Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(17,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bc (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 14 x^{10} - 32 x^{9} + 70 x^{8} + 224 x^{7} - 50 x^{6} + 2016 x^{5} + 5670 x^{4} + \cdots + 531441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{7} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.4 | ||
Root | \(-2.92030 + 0.686929i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.17 |
Dual form | 336.4.bc.c.257.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.18980 | + | 5.05810i | 0.228976 | + | 0.973432i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.619556 | + | 1.07310i | 0.0554148 | + | 0.0959812i | 0.892402 | − | 0.451241i | \(-0.149019\pi\) |
−0.836987 | + | 0.547222i | \(0.815685\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.82127 | + | 16.2845i | −0.476304 | + | 0.879281i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −24.1688 | + | 12.0362i | −0.895140 | + | 0.445786i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 56.1748 | + | 32.4325i | 1.53976 | + | 0.888980i | 0.998852 | + | 0.0478964i | \(0.0152517\pi\) |
0.540906 | + | 0.841083i | \(0.318082\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 54.9296i | − | 1.17190i | −0.810346 | − | 0.585952i | \(-0.800721\pi\) | ||
0.810346 | − | 0.585952i | \(-0.199279\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.69072 | + | 4.41055i | −0.0807425 | + | 0.0759200i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −47.9159 | + | 82.9928i | −0.683607 | + | 1.18404i | 0.290265 | + | 0.956946i | \(0.406256\pi\) |
−0.973872 | + | 0.227096i | \(0.927077\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −23.2913 | + | 13.4472i | −0.281231 | + | 0.162369i | −0.633980 | − | 0.773349i | \(-0.718580\pi\) |
0.352750 | + | 0.935718i | \(0.385247\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −92.8642 | − | 25.2436i | −0.964982 | − | 0.262315i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −150.137 | + | 86.6815i | −1.36112 | + | 0.785841i | −0.989773 | − | 0.142654i | \(-0.954436\pi\) |
−0.371345 | + | 0.928495i | \(0.621103\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 61.7323 | − | 106.923i | 0.493858 | − | 0.855388i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −89.6363 | − | 107.927i | −0.638908 | − | 0.769283i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 16.9397i | 0.108470i | 0.998528 | + | 0.0542349i | \(0.0172720\pi\) | ||||
−0.998528 | + | 0.0542349i | \(0.982728\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −66.1489 | − | 38.1911i | −0.383248 | − | 0.221268i | 0.295982 | − | 0.955193i | \(-0.404353\pi\) |
−0.679231 | + | 0.733925i | \(0.737686\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −97.2105 | + | 322.726i | −0.512793 | + | 1.70241i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −22.9402 | + | 0.623042i | −0.110789 | + | 0.00300895i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 69.3842 | + | 120.177i | 0.308289 | + | 0.533972i | 0.977988 | − | 0.208660i | \(-0.0669103\pi\) |
−0.669699 | + | 0.742632i | \(0.733577\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 277.840 | − | 65.3551i | 1.14077 | − | 0.268338i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 100.811 | 0.383999 | 0.192000 | − | 0.981395i | \(-0.438503\pi\) | ||||
0.192000 | + | 0.981395i | \(0.438503\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −197.789 | −0.701454 | −0.350727 | − | 0.936478i | \(-0.614066\pi\) | ||||
−0.350727 | + | 0.936478i | \(0.614066\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −27.8900 | − | 18.4785i | −0.0923911 | − | 0.0612135i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −161.676 | − | 280.031i | −0.501762 | − | 0.869078i | −0.999998 | − | 0.00203631i | \(-0.999352\pi\) |
0.498235 | − | 0.867042i | \(-0.333982\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −187.370 | − | 287.300i | −0.546270 | − | 0.837609i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −476.796 | − | 143.619i | −1.30911 | − | 0.394327i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −248.397 | − | 143.412i | −0.643772 | − | 0.371682i | 0.142294 | − | 0.989824i | \(-0.454552\pi\) |
−0.786066 | + | 0.618143i | \(0.787885\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 80.3751i | 0.197051i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −95.7292 | − | 101.810i | −0.222450 | − | 0.236580i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −84.2538 | + | 145.932i | −0.185914 | + | 0.322012i | −0.943884 | − | 0.330277i | \(-0.892858\pi\) |
0.757970 | + | 0.652289i | \(0.226191\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −166.581 | + | 96.1756i | −0.349648 | + | 0.201869i | −0.664530 | − | 0.747261i | \(-0.731368\pi\) |
0.314882 | + | 0.949131i | \(0.398035\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 17.1953 | − | 499.751i | 0.0343873 | − | 0.999409i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 58.9452 | − | 34.0320i | 0.112481 | − | 0.0649408i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −442.197 | + | 765.908i | −0.806313 | + | 1.39657i | 0.109088 | + | 0.994032i | \(0.465207\pi\) |
−0.915401 | + | 0.402543i | \(0.868126\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −617.076 | − | 656.274i | −1.07663 | − | 1.14502i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 661.451i | 1.10563i | 0.833304 | + | 0.552815i | \(0.186446\pi\) | ||||
−0.833304 | + | 0.552815i | \(0.813554\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 125.139 | + | 72.2493i | 0.200637 | + | 0.115838i | 0.596952 | − | 0.802277i | \(-0.296378\pi\) |
−0.396316 | + | 0.918114i | \(0.629711\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 614.279 | + | 185.031i | 0.945744 | + | 0.284874i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1023.68 | + | 628.683i | −1.51506 | + | 0.930455i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −228.592 | − | 395.933i | −0.325552 | − | 0.563872i | 0.656072 | − | 0.754698i | \(-0.272217\pi\) |
−0.981624 | + | 0.190826i | \(0.938883\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 439.259 | − | 581.801i | 0.602550 | − | 0.798081i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 967.789 | 1.27986 | 0.639931 | − | 0.768432i | \(-0.278963\pi\) | ||||
0.639931 | + | 0.768432i | \(0.278963\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −118.746 | −0.151528 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −85.6827 | + | 20.1548i | −0.105588 | + | 0.0248370i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 605.448 | + | 1048.67i | 0.721094 | + | 1.24897i | 0.960562 | + | 0.278067i | \(0.0896937\pi\) |
−0.239468 | + | 0.970904i | \(0.576973\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 894.502 | + | 484.549i | 1.03043 | + | 0.558182i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 114.471 | − | 380.027i | 0.127635 | − | 0.423731i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −28.8605 | − | 16.6626i | −0.0311687 | − | 0.0179952i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 777.582i | 0.813933i | 0.913443 | + | 0.406967i | \(0.133413\pi\) | ||||
−0.913443 | + | 0.406967i | \(0.866587\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1748.04 | − | 107.722i | −1.77459 | − | 0.109359i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 866.580 | − | 1500.96i | 0.853742 | − | 1.47872i | −0.0240654 | − | 0.999710i | \(-0.507661\pi\) |
0.877807 | − | 0.479014i | \(-0.159006\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1106.65 | − | 638.925i | 1.05866 | − | 0.611215i | 0.133595 | − | 0.991036i | \(-0.457348\pi\) |
0.925060 | + | 0.379821i | \(0.124014\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −30.4456 | − | 115.293i | −0.0282970 | − | 0.107156i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1131.68 | + | 653.374i | −1.02246 | + | 0.590318i | −0.914816 | − | 0.403871i | \(-0.867664\pi\) |
−0.107645 | + | 0.994189i | \(0.534331\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −508.523 | + | 880.787i | −0.446859 | + | 0.773983i | −0.998180 | − | 0.0603107i | \(-0.980791\pi\) |
0.551320 | + | 0.834294i | \(0.314124\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −525.314 | + | 493.938i | −0.449194 | + | 0.422365i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 114.438i | 0.0952693i | 0.998865 | + | 0.0476346i | \(0.0151683\pi\) | ||||
−0.998865 | + | 0.0476346i | \(0.984832\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −186.036 | − | 107.408i | −0.150852 | − | 0.0870945i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 661.145 | + | 1327.58i | 0.522418 | + | 1.04902i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −928.818 | − | 1512.39i | −0.715501 | − | 1.16505i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1438.24 | + | 2491.10i | 1.08057 | + | 1.87160i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 119.944 | + | 509.910i | 0.0879268 | + | 0.373797i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 307.876 | 0.220298 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2154.75 | 1.50554 | 0.752768 | − | 0.658286i | \(-0.228718\pi\) | ||||
0.752768 | + | 0.658286i | \(0.228718\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −235.328 | − | 1000.44i | −0.160616 | − | 0.682818i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 449.460 | + | 778.487i | 0.299767 | + | 0.519212i | 0.976083 | − | 0.217400i | \(-0.0697577\pi\) |
−0.676315 | + | 0.736612i | \(0.736424\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.5229 | − | 497.908i | −0.00881641 | − | 0.324617i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 60.2825 | − | 163.056i | 0.0384318 | − | 0.103953i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −494.836 | − | 285.694i | −0.308589 | − | 0.178164i | 0.337706 | − | 0.941252i | \(-0.390349\pi\) |
−0.646295 | + | 0.763088i | \(0.723682\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1078.72i | − | 0.658244i | −0.944287 | − | 0.329122i | \(-0.893247\pi\) | ||
0.944287 | − | 0.329122i | \(-0.106753\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1224.06 | − | 1150.95i | 0.731097 | − | 0.687430i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1781.51 | − | 3085.66i | 1.04180 | − | 1.80445i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.1780 | + | 10.4951i | −0.0104111 | + | 0.00601083i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1230.26 | − | 1289.57i | 0.690273 | − | 0.723549i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 841.243 | − | 485.692i | 0.462532 | − | 0.267043i | −0.250576 | − | 0.968097i | \(-0.580620\pi\) |
0.713108 | + | 0.701054i | \(0.247287\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −730.013 | + | 1264.42i | −0.393428 | + | 0.681437i | −0.992899 | − | 0.118959i | \(-0.962044\pi\) |
0.599471 | + | 0.800396i | \(0.295378\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 159.149 | − | 2582.56i | 0.0840946 | − | 1.36463i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 94.6461i | − | 0.0490462i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1878.50 | + | 1084.55i | 0.954909 | + | 0.551317i | 0.894602 | − | 0.446863i | \(-0.147459\pi\) |
0.0603065 | + | 0.998180i | \(0.480792\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 429.850 | − | 1427.05i | 0.214398 | − | 0.711774i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −87.1693 | − | 3209.55i | −0.0426702 | − | 1.57110i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1693.30 | + | 2932.89i | 0.813680 | + | 1.40933i | 0.910272 | + | 0.414011i | \(0.135872\pi\) |
−0.0965924 | + | 0.995324i | \(0.530794\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −406.545 | + | 95.6300i | −0.191815 | + | 0.0451199i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1261.28 | −0.584436 | −0.292218 | − | 0.956352i | \(-0.594393\pi\) | ||||
−0.292218 | + | 0.956352i | \(0.594393\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −820.265 | −0.373357 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 401.068 | − | 605.341i | 0.179359 | − | 0.270711i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 67.8201 | + | 117.468i | 0.0298050 | + | 0.0516238i | 0.880543 | − | 0.473966i | \(-0.157178\pi\) |
−0.850738 | + | 0.525590i | \(0.823845\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1196.64 | + | 1948.48i | 0.516900 | + | 0.841665i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −838.383 | − | 252.535i | −0.356027 | − | 0.107241i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2940.82 | + | 1697.88i | 1.22797 | + | 0.708971i | 0.966606 | − | 0.256268i | \(-0.0824929\pi\) |
0.261368 | + | 0.965239i | \(0.415826\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1271.84i | 0.522294i | 0.965299 | + | 0.261147i | \(0.0841007\pi\) | ||||
−0.965299 | + | 0.261147i | \(0.915899\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −684.664 | − | 728.154i | −0.276567 | − | 0.294135i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −85.9748 | + | 148.913i | −0.0341675 | + | 0.0591799i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5383.34 | + | 3108.07i | −2.10518 | + | 1.21543i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2548.25 | − | 507.627i | 0.980730 | − | 0.195367i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2509.87 | − | 1449.08i | 0.950827 | − | 0.548960i | 0.0574895 | − | 0.998346i | \(-0.481690\pi\) |
0.893338 | + | 0.449386i | \(0.148357\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 636.386 | − | 1102.25i | 0.237348 | − | 0.411098i | −0.722605 | − | 0.691261i | \(-0.757055\pi\) |
0.959952 | + | 0.280163i | \(0.0903887\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 242.270 | + | 257.659i | 0.0889709 | + | 0.0946224i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1931.73i | 0.698630i | 0.937005 | + | 0.349315i | \(0.113586\pi\) | ||||
−0.937005 | + | 0.349315i | \(0.886414\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2875.45 | + | 1660.14i | 1.02430 | + | 0.591378i | 0.915346 | − | 0.402669i | \(-0.131917\pi\) |
0.108951 | + | 0.994047i | \(0.465251\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4400.16 | − | 1325.40i | −1.54410 | − | 0.465108i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −275.855 | − | 149.430i | −0.0953754 | − | 0.0516645i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 62.4579 | + | 108.180i | 0.0212793 | + | 0.0368567i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2585.30 | − | 3902.07i | 0.868073 | − | 1.31020i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1744.51 | −0.577370 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1337.20 | −0.436288 | −0.218144 | − | 0.975917i | \(-0.570000\pi\) | ||||
−0.218144 | + | 0.975917i | \(0.570000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3345.68 | + | 786.991i | −1.07626 | + | 0.253163i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −122.541 | − | 212.248i | −0.0388709 | − | 0.0673264i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1205.44 | − | 740.309i | 0.377100 | − | 0.231592i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −216.554 | + | 718.930i | −0.0668190 | + | 0.221830i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4558.77 | + | 2632.01i | 1.38758 | + | 0.801121i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3883.82i | − | 1.16628i | −0.812373 | − | 0.583138i | \(-0.801825\pi\) | ||
0.812373 | − | 0.583138i | \(-0.198175\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −205.039 | + | 3327.23i | −0.0607524 | + | 0.985847i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2196.76 | + | 3804.90i | −0.642309 | + | 1.11251i | 0.342607 | + | 0.939479i | \(0.388690\pi\) |
−0.984916 | + | 0.173033i | \(0.944643\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4125.28 | − | 2381.73i | 1.19042 | − | 0.687290i | 0.232018 | − | 0.972711i | \(-0.425467\pi\) |
0.958402 | + | 0.285422i | \(0.0921337\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4397.91 | − | 4429.88i | −1.25265 | − | 1.26175i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −977.023 | + | 564.085i | −0.274708 | + | 0.158603i | −0.631025 | − | 0.775762i | \(-0.717366\pi\) |
0.356317 | + | 0.934365i | \(0.384032\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 200.334 | − | 346.989i | 0.0556101 | − | 0.0963196i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1730.69 | − | 1627.32i | 0.474348 | − | 0.446016i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2668.99i | 0.722355i | 0.932497 | + | 0.361177i | \(0.117625\pi\) | ||||
−0.932497 | + | 0.361177i | \(0.882375\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4978.44 | + | 2874.31i | 1.33066 | + | 0.768259i | 0.985401 | − | 0.170248i | \(-0.0544568\pi\) |
0.345262 | + | 0.938506i | \(0.387790\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3465.44 | + | 1529.59i | 0.914847 | + | 0.403800i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 192.216 | − | 379.066i | 0.0501234 | − | 0.0988476i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 738.651 | + | 1279.38i | 0.190280 | + | 0.329575i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1151.47 | + | 4895.17i | 0.293058 | + | 1.24586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7376.76 | −1.85505 | −0.927524 | − | 0.373763i | \(-0.878067\pi\) | ||||
−0.927524 | + | 0.373763i | \(0.878067\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11245.2 | −2.79439 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −141.284 | − | 600.632i | −0.0346963 | − | 0.147502i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1148.07 | − | 1988.51i | −0.278655 | − | 0.482645i | 0.692396 | − | 0.721518i | \(-0.256555\pi\) |
−0.971051 | + | 0.238873i | \(0.923222\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2569.08 | + | 69.7746i | −0.616350 | + | 0.0167397i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −203.890 | − | 409.412i | −0.0483543 | − | 0.0970956i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6321.86 | − | 3649.93i | −1.48222 | − | 0.855758i | −0.482420 | − | 0.875940i | \(-0.660242\pi\) |
−0.999796 | + | 0.0201823i | \(0.993575\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 355.407i | − | 0.0823867i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4583.90 | + | 4310.12i | −1.05068 | + | 0.987921i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −801.460 | + | 1388.17i | −0.181657 | + | 0.314640i | −0.942445 | − | 0.334361i | \(-0.891480\pi\) |
0.760788 | + | 0.649001i | \(0.224813\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1676.27 | + | 967.793i | −0.375741 | + | 0.216934i | −0.675964 | − | 0.736935i | \(-0.736272\pi\) |
0.300222 | + | 0.953869i | \(0.402939\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1386.62 | + | 5101.00i | −0.307407 | + | 1.13087i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6935.60 | − | 4004.27i | 1.52084 | − | 0.878060i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1429.42 | + | 2475.83i | −0.310056 | + | 0.537033i | −0.978374 | − | 0.206843i | \(-0.933681\pi\) |
0.668318 | + | 0.743876i | \(0.267014\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2058.41 | + | 126.849i | 0.441699 | + | 0.0272195i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3286.82i | 0.697777i | 0.937164 | + | 0.348889i | \(0.113441\pi\) | ||||
−0.937164 | + | 0.348889i | \(0.886559\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1070.70 | − | 618.169i | −0.224900 | − | 0.129846i | 0.383317 | − | 0.923617i | \(-0.374782\pi\) |
−0.608217 | + | 0.793771i | \(0.708115\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 49.9431 | − | 165.804i | 0.0103803 | − | 0.0344611i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −889.278 | + | 1641.65i | −0.182900 | + | 0.337643i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2135.37 | − | 3698.58i | −0.434638 | − | 0.752814i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3933.09 | + | 925.164i | −0.792308 | + | 0.186371i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9667.17 | −1.92752 | −0.963758 | − | 0.266778i | \(-0.914041\pi\) | ||||
−0.963758 | + | 0.266778i | \(0.914041\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −208.800 | −0.0412095 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1534.94 | − | 8969.93i | −0.299887 | − | 1.75249i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4761.39 | + | 8246.96i | 0.920930 | + | 1.59510i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1744.75 | − | 3220.90i | 0.334105 | − | 0.616775i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8623.06 | + | 2597.41i | 1.63492 | + | 0.492467i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −206.413 | − | 119.172i | −0.0387513 | − | 0.0223731i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8175.07i | − | 1.51979i | −0.650045 | − | 0.759896i | \(-0.725250\pi\) | ||
0.650045 | − | 0.759896i | \(-0.274750\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4548.43 | + | 4837.36i | 0.837383 | + | 0.890575i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −359.769 | + | 623.138i | −0.0655969 | + | 0.113617i | −0.896959 | − | 0.442115i | \(-0.854228\pi\) |
0.831362 | + | 0.555732i | \(0.187562\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6310.26 | − | 3643.23i | 1.13954 | − | 0.657915i | 0.193226 | − | 0.981154i | \(-0.438105\pi\) |
0.946317 | + | 0.323239i | \(0.104772\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 546.938 | − | 291.172i | 0.0978300 | − | 0.0520815i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2155.25 | − | 1244.34i | 0.381864 | − | 0.220470i | −0.296765 | − | 0.954951i | \(-0.595908\pi\) |
0.678629 | + | 0.734481i | \(0.262574\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −549.397 | + | 951.584i | −0.0964274 | + | 0.167017i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4651.30 | − | 4946.75i | −0.808754 | − | 0.860127i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2577.34i | − | 0.443985i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5873.27 | − | 3390.93i | −1.00243 | − | 0.578754i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5060.15 | − | 1524.20i | −0.855740 | − | 0.257763i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5986.35 | − | 162.585i | 1.00316 | − | 0.0272451i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1853.27 | − | 3209.96i | −0.307749 | − | 0.533037i | 0.670121 | − | 0.742252i | \(-0.266242\pi\) |
−0.977870 | + | 0.209215i | \(0.932909\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3123.41 | − | 2069.41i | −0.513999 | − | 0.340549i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1095.86 | −0.178727 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5344.50 | −0.863898 | −0.431949 | − | 0.901898i | \(-0.642174\pi\) | ||||
−0.431949 | + | 0.901898i | \(0.642174\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −578.839 | + | 136.158i | −0.0927382 | + | 0.0218144i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2477.27 | − | 4290.75i | −0.393406 | − | 0.681400i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6331.38 | − | 516.886i | 0.996684 | − | 0.0813680i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 321.936 | − | 1068.78i | 0.0502390 | − | 0.166787i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2720.97 | + | 1570.95i | 0.420949 | + | 0.243035i | 0.695483 | − | 0.718542i | \(-0.255190\pi\) |
−0.274534 | + | 0.961577i | \(0.588524\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1019.37i | − | 0.156348i | −0.996940 | − | 0.0781741i | \(-0.975091\pi\) | ||
0.996940 | − | 0.0781741i | \(-0.0249090\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5928.41 | + | 4923.69i | −0.901525 | + | 0.748738i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3352.27 | + | 5806.30i | −0.505448 | + | 0.875462i | 0.494532 | + | 0.869160i | \(0.335340\pi\) |
−0.999980 | + | 0.00630284i | \(0.997994\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −709.805 | + | 409.806i | −0.106120 | + | 0.0612683i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6544.71 | − | 6497.49i | 0.970261 | − | 0.963260i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1032.81 | + | 596.291i | −0.151837 | + | 0.0876631i | −0.573994 | − | 0.818860i | \(-0.694607\pi\) |
0.422157 | + | 0.906523i | \(0.361273\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3067.84 | + | 5313.66i | −0.447273 | + | 0.774699i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10889.0 | + | 10238.7i | −1.57445 | + | 1.48041i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 179.050i | 0.0256765i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3581.98 | − | 2068.05i | −0.509476 | − | 0.294146i | 0.223142 | − | 0.974786i | \(-0.428369\pi\) |
−0.732618 | + | 0.680640i | \(0.761702\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2436.47 | + | 1213.38i | −0.343733 | + | 0.171182i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4526.56 | − | 2779.94i | 0.633443 | − | 0.389023i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 696.094 | + | 1205.67i | 0.0966283 | + | 0.167365i | 0.910287 | − | 0.413978i | \(-0.135861\pi\) |
−0.813659 | + | 0.581343i | \(0.802528\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 366.309 | + | 1557.27i | 0.0504430 | + | 0.214445i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 930.491 | 0.127116 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6840.24 | 0.927070 | 0.463535 | − | 0.886079i | \(-0.346581\pi\) | ||||
0.463535 | + | 0.886079i | \(0.346581\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2563.71 | + | 10898.9i | 0.344732 | + | 1.46554i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4912.29 | − | 8508.33i | −0.655369 | − | 1.13513i | −0.981801 | − | 0.189912i | \(-0.939180\pi\) |
0.326432 | − | 0.945221i | \(-0.394153\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1308.87 | − | 709.010i | −0.173263 | − | 0.0938559i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4780.32 | − | 2380.63i | 0.627899 | − | 0.312698i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 246.932 | + | 142.566i | 0.0321850 | + | 0.0185820i | 0.516006 | − | 0.856585i | \(-0.327418\pi\) |
−0.483821 | + | 0.875167i | \(0.660751\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 16613.7i | − | 2.14883i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3402.90 | + | 3199.65i | −0.436778 | + | 0.410690i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 283.251 | − | 490.605i | 0.0360808 | − | 0.0624938i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10717.4 | + | 6187.70i | −1.35489 | + | 0.782247i | −0.988930 | − | 0.148384i | \(-0.952593\pi\) |
−0.365961 | + | 0.930630i | \(0.619260\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2502.38 | − | 660.809i | 0.313974 | − | 0.0829119i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8479.92 | − | 4895.88i | 1.05603 | − | 0.609697i | 0.131696 | − | 0.991290i | \(-0.457958\pi\) |
0.924331 | + | 0.381593i | \(0.124624\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2097.82 | + | 3633.53i | −0.259305 | + | 0.449130i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 896.478 | + | 110.911i | 0.109991 | + | 0.0136080i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9001.22i | 1.09625i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7947.38 | + | 4588.42i | 0.960813 | + | 0.554726i | 0.896423 | − | 0.443199i | \(-0.146156\pi\) |
0.0643901 | + | 0.997925i | \(0.479490\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 856.314 | − | 2842.85i | 0.102771 | − | 0.341186i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1633.20 | − | 2659.33i | −0.194588 | − | 0.316846i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 599.600 | + | 1038.54i | 0.0709233 | + | 0.122843i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5456.28 | − | 1283.46i | 0.640756 | − | 0.150722i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11642.2 | −1.35742 | −0.678711 | − | 0.734405i | \(-0.737461\pi\) | ||||
−0.678711 | + | 0.734405i | \(0.737461\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4218.54 | 0.488359 | 0.244179 | − | 0.969730i | \(-0.421481\pi\) | ||||
0.244179 | + | 0.969730i | \(0.421481\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7278.01 | + | 4822.03i | 0.836570 | + | 0.554268i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5915.92 | + | 10246.7i | 0.675210 | + | 1.16950i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −96.7168 | − | 3561.08i | −0.0109612 | − | 0.403590i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17727.2 | + | 5339.74i | 1.99505 | + | 0.600944i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7697.77 | + | 4444.31i | 0.860298 | + | 0.496693i | 0.864112 | − | 0.503300i | \(-0.167881\pi\) |
−0.00381421 | + | 0.999993i | \(0.501214\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8521.56i | − | 0.945774i | −0.881123 | − | 0.472887i | \(-0.843212\pi\) | ||
0.881123 | − | 0.472887i | \(-0.156788\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −74.7134 | − | 79.4593i | −0.00823502 | − | 0.00875812i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2331.25 | − | 4037.85i | 0.255192 | − | 0.442005i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 530.773 | − | 306.442i | 0.0577048 | − | 0.0333159i | −0.470870 | − | 0.882203i | \(-0.656060\pi\) |
0.528575 | + | 0.848887i | \(0.322727\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7986.52 | + | 4688.46i | 0.862382 | + | 0.506258i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −319.307 | + | 184.352i | −0.0342454 | + | 0.0197716i | −0.517025 | − | 0.855970i | \(-0.672961\pi\) |
0.482780 | + | 0.875742i | \(0.339627\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −750.218 | + | 1299.42i | −0.0799185 | + | 0.138423i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3457.59 | + | 3677.22i | 0.365857 | + | 0.389097i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6042.70i | 0.635128i | 0.948237 | + | 0.317564i | \(0.102865\pi\) | ||||
−0.948237 | + | 0.317564i | \(0.897135\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5663.02 | + | 3269.54i | 0.591266 | + | 0.341368i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7264.13 | − | 2188.08i | −0.753419 | − | 0.226942i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 34.2235 | + | 1260.10i | 0.00352620 | + | 0.129834i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6521.04 | + | 11294.8i | 0.667487 | + | 1.15612i | 0.978605 | + | 0.205750i | \(0.0659633\pi\) |
−0.311118 | + | 0.950371i | \(0.600703\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13252.2 | − | 2267.73i | 1.34763 | − | 0.230607i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2429.28 | 0.245429 | 0.122714 | − | 0.992442i | \(-0.460840\pi\) | ||||
0.122714 | + | 0.992442i | \(0.460840\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9114.64 | −0.914889 | −0.457444 | − | 0.889238i | \(-0.651235\pi\) | ||||
−0.457444 | + | 0.889238i | \(0.651235\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 478.730 | − | 112.610i | 0.0477431 | − | 0.0112304i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5344.99 | − | 9257.79i | −0.529629 | − | 0.917344i | −0.999403 | − | 0.0345570i | \(-0.988998\pi\) |
0.469774 | − | 0.882787i | \(-0.344335\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8571.69 | − | 13957.2i | −0.843932 | − | 1.37417i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3250.75 | + | 10792.0i | −0.318018 | + | 1.05578i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11110.8 | − | 6414.80i | −1.08007 | − | 0.623578i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3320.51i | 0.320748i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7729.58 | + | 476.332i | 0.741956 | + | 0.0457228i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3221.06 | − | 5579.04i | 0.307253 | − | 0.532177i | −0.670508 | − | 0.741903i | \(-0.733924\pi\) |
0.977760 | + | 0.209725i | \(0.0672570\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6601.27 | − | 3811.25i | 0.625763 | − | 0.361285i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16130.5 | − | 4259.62i | 1.51959 | − | 0.401282i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −834.426 | + | 481.756i | −0.0781223 | + | 0.0451039i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7920.17 | + | 13718.1i | −0.736956 | + | 1.27644i | 0.216905 | + | 0.976193i | \(0.430404\pi\) |
−0.953860 | + | 0.300252i | \(0.902929\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12820.2 | + | 12054.4i | −1.18558 | + | 1.11477i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 174.783i | 0.0160649i | 0.999968 | + | 0.00803244i | \(0.00255683\pi\) | ||||
−0.999968 | + | 0.00803244i | \(0.997443\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1405.87 | − | 811.681i | −0.128433 | − | 0.0741507i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −967.412 | − | 1942.57i | −0.0878423 | − | 0.176388i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10771.4 | − | 5834.83i | −0.972159 | − | 0.526616i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1298.61 | + | 2249.26i | 0.116501 | + | 0.201785i | 0.918379 | − | 0.395703i | \(-0.129499\pi\) |
−0.801878 | + | 0.597488i | \(0.796166\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1500.67 | − | 6379.68i | −0.133822 | − | 0.568908i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21636.9 | 1.91797 | 0.958987 | − | 0.283449i | \(-0.0914787\pi\) | ||||
0.958987 | + | 0.283449i | \(0.0914787\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2147.58 | 0.189240 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −975.948 | − | 4148.98i | −0.0854899 | − | 0.363438i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2572.24 | − | 4455.26i | −0.223994 | − | 0.387968i | 0.732023 | − | 0.681279i | \(-0.238576\pi\) |
−0.956017 | + | 0.293311i | \(0.905243\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2280.43 | + | 1400.50i | −0.197418 | + | 0.121242i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3539.07 | + | 1308.41i | 0.304588 | + | 0.112607i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1371.26 | + | 791.700i | 0.117330 | + | 0.0677407i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 20974.2i | − | 1.78423i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −513.472 | + | 482.804i | −0.0434276 | + | 0.0408338i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10107.3 | − | 17506.4i | 0.849924 | − | 1.47211i | −0.0313516 | − | 0.999508i | \(-0.509981\pi\) |
0.881275 | − | 0.472603i | \(-0.156686\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11073.3 | − | 6393.15i | 0.925813 | − | 0.534518i | 0.0403281 | − | 0.999186i | \(-0.487160\pi\) |
0.885485 | + | 0.464668i | \(0.153826\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8431.86 | + | 8371.02i | −0.700945 | + | 0.695888i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6339.17 | − | 3659.92i | 0.523982 | − | 0.302521i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8943.88 | − | 15491.3i | 0.735093 | − | 1.27322i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 279.843 | − | 4541.09i | 0.0228703 | − | 0.371123i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 5537.49i | − | 0.450010i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1402.27 | − | 809.604i | −0.113319 | − | 0.0654247i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5089.09 | + | 16895.1i | −0.408958 | + | 1.35769i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1207.63 | − | 22215.9i | −0.0965053 | − | 1.77534i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 652.252 | + | 1129.73i | 0.0518346 | + | 0.0897801i | 0.890778 | − | 0.454438i | \(-0.150160\pi\) |
−0.838944 | + | 0.544218i | \(0.816826\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6433.10 | + | 1513.23i | −0.508418 | + | 0.119593i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1260.23 | −0.0990504 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5425.06 | −0.424056 | −0.212028 | − | 0.977264i | \(-0.568007\pi\) | ||||
−0.212028 | + | 0.977264i | \(0.568007\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2868.47 | − | 4329.45i | 0.222993 | − | 0.336569i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −227.792 | − | 394.547i | −0.0176121 | − | 0.0305050i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8464.04 | − | 229.878i | 0.650864 | − | 0.0176771i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −855.508 | − | 257.693i | −0.0654312 | − | 0.0197090i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21651.8 | + | 12500.7i | 1.64707 | + | 0.950936i | 0.978228 | + | 0.207531i | \(0.0665429\pi\) |
0.668842 | + | 0.743405i | \(0.266790\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10864.5i | 0.822036i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22126.0 | − | 23531.5i | −1.66517 | − | 1.77095i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 252.273 | − | 436.949i | 0.0188846 | − | 0.0327091i | −0.856429 | − | 0.516265i | \(-0.827322\pi\) |
0.875313 | + | 0.483556i | \(0.160655\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −122.804 | + | 70.9008i | −0.00914406 | + | 0.00527933i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5599.53 | + | 12285.3i | 0.414741 | + | 0.909940i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13368.2 | − | 7718.14i | 0.984928 | − | 0.568649i | 0.0811739 | − | 0.996700i | \(-0.474133\pi\) |
0.903754 | + | 0.428051i | \(0.140800\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 200.620 | − | 347.484i | 0.0147035 | − | 0.0254672i | −0.858580 | − | 0.512680i | \(-0.828653\pi\) |
0.873284 | + | 0.487212i | \(0.161986\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10315.8 | + | 10971.1i | 0.752093 | + | 0.799867i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21404.2i | 1.55238i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13087.8 | + | 7556.24i | 0.944284 | + | 0.545182i | 0.891301 | − | 0.453413i | \(-0.149794\pi\) |
0.0529832 | + | 0.998595i | \(0.483127\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6332.48 | + | 1907.45i | 0.454523 | + | 0.136910i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8537.12 | + | 15760.0i | −0.609603 | + | 1.12536i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9302.42 | − | 16112.3i | −0.660835 | − | 1.14460i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1015.02 | + | 1531.99i | −0.0717363 | + | 0.108273i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −92.4546 | −0.00650087 | −0.00325043 | − | 0.999995i | \(-0.501035\pi\) | ||||
−0.00325043 | + | 0.999995i | \(0.501035\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2054.26 | 0.143708 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9770.89 | + | 2298.37i | −0.680069 | + | 0.159970i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 183.749 | + | 318.262i | 0.0127245 | + | 0.0220396i | 0.872318 | − | 0.488940i | \(-0.162616\pi\) |
−0.859593 | + | 0.510979i | \(0.829283\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1047.49 | − | 1933.73i | 0.0721733 | − | 0.133236i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4975.96 | + | 16519.5i | −0.341126 | + | 1.13249i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3689.70 | + | 2130.25i | 0.251681 | + | 0.145308i | 0.620534 | − | 0.784180i | \(-0.286916\pi\) |
−0.368853 | + | 0.929488i | \(0.620249\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 799.579i | − | 0.0542687i | −0.999632 | − | 0.0271343i | \(-0.991362\pi\) | ||
0.999632 | − | 0.0271343i | \(-0.00863819\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1468.73 | − | 23833.4i | 0.0991893 | − | 1.60957i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1782.14 | + | 3086.76i | −0.119759 | + | 0.207429i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11078.7 | − | 6396.27i | 0.740806 | − | 0.427704i | −0.0815566 | − | 0.996669i | \(-0.525989\pi\) |
0.822362 | + | 0.568964i | \(0.192656\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 427.619 | − | 1573.09i | 0.0284532 | − | 0.104671i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15382.0 | + | 8880.79i | −1.01848 | + | 0.588017i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10022.5 | + | 17359.4i | −0.660365 | + | 1.14379i | 0.320155 | + | 0.947365i | \(0.396265\pi\) |
−0.980520 | + | 0.196420i | \(0.937068\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −472.874 | + | 444.631i | −0.0310051 | + | 0.0291532i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17082.6i | 1.11462i | 0.830305 | + | 0.557309i | \(0.188166\pi\) | ||||
−0.830305 | + | 0.557309i | \(0.811834\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14708.7 | + | 8492.05i | 0.955074 | + | 0.551412i | 0.894653 | − | 0.446761i | \(-0.147422\pi\) |
0.0604206 | + | 0.998173i | \(0.480756\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22813.0 | + | 8434.07i | 1.47416 | + | 0.545004i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −22417.8 | + | 608.855i | −1.44166 | + | 0.0391545i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7525.79 | − | 13035.1i | −0.481651 | − | 0.834243i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2075.61 | − | 8823.90i | −0.132204 | − | 0.562030i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13298.4 | −0.842994 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20829.5 | −1.31412 | −0.657061 | − | 0.753837i | \(-0.728201\pi\) | ||||
−0.657061 | + | 0.753837i | \(0.728201\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1591.00 | − | 6763.71i | −0.0998998 | − | 0.424697i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1334.99 | + | 2312.27i | 0.0834290 | + | 0.144503i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15781.3 | + | 10292.2i | −0.981597 | + | 0.640175i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7961.36 | − | 15986.4i | −0.492874 | − | 0.989693i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21862.6 | − | 12622.4i | −1.34714 | − | 0.777774i | −0.359299 | − | 0.933222i | \(-0.616984\pi\) |
−0.987844 | + | 0.155449i | \(0.950318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 17905.6i | − | 1.09818i | −0.835764 | − | 0.549089i | \(-0.814975\pi\) | ||
0.835764 | − | 0.549089i | \(-0.185025\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 927.772 | − | 872.358i | 0.0566372 | − | 0.0532544i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3777.94 | + | 6543.58i | −0.229561 | + | 0.397612i | −0.957678 | − | 0.287841i | \(-0.907062\pi\) |
0.728117 | + | 0.685453i | \(0.240396\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9465.88 | + | 5465.13i | −0.572524 | + | 0.330547i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5178.78 | + | 5216.42i | 0.311786 | + | 0.314052i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8162.19 | − | 4712.44i | 0.489144 | − | 0.282408i | −0.235075 | − | 0.971977i | \(-0.575534\pi\) |
0.724219 | + | 0.689570i | \(0.242200\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −556.931 | + | 964.633i | −0.0332231 | + | 0.0575440i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3894.08 | − | 239.971i | −0.231236 | − | 0.0142499i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 14519.0i | − | 0.858240i | −0.903248 | − | 0.429120i | \(-0.858824\pi\) | ||
0.903248 | − | 0.429120i | \(-0.141176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13331.6 | − | 7696.97i | −0.784474 | − | 0.452916i | 0.0535396 | − | 0.998566i | \(-0.482950\pi\) |
−0.838013 | + | 0.545650i | \(0.816283\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7888.94 | + | 26190.3i | −0.462113 | + | 1.53416i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 525.929 | − | 322.994i | 0.0306686 | − | 0.0188348i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1468.36 | − | 2543.27i | −0.0852400 | − | 0.147640i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19644.7 | − | 4620.95i | 1.13529 | − | 0.267050i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12476.9 | −0.717831 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9948.76 | 0.569831 | 0.284916 | − | 0.958553i | \(-0.408034\pi\) | ||||
0.284916 | + | 0.958553i | \(0.408034\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17073.4 | + | 2921.62i | −0.973566 | + | 0.166597i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7731.79 | + | 13391.9i | 0.438932 | + | 0.760252i | 0.997607 | − | 0.0691341i | \(-0.0220236\pi\) |
−0.558676 | + | 0.829386i | \(0.688690\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12662.5 | − | 6859.26i | −0.715676 | − | 0.387679i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21859.3 | − | 6584.38i | −1.23003 | − | 0.370505i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10282.5 | − | 5936.60i | −0.576060 | − | 0.332588i | 0.183506 | − | 0.983019i | \(-0.441255\pi\) |
−0.759566 | + | 0.650430i | \(0.774589\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 708.014i | − | 0.0394917i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16955.3 | + | 18032.3i | 0.941608 | + | 1.00142i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7877.56 | + | 13644.3i | −0.435575 | + | 0.754438i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4156.18 | − | 2399.57i | 0.228811 | − | 0.132104i | −0.381212 | − | 0.924488i | \(-0.624493\pi\) |
0.610024 | + | 0.792383i | \(0.291160\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17174.1 | − | 27515.7i | 0.941402 | − | 1.50828i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1157.58 | − | 668.329i | 0.0631791 | − | 0.0364765i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4830.44 | + | 8366.56i | −0.262505 | + | 0.454672i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4015.66 | − | 4270.74i | −0.217291 | − | 0.231093i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 8788.82i | − | 0.473536i | −0.971566 | − | 0.236768i | \(-0.923912\pi\) | ||
0.971566 | − | 0.236768i | \(-0.0760882\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3232.09 | − | 1866.05i | −0.173401 | − | 0.100113i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1993.47 | + | 600.465i | 0.106494 | + | 0.0320778i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16798.1 | + | 27352.2i | 0.893574 | + | 1.45500i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8501.87 | − | 14725.7i | −0.450345 | − | 0.780020i | 0.548063 | − | 0.836437i | \(-0.315366\pi\) |
−0.998407 | + | 0.0564176i | \(0.982032\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10290.3 | + | 6817.83i | 0.542781 | + | 0.359618i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13241.8 | 0.695527 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4414.98 | 0.230924 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13500.0 | + | 3175.56i | −0.703163 | + | 0.165402i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11003.9 | + | 19059.3i | 0.570760 | + | 0.988586i | 0.996488 | + | 0.0837345i | \(0.0266848\pi\) |
−0.425728 | + | 0.904851i | \(0.639982\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 642.520 | + | 23657.4i | 0.0331882 | + | 1.22198i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8615.20 | + | 28601.3i | −0.443157 | + | 1.47122i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1811.25 | + | 1045.73i | 0.0927837 | + | 0.0535687i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20005.6i | 1.02059i | 0.860001 | + | 0.510293i | \(0.170463\pi\) | ||||
−0.860001 | + | 0.510293i | \(0.829537\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3613.66 | + | 19348.4i | −0.183593 | + | 0.983002i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9477.24 | − | 16415.1i | 0.479519 | − | 0.830551i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7493.92 | + | 4326.62i | −0.377619 | + | 0.218018i | −0.676782 | − | 0.736184i | \(-0.736626\pi\) |
0.299163 | + | 0.954202i | \(0.403293\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2146.05 | + | 521.236i | 0.107698 | + | 0.0261579i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −49680.6 | + | 28683.1i | −2.48305 | + | 1.43359i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2518.09 | + | 4361.46i | −0.125344 | + | 0.217103i | −0.921867 | − | 0.387505i | \(-0.873337\pi\) |
0.796523 | + | 0.604608i | \(0.206670\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5592.39 | + | 5258.37i | −0.277249 | + | 0.260690i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4822.04i | 0.238093i | 0.992889 | + | 0.119047i | \(0.0379838\pi\) | ||||
−0.992889 | + | 0.119047i | \(0.962016\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1042.39 | + | 601.827i | 0.0512623 | + | 0.0295963i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −23390.3 | + | 11648.5i | −1.14566 | + | 0.570545i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −657.050 | − | 24192.4i | −0.0320535 | − | 1.18020i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10017.2 | + | 17350.3i | 0.486729 | + | 0.843039i | 0.999884 | − | 0.0152569i | \(-0.00485662\pi\) |
−0.513155 | + | 0.858296i | \(0.671523\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8776.85 | − | 37312.4i | −0.424762 | − | 1.80576i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1809.14 | −0.0872069 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6092.75 | 0.292530 | 0.146265 | − | 0.989245i | \(-0.453275\pi\) | ||||
0.146265 | + | 0.989245i | \(0.453275\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13379.5 | − | 56879.4i | −0.639849 | − | 2.72015i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3738.26 | − | 6474.85i | −0.178071 | − | 0.308427i | 0.763149 | − | 0.646223i | \(-0.223652\pi\) |
−0.941220 | + | 0.337795i | \(0.890319\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9857.37 | − | 16050.7i | −0.467708 | − | 0.761566i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2869.96 | − | 1429.26i | 0.135639 | − | 0.0675490i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8015.98 | + | 4628.03i | 0.377367 | + | 0.217873i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 24997.9i | − | 1.17223i | −0.810227 | − | 0.586117i | \(-0.800656\pi\) | ||
0.810227 | − | 0.586117i | \(-0.199344\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8692.11 | − | 8172.95i | 0.406017 | − | 0.381766i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2912.70 | + | 5044.94i | −0.135527 | + | 0.234740i | −0.925799 | − | 0.378017i | \(-0.876606\pi\) |
0.790272 | + | 0.612757i | \(0.209939\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8167.05 | + | 4715.25i | −0.378541 | + | 0.218551i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3409.61 | − | 12911.6i | −0.157425 | − | 0.596142i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2348.01 | + | 1355.62i | −0.107992 | + | 0.0623495i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21452.5 | + | 37156.8i | −0.982883 | + | 1.70240i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1828.26 | − | 1518.41i | 0.0834439 | − | 0.0693022i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2687.77i | 0.122204i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15489.8 | + | 8943.04i | 0.701590 | + | 0.405063i | 0.807940 | − | 0.589265i | \(-0.200583\pi\) |
−0.106349 | + | 0.994329i | \(0.533916\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10940.0 | − | 36319.3i | 0.493630 | − | 1.63878i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1863.57 | − | 1009.49i | −0.0837684 | − | 0.0453771i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5282.89 | + | 9150.24i | 0.236571 | + | 0.409753i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1797.68 | − | 422.862i | 0.0801978 | − | 0.0188646i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25339.1 | 1.12617 | 0.563085 | − | 0.826399i | \(-0.309614\pi\) | ||||
0.563085 | + | 0.826399i | \(0.309614\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30987.4 | 1.37203 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −27254.9 | − | 18057.7i | −1.20225 | − | 0.796550i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4686.46 | + | 8117.18i | 0.205954 | + | 0.356724i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3390.17 | − | 2082.04i | 0.148432 | − | 0.0911579i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7975.07 | − | 2402.23i | −0.347876 | − | 0.104786i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17555.7 | + | 10135.8i | 0.762947 | + | 0.440487i | 0.830353 | − | 0.557238i | \(-0.188139\pi\) |
−0.0674061 | + | 0.997726i | \(0.521472\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 881.011i | − | 0.0381461i | −0.999818 | − | 0.0190731i | \(-0.993928\pi\) | ||
0.999818 | − | 0.0190731i | \(-0.00607151\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6889.61 | − | 7327.25i | −0.297207 | − | 0.316086i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2098.19 | + | 3634.18i | −0.0901798 | + | 0.156196i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4606.75 | − | 2659.71i | 0.197270 | − | 0.113894i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −27451.2 | − | 944.530i | −1.17121 | − | 0.0402986i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29088.6 | + | 16794.3i | −1.23654 | + | 0.713916i | −0.968385 | − | 0.249460i | \(-0.919747\pi\) |
−0.268154 | + | 0.963376i | \(0.586414\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15791.4 | − | 27351.5i | 0.668838 | − | 1.15846i | −0.309392 | − | 0.950935i | \(-0.600125\pi\) |
0.978229 | − | 0.207526i | \(-0.0665413\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 28505.9 | + | 30316.7i | 1.20297 | + | 1.27938i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 29539.1i | − | 1.24205i | −0.783791 | − | 0.621024i | \(-0.786717\pi\) | ||
0.783791 | − | 0.621024i | \(-0.213283\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4256.59 | + | 2457.54i | 0.178332 | + | 0.102960i | 0.586509 | − | 0.809943i | \(-0.300502\pi\) |
−0.408177 | + | 0.912903i | \(0.633835\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14223.7 | − | 4284.42i | −0.593760 | − | 0.178851i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 32821.9 | − | 1784.16i | 1.36520 | − | 0.0742106i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −781.434 | − | 1353.48i | −0.0323864 | − | 0.0560948i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1807.48 | + | 10562.6i | 0.0746422 | + | 0.436196i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6724.37 | 0.276700 | 0.138350 | − | 0.990383i | \(-0.455820\pi\) | ||||
0.138350 | + | 0.990383i | \(0.455820\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24102.0 | 0.988234 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16625.1 | + | 3910.65i | −0.679238 | + | 0.159774i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −508.200 | − | 880.229i | −0.0206895 | − | 0.0358353i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −53253.5 | + | 1446.33i | −2.16034 | + | 0.0586736i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1852.85 | − | 6151.21i | 0.0748994 | − | 0.248656i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20834.2 | − | 12028.7i | −0.839234 | − | 0.484532i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8582.65i | 0.344507i | 0.985053 | + | 0.172253i | \(0.0551048\pi\) | ||||
−0.985053 | + | 0.172253i | \(0.944895\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 898.078 | + | 55.3437i | 0.0359223 | + | 0.00221370i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20184.4 | − | 34960.3i | 0.804532 | − | 1.39349i | −0.112074 | − | 0.993700i | \(-0.535749\pi\) |
0.916606 | − | 0.399791i | \(-0.130917\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22420.1 | − | 12944.2i | 0.890528 | − | 0.514146i | 0.0164125 | − | 0.999865i | \(-0.494775\pi\) |
0.874115 | + | 0.485719i | \(0.161442\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9361.70 | − | 2544.83i | −0.370553 | − | 0.100729i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19554.1 | + | 11289.6i | −0.771298 | + | 0.445309i | −0.833338 | − | 0.552764i | \(-0.813573\pi\) |
0.0620392 | + | 0.998074i | \(0.480240\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −84.0367 | + | 145.556i | −0.00330328 | + | 0.00572144i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16167.1 | − | 15201.5i | 0.633292 | − | 0.595467i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 29655.3i | − | 1.15764i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42071.0 | + | 24289.7i | 1.63665 | + | 0.944921i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9359.15 | − | 18793.2i | −0.362840 | − | 0.728584i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2715.85 | + | 5013.60i | −0.104929 | + | 0.193704i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7718.29 | − | 13368.5i | −0.297182 | − | 0.514734i | 0.678308 | − | 0.734777i | \(-0.262713\pi\) |
−0.975490 | + | 0.220044i | \(0.929380\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11502.0 | − | 48897.5i | −0.441356 | − | 1.87631i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12878.8 | 0.492505 | 0.246253 | − | 0.969206i | \(-0.420801\pi\) | ||||
0.246253 | + | 0.969206i | \(0.420801\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29072.1 | −1.10799 | −0.553994 | − | 0.832521i | \(-0.686897\pi\) | ||||
−0.553994 | + | 0.832521i | \(0.686897\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −248.429 | − | 1056.13i | −0.00943600 | − | 0.0401146i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6245.78 | − | 10818.0i | −0.236429 | − | 0.409507i | 0.723258 | − | 0.690578i | \(-0.242644\pi\) |
−0.959687 | + | 0.281071i | \(0.909310\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19007.6 | + | 35089.0i | −0.717092 | + | 1.32379i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 43544.6 | − | 18436.3i | 1.63726 | − | 0.693197i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7531.27 | + | 4348.18i | 0.282222 | + | 0.162941i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4207.74i | 0.157150i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −36048.9 | + | 33895.8i | −1.34185 | + | 1.26170i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 646.945 | − | 1120.54i | 0.0240009 | − | 0.0415708i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23804.3 | − | 13743.4i | 0.880174 | − | 0.508169i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 18367.5 | + | 4992.91i | 0.676891 | + | 0.184002i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1364.82 | + | 787.977i | −0.0501304 | + | 0.0289428i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6202.64 | + | 10743.3i | −0.227073 | + | 0.393302i | −0.956939 | − | 0.290288i | \(-0.906249\pi\) |
0.729866 | + | 0.683590i | \(0.239582\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2878.28 | + | 46706.7i | −0.105024 | + | 1.70425i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 42362.8i | − | 1.54066i | −0.637645 | − | 0.770331i | \(-0.720091\pi\) | ||
0.637645 | − | 0.770331i | \(-0.279909\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 54365.3 | + | 31387.8i | 1.97068 | + | 1.13777i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 357.197 | − | 1185.85i | 0.0129055 | − | 0.0428447i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16642.1 | + | 451.989i | −0.599313 | + | 0.0162770i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17133.8 | + | 29676.6i | 0.615007 | + | 1.06522i | 0.990383 | + | 0.138351i | \(0.0441802\pi\) |
−0.375376 | + | 0.926873i | \(0.622486\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 41350.3 | − | 9726.67i | 1.47941 | − | 0.347996i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36333.2 | 1.29569 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17133.0 | 0.609004 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19056.1 | + | 28761.9i | −0.675173 | + | 1.01906i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11062.6 | − | 19160.9i | −0.390690 | − | 0.676695i | 0.601851 | − | 0.798609i | \(-0.294430\pi\) |
−0.992541 | + | 0.121914i | \(0.961097\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8227.48 | + | 4171.97i | 0.289629 | + | 0.146864i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3579.95 | − | 1078.34i | −0.125619 | − | 0.0378385i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6670.56 | − | 3851.25i | −0.233316 | − | 0.134705i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4555.00i | 0.158810i | 0.996842 | + | 0.0794052i | \(0.0253021\pi\) | ||||
−0.996842 | + | 0.0794052i | \(0.974698\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25935.7 | + | 27583.2i | 0.901364 | + | 0.958620i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26750.6 | + | 46333.4i | −0.926721 | + | 1.60513i | −0.137951 | + | 0.990439i | \(0.544052\pi\) |
−0.788770 | + | 0.614689i | \(0.789282\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15135.4 | + | 8738.42i | −0.522668 | + | 0.301763i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2123.52 | + | 2420.03i | 0.0730986 | + | 0.0833055i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 108.948 | − | 62.9013i | 0.00373848 | − | 0.00215841i | −0.498130 | − | 0.867103i | \(-0.665980\pi\) |
0.501868 | + | 0.864944i | \(0.332646\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3968.63 | − | 6873.87i | 0.135750 | − | 0.235127i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8858.28 | + | 9420.98i | 0.302050 | + | 0.321237i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 24924.7i | − | 0.847209i | −0.905847 | − | 0.423604i | \(-0.860765\pi\) | ||
0.905847 | − | 0.423604i | \(-0.139235\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3110.01 | + | 1795.57i | 0.105380 | + | 0.0608411i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5466.88 | − | 1646.72i | −0.184659 | − | 0.0556225i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9017.47 | − | 5537.99i | 0.303639 | − | 0.186476i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11978.4 | − | 20747.2i | −0.402081 | − | 0.696424i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19487.1 | − | 29412.3i | 0.652090 | − | 0.984216i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1577.11 | 0.0526103 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19897.4 | 0.661692 | 0.330846 | − | 0.943685i | \(-0.392666\pi\) | ||||
0.330846 | + | 0.943685i | \(0.392666\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13036.5 | − | 3066.51i | 0.432190 | − | 0.101662i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19064.3 | + | 33020.3i | 0.630075 | + | 1.09132i | 0.987536 | + | 0.157393i | \(0.0503090\pi\) |
−0.357462 | + | 0.933928i | \(0.616358\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17566.5 | + | 9515.69i | 0.578782 | + | 0.313524i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10163.7 | − | 33742.1i | 0.333845 | − | 1.10832i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4321.33 | + | 2494.92i | 0.141506 | + | 0.0816986i | 0.569082 | − | 0.822281i | \(-0.307299\pi\) |
−0.427575 | + | 0.903980i | \(0.640632\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 78544.8i | 2.56415i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1689.02 | − | 27408.2i | 0.0549708 | − | 0.892026i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8880.48 | + | 15381.4i | −0.288142 | + | 0.499076i | −0.973366 | − | 0.229256i | \(-0.926371\pi\) |
0.685225 | + | 0.728332i | \(0.259704\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2072.95 | + | 1196.82i | −0.0670554 | + | 0.0387144i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7944.91 | + | 30086.1i | 0.256220 | + | 0.970265i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29695.4 | − | 17144.6i | 0.954761 | − | 0.551232i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23134.6 | + | 40070.2i | −0.741568 | + | 1.28443i | 0.210214 | + | 0.977655i | \(0.432584\pi\) |
−0.951781 | + | 0.306777i | \(0.900749\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14031.3 | − | 13193.2i | 0.448408 | − | 0.421626i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4114.20i | 0.131084i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41387.9 | − | 23895.3i | −1.31471 | − | 0.759049i | −0.331839 | − | 0.943336i | \(-0.607669\pi\) |
−0.982872 | + | 0.184288i | \(0.941002\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6751.04 | − | 18260.7i | 0.213807 | − | 0.578320i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 336.4.bc.c.17.4 | 12 | ||
3.2 | odd | 2 | inner | 336.4.bc.c.17.6 | 12 | ||
4.3 | odd | 2 | 84.4.k.c.17.3 | yes | 12 | ||
7.5 | odd | 6 | inner | 336.4.bc.c.257.6 | 12 | ||
12.11 | even | 2 | 84.4.k.c.17.1 | yes | 12 | ||
21.5 | even | 6 | inner | 336.4.bc.c.257.4 | 12 | ||
28.3 | even | 6 | 588.4.f.c.293.7 | 12 | |||
28.11 | odd | 6 | 588.4.f.c.293.6 | 12 | |||
28.19 | even | 6 | 84.4.k.c.5.1 | ✓ | 12 | ||
28.23 | odd | 6 | 588.4.k.c.509.6 | 12 | |||
28.27 | even | 2 | 588.4.k.c.521.4 | 12 | |||
84.11 | even | 6 | 588.4.f.c.293.8 | 12 | |||
84.23 | even | 6 | 588.4.k.c.509.4 | 12 | |||
84.47 | odd | 6 | 84.4.k.c.5.3 | yes | 12 | ||
84.59 | odd | 6 | 588.4.f.c.293.5 | 12 | |||
84.83 | odd | 2 | 588.4.k.c.521.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.k.c.5.1 | ✓ | 12 | 28.19 | even | 6 | ||
84.4.k.c.5.3 | yes | 12 | 84.47 | odd | 6 | ||
84.4.k.c.17.1 | yes | 12 | 12.11 | even | 2 | ||
84.4.k.c.17.3 | yes | 12 | 4.3 | odd | 2 | ||
336.4.bc.c.17.4 | 12 | 1.1 | even | 1 | trivial | ||
336.4.bc.c.17.6 | 12 | 3.2 | odd | 2 | inner | ||
336.4.bc.c.257.4 | 12 | 21.5 | even | 6 | inner | ||
336.4.bc.c.257.6 | 12 | 7.5 | odd | 6 | inner | ||
588.4.f.c.293.5 | 12 | 84.59 | odd | 6 | |||
588.4.f.c.293.6 | 12 | 28.11 | odd | 6 | |||
588.4.f.c.293.7 | 12 | 28.3 | even | 6 | |||
588.4.f.c.293.8 | 12 | 84.11 | even | 6 | |||
588.4.k.c.509.4 | 12 | 84.23 | even | 6 | |||
588.4.k.c.509.6 | 12 | 28.23 | odd | 6 | |||
588.4.k.c.521.4 | 12 | 28.27 | even | 2 | |||
588.4.k.c.521.6 | 12 | 84.83 | odd | 2 |