Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,4,Mod(181,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.181");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.k (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: | \(21.2406876021\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{11} + 7x^{10} - 12x^{9} + 21x^{8} - 68x^{6} + 336x^{4} - 768x^{3} + 1792x^{2} - 4096x + 4096 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14}\cdot 5^{4} \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 181.9 | ||
Root | \(-0.650488 + 1.89126i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 360.181 |
Dual form | 360.4.k.c.181.10 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.54175 | − | 1.24077i | 0.898644 | − | 0.438679i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.92097 | − | 6.30746i | 0.615121 | − | 0.788433i | ||||
\(5\) | 5.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 26.6173 | 1.43720 | 0.718600 | − | 0.695424i | \(-0.244783\pi\) | ||||
0.718600 | + | 0.695424i | \(0.244783\pi\) | |||||||
\(8\) | 4.68175 | − | 22.1378i | 0.206906 | − | 0.978361i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.20386 | + | 12.7087i | 0.196183 | + | 0.401886i | ||||
\(11\) | 61.7277i | 1.69196i | 0.533212 | + | 0.845982i | \(0.320985\pi\) | ||||
−0.533212 | + | 0.845982i | \(0.679015\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 45.0627i | 0.961396i | 0.876886 | + | 0.480698i | \(0.159617\pi\) | ||||
−0.876886 | + | 0.480698i | \(0.840383\pi\) | |||||||
\(14\) | 67.6545 | − | 33.0260i | 1.29153 | − | 0.630470i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −15.5681 | − | 62.0776i | −0.243252 | − | 0.969963i | ||||
\(17\) | 71.8754 | 1.02543 | 0.512716 | − | 0.858558i | \(-0.328639\pi\) | ||||
0.512716 | + | 0.858558i | \(0.328639\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 17.6319i | − | 0.212897i | −0.994318 | − | 0.106449i | \(-0.966052\pi\) | ||
0.994318 | − | 0.106449i | \(-0.0339480\pi\) | |||||||
\(20\) | 31.5373 | + | 24.6049i | 0.352598 | + | 0.275091i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 76.5900 | + | 156.896i | 0.742229 | + | 1.52047i | ||||
\(23\) | −43.4131 | −0.393577 | −0.196788 | − | 0.980446i | \(-0.563051\pi\) | ||||
−0.196788 | + | 0.980446i | \(0.563051\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −25.0000 | −0.200000 | ||||||||
\(26\) | 55.9125 | + | 114.538i | 0.421744 | + | 0.863952i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 130.983 | − | 167.888i | 0.884052 | − | 1.13314i | ||||
\(29\) | − | 267.633i | − | 1.71373i | −0.515540 | − | 0.856866i | \(-0.672409\pi\) | ||
0.515540 | − | 0.856866i | \(-0.327591\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 50.2133 | 0.290922 | 0.145461 | − | 0.989364i | \(-0.453533\pi\) | ||||
0.145461 | + | 0.989364i | \(0.453533\pi\) | |||||||
\(32\) | −116.594 | − | 138.469i | −0.644099 | − | 0.764942i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 182.689 | − | 89.1810i | 0.921498 | − | 0.449836i | ||||
\(35\) | 133.087i | 0.642735i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 75.0720i | 0.333561i | 0.985994 | + | 0.166781i | \(0.0533372\pi\) | ||||
−0.985994 | + | 0.166781i | \(0.946663\pi\) | |||||||
\(38\) | −21.8772 | − | 44.8160i | −0.0933935 | − | 0.191319i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 110.689 | + | 23.4087i | 0.437536 | + | 0.0925312i | ||||
\(41\) | 221.685 | 0.844425 | 0.422213 | − | 0.906497i | \(-0.361254\pi\) | ||||
0.422213 | + | 0.906497i | \(0.361254\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 188.998i | 0.670277i | 0.942169 | + | 0.335139i | \(0.108783\pi\) | ||||
−0.942169 | + | 0.335139i | \(0.891217\pi\) | |||||||
\(44\) | 389.345 | + | 303.760i | 1.33400 | + | 1.04076i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −110.345 | + | 53.8658i | −0.353685 | + | 0.172654i | ||||
\(47\) | 384.142 | 1.19219 | 0.596094 | − | 0.802914i | \(-0.296718\pi\) | ||||
0.596094 | + | 0.802914i | \(0.296718\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 365.481 | 1.06554 | ||||||||
\(50\) | −63.5437 | + | 31.0193i | −0.179729 | + | 0.0877358i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 284.231 | + | 221.752i | 0.757996 | + | 0.591375i | ||||
\(53\) | 247.445i | 0.641306i | 0.947197 | + | 0.320653i | \(0.103902\pi\) | ||||
−0.947197 | + | 0.320653i | \(0.896098\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −308.638 | −0.756669 | ||||||||
\(56\) | 124.616 | − | 589.248i | 0.297365 | − | 1.40610i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −332.072 | − | 680.256i | −0.751778 | − | 1.54003i | ||||
\(59\) | − | 518.596i | − | 1.14433i | −0.820139 | − | 0.572165i | \(-0.806104\pi\) | ||
0.820139 | − | 0.572165i | \(-0.193896\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 62.0042i | − | 0.130145i | −0.997881 | − | 0.0650723i | \(-0.979272\pi\) | ||
0.997881 | − | 0.0650723i | \(-0.0207278\pi\) | |||||||
\(62\) | 127.630 | − | 62.3033i | 0.261435 | − | 0.127621i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −468.162 | − | 207.287i | −0.914380 | − | 0.404858i | ||||
\(65\) | −225.314 | −0.429949 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 558.476i | − | 1.01834i | −0.860666 | − | 0.509169i | \(-0.829953\pi\) | ||
0.860666 | − | 0.509169i | \(-0.170047\pi\) | |||||||
\(68\) | 353.697 | − | 453.351i | 0.630765 | − | 0.808484i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 165.130 | + | 338.273i | 0.281955 | + | 0.577590i | ||||
\(71\) | −313.194 | −0.523512 | −0.261756 | − | 0.965134i | \(-0.584301\pi\) | ||||
−0.261756 | + | 0.965134i | \(0.584301\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −263.926 | −0.423153 | −0.211576 | − | 0.977361i | \(-0.567860\pi\) | ||||
−0.211576 | + | 0.977361i | \(0.567860\pi\) | |||||||
\(74\) | 93.1472 | + | 190.814i | 0.146326 | + | 0.299753i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −111.213 | − | 86.7663i | −0.167855 | − | 0.130958i | ||||
\(77\) | 1643.03i | 2.43169i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −732.940 | −1.04383 | −0.521913 | − | 0.852999i | \(-0.674781\pi\) | ||||
−0.521913 | + | 0.852999i | \(0.674781\pi\) | |||||||
\(80\) | 310.388 | − | 77.8405i | 0.433781 | − | 0.108785i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 563.468 | − | 275.061i | 0.758837 | − | 0.370432i | ||||
\(83\) | − | 717.705i | − | 0.949137i | −0.880218 | − | 0.474569i | \(-0.842604\pi\) | ||
0.880218 | − | 0.474569i | \(-0.157396\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 359.377i | 0.458587i | ||||||||
\(86\) | 234.503 | + | 480.385i | 0.294037 | + | 0.602341i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1366.51 | + | 288.994i | 1.65535 | + | 0.350077i | ||||
\(89\) | −1634.69 | −1.94693 | −0.973463 | − | 0.228845i | \(-0.926505\pi\) | ||||
−0.973463 | + | 0.228845i | \(0.926505\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1199.45i | 1.38172i | ||||||||
\(92\) | −213.635 | + | 273.827i | −0.242097 | + | 0.310309i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 976.392 | − | 476.633i | 1.07135 | − | 0.522988i | ||||
\(95\) | 88.1597 | 0.0952105 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1367.12 | −1.43103 | −0.715516 | − | 0.698596i | \(-0.753809\pi\) | ||||
−0.715516 | + | 0.698596i | \(0.753809\pi\) | |||||||
\(98\) | 928.962 | − | 453.479i | 0.957544 | − | 0.467432i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −123.024 | + | 157.687i | −0.123024 | + | 0.157687i | ||||
\(101\) | − | 58.3234i | − | 0.0574594i | −0.999587 | − | 0.0287297i | \(-0.990854\pi\) | ||
0.999587 | − | 0.0287297i | \(-0.00914620\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.69032 | −0.00927005 | −0.00463503 | − | 0.999989i | \(-0.501475\pi\) | ||||
−0.00463503 | + | 0.999989i | \(0.501475\pi\) | |||||||
\(104\) | 997.588 | + | 210.972i | 0.940592 | + | 0.198919i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 307.023 | + | 628.944i | 0.281328 | + | 0.576306i | ||||
\(107\) | − | 439.045i | − | 0.396674i | −0.980134 | − | 0.198337i | \(-0.936446\pi\) | ||
0.980134 | − | 0.198337i | \(-0.0635540\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1616.51i | 1.42049i | 0.703955 | + | 0.710245i | \(0.251416\pi\) | ||||
−0.703955 | + | 0.710245i | \(0.748584\pi\) | |||||||
\(110\) | −784.481 | + | 382.950i | −0.679976 | + | 0.331935i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −414.381 | − | 1652.34i | −0.349601 | − | 1.39403i | ||||
\(113\) | 1281.25 | 1.06663 | 0.533316 | − | 0.845916i | \(-0.320946\pi\) | ||||
0.533316 | + | 0.845916i | \(0.320946\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 217.066i | − | 0.176013i | ||||||
\(116\) | −1688.08 | − | 1317.01i | −1.35116 | − | 1.05415i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −643.459 | − | 1318.14i | −0.501993 | − | 1.02834i | ||||
\(119\) | 1913.13 | 1.47375 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2479.31 | −1.86274 | ||||||||
\(122\) | −76.9330 | − | 157.599i | −0.0570917 | − | 0.116954i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 247.098 | − | 316.718i | 0.178952 | − | 0.229372i | ||||
\(125\) | − | 125.000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 235.326 | 0.164423 | 0.0822117 | − | 0.996615i | \(-0.473802\pi\) | ||||
0.0822117 | + | 0.996615i | \(0.473802\pi\) | |||||||
\(128\) | −1447.15 | + | 54.0113i | −0.999304 | + | 0.0372966i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −572.690 | + | 279.563i | −0.386371 | + | 0.188610i | ||||
\(131\) | 993.121i | 0.662362i | 0.943567 | + | 0.331181i | \(0.107447\pi\) | ||||
−0.943567 | + | 0.331181i | \(0.892553\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 469.315i | − | 0.305976i | ||||||
\(134\) | −692.941 | − | 1419.51i | −0.446724 | − | 0.915124i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 336.503 | − | 1591.16i | 0.212168 | − | 1.00324i | ||||
\(137\) | −2070.09 | −1.29095 | −0.645474 | − | 0.763782i | \(-0.723340\pi\) | ||||
−0.645474 | + | 0.763782i | \(0.723340\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 288.330i | − | 0.175941i | −0.996123 | − | 0.0879707i | \(-0.971962\pi\) | ||
0.996123 | − | 0.0879707i | \(-0.0280382\pi\) | |||||||
\(140\) | 839.438 | + | 654.915i | 0.506753 | + | 0.395360i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −796.061 | + | 388.603i | −0.470450 | + | 0.229654i | ||||
\(143\) | −2781.62 | −1.62665 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1338.17 | 0.766404 | ||||||||
\(146\) | −670.832 | + | 327.471i | −0.380264 | + | 0.185628i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 473.514 | + | 369.427i | 0.262990 | + | 0.205181i | ||||
\(149\) | 900.665i | 0.495204i | 0.968862 | + | 0.247602i | \(0.0796425\pi\) | ||||
−0.968862 | + | 0.247602i | \(0.920358\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2005.71 | 1.08094 | 0.540472 | − | 0.841362i | \(-0.318246\pi\) | ||||
0.540472 | + | 0.841362i | \(0.318246\pi\) | |||||||
\(152\) | −390.332 | − | 82.5483i | −0.208290 | − | 0.0440497i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2038.62 | + | 4176.16i | 1.06673 | + | 2.18522i | ||||
\(155\) | 251.067i | 0.130104i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3098.13i | 1.57489i | 0.616385 | + | 0.787445i | \(0.288597\pi\) | ||||
−0.616385 | + | 0.787445i | \(0.711403\pi\) | |||||||
\(158\) | −1862.95 | + | 909.412i | −0.938027 | + | 0.457905i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 692.346 | − | 582.972i | 0.342092 | − | 0.288050i | ||||
\(161\) | −1155.54 | −0.565648 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3566.57i | − | 1.71383i | −0.515454 | − | 0.856917i | \(-0.672377\pi\) | ||
0.515454 | − | 0.856917i | \(-0.327623\pi\) | |||||||
\(164\) | 1090.91 | − | 1398.27i | 0.519424 | − | 0.665772i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −890.509 | − | 1824.23i | −0.416367 | − | 0.852936i | ||||
\(167\) | −1326.87 | −0.614830 | −0.307415 | − | 0.951576i | \(-0.599464\pi\) | ||||
−0.307415 | + | 0.951576i | \(0.599464\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 166.353 | 0.0757180 | ||||||||
\(170\) | 445.905 | + | 913.446i | 0.201173 | + | 0.412106i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1192.10 | + | 930.054i | 0.528469 | + | 0.412302i | ||||
\(173\) | 1035.22i | 0.454952i | 0.973784 | + | 0.227476i | \(0.0730473\pi\) | ||||
−0.973784 | + | 0.227476i | \(0.926953\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −665.433 | −0.287440 | ||||||||
\(176\) | 3831.91 | − | 960.983i | 1.64114 | − | 0.411573i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4154.96 | + | 2028.27i | −1.74959 | + | 0.854076i | ||||
\(179\) | 1811.28i | 0.756319i | 0.925740 | + | 0.378160i | \(0.123443\pi\) | ||||
−0.925740 | + | 0.378160i | \(0.876557\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2286.18i | − | 0.938842i | −0.882975 | − | 0.469421i | \(-0.844463\pi\) | ||
0.882975 | − | 0.469421i | \(-0.155537\pi\) | |||||||
\(182\) | 1488.24 | + | 3048.70i | 0.606131 | + | 1.24167i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −203.249 | + | 961.070i | −0.0814334 | + | 0.385060i | ||||
\(185\) | −375.360 | −0.149173 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4436.70i | 1.73499i | ||||||||
\(188\) | 1890.35 | − | 2422.96i | 0.733341 | − | 0.939960i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 224.080 | − | 109.386i | 0.0855603 | − | 0.0417669i | ||||
\(191\) | 2392.90 | 0.906513 | 0.453256 | − | 0.891380i | \(-0.350262\pi\) | ||||
0.453256 | + | 0.891380i | \(0.350262\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −638.414 | −0.238104 | −0.119052 | − | 0.992888i | \(-0.537985\pi\) | ||||
−0.119052 | + | 0.992888i | \(0.537985\pi\) | |||||||
\(194\) | −3474.88 | + | 1696.29i | −1.28599 | + | 0.627764i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1798.52 | − | 2305.26i | 0.655438 | − | 0.840109i | ||||
\(197\) | 654.303i | 0.236635i | 0.992976 | + | 0.118318i | \(0.0377501\pi\) | ||||
−0.992976 | + | 0.118318i | \(0.962250\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1637.06 | −0.583155 | −0.291578 | − | 0.956547i | \(-0.594180\pi\) | ||||
−0.291578 | + | 0.956547i | \(0.594180\pi\) | |||||||
\(200\) | −117.044 | + | 553.444i | −0.0413812 | + | 0.195672i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −72.3661 | − | 148.243i | −0.0252062 | − | 0.0516355i | ||||
\(203\) | − | 7123.67i | − | 2.46297i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1108.43i | 0.377638i | ||||||||
\(206\) | −24.6304 | + | 12.0235i | −0.00833048 | + | 0.00406658i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2797.39 | − | 701.541i | 0.932519 | − | 0.233861i | ||||
\(209\) | 1088.38 | 0.360214 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 2769.26i | − | 0.903524i | −0.892139 | − | 0.451762i | \(-0.850796\pi\) | ||
0.892139 | − | 0.451762i | \(-0.149204\pi\) | |||||||
\(212\) | 1560.75 | + | 1217.67i | 0.505627 | + | 0.394481i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −544.755 | − | 1115.94i | −0.174012 | − | 0.356468i | ||||
\(215\) | −944.990 | −0.299757 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1336.54 | 0.418113 | ||||||||
\(218\) | 2005.72 | + | 4108.76i | 0.623139 | + | 1.27651i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1518.80 | + | 1946.72i | −0.465443 | + | 0.596582i | ||||
\(221\) | 3238.90i | 0.985846i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4312.57 | −1.29503 | −0.647514 | − | 0.762054i | \(-0.724191\pi\) | ||||
−0.647514 | + | 0.762054i | \(0.724191\pi\) | |||||||
\(224\) | −3103.43 | − | 3685.68i | −0.925699 | − | 1.09937i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3256.60 | − | 1589.73i | 0.958523 | − | 0.467909i | ||||
\(227\) | − | 575.097i | − | 0.168152i | −0.996459 | − | 0.0840761i | \(-0.973206\pi\) | ||
0.996459 | − | 0.0840761i | \(-0.0267939\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2396.42i | 0.691529i | 0.938321 | + | 0.345765i | \(0.112380\pi\) | ||||
−0.938321 | + | 0.345765i | \(0.887620\pi\) | |||||||
\(230\) | −269.329 | − | 551.726i | −0.0772132 | − | 0.158173i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5924.80 | − | 1252.99i | −1.67665 | − | 0.354581i | ||||
\(233\) | −3307.22 | −0.929885 | −0.464943 | − | 0.885341i | \(-0.653925\pi\) | ||||
−0.464943 | + | 0.885341i | \(0.653925\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1920.71i | 0.533163i | ||||||||
\(236\) | −3271.02 | − | 2551.99i | −0.902227 | − | 0.703901i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4862.69 | − | 2373.76i | 1.32438 | − | 0.646504i | ||||
\(239\) | 1534.33 | 0.415262 | 0.207631 | − | 0.978207i | \(-0.433425\pi\) | ||||
0.207631 | + | 0.978207i | \(0.433425\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −461.143 | −0.123257 | −0.0616283 | − | 0.998099i | \(-0.519629\pi\) | ||||
−0.0616283 | + | 0.998099i | \(0.519629\pi\) | |||||||
\(242\) | −6301.77 | + | 3076.25i | −1.67394 | + | 0.817145i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −391.089 | − | 305.121i | −0.102610 | − | 0.0800547i | ||||
\(245\) | 1827.41i | 0.476526i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 794.543 | 0.204678 | ||||||||
\(248\) | 235.086 | − | 1111.61i | 0.0601935 | − | 0.284627i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −155.096 | − | 317.719i | −0.0392367 | − | 0.0803771i | ||||
\(251\) | − | 6200.39i | − | 1.55922i | −0.626263 | − | 0.779612i | \(-0.715416\pi\) | ||
0.626263 | − | 0.779612i | \(-0.284584\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2679.79i | − | 0.665917i | ||||||
\(254\) | 598.139 | − | 291.986i | 0.147758 | − | 0.0721291i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3611.27 | + | 1932.86i | −0.881657 | + | 0.471890i | ||||
\(257\) | 2381.71 | 0.578082 | 0.289041 | − | 0.957317i | \(-0.406664\pi\) | ||||
0.289041 | + | 0.957317i | \(0.406664\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1998.22i | 0.479394i | ||||||||
\(260\) | −1108.76 | + | 1421.16i | −0.264471 | + | 0.338986i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1232.24 | + | 2524.26i | 0.290564 | + | 0.595227i | ||||
\(263\) | 420.996 | 0.0987061 | 0.0493531 | − | 0.998781i | \(-0.484284\pi\) | ||||
0.0493531 | + | 0.998781i | \(0.484284\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1237.23 | −0.286801 | ||||||||
\(266\) | −582.313 | − | 1192.88i | −0.134225 | − | 0.274963i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3522.56 | − | 2748.24i | −0.802891 | − | 0.626402i | ||||
\(269\) | 6748.92i | 1.52970i | 0.644209 | + | 0.764849i | \(0.277187\pi\) | ||||
−0.644209 | + | 0.764849i | \(0.722813\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5718.47 | 1.28182 | 0.640908 | − | 0.767618i | \(-0.278558\pi\) | ||||
0.640908 | + | 0.767618i | \(0.278558\pi\) | |||||||
\(272\) | −1118.96 | − | 4461.86i | −0.249438 | − | 0.994631i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5261.65 | + | 2568.51i | −1.16010 | + | 0.566312i | ||||
\(275\) | − | 1543.19i | − | 0.338393i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 6245.97i | − | 1.35481i | −0.735608 | − | 0.677407i | \(-0.763103\pi\) | ||
0.735608 | − | 0.677407i | \(-0.236897\pi\) | |||||||
\(278\) | −357.752 | − | 732.863i | −0.0771818 | − | 0.158109i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2946.24 | + | 623.078i | 0.628827 | + | 0.132986i | ||||
\(281\) | −2883.17 | −0.612084 | −0.306042 | − | 0.952018i | \(-0.599005\pi\) | ||||
−0.306042 | + | 0.952018i | \(0.599005\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 7520.83i | − | 1.57974i | −0.613273 | − | 0.789871i | \(-0.710148\pi\) | ||
0.613273 | − | 0.789871i | \(-0.289852\pi\) | |||||||
\(284\) | −1541.22 | + | 1975.46i | −0.322023 | + | 0.412754i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7070.17 | + | 3451.35i | −1.46178 | + | 0.713576i | ||||
\(287\) | 5900.67 | 1.21361 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 253.072 | 0.0515107 | ||||||||
\(290\) | 3401.28 | − | 1660.36i | 0.688724 | − | 0.336205i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1298.77 | + | 1664.70i | −0.260290 | + | 0.333627i | ||||
\(293\) | − | 6762.89i | − | 1.34844i | −0.738531 | − | 0.674219i | \(-0.764480\pi\) | ||
0.738531 | − | 0.674219i | \(-0.235520\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2592.98 | 0.511760 | ||||||||
\(296\) | 1661.93 | + | 351.468i | 0.326343 | + | 0.0690158i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1117.52 | + | 2289.26i | 0.217236 | + | 0.445012i | ||||
\(299\) | − | 1956.31i | − | 0.378383i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5030.62i | 0.963323i | ||||||||
\(302\) | 5098.01 | − | 2488.63i | 0.971383 | − | 0.474187i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1094.55 | + | 274.496i | −0.206502 | + | 0.0517876i | ||||
\(305\) | 310.021 | 0.0582024 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10085.5i | − | 1.87495i | −0.348058 | − | 0.937473i | \(-0.613159\pi\) | ||
0.348058 | − | 0.937473i | \(-0.386841\pi\) | |||||||
\(308\) | 10363.3 | + | 8085.28i | 1.91722 | + | 1.49578i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 311.516 | + | 638.148i | 0.0570740 | + | 0.116917i | ||||
\(311\) | 7683.50 | 1.40094 | 0.700469 | − | 0.713683i | \(-0.252974\pi\) | ||||
0.700469 | + | 0.713683i | \(0.252974\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1253.17 | 0.226304 | 0.113152 | − | 0.993578i | \(-0.463905\pi\) | ||||
0.113152 | + | 0.993578i | \(0.463905\pi\) | |||||||
\(314\) | 3844.07 | + | 7874.67i | 0.690872 | + | 1.41527i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3606.78 | + | 4622.99i | −0.642079 | + | 0.822986i | ||||
\(317\) | − | 958.616i | − | 0.169846i | −0.996388 | − | 0.0849231i | \(-0.972936\pi\) | ||
0.996388 | − | 0.0849231i | \(-0.0270645\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16520.4 | 2.89957 | ||||||||
\(320\) | 1036.44 | − | 2340.81i | 0.181058 | − | 0.408923i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2937.09 | + | 1433.76i | −0.508316 | + | 0.248138i | ||||
\(323\) | − | 1267.30i | − | 0.218312i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1126.57i | − | 0.192279i | ||||||
\(326\) | −4425.29 | − | 9065.31i | −0.751823 | − | 1.54013i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1037.87 | − | 4907.62i | 0.174717 | − | 0.826152i | ||||
\(329\) | 10224.8 | 1.71341 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 4252.70i | − | 0.706192i | −0.935587 | − | 0.353096i | \(-0.885129\pi\) | ||
0.935587 | − | 0.353096i | \(-0.114871\pi\) | |||||||
\(332\) | −4526.90 | − | 3531.81i | −0.748331 | − | 0.583835i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3372.58 | + | 1646.35i | −0.552513 | + | 0.269713i | ||||
\(335\) | 2792.38 | 0.455415 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7662.86 | 1.23864 | 0.619321 | − | 0.785138i | \(-0.287408\pi\) | ||||
0.619321 | + | 0.785138i | \(0.287408\pi\) | |||||||
\(338\) | 422.826 | − | 206.406i | 0.0680435 | − | 0.0332159i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2266.76 | + | 1768.48i | 0.361565 | + | 0.282087i | ||||
\(341\) | 3099.55i | 0.492229i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 598.394 | 0.0941990 | ||||||||
\(344\) | 4184.00 | + | 884.841i | 0.655773 | + | 0.138684i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1284.48 | + | 2631.28i | 0.199578 | + | 0.408840i | ||||
\(347\) | 3626.75i | 0.561078i | 0.959843 | + | 0.280539i | \(0.0905132\pi\) | ||||
−0.959843 | + | 0.280539i | \(0.909487\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8867.03i | 1.36000i | 0.733210 | + | 0.680002i | \(0.238021\pi\) | ||||
−0.733210 | + | 0.680002i | \(0.761979\pi\) | |||||||
\(350\) | −1691.36 | + | 825.650i | −0.258306 | + | 0.126094i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8547.39 | − | 7197.10i | 1.29425 | − | 1.08979i | ||||
\(353\) | −8775.59 | −1.32317 | −0.661583 | − | 0.749872i | \(-0.730115\pi\) | ||||
−0.661583 | + | 0.749872i | \(0.730115\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1565.97i | − | 0.234121i | ||||||
\(356\) | −8044.24 | + | 10310.7i | −1.19760 | + | 1.53502i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2247.38 | + | 4603.81i | 0.331782 | + | 0.679662i | ||||
\(359\) | −7668.51 | −1.12738 | −0.563688 | − | 0.825988i | \(-0.690618\pi\) | ||||
−0.563688 | + | 0.825988i | \(0.690618\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6548.11 | 0.954675 | ||||||||
\(362\) | −2836.63 | − | 5810.89i | −0.411850 | − | 0.843684i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7565.47 | + | 5902.45i | 1.08939 | + | 0.849924i | ||||
\(365\) | − | 1319.63i | − | 0.189240i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8276.28 | −1.17716 | −0.588581 | − | 0.808438i | \(-0.700313\pi\) | ||||
−0.588581 | + | 0.808438i | \(0.700313\pi\) | |||||||
\(368\) | 675.860 | + | 2694.99i | 0.0957382 | + | 0.381755i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −954.071 | + | 465.736i | −0.134053 | + | 0.0654391i | ||||
\(371\) | 6586.33i | 0.921685i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 270.669i | 0.0375730i | 0.999824 | + | 0.0187865i | \(0.00598028\pi\) | ||||
−0.999824 | + | 0.0187865i | \(0.994020\pi\) | |||||||
\(374\) | 5504.93 | + | 11277.0i | 0.761105 | + | 1.55914i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1798.46 | − | 8504.05i | 0.246671 | − | 1.16639i | ||||
\(377\) | 12060.3 | 1.64757 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8455.66i | 1.14601i | 0.819551 | + | 0.573006i | \(0.194223\pi\) | ||||
−0.819551 | + | 0.573006i | \(0.805777\pi\) | |||||||
\(380\) | 433.831 | − | 556.064i | 0.0585660 | − | 0.0750671i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6082.14 | − | 2969.04i | 0.814632 | − | 0.397668i | ||||
\(383\) | 6527.25 | 0.870827 | 0.435414 | − | 0.900231i | \(-0.356602\pi\) | ||||
0.435414 | + | 0.900231i | \(0.356602\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8215.13 | −1.08748 | ||||||||
\(386\) | −1622.69 | + | 792.126i | −0.213971 | + | 0.104451i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6727.57 | + | 8623.07i | −0.880259 | + | 1.12827i | ||||
\(389\) | 683.173i | 0.0890443i | 0.999008 | + | 0.0445222i | \(0.0141765\pi\) | ||||
−0.999008 | + | 0.0445222i | \(0.985823\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3120.34 | −0.403586 | ||||||||
\(392\) | 1711.09 | − | 8090.95i | 0.220467 | − | 1.04249i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 811.840 | + | 1663.07i | 0.103807 | + | 0.212651i | ||||
\(395\) | − | 3664.70i | − | 0.466813i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2579.34i | − | 0.326079i | −0.986620 | − | 0.163040i | \(-0.947870\pi\) | ||
0.986620 | − | 0.163040i | \(-0.0521298\pi\) | |||||||
\(398\) | −4160.99 | + | 2031.21i | −0.524049 | + | 0.255818i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 389.203 | + | 1551.94i | 0.0486503 | + | 0.193993i | ||||
\(401\) | 8344.02 | 1.03910 | 0.519552 | − | 0.854439i | \(-0.326099\pi\) | ||||
0.519552 | + | 0.854439i | \(0.326099\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2262.75i | 0.279691i | ||||||||
\(404\) | −367.873 | − | 287.008i | −0.0453028 | − | 0.0353445i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8838.85 | − | 18106.6i | −1.08046 | − | 2.21334i | ||||
\(407\) | −4634.02 | −0.564373 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1939.68 | 0.234501 | 0.117251 | − | 0.993102i | \(-0.462592\pi\) | ||||
0.117251 | + | 0.993102i | \(0.462592\pi\) | |||||||
\(410\) | 1375.30 | + | 2817.34i | 0.165662 | + | 0.339362i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −47.6858 | + | 61.1213i | −0.00570221 | + | 0.00730881i | ||||
\(413\) | − | 13803.6i | − | 1.64463i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3588.53 | 0.424467 | ||||||||
\(416\) | 6239.80 | − | 5254.06i | 0.735412 | − | 0.619234i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2766.39 | − | 1350.43i | 0.323704 | − | 0.158018i | ||||
\(419\) | − | 4046.49i | − | 0.471799i | −0.971777 | − | 0.235900i | \(-0.924196\pi\) | ||
0.971777 | − | 0.235900i | \(-0.0758037\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 3305.28i | − | 0.382636i | −0.981528 | − | 0.191318i | \(-0.938724\pi\) | ||
0.981528 | − | 0.191318i | \(-0.0612761\pi\) | |||||||
\(422\) | −3436.02 | − | 7038.76i | −0.396357 | − | 0.811946i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5477.89 | + | 1158.48i | 0.627429 | + | 0.132690i | ||||
\(425\) | −1796.88 | −0.205086 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1650.38i | − | 0.187044i | ||||||
\(428\) | −2769.26 | − | 2160.53i | −0.312750 | − | 0.244002i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2401.93 | + | 1172.52i | −0.269375 | + | 0.131497i | ||||
\(431\) | 2953.12 | 0.330038 | 0.165019 | − | 0.986290i | \(-0.447231\pi\) | ||||
0.165019 | + | 0.986290i | \(0.447231\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1380.70 | 0.153239 | 0.0766193 | − | 0.997060i | \(-0.475587\pi\) | ||||
0.0766193 | + | 0.997060i | \(0.475587\pi\) | |||||||
\(434\) | 3397.16 | − | 1658.35i | 0.375735 | − | 0.183417i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10196.1 | + | 7954.79i | 1.11996 | + | 0.873774i | ||||
\(437\) | 765.458i | 0.0837914i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14233.4 | −1.54743 | −0.773717 | − | 0.633532i | \(-0.781605\pi\) | ||||
−0.773717 | + | 0.633532i | \(0.781605\pi\) | |||||||
\(440\) | −1444.97 | + | 6832.57i | −0.156559 | + | 0.740295i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4018.74 | + | 8232.47i | 0.432470 | + | 0.885924i | ||||
\(443\) | 8541.25i | 0.916042i | 0.888941 | + | 0.458021i | \(0.151442\pi\) | ||||
−0.888941 | + | 0.458021i | \(0.848558\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 8173.43i | − | 0.870692i | ||||||
\(446\) | −10961.5 | + | 5350.92i | −1.16377 | + | 0.568101i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −12461.2 | − | 5517.42i | −1.31415 | − | 0.581861i | ||||
\(449\) | −9994.76 | −1.05052 | −0.525258 | − | 0.850943i | \(-0.676031\pi\) | ||||
−0.525258 | + | 0.850943i | \(0.676031\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13684.1i | 1.42874i | ||||||||
\(452\) | 6304.97 | − | 8081.41i | 0.656108 | − | 0.840968i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −713.564 | − | 1461.75i | −0.0737648 | − | 0.151109i | ||||
\(455\) | −5997.24 | −0.617923 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6435.58 | 0.658739 | 0.329370 | − | 0.944201i | \(-0.393164\pi\) | ||||
0.329370 | + | 0.944201i | \(0.393164\pi\) | |||||||
\(458\) | 2973.42 | + | 6091.11i | 0.303359 | + | 0.621438i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1369.13 | − | 1068.17i | −0.138774 | − | 0.108269i | ||||
\(461\) | 7851.78i | 0.793262i | 0.917978 | + | 0.396631i | \(0.129821\pi\) | ||||
−0.917978 | + | 0.396631i | \(0.870179\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7073.58 | 0.710016 | 0.355008 | − | 0.934863i | \(-0.384478\pi\) | ||||
0.355008 | + | 0.934863i | \(0.384478\pi\) | |||||||
\(464\) | −16614.0 | + | 4166.54i | −1.66226 | + | 0.416868i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8406.12 | + | 4103.51i | −0.835635 | + | 0.407921i | ||||
\(467\) | − | 15753.8i | − | 1.56102i | −0.625142 | − | 0.780511i | \(-0.714959\pi\) | ||
0.625142 | − | 0.780511i | \(-0.285041\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 14865.1i | − | 1.46356i | ||||||
\(470\) | 2383.16 | + | 4881.96i | 0.233887 | + | 0.479124i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11480.6 | − | 2427.94i | −1.11957 | − | 0.236769i | ||||
\(473\) | −11666.4 | −1.13408 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 440.799i | 0.0425794i | ||||||||
\(476\) | 9414.46 | − | 12067.0i | 0.906535 | − | 1.16195i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3899.88 | − | 1903.75i | 0.373172 | − | 0.182167i | ||||
\(479\) | −14747.9 | −1.40678 | −0.703391 | − | 0.710803i | \(-0.748332\pi\) | ||||
−0.703391 | + | 0.710803i | \(0.748332\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3382.95 | −0.320684 | ||||||||
\(482\) | −1172.11 | + | 572.173i | −0.110764 | + | 0.0540701i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12200.6 | + | 15638.1i | −1.14581 | + | 1.46864i | ||||
\(485\) | − | 6835.61i | − | 0.639977i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5631.77 | 0.524024 | 0.262012 | − | 0.965065i | \(-0.415614\pi\) | ||||
0.262012 | + | 0.965065i | \(0.415614\pi\) | |||||||
\(488\) | −1372.63 | − | 290.288i | −0.127328 | − | 0.0269277i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2267.40 | + | 4644.81i | 0.209042 | + | 0.428227i | ||||
\(491\) | 18259.0i | 1.67824i | 0.543945 | + | 0.839121i | \(0.316930\pi\) | ||||
−0.543945 | + | 0.839121i | \(0.683070\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 19236.2i | − | 1.75731i | ||||||
\(494\) | 2019.53 | − | 985.847i | 0.183933 | − | 0.0897882i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −781.726 | − | 3117.12i | −0.0707672 | − | 0.282183i | ||||
\(497\) | −8336.39 | −0.752391 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 729.599i | − | 0.0654536i | −0.999464 | − | 0.0327268i | \(-0.989581\pi\) | ||
0.999464 | − | 0.0327268i | \(-0.0104191\pi\) | |||||||
\(500\) | −788.433 | − | 615.121i | −0.0705195 | − | 0.0550181i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7693.27 | − | 15759.8i | −0.683999 | − | 1.40119i | ||||
\(503\) | −1551.81 | −0.137558 | −0.0687790 | − | 0.997632i | \(-0.521910\pi\) | ||||
−0.0687790 | + | 0.997632i | \(0.521910\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 291.617 | 0.0256966 | ||||||||
\(506\) | −3325.01 | − | 6811.36i | −0.292124 | − | 0.598423i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1158.03 | − | 1484.31i | 0.101140 | − | 0.129637i | ||||
\(509\) | − | 6145.59i | − | 0.535164i | −0.963535 | − | 0.267582i | \(-0.913775\pi\) | ||
0.963535 | − | 0.267582i | \(-0.0862247\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7024.99 | −0.608155 | ||||||||
\(512\) | −6780.69 | + | 9393.61i | −0.585287 | + | 0.810826i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6053.71 | − | 2955.16i | 0.519490 | − | 0.253593i | ||||
\(515\) | − | 48.4516i | − | 0.00414569i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23712.2i | 2.01714i | ||||||||
\(518\) | 2479.33 | + | 5078.96i | 0.210300 | + | 0.430804i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1054.86 | + | 4987.94i | −0.0889591 | + | 0.420646i | ||||
\(521\) | −588.432 | −0.0494812 | −0.0247406 | − | 0.999694i | \(-0.507876\pi\) | ||||
−0.0247406 | + | 0.999694i | \(0.507876\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 866.147i | 0.0724168i | 0.999344 | + | 0.0362084i | \(0.0115280\pi\) | ||||
−0.999344 | + | 0.0362084i | \(0.988472\pi\) | |||||||
\(524\) | 6264.07 | + | 4887.12i | 0.522228 | + | 0.407433i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1070.07 | − | 522.360i | 0.0887016 | − | 0.0433003i | ||||
\(527\) | 3609.10 | 0.298321 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10282.3 | −0.845097 | ||||||||
\(530\) | −3144.72 | + | 1535.12i | −0.257732 | + | 0.125814i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2960.19 | − | 2309.49i | −0.241241 | − | 0.188212i | ||||
\(533\) | 9989.74i | 0.811827i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2195.22 | 0.177398 | ||||||||
\(536\) | −12363.4 | − | 2614.64i | −0.996303 | − | 0.210700i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8373.87 | + | 17154.1i | 0.671047 | + | 1.37465i | ||||
\(539\) | 22560.3i | 1.80286i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10380.3i | 0.824926i | 0.910974 | + | 0.412463i | \(0.135331\pi\) | ||||
−0.910974 | + | 0.412463i | \(0.864669\pi\) | |||||||
\(542\) | 14534.9 | − | 7095.31i | 1.15190 | − | 0.562306i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8380.27 | − | 9952.53i | −0.660480 | − | 0.784396i | ||||
\(545\) | −8082.54 | −0.635262 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1208.43i | 0.0944584i | 0.998884 | + | 0.0472292i | \(0.0150391\pi\) | ||||
−0.998884 | + | 0.0472292i | \(0.984961\pi\) | |||||||
\(548\) | −10186.9 | + | 13057.0i | −0.794090 | + | 1.01783i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1914.75 | − | 3922.41i | −0.148446 | − | 0.304094i | ||||
\(551\) | −4718.89 | −0.364849 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19508.9 | −1.50019 | ||||||||
\(554\) | −7749.82 | − | 15875.7i | −0.594329 | − | 1.21750i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1818.63 | − | 1418.86i | −0.138718 | − | 0.108225i | ||||
\(557\) | 10284.9i | 0.782379i | 0.920310 | + | 0.391190i | \(0.127936\pi\) | ||||
−0.920310 | + | 0.391190i | \(0.872064\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8516.76 | −0.644402 | ||||||||
\(560\) | 8261.70 | − | 2071.91i | 0.623430 | − | 0.156346i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7328.29 | + | 3577.36i | −0.550045 | + | 0.268508i | ||||
\(563\) | − | 18420.7i | − | 1.37894i | −0.724316 | − | 0.689469i | \(-0.757844\pi\) | ||
0.724316 | − | 0.689469i | \(-0.242156\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6406.23i | 0.477013i | ||||||||
\(566\) | −9331.63 | − | 19116.1i | −0.693000 | − | 1.41963i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1466.30 | + | 6933.43i | −0.108318 | + | 0.512183i | ||||
\(569\) | 13111.3 | 0.966002 | 0.483001 | − | 0.875620i | \(-0.339547\pi\) | ||||
0.483001 | + | 0.875620i | \(0.339547\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12226.6i | 0.896088i | 0.894012 | + | 0.448044i | \(0.147879\pi\) | ||||
−0.894012 | + | 0.448044i | \(0.852121\pi\) | |||||||
\(572\) | −13688.3 | + | 17544.9i | −1.00058 | + | 1.28250i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14998.0 | − | 7321.38i | 1.09060 | − | 0.532384i | ||||
\(575\) | 1085.33 | 0.0787153 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3294.12 | 0.237671 | 0.118836 | − | 0.992914i | \(-0.462084\pi\) | ||||
0.118836 | + | 0.992914i | \(0.462084\pi\) | |||||||
\(578\) | 643.246 | − | 314.005i | 0.0462898 | − | 0.0225967i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6585.07 | − | 8440.42i | 0.471431 | − | 0.604258i | ||||
\(581\) | − | 19103.4i | − | 1.36410i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15274.2 | −1.08507 | ||||||||
\(584\) | −1235.63 | + | 5842.73i | −0.0875529 | + | 0.413996i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8391.21 | − | 17189.6i | −0.591532 | − | 1.21177i | ||||
\(587\) | 16607.6i | 1.16775i | 0.811844 | + | 0.583874i | \(0.198464\pi\) | ||||
−0.811844 | + | 0.583874i | \(0.801536\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 885.358i | − | 0.0619364i | ||||||
\(590\) | 6590.70 | − | 3217.30i | 0.459890 | − | 0.224498i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4660.29 | − | 1168.73i | 0.323542 | − | 0.0811393i | ||||
\(593\) | 15288.4 | 1.05872 | 0.529359 | − | 0.848398i | \(-0.322433\pi\) | ||||
0.529359 | + | 0.848398i | \(0.322433\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9565.65i | 0.659081i | ||||||||
\(596\) | 5680.91 | + | 4432.15i | 0.390435 | + | 0.304610i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2427.34 | − | 4972.46i | −0.165989 | − | 0.340032i | ||||
\(599\) | 23543.0 | 1.60591 | 0.802955 | − | 0.596040i | \(-0.203260\pi\) | ||||
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15689.7 | −1.06488 | −0.532442 | − | 0.846467i | \(-0.678725\pi\) | ||||
−0.532442 | + | 0.846467i | \(0.678725\pi\) | |||||||
\(602\) | 6241.85 | + | 12786.6i | 0.422590 | + | 0.865684i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9870.05 | − | 12650.9i | 0.664911 | − | 0.852251i | ||||
\(605\) | − | 12396.5i | − | 0.833043i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26462.9 | −1.76952 | −0.884759 | − | 0.466048i | \(-0.845677\pi\) | ||||
−0.884759 | + | 0.466048i | \(0.845677\pi\) | |||||||
\(608\) | −2441.48 | + | 2055.79i | −0.162854 | + | 0.137127i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 787.995 | − | 384.665i | 0.0523032 | − | 0.0255322i | ||||
\(611\) | 17310.5i | 1.14617i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18256.6i | 1.20290i | 0.798912 | + | 0.601448i | \(0.205409\pi\) | ||||
−0.798912 | + | 0.601448i | \(0.794591\pi\) | |||||||
\(614\) | −12513.8 | − | 25634.7i | −0.822500 | − | 1.68491i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 36372.9 | + | 7692.23i | 2.37907 | + | 0.503131i | ||||
\(617\) | −393.579 | −0.0256805 | −0.0128403 | − | 0.999918i | \(-0.504087\pi\) | ||||
−0.0128403 | + | 0.999918i | \(0.504087\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 23039.6i | − | 1.49602i | −0.663685 | − | 0.748012i | \(-0.731009\pi\) | ||
0.663685 | − | 0.748012i | \(-0.268991\pi\) | |||||||
\(620\) | 1583.59 | + | 1235.49i | 0.102578 | + | 0.0800299i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19529.5 | − | 9533.47i | 1.25894 | − | 0.614562i | ||||
\(623\) | −43511.0 | −2.79812 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 3185.24 | − | 1554.90i | 0.203367 | − | 0.0992750i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19541.3 | + | 15245.8i | 1.24169 | + | 0.968749i | ||||
\(629\) | 5395.83i | 0.342044i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28960.4 | 1.82709 | 0.913547 | − | 0.406734i | \(-0.133332\pi\) | ||||
0.913547 | + | 0.406734i | \(0.133332\pi\) | |||||||
\(632\) | −3431.44 | + | 16225.7i | −0.215974 | + | 1.02124i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1189.42 | − | 2436.56i | −0.0745080 | − | 0.152631i | ||||
\(635\) | 1176.63i | 0.0735324i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16469.6i | 1.02441i | ||||||||
\(638\) | 41990.6 | − | 20498.0i | 2.60568 | − | 1.27198i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −270.057 | − | 7235.74i | −0.0166796 | − | 0.446902i | ||||
\(641\) | 7160.30 | 0.441209 | 0.220604 | − | 0.975363i | \(-0.429197\pi\) | ||||
0.220604 | + | 0.975363i | \(0.429197\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1843.33i | − | 0.113054i | −0.998401 | − | 0.0565270i | \(-0.981997\pi\) | ||
0.998401 | − | 0.0565270i | \(-0.0180027\pi\) | |||||||
\(644\) | −5686.38 | + | 7288.53i | −0.347942 | + | 0.445976i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1572.43 | − | 3221.17i | −0.0957687 | − | 0.196184i | ||||
\(647\) | −28494.4 | −1.73142 | −0.865712 | − | 0.500542i | \(-0.833134\pi\) | ||||
−0.865712 | + | 0.500542i | \(0.833134\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32011.7 | 1.93616 | ||||||||
\(650\) | −1397.81 | − | 2863.45i | −0.0843489 | − | 0.172790i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −22496.0 | − | 17551.0i | −1.35124 | − | 1.05422i | ||||
\(653\) | − | 15898.2i | − | 0.952746i | −0.879243 | − | 0.476373i | \(-0.841951\pi\) | ||
0.879243 | − | 0.476373i | \(-0.158049\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4965.61 | −0.296217 | ||||||||
\(656\) | −3451.22 | − | 13761.7i | −0.205408 | − | 0.819061i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 25988.9 | − | 12686.7i | 1.53975 | − | 0.751639i | ||||
\(659\) | − | 6729.26i | − | 0.397776i | −0.980022 | − | 0.198888i | \(-0.936267\pi\) | ||
0.980022 | − | 0.198888i | \(-0.0637331\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 24516.3i | − | 1.44262i | −0.692611 | − | 0.721311i | \(-0.743540\pi\) | ||
0.692611 | − | 0.721311i | \(-0.256460\pi\) | |||||||
\(662\) | −5276.63 | − | 10809.3i | −0.309792 | − | 0.634615i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15888.4 | − | 3360.12i | −0.928599 | − | 0.196382i | ||||
\(665\) | 2346.58 | 0.136837 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11618.8i | 0.674485i | ||||||||
\(668\) | −6529.51 | + | 8369.20i | −0.378195 | + | 0.484752i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7097.53 | − | 3464.71i | 0.409256 | − | 0.199781i | ||||
\(671\) | 3827.37 | 0.220200 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8192.84 | −0.469258 | −0.234629 | − | 0.972085i | \(-0.575388\pi\) | ||||
−0.234629 | + | 0.972085i | \(0.575388\pi\) | |||||||
\(674\) | 19477.1 | − | 9507.86i | 1.11310 | − | 0.543367i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 818.616 | − | 1049.26i | 0.0465758 | − | 0.0596986i | ||||
\(677\) | 5219.11i | 0.296287i | 0.988966 | + | 0.148144i | \(0.0473298\pi\) | ||||
−0.988966 | + | 0.148144i | \(0.952670\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36389.1 | −2.05668 | ||||||||
\(680\) | 7955.81 | + | 1682.51i | 0.448664 | + | 0.0948844i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3845.84 | + | 7878.28i | 0.215931 | + | 0.442339i | ||||
\(683\) | 7903.11i | 0.442759i | 0.975188 | + | 0.221379i | \(0.0710559\pi\) | ||||
−0.975188 | + | 0.221379i | \(0.928944\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 10350.5i | − | 0.577330i | ||||||
\(686\) | 1520.97 | − | 742.471i | 0.0846513 | − | 0.0413231i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11732.6 | − | 2942.34i | 0.650144 | − | 0.163046i | ||||
\(689\) | −11150.6 | −0.616549 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13969.2i | 0.769051i | 0.923114 | + | 0.384526i | \(0.125635\pi\) | ||||
−0.923114 | + | 0.384526i | \(0.874365\pi\) | |||||||
\(692\) | 6529.64 | + | 5094.31i | 0.358699 | + | 0.279851i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4499.97 | + | 9218.28i | 0.246133 | + | 0.504209i | ||||
\(695\) | 1441.65 | 0.0786834 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15933.7 | 0.865900 | ||||||||
\(698\) | 11002.0 | + | 22537.8i | 0.596605 | + | 1.22216i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3274.58 | + | 4197.19i | −0.176810 | + | 0.226627i | ||||
\(701\) | − | 1929.28i | − | 0.103948i | −0.998648 | − | 0.0519742i | \(-0.983449\pi\) | ||
0.998648 | − | 0.0519742i | \(-0.0165514\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1323.67 | 0.0710142 | ||||||||
\(704\) | 12795.3 | − | 28898.6i | 0.685004 | − | 1.54710i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22305.3 | + | 10888.5i | −1.18905 | + | 0.580445i | ||||
\(707\) | − | 1552.41i | − | 0.0825806i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33077.6i | 1.75213i | 0.482197 | + | 0.876063i | \(0.339839\pi\) | ||||
−0.482197 | + | 0.876063i | \(0.660161\pi\) | |||||||
\(710\) | −1943.01 | − | 3980.31i | −0.102704 | − | 0.210392i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7653.19 | + | 36188.3i | −0.402831 | + | 1.90480i | ||||
\(713\) | −2179.92 | −0.114500 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 13908.1i | − | 0.727458i | ||||||
\(716\) | 11424.6 | + | 8913.24i | 0.596307 | + | 0.465228i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19491.4 | + | 9514.87i | −1.01311 | + | 0.494557i | ||||
\(719\) | 5643.22 | 0.292707 | 0.146354 | − | 0.989232i | \(-0.453246\pi\) | ||||
0.146354 | + | 0.989232i | \(0.453246\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −257.930 | −0.0133229 | ||||||||
\(722\) | 16643.7 | − | 8124.72i | 0.857913 | − | 0.418796i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14420.0 | − | 11250.2i | −0.740213 | − | 0.577502i | ||||
\(725\) | 6690.83i | 0.342746i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17112.0 | 0.872969 | 0.436484 | − | 0.899712i | \(-0.356223\pi\) | ||||
0.436484 | + | 0.899712i | \(0.356223\pi\) | |||||||
\(728\) | 26553.1 | + | 5615.52i | 1.35182 | + | 0.285886i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1637.36 | − | 3354.16i | −0.0830155 | − | 0.170059i | ||||
\(731\) | 13584.3i | 0.687324i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 20314.2i | − | 1.02363i | −0.859095 | − | 0.511817i | \(-0.828973\pi\) | ||
0.859095 | − | 0.511817i | \(-0.171027\pi\) | |||||||
\(734\) | −21036.2 | + | 10269.0i | −1.05785 | + | 0.516396i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5061.73 | + | 6011.39i | 0.253502 | + | 0.301063i | ||||
\(737\) | 34473.4 | 1.72299 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 5845.97i | − | 0.290998i | −0.989358 | − | 0.145499i | \(-0.953521\pi\) | ||
0.989358 | − | 0.145499i | \(-0.0464788\pi\) | |||||||
\(740\) | −1847.14 | + | 2367.57i | −0.0917595 | + | 0.117613i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8172.13 | + | 16740.8i | 0.404324 | + | 0.828267i | ||||
\(743\) | −4964.00 | −0.245103 | −0.122551 | − | 0.992462i | \(-0.539108\pi\) | ||||
−0.122551 | + | 0.992462i | \(0.539108\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4503.32 | −0.221462 | ||||||||
\(746\) | 335.839 | + | 687.973i | 0.0164825 | + | 0.0337647i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 27984.3 | + | 21832.9i | 1.36793 | + | 1.06723i | ||||
\(749\) | − | 11686.2i | − | 0.570099i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30765.7 | 1.49488 | 0.747441 | − | 0.664329i | \(-0.231282\pi\) | ||||
0.747441 | + | 0.664329i | \(0.231282\pi\) | |||||||
\(752\) | −5980.36 | − | 23846.6i | −0.290002 | − | 1.15638i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 30654.2 | − | 14964.0i | 1.48058 | − | 0.722756i | ||||
\(755\) | 10028.6i | 0.483413i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 34346.8i | − | 1.64908i | −0.565801 | − | 0.824542i | \(-0.691433\pi\) | ||
0.565801 | − | 0.824542i | \(-0.308567\pi\) | |||||||
\(758\) | 10491.5 | + | 21492.2i | 0.502731 | + | 1.02986i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 412.742 | − | 1951.66i | 0.0196996 | − | 0.0931502i | ||||
\(761\) | 12083.9 | 0.575610 | 0.287805 | − | 0.957689i | \(-0.407074\pi\) | ||||
0.287805 | + | 0.957689i | \(0.407074\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43027.1i | 2.04153i | ||||||||
\(764\) | 11775.4 | − | 15093.1i | 0.557615 | − | 0.714724i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16590.6 | − | 8098.82i | 0.782563 | − | 0.382014i | ||||
\(767\) | 23369.3 | 1.10015 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9054.84 | 0.424611 | 0.212305 | − | 0.977203i | \(-0.431903\pi\) | ||||
0.212305 | + | 0.977203i | \(0.431903\pi\) | |||||||
\(770\) | −20880.8 | + | 10193.1i | −0.977261 | + | 0.477057i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3141.62 | + | 4026.77i | −0.146463 | + | 0.187729i | ||||
\(773\) | − | 13846.2i | − | 0.644260i | −0.946695 | − | 0.322130i | \(-0.895601\pi\) | ||
0.946695 | − | 0.322130i | \(-0.104399\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1255.33 | −0.0581844 | ||||||||
\(776\) | −6400.52 | + | 30265.0i | −0.296089 | + | 1.40007i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 847.662 | + | 1736.45i | 0.0390619 | + | 0.0800191i | ||||
\(779\) | − | 3908.74i | − | 0.179776i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 19332.8i | − | 0.885762i | ||||||
\(782\) | −7931.11 | + | 3871.63i | −0.362680 | + | 0.177045i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5689.85 | − | 22688.2i | −0.259195 | − | 1.03354i | ||||
\(785\) | −15490.7 | −0.704312 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9393.21i | 0.425454i | 0.977112 | + | 0.212727i | \(0.0682344\pi\) | ||||
−0.977112 | + | 0.212727i | \(0.931766\pi\) | |||||||
\(788\) | 4126.99 | + | 3219.80i | 0.186571 | + | 0.145559i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4547.06 | − | 9314.75i | −0.204781 | − | 0.419499i | ||||
\(791\) | 34103.3 | 1.53296 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2794.08 | 0.125120 | ||||||||
\(794\) | −3200.37 | − | 6556.04i | −0.143044 | − | 0.293029i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8055.91 | + | 10325.7i | −0.358711 | + | 0.459779i | ||||
\(797\) | − | 7921.92i | − | 0.352081i | −0.984383 | − | 0.176041i | \(-0.943671\pi\) | ||
0.984383 | − | 0.176041i | \(-0.0563290\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27610.4 | 1.22251 | ||||||||
\(800\) | 2914.86 | + | 3461.73i | 0.128820 | + | 0.152988i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21208.4 | − | 10353.0i | 0.933784 | − | 0.455833i | ||||
\(803\) | − | 16291.5i | − | 0.715959i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 5777.71i | − | 0.252966i | ||||||
\(806\) | 2807.55 | + | 5751.34i | 0.122695 | + | 0.251343i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1291.15 | − | 273.056i | −0.0562160 | − | 0.0118887i | ||||
\(809\) | −8042.02 | −0.349496 | −0.174748 | − | 0.984613i | \(-0.555911\pi\) | ||||
−0.174748 | + | 0.984613i | \(0.555911\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28973.7i | 1.25451i | 0.778816 | + | 0.627253i | \(0.215821\pi\) | ||||
−0.778816 | + | 0.627253i | \(0.784179\pi\) | |||||||
\(812\) | −44932.3 | − | 35055.4i | −1.94189 | − | 1.51503i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11778.5 | + | 5749.76i | −0.507170 | + | 0.247579i | ||||
\(815\) | 17832.8 | 0.766450 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3332.40 | 0.142700 | ||||||||
\(818\) | 4930.18 | − | 2406.70i | 0.210733 | − | 0.102871i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6991.36 | + | 5454.53i | 0.297742 | + | 0.232293i | ||||
\(821\) | 11126.0i | 0.472960i | 0.971636 | + | 0.236480i | \(0.0759937\pi\) | ||||
−0.971636 | + | 0.236480i | \(0.924006\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3077.71 | 0.130355 | 0.0651775 | − | 0.997874i | \(-0.479239\pi\) | ||||
0.0651775 | + | 0.997874i | \(0.479239\pi\) | |||||||
\(824\) | −45.3676 | + | 214.522i | −0.00191803 | + | 0.00906946i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17127.2 | − | 35085.4i | −0.721465 | − | 1.47794i | ||||
\(827\) | 37902.1i | 1.59369i | 0.604181 | + | 0.796847i | \(0.293501\pi\) | ||||
−0.604181 | + | 0.796847i | \(0.706499\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 38596.7i | − | 1.61703i | −0.588474 | − | 0.808516i | \(-0.700271\pi\) | ||
0.588474 | − | 0.808516i | \(-0.299729\pi\) | |||||||
\(830\) | 9121.13 | − | 4452.54i | 0.381445 | − | 0.186205i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9340.92 | − | 21096.7i | 0.389228 | − | 0.879081i | ||||
\(833\) | 26269.1 | 1.09264 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 6634.37i | − | 0.274960i | ||||||
\(836\) | 5355.88 | − | 6864.91i | 0.221575 | − | 0.284005i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5020.77 | − | 10285.2i | −0.206968 | − | 0.423979i | ||||
\(839\) | 7585.24 | 0.312123 | 0.156062 | − | 0.987747i | \(-0.450120\pi\) | ||||
0.156062 | + | 0.987747i | \(0.450120\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −47238.4 | −1.93687 | ||||||||
\(842\) | −4101.10 | − | 8401.20i | −0.167854 | − | 0.343853i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17467.0 | − | 13627.4i | −0.712368 | − | 0.555777i | ||||
\(845\) | 831.763i | 0.0338621i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −65992.5 | −2.67713 | ||||||||
\(848\) | 15360.8 | − | 3852.26i | 0.622044 | − | 0.155999i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4567.23 | + | 2229.52i | −0.184300 | + | 0.0899671i | ||||
\(851\) | − | 3259.11i | − | 0.131282i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37228.6i | 1.49435i | 0.664625 | + | 0.747177i | \(0.268591\pi\) | ||||
−0.664625 | + | 0.747177i | \(0.731409\pi\) | |||||||
\(854\) | −2047.75 | − | 4194.86i | −0.0820522 | − | 0.168086i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9719.48 | − | 2055.50i | −0.388090 | − | 0.0820741i | ||||
\(857\) | −7510.28 | −0.299354 | −0.149677 | − | 0.988735i | \(-0.547823\pi\) | ||||
−0.149677 | + | 0.988735i | \(0.547823\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19383.6i | 0.769918i | 0.922934 | + | 0.384959i | \(0.125784\pi\) | ||||
−0.922934 | + | 0.384959i | \(0.874216\pi\) | |||||||
\(860\) | −4650.27 | + | 5960.49i | −0.184387 | + | 0.236338i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7506.08 | − | 3664.14i | 0.296587 | − | 0.144781i | ||||
\(863\) | −7835.20 | −0.309054 | −0.154527 | − | 0.987989i | \(-0.549385\pi\) | ||||
−0.154527 | + | 0.987989i | \(0.549385\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5176.12 | −0.203461 | ||||||||
\(866\) | 3509.40 | − | 1713.14i | 0.137707 | − | 0.0672226i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6577.09 | − | 8430.20i | 0.257190 | − | 0.329654i | ||||
\(869\) | − | 45242.7i | − | 1.76611i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25166.4 | 0.979026 | ||||||||
\(872\) | 35785.9 | + | 7568.09i | 1.38975 | + | 0.293908i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 949.759 | + | 1945.60i | 0.0367575 | + | 0.0752986i | ||||
\(875\) | − | 3327.16i | − | 0.128547i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8353.53i | 0.321640i | 0.986984 | + | 0.160820i | \(0.0514139\pi\) | ||||
−0.986984 | + | 0.160820i | \(0.948586\pi\) | |||||||
\(878\) | −36177.7 | + | 17660.4i | −1.39059 | + | 0.678827i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4804.92 | + | 19159.5i | 0.184061 | + | 0.733941i | ||||
\(881\) | −17964.9 | −0.687008 | −0.343504 | − | 0.939151i | \(-0.611614\pi\) | ||||
−0.343504 | + | 0.939151i | \(0.611614\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 34012.6i | − | 1.29628i | −0.761521 | − | 0.648140i | \(-0.775547\pi\) | ||
0.761521 | − | 0.648140i | \(-0.224453\pi\) | |||||||
\(884\) | 20429.2 | + | 15938.5i | 0.777273 | + | 0.606415i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10597.7 | + | 21709.7i | 0.401849 | + | 0.823196i | ||||
\(887\) | −32352.3 | −1.22467 | −0.612335 | − | 0.790598i | \(-0.709770\pi\) | ||||
−0.612335 | + | 0.790598i | \(0.709770\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6263.74 | 0.236309 | ||||||||
\(890\) | −10141.4 | − | 20774.8i | −0.381954 | − | 0.782442i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −21222.0 | + | 27201.4i | −0.796599 | + | 1.02104i | ||||
\(893\) | − | 6773.17i | − | 0.253814i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9056.38 | −0.338236 | ||||||||
\(896\) | −38519.2 | + | 1437.64i | −1.43620 | + | 0.0536027i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −25404.2 | + | 12401.2i | −0.944040 | + | 0.460840i | ||||
\(899\) | − | 13438.7i | − | 0.498562i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17785.2i | 0.657616i | ||||||||
\(902\) | 16978.9 | + | 34781.6i | 0.626757 | + | 1.28392i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5998.47 | − | 28363.9i | 0.220693 | − | 1.04355i | ||||
\(905\) | 11430.9 | 0.419863 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 15523.0i | − | 0.568284i | −0.958782 | − | 0.284142i | \(-0.908291\pi\) | ||
0.958782 | − | 0.284142i | \(-0.0917088\pi\) | |||||||
\(908\) | −3627.40 | − | 2830.04i | −0.132577 | − | 0.103434i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −15243.5 | + | 7441.21i | −0.555293 | + | 0.271070i | ||||
\(911\) | −8000.66 | −0.290970 | −0.145485 | − | 0.989360i | \(-0.546474\pi\) | ||||
−0.145485 | + | 0.989360i | \(0.546474\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44302.3 | 1.60591 | ||||||||
\(914\) | 16357.6 | − | 7985.09i | 0.591972 | − | 0.288975i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15115.4 | + | 11792.7i | 0.545224 | + | 0.425374i | ||||
\(917\) | 26434.2i | 0.951946i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23631.8 | −0.848251 | −0.424125 | − | 0.905603i | \(-0.639418\pi\) | ||||
−0.424125 | + | 0.905603i | \(0.639418\pi\) | |||||||
\(920\) | −4805.35 | − | 1016.25i | −0.172204 | − | 0.0364181i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9742.27 | + | 19957.2i | 0.347987 | + | 0.712860i | ||||
\(923\) | − | 14113.4i | − | 0.503302i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1876.80i | − | 0.0667122i | ||||||
\(926\) | 17979.3 | − | 8776.70i | 0.638051 | − | 0.311469i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −37059.0 | + | 31204.5i | −1.31091 | + | 1.10381i | ||||
\(929\) | 7564.75 | 0.267160 | 0.133580 | − | 0.991038i | \(-0.457353\pi\) | ||||
0.133580 | + | 0.991038i | \(0.457353\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 6444.15i | − | 0.226851i | ||||||
\(932\) | −16274.7 | + | 20860.2i | −0.571992 | + | 0.733152i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −19546.8 | − | 40042.1i | −0.684788 | − | 1.40280i | ||||
\(935\) | −22183.5 | −0.775913 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6226.13 | 0.217074 | 0.108537 | − | 0.994092i | \(-0.465383\pi\) | ||||
0.108537 | + | 0.994092i | \(0.465383\pi\) | |||||||
\(938\) | −18444.2 | − | 37783.4i | −0.642031 | − | 1.31522i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12114.8 | + | 9451.76i | 0.420363 | + | 0.327960i | ||||
\(941\) | 14012.2i | 0.485426i | 0.970098 | + | 0.242713i | \(0.0780373\pi\) | ||||
−0.970098 | + | 0.242713i | \(0.921963\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9624.05 | −0.332346 | ||||||||
\(944\) | −32193.2 | + | 8073.56i | −1.10996 | + | 0.278360i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29653.1 | + | 14475.4i | −1.01914 | + | 0.497499i | ||||
\(947\) | 39575.5i | 1.35801i | 0.734135 | + | 0.679003i | \(0.237588\pi\) | ||||
−0.734135 | + | 0.679003i | \(0.762412\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 11893.2i | − | 0.406817i | ||||||
\(950\) | 546.931 | + | 1120.40i | 0.0186787 | + | 0.0382637i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8956.79 | − | 42352.4i | 0.304928 | − | 1.44186i | ||||
\(953\) | −36806.3 | −1.25107 | −0.625537 | − | 0.780194i | \(-0.715120\pi\) | ||||
−0.625537 | + | 0.780194i | \(0.715120\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11964.5i | 0.405405i | ||||||||
\(956\) | 7550.39 | − | 9677.73i | 0.255436 | − | 0.327406i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −37485.4 | + | 18298.8i | −1.26420 | + | 0.617126i | ||||
\(959\) | −55100.3 | −1.85535 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27269.6 | −0.915364 | ||||||||
\(962\) | −8598.60 | + | 4197.47i | −0.288181 | + | 0.140678i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2269.27 | + | 2908.64i | −0.0758177 | + | 0.0971795i | ||||
\(965\) | − | 3192.07i | − | 0.106483i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33422.7 | 1.11148 | 0.555740 | − | 0.831356i | \(-0.312435\pi\) | ||||
0.555740 | + | 0.831356i | \(0.312435\pi\) | |||||||
\(968\) | −11607.5 | + | 54886.3i | −0.385412 | + | 1.82243i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8481.43 | − | 17374.4i | −0.280745 | − | 0.575112i | ||||
\(971\) | − | 35405.1i | − | 1.17014i | −0.810983 | − | 0.585069i | \(-0.801067\pi\) | ||
0.810983 | − | 0.585069i | \(-0.198933\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 7674.58i | − | 0.252863i | ||||||
\(974\) | 14314.5 | − | 6987.74i | 0.470911 | − | 0.229878i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3849.07 | + | 965.287i | −0.126235 | + | 0.0316579i | ||||
\(977\) | 45772.5 | 1.49887 | 0.749433 | − | 0.662080i | \(-0.230326\pi\) | ||||
0.749433 | + | 0.662080i | \(0.230326\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 100905.i | − | 3.29413i | ||||||
\(980\) | 11526.3 | + | 8992.62i | 0.375708 | + | 0.293121i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 22655.2 | + | 46409.8i | 0.736210 | + | 1.50814i | ||||
\(983\) | 18452.9 | 0.598736 | 0.299368 | − | 0.954138i | \(-0.403224\pi\) | ||||
0.299368 | + | 0.954138i | \(0.403224\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3271.51 | −0.105826 | ||||||||
\(986\) | −23867.8 | − | 48893.7i | −0.770897 | − | 1.57920i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3909.92 | − | 5011.55i | 0.125902 | − | 0.161375i | ||||
\(989\) | − | 8205.00i | − | 0.263806i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34921.1 | 1.11938 | 0.559689 | − | 0.828703i | \(-0.310920\pi\) | ||||
0.559689 | + | 0.828703i | \(0.310920\pi\) | |||||||
\(992\) | −5854.59 | − | 6953.00i | −0.187383 | − | 0.222538i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −21189.0 | + | 10343.6i | −0.676131 | + | 0.330058i | ||||
\(995\) | − | 8185.29i | − | 0.260795i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18316.5i | 0.581835i | 0.956748 | + | 0.290917i | \(0.0939605\pi\) | ||||
−0.956748 | + | 0.290917i | \(0.906039\pi\) | |||||||
\(998\) | −905.266 | − | 1854.46i | −0.0287131 | − | 0.0588195i | ||||
\(999\) | 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 | 360.4.k.c.181.9 | 12 | ||
3.2 | odd | 2 | 40.4.d.a.21.4 | yes | 12 | ||
4.3 | odd | 2 | 1440.4.k.c.721.7 | 12 | |||
8.3 | odd | 2 | 1440.4.k.c.721.1 | 12 | |||
8.5 | even | 2 | inner | 360.4.k.c.181.10 | 12 | ||
12.11 | even | 2 | 160.4.d.a.81.7 | 12 | |||
15.2 | even | 4 | 200.4.f.b.149.5 | 12 | |||
15.8 | even | 4 | 200.4.f.c.149.8 | 12 | |||
15.14 | odd | 2 | 200.4.d.b.101.9 | 12 | |||
24.5 | odd | 2 | 40.4.d.a.21.3 | ✓ | 12 | ||
24.11 | even | 2 | 160.4.d.a.81.6 | 12 | |||
48.5 | odd | 4 | 1280.4.a.bb.1.4 | 6 | |||
48.11 | even | 4 | 1280.4.a.bd.1.3 | 6 | |||
48.29 | odd | 4 | 1280.4.a.bc.1.3 | 6 | |||
48.35 | even | 4 | 1280.4.a.ba.1.4 | 6 | |||
60.23 | odd | 4 | 800.4.f.b.49.8 | 12 | |||
60.47 | odd | 4 | 800.4.f.c.49.5 | 12 | |||
60.59 | even | 2 | 800.4.d.d.401.6 | 12 | |||
120.29 | odd | 2 | 200.4.d.b.101.10 | 12 | |||
120.53 | even | 4 | 200.4.f.b.149.6 | 12 | |||
120.59 | even | 2 | 800.4.d.d.401.7 | 12 | |||
120.77 | even | 4 | 200.4.f.c.149.7 | 12 | |||
120.83 | odd | 4 | 800.4.f.c.49.6 | 12 | |||
120.107 | odd | 4 | 800.4.f.b.49.7 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.4.d.a.21.3 | ✓ | 12 | 24.5 | odd | 2 | ||
40.4.d.a.21.4 | yes | 12 | 3.2 | odd | 2 | ||
160.4.d.a.81.6 | 12 | 24.11 | even | 2 | |||
160.4.d.a.81.7 | 12 | 12.11 | even | 2 | |||
200.4.d.b.101.9 | 12 | 15.14 | odd | 2 | |||
200.4.d.b.101.10 | 12 | 120.29 | odd | 2 | |||
200.4.f.b.149.5 | 12 | 15.2 | even | 4 | |||
200.4.f.b.149.6 | 12 | 120.53 | even | 4 | |||
200.4.f.c.149.7 | 12 | 120.77 | even | 4 | |||
200.4.f.c.149.8 | 12 | 15.8 | even | 4 | |||
360.4.k.c.181.9 | 12 | 1.1 | even | 1 | trivial | ||
360.4.k.c.181.10 | 12 | 8.5 | even | 2 | inner | ||
800.4.d.d.401.6 | 12 | 60.59 | even | 2 | |||
800.4.d.d.401.7 | 12 | 120.59 | even | 2 | |||
800.4.f.b.49.7 | 12 | 120.107 | odd | 4 | |||
800.4.f.b.49.8 | 12 | 60.23 | odd | 4 | |||
800.4.f.c.49.5 | 12 | 60.47 | odd | 4 | |||
800.4.f.c.49.6 | 12 | 120.83 | odd | 4 | |||
1280.4.a.ba.1.4 | 6 | 48.35 | even | 4 | |||
1280.4.a.bb.1.4 | 6 | 48.5 | odd | 4 | |||
1280.4.a.bc.1.3 | 6 | 48.29 | odd | 4 | |||
1280.4.a.bd.1.3 | 6 | 48.11 | even | 4 | |||
1440.4.k.c.721.1 | 12 | 8.3 | odd | 2 | |||
1440.4.k.c.721.7 | 12 | 4.3 | odd | 2 |