Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,4,Mod(49,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.f (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: | \(70.8022920069\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 9x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Root | \(2.17945 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.49 |
Dual form | 1200.4.f.v.49.1 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.43560i | 0.239500i | 0.992804 | + | 0.119750i | \(0.0382092\pi\) | ||||
−0.992804 | + | 0.119750i | \(0.961791\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.43560 | 0.0941701 | 0.0470851 | − | 0.998891i | \(-0.485007\pi\) | ||||
0.0470851 | + | 0.998891i | \(0.485007\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 78.7424i | − 1.67994i | −0.542634 | − | 0.839970i | \(-0.682573\pi\) | ||||
0.542634 | − | 0.839970i | \(-0.317427\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 53.1780i | 0.758680i | 0.925257 | + | 0.379340i | \(0.123849\pi\) | ||||
−0.925257 | + | 0.379340i | \(0.876151\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 20.4356 | 0.246750 | 0.123375 | − | 0.992360i | \(-0.460628\pi\) | ||||
0.123375 | + | 0.992360i | \(0.460628\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −13.3068 | −0.138275 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 118.307i | 1.07255i | 0.844043 | + | 0.536275i | \(0.180169\pi\) | ||||
−0.844043 | + | 0.536275i | \(0.819831\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −168.049 | −1.07607 | −0.538034 | − | 0.842923i | \(-0.680833\pi\) | ||||
−0.538034 | + | 0.842923i | \(0.680833\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 61.0492 | 0.353702 | 0.176851 | − | 0.984238i | \(-0.443409\pi\) | ||||
0.176851 | + | 0.984238i | \(0.443409\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.3068i | 0.0543691i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 246.614i | − 1.09576i | −0.836558 | − | 0.547879i | \(-0.815436\pi\) | ||||
0.836558 | − | 0.547879i | \(-0.184564\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 236.227 | 0.969913 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 422.663 | 1.60997 | 0.804986 | − | 0.593294i | \(-0.202173\pi\) | ||||
0.804986 | + | 0.593294i | \(0.202173\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 362.436i | 1.28537i | 0.766131 | + | 0.642685i | \(0.222180\pi\) | ||||
−0.766131 | + | 0.642685i | \(0.777820\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 170.515i | 0.529196i | 0.964359 | + | 0.264598i | \(0.0852392\pi\) | ||||
−0.964359 | + | 0.264598i | \(0.914761\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 323.325 | 0.942640 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −159.534 | −0.438024 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 546.049i | 1.41520i | 0.706613 | + | 0.707600i | \(0.250222\pi\) | ||||
−0.706613 | + | 0.707600i | \(0.749778\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 61.3068i | 0.142461i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −216.970 | −0.478763 | −0.239382 | − | 0.970926i | \(-0.576945\pi\) | ||||
−0.239382 | + | 0.970926i | \(0.576945\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 130.902 | 0.274758 | 0.137379 | − | 0.990519i | \(-0.456132\pi\) | ||||
0.137379 | + | 0.990519i | \(0.456132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 39.9204i | − 0.0798332i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 614.890i | 1.12121i | 0.828085 | + | 0.560603i | \(0.189430\pi\) | ||||
−0.828085 | + | 0.560603i | \(0.810570\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −354.920 | −0.619238 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −324.822 | −0.542948 | −0.271474 | − | 0.962446i | \(-0.587511\pi\) | ||||
−0.271474 | + | 0.962446i | \(0.587511\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 88.8712i | 0.142487i | 0.997459 | + | 0.0712437i | \(0.0226968\pi\) | ||||
−0.997459 | + | 0.0712437i | \(0.977303\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.2389i | 0.0225537i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1137.42 | −1.61988 | −0.809938 | − | 0.586516i | \(-0.800499\pi\) | ||||
−0.809938 | + | 0.586516i | \(0.800499\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 758.909i | − 1.00363i | −0.864976 | − | 0.501813i | \(-0.832666\pi\) | ||||
0.864976 | − | 0.501813i | \(-0.167334\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 504.148i | − 0.621268i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −195.681 | −0.233058 | −0.116529 | − | 0.993187i | \(-0.537177\pi\) | ||||
−0.116529 | + | 0.993187i | \(0.537177\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 349.269 | 0.402345 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 183.148i | 0.204210i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 521.000i | 0.545356i | 0.962105 | + | 0.272678i | \(0.0879094\pi\) | ||||
−0.962105 | + | 0.272678i | \(0.912091\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −30.9204 | −0.0313900 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 660.920 | 0.651129 | 0.325565 | − | 0.945520i | \(-0.394446\pi\) | ||||
0.325565 | + | 0.945520i | \(0.394446\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1530.75i | 1.46436i | 0.681110 | + | 0.732181i | \(0.261497\pi\) | ||||
−0.681110 | + | 0.732181i | \(0.738503\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 264.625i | 0.239087i | 0.992829 | + | 0.119543i | \(0.0381431\pi\) | ||||
−0.992829 | + | 0.119543i | \(0.961857\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1117.61 | −0.982091 | −0.491046 | − | 0.871134i | \(-0.663385\pi\) | ||||
−0.491046 | + | 0.871134i | \(0.663385\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 739.841 | 0.632636 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 934.061i | 0.777602i | 0.921322 | + | 0.388801i | \(0.127111\pi\) | ||||
−0.921322 | + | 0.388801i | \(0.872889\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 708.681i | 0.559980i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −235.876 | −0.181704 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1319.20 | −0.991132 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1267.99i | 0.929517i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 630.356i | − 0.440433i | −0.975451 | − | 0.220217i | \(-0.929324\pi\) | ||||
0.975451 | − | 0.220217i | \(-0.0706765\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1087.31 | −0.742109 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2163.06 | 1.44265 | 0.721325 | − | 0.692597i | \(-0.243534\pi\) | ||||
0.721325 | + | 0.692597i | \(0.243534\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 90.6440i | 0.0590965i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1118.61i | 0.697588i | 0.937199 | + | 0.348794i | \(0.113409\pi\) | ||||
−0.937199 | + | 0.348794i | \(0.886591\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −166.478 | −0.101586 | −0.0507930 | − | 0.998709i | \(-0.516175\pi\) | ||||
−0.0507930 | + | 0.998709i | \(0.516175\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −511.546 | −0.305531 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 270.527i | − 0.158200i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 969.976i | 0.544233i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 653.143 | 0.359111 | 0.179555 | − | 0.983748i | \(-0.442534\pi\) | ||||
0.179555 | + | 0.983748i | \(0.442534\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1929.38 | 1.03981 | 0.519903 | − | 0.854225i | \(-0.325968\pi\) | ||||
0.519903 | + | 0.854225i | \(0.325968\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 478.602i | − 0.252893i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2169.75i | 1.10296i | 0.834188 | + | 0.551480i | \(0.185937\pi\) | ||||
−0.834188 | + | 0.551480i | \(0.814063\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1638.15 | −0.817066 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −524.761 | −0.256876 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 763.738i | − 0.366997i | −0.983020 | − | 0.183499i | \(-0.941258\pi\) | ||||
0.983020 | − | 0.183499i | \(-0.0587423\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2564.28i | 1.18820i | 0.804389 | + | 0.594102i | \(0.202493\pi\) | ||||
−0.804389 | + | 0.594102i | \(0.797507\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4003.36 | −1.82220 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −183.920 | −0.0822500 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 51.8290i | − 0.0227774i | −0.999935 | − | 0.0113887i | \(-0.996375\pi\) | ||||
0.999935 | − | 0.0113887i | \(-0.00362521\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 650.909i | − 0.276414i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3956.63 | −1.65214 | −0.826068 | − | 0.563571i | \(-0.809427\pi\) | ||||
−0.826068 | + | 0.563571i | \(0.809427\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1804.04 | 0.740848 | 0.370424 | − | 0.928863i | \(-0.379212\pi\) | ||||
0.370424 | + | 0.928863i | \(0.379212\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 392.705i | 0.158632i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 182.698i | 0.0714449i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 119.761 | 0.0460917 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3666.75 | −1.38909 | −0.694547 | − | 0.719448i | \(-0.744395\pi\) | ||||
−0.694547 | + | 0.719448i | \(0.744395\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2716.98i | 1.01333i | 0.862144 | + | 0.506664i | \(0.169121\pi\) | ||||
−0.862144 | + | 0.506664i | \(0.830879\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2034.30i | 0.735723i | 0.929881 | + | 0.367862i | \(0.119910\pi\) | ||||
−0.929881 | + | 0.367862i | \(0.880090\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1551.27 | −0.552596 | −0.276298 | − | 0.961072i | \(-0.589108\pi\) | ||||
−0.276298 | + | 0.961072i | \(0.589108\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1844.67 | −0.647328 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 745.398i | − 0.257718i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 1064.76i | − 0.357517i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 70.2084 | 0.0232365 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3192.51 | −1.04162 | −0.520809 | − | 0.853673i | \(-0.674370\pi\) | ||||
−0.520809 | + | 0.853673i | \(0.674370\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 974.466i | − 0.313471i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 270.789i | 0.0847115i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −266.614 | −0.0822652 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4187.36 | 1.27454 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1555.55i | − 0.467120i | −0.972342 | − | 0.233560i | \(-0.924963\pi\) | ||||
0.972342 | − | 0.233560i | \(-0.0750374\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6206.86i | 1.81482i | 0.420248 | + | 0.907409i | \(0.361943\pi\) | ||||
−0.420248 | + | 0.907409i | \(0.638057\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4679.51 | −1.35035 | −0.675176 | − | 0.737657i | \(-0.735932\pi\) | ||||
−0.675176 | + | 0.737657i | \(0.735932\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −45.7167 | −0.0130214 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3244.53i | 0.912259i | 0.889913 | + | 0.456129i | \(0.150765\pi\) | ||||
−0.889913 | + | 0.456129i | \(0.849235\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 3412.27i | − 0.935236i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3658.62 | −0.990193 | −0.495097 | − | 0.868838i | \(-0.664867\pi\) | ||||
−0.495097 | + | 0.868838i | \(0.664867\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1931.01 | 0.516131 | 0.258065 | − | 0.966127i | \(-0.416915\pi\) | ||||
0.258065 | + | 0.966127i | \(0.416915\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1609.15i | − 0.414525i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2276.73 | 0.579444 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5843.34 | 1.46944 | 0.734718 | − | 0.678373i | \(-0.237315\pi\) | ||||
0.734718 | + | 0.678373i | \(0.237315\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 406.454i | 0.101002i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4506.11i | 1.09371i | 0.837227 | + | 0.546855i | \(0.184175\pi\) | ||||
−0.837227 | + | 0.546855i | \(0.815825\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1093.88 | 0.262434 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1512.44 | 0.358689 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5340.16i | 1.25205i | 0.779804 | + | 0.626024i | \(0.215319\pi\) | ||||
−0.779804 | + | 0.626024i | \(0.784681\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 587.044i | − 0.134556i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2809.79 | −0.636863 | −0.318431 | − | 0.947946i | \(-0.603156\pi\) | ||||
−0.318431 | + | 0.947946i | \(0.603156\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3102.95 | −0.695537 | −0.347769 | − | 0.937580i | \(-0.613060\pi\) | ||||
−0.347769 | + | 0.937580i | \(0.613060\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1047.81i | 0.232294i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 4598.93i | − 0.997555i | −0.866730 | − | 0.498777i | \(-0.833783\pi\) | ||||
0.866730 | − | 0.498777i | \(-0.166217\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −549.443 | −0.117901 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2571.83 | 0.545987 | 0.272994 | − | 0.962016i | \(-0.411986\pi\) | ||||
0.272994 | + | 0.962016i | \(0.411986\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5575.31i | 1.17109i | 0.810641 | + | 0.585544i | \(0.199119\pi\) | ||||
−0.810641 | + | 0.585544i | \(0.800881\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1874.76i | 0.385588i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2085.10 | 0.424405 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1563.00 | −0.314861 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 5794.27i | − 1.15531i | −0.816282 | − | 0.577654i | \(-0.803968\pi\) | ||||
0.816282 | − | 0.577654i | \(-0.196032\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 92.7611i | − 0.0181230i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9315.76 | 1.80182 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1607.62 | −0.307846 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1982.76i | 0.375930i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1404.47i | 0.261099i | 0.991442 | + | 0.130550i | \(0.0416742\pi\) | ||||
−0.991442 | + | 0.130550i | \(0.958326\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4592.25 | −0.845449 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4096.75 | 0.746963 | 0.373481 | − | 0.927638i | \(-0.378164\pi\) | ||||
0.373481 | + | 0.927638i | \(0.378164\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 974.611i | − 0.176001i | −0.996120 | − | 0.0880004i | \(-0.971952\pi\) | ||||
0.996120 | − | 0.0880004i | \(-0.0280477\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2071.69i | − 0.367058i | −0.983014 | − | 0.183529i | \(-0.941248\pi\) | ||||
0.983014 | − | 0.183529i | \(-0.0587522\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −577.349 | −0.101333 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −793.876 | −0.138037 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1086.72i | 0.187204i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 3352.84i | − 0.567011i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −756.337 | −0.126742 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6159.17 | 1.02278 | 0.511388 | − | 0.859350i | \(-0.329132\pi\) | ||||
0.511388 | + | 0.859350i | \(0.329132\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2219.52i | 0.365252i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2791.26i | 0.451186i | 0.974222 | + | 0.225593i | \(0.0724320\pi\) | ||||
−0.974222 | + | 0.225593i | \(0.927568\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2802.18 | −0.448949 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 209.740 | 0.0333081 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2955.55i | 0.465262i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 940.848i | − 0.145554i | −0.997348 | − | 0.0727772i | \(-0.976814\pi\) | ||||
0.997348 | − | 0.0727772i | \(-0.0231862\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3519.62 | 0.539831 | 0.269915 | − | 0.962884i | \(-0.413004\pi\) | ||||
0.269915 | + | 0.962884i | \(0.413004\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2126.04 | −0.323304 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 5021.60i | − 0.757147i | −0.925571 | − | 0.378573i | \(-0.876415\pi\) | ||||
0.925571 | − | 0.378573i | \(-0.123585\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 707.628i | − 0.104907i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6811.99 | 1.00146 | 0.500728 | − | 0.865604i | \(-0.333066\pi\) | ||||
0.500728 | + | 0.865604i | \(0.333066\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6441.39 | −0.939115 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 3957.59i | − 0.572230i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 3748.07i | − 0.533099i | −0.963821 | − | 0.266550i | \(-0.914116\pi\) | ||||
0.963821 | − | 0.266550i | \(-0.0858836\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3803.96 | −0.536657 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2422.05 | −0.338940 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 898.302i | 0.124698i | 0.998054 | + | 0.0623489i | \(0.0198592\pi\) | ||||
−0.998054 | + | 0.0623489i | \(0.980141\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13232.6i | 1.80773i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9378.99 | −1.27115 | −0.635576 | − | 0.772038i | \(-0.719237\pi\) | ||||
−0.635576 | + | 0.772038i | \(0.719237\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1891.07 | 0.254284 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 9446.29i | − 1.26027i | −0.776486 | − | 0.630134i | \(-0.783000\pi\) | ||||
0.776486 | − | 0.630134i | \(-0.217000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 3261.92i | − 0.428457i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7643.23 | 0.996214 | 0.498107 | − | 0.867116i | \(-0.334029\pi\) | ||||
0.498107 | + | 0.867116i | \(0.334029\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6291.32 | −0.813723 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6489.17i | 0.832914i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 12013.6i | − 1.51876i | −0.650650 | − | 0.759378i | \(-0.725503\pi\) | ||||
0.650650 | − | 0.759378i | \(-0.274497\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −271.932 | −0.0341194 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8538.51 | −1.06332 | −0.531662 | − | 0.846957i | \(-0.678432\pi\) | ||||
−0.531662 | + | 0.846957i | \(0.678432\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 4807.16i | − 0.594197i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 847.265i | − 0.103188i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12267.6 | 1.48312 | 0.741558 | − | 0.670889i | \(-0.234087\pi\) | ||||
0.741558 | + | 0.670889i | \(0.234087\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3355.84 | −0.402753 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 962.389i | − 0.114664i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 499.433i | − 0.0586508i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15493.0 | 1.80641 | 0.903204 | − | 0.429212i | \(-0.141209\pi\) | ||||
0.903204 | + | 0.429212i | \(0.141209\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7510.67 | 0.869472 | 0.434736 | − | 0.900558i | \(-0.356842\pi\) | ||||
0.434736 | + | 0.900558i | \(0.356842\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 1534.64i | − 0.176399i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 580.627i | 0.0658045i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 811.581 | 0.0913368 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15675.3 | 1.75186 | 0.875932 | − | 0.482434i | \(-0.160247\pi\) | ||||
0.875932 | + | 0.482434i | \(0.160247\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9604.78i | 1.06600i | 0.846117 | + | 0.532998i | \(0.178935\pi\) | ||||
−0.846117 | + | 0.532998i | \(0.821065\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2417.67i | 0.264652i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6362.06 | −0.691673 | −0.345837 | − | 0.938295i | \(-0.612405\pi\) | ||||
−0.345837 | + | 0.938295i | \(0.612405\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2909.93 | −0.314213 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 931.658i | 0.0999196i | 0.998751 | + | 0.0499598i | \(0.0159093\pi\) | ||||
−0.998751 | + | 0.0499598i | \(0.984091\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1959.43i | 0.207333i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18684.1 | 1.96383 | 0.981914 | − | 0.189329i | \(-0.0606314\pi\) | ||||
0.981914 | + | 0.189329i | \(0.0606314\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1452.10 | 0.151611 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5788.14i | 0.600333i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 11565.9i | − 1.18387i | −0.805985 | − | 0.591936i | \(-0.798364\pi\) | ||||
0.805985 | − | 0.591936i | \(-0.201636\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1435.81 | 0.146008 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19401.0 | 1.96008 | 0.980039 | − | 0.198806i | \(-0.0637062\pi\) | ||||
0.980039 | + | 0.198806i | \(0.0637062\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1576.28i | 0.158220i | 0.996866 | + | 0.0791099i | \(0.0252078\pi\) | ||||
−0.996866 | + | 0.0791099i | \(0.974792\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 3256.55i | − 0.322687i | −0.986898 | − | 0.161344i | \(-0.948417\pi\) | ||||
0.986898 | − | 0.161344i | \(-0.0515827\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2727.40 | −0.268528 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6509.25 | −0.636795 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1245.18i | 0.121043i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 4914.44i | − 0.471733i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8291.59 | 0.790924 | 0.395462 | − | 0.918482i | \(-0.370585\pi\) | ||||
0.395462 | + | 0.918482i | \(0.370585\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19418.9 | −1.84081 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1574.28i | − 0.148307i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 4758.55i | − 0.442773i | −0.975186 | − | 0.221387i | \(-0.928942\pi\) | ||||
0.975186 | − | 0.221387i | \(-0.0710583\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2291.21 | 0.211886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3906.46 | −0.359055 | −0.179528 | − | 0.983753i | \(-0.557457\pi\) | ||||
−0.179528 | + | 0.983753i | \(0.557457\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 8936.52i | − 0.816390i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 1440.78i | − 0.130036i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3093.31 | −0.277506 | −0.138753 | − | 0.990327i | \(-0.544309\pi\) | ||||
−0.138753 | + | 0.990327i | \(0.544309\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7692.85 | −0.686010 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 18153.9i | − 1.60923i | −0.593796 | − | 0.804616i | \(-0.702371\pi\) | ||||
0.593796 | − | 0.804616i | \(-0.297629\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 12010.1i | − 1.05204i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2281.32 | −0.198660 | −0.0993298 | − | 0.995055i | \(-0.531670\pi\) | ||||
−0.0993298 | + | 0.995055i | \(0.531670\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −394.197 | −0.0341257 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 551.761i | − 0.0474870i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 585.821i | 0.0498344i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 155.487 | 0.0131505 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16691.9 | −1.40362 | −0.701809 | − | 0.712366i | \(-0.747624\pi\) | ||||
−0.701809 | + | 0.712366i | \(0.747624\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 17090.4i | − 1.42889i | −0.699690 | − | 0.714446i | \(-0.746679\pi\) | ||||
0.699690 | − | 0.714446i | \(-0.253321\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3246.47i | 0.268346i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1829.50 | −0.150365 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1952.73 | 0.159588 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 33281.5i | − 2.70465i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 11869.9i | − 0.953861i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1110.82 | 0.0887685 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5271.40 | 0.418919 | 0.209459 | − | 0.977817i | \(-0.432830\pi\) | ||||
0.209459 | + | 0.977817i | \(0.432830\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5412.13i | 0.427729i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 15182.2i | − 1.18673i | −0.804933 | − | 0.593366i | \(-0.797799\pi\) | ||||
0.804933 | − | 0.593366i | \(-0.202201\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1178.11 | −0.0915860 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3434.18 | −0.265519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 5045.15i | − 0.387960i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12241.2i | 0.931198i | 0.884996 | + | 0.465599i | \(0.154161\pi\) | ||||
−0.884996 | + | 0.465599i | \(0.845839\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28539.0 | 2.15934 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −548.094 | −0.0412488 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14196.4i | 1.06271i | 0.847149 | + | 0.531355i | \(0.178317\pi\) | ||||
−0.847149 | + | 0.531355i | \(0.821683\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 359.283i | 0.0266111i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9150.05 | −0.674148 | −0.337074 | − | 0.941478i | \(-0.609437\pi\) | ||||
−0.337074 | + | 0.941478i | \(0.609437\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23582.1 | −1.72833 | −0.864167 | − | 0.503206i | \(-0.832154\pi\) | ||||
−0.864167 | + | 0.503206i | \(0.832154\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 11000.3i | − 0.801993i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3906.22i | 0.281834i | 0.990021 | + | 0.140917i | \(0.0450050\pi\) | ||||
−0.990021 | + | 0.140917i | \(0.954995\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8150.93 | −0.585045 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3366.21 | 0.240368 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1876.00i | 0.133270i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25938.0i | 1.82381i | 0.410401 | + | 0.911905i | \(0.365389\pi\) | ||||
−0.410401 | + | 0.911905i | \(0.634611\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1247.58 | 0.0872759 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6102.89 | −0.424770 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 1908.23i | − 0.132145i | −0.997815 | − | 0.0660723i | \(-0.978953\pi\) | ||||
0.997815 | − | 0.0660723i | \(-0.0210468\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 4653.81i | − 0.319041i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3495.41 | −0.238429 | −0.119214 | − | 0.992869i | \(-0.538038\pi\) | ||||
−0.119214 | + | 0.992869i | \(0.538038\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18267.2 | −1.23983 | −0.619913 | − | 0.784671i | \(-0.712832\pi\) | ||||
−0.619913 | + | 0.784671i | \(0.712832\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 5534.01i | − 0.373735i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 11538.2i | − 0.771534i | −0.922596 | − | 0.385767i | \(-0.873937\pi\) | ||||
0.922596 | − | 0.385767i | \(-0.126063\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2236.19 | 0.148793 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13426.8 | 0.889017 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 21136.9i | − 1.39268i | −0.717713 | − | 0.696340i | \(-0.754811\pi\) | ||||
0.717713 | − | 0.696340i | \(-0.245189\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15673.2i | 1.02266i | 0.859385 | + | 0.511329i | \(0.170847\pi\) | ||||
−0.859385 | + | 0.511329i | \(0.829153\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22923.7 | 1.48850 | 0.744249 | − | 0.667902i | \(-0.232807\pi\) | ||||
0.744249 | + | 0.667902i | \(0.232807\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3194.28 | 0.206413 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 867.964i | − 0.0558174i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 210.625i | 0.0134156i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13114.4 | 0.831329 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9108.23 | −0.574632 | −0.287316 | − | 0.957836i | \(-0.592763\pi\) | ||||
−0.287316 | + | 0.957836i | \(0.592763\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 9577.53i | − 0.601379i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 25459.4i | − 1.58358i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2923.40 | 0.180983 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20103.5 | 1.23875 | 0.619375 | − | 0.785095i | \(-0.287386\pi\) | ||||
0.619375 | + | 0.785095i | \(0.287386\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5934.92i | 0.363997i | 0.983299 | + | 0.181999i | \(0.0582567\pi\) | ||||
−0.983299 | + | 0.181999i | \(0.941743\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14193.7i | 0.862460i | 0.902242 | + | 0.431230i | \(0.141920\pi\) | ||||
−0.902242 | + | 0.431230i | \(0.858080\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −745.420 | −0.0450852 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −812.368 | −0.0489082 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4795.80i | 0.287403i | 0.989621 | + | 0.143701i | \(0.0459005\pi\) | ||||
−0.989621 | + | 0.143701i | \(0.954100\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 799.841i | − 0.0474958i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4399.57 | 0.260065 | 0.130032 | − | 0.991510i | \(-0.458492\pi\) | ||||
0.130032 | + | 0.991510i | \(0.458492\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24096.0 | 1.41789 | 0.708945 | − | 0.705263i | \(-0.249171\pi\) | ||||
0.708945 | + | 0.705263i | \(0.249171\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12562.1i | 0.735853i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 19881.4i | − 1.15414i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4666.66 | 0.269692 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 449.725 | 0.0258740 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27648.3i | 1.58360i | 0.610781 | + | 0.791800i | \(0.290856\pi\) | ||||
−0.610781 | + | 0.791800i | \(0.709144\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 27605.5i | − 1.56716i | −0.621292 | − | 0.783580i | \(-0.713392\pi\) | ||||
0.621292 | − | 0.783580i | \(-0.286608\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2310.95 | −0.130613 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18620.6 | −1.04779 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 14949.4i | − 0.837513i | −0.908099 | − | 0.418756i | \(-0.862466\pi\) | ||||
0.908099 | − | 0.418756i | \(-0.137534\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 14038.5i | − 0.779626i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 42997.2 | 2.37745 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8884.30 | −0.489110 | −0.244555 | − | 0.969635i | \(-0.578642\pi\) | ||||
−0.244555 | + | 0.969635i | \(0.578642\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 137.150i | − 0.00751790i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22476.4i | 1.22145i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9733.59 | −0.526693 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10556.9 | 0.568798 | 0.284399 | − | 0.958706i | \(-0.408206\pi\) | ||||
0.284399 | + | 0.958706i | \(0.408206\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 5039.70i | − 0.270378i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2931.58i | 0.155945i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25351.9 | −1.34289 | −0.671445 | − | 0.741055i | \(-0.734326\pi\) | ||||
−0.671445 | + | 0.741055i | \(0.734326\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10236.8 | 0.539959 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7222.53i | 0.379363i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 10975.8i | − 0.571688i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9719.94 | 0.504162 | 0.252081 | − | 0.967706i | \(-0.418885\pi\) | ||||
0.252081 | + | 0.967706i | \(0.418885\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6789.79 | −0.350714 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5793.04i | 0.297988i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27509.3i | 1.40339i | 0.712479 | + | 0.701694i | \(0.247572\pi\) | ||||
−0.712479 | + | 0.701694i | \(0.752428\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19273.6 | −0.975184 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7240.49i | 0.364848i | 0.983220 | + | 0.182424i | \(0.0583944\pi\) | ||||
−0.983220 | + | 0.182424i | \(0.941606\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2112.51i | 0.105584i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15875.3 | −0.790234 | −0.395117 | − | 0.918631i | \(-0.629296\pi\) | ||||
−0.395117 | + | 0.918631i | \(0.629296\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4827.44 | 0.239326 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 25714.3i | − 1.26967i | −0.772647 | − | 0.634836i | \(-0.781068\pi\) | ||||
0.772647 | − | 0.634836i | \(-0.218932\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6830.18i | 0.334542i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1173.77 | −0.0572612 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9709.09 | 0.471757 | 0.235879 | − | 0.971783i | \(-0.424203\pi\) | ||||
0.235879 | + | 0.971783i | \(0.424203\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17530.0i | 0.848379i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 9567.13i | − 0.459344i | −0.973268 | − | 0.229672i | \(-0.926235\pi\) | ||||
0.973268 | − | 0.229672i | \(-0.0737653\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1219.36 | −0.0583137 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12322.5 | −0.586980 | −0.293490 | − | 0.955962i | \(-0.594817\pi\) | ||||
−0.293490 | + | 0.955962i | \(0.594817\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 4957.28i | − 0.235211i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17084.7i | 0.804293i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2575.56 | −0.120776 | −0.0603881 | − | 0.998175i | \(-0.519234\pi\) | ||||
−0.0603881 | + | 0.998175i | \(0.519234\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13518.3 | −0.631454 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6606.23i | 0.307386i | 0.988119 | + | 0.153693i | \(0.0491167\pi\) | ||||
−0.988119 | + | 0.153693i | \(0.950883\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3281.63i | 0.151516i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8637.37 | 0.397260 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1115.96 | −0.0511294 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4537.33i | 0.207089i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 16417.0i | − 0.743587i | −0.928315 | − | 0.371793i | \(-0.878743\pi\) | ||||
0.928315 | − | 0.371793i | \(-0.121257\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16020.5 | −0.722870 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4143.12 | −0.186235 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 10307.5i | − 0.461577i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 3944.19i | − 0.175295i | −0.996152 | − | 0.0876477i | \(-0.972065\pi\) | ||||
0.996152 | − | 0.0876477i | \(-0.0279350\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9067.66 | −0.401490 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1761.13 | 0.0776861 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 305.325i | 0.0134181i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 8429.37i | − 0.367693i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17960.7 | 0.780549 | 0.390275 | − | 0.920699i | \(-0.372380\pi\) | ||||
0.390275 | + | 0.920699i | \(0.372380\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13162.5 | 0.569912 | 0.284956 | − | 0.958541i | \(-0.408021\pi\) | ||||
0.284956 | + | 0.958541i | \(0.408021\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 9308.84i | − 0.401569i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7406.59i | 0.317165i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3143.42 | −0.134115 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26502.4 | 1.12660 | 0.563302 | − | 0.826251i | \(-0.309531\pi\) | ||||
0.563302 | + | 0.826251i | \(0.309531\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6937.86i | 0.293850i | 0.989148 | + | 0.146925i | \(0.0469376\pi\) | ||||
−0.989148 | + | 0.146925i | \(0.953062\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 41197.9i | − 1.73228i | −0.499805 | − | 0.866138i | \(-0.666595\pi\) | ||||
0.499805 | − | 0.866138i | \(-0.333405\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 693.324 | 0.0290472 | 0.0145236 | − | 0.999895i | \(-0.495377\pi\) | ||||
0.0145236 | + | 0.999895i | \(0.495377\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13796.8 | 0.575938 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17193.8i | 0.715162i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 1648.33i | − 0.0680699i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6491.28 | −0.267108 | −0.133554 | − | 0.991042i | \(-0.542639\pi\) | ||||
−0.133554 | + | 0.991042i | \(0.542639\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3851.52 | 0.157921 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7715.49i | 0.315226i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 5851.42i | − 0.237376i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16725.9 | −0.676128 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29176.1 | 1.17526 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1116.68i | 0.0448233i | 0.999749 | + | 0.0224117i | \(0.00713445\pi\) | ||||
−0.999749 | + | 0.0224117i | \(0.992866\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44383.9i | 1.76911i | 0.466438 | + | 0.884554i | \(0.345537\pi\) | ||||
−0.466438 | + | 0.884554i | \(0.654463\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25579.3 | −1.01601 | −0.508006 | − | 0.861354i | \(-0.669617\pi\) | ||||
−0.508006 | + | 0.861354i | \(0.669617\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5624.28 | −0.222619 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 11194.8i | − 0.441570i | −0.975323 | − | 0.220785i | \(-0.929138\pi\) | ||||
0.975323 | − | 0.220785i | \(-0.0708619\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6255.31i | 0.245030i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3907.73 | −0.152544 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 48417.9 | 1.88356 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 4689.00i | − 0.181785i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 5721.75i | − 0.220308i | −0.993915 | − | 0.110154i | \(-0.964866\pi\) | ||||
0.993915 | − | 0.110154i | \(-0.0351344\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17382.8 | 0.667017 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34682.8 | −1.32633 | −0.663163 | − | 0.748475i | \(-0.730786\pi\) | ||||
−0.663163 | + | 0.748475i | \(0.730786\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37990.4i | 1.44788i | 0.689862 | + | 0.723941i | \(0.257671\pi\) | ||||
−0.689862 | + | 0.723941i | \(0.742329\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28299.0i | 1.07124i | 0.844460 | + | 0.535618i | \(0.179921\pi\) | ||||
−0.844460 | + | 0.535618i | \(0.820079\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2796.00 | 0.105484 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 278.283 | 0.0104633 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3484.58i | 0.130579i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27947.3i | 1.04028i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10259.3 | −0.380607 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29037.8 | −1.07368 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 4822.85i | − 0.177735i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17388.0i | 0.636559i | 0.947997 | + | 0.318280i | \(0.103105\pi\) | ||||
−0.947997 | + | 0.318280i | \(0.896895\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5948.28 | −0.217043 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23555.3 | −0.856663 | −0.428332 | − | 0.903622i | \(-0.640899\pi\) | ||||
−0.428332 | + | 0.903622i | \(0.640899\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 2607.30i | − 0.0945117i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9594.44i | 0.345514i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5983.09 | −0.214760 | −0.107380 | − | 0.994218i | \(-0.534246\pi\) | ||||
−0.107380 | + | 0.994218i | \(0.534246\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4213.42 | −0.150746 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25577.3i | 0.912119i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 13776.7i | − 0.488120i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20576.7 | −0.726694 | −0.363347 | − | 0.931654i | \(-0.618366\pi\) | ||||
−0.363347 | + | 0.931654i | \(0.618366\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6607.35 | 0.232596 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12290.2i | 0.431259i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 11228.6i | − 0.391485i | −0.980655 | − | 0.195743i | \(-0.937288\pi\) | ||||
0.980655 | − | 0.195743i | \(-0.0627117\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2923.83 | 0.101614 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38567.6 | 1.33610 | 0.668049 | − | 0.744118i | \(-0.267130\pi\) | ||||
0.668049 | + | 0.744118i | \(0.267130\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 50003.9i | 1.72678i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 4606.17i | − 0.158057i | −0.996872 | − | 0.0790287i | \(-0.974818\pi\) | ||||
0.996872 | − | 0.0790287i | \(-0.0251819\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6997.93 | 0.239370 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6215.06 | 0.211921 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25559.7i | 0.868795i | 0.900721 | + | 0.434397i | \(0.143039\pi\) | ||||
−0.900721 | + | 0.434397i | \(0.856961\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1732.05i | − 0.0585048i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4961.72 | −0.167072 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26064.0 | −0.874895 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 2381.63i | − 0.0796956i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 37895.8i | − 1.26023i | −0.776500 | − | 0.630117i | \(-0.783007\pi\) | ||||
0.776500 | − | 0.630117i | \(-0.216993\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3260.17 | −0.108082 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46761.0 | 1.54545 | 0.772726 | − | 0.634740i | \(-0.218893\pi\) | ||||
0.772726 | + | 0.634740i | \(0.218893\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 738.428i | − 0.0243298i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3070.29i | 0.100540i | 0.998736 | + | 0.0502698i | \(0.0160081\pi\) | ||||
−0.998736 | + | 0.0502698i | \(0.983992\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −672.282 | −0.0219471 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10058.5 | 0.327364 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16319.0i | 0.529498i | 0.964317 | + | 0.264749i | \(0.0852891\pi\) | ||||
−0.964317 | + | 0.264749i | \(0.914711\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 2269.01i | − 0.0731747i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42878.6 | −1.37862 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5105.79 | −0.163664 | −0.0818319 | − | 0.996646i | \(-0.526077\pi\) | ||||
−0.0818319 | + | 0.996646i | \(0.526077\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18477.5i | 0.590500i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7206.97i | 0.228934i | 0.993427 | + | 0.114467i | \(0.0365160\pi\) | ||||
−0.993427 | + | 0.114467i | \(0.963484\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6658.57 | −0.210879 |
(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 | 1200.4.f.v.49.4 | 4 | ||
4.3 | odd | 2 | 75.4.b.c.49.1 | 4 | |||
5.2 | odd | 4 | 1200.4.a.bu.1.1 | 2 | |||
5.3 | odd | 4 | 1200.4.a.bl.1.2 | 2 | |||
5.4 | even | 2 | inner | 1200.4.f.v.49.1 | 4 | ||
12.11 | even | 2 | 225.4.b.h.199.4 | 4 | |||
20.3 | even | 4 | 75.4.a.d.1.1 | ✓ | 2 | ||
20.7 | even | 4 | 75.4.a.e.1.2 | yes | 2 | ||
20.19 | odd | 2 | 75.4.b.c.49.4 | 4 | |||
60.23 | odd | 4 | 225.4.a.n.1.2 | 2 | |||
60.47 | odd | 4 | 225.4.a.j.1.1 | 2 | |||
60.59 | even | 2 | 225.4.b.h.199.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.a.d.1.1 | ✓ | 2 | 20.3 | even | 4 | ||
75.4.a.e.1.2 | yes | 2 | 20.7 | even | 4 | ||
75.4.b.c.49.1 | 4 | 4.3 | odd | 2 | |||
75.4.b.c.49.4 | 4 | 20.19 | odd | 2 | |||
225.4.a.j.1.1 | 2 | 60.47 | odd | 4 | |||
225.4.a.n.1.2 | 2 | 60.23 | odd | 4 | |||
225.4.b.h.199.1 | 4 | 60.59 | even | 2 | |||
225.4.b.h.199.4 | 4 | 12.11 | even | 2 | |||
1200.4.a.bl.1.2 | 2 | 5.3 | odd | 4 | |||
1200.4.a.bu.1.1 | 2 | 5.2 | odd | 4 | |||
1200.4.f.v.49.1 | 4 | 5.4 | even | 2 | inner | ||
1200.4.f.v.49.4 | 4 | 1.1 | even | 1 | trivial |