Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(361,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.g (of order \(3\), 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: | \(52.0396846251\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.361 |
Dual form | 882.4.g.u.667.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.73205i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | 4.50000 | + | 7.79423i | 0.402492 | + | 0.697137i | 0.994026 | − | 0.109143i | \(-0.0348107\pi\) |
−0.591534 | + | 0.806280i | \(0.701477\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −9.00000 | + | 15.5885i | −0.284605 | + | 0.492950i | ||||
\(11\) | −28.5000 | + | 49.3634i | −0.781188 | + | 1.35306i | 0.150061 | + | 0.988677i | \(0.452053\pi\) |
−0.931250 | + | 0.364381i | \(0.881280\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 70.0000 | 1.49342 | 0.746712 | − | 0.665148i | \(-0.231631\pi\) | ||||
0.746712 | + | 0.665148i | \(0.231631\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | −25.5000 | + | 44.1673i | −0.363803 | + | 0.630126i | −0.988583 | − | 0.150675i | \(-0.951855\pi\) |
0.624780 | + | 0.780801i | \(0.285189\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.50000 | + | 4.33013i | 0.0301863 | + | 0.0522842i | 0.880724 | − | 0.473630i | \(-0.157057\pi\) |
−0.850538 | + | 0.525914i | \(0.823723\pi\) | |||||||
\(20\) | −36.0000 | −0.402492 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −114.000 | −1.10477 | ||||||||
\(23\) | 34.5000 | + | 59.7558i | 0.312772 | + | 0.541736i | 0.978961 | − | 0.204046i | \(-0.0654092\pi\) |
−0.666190 | + | 0.745782i | \(0.732076\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 22.0000 | − | 38.1051i | 0.176000 | − | 0.304841i | ||||
\(26\) | 70.0000 | + | 121.244i | 0.528005 | + | 0.914531i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −114.000 | −0.729975 | −0.364987 | − | 0.931012i | \(-0.618927\pi\) | ||||
−0.364987 | + | 0.931012i | \(0.618927\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 11.5000 | − | 19.9186i | 0.0666278 | − | 0.115403i | −0.830787 | − | 0.556590i | \(-0.812109\pi\) |
0.897415 | + | 0.441188i | \(0.145443\pi\) | |||||||
\(32\) | 16.0000 | − | 27.7128i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −102.000 | −0.514496 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 126.500 | + | 219.104i | 0.562067 | + | 0.973528i | 0.997316 | + | 0.0732182i | \(0.0233270\pi\) |
−0.435249 | + | 0.900310i | \(0.643340\pi\) | |||||||
\(38\) | −5.00000 | + | 8.66025i | −0.0213449 | + | 0.0369705i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −36.0000 | − | 62.3538i | −0.142302 | − | 0.246475i | ||||
\(41\) | −42.0000 | −0.159983 | −0.0799914 | − | 0.996796i | \(-0.525489\pi\) | ||||
−0.0799914 | + | 0.996796i | \(0.525489\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −124.000 | −0.439763 | −0.219882 | − | 0.975527i | \(-0.570567\pi\) | ||||
−0.219882 | + | 0.975527i | \(0.570567\pi\) | |||||||
\(44\) | −114.000 | − | 197.454i | −0.390594 | − | 0.676529i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −69.0000 | + | 119.512i | −0.221163 | + | 0.383065i | ||||
\(47\) | −100.500 | − | 174.071i | −0.311903 | − | 0.540231i | 0.666871 | − | 0.745173i | \(-0.267633\pi\) |
−0.978774 | + | 0.204941i | \(0.934300\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 88.0000 | 0.248902 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −140.000 | + | 242.487i | −0.373356 | + | 0.646671i | ||||
\(53\) | −196.500 | + | 340.348i | −0.509271 | + | 0.882083i | 0.490672 | + | 0.871345i | \(0.336751\pi\) |
−0.999942 | + | 0.0107383i | \(0.996582\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −513.000 | −1.25769 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −114.000 | − | 197.454i | −0.258085 | − | 0.447016i | ||||
\(59\) | −109.500 | + | 189.660i | −0.241622 | + | 0.418501i | −0.961176 | − | 0.275935i | \(-0.911013\pi\) |
0.719555 | + | 0.694436i | \(0.244346\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −354.500 | − | 614.012i | −0.744083 | − | 1.28879i | −0.950622 | − | 0.310351i | \(-0.899553\pi\) |
0.206539 | − | 0.978438i | \(-0.433780\pi\) | |||||||
\(62\) | 46.0000 | 0.0942259 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 315.000 | + | 545.596i | 0.601091 | + | 1.04112i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −209.500 | + | 362.865i | −0.382007 | + | 0.661656i | −0.991349 | − | 0.131251i | \(-0.958100\pi\) |
0.609342 | + | 0.792908i | \(0.291434\pi\) | |||||||
\(68\) | −102.000 | − | 176.669i | −0.181902 | − | 0.315063i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 96.0000 | 0.160466 | 0.0802331 | − | 0.996776i | \(-0.474434\pi\) | ||||
0.0802331 | + | 0.996776i | \(0.474434\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −156.500 | + | 271.066i | −0.250917 | + | 0.434601i | −0.963779 | − | 0.266704i | \(-0.914065\pi\) |
0.712862 | + | 0.701305i | \(0.247399\pi\) | |||||||
\(74\) | −253.000 | + | 438.209i | −0.397441 | + | 0.688388i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −20.0000 | −0.0301863 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −230.500 | − | 399.238i | −0.328269 | − | 0.568579i | 0.653899 | − | 0.756582i | \(-0.273132\pi\) |
−0.982169 | + | 0.188003i | \(0.939799\pi\) | |||||||
\(80\) | 72.0000 | − | 124.708i | 0.100623 | − | 0.174284i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −42.0000 | − | 72.7461i | −0.0565625 | − | 0.0979691i | ||||
\(83\) | −588.000 | −0.777607 | −0.388804 | − | 0.921321i | \(-0.627112\pi\) | ||||
−0.388804 | + | 0.921321i | \(0.627112\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −459.000 | −0.585712 | ||||||||
\(86\) | −124.000 | − | 214.774i | −0.155480 | − | 0.269299i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 228.000 | − | 394.908i | 0.276192 | − | 0.478378i | ||||
\(89\) | 508.500 | + | 880.748i | 0.605628 | + | 1.04898i | 0.991952 | + | 0.126615i | \(0.0404114\pi\) |
−0.386324 | + | 0.922363i | \(0.626255\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −276.000 | −0.312772 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 201.000 | − | 348.142i | 0.220549 | − | 0.382001i | ||||
\(95\) | −22.5000 | + | 38.9711i | −0.0242995 | + | 0.0420879i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1834.00 | 1.91974 | 0.959868 | − | 0.280451i | \(-0.0904839\pi\) | ||||
0.959868 | + | 0.280451i | \(0.0904839\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 88.0000 | + | 152.420i | 0.0880000 | + | 0.152420i | ||||
\(101\) | 142.500 | − | 246.817i | 0.140389 | − | 0.243161i | −0.787254 | − | 0.616629i | \(-0.788498\pi\) |
0.927643 | + | 0.373468i | \(0.121831\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −249.500 | − | 432.147i | −0.238679 | − | 0.413405i | 0.721656 | − | 0.692252i | \(-0.243381\pi\) |
−0.960336 | + | 0.278847i | \(0.910048\pi\) | |||||||
\(104\) | −560.000 | −0.528005 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −786.000 | −0.720218 | ||||||||
\(107\) | −553.500 | − | 958.690i | −0.500083 | − | 0.866169i | −1.00000 | 9.56665e-5i | \(-0.999970\pi\) | |
0.499917 | − | 0.866073i | \(-0.333364\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −461.500 | + | 799.341i | −0.405538 | + | 0.702413i | −0.994384 | − | 0.105832i | \(-0.966249\pi\) |
0.588846 | + | 0.808246i | \(0.299583\pi\) | |||||||
\(110\) | −513.000 | − | 888.542i | −0.444660 | − | 0.770174i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1542.00 | −1.28371 | −0.641855 | − | 0.766826i | \(-0.721835\pi\) | ||||
−0.641855 | + | 0.766826i | \(0.721835\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −310.500 | + | 537.802i | −0.251776 | + | 0.436089i | ||||
\(116\) | 228.000 | − | 394.908i | 0.182494 | − | 0.316088i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −438.000 | −0.341705 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −959.000 | − | 1661.04i | −0.720511 | − | 1.24796i | ||||
\(122\) | 709.000 | − | 1228.02i | 0.526146 | − | 0.911312i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 46.0000 | + | 79.6743i | 0.0333139 | + | 0.0577013i | ||||
\(125\) | 1521.00 | 1.08834 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2056.00 | −1.43654 | −0.718270 | − | 0.695765i | \(-0.755066\pi\) | ||||
−0.718270 | + | 0.695765i | \(0.755066\pi\) | |||||||
\(128\) | 64.0000 | + | 110.851i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −630.000 | + | 1091.19i | −0.425036 | + | 0.736184i | ||||
\(131\) | −1024.50 | − | 1774.49i | −0.683290 | − | 1.18349i | −0.973971 | − | 0.226673i | \(-0.927215\pi\) |
0.290681 | − | 0.956820i | \(-0.406118\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −838.000 | −0.540240 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 204.000 | − | 353.338i | 0.128624 | − | 0.222783i | ||||
\(137\) | −70.5000 | + | 122.110i | −0.0439651 | + | 0.0761498i | −0.887171 | − | 0.461442i | \(-0.847332\pi\) |
0.843205 | + | 0.537591i | \(0.180666\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1484.00 | −0.905548 | −0.452774 | − | 0.891625i | \(-0.649566\pi\) | ||||
−0.452774 | + | 0.891625i | \(0.649566\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 96.0000 | + | 166.277i | 0.0567334 | + | 0.0982651i | ||||
\(143\) | −1995.00 | + | 3455.44i | −1.16665 | + | 2.02069i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −513.000 | − | 888.542i | −0.293809 | − | 0.508892i | ||||
\(146\) | −626.000 | −0.354850 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1012.00 | −0.562067 | ||||||||
\(149\) | −28.5000 | − | 49.3634i | −0.0156699 | − | 0.0271410i | 0.858084 | − | 0.513509i | \(-0.171655\pi\) |
−0.873754 | + | 0.486368i | \(0.838321\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −419.500 | + | 726.595i | −0.226082 | + | 0.391586i | −0.956644 | − | 0.291261i | \(-0.905925\pi\) |
0.730561 | + | 0.682847i | \(0.239258\pi\) | |||||||
\(152\) | −20.0000 | − | 34.6410i | −0.0106725 | − | 0.0184852i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 207.000 | 0.107269 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1416.50 | + | 2453.45i | −0.720057 | + | 1.24718i | 0.240919 | + | 0.970545i | \(0.422551\pi\) |
−0.960976 | + | 0.276631i | \(0.910782\pi\) | |||||||
\(158\) | 461.000 | − | 798.475i | 0.232121 | − | 0.402046i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 288.000 | 0.142302 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1155.50 | + | 2001.38i | 0.555250 | + | 0.961721i | 0.997884 | + | 0.0650188i | \(0.0207107\pi\) |
−0.442634 | + | 0.896702i | \(0.645956\pi\) | |||||||
\(164\) | 84.0000 | − | 145.492i | 0.0399957 | − | 0.0692746i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −588.000 | − | 1018.45i | −0.274926 | − | 0.476185i | ||||
\(167\) | 1260.00 | 0.583843 | 0.291921 | − | 0.956442i | \(-0.405705\pi\) | ||||
0.291921 | + | 0.956442i | \(0.405705\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2703.00 | 1.23031 | ||||||||
\(170\) | −459.000 | − | 795.011i | −0.207081 | − | 0.358674i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 248.000 | − | 429.549i | 0.109941 | − | 0.190423i | ||||
\(173\) | −1633.50 | − | 2829.30i | −0.717877 | − | 1.24340i | −0.961839 | − | 0.273615i | \(-0.911781\pi\) |
0.243962 | − | 0.969785i | \(-0.421553\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 912.000 | 0.390594 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1017.00 | + | 1761.50i | −0.428244 | + | 0.741740i | ||||
\(179\) | 643.500 | − | 1114.57i | 0.268701 | − | 0.465403i | −0.699826 | − | 0.714314i | \(-0.746739\pi\) |
0.968527 | + | 0.248910i | \(0.0800724\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2674.00 | 1.09810 | 0.549052 | − | 0.835788i | \(-0.314989\pi\) | ||||
0.549052 | + | 0.835788i | \(0.314989\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −276.000 | − | 478.046i | −0.110581 | − | 0.191533i | ||||
\(185\) | −1138.50 | + | 1971.94i | −0.452455 | + | 0.783675i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1453.50 | − | 2517.54i | −0.568398 | − | 0.984494i | ||||
\(188\) | 804.000 | 0.311903 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −90.0000 | −0.0343647 | ||||||||
\(191\) | 2092.50 | + | 3624.32i | 0.792712 | + | 1.37302i | 0.924282 | + | 0.381711i | \(0.124665\pi\) |
−0.131570 | + | 0.991307i | \(0.542002\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 42.5000 | − | 73.6122i | 0.0158509 | − | 0.0274545i | −0.857991 | − | 0.513664i | \(-0.828288\pi\) |
0.873842 | + | 0.486210i | \(0.161621\pi\) | |||||||
\(194\) | 1834.00 | + | 3176.58i | 0.678730 | + | 1.17559i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 390.000 | 0.141047 | 0.0705237 | − | 0.997510i | \(-0.477533\pi\) | ||||
0.0705237 | + | 0.997510i | \(0.477533\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1416.50 | + | 2453.45i | −0.504588 | + | 0.873972i | 0.495398 | + | 0.868666i | \(0.335022\pi\) |
−0.999986 | + | 0.00530596i | \(0.998311\pi\) | |||||||
\(200\) | −176.000 | + | 304.841i | −0.0622254 | + | 0.107778i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 570.000 | 0.198540 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −189.000 | − | 327.358i | −0.0643919 | − | 0.111530i | ||||
\(206\) | 499.000 | − | 864.293i | 0.168772 | − | 0.292321i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −560.000 | − | 969.948i | −0.186678 | − | 0.323336i | ||||
\(209\) | −285.000 | −0.0943247 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −124.000 | −0.0404574 | −0.0202287 | − | 0.999795i | \(-0.506439\pi\) | ||||
−0.0202287 | + | 0.999795i | \(0.506439\pi\) | |||||||
\(212\) | −786.000 | − | 1361.39i | −0.254635 | − | 0.441041i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1107.00 | − | 1917.38i | 0.353612 | − | 0.612474i | ||||
\(215\) | −558.000 | − | 966.484i | −0.177001 | − | 0.306575i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1846.00 | −0.573518 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1026.00 | − | 1777.08i | 0.314422 | − | 0.544595i | ||||
\(221\) | −1785.00 | + | 3091.71i | −0.543313 | + | 0.941045i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −56.0000 | −0.0168163 | −0.00840816 | − | 0.999965i | \(-0.502676\pi\) | ||||
−0.00840816 | + | 0.999965i | \(0.502676\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1542.00 | − | 2670.82i | −0.453860 | − | 0.786108i | ||||
\(227\) | 1528.50 | − | 2647.44i | 0.446917 | − | 0.774083i | −0.551267 | − | 0.834329i | \(-0.685855\pi\) |
0.998184 | + | 0.0602465i | \(0.0191887\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −480.500 | − | 832.250i | −0.138656 | − | 0.240160i | 0.788332 | − | 0.615250i | \(-0.210945\pi\) |
−0.926988 | + | 0.375090i | \(0.877612\pi\) | |||||||
\(230\) | −1242.00 | −0.356065 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 912.000 | 0.258085 | ||||||||
\(233\) | −1414.50 | − | 2449.99i | −0.397712 | − | 0.688858i | 0.595731 | − | 0.803184i | \(-0.296862\pi\) |
−0.993443 | + | 0.114326i | \(0.963529\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 904.500 | − | 1566.64i | 0.251077 | − | 0.434878i | ||||
\(236\) | −438.000 | − | 758.638i | −0.120811 | − | 0.209251i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3540.00 | 0.958090 | 0.479045 | − | 0.877790i | \(-0.340983\pi\) | ||||
0.479045 | + | 0.877790i | \(0.340983\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2615.50 | − | 4530.18i | 0.699084 | − | 1.21085i | −0.269701 | − | 0.962944i | \(-0.586925\pi\) |
0.968785 | − | 0.247904i | \(-0.0797419\pi\) | |||||||
\(242\) | 1918.00 | − | 3322.07i | 0.509478 | − | 0.882442i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2836.00 | 0.744083 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 175.000 | + | 303.109i | 0.0450809 | + | 0.0780824i | ||||
\(248\) | −92.0000 | + | 159.349i | −0.0235565 | + | 0.0408010i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1521.00 | + | 2634.45i | 0.384786 | + | 0.666469i | ||||
\(251\) | 5040.00 | 1.26742 | 0.633709 | − | 0.773571i | \(-0.281532\pi\) | ||||
0.633709 | + | 0.773571i | \(0.281532\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3933.00 | −0.977334 | ||||||||
\(254\) | −2056.00 | − | 3561.10i | −0.507893 | − | 0.879697i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 718.500 | + | 1244.48i | 0.174392 | + | 0.302056i | 0.939951 | − | 0.341310i | \(-0.110871\pi\) |
−0.765559 | + | 0.643366i | \(0.777537\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2520.00 | −0.601091 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2049.00 | − | 3548.97i | 0.483159 | − | 0.836856i | ||||
\(263\) | −1162.50 | + | 2013.51i | −0.272558 | + | 0.472085i | −0.969516 | − | 0.245027i | \(-0.921203\pi\) |
0.696958 | + | 0.717112i | \(0.254536\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3537.00 | −0.819910 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −838.000 | − | 1451.46i | −0.191004 | − | 0.330828i | ||||
\(269\) | 1192.50 | − | 2065.47i | 0.270290 | − | 0.468156i | −0.698646 | − | 0.715467i | \(-0.746214\pi\) |
0.968936 | + | 0.247311i | \(0.0795471\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −165.500 | − | 286.654i | −0.0370975 | − | 0.0642547i | 0.846881 | − | 0.531783i | \(-0.178478\pi\) |
−0.883978 | + | 0.467528i | \(0.845145\pi\) | |||||||
\(272\) | 816.000 | 0.181902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −282.000 | −0.0621761 | ||||||||
\(275\) | 1254.00 | + | 2171.99i | 0.274978 | + | 0.476276i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2435.50 | + | 4218.41i | −0.528285 | + | 0.915017i | 0.471171 | + | 0.882042i | \(0.343831\pi\) |
−0.999456 | + | 0.0329750i | \(0.989502\pi\) | |||||||
\(278\) | −1484.00 | − | 2570.36i | −0.320160 | − | 0.554533i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7026.00 | 1.49159 | 0.745794 | − | 0.666177i | \(-0.232070\pi\) | ||||
0.745794 | + | 0.666177i | \(0.232070\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2676.50 | + | 4635.83i | −0.562196 | + | 0.973752i | 0.435109 | + | 0.900378i | \(0.356710\pi\) |
−0.997305 | + | 0.0733738i | \(0.976623\pi\) | |||||||
\(284\) | −192.000 | + | 332.554i | −0.0401166 | + | 0.0694839i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7980.00 | −1.64989 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1156.00 | + | 2002.25i | 0.235294 | + | 0.407541i | ||||
\(290\) | 1026.00 | − | 1777.08i | 0.207754 | − | 0.359841i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −626.000 | − | 1084.26i | −0.125458 | − | 0.217300i | ||||
\(293\) | 4158.00 | 0.829054 | 0.414527 | − | 0.910037i | \(-0.363947\pi\) | ||||
0.414527 | + | 0.910037i | \(0.363947\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1971.00 | −0.389004 | ||||||||
\(296\) | −1012.00 | − | 1752.84i | −0.198721 | − | 0.344194i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 57.0000 | − | 98.7269i | 0.0110803 | − | 0.0191916i | ||||
\(299\) | 2415.00 | + | 4182.90i | 0.467101 | + | 0.809042i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1678.00 | −0.319729 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 40.0000 | − | 69.2820i | 0.00754657 | − | 0.0130710i | ||||
\(305\) | 3190.50 | − | 5526.11i | 0.598975 | − | 1.03746i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9604.00 | 1.78544 | 0.892719 | − | 0.450615i | \(-0.148795\pi\) | ||||
0.892719 | + | 0.450615i | \(0.148795\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 207.000 | + | 358.535i | 0.0379252 | + | 0.0656884i | ||||
\(311\) | −5065.50 | + | 8773.70i | −0.923595 | + | 1.59971i | −0.129791 | + | 0.991541i | \(0.541430\pi\) |
−0.793805 | + | 0.608173i | \(0.791903\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5399.50 | + | 9352.21i | 0.975073 | + | 1.68888i | 0.679695 | + | 0.733495i | \(0.262112\pi\) |
0.295378 | + | 0.955380i | \(0.404554\pi\) | |||||||
\(314\) | −5666.00 | −1.01831 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1844.00 | 0.328269 | ||||||||
\(317\) | 265.500 | + | 459.859i | 0.0470409 | + | 0.0814772i | 0.888587 | − | 0.458708i | \(-0.151688\pi\) |
−0.841546 | + | 0.540185i | \(0.818354\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3249.00 | − | 5627.43i | 0.570248 | − | 0.987698i | ||||
\(320\) | 288.000 | + | 498.831i | 0.0503115 | + | 0.0871421i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −255.000 | −0.0439275 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1540.00 | − | 2667.36i | 0.262843 | − | 0.455257i | ||||
\(326\) | −2311.00 | + | 4002.77i | −0.392621 | + | 0.680040i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 336.000 | 0.0565625 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3507.50 | + | 6075.17i | 0.582446 | + | 1.00883i | 0.995189 | + | 0.0979784i | \(0.0312376\pi\) |
−0.412743 | + | 0.910848i | \(0.635429\pi\) | |||||||
\(332\) | 1176.00 | − | 2036.89i | 0.194402 | − | 0.336714i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1260.00 | + | 2182.38i | 0.206420 | + | 0.357529i | ||||
\(335\) | −3771.00 | −0.615020 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8990.00 | 1.45316 | 0.726582 | − | 0.687079i | \(-0.241108\pi\) | ||||
0.726582 | + | 0.687079i | \(0.241108\pi\) | |||||||
\(338\) | 2703.00 | + | 4681.73i | 0.434982 | + | 0.753410i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 918.000 | − | 1590.02i | 0.146428 | − | 0.253621i | ||||
\(341\) | 655.500 | + | 1135.36i | 0.104098 | + | 0.180303i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 992.000 | 0.155480 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3267.00 | − | 5658.61i | 0.507616 | − | 0.879216i | ||||
\(347\) | −4354.50 | + | 7542.22i | −0.673665 | + | 1.16682i | 0.303192 | + | 0.952929i | \(0.401948\pi\) |
−0.976857 | + | 0.213893i | \(0.931386\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6482.00 | −0.994193 | −0.497097 | − | 0.867695i | \(-0.665601\pi\) | ||||
−0.497097 | + | 0.867695i | \(0.665601\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 912.000 | + | 1579.63i | 0.138096 | + | 0.239189i | ||||
\(353\) | 1066.50 | − | 1847.23i | 0.160805 | − | 0.278522i | −0.774353 | − | 0.632754i | \(-0.781924\pi\) |
0.935158 | + | 0.354232i | \(0.115258\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 432.000 | + | 748.246i | 0.0645864 | + | 0.111867i | ||||
\(356\) | −4068.00 | −0.605628 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2574.00 | 0.380000 | ||||||||
\(359\) | 1924.50 | + | 3333.33i | 0.282928 | + | 0.490046i | 0.972105 | − | 0.234548i | \(-0.0753608\pi\) |
−0.689176 | + | 0.724594i | \(0.742028\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3417.00 | − | 5918.42i | 0.498178 | − | 0.862869i | ||||
\(362\) | 2674.00 | + | 4631.50i | 0.388238 | + | 0.672449i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2817.00 | −0.403969 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3245.50 | − | 5621.37i | 0.461618 | − | 0.799545i | −0.537424 | − | 0.843312i | \(-0.680603\pi\) |
0.999042 | + | 0.0437668i | \(0.0139358\pi\) | |||||||
\(368\) | 552.000 | − | 956.092i | 0.0781929 | − | 0.135434i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4554.00 | −0.639868 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −461.500 | − | 799.341i | −0.0640632 | − | 0.110961i | 0.832215 | − | 0.554453i | \(-0.187073\pi\) |
−0.896278 | + | 0.443493i | \(0.853739\pi\) | |||||||
\(374\) | 2907.00 | − | 5035.07i | 0.401918 | − | 0.696143i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 804.000 | + | 1392.57i | 0.110274 | + | 0.191001i | ||||
\(377\) | −7980.00 | −1.09016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6344.00 | 0.859814 | 0.429907 | − | 0.902873i | \(-0.358546\pi\) | ||||
0.429907 | + | 0.902873i | \(0.358546\pi\) | |||||||
\(380\) | −90.0000 | − | 155.885i | −0.0121497 | − | 0.0210440i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4185.00 | + | 7248.63i | −0.560532 | + | 0.970870i | ||||
\(383\) | 2503.50 | + | 4336.19i | 0.334002 | + | 0.578509i | 0.983293 | − | 0.182032i | \(-0.0582673\pi\) |
−0.649290 | + | 0.760541i | \(0.724934\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 170.000 | 0.0224165 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3668.00 | + | 6353.16i | −0.479934 | + | 0.831270i | ||||
\(389\) | 6145.50 | − | 10644.3i | 0.801001 | − | 1.38737i | −0.117958 | − | 0.993019i | \(-0.537635\pi\) |
0.918958 | − | 0.394355i | \(-0.129032\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3519.00 | −0.455150 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 390.000 | + | 675.500i | 0.0498678 | + | 0.0863736i | ||||
\(395\) | 2074.50 | − | 3593.14i | 0.264252 | − | 0.457697i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 443.500 | + | 768.165i | 0.0560671 | + | 0.0971110i | 0.892697 | − | 0.450658i | \(-0.148811\pi\) |
−0.836630 | + | 0.547769i | \(0.815477\pi\) | |||||||
\(398\) | −5666.00 | −0.713595 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −704.000 | −0.0880000 | ||||||||
\(401\) | 5977.50 | + | 10353.3i | 0.744394 | + | 1.28933i | 0.950477 | + | 0.310794i | \(0.100595\pi\) |
−0.206083 | + | 0.978535i | \(0.566072\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 805.000 | − | 1394.30i | 0.0995035 | − | 0.172345i | ||||
\(404\) | 570.000 | + | 987.269i | 0.0701945 | + | 0.121580i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14421.0 | −1.75632 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1710.50 | + | 2962.67i | −0.206794 | + | 0.358178i | −0.950703 | − | 0.310103i | \(-0.899636\pi\) |
0.743909 | + | 0.668281i | \(0.232970\pi\) | |||||||
\(410\) | 378.000 | − | 654.715i | 0.0455319 | − | 0.0788636i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1996.00 | 0.238679 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2646.00 | − | 4583.01i | −0.312981 | − | 0.542099i | ||||
\(416\) | 1120.00 | − | 1939.90i | 0.132001 | − | 0.228633i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −285.000 | − | 493.634i | −0.0333488 | − | 0.0577618i | ||||
\(419\) | −5460.00 | −0.636607 | −0.318304 | − | 0.947989i | \(-0.603113\pi\) | ||||
−0.318304 | + | 0.947989i | \(0.603113\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7730.00 | 0.894863 | 0.447431 | − | 0.894318i | \(-0.352339\pi\) | ||||
0.447431 | + | 0.894318i | \(0.352339\pi\) | |||||||
\(422\) | −124.000 | − | 214.774i | −0.0143039 | − | 0.0247750i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1572.00 | − | 2722.78i | 0.180054 | − | 0.311863i | ||||
\(425\) | 1122.00 | + | 1943.36i | 0.128059 | + | 0.221804i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4428.00 | 0.500083 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1116.00 | − | 1932.97i | 0.125159 | − | 0.216781i | ||||
\(431\) | −5656.50 | + | 9797.35i | −0.632167 | + | 1.09495i | 0.354941 | + | 0.934889i | \(0.384501\pi\) |
−0.987108 | + | 0.160057i | \(0.948832\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4214.00 | −0.467695 | −0.233847 | − | 0.972273i | \(-0.575132\pi\) | ||||
−0.233847 | + | 0.972273i | \(0.575132\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1846.00 | − | 3197.37i | −0.202769 | − | 0.351207i | ||||
\(437\) | −172.500 | + | 298.779i | −0.0188828 | + | 0.0327060i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8276.50 | + | 14335.3i | 0.899808 | + | 1.55851i | 0.827739 | + | 0.561114i | \(0.189627\pi\) |
0.0720696 | + | 0.997400i | \(0.477040\pi\) | |||||||
\(440\) | 4104.00 | 0.444660 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7140.00 | −0.768360 | ||||||||
\(443\) | −8197.50 | − | 14198.5i | −0.879176 | − | 1.52278i | −0.852247 | − | 0.523140i | \(-0.824760\pi\) |
−0.0269294 | − | 0.999637i | \(-0.508573\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4576.50 | + | 7926.73i | −0.487521 | + | 0.844411i | ||||
\(446\) | −56.0000 | − | 96.9948i | −0.00594546 | − | 0.0102978i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15090.0 | 1.58606 | 0.793030 | − | 0.609182i | \(-0.208502\pi\) | ||||
0.793030 | + | 0.609182i | \(0.208502\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1197.00 | − | 2073.26i | 0.124977 | − | 0.216466i | ||||
\(452\) | 3084.00 | − | 5341.64i | 0.320927 | − | 0.555862i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6114.00 | 0.632036 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7392.50 | + | 12804.2i | 0.756688 | + | 1.31062i | 0.944531 | + | 0.328423i | \(0.106517\pi\) |
−0.187842 | + | 0.982199i | \(0.560149\pi\) | |||||||
\(458\) | 961.000 | − | 1664.50i | 0.0980449 | − | 0.169819i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1242.00 | − | 2151.21i | −0.125888 | − | 0.218045i | ||||
\(461\) | 2898.00 | 0.292784 | 0.146392 | − | 0.989227i | \(-0.453234\pi\) | ||||
0.146392 | + | 0.989227i | \(0.453234\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 464.000 | 0.0465743 | 0.0232872 | − | 0.999729i | \(-0.492587\pi\) | ||||
0.0232872 | + | 0.999729i | \(0.492587\pi\) | |||||||
\(464\) | 912.000 | + | 1579.63i | 0.0912468 | + | 0.158044i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2829.00 | − | 4899.97i | 0.281225 | − | 0.487096i | ||||
\(467\) | −2116.50 | − | 3665.89i | −0.209721 | − | 0.363248i | 0.741905 | − | 0.670505i | \(-0.233922\pi\) |
−0.951627 | + | 0.307256i | \(0.900589\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3618.00 | 0.355076 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 876.000 | − | 1517.28i | 0.0854262 | − | 0.147963i | ||||
\(473\) | 3534.00 | − | 6121.07i | 0.343538 | − | 0.595025i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 220.000 | 0.0212511 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3540.00 | + | 6131.46i | 0.338736 | + | 0.586708i | ||||
\(479\) | −1369.50 | + | 2372.04i | −0.130635 | + | 0.226266i | −0.923921 | − | 0.382582i | \(-0.875035\pi\) |
0.793287 | + | 0.608848i | \(0.208368\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8855.00 | + | 15337.3i | 0.839404 | + | 1.45389i | ||||
\(482\) | 10462.0 | 0.988654 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7672.00 | 0.720511 | ||||||||
\(485\) | 8253.00 | + | 14294.6i | 0.772679 | + | 1.33832i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8525.50 | + | 14766.6i | −0.793280 | + | 1.37400i | 0.130646 | + | 0.991429i | \(0.458295\pi\) |
−0.923926 | + | 0.382572i | \(0.875038\pi\) | |||||||
\(488\) | 2836.00 | + | 4912.10i | 0.263073 | + | 0.455656i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4296.00 | 0.394859 | 0.197429 | − | 0.980317i | \(-0.436741\pi\) | ||||
0.197429 | + | 0.980317i | \(0.436741\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2907.00 | − | 5035.07i | 0.265567 | − | 0.459976i | ||||
\(494\) | −350.000 | + | 606.218i | −0.0318770 | + | 0.0552126i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −368.000 | −0.0333139 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1700.50 | − | 2945.35i | −0.152555 | − | 0.264233i | 0.779611 | − | 0.626264i | \(-0.215417\pi\) |
−0.932166 | + | 0.362031i | \(0.882083\pi\) | |||||||
\(500\) | −3042.00 | + | 5268.90i | −0.272085 | + | 0.471265i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5040.00 | + | 8729.54i | 0.448100 | + | 0.776132i | ||||
\(503\) | 16800.0 | 1.48921 | 0.744607 | − | 0.667503i | \(-0.232637\pi\) | ||||
0.744607 | + | 0.667503i | \(0.232637\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2565.00 | 0.226022 | ||||||||
\(506\) | −3933.00 | − | 6812.16i | −0.345540 | − | 0.598493i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4112.00 | − | 7122.19i | 0.359135 | − | 0.622040i | ||||
\(509\) | −919.500 | − | 1592.62i | −0.0800710 | − | 0.138687i | 0.823209 | − | 0.567738i | \(-0.192181\pi\) |
−0.903280 | + | 0.429051i | \(0.858848\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1437.00 | + | 2488.96i | −0.123314 | + | 0.213586i | ||||
\(515\) | 2245.50 | − | 3889.32i | 0.192133 | − | 0.332784i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11457.0 | 0.974620 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2520.00 | − | 4364.77i | −0.212518 | − | 0.368092i | ||||
\(521\) | −151.500 | + | 262.406i | −0.0127396 | + | 0.0220656i | −0.872325 | − | 0.488927i | \(-0.837389\pi\) |
0.859585 | + | 0.510992i | \(0.170722\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10833.5 | − | 18764.2i | −0.905767 | − | 1.56883i | −0.819885 | − | 0.572528i | \(-0.805963\pi\) |
−0.0858815 | − | 0.996305i | \(-0.527371\pi\) | |||||||
\(524\) | 8196.00 | 0.683290 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4650.00 | −0.385456 | ||||||||
\(527\) | 586.500 | + | 1015.85i | 0.0484788 | + | 0.0839678i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3703.00 | − | 6413.78i | 0.304348 | − | 0.527146i | ||||
\(530\) | −3537.00 | − | 6126.26i | −0.289882 | − | 0.502090i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2940.00 | −0.238922 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4981.50 | − | 8628.21i | 0.402559 | − | 0.697253i | ||||
\(536\) | 1676.00 | − | 2902.92i | 0.135060 | − | 0.233931i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4770.00 | 0.382248 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2519.50 | − | 4363.90i | −0.200225 | − | 0.346800i | 0.748376 | − | 0.663275i | \(-0.230834\pi\) |
−0.948601 | + | 0.316475i | \(0.897501\pi\) | |||||||
\(542\) | 331.000 | − | 573.309i | 0.0262319 | − | 0.0454349i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 816.000 | + | 1413.35i | 0.0643120 | + | 0.111392i | ||||
\(545\) | −8307.00 | −0.652904 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2392.00 | −0.186974 | −0.0934868 | − | 0.995621i | \(-0.529801\pi\) | ||||
−0.0934868 | + | 0.995621i | \(0.529801\pi\) | |||||||
\(548\) | −282.000 | − | 488.438i | −0.0219826 | − | 0.0380749i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2508.00 | + | 4343.98i | −0.194439 | + | 0.336778i | ||||
\(551\) | −285.000 | − | 493.634i | −0.0220352 | − | 0.0381661i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −9742.00 | −0.747108 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2968.00 | − | 5140.73i | 0.226387 | − | 0.392114i | ||||
\(557\) | −11074.5 | + | 19181.6i | −0.842445 | + | 1.45916i | 0.0453775 | + | 0.998970i | \(0.485551\pi\) |
−0.887822 | + | 0.460187i | \(0.847782\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8680.00 | −0.656753 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7026.00 | + | 12169.4i | 0.527356 | + | 0.913407i | ||||
\(563\) | 4174.50 | − | 7230.45i | 0.312494 | − | 0.541256i | −0.666408 | − | 0.745588i | \(-0.732169\pi\) |
0.978902 | + | 0.204332i | \(0.0655022\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6939.00 | − | 12018.7i | −0.516683 | − | 0.894921i | ||||
\(566\) | −10706.0 | −0.795065 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −768.000 | −0.0567334 | ||||||||
\(569\) | −7672.50 | − | 13289.2i | −0.565286 | − | 0.979105i | −0.997023 | − | 0.0771050i | \(-0.975432\pi\) |
0.431737 | − | 0.902000i | \(-0.357901\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5796.50 | − | 10039.8i | 0.424827 | − | 0.735821i | −0.571578 | − | 0.820548i | \(-0.693668\pi\) |
0.996404 | + | 0.0847268i | \(0.0270017\pi\) | |||||||
\(572\) | −7980.00 | − | 13821.8i | −0.583323 | − | 1.01034i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3036.00 | 0.220191 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7296.50 | + | 12637.9i | −0.526442 | + | 0.911825i | 0.473083 | + | 0.881018i | \(0.343141\pi\) |
−0.999525 | + | 0.0308071i | \(0.990192\pi\) | |||||||
\(578\) | −2312.00 | + | 4004.50i | −0.166378 | + | 0.288175i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4104.00 | 0.293809 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11200.5 | − | 19399.8i | −0.795673 | − | 1.37815i | ||||
\(584\) | 1252.00 | − | 2168.53i | 0.0887125 | − | 0.153655i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4158.00 | + | 7201.87i | 0.293115 | + | 0.507690i | ||||
\(587\) | −15372.0 | −1.08087 | −0.540435 | − | 0.841386i | \(-0.681740\pi\) | ||||
−0.540435 | + | 0.841386i | \(0.681740\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 115.000 | 0.00804498 | ||||||||
\(590\) | −1971.00 | − | 3413.87i | −0.137534 | − | 0.238215i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2024.00 | − | 3505.67i | 0.140517 | − | 0.243382i | ||||
\(593\) | 7186.50 | + | 12447.4i | 0.497663 | + | 0.861978i | 0.999996 | − | 0.00269639i | \(-0.000858288\pi\) |
−0.502333 | + | 0.864674i | \(0.667525\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 228.000 | 0.0156699 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4830.00 | + | 8365.81i | −0.330290 | + | 0.572079i | ||||
\(599\) | 1273.50 | − | 2205.77i | 0.0868678 | − | 0.150459i | −0.819318 | − | 0.573340i | \(-0.805648\pi\) |
0.906186 | + | 0.422880i | \(0.138981\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7042.00 | 0.477952 | 0.238976 | − | 0.971025i | \(-0.423188\pi\) | ||||
0.238976 | + | 0.971025i | \(0.423188\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1678.00 | − | 2906.38i | −0.113041 | − | 0.195793i | ||||
\(605\) | 8631.00 | − | 14949.3i | 0.580000 | − | 1.00459i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11295.5 | − | 19564.4i | −0.755305 | − | 1.30823i | −0.945223 | − | 0.326427i | \(-0.894155\pi\) |
0.189917 | − | 0.981800i | \(-0.439178\pi\) | |||||||
\(608\) | 160.000 | 0.0106725 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12762.0 | 0.847079 | ||||||||
\(611\) | −7035.00 | − | 12185.0i | −0.465803 | − | 0.806794i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4242.50 | − | 7348.23i | 0.279532 | − | 0.484163i | −0.691737 | − | 0.722150i | \(-0.743154\pi\) |
0.971268 | + | 0.237987i | \(0.0764874\pi\) | |||||||
\(614\) | 9604.00 | + | 16634.6i | 0.631247 | + | 1.09335i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18282.0 | 1.19288 | 0.596439 | − | 0.802658i | \(-0.296582\pi\) | ||||
0.596439 | + | 0.802658i | \(0.296582\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1145.50 | − | 1984.06i | 0.0743805 | − | 0.128831i | −0.826436 | − | 0.563030i | \(-0.809635\pi\) |
0.900817 | + | 0.434200i | \(0.142969\pi\) | |||||||
\(620\) | −414.000 | + | 717.069i | −0.0268172 | + | 0.0464487i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −20262.0 | −1.30616 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4094.50 | + | 7091.88i | 0.262048 | + | 0.453880i | ||||
\(626\) | −10799.0 | + | 18704.4i | −0.689481 | + | 1.19422i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5666.00 | − | 9813.80i | −0.360029 | − | 0.623588i | ||||
\(629\) | −12903.0 | −0.817927 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6928.00 | −0.437083 | −0.218541 | − | 0.975828i | \(-0.570130\pi\) | ||||
−0.218541 | + | 0.975828i | \(0.570130\pi\) | |||||||
\(632\) | 1844.00 | + | 3193.90i | 0.116061 | + | 0.201023i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −531.000 | + | 919.719i | −0.0332629 | + | 0.0576131i | ||||
\(635\) | −9252.00 | − | 16024.9i | −0.578196 | − | 1.00146i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12996.0 | 0.806452 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −576.000 | + | 997.661i | −0.0355756 | + | 0.0616188i | ||||
\(641\) | 12487.5 | − | 21629.0i | 0.769464 | − | 1.33275i | −0.168390 | − | 0.985721i | \(-0.553857\pi\) |
0.937854 | − | 0.347031i | \(-0.112810\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9548.00 | −0.585593 | −0.292797 | − | 0.956175i | \(-0.594586\pi\) | ||||
−0.292797 | + | 0.956175i | \(0.594586\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −255.000 | − | 441.673i | −0.0155307 | − | 0.0269000i | ||||
\(647\) | −5065.50 | + | 8773.70i | −0.307798 | + | 0.533122i | −0.977880 | − | 0.209165i | \(-0.932925\pi\) |
0.670082 | + | 0.742287i | \(0.266259\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6241.50 | − | 10810.6i | −0.377504 | − | 0.653857i | ||||
\(650\) | 6160.00 | 0.371716 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9244.00 | −0.555250 | ||||||||
\(653\) | 8329.50 | + | 14427.1i | 0.499171 | + | 0.864589i | 1.00000 | 0.000957229i | \(-0.000304695\pi\) | |
−0.500829 | + | 0.865546i | \(0.666971\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9220.50 | − | 15970.4i | 0.550038 | − | 0.952693i | ||||
\(656\) | 336.000 | + | 581.969i | 0.0199979 | + | 0.0346373i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29556.0 | −1.74710 | −0.873550 | − | 0.486735i | \(-0.838188\pi\) | ||||
−0.873550 | + | 0.486735i | \(0.838188\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 95.5000 | − | 165.411i | 0.00561955 | − | 0.00973334i | −0.863202 | − | 0.504859i | \(-0.831545\pi\) |
0.868822 | + | 0.495125i | \(0.164878\pi\) | |||||||
\(662\) | −7015.00 | + | 12150.3i | −0.411852 | + | 0.713348i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4704.00 | 0.274926 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3933.00 | − | 6812.16i | −0.228315 | − | 0.395454i | ||||
\(668\) | −2520.00 | + | 4364.77i | −0.145961 | + | 0.252811i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3771.00 | − | 6531.56i | −0.217442 | − | 0.376621i | ||||
\(671\) | 40413.0 | 2.32508 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2606.00 | 0.149263 | 0.0746314 | − | 0.997211i | \(-0.476222\pi\) | ||||
0.0746314 | + | 0.997211i | \(0.476222\pi\) | |||||||
\(674\) | 8990.00 | + | 15571.1i | 0.513771 | + | 0.889878i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5406.00 | + | 9363.47i | −0.307579 | + | 0.532742i | ||||
\(677\) | 2104.50 | + | 3645.10i | 0.119472 | + | 0.206931i | 0.919559 | − | 0.392953i | \(-0.128547\pi\) |
−0.800087 | + | 0.599885i | \(0.795213\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3672.00 | 0.207081 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1311.00 | + | 2270.72i | −0.0736082 | + | 0.127493i | ||||
\(683\) | 12151.5 | − | 21047.0i | 0.680768 | − | 1.17912i | −0.293979 | − | 0.955812i | \(-0.594980\pi\) |
0.974747 | − | 0.223312i | \(-0.0716869\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1269.00 | −0.0707825 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 992.000 | + | 1718.19i | 0.0549704 | + | 0.0952116i | ||||
\(689\) | −13755.0 | + | 23824.4i | −0.760557 | + | 1.31732i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7520.50 | + | 13025.9i | 0.414028 | + | 0.717117i | 0.995326 | − | 0.0965734i | \(-0.0307882\pi\) |
−0.581298 | + | 0.813691i | \(0.697455\pi\) | |||||||
\(692\) | 13068.0 | 0.717877 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17418.0 | −0.952706 | ||||||||
\(695\) | −6678.00 | − | 11566.6i | −0.364476 | − | 0.631291i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1071.00 | − | 1855.03i | 0.0582023 | − | 0.100809i | ||||
\(698\) | −6482.00 | − | 11227.2i | −0.351500 | − | 0.608817i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24726.0 | −1.33222 | −0.666111 | − | 0.745852i | \(-0.732042\pi\) | ||||
−0.666111 | + | 0.745852i | \(0.732042\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −632.500 | + | 1095.52i | −0.0339334 | + | 0.0587744i | ||||
\(704\) | −1824.00 | + | 3159.26i | −0.0976486 | + | 0.169132i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4266.00 | 0.227412 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2478.50 | + | 4292.89i | 0.131286 | + | 0.227395i | 0.924173 | − | 0.381975i | \(-0.124756\pi\) |
−0.792886 | + | 0.609370i | \(0.791423\pi\) | |||||||
\(710\) | −864.000 | + | 1496.49i | −0.0456695 | + | 0.0791019i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4068.00 | − | 7045.98i | −0.214122 | − | 0.370870i | ||||
\(713\) | 1587.00 | 0.0833571 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −35910.0 | −1.87826 | ||||||||
\(716\) | 2574.00 | + | 4458.30i | 0.134350 | + | 0.232702i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3849.00 | + | 6666.66i | −0.200060 | + | 0.346515i | ||||
\(719\) | −13834.5 | − | 23962.1i | −0.717580 | − | 1.24288i | −0.961956 | − | 0.273204i | \(-0.911917\pi\) |
0.244376 | − | 0.969680i | \(-0.421417\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13668.0 | 0.704529 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5348.00 | + | 9263.01i | −0.274526 | + | 0.475493i | ||||
\(725\) | −2508.00 | + | 4343.98i | −0.128476 | + | 0.222526i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13888.0 | 0.708497 | 0.354249 | − | 0.935151i | \(-0.384737\pi\) | ||||
0.354249 | + | 0.935151i | \(0.384737\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2817.00 | − | 4879.19i | −0.142824 | − | 0.247379i | ||||
\(731\) | 3162.00 | − | 5476.74i | 0.159987 | − | 0.277106i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7121.50 | + | 12334.8i | 0.358852 | + | 0.621550i | 0.987769 | − | 0.155922i | \(-0.0498349\pi\) |
−0.628917 | + | 0.777472i | \(0.716502\pi\) | |||||||
\(734\) | 12982.0 | 0.652826 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2208.00 | 0.110581 | ||||||||
\(737\) | −11941.5 | − | 20683.3i | −0.596840 | − | 1.03376i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18479.5 | + | 32007.4i | −0.919864 | + | 1.59325i | −0.120244 | + | 0.992744i | \(0.538368\pi\) |
−0.799620 | + | 0.600507i | \(0.794966\pi\) | |||||||
\(740\) | −4554.00 | − | 7887.76i | −0.226228 | − | 0.391838i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12528.0 | 0.618584 | 0.309292 | − | 0.950967i | \(-0.399908\pi\) | ||||
0.309292 | + | 0.950967i | \(0.399908\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 256.500 | − | 444.271i | 0.0126140 | − | 0.0218481i | ||||
\(746\) | 923.000 | − | 1598.68i | 0.0452995 | − | 0.0784610i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11628.0 | 0.568398 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8883.50 | + | 15386.7i | 0.431643 | + | 0.747627i | 0.997015 | − | 0.0772090i | \(-0.0246009\pi\) |
−0.565372 | + | 0.824836i | \(0.691268\pi\) | |||||||
\(752\) | −1608.00 | + | 2785.14i | −0.0779757 | + | 0.135058i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7980.00 | − | 13821.8i | −0.385430 | − | 0.667585i | ||||
\(755\) | −7551.00 | −0.363985 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28726.0 | −1.37921 | −0.689606 | − | 0.724184i | \(-0.742216\pi\) | ||||
−0.689606 | + | 0.724184i | \(0.742216\pi\) | |||||||
\(758\) | 6344.00 | + | 10988.1i | 0.303990 | + | 0.526526i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 180.000 | − | 311.769i | 0.00859117 | − | 0.0148803i | ||||
\(761\) | 13234.5 | + | 22922.8i | 0.630421 | + | 1.09192i | 0.987466 | + | 0.157834i | \(0.0504510\pi\) |
−0.357045 | + | 0.934087i | \(0.616216\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −16740.0 | −0.792712 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5007.00 | + | 8672.38i | −0.236175 | + | 0.409068i | ||||
\(767\) | −7665.00 | + | 13276.2i | −0.360844 | + | 0.625000i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5054.00 | −0.236999 | −0.118499 | − | 0.992954i | \(-0.537808\pi\) | ||||
−0.118499 | + | 0.992954i | \(0.537808\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 170.000 | + | 294.449i | 0.00792543 | + | 0.0137273i | ||||
\(773\) | 17782.5 | − | 30800.2i | 0.827415 | − | 1.43313i | −0.0726439 | − | 0.997358i | \(-0.523144\pi\) |
0.900059 | − | 0.435767i | \(-0.143523\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −506.000 | − | 876.418i | −0.0234530 | − | 0.0406217i | ||||
\(776\) | −14672.0 | −0.678730 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24582.0 | 1.13279 | ||||||||
\(779\) | −105.000 | − | 181.865i | −0.00482929 | − | 0.00836457i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2736.00 | + | 4738.89i | −0.125354 | + | 0.217120i | ||||
\(782\) | −3519.00 | − | 6095.09i | −0.160920 | − | 0.278721i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25497.0 | −1.15927 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4314.50 | + | 7472.93i | −0.195420 | + | 0.338477i | −0.947038 | − | 0.321121i | \(-0.895940\pi\) |
0.751618 | + | 0.659598i | \(0.229274\pi\) | |||||||
\(788\) | −780.000 | + | 1351.00i | −0.0352619 | + | 0.0610753i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8298.00 | 0.373708 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24815.0 | − | 42980.8i | −1.11123 | − | 1.92471i | ||||
\(794\) | −887.000 | + | 1536.33i | −0.0396454 | + | 0.0686679i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5666.00 | − | 9813.80i | −0.252294 | − | 0.436986i | ||||
\(797\) | 20706.0 | 0.920256 | 0.460128 | − | 0.887853i | \(-0.347803\pi\) | ||||
0.460128 | + | 0.887853i | \(0.347803\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10251.0 | 0.453885 | ||||||||
\(800\) | −704.000 | − | 1219.36i | −0.0311127 | − | 0.0538888i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11955.0 | + | 20706.7i | −0.526366 | + | 0.911693i | ||||
\(803\) | −8920.50 | − | 15450.8i | −0.392027 | − | 0.679011i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3220.00 | 0.140719 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1140.00 | + | 1974.54i | −0.0496350 | + | 0.0859703i | ||||
\(809\) | −8092.50 | + | 14016.6i | −0.351690 | + | 0.609145i | −0.986546 | − | 0.163486i | \(-0.947726\pi\) |
0.634856 | + | 0.772631i | \(0.281060\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11788.0 | 0.510398 | 0.255199 | − | 0.966889i | \(-0.417859\pi\) | ||||
0.255199 | + | 0.966889i | \(0.417859\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −14421.0 | − | 24977.9i | −0.620953 | − | 1.07552i | ||||
\(815\) | −10399.5 | + | 18012.5i | −0.446968 | + | 0.774171i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −310.000 | − | 536.936i | −0.0132748 | − | 0.0229927i | ||||
\(818\) | −6842.00 | −0.292451 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1512.00 | 0.0643919 | ||||||||
\(821\) | −14896.5 | − | 25801.5i | −0.633242 | − | 1.09681i | −0.986885 | − | 0.161426i | \(-0.948391\pi\) |
0.353643 | − | 0.935380i | \(-0.384943\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15161.5 | + | 26260.5i | −0.642159 | + | 1.11225i | 0.342791 | + | 0.939412i | \(0.388628\pi\) |
−0.984950 | + | 0.172840i | \(0.944706\pi\) | |||||||
\(824\) | 1996.00 | + | 3457.17i | 0.0843859 | + | 0.146161i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21156.0 | −0.889560 | −0.444780 | − | 0.895640i | \(-0.646718\pi\) | ||||
−0.444780 | + | 0.895640i | \(0.646718\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2634.50 | + | 4563.09i | −0.110374 | + | 0.191173i | −0.915921 | − | 0.401358i | \(-0.868538\pi\) |
0.805547 | + | 0.592532i | \(0.201871\pi\) | |||||||
\(830\) | 5292.00 | − | 9166.01i | 0.221311 | − | 0.383322i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4480.00 | 0.186678 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5670.00 | + | 9820.73i | 0.234992 | + | 0.407018i | ||||
\(836\) | 570.000 | − | 987.269i | 0.0235812 | − | 0.0408438i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5460.00 | − | 9457.00i | −0.225075 | − | 0.389841i | ||||
\(839\) | −39816.0 | −1.63838 | −0.819190 | − | 0.573522i | \(-0.805577\pi\) | ||||
−0.819190 | + | 0.573522i | \(0.805577\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11393.0 | −0.467137 | ||||||||
\(842\) | 7730.00 | + | 13388.8i | 0.316382 | + | 0.547989i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 248.000 | − | 429.549i | 0.0101144 | − | 0.0175186i | ||||
\(845\) | 12163.5 | + | 21067.8i | 0.495192 | + | 0.857697i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6288.00 | 0.254635 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2244.00 | + | 3886.72i | −0.0905513 | + | 0.156839i | ||||
\(851\) | −8728.50 | + | 15118.2i | −0.351597 | + | 0.608984i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14546.0 | −0.583875 | −0.291938 | − | 0.956437i | \(-0.594300\pi\) | ||||
−0.291938 | + | 0.956437i | \(0.594300\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4428.00 | + | 7669.52i | 0.176806 | + | 0.306237i | ||||
\(857\) | 15724.5 | − | 27235.6i | 0.626766 | − | 1.08559i | −0.361430 | − | 0.932399i | \(-0.617711\pi\) |
0.988196 | − | 0.153192i | \(-0.0489552\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12261.5 | − | 21237.5i | −0.487028 | − | 0.843557i | 0.512861 | − | 0.858472i | \(-0.328586\pi\) |
−0.999889 | + | 0.0149147i | \(0.995252\pi\) | |||||||
\(860\) | 4464.00 | 0.177001 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22626.0 | −0.894019 | ||||||||
\(863\) | −4081.50 | − | 7069.37i | −0.160992 | − | 0.278846i | 0.774233 | − | 0.632901i | \(-0.218136\pi\) |
−0.935225 | + | 0.354055i | \(0.884803\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14701.5 | − | 25463.7i | 0.577880 | − | 1.00092i | ||||
\(866\) | −4214.00 | − | 7298.86i | −0.165355 | − | 0.286403i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26277.0 | 1.02576 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14665.0 | + | 25400.5i | −0.570499 | + | 0.988133i | ||||
\(872\) | 3692.00 | − | 6394.73i | 0.143379 | − | 0.248341i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −690.000 | −0.0267043 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2183.50 | − | 3781.93i | −0.0840725 | − | 0.145618i | 0.820923 | − | 0.571039i | \(-0.193459\pi\) |
−0.904996 | + | 0.425421i | \(0.860126\pi\) | |||||||
\(878\) | −16553.0 | + | 28670.6i | −0.636260 | + | 1.10204i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4104.00 | + | 7108.34i | 0.157211 | + | 0.272298i | ||||
\(881\) | −50190.0 | −1.91935 | −0.959673 | − | 0.281118i | \(-0.909295\pi\) | ||||
−0.959673 | + | 0.281118i | \(0.909295\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12308.0 | 0.469079 | 0.234540 | − | 0.972107i | \(-0.424642\pi\) | ||||
0.234540 | + | 0.972107i | \(0.424642\pi\) | |||||||
\(884\) | −7140.00 | − | 12366.8i | −0.271656 | − | 0.470523i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16395.0 | − | 28397.0i | 0.621671 | − | 1.07677i | ||||
\(887\) | −15808.5 | − | 27381.1i | −0.598419 | − | 1.03649i | −0.993055 | − | 0.117654i | \(-0.962463\pi\) |
0.394636 | − | 0.918838i | \(-0.370871\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −18306.0 | −0.689459 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 112.000 | − | 193.990i | 0.00420408 | − | 0.00728168i | ||||
\(893\) | 502.500 | − | 870.356i | 0.0188304 | − | 0.0326152i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11583.0 | 0.432600 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15090.0 | + | 26136.6i | 0.560757 | + | 0.971260i | ||||
\(899\) | −1311.00 | + | 2270.72i | −0.0486366 | + | 0.0842411i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10021.5 | − | 17357.7i | −0.370549 | − | 0.641810i | ||||
\(902\) | 4788.00 | 0.176744 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12336.0 | 0.453860 | ||||||||
\(905\) | 12033.0 | + | 20841.8i | 0.441978 | + | 0.765529i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6762.50 | − | 11713.0i | 0.247569 | − | 0.428802i | −0.715282 | − | 0.698836i | \(-0.753702\pi\) |
0.962851 | + | 0.270034i | \(0.0870350\pi\) | |||||||
\(908\) | 6114.00 | + | 10589.8i | 0.223458 | + | 0.387041i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19248.0 | 0.700016 | 0.350008 | − | 0.936747i | \(-0.386179\pi\) | ||||
0.350008 | + | 0.936747i | \(0.386179\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16758.0 | − | 29025.7i | 0.607458 | − | 1.05215i | ||||
\(914\) | −14785.0 | + | 25608.4i | −0.535059 | + | 0.926750i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3844.00 | 0.138656 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4347.50 | + | 7530.09i | 0.156051 | + | 0.270288i | 0.933441 | − | 0.358730i | \(-0.116790\pi\) |
−0.777390 | + | 0.629019i | \(0.783457\pi\) | |||||||
\(920\) | 2484.00 | − | 4302.41i | 0.0890164 | − | 0.154181i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2898.00 | + | 5019.48i | 0.103515 | + | 0.179293i | ||||
\(923\) | 6720.00 | 0.239644 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11132.0 | 0.395695 | ||||||||
\(926\) | 464.000 | + | 803.672i | 0.0164665 | + | 0.0285208i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1824.00 | + | 3159.26i | −0.0645213 | + | 0.111754i | ||||
\(929\) | −9739.50 | − | 16869.3i | −0.343964 | − | 0.595763i | 0.641201 | − | 0.767373i | \(-0.278437\pi\) |
−0.985165 | + | 0.171610i | \(0.945103\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 11316.0 | 0.397712 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4233.00 | − | 7331.77i | 0.148295 | − | 0.256855i | ||||
\(935\) | 13081.5 | − | 22657.8i | 0.457552 | − | 0.792503i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12502.0 | 0.435883 | 0.217942 | − | 0.975962i | \(-0.430066\pi\) | ||||
0.217942 | + | 0.975962i | \(0.430066\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3618.00 | + | 6266.56i | 0.125538 | + | 0.217439i | ||||
\(941\) | 7996.50 | − | 13850.3i | 0.277023 | − | 0.479818i | −0.693621 | − | 0.720340i | \(-0.743986\pi\) |
0.970643 | + | 0.240523i | \(0.0773189\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1449.00 | − | 2509.74i | −0.0500381 | − | 0.0866685i | ||||
\(944\) | 3504.00 | 0.120811 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14136.0 | 0.485836 | ||||||||
\(947\) | 22000.5 | + | 38106.0i | 0.754932 | + | 1.30758i | 0.945408 | + | 0.325888i | \(0.105663\pi\) |
−0.190477 | + | 0.981692i | \(0.561003\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10955.0 | + | 18974.6i | −0.374725 | + | 0.649043i | ||||
\(950\) | 220.000 | + | 381.051i | 0.00751341 | + | 0.0130136i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4002.00 | 0.136031 | 0.0680155 | − | 0.997684i | \(-0.478333\pi\) | ||||
0.0680155 | + | 0.997684i | \(0.478333\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18832.5 | + | 32618.8i | −0.638121 | + | 1.10526i | ||||
\(956\) | −7080.00 | + | 12262.9i | −0.239523 | + | 0.414865i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5478.00 | −0.184745 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14631.0 | + | 25341.6i | 0.491121 | + | 0.850647i | ||||
\(962\) | −17710.0 | + | 30674.6i | −0.593548 | + | 1.02806i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10462.0 | + | 18120.7i | 0.349542 | + | 0.605424i | ||||
\(965\) | 765.000 | 0.0255194 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10544.0 | 0.350643 | 0.175322 | − | 0.984511i | \(-0.443903\pi\) | ||||
0.175322 | + | 0.984511i | \(0.443903\pi\) | |||||||
\(968\) | 7672.00 | + | 13288.3i | 0.254739 | + | 0.441221i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −16506.0 | + | 28589.2i | −0.546367 | + | 0.946335i | ||||
\(971\) | 3091.50 | + | 5354.64i | 0.102174 | + | 0.176971i | 0.912580 | − | 0.408898i | \(-0.134087\pi\) |
−0.810406 | + | 0.585869i | \(0.800753\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −34102.0 | −1.12187 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5672.00 | + | 9824.19i | −0.186021 | + | 0.322197i | ||||
\(977\) | 1861.50 | − | 3224.21i | 0.0609567 | − | 0.105580i | −0.833937 | − | 0.551860i | \(-0.813918\pi\) |
0.894893 | + | 0.446280i | \(0.147252\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −57969.0 | −1.89244 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4296.00 | + | 7440.89i | 0.139604 | + | 0.241801i | ||||
\(983\) | 22948.5 | − | 39748.0i | 0.744602 | − | 1.28969i | −0.205779 | − | 0.978599i | \(-0.565973\pi\) |
0.950381 | − | 0.311089i | \(-0.100694\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1755.00 | + | 3039.75i | 0.0567705 | + | 0.0983294i | ||||
\(986\) | 11628.0 | 0.375569 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1400.00 | −0.0450809 | ||||||||
\(989\) | −4278.00 | − | 7409.71i | −0.137545 | − | 0.238236i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3233.50 | + | 5600.59i | −0.103648 | + | 0.179524i | −0.913185 | − | 0.407545i | \(-0.866385\pi\) |
0.809537 | + | 0.587069i | \(0.199718\pi\) | |||||||
\(992\) | −368.000 | − | 637.395i | −0.0117782 | − | 0.0204005i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25497.0 | −0.812371 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11519.5 | − | 19952.4i | 0.365924 | − | 0.633799i | −0.623000 | − | 0.782222i | \(-0.714086\pi\) |
0.988924 | + | 0.148423i | \(0.0474197\pi\) | |||||||
\(998\) | 3401.00 | − | 5890.70i | 0.107873 | − | 0.186841i | ||||
\(999\) | 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 | 882.4.g.u.361.1 | 2 | ||
3.2 | odd | 2 | 98.4.c.a.67.1 | 2 | |||
7.2 | even | 3 | inner | 882.4.g.u.667.1 | 2 | ||
7.3 | odd | 6 | 882.4.a.f.1.1 | 1 | |||
7.4 | even | 3 | 882.4.a.c.1.1 | 1 | |||
7.5 | odd | 6 | 126.4.g.d.37.1 | 2 | |||
7.6 | odd | 2 | 126.4.g.d.109.1 | 2 | |||
21.2 | odd | 6 | 98.4.c.a.79.1 | 2 | |||
21.5 | even | 6 | 14.4.c.a.9.1 | ✓ | 2 | ||
21.11 | odd | 6 | 98.4.a.f.1.1 | 1 | |||
21.17 | even | 6 | 98.4.a.d.1.1 | 1 | |||
21.20 | even | 2 | 14.4.c.a.11.1 | yes | 2 | ||
84.11 | even | 6 | 784.4.a.c.1.1 | 1 | |||
84.47 | odd | 6 | 112.4.i.a.65.1 | 2 | |||
84.59 | odd | 6 | 784.4.a.p.1.1 | 1 | |||
84.83 | odd | 2 | 112.4.i.a.81.1 | 2 | |||
105.47 | odd | 12 | 350.4.j.b.149.1 | 4 | |||
105.59 | even | 6 | 2450.4.a.q.1.1 | 1 | |||
105.62 | odd | 4 | 350.4.j.b.249.2 | 4 | |||
105.68 | odd | 12 | 350.4.j.b.149.2 | 4 | |||
105.74 | odd | 6 | 2450.4.a.d.1.1 | 1 | |||
105.83 | odd | 4 | 350.4.j.b.249.1 | 4 | |||
105.89 | even | 6 | 350.4.e.e.51.1 | 2 | |||
105.104 | even | 2 | 350.4.e.e.151.1 | 2 | |||
168.5 | even | 6 | 448.4.i.b.65.1 | 2 | |||
168.83 | odd | 2 | 448.4.i.e.193.1 | 2 | |||
168.125 | even | 2 | 448.4.i.b.193.1 | 2 | |||
168.131 | odd | 6 | 448.4.i.e.65.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.4.c.a.9.1 | ✓ | 2 | 21.5 | even | 6 | ||
14.4.c.a.11.1 | yes | 2 | 21.20 | even | 2 | ||
98.4.a.d.1.1 | 1 | 21.17 | even | 6 | |||
98.4.a.f.1.1 | 1 | 21.11 | odd | 6 | |||
98.4.c.a.67.1 | 2 | 3.2 | odd | 2 | |||
98.4.c.a.79.1 | 2 | 21.2 | odd | 6 | |||
112.4.i.a.65.1 | 2 | 84.47 | odd | 6 | |||
112.4.i.a.81.1 | 2 | 84.83 | odd | 2 | |||
126.4.g.d.37.1 | 2 | 7.5 | odd | 6 | |||
126.4.g.d.109.1 | 2 | 7.6 | odd | 2 | |||
350.4.e.e.51.1 | 2 | 105.89 | even | 6 | |||
350.4.e.e.151.1 | 2 | 105.104 | even | 2 | |||
350.4.j.b.149.1 | 4 | 105.47 | odd | 12 | |||
350.4.j.b.149.2 | 4 | 105.68 | odd | 12 | |||
350.4.j.b.249.1 | 4 | 105.83 | odd | 4 | |||
350.4.j.b.249.2 | 4 | 105.62 | odd | 4 | |||
448.4.i.b.65.1 | 2 | 168.5 | even | 6 | |||
448.4.i.b.193.1 | 2 | 168.125 | even | 2 | |||
448.4.i.e.65.1 | 2 | 168.131 | odd | 6 | |||
448.4.i.e.193.1 | 2 | 168.83 | odd | 2 | |||
784.4.a.c.1.1 | 1 | 84.11 | even | 6 | |||
784.4.a.p.1.1 | 1 | 84.59 | odd | 6 | |||
882.4.a.c.1.1 | 1 | 7.4 | even | 3 | |||
882.4.a.f.1.1 | 1 | 7.3 | odd | 6 | |||
882.4.g.u.361.1 | 2 | 1.1 | even | 1 | trivial | ||
882.4.g.u.667.1 | 2 | 7.2 | even | 3 | inner | ||
2450.4.a.d.1.1 | 1 | 105.74 | odd | 6 | |||
2450.4.a.q.1.1 | 1 | 105.59 | even | 6 |