Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1560,2,Mod(1249,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1560.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.l (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(12.4566627153\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1698758656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.7 | ||
Root | \(-1.69230i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.1249 |
Dual form | 1560.2.l.e.1249.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times\).
\(n\) | \(391\) | \(521\) | \(781\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.489528 | + | 2.18183i | 0.218924 | + | 0.975742i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843i | 1.06904i | 0.845154 | + | 0.534522i | \(0.179509\pi\) | ||||
−0.845154 | + | 0.534522i | \(0.820491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.97906 | −0.898219 | −0.449110 | − | 0.893477i | \(-0.648259\pi\) | ||||
−0.449110 | + | 0.893477i | \(0.648259\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.00000i | − | 0.277350i | ||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.18183 | + | 0.489528i | −0.563345 | + | 0.126396i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.44383i | − | 0.350181i | −0.984552 | − | 0.175090i | \(-0.943978\pi\) | ||
0.984552 | − | 0.175090i | \(-0.0560218\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.17113 | −0.956924 | −0.478462 | − | 0.878108i | \(-0.658806\pi\) | ||||
−0.478462 | + | 0.878108i | \(0.658806\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.82843 | −0.617213 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.21302i | 1.29550i | 0.761851 | + | 0.647752i | \(0.224291\pi\) | ||||
−0.761851 | + | 0.647752i | \(0.775709\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.52072 | + | 2.13613i | −0.904145 | + | 0.427226i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.828427 | 0.153835 | 0.0769175 | − | 0.997037i | \(-0.475492\pi\) | ||||
0.0769175 | + | 0.997037i | \(0.475492\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.65685 | 0.297580 | 0.148790 | − | 0.988869i | \(-0.452462\pi\) | ||||
0.148790 | + | 0.988869i | \(0.452462\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.97906i | − | 0.518587i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.17113 | + | 1.38459i | −1.04311 | + | 0.234039i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.0418875i | 0.00688626i | 0.999994 | + | 0.00344313i | \(0.00109599\pi\) | ||||
−0.999994 | + | 0.00344313i | \(0.998904\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.36365 | −0.681488 | −0.340744 | − | 0.940156i | \(-0.610679\pi\) | ||||
−0.340744 | + | 0.940156i | \(0.610679\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.99956i | − | 1.37242i | −0.727403 | − | 0.686210i | \(-0.759273\pi\) | ||
0.727403 | − | 0.686210i | \(-0.240727\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.489528 | − | 2.18183i | −0.0729745 | − | 0.325247i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.40554i | 0.642614i | 0.946975 | + | 0.321307i | \(0.104122\pi\) | ||||
−0.946975 | + | 0.321307i | \(0.895878\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.44383 | 0.202177 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.72730i | − | 0.924066i | −0.886863 | − | 0.462033i | \(-0.847120\pi\) | ||
0.886863 | − | 0.462033i | \(-0.152880\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.45833 | − | 6.49978i | −0.196641 | − | 0.876430i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4.17113i | − | 0.552480i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.97906 | 0.387840 | 0.193920 | − | 0.981017i | \(-0.437880\pi\) | ||||
0.193920 | + | 0.981017i | \(0.437880\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.27226 | 0.803081 | 0.401540 | − | 0.915841i | \(-0.368475\pi\) | ||||
0.401540 | + | 0.915841i | \(0.368475\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.82843i | − | 0.356348i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.18183 | − | 0.489528i | 0.270622 | − | 0.0607185i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 0.727302i | − | 0.0888540i | −0.999013 | − | 0.0444270i | \(-0.985854\pi\) | ||
0.999013 | − | 0.0444270i | \(-0.0141462\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.21302 | −0.747960 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.32176 | −0.987612 | −0.493806 | − | 0.869572i | \(-0.664395\pi\) | ||||
−0.493806 | + | 0.869572i | \(0.664395\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.87031i | − | 0.804110i | −0.915616 | − | 0.402055i | \(-0.868296\pi\) | ||
0.915616 | − | 0.402055i | \(-0.131704\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.13613 | − | 4.52072i | −0.246659 | − | 0.522008i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 8.42604i | − | 0.960237i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.11190 | −0.687642 | −0.343821 | − | 0.939035i | \(-0.611721\pi\) | ||||
−0.343821 | + | 0.939035i | \(0.611721\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.7059i | 1.61418i | 0.590425 | + | 0.807092i | \(0.298960\pi\) | ||||
−0.590425 | + | 0.807092i | \(0.701040\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.15019 | − | 0.706797i | 0.341686 | − | 0.0766629i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.828427i | 0.0888167i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.7478 | −1.56326 | −0.781632 | − | 0.623740i | \(-0.785613\pi\) | ||||
−0.781632 | + | 0.623740i | \(0.785613\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.82843 | 0.296500 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.65685i | 0.171808i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.04189 | − | 9.10069i | −0.209493 | − | 0.933711i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.78654i | 0.689069i | 0.938774 | + | 0.344534i | \(0.111963\pi\) | ||||
−0.938774 | + | 0.344534i | \(0.888037\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.97906 | 0.299406 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.1421 | 1.20819 | 0.604094 | − | 0.796913i | \(-0.293535\pi\) | ||||
0.604094 | + | 0.796913i | \(0.293535\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.81108i | 0.276984i | 0.990364 | + | 0.138492i | \(0.0442255\pi\) | ||||
−0.990364 | + | 0.138492i | \(0.955775\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.38459 | − | 6.17113i | −0.135123 | − | 0.602241i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.3842i | 1.77726i | 0.458621 | + | 0.888632i | \(0.348343\pi\) | ||||
−0.458621 | + | 0.888632i | \(0.651657\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.44383 | −0.138294 | −0.0691470 | − | 0.997606i | \(-0.522028\pi\) | ||||
−0.0691470 | + | 0.997606i | \(0.522028\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0418875 | −0.00397579 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.40194i | − | 0.320028i | −0.987115 | − | 0.160014i | \(-0.948846\pi\) | ||
0.987115 | − | 0.160014i | \(-0.0511539\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.5557 | + | 3.04145i | −1.26408 | + | 0.283617i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000i | 0.0924500i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.08378 | 0.374359 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.12522 | −0.193202 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 4.36365i | − | 0.393457i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.87368 | − | 8.81774i | −0.614801 | − | 0.788682i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.8106i | 1.40297i | 0.712686 | + | 0.701484i | \(0.247479\pi\) | ||||
−0.712686 | + | 0.701484i | \(0.752521\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.99956 | 0.792367 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.1707 | −1.67495 | −0.837476 | − | 0.546475i | \(-0.815970\pi\) | ||||
−0.837476 | + | 0.546475i | \(0.815970\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 11.7977i | − | 1.02299i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.18183 | − | 0.489528i | 0.187782 | − | 0.0421319i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.67824i | 0.143381i | 0.997427 | + | 0.0716907i | \(0.0228395\pi\) | ||||
−0.997427 | + | 0.0716907i | \(0.977161\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.3423 | 1.04686 | 0.523429 | − | 0.852069i | \(-0.324653\pi\) | ||||
0.523429 | + | 0.852069i | \(0.324653\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.40554 | −0.371013 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.97906i | 0.249121i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.405538 | + | 1.80748i | 0.0336781 | + | 0.150103i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.00000i | − | 0.0824786i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.677798 | −0.0555274 | −0.0277637 | − | 0.999615i | \(-0.508839\pi\) | ||||
−0.0277637 | + | 0.999615i | \(0.508839\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.9991 | −1.46475 | −0.732374 | − | 0.680903i | \(-0.761588\pi\) | ||||
−0.732374 | + | 0.680903i | \(0.761588\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.44383i | 0.116727i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.811077 | + | 3.61497i | 0.0651473 | + | 0.290361i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 12.8392i | − | 1.02468i | −0.858783 | − | 0.512340i | \(-0.828779\pi\) | ||
0.858783 | − | 0.512340i | \(-0.171221\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.72730 | 0.533510 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.5731 | −1.38495 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 15.3137i | − | 1.19946i | −0.800202 | − | 0.599731i | \(-0.795274\pi\) | ||
0.800202 | − | 0.599731i | \(-0.204726\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.49978 | − | 1.45833i | 0.506007 | − | 0.113531i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.3922i | 1.19109i | 0.803324 | + | 0.595543i | \(0.203063\pi\) | ||||
−0.803324 | + | 0.595543i | \(0.796937\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.17113 | 0.318975 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.9706i | 1.13819i | 0.822272 | + | 0.569095i | \(0.192706\pi\) | ||||
−0.822272 | + | 0.569095i | \(0.807294\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.04189 | − | 12.7865i | −0.456724 | − | 0.966572i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.97906i | 0.223920i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.63950 | 0.571003 | 0.285502 | − | 0.958378i | \(-0.407840\pi\) | ||||
0.285502 | + | 0.958378i | \(0.407840\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.0286 | 1.11706 | 0.558532 | − | 0.829483i | \(-0.311365\pi\) | ||||
0.558532 | + | 0.829483i | \(0.311365\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.27226i | 0.463659i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0913912 | + | 0.0205051i | −0.00671922 | + | 0.00150757i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.30126i | 0.314539i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.82843 | 0.205738 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.8877 | −0.787804 | −0.393902 | − | 0.919152i | \(-0.628875\pi\) | ||||
−0.393902 | + | 0.919152i | \(0.628875\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.94690i | − | 0.356086i | −0.984023 | − | 0.178043i | \(-0.943023\pi\) | ||
0.984023 | − | 0.178043i | \(-0.0569766\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.489528 | + | 2.18183i | 0.0350558 | + | 0.156244i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.3628i | 1.87827i | 0.343549 | + | 0.939135i | \(0.388371\pi\) | ||||
−0.343549 | + | 0.939135i | \(0.611629\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.11190 | −0.433261 | −0.216630 | − | 0.976254i | \(-0.569507\pi\) | ||||
−0.216630 | + | 0.976254i | \(0.569507\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.727302 | 0.0512999 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.34315i | 0.164457i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.13613 | − | 9.52072i | −0.149194 | − | 0.664956i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.21302i | − | 0.431835i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.4260 | 0.859527 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.68585 | 0.666802 | 0.333401 | − | 0.942785i | \(-0.391804\pi\) | ||||
0.333401 | + | 0.942785i | \(0.391804\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 8.32176i | − | 0.570198i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.6355 | − | 4.40554i | 1.33913 | − | 0.300455i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.68629i | 0.318126i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.87031 | 0.464253 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.44383 | −0.0971227 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 9.21258i | − | 0.616920i | −0.951237 | − | 0.308460i | \(-0.900186\pi\) | ||
0.951237 | − | 0.308460i | \(-0.0998136\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.52072 | − | 2.13613i | 0.301382 | − | 0.142409i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.3218i | 1.34880i | 0.738365 | + | 0.674401i | \(0.235598\pi\) | ||||
−0.738365 | + | 0.674401i | \(0.764402\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.4715 | 1.08847 | 0.544234 | − | 0.838933i | \(-0.316820\pi\) | ||||
0.544234 | + | 0.838933i | \(0.316820\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.42604 | 0.554393 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 2.37339i | − | 0.155486i | −0.996973 | − | 0.0777428i | \(-0.975229\pi\) | ||
0.996973 | − | 0.0777428i | \(-0.0247713\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.61212 | + | 2.15663i | −0.627025 | + | 0.140683i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 6.11190i | − | 0.397010i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.6363 | 0.882062 | 0.441031 | − | 0.897492i | \(-0.354613\pi\) | ||||
0.441031 | + | 0.897492i | \(0.354613\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.07045 | 0.0689536 | 0.0344768 | − | 0.999405i | \(-0.489024\pi\) | ||||
0.0344768 | + | 0.999405i | \(0.489024\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.489528 | − | 2.18183i | −0.0312748 | − | 0.139392i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.17113i | 0.265403i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.7059 | −0.931950 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.6262 | 0.923196 | 0.461598 | − | 0.887089i | \(-0.347276\pi\) | ||||
0.461598 | + | 0.887089i | \(0.347276\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 18.5089i | − | 1.16365i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.706797 | + | 3.15019i | 0.0442613 | + | 0.197273i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.9403i | 1.55573i | 0.628429 | + | 0.777867i | \(0.283698\pi\) | ||||
−0.628429 | + | 0.777867i | \(0.716302\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.118476 | −0.00736173 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.828427 | −0.0512784 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.01691i | 0.556007i | 0.960580 | + | 0.278003i | \(0.0896726\pi\) | ||||
−0.960580 | + | 0.278003i | \(0.910327\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.6778 | − | 3.29320i | 0.901650 | − | 0.202300i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 14.7478i | − | 0.902551i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.28391 | −0.505079 | −0.252539 | − | 0.967587i | \(-0.581266\pi\) | ||||
−0.252539 | + | 0.967587i | \(0.581266\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.9572 | −1.21232 | −0.606158 | − | 0.795344i | \(-0.707290\pi\) | ||||
−0.606158 | + | 0.795344i | \(0.707290\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.82843i | 0.171184i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.4675 | − | 6.36365i | 0.812120 | − | 0.383743i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 22.6145i | − | 1.35878i | −0.733780 | − | 0.679388i | \(-0.762245\pi\) | ||
0.733780 | − | 0.679388i | \(-0.237755\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.65685 | −0.0991933 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.89572 | −0.113089 | −0.0565446 | − | 0.998400i | \(-0.518008\pi\) | ||||
−0.0565446 | + | 0.998400i | \(0.518008\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.2299i | 0.667550i | 0.942653 | + | 0.333775i | \(0.108323\pi\) | ||||
−0.942653 | + | 0.333775i | \(0.891677\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.10069 | − | 2.04189i | 0.539078 | − | 0.120951i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 12.3423i | − | 0.728541i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.9153 | 0.877373 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.78654 | −0.397834 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 27.6774i | − | 1.61693i | −0.588545 | − | 0.808464i | \(-0.700299\pi\) | ||
0.588545 | − | 0.808464i | \(-0.299701\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.45833 | + | 6.49978i | 0.0849074 | + | 0.378432i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.97906i | 0.172862i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.21302 | 0.359308 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.4546 | 1.46718 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.1421i | 0.697547i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.07045 | + | 13.6850i | 0.175813 | + | 0.783599i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.9858i | 1.42601i | 0.701157 | + | 0.713007i | \(0.252667\pi\) | ||||
−0.701157 | + | 0.713007i | \(0.747333\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.81108 | −0.159917 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.3842 | 1.04247 | 0.521235 | − | 0.853413i | \(-0.325472\pi\) | ||||
0.521235 | + | 0.853413i | \(0.325472\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.61453i | 0.486922i | 0.969911 | + | 0.243461i | \(0.0782828\pi\) | ||||
−0.969911 | + | 0.243461i | \(0.921717\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.17113 | − | 1.38459i | 0.347704 | − | 0.0780131i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.0491i | 0.845240i | 0.906307 | + | 0.422620i | \(0.138889\pi\) | ||||
−0.906307 | + | 0.422620i | \(0.861111\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.46793 | −0.138178 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.3842 | −1.02610 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.02242i | 0.335096i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.13613 | + | 4.52072i | 0.118491 | + | 0.250765i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 1.44383i | − | 0.0798441i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.4607 | −0.686983 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.6738 | 1.24626 | 0.623131 | − | 0.782117i | \(-0.285860\pi\) | ||||
0.623131 | + | 0.782117i | \(0.285860\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 0.0418875i | − | 0.00229542i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.58685 | − | 0.356035i | 0.0866986 | − | 0.0194523i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.9282i | 1.52135i | 0.649134 | + | 0.760674i | \(0.275131\pi\) | ||||
−0.649134 | + | 0.760674i | \(0.724869\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.40194 | 0.184768 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.93586 | −0.267292 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706i | 0.916324i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.04145 | − | 13.5557i | −0.163746 | − | 0.729816i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.7398i | 1.05969i | 0.848096 | + | 0.529843i | \(0.177749\pi\) | ||||
−0.848096 | + | 0.529843i | \(0.822251\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.7157 | −1.64417 | −0.822086 | − | 0.569364i | \(-0.807190\pi\) | ||||
−0.822086 | + | 0.569364i | \(0.807190\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.0072i | 0.905201i | 0.891713 | + | 0.452600i | \(0.149504\pi\) | ||||
−0.891713 | + | 0.452600i | \(0.850496\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.07374 | − | 18.1566i | −0.216212 | − | 0.963654i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.08378i | 0.216136i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.90203 | 0.417053 | 0.208527 | − | 0.978017i | \(-0.433133\pi\) | ||||
0.208527 | + | 0.978017i | \(0.433133\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.60164 | −0.0842968 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 2.12522i | − | 0.111545i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.9898 | − | 3.36321i | 0.784603 | − | 0.176039i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 34.1810i | − | 1.78424i | −0.451803 | − | 0.892118i | \(-0.649219\pi\) | ||
0.451803 | − | 0.892118i | \(-0.350781\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.36365 | 0.227163 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.0277 | 0.987868 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 18.5098i | − | 0.958402i | −0.877705 | − | 0.479201i | \(-0.840926\pi\) | ||
0.877705 | − | 0.479201i | \(-0.159074\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.81774 | − | 6.87368i | 0.455346 | − | 0.354956i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 0.828427i | − | 0.0426662i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.7994 | 0.657462 | 0.328731 | − | 0.944424i | \(-0.393379\pi\) | ||||
0.328731 | + | 0.944424i | \(0.393379\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.8106 | −0.810004 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.664032i | 0.0339304i | 0.999856 | + | 0.0169652i | \(0.00540046\pi\) | ||||
−0.999856 | + | 0.0169652i | \(0.994600\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.3842 | − | 4.12479i | 0.936943 | − | 0.210219i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.99956i | 0.457473i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.32580 | −0.117923 | −0.0589613 | − | 0.998260i | \(-0.518779\pi\) | ||||
−0.0589613 | + | 0.998260i | \(0.518779\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.97056 | 0.453661 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 19.1707i | − | 0.967034i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.99195 | − | 13.3351i | −0.150541 | − | 0.670961i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2433i | 0.915603i | 0.889054 | + | 0.457802i | \(0.151363\pi\) | ||||
−0.889054 | + | 0.457802i | \(0.848637\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.7977 | 0.590626 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.9919 | 0.848537 | 0.424269 | − | 0.905536i | \(-0.360531\pi\) | ||||
0.424269 | + | 0.905536i | \(0.360531\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1.65685i | − | 0.0825338i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.489528 | + | 2.18183i | 0.0243248 | + | 0.108416i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.124785i | − | 0.00618538i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.8111 | 0.534573 | 0.267287 | − | 0.963617i | \(-0.413873\pi\) | ||||
0.267287 | + | 0.963617i | \(0.413873\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.67824 | −0.0827813 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.42604i | 0.414618i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −32.0857 | + | 7.19896i | −1.57503 | + | 0.353383i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.3423i | 0.604403i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.08780 | 0.248555 | 0.124278 | − | 0.992247i | \(-0.460339\pi\) | ||||
0.124278 | + | 0.992247i | \(0.460339\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.0945 | 0.589452 | 0.294726 | − | 0.955582i | \(-0.404772\pi\) | ||||
0.294726 | + | 0.955582i | \(0.404772\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 4.40554i | − | 0.214205i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.08421 | + | 6.52717i | 0.149606 | + | 0.316614i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.7406i | 0.858529i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.97906 | −0.143830 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.48931 | −0.408916 | −0.204458 | − | 0.978875i | \(-0.565543\pi\) | ||||
−0.204458 | + | 0.978875i | \(0.565543\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.8453i | 0.665365i | 0.943039 | + | 0.332682i | \(0.107954\pi\) | ||||
−0.943039 | + | 0.332682i | \(0.892046\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.80748 | + | 0.405538i | −0.0866622 | + | 0.0194441i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 25.9153i | − | 1.23970i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.602516 | −0.0287565 | −0.0143783 | − | 0.999897i | \(-0.504577\pi\) | ||||
−0.0143783 | + | 0.999897i | \(0.504577\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 17.6721i | − | 0.839626i | −0.907611 | − | 0.419813i | \(-0.862096\pi\) | ||
0.907611 | − | 0.419813i | \(-0.137904\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.21947 | − | 32.1771i | −0.342236 | − | 1.52534i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 0.677798i | − | 0.0320587i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.33509 | −0.157393 | −0.0786963 | − | 0.996899i | \(-0.525076\pi\) | ||||
−0.0786963 | + | 0.996899i | \(0.525076\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.9996 | 0.612125 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 17.9991i | − | 0.845673i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.38459 | + | 6.17113i | 0.0649108 | + | 0.289307i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.9266i | 1.82091i | 0.413611 | + | 0.910454i | \(0.364267\pi\) | ||||
−0.413611 | + | 0.910454i | \(0.635733\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.44383 | −0.0673923 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.3918 | 1.32234 | 0.661168 | − | 0.750238i | \(-0.270061\pi\) | ||||
0.661168 | + | 0.750238i | \(0.270061\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.2259i | 0.475238i | 0.971358 | + | 0.237619i | \(0.0763670\pi\) | ||||
−0.971358 | + | 0.237619i | \(0.923633\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.61497 | + | 0.811077i | −0.167640 | + | 0.0376128i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.61584i | 0.259870i | 0.991522 | + | 0.129935i | \(0.0414769\pi\) | ||||
−0.991522 | + | 0.129935i | \(0.958523\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.05712 | 0.0949890 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.8392 | 0.591599 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 26.8102i | 1.23273i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.8565 | − | 8.91008i | 0.865198 | − | 0.408823i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.72730i | 0.308022i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.95006 | 0.408939 | 0.204469 | − | 0.978873i | \(-0.434453\pi\) | ||||
0.204469 | + | 0.978873i | \(0.434453\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0418875 | 0.00190991 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 17.5731i | − | 0.799603i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.8070 | + | 3.32220i | −0.672353 | + | 0.150853i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 18.3596i | − | 0.831954i | −0.909375 | − | 0.415977i | \(-0.863440\pi\) | ||
0.909375 | − | 0.415977i | \(-0.136560\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.3137 | 0.692510 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.7981 | −1.52529 | −0.762644 | − | 0.646819i | \(-0.776099\pi\) | ||||
−0.762644 | + | 0.646819i | \(0.776099\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.19611i | − | 0.0538701i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.45833 | + | 6.49978i | 0.0655471 | + | 0.292143i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 23.5375i | − | 1.05580i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.72898 | −0.256464 | −0.128232 | − | 0.991744i | \(-0.540930\pi\) | ||||
−0.128232 | + | 0.991744i | \(0.540930\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.3922 | −0.687673 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 20.2121i | − | 0.901215i | −0.892722 | − | 0.450607i | \(-0.851207\pi\) | ||
0.892722 | − | 0.450607i | \(-0.148793\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.94392 | + | 26.4920i | 0.264501 | + | 1.17888i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.00000i | − | 0.0444116i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.02708 | −0.267146 | −0.133573 | − | 0.991039i | \(-0.542645\pi\) | ||||
−0.133573 | + | 0.991039i | \(0.542645\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.4322 | 0.859629 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.17113i | 0.184160i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.13328 | + | 1.37610i | −0.270265 | + | 0.0606383i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 13.1243i | − | 0.577208i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.9706 | −0.657135 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.95899 | −0.0858249 | −0.0429125 | − | 0.999079i | \(-0.513664\pi\) | ||||
−0.0429125 | + | 0.999079i | \(0.513664\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 21.6859i | − | 0.948256i | −0.880456 | − | 0.474128i | \(-0.842763\pi\) | ||
0.880456 | − | 0.474128i | \(-0.157237\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.7865 | − | 6.04189i | 0.558050 | − | 0.263690i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 2.39222i | − | 0.104207i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.6016 | −0.678332 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.97906 | −0.129280 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.36365i | 0.189011i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −40.1110 | + | 8.99956i | −1.73415 | + | 0.389085i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.63950i | 0.329669i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.97906 | 0.128317 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.3245 | 1.69069 | 0.845346 | − | 0.534220i | \(-0.179394\pi\) | ||||
0.845346 | + | 0.534220i | \(0.179394\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.0286i | 0.644937i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.706797 | − | 3.15019i | −0.0302758 | − | 0.134939i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 14.1466i | − | 0.604865i | −0.953171 | − | 0.302432i | \(-0.902201\pi\) | ||
0.953171 | − | 0.302432i | \(-0.0977987\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.27226 | −0.267694 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.45548 | −0.147208 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 17.2871i | − | 0.735120i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.0205051 | − | 0.0913912i | −0.000870394 | − | 0.00387934i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.7603i | 1.26098i | 0.776196 | + | 0.630491i | \(0.217147\pi\) | ||||
−0.776196 | + | 0.630491i | \(0.782853\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.99956 | −0.380641 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.30126 | −0.181599 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 28.6498i | − | 1.20745i | −0.797194 | − | 0.603723i | \(-0.793683\pi\) | ||
0.797194 | − | 0.603723i | \(-0.206317\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.42245 | − | 1.66535i | 0.312265 | − | 0.0700617i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.82843i | 0.118783i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −39.7326 | −1.66568 | −0.832838 | − | 0.553517i | \(-0.813285\pi\) | ||||
−0.832838 | + | 0.553517i | \(0.813285\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.5726 | 1.27943 | 0.639713 | − | 0.768614i | \(-0.279053\pi\) | ||||
0.639713 | + | 0.768614i | \(0.279053\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 10.8877i | − | 0.454839i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.2718 | − | 28.0874i | −0.553473 | − | 1.17132i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.3116i | 1.47004i | 0.678045 | + | 0.735020i | \(0.262827\pi\) | ||||
−0.678045 | + | 0.735020i | \(0.737173\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.94690 | 0.205586 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −41.5946 | −1.72564 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.0410i | 0.830014i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.18183 | + | 0.489528i | −0.0902074 | + | 0.0202395i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 19.5517i | − | 0.806985i | −0.914983 | − | 0.403492i | \(-0.867796\pi\) | ||
0.914983 | − | 0.403492i | \(-0.132204\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.91096 | −0.284761 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.3628 | −1.08442 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.66491i | 0.191565i | 0.995402 | + | 0.0957824i | \(0.0305353\pi\) | ||||
−0.995402 | + | 0.0957824i | \(0.969465\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.99912 | + | 8.91008i | 0.0819560 | + | 0.365278i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 6.11190i | − | 0.250143i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.6497 | 0.802864 | 0.401432 | − | 0.915889i | \(-0.368513\pi\) | ||||
0.401432 | + | 0.915889i | \(0.368513\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.2714 | 1.80587 | 0.902934 | − | 0.429780i | \(-0.141409\pi\) | ||||
0.902934 | + | 0.429780i | \(0.141409\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.727302i | 0.0296180i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.04036 | − | 4.63687i | −0.0422965 | − | 0.188515i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 34.2648i | − | 1.39077i | −0.718640 | − | 0.695383i | \(-0.755235\pi\) | ||
0.718640 | − | 0.695383i | \(-0.244765\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.34315 | −0.0949491 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.40554 | 0.178229 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.7203i | 1.36195i | 0.732307 | + | 0.680975i | \(0.238444\pi\) | ||||
−0.732307 | + | 0.680975i | \(0.761556\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.52072 | − | 2.13613i | 0.383913 | − | 0.0861371i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.0901i | 1.41267i | 0.707876 | + | 0.706337i | \(0.249653\pi\) | ||||
−0.707876 | + | 0.706337i | \(0.750347\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.63907 | −0.106073 | −0.0530365 | − | 0.998593i | \(-0.516890\pi\) | ||||
−0.0530365 | + | 0.998593i | \(0.516890\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.21302 | 0.249320 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 41.7131i | − | 1.67120i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.8739 | − | 19.3137i | 0.634956 | − | 0.772548i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.4260i | 0.496248i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.0604785 | 0.00241144 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.7683 | −1.14525 | −0.572624 | − | 0.819818i | \(-0.694075\pi\) | ||||
−0.572624 | + | 0.819818i | \(0.694075\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.68585i | 0.384978i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −34.4961 | + | 7.73975i | −1.36893 | + | 0.307143i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000i | 0.0396214i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.32176 | 0.329204 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.1944 | 1.39009 | 0.695047 | − | 0.718965i | \(-0.255384\pi\) | ||||
0.695047 | + | 0.718965i | \(0.255384\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 27.2709i | − | 1.07546i | −0.843117 | − | 0.537731i | \(-0.819282\pi\) | ||
0.843117 | − | 0.537731i | \(-0.180718\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.40554 | + | 19.6355i | 0.173468 | + | 0.773146i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.22913i | 0.166264i | 0.996539 | + | 0.0831322i | \(0.0264924\pi\) | ||||
−0.996539 | + | 0.0831322i | \(0.973508\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.87478 | −0.348365 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.68629 | −0.183670 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 22.1400i | − | 0.866406i | −0.901296 | − | 0.433203i | \(-0.857383\pi\) | ||
0.901296 | − | 0.433203i | \(-0.142617\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.38459 | − | 41.8271i | −0.366686 | − | 1.63432i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.87031i | 0.268037i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.0932 | −1.05540 | −0.527701 | − | 0.849430i | \(-0.676946\pi\) | ||||
−0.527701 | + | 0.849430i | \(0.676946\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.0597 | 0.741335 | 0.370668 | − | 0.928766i | \(-0.379129\pi\) | ||||
0.370668 | + | 0.928766i | \(0.379129\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 1.44383i | − | 0.0560738i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 25.7406 | − | 5.77533i | 0.998179 | − | 0.223958i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.14704i | 0.199294i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.21258 | 0.356179 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.6854 | −0.721342 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.6213i | 0.910533i | 0.890355 | + | 0.455267i | \(0.150456\pi\) | ||||
−0.890355 | + | 0.455267i | \(0.849544\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.13613 | + | 4.52072i | 0.0822197 | + | 0.174003i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 18.8111i | − | 0.722968i | −0.932378 | − | 0.361484i | \(-0.882270\pi\) | ||
0.932378 | − | 0.361484i | \(-0.117730\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.1952 | −0.736645 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.3218 | −0.778732 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 33.7827i | − | 1.29266i | −0.763059 | − | 0.646329i | \(-0.776303\pi\) | ||
0.763059 | − | 0.646329i | \(-0.223697\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.66162 | + | 0.821544i | −0.139903 | + | 0.0313896i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.4715i | 0.628428i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.72730 | −0.256290 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −47.3236 | −1.80027 | −0.900137 | − | 0.435606i | \(-0.856534\pi\) | ||||
−0.900137 | + | 0.435606i | \(0.856534\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.42604i | 0.320079i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.04189 | + | 26.9287i | 0.229182 | + | 1.02146i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.30038i | 0.238644i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.37339 | 0.0897697 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.29636 | −0.124502 | −0.0622509 | − | 0.998061i | \(-0.519828\pi\) | ||||
−0.0622509 | + | 0.998061i | \(0.519828\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.174718i | − | 0.00658963i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.15663 | − | 9.61212i | −0.0812236 | − | 0.362013i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 34.3431i | 1.29161i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −46.8404 | −1.75913 | −0.879565 | − | 0.475779i | \(-0.842166\pi\) | ||||
−0.879565 | + | 0.475779i | \(0.842166\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.11190 | 0.229214 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.2941i | 0.385516i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.49978 | + | 1.45833i | −0.243078 | + | 0.0545385i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.6363i | 0.509259i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.0152 | 0.746442 | 0.373221 | − | 0.927742i | \(-0.378253\pi\) | ||||
0.373221 | + | 0.927742i | \(0.378253\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.95093 | −0.296108 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.07045i | 0.0398104i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.74509 | + | 1.76963i | −0.139089 | + | 0.0657223i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.8383i | 0.401971i | 0.979594 | + | 0.200986i | \(0.0644144\pi\) | ||||
−0.979594 | + | 0.200986i | \(0.935586\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.9939 | −0.480595 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.1952i | 0.782864i | 0.920207 | + | 0.391432i | \(0.128020\pi\) | ||||
−0.920207 | + | 0.391432i | \(0.871980\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.18183 | − | 0.489528i | 0.0804778 | − | 0.0180565i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.16667i | 0.0798104i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.07403 | −0.260222 | −0.130111 | − | 0.991499i | \(-0.541533\pi\) | ||||
−0.130111 | + | 0.991499i | \(0.541533\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.17113 | −0.153230 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.3913i | 0.784772i | 0.919801 | + | 0.392386i | \(0.128350\pi\) | ||||
−0.919801 | + | 0.392386i | \(0.871650\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.331801 | − | 1.47884i | −0.0121563 | − | 0.0541804i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 14.7059i | − | 0.538061i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −51.9982 | −1.89997 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.2247 | 0.665028 | 0.332514 | − | 0.943098i | \(-0.392103\pi\) | ||||
0.332514 | + | 0.943098i | \(0.392103\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.6262i | 0.533007i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.81108 | − | 39.2709i | −0.320668 | − | 1.42922i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.3708i | 1.43096i | 0.698635 | + | 0.715479i | \(0.253791\pi\) | ||||
−0.698635 | + | 0.715479i | \(0.746209\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18.5089 | 0.671832 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.8610 | −0.502462 | −0.251231 | − | 0.967927i | \(-0.580835\pi\) | ||||
−0.251231 | + | 0.967927i | \(0.580835\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 4.08378i | − | 0.147843i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.15019 | + | 0.706797i | −0.113895 | + | 0.0255543i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 2.97906i | − | 0.107567i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.6274 | 0.455356 | 0.227678 | − | 0.973736i | \(-0.426887\pi\) | ||||
0.227678 | + | 0.973736i | \(0.426887\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.9403 | −0.898204 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 34.7825i | − | 1.25104i | −0.780208 | − | 0.625520i | \(-0.784887\pi\) | ||
0.780208 | − | 0.625520i | \(-0.215113\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.49018 | + | 3.53926i | −0.269055 | + | 0.127134i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 0.118476i | − | 0.00425029i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.2014 | 0.652132 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.7910 | 0.887092 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 0.828427i | − | 0.0296056i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.0129 | − | 6.28515i | 0.999823 | − | 0.224327i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 36.7835i | − | 1.31119i | −0.755112 | − | 0.655596i | \(-0.772418\pi\) | ||
0.755112 | − | 0.655596i | \(-0.227582\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.01691 | −0.321011 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.62215 | 0.342124 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 6.27226i | − | 0.222734i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.29320 | + | 14.6778i | 0.116798 | + | 0.520568i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 42.4413i | − | 1.50335i | −0.659535 | − | 0.751674i | \(-0.729247\pi\) | ||
0.659535 | − | 0.751674i | \(-0.270753\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.36086 | 0.225031 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.7478 | 0.521088 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.4671i | 0.722267i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.60252 | − | 38.3414i | −0.303199 | − | 1.35136i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 8.28391i | − | 0.291607i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −55.3771 | −1.94696 | −0.973478 | − | 0.228780i | \(-0.926526\pi\) | ||||
−0.973478 | + | 0.228780i | \(0.926526\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.1159 | −0.601021 | −0.300511 | − | 0.953778i | \(-0.597157\pi\) | ||||
−0.300511 | + | 0.953778i | \(0.597157\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 19.9572i | − | 0.699931i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 33.4118 | − | 7.49649i | 1.17037 | − | 0.262591i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37.5384i | 1.31330i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.82843 | −0.0988332 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.5460 | 0.542559 | 0.271279 | − | 0.962501i | \(-0.412553\pi\) | ||||
0.271279 | + | 0.962501i | \(0.412553\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 0.0998847i | − | 0.00348176i | −0.999998 | − | 0.00174088i | \(-0.999446\pi\) | ||
0.999998 | − | 0.00174088i | \(-0.000554140\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.36365 | + | 13.4675i | 0.221554 | + | 0.468878i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 9.53311i | − | 0.331499i | −0.986168 | − | 0.165749i | \(-0.946996\pi\) | ||
0.986168 | − | 0.165749i | \(-0.0530042\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.6361 | −1.75866 | −0.879332 | − | 0.476210i | \(-0.842010\pi\) | ||||
−0.879332 | + | 0.476210i | \(0.842010\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.6145 | 0.784489 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.44383i | 0.0500258i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −33.5831 | + | 7.53492i | −1.16219 | + | 0.260757i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 1.65685i | − | 0.0572693i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43.2310 | 1.49250 | 0.746249 | − | 0.665666i | \(-0.231853\pi\) | ||||
0.746249 | + | 0.665666i | \(0.231853\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3137 | −0.976335 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 1.89572i | − | 0.0652921i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.489528 | − | 2.18183i | −0.0168403 | − | 0.0750571i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6.01104i | − | 0.206542i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.2299 | −0.385410 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.260248 | −0.00892119 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.6979i | 1.08531i | 0.839954 | + | 0.542657i | \(0.182582\pi\) | ||||
−0.839954 | + | 0.542657i | \(0.817418\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.04189 | + | 9.10069i | 0.0698311 | + | 0.311237i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 28.8912i | − | 0.986906i | −0.869772 | − | 0.493453i | \(-0.835734\pi\) | ||
0.869772 | − | 0.493453i | \(-0.164266\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.7099 | −1.69608 | −0.848040 | − | 0.529933i | \(-0.822217\pi\) | ||||
−0.848040 | + | 0.529933i | \(0.822217\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.3423 | 0.420623 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.56502i | 0.155395i | 0.996977 | + | 0.0776976i | \(0.0247569\pi\) | ||||
−0.996977 | + | 0.0776976i | \(0.975243\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.6632 | + | 7.32851i | −1.11058 | + | 0.249177i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.9153i | 0.506552i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.2077 | 0.617653 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.727302 | −0.0246437 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 6.78654i | − | 0.229690i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.9403 | − | 19.4417i | 0.843137 | − | 0.657250i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.5312i | 0.456916i | 0.973554 | + | 0.228458i | \(0.0733683\pi\) | ||||
−0.973554 | + | 0.228458i | \(0.926632\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27.6774 | 0.933534 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.0634 | −0.945481 | −0.472740 | − | 0.881202i | \(-0.656735\pi\) | ||||
−0.472740 | + | 0.881202i | \(0.656735\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.3700i | 1.59413i | 0.603896 | + | 0.797063i | \(0.293614\pi\) | ||||
−0.603896 | + | 0.797063i | \(0.706386\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.49978 | + | 1.45833i | −0.218488 | + | 0.0490213i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 0.606101i | − | 0.0203509i | −0.999948 | − | 0.0101754i | \(-0.996761\pi\) | ||
0.999948 | − | 0.0101754i | \(-0.00323900\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −44.7192 | −1.49984 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.97906 | −0.0998021 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 18.3761i | − | 0.614932i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.73975 | + | 16.6681i | 0.125006 | + | 0.557152i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.21302i | 0.207447i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.37258 | 0.0457782 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.71310 | −0.323590 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.4546i | 0.847076i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.35690 | + | 32.7897i | 0.244552 | + | 1.08997i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 11.8582i | − | 0.393746i | −0.980429 | − | 0.196873i | \(-0.936921\pi\) | ||
0.980429 | − | 0.196873i | \(-0.0630787\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.1421 | −0.402729 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.5642 | −1.11203 | −0.556015 | − | 0.831172i | \(-0.687670\pi\) | ||||
−0.556015 | + | 0.831172i | \(0.687670\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 43.8098i | − | 1.44989i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.6850 | + | 3.07045i | −0.452411 | + | 0.101506i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 54.2229i | − | 1.79060i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.2242 | 0.634149 | 0.317074 | − | 0.948401i | \(-0.397299\pi\) | ||||
0.317074 | + | 0.948401i | \(0.397299\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.9858 | −0.823310 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.32176i | 0.273914i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.0894772 | − | 0.189362i | −0.00294199 | − | 0.00622618i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 2.81108i | − | 0.0923279i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.0349 | 1.18227 | 0.591133 | − | 0.806574i | \(-0.298681\pi\) | ||||
0.591133 | + | 0.806574i | \(0.298681\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.17113 | 0.136703 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.3842i | 0.601870i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.38459 | + | 2.10559i | −0.306909 | + | 0.0688601i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 41.5851i | − | 1.35853i | −0.733895 | − | 0.679263i | \(-0.762300\pi\) | ||
0.733895 | − | 0.679263i | \(-0.237700\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.61453 | −0.281124 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −56.4933 | −1.84163 | −0.920814 | − | 0.390002i | \(-0.872474\pi\) | ||||
−0.920814 | + | 0.390002i | \(0.872474\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 27.1115i | − | 0.882871i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.38459 | + | 6.17113i | 0.0450409 | + | 0.200747i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.3922i | 0.370197i | 0.982720 | + | 0.185099i | \(0.0592604\pi\) | ||||
−0.982720 | + | 0.185099i | \(0.940740\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.87031 | −0.223020 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.0491 | −0.487999 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56.7986i | 1.83989i | 0.392053 | + | 0.919943i | \(0.371765\pi\) | ||||
−0.392053 | + | 0.919943i | \(0.628235\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.32982 | − | 23.7550i | −0.172469 | − | 0.768693i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 2.46793i | − | 0.0797769i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.74677 | −0.153281 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.2548 | −0.911446 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 18.3842i | − | 0.592421i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.7933 | − | 2.42165i | 0.347448 | − | 0.0779556i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.7224i | 0.827177i | 0.910464 | + | 0.413588i | \(0.135725\pi\) | ||||
−0.910464 | + | 0.413588i | \(0.864275\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.02242 | −0.193468 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.8703 | −1.05486 | −0.527429 | − | 0.849599i | \(-0.676844\pi\) | ||||
−0.527429 | + | 0.849599i | \(0.676844\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.9092i | 1.11914i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.52072 | + | 2.13613i | −0.144779 | + | 0.0684109i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 30.1453i | − | 0.964433i | −0.876052 | − | 0.482217i | \(-0.839832\pi\) | ||
0.876052 | − | 0.482217i | \(-0.160168\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43.9345 | 1.40415 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.44383 | 0.0460980 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 32.4965i | − | 1.03648i | −0.855236 | − | 0.518238i | \(-0.826588\pi\) | ||
0.855236 | − | 0.518238i | \(-0.173412\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −57.5190 | + | 12.9053i | −1.83271 | + | 0.411198i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 12.4607i | − | 0.396630i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 55.9145 | 1.77798 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.4893 | 1.19089 | 0.595443 | − | 0.803397i | \(-0.296976\pi\) | ||||
0.595443 | + | 0.803397i | \(0.296976\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.6738i | 0.719530i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.99195 | − | 13.3351i | −0.0948510 | − | 0.422751i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.8659i | 0.597488i | 0.954333 | + | 0.298744i | \(0.0965676\pi\) | ||||
−0.954333 | + | 0.298744i | \(0.903432\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.0418875 | 0.00132526 |
(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 | 1560.2.l.e.1249.7 | yes | 8 | |
3.2 | odd | 2 | 4680.2.l.f.2809.3 | 8 | |||
4.3 | odd | 2 | 3120.2.l.o.1249.3 | 8 | |||
5.2 | odd | 4 | 7800.2.a.bw.1.1 | 4 | |||
5.3 | odd | 4 | 7800.2.a.bv.1.3 | 4 | |||
5.4 | even | 2 | inner | 1560.2.l.e.1249.3 | ✓ | 8 | |
15.14 | odd | 2 | 4680.2.l.f.2809.4 | 8 | |||
20.19 | odd | 2 | 3120.2.l.o.1249.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.l.e.1249.3 | ✓ | 8 | 5.4 | even | 2 | inner | |
1560.2.l.e.1249.7 | yes | 8 | 1.1 | even | 1 | trivial | |
3120.2.l.o.1249.3 | 8 | 4.3 | odd | 2 | |||
3120.2.l.o.1249.7 | 8 | 20.19 | odd | 2 | |||
4680.2.l.f.2809.3 | 8 | 3.2 | odd | 2 | |||
4680.2.l.f.2809.4 | 8 | 15.14 | odd | 2 | |||
7800.2.a.bv.1.3 | 4 | 5.3 | odd | 4 | |||
7800.2.a.bw.1.1 | 4 | 5.2 | odd | 4 |