Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7225,2,Mod(1,7225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7225, 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("7225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7225 = 5^{2} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7225.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: | \(57.6919154604\) |
Analytic rank: | \(1\) |
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: |
\( x^{15} - 21 x^{13} - 2 x^{12} + 171 x^{11} + 30 x^{10} - 678 x^{9} - 153 x^{8} + 1350 x^{7} + 301 x^{6} + \cdots + 3 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.567962\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.567962 | −0.401610 | −0.200805 | − | 0.979631i | \(-0.564356\pi\) | ||||
−0.200805 | + | 0.979631i | \(0.564356\pi\) | |||||||
\(3\) | −2.88559 | −1.66600 | −0.832998 | − | 0.553276i | \(-0.813377\pi\) | ||||
−0.832998 | + | 0.553276i | \(0.813377\pi\) | |||||||
\(4\) | −1.67742 | −0.838710 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.63891 | 0.669080 | ||||||||
\(7\) | −5.00907 | −1.89325 | −0.946626 | − | 0.322335i | \(-0.895532\pi\) | ||||
−0.946626 | + | 0.322335i | \(0.895532\pi\) | |||||||
\(8\) | 2.08863 | 0.738444 | ||||||||
\(9\) | 5.32662 | 1.77554 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.17554 | 1.25897 | 0.629487 | − | 0.777011i | \(-0.283265\pi\) | ||||
0.629487 | + | 0.777011i | \(0.283265\pi\) | |||||||
\(12\) | 4.84034 | 1.39729 | ||||||||
\(13\) | 0.657310 | 0.182305 | 0.0911526 | − | 0.995837i | \(-0.470945\pi\) | ||||
0.0911526 | + | 0.995837i | \(0.470945\pi\) | |||||||
\(14\) | 2.84496 | 0.760348 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.16857 | 0.542143 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −3.02532 | −0.713075 | ||||||||
\(19\) | −5.62036 | −1.28940 | −0.644700 | − | 0.764436i | \(-0.723018\pi\) | ||||
−0.644700 | + | 0.764436i | \(0.723018\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14.4541 | 3.15415 | ||||||||
\(22\) | −2.37155 | −0.505616 | ||||||||
\(23\) | −4.27833 | −0.892093 | −0.446046 | − | 0.895010i | \(-0.647168\pi\) | ||||
−0.446046 | + | 0.895010i | \(0.647168\pi\) | |||||||
\(24\) | −6.02694 | −1.23024 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.373327 | −0.0732155 | ||||||||
\(27\) | −6.71368 | −1.29205 | ||||||||
\(28\) | 8.40231 | 1.58789 | ||||||||
\(29\) | −5.59957 | −1.03981 | −0.519907 | − | 0.854223i | \(-0.674033\pi\) | ||||
−0.519907 | + | 0.854223i | \(0.674033\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.143757 | 0.0258195 | 0.0129098 | − | 0.999917i | \(-0.495891\pi\) | ||||
0.0129098 | + | 0.999917i | \(0.495891\pi\) | |||||||
\(32\) | −5.40894 | −0.956174 | ||||||||
\(33\) | −12.0489 | −2.09744 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −8.93498 | −1.48916 | ||||||||
\(37\) | −4.88950 | −0.803828 | −0.401914 | − | 0.915677i | \(-0.631655\pi\) | ||||
−0.401914 | + | 0.915677i | \(0.631655\pi\) | |||||||
\(38\) | 3.19215 | 0.517836 | ||||||||
\(39\) | −1.89673 | −0.303720 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.55997 | −0.243627 | −0.121813 | − | 0.992553i | \(-0.538871\pi\) | ||||
−0.121813 | + | 0.992553i | \(0.538871\pi\) | |||||||
\(42\) | −8.20939 | −1.26674 | ||||||||
\(43\) | −2.97180 | −0.453196 | −0.226598 | − | 0.973988i | \(-0.572760\pi\) | ||||
−0.226598 | + | 0.973988i | \(0.572760\pi\) | |||||||
\(44\) | −7.00414 | −1.05591 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.42993 | 0.358273 | ||||||||
\(47\) | −11.4416 | −1.66893 | −0.834466 | − | 0.551060i | \(-0.814223\pi\) | ||||
−0.834466 | + | 0.551060i | \(0.814223\pi\) | |||||||
\(48\) | −6.25761 | −0.903208 | ||||||||
\(49\) | 18.0908 | 2.58440 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.10259 | −0.152901 | ||||||||
\(53\) | 13.3194 | 1.82956 | 0.914778 | − | 0.403957i | \(-0.132365\pi\) | ||||
0.914778 | + | 0.403957i | \(0.132365\pi\) | |||||||
\(54\) | 3.81312 | 0.518900 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −10.4621 | −1.39806 | ||||||||
\(57\) | 16.2181 | 2.14813 | ||||||||
\(58\) | 3.18034 | 0.417599 | ||||||||
\(59\) | 10.1079 | 1.31594 | 0.657968 | − | 0.753045i | \(-0.271416\pi\) | ||||
0.657968 | + | 0.753045i | \(0.271416\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.961538 | −0.123112 | −0.0615562 | − | 0.998104i | \(-0.519606\pi\) | ||||
−0.0615562 | + | 0.998104i | \(0.519606\pi\) | |||||||
\(62\) | −0.0816486 | −0.0103694 | ||||||||
\(63\) | −26.6814 | −3.36155 | ||||||||
\(64\) | −1.26508 | −0.158135 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.84332 | 0.842354 | ||||||||
\(67\) | 0.747944 | 0.0913759 | 0.0456880 | − | 0.998956i | \(-0.485452\pi\) | ||||
0.0456880 | + | 0.998956i | \(0.485452\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.3455 | 1.48622 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.0687573 | 0.00815999 | 0.00408000 | − | 0.999992i | \(-0.498701\pi\) | ||||
0.00408000 | + | 0.999992i | \(0.498701\pi\) | |||||||
\(72\) | 11.1254 | 1.31114 | ||||||||
\(73\) | −1.46435 | −0.171389 | −0.0856944 | − | 0.996321i | \(-0.527311\pi\) | ||||
−0.0856944 | + | 0.996321i | \(0.527311\pi\) | |||||||
\(74\) | 2.77705 | 0.322825 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.42771 | 1.08143 | ||||||||
\(77\) | −20.9156 | −2.38355 | ||||||||
\(78\) | 1.07727 | 0.121977 | ||||||||
\(79\) | 6.72529 | 0.756654 | 0.378327 | − | 0.925672i | \(-0.376500\pi\) | ||||
0.378327 | + | 0.925672i | \(0.376500\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.39306 | 0.377007 | ||||||||
\(82\) | 0.886004 | 0.0978428 | ||||||||
\(83\) | 6.20936 | 0.681566 | 0.340783 | − | 0.940142i | \(-0.389308\pi\) | ||||
0.340783 | + | 0.940142i | \(0.389308\pi\) | |||||||
\(84\) | −24.2456 | −2.64541 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.68787 | 0.182008 | ||||||||
\(87\) | 16.1581 | 1.73233 | ||||||||
\(88\) | 8.72118 | 0.929681 | ||||||||
\(89\) | 10.9442 | 1.16008 | 0.580041 | − | 0.814587i | \(-0.303037\pi\) | ||||
0.580041 | + | 0.814587i | \(0.303037\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.29252 | −0.345149 | ||||||||
\(92\) | 7.17655 | 0.748207 | ||||||||
\(93\) | −0.414824 | −0.0430153 | ||||||||
\(94\) | 6.49840 | 0.670259 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 15.6080 | 1.59298 | ||||||||
\(97\) | 7.76437 | 0.788352 | 0.394176 | − | 0.919035i | \(-0.371030\pi\) | ||||
0.394176 | + | 0.919035i | \(0.371030\pi\) | |||||||
\(98\) | −10.2749 | −1.03792 | ||||||||
\(99\) | 22.2416 | 2.23536 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.07228 | 0.604215 | 0.302107 | − | 0.953274i | \(-0.402310\pi\) | ||||
0.302107 | + | 0.953274i | \(0.402310\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.0314 | 1.18549 | 0.592744 | − | 0.805391i | \(-0.298044\pi\) | ||||
0.592744 | + | 0.805391i | \(0.298044\pi\) | |||||||
\(104\) | 1.37288 | 0.134622 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.56490 | −0.734768 | ||||||||
\(107\) | 10.9225 | 1.05591 | 0.527957 | − | 0.849271i | \(-0.322958\pi\) | ||||
0.527957 | + | 0.849271i | \(0.322958\pi\) | |||||||
\(108\) | 11.2617 | 1.08365 | ||||||||
\(109\) | −14.5989 | −1.39832 | −0.699162 | − | 0.714964i | \(-0.746443\pi\) | ||||
−0.699162 | + | 0.714964i | \(0.746443\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.1091 | 1.33917 | ||||||||
\(112\) | −10.8625 | −1.02641 | ||||||||
\(113\) | 1.40986 | 0.132628 | 0.0663141 | − | 0.997799i | \(-0.478876\pi\) | ||||
0.0663141 | + | 0.997799i | \(0.478876\pi\) | |||||||
\(114\) | −9.21124 | −0.862712 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.39282 | 0.872102 | ||||||||
\(117\) | 3.50125 | 0.323690 | ||||||||
\(118\) | −5.74091 | −0.528493 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.43516 | 0.585015 | ||||||||
\(122\) | 0.546117 | 0.0494431 | ||||||||
\(123\) | 4.50143 | 0.405881 | ||||||||
\(124\) | −0.241141 | −0.0216551 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 15.1541 | 1.35003 | ||||||||
\(127\) | 1.54162 | 0.136797 | 0.0683984 | − | 0.997658i | \(-0.478211\pi\) | ||||
0.0683984 | + | 0.997658i | \(0.478211\pi\) | |||||||
\(128\) | 11.5364 | 1.01968 | ||||||||
\(129\) | 8.57540 | 0.755022 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.08132 | −0.181845 | −0.0909227 | − | 0.995858i | \(-0.528982\pi\) | ||||
−0.0909227 | + | 0.995858i | \(0.528982\pi\) | |||||||
\(132\) | 20.2111 | 1.75915 | ||||||||
\(133\) | 28.1528 | 2.44116 | ||||||||
\(134\) | −0.424804 | −0.0366975 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.1320 | 0.951072 | 0.475536 | − | 0.879696i | \(-0.342254\pi\) | ||||
0.475536 | + | 0.879696i | \(0.342254\pi\) | |||||||
\(138\) | −7.01177 | −0.596882 | ||||||||
\(139\) | −15.0404 | −1.27571 | −0.637853 | − | 0.770158i | \(-0.720177\pi\) | ||||
−0.637853 | + | 0.770158i | \(0.720177\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 33.0158 | 2.78043 | ||||||||
\(142\) | −0.0390515 | −0.00327713 | ||||||||
\(143\) | 2.74463 | 0.229517 | ||||||||
\(144\) | 11.5512 | 0.962598 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.831694 | 0.0688314 | ||||||||
\(147\) | −52.2026 | −4.30560 | ||||||||
\(148\) | 8.20174 | 0.674178 | ||||||||
\(149\) | 9.68788 | 0.793662 | 0.396831 | − | 0.917892i | \(-0.370110\pi\) | ||||
0.396831 | + | 0.917892i | \(0.370110\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.9184 | 1.05129 | 0.525644 | − | 0.850705i | \(-0.323824\pi\) | ||||
0.525644 | + | 0.850705i | \(0.323824\pi\) | |||||||
\(152\) | −11.7389 | −0.952149 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 11.8793 | 0.957259 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.18161 | 0.254732 | ||||||||
\(157\) | −14.3030 | −1.14150 | −0.570752 | − | 0.821122i | \(-0.693348\pi\) | ||||
−0.570752 | + | 0.821122i | \(0.693348\pi\) | |||||||
\(158\) | −3.81971 | −0.303880 | ||||||||
\(159\) | −38.4342 | −3.04803 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 21.4304 | 1.68896 | ||||||||
\(162\) | −1.92713 | −0.151410 | ||||||||
\(163\) | −14.2490 | −1.11607 | −0.558035 | − | 0.829817i | \(-0.688445\pi\) | ||||
−0.558035 | + | 0.829817i | \(0.688445\pi\) | |||||||
\(164\) | 2.61672 | 0.204332 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.52668 | −0.273724 | ||||||||
\(167\) | 0.117789 | 0.00911480 | 0.00455740 | − | 0.999990i | \(-0.498549\pi\) | ||||
0.00455740 | + | 0.999990i | \(0.498549\pi\) | |||||||
\(168\) | 30.1894 | 2.32916 | ||||||||
\(169\) | −12.5679 | −0.966765 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −29.9376 | −2.28938 | ||||||||
\(172\) | 4.98496 | 0.380099 | ||||||||
\(173\) | 12.6922 | 0.964971 | 0.482486 | − | 0.875904i | \(-0.339734\pi\) | ||||
0.482486 | + | 0.875904i | \(0.339734\pi\) | |||||||
\(174\) | −9.17716 | −0.695719 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.05497 | 0.682544 | ||||||||
\(177\) | −29.1673 | −2.19235 | ||||||||
\(178\) | −6.21588 | −0.465900 | ||||||||
\(179\) | 10.8855 | 0.813618 | 0.406809 | − | 0.913513i | \(-0.366641\pi\) | ||||
0.406809 | + | 0.913513i | \(0.366641\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.1464 | 0.977163 | 0.488581 | − | 0.872518i | \(-0.337515\pi\) | ||||
0.488581 | + | 0.872518i | \(0.337515\pi\) | |||||||
\(182\) | 1.87002 | 0.138615 | ||||||||
\(183\) | 2.77460 | 0.205105 | ||||||||
\(184\) | −8.93586 | −0.658760 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.235604 | 0.0172753 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 19.1924 | 1.39975 | ||||||||
\(189\) | 33.6293 | 2.44617 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.1085 | −1.09321 | −0.546605 | − | 0.837391i | \(-0.684080\pi\) | ||||
−0.546605 | + | 0.837391i | \(0.684080\pi\) | |||||||
\(192\) | 3.65049 | 0.263451 | ||||||||
\(193\) | −12.5625 | −0.904266 | −0.452133 | − | 0.891950i | \(-0.649337\pi\) | ||||
−0.452133 | + | 0.891950i | \(0.649337\pi\) | |||||||
\(194\) | −4.40987 | −0.316610 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −30.3459 | −2.16756 | ||||||||
\(197\) | 11.4550 | 0.816134 | 0.408067 | − | 0.912952i | \(-0.366203\pi\) | ||||
0.408067 | + | 0.912952i | \(0.366203\pi\) | |||||||
\(198\) | −12.6324 | −0.897743 | ||||||||
\(199\) | −5.54827 | −0.393306 | −0.196653 | − | 0.980473i | \(-0.563007\pi\) | ||||
−0.196653 | + | 0.980473i | \(0.563007\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.15826 | −0.152232 | ||||||||
\(202\) | −3.44883 | −0.242658 | ||||||||
\(203\) | 28.0486 | 1.96863 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.83338 | −0.476104 | ||||||||
\(207\) | −22.7890 | −1.58395 | ||||||||
\(208\) | 1.42543 | 0.0988355 | ||||||||
\(209\) | −23.4681 | −1.62332 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.30121 | 0.227265 | 0.113632 | − | 0.993523i | \(-0.463751\pi\) | ||||
0.113632 | + | 0.993523i | \(0.463751\pi\) | |||||||
\(212\) | −22.3422 | −1.53447 | ||||||||
\(213\) | −0.198405 | −0.0135945 | ||||||||
\(214\) | −6.20354 | −0.424065 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −14.0224 | −0.954106 | ||||||||
\(217\) | −0.720090 | −0.0488829 | ||||||||
\(218\) | 8.29163 | 0.561580 | ||||||||
\(219\) | 4.22550 | 0.285533 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −8.01342 | −0.537826 | ||||||||
\(223\) | −18.2613 | −1.22287 | −0.611434 | − | 0.791295i | \(-0.709407\pi\) | ||||
−0.611434 | + | 0.791295i | \(0.709407\pi\) | |||||||
\(224\) | 27.0938 | 1.81028 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.800745 | −0.0532648 | ||||||||
\(227\) | −12.4335 | −0.825237 | −0.412619 | − | 0.910904i | \(-0.635386\pi\) | ||||
−0.412619 | + | 0.910904i | \(0.635386\pi\) | |||||||
\(228\) | −27.2045 | −1.80166 | ||||||||
\(229\) | −18.6762 | −1.23416 | −0.617080 | − | 0.786900i | \(-0.711685\pi\) | ||||
−0.617080 | + | 0.786900i | \(0.711685\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 60.3538 | 3.97099 | ||||||||
\(232\) | −11.6955 | −0.767844 | ||||||||
\(233\) | 1.53341 | 0.100457 | 0.0502284 | − | 0.998738i | \(-0.484005\pi\) | ||||
0.0502284 | + | 0.998738i | \(0.484005\pi\) | |||||||
\(234\) | −1.98857 | −0.129997 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −16.9552 | −1.10369 | ||||||||
\(237\) | −19.4064 | −1.26058 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.27893 | −0.600204 | −0.300102 | − | 0.953907i | \(-0.597021\pi\) | ||||
−0.300102 | + | 0.953907i | \(0.597021\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.0757 | 1.80851 | 0.904257 | − | 0.426988i | \(-0.140425\pi\) | ||||
0.904257 | + | 0.426988i | \(0.140425\pi\) | |||||||
\(242\) | −3.65493 | −0.234948 | ||||||||
\(243\) | 10.3501 | 0.663958 | ||||||||
\(244\) | 1.61290 | 0.103256 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.55664 | −0.163006 | ||||||||
\(247\) | −3.69432 | −0.235064 | ||||||||
\(248\) | 0.300256 | 0.0190663 | ||||||||
\(249\) | −17.9177 | −1.13549 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.3009 | −0.650189 | −0.325094 | − | 0.945682i | \(-0.605396\pi\) | ||||
−0.325094 | + | 0.945682i | \(0.605396\pi\) | |||||||
\(252\) | 44.7560 | 2.81936 | ||||||||
\(253\) | −17.8643 | −1.12312 | ||||||||
\(254\) | −0.875582 | −0.0549389 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.02208 | −0.251380 | ||||||||
\(257\) | 24.5419 | 1.53088 | 0.765441 | − | 0.643506i | \(-0.222521\pi\) | ||||
0.765441 | + | 0.643506i | \(0.222521\pi\) | |||||||
\(258\) | −4.87050 | −0.303224 | ||||||||
\(259\) | 24.4918 | 1.52185 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −29.8268 | −1.84623 | ||||||||
\(262\) | 1.18211 | 0.0730309 | ||||||||
\(263\) | 2.84217 | 0.175256 | 0.0876279 | − | 0.996153i | \(-0.472071\pi\) | ||||
0.0876279 | + | 0.996153i | \(0.472071\pi\) | |||||||
\(264\) | −25.1658 | −1.54884 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −15.9897 | −0.980393 | ||||||||
\(267\) | −31.5804 | −1.93269 | ||||||||
\(268\) | −1.25462 | −0.0766378 | ||||||||
\(269\) | 25.6796 | 1.56571 | 0.782857 | − | 0.622201i | \(-0.213761\pi\) | ||||
0.782857 | + | 0.622201i | \(0.213761\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.7663 | −0.714752 | −0.357376 | − | 0.933961i | \(-0.616329\pi\) | ||||
−0.357376 | + | 0.933961i | \(0.616329\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.50085 | 0.575017 | ||||||||
\(274\) | −6.32256 | −0.381960 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −20.7086 | −1.24651 | ||||||||
\(277\) | 11.5928 | 0.696545 | 0.348273 | − | 0.937393i | \(-0.386768\pi\) | ||||
0.348273 | + | 0.937393i | \(0.386768\pi\) | |||||||
\(278\) | 8.54235 | 0.512336 | ||||||||
\(279\) | 0.765741 | 0.0458437 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.5107 | 1.76046 | 0.880229 | − | 0.474549i | \(-0.157389\pi\) | ||||
0.880229 | + | 0.474549i | \(0.157389\pi\) | |||||||
\(282\) | −18.7517 | −1.11665 | ||||||||
\(283\) | −0.0152294 | −0.000905295 0 | −0.000452648 | − | 1.00000i | \(-0.500144\pi\) | ||||
−0.000452648 | 1.00000i | \(0.500144\pi\) | ||||||||
\(284\) | −0.115335 | −0.00684386 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.55884 | −0.0921764 | ||||||||
\(287\) | 7.81401 | 0.461246 | ||||||||
\(288\) | −28.8114 | −1.69773 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.4048 | −1.31339 | ||||||||
\(292\) | 2.45632 | 0.143745 | ||||||||
\(293\) | −3.52542 | −0.205957 | −0.102979 | − | 0.994684i | \(-0.532837\pi\) | ||||
−0.102979 | + | 0.994684i | \(0.532837\pi\) | |||||||
\(294\) | 29.6491 | 1.72917 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −10.2124 | −0.593582 | ||||||||
\(297\) | −28.0333 | −1.62666 | ||||||||
\(298\) | −5.50235 | −0.318743 | ||||||||
\(299\) | −2.81219 | −0.162633 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.8860 | 0.858013 | ||||||||
\(302\) | −7.33719 | −0.422208 | ||||||||
\(303\) | −17.5221 | −1.00662 | ||||||||
\(304\) | −12.1882 | −0.699040 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.7368 | −1.24058 | −0.620292 | − | 0.784371i | \(-0.712986\pi\) | ||||
−0.620292 | + | 0.784371i | \(0.712986\pi\) | |||||||
\(308\) | 35.0842 | 1.99911 | ||||||||
\(309\) | −34.7177 | −1.97502 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.74863 | −0.0991556 | −0.0495778 | − | 0.998770i | \(-0.515788\pi\) | ||||
−0.0495778 | + | 0.998770i | \(0.515788\pi\) | |||||||
\(312\) | −3.96157 | −0.224280 | ||||||||
\(313\) | 16.6552 | 0.941406 | 0.470703 | − | 0.882292i | \(-0.344000\pi\) | ||||
0.470703 | + | 0.882292i | \(0.344000\pi\) | |||||||
\(314\) | 8.12357 | 0.458440 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.2811 | −0.634613 | ||||||||
\(317\) | 21.9922 | 1.23520 | 0.617602 | − | 0.786491i | \(-0.288104\pi\) | ||||
0.617602 | + | 0.786491i | \(0.288104\pi\) | |||||||
\(318\) | 21.8292 | 1.22412 | ||||||||
\(319\) | −23.3812 | −1.30910 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −31.5177 | −1.75915 | ||||||||
\(322\) | −12.1717 | −0.678301 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −5.69158 | −0.316199 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.09291 | 0.448225 | ||||||||
\(327\) | 42.1265 | 2.32960 | ||||||||
\(328\) | −3.25821 | −0.179904 | ||||||||
\(329\) | 57.3119 | 3.15971 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.73526 | 0.315238 | 0.157619 | − | 0.987500i | \(-0.449618\pi\) | ||||
0.157619 | + | 0.987500i | \(0.449618\pi\) | |||||||
\(332\) | −10.4157 | −0.571636 | ||||||||
\(333\) | −26.0445 | −1.42723 | ||||||||
\(334\) | −0.0668998 | −0.00366059 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 31.3448 | 1.71000 | ||||||||
\(337\) | 8.30683 | 0.452502 | 0.226251 | − | 0.974069i | \(-0.427353\pi\) | ||||
0.226251 | + | 0.974069i | \(0.427353\pi\) | |||||||
\(338\) | 7.13811 | 0.388262 | ||||||||
\(339\) | −4.06827 | −0.220958 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.600264 | 0.0325061 | ||||||||
\(342\) | 17.0034 | 0.919439 | ||||||||
\(343\) | −55.5547 | −2.99967 | ||||||||
\(344\) | −6.20701 | −0.334659 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.20870 | −0.387542 | ||||||||
\(347\) | −16.6251 | −0.892485 | −0.446242 | − | 0.894912i | \(-0.647238\pi\) | ||||
−0.446242 | + | 0.894912i | \(0.647238\pi\) | |||||||
\(348\) | −27.1038 | −1.45292 | ||||||||
\(349\) | −18.6990 | −1.00093 | −0.500467 | − | 0.865755i | \(-0.666839\pi\) | ||||
−0.500467 | + | 0.865755i | \(0.666839\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.41297 | −0.235547 | ||||||||
\(352\) | −22.5852 | −1.20380 | ||||||||
\(353\) | 5.78418 | 0.307861 | 0.153930 | − | 0.988082i | \(-0.450807\pi\) | ||||
0.153930 | + | 0.988082i | \(0.450807\pi\) | |||||||
\(354\) | 16.5659 | 0.880467 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −18.3580 | −0.972971 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.18253 | −0.326757 | ||||||||
\(359\) | 34.2408 | 1.80716 | 0.903581 | − | 0.428417i | \(-0.140928\pi\) | ||||
0.903581 | + | 0.428417i | \(0.140928\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.5885 | 0.662552 | ||||||||
\(362\) | −7.46665 | −0.392438 | ||||||||
\(363\) | −18.5692 | −0.974632 | ||||||||
\(364\) | 5.52293 | 0.289480 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.57587 | −0.0823720 | ||||||||
\(367\) | −17.4496 | −0.910860 | −0.455430 | − | 0.890272i | \(-0.650514\pi\) | ||||
−0.455430 | + | 0.890272i | \(0.650514\pi\) | |||||||
\(368\) | −9.27787 | −0.483642 | ||||||||
\(369\) | −8.30938 | −0.432569 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −66.7177 | −3.46381 | ||||||||
\(372\) | 0.695834 | 0.0360773 | ||||||||
\(373\) | −3.90239 | −0.202058 | −0.101029 | − | 0.994883i | \(-0.532213\pi\) | ||||
−0.101029 | + | 0.994883i | \(0.532213\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −23.8974 | −1.23241 | ||||||||
\(377\) | −3.68065 | −0.189563 | ||||||||
\(378\) | −19.1002 | −0.982407 | ||||||||
\(379\) | 32.4372 | 1.66619 | 0.833094 | − | 0.553132i | \(-0.186567\pi\) | ||||
0.833094 | + | 0.553132i | \(0.186567\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.44848 | −0.227903 | ||||||||
\(382\) | 8.58103 | 0.439044 | ||||||||
\(383\) | 12.4887 | 0.638140 | 0.319070 | − | 0.947731i | \(-0.396629\pi\) | ||||
0.319070 | + | 0.947731i | \(0.396629\pi\) | |||||||
\(384\) | −33.2893 | −1.69879 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.13501 | 0.363162 | ||||||||
\(387\) | −15.8297 | −0.804668 | ||||||||
\(388\) | −13.0241 | −0.661199 | ||||||||
\(389\) | −12.0159 | −0.609232 | −0.304616 | − | 0.952475i | \(-0.598528\pi\) | ||||
−0.304616 | + | 0.952475i | \(0.598528\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 37.7851 | 1.90843 | ||||||||
\(393\) | 6.00582 | 0.302954 | ||||||||
\(394\) | −6.50600 | −0.327768 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −37.3084 | −1.87482 | ||||||||
\(397\) | 10.6585 | 0.534934 | 0.267467 | − | 0.963567i | \(-0.413813\pi\) | ||||
0.267467 | + | 0.963567i | \(0.413813\pi\) | |||||||
\(398\) | 3.15121 | 0.157956 | ||||||||
\(399\) | −81.2374 | −4.06696 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.0381 | −0.501278 | −0.250639 | − | 0.968081i | \(-0.580641\pi\) | ||||
−0.250639 | + | 0.968081i | \(0.580641\pi\) | |||||||
\(402\) | 1.22581 | 0.0611378 | ||||||||
\(403\) | 0.0944931 | 0.00470704 | ||||||||
\(404\) | −10.1858 | −0.506761 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.9306 | −0.790621 | ||||||||
\(407\) | −20.4163 | −1.01200 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.1053 | −0.648017 | −0.324008 | − | 0.946054i | \(-0.605031\pi\) | ||||
−0.324008 | + | 0.946054i | \(0.605031\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −32.1224 | −1.58448 | ||||||||
\(412\) | −20.1817 | −0.994281 | ||||||||
\(413\) | −50.6312 | −2.49140 | ||||||||
\(414\) | 12.9433 | 0.636129 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.55535 | −0.174315 | ||||||||
\(417\) | 43.4003 | 2.12532 | ||||||||
\(418\) | 13.3290 | 0.651941 | ||||||||
\(419\) | −37.0499 | −1.81001 | −0.905003 | − | 0.425406i | \(-0.860131\pi\) | ||||
−0.905003 | + | 0.425406i | \(0.860131\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.49427 | −0.219037 | −0.109519 | − | 0.993985i | \(-0.534931\pi\) | ||||
−0.109519 | + | 0.993985i | \(0.534931\pi\) | |||||||
\(422\) | −1.87496 | −0.0912717 | ||||||||
\(423\) | −60.9452 | −2.96326 | ||||||||
\(424\) | 27.8193 | 1.35102 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.112687 | 0.00545969 | ||||||||
\(427\) | 4.81642 | 0.233083 | ||||||||
\(428\) | −18.3215 | −0.885605 | ||||||||
\(429\) | −7.91987 | −0.382375 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 39.1192 | 1.88430 | 0.942152 | − | 0.335185i | \(-0.108799\pi\) | ||||
0.942152 | + | 0.335185i | \(0.108799\pi\) | |||||||
\(432\) | −14.5591 | −0.700476 | ||||||||
\(433\) | 8.46352 | 0.406731 | 0.203366 | − | 0.979103i | \(-0.434812\pi\) | ||||
0.203366 | + | 0.979103i | \(0.434812\pi\) | |||||||
\(434\) | 0.408984 | 0.0196319 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 24.4885 | 1.17279 | ||||||||
\(437\) | 24.0458 | 1.15026 | ||||||||
\(438\) | −2.39993 | −0.114673 | ||||||||
\(439\) | −32.1434 | −1.53412 | −0.767061 | − | 0.641574i | \(-0.778282\pi\) | ||||
−0.767061 | + | 0.641574i | \(0.778282\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 96.3629 | 4.58871 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.3440 | −1.15662 | −0.578308 | − | 0.815818i | \(-0.696287\pi\) | ||||
−0.578308 | + | 0.815818i | \(0.696287\pi\) | |||||||
\(444\) | −23.6668 | −1.12318 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.3717 | 0.491116 | ||||||||
\(447\) | −27.9553 | −1.32224 | ||||||||
\(448\) | 6.33686 | 0.299388 | ||||||||
\(449\) | −13.6669 | −0.644980 | −0.322490 | − | 0.946573i | \(-0.604520\pi\) | ||||
−0.322490 | + | 0.946573i | \(0.604520\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.51373 | −0.306719 | ||||||||
\(452\) | −2.36492 | −0.111237 | ||||||||
\(453\) | −37.2773 | −1.75144 | ||||||||
\(454\) | 7.06173 | 0.331423 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 33.8736 | 1.58628 | ||||||||
\(457\) | 9.61288 | 0.449672 | 0.224836 | − | 0.974397i | \(-0.427815\pi\) | ||||
0.224836 | + | 0.974397i | \(0.427815\pi\) | |||||||
\(458\) | 10.6074 | 0.495651 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.3179 | 0.899725 | 0.449862 | − | 0.893098i | \(-0.351473\pi\) | ||||
0.449862 | + | 0.893098i | \(0.351473\pi\) | |||||||
\(462\) | −34.2787 | −1.59479 | ||||||||
\(463\) | 20.8479 | 0.968883 | 0.484442 | − | 0.874824i | \(-0.339023\pi\) | ||||
0.484442 | + | 0.874824i | \(0.339023\pi\) | |||||||
\(464\) | −12.1431 | −0.563728 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.870916 | −0.0403444 | ||||||||
\(467\) | 22.0407 | 1.01992 | 0.509962 | − | 0.860197i | \(-0.329659\pi\) | ||||
0.509962 | + | 0.860197i | \(0.329659\pi\) | |||||||
\(468\) | −5.87306 | −0.271482 | ||||||||
\(469\) | −3.74651 | −0.172998 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 41.2726 | 1.90174 | ||||||||
\(472\) | 21.1117 | 0.971745 | ||||||||
\(473\) | −12.4089 | −0.570561 | ||||||||
\(474\) | 11.0221 | 0.506262 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 70.9473 | 3.24845 | ||||||||
\(478\) | 5.27008 | 0.241048 | ||||||||
\(479\) | 8.16793 | 0.373202 | 0.186601 | − | 0.982436i | \(-0.440253\pi\) | ||||
0.186601 | + | 0.982436i | \(0.440253\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.21392 | −0.146542 | ||||||||
\(482\) | −15.9459 | −0.726317 | ||||||||
\(483\) | −61.8395 | −2.81379 | ||||||||
\(484\) | −10.7945 | −0.490657 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −5.87845 | −0.266652 | ||||||||
\(487\) | −13.5824 | −0.615476 | −0.307738 | − | 0.951471i | \(-0.599572\pi\) | ||||
−0.307738 | + | 0.951471i | \(0.599572\pi\) | |||||||
\(488\) | −2.00830 | −0.0909116 | ||||||||
\(489\) | 41.1169 | 1.85937 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 41.4309 | 1.86975 | 0.934875 | − | 0.354978i | \(-0.115512\pi\) | ||||
0.934875 | + | 0.354978i | \(0.115512\pi\) | |||||||
\(492\) | −7.55079 | −0.340416 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 2.09824 | 0.0944041 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.311748 | 0.0139979 | ||||||||
\(497\) | −0.344410 | −0.0154489 | ||||||||
\(498\) | 10.1766 | 0.456022 | ||||||||
\(499\) | 2.98794 | 0.133759 | 0.0668793 | − | 0.997761i | \(-0.478696\pi\) | ||||
0.0668793 | + | 0.997761i | \(0.478696\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.339891 | −0.0151852 | ||||||||
\(502\) | 5.85053 | 0.261122 | ||||||||
\(503\) | −22.7093 | −1.01256 | −0.506279 | − | 0.862370i | \(-0.668979\pi\) | ||||
−0.506279 | + | 0.862370i | \(0.668979\pi\) | |||||||
\(504\) | −55.7278 | −2.48231 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.1463 | 0.451057 | ||||||||
\(507\) | 36.2659 | 1.61063 | ||||||||
\(508\) | −2.58594 | −0.114733 | ||||||||
\(509\) | 12.4475 | 0.551727 | 0.275863 | − | 0.961197i | \(-0.411036\pi\) | ||||
0.275863 | + | 0.961197i | \(0.411036\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.33502 | 0.324482 | ||||||||
\(512\) | −20.7884 | −0.918726 | ||||||||
\(513\) | 37.7333 | 1.66597 | ||||||||
\(514\) | −13.9389 | −0.614817 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −14.3845 | −0.633244 | ||||||||
\(517\) | −47.7750 | −2.10114 | ||||||||
\(518\) | −13.9104 | −0.611189 | ||||||||
\(519\) | −36.6245 | −1.60764 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.89567 | 0.126862 | 0.0634308 | − | 0.997986i | \(-0.479796\pi\) | ||||
0.0634308 | + | 0.997986i | \(0.479796\pi\) | |||||||
\(522\) | 16.9405 | 0.741465 | ||||||||
\(523\) | 43.9292 | 1.92089 | 0.960444 | − | 0.278472i | \(-0.0898281\pi\) | ||||
0.960444 | + | 0.278472i | \(0.0898281\pi\) | |||||||
\(524\) | 3.49124 | 0.152515 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.61424 | −0.0703844 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −26.1289 | −1.13712 | ||||||||
\(529\) | −4.69592 | −0.204170 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 53.8410 | 2.33650 | ||||||||
\(532\) | −47.2241 | −2.04742 | ||||||||
\(533\) | −1.02538 | −0.0444144 | ||||||||
\(534\) | 17.9365 | 0.776188 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.56218 | 0.0674760 | ||||||||
\(537\) | −31.4110 | −1.35548 | ||||||||
\(538\) | −14.5851 | −0.628806 | ||||||||
\(539\) | 75.5389 | 3.25369 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.3972 | −1.17790 | −0.588949 | − | 0.808170i | \(-0.700458\pi\) | ||||
−0.588949 | + | 0.808170i | \(0.700458\pi\) | |||||||
\(542\) | 6.68281 | 0.287051 | ||||||||
\(543\) | −37.9351 | −1.62795 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.39612 | −0.230933 | ||||||||
\(547\) | 26.0311 | 1.11301 | 0.556506 | − | 0.830844i | \(-0.312142\pi\) | ||||
0.556506 | + | 0.830844i | \(0.312142\pi\) | |||||||
\(548\) | −18.6731 | −0.797674 | ||||||||
\(549\) | −5.12175 | −0.218591 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.4716 | 1.34074 | ||||||||
\(552\) | 25.7852 | 1.09749 | ||||||||
\(553\) | −33.6874 | −1.43254 | ||||||||
\(554\) | −6.58428 | −0.279739 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 25.2290 | 1.06995 | ||||||||
\(557\) | −28.7744 | −1.21921 | −0.609605 | − | 0.792705i | \(-0.708672\pi\) | ||||
−0.609605 | + | 0.792705i | \(0.708672\pi\) | |||||||
\(558\) | −0.434912 | −0.0184113 | ||||||||
\(559\) | −1.95340 | −0.0826199 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.7609 | −0.707017 | ||||||||
\(563\) | −15.0383 | −0.633790 | −0.316895 | − | 0.948461i | \(-0.602640\pi\) | ||||
−0.316895 | + | 0.948461i | \(0.602640\pi\) | |||||||
\(564\) | −55.3813 | −2.33197 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.00864974 | 0.000363576 0 | ||||||||
\(567\) | −16.9961 | −0.713768 | ||||||||
\(568\) | 0.143609 | 0.00602570 | ||||||||
\(569\) | 37.3329 | 1.56508 | 0.782539 | − | 0.622602i | \(-0.213924\pi\) | ||||
0.782539 | + | 0.622602i | \(0.213924\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.0534 | −1.59248 | −0.796242 | − | 0.604978i | \(-0.793182\pi\) | ||||
−0.796242 | + | 0.604978i | \(0.793182\pi\) | |||||||
\(572\) | −4.60389 | −0.192498 | ||||||||
\(573\) | 43.5968 | 1.82128 | ||||||||
\(574\) | −4.43806 | −0.185241 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.73859 | −0.280774 | ||||||||
\(577\) | −37.8644 | −1.57632 | −0.788159 | − | 0.615472i | \(-0.788965\pi\) | ||||
−0.788159 | + | 0.615472i | \(0.788965\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 36.2501 | 1.50650 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.1031 | −1.29038 | ||||||||
\(582\) | 12.7251 | 0.527471 | ||||||||
\(583\) | 55.6156 | 2.30336 | ||||||||
\(584\) | −3.05849 | −0.126561 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.00231 | 0.0827145 | ||||||||
\(587\) | 32.8884 | 1.35745 | 0.678725 | − | 0.734393i | \(-0.262533\pi\) | ||||
0.678725 | + | 0.734393i | \(0.262533\pi\) | |||||||
\(588\) | 87.5657 | 3.61115 | ||||||||
\(589\) | −0.807968 | −0.0332917 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −33.0544 | −1.35968 | ||||||||
\(592\) | −10.6032 | −0.435790 | ||||||||
\(593\) | −29.6499 | −1.21757 | −0.608787 | − | 0.793334i | \(-0.708344\pi\) | ||||
−0.608787 | + | 0.793334i | \(0.708344\pi\) | |||||||
\(594\) | 15.9218 | 0.653281 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16.2506 | −0.665652 | ||||||||
\(597\) | 16.0100 | 0.655247 | ||||||||
\(598\) | 1.59722 | 0.0653150 | ||||||||
\(599\) | −7.52613 | −0.307509 | −0.153755 | − | 0.988109i | \(-0.549137\pi\) | ||||
−0.153755 | + | 0.988109i | \(0.549137\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.0062 | 0.734488 | 0.367244 | − | 0.930125i | \(-0.380301\pi\) | ||||
0.367244 | + | 0.930125i | \(0.380301\pi\) | |||||||
\(602\) | −8.45467 | −0.344586 | ||||||||
\(603\) | 3.98402 | 0.162242 | ||||||||
\(604\) | −21.6696 | −0.881725 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.95189 | 0.404268 | ||||||||
\(607\) | −1.75527 | −0.0712444 | −0.0356222 | − | 0.999365i | \(-0.511341\pi\) | ||||
−0.0356222 | + | 0.999365i | \(0.511341\pi\) | |||||||
\(608\) | 30.4002 | 1.23289 | ||||||||
\(609\) | −80.9369 | −3.27973 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.52069 | −0.304255 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.6412 | −0.672131 | −0.336066 | − | 0.941839i | \(-0.609096\pi\) | ||||
−0.336066 | + | 0.941839i | \(0.609096\pi\) | |||||||
\(614\) | 12.3457 | 0.498231 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −43.6850 | −1.76012 | ||||||||
\(617\) | 41.7577 | 1.68110 | 0.840551 | − | 0.541733i | \(-0.182232\pi\) | ||||
0.840551 | + | 0.541733i | \(0.182232\pi\) | |||||||
\(618\) | 19.7183 | 0.793187 | ||||||||
\(619\) | 9.18747 | 0.369276 | 0.184638 | − | 0.982807i | \(-0.440889\pi\) | ||||
0.184638 | + | 0.982807i | \(0.440889\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.7233 | 1.15263 | ||||||||
\(622\) | 0.993154 | 0.0398219 | ||||||||
\(623\) | −54.8202 | −2.19633 | ||||||||
\(624\) | −4.11319 | −0.164660 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.45950 | −0.378078 | ||||||||
\(627\) | 67.7192 | 2.70444 | ||||||||
\(628\) | 23.9922 | 0.957391 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.9015 | −1.19036 | −0.595181 | − | 0.803592i | \(-0.702920\pi\) | ||||
−0.595181 | + | 0.803592i | \(0.702920\pi\) | |||||||
\(632\) | 14.0467 | 0.558746 | ||||||||
\(633\) | −9.52593 | −0.378622 | ||||||||
\(634\) | −12.4907 | −0.496070 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 64.4703 | 2.55641 | ||||||||
\(637\) | 11.8913 | 0.471149 | ||||||||
\(638\) | 13.2797 | 0.525747 | ||||||||
\(639\) | 0.366244 | 0.0144884 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.2872 | −0.524811 | −0.262406 | − | 0.964958i | \(-0.584516\pi\) | ||||
−0.262406 | + | 0.964958i | \(0.584516\pi\) | |||||||
\(642\) | 17.9009 | 0.706491 | ||||||||
\(643\) | 13.1341 | 0.517959 | 0.258979 | − | 0.965883i | \(-0.416614\pi\) | ||||
0.258979 | + | 0.965883i | \(0.416614\pi\) | |||||||
\(644\) | −35.9478 | −1.41654 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.8117 | 0.818191 | 0.409095 | − | 0.912492i | \(-0.365844\pi\) | ||||
0.409095 | + | 0.912492i | \(0.365844\pi\) | |||||||
\(648\) | 7.08686 | 0.278398 | ||||||||
\(649\) | 42.2060 | 1.65673 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.07788 | 0.0814387 | ||||||||
\(652\) | 23.9016 | 0.936059 | ||||||||
\(653\) | 35.4359 | 1.38671 | 0.693356 | − | 0.720595i | \(-0.256131\pi\) | ||||
0.693356 | + | 0.720595i | \(0.256131\pi\) | |||||||
\(654\) | −23.9262 | −0.935590 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.38291 | −0.132080 | ||||||||
\(657\) | −7.80003 | −0.304308 | ||||||||
\(658\) | −32.5510 | −1.26897 | ||||||||
\(659\) | −22.4546 | −0.874706 | −0.437353 | − | 0.899290i | \(-0.644084\pi\) | ||||
−0.437353 | + | 0.899290i | \(0.644084\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.69679 | −0.221579 | −0.110790 | − | 0.993844i | \(-0.535338\pi\) | ||||
−0.110790 | + | 0.993844i | \(0.535338\pi\) | |||||||
\(662\) | −3.25741 | −0.126603 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.9691 | 0.503298 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 14.7923 | 0.573190 | ||||||||
\(667\) | 23.9568 | 0.927610 | ||||||||
\(668\) | −0.197582 | −0.00764467 | ||||||||
\(669\) | 52.6947 | 2.03729 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.01495 | −0.154995 | ||||||||
\(672\) | −78.1814 | −3.01591 | ||||||||
\(673\) | −15.1352 | −0.583420 | −0.291710 | − | 0.956507i | \(-0.594224\pi\) | ||||
−0.291710 | + | 0.956507i | \(0.594224\pi\) | |||||||
\(674\) | −4.71796 | −0.181729 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.0817 | 0.810835 | ||||||||
\(677\) | −19.9248 | −0.765774 | −0.382887 | − | 0.923795i | \(-0.625070\pi\) | ||||
−0.382887 | + | 0.923795i | \(0.625070\pi\) | |||||||
\(678\) | 2.31062 | 0.0887389 | ||||||||
\(679\) | −38.8923 | −1.49255 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 35.8778 | 1.37484 | ||||||||
\(682\) | −0.340927 | −0.0130548 | ||||||||
\(683\) | 14.2091 | 0.543694 | 0.271847 | − | 0.962340i | \(-0.412365\pi\) | ||||
0.271847 | + | 0.962340i | \(0.412365\pi\) | |||||||
\(684\) | 50.2179 | 1.92013 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 31.5529 | 1.20470 | ||||||||
\(687\) | 53.8920 | 2.05611 | ||||||||
\(688\) | −6.44457 | −0.245697 | ||||||||
\(689\) | 8.75496 | 0.333537 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.5099 | −1.35086 | −0.675431 | − | 0.737424i | \(-0.736042\pi\) | ||||
−0.675431 | + | 0.737424i | \(0.736042\pi\) | |||||||
\(692\) | −21.2902 | −0.809331 | ||||||||
\(693\) | −111.410 | −4.23210 | ||||||||
\(694\) | 9.44245 | 0.358431 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 33.7483 | 1.27922 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 10.6203 | 0.401985 | ||||||||
\(699\) | −4.42478 | −0.167360 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −51.3506 | −1.93949 | −0.969743 | − | 0.244130i | \(-0.921498\pi\) | ||||
−0.969743 | + | 0.244130i | \(0.921498\pi\) | |||||||
\(702\) | 2.50640 | 0.0945980 | ||||||||
\(703\) | 27.4807 | 1.03646 | ||||||||
\(704\) | −5.28238 | −0.199087 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.28519 | −0.123640 | ||||||||
\(707\) | −30.4165 | −1.14393 | ||||||||
\(708\) | 48.9257 | 1.83874 | ||||||||
\(709\) | −2.35324 | −0.0883780 | −0.0441890 | − | 0.999023i | \(-0.514070\pi\) | ||||
−0.0441890 | + | 0.999023i | \(0.514070\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 35.8231 | 1.34347 | ||||||||
\(712\) | 22.8584 | 0.856655 | ||||||||
\(713\) | −0.615040 | −0.0230334 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.2595 | −0.682389 | ||||||||
\(717\) | 26.7752 | 0.999937 | ||||||||
\(718\) | −19.4475 | −0.725774 | ||||||||
\(719\) | −19.2163 | −0.716648 | −0.358324 | − | 0.933597i | \(-0.616652\pi\) | ||||
−0.358324 | + | 0.933597i | \(0.616652\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −60.2661 | −2.24443 | ||||||||
\(722\) | −7.14978 | −0.266087 | ||||||||
\(723\) | −81.0149 | −3.01298 | ||||||||
\(724\) | −22.0520 | −0.819556 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 10.5466 | 0.391422 | ||||||||
\(727\) | 16.4927 | 0.611680 | 0.305840 | − | 0.952083i | \(-0.401063\pi\) | ||||
0.305840 | + | 0.952083i | \(0.401063\pi\) | |||||||
\(728\) | −6.87686 | −0.254873 | ||||||||
\(729\) | −40.0452 | −1.48316 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −4.65418 | −0.172023 | ||||||||
\(733\) | 6.80546 | 0.251365 | 0.125683 | − | 0.992070i | \(-0.459888\pi\) | ||||
0.125683 | + | 0.992070i | \(0.459888\pi\) | |||||||
\(734\) | 9.91069 | 0.365810 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 23.1412 | 0.852996 | ||||||||
\(737\) | 3.12307 | 0.115040 | ||||||||
\(738\) | 4.71941 | 0.173724 | ||||||||
\(739\) | −24.7430 | −0.910188 | −0.455094 | − | 0.890443i | \(-0.650394\pi\) | ||||
−0.455094 | + | 0.890443i | \(0.650394\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.6603 | 0.391616 | ||||||||
\(742\) | 37.8931 | 1.39110 | ||||||||
\(743\) | −27.0871 | −0.993729 | −0.496865 | − | 0.867828i | \(-0.665515\pi\) | ||||
−0.496865 | + | 0.867828i | \(0.665515\pi\) | |||||||
\(744\) | −0.866416 | −0.0317643 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.21641 | 0.0811485 | ||||||||
\(747\) | 33.0749 | 1.21015 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −54.7114 | −1.99911 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.6034 | −0.532885 | −0.266443 | − | 0.963851i | \(-0.585848\pi\) | ||||
−0.266443 | + | 0.963851i | \(0.585848\pi\) | |||||||
\(752\) | −24.8120 | −0.904800 | ||||||||
\(753\) | 29.7242 | 1.08321 | ||||||||
\(754\) | 2.09047 | 0.0761305 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −56.4105 | −2.05163 | ||||||||
\(757\) | −5.50378 | −0.200038 | −0.100019 | − | 0.994986i | \(-0.531890\pi\) | ||||
−0.100019 | + | 0.994986i | \(0.531890\pi\) | |||||||
\(758\) | −18.4231 | −0.669157 | ||||||||
\(759\) | 51.5491 | 1.87112 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.4420 | −0.451023 | −0.225512 | − | 0.974240i | \(-0.572405\pi\) | ||||
−0.225512 | + | 0.974240i | \(0.572405\pi\) | |||||||
\(762\) | 2.52657 | 0.0915280 | ||||||||
\(763\) | 73.1271 | 2.64738 | ||||||||
\(764\) | 25.3432 | 0.916885 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.09308 | −0.256283 | ||||||||
\(767\) | 6.64403 | 0.239902 | ||||||||
\(768\) | 11.6061 | 0.418798 | ||||||||
\(769\) | −25.9053 | −0.934170 | −0.467085 | − | 0.884212i | \(-0.654696\pi\) | ||||
−0.467085 | + | 0.884212i | \(0.654696\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −70.8179 | −2.55044 | ||||||||
\(772\) | 21.0725 | 0.758417 | ||||||||
\(773\) | −10.7423 | −0.386372 | −0.193186 | − | 0.981162i | \(-0.561882\pi\) | ||||
−0.193186 | + | 0.981162i | \(0.561882\pi\) | |||||||
\(774\) | 8.99065 | 0.323162 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 16.2169 | 0.582154 | ||||||||
\(777\) | −70.6734 | −2.53539 | ||||||||
\(778\) | 6.82459 | 0.244673 | ||||||||
\(779\) | 8.76760 | 0.314132 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.287099 | 0.0102732 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 37.5937 | 1.34349 | ||||||||
\(784\) | 39.2312 | 1.40112 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.41108 | −0.121669 | ||||||||
\(787\) | 13.9051 | 0.495662 | 0.247831 | − | 0.968803i | \(-0.420282\pi\) | ||||
0.247831 | + | 0.968803i | \(0.420282\pi\) | |||||||
\(788\) | −19.2148 | −0.684500 | ||||||||
\(789\) | −8.20134 | −0.291975 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.06208 | −0.251099 | ||||||||
\(792\) | 46.4545 | 1.65069 | ||||||||
\(793\) | −0.632029 | −0.0224440 | ||||||||
\(794\) | −6.05361 | −0.214835 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.30677 | 0.329870 | ||||||||
\(797\) | −36.5024 | −1.29298 | −0.646490 | − | 0.762922i | \(-0.723764\pi\) | ||||
−0.646490 | + | 0.762922i | \(0.723764\pi\) | |||||||
\(798\) | 46.1398 | 1.63333 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 58.2956 | 2.05977 | ||||||||
\(802\) | 5.70126 | 0.201318 | ||||||||
\(803\) | −6.11444 | −0.215774 | ||||||||
\(804\) | 3.62031 | 0.127678 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.0536685 | −0.00189039 | ||||||||
\(807\) | −74.1009 | −2.60847 | ||||||||
\(808\) | 12.6828 | 0.446179 | ||||||||
\(809\) | 10.9881 | 0.386321 | 0.193161 | − | 0.981167i | \(-0.438126\pi\) | ||||
0.193161 | + | 0.981167i | \(0.438126\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.3689 | −1.31220 | −0.656100 | − | 0.754674i | \(-0.727795\pi\) | ||||
−0.656100 | + | 0.754674i | \(0.727795\pi\) | |||||||
\(812\) | −47.0493 | −1.65111 | ||||||||
\(813\) | 33.9527 | 1.19077 | ||||||||
\(814\) | 11.5957 | 0.406429 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.7026 | 0.584350 | ||||||||
\(818\) | 7.44333 | 0.260250 | ||||||||
\(819\) | −17.5380 | −0.612827 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.68224 | −0.0936107 | −0.0468054 | − | 0.998904i | \(-0.514904\pi\) | ||||
−0.0468054 | + | 0.998904i | \(0.514904\pi\) | |||||||
\(822\) | 18.2443 | 0.636344 | ||||||||
\(823\) | 33.0593 | 1.15237 | 0.576187 | − | 0.817318i | \(-0.304540\pi\) | ||||
0.576187 | + | 0.817318i | \(0.304540\pi\) | |||||||
\(824\) | 25.1292 | 0.875417 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 28.7566 | 1.00057 | ||||||||
\(827\) | −2.05218 | −0.0713614 | −0.0356807 | − | 0.999363i | \(-0.511360\pi\) | ||||
−0.0356807 | + | 0.999363i | \(0.511360\pi\) | |||||||
\(828\) | 38.2268 | 1.32847 | ||||||||
\(829\) | −11.7740 | −0.408928 | −0.204464 | − | 0.978874i | \(-0.565545\pi\) | ||||
−0.204464 | + | 0.978874i | \(0.565545\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −33.4521 | −1.16044 | ||||||||
\(832\) | −0.831548 | −0.0288287 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −24.6497 | −0.853550 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 39.3658 | 1.36149 | ||||||||
\(837\) | −0.965140 | −0.0333601 | ||||||||
\(838\) | 21.0429 | 0.726916 | ||||||||
\(839\) | −51.0024 | −1.76080 | −0.880400 | − | 0.474232i | \(-0.842726\pi\) | ||||
−0.880400 | + | 0.474232i | \(0.842726\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.35516 | 0.0812126 | ||||||||
\(842\) | 2.55258 | 0.0879676 | ||||||||
\(843\) | −85.1556 | −2.93292 | ||||||||
\(844\) | −5.53751 | −0.190609 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 34.6146 | 1.19007 | ||||||||
\(847\) | −32.2342 | −1.10758 | ||||||||
\(848\) | 28.8840 | 0.991882 | ||||||||
\(849\) | 0.0439459 | 0.00150822 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.9189 | 0.717089 | ||||||||
\(852\) | 0.332809 | 0.0114018 | ||||||||
\(853\) | −6.87916 | −0.235538 | −0.117769 | − | 0.993041i | \(-0.537574\pi\) | ||||
−0.117769 | + | 0.993041i | \(0.537574\pi\) | |||||||
\(854\) | −2.73554 | −0.0936083 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22.8130 | 0.779733 | ||||||||
\(857\) | 22.0791 | 0.754207 | 0.377103 | − | 0.926171i | \(-0.376920\pi\) | ||||
0.377103 | + | 0.926171i | \(0.376920\pi\) | |||||||
\(858\) | 4.49818 | 0.153565 | ||||||||
\(859\) | −27.4713 | −0.937308 | −0.468654 | − | 0.883382i | \(-0.655261\pi\) | ||||
−0.468654 | + | 0.883382i | \(0.655261\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.5480 | −0.768434 | ||||||||
\(862\) | −22.2182 | −0.756755 | ||||||||
\(863\) | 4.04381 | 0.137653 | 0.0688265 | − | 0.997629i | \(-0.478075\pi\) | ||||
0.0688265 | + | 0.997629i | \(0.478075\pi\) | |||||||
\(864\) | 36.3139 | 1.23542 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.80696 | −0.163347 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.20789 | 0.0409986 | ||||||||
\(869\) | 28.0817 | 0.952607 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.491631 | 0.0166583 | ||||||||
\(872\) | −30.4918 | −1.03258 | ||||||||
\(873\) | 41.3579 | 1.39975 | ||||||||
\(874\) | −13.6571 | −0.461957 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.08794 | −0.239479 | ||||||||
\(877\) | 16.7190 | 0.564560 | 0.282280 | − | 0.959332i | \(-0.408909\pi\) | ||||
0.282280 | + | 0.959332i | \(0.408909\pi\) | |||||||
\(878\) | 18.2563 | 0.616119 | ||||||||
\(879\) | 10.1729 | 0.343124 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.2673 | −1.49140 | −0.745702 | − | 0.666279i | \(-0.767886\pi\) | ||||
−0.745702 | + | 0.666279i | \(0.767886\pi\) | |||||||
\(882\) | −54.7305 | −1.84287 | ||||||||
\(883\) | −2.86400 | −0.0963812 | −0.0481906 | − | 0.998838i | \(-0.515345\pi\) | ||||
−0.0481906 | + | 0.998838i | \(0.515345\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.8264 | 0.464509 | ||||||||
\(887\) | 4.69527 | 0.157652 | 0.0788259 | − | 0.996888i | \(-0.474883\pi\) | ||||
0.0788259 | + | 0.996888i | \(0.474883\pi\) | |||||||
\(888\) | 29.4687 | 0.988905 | ||||||||
\(889\) | −7.72209 | −0.258991 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.1679 | 0.474641 | ||||||||
\(892\) | 30.6319 | 1.02563 | ||||||||
\(893\) | 64.3060 | 2.15192 | ||||||||
\(894\) | 15.8775 | 0.531024 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −57.7866 | −1.93051 | ||||||||
\(897\) | 8.11482 | 0.270946 | ||||||||
\(898\) | 7.76227 | 0.259030 | ||||||||
\(899\) | −0.804978 | −0.0268475 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 3.69955 | 0.123181 | ||||||||
\(903\) | −42.9548 | −1.42945 | ||||||||
\(904\) | 2.94468 | 0.0979385 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 21.1721 | 0.703396 | ||||||||
\(907\) | 17.4972 | 0.580985 | 0.290493 | − | 0.956877i | \(-0.406181\pi\) | ||||
0.290493 | + | 0.956877i | \(0.406181\pi\) | |||||||
\(908\) | 20.8561 | 0.692135 | ||||||||
\(909\) | 32.3448 | 1.07281 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.2233 | −0.471238 | −0.235619 | − | 0.971846i | \(-0.575712\pi\) | ||||
−0.235619 | + | 0.971846i | \(0.575712\pi\) | |||||||
\(912\) | 35.1701 | 1.16460 | ||||||||
\(913\) | 25.9275 | 0.858073 | ||||||||
\(914\) | −5.45975 | −0.180593 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 31.3279 | 1.03510 | ||||||||
\(917\) | 10.4255 | 0.344279 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.1242 | 0.993707 | 0.496854 | − | 0.867834i | \(-0.334489\pi\) | ||||
0.496854 | + | 0.867834i | \(0.334489\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 62.7235 | 2.06681 | ||||||||
\(922\) | −10.9718 | −0.361338 | ||||||||
\(923\) | 0.0451949 | 0.00148761 | ||||||||
\(924\) | −101.239 | −3.33051 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −11.8408 | −0.389113 | ||||||||
\(927\) | 64.0867 | 2.10488 | ||||||||
\(928\) | 30.2877 | 0.994243 | ||||||||
\(929\) | −1.83388 | −0.0601675 | −0.0300838 | − | 0.999547i | \(-0.509577\pi\) | ||||
−0.0300838 | + | 0.999547i | \(0.509577\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −101.677 | −3.33233 | ||||||||
\(932\) | −2.57216 | −0.0842540 | ||||||||
\(933\) | 5.04582 | 0.165193 | ||||||||
\(934\) | −12.5183 | −0.409612 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.31282 | 0.239027 | ||||||||
\(937\) | −53.6062 | −1.75124 | −0.875618 | − | 0.483004i | \(-0.839546\pi\) | ||||
−0.875618 | + | 0.483004i | \(0.839546\pi\) | |||||||
\(938\) | 2.12787 | 0.0694775 | ||||||||
\(939\) | −48.0600 | −1.56838 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.39257 | −0.208392 | −0.104196 | − | 0.994557i | \(-0.533227\pi\) | ||||
−0.104196 | + | 0.994557i | \(0.533227\pi\) | |||||||
\(942\) | −23.4413 | −0.763758 | ||||||||
\(943\) | 6.67406 | 0.217337 | ||||||||
\(944\) | 21.9197 | 0.713426 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.04778 | 0.229143 | ||||||||
\(947\) | 49.7691 | 1.61728 | 0.808640 | − | 0.588304i | \(-0.200204\pi\) | ||||
0.808640 | + | 0.588304i | \(0.200204\pi\) | |||||||
\(948\) | 32.5527 | 1.05726 | ||||||||
\(949\) | −0.962531 | −0.0312451 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −63.4604 | −2.05784 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.67955 | 0.216372 | 0.108186 | − | 0.994131i | \(-0.465496\pi\) | ||||
0.108186 | + | 0.994131i | \(0.465496\pi\) | |||||||
\(954\) | −40.2954 | −1.30461 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 15.5646 | 0.503397 | ||||||||
\(957\) | 67.4687 | 2.18095 | ||||||||
\(958\) | −4.63907 | −0.149882 | ||||||||
\(959\) | −55.7611 | −1.80062 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9793 | −0.999333 | ||||||||
\(962\) | 1.82538 | 0.0588527 | ||||||||
\(963\) | 58.1799 | 1.87482 | ||||||||
\(964\) | −47.0947 | −1.51682 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 35.1225 | 1.13005 | ||||||||
\(967\) | −3.07928 | −0.0990230 | −0.0495115 | − | 0.998774i | \(-0.515766\pi\) | ||||
−0.0495115 | + | 0.998774i | \(0.515766\pi\) | |||||||
\(968\) | 13.4407 | 0.432000 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.8610 | −0.605279 | −0.302640 | − | 0.953105i | \(-0.597868\pi\) | ||||
−0.302640 | + | 0.953105i | \(0.597868\pi\) | |||||||
\(972\) | −17.3614 | −0.556868 | ||||||||
\(973\) | 75.3382 | 2.41523 | ||||||||
\(974\) | 7.71427 | 0.247181 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.08517 | −0.0667446 | ||||||||
\(977\) | 12.5553 | 0.401679 | 0.200839 | − | 0.979624i | \(-0.435633\pi\) | ||||
0.200839 | + | 0.979624i | \(0.435633\pi\) | |||||||
\(978\) | −23.3528 | −0.746741 | ||||||||
\(979\) | 45.6979 | 1.46051 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −77.7630 | −2.48278 | ||||||||
\(982\) | −23.5312 | −0.750910 | ||||||||
\(983\) | −9.84262 | −0.313931 | −0.156965 | − | 0.987604i | \(-0.550171\pi\) | ||||
−0.156965 | + | 0.987604i | \(0.550171\pi\) | |||||||
\(984\) | 9.40185 | 0.299720 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −165.379 | −5.26406 | ||||||||
\(988\) | 6.19693 | 0.197151 | ||||||||
\(989\) | 12.7143 | 0.404293 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.29887 | −0.231856 | −0.115928 | − | 0.993258i | \(-0.536984\pi\) | ||||
−0.115928 | + | 0.993258i | \(0.536984\pi\) | |||||||
\(992\) | −0.777573 | −0.0246880 | ||||||||
\(993\) | −16.5496 | −0.525186 | ||||||||
\(994\) | 0.195612 | 0.00620444 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 30.0554 | 0.952343 | ||||||||
\(997\) | −62.4018 | −1.97629 | −0.988143 | − | 0.153537i | \(-0.950934\pi\) | ||||
−0.988143 | + | 0.153537i | \(0.950934\pi\) | |||||||
\(998\) | −1.69704 | −0.0537187 | ||||||||
\(999\) | 32.8265 | 1.03859 |
(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 | 7225.2.a.bu.1.7 | yes | 15 | |
5.4 | even | 2 | 7225.2.a.bw.1.9 | yes | 15 | ||
17.16 | even | 2 | 7225.2.a.bv.1.7 | yes | 15 | ||
85.84 | even | 2 | 7225.2.a.bt.1.9 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7225.2.a.bt.1.9 | ✓ | 15 | 85.84 | even | 2 | ||
7225.2.a.bu.1.7 | yes | 15 | 1.1 | even | 1 | trivial | |
7225.2.a.bv.1.7 | yes | 15 | 17.16 | even | 2 | ||
7225.2.a.bw.1.9 | yes | 15 | 5.4 | even | 2 |