Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,4,Mod(125,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, 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("756.125");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.x (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: | \(44.6054439643\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 125.19 | ||
Character | \(\chi\) | \(=\) | 756.125 |
Dual form | 756.4.x.a.629.19 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 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 | ||||||||
\(7\) | −18.3277 | − | 2.66385i | −0.989602 | − | 0.143834i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −13.8268 | + | 7.98293i | −0.378996 | + | 0.218813i | −0.677381 | − | 0.735632i | \(-0.736885\pi\) |
0.298386 | + | 0.954445i | \(0.403552\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 77.4289 | + | 44.7036i | 1.65192 | + | 0.953734i | 0.976283 | + | 0.216496i | \(0.0694629\pi\) |
0.675633 | + | 0.737238i | \(0.263870\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 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 | \(0.0159884\pi\) | ||||
−0.998739 | + | 0.0502079i | \(0.984012\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 123.893 | + | 71.5294i | 1.12319 | + | 0.648474i | 0.942214 | − | 0.335013i | \(-0.108741\pi\) |
0.180977 | + | 0.983487i | \(0.442074\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.06812 | + | 3.58208i | 0.0165449 | + | 0.0286567i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −129.721 | + | 74.8943i | −0.830639 | + | 0.479570i | −0.854072 | − | 0.520156i | \(-0.825874\pi\) |
0.0234322 | + | 0.999725i | \(0.492541\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 37.1952 | + | 21.4747i | 0.215499 | + | 0.124418i | 0.603864 | − | 0.797087i | \(-0.293627\pi\) |
−0.388366 | + | 0.921505i | \(0.626960\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 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 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 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 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 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 | ||||||||
\(49\) | 328.808 | + | 97.6442i | 0.958623 | + | 0.284677i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 445.230i | − | 1.15391i | −0.816777 | − | 0.576954i | \(-0.804241\pi\) | ||
0.816777 | − | 0.576954i | \(-0.195759\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 175.526i | 0.430325i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 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 | 0.0115982 | − | 0.999933i | \(-0.496308\pi\) |
0.871766 | + | 0.489922i | \(0.162975\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 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 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 751.418i | 1.25601i | 0.778208 | + | 0.628007i | \(0.216129\pi\) | ||||
−0.778208 | + | 0.628007i | \(0.783871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 507.533i | − | 0.813729i | −0.913489 | − | 0.406865i | \(-0.866622\pi\) | ||
0.913489 | − | 0.406865i | \(-0.133378\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 274.679 | − | 109.476i | 0.406528 | − | 0.162025i | ||||
\(78\) | 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 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 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 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 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 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 79.1792 | + | 45.7141i | 0.0855117 | + | 0.0493702i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −494.582 | + | 285.547i | −0.517703 | + | 0.298896i | −0.735994 | − | 0.676988i | \(-0.763285\pi\) |
0.218291 | + | 0.975884i | \(0.429952\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 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 | 0.600460 | − | 0.799655i | \(-0.294984\pi\) |
−0.392291 | + | 0.919841i | \(0.628317\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 739.962i | 0.668549i | 0.942476 | + | 0.334275i | \(0.108491\pi\) | ||||
−0.942476 | + | 0.334275i | \(0.891509\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1497.38 | 1.31580 | 0.657902 | − | 0.753104i | \(-0.271444\pi\) | ||||
0.657902 | + | 0.753104i | \(0.271444\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 861.916 | + | 497.627i | 0.717542 | + | 0.414273i | 0.813847 | − | 0.581079i | \(-0.197369\pi\) |
−0.0963056 | + | 0.995352i | \(0.530703\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1362.05 | − | 786.380i | 1.10445 | − | 0.637655i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1960.20 | + | 284.906i | 1.51001 | + | 0.219473i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −538.046 | + | 931.922i | −0.404242 | + | 0.700167i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 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 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | ||||||||
\(133\) | 22.1534 | − | 152.419i | 0.0144432 | − | 0.0993716i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1419.80 | − | 819.722i | 0.885414 | − | 0.511194i | 0.0129744 | − | 0.999916i | \(-0.495870\pi\) |
0.872440 | + | 0.488722i | \(0.162537\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 899.533 | + | 519.345i | 0.548902 | + | 0.316909i | 0.748679 | − | 0.662933i | \(-0.230688\pi\) |
−0.199777 | + | 0.979841i | \(0.564022\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1427.46 | −0.834759 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1646.75i | 0.943137i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1523.17 | + | 879.401i | 0.837468 | + | 0.483512i | 0.856403 | − | 0.516308i | \(-0.172694\pi\) |
−0.0189346 | + | 0.999821i | \(0.506027\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 408.917 | − | 236.088i | 0.211903 | − | 0.122342i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −579.051 | − | 334.315i | −0.294352 | − | 0.169944i | 0.345551 | − | 0.938400i | \(-0.387692\pi\) |
−0.639903 | + | 0.768456i | \(0.721025\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 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 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 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 | ||||||||
\(175\) | −28.3617 | − | 71.1604i | −0.0122511 | − | 0.0307384i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1175.15i | 0.490697i | 0.969435 | + | 0.245349i | \(0.0789024\pi\) | ||||
−0.969435 | + | 0.245349i | \(0.921098\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3506.89i | − | 1.44014i | −0.693902 | − | 0.720070i | \(-0.744110\pi\) | ||
0.693902 | − | 0.720070i | \(-0.255890\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 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 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1228.14 | + | 709.068i | −0.465263 | + | 0.268620i | −0.714255 | − | 0.699886i | \(-0.753234\pi\) |
0.248992 | + | 0.968506i | \(0.419901\pi\) | |||||||
\(192\) | 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 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2384.42i | 0.862351i | 0.902268 | + | 0.431175i | \(0.141901\pi\) | ||||
−0.902268 | + | 0.431175i | \(0.858099\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4960.24i | 1.76695i | 0.468482 | + | 0.883473i | \(0.344801\pi\) | ||||
−0.468482 | + | 0.883473i | \(0.655199\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2576.99 | − | 1027.08i | 0.890981 | − | 0.355109i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1896.28 | − | 3284.46i | −0.646059 | − | 1.11901i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 627.950 | 0.199190 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −624.497 | − | 492.663i | −0.195362 | − | 0.154121i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8281.26 | − | 4781.19i | −2.52062 | − | 1.45528i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1397.46 | − | 806.825i | 0.419646 | − | 0.242283i | −0.275280 | − | 0.961364i | \(-0.588771\pi\) |
0.694926 | + | 0.719082i | \(0.255437\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 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 | 0.719316 | − | 0.694683i | \(-0.244456\pi\) |
−0.241956 | + | 0.970287i | \(0.577789\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4408.26i | 1.23946i | 0.784814 | + | 0.619731i | \(0.212758\pi\) | ||||
−0.784814 | + | 0.619731i | \(0.787242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 178.821 | 0.0496383 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3715.64 | − | 2145.23i | −1.00563 | − | 0.580599i | −0.0957187 | − | 0.995408i | \(-0.530515\pi\) |
−0.909908 | + | 0.414809i | \(0.863848\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1413.43 | − | 816.047i | 0.377790 | − | 0.218117i | −0.299066 | − | 0.954232i | \(-0.596675\pi\) |
0.676856 | + | 0.736115i | \(0.263342\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2737.09 | − | 2593.81i | 0.713739 | − | 0.676378i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −371.770 | + | 643.925i | −0.0957700 | + | 0.165878i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 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 | ||||||||
\(259\) | −7160.74 | − | 1040.78i | −1.71794 | − | 0.249695i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3827.74 | + | 2209.95i | −0.897448 | + | 0.518142i | −0.876371 | − | 0.481636i | \(-0.840043\pi\) |
−0.0210765 | + | 0.999778i | \(0.506709\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4239.00 | − | 2447.39i | −0.982641 | − | 0.567328i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 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 | \(-0.995427\pi\) | ||
0.999897 | − | 0.0143671i | \(-0.00457334\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 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 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1506.57 | + | 869.820i | −0.319838 | + | 0.184659i | −0.651321 | − | 0.758803i | \(-0.725785\pi\) |
0.331482 | + | 0.943462i | \(0.392451\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1080.52 | − | 623.836i | −0.226961 | − | 0.131036i | 0.382208 | − | 0.924076i | \(-0.375164\pi\) |
−0.609169 | + | 0.793040i | \(0.708497\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3957.11 | + | 5016.01i | −0.813871 | + | 1.03166i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6525.95 | 1.32830 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 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 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6395.24 | + | 11076.9i | 1.23694 | + | 2.14245i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −391.655 | − | 982.676i | −0.0749987 | − | 0.188175i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 5342.59i | − | 1.00300i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4679.41i | 0.869929i | 0.900448 | + | 0.434965i | \(0.143239\pi\) | ||||
−0.900448 | + | 0.434965i | \(0.856761\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | −0.887395 | − | 0.461010i | \(-0.847487\pi\) |
−0.0444510 | + | 0.999012i | \(0.514154\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8986.17 | − | 5188.17i | 1.59216 | − | 0.919232i | 0.599220 | − | 0.800584i | \(-0.295477\pi\) |
0.992936 | − | 0.118648i | \(-0.0378559\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1195.75 | − | 2071.10i | 0.209872 | − | 0.363510i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 889.458i | − | 0.153222i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 369.809i | 0.0631179i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −111.532 | − | 279.837i | −0.0186898 | − | 0.0468933i | ||||
\(330\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −685.723 | −0.108897 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5766.18 | − | 2665.49i | −0.907709 | − | 0.419600i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3834.85 | − | 2214.05i | −0.593273 | − | 0.342526i | 0.173118 | − | 0.984901i | \(-0.444616\pi\) |
−0.766391 | + | 0.642375i | \(0.777949\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1980.13 | + | 1143.23i | −0.303707 | + | 0.175345i | −0.644107 | − | 0.764935i | \(-0.722771\pi\) |
0.340400 | + | 0.940281i | \(0.389438\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 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 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 5537.25i | − | 0.814053i | −0.913416 | − | 0.407027i | \(-0.866566\pi\) | ||
0.913416 | − | 0.407027i | \(-0.133434\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6789.84 | 0.989917 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4832.18 | − | 2789.86i | −0.692953 | − | 0.400076i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4668.87 | + | 2695.58i | −0.664069 | + | 0.383400i | −0.793825 | − | 0.608146i | \(-0.791914\pi\) |
0.129757 | + | 0.991546i | \(0.458580\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1186.03 | + | 8160.04i | −0.165971 | + | 1.14191i | ||||
\(372\) | 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 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 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 | ||||||||
\(385\) | 467.573 | − | 3216.98i | 0.0618954 | − | 0.425850i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1416.25 | + | 817.670i | −0.184593 | + | 0.106575i | −0.589449 | − | 0.807806i | \(-0.700655\pi\) |
0.404856 | + | 0.914380i | \(0.367322\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13250.7 | − | 7650.29i | −1.71385 | − | 0.989493i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8389.82 | 1.06870 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 7694.41i | − | 0.972724i | −0.873757 | − | 0.486362i | \(-0.838324\pi\) | ||
0.873757 | − | 0.486362i | \(-0.161676\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4800.46 | − | 2771.55i | −0.597815 | − | 0.345148i | 0.170367 | − | 0.985381i | \(-0.445505\pi\) |
−0.768181 | + | 0.640232i | \(0.778838\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1919.99 | + | 3325.52i | 0.237324 | + | 0.411057i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5402.24 | + | 3118.98i | −0.657934 | + | 0.379858i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6361.70 | − | 3672.93i | −0.769109 | − | 0.444045i | 0.0634474 | − | 0.997985i | \(-0.479790\pi\) |
−0.832557 | + | 0.553940i | \(0.813124\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4435.75 | + | 5622.74i | −0.528497 | + | 0.669920i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13351.8 | −1.57931 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −221.191 | − | 383.115i | −0.0252455 | − | 0.0437266i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8360.60 | + | 3332.20i | −0.947536 | + | 0.377650i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13632.5i | 1.52356i | 0.647839 | + | 0.761778i | \(0.275673\pi\) | ||||
−0.647839 | + | 0.761778i | \(0.724327\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 6735.48i | − | 0.747544i | −0.927521 | − | 0.373772i | \(-0.878064\pi\) | ||
0.927521 | − | 0.373772i | \(-0.121936\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −594.863 | + | 1030.33i | −0.0651170 | + | 0.112786i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9181.17 | + | 5300.75i | −0.998162 | + | 0.576289i | −0.907704 | − | 0.419611i | \(-0.862166\pi\) |
−0.0904581 | + | 0.995900i | \(0.528833\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3111.86 | − | 1796.64i | 0.333745 | − | 0.192688i | −0.323757 | − | 0.946140i | \(-0.604946\pi\) |
0.657503 | + | 0.753452i | \(0.271613\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2340.18 | − | 4053.31i | 0.249293 | − | 0.431788i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 8675.98i | − | 0.911904i | −0.890004 | − | 0.455952i | \(-0.849299\pi\) | ||
0.890004 | − | 0.455952i | \(-0.150701\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5507.79i | 0.575059i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16910.4 | + | 6739.80i | −1.74236 | + | 0.694433i | ||||
\(456\) | 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 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 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 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 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 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 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 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 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 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −653.319 | − | 377.194i | −0.0600486 | − | 0.0346691i | 0.469675 | − | 0.882839i | \(-0.344371\pi\) |
−0.529724 | + | 0.848170i | \(0.677704\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13874.0 | − | 8010.17i | 1.26745 | − | 0.731765i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2001.66 | − | 13771.8i | 0.180658 | − | 1.24295i | ||||
\(498\) | 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 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 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 | ||||||||
\(511\) | −1351.99 | + | 9301.90i | −0.117042 | + | 0.805268i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 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 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 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 | \(0.330633\pi\) | ||||
−0.507330 | + | 0.861752i | \(0.669367\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 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 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 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 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 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 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −622.847 | − | 1078.80i | −0.0481564 | − | 0.0834093i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5232.77 | − | 13129.2i | −0.402387 | − | 1.00960i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15368.4i | 1.16908i | 0.811364 | + | 0.584541i | \(0.198725\pi\) | ||||
−0.811364 | + | 0.584541i | \(0.801275\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5106.81i | 0.386395i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 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 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20989.2 | + | 12118.1i | −1.54642 | + | 0.892824i | −0.548005 | + | 0.836475i | \(0.684613\pi\) |
−0.998411 | + | 0.0563492i | \(0.982054\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 591.724i | 0.0429158i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11928.2i | 0.860617i | 0.902682 | + | 0.430308i | \(0.141595\pi\) | ||||
−0.902682 | + | 0.430308i | \(0.858405\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8327.56 | + | 20894.1i | 0.594639 | + | 1.49197i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3554.24 | + | 6156.13i | 0.252490 | + | 0.437326i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 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 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 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 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8568.78 | + | 4947.19i | 0.584492 | + | 0.337457i | 0.762917 | − | 0.646497i | \(-0.223767\pi\) |
−0.178424 | + | 0.983954i | \(0.557100\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2305.57 | + | 1331.12i | −0.156483 | + | 0.0903454i | −0.576197 | − | 0.817311i | \(-0.695464\pi\) |
0.419714 | + | 0.907656i | \(0.362130\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5915.17 | + | 10245.4i | 0.397497 | + | 0.688485i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9797.65 | + | 5656.68i | 0.655147 | + | 0.378249i | 0.790425 | − | 0.612558i | \(-0.209859\pi\) |
−0.135278 | + | 0.990808i | \(0.543193\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14063.1 | + | 8119.31i | 0.917597 | + | 0.529775i | 0.882868 | − | 0.469622i | \(-0.155610\pi\) |
0.0347291 | + | 0.999397i | \(0.488943\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14971.6 | − | 8643.88i | 0.972150 | − | 0.561271i | 0.0722590 | − | 0.997386i | \(-0.476979\pi\) |
0.899891 | + | 0.436115i | \(0.143646\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7802.60 | − | 1134.07i | −0.501773 | − | 0.0729304i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7545.43 | − | 13069.1i | 0.482908 | − | 0.836421i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13574.1 | − | 23511.0i | 0.848302 | − | 1.46930i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21094.2 | + | 22259.4i | 1.31206 | + | 1.38453i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14508.8 | − | 8376.64i | 0.894013 | − | 0.516158i | 0.0187597 | − | 0.999824i | \(-0.494028\pi\) |
0.875253 | + | 0.483666i | \(0.160695\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10660.5 | − | 6154.87i | −0.653827 | − | 0.377487i | 0.136094 | − | 0.990696i | \(-0.456545\pi\) |
−0.789921 | + | 0.613209i | \(0.789878\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15436.6 | + | 8912.32i | 0.925085 | + | 0.534098i | 0.885254 | − | 0.465108i | \(-0.153985\pi\) |
0.0398315 | + | 0.999206i | \(0.487318\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8462.89 | − | 14658.2i | −0.504843 | − | 0.874415i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17782.9 | + | 10267.0i | −1.05117 | + | 0.606895i | −0.922978 | − | 0.384853i | \(-0.874252\pi\) |
−0.128196 | + | 0.991749i | \(0.540919\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8819.60 | − | 5092.00i | −0.518975 | − | 0.299630i | 0.217540 | − | 0.976051i | \(-0.430197\pi\) |
−0.736515 | + | 0.676421i | \(0.763530\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1329.40 | − | 1048.75i | −0.0775214 | − | 0.0611563i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21428.6 | −1.24395 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 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 | ||||||||
\(679\) | 9825.20 | − | 3915.93i | 0.555311 | − | 0.221325i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 4376.97i | − | 0.245213i | −0.992455 | − | 0.122606i | \(-0.960875\pi\) | ||
0.992455 | − | 0.122606i | \(-0.0391253\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 18023.7i | − | 1.00533i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19903.4 | − | 34473.7i | 1.10052 | − | 1.90616i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17526.8 | − | 10119.1i | 0.964905 | − | 0.557088i | 0.0672260 | − | 0.997738i | \(-0.478585\pi\) |
0.897679 | + | 0.440649i | \(0.145252\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 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 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 33130.3i | − | 1.78504i | −0.451004 | − | 0.892522i | \(-0.648934\pi\) | ||
0.451004 | − | 0.892522i | \(-0.351066\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3249.25i | 0.174321i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4846.24 | − | 12159.4i | −0.257796 | − | 0.646818i | ||||
\(708\) | 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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 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 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −536.555 | − | 309.780i | −0.0274857 | − | 0.0158689i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −685.180 | + | 395.589i | −0.0349545 | + | 0.0201810i | −0.517375 | − | 0.855759i | \(-0.673091\pi\) |
0.482421 | + | 0.875940i | \(0.339758\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3054.50 | − | 5290.55i | −0.154548 | − | 0.267685i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −195.132 | − | 112.659i | −0.00983269 | − | 0.00567691i | 0.495076 | − | 0.868850i | \(-0.335140\pi\) |
−0.504908 | + | 0.863173i | \(0.668474\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 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 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30419.9 | + | 17563.0i | 1.50202 | + | 0.867190i | 0.999997 | + | 0.00233421i | \(0.000743004\pi\) |
0.502020 | + | 0.864856i | \(0.332590\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16745.4 | − | 9667.97i | 0.823496 | − | 0.475446i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1971.14 | − | 13561.8i | 0.0961602 | − | 0.661598i | ||||
\(750\) | 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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 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 | ||||||||
\(763\) | −27443.4 | − | 3988.78i | −1.30212 | − | 0.189258i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 29941.7 | − | 17286.9i | 1.40956 | − | 0.813811i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17962.0 | − | 10370.3i | −0.842295 | − | 0.486299i | 0.0157486 | − | 0.999876i | \(-0.494987\pi\) |
−0.858044 | + | 0.513577i | \(0.828320\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 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 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6365.97 | + | 3675.40i | −0.289441 | + | 0.167109i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14417.6 | + | 8323.99i | 0.653025 | + | 0.377024i | 0.789614 | − | 0.613603i | \(-0.210281\pi\) |
−0.136589 | + | 0.990628i | \(0.543614\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14471.3 | − | 11416.4i | −0.650494 | − | 0.513172i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43448.7 | 1.94566 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 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 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4051.60 | + | 7017.58i | 0.178055 | + | 0.308400i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27058.0 | + | 10784.2i | −1.18468 | + | 0.472167i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.4260i | 0.00214799i | 0.999999 | + | 0.00107400i | \(0.000341863\pi\) | ||||
−0.999999 | + | 0.00107400i | \(0.999658\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 37292.7i | − | 1.61470i | −0.590072 | − | 0.807350i | \(-0.700901\pi\) | ||
0.590072 | − | 0.807350i | \(-0.299099\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 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 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 699.390 | − | 403.793i | 0.0297307 | − | 0.0171650i | −0.485061 | − | 0.874480i | \(-0.661203\pi\) |
0.514792 | + | 0.857315i | \(0.327869\pi\) | |||||||
\(822\) | 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 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44485.5i | 1.87051i | 0.353976 | + | 0.935255i | \(0.384830\pi\) | ||||
−0.353976 | + | 0.935255i | \(0.615170\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7797.19i | 0.326668i | 0.986571 | + | 0.163334i | \(0.0522248\pi\) | ||||
−0.986571 | + | 0.163334i | \(0.947775\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −35167.0 | − | 10443.3i | −1.46274 | − | 0.434382i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10628.8 | + | 18409.7i | 0.440509 | + | 0.762985i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 63727.2 | 2.59442 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12343.6 | − | 15646.7i | 0.500746 | − | 0.634743i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 48405.6 | + | 27947.0i | 1.94985 | + | 1.12575i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8459.43 | − | 4884.05i | 0.339561 | − | 0.196045i | −0.320517 | − | 0.947243i | \(-0.603857\pi\) |
0.660078 | + | 0.751197i | \(0.270523\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 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 | 0.965665 | − | 0.259790i | \(-0.0836533\pi\) |
0.257848 | + | 0.966186i | \(0.416987\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 34594.9i | − | 1.36457i | −0.731087 | − | 0.682285i | \(-0.760986\pi\) | ||
0.731087 | − | 0.682285i | \(-0.239014\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18689.9 | −0.734653 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 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 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26019.8 | − | 3781.86i | −1.00529 | − | 0.146114i | ||||
\(876\) | 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 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 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 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 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 | ||||||||
\(889\) | −45258.6 | − | 6578.13i | −1.70745 | − | 0.248170i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 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 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6433.32 | −0.238669 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47618.7i | 1.76072i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 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 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45460.5 | + | 26246.6i | −1.65332 | + | 0.954543i | −0.677622 | + | 0.735410i | \(0.736989\pi\) |
−0.975695 | + | 0.219133i | \(0.929677\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16792.5 | + | 9695.13i | 0.608707 | + | 0.351437i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 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 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 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 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 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 | ||||||||
\(931\) | −812.043 | + | 2734.48i | −0.0285861 | + | 0.0962609i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 18773.0i | − | 0.656623i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4717.18i | 0.164465i | 0.996613 | + | 0.0822325i | \(0.0262050\pi\) | ||||
−0.996613 | + | 0.0822325i | \(0.973795\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 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 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21626.2 | + | 12485.9i | −0.742088 | + | 0.428445i | −0.822828 | − | 0.568290i | \(-0.807605\pi\) |
0.0807398 | + | 0.996735i | \(0.474272\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22688.5 | − | 39297.7i | 0.776081 | − | 1.34421i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14607.3i | 0.496512i | 0.968694 | + | 0.248256i | \(0.0798574\pi\) | ||||
−0.968694 | + | 0.248256i | \(0.920143\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15590.7i | 0.528276i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28205.3 | + | 11241.5i | −0.949735 | + | 0.378526i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13973.2 | − | 24202.3i | −0.469040 | − | 0.812402i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 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 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3972.26 | − | 2293.38i | −0.130076 | − | 0.0750991i | 0.433550 | − | 0.901129i | \(-0.357261\pi\) |
−0.563626 | + | 0.826030i | \(0.690594\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5886.47 | + | 3398.55i | −0.192168 | + | 0.110948i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 47226.0 | + | 27266.0i | 1.50469 | + | 0.868733i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12254.1 | + | 7074.88i | −0.389258 | + | 0.224738i | −0.681838 | − | 0.731503i | \(-0.738819\pi\) |
0.292581 | + | 0.956241i | \(0.405486\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 756.4.x.a.125.19 | 48 | ||
3.2 | odd | 2 | 252.4.x.a.41.11 | ✓ | 48 | ||
7.6 | odd | 2 | inner | 756.4.x.a.125.6 | 48 | ||
9.2 | odd | 6 | inner | 756.4.x.a.629.6 | 48 | ||
9.4 | even | 3 | 2268.4.f.a.1133.11 | 48 | |||
9.5 | odd | 6 | 2268.4.f.a.1133.38 | 48 | |||
9.7 | even | 3 | 252.4.x.a.209.14 | yes | 48 | ||
21.20 | even | 2 | 252.4.x.a.41.14 | yes | 48 | ||
63.13 | odd | 6 | 2268.4.f.a.1133.37 | 48 | |||
63.20 | even | 6 | inner | 756.4.x.a.629.19 | 48 | ||
63.34 | odd | 6 | 252.4.x.a.209.11 | yes | 48 | ||
63.41 | even | 6 | 2268.4.f.a.1133.12 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.x.a.41.11 | ✓ | 48 | 3.2 | odd | 2 | ||
252.4.x.a.41.14 | yes | 48 | 21.20 | even | 2 | ||
252.4.x.a.209.11 | yes | 48 | 63.34 | odd | 6 | ||
252.4.x.a.209.14 | yes | 48 | 9.7 | even | 3 | ||
756.4.x.a.125.6 | 48 | 7.6 | odd | 2 | inner | ||
756.4.x.a.125.19 | 48 | 1.1 | even | 1 | trivial | ||
756.4.x.a.629.6 | 48 | 9.2 | odd | 6 | inner | ||
756.4.x.a.629.19 | 48 | 63.20 | even | 6 | inner | ||
2268.4.f.a.1133.11 | 48 | 9.4 | even | 3 | |||
2268.4.f.a.1133.12 | 48 | 63.41 | even | 6 | |||
2268.4.f.a.1133.37 | 48 | 63.13 | odd | 6 | |||
2268.4.f.a.1133.38 | 48 | 9.5 | odd | 6 |