Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1560,2,Mod(961,1560)]
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, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1560.961");
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.g (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: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{41})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 21x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 961.2 | ||
Root | \(2.70156i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.961 |
Dual form | 1560.2.g.f.961.3 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.70156i | 0.643130i | 0.946888 | + | 0.321565i | \(0.104209\pi\) | ||||
−0.946888 | + | 0.321565i | \(0.895791\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.70156i | − | 1.11606i | −0.829820 | − | 0.558031i | \(-0.811557\pi\) | ||
0.829820 | − | 0.558031i | \(-0.188443\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | + | 3.00000i | 0.554700 | + | 0.832050i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.298438 | 0.0723818 | 0.0361909 | − | 0.999345i | \(-0.488478\pi\) | ||||
0.0361909 | + | 0.999345i | \(0.488478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.40312i | − | 1.23956i | −0.784775 | − | 0.619781i | \(-0.787221\pi\) | ||
0.784775 | − | 0.619781i | \(-0.212779\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.70156i | − | 0.371311i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.70156 | −0.771829 | −0.385915 | − | 0.922535i | \(-0.626114\pi\) | ||||
−0.385915 | + | 0.922535i | \(0.626114\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.40312i | 0.611219i | 0.952157 | + | 0.305610i | \(0.0988602\pi\) | ||||
−0.952157 | + | 0.305610i | \(0.901140\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.70156i | 0.644359i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.70156 | 0.287616 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.70156i | 0.608533i | 0.952587 | + | 0.304267i | \(0.0984113\pi\) | ||||
−0.952587 | + | 0.304267i | \(0.901589\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.00000 | − | 3.00000i | −0.320256 | − | 0.480384i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.29844i | − | 0.358956i | −0.983762 | − | 0.179478i | \(-0.942559\pi\) | ||
0.983762 | − | 0.179478i | \(-0.0574408\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.4031 | 1.73896 | 0.869480 | − | 0.493968i | \(-0.164454\pi\) | ||||
0.869480 | + | 0.493968i | \(0.164454\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 8.00000i | − | 1.16692i | −0.812142 | − | 0.583460i | \(-0.801699\pi\) | ||
0.812142 | − | 0.583460i | \(-0.198301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.10469 | 0.586384 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.298438 | −0.0417897 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.29844 | 0.315715 | 0.157857 | − | 0.987462i | \(-0.449541\pi\) | ||||
0.157857 | + | 0.987462i | \(0.449541\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.70156 | −0.499119 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.40312i | 0.715661i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 13.4031i | − | 1.74494i | −0.488669 | − | 0.872469i | \(-0.662518\pi\) | ||
0.488669 | − | 0.872469i | \(-0.337482\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.298438 | 0.0382111 | 0.0191055 | − | 0.999817i | \(-0.493918\pi\) | ||||
0.0191055 | + | 0.999817i | \(0.493918\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.70156i | 0.214377i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.00000 | − | 2.00000i | 0.372104 | − | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.00000i | − | 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.70156 | 0.445616 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.70156i | − | 0.676651i | −0.941029 | − | 0.338325i | \(-0.890140\pi\) | ||
0.941029 | − | 0.338325i | \(-0.109860\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.8062i | − | 1.49886i | −0.662085 | − | 0.749429i | \(-0.730328\pi\) | ||
0.662085 | − | 0.749429i | \(-0.269672\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.29844 | 0.717774 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.70156 | −1.09151 | −0.545756 | − | 0.837944i | \(-0.683757\pi\) | ||||
−0.545756 | + | 0.837944i | \(0.683757\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.40312i | 0.373541i | 0.982404 | + | 0.186771i | \(0.0598021\pi\) | ||||
−0.982404 | + | 0.186771i | \(0.940198\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 0.298438i | − | 0.0323701i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.70156i | 0.180365i | 0.995925 | + | 0.0901826i | \(0.0287451\pi\) | ||||
−0.995925 | + | 0.0901826i | \(0.971255\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.10469 | + | 3.40312i | −0.535117 | + | 0.356744i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 3.40312i | − | 0.352888i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.40312 | −0.554349 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.10469i | − | 0.315233i | −0.987500 | − | 0.157617i | \(-0.949619\pi\) | ||
0.987500 | − | 0.157617i | \(-0.0503810\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.70156i | − | 0.372021i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.8062 | 1.67228 | 0.836142 | − | 0.548513i | \(-0.184806\pi\) | ||||
0.836142 | + | 0.548513i | \(0.184806\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.40312 | 0.926517 | 0.463259 | − | 0.886223i | \(-0.346680\pi\) | ||||
0.463259 | + | 0.886223i | \(0.346680\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.70156 | −0.166055 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.1047 | 1.26688 | 0.633439 | − | 0.773793i | \(-0.281643\pi\) | ||||
0.633439 | + | 0.773793i | \(0.281643\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.00000i | − | 0.574696i | −0.957826 | − | 0.287348i | \(-0.907226\pi\) | ||
0.957826 | − | 0.287348i | \(-0.0927736\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 3.70156i | − | 0.351337i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.70156i | 0.345172i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000 | + | 3.00000i | 0.184900 | + | 0.277350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.507811i | 0.0465509i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.70156 | −0.245597 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.29844i | 0.207243i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.8062 | −1.49131 | −0.745657 | − | 0.666330i | \(-0.767864\pi\) | ||||
−0.745657 | + | 0.666330i | \(0.767864\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.4031 | −1.00399 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.19375 | 0.797199 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 16.8062i | − | 1.43585i | −0.696118 | − | 0.717927i | \(-0.745091\pi\) | ||
0.696118 | − | 0.717927i | \(-0.254909\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.10469 | −0.772249 | −0.386125 | − | 0.922447i | \(-0.626187\pi\) | ||||
−0.386125 | + | 0.922447i | \(0.626187\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000i | 0.673722i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.1047 | − | 7.40312i | 0.928621 | − | 0.619080i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2.00000i | − | 0.166091i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.10469 | −0.338549 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 8.29844i | − | 0.679835i | −0.940455 | − | 0.339917i | \(-0.889601\pi\) | ||
0.940455 | − | 0.339917i | \(-0.110399\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 7.40312i | − | 0.602458i | −0.953552 | − | 0.301229i | \(-0.902603\pi\) | ||
0.953552 | − | 0.301229i | \(-0.0973968\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.298438 | 0.0241273 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.40312 | 0.273346 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.80625 | 0.223963 | 0.111982 | − | 0.993710i | \(-0.464280\pi\) | ||||
0.111982 | + | 0.993710i | \(0.464280\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.29844 | −0.182278 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.29844i | − | 0.496386i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.7016i | 1.07319i | 0.843840 | + | 0.536595i | \(0.180290\pi\) | ||||
−0.843840 | + | 0.536595i | \(0.819710\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.70156 | 0.288166 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 8.00000i | − | 0.619059i | −0.950890 | − | 0.309529i | \(-0.899829\pi\) | ||
0.950890 | − | 0.309529i | \(-0.100171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | + | 12.0000i | −0.384615 | + | 0.923077i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 5.40312i | − | 0.413187i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.4031 | 1.77931 | 0.889653 | − | 0.456637i | \(-0.150946\pi\) | ||||
0.889653 | + | 0.456637i | \(0.150946\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.70156i | − | 0.128626i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.4031i | 1.00744i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.8062 | −1.40565 | −0.702823 | − | 0.711365i | \(-0.748077\pi\) | ||||
−0.702823 | + | 0.711365i | \(0.748077\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.1047 | −0.825405 | −0.412702 | − | 0.910866i | \(-0.635415\pi\) | ||||
−0.412702 | + | 0.910866i | \(0.635415\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.298438 | −0.0220612 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.70156 | 0.272144 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.10469i | − | 0.0807827i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 1.70156i | − | 0.123770i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.00000 | 0.289430 | 0.144715 | − | 0.989473i | \(-0.453773\pi\) | ||||
0.144715 | + | 0.989473i | \(0.453773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.50781i | 0.468442i | 0.972183 | + | 0.234221i | \(0.0752540\pi\) | ||||
−0.972183 | + | 0.234221i | \(0.924746\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.00000 | + | 2.00000i | −0.214834 | + | 0.143223i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.8062i | 0.912407i | 0.889875 | + | 0.456204i | \(0.150791\pi\) | ||||
−0.889875 | + | 0.456204i | \(0.849209\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.8062 | 0.766035 | 0.383017 | − | 0.923741i | \(-0.374885\pi\) | ||||
0.383017 | + | 0.923741i | \(0.374885\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000i | 0.564276i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.40312i | 0.238852i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.29844 | −0.160530 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.70156 | −0.257276 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.0000 | −1.38343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.6125 | 1.76324 | 0.881619 | − | 0.471963i | \(-0.156454\pi\) | ||||
0.881619 | + | 0.471963i | \(0.156454\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.70156i | 0.390665i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 11.4031i | − | 0.777687i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.79063 | −0.393093 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.8062i | 0.865366i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.596876 | + | 0.895314i | 0.0401502 | + | 0.0602253i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0000i | 1.60716i | 0.595198 | + | 0.803579i | \(0.297074\pi\) | ||||
−0.595198 | + | 0.803579i | \(0.702926\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.8062i | 0.982725i | 0.870955 | + | 0.491363i | \(0.163501\pi\) | ||||
−0.870955 | + | 0.491363i | \(0.836499\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.80625i | 0.581933i | 0.956733 | + | 0.290967i | \(0.0939769\pi\) | ||||
−0.956733 | + | 0.290967i | \(0.906023\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.29844 | −0.414407 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.70156 | 0.242497 | 0.121249 | − | 0.992622i | \(-0.461310\pi\) | ||||
0.121249 | + | 0.992622i | \(0.461310\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | −0.521862 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.70156 | 0.630184 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 9.70156i | − | 0.627542i | −0.949499 | − | 0.313771i | \(-0.898408\pi\) | ||
0.949499 | − | 0.313771i | \(-0.101592\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.4031i | 0.734540i | 0.930114 | + | 0.367270i | \(0.119707\pi\) | ||||
−0.930114 | + | 0.367270i | \(0.880293\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 4.10469i | − | 0.262239i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.2094 | − | 10.8062i | 1.03138 | − | 0.687585i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 3.40312i | − | 0.215664i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.5969 | 1.04759 | 0.523793 | − | 0.851846i | \(-0.324517\pi\) | ||||
0.523793 | + | 0.851846i | \(0.324517\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.7016i | 0.861410i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.298438i | 0.0186889i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.80625 | −0.299806 | −0.149903 | − | 0.988701i | \(-0.547896\pi\) | ||||
−0.149903 | + | 0.988701i | \(0.547896\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.29844 | −0.391366 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.2094 | −1.24616 | −0.623082 | − | 0.782157i | \(-0.714120\pi\) | ||||
−0.623082 | + | 0.782157i | \(0.714120\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.29844i | − | 0.141192i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 1.70156i | − | 0.104134i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.4031 | −0.817203 | −0.408601 | − | 0.912713i | \(-0.633983\pi\) | ||||
−0.408601 | + | 0.912713i | \(0.633983\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.4031i | 0.935673i | 0.883815 | + | 0.467837i | \(0.154966\pi\) | ||||
−0.883815 | + | 0.467837i | \(0.845034\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.10469 | − | 3.40312i | 0.308950 | − | 0.205966i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.70156i | 0.223213i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.8062 | −0.889621 | −0.444811 | − | 0.895625i | \(-0.646729\pi\) | ||||
−0.444811 | + | 0.895625i | \(0.646729\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.40312i | 0.203740i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.59688i | 0.274227i | 0.990555 | + | 0.137113i | \(0.0437824\pi\) | ||||
−0.990555 | + | 0.137113i | \(0.956218\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.596876 | 0.0354806 | 0.0177403 | − | 0.999843i | \(-0.494353\pi\) | ||||
0.0177403 | + | 0.999843i | \(0.494353\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.40312 | 0.320053 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.91093 | 0.230855 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9109 | −0.994761 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.10469i | 0.182000i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.00000i | 0.350524i | 0.984522 | + | 0.175262i | \(0.0560772\pi\) | ||||
−0.984522 | + | 0.175262i | \(0.943923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.4031 | −0.780360 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.70156i | 0.214786i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.40312 | − | 11.1047i | −0.428134 | − | 0.642201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.4031i | 1.11838i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.8062 | −0.965494 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 0.298438i | − | 0.0170885i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.10469i | − | 0.519632i | −0.965658 | − | 0.259816i | \(-0.916338\pi\) | ||
0.965658 | − | 0.259816i | \(-0.0836619\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.40312 | −0.534925 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.40312 | −0.419793 | −0.209896 | − | 0.977724i | \(-0.567313\pi\) | ||||
−0.209896 | + | 0.977724i | \(0.567313\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.2094 | −1.82058 | −0.910291 | − | 0.413970i | \(-0.864142\pi\) | ||||
−0.910291 | + | 0.413970i | \(0.864142\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.70156 | 0.0958722 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.19375i | 0.179379i | 0.995970 | + | 0.0896895i | \(0.0285875\pi\) | ||||
−0.995970 | + | 0.0896895i | \(0.971413\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 7.40312i | − | 0.414495i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.1047 | −0.731432 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.61250i | − | 0.0897217i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.00000 | − | 3.00000i | −0.110940 | − | 0.166410i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.00000i | 0.331801i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.6125 | 0.750481 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.59688i | 0.142737i | 0.997450 | + | 0.0713686i | \(0.0227367\pi\) | ||||
−0.997450 | + | 0.0713686i | \(0.977263\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.70156i | 0.202844i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.00000 | −0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.8062 | −1.78707 | −0.893535 | − | 0.448993i | \(-0.851783\pi\) | ||||
−0.893535 | + | 0.448993i | \(0.851783\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.0000 | −0.760376 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.5969 | 0.682159 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.8953i | 1.02025i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 3.70156i | − | 0.199285i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.507811 | −0.0272607 | −0.0136304 | − | 0.999907i | \(-0.504339\pi\) | ||||
−0.0136304 | + | 0.999907i | \(0.504339\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 16.8062i | − | 0.899618i | −0.893125 | − | 0.449809i | \(-0.851492\pi\) | ||
0.893125 | − | 0.449809i | \(-0.148508\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | − | 3.00000i | −0.106752 | − | 0.160128i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.20937i | 0.436941i | 0.975844 | + | 0.218470i | \(0.0701067\pi\) | ||||
−0.975844 | + | 0.218470i | \(0.929893\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.70156 | −0.302607 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 0.507811i | − | 0.0268762i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 16.0000i | − | 0.844448i | −0.906492 | − | 0.422224i | \(-0.861250\pi\) | ||
0.906492 | − | 0.422224i | \(-0.138750\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.1938 | −0.536513 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.70156 | 0.141795 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.8062 | −0.670310 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.0000 | 0.939592 | 0.469796 | − | 0.882775i | \(-0.344327\pi\) | ||||
0.469796 | + | 0.882775i | \(0.344327\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 2.29844i | − | 0.119652i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.91093i | 0.203046i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.6125 | 0.911941 | 0.455970 | − | 0.889995i | \(-0.349292\pi\) | ||||
0.455970 | + | 0.889995i | \(0.349292\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1.00000i | − | 0.0516398i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.00000 | + | 6.00000i | 0.206010 | + | 0.309016i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.8062i | 1.06875i | 0.845249 | + | 0.534373i | \(0.179452\pi\) | ||||
−0.845249 | + | 0.534373i | \(0.820548\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.8062 | 0.861010 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.4031i | 0.991453i | 0.868479 | + | 0.495727i | \(0.165098\pi\) | ||||
−0.868479 | + | 0.495727i | \(0.834902\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 6.29844i | − | 0.320998i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.4031 | 0.579653 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.0000 | −0.507020 | −0.253510 | − | 0.967333i | \(-0.581585\pi\) | ||||
−0.253510 | + | 0.967333i | \(0.581585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.10469 | −0.0558664 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0000 | 0.605320 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.70156i | 0.488139i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.7016i | 1.18955i | 0.803893 | + | 0.594774i | \(0.202758\pi\) | ||||
−0.803893 | + | 0.594774i | \(0.797242\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.19375 | −0.460263 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 10.2094i | − | 0.509832i | −0.966963 | − | 0.254916i | \(-0.917952\pi\) | ||
0.966963 | − | 0.254916i | \(-0.0820478\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.2094 | + | 6.80625i | −0.508565 | + | 0.339043i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1.00000i | − | 0.0496904i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.7016 | 0.679161 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 18.8062i | − | 0.929909i | −0.885335 | − | 0.464955i | \(-0.846071\pi\) | ||
0.885335 | − | 0.464955i | \(-0.153929\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.8062i | 0.828991i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.8062 | 1.12222 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.40312 | 0.167053 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.10469 | 0.445858 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.59688 | −0.419985 | −0.209992 | − | 0.977703i | \(-0.567344\pi\) | ||||
−0.209992 | + | 0.977703i | \(0.567344\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 12.8062i | − | 0.624138i | −0.950059 | − | 0.312069i | \(-0.898978\pi\) | ||
0.950059 | − | 0.312069i | \(-0.101022\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 8.00000i | − | 0.388973i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.298438 | −0.0144764 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.507811i | 0.0245747i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.1047 | + | 7.40312i | −0.536139 | + | 0.357426i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.19375i | 0.250174i | 0.992146 | + | 0.125087i | \(0.0399210\pi\) | ||||
−0.992146 | + | 0.125087i | \(0.960079\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.6125 | 1.32697 | 0.663486 | − | 0.748189i | \(-0.269076\pi\) | ||||
0.663486 | + | 0.748189i | \(0.269076\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.00000i | 0.0958927i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.0000i | 0.956730i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.1047 | 1.38909 | 0.694545 | − | 0.719449i | \(-0.255606\pi\) | ||||
0.694545 | + | 0.719449i | \(0.255606\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.10469 | 0.195461 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.7016 | −0.841027 | −0.420513 | − | 0.907286i | \(-0.638150\pi\) | ||||
−0.420513 | + | 0.907286i | \(0.638150\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.70156 | 0.0806618 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.29844i | 0.392503i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.9109i | 1.31720i | 0.752494 | + | 0.658599i | \(0.228851\pi\) | ||||
−0.752494 | + | 0.658599i | \(0.771149\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.50781 | −0.400617 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.40312i | 0.347829i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.40312 | + | 5.10469i | 0.159541 | + | 0.239311i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 35.1047i | − | 1.64213i | −0.570836 | − | 0.821064i | \(-0.693381\pi\) | ||
0.570836 | − | 0.821064i | \(-0.306619\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.298438 | −0.0139299 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.7172i | 1.71009i | 0.518554 | + | 0.855045i | \(0.326471\pi\) | ||||
−0.518554 | + | 0.855045i | \(0.673529\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.5078i | 1.13897i | 0.822000 | + | 0.569487i | \(0.192858\pi\) | ||||
−0.822000 | + | 0.569487i | \(0.807142\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.40312 | −0.157816 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.8953 | 0.504175 | 0.252087 | − | 0.967704i | \(-0.418883\pi\) | ||||
0.252087 | + | 0.967704i | \(0.418883\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.6125 | 0.628567 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.80625 | −0.129305 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 42.2094i | − | 1.94079i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.40312i | 0.247912i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.29844 | 0.105238 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 31.3141i | − | 1.43078i | −0.698727 | − | 0.715388i | \(-0.746250\pi\) | ||
0.698727 | − | 0.715388i | \(-0.253750\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.1047 | + | 7.40312i | −0.506330 | + | 0.337553i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.29844i | 0.286589i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.10469 | −0.140977 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.5078i | 0.748040i | 0.927421 | + | 0.374020i | \(0.122021\pi\) | ||||
−0.927421 | + | 0.374020i | \(0.877979\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 13.7016i | − | 0.619606i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.6125 | 0.794841 | 0.397420 | − | 0.917637i | \(-0.369905\pi\) | ||||
0.397420 | + | 0.917637i | \(0.369905\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.596876 | 0.0268819 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.70156 | −0.166373 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.70156 | 0.435175 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.5969i | 0.653446i | 0.945120 | + | 0.326723i | \(0.105944\pi\) | ||||
−0.945120 | + | 0.326723i | \(0.894056\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.00000i | 0.357414i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.5969 | −0.472491 | −0.236246 | − | 0.971693i | \(-0.575917\pi\) | ||||
−0.236246 | + | 0.971693i | \(0.575917\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 16.8062i | − | 0.747868i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.00000 | − | 12.0000i | 0.222058 | − | 0.532939i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 36.7172i | − | 1.62746i | −0.581243 | − | 0.813730i | \(-0.697433\pi\) | ||
0.581243 | − | 0.813730i | \(-0.302567\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.7906 | 0.963961 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.40312i | 0.238554i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 9.40312i | − | 0.414351i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −29.6125 | −1.30236 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.4031 | −1.02728 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.2094 | −1.41112 | −0.705559 | − | 0.708651i | \(-0.749304\pi\) | ||||
−0.705559 | + | 0.708651i | \(0.749304\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.4031 | 0.848439 | 0.424220 | − | 0.905559i | \(-0.360548\pi\) | ||||
0.424220 | + | 0.905559i | \(0.360548\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.70156i | 0.0742623i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.01562i | 0.0442412i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.29844 | −0.404280 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 13.4031i | − | 0.581646i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.89531 | − | 4.59688i | 0.298669 | − | 0.199113i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 13.1047i | − | 0.566565i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.8062 | 0.811550 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 15.1938i | − | 0.654441i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.5969i | 0.627569i | 0.949494 | + | 0.313784i | \(0.101597\pi\) | ||||
−0.949494 | + | 0.313784i | \(0.898403\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.1047 | 0.476548 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.00000 | −0.257012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.4031 | −1.34270 | −0.671350 | − | 0.741140i | \(-0.734285\pi\) | ||||
−0.671350 | + | 0.741140i | \(0.734285\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.298438 | 0.0127370 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10.8062i | − | 0.460362i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 16.5078i | − | 0.701984i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.70156 | −0.157123 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.0000i | 0.593199i | 0.955002 | + | 0.296600i | \(0.0958526\pi\) | ||||
−0.955002 | + | 0.296600i | \(0.904147\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.8062 | + | 34.2094i | 0.964602 | + | 1.44690i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.10469i | 0.0466399i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.8953 | 0.796343 | 0.398171 | − | 0.917311i | \(-0.369645\pi\) | ||||
0.398171 | + | 0.917311i | \(0.369645\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 14.0000i | − | 0.588984i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.70156i | 0.0714589i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.0000 | −1.08998 | −0.544988 | − | 0.838444i | \(-0.683466\pi\) | ||||
−0.544988 | + | 0.838444i | \(0.683466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.3141 | 0.808268 | 0.404134 | − | 0.914700i | \(-0.367573\pi\) | ||||
0.404134 | + | 0.914700i | \(0.367573\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.00000 | −0.167102 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.70156 | 0.154366 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.49219i | − | 0.0621207i | −0.999518 | − | 0.0310603i | \(-0.990112\pi\) | ||
0.999518 | − | 0.0310603i | \(-0.00988840\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 6.50781i | − | 0.270455i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.79063 | −0.240236 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 8.50781i | − | 0.352358i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.00000 | − | 2.00000i | 0.124035 | − | 0.0826898i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 6.20937i | − | 0.256288i | −0.991756 | − | 0.128144i | \(-0.959098\pi\) | ||
0.991756 | − | 0.128144i | \(-0.0409020\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.3875 | 0.757644 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 12.8062i | − | 0.526779i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 22.0000i | − | 0.903432i | −0.892162 | − | 0.451716i | \(-0.850812\pi\) | ||
0.892162 | − | 0.451716i | \(-0.149188\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.507811 | 0.0208182 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.8062 | −0.442270 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.1938 | −0.702518 | −0.351259 | − | 0.936278i | \(-0.614246\pi\) | ||||
−0.351259 | + | 0.936278i | \(0.614246\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.1203 | 1.47338 | 0.736689 | − | 0.676232i | \(-0.236388\pi\) | ||||
0.736689 | + | 0.676232i | \(0.236388\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 8.00000i | − | 0.325785i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.70156i | 0.109834i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.20937 | −0.170853 | −0.0854266 | − | 0.996344i | \(-0.527225\pi\) | ||||
−0.0854266 | + | 0.996344i | \(0.527225\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 3.40312i | − | 0.137902i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.0000 | − | 16.0000i | 0.970936 | − | 0.647291i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 3.10469i | − | 0.125397i | −0.998033 | − | 0.0626986i | \(-0.980029\pi\) | ||
0.998033 | − | 0.0626986i | \(-0.0199707\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.29844 | 0.0926820 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.6125i | 1.11164i | 0.831304 | + | 0.555819i | \(0.187595\pi\) | ||||
−0.831304 | + | 0.555819i | \(0.812405\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 22.0000i | − | 0.884255i | −0.896952 | − | 0.442127i | \(-0.854224\pi\) | ||
0.896952 | − | 0.442127i | \(-0.145776\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.70156 | 0.148539 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.89531 | −0.115998 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.0000 | 0.798723 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.10469i | 0.0440467i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 6.20937i | − | 0.247191i | −0.992333 | − | 0.123596i | \(-0.960557\pi\) | ||
0.992333 | − | 0.123596i | \(-0.0394426\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −25.6125 | −1.01801 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.8062i | 0.666936i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.20937 | + | 12.3141i | 0.325267 | + | 0.487901i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 5.70156i | − | 0.225550i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.0156 | −0.751072 | −0.375536 | − | 0.926808i | \(-0.622541\pi\) | ||||
−0.375536 | + | 0.926808i | \(0.622541\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 24.5078i | − | 0.966494i | −0.875484 | − | 0.483247i | \(-0.839457\pi\) | ||
0.875484 | − | 0.483247i | \(-0.160543\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.4031i | 0.448998i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.9109 | −1.17592 | −0.587960 | − | 0.808890i | \(-0.700069\pi\) | ||||
−0.587960 | + | 0.808890i | \(0.700069\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −49.6125 | −1.94746 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.79063 | 0.226953 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.4031 | 0.446239 | 0.223119 | − | 0.974791i | \(-0.428376\pi\) | ||||
0.223119 | + | 0.974791i | \(0.428376\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.0000i | 0.468879i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 12.8062i | − | 0.499619i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.0156 | 0.818652 | 0.409326 | − | 0.912388i | \(-0.365764\pi\) | ||||
0.409326 | + | 0.912388i | \(0.365764\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 25.4031i | − | 0.988067i | −0.869443 | − | 0.494034i | \(-0.835522\pi\) | ||
0.869443 | − | 0.494034i | \(-0.164478\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.596876 | − | 0.895314i | −0.0231807 | − | 0.0347711i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 9.19375i | − | 0.356518i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.40312 | −0.286650 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 24.0000i | − | 0.927894i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.10469i | − | 0.0426459i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.5969 | 0.562668 | 0.281334 | − | 0.959610i | \(-0.409223\pi\) | ||||
0.281334 | + | 0.959610i | \(0.409223\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.70156 | −0.372861 | −0.186431 | − | 0.982468i | \(-0.559692\pi\) | ||||
−0.186431 | + | 0.982468i | \(0.559692\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.28282 | 0.202736 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 14.8062i | − | 0.567377i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.5969i | 1.40034i | 0.713976 | + | 0.700170i | \(0.246893\pi\) | ||||
−0.713976 | + | 0.700170i | \(0.753107\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.8062 | −0.642134 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 8.80625i | − | 0.335979i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.59688 | + | 6.89531i | 0.175127 | + | 0.262691i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 31.6125i | − | 1.20260i | −0.799025 | − | 0.601298i | \(-0.794650\pi\) | ||
0.799025 | − | 0.601298i | \(-0.205350\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.29844 | 0.239258 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.10469i | 0.345360i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 0.685941i | − | 0.0259819i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.70156 | −0.140006 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.0156 | 1.32252 | 0.661261 | − | 0.750156i | \(-0.270022\pi\) | ||||
0.661261 | + | 0.750156i | \(0.270022\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.0000 | 0.754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.00000 | 0.301297 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.5969i | 1.07550i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.2094i | 1.05943i | 0.848177 | + | 0.529713i | \(0.177700\pi\) | ||||
−0.848177 | + | 0.529713i | \(0.822300\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.70156 | −0.363837 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 12.5969i | − | 0.471757i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.40312 | − | 11.1047i | −0.276861 | − | 0.415292i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.70156i | 0.362311i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.4031 | 0.574440 | 0.287220 | − | 0.957865i | \(-0.407269\pi\) | ||||
0.287220 | + | 0.957865i | \(0.407269\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000i | 0.595871i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 11.4031i | − | 0.424087i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.00000 | −0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.1938 | −0.415153 | −0.207577 | − | 0.978219i | \(-0.566558\pi\) | ||||
−0.207577 | + | 0.978219i | \(0.566558\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.40312 | 0.125869 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 43.7016i | − | 1.61415i | −0.590446 | − | 0.807077i | \(-0.701048\pi\) | ||
0.590446 | − | 0.807077i | \(-0.298952\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.10469i | 0.151404i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.6125 | −1.09079 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.8062i | 1.35394i | 0.736011 | + | 0.676970i | \(0.236707\pi\) | ||||
−0.736011 | + | 0.676970i | \(0.763293\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.2094 | + | 10.8062i | −0.595466 | + | 0.396977i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.0000i | 1.46746i | 0.679442 | + | 0.733729i | \(0.262222\pi\) | ||||
−0.679442 | + | 0.733729i | \(0.737778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.29844 | −0.304031 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.40312i | 0.124514i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.2984i | 0.814767i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.2984 | 1.54349 | 0.771746 | − | 0.635931i | \(-0.219384\pi\) | ||||
0.771746 | + | 0.635931i | \(0.219384\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.5969 | −0.604824 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.40312 | −0.269427 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.80625 | 0.247377 | 0.123689 | − | 0.992321i | \(-0.460528\pi\) | ||||
0.123689 | + | 0.992321i | \(0.460528\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 13.7016i | − | 0.497335i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.4031i | 0.413363i | 0.978408 | + | 0.206681i | \(0.0662664\pi\) | ||||
−0.978408 | + | 0.206681i | \(0.933734\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.2094 | 0.369604 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 0.298438i | − | 0.0107900i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 40.2094 | − | 26.8062i | 1.45188 | − | 0.967918i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 30.8062i | − | 1.11090i | −0.831549 | − | 0.555451i | \(-0.812546\pi\) | ||
0.831549 | − | 0.555451i | \(-0.187454\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.80625 | 0.173093 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 44.8062i | − | 1.61157i | −0.592209 | − | 0.805784i | \(-0.701744\pi\) | ||
0.592209 | − | 0.805784i | \(-0.298256\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.40312i | − | 0.122244i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.29844 | 0.225955 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.4187 | −0.444948 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.1047 | −0.755185 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2.80625i | − | 0.100159i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 52.0000i | − | 1.85360i | −0.375555 | − | 0.926800i | \(-0.622548\pi\) | ||
0.375555 | − | 0.926800i | \(-0.377452\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.2094 | 0.719473 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.8219i | 0.847008i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.596876 | + | 0.895314i | 0.0211957 | + | 0.0317935i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.29844i | 0.0815172i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 53.5234 | 1.89590 | 0.947949 | − | 0.318423i | \(-0.103153\pi\) | ||||
0.947949 | + | 0.318423i | \(0.103153\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.38750i | − | 0.0844638i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.70156i | 0.0601217i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −47.4031 | −1.67282 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.29844 | −0.221991 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.4031 | 0.471812 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.4031 | −1.03376 | −0.516879 | − | 0.856058i | \(-0.672906\pi\) | ||||
−0.516879 | + | 0.856058i | \(0.672906\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.8062i | 1.15198i | 0.817456 | + | 0.575992i | \(0.195384\pi\) | ||||
−0.817456 | + | 0.575992i | \(0.804616\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 15.4031i | − | 0.540211i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.7016 | 0.479945 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 61.6125i | − | 2.15555i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.10469 | + | 3.40312i | −0.178372 | + | 0.118915i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 6.50781i | − | 0.227124i | −0.993531 | − | 0.113562i | \(-0.963774\pi\) | ||
0.993531 | − | 0.113562i | \(-0.0362261\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47.6125 | 1.65967 | 0.829834 | − | 0.558011i | \(-0.188435\pi\) | ||||
0.829834 | + | 0.558011i | \(0.188435\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 3.70156i | − | 0.128872i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.19375i | 0.180604i | 0.995914 | + | 0.0903022i | \(0.0287833\pi\) | ||||
−0.995914 | + | 0.0903022i | \(0.971217\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.0000 | 0.486240 | 0.243120 | − | 0.969996i | \(-0.421829\pi\) | ||||
0.243120 | + | 0.969996i | \(0.421829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.8062 | 0.513623 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.22499 | 0.0424435 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.00000 | −0.276851 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 3.40312i | − | 0.117629i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 2.29844i | − | 0.0793509i | −0.999213 | − | 0.0396754i | \(-0.987368\pi\) | ||
0.999213 | − | 0.0396754i | \(-0.0126324\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 4.59688i | − | 0.158325i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.0000 | + | 5.00000i | 0.412813 | + | 0.172005i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4.59688i | − | 0.157951i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.596876 | −0.0204847 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 13.7016i | − | 0.469684i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.10469i | 0.243260i | 0.992576 | + | 0.121630i | \(0.0388121\pi\) | ||||
−0.992576 | + | 0.121630i | \(0.961188\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.40312 | −0.184783 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.3141 | 1.54790 | 0.773949 | − | 0.633247i | \(-0.218278\pi\) | ||||
0.773949 | + | 0.633247i | \(0.218278\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.5078 | 0.426761 | 0.213380 | − | 0.976969i | \(-0.431553\pi\) | ||||
0.213380 | + | 0.976969i | \(0.431553\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.91093 | −0.133284 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 43.4031i | 1.47746i | 0.674002 | + | 0.738730i | \(0.264574\pi\) | ||||
−0.674002 | + | 0.738730i | \(0.735426\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 23.4031i | − | 0.795730i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.9109 | 0.574325 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35.9109i | 1.21820i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.0000 | − | 16.0000i | 0.813209 | − | 0.542139i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 3.10469i | − | 0.105078i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.70156 | −0.0575233 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.387503i | 0.0130850i | 0.999979 | + | 0.00654252i | \(0.00208256\pi\) | ||||
−0.999979 | + | 0.00654252i | \(0.997917\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 6.00000i | − | 0.202375i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.209373 | 0.00705395 | 0.00352697 | − | 0.999994i | \(-0.498877\pi\) | ||||
0.00352697 | + | 0.999994i | \(0.498877\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.4187 | −1.49481 | −0.747405 | − | 0.664369i | \(-0.768700\pi\) | ||||
−0.747405 | + | 0.664369i | \(0.768700\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.4031 | 0.450541 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.31406 | −0.178429 | −0.0892143 | − | 0.996012i | \(-0.528436\pi\) | ||||
−0.0892143 | + | 0.996012i | \(0.528436\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 28.5969i | − | 0.959108i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 3.70156i | − | 0.124007i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −43.2250 | −1.44647 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.8062i | 0.628624i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.40312 | + | 11.1047i | 0.247183 | + | 0.370775i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.80625i | 0.227001i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.685941 | 0.0228520 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 19.4031i | − | 0.645696i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.1047i | 0.369132i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.0000 | 0.796907 | 0.398453 | − | 0.917189i | \(-0.369547\pi\) | ||||
0.398453 | + | 0.917189i | \(0.369547\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.8062 | 0.557428 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.8219 | −1.71694 | −0.858468 | − | 0.512868i | \(-0.828583\pi\) | ||||
−0.858468 | + | 0.512868i | \(0.828583\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.5969 | 0.416896 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.298438i | 0.00986605i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 20.4187i | − | 0.674286i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.7016 | −0.451973 | −0.225986 | − | 0.974130i | \(-0.572560\pi\) | ||||
−0.225986 | + | 0.974130i | \(0.572560\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.10469i | 0.300010i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.1047 | − | 11.4031i | 0.563008 | − | 0.375338i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 3.70156i | − | 0.121707i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.40312 | 0.308839 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 24.5078i | − | 0.804075i | −0.915623 | − | 0.402038i | \(-0.868302\pi\) | ||
0.915623 | − | 0.402038i | \(-0.131698\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 22.1781i | − | 0.726859i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.40312 | 0.242367 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.10469 | −0.0361271 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −59.6125 | −1.94746 | −0.973728 | − | 0.227716i | \(-0.926874\pi\) | ||||
−0.973728 | + | 0.227716i | \(0.926874\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.2094 | 1.05111 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.49219i | − | 0.0486440i | −0.999704 | − | 0.0243220i | \(-0.992257\pi\) | ||
0.999704 | − | 0.0243220i | \(-0.00774269\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.50781i | 0.277052i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.70156 | −0.0553518 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.0000i | 0.649913i | 0.945729 | + | 0.324956i | \(0.105350\pi\) | ||||
−0.945729 | + | 0.324956i | \(0.894650\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38.4187 | − | 25.6125i | 1.24713 | − | 0.831417i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 3.19375i | − | 0.103564i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −56.1203 | −1.81792 | −0.908958 | − | 0.416889i | \(-0.863120\pi\) | ||||
−0.908958 | + | 0.416889i | \(0.863120\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 4.00000i | − | 0.129437i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.40312i | 0.239309i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28.5969 | 0.923441 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.4187 | 0.626411 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.1047 | 0.422293 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.50781 | 0.209494 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.00000i | 0.257263i | 0.991692 | + | 0.128631i | \(0.0410584\pi\) | ||||
−0.991692 | + | 0.128631i | \(0.958942\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.61250i | 0.0518009i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.2094 | 1.22620 | 0.613099 | − | 0.790006i | \(-0.289923\pi\) | ||||
0.613099 | + | 0.790006i | \(0.289923\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 15.4922i | − | 0.496657i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.00000 | + | 3.00000i | 0.0640513 | + | 0.0960769i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 25.4031i | − | 0.812718i | −0.913714 | − | 0.406359i | \(-0.866798\pi\) | ||
0.913714 | − | 0.406359i | \(-0.133202\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.29844 | 0.201299 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 6.00000i | − | 0.191565i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.4187i | 0.906417i | 0.891404 | + | 0.453209i | \(0.149721\pi\) | ||||
−0.891404 | + | 0.453209i | \(0.850279\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.8062 | 0.408041 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.6125 | −0.433291 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42.2094 | −1.34218 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.8953 | 0.473165 | 0.236583 | − | 0.971611i | \(-0.423973\pi\) | ||||
0.236583 | + | 0.971611i | \(0.423973\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 2.59688i | − | 0.0824094i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 10.8062i | − | 0.342581i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.0000 | −1.39349 | −0.696747 | − | 0.717317i | \(-0.745370\pi\) | ||||
−0.696747 | + | 0.717317i | \(0.745370\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 3.70156i | − | 0.117112i |
(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.g.f.961.2 | ✓ | 4 | |
3.2 | odd | 2 | 4680.2.g.h.2521.4 | 4 | |||
4.3 | odd | 2 | 3120.2.g.r.961.1 | 4 | |||
13.12 | even | 2 | inner | 1560.2.g.f.961.3 | yes | 4 | |
39.38 | odd | 2 | 4680.2.g.h.2521.1 | 4 | |||
52.51 | odd | 2 | 3120.2.g.r.961.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.g.f.961.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1560.2.g.f.961.3 | yes | 4 | 13.12 | even | 2 | inner | |
3120.2.g.r.961.1 | 4 | 4.3 | odd | 2 | |||
3120.2.g.r.961.4 | 4 | 52.51 | odd | 2 | |||
4680.2.g.h.2521.1 | 4 | 39.38 | odd | 2 | |||
4680.2.g.h.2521.4 | 4 | 3.2 | odd | 2 |