Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6525,2,Mod(1,6525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6525, 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("6525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6525 = 3^{2} \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6525.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: | \(52.1023873189\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.246832.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 435) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.71250\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.712495 | −0.503810 | −0.251905 | − | 0.967752i | \(-0.581057\pi\) | ||||
−0.251905 | + | 0.967752i | \(0.581057\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.49235 | −0.746175 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.77986 | −1.05069 | −0.525343 | − | 0.850890i | \(-0.676063\pi\) | ||||
−0.525343 | + | 0.850890i | \(0.676063\pi\) | |||||||
\(8\) | 2.48828 | 0.879741 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.26814 | −1.28689 | −0.643446 | − | 0.765491i | \(-0.722496\pi\) | ||||
−0.643446 | + | 0.765491i | \(0.722496\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.779856 | 0.216293 | 0.108147 | − | 0.994135i | \(-0.465508\pi\) | ||||
0.108147 | + | 0.994135i | \(0.465508\pi\) | |||||||
\(14\) | 1.98063 | 0.529347 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.21181 | 0.302953 | ||||||||
\(17\) | 1.90354 | 0.461677 | 0.230838 | − | 0.972992i | \(-0.425853\pi\) | ||||
0.230838 | + | 0.972992i | \(0.425853\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.72036 | 1.54176 | 0.770878 | − | 0.636983i | \(-0.219818\pi\) | ||||
0.770878 | + | 0.636983i | \(0.219818\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.04103 | 0.648349 | ||||||||
\(23\) | −2.17168 | −0.452827 | −0.226413 | − | 0.974031i | \(-0.572700\pi\) | ||||
−0.226413 | + | 0.974031i | \(0.572700\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.555643 | −0.108971 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.14852 | 0.783997 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.82061 | −1.58423 | −0.792114 | − | 0.610373i | \(-0.791020\pi\) | ||||
−0.792114 | + | 0.610373i | \(0.791020\pi\) | |||||||
\(32\) | −5.83998 | −1.03237 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.35626 | −0.232597 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.48402 | 0.243971 | 0.121986 | − | 0.992532i | \(-0.461074\pi\) | ||||
0.121986 | + | 0.992532i | \(0.461074\pi\) | |||||||
\(38\) | −4.78822 | −0.776752 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.71389 | 1.20471 | 0.602354 | − | 0.798229i | \(-0.294230\pi\) | ||||
0.602354 | + | 0.798229i | \(0.294230\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.19624 | −1.24991 | −0.624957 | − | 0.780659i | \(-0.714884\pi\) | ||||
−0.624957 | + | 0.780659i | \(0.714884\pi\) | |||||||
\(44\) | 6.36956 | 0.960247 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.54731 | 0.228139 | ||||||||
\(47\) | 5.19381 | 0.757595 | 0.378798 | − | 0.925480i | \(-0.376338\pi\) | ||||
0.378798 | + | 0.925480i | \(0.376338\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.727598 | 0.103943 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.16382 | −0.161393 | ||||||||
\(53\) | 11.7853 | 1.61884 | 0.809419 | − | 0.587231i | \(-0.199782\pi\) | ||||
0.809419 | + | 0.587231i | \(0.199782\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.91707 | −0.924332 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.712495 | 0.0935552 | ||||||||
\(59\) | 4.46028 | 0.580679 | 0.290339 | − | 0.956924i | \(-0.406232\pi\) | ||||
0.290339 | + | 0.956924i | \(0.406232\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.24905 | −0.672071 | −0.336036 | − | 0.941849i | \(-0.609086\pi\) | ||||
−0.336036 | + | 0.941849i | \(0.609086\pi\) | |||||||
\(62\) | 6.28464 | 0.798150 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.73733 | 0.217166 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.49375 | −1.03768 | −0.518838 | − | 0.854872i | \(-0.673635\pi\) | ||||
−0.518838 | + | 0.854872i | \(0.673635\pi\) | |||||||
\(68\) | −2.84075 | −0.344492 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.663102 | −0.0786957 | −0.0393479 | − | 0.999226i | \(-0.512528\pi\) | ||||
−0.0393479 | + | 0.999226i | \(0.512528\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.5345 | 1.93522 | 0.967609 | − | 0.252455i | \(-0.0812380\pi\) | ||||
0.967609 | + | 0.252455i | \(0.0812380\pi\) | |||||||
\(74\) | −1.05736 | −0.122915 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.0291 | −1.15042 | ||||||||
\(77\) | 11.8648 | 1.35212 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.54554 | 1.07396 | 0.536978 | − | 0.843596i | \(-0.319566\pi\) | ||||
0.536978 | + | 0.843596i | \(0.319566\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.49611 | −0.606944 | ||||||||
\(83\) | 0.0123998 | 0.00136106 | 0.000680528 | − | 1.00000i | \(-0.499783\pi\) | ||||
0.000680528 | 1.00000i | \(0.499783\pi\) | ||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.83978 | 0.629720 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.6203 | −1.13213 | ||||||||
\(89\) | 5.46783 | 0.579588 | 0.289794 | − | 0.957089i | \(-0.406413\pi\) | ||||
0.289794 | + | 0.957089i | \(0.406413\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.16789 | −0.227256 | ||||||||
\(92\) | 3.24091 | 0.337888 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.70056 | −0.381684 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.952006 | −0.0966615 | −0.0483308 | − | 0.998831i | \(-0.515390\pi\) | ||||
−0.0483308 | + | 0.998831i | \(0.515390\pi\) | |||||||
\(98\) | −0.518410 | −0.0523673 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.31781 | −0.827653 | −0.413826 | − | 0.910356i | \(-0.635808\pi\) | ||||
−0.413826 | + | 0.910356i | \(0.635808\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.4091 | 1.22271 | 0.611355 | − | 0.791357i | \(-0.290625\pi\) | ||||
0.611355 | + | 0.791357i | \(0.290625\pi\) | |||||||
\(104\) | 1.94050 | 0.190282 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.39698 | −0.815587 | ||||||||
\(107\) | 17.5579 | 1.69739 | 0.848695 | − | 0.528883i | \(-0.177389\pi\) | ||||
0.848695 | + | 0.528883i | \(0.177389\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00973 | 0.0967146 | 0.0483573 | − | 0.998830i | \(-0.484601\pi\) | ||||
0.0483573 | + | 0.998830i | \(0.484601\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.36866 | −0.318309 | ||||||||
\(113\) | 15.5787 | 1.46552 | 0.732761 | − | 0.680487i | \(-0.238232\pi\) | ||||
0.732761 | + | 0.680487i | \(0.238232\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.49235 | 0.138561 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.17792 | −0.292552 | ||||||||
\(119\) | −5.29157 | −0.485078 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.21701 | 0.656091 | ||||||||
\(122\) | 3.73992 | 0.338596 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 13.1634 | 1.18211 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.9536 | −1.50438 | −0.752192 | − | 0.658943i | \(-0.771004\pi\) | ||||
−0.752192 | + | 0.658943i | \(0.771004\pi\) | |||||||
\(128\) | 10.4421 | 0.922961 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.9324 | −1.04254 | −0.521268 | − | 0.853393i | \(-0.674541\pi\) | ||||
−0.521268 | + | 0.853393i | \(0.674541\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.6816 | −1.61990 | ||||||||
\(134\) | 6.05175 | 0.522792 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.73655 | 0.406156 | ||||||||
\(137\) | 0.239785 | 0.0204862 | 0.0102431 | − | 0.999948i | \(-0.496739\pi\) | ||||
0.0102431 | + | 0.999948i | \(0.496739\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.0255 | −1.44408 | −0.722040 | − | 0.691851i | \(-0.756795\pi\) | ||||
−0.722040 | + | 0.691851i | \(0.756795\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.472457 | 0.0396477 | ||||||||
\(143\) | −3.32853 | −0.278346 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.7808 | −0.974982 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.21468 | −0.182045 | ||||||||
\(149\) | 4.13046 | 0.338380 | 0.169190 | − | 0.985583i | \(-0.445885\pi\) | ||||
0.169190 | + | 0.985583i | \(0.445885\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.21580 | −0.261698 | −0.130849 | − | 0.991402i | \(-0.541770\pi\) | ||||
−0.130849 | + | 0.991402i | \(0.541770\pi\) | |||||||
\(152\) | 16.7221 | 1.35635 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.45362 | −0.681212 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.84237 | 0.546081 | 0.273040 | − | 0.962003i | \(-0.411971\pi\) | ||||
0.273040 | + | 0.962003i | \(0.411971\pi\) | |||||||
\(158\) | −6.80115 | −0.541070 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.03696 | 0.475779 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.0502 | −1.10050 | −0.550248 | − | 0.835001i | \(-0.685467\pi\) | ||||
−0.550248 | + | 0.835001i | \(0.685467\pi\) | |||||||
\(164\) | −11.5118 | −0.898923 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.00883480 | −0.000685713 0 | ||||||||
\(167\) | −17.8725 | −1.38301 | −0.691507 | − | 0.722370i | \(-0.743053\pi\) | ||||
−0.691507 | + | 0.722370i | \(0.743053\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3918 | −0.953217 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.2317 | 0.932656 | ||||||||
\(173\) | 2.82518 | 0.214795 | 0.107397 | − | 0.994216i | \(-0.465748\pi\) | ||||
0.107397 | + | 0.994216i | \(0.465748\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.17218 | −0.389868 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.89580 | −0.292002 | ||||||||
\(179\) | −20.2829 | −1.51601 | −0.758006 | − | 0.652247i | \(-0.773826\pi\) | ||||
−0.758006 | + | 0.652247i | \(0.773826\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.63783 | −0.642045 | −0.321023 | − | 0.947072i | \(-0.604027\pi\) | ||||
−0.321023 | + | 0.947072i | \(0.604027\pi\) | |||||||
\(182\) | 1.54461 | 0.114494 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.40376 | −0.398370 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.12458 | −0.594128 | ||||||||
\(188\) | −7.75099 | −0.565299 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.896850 | −0.0648938 | −0.0324469 | − | 0.999473i | \(-0.510330\pi\) | ||||
−0.0324469 | + | 0.999473i | \(0.510330\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.4506 | −0.752251 | −0.376126 | − | 0.926569i | \(-0.622744\pi\) | ||||
−0.376126 | + | 0.926569i | \(0.622744\pi\) | |||||||
\(194\) | 0.678299 | 0.0486991 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.08583 | −0.0775594 | ||||||||
\(197\) | −9.57740 | −0.682361 | −0.341181 | − | 0.939998i | \(-0.610827\pi\) | ||||
−0.341181 | + | 0.939998i | \(0.610827\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.61768 | 0.398227 | 0.199113 | − | 0.979976i | \(-0.436194\pi\) | ||||
0.199113 | + | 0.979976i | \(0.436194\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.92640 | 0.416980 | ||||||||
\(203\) | 2.77986 | 0.195108 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.84145 | −0.616013 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.945039 | 0.0655267 | ||||||||
\(209\) | −28.6834 | −1.98407 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.605216 | −0.0416648 | −0.0208324 | − | 0.999783i | \(-0.506632\pi\) | ||||
−0.0208324 | + | 0.999783i | \(0.506632\pi\) | |||||||
\(212\) | −17.5878 | −1.20794 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.5099 | −0.855162 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.5200 | 1.66453 | ||||||||
\(218\) | −0.719428 | −0.0487258 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.48449 | 0.0998575 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.5537 | 1.10852 | 0.554260 | − | 0.832344i | \(-0.313001\pi\) | ||||
0.554260 | + | 0.832344i | \(0.313001\pi\) | |||||||
\(224\) | 16.2343 | 1.08470 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.0997 | −0.738344 | ||||||||
\(227\) | 22.0061 | 1.46060 | 0.730299 | − | 0.683128i | \(-0.239381\pi\) | ||||
0.730299 | + | 0.683128i | \(0.239381\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.5647 | −1.62328 | −0.811641 | − | 0.584157i | \(-0.801425\pi\) | ||||
−0.811641 | + | 0.584157i | \(0.801425\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.48828 | −0.163364 | ||||||||
\(233\) | 5.56824 | 0.364787 | 0.182394 | − | 0.983226i | \(-0.441615\pi\) | ||||
0.182394 | + | 0.983226i | \(0.441615\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.65630 | −0.433288 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.77022 | 0.244387 | ||||||||
\(239\) | −6.90640 | −0.446738 | −0.223369 | − | 0.974734i | \(-0.571705\pi\) | ||||
−0.223369 | + | 0.974734i | \(0.571705\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.1989 | −1.62320 | −0.811602 | − | 0.584210i | \(-0.801404\pi\) | ||||
−0.811602 | + | 0.584210i | \(0.801404\pi\) | |||||||
\(242\) | −5.14208 | −0.330545 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.83342 | 0.501483 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.24091 | 0.333471 | ||||||||
\(248\) | −21.9482 | −1.39371 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.3687 | −1.79062 | −0.895309 | − | 0.445446i | \(-0.853045\pi\) | ||||
−0.895309 | + | 0.445446i | \(0.853045\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.26903 | 0.582739 | ||||||||
\(254\) | 12.0793 | 0.757924 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.9146 | −0.682163 | ||||||||
\(257\) | −8.71100 | −0.543377 | −0.271688 | − | 0.962385i | \(-0.587582\pi\) | ||||
−0.271688 | + | 0.962385i | \(0.587582\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.12536 | −0.256337 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.50175 | 0.525240 | ||||||||
\(263\) | 13.2128 | 0.814736 | 0.407368 | − | 0.913264i | \(-0.366447\pi\) | ||||
0.407368 | + | 0.913264i | \(0.366447\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 13.3106 | 0.816123 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.6757 | 0.774289 | ||||||||
\(269\) | 10.3447 | 0.630725 | 0.315363 | − | 0.948971i | \(-0.397874\pi\) | ||||
0.315363 | + | 0.948971i | \(0.397874\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.76022 | 0.592891 | 0.296445 | − | 0.955050i | \(-0.404199\pi\) | ||||
0.296445 | + | 0.955050i | \(0.404199\pi\) | |||||||
\(272\) | 2.30674 | 0.139866 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.170845 | −0.0103212 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.87503 | 0.112659 | 0.0563297 | − | 0.998412i | \(-0.482060\pi\) | ||||
0.0563297 | + | 0.998412i | \(0.482060\pi\) | |||||||
\(278\) | 12.1306 | 0.727542 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.2930 | 1.27024 | 0.635118 | − | 0.772415i | \(-0.280951\pi\) | ||||
0.635118 | + | 0.772415i | \(0.280951\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.8729 | −0.943544 | −0.471772 | − | 0.881721i | \(-0.656385\pi\) | ||||
−0.471772 | + | 0.881721i | \(0.656385\pi\) | |||||||
\(284\) | 0.989581 | 0.0587208 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.37156 | 0.140233 | ||||||||
\(287\) | −21.4435 | −1.26577 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.3765 | −0.786855 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −24.6753 | −1.44401 | ||||||||
\(293\) | 33.1369 | 1.93588 | 0.967938 | − | 0.251189i | \(-0.0808216\pi\) | ||||
0.967938 | + | 0.251189i | \(0.0808216\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.69266 | 0.214631 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.94293 | −0.170479 | ||||||||
\(299\) | −1.69360 | −0.0979433 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.7844 | 1.31327 | ||||||||
\(302\) | 2.29124 | 0.131846 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.14381 | 0.467080 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.2605 | −0.985109 | −0.492555 | − | 0.870282i | \(-0.663937\pi\) | ||||
−0.492555 | + | 0.870282i | \(0.663937\pi\) | |||||||
\(308\) | −17.7065 | −1.00892 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.5116 | 1.84356 | 0.921781 | − | 0.387711i | \(-0.126734\pi\) | ||||
0.921781 | + | 0.387711i | \(0.126734\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.26304 | −0.354008 | −0.177004 | − | 0.984210i | \(-0.556641\pi\) | ||||
−0.177004 | + | 0.984210i | \(0.556641\pi\) | |||||||
\(314\) | −4.87516 | −0.275121 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.2453 | −0.801360 | ||||||||
\(317\) | −18.8523 | −1.05885 | −0.529426 | − | 0.848356i | \(-0.677593\pi\) | ||||
−0.529426 | + | 0.848356i | \(0.677593\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.26814 | 0.238970 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.30130 | −0.239702 | ||||||||
\(323\) | 12.7925 | 0.711793 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.0107 | 0.554441 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 19.1943 | 1.05983 | ||||||||
\(329\) | −14.4380 | −0.795995 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.596245 | −0.0327726 | −0.0163863 | − | 0.999866i | \(-0.505216\pi\) | ||||
−0.0163863 | + | 0.999866i | \(0.505216\pi\) | |||||||
\(332\) | −0.0185049 | −0.00101559 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.7341 | 0.696776 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.6414 | −1.77809 | −0.889046 | − | 0.457818i | \(-0.848631\pi\) | ||||
−0.889046 | + | 0.457818i | \(0.848631\pi\) | |||||||
\(338\) | 8.82911 | 0.480240 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 37.6476 | 2.03873 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.4364 | 0.941476 | ||||||||
\(344\) | −20.3946 | −1.09960 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.01293 | −0.108216 | ||||||||
\(347\) | −13.1985 | −0.708531 | −0.354265 | − | 0.935145i | \(-0.615269\pi\) | ||||
−0.354265 | + | 0.935145i | \(0.615269\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.6412 | 0.837255 | 0.418628 | − | 0.908158i | \(-0.362511\pi\) | ||||
0.418628 | + | 0.908158i | \(0.362511\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 24.9258 | 1.32855 | ||||||||
\(353\) | −5.65486 | −0.300978 | −0.150489 | − | 0.988612i | \(-0.548085\pi\) | ||||
−0.150489 | + | 0.988612i | \(0.548085\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8.15991 | −0.432475 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.4514 | 0.763782 | ||||||||
\(359\) | −25.2693 | −1.33366 | −0.666832 | − | 0.745208i | \(-0.732350\pi\) | ||||
−0.666832 | + | 0.745208i | \(0.732350\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.1632 | 1.37701 | ||||||||
\(362\) | 6.15441 | 0.323469 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.23525 | 0.169573 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.2788 | 1.37174 | 0.685872 | − | 0.727722i | \(-0.259421\pi\) | ||||
0.685872 | + | 0.727722i | \(0.259421\pi\) | |||||||
\(368\) | −2.63167 | −0.137185 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −32.7615 | −1.70089 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.43033 | 0.0740596 | 0.0370298 | − | 0.999314i | \(-0.488210\pi\) | ||||
0.0370298 | + | 0.999314i | \(0.488210\pi\) | |||||||
\(374\) | 5.78872 | 0.299328 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.9237 | 0.666487 | ||||||||
\(377\) | −0.779856 | −0.0401646 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.2336 | −1.80983 | −0.904915 | − | 0.425591i | \(-0.860066\pi\) | ||||
−0.904915 | + | 0.425591i | \(0.860066\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.639001 | 0.0326941 | ||||||||
\(383\) | −32.0701 | −1.63870 | −0.819352 | − | 0.573291i | \(-0.805666\pi\) | ||||
−0.819352 | + | 0.573291i | \(0.805666\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.44601 | 0.378992 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.42073 | 0.0721265 | ||||||||
\(389\) | −1.63922 | −0.0831117 | −0.0415558 | − | 0.999136i | \(-0.513231\pi\) | ||||
−0.0415558 | + | 0.999136i | \(0.513231\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.13389 | −0.209060 | ||||||||
\(392\) | 1.81047 | 0.0914425 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.82385 | 0.343781 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.04098 | −0.102434 | −0.0512170 | − | 0.998688i | \(-0.516310\pi\) | ||||
−0.0512170 | + | 0.998688i | \(0.516310\pi\) | |||||||
\(398\) | −4.00257 | −0.200631 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.4108 | −0.869455 | −0.434727 | − | 0.900562i | \(-0.643155\pi\) | ||||
−0.434727 | + | 0.900562i | \(0.643155\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.87880 | −0.342658 | ||||||||
\(404\) | 12.4131 | 0.617574 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.98063 | −0.0982972 | ||||||||
\(407\) | −6.33400 | −0.313965 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −37.3010 | −1.84441 | −0.922207 | − | 0.386696i | \(-0.873616\pi\) | ||||
−0.922207 | + | 0.386696i | \(0.873616\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −18.5188 | −0.912356 | ||||||||
\(413\) | −12.3989 | −0.610111 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.55434 | −0.223295 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 20.4368 | 0.999596 | ||||||||
\(419\) | −4.32941 | −0.211506 | −0.105753 | − | 0.994392i | \(-0.533725\pi\) | ||||
−0.105753 | + | 0.994392i | \(0.533725\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.2505 | −1.66927 | −0.834634 | − | 0.550806i | \(-0.814321\pi\) | ||||
−0.834634 | + | 0.550806i | \(0.814321\pi\) | |||||||
\(422\) | 0.431214 | 0.0209911 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 29.3252 | 1.42416 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.5916 | 0.706137 | ||||||||
\(428\) | −26.2026 | −1.26655 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.4885 | −1.66125 | −0.830626 | − | 0.556831i | \(-0.812017\pi\) | ||||
−0.830626 | + | 0.556831i | \(0.812017\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.02258 | −0.145256 | −0.0726279 | − | 0.997359i | \(-0.523139\pi\) | ||||
−0.0726279 | + | 0.997359i | \(0.523139\pi\) | |||||||
\(434\) | −17.4704 | −0.838606 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.50687 | −0.0721661 | ||||||||
\(437\) | −14.5945 | −0.698148 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.37392 | 0.399665 | 0.199833 | − | 0.979830i | \(-0.435960\pi\) | ||||
0.199833 | + | 0.979830i | \(0.435960\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.05769 | −0.0503092 | ||||||||
\(443\) | −29.8770 | −1.41950 | −0.709749 | − | 0.704454i | \(-0.751192\pi\) | ||||
−0.709749 | + | 0.704454i | \(0.751192\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.7945 | −0.558484 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.82952 | −0.228174 | ||||||||
\(449\) | −12.0780 | −0.569994 | −0.284997 | − | 0.958528i | \(-0.591993\pi\) | ||||
−0.284997 | + | 0.958528i | \(0.591993\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.9240 | −1.55033 | ||||||||
\(452\) | −23.2489 | −1.09354 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −15.6793 | −0.735864 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.03357 | −0.141905 | −0.0709523 | − | 0.997480i | \(-0.522604\pi\) | ||||
−0.0709523 | + | 0.997480i | \(0.522604\pi\) | |||||||
\(458\) | 17.5022 | 0.817826 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.44508 | 0.207028 | 0.103514 | − | 0.994628i | \(-0.466991\pi\) | ||||
0.103514 | + | 0.994628i | \(0.466991\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.04875 | 0.420531 | 0.210266 | − | 0.977644i | \(-0.432567\pi\) | ||||
0.210266 | + | 0.977644i | \(0.432567\pi\) | |||||||
\(464\) | −1.21181 | −0.0562570 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.96734 | −0.183784 | ||||||||
\(467\) | 8.11327 | 0.375437 | 0.187719 | − | 0.982223i | \(-0.439891\pi\) | ||||
0.187719 | + | 0.982223i | \(0.439891\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.6114 | 1.09027 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.0984 | 0.510847 | ||||||||
\(473\) | 34.9827 | 1.60851 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.89688 | 0.361953 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.92078 | 0.225071 | ||||||||
\(479\) | −6.62947 | −0.302908 | −0.151454 | − | 0.988464i | \(-0.548396\pi\) | ||||
−0.151454 | + | 0.988464i | \(0.548396\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.15732 | 0.0527693 | ||||||||
\(482\) | 17.9541 | 0.817787 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.7703 | −0.489559 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.2047 | 1.32339 | 0.661695 | − | 0.749773i | \(-0.269837\pi\) | ||||
0.661695 | + | 0.749773i | \(0.269837\pi\) | |||||||
\(488\) | −13.0611 | −0.591249 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.32464 | 0.195168 | 0.0975841 | − | 0.995227i | \(-0.468889\pi\) | ||||
0.0975841 | + | 0.995227i | \(0.468889\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.90354 | −0.0857312 | ||||||||
\(494\) | −3.73412 | −0.168006 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.6889 | −0.479947 | ||||||||
\(497\) | 1.84333 | 0.0826846 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.29688 | 0.192355 | 0.0961774 | − | 0.995364i | \(-0.469338\pi\) | ||||
0.0961774 | + | 0.995364i | \(0.469338\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.2126 | 0.902131 | ||||||||
\(503\) | −14.2512 | −0.635429 | −0.317715 | − | 0.948186i | \(-0.602915\pi\) | ||||
−0.317715 | + | 0.948186i | \(0.602915\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.60414 | −0.293590 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 25.3007 | 1.12254 | ||||||||
\(509\) | 19.4974 | 0.864206 | 0.432103 | − | 0.901824i | \(-0.357772\pi\) | ||||
0.432103 | + | 0.901824i | \(0.357772\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −45.9635 | −2.03331 | ||||||||
\(512\) | −13.1076 | −0.579280 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.20654 | 0.273759 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.1679 | −0.974943 | ||||||||
\(518\) | 2.93930 | 0.129145 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.5229 | −1.07437 | −0.537185 | − | 0.843465i | \(-0.680512\pi\) | ||||
−0.537185 | + | 0.843465i | \(0.680512\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.8566 | 0.474725 | 0.237362 | − | 0.971421i | \(-0.423717\pi\) | ||||
0.237362 | + | 0.971421i | \(0.423717\pi\) | |||||||
\(524\) | 17.8073 | 0.777914 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.41406 | −0.410472 | ||||||||
\(527\) | −16.7904 | −0.731401 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.2838 | −0.794948 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 27.8795 | 1.20873 | ||||||||
\(533\) | 6.01572 | 0.260570 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −21.1348 | −0.912886 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.37052 | −0.317766 | ||||||||
\(539\) | −3.10549 | −0.133763 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.7032 | −0.976085 | −0.488043 | − | 0.872820i | \(-0.662289\pi\) | ||||
−0.488043 | + | 0.872820i | \(0.662289\pi\) | |||||||
\(542\) | −6.95410 | −0.298704 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −11.1166 | −0.476622 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.8229 | 1.40340 | 0.701702 | − | 0.712471i | \(-0.252424\pi\) | ||||
0.701702 | + | 0.712471i | \(0.252424\pi\) | |||||||
\(548\) | −0.357843 | −0.0152863 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.72036 | −0.286297 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.5352 | −1.12839 | ||||||||
\(554\) | −1.33595 | −0.0567590 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 25.4080 | 1.07754 | ||||||||
\(557\) | 26.3234 | 1.11536 | 0.557679 | − | 0.830057i | \(-0.311692\pi\) | ||||
0.557679 | + | 0.830057i | \(0.311692\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.39189 | −0.270348 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.1712 | −0.639958 | ||||||||
\(563\) | 28.4750 | 1.20008 | 0.600039 | − | 0.799971i | \(-0.295152\pi\) | ||||
0.600039 | + | 0.799971i | \(0.295152\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.3093 | 0.475367 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.64999 | −0.0692318 | ||||||||
\(569\) | 14.7555 | 0.618582 | 0.309291 | − | 0.950967i | \(-0.399908\pi\) | ||||
0.309291 | + | 0.950967i | \(0.399908\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.204397 | −0.00855376 | −0.00427688 | − | 0.999991i | \(-0.501361\pi\) | ||||
−0.00427688 | + | 0.999991i | \(0.501361\pi\) | |||||||
\(572\) | 4.96734 | 0.207695 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 15.2784 | 0.637708 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.3300 | 1.55407 | 0.777035 | − | 0.629457i | \(-0.216723\pi\) | ||||
0.777035 | + | 0.629457i | \(0.216723\pi\) | |||||||
\(578\) | 9.53071 | 0.396425 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.0344697 | −0.00143004 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −50.3014 | −2.08327 | ||||||||
\(584\) | 41.1425 | 1.70249 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.6098 | −0.975314 | ||||||||
\(587\) | −10.8497 | −0.447813 | −0.223907 | − | 0.974611i | \(-0.571881\pi\) | ||||
−0.223907 | + | 0.974611i | \(0.571881\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −59.2776 | −2.44249 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.79835 | 0.0739119 | ||||||||
\(593\) | 14.0575 | 0.577272 | 0.288636 | − | 0.957439i | \(-0.406798\pi\) | ||||
0.288636 | + | 0.957439i | \(0.406798\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.16409 | −0.252491 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.20668 | 0.0493448 | ||||||||
\(599\) | 5.52446 | 0.225724 | 0.112862 | − | 0.993611i | \(-0.463998\pi\) | ||||
0.112862 | + | 0.993611i | \(0.463998\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.85394 | −0.279578 | −0.139789 | − | 0.990181i | \(-0.544642\pi\) | ||||
−0.139789 | + | 0.990181i | \(0.544642\pi\) | |||||||
\(602\) | −16.2337 | −0.661638 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.79910 | 0.195273 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.4979 | −1.23787 | −0.618935 | − | 0.785442i | \(-0.712436\pi\) | ||||
−0.618935 | + | 0.785442i | \(0.712436\pi\) | |||||||
\(608\) | −39.2467 | −1.59166 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.05042 | 0.163863 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.9211 | −1.20850 | −0.604250 | − | 0.796794i | \(-0.706527\pi\) | ||||
−0.604250 | + | 0.796794i | \(0.706527\pi\) | |||||||
\(614\) | 12.2980 | 0.496308 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 29.5230 | 1.18952 | ||||||||
\(617\) | −1.04305 | −0.0419917 | −0.0209959 | − | 0.999780i | \(-0.506684\pi\) | ||||
−0.0209959 | + | 0.999780i | \(0.506684\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.1661 | 0.890930 | 0.445465 | − | 0.895299i | \(-0.353038\pi\) | ||||
0.445465 | + | 0.895299i | \(0.353038\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −23.1643 | −0.928805 | ||||||||
\(623\) | −15.1998 | −0.608966 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.46238 | 0.178353 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.2112 | −0.407472 | ||||||||
\(629\) | 2.82489 | 0.112636 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.1089 | 0.800524 | 0.400262 | − | 0.916401i | \(-0.368919\pi\) | ||||
0.400262 | + | 0.916401i | \(0.368919\pi\) | |||||||
\(632\) | 23.7520 | 0.944804 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.4322 | 0.533460 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.567422 | 0.0224821 | ||||||||
\(638\) | −3.04103 | −0.120395 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.93422 | −0.234388 | −0.117194 | − | 0.993109i | \(-0.537390\pi\) | ||||
−0.117194 | + | 0.993109i | \(0.537390\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.951317 | −0.0375163 | −0.0187581 | − | 0.999824i | \(-0.505971\pi\) | ||||
−0.0187581 | + | 0.999824i | \(0.505971\pi\) | |||||||
\(644\) | −9.00926 | −0.355015 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.11458 | −0.358608 | ||||||||
\(647\) | −35.1384 | −1.38143 | −0.690716 | − | 0.723126i | \(-0.742705\pi\) | ||||
−0.690716 | + | 0.723126i | \(0.742705\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.0371 | −0.747271 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.9678 | 0.821163 | ||||||||
\(653\) | −45.9930 | −1.79984 | −0.899922 | − | 0.436050i | \(-0.856377\pi\) | ||||
−0.899922 | + | 0.436050i | \(0.856377\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.34779 | 0.364970 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 10.2870 | 0.401030 | ||||||||
\(659\) | 19.3162 | 0.752451 | 0.376226 | − | 0.926528i | \(-0.377222\pi\) | ||||
0.376226 | + | 0.926528i | \(0.377222\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.3224 | 1.72394 | 0.861970 | − | 0.506959i | \(-0.169230\pi\) | ||||
0.861970 | + | 0.506959i | \(0.169230\pi\) | |||||||
\(662\) | 0.424821 | 0.0165111 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.0308542 | 0.00119738 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.17168 | 0.0840878 | ||||||||
\(668\) | 26.6720 | 1.03197 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.4037 | 0.864883 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.7421 | −0.491170 | −0.245585 | − | 0.969375i | \(-0.578980\pi\) | ||||
−0.245585 | + | 0.969375i | \(0.578980\pi\) | |||||||
\(674\) | 23.2569 | 0.895821 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.4930 | 0.711267 | ||||||||
\(677\) | −9.41654 | −0.361907 | −0.180954 | − | 0.983492i | \(-0.557918\pi\) | ||||
−0.180954 | + | 0.983492i | \(0.557918\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.64644 | 0.101561 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −26.8237 | −1.02713 | ||||||||
\(683\) | 6.92316 | 0.264907 | 0.132454 | − | 0.991189i | \(-0.457714\pi\) | ||||
0.132454 | + | 0.991189i | \(0.457714\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12.4233 | −0.474325 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.93231 | −0.378666 | ||||||||
\(689\) | 9.19085 | 0.350144 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −48.7272 | −1.85367 | −0.926835 | − | 0.375469i | \(-0.877482\pi\) | ||||
−0.926835 | + | 0.375469i | \(0.877482\pi\) | |||||||
\(692\) | −4.21616 | −0.160274 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.40384 | 0.356965 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.6837 | 0.556186 | ||||||||
\(698\) | −11.1443 | −0.421818 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.88580 | −0.108995 | −0.0544975 | − | 0.998514i | \(-0.517356\pi\) | ||||
−0.0544975 | + | 0.998514i | \(0.517356\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.97314 | 0.376144 | ||||||||
\(704\) | −7.41516 | −0.279469 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.02906 | 0.151636 | ||||||||
\(707\) | 23.1223 | 0.869604 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.73056 | −0.0649924 | −0.0324962 | − | 0.999472i | \(-0.510346\pi\) | ||||
−0.0324962 | + | 0.999472i | \(0.510346\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.6055 | 0.509887 | ||||||||
\(713\) | 19.1555 | 0.717381 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 30.2692 | 1.13121 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.0043 | 0.671913 | ||||||||
\(719\) | 12.9089 | 0.481420 | 0.240710 | − | 0.970597i | \(-0.422620\pi\) | ||||
0.240710 | + | 0.970597i | \(0.422620\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34.4956 | −1.28468 | ||||||||
\(722\) | −18.6412 | −0.693752 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.8907 | 0.479078 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.3405 | 1.42197 | 0.710985 | − | 0.703207i | \(-0.248249\pi\) | ||||
0.710985 | + | 0.703207i | \(0.248249\pi\) | |||||||
\(728\) | −5.39431 | −0.199927 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.6019 | −0.577057 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.8966 | 1.28894 | 0.644468 | − | 0.764631i | \(-0.277079\pi\) | ||||
0.644468 | + | 0.764631i | \(0.277079\pi\) | |||||||
\(734\) | −18.7235 | −0.691098 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.6826 | 0.467485 | ||||||||
\(737\) | 36.2525 | 1.33538 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.2969 | 0.525921 | 0.262960 | − | 0.964807i | \(-0.415301\pi\) | ||||
0.262960 | + | 0.964807i | \(0.415301\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 23.3424 | 0.856927 | ||||||||
\(743\) | −44.1357 | −1.61918 | −0.809591 | − | 0.586995i | \(-0.800311\pi\) | ||||
−0.809591 | + | 0.586995i | \(0.800311\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.01910 | −0.0373120 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.1247 | 0.443324 | ||||||||
\(749\) | −48.8085 | −1.78343 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.56375 | 0.348986 | 0.174493 | − | 0.984658i | \(-0.444171\pi\) | ||||
0.174493 | + | 0.984658i | \(0.444171\pi\) | |||||||
\(752\) | 6.29393 | 0.229516 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.555643 | 0.0202353 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.1910 | −1.09731 | −0.548656 | − | 0.836048i | \(-0.684860\pi\) | ||||
−0.548656 | + | 0.836048i | \(0.684860\pi\) | |||||||
\(758\) | 25.1038 | 0.911811 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.27038 | −0.299801 | −0.149900 | − | 0.988701i | \(-0.547895\pi\) | ||||
−0.149900 | + | 0.988701i | \(0.547895\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.80690 | −0.101617 | ||||||||
\(764\) | 1.33841 | 0.0484221 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.8498 | 0.825595 | ||||||||
\(767\) | 3.47837 | 0.125597 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.4592 | −0.809901 | −0.404950 | − | 0.914339i | \(-0.632711\pi\) | ||||
−0.404950 | + | 0.914339i | \(0.632711\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 15.5960 | 0.561311 | ||||||||
\(773\) | −26.9520 | −0.969398 | −0.484699 | − | 0.874681i | \(-0.661071\pi\) | ||||
−0.484699 | + | 0.874681i | \(0.661071\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.36886 | −0.0850371 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.16794 | 0.0418725 | ||||||||
\(779\) | 51.8401 | 1.85737 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.83021 | 0.101273 | ||||||||
\(782\) | 2.94537 | 0.105326 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.881713 | 0.0314897 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.16423 | −0.0415004 | −0.0207502 | − | 0.999785i | \(-0.506605\pi\) | ||||
−0.0207502 | + | 0.999785i | \(0.506605\pi\) | |||||||
\(788\) | 14.2928 | 0.509161 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −43.3065 | −1.53980 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.09350 | −0.145364 | ||||||||
\(794\) | 1.45419 | 0.0516073 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.38354 | −0.297147 | ||||||||
\(797\) | 15.9624 | 0.565418 | 0.282709 | − | 0.959206i | \(-0.408767\pi\) | ||||
0.282709 | + | 0.959206i | \(0.408767\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.88664 | 0.349764 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.4051 | 0.438040 | ||||||||
\(803\) | −70.5715 | −2.49042 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.90111 | 0.172634 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −20.6971 | −0.728120 | ||||||||
\(809\) | 7.83605 | 0.275501 | 0.137750 | − | 0.990467i | \(-0.456013\pi\) | ||||
0.137750 | + | 0.990467i | \(0.456013\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.9935 | −0.842526 | −0.421263 | − | 0.906939i | \(-0.638413\pi\) | ||||
−0.421263 | + | 0.906939i | \(0.638413\pi\) | |||||||
\(812\) | −4.14852 | −0.145585 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.51294 | 0.158179 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −55.0817 | −1.92706 | ||||||||
\(818\) | 26.5768 | 0.929235 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.8804 | 0.449528 | 0.224764 | − | 0.974413i | \(-0.427839\pi\) | ||||
0.224764 | + | 0.974413i | \(0.427839\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.8165 | −1.66678 | −0.833389 | − | 0.552687i | \(-0.813603\pi\) | ||||
−0.833389 | + | 0.552687i | \(0.813603\pi\) | |||||||
\(824\) | 30.8775 | 1.07567 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.83417 | 0.307380 | ||||||||
\(827\) | −14.6873 | −0.510726 | −0.255363 | − | 0.966845i | \(-0.582195\pi\) | ||||
−0.255363 | + | 0.966845i | \(0.582195\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.9876 | 1.45829 | 0.729145 | − | 0.684359i | \(-0.239918\pi\) | ||||
0.729145 | + | 0.684359i | \(0.239918\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.35487 | 0.0469715 | ||||||||
\(833\) | 1.38501 | 0.0479879 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 42.8057 | 1.48047 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.08468 | 0.106559 | ||||||||
\(839\) | 4.04408 | 0.139617 | 0.0698085 | − | 0.997560i | \(-0.477761\pi\) | ||||
0.0698085 | + | 0.997560i | \(0.477761\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 24.4033 | 0.840994 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.903195 | 0.0310892 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.0622 | −0.689347 | ||||||||
\(848\) | 14.2816 | 0.490432 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.22282 | −0.110477 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.8299 | 1.50071 | 0.750353 | − | 0.661037i | \(-0.229883\pi\) | ||||
0.750353 | + | 0.661037i | \(0.229883\pi\) | |||||||
\(854\) | −10.3964 | −0.355759 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 43.6891 | 1.49326 | ||||||||
\(857\) | 2.09275 | 0.0714868 | 0.0357434 | − | 0.999361i | \(-0.488620\pi\) | ||||
0.0357434 | + | 0.999361i | \(0.488620\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.5885 | 1.58958 | 0.794790 | − | 0.606885i | \(-0.207581\pi\) | ||||
0.794790 | + | 0.606885i | \(0.207581\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.5729 | 0.836955 | ||||||||
\(863\) | 32.1466 | 1.09428 | 0.547141 | − | 0.837040i | \(-0.315716\pi\) | ||||
0.547141 | + | 0.837040i | \(0.315716\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.15357 | 0.0731814 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −36.5925 | −1.24203 | ||||||||
\(869\) | −40.7417 | −1.38207 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.62390 | −0.224442 | ||||||||
\(872\) | 2.51249 | 0.0850838 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 10.3985 | 0.351734 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −48.0544 | −1.62268 | −0.811342 | − | 0.584572i | \(-0.801262\pi\) | ||||
−0.811342 | + | 0.584572i | \(0.801262\pi\) | |||||||
\(878\) | −5.96637 | −0.201355 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.9846 | 1.04390 | 0.521950 | − | 0.852976i | \(-0.325205\pi\) | ||||
0.521950 | + | 0.852976i | \(0.325205\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.60378 | −0.323193 | −0.161597 | − | 0.986857i | \(-0.551664\pi\) | ||||
−0.161597 | + | 0.986857i | \(0.551664\pi\) | |||||||
\(884\) | −2.21538 | −0.0745112 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.2872 | 0.715158 | ||||||||
\(887\) | −29.7279 | −0.998165 | −0.499083 | − | 0.866554i | \(-0.666330\pi\) | ||||
−0.499083 | + | 0.866554i | \(0.666330\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 47.1284 | 1.58064 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −24.7040 | −0.827150 | ||||||||
\(893\) | 34.9043 | 1.16803 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −29.0276 | −0.969743 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.60548 | 0.287169 | ||||||||
\(899\) | 8.82061 | 0.294184 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.4339 | 0.747380 | ||||||||
\(902\) | 23.4582 | 0.781071 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 38.7642 | 1.28928 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.35876 | −0.144730 | −0.0723651 | − | 0.997378i | \(-0.523055\pi\) | ||||
−0.0723651 | + | 0.997378i | \(0.523055\pi\) | |||||||
\(908\) | −32.8409 | −1.08986 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.389317 | 0.0128986 | 0.00644932 | − | 0.999979i | \(-0.497947\pi\) | ||||
0.00644932 | + | 0.999979i | \(0.497947\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.0529241 | −0.00175153 | ||||||||
\(914\) | 2.16141 | 0.0714930 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 36.6592 | 1.21125 | ||||||||
\(917\) | 33.1703 | 1.09538 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −54.9915 | −1.81400 | −0.907001 | − | 0.421128i | \(-0.861634\pi\) | ||||
−0.907001 | + | 0.421128i | \(0.861634\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.16710 | −0.104303 | ||||||||
\(923\) | −0.517124 | −0.0170213 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.44719 | −0.211868 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.83998 | 0.191707 | ||||||||
\(929\) | −17.4617 | −0.572901 | −0.286450 | − | 0.958095i | \(-0.592475\pi\) | ||||
−0.286450 | + | 0.958095i | \(0.592475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.88972 | 0.160254 | ||||||||
\(932\) | −8.30977 | −0.272195 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.78066 | −0.189149 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.4261 | −0.895970 | −0.447985 | − | 0.894041i | \(-0.647858\pi\) | ||||
−0.447985 | + | 0.894041i | \(0.647858\pi\) | |||||||
\(938\) | −16.8230 | −0.549291 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.1587 | 1.14614 | 0.573070 | − | 0.819506i | \(-0.305752\pi\) | ||||
0.573070 | + | 0.819506i | \(0.305752\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.7521 | −0.545524 | ||||||||
\(944\) | 5.40502 | 0.175918 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.9250 | −0.810381 | ||||||||
\(947\) | −44.1438 | −1.43448 | −0.717240 | − | 0.696827i | \(-0.754595\pi\) | ||||
−0.717240 | + | 0.696827i | \(0.754595\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.8945 | 0.418574 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −13.1669 | −0.426743 | ||||||||
\(953\) | −27.3169 | −0.884881 | −0.442441 | − | 0.896798i | \(-0.645887\pi\) | ||||
−0.442441 | + | 0.896798i | \(0.645887\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.3068 | 0.333345 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.72346 | 0.152608 | ||||||||
\(959\) | −0.666567 | −0.0215246 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.8031 | 1.50978 | ||||||||
\(962\) | −0.824585 | −0.0265857 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 37.6056 | 1.21120 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −54.3910 | −1.74910 | −0.874548 | − | 0.484939i | \(-0.838842\pi\) | ||||
−0.874548 | + | 0.484939i | \(0.838842\pi\) | |||||||
\(968\) | 17.9579 | 0.577190 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.2906 | 0.458606 | 0.229303 | − | 0.973355i | \(-0.426355\pi\) | ||||
0.229303 | + | 0.973355i | \(0.426355\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 47.3283 | 1.51728 | ||||||||
\(974\) | −20.8082 | −0.666737 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.36086 | −0.203606 | ||||||||
\(977\) | −8.94905 | −0.286306 | −0.143153 | − | 0.989701i | \(-0.545724\pi\) | ||||
−0.143153 | + | 0.989701i | \(0.545724\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.3374 | −0.745868 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.08128 | −0.0983277 | ||||||||
\(983\) | −22.1981 | −0.708010 | −0.354005 | − | 0.935244i | \(-0.615180\pi\) | ||||
−0.354005 | + | 0.935244i | \(0.615180\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.35626 | 0.0431923 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.82128 | −0.248828 | ||||||||
\(989\) | 17.7996 | 0.565995 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.2764 | −0.421740 | −0.210870 | − | 0.977514i | \(-0.567630\pi\) | ||||
−0.210870 | + | 0.977514i | \(0.567630\pi\) | |||||||
\(992\) | 51.5121 | 1.63551 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.31336 | −0.0416573 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.6929 | 0.623682 | 0.311841 | − | 0.950134i | \(-0.399054\pi\) | ||||
0.311841 | + | 0.950134i | \(0.399054\pi\) | |||||||
\(998\) | −3.06150 | −0.0969102 | ||||||||
\(999\) | 0 | 0 |
(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 | 6525.2.a.bs.1.2 | 5 | ||
3.2 | odd | 2 | 2175.2.a.w.1.4 | 5 | |||
5.2 | odd | 4 | 1305.2.c.j.784.5 | 10 | |||
5.3 | odd | 4 | 1305.2.c.j.784.6 | 10 | |||
5.4 | even | 2 | 6525.2.a.bl.1.4 | 5 | |||
15.2 | even | 4 | 435.2.c.e.349.6 | yes | 10 | ||
15.8 | even | 4 | 435.2.c.e.349.5 | ✓ | 10 | ||
15.14 | odd | 2 | 2175.2.a.z.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
435.2.c.e.349.5 | ✓ | 10 | 15.8 | even | 4 | ||
435.2.c.e.349.6 | yes | 10 | 15.2 | even | 4 | ||
1305.2.c.j.784.5 | 10 | 5.2 | odd | 4 | |||
1305.2.c.j.784.6 | 10 | 5.3 | odd | 4 | |||
2175.2.a.w.1.4 | 5 | 3.2 | odd | 2 | |||
2175.2.a.z.1.2 | 5 | 15.14 | odd | 2 | |||
6525.2.a.bl.1.4 | 5 | 5.4 | even | 2 | |||
6525.2.a.bs.1.2 | 5 | 1.1 | even | 1 | trivial |