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 | 53.8 | ||
Root | \(-0.651388 + 0.158947i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 72.53 |
Dual form | 72.3.h.a.53.7 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.77521 | + | 0.921201i | 0.887607 | + | 0.460601i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.30278 | + | 3.27066i | 0.575694 | + | 0.817665i | ||||
\(5\) | −1.07498 | −0.214997 | −0.107498 | − | 0.994205i | \(-0.534284\pi\) | ||||
−0.107498 | + | 0.994205i | \(0.534284\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.21110 | 1.03016 | 0.515079 | − | 0.857143i | \(-0.327763\pi\) | ||||
0.515079 | + | 0.857143i | \(0.327763\pi\) | |||||||
\(8\) | 1.07498 | + | 7.92745i | 0.134373 | + | 0.990931i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.90833 | − | 0.990277i | −0.190833 | − | 0.0990277i | ||||
\(11\) | −16.3517 | −1.48652 | −0.743258 | − | 0.669004i | \(-0.766721\pi\) | ||||
−0.743258 | + | 0.669004i | \(0.766721\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 21.6045i | − | 1.66189i | −0.556357 | − | 0.830943i | \(-0.687801\pi\) | ||
0.556357 | − | 0.830943i | \(-0.312199\pi\) | |||||||
\(14\) | 12.8013 | + | 6.64288i | 0.914375 | + | 0.474491i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.39445 | + | 15.0632i | −0.337153 | + | 0.941450i | ||||
\(17\) | − | 18.9819i | − | 1.11658i | −0.829646 | − | 0.558290i | \(-0.811458\pi\) | ||
0.829646 | − | 0.558290i | \(-0.188542\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.0438i | 0.897040i | 0.893773 | + | 0.448520i | \(0.148049\pi\) | ||||
−0.893773 | + | 0.448520i | \(0.851951\pi\) | |||||||
\(20\) | −2.47545 | − | 3.51591i | −0.123772 | − | 0.175795i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −29.0278 | − | 15.0632i | −1.31944 | − | 0.684691i | ||||
\(23\) | − | 1.11567i | − | 0.0485074i | −0.999706 | − | 0.0242537i | \(-0.992279\pi\) | ||
0.999706 | − | 0.0242537i | \(-0.00772094\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −23.8444 | −0.953776 | ||||||||
\(26\) | 19.9021 | − | 38.3527i | 0.765466 | − | 1.47510i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 16.6056 | + | 23.5851i | 0.593055 | + | 0.842324i | ||||
\(29\) | 29.4784 | 1.01650 | 0.508249 | − | 0.861210i | \(-0.330293\pi\) | ||||
0.508249 | + | 0.861210i | \(0.330293\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.63331 | 0.181720 | 0.0908598 | − | 0.995864i | \(-0.471038\pi\) | ||||
0.0908598 | + | 0.995864i | \(0.471038\pi\) | |||||||
\(32\) | −23.4525 | + | 21.7710i | −0.732892 | + | 0.680345i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 17.4861 | − | 33.6969i | 0.514298 | − | 0.991085i | ||||
\(35\) | −7.75182 | −0.221480 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 17.0438i | − | 0.460642i | −0.973115 | − | 0.230321i | \(-0.926022\pi\) | ||
0.973115 | − | 0.230321i | \(-0.0739776\pi\) | |||||||
\(38\) | −15.7007 | + | 30.2563i | −0.413177 | + | 0.796219i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.15559 | − | 8.52188i | −0.0288897 | − | 0.213047i | ||||
\(41\) | 27.4671i | 0.669930i | 0.942231 | + | 0.334965i | \(0.108725\pi\) | ||||
−0.942231 | + | 0.334965i | \(0.891275\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 52.3306i | 1.21699i | 0.793558 | + | 0.608495i | \(0.208226\pi\) | ||||
−0.793558 | + | 0.608495i | \(0.791774\pi\) | |||||||
\(44\) | −37.6543 | − | 53.4808i | −0.855779 | − | 1.21547i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.02776 | − | 1.98055i | 0.0223425 | − | 0.0430555i | ||||
\(47\) | 64.5352i | 1.37309i | 0.727087 | + | 0.686545i | \(0.240874\pi\) | ||||
−0.727087 | + | 0.686545i | \(0.759126\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.0612245 | ||||||||
\(50\) | −42.3290 | − | 21.9655i | −0.846579 | − | 0.439310i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 70.6611 | − | 49.7504i | 1.35887 | − | 0.956738i | ||||
\(53\) | 35.9283 | 0.677893 | 0.338946 | − | 0.940806i | \(-0.389929\pi\) | ||||
0.338946 | + | 0.940806i | \(0.389929\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.5778 | 0.319596 | ||||||||
\(56\) | 7.75182 | + | 57.1656i | 0.138425 | + | 1.02081i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 52.3305 | + | 27.1556i | 0.902251 | + | 0.468199i | ||||
\(59\) | 56.8069 | 0.962828 | 0.481414 | − | 0.876493i | \(-0.340123\pi\) | ||||
0.481414 | + | 0.876493i | \(0.340123\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 69.3743i | 1.13728i | 0.822585 | + | 0.568642i | \(0.192531\pi\) | ||||
−0.822585 | + | 0.568642i | \(0.807469\pi\) | |||||||
\(62\) | 10.0003 | + | 5.18941i | 0.161296 | + | 0.0837002i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −61.6888 | + | 17.0438i | −0.963888 | + | 0.266309i | ||||
\(65\) | 23.2245i | 0.357300i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 69.3743i | − | 1.03544i | −0.855551 | − | 0.517719i | \(-0.826781\pi\) | ||
0.855551 | − | 0.517719i | \(-0.173219\pi\) | |||||||
\(68\) | 62.0832 | − | 43.7110i | 0.912989 | − | 0.642808i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −13.7611 | − | 7.14099i | −0.196588 | − | 0.102014i | ||||
\(71\) | − | 98.4764i | − | 1.38699i | −0.720461 | − | 0.693496i | \(-0.756070\pi\) | ||
0.720461 | − | 0.693496i | \(-0.243930\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 37.6888 | 0.516285 | 0.258143 | − | 0.966107i | \(-0.416890\pi\) | ||||
0.258143 | + | 0.966107i | \(0.416890\pi\) | |||||||
\(74\) | 15.7007 | − | 30.2563i | 0.212172 | − | 0.408869i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −55.7443 | + | 39.2479i | −0.733478 | + | 0.516420i | ||||
\(77\) | −117.914 | −1.53135 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −127.322 | −1.61167 | −0.805836 | − | 0.592138i | \(-0.798284\pi\) | ||||
−0.805836 | + | 0.592138i | \(0.798284\pi\) | |||||||
\(80\) | 5.79894 | − | 16.1927i | 0.0724868 | − | 0.202409i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −25.3028 | + | 48.7601i | −0.308570 | + | 0.594635i | ||||
\(83\) | 7.75182 | 0.0933954 | 0.0466977 | − | 0.998909i | \(-0.485130\pi\) | ||||
0.0466977 | + | 0.998909i | \(0.485130\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.4052i | 0.240061i | ||||||||
\(86\) | −48.2070 | + | 92.8980i | −0.560547 | + | 1.08021i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −17.5778 | − | 129.627i | −0.199748 | − | 1.47304i | ||||
\(89\) | − | 76.1475i | − | 0.855590i | −0.903876 | − | 0.427795i | \(-0.859291\pi\) | ||
0.903876 | − | 0.427795i | \(-0.140709\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 155.792i | − | 1.71200i | ||||||
\(92\) | 3.64898 | − | 2.56914i | 0.0396628 | − | 0.0279254i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −59.4500 | + | 114.564i | −0.632446 | + | 1.21877i | ||||
\(95\) | − | 18.3218i | − | 0.192861i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.84441 | 0.0499424 | 0.0249712 | − | 0.999688i | \(-0.492051\pi\) | ||||
0.0249712 | + | 0.999688i | \(0.492051\pi\) | |||||||
\(98\) | 5.32564 | + | 2.76360i | 0.0543433 | + | 0.0282000i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −54.9083 | − | 77.9870i | −0.549083 | − | 0.779870i | ||||
\(101\) | −105.635 | −1.04589 | −0.522946 | − | 0.852366i | \(-0.675167\pi\) | ||||
−0.522946 | + | 0.852366i | \(0.675167\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 104.789 | 1.01737 | 0.508684 | − | 0.860953i | \(-0.330132\pi\) | ||||
0.508684 | + | 0.860953i | \(0.330132\pi\) | |||||||
\(104\) | 171.269 | − | 23.2245i | 1.64681 | − | 0.223313i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 63.7805 | + | 33.0972i | 0.601703 | + | 0.312238i | ||||
\(107\) | −65.4067 | −0.611278 | −0.305639 | − | 0.952147i | \(-0.598870\pi\) | ||||
−0.305639 | + | 0.952147i | \(0.598870\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.36144i | 0.0308389i | 0.999881 | + | 0.0154195i | \(0.00490836\pi\) | ||||
−0.999881 | + | 0.0154195i | \(0.995092\pi\) | |||||||
\(110\) | 31.2044 | + | 16.1927i | 0.283676 | + | 0.147206i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −38.8999 | + | 108.622i | −0.347321 | + | 0.969842i | ||||
\(113\) | 84.1927i | 0.745068i | 0.928019 | + | 0.372534i | \(0.121511\pi\) | ||||
−0.928019 | + | 0.372534i | \(0.878489\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.19933i | 0.0104289i | ||||||||
\(116\) | 67.8822 | + | 96.4139i | 0.585191 | + | 0.831155i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 100.844 | + | 52.3306i | 0.854614 | + | 0.443479i | ||||
\(119\) | − | 136.880i | − | 1.15025i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 146.378 | 1.20973 | ||||||||
\(122\) | −63.9077 | + | 123.154i | −0.523834 | + | 1.00946i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.9722 | + | 18.4246i | 0.104615 | + | 0.148586i | ||||
\(125\) | 52.5069 | 0.420056 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −45.5223 | −0.358443 | −0.179222 | − | 0.983809i | \(-0.557358\pi\) | ||||
−0.179222 | + | 0.983809i | \(0.557358\pi\) | |||||||
\(128\) | −125.212 | − | 26.5715i | −0.978216 | − | 0.207590i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −21.3944 | + | 41.2285i | −0.164573 | + | 0.317142i | ||||
\(131\) | 129.117 | 0.985629 | 0.492814 | − | 0.870134i | \(-0.335968\pi\) | ||||
0.492814 | + | 0.870134i | \(0.335968\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 122.904i | 0.924092i | ||||||||
\(134\) | 63.9077 | − | 123.154i | 0.476923 | − | 0.919062i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 150.478 | − | 20.4052i | 1.10645 | − | 0.150038i | ||||
\(137\) | 10.9367i | 0.0798296i | 0.999203 | + | 0.0399148i | \(0.0127087\pi\) | ||||
−0.999203 | + | 0.0399148i | \(0.987291\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.19933i | − | 0.00862825i | −0.999991 | − | 0.00431412i | \(-0.998627\pi\) | ||
0.999991 | − | 0.00431412i | \(-0.00137323\pi\) | |||||||
\(140\) | −17.8507 | − | 25.3536i | −0.127505 | − | 0.181097i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 90.7166 | − | 174.817i | 0.638849 | − | 1.23110i | ||||
\(143\) | 353.270i | 2.47042i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −31.6888 | −0.218544 | ||||||||
\(146\) | 66.9058 | + | 34.7190i | 0.458259 | + | 0.237801i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 55.7443 | − | 39.2479i | 0.376651 | − | 0.265189i | ||||
\(149\) | −29.9323 | −0.200888 | −0.100444 | − | 0.994943i | \(-0.532026\pi\) | ||||
−0.100444 | + | 0.994943i | \(0.532026\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 61.5223 | 0.407432 | 0.203716 | − | 0.979030i | \(-0.434698\pi\) | ||||
0.203716 | + | 0.979030i | \(0.434698\pi\) | |||||||
\(152\) | −135.113 | + | 18.3218i | −0.888904 | + | 0.120538i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −209.322 | − | 108.622i | −1.35923 | − | 0.705339i | ||||
\(155\) | −6.05571 | −0.0390691 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 137.549i | − | 0.876110i | −0.898948 | − | 0.438055i | \(-0.855667\pi\) | ||
0.898948 | − | 0.438055i | \(-0.144333\pi\) | |||||||
\(158\) | −226.024 | − | 117.289i | −1.43053 | − | 0.742338i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 25.2111 | − | 23.4035i | 0.157569 | − | 0.146272i | ||||
\(161\) | − | 8.04521i | − | 0.0499702i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 191.079i | 1.17227i | 0.810215 | + | 0.586133i | \(0.199350\pi\) | ||||
−0.810215 | + | 0.586133i | \(0.800650\pi\) | |||||||
\(164\) | −89.8357 | + | 63.2507i | −0.547779 | + | 0.385675i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.7611 | + | 7.14099i | 0.0828984 | + | 0.0430180i | ||||
\(167\) | − | 233.125i | − | 1.39596i | −0.716118 | − | 0.697980i | \(-0.754083\pi\) | ||
0.716118 | − | 0.697980i | \(-0.245917\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −297.755 | −1.76187 | ||||||||
\(170\) | −18.7973 | + | 36.2236i | −0.110572 | + | 0.213080i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −171.156 | + | 120.506i | −0.995091 | + | 0.700614i | ||||
\(173\) | 323.809 | 1.87173 | 0.935864 | − | 0.352363i | \(-0.114622\pi\) | ||||
0.935864 | + | 0.352363i | \(0.114622\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −171.944 | −0.982540 | ||||||||
\(176\) | 88.2083 | − | 246.309i | 0.501184 | − | 1.39948i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 70.1472 | − | 135.178i | 0.394085 | − | 0.759428i | ||||
\(179\) | −185.924 | −1.03868 | −0.519342 | − | 0.854567i | \(-0.673823\pi\) | ||||
−0.519342 | + | 0.854567i | \(0.673823\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 126.266i | − | 0.697600i | −0.937197 | − | 0.348800i | \(-0.886589\pi\) | ||
0.937197 | − | 0.348800i | \(-0.113411\pi\) | |||||||
\(182\) | 143.516 | − | 276.565i | 0.788551 | − | 1.51959i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.84441 | − | 1.19933i | 0.0480674 | − | 0.00651808i | ||||
\(185\) | 18.3218i | 0.0990365i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 310.385i | 1.65982i | ||||||||
\(188\) | −211.073 | + | 148.610i | −1.12273 | + | 0.790480i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.8780 | − | 32.5250i | 0.0888317 | − | 0.171184i | ||||
\(191\) | 233.125i | 1.22055i | 0.792189 | + | 0.610275i | \(0.208941\pi\) | ||||
−0.792189 | + | 0.610275i | \(0.791059\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −117.378 | −0.608174 | −0.304087 | − | 0.952644i | \(-0.598351\pi\) | ||||
−0.304087 | + | 0.952644i | \(0.598351\pi\) | |||||||
\(194\) | 8.59987 | + | 4.46268i | 0.0443292 | + | 0.0230035i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.90833 | + | 9.81198i | 0.0352466 | + | 0.0500611i | ||||
\(197\) | 296.313 | 1.50413 | 0.752064 | − | 0.659091i | \(-0.229059\pi\) | ||||
0.752064 | + | 0.659091i | \(0.229059\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 233.011 | 1.17091 | 0.585455 | − | 0.810705i | \(-0.300916\pi\) | ||||
0.585455 | + | 0.810705i | \(0.300916\pi\) | |||||||
\(200\) | −25.6324 | − | 189.025i | −0.128162 | − | 0.945126i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −187.525 | − | 97.3111i | −0.928341 | − | 0.481738i | ||||
\(203\) | 212.572 | 1.04715 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 29.5267i | − | 0.144033i | ||||||
\(206\) | 186.023 | + | 96.5317i | 0.903023 | + | 0.468600i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 325.433 | + | 116.544i | 1.56458 | + | 0.560310i | ||||
\(209\) | − | 278.694i | − | 1.33346i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 35.2868i | − | 0.167236i | −0.996498 | − | 0.0836181i | \(-0.973352\pi\) | ||
0.996498 | − | 0.0836181i | \(-0.0266476\pi\) | |||||||
\(212\) | 82.7349 | + | 117.509i | 0.390259 | + | 0.554289i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −116.111 | − | 60.2528i | −0.542575 | − | 0.281555i | ||||
\(215\) | − | 56.2545i | − | 0.261649i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 40.6224 | 0.187200 | ||||||||
\(218\) | −3.09657 | + | 5.96728i | −0.0142044 | + | 0.0273729i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 40.4777 | + | 57.4910i | 0.183990 | + | 0.261323i | ||||
\(221\) | −410.094 | −1.85563 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −51.8335 | −0.232437 | −0.116219 | − | 0.993224i | \(-0.537077\pi\) | ||||
−0.116219 | + | 0.993224i | \(0.537077\pi\) | |||||||
\(224\) | −169.119 | + | 156.993i | −0.754994 | + | 0.700862i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −77.5584 | + | 149.460i | −0.343179 | + | 0.661328i | ||||
\(227\) | −334.786 | −1.47483 | −0.737413 | − | 0.675442i | \(-0.763953\pi\) | ||||
−0.737413 | + | 0.675442i | \(0.763953\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 219.407i | − | 0.958108i | −0.877786 | − | 0.479054i | \(-0.840980\pi\) | ||
0.877786 | − | 0.479054i | \(-0.159020\pi\) | |||||||
\(230\) | −1.10482 | + | 2.12906i | −0.00480357 | + | 0.00925679i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 31.6888 | + | 233.689i | 0.136590 | + | 1.00728i | ||||
\(233\) | 203.867i | 0.874965i | 0.899227 | + | 0.437482i | \(0.144130\pi\) | ||||
−0.899227 | + | 0.437482i | \(0.855870\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 69.3743i | − | 0.295210i | ||||||
\(236\) | 130.813 | + | 185.796i | 0.554294 | + | 0.787271i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 126.094 | − | 242.992i | 0.529808 | − | 1.02097i | ||||
\(239\) | 54.0232i | 0.226038i | 0.993593 | + | 0.113019i | \(0.0360522\pi\) | ||||
−0.993593 | + | 0.113019i | \(0.963948\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 327.600 | 1.35933 | 0.679667 | − | 0.733520i | \(-0.262124\pi\) | ||||
0.679667 | + | 0.733520i | \(0.262124\pi\) | |||||||
\(242\) | 259.852 | + | 134.843i | 1.07377 | + | 0.557204i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −226.900 | + | 159.754i | −0.929918 | + | 0.654728i | ||||
\(245\) | −3.22495 | −0.0131631 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 368.222 | 1.49078 | ||||||||
\(248\) | 6.05571 | + | 44.6577i | 0.0244182 | + | 0.180072i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 93.2111 | + | 48.3695i | 0.372844 | + | 0.193478i | ||||
\(251\) | −362.281 | −1.44335 | −0.721676 | − | 0.692231i | \(-0.756628\pi\) | ||||
−0.721676 | + | 0.692231i | \(0.756628\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.2431i | 0.0721070i | ||||||||
\(254\) | −80.8118 | − | 41.9352i | −0.318157 | − | 0.165099i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −197.800 | − | 162.515i | −0.772656 | − | 0.634825i | ||||
\(257\) | 21.2132i | 0.0825416i | 0.999148 | + | 0.0412708i | \(0.0131406\pi\) | ||||
−0.999148 | + | 0.0412708i | \(0.986859\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 122.904i | − | 0.474534i | ||||||
\(260\) | −75.9595 | + | 53.4808i | −0.292152 | + | 0.205695i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 229.211 | + | 118.943i | 0.874852 | + | 0.453981i | ||||
\(263\) | − | 205.878i | − | 0.782806i | −0.920219 | − | 0.391403i | \(-0.871990\pi\) | ||
0.920219 | − | 0.391403i | \(-0.128010\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −38.6224 | −0.145745 | ||||||||
\(266\) | −113.220 | + | 218.181i | −0.425637 | + | 0.820231i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 226.900 | − | 159.754i | 0.846642 | − | 0.596095i | ||||
\(269\) | −2.77109 | −0.0103014 | −0.00515072 | − | 0.999987i | \(-0.501640\pi\) | ||||
−0.00515072 | + | 0.999987i | \(0.501640\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −125.744 | −0.464001 | −0.232001 | − | 0.972716i | \(-0.574527\pi\) | ||||
−0.232001 | + | 0.972716i | \(0.574527\pi\) | |||||||
\(272\) | 285.928 | + | 102.397i | 1.05120 | + | 0.376458i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.0749 | + | 19.4149i | −0.0367696 | + | 0.0708574i | ||||
\(275\) | 389.896 | 1.41780 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 162.752i | − | 0.587552i | −0.955874 | − | 0.293776i | \(-0.905088\pi\) | ||
0.955874 | − | 0.293776i | \(-0.0949119\pi\) | |||||||
\(278\) | 1.10482 | − | 2.12906i | 0.00397418 | − | 0.00765850i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.33308 | − | 61.4521i | −0.0297610 | − | 0.219472i | ||||
\(281\) | − | 301.227i | − | 1.07198i | −0.844223 | − | 0.535992i | \(-0.819938\pi\) | ||
0.844223 | − | 0.535992i | \(-0.180062\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 31.6888i | − | 0.111975i | −0.998431 | − | 0.0559874i | \(-0.982169\pi\) | ||
0.998431 | − | 0.0559874i | \(-0.0178307\pi\) | |||||||
\(284\) | 322.083 | − | 226.769i | 1.13409 | − | 0.798482i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −325.433 | + | 627.131i | −1.13788 | + | 2.19276i | ||||
\(287\) | 198.068i | 0.690134i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −71.3112 | −0.246751 | ||||||||
\(290\) | −56.2545 | − | 29.1918i | −0.193981 | − | 0.100661i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 86.7889 | + | 123.267i | 0.297222 | + | 0.422148i | ||||
\(293\) | −304.913 | −1.04066 | −0.520329 | − | 0.853966i | \(-0.674191\pi\) | ||||
−0.520329 | + | 0.853966i | \(0.674191\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −61.0665 | −0.207005 | ||||||||
\(296\) | 135.113 | − | 18.3218i | 0.456464 | − | 0.0618978i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −53.1362 | − | 27.5737i | −0.178310 | − | 0.0925291i | ||||
\(299\) | −24.1035 | −0.0806137 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 377.361i | 1.25369i | ||||||||
\(302\) | 109.215 | + | 56.6744i | 0.361640 | + | 0.187664i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −256.733 | − | 91.9416i | −0.844518 | − | 0.302440i | ||||
\(305\) | − | 74.5763i | − | 0.244512i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 105.860i | − | 0.344822i | −0.985025 | − | 0.172411i | \(-0.944844\pi\) | ||
0.985025 | − | 0.172411i | \(-0.0551558\pi\) | |||||||
\(308\) | −271.529 | − | 385.656i | −0.881587 | − | 1.25213i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.7502 | − | 5.57853i | −0.0346780 | − | 0.0179953i | ||||
\(311\) | − | 555.157i | − | 1.78507i | −0.450978 | − | 0.892535i | \(-0.648925\pi\) | ||
0.450978 | − | 0.892535i | \(-0.351075\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 158.000 | 0.504792 | 0.252396 | − | 0.967624i | \(-0.418781\pi\) | ||||
0.252396 | + | 0.967624i | \(0.418781\pi\) | |||||||
\(314\) | 126.711 | − | 244.180i | 0.403537 | − | 0.777642i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −293.194 | − | 416.428i | −0.927830 | − | 1.31781i | ||||
\(317\) | 97.0351 | 0.306105 | 0.153052 | − | 0.988218i | \(-0.451090\pi\) | ||||
0.153052 | + | 0.988218i | \(0.451090\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −482.022 | −1.51104 | ||||||||
\(320\) | 66.3145 | − | 18.3218i | 0.207233 | − | 0.0572555i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.41126 | − | 14.2820i | 0.0230163 | − | 0.0443539i | ||||
\(323\) | 323.522 | 1.00162 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 515.147i | 1.58507i | ||||||||
\(326\) | −176.022 | + | 339.207i | −0.539946 | + | 1.04051i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −217.744 | + | 29.5267i | −0.663855 | + | 0.0900205i | ||||
\(329\) | 465.370i | 1.41450i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 619.572i | − | 1.87182i | −0.352242 | − | 0.935909i | \(-0.614581\pi\) | ||
0.352242 | − | 0.935909i | \(-0.385419\pi\) | |||||||
\(332\) | 17.8507 | + | 25.3536i | 0.0537672 | + | 0.0763662i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 214.755 | − | 413.847i | 0.642980 | − | 1.23906i | ||||
\(335\) | 74.5763i | 0.222616i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −170.755 | −0.506692 | −0.253346 | − | 0.967376i | \(-0.581531\pi\) | ||||
−0.253346 | + | 0.967376i | \(0.581531\pi\) | |||||||
\(338\) | −528.580 | − | 274.293i | −1.56384 | − | 0.811517i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −66.7385 | + | 46.9886i | −0.196290 | + | 0.138202i | ||||
\(341\) | −92.1141 | −0.270129 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −331.711 | −0.967087 | ||||||||
\(344\) | −414.848 | + | 56.2545i | −1.20595 | + | 0.163531i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 574.830 | + | 298.293i | 1.66136 | + | 0.862119i | ||||
\(347\) | 300.386 | 0.865666 | 0.432833 | − | 0.901474i | \(-0.357514\pi\) | ||||
0.432833 | + | 0.901474i | \(0.357514\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 53.5299i | − | 0.153381i | −0.997055 | − | 0.0766904i | \(-0.975565\pi\) | ||
0.997055 | − | 0.0766904i | \(-0.0244353\pi\) | |||||||
\(350\) | −305.238 | − | 158.396i | −0.872110 | − | 0.452559i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 383.489 | − | 355.993i | 1.08946 | − | 1.01134i | ||||
\(353\) | 600.475i | 1.70106i | 0.525925 | + | 0.850531i | \(0.323719\pi\) | ||||
−0.525925 | + | 0.850531i | \(0.676281\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 105.860i | 0.298199i | ||||||||
\(356\) | 249.053 | − | 175.351i | 0.699586 | − | 0.492558i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −330.056 | − | 171.274i | −0.921943 | − | 0.478418i | ||||
\(359\) | 148.508i | 0.413671i | 0.978376 | + | 0.206836i | \(0.0663165\pi\) | ||||
−0.978376 | + | 0.206836i | \(0.933683\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 70.5106 | 0.195320 | ||||||||
\(362\) | 116.316 | − | 224.149i | 0.321315 | − | 0.619195i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 509.544 | − | 358.755i | 1.39985 | − | 0.985591i | ||||
\(365\) | −40.5149 | −0.111000 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 316.389 | 0.862094 | 0.431047 | − | 0.902329i | \(-0.358144\pi\) | ||||
0.431047 | + | 0.902329i | \(0.358144\pi\) | |||||||
\(368\) | 16.8055 | + | 6.01842i | 0.0456673 | + | 0.0163544i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −16.8780 | + | 32.5250i | −0.0456163 | + | 0.0879055i | ||||
\(371\) | 259.083 | 0.698336 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 626.768i | 1.68034i | 0.542321 | + | 0.840171i | \(0.317545\pi\) | ||||
−0.542321 | + | 0.840171i | \(0.682455\pi\) | |||||||
\(374\) | −285.928 | + | 551.001i | −0.764512 | + | 1.47326i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −511.600 | + | 69.3743i | −1.36064 | + | 0.184506i | ||||
\(377\) | − | 636.867i | − | 1.68930i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 331.027i | 0.873423i | 0.899602 | + | 0.436711i | \(0.143857\pi\) | ||||
−0.899602 | + | 0.436711i | \(0.856143\pi\) | |||||||
\(380\) | 59.9242 | − | 42.1909i | 0.157695 | − | 0.111029i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −214.755 | + | 413.847i | −0.562187 | + | 1.08337i | ||||
\(383\) | 407.765i | 1.06466i | 0.846537 | + | 0.532330i | \(0.178683\pi\) | ||||
−0.846537 | + | 0.532330i | \(0.821317\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 126.755 | 0.329234 | ||||||||
\(386\) | −208.371 | − | 108.128i | −0.539820 | − | 0.280126i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.1556 | + | 15.8444i | 0.0287515 | + | 0.0408361i | ||||
\(389\) | 53.5819 | 0.137743 | 0.0688714 | − | 0.997626i | \(-0.478060\pi\) | ||||
0.0688714 | + | 0.997626i | \(0.478060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.1775 | −0.0541624 | ||||||||
\(392\) | 3.22495 | + | 23.7823i | 0.00822692 | + | 0.0606692i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 526.019 | + | 272.964i | 1.33507 | + | 0.692802i | ||||
\(395\) | 136.869 | 0.346504 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 289.744i | − | 0.729833i | −0.931040 | − | 0.364917i | \(-0.881098\pi\) | ||
0.931040 | − | 0.364917i | \(-0.118902\pi\) | |||||||
\(398\) | 413.644 | + | 214.650i | 1.03931 | + | 0.539322i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 128.627 | − | 359.173i | 0.321569 | − | 0.897933i | ||||
\(401\) | 203.458i | 0.507376i | 0.967286 | + | 0.253688i | \(0.0816436\pi\) | ||||
−0.967286 | + | 0.253688i | \(0.918356\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 121.705i | − | 0.301997i | ||||||
\(404\) | −243.254 | − | 345.496i | −0.602113 | − | 0.855189i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 377.361 | + | 195.822i | 0.929460 | + | 0.482319i | ||||
\(407\) | 278.694i | 0.684752i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 412.844 | 1.00940 | 0.504700 | − | 0.863295i | \(-0.331603\pi\) | ||||
0.504700 | + | 0.863295i | \(0.331603\pi\) | |||||||
\(410\) | 27.2001 | − | 52.4163i | 0.0663416 | − | 0.127845i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 241.305 | + | 342.729i | 0.585693 | + | 0.831866i | ||||
\(413\) | 409.640 | 0.991865 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.33308 | −0.0200797 | ||||||||
\(416\) | 470.353 | + | 506.681i | 1.13066 | + | 1.21798i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 256.733 | − | 494.742i | 0.614195 | − | 1.18359i | ||||
\(419\) | −336.482 | −0.803059 | −0.401529 | − | 0.915846i | \(-0.631521\pi\) | ||||
−0.401529 | + | 0.915846i | \(0.631521\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 217.481i | − | 0.516582i | −0.966067 | − | 0.258291i | \(-0.916841\pi\) | ||
0.966067 | − | 0.258291i | \(-0.0831594\pi\) | |||||||
\(422\) | 32.5063 | − | 62.6417i | 0.0770291 | − | 0.148440i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 38.6224 | + | 284.820i | 0.0910905 | + | 0.671745i | ||||
\(425\) | 452.611i | 1.06497i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 500.265i | 1.17158i | ||||||||
\(428\) | −150.617 | − | 213.923i | −0.351909 | − | 0.499821i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 51.8217 | − | 99.8639i | 0.120516 | − | 0.232242i | ||||
\(431\) | − | 750.994i | − | 1.74245i | −0.490888 | − | 0.871223i | \(-0.663328\pi\) | ||
0.490888 | − | 0.871223i | \(-0.336672\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −176.133 | −0.406773 | −0.203387 | − | 0.979098i | \(-0.565195\pi\) | ||||
−0.203387 | + | 0.979098i | \(0.565195\pi\) | |||||||
\(434\) | 72.1134 | + | 37.4214i | 0.166160 | + | 0.0862244i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.9941 | + | 7.74065i | −0.0252159 | + | 0.0177538i | ||||
\(437\) | 19.0152 | 0.0435130 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 417.788 | 0.951681 | 0.475841 | − | 0.879531i | \(-0.342144\pi\) | ||||
0.475841 | + | 0.879531i | \(0.342144\pi\) | |||||||
\(440\) | 18.8958 | + | 139.347i | 0.0429451 | + | 0.316698i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −728.005 | − | 377.779i | −1.64707 | − | 0.854704i | ||||
\(443\) | 61.0471 | 0.137804 | 0.0689020 | − | 0.997623i | \(-0.478050\pi\) | ||||
0.0689020 | + | 0.997623i | \(0.478050\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 81.8573i | 0.183949i | ||||||||
\(446\) | −92.0155 | − | 47.7491i | −0.206313 | − | 0.107061i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −444.844 | + | 122.904i | −0.992956 | + | 0.274340i | ||||
\(449\) | − | 182.905i | − | 0.407360i | −0.979038 | − | 0.203680i | \(-0.934710\pi\) | ||
0.979038 | − | 0.203680i | \(-0.0652902\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 449.134i | − | 0.995863i | ||||||
\(452\) | −275.366 | + | 193.877i | −0.609216 | + | 0.428931i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −594.316 | − | 308.405i | −1.30907 | − | 0.679306i | ||||
\(455\) | 167.474i | 0.368075i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −443.600 | −0.970678 | −0.485339 | − | 0.874326i | \(-0.661304\pi\) | ||||
−0.485339 | + | 0.874326i | \(0.661304\pi\) | |||||||
\(458\) | 202.118 | − | 389.494i | 0.441305 | − | 0.850423i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.92259 | + | 2.76178i | −0.00852737 | + | 0.00600387i | ||||
\(461\) | −728.241 | −1.57970 | −0.789850 | − | 0.613301i | \(-0.789841\pi\) | ||||
−0.789850 | + | 0.613301i | \(0.789841\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −107.722 | −0.232662 | −0.116331 | − | 0.993211i | \(-0.537113\pi\) | ||||
−0.116331 | + | 0.993211i | \(0.537113\pi\) | |||||||
\(464\) | −159.020 | + | 444.039i | −0.342715 | + | 0.956981i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −187.802 | + | 361.907i | −0.403009 | + | 0.776625i | ||||
\(467\) | −820.248 | −1.75642 | −0.878210 | − | 0.478276i | \(-0.841262\pi\) | ||||
−0.878210 | + | 0.478276i | \(0.841262\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 500.265i | − | 1.06666i | ||||||
\(470\) | 63.9077 | − | 123.154i | 0.135974 | − | 0.262031i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 61.0665 | + | 450.333i | 0.129378 | + | 0.954096i | ||||
\(473\) | − | 855.693i | − | 1.80908i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 406.398i | − | 0.855575i | ||||||
\(476\) | 447.689 | − | 315.204i | 0.940522 | − | 0.662194i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −49.7662 | + | 95.9027i | −0.104113 | + | 0.200633i | ||||
\(479\) | − | 120.790i | − | 0.252171i | −0.992019 | − | 0.126085i | \(-0.959759\pi\) | ||
0.992019 | − | 0.126085i | \(-0.0402413\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −368.222 | −0.765534 | ||||||||
\(482\) | 581.560 | + | 301.785i | 1.20656 | + | 0.626111i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 337.075 | + | 478.752i | 0.696436 | + | 0.989156i | ||||
\(485\) | −5.20766 | −0.0107374 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −128.234 | −0.263314 | −0.131657 | − | 0.991295i | \(-0.542030\pi\) | ||||
−0.131657 | + | 0.991295i | \(0.542030\pi\) | |||||||
\(488\) | −549.961 | + | 74.5763i | −1.12697 | + | 0.152820i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.72498 | − | 2.97083i | −0.0116836 | − | 0.00606292i | ||||
\(491\) | −382.144 | −0.778298 | −0.389149 | − | 0.921175i | \(-0.627231\pi\) | ||||
−0.389149 | + | 0.921175i | \(0.627231\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 559.555i | − | 1.13500i | ||||||
\(494\) | 653.673 | + | 339.207i | 1.32323 | + | 0.686653i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −30.3886 | + | 84.8556i | −0.0612673 | + | 0.171080i | ||||
\(497\) | − | 710.123i | − | 1.42882i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 554.995i | 1.11221i | 0.831111 | + | 0.556107i | \(0.187705\pi\) | ||||
−0.831111 | + | 0.556107i | \(0.812295\pi\) | |||||||
\(500\) | 120.912 | + | 171.732i | 0.241823 | + | 0.343465i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −643.127 | − | 333.734i | −1.28113 | − | 0.664809i | ||||
\(503\) | − | 78.3943i | − | 0.155854i | −0.996959 | − | 0.0779268i | \(-0.975170\pi\) | ||
0.996959 | − | 0.0779268i | \(-0.0248300\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 113.556 | 0.224863 | ||||||||
\(506\) | −16.8055 | + | 32.3854i | −0.0332125 | + | 0.0640027i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −104.828 | − | 148.888i | −0.206354 | − | 0.293087i | ||||
\(509\) | 514.941 | 1.01167 | 0.505836 | − | 0.862630i | \(-0.331184\pi\) | ||||
0.505836 | + | 0.862630i | \(0.331184\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 271.778 | 0.531855 | ||||||||
\(512\) | −201.428 | − | 470.713i | −0.393414 | − | 0.919361i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.5416 | + | 37.6580i | −0.0380187 | + | 0.0732646i | ||||
\(515\) | −112.646 | −0.218731 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1055.26i | − | 2.04112i | ||||||
\(518\) | 113.220 | − | 218.181i | 0.218571 | − | 0.421200i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −184.111 | + | 24.9660i | −0.354060 | + | 0.0480115i | ||||
\(521\) | 489.695i | 0.939914i | 0.882689 | + | 0.469957i | \(0.155730\pi\) | ||||
−0.882689 | + | 0.469957i | \(0.844270\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 774.165i | 1.48024i | 0.672476 | + | 0.740119i | \(0.265231\pi\) | ||||
−0.672476 | + | 0.740119i | \(0.734769\pi\) | |||||||
\(524\) | 297.328 | + | 422.299i | 0.567421 | + | 0.805915i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 189.655 | − | 365.478i | 0.360561 | − | 0.694825i | ||||
\(527\) | − | 106.931i | − | 0.202905i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 527.755 | 0.997647 | ||||||||
\(530\) | −68.5630 | − | 35.5790i | −0.129364 | − | 0.0671301i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −401.978 | + | 283.021i | −0.755598 | + | 0.531994i | ||||
\(533\) | 593.415 | 1.11335 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 70.3112 | 0.131423 | ||||||||
\(536\) | 549.961 | − | 74.5763i | 1.02605 | − | 0.139135i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.91928 | − | 2.55273i | −0.00914363 | − | 0.00474485i | ||||
\(539\) | −49.0551 | −0.0910112 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 590.045i | 1.09066i | 0.838223 | + | 0.545328i | \(0.183595\pi\) | ||||
−0.838223 | + | 0.545328i | \(0.816405\pi\) | |||||||
\(542\) | −223.223 | − | 115.836i | −0.411851 | − | 0.213719i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 413.255 | + | 445.173i | 0.759660 | + | 0.818333i | ||||
\(545\) | − | 3.61350i | − | 0.00663027i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 707.189i | 1.29285i | 0.762977 | + | 0.646425i | \(0.223737\pi\) | ||||
−0.762977 | + | 0.646425i | \(0.776263\pi\) | |||||||
\(548\) | −35.7701 | + | 25.1847i | −0.0652739 | + | 0.0459574i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 692.150 | + | 359.173i | 1.25845 | + | 0.653042i | ||||
\(551\) | 502.423i | 0.911838i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −918.133 | −1.66028 | ||||||||
\(554\) | 149.927 | − | 288.919i | 0.270627 | − | 0.521515i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.92259 | − | 2.76178i | 0.00705502 | − | 0.00496723i | ||||
\(557\) | −75.0816 | −0.134796 | −0.0673982 | − | 0.997726i | \(-0.521470\pi\) | ||||
−0.0673982 | + | 0.997726i | \(0.521470\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1130.58 | 2.02250 | ||||||||
\(560\) | 41.8168 | − | 116.767i | 0.0746728 | − | 0.208513i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 277.491 | − | 534.744i | 0.493757 | − | 0.951501i | ||||
\(563\) | −114.462 | −0.203307 | −0.101653 | − | 0.994820i | \(-0.532413\pi\) | ||||
−0.101653 | + | 0.994820i | \(0.532413\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 90.5058i | − | 0.160187i | ||||||
\(566\) | 29.1918 | − | 56.2545i | 0.0515756 | − | 0.0993896i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 780.666 | − | 105.860i | 1.37441 | − | 0.186374i | ||||
\(569\) | 45.8199i | 0.0805270i | 0.999189 | + | 0.0402635i | \(0.0128197\pi\) | ||||
−0.999189 | + | 0.0402635i | \(0.987180\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 830.093i | − | 1.45375i | −0.686768 | − | 0.726877i | \(-0.740971\pi\) | ||
0.686768 | − | 0.726877i | \(-0.259029\pi\) | |||||||
\(572\) | −1155.43 | + | 813.502i | −2.01998 | + | 1.42221i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −182.461 | + | 351.614i | −0.317876 | + | 0.612568i | ||||
\(575\) | 26.6025i | 0.0462652i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −69.3776 | −0.120239 | −0.0601193 | − | 0.998191i | \(-0.519148\pi\) | ||||
−0.0601193 | + | 0.998191i | \(0.519148\pi\) | |||||||
\(578\) | −126.593 | − | 65.6920i | −0.219018 | − | 0.113654i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −72.9722 | − | 103.643i | −0.125814 | − | 0.178696i | ||||
\(581\) | 55.8991 | 0.0962120 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −587.489 | −1.00770 | ||||||||
\(584\) | 40.5149 | + | 298.776i | 0.0693748 | + | 0.511603i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −541.286 | − | 280.886i | −0.923696 | − | 0.479328i | ||||
\(587\) | −428.655 | −0.730248 | −0.365124 | − | 0.930959i | \(-0.618973\pi\) | ||||
−0.365124 | + | 0.930959i | \(0.618973\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 96.0127i | 0.163010i | ||||||||
\(590\) | −108.406 | − | 56.2545i | −0.183739 | − | 0.0953466i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 256.733 | + | 91.9416i | 0.433671 | + | 0.155307i | ||||
\(593\) | − | 77.0276i | − | 0.129895i | −0.997889 | − | 0.0649474i | \(-0.979312\pi\) | ||
0.997889 | − | 0.0649474i | \(-0.0206880\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 147.144i | 0.247301i | ||||||||
\(596\) | −68.9273 | − | 97.8984i | −0.115650 | − | 0.164259i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −42.7889 | − | 22.2042i | −0.0715533 | − | 0.0371307i | ||||
\(599\) | 963.566i | 1.60862i | 0.594207 | + | 0.804312i | \(0.297466\pi\) | ||||
−0.594207 | + | 0.804312i | \(0.702534\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 840.133 | 1.39789 | 0.698946 | − | 0.715175i | \(-0.253653\pi\) | ||||
0.698946 | + | 0.715175i | \(0.253653\pi\) | |||||||
\(602\) | −347.626 | + | 669.897i | −0.577451 | + | 1.11279i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 141.672 | + | 201.219i | 0.234556 | + | 0.333143i | ||||
\(605\) | −157.354 | −0.260089 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 156.611 | 0.258008 | 0.129004 | − | 0.991644i | \(-0.458822\pi\) | ||||
0.129004 | + | 0.991644i | \(0.458822\pi\) | |||||||
\(608\) | −371.060 | − | 399.719i | −0.610296 | − | 0.657433i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 68.6998 | − | 132.389i | 0.112623 | − | 0.217031i | ||||
\(611\) | 1394.25 | 2.28192 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 426.094i | 0.695096i | 0.937662 | + | 0.347548i | \(0.112986\pi\) | ||||
−0.937662 | + | 0.347548i | \(0.887014\pi\) | |||||||
\(614\) | 97.5188 | − | 187.925i | 0.158825 | − | 0.306067i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −126.755 | − | 934.754i | −0.205772 | − | 1.51746i | ||||
\(617\) | 963.520i | 1.56162i | 0.624769 | + | 0.780810i | \(0.285193\pi\) | ||||
−0.624769 | + | 0.780810i | \(0.714807\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 175.235i | 0.283093i | 0.989932 | + | 0.141547i | \(0.0452075\pi\) | ||||
−0.989932 | + | 0.141547i | \(0.954792\pi\) | |||||||
\(620\) | −13.9449 | − | 19.8062i | −0.0224919 | − | 0.0319455i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 511.411 | − | 985.523i | 0.822205 | − | 1.58444i | ||||
\(623\) | − | 549.107i | − | 0.881392i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 539.666 | 0.863466 | ||||||||
\(626\) | 280.484 | + | 145.550i | 0.448057 | + | 0.232508i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 449.877 | − | 316.745i | 0.716365 | − | 0.504371i | ||||
\(629\) | −323.522 | −0.514344 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1140.72 | −1.80780 | −0.903900 | − | 0.427744i | \(-0.859308\pi\) | ||||
−0.903900 | + | 0.427744i | \(0.859308\pi\) | |||||||
\(632\) | −136.869 | − | 1009.34i | −0.216565 | − | 1.59706i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 172.258 | + | 89.3889i | 0.271701 | + | 0.140992i | ||||
\(635\) | 48.9357 | 0.0770641 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 64.8136i | − | 0.101748i | ||||||
\(638\) | −855.692 | − | 444.039i | −1.34121 | − | 0.695986i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 134.600 | + | 28.5639i | 0.210313 | + | 0.0446312i | ||||
\(641\) | 351.730i | 0.548721i | 0.961627 | + | 0.274360i | \(0.0884661\pi\) | ||||
−0.961627 | + | 0.274360i | \(0.911534\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 86.4181i | − | 0.134398i | −0.997740 | − | 0.0671991i | \(-0.978594\pi\) | ||
0.997740 | − | 0.0671991i | \(-0.0214063\pi\) | |||||||
\(644\) | 26.3131 | − | 18.5263i | 0.0408589 | − | 0.0287676i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 574.321 | + | 298.029i | 0.889042 | + | 0.461345i | ||||
\(647\) | 430.723i | 0.665723i | 0.942976 | + | 0.332861i | \(0.108014\pi\) | ||||
−0.942976 | + | 0.332861i | \(0.891986\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −928.888 | −1.43126 | ||||||||
\(650\) | −474.554 | + | 914.497i | −0.730083 | + | 1.40692i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −624.955 | + | 440.013i | −0.958521 | + | 0.674866i | ||||
\(653\) | 886.670 | 1.35784 | 0.678920 | − | 0.734212i | \(-0.262448\pi\) | ||||
0.678920 | + | 0.734212i | \(0.262448\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −138.799 | −0.211907 | ||||||||
\(656\) | −413.743 | − | 148.170i | −0.630706 | − | 0.225869i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −428.700 | + | 826.132i | −0.651519 | + | 1.25552i | ||||
\(659\) | 352.833 | 0.535407 | 0.267704 | − | 0.963501i | \(-0.413735\pi\) | ||||
0.267704 | + | 0.963501i | \(0.413735\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1206.26i | 1.82489i | 0.409195 | + | 0.912447i | \(0.365810\pi\) | ||||
−0.409195 | + | 0.912447i | \(0.634190\pi\) | |||||||
\(662\) | 570.750 | − | 1099.87i | 0.862161 | − | 1.66144i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.33308 | + | 61.4521i | 0.0125498 | + | 0.0925484i | ||||
\(665\) | − | 132.120i | − | 0.198677i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 32.8882i | − | 0.0493076i | ||||||
\(668\) | 762.474 | − | 536.835i | 1.14143 | − | 0.803645i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −68.6998 | + | 132.389i | −0.102537 | + | 0.197595i | ||||
\(671\) | − | 1134.39i | − | 1.69059i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −956.133 | −1.42070 | −0.710351 | − | 0.703847i | \(-0.751464\pi\) | ||||
−0.710351 | + | 0.703847i | \(0.751464\pi\) | |||||||
\(674\) | −303.127 | − | 157.300i | −0.449744 | − | 0.233383i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −685.664 | − | 973.857i | −1.01430 | − | 1.44062i | ||||
\(677\) | 420.557 | 0.621207 | 0.310604 | − | 0.950540i | \(-0.399469\pi\) | ||||
0.310604 | + | 0.950540i | \(0.399469\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34.9335 | 0.0514485 | ||||||||
\(680\) | −161.761 | + | 21.9352i | −0.237884 | + | 0.0322577i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −163.522 | − | 84.8556i | −0.239769 | − | 0.124422i | ||||
\(683\) | 539.725 | 0.790227 | 0.395113 | − | 0.918632i | \(-0.370705\pi\) | ||||
0.395113 | + | 0.918632i | \(0.370705\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 11.7567i | − | 0.0171631i | ||||||
\(686\) | −588.858 | − | 305.572i | −0.858393 | − | 0.445441i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −788.266 | − | 282.295i | −1.14574 | − | 0.410312i | ||||
\(689\) | − | 776.214i | − | 1.12658i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 432.090i | − | 0.625312i | −0.949866 | − | 0.312656i | \(-0.898781\pi\) | ||
0.949866 | − | 0.312656i | \(-0.101219\pi\) | |||||||
\(692\) | 745.659 | + | 1059.07i | 1.07754 | + | 1.53045i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 533.250 | + | 276.716i | 0.768371 | + | 0.398726i | ||||
\(695\) | 1.28926i | 0.00185504i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 521.378 | 0.748031 | ||||||||
\(698\) | 49.3118 | − | 95.0271i | 0.0706473 | − | 0.136142i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −395.950 | − | 562.372i | −0.565642 | − | 0.803389i | ||||
\(701\) | −880.339 | −1.25583 | −0.627917 | − | 0.778280i | \(-0.716092\pi\) | ||||
−0.627917 | + | 0.778280i | \(0.716092\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 290.489 | 0.413214 | ||||||||
\(704\) | 1008.72 | − | 278.694i | 1.43284 | − | 0.395872i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −553.158 | + | 1065.97i | −0.783510 | + | 1.50987i | ||||
\(707\) | −761.745 | −1.07743 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 799.367i | 1.12746i | 0.825960 | + | 0.563729i | \(0.190634\pi\) | ||||
−0.825960 | + | 0.563729i | \(0.809366\pi\) | |||||||
\(710\) | −97.5188 | + | 187.925i | −0.137350 | + | 0.264683i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 603.655 | − | 81.8573i | 0.847830 | − | 0.114968i | ||||
\(713\) | − | 6.28491i | − | 0.00881474i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 379.760i | − | 0.531133i | ||||||
\(716\) | −428.142 | − | 608.095i | −0.597963 | − | 0.849295i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −136.806 | + | 263.633i | −0.190537 | + | 0.367178i | ||||
\(719\) | − | 258.786i | − | 0.359924i | −0.983674 | − | 0.179962i | \(-0.942402\pi\) | ||
0.983674 | − | 0.179962i | \(-0.0575975\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 755.643 | 1.04805 | ||||||||
\(722\) | 125.171 | + | 64.9544i | 0.173368 | + | 0.0899646i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 412.972 | − | 290.762i | 0.570404 | − | 0.401604i | ||||
\(725\) | −702.896 | −0.969511 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −663.211 | −0.912257 | −0.456129 | − | 0.889914i | \(-0.650764\pi\) | ||||
−0.456129 | + | 0.889914i | \(0.650764\pi\) | |||||||
\(728\) | 1235.04 | − | 167.474i | 1.69648 | − | 0.230047i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −71.9226 | − | 37.3224i | −0.0985241 | − | 0.0511265i | ||||
\(731\) | 993.332 | 1.35887 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 908.826i | − | 1.23987i | −0.784653 | − | 0.619936i | \(-0.787159\pi\) | ||
0.784653 | − | 0.619936i | \(-0.212841\pi\) | |||||||
\(734\) | 561.658 | + | 291.458i | 0.765201 | + | 0.397081i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24.2893 | + | 26.1653i | 0.0330017 | + | 0.0355507i | ||||
\(737\) | 1134.39i | 1.53920i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1112.39i | − | 1.50526i | −0.658443 | − | 0.752631i | \(-0.728785\pi\) | ||
0.658443 | − | 0.752631i | \(-0.271215\pi\) | |||||||
\(740\) | −59.9242 | + | 42.1909i | −0.0809787 | + | 0.0570147i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 459.928 | + | 238.667i | 0.619849 | + | 0.321654i | ||||
\(743\) | 541.298i | 0.728530i | 0.931295 | + | 0.364265i | \(0.118680\pi\) | ||||
−0.931295 | + | 0.364265i | \(0.881320\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32.1767 | 0.0431902 | ||||||||
\(746\) | −577.379 | + | 1112.65i | −0.773967 | + | 1.49148i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1015.17 | + | 714.748i | −1.35717 | + | 0.955546i | ||||
\(749\) | −471.655 | −0.629713 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −763.699 | −1.01691 | −0.508455 | − | 0.861089i | \(-0.669783\pi\) | ||||
−0.508455 | + | 0.861089i | \(0.669783\pi\) | |||||||
\(752\) | −972.107 | − | 348.132i | −1.29270 | − | 0.462942i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 586.683 | − | 1130.58i | 0.778094 | − | 1.49944i | ||||
\(755\) | −66.1354 | −0.0875966 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 419.134i | − | 0.553678i | −0.960916 | − | 0.276839i | \(-0.910713\pi\) | ||
0.960916 | − | 0.276839i | \(-0.0892869\pi\) | |||||||
\(758\) | −304.943 | + | 587.644i | −0.402299 | + | 0.775257i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 145.245 | − | 19.6956i | 0.191111 | − | 0.0259152i | ||||
\(761\) | − | 1330.24i | − | 1.74802i | −0.485912 | − | 0.874008i | \(-0.661512\pi\) | ||
0.485912 | − | 0.874008i | \(-0.338488\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.2397i | 0.0317690i | ||||||||
\(764\) | −762.474 | + | 536.835i | −0.998002 | + | 0.702664i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −375.633 | + | 723.870i | −0.490383 | + | 0.945000i | ||||
\(767\) | − | 1227.29i | − | 1.60011i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 671.511 | 0.873226 | 0.436613 | − | 0.899649i | \(-0.356178\pi\) | ||||
0.436613 | + | 0.899649i | \(0.356178\pi\) | |||||||
\(770\) | 225.018 | + | 116.767i | 0.292231 | + | 0.151646i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −270.294 | − | 383.902i | −0.350122 | − | 0.497283i | ||||
\(773\) | −1421.13 | −1.83846 | −0.919229 | − | 0.393724i | \(-0.871187\pi\) | ||||
−0.919229 | + | 0.393724i | \(0.871187\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −134.323 | −0.173320 | ||||||||
\(776\) | 5.20766 | + | 38.4038i | 0.00671090 | + | 0.0494894i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 95.1194 | + | 49.3597i | 0.122261 | + | 0.0634444i | ||||
\(779\) | −468.143 | −0.600954 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1610.25i | 2.06179i | ||||||||
\(782\) | −37.5946 | − | 19.5087i | −0.0480749 | − | 0.0249472i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −16.1833 | + | 45.1896i | −0.0206420 | + | 0.0576398i | ||||
\(785\) | 147.863i | 0.188361i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 649.808i | − | 0.825677i | −0.910804 | − | 0.412839i | \(-0.864537\pi\) | ||
0.910804 | − | 0.412839i | \(-0.135463\pi\) | |||||||
\(788\) | 682.343 | + | 969.140i | 0.865917 | + | 1.22987i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 242.972 | + | 126.084i | 0.307560 | + | 0.159600i | ||||
\(791\) | 607.122i | 0.767538i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1498.80 | 1.89004 | ||||||||
\(794\) | 266.912 | − | 514.357i | 0.336162 | − | 0.647805i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 536.572 | + | 762.100i | 0.674085 | + | 0.957412i | ||||
\(797\) | 422.946 | 0.530672 | 0.265336 | − | 0.964156i | \(-0.414517\pi\) | ||||
0.265336 | + | 0.964156i | \(0.414517\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1225.00 | 1.53317 | ||||||||
\(800\) | 559.212 | − | 519.118i | 0.699015 | − | 0.648897i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −187.426 | + | 361.181i | −0.233698 | + | 0.450351i | ||||
\(803\) | −616.276 | −0.767467 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.64847i | 0.0107434i | ||||||||
\(806\) | 112.115 | − | 216.052i | 0.139100 | − | 0.268055i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −113.556 | − | 837.416i | −0.140539 | − | 1.03641i | ||||
\(809\) | 1353.87i | 1.67351i | 0.547574 | + | 0.836757i | \(0.315552\pi\) | ||||
−0.547574 | + | 0.836757i | \(0.684448\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 842.340i | − | 1.03864i | −0.854579 | − | 0.519322i | \(-0.826185\pi\) | ||
0.854579 | − | 0.519322i | \(-0.173815\pi\) | |||||||
\(812\) | 489.505 | + | 695.251i | 0.602839 | + | 0.856220i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −256.733 | + | 494.742i | −0.315397 | + | 0.607791i | ||||
\(815\) | − | 205.407i | − | 0.252033i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −891.909 | −1.09169 | ||||||||
\(818\) | 732.888 | + | 380.313i | 0.895951 | + | 0.464930i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 96.5719 | − | 67.9934i | 0.117771 | − | 0.0829188i | ||||
\(821\) | −616.897 | −0.751397 | −0.375698 | − | 0.926742i | \(-0.622597\pi\) | ||||
−0.375698 | + | 0.926742i | \(0.622597\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 980.500 | 1.19137 | 0.595686 | − | 0.803217i | \(-0.296880\pi\) | ||||
0.595686 | + | 0.803217i | \(0.296880\pi\) | |||||||
\(824\) | 112.646 | + | 830.708i | 0.136707 | + | 1.00814i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 727.199 | + | 377.361i | 0.880387 | + | 0.456854i | ||||
\(827\) | −70.4951 | −0.0852419 | −0.0426210 | − | 0.999091i | \(-0.513571\pi\) | ||||
−0.0426210 | + | 0.999091i | \(0.513571\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 515.147i | − | 0.621408i | −0.950507 | − | 0.310704i | \(-0.899435\pi\) | ||
0.950507 | − | 0.310704i | \(-0.100565\pi\) | |||||||
\(830\) | −14.7930 | − | 7.67644i | −0.0178229 | − | 0.00924873i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 368.222 | + | 1332.76i | 0.442575 | + | 1.60187i | ||||
\(833\) | − | 56.9456i | − | 0.0683621i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 250.606i | 0.300127i | ||||||||
\(836\) | 911.514 | − | 641.770i | 1.09033 | − | 0.767667i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −597.327 | − | 309.967i | −0.712801 | − | 0.369889i | ||||
\(839\) | − | 47.1556i | − | 0.0562045i | −0.999605 | − | 0.0281022i | \(-0.991054\pi\) | ||
0.999605 | − | 0.0281022i | \(-0.00894640\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.9773 | 0.0332667 | ||||||||
\(842\) | 200.344 | − | 386.076i | 0.237938 | − | 0.458522i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 115.411 | − | 81.2576i | 0.136743 | − | 0.0962768i | ||||
\(845\) | 320.082 | 0.378795 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1055.54 | 1.24622 | ||||||||
\(848\) | −193.813 | + | 541.195i | −0.228554 | + | 0.638202i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −416.946 | + | 803.482i | −0.490525 | + | 0.945273i | ||||
\(851\) | −19.0152 | −0.0223445 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 763.118i | − | 0.894628i | −0.894377 | − | 0.447314i | \(-0.852381\pi\) | ||
0.894377 | − | 0.447314i | \(-0.147619\pi\) | |||||||
\(854\) | −460.845 | + | 888.079i | −0.539631 | + | 1.03990i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −70.3112 | − | 518.508i | −0.0821392 | − | 0.605734i | ||||
\(857\) | − | 1641.05i | − | 1.91488i | −0.288631 | − | 0.957440i | \(-0.593200\pi\) | ||
0.288631 | − | 0.957440i | \(-0.406800\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1366.84i | 1.59120i | 0.605819 | + | 0.795602i | \(0.292845\pi\) | ||||
−0.605819 | + | 0.795602i | \(0.707155\pi\) | |||||||
\(860\) | 183.989 | − | 129.542i | 0.213941 | − | 0.150630i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 691.817 | − | 1333.18i | 0.802572 | − | 1.54661i | ||||
\(863\) | − | 836.082i | − | 0.968809i | −0.874844 | − | 0.484405i | \(-0.839036\pi\) | ||
0.874844 | − | 0.484405i | \(-0.160964\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −348.089 | −0.402415 | ||||||||
\(866\) | −312.674 | − | 162.254i | −0.361055 | − | 0.187360i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 93.5442 | + | 132.862i | 0.107770 | + | 0.153067i | ||||
\(869\) | 2081.93 | 2.39578 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1498.80 | −1.72078 | ||||||||
\(872\) | −26.6477 | + | 3.61350i | −0.0305592 | + | 0.00414392i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 33.7561 | + | 17.5168i | 0.0386225 | + | 0.0200421i | ||||
\(875\) | 378.633 | 0.432723 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 158.191i | − | 0.180377i | −0.995925 | − | 0.0901887i | \(-0.971253\pi\) | ||
0.995925 | − | 0.0901887i | \(-0.0287470\pi\) | |||||||
\(878\) | 741.664 | + | 384.867i | 0.844719 | + | 0.438345i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −94.8225 | + | 264.778i | −0.107753 | + | 0.300884i | ||||
\(881\) | 237.430i | 0.269500i | 0.990880 | + | 0.134750i | \(0.0430232\pi\) | ||||
−0.990880 | + | 0.134750i | \(0.956977\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 592.933i | 0.671499i | 0.941951 | + | 0.335749i | \(0.108989\pi\) | ||||
−0.941951 | + | 0.335749i | \(0.891011\pi\) | |||||||
\(884\) | −944.355 | − | 1341.28i | −1.06827 | − | 1.51728i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 108.372 | + | 56.2367i | 0.122316 | + | 0.0634726i | ||||
\(887\) | 1420.72i | 1.60171i | 0.598858 | + | 0.800855i | \(0.295621\pi\) | ||||
−0.598858 | + | 0.800855i | \(0.704379\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −328.266 | −0.369253 | ||||||||
\(890\) | −75.4071 | + | 145.314i | −0.0847271 | + | 0.163275i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −119.361 | − | 169.530i | −0.133813 | − | 0.190056i | ||||
\(893\) | −1099.92 | −1.23172 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 199.866 | 0.223313 | ||||||||
\(896\) | −902.914 | − | 191.610i | −1.00772 | − | 0.213850i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 168.492 | − | 324.695i | 0.187630 | − | 0.361576i | ||||
\(899\) | 166.061 | 0.184717 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 681.987i | − | 0.756922i | ||||||
\(902\) | 413.743 | − | 797.310i | 0.458695 | − | 0.883935i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −667.433 | + | 90.5058i | −0.738311 | + | 0.100117i | ||||
\(905\) | 135.734i | 0.149982i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 816.648i | 0.900383i | 0.892932 | + | 0.450192i | \(0.148644\pi\) | ||||
−0.892932 | + | 0.450192i | \(0.851356\pi\) | |||||||
\(908\) | −770.936 | − | 1094.97i | −0.849048 | − | 1.20591i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −154.278 | + | 297.303i | −0.169536 | + | 0.326706i | ||||
\(911\) | 469.895i | 0.515801i | 0.966171 | + | 0.257901i | \(0.0830307\pi\) | ||||
−0.966171 | + | 0.257901i | \(0.916969\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −126.755 | −0.138834 | ||||||||
\(914\) | −787.485 | − | 408.645i | −0.861581 | − | 0.447095i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 717.605 | − | 505.244i | 0.783411 | − | 0.551577i | ||||
\(917\) | 931.079 | 1.01535 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1648.21 | −1.79348 | −0.896741 | − | 0.442555i | \(-0.854072\pi\) | ||||
−0.896741 | + | 0.442555i | \(0.854072\pi\) | |||||||
\(920\) | −9.50760 | + | 1.28926i | −0.0103343 | + | 0.00140137i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1292.78 | − | 670.857i | −1.40215 | − | 0.727611i | ||||
\(923\) | −2127.53 | −2.30502 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 406.398i | 0.439349i | ||||||||
\(926\) | −191.230 | − | 99.2341i | −0.206512 | − | 0.107164i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −691.344 | + | 641.776i | −0.744983 | + | 0.691569i | ||||
\(929\) | 421.311i | 0.453510i | 0.973952 | + | 0.226755i | \(0.0728116\pi\) | ||||
−0.973952 | + | 0.226755i | \(0.927188\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51.1313i | 0.0549208i | ||||||||
\(932\) | −666.779 | + | 469.459i | −0.715428 | + | 0.503712i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1456.12 | − | 755.614i | −1.55901 | − | 0.809008i | ||||
\(935\) | − | 333.659i | − | 0.356855i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1434.27 | −1.53070 | −0.765350 | − | 0.643614i | \(-0.777434\pi\) | ||||
−0.765350 | + | 0.643614i | \(0.777434\pi\) | |||||||
\(938\) | 460.845 | − | 888.079i | 0.491306 | − | 0.946779i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 226.900 | − | 159.754i | 0.241383 | − | 0.169951i | ||||
\(941\) | 732.876 | 0.778827 | 0.389413 | − | 0.921063i | \(-0.372678\pi\) | ||||
0.389413 | + | 0.921063i | \(0.372678\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.6443 | 0.0324966 | ||||||||
\(944\) | −306.442 | + | 855.693i | −0.324621 | + | 0.906455i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 788.266 | − | 1519.04i | 0.833262 | − | 1.60575i | ||||
\(947\) | 1385.53 | 1.46308 | 0.731538 | − | 0.681800i | \(-0.238803\pi\) | ||||
0.731538 | + | 0.681800i | \(0.238803\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 814.249i | − | 0.858007i | ||||||
\(950\) | 374.375 | − | 721.444i | 0.394079 | − | 0.759415i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1085.11 | − | 147.144i | 1.13982 | − | 0.154563i | ||||
\(953\) | − | 957.328i | − | 1.00454i | −0.864711 | − | 0.502270i | \(-0.832498\pi\) | ||
0.864711 | − | 0.502270i | \(-0.167502\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 250.606i | − | 0.262414i | ||||||
\(956\) | −176.692 | + | 124.403i | −0.184824 | + | 0.130129i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 111.272 | − | 214.428i | 0.116150 | − | 0.223829i | ||||
\(959\) | 78.8654i | 0.0822371i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −929.266 | −0.966978 | ||||||||
\(962\) | −653.673 | − | 339.207i | −0.679494 | − | 0.352606i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 754.389 | + | 1071.47i | 0.782561 | + | 1.11148i | ||||
\(965\) | 126.179 | 0.130755 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1225.90 | 1.26773 | 0.633867 | − | 0.773442i | \(-0.281467\pi\) | ||||
0.633867 | + | 0.773442i | \(0.281467\pi\) | |||||||
\(968\) | 157.354 | + | 1160.40i | 0.162555 | + | 1.19876i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.24472 | − | 4.79731i | −0.00953064 | − | 0.00494568i | ||||
\(971\) | 752.906 | 0.775393 | 0.387696 | − | 0.921787i | \(-0.373271\pi\) | ||||
0.387696 | + | 0.921787i | \(0.373271\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 8.64847i | − | 0.00888845i | ||||||
\(974\) | −227.642 | − | 118.129i | −0.233719 | − | 0.121282i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1045.00 | − | 374.236i | −1.07070 | − | 0.383439i | ||||
\(977\) | − | 642.932i | − | 0.658068i | −0.944318 | − | 0.329034i | \(-0.893277\pi\) | ||
0.944318 | − | 0.329034i | \(-0.106723\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1245.14i | 1.27185i | ||||||||
\(980\) | −7.42634 | − | 10.5477i | −0.00757790 | − | 0.0107630i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −678.389 | − | 352.032i | −0.690823 | − | 0.358485i | ||||
\(983\) | 161.251i | 0.164040i | 0.996631 | + | 0.0820200i | \(0.0261371\pi\) | ||||
−0.996631 | + | 0.0820200i | \(0.973863\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −318.532 | −0.323382 | ||||||||
\(986\) | 515.463 | − | 993.331i | 0.522782 | − | 1.00744i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 847.933 | + | 1204.33i | 0.858232 | + | 1.21896i | ||||
\(989\) | 58.3836 | 0.0590330 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 811.500 | 0.818870 | 0.409435 | − | 0.912339i | \(-0.365726\pi\) | ||||
0.409435 | + | 0.912339i | \(0.365726\pi\) | |||||||
\(992\) | −132.115 | + | 122.643i | −0.133181 | + | 0.123632i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 654.167 | − | 1260.62i | 0.658115 | − | 1.26823i | ||||
\(995\) | −250.483 | −0.251742 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 390.554i | 0.391729i | 0.980631 | + | 0.195864i | \(0.0627513\pi\) | ||||
−0.980631 | + | 0.195864i | \(0.937249\pi\) | |||||||
\(998\) | −511.262 | + | 985.235i | −0.512286 | + | 0.987209i | ||||
\(999\) | 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.53.8 | yes | 8 | |
3.2 | odd | 2 | inner | 72.3.h.a.53.1 | ✓ | 8 | |
4.3 | odd | 2 | 288.3.h.a.17.3 | 8 | |||
8.3 | odd | 2 | 288.3.h.a.17.6 | 8 | |||
8.5 | even | 2 | inner | 72.3.h.a.53.2 | yes | 8 | |
12.11 | even | 2 | 288.3.h.a.17.5 | 8 | |||
16.3 | odd | 4 | 2304.3.e.o.1025.6 | 8 | |||
16.5 | even | 4 | 2304.3.e.n.1025.3 | 8 | |||
16.11 | odd | 4 | 2304.3.e.o.1025.3 | 8 | |||
16.13 | even | 4 | 2304.3.e.n.1025.6 | 8 | |||
24.5 | odd | 2 | inner | 72.3.h.a.53.7 | yes | 8 | |
24.11 | even | 2 | 288.3.h.a.17.4 | 8 | |||
48.5 | odd | 4 | 2304.3.e.n.1025.5 | 8 | |||
48.11 | even | 4 | 2304.3.e.o.1025.5 | 8 | |||
48.29 | odd | 4 | 2304.3.e.n.1025.4 | 8 | |||
48.35 | even | 4 | 2304.3.e.o.1025.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.h.a.53.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
72.3.h.a.53.2 | yes | 8 | 8.5 | even | 2 | inner | |
72.3.h.a.53.7 | yes | 8 | 24.5 | odd | 2 | inner | |
72.3.h.a.53.8 | yes | 8 | 1.1 | even | 1 | trivial | |
288.3.h.a.17.3 | 8 | 4.3 | odd | 2 | |||
288.3.h.a.17.4 | 8 | 24.11 | even | 2 | |||
288.3.h.a.17.5 | 8 | 12.11 | even | 2 | |||
288.3.h.a.17.6 | 8 | 8.3 | odd | 2 | |||
2304.3.e.n.1025.3 | 8 | 16.5 | even | 4 | |||
2304.3.e.n.1025.4 | 8 | 48.29 | odd | 4 | |||
2304.3.e.n.1025.5 | 8 | 48.5 | odd | 4 | |||
2304.3.e.n.1025.6 | 8 | 16.13 | even | 4 | |||
2304.3.e.o.1025.3 | 8 | 16.11 | odd | 4 | |||
2304.3.e.o.1025.4 | 8 | 48.35 | even | 4 | |||
2304.3.e.o.1025.5 | 8 | 48.11 | even | 4 | |||
2304.3.e.o.1025.6 | 8 | 16.3 | odd | 4 |