Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3800,2,Mod(3649,3800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3800.3649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3800.d (of order \(2\), degree \(1\), not 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: | \(30.3431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.59105344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 21x^{4} + 116x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3649.2 | ||
Root | \(0.786802i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3800.3649 |
Dual form | 3800.2.d.j.3649.5 |
$q$-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 \(\left(\mathbb{Z}/3800\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(951\) | \(1901\) | \(1977\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 3.08387i | − 1.78047i | −0.455497 | − | 0.890237i | \(-0.650538\pi\) | ||||
0.455497 | − | 0.890237i | \(-0.349462\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 4.29707i | − 1.62414i | −0.583560 | − | 0.812070i | \(-0.698341\pi\) | ||||
0.583560 | − | 0.812070i | \(-0.301659\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.51027 | −2.17009 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.21320 | −0.365793 | −0.182897 | − | 0.983132i | \(-0.558547\pi\) | ||||
−0.182897 | + | 0.983132i | \(0.558547\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.08387i | 1.41001i | 0.709201 | + | 0.705006i | \(0.249056\pi\) | ||||
−0.709201 | + | 0.705006i | \(0.750944\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.29707i | 0.557121i | 0.960419 | + | 0.278561i | \(0.0898573\pi\) | ||||
−0.960419 | + | 0.278561i | \(0.910143\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −13.2516 | −2.89174 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.67801i | 1.60098i | 0.599348 | + | 0.800488i | \(0.295426\pi\) | ||||
−0.599348 | + | 0.800488i | \(0.704574\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.8252i | 2.08331i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.489731 | 0.0909408 | 0.0454704 | − | 0.998966i | \(-0.485521\pi\) | ||||
0.0454704 | + | 0.998966i | \(0.485521\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.74135i | 0.651285i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 15.6780 | 2.51049 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.16774 | −0.650892 | −0.325446 | − | 0.945561i | \(-0.605514\pi\) | ||||
−0.325446 | + | 0.945561i | \(0.605514\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.9545i | 1.97555i | 0.155887 | + | 0.987775i | \(0.450176\pi\) | ||||
−0.155887 | + | 0.987775i | \(0.549824\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.80734i | 0.847087i | 0.905876 | + | 0.423544i | \(0.139214\pi\) | ||||
−0.905876 | + | 0.423544i | \(0.860786\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11.4648 | −1.63783 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.08387 | 0.991941 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.93667i | 0.266021i | 0.991115 | + | 0.133011i | \(0.0424645\pi\) | ||||
−0.991115 | + | 0.133011i | \(0.957536\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 3.08387i | − 0.408469i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.0839 | 1.44300 | 0.721499 | − | 0.692416i | \(-0.243454\pi\) | ||||
0.721499 | + | 0.692416i | \(0.243454\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.38094 | −0.688959 | −0.344480 | − | 0.938794i | \(-0.611945\pi\) | ||||
−0.344480 | + | 0.938794i | \(0.611945\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 27.9751i | 3.52453i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 2.48973i | − 0.304169i | −0.988367 | − | 0.152085i | \(-0.951401\pi\) | ||||
0.988367 | − | 0.152085i | \(-0.0485986\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 23.6780 | 2.85050 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.7413 | −1.39344 | −0.696721 | − | 0.717342i | \(-0.745358\pi\) | ||||
−0.696721 | + | 0.717342i | \(0.745358\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 8.46482i | − 0.990732i | −0.868684 | − | 0.495366i | \(-0.835034\pi\) | ||||
0.868684 | − | 0.495366i | \(-0.164966\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.21320i | 0.594099i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.83226 | −0.206145 | −0.103072 | − | 0.994674i | \(-0.532867\pi\) | ||||
−0.103072 | + | 0.994674i | \(0.532867\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 13.8528 | 1.53920 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 7.02054i | − 0.770604i | −0.922791 | − | 0.385302i | \(-0.874097\pi\) | ||||
0.922791 | − | 0.385302i | \(-0.125903\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 1.51027i | − 0.161918i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.7413 | −1.45658 | −0.728290 | − | 0.685269i | \(-0.759685\pi\) | ||||
−0.728290 | + | 0.685269i | \(0.759685\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21.8458 | 2.29006 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.57360i | 0.362844i | 0.983405 | + | 0.181422i | \(0.0580701\pi\) | ||||
−0.983405 | + | 0.181422i | \(0.941930\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.89825 | 0.793804 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.33549 | −0.630405 | −0.315202 | − | 0.949024i | \(-0.602072\pi\) | ||||
−0.315202 | + | 0.949024i | \(0.602072\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 5.44693i | − 0.536702i | −0.963321 | − | 0.268351i | \(-0.913521\pi\) | ||||
0.963321 | − | 0.268351i | \(-0.0864788\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 3.08387i | − 0.298129i | −0.988827 | − | 0.149065i | \(-0.952374\pi\) | ||||
0.988827 | − | 0.149065i | \(-0.0476262\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.10441 | −0.776262 | −0.388131 | − | 0.921604i | \(-0.626879\pi\) | ||||
−0.388131 | + | 0.921604i | \(0.626879\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.16774 | 0.585416 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.3355i | 1.34857i | 0.738471 | + | 0.674285i | \(0.235548\pi\) | ||||
−0.738471 | + | 0.674285i | \(0.764452\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 33.0974i | − 3.05985i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.87067 | 0.904843 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.52815 | −0.866195 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.8528i | 1.15890i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.74135i | 0.331991i | 0.986127 | + | 0.165995i | \(0.0530837\pi\) | ||||
−0.986127 | + | 0.165995i | \(0.946916\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 39.9502 | 3.51742 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.9545 | −1.13184 | −0.565922 | − | 0.824459i | \(-0.691480\pi\) | ||||
−0.565922 | + | 0.824459i | \(0.691480\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4.29707i | − 0.372603i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.63256i | 0.566658i | 0.959023 | + | 0.283329i | \(0.0914388\pi\) | ||||
−0.959023 | + | 0.283329i | \(0.908561\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.23374 | 0.359101 | 0.179550 | − | 0.983749i | \(-0.442536\pi\) | ||||
0.179550 | + | 0.983749i | \(0.442536\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.9091 | 1.50822 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 6.16774i | − 0.515773i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 35.3560i | 2.91612i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.63959 | 0.789706 | 0.394853 | − | 0.918744i | \(-0.370795\pi\) | ||||
0.394853 | + | 0.918744i | \(0.370795\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.44693 | −0.443265 | −0.221633 | − | 0.975130i | \(-0.571139\pi\) | ||||
−0.221633 | + | 0.975130i | \(0.571139\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 14.9545i | − 1.20900i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 14.0000i | − 1.11732i | −0.829396 | − | 0.558661i | \(-0.811315\pi\) | ||||
0.829396 | − | 0.558661i | \(-0.188685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.97243 | 0.473644 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 32.9930 | 2.60021 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 16.3355i | − 1.27949i | −0.768585 | − | 0.639747i | \(-0.779039\pi\) | ||||
0.768585 | − | 0.639747i | \(-0.220961\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.5736i | 1.05036i | 0.850992 | + | 0.525178i | \(0.176001\pi\) | ||||
−0.850992 | + | 0.525178i | \(0.823999\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8458 | −0.988135 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.51027 | −0.497853 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.3355i | 1.39402i | 0.717061 | + | 0.697011i | \(0.245487\pi\) | ||||
−0.717061 | + | 0.697011i | \(0.754513\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 34.1812i | − 2.56922i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.9502 | −1.49115 | −0.745573 | − | 0.666424i | \(-0.767824\pi\) | ||||
−0.745573 | + | 0.666424i | \(0.767824\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.85279 | −0.509364 | −0.254682 | − | 0.967025i | \(-0.581971\pi\) | ||||
−0.254682 | + | 0.967025i | \(0.581971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.5941i | 1.22667i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2.78680i | − 0.203791i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 46.5167 | 3.38359 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.7798 | 1.43121 | 0.715607 | − | 0.698503i | \(-0.246150\pi\) | ||||
0.715607 | + | 0.698503i | \(0.246150\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 9.61468i | − 0.692080i | −0.938220 | − | 0.346040i | \(-0.887526\pi\) | ||||
0.938220 | − | 0.346040i | \(-0.112474\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 4.16774i | − 0.296940i | −0.988917 | − | 0.148470i | \(-0.952565\pi\) | ||||
0.988917 | − | 0.148470i | \(-0.0474348\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.48535 | −0.388846 | −0.194423 | − | 0.980918i | \(-0.562283\pi\) | ||||
−0.194423 | + | 0.980918i | \(0.562283\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.67801 | −0.541565 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 2.10441i | − 0.147701i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 49.9859i | − 3.47426i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.21320 | −0.0839187 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.89559 | −0.130498 | −0.0652489 | − | 0.997869i | \(-0.520784\pi\) | ||||
−0.0652489 | + | 0.997869i | \(0.520784\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 36.2088i | 2.48099i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −26.1044 | −1.76397 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.6780 | −0.785548 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.74135i | 0.250539i | 0.992123 | + | 0.125270i | \(0.0399796\pi\) | ||||
−0.992123 | + | 0.125270i | \(0.960020\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 19.6780i | − 1.30608i | −0.757325 | − | 0.653038i | \(-0.773494\pi\) | ||||
0.757325 | − | 0.653038i | \(-0.226506\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.7164 | −1.43506 | −0.717531 | − | 0.696526i | \(-0.754728\pi\) | ||||
−0.717531 | + | 0.696526i | \(0.754728\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.0768 | 1.05778 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 10.5692i | − 0.692413i | −0.938158 | − | 0.346206i | \(-0.887470\pi\) | ||||
0.938158 | − | 0.346206i | \(-0.112530\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.65044i | 0.367036i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.0384 | 1.03744 | 0.518720 | − | 0.854944i | \(-0.326409\pi\) | ||||
0.518720 | + | 0.854944i | \(0.326409\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.0205 | −1.09639 | −0.548195 | − | 0.836351i | \(-0.684685\pi\) | ||||
−0.548195 | + | 0.836351i | \(0.684685\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 10.2446i | − 0.657190i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.08387i | 0.323479i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −21.6504 | −1.37204 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.1223 | −1.20699 | −0.603494 | − | 0.797367i | \(-0.706225\pi\) | ||||
−0.603494 | + | 0.797367i | \(0.706225\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 9.31495i | − 0.585626i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.553066i | 0.0344993i | 0.999851 | + | 0.0172497i | \(0.00549101\pi\) | ||||
−0.999851 | + | 0.0172497i | \(0.994509\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.59414 | 0.534014 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.18828 | −0.197350 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.04545i | 0.434441i | 0.976123 | + | 0.217221i | \(0.0696991\pi\) | ||||
−0.976123 | + | 0.217221i | \(0.930301\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 42.3766i | 2.59340i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.7619 | −0.778106 | −0.389053 | − | 0.921215i | \(-0.627198\pi\) | ||||
−0.389053 | + | 0.921215i | \(0.627198\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.6780 | 0.952371 | 0.476186 | − | 0.879345i | \(-0.342019\pi\) | ||||
0.476186 | + | 0.879345i | \(0.342019\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 67.3695i | − 4.07739i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.97508i | 0.359008i | 0.983757 | + | 0.179504i | \(0.0574493\pi\) | ||||
−0.983757 | + | 0.179504i | \(0.942551\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.2088 | 1.80211 | 0.901054 | − | 0.433708i | \(-0.142795\pi\) | ||||
0.901054 | + | 0.433708i | \(0.142795\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1.21320i | − 0.0721171i | −0.999350 | − | 0.0360586i | \(-0.988520\pi\) | ||||
0.999350 | − | 0.0360586i | \(-0.0114803\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.9091i | 1.05714i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.7235 | 0.689616 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.0205 | 0.646035 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.104410i | 0.00609969i | 0.999995 | + | 0.00304984i | \(0.000970797\pi\) | ||||
−0.999995 | + | 0.00304984i | \(0.999029\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 13.1331i | − 0.762062i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −39.0340 | −2.25740 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 55.6666 | 3.20857 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.5378i | 1.12242i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 0.852793i | − 0.0486715i | −0.999704 | − | 0.0243357i | \(-0.992253\pi\) | ||||
0.999704 | − | 0.0243357i | \(-0.00774707\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.7976 | −0.955585 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.12933 | −0.347562 | −0.173781 | − | 0.984784i | \(-0.555599\pi\) | ||||
−0.173781 | + | 0.984784i | \(0.555599\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 3.17478i | − 0.179449i | −0.995967 | − | 0.0897246i | \(-0.971401\pi\) | ||||
0.995967 | − | 0.0897246i | \(-0.0285987\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.6986i | 1.16255i | 0.813708 | + | 0.581273i | \(0.197445\pi\) | ||||
−0.813708 | + | 0.581273i | \(0.802555\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.594141 | −0.0332655 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.51027 | −0.530811 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.29707i | 0.127812i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 24.9930i | 1.38211i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.9545 | 1.37579 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.84576 | 0.541172 | 0.270586 | − | 0.962696i | \(-0.412783\pi\) | ||||
0.270586 | + | 0.962696i | \(0.412783\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 13.0205i | − 0.713521i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.9296i | 1.03116i | 0.856841 | + | 0.515581i | \(0.172424\pi\) | ||||
−0.856841 | + | 0.515581i | \(0.827576\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 44.2088 | 2.40109 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.1856i | 1.03593i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.78680i | 0.364335i | 0.983268 | + | 0.182167i | \(0.0583112\pi\) | ||||
−0.983268 | + | 0.182167i | \(0.941689\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.23374 | −0.333684 | −0.166842 | − | 0.985984i | \(-0.553357\pi\) | ||||
−0.166842 | + | 0.985984i | \(0.553357\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −55.0340 | −2.93750 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.7191i | 1.68824i | 0.536157 | + | 0.844118i | \(0.319876\pi\) | ||||
−0.536157 | + | 0.844118i | \(0.680124\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 30.4399i | − 1.61105i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.3944 | 1.23471 | 0.617356 | − | 0.786684i | \(-0.288204\pi\) | ||||
0.617356 | + | 0.786684i | \(0.288204\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 29.3836i | 1.54224i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.3355i | 1.06150i | 0.847527 | + | 0.530752i | \(0.178090\pi\) | ||||
−0.847527 | + | 0.530752i | \(0.821910\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 27.1331 | 1.41249 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.32199 | 0.432056 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 36.9021i | − 1.91072i | −0.295450 | − | 0.955358i | \(-0.595470\pi\) | ||||
0.295450 | − | 0.955358i | \(-0.404530\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.48973i | 0.128228i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.9367 | 0.818611 | 0.409306 | − | 0.912397i | \(-0.365771\pi\) | ||||
0.409306 | + | 0.912397i | \(0.365771\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.5378 | 0.591101 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 19.0205i | − 0.971904i | −0.873985 | − | 0.485952i | \(-0.838473\pi\) | ||||
0.873985 | − | 0.485952i | \(-0.161527\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 84.3376i | − 4.28712i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.61906 | −0.132791 | −0.0663957 | − | 0.997793i | \(-0.521150\pi\) | ||||
−0.0663957 | + | 0.997793i | \(0.521150\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.6369 | −0.891938 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 39.9502i | 2.01522i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.1634i | 1.56404i | 0.623251 | + | 0.782022i | \(0.285812\pi\) | ||||
−0.623251 | + | 0.782022i | \(0.714188\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.2516 | −0.663411 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.7413 | 1.08571 | 0.542856 | − | 0.839826i | \(-0.317343\pi\) | ||||
0.542856 | + | 0.839826i | \(0.317343\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 2.42640i | − 0.120272i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.2651 | 1.15039 | 0.575193 | − | 0.818018i | \(-0.304927\pi\) | ||||
0.575193 | + | 0.818018i | \(0.304927\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.4540 | 1.00892 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 47.6282i | − 2.34363i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 13.0563i | − 0.639370i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.33549 | −0.407215 | −0.203608 | − | 0.979053i | \(-0.565267\pi\) | ||||
−0.203608 | + | 0.979053i | \(0.565267\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.748383 | 0.0364740 | 0.0182370 | − | 0.999834i | \(-0.494195\pi\) | ||||
0.0182370 | + | 0.999834i | \(0.494195\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 37.8073i | − 1.83826i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.1223i | 1.11897i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −19.0205 | −0.918320 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.3560 | 1.51037 | 0.755183 | − | 0.655514i | \(-0.227548\pi\) | ||||
0.755183 | + | 0.655514i | \(0.227548\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.48270i | 0.455709i | 0.973695 | + | 0.227855i | \(0.0731711\pi\) | ||||
−0.973695 | + | 0.227855i | \(0.926829\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.67801i | 0.367289i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.9502 | 1.52490 | 0.762449 | − | 0.647048i | \(-0.223997\pi\) | ||||
0.762449 | + | 0.647048i | \(0.223997\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 74.6390 | 3.55424 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.91878i | 0.138676i | 0.997593 | + | 0.0693378i | \(0.0220886\pi\) | ||||
−0.997593 | + | 0.0693378i | \(0.977911\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 29.7273i | − 1.40605i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.0909069 | −0.00429016 | −0.00214508 | − | 0.999998i | \(-0.500683\pi\) | ||||
−0.00214508 | + | 0.999998i | \(0.500683\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.05630 | 0.238092 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.7976i | 0.789222i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 19.1499i | − 0.895793i | −0.894085 | − | 0.447896i | \(-0.852173\pi\) | ||||
0.894085 | − | 0.447896i | \(-0.147827\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −24.8663 | −1.16066 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.9253 | 1.58006 | 0.790028 | − | 0.613070i | \(-0.210066\pi\) | ||||
0.790028 | + | 0.613070i | \(0.210066\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.3809i | 1.27250i | 0.771483 | + | 0.636250i | \(0.219515\pi\) | ||||
−0.771483 | + | 0.636250i | \(0.780485\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 17.2132i | − 0.796532i | −0.917270 | − | 0.398266i | \(-0.869612\pi\) | ||||
0.917270 | − | 0.398266i | \(-0.130388\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.6986 | −0.494013 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −43.1742 | −1.98936 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 15.7164i | − 0.722642i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 12.6082i | − 0.577290i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.4827 | −0.707422 | −0.353711 | − | 0.935355i | \(-0.615080\pi\) | ||||
−0.353711 | + | 0.935355i | \(0.615080\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.1677 | −0.463609 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 101.746i | − 4.62961i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 30.1179i | − 1.36477i | −0.730992 | − | 0.682386i | \(-0.760942\pi\) | ||||
0.730992 | − | 0.682386i | \(-0.239058\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −50.3766 | −2.27811 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.2944 | −0.825615 | −0.412808 | − | 0.910818i | \(-0.635452\pi\) | ||||
−0.412808 | + | 0.910818i | \(0.635452\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.12495i | 0.0506651i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 50.4534i | 2.26314i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.5282 | −0.471305 | −0.235652 | − | 0.971837i | \(-0.575723\pi\) | ||||
−0.235652 | + | 0.971837i | \(0.575723\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 41.8593 | 1.87013 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.2018i | 1.65875i | 0.558696 | + | 0.829373i | \(0.311302\pi\) | ||||
−0.558696 | + | 0.829373i | \(0.688698\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 39.6147i | 1.75935i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.4264 | 0.905384 | 0.452692 | − | 0.891667i | \(-0.350464\pi\) | ||||
0.452692 | + | 0.891667i | \(0.350464\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.3739 | −1.60909 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.8252i | 0.477945i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 7.04545i | − 0.309859i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 56.5443 | 2.48202 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.8235 | −1.65708 | −0.828539 | − | 0.559932i | \(-0.810827\pi\) | ||||
−0.828539 | + | 0.559932i | \(0.810827\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.0428i | 0.570322i | 0.958480 | + | 0.285161i | \(0.0920470\pi\) | ||||
−0.958480 | + | 0.285161i | \(0.907953\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −35.9519 | −1.56313 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −72.1590 | −3.13143 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 21.1883i | − 0.917766i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 61.5238i | 2.65495i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.9091 | 0.599107 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.6754 | −1.18986 | −0.594928 | − | 0.803779i | \(-0.702820\pi\) | ||||
−0.594928 | + | 0.803779i | \(0.702820\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.1331i | 0.906910i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 12.0000i | − 0.513083i | −0.966533 | − | 0.256541i | \(-0.917417\pi\) | ||||
0.966533 | − | 0.256541i | \(-0.0825830\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 35.0314 | 1.49510 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.489731 | 0.0208633 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.87333i | 0.334808i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.2695i | 1.53679i | 0.639977 | + | 0.768394i | \(0.278944\pi\) | ||||
−0.639977 | + | 0.768394i | \(0.721056\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −65.8593 | −2.78555 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.59414 | −0.362845 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.9091i | 0.586198i | 0.956082 | + | 0.293099i | \(0.0946866\pi\) | ||||
−0.956082 | + | 0.293099i | \(0.905313\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 59.5264i | − 2.49987i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.7413 | −1.24682 | −0.623411 | − | 0.781894i | \(-0.714254\pi\) | ||||
−0.623411 | + | 0.781894i | \(0.714254\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.6710 | −1.53463 | −0.767316 | − | 0.641269i | \(-0.778408\pi\) | ||||
−0.767316 | + | 0.641269i | \(0.778408\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 60.9983i | − 2.54824i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 20.4648i | − 0.851961i | −0.904732 | − | 0.425981i | \(-0.859929\pi\) | ||||
0.904732 | − | 0.425981i | \(-0.140071\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −29.6504 | −1.23223 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30.1677 | −1.25157 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 2.34956i | − 0.0973088i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 18.2748i | − 0.754282i | −0.926156 | − | 0.377141i | \(-0.876907\pi\) | ||||
0.926156 | − | 0.377141i | \(-0.123093\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.8528 | −0.528693 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.5238i | 1.29453i | 0.762267 | + | 0.647263i | \(0.224086\pi\) | ||||
−0.762267 | + | 0.647263i | \(0.775914\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.9161i | 0.692331i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.3766 | 1.07772 | 0.538859 | − | 0.842396i | \(-0.318856\pi\) | ||||
0.538859 | + | 0.842396i | \(0.318856\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.3971 | −1.11755 | −0.558776 | − | 0.829319i | \(-0.688729\pi\) | ||||
−0.558776 | + | 0.829319i | \(0.688729\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.2088i | 0.660074i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 33.9859i | − 1.37945i | −0.724073 | − | 0.689723i | \(-0.757732\pi\) | ||||
0.724073 | − | 0.689723i | \(-0.242268\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.48973 | −0.262977 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.5238 | −1.19440 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.08653i | 0.124664i | 0.998055 | + | 0.0623319i | \(0.0198537\pi\) | ||||
−0.998055 | + | 0.0623319i | \(0.980146\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.1018i | 1.05082i | 0.850850 | + | 0.525409i | \(0.176087\pi\) | ||||
−0.850850 | + | 0.525409i | \(0.823913\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.0616 | −1.16808 | −0.584042 | − | 0.811723i | \(-0.698530\pi\) | ||||
−0.584042 | + | 0.811723i | \(0.698530\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −83.1162 | −3.33534 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 59.0475i | 2.36569i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.74135i | 0.149415i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.59414 | −0.183180 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.1018 | 0.800238 | 0.400119 | − | 0.916463i | \(-0.368969\pi\) | ||||
0.400119 | + | 0.916463i | \(0.368969\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.84576i | 0.232348i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 58.2857i | − 2.30936i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 76.4393 | 3.02389 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.7619 | 0.978036 | 0.489018 | − | 0.872274i | \(-0.337355\pi\) | ||||
0.489018 | + | 0.872274i | \(0.337355\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 11.8431i | − 0.467046i | −0.972351 | − | 0.233523i | \(-0.924975\pi\) | ||||
0.972351 | − | 0.233523i | \(-0.0750255\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 37.4854i | − 1.47370i | −0.676056 | − | 0.736851i | \(-0.736312\pi\) | ||||
0.676056 | − | 0.736851i | \(-0.263688\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.4469 | −0.527838 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 34.8279i | − 1.36292i | −0.731855 | − | 0.681460i | \(-0.761345\pi\) | ||||
0.731855 | − | 0.681460i | \(-0.238655\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 55.1082i | 2.14998i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28.2722 | −1.10133 | −0.550663 | − | 0.834727i | \(-0.685625\pi\) | ||||
−0.550663 | + | 0.834727i | \(0.685625\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.58064 | 0.100375 | 0.0501876 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501876 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 36.0135i | 1.39865i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.76016i | 0.145594i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.5378 | 0.446079 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.52815 | 0.252016 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 50.5443i | 1.94834i | 0.225816 | + | 0.974170i | \(0.427495\pi\) | ||||
−0.225816 | + | 0.974170i | \(0.572505\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 0.825221i | − 0.0317158i | −0.999874 | − | 0.0158579i | \(-0.994952\pi\) | ||||
0.999874 | − | 0.0158579i | \(-0.00504794\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.3560 | 0.589310 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −60.6845 | −2.32543 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 12.0000i | − 0.459167i | −0.973289 | − | 0.229584i | \(-0.926264\pi\) | ||||
0.973289 | − | 0.229584i | \(-0.0737364\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 66.9707i | 2.55509i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.84576 | −0.375094 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.0249160 | 0.000947850 0 | 0.000473925 | − | 1.00000i | \(-0.499849\pi\) | ||||
0.000473925 | 1.00000i | \(0.499849\pi\) | ||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 33.9393i | − 1.28925i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 9.57360i | − 0.362626i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −32.5941 | −1.23282 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.3560 | 1.10876 | 0.554381 | − | 0.832263i | \(-0.312955\pi\) | ||||
0.554381 | + | 0.832263i | \(0.312955\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.00000i | 0.0754314i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.2240i | 1.02387i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.4827 | 0.656576 | 0.328288 | − | 0.944578i | \(-0.393528\pi\) | ||||
0.328288 | + | 0.944578i | \(0.393528\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.9285 | 0.447353 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 49.4604i | − 1.84713i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.5915 | −0.693345 | −0.346673 | − | 0.937986i | \(-0.612689\pi\) | ||||
−0.346673 | + | 0.937986i | \(0.612689\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.4059 | −0.871680 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 52.4892i | 1.95209i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.50589i | 0.315466i | 0.987482 | + | 0.157733i | \(0.0504185\pi\) | ||||
−0.987482 | + | 0.157733i | \(0.949581\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.96539 | 0.369089 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29.7575 | −1.10062 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.5032i | 0.905048i | 0.891752 | + | 0.452524i | \(0.149476\pi\) | ||||
−0.891752 | + | 0.452524i | \(0.850524\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.02054i | 0.111263i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.9047 | 0.768992 | 0.384496 | − | 0.923127i | \(-0.374375\pi\) | ||||
0.384496 | + | 0.923127i | \(0.374375\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.6780 | 0.575946 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.5238i | 0.789631i | 0.918761 | + | 0.394815i | \(0.129191\pi\) | ||||
−0.918761 | + | 0.394815i | \(0.870809\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 45.7056i | 1.67228i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.2516 | −0.484204 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.37656 | 0.0867221 | 0.0433610 | − | 0.999059i | \(-0.486193\pi\) | ||||
0.0433610 | + | 0.999059i | \(0.486193\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 58.9707i | 2.14901i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 46.9545i | − 1.70659i | −0.521427 | − | 0.853296i | \(-0.674600\pi\) | ||||
0.521427 | − | 0.853296i | \(-0.325400\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −28.7261 | −1.04269 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.44428 | −0.197355 | −0.0986775 | − | 0.995119i | \(-0.531461\pi\) | ||||
−0.0986775 | + | 0.995119i | \(0.531461\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.8252i | 1.26076i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 56.3490i | 2.03464i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.92697 | −0.321915 | −0.160957 | − | 0.986961i | \(-0.551458\pi\) | ||||
−0.160957 | + | 0.986961i | \(0.551458\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.70559 | 0.0614252 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 17.8047i | − 0.640390i | −0.947352 | − | 0.320195i | \(-0.896252\pi\) | ||||
0.947352 | − | 0.320195i | \(-0.103748\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 26.5032i | − 0.950798i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.16774 | −0.149325 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.2446 | 0.509711 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.30145i | 0.189458i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 13.3836i | − 0.477074i | −0.971133 | − | 0.238537i | \(-0.923332\pi\) | ||||
0.971133 | − | 0.238537i | \(-0.0766678\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.7273 | 0.773512 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 61.6006 | 2.19027 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 27.3560i | − 0.971441i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 28.5666i | − 1.01188i | −0.862569 | − | 0.505940i | \(-0.831146\pi\) | ||||
0.862569 | − | 0.505940i | \(-0.168854\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.3399 | −0.471931 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 89.4599 | 3.16091 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.2695i | 0.362403i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 39.3560i | 1.38540i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.2625 | −1.59134 | −0.795672 | − | 0.605728i | \(-0.792882\pi\) | ||||
−0.795672 | + | 0.605728i | \(0.792882\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.4551 | −1.73660 | −0.868302 | − | 0.496036i | \(-0.834789\pi\) | ||||
−0.868302 | + | 0.496036i | \(0.834789\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 48.3490i | − 1.69567i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.9545i | 0.453222i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −142.222 | −4.96963 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.7933 | −1.45860 | −0.729298 | − | 0.684197i | \(-0.760153\pi\) | ||||
−0.729298 | + | 0.684197i | \(0.760153\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 8.68239i | − 0.302649i | −0.988484 | − | 0.151325i | \(-0.951646\pi\) | ||||
0.988484 | − | 0.151325i | \(-0.0483539\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 13.1196i | − 0.456214i | −0.973636 | − | 0.228107i | \(-0.926746\pi\) | ||||
0.973636 | − | 0.228107i | \(-0.0732537\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.83053 | 0.306697 | 0.153349 | − | 0.988172i | \(-0.450994\pi\) | ||||
0.153349 | + | 0.988172i | \(0.450994\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.4264 | 0.639205 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 26.3355i | − 0.912471i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.80296 | −0.165817 | −0.0829083 | − | 0.996557i | \(-0.526421\pi\) | ||||
−0.0829083 | + | 0.996557i | \(0.526421\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7602 | −0.991730 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 93.1601i | − 3.20861i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 40.9431i | 1.40682i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.74135 | −0.128403 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.3560 | −0.526398 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.51730i | − 0.0861908i | −0.999071 | − | 0.0430954i | \(-0.986278\pi\) | ||||
0.999071 | − | 0.0430954i | \(-0.0137219\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.3560i | 1.27606i | 0.770013 | + | 0.638029i | \(0.220250\pi\) | ||||
−0.770013 | + | 0.638029i | \(0.779750\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.6461 | −1.38683 | −0.693413 | − | 0.720540i | \(-0.743894\pi\) | ||||
−0.693413 | + | 0.720540i | \(0.743894\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 55.2294 | 1.88221 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 7.40586i | − 0.252098i | −0.992024 | − | 0.126049i | \(-0.959770\pi\) | ||||
0.992024 | − | 0.126049i | \(-0.0402297\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 36.1537i | − 1.22784i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.22289 | 0.0754063 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.6575 | 0.428882 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 23.2651i | − 0.787405i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 50.5308i | − 1.70630i | −0.521662 | − | 0.853152i | \(-0.674688\pi\) | ||||
0.521662 | − | 0.853152i | \(-0.325312\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.321987 | 0.0108603 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.4631 | 1.12740 | 0.563700 | − | 0.825980i | \(-0.309377\pi\) | ||||
0.563700 | + | 0.825980i | \(0.309377\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.0162i | 1.01012i | 0.863083 | + | 0.505062i | \(0.168530\pi\) | ||||
−0.863083 | + | 0.505062i | \(0.831470\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 19.0704i | − 0.640320i | −0.947363 | − | 0.320160i | \(-0.896263\pi\) | ||||
0.947363 | − | 0.320160i | \(-0.103737\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0768 | 0.539200 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.8062 | −0.563028 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.80734i | 0.194335i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 120.376i | 4.01924i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.44866 | −0.148206 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 171.669i | − 5.71278i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.0135i | 1.59426i | 0.603806 | + | 0.797131i | \(0.293650\pi\) | ||||
−0.603806 | + | 0.797131i | \(0.706350\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 41.2457 | 1.36803 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.2446 | −1.53215 | −0.766076 | − | 0.642750i | \(-0.777793\pi\) | ||||
−0.766076 | + | 0.642750i | \(0.777793\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.51730i | 0.281882i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 55.6666i | 1.83827i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.5103 | −1.36930 | −0.684649 | − | 0.728873i | \(-0.740044\pi\) | ||||
−0.684649 | + | 0.728873i | \(0.740044\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.62990 | −0.0866583 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 59.6915i | − 1.96477i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 35.4610i | 1.16469i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −55.4551 | −1.81942 | −0.909712 | − | 0.415240i | \(-0.863698\pi\) | ||||
−0.909712 | + | 0.415240i | \(0.863698\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.4648 | −0.375744 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.9021i | 0.618826i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.08825i | 0.198894i | 0.995043 | + | 0.0994472i | \(0.0317075\pi\) | ||||
−0.995043 | + | 0.0994472i | \(0.968293\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.79061 | −0.319505 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.3836 | −0.371095 | −0.185547 | − | 0.982635i | \(-0.559406\pi\) | ||||
−0.185547 | + | 0.982635i | \(0.559406\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 32.0000i | − 1.04206i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.3766i | 1.24707i | 0.781795 | + | 0.623535i | \(0.214304\pi\) | ||||
−0.781795 | + | 0.623535i | \(0.785696\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 43.0340 | 1.39694 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 63.8317 | 2.06988 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.2857i | 0.981049i | 0.871427 | + | 0.490524i | \(0.163195\pi\) | ||||
−0.871427 | + | 0.490524i | \(0.836805\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.83226i | 0.0592284i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28.5006 | 0.920332 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.0768i | 0.646967i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.6710i | 0.793365i | 0.917956 | + | 0.396683i | \(0.129839\pi\) | ||||
−0.917956 | + | 0.396683i | \(0.870161\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.08387 | 0.227567 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.0000 | 0.641831 | 0.320915 | − | 0.947108i | \(-0.396010\pi\) | ||||
0.320915 | + | 0.947108i | \(0.396010\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 18.1927i | − 0.583230i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.4059i | 0.684834i | 0.939548 | + | 0.342417i | \(0.111246\pi\) | ||||
−0.939548 | + | 0.342417i | \(0.888754\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.6710 | 0.532807 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 52.7619 | 1.68456 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38.1677i | 1.21736i | 0.793415 | + | 0.608681i | \(0.208301\pi\) | ||||
−0.793415 | + | 0.608681i | \(0.791699\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 76.9566i | − 2.44956i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −99.4652 | −3.16281 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.4675 | 0.523106 | 0.261553 | − | 0.965189i | \(-0.415765\pi\) | ||||
0.261553 | + | 0.965189i | \(0.415765\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 30.3631i | − 0.963543i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 13.8431i | − 0.438415i | −0.975678 | − | 0.219208i | \(-0.929653\pi\) | ||||
0.975678 | − | 0.219208i | \(-0.0703472\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.6504 | −0.684990 |
(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 | 3800.2.d.j.3649.2 | 6 | ||
5.2 | odd | 4 | 152.2.a.c.1.1 | ✓ | 3 | ||
5.3 | odd | 4 | 3800.2.a.r.1.3 | 3 | |||
5.4 | even | 2 | inner | 3800.2.d.j.3649.5 | 6 | ||
15.2 | even | 4 | 1368.2.a.n.1.2 | 3 | |||
20.3 | even | 4 | 7600.2.a.bv.1.1 | 3 | |||
20.7 | even | 4 | 304.2.a.g.1.3 | 3 | |||
35.27 | even | 4 | 7448.2.a.bf.1.3 | 3 | |||
40.27 | even | 4 | 1216.2.a.v.1.1 | 3 | |||
40.37 | odd | 4 | 1216.2.a.u.1.3 | 3 | |||
60.47 | odd | 4 | 2736.2.a.bd.1.2 | 3 | |||
95.37 | even | 4 | 2888.2.a.o.1.3 | 3 | |||
380.227 | odd | 4 | 5776.2.a.bp.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.a.c.1.1 | ✓ | 3 | 5.2 | odd | 4 | ||
304.2.a.g.1.3 | 3 | 20.7 | even | 4 | |||
1216.2.a.u.1.3 | 3 | 40.37 | odd | 4 | |||
1216.2.a.v.1.1 | 3 | 40.27 | even | 4 | |||
1368.2.a.n.1.2 | 3 | 15.2 | even | 4 | |||
2736.2.a.bd.1.2 | 3 | 60.47 | odd | 4 | |||
2888.2.a.o.1.3 | 3 | 95.37 | even | 4 | |||
3800.2.a.r.1.3 | 3 | 5.3 | odd | 4 | |||
3800.2.d.j.3649.2 | 6 | 1.1 | even | 1 | trivial | ||
3800.2.d.j.3649.5 | 6 | 5.4 | even | 2 | inner | ||
5776.2.a.bp.1.1 | 3 | 380.227 | odd | 4 | |||
7448.2.a.bf.1.3 | 3 | 35.27 | even | 4 | |||
7600.2.a.bv.1.1 | 3 | 20.3 | even | 4 |