Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(241,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.q (of order \(3\), 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: | \(5.74922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.856615824.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 481.2 | ||
Root | \(2.33086i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.481 |
Dual form | 720.2.q.l.241.2 |
$q$-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 \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | −1.05903 | + | 1.37057i | −0.611432 | + | 0.791297i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.51859 | + | 2.63027i | 0.573972 | + | 0.994148i | 0.996153 | + | 0.0876366i | \(0.0279314\pi\) |
−0.422181 | + | 0.906512i | \(0.638735\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.756906 | − | 2.90295i | −0.252302 | − | 0.967649i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.63557 | + | 4.56494i | 0.794655 | + | 1.37638i | 0.923058 | + | 0.384660i | \(0.125681\pi\) |
−0.128403 | + | 0.991722i | \(0.540985\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.256906 | − | 0.444974i | 0.0712528 | − | 0.123414i | −0.828198 | − | 0.560436i | \(-0.810634\pi\) |
0.899451 | + | 0.437022i | \(0.143967\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.657430 | − | 1.60243i | −0.169748 | − | 0.413746i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.80320 | 0.679876 | 0.339938 | − | 0.940448i | \(-0.389594\pi\) | ||||
0.339938 | + | 0.940448i | \(0.389594\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.29877 | −1.90387 | −0.951934 | − | 0.306304i | \(-0.900908\pi\) | ||||
−0.951934 | + | 0.306304i | \(0.900908\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.21319 | − | 0.704213i | −1.13761 | − | 0.153672i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.51859 | − | 4.36232i | 0.525162 | − | 0.909607i | −0.474409 | − | 0.880305i | \(-0.657338\pi\) |
0.999571 | − | 0.0293020i | \(-0.00932846\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.78027 | + | 2.03692i | 0.919963 | + | 0.392005i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.39248 | + | 4.14389i | 0.444272 | + | 0.769502i | 0.998001 | − | 0.0631952i | \(-0.0201291\pi\) |
−0.553729 | + | 0.832697i | \(0.686796\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.29408 | + | 7.43756i | −0.771239 | + | 1.33583i | 0.165645 | + | 0.986185i | \(0.447030\pi\) |
−0.936884 | + | 0.349640i | \(0.886304\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.04771 | − | 1.22219i | −1.57500 | − | 0.212756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.03717 | −0.513376 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.58816 | −1.08309 | −0.541543 | − | 0.840673i | \(-0.682160\pi\) | ||||
−0.541543 | + | 0.840673i | \(0.682160\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.337795 | + | 0.823348i | 0.0540905 | + | 0.131841i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.99088 | + | 6.91240i | −0.623270 | + | 1.07954i | 0.365602 | + | 0.930771i | \(0.380863\pi\) |
−0.988873 | + | 0.148765i | \(0.952470\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.598399 | − | 1.03646i | −0.0912549 | − | 0.158058i | 0.816784 | − | 0.576943i | \(-0.195754\pi\) |
−0.908039 | + | 0.418885i | \(0.862421\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.89248 | + | 0.795973i | 0.431185 | + | 0.118657i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.81267 | − | 8.33578i | −0.701999 | − | 1.21590i | −0.967764 | − | 0.251861i | \(-0.918958\pi\) |
0.265764 | − | 0.964038i | \(-0.414376\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.11221 | + | 1.92640i | −0.158887 | + | 0.275201i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.96868 | + | 3.84198i | −0.415698 | + | 0.537984i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.467941 | −0.0642766 | −0.0321383 | − | 0.999483i | \(-0.510232\pi\) | ||||
−0.0321383 | + | 0.999483i | \(0.510232\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.27114 | −0.710761 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.78865 | − | 11.3740i | 1.16409 | − | 1.50652i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.378666 | + | 0.655869i | −0.0492981 | + | 0.0853868i | −0.889621 | − | 0.456699i | \(-0.849032\pi\) |
0.840323 | + | 0.542085i | \(0.182365\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.135572 | + | 0.234817i | 0.0173582 | + | 0.0300653i | 0.874574 | − | 0.484892i | \(-0.161141\pi\) |
−0.857216 | + | 0.514957i | \(0.827808\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.48610 | − | 6.39924i | 0.817172 | − | 0.806228i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.256906 | + | 0.444974i | 0.0318652 | + | 0.0551922i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.63080 | + | 6.28872i | −0.443572 | + | 0.768290i | −0.997952 | − | 0.0639743i | \(-0.979622\pi\) |
0.554379 | + | 0.832264i | \(0.312956\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.31159 | + | 8.07172i | 0.398668 | + | 0.971721i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.48619 | −0.176378 | −0.0881891 | − | 0.996104i | \(-0.528108\pi\) | ||||
−0.0881891 | + | 0.996104i | \(0.528108\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.31701 | 0.622309 | 0.311155 | − | 0.950359i | \(-0.399284\pi\) | ||||
0.311155 | + | 0.950359i | \(0.399284\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.71646 | + | 0.231865i | 0.198200 | + | 0.0267734i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.00469 | + | 13.8645i | −0.912219 | + | 1.58001i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.98175 | − | 13.8248i | −0.898017 | − | 1.55541i | −0.830025 | − | 0.557726i | \(-0.811674\pi\) |
−0.0679921 | − | 0.997686i | \(-0.521659\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.85419 | + | 4.39451i | −0.872687 | + | 0.488279i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.03240 | + | 10.4484i | 0.662142 | + | 1.14686i | 0.980052 | + | 0.198742i | \(0.0636857\pi\) |
−0.317910 | + | 0.948121i | \(0.602981\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.40160 | + | 2.42764i | −0.152025 | + | 0.263315i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.21319 | − | 1.10946i | −0.880546 | − | 0.118947i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.2529 | 1.61680 | 0.808402 | − | 0.588631i | \(-0.200333\pi\) | ||||
0.808402 | + | 0.588631i | \(0.200333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.56053 | 0.163588 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.64611 | − | 13.7619i | −0.585475 | − | 1.42705i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.14938 | − | 7.18694i | 0.425718 | − | 0.737365i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.18187 | + | 5.51116i | 0.323070 | + | 0.559573i | 0.981120 | − | 0.193401i | \(-0.0619518\pi\) |
−0.658050 | + | 0.752974i | \(0.728618\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.2569 | − | 11.1062i | 1.13136 | − | 1.11621i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.03717 | + | 1.79644i | 0.103203 | + | 0.178752i | 0.913002 | − | 0.407954i | \(-0.133758\pi\) |
−0.809800 | + | 0.586706i | \(0.800424\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.52805 | − | 4.37871i | 0.249096 | − | 0.431447i | −0.714179 | − | 0.699963i | \(-0.753200\pi\) |
0.963275 | + | 0.268516i | \(0.0865332\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.21646 | − | 4.16265i | 0.313894 | − | 0.406233i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.2901 | 1.28480 | 0.642400 | − | 0.766370i | \(-0.277939\pi\) | ||||
0.642400 | + | 0.766370i | \(0.277939\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.34549 | 0.799353 | 0.399676 | − | 0.916656i | \(-0.369122\pi\) | ||||
0.399676 | + | 0.916656i | \(0.369122\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.97706 | − | 9.02951i | 0.662234 | − | 0.857043i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.55098 | − | 4.41844i | 0.239976 | − | 0.415651i | −0.720731 | − | 0.693215i | \(-0.756194\pi\) |
0.960707 | + | 0.277564i | \(0.0895269\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.51859 | + | 4.36232i | 0.234859 | + | 0.406788i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.48619 | − | 0.408980i | −0.137398 | − | 0.0378102i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.25691 | + | 7.37318i | 0.390230 | + | 0.675898i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.39248 | + | 14.5362i | −0.762953 | + | 1.32147i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.24744 | − | 12.7902i | −0.473146 | − | 1.15325i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.0830 | 0.983461 | 0.491731 | − | 0.870747i | \(-0.336365\pi\) | ||||
0.491731 | + | 0.870747i | \(0.336365\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.05426 | + | 0.277495i | 0.180867 | + | 0.0244321i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.775579 | − | 1.34334i | 0.0677627 | − | 0.117368i | −0.830153 | − | 0.557535i | \(-0.811747\pi\) |
0.897916 | + | 0.440167i | \(0.145081\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.6024 | − | 21.8280i | −1.09277 | − | 1.89273i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.15416 | + | 3.12137i | −0.357533 | + | 0.268645i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.40629 | + | 4.16782i | 0.205583 | + | 0.356080i | 0.950318 | − | 0.311280i | \(-0.100758\pi\) |
−0.744735 | + | 0.667360i | \(0.767424\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.7329 | + | 18.5898i | −0.910349 | + | 1.57677i | −0.0967767 | + | 0.995306i | \(0.530853\pi\) |
−0.813572 | + | 0.581464i | \(0.802480\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.5215 | + | 2.23177i | 1.39136 | + | 0.187949i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.70837 | 0.226486 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.78496 | −0.397369 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.46240 | − | 3.56448i | −0.120617 | − | 0.293993i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.39717 | − | 12.8123i | 0.605999 | − | 1.04962i | −0.385893 | − | 0.922543i | \(-0.626107\pi\) |
0.991893 | − | 0.127078i | \(-0.0405600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.490876 | + | 0.850223i | 0.0399469 | + | 0.0691901i | 0.885308 | − | 0.465006i | \(-0.153948\pi\) |
−0.845361 | + | 0.534196i | \(0.820614\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.12176 | − | 8.13754i | −0.171534 | − | 0.657882i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.29408 | − | 7.43756i | −0.344909 | − | 0.597399i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.43077 | − | 5.94226i | 0.273805 | − | 0.474244i | −0.696028 | − | 0.718015i | \(-0.745051\pi\) |
0.969833 | + | 0.243770i | \(0.0783843\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.495564 | − | 0.641344i | 0.0393008 | − | 0.0508619i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.2988 | 1.20571 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.90741 | 0.384378 | 0.192189 | − | 0.981358i | \(-0.438441\pi\) | ||||
0.192189 | + | 0.981358i | \(0.438441\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.58231 | − | 7.22445i | 0.434582 | − | 0.562423i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.73832 | − | 3.01086i | 0.134515 | − | 0.232987i | −0.790897 | − | 0.611949i | \(-0.790386\pi\) |
0.925412 | + | 0.378962i | \(0.123719\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.36800 | + | 11.0297i | 0.489846 | + | 0.848438i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.28138 | + | 24.0909i | 0.480349 | + | 1.84227i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.27114 | − | 9.12989i | −0.400758 | − | 0.694133i | 0.593060 | − | 0.805158i | \(-0.297920\pi\) |
−0.993818 | + | 0.111026i | \(0.964586\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.51859 | − | 2.63027i | 0.114794 | − | 0.198830i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.497893 | − | 1.21357i | −0.0374239 | − | 0.0912177i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.90741 | −0.366797 | −0.183398 | − | 0.983039i | \(-0.558710\pi\) | ||||
−0.183398 | + | 0.983039i | \(0.558710\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.21504 | 0.387631 | 0.193816 | − | 0.981038i | \(-0.437914\pi\) | ||||
0.193816 | + | 0.981038i | \(0.437914\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.465408 | − | 0.0628686i | −0.0344039 | − | 0.00464738i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.29408 | − | 5.70551i | 0.242185 | − | 0.419478i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.38804 | + | 12.7965i | 0.540267 | + | 0.935770i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.90160 | + | 15.6666i | 0.138321 | + | 1.13958i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.8451 | + | 22.2483i | 0.929436 | + | 1.60983i | 0.784267 | + | 0.620424i | \(0.213039\pi\) |
0.145170 | + | 0.989407i | \(0.453627\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.59840 | + | 2.76851i | −0.115055 | + | 0.199282i | −0.917802 | − | 0.397039i | \(-0.870038\pi\) |
0.802747 | + | 0.596320i | \(0.203371\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.881938 | − | 0.119135i | −0.0631569 | − | 0.00853141i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.6808 | 0.974713 | 0.487357 | − | 0.873203i | \(-0.337961\pi\) | ||||
0.487357 | + | 0.873203i | \(0.337961\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.95413 | 0.422077 | 0.211039 | − | 0.977478i | \(-0.432315\pi\) | ||||
0.211039 | + | 0.977478i | \(0.432315\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.77399 | − | 11.6362i | −0.336731 | − | 0.820755i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.26637 | + | 12.5857i | −0.509999 | + | 0.883344i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.99088 | − | 6.91240i | −0.278735 | − | 0.482783i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.5699 | − | 4.00945i | −1.01268 | − | 0.278676i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.8720 | − | 37.8834i | −1.51292 | − | 2.62045i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.29408 | − | 12.6337i | 0.502145 | − | 0.869741i | −0.497852 | − | 0.867262i | \(-0.665878\pi\) |
0.999997 | − | 0.00247872i | \(-0.000789002\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.57392 | − | 2.03692i | 0.107843 | − | 0.139567i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.19680 | 0.0816209 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −26.0837 | −1.77068 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.63088 | + | 7.28732i | −0.380500 | + | 0.492432i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.720159 | − | 1.24735i | 0.0484431 | − | 0.0839060i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.8870 | − | 24.0530i | −0.929943 | − | 1.61071i | −0.783412 | − | 0.621503i | \(-0.786523\pi\) |
−0.146531 | − | 0.989206i | \(-0.546811\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.13557 | + | 2.10697i | −0.142371 | + | 0.140465i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.42053 | + | 11.1207i | 0.426145 | + | 0.738105i | 0.996527 | − | 0.0832747i | \(-0.0265379\pi\) |
−0.570381 | + | 0.821380i | \(0.693205\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.9530 | + | 22.4353i | −0.855959 | + | 1.48256i | 0.0197932 | + | 0.999804i | \(0.493699\pi\) |
−0.875752 | + | 0.482761i | \(0.839634\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.5250 | − | 25.6539i | −0.692497 | − | 1.68790i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.71998 | 0.374729 | 0.187364 | − | 0.982290i | \(-0.440006\pi\) | ||||
0.187364 | + | 0.982290i | \(0.440006\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.62533 | 0.627887 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 27.4007 | + | 3.70137i | 1.77987 | + | 0.240430i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.52336 | − | 9.56674i | 0.357277 | − | 0.618821i | −0.630228 | − | 0.776410i | \(-0.717039\pi\) |
0.987505 | + | 0.157589i | \(0.0503720\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.24309 | − | 10.8134i | −0.402153 | − | 0.696550i | 0.591832 | − | 0.806061i | \(-0.298405\pi\) |
−0.993986 | + | 0.109511i | \(0.965071\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.29486 | − | 15.4186i | 0.147215 | − | 0.989104i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.11221 | − | 1.92640i | −0.0710565 | − | 0.123073i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.13200 | + | 3.69273i | −0.135656 | + | 0.234963i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −20.7088 | − | 2.79740i | −1.31236 | − | 0.177278i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.22442 | −0.519121 | −0.259560 | − | 0.965727i | \(-0.583578\pi\) | ||||
−0.259560 | + | 0.965727i | \(0.583578\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.5517 | 1.66929 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.84291 | − | 4.49194i | −0.115407 | − | 0.281296i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.41584 | + | 14.5767i | −0.524966 | + | 0.909267i | 0.474612 | + | 0.880195i | \(0.342588\pi\) |
−0.999577 | + | 0.0290718i | \(0.990745\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.0047 | − | 17.3286i | −0.621661 | − | 1.07675i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.2186 | − | 10.0818i | 0.632516 | − | 0.624046i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.06011 | + | 10.4964i | 0.373682 | + | 0.647237i | 0.990129 | − | 0.140160i | \(-0.0447617\pi\) |
−0.616447 | + | 0.787397i | \(0.711428\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.233971 | − | 0.405249i | 0.0143727 | − | 0.0248942i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.1533 | + | 20.9051i | −0.988565 | + | 1.27937i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.5859 | −1.37709 | −0.688544 | − | 0.725195i | \(-0.741750\pi\) | ||||
−0.688544 | + | 0.725195i | \(0.741750\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9818 | 0.667094 | 0.333547 | − | 0.942733i | \(-0.391754\pi\) | ||||
0.333547 | + | 0.942733i | \(0.391754\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.65265 | + | 2.13882i | −0.100023 | + | 0.129447i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.63557 | − | 4.56494i | 0.158931 | − | 0.275276i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.3589 | − | 24.8703i | −0.862741 | − | 1.49431i | −0.869273 | − | 0.494333i | \(-0.835412\pi\) |
0.00653148 | − | 0.999979i | \(-0.497921\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24.8411 | + | 6.83594i | 1.48720 | + | 0.409257i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.1545 | + | 21.0522i | 0.725077 | + | 1.25587i | 0.958943 | + | 0.283601i | \(0.0915290\pi\) |
−0.233866 | + | 0.972269i | \(0.575138\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.31224 | − | 12.6652i | 0.434668 | − | 0.752866i | −0.562601 | − | 0.826729i | \(-0.690199\pi\) |
0.997268 | + | 0.0738624i | \(0.0235326\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.45586 | + | 13.2982i | 0.323177 | + | 0.787718i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −24.2420 | −1.43096 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.14206 | −0.537768 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.9231 | − | 1.47553i | −0.640324 | − | 0.0864968i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.84506 | + | 13.5880i | −0.458314 | + | 0.793822i | −0.998872 | − | 0.0474842i | \(-0.984880\pi\) |
0.540558 | + | 0.841306i | \(0.318213\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.378666 | − | 0.655869i | −0.0220468 | − | 0.0381862i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.30031 | + | 27.1901i | 0.191503 | + | 1.57773i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.29408 | − | 2.24141i | −0.0748385 | − | 0.129624i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.81744 | − | 3.14790i | 0.104756 | − | 0.181442i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.56053 | − | 0.480967i | −0.204547 | − | 0.0276309i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.271144 | −0.0155256 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.3920 | 1.50627 | 0.753137 | − | 0.657864i | \(-0.228540\pi\) | ||||
0.753137 | + | 0.657864i | \(0.228540\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.32403 | + | 8.10205i | 0.189097 | + | 0.460910i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.01424 | + | 12.1490i | −0.397741 | + | 0.688908i | −0.993447 | − | 0.114295i | \(-0.963539\pi\) |
0.595706 | + | 0.803203i | \(0.296872\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.2055 | + | 29.8008i | 0.972511 | + | 1.68444i | 0.687914 | + | 0.725792i | \(0.258526\pi\) |
0.284597 | + | 0.958647i | \(0.408140\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.29885 | + | 8.81675i | 0.129526 | + | 0.496768i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.09728 | + | 1.90055i | 0.0616295 | + | 0.106745i | 0.895194 | − | 0.445677i | \(-0.147037\pi\) |
−0.833564 | + | 0.552422i | \(0.813704\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.6111 | + | 21.8431i | −0.706086 | + | 1.22298i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.0746 | + | 18.2149i | −0.785567 | + | 1.01666i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.2631 | −1.29439 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.513812 | −0.0285011 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.83813 | + | 11.4380i | −0.488750 | + | 0.632526i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.6169 | − | 25.3172i | 0.805856 | − | 1.39578i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.44902 | + | 11.1700i | 0.354470 | + | 0.613960i | 0.987027 | − | 0.160554i | \(-0.0513280\pi\) |
−0.632557 | + | 0.774514i | \(0.717995\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.98661 | + | 19.1251i | 0.273265 | + | 1.04805i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.63080 | − | 6.28872i | −0.198372 | − | 0.343590i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.40629 | + | 11.0960i | −0.348973 | + | 0.604439i | −0.986067 | − | 0.166347i | \(-0.946803\pi\) |
0.637094 | + | 0.770786i | \(0.280136\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.35419 | + | 8.17556i | 0.182174 | + | 0.444035i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −45.2694 | −2.45148 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.5043 | 0.783157 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.64611 | − | 1.16794i | −0.465491 | − | 0.0628799i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.09396 | − | 7.09095i | 0.219775 | − | 0.380662i | −0.734964 | − | 0.678106i | \(-0.762801\pi\) |
0.954739 | + | 0.297444i | \(0.0961342\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.67232 | − | 4.62859i | −0.143046 | − | 0.247763i | 0.785596 | − | 0.618739i | \(-0.212356\pi\) |
−0.928642 | + | 0.370977i | \(0.879023\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.13445 | − | 1.60380i | 0.113929 | − | 0.0856044i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.41584 | + | 12.8446i | 0.394705 | + | 0.683650i | 0.993064 | − | 0.117579i | \(-0.0375134\pi\) |
−0.598358 | + | 0.801229i | \(0.704180\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.743094 | − | 1.28708i | 0.0394393 | − | 0.0683110i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.6136 | − | 1.97405i | −0.773435 | − | 0.104478i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.55031 | −0.345712 | −0.172856 | − | 0.984947i | \(-0.555300\pi\) | ||||
−0.172856 | + | 0.984947i | \(0.555300\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 49.8695 | 2.62471 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.0349 | − | 26.8967i | −0.579184 | − | 1.41171i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.65851 | + | 4.60467i | −0.139153 | + | 0.241019i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.0601 | − | 24.3528i | −0.733932 | − | 1.27121i | −0.955190 | − | 0.295992i | \(-0.904350\pi\) |
0.221259 | − | 0.975215i | \(-0.428983\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 23.0870 | + | 6.35326i | 1.20186 | + | 0.330738i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.710609 | − | 1.23081i | −0.0368930 | − | 0.0639005i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.86800 | − | 15.3598i | 0.459168 | − | 0.795302i | −0.539750 | − | 0.841826i | \(-0.681481\pi\) |
0.998917 | + | 0.0465241i | \(0.0148144\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.05903 | + | 1.37057i | −0.0546881 | + | 0.0707758i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.45857 | 0.126623 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.8228 | −0.812763 | −0.406381 | − | 0.913703i | \(-0.633210\pi\) | ||||
−0.406381 | + | 0.913703i | \(0.633210\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.7373 | + | 15.1900i | −0.601320 | + | 0.778210i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.55567 | + | 6.15861i | −0.181686 | + | 0.314690i | −0.942455 | − | 0.334333i | \(-0.891489\pi\) |
0.760769 | + | 0.649023i | \(0.224822\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00469 | − | 13.8645i | −0.407957 | − | 0.706602i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.55585 | + | 2.52162i | −0.129921 | + | 0.128181i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.87380 | − | 4.97757i | −0.145708 | − | 0.252373i | 0.783929 | − | 0.620850i | \(-0.213213\pi\) |
−0.929637 | + | 0.368477i | \(0.879879\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.06011 | − | 12.2285i | 0.357045 | − | 0.618420i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.01978 | + | 2.48563i | 0.0514410 | + | 0.125383i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.9635 | 0.803211 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.35710 | 0.319054 | 0.159527 | − | 0.987194i | \(-0.449003\pi\) | ||||
0.159527 | + | 0.987194i | \(0.449003\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 43.2630 | + | 5.84410i | 2.16586 | + | 0.292571i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.5550 | − | 30.4061i | 0.876654 | − | 1.51841i | 0.0216636 | − | 0.999765i | \(-0.493104\pi\) |
0.854990 | − | 0.518644i | \(-0.173563\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.20635 | + | 3.82151i | 0.109906 | + | 0.190363i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.121334 | − | 8.99918i | 0.00602913 | − | 0.447173i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.3636 | − | 30.0746i | −0.860680 | − | 1.49074i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.4252 | + | 21.5211i | −0.614387 | + | 1.06415i | 0.376104 | + | 0.926577i | \(0.377263\pi\) |
−0.990492 | + | 0.137573i | \(0.956070\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.26060 | − | 1.11587i | −0.407466 | − | 0.0550416i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.30015 | −0.113183 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0648 | −0.592238 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.1122 | − | 34.3973i | −0.691077 | − | 1.68444i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.68767 | − | 2.92314i | 0.0824483 | − | 0.142805i | −0.821853 | − | 0.569700i | \(-0.807059\pi\) |
0.904301 | + | 0.426895i | \(0.140393\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.98175 | + | 3.43250i | 0.0965847 | + | 0.167290i | 0.910269 | − | 0.414018i | \(-0.135875\pi\) |
−0.813684 | + | 0.581307i | \(0.802541\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −20.5556 | + | 20.2803i | −0.999447 | + | 0.986062i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.40160 | − | 2.42764i | −0.0679876 | − | 0.117758i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.411755 | + | 0.713181i | −0.0199262 | + | 0.0345132i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.86825 | + | 3.71201i | −0.138481 | + | 0.179217i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.62516 | −0.367291 | −0.183645 | − | 0.982993i | \(-0.558790\pi\) | ||||
−0.183645 | + | 0.982993i | \(0.558790\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.29024 | −0.350347 | −0.175173 | − | 0.984538i | \(-0.556049\pi\) | ||||
−0.175173 | + | 0.984538i | \(0.556049\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.06742 | − | 6.55810i | 0.242964 | − | 0.314437i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.9012 | + | 36.2019i | −0.999838 | + | 1.73177i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.1952 | + | 31.5151i | 0.868411 | + | 1.50413i | 0.863619 | + | 0.504144i | \(0.168192\pi\) |
0.00479205 | + | 0.999989i | \(0.498475\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.43409 | + | 1.77058i | 0.306385 | + | 0.0843133i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.6869 | − | 30.6346i | −0.840330 | − | 1.45549i | −0.889616 | − | 0.456709i | \(-0.849028\pi\) |
0.0492863 | − | 0.998785i | \(-0.484305\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.62645 | + | 13.2094i | −0.361528 | + | 0.626185i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.72624 | + | 23.7069i | 0.460035 | + | 1.12130i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.9425 | −0.705181 | −0.352591 | − | 0.935778i | \(-0.614699\pi\) | ||||
−0.352591 | + | 0.935778i | \(0.614699\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −42.0730 | −1.98114 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.68514 | − | 0.227634i | −0.0791748 | − | 0.0106952i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.780267 | + | 1.35146i | −0.0365795 | + | 0.0633575i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.39205 | + | 11.0714i | 0.299008 | + | 0.517896i | 0.975909 | − | 0.218177i | \(-0.0700111\pi\) |
−0.676902 | + | 0.736074i | \(0.736678\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.4001 | + | 5.70990i | 0.625461 | + | 0.266515i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.05722 | − | 7.02730i | −0.188963 | − | 0.327294i | 0.755942 | − | 0.654639i | \(-0.227179\pi\) |
−0.944905 | + | 0.327345i | \(0.893846\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.7803 | + | 18.6720i | −0.501002 | + | 0.867760i | 0.498998 | + | 0.866603i | \(0.333702\pi\) |
−0.999999 | + | 0.00115683i | \(0.999632\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14.7412 | + | 1.99129i | 0.683609 | + | 0.0923439i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.8602 | 1.42804 | 0.714019 | − | 0.700127i | \(-0.246873\pi\) | ||||
0.714019 | + | 0.700127i | \(0.246873\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.0547 | −1.01839 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.51098 | + | 10.9951i | 0.207855 | + | 0.506629i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.15425 | − | 5.46331i | 0.145032 | − | 0.251203i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.14938 | + | 7.18694i | 0.190387 | + | 0.329760i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.354187 | + | 1.35841i | 0.0162171 | + | 0.0621972i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.532059 | − | 0.921553i | −0.0243104 | − | 0.0421068i | 0.853614 | − | 0.520906i | \(-0.174406\pi\) |
−0.877925 | + | 0.478799i | \(0.841072\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.69254 | + | 2.93156i | −0.0771730 | + | 0.133668i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.2019 | + | 20.9680i | −0.737211 | + | 0.954076i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.36374 | −0.288962 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.0182 | 1.22431 | 0.612157 | − | 0.790736i | \(-0.290302\pi\) | ||||
0.612157 | + | 0.790736i | \(0.290302\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.19710 | + | 6.72593i | −0.235021 | + | 0.304157i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.11690 | − | 14.0589i | 0.366310 | − | 0.634468i | −0.622675 | − | 0.782481i | \(-0.713954\pi\) |
0.988986 | + | 0.148012i | \(0.0472875\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.70660 | + | 11.6162i | 0.302050 | + | 0.523166i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.98976 | + | 15.3018i | 0.179326 | + | 0.687767i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.25691 | − | 3.90908i | −0.101236 | − | 0.175346i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.3604 | − | 17.9448i | 0.463796 | − | 0.803318i | −0.535350 | − | 0.844630i | \(-0.679820\pi\) |
0.999146 | + | 0.0413119i | \(0.0131537\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.28565 | + | 5.57107i | 0.102115 | + | 0.248897i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.47834 | 0.244267 | 0.122134 | − | 0.992514i | \(-0.461026\pi\) | ||||
0.122134 | + | 0.992514i | \(0.461026\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.07435 | −0.0923072 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.8608 | − | 2.95303i | −0.970874 | − | 0.131149i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.35530 | − | 7.54361i | 0.193045 | − | 0.334365i | −0.753213 | − | 0.657777i | \(-0.771497\pi\) |
0.946258 | + | 0.323413i | \(0.104830\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.07435 | + | 13.9852i | 0.357188 | + | 0.618668i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −39.6703 | − | 16.9039i | −1.75149 | − | 0.746327i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.52805 | + | 4.37871i | 0.111399 | + | 0.192949i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.3683 | − | 43.9391i | 1.11569 | − | 1.93244i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.0954 | + | 2.44438i | 0.794301 | + | 0.107297i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.87041 | −0.125755 | −0.0628774 | − | 0.998021i | \(-0.520028\pi\) | ||||
−0.0628774 | + | 0.998021i | \(0.520028\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.65295 | 0.290913 | 0.145457 | − | 0.989365i | \(-0.453535\pi\) | ||||
0.145457 | + | 0.989365i | \(0.453535\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.99673 | + | 4.86686i | 0.0871444 | + | 0.212407i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.0372 | + | 20.8490i | −0.524347 | + | 0.908197i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.18656 | − | 2.05518i | −0.0515894 | − | 0.0893555i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.19057 | + | 0.602816i | 0.0950625 | + | 0.0261600i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.05056 | + | 3.55167i | 0.0888195 | + | 0.153840i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.64503 | + | 11.5095i | −0.287290 | + | 0.497601i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.19710 | − | 6.72593i | 0.224271 | − | 0.290245i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.7252 | −0.505042 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.79348 | 0.335068 | 0.167534 | − | 0.985866i | \(-0.446420\pi\) | ||||
0.167534 | + | 0.985866i | \(0.446420\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.52290 | + | 7.14757i | −0.237010 | + | 0.306731i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.17274 | + | 7.22741i | −0.178741 | + | 0.309588i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.87901 | − | 10.1827i | −0.251368 | − | 0.435382i | 0.712535 | − | 0.701637i | \(-0.247547\pi\) |
−0.963903 | + | 0.266255i | \(0.914214\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.579047 | − | 0.571292i | 0.0247131 | − | 0.0243822i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.8546 | − | 34.3892i | −0.845835 | − | 1.46503i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.2420 | − | 41.9883i | 1.03087 | − | 1.78552i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.33125 | + | 10.5571i | 0.183851 | + | 0.448123i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.7827 | 0.711107 | 0.355553 | − | 0.934656i | \(-0.384292\pi\) | ||||
0.355553 | + | 0.934656i | \(0.384292\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.614928 | −0.0260087 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25.3626 | − | 3.42605i | −1.07081 | − | 0.144648i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.8743 | + | 22.2990i | −0.542588 | + | 0.939790i | 0.456167 | + | 0.889894i | \(0.349222\pi\) |
−0.998754 | + | 0.0498953i | \(0.984111\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.55098 | + | 4.41844i | 0.107321 | + | 0.185885i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.4860 | − | 13.9852i | −0.986320 | − | 0.587322i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.55654 | + | 4.42805i | 0.107176 | + | 0.185634i | 0.914625 | − | 0.404303i | \(-0.132486\pi\) |
−0.807449 | + | 0.589937i | \(0.799153\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.7329 | − | 22.0539i | 0.532853 | − | 0.922929i | −0.466411 | − | 0.884568i | \(-0.654453\pi\) |
0.999264 | − | 0.0383607i | \(-0.0122136\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −44.0961 | − | 5.95663i | −1.84214 | − | 0.248842i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.03717 | −0.210065 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.7164 | 1.86157 | 0.930783 | − | 0.365571i | \(-0.119126\pi\) | ||||
0.930783 | + | 0.365571i | \(0.119126\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.10167 | − | 5.12265i | −0.0873424 | − | 0.212890i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.3214 | + | 31.7337i | −0.760101 | + | 1.31653i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.23329 | − | 2.13612i | −0.0510777 | − | 0.0884692i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.09728 | − | 1.08259i | 0.0453670 | − | 0.0447595i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.4578 | − | 35.4339i | −0.844383 | − | 1.46251i | −0.886156 | − | 0.463388i | \(-0.846634\pi\) |
0.0417725 | − | 0.999127i | \(-0.486700\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.6356 | − | 61.7226i | 1.46834 | − | 2.54324i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.4883 | + | 18.7504i | −0.595971 | + | 0.771288i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.9729 | −0.491667 | −0.245834 | − | 0.969312i | \(-0.579062\pi\) | ||||
−0.245834 | + | 0.969312i | \(0.579062\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.51381 | −0.349032 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.30561 | + | 8.16053i | −0.258071 | + | 0.333988i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.17855 | − | 12.4336i | 0.293308 | − | 0.508024i | −0.681282 | − | 0.732021i | \(-0.738577\pi\) |
0.974590 | + | 0.223997i | \(0.0719107\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.3210 | − | 38.6611i | −0.910493 | − | 1.57702i | −0.813369 | − | 0.581748i | \(-0.802369\pi\) |
−0.0971239 | − | 0.995272i | \(-0.530964\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.0040 | + | 5.78003i | 0.855349 | + | 0.235381i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.39248 | − | 14.5362i | −0.341203 | − | 0.590980i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.8870 | + | 25.7851i | −0.604245 | + | 1.04658i | 0.387925 | + | 0.921691i | \(0.373192\pi\) |
−0.992170 | + | 0.124892i | \(0.960141\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.55426 | − | 23.2877i | −0.387158 | − | 0.943666i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.94561 | −0.200078 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.4132 | 1.34955 | 0.674773 | − | 0.738025i | \(-0.264241\pi\) | ||||
0.674773 | + | 0.738025i | \(0.264241\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.7004 | + | 1.85069i | 0.552452 | + | 0.0746269i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.2941 | − | 38.6145i | 0.897525 | − | 1.55456i | 0.0668776 | − | 0.997761i | \(-0.478696\pi\) |
0.830648 | − | 0.556798i | \(-0.187970\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.4766 | − | 32.0025i | −0.742638 | − | 1.28629i | −0.951290 | − | 0.308297i | \(-0.900241\pi\) |
0.208652 | − | 0.977990i | \(-0.433092\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.9252 | − | 15.7229i | 0.839700 | − | 0.630938i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.1628 | + | 40.1192i | 0.928000 | + | 1.60734i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 75.0849 | + | 10.1427i | 2.99860 | + | 0.405060i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.4679 | −0.736365 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.10197 | 0.0438687 | 0.0219344 | − | 0.999759i | \(-0.493018\pi\) | ||||
0.0219344 | + | 0.999759i | \(0.493018\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.59069 | + | 23.3765i | 0.381196 | + | 0.929133i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.54152 | + | 9.59820i | −0.219909 | + | 0.380893i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.571466 | + | 0.989809i | 0.0226423 | + | 0.0392177i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.12490 | + | 4.31432i | 0.0445005 | + | 0.170672i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.78453 | + | 11.7511i | 0.267973 | + | 0.464142i | 0.968338 | − | 0.249642i | \(-0.0803129\pi\) |
−0.700365 | + | 0.713784i | \(0.746980\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.86477 | − | 8.42602i | 0.191848 | − | 0.332290i | −0.754015 | − | 0.656857i | \(-0.771885\pi\) |
0.945863 | + | 0.324567i | \(0.105219\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.26745 | + | 1.64029i | −0.0499056 | + | 0.0645864i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.5786 | 1.51668 | 0.758341 | − | 0.651858i | \(-0.226010\pi\) | ||||
0.758341 | + | 0.651858i | \(0.226010\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.99201 | −0.156700 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 27.6235 | − | 35.7495i | 1.08265 | − | 1.40113i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.56522 | + | 14.8354i | −0.335183 | + | 0.580554i | −0.983520 | − | 0.180799i | \(-0.942132\pi\) |
0.648337 | + | 0.761354i | \(0.275465\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.775579 | + | 1.34334i | 0.0303044 | + | 0.0524888i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.02448 | − | 15.4350i | −0.157010 | − | 0.602177i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.8315 | − | 20.4928i | −0.460890 | − | 0.798285i | 0.538116 | − | 0.842871i | \(-0.319136\pi\) |
−0.999006 | + | 0.0445862i | \(0.985803\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.21504 | + | 15.9609i | −0.358424 | + | 0.620808i | −0.987698 | − | 0.156375i | \(-0.950019\pi\) |
0.629274 | + | 0.777184i | \(0.283352\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.946908 | + | 2.30801i | 0.0367749 | + | 0.0896357i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 25.2048 | 0.977400 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.1026 | 0.933258 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 47.6730 | + | 6.43981i | 1.84315 | + | 0.248978i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.714619 | + | 1.23776i | −0.0275875 | + | 0.0477830i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.24821 | + | 14.2863i | 0.317945 | + | 0.550697i | 0.980059 | − | 0.198706i | \(-0.0636739\pi\) |
−0.662114 | + | 0.749403i | \(0.730341\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.626109 | − | 5.15829i | −0.0240989 | − | 0.198543i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.05141 | − | 8.74930i | −0.194141 | − | 0.336263i | 0.752477 | − | 0.658618i | \(-0.228859\pi\) |
−0.946619 | + | 0.322355i | \(0.895525\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.66389 | + | 16.7383i | −0.370866 | + | 0.642359i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.0412 | − | 2.97739i | −0.844619 | − | 0.114094i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.16917 | 0.312585 | 0.156292 | − | 0.987711i | \(-0.450046\pi\) | ||||
0.156292 | + | 0.987711i | \(0.450046\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.81258 | −0.183879 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.0314 | − | 41.5126i | −0.649788 | − | 1.58381i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.120217 | + | 0.208222i | −0.00457989 | + | 0.00793261i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.75733 | − | 3.04379i | −0.0668521 | − | 0.115791i | 0.830662 | − | 0.556777i | \(-0.187962\pi\) |
−0.897514 | + | 0.440986i | \(0.854629\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 46.3068 | + | 12.7430i | 1.75905 | + | 0.484068i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.7329 | − | 18.5898i | −0.407120 | − | 0.705153i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.1872 | + | 19.3769i | −0.423747 | + | 0.733951i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.05764 | + | 7.83962i | −0.229121 | + | 0.296522i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.9897 | 1.28378 | 0.641888 | − | 0.766799i | \(-0.278152\pi\) | ||||
0.641888 | + | 0.766799i | \(0.278152\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 54.6736 | 2.06205 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.1935 | + | 13.1922i | −0.383910 | + | 0.496845i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.15007 | + | 5.45609i | −0.118471 | + | 0.205197i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.99888 | + | 3.46217i | 0.0750696 | + | 0.130024i | 0.901117 | − | 0.433577i | \(-0.142749\pi\) |
−0.826047 | + | 0.563601i | \(0.809415\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −34.0912 | + | 33.6347i | −1.27852 | + | 1.26140i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.6300 | + | 37.4643i | 0.810051 | + | 1.40305i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.35419 | + | 2.34552i | −0.0506437 | + | 0.0877175i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.26245 | + | 17.7016i | 0.271221 | + | 0.661079i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.2142 | 1.23868 | 0.619340 | − | 0.785123i | \(-0.287400\pi\) | ||||
0.619340 | + | 0.785123i | \(0.287400\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3562 | 0.571897 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.4321 | + | 2.89511i | 0.797067 | + | 0.107670i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.39248 | − | 4.14389i | 0.0888544 | − | 0.153900i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.7944 | − | 23.8926i | −0.511607 | − | 0.886129i | −0.999909 | − | 0.0134545i | \(-0.995717\pi\) |
0.488303 | − | 0.872674i | \(-0.337616\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.7019 | + | 19.4740i | 0.692663 | + | 0.721261i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.67743 | − | 2.90540i | −0.0620421 | − | 0.107460i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.85930 | + | 8.41656i | −0.179482 | + | 0.310873i | −0.941703 | − | 0.336444i | \(-0.890776\pi\) |
0.762221 | + | 0.647317i | \(0.224109\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.81813 | + | 0.515764i | 0.140834 | + | 0.0190243i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −38.2769 | −1.40995 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.2355 | −1.33294 | −0.666472 | − | 0.745530i | \(-0.732197\pi\) | ||||
−0.666472 | + | 0.745530i | \(0.732197\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.80328 | − | 6.83277i | −0.102981 | − | 0.251008i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.3407 | − | 17.9106i | 0.379364 | − | 0.657078i | −0.611606 | − | 0.791163i | \(-0.709476\pi\) |
0.990970 | + | 0.134085i | \(0.0428095\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.39717 | + | 12.8123i | 0.271011 | + | 0.469405i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.7652 | − | 25.4202i | 0.942701 | − | 0.930076i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.1821 | + | 34.9565i | 0.737439 | + | 1.27728i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.5374 | − | 25.1796i | 0.530478 | − | 0.918815i | −0.468889 | − | 0.883257i | \(-0.655346\pi\) |
0.999368 | − | 0.0355583i | \(-0.0113209\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.70992 | − | 11.2721i | 0.317407 | − | 0.410779i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.981753 | −0.0357296 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.1202 | −0.803973 | −0.401986 | − | 0.915646i | \(-0.631680\pi\) | ||||
−0.401986 | + | 0.915646i | \(0.631680\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −28.1190 | + | 36.3908i | −1.02066 | + | 1.32090i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.64537 | + | 13.2422i | −0.277145 | + | 0.480029i | −0.970674 | − | 0.240400i | \(-0.922721\pi\) |
0.693529 | + | 0.720428i | \(0.256055\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.6733 | + | 21.9509i | 0.458806 | + | 0.794675i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.10820 | + | 2.23127i | 0.293153 | + | 0.0806719i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.194563 | + | 0.336993i | 0.00702526 | + | 0.0121681i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.9989 | + | 24.2468i | −0.504813 | + | 0.874361i | 0.495172 | + | 0.868795i | \(0.335105\pi\) |
−0.999985 | + | 0.00556608i | \(0.998228\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.0656 | − | 26.9716i | −0.398520 | − | 0.971359i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.4853 | −0.664871 | −0.332436 | − | 0.943126i | \(-0.607870\pi\) | ||||
−0.332436 | + | 0.943126i | \(0.607870\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.58816 | 0.308496 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 34.3453 | + | 4.63947i | 1.23213 | + | 0.166440i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.1194 | − | 57.3644i | 1.18662 | − | 2.05529i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.91696 | − | 6.78437i | −0.140160 | − | 0.242764i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.99590 | + | 24.6822i | 0.107065 | + | 0.882070i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.43077 | + | 5.94226i | 0.122449 | + | 0.212089i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.46308 | − | 7.73028i | 0.159092 | − | 0.275555i | −0.775450 | − | 0.631409i | \(-0.782477\pi\) |
0.934541 | + | 0.355855i | \(0.115810\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.8039 | − | 2.81025i | −0.740638 | − | 0.100048i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.4956 | 0.550959 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.139317 | 0.00494728 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.307638 | + | 0.749843i | 0.0109108 | + | 0.0265942i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.2277 | − | 28.1072i | 0.574816 | − | 0.995610i | −0.421246 | − | 0.906946i | \(-0.638407\pi\) |
0.996062 | − | 0.0886634i | \(-0.0282595\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.4909 | − | 23.3669i | −0.477273 | − | 0.826661i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.5450 | − | 44.2783i | −0.407923 | − | 1.56450i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.0134 | + | 24.2719i | 0.494521 | + | 0.856536i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.64938 | + | 13.2491i | −0.269605 | + | 0.466970i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.9192 | − | 30.9555i | 0.841996 | − | 1.08969i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.4759 | 0.438631 | 0.219315 | − | 0.975654i | \(-0.429618\pi\) | ||||
0.219315 | + | 0.975654i | \(0.429618\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.0632 | 0.564057 | 0.282028 | − | 0.959406i | \(-0.408993\pi\) | ||||
0.282028 | + | 0.959406i | \(0.408993\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.6300 | + | 15.0512i | −0.407883 | + | 0.527869i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.45370 | + | 4.24994i | −0.0859495 | + | 0.148869i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.96597 | + | 8.60131i | 0.173737 | + | 0.300922i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.18118 | − | 4.53015i | −0.0412737 | − | 0.158296i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.8075 | − | 41.2357i | −0.830886 | − | 1.43914i | −0.897337 | − | 0.441347i | \(-0.854501\pi\) |
0.0664509 | − | 0.997790i | \(-0.478832\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.87764 | − | 15.3765i | 0.309455 | − | 0.535992i | −0.668788 | − | 0.743453i | \(-0.733187\pi\) |
0.978243 | + | 0.207461i | \(0.0665201\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.46541 | + | 8.44665i | 0.120650 | + | 0.294074i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.2420 | −0.842976 | −0.421488 | − | 0.906834i | \(-0.638492\pi\) | ||||
−0.421488 | + | 0.906834i | \(0.638492\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.3816 | −1.05520 | −0.527599 | − | 0.849494i | \(-0.676908\pi\) | ||||
−0.527599 | + | 0.849494i | \(0.676908\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 49.2929 | + | 6.65863i | 1.70995 | + | 0.230985i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.11775 | + | 5.40010i | −0.108024 | + | 0.187102i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.73832 | + | 3.01086i | 0.0601570 | + | 0.104195i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −35.6766 | + | 26.8068i | −1.23316 | + | 0.926580i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.32170 | − | 9.21746i | −0.183726 | − | 0.318222i | 0.759421 | − | 0.650600i | \(-0.225482\pi\) |
−0.943146 | + | 0.332378i | \(0.892149\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.05210 | − | 5.28640i | 0.105245 | − | 0.182290i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −41.7254 | − | 5.63640i | −1.43710 | − | 0.194128i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.7360 | −0.438132 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −50.9788 | −1.75165 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.61457 | + | 23.4347i | 0.329971 | + | 0.804278i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.5928 | + | 28.7397i | −0.568795 | + | 0.985183i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.5746 | − | 23.5119i | −0.464785 | − | 0.805032i | 0.534406 | − | 0.845228i | \(-0.320535\pi\) |
−0.999192 | + | 0.0401957i | \(0.987202\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −24.0040 | − | 6.60560i | −0.820919 | − | 0.225907i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.5833 | − | 37.3834i | −0.737271 | − | 1.27699i | −0.953720 | − | 0.300697i | \(-0.902781\pi\) |
0.216448 | − | 0.976294i | \(-0.430553\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.30986 | + | 5.73285i | −0.112931 | + | 0.195602i | −0.916951 | − | 0.399000i | \(-0.869357\pi\) |
0.804020 | + | 0.594603i | \(0.202691\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 25.6730 | − | 33.2252i | 0.874933 | − | 1.13231i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.31055 | −0.180773 | −0.0903866 | − | 0.995907i | \(-0.528810\pi\) | ||||
−0.0903866 | + | 0.995907i | \(0.528810\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.5423 | 0.358449 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.68172 | − | 12.5298i | 0.328809 | − | 0.425534i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 42.0730 | − | 72.8725i | 1.42723 | − | 2.47203i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.86555 | + | 3.23122i | 0.0632116 | + | 0.109486i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.5902 | − | 13.4082i | 0.459959 | − | 0.453799i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.51859 | + | 2.63027i | 0.0513376 | + | 0.0889193i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.06011 | − | 1.83616i | 0.0357973 | − | 0.0620028i | −0.847572 | − | 0.530681i | \(-0.821936\pi\) |
0.883369 | + | 0.468678i | \(0.155270\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.3152 | − | 25.1424i | −0.347922 | − | 0.848030i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.5668 | 0.760296 | 0.380148 | − | 0.924926i | \(-0.375873\pi\) | ||||
0.380148 | + | 0.924926i | \(0.375873\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.5399 | −1.39793 | −0.698964 | − | 0.715157i | \(-0.746355\pi\) | ||||
−0.698964 | + | 0.715157i | \(0.746355\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.29993 | + | 0.175599i | 0.0436967 | + | 0.00590268i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.7248 | + | 37.6285i | −0.729449 | + | 1.26344i | 0.227667 | + | 0.973739i | \(0.426890\pi\) |
−0.957116 | + | 0.289704i | \(0.906443\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.8306 | + | 29.1514i | 0.564479 | + | 0.977706i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40.7610 | − | 24.2719i | −1.36554 | − | 0.813138i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 39.9392 | + | 69.1767i | 1.33651 | + | 2.31491i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.45370 | − | 4.24994i | 0.0820183 | − | 0.142060i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.44247 | + | 0.600102i | 0.148330 | + | 0.0200368i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41.0940 | −1.37056 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.31173 | −0.0437002 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.38968 | + | 5.82465i | 0.0795236 | + | 0.193832i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.60752 | + | 4.51636i | −0.0866770 | + | 0.150129i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.19133 | + | 3.79550i | 0.0727620 | + | 0.126027i | 0.900111 | − | 0.435661i | \(-0.143485\pi\) |
−0.827349 | + | 0.561688i | \(0.810152\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.42992 | − | 4.37059i | 0.146931 | − | 0.144963i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.33594 | + | 12.7062i | 0.243051 | + | 0.420976i | 0.961582 | − | 0.274519i | \(-0.0885186\pi\) |
−0.718531 | + | 0.695495i | \(0.755185\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.7976 | + | 55.0751i | −1.05235 | + | 1.82272i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.287150 | − | 0.371620i | 0.00949287 | − | 0.0122854i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.71114 | 0.155575 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.3233 | 1.23118 | 0.615591 | − | 0.788066i | \(-0.288917\pi\) | ||||
0.615591 | + | 0.788066i | \(0.288917\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.9500 | + | 36.1720i | −0.920984 | + | 1.19191i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.381810 | + | 0.661315i | −0.0125674 | + | 0.0217674i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.29408 | + | 5.70551i | 0.108309 | + | 0.187596i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.6247 | − | 4.02452i | −0.480337 | − | 0.132183i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.66250 | + | 16.7359i | 0.317016 | + | 0.549089i | 0.979864 | − | 0.199666i | \(-0.0639856\pi\) |
−0.662848 | + | 0.748754i | \(0.730652\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.22997 | − | 15.9868i | 0.302500 | − | 0.523946i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.22274 | − | 22.4797i | −0.301939 | − | 0.735951i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.7761 | −0.483230 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.8339 | −0.517271 | −0.258636 | − | 0.965975i | \(-0.583273\pi\) | ||||
−0.258636 | + | 0.965975i | \(0.583273\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −59.0651 | − | 7.97869i | −1.92752 | − | 0.260375i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.17967 | − | 3.77529i | 0.0710551 | − | 0.123071i | −0.828309 | − | 0.560272i | \(-0.810697\pi\) |
0.899364 | + | 0.437201i | \(0.144030\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.1027 | + | 34.8190i | 0.654635 | + | 1.13386i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −14.5185 | − | 6.18648i | −0.472287 | − | 0.201246i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.8158 | + | 34.3220i | 0.643927 | + | 1.11531i | 0.984548 | + | 0.175114i | \(0.0560294\pi\) |
−0.340621 | + | 0.940201i | \(0.610637\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.36597 | − | 2.36593i | 0.0443413 | − | 0.0768014i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.76688 | − | 0.508842i | −0.122150 | − | 0.0165003i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.3922 | −1.24365 | −0.621823 | − | 0.783158i | \(-0.713608\pi\) | ||||
−0.621823 | + | 0.783158i | \(0.713608\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.6901 | −0.831313 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.5818 | − | 40.4168i | −0.536014 | − | 1.30649i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.30832 | + | 12.6584i | −0.235998 | + | 0.408760i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.3782 | − | 37.0282i | −0.689620 | − | 1.19446i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.0593 | − | 38.5803i | −0.324157 | − | 1.24323i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.59840 | − | 2.76851i | −0.0514543 | − | 0.0891214i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.1628 | + | 45.3154i | −0.841340 | + | 1.45724i | 0.0474216 | + | 0.998875i | \(0.484900\pi\) |
−0.888762 | + | 0.458369i | \(0.848434\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 24.6364 | − | 31.8837i | 0.791434 | − | 1.02425i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.4831 | 1.45962 | 0.729811 | − | 0.683649i | \(-0.239608\pi\) | ||||
0.729811 | + | 0.683649i | \(0.239608\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −65.1951 | −2.09006 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.544142 | − | 0.704213i | 0.0174265 | − | 0.0225529i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.01756 | + | 1.76246i | −0.0325545 | + | 0.0563861i | −0.881844 | − | 0.471542i | \(-0.843698\pi\) |
0.849289 | + | 0.527928i | \(0.177031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40.2001 | + | 69.6286i | 1.28480 | + | 2.22534i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.31675 | − | 24.2265i | −0.201678 | − | 0.773493i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.7065 | + | 22.0083i | 0.405275 | + | 0.701957i | 0.994353 | − | 0.106119i | \(-0.0338425\pi\) |
−0.589079 | + | 0.808076i | \(0.700509\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.84038 | + | 11.8479i | −0.217952 | + | 0.377505i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19.2192 | + | 46.8451i | 0.611753 | + | 1.49110i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.02848 | −0.191694 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.259533 | 0.00824435 | 0.00412218 | − | 0.999992i | \(-0.498688\pi\) | ||||
0.00412218 | + | 0.999992i | \(0.498688\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22.1390 | − | 2.99060i | −0.702559 | − | 0.0949037i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.97706 | + | 5.15643i | −0.0943793 | + | 0.163470i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.4570 | + | 42.3608i | 0.774561 | + | 1.34158i | 0.935041 | + | 0.354540i | \(0.115363\pi\) |
−0.160479 | + | 0.987039i | \(0.551304\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −31.4932 | − | 13.4196i | −0.996399 | − | 0.424576i |
(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 | 720.2.q.l.481.2 | 8 | ||
3.2 | odd | 2 | 2160.2.q.l.1441.4 | 8 | |||
4.3 | odd | 2 | 360.2.q.e.121.3 | ✓ | 8 | ||
9.2 | odd | 6 | 2160.2.q.l.721.4 | 8 | |||
9.4 | even | 3 | 6480.2.a.cb.1.1 | 4 | |||
9.5 | odd | 6 | 6480.2.a.bz.1.1 | 4 | |||
9.7 | even | 3 | inner | 720.2.q.l.241.2 | 8 | ||
12.11 | even | 2 | 1080.2.q.e.361.1 | 8 | |||
36.7 | odd | 6 | 360.2.q.e.241.3 | yes | 8 | ||
36.11 | even | 6 | 1080.2.q.e.721.1 | 8 | |||
36.23 | even | 6 | 3240.2.a.s.1.4 | 4 | |||
36.31 | odd | 6 | 3240.2.a.u.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.q.e.121.3 | ✓ | 8 | 4.3 | odd | 2 | ||
360.2.q.e.241.3 | yes | 8 | 36.7 | odd | 6 | ||
720.2.q.l.241.2 | 8 | 9.7 | even | 3 | inner | ||
720.2.q.l.481.2 | 8 | 1.1 | even | 1 | trivial | ||
1080.2.q.e.361.1 | 8 | 12.11 | even | 2 | |||
1080.2.q.e.721.1 | 8 | 36.11 | even | 6 | |||
2160.2.q.l.721.4 | 8 | 9.2 | odd | 6 | |||
2160.2.q.l.1441.4 | 8 | 3.2 | odd | 2 | |||
3240.2.a.s.1.4 | 4 | 36.23 | even | 6 | |||
3240.2.a.u.1.4 | 4 | 36.31 | odd | 6 | |||
6480.2.a.bz.1.1 | 4 | 9.5 | odd | 6 | |||
6480.2.a.cb.1.1 | 4 | 9.4 | even | 3 |