Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6000,2,Mod(1249,6000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6000, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6000.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6000 = 2^{4} \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6000.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: | \(47.9102412128\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 750) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.4 | ||
Root | \(0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6000.1249 |
Dual form | 6000.2.f.a.1249.1 |
$q$-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 \(\left(\mathbb{Z}/6000\mathbb{Z}\right)^\times\).
\(n\) | \(751\) | \(4001\) | \(4501\) | \(5377\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.23607i | 0.467190i | 0.972334 | + | 0.233595i | \(0.0750489\pi\) | ||||
−0.972334 | + | 0.233595i | \(0.924951\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.38197 | −0.416678 | −0.208339 | − | 0.978057i | \(-0.566806\pi\) | ||||
−0.208339 | + | 0.978057i | \(0.566806\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.85410i | − 0.791585i | −0.918340 | − | 0.395793i | \(-0.870470\pi\) | ||||
0.918340 | − | 0.395793i | \(-0.129530\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 4.85410i | − 1.17729i | −0.808391 | − | 0.588646i | \(-0.799661\pi\) | ||||
0.808391 | − | 0.588646i | \(-0.200339\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.23607 | −0.269732 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.09017i | 0.644345i | 0.946681 | + | 0.322172i | \(0.104413\pi\) | ||||
−0.946681 | + | 0.322172i | \(0.895587\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.32624 | −1.73184 | −0.865919 | − | 0.500183i | \(-0.833266\pi\) | ||||
−0.865919 | + | 0.500183i | \(0.833266\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.14590 | −0.385415 | −0.192707 | − | 0.981256i | \(-0.561727\pi\) | ||||
−0.192707 | + | 0.981256i | \(0.561727\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 1.38197i | − 0.240569i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.85410i | 1.29121i | 0.763673 | + | 0.645603i | \(0.223394\pi\) | ||||
−0.763673 | + | 0.645603i | \(0.776606\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.85410 | 0.457022 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.23607 | −0.505389 | −0.252694 | − | 0.967546i | \(-0.581317\pi\) | ||||
−0.252694 | + | 0.967546i | \(0.581317\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.145898i | 0.0222492i | 0.999938 | + | 0.0111246i | \(0.00354115\pi\) | ||||
−0.999938 | + | 0.0111246i | \(0.996459\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.8541i | 1.58323i | 0.611018 | + | 0.791617i | \(0.290760\pi\) | ||||
−0.611018 | + | 0.791617i | \(0.709240\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.47214 | 0.781734 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.85410 | 0.679710 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.23607i | 0.444508i | 0.974989 | + | 0.222254i | \(0.0713414\pi\) | ||||
−0.974989 | + | 0.222254i | \(0.928659\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000i | 0.794719i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.38197 | 0.830861 | 0.415431 | − | 0.909625i | \(-0.363631\pi\) | ||||
0.415431 | + | 0.909625i | \(0.363631\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.4164 | 1.71780 | 0.858898 | − | 0.512148i | \(-0.171150\pi\) | ||||
0.858898 | + | 0.512148i | \(0.171150\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 1.23607i | − 0.155730i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 2.38197i | − 0.291003i | −0.989358 | − | 0.145502i | \(-0.953520\pi\) | ||||
0.989358 | − | 0.145502i | \(-0.0464796\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.09017 | −0.372013 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.94427 | 1.06149 | 0.530745 | − | 0.847532i | \(-0.321912\pi\) | ||||
0.530745 | + | 0.847532i | \(0.321912\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 12.0000i | − 1.40449i | −0.711934 | − | 0.702247i | \(-0.752180\pi\) | ||||
0.711934 | − | 0.702247i | \(-0.247820\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.70820i | − 0.194668i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.14590 | −0.128924 | −0.0644618 | − | 0.997920i | \(-0.520533\pi\) | ||||
−0.0644618 | + | 0.997920i | \(0.520533\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.18034i | 0.897909i | 0.893555 | + | 0.448954i | \(0.148203\pi\) | ||||
−0.893555 | + | 0.448954i | \(0.851797\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 9.32624i | − 0.999878i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.23607 | 0.979021 | 0.489511 | − | 0.871997i | \(-0.337175\pi\) | ||||
0.489511 | + | 0.871997i | \(0.337175\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.52786 | 0.369821 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 2.14590i | − 0.222519i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.1803i | 1.84593i | 0.384879 | + | 0.922967i | \(0.374243\pi\) | ||||
−0.384879 | + | 0.922967i | \(0.625757\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.38197 | 0.138893 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.32624 | −0.231469 | −0.115735 | − | 0.993280i | \(-0.536922\pi\) | ||||
−0.115735 | + | 0.993280i | \(0.536922\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 4.00000i | − 0.394132i | −0.980390 | − | 0.197066i | \(-0.936859\pi\) | ||||
0.980390 | − | 0.197066i | \(-0.0631413\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.18034i | 0.790823i | 0.918504 | + | 0.395412i | \(0.129398\pi\) | ||||
−0.918504 | + | 0.395412i | \(0.870602\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.4164 | 1.28506 | 0.642529 | − | 0.766261i | \(-0.277885\pi\) | ||||
0.642529 | + | 0.766261i | \(0.277885\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.85410 | −0.745478 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 12.3262i | − 1.15955i | −0.814775 | − | 0.579777i | \(-0.803139\pi\) | ||||
0.814775 | − | 0.579777i | \(-0.196861\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.85410i | 0.263862i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.00000 | 0.550019 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.09017 | −0.826379 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 3.23607i | − 0.291786i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.4164i | 1.19051i | 0.803535 | + | 0.595257i | \(0.202950\pi\) | ||||
−0.803535 | + | 0.595257i | \(0.797050\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.145898 | −0.0128456 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.8885 | −1.56293 | −0.781465 | − | 0.623949i | \(-0.785527\pi\) | ||||
−0.781465 | + | 0.623949i | \(0.785527\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.41641i | 0.643084i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.61803i | 0.394545i | 0.980349 | + | 0.197273i | \(0.0632084\pi\) | ||||
−0.980349 | + | 0.197273i | \(0.936792\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.2361 | −1.80122 | −0.900610 | − | 0.434628i | \(-0.856880\pi\) | ||||
−0.900610 | + | 0.434628i | \(0.856880\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.8541 | −0.914080 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.94427i | 0.329837i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.47214i | 0.451334i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.4721 | 1.67714 | 0.838571 | − | 0.544792i | \(-0.183391\pi\) | ||||
0.838571 | + | 0.544792i | \(0.183391\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.8541 | 1.45295 | 0.726473 | − | 0.687195i | \(-0.241158\pi\) | ||||
0.726473 | + | 0.687195i | \(0.241158\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.85410i | 0.392431i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 0.437694i | − 0.0349318i | −0.999847 | − | 0.0174659i | \(-0.994440\pi\) | ||||
0.999847 | − | 0.0174659i | \(-0.00555985\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.23607 | −0.256637 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.81966 | −0.301031 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.2705i | 1.58771i | 0.608108 | + | 0.793854i | \(0.291929\pi\) | ||||
−0.608108 | + | 0.793854i | \(0.708071\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.0902i | 1.78677i | 0.449291 | + | 0.893385i | \(0.351677\pi\) | ||||
−0.449291 | + | 0.893385i | \(0.648323\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.85410 | 0.373392 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.00000 | −0.458831 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.23607i | 0.702205i | 0.936337 | + | 0.351103i | \(0.114193\pi\) | ||||
−0.936337 | + | 0.351103i | \(0.885807\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.38197i | 0.479698i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.41641 | 0.554328 | 0.277164 | − | 0.960823i | \(-0.410605\pi\) | ||||
0.277164 | + | 0.960823i | \(0.410605\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.41641 | 0.551257 | 0.275629 | − | 0.961264i | \(-0.411114\pi\) | ||||
0.275629 | + | 0.961264i | \(0.411114\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.4164i | 0.991769i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.70820i | 0.490552i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.23607 | 0.0899107 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00000 | −0.434145 | −0.217072 | − | 0.976156i | \(-0.569651\pi\) | ||||
−0.217072 | + | 0.976156i | \(0.569651\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.1246i | 1.23266i | 0.787489 | + | 0.616328i | \(0.211381\pi\) | ||||
−0.787489 | + | 0.616328i | \(0.788619\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.52786i | − 0.108856i | −0.998518 | − | 0.0544279i | \(-0.982666\pi\) | ||||
0.998518 | − | 0.0544279i | \(-0.0173335\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.6180 | −1.10713 | −0.553567 | − | 0.832805i | \(-0.686734\pi\) | ||||
−0.553567 | + | 0.832805i | \(0.686734\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.38197 | 0.168011 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 11.5279i | − 0.809097i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 3.09017i | − 0.214782i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.29180 | −0.573556 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.41641 | −0.235195 | −0.117598 | − | 0.993061i | \(-0.537519\pi\) | ||||
−0.117598 | + | 0.993061i | \(0.537519\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.94427i | 0.612851i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 2.65248i | − 0.180062i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.0000 | 0.810885 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.8541 | −0.931928 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 21.7082i | − 1.45369i | −0.686802 | − | 0.726844i | \(-0.740986\pi\) | ||||
0.686802 | − | 0.726844i | \(-0.259014\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.4721i | 1.09329i | 0.837363 | + | 0.546647i | \(0.184096\pi\) | ||||
−0.837363 | + | 0.546647i | \(0.815904\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.70820 | 0.112881 | 0.0564406 | − | 0.998406i | \(-0.482025\pi\) | ||||
0.0564406 | + | 0.998406i | \(0.482025\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.70820 | 0.112392 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 7.32624i | − 0.479958i | −0.970778 | − | 0.239979i | \(-0.922859\pi\) | ||||
0.970778 | − | 0.239979i | \(-0.0771405\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.14590i | − 0.0744341i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.6525 | −1.72401 | −0.862003 | − | 0.506904i | \(-0.830790\pi\) | ||||
−0.862003 | + | 0.506904i | \(0.830790\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0901699 | 0.00580836 | 0.00290418 | − | 0.999996i | \(-0.499076\pi\) | ||||
0.00290418 | + | 0.999996i | \(0.499076\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 17.1246i | − 1.08961i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.18034 | −0.518408 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.90983 | −0.499264 | −0.249632 | − | 0.968341i | \(-0.580310\pi\) | ||||
−0.249632 | + | 0.968341i | \(0.580310\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 4.27051i | − 0.268485i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.5066i | 1.46630i | 0.680067 | + | 0.733150i | \(0.261951\pi\) | ||||
−0.680067 | + | 0.733150i | \(0.738049\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.70820 | −0.603238 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.32624 | 0.577280 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 15.9787i | − 0.985290i | −0.870230 | − | 0.492645i | \(-0.836030\pi\) | ||||
0.870230 | − | 0.492645i | \(-0.163970\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.23607i | 0.565238i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.6180 | −1.37905 | −0.689523 | − | 0.724264i | \(-0.742180\pi\) | ||||
−0.689523 | + | 0.724264i | \(0.742180\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.56231 | 0.520123 | 0.260062 | − | 0.965592i | \(-0.416257\pi\) | ||||
0.260062 | + | 0.965592i | \(0.416257\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.52786i | 0.213516i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.3607i | 0.862850i | 0.902149 | + | 0.431425i | \(0.141989\pi\) | ||||
−0.902149 | + | 0.431425i | \(0.858011\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.14590 | 0.128472 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.4721 | 1.34058 | 0.670288 | − | 0.742101i | \(-0.266171\pi\) | ||||
0.670288 | + | 0.742101i | \(0.266171\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 21.0902i | − 1.25368i | −0.779148 | − | 0.626840i | \(-0.784348\pi\) | ||||
0.779148 | − | 0.626840i | \(-0.215652\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 4.00000i | − 0.236113i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.56231 | −0.386018 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.1803 | −1.06575 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.5967i | 0.911172i | 0.890192 | + | 0.455586i | \(0.150570\pi\) | ||||
−0.890192 | + | 0.455586i | \(0.849430\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.38197i | 0.0801898i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.81966 | 0.510054 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.180340 | −0.0103946 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 2.32624i | − 0.133639i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 33.0902i | 1.88856i | 0.329149 | + | 0.944278i | \(0.393238\pi\) | ||||
−0.329149 | + | 0.944278i | \(0.606762\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.00000 | 0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.47214 | 0.253592 | 0.126796 | − | 0.991929i | \(-0.459531\pi\) | ||||
0.126796 | + | 0.991929i | \(0.459531\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 30.9443i | − 1.74907i | −0.484959 | − | 0.874537i | \(-0.661166\pi\) | ||||
0.484959 | − | 0.874537i | \(-0.338834\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.70820i | 0.545267i | 0.962118 | + | 0.272634i | \(0.0878947\pi\) | ||||
−0.962118 | + | 0.272634i | \(0.912105\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.8885 | 0.721620 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.18034 | −0.456582 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 29.1246i | − 1.62054i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.4164i | 0.741929i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.4164 | −0.739671 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.4164 | 1.17715 | 0.588576 | − | 0.808442i | \(-0.299689\pi\) | ||||
0.588576 | + | 0.808442i | \(0.299689\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 7.85410i | − 0.430402i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 12.9443i | − 0.705119i | −0.935789 | − | 0.352560i | \(-0.885311\pi\) | ||||
0.935789 | − | 0.352560i | \(-0.114689\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.3262 | 0.669469 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.96556 | 0.160594 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.4164i | 0.832408i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 24.3607i | − 1.30775i | −0.756603 | − | 0.653875i | \(-0.773142\pi\) | ||||
0.756603 | − | 0.653875i | \(-0.226858\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.85410 | −0.152341 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 1.20163i | − 0.0639561i | −0.999489 | − | 0.0319781i | \(-0.989819\pi\) | ||||
0.999489 | − | 0.0319781i | \(-0.0101807\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.00000i | 0.317554i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.8885 | 1.26079 | 0.630395 | − | 0.776275i | \(-0.282893\pi\) | ||||
0.630395 | + | 0.776275i | \(0.282893\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 9.09017i | − 0.477110i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 10.2918i | − 0.537227i | −0.963248 | − | 0.268614i | \(-0.913434\pi\) | ||||
0.963248 | − | 0.268614i | \(-0.0865655\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.23607 | 0.168463 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.00000 | −0.207670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.7426i | 1.69535i | 0.530516 | + | 0.847675i | \(0.321998\pi\) | ||||
−0.530516 | + | 0.847675i | \(0.678002\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.6180i | 1.37090i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.23607 | −0.0634925 | −0.0317463 | − | 0.999496i | \(-0.510107\pi\) | ||||
−0.0317463 | + | 0.999496i | \(0.510107\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.4164 | −0.687343 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.8885i | 0.914062i | 0.889451 | + | 0.457031i | \(0.151087\pi\) | ||||
−0.889451 | + | 0.457031i | \(0.848913\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 0.145898i | − 0.00741641i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.2705 | −0.926352 | −0.463176 | − | 0.886266i | \(-0.653290\pi\) | ||||
−0.463176 | + | 0.886266i | \(0.653290\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.0000 | 0.758583 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 17.8885i | − 0.902358i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.4721i | 1.62973i | 0.579651 | + | 0.814865i | \(0.303189\pi\) | ||||
−0.579651 | + | 0.814865i | \(0.696811\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.41641 | −0.371285 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.4721 | −0.522954 | −0.261477 | − | 0.965210i | \(-0.584209\pi\) | ||||
−0.261477 | + | 0.965210i | \(0.584209\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.12461i | 0.305089i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 10.8541i | − 0.538018i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.5623 | −0.670613 | −0.335306 | − | 0.942109i | \(-0.608840\pi\) | ||||
−0.335306 | + | 0.942109i | \(0.608840\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.61803 | −0.227791 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.88854i | 0.388170i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 21.2361i | − 1.03993i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.94427 | −0.436956 | −0.218478 | − | 0.975842i | \(-0.570109\pi\) | ||||
−0.218478 | + | 0.975842i | \(0.570109\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.4721 | 0.705329 | 0.352664 | − | 0.935750i | \(-0.385276\pi\) | ||||
0.352664 | + | 0.935750i | \(0.385276\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 10.8541i | − 0.527744i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.5836i | 0.802536i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.94427 | −0.190431 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.7082 | 1.04565 | 0.522824 | − | 0.852441i | \(-0.324879\pi\) | ||||
0.522824 | + | 0.852441i | \(0.324879\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.180340i | 0.00866658i | 0.999991 | + | 0.00433329i | \(0.00137933\pi\) | ||||
−0.999991 | + | 0.00433329i | \(0.998621\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.5410i | 0.886937i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.3262 | 1.35194 | 0.675969 | − | 0.736930i | \(-0.263725\pi\) | ||||
0.675969 | + | 0.736930i | \(0.263725\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.47214 | −0.260578 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.6525i | 1.55137i | 0.631123 | + | 0.775683i | \(0.282594\pi\) | ||||
−0.631123 | + | 0.775683i | \(0.717406\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.4721i | 0.968299i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.94427 | −0.138949 | −0.0694744 | − | 0.997584i | \(-0.522132\pi\) | ||||
−0.0694744 | + | 0.997584i | \(0.522132\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.47214 | 0.210585 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.8541i | 0.838859i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 22.9443i | − 1.07329i | −0.843809 | − | 0.536644i | \(-0.819692\pi\) | ||||
0.843809 | − | 0.536644i | \(-0.180308\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.85410 | −0.226570 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.9787 | −0.744203 | −0.372101 | − | 0.928192i | \(-0.621363\pi\) | ||||
−0.372101 | + | 0.928192i | \(0.621363\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 2.29180i | − 0.106509i | −0.998581 | − | 0.0532544i | \(-0.983041\pi\) | ||||
0.998581 | − | 0.0532544i | \(-0.0169594\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 2.29180i | − 0.106052i | −0.998593 | − | 0.0530258i | \(-0.983113\pi\) | ||||
0.998593 | − | 0.0530258i | \(-0.0168866\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.94427 | 0.135954 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.437694 | 0.0201679 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 0.201626i | − 0.00927078i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 3.23607i | − 0.148169i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.65248 | 0.303959 | 0.151980 | − | 0.988384i | \(-0.451435\pi\) | ||||
0.151980 | + | 0.988384i | \(0.451435\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.4164 | 1.02210 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 3.81966i | − 0.173801i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.5967i | 0.797385i | 0.917085 | + | 0.398692i | \(0.130536\pi\) | ||||
−0.917085 | + | 0.398692i | \(0.869464\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.2705 | −0.916664 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.61803 | −0.118150 | −0.0590751 | − | 0.998254i | \(-0.518815\pi\) | ||||
−0.0590751 | + | 0.998254i | \(0.518815\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 45.2705i | 2.03888i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.0557i | 0.495917i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.2361 | 0.592528 | 0.296264 | − | 0.955106i | \(-0.404259\pi\) | ||||
0.296264 | + | 0.955106i | \(0.404259\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.0902 | −1.03159 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 10.4721i | − 0.466929i | −0.972365 | − | 0.233465i | \(-0.924994\pi\) | ||||
0.972365 | − | 0.233465i | \(-0.0750063\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.85410i | 0.215578i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.94427 | −0.130503 | −0.0652513 | − | 0.997869i | \(-0.520785\pi\) | ||||
−0.0652513 | + | 0.997869i | \(0.520785\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.8328 | 0.656165 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 6.00000i | − 0.264906i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 15.0000i | − 0.659699i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.23607 | −0.405418 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.18034 | −0.358387 | −0.179194 | − | 0.983814i | \(-0.557349\pi\) | ||||
−0.179194 | + | 0.983814i | \(0.557349\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.9098i | 0.520781i | 0.965503 | + | 0.260390i | \(0.0838512\pi\) | ||||
−0.965503 | + | 0.260390i | \(0.916149\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.4164i | 0.453746i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.4508 | 0.584820 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.38197 | −0.276954 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.23607i | 0.400059i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.41641i | 0.320042i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.56231 | −0.325732 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.7082 | 0.503375 | 0.251688 | − | 0.967809i | \(-0.419014\pi\) | ||||
0.251688 | + | 0.967809i | \(0.419014\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.41641i | 0.318269i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.43769i | 0.232499i | 0.993220 | + | 0.116250i | \(0.0370872\pi\) | ||||
−0.993220 | + | 0.116250i | \(0.962913\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.4164 | −0.572598 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −55.9574 | −2.38387 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 1.41641i | − 0.0602318i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.3607i | 0.438996i | 0.975613 | + | 0.219498i | \(0.0704420\pi\) | ||||
−0.975613 | + | 0.219498i | \(0.929558\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.416408 | 0.0176122 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.70820 | −0.283221 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 12.6525i | − 0.533238i | −0.963802 | − | 0.266619i | \(-0.914093\pi\) | ||||
0.963802 | − | 0.266619i | \(-0.0859066\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.23607i | 0.0519100i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.0557 | 0.547325 | 0.273662 | − | 0.961826i | \(-0.411765\pi\) | ||||
0.273662 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.3607 | −0.517278 | −0.258639 | − | 0.965974i | \(-0.583274\pi\) | ||||
−0.258639 | + | 0.965974i | \(0.583274\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 6.00000i | − 0.250654i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.11146i | 0.171162i | 0.996331 | + | 0.0855811i | \(0.0272747\pi\) | ||||
−0.996331 | + | 0.0855811i | \(0.972725\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.1246 | −0.711675 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.1115 | −0.419494 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 4.47214i | − 0.185217i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 18.6525i | − 0.769870i | −0.922944 | − | 0.384935i | \(-0.874224\pi\) | ||||
0.922944 | − | 0.384935i | \(-0.125776\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.8754 | −0.530521 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.52786 | 0.0628479 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 34.7984i | − 1.42900i | −0.699636 | − | 0.714499i | \(-0.746655\pi\) | ||||
0.699636 | − | 0.714499i | \(-0.253345\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 15.6180i | − 0.639204i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.8885 | −1.30293 | −0.651465 | − | 0.758678i | \(-0.725845\pi\) | ||||
−0.651465 | + | 0.758678i | \(0.725845\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.6869 | 1.65965 | 0.829827 | − | 0.558021i | \(-0.188439\pi\) | ||||
0.829827 | + | 0.558021i | \(0.188439\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.38197i | 0.0970012i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 47.4164i | 1.92457i | 0.272039 | + | 0.962286i | \(0.412302\pi\) | ||||
−0.272039 | + | 0.962286i | \(0.587698\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.5279 | 0.467133 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.9787 | 1.25326 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 37.7771i | − 1.52580i | −0.646515 | − | 0.762901i | \(-0.723774\pi\) | ||||
0.646515 | − | 0.762901i | \(-0.276226\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 31.3050i | − 1.26029i | −0.776478 | − | 0.630145i | \(-0.782995\pi\) | ||||
0.776478 | − | 0.630145i | \(-0.217005\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −47.7082 | −1.91755 | −0.958777 | − | 0.284159i | \(-0.908286\pi\) | ||||
−0.958777 | + | 0.284159i | \(0.908286\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.09017 | 0.124004 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.4164i | 0.457389i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 8.29180i | − 0.331142i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 38.1246 | 1.52013 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.0344 | 0.598512 | 0.299256 | − | 0.954173i | \(-0.403262\pi\) | ||||
0.299256 | + | 0.954173i | \(0.403262\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 3.41641i | − 0.135790i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 15.6180i | − 0.618809i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.94427 | −0.353830 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.6525 | −1.21070 | −0.605350 | − | 0.795959i | \(-0.706967\pi\) | ||||
−0.605350 | + | 0.795959i | \(0.706967\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 31.5623i | − 1.24470i | −0.782741 | − | 0.622348i | \(-0.786179\pi\) | ||||
0.782741 | − | 0.622348i | \(-0.213821\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 12.6180i | − 0.496066i | −0.968752 | − | 0.248033i | \(-0.920216\pi\) | ||||
0.968752 | − | 0.248033i | \(-0.0797842\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.81966 | −0.346202 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.65248 | 0.103959 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.88854i | 0.386969i | 0.981103 | + | 0.193484i | \(0.0619789\pi\) | ||||
−0.981103 | + | 0.193484i | \(0.938021\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.0000i | 0.468165i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.02129 | 0.0787381 | 0.0393691 | − | 0.999225i | \(-0.487465\pi\) | ||||
0.0393691 | + | 0.999225i | \(0.487465\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.70820 | 0.222023 | 0.111012 | − | 0.993819i | \(-0.464591\pi\) | ||||
0.111012 | + | 0.993819i | \(0.464591\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 13.8541i | − 0.538049i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 28.8197i | − 1.11590i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.7082 | 0.839288 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.5410 | −0.715768 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 47.3050i | − 1.82347i | −0.410777 | − | 0.911736i | \(-0.634742\pi\) | ||||
0.410777 | − | 0.911736i | \(-0.365258\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.2361i | 1.20050i | 0.799813 | + | 0.600250i | \(0.204932\pi\) | ||||
−0.799813 | + | 0.600250i | \(0.795068\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.4721 | −0.862401 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.4721 | −0.631214 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.7639i | 0.411870i | 0.978566 | + | 0.205935i | \(0.0660236\pi\) | ||||
−0.978566 | + | 0.205935i | \(0.933976\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.70820i | 0.0651720i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.23607 | 0.351866 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.7639 | −1.01815 | −0.509074 | − | 0.860723i | \(-0.670012\pi\) | ||||
−0.509074 | + | 0.860723i | \(0.670012\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.70820i | 0.0648893i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.7082i | 0.594991i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.32624 | 0.277104 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.2148 | 0.461346 | 0.230673 | − | 0.973031i | \(-0.425907\pi\) | ||||
0.230673 | + | 0.973031i | \(0.425907\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 47.1246i | 1.77734i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2.87539i | − 0.108140i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.87539 | 0.258211 | 0.129105 | − | 0.991631i | \(-0.458789\pi\) | ||||
0.129105 | + | 0.991631i | \(0.458789\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.14590 | 0.0429745 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 6.63119i | − 0.248340i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 26.6525i | − 0.995355i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.23607 | −0.269860 | −0.134930 | − | 0.990855i | \(-0.543081\pi\) | ||||
−0.134930 | + | 0.990855i | \(0.543081\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.94427 | 0.184134 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.0901699i | 0.00335346i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.34752i | 0.272505i | 0.990674 | + | 0.136252i | \(0.0435058\pi\) | ||||
−0.990674 | + | 0.136252i | \(0.956494\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.708204 | 0.0261939 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.6869i | 1.28119i | 0.767879 | + | 0.640595i | \(0.221312\pi\) | ||||
−0.767879 | + | 0.640595i | \(0.778688\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.29180i | 0.121255i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.65248 | 0.318286 | 0.159143 | − | 0.987256i | \(-0.449127\pi\) | ||||
0.159143 | + | 0.987256i | \(0.449127\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.1246 | 0.629088 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.6180i | 0.719716i | 0.933007 | + | 0.359858i | \(0.117175\pi\) | ||||
−0.933007 | + | 0.359858i | \(0.882825\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 8.18034i | − 0.299303i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.1115 | −0.369465 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.4164 | 1.58429 | 0.792144 | − | 0.610335i | \(-0.208965\pi\) | ||||
0.792144 | + | 0.610335i | \(0.208965\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 7.90983i | − 0.288250i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 4.83282i | − 0.175652i | −0.996136 | − | 0.0878258i | \(-0.972008\pi\) | ||||
0.996136 | − | 0.0878258i | \(-0.0279919\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.27051 | 0.155010 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.6525 | −1.18365 | −0.591826 | − | 0.806066i | \(-0.701593\pi\) | ||||
−0.591826 | + | 0.806066i | \(0.701593\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.5836i | 0.600366i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 18.2148i | − 0.657698i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.9230 | 0.826624 | 0.413312 | − | 0.910589i | \(-0.364372\pi\) | ||||
0.413312 | + | 0.910589i | \(0.364372\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.5066 | −0.846569 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 6.47214i | − 0.232787i | −0.993203 | − | 0.116393i | \(-0.962867\pi\) | ||||
0.993203 | − | 0.116393i | \(-0.0371333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 9.70820i | − 0.348280i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.4164 | −0.695665 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.3607 | −0.442300 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.32624i | 0.333293i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 38.5623i | − 1.37460i | −0.726375 | − | 0.687299i | \(-0.758796\pi\) | ||||
0.726375 | − | 0.687299i | \(-0.241204\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.9787 | 0.568857 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.2361 | 0.541732 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 38.2918i | − 1.35978i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 34.4721i | − 1.22107i | −0.791991 | − | 0.610533i | \(-0.790955\pi\) | ||||
0.791991 | − | 0.610533i | \(-0.209045\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 52.6869 | 1.86393 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.23607 | −0.326340 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.5836i | 0.585222i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 22.6180i | − 0.796193i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.5279 | 1.03814 | 0.519072 | − | 0.854730i | \(-0.326278\pi\) | ||||
0.519072 | + | 0.854730i | \(0.326278\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.0000 | 1.19390 | 0.596951 | − | 0.802278i | \(-0.296379\pi\) | ||||
0.596951 | + | 0.802278i | \(0.296379\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.56231i | 0.300293i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.875388i | 0.0306260i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.52786 | −0.123274 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.2148 | 1.26390 | 0.631952 | − | 0.775007i | \(-0.282254\pi\) | ||||
0.631952 | + | 0.775007i | \(0.282254\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 15.1246i | − 0.527211i | −0.964631 | − | 0.263605i | \(-0.915088\pi\) | ||||
0.964631 | − | 0.263605i | \(-0.0849117\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.0000i | 0.625921i | 0.949766 | + | 0.312961i | \(0.101321\pi\) | ||||
−0.949766 | + | 0.312961i | \(0.898679\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.1803 | −1.18713 | −0.593566 | − | 0.804785i | \(-0.702280\pi\) | ||||
−0.593566 | + | 0.804785i | \(0.702280\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.3607 | −0.498166 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 26.5623i | − 0.920329i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.14590i | 0.0741731i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.1246 | −0.384064 | −0.192032 | − | 0.981389i | \(-0.561508\pi\) | ||||
−0.192032 | + | 0.981389i | \(0.561508\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57.9787 | 1.99927 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.4721i | 0.773981i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 11.2361i | − 0.386076i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.0902 | 0.723813 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.2705 | −0.831982 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.0902i | 0.996028i | 0.867169 | + | 0.498014i | \(0.165937\pi\) | ||||
−0.867169 | + | 0.498014i | \(0.834063\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.3262i | 0.421056i | 0.977588 | + | 0.210528i | \(0.0675184\pi\) | ||||
−0.977588 | + | 0.210528i | \(0.932482\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.7082 | −0.535957 | −0.267979 | − | 0.963425i | \(-0.586356\pi\) | ||||
−0.267979 | + | 0.963425i | \(0.586356\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.00000 | 0.136320 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 8.56231i | − 0.291464i | −0.989324 | − | 0.145732i | \(-0.953446\pi\) | ||||
0.989324 | − | 0.145732i | \(-0.0465538\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 6.56231i | − 0.222868i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.58359 | 0.0537197 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.79837 | −0.230354 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 18.1803i | − 0.615311i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.3951i | 0.891300i | 0.895207 | + | 0.445650i | \(0.147027\pi\) | ||||
−0.895207 | + | 0.445650i | \(0.852973\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.5967 | −0.526065 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.05573 | −0.170332 | −0.0851659 | − | 0.996367i | \(-0.527142\pi\) | ||||
−0.0851659 | + | 0.996367i | \(0.527142\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.9787i | 1.58096i | 0.612488 | + | 0.790480i | \(0.290169\pi\) | ||||
−0.612488 | + | 0.790480i | \(0.709831\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 54.4721i | − 1.82900i | −0.404591 | − | 0.914498i | \(-0.632586\pi\) | ||||
0.404591 | − | 0.914498i | \(-0.367414\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.5836 | −0.556196 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.38197 | −0.0462976 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 65.1246i | 2.17931i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.81966i | 0.294480i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.0132 | 0.667476 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.7082 | 0.523316 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 0.180340i | − 0.00600134i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 23.1459i | − 0.768547i | −0.923219 | − | 0.384273i | \(-0.874452\pi\) | ||||
0.923219 | − | 0.384273i | \(-0.125548\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.32624 | 0.0771564 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.5279 | −1.24335 | −0.621677 | − | 0.783274i | \(-0.713548\pi\) | ||||
−0.621677 | + | 0.783274i | \(0.713548\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 11.3050i | − 0.374139i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 22.1115i | − 0.730185i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.8885 | 0.722036 | 0.361018 | − | 0.932559i | \(-0.382429\pi\) | ||||
0.361018 | + | 0.932559i | \(0.382429\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.0902 | −1.09036 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 25.5279i | − 0.840260i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.00000i | 0.131377i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.5410 | 0.805165 | 0.402582 | − | 0.915384i | \(-0.368113\pi\) | ||||
0.402582 | + | 0.915384i | \(0.368113\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.8328 | 1.07605 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.47214i | 0.146411i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 27.4164i | − 0.895655i | −0.894120 | − | 0.447828i | \(-0.852198\pi\) | ||||
0.894120 | − | 0.447828i | \(-0.147802\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.9443 | 1.00983 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.4508 | −0.731877 | −0.365938 | − | 0.930639i | \(-0.619252\pi\) | ||||
−0.365938 | + | 0.930639i | \(0.619252\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 10.0000i | − 0.325645i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 55.3050i | 1.79717i | 0.438800 | + | 0.898585i | \(0.355404\pi\) | ||||
−0.438800 | + | 0.898585i | \(0.644596\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34.2492 | −1.11178 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.70820 | −0.314810 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.63932i | 0.0531028i | 0.999647 | + | 0.0265514i | \(0.00845257\pi\) | ||||
−0.999647 | + | 0.0265514i | \(0.991547\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.8885i | 0.416627i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.70820 | −0.184328 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.3951 | −0.851456 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 8.18034i | − 0.263608i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 39.0132i | − 1.25458i | −0.778786 | − | 0.627289i | \(-0.784164\pi\) | ||||
0.778786 | − | 0.627289i | \(-0.215836\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 29.1246 | 0.935617 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −52.0902 | −1.67165 | −0.835827 | − | 0.548994i | \(-0.815011\pi\) | ||||
−0.835827 | + | 0.548994i | \(0.815011\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 26.2492i | − 0.841511i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 54.2837i | − 1.73669i | −0.495962 | − | 0.868344i | \(-0.665185\pi\) | ||||
0.495962 | − | 0.868344i | \(-0.334815\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.7639 | −0.407937 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.4164 | −0.428353 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 24.9787i | − 0.796697i | −0.917234 | − | 0.398349i | \(-0.869583\pi\) | ||||
0.917234 | − | 0.398349i | \(-0.130417\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 13.4164i | − 0.427049i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.450850 | −0.0143362 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.68692 | 0.275949 | 0.137975 | − | 0.990436i | \(-0.455941\pi\) | ||||
0.137975 | + | 0.990436i | \(0.455941\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.4164i | 0.679629i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 38.2705i | − 1.21204i | −0.795450 | − | 0.606020i | \(-0.792765\pi\) | ||||
0.795450 | − | 0.606020i | \(-0.207235\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.85410 | 0.248493 |
(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 | 6000.2.f.a.1249.4 | 4 | ||
4.3 | odd | 2 | 750.2.c.b.499.1 | 4 | |||
5.2 | odd | 4 | 6000.2.a.y.1.1 | 2 | |||
5.3 | odd | 4 | 6000.2.a.d.1.2 | 2 | |||
5.4 | even | 2 | inner | 6000.2.f.a.1249.1 | 4 | ||
12.11 | even | 2 | 2250.2.c.b.1999.3 | 4 | |||
20.3 | even | 4 | 750.2.a.c.1.1 | ✓ | 2 | ||
20.7 | even | 4 | 750.2.a.f.1.2 | yes | 2 | ||
20.19 | odd | 2 | 750.2.c.b.499.4 | 4 | |||
60.23 | odd | 4 | 2250.2.a.n.1.1 | 2 | |||
60.47 | odd | 4 | 2250.2.a.c.1.2 | 2 | |||
60.59 | even | 2 | 2250.2.c.b.1999.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
750.2.a.c.1.1 | ✓ | 2 | 20.3 | even | 4 | ||
750.2.a.f.1.2 | yes | 2 | 20.7 | even | 4 | ||
750.2.c.b.499.1 | 4 | 4.3 | odd | 2 | |||
750.2.c.b.499.4 | 4 | 20.19 | odd | 2 | |||
2250.2.a.c.1.2 | 2 | 60.47 | odd | 4 | |||
2250.2.a.n.1.1 | 2 | 60.23 | odd | 4 | |||
2250.2.c.b.1999.2 | 4 | 60.59 | even | 2 | |||
2250.2.c.b.1999.3 | 4 | 12.11 | even | 2 | |||
6000.2.a.d.1.2 | 2 | 5.3 | odd | 4 | |||
6000.2.a.y.1.1 | 2 | 5.2 | odd | 4 | |||
6000.2.f.a.1249.1 | 4 | 5.4 | even | 2 | inner | ||
6000.2.f.a.1249.4 | 4 | 1.1 | even | 1 | trivial |