Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4003,2,Mod(1,4003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4003.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: | \(31.9641159291\) |
Analytic rank: | \(0\) |
Dimension: | \(179\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 4003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.33012 | −1.64764 | −0.823822 | − | 0.566849i | \(-0.808162\pi\) | ||||
−0.823822 | + | 0.566849i | \(0.808162\pi\) | |||||||
\(3\) | −0.602166 | −0.347661 | −0.173830 | − | 0.984776i | \(-0.555614\pi\) | ||||
−0.173830 | + | 0.984776i | \(0.555614\pi\) | |||||||
\(4\) | 3.42946 | 1.71473 | ||||||||
\(5\) | 1.32408 | 0.592146 | 0.296073 | − | 0.955165i | \(-0.404323\pi\) | ||||
0.296073 | + | 0.955165i | \(0.404323\pi\) | |||||||
\(6\) | 1.40312 | 0.572821 | ||||||||
\(7\) | −1.36511 | −0.515962 | −0.257981 | − | 0.966150i | \(-0.583057\pi\) | ||||
−0.257981 | + | 0.966150i | \(0.583057\pi\) | |||||||
\(8\) | −3.33081 | −1.17762 | ||||||||
\(9\) | −2.63740 | −0.879132 | ||||||||
\(10\) | −3.08526 | −0.975646 | ||||||||
\(11\) | −0.0777918 | −0.0234551 | −0.0117276 | − | 0.999931i | \(-0.503733\pi\) | ||||
−0.0117276 | + | 0.999931i | \(0.503733\pi\) | |||||||
\(12\) | −2.06510 | −0.596144 | ||||||||
\(13\) | −4.41950 | −1.22575 | −0.612875 | − | 0.790180i | \(-0.709987\pi\) | ||||
−0.612875 | + | 0.790180i | \(0.709987\pi\) | |||||||
\(14\) | 3.18086 | 0.850121 | ||||||||
\(15\) | −0.797315 | −0.205866 | ||||||||
\(16\) | 0.902278 | 0.225569 | ||||||||
\(17\) | 1.21540 | 0.294779 | 0.147389 | − | 0.989079i | \(-0.452913\pi\) | ||||
0.147389 | + | 0.989079i | \(0.452913\pi\) | |||||||
\(18\) | 6.14545 | 1.44850 | ||||||||
\(19\) | 0.960375 | 0.220325 | 0.110163 | − | 0.993914i | \(-0.464863\pi\) | ||||
0.110163 | + | 0.993914i | \(0.464863\pi\) | |||||||
\(20\) | 4.54088 | 1.01537 | ||||||||
\(21\) | 0.822021 | 0.179380 | ||||||||
\(22\) | 0.181264 | 0.0386457 | ||||||||
\(23\) | −8.67641 | −1.80916 | −0.904578 | − | 0.426308i | \(-0.859814\pi\) | ||||
−0.904578 | + | 0.426308i | \(0.859814\pi\) | |||||||
\(24\) | 2.00570 | 0.409412 | ||||||||
\(25\) | −3.24682 | −0.649363 | ||||||||
\(26\) | 10.2980 | 2.01960 | ||||||||
\(27\) | 3.39465 | 0.653300 | ||||||||
\(28\) | −4.68158 | −0.884735 | ||||||||
\(29\) | −7.04953 | −1.30906 | −0.654532 | − | 0.756034i | \(-0.727134\pi\) | ||||
−0.654532 | + | 0.756034i | \(0.727134\pi\) | |||||||
\(30\) | 1.85784 | 0.339194 | ||||||||
\(31\) | −1.89745 | −0.340792 | −0.170396 | − | 0.985376i | \(-0.554505\pi\) | ||||
−0.170396 | + | 0.985376i | \(0.554505\pi\) | |||||||
\(32\) | 4.55921 | 0.805963 | ||||||||
\(33\) | 0.0468436 | 0.00815442 | ||||||||
\(34\) | −2.83204 | −0.485690 | ||||||||
\(35\) | −1.80751 | −0.305525 | ||||||||
\(36\) | −9.04485 | −1.50747 | ||||||||
\(37\) | 7.32980 | 1.20501 | 0.602506 | − | 0.798114i | \(-0.294169\pi\) | ||||
0.602506 | + | 0.798114i | \(0.294169\pi\) | |||||||
\(38\) | −2.23779 | −0.363017 | ||||||||
\(39\) | 2.66127 | 0.426145 | ||||||||
\(40\) | −4.41026 | −0.697323 | ||||||||
\(41\) | −7.66124 | −1.19649 | −0.598243 | − | 0.801315i | \(-0.704134\pi\) | ||||
−0.598243 | + | 0.801315i | \(0.704134\pi\) | |||||||
\(42\) | −1.91541 | −0.295554 | ||||||||
\(43\) | 5.26894 | 0.803505 | 0.401753 | − | 0.915748i | \(-0.368401\pi\) | ||||
0.401753 | + | 0.915748i | \(0.368401\pi\) | |||||||
\(44\) | −0.266784 | −0.0402192 | ||||||||
\(45\) | −3.49212 | −0.520575 | ||||||||
\(46\) | 20.2171 | 2.98085 | ||||||||
\(47\) | −12.8976 | −1.88131 | −0.940654 | − | 0.339367i | \(-0.889787\pi\) | ||||
−0.940654 | + | 0.339367i | \(0.889787\pi\) | |||||||
\(48\) | −0.543321 | −0.0784216 | ||||||||
\(49\) | −5.13648 | −0.733783 | ||||||||
\(50\) | 7.56547 | 1.06992 | ||||||||
\(51\) | −0.731874 | −0.102483 | ||||||||
\(52\) | −15.1565 | −2.10183 | ||||||||
\(53\) | 7.76041 | 1.06597 | 0.532987 | − | 0.846123i | \(-0.321069\pi\) | ||||
0.532987 | + | 0.846123i | \(0.321069\pi\) | |||||||
\(54\) | −7.90994 | −1.07641 | ||||||||
\(55\) | −0.103002 | −0.0138889 | ||||||||
\(56\) | 4.54692 | 0.607607 | ||||||||
\(57\) | −0.578305 | −0.0765983 | ||||||||
\(58\) | 16.4263 | 2.15687 | ||||||||
\(59\) | 10.6714 | 1.38930 | 0.694650 | − | 0.719348i | \(-0.255559\pi\) | ||||
0.694650 | + | 0.719348i | \(0.255559\pi\) | |||||||
\(60\) | −2.73436 | −0.353004 | ||||||||
\(61\) | −7.38442 | −0.945478 | −0.472739 | − | 0.881203i | \(-0.656735\pi\) | ||||
−0.472739 | + | 0.881203i | \(0.656735\pi\) | |||||||
\(62\) | 4.42129 | 0.561504 | ||||||||
\(63\) | 3.60033 | 0.453599 | ||||||||
\(64\) | −12.4281 | −1.55351 | ||||||||
\(65\) | −5.85177 | −0.725823 | ||||||||
\(66\) | −0.109151 | −0.0134356 | ||||||||
\(67\) | −6.57719 | −0.803531 | −0.401766 | − | 0.915743i | \(-0.631603\pi\) | ||||
−0.401766 | + | 0.915743i | \(0.631603\pi\) | |||||||
\(68\) | 4.16818 | 0.505466 | ||||||||
\(69\) | 5.22464 | 0.628972 | ||||||||
\(70\) | 4.21171 | 0.503396 | ||||||||
\(71\) | 6.73510 | 0.799309 | 0.399655 | − | 0.916666i | \(-0.369130\pi\) | ||||
0.399655 | + | 0.916666i | \(0.369130\pi\) | |||||||
\(72\) | 8.78468 | 1.03528 | ||||||||
\(73\) | 6.88195 | 0.805471 | 0.402736 | − | 0.915316i | \(-0.368059\pi\) | ||||
0.402736 | + | 0.915316i | \(0.368059\pi\) | |||||||
\(74\) | −17.0793 | −1.98543 | ||||||||
\(75\) | 1.95512 | 0.225758 | ||||||||
\(76\) | 3.29357 | 0.377798 | ||||||||
\(77\) | 0.106194 | 0.0121019 | ||||||||
\(78\) | −6.20109 | −0.702135 | ||||||||
\(79\) | 3.73122 | 0.419795 | 0.209897 | − | 0.977723i | \(-0.432687\pi\) | ||||
0.209897 | + | 0.977723i | \(0.432687\pi\) | |||||||
\(80\) | 1.19469 | 0.133570 | ||||||||
\(81\) | 5.86805 | 0.652005 | ||||||||
\(82\) | 17.8516 | 1.97138 | ||||||||
\(83\) | 4.04725 | 0.444243 | 0.222122 | − | 0.975019i | \(-0.428702\pi\) | ||||
0.222122 | + | 0.975019i | \(0.428702\pi\) | |||||||
\(84\) | 2.81909 | 0.307588 | ||||||||
\(85\) | 1.60929 | 0.174552 | ||||||||
\(86\) | −12.2773 | −1.32389 | ||||||||
\(87\) | 4.24499 | 0.455110 | ||||||||
\(88\) | 0.259110 | 0.0276212 | ||||||||
\(89\) | 11.3044 | 1.19826 | 0.599132 | − | 0.800650i | \(-0.295512\pi\) | ||||
0.599132 | + | 0.800650i | \(0.295512\pi\) | |||||||
\(90\) | 8.13706 | 0.857721 | ||||||||
\(91\) | 6.03309 | 0.632440 | ||||||||
\(92\) | −29.7554 | −3.10222 | ||||||||
\(93\) | 1.14258 | 0.118480 | ||||||||
\(94\) | 30.0530 | 3.09973 | ||||||||
\(95\) | 1.27161 | 0.130465 | ||||||||
\(96\) | −2.74540 | −0.280201 | ||||||||
\(97\) | −13.5334 | −1.37411 | −0.687054 | − | 0.726607i | \(-0.741096\pi\) | ||||
−0.687054 | + | 0.726607i | \(0.741096\pi\) | |||||||
\(98\) | 11.9686 | 1.20901 | ||||||||
\(99\) | 0.205168 | 0.0206201 | ||||||||
\(100\) | −11.1348 | −1.11348 | ||||||||
\(101\) | −6.21352 | −0.618268 | −0.309134 | − | 0.951018i | \(-0.600039\pi\) | ||||
−0.309134 | + | 0.951018i | \(0.600039\pi\) | |||||||
\(102\) | 1.70536 | 0.168855 | ||||||||
\(103\) | 13.9862 | 1.37810 | 0.689050 | − | 0.724714i | \(-0.258028\pi\) | ||||
0.689050 | + | 0.724714i | \(0.258028\pi\) | |||||||
\(104\) | 14.7205 | 1.44347 | ||||||||
\(105\) | 1.08842 | 0.106219 | ||||||||
\(106\) | −18.0827 | −1.75635 | ||||||||
\(107\) | 3.52256 | 0.340539 | 0.170269 | − | 0.985398i | \(-0.445536\pi\) | ||||
0.170269 | + | 0.985398i | \(0.445536\pi\) | |||||||
\(108\) | 11.6418 | 1.12023 | ||||||||
\(109\) | 12.7414 | 1.22041 | 0.610204 | − | 0.792244i | \(-0.291087\pi\) | ||||
0.610204 | + | 0.792244i | \(0.291087\pi\) | |||||||
\(110\) | 0.240008 | 0.0228839 | ||||||||
\(111\) | −4.41376 | −0.418935 | ||||||||
\(112\) | −1.23171 | −0.116385 | ||||||||
\(113\) | 15.9631 | 1.50168 | 0.750840 | − | 0.660484i | \(-0.229649\pi\) | ||||
0.750840 | + | 0.660484i | \(0.229649\pi\) | |||||||
\(114\) | 1.34752 | 0.126207 | ||||||||
\(115\) | −11.4882 | −1.07128 | ||||||||
\(116\) | −24.1761 | −2.24469 | ||||||||
\(117\) | 11.6560 | 1.07760 | ||||||||
\(118\) | −24.8657 | −2.28907 | ||||||||
\(119\) | −1.65915 | −0.152094 | ||||||||
\(120\) | 2.65571 | 0.242432 | ||||||||
\(121\) | −10.9939 | −0.999450 | ||||||||
\(122\) | 17.2066 | 1.55781 | ||||||||
\(123\) | 4.61334 | 0.415971 | ||||||||
\(124\) | −6.50723 | −0.584366 | ||||||||
\(125\) | −10.9194 | −0.976664 | ||||||||
\(126\) | −8.38920 | −0.747369 | ||||||||
\(127\) | 9.26656 | 0.822275 | 0.411137 | − | 0.911573i | \(-0.365132\pi\) | ||||
0.411137 | + | 0.911573i | \(0.365132\pi\) | |||||||
\(128\) | 19.8405 | 1.75367 | ||||||||
\(129\) | −3.17277 | −0.279347 | ||||||||
\(130\) | 13.6353 | 1.19590 | ||||||||
\(131\) | 3.55953 | 0.310997 | 0.155499 | − | 0.987836i | \(-0.450302\pi\) | ||||
0.155499 | + | 0.987836i | \(0.450302\pi\) | |||||||
\(132\) | 0.160648 | 0.0139826 | ||||||||
\(133\) | −1.31101 | −0.113679 | ||||||||
\(134\) | 15.3256 | 1.32393 | ||||||||
\(135\) | 4.49478 | 0.386849 | ||||||||
\(136\) | −4.04828 | −0.347137 | ||||||||
\(137\) | 21.2859 | 1.81858 | 0.909288 | − | 0.416167i | \(-0.136627\pi\) | ||||
0.909288 | + | 0.416167i | \(0.136627\pi\) | |||||||
\(138\) | −12.1740 | −1.03632 | ||||||||
\(139\) | −13.2048 | −1.12001 | −0.560006 | − | 0.828488i | \(-0.689201\pi\) | ||||
−0.560006 | + | 0.828488i | \(0.689201\pi\) | |||||||
\(140\) | −6.19878 | −0.523892 | ||||||||
\(141\) | 7.76649 | 0.654057 | ||||||||
\(142\) | −15.6936 | −1.31698 | ||||||||
\(143\) | 0.343801 | 0.0287501 | ||||||||
\(144\) | −2.37966 | −0.198305 | ||||||||
\(145\) | −9.33413 | −0.775157 | ||||||||
\(146\) | −16.0358 | −1.32713 | ||||||||
\(147\) | 3.09302 | 0.255108 | ||||||||
\(148\) | 25.1373 | 2.06627 | ||||||||
\(149\) | −9.52196 | −0.780069 | −0.390035 | − | 0.920800i | \(-0.627537\pi\) | ||||
−0.390035 | + | 0.920800i | \(0.627537\pi\) | |||||||
\(150\) | −4.55567 | −0.371969 | ||||||||
\(151\) | −5.51607 | −0.448892 | −0.224446 | − | 0.974487i | \(-0.572057\pi\) | ||||
−0.224446 | + | 0.974487i | \(0.572057\pi\) | |||||||
\(152\) | −3.19883 | −0.259459 | ||||||||
\(153\) | −3.20550 | −0.259149 | ||||||||
\(154\) | −0.247445 | −0.0199397 | ||||||||
\(155\) | −2.51237 | −0.201799 | ||||||||
\(156\) | 9.12673 | 0.730723 | ||||||||
\(157\) | 18.4394 | 1.47162 | 0.735812 | − | 0.677186i | \(-0.236801\pi\) | ||||
0.735812 | + | 0.677186i | \(0.236801\pi\) | |||||||
\(158\) | −8.69418 | −0.691672 | ||||||||
\(159\) | −4.67305 | −0.370597 | ||||||||
\(160\) | 6.03676 | 0.477248 | ||||||||
\(161\) | 11.8442 | 0.933456 | ||||||||
\(162\) | −13.6733 | −1.07427 | ||||||||
\(163\) | −15.0090 | −1.17560 | −0.587799 | − | 0.809007i | \(-0.700005\pi\) | ||||
−0.587799 | + | 0.809007i | \(0.700005\pi\) | |||||||
\(164\) | −26.2739 | −2.05165 | ||||||||
\(165\) | 0.0620246 | 0.00482861 | ||||||||
\(166\) | −9.43057 | −0.731954 | ||||||||
\(167\) | 1.40736 | 0.108905 | 0.0544524 | − | 0.998516i | \(-0.482659\pi\) | ||||
0.0544524 | + | 0.998516i | \(0.482659\pi\) | |||||||
\(168\) | −2.73800 | −0.211241 | ||||||||
\(169\) | 6.53201 | 0.502462 | ||||||||
\(170\) | −3.74984 | −0.287599 | ||||||||
\(171\) | −2.53289 | −0.193695 | ||||||||
\(172\) | 18.0696 | 1.37779 | ||||||||
\(173\) | −18.1572 | −1.38047 | −0.690234 | − | 0.723586i | \(-0.742492\pi\) | ||||
−0.690234 | + | 0.723586i | \(0.742492\pi\) | |||||||
\(174\) | −9.89133 | −0.749860 | ||||||||
\(175\) | 4.43225 | 0.335047 | ||||||||
\(176\) | −0.0701898 | −0.00529076 | ||||||||
\(177\) | −6.42596 | −0.483005 | ||||||||
\(178\) | −26.3406 | −1.97431 | ||||||||
\(179\) | −12.0069 | −0.897435 | −0.448717 | − | 0.893674i | \(-0.648119\pi\) | ||||
−0.448717 | + | 0.893674i | \(0.648119\pi\) | |||||||
\(180\) | −11.9761 | −0.892645 | ||||||||
\(181\) | −6.56194 | −0.487745 | −0.243873 | − | 0.969807i | \(-0.578418\pi\) | ||||
−0.243873 | + | 0.969807i | \(0.578418\pi\) | |||||||
\(182\) | −14.0578 | −1.04204 | ||||||||
\(183\) | 4.44664 | 0.328705 | ||||||||
\(184\) | 28.8995 | 2.13050 | ||||||||
\(185\) | 9.70524 | 0.713543 | ||||||||
\(186\) | −2.66235 | −0.195213 | ||||||||
\(187\) | −0.0945484 | −0.00691407 | ||||||||
\(188\) | −44.2318 | −3.22594 | ||||||||
\(189\) | −4.63406 | −0.337078 | ||||||||
\(190\) | −2.96301 | −0.214959 | ||||||||
\(191\) | −2.35110 | −0.170119 | −0.0850597 | − | 0.996376i | \(-0.527108\pi\) | ||||
−0.0850597 | + | 0.996376i | \(0.527108\pi\) | |||||||
\(192\) | 7.48376 | 0.540094 | ||||||||
\(193\) | −5.42724 | −0.390662 | −0.195331 | − | 0.980737i | \(-0.562578\pi\) | ||||
−0.195331 | + | 0.980737i | \(0.562578\pi\) | |||||||
\(194\) | 31.5344 | 2.26404 | ||||||||
\(195\) | 3.52374 | 0.252340 | ||||||||
\(196\) | −17.6154 | −1.25824 | ||||||||
\(197\) | −0.545520 | −0.0388667 | −0.0194334 | − | 0.999811i | \(-0.506186\pi\) | ||||
−0.0194334 | + | 0.999811i | \(0.506186\pi\) | |||||||
\(198\) | −0.478066 | −0.0339747 | ||||||||
\(199\) | −12.7766 | −0.905709 | −0.452855 | − | 0.891584i | \(-0.649594\pi\) | ||||
−0.452855 | + | 0.891584i | \(0.649594\pi\) | |||||||
\(200\) | 10.8145 | 0.764704 | ||||||||
\(201\) | 3.96056 | 0.279356 | ||||||||
\(202\) | 14.4782 | 1.01869 | ||||||||
\(203\) | 9.62336 | 0.675427 | ||||||||
\(204\) | −2.50993 | −0.175731 | ||||||||
\(205\) | −10.1441 | −0.708494 | ||||||||
\(206\) | −32.5895 | −2.27062 | ||||||||
\(207\) | 22.8831 | 1.59049 | ||||||||
\(208\) | −3.98762 | −0.276492 | ||||||||
\(209\) | −0.0747093 | −0.00516775 | ||||||||
\(210\) | −2.53615 | −0.175011 | ||||||||
\(211\) | −12.0368 | −0.828645 | −0.414322 | − | 0.910130i | \(-0.635981\pi\) | ||||
−0.414322 | + | 0.910130i | \(0.635981\pi\) | |||||||
\(212\) | 26.6140 | 1.82786 | ||||||||
\(213\) | −4.05565 | −0.277888 | ||||||||
\(214\) | −8.20799 | −0.561087 | ||||||||
\(215\) | 6.97649 | 0.475792 | ||||||||
\(216\) | −11.3069 | −0.769340 | ||||||||
\(217\) | 2.59022 | 0.175836 | ||||||||
\(218\) | −29.6891 | −2.01080 | ||||||||
\(219\) | −4.14407 | −0.280031 | ||||||||
\(220\) | −0.353243 | −0.0238156 | ||||||||
\(221\) | −5.37148 | −0.361325 | ||||||||
\(222\) | 10.2846 | 0.690256 | ||||||||
\(223\) | 8.10464 | 0.542727 | 0.271363 | − | 0.962477i | \(-0.412525\pi\) | ||||
0.271363 | + | 0.962477i | \(0.412525\pi\) | |||||||
\(224\) | −6.22381 | −0.415846 | ||||||||
\(225\) | 8.56314 | 0.570876 | ||||||||
\(226\) | −37.1959 | −2.47423 | ||||||||
\(227\) | −17.0681 | −1.13285 | −0.566423 | − | 0.824115i | \(-0.691673\pi\) | ||||
−0.566423 | + | 0.824115i | \(0.691673\pi\) | |||||||
\(228\) | −1.98327 | −0.131345 | ||||||||
\(229\) | 1.22546 | 0.0809808 | 0.0404904 | − | 0.999180i | \(-0.487108\pi\) | ||||
0.0404904 | + | 0.999180i | \(0.487108\pi\) | |||||||
\(230\) | 26.7690 | 1.76510 | ||||||||
\(231\) | −0.0639465 | −0.00420737 | ||||||||
\(232\) | 23.4807 | 1.54158 | ||||||||
\(233\) | −4.88188 | −0.319822 | −0.159911 | − | 0.987131i | \(-0.551121\pi\) | ||||
−0.159911 | + | 0.987131i | \(0.551121\pi\) | |||||||
\(234\) | −27.1598 | −1.77549 | ||||||||
\(235\) | −17.0774 | −1.11401 | ||||||||
\(236\) | 36.5972 | 2.38227 | ||||||||
\(237\) | −2.24681 | −0.145946 | ||||||||
\(238\) | 3.86603 | 0.250598 | ||||||||
\(239\) | 11.8024 | 0.763436 | 0.381718 | − | 0.924279i | \(-0.375332\pi\) | ||||
0.381718 | + | 0.924279i | \(0.375332\pi\) | |||||||
\(240\) | −0.719400 | −0.0464370 | ||||||||
\(241\) | 23.0757 | 1.48644 | 0.743219 | − | 0.669048i | \(-0.233298\pi\) | ||||
0.743219 | + | 0.669048i | \(0.233298\pi\) | |||||||
\(242\) | 25.6172 | 1.64674 | ||||||||
\(243\) | −13.7175 | −0.879977 | ||||||||
\(244\) | −25.3246 | −1.62124 | ||||||||
\(245\) | −6.80111 | −0.434507 | ||||||||
\(246\) | −10.7496 | −0.685372 | ||||||||
\(247\) | −4.24438 | −0.270063 | ||||||||
\(248\) | 6.32005 | 0.401324 | ||||||||
\(249\) | −2.43711 | −0.154446 | ||||||||
\(250\) | 25.4436 | 1.60919 | ||||||||
\(251\) | −11.6615 | −0.736065 | −0.368033 | − | 0.929813i | \(-0.619969\pi\) | ||||
−0.368033 | + | 0.929813i | \(0.619969\pi\) | |||||||
\(252\) | 12.3472 | 0.777799 | ||||||||
\(253\) | 0.674954 | 0.0424340 | ||||||||
\(254\) | −21.5922 | −1.35482 | ||||||||
\(255\) | −0.969059 | −0.0606848 | ||||||||
\(256\) | −21.3745 | −1.33591 | ||||||||
\(257\) | 16.3711 | 1.02120 | 0.510600 | − | 0.859818i | \(-0.329423\pi\) | ||||
0.510600 | + | 0.859818i | \(0.329423\pi\) | |||||||
\(258\) | 7.39294 | 0.460265 | ||||||||
\(259\) | −10.0060 | −0.621740 | ||||||||
\(260\) | −20.0684 | −1.24459 | ||||||||
\(261\) | 18.5924 | 1.15084 | ||||||||
\(262\) | −8.29412 | −0.512413 | ||||||||
\(263\) | 22.4755 | 1.38590 | 0.692950 | − | 0.720986i | \(-0.256311\pi\) | ||||
0.692950 | + | 0.720986i | \(0.256311\pi\) | |||||||
\(264\) | −0.156027 | −0.00960281 | ||||||||
\(265\) | 10.2754 | 0.631212 | ||||||||
\(266\) | 3.05482 | 0.187303 | ||||||||
\(267\) | −6.80712 | −0.416589 | ||||||||
\(268\) | −22.5562 | −1.37784 | ||||||||
\(269\) | 2.19773 | 0.133998 | 0.0669989 | − | 0.997753i | \(-0.478658\pi\) | ||||
0.0669989 | + | 0.997753i | \(0.478658\pi\) | |||||||
\(270\) | −10.4734 | −0.637390 | ||||||||
\(271\) | 1.07274 | 0.0651642 | 0.0325821 | − | 0.999469i | \(-0.489627\pi\) | ||||
0.0325821 | + | 0.999469i | \(0.489627\pi\) | |||||||
\(272\) | 1.09663 | 0.0664930 | ||||||||
\(273\) | −3.63292 | −0.219874 | ||||||||
\(274\) | −49.5987 | −2.99637 | ||||||||
\(275\) | 0.252576 | 0.0152309 | ||||||||
\(276\) | 17.9177 | 1.07852 | ||||||||
\(277\) | 4.69125 | 0.281870 | 0.140935 | − | 0.990019i | \(-0.454989\pi\) | ||||
0.140935 | + | 0.990019i | \(0.454989\pi\) | |||||||
\(278\) | 30.7687 | 1.84538 | ||||||||
\(279\) | 5.00433 | 0.299601 | ||||||||
\(280\) | 6.02048 | 0.359792 | ||||||||
\(281\) | 33.3377 | 1.98876 | 0.994379 | − | 0.105875i | \(-0.0337643\pi\) | ||||
0.994379 | + | 0.105875i | \(0.0337643\pi\) | |||||||
\(282\) | −18.0969 | −1.07765 | ||||||||
\(283\) | −26.4146 | −1.57019 | −0.785093 | − | 0.619377i | \(-0.787385\pi\) | ||||
−0.785093 | + | 0.619377i | \(0.787385\pi\) | |||||||
\(284\) | 23.0978 | 1.37060 | ||||||||
\(285\) | −0.765721 | −0.0453574 | ||||||||
\(286\) | −0.801098 | −0.0473699 | ||||||||
\(287\) | 10.4584 | 0.617341 | ||||||||
\(288\) | −12.0245 | −0.708548 | ||||||||
\(289\) | −15.5228 | −0.913106 | ||||||||
\(290\) | 21.7496 | 1.27718 | ||||||||
\(291\) | 8.14934 | 0.477723 | ||||||||
\(292\) | 23.6014 | 1.38117 | ||||||||
\(293\) | 9.68309 | 0.565692 | 0.282846 | − | 0.959165i | \(-0.408721\pi\) | ||||
0.282846 | + | 0.959165i | \(0.408721\pi\) | |||||||
\(294\) | −7.20710 | −0.420326 | ||||||||
\(295\) | 14.1298 | 0.822668 | ||||||||
\(296\) | −24.4142 | −1.41905 | ||||||||
\(297\) | −0.264076 | −0.0153232 | ||||||||
\(298\) | 22.1873 | 1.28528 | ||||||||
\(299\) | 38.3454 | 2.21757 | ||||||||
\(300\) | 6.70501 | 0.387114 | ||||||||
\(301\) | −7.19266 | −0.414578 | ||||||||
\(302\) | 12.8531 | 0.739614 | ||||||||
\(303\) | 3.74157 | 0.214948 | ||||||||
\(304\) | 0.866525 | 0.0496986 | ||||||||
\(305\) | −9.77755 | −0.559861 | ||||||||
\(306\) | 7.46920 | 0.426986 | ||||||||
\(307\) | 13.7834 | 0.786658 | 0.393329 | − | 0.919398i | \(-0.371323\pi\) | ||||
0.393329 | + | 0.919398i | \(0.371323\pi\) | |||||||
\(308\) | 0.364189 | 0.0207516 | ||||||||
\(309\) | −8.42200 | −0.479111 | ||||||||
\(310\) | 5.85413 | 0.332492 | ||||||||
\(311\) | 17.3375 | 0.983117 | 0.491558 | − | 0.870845i | \(-0.336427\pi\) | ||||
0.491558 | + | 0.870845i | \(0.336427\pi\) | |||||||
\(312\) | −8.86421 | −0.501837 | ||||||||
\(313\) | −6.82737 | −0.385906 | −0.192953 | − | 0.981208i | \(-0.561806\pi\) | ||||
−0.192953 | + | 0.981208i | \(0.561806\pi\) | |||||||
\(314\) | −42.9660 | −2.42471 | ||||||||
\(315\) | 4.76712 | 0.268597 | ||||||||
\(316\) | 12.7961 | 0.719834 | ||||||||
\(317\) | 25.7736 | 1.44759 | 0.723794 | − | 0.690016i | \(-0.242396\pi\) | ||||
0.723794 | + | 0.690016i | \(0.242396\pi\) | |||||||
\(318\) | 10.8888 | 0.610612 | ||||||||
\(319\) | 0.548396 | 0.0307043 | ||||||||
\(320\) | −16.4557 | −0.919904 | ||||||||
\(321\) | −2.12117 | −0.118392 | ||||||||
\(322\) | −27.5985 | −1.53800 | ||||||||
\(323\) | 1.16724 | 0.0649471 | ||||||||
\(324\) | 20.1242 | 1.11801 | ||||||||
\(325\) | 14.3493 | 0.795957 | ||||||||
\(326\) | 34.9728 | 1.93697 | ||||||||
\(327\) | −7.67246 | −0.424288 | ||||||||
\(328\) | 25.5182 | 1.40901 | ||||||||
\(329\) | 17.6066 | 0.970683 | ||||||||
\(330\) | −0.144525 | −0.00795582 | ||||||||
\(331\) | −12.7055 | −0.698355 | −0.349178 | − | 0.937057i | \(-0.613539\pi\) | ||||
−0.349178 | + | 0.937057i | \(0.613539\pi\) | |||||||
\(332\) | 13.8799 | 0.761757 | ||||||||
\(333\) | −19.3316 | −1.05937 | ||||||||
\(334\) | −3.27932 | −0.179436 | ||||||||
\(335\) | −8.70871 | −0.475808 | ||||||||
\(336\) | 0.741691 | 0.0404626 | ||||||||
\(337\) | −13.8969 | −0.757014 | −0.378507 | − | 0.925599i | \(-0.623562\pi\) | ||||
−0.378507 | + | 0.925599i | \(0.623562\pi\) | |||||||
\(338\) | −15.2204 | −0.827878 | ||||||||
\(339\) | −9.61242 | −0.522075 | ||||||||
\(340\) | 5.51899 | 0.299309 | ||||||||
\(341\) | 0.147606 | 0.00799332 | ||||||||
\(342\) | 5.90193 | 0.319140 | ||||||||
\(343\) | 16.5676 | 0.894566 | ||||||||
\(344\) | −17.5498 | −0.946224 | ||||||||
\(345\) | 6.91783 | 0.372444 | ||||||||
\(346\) | 42.3085 | 2.27452 | ||||||||
\(347\) | 13.6074 | 0.730483 | 0.365242 | − | 0.930913i | \(-0.380986\pi\) | ||||
0.365242 | + | 0.930913i | \(0.380986\pi\) | |||||||
\(348\) | 14.5580 | 0.780391 | ||||||||
\(349\) | −10.3719 | −0.555197 | −0.277599 | − | 0.960697i | \(-0.589539\pi\) | ||||
−0.277599 | + | 0.960697i | \(0.589539\pi\) | |||||||
\(350\) | −10.3277 | −0.552037 | ||||||||
\(351\) | −15.0027 | −0.800782 | ||||||||
\(352\) | −0.354670 | −0.0189039 | ||||||||
\(353\) | 2.15599 | 0.114752 | 0.0573760 | − | 0.998353i | \(-0.481727\pi\) | ||||
0.0573760 | + | 0.998353i | \(0.481727\pi\) | |||||||
\(354\) | 14.9733 | 0.795820 | ||||||||
\(355\) | 8.91780 | 0.473308 | ||||||||
\(356\) | 38.7680 | 2.05470 | ||||||||
\(357\) | 0.999086 | 0.0528773 | ||||||||
\(358\) | 27.9774 | 1.47865 | ||||||||
\(359\) | 35.7983 | 1.88936 | 0.944680 | − | 0.327993i | \(-0.106372\pi\) | ||||
0.944680 | + | 0.327993i | \(0.106372\pi\) | |||||||
\(360\) | 11.6316 | 0.613039 | ||||||||
\(361\) | −18.0777 | −0.951457 | ||||||||
\(362\) | 15.2901 | 0.803630 | ||||||||
\(363\) | 6.62018 | 0.347469 | ||||||||
\(364\) | 20.6903 | 1.08446 | ||||||||
\(365\) | 9.11224 | 0.476956 | ||||||||
\(366\) | −10.3612 | −0.541589 | ||||||||
\(367\) | −22.5101 | −1.17502 | −0.587509 | − | 0.809218i | \(-0.699891\pi\) | ||||
−0.587509 | + | 0.809218i | \(0.699891\pi\) | |||||||
\(368\) | −7.82853 | −0.408090 | ||||||||
\(369\) | 20.2057 | 1.05187 | ||||||||
\(370\) | −22.6144 | −1.17567 | ||||||||
\(371\) | −10.5938 | −0.550002 | ||||||||
\(372\) | 3.91843 | 0.203161 | ||||||||
\(373\) | −4.74914 | −0.245901 | −0.122951 | − | 0.992413i | \(-0.539236\pi\) | ||||
−0.122951 | + | 0.992413i | \(0.539236\pi\) | |||||||
\(374\) | 0.220309 | 0.0113919 | ||||||||
\(375\) | 6.57531 | 0.339548 | ||||||||
\(376\) | 42.9595 | 2.21547 | ||||||||
\(377\) | 31.1554 | 1.60459 | ||||||||
\(378\) | 10.7979 | 0.555384 | ||||||||
\(379\) | 7.76279 | 0.398748 | 0.199374 | − | 0.979923i | \(-0.436109\pi\) | ||||
0.199374 | + | 0.979923i | \(0.436109\pi\) | |||||||
\(380\) | 4.36094 | 0.223712 | ||||||||
\(381\) | −5.58001 | −0.285872 | ||||||||
\(382\) | 5.47834 | 0.280296 | ||||||||
\(383\) | 5.15905 | 0.263615 | 0.131808 | − | 0.991275i | \(-0.457922\pi\) | ||||
0.131808 | + | 0.991275i | \(0.457922\pi\) | |||||||
\(384\) | −11.9473 | −0.609681 | ||||||||
\(385\) | 0.140609 | 0.00716612 | ||||||||
\(386\) | 12.6461 | 0.643671 | ||||||||
\(387\) | −13.8963 | −0.706387 | ||||||||
\(388\) | −46.4122 | −2.35622 | ||||||||
\(389\) | 21.9624 | 1.11354 | 0.556768 | − | 0.830668i | \(-0.312041\pi\) | ||||
0.556768 | + | 0.830668i | \(0.312041\pi\) | |||||||
\(390\) | −8.21073 | −0.415766 | ||||||||
\(391\) | −10.5453 | −0.533301 | ||||||||
\(392\) | 17.1087 | 0.864119 | ||||||||
\(393\) | −2.14342 | −0.108121 | ||||||||
\(394\) | 1.27113 | 0.0640385 | ||||||||
\(395\) | 4.94042 | 0.248580 | ||||||||
\(396\) | 0.703615 | 0.0353580 | ||||||||
\(397\) | 35.4778 | 1.78058 | 0.890291 | − | 0.455392i | \(-0.150501\pi\) | ||||
0.890291 | + | 0.455392i | \(0.150501\pi\) | |||||||
\(398\) | 29.7710 | 1.49229 | ||||||||
\(399\) | 0.789448 | 0.0395218 | ||||||||
\(400\) | −2.92953 | −0.146476 | ||||||||
\(401\) | 10.8155 | 0.540099 | 0.270049 | − | 0.962846i | \(-0.412960\pi\) | ||||
0.270049 | + | 0.962846i | \(0.412960\pi\) | |||||||
\(402\) | −9.22857 | −0.460279 | ||||||||
\(403\) | 8.38579 | 0.417726 | ||||||||
\(404\) | −21.3090 | −1.06016 | ||||||||
\(405\) | 7.76976 | 0.386082 | ||||||||
\(406\) | −22.4236 | −1.11286 | ||||||||
\(407\) | −0.570199 | −0.0282637 | ||||||||
\(408\) | 2.43774 | 0.120686 | ||||||||
\(409\) | −0.103382 | −0.00511192 | −0.00255596 | − | 0.999997i | \(-0.500814\pi\) | ||||
−0.00255596 | + | 0.999997i | \(0.500814\pi\) | |||||||
\(410\) | 23.6369 | 1.16735 | ||||||||
\(411\) | −12.8176 | −0.632247 | ||||||||
\(412\) | 47.9651 | 2.36307 | ||||||||
\(413\) | −14.5676 | −0.716826 | ||||||||
\(414\) | −53.3205 | −2.62056 | ||||||||
\(415\) | 5.35887 | 0.263057 | ||||||||
\(416\) | −20.1495 | −0.987908 | ||||||||
\(417\) | 7.95145 | 0.389384 | ||||||||
\(418\) | 0.174082 | 0.00851461 | ||||||||
\(419\) | −13.3064 | −0.650062 | −0.325031 | − | 0.945703i | \(-0.605375\pi\) | ||||
−0.325031 | + | 0.945703i | \(0.605375\pi\) | |||||||
\(420\) | 3.73269 | 0.182137 | ||||||||
\(421\) | 20.6781 | 1.00779 | 0.503894 | − | 0.863765i | \(-0.331900\pi\) | ||||
0.503894 | + | 0.863765i | \(0.331900\pi\) | |||||||
\(422\) | 28.0471 | 1.36531 | ||||||||
\(423\) | 34.0161 | 1.65392 | ||||||||
\(424\) | −25.8485 | −1.25531 | ||||||||
\(425\) | −3.94619 | −0.191418 | ||||||||
\(426\) | 9.45014 | 0.457861 | ||||||||
\(427\) | 10.0805 | 0.487831 | ||||||||
\(428\) | 12.0805 | 0.583932 | ||||||||
\(429\) | −0.207025 | −0.00999528 | ||||||||
\(430\) | −16.2561 | −0.783936 | ||||||||
\(431\) | 12.7856 | 0.615860 | 0.307930 | − | 0.951409i | \(-0.400364\pi\) | ||||
0.307930 | + | 0.951409i | \(0.400364\pi\) | |||||||
\(432\) | 3.06291 | 0.147365 | ||||||||
\(433\) | 38.3209 | 1.84158 | 0.920792 | − | 0.390053i | \(-0.127543\pi\) | ||||
0.920792 | + | 0.390053i | \(0.127543\pi\) | |||||||
\(434\) | −6.03553 | −0.289715 | ||||||||
\(435\) | 5.62069 | 0.269492 | ||||||||
\(436\) | 43.6963 | 2.09267 | ||||||||
\(437\) | −8.33260 | −0.398603 | ||||||||
\(438\) | 9.65619 | 0.461391 | ||||||||
\(439\) | −40.3093 | −1.92386 | −0.961930 | − | 0.273297i | \(-0.911886\pi\) | ||||
−0.961930 | + | 0.273297i | \(0.911886\pi\) | |||||||
\(440\) | 0.343082 | 0.0163558 | ||||||||
\(441\) | 13.5469 | 0.645093 | ||||||||
\(442\) | 12.5162 | 0.595334 | ||||||||
\(443\) | −7.67688 | −0.364740 | −0.182370 | − | 0.983230i | \(-0.558377\pi\) | ||||
−0.182370 | + | 0.983230i | \(0.558377\pi\) | |||||||
\(444\) | −15.1368 | −0.718361 | ||||||||
\(445\) | 14.9679 | 0.709547 | ||||||||
\(446\) | −18.8848 | −0.894221 | ||||||||
\(447\) | 5.73380 | 0.271199 | ||||||||
\(448\) | 16.9656 | 0.801551 | ||||||||
\(449\) | −28.6328 | −1.35126 | −0.675632 | − | 0.737239i | \(-0.736129\pi\) | ||||
−0.675632 | + | 0.737239i | \(0.736129\pi\) | |||||||
\(450\) | −19.9531 | −0.940600 | ||||||||
\(451\) | 0.595982 | 0.0280637 | ||||||||
\(452\) | 54.7448 | 2.57498 | ||||||||
\(453\) | 3.32159 | 0.156062 | ||||||||
\(454\) | 39.7706 | 1.86653 | ||||||||
\(455\) | 7.98829 | 0.374497 | ||||||||
\(456\) | 1.92623 | 0.0902038 | ||||||||
\(457\) | −9.94190 | −0.465062 | −0.232531 | − | 0.972589i | \(-0.574701\pi\) | ||||
−0.232531 | + | 0.972589i | \(0.574701\pi\) | |||||||
\(458\) | −2.85547 | −0.133427 | ||||||||
\(459\) | 4.12587 | 0.192579 | ||||||||
\(460\) | −39.3985 | −1.83696 | ||||||||
\(461\) | −10.3989 | −0.484327 | −0.242163 | − | 0.970235i | \(-0.577857\pi\) | ||||
−0.242163 | + | 0.970235i | \(0.577857\pi\) | |||||||
\(462\) | 0.149003 | 0.00693225 | ||||||||
\(463\) | 7.32945 | 0.340628 | 0.170314 | − | 0.985390i | \(-0.445522\pi\) | ||||
0.170314 | + | 0.985390i | \(0.445522\pi\) | |||||||
\(464\) | −6.36063 | −0.295285 | ||||||||
\(465\) | 1.51287 | 0.0701574 | ||||||||
\(466\) | 11.3754 | 0.526953 | ||||||||
\(467\) | −5.35459 | −0.247781 | −0.123890 | − | 0.992296i | \(-0.539537\pi\) | ||||
−0.123890 | + | 0.992296i | \(0.539537\pi\) | |||||||
\(468\) | 39.9737 | 1.84779 | ||||||||
\(469\) | 8.97856 | 0.414591 | ||||||||
\(470\) | 39.7925 | 1.83549 | ||||||||
\(471\) | −11.1036 | −0.511625 | ||||||||
\(472\) | −35.5445 | −1.63607 | ||||||||
\(473\) | −0.409880 | −0.0188463 | ||||||||
\(474\) | 5.23534 | 0.240467 | ||||||||
\(475\) | −3.11816 | −0.143071 | ||||||||
\(476\) | −5.69001 | −0.260801 | ||||||||
\(477\) | −20.4673 | −0.937132 | ||||||||
\(478\) | −27.5011 | −1.25787 | ||||||||
\(479\) | 31.7796 | 1.45205 | 0.726023 | − | 0.687671i | \(-0.241367\pi\) | ||||
0.726023 | + | 0.687671i | \(0.241367\pi\) | |||||||
\(480\) | −3.63513 | −0.165920 | ||||||||
\(481\) | −32.3941 | −1.47704 | ||||||||
\(482\) | −53.7692 | −2.44912 | ||||||||
\(483\) | −7.13219 | −0.324526 | ||||||||
\(484\) | −37.7033 | −1.71379 | ||||||||
\(485\) | −17.9193 | −0.813672 | ||||||||
\(486\) | 31.9634 | 1.44989 | ||||||||
\(487\) | 3.14020 | 0.142296 | 0.0711481 | − | 0.997466i | \(-0.477334\pi\) | ||||
0.0711481 | + | 0.997466i | \(0.477334\pi\) | |||||||
\(488\) | 24.5961 | 1.11341 | ||||||||
\(489\) | 9.03792 | 0.408709 | ||||||||
\(490\) | 15.8474 | 0.715913 | ||||||||
\(491\) | 23.5419 | 1.06243 | 0.531215 | − | 0.847237i | \(-0.321736\pi\) | ||||
0.531215 | + | 0.847237i | \(0.321736\pi\) | |||||||
\(492\) | 15.8213 | 0.713278 | ||||||||
\(493\) | −8.56802 | −0.385884 | ||||||||
\(494\) | 9.88991 | 0.444968 | ||||||||
\(495\) | 0.271658 | 0.0122101 | ||||||||
\(496\) | −1.71203 | −0.0768723 | ||||||||
\(497\) | −9.19413 | −0.412413 | ||||||||
\(498\) | 5.67877 | 0.254472 | ||||||||
\(499\) | −5.86590 | −0.262594 | −0.131297 | − | 0.991343i | \(-0.541914\pi\) | ||||
−0.131297 | + | 0.991343i | \(0.541914\pi\) | |||||||
\(500\) | −37.4478 | −1.67471 | ||||||||
\(501\) | −0.847464 | −0.0378619 | ||||||||
\(502\) | 27.1726 | 1.21277 | ||||||||
\(503\) | 28.3501 | 1.26407 | 0.632034 | − | 0.774941i | \(-0.282220\pi\) | ||||
0.632034 | + | 0.774941i | \(0.282220\pi\) | |||||||
\(504\) | −11.9920 | −0.534167 | ||||||||
\(505\) | −8.22719 | −0.366105 | ||||||||
\(506\) | −1.57272 | −0.0699161 | ||||||||
\(507\) | −3.93335 | −0.174686 | ||||||||
\(508\) | 31.7793 | 1.40998 | ||||||||
\(509\) | −21.0958 | −0.935054 | −0.467527 | − | 0.883979i | \(-0.654855\pi\) | ||||
−0.467527 | + | 0.883979i | \(0.654855\pi\) | |||||||
\(510\) | 2.25802 | 0.0999870 | ||||||||
\(511\) | −9.39459 | −0.415592 | ||||||||
\(512\) | 10.1243 | 0.447436 | ||||||||
\(513\) | 3.26013 | 0.143938 | ||||||||
\(514\) | −38.1466 | −1.68257 | ||||||||
\(515\) | 18.5188 | 0.816036 | ||||||||
\(516\) | −10.8809 | −0.479005 | ||||||||
\(517\) | 1.00333 | 0.0441263 | ||||||||
\(518\) | 23.3151 | 1.02441 | ||||||||
\(519\) | 10.9337 | 0.479934 | ||||||||
\(520\) | 19.4912 | 0.854744 | ||||||||
\(521\) | −14.4116 | −0.631384 | −0.315692 | − | 0.948862i | \(-0.602237\pi\) | ||||
−0.315692 | + | 0.948862i | \(0.602237\pi\) | |||||||
\(522\) | −43.3225 | −1.89618 | ||||||||
\(523\) | 26.7550 | 1.16991 | 0.584956 | − | 0.811065i | \(-0.301112\pi\) | ||||
0.584956 | + | 0.811065i | \(0.301112\pi\) | |||||||
\(524\) | 12.2073 | 0.533276 | ||||||||
\(525\) | −2.66895 | −0.116483 | ||||||||
\(526\) | −52.3707 | −2.28347 | ||||||||
\(527\) | −2.30617 | −0.100458 | ||||||||
\(528\) | 0.0422659 | 0.00183939 | ||||||||
\(529\) | 52.2801 | 2.27305 | ||||||||
\(530\) | −23.9429 | −1.04001 | ||||||||
\(531\) | −28.1447 | −1.22138 | ||||||||
\(532\) | −4.49607 | −0.194929 | ||||||||
\(533\) | 33.8589 | 1.46659 | ||||||||
\(534\) | 15.8614 | 0.686391 | ||||||||
\(535\) | 4.66415 | 0.201649 | ||||||||
\(536\) | 21.9074 | 0.946255 | ||||||||
\(537\) | 7.23012 | 0.312003 | ||||||||
\(538\) | −5.12097 | −0.220781 | ||||||||
\(539\) | 0.399576 | 0.0172110 | ||||||||
\(540\) | 15.4147 | 0.663342 | ||||||||
\(541\) | 17.0096 | 0.731300 | 0.365650 | − | 0.930752i | \(-0.380847\pi\) | ||||
0.365650 | + | 0.930752i | \(0.380847\pi\) | |||||||
\(542\) | −2.49961 | −0.107367 | ||||||||
\(543\) | 3.95138 | 0.169570 | ||||||||
\(544\) | 5.54128 | 0.237581 | ||||||||
\(545\) | 16.8707 | 0.722660 | ||||||||
\(546\) | 8.46515 | 0.362275 | ||||||||
\(547\) | −27.9256 | −1.19401 | −0.597005 | − | 0.802237i | \(-0.703643\pi\) | ||||
−0.597005 | + | 0.802237i | \(0.703643\pi\) | |||||||
\(548\) | 72.9991 | 3.11837 | ||||||||
\(549\) | 19.4756 | 0.831200 | ||||||||
\(550\) | −0.588532 | −0.0250951 | ||||||||
\(551\) | −6.77019 | −0.288420 | ||||||||
\(552\) | −17.4023 | −0.740691 | ||||||||
\(553\) | −5.09351 | −0.216598 | ||||||||
\(554\) | −10.9312 | −0.464421 | ||||||||
\(555\) | −5.84416 | −0.248071 | ||||||||
\(556\) | −45.2852 | −1.92052 | ||||||||
\(557\) | 30.8316 | 1.30638 | 0.653189 | − | 0.757195i | \(-0.273431\pi\) | ||||
0.653189 | + | 0.757195i | \(0.273431\pi\) | |||||||
\(558\) | −11.6607 | −0.493636 | ||||||||
\(559\) | −23.2861 | −0.984896 | ||||||||
\(560\) | −1.63087 | −0.0689170 | ||||||||
\(561\) | 0.0569338 | 0.00240375 | ||||||||
\(562\) | −77.6808 | −3.27677 | ||||||||
\(563\) | 12.2705 | 0.517139 | 0.258569 | − | 0.965993i | \(-0.416749\pi\) | ||||
0.258569 | + | 0.965993i | \(0.416749\pi\) | |||||||
\(564\) | 26.6349 | 1.12153 | ||||||||
\(565\) | 21.1364 | 0.889214 | ||||||||
\(566\) | 61.5493 | 2.58711 | ||||||||
\(567\) | −8.01051 | −0.336410 | ||||||||
\(568\) | −22.4334 | −0.941283 | ||||||||
\(569\) | 31.8746 | 1.33625 | 0.668127 | − | 0.744047i | \(-0.267096\pi\) | ||||
0.668127 | + | 0.744047i | \(0.267096\pi\) | |||||||
\(570\) | 1.78422 | 0.0747328 | ||||||||
\(571\) | −41.8752 | −1.75242 | −0.876212 | − | 0.481927i | \(-0.839937\pi\) | ||||
−0.876212 | + | 0.481927i | \(0.839937\pi\) | |||||||
\(572\) | 1.17905 | 0.0492987 | ||||||||
\(573\) | 1.41575 | 0.0591438 | ||||||||
\(574\) | −24.3694 | −1.01716 | ||||||||
\(575\) | 28.1707 | 1.17480 | ||||||||
\(576\) | 32.7777 | 1.36574 | ||||||||
\(577\) | −33.2442 | −1.38398 | −0.691988 | − | 0.721909i | \(-0.743265\pi\) | ||||
−0.691988 | + | 0.721909i | \(0.743265\pi\) | |||||||
\(578\) | 36.1700 | 1.50447 | ||||||||
\(579\) | 3.26810 | 0.135818 | ||||||||
\(580\) | −32.0110 | −1.32919 | ||||||||
\(581\) | −5.52492 | −0.229212 | ||||||||
\(582\) | −18.9889 | −0.787117 | ||||||||
\(583\) | −0.603696 | −0.0250026 | ||||||||
\(584\) | −22.9225 | −0.948539 | ||||||||
\(585\) | 15.4334 | 0.638094 | ||||||||
\(586\) | −22.5628 | −0.932059 | ||||||||
\(587\) | −37.7145 | −1.55664 | −0.778322 | − | 0.627865i | \(-0.783929\pi\) | ||||
−0.778322 | + | 0.627865i | \(0.783929\pi\) | |||||||
\(588\) | 10.6074 | 0.437441 | ||||||||
\(589\) | −1.82226 | −0.0750850 | ||||||||
\(590\) | −32.9241 | −1.35546 | ||||||||
\(591\) | 0.328494 | 0.0135124 | ||||||||
\(592\) | 6.61352 | 0.271814 | ||||||||
\(593\) | 32.4179 | 1.33124 | 0.665621 | − | 0.746290i | \(-0.268167\pi\) | ||||
0.665621 | + | 0.746290i | \(0.268167\pi\) | |||||||
\(594\) | 0.615328 | 0.0252472 | ||||||||
\(595\) | −2.19685 | −0.0900621 | ||||||||
\(596\) | −32.6552 | −1.33761 | ||||||||
\(597\) | 7.69363 | 0.314879 | ||||||||
\(598\) | −89.3494 | −3.65377 | ||||||||
\(599\) | −18.3584 | −0.750105 | −0.375052 | − | 0.927004i | \(-0.622375\pi\) | ||||
−0.375052 | + | 0.927004i | \(0.622375\pi\) | |||||||
\(600\) | −6.51215 | −0.265857 | ||||||||
\(601\) | −37.7899 | −1.54148 | −0.770741 | − | 0.637149i | \(-0.780114\pi\) | ||||
−0.770741 | + | 0.637149i | \(0.780114\pi\) | |||||||
\(602\) | 16.7598 | 0.683077 | ||||||||
\(603\) | 17.3466 | 0.706410 | ||||||||
\(604\) | −18.9172 | −0.769728 | ||||||||
\(605\) | −14.5569 | −0.591820 | ||||||||
\(606\) | −8.71830 | −0.354157 | ||||||||
\(607\) | 24.8244 | 1.00759 | 0.503795 | − | 0.863823i | \(-0.331937\pi\) | ||||
0.503795 | + | 0.863823i | \(0.331937\pi\) | |||||||
\(608\) | 4.37855 | 0.177574 | ||||||||
\(609\) | −5.79486 | −0.234820 | ||||||||
\(610\) | 22.7829 | 0.922451 | ||||||||
\(611\) | 57.0010 | 2.30601 | ||||||||
\(612\) | −10.9931 | −0.444371 | ||||||||
\(613\) | −31.0163 | −1.25274 | −0.626368 | − | 0.779527i | \(-0.715459\pi\) | ||||
−0.626368 | + | 0.779527i | \(0.715459\pi\) | |||||||
\(614\) | −32.1169 | −1.29613 | ||||||||
\(615\) | 6.10842 | 0.246315 | ||||||||
\(616\) | −0.353713 | −0.0142515 | ||||||||
\(617\) | 35.0353 | 1.41047 | 0.705234 | − | 0.708975i | \(-0.250842\pi\) | ||||
0.705234 | + | 0.708975i | \(0.250842\pi\) | |||||||
\(618\) | 19.6243 | 0.789404 | ||||||||
\(619\) | 10.8811 | 0.437348 | 0.218674 | − | 0.975798i | \(-0.429827\pi\) | ||||
0.218674 | + | 0.975798i | \(0.429827\pi\) | |||||||
\(620\) | −8.61608 | −0.346030 | ||||||||
\(621\) | −29.4534 | −1.18192 | ||||||||
\(622\) | −40.3983 | −1.61983 | ||||||||
\(623\) | −15.4317 | −0.618258 | ||||||||
\(624\) | 2.40121 | 0.0961253 | ||||||||
\(625\) | 1.77589 | 0.0710357 | ||||||||
\(626\) | 15.9086 | 0.635835 | ||||||||
\(627\) | 0.0449874 | 0.00179662 | ||||||||
\(628\) | 63.2371 | 2.52344 | ||||||||
\(629\) | 8.90867 | 0.355212 | ||||||||
\(630\) | −11.1080 | −0.442552 | ||||||||
\(631\) | 5.71731 | 0.227603 | 0.113801 | − | 0.993504i | \(-0.463697\pi\) | ||||
0.113801 | + | 0.993504i | \(0.463697\pi\) | |||||||
\(632\) | −12.4280 | −0.494359 | ||||||||
\(633\) | 7.24812 | 0.288087 | ||||||||
\(634\) | −60.0556 | −2.38511 | ||||||||
\(635\) | 12.2697 | 0.486907 | ||||||||
\(636\) | −16.0261 | −0.635474 | ||||||||
\(637\) | 22.7007 | 0.899435 | ||||||||
\(638\) | −1.27783 | −0.0505897 | ||||||||
\(639\) | −17.7631 | −0.702698 | ||||||||
\(640\) | 26.2703 | 1.03843 | ||||||||
\(641\) | −4.21327 | −0.166414 | −0.0832072 | − | 0.996532i | \(-0.526516\pi\) | ||||
−0.0832072 | + | 0.996532i | \(0.526516\pi\) | |||||||
\(642\) | 4.94257 | 0.195068 | ||||||||
\(643\) | −29.4539 | −1.16155 | −0.580774 | − | 0.814065i | \(-0.697250\pi\) | ||||
−0.580774 | + | 0.814065i | \(0.697250\pi\) | |||||||
\(644\) | 40.6193 | 1.60062 | ||||||||
\(645\) | −4.20100 | −0.165414 | ||||||||
\(646\) | −2.71981 | −0.107010 | ||||||||
\(647\) | 11.1428 | 0.438067 | 0.219034 | − | 0.975717i | \(-0.429710\pi\) | ||||
0.219034 | + | 0.975717i | \(0.429710\pi\) | |||||||
\(648\) | −19.5454 | −0.767815 | ||||||||
\(649\) | −0.830149 | −0.0325862 | ||||||||
\(650\) | −33.4356 | −1.31145 | ||||||||
\(651\) | −1.55974 | −0.0611311 | ||||||||
\(652\) | −51.4728 | −2.01583 | ||||||||
\(653\) | 5.72977 | 0.224223 | 0.112112 | − | 0.993696i | \(-0.464239\pi\) | ||||
0.112112 | + | 0.993696i | \(0.464239\pi\) | |||||||
\(654\) | 17.8778 | 0.699075 | ||||||||
\(655\) | 4.71309 | 0.184156 | ||||||||
\(656\) | −6.91257 | −0.269890 | ||||||||
\(657\) | −18.1504 | −0.708115 | ||||||||
\(658\) | −41.0255 | −1.59934 | ||||||||
\(659\) | −12.3162 | −0.479771 | −0.239886 | − | 0.970801i | \(-0.577110\pi\) | ||||
−0.239886 | + | 0.970801i | \(0.577110\pi\) | |||||||
\(660\) | 0.212711 | 0.00827976 | ||||||||
\(661\) | 34.8939 | 1.35721 | 0.678607 | − | 0.734502i | \(-0.262584\pi\) | ||||
0.678607 | + | 0.734502i | \(0.262584\pi\) | |||||||
\(662\) | 29.6053 | 1.15064 | ||||||||
\(663\) | 3.23452 | 0.125618 | ||||||||
\(664\) | −13.4806 | −0.523150 | ||||||||
\(665\) | −1.73589 | −0.0673147 | ||||||||
\(666\) | 45.0450 | 1.74546 | ||||||||
\(667\) | 61.1646 | 2.36830 | ||||||||
\(668\) | 4.82648 | 0.186742 | ||||||||
\(669\) | −4.88034 | −0.188685 | ||||||||
\(670\) | 20.2923 | 0.783962 | ||||||||
\(671\) | 0.574447 | 0.0221763 | ||||||||
\(672\) | 3.74777 | 0.144573 | ||||||||
\(673\) | 0.911582 | 0.0351389 | 0.0175694 | − | 0.999846i | \(-0.494407\pi\) | ||||
0.0175694 | + | 0.999846i | \(0.494407\pi\) | |||||||
\(674\) | 32.3815 | 1.24729 | ||||||||
\(675\) | −11.0218 | −0.424229 | ||||||||
\(676\) | 22.4013 | 0.861587 | ||||||||
\(677\) | 20.8095 | 0.799774 | 0.399887 | − | 0.916564i | \(-0.369049\pi\) | ||||
0.399887 | + | 0.916564i | \(0.369049\pi\) | |||||||
\(678\) | 22.3981 | 0.860194 | ||||||||
\(679\) | 18.4745 | 0.708987 | ||||||||
\(680\) | −5.36024 | −0.205556 | ||||||||
\(681\) | 10.2778 | 0.393846 | ||||||||
\(682\) | −0.343940 | −0.0131701 | ||||||||
\(683\) | 23.1134 | 0.884410 | 0.442205 | − | 0.896914i | \(-0.354196\pi\) | ||||
0.442205 | + | 0.896914i | \(0.354196\pi\) | |||||||
\(684\) | −8.68644 | −0.332134 | ||||||||
\(685\) | 28.1842 | 1.07686 | ||||||||
\(686\) | −38.6045 | −1.47393 | ||||||||
\(687\) | −0.737931 | −0.0281538 | ||||||||
\(688\) | 4.75404 | 0.181246 | ||||||||
\(689\) | −34.2972 | −1.30662 | ||||||||
\(690\) | −16.1194 | −0.613654 | ||||||||
\(691\) | 23.7898 | 0.905005 | 0.452503 | − | 0.891763i | \(-0.350531\pi\) | ||||
0.452503 | + | 0.891763i | \(0.350531\pi\) | |||||||
\(692\) | −62.2695 | −2.36713 | ||||||||
\(693\) | −0.280076 | −0.0106392 | ||||||||
\(694\) | −31.7069 | −1.20358 | ||||||||
\(695\) | −17.4841 | −0.663211 | ||||||||
\(696\) | −14.1393 | −0.535947 | ||||||||
\(697\) | −9.31150 | −0.352698 | ||||||||
\(698\) | 24.1679 | 0.914767 | ||||||||
\(699\) | 2.93970 | 0.111190 | ||||||||
\(700\) | 15.2002 | 0.574515 | ||||||||
\(701\) | 10.7114 | 0.404565 | 0.202283 | − | 0.979327i | \(-0.435164\pi\) | ||||
0.202283 | + | 0.979327i | \(0.435164\pi\) | |||||||
\(702\) | 34.9580 | 1.31940 | ||||||||
\(703\) | 7.03936 | 0.265494 | ||||||||
\(704\) | 0.966802 | 0.0364377 | ||||||||
\(705\) | 10.2834 | 0.387297 | ||||||||
\(706\) | −5.02372 | −0.189070 | ||||||||
\(707\) | 8.48212 | 0.319003 | ||||||||
\(708\) | −22.0376 | −0.828223 | ||||||||
\(709\) | 22.3840 | 0.840648 | 0.420324 | − | 0.907374i | \(-0.361916\pi\) | ||||
0.420324 | + | 0.907374i | \(0.361916\pi\) | |||||||
\(710\) | −20.7795 | −0.779842 | ||||||||
\(711\) | −9.84069 | −0.369055 | ||||||||
\(712\) | −37.6529 | −1.41110 | ||||||||
\(713\) | 16.4631 | 0.616546 | ||||||||
\(714\) | −2.32799 | −0.0871229 | ||||||||
\(715\) | 0.455220 | 0.0170243 | ||||||||
\(716\) | −41.1770 | −1.53886 | ||||||||
\(717\) | −7.10703 | −0.265417 | ||||||||
\(718\) | −83.4143 | −3.11299 | ||||||||
\(719\) | −12.4489 | −0.464267 | −0.232134 | − | 0.972684i | \(-0.574571\pi\) | ||||
−0.232134 | + | 0.972684i | \(0.574571\pi\) | |||||||
\(720\) | −3.15086 | −0.117426 | ||||||||
\(721\) | −19.0926 | −0.711047 | ||||||||
\(722\) | 42.1232 | 1.56766 | ||||||||
\(723\) | −13.8954 | −0.516776 | ||||||||
\(724\) | −22.5039 | −0.836351 | ||||||||
\(725\) | 22.8885 | 0.850058 | ||||||||
\(726\) | −15.4258 | −0.572506 | ||||||||
\(727\) | 42.6429 | 1.58154 | 0.790768 | − | 0.612116i | \(-0.209681\pi\) | ||||
0.790768 | + | 0.612116i | \(0.209681\pi\) | |||||||
\(728\) | −20.0951 | −0.744774 | ||||||||
\(729\) | −9.34395 | −0.346072 | ||||||||
\(730\) | −21.2326 | −0.785854 | ||||||||
\(731\) | 6.40388 | 0.236856 | ||||||||
\(732\) | 15.2496 | 0.563641 | ||||||||
\(733\) | 33.0759 | 1.22169 | 0.610843 | − | 0.791751i | \(-0.290830\pi\) | ||||
0.610843 | + | 0.791751i | \(0.290830\pi\) | |||||||
\(734\) | 52.4512 | 1.93601 | ||||||||
\(735\) | 4.09540 | 0.151061 | ||||||||
\(736\) | −39.5576 | −1.45811 | ||||||||
\(737\) | 0.511651 | 0.0188469 | ||||||||
\(738\) | −47.0818 | −1.73310 | ||||||||
\(739\) | 4.68863 | 0.172474 | 0.0862371 | − | 0.996275i | \(-0.472516\pi\) | ||||
0.0862371 | + | 0.996275i | \(0.472516\pi\) | |||||||
\(740\) | 33.2837 | 1.22353 | ||||||||
\(741\) | 2.55582 | 0.0938904 | ||||||||
\(742\) | 24.6848 | 0.906207 | ||||||||
\(743\) | −16.3647 | −0.600362 | −0.300181 | − | 0.953882i | \(-0.597047\pi\) | ||||
−0.300181 | + | 0.953882i | \(0.597047\pi\) | |||||||
\(744\) | −3.80572 | −0.139524 | ||||||||
\(745\) | −12.6078 | −0.461915 | ||||||||
\(746\) | 11.0661 | 0.405158 | ||||||||
\(747\) | −10.6742 | −0.390548 | ||||||||
\(748\) | −0.324250 | −0.0118558 | ||||||||
\(749\) | −4.80867 | −0.175705 | ||||||||
\(750\) | −15.3213 | −0.559453 | ||||||||
\(751\) | −38.3167 | −1.39820 | −0.699098 | − | 0.715026i | \(-0.746415\pi\) | ||||
−0.699098 | + | 0.715026i | \(0.746415\pi\) | |||||||
\(752\) | −11.6372 | −0.424366 | ||||||||
\(753\) | 7.02214 | 0.255901 | ||||||||
\(754\) | −72.5959 | −2.64379 | ||||||||
\(755\) | −7.30371 | −0.265809 | ||||||||
\(756\) | −15.8923 | −0.577998 | ||||||||
\(757\) | 11.8814 | 0.431836 | 0.215918 | − | 0.976411i | \(-0.430726\pi\) | ||||
0.215918 | + | 0.976411i | \(0.430726\pi\) | |||||||
\(758\) | −18.0882 | −0.656994 | ||||||||
\(759\) | −0.406434 | −0.0147526 | ||||||||
\(760\) | −4.23550 | −0.153638 | ||||||||
\(761\) | −32.5677 | −1.18058 | −0.590289 | − | 0.807192i | \(-0.700986\pi\) | ||||
−0.590289 | + | 0.807192i | \(0.700986\pi\) | |||||||
\(762\) | 13.0021 | 0.471016 | ||||||||
\(763\) | −17.3934 | −0.629684 | ||||||||
\(764\) | −8.06299 | −0.291709 | ||||||||
\(765\) | −4.24433 | −0.153454 | ||||||||
\(766\) | −12.0212 | −0.434344 | ||||||||
\(767\) | −47.1623 | −1.70293 | ||||||||
\(768\) | 12.8710 | 0.464443 | ||||||||
\(769\) | 10.4032 | 0.375150 | 0.187575 | − | 0.982250i | \(-0.439937\pi\) | ||||
0.187575 | + | 0.982250i | \(0.439937\pi\) | |||||||
\(770\) | −0.327637 | −0.0118072 | ||||||||
\(771\) | −9.85811 | −0.355031 | ||||||||
\(772\) | −18.6125 | −0.669879 | ||||||||
\(773\) | 6.61323 | 0.237861 | 0.118931 | − | 0.992903i | \(-0.462053\pi\) | ||||
0.118931 | + | 0.992903i | \(0.462053\pi\) | |||||||
\(774\) | 32.3800 | 1.16387 | ||||||||
\(775\) | 6.16067 | 0.221298 | ||||||||
\(776\) | 45.0772 | 1.61818 | ||||||||
\(777\) | 6.02525 | 0.216155 | ||||||||
\(778\) | −51.1750 | −1.83471 | ||||||||
\(779\) | −7.35766 | −0.263616 | ||||||||
\(780\) | 12.0845 | 0.432695 | ||||||||
\(781\) | −0.523936 | −0.0187479 | ||||||||
\(782\) | 24.5719 | 0.878689 | ||||||||
\(783\) | −23.9307 | −0.855212 | ||||||||
\(784\) | −4.63454 | −0.165519 | ||||||||
\(785\) | 24.4152 | 0.871416 | ||||||||
\(786\) | 4.99444 | 0.178146 | ||||||||
\(787\) | −17.2256 | −0.614025 | −0.307013 | − | 0.951705i | \(-0.599329\pi\) | ||||
−0.307013 | + | 0.951705i | \(0.599329\pi\) | |||||||
\(788\) | −1.87084 | −0.0666459 | ||||||||
\(789\) | −13.5340 | −0.481823 | ||||||||
\(790\) | −11.5118 | −0.409571 | ||||||||
\(791\) | −21.7913 | −0.774810 | ||||||||
\(792\) | −0.683376 | −0.0242827 | ||||||||
\(793\) | 32.6355 | 1.15892 | ||||||||
\(794\) | −82.6676 | −2.93376 | ||||||||
\(795\) | −6.18749 | −0.219448 | ||||||||
\(796\) | −43.8168 | −1.55305 | ||||||||
\(797\) | −1.88961 | −0.0669334 | −0.0334667 | − | 0.999440i | \(-0.510655\pi\) | ||||
−0.0334667 | + | 0.999440i | \(0.510655\pi\) | |||||||
\(798\) | −1.83951 | −0.0651179 | ||||||||
\(799\) | −15.6758 | −0.554569 | ||||||||
\(800\) | −14.8029 | −0.523362 | ||||||||
\(801\) | −29.8142 | −1.05343 | ||||||||
\(802\) | −25.2013 | −0.889891 | ||||||||
\(803\) | −0.535359 | −0.0188924 | ||||||||
\(804\) | 13.5826 | 0.479020 | ||||||||
\(805\) | 15.6827 | 0.552742 | ||||||||
\(806\) | −19.5399 | −0.688263 | ||||||||
\(807\) | −1.32340 | −0.0465858 | ||||||||
\(808\) | 20.6961 | 0.728086 | ||||||||
\(809\) | 10.6848 | 0.375656 | 0.187828 | − | 0.982202i | \(-0.439855\pi\) | ||||
0.187828 | + | 0.982202i | \(0.439855\pi\) | |||||||
\(810\) | −18.1045 | −0.636126 | ||||||||
\(811\) | −28.0525 | −0.985056 | −0.492528 | − | 0.870297i | \(-0.663927\pi\) | ||||
−0.492528 | + | 0.870297i | \(0.663927\pi\) | |||||||
\(812\) | 33.0029 | 1.15818 | ||||||||
\(813\) | −0.645967 | −0.0226550 | ||||||||
\(814\) | 1.32863 | 0.0465685 | ||||||||
\(815\) | −19.8731 | −0.696125 | ||||||||
\(816\) | −0.660354 | −0.0231170 | ||||||||
\(817\) | 5.06015 | 0.177032 | ||||||||
\(818\) | 0.240893 | 0.00842262 | ||||||||
\(819\) | −15.9117 | −0.555998 | ||||||||
\(820\) | −34.7887 | −1.21488 | ||||||||
\(821\) | −35.8701 | −1.25188 | −0.625938 | − | 0.779873i | \(-0.715284\pi\) | ||||
−0.625938 | + | 0.779873i | \(0.715284\pi\) | |||||||
\(822\) | 29.8666 | 1.04172 | ||||||||
\(823\) | 9.41093 | 0.328044 | 0.164022 | − | 0.986457i | \(-0.447553\pi\) | ||||
0.164022 | + | 0.986457i | \(0.447553\pi\) | |||||||
\(824\) | −46.5854 | −1.62288 | ||||||||
\(825\) | −0.152092 | −0.00529518 | ||||||||
\(826\) | 33.9443 | 1.18107 | ||||||||
\(827\) | −20.2417 | −0.703873 | −0.351936 | − | 0.936024i | \(-0.614477\pi\) | ||||
−0.351936 | + | 0.936024i | \(0.614477\pi\) | |||||||
\(828\) | 78.4768 | 2.72726 | ||||||||
\(829\) | 33.2249 | 1.15395 | 0.576975 | − | 0.816762i | \(-0.304233\pi\) | ||||
0.576975 | + | 0.816762i | \(0.304233\pi\) | |||||||
\(830\) | −12.4868 | −0.433424 | ||||||||
\(831\) | −2.82491 | −0.0979951 | ||||||||
\(832\) | 54.9259 | 1.90421 | ||||||||
\(833\) | −6.24290 | −0.216304 | ||||||||
\(834\) | −18.5278 | −0.641567 | ||||||||
\(835\) | 1.86346 | 0.0644875 | ||||||||
\(836\) | −0.256213 | −0.00886130 | ||||||||
\(837\) | −6.44117 | −0.222640 | ||||||||
\(838\) | 31.0056 | 1.07107 | ||||||||
\(839\) | 0.321810 | 0.0111101 | 0.00555506 | − | 0.999985i | \(-0.498232\pi\) | ||||
0.00555506 | + | 0.999985i | \(0.498232\pi\) | |||||||
\(840\) | −3.62532 | −0.125086 | ||||||||
\(841\) | 20.6959 | 0.713650 | ||||||||
\(842\) | −48.1824 | −1.66048 | ||||||||
\(843\) | −20.0748 | −0.691413 | ||||||||
\(844\) | −41.2796 | −1.42090 | ||||||||
\(845\) | 8.64889 | 0.297531 | ||||||||
\(846\) | −79.2615 | −2.72507 | ||||||||
\(847\) | 15.0079 | 0.515678 | ||||||||
\(848\) | 7.00205 | 0.240451 | ||||||||
\(849\) | 15.9060 | 0.545892 | ||||||||
\(850\) | 9.19510 | 0.315389 | ||||||||
\(851\) | −63.5964 | −2.18006 | ||||||||
\(852\) | −13.9087 | −0.476503 | ||||||||
\(853\) | 52.4751 | 1.79671 | 0.898356 | − | 0.439269i | \(-0.144762\pi\) | ||||
0.898356 | + | 0.439269i | \(0.144762\pi\) | |||||||
\(854\) | −23.4888 | −0.803771 | ||||||||
\(855\) | −3.35374 | −0.114696 | ||||||||
\(856\) | −11.7330 | −0.401026 | ||||||||
\(857\) | −23.3983 | −0.799271 | −0.399635 | − | 0.916674i | \(-0.630863\pi\) | ||||
−0.399635 | + | 0.916674i | \(0.630863\pi\) | |||||||
\(858\) | 0.482394 | 0.0164687 | ||||||||
\(859\) | 8.59949 | 0.293411 | 0.146705 | − | 0.989180i | \(-0.453133\pi\) | ||||
0.146705 | + | 0.989180i | \(0.453133\pi\) | |||||||
\(860\) | 23.9256 | 0.815856 | ||||||||
\(861\) | −6.29770 | −0.214625 | ||||||||
\(862\) | −29.7919 | −1.01472 | ||||||||
\(863\) | 5.71337 | 0.194485 | 0.0972427 | − | 0.995261i | \(-0.468998\pi\) | ||||
0.0972427 | + | 0.995261i | \(0.468998\pi\) | |||||||
\(864\) | 15.4769 | 0.526536 | ||||||||
\(865\) | −24.0416 | −0.817438 | ||||||||
\(866\) | −89.2923 | −3.03428 | ||||||||
\(867\) | 9.34730 | 0.317451 | ||||||||
\(868\) | 8.88306 | 0.301511 | ||||||||
\(869\) | −0.290258 | −0.00984633 | ||||||||
\(870\) | −13.0969 | −0.444026 | ||||||||
\(871\) | 29.0679 | 0.984928 | ||||||||
\(872\) | −42.4394 | −1.43718 | ||||||||
\(873\) | 35.6929 | 1.20802 | ||||||||
\(874\) | 19.4160 | 0.656755 | ||||||||
\(875\) | 14.9062 | 0.503921 | ||||||||
\(876\) | −14.2119 | −0.480177 | ||||||||
\(877\) | −46.9371 | −1.58495 | −0.792477 | − | 0.609902i | \(-0.791209\pi\) | ||||
−0.792477 | + | 0.609902i | \(0.791209\pi\) | |||||||
\(878\) | 93.9256 | 3.16984 | ||||||||
\(879\) | −5.83083 | −0.196669 | ||||||||
\(880\) | −0.0929369 | −0.00313290 | ||||||||
\(881\) | 4.32732 | 0.145791 | 0.0728955 | − | 0.997340i | \(-0.476776\pi\) | ||||
0.0728955 | + | 0.997340i | \(0.476776\pi\) | |||||||
\(882\) | −31.5660 | −1.06288 | ||||||||
\(883\) | −33.9603 | −1.14285 | −0.571427 | − | 0.820653i | \(-0.693610\pi\) | ||||
−0.571427 | + | 0.820653i | \(0.693610\pi\) | |||||||
\(884\) | −18.4213 | −0.619574 | ||||||||
\(885\) | −8.50848 | −0.286009 | ||||||||
\(886\) | 17.8881 | 0.600961 | ||||||||
\(887\) | −45.0169 | −1.51152 | −0.755759 | − | 0.654850i | \(-0.772732\pi\) | ||||
−0.755759 | + | 0.654850i | \(0.772732\pi\) | |||||||
\(888\) | 14.7014 | 0.493347 | ||||||||
\(889\) | −12.6498 | −0.424262 | ||||||||
\(890\) | −34.8770 | −1.16908 | ||||||||
\(891\) | −0.456486 | −0.0152929 | ||||||||
\(892\) | 27.7945 | 0.930630 | ||||||||
\(893\) | −12.3865 | −0.414499 | ||||||||
\(894\) | −13.3604 | −0.446840 | ||||||||
\(895\) | −15.8980 | −0.531412 | ||||||||
\(896\) | −27.0844 | −0.904825 | ||||||||
\(897\) | −23.0903 | −0.770963 | ||||||||
\(898\) | 66.7178 | 2.22640 | ||||||||
\(899\) | 13.3761 | 0.446119 | ||||||||
\(900\) | 29.3669 | 0.978898 | ||||||||
\(901\) | 9.43203 | 0.314226 | ||||||||
\(902\) | −1.38871 | −0.0462390 | ||||||||
\(903\) | 4.33117 | 0.144132 | ||||||||
\(904\) | −53.1701 | −1.76841 | ||||||||
\(905\) | −8.68852 | −0.288816 | ||||||||
\(906\) | −7.73971 | −0.257135 | ||||||||
\(907\) | −12.5106 | −0.415409 | −0.207705 | − | 0.978192i | \(-0.566599\pi\) | ||||
−0.207705 | + | 0.978192i | \(0.566599\pi\) | |||||||
\(908\) | −58.5342 | −1.94253 | ||||||||
\(909\) | 16.3875 | 0.543539 | ||||||||
\(910\) | −18.6137 | −0.617037 | ||||||||
\(911\) | −45.6519 | −1.51251 | −0.756257 | − | 0.654275i | \(-0.772974\pi\) | ||||
−0.756257 | + | 0.654275i | \(0.772974\pi\) | |||||||
\(912\) | −0.521792 | −0.0172782 | ||||||||
\(913\) | −0.314843 | −0.0104198 | ||||||||
\(914\) | 23.1658 | 0.766257 | ||||||||
\(915\) | 5.88771 | 0.194642 | ||||||||
\(916\) | 4.20267 | 0.138860 | ||||||||
\(917\) | −4.85913 | −0.160463 | ||||||||
\(918\) | −9.61376 | −0.317301 | ||||||||
\(919\) | 19.9639 | 0.658547 | 0.329274 | − | 0.944235i | \(-0.393196\pi\) | ||||
0.329274 | + | 0.944235i | \(0.393196\pi\) | |||||||
\(920\) | 38.2652 | 1.26157 | ||||||||
\(921\) | −8.29987 | −0.273490 | ||||||||
\(922\) | 24.2308 | 0.797998 | ||||||||
\(923\) | −29.7658 | −0.979753 | ||||||||
\(924\) | −0.219302 | −0.00721450 | ||||||||
\(925\) | −23.7985 | −0.782491 | ||||||||
\(926\) | −17.0785 | −0.561234 | ||||||||
\(927\) | −36.8871 | −1.21153 | ||||||||
\(928\) | −32.1403 | −1.05506 | ||||||||
\(929\) | 1.14632 | 0.0376096 | 0.0188048 | − | 0.999823i | \(-0.494014\pi\) | ||||
0.0188048 | + | 0.999823i | \(0.494014\pi\) | |||||||
\(930\) | −3.52516 | −0.115594 | ||||||||
\(931\) | −4.93295 | −0.161671 | ||||||||
\(932\) | −16.7422 | −0.548409 | ||||||||
\(933\) | −10.4400 | −0.341791 | ||||||||
\(934\) | 12.4768 | 0.408255 | ||||||||
\(935\) | −0.125190 | −0.00409414 | ||||||||
\(936\) | −38.8239 | −1.26900 | ||||||||
\(937\) | −31.0541 | −1.01449 | −0.507246 | − | 0.861801i | \(-0.669336\pi\) | ||||
−0.507246 | + | 0.861801i | \(0.669336\pi\) | |||||||
\(938\) | −20.9211 | −0.683099 | ||||||||
\(939\) | 4.11121 | 0.134164 | ||||||||
\(940\) | −58.5664 | −1.91022 | ||||||||
\(941\) | −15.5178 | −0.505865 | −0.252932 | − | 0.967484i | \(-0.581395\pi\) | ||||
−0.252932 | + | 0.967484i | \(0.581395\pi\) | |||||||
\(942\) | 25.8726 | 0.842976 | ||||||||
\(943\) | 66.4721 | 2.16463 | ||||||||
\(944\) | 9.62858 | 0.313384 | ||||||||
\(945\) | −6.13585 | −0.199599 | ||||||||
\(946\) | 0.955070 | 0.0310520 | ||||||||
\(947\) | 51.2678 | 1.66598 | 0.832990 | − | 0.553288i | \(-0.186627\pi\) | ||||
0.832990 | + | 0.553288i | \(0.186627\pi\) | |||||||
\(948\) | −7.70535 | −0.250258 | ||||||||
\(949\) | −30.4148 | −0.987306 | ||||||||
\(950\) | 7.26569 | 0.235730 | ||||||||
\(951\) | −15.5200 | −0.503270 | ||||||||
\(952\) | 5.52634 | 0.179110 | ||||||||
\(953\) | −41.7626 | −1.35282 | −0.676411 | − | 0.736524i | \(-0.736466\pi\) | ||||
−0.676411 | + | 0.736524i | \(0.736466\pi\) | |||||||
\(954\) | 47.6912 | 1.54406 | ||||||||
\(955\) | −3.11304 | −0.100736 | ||||||||
\(956\) | 40.4760 | 1.30909 | ||||||||
\(957\) | −0.330225 | −0.0106747 | ||||||||
\(958\) | −74.0502 | −2.39245 | ||||||||
\(959\) | −29.0575 | −0.938316 | ||||||||
\(960\) | 9.90909 | 0.319814 | ||||||||
\(961\) | −27.3997 | −0.883861 | ||||||||
\(962\) | 75.4821 | 2.43364 | ||||||||
\(963\) | −9.29039 | −0.299379 | ||||||||
\(964\) | 79.1373 | 2.54884 | ||||||||
\(965\) | −7.18610 | −0.231329 | ||||||||
\(966\) | 16.6189 | 0.534703 | ||||||||
\(967\) | 38.4958 | 1.23794 | 0.618971 | − | 0.785414i | \(-0.287550\pi\) | ||||
0.618971 | + | 0.785414i | \(0.287550\pi\) | |||||||
\(968\) | 36.6188 | 1.17697 | ||||||||
\(969\) | −0.702873 | −0.0225795 | ||||||||
\(970\) | 41.7540 | 1.34064 | ||||||||
\(971\) | 58.0340 | 1.86240 | 0.931200 | − | 0.364509i | \(-0.118763\pi\) | ||||
0.931200 | + | 0.364509i | \(0.118763\pi\) | |||||||
\(972\) | −47.0436 | −1.50892 | ||||||||
\(973\) | 18.0259 | 0.577884 | ||||||||
\(974\) | −7.31705 | −0.234453 | ||||||||
\(975\) | −8.64067 | −0.276723 | ||||||||
\(976\) | −6.66280 | −0.213271 | ||||||||
\(977\) | −18.3580 | −0.587324 | −0.293662 | − | 0.955909i | \(-0.594874\pi\) | ||||
−0.293662 | + | 0.955909i | \(0.594874\pi\) | |||||||
\(978\) | −21.0594 | −0.673407 | ||||||||
\(979\) | −0.879390 | −0.0281054 | ||||||||
\(980\) | −23.3241 | −0.745062 | ||||||||
\(981\) | −33.6042 | −1.07290 | ||||||||
\(982\) | −54.8554 | −1.75051 | ||||||||
\(983\) | 62.4558 | 1.99203 | 0.996015 | − | 0.0891866i | \(-0.0284267\pi\) | ||||
0.996015 | + | 0.0891866i | \(0.0284267\pi\) | |||||||
\(984\) | −15.3662 | −0.489856 | ||||||||
\(985\) | −0.722312 | −0.0230148 | ||||||||
\(986\) | 19.9645 | 0.635800 | ||||||||
\(987\) | −10.6021 | −0.337468 | ||||||||
\(988\) | −14.5559 | −0.463086 | ||||||||
\(989\) | −45.7155 | −1.45367 | ||||||||
\(990\) | −0.632997 | −0.0201180 | ||||||||
\(991\) | 5.20461 | 0.165330 | 0.0826649 | − | 0.996577i | \(-0.473657\pi\) | ||||
0.0826649 | + | 0.996577i | \(0.473657\pi\) | |||||||
\(992\) | −8.65088 | −0.274666 | ||||||||
\(993\) | 7.65080 | 0.242791 | ||||||||
\(994\) | 21.4234 | 0.679510 | ||||||||
\(995\) | −16.9172 | −0.536312 | ||||||||
\(996\) | −8.35799 | −0.264833 | ||||||||
\(997\) | −7.56919 | −0.239719 | −0.119859 | − | 0.992791i | \(-0.538244\pi\) | ||||
−0.119859 | + | 0.992791i | \(0.538244\pi\) | |||||||
\(998\) | 13.6682 | 0.432661 | ||||||||
\(999\) | 24.8821 | 0.787235 |
(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 | 4003.2.a.c.1.19 | ✓ | 179 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4003.2.a.c.1.19 | ✓ | 179 | 1.1 | even | 1 | trivial |