Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,3,Mod(53,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.53");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.h (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: | \(1.96185790339\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.33808912384.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 11x^{6} - 18x^{5} + 47x^{4} - 28x^{3} - 44x^{2} + 48x + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 53.6 | ||
Root | \(1.15139 - 0.593052i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 72.53 |
Dual form | 72.3.h.a.53.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.16130 | + | 1.62831i | 0.580649 | + | 0.814154i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.30278 | + | 3.78190i | −0.325694 | + | 0.945475i | ||||
\(5\) | 7.67101 | 1.53420 | 0.767101 | − | 0.641526i | \(-0.221698\pi\) | ||||
0.767101 | + | 0.641526i | \(0.221698\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.21110 | −1.03016 | −0.515079 | − | 0.857143i | \(-0.672237\pi\) | ||||
−0.515079 | + | 0.857143i | \(0.672237\pi\) | |||||||
\(8\) | −7.67101 | + | 2.27059i | −0.958876 | + | 0.283824i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.90833 | + | 12.4908i | 0.890833 | + | 1.24908i | ||||
\(11\) | 6.05164 | 0.550149 | 0.275075 | − | 0.961423i | \(-0.411297\pi\) | ||||
0.275075 | + | 0.961423i | \(0.411297\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.29014i | 0.176164i | 0.996113 | + | 0.0880821i | \(0.0280738\pi\) | ||||
−0.996113 | + | 0.0880821i | \(0.971926\pi\) | |||||||
\(14\) | −8.37424 | − | 11.7419i | −0.598160 | − | 0.838707i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −12.6056 | − | 9.85394i | −0.787847 | − | 0.615871i | ||||
\(17\) | − | 21.8103i | − | 1.28296i | −0.767140 | − | 0.641479i | \(-0.778321\pi\) | ||
0.767140 | − | 0.641479i | \(-0.221679\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 34.8355i | − | 1.83345i | −0.399523 | − | 0.916723i | \(-0.630824\pi\) | ||
0.399523 | − | 0.916723i | \(-0.369176\pi\) | |||||||
\(20\) | −9.99361 | + | 29.0110i | −0.499680 | + | 1.45055i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.02776 | + | 9.85394i | 0.319443 | + | 0.447906i | ||||
\(23\) | 21.5117i | 0.935293i | 0.883915 | + | 0.467647i | \(0.154898\pi\) | ||||
−0.883915 | + | 0.467647i | \(0.845102\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 33.8444 | 1.35378 | ||||||||
\(26\) | −3.72905 | + | 2.65953i | −0.143425 | + | 0.102290i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 9.39445 | − | 27.2717i | 0.335516 | − | 0.973988i | ||||
\(29\) | 10.9098 | 0.376198 | 0.188099 | − | 0.982150i | \(-0.439767\pi\) | ||||
0.188099 | + | 0.982150i | \(0.439767\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −37.6333 | −1.21398 | −0.606989 | − | 0.794710i | \(-0.707623\pi\) | ||||
−0.606989 | + | 0.794710i | \(0.707623\pi\) | |||||||
\(32\) | 1.40645 | − | 31.9691i | 0.0439516 | − | 0.999034i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 35.5139 | − | 25.3282i | 1.04453 | − | 0.744948i | ||||
\(35\) | −55.3164 | −1.58047 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 34.8355i | 0.941499i | 0.882267 | + | 0.470750i | \(0.156017\pi\) | ||||
−0.882267 | + | 0.470750i | \(0.843983\pi\) | |||||||
\(38\) | 56.7229 | − | 40.4544i | 1.49271 | − | 1.06459i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −58.8444 | + | 17.4177i | −1.47111 | + | 0.435443i | ||||
\(41\) | 13.3250i | 0.325000i | 0.986709 | + | 0.162500i | \(0.0519558\pi\) | ||||
−0.986709 | + | 0.162500i | \(0.948044\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 60.5104i | 1.40722i | 0.710587 | + | 0.703609i | \(0.248430\pi\) | ||||
−0.710587 | + | 0.703609i | \(0.751570\pi\) | |||||||
\(44\) | −7.88393 | + | 22.8867i | −0.179180 | + | 0.520152i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −35.0278 | + | 24.9815i | −0.761473 | + | 0.543077i | ||||
\(47\) | − | 3.34701i | − | 0.0712129i | −0.999366 | − | 0.0356065i | \(-0.988664\pi\) | ||
0.999366 | − | 0.0356065i | \(-0.0113363\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.0612245 | ||||||||
\(50\) | 39.3034 | + | 55.1091i | 0.786069 | + | 1.10218i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.66106 | − | 2.98353i | −0.166559 | − | 0.0573756i | ||||
\(53\) | −35.1163 | −0.662572 | −0.331286 | − | 0.943530i | \(-0.607482\pi\) | ||||
−0.331286 | + | 0.943530i | \(0.607482\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 46.4222 | 0.844040 | ||||||||
\(56\) | 55.3164 | − | 16.3735i | 0.987794 | − | 0.292383i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12.6695 | + | 17.7644i | 0.218439 | + | 0.306283i | ||||
\(59\) | 37.1615 | 0.629856 | 0.314928 | − | 0.949116i | \(-0.398020\pi\) | ||||
0.314928 | + | 0.949116i | \(0.398020\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 25.6749i | 0.420901i | 0.977605 | + | 0.210450i | \(0.0674930\pi\) | ||||
−0.977605 | + | 0.210450i | \(0.932507\pi\) | |||||||
\(62\) | −43.7035 | − | 61.2786i | −0.704895 | − | 0.988365i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 53.6888 | − | 34.8355i | 0.838888 | − | 0.544304i | ||||
\(65\) | 17.5677i | 0.270272i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 25.6749i | − | 0.383208i | −0.981472 | − | 0.191604i | \(-0.938631\pi\) | ||
0.981472 | − | 0.191604i | \(-0.0613689\pi\) | |||||||
\(68\) | 82.4844 | + | 28.4139i | 1.21301 | + | 0.417852i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −64.2389 | − | 90.0722i | −0.917698 | − | 1.28675i | ||||
\(71\) | 37.2881i | 0.525185i | 0.964907 | + | 0.262592i | \(0.0845775\pi\) | ||||
−0.964907 | + | 0.262592i | \(0.915423\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −77.6888 | −1.06423 | −0.532115 | − | 0.846672i | \(-0.678603\pi\) | ||||
−0.532115 | + | 0.846672i | \(0.678603\pi\) | |||||||
\(74\) | −56.7229 | + | 40.4544i | −0.766526 | + | 0.546681i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 131.744 | + | 45.3828i | 1.73348 | + | 0.597142i | ||||
\(77\) | −43.6390 | −0.566740 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 31.3221 | 0.396483 | 0.198241 | − | 0.980153i | \(-0.436477\pi\) | ||||
0.198241 | + | 0.980153i | \(0.436477\pi\) | |||||||
\(80\) | −96.6973 | − | 75.5897i | −1.20872 | − | 0.944871i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −21.6972 | + | 15.4743i | −0.264600 | + | 0.188711i | ||||
\(83\) | 55.3164 | 0.666463 | 0.333232 | − | 0.942845i | \(-0.391861\pi\) | ||||
0.333232 | + | 0.942845i | \(0.391861\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 167.307i | − | 1.96832i | ||||||
\(86\) | −98.5296 | + | 70.2706i | −1.14569 | + | 0.817100i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −46.4222 | + | 13.7408i | −0.527525 | + | 0.156146i | ||||
\(89\) | − | 5.43682i | − | 0.0610878i | −0.999533 | − | 0.0305439i | \(-0.990276\pi\) | ||
0.999533 | − | 0.0305439i | \(-0.00972394\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 16.5144i | − | 0.181477i | ||||||
\(92\) | −81.3553 | − | 28.0250i | −0.884297 | − | 0.304619i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.44996 | − | 3.88687i | 0.0579783 | − | 0.0413497i | ||||
\(95\) | − | 267.223i | − | 2.81288i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −52.8444 | −0.544788 | −0.272394 | − | 0.962186i | \(-0.587815\pi\) | ||||
−0.272394 | + | 0.962186i | \(0.587815\pi\) | |||||||
\(98\) | 3.48389 | + | 4.88492i | 0.0355499 | + | 0.0498462i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −44.0917 | + | 127.996i | −0.440917 | + | 1.27996i | ||||
\(101\) | 90.0069 | 0.891158 | 0.445579 | − | 0.895243i | \(-0.352998\pi\) | ||||
0.445579 | + | 0.895243i | \(0.352998\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 119.211 | 1.15739 | 0.578695 | − | 0.815544i | \(-0.303562\pi\) | ||||
0.578695 | + | 0.815544i | \(0.303562\pi\) | |||||||
\(104\) | −5.19996 | − | 17.5677i | −0.0499996 | − | 0.168920i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −40.7805 | − | 57.1802i | −0.384722 | − | 0.539436i | ||||
\(107\) | 24.2066 | 0.226230 | 0.113115 | − | 0.993582i | \(-0.463917\pi\) | ||||
0.113115 | + | 0.993582i | \(0.463917\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 132.472i | − | 1.21533i | −0.794192 | − | 0.607667i | \(-0.792105\pi\) | ||
0.794192 | − | 0.607667i | \(-0.207895\pi\) | |||||||
\(110\) | 53.9100 | + | 75.5897i | 0.490091 | + | 0.687179i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 90.8999 | + | 71.0578i | 0.811606 | + | 0.634444i | ||||
\(113\) | 160.560i | 1.42089i | 0.703754 | + | 0.710444i | \(0.251506\pi\) | ||||
−0.703754 | + | 0.710444i | \(0.748494\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 165.017i | 1.43493i | ||||||||
\(116\) | −14.2130 | + | 41.2596i | −0.122525 | + | 0.355686i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 43.1556 | + | 60.5104i | 0.365725 | + | 0.512800i | ||||
\(119\) | 157.276i | 1.32165i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −84.3776 | −0.697336 | ||||||||
\(122\) | −41.8067 | + | 29.8162i | −0.342678 | + | 0.244395i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 49.0278 | − | 142.325i | 0.395385 | − | 1.14779i | ||||
\(125\) | 67.8456 | 0.542765 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −146.478 | −1.15337 | −0.576684 | − | 0.816967i | \(-0.695654\pi\) | ||||
−0.576684 | + | 0.816967i | \(0.695654\pi\) | |||||||
\(128\) | 119.072 | + | 46.9676i | 0.930247 | + | 0.366934i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −28.6056 | + | 20.4013i | −0.220043 | + | 0.156933i | ||||
\(131\) | 184.956 | 1.41188 | 0.705939 | − | 0.708273i | \(-0.250525\pi\) | ||||
0.705939 | + | 0.708273i | \(0.250525\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 251.202i | 1.88874i | ||||||||
\(134\) | 41.8067 | − | 29.8162i | 0.311990 | − | 0.222509i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 49.5223 | + | 167.307i | 0.364134 | + | 1.23020i | ||||
\(137\) | − | 133.313i | − | 0.973089i | −0.873656 | − | 0.486544i | \(-0.838257\pi\) | ||
0.873656 | − | 0.486544i | \(-0.161743\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 165.017i | − | 1.18717i | −0.804771 | − | 0.593586i | \(-0.797712\pi\) | ||
0.804771 | − | 0.593586i | \(-0.202288\pi\) | |||||||
\(140\) | 72.0649 | − | 209.201i | 0.514749 | − | 1.49430i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −60.7166 | + | 43.3026i | −0.427582 | + | 0.304948i | ||||
\(143\) | 13.8591i | 0.0969166i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 83.6888 | 0.577164 | ||||||||
\(146\) | −90.2198 | − | 126.501i | −0.617944 | − | 0.866448i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −131.744 | − | 45.3828i | −0.890164 | − | 0.306641i | ||||
\(149\) | −228.937 | −1.53649 | −0.768244 | − | 0.640157i | \(-0.778869\pi\) | ||||
−0.768244 | + | 0.640157i | \(0.778869\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 162.478 | 1.07601 | 0.538006 | − | 0.842941i | \(-0.319178\pi\) | ||||
0.538006 | + | 0.842941i | \(0.319178\pi\) | |||||||
\(152\) | 79.0972 | + | 267.223i | 0.520376 | + | 1.75805i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −50.6779 | − | 71.0578i | −0.329077 | − | 0.461414i | ||||
\(155\) | −288.686 | −1.86249 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 113.667i | 0.723993i | 0.932179 | + | 0.361997i | \(0.117905\pi\) | ||||
−0.932179 | + | 0.361997i | \(0.882095\pi\) | |||||||
\(158\) | 36.3743 | + | 51.0021i | 0.230217 | + | 0.322798i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 10.7889 | − | 245.235i | 0.0674306 | − | 1.53272i | ||||
\(161\) | − | 155.123i | − | 0.963499i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 111.860i | 0.686259i | 0.939288 | + | 0.343130i | \(0.111487\pi\) | ||||
−0.939288 | + | 0.343130i | \(0.888513\pi\) | |||||||
\(164\) | −50.3939 | − | 17.3595i | −0.307280 | − | 0.105851i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 64.2389 | + | 90.0722i | 0.386981 | + | 0.542604i | ||||
\(167\) | 151.541i | 0.907430i | 0.891147 | + | 0.453715i | \(0.149902\pi\) | ||||
−0.891147 | + | 0.453715i | \(0.850098\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 163.755 | 0.968966 | ||||||||
\(170\) | 272.427 | − | 194.293i | 1.60251 | − | 1.14290i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −228.844 | − | 78.8315i | −1.33049 | − | 0.458323i | ||||
\(173\) | −98.0198 | −0.566588 | −0.283294 | − | 0.959033i | \(-0.591427\pi\) | ||||
−0.283294 | + | 0.959033i | \(0.591427\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −244.056 | −1.39460 | ||||||||
\(176\) | −76.2843 | − | 59.6325i | −0.433433 | − | 0.338821i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.85281 | − | 6.31376i | 0.0497349 | − | 0.0354706i | ||||
\(179\) | −222.117 | −1.24088 | −0.620440 | − | 0.784254i | \(-0.713046\pi\) | ||||
−0.620440 | + | 0.784254i | \(0.713046\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 118.731i | − | 0.655971i | −0.944683 | − | 0.327985i | \(-0.893630\pi\) | ||
0.944683 | − | 0.327985i | \(-0.106370\pi\) | |||||||
\(182\) | 26.8905 | − | 19.1781i | 0.147750 | − | 0.105374i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −48.8444 | − | 165.017i | −0.265459 | − | 0.896831i | ||||
\(185\) | 267.223i | 1.44445i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 131.988i | − | 0.705818i | ||||||
\(188\) | 12.6581 | + | 4.36040i | 0.0673301 | + | 0.0231936i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 435.122 | − | 310.326i | 2.29012 | − | 1.63329i | ||||
\(191\) | − | 151.541i | − | 0.793408i | −0.917947 | − | 0.396704i | \(-0.870154\pi\) | ||
0.917947 | − | 0.396704i | \(-0.129846\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 113.378 | 0.587449 | 0.293724 | − | 0.955890i | \(-0.405105\pi\) | ||||
0.293724 | + | 0.955890i | \(0.405105\pi\) | |||||||
\(194\) | −61.3681 | − | 86.0470i | −0.316330 | − | 0.443541i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.90833 | + | 11.3457i | −0.0199404 | + | 0.0578862i | ||||
\(197\) | 319.454 | 1.62159 | 0.810796 | − | 0.585329i | \(-0.199035\pi\) | ||||
0.810796 | + | 0.585329i | \(0.199035\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −41.0109 | −0.206085 | −0.103043 | − | 0.994677i | \(-0.532858\pi\) | ||||
−0.103043 | + | 0.994677i | \(0.532858\pi\) | |||||||
\(200\) | −259.621 | + | 76.8469i | −1.29810 | + | 0.384234i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 104.525 | + | 146.559i | 0.517450 | + | 0.725540i | ||||
\(203\) | −78.6713 | −0.387544 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 102.216i | 0.498616i | ||||||||
\(206\) | 138.440 | + | 194.112i | 0.672037 | + | 0.942293i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 22.5668 | − | 28.8684i | 0.108494 | − | 0.138790i | ||||
\(209\) | − | 210.812i | − | 1.00867i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 95.3459i | − | 0.451876i | −0.974142 | − | 0.225938i | \(-0.927455\pi\) | ||
0.974142 | − | 0.225938i | \(-0.0725447\pi\) | |||||||
\(212\) | 45.7487 | − | 132.806i | 0.215796 | − | 0.626445i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 28.1110 | + | 39.4157i | 0.131360 | + | 0.184186i | ||||
\(215\) | 464.176i | 2.15896i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 271.378 | 1.25059 | ||||||||
\(218\) | 215.704 | − | 153.839i | 0.989470 | − | 0.705683i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −60.4777 | + | 175.564i | −0.274899 | + | 0.798019i | ||||
\(221\) | 49.9485 | 0.226011 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −268.167 | −1.20254 | −0.601270 | − | 0.799046i | \(-0.705338\pi\) | ||||
−0.601270 | + | 0.799046i | \(0.705338\pi\) | |||||||
\(224\) | −10.1421 | + | 230.532i | −0.0452770 | + | 1.02916i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −261.442 | + | 186.458i | −1.15682 | + | 0.825036i | ||||
\(227\) | 65.7164 | 0.289499 | 0.144750 | − | 0.989468i | \(-0.453762\pi\) | ||||
0.144750 | + | 0.989468i | \(0.453762\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 155.373i | 0.678484i | 0.940699 | + | 0.339242i | \(0.110171\pi\) | ||||
−0.940699 | + | 0.339242i | \(0.889829\pi\) | |||||||
\(230\) | −268.698 | + | 191.634i | −1.16825 | + | 0.833190i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −83.6888 | + | 24.7716i | −0.360728 | + | 0.106774i | ||||
\(233\) | − | 285.451i | − | 1.22511i | −0.790427 | − | 0.612556i | \(-0.790141\pi\) | ||
0.790427 | − | 0.612556i | \(-0.209859\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 25.6749i | − | 0.109255i | ||||||
\(236\) | −48.4131 | + | 140.541i | −0.205140 | + | 0.595514i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −256.094 | + | 182.645i | −1.07603 | + | 0.767414i | ||||
\(239\) | − | 421.153i | − | 1.76214i | −0.472982 | − | 0.881072i | \(-0.656822\pi\) | ||
0.472982 | − | 0.881072i | \(-0.343178\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −191.600 | −0.795019 | −0.397510 | − | 0.917598i | \(-0.630126\pi\) | ||||
−0.397510 | + | 0.917598i | \(0.630126\pi\) | |||||||
\(242\) | −97.9876 | − | 137.393i | −0.404907 | − | 0.567739i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −97.1001 | − | 33.4487i | −0.397951 | − | 0.137085i | ||||
\(245\) | 23.0130 | 0.0939307 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 79.7779 | 0.322988 | ||||||||
\(248\) | 288.686 | − | 85.4499i | 1.16405 | − | 0.344556i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 78.7889 | + | 110.473i | 0.315156 | + | 0.441894i | ||||
\(251\) | 483.190 | 1.92506 | 0.962529 | − | 0.271178i | \(-0.0874131\pi\) | ||||
0.962529 | + | 0.271178i | \(0.0874131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 130.181i | 0.514551i | ||||||||
\(254\) | −170.104 | − | 238.511i | −0.669702 | − | 0.939019i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 61.7998 | + | 248.429i | 0.241406 | + | 0.970424i | ||||
\(257\) | − | 21.2132i | − | 0.0825416i | −0.999148 | − | 0.0412708i | \(-0.986859\pi\) | ||
0.999148 | − | 0.0412708i | \(-0.0131406\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 251.202i | − | 0.969893i | ||||||
\(260\) | −66.4391 | − | 22.8867i | −0.255535 | − | 0.0880258i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 214.789 | + | 301.165i | 0.819805 | + | 1.14949i | ||||
\(263\) | 246.670i | 0.937910i | 0.883222 | + | 0.468955i | \(0.155369\pi\) | ||||
−0.883222 | + | 0.468955i | \(0.844631\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −269.378 | −1.01652 | ||||||||
\(266\) | −409.035 | + | 291.721i | −1.53772 | + | 1.09669i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 97.1001 | + | 33.4487i | 0.362314 | + | 0.124809i | ||||
\(269\) | 241.040 | 0.896060 | 0.448030 | − | 0.894019i | \(-0.352126\pi\) | ||||
0.448030 | + | 0.894019i | \(0.352126\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 61.7443 | 0.227839 | 0.113919 | − | 0.993490i | \(-0.463659\pi\) | ||||
0.113919 | + | 0.993490i | \(0.463659\pi\) | |||||||
\(272\) | −214.917 | + | 274.931i | −0.790137 | + | 1.01077i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 217.075 | − | 154.816i | 0.792244 | − | 0.565023i | ||||
\(275\) | 204.814 | 0.744779 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 379.093i | − | 1.36857i | −0.729215 | − | 0.684284i | \(-0.760115\pi\) | ||
0.729215 | − | 0.684284i | \(-0.239885\pi\) | |||||||
\(278\) | 268.698 | − | 191.634i | 0.966541 | − | 0.689330i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 424.333 | − | 125.601i | 1.51548 | − | 0.448575i | ||||
\(281\) | 301.227i | 1.07198i | 0.844223 | + | 0.535992i | \(0.180062\pi\) | ||||
−0.844223 | + | 0.535992i | \(0.819938\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 399.705i | 1.41238i | 0.708020 | + | 0.706192i | \(0.249588\pi\) | ||||
−0.708020 | + | 0.706192i | \(0.750412\pi\) | |||||||
\(284\) | −141.020 | − | 48.5781i | −0.496549 | − | 0.171050i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −22.5668 | + | 16.0945i | −0.0789051 | + | 0.0562745i | ||||
\(287\) | − | 96.0880i | − | 0.334801i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −186.689 | −0.645982 | ||||||||
\(290\) | 97.1876 | + | 136.271i | 0.335130 | + | 0.469901i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 101.211 | − | 293.811i | 0.346613 | − | 1.00620i | ||||
\(293\) | −258.085 | −0.880838 | −0.440419 | − | 0.897792i | \(-0.645170\pi\) | ||||
−0.440419 | + | 0.897792i | \(0.645170\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 285.066 | 0.966327 | ||||||||
\(296\) | −79.0972 | − | 267.223i | −0.267220 | − | 0.902782i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −265.864 | − | 372.780i | −0.892160 | − | 1.25094i | ||||
\(299\) | −49.2648 | −0.164765 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 436.347i | − | 1.44966i | ||||||
\(302\) | 188.685 | + | 264.564i | 0.624785 | + | 0.876039i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −343.267 | + | 439.120i | −1.12917 | + | 1.44448i | ||||
\(305\) | 196.953i | 0.645747i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 286.038i | − | 0.931719i | −0.884859 | − | 0.465859i | \(-0.845745\pi\) | ||
0.884859 | − | 0.465859i | \(-0.154255\pi\) | |||||||
\(308\) | 56.8518 | − | 165.038i | 0.184584 | − | 0.535839i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −335.250 | − | 470.069i | −1.08145 | − | 1.51635i | ||||
\(311\) | − | 464.647i | − | 1.49404i | −0.664800 | − | 0.747021i | \(-0.731483\pi\) | ||
0.664800 | − | 0.747021i | \(-0.268517\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 158.000 | 0.504792 | 0.252396 | − | 0.967624i | \(-0.418781\pi\) | ||||
0.252396 | + | 0.967624i | \(0.418781\pi\) | |||||||
\(314\) | −185.085 | + | 132.001i | −0.589442 | + | 0.420386i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −40.8057 | + | 118.457i | −0.129132 | + | 0.374865i | ||||
\(317\) | −28.6388 | −0.0903433 | −0.0451717 | − | 0.998979i | \(-0.514383\pi\) | ||||
−0.0451717 | + | 0.998979i | \(0.514383\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 66.0219 | 0.206965 | ||||||||
\(320\) | 411.848 | − | 267.223i | 1.28702 | − | 0.835073i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 252.589 | − | 180.144i | 0.784437 | − | 0.559455i | ||||
\(323\) | −759.772 | −2.35224 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 77.5083i | 0.238487i | ||||||||
\(326\) | −182.143 | + | 129.903i | −0.558721 | + | 0.398476i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −30.2557 | − | 102.216i | −0.0922429 | − | 0.311635i | ||||
\(329\) | 24.1356i | 0.0733605i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 428.993i | 1.29605i | 0.761619 | + | 0.648026i | \(0.224405\pi\) | ||||
−0.761619 | + | 0.648026i | \(0.775595\pi\) | |||||||
\(332\) | −72.0649 | + | 209.201i | −0.217063 | + | 0.630124i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −246.755 | + | 175.984i | −0.738788 | + | 0.526898i | ||||
\(335\) | − | 196.953i | − | 0.587919i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 290.755 | 0.862775 | 0.431388 | − | 0.902167i | \(-0.358024\pi\) | ||||
0.431388 | + | 0.902167i | \(0.358024\pi\) | |||||||
\(338\) | 190.169 | + | 266.644i | 0.562629 | + | 0.788888i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 632.738 | + | 217.963i | 1.86100 | + | 0.641069i | ||||
\(341\) | −227.743 | −0.667869 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 331.711 | 0.967087 | ||||||||
\(344\) | −137.394 | − | 464.176i | −0.399403 | − | 1.34935i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −113.830 | − | 159.606i | −0.328989 | − | 0.461290i | ||||
\(347\) | 179.756 | 0.518029 | 0.259014 | − | 0.965873i | \(-0.416602\pi\) | ||||
0.259014 | + | 0.965873i | \(0.416602\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 225.527i | − | 0.646210i | −0.946363 | − | 0.323105i | \(-0.895273\pi\) | ||
0.946363 | − | 0.323105i | \(-0.104727\pi\) | |||||||
\(350\) | −283.421 | − | 397.398i | −0.809775 | − | 1.13542i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.51133 | − | 193.465i | 0.0241799 | − | 0.549618i | ||||
\(353\) | 133.784i | 0.378992i | 0.981881 | + | 0.189496i | \(0.0606854\pi\) | ||||
−0.981881 | + | 0.189496i | \(0.939315\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 286.038i | 0.805740i | ||||||||
\(356\) | 20.5615 | + | 7.08295i | 0.0577570 | + | 0.0198959i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −257.944 | − | 361.676i | −0.720515 | − | 1.01027i | ||||
\(359\) | 239.018i | 0.665787i | 0.942964 | + | 0.332894i | \(0.108025\pi\) | ||||
−0.942964 | + | 0.332894i | \(0.891975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −852.511 | −2.36153 | ||||||||
\(362\) | 193.330 | − | 137.882i | 0.534061 | − | 0.380889i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 62.4558 | + | 21.5146i | 0.171582 | + | 0.0591059i | ||||
\(365\) | −595.952 | −1.63274 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −188.389 | −0.513320 | −0.256660 | − | 0.966502i | \(-0.582622\pi\) | ||||
−0.256660 | + | 0.966502i | \(0.582622\pi\) | |||||||
\(368\) | 211.975 | − | 271.167i | 0.576020 | − | 0.736868i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −435.122 | + | 310.326i | −1.17601 | + | 0.838718i | ||||
\(371\) | 253.227 | 0.682554 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 561.108i | 1.50431i | 0.658985 | + | 0.752156i | \(0.270986\pi\) | ||||
−0.658985 | + | 0.752156i | \(0.729014\pi\) | |||||||
\(374\) | 214.917 | − | 153.277i | 0.574645 | − | 0.409833i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.59969 | + | 25.6749i | 0.0202119 | + | 0.0682844i | ||||
\(377\) | 24.9848i | 0.0662727i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 328.227i | 0.866034i | 0.901386 | + | 0.433017i | \(0.142551\pi\) | ||||
−0.901386 | + | 0.433017i | \(0.857449\pi\) | |||||||
\(380\) | 1010.61 | + | 348.132i | 2.65951 | + | 0.916137i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 246.755 | − | 175.984i | 0.645956 | − | 0.460691i | ||||
\(383\) | 204.118i | 0.532945i | 0.963843 | + | 0.266472i | \(0.0858581\pi\) | ||||
−0.963843 | + | 0.266472i | \(0.914142\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −334.755 | −0.869494 | ||||||||
\(386\) | 131.665 | + | 184.614i | 0.341102 | + | 0.478274i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 68.8444 | − | 199.852i | 0.177434 | − | 0.515083i | ||||
\(389\) | 60.1746 | 0.154690 | 0.0773452 | − | 0.997004i | \(-0.475356\pi\) | ||||
0.0773452 | + | 0.997004i | \(0.475356\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 469.177 | 1.19994 | ||||||||
\(392\) | −23.0130 | + | 6.81178i | −0.0587067 | + | 0.0173770i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 370.981 | + | 520.169i | 0.941575 | + | 1.32023i | ||||
\(395\) | 240.272 | 0.608285 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 592.203i | 1.49170i | 0.666116 | + | 0.745848i | \(0.267955\pi\) | ||||
−0.666116 | + | 0.745848i | \(0.732045\pi\) | |||||||
\(398\) | −47.6259 | − | 66.7785i | −0.119663 | − | 0.167785i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −426.627 | − | 333.501i | −1.06657 | − | 0.833752i | ||||
\(401\) | 653.178i | 1.62887i | 0.580254 | + | 0.814436i | \(0.302953\pi\) | ||||
−0.580254 | + | 0.814436i | \(0.697047\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 86.1854i | − | 0.213859i | ||||||
\(404\) | −117.259 | + | 340.397i | −0.290245 | + | 0.842568i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −91.3608 | − | 128.101i | −0.225027 | − | 0.315520i | ||||
\(407\) | 210.812i | 0.517965i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 355.156 | 0.868351 | 0.434176 | − | 0.900828i | \(-0.357040\pi\) | ||||
0.434176 | + | 0.900828i | \(0.357040\pi\) | |||||||
\(410\) | −166.440 | + | 118.704i | −0.405950 | + | 0.289521i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −155.305 | + | 450.845i | −0.376955 | + | 1.09428i | ||||
\(413\) | −267.976 | −0.648851 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 424.333 | 1.02249 | ||||||||
\(416\) | 73.2135 | + | 3.22096i | 0.175994 | + | 0.00774270i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 343.267 | − | 244.815i | 0.821212 | − | 0.585682i | ||||
\(419\) | 299.085 | 0.713808 | 0.356904 | − | 0.934141i | \(-0.383832\pi\) | ||||
0.356904 | + | 0.934141i | \(0.383832\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 769.638i | − | 1.82812i | −0.405582 | − | 0.914059i | \(-0.632931\pi\) | ||
0.405582 | − | 0.914059i | \(-0.367069\pi\) | |||||||
\(422\) | 155.253 | − | 110.725i | 0.367897 | − | 0.262381i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 269.378 | − | 79.7348i | 0.635325 | − | 0.188054i | ||||
\(425\) | − | 738.156i | − | 1.73684i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 185.145i | − | 0.433594i | ||||||
\(428\) | −31.5357 | + | 91.5468i | −0.0736816 | + | 0.213894i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −755.822 | + | 539.047i | −1.75772 | + | 1.25360i | ||||
\(431\) | − | 411.583i | − | 0.954948i | −0.878646 | − | 0.477474i | \(-0.841552\pi\) | ||
0.878646 | − | 0.477474i | \(-0.158448\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 516.133 | 1.19199 | 0.595996 | − | 0.802987i | \(-0.296757\pi\) | ||||
0.595996 | + | 0.802987i | \(0.296757\pi\) | |||||||
\(434\) | 315.150 | + | 441.886i | 0.726153 | + | 1.01817i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 500.994 | + | 172.581i | 1.14907 | + | 0.395827i | ||||
\(437\) | 749.372 | 1.71481 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −865.788 | −1.97218 | −0.986091 | − | 0.166205i | \(-0.946849\pi\) | ||||
−0.986091 | + | 0.166205i | \(0.946849\pi\) | |||||||
\(440\) | −356.105 | + | 105.406i | −0.809330 | + | 0.239559i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 58.0051 | + | 81.3316i | 0.131233 | + | 0.184008i | ||||
\(443\) | −546.261 | −1.23310 | −0.616548 | − | 0.787318i | \(-0.711469\pi\) | ||||
−0.616548 | + | 0.787318i | \(0.711469\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 41.7059i | − | 0.0937211i | ||||||
\(446\) | −311.421 | − | 436.658i | −0.698254 | − | 0.979053i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −387.156 | + | 251.202i | −0.864187 | + | 0.560719i | ||||
\(449\) | − | 428.978i | − | 0.955407i | −0.878521 | − | 0.477704i | \(-0.841469\pi\) | ||
0.878521 | − | 0.477704i | \(-0.158531\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 80.6382i | 0.178799i | ||||||||
\(452\) | −607.223 | − | 209.174i | −1.34341 | − | 0.462774i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 76.3163 | + | 107.007i | 0.168098 | + | 0.235697i | ||||
\(455\) | − | 126.682i | − | 0.278422i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 75.5997 | 0.165426 | 0.0827130 | − | 0.996573i | \(-0.473642\pi\) | ||||
0.0827130 | + | 0.996573i | \(0.473642\pi\) | |||||||
\(458\) | −252.995 | + | 180.434i | −0.552391 | + | 0.393961i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −624.077 | − | 214.980i | −1.35669 | − | 0.467348i | ||||
\(461\) | 771.365 | 1.67324 | 0.836622 | − | 0.547781i | \(-0.184527\pi\) | ||||
0.836622 | + | 0.547781i | \(0.184527\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −468.278 | −1.01140 | −0.505699 | − | 0.862710i | \(-0.668765\pi\) | ||||
−0.505699 | + | 0.862710i | \(0.668765\pi\) | |||||||
\(464\) | −137.523 | − | 107.504i | −0.296387 | − | 0.231690i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 464.802 | − | 331.494i | 0.997430 | − | 0.711360i | ||||
\(467\) | −452.842 | −0.969682 | −0.484841 | − | 0.874602i | \(-0.661123\pi\) | ||||
−0.484841 | + | 0.874602i | \(0.661123\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 185.145i | 0.394765i | ||||||||
\(470\) | 41.8067 | − | 29.8162i | 0.0889505 | − | 0.0634388i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −285.066 | + | 84.3787i | −0.603954 | + | 0.178768i | ||||
\(473\) | 366.187i | 0.774180i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1178.99i | − | 2.48208i | ||||||
\(476\) | −594.803 | − | 204.896i | −1.24959 | − | 0.430453i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 685.766 | − | 489.083i | 1.43466 | − | 1.02319i | ||||
\(479\) | 467.523i | 0.976040i | 0.872832 | + | 0.488020i | \(0.162281\pi\) | ||||
−0.872832 | + | 0.488020i | \(0.837719\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −79.7779 | −0.165859 | ||||||||
\(482\) | −222.504 | − | 311.983i | −0.461627 | − | 0.647268i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 109.925 | − | 319.108i | 0.227118 | − | 0.659314i | ||||
\(485\) | −405.370 | −0.835815 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −863.766 | −1.77365 | −0.886824 | − | 0.462108i | \(-0.847093\pi\) | ||||
−0.886824 | + | 0.462108i | \(0.847093\pi\) | |||||||
\(488\) | −58.2973 | − | 196.953i | −0.119462 | − | 0.403592i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 26.7250 | + | 37.4723i | 0.0545408 | + | 0.0764741i | ||||
\(491\) | −149.498 | −0.304476 | −0.152238 | − | 0.988344i | \(-0.548648\pi\) | ||||
−0.152238 | + | 0.988344i | \(0.548648\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 237.945i | − | 0.482647i | ||||||
\(494\) | 92.6459 | + | 129.903i | 0.187542 | + | 0.262962i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 474.389 | + | 370.836i | 0.956429 | + | 0.747654i | ||||
\(497\) | − | 268.889i | − | 0.541023i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 205.400i | 0.411622i | 0.978592 | + | 0.205811i | \(0.0659833\pi\) | ||||
−0.978592 | + | 0.205811i | \(0.934017\pi\) | |||||||
\(500\) | −88.3876 | + | 256.585i | −0.176775 | + | 0.513170i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 561.127 | + | 786.782i | 1.11778 | + | 1.56729i | ||||
\(503\) | − | 349.923i | − | 0.695673i | −0.937555 | − | 0.347836i | \(-0.886916\pi\) | ||
0.937555 | − | 0.347836i | \(-0.113084\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 690.444 | 1.36722 | ||||||||
\(506\) | −211.975 | + | 151.179i | −0.418924 | + | 0.298773i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 190.828 | − | 553.964i | 0.375645 | − | 1.09048i | ||||
\(509\) | 529.468 | 1.04021 | 0.520106 | − | 0.854102i | \(-0.325892\pi\) | ||||
0.520106 | + | 0.854102i | \(0.325892\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 560.222 | 1.09632 | ||||||||
\(512\) | −332.750 | + | 389.129i | −0.649903 | + | 0.760017i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 34.5416 | − | 24.6348i | 0.0672016 | − | 0.0479277i | ||||
\(515\) | 914.470 | 1.77567 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 20.2549i | − | 0.0391777i | ||||||
\(518\) | 409.035 | − | 291.721i | 0.789642 | − | 0.563167i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −39.8890 | − | 134.762i | −0.0767096 | − | 0.259157i | ||||
\(521\) | − | 367.318i | − | 0.705026i | −0.935807 | − | 0.352513i | \(-0.885327\pi\) | ||
0.935807 | − | 0.352513i | \(-0.114673\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 577.495i | − | 1.10420i | −0.833779 | − | 0.552099i | \(-0.813827\pi\) | ||
0.833779 | − | 0.552099i | \(-0.186173\pi\) | |||||||
\(524\) | −240.956 | + | 699.485i | −0.459840 | + | 1.33490i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −401.655 | + | 286.458i | −0.763603 | + | 0.544596i | ||||
\(527\) | 820.793i | 1.55748i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 66.2447 | 0.125226 | ||||||||
\(530\) | −312.828 | − | 438.630i | −0.590241 | − | 0.827603i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −950.022 | − | 327.260i | −1.78576 | − | 0.615151i | ||||
\(533\) | −30.5161 | −0.0572534 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 185.689 | 0.347082 | ||||||||
\(536\) | 58.2973 | + | 196.953i | 0.108764 | + | 0.367449i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 279.919 | + | 392.488i | 0.520296 | + | 0.729531i | ||||
\(539\) | 18.1549 | 0.0336826 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 326.777i | − | 0.604023i | −0.953304 | − | 0.302012i | \(-0.902342\pi\) | ||
0.953304 | − | 0.302012i | \(-0.0976582\pi\) | |||||||
\(542\) | 71.7035 | + | 100.539i | 0.132294 | + | 0.185496i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −697.255 | − | 30.6751i | −1.28172 | − | 0.0563880i | ||||
\(545\) | − | 1016.19i | − | 1.86457i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 273.137i | − | 0.499336i | −0.968332 | − | 0.249668i | \(-0.919679\pi\) | ||
0.968332 | − | 0.249668i | \(-0.0803214\pi\) | |||||||
\(548\) | 504.177 | + | 173.677i | 0.920031 | + | 0.316929i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 237.850 | + | 333.501i | 0.432455 | + | 0.606365i | ||||
\(551\) | − | 380.046i | − | 0.689739i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −225.867 | −0.408440 | ||||||||
\(554\) | 617.281 | − | 440.240i | 1.11423 | − | 0.794658i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 624.077 | + | 214.980i | 1.12244 | + | 0.386655i | ||||
\(557\) | 93.2457 | 0.167407 | 0.0837035 | − | 0.996491i | \(-0.473325\pi\) | ||||
0.0837035 | + | 0.996491i | \(0.473325\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −138.577 | −0.247902 | ||||||||
\(560\) | 697.294 | + | 545.085i | 1.24517 | + | 0.973366i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −490.491 | + | 349.815i | −0.872760 | + | 0.622446i | ||||
\(563\) | 42.3615 | 0.0752424 | 0.0376212 | − | 0.999292i | \(-0.488022\pi\) | ||||
0.0376212 | + | 0.999292i | \(0.488022\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1231.66i | 2.17993i | ||||||||
\(566\) | −650.842 | + | 464.176i | −1.14990 | + | 0.820099i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −84.6662 | − | 286.038i | −0.149060 | − | 0.503587i | ||||
\(569\) | 1055.57i | 1.85513i | 0.373663 | + | 0.927564i | \(0.378102\pi\) | ||||
−0.373663 | + | 0.927564i | \(0.621898\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.9344i | 0.0384141i | 0.999816 | + | 0.0192070i | \(0.00611417\pi\) | ||||
−0.999816 | + | 0.0192070i | \(0.993886\pi\) | |||||||
\(572\) | −52.4137 | − | 18.0553i | −0.0916323 | − | 0.0315651i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 156.461 | − | 111.587i | 0.272580 | − | 0.194402i | ||||
\(575\) | 728.052i | 1.26618i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 161.378 | 0.279684 | 0.139842 | − | 0.990174i | \(-0.455341\pi\) | ||||
0.139842 | + | 0.990174i | \(0.455341\pi\) | |||||||
\(578\) | −216.801 | − | 303.987i | −0.375089 | − | 0.525929i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −109.028 | + | 316.503i | −0.187979 | + | 0.545695i | ||||
\(581\) | −398.893 | −0.686562 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −212.511 | −0.364513 | ||||||||
\(584\) | 595.952 | − | 176.400i | 1.02047 | − | 0.302054i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −299.714 | − | 420.243i | −0.511457 | − | 0.717138i | ||||
\(587\) | −481.396 | −0.820096 | −0.410048 | − | 0.912064i | \(-0.634488\pi\) | ||||
−0.410048 | + | 0.912064i | \(0.634488\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1310.97i | 2.22576i | ||||||||
\(590\) | 331.047 | + | 464.176i | 0.561097 | + | 0.786739i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 343.267 | − | 439.120i | 0.579842 | − | 0.741757i | ||||
\(593\) | 321.781i | 0.542632i | 0.962490 | + | 0.271316i | \(0.0874588\pi\) | ||||
−0.962490 | + | 0.271316i | \(0.912541\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1206.47i | 2.02768i | ||||||||
\(596\) | 298.253 | − | 865.816i | 0.500425 | − | 1.45271i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −57.2111 | − | 80.2183i | −0.0956707 | − | 0.134144i | ||||
\(599\) | 35.8419i | 0.0598362i | 0.999552 | + | 0.0299181i | \(0.00952464\pi\) | ||||
−0.999552 | + | 0.0299181i | \(0.990475\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 147.867 | 0.246035 | 0.123018 | − | 0.992404i | \(-0.460743\pi\) | ||||
0.123018 | + | 0.992404i | \(0.460743\pi\) | |||||||
\(602\) | 710.507 | − | 506.729i | 1.18024 | − | 0.841742i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −211.672 | + | 614.475i | −0.350450 | + | 1.01734i | ||||
\(605\) | −647.262 | −1.06985 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −636.611 | −1.04878 | −0.524391 | − | 0.851478i | \(-0.675707\pi\) | ||||
−0.524391 | + | 0.851478i | \(0.675707\pi\) | |||||||
\(608\) | −1113.66 | − | 48.9944i | −1.83167 | − | 0.0805829i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −320.700 | + | 228.721i | −0.525737 | + | 0.374952i | ||||
\(611\) | 7.66510 | 0.0125452 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 870.887i | − | 1.42070i | −0.703850 | − | 0.710348i | \(-0.748537\pi\) | ||
0.703850 | − | 0.710348i | \(-0.251463\pi\) | |||||||
\(614\) | 465.758 | − | 332.175i | 0.758563 | − | 0.541001i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 334.755 | − | 99.0864i | 0.543434 | − | 0.160855i | ||||
\(617\) | − | 1126.69i | − | 1.82607i | −0.407876 | − | 0.913037i | \(-0.633730\pi\) | ||
0.407876 | − | 0.913037i | \(-0.366270\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 311.713i | 0.503575i | 0.967783 | + | 0.251787i | \(0.0810183\pi\) | ||||
−0.967783 | + | 0.251787i | \(0.918982\pi\) | |||||||
\(620\) | 376.092 | − | 1091.78i | 0.606601 | − | 1.76094i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 756.589 | − | 539.594i | 1.21638 | − | 0.867514i | ||||
\(623\) | 39.2054i | 0.0629301i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −325.666 | −0.521066 | ||||||||
\(626\) | 183.485 | + | 257.273i | 0.293107 | + | 0.410979i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −429.877 | − | 148.083i | −0.684518 | − | 0.235800i | ||||
\(629\) | 759.772 | 1.20790 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −203.278 | −0.322153 | −0.161076 | − | 0.986942i | \(-0.551497\pi\) | ||||
−0.161076 | + | 0.986942i | \(0.551497\pi\) | |||||||
\(632\) | −240.272 | + | 71.1198i | −0.380178 | + | 0.112531i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −33.2582 | − | 46.6329i | −0.0524577 | − | 0.0735534i | ||||
\(635\) | −1123.63 | −1.76950 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.87041i | 0.0107856i | ||||||||
\(638\) | 76.6711 | + | 107.504i | 0.120174 | + | 0.168502i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 913.400 | + | 360.289i | 1.42719 | + | 0.562951i | ||||
\(641\) | 586.490i | 0.914960i | 0.889220 | + | 0.457480i | \(0.151248\pi\) | ||||
−0.889220 | + | 0.457480i | \(0.848752\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.16054i | 0.0142466i | 0.999975 | + | 0.00712328i | \(0.00226743\pi\) | ||||
−0.999975 | + | 0.00712328i | \(0.997733\pi\) | |||||||
\(644\) | 586.661 | + | 202.091i | 0.910965 | + | 0.313806i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −882.321 | − | 1237.14i | −1.36582 | − | 1.91508i | ||||
\(647\) | − | 859.040i | − | 1.32773i | −0.747853 | − | 0.663864i | \(-0.768915\pi\) | ||
0.747853 | − | 0.663864i | \(-0.231085\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 224.888 | 0.346515 | ||||||||
\(650\) | −126.207 | + | 90.0102i | −0.194165 | + | 0.138477i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −423.045 | − | 145.729i | −0.648841 | − | 0.223511i | ||||
\(653\) | −131.775 | −0.201799 | −0.100899 | − | 0.994897i | \(-0.532172\pi\) | ||||
−0.100899 | + | 0.994897i | \(0.532172\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1418.80 | 2.16611 | ||||||||
\(656\) | 131.304 | − | 167.969i | 0.200158 | − | 0.256050i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −39.3002 | + | 28.0286i | −0.0597268 | + | 0.0425967i | ||||
\(659\) | −305.137 | −0.463030 | −0.231515 | − | 0.972831i | \(-0.574368\pi\) | ||||
−0.231515 | + | 0.972831i | \(0.574368\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 623.298i | − | 0.942962i | −0.881876 | − | 0.471481i | \(-0.843720\pi\) | ||
0.881876 | − | 0.471481i | \(-0.156280\pi\) | |||||||
\(662\) | −698.533 | + | 498.189i | −1.05519 | + | 0.752551i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −424.333 | + | 125.601i | −0.639056 | + | 0.189158i | ||||
\(665\) | 1926.97i | 2.89771i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 234.688i | 0.351856i | ||||||||
\(668\) | −573.113 | − | 197.424i | −0.857953 | − | 0.295545i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 320.700 | − | 228.721i | 0.478656 | − | 0.341374i | ||||
\(671\) | 155.376i | 0.231558i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −263.867 | −0.392076 | −0.196038 | − | 0.980596i | \(-0.562808\pi\) | ||||
−0.196038 | + | 0.980596i | \(0.562808\pi\) | |||||||
\(674\) | 337.653 | + | 473.439i | 0.500969 | + | 0.702432i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −213.336 | + | 619.306i | −0.315586 | + | 0.916134i | ||||
\(677\) | −788.411 | −1.16457 | −0.582283 | − | 0.812986i | \(-0.697840\pi\) | ||||
−0.582283 | + | 0.812986i | \(0.697840\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 381.066 | 0.561217 | ||||||||
\(680\) | 379.886 | + | 1283.41i | 0.558656 | + | 1.88737i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −264.478 | − | 370.836i | −0.387797 | − | 0.543748i | ||||
\(683\) | 905.773 | 1.32617 | 0.663084 | − | 0.748545i | \(-0.269247\pi\) | ||||
0.663084 | + | 0.748545i | \(0.269247\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1022.65i | − | 1.49291i | ||||||
\(686\) | 385.215 | + | 540.127i | 0.561538 | + | 0.787358i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 596.266 | − | 762.767i | 0.866665 | − | 1.10867i | ||||
\(689\) | − | 80.4211i | − | 0.116721i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.8027i | 0.0662847i | 0.999451 | + | 0.0331423i | \(0.0105515\pi\) | ||||
−0.999451 | + | 0.0331423i | \(0.989449\pi\) | |||||||
\(692\) | 127.698 | − | 370.701i | 0.184534 | − | 0.535695i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 208.750 | + | 292.698i | 0.300793 | + | 0.421755i | ||||
\(695\) | − | 1265.85i | − | 1.82136i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 290.622 | 0.416962 | ||||||||
\(698\) | 367.228 | − | 261.904i | 0.526114 | − | 0.375221i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 317.950 | − | 922.994i | 0.454214 | − | 1.31856i | ||||
\(701\) | −1019.73 | −1.45468 | −0.727339 | − | 0.686279i | \(-0.759243\pi\) | ||||
−0.727339 | + | 0.686279i | \(0.759243\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1213.51 | 1.72619 | ||||||||
\(704\) | 324.905 | − | 210.812i | 0.461513 | − | 0.299449i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −217.842 | + | 155.363i | −0.308558 | + | 0.220061i | ||||
\(707\) | −649.049 | −0.918033 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 84.7350i | − | 0.119513i | −0.998213 | − | 0.0597567i | \(-0.980968\pi\) | ||
0.998213 | − | 0.0597567i | \(-0.0190325\pi\) | |||||||
\(710\) | −465.758 | + | 332.175i | −0.655997 | + | 0.467852i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.3448 | + | 41.7059i | 0.0173382 | + | 0.0585757i | ||||
\(713\) | − | 809.558i | − | 1.13543i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 106.313i | 0.148690i | ||||||||
\(716\) | 289.369 | − | 840.026i | 0.404147 | − | 1.17322i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −389.194 | + | 277.571i | −0.542053 | + | 0.386589i | ||||
\(719\) | 646.311i | 0.898903i | 0.893305 | + | 0.449451i | \(0.148381\pi\) | ||||
−0.893305 | + | 0.449451i | \(0.851619\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −859.643 | −1.19229 | ||||||||
\(722\) | −990.018 | − | 1388.15i | −1.37122 | − | 1.92265i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 449.028 | + | 154.679i | 0.620204 | + | 0.213646i | ||||
\(725\) | 369.234 | 0.509288 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −648.789 | −0.892419 | −0.446210 | − | 0.894928i | \(-0.647226\pi\) | ||||
−0.446210 | + | 0.894928i | \(0.647226\pi\) | |||||||
\(728\) | 37.4975 | + | 126.682i | 0.0515075 | + | 0.174014i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −692.077 | − | 970.393i | −0.948051 | − | 1.32931i | ||||
\(731\) | 1319.75 | 1.80540 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 696.353i | − | 0.950004i | −0.879985 | − | 0.475002i | \(-0.842447\pi\) | ||
0.879985 | − | 0.475002i | \(-0.157553\pi\) | |||||||
\(734\) | −218.775 | − | 306.755i | −0.298059 | − | 0.417922i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 687.711 | + | 30.2552i | 0.934390 | + | 0.0411076i | ||||
\(737\) | − | 155.376i | − | 0.210822i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 740.833i | − | 1.00248i | −0.865308 | − | 0.501240i | \(-0.832877\pi\) | ||
0.865308 | − | 0.501240i | \(-0.167123\pi\) | |||||||
\(740\) | −1010.61 | − | 348.132i | −1.36569 | − | 0.470449i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 294.072 | + | 412.332i | 0.396324 | + | 0.555704i | ||||
\(743\) | 111.377i | 0.149901i | 0.997187 | + | 0.0749507i | \(0.0238800\pi\) | ||||
−0.997187 | + | 0.0749507i | \(0.976120\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1756.18 | −2.35728 | ||||||||
\(746\) | −913.657 | + | 651.614i | −1.22474 | + | 0.873477i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 499.166 | + | 171.951i | 0.667334 | + | 0.229881i | ||||
\(749\) | −174.556 | −0.233052 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 923.699 | 1.22996 | 0.614979 | − | 0.788543i | \(-0.289164\pi\) | ||||
0.614979 | + | 0.788543i | \(0.289164\pi\) | |||||||
\(752\) | −32.9812 | + | 42.1909i | −0.0438580 | + | 0.0561049i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −40.6830 | + | 29.0148i | −0.0539562 | + | 0.0384812i | ||||
\(755\) | 1246.37 | 1.65082 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1233.47i | 1.62941i | 0.579873 | + | 0.814707i | \(0.303102\pi\) | ||||
−0.579873 | + | 0.814707i | \(0.696898\pi\) | |||||||
\(758\) | −534.455 | + | 381.169i | −0.705085 | + | 0.502862i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 606.755 | + | 2049.87i | 0.798362 | + | 2.69720i | ||||
\(761\) | − | 179.070i | − | 0.235309i | −0.993055 | − | 0.117654i | \(-0.962463\pi\) | ||
0.993055 | − | 0.117654i | \(-0.0375375\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 955.266i | 1.25199i | ||||||||
\(764\) | 573.113 | + | 197.424i | 0.750147 | + | 0.258408i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −332.367 | + | 237.042i | −0.433899 | + | 0.309454i | ||||
\(767\) | 85.1049i | 0.110958i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −251.511 | −0.327062 | −0.163531 | − | 0.986538i | \(-0.552288\pi\) | ||||
−0.163531 | + | 0.986538i | \(0.552288\pi\) | |||||||
\(770\) | −388.751 | − | 545.085i | −0.504871 | − | 0.707902i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −147.706 | + | 428.783i | −0.191329 | + | 0.555418i | ||||
\(773\) | 184.110 | 0.238176 | 0.119088 | − | 0.992884i | \(-0.462003\pi\) | ||||
0.119088 | + | 0.992884i | \(0.462003\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1273.68 | −1.64345 | ||||||||
\(776\) | 405.370 | − | 119.988i | 0.522384 | − | 0.154624i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 69.8806 | + | 97.9827i | 0.0898208 | + | 0.125942i | ||||
\(779\) | 464.183 | 0.595870 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 225.654i | 0.288930i | ||||||||
\(782\) | 544.855 | + | 763.966i | 0.696745 | + | 0.976938i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −37.8167 | − | 29.5618i | −0.0482355 | − | 0.0377064i | ||||
\(785\) | 871.941i | 1.11075i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1351.36i | − | 1.71710i | −0.512731 | − | 0.858550i | \(-0.671366\pi\) | ||
0.512731 | − | 0.858550i | \(-0.328634\pi\) | |||||||
\(788\) | −416.176 | + | 1208.14i | −0.528143 | + | 1.53317i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 279.028 | + | 391.238i | 0.353200 | + | 0.495237i | ||||
\(791\) | − | 1157.82i | − | 1.46374i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −58.7991 | −0.0741476 | ||||||||
\(794\) | −964.289 | + | 687.724i | −1.21447 | + | 0.866151i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 53.4281 | − | 155.099i | 0.0671207 | − | 0.194848i | ||||
\(797\) | 1407.20 | 1.76562 | 0.882812 | − | 0.469727i | \(-0.155648\pi\) | ||||
0.882812 | + | 0.469727i | \(0.155648\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −72.9992 | −0.0913632 | ||||||||
\(800\) | 47.6005 | − | 1081.97i | 0.0595006 | − | 1.35247i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1063.57 | + | 758.534i | −1.32615 | + | 0.945802i | ||||
\(803\) | −470.145 | −0.585485 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 1189.95i | − | 1.47820i | ||||||
\(806\) | 140.336 | − | 100.087i | 0.174115 | − | 0.124177i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −690.444 | + | 204.369i | −0.854510 | + | 0.252932i | ||||
\(809\) | − | 741.991i | − | 0.917171i | −0.888650 | − | 0.458585i | \(-0.848356\pi\) | ||
0.888650 | − | 0.458585i | \(-0.151644\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 716.837i | 0.883893i | 0.897041 | + | 0.441947i | \(0.145712\pi\) | ||||
−0.897041 | + | 0.441947i | \(0.854288\pi\) | |||||||
\(812\) | 102.491 | − | 297.527i | 0.126221 | − | 0.366413i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −343.267 | + | 244.815i | −0.421703 | + | 0.300756i | ||||
\(815\) | 858.082i | 1.05286i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2107.91 | 2.58006 | ||||||||
\(818\) | 412.441 | + | 578.303i | 0.504207 | + | 0.706972i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −386.572 | − | 133.165i | −0.471429 | − | 0.162396i | ||||
\(821\) | −244.447 | −0.297743 | −0.148871 | − | 0.988857i | \(-0.547564\pi\) | ||||
−0.148871 | + | 0.988857i | \(0.547564\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 331.500 | 0.402795 | 0.201398 | − | 0.979510i | \(-0.435452\pi\) | ||||
0.201398 | + | 0.979510i | \(0.435452\pi\) | |||||||
\(824\) | −914.470 | + | 270.680i | −1.10979 | + | 0.328495i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −311.199 | − | 436.347i | −0.376755 | − | 0.528265i | ||||
\(827\) | 724.314 | 0.875833 | 0.437916 | − | 0.899016i | \(-0.355717\pi\) | ||||
0.437916 | + | 0.899016i | \(0.355717\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 77.5083i | − | 0.0934961i | −0.998907 | − | 0.0467481i | \(-0.985114\pi\) | ||
0.998907 | − | 0.0467481i | \(-0.0148858\pi\) | |||||||
\(830\) | 492.777 | + | 690.945i | 0.593707 | + | 0.832464i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 79.7779 | + | 122.955i | 0.0958870 | + | 0.147782i | ||||
\(833\) | − | 65.4309i | − | 0.0785485i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1162.47i | 1.39218i | ||||||||
\(836\) | 797.269 | + | 274.640i | 0.953672 | + | 0.328517i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 347.327 | + | 487.003i | 0.414472 | + | 0.581150i | ||||
\(839\) | − | 952.252i | − | 1.13498i | −0.823379 | − | 0.567492i | \(-0.807914\pi\) | ||
0.823379 | − | 0.567492i | \(-0.192086\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −721.977 | −0.858475 | ||||||||
\(842\) | 1253.21 | − | 893.778i | 1.48837 | − | 1.06149i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 360.589 | + | 124.214i | 0.427238 | + | 0.147173i | ||||
\(845\) | 1256.17 | 1.48659 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 608.456 | 0.718366 | ||||||||
\(848\) | 442.661 | + | 346.034i | 0.522005 | + | 0.408059i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1201.95 | − | 857.219i | 1.41405 | − | 1.00849i | ||||
\(851\) | −749.372 | −0.880578 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 282.424i | − | 0.331095i | −0.986202 | − | 0.165548i | \(-0.947061\pi\) | ||
0.986202 | − | 0.165548i | \(-0.0529392\pi\) | |||||||
\(854\) | 301.473 | − | 215.008i | 0.353012 | − | 0.251766i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −185.689 | + | 54.9632i | −0.216926 | + | 0.0642094i | ||||
\(857\) | 539.665i | 0.629714i | 0.949139 | + | 0.314857i | \(0.101956\pi\) | ||||
−0.949139 | + | 0.314857i | \(0.898044\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.2837i | 0.0620299i | 0.999519 | + | 0.0310150i | \(0.00987395\pi\) | ||||
−0.999519 | + | 0.0310150i | \(0.990126\pi\) | |||||||
\(860\) | −1755.47 | − | 604.717i | −2.04124 | − | 0.703160i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 670.183 | − | 477.970i | 0.777475 | − | 0.554489i | ||||
\(863\) | − | 632.435i | − | 0.732834i | −0.930451 | − | 0.366417i | \(-0.880584\pi\) | ||
0.930451 | − | 0.366417i | \(-0.119416\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −751.911 | −0.869261 | ||||||||
\(866\) | 599.384 | + | 840.424i | 0.692129 | + | 0.970466i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −353.544 | + | 1026.32i | −0.407309 | + | 1.18240i | ||||
\(869\) | 189.550 | 0.218125 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 58.7991 | 0.0675075 | ||||||||
\(872\) | 300.789 | + | 1016.19i | 0.344941 | + | 1.16536i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 870.244 | + | 1220.21i | 0.995702 | + | 1.39612i | ||||
\(875\) | −489.241 | −0.559133 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 346.548i | − | 0.395152i | −0.980288 | − | 0.197576i | \(-0.936693\pi\) | ||
0.980288 | − | 0.197576i | \(-0.0633069\pi\) | |||||||
\(878\) | −1005.44 | − | 1409.77i | −1.14515 | − | 1.60566i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −585.177 | − | 457.441i | −0.664974 | − | 0.519820i | ||||
\(881\) | 1394.26i | 1.58258i | 0.611438 | + | 0.791292i | \(0.290591\pi\) | ||||
−0.611438 | + | 0.791292i | \(0.709409\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1714.29i | − | 1.94144i | −0.240212 | − | 0.970720i | \(-0.577217\pi\) | ||
0.240212 | − | 0.970720i | \(-0.422783\pi\) | |||||||
\(884\) | −65.0717 | + | 188.900i | −0.0736105 | + | 0.213688i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −634.372 | − | 889.482i | −0.715995 | − | 1.00393i | ||||
\(887\) | 1149.19i | 1.29559i | 0.761815 | + | 0.647795i | \(0.224309\pi\) | ||||
−0.761815 | + | 0.647795i | \(0.775691\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1056.27 | 1.18815 | ||||||||
\(890\) | 67.9100 | − | 48.4329i | 0.0763034 | − | 0.0544190i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 349.361 | − | 1014.18i | 0.391660 | − | 1.13697i | ||||
\(893\) | −116.595 | −0.130565 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1703.87 | −1.90376 | ||||||||
\(896\) | −858.638 | − | 338.688i | −0.958301 | − | 0.378000i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 698.508 | − | 498.171i | 0.777849 | − | 0.554756i | ||||
\(899\) | −410.570 | −0.456696 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 765.897i | 0.850052i | ||||||||
\(902\) | −131.304 | + | 93.6449i | −0.145570 | + | 0.103819i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −364.567 | − | 1231.66i | −0.403282 | − | 1.36246i | ||||
\(905\) | − | 910.785i | − | 1.00639i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 507.952i | 0.560035i | 0.959995 | + | 0.280017i | \(0.0903402\pi\) | ||||
−0.959995 | + | 0.280017i | \(0.909660\pi\) | |||||||
\(908\) | −85.6137 | + | 248.533i | −0.0942882 | + | 0.273715i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 206.278 | − | 147.116i | 0.226679 | − | 0.161666i | ||||
\(911\) | 1488.13i | 1.63351i | 0.576984 | + | 0.816756i | \(0.304230\pi\) | ||||
−0.576984 | + | 0.816756i | \(0.695770\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 334.755 | 0.366654 | ||||||||
\(914\) | 87.7937 | + | 123.100i | 0.0960544 | + | 0.134682i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −587.605 | − | 202.416i | −0.641490 | − | 0.220978i | ||||
\(917\) | −1333.74 | −1.45446 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −335.790 | −0.365386 | −0.182693 | − | 0.983170i | \(-0.558481\pi\) | ||||
−0.182693 | + | 0.983170i | \(0.558481\pi\) | |||||||
\(920\) | −374.686 | − | 1265.85i | −0.407267 | − | 1.37592i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 895.785 | + | 1256.02i | 0.971567 | + | 1.36228i | ||||
\(923\) | −85.3949 | −0.0925188 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1178.99i | 1.27458i | ||||||||
\(926\) | −543.810 | − | 762.500i | −0.587267 | − | 0.823434i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 15.3440 | − | 348.775i | 0.0165345 | − | 0.375835i | ||||
\(929\) | − | 1685.87i | − | 1.81471i | −0.420363 | − | 0.907356i | \(-0.638097\pi\) | ||
0.420363 | − | 0.907356i | \(-0.361903\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 104.506i | − | 0.112252i | ||||||
\(932\) | 1079.55 | + | 371.879i | 1.15831 | + | 0.399012i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −525.884 | − | 737.366i | −0.563045 | − | 0.789471i | ||||
\(935\) | − | 1012.48i | − | 1.08287i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.7342 | −0.0530781 | −0.0265390 | − | 0.999648i | \(-0.508449\pi\) | ||||
−0.0265390 | + | 0.999648i | \(0.508449\pi\) | |||||||
\(938\) | −301.473 | + | 215.008i | −0.321399 | + | 0.229220i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 97.1001 | + | 33.4487i | 0.103298 | + | 0.0355837i | ||||
\(941\) | −1689.50 | −1.79543 | −0.897715 | − | 0.440577i | \(-0.854774\pi\) | ||||
−0.897715 | + | 0.440577i | \(0.854774\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −286.644 | −0.303971 | ||||||||
\(944\) | −468.441 | − | 366.187i | −0.496230 | − | 0.387910i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −596.266 | + | 425.252i | −0.630302 | + | 0.449527i | ||||
\(947\) | −1036.44 | −1.09445 | −0.547225 | − | 0.836986i | \(-0.684316\pi\) | ||||
−0.547225 | + | 0.836986i | \(0.684316\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 177.918i | − | 0.187479i | ||||||
\(950\) | 1919.75 | − | 1369.15i | 2.02079 | − | 1.44121i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −357.110 | − | 1206.47i | −0.375116 | − | 1.26730i | ||||
\(953\) | − | 388.814i | − | 0.407989i | −0.978972 | − | 0.203995i | \(-0.934608\pi\) | ||
0.978972 | − | 0.203995i | \(-0.0653925\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1162.47i | − | 1.21725i | ||||||
\(956\) | 1592.76 | + | 548.667i | 1.66606 | + | 0.573920i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −761.272 | + | 542.933i | −0.794647 | + | 0.566736i | ||||
\(959\) | 961.335i | 1.00243i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 455.266 | 0.473742 | ||||||||
\(962\) | −92.6459 | − | 129.903i | −0.0963056 | − | 0.135034i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 249.611 | − | 724.611i | 0.258933 | − | 0.751671i | ||||
\(965\) | 869.721 | 0.901265 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −201.899 | −0.208789 | −0.104395 | − | 0.994536i | \(-0.533290\pi\) | ||||
−0.104395 | + | 0.994536i | \(0.533290\pi\) | |||||||
\(968\) | 647.262 | − | 191.587i | 0.668659 | − | 0.197921i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −470.755 | − | 660.067i | −0.485315 | − | 0.680482i | ||||
\(971\) | −1500.54 | −1.54535 | −0.772676 | − | 0.634800i | \(-0.781082\pi\) | ||||
−0.772676 | + | 0.634800i | \(0.781082\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1189.95i | 1.22297i | ||||||||
\(974\) | −1003.09 | − | 1406.48i | −1.02987 | − | 1.44402i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 252.999 | − | 323.647i | 0.259221 | − | 0.331605i | ||||
\(977\) | − | 866.378i | − | 0.886774i | −0.896330 | − | 0.443387i | \(-0.853777\pi\) | ||
0.896330 | − | 0.443387i | \(-0.146223\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 32.9017i | − | 0.0336074i | ||||||
\(980\) | −29.9808 | + | 87.0330i | −0.0305927 | + | 0.0888092i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −173.611 | − | 243.428i | −0.176794 | − | 0.247890i | ||||
\(983\) | 613.800i | 0.624415i | 0.950014 | + | 0.312207i | \(0.101068\pi\) | ||||
−0.950014 | + | 0.312207i | \(0.898932\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2450.53 | 2.48785 | ||||||||
\(986\) | 387.448 | − | 276.325i | 0.392949 | − | 0.280248i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −103.933 | + | 301.712i | −0.105195 | + | 0.305377i | ||||
\(989\) | −1301.68 | −1.31616 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1460.50 | 1.47376 | 0.736882 | − | 0.676022i | \(-0.236297\pi\) | ||||
0.736882 | + | 0.676022i | \(0.236297\pi\) | |||||||
\(992\) | −52.9294 | + | 1203.10i | −0.0533562 | + | 1.21280i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 437.833 | − | 312.260i | 0.440476 | − | 0.314145i | ||||
\(995\) | −314.595 | −0.316176 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1378.84i | 1.38299i | 0.722382 | + | 0.691494i | \(0.243047\pi\) | ||||
−0.722382 | + | 0.691494i | \(0.756953\pi\) | |||||||
\(998\) | −334.454 | + | 238.530i | −0.335124 | + | 0.239008i | ||||
\(999\) | 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 | 72.3.h.a.53.6 | yes | 8 | |
3.2 | odd | 2 | inner | 72.3.h.a.53.3 | ✓ | 8 | |
4.3 | odd | 2 | 288.3.h.a.17.8 | 8 | |||
8.3 | odd | 2 | 288.3.h.a.17.1 | 8 | |||
8.5 | even | 2 | inner | 72.3.h.a.53.4 | yes | 8 | |
12.11 | even | 2 | 288.3.h.a.17.2 | 8 | |||
16.3 | odd | 4 | 2304.3.e.o.1025.1 | 8 | |||
16.5 | even | 4 | 2304.3.e.n.1025.8 | 8 | |||
16.11 | odd | 4 | 2304.3.e.o.1025.8 | 8 | |||
16.13 | even | 4 | 2304.3.e.n.1025.1 | 8 | |||
24.5 | odd | 2 | inner | 72.3.h.a.53.5 | yes | 8 | |
24.11 | even | 2 | 288.3.h.a.17.7 | 8 | |||
48.5 | odd | 4 | 2304.3.e.n.1025.2 | 8 | |||
48.11 | even | 4 | 2304.3.e.o.1025.2 | 8 | |||
48.29 | odd | 4 | 2304.3.e.n.1025.7 | 8 | |||
48.35 | even | 4 | 2304.3.e.o.1025.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.h.a.53.3 | ✓ | 8 | 3.2 | odd | 2 | inner | |
72.3.h.a.53.4 | yes | 8 | 8.5 | even | 2 | inner | |
72.3.h.a.53.5 | yes | 8 | 24.5 | odd | 2 | inner | |
72.3.h.a.53.6 | yes | 8 | 1.1 | even | 1 | trivial | |
288.3.h.a.17.1 | 8 | 8.3 | odd | 2 | |||
288.3.h.a.17.2 | 8 | 12.11 | even | 2 | |||
288.3.h.a.17.7 | 8 | 24.11 | even | 2 | |||
288.3.h.a.17.8 | 8 | 4.3 | odd | 2 | |||
2304.3.e.n.1025.1 | 8 | 16.13 | even | 4 | |||
2304.3.e.n.1025.2 | 8 | 48.5 | odd | 4 | |||
2304.3.e.n.1025.7 | 8 | 48.29 | odd | 4 | |||
2304.3.e.n.1025.8 | 8 | 16.5 | even | 4 | |||
2304.3.e.o.1025.1 | 8 | 16.3 | odd | 4 | |||
2304.3.e.o.1025.2 | 8 | 48.11 | even | 4 | |||
2304.3.e.o.1025.7 | 8 | 48.35 | even | 4 | |||
2304.3.e.o.1025.8 | 8 | 16.11 | odd | 4 |