Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [208,4,Mod(17,208)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(208, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("208.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 208 = 2^{4} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 208.w (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: | \(12.2723972812\) |
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: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 208.49 |
Dual form | 208.4.w.b.17.1 |
$q$-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 \(\left(\mathbb{Z}/208\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(79\) | \(145\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | + | 1.73205i | 0.192450 | + | 0.333333i | 0.946062 | − | 0.323987i | \(-0.105023\pi\) |
−0.753612 | + | 0.657320i | \(0.771690\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.73205i | 0.154919i | 0.996995 | + | 0.0774597i | \(0.0246809\pi\) | ||||
−0.996995 | + | 0.0774597i | \(0.975319\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.0000 | + | 6.92820i | 0.647939 | + | 0.374088i | 0.787666 | − | 0.616102i | \(-0.211289\pi\) |
−0.139727 | + | 0.990190i | \(0.544623\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 11.5000 | − | 19.9186i | 0.425926 | − | 0.737725i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −12.0000 | + | 6.92820i | −0.328921 | + | 0.189903i | −0.655362 | − | 0.755315i | \(-0.727484\pi\) |
0.326441 | + | 0.945218i | \(0.394151\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 45.5000 | − | 11.2583i | 0.970725 | − | 0.240192i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.00000 | + | 1.73205i | −0.0516398 | + | 0.0298142i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −58.5000 | + | 101.325i | −0.834608 | + | 1.44558i | 0.0597414 | + | 0.998214i | \(0.480972\pi\) |
−0.894349 | + | 0.447369i | \(0.852361\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 99.0000 | + | 57.1577i | 1.19538 | + | 0.690151i | 0.959521 | − | 0.281637i | \(-0.0908774\pi\) |
0.235856 | + | 0.971788i | \(0.424211\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 27.7128i | 0.287973i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −39.0000 | − | 67.5500i | −0.353568 | − | 0.612398i | 0.633304 | − | 0.773903i | \(-0.281698\pi\) |
−0.986872 | + | 0.161506i | \(0.948365\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 122.000 | 0.976000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 100.000 | 0.712778 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 70.5000 | + | 122.110i | 0.451432 | + | 0.781903i | 0.998475 | − | 0.0552014i | \(-0.0175801\pi\) |
−0.547043 | + | 0.837104i | \(0.684247\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 155.885i | 0.903151i | 0.892233 | + | 0.451576i | \(0.149138\pi\) | ||||
−0.892233 | + | 0.451576i | \(0.850862\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −24.0000 | − | 13.8564i | −0.126602 | − | 0.0730937i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −12.0000 | + | 20.7846i | −0.0579534 | + | 0.100378i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −124.500 | + | 71.8801i | −0.553180 | + | 0.319379i | −0.750404 | − | 0.660980i | \(-0.770141\pi\) |
0.197223 | + | 0.980359i | \(0.436808\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 65.0000 | + | 67.5500i | 0.266880 | + | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 235.500 | − | 135.966i | 0.897047 | − | 0.517910i | 0.0208059 | − | 0.999784i | \(-0.493377\pi\) |
0.876241 | + | 0.481873i | \(0.160043\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 52.0000 | − | 90.0666i | 0.184417 | − | 0.319419i | −0.758963 | − | 0.651134i | \(-0.774294\pi\) |
0.943380 | + | 0.331714i | \(0.107627\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 34.5000 | + | 19.9186i | 0.114288 | + | 0.0659842i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 301.377i | 0.935326i | 0.883907 | + | 0.467663i | \(0.154904\pi\) | ||||
−0.883907 | + | 0.467663i | \(0.845096\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −75.5000 | − | 130.770i | −0.220117 | − | 0.381253i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −234.000 | −0.642481 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 93.0000 | 0.241029 | 0.120514 | − | 0.992712i | \(-0.461546\pi\) | ||||
0.120514 | + | 0.992712i | \(0.461546\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.0000 | − | 20.7846i | −0.0294196 | − | 0.0509563i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 228.631i | 0.531279i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 246.000 | + | 142.028i | 0.542822 | + | 0.313398i | 0.746222 | − | 0.665698i | \(-0.231866\pi\) |
−0.203400 | + | 0.979096i | \(0.565199\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −72.5000 | + | 125.574i | −0.152175 | + | 0.263575i | −0.932027 | − | 0.362389i | \(-0.881961\pi\) |
0.779852 | + | 0.625964i | \(0.215294\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 276.000 | − | 159.349i | 0.551948 | − | 0.318667i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 19.5000 | + | 78.8083i | 0.0372104 | + | 0.150384i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 681.000 | − | 393.176i | 1.24175 | − | 0.716926i | 0.272301 | − | 0.962212i | \(-0.412215\pi\) |
0.969451 | + | 0.245286i | \(0.0788819\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 78.0000 | − | 135.100i | 0.136088 | − | 0.235712i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −915.000 | − | 528.275i | −1.52944 | − | 0.883025i | −0.999385 | − | 0.0350641i | \(-0.988836\pi\) |
−0.530059 | − | 0.847961i | \(-0.677830\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 458.993i | − | 0.735906i | −0.929844 | − | 0.367953i | \(-0.880059\pi\) | ||
0.929844 | − | 0.367953i | \(-0.119941\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 122.000 | + | 211.310i | 0.187831 | + | 0.325333i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −192.000 | −0.284161 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1276.00 | −1.81723 | −0.908615 | − | 0.417634i | \(-0.862859\pi\) | ||||
−0.908615 | + | 0.417634i | \(0.862859\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −210.500 | − | 364.597i | −0.288752 | − | 0.500133i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 789.815i | − | 1.04450i | −0.852793 | − | 0.522250i | \(-0.825093\pi\) | ||
0.852793 | − | 0.522250i | \(-0.174907\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −175.500 | − | 101.325i | −0.223949 | − | 0.129297i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −141.000 | + | 244.219i | −0.173756 | + | 0.300955i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −846.000 | + | 488.438i | −1.00759 | + | 0.581734i | −0.910486 | − | 0.413540i | \(-0.864292\pi\) |
−0.0971073 | + | 0.995274i | \(0.530959\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 624.000 | + | 180.133i | 0.718824 | + | 0.207507i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −270.000 | + | 155.885i | −0.301050 | + | 0.173812i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −99.0000 | + | 171.473i | −0.106918 | + | 0.185187i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 174.000 | + | 100.459i | 0.182134 | + | 0.105155i | 0.588295 | − | 0.808646i | \(-0.299799\pi\) |
−0.406161 | + | 0.913802i | \(0.633133\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 318.697i | 0.323538i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −214.500 | − | 371.525i | −0.211322 | − | 0.366021i | 0.740806 | − | 0.671719i | \(-0.234444\pi\) |
−0.952129 | + | 0.305698i | \(0.901110\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −182.000 | −0.174107 | −0.0870534 | − | 0.996204i | \(-0.527745\pi\) | ||||
−0.0870534 | + | 0.996204i | \(0.527745\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −48.0000 | −0.0446126 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −753.000 | − | 1304.23i | −0.680330 | − | 1.17837i | −0.974880 | − | 0.222729i | \(-0.928503\pi\) |
0.294551 | − | 0.955636i | \(-0.404830\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1551.92i | − | 1.36373i | −0.731477 | − | 0.681866i | \(-0.761169\pi\) | ||
0.731477 | − | 0.681866i | \(-0.238831\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −249.000 | − | 143.760i | −0.212919 | − | 0.122929i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 343.500 | − | 594.959i | 0.285962 | − | 0.495302i | −0.686880 | − | 0.726771i | \(-0.741020\pi\) |
0.972842 | + | 0.231470i | \(0.0743534\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 117.000 | − | 67.5500i | 0.0948722 | − | 0.0547745i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 299.000 | − | 1035.77i | 0.236261 | − | 0.818433i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1404.00 | + | 810.600i | −1.08155 | + | 0.624433i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −569.500 | + | 986.403i | −0.427874 | + | 0.741099i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 471.000 | + | 271.932i | 0.345273 | + | 0.199344i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 427.817i | 0.306121i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 143.000 | + | 247.683i | 0.0999149 | + | 0.173058i | 0.911649 | − | 0.410969i | \(-0.134810\pi\) |
−0.811734 | + | 0.584027i | \(0.801476\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 208.000 | 0.141964 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1974.00 | 1.31656 | 0.658279 | − | 0.752774i | \(-0.271285\pi\) | ||||
0.658279 | + | 0.752774i | \(0.271285\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 792.000 | + | 1371.78i | 0.516354 | + | 0.894352i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 173.205i | 0.110423i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −733.500 | − | 423.486i | −0.457424 | − | 0.264094i | 0.253536 | − | 0.967326i | \(-0.418406\pi\) |
−0.710961 | + | 0.703232i | \(0.751740\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 118.000 | − | 204.382i | 0.0720045 | − | 0.124716i | −0.827775 | − | 0.561060i | \(-0.810394\pi\) |
0.899780 | + | 0.436344i | \(0.143727\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −522.000 | + | 301.377i | −0.311775 | + | 0.180004i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −468.000 | + | 450.333i | −0.273679 | + | 0.263348i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −211.500 | + | 122.110i | −0.121132 | + | 0.0699355i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 151.000 | − | 261.540i | 0.0847229 | − | 0.146744i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −40.5000 | − | 23.3827i | −0.0222677 | − | 0.0128563i | 0.488825 | − | 0.872382i | \(-0.337426\pi\) |
−0.511093 | + | 0.859526i | \(0.670759\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1770.16i | − | 0.953995i | −0.878905 | − | 0.476998i | \(-0.841725\pi\) | ||
0.878905 | − | 0.476998i | \(-0.158275\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1345.50 | + | 2330.47i | 0.710962 | + | 1.23142i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −270.000 | −0.139916 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1211.00 | 0.615594 | 0.307797 | − | 0.951452i | \(-0.400408\pi\) | ||||
0.307797 | + | 0.951452i | \(0.400408\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 93.0000 | + | 161.081i | 0.0463860 | + | 0.0803430i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1080.80i | − | 0.529062i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 870.000 | + | 502.295i | 0.418059 | + | 0.241367i | 0.694247 | − | 0.719737i | \(-0.255738\pi\) |
−0.276187 | + | 0.961104i | \(0.589071\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 24.0000 | − | 41.5692i | 0.0113236 | − | 0.0196131i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −792.000 | + | 457.261i | −0.366987 | + | 0.211880i | −0.672141 | − | 0.740423i | \(-0.734625\pi\) |
0.305154 | + | 0.952303i | \(0.401292\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1943.50 | − | 1024.51i | 0.884615 | − | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2277.00 | − | 1314.63i | 1.01828 | − | 0.587906i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1287.00 | + | 2229.15i | −0.565600 | + | 0.979648i | 0.431394 | + | 0.902164i | \(0.358022\pi\) |
−0.996994 | + | 0.0774841i | \(0.975311\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1464.00 | + | 845.241i | 0.632389 | + | 0.365110i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 568.113i | 0.241254i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1872.00 | + | 3242.40i | 0.781675 | + | 1.35390i | 0.930965 | + | 0.365108i | \(0.118968\pi\) |
−0.149290 | + | 0.988793i | \(0.547699\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −637.000 | −0.261590 | −0.130795 | − | 0.991409i | \(-0.541753\pi\) | ||||
−0.130795 | + | 0.991409i | \(0.541753\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −290.000 | −0.117144 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −124.500 | − | 215.640i | −0.0494780 | − | 0.0856983i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1621.20i | − | 0.633978i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1200.00 | + | 692.820i | 0.461837 | + | 0.266642i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1299.00 | + | 2249.93i | −0.492106 | + | 0.852353i | −0.999959 | − | 0.00909077i | \(-0.997106\pi\) |
0.507852 | + | 0.861444i | \(0.330440\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 967.500 | − | 558.586i | 0.360840 | − | 0.208331i | −0.308609 | − | 0.951189i | \(-0.599863\pi\) |
0.669449 | + | 0.742858i | \(0.266530\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −117.000 | + | 112.583i | −0.0429669 | + | 0.0413449i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1776.00 | − | 1025.37i | 0.642308 | − | 0.370837i | −0.143195 | − | 0.989695i | \(-0.545738\pi\) |
0.785503 | + | 0.618858i | \(0.212404\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1261.00 | + | 2184.12i | −0.449196 | + | 0.778030i | −0.998334 | − | 0.0577019i | \(-0.981623\pi\) |
0.549138 | + | 0.835732i | \(0.314956\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1362.00 | + | 786.351i | 0.477951 | + | 0.275945i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1953.75i | 0.675500i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 235.500 | + | 407.898i | 0.0802343 | + | 0.138970i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1794.00 | −0.602375 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1584.00 | −0.524247 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 521.000 | + | 902.398i | 0.169986 | + | 0.294425i | 0.938415 | − | 0.345511i | \(-0.112294\pi\) |
−0.768428 | + | 0.639936i | \(0.778961\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 2113.10i | − | 0.679753i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 156.000 | + | 90.0666i | 0.0494842 | + | 0.0285697i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1080.00 | + | 1870.61i | −0.337858 | + | 0.585187i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 795.000 | − | 458.993i | 0.245302 | − | 0.141625i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1521.00 | + | 5268.90i | −0.462957 | + | 1.60373i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2085.00 | − | 1203.78i | 0.626107 | − | 0.361483i | −0.153136 | − | 0.988205i | \(-0.548937\pi\) |
0.779243 | + | 0.626722i | \(0.215604\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1403.00 | − | 2430.07i | 0.415704 | − | 0.720020i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2085.00 | − | 1203.78i | −0.609631 | − | 0.351971i | 0.163190 | − | 0.986595i | \(-0.447822\pi\) |
−0.772821 | + | 0.634624i | \(0.781155\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2508.01i | − | 0.723729i | −0.932231 | − | 0.361864i | \(-0.882140\pi\) | ||
0.932231 | − | 0.361864i | \(-0.117860\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −192.000 | − | 332.554i | −0.0546869 | − | 0.0947205i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5850.00 | −1.64483 | −0.822417 | − | 0.568885i | \(-0.807375\pi\) | ||||
−0.822417 | + | 0.568885i | \(0.807375\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −522.000 | −0.144900 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1276.00 | − | 2210.10i | −0.349726 | − | 0.605744i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5383.21i | − | 1.45695i | −0.685072 | − | 0.728475i | \(-0.740229\pi\) | ||
0.685072 | − | 0.728475i | \(-0.259771\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4258.50 | + | 2458.65i | 1.13823 | + | 0.657159i | 0.945992 | − | 0.324189i | \(-0.105091\pi\) |
0.192240 | + | 0.981348i | \(0.438425\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1771.00 | − | 3067.46i | 0.467530 | − | 0.809785i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 226.500 | − | 130.770i | 0.0590635 | − | 0.0341003i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5148.00 | + | 1486.10i | 1.32615 | + | 0.382827i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1368.00 | − | 789.815i | 0.348167 | − | 0.201014i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1989.00 | + | 3445.05i | −0.500178 | + | 0.866333i | 0.499822 | + | 0.866128i | \(0.333399\pi\) |
−1.00000 | 0.000205037i | \(0.999935\pi\) | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 936.000 | + | 540.400i | 0.232592 | + | 0.134287i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 405.300i | − | 0.0995328i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1033.50 | − | 1790.07i | −0.250848 | − | 0.434482i | 0.712911 | − | 0.701254i | \(-0.247376\pi\) |
−0.963760 | + | 0.266772i | \(0.914043\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1992.00 | −0.477903 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3243.00 | 0.769106 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1026.00 | − | 1777.08i | −0.240555 | − | 0.416653i | 0.720318 | − | 0.693644i | \(-0.243996\pi\) |
−0.960872 | + | 0.276991i | \(0.910663\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 161.081i | 0.0373400i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1692.00 | − | 976.877i | −0.387823 | − | 0.223910i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1665.00 | + | 2883.86i | −0.377386 | + | 0.653652i | −0.990681 | − | 0.136202i | \(-0.956510\pi\) |
0.613295 | + | 0.789854i | \(0.289844\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2430.00 | + | 1402.96i | −0.544694 | + | 0.314479i | −0.746979 | − | 0.664848i | \(-0.768496\pi\) |
0.202285 | + | 0.979327i | \(0.435163\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 312.000 | + | 1260.93i | 0.0691689 | + | 0.279543i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1464.00 | + | 845.241i | −0.321027 | + | 0.185345i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −188.500 | + | 326.492i | −0.0408876 | + | 0.0708194i | −0.885745 | − | 0.464172i | \(-0.846352\pi\) |
0.844857 | + | 0.534992i | \(0.179685\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3105.00 | + | 1792.67i | 0.666278 | + | 0.384676i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 36.3731i | 0.00772183i | 0.999993 | + | 0.00386092i | \(0.00122897\pi\) | ||||
−0.999993 | + | 0.00386092i | \(0.998771\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3562.00 | − | 6169.56i | −0.748194 | − | 1.29591i | −0.948688 | − | 0.316215i | \(-0.897588\pi\) |
0.200493 | − | 0.979695i | \(-0.435745\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −396.000 | −0.0823053 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3768.00 | 0.774976 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4388.00 | − | 7600.24i | −0.893141 | − | 1.54696i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 401.836i | 0.0809486i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7207.50 | − | 4161.25i | −1.43709 | − | 0.829703i | −0.439441 | − | 0.898271i | \(-0.644823\pi\) |
−0.997646 | + | 0.0685685i | \(0.978157\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −246.000 | + | 426.084i | −0.0485514 | + | 0.0840936i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1200.00 | + | 692.820i | −0.234448 | + | 0.135359i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2535.00 | − | 2634.45i | −0.490310 | − | 0.509546i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1248.00 | − | 720.533i | 0.238982 | − | 0.137976i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 429.000 | − | 743.050i | 0.0813380 | − | 0.140882i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −217.500 | − | 125.574i | −0.0408328 | − | 0.0235748i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2220.49i | − | 0.412801i | −0.978468 | − | 0.206401i | \(-0.933825\pi\) | ||
0.978468 | − | 0.206401i | \(-0.0661750\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −182.000 | − | 315.233i | −0.0335069 | − | 0.0580356i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4914.00 | −0.895972 | −0.447986 | − | 0.894041i | \(-0.647859\pi\) | ||||
−0.447986 | + | 0.894041i | \(0.647859\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −518.000 | −0.0935434 | −0.0467717 | − | 0.998906i | \(-0.514893\pi\) | ||||
−0.0467717 | + | 0.998906i | \(0.514893\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 276.000 | + | 478.046i | 0.0493677 | + | 0.0855074i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 3916.17i | − | 0.693861i | −0.937891 | − | 0.346930i | \(-0.887224\pi\) | ||
0.937891 | − | 0.346930i | \(-0.112776\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1692.00 | − | 976.877i | −0.296971 | − | 0.171456i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1506.00 | − | 2608.47i | 0.261859 | − | 0.453553i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11583.0 | + | 6687.45i | −1.99534 | + | 1.15201i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5551.00 | − | 1373.52i | 0.947428 | − | 0.234428i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2688.00 | − | 1551.92i | 0.454577 | − | 0.262450i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2088.00 | + | 3616.52i | −0.349894 | + | 0.606034i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6456.00 | + | 3727.37i | 1.07207 | + | 0.618958i | 0.928745 | − | 0.370719i | \(-0.120889\pi\) |
0.143321 | + | 0.989676i | \(0.454222\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3306.48i | 0.544127i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 681.000 | + | 1179.53i | 0.111066 | + | 0.192371i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3575.00 | −0.577871 | −0.288936 | − | 0.957349i | \(-0.593301\pi\) | ||||
−0.288936 | + | 0.957349i | \(0.593301\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1374.00 | 0.220134 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1080.00 | − | 1870.61i | −0.171511 | − | 0.297066i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6845.06i | − | 1.07755i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 234.000 | + | 135.100i | 0.0365163 | + | 0.0210827i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3483.00 | + | 6032.73i | −0.538839 | + | 0.933297i | 0.460128 | + | 0.887853i | \(0.347804\pi\) |
−0.998967 | + | 0.0454442i | \(0.985530\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5760.00 | + | 3325.54i | −0.883455 | + | 0.510063i | −0.871796 | − | 0.489869i | \(-0.837045\pi\) |
−0.0116588 | + | 0.999932i | \(0.503711\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4550.00 | − | 1125.83i | 0.691912 | − | 0.171204i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4876.50 | − | 2815.45i | 0.735269 | − | 0.424508i | −0.0850777 | − | 0.996374i | \(-0.527114\pi\) |
0.820347 | + | 0.571867i | \(0.193781\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 915.000 | − | 1584.83i | 0.136798 | − | 0.236940i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2808.00 | − | 1621.20i | −0.416289 | − | 0.240344i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 7129.12i | − | 1.04808i | −0.851694 | − | 0.524040i | \(-0.824424\pi\) | ||
0.851694 | − | 0.524040i | \(-0.175576\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3104.50 | + | 5377.15i | 0.452617 | + | 0.783956i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2278.00 | −0.329377 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 795.000 | 0.114006 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.00000 | + | 1.73205i | 0.000142233 | + | 0.000246355i | 0.866097 | − | 0.499877i | \(-0.166621\pi\) |
−0.865954 | + | 0.500123i | \(0.833288\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 6254.44i | − | 0.882366i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1116.00 | + | 644.323i | 0.156172 | + | 0.0901660i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1749.50 | + | 3030.22i | −0.242857 | + | 0.420641i | −0.961527 | − | 0.274711i | \(-0.911418\pi\) |
0.718670 | + | 0.695351i | \(0.244751\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −741.000 | + | 427.817i | −0.102040 | + | 0.0589129i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4582.50 | + | 4762.27i | 0.626023 | + | 0.650582i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4779.00 | + | 2759.16i | −0.647706 | + | 0.373953i | −0.787577 | − | 0.616216i | \(-0.788665\pi\) |
0.139871 | + | 0.990170i | \(0.455331\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −286.000 | + | 495.367i | −0.0384573 | + | 0.0666100i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6378.00 | + | 3682.34i | 0.850915 | + | 0.491276i | 0.860960 | − | 0.508673i | \(-0.169864\pi\) |
−0.0100443 | + | 0.999950i | \(0.503197\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 332.554i | − | 0.0440221i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1196.00 | − | 2071.53i | −0.157096 | − | 0.272098i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1209.00 | −0.157580 | −0.0787901 | − | 0.996891i | \(-0.525106\pi\) | ||||
−0.0787901 | + | 0.996891i | \(0.525106\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9126.00 | 1.18036 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1974.00 | + | 3419.07i | 0.253372 | + | 0.438853i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 2210.10i | − | 0.281524i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10128.0 | + | 5847.40i | 1.28038 | + | 0.739226i | 0.976917 | − | 0.213618i | \(-0.0685248\pi\) |
0.303460 | + | 0.952844i | \(0.401858\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1584.00 | + | 2743.57i | −0.198745 | + | 0.344236i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2581.50 | + | 1490.43i | −0.321481 | + | 0.185607i | −0.652053 | − | 0.758174i | \(-0.726092\pi\) |
0.330571 | + | 0.943781i | \(0.392759\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1755.00 | + | 7092.75i | 0.216930 | + | 0.876712i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 631.500 | − | 364.597i | 0.0774802 | − | 0.0447332i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 996.000 | − | 1725.12i | 0.121302 | − | 0.210101i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.5000 | + | 21.6506i | 0.00453363 | + | 0.00261749i | 0.502265 | − | 0.864714i | \(-0.332500\pi\) |
−0.497731 | + | 0.867331i | \(0.665833\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 1693.95i | − | 0.203300i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1968.00 | + | 3408.68i | 0.234477 | + | 0.406126i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1368.00 | 0.161813 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 472.000 | 0.0554291 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4731.00 | − | 8194.33i | −0.551610 | − | 0.955416i | −0.998159 | − | 0.0606569i | \(-0.980680\pi\) |
0.446549 | − | 0.894759i | \(-0.352653\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 7068.50i | − | 0.818284i | −0.912471 | − | 0.409142i | \(-0.865828\pi\) | ||
0.912471 | − | 0.409142i | \(-0.134172\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6003.00 | + | 3465.83i | 0.690014 | + | 0.398380i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7137.00 | + | 12361.6i | −0.814577 | + | 1.41089i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1740.00 | + | 1004.59i | −0.197200 | + | 0.113854i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1248.00 | − | 360.267i | −0.140452 | − | 0.0405451i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8598.00 | − | 4964.06i | 0.960907 | − | 0.554780i | 0.0644552 | − | 0.997921i | \(-0.479469\pi\) |
0.896452 | + | 0.443140i | \(0.146136\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3308.50 | − | 5730.49i | 0.367197 | − | 0.636004i | −0.621929 | − | 0.783074i | \(-0.713651\pi\) |
0.989126 | + | 0.147070i | \(0.0469841\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −423.000 | − | 244.219i | −0.0466237 | − | 0.0269182i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 8916.60i | − | 0.976061i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6994.00 | + | 12114.0i | 0.760377 | + | 1.31701i | 0.942656 | + | 0.333765i | \(0.108319\pi\) |
−0.182280 | + | 0.983247i | \(0.558348\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3473.00 | −0.375013 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2004.00 | −0.214928 | −0.107464 | − | 0.994209i | \(-0.534273\pi\) | ||||
−0.107464 | + | 0.994209i | \(0.534273\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −846.000 | − | 1465.31i | −0.0901219 | − | 0.156096i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 93.5307i | − | 0.00989676i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7866.00 | + | 4541.44i | 0.826769 | + | 0.477336i | 0.852745 | − | 0.522327i | \(-0.174936\pi\) |
−0.0259758 | + | 0.999663i | \(0.508269\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1884.00 | + | 3263.18i | −0.196705 | + | 0.340704i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3066.00 | − | 1770.16i | 0.317998 | − | 0.183596i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −312.000 | + | 1080.80i | −0.0321468 | + | 0.111360i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2185.50 | − | 1261.80i | 0.223705 | − | 0.129156i | −0.383959 | − | 0.923350i | \(-0.625440\pi\) |
0.607665 | + | 0.794194i | \(0.292106\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5850.00 | + | 10132.5i | −0.594890 | + | 1.03038i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16963.5 | + | 9793.88i | 1.71382 | + | 0.989472i | 0.929270 | + | 0.369400i | \(0.120437\pi\) |
0.784545 | + | 0.620072i | \(0.212897\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8632.54i | 0.866497i | 0.901274 | + | 0.433249i | \(0.142633\pi\) | ||||
−0.901274 | + | 0.433249i | \(0.857367\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −270.000 | − | 467.654i | −0.0269268 | − | 0.0466385i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5460.00 | −0.541025 | −0.270512 | − | 0.962716i | \(-0.587193\pi\) | ||||
−0.270512 | + | 0.962716i | \(0.587193\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10896.0 | 1.07277 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1211.00 | + | 2097.51i | 0.118471 | + | 0.205198i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1441.07i | 0.140085i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12078.0 | + | 6973.24i | 1.16669 | + | 0.673587i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1069.50 | − | 1852.43i | 0.102660 | − | 0.177813i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2211.00 | − | 1276.52i | 0.210904 | − | 0.121766i | −0.390827 | − | 0.920464i | \(-0.627811\pi\) |
0.601732 | + | 0.798698i | \(0.294478\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4855.50 | + | 4672.21i | −0.460274 | + | 0.442899i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1872.00 | − | 1080.80i | 0.176354 | − | 0.101818i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −174.000 | + | 301.377i | −0.0162906 | + | 0.0282161i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9378.00 | − | 5414.39i | −0.872603 | − | 0.503798i | −0.00439074 | − | 0.999990i | \(-0.501398\pi\) |
−0.868212 | + | 0.496193i | \(0.834731\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2009.18i | 0.185804i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5694.00 | + | 9862.30i | 0.523354 | + | 0.906475i | 0.999631 | + | 0.0271797i | \(0.00865264\pi\) |
−0.476277 | + | 0.879295i | \(0.658014\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16497.0 | −1.50707 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −552.000 | −0.0501223 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7320.00 | − | 12678.6i | −0.660658 | − | 1.14429i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 17677.3i | − | 1.58586i | −0.609311 | − | 0.792931i | \(-0.708554\pi\) | ||
0.609311 | − | 0.792931i | \(-0.291446\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1584.00 | − | 914.523i | −0.141253 | − | 0.0815526i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1938.00 | − | 3356.71i | 0.171792 | − | 0.297552i | −0.767255 | − | 0.641343i | \(-0.778378\pi\) |
0.939046 | + | 0.343791i | \(0.111711\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 643.500 | − | 371.525i | 0.0567037 | − | 0.0327379i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3718.00 | + | 2341.73i | 0.325685 | + | 0.205128i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14779.5 | + | 8532.95i | −1.28701 | + | 0.743058i | −0.978120 | − | 0.208039i | \(-0.933292\pi\) |
−0.308893 | + | 0.951097i | \(0.599958\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3180.00 | − | 5507.92i | 0.275293 | − | 0.476822i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9900.00 | + | 5715.77i | 0.852038 | + | 0.491925i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 315.233i | − | 0.0269725i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2088.00 | − | 3616.52i | −0.177621 | − | 0.307649i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5148.00 | −0.435399 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2121.00 | 0.178355 | 0.0891773 | − | 0.996016i | \(-0.471576\pi\) | ||||
0.0891773 | + | 0.996016i | \(0.471576\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5732.00 | − | 9928.12i | −0.479241 | − | 0.830069i | 0.520476 | − | 0.853876i | \(-0.325755\pi\) |
−0.999717 | + | 0.0238072i | \(0.992421\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3380.96i | 0.281062i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15795.0 | − | 9119.25i | −1.30558 | − | 0.753777i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3041.50 | − | 5268.03i | 0.249979 | − | 0.432977i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5658.00 | − | 3266.65i | 0.462404 | − | 0.266969i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9184.50 | − | 8837.79i | 0.746388 | − | 0.718212i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2259.00 | − | 1304.23i | 0.182552 | − | 0.105396i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3744.00 | + | 6484.80i | −0.300867 | + | 0.521117i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1812.00 | + | 1046.16i | 0.144802 | + | 0.0836016i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4764.87i | 0.378665i | 0.981913 | + | 0.189333i | \(0.0606324\pi\) | ||||
−0.981913 | + | 0.189333i | \(0.939368\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −637.000 | − | 1103.32i | −0.0503431 | − | 0.0871968i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2688.00 | 0.211268 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6554.00 | −0.512301 | −0.256151 | − | 0.966637i | \(-0.582454\pi\) | ||||
−0.256151 | + | 0.966637i | \(0.582454\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1667.50 | + | 2888.19i | 0.129631 | + | 0.224527i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16118.5i | 1.24622i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15312.0 | − | 8840.39i | −1.17745 | − | 0.679804i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 249.000 | − | 431.281i | 0.0190441 | − | 0.0329853i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15685.5 | + | 9056.03i | −1.19321 | + | 0.688898i | −0.959032 | − | 0.283297i | \(-0.908572\pi\) |
−0.234174 | + | 0.972195i | \(0.575239\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1352.00 | − | 4683.47i | 0.102296 | − | 0.354364i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2808.00 | − | 1621.20i | 0.211326 | − | 0.122009i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6084.00 | + | 10537.8i | −0.455435 | + | 0.788837i | −0.998713 | − | 0.0507160i | \(-0.983850\pi\) |
0.543278 | + | 0.839553i | \(0.317183\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1030.50 | + | 594.959i | 0.0767318 | + | 0.0443011i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 5833.55i | − | 0.432074i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3861.00 | + | 6687.45i | 0.284467 | + | 0.492711i | 0.972480 | − | 0.232988i | \(-0.0748502\pi\) |
−0.688013 | + | 0.725698i | \(0.741517\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11440.0 | −0.838440 | −0.419220 | − | 0.907885i | \(-0.637696\pi\) | ||||
−0.419220 | + | 0.907885i | \(0.637696\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5196.00 | −0.378824 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4758.00 | − | 8241.10i | −0.345082 | − | 0.597700i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 15444.7i | − | 1.11433i | −0.830400 | − | 0.557167i | \(-0.811888\pi\) | ||
0.830400 | − | 0.557167i | \(-0.188112\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1935.00 | + | 1117.17i | 0.138887 | + | 0.0801867i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5472.00 | − | 9477.78i | 0.390735 | − | 0.676772i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1116.00 | + | 644.323i | −0.0792796 | + | 0.0457721i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1794.00 | + | 517.883i | 0.126791 | + | 0.0366014i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12186.0 | − | 7035.59i | 0.856848 | − | 0.494702i | −0.00610719 | − | 0.999981i | \(-0.501944\pi\) |
0.862956 | + | 0.505280i | \(0.168611\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8910.00 | + | 15432.6i | −0.623311 | + | 1.07961i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3552.00 | + | 2050.75i | 0.247225 | + | 0.142735i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 26938.6i | − | 1.86549i | −0.360538 | − | 0.932745i | \(-0.617407\pi\) | ||
0.360538 | − | 0.932745i | \(-0.382593\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1404.00 | − | 2431.80i | −0.0967368 | − | 0.167553i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5044.00 | −0.345791 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10554.0 | 0.719908 | 0.359954 | − | 0.932970i | \(-0.382792\pi\) | ||||
0.359954 | + | 0.932970i | \(0.382792\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7415.50 | + | 12844.0i | 0.503302 | + | 0.871745i | 0.999993 | + | 0.00381713i | \(0.00121503\pi\) |
−0.496691 | + | 0.867928i | \(0.665452\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 18086.1i | − | 1.22143i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1708.50 | − | 986.403i | −0.114811 | − | 0.0662859i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3977.00 | + | 6888.37i | −0.265933 | + | 0.460610i | −0.967808 | − | 0.251691i | \(-0.919013\pi\) |
0.701874 | + | 0.712301i | \(0.252347\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3384.00 | + | 1953.75i | −0.225167 | + | 0.130000i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3393.00 | + | 13712.6i | 0.224658 | + | 0.907945i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21841.5 | − | 12610.2i | 1.43910 | − | 0.830866i | 0.441315 | − | 0.897352i | \(-0.354512\pi\) |
0.997787 | + | 0.0664859i | \(0.0211787\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −471.000 | + | 815.796i | −0.0308822 | + | 0.0534895i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15055.5 | − | 8692.30i | −0.982353 | − | 0.567162i | −0.0793731 | − | 0.996845i | \(-0.525292\pi\) |
−0.902980 | + | 0.429683i | \(0.858625\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 8209.92i | − | 0.533093i | −0.963822 | − | 0.266547i | \(-0.914117\pi\) | ||
0.963822 | − | 0.266547i | \(-0.0858826\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3900.00 | − | 6755.00i | −0.252015 | − | 0.436504i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13536.0 | −0.870479 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14509.0 | 0.928576 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1584.00 | − | 2743.57i | −0.100891 | − | 0.174749i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 16819.9i | − | 1.06622i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11142.0 | − | 6432.84i | −0.702941 | − | 0.405843i | 0.105501 | − | 0.994419i | \(-0.466355\pi\) |
−0.808442 | + | 0.588576i | \(0.799689\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1042.00 | + | 1804.80i | −0.0654278 | + | 0.113324i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −429.000 | + | 247.683i | −0.0268100 | + | 0.0154788i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4907.50 | − | 5100.02i | −0.305247 | − | 0.317222i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −21045.0 | + | 12150.3i | −1.30286 | + | 0.752206i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3100.50 | + | 5370.22i | −0.191049 | + | 0.330907i | −0.945598 | − | 0.325337i | \(-0.894522\pi\) |
0.754549 | + | 0.656244i | \(0.227856\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14568.0 | + | 8410.84i | 0.893477 | + | 0.515849i | 0.875078 | − | 0.483981i | \(-0.160810\pi\) |
0.0183989 | + | 0.999831i | \(0.494143\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 360.267i | 0.0219930i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6747.00 | − | 11686.1i | −0.409972 | − | 0.710092i | 0.584914 | − | 0.811095i | \(-0.301128\pi\) |
−0.994886 | + | 0.101003i | \(0.967795\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3936.00 | −0.238061 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4320.00 | −0.260083 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5667.00 | + | 9815.53i | 0.339612 | + | 0.588226i | 0.984360 | − | 0.176170i | \(-0.0563708\pi\) |
−0.644747 | + | 0.764396i | \(0.723037\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3419.07i | 0.203960i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9142.50 | − | 5278.42i | −0.542896 | − | 0.313441i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6618.00 | − | 11462.7i | 0.391200 | − | 0.677578i | −0.601408 | − | 0.798942i | \(-0.705393\pi\) |
0.992608 | + | 0.121364i | \(0.0387268\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10264.5 | + | 5926.21i | −0.603998 | + | 0.348718i | −0.770613 | − | 0.637304i | \(-0.780050\pi\) |
0.166615 | + | 0.986022i | \(0.446716\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10647.0 | + | 2634.45i | −0.623673 | + | 0.154319i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2376.00 | + | 1371.78i | −0.138552 | + | 0.0799932i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5499.00 | − | 9524.55i | 0.319224 | − | 0.552911i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4170.00 | + | 2407.55i | 0.240989 | + | 0.139135i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2009.18i | − | 0.115594i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4010.50 | − | 6946.39i | −0.229708 | − | 0.397866i | 0.728014 | − | 0.685563i | \(-0.240444\pi\) |
−0.957722 | + | 0.287697i | \(0.907110\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12200.0 | 0.695671 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21630.0 | −1.22793 | −0.613965 | − | 0.789333i | \(-0.710426\pi\) | ||||
−0.613965 | + | 0.789333i | \(0.710426\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1392.00 | + | 2411.01i | 0.0786746 | + | 0.136268i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 4815.10i | − | 0.270947i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22983.0 | + | 13269.2i | 1.28758 | + | 0.743387i | 0.978223 | − | 0.207557i | \(-0.0665514\pi\) |
0.309361 | + | 0.950945i | \(0.399885\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 733.500 | − | 1270.46i | 0.0409133 | − | 0.0708639i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4344.00 | − | 2508.01i | 0.241243 | − | 0.139282i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4231.50 | − | 1047.02i | 0.233973 | − | 0.0578933i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 720.000 | − | 415.692i | 0.0396383 | − | 0.0228852i | −0.480050 | − | 0.877241i | \(-0.659381\pi\) |
0.519688 | + | 0.854356i | \(0.326048\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2208.00 | + | 3824.37i | −0.121032 | + | 0.209633i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 354.000 | + | 204.382i | 0.0193208 | + | 0.0111549i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31816.0i | 1.72901i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5850.00 | − | 10132.5i | −0.316548 | − | 0.548278i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30186.0 | 1.62640 | 0.813202 | − | 0.581981i | \(-0.197722\pi\) | ||||
0.813202 | + | 0.581981i | \(0.197722\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16434.0 | −0.881679 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −522.000 | − | 904.131i | −0.0278860 | − | 0.0483000i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 5944.40i | − | 0.316212i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10288.5 | − | 5940.07i | −0.544983 | − | 0.314646i | 0.202113 | − | 0.979362i | \(-0.435219\pi\) |
−0.747096 | + | 0.664716i | \(0.768552\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14674.0 | + | 25416.1i | −0.774006 | + | 1.34062i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10530.0 | − | 6079.50i | 0.553088 | − | 0.319325i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −780.000 | − | 810.600i | −0.0407977 | − | 0.0423982i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9324.00 | − | 5383.21i | 0.485650 | − | 0.280390i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9204.00 | − | 15941.8i | 0.477401 | − | 0.826883i | −0.522264 | − | 0.852784i | \(-0.674912\pi\) |
0.999665 | + | 0.0259014i | \(0.00824561\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2184.00 | − | 1260.93i | −0.112811 | − | 0.0651312i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9834.58i | 0.505881i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8601.00 | + | 14897.4i | 0.440597 | + | 0.763137i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21112.0 | −1.07703 | −0.538515 | − | 0.842616i | \(-0.681014\pi\) | ||||
−0.538515 | + | 0.842616i | \(0.681014\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4283.00 | −0.217599 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6084.00 | + | 10537.8i | 0.307832 | + | 0.533180i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23959.5i | 1.20732i | 0.797243 | + | 0.603658i | \(0.206291\pi\) | ||||
−0.797243 | + | 0.603658i | \(0.793709\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 453.000 | + | 261.540i | 0.0227335 | + | 0.0131252i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5448.00 | + | 9436.21i | −0.272293 | + | 0.471625i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2742.00 | + | 1583.09i | −0.136490 | + | 0.0788025i | −0.566690 | − | 0.823931i | \(-0.691776\pi\) |
0.430200 | + | 0.902734i | \(0.358443\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2574.00 | + | 10402.7i | 0.127609 | + | 0.515726i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26070.0 | − | 15051.5i | 1.28723 | − | 0.743185i | 0.309075 | − | 0.951038i | \(-0.399981\pi\) |
0.978160 | + | 0.207852i | \(0.0666474\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40.5000 | − | 70.1481i | 0.00199168 | − | 0.00344970i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15732.0 | − | 9082.87i | −0.770554 | − | 0.444880i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 20867.7i | − | 1.01801i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14248.0 | + | 24678.3i | 0.692299 | + | 1.19910i | 0.971083 | + | 0.238744i | \(0.0767356\pi\) |
−0.278783 | + | 0.960354i | \(0.589931\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7956.00 | −0.385037 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3066.00 | 0.147792 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8711.00 | − | 15087.9i | −0.418239 | − | 0.724411i | 0.577524 | − | 0.816374i | \(-0.304019\pi\) |
−0.995762 | + | 0.0919633i | \(0.970686\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2161.60i | 0.103374i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35790.0 | + | 20663.4i | 1.70484 | + | 0.984292i | 0.940695 | + | 0.339252i | \(0.110174\pi\) |
0.764149 | + | 0.645040i | \(0.223159\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10752.0 | − | 18623.0i | 0.510155 | − | 0.883615i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4036.50 | + | 2330.47i | −0.190771 | + | 0.110142i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12792.0 | + | 3692.73i | 0.602206 | + | 0.173842i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12186.0 | + | 7035.59i | −0.571441 | + | 0.329922i | −0.757725 | − | 0.652574i | \(-0.773689\pi\) |
0.186283 | + | 0.982496i | \(0.440356\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2067.00 | − | 3580.15i | 0.0965515 | − | 0.167232i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 174.000 | + | 100.459i | 0.00809618 | + | 0.00467433i | 0.504043 | − | 0.863679i | \(-0.331845\pi\) |
−0.495946 | + | 0.868353i | \(0.665179\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19017.9i | 0.881476i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1992.00 | − | 3450.25i | −0.0919725 | − | 0.159301i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31086.0 | 1.42975 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14640.0 | 0.670756 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7050.00 | + | 12211.0i | 0.321771 | + | 0.557323i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2097.51i | 0.0953675i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5979.00 | + | 3451.98i | 0.270811 | + | 0.156353i | 0.629256 | − | 0.777198i | \(-0.283360\pi\) |
−0.358445 | + | 0.933551i | \(0.616693\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2052.00 | − | 3554.17i | 0.0925895 | − | 0.160370i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8244.00 | − | 4759.68i | 0.370573 | − | 0.213950i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1885.00 | + | 6529.83i | −0.0844115 | + | 0.292410i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −279.000 | + | 161.081i | −0.0124467 | + | 0.00718609i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15639.0 | − | 27087.5i | 0.695059 | − | 1.20388i | −0.275102 | − | 0.961415i | \(-0.588712\pi\) |
0.970161 | − | 0.242462i | \(-0.0779550\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30537.0 | − | 17630.5i | −1.35209 | − | 0.780631i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22468.2i | 0.991103i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3180.00 | + | 5507.92i | 0.139751 | + | 0.242055i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1872.00 | 0.0819619 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6660.00 | −0.290512 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4024.50 | − | 6970.64i | −0.174900 | − | 0.302935i | 0.765227 | − | 0.643761i | \(-0.222627\pi\) |
−0.940127 | + | 0.340826i | \(0.889293\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14026.1i | 0.607305i | 0.952783 | + | 0.303653i | \(0.0982062\pi\) | ||||
−0.952783 | + | 0.303653i | \(0.901794\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4860.00 | − | 2805.92i | −0.209653 | − | 0.121043i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −870.000 | + | 1506.88i | −0.0373924 | + | 0.0647655i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10296.0 | − | 5944.40i | 0.440895 | − | 0.254551i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10764.0 | − | 10357.7i | 0.459249 | − | 0.441912i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6960.00 | + | 4018.36i | −0.295866 | + | 0.170818i | −0.640584 | − | 0.767888i | \(-0.721308\pi\) |
0.344718 | + | 0.938706i | \(0.387974\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20150.0 | + | 34900.8i | −0.853445 | + | 1.47821i | 0.0246361 | + | 0.999696i | \(0.492157\pi\) |
−0.878081 | + | 0.478513i | \(0.841176\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2928.00 | − | 1690.48i | −0.123563 | − | 0.0713394i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39525.4i | 1.66195i | 0.556310 | + | 0.830975i | \(0.312217\pi\) | ||||
−0.556310 | + | 0.830975i | \(0.687783\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6155.50 | + | 10661.6i | 0.257888 | + | 0.446676i | 0.965676 | − | 0.259750i | \(-0.0836400\pi\) |
−0.707788 | + | 0.706425i | \(0.750307\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −754.000 | −0.0314753 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17667.0 | 0.734844 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −792.000 | − | 1371.78i | −0.0328243 | − | 0.0568534i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15588.5i | 0.643747i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18591.0 | − | 10733.5i | −0.764997 | − | 0.441671i | 0.0660899 | − | 0.997814i | \(-0.478948\pi\) |
−0.831087 | + | 0.556142i | \(0.812281\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2254.00 | − | 3904.04i | 0.0924187 | − | 0.160074i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −63.0000 | + | 36.3731i | −0.00257394 | + | 0.00148607i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1774.50 | + | 3366.24i | 0.0722422 | + | 0.137044i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13668.0 | + | 7891.22i | −0.554472 | + | 0.320125i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7124.00 | − | 12339.1i | 0.287980 | − | 0.498796i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9711.00 | + | 5606.65i | 0.391174 | + | 0.225844i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 774.227i | − | 0.0310774i | −0.999879 | − | 0.0155387i | \(-0.995054\pi\) | ||
0.999879 | − | 0.0155387i | \(-0.00494632\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2277.00 | + | 3943.88i | 0.0910781 | + | 0.157752i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13923.0 | 0.554960 | 0.277480 | − | 0.960731i | \(-0.410501\pi\) | ||||
0.277480 | + | 0.960731i | \(0.410501\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22358.0 | 0.888062 | 0.444031 | − | 0.896011i | \(-0.353548\pi\) | ||||
0.444031 | + | 0.896011i | \(0.353548\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3768.00 | + | 6526.37i | 0.149144 | + | 0.258325i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2230.88i | − | 0.0879955i | −0.999032 | − | 0.0439977i | \(-0.985991\pi\) | ||
0.999032 | − | 0.0439977i | \(-0.0140094\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3861.00 | − | 2229.15i | −0.151766 | − | 0.0876224i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8776.00 | − | 15200.5i | 0.343770 | − | 0.595427i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15312.0 | − | 8840.39i | 0.597726 | − | 0.345097i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26559.0 | − | 25556.4i | 1.03320 | − | 0.994197i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4002.00 | − | 2310.56i | 0.155151 | − | 0.0895767i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2964.00 | + | 5133.80i | −0.114516 | + | 0.198348i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14509.5 | − | 8377.06i | −0.558667 | − | 0.322547i | 0.193943 | − | 0.981013i | \(-0.437872\pi\) |
−0.752610 | + | 0.658466i | \(0.771206\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 16645.0i | − | 0.638706i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8677.50 | − | 15029.9i | −0.331842 | − | 0.574766i | 0.651031 | − | 0.759051i | \(-0.274337\pi\) |
−0.982873 | + | 0.184284i | \(0.941003\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46982.0 | 1.79057 | 0.895283 | − | 0.445497i | \(-0.146973\pi\) | ||||
0.895283 | + | 0.445497i | \(0.146973\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −984.000 | −0.0373749 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4458.00 | − | 7721.48i | −0.168754 | − | 0.292291i | 0.769228 | − | 0.638975i | \(-0.220641\pi\) |
−0.937982 | + | 0.346684i | \(0.887308\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3962.93i | 0.149508i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5052.00 | + | 2916.77i | 0.189953 | + | 0.109670i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17226.0 | + | 29836.3i | −0.645516 | + | 1.11807i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5616.00 | + | 3242.40i | −0.209745 | + | 0.121097i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2028.00 | − | 7025.20i | 0.0754882 | − | 0.261499i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19035.0 | + | 10989.9i | −0.706177 | + | 0.407711i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5440.50 | + | 9423.22i | −0.201165 | + | 0.348427i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2496.00 | + | 1441.07i | 0.0919841 | + | 0.0531071i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1103.32i | − | 0.0405254i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15418.0 | − | 26704.8i | −0.564439 | − | 0.977637i | −0.997102 | − | 0.0760813i | \(-0.975759\pi\) |
0.432662 | − | 0.901556i | \(-0.357574\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9867.00 | −0.360031 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27480.0 | 0.999400 | 0.499700 | − | 0.866199i | \(-0.333444\pi\) | ||||
0.499700 | + | 0.866199i | \(0.333444\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5472.00 | + | 9477.78i | 0.198354 | + | 0.343558i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 502.295i | − | 0.0181479i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23688.0 | + | 13676.3i | 0.853050 | + | 0.492509i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14221.0 | + | 24631.5i | −0.510454 | + | 0.884133i | 0.489472 | + | 0.872019i | \(0.337189\pi\) |
−0.999927 | + | 0.0121140i | \(0.996144\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3846.00 | − | 2220.49i | 0.137600 | − | 0.0794437i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −47580.0 | − | 13735.2i | −1.69677 | − | 0.489814i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15189.0 | + | 8769.37i | −0.539904 | + | 0.311714i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2093.00 | + | 3625.18i | −0.0741566 | + | 0.128443i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6043.50 | + | 3489.22i | 0.213435 | + | 0.123227i | 0.602907 | − | 0.797812i | \(-0.294009\pi\) |
−0.389472 | + | 0.921038i | \(0.627342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 17261.6i | − | 0.607655i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4914.00 | − | 8511.30i | −0.172430 | − | 0.298657i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2808.00 | 0.0982154 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38465.0 | −1.34109 | −0.670543 | − | 0.741871i | \(-0.733939\pi\) | ||||
−0.670543 | + | 0.741871i | \(0.733939\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −518.000 | − | 897.202i | −0.0180024 | − | 0.0311811i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 4884.38i | − | 0.169210i | −0.996415 | − | 0.0846049i | \(-0.973037\pi\) | ||
0.996415 | − | 0.0846049i | \(-0.0269628\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18369.0 | − | 10605.3i | −0.634334 | − | 0.366233i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1200.00 | + | 2078.46i | −0.0413079 | + | 0.0715475i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18849.0 | + | 10882.5i | −0.646790 | + | 0.373424i | −0.787225 | − | 0.616665i | \(-0.788483\pi\) |
0.140435 | + | 0.990090i | \(0.455150\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5167.50 | − | 20884.2i | −0.176759 | − | 0.714362i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6783.00 | − | 3916.17i | 0.231287 | − | 0.133534i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3237.00 | + | 5606.65i | −0.110028 | + | 0.190574i | −0.915781 | − | 0.401677i | \(-0.868427\pi\) |
0.805753 | + | 0.592251i | \(0.201761\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3897.00 | − | 2249.93i | −0.132046 | − | 0.0762368i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 3907.51i | − | 0.131987i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5868.00 | − | 10163.7i | −0.197589 | − | 0.342234i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5491.00 | 0.184317 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −34638.0 | −1.15908 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 967.500 | + | 1675.76i | 0.0322745 | + | 0.0559011i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7541.35i | 0.250789i | 0.992107 | + | 0.125395i | \(0.0400197\pi\) | ||||
−0.992107 | + | 0.125395i | \(0.959980\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23166.0 | − | 13374.9i | −0.768007 | − | 0.443409i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17499.0 | − | 30309.2i | 0.578342 | − | 1.00172i | −0.417328 | − | 0.908756i | \(-0.637033\pi\) |
0.995670 | − | 0.0929611i | \(-0.0296332\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2832.00 | − | 1635.06i | 0.0933091 | − | 0.0538720i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7930.00 | + | 8241.10i | 0.260475 | + | 0.270694i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21838.5 | + | 12608.5i | −0.715123 | + | 0.412877i | −0.812955 | − | 0.582326i | \(-0.802143\pi\) |
0.0978318 | + | 0.995203i | \(0.468809\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6768.00 | − | 11722.5i | 0.220946 | − | 0.382690i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30912.0 | − | 17847.1i | −1.00606 | − | 0.580849i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 56440.6i | − | 1.83131i | −0.401967 | − | 0.915654i | \(-0.631673\pi\) | ||
0.401967 | − | 0.915654i | \(-0.368327\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1776.00 | + | 3076.12i | 0.0574498 | + | 0.0995060i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8352.00 | −0.269349 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8112.00 | −0.260816 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29641.0 | + | 51339.7i | 0.950129 | + | 1.64567i | 0.745142 | + | 0.666906i | \(0.232382\pi\) |
0.204987 | + | 0.978765i | \(0.434285\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14909.5i | 0.476474i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3783.00 | − | 2184.12i | −0.120532 | − | 0.0695891i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18855.5 | − | 32658.7i | 0.598957 | − | 1.03742i | −0.394019 | − | 0.919102i | \(-0.628916\pi\) |
0.992975 | − | 0.118321i | \(-0.0377511\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12450.0 | + | 7188.01i | −0.394295 | + | 0.227646i |
(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 | 208.4.w.b.49.1 | 2 | ||
4.3 | odd | 2 | 13.4.e.b.10.1 | yes | 2 | ||
12.11 | even | 2 | 117.4.q.a.10.1 | 2 | |||
13.4 | even | 6 | inner | 208.4.w.b.17.1 | 2 | ||
52.3 | odd | 6 | 169.4.b.d.168.2 | 2 | |||
52.7 | even | 12 | 169.4.c.h.22.2 | 4 | |||
52.11 | even | 12 | 169.4.a.i.1.1 | 2 | |||
52.15 | even | 12 | 169.4.a.i.1.2 | 2 | |||
52.19 | even | 12 | 169.4.c.h.22.1 | 4 | |||
52.23 | odd | 6 | 169.4.b.d.168.1 | 2 | |||
52.31 | even | 4 | 169.4.c.h.146.1 | 4 | |||
52.35 | odd | 6 | 169.4.e.a.147.1 | 2 | |||
52.43 | odd | 6 | 13.4.e.b.4.1 | ✓ | 2 | ||
52.47 | even | 4 | 169.4.c.h.146.2 | 4 | |||
52.51 | odd | 2 | 169.4.e.a.23.1 | 2 | |||
156.11 | odd | 12 | 1521.4.a.o.1.2 | 2 | |||
156.95 | even | 6 | 117.4.q.a.82.1 | 2 | |||
156.119 | odd | 12 | 1521.4.a.o.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.e.b.4.1 | ✓ | 2 | 52.43 | odd | 6 | ||
13.4.e.b.10.1 | yes | 2 | 4.3 | odd | 2 | ||
117.4.q.a.10.1 | 2 | 12.11 | even | 2 | |||
117.4.q.a.82.1 | 2 | 156.95 | even | 6 | |||
169.4.a.i.1.1 | 2 | 52.11 | even | 12 | |||
169.4.a.i.1.2 | 2 | 52.15 | even | 12 | |||
169.4.b.d.168.1 | 2 | 52.23 | odd | 6 | |||
169.4.b.d.168.2 | 2 | 52.3 | odd | 6 | |||
169.4.c.h.22.1 | 4 | 52.19 | even | 12 | |||
169.4.c.h.22.2 | 4 | 52.7 | even | 12 | |||
169.4.c.h.146.1 | 4 | 52.31 | even | 4 | |||
169.4.c.h.146.2 | 4 | 52.47 | even | 4 | |||
169.4.e.a.23.1 | 2 | 52.51 | odd | 2 | |||
169.4.e.a.147.1 | 2 | 52.35 | odd | 6 | |||
208.4.w.b.17.1 | 2 | 13.4 | even | 6 | inner | ||
208.4.w.b.49.1 | 2 | 1.1 | even | 1 | trivial | ||
1521.4.a.o.1.1 | 2 | 156.119 | odd | 12 | |||
1521.4.a.o.1.2 | 2 | 156.11 | odd | 12 |