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 | 209.9 | ||
Character | \(\chi\) | \(=\) | 252.209 |
Dual form | 252.4.x.a.41.9 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −2.29905 | − | 4.65987i | −0.442452 | − | 0.896792i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.03570 | − | 10.4541i | −0.539850 | − | 0.935047i | −0.998912 | − | 0.0466430i | \(-0.985148\pi\) |
0.459062 | − | 0.888404i | \(-0.348186\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.9871 | + | 7.37834i | −0.917215 | + | 0.398393i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −16.4287 | + | 21.4265i | −0.608472 | + | 0.793575i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.00221312 | + | 0.00127775i | 6.06619e−5 | + | 3.50232e-5i | 0.500030 | − | 0.866008i | \(-0.333322\pi\) |
−0.499970 | + | 0.866043i | \(0.666656\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.06841 | + | 3.50360i | −0.129467 | + | 0.0747479i | −0.563335 | − | 0.826229i | \(-0.690482\pi\) |
0.433868 | + | 0.900977i | \(0.357149\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −34.8386 | + | 52.1602i | −0.599685 | + | 0.897847i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 28.3143 | 0.403955 | 0.201977 | − | 0.979390i | \(-0.435263\pi\) | ||||
0.201977 | + | 0.979390i | \(0.435263\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 49.1973i | 0.594033i | 0.954872 | + | 0.297016i | \(0.0959916\pi\) | ||||
−0.954872 | + | 0.297016i | \(0.904008\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 73.4362 | + | 62.1943i | 0.763099 | + | 0.646281i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 44.4689 | − | 25.6741i | 0.403148 | − | 0.232758i | −0.284693 | − | 0.958619i | \(-0.591892\pi\) |
0.687841 | + | 0.725861i | \(0.258558\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.3594 | + | 17.9431i | −0.0828756 | + | 0.143545i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 137.615 | + | 27.2951i | 0.980892 | + | 0.194554i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 97.9469 | + | 56.5497i | 0.627182 | + | 0.362104i | 0.779660 | − | 0.626203i | \(-0.215392\pi\) |
−0.152478 | + | 0.988307i | \(0.548725\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 28.4271 | − | 16.4124i | 0.164699 | − | 0.0950889i | −0.415385 | − | 0.909646i | \(-0.636353\pi\) |
0.580084 | + | 0.814557i | \(0.303020\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.000866054 | − | 0.0132505i | 4.56850e−6 | − | 6.98972e-5i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 179.663 | + | 133.052i | 0.867674 | + | 0.642567i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −101.961 | −0.453034 | −0.226517 | − | 0.974007i | \(-0.572734\pi\) | ||||
−0.226517 | + | 0.974007i | \(0.572734\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 30.2779 | + | 20.2230i | 0.124316 | + | 0.0830328i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.2449 | + | 19.4767i | 0.0428331 | + | 0.0741891i | 0.886647 | − | 0.462447i | \(-0.153028\pi\) |
−0.843814 | + | 0.536636i | \(0.819695\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −227.203 | + | 393.527i | −0.805771 | + | 1.39564i | 0.109998 | + | 0.993932i | \(0.464916\pi\) |
−0.915769 | + | 0.401705i | \(0.868418\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 323.155 | + | 42.4243i | 1.07051 | + | 0.140539i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −231.260 | + | 400.554i | −0.717717 | + | 1.24312i | 0.244185 | + | 0.969729i | \(0.421480\pi\) |
−0.961902 | + | 0.273394i | \(0.911854\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 234.120 | − | 250.672i | 0.682567 | − | 0.730823i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −65.0960 | − | 131.941i | −0.178731 | − | 0.362263i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 567.586i | 1.47102i | 0.677515 | + | 0.735509i | \(0.263057\pi\) | ||||
−0.677515 | + | 0.735509i | \(0.736943\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.0308484i | − | 7.56290e-5i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 229.253 | − | 113.107i | 0.532724 | − | 0.262831i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 145.654 | + | 252.280i | 0.321399 | + | 0.556680i | 0.980777 | − | 0.195132i | \(-0.0625136\pi\) |
−0.659378 | + | 0.751812i | \(0.729180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −592.003 | − | 341.793i | −1.24259 | − | 0.717412i | −0.272972 | − | 0.962022i | \(-0.588007\pi\) |
−0.969621 | + | 0.244610i | \(0.921340\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 120.984 | − | 485.191i | 0.241945 | − | 0.970290i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 73.2542 | + | 42.2933i | 0.139786 | + | 0.0807053i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 269.780 | + | 467.273i | 0.491924 | + | 0.852037i | 0.999957 | − | 0.00930051i | \(-0.00296049\pi\) |
−0.508033 | + | 0.861338i | \(0.669627\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −221.874 | − | 148.193i | −0.387109 | − | 0.258556i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 307.517i | − | 0.514022i | −0.966408 | − | 0.257011i | \(-0.917262\pi\) | ||
0.966408 | − | 0.257011i | \(-0.0827377\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 495.192i | − | 0.793943i | −0.917831 | − | 0.396971i | \(-0.870061\pi\) | ||
0.917831 | − | 0.396971i | \(-0.129939\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 107.429 | + | 7.02162i | 0.165398 | + | 0.0108105i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0470221 | − | 0.00537600i | −6.95930e−5 | − | 7.95652e-6i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −324.865 | + | 562.683i | −0.462661 | + | 0.801352i | −0.999093 | − | 0.0425920i | \(-0.986438\pi\) |
0.536432 | + | 0.843944i | \(0.319772\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −189.193 | − | 704.022i | −0.259524 | − | 0.965737i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −565.581 | + | 979.615i | −0.747959 | + | 1.29550i | 0.200841 | + | 0.979624i | \(0.435633\pi\) |
−0.948800 | + | 0.315879i | \(0.897701\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −170.897 | − | 296.002i | −0.218075 | − | 0.377717i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 38.3293 | − | 586.430i | 0.0472336 | − | 0.722665i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −130.217 | −0.155089 | −0.0775447 | − | 0.996989i | \(-0.524708\pi\) | ||||
−0.0775447 | + | 0.996989i | \(0.524708\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 77.2337 | − | 104.291i | 0.0889702 | − | 0.120139i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −141.835 | − | 94.7337i | −0.158146 | − | 0.105628i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 514.315 | − | 296.940i | 0.555449 | − | 0.320688i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1260.41 | − | 727.696i | −1.31933 | − | 0.761715i | −0.335709 | − | 0.941966i | \(-0.608976\pi\) |
−0.983621 | + | 0.180251i | \(0.942309\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.0637365 | + | 0.0264277i | −6.47046e−5 | + | 2.68292e-5i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −197.600 | + | 342.254i | −0.194673 | + | 0.337183i | −0.946793 | − | 0.321842i | \(-0.895698\pi\) |
0.752120 | + | 0.659026i | \(0.229031\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −545.260 | + | 314.806i | −0.521612 | + | 0.301153i | −0.737594 | − | 0.675244i | \(-0.764038\pi\) |
0.215982 | + | 0.976397i | \(0.430705\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 206.949 | − | 1143.10i | 0.192345 | − | 1.06243i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 515.616i | − | 0.465855i | −0.972494 | − | 0.232927i | \(-0.925170\pi\) | ||
0.972494 | − | 0.232927i | \(-0.0748305\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 794.011 | 0.697729 | 0.348864 | − | 0.937173i | \(-0.386567\pi\) | ||||
0.348864 | + | 0.937173i | \(0.386567\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 234.413 | + | 475.124i | 0.200446 | + | 0.406277i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1782.31 | − | 1029.02i | 1.48377 | − | 0.856654i | 0.483939 | − | 0.875102i | \(-0.339206\pi\) |
0.999830 | + | 0.0184476i | \(0.00587238\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −536.802 | − | 309.923i | −0.435279 | − | 0.251308i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 24.6264 | − | 187.585i | 0.0194591 | − | 0.148224i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −480.977 | + | 208.912i | −0.370513 | + | 0.160933i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −665.500 | − | 1152.68i | −0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 64.9064 | − | 97.1776i | 0.0475806 | − | 0.0712375i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1258.82 | −0.900738 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2071.63 | −1.44746 | −0.723729 | − | 0.690084i | \(-0.757573\pi\) | ||||
−0.723729 | + | 0.690084i | \(0.757573\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2356.14 | + | 153.998i | 1.60811 | + | 0.105107i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 467.210 | + | 809.232i | 0.311606 | + | 0.539717i | 0.978710 | − | 0.205247i | \(-0.0657999\pi\) |
−0.667104 | + | 0.744964i | \(0.732467\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −362.994 | − | 835.717i | −0.236658 | − | 0.544856i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −545.258 | − | 1603.40i | −0.347617 | − | 1.02221i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2320.59 | + | 1339.79i | 1.44716 | + | 0.835521i | 0.998312 | − | 0.0580849i | \(-0.0184994\pi\) |
0.448853 | + | 0.893606i | \(0.351833\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −794.727 | + | 458.836i | −0.484949 | + | 0.279985i | −0.722476 | − | 0.691395i | \(-0.756996\pi\) |
0.237528 | + | 0.971381i | \(0.423663\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2398.21 | + | 156.748i | 1.43238 | + | 0.0936207i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.0179068 | −1.04716e−5 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1365.27i | − | 0.781926i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1706.35 | − | 514.662i | −0.957400 | − | 0.288766i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1187.44 | − | 685.572i | 0.652881 | − | 0.376941i | −0.136678 | − | 0.990616i | \(-0.543643\pi\) |
0.789559 | + | 0.613674i | \(0.210309\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 127.186 | − | 220.292i | 0.0685445 | − | 0.118723i | −0.829716 | − | 0.558185i | \(-0.811498\pi\) |
0.898261 | + | 0.439463i | \(0.144831\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −465.169 | + | 606.678i | −0.245795 | + | 0.320568i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −343.155 | − | 198.121i | −0.177825 | − | 0.102667i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −511.747 | + | 295.457i | −0.260139 | + | 0.150191i | −0.624398 | − | 0.781106i | \(-0.714656\pi\) |
0.364259 | + | 0.931298i | \(0.381322\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2644.87 | − | 1304.91i | 1.31920 | − | 0.650855i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −565.963 | + | 764.234i | −0.277044 | + | 0.374100i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2197.17 | −1.05580 | −0.527901 | − | 0.849306i | \(-0.677021\pi\) | ||||
−0.527901 | + | 0.849306i | \(0.677021\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.143749 | + | 0.0709220i | −6.78235e−5 | + | 3.34622e-5i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −210.903 | − | 365.295i | −0.0977256 | − | 0.169266i | 0.813017 | − | 0.582240i | \(-0.197823\pi\) |
−0.910743 | + | 0.412974i | \(0.864490\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1073.95 | + | 1860.14i | −0.488826 | + | 0.846671i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1054.13 | − | 808.249i | −0.471410 | − | 0.361452i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −872.428 | + | 1511.09i | −0.383407 | + | 0.664081i | −0.991547 | − | 0.129749i | \(-0.958583\pi\) |
0.608139 | + | 0.793830i | \(0.291916\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 43.5864 | − | 381.236i | 0.0188276 | − | 0.164678i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 840.727 | − | 1258.73i | 0.357022 | − | 0.534532i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4311.61i | 1.80036i | 0.435518 | + | 0.900180i | \(0.356565\pi\) | ||||
−0.435518 | + | 0.900180i | \(0.643435\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1307.99i | − | 0.537141i | −0.963260 | − | 0.268570i | \(-0.913449\pi\) | ||
0.963260 | − | 0.268570i | \(-0.0865512\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −231.667 | + | 3544.45i | −0.0935808 | + | 1.43177i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 615.405 | + | 1065.91i | 0.244570 | + | 0.423608i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0626630 | + | 0.0361785i | 2.45047e−5 | + | 1.41478e-5i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2539.07 | + | 551.708i | −0.977197 | + | 0.212333i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3495.99 | − | 2018.41i | −1.32440 | − | 0.764644i | −0.339975 | − | 0.940435i | \(-0.610419\pi\) |
−0.984428 | + | 0.175791i | \(0.943752\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2209.64 | + | 3827.21i | 0.824112 | + | 1.42740i | 0.902596 | + | 0.430488i | \(0.141658\pi\) |
−0.0784849 | + | 0.996915i | \(0.525008\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 28.6663 | − | 438.589i | 0.0105274 | − | 0.161067i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 151.673i | 0.0548540i | 0.999624 | + | 0.0274270i | \(0.00873138\pi\) | ||||
−0.999624 | + | 0.0274270i | \(0.991269\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1838.65i | − | 0.654966i | −0.944857 | − | 0.327483i | \(-0.893800\pi\) | ||
0.944857 | − | 0.327483i | \(-0.106200\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1557.19 | − | 2331.42i | 0.546447 | − | 0.818139i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2081.07 | − | 237.927i | −0.719520 | − | 0.0822622i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 135.742 | − | 235.111i | 0.0462468 | − | 0.0801019i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −180.461 | + | 1374.61i | −0.0605936 | + | 0.461555i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0628616 | + | 0.108879i | −2.08049e−5 | + | 3.60352e-5i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1229.27 | + | 2129.15i | 0.401072 | + | 0.694678i | 0.993856 | − | 0.110684i | \(-0.0353042\pi\) |
−0.592783 | + | 0.805362i | \(0.701971\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1432.99 | + | 706.997i | −0.460971 | + | 0.227430i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5485.32 | 1.73998 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −361.797 | + | 488.543i | −0.113181 | + | 0.152832i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2307.53 | + | 1138.47i | −0.712002 | + | 0.351282i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −171.823 | + | 99.2019i | −0.0522989 | + | 0.0301948i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4491.19 | + | 2592.99i | 1.34867 | + | 0.778653i | 0.988061 | − | 0.154066i | \(-0.0492367\pi\) |
0.360606 | + | 0.932718i | \(0.382570\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −214.266 | − | 516.750i | −0.0634861 | − | 0.153111i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −497.531 | + | 861.749i | −0.145473 | + | 0.251966i | −0.929549 | − | 0.368698i | \(-0.879804\pi\) |
0.784077 | + | 0.620664i | \(0.213137\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −101.864 | + | 58.8111i | −0.0293946 | + | 0.0169710i | −0.514625 | − | 0.857415i | \(-0.672069\pi\) |
0.485231 | + | 0.874386i | \(0.338736\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0830546 | + | 0.231476i | 2.36562e−5 | + | 6.59308e-5i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1484.08i | 0.417276i | 0.977993 | + | 0.208638i | \(0.0669030\pi\) | ||||
−0.977993 | + | 0.208638i | \(0.933097\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5583.26 | 1.54984 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3368.91 | + | 220.193i | 0.923351 | + | 0.0603505i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2392.08 | − | 1381.07i | 0.647409 | − | 0.373782i | −0.140054 | − | 0.990144i | \(-0.544728\pi\) |
0.787463 | + | 0.616362i | \(0.211394\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3362.99 | + | 1941.62i | 0.898877 | + | 0.518967i | 0.876836 | − | 0.480790i | \(-0.159650\pi\) |
0.0220413 | + | 0.999757i | \(0.492983\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2845.69 | + | 2500.19i | −0.751238 | + | 0.660031i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4033.65 | − | 934.544i | −1.05184 | − | 0.243697i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −172.367 | − | 298.549i | −0.0444027 | − | 0.0769078i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5865.18 | + | 383.350i | 1.49273 | + | 0.0975655i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5549.57 | 1.39556 | 0.697780 | − | 0.716312i | \(-0.254171\pi\) | ||||
0.697780 | + | 0.716312i | \(0.254171\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.131220 | 3.26076e−5 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −986.430 | + | 1476.88i | −0.242246 | + | 0.362689i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −809.585 | − | 1402.24i | −0.196500 | − | 0.340348i | 0.750891 | − | 0.660426i | \(-0.229624\pi\) |
−0.947391 | + | 0.320078i | \(0.896291\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1732.01 | − | 752.301i | 0.415529 | − | 0.180485i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2820.81 | + | 1169.62i | −0.668979 | + | 0.277386i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −594.813 | − | 343.415i | −0.139459 | − | 0.0805167i | 0.428647 | − | 0.903472i | \(-0.358990\pi\) |
−0.568106 | + | 0.822955i | \(0.692324\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5933.62 | − | 3425.78i | 1.37547 | − | 0.794128i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 299.375 | + | 606.793i | 0.0686196 | + | 0.139083i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1805.03 | 0.409124 | 0.204562 | − | 0.978854i | \(-0.434423\pi\) | ||||
0.204562 | + | 0.978854i | \(0.434423\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6726.19i | 1.50770i | 0.657046 | + | 0.753851i | \(0.271806\pi\) | ||||
−0.657046 | + | 0.753851i | \(0.728194\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −663.544 | − | 120.130i | −0.147104 | − | 0.0266322i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.0458534 | + | 0.0264735i | −1.00548e−5 | + | 5.80513e-6i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −336.124 | + | 582.184i | −0.0729088 | + | 0.126282i | −0.900175 | − | 0.435528i | \(-0.856562\pi\) |
0.827266 | + | 0.561810i | \(0.189895\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −115.361 | + | 878.730i | −0.0247544 | + | 0.188560i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2007.12 | − | 1158.81i | −0.426102 | − | 0.246010i | 0.271583 | − | 0.962415i | \(-0.412453\pi\) |
−0.697685 | + | 0.716405i | \(0.745786\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8014.87 | + | 4627.39i | −1.68352 | + | 0.971978i | −0.724222 | + | 0.689567i | \(0.757801\pi\) |
−0.959294 | + | 0.282411i | \(0.908866\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2566.14 | − | 1713.96i | −0.533350 | − | 0.356233i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −334.723 | − | 247.883i | −0.0688435 | − | 0.0509829i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4111.30 | −0.836821 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −493.231 | + | 7546.34i | −0.0993599 | + | 1.52019i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4392.72 | − | 7608.42i | −0.875855 | − | 1.51703i | −0.855849 | − | 0.517225i | \(-0.826965\pi\) |
−0.0200056 | − | 0.999800i | \(-0.506368\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1758.25 | − | 3045.38i | 0.347015 | − | 0.601047i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.269683 | + | 0.236245i | 5.26889e−5 | + | 4.61559e-5i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −179.904 | + | 311.602i | −0.0347963 | + | 0.0602689i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 955.936 | − | 8361.25i | 0.183054 | − | 1.60111i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2049.15 | + | 133.933i | 0.388517 | + | 0.0253936i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8251.85i | 1.54918i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 599.516i | − | 0.111453i | −0.998446 | − | 0.0557267i | \(-0.982252\pi\) | ||
0.998446 | − | 0.0557267i | \(-0.0177476\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2720.53 | + | 1817.08i | 0.500860 | + | 0.334532i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4494.29 | − | 7784.34i | −0.819447 | − | 1.41932i | −0.906090 | − | 0.423084i | \(-0.860948\pi\) |
0.0866437 | − | 0.996239i | \(-0.472386\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7102.69 | − | 4100.74i | −1.28264 | − | 0.740535i | −0.305314 | − | 0.952252i | \(-0.598761\pi\) |
−0.977331 | + | 0.211717i | \(0.932095\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5802.48 | + | 1663.68i | −1.03788 | + | 0.297581i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5894.42 | − | 3403.15i | −1.04436 | − | 0.602964i | −0.123298 | − | 0.992370i | \(-0.539347\pi\) |
−0.921066 | + | 0.389405i | \(0.872681\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.144512 | + | 0.250302i | 2.53640e−5 | + | 4.39318e-5i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2402.70 | + | 1185.43i | −0.417775 | + | 0.206118i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1392.99i | 0.239962i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 145.181i | − | 0.0247791i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1825.47 | − | 3699.99i | −0.308712 | − | 0.625718i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 973.004 | − | 8510.54i | 0.163050 | − | 1.42614i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3875.41 | − | 6712.41i | 0.643540 | − | 1.11464i | −0.341097 | − | 0.940028i | \(-0.610798\pi\) |
0.984637 | − | 0.174616i | \(-0.0558684\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1675.09 | − | 2184.67i | 0.275658 | − | 0.359517i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3256.63 | − | 5640.64i | 0.531130 | − | 0.919944i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1544.24 | − | 2674.70i | −0.249614 | − | 0.432344i | 0.713805 | − | 0.700345i | \(-0.246970\pi\) |
−0.963419 | + | 0.268001i | \(0.913637\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8892.72 | − | 5939.58i | −1.42474 | − | 0.951603i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.0838835 | 1.33213e−5 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2127.47 | + | 5985.61i | −0.334906 | + | 0.942252i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −210.065 | + | 3213.95i | −0.0327812 | + | 0.501546i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10112.9 | − | 5838.71i | 1.56453 | − | 0.903281i | 0.567739 | − | 0.823209i | \(-0.307818\pi\) |
0.996789 | − | 0.0800721i | \(-0.0255151\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6683.19 | + | 3858.54i | 1.02505 | + | 0.591814i | 0.915563 | − | 0.402174i | \(-0.131745\pi\) |
0.109489 | + | 0.993988i | \(0.465079\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −930.737 | + | 316.511i | −0.141536 | + | 0.0481313i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2760.12 | + | 4780.66i | −0.416165 | + | 0.720818i | −0.995550 | − | 0.0942355i | \(-0.969959\pi\) |
0.579385 | + | 0.815054i | \(0.303293\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3214.83 | + | 1856.08i | −0.480635 | + | 0.277495i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2079.29 | + | 1760.99i | 0.308257 | + | 0.261068i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6290.95i | − | 0.924857i | −0.886657 | − | 0.462429i | \(-0.846978\pi\) | ||
0.886657 | − | 0.462429i | \(-0.153022\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4438.63 | 0.647125 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3841.32 | + | 5751.21i | −0.555419 | + | 0.831571i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5176.81 | + | 2988.83i | −0.742374 | + | 0.428610i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3342.42 | + | 1929.75i | 0.475404 | + | 0.274474i | 0.718499 | − | 0.695528i | \(-0.244829\pi\) |
−0.243095 | + | 0.970002i | \(0.578163\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −602.058 | − | 79.0390i | −0.0849373 | − | 0.0111507i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4187.84 | − | 9641.61i | −0.586042 | − | 1.34924i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4308.29 | − | 7462.17i | −0.598055 | − | 1.03586i | −0.993108 | − | 0.117204i | \(-0.962607\pi\) |
0.395052 | − | 0.918659i | \(-0.370726\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2894.09 | + | 5865.93i | 0.398534 | + | 0.807775i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −792.509 | −0.108266 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11100.5 | 1.50447 | 0.752237 | − | 0.658893i | \(-0.228975\pi\) | ||||
0.752237 | + | 0.658893i | \(0.228975\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4762.77 | + | 9653.51i | 0.640431 | + | 1.29807i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3294.29 | + | 5705.87i | 0.439505 | + | 0.761244i | 0.997651 | − | 0.0684980i | \(-0.0218207\pi\) |
−0.558147 | + | 0.829742i | \(0.688487\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.227610 | + | 0.524023i | 3.01300e−5 | + | 6.93681e-5i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4699.27 | − | 11333.3i | −0.617253 | − | 1.48865i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6913.20 | − | 3991.34i | −0.901062 | − | 0.520228i | −0.0235174 | − | 0.999723i | \(-0.507487\pi\) |
−0.877545 | + | 0.479495i | \(0.840820\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1259.11 | − | 726.945i | 0.162854 | − | 0.0940235i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2696.77 | − | 4037.60i | 0.346143 | − | 0.518245i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7843.16 | 0.999069 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9040.06i | 1.14284i | 0.820658 | + | 0.571420i | \(0.193607\pi\) | ||||
−0.820658 | + | 0.571420i | \(0.806393\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3059.79 | + | 3612.86i | −0.383912 | + | 0.453306i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −836.173 | + | 482.765i | −0.104131 | + | 0.0601200i | −0.551161 | − | 0.834399i | \(-0.685815\pi\) |
0.447030 | + | 0.894519i | \(0.352482\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −115.005 | + | 199.194i | −0.0142154 | + | 0.0246218i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6218.04 | + | 6227.12i | −0.762906 | + | 0.764020i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.225652 | − | 0.130280i | −2.74819e−5 | − | 1.58667e-5i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2868.77 | − | 1656.28i | 0.346825 | − | 0.200240i | −0.316461 | − | 0.948606i | \(-0.602495\pi\) |
0.663286 | + | 0.748366i | \(0.269161\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 908.110 | − | 13893.9i | 0.108987 | − | 1.66748i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4335.64 | − | 3210.82i | −0.516569 | − | 0.382552i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13654.7 | 1.61514 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3965.23 | + | 2648.44i | 0.465655 | + | 0.311018i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4172.32 | − | 7226.67i | −0.486470 | − | 0.842591i | 0.513409 | − | 0.858144i | \(-0.328382\pi\) |
−0.999879 | + | 0.0155530i | \(0.995049\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3350.59 | − | 5803.38i | 0.387880 | − | 0.671828i | −0.604284 | − | 0.796769i | \(-0.706541\pi\) |
0.992164 | + | 0.124941i | \(0.0398741\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4783.17 | − | 11535.7i | −0.549801 | − | 1.32597i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −293.321 | + | 508.046i | −0.0334780 | + | 0.0579856i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12578.2 | + | 1438.06i | 1.42554 | + | 0.162981i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.0411687 | + | 0.0834434i | 4.63320e−6 | + | 9.39088e-6i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 9168.55i | − | 1.02467i | −0.858785 | − | 0.512336i | \(-0.828780\pi\) | ||
0.858785 | − | 0.512336i | \(-0.171220\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1346.90i | 0.149487i | 0.997203 | + | 0.0747436i | \(0.0238138\pi\) | ||||
−0.997203 | + | 0.0747436i | \(0.976186\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6361.97 | + | 3138.82i | −0.701225 | + | 0.345965i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1263.10 | + | 2187.75i | 0.138266 | + | 0.239483i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4892.07 | − | 2824.44i | −0.531858 | − | 0.307069i | 0.209914 | − | 0.977720i | \(-0.432681\pi\) |
−0.741773 | + | 0.670651i | \(0.766015\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1524.74 | + | 9134.62i | 0.164641 | + | 0.986354i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7525.68 | − | 4344.95i | −0.807124 | − | 0.465993i | 0.0388322 | − | 0.999246i | \(-0.487636\pi\) |
−0.845956 | + | 0.533253i | \(0.820970\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 785.950 | + | 1361.31i | 0.0837249 | + | 0.145016i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5924.67 | − | 3957.17i | −0.626906 | − | 0.418720i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14492.3i | 1.52324i | 0.648026 | + | 0.761618i | \(0.275595\pi\) | ||||
−0.648026 | + | 0.761618i | \(0.724405\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0574724i | 6.00060e-6i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1318.94 | − | 86.2062i | −0.136797 | − | 0.00894111i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1556.43 | − | 177.945i | −0.160366 | − | 0.0183345i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4131.68 | + | 7156.27i | −0.422914 | + | 0.732508i | −0.996223 | − | 0.0868308i | \(-0.972326\pi\) |
0.573309 | + | 0.819339i | \(0.305659\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3896.48 | + | 772.843i | 0.396236 | + | 0.0785909i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4948.33 | + | 8570.75i | −0.499928 | + | 0.865900i | −1.00000 | 8.36677e-5i | \(-0.999973\pi\) | |
0.500072 | + | 0.865984i | \(0.333307\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1987.79 | + | 3442.95i | 0.199525 | + | 0.345588i | 0.948375 | − | 0.317152i | \(-0.102727\pi\) |
−0.748849 | + | 0.662740i | \(0.769393\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −134.286 | + | 2054.55i | −0.0133922 | + | 0.204898i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17044.5 | 1.68892 | 0.844460 | − | 0.535619i | \(-0.179921\pi\) | ||||
0.844460 | + | 0.535619i | \(0.179921\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8030.47 | − | 5947.07i | −0.790645 | − | 0.585522i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2553.32 | + | 1705.40i | 0.249790 | + | 0.166838i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.00566 | + | 0.580616i | −9.77592e−5 | + | 5.64413e-5i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −882.751 | − | 509.656i | −0.0852703 | − | 0.0492308i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12161.4 | − | 9324.72i | −1.16736 | − | 0.895073i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5364.93 | − | 9292.33i | 0.511753 | − | 0.886383i | −0.488154 | − | 0.872758i | \(-0.662330\pi\) |
0.999907 | − | 0.0136250i | \(-0.00433712\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 618.740 | − | 357.230i | 0.0586530 | − | 0.0338633i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4862.41 | + | 880.302i | 0.458069 | + | 0.0829299i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17568.6i | 1.64485i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12461.1 | −1.15948 | −0.579741 | − | 0.814801i | \(-0.696846\pi\) | ||||
−0.579741 | + | 0.814801i | \(0.696846\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5051.40 | + | 10238.5i | 0.467142 | + | 0.946834i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4052.21 | + | 2339.55i | −0.372452 | + | 0.215035i | −0.674529 | − | 0.738248i | \(-0.735653\pi\) |
0.302077 | + | 0.953283i | \(0.402320\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2773.30 | + | 1601.16i | 0.253353 | + | 0.146273i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.660974 | + | 0.506800i | 6.00173e−5 | + | 4.60181e-5i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2268.96 | + | 5223.81i | 0.204783 | + | 0.471469i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2685.54 | + | 4651.49i | 0.240924 | + | 0.417293i | 0.960978 | − | 0.276625i | \(-0.0892161\pi\) |
−0.720054 | + | 0.693918i | \(0.755883\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1217.35 | + | 1822.61i | −0.108557 | + | 0.162532i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22263.9 | −1.97355 | −0.986777 | − | 0.162086i | \(-0.948178\pi\) | ||||
−0.986777 | + | 0.162086i | \(0.948178\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4770.63 | 0.420376 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11137.0 | + | 727.921i | 0.975569 | + | 0.0637635i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7249.76 | + | 12556.9i | 0.631316 | + | 1.09347i | 0.987283 | + | 0.158973i | \(0.0508182\pi\) |
−0.355967 | + | 0.934498i | \(0.615848\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3653.69 | + | 8411.85i | 0.316301 | + | 0.728216i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1342.85 | + | 6770.30i | −0.115571 | + | 0.582682i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6582.05 | + | 3800.15i | 0.563184 | + | 0.325155i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.02361 | + | 0.590983i | −8.70762e−5 | + | 5.02735e-5i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9047.24 | + | 591.330i | 0.765182 | + | 0.0500126i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7009.79 | 0.589452 | 0.294726 | − | 0.955582i | \(-0.404772\pi\) | ||||
0.294726 | + | 0.955582i | \(0.404772\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3631.76i | 0.303644i | 0.988408 | + | 0.151822i | \(0.0485141\pi\) | ||||
−0.988408 | + | 0.151822i | \(0.951486\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1876.72 | + | 673.373i | −0.156013 | + | 0.0559779i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 804.894 | − | 464.706i | 0.0665308 | − | 0.0384116i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4765.18 | + | 8253.53i | −0.391648 | + | 0.678354i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7798.41 | − | 1023.79i | −0.637330 | − | 0.0836696i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −136.477 | − | 78.7951i | −0.0110910 | − | 0.00640336i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5390.32 | + | 3112.10i | −0.435596 | + | 0.251492i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20091.5 | − | 9912.59i | 1.61455 | − | 0.796573i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.838432 | − | 0.255622i | 6.70015e−5 | − | 2.04275e-5i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12760.4 | −1.01407 | −0.507037 | − | 0.861925i | \(-0.669259\pi\) | ||||
−0.507037 | + | 0.861925i | \(0.669259\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6095.08 | + | 3007.14i | −0.481704 | + | 0.237659i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4792.42 | − | 8300.71i | −0.376669 | − | 0.652410i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3919.62 | + | 6788.98i | −0.306382 | + | 0.530669i | −0.977568 | − | 0.210620i | \(-0.932452\pi\) |
0.671186 | + | 0.741289i | \(0.265785\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17049.3 | − | 7069.34i | 1.32540 | − | 0.549566i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2782.09 | + | 4818.72i | −0.215101 | + | 0.372567i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1366.84 | − | 11955.3i | 0.105107 | − | 0.919332i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3552.17 | − | 5318.29i | 0.271678 | − | 0.406755i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9443.19i | 0.718350i | 0.933270 | + | 0.359175i | \(0.116942\pi\) | ||||
−0.933270 | + | 0.359175i | \(0.883058\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3184.11i | − | 0.240919i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0245217 | − | 0.375177i | 1.84547e−6 | − | 2.82353e-5i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8022.13 | + | 13894.7i | 0.600519 | + | 1.04013i | 0.992742 | + | 0.120260i | \(0.0383728\pi\) |
−0.392223 | + | 0.919870i | \(0.628294\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21515.0 | − | 12421.7i | −1.60202 | − | 0.924929i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8408.34 | + | 10563.3i | 0.622781 | + | 0.782396i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19213.9 | + | 11093.2i | 1.41562 | + | 0.817310i | 0.995910 | − | 0.0903469i | \(-0.0287976\pi\) |
0.419712 | + | 0.907657i | \(0.362131\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3211.11 | − | 5561.80i | −0.235343 | − | 0.407625i | 0.724030 | − | 0.689769i | \(-0.242288\pi\) |
−0.959372 | + | 0.282144i | \(0.908955\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1368.07 | + | 20931.3i | −0.0997419 | + | 1.52603i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1063.88i | 0.0771597i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 21441.1i | − | 1.54697i | −0.633813 | − | 0.773486i | \(-0.718511\pi\) | ||
0.633813 | − | 0.773486i | \(-0.281489\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12754.2 | − | 19095.6i | 0.915454 | − | 1.37061i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2379.63 | − | 20813.8i | 0.169920 | − | 1.48624i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.725230 | + | 1.25614i | −5.15197e−5 | + | 8.92347e-5i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2109.67 | + | 874.757i | −0.149101 | + | 0.0618235i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −342.762 | + | 593.681i | −0.0241010 | + | 0.0417442i | −0.877824 | − | 0.478983i | \(-0.841006\pi\) |
0.853723 | + | 0.520727i | \(0.174339\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 807.445 | + | 1398.54i | 0.0564859 | + | 0.0978365i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 706.775 | − | 348.703i | 0.0491926 | − | 0.0242703i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11503.8 | 0.796635 | 0.398317 | − | 0.917248i | \(-0.369594\pi\) | ||||
0.398317 | + | 0.917248i | \(0.369594\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5087.04 | + | 3767.27i | 0.350501 | + | 0.259568i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8567.85 | + | 4227.14i | −0.587368 | + | 0.289791i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5124.45 | − | 2958.60i | 0.349548 | − | 0.201812i | −0.314938 | − | 0.949112i | \(-0.601984\pi\) |
0.664486 | + | 0.747300i | \(0.268650\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10168.3 | + | 5870.67i | 0.690139 | + | 0.398452i | 0.803664 | − | 0.595083i | \(-0.202881\pi\) |
−0.113525 | + | 0.993535i | \(0.536214\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14444.2 | − | 1896.25i | −0.975478 | − | 0.128062i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8033.52 | + | 13914.5i | −0.539850 | + | 0.935047i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24018.0 | + | 13866.8i | −1.60603 | + | 0.927241i | −0.615782 | + | 0.787916i | \(0.711160\pi\) |
−0.990247 | + | 0.139325i | \(0.955507\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3675.78 | + | 10244.5i | 0.244581 | + | 0.681657i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 3240.96i | − | 0.214592i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19338.2 | −1.27416 | −0.637081 | − | 0.770797i | \(-0.719858\pi\) | ||||
−0.637081 | + | 0.770797i | \(0.719858\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1407.66 | − | 92.0054i | −0.0922968 | − | 0.00603255i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9927.33 | − | 5731.55i | 0.647746 | − | 0.373976i | −0.139846 | − | 0.990173i | \(-0.544661\pi\) |
0.787592 | + | 0.616197i | \(0.211327\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3429.59 | + | 1980.07i | 0.222693 | + | 0.128572i | 0.607196 | − | 0.794552i | \(-0.292294\pi\) |
−0.384504 | + | 0.923123i | \(0.625627\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6820.38 | − | 2319.37i | 0.440728 | − | 0.149876i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2212.00 | − | 960.783i | 0.142250 | − | 0.0617865i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8892.79 | + | 15402.8i | 0.569139 | + | 0.985777i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.651886 | + | 0.0426075i | 4.15212e−5 | + | 2.71384e-6i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2886.95 | −0.183005 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5409.20 | −0.341263 | −0.170631 | − | 0.985335i | \(-0.554581\pi\) | ||||
−0.170631 | + | 0.985335i | \(0.554581\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7095.43 | − | 10623.3i | 0.445526 | − | 0.667040i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12503.7 | + | 21657.1i | 0.781410 | + | 1.35344i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −542.482 | + | 2341.45i | −0.0337424 | + | 0.145638i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6589.02 | + | 5052.12i | 0.407915 | + | 0.312768i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20809.6 | − | 12014.4i | −1.28226 | − | 0.740313i | −0.304999 | − | 0.952353i | \(-0.598656\pi\) |
−0.977261 | + | 0.212040i | \(0.931989\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3581.87 | − | 2068.00i | 0.219682 | − | 0.126833i | −0.386121 | − | 0.922448i | \(-0.626185\pi\) |
0.605803 | + | 0.795615i | \(0.292852\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12611.0 | − | 25560.9i | −0.769859 | − | 1.56040i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1393.75 | −0.0846895 | −0.0423447 | − | 0.999103i | \(-0.513483\pi\) | ||||
−0.0423447 | + | 0.999103i | \(0.513483\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.744436i | 4.50257e-5i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3108.34 | + | 562.741i | 0.187136 | + | 0.0338795i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7846.10 | − | 4529.95i | 0.470202 | − | 0.271471i | −0.246122 | − | 0.969239i | \(-0.579157\pi\) |
0.716324 | + | 0.697768i | \(0.245823\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5639.89 | − | 9768.57i | 0.336441 | − | 0.582732i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10610.2 | + | 8135.38i | 0.630053 | + | 0.483092i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14018.1 | + | 8093.34i | 0.828629 | + | 0.478409i | 0.853383 | − | 0.521284i | \(-0.174547\pi\) |
−0.0247539 | + | 0.999694i | \(0.507880\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24821.5 | + | 14330.7i | −1.46058 | + | 0.843269i | −0.999038 | − | 0.0438473i | \(-0.986038\pi\) |
−0.461546 | + | 0.887116i | \(0.652705\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 857.297 | + | 572.601i | 0.0502182 | + | 0.0335415i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6545.78 | + | 8838.93i | −0.381706 | + | 0.515427i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5807.45 | 0.337130 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1757.53 | − | 26889.8i | 0.101569 | − | 1.55399i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.873449 | − | 1.51286i | −5.02521e−5 | − | 8.70391e-5i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3670.88 | − | 6358.15i | 0.210255 | − | 0.364173i | −0.741539 | − | 0.670910i | \(-0.765904\pi\) |
0.951794 | + | 0.306737i | \(0.0992371\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1915.38 | + | 2186.48i | −0.109219 | + | 0.124678i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16478.4 | + | 28541.4i | −0.935474 | + | 1.62029i | −0.161687 | + | 0.986842i | \(0.551693\pi\) |
−0.773787 | + | 0.633446i | \(0.781640\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26779.8 | + | 3061.71i | 1.51357 | + | 0.173045i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5159.48 | + | 337.226i | 0.290326 | + | 0.0189758i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 22213.0i | − | 1.24444i | −0.782841 | − | 0.622222i | \(-0.786230\pi\) | ||
0.782841 | − | 0.622222i | \(-0.213770\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 32346.4i | − | 1.80422i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 508.242 | + | 339.463i | 0.0282251 | + | 0.0188520i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1988.59 | − | 3444.34i | −0.109955 | − | 0.190448i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22072.1 | − | 12743.3i | −1.21514 | − | 0.701563i | −0.251267 | − | 0.967918i | \(-0.580847\pi\) |
−0.963875 | + | 0.266355i | \(0.914181\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.887702 | − | 0.919199i | 4.86595e−5 | − | 5.03860e-5i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9593.47 | + | 5538.79i | 0.523599 | + | 0.302300i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 318.391 | + | 551.470i | 0.0173026 | + | 0.0299690i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6915.61 | − | 3411.97i | 0.374209 | − | 0.184625i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 22316.4i | − | 1.20239i | −0.799101 | − | 0.601197i | \(-0.794691\pi\) | ||
0.799101 | − | 0.601197i | \(-0.205309\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 5016.19i | − | 0.269117i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12836.2 | − | 26017.3i | −0.685729 | − | 1.38988i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 831.385 | − | 7271.84i | 0.0442255 | − | 0.386826i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −620.251 | + | 1074.31i | −0.0328547 | + | 0.0569061i | −0.881985 | − | 0.471277i | \(-0.843793\pi\) |
0.849130 | + | 0.528183i | \(0.177127\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6719.22 | − | 16204.9i | −0.354417 | − | 0.854756i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 842.748 | − | 1459.68i | 0.0442653 | − | 0.0766698i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.108080 | + | 0.187201i | 5.65311e−6 | + | 9.79147e-6i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11935.1 | − | 7971.63i | −0.621652 | − | 0.415211i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1718.52 | −0.0891374 | −0.0445687 | − | 0.999006i | \(-0.514191\pi\) | ||||
−0.0445687 | + | 0.999006i | \(0.514191\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6939.62 | − | 9370.74i | 0.358453 | − | 0.484028i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1316.03 | − | 20135.0i | 0.0676952 | − | 1.03572i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2029.35 | + | 1171.65i | −0.103956 | + | 0.0600191i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2204.74 | − | 1272.91i | −0.112475 | − | 0.0649376i | 0.442707 | − | 0.896666i | \(-0.354018\pi\) |
−0.555182 | + | 0.831729i | \(0.687351\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18193.0 | + | 7512.46i | 0.924298 | + | 0.381672i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6433.10 | + | 11142.5i | −0.325495 | + | 0.563774i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19126.0 | + | 11042.4i | −0.963761 | + | 0.556427i | −0.897328 | − | 0.441363i | \(-0.854495\pi\) |
−0.0664323 | + | 0.997791i | \(0.521162\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4918.70 | + | 20944.8i | 0.246842 | + | 1.05110i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.37884i | 6.89149e-5i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5401.50 | −0.268873 | −0.134437 | − | 0.990922i | \(-0.542922\pi\) | ||||
−0.134437 | + | 0.990922i | \(0.542922\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −994.918 | + | 1489.59i | −0.0493242 | + | 0.0738480i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26971.1 | + | 15571.7i | −1.33173 | + | 0.768872i | −0.985564 | − | 0.169303i | \(-0.945848\pi\) |
−0.346161 | + | 0.938175i | \(0.612515\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14334.1 | − | 8275.82i | −0.704915 | − | 0.406983i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11698.0 | − | 28212.3i | −0.572967 | − | 1.38184i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3804.39 | + | 8758.80i | 0.185593 | + | 0.427289i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2644.61 | − | 4580.61i | −0.128500 | − | 0.222568i | 0.794596 | − | 0.607139i | \(-0.207683\pi\) |
−0.923096 | + | 0.384571i | \(0.874350\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12758.7 | − | 25860.2i | −0.617468 | − | 1.25153i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3070.62 | −0.148015 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20794.2 | −0.998384 | −0.499192 | − | 0.866491i | \(-0.666370\pi\) | ||||
−0.499192 | + | 0.866491i | \(0.666370\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.301681 | − | 0.611468i | −1.44273e−5 | − | 2.92423e-5i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9126.94 | + | 15808.3i | 0.434759 | + | 0.753024i | 0.997276 | − | 0.0737616i | \(-0.0235004\pi\) |
−0.562517 | + | 0.826785i | \(0.690167\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13487.9 | + | 5858.48i | −0.639967 | + | 0.277970i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9149.92 | + | 1201.21i | 0.432439 | + | 0.0567712i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1767.78 | − | 1020.63i | −0.0832213 | − | 0.0480478i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28098.3 | − | 16222.6i | 1.31762 | − | 0.760730i | 0.334278 | − | 0.942475i | \(-0.391508\pi\) |
0.983346 | + | 0.181745i | \(0.0581744\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4672.99 | + | 6996.39i | −0.218280 | + | 0.326808i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20600.1 | −0.958519 | −0.479259 | − | 0.877673i | \(-0.659095\pi\) | ||||
−0.479259 | + | 0.877673i | \(0.659095\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 680.094i | 0.0315222i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7487.61 | − | 6341.38i | −0.345710 | − | 0.292787i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −958.201 | + | 553.217i | −0.0440707 | + | 0.0254442i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.392929 | − | 0.680572i | 1.80027e−5 | − | 3.11816e-5i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11935.5 | + | 10455.6i | 0.544749 | + | 0.477205i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6177.51 | + | 3566.59i | 0.280872 | + | 0.162162i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12253.1 | + | 7074.35i | −0.554990 | + | 0.320424i | −0.751132 | − | 0.660152i | \(-0.770492\pi\) |
0.196142 | + | 0.980575i | \(0.437159\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −232.766 | + | 3561.28i | −0.0105028 | + | 0.160691i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22683.8 | + | 30630.5i | −1.01965 | + | 1.37686i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4790.02 | 0.214500 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −29605.4 | − | 19773.9i | −1.32075 | − | 0.882147i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9980.73 | − | 17287.1i | −0.443583 | − | 0.768308i | 0.554369 | − | 0.832271i | \(-0.312959\pi\) |
−0.997952 | + | 0.0639626i | \(0.979626\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6547.96 | + | 11341.4i | −0.289925 | + | 0.502165i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2139.30 | − | 2790.09i | 0.0943675 | − | 0.123075i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.632729 | − | 1.09592i | 2.78064e−5 | − | 4.81621e-5i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11405.4 | + | 1303.97i | 0.499364 | + | 0.0570919i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4149.84 | − | 8411.18i | −0.181018 | − | 0.366899i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13027.7i | 0.566169i | 0.959095 | + | 0.283085i | \(0.0913578\pi\) | ||||
−0.959095 | + | 0.283085i | \(0.908642\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2467.58i | 0.106841i | 0.998572 | + | 0.0534207i | \(0.0170124\pi\) | ||||
−0.998572 | + | 0.0534207i | \(0.982988\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 31343.2 | − | 15463.8i | 1.35209 | − | 0.667086i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13261.5 | + | 22969.5i | 0.569974 | + | 0.987224i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19360.5 | − | 11177.8i | −0.829054 | − | 0.478654i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 965.732 | + | 3368.21i | 0.0412032 | + | 0.143706i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17302.8 | + | 9989.80i | 0.735534 | + | 0.424661i | 0.820443 | − | 0.571728i | \(-0.193727\pi\) |
−0.0849092 | + | 0.996389i | \(0.527060\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20481.8 | − | 35475.5i | −0.867497 | − | 1.50255i | −0.864546 | − | 0.502553i | \(-0.832394\pi\) |
−0.00295098 | − | 0.999996i | \(-0.500939\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.228782 | + | 0.152807i | 9.65476e−6 | + | 6.44856e-6i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 38066.2i | − | 1.60059i | −0.599604 | − | 0.800297i | \(-0.704675\pi\) | ||
0.599604 | − | 0.800297i | \(-0.295325\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5157.09i | − | 0.216059i | −0.994148 | − | 0.108030i | \(-0.965546\pi\) | ||
0.994148 | − | 0.108030i | \(-0.0344542\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3485.67 | + | 227.824i | 0.145507 | + | 0.00951039i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6628.96 | − | 7097.62i | 0.275726 | − | 0.295220i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2545.90 | + | 4409.62i | −0.105514 | + | 0.182756i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4359.99 | − | 1482.68i | 0.180052 | − | 0.0612291i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12192.2 | − | 21117.5i | 0.501695 | − | 0.868960i | −0.498304 | − | 0.867003i | \(-0.666043\pi\) |
0.999998 | − | 0.00195781i | \(-0.000623192\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5798.77 | − | 10043.8i | −0.237762 | − | 0.411816i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −785.439 | + | 12017.1i | −0.0320901 | + | 0.490972i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25928.2 | 1.05557 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19809.7 | + | 14670.4i | 0.803626 | + | 0.595135i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 39989.6 | + | 26709.7i | 1.61654 | + | 1.07971i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4534.08 | + | 2617.75i | −0.182640 | + | 0.105447i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35213.6 | + | 20330.6i | 1.41347 | + | 0.816068i | 0.995714 | − | 0.0924912i | \(-0.0294830\pi\) |
0.417757 | + | 0.908559i | \(0.362816\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2087.16 | + | 15898.3i | −0.0834846 | + | 0.635920i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5424.95 | − | 9396.29i | 0.216234 | − | 0.374529i | −0.737419 | − | 0.675435i | \(-0.763956\pi\) |
0.953654 | + | 0.300906i | \(0.0972892\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29442.4 | + | 16998.6i | −1.16945 | + | 0.675184i | −0.953551 | − | 0.301230i | \(-0.902603\pi\) |
−0.215902 | + | 0.976415i | \(0.569269\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −385.559 | + | 2129.66i | −0.0152611 | + | 0.0842958i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 21617.2i | − | 0.852675i | −0.904564 | − | 0.426337i | \(-0.859804\pi\) | ||
0.904564 | − | 0.426337i | \(-0.140196\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21062.9 | 0.827930 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9452.08 | + | 19158.1i | 0.370253 | + | 0.750454i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.43793 | + | 0.830190i | −5.61317e−5 | + | 3.24077e-5i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3274.27 | − | 1890.40i | −0.127376 | − | 0.0735406i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 36298.9 | − | 15051.0i | 1.40725 | − | 0.583505i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 21383.6 | − | 9287.99i | 0.826170 | − | 0.358847i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7452.42 | + | 12908.0i | 0.286945 | + | 0.497003i | 0.973079 | − | 0.230472i | \(-0.0740271\pi\) |
−0.686134 | + | 0.727475i | \(0.740694\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25355.1 | + | 37961.6i | −0.972932 | + | 1.45667i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18956.5 | −0.724928 | −0.362464 | − | 0.931998i | \(-0.618064\pi\) | ||||
−0.362464 | + | 0.931998i | \(0.618064\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35931.1 | −1.36940 | −0.684700 | − | 0.728825i | \(-0.740067\pi\) | ||||
−0.684700 | + | 0.728825i | \(0.740067\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18233.4 | − | 1191.74i | −0.692551 | − | 0.0452654i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19322.4 | + | 33467.3i | 0.731434 | + | 1.26688i | 0.956270 | + | 0.292484i | \(0.0944819\pi\) |
−0.224837 | + | 0.974396i | \(0.572185\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35190.8 | − | 15285.2i | 1.32763 | − | 0.576657i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.480855 | − | 1.79983i | 1.80800e−5 | − | 6.76728e-5i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −19706.1 | − | 11377.3i | −0.738456 | − | 0.426348i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45074.2 | − | 26023.6i | 1.68342 | − | 0.971924i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1865.63 | + | 121.938i | 0.0694444 | + | 0.00453891i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3712.46 | 0.137728 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16070.8i | 0.594224i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −41160.1 | + | 14768.4i | −1.51686 | + | 0.544254i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13674.0 | + | 7894.67i | −0.502252 | + | 0.289975i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −286.156 | + | 495.636i | −0.0104759 | + | 0.0181448i | −0.871216 | − | 0.490900i | \(-0.836668\pi\) |
0.860740 | + | 0.509045i | \(0.170001\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4086.99 | − | 9856.69i | −0.149127 | − | 0.359654i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24634.1 | + | 14222.5i | 0.895901 | + | 0.517248i | 0.875868 | − | 0.482551i | \(-0.160290\pi\) |
0.0200327 | + | 0.999799i | \(0.493623\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.50340 | + | 1.44534i | −9.07452e−5 | + | 5.23918e-5i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 38452.5 | − | 18971.4i | 1.38929 | − | 0.685437i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13907.3 | − | 10299.2i | −0.500829 | − | 0.370895i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20019.4 | 0.718585 | 0.359292 | − | 0.933225i | \(-0.383018\pi\) | ||||
0.359292 | + | 0.933225i | \(0.383018\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2793.67 | + | 1378.32i | −0.0999506 | + | 0.0493128i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1077.42 | + | 1866.14i | 0.0384221 | + | 0.0665490i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1056.26 | − | 1829.49i | 0.0375455 | − | 0.0650306i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2212.74 | − | 16854.9i | 0.0783989 | − | 0.597182i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15791.3 | − | 27351.3i | 0.557690 | − | 0.965948i | −0.439999 | − | 0.897999i | \(-0.645021\pi\) |
0.997689 | − | 0.0679494i | \(-0.0216456\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12332.4 | + | 11518.1i | 0.434133 | + | 0.405467i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −25941.4 | + | 38839.4i | −0.910272 | + | 1.36286i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 0.873451i | − | 3.05507e-5i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39841.1i | 1.38906i | 0.719463 | + | 0.694531i | \(0.244388\pi\) | ||||
−0.719463 | + | 0.694531i | \(0.755612\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2779.47 | + | 42525.4i | −0.0965971 | + | 1.47792i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5443.60 | + | 9428.59i | 0.188583 | + | 0.326635i | 0.944778 | − | 0.327711i | \(-0.106277\pi\) |
−0.756195 | + | 0.654346i | \(0.772944\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1000.09 | + | 577.405i | 0.0345361 | + | 0.0199394i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 21092.7 | + | 23213.9i | 0.726081 | + | 0.799098i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19780.5 | + | 11420.3i | 0.678755 | + | 0.391879i | 0.799386 | − | 0.600818i | \(-0.205158\pi\) |
−0.120631 | + | 0.992697i | \(0.538492\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1734.95 | + | 3005.03i | 0.0593456 | + | 0.102790i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2306.65 | + | 35291.2i | −0.0786521 | + | 1.20336i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 51243.3i | − | 1.74180i | −0.491462 | − | 0.870899i | \(-0.663537\pi\) | ||
0.491462 | − | 0.870899i | \(-0.336463\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48730.1i | 1.65117i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.834136 | − | 1.24887i | 2.81753e−5 | − | 4.21840e-5i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −49305.5 | − | 5637.06i | −1.66023 | − | 0.189812i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14356.8 | + | 24866.6i | −0.481916 | + | 0.834703i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11047.9 | + | 8470.92i | 0.369691 | + | 0.283460i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26673.5 | − | 46199.8i | 0.889793 | − | 1.54117i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7489.56 | − | 12972.3i | −0.249067 | − | 0.431397i | 0.714200 | − | 0.699942i | \(-0.246791\pi\) |
−0.963267 | + | 0.268544i | \(0.913457\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6491.13 | − | 3202.54i | 0.215196 | − | 0.106172i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12705.2 | 0.419908 | 0.209954 | − | 0.977711i | \(-0.432669\pi\) | ||||
0.209954 | + | 0.977711i | \(0.432669\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10114.6 | − | 13658.0i | 0.333258 | − | 0.450007i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −676.526 | + | 333.779i | −0.0222217 | + | 0.0109636i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17602.3 | + | 10162.7i | −0.576405 | + | 0.332788i | −0.759703 | − | 0.650270i | \(-0.774656\pi\) |
0.183298 | + | 0.983057i | \(0.441323\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.288185 | − | 0.166384i | −9.40802e−6 | − | 5.43172e-6i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13044.6 | + | 17012.9i | −0.424549 | + | 0.553700i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20257.1 | − | 35086.3i | 0.657274 | − | 1.13843i | −0.324044 | − | 0.946042i | \(-0.605043\pi\) |
0.981318 | − | 0.192390i | \(-0.0616240\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1585.61 | − | 915.452i | 0.0512911 | − | 0.0296129i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −41895.0 | + | 15032.1i | −1.35110 | + | 0.484779i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23333.0i | 0.750197i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5083.59 | −0.162952 | −0.0814761 | − | 0.996675i | \(-0.525963\pi\) | ||||
−0.0814761 | + | 0.996675i | \(0.525963\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −40188.7 | − | 2626.75i | −1.28434 | − | 0.0839449i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19221.5 | + | 11097.5i | −0.612424 | + | 0.353583i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15996.3 | − | 9235.49i | −0.508133 | − | 0.293371i | 0.223933 | − | 0.974605i | \(-0.428110\pi\) |
−0.732066 | + | 0.681234i | \(0.761444\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14031.4 | − | 2783.03i | −0.444377 | − | 0.0881394i |
(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.209.9 | yes | 48 | |
3.2 | odd | 2 | 756.4.x.a.629.20 | 48 | |||
7.6 | odd | 2 | inner | 252.4.x.a.209.16 | yes | 48 | |
9.2 | odd | 6 | 2268.4.f.a.1133.9 | 48 | |||
9.4 | even | 3 | 756.4.x.a.125.5 | 48 | |||
9.5 | odd | 6 | inner | 252.4.x.a.41.16 | yes | 48 | |
9.7 | even | 3 | 2268.4.f.a.1133.40 | 48 | |||
21.20 | even | 2 | 756.4.x.a.629.5 | 48 | |||
63.13 | odd | 6 | 756.4.x.a.125.20 | 48 | |||
63.20 | even | 6 | 2268.4.f.a.1133.39 | 48 | |||
63.34 | odd | 6 | 2268.4.f.a.1133.10 | 48 | |||
63.41 | even | 6 | inner | 252.4.x.a.41.9 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.x.a.41.9 | ✓ | 48 | 63.41 | even | 6 | inner | |
252.4.x.a.41.16 | yes | 48 | 9.5 | odd | 6 | inner | |
252.4.x.a.209.9 | yes | 48 | 1.1 | even | 1 | trivial | |
252.4.x.a.209.16 | yes | 48 | 7.6 | odd | 2 | inner | |
756.4.x.a.125.5 | 48 | 9.4 | even | 3 | |||
756.4.x.a.125.20 | 48 | 63.13 | odd | 6 | |||
756.4.x.a.629.5 | 48 | 21.20 | even | 2 | |||
756.4.x.a.629.20 | 48 | 3.2 | odd | 2 | |||
2268.4.f.a.1133.9 | 48 | 9.2 | odd | 6 | |||
2268.4.f.a.1133.10 | 48 | 63.34 | odd | 6 | |||
2268.4.f.a.1133.39 | 48 | 63.20 | even | 6 | |||
2268.4.f.a.1133.40 | 48 | 9.7 | even | 3 |