Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(190,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.190");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.f (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: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 189) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 379.2 | ||
Root | \(1.32288 - 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.379 |
Dual form | 567.2.f.i.190.2 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.32288 | − | 2.29129i | 0.935414 | − | 1.62019i | 0.161521 | − | 0.986869i | \(-0.448360\pi\) |
0.773893 | − | 0.633316i | \(-0.218307\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.50000 | − | 4.33013i | −1.25000 | − | 2.16506i | ||||
\(5\) | −1.32288 | − | 2.29129i | −0.591608 | − | 1.02470i | −0.994016 | − | 0.109235i | \(-0.965160\pi\) |
0.402408 | − | 0.915460i | \(-0.368173\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | ||||
\(8\) | −7.93725 | −2.80624 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.00000 | −2.21359 | ||||||||
\(11\) | −1.32288 | + | 2.29129i | −0.398862 | + | 0.690849i | −0.993586 | − | 0.113081i | \(-0.963928\pi\) |
0.594724 | + | 0.803930i | \(0.297261\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | + | 1.73205i | 0.277350 | + | 0.480384i | 0.970725 | − | 0.240192i | \(-0.0772105\pi\) |
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | −1.32288 | − | 2.29129i | −0.353553 | − | 0.612372i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.50000 | + | 9.52628i | −1.37500 | + | 2.38157i | ||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.00000 | 1.60591 | 0.802955 | − | 0.596040i | \(-0.203260\pi\) | ||||
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | −6.61438 | + | 11.4564i | −1.47902 | + | 2.56174i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.50000 | + | 6.06218i | 0.746203 | + | 1.29246i | ||||
\(23\) | −3.96863 | − | 6.87386i | −0.827516 | − | 1.43330i | −0.899981 | − | 0.435929i | \(-0.856420\pi\) |
0.0724653 | − | 0.997371i | \(-0.476913\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | ||||
\(26\) | 5.29150 | 1.03775 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.00000 | −0.944911 | ||||||||
\(29\) | 2.64575 | − | 4.58258i | 0.491304 | − | 0.850963i | −0.508646 | − | 0.860976i | \(-0.669854\pi\) |
0.999950 | + | 0.0100127i | \(0.00318719\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | − | 2.59808i | −0.269408 | − | 0.466628i | 0.699301 | − | 0.714827i | \(-0.253495\pi\) |
−0.968709 | + | 0.248199i | \(0.920161\pi\) | |||||||
\(32\) | 6.61438 | + | 11.4564i | 1.16927 | + | 2.02523i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.64575 | −0.447214 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | −0.493197 | −0.246598 | − | 0.969118i | \(-0.579313\pi\) | ||||
−0.246598 | + | 0.969118i | \(0.579313\pi\) | |||||||
\(38\) | 9.26013 | − | 16.0390i | 1.50219 | − | 2.60187i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 10.5000 | + | 18.1865i | 1.66020 | + | 2.87554i | ||||
\(41\) | 1.32288 | + | 2.29129i | 0.206598 | + | 0.357839i | 0.950641 | − | 0.310293i | \(-0.100427\pi\) |
−0.744042 | + | 0.668132i | \(0.767094\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | + | 6.92820i | −0.609994 | + | 1.05654i | 0.381246 | + | 0.924473i | \(0.375495\pi\) |
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | 13.2288 | 1.99431 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −21.0000 | −3.09628 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 2.64575 | + | 4.58258i | 0.374166 | + | 0.648074i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.00000 | − | 8.66025i | 0.693375 | − | 1.20096i | ||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.00000 | 0.943880 | ||||||||
\(56\) | −3.96863 | + | 6.87386i | −0.530330 | + | 0.918559i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.00000 | − | 12.1244i | −0.919145 | − | 1.59201i | ||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | − | 6.92820i | 0.512148 | − | 0.887066i | −0.487753 | − | 0.872982i | \(-0.662183\pi\) |
0.999901 | − | 0.0140840i | \(-0.00448323\pi\) | |||||||
\(62\) | −7.93725 | −1.00803 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 13.0000 | 1.62500 | ||||||||
\(65\) | 2.64575 | − | 4.58258i | 0.328165 | − | 0.568399i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000 | + | 1.73205i | 0.122169 | + | 0.211604i | 0.920623 | − | 0.390453i | \(-0.127682\pi\) |
−0.798454 | + | 0.602056i | \(0.794348\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.50000 | + | 6.06218i | −0.418330 | + | 0.724569i | ||||
\(71\) | −7.93725 | −0.941979 | −0.470989 | − | 0.882139i | \(-0.656103\pi\) | ||||
−0.470989 | + | 0.882139i | \(0.656103\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(74\) | −3.96863 | + | 6.87386i | −0.461344 | + | 0.799070i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −17.5000 | − | 30.3109i | −2.00739 | − | 3.47690i | ||||
\(77\) | 1.32288 | + | 2.29129i | 0.150756 | + | 0.261116i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | − | 3.46410i | 0.225018 | − | 0.389742i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
0.956325 | + | 0.292306i | \(0.0944227\pi\) | |||||||
\(80\) | 29.1033 | 3.25384 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.00000 | 0.773021 | ||||||||
\(83\) | 7.93725 | − | 13.7477i | 0.871227 | − | 1.50901i | 0.0104983 | − | 0.999945i | \(-0.496658\pi\) |
0.860729 | − | 0.509064i | \(-0.170008\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.5830 | + | 18.3303i | 1.14119 | + | 1.97661i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.5000 | − | 18.1865i | 1.11930 | − | 1.93869i | ||||
\(89\) | 18.5203 | 1.96314 | 0.981572 | − | 0.191094i | \(-0.0612035\pi\) | ||||
0.981572 | + | 0.191094i | \(0.0612035\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | −19.8431 | + | 34.3693i | −2.06879 | + | 3.58325i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.26013 | − | 16.0390i | −0.950069 | − | 1.64557i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | − | 10.3923i | 0.609208 | − | 1.05518i | −0.382164 | − | 0.924095i | \(-0.624821\pi\) |
0.991371 | − | 0.131084i | \(-0.0418458\pi\) | |||||||
\(98\) | −2.64575 | −0.267261 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10.0000 | 1.00000 | ||||||||
\(101\) | 5.29150 | − | 9.16515i | 0.526524 | − | 0.911967i | −0.472998 | − | 0.881063i | \(-0.656828\pi\) |
0.999522 | − | 0.0309033i | \(-0.00983838\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.50000 | + | 11.2583i | 0.640464 | + | 1.10932i | 0.985329 | + | 0.170664i | \(0.0545913\pi\) |
−0.344865 | + | 0.938652i | \(0.612075\pi\) | |||||||
\(104\) | −7.93725 | − | 13.7477i | −0.778312 | − | 1.34808i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.29150 | −0.511549 | −0.255774 | − | 0.966736i | \(-0.582330\pi\) | ||||
−0.255774 | + | 0.966736i | \(0.582330\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.00000 | 0.862044 | 0.431022 | − | 0.902342i | \(-0.358153\pi\) | ||||
0.431022 | + | 0.902342i | \(0.358153\pi\) | |||||||
\(110\) | 9.26013 | − | 16.0390i | 0.882919 | − | 1.52926i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.50000 | + | 9.52628i | 0.519701 | + | 0.900149i | ||||
\(113\) | 2.64575 | + | 4.58258i | 0.248891 | + | 0.431092i | 0.963218 | − | 0.268719i | \(-0.0866005\pi\) |
−0.714327 | + | 0.699812i | \(0.753267\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.5000 | + | 18.1865i | −0.979130 | + | 1.69590i | ||||
\(116\) | −26.4575 | −2.45652 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.00000 | + | 3.46410i | 0.181818 | + | 0.314918i | ||||
\(122\) | −10.5830 | − | 18.3303i | −0.958140 | − | 1.65955i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.50000 | + | 12.9904i | −0.673520 | + | 1.16657i | ||||
\(125\) | −7.93725 | −0.709930 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.00000 | 0.532414 | 0.266207 | − | 0.963916i | \(-0.414230\pi\) | ||||
0.266207 | + | 0.963916i | \(0.414230\pi\) | |||||||
\(128\) | 3.96863 | − | 6.87386i | 0.350780 | − | 0.607569i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.00000 | − | 12.1244i | −0.613941 | − | 1.06338i | ||||
\(131\) | 10.5830 | + | 18.3303i | 0.924641 | + | 1.60153i | 0.792137 | + | 0.610344i | \(0.208969\pi\) |
0.132505 | + | 0.991182i | \(0.457698\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.50000 | − | 6.06218i | 0.303488 | − | 0.525657i | ||||
\(134\) | 5.29150 | 0.457116 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.93725 | + | 13.7477i | −0.678125 | + | 1.17455i | 0.297419 | + | 0.954747i | \(0.403874\pi\) |
−0.975545 | + | 0.219801i | \(0.929459\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.00000 | + | 10.3923i | 0.508913 | + | 0.881464i | 0.999947 | + | 0.0103230i | \(0.00328598\pi\) |
−0.491033 | + | 0.871141i | \(0.663381\pi\) | |||||||
\(140\) | 6.61438 | + | 11.4564i | 0.559017 | + | 0.968246i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.5000 | + | 18.1865i | −0.881140 | + | 1.52618i | ||||
\(143\) | −5.29150 | −0.442498 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.0000 | −1.16264 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.50000 | + | 12.9904i | 0.616496 | + | 1.06780i | ||||
\(149\) | −7.93725 | − | 13.7477i | −0.650245 | − | 1.12626i | −0.983063 | − | 0.183267i | \(-0.941333\pi\) |
0.332818 | − | 0.942991i | \(-0.392000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.00000 | + | 1.73205i | −0.0813788 | + | 0.140952i | −0.903842 | − | 0.427865i | \(-0.859266\pi\) |
0.822464 | + | 0.568818i | \(0.192599\pi\) | |||||||
\(152\) | −55.5608 | −4.50657 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.00000 | 0.564076 | ||||||||
\(155\) | −3.96863 | + | 6.87386i | −0.318768 | + | 0.552122i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.00000 | + | 12.1244i | 0.558661 | + | 0.967629i | 0.997609 | + | 0.0691164i | \(0.0220180\pi\) |
−0.438948 | + | 0.898513i | \(0.644649\pi\) | |||||||
\(158\) | −5.29150 | − | 9.16515i | −0.420969 | − | 0.729140i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 17.5000 | − | 30.3109i | 1.38350 | − | 2.39629i | ||||
\(161\) | −7.93725 | −0.625543 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0000 | 0.783260 | 0.391630 | − | 0.920123i | \(-0.371911\pi\) | ||||
0.391630 | + | 0.920123i | \(0.371911\pi\) | |||||||
\(164\) | 6.61438 | − | 11.4564i | 0.516496 | − | 0.894598i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −21.0000 | − | 36.3731i | −1.62992 | − | 2.82310i | ||||
\(167\) | 2.64575 | + | 4.58258i | 0.204734 | + | 0.354610i | 0.950048 | − | 0.312104i | \(-0.101034\pi\) |
−0.745314 | + | 0.666714i | \(0.767700\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | − | 7.79423i | 0.346154 | − | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 40.0000 | 3.04997 | ||||||||
\(173\) | −6.61438 | + | 11.4564i | −0.502882 | + | 0.871017i | 0.497113 | + | 0.867686i | \(0.334394\pi\) |
−0.999994 | + | 0.00333090i | \(0.998940\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | + | 1.73205i | 0.0755929 | + | 0.130931i | ||||
\(176\) | −14.5516 | − | 25.2042i | −1.09687 | − | 1.89984i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 24.5000 | − | 42.4352i | 1.83635 | − | 3.18066i | ||||
\(179\) | 5.29150 | 0.395505 | 0.197753 | − | 0.980252i | \(-0.436636\pi\) | ||||
0.197753 | + | 0.980252i | \(0.436636\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 2.64575 | − | 4.58258i | 0.196116 | − | 0.339683i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 31.5000 | + | 54.5596i | 2.32221 | + | 4.02219i | ||||
\(185\) | 3.96863 | + | 6.87386i | 0.291779 | + | 0.505376i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −49.0000 | −3.55483 | ||||||||
\(191\) | −1.32288 | + | 2.29129i | −0.0957199 | + | 0.165792i | −0.909909 | − | 0.414808i | \(-0.863849\pi\) |
0.814189 | + | 0.580600i | \(0.197182\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | − | 1.73205i | −0.0719816 | − | 0.124676i | 0.827788 | − | 0.561041i | \(-0.189599\pi\) |
−0.899770 | + | 0.436365i | \(0.856266\pi\) | |||||||
\(194\) | −15.8745 | − | 27.4955i | −1.13972 | − | 1.97406i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.50000 | + | 4.33013i | −0.178571 | + | 0.309295i | ||||
\(197\) | 26.4575 | 1.88502 | 0.942510 | − | 0.334178i | \(-0.108459\pi\) | ||||
0.942510 | + | 0.334178i | \(0.108459\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.00000 | −0.212664 | −0.106332 | − | 0.994331i | \(-0.533911\pi\) | ||||
−0.106332 | + | 0.994331i | \(0.533911\pi\) | |||||||
\(200\) | 7.93725 | − | 13.7477i | 0.561249 | − | 0.972111i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.0000 | − | 24.2487i | −0.985037 | − | 1.70613i | ||||
\(203\) | −2.64575 | − | 4.58258i | −0.185695 | − | 0.321634i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.50000 | − | 6.06218i | 0.244451 | − | 0.423401i | ||||
\(206\) | 34.3948 | 2.39640 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −22.0000 | −1.52543 | ||||||||
\(209\) | −9.26013 | + | 16.0390i | −0.640537 | + | 1.10944i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.0000 | − | 19.0526i | −0.757271 | − | 1.31163i | −0.944237 | − | 0.329266i | \(-0.893199\pi\) |
0.186966 | − | 0.982366i | \(-0.440135\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.00000 | + | 12.1244i | −0.478510 | + | 0.828804i | ||||
\(215\) | 21.1660 | 1.44351 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | −0.203653 | ||||||||
\(218\) | 11.9059 | − | 20.6216i | 0.806368 | − | 1.39667i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −17.5000 | − | 30.3109i | −1.17985 | − | 2.04356i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.50000 | + | 6.06218i | −0.234377 | + | 0.405953i | −0.959092 | − | 0.283096i | \(-0.908638\pi\) |
0.724714 | + | 0.689050i | \(0.241972\pi\) | |||||||
\(224\) | 13.2288 | 0.883883 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.0000 | 0.931266 | ||||||||
\(227\) | −7.93725 | + | 13.7477i | −0.526814 | + | 0.912469i | 0.472698 | + | 0.881225i | \(0.343280\pi\) |
−0.999512 | + | 0.0312441i | \(0.990053\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | − | 17.3205i | −0.660819 | − | 1.14457i | −0.980401 | − | 0.197013i | \(-0.936876\pi\) |
0.319582 | − | 0.947559i | \(-0.396457\pi\) | |||||||
\(230\) | 27.7804 | + | 48.1170i | 1.83178 | + | 3.17274i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −21.0000 | + | 36.3731i | −1.37872 | + | 2.38801i | ||||
\(233\) | −15.8745 | −1.03997 | −0.519987 | − | 0.854174i | \(-0.674063\pi\) | ||||
−0.519987 | + | 0.854174i | \(0.674063\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.93725 | + | 13.7477i | 0.513418 | + | 0.889267i | 0.999879 | + | 0.0155640i | \(0.00495438\pi\) |
−0.486461 | + | 0.873703i | \(0.661712\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | − | 3.46410i | 0.128831 | − | 0.223142i | −0.794393 | − | 0.607404i | \(-0.792211\pi\) |
0.923224 | + | 0.384262i | \(0.125544\pi\) | |||||||
\(242\) | 10.5830 | 0.680301 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −40.0000 | −2.56074 | ||||||||
\(245\) | −1.32288 | + | 2.29129i | −0.0845154 | + | 0.146385i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.00000 | + | 12.1244i | 0.445399 | + | 0.771454i | ||||
\(248\) | 11.9059 | + | 20.6216i | 0.756024 | + | 1.30947i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.5000 | + | 18.1865i | −0.664078 | + | 1.15022i | ||||
\(251\) | 10.5830 | 0.667993 | 0.333997 | − | 0.942574i | \(-0.391603\pi\) | ||||
0.333997 | + | 0.942574i | \(0.391603\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.0000 | 1.32026 | ||||||||
\(254\) | 7.93725 | − | 13.7477i | 0.498028 | − | 0.862609i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.50000 | + | 4.33013i | 0.156250 | + | 0.270633i | ||||
\(257\) | 9.26013 | + | 16.0390i | 0.577631 | + | 1.00049i | 0.995750 | + | 0.0920941i | \(0.0293561\pi\) |
−0.418119 | + | 0.908392i | \(0.637311\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.50000 | + | 2.59808i | −0.0932055 | + | 0.161437i | ||||
\(260\) | −26.4575 | −1.64083 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 56.0000 | 3.45969 | ||||||||
\(263\) | −9.26013 | + | 16.0390i | −0.571004 | + | 0.989008i | 0.425459 | + | 0.904978i | \(0.360113\pi\) |
−0.996463 | + | 0.0840304i | \(0.973221\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.26013 | − | 16.0390i | −0.567775 | − | 0.983415i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.00000 | − | 8.66025i | 0.305424 | − | 0.529009i | ||||
\(269\) | −23.8118 | −1.45183 | −0.725914 | − | 0.687785i | \(-0.758583\pi\) | ||||
−0.725914 | + | 0.687785i | \(0.758583\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.0000 | −1.21491 | −0.607457 | − | 0.794353i | \(-0.707810\pi\) | ||||
−0.607457 | + | 0.794353i | \(0.707810\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 21.0000 | + | 36.3731i | 1.26866 | + | 2.19738i | ||||
\(275\) | −2.64575 | − | 4.58258i | −0.159545 | − | 0.276340i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.5000 | − | 19.9186i | 0.690968 | − | 1.19679i | −0.280553 | − | 0.959839i | \(-0.590518\pi\) |
0.971521 | − | 0.236953i | \(-0.0761488\pi\) | |||||||
\(278\) | 31.7490 | 1.90418 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 21.0000 | 1.25499 | ||||||||
\(281\) | 5.29150 | − | 9.16515i | 0.315665 | − | 0.546747i | −0.663914 | − | 0.747809i | \(-0.731106\pi\) |
0.979579 | + | 0.201062i | \(0.0644392\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.00000 | − | 3.46410i | −0.118888 | − | 0.205919i | 0.800439 | − | 0.599414i | \(-0.204600\pi\) |
−0.919327 | + | 0.393494i | \(0.871266\pi\) | |||||||
\(284\) | 19.8431 | + | 34.3693i | 1.17747 | + | 2.03944i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.00000 | + | 12.1244i | −0.413919 | + | 0.716928i | ||||
\(287\) | 2.64575 | 0.156174 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | −18.5203 | + | 32.0780i | −1.08755 | + | 1.88369i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.29150 | + | 9.16515i | 0.309133 | + | 0.535434i | 0.978173 | − | 0.207792i | \(-0.0666279\pi\) |
−0.669040 | + | 0.743226i | \(0.733295\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 23.8118 | 1.38403 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −42.0000 | −2.43299 | ||||||||
\(299\) | 7.93725 | − | 13.7477i | 0.459023 | − | 0.795052i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | + | 6.92820i | 0.230556 | + | 0.399335i | ||||
\(302\) | 2.64575 | + | 4.58258i | 0.152246 | + | 0.263698i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −38.5000 | + | 66.6840i | −2.20813 | + | 3.82459i | ||||
\(305\) | −21.1660 | −1.21196 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.0000 | 1.08439 | 0.542194 | − | 0.840254i | \(-0.317594\pi\) | ||||
0.542194 | + | 0.840254i | \(0.317594\pi\) | |||||||
\(308\) | 6.61438 | − | 11.4564i | 0.376889 | − | 0.652791i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.5000 | + | 18.1865i | 0.596360 | + | 1.03293i | ||||
\(311\) | 7.93725 | + | 13.7477i | 0.450080 | + | 0.779562i | 0.998391 | − | 0.0567130i | \(-0.0180620\pi\) |
−0.548310 | + | 0.836275i | \(0.684729\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.00000 | + | 12.1244i | −0.395663 | + | 0.685309i | −0.993186 | − | 0.116543i | \(-0.962819\pi\) |
0.597522 | + | 0.801852i | \(0.296152\pi\) | |||||||
\(314\) | 37.0405 | 2.09032 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.0000 | −1.12509 | ||||||||
\(317\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.00000 | + | 12.1244i | 0.391925 | + | 0.678834i | ||||
\(320\) | −17.1974 | − | 29.7867i | −0.961363 | − | 1.66513i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.5000 | + | 18.1865i | −0.585142 | + | 1.01350i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | 13.2288 | − | 22.9129i | 0.732673 | − | 1.26903i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.5000 | − | 18.1865i | −0.579766 | − | 1.00418i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0000 | + | 17.3205i | −0.549650 | + | 0.952021i | 0.448649 | + | 0.893708i | \(0.351905\pi\) |
−0.998298 | + | 0.0583130i | \(0.981428\pi\) | |||||||
\(332\) | −79.3725 | −4.35613 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.0000 | 0.766046 | ||||||||
\(335\) | 2.64575 | − | 4.58258i | 0.144553 | − | 0.250373i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.50000 | − | 16.4545i | −0.517498 | − | 0.896333i | −0.999793 | − | 0.0203242i | \(-0.993530\pi\) |
0.482295 | − | 0.876009i | \(-0.339803\pi\) | |||||||
\(338\) | −11.9059 | − | 20.6216i | −0.647595 | − | 1.12167i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.93725 | 0.429826 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 31.7490 | − | 54.9909i | 1.71179 | − | 2.96491i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.5000 | + | 30.3109i | 0.940806 | + | 1.62952i | ||||
\(347\) | 1.32288 | + | 2.29129i | 0.0710157 | + | 0.123003i | 0.899347 | − | 0.437236i | \(-0.144043\pi\) |
−0.828331 | + | 0.560239i | \(0.810709\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.00000 | − | 1.73205i | 0.0535288 | − | 0.0927146i | −0.838019 | − | 0.545640i | \(-0.816286\pi\) |
0.891548 | + | 0.452926i | \(0.149620\pi\) | |||||||
\(350\) | 5.29150 | 0.282843 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −35.0000 | −1.86551 | ||||||||
\(353\) | −1.32288 | + | 2.29129i | −0.0704096 | + | 0.121953i | −0.899081 | − | 0.437783i | \(-0.855764\pi\) |
0.828671 | + | 0.559736i | \(0.189097\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.5000 | + | 18.1865i | 0.557282 | + | 0.965241i | ||||
\(356\) | −46.3006 | − | 80.1951i | −2.45393 | − | 4.25033i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.00000 | − | 12.1244i | 0.369961 | − | 0.640792i | ||||
\(359\) | 5.29150 | 0.279275 | 0.139637 | − | 0.990203i | \(-0.455406\pi\) | ||||
0.139637 | + | 0.990203i | \(0.455406\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.0000 | 1.57895 | ||||||||
\(362\) | −18.5203 | + | 32.0780i | −0.973403 | + | 1.68598i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.00000 | − | 8.66025i | −0.262071 | − | 0.453921i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.5000 | + | 18.1865i | −0.548096 | + | 0.949329i | 0.450310 | + | 0.892873i | \(0.351314\pi\) |
−0.998405 | + | 0.0564568i | \(0.982020\pi\) | |||||||
\(368\) | 87.3098 | 4.55134 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21.0000 | 1.09174 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.5000 | − | 25.1147i | −0.750782 | − | 1.30039i | −0.947444 | − | 0.319921i | \(-0.896344\pi\) |
0.196663 | − | 0.980471i | \(-0.436990\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.5830 | 0.545053 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.0000 | 1.84920 | 0.924598 | − | 0.380945i | \(-0.124401\pi\) | ||||
0.924598 | + | 0.380945i | \(0.124401\pi\) | |||||||
\(380\) | −46.3006 | + | 80.1951i | −2.37517 | + | 4.11392i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.50000 | + | 6.06218i | 0.179076 | + | 0.310168i | ||||
\(383\) | 7.93725 | + | 13.7477i | 0.405575 | + | 0.702476i | 0.994388 | − | 0.105793i | \(-0.0337381\pi\) |
−0.588813 | + | 0.808269i | \(0.700405\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.50000 | − | 6.06218i | 0.178377 | − | 0.308957i | ||||
\(386\) | −5.29150 | −0.269330 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −60.0000 | −3.04604 | ||||||||
\(389\) | 15.8745 | − | 27.4955i | 0.804869 | − | 1.39407i | −0.111510 | − | 0.993763i | \(-0.535569\pi\) |
0.916379 | − | 0.400312i | \(-0.131098\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 3.96863 | + | 6.87386i | 0.200446 | + | 0.347183i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 35.0000 | − | 60.6218i | 1.76327 | − | 3.05408i | ||||
\(395\) | −10.5830 | −0.532489 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.00000 | −0.301131 | −0.150566 | − | 0.988600i | \(-0.548110\pi\) | ||||
−0.150566 | + | 0.988600i | \(0.548110\pi\) | |||||||
\(398\) | −3.96863 | + | 6.87386i | −0.198929 | + | 0.344556i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11.0000 | − | 19.0526i | −0.550000 | − | 0.952628i | ||||
\(401\) | 7.93725 | + | 13.7477i | 0.396368 | + | 0.686529i | 0.993275 | − | 0.115782i | \(-0.0369373\pi\) |
−0.596907 | + | 0.802310i | \(0.703604\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.00000 | − | 5.19615i | 0.149441 | − | 0.258839i | ||||
\(404\) | −52.9150 | −2.63262 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.0000 | −0.694808 | ||||||||
\(407\) | 3.96863 | − | 6.87386i | 0.196718 | − | 0.340725i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0000 | − | 27.7128i | −0.791149 | − | 1.37031i | −0.925256 | − | 0.379344i | \(-0.876150\pi\) |
0.134107 | − | 0.990967i | \(-0.457183\pi\) | |||||||
\(410\) | −9.26013 | − | 16.0390i | −0.457325 | − | 0.792110i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 32.5000 | − | 56.2917i | 1.60116 | − | 2.77329i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −42.0000 | −2.06170 | ||||||||
\(416\) | −13.2288 | + | 22.9129i | −0.648593 | + | 1.12340i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 24.5000 | + | 42.4352i | 1.19833 | + | 2.07558i | ||||
\(419\) | −7.93725 | − | 13.7477i | −0.387760 | − | 0.671620i | 0.604388 | − | 0.796690i | \(-0.293418\pi\) |
−0.992148 | + | 0.125070i | \(0.960084\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.50000 | − | 16.4545i | 0.463002 | − | 0.801942i | −0.536107 | − | 0.844150i | \(-0.680106\pi\) |
0.999109 | + | 0.0422075i | \(0.0134391\pi\) | |||||||
\(422\) | −58.2065 | −2.83345 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.00000 | − | 6.92820i | −0.193574 | − | 0.335279i | ||||
\(428\) | 13.2288 | + | 22.9129i | 0.639436 | + | 1.10754i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 28.0000 | − | 48.4974i | 1.35028 | − | 2.33875i | ||||
\(431\) | −39.6863 | −1.91162 | −0.955810 | − | 0.293985i | \(-0.905019\pi\) | ||||
−0.955810 | + | 0.293985i | \(0.905019\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.0000 | −1.24948 | −0.624740 | − | 0.780833i | \(-0.714795\pi\) | ||||
−0.624740 | + | 0.780833i | \(0.714795\pi\) | |||||||
\(434\) | −3.96863 | + | 6.87386i | −0.190500 | + | 0.329956i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −22.5000 | − | 38.9711i | −1.07755 | − | 1.86638i | ||||
\(437\) | −27.7804 | − | 48.1170i | −1.32892 | − | 2.30175i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(440\) | −55.5608 | −2.64876 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.96863 | + | 6.87386i | −0.188555 | + | 0.326587i | −0.944769 | − | 0.327738i | \(-0.893714\pi\) |
0.756214 | + | 0.654325i | \(0.227047\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.5000 | − | 42.4352i | −1.16141 | − | 2.01162i | ||||
\(446\) | 9.26013 | + | 16.0390i | 0.438480 | + | 0.759469i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.50000 | − | 11.2583i | 0.307096 | − | 0.531906i | ||||
\(449\) | 15.8745 | 0.749164 | 0.374582 | − | 0.927194i | \(-0.377786\pi\) | ||||
0.374582 | + | 0.927194i | \(0.377786\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.00000 | −0.329617 | ||||||||
\(452\) | 13.2288 | − | 22.9129i | 0.622228 | − | 1.07773i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.0000 | + | 36.3731i | 0.985579 | + | 1.70707i | ||||
\(455\) | −2.64575 | − | 4.58258i | −0.124035 | − | 0.214834i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5000 | + | 21.6506i | −0.584725 | + | 1.01277i | 0.410184 | + | 0.912003i | \(0.365464\pi\) |
−0.994910 | + | 0.100771i | \(0.967869\pi\) | |||||||
\(458\) | −52.9150 | −2.47256 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 105.000 | 4.89565 | ||||||||
\(461\) | 9.26013 | − | 16.0390i | 0.431287 | − | 0.747011i | −0.565697 | − | 0.824613i | \(-0.691393\pi\) |
0.996984 | + | 0.0776016i | \(0.0247262\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.0000 | + | 22.5167i | 0.604161 | + | 1.04644i | 0.992183 | + | 0.124788i | \(0.0398251\pi\) |
−0.388022 | + | 0.921650i | \(0.626842\pi\) | |||||||
\(464\) | 29.1033 | + | 50.4083i | 1.35109 | + | 2.34015i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.0000 | + | 36.3731i | −0.972806 | + | 1.68495i | ||||
\(467\) | 31.7490 | 1.46917 | 0.734585 | − | 0.678517i | \(-0.237377\pi\) | ||||
0.734585 | + | 0.678517i | \(0.237377\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.00000 | 0.0923514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.5830 | − | 18.3303i | −0.486607 | − | 0.842828i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.00000 | + | 12.1244i | −0.321182 | + | 0.556304i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 42.0000 | 1.92104 | ||||||||
\(479\) | −10.5830 | + | 18.3303i | −0.483550 | + | 0.837533i | −0.999822 | − | 0.0188920i | \(-0.993986\pi\) |
0.516272 | + | 0.856425i | \(0.327319\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.00000 | − | 5.19615i | −0.136788 | − | 0.236924i | ||||
\(482\) | −5.29150 | − | 9.16515i | −0.241021 | − | 0.417461i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.0000 | − | 17.3205i | 0.454545 | − | 0.787296i | ||||
\(485\) | −31.7490 | −1.44165 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.0000 | −1.45006 | −0.725029 | − | 0.688718i | \(-0.758174\pi\) | ||||
−0.725029 | + | 0.688718i | \(0.758174\pi\) | |||||||
\(488\) | −31.7490 | + | 54.9909i | −1.43721 | + | 2.48932i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.50000 | + | 6.06218i | 0.158114 | + | 0.273861i | ||||
\(491\) | 1.32288 | + | 2.29129i | 0.0597005 | + | 0.103404i | 0.894331 | − | 0.447406i | \(-0.147652\pi\) |
−0.834630 | + | 0.550810i | \(0.814319\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 37.0405 | 1.66653 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 33.0000 | 1.48174 | ||||||||
\(497\) | −3.96863 | + | 6.87386i | −0.178017 | + | 0.308335i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.00000 | − | 3.46410i | −0.0895323 | − | 0.155074i | 0.817781 | − | 0.575529i | \(-0.195204\pi\) |
−0.907314 | + | 0.420455i | \(0.861871\pi\) | |||||||
\(500\) | 19.8431 | + | 34.3693i | 0.887412 | + | 1.53704i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.0000 | − | 24.2487i | 0.624851 | − | 1.08227i | ||||
\(503\) | 15.8745 | 0.707809 | 0.353905 | − | 0.935282i | \(-0.384854\pi\) | ||||
0.353905 | + | 0.935282i | \(0.384854\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.0000 | −1.24598 | ||||||||
\(506\) | 27.7804 | − | 48.1170i | 1.23499 | − | 2.13906i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.0000 | − | 25.9808i | −0.665517 | − | 1.15271i | ||||
\(509\) | 5.29150 | + | 9.16515i | 0.234542 | + | 0.406238i | 0.959139 | − | 0.282934i | \(-0.0913077\pi\) |
−0.724598 | + | 0.689172i | \(0.757974\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 29.1033 | 1.28619 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 49.0000 | 2.16130 | ||||||||
\(515\) | 17.1974 | − | 29.7867i | 0.757807 | − | 1.31256i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.96863 | + | 6.87386i | 0.174371 | + | 0.302020i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −21.0000 | + | 36.3731i | −0.920911 | + | 1.59506i | ||||
\(521\) | 39.6863 | 1.73869 | 0.869344 | − | 0.494208i | \(-0.164542\pi\) | ||||
0.869344 | + | 0.494208i | \(0.164542\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.0000 | 0.568450 | 0.284225 | − | 0.958758i | \(-0.408264\pi\) | ||||
0.284225 | + | 0.958758i | \(0.408264\pi\) | |||||||
\(524\) | 52.9150 | − | 91.6515i | 2.31160 | − | 4.00381i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.5000 | + | 42.4352i | 1.06825 | + | 1.85026i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.0000 | + | 34.6410i | −0.869565 | + | 1.50613i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −35.0000 | −1.51744 | ||||||||
\(533\) | −2.64575 | + | 4.58258i | −0.114600 | + | 0.198493i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.00000 | + | 12.1244i | 0.302636 | + | 0.524182i | ||||
\(536\) | −7.93725 | − | 13.7477i | −0.342837 | − | 0.593811i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −31.5000 | + | 54.5596i | −1.35806 | + | 2.35223i | ||||
\(539\) | 2.64575 | 0.113961 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.0000 | 1.24681 | 0.623404 | − | 0.781900i | \(-0.285749\pi\) | ||||
0.623404 | + | 0.781900i | \(0.285749\pi\) | |||||||
\(542\) | −26.4575 | + | 45.8258i | −1.13645 | + | 1.96838i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.9059 | − | 20.6216i | −0.509992 | − | 0.883332i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.00000 | − | 6.92820i | 0.171028 | − | 0.296229i | −0.767752 | − | 0.640747i | \(-0.778625\pi\) |
0.938779 | + | 0.344519i | \(0.111958\pi\) | |||||||
\(548\) | 79.3725 | 3.39063 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −14.0000 | −0.596962 | ||||||||
\(551\) | 18.5203 | − | 32.0780i | 0.788990 | − | 1.36657i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.00000 | − | 3.46410i | −0.0850487 | − | 0.147309i | ||||
\(554\) | −30.4261 | − | 52.6996i | −1.29268 | − | 2.23899i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 30.0000 | − | 51.9615i | 1.27228 | − | 2.20366i | ||||
\(557\) | −5.29150 | −0.224208 | −0.112104 | − | 0.993696i | \(-0.535759\pi\) | ||||
−0.112104 | + | 0.993696i | \(0.535759\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.0000 | −0.676728 | ||||||||
\(560\) | 14.5516 | − | 25.2042i | 0.614919 | − | 1.06507i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.0000 | − | 24.2487i | −0.590554 | − | 1.02287i | ||||
\(563\) | −13.2288 | − | 22.9129i | −0.557526 | − | 0.965663i | −0.997702 | − | 0.0677515i | \(-0.978418\pi\) |
0.440177 | − | 0.897911i | \(-0.354916\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.00000 | − | 12.1244i | 0.294492 | − | 0.510075i | ||||
\(566\) | −10.5830 | −0.444837 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 63.0000 | 2.64342 | ||||||||
\(569\) | −13.2288 | + | 22.9129i | −0.554578 | + | 0.960558i | 0.443358 | + | 0.896345i | \(0.353787\pi\) |
−0.997936 | + | 0.0642132i | \(0.979546\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.00000 | + | 8.66025i | 0.209243 | + | 0.362420i | 0.951476 | − | 0.307722i | \(-0.0995665\pi\) |
−0.742233 | + | 0.670142i | \(0.766233\pi\) | |||||||
\(572\) | 13.2288 | + | 22.9129i | 0.553122 | + | 0.958036i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.50000 | − | 6.06218i | 0.146087 | − | 0.253030i | ||||
\(575\) | 15.8745 | 0.662013 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.0000 | −1.58196 | −0.790980 | − | 0.611842i | \(-0.790429\pi\) | ||||
−0.790980 | + | 0.611842i | \(0.790429\pi\) | |||||||
\(578\) | −22.4889 | + | 38.9519i | −0.935414 | + | 1.62019i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 35.0000 | + | 60.6218i | 1.45330 | + | 2.51718i | ||||
\(581\) | −7.93725 | − | 13.7477i | −0.329293 | − | 0.570352i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.0000 | 1.15667 | ||||||||
\(587\) | −13.2288 | + | 22.9129i | −0.546009 | + | 0.945716i | 0.452533 | + | 0.891747i | \(0.350520\pi\) |
−0.998543 | + | 0.0539683i | \(0.982813\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.5000 | − | 18.1865i | −0.432645 | − | 0.749363i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 16.5000 | − | 28.5788i | 0.678146 | − | 1.17458i | ||||
\(593\) | −23.8118 | −0.977832 | −0.488916 | − | 0.872331i | \(-0.662608\pi\) | ||||
−0.488916 | + | 0.872331i | \(0.662608\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −39.6863 | + | 68.7386i | −1.62561 | + | 2.81564i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −21.0000 | − | 36.3731i | −0.858754 | − | 1.48741i | ||||
\(599\) | 3.96863 | + | 6.87386i | 0.162154 | + | 0.280858i | 0.935641 | − | 0.352954i | \(-0.114823\pi\) |
−0.773487 | + | 0.633812i | \(0.781489\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.0000 | − | 25.9808i | 0.611863 | − | 1.05978i | −0.379063 | − | 0.925371i | \(-0.623754\pi\) |
0.990926 | − | 0.134407i | \(-0.0429129\pi\) | |||||||
\(602\) | 21.1660 | 0.862662 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.0000 | 0.406894 | ||||||||
\(605\) | 5.29150 | − | 9.16515i | 0.215130 | − | 0.372616i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.0000 | + | 24.2487i | 0.568242 | + | 0.984225i | 0.996740 | + | 0.0806818i | \(0.0257098\pi\) |
−0.428497 | + | 0.903543i | \(0.640957\pi\) | |||||||
\(608\) | 46.3006 | + | 80.1951i | 1.87774 | + | 3.25234i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −28.0000 | + | 48.4974i | −1.13369 | + | 1.96360i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.0000 | 0.767403 | 0.383701 | − | 0.923457i | \(-0.374649\pi\) | ||||
0.383701 | + | 0.923457i | \(0.374649\pi\) | |||||||
\(614\) | 25.1346 | − | 43.5345i | 1.01435 | − | 1.75691i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.5000 | − | 18.1865i | −0.423057 | − | 0.732756i | ||||
\(617\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.5000 | + | 26.8468i | −0.622998 | + | 1.07906i | 0.365927 | + | 0.930644i | \(0.380752\pi\) |
−0.988924 | + | 0.148420i | \(0.952581\pi\) | |||||||
\(620\) | 39.6863 | 1.59384 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 42.0000 | 1.68405 | ||||||||
\(623\) | 9.26013 | − | 16.0390i | 0.370999 | − | 0.642590i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5000 | + | 26.8468i | 0.620000 | + | 1.07387i | ||||
\(626\) | 18.5203 | + | 32.0780i | 0.740218 | + | 1.28210i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 35.0000 | − | 60.6218i | 1.39665 | − | 2.41907i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | −15.8745 | + | 27.4955i | −0.631454 | + | 1.09371i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.93725 | − | 13.7477i | −0.314980 | − | 0.545562i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | − | 1.73205i | 0.0396214 | − | 0.0686264i | ||||
\(638\) | 37.0405 | 1.46645 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −21.0000 | −0.830098 | ||||||||
\(641\) | 7.93725 | − | 13.7477i | 0.313503 | − | 0.543003i | −0.665615 | − | 0.746295i | \(-0.731831\pi\) |
0.979118 | + | 0.203292i | \(0.0651642\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.5000 | − | 19.9186i | −0.453516 | − | 0.785512i | 0.545086 | − | 0.838380i | \(-0.316497\pi\) |
−0.998602 | + | 0.0528680i | \(0.983164\pi\) | |||||||
\(644\) | 19.8431 | + | 34.3693i | 0.781929 | + | 1.35434i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.5830 | −0.416061 | −0.208030 | − | 0.978122i | \(-0.566705\pi\) | ||||
−0.208030 | + | 0.978122i | \(0.566705\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −5.29150 | + | 9.16515i | −0.207550 | + | 0.359487i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −25.0000 | − | 43.3013i | −0.979076 | − | 1.69581i | ||||
\(653\) | −15.8745 | − | 27.4955i | −0.621217 | − | 1.07598i | −0.989259 | − | 0.146171i | \(-0.953305\pi\) |
0.368042 | − | 0.929809i | \(-0.380028\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.0000 | − | 48.4974i | 1.09405 | − | 1.89495i | ||||
\(656\) | −29.1033 | −1.13629 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.9059 | + | 20.6216i | −0.463787 | + | 0.803303i | −0.999146 | − | 0.0413217i | \(-0.986843\pi\) |
0.535359 | + | 0.844625i | \(0.320176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.00000 | + | 12.1244i | 0.272268 | + | 0.471583i | 0.969442 | − | 0.245319i | \(-0.0788928\pi\) |
−0.697174 | + | 0.716902i | \(0.745559\pi\) | |||||||
\(662\) | 26.4575 | + | 45.8258i | 1.02830 | + | 1.78107i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −63.0000 | + | 109.119i | −2.44487 | + | 4.23465i | ||||
\(665\) | −18.5203 | −0.718185 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −42.0000 | −1.62625 | ||||||||
\(668\) | 13.2288 | − | 22.9129i | 0.511836 | − | 0.886526i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.00000 | − | 12.1244i | −0.270434 | − | 0.468405i | ||||
\(671\) | 10.5830 | + | 18.3303i | 0.408552 | + | 0.707633i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.00000 | − | 1.73205i | 0.0385472 | − | 0.0667657i | −0.846108 | − | 0.533011i | \(-0.821060\pi\) |
0.884655 | + | 0.466246i | \(0.154394\pi\) | |||||||
\(674\) | −50.2693 | −1.93630 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −45.0000 | −1.73077 | ||||||||
\(677\) | −3.96863 | + | 6.87386i | −0.152527 | + | 0.264184i | −0.932156 | − | 0.362058i | \(-0.882074\pi\) |
0.779629 | + | 0.626242i | \(0.215408\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.00000 | − | 10.3923i | −0.230259 | − | 0.398820i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.5000 | − | 18.1865i | 0.402066 | − | 0.696398i | ||||
\(683\) | −23.8118 | −0.911132 | −0.455566 | − | 0.890202i | \(-0.650563\pi\) | ||||
−0.455566 | + | 0.890202i | \(0.650563\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 42.0000 | 1.60474 | ||||||||
\(686\) | −1.32288 | + | 2.29129i | −0.0505076 | + | 0.0874818i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −44.0000 | − | 76.2102i | −1.67748 | − | 2.90549i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00000 | + | 6.92820i | −0.152167 | + | 0.263561i | −0.932024 | − | 0.362397i | \(-0.881959\pi\) |
0.779857 | + | 0.625958i | \(0.215292\pi\) | |||||||
\(692\) | 66.1438 | 2.51441 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.00000 | 0.265716 | ||||||||
\(695\) | 15.8745 | − | 27.4955i | 0.602154 | − | 1.04296i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −2.64575 | − | 4.58258i | −0.100143 | − | 0.173453i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.00000 | − | 8.66025i | 0.188982 | − | 0.327327i | ||||
\(701\) | 15.8745 | 0.599572 | 0.299786 | − | 0.954006i | \(-0.403085\pi\) | ||||
0.299786 | + | 0.954006i | \(0.403085\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.0000 | −0.792030 | ||||||||
\(704\) | −17.1974 | + | 29.7867i | −0.648151 | + | 1.12263i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.50000 | + | 6.06218i | 0.131724 | + | 0.228153i | ||||
\(707\) | −5.29150 | − | 9.16515i | −0.199007 | − | 0.344691i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.50000 | − | 2.59808i | 0.0563337 | − | 0.0975728i | −0.836483 | − | 0.547992i | \(-0.815392\pi\) |
0.892817 | + | 0.450420i | \(0.148726\pi\) | |||||||
\(710\) | 55.5608 | 2.08516 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −147.000 | −5.50906 | ||||||||
\(713\) | −11.9059 | + | 20.6216i | −0.445879 | + | 0.772285i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.00000 | + | 12.1244i | 0.261785 | + | 0.453425i | ||||
\(716\) | −13.2288 | − | 22.9129i | −0.494382 | − | 0.856294i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.00000 | − | 12.1244i | 0.261238 | − | 0.452477i | ||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.0000 | 0.484145 | ||||||||
\(722\) | 39.6863 | − | 68.7386i | 1.47697 | − | 2.55819i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 35.0000 | + | 60.6218i | 1.30076 | + | 2.25299i | ||||
\(725\) | 5.29150 | + | 9.16515i | 0.196521 | + | 0.340385i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.0000 | − | 34.6410i | 0.741759 | − | 1.28476i | −0.209935 | − | 0.977715i | \(-0.567325\pi\) |
0.951694 | − | 0.307049i | \(-0.0993415\pi\) | |||||||
\(728\) | −15.8745 | −0.588348 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.0000 | − | 31.1769i | −0.664845 | − | 1.15155i | −0.979327 | − | 0.202282i | \(-0.935164\pi\) |
0.314482 | − | 0.949263i | \(-0.398169\pi\) | |||||||
\(734\) | 27.7804 | + | 48.1170i | 1.02539 | + | 1.77603i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 52.5000 | − | 90.9327i | 1.93518 | − | 3.35182i | ||||
\(737\) | −5.29150 | −0.194915 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.0000 | −1.10357 | −0.551784 | − | 0.833987i | \(-0.686053\pi\) | ||||
−0.551784 | + | 0.833987i | \(0.686053\pi\) | |||||||
\(740\) | 19.8431 | − | 34.3693i | 0.729448 | − | 1.26344i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.9059 | − | 20.6216i | −0.436784 | − | 0.756533i | 0.560655 | − | 0.828050i | \(-0.310549\pi\) |
−0.997439 | + | 0.0715167i | \(0.977216\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.0000 | + | 36.3731i | −0.769380 | + | 1.33261i | ||||
\(746\) | −76.7268 | −2.80917 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.64575 | + | 4.58258i | −0.0966736 | + | 0.167444i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.00000 | + | 6.92820i | 0.145962 | + | 0.252814i | 0.929731 | − | 0.368238i | \(-0.120039\pi\) |
−0.783769 | + | 0.621052i | \(0.786706\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14.0000 | − | 24.2487i | 0.509850 | − | 0.883086i | ||||
\(755\) | 5.29150 | 0.192577 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.0000 | −1.23575 | −0.617876 | − | 0.786276i | \(-0.712006\pi\) | ||||
−0.617876 | + | 0.786276i | \(0.712006\pi\) | |||||||
\(758\) | 47.6235 | − | 82.4864i | 1.72976 | − | 2.99604i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 73.5000 | + | 127.306i | 2.66613 | + | 4.61786i | ||||
\(761\) | 15.8745 | + | 27.4955i | 0.575450 | + | 0.996709i | 0.995993 | + | 0.0894364i | \(0.0285066\pi\) |
−0.420542 | + | 0.907273i | \(0.638160\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.50000 | − | 7.79423i | 0.162911 | − | 0.282170i | ||||
\(764\) | 13.2288 | 0.478600 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 42.0000 | 1.51752 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.00000 | − | 12.1244i | −0.252426 | − | 0.437215i | 0.711767 | − | 0.702416i | \(-0.247895\pi\) |
−0.964193 | + | 0.265200i | \(0.914562\pi\) | |||||||
\(770\) | −9.26013 | − | 16.0390i | −0.333712 | − | 0.578006i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.00000 | + | 8.66025i | −0.179954 | + | 0.311689i | ||||
\(773\) | −2.64575 | −0.0951611 | −0.0475805 | − | 0.998867i | \(-0.515151\pi\) | ||||
−0.0475805 | + | 0.998867i | \(0.515151\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.00000 | 0.215526 | ||||||||
\(776\) | −47.6235 | + | 82.4864i | −1.70958 | + | 2.96109i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −42.0000 | − | 72.7461i | −1.50577 | − | 2.60808i | ||||
\(779\) | 9.26013 | + | 16.0390i | 0.331779 | + | 0.574657i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.5000 | − | 18.1865i | 0.375720 | − | 0.650765i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11.0000 | 0.392857 | ||||||||
\(785\) | 18.5203 | − | 32.0780i | 0.661016 | − | 1.14491i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.00000 | − | 3.46410i | −0.0712923 | − | 0.123482i | 0.828176 | − | 0.560469i | \(-0.189379\pi\) |
−0.899468 | + | 0.436987i | \(0.856046\pi\) | |||||||
\(788\) | −66.1438 | − | 114.564i | −2.35627 | − | 4.08119i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −14.0000 | + | 24.2487i | −0.498098 | + | 0.862730i | ||||
\(791\) | 5.29150 | 0.188144 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.0000 | 0.568177 | ||||||||
\(794\) | −7.93725 | + | 13.7477i | −0.281683 | + | 0.487889i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.50000 | + | 12.9904i | 0.265830 | + | 0.460432i | ||||
\(797\) | 22.4889 | + | 38.9519i | 0.796597 | + | 1.37975i | 0.921820 | + | 0.387618i | \(0.126702\pi\) |
−0.125223 | + | 0.992129i | \(0.539965\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −26.4575 | −0.935414 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 42.0000 | 1.48307 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.5000 | + | 18.1865i | 0.370076 | + | 0.640991i | ||||
\(806\) | −7.93725 | − | 13.7477i | −0.279578 | − | 0.484243i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −42.0000 | + | 72.7461i | −1.47755 | + | 2.55920i | ||||
\(809\) | 15.8745 | 0.558118 | 0.279059 | − | 0.960274i | \(-0.409977\pi\) | ||||
0.279059 | + | 0.960274i | \(0.409977\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.0000 | 1.22902 | 0.614508 | − | 0.788911i | \(-0.289355\pi\) | ||||
0.614508 | + | 0.788911i | \(0.289355\pi\) | |||||||
\(812\) | −13.2288 | + | 22.9129i | −0.464238 | + | 0.804084i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.5000 | − | 18.1865i | −0.368025 | − | 0.637438i | ||||
\(815\) | −13.2288 | − | 22.9129i | −0.463383 | − | 0.802603i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.0000 | + | 48.4974i | −0.979596 | + | 1.69671i | ||||
\(818\) | −84.6640 | −2.96021 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −35.0000 | −1.22225 | ||||||||
\(821\) | −10.5830 | + | 18.3303i | −0.369349 | + | 0.639732i | −0.989464 | − | 0.144779i | \(-0.953753\pi\) |
0.620115 | + | 0.784511i | \(0.287086\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.0000 | + | 25.9808i | 0.522867 | + | 0.905632i | 0.999646 | + | 0.0266091i | \(0.00847095\pi\) |
−0.476779 | + | 0.879023i | \(0.658196\pi\) | |||||||
\(824\) | −51.5922 | − | 89.3602i | −1.79730 | − | 3.11301i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.6863 | −1.38003 | −0.690013 | − | 0.723797i | \(-0.742395\pi\) | ||||
−0.690013 | + | 0.723797i | \(0.742395\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.0000 | −0.972480 | −0.486240 | − | 0.873825i | \(-0.661632\pi\) | ||||
−0.486240 | + | 0.873825i | \(0.661632\pi\) | |||||||
\(830\) | −55.5608 | + | 96.2341i | −1.92854 | + | 3.34033i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13.0000 | + | 22.5167i | 0.450694 | + | 0.780625i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.00000 | − | 12.1244i | 0.242245 | − | 0.419581i | ||||
\(836\) | 92.6013 | 3.20268 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −42.0000 | −1.45087 | ||||||||
\(839\) | 2.64575 | − | 4.58258i | 0.0913415 | − | 0.158208i | −0.816734 | − | 0.577014i | \(-0.804218\pi\) |
0.908076 | + | 0.418806i | \(0.137551\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.500000 | + | 0.866025i | 0.0172414 | + | 0.0298629i | ||||
\(842\) | −25.1346 | − | 43.5345i | −0.866197 | − | 1.50030i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −55.0000 | + | 95.2628i | −1.89318 | + | 3.27908i | ||||
\(845\) | −23.8118 | −0.819150 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.00000 | 0.137442 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.9059 | + | 20.6216i | 0.408128 | + | 0.706899i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.0000 | − | 24.2487i | 0.479351 | − | 0.830260i | −0.520369 | − | 0.853942i | \(-0.674205\pi\) |
0.999720 | + | 0.0236816i | \(0.00753881\pi\) | |||||||
\(854\) | −21.1660 | −0.724286 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 42.0000 | 1.43553 | ||||||||
\(857\) | 6.61438 | − | 11.4564i | 0.225943 | − | 0.391345i | −0.730659 | − | 0.682743i | \(-0.760787\pi\) |
0.956602 | + | 0.291398i | \(0.0941204\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.50000 | + | 11.2583i | 0.221777 | + | 0.384129i | 0.955348 | − | 0.295484i | \(-0.0954809\pi\) |
−0.733571 | + | 0.679613i | \(0.762148\pi\) | |||||||
\(860\) | −52.9150 | − | 91.6515i | −1.80439 | − | 3.12529i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −52.5000 | + | 90.9327i | −1.78816 | + | 3.09718i | ||||
\(863\) | −15.8745 | −0.540375 | −0.270187 | − | 0.962808i | \(-0.587086\pi\) | ||||
−0.270187 | + | 0.962808i | \(0.587086\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.0000 | 1.19004 | ||||||||
\(866\) | −34.3948 | + | 59.5735i | −1.16878 | + | 2.02439i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.50000 | + | 12.9904i | 0.254567 | + | 0.440922i | ||||
\(869\) | 5.29150 | + | 9.16515i | 0.179502 | + | 0.310906i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.00000 | + | 3.46410i | −0.0677674 | + | 0.117377i | ||||
\(872\) | −71.4353 | −2.41910 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −147.000 | −4.97235 | ||||||||
\(875\) | −3.96863 | + | 6.87386i | −0.134164 | + | 0.232379i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.00000 | − | 8.66025i | −0.168838 | − | 0.292436i | 0.769174 | − | 0.639040i | \(-0.220668\pi\) |
−0.938012 | + | 0.346604i | \(0.887335\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −38.5000 | + | 66.6840i | −1.29783 | + | 2.24792i | ||||
\(881\) | 23.8118 | 0.802239 | 0.401119 | − | 0.916026i | \(-0.368621\pi\) | ||||
0.401119 | + | 0.916026i | \(0.368621\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.0000 | −0.538443 | −0.269221 | − | 0.963078i | \(-0.586766\pi\) | ||||
−0.269221 | + | 0.963078i | \(0.586766\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.5000 | + | 18.1865i | 0.352754 | + | 0.610989i | ||||
\(887\) | −18.5203 | − | 32.0780i | −0.621849 | − | 1.07707i | −0.989141 | − | 0.146969i | \(-0.953048\pi\) |
0.367292 | − | 0.930106i | \(-0.380285\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.00000 | − | 5.19615i | 0.100617 | − | 0.174273i | ||||
\(890\) | −129.642 | −4.34560 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 35.0000 | 1.17189 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.00000 | − | 12.1244i | −0.233984 | − | 0.405273i | ||||
\(896\) | −3.96863 | − | 6.87386i | −0.132583 | − | 0.229640i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.0000 | − | 36.3731i | 0.700779 | − | 1.21378i | ||||
\(899\) | −15.8745 | −0.529444 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −9.26013 | + | 16.0390i | −0.308329 | + | 0.534041i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −21.0000 | − | 36.3731i | −0.698450 | − | 1.20975i | ||||
\(905\) | 18.5203 | + | 32.0780i | 0.615634 | + | 1.06631i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.00000 | + | 1.73205i | −0.0332045 | + | 0.0575118i | −0.882150 | − | 0.470968i | \(-0.843905\pi\) |
0.848946 | + | 0.528480i | \(0.177238\pi\) | |||||||
\(908\) | 79.3725 | 2.63407 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −14.0000 | −0.464095 | ||||||||
\(911\) | −23.8118 | + | 41.2432i | −0.788919 | + | 1.36645i | 0.137711 | + | 0.990472i | \(0.456026\pi\) |
−0.926630 | + | 0.375975i | \(0.877308\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.0000 | + | 36.3731i | 0.694999 | + | 1.20377i | ||||
\(914\) | 33.0719 | + | 57.2822i | 1.09392 | + | 1.89473i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −50.0000 | + | 86.6025i | −1.65205 | + | 2.86143i | ||||
\(917\) | 21.1660 | 0.698963 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.0000 | 1.05558 | 0.527791 | − | 0.849374i | \(-0.323020\pi\) | ||||
0.527791 | + | 0.849374i | \(0.323020\pi\) | |||||||
\(920\) | 83.3412 | − | 144.351i | 2.74768 | − | 4.75912i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −24.5000 | − | 42.4352i | −0.806865 | − | 1.39753i | ||||
\(923\) | −7.93725 | − | 13.7477i | −0.261258 | − | 0.452512i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.00000 | − | 5.19615i | 0.0986394 | − | 0.170848i | ||||
\(926\) | 68.7895 | 2.26056 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 70.0000 | 2.29786 | ||||||||
\(929\) | 21.1660 | − | 36.6606i | 0.694434 | − | 1.20280i | −0.275937 | − | 0.961176i | \(-0.588988\pi\) |
0.970371 | − | 0.241620i | \(-0.0776786\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.50000 | − | 6.06218i | −0.114708 | − | 0.198680i | ||||
\(932\) | 39.6863 | + | 68.7386i | 1.29997 | + | 2.25161i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 42.0000 | − | 72.7461i | 1.37428 | − | 2.38033i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.0000 | −0.392023 | −0.196011 | − | 0.980602i | \(-0.562799\pi\) | ||||
−0.196011 | + | 0.980602i | \(0.562799\pi\) | |||||||
\(938\) | 2.64575 | − | 4.58258i | 0.0863868 | − | 0.149626i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.1346 | + | 43.5345i | 0.819366 | + | 1.41918i | 0.906150 | + | 0.422956i | \(0.139008\pi\) |
−0.0867844 | + | 0.996227i | \(0.527659\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.5000 | − | 18.1865i | 0.341927 | − | 0.592235i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −56.0000 | −1.82072 | ||||||||
\(947\) | 9.26013 | − | 16.0390i | 0.300914 | − | 0.521198i | −0.675429 | − | 0.737425i | \(-0.736042\pi\) |
0.976343 | + | 0.216227i | \(0.0693750\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 18.5203 | + | 32.0780i | 0.600877 | + | 1.04075i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.4575 | −0.857043 | −0.428521 | − | 0.903532i | \(-0.640965\pi\) | ||||
−0.428521 | + | 0.903532i | \(0.640965\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.00000 | 0.226515 | ||||||||
\(956\) | 39.6863 | − | 68.7386i | 1.28355 | − | 2.22317i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.0000 | + | 48.4974i | 0.904639 | + | 1.56688i | ||||
\(959\) | 7.93725 | + | 13.7477i | 0.256307 | + | 0.443937i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | − | 19.0526i | 0.354839 | − | 0.614599i | ||||
\(962\) | −15.8745 | −0.511815 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −20.0000 | −0.644157 | ||||||||
\(965\) | −2.64575 | + | 4.58258i | −0.0851697 | + | 0.147518i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.0000 | + | 43.3013i | 0.803946 | + | 1.39247i | 0.917000 | + | 0.398886i | \(0.130603\pi\) |
−0.113055 | + | 0.993589i | \(0.536064\pi\) | |||||||
\(968\) | −15.8745 | − | 27.4955i | −0.510226 | − | 0.883737i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −42.0000 | + | 72.7461i | −1.34854 | + | 2.33574i | ||||
\(971\) | 15.8745 | 0.509437 | 0.254719 | − | 0.967015i | \(-0.418017\pi\) | ||||
0.254719 | + | 0.967015i | \(0.418017\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0000 | 0.384702 | ||||||||
\(974\) | −42.3320 | + | 73.3212i | −1.35641 | + | 2.34936i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 44.0000 | + | 76.2102i | 1.40841 | + | 2.43943i | ||||
\(977\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.5000 | + | 42.4352i | −0.783023 | + | 1.35624i | ||||
\(980\) | 13.2288 | 0.422577 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.00000 | 0.223379 | ||||||||
\(983\) | 15.8745 | − | 27.4955i | 0.506318 | − | 0.876969i | −0.493655 | − | 0.869658i | \(-0.664339\pi\) |
0.999973 | − | 0.00731102i | \(-0.00232719\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35.0000 | − | 60.6218i | −1.11519 | − | 1.93157i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 35.0000 | − | 60.6218i | 1.11350 | − | 1.92864i | ||||
\(989\) | 63.4980 | 2.01912 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.00000 | 0.0635321 | 0.0317660 | − | 0.999495i | \(-0.489887\pi\) | ||||
0.0317660 | + | 0.999495i | \(0.489887\pi\) | |||||||
\(992\) | 19.8431 | − | 34.3693i | 0.630020 | − | 1.09123i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.5000 | + | 18.1865i | 0.333040 | + | 0.576842i | ||||
\(995\) | 3.96863 | + | 6.87386i | 0.125814 | + | 0.217916i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.0000 | − | 32.9090i | 0.601736 | − | 1.04224i | −0.390822 | − | 0.920466i | \(-0.627809\pi\) |
0.992558 | − | 0.121771i | \(-0.0388574\pi\) | |||||||
\(998\) | −10.5830 | −0.334999 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 567.2.f.i.379.2 | 4 | ||
3.2 | odd | 2 | inner | 567.2.f.i.379.1 | 4 | ||
9.2 | odd | 6 | 189.2.a.f.1.2 | yes | 2 | ||
9.4 | even | 3 | inner | 567.2.f.i.190.2 | 4 | ||
9.5 | odd | 6 | inner | 567.2.f.i.190.1 | 4 | ||
9.7 | even | 3 | 189.2.a.f.1.1 | ✓ | 2 | ||
36.7 | odd | 6 | 3024.2.a.bi.1.2 | 2 | |||
36.11 | even | 6 | 3024.2.a.bi.1.1 | 2 | |||
45.29 | odd | 6 | 4725.2.a.bb.1.1 | 2 | |||
45.34 | even | 6 | 4725.2.a.bb.1.2 | 2 | |||
63.20 | even | 6 | 1323.2.a.w.1.2 | 2 | |||
63.34 | odd | 6 | 1323.2.a.w.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.a.f.1.1 | ✓ | 2 | 9.7 | even | 3 | ||
189.2.a.f.1.2 | yes | 2 | 9.2 | odd | 6 | ||
567.2.f.i.190.1 | 4 | 9.5 | odd | 6 | inner | ||
567.2.f.i.190.2 | 4 | 9.4 | even | 3 | inner | ||
567.2.f.i.379.1 | 4 | 3.2 | odd | 2 | inner | ||
567.2.f.i.379.2 | 4 | 1.1 | even | 1 | trivial | ||
1323.2.a.w.1.1 | 2 | 63.34 | odd | 6 | |||
1323.2.a.w.1.2 | 2 | 63.20 | even | 6 | |||
3024.2.a.bi.1.1 | 2 | 36.11 | even | 6 | |||
3024.2.a.bi.1.2 | 2 | 36.7 | odd | 6 | |||
4725.2.a.bb.1.1 | 2 | 45.29 | odd | 6 | |||
4725.2.a.bb.1.2 | 2 | 45.34 | even | 6 |