Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6028,2,Mod(1,6028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6028, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6028.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6028 = 2^{2} \cdot 11 \cdot 137 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6028.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: | \(48.1338223384\) |
Analytic rank: | \(0\) |
Dimension: | \(29\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 6028.1 |
$q$-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 | 0 | ||||||||
\(3\) | −2.00219 | −1.15597 | −0.577983 | − | 0.816049i | \(-0.696160\pi\) | ||||
−0.577983 | + | 0.816049i | \(0.696160\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.977497 | 0.437150 | 0.218575 | − | 0.975820i | \(-0.429859\pi\) | ||||
0.218575 | + | 0.975820i | \(0.429859\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.03319 | −1.14644 | −0.573219 | − | 0.819402i | \(-0.694305\pi\) | ||||
−0.573219 | + | 0.819402i | \(0.694305\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00878 | 0.336259 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.12665 | −1.14453 | −0.572264 | − | 0.820070i | \(-0.693935\pi\) | ||||
−0.572264 | + | 0.820070i | \(0.693935\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.95714 | −0.505331 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.328908 | −0.0797719 | −0.0398859 | − | 0.999204i | \(-0.512699\pi\) | ||||
−0.0398859 | + | 0.999204i | \(0.512699\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.36999 | −1.92021 | −0.960104 | − | 0.279645i | \(-0.909783\pi\) | ||||
−0.960104 | + | 0.279645i | \(0.909783\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.07303 | 1.32524 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.85060 | 0.594392 | 0.297196 | − | 0.954817i | \(-0.403949\pi\) | ||||
0.297196 | + | 0.954817i | \(0.403949\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.04450 | −0.808900 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.98681 | 0.767263 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.72310 | 0.319971 | 0.159986 | − | 0.987119i | \(-0.448855\pi\) | ||||
0.159986 | + | 0.987119i | \(0.448855\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.02515 | 0.902544 | 0.451272 | − | 0.892386i | \(-0.350970\pi\) | ||||
0.451272 | + | 0.892386i | \(0.350970\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.00219 | −0.348537 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.96493 | −0.501165 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.87184 | −0.636527 | −0.318264 | − | 0.948002i | \(-0.603100\pi\) | ||||
−0.318264 | + | 0.948002i | \(0.603100\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.26235 | 1.32304 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.5021 | −1.95250 | −0.976248 | − | 0.216656i | \(-0.930485\pi\) | ||||
−0.976248 | + | 0.216656i | \(0.930485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.5086 | −1.60254 | −0.801272 | − | 0.598300i | \(-0.795843\pi\) | ||||
−0.801272 | + | 0.598300i | \(0.795843\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.986076 | 0.146996 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.81610 | 0.848365 | 0.424183 | − | 0.905577i | \(-0.360561\pi\) | ||||
0.424183 | + | 0.905577i | \(0.360561\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.20023 | 0.314319 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.658537 | 0.0922136 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.3047 | −1.82754 | −0.913771 | − | 0.406230i | \(-0.866843\pi\) | ||||
−0.913771 | + | 0.406230i | \(0.866843\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.977497 | 0.131806 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.7583 | 2.21970 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.50069 | −0.585940 | −0.292970 | − | 0.956122i | \(-0.594644\pi\) | ||||
−0.292970 | + | 0.956122i | \(0.594644\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.17394 | 1.04657 | 0.523283 | − | 0.852159i | \(-0.324707\pi\) | ||||
0.523283 | + | 0.852159i | \(0.324707\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.05981 | −0.385500 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.03379 | −0.500330 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.37395 | 0.778702 | 0.389351 | − | 0.921090i | \(-0.372699\pi\) | ||||
0.389351 | + | 0.921090i | \(0.372699\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.70746 | −0.687097 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.0597 | 1.66857 | 0.834287 | − | 0.551330i | \(-0.185880\pi\) | ||||
0.834287 | + | 0.551330i | \(0.185880\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.78699 | −0.326192 | −0.163096 | − | 0.986610i | \(-0.552148\pi\) | ||||
−0.163096 | + | 0.986610i | \(0.552148\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.09787 | 0.935061 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.03319 | −0.345664 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.40230 | −0.495297 | −0.247649 | − | 0.968850i | \(-0.579658\pi\) | ||||
−0.247649 | + | 0.968850i | \(0.579658\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0087 | −1.22319 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.44808 | 0.817533 | 0.408767 | − | 0.912639i | \(-0.365959\pi\) | ||||
0.408767 | + | 0.912639i | \(0.365959\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.321506 | −0.0348723 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.44997 | −0.369876 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.2301 | −1.61438 | −0.807192 | − | 0.590288i | \(-0.799014\pi\) | ||||
−0.807192 | + | 0.590288i | \(0.799014\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.5169 | 1.31213 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.0613 | −1.04331 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.18164 | −0.839418 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.5413 | 1.37491 | 0.687456 | − | 0.726226i | \(-0.258727\pi\) | ||||
0.687456 | + | 0.726226i | \(0.258727\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00878 | 0.101386 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.59880 | −0.557102 | −0.278551 | − | 0.960421i | \(-0.589854\pi\) | ||||
−0.278551 | + | 0.960421i | \(0.589854\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.2952 | 1.80268 | 0.901338 | − | 0.433117i | \(-0.142586\pi\) | ||||
0.901338 | + | 0.433117i | \(0.142586\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.93637 | 0.579330 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.55388 | −0.343567 | −0.171783 | − | 0.985135i | \(-0.554953\pi\) | ||||
−0.171783 | + | 0.985135i | \(0.554953\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.8476 | 1.23058 | 0.615288 | − | 0.788302i | \(-0.289040\pi\) | ||||
0.615288 | + | 0.788302i | \(0.289040\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.75218 | 0.735804 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.4453 | −1.82926 | −0.914630 | − | 0.404293i | \(-0.867518\pi\) | ||||
−0.914630 | + | 0.404293i | \(0.867518\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.78645 | 0.259838 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.16287 | −0.384858 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.997639 | 0.0914535 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 25.0316 | 2.25702 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.84097 | −0.790760 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.2060 | 1.43805 | 0.719027 | − | 0.694983i | \(-0.244588\pi\) | ||||
0.719027 | + | 0.694983i | \(0.244588\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 21.0402 | 1.85249 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.9613 | −1.83139 | −0.915697 | − | 0.401870i | \(-0.868360\pi\) | ||||
−0.915697 | + | 0.401870i | \(0.868360\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 25.3878 | 2.20140 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.89710 | 0.335409 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.00000 | 0.0854358 | ||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.7907 | −1.59381 | −0.796904 | − | 0.604106i | \(-0.793530\pi\) | ||||
−0.796904 | + | 0.604106i | \(0.793530\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.6450 | −0.980682 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.12665 | −0.345088 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.68432 | 0.139875 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.40529 | −0.363343 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.74776 | −0.798567 | −0.399284 | − | 0.916827i | \(-0.630741\pi\) | ||||
−0.399284 | + | 0.916827i | \(0.630741\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.5230 | −0.937726 | −0.468863 | − | 0.883271i | \(-0.655336\pi\) | ||||
−0.468863 | + | 0.883271i | \(0.655336\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.331795 | −0.0268240 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.91207 | 0.394547 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.2000 | 1.37271 | 0.686356 | − | 0.727266i | \(-0.259209\pi\) | ||||
0.686356 | + | 0.727266i | \(0.259209\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 26.6386 | 2.11258 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.64641 | −0.681433 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.54825 | 0.747876 | 0.373938 | − | 0.927454i | \(-0.378007\pi\) | ||||
0.373938 | + | 0.927454i | \(0.378007\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.95714 | −0.152363 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.0646 | 0.856207 | 0.428103 | − | 0.903730i | \(-0.359182\pi\) | ||||
0.428103 | + | 0.903730i | \(0.359182\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.02925 | 0.309942 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.44345 | −0.645687 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.86589 | 0.598033 | 0.299016 | − | 0.954248i | \(-0.403341\pi\) | ||||
0.299016 | + | 0.954248i | \(0.403341\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.2677 | 0.927353 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.01125 | 0.677327 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.1201 | 0.980645 | 0.490322 | − | 0.871541i | \(-0.336879\pi\) | ||||
0.490322 | + | 0.871541i | \(0.336879\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.19900 | −0.237780 | −0.118890 | − | 0.992907i | \(-0.537934\pi\) | ||||
−0.118890 | + | 0.992907i | \(0.537934\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.3658 | −1.20979 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.78472 | −0.278258 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.328908 | −0.0240521 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.0928 | −0.879619 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.31823 | 0.167741 | 0.0838706 | − | 0.996477i | \(-0.473272\pi\) | ||||
0.0838706 | + | 0.996477i | \(0.473272\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.9716 | −1.43759 | −0.718793 | − | 0.695224i | \(-0.755305\pi\) | ||||
−0.718793 | + | 0.695224i | \(0.755305\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.07642 | 0.578365 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.99517 | 0.427138 | 0.213569 | − | 0.976928i | \(-0.431491\pi\) | ||||
0.213569 | + | 0.976928i | \(0.431491\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.48710 | 0.105418 | 0.0527090 | − | 0.998610i | \(-0.483214\pi\) | ||||
0.0527090 | + | 0.998610i | \(0.483214\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.7619 | −0.900153 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.22648 | −0.366827 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.2207 | −0.853533 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.87562 | 0.199870 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.36999 | −0.578964 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.8499 | −1.43537 | −0.717684 | − | 0.696369i | \(-0.754798\pi\) | ||||
−0.717684 | + | 0.696369i | \(0.754798\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −28.1501 | −1.92882 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.2721 | −0.700552 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.2422 | −1.03471 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.58009 | 0.377068 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.35729 | 0.0913011 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.6100 | −1.17925 | −0.589625 | − | 0.807677i | \(-0.700725\pi\) | ||||
−0.589625 | + | 0.807677i | \(0.700725\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.08000 | −0.272000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.20216 | −0.478024 | −0.239012 | − | 0.971017i | \(-0.576824\pi\) | ||||
−0.239012 | + | 0.971017i | \(0.576824\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.2665 | 1.07492 | 0.537459 | − | 0.843290i | \(-0.319384\pi\) | ||||
0.537459 | + | 0.843290i | \(0.319384\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.07303 | 0.399576 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.64502 | −0.435330 | −0.217665 | − | 0.976024i | \(-0.569844\pi\) | ||||
−0.217665 | + | 0.976024i | \(0.569844\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.68522 | 0.370863 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.81425 | 0.572547 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.7141 | 1.46925 | 0.734627 | − | 0.678471i | \(-0.237357\pi\) | ||||
0.734627 | + | 0.678471i | \(0.237357\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.8268 | 1.21274 | 0.606371 | − | 0.795182i | \(-0.292625\pi\) | ||||
0.606371 | + | 0.795182i | \(0.292625\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.0811 | 0.646703 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.15072 | 0.137405 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 34.5400 | 2.19773 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.9125 | −0.945041 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.39230 | 0.214120 | 0.107060 | − | 0.994253i | \(-0.465856\pi\) | ||||
0.107060 | + | 0.994253i | \(0.465856\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.85060 | 0.179216 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.643718 | 0.0403112 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.7136 | 1.54159 | 0.770796 | − | 0.637083i | \(-0.219859\pi\) | ||||
0.770796 | + | 0.637083i | \(0.219859\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.7440 | 0.729739 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.73822 | 0.107593 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.9557 | 0.983871 | 0.491936 | − | 0.870632i | \(-0.336290\pi\) | ||||
0.491936 | + | 0.870632i | \(0.336290\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.0053 | −0.798910 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 30.4936 | 1.86618 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.78458 | −0.352692 | −0.176346 | − | 0.984328i | \(-0.556428\pi\) | ||||
−0.176346 | + | 0.984328i | \(0.556428\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.88186 | −0.418043 | −0.209022 | − | 0.977911i | \(-0.567028\pi\) | ||||
−0.209022 | + | 0.977911i | \(0.567028\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −25.0613 | −1.51678 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.04450 | −0.243893 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.0005 | −0.781125 | −0.390563 | − | 0.920576i | \(-0.627720\pi\) | ||||
−0.390563 | + | 0.920576i | \(0.627720\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.06926 | 0.303489 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.3084 | 0.972878 | 0.486439 | − | 0.873715i | \(-0.338296\pi\) | ||||
0.486439 | + | 0.873715i | \(0.338296\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.1041 | 0.897847 | 0.448923 | − | 0.893570i | \(-0.351808\pi\) | ||||
0.448923 | + | 0.893570i | \(0.351808\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 16.3812 | 0.970340 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 37.9212 | 2.23841 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8918 | −0.993636 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −27.1123 | −1.58935 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.6206 | 0.912568 | 0.456284 | − | 0.889834i | \(-0.349180\pi\) | ||||
0.456284 | + | 0.889834i | \(0.349180\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.39941 | −0.256144 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.98681 | 0.231338 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.7634 | −0.680297 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31.8745 | 1.83722 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.2099 | 0.643991 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.99000 | 0.457506 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.85495 | 0.505378 | 0.252689 | − | 0.967547i | \(-0.418685\pi\) | ||||
0.252689 | + | 0.967547i | \(0.418685\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −36.6304 | −2.08383 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.2638 | −0.865533 | −0.432766 | − | 0.901506i | \(-0.642462\pi\) | ||||
−0.432766 | + | 0.901506i | \(0.642462\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.5499 | 1.33112 | 0.665559 | − | 0.746345i | \(-0.268193\pi\) | ||||
0.665559 | + | 0.746345i | \(0.268193\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.99096 | −0.168521 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.4581 | 1.03671 | 0.518354 | − | 0.855166i | \(-0.326545\pi\) | ||||
0.518354 | + | 0.855166i | \(0.326545\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.72310 | 0.0964749 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.11556 | 0.397152 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.75295 | 0.153179 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.6902 | 0.925808 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −25.7234 | −1.42251 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.6413 | −0.972598 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.2499 | −1.11303 | −0.556517 | − | 0.830836i | \(-0.687862\pi\) | ||||
−0.556517 | + | 0.830836i | \(0.687862\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.90583 | −0.214038 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.23052 | 0.340409 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.87065 | 0.483215 | 0.241608 | − | 0.970374i | \(-0.422325\pi\) | ||||
0.241608 | + | 0.970374i | \(0.422325\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 38.9332 | 2.11456 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.02515 | 0.272127 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.5586 | 0.786090 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.57902 | −0.300364 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.02668 | 0.162481 | 0.0812404 | − | 0.996695i | \(-0.474112\pi\) | ||||
0.0812404 | + | 0.996695i | \(0.474112\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.9226 | 0.798791 | 0.399395 | − | 0.916779i | \(-0.369220\pi\) | ||||
0.399395 | + | 0.916779i | \(0.369220\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.4522 | −0.878153 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.2247 | 1.07645 | 0.538227 | − | 0.842800i | \(-0.319094\pi\) | ||||
0.538227 | + | 0.842800i | \(0.319094\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.7433 | 0.729417 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.99747 | −0.105717 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.0082 | 0.686548 | 0.343274 | − | 0.939235i | \(-0.388464\pi\) | ||||
0.343274 | + | 0.939235i | \(0.388464\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 51.0567 | 2.68720 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.00219 | −0.105088 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.72427 | −0.142595 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.55269 | 0.446447 | 0.223223 | − | 0.974767i | \(-0.428342\pi\) | ||||
0.223223 | + | 0.974767i | \(0.428342\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.6118 | −0.656544 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 40.3557 | 2.09516 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.7305 | −0.607382 | −0.303691 | − | 0.952771i | \(-0.598219\pi\) | ||||
−0.303691 | + | 0.952771i | \(0.598219\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.7013 | 0.914093 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.11062 | −0.366216 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.9245 | 1.07482 | 0.537411 | − | 0.843321i | \(-0.319403\pi\) | ||||
0.537411 | + | 0.843321i | \(0.319403\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −32.4476 | −1.66234 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.27724 | −0.320752 | −0.160376 | − | 0.987056i | \(-0.551271\pi\) | ||||
−0.160376 | + | 0.987056i | \(0.551271\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.96493 | −0.151107 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.6008 | −0.538870 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.3789 | −0.982551 | −0.491276 | − | 0.871004i | \(-0.663469\pi\) | ||||
−0.491276 | + | 0.871004i | \(0.663469\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.937585 | −0.0474157 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 41.9685 | 2.11703 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.30323 | −0.216519 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.1112 | 1.00935 | 0.504677 | − | 0.863308i | \(-0.331612\pi\) | ||||
0.504677 | + | 0.863308i | \(0.331612\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −50.8312 | −2.54474 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.4657 | −0.772321 | −0.386160 | − | 0.922432i | \(-0.626199\pi\) | ||||
−0.386160 | + | 0.922432i | \(0.626199\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.7371 | −1.03299 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.7610 | −0.534717 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.87184 | −0.191920 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.32781 | −0.115103 | −0.0575514 | − | 0.998343i | \(-0.518329\pi\) | ||||
−0.0575514 | + | 0.998343i | \(0.518329\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.00219 | −0.0987609 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.6514 | 0.671743 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.28048 | 0.357385 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 37.6227 | 1.84239 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.20899 | −0.156769 | −0.0783847 | − | 0.996923i | \(-0.524976\pi\) | ||||
−0.0783847 | + | 0.996923i | \(0.524976\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.39568 | −0.214232 | −0.107116 | − | 0.994247i | \(-0.534162\pi\) | ||||
−0.107116 | + | 0.994247i | \(0.534162\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.86715 | 0.285270 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.33027 | 0.0645275 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.7931 | −1.19982 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.26235 | 0.398910 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.09241 | −0.389798 | −0.194899 | − | 0.980823i | \(-0.562438\pi\) | ||||
−0.194899 | + | 0.980823i | \(0.562438\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.07296 | −0.291848 | −0.145924 | − | 0.989296i | \(-0.546615\pi\) | ||||
−0.145924 | + | 0.989296i | \(0.546615\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.37234 | −0.161691 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −23.8595 | −1.14136 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.4709 | 1.35884 | 0.679422 | − | 0.733748i | \(-0.262231\pi\) | ||||
0.679422 | + | 0.733748i | \(0.262231\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.21955 | 0.105693 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.1690 | 0.768213 | 0.384107 | − | 0.923289i | \(-0.374510\pi\) | ||||
0.384107 | + | 0.923289i | \(0.374510\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.8874 | −0.705728 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.5169 | 0.923117 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.0987 | 0.712551 | 0.356276 | − | 0.934381i | \(-0.384046\pi\) | ||||
0.356276 | + | 0.934381i | \(0.384046\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.5021 | −0.588700 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.0712 | 1.08398 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.2352 | 0.573597 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.75977 | 0.0823188 | 0.0411594 | − | 0.999153i | \(-0.486895\pi\) | ||||
0.0411594 | + | 0.999153i | \(0.486895\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.31129 | −0.0612060 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.4532 | 1.37177 | 0.685887 | − | 0.727708i | \(-0.259414\pi\) | ||||
0.685887 | + | 0.727708i | \(0.259414\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.1996 | −0.520491 | −0.260245 | − | 0.965543i | \(-0.583803\pi\) | ||||
−0.260245 | + | 0.965543i | \(0.583803\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.83492 | −0.456083 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.64000 | 0.214713 | 0.107357 | − | 0.994221i | \(-0.465761\pi\) | ||||
0.107357 | + | 0.994221i | \(0.465761\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.3334 | −0.892733 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −34.4378 | −1.58681 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.5086 | −0.483185 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 33.8524 | 1.55326 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.4215 | −0.614527 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.7125 | −1.03776 | −0.518880 | − | 0.854847i | \(-0.673651\pi\) | ||||
−0.518880 | + | 0.854847i | \(0.673651\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.9778 | 0.728523 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.3118 | 0.787714 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.2366 | 0.601043 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.5797 | 0.796614 | 0.398307 | − | 0.917252i | \(-0.369598\pi\) | ||||
0.398307 | + | 0.917252i | \(0.369598\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.1174 | −0.864520 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.0696 | 0.950860 | 0.475430 | − | 0.879754i | \(-0.342293\pi\) | ||||
0.475430 | + | 0.879754i | \(0.342293\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.566740 | −0.0255247 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.986076 | 0.0443208 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −42.6456 | −1.91292 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.3214 | 1.67074 | 0.835369 | − | 0.549690i | \(-0.185254\pi\) | ||||
0.835369 | + | 0.549690i | \(0.185254\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22.1535 | −0.989747 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.5940 | −1.05200 | −0.526002 | − | 0.850483i | \(-0.676310\pi\) | ||||
−0.526002 | + | 0.850483i | \(0.676310\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.47281 | −0.243537 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.06734 | −0.358283 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.134884 | −0.00597864 | −0.00298932 | − | 0.999996i | \(-0.500952\pi\) | ||||
−0.00298932 | + | 0.999996i | \(0.500952\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.45347 | 0.373959 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −33.3696 | −1.47330 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.8835 | 0.788039 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.81610 | 0.255792 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.7490 | −0.691306 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.7979 | 1.69977 | 0.849883 | − | 0.526972i | \(-0.176673\pi\) | ||||
0.849883 | + | 0.526972i | \(0.176673\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.45738 | 0.107454 | 0.0537270 | − | 0.998556i | \(-0.482890\pi\) | ||||
0.0537270 | + | 0.998556i | \(0.482890\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −24.5624 | −1.07199 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.65281 | −0.0719976 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.8741 | −0.646699 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.54019 | −0.197027 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 51.5917 | 2.23468 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.47391 | −0.150190 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.2690 | −1.13359 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.20023 | 0.0947708 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.7999 | −1.28120 | −0.640599 | − | 0.767875i | \(-0.721314\pi\) | ||||
−0.640599 | + | 0.767875i | \(0.721314\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.40502 | 0.274866 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.5585 | 0.537946 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.5484 | −1.30615 | −0.653077 | − | 0.757292i | \(-0.726522\pi\) | ||||
−0.653077 | + | 0.757292i | \(0.726522\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.24568 | 0.351917 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.4223 | −0.614411 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.3530 | 0.567827 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.57773 | 0.321657 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.3934 | 0.609866 | 0.304933 | − | 0.952374i | \(-0.401366\pi\) | ||||
0.304933 | + | 0.952374i | \(0.401366\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43.3653 | 1.83416 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.658537 | 0.0278035 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.9249 | 1.42976 | 0.714882 | − | 0.699245i | \(-0.246480\pi\) | ||||
0.714882 | + | 0.699245i | \(0.246480\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.0077 | −0.799660 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 33.3915 | 1.40231 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.1419 | −0.802470 | −0.401235 | − | 0.915975i | \(-0.631419\pi\) | ||||
−0.401235 | + | 0.915975i | \(0.631419\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.5075 | 0.690816 | 0.345408 | − | 0.938453i | \(-0.387741\pi\) | ||||
0.345408 | + | 0.938453i | \(0.387741\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.64154 | −0.193903 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.5293 | −0.480803 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.0245 | −0.708740 | −0.354370 | − | 0.935105i | \(-0.615305\pi\) | ||||
−0.354370 | + | 0.935105i | \(0.615305\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 39.9870 | 1.66180 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.5914 | −0.937251 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.3047 | −0.551025 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.06919 | −0.168240 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.77851 | 0.403602 | 0.201801 | − | 0.979427i | \(-0.435321\pi\) | ||||
0.201801 | + | 0.979427i | \(0.435321\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.0605 | −1.73307 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.0035 | −0.493758 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.49585 | −0.0614274 | −0.0307137 | − | 0.999528i | \(-0.509778\pi\) | ||||
−0.0307137 | + | 0.999528i | \(0.509778\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.975190 | 0.0399789 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.97747 | −0.121860 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.61882 | −0.188720 | −0.0943599 | − | 0.995538i | \(-0.530080\pi\) | ||||
−0.0943599 | + | 0.995538i | \(0.530080\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −42.5865 | −1.73714 | −0.868570 | − | 0.495567i | \(-0.834960\pi\) | ||||
−0.868570 | + | 0.495567i | \(0.834960\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.42989 | 0.261845 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.977497 | 0.0397409 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.4872 | −1.11567 | −0.557836 | − | 0.829951i | \(-0.688368\pi\) | ||||
−0.557836 | + | 0.829951i | \(0.688368\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.4644 | 0.424040 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.0010 | −0.970977 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.2387 | −0.736652 | −0.368326 | − | 0.929697i | \(-0.620069\pi\) | ||||
−0.368326 | + | 0.929697i | \(0.620069\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.4683 | 0.986656 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.9697 | −1.64938 | −0.824688 | − | 0.565587i | \(-0.808650\pi\) | ||||
−0.824688 | + | 0.565587i | \(0.808650\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.8199 | 0.434887 | 0.217443 | − | 0.976073i | \(-0.430228\pi\) | ||||
0.217443 | + | 0.976073i | \(0.430228\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.3648 | 0.456054 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 46.1957 | 1.85079 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.5805 | 0.463219 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.7583 | 0.669263 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.27348 | 0.0507770 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.5163 | −1.01579 | −0.507894 | − | 0.861420i | \(-0.669576\pi\) | ||||
−0.507894 | + | 0.861420i | \(0.669576\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 41.7456 | 1.65924 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.8414 | 0.628645 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.07960 | −0.359747 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.1831 | 0.561073 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.5303 | 1.60085 | 0.800424 | − | 0.599434i | \(-0.204608\pi\) | ||||
0.800424 | + | 0.599434i | \(0.204608\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.0951 | 1.46289 | 0.731444 | − | 0.681901i | \(-0.238847\pi\) | ||||
0.731444 | + | 0.681901i | \(0.238847\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20.5667 | 0.809815 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.4603 | 0.765065 | 0.382533 | − | 0.923942i | \(-0.375052\pi\) | ||||
0.382533 | + | 0.923942i | \(0.375052\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.50069 | −0.176667 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 30.5179 | 1.19609 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.2969 | −0.872544 | −0.436272 | − | 0.899815i | \(-0.643702\pi\) | ||||
−0.436272 | + | 0.899815i | \(0.643702\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.4896 | −0.800594 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.81145 | −0.109685 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.38133 | −0.209627 | −0.104814 | − | 0.994492i | \(-0.533425\pi\) | ||||
−0.104814 | + | 0.994492i | \(0.533425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.1394 | −0.627751 | −0.313875 | − | 0.949464i | \(-0.601627\pi\) | ||||
−0.313875 | + | 0.949464i | \(0.601627\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.71755 | −0.105541 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.8165 | 0.962341 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.91186 | 0.190188 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 35.2585 | 1.36317 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.17394 | 0.315551 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.52981 | −0.367347 | −0.183674 | − | 0.982987i | \(-0.558799\pi\) | ||||
−0.183674 | + | 0.982987i | \(0.558799\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.1247 | −0.620639 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.6949 | −1.02597 | −0.512984 | − | 0.858398i | \(-0.671460\pi\) | ||||
−0.512984 | + | 0.858398i | \(0.671460\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −41.0734 | −1.57625 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.4201 | 0.552580 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.2958 | −0.508749 | −0.254374 | − | 0.967106i | \(-0.581870\pi\) | ||||
−0.254374 | + | 0.967106i | \(0.581870\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.977497 | 0.0373482 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −32.5686 | −1.24257 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 54.9039 | 2.09167 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.0819 | −0.649825 | −0.324913 | − | 0.945744i | \(-0.605335\pi\) | ||||
−0.324913 | + | 0.945744i | \(0.605335\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.05981 | −0.116233 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.3679 | −0.696733 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.11203 | 0.155754 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.3046 | 0.503227 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.13965 | 0.156353 | 0.0781763 | − | 0.996940i | \(-0.475090\pi\) | ||||
0.0781763 | + | 0.996940i | \(0.475090\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.4073 | 1.22226 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.3829 | −0.428705 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.9822 | 0.638683 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.99415 | 0.300226 | 0.150113 | − | 0.988669i | \(-0.452036\pi\) | ||||
0.150113 | + | 0.988669i | \(0.452036\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.44094 | −0.166548 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.3247 | 0.536465 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.03379 | −0.150855 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −45.4780 | −1.69841 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.7584 | −0.886040 | −0.443020 | − | 0.896512i | \(-0.646093\pi\) | ||||
−0.443020 | + | 0.896512i | \(0.646093\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −55.4927 | −2.06665 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −37.6949 | −1.40189 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.96906 | −0.258825 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.3570 | −1.23714 | −0.618572 | − | 0.785728i | \(-0.712289\pi\) | ||||
−0.618572 | + | 0.785728i | \(0.712289\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.8418 | 0.475622 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.45636 | 0.127838 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.2988 | 0.491203 | 0.245601 | − | 0.969371i | \(-0.421015\pi\) | ||||
0.245601 | + | 0.969371i | \(0.421015\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.30616 | −0.158835 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.37395 | 0.234787 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.2207 | 1.44276 | 0.721379 | − | 0.692541i | \(-0.243509\pi\) | ||||
0.721379 | + | 0.692541i | \(0.243509\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −69.1558 | −2.54050 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.2666 | 1.47724 | 0.738619 | − | 0.674123i | \(-0.235478\pi\) | ||||
0.738619 | + | 0.674123i | \(0.235478\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.52840 | −0.349094 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.51346 | 0.274903 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.7796 | 0.393878 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.8856 | −1.09054 | −0.545271 | − | 0.838260i | \(-0.683573\pi\) | ||||
−0.545271 | + | 0.838260i | \(0.683573\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.79204 | −0.247516 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.2637 | −0.409927 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.3272 | −1.42937 | −0.714686 | − | 0.699445i | \(-0.753431\pi\) | ||||
−0.714686 | + | 0.699445i | \(0.753431\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.70746 | −0.207168 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.2195 | 0.551706 | 0.275853 | − | 0.961200i | \(-0.411040\pi\) | ||||
0.275853 | + | 0.961200i | \(0.411040\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38.9692 | −1.41078 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.324328 | −0.0117261 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.5728 | 0.670624 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.2618 | 1.27157 | 0.635787 | − | 0.771865i | \(-0.280676\pi\) | ||||
0.635787 | + | 0.771865i | \(0.280676\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −49.4814 | −1.78203 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −48.1191 | −1.73072 | −0.865361 | − | 0.501149i | \(-0.832911\pi\) | ||||
−0.865361 | + | 0.501149i | \(0.832911\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.3242 | −0.730068 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −23.5138 | −0.843554 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 104.642 | 3.74920 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.0597 | 0.503094 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.86966 | 0.245502 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.8130 | 0.600081 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.6998 | 0.488347 | 0.244173 | − | 0.969732i | \(-0.421483\pi\) | ||||
0.244173 | + | 0.969732i | \(0.421483\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −31.9464 | −1.13732 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 58.9812 | 2.09713 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.7310 | −1.19782 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 26.0391 | 0.923513 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.92621 | −0.209917 | −0.104959 | − | 0.994477i | \(-0.533471\pi\) | ||||
−0.104959 | + | 0.994477i | \(0.533471\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.91296 | −0.0676757 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.3638 | −0.542851 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.78699 | −0.0983507 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.45184 | −0.297888 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.5818 | 0.407700 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.0552 | −0.599629 | −0.299814 | − | 0.953998i | \(-0.596925\pi\) | ||||
−0.299814 | + | 0.953998i | \(0.596925\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.9900 | 0.807289 | 0.403644 | − | 0.914916i | \(-0.367743\pi\) | ||||
0.403644 | + | 0.914916i | \(0.367743\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.7788 | 0.483244 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.33338 | 0.326934 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 87.9568 | 3.07722 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.6268 | 0.441215 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.539841 | −0.0188406 | −0.00942029 | − | 0.999956i | \(-0.502999\pi\) | ||||
−0.00942029 | + | 0.999956i | \(0.502999\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.0813 | 0.595418 | 0.297709 | − | 0.954657i | \(-0.403777\pi\) | ||||
0.297709 | + | 0.954657i | \(0.403777\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.09787 | 0.281932 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.2959 | −0.566666 | −0.283333 | − | 0.959022i | \(-0.591440\pi\) | ||||
−0.283333 | + | 0.959022i | \(0.591440\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.4427 | 1.47410 | 0.737048 | − | 0.675840i | \(-0.236219\pi\) | ||||
0.737048 | + | 0.675840i | \(0.236219\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.0295 | 0.902955 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.723674 | −0.0250738 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.8156 | 0.374291 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.0343 | 0.692488 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.8648 | −0.892950 | −0.446475 | − | 0.894796i | \(-0.647321\pi\) | ||||
−0.446475 | + | 0.894796i | \(0.647321\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0309 | −0.897619 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32.6526 | −1.12461 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.93858 | 0.135491 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.03319 | −0.104222 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −30.2414 | −1.03788 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.0371 | −0.378347 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.1039 | 1.40737 | 0.703685 | − | 0.710512i | \(-0.251537\pi\) | ||||
0.703685 | + | 0.710512i | \(0.251537\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.25345 | −0.282262 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40.5227 | 1.38423 | 0.692115 | − | 0.721787i | \(-0.256679\pi\) | ||||
0.692115 | + | 0.721787i | \(0.256679\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.0346 | −0.854168 | −0.427084 | − | 0.904212i | \(-0.640459\pi\) | ||||
−0.427084 | + | 0.904212i | \(0.640459\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −75.9255 | −2.58753 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.7230 | 0.909662 | 0.454831 | − | 0.890578i | \(-0.349700\pi\) | ||||
0.454831 | + | 0.890578i | \(0.349700\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.68888 | 0.261430 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 33.8207 | 1.14861 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.40230 | −0.149338 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.3031 | −0.891245 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.6602 | 0.462326 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 26.8163 | 0.906558 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.5316 | 1.13228 | 0.566140 | − | 0.824309i | \(-0.308436\pi\) | ||||
0.566140 | + | 0.824309i | \(0.308436\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31.2756 | −1.05490 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.2863 | 1.35728 | 0.678641 | − | 0.734470i | \(-0.262569\pi\) | ||||
0.678641 | + | 0.734470i | \(0.262569\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.202900 | 0.00682812 | 0.00341406 | − | 0.999994i | \(-0.498913\pi\) | ||||
0.00341406 | + | 0.999994i | \(0.498913\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.80847 | 0.296093 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.5107 | −0.554376 | −0.277188 | − | 0.960816i | \(-0.589402\pi\) | ||||
−0.277188 | + | 0.960816i | \(0.589402\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −49.1560 | −1.64864 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.0087 | −0.368805 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −48.6807 | −1.62904 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.8249 | 0.428689 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.5527 | 0.786401 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.65883 | 0.288788 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.37602 | 0.145786 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −63.8190 | −2.12376 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.12701 | −0.103945 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46.2763 | −1.53658 | −0.768290 | − | 0.640102i | \(-0.778892\pi\) | ||||
−0.768290 | + | 0.640102i | \(0.778892\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.64794 | −0.187331 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.1774 | −0.734770 | −0.367385 | − | 0.930069i | \(-0.619747\pi\) | ||||
−0.367385 | + | 0.930069i | \(0.619747\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.44808 | 0.246496 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.9975 | −0.528862 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 63.5795 | 2.09958 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.2421 | 0.865646 | 0.432823 | − | 0.901479i | \(-0.357518\pi\) | ||||
0.432823 | + | 0.901479i | \(0.357518\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.7293 | −0.584201 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −58.0193 | −1.90973 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.6597 | 0.514887 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.4557 | 0.606166 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46.7248 | 1.53299 | 0.766495 | − | 0.642250i | \(-0.221999\pi\) | ||||
0.766495 | + | 0.642250i | \(0.221999\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.4159 | −0.603558 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 30.5611 | 1.00053 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.321506 | −0.0105144 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.4290 | −0.471373 | −0.235687 | − | 0.971829i | \(-0.575734\pi\) | ||||
−0.235687 | + | 0.971829i | \(0.575734\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −47.1514 | −1.53873 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.4566 | −1.38404 | −0.692022 | − | 0.721876i | \(-0.743280\pi\) | ||||
−0.692022 | + | 0.721876i | \(0.743280\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.6384 | −1.16055 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.8206 | −0.384525 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −59.4759 | −1.93271 | −0.966354 | − | 0.257215i | \(-0.917195\pi\) | ||||
−0.966354 | + | 0.257215i | \(0.917195\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.5009 | 0.373336 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −36.9566 | −1.19840 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.7903 | −0.738250 | −0.369125 | − | 0.929380i | \(-0.620343\pi\) | ||||
−0.369125 | + | 0.929380i | \(0.620343\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.26606 | 0.0733281 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.44997 | −0.111522 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.03319 | −0.0979468 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.74784 | −0.185414 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.58507 | −0.115527 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.5222 | −0.628441 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.35057 | 0.268536 | 0.134268 | − | 0.990945i | \(-0.457132\pi\) | ||||
0.134268 | + | 0.990945i | \(0.457132\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.51195 | −0.177069 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.0833 | −0.997512 | −0.498756 | − | 0.866742i | \(-0.666210\pi\) | ||||
−0.498756 | + | 0.866742i | \(0.666210\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 56.9958 | 1.82720 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −33.4171 | −1.07020 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.6117 | −0.531455 | −0.265727 | − | 0.964048i | \(-0.585612\pi\) | ||||
−0.265727 | + | 0.964048i | \(0.585612\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.2301 | −0.486755 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.9604 | 0.413792 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.2096 | 0.899748 | 0.449874 | − | 0.893092i | \(-0.351469\pi\) | ||||
0.449874 | + | 0.893092i | \(0.351469\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.86026 | 0.186724 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 35.3213 | 1.12429 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −29.9558 | −0.952539 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 58.7449 | 1.86609 | 0.933047 | − | 0.359755i | \(-0.117140\pi\) | ||||
0.933047 | + | 0.359755i | \(0.117140\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 40.5441 | 1.28663 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.45364 | 0.0460835 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.42598 | 0.0768317 | 0.0384158 | − | 0.999262i | \(-0.487769\pi\) | ||||
0.0384158 | + | 0.999262i | \(0.487769\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −15.4363 | −0.488384 |
(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 | 6028.2.a.f.1.5 | ✓ | 29 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6028.2.a.f.1.5 | ✓ | 29 | 1.1 | even | 1 | trivial |