Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,3,Mod(793,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.793");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.v (of order \(4\), degree \(2\), 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: | \(49.0464475849\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 600) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1657.2 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.1657 |
Dual form | 1800.3.v.m.793.2 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.22474 | + | 3.22474i | 0.460678 | + | 0.460678i | 0.898878 | − | 0.438200i | \(-0.144384\pi\) |
−0.438200 | + | 0.898878i | \(0.644384\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.89898 | 0.627180 | 0.313590 | − | 0.949558i | \(-0.398468\pi\) | ||||
0.313590 | + | 0.949558i | \(0.398468\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.1237 | − | 18.1237i | 1.39413 | − | 1.39413i | 0.578329 | − | 0.815804i | \(-0.303705\pi\) |
0.815804 | − | 0.578329i | \(-0.196295\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.449490 | + | 0.449490i | 0.0264406 | + | 0.0264406i | 0.720203 | − | 0.693763i | \(-0.244048\pi\) |
−0.693763 | + | 0.720203i | \(0.744048\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.89898i | 0.520999i | 0.965474 | + | 0.260499i | \(0.0838872\pi\) | ||||
−0.965474 | + | 0.260499i | \(0.916113\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −10.6515 | + | 10.6515i | −0.463110 | + | 0.463110i | −0.899673 | − | 0.436563i | \(-0.856195\pi\) |
0.436563 | + | 0.899673i | \(0.356195\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 36.2929i | − | 1.25148i | −0.780033 | − | 0.625739i | \(-0.784798\pi\) | ||
0.780033 | − | 0.625739i | \(-0.215202\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 25.6969 | 0.828933 | 0.414467 | − | 0.910064i | \(-0.363968\pi\) | ||||
0.414467 | + | 0.910064i | \(0.363968\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13.3031 | + | 13.3031i | 0.359542 | + | 0.359542i | 0.863644 | − | 0.504102i | \(-0.168176\pi\) |
−0.504102 | + | 0.863644i | \(0.668176\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.10102 | 0.0756346 | 0.0378173 | − | 0.999285i | \(-0.487960\pi\) | ||||
0.0378173 | + | 0.999285i | \(0.487960\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.72985 | − | 2.72985i | 0.0634848 | − | 0.0634848i | −0.674652 | − | 0.738136i | \(-0.735706\pi\) |
0.738136 | + | 0.674652i | \(0.235706\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −37.1464 | − | 37.1464i | −0.790350 | − | 0.790350i | 0.191201 | − | 0.981551i | \(-0.438762\pi\) |
−0.981551 | + | 0.191201i | \(0.938762\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 28.2020i | − | 0.575552i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −65.1918 | + | 65.1918i | −1.23003 | + | 1.23003i | −0.266085 | + | 0.963950i | \(0.585730\pi\) |
−0.963950 | + | 0.266085i | \(0.914270\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 80.3837i | − | 1.36244i | −0.732081 | − | 0.681218i | \(-0.761451\pi\) | ||
0.732081 | − | 0.681218i | \(-0.238549\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.7878 | 0.226029 | 0.113014 | − | 0.993593i | \(-0.463949\pi\) | ||||
0.113014 | + | 0.993593i | \(0.463949\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 84.3712 | + | 84.3712i | 1.25927 | + | 1.25927i | 0.951441 | + | 0.307830i | \(0.0996027\pi\) |
0.307830 | + | 0.951441i | \(0.400397\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −98.2929 | −1.38441 | −0.692203 | − | 0.721703i | \(-0.743360\pi\) | ||||
−0.692203 | + | 0.721703i | \(0.743360\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 52.4949 | − | 52.4949i | 0.719108 | − | 0.719108i | −0.249314 | − | 0.968423i | \(-0.580205\pi\) |
0.968423 | + | 0.249314i | \(0.0802053\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22.2474 | + | 22.2474i | 0.288928 | + | 0.288928i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 68.2020i | 0.863317i | 0.902037 | + | 0.431658i | \(0.142071\pi\) | ||||
−0.902037 | + | 0.431658i | \(0.857929\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 89.7321 | − | 89.7321i | 1.08111 | − | 1.08111i | 0.0847040 | − | 0.996406i | \(-0.473006\pi\) |
0.996406 | − | 0.0847040i | \(-0.0269945\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 40.5857i | − | 0.456019i | −0.973659 | − | 0.228010i | \(-0.926778\pi\) | ||
0.973659 | − | 0.228010i | \(-0.0732218\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 116.889 | 1.28449 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 105.720 | + | 105.720i | 1.08989 | + | 1.08989i | 0.995539 | + | 0.0943546i | \(0.0300787\pi\) |
0.0943546 | + | 0.995539i | \(0.469921\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 197.485 | 1.95529 | 0.977647 | − | 0.210253i | \(-0.0674288\pi\) | ||||
0.977647 | + | 0.210253i | \(0.0674288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 45.7980 | − | 45.7980i | 0.444640 | − | 0.444640i | −0.448928 | − | 0.893568i | \(-0.648194\pi\) |
0.893568 | + | 0.448928i | \(0.148194\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 139.485 | + | 139.485i | 1.30360 | + | 1.30360i | 0.925951 | + | 0.377645i | \(0.123266\pi\) |
0.377645 | + | 0.925951i | \(0.376734\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 140.576i | − | 1.28968i | −0.764316 | − | 0.644842i | \(-0.776923\pi\) | ||
0.764316 | − | 0.644842i | \(-0.223077\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −105.980 | + | 105.980i | −0.937872 | + | 0.937872i | −0.998180 | − | 0.0603074i | \(-0.980792\pi\) |
0.0603074 | + | 0.998180i | \(0.480792\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.89898i | 0.0243612i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −73.4041 | −0.606645 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 66.6969 | + | 66.6969i | 0.525173 | + | 0.525173i | 0.919129 | − | 0.393956i | \(-0.128894\pi\) |
−0.393956 | + | 0.919129i | \(0.628894\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 32.6765 | 0.249439 | 0.124720 | − | 0.992192i | \(-0.460197\pi\) | ||||
0.124720 | + | 0.992192i | \(0.460197\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −31.9217 | + | 31.9217i | −0.240013 | + | 0.240013i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −45.3281 | − | 45.3281i | −0.330862 | − | 0.330862i | 0.522052 | − | 0.852914i | \(-0.325167\pi\) |
−0.852914 | + | 0.522052i | \(0.825167\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 252.747i | − | 1.81832i | −0.416443 | − | 0.909162i | \(-0.636724\pi\) | ||
0.416443 | − | 0.909162i | \(-0.363276\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 125.035 | − | 125.035i | 0.874372 | − | 0.874372i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 75.2122i | − | 0.504780i | −0.967626 | − | 0.252390i | \(-0.918783\pi\) | ||
0.967626 | − | 0.252390i | \(-0.0812166\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 187.091 | 1.23901 | 0.619506 | − | 0.784992i | \(-0.287333\pi\) | ||||
0.619506 | + | 0.784992i | \(0.287333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −119.452 | − | 119.452i | −0.760839 | − | 0.760839i | 0.215635 | − | 0.976474i | \(-0.430818\pi\) |
−0.976474 | + | 0.215635i | \(0.930818\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −68.6969 | −0.426689 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −104.866 | + | 104.866i | −0.643350 | + | 0.643350i | −0.951377 | − | 0.308027i | \(-0.900331\pi\) |
0.308027 | + | 0.951377i | \(0.400331\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 67.3031 | + | 67.3031i | 0.403012 | + | 0.403012i | 0.879293 | − | 0.476281i | \(-0.158015\pi\) |
−0.476281 | + | 0.879293i | \(0.658015\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 487.939i | − | 2.88721i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 47.8638 | − | 47.8638i | 0.276669 | − | 0.276669i | −0.555109 | − | 0.831778i | \(-0.687323\pi\) |
0.831778 | + | 0.555109i | \(0.187323\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 134.000i | 0.748603i | 0.927307 | + | 0.374302i | \(0.122118\pi\) | ||||
−0.927307 | + | 0.374302i | \(0.877882\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −34.4143 | −0.190134 | −0.0950671 | − | 0.995471i | \(-0.530307\pi\) | ||||
−0.0950671 | + | 0.995471i | \(0.530307\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.10102 | + | 3.10102i | 0.0165830 | + | 0.0165830i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 238.272 | 1.24750 | 0.623750 | − | 0.781624i | \(-0.285608\pi\) | ||||
0.623750 | + | 0.781624i | \(0.285608\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −61.8763 | + | 61.8763i | −0.320602 | + | 0.320602i | −0.848998 | − | 0.528396i | \(-0.822794\pi\) |
0.528396 | + | 0.848998i | \(0.322794\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 72.2474 | + | 72.2474i | 0.366738 | + | 0.366738i | 0.866286 | − | 0.499548i | \(-0.166501\pi\) |
−0.499548 | + | 0.866286i | \(0.666501\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 85.4541i | − | 0.429417i | −0.976678 | − | 0.214709i | \(-0.931120\pi\) | ||
0.976678 | − | 0.214709i | \(-0.0688802\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 117.035 | − | 117.035i | 0.576528 | − | 0.576528i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 68.2929i | 0.326760i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 99.4745 | 0.471443 | 0.235722 | − | 0.971821i | \(-0.424255\pi\) | ||||
0.235722 | + | 0.971821i | \(0.424255\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 82.8661 | + | 82.8661i | 0.381871 | + | 0.381871i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.2929 | 0.0737233 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.35076 | − | 2.35076i | 0.0105415 | − | 0.0105415i | −0.701816 | − | 0.712358i | \(-0.747627\pi\) |
0.712358 | + | 0.701816i | \(0.247627\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 204.474 | + | 204.474i | 0.900769 | + | 0.900769i | 0.995503 | − | 0.0947340i | \(-0.0302000\pi\) |
−0.0947340 | + | 0.995503i | \(0.530200\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 131.808i | 0.575582i | 0.957693 | + | 0.287791i | \(0.0929208\pi\) | ||||
−0.957693 | + | 0.287791i | \(0.907079\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 139.616 | − | 139.616i | 0.599212 | − | 0.599212i | −0.340891 | − | 0.940103i | \(-0.610729\pi\) |
0.940103 | + | 0.340891i | \(0.110729\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 118.697i | 0.496640i | 0.968678 | + | 0.248320i | \(0.0798784\pi\) | ||||
−0.968678 | + | 0.248320i | \(0.920122\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 277.384 | 1.15097 | 0.575485 | − | 0.817812i | \(-0.304813\pi\) | ||||
0.575485 | + | 0.817812i | \(0.304813\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 179.406 | + | 179.406i | 0.726342 | + | 0.726342i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −37.5755 | −0.149703 | −0.0748516 | − | 0.997195i | \(-0.523848\pi\) | ||||
−0.0748516 | + | 0.997195i | \(0.523848\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −73.4847 | + | 73.4847i | −0.290453 | + | 0.290453i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −79.8684 | − | 79.8684i | −0.310772 | − | 0.310772i | 0.534437 | − | 0.845209i | \(-0.320524\pi\) |
−0.845209 | + | 0.534437i | \(0.820524\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 85.7980i | 0.331266i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 222.767 | − | 222.767i | 0.847024 | − | 0.847024i | −0.142737 | − | 0.989761i | \(-0.545590\pi\) |
0.989761 | + | 0.142737i | \(0.0455902\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 450.091i | − | 1.67320i | −0.547814 | − | 0.836600i | \(-0.684540\pi\) | ||
0.547814 | − | 0.836600i | \(-0.315460\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −99.2122 | −0.366097 | −0.183048 | − | 0.983104i | \(-0.558597\pi\) | ||||
−0.183048 | + | 0.983104i | \(0.558597\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.5936 | + | 26.5936i | 0.0960059 | + | 0.0960059i | 0.753478 | − | 0.657473i | \(-0.228374\pi\) |
−0.657473 | + | 0.753478i | \(0.728374\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −325.101 | −1.15694 | −0.578472 | − | 0.815703i | \(-0.696351\pi\) | ||||
−0.578472 | + | 0.815703i | \(0.696351\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 158.351 | − | 158.351i | 0.559543 | − | 0.559543i | −0.369634 | − | 0.929177i | \(-0.620517\pi\) |
0.929177 | + | 0.369634i | \(0.120517\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.0000 | + | 10.0000i | 0.0348432 | + | 0.0348432i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 288.596i | − | 0.998602i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −347.126 | + | 347.126i | −1.18473 | + | 1.18473i | −0.206226 | + | 0.978504i | \(0.566118\pi\) |
−0.978504 | + | 0.206226i | \(0.933882\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 386.091i | 1.29127i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.6061 | 0.0584921 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 107.250 | + | 107.250i | 0.349348 | + | 0.349348i | 0.859867 | − | 0.510519i | \(-0.170547\pi\) |
−0.510519 | + | 0.859867i | \(0.670547\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 356.788 | 1.14723 | 0.573614 | − | 0.819126i | \(-0.305541\pi\) | ||||
0.573614 | + | 0.819126i | \(0.305541\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −103.386 | + | 103.386i | −0.330307 | + | 0.330307i | −0.852703 | − | 0.522396i | \(-0.825038\pi\) |
0.522396 | + | 0.852703i | \(0.325038\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 207.060 | + | 207.060i | 0.653187 | + | 0.653187i | 0.953759 | − | 0.300572i | \(-0.0971777\pi\) |
−0.300572 | + | 0.953759i | \(0.597178\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 250.384i | − | 0.784902i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.44949 | + | 4.44949i | −0.0137755 | + | 0.0137755i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 239.576i | − | 0.728193i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −565.555 | −1.70863 | −0.854313 | − | 0.519759i | \(-0.826022\pi\) | ||||
−0.854313 | + | 0.519759i | \(0.826022\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 65.6538 | + | 65.6538i | 0.194818 | + | 0.194818i | 0.797774 | − | 0.602956i | \(-0.206011\pi\) |
−0.602956 | + | 0.797774i | \(0.706011\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 177.283 | 0.519890 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 248.957 | − | 248.957i | 0.725822 | − | 0.725822i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −106.177 | − | 106.177i | −0.305986 | − | 0.305986i | 0.537364 | − | 0.843350i | \(-0.319420\pi\) |
−0.843350 | + | 0.537364i | \(0.819420\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 335.980i | 0.962692i | 0.876531 | + | 0.481346i | \(0.159852\pi\) | ||||
−0.876531 | + | 0.481346i | \(0.840148\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −419.328 | + | 419.328i | −1.18790 | + | 1.18790i | −0.210251 | + | 0.977648i | \(0.567428\pi\) |
−0.977648 | + | 0.210251i | \(0.932572\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 191.019i | − | 0.532087i | −0.963961 | − | 0.266044i | \(-0.914283\pi\) | ||
0.963961 | − | 0.266044i | \(-0.0857166\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 263.010 | 0.728560 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −207.341 | − | 207.341i | −0.564961 | − | 0.564961i | 0.365752 | − | 0.930712i | \(-0.380812\pi\) |
−0.930712 | + | 0.365752i | \(0.880812\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −420.454 | −1.13330 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −353.052 | + | 353.052i | −0.946521 | + | 0.946521i | −0.998641 | − | 0.0521200i | \(-0.983402\pi\) |
0.0521200 | + | 0.998641i | \(0.483402\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −657.762 | − | 657.762i | −1.74473 | − | 1.74473i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 607.393i | 1.60262i | 0.598250 | + | 0.801310i | \(0.295863\pi\) | ||||
−0.598250 | + | 0.801310i | \(0.704137\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −207.414 | + | 207.414i | −0.541552 | + | 0.541552i | −0.923984 | − | 0.382432i | \(-0.875087\pi\) |
0.382432 | + | 0.923984i | \(0.375087\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 593.889i | − | 1.52671i | −0.645981 | − | 0.763353i | \(-0.723552\pi\) | ||
0.645981 | − | 0.763353i | \(-0.276448\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.57551 | −0.0244898 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −288.062 | − | 288.062i | −0.725598 | − | 0.725598i | 0.244141 | − | 0.969740i | \(-0.421494\pi\) |
−0.969740 | + | 0.244141i | \(0.921494\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −129.748 | −0.323561 | −0.161781 | − | 0.986827i | \(-0.551724\pi\) | ||||
−0.161781 | + | 0.986827i | \(0.551724\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 465.724 | − | 465.724i | 1.15564 | − | 1.15564i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 91.7775 | + | 91.7775i | 0.225498 | + | 0.225498i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 262.696i | 0.642288i | 0.947030 | + | 0.321144i | \(0.104067\pi\) | ||||
−0.947030 | + | 0.321144i | \(0.895933\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 259.217 | − | 259.217i | 0.627644 | − | 0.627644i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 638.030i | 1.52274i | 0.648315 | + | 0.761372i | \(0.275474\pi\) | ||||
−0.648315 | + | 0.761372i | \(0.724526\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −272.606 | −0.647520 | −0.323760 | − | 0.946139i | \(-0.604947\pi\) | ||||
−0.323760 | + | 0.946139i | \(0.604947\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 44.4620 | + | 44.4620i | 0.104126 | + | 0.104126i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 264.960 | 0.614757 | 0.307378 | − | 0.951587i | \(-0.400548\pi\) | ||||
0.307378 | + | 0.951587i | \(0.400548\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 210.619 | − | 210.619i | 0.486417 | − | 0.486417i | −0.420756 | − | 0.907174i | \(-0.638235\pi\) |
0.907174 | + | 0.420756i | \(0.138235\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −105.439 | − | 105.439i | −0.241280 | − | 0.241280i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 423.999i | 0.965829i | 0.875667 | + | 0.482915i | \(0.160422\pi\) | ||||
−0.875667 | + | 0.482915i | \(0.839578\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −533.040 | + | 533.040i | −1.20325 | + | 1.20325i | −0.230078 | + | 0.973172i | \(0.573898\pi\) |
−0.973172 | + | 0.230078i | \(0.926102\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.23266i | 0.0161084i | 0.999968 | + | 0.00805418i | \(0.00256375\pi\) | ||||
−0.999968 | + | 0.00805418i | \(0.997436\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.3939 | 0.0474365 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 183.918 | + | 183.918i | 0.402447 | + | 0.402447i | 0.879095 | − | 0.476647i | \(-0.158148\pi\) |
−0.476647 | + | 0.879095i | \(0.658148\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −632.595 | −1.37222 | −0.686112 | − | 0.727496i | \(-0.740684\pi\) | ||||
−0.686112 | + | 0.727496i | \(0.740684\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 382.838 | − | 382.838i | 0.826863 | − | 0.826863i | −0.160218 | − | 0.987082i | \(-0.551220\pi\) |
0.987082 | + | 0.160218i | \(0.0512198\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −164.581 | − | 164.581i | −0.352422 | − | 0.352422i | 0.508588 | − | 0.861010i | \(-0.330168\pi\) |
−0.861010 | + | 0.508588i | \(0.830168\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 544.151i | 1.16024i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.8332 | − | 18.8332i | 0.0398164 | − | 0.0398164i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 356.606i | 0.744480i | 0.928136 | + | 0.372240i | \(0.121410\pi\) | ||||
−0.928136 | + | 0.372240i | \(0.878590\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 482.202 | 1.00250 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −170.103 | − | 170.103i | −0.349288 | − | 0.349288i | 0.510556 | − | 0.859844i | \(-0.329440\pi\) |
−0.859844 | + | 0.510556i | \(0.829440\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 439.514 | 0.895141 | 0.447571 | − | 0.894249i | \(-0.352289\pi\) | ||||
0.447571 | + | 0.894249i | \(0.352289\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.3133 | − | 16.3133i | 0.0330898 | − | 0.0330898i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −316.969 | − | 316.969i | −0.637765 | − | 0.637765i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 751.413i | 1.50584i | 0.658113 | + | 0.752919i | \(0.271355\pi\) | ||||
−0.658113 | + | 0.752919i | \(0.728645\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 543.626 | − | 543.626i | 1.08077 | − | 1.08077i | 0.0843284 | − | 0.996438i | \(-0.473126\pi\) |
0.996438 | − | 0.0843284i | \(-0.0268745\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 471.798i | − | 0.926912i | −0.886120 | − | 0.463456i | \(-0.846609\pi\) | ||
0.886120 | − | 0.463456i | \(-0.153391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 338.565 | 0.662554 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −256.272 | − | 256.272i | −0.495691 | − | 0.495691i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −881.928 | −1.69276 | −0.846380 | − | 0.532580i | \(-0.821223\pi\) | ||||
−0.846380 | + | 0.532580i | \(0.821223\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −305.493 | + | 305.493i | −0.584116 | + | 0.584116i | −0.936032 | − | 0.351916i | \(-0.885530\pi\) |
0.351916 | + | 0.936032i | \(0.385530\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.5505 | + | 11.5505i | 0.0219175 | + | 0.0219175i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 302.090i | 0.571058i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 56.2020 | − | 56.2020i | 0.105445 | − | 0.105445i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 194.565i | − | 0.360975i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −761.867 | −1.40826 | −0.704129 | − | 0.710072i | \(-0.748662\pi\) | ||||
−0.704129 | + | 0.710072i | \(0.748662\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −178.020 | − | 178.020i | −0.325449 | − | 0.325449i | 0.525404 | − | 0.850853i | \(-0.323914\pi\) |
−0.850853 | + | 0.525404i | \(0.823914\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 359.262 | 0.652019 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −219.934 | + | 219.934i | −0.397711 | + | 0.397711i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −82.9852 | − | 82.9852i | −0.148986 | − | 0.148986i | 0.628679 | − | 0.777665i | \(-0.283596\pi\) |
−0.777665 | + | 0.628679i | \(0.783596\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 98.9500i | − | 0.177013i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −228.227 | + | 228.227i | −0.405377 | + | 0.405377i | −0.880123 | − | 0.474746i | \(-0.842540\pi\) |
0.474746 | + | 0.880123i | \(0.342540\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 613.787i | 1.07871i | 0.842078 | + | 0.539356i | \(0.181332\pi\) | ||||
−0.842078 | + | 0.539356i | \(0.818668\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −541.656 | −0.948610 | −0.474305 | − | 0.880361i | \(-0.657301\pi\) | ||||
−0.474305 | + | 0.880361i | \(0.657301\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −341.967 | − | 341.967i | −0.592664 | − | 0.592664i | 0.345686 | − | 0.938350i | \(-0.387646\pi\) |
−0.938350 | + | 0.345686i | \(0.887646\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 578.727 | 0.996087 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −449.757 | + | 449.757i | −0.771453 | + | 0.771453i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 454.141 | + | 454.141i | 0.773664 | + | 0.773664i | 0.978745 | − | 0.205081i | \(-0.0657458\pi\) |
−0.205081 | + | 0.978745i | \(0.565746\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 254.373i | 0.431873i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −50.6357 | + | 50.6357i | −0.0853891 | + | 0.0853891i | −0.748511 | − | 0.663122i | \(-0.769231\pi\) |
0.663122 | + | 0.748511i | \(0.269231\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 506.443i | 0.845481i | 0.906251 | + | 0.422740i | \(0.138932\pi\) | ||||
−0.906251 | + | 0.422740i | \(0.861068\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −785.120 | −1.30636 | −0.653178 | − | 0.757204i | \(-0.726565\pi\) | ||||
−0.653178 | + | 0.757204i | \(0.726565\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −766.252 | − | 766.252i | −1.26236 | − | 1.26236i | −0.949946 | − | 0.312413i | \(-0.898863\pi\) |
−0.312413 | − | 0.949946i | \(-0.601137\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1346.46 | −2.20370 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −182.697 | + | 182.697i | −0.298037 | + | 0.298037i | −0.840245 | − | 0.542207i | \(-0.817589\pi\) |
0.542207 | + | 0.840245i | \(0.317589\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 71.1214 | + | 71.1214i | 0.115270 | + | 0.115270i | 0.762389 | − | 0.647119i | \(-0.224026\pi\) |
−0.647119 | + | 0.762389i | \(0.724026\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1031.35i | − | 1.66616i | −0.553154 | − | 0.833079i | \(-0.686576\pi\) | ||
0.553154 | − | 0.833079i | \(-0.313424\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 130.879 | − | 130.879i | 0.210078 | − | 0.210078i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.9592i | 0.0190130i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −374.201 | −0.593029 | −0.296514 | − | 0.955028i | \(-0.595824\pi\) | ||||
−0.296514 | + | 0.955028i | \(0.595824\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −511.126 | − | 511.126i | −0.802396 | − | 0.802396i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 884.827 | 1.38038 | 0.690192 | − | 0.723626i | \(-0.257526\pi\) | ||||
0.690192 | + | 0.723626i | \(0.257526\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −683.787 | + | 683.787i | −1.06343 | + | 1.06343i | −0.0655849 | + | 0.997847i | \(0.520891\pi\) |
−0.997847 | + | 0.0655849i | \(0.979109\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −597.898 | − | 597.898i | −0.924108 | − | 0.924108i | 0.0732085 | − | 0.997317i | \(-0.476676\pi\) |
−0.997317 | + | 0.0732085i | \(0.976676\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 554.565i | − | 0.854492i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −282.136 | + | 282.136i | −0.432062 | + | 0.432062i | −0.889329 | − | 0.457268i | \(-0.848828\pi\) |
0.457268 | + | 0.889329i | \(0.348828\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 503.505i | − | 0.764044i | −0.924153 | − | 0.382022i | \(-0.875228\pi\) | ||
0.924153 | − | 0.382022i | \(-0.124772\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.7673 | 0.0586495 | 0.0293248 | − | 0.999570i | \(-0.490664\pi\) | ||||
0.0293248 | + | 0.999570i | \(0.490664\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 386.574 | + | 386.574i | 0.579572 | + | 0.579572i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 95.1214 | 0.141761 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −359.728 | + | 359.728i | −0.534513 | + | 0.534513i | −0.921912 | − | 0.387399i | \(-0.873374\pi\) |
0.387399 | + | 0.921912i | \(0.373374\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.0454 | − | 40.0454i | −0.0591513 | − | 0.0591513i | 0.676912 | − | 0.736064i | \(-0.263318\pi\) |
−0.736064 | + | 0.676912i | \(0.763318\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 681.838i | 1.00418i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 502.243 | − | 502.243i | 0.735348 | − | 0.735348i | −0.236326 | − | 0.971674i | \(-0.575943\pi\) |
0.971674 | + | 0.236326i | \(0.0759432\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2363.04i | 3.42966i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −242.241 | −0.350566 | −0.175283 | − | 0.984518i | \(-0.556084\pi\) | ||||
−0.175283 | + | 0.984518i | \(0.556084\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.39388 | + | 1.39388i | 0.00199982 | + | 0.00199982i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −619.181 | −0.883282 | −0.441641 | − | 0.897192i | \(-0.645603\pi\) | ||||
−0.441641 | + | 0.897192i | \(0.645603\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −131.687 | + | 131.687i | −0.187321 | + | 0.187321i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 636.838 | + | 636.838i | 0.900761 | + | 0.900761i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 618.514i | 0.872376i | 0.899856 | + | 0.436188i | \(0.143672\pi\) | ||||
−0.899856 | + | 0.436188i | \(0.856328\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −273.712 | + | 273.712i | −0.383887 | + | 0.383887i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 555.989i | 0.773281i | 0.922231 | + | 0.386640i | \(0.126365\pi\) | ||||
−0.922231 | + | 0.386640i | \(0.873635\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 295.373 | 0.409672 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −103.992 | − | 103.992i | −0.143043 | − | 0.143043i | 0.631959 | − | 0.775002i | \(-0.282251\pi\) |
−0.775002 | + | 0.631959i | \(0.782251\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.45408 | 0.00335715 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 462.979 | − | 462.979i | 0.631621 | − | 0.631621i | −0.316853 | − | 0.948475i | \(-0.602626\pi\) |
0.948475 | + | 0.316853i | \(0.102626\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 582.075 | + | 582.075i | 0.789790 | + | 0.789790i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 701.414i | 0.949140i | 0.880218 | + | 0.474570i | \(0.157396\pi\) | ||||
−0.880218 | + | 0.474570i | \(0.842604\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 634.534 | − | 634.534i | 0.854016 | − | 0.854016i | −0.136609 | − | 0.990625i | \(-0.543620\pi\) |
0.990625 | + | 0.136609i | \(0.0436205\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 899.605i | 1.20107i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −934.241 | −1.24400 | −0.621998 | − | 0.783019i | \(-0.713679\pi\) | ||||
−0.621998 | + | 0.783019i | \(0.713679\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −656.598 | − | 656.598i | −0.867369 | − | 0.867369i | 0.124812 | − | 0.992180i | \(-0.460167\pi\) |
−0.992180 | + | 0.124812i | \(0.960167\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 911.292 | 1.19749 | 0.598746 | − | 0.800939i | \(-0.295666\pi\) | ||||
0.598746 | + | 0.800939i | \(0.295666\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 453.320 | − | 453.320i | 0.594129 | − | 0.594129i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1456.85 | − | 1456.85i | −1.89942 | − | 1.89942i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 769.847i | − | 1.00110i | −0.865707 | − | 0.500551i | \(-0.833131\pi\) | ||
0.865707 | − | 0.500551i | \(-0.166869\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 480.515 | − | 480.515i | 0.621624 | − | 0.621624i | −0.324323 | − | 0.945947i | \(-0.605136\pi\) |
0.945947 | + | 0.324323i | \(0.105136\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.6969i | 0.0394056i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −678.120 | −0.868272 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −48.0079 | − | 48.0079i | −0.0610012 | − | 0.0610012i | 0.675948 | − | 0.736949i | \(-0.263734\pi\) |
−0.736949 | + | 0.675948i | \(0.763734\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −683.514 | −0.864114 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 249.885 | − | 249.885i | 0.315114 | − | 0.315114i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 650.080 | + | 650.080i | 0.815658 | + | 0.815658i | 0.985476 | − | 0.169817i | \(-0.0543178\pi\) |
−0.169817 | + | 0.985476i | \(0.554318\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 33.3939i | − | 0.0417946i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 362.161 | − | 362.161i | 0.451010 | − | 0.451010i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 941.281i | − | 1.16351i | −0.813364 | − | 0.581756i | \(-0.802366\pi\) | ||
0.813364 | − | 0.581756i | \(-0.197634\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 657.674 | 0.810943 | 0.405471 | − | 0.914108i | \(-0.367107\pi\) | ||||
0.405471 | + | 0.914108i | \(0.367107\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.0227 | + | 27.0227i | 0.0330755 | + | 0.0330755i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 574.041 | 0.699197 | 0.349599 | − | 0.936900i | \(-0.386318\pi\) | ||||
0.349599 | + | 0.936900i | \(0.386318\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −547.027 | + | 547.027i | −0.664675 | + | 0.664675i | −0.956478 | − | 0.291804i | \(-0.905745\pi\) |
0.291804 | + | 0.956478i | \(0.405745\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 959.271 | + | 959.271i | 1.15994 | + | 1.15994i | 0.984488 | + | 0.175454i | \(0.0561392\pi\) |
0.175454 | + | 0.984488i | \(0.443861\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 156.020i | − | 0.188203i | −0.995563 | − | 0.0941016i | \(-0.970002\pi\) | ||
0.995563 | − | 0.0941016i | \(-0.0299978\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.6765 | − | 12.6765i | 0.0152179 | − | 0.0152179i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 771.566i | − | 0.919626i | −0.888016 | − | 0.459813i | \(-0.847916\pi\) | ||
0.888016 | − | 0.459813i | \(-0.152084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −476.171 | −0.566197 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −236.709 | − | 236.709i | −0.279468 | − | 0.279468i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −283.396 | −0.333015 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −162.553 | + | 162.553i | −0.190566 | + | 0.190566i | −0.795941 | − | 0.605375i | \(-0.793023\pi\) |
0.605375 | + | 0.795941i | \(0.293023\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −426.434 | − | 426.434i | −0.497589 | − | 0.497589i | 0.413098 | − | 0.910687i | \(-0.364447\pi\) |
−0.910687 | + | 0.413098i | \(0.864447\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 155.453i | 0.180970i | 0.995898 | + | 0.0904849i | \(0.0288417\pi\) | ||||
−0.995898 | + | 0.0904849i | \(0.971158\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.30409 | − | 8.30409i | 0.00962236 | − | 0.00962236i | −0.702279 | − | 0.711902i | \(-0.747834\pi\) |
0.711902 | + | 0.702279i | \(0.247834\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 470.524i | 0.541455i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3058.24 | 3.51118 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 485.654 | + | 485.654i | 0.553767 | + | 0.553767i | 0.927526 | − | 0.373759i | \(-0.121931\pi\) |
−0.373759 | + | 0.927526i | \(0.621931\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1068.34 | −1.21265 | −0.606323 | − | 0.795219i | \(-0.707356\pi\) | ||||
−0.606323 | + | 0.795219i | \(0.707356\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1022.15 | + | 1022.15i | −1.15758 | + | 1.15758i | −0.172590 | + | 0.984994i | \(0.555214\pi\) |
−0.984994 | + | 0.172590i | \(0.944786\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −580.711 | − | 580.711i | −0.654691 | − | 0.654691i | 0.299428 | − | 0.954119i | \(-0.403204\pi\) |
−0.954119 | + | 0.299428i | \(0.903204\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 430.161i | 0.483871i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 367.712 | − | 367.712i | 0.411771 | − | 0.411771i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 932.615i | − | 1.03739i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −58.6061 | −0.0650456 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −222.979 | − | 222.979i | −0.245842 | − | 0.245842i | 0.573420 | − | 0.819262i | \(-0.305616\pi\) |
−0.819262 | + | 0.573420i | \(0.805616\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 710.849 | 0.780295 | 0.390148 | − | 0.920752i | \(-0.372424\pi\) | ||||
0.390148 | + | 0.920752i | \(0.372424\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 619.060 | − | 619.060i | 0.678051 | − | 0.678051i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 105.373 | + | 105.373i | 0.114911 | + | 0.114911i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 535.595i | − | 0.582802i | −0.956601 | − | 0.291401i | \(-0.905879\pi\) | ||
0.956601 | − | 0.291401i | \(-0.0941214\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1781.43 | + | 1781.43i | −1.93005 | + | 1.93005i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1482.43i | − | 1.59573i | −0.602837 | − | 0.797864i | \(-0.705963\pi\) | ||
0.602837 | − | 0.797864i | \(-0.294037\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 279.171 | 0.299862 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 329.109 | + | 329.109i | 0.351237 | + | 0.351237i | 0.860570 | − | 0.509333i | \(-0.170108\pi\) |
−0.509333 | + | 0.860570i | \(0.670108\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1330.38 | 1.41380 | 0.706898 | − | 0.707316i | \(-0.250094\pi\) | ||||
0.706898 | + | 0.707316i | \(0.250094\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33.0306 | + | 33.0306i | −0.0350272 | + | 0.0350272i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −310.652 | − | 310.652i | −0.328038 | − | 0.328038i | 0.523802 | − | 0.851840i | \(-0.324513\pi\) |
−0.851840 | + | 0.523802i | \(0.824513\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1902.81i | − | 2.00506i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.8990 | − | 40.8990i | 0.0429160 | − | 0.0429160i | −0.685323 | − | 0.728239i | \(-0.740339\pi\) |
0.728239 | + | 0.685323i | \(0.240339\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 292.343i | − | 0.304841i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −300.667 | −0.312869 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −106.656 | − | 106.656i | −0.110296 | − | 0.110296i | 0.649805 | − | 0.760101i | \(-0.274851\pi\) |
−0.760101 | + | 0.649805i | \(0.774851\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1529.61 | −1.57530 | −0.787649 | − | 0.616124i | \(-0.788702\pi\) | ||||
−0.787649 | + | 0.616124i | \(0.788702\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 815.044 | − | 815.044i | 0.837661 | − | 0.837661i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 148.974 | + | 148.974i | 0.152481 | + | 0.152481i | 0.779225 | − | 0.626744i | \(-0.215613\pi\) |
−0.626744 | + | 0.779225i | \(0.715613\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 280.000i | − | 0.286006i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −449.930 | + | 449.930i | −0.457711 | + | 0.457711i | −0.897903 | − | 0.440193i | \(-0.854910\pi\) |
0.440193 | + | 0.897903i | \(0.354910\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 58.1541i | 0.0588009i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1430.89 | −1.44388 | −0.721941 | − | 0.691955i | \(-0.756750\pi\) | ||||
−0.721941 | + | 0.691955i | \(0.756750\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 588.191 | + | 588.191i | 0.589961 | + | 0.589961i | 0.937621 | − | 0.347660i | \(-0.113024\pi\) |
−0.347660 | + | 0.937621i | \(0.613024\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1800.3.v.m.1657.2 | 4 | ||
3.2 | odd | 2 | 600.3.u.d.457.1 | yes | 4 | ||
5.2 | odd | 4 | 1800.3.v.l.793.1 | 4 | |||
5.3 | odd | 4 | inner | 1800.3.v.m.793.2 | 4 | ||
5.4 | even | 2 | 1800.3.v.l.1657.1 | 4 | |||
12.11 | even | 2 | 1200.3.bg.f.1057.2 | 4 | |||
15.2 | even | 4 | 600.3.u.c.193.2 | ✓ | 4 | ||
15.8 | even | 4 | 600.3.u.d.193.1 | yes | 4 | ||
15.14 | odd | 2 | 600.3.u.c.457.2 | yes | 4 | ||
60.23 | odd | 4 | 1200.3.bg.f.193.2 | 4 | |||
60.47 | odd | 4 | 1200.3.bg.l.193.1 | 4 | |||
60.59 | even | 2 | 1200.3.bg.l.1057.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.3.u.c.193.2 | ✓ | 4 | 15.2 | even | 4 | ||
600.3.u.c.457.2 | yes | 4 | 15.14 | odd | 2 | ||
600.3.u.d.193.1 | yes | 4 | 15.8 | even | 4 | ||
600.3.u.d.457.1 | yes | 4 | 3.2 | odd | 2 | ||
1200.3.bg.f.193.2 | 4 | 60.23 | odd | 4 | |||
1200.3.bg.f.1057.2 | 4 | 12.11 | even | 2 | |||
1200.3.bg.l.193.1 | 4 | 60.47 | odd | 4 | |||
1200.3.bg.l.1057.1 | 4 | 60.59 | even | 2 | |||
1800.3.v.l.793.1 | 4 | 5.2 | odd | 4 | |||
1800.3.v.l.1657.1 | 4 | 5.4 | even | 2 | |||
1800.3.v.m.793.2 | 4 | 5.3 | odd | 4 | inner | ||
1800.3.v.m.1657.2 | 4 | 1.1 | even | 1 | trivial |