Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(17,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bc (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 257.2 | ||
Root | \(0.00299931 - 3.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.257 |
Dual form | 336.4.bc.d.17.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.59358 | + | 4.50260i | −0.499134 | + | 0.866525i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.05907 | + | 13.9587i | −0.720825 | + | 1.24851i | 0.239845 | + | 0.970811i | \(0.422903\pi\) |
−0.960670 | + | 0.277694i | \(0.910430\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.67909 | − | 17.6280i | 0.306642 | − | 0.951825i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −13.5467 | − | 23.3556i | −0.501731 | − | 0.865024i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −30.8296 | + | 17.7995i | −0.845043 | + | 0.487886i | −0.858975 | − | 0.512017i | \(-0.828898\pi\) |
0.0139322 | + | 0.999903i | \(0.495565\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.40831i | 0.158054i | 0.996872 | + | 0.0790268i | \(0.0251813\pi\) | ||||
−0.996872 | + | 0.0790268i | \(0.974819\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −41.9486 | − | 72.4897i | −0.722073 | − | 1.24778i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −14.4601 | − | 25.0457i | −0.206300 | − | 0.357322i | 0.744246 | − | 0.667905i | \(-0.232809\pi\) |
−0.950546 | + | 0.310584i | \(0.899476\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −30.4580 | − | 17.5849i | −0.367765 | − | 0.212329i | 0.304716 | − | 0.952443i | \(-0.401438\pi\) |
−0.672482 | + | 0.740114i | \(0.734772\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 64.6428 | + | 71.2903i | 0.671725 | + | 0.740801i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −48.0017 | − | 27.7138i | −0.435175 | − | 0.251249i | 0.266374 | − | 0.963870i | \(-0.414175\pi\) |
−0.701549 | + | 0.712621i | \(0.747508\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −67.3971 | − | 116.735i | −0.539177 | − | 0.933881i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 140.295 | − | 0.420792i | 0.999996 | − | 0.00299931i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 68.1510i | 0.436390i | 0.975905 | + | 0.218195i | \(0.0700169\pi\) | ||||
−0.975905 | + | 0.218195i | \(0.929983\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 154.734 | − | 89.3356i | 0.896484 | − | 0.517585i | 0.0204262 | − | 0.999791i | \(-0.493498\pi\) |
0.876058 | + | 0.482206i | \(0.160164\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.184935 | − | 184.977i | −0.000975549 | − | 0.975771i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 200.297 | + | 221.338i | 0.967323 | + | 1.06894i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 116.838 | − | 202.370i | 0.519137 | − | 0.899172i | −0.480615 | − | 0.876931i | \(-0.659587\pi\) |
0.999753 | − | 0.0222405i | \(-0.00707996\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −33.3566 | − | 19.2140i | −0.136957 | − | 0.0788899i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 370.068 | 1.40963 | 0.704816 | − | 0.709390i | \(-0.251030\pi\) | ||||
0.704816 | + | 0.709390i | \(0.251030\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 187.068 | 0.663432 | 0.331716 | − | 0.943379i | \(-0.392372\pi\) | ||||
0.331716 | + | 0.943379i | \(0.392372\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 435.189 | − | 0.870180i | 1.44165 | − | 0.00288264i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 87.3726 | − | 151.334i | 0.271162 | − | 0.469666i | −0.697998 | − | 0.716100i | \(-0.745925\pi\) |
0.969160 | + | 0.246434i | \(0.0792588\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −278.496 | − | 200.222i | −0.811942 | − | 0.583739i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 150.274 | − | 0.150240i | 0.412599 | − | 0.000412505i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −235.715 | + | 136.090i | −0.610905 | + | 0.352706i | −0.773319 | − | 0.634017i | \(-0.781405\pi\) |
0.162415 | + | 0.986723i | \(0.448072\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 573.789i | − | 1.40672i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 158.173 | − | 91.5321i | 0.367553 | − | 0.212697i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 48.4354 | + | 83.8926i | 0.106877 | + | 0.185117i | 0.914504 | − | 0.404578i | \(-0.132581\pi\) |
−0.807626 | + | 0.589695i | \(0.799248\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −333.882 | − | 192.767i | −0.700807 | − | 0.404611i | 0.106841 | − | 0.994276i | \(-0.465927\pi\) |
−0.807648 | + | 0.589665i | \(0.799260\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −488.647 | + | 106.164i | −0.977203 | + | 0.212307i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −103.411 | − | 59.7041i | −0.197331 | − | 0.113929i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −509.009 | − | 881.630i | −0.928140 | − | 1.60759i | −0.786432 | − | 0.617677i | \(-0.788074\pi\) |
−0.141708 | − | 0.989908i | \(-0.545259\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 249.280 | − | 144.254i | 0.434924 | − | 0.251684i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 125.333i | − | 0.209497i | −0.994499 | − | 0.104749i | \(-0.966596\pi\) | ||
0.994499 | − | 0.104749i | \(-0.0334038\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 195.346 | − | 112.783i | 0.313199 | − | 0.180825i | −0.335158 | − | 0.942162i | \(-0.608790\pi\) |
0.648357 | + | 0.761337i | \(0.275456\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 700.411 | − | 0.700251i | 1.07835 | − | 0.00107811i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 138.686 | + | 644.550i | 0.205256 | + | 0.953939i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −532.154 | + | 921.718i | −0.757874 | + | 1.31268i | 0.186059 | + | 0.982539i | \(0.440428\pi\) |
−0.943933 | + | 0.330138i | \(0.892905\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −361.972 | + | 632.785i | −0.496533 | + | 0.868018i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 601.040 | 0.794852 | 0.397426 | − | 0.917634i | \(-0.369904\pi\) | ||||
0.397426 | + | 0.917634i | \(0.369904\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 466.140 | 0.594824 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −306.856 | − | 176.755i | −0.378143 | − | 0.217817i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 752.606 | − | 1303.55i | 0.896360 | − | 1.55254i | 0.0642474 | − | 0.997934i | \(-0.479535\pi\) |
0.832112 | − | 0.554607i | \(-0.187131\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 130.594 | + | 42.0725i | 0.150439 | + | 0.0484658i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.928190 | + | 928.402i | 0.00103493 | + | 1.03517i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 490.926 | − | 283.436i | 0.530189 | − | 0.306105i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 327.463i | − | 0.342771i | −0.985204 | − | 0.171386i | \(-0.945176\pi\) | ||
0.985204 | − | 0.171386i | \(-0.0548244\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 833.358 | + | 478.920i | 0.846017 | + | 0.486195i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −547.845 | − | 948.895i | −0.539729 | − | 0.934837i | −0.998918 | − | 0.0464990i | \(-0.985194\pi\) |
0.459190 | − | 0.888338i | \(-0.348140\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −179.848 | − | 103.835i | −0.172048 | − | 0.0993318i | 0.411503 | − | 0.911408i | \(-0.365004\pi\) |
−0.583551 | + | 0.812076i | \(0.698337\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1516.08 | + | 327.797i | −1.40909 | + | 0.304664i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1561.25 | − | 901.391i | −1.41058 | − | 0.814399i | −0.415138 | − | 0.909759i | \(-0.636267\pi\) |
−0.995443 | + | 0.0953593i | \(0.969600\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −141.825 | − | 245.647i | −0.124627 | − | 0.215860i | 0.796960 | − | 0.604032i | \(-0.206440\pi\) |
−0.921587 | + | 0.388172i | \(0.873107\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 608.160 | + | 1050.94i | 0.520036 | + | 0.898652i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1037.39i | 0.863627i | 0.901963 | + | 0.431814i | \(0.142126\pi\) | ||||
−0.901963 | + | 0.431814i | \(0.857874\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 773.697 | − | 446.694i | 0.627371 | − | 0.362213i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 173.026 | − | 100.358i | 0.136720 | − | 0.0793003i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −523.626 | + | 112.667i | −0.403368 | + | 0.0867915i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −31.8573 | + | 55.1785i | −0.0239349 | + | 0.0414564i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −959.799 | + | 1666.27i | −0.703595 | + | 1.22148i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 157.864 | 0.112958 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1645.81 | −1.14994 | −0.574968 | − | 0.818176i | \(-0.694985\pi\) | ||||
−0.574968 | + | 0.818176i | \(0.694985\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −485.175 | + | 842.291i | −0.331142 | + | 0.574881i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −314.185 | + | 544.184i | −0.209545 | + | 0.362943i | −0.951571 | − | 0.307428i | \(-0.900532\pi\) |
0.742026 | + | 0.670371i | \(0.233865\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −482.961 | + | 437.048i | −0.314873 | + | 0.284939i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1124.78 | + | 1961.74i | −0.717077 | + | 1.25066i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 432.079 | − | 249.461i | 0.269453 | − | 0.155569i | −0.359186 | − | 0.933266i | \(-0.616946\pi\) |
0.628639 | + | 0.777697i | \(0.283612\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1216.65i | − | 0.742410i | −0.928551 | − | 0.371205i | \(-0.878945\pi\) | ||
0.928551 | − | 0.371205i | \(-0.121055\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 454.788 | + | 785.900i | 0.271631 | + | 0.469395i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −131.864 | − | 228.395i | −0.0771121 | − | 0.133562i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −951.300 | − | 549.233i | −0.544835 | − | 0.314561i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1623.82 | − | 734.663i | 0.911092 | − | 0.412204i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2010.18 | − | 1160.58i | −1.10524 | − | 0.638111i | −0.167648 | − | 0.985847i | \(-0.553617\pi\) |
−0.937592 | + | 0.347736i | \(0.886950\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 488.726 | + | 846.497i | 0.263390 | + | 0.456205i | 0.967141 | − | 0.254242i | \(-0.0818260\pi\) |
−0.703750 | + | 0.710447i | \(0.748493\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −389.070 | + | 677.012i | −0.205585 | + | 0.357733i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2879.85i | 1.49235i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −143.752 | + | 82.9950i | −0.0730740 | + | 0.0421893i | −0.536092 | − | 0.844160i | \(-0.680100\pi\) |
0.463018 | + | 0.886349i | \(0.346767\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.41397 | − | 1414.29i | −0.000705251 | − | 0.705412i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −761.145 | + | 688.786i | −0.372588 | + | 0.337168i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 488.511 | − | 846.127i | 0.234743 | − | 0.406587i | −0.724455 | − | 0.689322i | \(-0.757908\pi\) |
0.959198 | + | 0.282735i | \(0.0912417\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2583.54 | + | 1488.16i | 1.21896 | + | 0.702142i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00709 | −0.000466651 | −0.000233326 | − | 1.00000i | \(-0.500074\pi\) | ||||
−0.000233326 | 1.00000i | \(0.500074\pi\) | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2142.12 | 0.975019 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.89874 | + | 949.584i | 0.000849123 | + | 0.424658i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1978.27 | + | 3426.47i | −0.869395 | + | 1.50584i | −0.00677983 | + | 0.999977i | \(0.502158\pi\) |
−0.862616 | + | 0.505860i | \(0.831175\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2440.57 | + | 525.130i | −1.05423 | + | 0.226835i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −503.356 | + | 0.503241i | −0.213754 | + | 0.000213706i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2423.54 | − | 1399.23i | 1.01198 | − | 0.584266i | 0.100208 | − | 0.994967i | \(-0.468049\pi\) |
0.911770 | + | 0.410701i | \(0.134716\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1506.74i | − | 0.618758i | −0.950939 | − | 0.309379i | \(-0.899879\pi\) | ||
0.950939 | − | 0.309379i | \(-0.100121\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1733.90 | − | 1003.38i | 0.700403 | − | 0.405312i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1883.21 | + | 3261.82i | 0.748414 | + | 1.29629i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 891.599 | + | 514.765i | 0.348664 | + | 0.201301i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 789.332 | − | 2475.52i | 0.303786 | − | 0.952740i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3184.51 | − | 1838.58i | −1.20640 | − | 0.696518i | −0.244433 | − | 0.969666i | \(-0.578602\pi\) |
−0.961972 | + | 0.273148i | \(0.911935\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 64.7335 | + | 112.122i | 0.0241431 | + | 0.0418171i | 0.877845 | − | 0.478946i | \(-0.158981\pi\) |
−0.853701 | + | 0.520763i | \(0.825648\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 537.026 | − | 310.769i | 0.197217 | − | 0.114126i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3044.81i | − | 1.10119i | −0.834774 | − | 0.550593i | \(-0.814402\pi\) | ||
0.834774 | − | 0.550593i | \(-0.185598\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3458.29 | + | 1996.64i | −1.23192 | + | 0.711248i | −0.967429 | − | 0.253141i | \(-0.918536\pi\) |
−0.264488 | + | 0.964389i | \(0.585203\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5289.78 | − | 5.28857i | 1.85628 | − | 0.00185586i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1201.37 | + | 387.035i | 0.415367 | + | 0.133815i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2982.40 | + | 5165.67i | −1.01610 | + | 1.75993i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.99240 | + | 1496.54i | 0.00100476 | + | 0.502496i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1252.01 | 0.414370 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4383.67 | 1.43026 | 0.715129 | − | 0.698992i | \(-0.246368\pi\) | ||||
0.715129 | + | 0.698992i | \(0.246368\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 564.324 | + | 325.061i | 0.181534 | + | 0.104567i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1507.59 | + | 2611.23i | −0.478219 | + | 0.828299i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −696.065 | − | 3235.00i | −0.217751 | − | 1.01201i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.17181 | + | 1172.07i | 0.000361568 | + | 0.361650i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 185.546 | − | 107.125i | 0.0564759 | − | 0.0326064i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4851.53i | − | 1.45687i | −0.685114 | − | 0.728436i | \(-0.740247\pi\) | ||
0.685114 | − | 0.728436i | \(-0.259753\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1813.42 | + | 3155.48i | −0.537308 | + | 0.934958i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1184.05 | + | 2050.83i | 0.346203 | + | 0.599642i | 0.985572 | − | 0.169259i | \(-0.0541374\pi\) |
−0.639368 | + | 0.768901i | \(0.720804\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3737.27 | − | 2157.72i | −1.07845 | − | 0.622646i | −0.147975 | − | 0.988991i | \(-0.547276\pi\) |
−0.930479 | + | 0.366345i | \(0.880609\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3261.84 | − | 1047.24i | −0.929062 | − | 0.298284i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4826.98 | − | 2786.86i | −1.35719 | − | 0.783576i | −0.367949 | − | 0.929846i | \(-0.619940\pi\) |
−0.989245 | + | 0.146270i | \(0.953273\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1408.28 | + | 2439.22i | 0.390920 | + | 0.677094i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2769.94 | − | 4786.62i | −0.759186 | − | 1.31192i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 4683.70i | − | 1.26763i | −0.773485 | − | 0.633814i | \(-0.781488\pi\) | ||
0.773485 | − | 0.633814i | \(-0.218512\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1896.77 | + | 1095.10i | −0.506977 | + | 0.292703i | −0.731590 | − | 0.681745i | \(-0.761222\pi\) |
0.224613 | + | 0.974448i | \(0.427888\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1910.37 | − | 3270.99i | −0.504323 | − | 0.863515i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5039.26 | − | 2273.84i | 1.31407 | − | 0.592940i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 130.275 | − | 225.642i | 0.0335594 | − | 0.0581266i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1558.84 | + | 2706.24i | −0.396738 | + | 0.688759i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2240.70 | −0.563473 | −0.281736 | − | 0.959492i | \(-0.590910\pi\) | ||||
−0.281736 | + | 0.959492i | \(0.590910\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1973.16 | 0.490323 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1208.97 | + | 2098.84i | −0.296897 | + | 0.515429i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −555.785 | + | 962.648i | −0.134898 | + | 0.233651i | −0.925559 | − | 0.378604i | \(-0.876404\pi\) |
0.790660 | + | 0.612255i | \(0.209737\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2903.85 | − | 3208.90i | −0.696665 | − | 0.769851i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1591.71 | − | 923.223i | 0.377488 | − | 0.218950i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1782.86 | + | 1029.34i | −0.418007 | + | 0.241337i | −0.694224 | − | 0.719759i | \(-0.744252\pi\) |
0.276217 | + | 0.961095i | \(0.410919\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4387.04i | − | 1.01696i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3917.42 | + | 6769.54i | 0.897912 | + | 1.55164i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2414.62 | − | 4182.24i | −0.547294 | − | 0.947940i | −0.998459 | − | 0.0554999i | \(-0.982325\pi\) |
0.451165 | − | 0.892441i | \(-0.351009\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 191.772 | + | 110.720i | 0.0429865 | + | 0.0248183i | 0.521339 | − | 0.853350i | \(-0.325433\pi\) |
−0.478353 | + | 0.878168i | \(0.658766\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −528.141 | + | 478.894i | −0.117086 | + | 0.106168i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4155.65 | + | 2399.27i | 0.911255 | + | 0.526113i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1233.58 | − | 2136.62i | −0.267576 | − | 0.463455i | 0.700660 | − | 0.713496i | \(-0.252889\pi\) |
−0.968235 | + | 0.250041i | \(0.919556\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4182.63 | − | 2403.70i | −0.897517 | − | 0.515792i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4174.76i | 0.886282i | 0.896452 | + | 0.443141i | \(0.146136\pi\) | ||||
−0.896452 | + | 0.443141i | \(0.853864\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5628.39 | − | 3249.55i | 1.18224 | − | 0.682565i | 0.225706 | − | 0.974195i | \(-0.427531\pi\) |
0.956531 | + | 0.291630i | \(0.0941977\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.94488 | + | 2945.55i | 0.000612069 | + | 0.612209i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2101.65 | − | 6523.57i | 0.432252 | − | 1.34172i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2038.31 | − | 3530.46i | 0.414881 | − | 0.718595i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1474.43 | + | 849.300i | 0.297020 | + | 0.171089i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5637.32 | 1.12401 | 0.562007 | − | 0.827133i | \(-0.310030\pi\) | ||||
0.562007 | + | 0.827133i | \(0.310030\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1561.38 | −0.308159 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4317.76 | + | 2510.16i | −0.843576 | + | 0.490418i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 205.312 | − | 355.611i | 0.0397108 | − | 0.0687810i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1062.38 | − | 3297.64i | 0.203436 | − | 0.631472i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5693.37 | − | 5.69207i | 1.07946 | − | 0.00107921i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5381.56 | − | 3107.05i | 1.01032 | − | 0.583308i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3442.95i | − | 0.640064i | −0.947407 | − | 0.320032i | \(-0.896306\pi\) | ||
0.947407 | − | 0.320032i | \(-0.103694\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 933.976 | − | 540.477i | 0.171948 | − | 0.0995037i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 75.7324 | + | 131.172i | 0.0138083 | + | 0.0239167i | 0.872847 | − | 0.487994i | \(-0.162271\pi\) |
−0.859039 | + | 0.511911i | \(0.828938\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8335.31 | + | 4812.40i | 1.50524 | + | 0.869050i | 0.999982 | + | 0.00608123i | \(0.00193573\pi\) |
0.505257 | + | 0.862969i | \(0.331398\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2456.13 | − | 7676.47i | 0.439325 | − | 1.37308i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7866.93 | + | 4541.98i | 1.39385 | + | 0.804741i | 0.993739 | − | 0.111726i | \(-0.0356377\pi\) |
0.400112 | + | 0.916466i | \(0.368971\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1213.05 | − | 2101.07i | −0.212909 | − | 0.368768i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8107.83 | − | 4691.87i | 1.40977 | − | 0.815809i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1017.12i | 0.175214i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 864.811 | − | 499.299i | 0.147603 | − | 0.0852188i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1473.88 | − | 1.47355i | 0.249254 | − | 0.000249197i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2171.52 | − | 2399.65i | −0.363890 | − | 0.402118i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −702.788 | + | 1217.26i | −0.116703 | + | 0.202136i | −0.918459 | − | 0.395516i | \(-0.870566\pi\) |
0.801756 | + | 0.597651i | \(0.203899\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6309.25 | + | 12.6156i | −1.03827 | + | 0.00207607i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16408.6 | 2.67611 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7983.35 | 1.29045 | 0.645223 | − | 0.763994i | \(-0.276764\pi\) | ||||
0.645223 | + | 0.763994i | \(0.276764\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4670.97 | − | 2690.56i | −0.748354 | − | 0.431066i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3180.25 | + | 5508.36i | −0.505045 | + | 0.874764i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5111.13 | + | 3772.26i | −0.804592 | + | 0.593828i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.64112 | + | 4642.18i | 0.000724260 | + | 0.724425i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2268.41 | + | 1309.67i | −0.350935 | + | 0.202612i | −0.665097 | − | 0.746757i | \(-0.731610\pi\) |
0.314162 | + | 0.949369i | \(0.398276\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6032.33i | 0.925224i | 0.886561 | + | 0.462612i | \(0.153088\pi\) | ||||
−0.886561 | + | 0.462612i | \(0.846912\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.11736 | + | 1039.35i | 0.000474052 | + | 0.158053i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2658.15 | − | 4604.06i | −0.400791 | − | 0.694190i | 0.593031 | − | 0.805180i | \(-0.297931\pi\) |
−0.993822 | + | 0.110990i | \(0.964598\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1749.49 | + | 1010.07i | 0.261558 | + | 0.151011i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 850.770 | − | 2649.89i | 0.126128 | − | 0.392849i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1612.51 | − | 930.982i | −0.237061 | − | 0.136867i | 0.376764 | − | 0.926309i | \(-0.377037\pi\) |
−0.613825 | + | 0.789442i | \(0.710370\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2811.04 | − | 4868.87i | −0.409832 | − | 0.709851i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −165.822 | − | 286.550i | −0.0239763 | − | 0.0414325i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3635.70i | 0.521373i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1675.89 | − | 967.574i | 0.238367 | − | 0.137621i | −0.376059 | − | 0.926596i | \(-0.622721\pi\) |
0.614426 | + | 0.788975i | \(0.289388\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5013.21 | − | 8643.18i | −0.707255 | − | 1.21937i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1060.36 | + | 4928.06i | 0.148385 | + | 0.689629i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3871.04 | + | 6704.83i | −0.537359 | + | 0.930732i | 0.461687 | + | 0.887043i | \(0.347244\pi\) |
−0.999045 | + | 0.0436892i | \(0.986089\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −409.432 | + | 710.797i | −0.0563812 | + | 0.0978810i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −504.884 | −0.0689730 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3722.15 | 0.504470 | 0.252235 | − | 0.967666i | \(-0.418834\pi\) | ||||
0.252235 | + | 0.967666i | \(0.418834\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4268.53 | − | 7410.41i | 0.573972 | − | 0.996448i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3546.73 | + | 6143.12i | −0.473184 | + | 0.819578i | −0.999529 | − | 0.0306926i | \(-0.990229\pi\) |
0.526345 | + | 0.850271i | \(0.323562\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10114.8 | − | 3258.60i | −1.33895 | − | 0.431359i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2534.16 | − | 4369.09i | −0.332864 | − | 0.573885i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6173.12 | + | 3564.05i | −0.804601 | + | 0.464537i | −0.845077 | − | 0.534644i | \(-0.820446\pi\) |
0.0404765 | + | 0.999180i | \(0.487112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1602.98i | 0.207330i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1635.38 | − | 2826.03i | −0.209908 | − | 0.362733i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8577.33 | − | 14856.4i | −1.09259 | − | 1.89242i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7738.99 | + | 4468.11i | 0.978360 | + | 0.564857i | 0.901775 | − | 0.432206i | \(-0.142265\pi\) |
0.0765855 | + | 0.997063i | \(0.475598\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −715.255 | − | 3308.10i | −0.0897432 | − | 0.415068i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7719.60 | − | 4456.91i | −0.961343 | − | 0.555032i | −0.0647568 | − | 0.997901i | \(-0.520627\pi\) |
−0.896586 | + | 0.442869i | \(0.853961\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 661.826 | + | 1146.32i | 0.0818062 | + | 0.141692i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5915.71 | − | 10152.3i | −0.725812 | − | 1.24561i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8318.63i | 1.01312i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2680.13 | + | 1547.37i | −0.324019 | + | 0.187073i | −0.653183 | − | 0.757200i | \(-0.726567\pi\) |
0.329163 | + | 0.944273i | \(0.393233\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.59188 | + | 2592.47i | 0.000311066 | + | 0.311137i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1753.93 | − | 377.389i | 0.208972 | − | 0.0449639i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4843.82 | + | 8389.74i | −0.572949 | + | 0.992377i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5478.09 | + | 3155.48i | 0.643317 | + | 0.370562i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7234.25 | −0.843476 | −0.421738 | − | 0.906718i | \(-0.638580\pi\) | ||||
−0.421738 | + | 0.906718i | \(0.638580\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 406.124 | 0.0470148 | 0.0235074 | − | 0.999724i | \(-0.492517\pi\) | ||||
0.0235074 | + | 0.999724i | \(0.492517\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4718.11 | + | 9.43408i | −0.542323 | + | 0.00108440i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1949.14 | + | 3376.01i | −0.222464 | + | 0.385319i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5294.25 | + | 4790.95i | −0.600016 | + | 0.542975i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1370.37 | − | 1.37006i | 0.154224 | − | 0.000154189i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10590.4 | + | 6114.37i | −1.18358 | + | 0.683338i | −0.956839 | − | 0.290618i | \(-0.906139\pi\) |
−0.226737 | + | 0.973956i | \(0.572806\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3252.79i | 0.361014i | 0.983574 | + | 0.180507i | \(0.0577738\pi\) | ||||
−0.983574 | + | 0.180507i | \(0.942226\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4940.24 | − | 2858.84i | 0.544521 | − | 0.315105i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 974.689 | + | 1688.21i | 0.106695 | + | 0.184801i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13036.8 | + | 7526.81i | 1.41734 | + | 0.818303i | 0.996065 | − | 0.0886287i | \(-0.0282485\pi\) |
0.421278 | + | 0.906932i | \(0.361582\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −903.614 | + | 9216.81i | −0.0975720 | + | 0.995228i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −204.373 | − | 117.995i | −0.0219189 | − | 0.0126549i | 0.489001 | − | 0.872283i | \(-0.337362\pi\) |
−0.510919 | + | 0.859629i | \(0.670695\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12130.6 | + | 21010.8i | 1.29224 | + | 2.23822i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10439.2 | − | 6040.99i | 1.10460 | − | 0.639215i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5874.66i | − | 0.617466i | −0.951149 | − | 0.308733i | \(-0.900095\pi\) | ||
0.951149 | − | 0.308733i | \(-0.0999049\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11409.0 | + | 6587.02i | −1.19120 | + | 0.687739i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5078.98 | + | 5.07782i | −0.526780 | + | 0.000526660i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1639.74 | + | 1483.86i | −0.168950 | + | 0.152889i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −153.883 | + | 266.533i | −0.0157513 | + | 0.0272821i | −0.873794 | − | 0.486297i | \(-0.838347\pi\) |
0.858042 | + | 0.513579i | \(0.171681\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2039.23 | − | 3507.71i | −0.207370 | − | 0.356701i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4752.26 | −0.480119 | −0.240060 | − | 0.970758i | \(-0.577167\pi\) | ||||
−0.240060 | + | 0.970758i | \(0.577167\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9529.43 | 0.956523 | 0.478261 | − | 0.878218i | \(-0.341267\pi\) | ||||
0.478261 | + | 0.878218i | \(0.341267\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12966.8 | − | 7469.10i | −1.29316 | − | 0.744884i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3269.28 | − | 5662.56i | 0.323949 | − | 0.561097i | −0.657350 | − | 0.753586i | \(-0.728323\pi\) |
0.981299 | + | 0.192489i | \(0.0616559\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18432.1 | + | 3965.99i | −1.81475 | + | 0.390474i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.862312 | − | 862.509i | −8.43593e−5 | − | 0.0843786i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5767.23 | + | 3329.71i | −0.560629 | + | 0.323679i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4740.69i | 0.457932i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6371.64 | + | 3661.70i | 0.611609 | + | 0.351484i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3671.28 | − | 6358.85i | −0.350199 | − | 0.606562i | 0.636085 | − | 0.771619i | \(-0.280553\pi\) |
−0.986284 | + | 0.165057i | \(0.947219\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1499.22 | + | 865.574i | 0.142117 | + | 0.0820515i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1127.24 | − | 5213.55i | −0.106193 | − | 0.491148i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4570.96 | + | 2639.05i | 0.427952 | + | 0.247078i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3508.78 | + | 6077.39i | 0.326485 | + | 0.565489i | 0.981812 | − | 0.189857i | \(-0.0608024\pi\) |
−0.655327 | + | 0.755345i | \(0.727469\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2542.77 | + | 4394.06i | 0.235150 | + | 0.406352i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 224.222i | 0.0206089i | 0.999947 | + | 0.0103045i | \(0.00328007\pi\) | ||||
−0.999947 | + | 0.0103045i | \(0.996720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1706.89 | − | 985.471i | 0.155932 | − | 0.0900272i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13401.2 | + | 7772.96i | −1.21685 | + | 0.705795i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2209.38 | − | 711.777i | −0.199405 | − | 0.0642406i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10396.1 | + | 18006.6i | −0.932651 | + | 1.61540i | −0.153881 | + | 0.988089i | \(0.549177\pi\) |
−0.778770 | + | 0.627309i | \(0.784156\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.61196 | − | 4.53451i | 0.000232922 | − | 0.000404365i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7341.52 | 0.650780 | 0.325390 | − | 0.945580i | \(-0.394504\pi\) | ||||
0.325390 | + | 0.945580i | \(0.394504\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17660.5 | 1.55620 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5555.74 | + | 9645.09i | −0.486665 | + | 0.844878i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9956.11 | − | 17244.5i | 0.866988 | − | 1.50167i | 0.00192778 | − | 0.999998i | \(-0.499386\pi\) |
0.865060 | − | 0.501669i | \(-0.167280\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −878.757 | − | 4084.07i | −0.0760742 | − | 0.353559i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4280.52 | − | 2454.27i | −0.368400 | − | 0.211225i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2898.81 | − | 1673.63i | 0.248032 | − | 0.143202i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6220.75i | 0.529184i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10297.2 | − | 17794.2i | −0.870900 | − | 1.50497i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3745.90 | + | 6488.08i | 0.314992 | + | 0.545582i | 0.979436 | − | 0.201756i | \(-0.0646649\pi\) |
−0.664444 | + | 0.747338i | \(0.731332\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −249.515 | − | 144.058i | −0.0208614 | − | 0.0120444i | 0.489533 | − | 0.871985i | \(-0.337167\pi\) |
−0.510394 | + | 0.859940i | \(0.670501\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3965.35 | − | 12350.8i | 0.329642 | − | 1.02673i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4474.94 | − | 2583.61i | −0.369889 | − | 0.213555i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4547.39 | − | 7876.32i | −0.373748 | − | 0.647351i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1303.23 | − | 2267.71i | 0.106507 | − | 0.185330i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2741.58i | 0.222797i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25164.5 | − | 14528.7i | 2.03356 | − | 1.17408i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.5379 | + | 14541.2i | 0.00116826 | + | 1.16853i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12149.8 | + | 1215.69i | 0.970923 | + | 0.0971496i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7400.87 | + | 12818.7i | −0.588149 | + | 1.01870i | 0.406326 | + | 0.913728i | \(0.366810\pi\) |
−0.994475 | + | 0.104975i | \(0.966524\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6784.24 | + | 3907.85i | 0.536169 | + | 0.308843i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4571.90 | 0.359337 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4036.80 | 0.315541 | 0.157771 | − | 0.987476i | \(-0.449569\pi\) | ||||
0.157771 | + | 0.987476i | \(0.449569\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20.8141 | + | 10409.4i | 0.00161807 | + | 0.809221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1198.43 | − | 2075.74i | 0.0926585 | − | 0.160489i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13225.9 | + | 14615.4i | 1.01704 | + | 1.12388i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19570.9 | + | 19.5664i | −1.49683 | + | 0.00149649i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14891.1 | + | 8597.36i | −1.13277 | + | 0.654007i | −0.944631 | − | 0.328135i | \(-0.893580\pi\) |
−0.188142 | + | 0.982142i | \(0.560246\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1385.86i | 0.104858i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4630.21 | + | 2679.43i | −0.348463 | + | 0.201650i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9453.63 | + | 16374.2i | 0.707678 | + | 1.22573i | 0.965716 | + | 0.259600i | \(0.0835907\pi\) |
−0.258038 | + | 0.966135i | \(0.583076\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14480.7 | − | 8360.43i | −1.07824 | − | 0.622524i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9099.09 | + | 9974.51i | 0.673944 | + | 0.738783i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6255.57 | + | 3611.66i | 0.460891 | + | 0.266096i | 0.712419 | − | 0.701754i | \(-0.247600\pi\) |
−0.251528 | + | 0.967850i | \(0.580933\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4965.17 | − | 8599.93i | −0.363898 | − | 0.630290i | 0.624700 | − | 0.780865i | \(-0.285221\pi\) |
−0.988599 | + | 0.150574i | \(0.951888\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16537.7 | − | 9570.08i | 1.20571 | − | 0.697724i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7471.31i | 0.541870i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7254.16 | − | 4188.19i | 0.523388 | − | 0.302178i | −0.214932 | − | 0.976629i | \(-0.568953\pi\) |
0.738320 | + | 0.674451i | \(0.235620\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −672.730 | + | 0.672576i | −0.0482862 | + | 4.82752e-5i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3413.36 | − | 10595.2i | 0.243735 | − | 0.756560i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4844.67 | − | 8391.21i | 0.344161 | − | 0.596104i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.44656 | + | 3224.01i | 0.000455611 | + | 0.227857i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21277.2 | −1.49609 | −0.748043 | − | 0.663650i | \(-0.769006\pi\) | ||||
−0.748043 | + | 0.663650i | \(0.769006\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6283.84 | −0.439594 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13709.5 | + | 7896.94i | 0.954204 | + | 0.549639i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1424.49 | − | 2467.29i | 0.0986454 | − | 0.170859i | −0.812479 | − | 0.582991i | \(-0.801882\pi\) |
0.911124 | + | 0.412132i | \(0.135216\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2647.25 | − | 8217.14i | 0.182398 | − | 0.566168i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.7450 | − | 20749.7i | −0.00142217 | − | 1.42249i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3844.40 | − | 2219.57i | 0.262234 | − | 0.151401i | −0.363119 | − | 0.931743i | \(-0.618288\pi\) |
0.625353 | + | 0.780342i | \(0.284955\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 7868.29i | − | 0.534033i | −0.963692 | − | 0.267017i | \(-0.913962\pi\) | ||
0.963692 | − | 0.267017i | \(-0.0860379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13695.6 | + | 23831.4i | −0.924924 | + | 1.60944i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −513.480 | − | 889.374i | −0.0345057 | − | 0.0597656i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15144.9 | + | 8743.92i | 1.01271 | + | 0.584686i | 0.911983 | − | 0.410228i | \(-0.134551\pi\) |
0.100724 | + | 0.994914i | \(0.467884\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4858.50 | + | 4405.47i | −0.323278 | + | 0.293134i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1121.13 | + | 647.284i | 0.0742324 | + | 0.0428581i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6422.07 | − | 11123.3i | −0.423140 | − | 0.732900i | 0.573105 | − | 0.819482i | \(-0.305739\pi\) |
−0.996245 | + | 0.0865820i | \(0.972406\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15523.8 | − | 26826.1i | −1.01786 | − | 1.75892i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23625.5i | 1.54153i | 0.637117 | + | 0.770767i | \(0.280127\pi\) | ||||
−0.637117 | + | 0.770767i | \(0.719873\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16529.1 | + | 9543.05i | −1.07328 | + | 0.619657i | −0.929075 | − | 0.369891i | \(-0.879395\pi\) |
−0.144202 | + | 0.989548i | \(0.546062\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6746.08 | − | 3867.92i | −0.435927 | − | 0.249942i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18704.9 | − | 20669.9i | −1.20289 | − | 1.32925i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7152.40 | − | 12388.3i | 0.457754 | − | 0.792853i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3247.18 | + | 5637.29i | −0.206826 | + | 0.359062i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6757.98 | −0.428391 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.3893 | −0.00204342 | −0.00102171 | − | 0.999999i | \(-0.500325\pi\) | ||||
−0.00102171 | + | 0.999999i | \(0.500325\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11369.4 | + | 19737.9i | −0.713891 | + | 1.23935i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13263.7 | − | 22973.4i | 0.828902 | − | 1.43570i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1483.31 | − | 2063.19i | 0.0922620 | − | 0.128330i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2927.23 | + | 1697.85i | −0.181220 | + | 0.105111i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18742.7 | − | 10821.1i | 1.15490 | − | 0.666784i | 0.204827 | − | 0.978798i | \(-0.434337\pi\) |
0.950078 | + | 0.312014i | \(0.101004\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19867.3i | 1.21849i | 0.792982 | + | 0.609246i | \(0.208528\pi\) | ||||
−0.792982 | + | 0.609246i | \(0.791472\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7847.24 | − | 13560.5i | −0.479046 | − | 0.827820i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11212.2 | + | 19420.1i | 0.681294 | + | 1.18004i | 0.974586 | + | 0.224012i | \(0.0719156\pi\) |
−0.293293 | + | 0.956023i | \(0.594751\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2986.49 | − | 1724.25i | −0.180632 | − | 0.104288i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16371.2 | + | 5256.11i | 0.985618 | + | 0.316441i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17358.5 | − | 10021.9i | −1.04026 | − | 0.600594i | −0.120353 | − | 0.992731i | \(-0.538403\pi\) |
−0.919907 | + | 0.392137i | \(0.871736\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5064.07 | − | 8771.22i | −0.302091 | − | 0.523237i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5280.41 | − | 3034.59i | −0.313559 | − | 0.180199i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 13217.9i | − | 0.781327i | −0.920533 | − | 0.390664i | \(-0.872246\pi\) | ||
0.920533 | − | 0.390664i | \(-0.127754\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8470.90 | − | 4890.68i | 0.498457 | − | 0.287784i | −0.229619 | − | 0.973281i | \(-0.573748\pi\) |
0.728076 | + | 0.685496i | \(0.240415\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.11302 | + | 1113.28i | 6.51979e−5 | + | 0.0652128i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2208.41 | − | 10263.7i | −0.128780 | − | 0.598511i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1888.72 | − | 3271.36i | 0.109642 | − | 0.189906i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21844.5 | + | 12582.8i | 1.26242 | + | 0.727174i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13724.6 | 0.789617 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4670.73 | −0.267524 | −0.133762 | − | 0.991014i | \(-0.542706\pi\) | ||||
−0.133762 | + | 0.991014i | \(0.542706\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9504.63 | − | 16349.1i | −0.541975 | − | 0.932260i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13521.0 | − | 23419.1i | 0.767584 | − | 1.32949i | −0.171286 | − | 0.985221i | \(-0.554792\pi\) |
0.938870 | − | 0.344273i | \(-0.111875\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5772.53 | − | 1859.69i | −0.326258 | − | 0.105108i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12305.0 | + | 12.3022i | −0.692406 | + | 0.000692248i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11596.9 | − | 6695.45i | 0.649694 | − | 0.375101i | −0.138645 | − | 0.990342i | \(-0.544275\pi\) |
0.788339 | + | 0.615241i | \(0.210941\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8041.69i | 0.448551i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19408.2 | − | 11231.2i | 1.07783 | − | 0.623724i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1008.20 | − | 1746.25i | −0.0557464 | − | 0.0965557i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26837.3 | − | 15494.6i | −1.47748 | − | 0.853025i | −0.477807 | − | 0.878465i | \(-0.658568\pi\) |
−0.999676 | + | 0.0254396i | \(0.991901\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13175.1 | − | 11970.6i | 0.722197 | − | 0.656172i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16982.9 | + | 9805.07i | 0.926903 | + | 0.535147i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5351.23 | − | 9268.60i | −0.290807 | − | 0.503692i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25067.3 | − | 14506.0i | 1.35641 | − | 0.784933i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2892.67i | 0.155855i | 0.996959 | + | 0.0779277i | \(0.0248303\pi\) | ||||
−0.996959 | + | 0.0779277i | \(0.975170\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7117.31 | + | 4109.18i | −0.381841 | + | 0.220456i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14635.3 | + | 14.6320i | −0.781841 | + | 0.000781662i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19838.4 | + | 4268.57i | −1.05530 | + | 0.227067i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7965.19 | + | 13796.1i | −0.421917 | + | 0.730781i | −0.996127 | − | 0.0879267i | \(-0.971976\pi\) |
0.574210 | + | 0.818708i | \(0.305309\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 28736.3 | − | 57.4595i | 1.51574 | − | 0.00303080i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9903.30 | −0.520171 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4250.81 | 0.222337 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21088.8 | + | 12147.5i | 1.09843 | + | 0.632716i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5938.87 | + | 10286.4i | −0.308042 | + | 0.533545i | −0.977934 | − | 0.208914i | \(-0.933007\pi\) |
0.669892 | + | 0.742459i | \(0.266341\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2851.78 | + | 2580.67i | −0.147303 | + | 0.133300i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.3780 | − | 11380.6i | −0.000585273 | − | 0.585407i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7955.61 | − | 4593.18i | 0.407537 | − | 0.235291i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 16795.8i | − | 0.856839i | −0.903580 | − | 0.428419i | \(-0.859071\pi\) | ||
0.903580 | − | 0.428419i | \(-0.140929\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19682.6 | − | 118.070i | 0.999982 | − | 0.00599859i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2705.03 | − | 4685.24i | −0.136866 | − | 0.237059i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22048.4 | + | 12729.7i | 1.11102 | + | 0.641447i | 0.939093 | − | 0.343663i | \(-0.111668\pi\) |
0.171926 | + | 0.985110i | \(0.445001\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2831.54 | + | 28587.1i | −0.142099 | + | 1.43463i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31385.1 | + | 18120.2i | 1.56864 | + | 0.905653i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9319.48 | − | 16141.8i | −0.463901 | − | 0.803499i | 0.535251 | − | 0.844693i | \(-0.320217\pi\) |
−0.999151 | + | 0.0411940i | \(0.986884\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 678.099 | + | 1171.79i | 0.0336175 | + | 0.0580930i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14043.3i | 0.693401i | 0.937976 | + | 0.346700i | \(0.112698\pi\) | ||||
−0.937976 | + | 0.346700i | \(0.887302\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32400.4 | − | 18706.4i | 1.59337 | − | 0.919932i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8142.12 | − | 14037.7i | −0.398802 | − | 0.687566i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24756.3 | + | 22402.8i | −1.20771 | + | 1.09290i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8115.13 | − | 14055.8i | 0.394308 | − | 0.682961i | −0.598705 | − | 0.800970i | \(-0.704318\pi\) |
0.993013 | + | 0.118009i | \(0.0376510\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5811.43 | − | 10089.0i | 0.281248 | − | 0.488263i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15754.7 | −0.759433 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33345.7 | −1.60102 | −0.800508 | − | 0.599322i | \(-0.795437\pi\) | ||||
−0.800508 | + | 0.599322i | \(0.795437\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5117.55 | + | 8884.35i | −0.244737 | + | 0.424877i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5394.02 | + | 9342.71i | −0.256942 | + | 0.445037i | −0.965421 | − | 0.260695i | \(-0.916048\pi\) |
0.708479 | + | 0.705732i | \(0.249382\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5135.72 | + | 1105.04i | −0.243677 | + | 0.0524313i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6314.68 | − | 10887.0i | −0.298441 | − | 0.514537i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −621.503 | + | 358.825i | −0.0292584 | + | 0.0168923i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 35799.6i | − | 1.67876i | −0.543543 | − | 0.839381i | \(-0.682918\pi\) | ||
0.543543 | − | 0.839381i | \(-0.317082\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2892.94 | − | 4999.17i | −0.135132 | − | 0.233516i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18306.3 | + | 31707.5i | 0.851788 | + | 1.47534i | 0.879593 | + | 0.475727i | \(0.157815\pi\) |
−0.0278053 | + | 0.999613i | \(0.508852\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20857.2 | − | 12041.9i | −0.966727 | − | 0.558140i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21979.7 | − | 4752.31i | 1.01482 | − | 0.219419i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11271.5 | − | 6507.62i | −0.518414 | − | 0.299306i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2230.86 | + | 3863.97i | 0.102211 | + | 0.177034i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 28.6773 | + | 9561.27i | 0.00130887 | + | 0.436388i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2675.45i | − | 0.121644i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34874.9 | − | 20135.0i | 1.57961 | − | 0.911990i | 0.584701 | − | 0.811249i | \(-0.301212\pi\) |
0.994913 | − | 0.100742i | \(-0.0321216\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.6947 | − | 10697.2i | −0.000482563 | − | 0.482673i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18287.2 | + | 5891.45i | 0.822022 | + | 0.264824i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1428.08 | − | 2473.51i | 0.0639503 | − | 0.110765i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19753.1 | + | 11378.1i | 0.881219 | + | 0.507598i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11444.6 | 0.508645 | 0.254323 | − | 0.967119i | \(-0.418148\pi\) | ||||
0.254323 | + | 0.967119i | \(0.418148\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5053.68 | −0.223762 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −40640.6 | + | 81.2628i | −1.79272 | + | 0.00358462i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4014.95 | + | 6954.10i | −0.176444 | + | 0.305610i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3480.45 | − | 16175.6i | −0.152385 | − | 0.708216i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25093.5 | − | 25.0877i | 1.09459 | − | 0.00109434i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2702.86 | − | 1560.50i | 0.117463 | − | 0.0678172i | −0.440117 | − | 0.897940i | \(-0.645063\pi\) |
0.557580 | + | 0.830123i | \(0.311730\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3571.23i | 0.154628i | 0.997007 | + | 0.0773138i | \(0.0246343\pi\) | ||||
−0.997007 | + | 0.0773138i | \(0.975366\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −995.903 | + | 576.313i | −0.0429617 | + | 0.0248612i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7873.89 | + | 13638.0i | 0.338418 | + | 0.586157i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5697.71 | − | 3289.58i | −0.243987 | − | 0.140866i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −786.493 | − | 3620.05i | −0.0335559 | − | 0.154450i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24420.3 | − | 14099.1i | −1.03809 | − | 0.599344i | −0.118801 | − | 0.992918i | \(-0.537905\pi\) |
−0.919293 | + | 0.393574i | \(0.871238\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5700.86 | − | 9874.18i | −0.241457 | − | 0.418217i | 0.719672 | − | 0.694314i | \(-0.244292\pi\) |
−0.961130 | + | 0.276097i | \(0.910959\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −21580.9 | + | 12488.5i | −0.910729 | + | 0.527024i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18948.2i | 0.796726i | 0.917228 | + | 0.398363i | \(0.130422\pi\) | ||||
−0.917228 | + | 0.398363i | \(0.869578\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 663.246 | − | 382.925i | 0.0277871 | − | 0.0160429i | −0.486042 | − | 0.873935i | \(-0.661560\pi\) |
0.513829 | + | 0.857893i | \(0.328227\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12819.7 | − | 12.8168i | 0.535151 | − | 0.000535029i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −987.617 | + | 9870.36i | −0.0410791 | + | 0.410549i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.11618 | − | 14.0576i | 0.000336374 | − | 0.000582617i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21670.9 | − | 12598.5i | 0.894928 | − | 0.520272i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5355.68 | −0.220380 | −0.110190 | − | 0.993911i | \(-0.535146\pi\) | ||||
−0.110190 | + | 0.993911i | \(0.535146\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19744.4 | 0.809564 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18797.3 | − | 10827.6i | −0.767986 | − | 0.442374i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17263.5 | + | 29901.2i | −0.702818 | + | 1.21732i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 791.768 | + | 874.946i | 0.0321198 | + | 0.0354941i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 33.7626 | + | 33770.3i | 0.00136482 | + | 1.36513i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11216.8 | + | 6476.05i | −0.451832 | + | 0.260865i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8591.74i | 0.344872i | 0.985021 | + | 0.172436i | \(0.0551638\pi\) | ||||
−0.985021 | + | 0.172436i | \(0.944836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13270.3 | − | 7626.26i | −0.530800 | − | 0.305044i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20273.3 | − | 35114.5i | −0.808080 | − | 1.39964i | −0.914192 | − | 0.405281i | \(-0.867174\pi\) |
0.106112 | − | 0.994354i | \(-0.466160\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8352.92 | + | 4822.56i | 0.331779 | + | 0.191553i | 0.656631 | − | 0.754212i | \(-0.271981\pi\) |
−0.324852 | + | 0.945765i | \(0.605314\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23922.2 | + | 26382.3i | 0.946884 | + | 1.04426i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9951.19 | − | 5745.32i | −0.392517 | − | 0.226620i | 0.290733 | − | 0.956804i | \(-0.406101\pi\) |
−0.683250 | + | 0.730184i | \(0.739434\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31886.1 | − | 55228.3i | −1.25336 | − | 2.17089i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10609.7 | + | 18334.2i | 0.415599 | + | 0.718180i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 37888.3i | − | 1.47902i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6531.39 | − | 3770.90i | 0.254085 | − | 0.146696i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7648.11 | + | 4436.05i | −0.296506 | + | 0.171979i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 896.522 | − | 2782.83i | 0.0346377 | − | 0.107516i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14714.7 | − | 25486.6i | 0.566568 | − | 0.981324i | −0.430334 | − | 0.902670i | \(-0.641604\pi\) |
0.996902 | − | 0.0786543i | \(-0.0250623\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14620.8 | + | 25382.6i | −0.561033 | + | 0.973986i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22330.5 | 0.853956 | 0.426978 | − | 0.904262i | \(-0.359578\pi\) | ||||
0.426978 | + | 0.904262i | \(0.359578\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15519.2 | −0.591463 | −0.295732 | − | 0.955271i | \(-0.595563\pi\) | ||||
−0.295732 | + | 0.955271i | \(0.595563\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4049.55 | − | 7030.25i | 0.153813 | − | 0.267027i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19107.9 | − | 33095.9i | 0.723316 | − | 1.25282i | −0.236347 | − | 0.971669i | \(-0.575950\pi\) |
0.959663 | − | 0.281152i | \(-0.0907165\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9346.69 | + | 29012.4i | −0.352618 | + | 1.09454i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −103.783 | − | 25951.4i | −0.00390218 | − | 0.975764i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5322.39 | + | 3072.88i | −0.199448 | + | 0.115151i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45106.0i | 1.68461i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1068.68 | + | 1846.74i | 0.0397795 | + | 0.0687413i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6088.31 | + | 10545.3i | 0.225869 | + | 0.391217i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6816.94 | + | 3935.76i | 0.252059 | + | 0.145526i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12092.6 | + | 13336.1i | 0.445644 | + | 0.491471i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21032.2 | + | 12142.9i | 0.772522 | + | 0.446016i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4432.30 | − | 7676.97i | −0.162262 | − | 0.281047i | 0.773417 | − | 0.633897i | \(-0.218546\pi\) |
−0.935680 | + | 0.352850i | \(0.885212\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14740.5 | + | 25649.7i | −0.537858 | + | 0.935915i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 15145.0i | − | 0.550798i | −0.961330 | − | 0.275399i | \(-0.911190\pi\) | ||
0.961330 | − | 0.275399i | \(-0.0888100\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18529.8 | + | 10698.2i | −0.671684 | + | 0.387797i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 32.2820 | + | 32289.3i | 0.00116635 | + | 1.16662i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7808.61 | + | 8628.93i | 0.281203 | + | 0.310744i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2244.07 | + | 3886.84i | −0.0805495 | + | 0.139516i | −0.903486 | − | 0.428617i | \(-0.859001\pi\) |
0.822937 | + | 0.568133i | \(0.192334\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15502.2 | + | 8929.55i | 0.554631 | + | 0.319477i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 928.506 | 0.0331118 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31498.2 | −1.11963 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.2116 | + | 5607.08i | 0.000397236 | + | 0.198663i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8911.93 | − | 15435.9i | 0.314737 | − | 0.545141i | −0.664644 | − | 0.747160i | \(-0.731417\pi\) |
0.979382 | + | 0.202019i | \(0.0647503\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4961.53 | + | 10995.7i | 0.174659 | + | 0.387078i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −787.033 | + | 0.786854i | −0.0276166 | + | 2.76103e-5i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14370.9 | + | 8297.05i | −0.502652 | + | 0.290206i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51270.5i | 1.78755i | 0.448516 | + | 0.893775i | \(0.351953\pi\) | ||||
−0.448516 | + | 0.893775i | \(0.648047\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −43286.5 | + | 25049.2i | −1.50437 | + | 0.870554i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5422.48 | + | 9392.01i | 0.187851 | + | 0.325367i | 0.944533 | − | 0.328415i | \(-0.106514\pi\) |
−0.756683 | + | 0.653782i | \(0.773181\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17763.9 | − | 10256.0i | −0.613437 | − | 0.354168i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 28193.9 | + | 30968.5i | 0.970525 | + | 1.06604i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36916.8 | + | 21313.9i | 1.26677 | + | 0.731372i | 0.974376 | − | 0.224926i | \(-0.0722139\pi\) |
0.292397 | + | 0.956297i | \(0.405547\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 835.531 | + | 1447.18i | 0.0285801 | + | 0.0495021i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −40854.2 | + | 23641.7i | −1.39305 | + | 0.806134i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 33229.0i | − | 1.12948i | −0.825269 | − | 0.564739i | \(-0.808977\pi\) | ||
0.825269 | − | 0.564739i | \(-0.191023\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 51328.4 | − | 29634.5i | 1.73921 | − | 1.00413i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12606.4 | − | 12.6035i | 0.425817 | − | 0.000425720i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1943.69 | − | 9033.42i | −0.0654486 | − | 0.304175i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1066.19 | − | 1846.70i | 0.0357891 | − | 0.0619885i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 97.3279 | + | 48675.0i | 0.00325685 | + | 1.62880i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2086.77 | −0.0696118 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16853.4 | 0.560464 | 0.280232 | − | 0.959932i | \(-0.409589\pi\) | ||||
0.280232 | + | 0.959932i | \(0.409589\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4579.68 | − | 2637.98i | −0.151827 | − | 0.0874552i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 634.824 | − | 1099.55i | 0.0209809 | − | 0.0363400i | −0.855344 | − | 0.518060i | \(-0.826654\pi\) |
0.876325 | + | 0.481720i | \(0.159988\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21447.2 | − | 6909.46i | −0.706644 | − | 0.227654i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.18768 | + | 5188.86i | 0.000170399 | + | 0.170438i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −49580.5 | + | 28625.3i | −1.62356 | + | 0.937364i | −0.637605 | + | 0.770363i | \(0.720075\pi\) |
−0.985957 | + | 0.167001i | \(0.946592\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 53583.9i | 1.74929i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3816.00 | + | 6640.13i | −0.124195 | + | 0.216109i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30733.8 | − | 53232.4i | −0.997207 | − | 1.72721i | −0.563283 | − | 0.826264i | \(-0.690462\pi\) |
−0.433924 | − | 0.900950i | \(-0.642871\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 42501.6 | + | 24538.3i | 1.37484 | + | 0.793762i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16436.7 | − | 3553.82i | 0.530075 | − | 0.114609i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8979.57 | − | 5184.36i | −0.288710 | − | 0.166687i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25996.6 | − | 45027.4i | −0.833308 | − | 1.44333i | −0.895401 | − | 0.445261i | \(-0.853111\pi\) |
0.0620930 | − | 0.998070i | \(-0.480222\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3658.12 | − | 6321.44i | −0.116905 | − | 0.202019i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 64364.3i | − | 2.05074i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29417.3 | − | 16984.1i | 0.934460 | − | 0.539510i | 0.0462403 | − | 0.998930i | \(-0.485276\pi\) |
0.888219 | + | 0.459420i | \(0.151943\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16306.7 | − | 28440.7i | 0.516438 | − | 0.900725i |
(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 | 336.4.bc.d.257.2 | 12 | ||
3.2 | odd | 2 | inner | 336.4.bc.d.257.1 | 12 | ||
4.3 | odd | 2 | 21.4.g.a.5.5 | yes | 12 | ||
7.3 | odd | 6 | inner | 336.4.bc.d.17.1 | 12 | ||
12.11 | even | 2 | 21.4.g.a.5.2 | ✓ | 12 | ||
21.17 | even | 6 | inner | 336.4.bc.d.17.2 | 12 | ||
28.3 | even | 6 | 21.4.g.a.17.2 | yes | 12 | ||
28.11 | odd | 6 | 147.4.g.d.80.2 | 12 | |||
28.19 | even | 6 | 147.4.c.a.146.3 | 12 | |||
28.23 | odd | 6 | 147.4.c.a.146.4 | 12 | |||
28.27 | even | 2 | 147.4.g.d.68.5 | 12 | |||
84.11 | even | 6 | 147.4.g.d.80.5 | 12 | |||
84.23 | even | 6 | 147.4.c.a.146.9 | 12 | |||
84.47 | odd | 6 | 147.4.c.a.146.10 | 12 | |||
84.59 | odd | 6 | 21.4.g.a.17.5 | yes | 12 | ||
84.83 | odd | 2 | 147.4.g.d.68.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.g.a.5.2 | ✓ | 12 | 12.11 | even | 2 | ||
21.4.g.a.5.5 | yes | 12 | 4.3 | odd | 2 | ||
21.4.g.a.17.2 | yes | 12 | 28.3 | even | 6 | ||
21.4.g.a.17.5 | yes | 12 | 84.59 | odd | 6 | ||
147.4.c.a.146.3 | 12 | 28.19 | even | 6 | |||
147.4.c.a.146.4 | 12 | 28.23 | odd | 6 | |||
147.4.c.a.146.9 | 12 | 84.23 | even | 6 | |||
147.4.c.a.146.10 | 12 | 84.47 | odd | 6 | |||
147.4.g.d.68.2 | 12 | 84.83 | odd | 2 | |||
147.4.g.d.68.5 | 12 | 28.27 | even | 2 | |||
147.4.g.d.80.2 | 12 | 28.11 | odd | 6 | |||
147.4.g.d.80.5 | 12 | 84.11 | even | 6 | |||
336.4.bc.d.17.1 | 12 | 7.3 | odd | 6 | inner | ||
336.4.bc.d.17.2 | 12 | 21.17 | even | 6 | inner | ||
336.4.bc.d.257.1 | 12 | 3.2 | odd | 2 | inner | ||
336.4.bc.d.257.2 | 12 | 1.1 | even | 1 | trivial |