Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.09514 | −0.774383 | −0.387191 | − | 0.921999i | \(-0.626555\pi\) | ||||
−0.387191 | + | 0.921999i | \(0.626555\pi\) | |||||||
\(3\) | −0.223927 | −0.129284 | −0.0646421 | − | 0.997909i | \(-0.520591\pi\) | ||||
−0.0646421 | + | 0.997909i | \(0.520591\pi\) | |||||||
\(4\) | −0.800662 | −0.400331 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.245232 | 0.100116 | ||||||||
\(7\) | −2.26365 | −0.855580 | −0.427790 | − | 0.903878i | \(-0.640708\pi\) | ||||
−0.427790 | + | 0.903878i | \(0.640708\pi\) | |||||||
\(8\) | 3.06713 | 1.08439 | ||||||||
\(9\) | −2.94986 | −0.983286 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.16701 | −0.954889 | −0.477444 | − | 0.878662i | \(-0.658437\pi\) | ||||
−0.477444 | + | 0.878662i | \(0.658437\pi\) | |||||||
\(12\) | 0.179290 | 0.0517565 | ||||||||
\(13\) | 0.0649874 | 0.0180243 | 0.00901213 | − | 0.999959i | \(-0.497131\pi\) | ||||
0.00901213 | + | 0.999959i | \(0.497131\pi\) | |||||||
\(14\) | 2.47902 | 0.662546 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.75761 | −0.439404 | ||||||||
\(17\) | −4.44087 | −1.07707 | −0.538534 | − | 0.842604i | \(-0.681022\pi\) | ||||
−0.538534 | + | 0.842604i | \(0.681022\pi\) | |||||||
\(18\) | 3.23051 | 0.761439 | ||||||||
\(19\) | 7.82407 | 1.79496 | 0.897482 | − | 0.441050i | \(-0.145394\pi\) | ||||
0.897482 | + | 0.441050i | \(0.145394\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.506893 | 0.110613 | ||||||||
\(22\) | 3.46833 | 0.739450 | ||||||||
\(23\) | 2.53175 | 0.527906 | 0.263953 | − | 0.964536i | \(-0.414974\pi\) | ||||
0.263953 | + | 0.964536i | \(0.414974\pi\) | |||||||
\(24\) | −0.686812 | −0.140195 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.0711705 | −0.0139577 | ||||||||
\(27\) | 1.33233 | 0.256408 | ||||||||
\(28\) | 1.81242 | 0.342515 | ||||||||
\(29\) | −6.53411 | −1.21335 | −0.606677 | − | 0.794949i | \(-0.707498\pi\) | ||||
−0.606677 | + | 0.794949i | \(0.707498\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.27459 | 1.48616 | 0.743080 | − | 0.669202i | \(-0.233364\pi\) | ||||
0.743080 | + | 0.669202i | \(0.233364\pi\) | |||||||
\(32\) | −4.20941 | −0.744126 | ||||||||
\(33\) | 0.709178 | 0.123452 | ||||||||
\(34\) | 4.86338 | 0.834063 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.36184 | 0.393640 | ||||||||
\(37\) | 2.73984 | 0.450428 | 0.225214 | − | 0.974309i | \(-0.427692\pi\) | ||||
0.225214 | + | 0.974309i | \(0.427692\pi\) | |||||||
\(38\) | −8.56847 | −1.38999 | ||||||||
\(39\) | −0.0145524 | −0.00233025 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.52088 | −1.17456 | −0.587282 | − | 0.809382i | \(-0.699802\pi\) | ||||
−0.587282 | + | 0.809382i | \(0.699802\pi\) | |||||||
\(42\) | −0.555120 | −0.0856568 | ||||||||
\(43\) | 10.7428 | 1.63827 | 0.819134 | − | 0.573603i | \(-0.194455\pi\) | ||||
0.819134 | + | 0.573603i | \(0.194455\pi\) | |||||||
\(44\) | 2.53570 | 0.382272 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.77262 | −0.408801 | ||||||||
\(47\) | −8.53037 | −1.24428 | −0.622141 | − | 0.782905i | \(-0.713737\pi\) | ||||
−0.622141 | + | 0.782905i | \(0.713737\pi\) | |||||||
\(48\) | 0.393577 | 0.0568080 | ||||||||
\(49\) | −1.87588 | −0.267983 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.994430 | 0.139248 | ||||||||
\(52\) | −0.0520330 | −0.00721567 | ||||||||
\(53\) | −0.0654906 | −0.00899583 | −0.00449791 | − | 0.999990i | \(-0.501432\pi\) | ||||
−0.00449791 | + | 0.999990i | \(0.501432\pi\) | |||||||
\(54\) | −1.45909 | −0.198558 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.94290 | −0.927784 | ||||||||
\(57\) | −1.75202 | −0.232061 | ||||||||
\(58\) | 7.15578 | 0.939600 | ||||||||
\(59\) | 11.9066 | 1.55011 | 0.775055 | − | 0.631894i | \(-0.217722\pi\) | ||||
0.775055 | + | 0.631894i | \(0.217722\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.88792 | 1.00995 | 0.504973 | − | 0.863135i | \(-0.331503\pi\) | ||||
0.504973 | + | 0.863135i | \(0.331503\pi\) | |||||||
\(62\) | −9.06186 | −1.15086 | ||||||||
\(63\) | 6.67745 | 0.841279 | ||||||||
\(64\) | 8.12514 | 1.01564 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.776651 | −0.0955992 | ||||||||
\(67\) | 13.3617 | 1.63240 | 0.816199 | − | 0.577771i | \(-0.196077\pi\) | ||||
0.816199 | + | 0.577771i | \(0.196077\pi\) | |||||||
\(68\) | 3.55564 | 0.431184 | ||||||||
\(69\) | −0.566926 | −0.0682499 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.56086 | −1.01599 | −0.507994 | − | 0.861361i | \(-0.669613\pi\) | ||||
−0.507994 | + | 0.861361i | \(0.669613\pi\) | |||||||
\(72\) | −9.04758 | −1.06627 | ||||||||
\(73\) | 16.6336 | 1.94682 | 0.973410 | − | 0.229068i | \(-0.0735680\pi\) | ||||
0.973410 | + | 0.229068i | \(0.0735680\pi\) | |||||||
\(74\) | −3.00052 | −0.348803 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.26444 | −0.718580 | ||||||||
\(77\) | 7.16900 | 0.816984 | ||||||||
\(78\) | 0.0159370 | 0.00180451 | ||||||||
\(79\) | −0.725508 | −0.0816260 | −0.0408130 | − | 0.999167i | \(-0.512995\pi\) | ||||
−0.0408130 | + | 0.999167i | \(0.512995\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.55123 | 0.950136 | ||||||||
\(82\) | 8.23644 | 0.909562 | ||||||||
\(83\) | 6.57206 | 0.721378 | 0.360689 | − | 0.932686i | \(-0.382542\pi\) | ||||
0.360689 | + | 0.932686i | \(0.382542\pi\) | |||||||
\(84\) | −0.405850 | −0.0442818 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11.7649 | −1.26865 | ||||||||
\(87\) | 1.46316 | 0.156868 | ||||||||
\(88\) | −9.71361 | −1.03547 | ||||||||
\(89\) | −10.8164 | −1.14654 | −0.573269 | − | 0.819367i | \(-0.694325\pi\) | ||||
−0.573269 | + | 0.819367i | \(0.694325\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.147109 | −0.0154212 | ||||||||
\(92\) | −2.02707 | −0.211337 | ||||||||
\(93\) | −1.85290 | −0.192137 | ||||||||
\(94\) | 9.34197 | 0.963551 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.942600 | 0.0962038 | ||||||||
\(97\) | 9.64642 | 0.979445 | 0.489723 | − | 0.871878i | \(-0.337098\pi\) | ||||
0.489723 | + | 0.871878i | \(0.337098\pi\) | |||||||
\(98\) | 2.05436 | 0.207521 | ||||||||
\(99\) | 9.34222 | 0.938928 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.4798 | −1.63980 | −0.819902 | − | 0.572504i | \(-0.805972\pi\) | ||||
−0.819902 | + | 0.572504i | \(0.805972\pi\) | |||||||
\(102\) | −1.08904 | −0.107831 | ||||||||
\(103\) | −10.7964 | −1.06380 | −0.531898 | − | 0.846808i | \(-0.678521\pi\) | ||||
−0.531898 | + | 0.846808i | \(0.678521\pi\) | |||||||
\(104\) | 0.199324 | 0.0195454 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.0717216 | 0.00696622 | ||||||||
\(107\) | −1.67365 | −0.161798 | −0.0808988 | − | 0.996722i | \(-0.525779\pi\) | ||||
−0.0808988 | + | 0.996722i | \(0.525779\pi\) | |||||||
\(108\) | −1.06675 | −0.102648 | ||||||||
\(109\) | −16.9594 | −1.62442 | −0.812208 | − | 0.583368i | \(-0.801735\pi\) | ||||
−0.812208 | + | 0.583368i | \(0.801735\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.613525 | −0.0582332 | ||||||||
\(112\) | 3.97863 | 0.375945 | ||||||||
\(113\) | 8.64948 | 0.813675 | 0.406837 | − | 0.913501i | \(-0.366632\pi\) | ||||
0.406837 | + | 0.913501i | \(0.366632\pi\) | |||||||
\(114\) | 1.91871 | 0.179704 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.23162 | 0.485743 | ||||||||
\(117\) | −0.191703 | −0.0177230 | ||||||||
\(118\) | −13.0394 | −1.20038 | ||||||||
\(119\) | 10.0526 | 0.921518 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.970060 | −0.0881872 | ||||||||
\(122\) | −8.63840 | −0.782084 | ||||||||
\(123\) | 1.68413 | 0.151853 | ||||||||
\(124\) | −6.62515 | −0.594956 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −7.31276 | −0.651472 | ||||||||
\(127\) | −6.06109 | −0.537835 | −0.268918 | − | 0.963163i | \(-0.586666\pi\) | ||||
−0.268918 | + | 0.963163i | \(0.586666\pi\) | |||||||
\(128\) | −0.479360 | −0.0423699 | ||||||||
\(129\) | −2.40561 | −0.211802 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.54103 | −0.571493 | −0.285746 | − | 0.958305i | \(-0.592241\pi\) | ||||
−0.285746 | + | 0.958305i | \(0.592241\pi\) | |||||||
\(132\) | −0.567812 | −0.0494217 | ||||||||
\(133\) | −17.7110 | −1.53574 | ||||||||
\(134\) | −14.6330 | −1.26410 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −13.6207 | −1.16797 | ||||||||
\(137\) | 8.14464 | 0.695844 | 0.347922 | − | 0.937524i | \(-0.386887\pi\) | ||||
0.347922 | + | 0.937524i | \(0.386887\pi\) | |||||||
\(138\) | 0.620865 | 0.0528515 | ||||||||
\(139\) | −6.38850 | −0.541865 | −0.270933 | − | 0.962598i | \(-0.587332\pi\) | ||||
−0.270933 | + | 0.962598i | \(0.587332\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.91018 | 0.160866 | ||||||||
\(142\) | 9.37537 | 0.786763 | ||||||||
\(143\) | −0.205816 | −0.0172112 | ||||||||
\(144\) | 5.18471 | 0.432059 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −18.2162 | −1.50758 | ||||||||
\(147\) | 0.420060 | 0.0346460 | ||||||||
\(148\) | −2.19369 | −0.180320 | ||||||||
\(149\) | 9.29157 | 0.761195 | 0.380598 | − | 0.924741i | \(-0.375718\pi\) | ||||
0.380598 | + | 0.924741i | \(0.375718\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.44437 | −0.361677 | −0.180839 | − | 0.983513i | \(-0.557881\pi\) | ||||
−0.180839 | + | 0.983513i | \(0.557881\pi\) | |||||||
\(152\) | 23.9974 | 1.94645 | ||||||||
\(153\) | 13.0999 | 1.05907 | ||||||||
\(154\) | −7.85108 | −0.632658 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.0116516 | 0.000932873 0 | ||||||||
\(157\) | 0.260484 | 0.0207889 | 0.0103944 | − | 0.999946i | \(-0.496691\pi\) | ||||
0.0103944 | + | 0.999946i | \(0.496691\pi\) | |||||||
\(158\) | 0.794534 | 0.0632098 | ||||||||
\(159\) | 0.0146651 | 0.00116302 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.73099 | −0.451666 | ||||||||
\(162\) | −9.36481 | −0.735769 | ||||||||
\(163\) | −5.42016 | −0.424539 | −0.212270 | − | 0.977211i | \(-0.568086\pi\) | ||||
−0.212270 | + | 0.977211i | \(0.568086\pi\) | |||||||
\(164\) | 6.02169 | 0.470215 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.19735 | −0.558623 | ||||||||
\(167\) | 22.0325 | 1.70492 | 0.852462 | − | 0.522789i | \(-0.175109\pi\) | ||||
0.852462 | + | 0.522789i | \(0.175109\pi\) | |||||||
\(168\) | 1.55470 | 0.119948 | ||||||||
\(169\) | −12.9958 | −0.999675 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −23.0799 | −1.76496 | ||||||||
\(172\) | −8.60139 | −0.655849 | ||||||||
\(173\) | −18.0964 | −1.37584 | −0.687922 | − | 0.725785i | \(-0.741477\pi\) | ||||
−0.687922 | + | 0.725785i | \(0.741477\pi\) | |||||||
\(174\) | −1.60237 | −0.121476 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.56638 | 0.419582 | ||||||||
\(177\) | −2.66621 | −0.200405 | ||||||||
\(178\) | 11.8455 | 0.887859 | ||||||||
\(179\) | −17.4131 | −1.30151 | −0.650757 | − | 0.759286i | \(-0.725548\pi\) | ||||
−0.650757 | + | 0.759286i | \(0.725548\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.69828 | 0.497879 | 0.248940 | − | 0.968519i | \(-0.419918\pi\) | ||||
0.248940 | + | 0.968519i | \(0.419918\pi\) | |||||||
\(182\) | 0.161105 | 0.0119419 | ||||||||
\(183\) | −1.76632 | −0.130570 | ||||||||
\(184\) | 7.76518 | 0.572457 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.02919 | 0.148788 | ||||||||
\(187\) | 14.0643 | 1.02848 | ||||||||
\(188\) | 6.82995 | 0.498125 | ||||||||
\(189\) | −3.01594 | −0.219377 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.2205 | 1.31839 | 0.659196 | − | 0.751971i | \(-0.270897\pi\) | ||||
0.659196 | + | 0.751971i | \(0.270897\pi\) | |||||||
\(192\) | −1.81944 | −0.131307 | ||||||||
\(193\) | 5.88201 | 0.423396 | 0.211698 | − | 0.977335i | \(-0.432101\pi\) | ||||
0.211698 | + | 0.977335i | \(0.432101\pi\) | |||||||
\(194\) | −10.5642 | −0.758466 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.50195 | 0.107282 | ||||||||
\(197\) | −18.3999 | −1.31094 | −0.655468 | − | 0.755223i | \(-0.727528\pi\) | ||||
−0.655468 | + | 0.755223i | \(0.727528\pi\) | |||||||
\(198\) | −10.2311 | −0.727090 | ||||||||
\(199\) | 11.8695 | 0.841404 | 0.420702 | − | 0.907199i | \(-0.361784\pi\) | ||||
0.420702 | + | 0.907199i | \(0.361784\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.99206 | −0.211043 | ||||||||
\(202\) | 18.0478 | 1.26984 | ||||||||
\(203\) | 14.7909 | 1.03812 | ||||||||
\(204\) | −0.796203 | −0.0557453 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 11.8235 | 0.823786 | ||||||||
\(207\) | −7.46829 | −0.519082 | ||||||||
\(208\) | −0.114223 | −0.00791992 | ||||||||
\(209\) | −24.7789 | −1.71399 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.3377 | 1.19358 | 0.596788 | − | 0.802399i | \(-0.296443\pi\) | ||||
0.596788 | + | 0.802399i | \(0.296443\pi\) | |||||||
\(212\) | 0.0524359 | 0.00360131 | ||||||||
\(213\) | 1.91701 | 0.131351 | ||||||||
\(214\) | 1.83288 | 0.125293 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.08643 | 0.278046 | ||||||||
\(217\) | −18.7308 | −1.27153 | ||||||||
\(218\) | 18.5730 | 1.25792 | ||||||||
\(219\) | −3.72472 | −0.251693 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.288600 | −0.0194134 | ||||||||
\(222\) | 0.671897 | 0.0450948 | ||||||||
\(223\) | 0.685671 | 0.0459159 | 0.0229580 | − | 0.999736i | \(-0.492692\pi\) | ||||
0.0229580 | + | 0.999736i | \(0.492692\pi\) | |||||||
\(224\) | 9.52864 | 0.636659 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.47242 | −0.630096 | ||||||||
\(227\) | 23.7034 | 1.57325 | 0.786626 | − | 0.617429i | \(-0.211826\pi\) | ||||
0.786626 | + | 0.617429i | \(0.211826\pi\) | |||||||
\(228\) | 1.40278 | 0.0929011 | ||||||||
\(229\) | −18.1670 | −1.20051 | −0.600254 | − | 0.799810i | \(-0.704934\pi\) | ||||
−0.600254 | + | 0.799810i | \(0.704934\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.60533 | −0.105623 | ||||||||
\(232\) | −20.0409 | −1.31575 | ||||||||
\(233\) | 1.69882 | 0.111293 | 0.0556466 | − | 0.998451i | \(-0.482278\pi\) | ||||
0.0556466 | + | 0.998451i | \(0.482278\pi\) | |||||||
\(234\) | 0.209943 | 0.0137244 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.53318 | −0.620557 | ||||||||
\(237\) | 0.162461 | 0.0105530 | ||||||||
\(238\) | −11.0090 | −0.713608 | ||||||||
\(239\) | 4.67855 | 0.302631 | 0.151315 | − | 0.988486i | \(-0.451649\pi\) | ||||
0.151315 | + | 0.988486i | \(0.451649\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | 1.06235 | 0.0682907 | ||||||||
\(243\) | −5.91185 | −0.379245 | ||||||||
\(244\) | −6.31556 | −0.404313 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.84436 | −0.117592 | ||||||||
\(247\) | 0.508466 | 0.0323529 | ||||||||
\(248\) | 25.3792 | 1.61158 | ||||||||
\(249\) | −1.47166 | −0.0932628 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.44769 | −0.406974 | −0.203487 | − | 0.979078i | \(-0.565228\pi\) | ||||
−0.203487 | + | 0.979078i | \(0.565228\pi\) | |||||||
\(252\) | −5.34638 | −0.336790 | ||||||||
\(253\) | −8.01806 | −0.504091 | ||||||||
\(254\) | 6.63776 | 0.416490 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.7253 | −0.982831 | ||||||||
\(257\) | 15.0125 | 0.936452 | 0.468226 | − | 0.883609i | \(-0.344893\pi\) | ||||
0.468226 | + | 0.883609i | \(0.344893\pi\) | |||||||
\(258\) | 2.63449 | 0.164016 | ||||||||
\(259\) | −6.20205 | −0.385377 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.2747 | 1.19307 | ||||||||
\(262\) | 7.16336 | 0.442554 | ||||||||
\(263\) | −11.1566 | −0.687945 | −0.343973 | − | 0.938980i | \(-0.611773\pi\) | ||||
−0.343973 | + | 0.938980i | \(0.611773\pi\) | |||||||
\(264\) | 2.17514 | 0.133871 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 19.3960 | 1.18925 | ||||||||
\(267\) | 2.42209 | 0.148229 | ||||||||
\(268\) | −10.6983 | −0.653500 | ||||||||
\(269\) | −13.5075 | −0.823569 | −0.411785 | − | 0.911281i | \(-0.635094\pi\) | ||||
−0.411785 | + | 0.911281i | \(0.635094\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.0987 | 0.795687 | 0.397844 | − | 0.917453i | \(-0.369759\pi\) | ||||
0.397844 | + | 0.917453i | \(0.369759\pi\) | |||||||
\(272\) | 7.80533 | 0.473268 | ||||||||
\(273\) | 0.0329416 | 0.00199372 | ||||||||
\(274\) | −8.91954 | −0.538849 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.453917 | 0.0273226 | ||||||||
\(277\) | −14.4487 | −0.868135 | −0.434068 | − | 0.900880i | \(-0.642922\pi\) | ||||
−0.434068 | + | 0.900880i | \(0.642922\pi\) | |||||||
\(278\) | 6.99631 | 0.419611 | ||||||||
\(279\) | −24.4089 | −1.46132 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.77667 | 0.105988 | 0.0529938 | − | 0.998595i | \(-0.483124\pi\) | ||||
0.0529938 | + | 0.998595i | \(0.483124\pi\) | |||||||
\(282\) | −2.09192 | −0.124572 | ||||||||
\(283\) | −18.4509 | −1.09679 | −0.548397 | − | 0.836218i | \(-0.684762\pi\) | ||||
−0.548397 | + | 0.836218i | \(0.684762\pi\) | |||||||
\(284\) | 6.85436 | 0.406732 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.225397 | 0.0133280 | ||||||||
\(287\) | 17.0247 | 1.00493 | ||||||||
\(288\) | 12.4172 | 0.731688 | ||||||||
\(289\) | 2.72130 | 0.160077 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.16009 | −0.126627 | ||||||||
\(292\) | −13.3179 | −0.779373 | ||||||||
\(293\) | 8.65394 | 0.505569 | 0.252784 | − | 0.967523i | \(-0.418654\pi\) | ||||
0.252784 | + | 0.967523i | \(0.418654\pi\) | |||||||
\(294\) | −0.460026 | −0.0268293 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.40345 | 0.488440 | ||||||||
\(297\) | −4.21951 | −0.244841 | ||||||||
\(298\) | −10.1756 | −0.589456 | ||||||||
\(299\) | 0.164532 | 0.00951511 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.3180 | −1.40167 | ||||||||
\(302\) | 4.86722 | 0.280077 | ||||||||
\(303\) | 3.69028 | 0.212001 | ||||||||
\(304\) | −13.7517 | −0.788714 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −14.3463 | −0.820123 | ||||||||
\(307\) | 6.61143 | 0.377334 | 0.188667 | − | 0.982041i | \(-0.439583\pi\) | ||||
0.188667 | + | 0.982041i | \(0.439583\pi\) | |||||||
\(308\) | −5.73995 | −0.327064 | ||||||||
\(309\) | 2.41759 | 0.137532 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.4206 | −1.10124 | −0.550622 | − | 0.834755i | \(-0.685609\pi\) | ||||
−0.550622 | + | 0.834755i | \(0.685609\pi\) | |||||||
\(312\) | −0.0446341 | −0.00252691 | ||||||||
\(313\) | −19.4518 | −1.09948 | −0.549740 | − | 0.835336i | \(-0.685273\pi\) | ||||
−0.549740 | + | 0.835336i | \(0.685273\pi\) | |||||||
\(314\) | −0.285267 | −0.0160986 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.580887 | 0.0326774 | ||||||||
\(317\) | −0.792618 | −0.0445179 | −0.0222589 | − | 0.999752i | \(-0.507086\pi\) | ||||
−0.0222589 | + | 0.999752i | \(0.507086\pi\) | |||||||
\(318\) | −0.0160604 | −0.000900622 0 | ||||||||
\(319\) | 20.6936 | 1.15862 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.374775 | 0.0209179 | ||||||||
\(322\) | 6.27626 | 0.349762 | ||||||||
\(323\) | −34.7457 | −1.93330 | ||||||||
\(324\) | −6.84664 | −0.380369 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.93584 | 0.328756 | ||||||||
\(327\) | 3.79767 | 0.210011 | ||||||||
\(328\) | −23.0675 | −1.27369 | ||||||||
\(329\) | 19.3098 | 1.06458 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.6988 | 0.807917 | 0.403958 | − | 0.914777i | \(-0.367634\pi\) | ||||
0.403958 | + | 0.914777i | \(0.367634\pi\) | |||||||
\(332\) | −5.26201 | −0.288790 | ||||||||
\(333\) | −8.08215 | −0.442899 | ||||||||
\(334\) | −24.1287 | −1.32026 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.890922 | −0.0486038 | ||||||||
\(337\) | 17.3385 | 0.944487 | 0.472244 | − | 0.881468i | \(-0.343444\pi\) | ||||
0.472244 | + | 0.881468i | \(0.343444\pi\) | |||||||
\(338\) | 14.2322 | 0.774131 | ||||||||
\(339\) | −1.93685 | −0.105195 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.2057 | −1.41912 | ||||||||
\(342\) | 25.2758 | 1.36676 | ||||||||
\(343\) | 20.0919 | 1.08486 | ||||||||
\(344\) | 32.9496 | 1.77652 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.8181 | 1.06543 | ||||||||
\(347\) | −13.9745 | −0.750188 | −0.375094 | − | 0.926987i | \(-0.622390\pi\) | ||||
−0.375094 | + | 0.926987i | \(0.622390\pi\) | |||||||
\(348\) | −1.17150 | −0.0627990 | ||||||||
\(349\) | 18.2257 | 0.975600 | 0.487800 | − | 0.872955i | \(-0.337800\pi\) | ||||
0.487800 | + | 0.872955i | \(0.337800\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.0865848 | 0.00462156 | ||||||||
\(352\) | 13.3312 | 0.710557 | ||||||||
\(353\) | 25.1550 | 1.33886 | 0.669432 | − | 0.742873i | \(-0.266537\pi\) | ||||
0.669432 | + | 0.742873i | \(0.266537\pi\) | |||||||
\(354\) | 2.91988 | 0.155190 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.66030 | 0.458995 | ||||||||
\(357\) | −2.25104 | −0.119138 | ||||||||
\(358\) | 19.0698 | 1.00787 | ||||||||
\(359\) | −6.05193 | −0.319409 | −0.159704 | − | 0.987165i | \(-0.551054\pi\) | ||||
−0.159704 | + | 0.987165i | \(0.551054\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 42.2161 | 2.22190 | ||||||||
\(362\) | −7.33558 | −0.385549 | ||||||||
\(363\) | 0.217222 | 0.0114012 | ||||||||
\(364\) | 0.117784 | 0.00617359 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.93437 | 0.101111 | ||||||||
\(367\) | −31.3055 | −1.63413 | −0.817067 | − | 0.576543i | \(-0.804401\pi\) | ||||
−0.817067 | + | 0.576543i | \(0.804401\pi\) | |||||||
\(368\) | −4.44984 | −0.231964 | ||||||||
\(369\) | 22.1855 | 1.15493 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.148248 | 0.00769665 | ||||||||
\(372\) | 1.48355 | 0.0769185 | ||||||||
\(373\) | −17.5060 | −0.906424 | −0.453212 | − | 0.891403i | \(-0.649722\pi\) | ||||
−0.453212 | + | 0.891403i | \(0.649722\pi\) | |||||||
\(374\) | −15.4024 | −0.796438 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −26.1637 | −1.34929 | ||||||||
\(377\) | −0.424635 | −0.0218698 | ||||||||
\(378\) | 3.30288 | 0.169882 | ||||||||
\(379\) | 0.569958 | 0.0292768 | 0.0146384 | − | 0.999893i | \(-0.495340\pi\) | ||||
0.0146384 | + | 0.999893i | \(0.495340\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.35724 | 0.0695336 | ||||||||
\(382\) | −19.9541 | −1.02094 | ||||||||
\(383\) | −24.0263 | −1.22769 | −0.613843 | − | 0.789428i | \(-0.710377\pi\) | ||||
−0.613843 | + | 0.789428i | \(0.710377\pi\) | |||||||
\(384\) | 0.107342 | 0.00547776 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.44164 | −0.327871 | ||||||||
\(387\) | −31.6898 | −1.61088 | ||||||||
\(388\) | −7.72353 | −0.392103 | ||||||||
\(389\) | −13.5820 | −0.688633 | −0.344317 | − | 0.938854i | \(-0.611889\pi\) | ||||
−0.344317 | + | 0.938854i | \(0.611889\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.2432 | −0.568591 | ||||||||
\(392\) | −5.75356 | −0.290599 | ||||||||
\(393\) | 1.46471 | 0.0738850 | ||||||||
\(394\) | 20.1505 | 1.01517 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.47997 | −0.375882 | ||||||||
\(397\) | −9.52930 | −0.478262 | −0.239131 | − | 0.970987i | \(-0.576863\pi\) | ||||
−0.239131 | + | 0.970987i | \(0.576863\pi\) | |||||||
\(398\) | −12.9988 | −0.651569 | ||||||||
\(399\) | 3.96596 | 0.198546 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.98608 | 0.498681 | 0.249341 | − | 0.968416i | \(-0.419786\pi\) | ||||
0.249341 | + | 0.968416i | \(0.419786\pi\) | |||||||
\(402\) | 3.27673 | 0.163428 | ||||||||
\(403\) | 0.537744 | 0.0267869 | ||||||||
\(404\) | 13.1948 | 0.656465 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16.1982 | −0.803903 | ||||||||
\(407\) | −8.67711 | −0.430108 | ||||||||
\(408\) | 3.05004 | 0.150999 | ||||||||
\(409\) | −1.85693 | −0.0918193 | −0.0459097 | − | 0.998946i | \(-0.514619\pi\) | ||||
−0.0459097 | + | 0.998946i | \(0.514619\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.82380 | −0.0899616 | ||||||||
\(412\) | 8.64424 | 0.425871 | ||||||||
\(413\) | −26.9524 | −1.32624 | ||||||||
\(414\) | 8.17884 | 0.401968 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.273559 | −0.0134123 | ||||||||
\(417\) | 1.43056 | 0.0700546 | ||||||||
\(418\) | 27.1364 | 1.32729 | ||||||||
\(419\) | −9.53574 | −0.465851 | −0.232926 | − | 0.972495i | \(-0.574830\pi\) | ||||
−0.232926 | + | 0.972495i | \(0.574830\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.1822 | −1.03235 | −0.516177 | − | 0.856482i | \(-0.672645\pi\) | ||||
−0.516177 | + | 0.856482i | \(0.672645\pi\) | |||||||
\(422\) | −18.9872 | −0.924284 | ||||||||
\(423\) | 25.1634 | 1.22348 | ||||||||
\(424\) | −0.200868 | −0.00975501 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.09940 | −0.101716 | ||||||||
\(427\) | −17.8555 | −0.864089 | ||||||||
\(428\) | 1.34003 | 0.0647726 | ||||||||
\(429\) | 0.0460876 | 0.00222513 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −35.7158 | −1.72037 | −0.860186 | − | 0.509981i | \(-0.829652\pi\) | ||||
−0.860186 | + | 0.509981i | \(0.829652\pi\) | |||||||
\(432\) | −2.34173 | −0.112666 | ||||||||
\(433\) | −11.8322 | −0.568618 | −0.284309 | − | 0.958733i | \(-0.591764\pi\) | ||||
−0.284309 | + | 0.958733i | \(0.591764\pi\) | |||||||
\(434\) | 20.5129 | 0.984650 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.5788 | 0.650305 | ||||||||
\(437\) | 19.8086 | 0.947572 | ||||||||
\(438\) | 4.07910 | 0.194907 | ||||||||
\(439\) | 2.11764 | 0.101069 | 0.0505347 | − | 0.998722i | \(-0.483907\pi\) | ||||
0.0505347 | + | 0.998722i | \(0.483907\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.53358 | 0.263504 | ||||||||
\(442\) | 0.316059 | 0.0150334 | ||||||||
\(443\) | −26.8075 | −1.27366 | −0.636832 | − | 0.771002i | \(-0.719756\pi\) | ||||
−0.636832 | + | 0.771002i | \(0.719756\pi\) | |||||||
\(444\) | 0.491226 | 0.0233126 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.750907 | −0.0355565 | ||||||||
\(447\) | −2.08063 | −0.0984106 | ||||||||
\(448\) | −18.3925 | −0.868963 | ||||||||
\(449\) | −35.6307 | −1.68152 | −0.840759 | − | 0.541409i | \(-0.817891\pi\) | ||||
−0.840759 | + | 0.541409i | \(0.817891\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.8187 | 1.12158 | ||||||||
\(452\) | −6.92532 | −0.325739 | ||||||||
\(453\) | 0.995213 | 0.0467592 | ||||||||
\(454\) | −25.9587 | −1.21830 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.37366 | −0.251645 | ||||||||
\(457\) | 4.37323 | 0.204571 | 0.102286 | − | 0.994755i | \(-0.467384\pi\) | ||||
0.102286 | + | 0.994755i | \(0.467384\pi\) | |||||||
\(458\) | 19.8954 | 0.929652 | ||||||||
\(459\) | −5.91671 | −0.276169 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.32865 | 0.108456 | 0.0542281 | − | 0.998529i | \(-0.482730\pi\) | ||||
0.0542281 | + | 0.998529i | \(0.482730\pi\) | |||||||
\(462\) | 1.75807 | 0.0817927 | ||||||||
\(463\) | 24.3683 | 1.13249 | 0.566246 | − | 0.824236i | \(-0.308395\pi\) | ||||
0.566246 | + | 0.824236i | \(0.308395\pi\) | |||||||
\(464\) | 11.4844 | 0.533152 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.86045 | −0.0861835 | ||||||||
\(467\) | −42.0547 | −1.94606 | −0.973030 | − | 0.230678i | \(-0.925906\pi\) | ||||
−0.973030 | + | 0.230678i | \(0.925906\pi\) | |||||||
\(468\) | 0.153490 | 0.00709507 | ||||||||
\(469\) | −30.2463 | −1.39665 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.0583294 | −0.00268768 | ||||||||
\(472\) | 36.5191 | 1.68093 | ||||||||
\(473\) | −34.0226 | −1.56436 | ||||||||
\(474\) | −0.177918 | −0.00817203 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.04872 | −0.368913 | ||||||||
\(477\) | 0.193188 | 0.00884547 | ||||||||
\(478\) | −5.12369 | −0.234352 | ||||||||
\(479\) | −30.3166 | −1.38520 | −0.692600 | − | 0.721322i | \(-0.743535\pi\) | ||||
−0.692600 | + | 0.721322i | \(0.743535\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.178055 | 0.00811862 | ||||||||
\(482\) | −1.09514 | −0.0498824 | ||||||||
\(483\) | 1.28332 | 0.0583932 | ||||||||
\(484\) | 0.776690 | 0.0353041 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 6.47432 | 0.293681 | ||||||||
\(487\) | −16.4118 | −0.743692 | −0.371846 | − | 0.928295i | \(-0.621275\pi\) | ||||
−0.371846 | + | 0.928295i | \(0.621275\pi\) | |||||||
\(488\) | 24.1932 | 1.09518 | ||||||||
\(489\) | 1.21372 | 0.0548863 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.561056 | −0.0253201 | −0.0126600 | − | 0.999920i | \(-0.504030\pi\) | ||||
−0.0126600 | + | 0.999920i | \(0.504030\pi\) | |||||||
\(492\) | −1.34842 | −0.0607914 | ||||||||
\(493\) | 29.0171 | 1.30686 | ||||||||
\(494\) | −0.556843 | −0.0250535 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.5435 | −0.653024 | ||||||||
\(497\) | 19.3788 | 0.869258 | ||||||||
\(498\) | 1.61168 | 0.0722211 | ||||||||
\(499\) | −39.1100 | −1.75080 | −0.875401 | − | 0.483397i | \(-0.839403\pi\) | ||||
−0.875401 | + | 0.483397i | \(0.839403\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.93366 | −0.220420 | ||||||||
\(502\) | 7.06114 | 0.315154 | ||||||||
\(503\) | 36.7064 | 1.63666 | 0.818329 | − | 0.574750i | \(-0.194901\pi\) | ||||
0.818329 | + | 0.574750i | \(0.194901\pi\) | |||||||
\(504\) | 20.4806 | 0.912277 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8.78092 | 0.390360 | ||||||||
\(507\) | 2.91010 | 0.129242 | ||||||||
\(508\) | 4.85289 | 0.215312 | ||||||||
\(509\) | −20.8479 | −0.924065 | −0.462033 | − | 0.886863i | \(-0.652880\pi\) | ||||
−0.462033 | + | 0.886863i | \(0.652880\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −37.6528 | −1.66566 | ||||||||
\(512\) | 18.1802 | 0.803458 | ||||||||
\(513\) | 10.4243 | 0.460243 | ||||||||
\(514\) | −16.4408 | −0.725172 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.92608 | 0.0847910 | ||||||||
\(517\) | 27.0158 | 1.18815 | ||||||||
\(518\) | 6.79213 | 0.298429 | ||||||||
\(519\) | 4.05227 | 0.177875 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.2776 | −1.01981 | −0.509904 | − | 0.860231i | \(-0.670319\pi\) | ||||
−0.509904 | + | 0.860231i | \(0.670319\pi\) | |||||||
\(522\) | −21.1085 | −0.923895 | ||||||||
\(523\) | −16.3641 | −0.715552 | −0.357776 | − | 0.933807i | \(-0.616465\pi\) | ||||
−0.357776 | + | 0.933807i | \(0.616465\pi\) | |||||||
\(524\) | 5.23716 | 0.228786 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.2181 | 0.532733 | ||||||||
\(527\) | −36.7464 | −1.60070 | ||||||||
\(528\) | −1.24646 | −0.0542453 | ||||||||
\(529\) | −16.5903 | −0.721316 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35.1228 | −1.52420 | ||||||||
\(532\) | 14.1805 | 0.614803 | ||||||||
\(533\) | −0.488762 | −0.0211706 | ||||||||
\(534\) | −2.65253 | −0.114786 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 40.9822 | 1.77016 | ||||||||
\(537\) | 3.89926 | 0.168265 | ||||||||
\(538\) | 14.7927 | 0.637758 | ||||||||
\(539\) | 5.94093 | 0.255894 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.0819 | −0.992369 | −0.496184 | − | 0.868217i | \(-0.665266\pi\) | ||||
−0.496184 | + | 0.868217i | \(0.665266\pi\) | |||||||
\(542\) | −14.3449 | −0.616166 | ||||||||
\(543\) | −1.49993 | −0.0643680 | ||||||||
\(544\) | 18.6934 | 0.801475 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.0360758 | −0.00154390 | ||||||||
\(547\) | −17.3551 | −0.742049 | −0.371024 | − | 0.928623i | \(-0.620993\pi\) | ||||
−0.371024 | + | 0.928623i | \(0.620993\pi\) | |||||||
\(548\) | −6.52111 | −0.278568 | ||||||||
\(549\) | −23.2682 | −0.993064 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −51.1233 | −2.17793 | ||||||||
\(552\) | −1.73883 | −0.0740097 | ||||||||
\(553\) | 1.64230 | 0.0698376 | ||||||||
\(554\) | 15.8233 | 0.672269 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.11503 | 0.216926 | ||||||||
\(557\) | 6.28655 | 0.266370 | 0.133185 | − | 0.991091i | \(-0.457480\pi\) | ||||
0.133185 | + | 0.991091i | \(0.457480\pi\) | |||||||
\(558\) | 26.7312 | 1.13162 | ||||||||
\(559\) | 0.698149 | 0.0295285 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.14937 | −0.132966 | ||||||||
\(562\) | −1.94571 | −0.0820749 | ||||||||
\(563\) | −6.26725 | −0.264133 | −0.132067 | − | 0.991241i | \(-0.542161\pi\) | ||||
−0.132067 | + | 0.991241i | \(0.542161\pi\) | |||||||
\(564\) | −1.52941 | −0.0643997 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 20.2064 | 0.849338 | ||||||||
\(567\) | −19.3570 | −0.812917 | ||||||||
\(568\) | −26.2572 | −1.10173 | ||||||||
\(569\) | 21.6171 | 0.906234 | 0.453117 | − | 0.891451i | \(-0.350312\pi\) | ||||
0.453117 | + | 0.891451i | \(0.350312\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.4039 | −1.52345 | −0.761727 | − | 0.647898i | \(-0.775648\pi\) | ||||
−0.761727 | + | 0.647898i | \(0.775648\pi\) | |||||||
\(572\) | 0.164789 | 0.00689017 | ||||||||
\(573\) | −4.08007 | −0.170447 | ||||||||
\(574\) | −18.6444 | −0.778203 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −23.9680 | −0.998666 | ||||||||
\(577\) | −31.3479 | −1.30503 | −0.652514 | − | 0.757776i | \(-0.726286\pi\) | ||||
−0.652514 | + | 0.757776i | \(0.726286\pi\) | |||||||
\(578\) | −2.98022 | −0.123961 | ||||||||
\(579\) | −1.31714 | −0.0547385 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.8769 | −0.617196 | ||||||||
\(582\) | 2.36561 | 0.0980577 | ||||||||
\(583\) | 0.207409 | 0.00859002 | ||||||||
\(584\) | 51.0175 | 2.11112 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.47730 | −0.391504 | ||||||||
\(587\) | 44.4381 | 1.83416 | 0.917079 | − | 0.398705i | \(-0.130540\pi\) | ||||
0.917079 | + | 0.398705i | \(0.130540\pi\) | |||||||
\(588\) | −0.336326 | −0.0138699 | ||||||||
\(589\) | 64.7410 | 2.66761 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.12022 | 0.169483 | ||||||||
\(592\) | −4.81559 | −0.197920 | ||||||||
\(593\) | 6.62491 | 0.272052 | 0.136026 | − | 0.990705i | \(-0.456567\pi\) | ||||
0.136026 | + | 0.990705i | \(0.456567\pi\) | |||||||
\(594\) | 4.62096 | 0.189600 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.43941 | −0.304730 | ||||||||
\(597\) | −2.65789 | −0.108780 | ||||||||
\(598\) | −0.180186 | −0.00736834 | ||||||||
\(599\) | 24.8397 | 1.01492 | 0.507460 | − | 0.861675i | \(-0.330584\pi\) | ||||
0.507460 | + | 0.861675i | \(0.330584\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.70931 | −0.273679 | −0.136839 | − | 0.990593i | \(-0.543694\pi\) | ||||
−0.136839 | + | 0.990593i | \(0.543694\pi\) | |||||||
\(602\) | 26.6317 | 1.08543 | ||||||||
\(603\) | −39.4152 | −1.60511 | ||||||||
\(604\) | 3.55844 | 0.144791 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.04138 | −0.164170 | ||||||||
\(607\) | 18.3020 | 0.742857 | 0.371428 | − | 0.928462i | \(-0.378868\pi\) | ||||
0.371428 | + | 0.928462i | \(0.378868\pi\) | |||||||
\(608\) | −32.9347 | −1.33568 | ||||||||
\(609\) | −3.31209 | −0.134213 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.554366 | −0.0224273 | ||||||||
\(612\) | −10.4886 | −0.423977 | ||||||||
\(613\) | 26.7397 | 1.08000 | 0.540002 | − | 0.841664i | \(-0.318423\pi\) | ||||
0.540002 | + | 0.841664i | \(0.318423\pi\) | |||||||
\(614\) | −7.24045 | −0.292201 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 21.9882 | 0.885931 | ||||||||
\(617\) | 44.9237 | 1.80856 | 0.904280 | − | 0.426939i | \(-0.140408\pi\) | ||||
0.904280 | + | 0.426939i | \(0.140408\pi\) | |||||||
\(618\) | −2.64761 | −0.106503 | ||||||||
\(619\) | 34.7225 | 1.39562 | 0.697808 | − | 0.716285i | \(-0.254159\pi\) | ||||
0.697808 | + | 0.716285i | \(0.254159\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.37313 | 0.135359 | ||||||||
\(622\) | 21.2684 | 0.852784 | ||||||||
\(623\) | 24.4846 | 0.980954 | ||||||||
\(624\) | 0.0255776 | 0.00102392 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 21.3025 | 0.851418 | ||||||||
\(627\) | 5.54866 | 0.221592 | ||||||||
\(628\) | −0.208560 | −0.00832244 | ||||||||
\(629\) | −12.1673 | −0.485142 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.3033 | −1.20635 | −0.603177 | − | 0.797607i | \(-0.706099\pi\) | ||||
−0.603177 | + | 0.797607i | \(0.706099\pi\) | |||||||
\(632\) | −2.22522 | −0.0885146 | ||||||||
\(633\) | −3.88237 | −0.154311 | ||||||||
\(634\) | 0.868030 | 0.0344739 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.0117418 | −0.000465593 0 | ||||||||
\(637\) | −0.121909 | −0.00483019 | ||||||||
\(638\) | −22.6624 | −0.897214 | ||||||||
\(639\) | 25.2533 | 0.999006 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 44.8929 | 1.77316 | 0.886582 | − | 0.462571i | \(-0.153073\pi\) | ||||
0.886582 | + | 0.462571i | \(0.153073\pi\) | |||||||
\(642\) | −0.410432 | −0.0161984 | ||||||||
\(643\) | 0.746188 | 0.0294268 | 0.0147134 | − | 0.999892i | \(-0.495316\pi\) | ||||
0.0147134 | + | 0.999892i | \(0.495316\pi\) | |||||||
\(644\) | 4.58859 | 0.180816 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 38.0515 | 1.49711 | ||||||||
\(647\) | −25.5099 | −1.00290 | −0.501448 | − | 0.865188i | \(-0.667199\pi\) | ||||
−0.501448 | + | 0.865188i | \(0.667199\pi\) | |||||||
\(648\) | 26.2277 | 1.03032 | ||||||||
\(649\) | −37.7084 | −1.48018 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.19433 | 0.164389 | ||||||||
\(652\) | 4.33972 | 0.169956 | ||||||||
\(653\) | 28.7035 | 1.12325 | 0.561627 | − | 0.827391i | \(-0.310176\pi\) | ||||
0.561627 | + | 0.827391i | \(0.310176\pi\) | |||||||
\(654\) | −4.15899 | −0.162629 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 13.2188 | 0.516108 | ||||||||
\(657\) | −49.0669 | −1.91428 | ||||||||
\(658\) | −21.1470 | −0.824395 | ||||||||
\(659\) | 15.5090 | 0.604146 | 0.302073 | − | 0.953285i | \(-0.402321\pi\) | ||||
0.302073 | + | 0.953285i | \(0.402321\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.9524 | −1.12612 | −0.563058 | − | 0.826417i | \(-0.690375\pi\) | ||||
−0.563058 | + | 0.826417i | \(0.690375\pi\) | |||||||
\(662\) | −16.0972 | −0.625637 | ||||||||
\(663\) | 0.0646254 | 0.00250984 | ||||||||
\(664\) | 20.1573 | 0.782257 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.85111 | 0.342973 | ||||||||
\(667\) | −16.5427 | −0.640536 | ||||||||
\(668\) | −17.6406 | −0.682534 | ||||||||
\(669\) | −0.153540 | −0.00593620 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.9811 | −0.964385 | ||||||||
\(672\) | −2.13372 | −0.0823100 | ||||||||
\(673\) | −35.4119 | −1.36503 | −0.682513 | − | 0.730873i | \(-0.739113\pi\) | ||||
−0.682513 | + | 0.730873i | \(0.739113\pi\) | |||||||
\(674\) | −18.9881 | −0.731395 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.4052 | 0.400201 | ||||||||
\(677\) | −17.5836 | −0.675791 | −0.337896 | − | 0.941184i | \(-0.609715\pi\) | ||||
−0.337896 | + | 0.941184i | \(0.609715\pi\) | |||||||
\(678\) | 2.12113 | 0.0814615 | ||||||||
\(679\) | −21.8361 | −0.837994 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.30784 | −0.203397 | ||||||||
\(682\) | 28.6990 | 1.09894 | ||||||||
\(683\) | 29.9328 | 1.14535 | 0.572674 | − | 0.819783i | \(-0.305906\pi\) | ||||
0.572674 | + | 0.819783i | \(0.305906\pi\) | |||||||
\(684\) | 18.4792 | 0.706570 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −22.0035 | −0.840098 | ||||||||
\(687\) | 4.06807 | 0.155207 | ||||||||
\(688\) | −18.8818 | −0.719861 | ||||||||
\(689\) | −0.00425606 | −0.000162143 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.2291 | 0.503260 | 0.251630 | − | 0.967823i | \(-0.419033\pi\) | ||||
0.251630 | + | 0.967823i | \(0.419033\pi\) | |||||||
\(692\) | 14.4891 | 0.550793 | ||||||||
\(693\) | −21.1475 | −0.803328 | ||||||||
\(694\) | 15.3040 | 0.580933 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.48770 | 0.170106 | ||||||||
\(697\) | 33.3992 | 1.26509 | ||||||||
\(698\) | −19.9598 | −0.755488 | ||||||||
\(699\) | −0.380411 | −0.0143884 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.9444 | 0.602214 | 0.301107 | − | 0.953590i | \(-0.402644\pi\) | ||||
0.301107 | + | 0.953590i | \(0.402644\pi\) | |||||||
\(702\) | −0.0948228 | −0.00357885 | ||||||||
\(703\) | 21.4367 | 0.808502 | ||||||||
\(704\) | −25.7324 | −0.969825 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −27.5483 | −1.03679 | ||||||||
\(707\) | 37.3046 | 1.40298 | ||||||||
\(708\) | 2.13474 | 0.0802283 | ||||||||
\(709\) | 37.1049 | 1.39351 | 0.696753 | − | 0.717312i | \(-0.254628\pi\) | ||||
0.696753 | + | 0.717312i | \(0.254628\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.14014 | 0.0802617 | ||||||||
\(712\) | −33.1753 | −1.24330 | ||||||||
\(713\) | 20.9492 | 0.784552 | ||||||||
\(714\) | 2.46521 | 0.0922583 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13.9420 | 0.521037 | ||||||||
\(717\) | −1.04765 | −0.0391254 | ||||||||
\(718\) | 6.62773 | 0.247345 | ||||||||
\(719\) | 5.70240 | 0.212664 | 0.106332 | − | 0.994331i | \(-0.466089\pi\) | ||||
0.106332 | + | 0.994331i | \(0.466089\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.4392 | 0.910163 | ||||||||
\(722\) | −46.2326 | −1.72060 | ||||||||
\(723\) | −0.223927 | −0.00832793 | ||||||||
\(724\) | −5.36306 | −0.199317 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.237890 | −0.00882891 | ||||||||
\(727\) | 5.81600 | 0.215703 | 0.107852 | − | 0.994167i | \(-0.465603\pi\) | ||||
0.107852 | + | 0.994167i | \(0.465603\pi\) | |||||||
\(728\) | −0.451201 | −0.0167226 | ||||||||
\(729\) | −24.3299 | −0.901106 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −47.7075 | −1.76453 | ||||||||
\(732\) | 1.41422 | 0.0522712 | ||||||||
\(733\) | −43.9492 | −1.62330 | −0.811651 | − | 0.584143i | \(-0.801431\pi\) | ||||
−0.811651 | + | 0.584143i | \(0.801431\pi\) | |||||||
\(734\) | 34.2840 | 1.26545 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −10.6572 | −0.392828 | ||||||||
\(737\) | −42.3168 | −1.55876 | ||||||||
\(738\) | −24.2963 | −0.894359 | ||||||||
\(739\) | −22.5626 | −0.829979 | −0.414989 | − | 0.909826i | \(-0.636215\pi\) | ||||
−0.414989 | + | 0.909826i | \(0.636215\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.113859 | −0.00418272 | ||||||||
\(742\) | −0.162353 | −0.00596015 | ||||||||
\(743\) | −7.18672 | −0.263655 | −0.131828 | − | 0.991273i | \(-0.542085\pi\) | ||||
−0.131828 | + | 0.991273i | \(0.542085\pi\) | |||||||
\(744\) | −5.68309 | −0.208352 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 19.1715 | 0.701919 | ||||||||
\(747\) | −19.3866 | −0.709320 | ||||||||
\(748\) | −11.2607 | −0.411733 | ||||||||
\(749\) | 3.78855 | 0.138431 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.0828 | 1.09774 | 0.548868 | − | 0.835909i | \(-0.315059\pi\) | ||||
0.548868 | + | 0.835909i | \(0.315059\pi\) | |||||||
\(752\) | 14.9931 | 0.546742 | ||||||||
\(753\) | 1.44381 | 0.0526154 | ||||||||
\(754\) | 0.465036 | 0.0169356 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.41475 | 0.0878235 | ||||||||
\(757\) | 6.52000 | 0.236973 | 0.118487 | − | 0.992956i | \(-0.462196\pi\) | ||||
0.118487 | + | 0.992956i | \(0.462196\pi\) | |||||||
\(758\) | −0.624185 | −0.0226714 | ||||||||
\(759\) | 1.79546 | 0.0651711 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.1010 | 0.511162 | 0.255581 | − | 0.966788i | \(-0.417733\pi\) | ||||
0.255581 | + | 0.966788i | \(0.417733\pi\) | |||||||
\(762\) | −1.48637 | −0.0538456 | ||||||||
\(763\) | 38.3902 | 1.38982 | ||||||||
\(764\) | −14.5885 | −0.527793 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.3122 | 0.950699 | ||||||||
\(767\) | 0.773780 | 0.0279396 | ||||||||
\(768\) | 3.52132 | 0.127065 | ||||||||
\(769\) | 18.1800 | 0.655589 | 0.327795 | − | 0.944749i | \(-0.393695\pi\) | ||||
0.327795 | + | 0.944749i | \(0.393695\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.36169 | −0.121068 | ||||||||
\(772\) | −4.70950 | −0.169499 | ||||||||
\(773\) | −43.7032 | −1.57190 | −0.785948 | − | 0.618293i | \(-0.787825\pi\) | ||||
−0.785948 | + | 0.618293i | \(0.787825\pi\) | |||||||
\(774\) | 34.7049 | 1.24744 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 29.5868 | 1.06210 | ||||||||
\(777\) | 1.38881 | 0.0498232 | ||||||||
\(778\) | 14.8742 | 0.533266 | ||||||||
\(779\) | −58.8439 | −2.10830 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.1123 | 0.970155 | ||||||||
\(782\) | 12.3129 | 0.440307 | ||||||||
\(783\) | −8.70561 | −0.311113 | ||||||||
\(784\) | 3.29708 | 0.117753 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.60407 | −0.0572153 | ||||||||
\(787\) | −20.3278 | −0.724608 | −0.362304 | − | 0.932060i | \(-0.618010\pi\) | ||||
−0.362304 | + | 0.932060i | \(0.618010\pi\) | |||||||
\(788\) | 14.7321 | 0.524808 | ||||||||
\(789\) | 2.49826 | 0.0889405 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.5794 | −0.696164 | ||||||||
\(792\) | 28.6538 | 1.01817 | ||||||||
\(793\) | 0.512615 | 0.0182035 | ||||||||
\(794\) | 10.4359 | 0.370358 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.50343 | −0.336840 | ||||||||
\(797\) | 8.91772 | 0.315882 | 0.157941 | − | 0.987449i | \(-0.449514\pi\) | ||||
0.157941 | + | 0.987449i | \(0.449514\pi\) | |||||||
\(798\) | −4.34329 | −0.153751 | ||||||||
\(799\) | 37.8822 | 1.34018 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 31.9069 | 1.12737 | ||||||||
\(802\) | −10.9362 | −0.386170 | ||||||||
\(803\) | −52.6789 | −1.85900 | ||||||||
\(804\) | 2.39563 | 0.0844872 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.588906 | −0.0207433 | ||||||||
\(807\) | 3.02470 | 0.106475 | ||||||||
\(808\) | −50.5457 | −1.77819 | ||||||||
\(809\) | −23.4279 | −0.823680 | −0.411840 | − | 0.911256i | \(-0.635114\pi\) | ||||
−0.411840 | + | 0.911256i | \(0.635114\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.8208 | 0.625774 | 0.312887 | − | 0.949790i | \(-0.398704\pi\) | ||||
0.312887 | + | 0.949790i | \(0.398704\pi\) | |||||||
\(812\) | −11.8426 | −0.415592 | ||||||||
\(813\) | −2.93314 | −0.102870 | ||||||||
\(814\) | 9.50267 | 0.333069 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.74782 | −0.0611861 | ||||||||
\(817\) | 84.0527 | 2.94063 | ||||||||
\(818\) | 2.03360 | 0.0711033 | ||||||||
\(819\) | 0.433950 | 0.0151634 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.2196 | 1.15937 | 0.579686 | − | 0.814840i | \(-0.303175\pi\) | ||||
0.579686 | + | 0.814840i | \(0.303175\pi\) | |||||||
\(822\) | 1.99733 | 0.0696647 | ||||||||
\(823\) | −13.2155 | −0.460663 | −0.230331 | − | 0.973112i | \(-0.573981\pi\) | ||||
−0.230331 | + | 0.973112i | \(0.573981\pi\) | |||||||
\(824\) | −33.1138 | −1.15357 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 29.5168 | 1.02702 | ||||||||
\(827\) | −47.8885 | −1.66525 | −0.832623 | − | 0.553840i | \(-0.813162\pi\) | ||||
−0.832623 | + | 0.553840i | \(0.813162\pi\) | |||||||
\(828\) | 5.97958 | 0.207805 | ||||||||
\(829\) | 50.0186 | 1.73722 | 0.868609 | − | 0.495498i | \(-0.165015\pi\) | ||||
0.868609 | + | 0.495498i | \(0.165015\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.23544 | 0.112236 | ||||||||
\(832\) | 0.528031 | 0.0183062 | ||||||||
\(833\) | 8.33054 | 0.288636 | ||||||||
\(834\) | −1.56666 | −0.0542491 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 19.8395 | 0.686164 | ||||||||
\(837\) | 11.0245 | 0.381063 | ||||||||
\(838\) | 10.4430 | 0.360747 | ||||||||
\(839\) | −23.0264 | −0.794958 | −0.397479 | − | 0.917611i | \(-0.630115\pi\) | ||||
−0.397479 | + | 0.917611i | \(0.630115\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.6946 | 0.472227 | ||||||||
\(842\) | 23.1975 | 0.799438 | ||||||||
\(843\) | −0.397845 | −0.0137025 | ||||||||
\(844\) | −13.8816 | −0.477826 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −27.5575 | −0.947446 | ||||||||
\(847\) | 2.19588 | 0.0754512 | ||||||||
\(848\) | 0.115107 | 0.00395280 | ||||||||
\(849\) | 4.13166 | 0.141798 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.93659 | 0.237783 | ||||||||
\(852\) | −1.53488 | −0.0525840 | ||||||||
\(853\) | 39.2071 | 1.34243 | 0.671213 | − | 0.741265i | \(-0.265774\pi\) | ||||
0.671213 | + | 0.741265i | \(0.265774\pi\) | |||||||
\(854\) | 19.5543 | 0.669135 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.13328 | −0.175452 | ||||||||
\(857\) | 36.7331 | 1.25478 | 0.627389 | − | 0.778706i | \(-0.284124\pi\) | ||||
0.627389 | + | 0.778706i | \(0.284124\pi\) | |||||||
\(858\) | −0.0504725 | −0.00172310 | ||||||||
\(859\) | −47.6475 | −1.62571 | −0.812856 | − | 0.582465i | \(-0.802088\pi\) | ||||
−0.812856 | + | 0.582465i | \(0.802088\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.81228 | −0.129922 | ||||||||
\(862\) | 39.1139 | 1.33223 | ||||||||
\(863\) | 35.6174 | 1.21243 | 0.606215 | − | 0.795301i | \(-0.292687\pi\) | ||||
0.606215 | + | 0.795301i | \(0.292687\pi\) | |||||||
\(864\) | −5.60834 | −0.190800 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.9579 | 0.440328 | ||||||||
\(867\) | −0.609373 | −0.0206954 | ||||||||
\(868\) | 14.9970 | 0.509033 | ||||||||
\(869\) | 2.29769 | 0.0779438 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.868345 | 0.0294228 | ||||||||
\(872\) | −52.0166 | −1.76150 | ||||||||
\(873\) | −28.4556 | −0.963075 | ||||||||
\(874\) | −21.6932 | −0.733784 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.98224 | 0.100761 | ||||||||
\(877\) | −39.1576 | −1.32226 | −0.661129 | − | 0.750272i | \(-0.729922\pi\) | ||||
−0.661129 | + | 0.750272i | \(0.729922\pi\) | |||||||
\(878\) | −2.31912 | −0.0782664 | ||||||||
\(879\) | −1.93785 | −0.0653621 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.9027 | −1.04114 | −0.520569 | − | 0.853820i | \(-0.674280\pi\) | ||||
−0.520569 | + | 0.853820i | \(0.674280\pi\) | |||||||
\(882\) | −6.06006 | −0.204053 | ||||||||
\(883\) | 9.36408 | 0.315126 | 0.157563 | − | 0.987509i | \(-0.449636\pi\) | ||||
0.157563 | + | 0.987509i | \(0.449636\pi\) | |||||||
\(884\) | 0.231071 | 0.00777177 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 29.3581 | 0.986304 | ||||||||
\(887\) | −48.6485 | −1.63346 | −0.816728 | − | 0.577023i | \(-0.804214\pi\) | ||||
−0.816728 | + | 0.577023i | \(0.804214\pi\) | |||||||
\(888\) | −1.88176 | −0.0631477 | ||||||||
\(889\) | 13.7202 | 0.460161 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27.0818 | −0.907274 | ||||||||
\(892\) | −0.548991 | −0.0183816 | ||||||||
\(893\) | −66.7422 | −2.23344 | ||||||||
\(894\) | 2.27859 | 0.0762074 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.08510 | 0.0362508 | ||||||||
\(897\) | −0.0368431 | −0.00123015 | ||||||||
\(898\) | 39.0207 | 1.30214 | ||||||||
\(899\) | −54.0671 | −1.80324 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.290835 | 0.00968913 | ||||||||
\(902\) | −26.0849 | −0.868531 | ||||||||
\(903\) | 5.44546 | 0.181214 | ||||||||
\(904\) | 26.5290 | 0.882343 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.08990 | −0.0362095 | ||||||||
\(907\) | −42.3130 | −1.40498 | −0.702489 | − | 0.711694i | \(-0.747928\pi\) | ||||
−0.702489 | + | 0.711694i | \(0.747928\pi\) | |||||||
\(908\) | −18.9785 | −0.629822 | ||||||||
\(909\) | 48.6131 | 1.61240 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.03059 | 0.0672763 | 0.0336382 | − | 0.999434i | \(-0.489291\pi\) | ||||
0.0336382 | + | 0.999434i | \(0.489291\pi\) | |||||||
\(912\) | 3.07938 | 0.101968 | ||||||||
\(913\) | −20.8138 | −0.688836 | ||||||||
\(914\) | −4.78931 | −0.158416 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.5456 | 0.480601 | ||||||||
\(917\) | 14.8066 | 0.488958 | ||||||||
\(918\) | 6.47965 | 0.213860 | ||||||||
\(919\) | −24.5581 | −0.810097 | −0.405048 | − | 0.914295i | \(-0.632745\pi\) | ||||
−0.405048 | + | 0.914295i | \(0.632745\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.48048 | −0.0487833 | ||||||||
\(922\) | −2.55021 | −0.0839866 | ||||||||
\(923\) | −0.556348 | −0.0183124 | ||||||||
\(924\) | 1.28533 | 0.0422842 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −26.6868 | −0.876983 | ||||||||
\(927\) | 31.8477 | 1.04602 | ||||||||
\(928\) | 27.5048 | 0.902888 | ||||||||
\(929\) | 6.26058 | 0.205403 | 0.102702 | − | 0.994712i | \(-0.467251\pi\) | ||||
0.102702 | + | 0.994712i | \(0.467251\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.6770 | −0.481020 | ||||||||
\(932\) | −1.36018 | −0.0445541 | ||||||||
\(933\) | 4.34881 | 0.142374 | ||||||||
\(934\) | 46.0559 | 1.50700 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.587979 | −0.0192187 | ||||||||
\(937\) | −21.1381 | −0.690552 | −0.345276 | − | 0.938501i | \(-0.612215\pi\) | ||||
−0.345276 | + | 0.938501i | \(0.612215\pi\) | |||||||
\(938\) | 33.1241 | 1.08154 | ||||||||
\(939\) | 4.35577 | 0.142145 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.32725 | −0.108465 | −0.0542327 | − | 0.998528i | \(-0.517271\pi\) | ||||
−0.0542327 | + | 0.998528i | \(0.517271\pi\) | |||||||
\(942\) | 0.0638790 | 0.00208129 | ||||||||
\(943\) | −19.0410 | −0.620059 | ||||||||
\(944\) | −20.9272 | −0.681124 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 37.2597 | 1.21142 | ||||||||
\(947\) | −3.04446 | −0.0989318 | −0.0494659 | − | 0.998776i | \(-0.515752\pi\) | ||||
−0.0494659 | + | 0.998776i | \(0.515752\pi\) | |||||||
\(948\) | −0.130076 | −0.00422468 | ||||||||
\(949\) | 1.08098 | 0.0350900 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.177489 | 0.00575546 | ||||||||
\(952\) | 30.8325 | 0.999287 | ||||||||
\(953\) | 9.75807 | 0.316095 | 0.158047 | − | 0.987432i | \(-0.449480\pi\) | ||||
0.158047 | + | 0.987432i | \(0.449480\pi\) | |||||||
\(954\) | −0.211568 | −0.00684978 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.74594 | −0.121152 | ||||||||
\(957\) | −4.63385 | −0.149791 | ||||||||
\(958\) | 33.2010 | 1.07267 | ||||||||
\(959\) | −18.4366 | −0.595350 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.4688 | 1.20867 | ||||||||
\(962\) | −0.194996 | −0.00628692 | ||||||||
\(963\) | 4.93702 | 0.159093 | ||||||||
\(964\) | −0.800662 | −0.0257876 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.40542 | −0.0452187 | ||||||||
\(967\) | −8.16066 | −0.262429 | −0.131215 | − | 0.991354i | \(-0.541888\pi\) | ||||
−0.131215 | + | 0.991354i | \(0.541888\pi\) | |||||||
\(968\) | −2.97529 | −0.0956296 | ||||||||
\(969\) | 7.78049 | 0.249945 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.0914 | 0.516398 | 0.258199 | − | 0.966092i | \(-0.416871\pi\) | ||||
0.258199 | + | 0.966092i | \(0.416871\pi\) | |||||||
\(972\) | 4.73340 | 0.151824 | ||||||||
\(973\) | 14.4613 | 0.463609 | ||||||||
\(974\) | 17.9733 | 0.575902 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.8639 | −0.443774 | ||||||||
\(977\) | 23.1058 | 0.739220 | 0.369610 | − | 0.929187i | \(-0.379491\pi\) | ||||
0.369610 | + | 0.929187i | \(0.379491\pi\) | |||||||
\(978\) | −1.32920 | −0.0425030 | ||||||||
\(979\) | 34.2557 | 1.09482 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 50.0278 | 1.59727 | ||||||||
\(982\) | 0.614436 | 0.0196074 | ||||||||
\(983\) | 44.1346 | 1.40768 | 0.703838 | − | 0.710361i | \(-0.251468\pi\) | ||||
0.703838 | + | 0.710361i | \(0.251468\pi\) | |||||||
\(984\) | 5.16543 | 0.164668 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −31.7779 | −1.01201 | ||||||||
\(987\) | −4.32398 | −0.137634 | ||||||||
\(988\) | −0.407110 | −0.0129519 | ||||||||
\(989\) | 27.1981 | 0.864851 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.42300 | −0.172267 | −0.0861337 | − | 0.996284i | \(-0.527451\pi\) | ||||
−0.0861337 | + | 0.996284i | \(0.527451\pi\) | |||||||
\(992\) | −34.8312 | −1.10589 | ||||||||
\(993\) | −3.29145 | −0.104451 | ||||||||
\(994\) | −21.2226 | −0.673139 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.17830 | 0.0373360 | ||||||||
\(997\) | −56.5705 | −1.79161 | −0.895803 | − | 0.444451i | \(-0.853399\pi\) | ||||
−0.895803 | + | 0.444451i | \(0.853399\pi\) | |||||||
\(998\) | 42.8310 | 1.35579 | ||||||||
\(999\) | 3.65039 | 0.115493 |
(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 | 6025.2.a.p.1.15 | 46 | ||
5.2 | odd | 4 | 1205.2.b.c.724.15 | ✓ | 46 | ||
5.3 | odd | 4 | 1205.2.b.c.724.32 | yes | 46 | ||
5.4 | even | 2 | inner | 6025.2.a.p.1.32 | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.b.c.724.15 | ✓ | 46 | 5.2 | odd | 4 | ||
1205.2.b.c.724.32 | yes | 46 | 5.3 | odd | 4 | ||
6025.2.a.p.1.15 | 46 | 1.1 | even | 1 | trivial | ||
6025.2.a.p.1.32 | 46 | 5.4 | even | 2 | inner |