Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [322,2,Mod(321,322)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(322, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("322.321");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 322.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: | \(2.57118294509\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.2312.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 321.3 | ||
Root | \(1.28078 + 0.599676i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 322.321 |
Dual form | 322.2.c.d.321.2 |
$q$-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 \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).
\(n\) | \(185\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.936426i | 0.540646i | 0.962770 | + | 0.270323i | \(0.0871305\pi\) | ||||
−0.962770 | + | 0.270323i | \(0.912870\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0.936426i | 0.382294i | ||||||||
\(7\) | −1.56155 | − | 2.13578i | −0.590211 | − | 0.807249i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.12311 | 0.707702 | ||||||||
\(10\) | 2.00000 | 0.632456 | ||||||||
\(11\) | − | 0.936426i | − | 0.282343i | −0.989985 | − | 0.141172i | \(-0.954913\pi\) | ||
0.989985 | − | 0.141172i | \(-0.0450869\pi\) | |||||||
\(12\) | 0.936426i | 0.270323i | ||||||||
\(13\) | 3.33513i | 0.924999i | 0.886619 | + | 0.462500i | \(0.153047\pi\) | ||||
−0.886619 | + | 0.462500i | \(0.846953\pi\) | |||||||
\(14\) | −1.56155 | − | 2.13578i | −0.417343 | − | 0.570811i | ||||
\(15\) | 1.87285i | 0.483569i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.12311 | 0.272393 | 0.136197 | − | 0.990682i | \(-0.456512\pi\) | ||||
0.136197 | + | 0.990682i | \(0.456512\pi\) | |||||||
\(18\) | 2.12311 | 0.500421 | ||||||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | 2.00000 | 0.447214 | ||||||||
\(21\) | 2.00000 | − | 1.46228i | 0.436436 | − | 0.319095i | ||||
\(22\) | − | 0.936426i | − | 0.199647i | ||||||
\(23\) | −1.56155 | + | 4.53448i | −0.325606 | + | 0.945505i | ||||
\(24\) | 0.936426i | 0.191147i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 3.33513i | 0.654073i | ||||||||
\(27\) | 4.79741i | 0.923262i | ||||||||
\(28\) | −1.56155 | − | 2.13578i | −0.295106 | − | 0.403624i | ||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 1.87285i | 0.341935i | ||||||||
\(31\) | − | 9.06897i | − | 1.62884i | −0.580279 | − | 0.814418i | \(-0.697057\pi\) | ||
0.580279 | − | 0.814418i | \(-0.302943\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.876894 | 0.152648 | ||||||||
\(34\) | 1.12311 | 0.192611 | ||||||||
\(35\) | −3.12311 | − | 4.27156i | −0.527901 | − | 0.722025i | ||||
\(36\) | 2.12311 | 0.353851 | ||||||||
\(37\) | 3.33513i | 0.548292i | 0.961688 | + | 0.274146i | \(0.0883952\pi\) | ||||
−0.961688 | + | 0.274146i | \(0.911605\pi\) | |||||||
\(38\) | −4.00000 | −0.648886 | ||||||||
\(39\) | −3.12311 | −0.500097 | ||||||||
\(40\) | 2.00000 | 0.316228 | ||||||||
\(41\) | − | 6.67026i | − | 1.04172i | −0.853642 | − | 0.520860i | \(-0.825611\pi\) | ||
0.853642 | − | 0.520860i | \(-0.174389\pi\) | |||||||
\(42\) | 2.00000 | − | 1.46228i | 0.308607 | − | 0.225635i | ||||
\(43\) | − | 0.936426i | − | 0.142804i | −0.997448 | − | 0.0714018i | \(-0.977253\pi\) | ||
0.997448 | − | 0.0714018i | \(-0.0227473\pi\) | |||||||
\(44\) | − | 0.936426i | − | 0.141172i | ||||||
\(45\) | 4.24621 | 0.632988 | ||||||||
\(46\) | −1.56155 | + | 4.53448i | −0.230238 | + | 0.668573i | ||||
\(47\) | − | 6.14441i | − | 0.896254i | −0.893970 | − | 0.448127i | \(-0.852091\pi\) | ||
0.893970 | − | 0.448127i | \(-0.147909\pi\) | |||||||
\(48\) | 0.936426i | 0.135162i | ||||||||
\(49\) | −2.12311 | + | 6.67026i | −0.303301 | + | 0.952895i | ||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 1.05171i | 0.147268i | ||||||||
\(52\) | 3.33513i | 0.462500i | ||||||||
\(53\) | 0.410574i | 0.0563966i | 0.999602 | + | 0.0281983i | \(0.00897699\pi\) | ||||
−0.999602 | + | 0.0281983i | \(0.991023\pi\) | |||||||
\(54\) | 4.79741i | 0.652845i | ||||||||
\(55\) | − | 1.87285i | − | 0.252535i | ||||||
\(56\) | −1.56155 | − | 2.13578i | −0.208671 | − | 0.285406i | ||||
\(57\) | − | 3.74571i | − | 0.496131i | ||||||
\(58\) | −2.00000 | −0.262613 | ||||||||
\(59\) | − | 2.80928i | − | 0.365737i | −0.983137 | − | 0.182868i | \(-0.941462\pi\) | ||
0.983137 | − | 0.182868i | \(-0.0585383\pi\) | |||||||
\(60\) | 1.87285i | 0.241784i | ||||||||
\(61\) | −12.2462 | −1.56797 | −0.783983 | − | 0.620782i | \(-0.786815\pi\) | ||||
−0.783983 | + | 0.620782i | \(0.786815\pi\) | |||||||
\(62\) | − | 9.06897i | − | 1.15176i | ||||||
\(63\) | −3.31534 | − | 4.53448i | −0.417694 | − | 0.571291i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.67026i | 0.827344i | ||||||||
\(66\) | 0.876894 | 0.107938 | ||||||||
\(67\) | − | 7.60669i | − | 0.929305i | −0.885493 | − | 0.464653i | \(-0.846179\pi\) | ||
0.885493 | − | 0.464653i | \(-0.153821\pi\) | |||||||
\(68\) | 1.12311 | 0.136197 | ||||||||
\(69\) | −4.24621 | − | 1.46228i | −0.511184 | − | 0.176038i | ||||
\(70\) | −3.12311 | − | 4.27156i | −0.373283 | − | 0.510549i | ||||
\(71\) | −9.36932 | −1.11193 | −0.555967 | − | 0.831205i | \(-0.687652\pi\) | ||||
−0.555967 | + | 0.831205i | \(0.687652\pi\) | |||||||
\(72\) | 2.12311 | 0.250210 | ||||||||
\(73\) | 3.74571i | 0.438402i | 0.975680 | + | 0.219201i | \(0.0703450\pi\) | ||||
−0.975680 | + | 0.219201i | \(0.929655\pi\) | |||||||
\(74\) | 3.33513i | 0.387701i | ||||||||
\(75\) | − | 0.936426i | − | 0.108129i | ||||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | −2.00000 | + | 1.46228i | −0.227921 | + | 0.166642i | ||||
\(78\) | −3.12311 | −0.353622 | ||||||||
\(79\) | 12.8147i | 1.44176i | 0.693058 | + | 0.720882i | \(0.256263\pi\) | ||||
−0.693058 | + | 0.720882i | \(0.743737\pi\) | |||||||
\(80\) | 2.00000 | 0.223607 | ||||||||
\(81\) | 1.87689 | 0.208544 | ||||||||
\(82\) | − | 6.67026i | − | 0.736607i | ||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | 2.00000 | − | 1.46228i | 0.218218 | − | 0.159548i | ||||
\(85\) | 2.24621 | 0.243636 | ||||||||
\(86\) | − | 0.936426i | − | 0.100977i | ||||||
\(87\) | − | 1.87285i | − | 0.200791i | ||||||
\(88\) | − | 0.936426i | − | 0.0998234i | ||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 4.24621 | 0.447590 | ||||||||
\(91\) | 7.12311 | − | 5.20798i | 0.746704 | − | 0.545945i | ||||
\(92\) | −1.56155 | + | 4.53448i | −0.162803 | + | 0.472753i | ||||
\(93\) | 8.49242 | 0.880623 | ||||||||
\(94\) | − | 6.14441i | − | 0.633748i | ||||||
\(95\) | −8.00000 | −0.820783 | ||||||||
\(96\) | 0.936426i | 0.0955736i | ||||||||
\(97\) | 12.2462 | 1.24341 | 0.621707 | − | 0.783250i | \(-0.286439\pi\) | ||||
0.621707 | + | 0.783250i | \(0.286439\pi\) | |||||||
\(98\) | −2.12311 | + | 6.67026i | −0.214466 | + | 0.673798i | ||||
\(99\) | − | 1.98813i | − | 0.199815i | ||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 10.0054i | 0.995574i | 0.867299 | + | 0.497787i | \(0.165854\pi\) | ||||
−0.867299 | + | 0.497787i | \(0.834146\pi\) | |||||||
\(102\) | 1.05171i | 0.104134i | ||||||||
\(103\) | 19.1231 | 1.88426 | 0.942128 | − | 0.335254i | \(-0.108822\pi\) | ||||
0.942128 | + | 0.335254i | \(0.108822\pi\) | |||||||
\(104\) | 3.33513i | 0.327037i | ||||||||
\(105\) | 4.00000 | − | 2.92456i | 0.390360 | − | 0.285408i | ||||
\(106\) | 0.410574i | 0.0398784i | ||||||||
\(107\) | 19.8955i | 1.92337i | 0.274154 | + | 0.961686i | \(0.411602\pi\) | ||||
−0.274154 | + | 0.961686i | \(0.588398\pi\) | |||||||
\(108\) | 4.79741i | 0.461631i | ||||||||
\(109\) | − | 6.25969i | − | 0.599570i | −0.954007 | − | 0.299785i | \(-0.903085\pi\) | ||
0.954007 | − | 0.299785i | \(-0.0969149\pi\) | |||||||
\(110\) | − | 1.87285i | − | 0.178570i | ||||||
\(111\) | −3.12311 | −0.296432 | ||||||||
\(112\) | −1.56155 | − | 2.13578i | −0.147553 | − | 0.201812i | ||||
\(113\) | − | 13.3405i | − | 1.25497i | −0.778628 | − | 0.627486i | \(-0.784084\pi\) | ||
0.778628 | − | 0.627486i | \(-0.215916\pi\) | |||||||
\(114\) | − | 3.74571i | − | 0.350817i | ||||||
\(115\) | −3.12311 | + | 9.06897i | −0.291231 | + | 0.845686i | ||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | 7.08084i | 0.654624i | ||||||||
\(118\) | − | 2.80928i | − | 0.258615i | ||||||
\(119\) | −1.75379 | − | 2.39871i | −0.160770 | − | 0.219889i | ||||
\(120\) | 1.87285i | 0.170967i | ||||||||
\(121\) | 10.1231 | 0.920282 | ||||||||
\(122\) | −12.2462 | −1.10872 | ||||||||
\(123\) | 6.24621 | 0.563202 | ||||||||
\(124\) | − | 9.06897i | − | 0.814418i | ||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | −3.31534 | − | 4.53448i | −0.295354 | − | 0.403964i | ||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.876894 | 0.0772062 | ||||||||
\(130\) | 6.67026i | 0.585021i | ||||||||
\(131\) | 0.936426i | 0.0818160i | 0.999163 | + | 0.0409080i | \(0.0130250\pi\) | ||||
−0.999163 | + | 0.0409080i | \(0.986975\pi\) | |||||||
\(132\) | 0.876894 | 0.0763239 | ||||||||
\(133\) | 6.24621 | + | 8.54312i | 0.541615 | + | 0.740782i | ||||
\(134\) | − | 7.60669i | − | 0.657118i | ||||||
\(135\) | 9.59482i | 0.825791i | ||||||||
\(136\) | 1.12311 | 0.0963055 | ||||||||
\(137\) | − | 14.1617i | − | 1.20991i | −0.796258 | − | 0.604957i | \(-0.793190\pi\) | ||
0.796258 | − | 0.604957i | \(-0.206810\pi\) | |||||||
\(138\) | −4.24621 | − | 1.46228i | −0.361462 | − | 0.124477i | ||||
\(139\) | 4.68213i | 0.397133i | 0.980087 | + | 0.198567i | \(0.0636286\pi\) | ||||
−0.980087 | + | 0.198567i | \(0.936371\pi\) | |||||||
\(140\) | −3.12311 | − | 4.27156i | −0.263951 | − | 0.361013i | ||||
\(141\) | 5.75379 | 0.484556 | ||||||||
\(142\) | −9.36932 | −0.786256 | ||||||||
\(143\) | 3.12311 | 0.261167 | ||||||||
\(144\) | 2.12311 | 0.176925 | ||||||||
\(145\) | −4.00000 | −0.332182 | ||||||||
\(146\) | 3.74571i | 0.309997i | ||||||||
\(147\) | −6.24621 | − | 1.98813i | −0.515179 | − | 0.163978i | ||||
\(148\) | 3.33513i | 0.274146i | ||||||||
\(149\) | 6.25969i | 0.512814i | 0.966569 | + | 0.256407i | \(0.0825387\pi\) | ||||
−0.966569 | + | 0.256407i | \(0.917461\pi\) | |||||||
\(150\) | − | 0.936426i | − | 0.0764589i | ||||||
\(151\) | −3.12311 | −0.254155 | −0.127077 | − | 0.991893i | \(-0.540560\pi\) | ||||
−0.127077 | + | 0.991893i | \(0.540560\pi\) | |||||||
\(152\) | −4.00000 | −0.324443 | ||||||||
\(153\) | 2.38447 | 0.192773 | ||||||||
\(154\) | −2.00000 | + | 1.46228i | −0.161165 | + | 0.117834i | ||||
\(155\) | − | 18.1379i | − | 1.45687i | ||||||
\(156\) | −3.12311 | −0.250049 | ||||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | 12.8147i | 1.01948i | ||||||||
\(159\) | −0.384472 | −0.0304906 | ||||||||
\(160\) | 2.00000 | 0.158114 | ||||||||
\(161\) | 12.1231 | − | 3.74571i | 0.955435 | − | 0.295203i | ||||
\(162\) | 1.87689 | 0.147463 | ||||||||
\(163\) | 16.4924 | 1.29179 | 0.645893 | − | 0.763428i | \(-0.276485\pi\) | ||||
0.645893 | + | 0.763428i | \(0.276485\pi\) | |||||||
\(164\) | − | 6.67026i | − | 0.520860i | ||||||
\(165\) | 1.75379 | 0.136532 | ||||||||
\(166\) | −4.00000 | −0.310460 | ||||||||
\(167\) | − | 9.89012i | − | 0.765320i | −0.923889 | − | 0.382660i | \(-0.875008\pi\) | ||
0.923889 | − | 0.382660i | \(-0.124992\pi\) | |||||||
\(168\) | 2.00000 | − | 1.46228i | 0.154303 | − | 0.112817i | ||||
\(169\) | 1.87689 | 0.144376 | ||||||||
\(170\) | 2.24621 | 0.172277 | ||||||||
\(171\) | −8.49242 | −0.649432 | ||||||||
\(172\) | − | 0.936426i | − | 0.0714018i | ||||||
\(173\) | 13.7511i | 1.04548i | 0.852493 | + | 0.522738i | \(0.175090\pi\) | ||||
−0.852493 | + | 0.522738i | \(0.824910\pi\) | |||||||
\(174\) | − | 1.87285i | − | 0.141981i | ||||||
\(175\) | 1.56155 | + | 2.13578i | 0.118042 | + | 0.161450i | ||||
\(176\) | − | 0.936426i | − | 0.0705858i | ||||||
\(177\) | 2.63068 | 0.197734 | ||||||||
\(178\) | −2.00000 | −0.149906 | ||||||||
\(179\) | −2.24621 | −0.167890 | −0.0839449 | − | 0.996470i | \(-0.526752\pi\) | ||||
−0.0839449 | + | 0.996470i | \(0.526752\pi\) | |||||||
\(180\) | 4.24621 | 0.316494 | ||||||||
\(181\) | 8.24621 | 0.612936 | 0.306468 | − | 0.951881i | \(-0.400853\pi\) | ||||
0.306468 | + | 0.951881i | \(0.400853\pi\) | |||||||
\(182\) | 7.12311 | − | 5.20798i | 0.528000 | − | 0.386042i | ||||
\(183\) | − | 11.4677i | − | 0.847715i | ||||||
\(184\) | −1.56155 | + | 4.53448i | −0.115119 | + | 0.334287i | ||||
\(185\) | 6.67026i | 0.490408i | ||||||||
\(186\) | 8.49242 | 0.622695 | ||||||||
\(187\) | − | 1.05171i | − | 0.0769083i | ||||||
\(188\) | − | 6.14441i | − | 0.448127i | ||||||
\(189\) | 10.2462 | − | 7.49141i | 0.745302 | − | 0.544920i | ||||
\(190\) | −8.00000 | −0.580381 | ||||||||
\(191\) | 5.32326i | 0.385178i | 0.981280 | + | 0.192589i | \(0.0616884\pi\) | ||||
−0.981280 | + | 0.192589i | \(0.938312\pi\) | |||||||
\(192\) | 0.936426i | 0.0675808i | ||||||||
\(193\) | 19.3693 | 1.39423 | 0.697117 | − | 0.716957i | \(-0.254466\pi\) | ||||
0.697117 | + | 0.716957i | \(0.254466\pi\) | |||||||
\(194\) | 12.2462 | 0.879227 | ||||||||
\(195\) | −6.24621 | −0.447300 | ||||||||
\(196\) | −2.12311 | + | 6.67026i | −0.151650 | + | 0.476447i | ||||
\(197\) | −3.75379 | −0.267446 | −0.133723 | − | 0.991019i | \(-0.542693\pi\) | ||||
−0.133723 | + | 0.991019i | \(0.542693\pi\) | |||||||
\(198\) | − | 1.98813i | − | 0.141290i | ||||||
\(199\) | −20.4924 | −1.45267 | −0.726335 | − | 0.687341i | \(-0.758778\pi\) | ||||
−0.726335 | + | 0.687341i | \(0.758778\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 7.12311 | 0.502425 | ||||||||
\(202\) | 10.0054i | 0.703977i | ||||||||
\(203\) | 3.12311 | + | 4.27156i | 0.219199 | + | 0.299805i | ||||
\(204\) | 1.05171i | 0.0736341i | ||||||||
\(205\) | − | 13.3405i | − | 0.931743i | ||||||
\(206\) | 19.1231 | 1.33237 | ||||||||
\(207\) | −3.31534 | + | 9.62719i | −0.230432 | + | 0.669136i | ||||
\(208\) | 3.33513i | 0.231250i | ||||||||
\(209\) | 3.74571i | 0.259096i | ||||||||
\(210\) | 4.00000 | − | 2.92456i | 0.276026 | − | 0.201814i | ||||
\(211\) | 10.2462 | 0.705378 | 0.352689 | − | 0.935741i | \(-0.385267\pi\) | ||||
0.352689 | + | 0.935741i | \(0.385267\pi\) | |||||||
\(212\) | 0.410574i | 0.0281983i | ||||||||
\(213\) | − | 8.77368i | − | 0.601162i | ||||||
\(214\) | 19.8955i | 1.36003i | ||||||||
\(215\) | − | 1.87285i | − | 0.127727i | ||||||
\(216\) | 4.79741i | 0.326422i | ||||||||
\(217\) | −19.3693 | + | 14.1617i | −1.31487 | + | 0.961357i | ||||
\(218\) | − | 6.25969i | − | 0.423960i | ||||||
\(219\) | −3.50758 | −0.237020 | ||||||||
\(220\) | − | 1.87285i | − | 0.126268i | ||||||
\(221\) | 3.74571i | 0.251963i | ||||||||
\(222\) | −3.12311 | −0.209609 | ||||||||
\(223\) | 28.0281i | 1.87690i | 0.345419 | + | 0.938449i | \(0.387737\pi\) | ||||
−0.345419 | + | 0.938449i | \(0.612263\pi\) | |||||||
\(224\) | −1.56155 | − | 2.13578i | −0.104336 | − | 0.142703i | ||||
\(225\) | −2.12311 | −0.141540 | ||||||||
\(226\) | − | 13.3405i | − | 0.887399i | ||||||
\(227\) | −10.2462 | −0.680065 | −0.340032 | − | 0.940414i | \(-0.610438\pi\) | ||||
−0.340032 | + | 0.940414i | \(0.610438\pi\) | |||||||
\(228\) | − | 3.74571i | − | 0.248065i | ||||||
\(229\) | 24.2462 | 1.60223 | 0.801117 | − | 0.598507i | \(-0.204239\pi\) | ||||
0.801117 | + | 0.598507i | \(0.204239\pi\) | |||||||
\(230\) | −3.12311 | + | 9.06897i | −0.205931 | + | 0.597990i | ||||
\(231\) | −1.36932 | − | 1.87285i | −0.0900944 | − | 0.123225i | ||||
\(232\) | −2.00000 | −0.131306 | ||||||||
\(233\) | 0.246211 | 0.0161298 | 0.00806492 | − | 0.999967i | \(-0.497433\pi\) | ||||
0.00806492 | + | 0.999967i | \(0.497433\pi\) | |||||||
\(234\) | 7.08084i | 0.462889i | ||||||||
\(235\) | − | 12.2888i | − | 0.801634i | ||||||
\(236\) | − | 2.80928i | − | 0.182868i | ||||||
\(237\) | −12.0000 | −0.779484 | ||||||||
\(238\) | −1.75379 | − | 2.39871i | −0.113681 | − | 0.155485i | ||||
\(239\) | −23.6155 | −1.52756 | −0.763781 | − | 0.645476i | \(-0.776659\pi\) | ||||
−0.763781 | + | 0.645476i | \(0.776659\pi\) | |||||||
\(240\) | 1.87285i | 0.120892i | ||||||||
\(241\) | −3.75379 | −0.241803 | −0.120901 | − | 0.992665i | \(-0.538578\pi\) | ||||
−0.120901 | + | 0.992665i | \(0.538578\pi\) | |||||||
\(242\) | 10.1231 | 0.650738 | ||||||||
\(243\) | 16.1498i | 1.03601i | ||||||||
\(244\) | −12.2462 | −0.783983 | ||||||||
\(245\) | −4.24621 | + | 13.3405i | −0.271280 | + | 0.852295i | ||||
\(246\) | 6.24621 | 0.398244 | ||||||||
\(247\) | − | 13.3405i | − | 0.848837i | ||||||
\(248\) | − | 9.06897i | − | 0.575880i | ||||||
\(249\) | − | 3.74571i | − | 0.237374i | ||||||
\(250\) | −12.0000 | −0.758947 | ||||||||
\(251\) | 22.7386 | 1.43525 | 0.717625 | − | 0.696430i | \(-0.245229\pi\) | ||||
0.717625 | + | 0.696430i | \(0.245229\pi\) | |||||||
\(252\) | −3.31534 | − | 4.53448i | −0.208847 | − | 0.285646i | ||||
\(253\) | 4.24621 | + | 1.46228i | 0.266957 | + | 0.0919327i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.10341i | 0.131721i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 20.8319i | − | 1.29946i | −0.760165 | − | 0.649730i | \(-0.774882\pi\) | ||
0.760165 | − | 0.649730i | \(-0.225118\pi\) | |||||||
\(258\) | 0.876894 | 0.0545931 | ||||||||
\(259\) | 7.12311 | − | 5.20798i | 0.442608 | − | 0.323608i | ||||
\(260\) | 6.67026i | 0.413672i | ||||||||
\(261\) | −4.24621 | −0.262834 | ||||||||
\(262\) | 0.936426i | 0.0578526i | ||||||||
\(263\) | 6.14441i | 0.378881i | 0.981892 | + | 0.189440i | \(0.0606674\pi\) | ||||
−0.981892 | + | 0.189440i | \(0.939333\pi\) | |||||||
\(264\) | 0.876894 | 0.0539691 | ||||||||
\(265\) | 0.821147i | 0.0504427i | ||||||||
\(266\) | 6.24621 | + | 8.54312i | 0.382980 | + | 0.523812i | ||||
\(267\) | − | 1.87285i | − | 0.114617i | ||||||
\(268\) | − | 7.60669i | − | 0.464653i | ||||||
\(269\) | − | 17.4968i | − | 1.06680i | −0.845863 | − | 0.533400i | \(-0.820914\pi\) | ||
0.845863 | − | 0.533400i | \(-0.179086\pi\) | |||||||
\(270\) | 9.59482i | 0.583922i | ||||||||
\(271\) | 4.27156i | 0.259479i | 0.991548 | + | 0.129739i | \(0.0414141\pi\) | ||||
−0.991548 | + | 0.129739i | \(0.958586\pi\) | |||||||
\(272\) | 1.12311 | 0.0680983 | ||||||||
\(273\) | 4.87689 | + | 6.67026i | 0.295163 | + | 0.403703i | ||||
\(274\) | − | 14.1617i | − | 0.855538i | ||||||
\(275\) | 0.936426i | 0.0564686i | ||||||||
\(276\) | −4.24621 | − | 1.46228i | −0.255592 | − | 0.0880189i | ||||
\(277\) | −10.0000 | −0.600842 | −0.300421 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300421 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(278\) | 4.68213i | 0.280816i | ||||||||
\(279\) | − | 19.2544i | − | 1.15273i | ||||||
\(280\) | −3.12311 | − | 4.27156i | −0.186641 | − | 0.255274i | ||||
\(281\) | − | 17.0862i | − | 1.01928i | −0.860388 | − | 0.509640i | \(-0.829779\pi\) | ||
0.860388 | − | 0.509640i | \(-0.170221\pi\) | |||||||
\(282\) | 5.75379 | 0.342633 | ||||||||
\(283\) | 20.0000 | 1.18888 | 0.594438 | − | 0.804141i | \(-0.297374\pi\) | ||||
0.594438 | + | 0.804141i | \(0.297374\pi\) | |||||||
\(284\) | −9.36932 | −0.555967 | ||||||||
\(285\) | − | 7.49141i | − | 0.443753i | ||||||
\(286\) | 3.12311 | 0.184673 | ||||||||
\(287\) | −14.2462 | + | 10.4160i | −0.840927 | + | 0.614835i | ||||
\(288\) | 2.12311 | 0.125105 | ||||||||
\(289\) | −15.7386 | −0.925802 | ||||||||
\(290\) | −4.00000 | −0.234888 | ||||||||
\(291\) | 11.4677i | 0.672247i | ||||||||
\(292\) | 3.74571i | 0.219201i | ||||||||
\(293\) | 14.4924 | 0.846656 | 0.423328 | − | 0.905976i | \(-0.360862\pi\) | ||||
0.423328 | + | 0.905976i | \(0.360862\pi\) | |||||||
\(294\) | −6.24621 | − | 1.98813i | −0.364286 | − | 0.115950i | ||||
\(295\) | − | 5.61856i | − | 0.327125i | ||||||
\(296\) | 3.33513i | 0.193851i | ||||||||
\(297\) | 4.49242 | 0.260677 | ||||||||
\(298\) | 6.25969i | 0.362614i | ||||||||
\(299\) | −15.1231 | − | 5.20798i | −0.874592 | − | 0.301186i | ||||
\(300\) | − | 0.936426i | − | 0.0540646i | ||||||
\(301\) | −2.00000 | + | 1.46228i | −0.115278 | + | 0.0842844i | ||||
\(302\) | −3.12311 | −0.179715 | ||||||||
\(303\) | −9.36932 | −0.538253 | ||||||||
\(304\) | −4.00000 | −0.229416 | ||||||||
\(305\) | −24.4924 | −1.40243 | ||||||||
\(306\) | 2.38447 | 0.136311 | ||||||||
\(307\) | − | 1.98813i | − | 0.113469i | −0.998389 | − | 0.0567343i | \(-0.981931\pi\) | ||
0.998389 | − | 0.0567343i | \(-0.0180688\pi\) | |||||||
\(308\) | −2.00000 | + | 1.46228i | −0.113961 | + | 0.0833211i | ||||
\(309\) | 17.9074i | 1.01872i | ||||||||
\(310\) | − | 18.1379i | − | 1.03017i | ||||||
\(311\) | − | 23.2306i | − | 1.31729i | −0.752454 | − | 0.658645i | \(-0.771130\pi\) | ||
0.752454 | − | 0.658645i | \(-0.228870\pi\) | |||||||
\(312\) | −3.12311 | −0.176811 | ||||||||
\(313\) | −14.4924 | −0.819160 | −0.409580 | − | 0.912274i | \(-0.634325\pi\) | ||||
−0.409580 | + | 0.912274i | \(0.634325\pi\) | |||||||
\(314\) | 10.0000 | 0.564333 | ||||||||
\(315\) | −6.63068 | − | 9.06897i | −0.373597 | − | 0.510979i | ||||
\(316\) | 12.8147i | 0.720882i | ||||||||
\(317\) | −24.2462 | −1.36180 | −0.680901 | − | 0.732375i | \(-0.738412\pi\) | ||||
−0.680901 | + | 0.732375i | \(0.738412\pi\) | |||||||
\(318\) | −0.384472 | −0.0215601 | ||||||||
\(319\) | 1.87285i | 0.104860i | ||||||||
\(320\) | 2.00000 | 0.111803 | ||||||||
\(321\) | −18.6307 | −1.03986 | ||||||||
\(322\) | 12.1231 | − | 3.74571i | 0.675594 | − | 0.208740i | ||||
\(323\) | −4.49242 | −0.249965 | ||||||||
\(324\) | 1.87689 | 0.104272 | ||||||||
\(325\) | − | 3.33513i | − | 0.185000i | ||||||
\(326\) | 16.4924 | 0.913431 | ||||||||
\(327\) | 5.86174 | 0.324155 | ||||||||
\(328\) | − | 6.67026i | − | 0.368304i | ||||||
\(329\) | −13.1231 | + | 9.59482i | −0.723500 | + | 0.528980i | ||||
\(330\) | 1.75379 | 0.0965429 | ||||||||
\(331\) | 2.24621 | 0.123463 | 0.0617315 | − | 0.998093i | \(-0.480338\pi\) | ||||
0.0617315 | + | 0.998093i | \(0.480338\pi\) | |||||||
\(332\) | −4.00000 | −0.219529 | ||||||||
\(333\) | 7.08084i | 0.388028i | ||||||||
\(334\) | − | 9.89012i | − | 0.541163i | ||||||
\(335\) | − | 15.2134i | − | 0.831196i | ||||||
\(336\) | 2.00000 | − | 1.46228i | 0.109109 | − | 0.0797739i | ||||
\(337\) | 34.1725i | 1.86149i | 0.365665 | + | 0.930746i | \(0.380842\pi\) | ||||
−0.365665 | + | 0.930746i | \(0.619158\pi\) | |||||||
\(338\) | 1.87689 | 0.102090 | ||||||||
\(339\) | 12.4924 | 0.678495 | ||||||||
\(340\) | 2.24621 | 0.121818 | ||||||||
\(341\) | −8.49242 | −0.459890 | ||||||||
\(342\) | −8.49242 | −0.459218 | ||||||||
\(343\) | 17.5616 | − | 5.88148i | 0.948235 | − | 0.317570i | ||||
\(344\) | − | 0.936426i | − | 0.0504887i | ||||||
\(345\) | −8.49242 | − | 2.92456i | −0.457217 | − | 0.157453i | ||||
\(346\) | 13.7511i | 0.739264i | ||||||||
\(347\) | −16.4924 | −0.885360 | −0.442680 | − | 0.896680i | \(-0.645972\pi\) | ||||
−0.442680 | + | 0.896680i | \(0.645972\pi\) | |||||||
\(348\) | − | 1.87285i | − | 0.100395i | ||||||
\(349\) | − | 30.8373i | − | 1.65068i | −0.564633 | − | 0.825342i | \(-0.690982\pi\) | ||
0.564633 | − | 0.825342i | \(-0.309018\pi\) | |||||||
\(350\) | 1.56155 | + | 2.13578i | 0.0834685 | + | 0.114162i | ||||
\(351\) | −16.0000 | −0.854017 | ||||||||
\(352\) | − | 0.936426i | − | 0.0499117i | ||||||
\(353\) | 26.6811i | 1.42009i | 0.704157 | + | 0.710045i | \(0.251325\pi\) | ||||
−0.704157 | + | 0.710045i | \(0.748675\pi\) | |||||||
\(354\) | 2.63068 | 0.139819 | ||||||||
\(355\) | −18.7386 | −0.994543 | ||||||||
\(356\) | −2.00000 | −0.106000 | ||||||||
\(357\) | 2.24621 | − | 1.64229i | 0.118882 | − | 0.0869194i | ||||
\(358\) | −2.24621 | −0.118716 | ||||||||
\(359\) | 11.9935i | 0.632994i | 0.948593 | + | 0.316497i | \(0.102507\pi\) | ||||
−0.948593 | + | 0.316497i | \(0.897493\pi\) | |||||||
\(360\) | 4.24621 | 0.223795 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 8.24621 | 0.433411 | ||||||||
\(363\) | 9.47954i | 0.497547i | ||||||||
\(364\) | 7.12311 | − | 5.20798i | 0.373352 | − | 0.272973i | ||||
\(365\) | 7.49141i | 0.392118i | ||||||||
\(366\) | − | 11.4677i | − | 0.599425i | ||||||
\(367\) | −11.1231 | −0.580621 | −0.290311 | − | 0.956932i | \(-0.593759\pi\) | ||||
−0.290311 | + | 0.956932i | \(0.593759\pi\) | |||||||
\(368\) | −1.56155 | + | 4.53448i | −0.0814016 | + | 0.236376i | ||||
\(369\) | − | 14.1617i | − | 0.737227i | ||||||
\(370\) | 6.67026i | 0.346771i | ||||||||
\(371\) | 0.876894 | − | 0.641132i | 0.0455261 | − | 0.0332859i | ||||
\(372\) | 8.49242 | 0.440312 | ||||||||
\(373\) | − | 36.6865i | − | 1.89955i | −0.312930 | − | 0.949776i | \(-0.601310\pi\) | ||
0.312930 | − | 0.949776i | \(-0.398690\pi\) | |||||||
\(374\) | − | 1.05171i | − | 0.0543824i | ||||||
\(375\) | − | 11.2371i | − | 0.580282i | ||||||
\(376\) | − | 6.14441i | − | 0.316874i | ||||||
\(377\) | − | 6.67026i | − | 0.343536i | ||||||
\(378\) | 10.2462 | − | 7.49141i | 0.527008 | − | 0.385317i | ||||
\(379\) | 1.98813i | 0.102123i | 0.998695 | + | 0.0510617i | \(0.0162605\pi\) | ||||
−0.998695 | + | 0.0510617i | \(0.983739\pi\) | |||||||
\(380\) | −8.00000 | −0.410391 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.32326i | 0.272362i | ||||||||
\(383\) | −27.1231 | −1.38593 | −0.692963 | − | 0.720973i | \(-0.743695\pi\) | ||||
−0.692963 | + | 0.720973i | \(0.743695\pi\) | |||||||
\(384\) | 0.936426i | 0.0477868i | ||||||||
\(385\) | −4.00000 | + | 2.92456i | −0.203859 | + | 0.149049i | ||||
\(386\) | 19.3693 | 0.985872 | ||||||||
\(387\) | − | 1.98813i | − | 0.101062i | ||||||
\(388\) | 12.2462 | 0.621707 | ||||||||
\(389\) | − | 23.3459i | − | 1.18369i | −0.806054 | − | 0.591843i | \(-0.798401\pi\) | ||
0.806054 | − | 0.591843i | \(-0.201599\pi\) | |||||||
\(390\) | −6.24621 | −0.316289 | ||||||||
\(391\) | −1.75379 | + | 5.09271i | −0.0886929 | + | 0.257549i | ||||
\(392\) | −2.12311 | + | 6.67026i | −0.107233 | + | 0.336899i | ||||
\(393\) | −0.876894 | −0.0442335 | ||||||||
\(394\) | −3.75379 | −0.189113 | ||||||||
\(395\) | 25.6294i | 1.28955i | ||||||||
\(396\) | − | 1.98813i | − | 0.0999074i | ||||||
\(397\) | 19.6002i | 0.983707i | 0.870678 | + | 0.491853i | \(0.163680\pi\) | ||||
−0.870678 | + | 0.491853i | \(0.836320\pi\) | |||||||
\(398\) | −20.4924 | −1.02719 | ||||||||
\(399\) | −8.00000 | + | 5.84912i | −0.400501 | + | 0.292822i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | − | 2.92456i | − | 0.146045i | −0.997330 | − | 0.0730227i | \(-0.976735\pi\) | ||
0.997330 | − | 0.0730227i | \(-0.0232646\pi\) | |||||||
\(402\) | 7.12311 | 0.355268 | ||||||||
\(403\) | 30.2462 | 1.50667 | ||||||||
\(404\) | 10.0054i | 0.497787i | ||||||||
\(405\) | 3.75379 | 0.186527 | ||||||||
\(406\) | 3.12311 | + | 4.27156i | 0.154997 | + | 0.211994i | ||||
\(407\) | 3.12311 | 0.154807 | ||||||||
\(408\) | 1.05171i | 0.0520672i | ||||||||
\(409\) | 6.67026i | 0.329823i | 0.986308 | + | 0.164912i | \(0.0527339\pi\) | ||||
−0.986308 | + | 0.164912i | \(0.947266\pi\) | |||||||
\(410\) | − | 13.3405i | − | 0.658842i | ||||||
\(411\) | 13.2614 | 0.654135 | ||||||||
\(412\) | 19.1231 | 0.942128 | ||||||||
\(413\) | −6.00000 | + | 4.38684i | −0.295241 | + | 0.215862i | ||||
\(414\) | −3.31534 | + | 9.62719i | −0.162940 | + | 0.473151i | ||||
\(415\) | −8.00000 | −0.392705 | ||||||||
\(416\) | 3.33513i | 0.163518i | ||||||||
\(417\) | −4.38447 | −0.214709 | ||||||||
\(418\) | 3.74571i | 0.183208i | ||||||||
\(419\) | 24.4924 | 1.19653 | 0.598267 | − | 0.801297i | \(-0.295856\pi\) | ||||
0.598267 | + | 0.801297i | \(0.295856\pi\) | |||||||
\(420\) | 4.00000 | − | 2.92456i | 0.195180 | − | 0.142704i | ||||
\(421\) | 19.6002i | 0.955256i | 0.878562 | + | 0.477628i | \(0.158503\pi\) | ||||
−0.878562 | + | 0.477628i | \(0.841497\pi\) | |||||||
\(422\) | 10.2462 | 0.498778 | ||||||||
\(423\) | − | 13.0452i | − | 0.634281i | ||||||
\(424\) | 0.410574i | 0.0199392i | ||||||||
\(425\) | −1.12311 | −0.0544786 | ||||||||
\(426\) | − | 8.77368i | − | 0.425086i | ||||||
\(427\) | 19.1231 | + | 26.1552i | 0.925432 | + | 1.26574i | ||||
\(428\) | 19.8955i | 0.961686i | ||||||||
\(429\) | 2.92456i | 0.141199i | ||||||||
\(430\) | − | 1.87285i | − | 0.0903170i | ||||||
\(431\) | − | 24.2824i | − | 1.16964i | −0.811163 | − | 0.584820i | \(-0.801165\pi\) | ||
0.811163 | − | 0.584820i | \(-0.198835\pi\) | |||||||
\(432\) | 4.79741i | 0.230816i | ||||||||
\(433\) | 13.6155 | 0.654321 | 0.327160 | − | 0.944969i | \(-0.393908\pi\) | ||||
0.327160 | + | 0.944969i | \(0.393908\pi\) | |||||||
\(434\) | −19.3693 | + | 14.1617i | −0.929757 | + | 0.679782i | ||||
\(435\) | − | 3.74571i | − | 0.179593i | ||||||
\(436\) | − | 6.25969i | − | 0.299785i | ||||||
\(437\) | 6.24621 | − | 18.1379i | 0.298797 | − | 0.867655i | ||||
\(438\) | −3.50758 | −0.167599 | ||||||||
\(439\) | − | 18.6638i | − | 0.890774i | −0.895338 | − | 0.445387i | \(-0.853066\pi\) | ||
0.895338 | − | 0.445387i | \(-0.146934\pi\) | |||||||
\(440\) | − | 1.87285i | − | 0.0892848i | ||||||
\(441\) | −4.50758 | + | 14.1617i | −0.214647 | + | 0.674365i | ||||
\(442\) | 3.74571i | 0.178165i | ||||||||
\(443\) | 40.4924 | 1.92385 | 0.961927 | − | 0.273308i | \(-0.0881179\pi\) | ||||
0.961927 | + | 0.273308i | \(0.0881179\pi\) | |||||||
\(444\) | −3.12311 | −0.148216 | ||||||||
\(445\) | −4.00000 | −0.189618 | ||||||||
\(446\) | 28.0281i | 1.32717i | ||||||||
\(447\) | −5.86174 | −0.277251 | ||||||||
\(448\) | −1.56155 | − | 2.13578i | −0.0737764 | − | 0.100906i | ||||
\(449\) | 6.87689 | 0.324541 | 0.162270 | − | 0.986746i | \(-0.448118\pi\) | ||||
0.162270 | + | 0.986746i | \(0.448118\pi\) | |||||||
\(450\) | −2.12311 | −0.100084 | ||||||||
\(451\) | −6.24621 | −0.294123 | ||||||||
\(452\) | − | 13.3405i | − | 0.627486i | ||||||
\(453\) | − | 2.92456i | − | 0.137408i | ||||||
\(454\) | −10.2462 | −0.480879 | ||||||||
\(455\) | 14.2462 | − | 10.4160i | 0.667873 | − | 0.488308i | ||||
\(456\) | − | 3.74571i | − | 0.175409i | ||||||
\(457\) | − | 25.8599i | − | 1.20968i | −0.796349 | − | 0.604838i | \(-0.793238\pi\) | ||
0.796349 | − | 0.604838i | \(-0.206762\pi\) | |||||||
\(458\) | 24.2462 | 1.13295 | ||||||||
\(459\) | 5.38800i | 0.251490i | ||||||||
\(460\) | −3.12311 | + | 9.06897i | −0.145616 | + | 0.422843i | ||||
\(461\) | 24.1671i | 1.12557i | 0.826602 | + | 0.562786i | \(0.190271\pi\) | ||||
−0.826602 | + | 0.562786i | \(0.809729\pi\) | |||||||
\(462\) | −1.36932 | − | 1.87285i | −0.0637064 | − | 0.0871330i | ||||
\(463\) | 33.3693 | 1.55080 | 0.775402 | − | 0.631468i | \(-0.217547\pi\) | ||||
0.775402 | + | 0.631468i | \(0.217547\pi\) | |||||||
\(464\) | −2.00000 | −0.0928477 | ||||||||
\(465\) | 16.9848 | 0.787653 | ||||||||
\(466\) | 0.246211 | 0.0114055 | ||||||||
\(467\) | 40.4924 | 1.87377 | 0.936883 | − | 0.349643i | \(-0.113697\pi\) | ||||
0.936883 | + | 0.349643i | \(0.113697\pi\) | |||||||
\(468\) | 7.08084i | 0.327312i | ||||||||
\(469\) | −16.2462 | + | 11.8782i | −0.750180 | + | 0.548487i | ||||
\(470\) | − | 12.2888i | − | 0.566841i | ||||||
\(471\) | 9.36426i | 0.431483i | ||||||||
\(472\) | − | 2.80928i | − | 0.129308i | ||||||
\(473\) | −0.876894 | −0.0403196 | ||||||||
\(474\) | −12.0000 | −0.551178 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | −1.75379 | − | 2.39871i | −0.0803848 | − | 0.109944i | ||||
\(477\) | 0.871691i | 0.0399120i | ||||||||
\(478\) | −23.6155 | −1.08015 | ||||||||
\(479\) | 4.87689 | 0.222831 | 0.111415 | − | 0.993774i | \(-0.464462\pi\) | ||||
0.111415 | + | 0.993774i | \(0.464462\pi\) | |||||||
\(480\) | 1.87285i | 0.0854836i | ||||||||
\(481\) | −11.1231 | −0.507170 | ||||||||
\(482\) | −3.75379 | −0.170980 | ||||||||
\(483\) | 3.50758 | + | 11.3524i | 0.159600 | + | 0.516552i | ||||
\(484\) | 10.1231 | 0.460141 | ||||||||
\(485\) | 24.4924 | 1.11214 | ||||||||
\(486\) | 16.1498i | 0.732570i | ||||||||
\(487\) | −4.49242 | −0.203571 | −0.101786 | − | 0.994806i | \(-0.532456\pi\) | ||||
−0.101786 | + | 0.994806i | \(0.532456\pi\) | |||||||
\(488\) | −12.2462 | −0.554360 | ||||||||
\(489\) | 15.4439i | 0.698399i | ||||||||
\(490\) | −4.24621 | + | 13.3405i | −0.191824 | + | 0.602664i | ||||
\(491\) | 14.7386 | 0.665145 | 0.332573 | − | 0.943078i | \(-0.392083\pi\) | ||||
0.332573 | + | 0.943078i | \(0.392083\pi\) | |||||||
\(492\) | 6.24621 | 0.281601 | ||||||||
\(493\) | −2.24621 | −0.101164 | ||||||||
\(494\) | − | 13.3405i | − | 0.600219i | ||||||
\(495\) | − | 3.97626i | − | 0.178720i | ||||||
\(496\) | − | 9.06897i | − | 0.407209i | ||||||
\(497\) | 14.6307 | + | 20.0108i | 0.656276 | + | 0.897607i | ||||
\(498\) | − | 3.74571i | − | 0.167849i | ||||||
\(499\) | 7.50758 | 0.336085 | 0.168043 | − | 0.985780i | \(-0.446255\pi\) | ||||
0.168043 | + | 0.985780i | \(0.446255\pi\) | |||||||
\(500\) | −12.0000 | −0.536656 | ||||||||
\(501\) | 9.26137 | 0.413767 | ||||||||
\(502\) | 22.7386 | 1.01487 | ||||||||
\(503\) | −31.6155 | −1.40967 | −0.704833 | − | 0.709373i | \(-0.748978\pi\) | ||||
−0.704833 | + | 0.709373i | \(0.748978\pi\) | |||||||
\(504\) | −3.31534 | − | 4.53448i | −0.147677 | − | 0.201982i | ||||
\(505\) | 20.0108i | 0.890469i | ||||||||
\(506\) | 4.24621 | + | 1.46228i | 0.188767 | + | 0.0650062i | ||||
\(507\) | 1.75757i | 0.0780566i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.6757i | 0.739136i | 0.929204 | + | 0.369568i | \(0.120494\pi\) | ||||
−0.929204 | + | 0.369568i | \(0.879506\pi\) | |||||||
\(510\) | 2.10341i | 0.0931406i | ||||||||
\(511\) | 8.00000 | − | 5.84912i | 0.353899 | − | 0.258750i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | − | 19.1896i | − | 0.847244i | ||||||
\(514\) | − | 20.8319i | − | 0.918857i | ||||||
\(515\) | 38.2462 | 1.68533 | ||||||||
\(516\) | 0.876894 | 0.0386031 | ||||||||
\(517\) | −5.75379 | −0.253051 | ||||||||
\(518\) | 7.12311 | − | 5.20798i | 0.312971 | − | 0.228826i | ||||
\(519\) | −12.8769 | −0.565233 | ||||||||
\(520\) | 6.67026i | 0.292510i | ||||||||
\(521\) | −3.36932 | −0.147612 | −0.0738062 | − | 0.997273i | \(-0.523515\pi\) | ||||
−0.0738062 | + | 0.997273i | \(0.523515\pi\) | |||||||
\(522\) | −4.24621 | −0.185852 | ||||||||
\(523\) | 16.4924 | 0.721163 | 0.360582 | − | 0.932728i | \(-0.382578\pi\) | ||||
0.360582 | + | 0.932728i | \(0.382578\pi\) | |||||||
\(524\) | 0.936426i | 0.0409080i | ||||||||
\(525\) | −2.00000 | + | 1.46228i | −0.0872872 | + | 0.0638191i | ||||
\(526\) | 6.14441i | 0.267909i | ||||||||
\(527\) | − | 10.1854i | − | 0.443683i | ||||||
\(528\) | 0.876894 | 0.0381619 | ||||||||
\(529\) | −18.1231 | − | 14.1617i | −0.787961 | − | 0.615725i | ||||
\(530\) | 0.821147i | 0.0356683i | ||||||||
\(531\) | − | 5.96440i | − | 0.258833i | ||||||
\(532\) | 6.24621 | + | 8.54312i | 0.270808 | + | 0.370391i | ||||
\(533\) | 22.2462 | 0.963590 | ||||||||
\(534\) | − | 1.87285i | − | 0.0810463i | ||||||
\(535\) | 39.7910i | 1.72032i | ||||||||
\(536\) | − | 7.60669i | − | 0.328559i | ||||||
\(537\) | − | 2.10341i | − | 0.0907689i | ||||||
\(538\) | − | 17.4968i | − | 0.754341i | ||||||
\(539\) | 6.24621 | + | 1.98813i | 0.269043 | + | 0.0856349i | ||||
\(540\) | 9.59482i | 0.412895i | ||||||||
\(541\) | −36.7386 | −1.57952 | −0.789759 | − | 0.613418i | \(-0.789794\pi\) | ||||
−0.789759 | + | 0.613418i | \(0.789794\pi\) | |||||||
\(542\) | 4.27156i | 0.183479i | ||||||||
\(543\) | 7.72197i | 0.331381i | ||||||||
\(544\) | 1.12311 | 0.0481528 | ||||||||
\(545\) | − | 12.5194i | − | 0.536271i | ||||||
\(546\) | 4.87689 | + | 6.67026i | 0.208712 | + | 0.285461i | ||||
\(547\) | 16.4924 | 0.705165 | 0.352583 | − | 0.935781i | \(-0.385304\pi\) | ||||
0.352583 | + | 0.935781i | \(0.385304\pi\) | |||||||
\(548\) | − | 14.1617i | − | 0.604957i | ||||||
\(549\) | −26.0000 | −1.10965 | ||||||||
\(550\) | 0.936426i | 0.0399294i | ||||||||
\(551\) | 8.00000 | 0.340811 | ||||||||
\(552\) | −4.24621 | − | 1.46228i | −0.180731 | − | 0.0622387i | ||||
\(553\) | 27.3693 | − | 20.0108i | 1.16386 | − | 0.850945i | ||||
\(554\) | −10.0000 | −0.424859 | ||||||||
\(555\) | −6.24621 | −0.265137 | ||||||||
\(556\) | 4.68213i | 0.198567i | ||||||||
\(557\) | − | 43.3567i | − | 1.83708i | −0.395325 | − | 0.918542i | \(-0.629368\pi\) | ||
0.395325 | − | 0.918542i | \(-0.370632\pi\) | |||||||
\(558\) | − | 19.2544i | − | 0.815103i | ||||||
\(559\) | 3.12311 | 0.132093 | ||||||||
\(560\) | −3.12311 | − | 4.27156i | −0.131975 | − | 0.180506i | ||||
\(561\) | 0.984845 | 0.0415802 | ||||||||
\(562\) | − | 17.0862i | − | 0.720739i | ||||||
\(563\) | −6.73863 | −0.284000 | −0.142000 | − | 0.989867i | \(-0.545353\pi\) | ||||
−0.142000 | + | 0.989867i | \(0.545353\pi\) | |||||||
\(564\) | 5.75379 | 0.242278 | ||||||||
\(565\) | − | 26.6811i | − | 1.12248i | ||||||
\(566\) | 20.0000 | 0.840663 | ||||||||
\(567\) | −2.93087 | − | 4.00863i | −0.123085 | − | 0.168347i | ||||
\(568\) | −9.36932 | −0.393128 | ||||||||
\(569\) | − | 6.67026i | − | 0.279632i | −0.990178 | − | 0.139816i | \(-0.955349\pi\) | ||
0.990178 | − | 0.139816i | \(-0.0446511\pi\) | |||||||
\(570\) | − | 7.49141i | − | 0.313781i | ||||||
\(571\) | − | 3.86098i | − | 0.161577i | −0.996731 | − | 0.0807886i | \(-0.974256\pi\) | ||
0.996731 | − | 0.0807886i | \(-0.0257439\pi\) | |||||||
\(572\) | 3.12311 | 0.130584 | ||||||||
\(573\) | −4.98485 | −0.208245 | ||||||||
\(574\) | −14.2462 | + | 10.4160i | −0.594625 | + | 0.434754i | ||||
\(575\) | 1.56155 | − | 4.53448i | 0.0651213 | − | 0.189101i | ||||
\(576\) | 2.12311 | 0.0884627 | ||||||||
\(577\) | − | 41.6639i | − | 1.73449i | −0.497882 | − | 0.867245i | \(-0.665889\pi\) | ||
0.497882 | − | 0.867245i | \(-0.334111\pi\) | |||||||
\(578\) | −15.7386 | −0.654641 | ||||||||
\(579\) | 18.1379i | 0.753787i | ||||||||
\(580\) | −4.00000 | −0.166091 | ||||||||
\(581\) | 6.24621 | + | 8.54312i | 0.259137 | + | 0.354428i | ||||
\(582\) | 11.4677i | 0.475350i | ||||||||
\(583\) | 0.384472 | 0.0159232 | ||||||||
\(584\) | 3.74571i | 0.154998i | ||||||||
\(585\) | 14.1617i | 0.585513i | ||||||||
\(586\) | 14.4924 | 0.598676 | ||||||||
\(587\) | 41.7792i | 1.72441i | 0.506559 | + | 0.862205i | \(0.330917\pi\) | ||||
−0.506559 | + | 0.862205i | \(0.669083\pi\) | |||||||
\(588\) | −6.24621 | − | 1.98813i | −0.257589 | − | 0.0819892i | ||||
\(589\) | 36.2759i | 1.49472i | ||||||||
\(590\) | − | 5.61856i | − | 0.231312i | ||||||
\(591\) | − | 3.51515i | − | 0.144594i | ||||||
\(592\) | 3.33513i | 0.137073i | ||||||||
\(593\) | 7.49141i | 0.307635i | 0.988099 | + | 0.153818i | \(0.0491568\pi\) | ||||
−0.988099 | + | 0.153818i | \(0.950843\pi\) | |||||||
\(594\) | 4.49242 | 0.184326 | ||||||||
\(595\) | −3.50758 | − | 4.79741i | −0.143797 | − | 0.196675i | ||||
\(596\) | 6.25969i | 0.256407i | ||||||||
\(597\) | − | 19.1896i | − | 0.785380i | ||||||
\(598\) | −15.1231 | − | 5.20798i | −0.618430 | − | 0.212970i | ||||
\(599\) | −20.4924 | −0.837298 | −0.418649 | − | 0.908148i | \(-0.637496\pi\) | ||||
−0.418649 | + | 0.908148i | \(0.637496\pi\) | |||||||
\(600\) | − | 0.936426i | − | 0.0382294i | ||||||
\(601\) | 2.10341i | 0.0857999i | 0.999079 | + | 0.0429000i | \(0.0136597\pi\) | ||||
−0.999079 | + | 0.0429000i | \(0.986340\pi\) | |||||||
\(602\) | −2.00000 | + | 1.46228i | −0.0815139 | + | 0.0595981i | ||||
\(603\) | − | 16.1498i | − | 0.657671i | ||||||
\(604\) | −3.12311 | −0.127077 | ||||||||
\(605\) | 20.2462 | 0.823126 | ||||||||
\(606\) | −9.36932 | −0.380602 | ||||||||
\(607\) | 7.19612i | 0.292081i | 0.989279 | + | 0.146041i | \(0.0466530\pi\) | ||||
−0.989279 | + | 0.146041i | \(0.953347\pi\) | |||||||
\(608\) | −4.00000 | −0.162221 | ||||||||
\(609\) | −4.00000 | + | 2.92456i | −0.162088 | + | 0.118509i | ||||
\(610\) | −24.4924 | −0.991669 | ||||||||
\(611\) | 20.4924 | 0.829035 | ||||||||
\(612\) | 2.38447 | 0.0963866 | ||||||||
\(613\) | 24.1671i | 0.976099i | 0.872816 | + | 0.488049i | \(0.162291\pi\) | ||||
−0.872816 | + | 0.488049i | \(0.837709\pi\) | |||||||
\(614\) | − | 1.98813i | − | 0.0802345i | ||||||
\(615\) | 12.4924 | 0.503743 | ||||||||
\(616\) | −2.00000 | + | 1.46228i | −0.0805823 | + | 0.0589169i | ||||
\(617\) | 17.0862i | 0.687866i | 0.938994 | + | 0.343933i | \(0.111759\pi\) | ||||
−0.938994 | + | 0.343933i | \(0.888241\pi\) | |||||||
\(618\) | 17.9074i | 0.720340i | ||||||||
\(619\) | −5.75379 | −0.231264 | −0.115632 | − | 0.993292i | \(-0.536889\pi\) | ||||
−0.115632 | + | 0.993292i | \(0.536889\pi\) | |||||||
\(620\) | − | 18.1379i | − | 0.728437i | ||||||
\(621\) | −21.7538 | − | 7.49141i | −0.872949 | − | 0.300620i | ||||
\(622\) | − | 23.2306i | − | 0.931464i | ||||||
\(623\) | 3.12311 | + | 4.27156i | 0.125125 | + | 0.171136i | ||||
\(624\) | −3.12311 | −0.125024 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | −14.4924 | −0.579234 | ||||||||
\(627\) | −3.50758 | −0.140079 | ||||||||
\(628\) | 10.0000 | 0.399043 | ||||||||
\(629\) | 3.74571i | 0.149351i | ||||||||
\(630\) | −6.63068 | − | 9.06897i | −0.264173 | − | 0.361316i | ||||
\(631\) | 25.3341i | 1.00853i | 0.863548 | + | 0.504266i | \(0.168237\pi\) | ||||
−0.863548 | + | 0.504266i | \(0.831763\pi\) | |||||||
\(632\) | 12.8147i | 0.509740i | ||||||||
\(633\) | 9.59482i | 0.381360i | ||||||||
\(634\) | −24.2462 | −0.962940 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.384472 | −0.0152453 | ||||||||
\(637\) | −22.2462 | − | 7.08084i | −0.881427 | − | 0.280553i | ||||
\(638\) | 1.87285i | 0.0741470i | ||||||||
\(639\) | −19.8920 | −0.786917 | ||||||||
\(640\) | 2.00000 | 0.0790569 | ||||||||
\(641\) | − | 16.2651i | − | 0.642432i | −0.947006 | − | 0.321216i | \(-0.895908\pi\) | ||
0.947006 | − | 0.321216i | \(-0.104092\pi\) | |||||||
\(642\) | −18.6307 | −0.735294 | ||||||||
\(643\) | −22.7386 | −0.896724 | −0.448362 | − | 0.893852i | \(-0.647992\pi\) | ||||
−0.448362 | + | 0.893852i | \(0.647992\pi\) | |||||||
\(644\) | 12.1231 | − | 3.74571i | 0.477717 | − | 0.147601i | ||||
\(645\) | 1.75379 | 0.0690554 | ||||||||
\(646\) | −4.49242 | −0.176752 | ||||||||
\(647\) | 21.3578i | 0.839661i | 0.907602 | + | 0.419831i | \(0.137911\pi\) | ||||
−0.907602 | + | 0.419831i | \(0.862089\pi\) | |||||||
\(648\) | 1.87689 | 0.0737314 | ||||||||
\(649\) | −2.63068 | −0.103263 | ||||||||
\(650\) | − | 3.33513i | − | 0.130815i | ||||||
\(651\) | −13.2614 | − | 18.1379i | −0.519754 | − | 0.710882i | ||||
\(652\) | 16.4924 | 0.645893 | ||||||||
\(653\) | −20.7386 | −0.811565 | −0.405783 | − | 0.913970i | \(-0.633001\pi\) | ||||
−0.405783 | + | 0.913970i | \(0.633001\pi\) | |||||||
\(654\) | 5.86174 | 0.229212 | ||||||||
\(655\) | 1.87285i | 0.0731784i | ||||||||
\(656\) | − | 6.67026i | − | 0.260430i | ||||||
\(657\) | 7.95253i | 0.310258i | ||||||||
\(658\) | −13.1231 | + | 9.59482i | −0.511592 | + | 0.374045i | ||||
\(659\) | − | 0.115279i | − | 0.00449065i | −0.999997 | − | 0.00224532i | \(-0.999285\pi\) | ||
0.999997 | − | 0.00224532i | \(-0.000714709\pi\) | |||||||
\(660\) | 1.75379 | 0.0682661 | ||||||||
\(661\) | 5.50758 | 0.214220 | 0.107110 | − | 0.994247i | \(-0.465840\pi\) | ||||
0.107110 | + | 0.994247i | \(0.465840\pi\) | |||||||
\(662\) | 2.24621 | 0.0873015 | ||||||||
\(663\) | −3.50758 | −0.136223 | ||||||||
\(664\) | −4.00000 | −0.155230 | ||||||||
\(665\) | 12.4924 | + | 17.0862i | 0.484435 | + | 0.662576i | ||||
\(666\) | 7.08084i | 0.274377i | ||||||||
\(667\) | 3.12311 | − | 9.06897i | 0.120927 | − | 0.351152i | ||||
\(668\) | − | 9.89012i | − | 0.382660i | ||||||
\(669\) | −26.2462 | −1.01474 | ||||||||
\(670\) | − | 15.2134i | − | 0.587744i | ||||||
\(671\) | 11.4677i | 0.442705i | ||||||||
\(672\) | 2.00000 | − | 1.46228i | 0.0771517 | − | 0.0564086i | ||||
\(673\) | −25.1231 | −0.968425 | −0.484212 | − | 0.874951i | \(-0.660894\pi\) | ||||
−0.484212 | + | 0.874951i | \(0.660894\pi\) | |||||||
\(674\) | 34.1725i | 1.31627i | ||||||||
\(675\) | − | 4.79741i | − | 0.184652i | ||||||
\(676\) | 1.87689 | 0.0721882 | ||||||||
\(677\) | 14.4924 | 0.556989 | 0.278495 | − | 0.960438i | \(-0.410165\pi\) | ||||
0.278495 | + | 0.960438i | \(0.410165\pi\) | |||||||
\(678\) | 12.4924 | 0.479769 | ||||||||
\(679\) | −19.1231 | − | 26.1552i | −0.733877 | − | 1.00374i | ||||
\(680\) | 2.24621 | 0.0861383 | ||||||||
\(681\) | − | 9.59482i | − | 0.367674i | ||||||
\(682\) | −8.49242 | −0.325192 | ||||||||
\(683\) | 24.4924 | 0.937177 | 0.468588 | − | 0.883417i | \(-0.344763\pi\) | ||||
0.468588 | + | 0.883417i | \(0.344763\pi\) | |||||||
\(684\) | −8.49242 | −0.324716 | ||||||||
\(685\) | − | 28.3234i | − | 1.08218i | ||||||
\(686\) | 17.5616 | − | 5.88148i | 0.670503 | − | 0.224556i | ||||
\(687\) | 22.7048i | 0.866242i | ||||||||
\(688\) | − | 0.936426i | − | 0.0357009i | ||||||
\(689\) | −1.36932 | −0.0521668 | ||||||||
\(690\) | −8.49242 | − | 2.92456i | −0.323301 | − | 0.111336i | ||||
\(691\) | 9.71010i | 0.369390i | 0.982796 | + | 0.184695i | \(0.0591297\pi\) | ||||
−0.982796 | + | 0.184695i | \(0.940870\pi\) | |||||||
\(692\) | 13.7511i | 0.522738i | ||||||||
\(693\) | −4.24621 | + | 3.10457i | −0.161300 | + | 0.117933i | ||||
\(694\) | −16.4924 | −0.626044 | ||||||||
\(695\) | 9.36426i | 0.355207i | ||||||||
\(696\) | − | 1.87285i | − | 0.0709903i | ||||||
\(697\) | − | 7.49141i | − | 0.283757i | ||||||
\(698\) | − | 30.8373i | − | 1.16721i | ||||||
\(699\) | 0.230559i | 0.00872053i | ||||||||
\(700\) | 1.56155 | + | 2.13578i | 0.0590211 | + | 0.0807249i | ||||
\(701\) | 27.9128i | 1.05425i | 0.849787 | + | 0.527126i | \(0.176730\pi\) | ||||
−0.849787 | + | 0.527126i | \(0.823270\pi\) | |||||||
\(702\) | −16.0000 | −0.603881 | ||||||||
\(703\) | − | 13.3405i | − | 0.503148i | ||||||
\(704\) | − | 0.936426i | − | 0.0352929i | ||||||
\(705\) | 11.5076 | 0.433400 | ||||||||
\(706\) | 26.6811i | 1.00415i | ||||||||
\(707\) | 21.3693 | − | 15.6240i | 0.803676 | − | 0.587599i | ||||
\(708\) | 2.63068 | 0.0988671 | ||||||||
\(709\) | − | 27.9128i | − | 1.04829i | −0.851630 | − | 0.524143i | \(-0.824386\pi\) | ||
0.851630 | − | 0.524143i | \(-0.175614\pi\) | |||||||
\(710\) | −18.7386 | −0.703248 | ||||||||
\(711\) | 27.2069i | 1.02034i | ||||||||
\(712\) | −2.00000 | −0.0749532 | ||||||||
\(713\) | 41.1231 | + | 14.1617i | 1.54007 | + | 0.530359i | ||||
\(714\) | 2.24621 | − | 1.64229i | 0.0840623 | − | 0.0614613i | ||||
\(715\) | 6.24621 | 0.233595 | ||||||||
\(716\) | −2.24621 | −0.0839449 | ||||||||
\(717\) | − | 22.1142i | − | 0.825870i | ||||||
\(718\) | 11.9935i | 0.447594i | ||||||||
\(719\) | − | 28.2586i | − | 1.05387i | −0.849906 | − | 0.526934i | \(-0.823341\pi\) | ||
0.849906 | − | 0.526934i | \(-0.176659\pi\) | |||||||
\(720\) | 4.24621 | 0.158247 | ||||||||
\(721\) | −29.8617 | − | 40.8427i | −1.11211 | − | 1.52106i | ||||
\(722\) | −3.00000 | −0.111648 | ||||||||
\(723\) | − | 3.51515i | − | 0.130730i | ||||||
\(724\) | 8.24621 | 0.306468 | ||||||||
\(725\) | 2.00000 | 0.0742781 | ||||||||
\(726\) | 9.47954i | 0.351819i | ||||||||
\(727\) | 8.00000 | 0.296704 | 0.148352 | − | 0.988935i | \(-0.452603\pi\) | ||||
0.148352 | + | 0.988935i | \(0.452603\pi\) | |||||||
\(728\) | 7.12311 | − | 5.20798i | 0.264000 | − | 0.193021i | ||||
\(729\) | −9.49242 | −0.351571 | ||||||||
\(730\) | 7.49141i | 0.277270i | ||||||||
\(731\) | − | 1.05171i | − | 0.0388987i | ||||||
\(732\) | − | 11.4677i | − | 0.423857i | ||||||
\(733\) | −9.50758 | −0.351170 | −0.175585 | − | 0.984464i | \(-0.556182\pi\) | ||||
−0.175585 | + | 0.984464i | \(0.556182\pi\) | |||||||
\(734\) | −11.1231 | −0.410561 | ||||||||
\(735\) | −12.4924 | − | 3.97626i | −0.460790 | − | 0.146667i | ||||
\(736\) | −1.56155 | + | 4.53448i | −0.0575596 | + | 0.167143i | ||||
\(737\) | −7.12311 | −0.262383 | ||||||||
\(738\) | − | 14.1617i | − | 0.521298i | ||||||
\(739\) | −28.0000 | −1.03000 | −0.514998 | − | 0.857191i | \(-0.672207\pi\) | ||||
−0.514998 | + | 0.857191i | \(0.672207\pi\) | |||||||
\(740\) | 6.67026i | 0.245204i | ||||||||
\(741\) | 12.4924 | 0.458921 | ||||||||
\(742\) | 0.876894 | − | 0.641132i | 0.0321918 | − | 0.0235367i | ||||
\(743\) | − | 45.9354i | − | 1.68521i | −0.538534 | − | 0.842604i | \(-0.681022\pi\) | ||
0.538534 | − | 0.842604i | \(-0.318978\pi\) | |||||||
\(744\) | 8.49242 | 0.311347 | ||||||||
\(745\) | 12.5194i | 0.458675i | ||||||||
\(746\) | − | 36.6865i | − | 1.34319i | ||||||
\(747\) | −8.49242 | −0.310721 | ||||||||
\(748\) | − | 1.05171i | − | 0.0384542i | ||||||
\(749\) | 42.4924 | − | 31.0679i | 1.55264 | − | 1.13520i | ||||
\(750\) | − | 11.2371i | − | 0.410321i | ||||||
\(751\) | 6.96556i | 0.254177i | 0.991891 | + | 0.127088i | \(0.0405632\pi\) | ||||
−0.991891 | + | 0.127088i | \(0.959437\pi\) | |||||||
\(752\) | − | 6.14441i | − | 0.224064i | ||||||
\(753\) | 21.2931i | 0.775962i | ||||||||
\(754\) | − | 6.67026i | − | 0.242917i | ||||||
\(755\) | −6.24621 | −0.227323 | ||||||||
\(756\) | 10.2462 | − | 7.49141i | 0.372651 | − | 0.272460i | ||||
\(757\) | 37.5076i | 1.36324i | 0.731708 | + | 0.681618i | \(0.238724\pi\) | ||||
−0.731708 | + | 0.681618i | \(0.761276\pi\) | |||||||
\(758\) | 1.98813i | 0.0722122i | ||||||||
\(759\) | −1.36932 | + | 3.97626i | −0.0497031 | + | 0.144329i | ||||
\(760\) | −8.00000 | −0.290191 | ||||||||
\(761\) | 33.3513i | 1.20898i | 0.796611 | + | 0.604492i | \(0.206624\pi\) | ||||
−0.796611 | + | 0.604492i | \(0.793376\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.3693 | + | 9.77484i | −0.484002 | + | 0.353873i | ||||
\(764\) | 5.32326i | 0.192589i | ||||||||
\(765\) | 4.76894 | 0.172422 | ||||||||
\(766\) | −27.1231 | −0.979998 | ||||||||
\(767\) | 9.36932 | 0.338306 | ||||||||
\(768\) | 0.936426i | 0.0337904i | ||||||||
\(769\) | −27.3693 | −0.986963 | −0.493481 | − | 0.869756i | \(-0.664276\pi\) | ||||
−0.493481 | + | 0.869756i | \(0.664276\pi\) | |||||||
\(770\) | −4.00000 | + | 2.92456i | −0.144150 | + | 0.105394i | ||||
\(771\) | 19.5076 | 0.702548 | ||||||||
\(772\) | 19.3693 | 0.697117 | ||||||||
\(773\) | −52.2462 | −1.87917 | −0.939583 | − | 0.342322i | \(-0.888787\pi\) | ||||
−0.939583 | + | 0.342322i | \(0.888787\pi\) | |||||||
\(774\) | − | 1.98813i | − | 0.0714619i | ||||||
\(775\) | 9.06897i | 0.325767i | ||||||||
\(776\) | 12.2462 | 0.439613 | ||||||||
\(777\) | 4.87689 | + | 6.67026i | 0.174958 | + | 0.239294i | ||||
\(778\) | − | 23.3459i | − | 0.836992i | ||||||
\(779\) | 26.6811i | 0.955948i | ||||||||
\(780\) | −6.24621 | −0.223650 | ||||||||
\(781\) | 8.77368i | 0.313947i | ||||||||
\(782\) | −1.75379 | + | 5.09271i | −0.0627154 | + | 0.182115i | ||||
\(783\) | − | 9.59482i | − | 0.342891i | ||||||
\(784\) | −2.12311 | + | 6.67026i | −0.0758252 | + | 0.238224i | ||||
\(785\) | 20.0000 | 0.713831 | ||||||||
\(786\) | −0.876894 | −0.0312778 | ||||||||
\(787\) | −4.00000 | −0.142585 | −0.0712923 | − | 0.997455i | \(-0.522712\pi\) | ||||
−0.0712923 | + | 0.997455i | \(0.522712\pi\) | |||||||
\(788\) | −3.75379 | −0.133723 | ||||||||
\(789\) | −5.75379 | −0.204840 | ||||||||
\(790\) | 25.6294i | 0.911851i | ||||||||
\(791\) | −28.4924 | + | 20.8319i | −1.01307 | + | 0.740698i | ||||
\(792\) | − | 1.98813i | − | 0.0706452i | ||||||
\(793\) | − | 40.8427i | − | 1.45037i | ||||||
\(794\) | 19.6002i | 0.695586i | ||||||||
\(795\) | −0.768944 | −0.0272716 | ||||||||
\(796\) | −20.4924 | −0.726335 | ||||||||
\(797\) | −34.4924 | −1.22178 | −0.610892 | − | 0.791714i | \(-0.709189\pi\) | ||||
−0.610892 | + | 0.791714i | \(0.709189\pi\) | |||||||
\(798\) | −8.00000 | + | 5.84912i | −0.283197 | + | 0.207056i | ||||
\(799\) | − | 6.90082i | − | 0.244134i | ||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −4.24621 | −0.150032 | ||||||||
\(802\) | − | 2.92456i | − | 0.103270i | ||||||
\(803\) | 3.50758 | 0.123780 | ||||||||
\(804\) | 7.12311 | 0.251213 | ||||||||
\(805\) | 24.2462 | − | 7.49141i | 0.854567 | − | 0.264038i | ||||
\(806\) | 30.2462 | 1.06538 | ||||||||
\(807\) | 16.3845 | 0.576761 | ||||||||
\(808\) | 10.0054i | 0.351989i | ||||||||
\(809\) | 14.8769 | 0.523044 | 0.261522 | − | 0.965198i | \(-0.415776\pi\) | ||||
0.261522 | + | 0.965198i | \(0.415776\pi\) | |||||||
\(810\) | 3.75379 | 0.131895 | ||||||||
\(811\) | − | 47.3977i | − | 1.66436i | −0.554506 | − | 0.832179i | \(-0.687093\pi\) | ||
0.554506 | − | 0.832179i | \(-0.312907\pi\) | |||||||
\(812\) | 3.12311 | + | 4.27156i | 0.109600 | + | 0.149902i | ||||
\(813\) | −4.00000 | −0.140286 | ||||||||
\(814\) | 3.12311 | 0.109465 | ||||||||
\(815\) | 32.9848 | 1.15541 | ||||||||
\(816\) | 1.05171i | 0.0368171i | ||||||||
\(817\) | 3.74571i | 0.131046i | ||||||||
\(818\) | 6.67026i | 0.233220i | ||||||||
\(819\) | 15.1231 | − | 11.0571i | 0.528444 | − | 0.386366i | ||||
\(820\) | − | 13.3405i | − | 0.465871i | ||||||
\(821\) | 37.2311 | 1.29937 | 0.649686 | − | 0.760202i | \(-0.274900\pi\) | ||||
0.649686 | + | 0.760202i | \(0.274900\pi\) | |||||||
\(822\) | 13.2614 | 0.462543 | ||||||||
\(823\) | 36.4924 | 1.27205 | 0.636023 | − | 0.771670i | \(-0.280578\pi\) | ||||
0.636023 | + | 0.771670i | \(0.280578\pi\) | |||||||
\(824\) | 19.1231 | 0.666185 | ||||||||
\(825\) | −0.876894 | −0.0305295 | ||||||||
\(826\) | −6.00000 | + | 4.38684i | −0.208767 | + | 0.152638i | ||||
\(827\) | − | 3.86098i | − | 0.134260i | −0.997744 | − | 0.0671298i | \(-0.978616\pi\) | ||
0.997744 | − | 0.0671298i | \(-0.0213842\pi\) | |||||||
\(828\) | −3.31534 | + | 9.62719i | −0.115216 | + | 0.334568i | ||||
\(829\) | − | 41.2533i | − | 1.43279i | −0.697697 | − | 0.716393i | \(-0.745792\pi\) | ||
0.697697 | − | 0.716393i | \(-0.254208\pi\) | |||||||
\(830\) | −8.00000 | −0.277684 | ||||||||
\(831\) | − | 9.36426i | − | 0.324843i | ||||||
\(832\) | 3.33513i | 0.115625i | ||||||||
\(833\) | −2.38447 | + | 7.49141i | −0.0826171 | + | 0.259562i | ||||
\(834\) | −4.38447 | −0.151822 | ||||||||
\(835\) | − | 19.7802i | − | 0.684523i | ||||||
\(836\) | 3.74571i | 0.129548i | ||||||||
\(837\) | 43.5076 | 1.50384 | ||||||||
\(838\) | 24.4924 | 0.846077 | ||||||||
\(839\) | −37.8617 | −1.30713 | −0.653566 | − | 0.756869i | \(-0.726728\pi\) | ||||
−0.653566 | + | 0.756869i | \(0.726728\pi\) | |||||||
\(840\) | 4.00000 | − | 2.92456i | 0.138013 | − | 0.100907i | ||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 19.6002i | 0.675468i | ||||||||
\(843\) | 16.0000 | 0.551069 | ||||||||
\(844\) | 10.2462 | 0.352689 | ||||||||
\(845\) | 3.75379 | 0.129134 | ||||||||
\(846\) | − | 13.0452i | − | 0.448504i | ||||||
\(847\) | −15.8078 | − | 21.6207i | −0.543161 | − | 0.742897i | ||||
\(848\) | 0.410574i | 0.0140992i | ||||||||
\(849\) | 18.7285i | 0.642761i | ||||||||
\(850\) | −1.12311 | −0.0385222 | ||||||||
\(851\) | −15.1231 | − | 5.20798i | −0.518413 | − | 0.178527i | ||||
\(852\) | − | 8.77368i | − | 0.300581i | ||||||
\(853\) | 27.9128i | 0.955715i | 0.878437 | + | 0.477858i | \(0.158587\pi\) | ||||
−0.878437 | + | 0.477858i | \(0.841413\pi\) | |||||||
\(854\) | 19.1231 | + | 26.1552i | 0.654379 | + | 0.895013i | ||||
\(855\) | −16.9848 | −0.580869 | ||||||||
\(856\) | 19.8955i | 0.680015i | ||||||||
\(857\) | 27.5022i | 0.939457i | 0.882811 | + | 0.469729i | \(0.155648\pi\) | ||||
−0.882811 | + | 0.469729i | \(0.844352\pi\) | |||||||
\(858\) | 2.92456i | 0.0998428i | ||||||||
\(859\) | 44.7037i | 1.52527i | 0.646828 | + | 0.762636i | \(0.276095\pi\) | ||||
−0.646828 | + | 0.762636i | \(0.723905\pi\) | |||||||
\(860\) | − | 1.87285i | − | 0.0638637i | ||||||
\(861\) | −9.75379 | − | 13.3405i | −0.332408 | − | 0.454644i | ||||
\(862\) | − | 24.2824i | − | 0.827060i | ||||||
\(863\) | −32.0000 | −1.08929 | −0.544646 | − | 0.838666i | \(-0.683336\pi\) | ||||
−0.544646 | + | 0.838666i | \(0.683336\pi\) | |||||||
\(864\) | 4.79741i | 0.163211i | ||||||||
\(865\) | 27.5022i | 0.935103i | ||||||||
\(866\) | 13.6155 | 0.462674 | ||||||||
\(867\) | − | 14.7381i | − | 0.500531i | ||||||
\(868\) | −19.3693 | + | 14.1617i | −0.657437 | + | 0.480679i | ||||
\(869\) | 12.0000 | 0.407072 | ||||||||
\(870\) | − | 3.74571i | − | 0.126991i | ||||||
\(871\) | 25.3693 | 0.859607 | ||||||||
\(872\) | − | 6.25969i | − | 0.211980i | ||||||
\(873\) | 26.0000 | 0.879967 | ||||||||
\(874\) | 6.24621 | − | 18.1379i | 0.211281 | − | 0.613525i | ||||
\(875\) | 18.7386 | + | 25.6294i | 0.633481 | + | 0.866430i | ||||
\(876\) | −3.50758 | −0.118510 | ||||||||
\(877\) | −30.4924 | −1.02966 | −0.514828 | − | 0.857294i | \(-0.672144\pi\) | ||||
−0.514828 | + | 0.857294i | \(0.672144\pi\) | |||||||
\(878\) | − | 18.6638i | − | 0.629872i | ||||||
\(879\) | 13.5711i | 0.457741i | ||||||||
\(880\) | − | 1.87285i | − | 0.0631339i | ||||||
\(881\) | 23.3693 | 0.787332 | 0.393666 | − | 0.919253i | \(-0.371207\pi\) | ||||
0.393666 | + | 0.919253i | \(0.371207\pi\) | |||||||
\(882\) | −4.50758 | + | 14.1617i | −0.151778 | + | 0.476848i | ||||
\(883\) | −12.0000 | −0.403832 | −0.201916 | − | 0.979403i | \(-0.564717\pi\) | ||||
−0.201916 | + | 0.979403i | \(0.564717\pi\) | |||||||
\(884\) | 3.74571i | 0.125982i | ||||||||
\(885\) | 5.26137 | 0.176859 | ||||||||
\(886\) | 40.4924 | 1.36037 | ||||||||
\(887\) | − | 2.39871i | − | 0.0805407i | −0.999189 | − | 0.0402703i | \(-0.987178\pi\) | ||
0.999189 | − | 0.0402703i | \(-0.0128219\pi\) | |||||||
\(888\) | −3.12311 | −0.104805 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.00000 | −0.134080 | ||||||||
\(891\) | − | 1.75757i | − | 0.0588809i | ||||||
\(892\) | 28.0281i | 0.938449i | ||||||||
\(893\) | 24.5776i | 0.822460i | ||||||||
\(894\) | −5.86174 | −0.196046 | ||||||||
\(895\) | −4.49242 | −0.150165 | ||||||||
\(896\) | −1.56155 | − | 2.13578i | −0.0521678 | − | 0.0713514i | ||||
\(897\) | 4.87689 | − | 14.1617i | 0.162835 | − | 0.472845i | ||||
\(898\) | 6.87689 | 0.229485 | ||||||||
\(899\) | 18.1379i | 0.604934i | ||||||||
\(900\) | −2.12311 | −0.0707702 | ||||||||
\(901\) | 0.461117i | 0.0153620i | ||||||||
\(902\) | −6.24621 | −0.207976 | ||||||||
\(903\) | −1.36932 | − | 1.87285i | −0.0455680 | − | 0.0623246i | ||||
\(904\) | − | 13.3405i | − | 0.443699i | ||||||
\(905\) | 16.4924 | 0.548227 | ||||||||
\(906\) | − | 2.92456i | − | 0.0971619i | ||||||
\(907\) | 46.5766i | 1.54655i | 0.634071 | + | 0.773275i | \(0.281383\pi\) | ||||
−0.634071 | + | 0.773275i | \(0.718617\pi\) | |||||||
\(908\) | −10.2462 | −0.340032 | ||||||||
\(909\) | 21.2425i | 0.704570i | ||||||||
\(910\) | 14.2462 | − | 10.4160i | 0.472257 | − | 0.345286i | ||||
\(911\) | − | 24.2824i | − | 0.804510i | −0.915528 | − | 0.402255i | \(-0.868226\pi\) | ||
0.915528 | − | 0.402255i | \(-0.131774\pi\) | |||||||
\(912\) | − | 3.74571i | − | 0.124033i | ||||||
\(913\) | 3.74571i | 0.123965i | ||||||||
\(914\) | − | 25.8599i | − | 0.855370i | ||||||
\(915\) | − | 22.9354i | − | 0.758219i | ||||||
\(916\) | 24.2462 | 0.801117 | ||||||||
\(917\) | 2.00000 | − | 1.46228i | 0.0660458 | − | 0.0482887i | ||||
\(918\) | 5.38800i | 0.177830i | ||||||||
\(919\) | 35.7500i | 1.17928i | 0.807665 | + | 0.589642i | \(0.200731\pi\) | ||||
−0.807665 | + | 0.589642i | \(0.799269\pi\) | |||||||
\(920\) | −3.12311 | + | 9.06897i | −0.102966 | + | 0.298995i | ||||
\(921\) | 1.86174 | 0.0613464 | ||||||||
\(922\) | 24.1671i | 0.795900i | ||||||||
\(923\) | − | 31.2479i | − | 1.02854i | ||||||
\(924\) | −1.36932 | − | 1.87285i | −0.0450472 | − | 0.0616123i | ||||
\(925\) | − | 3.33513i | − | 0.109658i | ||||||
\(926\) | 33.3693 | 1.09658 | ||||||||
\(927\) | 40.6004 | 1.33349 | ||||||||
\(928\) | −2.00000 | −0.0656532 | ||||||||
\(929\) | − | 42.9461i | − | 1.40902i | −0.709695 | − | 0.704509i | \(-0.751167\pi\) | ||
0.709695 | − | 0.704509i | \(-0.248833\pi\) | |||||||
\(930\) | 16.9848 | 0.556955 | ||||||||
\(931\) | 8.49242 | − | 26.6811i | 0.278328 | − | 0.874436i | ||||
\(932\) | 0.246211 | 0.00806492 | ||||||||
\(933\) | 21.7538 | 0.712187 | ||||||||
\(934\) | 40.4924 | 1.32495 | ||||||||
\(935\) | − | 2.10341i | − | 0.0687889i | ||||||
\(936\) | 7.08084i | 0.231444i | ||||||||
\(937\) | −18.0000 | −0.588034 | −0.294017 | − | 0.955800i | \(-0.594992\pi\) | ||||
−0.294017 | + | 0.955800i | \(0.594992\pi\) | |||||||
\(938\) | −16.2462 | + | 11.8782i | −0.530458 | + | 0.387839i | ||||
\(939\) | − | 13.5711i | − | 0.442876i | ||||||
\(940\) | − | 12.2888i | − | 0.400817i | ||||||
\(941\) | −40.7386 | −1.32804 | −0.664021 | − | 0.747714i | \(-0.731151\pi\) | ||||
−0.664021 | + | 0.747714i | \(0.731151\pi\) | |||||||
\(942\) | 9.36426i | 0.305104i | ||||||||
\(943\) | 30.2462 | + | 10.4160i | 0.984952 | + | 0.339191i | ||||
\(944\) | − | 2.80928i | − | 0.0914342i | ||||||
\(945\) | 20.4924 | − | 14.9828i | 0.666619 | − | 0.487391i | ||||
\(946\) | −0.876894 | −0.0285103 | ||||||||
\(947\) | 12.9848 | 0.421951 | 0.210975 | − | 0.977491i | \(-0.432336\pi\) | ||||
0.210975 | + | 0.977491i | \(0.432336\pi\) | |||||||
\(948\) | −12.0000 | −0.389742 | ||||||||
\(949\) | −12.4924 | −0.405521 | ||||||||
\(950\) | 4.00000 | 0.129777 | ||||||||
\(951\) | − | 22.7048i | − | 0.736253i | ||||||
\(952\) | −1.75379 | − | 2.39871i | −0.0568406 | − | 0.0777425i | ||||
\(953\) | − | 48.3341i | − | 1.56570i | −0.622213 | − | 0.782848i | \(-0.713766\pi\) | ||
0.622213 | − | 0.782848i | \(-0.286234\pi\) | |||||||
\(954\) | 0.871691i | 0.0282220i | ||||||||
\(955\) | 10.6465i | 0.344514i | ||||||||
\(956\) | −23.6155 | −0.763781 | ||||||||
\(957\) | −1.75379 | −0.0566919 | ||||||||
\(958\) | 4.87689 | 0.157565 | ||||||||
\(959\) | −30.2462 | + | 22.1142i | −0.976701 | + | 0.714105i | ||||
\(960\) | 1.87285i | 0.0604461i | ||||||||
\(961\) | −51.2462 | −1.65310 | ||||||||
\(962\) | −11.1231 | −0.358623 | ||||||||
\(963\) | 42.2403i | 1.36117i | ||||||||
\(964\) | −3.75379 | −0.120901 | ||||||||
\(965\) | 38.7386 | 1.24704 | ||||||||
\(966\) | 3.50758 | + | 11.3524i | 0.112854 | + | 0.365257i | ||||
\(967\) | 5.86174 | 0.188501 | 0.0942504 | − | 0.995549i | \(-0.469955\pi\) | ||||
0.0942504 | + | 0.995549i | \(0.469955\pi\) | |||||||
\(968\) | 10.1231 | 0.325369 | ||||||||
\(969\) | − | 4.20682i | − | 0.135143i | ||||||
\(970\) | 24.4924 | 0.786404 | ||||||||
\(971\) | −43.2311 | −1.38735 | −0.693675 | − | 0.720288i | \(-0.744010\pi\) | ||||
−0.693675 | + | 0.720288i | \(0.744010\pi\) | |||||||
\(972\) | 16.1498i | 0.518005i | ||||||||
\(973\) | 10.0000 | − | 7.31140i | 0.320585 | − | 0.234393i | ||||
\(974\) | −4.49242 | −0.143947 | ||||||||
\(975\) | 3.12311 | 0.100019 | ||||||||
\(976\) | −12.2462 | −0.391992 | ||||||||
\(977\) | 17.9074i | 0.572908i | 0.958094 | + | 0.286454i | \(0.0924765\pi\) | ||||
−0.958094 | + | 0.286454i | \(0.907523\pi\) | |||||||
\(978\) | 15.4439i | 0.493843i | ||||||||
\(979\) | 1.87285i | 0.0598566i | ||||||||
\(980\) | −4.24621 | + | 13.3405i | −0.135640 | + | 0.426148i | ||||
\(981\) | − | 13.2900i | − | 0.424317i | ||||||
\(982\) | 14.7386 | 0.470329 | ||||||||
\(983\) | −11.5076 | −0.367035 | −0.183517 | − | 0.983016i | \(-0.558748\pi\) | ||||
−0.183517 | + | 0.983016i | \(0.558748\pi\) | |||||||
\(984\) | 6.24621 | 0.199122 | ||||||||
\(985\) | −7.50758 | −0.239211 | ||||||||
\(986\) | −2.24621 | −0.0715339 | ||||||||
\(987\) | −8.98485 | − | 12.2888i | −0.285991 | − | 0.391158i | ||||
\(988\) | − | 13.3405i | − | 0.424419i | ||||||
\(989\) | 4.24621 | + | 1.46228i | 0.135022 | + | 0.0464978i | ||||
\(990\) | − | 3.97626i | − | 0.126374i | ||||||
\(991\) | −32.0000 | −1.01651 | −0.508257 | − | 0.861206i | \(-0.669710\pi\) | ||||
−0.508257 | + | 0.861206i | \(0.669710\pi\) | |||||||
\(992\) | − | 9.06897i | − | 0.287940i | ||||||
\(993\) | 2.10341i | 0.0667497i | ||||||||
\(994\) | 14.6307 | + | 20.0108i | 0.464057 | + | 0.634704i | ||||
\(995\) | −40.9848 | −1.29931 | ||||||||
\(996\) | − | 3.74571i | − | 0.118687i | ||||||
\(997\) | 10.0054i | 0.316874i | 0.987369 | + | 0.158437i | \(0.0506455\pi\) | ||||
−0.987369 | + | 0.158437i | \(0.949355\pi\) | |||||||
\(998\) | 7.50758 | 0.237648 | ||||||||
\(999\) | −16.0000 | −0.506218 |
(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 | 322.2.c.d.321.3 | yes | 4 | |
3.2 | odd | 2 | 2898.2.g.a.2575.1 | 4 | |||
4.3 | odd | 2 | 2576.2.f.e.321.2 | 4 | |||
7.6 | odd | 2 | 322.2.c.c.321.2 | ✓ | 4 | ||
21.20 | even | 2 | 2898.2.g.b.2575.3 | 4 | |||
23.22 | odd | 2 | 322.2.c.c.321.3 | yes | 4 | ||
28.27 | even | 2 | 2576.2.f.b.321.3 | 4 | |||
69.68 | even | 2 | 2898.2.g.b.2575.4 | 4 | |||
92.91 | even | 2 | 2576.2.f.b.321.2 | 4 | |||
161.160 | even | 2 | inner | 322.2.c.d.321.2 | yes | 4 | |
483.482 | odd | 2 | 2898.2.g.a.2575.2 | 4 | |||
644.643 | odd | 2 | 2576.2.f.e.321.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.2.c.c.321.2 | ✓ | 4 | 7.6 | odd | 2 | ||
322.2.c.c.321.3 | yes | 4 | 23.22 | odd | 2 | ||
322.2.c.d.321.2 | yes | 4 | 161.160 | even | 2 | inner | |
322.2.c.d.321.3 | yes | 4 | 1.1 | even | 1 | trivial | |
2576.2.f.b.321.2 | 4 | 92.91 | even | 2 | |||
2576.2.f.b.321.3 | 4 | 28.27 | even | 2 | |||
2576.2.f.e.321.2 | 4 | 4.3 | odd | 2 | |||
2576.2.f.e.321.3 | 4 | 644.643 | odd | 2 | |||
2898.2.g.a.2575.1 | 4 | 3.2 | odd | 2 | |||
2898.2.g.a.2575.2 | 4 | 483.482 | odd | 2 | |||
2898.2.g.b.2575.3 | 4 | 21.20 | even | 2 | |||
2898.2.g.b.2575.4 | 4 | 69.68 | even | 2 |