475867 | + | 0.879517i | \(0.342134\pi\) | |||||||
\(264\) | −7.72409 | −0.475385 | ||||||||
\(265\) | 0.285395 | 0.0175317 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.5321 | 0.950550 | ||||||||
\(268\) | 1.20331 | 0.0735040 | ||||||||
\(269\) | −13.0407 | −0.795106 | −0.397553 | − | 0.917579i | \(-0.630141\pi\) | ||||
−0.397553 | + | 0.917579i | \(0.630141\pi\) | |||||||
\(270\) | −17.6822 | −1.07610 | ||||||||
\(271\) | 26.9706 | 1.63835 | 0.819174 | − | 0.573544i | \(-0.194432\pi\) | ||||
0.819174 | + | 0.573544i | \(0.194432\pi\) | |||||||
\(272\) | −27.7298 | −1.68136 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −23.7174 | −1.43282 | ||||||||
\(275\) | −9.88289 | −0.595961 | ||||||||
\(276\) | −0.642883 | −0.0386970 | ||||||||
\(277\) | 12.7015 | 0.763156 | 0.381578 | − | 0.924337i | \(-0.375381\pi\) | ||||
0.381578 | + | 0.924337i | \(0.375381\pi\) | |||||||
\(278\) | 7.87912 | 0.472558 | ||||||||
\(279\) | 6.19770 | 0.371047 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.7216 | 1.59408 | 0.797038 | − | 0.603930i | \(-0.206399\pi\) | ||||
0.797038 | + | 0.603930i | \(0.206399\pi\) | |||||||
\(282\) | −2.46612 | −0.146855 | ||||||||
\(283\) | 14.7423 | 0.876336 | 0.438168 | − | 0.898893i | \(-0.355627\pi\) | ||||
0.438168 | + | 0.898893i | \(0.355627\pi\) | |||||||
\(284\) | 2.17474 | 0.129047 | ||||||||
\(285\) | −6.90382 | −0.408947 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.29085 | −0.0760641 | ||||||||
\(289\) | 42.8952 | 2.52324 | ||||||||
\(290\) | 19.4131 | 1.13997 | ||||||||
\(291\) | 0.981092 | 0.0575126 | ||||||||
\(292\) | 0.144775 | 0.00847230 | ||||||||
\(293\) | −11.5831 | −0.676689 | −0.338345 | − | 0.941022i | \(-0.609867\pi\) | ||||
−0.338345 | + | 0.941022i | \(0.609867\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 39.9046 | 2.32334 | ||||||||
\(296\) | 3.11179 | 0.180869 | ||||||||
\(297\) | 4.71087 | 0.273353 | ||||||||
\(298\) | −14.0966 | −0.816593 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.01641 | −0.174153 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.34147 | −0.364911 | ||||||||
\(303\) | 5.90093 | 0.339000 | ||||||||
\(304\) | −3.38194 | −0.193968 | ||||||||
\(305\) | 27.2004 | 1.55749 | ||||||||
\(306\) | −12.5236 | −0.715927 | ||||||||
\(307\) | 29.3335 | 1.67415 | 0.837076 | − | 0.547086i | \(-0.184263\pi\) | ||||
0.837076 | + | 0.547086i | \(0.184263\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −23.2381 | −1.32197 | ||||||||
\(310\) | 24.7278 | 1.40444 | ||||||||
\(311\) | −0.150654 | −0.00854282 | −0.00427141 | − | 0.999991i | \(-0.501360\pi\) | ||||
−0.00427141 | + | 0.999991i | \(0.501360\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.5211 | −0.594690 | −0.297345 | − | 0.954770i | \(-0.596101\pi\) | ||||
−0.297345 | + | 0.954770i | \(0.596101\pi\) | |||||||
\(314\) | −12.1099 | −0.683399 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.543555 | 0.0305773 | ||||||||
\(317\) | −1.50676 | −0.0846281 | −0.0423140 | − | 0.999104i | \(-0.513473\pi\) | ||||
−0.0423140 | + | 0.999104i | \(0.513473\pi\) | |||||||
\(318\) | 0.220607 | 0.0123710 | ||||||||
\(319\) | −5.17202 | −0.289578 | ||||||||
\(320\) | −30.7172 | −1.71714 | ||||||||
\(321\) | −13.4734 | −0.752012 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.30486 | 0.406453 | ||||||||
\(324\) | 2.12482 | 0.118046 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.1863 | 0.896475 | ||||||||
\(327\) | −11.9708 | −0.661989 | ||||||||
\(328\) | −12.3720 | −0.683129 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −12.5814 | −0.692582 | ||||||||
\(331\) | −25.2509 | −1.38791 | −0.693957 | − | 0.720017i | \(-0.744134\pi\) | ||||
−0.693957 | + | 0.720017i | \(0.744134\pi\) | |||||||
\(332\) | −0.442569 | −0.0242891 | ||||||||
\(333\) | 1.27039 | 0.0696167 | ||||||||
\(334\) | −26.1270 | −1.42960 | ||||||||
\(335\) | 22.5520 | 1.23215 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.1811 | −1.75302 | −0.876509 | − | 0.481386i | \(-0.840134\pi\) | ||||
−0.876509 | + | 0.481386i | \(0.840134\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.3920 | 0.727351 | ||||||||
\(340\) | 5.25634 | 0.285065 | ||||||||
\(341\) | −6.58797 | −0.356759 | ||||||||
\(342\) | −1.52739 | −0.0825917 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 11.2871 | 0.608562 | ||||||||
\(345\) | −12.0487 | −0.648679 | ||||||||
\(346\) | −19.3437 | −1.03992 | ||||||||
\(347\) | 24.7638 | 1.32939 | 0.664695 | − | 0.747115i | \(-0.268562\pi\) | ||||
0.664695 | + | 0.747115i | \(0.268562\pi\) | |||||||
\(348\) | −1.57858 | −0.0846209 | ||||||||
\(349\) | 11.5556 | 0.618559 | 0.309280 | − | 0.950971i | \(-0.399912\pi\) | ||||
0.309280 | + | 0.950971i | \(0.399912\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.37213 | 0.0731350 | ||||||||
\(353\) | 20.0884 | 1.06920 | 0.534599 | − | 0.845106i | \(-0.320463\pi\) | ||||
0.534599 | + | 0.845106i | \(0.320463\pi\) | |||||||
\(354\) | 30.8459 | 1.63944 | ||||||||
\(355\) | 40.7582 | 2.16322 | ||||||||
\(356\) | −1.44227 | −0.0764399 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.29928 | −0.385779 | ||||||||
\(359\) | 15.0510 | 0.794363 | 0.397181 | − | 0.917740i | \(-0.369988\pi\) | ||||
0.397181 | + | 0.917740i | \(0.369988\pi\) | |||||||
\(360\) | −12.6458 | −0.666495 | ||||||||
\(361\) | −18.1091 | −0.953110 | ||||||||
\(362\) | −20.8378 | −1.09521 | ||||||||
\(363\) | −19.1992 | −1.00770 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.71331 | 0.142021 | ||||||||
\(366\) | 21.0257 | 1.09903 | ||||||||
\(367\) | 9.00355 | 0.469982 | 0.234991 | − | 0.971998i | \(-0.424494\pi\) | ||||
0.234991 | + | 0.971998i | \(0.424494\pi\) | |||||||
\(368\) | −5.90223 | −0.307675 | ||||||||
\(369\) | −5.05087 | −0.262938 | ||||||||
\(370\) | 5.06863 | 0.263506 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.01075 | −0.104253 | ||||||||
\(373\) | −16.1391 | −0.835649 | −0.417824 | − | 0.908528i | \(-0.637207\pi\) | ||||
−0.417824 | + | 0.908528i | \(0.637207\pi\) | |||||||
\(374\) | 13.3122 | 0.688358 | ||||||||
\(375\) | −19.9610 | −1.03078 | ||||||||
\(376\) | 2.63484 | 0.135882 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.6655 | −0.804685 | −0.402342 | − | 0.915489i | \(-0.631804\pi\) | ||||
−0.402342 | + | 0.915489i | \(0.631804\pi\) | |||||||
\(380\) | 0.641068 | 0.0328861 | ||||||||
\(381\) | 30.1700 | 1.54566 | ||||||||
\(382\) | −6.38474 | −0.326672 | ||||||||
\(383\) | 24.6328 | 1.25868 | 0.629339 | − | 0.777131i | \(-0.283326\pi\) | ||||
0.629339 | + | 0.777131i | \(0.283326\pi\) | |||||||
\(384\) | −19.3441 | −0.987151 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −28.3024 | −1.44055 | ||||||||
\(387\) | 4.60798 | 0.234237 | ||||||||
\(388\) | −0.0911013 | −0.00462497 | ||||||||
\(389\) | −18.8567 | −0.956071 | −0.478036 | − | 0.878340i | \(-0.658651\pi\) | ||||
−0.478036 | + | 0.878340i | \(0.658651\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.7486 | 0.644724 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22.9339 | 1.15686 | ||||||||
\(394\) | −7.81857 | −0.393894 | ||||||||
\(395\) | 10.1871 | 0.512569 | ||||||||
\(396\) | 0.292811 | 0.0147143 | ||||||||
\(397\) | 14.5030 | 0.727884 | 0.363942 | − | 0.931422i | \(-0.381431\pi\) | ||||
0.363942 | + | 0.931422i | \(0.381431\pi\) | |||||||
\(398\) | −14.2839 | −0.715985 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −27.6933 | −1.38467 | ||||||||
\(401\) | 20.9889 | 1.04814 | 0.524069 | − | 0.851676i | \(-0.324413\pi\) | ||||
0.524069 | + | 0.851676i | \(0.324413\pi\) | |||||||
\(402\) | 17.4325 | 0.869453 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.547943 | −0.0272612 | ||||||||
\(405\) | 39.8226 | 1.97880 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.35038 | −0.0669360 | ||||||||
\(408\) | 46.7502 | 2.31448 | ||||||||
\(409\) | −21.4276 | −1.05953 | −0.529763 | − | 0.848146i | \(-0.677719\pi\) | ||||
−0.529763 | + | 0.848146i | \(0.677719\pi\) | |||||||
\(410\) | −20.1521 | −0.995242 | ||||||||
\(411\) | 36.1450 | 1.78290 | ||||||||
\(412\) | 2.15782 | 0.106308 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.66563 | −0.131009 | ||||||||
\(415\) | −8.29446 | −0.407159 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.0077 | −0.588018 | ||||||||
\(418\) | 1.62357 | 0.0794113 | ||||||||
\(419\) | 7.96406 | 0.389070 | 0.194535 | − | 0.980896i | \(-0.437680\pi\) | ||||
0.194535 | + | 0.980896i | \(0.437680\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.81786 | 0.137334 | 0.0686670 | − | 0.997640i | \(-0.478125\pi\) | ||||
0.0686670 | + | 0.997640i | \(0.478125\pi\) | |||||||
\(422\) | 6.27614 | 0.305518 | ||||||||
\(423\) | 1.07568 | 0.0523011 | ||||||||
\(424\) | −0.235700 | −0.0114466 | ||||||||
\(425\) | 59.8165 | 2.90152 | ||||||||
\(426\) | 31.5057 | 1.52645 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.25110 | 0.0604742 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.3851 | 0.886606 | ||||||||
\(431\) | −5.73626 | −0.276306 | −0.138153 | − | 0.990411i | \(-0.544117\pi\) | ||||
−0.138153 | + | 0.990411i | \(0.544117\pi\) | |||||||
\(432\) | 13.2006 | 0.635112 | ||||||||
\(433\) | −24.5257 | −1.17863 | −0.589314 | − | 0.807904i | \(-0.700602\pi\) | ||||
−0.589314 | + | 0.807904i | \(0.700602\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −29.5852 | −1.41850 | ||||||||
\(436\) | 1.11158 | 0.0532349 | ||||||||
\(437\) | 1.55483 | 0.0743774 | ||||||||
\(438\) | 2.09736 | 0.100216 | ||||||||
\(439\) | 36.6423 | 1.74884 | 0.874420 | − | 0.485169i | \(-0.161242\pi\) | ||||
0.874420 | + | 0.485169i | \(0.161242\pi\) | |||||||
\(440\) | 13.4422 | 0.640830 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.0933 | 1.28724 | 0.643622 | − | 0.765344i | \(-0.277431\pi\) | ||||
0.643622 | + | 0.765344i | \(0.277431\pi\) | |||||||
\(444\) | −0.412158 | −0.0195602 | ||||||||
\(445\) | −27.0304 | −1.28136 | ||||||||
\(446\) | −32.5886 | −1.54312 | ||||||||
\(447\) | 21.4830 | 1.01611 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.4324 | 1.29461 | 0.647307 | − | 0.762229i | \(-0.275895\pi\) | ||||
0.647307 | + | 0.762229i | \(0.275895\pi\) | |||||||
\(450\) | −12.5072 | −0.589593 | ||||||||
\(451\) | 5.36892 | 0.252812 | ||||||||
\(452\) | −1.24354 | −0.0584911 | ||||||||
\(453\) | 9.66431 | 0.454069 | ||||||||
\(454\) | 20.6832 | 0.970712 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.70169 | 0.267006 | ||||||||
\(457\) | 39.6639 | 1.85540 | 0.927700 | − | 0.373327i | \(-0.121783\pi\) | ||||
0.927700 | + | 0.373327i | \(0.121783\pi\) | |||||||
\(458\) | 21.9964 | 1.02783 | ||||||||
\(459\) | −28.5127 | −1.33086 | ||||||||
\(460\) | 1.11880 | 0.0521645 | ||||||||
\(461\) | 4.89580 | 0.228020 | 0.114010 | − | 0.993480i | \(-0.463630\pi\) | ||||
0.114010 | + | 0.993480i | \(0.463630\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.71193 | 0.218982 | 0.109491 | − | 0.993988i | \(-0.465078\pi\) | ||||
0.109491 | + | 0.993988i | \(0.465078\pi\) | |||||||
\(464\) | −14.4928 | −0.672810 | ||||||||
\(465\) | −37.6848 | −1.74759 | ||||||||
\(466\) | 39.1605 | 1.81408 | ||||||||
\(467\) | 32.0161 | 1.48153 | 0.740765 | − | 0.671764i | \(-0.234463\pi\) | ||||
0.740765 | + | 0.671764i | \(0.234463\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.29176 | 0.197964 | ||||||||
\(471\) | 18.4552 | 0.850372 | ||||||||
\(472\) | −32.9563 | −1.51693 | ||||||||
\(473\) | −4.89814 | −0.225217 | ||||||||
\(474\) | 7.87452 | 0.361689 | ||||||||
\(475\) | 7.29526 | 0.334730 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.0962247 | −0.00440582 | ||||||||
\(478\) | 11.6417 | 0.532480 | ||||||||
\(479\) | 18.0245 | 0.823560 | 0.411780 | − | 0.911283i | \(-0.364907\pi\) | ||||
0.411780 | + | 0.911283i | \(0.364907\pi\) | |||||||
\(480\) | 7.84894 | 0.358253 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 24.4807 | 1.11506 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.78278 | 0.0810355 | ||||||||
\(485\) | −1.70739 | −0.0775284 | ||||||||
\(486\) | 15.9142 | 0.721885 | ||||||||
\(487\) | −17.6004 | −0.797550 | −0.398775 | − | 0.917049i | \(-0.630565\pi\) | ||||
−0.398775 | + | 0.917049i | \(0.630565\pi\) | |||||||
\(488\) | −22.4642 | −1.01691 | ||||||||
\(489\) | −24.6676 | −1.11551 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.86360 | 0.174362 | 0.0871810 | − | 0.996192i | \(-0.472214\pi\) | ||||
0.0871810 | + | 0.996192i | \(0.472214\pi\) | |||||||
\(492\) | 1.63868 | 0.0738773 | ||||||||
\(493\) | 31.3038 | 1.40985 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.48776 | 0.246656 | ||||||||
\(496\) | −18.4605 | −0.828899 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6.41153 | −0.287308 | ||||||||
\(499\) | 12.6473 | 0.566169 | 0.283084 | − | 0.959095i | \(-0.408642\pi\) | ||||
0.283084 | + | 0.959095i | \(0.408642\pi\) | |||||||
\(500\) | 1.85351 | 0.0828917 | ||||||||
\(501\) | 39.8171 | 1.77890 | ||||||||
\(502\) | −21.3514 | −0.952959 | ||||||||
\(503\) | 22.0360 | 0.982537 | 0.491268 | − | 0.871008i | \(-0.336533\pi\) | ||||
0.491268 | + | 0.871008i | \(0.336533\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.2693 | −0.456980 | ||||||||
\(506\) | 2.83348 | 0.125964 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.80150 | −0.124296 | ||||||||
\(509\) | 15.6702 | 0.694568 | 0.347284 | − | 0.937760i | \(-0.387104\pi\) | ||||
0.347284 | + | 0.937760i | \(0.387104\pi\) | |||||||
\(510\) | 76.1491 | 3.37194 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24.9600 | 1.10309 | ||||||||
\(513\) | −3.47743 | −0.153532 | ||||||||
\(514\) | 32.7249 | 1.44344 | ||||||||
\(515\) | 40.4411 | 1.78205 | ||||||||
\(516\) | −1.49499 | −0.0658132 | ||||||||
\(517\) | −1.14341 | −0.0502871 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.4795 | 1.29401 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.2415 | −1.10585 | −0.552925 | − | 0.833231i | \(-0.686488\pi\) | ||||
−0.552925 | + | 0.833231i | \(0.686488\pi\) | |||||||
\(522\) | −6.54538 | −0.286483 | ||||||||
\(523\) | −13.2477 | −0.579279 | −0.289640 | − | 0.957136i | \(-0.593535\pi\) | ||||
−0.289640 | + | 0.957136i | \(0.593535\pi\) | |||||||
\(524\) | −2.12957 | −0.0930307 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.7629 | −0.905307 | ||||||||
\(527\) | 39.8738 | 1.73693 | ||||||||
\(528\) | 9.39259 | 0.408760 | ||||||||
\(529\) | −20.2865 | −0.882021 | ||||||||
\(530\) | −0.383920 | −0.0166764 | ||||||||
\(531\) | −13.4544 | −0.583871 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −20.8942 | −0.904181 | ||||||||
\(535\) | 23.4477 | 1.01373 | ||||||||
\(536\) | −18.6252 | −0.804485 | ||||||||
\(537\) | 11.1240 | 0.480036 | ||||||||
\(538\) | 17.5427 | 0.756320 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.50225 | −0.107680 | ||||||||
\(541\) | −14.4034 | −0.619250 | −0.309625 | − | 0.950859i | \(-0.600204\pi\) | ||||
−0.309625 | + | 0.950859i | \(0.600204\pi\) | |||||||
\(542\) | −36.2816 | −1.55843 | ||||||||
\(543\) | 31.7565 | 1.36280 | ||||||||
\(544\) | −8.30488 | −0.356069 | ||||||||
\(545\) | 20.8328 | 0.892377 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.00679 | 0.0858042 | 0.0429021 | − | 0.999079i | \(-0.486340\pi\) | ||||
0.0429021 | + | 0.999079i | \(0.486340\pi\) | |||||||
\(548\) | −3.35631 | −0.143375 | ||||||||
\(549\) | −9.17100 | −0.391409 | ||||||||
\(550\) | 13.2947 | 0.566889 | ||||||||
\(551\) | 3.81783 | 0.162645 | ||||||||
\(552\) | 9.95071 | 0.423530 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −17.0863 | −0.725928 | ||||||||
\(555\) | −7.72451 | −0.327887 | ||||||||
\(556\) | 1.11499 | 0.0472863 | ||||||||
\(557\) | −8.57916 | −0.363511 | −0.181755 | − | 0.983344i | \(-0.558178\pi\) | ||||
−0.181755 | + | 0.983344i | \(0.558178\pi\) | |||||||
\(558\) | −8.33731 | −0.352946 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.2876 | −0.856543 | ||||||||
\(562\) | −35.9466 | −1.51631 | ||||||||
\(563\) | −12.7744 | −0.538375 | −0.269188 | − | 0.963088i | \(-0.586755\pi\) | ||||
−0.269188 | + | 0.963088i | \(0.586755\pi\) | |||||||
\(564\) | −0.348987 | −0.0146950 | ||||||||
\(565\) | −23.3059 | −0.980487 | ||||||||
\(566\) | −19.8317 | −0.833587 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −33.6612 | −1.41239 | ||||||||
\(569\) | −5.79116 | −0.242778 | −0.121389 | − | 0.992605i | \(-0.538735\pi\) | ||||
−0.121389 | + | 0.992605i | \(0.538735\pi\) | |||||||
\(570\) | 9.28720 | 0.388998 | ||||||||
\(571\) | −44.1332 | −1.84692 | −0.923458 | − | 0.383700i | \(-0.874650\pi\) | ||||
−0.923458 | + | 0.383700i | \(0.874650\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.73025 | 0.406487 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.7318 | 0.530954 | ||||||||
\(576\) | 10.3567 | 0.431529 | ||||||||
\(577\) | 11.9330 | 0.496776 | 0.248388 | − | 0.968661i | \(-0.420099\pi\) | ||||
0.248388 | + | 0.968661i | \(0.420099\pi\) | |||||||
\(578\) | −57.7037 | −2.40016 | ||||||||
\(579\) | 43.1324 | 1.79252 | ||||||||
\(580\) | 2.74719 | 0.114071 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.31979 | −0.0547071 | ||||||||
\(583\) | 0.102284 | 0.00423617 | ||||||||
\(584\) | −2.24086 | −0.0927274 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.5818 | 0.643679 | ||||||||
\(587\) | 20.3516 | 0.840000 | 0.420000 | − | 0.907524i | \(-0.362030\pi\) | ||||
0.420000 | + | 0.907524i | \(0.362030\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.86304 | 0.200378 | ||||||||
\(590\) | −53.6808 | −2.21000 | ||||||||
\(591\) | 11.9154 | 0.490133 | ||||||||
\(592\) | −3.78397 | −0.155520 | ||||||||
\(593\) | 18.1800 | 0.746563 | 0.373282 | − | 0.927718i | \(-0.378232\pi\) | ||||
0.373282 | + | 0.927718i | \(0.378232\pi\) | |||||||
\(594\) | −6.33719 | −0.260018 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.99484 | −0.0817120 | ||||||||
\(597\) | 21.7684 | 0.890920 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.2682 | −1.56359 | −0.781797 | − | 0.623532i | \(-0.785697\pi\) | ||||
−0.781797 | + | 0.623532i | \(0.785697\pi\) | |||||||
\(600\) | 46.6888 | 1.90606 | ||||||||
\(601\) | −26.8719 | −1.09613 | −0.548064 | − | 0.836436i | \(-0.684635\pi\) | ||||
−0.548064 | + | 0.836436i | \(0.684635\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.60372 | −0.309648 | ||||||||
\(604\) | −0.897398 | −0.0365146 | ||||||||
\(605\) | 33.4122 | 1.35840 | ||||||||
\(606\) | −7.93809 | −0.322463 | ||||||||
\(607\) | −9.40209 | −0.381619 | −0.190810 | − | 0.981627i | \(-0.561111\pi\) | ||||
−0.190810 | + | 0.981627i | \(0.561111\pi\) | |||||||
\(608\) | −1.01287 | −0.0410773 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −36.5908 | −1.48152 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.77225 | −0.0716389 | ||||||||
\(613\) | −13.2894 | −0.536753 | −0.268376 | − | 0.963314i | \(-0.586487\pi\) | ||||
−0.268376 | + | 0.963314i | \(0.586487\pi\) | |||||||
\(614\) | −39.4602 | −1.59248 | ||||||||
\(615\) | 30.7115 | 1.23841 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.2261 | 0.451947 | 0.225973 | − | 0.974133i | \(-0.427444\pi\) | ||||
0.225973 | + | 0.974133i | \(0.427444\pi\) | |||||||
\(618\) | 31.2606 | 1.25748 | ||||||||
\(619\) | 9.28505 | 0.373198 | 0.186599 | − | 0.982436i | \(-0.440254\pi\) | ||||
0.186599 | + | 0.982436i | \(0.440254\pi\) | |||||||
\(620\) | 3.49929 | 0.140535 | ||||||||
\(621\) | −6.06888 | −0.243536 | ||||||||
\(622\) | 0.202664 | 0.00812608 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.90726 | −0.156290 | ||||||||
\(626\) | 14.1533 | 0.565680 | ||||||||
\(627\) | −2.47429 | −0.0988137 | ||||||||
\(628\) | −1.71370 | −0.0683839 | ||||||||
\(629\) | 8.17322 | 0.325888 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.4026 | 0.414122 | 0.207061 | − | 0.978328i | \(-0.433610\pi\) | ||||
0.207061 | + | 0.978328i | \(0.433610\pi\) | |||||||
\(632\) | −8.41327 | −0.334662 | ||||||||
\(633\) | −9.56474 | −0.380164 | ||||||||
\(634\) | 2.02693 | 0.0804998 | ||||||||
\(635\) | −52.5046 | −2.08358 | ||||||||
\(636\) | 0.0312187 | 0.00123790 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.95754 | 0.275452 | ||||||||
\(639\) | −13.7422 | −0.543632 | ||||||||
\(640\) | 33.6644 | 1.33070 | ||||||||
\(641\) | 14.8591 | 0.586899 | 0.293449 | − | 0.955975i | \(-0.405197\pi\) | ||||
0.293449 | + | 0.955975i | \(0.405197\pi\) | |||||||
\(642\) | 18.1248 | 0.715328 | ||||||||
\(643\) | −2.29722 | −0.0905935 | −0.0452968 | − | 0.998974i | \(-0.514423\pi\) | ||||
−0.0452968 | + | 0.998974i | \(0.514423\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −28.0185 | −1.10323 | ||||||||
\(646\) | −9.82669 | −0.386626 | ||||||||
\(647\) | 7.99865 | 0.314459 | 0.157230 | − | 0.987562i | \(-0.449744\pi\) | ||||
0.157230 | + | 0.987562i | \(0.449744\pi\) | |||||||
\(648\) | −32.8885 | −1.29198 | ||||||||
\(649\) | 14.3016 | 0.561387 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.29056 | 0.0897053 | ||||||||
\(653\) | 3.98444 | 0.155923 | 0.0779615 | − | 0.996956i | \(-0.475159\pi\) | ||||
0.0779615 | + | 0.996956i | \(0.475159\pi\) | |||||||
\(654\) | 16.1035 | 0.629696 | ||||||||
\(655\) | −39.9116 | −1.55948 | ||||||||
\(656\) | 15.0445 | 0.587389 | ||||||||
\(657\) | −0.914831 | −0.0356910 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.5003 | −1.07126 | −0.535629 | − | 0.844453i | \(-0.679925\pi\) | ||||
−0.535629 | + | 0.844453i | \(0.679925\pi\) | |||||||
\(660\) | −1.78042 | −0.0693028 | ||||||||
\(661\) | 6.98621 | 0.271732 | 0.135866 | − | 0.990727i | \(-0.456618\pi\) | ||||
0.135866 | + | 0.990727i | \(0.456618\pi\) | |||||||
\(662\) | 33.9681 | 1.32021 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.85019 | 0.265839 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.70896 | −0.0662207 | ||||||||
\(667\) | 6.66296 | 0.257991 | ||||||||
\(668\) | −3.69729 | −0.143053 | ||||||||
\(669\) | 49.6646 | 1.92014 | ||||||||
\(670\) | −30.3376 | −1.17204 | ||||||||
\(671\) | 9.74849 | 0.376336 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.45566 | 0.210300 | 0.105150 | − | 0.994456i | \(-0.466468\pi\) | ||||
0.105150 | + | 0.994456i | \(0.466468\pi\) | |||||||
\(674\) | 43.2909 | 1.66750 | ||||||||
\(675\) | −28.4752 | −1.09601 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.7922 | 1.29874 | 0.649371 | − | 0.760472i | \(-0.275032\pi\) | ||||
0.649371 | + | 0.760472i | \(0.275032\pi\) | |||||||
\(678\) | −18.0152 | −0.691870 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −81.3590 | −3.11997 | ||||||||
\(681\) | −31.5209 | −1.20788 | ||||||||
\(682\) | 8.86231 | 0.339355 | ||||||||
\(683\) | 12.2988 | 0.470602 | 0.235301 | − | 0.971923i | \(-0.424392\pi\) | ||||
0.235301 | + | 0.971923i | \(0.424392\pi\) | |||||||
\(684\) | −0.216145 | −0.00826450 | ||||||||
\(685\) | −62.9028 | −2.40339 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33.5222 | −1.27895 | ||||||||
\(688\) | −13.7253 | −0.523272 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 16.2082 | 0.617036 | ||||||||
\(691\) | −11.0897 | −0.421871 | −0.210935 | − | 0.977500i | \(-0.567651\pi\) | ||||
−0.210935 | + | 0.977500i | \(0.567651\pi\) | |||||||
\(692\) | −2.73738 | −0.104059 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −33.3129 | −1.26454 | ||||||||
\(695\) | 20.8968 | 0.792662 | ||||||||
\(696\) | 24.4337 | 0.926156 | ||||||||
\(697\) | −32.4955 | −1.23086 | ||||||||
\(698\) | −15.5449 | −0.588385 | ||||||||
\(699\) | −59.6800 | −2.25731 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.6470 | −0.402133 | −0.201066 | − | 0.979578i | \(-0.564441\pi\) | ||||
−0.201066 | + | 0.979578i | \(0.564441\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.996813 | 0.0375955 | ||||||||
\(704\) | −11.0089 | −0.414912 | ||||||||
\(705\) | −6.54058 | −0.246333 | ||||||||
\(706\) | −27.0235 | −1.01704 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.36508 | 0.164050 | ||||||||
\(709\) | −40.7069 | −1.52878 | −0.764391 | − | 0.644754i | \(-0.776960\pi\) | ||||
−0.764391 | + | 0.644754i | \(0.776960\pi\) | |||||||
\(710\) | −54.8290 | −2.05770 | ||||||||
\(711\) | −3.43472 | −0.128812 | ||||||||
\(712\) | 22.3237 | 0.836618 | ||||||||
\(713\) | 8.48708 | 0.317844 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.03294 | −0.0386028 | ||||||||
\(717\) | −17.7418 | −0.662579 | ||||||||
\(718\) | −20.2470 | −0.755612 | ||||||||
\(719\) | −9.77537 | −0.364560 | −0.182280 | − | 0.983247i | \(-0.558348\pi\) | ||||
−0.182280 | + | 0.983247i | \(0.558348\pi\) | |||||||
\(720\) | 15.3775 | 0.573086 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 24.3608 | 0.906616 | ||||||||
\(723\) | −37.3081 | −1.38750 | ||||||||
\(724\) | −2.94881 | −0.109592 | ||||||||
\(725\) | 31.2627 | 1.16107 | ||||||||
\(726\) | 25.8273 | 0.958540 | ||||||||
\(727\) | 12.2091 | 0.452811 | 0.226406 | − | 0.974033i | \(-0.427303\pi\) | ||||
0.226406 | + | 0.974033i | \(0.427303\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.23219 | 0.341933 | ||||||||
\(730\) | −3.65002 | −0.135093 | ||||||||
\(731\) | 29.6461 | 1.09650 | ||||||||
\(732\) | 2.97539 | 0.109974 | ||||||||
\(733\) | 22.3153 | 0.824236 | 0.412118 | − | 0.911131i | \(-0.364789\pi\) | ||||
0.412118 | + | 0.911131i | \(0.364789\pi\) | |||||||
\(734\) | −12.1118 | −0.447055 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.76768 | −0.0651576 | ||||||||
\(737\) | 8.08253 | 0.297724 | ||||||||
\(738\) | 6.79456 | 0.250111 | ||||||||
\(739\) | −42.3729 | −1.55871 | −0.779357 | − | 0.626580i | \(-0.784454\pi\) | ||||
−0.779357 | + | 0.626580i | \(0.784454\pi\) | |||||||
\(740\) | 0.717275 | 0.0263675 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.9801 | −1.13655 | −0.568276 | − | 0.822838i | \(-0.692389\pi\) | ||||
−0.568276 | + | 0.822838i | \(0.692389\pi\) | |||||||
\(744\) | 31.1229 | 1.14102 | ||||||||
\(745\) | −37.3866 | −1.36974 | ||||||||
\(746\) | 21.7107 | 0.794885 | ||||||||
\(747\) | 2.79659 | 0.102322 | ||||||||
\(748\) | 1.88385 | 0.0688802 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 26.8520 | 0.980497 | ||||||||
\(751\) | 22.5660 | 0.823444 | 0.411722 | − | 0.911309i | \(-0.364927\pi\) | ||||
0.411722 | + | 0.911309i | \(0.364927\pi\) | |||||||
\(752\) | −3.20400 | −0.116838 | ||||||||
\(753\) | 32.5392 | 1.18579 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.8187 | −0.612095 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.2808 | 1.17327 | 0.586633 | − | 0.809853i | \(-0.300453\pi\) | ||||
0.586633 | + | 0.809853i | \(0.300453\pi\) | |||||||
\(758\) | 21.0737 | 0.765431 | ||||||||
\(759\) | −4.31818 | −0.156740 | ||||||||
\(760\) | −9.92260 | −0.359931 | ||||||||
\(761\) | 29.7517 | 1.07850 | 0.539249 | − | 0.842147i | \(-0.318708\pi\) | ||||
0.539249 | + | 0.842147i | \(0.318708\pi\) | |||||||
\(762\) | −40.5855 | −1.47026 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.903521 | −0.0326883 | ||||||||
\(765\) | −33.2148 | −1.20088 | ||||||||
\(766\) | −33.1367 | −1.19728 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −9.27895 | −0.334825 | ||||||||
\(769\) | −41.8105 | −1.50773 | −0.753863 | − | 0.657032i | \(-0.771812\pi\) | ||||
−0.753863 | + | 0.657032i | \(0.771812\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −49.8723 | −1.79611 | ||||||||
\(772\) | −4.00514 | −0.144148 | ||||||||
\(773\) | 41.4336 | 1.49026 | 0.745132 | − | 0.666917i | \(-0.232387\pi\) | ||||
0.745132 | + | 0.666917i | \(0.232387\pi\) | |||||||
\(774\) | −6.19877 | −0.222810 | ||||||||
\(775\) | 39.8215 | 1.43043 | ||||||||
\(776\) | 1.41009 | 0.0506192 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 25.3665 | 0.909433 | ||||||||
\(779\) | −3.96318 | −0.141996 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.6075 | 0.522698 | ||||||||
\(782\) | −17.1497 | −0.613273 | ||||||||
\(783\) | −14.9020 | −0.532552 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −32.1175 | −1.14632 | ||||||||
\(786\) | −30.8513 | −1.10043 | ||||||||
\(787\) | −23.8627 | −0.850612 | −0.425306 | − | 0.905050i | \(-0.639833\pi\) | ||||
−0.425306 | + | 0.905050i | \(0.639833\pi\) | |||||||
\(788\) | −1.10643 | −0.0394148 | ||||||||
\(789\) | 31.6424 | 1.12650 | ||||||||
\(790\) | −13.7040 | −0.487565 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.53221 | −0.161045 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −19.5098 | −0.692377 | ||||||||
\(795\) | 0.585088 | 0.0207509 | ||||||||
\(796\) | −2.02135 | −0.0716447 | ||||||||
\(797\) | 50.8231 | 1.80025 | 0.900123 | − | 0.435636i | \(-0.143476\pi\) | ||||
0.900123 | + | 0.435636i | \(0.143476\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.92052 | 0.244830 | ||||||||
\(800\) | −8.29397 | −0.293236 | ||||||||
\(801\) | 9.11367 | 0.322016 | ||||||||
\(802\) | −28.2349 | −0.997008 | ||||||||
\(803\) | 0.972438 | 0.0343166 | ||||||||
\(804\) | 2.46691 | 0.0870014 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.7348 | −0.941110 | ||||||||
\(808\) | 8.48119 | 0.298367 | ||||||||
\(809\) | 4.41176 | 0.155109 | 0.0775547 | − | 0.996988i | \(-0.475289\pi\) | ||||
0.0775547 | + | 0.996988i | \(0.475289\pi\) | |||||||
\(810\) | −53.5704 | −1.88227 | ||||||||
\(811\) | −17.6493 | −0.619750 | −0.309875 | − | 0.950777i | \(-0.600287\pi\) | ||||
−0.309875 | + | 0.950777i | \(0.600287\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 55.2926 | 1.93920 | ||||||||
\(814\) | 1.81657 | 0.0636707 | ||||||||
\(815\) | 42.9288 | 1.50373 | ||||||||
\(816\) | −56.8489 | −1.99011 | ||||||||
\(817\) | 3.61566 | 0.126496 | ||||||||
\(818\) | 28.8249 | 1.00784 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.85178 | −0.0995884 | ||||||||
\(821\) | −3.56043 | −0.124260 | −0.0621299 | − | 0.998068i | \(-0.519789\pi\) | ||||
−0.0621299 | + | 0.998068i | \(0.519789\pi\) | |||||||
\(822\) | −48.6232 | −1.69593 | ||||||||
\(823\) | 21.8665 | 0.762217 | 0.381109 | − | 0.924530i | \(-0.375542\pi\) | ||||
0.381109 | + | 0.924530i | \(0.375542\pi\) | |||||||
\(824\) | −33.3993 | −1.16352 | ||||||||
\(825\) | −20.2610 | −0.705396 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.1361 | 0.630653 | 0.315327 | − | 0.948983i | \(-0.397886\pi\) | ||||
0.315327 | + | 0.948983i | \(0.397886\pi\) | |||||||
\(828\) | −0.377220 | −0.0131093 | ||||||||
\(829\) | 30.8994 | 1.07318 | 0.536590 | − | 0.843843i | \(-0.319712\pi\) | ||||
0.536590 | + | 0.843843i | \(0.319712\pi\) | |||||||
\(830\) | 11.1579 | 0.387297 | ||||||||
\(831\) | 26.0393 | 0.903293 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 16.1530 | 0.559333 | ||||||||
\(835\) | −69.2933 | −2.39799 | ||||||||
\(836\) | 0.229755 | 0.00794625 | ||||||||
\(837\) | −18.9817 | −0.656103 | ||||||||
\(838\) | −10.7135 | −0.370090 | ||||||||
\(839\) | −15.3959 | −0.531526 | −0.265763 | − | 0.964038i | \(-0.585624\pi\) | ||||
−0.265763 | + | 0.964038i | \(0.585624\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.6393 | −0.435838 | ||||||||
\(842\) | −3.79065 | −0.130635 | ||||||||
\(843\) | 54.7820 | 1.88679 | ||||||||
\(844\) | 0.888153 | 0.0305715 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.44703 | −0.0497498 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.286615 | 0.00984239 | ||||||||
\(849\) | 30.2231 | 1.03726 | ||||||||
\(850\) | −80.4667 | −2.75998 | ||||||||
\(851\) | 1.73966 | 0.0596347 | ||||||||
\(852\) | 4.45845 | 0.152744 | ||||||||
\(853\) | −23.7772 | −0.814116 | −0.407058 | − | 0.913402i | \(-0.633445\pi\) | ||||
−0.407058 | + | 0.913402i | \(0.633445\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.05090 | −0.138538 | ||||||||
\(856\) | −19.3648 | −0.661877 | ||||||||
\(857\) | −30.1050 | −1.02837 | −0.514184 | − | 0.857680i | \(-0.671905\pi\) | ||||
−0.514184 | + | 0.857680i | \(0.671905\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.1343 | −0.516377 | −0.258188 | − | 0.966095i | \(-0.583126\pi\) | ||||
−0.258188 | + | 0.966095i | \(0.583126\pi\) | |||||||
\(860\) | 2.60172 | 0.0887178 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.71657 | 0.262827 | ||||||||
\(863\) | −18.2657 | −0.621773 | −0.310886 | − | 0.950447i | \(-0.600626\pi\) | ||||
−0.310886 | + | 0.950447i | \(0.600626\pi\) | |||||||
\(864\) | 3.95348 | 0.134500 | ||||||||
\(865\) | −51.3029 | −1.74435 | ||||||||
\(866\) | 32.9925 | 1.12113 | ||||||||
\(867\) | 87.9395 | 2.98658 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.65100 | 0.123852 | ||||||||
\(870\) | 39.7988 | 1.34931 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −17.2053 | −0.582643 | ||||||||
\(873\) | 0.575668 | 0.0194834 | ||||||||
\(874\) | −2.09159 | −0.0707492 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.296803 | 0.0100281 | ||||||||
\(877\) | −6.99639 | −0.236251 | −0.118126 | − | 0.992999i | \(-0.537689\pi\) | ||||
−0.118126 | + | 0.992999i | \(0.537689\pi\) | |||||||
\(878\) | −49.2922 | −1.66353 | ||||||||
\(879\) | −23.7465 | −0.800948 | ||||||||
\(880\) | −16.3458 | −0.551018 | ||||||||
\(881\) | 25.7746 | 0.868368 | 0.434184 | − | 0.900824i | \(-0.357037\pi\) | ||||
0.434184 | + | 0.900824i | \(0.357037\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.4526 | 0.553674 | 0.276837 | − | 0.960917i | \(-0.410714\pi\) | ||||
0.276837 | + | 0.960917i | \(0.410714\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 81.8086 | 2.74997 | ||||||||
\(886\) | −36.4467 | −1.22445 | ||||||||
\(887\) | 55.2455 | 1.85496 | 0.927481 | − | 0.373871i | \(-0.121970\pi\) | ||||
0.927481 | + | 0.373871i | \(0.121970\pi\) | |||||||
\(888\) | 6.37948 | 0.214081 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 36.3620 | 1.21886 | ||||||||
\(891\) | 14.2722 | 0.478137 | ||||||||
\(892\) | −4.61170 | −0.154411 | ||||||||
\(893\) | 0.844032 | 0.0282444 | ||||||||
\(894\) | −28.8995 | −0.966542 | ||||||||
\(895\) | −19.3590 | −0.647099 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −36.9028 | −1.23146 | ||||||||
\(899\) | 20.8398 | 0.695046 | ||||||||
\(900\) | −1.76992 | −0.0589973 | ||||||||
\(901\) | −0.619076 | −0.0206244 | ||||||||
\(902\) | −7.22241 | −0.240480 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.2478 | 0.640171 | ||||||||
\(905\) | −55.2655 | −1.83709 | ||||||||
\(906\) | −13.0007 | −0.431919 | ||||||||
\(907\) | 47.8424 | 1.58858 | 0.794290 | − | 0.607538i | \(-0.207843\pi\) | ||||
0.794290 | + | 0.607538i | \(0.207843\pi\) | |||||||
\(908\) | 2.92694 | 0.0971338 | ||||||||
\(909\) | 3.46245 | 0.114842 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.0711 | −0.764380 | −0.382190 | − | 0.924084i | \(-0.624830\pi\) | ||||
−0.382190 | + | 0.924084i | \(0.624830\pi\) | |||||||
\(912\) | −6.93333 | −0.229585 | ||||||||
\(913\) | −2.97269 | −0.0983817 | ||||||||
\(914\) | −53.3569 | −1.76489 | ||||||||
\(915\) | 55.7637 | 1.84349 | ||||||||
\(916\) | 3.11277 | 0.102849 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 38.3560 | 1.26594 | ||||||||
\(919\) | −43.4368 | −1.43285 | −0.716424 | − | 0.697665i | \(-0.754222\pi\) | ||||
−0.716424 | + | 0.697665i | \(0.754222\pi\) | |||||||
\(920\) | −17.3171 | −0.570929 | ||||||||
\(921\) | 60.1367 | 1.98157 | ||||||||
\(922\) | −6.58595 | −0.216897 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.16249 | 0.268381 | ||||||||
\(926\) | −6.33861 | −0.208300 | ||||||||
\(927\) | −13.6353 | −0.447841 | ||||||||
\(928\) | −4.34049 | −0.142484 | ||||||||
\(929\) | 12.7819 | 0.419361 | 0.209680 | − | 0.977770i | \(-0.432758\pi\) | ||||
0.209680 | + | 0.977770i | \(0.432758\pi\) | |||||||
\(930\) | 50.6945 | 1.66234 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5.54171 | 0.181525 | ||||||||
\(933\) | −0.308857 | −0.0101115 | ||||||||
\(934\) | −43.0689 | −1.40926 | ||||||||
\(935\) | 35.3063 | 1.15464 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.2533 | 0.530971 | 0.265486 | − | 0.964115i | \(-0.414468\pi\) | ||||
0.265486 | + | 0.964115i | \(0.414468\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.5694 | −0.703891 | ||||||||
\(940\) | 0.607339 | 0.0198092 | ||||||||
\(941\) | 45.1488 | 1.47181 | 0.735905 | − | 0.677085i | \(-0.236757\pi\) | ||||
0.735905 | + | 0.677085i | \(0.236757\pi\) | |||||||
\(942\) | −24.8265 | −0.808890 | ||||||||
\(943\) | −6.91662 | −0.225236 | ||||||||
\(944\) | 40.0752 | 1.30434 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.58911 | 0.214230 | ||||||||
\(947\) | 19.8557 | 0.645225 | 0.322612 | − | 0.946531i | \(-0.395439\pi\) | ||||
0.322612 | + | 0.946531i | \(0.395439\pi\) | |||||||
\(948\) | 1.11434 | 0.0361922 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −9.81378 | −0.318401 | ||||||||
\(951\) | −3.08901 | −0.100168 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.7287 | 0.509501 | 0.254751 | − | 0.967007i | \(-0.418007\pi\) | ||||
0.254751 | + | 0.967007i | \(0.418007\pi\) | |||||||
\(954\) | 0.129444 | 0.00419090 | ||||||||
\(955\) | −16.9335 | −0.547954 | ||||||||
\(956\) | 1.64745 | 0.0532823 | ||||||||
\(957\) | −10.6032 | −0.342752 | ||||||||
\(958\) | −24.2470 | −0.783385 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −62.9734 | −2.03246 | ||||||||
\(961\) | −4.45488 | −0.143706 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.90569 | −0.254757 | ||||||||
\(964\) | 3.46432 | 0.111578 | ||||||||
\(965\) | −75.0629 | −2.41636 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.1912 | 1.67835 | 0.839177 | − | 0.543858i | \(-0.183037\pi\) | ||||
0.839177 | + | 0.543858i | \(0.183037\pi\) | |||||||
\(968\) | −27.5943 | −0.886915 | ||||||||
\(969\) | 14.9757 | 0.481089 | ||||||||
\(970\) | 2.29682 | 0.0737465 | ||||||||
\(971\) | −22.4584 | −0.720724 | −0.360362 | − | 0.932813i | \(-0.617347\pi\) | ||||
−0.360362 | + | 0.932813i | \(0.617347\pi\) | |||||||
\(972\) | 2.25207 | 0.0722350 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 23.6765 | 0.758645 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 27.3167 | 0.874387 | ||||||||
\(977\) | 41.0345 | 1.31281 | 0.656405 | − | 0.754409i | \(-0.272076\pi\) | ||||
0.656405 | + | 0.754409i | \(0.272076\pi\) | |||||||
\(978\) | 33.1835 | 1.06109 | ||||||||
\(979\) | −9.68755 | −0.309616 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.02404 | −0.224260 | ||||||||
\(982\) | −5.19742 | −0.165856 | ||||||||
\(983\) | 26.8328 | 0.855832 | 0.427916 | − | 0.903818i | \(-0.359248\pi\) | ||||
0.427916 | + | 0.903818i | \(0.359248\pi\) | |||||||
\(984\) | −25.3639 | −0.808571 | ||||||||
\(985\) | −20.7362 | −0.660711 | ||||||||
\(986\) | −42.1107 | −1.34108 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.31013 | 0.200650 | ||||||||
\(990\) | −7.38228 | −0.234624 | ||||||||
\(991\) | 10.3751 | 0.329576 | 0.164788 | − | 0.986329i | \(-0.447306\pi\) | ||||
0.164788 | + | 0.986329i | \(0.447306\pi\) | |||||||
\(992\) | −5.52879 | −0.175539 | ||||||||
\(993\) | −51.7669 | −1.64277 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −37.8833 | −1.20098 | ||||||||
\(996\) | −0.907312 | −0.0287493 | ||||||||
\(997\) | −53.9097 | −1.70734 | −0.853669 | − | 0.520816i | \(-0.825628\pi\) | ||||
−0.853669 | + | 0.520816i | \(0.825628\pi\) | |||||||
\(998\) | −17.0134 | −0.538550 | ||||||||
\(999\) | −3.89081 | −0.123100 |
(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 | 8281.2.a.cp.1.4 | 12 | ||
7.2 | even | 3 | 1183.2.e.j.508.9 | 24 | |||
7.4 | even | 3 | 1183.2.e.j.170.9 | 24 | |||
7.6 | odd | 2 | 8281.2.a.co.1.4 | 12 | |||
13.2 | odd | 12 | 637.2.q.g.589.2 | 12 | |||
13.7 | odd | 12 | 637.2.q.g.491.2 | 12 | |||
13.12 | even | 2 | inner | 8281.2.a.cp.1.9 | 12 | ||
91.2 | odd | 12 | 91.2.k.b.4.5 | ✓ | 12 | ||
91.20 | even | 12 | 637.2.q.i.491.2 | 12 | |||
91.25 | even | 6 | 1183.2.e.j.170.4 | 24 | |||
91.33 | even | 12 | 637.2.u.g.361.5 | 12 | |||
91.41 | even | 12 | 637.2.q.i.589.2 | 12 | |||
91.46 | odd | 12 | 91.2.k.b.23.2 | yes | 12 | ||
91.51 | even | 6 | 1183.2.e.j.508.4 | 24 | |||
91.54 | even | 12 | 637.2.k.i.459.5 | 12 | |||
91.59 | even | 12 | 637.2.k.i.569.2 | 12 | |||
91.67 | odd | 12 | 91.2.u.b.30.5 | yes | 12 | ||
91.72 | odd | 12 | 91.2.u.b.88.5 | yes | 12 | ||
91.80 | even | 12 | 637.2.u.g.30.5 | 12 | |||
91.90 | odd | 2 | 8281.2.a.co.1.9 | 12 | |||
273.2 | even | 12 | 819.2.bm.f.550.2 | 12 | |||
273.137 | even | 12 | 819.2.bm.f.478.5 | 12 | |||
273.158 | even | 12 | 819.2.do.e.667.2 | 12 | |||
273.254 | even | 12 | 819.2.do.e.361.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.5 | ✓ | 12 | 91.2 | odd | 12 | ||
91.2.k.b.23.2 | yes | 12 | 91.46 | odd | 12 | ||
91.2.u.b.30.5 | yes | 12 | 91.67 | odd | 12 | ||
91.2.u.b.88.5 | yes | 12 | 91.72 | odd | 12 | ||
637.2.k.i.459.5 | 12 | 91.54 | even | 12 | |||
637.2.k.i.569.2 | 12 | 91.59 | even | 12 | |||
637.2.q.g.491.2 | 12 | 13.7 | odd | 12 | |||
637.2.q.g.589.2 | 12 | 13.2 | odd | 12 | |||
637.2.q.i.491.2 | 12 | 91.20 | even | 12 | |||
637.2.q.i.589.2 | 12 | 91.41 | even | 12 | |||
637.2.u.g.30.5 | 12 | 91.80 | even | 12 | |||
637.2.u.g.361.5 | 12 | 91.33 | even | 12 | |||
819.2.bm.f.478.5 | 12 | 273.137 | even | 12 | |||
819.2.bm.f.550.2 | 12 | 273.2 | even | 12 | |||
819.2.do.e.361.2 | 12 | 273.254 | even | 12 | |||
819.2.do.e.667.2 | 12 | 273.158 | even | 12 | |||
1183.2.e.j.170.4 | 24 | 91.25 | even | 6 | |||
1183.2.e.j.170.9 | 24 | 7.4 | even | 3 | |||
1183.2.e.j.508.4 | 24 | 91.51 | even | 6 | |||
1183.2.e.j.508.9 | 24 | 7.2 | even | 3 | |||
8281.2.a.co.1.4 | 12 | 7.6 | odd | 2 | |||
8281.2.a.co.1.9 | 12 | 91.90 | odd | 2 | |||
8281.2.a.cp.1.4 | 12 | 1.1 | even | 1 | trivial | ||
8281.2.a.cp.1.9 | 12 | 13.12 | even | 2 | inner |