Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(1,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, 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("1900.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.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: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.321.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.46050\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1 |
$q$-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 | ||||||||
\(3\) | 1.59358 | 0.920053 | 0.460027 | − | 0.887905i | \(-0.347840\pi\) | ||||
0.460027 | + | 0.887905i | \(0.347840\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.51459 | −1.70635 | −0.853177 | − | 0.521621i | \(-0.825327\pi\) | ||||
−0.853177 | + | 0.521621i | \(0.825327\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.460505 | −0.153502 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.593579 | 0.178971 | 0.0894855 | − | 0.995988i | \(-0.471478\pi\) | ||||
0.0894855 | + | 0.995988i | \(0.471478\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.05408 | 1.12440 | 0.562200 | − | 0.827001i | \(-0.309955\pi\) | ||||
0.562200 | + | 0.827001i | \(0.309955\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.32743 | 1.29209 | 0.646046 | − | 0.763299i | \(-0.276421\pi\) | ||||
0.646046 | + | 0.763299i | \(0.276421\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.19436 | −1.56994 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.46050 | 1.55562 | 0.777811 | − | 0.628498i | \(-0.216330\pi\) | ||||
0.777811 | + | 0.628498i | \(0.216330\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.51459 | −1.06128 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.32743 | −0.432193 | −0.216096 | − | 0.976372i | \(-0.569333\pi\) | ||||
−0.216096 | + | 0.976372i | \(0.569333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.97509 | 1.25276 | 0.626382 | − | 0.779516i | \(-0.284535\pi\) | ||||
0.626382 | + | 0.779516i | \(0.284535\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.945916 | 0.164663 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.40642 | −0.560012 | −0.280006 | − | 0.959998i | \(-0.590336\pi\) | ||||
−0.280006 | + | 0.959998i | \(0.590336\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.46050 | 1.03451 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.38151 | −1.15280 | −0.576399 | − | 0.817168i | \(-0.695543\pi\) | ||||
−0.576399 | + | 0.817168i | \(0.695543\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.18716 | 0.943533 | 0.471766 | − | 0.881724i | \(-0.343617\pi\) | ||||
0.471766 | + | 0.881724i | \(0.343617\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.7089 | 1.85379 | 0.926895 | − | 0.375321i | \(-0.122467\pi\) | ||||
0.926895 | + | 0.375321i | \(0.122467\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.3815 | 1.91164 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.48968 | 1.18879 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.84202 | −1.21454 | −0.607272 | − | 0.794494i | \(-0.707736\pi\) | ||||
−0.607272 | + | 0.794494i | \(0.707736\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.59358 | 0.211075 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.10817 | 0.534838 | 0.267419 | − | 0.963580i | \(-0.413829\pi\) | ||||
0.267419 | + | 0.963580i | \(0.413829\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.89610 | 1.26707 | 0.633533 | − | 0.773716i | \(-0.281604\pi\) | ||||
0.633533 | + | 0.773716i | \(0.281604\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.07899 | 0.261928 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0613 | 1.47352 | 0.736760 | − | 0.676154i | \(-0.236355\pi\) | ||||
0.736760 | + | 0.676154i | \(0.236355\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.8889 | 1.43126 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.10817 | −0.843584 | −0.421792 | − | 0.906693i | \(-0.638599\pi\) | ||||
−0.421792 | + | 0.906693i | \(0.638599\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.27335 | 0.617198 | 0.308599 | − | 0.951192i | \(-0.400140\pi\) | ||||
0.308599 | + | 0.951192i | \(0.400140\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.67977 | −0.305388 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.96790 | −0.446423 | −0.223212 | − | 0.974770i | \(-0.571654\pi\) | ||||
−0.223212 | + | 0.974770i | \(0.571654\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.40642 | −0.822936 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.53950 | 0.827567 | 0.413784 | − | 0.910375i | \(-0.364207\pi\) | ||||
0.413784 | + | 0.910375i | \(0.364207\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.70895 | −0.397641 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.19436 | 0.974600 | 0.487300 | − | 0.873235i | \(-0.337982\pi\) | ||||
0.487300 | + | 0.873235i | \(0.337982\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.3025 | −1.91863 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.1154 | 1.15261 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.42840 | 0.652705 | 0.326353 | − | 0.945248i | \(-0.394180\pi\) | ||||
0.326353 | + | 0.945248i | \(0.394180\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.273346 | −0.0274723 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.8099 | −1.17513 | −0.587565 | − | 0.809177i | \(-0.699913\pi\) | ||||
−0.587565 | + | 0.809177i | \(0.699913\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.4648 | 1.81939 | 0.909694 | − | 0.415279i | \(-0.136316\pi\) | ||||
0.909694 | + | 0.415279i | \(0.136316\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.431327 | 0.0416979 | 0.0208490 | − | 0.999783i | \(-0.493363\pi\) | ||||
0.0208490 | + | 0.999783i | \(0.493363\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.11537 | −0.681528 | −0.340764 | − | 0.940149i | \(-0.610686\pi\) | ||||
−0.340764 | + | 0.940149i | \(0.610686\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.42840 | −0.515241 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.16225 | −0.297480 | −0.148740 | − | 0.988876i | \(-0.547522\pi\) | ||||
−0.148740 | + | 0.988876i | \(0.547522\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.86693 | −0.172597 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24.0512 | −2.20477 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6477 | −0.967969 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.7630 | −1.06064 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.4107 | −1.36748 | −0.683739 | − | 0.729727i | \(-0.739647\pi\) | ||||
−0.683739 | + | 0.729727i | \(0.739647\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.85973 | 0.868101 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.0072 | 0.961703 | 0.480852 | − | 0.876802i | \(-0.340328\pi\) | ||||
0.480852 | + | 0.876802i | \(0.340328\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.51459 | −0.391465 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.72665 | 0.745568 | 0.372784 | − | 0.927918i | \(-0.378403\pi\) | ||||
0.372784 | + | 0.927918i | \(0.378403\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.64047 | −0.648056 | −0.324028 | − | 0.946048i | \(-0.605037\pi\) | ||||
−0.324028 | + | 0.946048i | \(0.605037\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.2527 | 1.70559 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.40642 | 0.201235 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 21.3245 | 1.75882 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.67684 | −0.546988 | −0.273494 | − | 0.961874i | \(-0.588179\pi\) | ||||
−0.273494 | + | 0.961874i | \(0.588179\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.1623 | −1.55940 | −0.779701 | − | 0.626152i | \(-0.784629\pi\) | ||||
−0.779701 | + | 0.626152i | \(0.784629\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.45331 | −0.198338 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.7558 | −1.33726 | −0.668630 | − | 0.743595i | \(-0.733119\pi\) | ||||
−0.668630 | + | 0.743595i | \(0.733119\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.0905 | −1.11745 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −33.6811 | −2.65444 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.32023 | 0.181735 | 0.0908673 | − | 0.995863i | \(-0.471036\pi\) | ||||
0.0908673 | + | 0.995863i | \(0.471036\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.56867 | 0.663064 | 0.331532 | − | 0.943444i | \(-0.392435\pi\) | ||||
0.331532 | + | 0.943444i | \(0.392435\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.43560 | 0.264277 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.460505 | −0.0352157 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.04689 | −0.687822 | −0.343911 | − | 0.939002i | \(-0.611752\pi\) | ||||
−0.343911 | + | 0.939002i | \(0.611752\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.54669 | 0.492080 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.4969 | 1.00880 | 0.504402 | − | 0.863469i | \(-0.331713\pi\) | ||||
0.504402 | + | 0.863469i | \(0.331713\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.00000 | −0.520306 | −0.260153 | − | 0.965567i | \(-0.583773\pi\) | ||||
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.7702 | 1.16577 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.16225 | 0.231247 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 24.8961 | 1.81093 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.4356 | −0.899808 | −0.449904 | − | 0.893077i | \(-0.648542\pi\) | ||||
−0.449904 | + | 0.893077i | \(0.648542\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.64766 | 0.118601 | 0.0593007 | − | 0.998240i | \(-0.481113\pi\) | ||||
0.0593007 | + | 0.998240i | \(0.481113\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.3566 | 1.52160 | 0.760798 | − | 0.648989i | \(-0.224808\pi\) | ||||
0.760798 | + | 0.648989i | \(0.224808\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.2632 | −0.869317 | −0.434658 | − | 0.900595i | \(-0.643131\pi\) | ||||
−0.434658 | + | 0.900595i | \(0.643131\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.2206 | 1.35572 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.5074 | 0.737474 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.43560 | −0.238791 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.593579 | 0.0410587 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.3743 | 1.33378 | 0.666892 | − | 0.745155i | \(-0.267624\pi\) | ||||
0.666892 | + | 0.745155i | \(0.267624\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.3274 | −0.776143 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −31.4897 | −2.13766 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.40350 | 0.567856 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.5979 | 1.45283 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.5117 | −1.37356 | −0.686781 | − | 0.726864i | \(-0.740977\pi\) | ||||
−0.686781 | + | 0.726864i | \(0.740977\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.91381 | −0.259769 | −0.129884 | − | 0.991529i | \(-0.541461\pi\) | ||||
−0.129884 | + | 0.991529i | \(0.541461\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.58638 | 0.236995 | 0.118497 | − | 0.992954i | \(-0.462192\pi\) | ||||
0.118497 | + | 0.992954i | \(0.462192\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.27042 | −0.280973 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.5294 | 0.820827 | 0.410413 | − | 0.911900i | \(-0.365384\pi\) | ||||
0.410413 | + | 0.911900i | \(0.365384\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.32316 | −0.410733 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.5218 | −1.52150 | −0.760749 | − | 0.649046i | \(-0.775168\pi\) | ||||
−0.760749 | + | 0.649046i | \(0.775168\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.22353 | 0.594140 | 0.297070 | − | 0.954856i | \(-0.403991\pi\) | ||||
0.297070 | + | 0.954856i | \(0.403991\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.74105 | 0.304138 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.05408 | 0.257955 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0148 | 0.761406 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.7237 | 1.18183 | 0.590916 | − | 0.806733i | \(-0.298767\pi\) | ||||
0.590916 | + | 0.806733i | \(0.298767\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.42840 | 0.278411 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.1196 | −1.69168 | −0.845838 | − | 0.533439i | \(-0.820899\pi\) | ||||
−0.845838 | + | 0.533439i | \(0.820899\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.3786 | 0.955579 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.07179 | 0.0663423 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.5510 | −1.14390 | −0.571951 | − | 0.820288i | \(-0.693813\pi\) | ||||
−0.571951 | + | 0.820288i | \(0.693813\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.6519 | 0.896684 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.1331 | −1.59336 | −0.796681 | − | 0.604400i | \(-0.793413\pi\) | ||||
−0.796681 | + | 0.604400i | \(0.793413\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.95311 | 0.118643 | 0.0593216 | − | 0.998239i | \(-0.481106\pi\) | ||||
0.0593216 | + | 0.998239i | \(0.481106\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −29.1665 | −1.76524 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.46770 | 0.148270 | 0.0741349 | − | 0.997248i | \(-0.476380\pi\) | ||||
0.0741349 | + | 0.997248i | \(0.476380\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.21206 | −0.192301 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.8712 | 1.48369 | 0.741846 | − | 0.670571i | \(-0.233951\pi\) | ||||
0.741846 | + | 0.670571i | \(0.233951\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.55389 | −0.567920 | −0.283960 | − | 0.958836i | \(-0.591648\pi\) | ||||
−0.283960 | + | 0.958836i | \(0.591648\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 33.3245 | 1.96708 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.3815 | 0.669501 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.2442 | 0.600524 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.2527 | 0.657390 | 0.328695 | − | 0.944436i | \(-0.393391\pi\) | ||||
0.328695 | + | 0.944436i | \(0.393391\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.27335 | −0.189939 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 30.2455 | 1.74914 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.9325 | −1.61000 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.8200 | −1.08118 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.2877 | 0.701298 | 0.350649 | − | 0.936507i | \(-0.385961\pi\) | ||||
0.350649 | + | 0.936507i | \(0.385961\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 29.4251 | 1.67393 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.1331 | 0.971528 | 0.485764 | − | 0.874090i | \(-0.338542\pi\) | ||||
0.485764 | + | 0.874090i | \(0.338542\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.98229 | −0.281616 | −0.140808 | − | 0.990037i | \(-0.544970\pi\) | ||||
−0.140808 | + | 0.990037i | \(0.544970\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.3963 | −1.25790 | −0.628951 | − | 0.777445i | \(-0.716515\pi\) | ||||
−0.628951 | + | 0.777445i | \(0.716515\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.38151 | −0.0773500 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.687353 | 0.0383643 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.32743 | 0.296426 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.3389 | −0.627043 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −57.3757 | −3.16322 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.06887 | 0.223645 | 0.111823 | − | 0.993728i | \(-0.464331\pi\) | ||||
0.111823 | + | 0.993728i | \(0.464331\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.56867 | 0.0859628 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.52179 | −0.518685 | −0.259342 | − | 0.965785i | \(-0.583506\pi\) | ||||
−0.259342 | + | 0.965785i | \(0.583506\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.03930 | −0.273697 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.14027 | 0.224208 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −28.8099 | −1.55559 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.1052 | −0.757209 | −0.378605 | − | 0.925559i | \(-0.623596\pi\) | ||||
−0.378605 | + | 0.925559i | \(0.623596\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.2704 | 0.817407 | 0.408703 | − | 0.912667i | \(-0.365981\pi\) | ||||
0.408703 | + | 0.912667i | \(0.365981\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.3566 | −1.19331 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.6591 | 1.68505 | 0.842523 | − | 0.538661i | \(-0.181070\pi\) | ||||
0.842523 | + | 0.538661i | \(0.181070\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −38.3274 | −2.02850 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.5366 | −1.40055 | −0.700273 | − | 0.713875i | \(-0.746939\pi\) | ||||
−0.700273 | + | 0.713875i | \(0.746939\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.9679 | −0.890584 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.2379 | 1.63061 | 0.815303 | − | 0.579034i | \(-0.196570\pi\) | ||||
0.815303 | + | 0.579034i | \(0.196570\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.39922 | 0.176957 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 39.9181 | 2.07244 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.8961 | −1.54796 | −0.773981 | − | 0.633209i | \(-0.781737\pi\) | ||||
−0.773981 | + | 0.633209i | \(0.781737\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.43560 | −0.485958 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −36.6093 | −1.88049 | −0.940247 | − | 0.340492i | \(-0.889406\pi\) | ||||
−0.940247 | + | 0.340492i | \(0.889406\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.5582 | −1.25815 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.9751 | 1.17397 | 0.586986 | − | 0.809597i | \(-0.300314\pi\) | ||||
0.586986 | + | 0.809597i | \(0.300314\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.84922 | −0.144834 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.4183 | −1.39016 | −0.695081 | − | 0.718931i | \(-0.744631\pi\) | ||||
−0.695081 | + | 0.718931i | \(0.744631\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 39.7453 | 2.01001 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.5408 | 0.884818 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.05408 | −0.454411 | −0.227206 | − | 0.973847i | \(-0.572959\pi\) | ||||
−0.227206 | + | 0.973847i | \(0.572959\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.19436 | −0.360168 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.21926 | 0.360513 | 0.180256 | − | 0.983620i | \(-0.442307\pi\) | ||||
0.180256 | + | 0.983620i | \(0.442307\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.2776 | 1.40861 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.02198 | −0.100226 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.08619 | 0.0537085 | 0.0268543 | − | 0.999639i | \(-0.491451\pi\) | ||||
0.0268543 | + | 0.999639i | \(0.491451\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.9066 | 0.685963 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.5467 | −0.912623 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.1757 | −0.596246 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.9899 | 0.536891 | 0.268445 | − | 0.963295i | \(-0.413490\pi\) | ||||
0.268445 | + | 0.963295i | \(0.413490\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.30545 | 0.258572 | 0.129286 | − | 0.991607i | \(-0.458732\pi\) | ||||
0.129286 | + | 0.991607i | \(0.458732\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.85253 | −0.284560 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −44.6768 | −2.16206 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.83482 | 0.185147 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.0905 | 0.534209 | 0.267104 | − | 0.963668i | \(-0.413933\pi\) | ||||
0.267104 | + | 0.963668i | \(0.413933\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.1652 | −0.584621 | −0.292311 | − | 0.956323i | \(-0.594424\pi\) | ||||
−0.292311 | + | 0.956323i | \(0.594424\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.46050 | 0.356884 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.5586 | 1.31530 | 0.657649 | − | 0.753325i | \(-0.271551\pi\) | ||||
0.657649 | + | 0.753325i | \(0.271551\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.16225 | −0.293441 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.1800 | 0.673710 | 0.336855 | − | 0.941556i | \(-0.390637\pi\) | ||||
0.336855 | + | 0.941556i | \(0.390637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.6401 | −0.503258 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.9895 | −0.707398 | −0.353699 | − | 0.935359i | \(-0.615076\pi\) | ||||
−0.353699 | + | 0.935359i | \(0.615076\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.38151 | −0.206317 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −30.5366 | −1.43473 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.1331 | −0.988564 | −0.494282 | − | 0.869302i | \(-0.664569\pi\) | ||||
−0.494282 | + | 0.869302i | \(0.664569\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −29.3786 | −1.37128 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.5801 | 1.89001 | 0.945003 | − | 0.327062i | \(-0.106059\pi\) | ||||
0.945003 | + | 0.327062i | \(0.106059\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.7381 | 0.591991 | 0.295995 | − | 0.955189i | \(-0.404349\pi\) | ||||
0.295995 | + | 0.955189i | \(0.404349\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.95739 | −0.414498 | −0.207249 | − | 0.978288i | \(-0.566451\pi\) | ||||
−0.207249 | + | 0.978288i | \(0.566451\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −54.4517 | −2.51435 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −26.7017 | −1.23035 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.67257 | 0.168865 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.07179 | 0.186435 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.32451 | 0.288974 | 0.144487 | − | 0.989507i | \(-0.453847\pi\) | ||||
0.144487 | + | 0.989507i | \(0.453847\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.8099 | −0.629678 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −53.6735 | −2.44223 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.4461 | 0.654616 | 0.327308 | − | 0.944918i | \(-0.393859\pi\) | ||||
0.327308 | + | 0.944918i | \(0.393859\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.69748 | 0.167206 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.28813 | 0.283779 | 0.141890 | − | 0.989882i | \(-0.454682\pi\) | ||||
0.141890 | + | 0.989882i | \(0.454682\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.3992 | −0.558433 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.0905 | 1.43945 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.9181 | −1.42885 | −0.714425 | − | 0.699712i | \(-0.753312\pi\) | ||||
−0.714425 | + | 0.699712i | \(0.753312\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.6549 | 0.610054 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.7601 | 0.702708 | 0.351354 | − | 0.936243i | \(-0.385721\pi\) | ||||
0.351354 | + | 0.936243i | \(0.385721\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.47490 | 0.243149 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.1885 | 1.16079 | 0.580393 | − | 0.814337i | \(-0.302899\pi\) | ||||
0.580393 | + | 0.814337i | \(0.302899\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.8070 | −1.05316 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.51459 | −0.243475 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.54377 | 0.331775 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.4169 | −0.632833 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −42.3245 | −1.85427 | −0.927135 | − | 0.374727i | \(-0.877736\pi\) | ||||
−0.927135 | + | 0.374727i | \(0.877736\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.3714 | −0.847052 | −0.423526 | − | 0.905884i | \(-0.639208\pi\) | ||||
−0.423526 | + | 0.905884i | \(0.639208\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 37.1593 | 1.61869 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.6591 | 1.41996 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.89183 | −0.0820985 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29.9253 | −1.29621 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.5083 | 0.928154 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.94299 | 0.342129 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.87451 | −0.252565 | −0.126282 | − | 0.991994i | \(-0.540305\pi\) | ||||
−0.126282 | + | 0.991994i | \(0.540305\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.1551 | −0.478709 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.2556 | −0.866069 | −0.433034 | − | 0.901377i | \(-0.642557\pi\) | ||||
−0.433034 | + | 0.901377i | \(0.642557\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.55720 | −0.194497 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.32743 | −0.0991519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.9134 | 0.761756 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.76010 | −0.159321 | −0.0796604 | − | 0.996822i | \(-0.525384\pi\) | ||||
−0.0796604 | + | 0.996822i | \(0.525384\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.0833 | 1.06091 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.03930 | 0.212759 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.2484 | 0.474065 | 0.237033 | − | 0.971502i | \(-0.423825\pi\) | ||||
0.237033 | + | 0.971502i | \(0.423825\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 33.4369 | 1.40422 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.2949 | 0.515431 | 0.257715 | − | 0.966221i | \(-0.417030\pi\) | ||||
0.257715 | + | 0.966221i | \(0.417030\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.8784 | 0.580793 | 0.290396 | − | 0.956906i | \(-0.406213\pi\) | ||||
0.290396 | + | 0.956906i | \(0.406213\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.8171 | −0.827872 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.1052 | 1.29493 | 0.647464 | − | 0.762096i | \(-0.275830\pi\) | ||||
0.647464 | + | 0.762096i | \(0.275830\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.62568 | 0.109120 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −34.0377 | −1.41212 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.24844 | −0.217368 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.7807 | 1.55938 | 0.779689 | − | 0.626167i | \(-0.215377\pi\) | ||||
0.779689 | + | 0.626167i | \(0.215377\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.97509 | 0.287404 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 34.0335 | 1.39995 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −40.5949 | −1.66703 | −0.833517 | − | 0.552494i | \(-0.813676\pi\) | ||||
−0.833517 | + | 0.552494i | \(0.813676\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.5424 | −0.799818 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.2776 | 0.746803 | 0.373402 | − | 0.927670i | \(-0.378191\pi\) | ||||
0.373402 | + | 0.927670i | \(0.378191\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.4313 | −0.547875 | −0.273938 | − | 0.961747i | \(-0.588326\pi\) | ||||
−0.273938 | + | 0.961747i | \(0.588326\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.55428 | −0.226188 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −47.2235 | −1.91674 | −0.958372 | − | 0.285522i | \(-0.907833\pi\) | ||||
−0.958372 | + | 0.285522i | \(0.907833\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.7444 | 0.678516 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 51.5231 | 2.08440 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.2268 | 0.413059 | 0.206529 | − | 0.978440i | \(-0.433783\pi\) | ||||
0.206529 | + | 0.978440i | \(0.433783\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.3829 | −1.30368 | −0.651842 | − | 0.758354i | \(-0.726004\pi\) | ||||
−0.651842 | + | 0.758354i | \(0.726004\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.8784 | 0.798980 | 0.399490 | − | 0.916738i | \(-0.369187\pi\) | ||||
0.399490 | + | 0.916738i | \(0.369187\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −41.1416 | −1.65096 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −41.5087 | −1.66301 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.945916 | 0.0377762 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.1475 | −0.723587 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.5103 | 0.577647 | 0.288823 | − | 0.957382i | \(-0.406736\pi\) | ||||
0.288823 | + | 0.957382i | \(0.406736\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 30.8745 | 1.22715 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 54.2498 | 2.14945 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.27335 | 0.129492 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.15798 | 0.124733 | 0.0623664 | − | 0.998053i | \(-0.480135\pi\) | ||||
0.0623664 | + | 0.998053i | \(0.480135\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.0000 | −0.867595 | −0.433798 | − | 0.901010i | \(-0.642827\pi\) | ||||
−0.433798 | + | 0.901010i | \(0.642827\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.36673 | −0.0537317 | −0.0268659 | − | 0.999639i | \(-0.508553\pi\) | ||||
−0.0268659 | + | 0.999639i | \(0.508553\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.43852 | 0.0957204 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −50.1813 | −1.96676 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.0220 | −0.666122 | −0.333061 | − | 0.942905i | \(-0.608081\pi\) | ||||
−0.333061 | + | 0.942905i | \(0.608081\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.42840 | −0.0947410 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.6883 | 0.572175 | 0.286088 | − | 0.958203i | \(-0.407645\pi\) | ||||
0.286088 | + | 0.958203i | \(0.407645\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.86693 | −0.0726150 | −0.0363075 | − | 0.999341i | \(-0.511560\pi\) | ||||
−0.0363075 | + | 0.999341i | \(0.511560\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 34.4179 | 1.33668 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.3638 | −0.672329 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −32.6870 | −1.26375 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.87412 | 0.226768 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.3465 | −0.591564 | −0.295782 | − | 0.955256i | \(-0.595580\pi\) | ||||
−0.295782 | + | 0.955256i | \(0.595580\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.3422 | 0.666515 | 0.333258 | − | 0.942836i | \(-0.391852\pi\) | ||||
0.333258 | + | 0.942836i | \(0.391852\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.0216 | −1.11375 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.23697 | −0.239001 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 40.9473 | 1.56680 | 0.783402 | − | 0.621516i | \(-0.213483\pi\) | ||||
0.783402 | + | 0.621516i | \(0.213483\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.71518 | 0.218048 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −35.8463 | −1.36563 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.65525 | 0.215136 | 0.107568 | − | 0.994198i | \(-0.465694\pi\) | ||||
0.107568 | + | 0.994198i | \(0.465694\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.23405 | 0.0468775 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −39.3245 | −1.48952 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.9665 | 0.755204 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.3786 | 1.33623 | 0.668115 | − | 0.744058i | \(-0.267101\pi\) | ||||
0.668115 | + | 0.744058i | \(0.267101\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.40642 | −0.128476 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 53.3169 | 2.00519 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.2852 | −1.55050 | −0.775249 | − | 0.631655i | \(-0.782376\pi\) | ||||
−0.775249 | + | 0.631655i | \(0.782376\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.82724 | 0.0685267 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 52.0377 | 1.94883 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −37.4838 | −1.39986 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.0689 | 0.636561 | 0.318281 | − | 0.947997i | \(-0.396895\pi\) | ||||
0.318281 | + | 0.947997i | \(0.396895\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −83.3609 | −3.10452 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.6984 | 0.546641 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.8741 | −1.03379 | −0.516897 | − | 0.856048i | \(-0.672913\pi\) | ||||
−0.516897 | + | 0.856048i | \(0.672913\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.7745 | 1.10276 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32.9617 | 1.21913 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.7922 | −1.28508 | −0.642540 | − | 0.766252i | \(-0.722119\pi\) | ||||
−0.642540 | + | 0.766252i | \(0.722119\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.15933 | 0.263717 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −49.0128 | −1.80297 | −0.901483 | − | 0.432815i | \(-0.857520\pi\) | ||||
−0.901483 | + | 0.432815i | \(0.857520\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.46050 | 0.237333 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.8142 | −0.763599 | −0.381799 | − | 0.924245i | \(-0.624695\pi\) | ||||
−0.381799 | + | 0.924245i | \(0.624695\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.47197 | −0.127033 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.94726 | −0.0711514 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.4457 | −0.527132 | −0.263566 | − | 0.964641i | \(-0.584899\pi\) | ||||
−0.263566 | + | 0.964641i | \(0.584899\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.8377 | 1.08735 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.11537 | 0.294958 | 0.147479 | − | 0.989065i | \(-0.452884\pi\) | ||||
0.147479 | + | 0.989065i | \(0.452884\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.05701 | 0.256153 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.2967 | 1.09825 | 0.549127 | − | 0.835739i | \(-0.314960\pi\) | ||||
0.549127 | + | 0.835739i | \(0.314960\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.1230 | 1.16293 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.6549 | 0.601372 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.4471 | 1.45856 | 0.729279 | − | 0.684216i | \(-0.239856\pi\) | ||||
0.729279 | + | 0.684216i | \(0.239856\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.2173 | −1.55643 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.16518 | −0.0778760 | −0.0389380 | − | 0.999242i | \(-0.512397\pi\) | ||||
−0.0389380 | + | 0.999242i | \(0.512397\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.5070 | 0.879184 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.38151 | −0.264470 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.21926 | −0.150977 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.8348 | 0.458679 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.4284 | −0.942071 | −0.471035 | − | 0.882114i | \(-0.656120\pi\) | ||||
−0.471035 | + | 0.882114i | \(0.656120\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −29.5624 | −1.05245 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.2763 | 0.507606 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.1196 | 1.42469 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39.5041 | −1.39931 | −0.699653 | − | 0.714483i | \(-0.746662\pi\) | ||||
−0.699653 | + | 0.714483i | \(0.746662\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 67.7060 | 2.39527 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.23405 | −0.149603 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.13015 | 0.110461 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −41.6451 | −1.46598 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.4078 | −0.963606 | −0.481803 | − | 0.876280i | \(-0.660018\pi\) | ||||
−0.481803 | + | 0.876280i | \(0.660018\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −50.7467 | −1.78196 | −0.890978 | − | 0.454046i | \(-0.849980\pi\) | ||||
−0.890978 | + | 0.454046i | \(0.849980\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.11244 | 0.109158 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.18716 | 0.216461 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.42840 | 0.294512 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.7410 | 0.444666 | 0.222333 | − | 0.974971i | \(-0.428633\pi\) | ||||
0.222333 | + | 0.974971i | \(0.428633\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.1623 | 0.598239 | 0.299119 | − | 0.954216i | \(-0.403307\pi\) | ||||
0.299119 | + | 0.954216i | \(0.403307\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 53.6735 | 1.86641 | 0.933206 | − | 0.359343i | \(-0.116999\pi\) | ||||
0.933206 | + | 0.359343i | \(0.116999\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.45331 | 0.258864 | 0.129432 | − | 0.991588i | \(-0.458685\pi\) | ||||
0.129432 | + | 0.991588i | \(0.458685\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.93248 | 0.136416 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 71.2891 | 2.47002 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −38.4648 | −1.32954 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 52.8257 | 1.82374 | 0.911872 | − | 0.410474i | \(-0.134637\pi\) | ||||
0.911872 | + | 0.410474i | \(0.134637\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.5831 | −0.813209 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 39.6342 | 1.36508 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48.0698 | 1.65170 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.2249 | −0.522517 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.4136 | −0.871168 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.6663 | −0.570644 | −0.285322 | − | 0.958432i | \(-0.592101\pi\) | ||||
−0.285322 | + | 0.958432i | \(0.592101\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.6654 | 0.569278 | 0.284639 | − | 0.958635i | \(-0.408126\pi\) | ||||
0.284639 | + | 0.958635i | \(0.408126\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.0010 | −1.02362 | −0.511810 | − | 0.859099i | \(-0.671025\pi\) | ||||
−0.511810 | + | 0.859099i | \(0.671025\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 53.1052 | 1.80982 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.0498 | 0.784625 | 0.392312 | − | 0.919832i | \(-0.371675\pi\) | ||||
0.392312 | + | 0.919832i | \(0.371675\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.1373 | 0.615977 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.35526 | −0.0798968 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 48.8975 | 1.65683 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.96031 | −0.100191 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.9938 | −0.843979 | −0.421990 | − | 0.906601i | \(-0.638668\pi\) | ||||
−0.421990 | + | 0.906601i | \(0.638668\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17.9321 | 0.604834 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.2590 | 0.480396 | 0.240198 | − | 0.970724i | \(-0.422788\pi\) | ||||
0.240198 | + | 0.970724i | \(0.422788\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.6021 | 1.60194 | 0.800970 | − | 0.598705i | \(-0.204318\pi\) | ||||
0.800970 | + | 0.598705i | \(0.204318\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.6959 | 1.13140 | 0.565699 | − | 0.824612i | \(-0.308607\pi\) | ||||
0.565699 | + | 0.824612i | \(0.308607\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 69.5729 | 2.33340 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.39630 | −0.147282 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.7089 | 0.425289 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 48.1986 | 1.60931 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.2340 | −0.541436 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −47.1052 | −1.56930 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −44.5126 | −1.48129 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.05701 | −0.267529 | −0.133764 | − | 0.991013i | \(-0.542707\pi\) | ||||
−0.133764 | + | 0.991013i | \(0.542707\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.43852 | 0.180384 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.6942 | −0.718760 | −0.359380 | − | 0.933191i | \(-0.617012\pi\) | ||||
−0.359380 | + | 0.933191i | \(0.617012\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.47529 | 0.148110 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −49.6930 | −1.64101 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.7525 | −1.41028 | −0.705138 | − | 0.709070i | \(-0.749115\pi\) | ||||
−0.705138 | + | 0.709070i | \(0.749115\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.5815 | 0.645232 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28.8171 | −0.948527 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.50312 | −0.279279 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.8290 | 1.07708 | 0.538542 | − | 0.842599i | \(-0.318975\pi\) | ||||
0.538542 | + | 0.842599i | \(0.318975\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.3815 | 0.438561 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27.3029 | 0.893857 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.6313 | −0.673995 | −0.336998 | − | 0.941505i | \(-0.609411\pi\) | ||||
−0.336998 | + | 0.941505i | \(0.609411\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.93968 | −0.259102 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.25271 | −0.0734363 | −0.0367182 | − | 0.999326i | \(-0.511690\pi\) | ||||
−0.0367182 | + | 0.999326i | \(0.511690\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −55.0698 | −1.79332 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −51.1387 | −1.66178 | −0.830892 | − | 0.556434i | \(-0.812169\pi\) | ||||
−0.830892 | + | 0.556434i | \(0.812169\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.3786 | 0.693978 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −35.6903 | −1.15734 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.14454 | −0.134255 | −0.0671275 | − | 0.997744i | \(-0.521383\pi\) | ||||
−0.0671275 | + | 0.997744i | \(0.521383\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.20155 | −0.0711661 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −39.3973 | −1.27220 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.6519 | 0.569417 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.198628 | −0.00640070 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.3202 | 0.942875 | 0.471438 | − | 0.881899i | \(-0.343735\pi\) | ||||
0.471438 | + | 0.881899i | \(0.343735\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.48968 | 0.272728 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.0144 | −0.321377 | −0.160689 | − | 0.987005i | \(-0.551371\pi\) | ||||
−0.160689 | + | 0.987005i | \(0.551371\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.4936 | 1.10581 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.2206 | 1.03083 | 0.515414 | − | 0.856941i | \(-0.327638\pi\) | ||||
0.515414 | + | 0.856941i | \(0.327638\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.45758 | 0.174425 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.27666 | 0.104616 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.7837 | 0.407736 | 0.203868 | − | 0.978998i | \(-0.434649\pi\) | ||||
0.203868 | + | 0.978998i | \(0.434649\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −91.4327 | −2.91033 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 46.1593 | 1.46778 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.4893 | −0.904992 | −0.452496 | − | 0.891766i | \(-0.649466\pi\) | ||||
−0.452496 | + | 0.891766i | \(0.649466\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.48406 | 0.205766 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.6122 | 1.34954 | 0.674772 | − | 0.738027i | \(-0.264242\pi\) | ||||
0.674772 | + | 0.738027i | \(0.264242\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18.7850 | 0.594331 |
(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 | 1900.2.a.i.1.2 | yes | 3 | |
4.3 | odd | 2 | 7600.2.a.bl.1.2 | 3 | |||
5.2 | odd | 4 | 1900.2.c.f.1749.3 | 6 | |||
5.3 | odd | 4 | 1900.2.c.f.1749.4 | 6 | |||
5.4 | even | 2 | 1900.2.a.g.1.2 | ✓ | 3 | ||
20.19 | odd | 2 | 7600.2.a.ca.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.2.a.g.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
1900.2.a.i.1.2 | yes | 3 | 1.1 | even | 1 | trivial | |
1900.2.c.f.1749.3 | 6 | 5.2 | odd | 4 | |||
1900.2.c.f.1749.4 | 6 | 5.3 | odd | 4 | |||
7600.2.a.bl.1.2 | 3 | 4.3 | odd | 2 | |||
7600.2.a.ca.1.2 | 3 | 20.19 | odd | 2 |