Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(569,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.569");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.c (of order \(2\), degree \(1\), 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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 569.1 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.569 |
Dual form | 570.2.c.d.569.5 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | −1.73205 | −1.00000 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.41421 | − | 1.73205i | −0.632456 | − | 0.774597i | ||||
\(6\) | 1.73205i | 0.707107i | ||||||||
\(7\) | − | 2.44949i | − | 0.925820i | −0.886405 | − | 0.462910i | \(-0.846805\pi\) | ||
0.886405 | − | 0.462910i | \(-0.153195\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | −1.73205 | + | 1.41421i | −0.547723 | + | 0.447214i | ||||
\(11\) | − | 3.46410i | − | 1.04447i | −0.852803 | − | 0.522233i | \(-0.825099\pi\) | ||
0.852803 | − | 0.522233i | \(-0.174901\pi\) | |||||||
\(12\) | 1.73205 | 0.500000 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | −2.44949 | −0.654654 | ||||||||
\(15\) | 2.44949 | + | 3.00000i | 0.632456 | + | 0.774597i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.07107 | −1.71499 | −0.857493 | − | 0.514496i | \(-0.827979\pi\) | ||||
−0.857493 | + | 0.514496i | \(0.827979\pi\) | |||||||
\(18\) | − | 3.00000i | − | 0.707107i | ||||||
\(19\) | −1.00000 | + | 4.24264i | −0.229416 | + | 0.973329i | ||||
\(20\) | 1.41421 | + | 1.73205i | 0.316228 | + | 0.387298i | ||||
\(21\) | 4.24264i | 0.925820i | ||||||||
\(22\) | −3.46410 | −0.738549 | ||||||||
\(23\) | 5.65685 | 1.17954 | 0.589768 | − | 0.807573i | \(-0.299219\pi\) | ||||
0.589768 | + | 0.807573i | \(0.299219\pi\) | |||||||
\(24\) | − | 1.73205i | − | 0.353553i | ||||||
\(25\) | −1.00000 | + | 4.89898i | −0.200000 | + | 0.979796i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 2.44949i | 0.462910i | ||||||||
\(29\) | −4.89898 | −0.909718 | −0.454859 | − | 0.890564i | \(-0.650310\pi\) | ||||
−0.454859 | + | 0.890564i | \(0.650310\pi\) | |||||||
\(30\) | 3.00000 | − | 2.44949i | 0.547723 | − | 0.447214i | ||||
\(31\) | 4.24264i | 0.762001i | 0.924575 | + | 0.381000i | \(0.124420\pi\) | ||||
−0.924575 | + | 0.381000i | \(0.875580\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 6.00000i | 1.04447i | ||||||||
\(34\) | 7.07107i | 1.21268i | ||||||||
\(35\) | −4.24264 | + | 3.46410i | −0.717137 | + | 0.585540i | ||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | −6.92820 | −1.13899 | −0.569495 | − | 0.821995i | \(-0.692861\pi\) | ||||
−0.569495 | + | 0.821995i | \(0.692861\pi\) | |||||||
\(38\) | 4.24264 | + | 1.00000i | 0.688247 | + | 0.162221i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.73205 | − | 1.41421i | 0.273861 | − | 0.223607i | ||||
\(41\) | 2.44949 | 0.382546 | 0.191273 | − | 0.981537i | \(-0.438738\pi\) | ||||
0.191273 | + | 0.981537i | \(0.438738\pi\) | |||||||
\(42\) | 4.24264 | 0.654654 | ||||||||
\(43\) | 9.79796i | 1.49417i | 0.664726 | + | 0.747087i | \(0.268548\pi\) | ||||
−0.664726 | + | 0.747087i | \(0.731452\pi\) | |||||||
\(44\) | 3.46410i | 0.522233i | ||||||||
\(45\) | −4.24264 | − | 5.19615i | −0.632456 | − | 0.774597i | ||||
\(46\) | − | 5.65685i | − | 0.834058i | ||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | −1.73205 | −0.250000 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.89898 | + | 1.00000i | 0.692820 | + | 0.141421i | ||||
\(51\) | 12.2474 | 1.71499 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 12.0000i | − | 1.64833i | −0.566352 | − | 0.824163i | \(-0.691646\pi\) | ||
0.566352 | − | 0.824163i | \(-0.308354\pi\) | |||||||
\(54\) | 5.19615i | 0.707107i | ||||||||
\(55\) | −6.00000 | + | 4.89898i | −0.809040 | + | 0.660578i | ||||
\(56\) | 2.44949 | 0.327327 | ||||||||
\(57\) | 1.73205 | − | 7.34847i | 0.229416 | − | 0.973329i | ||||
\(58\) | 4.89898i | 0.643268i | ||||||||
\(59\) | −7.34847 | −0.956689 | −0.478345 | − | 0.878172i | \(-0.658763\pi\) | ||||
−0.478345 | + | 0.878172i | \(0.658763\pi\) | |||||||
\(60\) | −2.44949 | − | 3.00000i | −0.316228 | − | 0.387298i | ||||
\(61\) | −10.0000 | −1.28037 | −0.640184 | − | 0.768221i | \(-0.721142\pi\) | ||||
−0.640184 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(62\) | 4.24264 | 0.538816 | ||||||||
\(63\) | − | 7.34847i | − | 0.925820i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.00000 | 0.738549 | ||||||||
\(67\) | 13.8564 | 1.69283 | 0.846415 | − | 0.532524i | \(-0.178756\pi\) | ||||
0.846415 | + | 0.532524i | \(0.178756\pi\) | |||||||
\(68\) | 7.07107 | 0.857493 | ||||||||
\(69\) | −9.79796 | −1.17954 | ||||||||
\(70\) | 3.46410 | + | 4.24264i | 0.414039 | + | 0.507093i | ||||
\(71\) | −4.89898 | −0.581402 | −0.290701 | − | 0.956814i | \(-0.593888\pi\) | ||||
−0.290701 | + | 0.956814i | \(0.593888\pi\) | |||||||
\(72\) | 3.00000i | 0.353553i | ||||||||
\(73\) | − | 9.79796i | − | 1.14676i | −0.819288 | − | 0.573382i | \(-0.805631\pi\) | ||
0.819288 | − | 0.573382i | \(-0.194369\pi\) | |||||||
\(74\) | 6.92820i | 0.805387i | ||||||||
\(75\) | 1.73205 | − | 8.48528i | 0.200000 | − | 0.979796i | ||||
\(76\) | 1.00000 | − | 4.24264i | 0.114708 | − | 0.486664i | ||||
\(77\) | −8.48528 | −0.966988 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.24264i | − | 0.477334i | −0.971101 | − | 0.238667i | \(-0.923290\pi\) | ||
0.971101 | − | 0.238667i | \(-0.0767105\pi\) | |||||||
\(80\) | −1.41421 | − | 1.73205i | −0.158114 | − | 0.193649i | ||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | − | 2.44949i | − | 0.270501i | ||||||
\(83\) | −1.41421 | −0.155230 | −0.0776151 | − | 0.996983i | \(-0.524731\pi\) | ||||
−0.0776151 | + | 0.996983i | \(0.524731\pi\) | |||||||
\(84\) | − | 4.24264i | − | 0.462910i | ||||||
\(85\) | 10.0000 | + | 12.2474i | 1.08465 | + | 1.32842i | ||||
\(86\) | 9.79796 | 1.05654 | ||||||||
\(87\) | 8.48528 | 0.909718 | ||||||||
\(88\) | 3.46410 | 0.369274 | ||||||||
\(89\) | −12.2474 | −1.29823 | −0.649113 | − | 0.760692i | \(-0.724860\pi\) | ||||
−0.649113 | + | 0.760692i | \(0.724860\pi\) | |||||||
\(90\) | −5.19615 | + | 4.24264i | −0.547723 | + | 0.447214i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.65685 | −0.589768 | ||||||||
\(93\) | − | 7.34847i | − | 0.762001i | ||||||
\(94\) | − | 2.82843i | − | 0.291730i | ||||||
\(95\) | 8.76268 | − | 4.26795i | 0.899032 | − | 0.437882i | ||||
\(96\) | 1.73205i | 0.176777i | ||||||||
\(97\) | 3.46410 | 0.351726 | 0.175863 | − | 0.984415i | \(-0.443728\pi\) | ||||
0.175863 | + | 0.984415i | \(0.443728\pi\) | |||||||
\(98\) | − | 1.00000i | − | 0.101015i | ||||||
\(99\) | − | 10.3923i | − | 1.04447i | ||||||
\(100\) | 1.00000 | − | 4.89898i | 0.100000 | − | 0.489898i | ||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | − | 12.2474i | − | 1.21268i | ||||||
\(103\) | −3.46410 | −0.341328 | −0.170664 | − | 0.985329i | \(-0.554591\pi\) | ||||
−0.170664 | + | 0.985329i | \(0.554591\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.34847 | − | 6.00000i | 0.717137 | − | 0.585540i | ||||
\(106\) | −12.0000 | −1.16554 | ||||||||
\(107\) | 12.0000i | 1.16008i | 0.814587 | + | 0.580042i | \(0.196964\pi\) | ||||
−0.814587 | + | 0.580042i | \(0.803036\pi\) | |||||||
\(108\) | 5.19615 | 0.500000 | ||||||||
\(109\) | − | 12.7279i | − | 1.21911i | −0.792742 | − | 0.609557i | \(-0.791347\pi\) | ||
0.792742 | − | 0.609557i | \(-0.208653\pi\) | |||||||
\(110\) | 4.89898 | + | 6.00000i | 0.467099 | + | 0.572078i | ||||
\(111\) | 12.0000 | 1.13899 | ||||||||
\(112\) | − | 2.44949i | − | 0.231455i | ||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | −7.34847 | − | 1.73205i | −0.688247 | − | 0.162221i | ||||
\(115\) | −8.00000 | − | 9.79796i | −0.746004 | − | 0.913664i | ||||
\(116\) | 4.89898 | 0.454859 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.34847i | 0.676481i | ||||||||
\(119\) | 17.3205i | 1.58777i | ||||||||
\(120\) | −3.00000 | + | 2.44949i | −0.273861 | + | 0.223607i | ||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 10.0000i | 0.905357i | ||||||||
\(123\) | −4.24264 | −0.382546 | ||||||||
\(124\) | − | 4.24264i | − | 0.381000i | ||||||
\(125\) | 9.89949 | − | 5.19615i | 0.885438 | − | 0.464758i | ||||
\(126\) | −7.34847 | −0.654654 | ||||||||
\(127\) | −3.46410 | −0.307389 | −0.153695 | − | 0.988118i | \(-0.549117\pi\) | ||||
−0.153695 | + | 0.988118i | \(0.549117\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | − | 16.9706i | − | 1.49417i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 3.46410i | − | 0.302660i | −0.988483 | − | 0.151330i | \(-0.951644\pi\) | ||
0.988483 | − | 0.151330i | \(-0.0483556\pi\) | |||||||
\(132\) | − | 6.00000i | − | 0.522233i | ||||||
\(133\) | 10.3923 | + | 2.44949i | 0.901127 | + | 0.212398i | ||||
\(134\) | − | 13.8564i | − | 1.19701i | ||||||
\(135\) | 7.34847 | + | 9.00000i | 0.632456 | + | 0.774597i | ||||
\(136\) | − | 7.07107i | − | 0.606339i | ||||||
\(137\) | −7.07107 | −0.604122 | −0.302061 | − | 0.953289i | \(-0.597675\pi\) | ||||
−0.302061 | + | 0.953289i | \(0.597675\pi\) | |||||||
\(138\) | 9.79796i | 0.834058i | ||||||||
\(139\) | −10.0000 | −0.848189 | −0.424094 | − | 0.905618i | \(-0.639408\pi\) | ||||
−0.424094 | + | 0.905618i | \(0.639408\pi\) | |||||||
\(140\) | 4.24264 | − | 3.46410i | 0.358569 | − | 0.292770i | ||||
\(141\) | −4.89898 | −0.412568 | ||||||||
\(142\) | 4.89898i | 0.411113i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 6.92820 | + | 8.48528i | 0.575356 | + | 0.704664i | ||||
\(146\) | −9.79796 | −0.810885 | ||||||||
\(147\) | −1.73205 | −0.142857 | ||||||||
\(148\) | 6.92820 | 0.569495 | ||||||||
\(149\) | − | 13.8564i | − | 1.13516i | −0.823318 | − | 0.567581i | \(-0.807880\pi\) | ||
0.823318 | − | 0.567581i | \(-0.192120\pi\) | |||||||
\(150\) | −8.48528 | − | 1.73205i | −0.692820 | − | 0.141421i | ||||
\(151\) | − | 12.7279i | − | 1.03578i | −0.855446 | − | 0.517892i | \(-0.826717\pi\) | ||
0.855446 | − | 0.517892i | \(-0.173283\pi\) | |||||||
\(152\) | −4.24264 | − | 1.00000i | −0.344124 | − | 0.0811107i | ||||
\(153\) | −21.2132 | −1.71499 | ||||||||
\(154\) | 8.48528i | 0.683763i | ||||||||
\(155\) | 7.34847 | − | 6.00000i | 0.590243 | − | 0.481932i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.34847i | 0.586472i | 0.956040 | + | 0.293236i | \(0.0947321\pi\) | ||||
−0.956040 | + | 0.293236i | \(0.905268\pi\) | |||||||
\(158\) | −4.24264 | −0.337526 | ||||||||
\(159\) | 20.7846i | 1.64833i | ||||||||
\(160\) | −1.73205 | + | 1.41421i | −0.136931 | + | 0.111803i | ||||
\(161\) | − | 13.8564i | − | 1.09204i | ||||||
\(162\) | − | 9.00000i | − | 0.707107i | ||||||
\(163\) | − | 14.6969i | − | 1.15115i | −0.817748 | − | 0.575577i | \(-0.804778\pi\) | ||
0.817748 | − | 0.575577i | \(-0.195222\pi\) | |||||||
\(164\) | −2.44949 | −0.191273 | ||||||||
\(165\) | 10.3923 | − | 8.48528i | 0.809040 | − | 0.660578i | ||||
\(166\) | 1.41421i | 0.109764i | ||||||||
\(167\) | − | 18.0000i | − | 1.39288i | −0.717614 | − | 0.696441i | \(-0.754766\pi\) | ||
0.717614 | − | 0.696441i | \(-0.245234\pi\) | |||||||
\(168\) | −4.24264 | −0.327327 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 12.2474 | − | 10.0000i | 0.939336 | − | 0.766965i | ||||
\(171\) | −3.00000 | + | 12.7279i | −0.229416 | + | 0.973329i | ||||
\(172\) | − | 9.79796i | − | 0.747087i | ||||||
\(173\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(174\) | − | 8.48528i | − | 0.643268i | ||||||
\(175\) | 12.0000 | + | 2.44949i | 0.907115 | + | 0.185164i | ||||
\(176\) | − | 3.46410i | − | 0.261116i | ||||||
\(177\) | 12.7279 | 0.956689 | ||||||||
\(178\) | 12.2474i | 0.917985i | ||||||||
\(179\) | −17.1464 | −1.28158 | −0.640792 | − | 0.767714i | \(-0.721394\pi\) | ||||
−0.640792 | + | 0.767714i | \(0.721394\pi\) | |||||||
\(180\) | 4.24264 | + | 5.19615i | 0.316228 | + | 0.387298i | ||||
\(181\) | 12.7279i | 0.946059i | 0.881047 | + | 0.473029i | \(0.156840\pi\) | ||||
−0.881047 | + | 0.473029i | \(0.843160\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.3205 | 1.28037 | ||||||||
\(184\) | 5.65685i | 0.417029i | ||||||||
\(185\) | 9.79796 | + | 12.0000i | 0.720360 | + | 0.882258i | ||||
\(186\) | −7.34847 | −0.538816 | ||||||||
\(187\) | 24.4949i | 1.79124i | ||||||||
\(188\) | −2.82843 | −0.206284 | ||||||||
\(189\) | 12.7279i | 0.925820i | ||||||||
\(190\) | −4.26795 | − | 8.76268i | −0.309630 | − | 0.635712i | ||||
\(191\) | 17.3205i | 1.25327i | 0.779314 | + | 0.626634i | \(0.215568\pi\) | ||||
−0.779314 | + | 0.626634i | \(0.784432\pi\) | |||||||
\(192\) | 1.73205 | 0.125000 | ||||||||
\(193\) | −20.7846 | −1.49611 | −0.748054 | − | 0.663637i | \(-0.769012\pi\) | ||||
−0.748054 | + | 0.663637i | \(0.769012\pi\) | |||||||
\(194\) | − | 3.46410i | − | 0.248708i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | −5.65685 | −0.403034 | −0.201517 | − | 0.979485i | \(-0.564587\pi\) | ||||
−0.201517 | + | 0.979485i | \(0.564587\pi\) | |||||||
\(198\) | −10.3923 | −0.738549 | ||||||||
\(199\) | 20.0000 | 1.41776 | 0.708881 | − | 0.705328i | \(-0.249200\pi\) | ||||
0.708881 | + | 0.705328i | \(0.249200\pi\) | |||||||
\(200\) | −4.89898 | − | 1.00000i | −0.346410 | − | 0.0707107i | ||||
\(201\) | −24.0000 | −1.69283 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.0000i | 0.842235i | ||||||||
\(204\) | −12.2474 | −0.857493 | ||||||||
\(205\) | −3.46410 | − | 4.24264i | −0.241943 | − | 0.296319i | ||||
\(206\) | 3.46410i | 0.241355i | ||||||||
\(207\) | 16.9706 | 1.17954 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.6969 | + | 3.46410i | 1.01661 | + | 0.239617i | ||||
\(210\) | −6.00000 | − | 7.34847i | −0.414039 | − | 0.507093i | ||||
\(211\) | − | 25.4558i | − | 1.75245i | −0.481900 | − | 0.876226i | \(-0.660053\pi\) | ||
0.481900 | − | 0.876226i | \(-0.339947\pi\) | |||||||
\(212\) | 12.0000i | 0.824163i | ||||||||
\(213\) | 8.48528 | 0.581402 | ||||||||
\(214\) | 12.0000 | 0.820303 | ||||||||
\(215\) | 16.9706 | − | 13.8564i | 1.15738 | − | 0.944999i | ||||
\(216\) | − | 5.19615i | − | 0.353553i | ||||||
\(217\) | 10.3923 | 0.705476 | ||||||||
\(218\) | −12.7279 | −0.862044 | ||||||||
\(219\) | 16.9706i | 1.14676i | ||||||||
\(220\) | 6.00000 | − | 4.89898i | 0.404520 | − | 0.330289i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | − | 12.0000i | − | 0.805387i | ||||||
\(223\) | −3.46410 | −0.231973 | −0.115987 | − | 0.993251i | \(-0.537003\pi\) | ||||
−0.115987 | + | 0.993251i | \(0.537003\pi\) | |||||||
\(224\) | −2.44949 | −0.163663 | ||||||||
\(225\) | −3.00000 | + | 14.6969i | −0.200000 | + | 0.979796i | ||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | − | 12.0000i | − | 0.796468i | −0.917284 | − | 0.398234i | \(-0.869623\pi\) | ||
0.917284 | − | 0.398234i | \(-0.130377\pi\) | |||||||
\(228\) | −1.73205 | + | 7.34847i | −0.114708 | + | 0.486664i | ||||
\(229\) | −22.0000 | −1.45380 | −0.726900 | − | 0.686743i | \(-0.759040\pi\) | ||||
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | −9.79796 | + | 8.00000i | −0.646058 | + | 0.527504i | ||||
\(231\) | 14.6969 | 0.966988 | ||||||||
\(232\) | − | 4.89898i | − | 0.321634i | ||||||
\(233\) | −7.07107 | −0.463241 | −0.231621 | − | 0.972806i | \(-0.574403\pi\) | ||||
−0.231621 | + | 0.972806i | \(0.574403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | − | 4.89898i | −0.260931 | − | 0.319574i | ||||
\(236\) | 7.34847 | 0.478345 | ||||||||
\(237\) | 7.34847i | 0.477334i | ||||||||
\(238\) | 17.3205 | 1.12272 | ||||||||
\(239\) | 6.92820i | 0.448148i | 0.974572 | + | 0.224074i | \(0.0719358\pi\) | ||||
−0.974572 | + | 0.224074i | \(0.928064\pi\) | |||||||
\(240\) | 2.44949 | + | 3.00000i | 0.158114 | + | 0.193649i | ||||
\(241\) | 8.48528i | 0.546585i | 0.961931 | + | 0.273293i | \(0.0881127\pi\) | ||||
−0.961931 | + | 0.273293i | \(0.911887\pi\) | |||||||
\(242\) | 1.00000i | 0.0642824i | ||||||||
\(243\) | −15.5885 | −1.00000 | ||||||||
\(244\) | 10.0000 | 0.640184 | ||||||||
\(245\) | −1.41421 | − | 1.73205i | −0.0903508 | − | 0.110657i | ||||
\(246\) | 4.24264i | 0.270501i | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −4.24264 | −0.269408 | ||||||||
\(249\) | 2.44949 | 0.155230 | ||||||||
\(250\) | −5.19615 | − | 9.89949i | −0.328634 | − | 0.626099i | ||||
\(251\) | 24.2487i | 1.53057i | 0.643695 | + | 0.765283i | \(0.277401\pi\) | ||||
−0.643695 | + | 0.765283i | \(0.722599\pi\) | |||||||
\(252\) | 7.34847i | 0.462910i | ||||||||
\(253\) | − | 19.5959i | − | 1.23198i | ||||||
\(254\) | 3.46410i | 0.217357i | ||||||||
\(255\) | −17.3205 | − | 21.2132i | −1.08465 | − | 1.32842i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.00000i | 0.374270i | 0.982334 | + | 0.187135i | \(0.0599201\pi\) | ||||
−0.982334 | + | 0.187135i | \(0.940080\pi\) | |||||||
\(258\) | −16.9706 | −1.05654 | ||||||||
\(259\) | 16.9706i | 1.05450i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.6969 | −0.909718 | ||||||||
\(262\) | −3.46410 | −0.214013 | ||||||||
\(263\) | 28.2843 | 1.74408 | 0.872041 | − | 0.489432i | \(-0.162796\pi\) | ||||
0.872041 | + | 0.489432i | \(0.162796\pi\) | |||||||
\(264\) | −6.00000 | −0.369274 | ||||||||
\(265\) | −20.7846 | + | 16.9706i | −1.27679 | + | 1.04249i | ||||
\(266\) | 2.44949 | − | 10.3923i | 0.150188 | − | 0.637193i | ||||
\(267\) | 21.2132 | 1.29823 | ||||||||
\(268\) | −13.8564 | −0.846415 | ||||||||
\(269\) | −19.5959 | −1.19478 | −0.597392 | − | 0.801949i | \(-0.703796\pi\) | ||||
−0.597392 | + | 0.801949i | \(0.703796\pi\) | |||||||
\(270\) | 9.00000 | − | 7.34847i | 0.547723 | − | 0.447214i | ||||
\(271\) | 28.0000 | 1.70088 | 0.850439 | − | 0.526073i | \(-0.176336\pi\) | ||||
0.850439 | + | 0.526073i | \(0.176336\pi\) | |||||||
\(272\) | −7.07107 | −0.428746 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.07107i | 0.427179i | ||||||||
\(275\) | 16.9706 | + | 3.46410i | 1.02336 | + | 0.208893i | ||||
\(276\) | 9.79796 | 0.589768 | ||||||||
\(277\) | − | 12.2474i | − | 0.735878i | −0.929850 | − | 0.367939i | \(-0.880064\pi\) | ||
0.929850 | − | 0.367939i | \(-0.119936\pi\) | |||||||
\(278\) | 10.0000i | 0.599760i | ||||||||
\(279\) | 12.7279i | 0.762001i | ||||||||
\(280\) | −3.46410 | − | 4.24264i | −0.207020 | − | 0.253546i | ||||
\(281\) | 31.8434 | 1.89962 | 0.949808 | − | 0.312833i | \(-0.101278\pi\) | ||||
0.949808 | + | 0.312833i | \(0.101278\pi\) | |||||||
\(282\) | 4.89898i | 0.291730i | ||||||||
\(283\) | − | 24.4949i | − | 1.45607i | −0.685540 | − | 0.728035i | \(-0.740434\pi\) | ||
0.685540 | − | 0.728035i | \(-0.259566\pi\) | |||||||
\(284\) | 4.89898 | 0.290701 | ||||||||
\(285\) | −15.1774 | + | 7.39230i | −0.899032 | + | 0.437882i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 6.00000i | − | 0.354169i | ||||||
\(288\) | − | 3.00000i | − | 0.176777i | ||||||
\(289\) | 33.0000 | 1.94118 | ||||||||
\(290\) | 8.48528 | − | 6.92820i | 0.498273 | − | 0.406838i | ||||
\(291\) | −6.00000 | −0.351726 | ||||||||
\(292\) | 9.79796i | 0.573382i | ||||||||
\(293\) | 6.00000i | 0.350524i | 0.984522 | + | 0.175262i | \(0.0560772\pi\) | ||||
−0.984522 | + | 0.175262i | \(0.943923\pi\) | |||||||
\(294\) | 1.73205i | 0.101015i | ||||||||
\(295\) | 10.3923 | + | 12.7279i | 0.605063 | + | 0.741048i | ||||
\(296\) | − | 6.92820i | − | 0.402694i | ||||||
\(297\) | 18.0000i | 1.04447i | ||||||||
\(298\) | −13.8564 | −0.802680 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.73205 | + | 8.48528i | −0.100000 | + | 0.489898i | ||||
\(301\) | 24.0000 | 1.38334 | ||||||||
\(302\) | −12.7279 | −0.732410 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | + | 4.24264i | −0.0573539 | + | 0.243332i | ||||
\(305\) | 14.1421 | + | 17.3205i | 0.809776 | + | 0.991769i | ||||
\(306\) | 21.2132i | 1.21268i | ||||||||
\(307\) | −6.92820 | −0.395413 | −0.197707 | − | 0.980261i | \(-0.563349\pi\) | ||||
−0.197707 | + | 0.980261i | \(0.563349\pi\) | |||||||
\(308\) | 8.48528 | 0.483494 | ||||||||
\(309\) | 6.00000 | 0.341328 | ||||||||
\(310\) | −6.00000 | − | 7.34847i | −0.340777 | − | 0.417365i | ||||
\(311\) | 3.46410i | 0.196431i | 0.995165 | + | 0.0982156i | \(0.0313135\pi\) | ||||
−0.995165 | + | 0.0982156i | \(0.968687\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.6969i | 0.830720i | 0.909657 | + | 0.415360i | \(0.136344\pi\) | ||||
−0.909657 | + | 0.415360i | \(0.863656\pi\) | |||||||
\(314\) | 7.34847 | 0.414698 | ||||||||
\(315\) | −12.7279 | + | 10.3923i | −0.717137 | + | 0.585540i | ||||
\(316\) | 4.24264i | 0.238667i | ||||||||
\(317\) | 6.00000i | 0.336994i | 0.985702 | + | 0.168497i | \(0.0538913\pi\) | ||||
−0.985702 | + | 0.168497i | \(0.946109\pi\) | |||||||
\(318\) | 20.7846 | 1.16554 | ||||||||
\(319\) | 16.9706i | 0.950169i | ||||||||
\(320\) | 1.41421 | + | 1.73205i | 0.0790569 | + | 0.0968246i | ||||
\(321\) | − | 20.7846i | − | 1.16008i | ||||||
\(322\) | −13.8564 | −0.772187 | ||||||||
\(323\) | 7.07107 | − | 30.0000i | 0.393445 | − | 1.66924i | ||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14.6969 | −0.813988 | ||||||||
\(327\) | 22.0454i | 1.21911i | ||||||||
\(328\) | 2.44949i | 0.135250i | ||||||||
\(329\) | − | 6.92820i | − | 0.381964i | ||||||
\(330\) | −8.48528 | − | 10.3923i | −0.467099 | − | 0.572078i | ||||
\(331\) | 8.48528i | 0.466393i | 0.972430 | + | 0.233197i | \(0.0749186\pi\) | ||||
−0.972430 | + | 0.233197i | \(0.925081\pi\) | |||||||
\(332\) | 1.41421 | 0.0776151 | ||||||||
\(333\) | −20.7846 | −1.13899 | ||||||||
\(334\) | −18.0000 | −0.984916 | ||||||||
\(335\) | −19.5959 | − | 24.0000i | −1.07064 | − | 1.31126i | ||||
\(336\) | 4.24264i | 0.231455i | ||||||||
\(337\) | −20.7846 | −1.13221 | −0.566105 | − | 0.824333i | \(-0.691550\pi\) | ||||
−0.566105 | + | 0.824333i | \(0.691550\pi\) | |||||||
\(338\) | 13.0000i | 0.707107i | ||||||||
\(339\) | − | 10.3923i | − | 0.564433i | ||||||
\(340\) | −10.0000 | − | 12.2474i | −0.542326 | − | 0.664211i | ||||
\(341\) | 14.6969 | 0.795884 | ||||||||
\(342\) | 12.7279 | + | 3.00000i | 0.688247 | + | 0.162221i | ||||
\(343\) | − | 19.5959i | − | 1.05808i | ||||||
\(344\) | −9.79796 | −0.528271 | ||||||||
\(345\) | 13.8564 | + | 16.9706i | 0.746004 | + | 0.913664i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.0416 | −1.29062 | −0.645311 | − | 0.763920i | \(-0.723272\pi\) | ||||
−0.645311 | + | 0.763920i | \(0.723272\pi\) | |||||||
\(348\) | −8.48528 | −0.454859 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 2.44949 | − | 12.0000i | 0.130931 | − | 0.641427i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.46410 | −0.184637 | ||||||||
\(353\) | −15.5563 | −0.827981 | −0.413990 | − | 0.910281i | \(-0.635865\pi\) | ||||
−0.413990 | + | 0.910281i | \(0.635865\pi\) | |||||||
\(354\) | − | 12.7279i | − | 0.676481i | ||||||
\(355\) | 6.92820 | + | 8.48528i | 0.367711 | + | 0.450352i | ||||
\(356\) | 12.2474 | 0.649113 | ||||||||
\(357\) | − | 30.0000i | − | 1.58777i | ||||||
\(358\) | 17.1464i | 0.906217i | ||||||||
\(359\) | 13.8564i | 0.731313i | 0.930750 | + | 0.365657i | \(0.119156\pi\) | ||||
−0.930750 | + | 0.365657i | \(0.880844\pi\) | |||||||
\(360\) | 5.19615 | − | 4.24264i | 0.273861 | − | 0.223607i | ||||
\(361\) | −17.0000 | − | 8.48528i | −0.894737 | − | 0.446594i | ||||
\(362\) | 12.7279 | 0.668965 | ||||||||
\(363\) | 1.73205 | 0.0909091 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.9706 | + | 13.8564i | −0.888280 | + | 0.725277i | ||||
\(366\) | − | 17.3205i | − | 0.905357i | ||||||
\(367\) | 7.34847i | 0.383587i | 0.981435 | + | 0.191793i | \(0.0614304\pi\) | ||||
−0.981435 | + | 0.191793i | \(0.938570\pi\) | |||||||
\(368\) | 5.65685 | 0.294884 | ||||||||
\(369\) | 7.34847 | 0.382546 | ||||||||
\(370\) | 12.0000 | − | 9.79796i | 0.623850 | − | 0.509372i | ||||
\(371\) | −29.3939 | −1.52605 | ||||||||
\(372\) | 7.34847i | 0.381000i | ||||||||
\(373\) | −6.92820 | −0.358729 | −0.179364 | − | 0.983783i | \(-0.557404\pi\) | ||||
−0.179364 | + | 0.983783i | \(0.557404\pi\) | |||||||
\(374\) | 24.4949 | 1.26660 | ||||||||
\(375\) | −17.1464 | + | 9.00000i | −0.885438 | + | 0.464758i | ||||
\(376\) | 2.82843i | 0.145865i | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 12.7279 | 0.654654 | ||||||||
\(379\) | − | 25.4558i | − | 1.30758i | −0.756677 | − | 0.653789i | \(-0.773178\pi\) | ||
0.756677 | − | 0.653789i | \(-0.226822\pi\) | |||||||
\(380\) | −8.76268 | + | 4.26795i | −0.449516 | + | 0.218941i | ||||
\(381\) | 6.00000 | 0.307389 | ||||||||
\(382\) | 17.3205 | 0.886194 | ||||||||
\(383\) | − | 24.0000i | − | 1.22634i | −0.789950 | − | 0.613171i | \(-0.789894\pi\) | ||
0.789950 | − | 0.613171i | \(-0.210106\pi\) | |||||||
\(384\) | − | 1.73205i | − | 0.0883883i | ||||||
\(385\) | 12.0000 | + | 14.6969i | 0.611577 | + | 0.749025i | ||||
\(386\) | 20.7846i | 1.05791i | ||||||||
\(387\) | 29.3939i | 1.49417i | ||||||||
\(388\) | −3.46410 | −0.175863 | ||||||||
\(389\) | 13.8564i | 0.702548i | 0.936273 | + | 0.351274i | \(0.114251\pi\) | ||||
−0.936273 | + | 0.351274i | \(0.885749\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −40.0000 | −2.02289 | ||||||||
\(392\) | 1.00000i | 0.0505076i | ||||||||
\(393\) | 6.00000i | 0.302660i | ||||||||
\(394\) | 5.65685i | 0.284988i | ||||||||
\(395\) | −7.34847 | + | 6.00000i | −0.369742 | + | 0.301893i | ||||
\(396\) | 10.3923i | 0.522233i | ||||||||
\(397\) | − | 26.9444i | − | 1.35230i | −0.736764 | − | 0.676150i | \(-0.763647\pi\) | ||
0.736764 | − | 0.676150i | \(-0.236353\pi\) | |||||||
\(398\) | − | 20.0000i | − | 1.00251i | ||||||
\(399\) | −18.0000 | − | 4.24264i | −0.901127 | − | 0.212398i | ||||
\(400\) | −1.00000 | + | 4.89898i | −0.0500000 | + | 0.244949i | ||||
\(401\) | −17.1464 | −0.856252 | −0.428126 | − | 0.903719i | \(-0.640826\pi\) | ||||
−0.428126 | + | 0.903719i | \(0.640826\pi\) | |||||||
\(402\) | 24.0000i | 1.19701i | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.7279 | − | 15.5885i | −0.632456 | − | 0.774597i | ||||
\(406\) | 12.0000 | 0.595550 | ||||||||
\(407\) | 24.0000i | 1.18964i | ||||||||
\(408\) | 12.2474i | 0.606339i | ||||||||
\(409\) | − | 33.9411i | − | 1.67828i | −0.543915 | − | 0.839140i | \(-0.683059\pi\) | ||
0.543915 | − | 0.839140i | \(-0.316941\pi\) | |||||||
\(410\) | −4.24264 | + | 3.46410i | −0.209529 | + | 0.171080i | ||||
\(411\) | 12.2474 | 0.604122 | ||||||||
\(412\) | 3.46410 | 0.170664 | ||||||||
\(413\) | 18.0000i | 0.885722i | ||||||||
\(414\) | − | 16.9706i | − | 0.834058i | ||||||
\(415\) | 2.00000 | + | 2.44949i | 0.0981761 | + | 0.120241i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.3205 | 0.848189 | ||||||||
\(418\) | 3.46410 | − | 14.6969i | 0.169435 | − | 0.718851i | ||||
\(419\) | − | 31.1769i | − | 1.52309i | −0.648111 | − | 0.761546i | \(-0.724441\pi\) | ||
0.648111 | − | 0.761546i | \(-0.275559\pi\) | |||||||
\(420\) | −7.34847 | + | 6.00000i | −0.358569 | + | 0.292770i | ||||
\(421\) | − | 4.24264i | − | 0.206774i | −0.994641 | − | 0.103387i | \(-0.967032\pi\) | ||
0.994641 | − | 0.103387i | \(-0.0329680\pi\) | |||||||
\(422\) | −25.4558 | −1.23917 | ||||||||
\(423\) | 8.48528 | 0.412568 | ||||||||
\(424\) | 12.0000 | 0.582772 | ||||||||
\(425\) | 7.07107 | − | 34.6410i | 0.342997 | − | 1.68034i | ||||
\(426\) | − | 8.48528i | − | 0.411113i | ||||||
\(427\) | 24.4949i | 1.18539i | ||||||||
\(428\) | − | 12.0000i | − | 0.580042i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.8564 | − | 16.9706i | −0.668215 | − | 0.818393i | ||||
\(431\) | −9.79796 | −0.471951 | −0.235976 | − | 0.971759i | \(-0.575829\pi\) | ||||
−0.235976 | + | 0.971759i | \(0.575829\pi\) | |||||||
\(432\) | −5.19615 | −0.250000 | ||||||||
\(433\) | 20.7846 | 0.998845 | 0.499422 | − | 0.866359i | \(-0.333546\pi\) | ||||
0.499422 | + | 0.866359i | \(0.333546\pi\) | |||||||
\(434\) | − | 10.3923i | − | 0.498847i | ||||||
\(435\) | −12.0000 | − | 14.6969i | −0.575356 | − | 0.704664i | ||||
\(436\) | 12.7279i | 0.609557i | ||||||||
\(437\) | −5.65685 | + | 24.0000i | −0.270604 | + | 1.14808i | ||||
\(438\) | 16.9706 | 0.810885 | ||||||||
\(439\) | 12.7279i | 0.607471i | 0.952756 | + | 0.303735i | \(0.0982338\pi\) | ||||
−0.952756 | + | 0.303735i | \(0.901766\pi\) | |||||||
\(440\) | −4.89898 | − | 6.00000i | −0.233550 | − | 0.286039i | ||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.5563 | −0.739104 | −0.369552 | − | 0.929210i | \(-0.620489\pi\) | ||||
−0.369552 | + | 0.929210i | \(0.620489\pi\) | |||||||
\(444\) | −12.0000 | −0.569495 | ||||||||
\(445\) | 17.3205 | + | 21.2132i | 0.821071 | + | 1.00560i | ||||
\(446\) | 3.46410i | 0.164030i | ||||||||
\(447\) | 24.0000i | 1.13516i | ||||||||
\(448\) | 2.44949i | 0.115728i | ||||||||
\(449\) | 22.0454 | 1.04039 | 0.520194 | − | 0.854048i | \(-0.325860\pi\) | ||||
0.520194 | + | 0.854048i | \(0.325860\pi\) | |||||||
\(450\) | 14.6969 | + | 3.00000i | 0.692820 | + | 0.141421i | ||||
\(451\) | − | 8.48528i | − | 0.399556i | ||||||
\(452\) | − | 6.00000i | − | 0.282216i | ||||||
\(453\) | 22.0454i | 1.03578i | ||||||||
\(454\) | −12.0000 | −0.563188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.34847 | + | 1.73205i | 0.344124 | + | 0.0811107i | ||||
\(457\) | − | 9.79796i | − | 0.458329i | −0.973388 | − | 0.229165i | \(-0.926401\pi\) | ||
0.973388 | − | 0.229165i | \(-0.0735994\pi\) | |||||||
\(458\) | 22.0000i | 1.02799i | ||||||||
\(459\) | 36.7423 | 1.71499 | ||||||||
\(460\) | 8.00000 | + | 9.79796i | 0.373002 | + | 0.456832i | ||||
\(461\) | − | 17.3205i | − | 0.806696i | −0.915047 | − | 0.403348i | \(-0.867846\pi\) | ||
0.915047 | − | 0.403348i | \(-0.132154\pi\) | |||||||
\(462\) | − | 14.6969i | − | 0.683763i | ||||||
\(463\) | − | 12.2474i | − | 0.569187i | −0.958648 | − | 0.284594i | \(-0.908141\pi\) | ||
0.958648 | − | 0.284594i | \(-0.0918587\pi\) | |||||||
\(464\) | −4.89898 | −0.227429 | ||||||||
\(465\) | −12.7279 | + | 10.3923i | −0.590243 | + | 0.481932i | ||||
\(466\) | 7.07107i | 0.327561i | ||||||||
\(467\) | −26.8701 | −1.24340 | −0.621699 | − | 0.783256i | \(-0.713557\pi\) | ||||
−0.621699 | + | 0.783256i | \(0.713557\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 33.9411i | − | 1.56726i | ||||||
\(470\) | −4.89898 | + | 4.00000i | −0.225973 | + | 0.184506i | ||||
\(471\) | − | 12.7279i | − | 0.586472i | ||||||
\(472\) | − | 7.34847i | − | 0.338241i | ||||||
\(473\) | 33.9411 | 1.56061 | ||||||||
\(474\) | 7.34847 | 0.337526 | ||||||||
\(475\) | −19.7846 | − | 9.14162i | −0.907780 | − | 0.419446i | ||||
\(476\) | − | 17.3205i | − | 0.793884i | ||||||
\(477\) | − | 36.0000i | − | 1.64833i | ||||||
\(478\) | 6.92820 | 0.316889 | ||||||||
\(479\) | − | 10.3923i | − | 0.474837i | −0.971408 | − | 0.237418i | \(-0.923699\pi\) | ||
0.971408 | − | 0.237418i | \(-0.0763012\pi\) | |||||||
\(480\) | 3.00000 | − | 2.44949i | 0.136931 | − | 0.111803i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 8.48528 | 0.386494 | ||||||||
\(483\) | 24.0000i | 1.09204i | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −4.89898 | − | 6.00000i | −0.222451 | − | 0.272446i | ||||
\(486\) | 15.5885i | 0.707107i | ||||||||
\(487\) | 3.46410 | 0.156973 | 0.0784867 | − | 0.996915i | \(-0.474991\pi\) | ||||
0.0784867 | + | 0.996915i | \(0.474991\pi\) | |||||||
\(488\) | − | 10.0000i | − | 0.452679i | ||||||
\(489\) | 25.4558i | 1.15115i | ||||||||
\(490\) | −1.73205 | + | 1.41421i | −0.0782461 | + | 0.0638877i | ||||
\(491\) | − | 10.3923i | − | 0.468998i | −0.972116 | − | 0.234499i | \(-0.924655\pi\) | ||
0.972116 | − | 0.234499i | \(-0.0753450\pi\) | |||||||
\(492\) | 4.24264 | 0.191273 | ||||||||
\(493\) | 34.6410 | 1.56015 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −18.0000 | + | 14.6969i | −0.809040 | + | 0.660578i | ||||
\(496\) | 4.24264i | 0.190500i | ||||||||
\(497\) | 12.0000i | 0.538274i | ||||||||
\(498\) | − | 2.44949i | − | 0.109764i | ||||||
\(499\) | 14.0000 | 0.626726 | 0.313363 | − | 0.949633i | \(-0.398544\pi\) | ||||
0.313363 | + | 0.949633i | \(0.398544\pi\) | |||||||
\(500\) | −9.89949 | + | 5.19615i | −0.442719 | + | 0.232379i | ||||
\(501\) | 31.1769i | 1.39288i | ||||||||
\(502\) | 24.2487 | 1.08227 | ||||||||
\(503\) | −5.65685 | −0.252227 | −0.126113 | − | 0.992016i | \(-0.540250\pi\) | ||||
−0.126113 | + | 0.992016i | \(0.540250\pi\) | |||||||
\(504\) | 7.34847 | 0.327327 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −19.5959 | −0.871145 | ||||||||
\(507\) | 22.5167 | 1.00000 | ||||||||
\(508\) | 3.46410 | 0.153695 | ||||||||
\(509\) | 24.4949 | 1.08572 | 0.542859 | − | 0.839824i | \(-0.317342\pi\) | ||||
0.542859 | + | 0.839824i | \(0.317342\pi\) | |||||||
\(510\) | −21.2132 | + | 17.3205i | −0.939336 | + | 0.766965i | ||||
\(511\) | −24.0000 | −1.06170 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 5.19615 | − | 22.0454i | 0.229416 | − | 0.973329i | ||||
\(514\) | 6.00000 | 0.264649 | ||||||||
\(515\) | 4.89898 | + | 6.00000i | 0.215875 | + | 0.264392i | ||||
\(516\) | 16.9706i | 0.747087i | ||||||||
\(517\) | − | 9.79796i | − | 0.430914i | ||||||
\(518\) | 16.9706 | 0.745644 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.0454 | −0.965827 | −0.482913 | − | 0.875668i | \(-0.660421\pi\) | ||||
−0.482913 | + | 0.875668i | \(0.660421\pi\) | |||||||
\(522\) | 14.6969i | 0.643268i | ||||||||
\(523\) | −13.8564 | −0.605898 | −0.302949 | − | 0.953007i | \(-0.597971\pi\) | ||||
−0.302949 | + | 0.953007i | \(0.597971\pi\) | |||||||
\(524\) | 3.46410i | 0.151330i | ||||||||
\(525\) | −20.7846 | − | 4.24264i | −0.907115 | − | 0.185164i | ||||
\(526\) | − | 28.2843i | − | 1.23325i | ||||||
\(527\) | − | 30.0000i | − | 1.30682i | ||||||
\(528\) | 6.00000i | 0.261116i | ||||||||
\(529\) | 9.00000 | 0.391304 | ||||||||
\(530\) | 16.9706 | + | 20.7846i | 0.737154 | + | 0.902826i | ||||
\(531\) | −22.0454 | −0.956689 | ||||||||
\(532\) | −10.3923 | − | 2.44949i | −0.450564 | − | 0.106199i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | − | 21.2132i | − | 0.917985i | ||||||
\(535\) | 20.7846 | − | 16.9706i | 0.898597 | − | 0.733701i | ||||
\(536\) | 13.8564i | 0.598506i | ||||||||
\(537\) | 29.6985 | 1.28158 | ||||||||
\(538\) | 19.5959i | 0.844840i | ||||||||
\(539\) | − | 3.46410i | − | 0.149209i | ||||||
\(540\) | −7.34847 | − | 9.00000i | −0.316228 | − | 0.387298i | ||||
\(541\) | 34.0000 | 1.46177 | 0.730887 | − | 0.682498i | \(-0.239107\pi\) | ||||
0.730887 | + | 0.682498i | \(0.239107\pi\) | |||||||
\(542\) | − | 28.0000i | − | 1.20270i | ||||||
\(543\) | − | 22.0454i | − | 0.946059i | ||||||
\(544\) | 7.07107i | 0.303170i | ||||||||
\(545\) | −22.0454 | + | 18.0000i | −0.944322 | + | 0.771035i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.6410 | 1.48114 | 0.740571 | − | 0.671978i | \(-0.234555\pi\) | ||||
0.740571 | + | 0.671978i | \(0.234555\pi\) | |||||||
\(548\) | 7.07107 | 0.302061 | ||||||||
\(549\) | −30.0000 | −1.28037 | ||||||||
\(550\) | 3.46410 | − | 16.9706i | 0.147710 | − | 0.723627i | ||||
\(551\) | 4.89898 | − | 20.7846i | 0.208704 | − | 0.885454i | ||||
\(552\) | − | 9.79796i | − | 0.417029i | ||||||
\(553\) | −10.3923 | −0.441926 | ||||||||
\(554\) | −12.2474 | −0.520344 | ||||||||
\(555\) | −16.9706 | − | 20.7846i | −0.720360 | − | 0.882258i | ||||
\(556\) | 10.0000 | 0.424094 | ||||||||
\(557\) | −5.65685 | −0.239689 | −0.119844 | − | 0.992793i | \(-0.538240\pi\) | ||||
−0.119844 | + | 0.992793i | \(0.538240\pi\) | |||||||
\(558\) | 12.7279 | 0.538816 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −4.24264 | + | 3.46410i | −0.179284 | + | 0.146385i | ||||
\(561\) | − | 42.4264i | − | 1.79124i | ||||||
\(562\) | − | 31.8434i | − | 1.34323i | ||||||
\(563\) | − | 12.0000i | − | 0.505740i | −0.967500 | − | 0.252870i | \(-0.918626\pi\) | ||
0.967500 | − | 0.252870i | \(-0.0813744\pi\) | |||||||
\(564\) | 4.89898 | 0.206284 | ||||||||
\(565\) | 10.3923 | − | 8.48528i | 0.437208 | − | 0.356978i | ||||
\(566\) | −24.4949 | −1.02960 | ||||||||
\(567\) | − | 22.0454i | − | 0.925820i | ||||||
\(568\) | − | 4.89898i | − | 0.205557i | ||||||
\(569\) | −2.44949 | −0.102688 | −0.0513440 | − | 0.998681i | \(-0.516350\pi\) | ||||
−0.0513440 | + | 0.998681i | \(0.516350\pi\) | |||||||
\(570\) | 7.39230 | + | 15.1774i | 0.309630 | + | 0.635712i | ||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 30.0000i | − | 1.25327i | ||||||
\(574\) | −6.00000 | −0.250435 | ||||||||
\(575\) | −5.65685 | + | 27.7128i | −0.235907 | + | 1.15570i | ||||
\(576\) | −3.00000 | −0.125000 | ||||||||
\(577\) | − | 4.89898i | − | 0.203947i | −0.994787 | − | 0.101974i | \(-0.967484\pi\) | ||
0.994787 | − | 0.101974i | \(-0.0325157\pi\) | |||||||
\(578\) | − | 33.0000i | − | 1.37262i | ||||||
\(579\) | 36.0000 | 1.49611 | ||||||||
\(580\) | −6.92820 | − | 8.48528i | −0.287678 | − | 0.352332i | ||||
\(581\) | 3.46410i | 0.143715i | ||||||||
\(582\) | 6.00000i | 0.248708i | ||||||||
\(583\) | −41.5692 | −1.72162 | ||||||||
\(584\) | 9.79796 | 0.405442 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.00000 | 0.247858 | ||||||||
\(587\) | −9.89949 | −0.408596 | −0.204298 | − | 0.978909i | \(-0.565491\pi\) | ||||
−0.204298 | + | 0.978909i | \(0.565491\pi\) | |||||||
\(588\) | 1.73205 | 0.0714286 | ||||||||
\(589\) | −18.0000 | − | 4.24264i | −0.741677 | − | 0.174815i | ||||
\(590\) | 12.7279 | − | 10.3923i | 0.524000 | − | 0.427844i | ||||
\(591\) | 9.79796 | 0.403034 | ||||||||
\(592\) | −6.92820 | −0.284747 | ||||||||
\(593\) | −18.3848 | −0.754972 | −0.377486 | − | 0.926015i | \(-0.623211\pi\) | ||||
−0.377486 | + | 0.926015i | \(0.623211\pi\) | |||||||
\(594\) | 18.0000 | 0.738549 | ||||||||
\(595\) | 30.0000 | − | 24.4949i | 1.22988 | − | 1.00419i | ||||
\(596\) | 13.8564i | 0.567581i | ||||||||
\(597\) | −34.6410 | −1.41776 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.1918 | 1.60134 | 0.800668 | − | 0.599109i | \(-0.204478\pi\) | ||||
0.800668 | + | 0.599109i | \(0.204478\pi\) | |||||||
\(600\) | 8.48528 | + | 1.73205i | 0.346410 | + | 0.0707107i | ||||
\(601\) | − | 25.4558i | − | 1.03837i | −0.854663 | − | 0.519183i | \(-0.826236\pi\) | ||
0.854663 | − | 0.519183i | \(-0.173764\pi\) | |||||||
\(602\) | − | 24.0000i | − | 0.978167i | ||||||
\(603\) | 41.5692 | 1.69283 | ||||||||
\(604\) | 12.7279i | 0.517892i | ||||||||
\(605\) | 1.41421 | + | 1.73205i | 0.0574960 | + | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.3923 | −0.421811 | −0.210905 | − | 0.977506i | \(-0.567641\pi\) | ||||
−0.210905 | + | 0.977506i | \(0.567641\pi\) | |||||||
\(608\) | 4.24264 | + | 1.00000i | 0.172062 | + | 0.0405554i | ||||
\(609\) | − | 20.7846i | − | 0.842235i | ||||||
\(610\) | 17.3205 | − | 14.1421i | 0.701287 | − | 0.572598i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 21.2132 | 0.857493 | ||||||||
\(613\) | 2.44949i | 0.0989340i | 0.998776 | + | 0.0494670i | \(0.0157523\pi\) | ||||
−0.998776 | + | 0.0494670i | \(0.984248\pi\) | |||||||
\(614\) | 6.92820i | 0.279600i | ||||||||
\(615\) | 6.00000 | + | 7.34847i | 0.241943 | + | 0.296319i | ||||
\(616\) | − | 8.48528i | − | 0.341882i | ||||||
\(617\) | 1.41421 | 0.0569341 | 0.0284670 | − | 0.999595i | \(-0.490937\pi\) | ||||
0.0284670 | + | 0.999595i | \(0.490937\pi\) | |||||||
\(618\) | − | 6.00000i | − | 0.241355i | ||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | −7.34847 | + | 6.00000i | −0.295122 | + | 0.240966i | ||||
\(621\) | −29.3939 | −1.17954 | ||||||||
\(622\) | 3.46410 | 0.138898 | ||||||||
\(623\) | 30.0000i | 1.20192i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.0000 | − | 9.79796i | −0.920000 | − | 0.391918i | ||||
\(626\) | 14.6969 | 0.587408 | ||||||||
\(627\) | −25.4558 | − | 6.00000i | −1.01661 | − | 0.239617i | ||||
\(628\) | − | 7.34847i | − | 0.293236i | ||||||
\(629\) | 48.9898 | 1.95335 | ||||||||
\(630\) | 10.3923 | + | 12.7279i | 0.414039 | + | 0.507093i | ||||
\(631\) | −4.00000 | −0.159237 | −0.0796187 | − | 0.996825i | \(-0.525370\pi\) | ||||
−0.0796187 | + | 0.996825i | \(0.525370\pi\) | |||||||
\(632\) | 4.24264 | 0.168763 | ||||||||
\(633\) | 44.0908i | 1.75245i | ||||||||
\(634\) | 6.00000 | 0.238290 | ||||||||
\(635\) | 4.89898 | + | 6.00000i | 0.194410 | + | 0.238103i | ||||
\(636\) | − | 20.7846i | − | 0.824163i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.9706 | 0.671871 | ||||||||
\(639\) | −14.6969 | −0.581402 | ||||||||
\(640\) | 1.73205 | − | 1.41421i | 0.0684653 | − | 0.0559017i | ||||
\(641\) | 17.1464 | 0.677243 | 0.338622 | − | 0.940923i | \(-0.390039\pi\) | ||||
0.338622 | + | 0.940923i | \(0.390039\pi\) | |||||||
\(642\) | −20.7846 | −0.820303 | ||||||||
\(643\) | 34.2929i | 1.35238i | 0.736728 | + | 0.676189i | \(0.236370\pi\) | ||||
−0.736728 | + | 0.676189i | \(0.763630\pi\) | |||||||
\(644\) | 13.8564i | 0.546019i | ||||||||
\(645\) | −29.3939 | + | 24.0000i | −1.15738 | + | 0.944999i | ||||
\(646\) | −30.0000 | − | 7.07107i | −1.18033 | − | 0.278207i | ||||
\(647\) | −11.3137 | −0.444788 | −0.222394 | − | 0.974957i | \(-0.571387\pi\) | ||||
−0.222394 | + | 0.974957i | \(0.571387\pi\) | |||||||
\(648\) | 9.00000i | 0.353553i | ||||||||
\(649\) | 25.4558i | 0.999229i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.0000 | −0.705476 | ||||||||
\(652\) | 14.6969i | 0.575577i | ||||||||
\(653\) | 36.7696 | 1.43890 | 0.719452 | − | 0.694542i | \(-0.244393\pi\) | ||||
0.719452 | + | 0.694542i | \(0.244393\pi\) | |||||||
\(654\) | 22.0454 | 0.862044 | ||||||||
\(655\) | −6.00000 | + | 4.89898i | −0.234439 | + | 0.191419i | ||||
\(656\) | 2.44949 | 0.0956365 | ||||||||
\(657\) | − | 29.3939i | − | 1.14676i | ||||||
\(658\) | −6.92820 | −0.270089 | ||||||||
\(659\) | −2.44949 | −0.0954186 | −0.0477093 | − | 0.998861i | \(-0.515192\pi\) | ||||
−0.0477093 | + | 0.998861i | \(0.515192\pi\) | |||||||
\(660\) | −10.3923 | + | 8.48528i | −0.404520 | + | 0.330289i | ||||
\(661\) | 38.1838i | 1.48518i | 0.669748 | + | 0.742588i | \(0.266402\pi\) | ||||
−0.669748 | + | 0.742588i | \(0.733598\pi\) | |||||||
\(662\) | 8.48528 | 0.329790 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 1.41421i | − | 0.0548821i | ||||||
\(665\) | −10.4543 | − | 21.4641i | −0.405400 | − | 0.832342i | ||||
\(666\) | 20.7846i | 0.805387i | ||||||||
\(667\) | −27.7128 | −1.07304 | ||||||||
\(668\) | 18.0000i | 0.696441i | ||||||||
\(669\) | 6.00000 | 0.231973 | ||||||||
\(670\) | −24.0000 | + | 19.5959i | −0.927201 | + | 0.757056i | ||||
\(671\) | 34.6410i | 1.33730i | ||||||||
\(672\) | 4.24264 | 0.163663 | ||||||||
\(673\) | 38.1051 | 1.46884 | 0.734422 | − | 0.678693i | \(-0.237453\pi\) | ||||
0.734422 | + | 0.678693i | \(0.237453\pi\) | |||||||
\(674\) | 20.7846i | 0.800593i | ||||||||
\(675\) | 5.19615 | − | 25.4558i | 0.200000 | − | 0.979796i | ||||
\(676\) | 13.0000 | 0.500000 | ||||||||
\(677\) | 42.0000i | 1.61419i | 0.590421 | + | 0.807096i | \(0.298962\pi\) | ||||
−0.590421 | + | 0.807096i | \(0.701038\pi\) | |||||||
\(678\) | −10.3923 | −0.399114 | ||||||||
\(679\) | − | 8.48528i | − | 0.325635i | ||||||
\(680\) | −12.2474 | + | 10.0000i | −0.469668 | + | 0.383482i | ||||
\(681\) | 20.7846i | 0.796468i | ||||||||
\(682\) | − | 14.6969i | − | 0.562775i | ||||||
\(683\) | 24.0000i | 0.918334i | 0.888350 | + | 0.459167i | \(0.151852\pi\) | ||||
−0.888350 | + | 0.459167i | \(0.848148\pi\) | |||||||
\(684\) | 3.00000 | − | 12.7279i | 0.114708 | − | 0.486664i | ||||
\(685\) | 10.0000 | + | 12.2474i | 0.382080 | + | 0.467951i | ||||
\(686\) | −19.5959 | −0.748176 | ||||||||
\(687\) | 38.1051 | 1.45380 | ||||||||
\(688\) | 9.79796i | 0.373544i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 16.9706 | − | 13.8564i | 0.646058 | − | 0.527504i | ||||
\(691\) | 28.0000 | 1.06517 | 0.532585 | − | 0.846376i | \(-0.321221\pi\) | ||||
0.532585 | + | 0.846376i | \(0.321221\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −25.4558 | −0.966988 | ||||||||
\(694\) | 24.0416i | 0.912608i | ||||||||
\(695\) | 14.1421 | + | 17.3205i | 0.536442 | + | 0.657004i | ||||
\(696\) | 8.48528i | 0.321634i | ||||||||
\(697\) | −17.3205 | −0.656061 | ||||||||
\(698\) | − | 2.00000i | − | 0.0757011i | ||||||
\(699\) | 12.2474 | 0.463241 | ||||||||
\(700\) | −12.0000 | − | 2.44949i | −0.453557 | − | 0.0925820i | ||||
\(701\) | − | 31.1769i | − | 1.17754i | −0.808302 | − | 0.588768i | \(-0.799613\pi\) | ||
0.808302 | − | 0.588768i | \(-0.200387\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.92820 | − | 29.3939i | 0.261302 | − | 1.10861i | ||||
\(704\) | 3.46410i | 0.130558i | ||||||||
\(705\) | 6.92820 | + | 8.48528i | 0.260931 | + | 0.319574i | ||||
\(706\) | 15.5563i | 0.585471i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −12.7279 | −0.478345 | ||||||||
\(709\) | −22.0000 | −0.826227 | −0.413114 | − | 0.910679i | \(-0.635559\pi\) | ||||
−0.413114 | + | 0.910679i | \(0.635559\pi\) | |||||||
\(710\) | 8.48528 | − | 6.92820i | 0.318447 | − | 0.260011i | ||||
\(711\) | − | 12.7279i | − | 0.477334i | ||||||
\(712\) | − | 12.2474i | − | 0.458993i | ||||||
\(713\) | 24.0000i | 0.898807i | ||||||||
\(714\) | −30.0000 | −1.12272 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 17.1464 | 0.640792 | ||||||||
\(717\) | − | 12.0000i | − | 0.448148i | ||||||
\(718\) | 13.8564 | 0.517116 | ||||||||
\(719\) | − | 13.8564i | − | 0.516757i | −0.966044 | − | 0.258378i | \(-0.916812\pi\) | ||
0.966044 | − | 0.258378i | \(-0.0831881\pi\) | |||||||
\(720\) | −4.24264 | − | 5.19615i | −0.158114 | − | 0.193649i | ||||
\(721\) | 8.48528i | 0.316008i | ||||||||
\(722\) | −8.48528 | + | 17.0000i | −0.315789 | + | 0.632674i | ||||
\(723\) | − | 14.6969i | − | 0.546585i | ||||||
\(724\) | − | 12.7279i | − | 0.473029i | ||||||
\(725\) | 4.89898 | − | 24.0000i | 0.181944 | − | 0.891338i | ||||
\(726\) | − | 1.73205i | − | 0.0642824i | ||||||
\(727\) | 41.6413i | 1.54439i | 0.635385 | + | 0.772196i | \(0.280841\pi\) | ||||
−0.635385 | + | 0.772196i | \(0.719159\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 13.8564 | + | 16.9706i | 0.512849 | + | 0.628109i | ||||
\(731\) | − | 69.2820i | − | 2.56249i | ||||||
\(732\) | −17.3205 | −0.640184 | ||||||||
\(733\) | 22.0454i | 0.814266i | 0.913369 | + | 0.407133i | \(0.133471\pi\) | ||||
−0.913369 | + | 0.407133i | \(0.866529\pi\) | |||||||
\(734\) | 7.34847 | 0.271237 | ||||||||
\(735\) | 2.44949 | + | 3.00000i | 0.0903508 | + | 0.110657i | ||||
\(736\) | − | 5.65685i | − | 0.208514i | ||||||
\(737\) | − | 48.0000i | − | 1.76810i | ||||||
\(738\) | − | 7.34847i | − | 0.270501i | ||||||
\(739\) | −20.0000 | −0.735712 | −0.367856 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367856 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(740\) | −9.79796 | − | 12.0000i | −0.360180 | − | 0.441129i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 29.3939i | 1.07908i | ||||||||
\(743\) | 18.0000i | 0.660356i | 0.943919 | + | 0.330178i | \(0.107109\pi\) | ||||
−0.943919 | + | 0.330178i | \(0.892891\pi\) | |||||||
\(744\) | 7.34847 | 0.269408 | ||||||||
\(745\) | −24.0000 | + | 19.5959i | −0.879292 | + | 0.717939i | ||||
\(746\) | 6.92820i | 0.253660i | ||||||||
\(747\) | −4.24264 | −0.155230 | ||||||||
\(748\) | − | 24.4949i | − | 0.895622i | ||||||
\(749\) | 29.3939 | 1.07403 | ||||||||
\(750\) | 9.00000 | + | 17.1464i | 0.328634 | + | 0.626099i | ||||
\(751\) | 21.2132i | 0.774081i | 0.922063 | + | 0.387040i | \(0.126503\pi\) | ||||
−0.922063 | + | 0.387040i | \(0.873497\pi\) | |||||||
\(752\) | 2.82843 | 0.103142 | ||||||||
\(753\) | − | 42.0000i | − | 1.53057i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.0454 | + | 18.0000i | −0.802315 | + | 0.655087i | ||||
\(756\) | − | 12.7279i | − | 0.462910i | ||||||
\(757\) | − | 17.1464i | − | 0.623198i | −0.950214 | − | 0.311599i | \(-0.899136\pi\) | ||
0.950214 | − | 0.311599i | \(-0.100864\pi\) | |||||||
\(758\) | −25.4558 | −0.924598 | ||||||||
\(759\) | 33.9411i | 1.23198i | ||||||||
\(760\) | 4.26795 | + | 8.76268i | 0.154815 | + | 0.317856i | ||||
\(761\) | 48.4974i | 1.75803i | 0.476794 | + | 0.879015i | \(0.341799\pi\) | ||||
−0.476794 | + | 0.879015i | \(0.658201\pi\) | |||||||
\(762\) | − | 6.00000i | − | 0.217357i | ||||||
\(763\) | −31.1769 | −1.12868 | ||||||||
\(764\) | − | 17.3205i | − | 0.626634i | ||||||
\(765\) | 30.0000 | + | 36.7423i | 1.08465 | + | 1.32842i | ||||
\(766\) | −24.0000 | −0.867155 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.73205 | −0.0625000 | ||||||||
\(769\) | −4.00000 | −0.144244 | −0.0721218 | − | 0.997396i | \(-0.522977\pi\) | ||||
−0.0721218 | + | 0.997396i | \(0.522977\pi\) | |||||||
\(770\) | 14.6969 | − | 12.0000i | 0.529641 | − | 0.432450i | ||||
\(771\) | − | 10.3923i | − | 0.374270i | ||||||
\(772\) | 20.7846 | 0.748054 | ||||||||
\(773\) | − | 24.0000i | − | 0.863220i | −0.902060 | − | 0.431610i | \(-0.857946\pi\) | ||
0.902060 | − | 0.431610i | \(-0.142054\pi\) | |||||||
\(774\) | 29.3939 | 1.05654 | ||||||||
\(775\) | −20.7846 | − | 4.24264i | −0.746605 | − | 0.152400i | ||||
\(776\) | 3.46410i | 0.124354i | ||||||||
\(777\) | − | 29.3939i | − | 1.05450i | ||||||
\(778\) | 13.8564 | 0.496776 | ||||||||
\(779\) | −2.44949 | + | 10.3923i | −0.0877621 | + | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.9706i | 0.607254i | ||||||||
\(782\) | 40.0000i | 1.43040i | ||||||||
\(783\) | 25.4558 | 0.909718 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 12.7279 | − | 10.3923i | 0.454279 | − | 0.370917i | ||||
\(786\) | 6.00000 | 0.214013 | ||||||||
\(787\) | 24.2487 | 0.864373 | 0.432187 | − | 0.901784i | \(-0.357742\pi\) | ||||
0.432187 | + | 0.901784i | \(0.357742\pi\) | |||||||
\(788\) | 5.65685 | 0.201517 | ||||||||
\(789\) | −48.9898 | −1.74408 | ||||||||
\(790\) | 6.00000 | + | 7.34847i | 0.213470 | + | 0.261447i | ||||
\(791\) | 14.6969 | 0.522563 | ||||||||
\(792\) | 10.3923 | 0.369274 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −26.9444 | −0.956221 | ||||||||
\(795\) | 36.0000 | − | 29.3939i | 1.27679 | − | 1.04249i | ||||
\(796\) | −20.0000 | −0.708881 | ||||||||
\(797\) | 30.0000i | 1.06265i | 0.847167 | + | 0.531327i | \(0.178307\pi\) | ||||
−0.847167 | + | 0.531327i | \(0.821693\pi\) | |||||||
\(798\) | −4.24264 | + | 18.0000i | −0.150188 | + | 0.637193i | ||||
\(799\) | −20.0000 | −0.707549 | ||||||||
\(800\) | 4.89898 | + | 1.00000i | 0.173205 | + | 0.0353553i | ||||
\(801\) | −36.7423 | −1.29823 | ||||||||
\(802\) | 17.1464i | 0.605461i | ||||||||
\(803\) | −33.9411 | −1.19776 | ||||||||
\(804\) | 24.0000 | 0.846415 | ||||||||
\(805\) | −24.0000 | + | 19.5959i | −0.845889 | + | 0.690665i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 33.9411 | 1.19478 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 48.4974i | − | 1.70508i | −0.522663 | − | 0.852539i | \(-0.675061\pi\) | ||
0.522663 | − | 0.852539i | \(-0.324939\pi\) | |||||||
\(810\) | −15.5885 | + | 12.7279i | −0.547723 | + | 0.447214i | ||||
\(811\) | 8.48528i | 0.297959i | 0.988840 | + | 0.148979i | \(0.0475988\pi\) | ||||
−0.988840 | + | 0.148979i | \(0.952401\pi\) | |||||||
\(812\) | − | 12.0000i | − | 0.421117i | ||||||
\(813\) | −48.4974 | −1.70088 | ||||||||
\(814\) | 24.0000 | 0.841200 | ||||||||
\(815\) | −25.4558 | + | 20.7846i | −0.891679 | + | 0.728053i | ||||
\(816\) | 12.2474 | 0.428746 | ||||||||
\(817\) | −41.5692 | − | 9.79796i | −1.45432 | − | 0.342787i | ||||
\(818\) | −33.9411 | −1.18672 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.46410 | + | 4.24264i | 0.120972 | + | 0.148159i | ||||
\(821\) | 27.7128i | 0.967184i | 0.875294 | + | 0.483592i | \(0.160668\pi\) | ||||
−0.875294 | + | 0.483592i | \(0.839332\pi\) | |||||||
\(822\) | − | 12.2474i | − | 0.427179i | ||||||
\(823\) | 12.2474i | 0.426919i | 0.976952 | + | 0.213460i | \(0.0684732\pi\) | ||||
−0.976952 | + | 0.213460i | \(0.931527\pi\) | |||||||
\(824\) | − | 3.46410i | − | 0.120678i | ||||||
\(825\) | −29.3939 | − | 6.00000i | −1.02336 | − | 0.208893i | ||||
\(826\) | 18.0000 | 0.626300 | ||||||||
\(827\) | 36.0000i | 1.25184i | 0.779886 | + | 0.625921i | \(0.215277\pi\) | ||||
−0.779886 | + | 0.625921i | \(0.784723\pi\) | |||||||
\(828\) | −16.9706 | −0.589768 | ||||||||
\(829\) | − | 46.6690i | − | 1.62088i | −0.585820 | − | 0.810442i | \(-0.699227\pi\) | ||
0.585820 | − | 0.810442i | \(-0.300773\pi\) | |||||||
\(830\) | 2.44949 | − | 2.00000i | 0.0850230 | − | 0.0694210i | ||||
\(831\) | 21.2132i | 0.735878i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.07107 | −0.244998 | ||||||||
\(834\) | − | 17.3205i | − | 0.599760i | ||||||
\(835\) | −31.1769 | + | 25.4558i | −1.07892 | + | 0.880936i | ||||
\(836\) | −14.6969 | − | 3.46410i | −0.508304 | − | 0.119808i | ||||
\(837\) | − | 22.0454i | − | 0.762001i | ||||||
\(838\) | −31.1769 | −1.07699 | ||||||||
\(839\) | 39.1918 | 1.35305 | 0.676526 | − | 0.736419i | \(-0.263485\pi\) | ||||
0.676526 | + | 0.736419i | \(0.263485\pi\) | |||||||
\(840\) | 6.00000 | + | 7.34847i | 0.207020 | + | 0.253546i | ||||
\(841\) | −5.00000 | −0.172414 | ||||||||
\(842\) | −4.24264 | −0.146211 | ||||||||
\(843\) | −55.1543 | −1.89962 | ||||||||
\(844\) | 25.4558i | 0.876226i | ||||||||
\(845\) | 18.3848 | + | 22.5167i | 0.632456 | + | 0.774597i | ||||
\(846\) | − | 8.48528i | − | 0.291730i | ||||||
\(847\) | 2.44949i | 0.0841655i | ||||||||
\(848\) | − | 12.0000i | − | 0.412082i | ||||||
\(849\) | 42.4264i | 1.45607i | ||||||||
\(850\) | −34.6410 | − | 7.07107i | −1.18818 | − | 0.242536i | ||||
\(851\) | −39.1918 | −1.34348 | ||||||||
\(852\) | −8.48528 | −0.290701 | ||||||||
\(853\) | 36.7423i | 1.25803i | 0.777392 | + | 0.629017i | \(0.216542\pi\) | ||||
−0.777392 | + | 0.629017i | \(0.783458\pi\) | |||||||
\(854\) | 24.4949 | 0.838198 | ||||||||
\(855\) | 26.2880 | − | 12.8038i | 0.899032 | − | 0.437882i | ||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | − | 54.0000i | − | 1.84460i | −0.386469 | − | 0.922302i | \(-0.626305\pi\) | ||
0.386469 | − | 0.922302i | \(-0.373695\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.00000 | 0.136478 | 0.0682391 | − | 0.997669i | \(-0.478262\pi\) | ||||
0.0682391 | + | 0.997669i | \(0.478262\pi\) | |||||||
\(860\) | −16.9706 | + | 13.8564i | −0.578691 | + | 0.472500i | ||||
\(861\) | 10.3923i | 0.354169i | ||||||||
\(862\) | 9.79796i | 0.333720i | ||||||||
\(863\) | − | 48.0000i | − | 1.63394i | −0.576681 | − | 0.816970i | \(-0.695652\pi\) | ||
0.576681 | − | 0.816970i | \(-0.304348\pi\) | |||||||
\(864\) | 5.19615i | 0.176777i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 20.7846i | − | 0.706290i | ||||||
\(867\) | −57.1577 | −1.94118 | ||||||||
\(868\) | −10.3923 | −0.352738 | ||||||||
\(869\) | −14.6969 | −0.498559 | ||||||||
\(870\) | −14.6969 | + | 12.0000i | −0.498273 | + | 0.406838i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 12.7279 | 0.431022 | ||||||||
\(873\) | 10.3923 | 0.351726 | ||||||||
\(874\) | 24.0000 | + | 5.65685i | 0.811812 | + | 0.191346i | ||||
\(875\) | −12.7279 | − | 24.2487i | −0.430282 | − | 0.819756i | ||||
\(876\) | − | 16.9706i | − | 0.573382i | ||||||
\(877\) | 41.5692 | 1.40369 | 0.701846 | − | 0.712328i | \(-0.252359\pi\) | ||||
0.701846 | + | 0.712328i | \(0.252359\pi\) | |||||||
\(878\) | 12.7279 | 0.429547 | ||||||||
\(879\) | − | 10.3923i | − | 0.350524i | ||||||
\(880\) | −6.00000 | + | 4.89898i | −0.202260 | + | 0.165145i | ||||
\(881\) | 13.8564i | 0.466834i | 0.972377 | + | 0.233417i | \(0.0749907\pi\) | ||||
−0.972377 | + | 0.233417i | \(0.925009\pi\) | |||||||
\(882\) | − | 3.00000i | − | 0.101015i | ||||||
\(883\) | 34.2929i | 1.15405i | 0.816728 | + | 0.577023i | \(0.195786\pi\) | ||||
−0.816728 | + | 0.577023i | \(0.804214\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.0000 | − | 22.0454i | −0.605063 | − | 0.741048i | ||||
\(886\) | 15.5563i | 0.522626i | ||||||||
\(887\) | 6.00000i | 0.201460i | 0.994914 | + | 0.100730i | \(0.0321179\pi\) | ||||
−0.994914 | + | 0.100730i | \(0.967882\pi\) | |||||||
\(888\) | 12.0000i | 0.402694i | ||||||||
\(889\) | 8.48528i | 0.284587i | ||||||||
\(890\) | 21.2132 | − | 17.3205i | 0.711068 | − | 0.580585i | ||||
\(891\) | − | 31.1769i | − | 1.04447i | ||||||
\(892\) | 3.46410 | 0.115987 | ||||||||
\(893\) | −2.82843 | + | 12.0000i | −0.0946497 | + | 0.401565i | ||||
\(894\) | 24.0000 | 0.802680 | ||||||||
\(895\) | 24.2487 | + | 29.6985i | 0.810545 | + | 0.992711i | ||||
\(896\) | 2.44949 | 0.0818317 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 22.0454i | − | 0.735665i | ||||||
\(899\) | − | 20.7846i | − | 0.693206i | ||||||
\(900\) | 3.00000 | − | 14.6969i | 0.100000 | − | 0.489898i | ||||
\(901\) | 84.8528i | 2.82686i | ||||||||
\(902\) | −8.48528 | −0.282529 | ||||||||
\(903\) | −41.5692 | −1.38334 | ||||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 22.0454 | − | 18.0000i | 0.732814 | − | 0.598340i | ||||
\(906\) | 22.0454 | 0.732410 | ||||||||
\(907\) | −17.3205 | −0.575118 | −0.287559 | − | 0.957763i | \(-0.592844\pi\) | ||||
−0.287559 | + | 0.957763i | \(0.592844\pi\) | |||||||
\(908\) | 12.0000i | 0.398234i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.3939 | −0.973863 | −0.486931 | − | 0.873440i | \(-0.661884\pi\) | ||||
−0.486931 | + | 0.873440i | \(0.661884\pi\) | |||||||
\(912\) | 1.73205 | − | 7.34847i | 0.0573539 | − | 0.243332i | ||||
\(913\) | 4.89898i | 0.162133i | ||||||||
\(914\) | −9.79796 | −0.324088 | ||||||||
\(915\) | −24.4949 | − | 30.0000i | −0.809776 | − | 0.991769i | ||||
\(916\) | 22.0000 | 0.726900 | ||||||||
\(917\) | −8.48528 | −0.280209 | ||||||||
\(918\) | − | 36.7423i | − | 1.21268i | ||||||
\(919\) | −8.00000 | −0.263896 | −0.131948 | − | 0.991257i | \(-0.542123\pi\) | ||||
−0.131948 | + | 0.991257i | \(0.542123\pi\) | |||||||
\(920\) | 9.79796 | − | 8.00000i | 0.323029 | − | 0.263752i | ||||
\(921\) | 12.0000 | 0.395413 | ||||||||
\(922\) | −17.3205 | −0.570421 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −14.6969 | −0.483494 | ||||||||
\(925\) | 6.92820 | − | 33.9411i | 0.227798 | − | 1.11598i | ||||
\(926\) | −12.2474 | −0.402476 | ||||||||
\(927\) | −10.3923 | −0.341328 | ||||||||
\(928\) | 4.89898i | 0.160817i | ||||||||
\(929\) | 20.7846i | 0.681921i | 0.940078 | + | 0.340960i | \(0.110752\pi\) | ||||
−0.940078 | + | 0.340960i | \(0.889248\pi\) | |||||||
\(930\) | 10.3923 | + | 12.7279i | 0.340777 | + | 0.417365i | ||||
\(931\) | −1.00000 | + | 4.24264i | −0.0327737 | + | 0.139047i | ||||
\(932\) | 7.07107 | 0.231621 | ||||||||
\(933\) | − | 6.00000i | − | 0.196431i | ||||||
\(934\) | 26.8701i | 0.879215i | ||||||||
\(935\) | 42.4264 | − | 34.6410i | 1.38749 | − | 1.13288i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 34.2929i | − | 1.12030i | −0.828392 | − | 0.560149i | \(-0.810744\pi\) | ||
0.828392 | − | 0.560149i | \(-0.189256\pi\) | |||||||
\(938\) | −33.9411 | −1.10822 | ||||||||
\(939\) | − | 25.4558i | − | 0.830720i | ||||||
\(940\) | 4.00000 | + | 4.89898i | 0.130466 | + | 0.159787i | ||||
\(941\) | 9.79796 | 0.319404 | 0.159702 | − | 0.987165i | \(-0.448947\pi\) | ||||
0.159702 | + | 0.987165i | \(0.448947\pi\) | |||||||
\(942\) | −12.7279 | −0.414698 | ||||||||
\(943\) | 13.8564 | 0.451227 | ||||||||
\(944\) | −7.34847 | −0.239172 | ||||||||
\(945\) | 22.0454 | − | 18.0000i | 0.717137 | − | 0.585540i | ||||
\(946\) | − | 33.9411i | − | 1.10352i | ||||||
\(947\) | 1.41421 | 0.0459558 | 0.0229779 | − | 0.999736i | \(-0.492685\pi\) | ||||
0.0229779 | + | 0.999736i | \(0.492685\pi\) | |||||||
\(948\) | − | 7.34847i | − | 0.238667i | ||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −9.14162 | + | 19.7846i | −0.296593 | + | 0.641898i | ||||
\(951\) | − | 10.3923i | − | 0.336994i | ||||||
\(952\) | −17.3205 | −0.561361 | ||||||||
\(953\) | 30.0000i | 0.971795i | 0.874016 | + | 0.485898i | \(0.161507\pi\) | ||||
−0.874016 | + | 0.485898i | \(0.838493\pi\) | |||||||
\(954\) | −36.0000 | −1.16554 | ||||||||
\(955\) | 30.0000 | − | 24.4949i | 0.970777 | − | 0.792636i | ||||
\(956\) | − | 6.92820i | − | 0.224074i | ||||||
\(957\) | − | 29.3939i | − | 0.950169i | ||||||
\(958\) | −10.3923 | −0.335760 | ||||||||
\(959\) | 17.3205i | 0.559308i | ||||||||
\(960\) | −2.44949 | − | 3.00000i | −0.0790569 | − | 0.0968246i | ||||
\(961\) | 13.0000 | 0.419355 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.0000i | 1.16008i | ||||||||
\(964\) | − | 8.48528i | − | 0.273293i | ||||||
\(965\) | 29.3939 | + | 36.0000i | 0.946222 | + | 1.15888i | ||||
\(966\) | 24.0000 | 0.772187 | ||||||||
\(967\) | 22.0454i | 0.708933i | 0.935069 | + | 0.354466i | \(0.115337\pi\) | ||||
−0.935069 | + | 0.354466i | \(0.884663\pi\) | |||||||
\(968\) | − | 1.00000i | − | 0.0321412i | ||||||
\(969\) | −12.2474 | + | 51.9615i | −0.393445 | + | 1.66924i | ||||
\(970\) | −6.00000 | + | 4.89898i | −0.192648 | + | 0.157297i | ||||
\(971\) | 26.9444 | 0.864687 | 0.432343 | − | 0.901709i | \(-0.357687\pi\) | ||||
0.432343 | + | 0.901709i | \(0.357687\pi\) | |||||||
\(972\) | 15.5885 | 0.500000 | ||||||||
\(973\) | 24.4949i | 0.785270i | ||||||||
\(974\) | − | 3.46410i | − | 0.110997i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.0000 | −0.320092 | ||||||||
\(977\) | 42.0000i | 1.34370i | 0.740688 | + | 0.671850i | \(0.234500\pi\) | ||||
−0.740688 | + | 0.671850i | \(0.765500\pi\) | |||||||
\(978\) | 25.4558 | 0.813988 | ||||||||
\(979\) | 42.4264i | 1.35595i | ||||||||
\(980\) | 1.41421 | + | 1.73205i | 0.0451754 | + | 0.0553283i | ||||
\(981\) | − | 38.1838i | − | 1.21911i | ||||||
\(982\) | −10.3923 | −0.331632 | ||||||||
\(983\) | − | 6.00000i | − | 0.191370i | −0.995412 | − | 0.0956851i | \(-0.969496\pi\) | ||
0.995412 | − | 0.0956851i | \(-0.0305042\pi\) | |||||||
\(984\) | − | 4.24264i | − | 0.135250i | ||||||
\(985\) | 8.00000 | + | 9.79796i | 0.254901 | + | 0.312189i | ||||
\(986\) | − | 34.6410i | − | 1.10319i | ||||||
\(987\) | 12.0000i | 0.381964i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 55.4256i | 1.76243i | ||||||||
\(990\) | 14.6969 | + | 18.0000i | 0.467099 | + | 0.572078i | ||||
\(991\) | − | 21.2132i | − | 0.673860i | −0.941530 | − | 0.336930i | \(-0.890611\pi\) | ||
0.941530 | − | 0.336930i | \(-0.109389\pi\) | |||||||
\(992\) | 4.24264 | 0.134704 | ||||||||
\(993\) | − | 14.6969i | − | 0.466393i | ||||||
\(994\) | 12.0000 | 0.380617 | ||||||||
\(995\) | −28.2843 | − | 34.6410i | −0.896672 | − | 1.09819i | ||||
\(996\) | −2.44949 | −0.0776151 | ||||||||
\(997\) | − | 17.1464i | − | 0.543033i | −0.962434 | − | 0.271516i | \(-0.912475\pi\) | ||
0.962434 | − | 0.271516i | \(-0.0875251\pi\) | |||||||
\(998\) | − | 14.0000i | − | 0.443162i | ||||||
\(999\) | 36.0000 | 1.13899 |
(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 | 570.2.c.d.569.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 570.2.c.d.569.6 | yes | 8 | |
5.4 | even | 2 | inner | 570.2.c.d.569.8 | yes | 8 | |
15.14 | odd | 2 | inner | 570.2.c.d.569.3 | yes | 8 | |
19.18 | odd | 2 | inner | 570.2.c.d.569.7 | yes | 8 | |
57.56 | even | 2 | inner | 570.2.c.d.569.4 | yes | 8 | |
95.94 | odd | 2 | inner | 570.2.c.d.569.2 | yes | 8 | |
285.284 | even | 2 | inner | 570.2.c.d.569.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.c.d.569.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
570.2.c.d.569.2 | yes | 8 | 95.94 | odd | 2 | inner | |
570.2.c.d.569.3 | yes | 8 | 15.14 | odd | 2 | inner | |
570.2.c.d.569.4 | yes | 8 | 57.56 | even | 2 | inner | |
570.2.c.d.569.5 | yes | 8 | 285.284 | even | 2 | inner | |
570.2.c.d.569.6 | yes | 8 | 3.2 | odd | 2 | inner | |
570.2.c.d.569.7 | yes | 8 | 19.18 | odd | 2 | inner | |
570.2.c.d.569.8 | yes | 8 | 5.4 | even | 2 | inner |