Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(41,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.41");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.x (of order \(6\), degree \(2\), 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: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 41.14 | ||
Character | \(\chi\) | \(=\) | 252.41 |
Dual form | 252.4.x.a.209.14 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.316211 | + | 5.18652i | 0.0608549 | + | 0.998147i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.49690 | − | 9.52092i | 0.491658 | − | 0.851577i | −0.508296 | − | 0.861182i | \(-0.669724\pi\) |
0.999954 | + | 0.00960594i | \(0.00305771\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.85688 | − | 17.2042i | 0.370237 | − | 0.928937i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.8000 | + | 3.28007i | −0.992593 | + | 0.121484i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.8268 | − | 7.98293i | 0.378996 | − | 0.218813i | −0.298386 | − | 0.954445i | \(-0.596448\pi\) |
0.677381 | + | 0.735632i | \(0.263115\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −77.4289 | − | 44.7036i | −1.65192 | − | 0.953734i | −0.976283 | − | 0.216496i | \(-0.930537\pi\) |
−0.675633 | − | 0.737238i | \(-0.736130\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 51.1186 | + | 25.4992i | 0.879918 | + | 0.438924i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −106.953 | −1.52588 | −0.762939 | − | 0.646471i | \(-0.776244\pi\) | ||||
−0.762939 | + | 0.646471i | \(0.776244\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 8.31634i | − | 0.100416i | −0.998739 | − | 0.0502079i | \(-0.984012\pi\) | ||
0.998739 | − | 0.0502079i | \(-0.0159884\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 91.3980 | + | 30.1232i | 0.949746 | + | 0.313020i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −123.893 | − | 71.5294i | −1.12319 | − | 0.648474i | −0.180977 | − | 0.983487i | \(-0.557926\pi\) |
−0.942214 | + | 0.335013i | \(0.891259\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.06812 | + | 3.58208i | 0.0165449 | + | 0.0286567i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −25.4866 | − | 137.962i | −0.181663 | − | 0.983361i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 129.721 | − | 74.8943i | 0.830639 | − | 0.479570i | −0.0234322 | − | 0.999725i | \(-0.507459\pi\) |
0.854072 | + | 0.520156i | \(0.174126\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −37.1952 | − | 21.4747i | −0.215499 | − | 0.124418i | 0.388366 | − | 0.921505i | \(-0.373040\pi\) |
−0.603864 | + | 0.797087i | \(0.706373\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 45.7759 | + | 69.1890i | 0.241471 | + | 0.364977i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −126.108 | − | 159.853i | −0.609031 | − | 0.772004i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 390.706 | 1.73599 | 0.867997 | − | 0.496570i | \(-0.165407\pi\) | ||||
0.867997 | + | 0.496570i | \(0.165407\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 207.372 | − | 415.722i | 0.851440 | − | 1.70689i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 172.486 | − | 298.755i | 0.657021 | − | 1.13799i | −0.324363 | − | 0.945933i | \(-0.605150\pi\) |
0.981383 | − | 0.192060i | \(-0.0615169\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 28.5593 | + | 49.4661i | 0.101285 | + | 0.175430i | 0.912214 | − | 0.409714i | \(-0.134371\pi\) |
−0.810929 | + | 0.585144i | \(0.801038\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −116.088 | + | 273.191i | −0.384563 | + | 0.904998i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.13282 | + | 14.0864i | 0.0252403 | + | 0.0437174i | 0.878370 | − | 0.477982i | \(-0.158632\pi\) |
−0.853129 | + | 0.521699i | \(0.825298\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −248.966 | − | 235.934i | −0.725849 | − | 0.687854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −33.8198 | − | 554.714i | −0.0928571 | − | 1.52305i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 445.230i | 1.15391i | 0.816777 | + | 0.576954i | \(0.195759\pi\) | ||||
−0.816777 | + | 0.576954i | \(0.804241\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 175.526i | − | 0.430325i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 43.1329 | − | 2.62972i | 0.100230 | − | 0.00611079i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 193.350 | − | 334.892i | 0.426644 | − | 0.738969i | −0.569928 | − | 0.821695i | \(-0.693029\pi\) |
0.996572 | + | 0.0827250i | \(0.0263623\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −420.857 | + | 242.982i | −0.883365 | + | 0.510011i | −0.871766 | − | 0.489922i | \(-0.837025\pi\) |
−0.0115982 | + | 0.999933i | \(0.503692\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −127.334 | + | 483.563i | −0.254643 | + | 0.967035i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −851.238 | + | 491.463i | −1.62436 | + | 0.937822i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −251.821 | + | 436.167i | −0.459177 | + | 0.795318i | −0.998918 | − | 0.0465137i | \(-0.985189\pi\) |
0.539741 | + | 0.841831i | \(0.318522\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 331.813 | − | 665.190i | 0.578921 | − | 1.16057i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 751.418i | − | 1.25601i | −0.778208 | − | 0.628007i | \(-0.783871\pi\) | ||
0.778208 | − | 0.628007i | \(-0.216129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 507.533i | 0.813729i | 0.913489 | + | 0.406865i | \(0.133378\pi\) | ||||
−0.913489 | + | 0.406865i | \(0.866622\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −17.9246 | + | 11.8590i | −0.0275967 | + | 0.0182582i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −42.5306 | − | 292.617i | −0.0629456 | − | 0.433076i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 381.570 | + | 660.899i | 0.543418 | + | 0.941228i | 0.998705 | + | 0.0508826i | \(0.0162034\pi\) |
−0.455287 | + | 0.890345i | \(0.650463\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 707.482 | − | 175.812i | 0.970483 | − | 0.241169i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −607.241 | − | 1051.77i | −0.803052 | − | 1.39093i | −0.917598 | − | 0.397509i | \(-0.869875\pi\) |
0.114546 | − | 0.993418i | \(-0.463459\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −587.911 | + | 1018.29i | −0.750210 | + | 1.29940i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 429.460 | + | 649.117i | 0.529229 | + | 0.799916i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 425.727 | 0.507045 | 0.253523 | − | 0.967329i | \(-0.418411\pi\) | ||||
0.253523 | + | 0.967329i | \(0.418411\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1300.01 | + | 1025.57i | −1.49756 | + | 1.18142i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 99.6173 | − | 199.704i | 0.111073 | − | 0.222671i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −79.1792 | − | 45.7141i | −0.0855117 | − | 0.0493702i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 494.582 | − | 285.547i | 0.517703 | − | 0.298896i | −0.218291 | − | 0.975884i | \(-0.570048\pi\) |
0.735994 | + | 0.676988i | \(0.236715\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −344.375 | + | 259.296i | −0.349606 | + | 0.263234i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 353.385 | + | 612.081i | 0.348150 | + | 0.603013i | 0.985921 | − | 0.167213i | \(-0.0534768\pi\) |
−0.637771 | + | 0.770226i | \(0.720143\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −217.607 | − | 125.635i | −0.208169 | − | 0.120187i | 0.392291 | − | 0.919841i | \(-0.371683\pi\) |
−0.600460 | + | 0.799655i | \(0.705016\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 789.207 | − | 704.608i | 0.733511 | − | 0.654883i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 739.962i | − | 0.668549i | −0.942476 | − | 0.334275i | \(-0.891509\pi\) | ||
0.942476 | − | 0.334275i | \(-0.108491\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1497.38 | 1.31580 | 0.657902 | − | 0.753104i | \(-0.271444\pi\) | ||||
0.657902 | + | 0.753104i | \(0.271444\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 123.546 | + | 2026.41i | 0.105644 | + | 1.73278i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −861.916 | − | 497.627i | −0.717542 | − | 0.414273i | 0.0963056 | − | 0.995352i | \(-0.469297\pi\) |
−0.813847 | + | 0.581079i | \(0.802631\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1362.05 | + | 786.380i | −1.10445 | + | 0.637655i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2221.73 | + | 944.085i | 1.75554 | + | 0.745989i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −733.365 | + | 1840.04i | −0.564936 | + | 1.41744i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −538.046 | + | 931.922i | −0.404242 | + | 0.700167i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1604.04 | + | 800.135i | 1.17587 | + | 0.586550i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1419.70 | 1.01585 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2469.41 | 1.72539 | 0.862696 | − | 0.505724i | \(-0.168774\pi\) | ||||
0.862696 | + | 0.505724i | \(0.168774\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −247.526 | + | 163.765i | −0.168942 | + | 0.111773i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 769.787 | − | 1333.31i | 0.513409 | − | 0.889251i | −0.486470 | − | 0.873697i | \(-0.661716\pi\) |
0.999879 | − | 0.0155535i | \(-0.00495103\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −143.076 | − | 57.0242i | −0.0932800 | − | 0.0371776i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1453.62 | − | 515.706i | −0.926723 | − | 0.328777i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1419.80 | + | 819.722i | −0.885414 | + | 0.511194i | −0.872440 | − | 0.488722i | \(-0.837463\pi\) |
−0.0129744 | + | 0.999916i | \(0.504130\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −899.533 | − | 519.345i | −0.548902 | − | 0.316909i | 0.199777 | − | 0.979841i | \(-0.435978\pi\) |
−0.748679 | + | 0.662933i | \(0.769312\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −70.4880 | + | 46.6353i | −0.0421004 | + | 0.0278539i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1427.46 | −0.834759 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1646.75i | − | 0.943137i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1144.95 | − | 1365.87i | 0.642407 | − | 0.766363i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1523.17 | − | 879.401i | −0.837468 | − | 0.483512i | 0.0189346 | − | 0.999821i | \(-0.493973\pi\) |
−0.856403 | + | 0.516308i | \(0.827306\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 352.401 | + | 610.376i | 0.189920 | + | 0.328952i | 0.945223 | − | 0.326424i | \(-0.105844\pi\) |
−0.755303 | + | 0.655376i | \(0.772510\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2866.34 | − | 350.814i | 1.51458 | − | 0.185370i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −408.917 | + | 236.088i | −0.211903 | + | 0.122342i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 579.051 | + | 334.315i | 0.294352 | + | 0.169944i | 0.639903 | − | 0.768456i | \(-0.278975\pi\) |
−0.345551 | + | 0.938400i | \(0.612308\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2309.20 | + | 140.787i | −1.15177 | + | 0.0702209i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2080.12 | + | 1641.00i | −1.01824 | + | 0.803285i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3926.19 | −1.88665 | −0.943323 | − | 0.331877i | \(-0.892318\pi\) | ||||
−0.943323 | + | 0.331877i | \(0.892318\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 910.368 | − | 55.5032i | 0.429527 | − | 0.0261874i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −966.800 | + | 1674.55i | −0.447984 | + | 0.775930i | −0.998255 | − | 0.0590557i | \(-0.981191\pi\) |
0.550271 | + | 0.834986i | \(0.314524\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2898.32 | + | 5020.04i | 1.31922 | + | 2.28495i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 27.2782 | + | 222.878i | 0.0121989 | + | 0.0996720i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −850.018 | − | 1472.27i | −0.373559 | − | 0.647023i | 0.616551 | − | 0.787315i | \(-0.288529\pi\) |
−0.990110 | + | 0.140292i | \(0.955196\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 75.8075 | − | 11.0183i | 0.0327458 | − | 0.00475945i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1798.06 | + | 896.917i | 0.763563 | + | 0.380884i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 1175.15i | − | 0.490697i | −0.969435 | − | 0.245349i | \(-0.921098\pi\) | ||
0.969435 | − | 0.245349i | \(-0.0789024\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3506.89i | 1.44014i | 0.693902 | + | 0.720070i | \(0.255890\pi\) | ||||
−0.693902 | + | 0.720070i | \(0.744110\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1393.31 | − | 2105.95i | −0.562823 | − | 0.850691i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2147.68 | − | 3719.88i | 0.853515 | − | 1.47833i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1478.82 | + | 853.799i | −0.578301 | + | 0.333882i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2548.27 | − | 507.511i | −0.980739 | − | 0.195323i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1228.14 | − | 709.068i | 0.465263 | − | 0.268620i | −0.248992 | − | 0.968506i | \(-0.580099\pi\) |
0.714255 | + | 0.699886i | \(0.246766\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 746.819 | − | 1293.53i | 0.278535 | − | 0.482436i | −0.692486 | − | 0.721431i | \(-0.743485\pi\) |
0.971021 | + | 0.238995i | \(0.0768179\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2818.15 | − | 4259.56i | −1.03493 | − | 1.56427i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2384.42i | − | 0.862351i | −0.902268 | − | 0.431175i | \(-0.858099\pi\) | ||
0.902268 | − | 0.431175i | \(-0.141901\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4960.24i | − | 1.76695i | −0.468482 | − | 0.883473i | \(-0.655199\pi\) | ||
0.468482 | − | 0.883473i | \(-0.344801\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2341.82 | − | 1168.15i | −0.821787 | − | 0.409927i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −399.014 | − | 2745.28i | −0.137957 | − | 0.949166i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1896.28 | − | 3284.46i | −0.646059 | − | 1.11901i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3554.94 | + | 1510.61i | 1.19365 | + | 0.507221i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −66.3888 | − | 114.989i | −0.0219723 | − | 0.0380571i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1973.64 | − | 3418.45i | 0.643939 | − | 1.11534i | −0.340606 | − | 0.940206i | \(-0.610632\pi\) |
0.984545 | − | 0.175129i | \(-0.0560343\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3897.25 | − | 237.607i | 1.25369 | − | 0.0764345i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 627.950 | 0.199190 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −624.497 | + | 492.663i | −0.195362 | + | 0.154121i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2632.33 | + | 160.488i | −0.812221 | + | 0.0495194i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8281.26 | + | 4781.19i | 2.52062 | + | 1.45528i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1397.46 | + | 806.825i | −0.419646 | + | 0.242283i | −0.694926 | − | 0.719082i | \(-0.744563\pi\) |
0.275280 | + | 0.961364i | \(0.411229\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −67.1750 | − | 89.2163i | −0.0199037 | − | 0.0264345i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1749.96 | + | 3031.01i | 0.511668 | + | 0.886235i | 0.999909 | + | 0.0135262i | \(0.00430565\pi\) |
−0.488240 | + | 0.872709i | \(0.662361\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1654.24 | − | 955.078i | −0.477360 | − | 0.275604i | 0.241956 | − | 0.970287i | \(-0.422211\pi\) |
−0.719316 | + | 0.694683i | \(0.755544\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1504.22 | − | 313.115i | 0.428443 | − | 0.0891837i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4408.26i | − | 1.23946i | −0.784814 | − | 0.619731i | \(-0.787242\pi\) | ||
0.784814 | − | 0.619731i | \(-0.212758\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 178.821 | 0.0496383 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3307.11 | + | 2188.01i | −0.906413 | + | 0.599689i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3715.64 | + | 2145.23i | 1.00563 | + | 0.580599i | 0.909908 | − | 0.414809i | \(-0.136152\pi\) |
0.0957187 | + | 0.995408i | \(0.469485\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1413.43 | + | 816.047i | −0.377790 | + | 0.218117i | −0.676856 | − | 0.736115i | \(-0.736658\pi\) |
0.299066 | + | 0.954232i | \(0.403325\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1135.57 | + | 3613.78i | 0.299780 | + | 0.954008i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3614.85 | + | 1073.48i | −0.942630 | + | 0.279927i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −371.770 | + | 643.925i | −0.0957700 | + | 0.165878i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5263.02 | − | 3482.05i | 1.33948 | − | 0.886209i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3912.60 | −0.983908 | −0.491954 | − | 0.870621i | \(-0.663717\pi\) | ||||
−0.491954 | + | 0.870621i | \(0.663717\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2284.06 | −0.567579 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5467.29 | − | 2727.22i | −1.34265 | − | 0.669745i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1054.61 | − | 1826.64i | 0.255971 | − | 0.443356i | −0.709187 | − | 0.705020i | \(-0.750938\pi\) |
0.965159 | + | 0.261664i | \(0.0842714\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2679.03 | − | 6721.78i | 0.642729 | − | 1.61263i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3230.86 | + | 2432.66i | −0.766227 | + | 0.576927i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3827.74 | − | 2209.95i | 0.897448 | − | 0.518142i | 0.0210765 | − | 0.999778i | \(-0.493291\pi\) |
0.876371 | + | 0.481636i | \(0.159957\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4239.00 | + | 2447.39i | 0.982641 | + | 0.567328i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 134.620 | + | 2208.04i | 0.0308562 | + | 0.506105i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4557.94 | −1.03309 | −0.516547 | − | 0.856259i | \(-0.672783\pi\) | ||||
−0.516547 | + | 0.856259i | \(0.672783\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 128.189i | 0.0287341i | 0.999897 | + | 0.0143671i | \(0.00457334\pi\) | ||||
−0.999897 | + | 0.0143671i | \(0.995427\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5730.23 | − | 6418.23i | −1.27036 | − | 1.42289i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 57.1910 | + | 33.0193i | 0.0125409 | + | 0.00724050i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1020.01 | + | 1766.71i | 0.221251 | + | 0.383218i | 0.955188 | − | 0.296000i | \(-0.0956527\pi\) |
−0.733937 | + | 0.679217i | \(0.762319\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1067.27 | + | 453.518i | 0.229017 | + | 0.0973170i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1506.57 | − | 869.820i | 0.319838 | − | 0.184659i | −0.331482 | − | 0.943462i | \(-0.607549\pi\) |
0.651321 | + | 0.758803i | \(0.274215\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1080.52 | + | 623.836i | 0.226961 | + | 0.131036i | 0.609169 | − | 0.793040i | \(-0.291503\pi\) |
−0.382208 | + | 0.924076i | \(0.624836\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 212.060 | − | 425.120i | 0.0440749 | − | 0.0883576i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3957.11 | − | 5016.01i | −0.813871 | − | 1.03166i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6525.95 | 1.32830 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1637.39 | + | 2474.87i | 0.329847 | + | 0.498554i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2395.59 | + | 4149.28i | −0.477651 | + | 0.827316i | −0.999672 | − | 0.0256168i | \(-0.991845\pi\) |
0.522021 | + | 0.852933i | \(0.325178\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2125.65 | − | 3681.74i | −0.419526 | − | 0.726640i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1453.74 | − | 1704.12i | −0.284022 | − | 0.332939i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6395.24 | + | 11076.9i | 1.23694 | + | 2.14245i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1046.85 | − | 152.155i | 0.200463 | − | 0.0291364i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3062.83 | + | 2026.39i | −0.580709 | + | 0.384201i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5342.59i | 1.00300i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4679.41i | − | 0.869929i | −0.900448 | − | 0.434965i | \(-0.856761\pi\) | ||
0.900448 | − | 0.434965i | \(-0.143239\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 582.801 | − | 1168.35i | 0.107296 | − | 0.215097i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 919.164 | − | 1592.04i | 0.167592 | − | 0.290277i | −0.769981 | − | 0.638067i | \(-0.779734\pi\) |
0.937573 | + | 0.347790i | \(0.113068\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5160.13 | − | 2979.20i | 0.931846 | − | 0.538001i | 0.0444510 | − | 0.999012i | \(-0.485846\pi\) |
0.887395 | + | 0.461010i | \(0.152513\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3904.02 | + | 3870.43i | 0.698307 | + | 0.692299i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8986.17 | + | 5188.17i | −1.59216 | + | 0.919232i | −0.599220 | + | 0.800584i | \(0.704523\pi\) |
−0.992936 | + | 0.118648i | \(0.962144\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1195.75 | − | 2071.10i | 0.209872 | − | 0.363510i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3837.83 | − | 233.984i | 0.667310 | − | 0.0406845i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 889.458i | 0.153222i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 369.809i | − | 0.0631179i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 473.487 | + | 7766.17i | 0.0800731 | + | 1.31337i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 298.111 | − | 43.3291i | 0.0499557 | − | 0.00726083i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2421.65 | − | 4194.42i | −0.402132 | − | 0.696514i | 0.591851 | − | 0.806048i | \(-0.298398\pi\) |
−0.993983 | + | 0.109534i | \(0.965064\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10470.9 | + | 1281.55i | −1.72314 | + | 0.210896i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2768.47 | + | 4795.13i | 0.451516 | + | 0.782048i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −559.013 | + | 968.240i | −0.0903602 | + | 0.156509i | −0.907663 | − | 0.419700i | \(-0.862135\pi\) |
0.817302 | + | 0.576209i | \(0.195469\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2308.41 | − | 4627.70i | 0.369839 | − | 0.741422i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −685.723 | −0.108897 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5766.18 | + | 2665.49i | −0.907709 | + | 0.419600i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4509.27 | − | 6815.64i | −0.703685 | − | 1.06360i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3834.85 | + | 2214.05i | 0.593273 | + | 0.342526i | 0.766391 | − | 0.642375i | \(-0.222051\pi\) |
−0.173118 | + | 0.984901i | \(0.555384\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1980.13 | − | 1143.23i | 0.303707 | − | 0.175345i | −0.340400 | − | 0.940281i | \(-0.610562\pi\) |
0.644107 | + | 0.764935i | \(0.277229\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4193.98 | + | 11821.6i | −0.637773 | + | 1.79769i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4027.88 | + | 6976.50i | 0.607316 | + | 1.05190i | 0.991681 | + | 0.128721i | \(0.0410873\pi\) |
−0.384364 | + | 0.923181i | \(0.625579\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7154.19 | − | 4130.47i | −1.06959 | − | 0.617529i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9775.29 | − | 3221.77i | −1.44920 | − | 0.477631i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5537.25i | 0.814053i | 0.913416 | + | 0.407027i | \(0.133434\pi\) | ||||
−0.913416 | + | 0.407027i | \(0.866566\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6789.84 | 0.989917 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5003.57 | − | 2495.90i | −0.723469 | − | 0.360884i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4832.18 | + | 2789.86i | 0.692953 | + | 0.400076i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4668.87 | − | 2695.58i | 0.664069 | − | 0.383400i | −0.129757 | − | 0.991546i | \(-0.541420\pi\) |
0.793825 | + | 0.608146i | \(0.208086\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3642.70 | + | 8572.41i | −0.513906 | + | 1.20938i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7659.81 | + | 3052.89i | 1.07191 | + | 0.427219i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1062.08 | − | 1839.58i | 0.147433 | − | 0.255362i | −0.782845 | − | 0.622217i | \(-0.786232\pi\) |
0.930278 | + | 0.366855i | \(0.119566\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 448.925 | + | 7363.30i | 0.0618196 | + | 1.01397i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13392.2 | −1.82953 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5358.80 | −0.726288 | −0.363144 | − | 0.931733i | \(-0.618297\pi\) | ||||
−0.363144 | + | 0.931733i | \(0.618297\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 780.855 | + | 12807.6i | 0.104998 | + | 1.72219i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2729.23 | − | 4727.16i | 0.364118 | − | 0.630670i | −0.624517 | − | 0.781012i | \(-0.714704\pi\) |
0.988634 | + | 0.150341i | \(0.0480373\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3019.77 | − | 1203.56i | −0.399745 | − | 0.159322i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −927.641 | − | 1232.02i | −0.121847 | − | 0.161827i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1416.25 | − | 817.670i | 0.184593 | − | 0.106575i | −0.404856 | − | 0.914380i | \(-0.632678\pi\) |
0.589449 | + | 0.807806i | \(0.299345\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13250.7 | + | 7650.29i | 1.71385 | + | 0.989493i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7158.66 | + | 3570.91i | 0.918846 | + | 0.458342i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8389.82 | 1.06870 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7694.41i | 0.972724i | 0.873757 | + | 0.486362i | \(0.161676\pi\) | ||||
−0.873757 | + | 0.486362i | \(0.838324\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 250.515 | − | 760.097i | 0.0314322 | − | 0.0953695i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4800.46 | + | 2771.55i | 0.597815 | + | 0.345148i | 0.768181 | − | 0.640232i | \(-0.221162\pi\) |
−0.170367 | + | 0.985381i | \(0.554495\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1919.99 | + | 3325.52i | 0.237324 | + | 0.411057i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2215.07 | − | 7702.30i | 0.271772 | − | 0.945013i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5402.24 | − | 3118.98i | 0.657934 | − | 0.379858i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6361.70 | + | 3672.93i | 0.769109 | + | 0.444045i | 0.832557 | − | 0.553940i | \(-0.186876\pi\) |
−0.0634474 | + | 0.997985i | \(0.520210\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4700.46 | − | 7104.62i | −0.564128 | − | 0.852664i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4435.75 | − | 5622.74i | −0.528497 | − | 0.669920i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13351.8 | −1.57931 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2409.15 | − | 4829.67i | 0.282918 | − | 0.567170i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1717.45 | − | 2974.72i | 0.200246 | − | 0.346836i | −0.748362 | − | 0.663291i | \(-0.769159\pi\) |
0.948608 | + | 0.316455i | \(0.102492\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7241.13 | − | 12542.0i | −0.838269 | − | 1.45192i | −0.891341 | − | 0.453334i | \(-0.850235\pi\) |
0.0530719 | − | 0.998591i | \(-0.483099\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −264.164 | − | 350.841i | −0.0303643 | − | 0.0403274i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −221.191 | − | 383.115i | −0.0252455 | − | 0.0437266i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1294.53 | + | 8906.59i | 0.146714 | + | 1.00942i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −451.380 | − | 7403.57i | −0.0507991 | − | 0.833212i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 13632.5i | − | 1.52356i | −0.647839 | − | 0.761778i | \(-0.724327\pi\) | ||
0.647839 | − | 0.761778i | \(-0.275673\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6735.48i | 0.747544i | 0.927521 | + | 0.373772i | \(0.121936\pi\) | ||||
−0.927521 | + | 0.373772i | \(0.878064\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8540.89 | − | 520.720i | 0.941389 | − | 0.0573945i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −594.863 | + | 1030.33i | −0.0651170 | + | 0.112786i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9181.17 | − | 5300.75i | 0.998162 | − | 0.576289i | 0.0904581 | − | 0.995900i | \(-0.471167\pi\) |
0.907704 | + | 0.419611i | \(0.137834\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7446.18 | + | 5506.40i | 0.804037 | + | 0.594580i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3111.86 | + | 1796.64i | −0.333745 | + | 0.192688i | −0.657503 | − | 0.753452i | \(-0.728387\pi\) |
0.323757 | + | 0.946140i | \(0.395054\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2340.18 | − | 4053.31i | 0.249293 | − | 0.431788i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4079.39 | − | 8178.02i | 0.431652 | − | 0.865340i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8675.98i | 0.911904i | 0.890004 | + | 0.455952i | \(0.150701\pi\) | ||||
−0.890004 | + | 0.455952i | \(0.849299\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 5507.79i | − | 0.575059i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3054.29 | + | 2020.74i | −0.316784 | + | 0.209587i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2618.36 | + | 18014.7i | 0.269782 | + | 1.85614i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1466.35 | − | 2539.79i | −0.150094 | − | 0.259970i | 0.781168 | − | 0.624321i | \(-0.214624\pi\) |
−0.931262 | + | 0.364351i | \(0.881291\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2725.87 | + | 14755.4i | 0.277196 | + | 1.50049i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3015.81 | + | 5223.53i | 0.304686 | + | 0.527731i | 0.977191 | − | 0.212361i | \(-0.0681152\pi\) |
−0.672506 | + | 0.740092i | \(0.734782\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 295.638 | − | 512.060i | 0.0296748 | − | 0.0513983i | −0.850807 | − | 0.525479i | \(-0.823886\pi\) |
0.880481 | + | 0.474081i | \(0.157219\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1353.78 | − | 2046.20i | −0.135011 | − | 0.204065i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16674.6 | 1.65227 | 0.826134 | − | 0.563473i | \(-0.190535\pi\) | ||||
0.826134 | + | 0.563473i | \(0.190535\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5777.18 | + | 7323.12i | 0.568796 | + | 0.721002i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1550.83 | + | 3108.98i | −0.151717 | + | 0.304149i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 789.769 | + | 455.973i | 0.0767730 | + | 0.0443249i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.7898 | − | 17.1992i | 0.00287758 | − | 0.00166137i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1460.39 | − | 11932.2i | −0.140181 | − | 1.14536i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8608.73 | − | 14910.8i | −0.821175 | − | 1.42232i | −0.904808 | − | 0.425820i | \(-0.859986\pi\) |
0.0836331 | − | 0.996497i | \(-0.473348\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30252.0 | − | 17466.0i | −2.86772 | − | 1.65568i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9168.83 | − | 10269.7i | −0.863761 | − | 0.967468i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 6278.50i | − | 0.587818i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8745.94 | 0.813792 | 0.406896 | − | 0.913475i | \(-0.366611\pi\) | ||||
0.406896 | + | 0.913475i | \(0.366611\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1241.51 | − | 20363.3i | −0.114812 | − | 1.88315i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 653.319 | + | 377.194i | 0.0600486 | + | 0.0346691i | 0.529724 | − | 0.848170i | \(-0.322296\pi\) |
−0.469675 | + | 0.882839i | \(0.655629\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13874.0 | + | 8010.17i | −1.26745 | + | 0.731765i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 575.737 | + | 4704.09i | 0.0522777 | + | 0.427138i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12927.5 | − | 5152.39i | −1.16676 | − | 0.465022i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2480.24 | + | 4295.90i | −0.222506 | + | 0.385392i | −0.955568 | − | 0.294769i | \(-0.904757\pi\) |
0.733062 | + | 0.680162i | \(0.238090\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8990.79 | − | 4484.82i | −0.801754 | − | 0.399934i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5299.83 | −0.469797 | −0.234898 | − | 0.972020i | \(-0.575476\pi\) | ||||
−0.234898 | + | 0.972020i | \(0.575476\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7770.09 | 0.684682 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −25120.1 | + | 16619.6i | −2.20044 | + | 1.45582i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9344.81 | − | 16185.7i | 0.813755 | − | 1.40947i | −0.0964627 | − | 0.995337i | \(-0.530753\pi\) |
0.910218 | − | 0.414129i | \(-0.135914\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8731.68 | + | 3480.09i | 0.755903 | + | 0.301273i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1147.34 | + | 211.956i | −0.0987449 | + | 0.0182418i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2392.33 | + | 1381.21i | −0.204696 | + | 0.118181i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 224.902 | + | 129.847i | 0.0191319 | + | 0.0110458i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7367.20 | − | 4874.19i | 0.623091 | − | 0.412241i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8964.93 | −0.753859 | −0.376930 | − | 0.926242i | \(-0.623020\pi\) | ||||
−0.376930 | + | 0.926242i | \(0.623020\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 20614.1i | − | 1.72350i | −0.507330 | − | 0.861752i | \(-0.669367\pi\) | ||
0.507330 | − | 0.861752i | \(-0.330633\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 81.1178 | + | 389.693i | 0.00674337 | + | 0.0323955i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3978.14 | + | 2296.78i | 0.328825 | + | 0.189847i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4149.41 | + | 7186.99i | 0.341038 | + | 0.590695i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4083.31 | + | 9609.31i | −0.333711 | + | 0.785327i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26710.9 | + | 15421.5i | −2.17069 | + | 1.25325i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7045.11 | − | 4067.50i | −0.569321 | − | 0.328698i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6094.94 | − | 371.595i | 0.489788 | − | 0.0298613i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5325.86 | − | 1274.74i | −0.425605 | − | 0.101868i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9376.65 | 0.745164 | 0.372582 | − | 0.927999i | \(-0.378473\pi\) | ||||
0.372582 | + | 0.927999i | \(0.378473\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18188.6 | + | 1108.92i | −1.43747 | + | 0.0876395i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8230.93 | − | 14256.4i | 0.646925 | − | 1.12051i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1172.25 | + | 2030.40i | 0.0916305 | + | 0.158709i | 0.908197 | − | 0.418542i | \(-0.137459\pi\) |
−0.816567 | + | 0.577251i | \(0.804125\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10482.0 | − | 7892.36i | 0.814864 | − | 0.613548i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −622.847 | − | 1078.80i | −0.0481564 | − | 0.0834093i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13986.6 | − | 2032.89i | 1.07553 | − | 0.156324i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19972.4 | + | 9962.70i | 1.52753 | + | 0.761969i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 15368.4i | − | 1.16908i | −0.811364 | − | 0.584541i | \(-0.801275\pi\) | ||
0.811364 | − | 0.584541i | \(-0.198725\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5106.81i | − | 0.386395i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4895.87 | − | 7399.97i | −0.368456 | − | 0.556911i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6447.73 | + | 11167.8i | −0.482664 | + | 0.835998i | −0.999802 | − | 0.0199041i | \(-0.993664\pi\) |
0.517138 | + | 0.855902i | \(0.326997\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9475.73 | + | 5470.82i | −0.705570 | + | 0.407361i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1826.42 | − | 13377.2i | 0.135278 | − | 0.990808i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20989.2 | − | 12118.1i | 1.54642 | − | 0.892824i | 0.548005 | − | 0.836475i | \(-0.315387\pi\) |
0.998411 | − | 0.0563492i | \(-0.0179460\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3678.38 | + | 6371.14i | −0.269589 | + | 0.466942i | −0.968756 | − | 0.248017i | \(-0.920221\pi\) |
0.699167 | + | 0.714959i | \(0.253555\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4065.95 | + | 6145.57i | 0.296435 | + | 0.448054i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 591.724i | − | 0.0429158i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 11928.2i | − | 0.860617i | −0.902682 | − | 0.430308i | \(-0.858405\pi\) | ||
0.902682 | − | 0.430308i | \(-0.141595\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6945.07 | + | 3464.37i | 0.498493 | + | 0.248660i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22258.6 | + | 3235.19i | −1.58940 | + | 0.231013i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3554.24 | + | 6156.13i | 0.252490 | + | 0.437326i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 21201.2 | − | 15963.3i | 1.49839 | − | 1.12821i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2638.36 | − | 4569.77i | −0.185514 | − | 0.321320i | 0.758236 | − | 0.651981i | \(-0.226062\pi\) |
−0.943750 | + | 0.330661i | \(0.892728\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −178.591 | + | 309.328i | −0.0124935 | + | 0.0216395i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12366.9 | − | 753.981i | 0.860752 | − | 0.0524782i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5290.53 | 0.366367 | 0.183184 | − | 0.983079i | \(-0.441360\pi\) | ||||
0.183184 | + | 0.983079i | \(0.441360\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13487.6 | + | 17096.8i | 0.929308 | + | 1.17798i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25726.4 | − | 1568.48i | 1.76367 | − | 0.107527i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8568.78 | − | 4947.19i | −0.584492 | − | 0.337457i | 0.178424 | − | 0.983954i | \(-0.442900\pi\) |
−0.762917 | + | 0.646497i | \(0.776233\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2305.57 | − | 1331.12i | 0.156483 | − | 0.0903454i | −0.419714 | − | 0.907656i | \(-0.637870\pi\) |
0.576197 | + | 0.817311i | \(0.304536\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5318.15 | − | 12515.3i | 0.359157 | − | 0.845210i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5915.17 | + | 10245.4i | 0.397497 | + | 0.688485i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9797.65 | − | 5656.68i | −0.655147 | − | 0.378249i | 0.135278 | − | 0.990808i | \(-0.456807\pi\) |
−0.790425 | + | 0.612558i | \(0.790141\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14112.3 | − | 2937.58i | 0.939012 | − | 0.195463i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1454.26i | − | 0.0962901i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23984.5 | −1.58030 | −0.790151 | − | 0.612912i | \(-0.789998\pi\) | ||||
−0.790151 | + | 0.612912i | \(0.789998\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16435.3 | − | 10873.7i | 1.07762 | − | 0.712958i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14063.1 | − | 8119.31i | −0.917597 | − | 0.529775i | −0.0347291 | − | 0.999397i | \(-0.511057\pi\) |
−0.882868 | + | 0.469622i | \(0.844390\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14971.6 | + | 8643.88i | −0.972150 | + | 0.561271i | −0.899891 | − | 0.436115i | \(-0.856354\pi\) |
−0.0722590 | + | 0.997386i | \(0.523021\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6710.71 | + | 18915.5i | −0.433642 | + | 1.22231i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2919.16 | − | 7324.28i | 0.187727 | − | 0.471013i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7545.43 | − | 13069.1i | 0.482908 | − | 0.836421i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 575.399 | − | 380.688i | 0.0366495 | − | 0.0242475i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −41787.2 | −2.64891 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 348.827 | 0.0220073 | 0.0110036 | − | 0.999939i | \(-0.496497\pi\) | ||||
0.0110036 | + | 0.999939i | \(0.496497\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18354.0 | + | 9155.39i | 1.15246 | + | 0.574872i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13574.1 | − | 23511.0i | 0.848302 | − | 1.46930i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8730.10 | + | 29397.8i | 0.543013 | + | 1.82854i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2464.71 | + | 20138.0i | 0.152586 | + | 1.24671i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14508.8 | + | 8376.64i | −0.894013 | + | 0.516158i | −0.875253 | − | 0.483666i | \(-0.839305\pi\) |
−0.0187597 | + | 0.999824i | \(0.505972\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10660.5 | + | 6154.87i | 0.653827 | + | 0.377487i | 0.789921 | − | 0.613209i | \(-0.210122\pi\) |
−0.136094 | + | 0.990696i | \(0.543455\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 198.565 | + | 3256.88i | 0.0121217 | + | 0.198821i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32197.6 | 1.95644 | 0.978220 | − | 0.207570i | \(-0.0665555\pi\) | ||||
0.978220 | + | 0.207570i | \(0.0665555\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 6174.00i | − | 0.373422i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2752.68 | − | 3083.18i | −0.165724 | − | 0.185621i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15436.6 | − | 8912.32i | −0.925085 | − | 0.534098i | −0.0398315 | − | 0.999206i | \(-0.512682\pi\) |
−0.885254 | + | 0.465108i | \(0.846015\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8462.89 | − | 14658.2i | −0.504843 | − | 0.874415i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1664.74 | − | 13601.9i | −0.0988552 | − | 0.807702i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17782.9 | − | 10267.0i | 1.05117 | − | 0.606895i | 0.128196 | − | 0.991749i | \(-0.459081\pi\) |
0.922978 | + | 0.384853i | \(0.125748\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8819.60 | + | 5092.00i | 0.518975 | + | 0.299630i | 0.736515 | − | 0.676421i | \(-0.236470\pi\) |
−0.217540 | + | 0.976051i | \(0.569803\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22179.1 | + | 44462.8i | −1.29919 | + | 2.60451i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1329.40 | + | 1048.75i | −0.0775214 | + | 0.0611563i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21428.6 | −1.24395 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4626.51 | − | 6992.84i | −0.267371 | − | 0.404124i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3879.42 | + | 6719.35i | −0.223194 | + | 0.386584i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8773.58 | + | 15196.3i | 0.502521 | + | 0.870392i | 0.999996 | + | 0.00291344i | \(0.000927377\pi\) |
−0.497475 | + | 0.867478i | \(0.665739\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 441.481 | − | 376.616i | 0.0251742 | − | 0.0214755i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4832.83 | + | 8370.70i | 0.274358 | + | 0.475203i | 0.969973 | − | 0.243212i | \(-0.0782012\pi\) |
−0.695615 | + | 0.718415i | \(0.744868\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1521.31 | − | 10466.8i | −0.0859829 | − | 0.591576i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15167.1 | + | 10034.6i | −0.853455 | + | 0.564652i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4376.97i | 0.245213i | 0.992455 | + | 0.122606i | \(0.0391253\pi\) | ||||
−0.992455 | + | 0.122606i | \(0.960875\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18023.7i | 1.00533i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4430.44 | − | 8881.77i | 0.246043 | − | 0.493247i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19903.4 | − | 34473.7i | 1.10052 | − | 1.90616i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17526.8 | + | 10119.1i | −0.964905 | + | 0.557088i | −0.897679 | − | 0.440649i | \(-0.854748\pi\) |
−0.0672260 | + | 0.997738i | \(0.521415\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2099.63 | + | 7702.65i | 0.115091 | + | 0.422221i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9889.29 | + | 5709.58i | −0.539744 | + | 0.311621i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18447.9 | + | 31952.8i | −1.00253 | + | 1.73644i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22863.5 | − | 1393.94i | 1.23717 | − | 0.0754273i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33130.3i | 1.78504i | 0.451004 | + | 0.892522i | \(0.351066\pi\) | ||||
−0.451004 | + | 0.892522i | \(0.648934\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3249.25i | − | 0.174321i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 56.5453 | + | 927.460i | 0.00302073 | + | 0.0495463i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12953.5 | − | 1882.73i | 0.689059 | − | 0.100152i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17606.6 | + | 30495.5i | 0.932623 | + | 1.61535i | 0.778819 | + | 0.627249i | \(0.215819\pi\) |
0.153804 | + | 0.988101i | \(0.450847\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12393.9 | − | 16460.5i | −0.653737 | − | 0.868240i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3072.14 | + | 5321.10i | 0.161364 | + | 0.279491i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7846.63 | + | 13590.8i | −0.410416 | + | 0.710861i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9951.34 | + | 19949.6i | −0.518326 | + | 1.03910i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21789.0 | 1.13017 | 0.565086 | − | 0.825032i | \(-0.308843\pi\) | ||||
0.565086 | + | 0.825032i | \(0.308843\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3653.55 | + | 2882.28i | −0.188718 | + | 0.148879i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4679.39 | − | 7072.77i | −0.240703 | − | 0.363816i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 536.555 | + | 309.780i | 0.0274857 | + | 0.0158689i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 685.180 | − | 395.589i | 0.0349545 | − | 0.0201810i | −0.482421 | − | 0.875940i | \(-0.660242\pi\) |
0.517375 | + | 0.855759i | \(0.326909\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18383.9 | + | 7032.36i | −0.933997 | + | 0.357281i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3054.50 | − | 5290.55i | −0.154548 | − | 0.267685i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 195.132 | + | 112.659i | 0.00983269 | + | 0.00567691i | 0.504908 | − | 0.863173i | \(-0.331526\pi\) |
−0.495076 | + | 0.868850i | \(0.664860\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6710.69 | − | 18409.1i | −0.336772 | − | 0.923848i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8041.08i | 0.401896i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2564.36 | −0.127648 | −0.0638238 | − | 0.997961i | \(-0.520330\pi\) | ||||
−0.0638238 | + | 0.997961i | \(0.520330\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3457.29 | − | 1724.58i | −0.171399 | − | 0.0854980i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30419.9 | − | 17563.0i | −1.50202 | − | 0.867190i | −0.999997 | − | 0.00233421i | \(-0.999257\pi\) |
−0.502020 | − | 0.864856i | \(-0.667410\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16745.4 | + | 9667.97i | −0.823496 | + | 0.475446i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19724.0 | + | 26195.7i | 0.966080 | + | 1.28307i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12730.4 | − | 5073.83i | −0.621041 | − | 0.247522i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5213.77 | + | 9030.52i | −0.253333 | + | 0.438786i | −0.964441 | − | 0.264297i | \(-0.914860\pi\) |
0.711108 | + | 0.703083i | \(0.248194\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1237.21 | − | 20292.8i | −0.0598756 | − | 0.982084i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7748.45 | 0.373503 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14031.2 | −0.673677 | −0.336838 | − | 0.941562i | \(-0.609358\pi\) | ||||
−0.336838 | + | 0.941562i | \(0.609358\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −722.245 | − | 11846.3i | −0.0345399 | − | 0.566527i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5435.63 | − | 9414.79i | 0.258924 | − | 0.448470i | −0.707030 | − | 0.707184i | \(-0.749965\pi\) |
0.965954 | + | 0.258714i | \(0.0832986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10267.3 | − | 25761.1i | 0.487159 | − | 1.22230i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12415.9 | − | 29218.6i | 0.586797 | − | 1.38092i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −29941.7 | + | 17286.9i | −1.40956 | + | 0.813811i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17962.0 | + | 10370.3i | 0.842295 | + | 0.486299i | 0.858044 | − | 0.513577i | \(-0.171680\pi\) |
−0.0157486 | + | 0.999876i | \(0.505013\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9807.36 | + | 4892.15i | 0.458111 | + | 0.228517i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7445.62 | 0.346443 | 0.173221 | − | 0.984883i | \(-0.444582\pi\) | ||||
0.173221 | + | 0.984883i | \(0.444582\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 177.648i | − | 0.00823396i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 35709.8 | + | 11769.3i | 1.64875 | + | 0.543401i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2484.55 | − | 1434.46i | −0.114272 | − | 0.0659752i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5998.52 | − | 10389.7i | −0.274832 | − | 0.476023i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13638.7 | − | 15987.7i | −0.622487 | − | 0.729698i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6365.97 | − | 3675.40i | 0.289441 | − | 0.167109i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14417.6 | − | 8323.99i | −0.653025 | − | 0.377024i | 0.136589 | − | 0.990628i | \(-0.456386\pi\) |
−0.789614 | + | 0.613603i | \(0.789719\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12672.3 | + | 19153.9i | 0.571796 | + | 0.864253i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14471.3 | + | 11416.4i | −0.650494 | + | 0.513172i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43448.7 | 1.94566 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11353.0 | + | 22759.6i | −0.506478 | + | 1.01534i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14318.8 | + | 24800.9i | −0.636383 | + | 1.10225i | 0.349837 | + | 0.936810i | \(0.386237\pi\) |
−0.986220 | + | 0.165437i | \(0.947097\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −869.829 | − | 1506.59i | −0.0385136 | − | 0.0667075i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11409.5 | + | 1396.42i | −0.503290 | + | 0.0615980i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4051.60 | + | 7017.58i | 0.178055 | + | 0.308400i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4189.59 | + | 28825.1i | 0.183433 | + | 1.26205i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1441.27 | − | 23639.8i | −0.0628688 | − | 1.03118i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 49.4260i | − | 0.00214799i | −0.999999 | − | 0.00107400i | \(-0.999658\pi\) | ||
0.999999 | − | 0.00107400i | \(-0.000341863\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37292.7i | 1.61470i | 0.590072 | + | 0.807350i | \(0.299099\pi\) | ||||
−0.590072 | + | 0.807350i | \(0.700901\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −664.857 | + | 40.5349i | −0.0286809 | + | 0.00174861i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21581.9 | + | 37380.9i | −0.927584 | + | 1.60662i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 411.377 | − | 237.509i | 0.0176160 | − | 0.0101706i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 31476.3 | − | 31749.5i | 1.34294 | − | 1.35460i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −699.390 | + | 403.793i | −0.0297307 | + | 0.0171650i | −0.514792 | − | 0.857315i | \(-0.672131\pi\) |
0.485061 | + | 0.874480i | \(0.338797\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10340.2 | − | 17909.8i | 0.437957 | − | 0.758563i | −0.559575 | − | 0.828780i | \(-0.689036\pi\) |
0.997532 | + | 0.0702164i | \(0.0223690\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −153.171 | + | 307.064i | −0.00646390 | + | 0.0129583i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 44485.5i | − | 1.87051i | −0.353976 | − | 0.935255i | \(-0.615170\pi\) | ||
0.353976 | − | 0.935255i | \(-0.384830\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 7797.19i | − | 0.326668i | −0.986571 | − | 0.163334i | \(-0.947775\pi\) | ||
0.986571 | − | 0.163334i | \(-0.0522248\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8840.54 | + | 5848.96i | −0.369043 | + | 0.244161i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26627.7 | + | 25233.8i | 1.10756 | + | 1.04958i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10628.8 | + | 18409.7i | 0.440509 | + | 0.762985i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2014.70 | + | 5678.83i | −0.0831998 | + | 0.234515i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14737.7 | − | 25526.4i | −0.606439 | − | 1.05038i | −0.991822 | − | 0.127626i | \(-0.959264\pi\) |
0.385384 | − | 0.922756i | \(-0.374069\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −976.184 | + | 1690.80i | −0.0400256 | + | 0.0693263i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4987.74 | + | 7538.83i | 0.203780 | + | 0.308008i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 63727.2 | 2.59442 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12343.6 | + | 15646.7i | 0.500746 | + | 0.634743i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2893.87 | + | 5801.38i | −0.116981 | + | 0.234515i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −48405.6 | − | 27947.0i | −1.94985 | − | 1.12575i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8459.43 | + | 4884.05i | −0.339561 | + | 0.196045i | −0.660078 | − | 0.751197i | \(-0.729477\pi\) |
0.320517 | + | 0.947243i | \(0.396143\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2271.95 | + | 965.426i | 0.0908761 | + | 0.0386162i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11406.2 | − | 19756.0i | −0.454641 | − | 0.787461i | 0.544027 | − | 0.839068i | \(-0.316899\pi\) |
−0.998667 | + | 0.0516072i | \(0.983566\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30803.4 | − | 17784.3i | −1.22351 | − | 0.706396i | −0.257848 | − | 0.966186i | \(-0.583013\pi\) |
−0.965665 | + | 0.259790i | \(0.916347\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24764.4 | − | 22109.8i | 0.980218 | − | 0.875144i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34594.9i | 1.36457i | 0.731087 | + | 0.682285i | \(0.239014\pi\) | ||||
−0.731087 | + | 0.682285i | \(0.760986\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18689.9 | −0.734653 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2063.58 | + | 33847.0i | 0.0808337 | + | 1.32584i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10551.8 | + | 6092.10i | 0.411906 | + | 0.237814i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38996.5 | − | 22514.6i | 1.51704 | − | 0.875865i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12318.2 | + | 9274.93i | −0.477558 | + | 0.359575i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9734.71 | − | 24424.7i | 0.376106 | − | 0.943664i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11651.8 | − | 20181.6i | 0.448637 | − | 0.777063i | −0.549660 | − | 0.835388i | \(-0.685243\pi\) |
0.998298 | + | 0.0583256i | \(0.0185762\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22277.9 | − | 11112.7i | −0.854850 | − | 0.426420i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8387.34 | 0.320745 | 0.160373 | − | 0.987057i | \(-0.448730\pi\) | ||||
0.160373 | + | 0.987057i | \(0.448730\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4287.17 | 0.163391 | 0.0816957 | − | 0.996657i | \(-0.473966\pi\) | ||||
0.0816957 | + | 0.996657i | \(0.473966\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18423.2 | − | 12188.9i | 0.699763 | − | 0.462968i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6730.67 | + | 11657.9i | −0.254784 | + | 0.441299i | −0.964837 | − | 0.262849i | \(-0.915338\pi\) |
0.710053 | + | 0.704149i | \(0.248671\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16932.5 | − | 42484.1i | 0.638803 | − | 1.60278i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8378.75 | − | 8078.71i | 0.315038 | − | 0.303756i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 117.148 | − | 67.6353i | 0.00438992 | − | 0.00253452i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11188.5 | − | 6459.68i | −0.417866 | − | 0.241255i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −55428.3 | + | 36671.7i | −2.06321 | + | 1.36503i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6433.32 | −0.238669 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 47618.7i | − | 1.76072i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1120.18 | + | 5381.40i | 0.0412816 | + | 0.198319i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33388.8 | + | 19277.0i | 1.22639 | + | 0.708056i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6942.32 | − | 12024.4i | −0.254152 | − | 0.440204i | 0.710513 | − | 0.703684i | \(-0.248463\pi\) |
−0.964665 | + | 0.263480i | \(0.915130\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11478.4 | − | 15244.6i | −0.418828 | − | 0.556252i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45460.5 | − | 26246.6i | 1.65332 | − | 0.954543i | 0.677622 | − | 0.735410i | \(-0.263011\pi\) |
0.975695 | − | 0.219133i | \(-0.0703228\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16792.5 | − | 9695.13i | −0.608707 | − | 0.351437i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −27709.5 | + | 1689.39i | −1.00114 | + | 0.0610376i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17660.1 | − | 22385.9i | −0.635975 | − | 0.806158i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29789.5 | 1.06928 | 0.534639 | − | 0.845081i | \(-0.320448\pi\) | ||||
0.534639 | + | 0.845081i | \(0.320448\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24269.9 | − | 1479.68i | 0.868317 | − | 0.0529394i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33591.1 | + | 58181.5i | −1.19790 | + | 2.07483i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 808.026 | + | 1399.54i | 0.0287219 | + | 0.0497478i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6243.96 | + | 2653.26i | 0.221228 | + | 0.0940071i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9157.11 | − | 15860.6i | −0.323396 | − | 0.560139i | 0.657790 | − | 0.753201i | \(-0.271491\pi\) |
−0.981186 | + | 0.193062i | \(0.938158\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1962.11 | + | 2070.49i | −0.0690714 | + | 0.0728867i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8547.79 | + | 4263.84i | 0.299938 | + | 0.149616i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18773.0i | 0.656623i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 4717.18i | − | 0.164465i | −0.996613 | − | 0.0822325i | \(-0.973795\pi\) | ||
0.996613 | − | 0.0822325i | \(-0.0262050\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17083.4 | + | 25821.1i | 0.593712 | + | 0.897379i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20464.4 | − | 35445.4i | 0.708950 | − | 1.22794i | −0.256298 | − | 0.966598i | \(-0.582503\pi\) |
0.965247 | − | 0.261339i | \(-0.0841640\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −42739.5 | + | 24675.7i | −1.47592 | + | 0.852122i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −18839.6 | + | 21472.2i | −0.648520 | + | 0.739142i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21626.2 | − | 12485.9i | 0.742088 | − | 0.428445i | −0.0807398 | − | 0.996735i | \(-0.525728\pi\) |
0.822828 | + | 0.568290i | \(0.192395\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22688.5 | − | 39297.7i | 0.776081 | − | 1.34421i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29750.1 | − | 44966.4i | −1.01442 | − | 1.53327i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 14607.3i | − | 0.496512i | −0.968694 | − | 0.248256i | \(-0.920143\pi\) | ||
0.968694 | − | 0.248256i | \(-0.0798574\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 15590.7i | − | 0.528276i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11119.9 | + | 5546.89i | 0.375608 | + | 0.187362i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4367.23 | + | 30047.2i | 0.147054 | + | 1.01176i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13973.2 | − | 24202.3i | −0.469040 | − | 0.812402i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2427.13 | + | 19831.0i | 0.0812182 | + | 0.663598i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8210.38 | − | 14220.8i | −0.273888 | − | 0.474387i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13828.2 | − | 23951.1i | 0.459859 | − | 0.796499i | −0.539094 | − | 0.842245i | \(-0.681233\pi\) |
0.998953 | + | 0.0457467i | \(0.0145667\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4613.19 | + | 281.257i | −0.152938 | + | 0.00932432i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5235.20 | 0.173023 | 0.0865117 | − | 0.996251i | \(-0.472428\pi\) | ||||
0.0865117 | + | 0.996251i | \(0.472428\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15102.9 | + | 11914.6i | −0.497612 | + | 0.392564i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1918.02 | − | 116.938i | 0.0630009 | − | 0.00384103i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3972.26 | + | 2293.38i | 0.130076 | + | 0.0750991i | 0.563626 | − | 0.826030i | \(-0.309406\pi\) |
−0.433550 | + | 0.901129i | \(0.642739\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5886.47 | − | 3398.55i | 0.192168 | − | 0.110948i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −40129.7 | + | 4911.50i | −1.30606 | + | 0.159849i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1967.14 | + | 3407.18i | 0.0638270 | + | 0.110552i | 0.896173 | − | 0.443705i | \(-0.146336\pi\) |
−0.832346 | + | 0.554256i | \(0.813003\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22701.9 | − | 13106.9i | −0.734358 | − | 0.423982i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 318.994 | + | 1532.46i | 0.0102874 | + | 0.0494212i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 8171.31i | − | 0.262722i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17434.1 | −0.558841 | −0.279421 | − | 0.960169i | \(-0.590142\pi\) | ||||
−0.279421 | + | 0.960169i | \(0.590142\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20988.7 | − | 13886.3i | 0.670751 | − | 0.443773i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −47226.0 | − | 27266.0i | −1.50469 | − | 0.868733i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12254.1 | − | 7074.88i | 0.389258 | − | 0.224738i | −0.292581 | − | 0.956241i | \(-0.594514\pi\) |
0.681838 | + | 0.731503i | \(0.261181\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9957.79 | − | 53902.5i | −0.315366 | − | 1.70711i |
(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 | 252.4.x.a.41.14 | yes | 48 | |
3.2 | odd | 2 | 756.4.x.a.125.6 | 48 | |||
7.6 | odd | 2 | inner | 252.4.x.a.41.11 | ✓ | 48 | |
9.2 | odd | 6 | inner | 252.4.x.a.209.11 | yes | 48 | |
9.4 | even | 3 | 2268.4.f.a.1133.12 | 48 | |||
9.5 | odd | 6 | 2268.4.f.a.1133.37 | 48 | |||
9.7 | even | 3 | 756.4.x.a.629.19 | 48 | |||
21.20 | even | 2 | 756.4.x.a.125.19 | 48 | |||
63.13 | odd | 6 | 2268.4.f.a.1133.38 | 48 | |||
63.20 | even | 6 | inner | 252.4.x.a.209.14 | yes | 48 | |
63.34 | odd | 6 | 756.4.x.a.629.6 | 48 | |||
63.41 | even | 6 | 2268.4.f.a.1133.11 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.x.a.41.11 | ✓ | 48 | 7.6 | odd | 2 | inner | |
252.4.x.a.41.14 | yes | 48 | 1.1 | even | 1 | trivial | |
252.4.x.a.209.11 | yes | 48 | 9.2 | odd | 6 | inner | |
252.4.x.a.209.14 | yes | 48 | 63.20 | even | 6 | inner | |
756.4.x.a.125.6 | 48 | 3.2 | odd | 2 | |||
756.4.x.a.125.19 | 48 | 21.20 | even | 2 | |||
756.4.x.a.629.6 | 48 | 63.34 | odd | 6 | |||
756.4.x.a.629.19 | 48 | 9.7 | even | 3 | |||
2268.4.f.a.1133.11 | 48 | 63.41 | even | 6 | |||
2268.4.f.a.1133.12 | 48 | 9.4 | even | 3 | |||
2268.4.f.a.1133.37 | 48 | 9.5 | odd | 6 | |||
2268.4.f.a.1133.38 | 48 | 63.13 | odd | 6 |