Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,3,Mod(193,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, 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("1200.193");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.bg (of order \(4\), degree \(2\), 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: | \(32.6976317232\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 600) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 193.2 | ||
Root | \(1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.193 |
Dual form | 1200.3.bg.f.1057.2 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.22474 | + | 1.22474i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.22474 | + | 3.22474i | −0.460678 | + | 0.460678i | −0.898878 | − | 0.438200i | \(-0.855616\pi\) |
0.438200 | + | 0.898878i | \(0.355616\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 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 | 0.815804 | + | 0.578329i | \(0.196295\pi\) |
0.578329 | + | 0.815804i | \(0.303705\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.449490 | + | 0.449490i | −0.0264406 | + | 0.0264406i | −0.720203 | − | 0.693763i | \(-0.755952\pi\) |
0.693763 | + | 0.720203i | \(0.255952\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.89898i | 0.520999i | 0.965474 | + | 0.260499i | \(0.0838872\pi\) | ||||
−0.965474 | + | 0.260499i | \(0.916113\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.89898 | −0.376142 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −10.6515 | − | 10.6515i | −0.463110 | − | 0.463110i | 0.436563 | − | 0.899673i | \(-0.356195\pi\) |
−0.899673 | + | 0.436563i | \(0.856195\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | 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 | \(-0.636032\pi\) | ||||
−0.414467 | + | 0.910064i | \(0.636032\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.44949 | + | 8.44949i | 0.256045 | + | 0.256045i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13.3031 | − | 13.3031i | 0.359542 | − | 0.359542i | −0.504102 | − | 0.863644i | \(-0.668176\pi\) |
0.863644 | + | 0.504102i | \(0.168176\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 44.3939i | 1.13830i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.10102 | −0.0756346 | −0.0378173 | − | 0.999285i | \(-0.512040\pi\) | ||||
−0.0378173 | + | 0.999285i | \(0.512040\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.72985 | − | 2.72985i | −0.0634848 | − | 0.0634848i | 0.674652 | − | 0.738136i | \(-0.264294\pi\) |
−0.738136 | + | 0.674652i | \(0.764294\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −37.1464 | + | 37.1464i | −0.790350 | + | 0.790350i | −0.981551 | − | 0.191201i | \(-0.938762\pi\) |
0.191201 | + | 0.981551i | \(0.438762\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 28.2020i | 0.575552i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.10102 | −0.0215886 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 65.1918 | + | 65.1918i | 1.23003 | + | 1.23003i | 0.963950 | + | 0.266085i | \(0.0857302\pi\) |
0.266085 | + | 0.963950i | \(0.414270\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.1237 | + | 12.1237i | −0.212697 | + | 0.212697i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 80.3837i | 1.36244i | 0.732081 | + | 0.681218i | \(0.238549\pi\) | ||||
−0.732081 | + | 0.681218i | \(0.761451\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.7878 | 0.226029 | 0.113014 | − | 0.993593i | \(-0.463949\pi\) | ||||
0.113014 | + | 0.993593i | \(0.463949\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.67423 | − | 9.67423i | −0.153559 | − | 0.153559i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −84.3712 | + | 84.3712i | −1.25927 | + | 1.25927i | −0.307830 | + | 0.951441i | \(0.599603\pi\) |
−0.951441 | + | 0.307830i | \(0.900397\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 26.0908i | − | 0.378128i | ||||||
\(70\) | 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 | 0.968423 | − | 0.249314i | \(-0.0802053\pi\) |
−0.249314 | + | 0.968423i | \(0.580205\pi\) | |||||||
\(74\) | 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 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 89.7321 | + | 89.7321i | 1.08111 | + | 1.08111i | 0.996406 | + | 0.0847040i | \(0.0269945\pi\) |
0.0847040 | + | 0.996406i | \(0.473006\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 44.4495 | − | 44.4495i | 0.510914 | − | 0.510914i | ||||
\(88\) | 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 | ||||||||
\(93\) | −31.4722 | − | 31.4722i | −0.338411 | − | 0.338411i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 105.720 | − | 105.720i | 1.08989 | − | 1.08989i | 0.0943546 | − | 0.995539i | \(-0.469921\pi\) |
0.995539 | − | 0.0943546i | \(-0.0300787\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 20.6969i | 0.209060i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −197.485 | −1.95529 | −0.977647 | − | 0.210253i | \(-0.932571\pi\) | ||||
−0.977647 | + | 0.210253i | \(0.932571\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −45.7980 | − | 45.7980i | −0.444640 | − | 0.444640i | 0.448928 | − | 0.893568i | \(-0.351806\pi\) |
−0.893568 | + | 0.448928i | \(0.851806\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 139.485 | − | 139.485i | 1.30360 | − | 1.30360i | 0.377645 | − | 0.925951i | \(-0.376734\pi\) |
0.925951 | − | 0.377645i | \(-0.123266\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 140.576i | 1.28968i | 0.764316 | + | 0.644842i | \(0.223077\pi\) | ||||
−0.764316 | + | 0.644842i | \(0.776923\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 32.5857 | 0.293565 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 105.980 | + | 105.980i | 0.937872 | + | 0.937872i | 0.998180 | − | 0.0603074i | \(-0.0192081\pi\) |
−0.0603074 | + | 0.998180i | \(0.519208\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −54.3712 | + | 54.3712i | −0.464711 | + | 0.464711i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.89898i | − | 0.0243612i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −73.4041 | −0.606645 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.79796 | − | 3.79796i | −0.0308777 | − | 0.0308777i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −66.6969 | + | 66.6969i | −0.525173 | + | 0.525173i | −0.919129 | − | 0.393956i | \(-0.871106\pi\) |
0.393956 | + | 0.919129i | \(0.371106\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 6.68673i | − | 0.0518351i | ||||||
\(130\) | 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 | \(-0.674833\pi\) |
0.852914 | + | 0.522052i | \(0.174833\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 252.747i | − | 1.81832i | −0.416443 | − | 0.909162i | \(-0.636724\pi\) | ||
0.416443 | − | 0.909162i | \(-0.363276\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −90.9898 | −0.645318 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 125.035 | + | 125.035i | 0.874372 | + | 0.874372i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −34.5403 | + | 34.5403i | −0.234968 | + | 0.234968i | ||||
\(148\) | 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 | \(-0.712667\pi\) | ||||
−0.619506 | + | 0.784992i | \(0.712667\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.34847 | − | 1.34847i | −0.00881352 | − | 0.00881352i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −119.452 | + | 119.452i | −0.760839 | + | 0.760839i | −0.976474 | − | 0.215635i | \(-0.930818\pi\) |
0.215635 | + | 0.976474i | \(0.430818\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 159.687i | 1.00432i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 68.6969 | 0.426689 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 104.866 | + | 104.866i | 0.643350 | + | 0.643350i | 0.951377 | − | 0.308027i | \(-0.0996688\pi\) |
−0.308027 | + | 0.951377i | \(0.599669\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 67.3031 | − | 67.3031i | 0.403012 | − | 0.403012i | −0.476281 | − | 0.879293i | \(-0.658015\pi\) |
0.879293 | + | 0.476281i | \(0.158015\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 487.939i | 2.88721i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −29.6969 | −0.173666 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −47.8638 | − | 47.8638i | −0.276669 | − | 0.276669i | 0.555109 | − | 0.831778i | \(-0.312677\pi\) |
−0.831778 | + | 0.555109i | \(0.812677\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −98.4495 | + | 98.4495i | −0.556212 | + | 0.556212i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 134.000i | − | 0.748603i | −0.927307 | − | 0.374302i | \(-0.877882\pi\) | ||
0.927307 | − | 0.374302i | \(-0.122118\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −34.4143 | −0.190134 | −0.0950671 | − | 0.995471i | \(-0.530307\pi\) | ||||
−0.0950671 | + | 0.995471i | \(0.530307\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.8865 | + | 16.8865i | 0.0922759 | + | 0.0922759i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.10102 | + | 3.10102i | −0.0165830 | + | 0.0165830i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 23.6969i | − | 0.125381i | ||||||
\(190\) | 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 | 0.528396 | − | 0.848998i | \(-0.322794\pi\) |
−0.848998 | + | 0.528396i | \(0.822794\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −72.2474 | + | 72.2474i | −0.366738 | + | 0.366738i | −0.866286 | − | 0.499548i | \(-0.833499\pi\) |
0.499548 | + | 0.866286i | \(0.333499\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 85.4541i | − | 0.429417i | −0.976678 | − | 0.214709i | \(-0.931120\pi\) | ||
0.976678 | − | 0.214709i | \(-0.0688802\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −206.666 | −1.02819 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 117.035 | + | 117.035i | 0.576528 | + | 0.576528i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 31.9546 | − | 31.9546i | 0.154370 | − | 0.154370i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 68.2929i | 0.326760i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −99.4745 | −0.471443 | −0.235722 | − | 0.971821i | \(-0.575745\pi\) | ||||
−0.235722 | + | 0.971821i | \(0.575745\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −120.384 | − | 120.384i | −0.565182 | − | 0.565182i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 82.8661 | − | 82.8661i | 0.381871 | − | 0.381871i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 128.586i | 0.587149i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.2929 | −0.0737233 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.35076 | − | 2.35076i | −0.0105415 | − | 0.0105415i | 0.701816 | − | 0.712358i | \(-0.252373\pi\) |
−0.712358 | + | 0.701816i | \(0.752373\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 204.474 | − | 204.474i | 0.900769 | − | 0.900769i | −0.0947340 | − | 0.995503i | \(-0.530200\pi\) |
0.995503 | + | 0.0947340i | \(0.0302000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 131.808i | − | 0.575582i | −0.957693 | − | 0.287791i | \(-0.907079\pi\) | ||
0.957693 | − | 0.287791i | \(-0.0929208\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −54.4949 | −0.235909 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −139.616 | − | 139.616i | −0.599212 | − | 0.599212i | 0.340891 | − | 0.940103i | \(-0.389271\pi\) |
−0.940103 | + | 0.340891i | \(0.889271\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −83.5301 | + | 83.5301i | −0.352448 | + | 0.352448i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 118.697i | − | 0.496640i | −0.968678 | − | 0.248320i | \(-0.920122\pi\) | ||
0.968678 | − | 0.248320i | \(-0.0798784\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 277.384 | 1.15097 | 0.575485 | − | 0.817812i | \(-0.304813\pi\) | ||||
0.575485 | + | 0.817812i | \(0.304813\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.0227 | − | 11.0227i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −179.406 | + | 179.406i | −0.726342 | + | 0.726342i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 219.798i | 0.882723i | ||||||||
\(250\) | 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 | \(-0.679476\pi\) |
0.845209 | + | 0.534437i | \(0.179476\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 85.7980i | 0.331266i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 108.879 | 0.417159 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 222.767 | + | 222.767i | 0.847024 | + | 0.847024i | 0.989761 | − | 0.142737i | \(-0.0455902\pi\) |
−0.142737 | + | 0.989761i | \(0.545590\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 49.7071 | − | 49.7071i | 0.186169 | − | 0.186169i | ||||
\(268\) | 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 | \(-0.441403\pi\) | ||||
0.183048 | + | 0.983104i | \(0.441403\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −143.159 | − | 143.159i | −0.524392 | − | 0.524392i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.5936 | − | 26.5936i | 0.0960059 | − | 0.0960059i | −0.657473 | − | 0.753478i | \(-0.728374\pi\) |
0.753478 | + | 0.657473i | \(0.228374\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 77.0908i | − | 0.276311i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 325.101 | 1.15694 | 0.578472 | − | 0.815703i | \(-0.303649\pi\) | ||||
0.578472 | + | 0.815703i | \(0.303649\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −158.351 | − | 158.351i | −0.559543 | − | 0.559543i | 0.369634 | − | 0.929177i | \(-0.379483\pi\) |
−0.929177 | + | 0.369634i | \(0.879483\pi\) | |||||||
\(284\) | 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 | ||||||||
\(291\) | 258.959 | 0.889894 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 347.126 | + | 347.126i | 1.18473 | + | 1.18473i | 0.978504 | + | 0.206226i | \(0.0661182\pi\) |
0.206226 | + | 0.978504i | \(0.433882\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −25.3485 | + | 25.3485i | −0.0853484 | + | 0.0853484i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 386.091i | − | 1.29127i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.6061 | 0.0584921 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −241.868 | − | 241.868i | −0.798245 | − | 0.798245i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −107.250 | + | 107.250i | −0.349348 | + | 0.349348i | −0.859867 | − | 0.510519i | \(-0.829453\pi\) |
0.510519 | + | 0.859867i | \(0.329453\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 112.182i | − | 0.363047i | ||||||
\(310\) | 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 | 0.522396 | − | 0.852703i | \(-0.325038\pi\) |
−0.852703 | + | 0.522396i | \(0.825038\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −207.060 | + | 207.060i | −0.653187 | + | 0.653187i | −0.953759 | − | 0.300572i | \(-0.902822\pi\) |
0.300572 | + | 0.953759i | \(0.402822\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 250.384i | − | 0.784902i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 341.666 | 1.06438 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.44949 | − | 4.44949i | −0.0137755 | − | 0.0137755i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −172.169 | + | 172.169i | −0.526511 | + | 0.526511i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 239.576i | − | 0.728193i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 565.555 | 1.70863 | 0.854313 | − | 0.519759i | \(-0.173978\pi\) | ||||
0.854313 | + | 0.519759i | \(0.173978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 39.9092 | + | 39.9092i | 0.119847 | + | 0.119847i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 65.6538 | − | 65.6538i | 0.194818 | − | 0.194818i | −0.602956 | − | 0.797774i | \(-0.706011\pi\) |
0.797774 | + | 0.602956i | \(0.206011\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 259.596i | 0.765770i | ||||||||
\(340\) | 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 | −0.843350 | − | 0.537364i | \(-0.819420\pi\) |
0.537364 | + | 0.843350i | \(0.319420\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 335.980i | − | 0.962692i | −0.876531 | − | 0.481346i | \(-0.840148\pi\) | ||
0.876531 | − | 0.481346i | \(-0.159852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −133.182 | −0.379435 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 419.328 | + | 419.328i | 1.18790 | + | 1.18790i | 0.977648 | + | 0.210251i | \(0.0674280\pi\) |
0.210251 | + | 0.977648i | \(0.432572\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.55051 | − | 3.55051i | 0.00994541 | − | 0.00994541i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 191.019i | 0.532087i | 0.963961 | + | 0.266044i | \(0.0857166\pi\) | ||||
−0.963961 | + | 0.266044i | \(0.914283\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 263.010 | 0.728560 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −89.9013 | − | 89.9013i | −0.247662 | − | 0.247662i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 207.341 | − | 207.341i | 0.564961 | − | 0.564961i | −0.365752 | − | 0.930712i | \(-0.619188\pi\) |
0.930712 | + | 0.365752i | \(0.119188\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 9.30306i | − | 0.0252115i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −420.454 | −1.13330 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −353.052 | − | 353.052i | −0.946521 | − | 0.946521i | 0.0521200 | − | 0.998641i | \(-0.483402\pi\) |
−0.998641 | + | 0.0521200i | \(0.983402\pi\) | |||||||
\(374\) | 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 | ||||||||
\(381\) | −163.373 | −0.428802 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −207.414 | − | 207.414i | −0.541552 | − | 0.541552i | 0.382432 | − | 0.923984i | \(-0.375087\pi\) |
−0.923984 | + | 0.382432i | \(0.875087\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.18954 | − | 8.18954i | 0.0211616 | − | 0.0211616i | ||||
\(388\) | 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 | ||||||||
\(393\) | 40.0204 | + | 40.0204i | 0.101833 | + | 0.101833i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −288.062 | + | 288.062i | −0.725598 | + | 0.725598i | −0.969740 | − | 0.244141i | \(-0.921494\pi\) |
0.244141 | + | 0.969740i | \(0.421494\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 78.1918i | − | 0.195970i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 129.748 | 0.323561 | 0.161781 | − | 0.986827i | \(-0.448276\pi\) | ||||
0.161781 | + | 0.986827i | \(0.448276\pi\) | |||||||
\(402\) | 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 | \(-0.895933\pi\) | ||
0.947030 | − | 0.321144i | \(-0.104067\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 111.031 | 0.270147 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −259.217 | − | 259.217i | −0.627644 | − | 0.627644i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 309.551 | − | 309.551i | 0.742327 | − | 0.742327i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 638.030i | − | 1.52274i | −0.648315 | − | 0.761372i | \(-0.724526\pi\) | ||
0.648315 | − | 0.761372i | \(-0.275474\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −272.606 | −0.647520 | −0.323760 | − | 0.946139i | \(-0.604947\pi\) | ||||
−0.323760 | + | 0.946139i | \(0.604947\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −111.439 | − | 111.439i | −0.263450 | − | 0.263450i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −44.4620 | + | 44.4620i | −0.104126 | + | 0.104126i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 306.272i | 0.713922i | ||||||||
\(430\) | 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 | 0.907174 | − | 0.420756i | \(-0.138235\pi\) |
−0.420756 | + | 0.907174i | \(0.638235\pi\) | |||||||
\(434\) | 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 | ||||||||
\(441\) | −84.6061 | −0.191851 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −533.040 | − | 533.040i | −1.20325 | − | 1.20325i | −0.973172 | − | 0.230078i | \(-0.926102\pi\) |
−0.230078 | − | 0.973172i | \(-0.573898\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 92.1158 | − | 92.1158i | 0.206076 | − | 0.206076i | ||||
\(448\) | 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 | ||||||||
\(453\) | −229.139 | − | 229.139i | −0.505825 | − | 0.505825i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 183.918 | − | 183.918i | 0.402447 | − | 0.402447i | −0.476647 | − | 0.879095i | \(-0.658148\pi\) |
0.879095 | + | 0.476647i | \(0.158148\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 3.30306i | − | 0.00719621i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 632.595 | 1.37222 | 0.686112 | − | 0.727496i | \(-0.259316\pi\) | ||||
0.686112 | + | 0.727496i | \(0.259316\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −382.838 | − | 382.838i | −0.826863 | − | 0.826863i | 0.160218 | − | 0.987082i | \(-0.448780\pi\) |
−0.987082 | + | 0.160218i | \(0.948780\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −164.581 | + | 164.581i | −0.352422 | + | 0.352422i | −0.861010 | − | 0.508588i | \(-0.830168\pi\) |
0.508588 | + | 0.861010i | \(0.330168\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 544.151i | − | 1.16024i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −292.596 | −0.621223 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.8332 | − | 18.8332i | −0.0398164 | − | 0.0398164i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −195.576 | + | 195.576i | −0.410012 | + | 0.410012i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 356.606i | − | 0.744480i | −0.928136 | − | 0.372240i | \(-0.878590\pi\) | ||
0.928136 | − | 0.372240i | \(-0.121410\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 482.202 | 1.00250 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 84.1362 | + | 84.1362i | 0.174195 | + | 0.174195i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 170.103 | − | 170.103i | 0.349288 | − | 0.349288i | −0.510556 | − | 0.859844i | \(-0.670560\pi\) |
0.859844 | + | 0.510556i | \(0.170560\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 256.868i | 0.525293i | ||||||||
\(490\) | 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 | ||||||||
\(501\) | 164.858 | 0.329058 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 543.626 | + | 543.626i | 1.08077 | + | 1.08077i | 0.996438 | + | 0.0843284i | \(0.0268745\pi\) |
0.0843284 | + | 0.996438i | \(0.473126\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −597.601 | + | 597.601i | −1.17870 | + | 1.17870i | ||||
\(508\) | 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 | ||||||||
\(513\) | −36.3712 | − | 36.3712i | −0.0708990 | − | 0.0708990i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −256.272 | + | 256.272i | −0.495691 | + | 0.495691i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 117.242i | − | 0.225899i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 881.928 | 1.69276 | 0.846380 | − | 0.532580i | \(-0.178777\pi\) | ||||
0.846380 | + | 0.532580i | \(0.178777\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 305.493 | + | 305.493i | 0.584116 | + | 0.584116i | 0.936032 | − | 0.351916i | \(-0.114470\pi\) |
−0.351916 | + | 0.936032i | \(0.614470\pi\) | |||||||
\(524\) | 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 | ||||||||
\(531\) | −241.151 | −0.454145 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −56.2020 | − | 56.2020i | −0.105445 | − | 0.105445i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 164.116 | − | 164.116i | 0.305616 | − | 0.305616i | ||||
\(538\) | 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 | ||||||||
\(543\) | −42.1487 | − | 42.1487i | −0.0776220 | − | 0.0776220i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 178.020 | − | 178.020i | 0.325449 | − | 0.325449i | −0.525404 | − | 0.850853i | \(-0.676086\pi\) |
0.850853 | + | 0.525404i | \(0.176086\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 41.3633i | 0.0753429i | ||||||||
\(550\) | 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 | \(-0.716404\pi\) |
0.777665 | + | 0.628679i | \(0.216404\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 98.9500i | − | 0.177013i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.59592 | −0.0135400 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −228.227 | − | 228.227i | −0.405377 | − | 0.405377i | 0.474746 | − | 0.880123i | \(-0.342540\pi\) |
−0.880123 | + | 0.474746i | \(0.842540\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 29.0227 | − | 29.0227i | 0.0511864 | − | 0.0511864i | ||||
\(568\) | 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 | \(-0.342699\pi\) | ||||
0.474305 | + | 0.880361i | \(0.342699\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 291.823 | + | 291.823i | 0.509290 | + | 0.509290i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −341.967 | + | 341.967i | −0.592664 | + | 0.592664i | −0.938350 | − | 0.345686i | \(-0.887646\pi\) |
0.345686 | + | 0.938350i | \(0.387646\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 151.565i | − | 0.261771i | ||||||
\(580\) | 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 | −0.205081 | − | 0.978745i | \(-0.565746\pi\) |
0.978745 | + | 0.205081i | \(0.0657458\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 254.373i | − | 0.431873i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −176.969 | −0.299441 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 50.6357 | + | 50.6357i | 0.0853891 | + | 0.0853891i | 0.748511 | − | 0.663122i | \(-0.230769\pi\) |
−0.663122 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 104.659 | − | 104.659i | 0.175309 | − | 0.175309i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 506.443i | − | 0.845481i | −0.906251 | − | 0.422740i | \(-0.861068\pi\) | ||
0.906251 | − | 0.422740i | \(-0.138932\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −785.120 | −1.30636 | −0.653178 | − | 0.757204i | \(-0.726565\pi\) | ||||
−0.653178 | + | 0.757204i | \(0.726565\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −253.114 | − | 253.114i | −0.419757 | − | 0.419757i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 766.252 | − | 766.252i | 1.26236 | − | 1.26236i | 0.312413 | − | 0.949946i | \(-0.398863\pi\) |
0.949946 | − | 0.312413i | \(-0.101137\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 286.677i | 0.470733i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1346.46 | −2.20370 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −182.697 | − | 182.697i | −0.298037 | − | 0.298037i | 0.542207 | − | 0.840245i | \(-0.317589\pi\) |
−0.840245 | + | 0.542207i | \(0.817589\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −71.1214 | + | 71.1214i | −0.115270 | + | 0.115270i | −0.762389 | − | 0.647119i | \(-0.775974\pi\) |
0.647119 | + | 0.762389i | \(0.275974\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1031.35i | − | 1.66616i | −0.553154 | − | 0.833079i | \(-0.686576\pi\) | ||
0.553154 | − | 0.833079i | \(-0.313424\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 78.2724 | 0.126043 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 130.879 | + | 130.879i | 0.210078 | + | 0.210078i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −83.6413 | + | 83.6413i | −0.133399 | + | 0.133399i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.9592i | 0.0190130i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 374.201 | 0.593029 | 0.296514 | − | 0.955028i | \(-0.404176\pi\) | ||||
0.296514 | + | 0.955028i | \(0.404176\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −121.831 | − | 121.831i | −0.192466 | − | 0.192466i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −511.126 | + | 511.126i | −0.802396 | + | 0.802396i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 294.879i | − | 0.461469i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −884.827 | −1.38038 | −0.690192 | − | 0.723626i | \(-0.742474\pi\) | ||||
−0.690192 | + | 0.723626i | \(0.742474\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 683.787 | + | 683.787i | 1.06343 | + | 1.06343i | 0.997847 | + | 0.0655849i | \(0.0208913\pi\) |
0.0655849 | + | 0.997847i | \(0.479109\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −597.898 | + | 597.898i | −0.924108 | + | 0.924108i | −0.997317 | − | 0.0732085i | \(-0.976676\pi\) |
0.0732085 | + | 0.997317i | \(0.476676\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 554.565i | 0.854492i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 202.980 | 0.311797 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 282.136 | + | 282.136i | 0.432062 | + | 0.432062i | 0.889329 | − | 0.457268i | \(-0.151172\pi\) |
−0.457268 | + | 0.889329i | \(0.651172\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −157.485 | + | 157.485i | −0.239703 | + | 0.239703i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 503.505i | 0.764044i | 0.924153 | + | 0.382022i | \(0.124772\pi\) | ||||
−0.924153 | + | 0.382022i | \(0.875228\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.7673 | 0.0586495 | 0.0293248 | − | 0.999570i | \(-0.490664\pi\) | ||||
0.0293248 | + | 0.999570i | \(0.490664\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.9546 | − | 19.9546i | −0.0300974 | − | 0.0300974i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −386.574 | + | 386.574i | −0.579572 | + | 0.579572i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 5.75817i | − | 0.00860713i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 95.1214 | 0.141761 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −359.728 | − | 359.728i | −0.534513 | − | 0.534513i | 0.387399 | − | 0.921912i | \(-0.373374\pi\) |
−0.921912 | + | 0.387399i | \(0.873374\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 40.0454 | − | 40.0454i | 0.0591513 | − | 0.0591513i | −0.676912 | − | 0.736064i | \(-0.736682\pi\) |
0.736064 | + | 0.676912i | \(0.236682\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 681.838i | 1.00418i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 500.858 | 0.735475 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 502.243 | + | 502.243i | 0.735348 | + | 0.735348i | 0.971674 | − | 0.236326i | \(-0.0759432\pi\) |
−0.236326 | + | 0.971674i | \(0.575943\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 161.431 | − | 161.431i | 0.234980 | − | 0.234980i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2363.04i | 3.42966i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 242.241 | 0.350566 | 0.175283 | − | 0.984518i | \(-0.443916\pi\) | ||||
0.175283 | + | 0.984518i | \(0.443916\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −66.7423 | − | 66.7423i | −0.0963093 | − | 0.0963093i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.39388 | − | 1.39388i | 0.00199982 | − | 0.00199982i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 341.989i | − | 0.489254i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 619.181 | 0.883282 | 0.441641 | − | 0.897192i | \(-0.354397\pi\) | ||||
0.441641 | + | 0.897192i | \(0.354397\pi\) | |||||||
\(702\) | 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 | \(-0.856328\pi\) | ||
0.899856 | − | 0.436188i | \(-0.143672\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −204.606 | −0.287772 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 273.712 | + | 273.712i | 0.383887 | + | 0.383887i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 145.373 | − | 145.373i | 0.202752 | − | 0.202752i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 555.989i | − | 0.773281i | −0.922231 | − | 0.386640i | \(-0.873635\pi\) | ||
0.922231 | − | 0.386640i | \(-0.126365\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 295.373 | 0.409672 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 339.724 | + | 339.724i | 0.469881 | + | 0.469881i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 103.992 | − | 103.992i | 0.143043 | − | 0.143043i | −0.631959 | − | 0.775002i | \(-0.717749\pi\) |
0.775002 | + | 0.631959i | \(0.217749\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.45408 | 0.00335715 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 462.979 | + | 462.979i | 0.631621 | + | 0.631621i | 0.948475 | − | 0.316853i | \(-0.102626\pi\) |
−0.316853 | + | 0.948475i | \(0.602626\pi\) | |||||||
\(734\) | 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 | ||||||||
\(741\) | −439.454 | −0.593055 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 634.534 | + | 634.534i | 0.854016 | + | 0.854016i | 0.990625 | − | 0.136609i | \(-0.0436205\pi\) |
−0.136609 | + | 0.990625i | \(0.543620\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −269.196 | + | 269.196i | −0.360370 | + | 0.360370i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 899.605i | 1.20107i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 934.241 | 1.24400 | 0.621998 | − | 0.783019i | \(-0.286321\pi\) | ||||
0.621998 | + | 0.783019i | \(0.286321\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −46.0204 | − | 46.0204i | −0.0611161 | − | 0.0611161i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −656.598 | + | 656.598i | −0.867369 | + | 0.867369i | −0.992180 | − | 0.124812i | \(-0.960167\pi\) |
0.124812 | + | 0.992180i | \(0.460167\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 180.000i | − | 0.237154i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −911.292 | −1.19749 | −0.598746 | − | 0.800939i | \(-0.704334\pi\) | ||||
−0.598746 | + | 0.800939i | \(0.704334\pi\) | |||||||
\(762\) | 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 | \(0.166869\pi\) | ||||
−0.865707 | + | 0.500551i | \(0.833131\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 195.637 | 0.253744 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −480.515 | − | 480.515i | −0.621624 | − | 0.621624i | 0.324323 | − | 0.945947i | \(-0.394864\pi\) |
−0.945947 | + | 0.324323i | \(0.894864\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −105.081 | + | 105.081i | −0.135239 | + | 0.135239i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 30.6969i | − | 0.0394056i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −678.120 | −0.868272 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 133.348 | + | 133.348i | 0.170305 | + | 0.170305i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.0079 | − | 48.0079i | 0.0610012 | − | 0.0610012i | −0.675948 | − | 0.736949i | \(-0.736266\pi\) |
0.736949 | + | 0.675948i | \(0.236266\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 545.666i | 0.691592i | ||||||||
\(790\) | 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 | \(-0.945682\pi\) |
0.169817 | + | 0.985476i | \(0.445682\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 33.3939i | − | 0.0417946i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 121.757 | 0.152006 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 362.161 | + | 362.161i | 0.451010 | + | 0.451010i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 551.246 | − | 551.246i | 0.683081 | − | 0.683081i | ||||
\(808\) | 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 | \(-0.632893\pi\) | ||||
−0.405471 | + | 0.914108i | \(0.632893\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 121.510 | + | 121.510i | 0.149458 | + | 0.149458i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.0227 | − | 27.0227i | 0.0330755 | − | 0.0330755i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 350.666i | − | 0.428164i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −574.041 | −0.699197 | −0.349599 | − | 0.936900i | \(-0.613682\pi\) | ||||
−0.349599 | + | 0.936900i | \(0.613682\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 547.027 | + | 547.027i | 0.664675 | + | 0.664675i | 0.956478 | − | 0.291804i | \(-0.0942554\pi\) |
−0.291804 | + | 0.956478i | \(0.594255\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 959.271 | − | 959.271i | 1.15994 | − | 1.15994i | 0.175454 | − | 0.984488i | \(-0.443861\pi\) |
0.984488 | − | 0.175454i | \(-0.0561392\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 156.020i | 0.188203i | 0.995563 | + | 0.0941016i | \(0.0299978\pi\) | ||||
−0.995563 | + | 0.0941016i | \(0.970002\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 65.1408 | 0.0783885 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.6765 | − | 12.6765i | −0.0152179 | − | 0.0152179i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 94.4166 | − | 94.4166i | 0.112804 | − | 0.112804i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 771.566i | 0.919626i | 0.888016 | + | 0.459813i | \(0.152084\pi\) | ||||
−0.888016 | + | 0.459813i | \(0.847916\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −476.171 | −0.566197 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 398.166 | + | 398.166i | 0.472320 | + | 0.472320i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 236.709 | − | 236.709i | 0.279468 | − | 0.279468i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 387.879i | − | 0.456865i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −283.396 | −0.333015 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −162.553 | − | 162.553i | −0.190566 | − | 0.190566i | 0.605375 | − | 0.795941i | \(-0.293023\pi\) |
−0.795941 | + | 0.605375i | \(0.793023\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 426.434 | − | 426.434i | 0.497589 | − | 0.497589i | −0.413098 | − | 0.910687i | \(-0.635553\pi\) |
0.910687 | + | 0.413098i | \(0.135553\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 155.453i | 0.180970i | 0.995898 | + | 0.0904849i | \(0.0288417\pi\) | ||||
−0.995898 | + | 0.0904849i | \(0.971158\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.4949 | 0.0284494 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.30409 | + | 8.30409i | 0.00962236 | + | 0.00962236i | 0.711902 | − | 0.702279i | \(-0.247834\pi\) |
−0.702279 | + | 0.711902i | \(0.747834\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −353.456 | + | 353.456i | −0.407677 | + | 0.407677i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 470.524i | 0.541455i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3058.24 | −3.51118 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 317.159 | + | 317.159i | 0.363298 | + | 0.363298i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 485.654 | − | 485.654i | 0.553767 | − | 0.553767i | −0.373759 | − | 0.927526i | \(-0.621931\pi\) |
0.927526 | + | 0.373759i | \(0.121931\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 850.282i | 0.967328i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1068.34 | 1.21265 | 0.606323 | − | 0.795219i | \(-0.292644\pi\) | ||||
0.606323 | + | 0.795219i | \(0.292644\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1022.15 | + | 1022.15i | 1.15758 | + | 1.15758i | 0.984994 | + | 0.172590i | \(0.0552137\pi\) |
0.172590 | + | 0.984994i | \(0.444786\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −580.711 | + | 580.711i | −0.654691 | + | 0.654691i | −0.954119 | − | 0.299428i | \(-0.903204\pi\) |
0.299428 | + | 0.954119i | \(0.403204\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 430.161i | − | 0.483871i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −62.0908 | −0.0696867 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −367.712 | − | 367.712i | −0.411771 | − | 0.411771i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 472.863 | − | 472.863i | 0.527160 | − | 0.527160i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 932.615i | 1.03739i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −58.6061 | −0.0650456 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.5630 | + | 21.5630i | 0.0238793 | + | 0.0238793i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 222.979 | − | 222.979i | 0.245842 | − | 0.245842i | −0.573420 | − | 0.819262i | \(-0.694384\pi\) |
0.819262 | + | 0.573420i | \(0.194384\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 592.454i | − | 0.651765i | ||||||
\(910\) | 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 | ||||||||
\(921\) | −262.707 | −0.285241 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1781.43 | − | 1781.43i | −1.93005 | − | 1.93005i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 137.394 | − | 137.394i | 0.148213 | − | 0.148213i | ||||
\(928\) | 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 | ||||||||
\(933\) | 436.974 | + | 436.974i | 0.468354 | + | 0.468354i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 329.109 | − | 329.109i | 0.351237 | − | 0.351237i | −0.509333 | − | 0.860570i | \(-0.670108\pi\) |
0.860570 | + | 0.509333i | \(0.170108\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 253.243i | − | 0.269694i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1330.38 | −1.41380 | −0.706898 | − | 0.707316i | \(-0.749906\pi\) | ||||
−0.706898 | + | 0.707316i | \(0.749906\pi\) | |||||||
\(942\) | 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 | −0.851840 | − | 0.523802i | \(-0.824513\pi\) |
0.523802 | + | 0.851840i | \(0.324513\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1902.81i | 2.00506i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −507.192 | −0.533325 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.8990 | − | 40.8990i | −0.0429160 | − | 0.0429160i | 0.685323 | − | 0.728239i | \(-0.259661\pi\) |
−0.728239 | + | 0.685323i | \(0.759661\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 306.656 | − | 306.656i | 0.320435 | − | 0.320435i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 292.343i | 0.304841i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −300.667 | −0.312869 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 418.454 | + | 418.454i | 0.434532 | + | 0.434532i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 106.656 | − | 106.656i | 0.110296 | − | 0.110296i | −0.649805 | − | 0.760101i | \(-0.725149\pi\) |
0.760101 | + | 0.649805i | \(0.225149\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 10.8990i | − | 0.0112477i | ||||||
\(970\) | 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 | \(-0.784387\pi\) |
0.626744 | + | 0.779225i | \(0.284387\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 280.000i | − | 0.286006i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −421.727 | −0.429895 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −449.930 | − | 449.930i | −0.457711 | − | 0.457711i | 0.440193 | − | 0.897903i | \(-0.354910\pi\) |
−0.897903 | + | 0.440193i | \(0.854910\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 293.419 | − | 293.419i | 0.297284 | − | 0.297284i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 58.1541i | 0.0588009i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1430.89 | 1.44388 | 0.721941 | − | 0.691955i | \(-0.243250\pi\) | ||||
0.721941 | + | 0.691955i | \(0.243250\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 692.661 | + | 692.661i | 0.697544 | + | 0.697544i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 588.191 | − | 588.191i | 0.589961 | − | 0.589961i | −0.347660 | − | 0.937621i | \(-0.613024\pi\) |
0.937621 | + | 0.347660i | \(0.113024\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 97.7571i | 0.0978550i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1200.3.bg.f.193.2 | 4 | ||
4.3 | odd | 2 | 600.3.u.d.193.1 | yes | 4 | ||
5.2 | odd | 4 | inner | 1200.3.bg.f.1057.2 | 4 | ||
5.3 | odd | 4 | 1200.3.bg.l.1057.1 | 4 | |||
5.4 | even | 2 | 1200.3.bg.l.193.1 | 4 | |||
12.11 | even | 2 | 1800.3.v.m.793.2 | 4 | |||
20.3 | even | 4 | 600.3.u.c.457.2 | yes | 4 | ||
20.7 | even | 4 | 600.3.u.d.457.1 | yes | 4 | ||
20.19 | odd | 2 | 600.3.u.c.193.2 | ✓ | 4 | ||
60.23 | odd | 4 | 1800.3.v.l.1657.1 | 4 | |||
60.47 | odd | 4 | 1800.3.v.m.1657.2 | 4 | |||
60.59 | even | 2 | 1800.3.v.l.793.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.3.u.c.193.2 | ✓ | 4 | 20.19 | odd | 2 | ||
600.3.u.c.457.2 | yes | 4 | 20.3 | even | 4 | ||
600.3.u.d.193.1 | yes | 4 | 4.3 | odd | 2 | ||
600.3.u.d.457.1 | yes | 4 | 20.7 | even | 4 | ||
1200.3.bg.f.193.2 | 4 | 1.1 | even | 1 | trivial | ||
1200.3.bg.f.1057.2 | 4 | 5.2 | odd | 4 | inner | ||
1200.3.bg.l.193.1 | 4 | 5.4 | even | 2 | |||
1200.3.bg.l.1057.1 | 4 | 5.3 | odd | 4 | |||
1800.3.v.l.793.1 | 4 | 60.59 | even | 2 | |||
1800.3.v.l.1657.1 | 4 | 60.23 | odd | 4 | |||
1800.3.v.m.793.2 | 4 | 12.11 | even | 2 | |||
1800.3.v.m.1657.2 | 4 | 60.47 | odd | 4 |