Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [100,4,Mod(9,100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(100, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("100.9");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 100 = 2^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 100.i (of order \(10\), degree \(4\), 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: | \(5.90019100057\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 9.4 | ||
Character | \(\chi\) | \(=\) | 100.9 |
Dual form | 100.4.i.a.89.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/100\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(77\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{7}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.776927 | + | 0.252439i | −0.149520 | + | 0.0485819i | −0.382821 | − | 0.923823i | \(-0.625047\pi\) |
0.233301 | + | 0.972405i | \(0.425047\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.16996 | − | 10.3736i | −0.372973 | − | 0.927842i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.56595i | 0.0845531i | 0.999106 | + | 0.0422766i | \(0.0134611\pi\) | ||||
−0.999106 | + | 0.0422766i | \(0.986539\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −21.3036 | + | 15.4779i | −0.789021 | + | 0.573257i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −28.6951 | − | 20.8482i | −0.786537 | − | 0.571453i | 0.120397 | − | 0.992726i | \(-0.461583\pi\) |
−0.906934 | + | 0.421273i | \(0.861583\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −34.1181 | − | 46.9595i | −0.727897 | − | 1.00186i | −0.999224 | − | 0.0393770i | \(-0.987463\pi\) |
0.271328 | − | 0.962487i | \(-0.412537\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.85845 | + | 7.00686i | 0.100843 | + | 0.120611i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −21.7409 | − | 7.06405i | −0.310173 | − | 0.100781i | 0.149794 | − | 0.988717i | \(-0.452139\pi\) |
−0.459967 | + | 0.887936i | \(0.652139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 44.6035 | − | 137.275i | 0.538565 | − | 1.65753i | −0.197252 | − | 0.980353i | \(-0.563202\pi\) |
0.735817 | − | 0.677180i | \(-0.236798\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.395306 | − | 1.21663i | −0.00410775 | − | 0.0126424i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −78.6996 | + | 108.321i | −0.713478 | + | 0.982018i | 0.286237 | + | 0.958159i | \(0.407595\pi\) |
−0.999715 | + | 0.0238596i | \(0.992405\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −90.2228 | + | 86.5150i | −0.721782 | + | 0.692120i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 25.6086 | − | 35.2472i | 0.182532 | − | 0.251234i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 15.4001 | + | 47.3967i | 0.0986115 | + | 0.303495i | 0.988178 | − | 0.153311i | \(-0.0489935\pi\) |
−0.889567 | + | 0.456806i | \(0.848994\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 46.9860 | − | 144.608i | 0.272224 | − | 0.837819i | −0.717717 | − | 0.696335i | \(-0.754813\pi\) |
0.989941 | − | 0.141483i | \(-0.0451872\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 27.5569 | + | 8.95379i | 0.145365 | + | 0.0472320i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 16.2445 | − | 6.52994i | 0.0784520 | − | 0.0315360i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 246.292 | + | 338.992i | 1.09433 | + | 1.50622i | 0.842693 | + | 0.538394i | \(0.180969\pi\) |
0.251636 | + | 0.967822i | \(0.419031\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 38.3617 | + | 27.8714i | 0.157507 | + | 0.114436i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.27027 | + | 6.00871i | −0.0315024 | + | 0.0228879i | −0.603425 | − | 0.797420i | \(-0.706198\pi\) |
0.571923 | + | 0.820308i | \(0.306198\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 151.479i | − | 0.537219i | −0.963249 | − | 0.268609i | \(-0.913436\pi\) | ||
0.963249 | − | 0.268609i | \(-0.0865641\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 249.397 | + | 156.452i | 0.826176 | + | 0.518278i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 179.302 | − | 58.2587i | 0.556465 | − | 0.180806i | −0.0172651 | − | 0.999851i | \(-0.505496\pi\) |
0.573730 | + | 0.819045i | \(0.305496\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 340.548 | 0.992851 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.6743 | 0.0512732 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −506.519 | + | 164.578i | −1.31275 | + | 0.426538i | −0.879999 | − | 0.474976i | \(-0.842457\pi\) |
−0.432751 | + | 0.901514i | \(0.642457\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −96.6134 | + | 384.608i | −0.236861 | + | 0.942919i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 117.913i | 0.273998i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 448.410 | − | 325.789i | 0.989458 | − | 0.718883i | 0.0296555 | − | 0.999560i | \(-0.490559\pi\) |
0.959802 | + | 0.280677i | \(0.0905590\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −434.696 | − | 315.825i | −0.912413 | − | 0.662907i | 0.0292111 | − | 0.999573i | \(-0.490700\pi\) |
−0.941624 | + | 0.336667i | \(0.890700\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −24.2376 | − | 33.3602i | −0.0484707 | − | 0.0667142i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −344.868 | + | 549.747i | −0.658086 | + | 1.04904i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 620.780 | + | 201.704i | 1.13195 | + | 0.367792i | 0.814315 | − | 0.580423i | \(-0.197113\pi\) |
0.317631 | + | 0.948214i | \(0.397113\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 33.7995 | − | 104.024i | 0.0589707 | − | 0.181493i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −192.972 | − | 593.908i | −0.322558 | − | 0.992731i | −0.972531 | − | 0.232774i | \(-0.925220\pi\) |
0.649973 | − | 0.759957i | \(-0.274780\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −180.947 | + | 249.052i | −0.290113 | + | 0.399306i | −0.929051 | − | 0.369952i | \(-0.879374\pi\) |
0.638938 | + | 0.769258i | \(0.279374\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 48.2568 | − | 89.9916i | 0.0742961 | − | 0.138551i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 32.6472 | − | 44.9350i | 0.0483181 | − | 0.0665042i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −201.806 | − | 621.096i | −0.287405 | − | 0.884541i | −0.985668 | − | 0.168700i | \(-0.946043\pi\) |
0.698263 | − | 0.715842i | \(-0.253957\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 208.707 | − | 642.335i | 0.286292 | − | 0.881118i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1006.07 | − | 326.891i | −1.33048 | − | 0.432300i | −0.444401 | − | 0.895828i | \(-0.646583\pi\) |
−0.886082 | + | 0.463528i | \(0.846583\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.3793 | + | 254.988i | 0.0221770 | + | 0.325381i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −23.9295 | − | 32.9362i | −0.0294887 | − | 0.0405877i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −190.914 | − | 138.707i | −0.227380 | − | 0.165201i | 0.468262 | − | 0.883590i | \(-0.344880\pi\) |
−0.695643 | + | 0.718388i | \(0.744880\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 73.5361 | − | 53.4271i | 0.0847108 | − | 0.0615460i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 124.211i | 0.138495i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1610.03 | + | 109.735i | −1.73880 | + | 0.118512i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −427.524 | + | 138.911i | −0.447510 | + | 0.145405i | −0.524098 | − | 0.851658i | \(-0.675598\pi\) |
0.0765876 | + | 0.997063i | \(0.475598\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 933.997 | 0.948184 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −779.325 | −0.767780 | −0.383890 | − | 0.923379i | \(-0.625416\pi\) | ||||
−0.383890 | + | 0.923379i | \(0.625416\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.2644 | − | 4.95969i | 0.0146024 | − | 0.00474459i | −0.301707 | − | 0.953401i | \(-0.597556\pi\) |
0.316309 | + | 0.948656i | \(0.397556\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.9724 | + | 9.17402i | −0.0101980 | + | 0.00852660i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 192.417i | − | 0.173847i | −0.996215 | − | 0.0869236i | \(-0.972296\pi\) | ||
0.996215 | − | 0.0869236i | \(-0.0277036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 170.017 | − | 123.524i | 0.149400 | − | 0.108546i | −0.510574 | − | 0.859834i | \(-0.670567\pi\) |
0.659974 | + | 0.751288i | \(0.270567\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −276.926 | − | 201.198i | −0.236799 | − | 0.172044i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −625.409 | − | 860.802i | −0.520651 | − | 0.716615i | 0.465019 | − | 0.885301i | \(-0.346048\pi\) |
−0.985670 | + | 0.168686i | \(0.946048\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1451.85 | + | 364.704i | 1.17727 | + | 0.295729i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1453.67 | + | 472.328i | 1.14865 | + | 0.373220i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.0619 | − | 34.0451i | 0.00852139 | − | 0.0262261i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −22.5397 | − | 69.3701i | −0.0169344 | − | 0.0521188i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.90857 | − | 6.75606i | 0.00359830 | − | 0.00495263i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1273.70 | + | 575.170i | 0.911384 | + | 0.411558i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −158.906 | + | 218.716i | −0.111029 | + | 0.152818i | −0.860915 | − | 0.508749i | \(-0.830108\pi\) |
0.749886 | + | 0.661567i | \(0.230108\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 38.2393 | + | 117.688i | 0.0260991 | + | 0.0803248i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −81.9275 | + | 252.147i | −0.0546415 | + | 0.168169i | −0.974653 | − | 0.223722i | \(-0.928179\pi\) |
0.920011 | + | 0.391892i | \(0.128179\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 214.966 | + | 69.8466i | 0.140150 | + | 0.0455374i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −472.427 | − | 118.673i | −0.301186 | − | 0.0756577i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1258.12 | + | 1731.66i | 0.784589 | + | 1.07989i | 0.994761 | + | 0.102229i | \(0.0325976\pi\) |
−0.210172 | + | 0.977664i | \(0.567402\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 649.615 | + | 471.973i | 0.396400 | + | 0.288001i | 0.768073 | − | 0.640362i | \(-0.221216\pi\) |
−0.371673 | + | 0.928364i | \(0.621216\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −124.598 | + | 90.5254i | −0.0744185 | + | 0.0540682i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2058.81i | 1.20396i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 427.456 | − | 357.397i | 0.244816 | − | 0.204691i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −264.581 | + | 85.9675i | −0.148451 | + | 0.0482346i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1322.85 | −0.727329 | −0.363664 | − | 0.931530i | \(-0.618474\pi\) | ||||
−0.363664 | + | 0.931530i | \(0.618474\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3124.98 | 1.68416 | 0.842078 | − | 0.539356i | \(-0.181332\pi\) | ||||
0.842078 | + | 0.539356i | \(0.181332\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 572.496 | − | 186.015i | 0.302507 | − | 0.0982905i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1696.03 | + | 115.597i | −0.878895 | + | 0.0599030i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2679.00i | − | 1.36183i | −0.732363 | − | 0.680915i | \(-0.761582\pi\) | ||
0.732363 | − | 0.680915i | \(-0.238418\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 351.982 | − | 255.730i | 0.175560 | − | 0.127552i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −169.624 | − | 123.239i | −0.0830327 | − | 0.0603268i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1470.51 | + | 2023.99i | 0.706622 | + | 0.972581i | 0.999863 | + | 0.0165430i | \(0.00526605\pi\) |
−0.293241 | + | 0.956038i | \(0.594734\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −22.0285 | − | 323.201i | −0.0103934 | − | 0.152492i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3182.68 | − | 1034.12i | −1.47475 | − | 0.479176i | −0.542211 | − | 0.840242i | \(-0.682413\pi\) |
−0.932540 | + | 0.361066i | \(0.882413\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −362.243 | + | 1114.87i | −0.164881 | + | 0.507451i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1174.53 | + | 3614.82i | 0.525254 | + | 1.61656i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1420.60 | − | 1955.29i | 0.624315 | − | 0.859295i | −0.373343 | − | 0.927693i | \(-0.621789\pi\) |
0.997658 | + | 0.0683977i | \(0.0217887\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −135.478 | − | 141.284i | −0.0585209 | − | 0.0610290i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −266.140 | + | 366.310i | −0.113019 | + | 0.155557i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.32806 | + | 19.4758i | 0.00264235 | + | 0.00813233i | 0.952369 | − | 0.304948i | \(-0.0986391\pi\) |
−0.949727 | + | 0.313080i | \(0.898639\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 495.928 | − | 1526.31i | 0.203658 | − | 0.626794i | −0.796108 | − | 0.605154i | \(-0.793111\pi\) |
0.999766 | − | 0.0216394i | \(-0.00688858\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 417.454 | + | 135.639i | 0.168629 | + | 0.0547908i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2489.54 | − | 3968.52i | 0.989375 | − | 1.57714i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 476.586 | + | 655.964i | 0.186371 | + | 0.256518i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 55.1952 | + | 40.1017i | 0.0212427 | + | 0.0154337i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3149.57 | + | 2288.29i | −1.19317 | + | 0.866886i | −0.993595 | − | 0.112998i | \(-0.963955\pi\) |
−0.199570 | + | 0.979883i | \(0.563955\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4353.01i | − | 1.62351i | −0.584000 | − | 0.811753i | \(-0.698513\pi\) | ||
0.584000 | − | 0.811753i | \(-0.301487\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 129.160 | − | 514.171i | 0.0474324 | − | 0.188823i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4717.04 | + | 1532.66i | −1.70596 | + | 0.554302i | −0.989653 | − | 0.143479i | \(-0.954171\pi\) |
−0.716312 | + | 0.697781i | \(0.754171\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2522.45 | −0.898552 | −0.449276 | − | 0.893393i | \(-0.648318\pi\) | ||||
−0.449276 | + | 0.893393i | \(0.648318\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −533.219 | −0.187116 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −74.2207 | + | 24.1158i | −0.0256614 | + | 0.00833791i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 96.8186 | + | 60.7364i | 0.0329859 | + | 0.0206927i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 3525.73i | − | 1.18384i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4141.85 | + | 3009.23i | −1.37080 | + | 0.995947i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −601.096 | − | 436.722i | −0.196119 | − | 0.142489i | 0.485392 | − | 0.874297i | \(-0.338677\pi\) |
−0.681511 | + | 0.731808i | \(0.738677\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 299.851 | + | 412.709i | 0.0964574 | + | 0.132762i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1571.39 | + | 631.664i | −0.498454 | + | 0.200368i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 226.448 | + | 73.5776i | 0.0708402 | + | 0.0230174i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 77.7121 | − | 239.173i | 0.0239785 | − | 0.0737984i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 410.034 | + | 1261.96i | 0.124805 | + | 0.384110i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −893.614 | + | 1229.95i | −0.268345 | + | 0.369345i | −0.921830 | − | 0.387594i | \(-0.873306\pi\) |
0.653485 | + | 0.756939i | \(0.273306\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 582.992 | − | 3239.54i | 0.172738 | − | 0.959864i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3636.30 | − | 5004.94i | 1.06322 | − | 1.46339i | 0.186456 | − | 0.982463i | \(-0.440300\pi\) |
0.876760 | − | 0.480928i | \(-0.159700\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 228.735 | + | 703.973i | 0.0660053 | + | 0.203143i | 0.978620 | − | 0.205678i | \(-0.0659399\pi\) |
−0.912614 | + | 0.408821i | \(0.865940\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.0212 | + | 43.1527i | −0.00399361 | + | 0.0122911i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3869.85 | + | 1257.39i | 1.08808 | + | 0.353539i | 0.797504 | − | 0.603313i | \(-0.206153\pi\) |
0.290576 | + | 0.956852i | \(0.406153\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1352.03 | − | 1617.07i | −0.375306 | − | 0.448876i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 313.578 | + | 431.602i | 0.0859454 | + | 0.118294i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1509.61 | − | 1096.80i | −0.408571 | − | 0.296844i | 0.364452 | − | 0.931222i | \(-0.381256\pi\) |
−0.773023 | + | 0.634378i | \(0.781256\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1663.23 | + | 1208.40i | −0.444555 | + | 0.322988i | −0.787442 | − | 0.616388i | \(-0.788595\pi\) |
0.342887 | + | 0.939377i | \(0.388595\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1728.07i | 0.456196i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1420.07 | − | 3532.70i | −0.370307 | − | 0.921209i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7968.17 | + | 2589.02i | −2.05264 | + | 0.666944i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 864.160 | 0.219935 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6414.16 | 1.61298 | 0.806490 | − | 0.591247i | \(-0.201364\pi\) | ||||
0.806490 | + | 0.591247i | \(0.201364\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4516.59 | − | 1467.53i | 1.12235 | − | 0.364675i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −77.8713 | − | 193.720i | −0.0191235 | − | 0.0475734i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2669.98i | − | 0.648050i | −0.946048 | − | 0.324025i | \(-0.894964\pi\) | ||
0.946048 | − | 0.324025i | \(-0.105036\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −530.844 | + | 385.680i | −0.127355 | + | 0.0925290i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1061.68 | − | 771.357i | −0.251787 | − | 0.182934i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1834.73 | − | 2525.30i | −0.430169 | − | 0.592077i | 0.537823 | − | 0.843058i | \(-0.319247\pi\) |
−0.967992 | + | 0.250981i | \(0.919247\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3819.43 | + | 4568.14i | 0.885380 | + | 1.05894i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 183.341 | + | 59.5712i | 0.0420236 | + | 0.0136543i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1221.38 | + | 3759.01i | −0.276835 | + | 0.852011i | 0.711893 | + | 0.702288i | \(0.247838\pi\) |
−0.988728 | + | 0.149723i | \(0.952162\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2211.00 | + | 6804.77i | 0.495605 | + | 1.52531i | 0.816012 | + | 0.578035i | \(0.196180\pi\) |
−0.320407 | + | 0.947280i | \(0.603820\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −43.6451 | + | 60.0723i | −0.00967590 | + | 0.0133177i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4392.64 | − | 601.574i | 0.963223 | − | 0.131914i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2073.39 | + | 2853.77i | −0.449739 | + | 0.619013i | −0.972341 | − | 0.233564i | \(-0.924961\pi\) |
0.522602 | + | 0.852577i | \(0.324961\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1237.27 | + | 3807.91i | 0.265495 | + | 0.817111i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −437.184 | + | 1345.52i | −0.0928122 | + | 0.285647i | −0.986677 | − | 0.162689i | \(-0.947983\pi\) |
0.893865 | + | 0.448336i | \(0.147983\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6802.11 | + | 2210.14i | 1.42878 | + | 0.464237i | 0.918379 | − | 0.395702i | \(-0.129499\pi\) |
0.510396 | + | 0.859939i | \(0.329499\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1223.18 | − | 491.691i | 0.254227 | − | 0.102194i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.40931 | − | 12.9508i | −0.00193524 | − | 0.00266363i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3551.93 | − | 2580.63i | −0.722966 | − | 0.525266i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 297.089 | − | 215.847i | 0.0598476 | − | 0.0434818i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 338.223i | − | 0.0674375i | −0.999431 | − | 0.0337188i | \(-0.989265\pi\) | ||
0.999431 | − | 0.0337188i | \(-0.0107351\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5249.45 | − | 3293.09i | −1.03605 | − | 0.649937i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1469.68 | + | 477.529i | −0.287137 | + | 0.0932965i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7771.77 | 1.50319 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 237.209 | 0.0454235 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 605.479 | − | 196.732i | 0.114798 | − | 0.0373002i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1463.58 | + | 5826.34i | −0.274767 | + | 1.09382i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6906.15i | − | 1.28389i | −0.766750 | − | 0.641946i | \(-0.778127\pi\) | ||
0.766750 | − | 0.641946i | \(-0.221873\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.6073 | + | 7.70664i | −0.00195284 | + | 0.00141882i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2107.51 | + | 1531.20i | 0.384264 | + | 0.279184i | 0.763101 | − | 0.646279i | \(-0.223676\pi\) |
−0.378837 | + | 0.925463i | \(0.623676\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1582.88 | + | 2178.64i | 0.285845 | + | 0.393432i | 0.927659 | − | 0.373429i | \(-0.121818\pi\) |
−0.641814 | + | 0.766860i | \(0.721818\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −244.995 | + | 390.542i | −0.0438220 | + | 0.0698558i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9301.43 | + | 3022.22i | 1.64801 | + | 0.535472i | 0.978308 | − | 0.207154i | \(-0.0664201\pi\) |
0.669706 | + | 0.742626i | \(0.266420\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 546.229 | − | 1681.12i | 0.0958714 | − | 0.295062i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 48.5735 | + | 149.494i | 0.00844582 | + | 0.0259936i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1939.44 | + | 2669.41i | −0.334097 | + | 0.459845i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7140.94 | + | 1285.09i | 1.21879 | + | 0.219336i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −100.908 | + | 138.888i | −0.0170649 | + | 0.0234879i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 91.2299 | + | 280.777i | 0.0152877 | + | 0.0470509i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2943.03 | − | 9057.71i | 0.488712 | − | 1.50410i | −0.337821 | − | 0.941210i | \(-0.609690\pi\) |
0.826532 | − | 0.562889i | \(-0.190310\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10493.8 | − | 3409.65i | −1.72690 | − | 0.561103i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −496.240 | − | 7280.82i | −0.0809328 | − | 1.18744i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5377.32 | + | 7401.25i | 0.869203 | + | 1.19635i | 0.979296 | + | 0.202434i | \(0.0648851\pi\) |
−0.110093 | + | 0.993921i | \(0.535115\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 703.197 | + | 510.903i | 0.112662 | + | 0.0818538i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4363.09 | + | 3169.97i | −0.692888 | + | 0.503412i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1070.40i | 0.168502i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1220.05 | + | 83.1549i | −0.190391 | + | 0.0129765i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3784.12 | + | 1229.54i | −0.585425 | + | 0.190216i | −0.586729 | − | 0.809783i | \(-0.699585\pi\) |
0.00130455 | + | 0.999999i | \(0.499585\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12466.3 | −1.91205 | −0.956025 | − | 0.293286i | \(-0.905251\pi\) | ||||
−0.956025 | + | 0.293286i | \(0.905251\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2528.91 | −0.384567 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4554.49 | + | 1479.84i | −0.686718 | + | 0.223128i | −0.631534 | − | 0.775348i | \(-0.717574\pi\) |
−0.0551835 | + | 0.998476i | \(0.517574\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5356.27 | + | 4478.39i | −0.800792 | + | 0.669545i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 29.2430i | 0.00433531i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6367.03 | − | 4625.92i | 0.936042 | − | 0.680074i | −0.0114230 | − | 0.999935i | \(-0.503636\pi\) |
0.947465 | + | 0.319861i | \(0.103636\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11306.0 | − | 8214.29i | −1.64835 | − | 1.19759i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 35.0234 | + | 48.2056i | 0.00506405 | + | 0.00697007i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3338.11 | + | 838.531i | 0.478697 | + | 0.120249i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1605.00 | + | 521.497i | 0.228285 | + | 0.0741742i | 0.420926 | − | 0.907095i | \(-0.361705\pi\) |
−0.192641 | + | 0.981269i | \(0.561705\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 83.1839 | − | 256.014i | 0.0117355 | − | 0.0361180i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −257.720 | − | 793.181i | −0.0360651 | − | 0.110997i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5649.85 | − | 7776.35i | 0.784285 | − | 1.07948i | −0.210512 | − | 0.977591i | \(-0.567513\pi\) |
0.994796 | − | 0.101884i | \(-0.0324870\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1134.76 | − | 125.334i | −0.156264 | − | 0.0172593i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1700.31 | − | 2340.27i | 0.232282 | − | 0.319708i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3329.83 | − | 10248.2i | −0.451298 | − | 1.38895i | −0.875427 | − | 0.483350i | \(-0.839420\pi\) |
0.424129 | − | 0.905602i | \(-0.360580\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 68.2462 | − | 210.040i | 0.00917680 | − | 0.0282433i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7462.73 | − | 2424.79i | −0.995634 | − | 0.323501i | −0.234515 | − | 0.972113i | \(-0.575350\pi\) |
−0.761120 | + | 0.648611i | \(0.775350\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −602.275 | − | 151.291i | −0.0797268 | − | 0.0200273i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2344.59 | + | 3227.05i | 0.307965 | + | 0.423877i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11716.3 | + | 8512.42i | 1.52710 | + | 1.10950i | 0.957824 | + | 0.287357i | \(0.0927764\pi\) |
0.569276 | + | 0.822146i | \(0.307224\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2476.18 | − | 1799.05i | 0.320271 | − | 0.232691i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 216.581i | − | 0.0277992i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5601.47 | + | 4683.41i | −0.713520 | + | 0.596576i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10826.5 | + | 3517.73i | −1.36868 | + | 0.444710i | −0.898931 | − | 0.438091i | \(-0.855655\pi\) |
−0.469747 | + | 0.882801i | \(0.655655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −184.645 | −0.0231674 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9387.67 | 1.16907 | 0.584536 | − | 0.811368i | \(-0.301277\pi\) | ||||
0.584536 | + | 0.811368i | \(0.301277\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8393.80 | + | 2727.31i | −1.03753 | + | 0.337114i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7533.62 | + | 513.470i | −0.924318 | + | 0.0629988i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 14862.2i | − | 1.81005i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2771.64 | − | 2013.71i | 0.335082 | − | 0.243452i | −0.407502 | − | 0.913204i | \(-0.633600\pi\) |
0.742584 | + | 0.669753i | \(0.233600\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1414.61 | − | 1027.77i | −0.169775 | − | 0.123349i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 510.168 | + | 702.186i | 0.0607838 | + | 0.0836618i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 804.230 | + | 11799.6i | 0.0951279 | + | 1.39571i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −623.847 | − | 202.700i | −0.0732612 | − | 0.0238040i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4711.09 | − | 14499.2i | 0.549288 | − | 1.69053i | −0.161282 | − | 0.986908i | \(-0.551563\pi\) |
0.710570 | − | 0.703626i | \(-0.248437\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1380.41 | − | 4248.48i | −0.159804 | − | 0.491825i | 0.838812 | − | 0.544421i | \(-0.183250\pi\) |
−0.998616 | + | 0.0525960i | \(0.983250\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2918.04 | + | 4016.34i | −0.335414 | + | 0.461658i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2572.67 | − | 1243.58i | 0.293630 | − | 0.141935i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 494.566 | − | 680.711i | 0.0560508 | − | 0.0771474i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −519.724 | − | 1599.55i | −0.0584907 | − | 0.180016i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2231.16 | − | 6866.80i | 0.249353 | − | 0.767430i | −0.745537 | − | 0.666464i | \(-0.767807\pi\) |
0.994890 | − | 0.100965i | \(-0.0321932\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3036.92 | − | 986.754i | −0.337055 | − | 0.109516i | 0.135599 | − | 0.990764i | \(-0.456704\pi\) |
−0.472654 | + | 0.881248i | \(0.656704\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −241.881 | + | 385.578i | −0.0266605 | + | 0.0424990i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11359.5 | + | 15635.0i | 1.24347 | + | 1.71149i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1051.45 | + | 763.925i | 0.114312 | + | 0.0830527i | 0.643473 | − | 0.765469i | \(-0.277493\pi\) |
−0.529160 | + | 0.848522i | \(0.677493\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7254.88 | + | 5270.98i | −0.783380 | + | 0.569159i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4847.79i | 0.519923i | 0.965619 | + | 0.259961i | \(0.0837098\pi\) | ||||
−0.965619 | + | 0.259961i | \(0.916290\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −642.786 | + | 2558.87i | −0.0684742 | + | 0.272589i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1027.76 | − | 333.938i | 0.108750 | − | 0.0353350i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2344.41 | 0.246414 | 0.123207 | − | 0.992381i | \(-0.460682\pi\) | ||||
0.123207 | + | 0.992381i | \(0.460682\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 362.588 | 0.0378572 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2427.88 | + | 788.867i | −0.251814 | + | 0.0818195i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −860.874 | − | 540.044i | −0.0886998 | − | 0.0556432i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8691.80i | 0.889684i | 0.895609 | + | 0.444842i | \(0.146740\pi\) | ||||
−0.895609 | + | 0.444842i | \(0.853260\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −805.742 | + | 585.406i | −0.0819365 | + | 0.0595303i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10813.3 | − | 7856.33i | −1.09246 | − | 0.793722i | −0.112651 | − | 0.993635i | \(-0.535934\pi\) |
−0.979814 | + | 0.199913i | \(0.935934\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2697.04 | − | 3712.16i | −0.270718 | − | 0.372611i | 0.651914 | − | 0.758293i | \(-0.273966\pi\) |
−0.922632 | + | 0.385682i | \(0.873966\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1288.51 | − | 517.955i | 0.128502 | − | 0.0516551i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18131.8 | + | 5891.39i | 1.79666 | + | 0.583770i | 0.999792 | − | 0.0203823i | \(-0.00648834\pi\) |
0.796869 | + | 0.604153i | \(0.206488\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −315.857 | + | 972.109i | −0.0310979 | + | 0.0957096i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 676.283 | + | 2081.39i | 0.0661602 | + | 0.203620i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3158.08 | + | 4346.72i | −0.306995 | + | 0.422543i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7852.13 | + | 16244.2i | 0.758485 | + | 1.56913i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8243.33 | − | 11346.0i | 0.791271 | − | 1.08909i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4236.57 | + | 13038.8i | 0.404120 | + | 1.24375i | 0.921627 | + | 0.388076i | \(0.126860\pi\) |
−0.517507 | + | 0.855679i | \(0.673140\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7515.89 | − | 23131.5i | 0.712464 | − | 2.19274i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 162.896 | + | 52.9282i | 0.0153458 | + | 0.00498616i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3223.77 | + | 3855.71i | 0.301822 | + | 0.360987i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6580.50 | + | 9057.28i | 0.612302 | + | 0.842761i | 0.996764 | − | 0.0803794i | \(-0.0256132\pi\) |
−0.384463 | + | 0.923141i | \(0.625613\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1653.41 | − | 1201.27i | −0.152904 | − | 0.111091i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8449.70 | + | 6139.07i | −0.776639 | + | 0.564261i | −0.903968 | − | 0.427599i | \(-0.859359\pi\) |
0.127329 | + | 0.991860i | \(0.459359\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1139.24i | − | 0.104074i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3894.73 | − | 9688.90i | −0.353647 | − | 0.879765i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 930.028 | − | 302.184i | 0.0839385 | − | 0.0272733i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13219.1 | 1.18591 | 0.592955 | − | 0.805236i | \(-0.297961\pi\) | ||||
0.592955 | + | 0.805236i | \(0.297961\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2733.76 | 0.243784 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10619.1 | − | 3450.37i | 0.941320 | − | 0.305853i | 0.202136 | − | 0.979357i | \(-0.435212\pi\) |
0.739184 | + | 0.673504i | \(0.235212\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3249.76 | + | 8084.40i | 0.286361 | + | 0.712378i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 957.617i | − | 0.0838841i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8386.76 | − | 6093.34i | 0.730328 | − | 0.530614i | −0.159339 | − | 0.987224i | \(-0.550936\pi\) |
0.889667 | + | 0.456610i | \(0.150936\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −390.002 | − | 283.353i | −0.0337626 | − | 0.0245300i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3696.34 | − | 5087.58i | −0.318124 | − | 0.437860i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −115.102 | − | 137.665i | −0.00984852 | − | 0.0117791i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6359.68 | − | 2066.38i | −0.541003 | − | 0.175782i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −610.113 | + | 1877.73i | −0.0516011 | + | 0.158812i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5294.58 | + | 16295.0i | 0.445220 | + | 1.37025i | 0.882242 | + | 0.470795i | \(0.156033\pi\) |
−0.437023 | + | 0.899451i | \(0.643967\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5599.83 | + | 7707.51i | −0.468190 | + | 0.644409i | −0.976182 | − | 0.216953i | \(-0.930388\pi\) |
0.507992 | + | 0.861362i | \(0.330388\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 140.922 | + | 75.5675i | 0.0117149 | + | 0.00628197i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2043.04 | + | 2812.00i | −0.168873 | + | 0.232434i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1779.94 | − | 5478.08i | −0.146292 | − | 0.450241i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4510.19 | + | 13880.9i | −0.368598 | + | 1.13443i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 564.332 | + | 183.363i | 0.0458610 | + | 0.0149012i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1996.05 | + | 802.372i | −0.161303 | + | 0.0648403i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.83288 | − | 13.5338i | −0.000790168 | − | 0.00108757i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9772.07 | − | 7099.82i | −0.780914 | − | 0.567367i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4918.39 | − | 3573.42i | 0.390865 | − | 0.283980i | −0.374945 | − | 0.927047i | \(-0.622338\pi\) |
0.765810 | + | 0.643067i | \(0.222338\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1311.02i | 0.103612i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1990.36 | − | 1248.59i | −0.156436 | − | 0.0981354i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20873.4 | + | 6782.18i | −1.63160 | + | 0.530138i | −0.974638 | − | 0.223789i | \(-0.928157\pi\) |
−0.656958 | + | 0.753927i | \(0.728157\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14148.9 | 1.09993 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7193.30 | 0.556161 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 972.603 | − | 316.018i | 0.0747907 | − | 0.0243010i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −932.379 | + | 3711.71i | −0.0713104 | + | 0.283880i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 16112.7i | − | 1.22571i | −0.790197 | − | 0.612853i | \(-0.790022\pi\) | ||
0.790197 | − | 0.612853i | \(-0.209978\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7113.41 | + | 5168.19i | −0.538220 | + | 0.391040i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −535.863 | − | 389.327i | −0.0403282 | − | 0.0293002i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5589.19 | − | 7692.85i | −0.418394 | − | 0.575871i | 0.546846 | − | 0.837233i | \(-0.315828\pi\) |
−0.965241 | + | 0.261362i | \(0.915828\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6321.68 | + | 10077.3i | −0.470717 | + | 0.750360i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1005.86 | + | 326.824i | 0.0745013 | + | 0.0242069i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3051.12 | + | 9390.39i | −0.224797 | + | 0.691855i | 0.773515 | + | 0.633778i | \(0.218497\pi\) |
−0.998312 | + | 0.0580769i | \(0.981503\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5095.76 | − | 15683.1i | −0.373469 | − | 1.14942i | −0.944506 | − | 0.328495i | \(-0.893459\pi\) |
0.571037 | − | 0.820925i | \(-0.306541\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1869.33 | − | 2572.91i | 0.136287 | − | 0.187583i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2270.87 | − | 16581.7i | −0.164699 | − | 1.20262i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −233.579 | + | 321.494i | −0.0168527 | + | 0.0231958i | −0.817360 | − | 0.576127i | \(-0.804563\pi\) |
0.800508 | + | 0.599323i | \(0.204563\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1098.87 | + | 3381.97i | 0.0788730 | + | 0.242746i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 511.893 | − | 1575.45i | 0.0365523 | − | 0.112497i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17965.8 | + | 5837.44i | 1.27627 | + | 0.414686i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1162.04 | − | 17049.4i | −0.0821272 | − | 1.20497i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2390.55 | − | 3290.30i | −0.168089 | − | 0.231355i | 0.716660 | − | 0.697423i | \(-0.245670\pi\) |
−0.884749 | + | 0.466068i | \(0.845670\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17755.4 | − | 12900.0i | −1.24210 | − | 0.902440i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3277.89 | − | 2381.53i | 0.228146 | − | 0.165758i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11135.7i | − | 0.771146i | −0.922677 | − | 0.385573i | \(-0.874004\pi\) | ||
0.922677 | − | 0.385573i | \(-0.125996\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −399.298 | + | 27.2150i | −0.0275120 | + | 0.00187514i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1959.76 | − | 636.765i | 0.134351 | − | 0.0436533i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12279.4 | −0.837603 | −0.418801 | − | 0.908078i | \(-0.637550\pi\) | ||||
−0.418801 | + | 0.908078i | \(0.637550\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1971.50 | −0.133809 | −0.0669045 | − | 0.997759i | \(-0.521312\pi\) | ||||
−0.0669045 | + | 0.997759i | \(0.521312\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16346.8 | + | 5311.40i | −1.10397 | + | 0.358701i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −625.627 | + | 523.088i | −0.0420419 | + | 0.0351513i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3978.46i | 0.266031i | 0.991114 | + | 0.133015i | \(0.0424660\pi\) | ||||
−0.991114 | + | 0.133015i | \(0.957534\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 51.5763 | − | 37.4724i | 0.00343182 | − | 0.00249336i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8853.24 | − | 6432.25i | −0.586192 | − | 0.425894i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11232.2 | + | 15459.8i | 0.740073 | + | 1.01862i | 0.998614 | + | 0.0526227i | \(0.0167581\pi\) |
−0.258542 | + | 0.966000i | \(0.583242\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −90.5532 | − | 22.7469i | −0.00593733 | − | 0.00149145i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −112.138 | − | 36.4359i | −0.00731687 | − | 0.00237740i | 0.305356 | − | 0.952238i | \(-0.401224\pi\) |
−0.312673 | + | 0.949861i | \(0.601224\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 195.101 | − | 600.460i | 0.0126685 | − | 0.0389895i | −0.944522 | − | 0.328447i | \(-0.893475\pi\) |
0.957191 | + | 0.289457i | \(0.0934748\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1802.62 | + | 5547.88i | 0.116484 | + | 0.358500i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 217.208 | − | 298.961i | 0.0139683 | − | 0.0192257i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 655.302 | − | 15611.3i | 0.0419393 | − | 0.999120i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2458.27 | − | 3383.52i | 0.156577 | − | 0.215510i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2959.96 | − | 9109.82i | −0.187633 | − | 0.577476i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2807.17 | + | 8639.59i | −0.177103 | + | 0.545066i | −0.999723 | − | 0.0235248i | \(-0.992511\pi\) |
0.822621 | + | 0.568591i | \(0.192511\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 577.253 | + | 187.561i | 0.0362461 | + | 0.0117771i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2931.50 | + | 736.392i | 0.183202 | + | 0.0460202i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11618.8 | − | 15992.0i | −0.722693 | − | 0.994702i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13303.5 | + | 9665.54i | 0.823595 | + | 0.598377i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3651.45 | + | 2652.93i | −0.224998 | + | 0.163470i | −0.694573 | − | 0.719422i | \(-0.744407\pi\) |
0.469576 | + | 0.882892i | \(0.344407\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 6553.26i | − | 0.401921i | −0.979599 | − | 0.200961i | \(-0.935594\pi\) | ||
0.979599 | − | 0.200961i | \(-0.0644063\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1061.40 | − | 887.436i | 0.0647944 | − | 0.0541748i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6759.24 | + | 2196.21i | −0.410716 | + | 0.133450i | −0.507085 | − | 0.861896i | \(-0.669277\pi\) |
0.0963691 | + | 0.995346i | \(0.469277\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19659.3 | −1.18905 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −194.508 | −0.0117102 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13453.8 | + | 4371.40i | −0.806259 | + | 0.261969i | −0.683013 | − | 0.730407i | \(-0.739331\pi\) |
−0.123247 | + | 0.992376i | \(0.539331\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2957.30 | − | 201.561i | 0.176414 | − | 0.0120239i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 8106.39i | − | 0.481370i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14599.7 | + | 10607.3i | −0.863012 | + | 0.627015i | −0.928703 | − | 0.370825i | \(-0.879075\pi\) |
0.0656910 | + | 0.997840i | \(0.479075\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22268.2 | + | 16178.8i | 1.31034 | + | 0.952017i | 0.999999 | + | 0.00139082i | \(0.000442713\pi\) |
0.310339 | + | 0.950626i | \(0.399557\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −637.133 | − | 876.939i | −0.0373216 | − | 0.0513687i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −171.840 | − | 2521.23i | −0.0100205 | − | 0.147021i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6346.03 | − | 2061.95i | −0.368395 | − | 0.119699i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 383.785 | − | 1181.17i | 0.0221793 | − | 0.0682610i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5889.27 | + | 18125.3i | 0.338827 | + | 1.04280i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13288.0 | − | 18289.3i | 0.761091 | − | 1.04755i | −0.236032 | − | 0.971745i | \(-0.575847\pi\) |
0.997123 | − | 0.0758065i | \(-0.0241531\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 738.934 | + | 5395.63i | 0.0421357 | + | 0.307671i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8113.39 | + | 11167.1i | −0.460595 | + | 0.633954i | −0.974632 | − | 0.223813i | \(-0.928149\pi\) |
0.514037 | + | 0.857768i | \(0.328149\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −217.527 | − | 669.480i | −0.0122944 | − | 0.0378384i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1561.70 | + | 4806.42i | −0.0878774 | + | 0.270459i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7746.21 | − | 2516.90i | −0.433969 | − | 0.141005i | 0.0838826 | − | 0.996476i | \(-0.473268\pi\) |
−0.517851 | + | 0.855471i | \(0.673268\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12717.2 | − | 20272.2i | 0.709341 | − | 1.13075i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −355.420 | − | 489.194i | −0.0197382 | − | 0.0271673i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25010.0 | + | 18170.8i | 1.38288 | + | 1.00472i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5632.18 | + | 4092.02i | −0.310070 | + | 0.225279i | −0.731926 | − | 0.681384i | \(-0.761379\pi\) |
0.421857 | + | 0.906662i | \(0.361379\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1462.59i | 0.0801719i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2187.18 | − | 8706.95i | 0.119373 | − | 0.475213i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 222.249 | − | 72.2131i | 0.0120779 | − | 0.00392434i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3324.01 | −0.179865 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17301.5 | −0.932193 | −0.466096 | − | 0.884734i | \(-0.654340\pi\) | ||||
−0.466096 | + | 0.884734i | \(0.654340\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 57520.8 | − | 18689.6i | 3.08597 | − | 1.00269i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1458.64 | + | 915.037i | 0.0779229 | + | 0.0488827i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 1220.38i | − | 0.0649182i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10399.9 | + | 7555.96i | −0.550883 | + | 0.400240i | −0.828111 | − | 0.560564i | \(-0.810584\pi\) |
0.277228 | + | 0.960804i | \(0.410584\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13912.5 | + | 10108.0i | 0.733838 | + | 0.533165i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11966.3 | + | 16470.2i | 0.628528 | + | 0.865094i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21357.3 | − | 8585.18i | 1.11709 | − | 0.449045i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1449.73 | + | 471.046i | 0.0755107 | + | 0.0245349i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7217.90 | + | 22214.4i | −0.374384 | + | 1.15224i | 0.569509 | + | 0.821985i | \(0.307133\pi\) |
−0.943893 | + | 0.330251i | \(0.892867\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.76661 | + | 23.9032i | 0.000401170 | + | 0.00123468i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 987.157 | − | 1358.70i | 0.0507784 | − | 0.0698904i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5489.97 | − | 2943.92i | −0.281231 | − | 0.150806i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13476.7 | + | 18549.0i | −0.687513 | + | 0.946281i | −0.999993 | − | 0.00364359i | \(-0.998840\pi\) |
0.312480 | + | 0.949924i | \(0.398840\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5198.86 | + | 16000.5i | 0.264130 | + | 0.812907i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1070.06 | + | 3293.30i | −0.0541417 | + | 0.166631i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20805.6 | + | 6760.13i | 1.04839 | + | 0.340643i | 0.782037 | − | 0.623232i | \(-0.214181\pi\) |
0.266354 | + | 0.963875i | \(0.414181\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1995.08 | + | 2386.17i | 0.100122 | + | 0.119749i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13608.2 | − | 18730.1i | −0.680142 | − | 0.936136i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20466.3 | − | 14869.7i | −1.01876 | − | 0.740175i | −0.0527349 | − | 0.998609i | \(-0.516794\pi\) |
−0.966029 | + | 0.258433i | \(0.916794\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5537.12 | − | 4022.95i | 0.274509 | − | 0.199442i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3971.78i | 0.196111i | 0.995181 | + | 0.0980555i | \(0.0312623\pi\) | ||||
−0.995181 | + | 0.0980555i | \(0.968738\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5516.23 | + | 13722.7i | 0.271274 | + | 0.674846i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 26492.4 | − | 8607.90i | 1.29760 | − | 0.421615i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 301.315 | 0.0146993 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31873.9 | 1.54873 | 0.774364 | − | 0.632740i | \(-0.218070\pi\) | ||||
0.774364 | + | 0.632740i | \(0.218070\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4983.33 | + | 1619.18i | −0.241172 | + | 0.0783616i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13031.1 | − | 32417.3i | −0.628145 | − | 1.56263i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 4967.00i | − | 0.238479i | −0.992866 | − | 0.119239i | \(-0.961954\pi\) | ||
0.992866 | − | 0.119239i | \(-0.0380456\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3138.60 | + | 2280.33i | −0.150097 | + | 0.109052i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20275.8 | + | 14731.2i | 0.965829 | + | 0.701716i | 0.954497 | − | 0.298220i | \(-0.0963928\pi\) |
0.0113320 | + | 0.999936i | \(0.496393\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 193.433 | + | 266.237i | 0.00917789 | + | 0.0126323i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4316.93 | − | 5163.16i | −0.204025 | − | 0.244019i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −30597.8 | − | 9941.83i | −1.44045 | − | 0.468029i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4397.19 | − | 13533.2i | 0.206199 | − | 0.634615i | −0.793463 | − | 0.608618i | \(-0.791724\pi\) |
0.999662 | − | 0.0259965i | \(-0.00827587\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 674.007 | + | 2074.38i | 0.0314835 | + | 0.0968963i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14147.6 | + | 19472.5i | −0.658283 | + | 0.906049i | −0.999423 | − | 0.0339639i | \(-0.989187\pi\) |
0.341140 | + | 0.940012i | \(0.389187\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8271.56 | + | 17111.9i | 0.383385 | + | 0.793134i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 315.066 | − | 433.651i | 0.0145469 | − | 0.0200221i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 455.964 | + | 1403.31i | 0.0209713 | + | 0.0645429i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6844.56 | + | 21065.4i | −0.313595 | + | 0.965146i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2064.98 | + | 670.952i | 0.0942481 | + | 0.0306231i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −27790.8 | + | 11171.3i | −1.26356 | + | 0.507926i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13080.1 | + | 18003.2i | 0.592445 | + | 0.815430i | 0.994990 | − | 0.0999696i | \(-0.0318746\pi\) |
−0.402546 | + | 0.915400i | \(0.631875\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2062.94 | + | 1498.81i | 0.0930830 | + | 0.0676288i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1347.97 | − | 979.358i | 0.0605920 | − | 0.0440227i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31188.5i | 1.39664i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4120.59 | − | 2584.93i | −0.183827 | − | 0.115318i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1809.10 | − | 587.811i | 0.0804033 | − | 0.0261246i | −0.268539 | − | 0.963269i | \(-0.586541\pi\) |
0.348942 | + | 0.937144i | \(0.386541\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4309.73 | −0.190822 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6214.05 | 0.274111 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10384.6 | − | 3374.16i | 0.456369 | − | 0.148283i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −571.107 | + | 2273.52i | −0.0250048 | + | 0.0995416i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 3228.80i | − | 0.140842i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11667.8 | − | 8477.13i | 0.507067 | − | 0.368405i | −0.304643 | − | 0.952467i | \(-0.598537\pi\) |
0.811710 | + | 0.584061i | \(0.198537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30961.9 | − | 22495.1i | −1.34059 | − | 0.973995i | −0.999422 | − | 0.0339929i | \(-0.989178\pi\) |
−0.341168 | − | 0.940003i | \(-0.610822\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3435.58 | − | 4728.67i | −0.148205 | − | 0.203987i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14864.0 | − | 23694.4i | 0.638851 | − | 1.01838i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20794.4 | − | 6756.51i | −0.890458 | − | 0.289327i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −739.640 | + | 2276.38i | −0.0315569 | + | 0.0971221i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3651.70 | + | 11238.8i | 0.155231 | + | 0.477753i | 0.998184 | − | 0.0602342i | \(-0.0191847\pi\) |
−0.842953 | + | 0.537988i | \(0.819185\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21930.1 | − | 30184.2i | 0.928841 | − | 1.27844i | −0.0314693 | − | 0.999505i | \(-0.510019\pi\) |
0.960310 | − | 0.278935i | \(-0.0899814\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3260.90 | + | 1576.25i | −0.137612 | + | 0.0665189i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19099.6 | − | 26288.3i | 0.803092 | − | 1.10536i | −0.189261 | − | 0.981927i | \(-0.560609\pi\) |
0.992353 | − | 0.123434i | \(-0.0393907\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 191.414 | + | 589.110i | 0.00801938 | + | 0.0246811i | 0.954986 | − | 0.296650i | \(-0.0958696\pi\) |
−0.946967 | + | 0.321332i | \(0.895870\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 890.467 | − | 2740.58i | 0.0371720 | − | 0.114404i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7403.82 | − | 2405.65i | −0.307956 | − | 0.100061i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2544.18 | + | 37328.1i | 0.105443 | + | 1.54706i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3893.78 | − | 5359.33i | −0.160799 | − | 0.221321i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5672.36 | − | 4121.21i | −0.233411 | − | 0.169583i | 0.464932 | − | 0.885346i | \(-0.346079\pi\) |
−0.698343 | + | 0.715764i | \(0.746079\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17721.8 | − | 12875.7i | 0.726632 | − | 0.527929i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 1155.73i | − | 0.0472188i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13075.7 | − | 891.206i | 0.532331 | − | 0.0362821i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 108.630 | − | 35.2960i | 0.00440680 | − | 0.00143186i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5842.67 | −0.236184 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −56103.0 | −2.25991 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5373.09 | + | 1745.82i | −0.215676 | + | 0.0700772i | −0.414862 | − | 0.909884i | \(-0.636170\pi\) |
0.199186 | + | 0.979962i | \(0.436170\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 32601.0 | − | 27257.8i | 1.30401 | − | 1.09029i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16445.6i | 0.655509i | 0.944763 | + | 0.327755i | \(0.106292\pi\) | ||||
−0.944763 | + | 0.327755i | \(0.893708\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8964.34 | + | 6512.97i | −0.356064 | + | 0.258696i | −0.751409 | − | 0.659837i | \(-0.770625\pi\) |
0.395344 | + | 0.918533i | \(0.370625\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.5796 | + | 7.68655i | 0.000418761 | + | 0.000304247i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23136.3 | − | 31844.4i | −0.912594 | − | 1.25608i | −0.966273 | − | 0.257520i | \(-0.917095\pi\) |
0.0536791 | − | 0.998558i | \(-0.482905\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26207.3 | − | 6583.25i | −1.03014 | − | 0.258772i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3411.04 | + | 1108.32i | 0.133616 | + | 0.0434145i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7157.90 | + | 22029.7i | −0.279419 | + | 0.859963i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11707.9 | − | 36033.3i | −0.455463 | − | 1.40177i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6957.74 | − | 9576.50i | 0.269741 | − | 0.371266i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −900.685 | + | 1994.54i | −0.0347985 | + | 0.0770603i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5869.40 | + | 8078.53i | −0.225993 | + | 0.311052i | −0.906923 | − | 0.421296i | \(-0.861575\pi\) |
0.680931 | + | 0.732348i | \(0.261575\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 85.3806 | + | 262.775i | 0.00327624 | + | 0.0100832i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6916.28 | + | 21286.1i | −0.264490 | + | 0.814015i | 0.727321 | + | 0.686297i | \(0.240765\pi\) |
−0.991811 | + | 0.127718i | \(0.959235\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31096.3 | − | 10103.8i | −1.18514 | − | 0.385074i | −0.350863 | − | 0.936427i | \(-0.614112\pi\) |
−0.834272 | + | 0.551353i | \(0.814112\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4909.75 | + | 1233.33i | 0.186485 | + | 0.0468450i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14028.5 | − | 19308.6i | −0.531039 | − | 0.730912i | 0.456249 | − | 0.889852i | \(-0.349193\pi\) |
−0.987288 | + | 0.158940i | \(0.949193\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −342.497 | − | 248.839i | −0.0129212 | − | 0.00938783i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19380.4 | + | 14080.7i | −0.728697 | + | 0.529429i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 27212.2i | − | 1.01973i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 175.646 | − | 146.858i | 0.00655999 | − | 0.00548483i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6038.10 | + | 1961.90i | −0.224756 | + | 0.0730277i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7577.54 | 0.281118 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12174.8 | 0.450167 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −184.294 | + | 59.8807i | −0.00679171 | + | 0.00220676i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17901.3 | + | 1220.10i | −0.657524 | + | 0.0448150i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50126.6i | 1.83509i | 0.397634 | + | 0.917544i | \(0.369831\pi\) | ||||
−0.397634 | + | 0.917544i | \(0.630169\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16602.4 | − | 12062.4i | 0.605794 | − | 0.440135i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15483.8 | + | 11249.7i | 0.563120 | + | 0.409131i | 0.832599 | − | 0.553876i | \(-0.186852\pi\) |
−0.269480 | + | 0.963006i | \(0.586852\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22054.1 | + | 30354.9i | 0.799435 | + | 1.10033i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −333.705 | − | 4896.11i | −0.0120568 | − | 0.176897i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −394.848 | − | 128.294i | −0.0142192 | − | 0.00462011i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1119.36 | + | 3445.05i | −0.0401789 | + | 0.123658i | −0.969134 | − | 0.246534i | \(-0.920708\pi\) |
0.928955 | + | 0.370192i | \(0.120708\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1743.38 | + | 5365.57i | 0.0623739 | + | 0.191967i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21305.8 | + | 29324.9i | −0.759793 | + | 1.04576i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −51549.1 | − | 9276.84i | −1.83235 | − | 0.329752i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −248.420 | + | 341.920i | −0.00880169 | + | 0.0121145i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15796.1 | − | 48615.5i | −0.557863 | − | 1.71692i | −0.688261 | − | 0.725463i | \(-0.741626\pi\) |
0.130399 | − | 0.991462i | \(-0.458374\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15189.6 | − | 46748.8i | 0.534715 | − | 1.64568i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2023.92 | − | 657.611i | −0.0710183 | − | 0.0230753i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4817.35 | − | 7679.25i | 0.168497 | − | 0.268597i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13605.4 | − | 18726.2i | −0.474352 | − | 0.652889i | 0.503055 | − | 0.864254i | \(-0.332209\pi\) |
−0.977407 | + | 0.211365i | \(0.932209\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1779.75 | − | 1293.07i | −0.0618531 | − | 0.0449389i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16989.1 | − | 12343.3i | 0.588553 | − | 0.427609i | −0.253245 | − | 0.967402i | \(-0.581498\pi\) |
0.841797 | + | 0.539794i | \(0.181498\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1368.72i | − | 0.0472660i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 185.836 | − | 739.795i | 0.00639709 | − | 0.0254662i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 49202.7 | − | 15986.9i | 1.68836 | − | 0.548580i | 0.701853 | − | 0.712322i | \(-0.252356\pi\) |
0.986503 | + | 0.163742i | \(0.0523564\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17868.9 | 0.611223 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7989.46 | −0.272425 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42977.6 | + | 13964.3i | −1.46084 | + | 0.474656i | −0.928327 | − | 0.371765i | \(-0.878753\pi\) |
−0.532514 | + | 0.846421i | \(0.678753\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36871.4 | + | 23130.2i | 1.24935 | + | 0.783745i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1444.00i | 0.0487751i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2711.68 | + | 1970.15i | −0.0913084 | + | 0.0663394i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5397.62 | + | 3921.60i | 0.181183 | + | 0.131637i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2978.22 | + | 4099.17i | 0.0996592 | + | 0.137169i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −45156.4 | + | 18151.9i | −1.50636 | + | 0.605524i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17108.4 | + | 5558.85i | 0.568944 | + | 0.184861i | 0.579342 | − | 0.815085i | \(-0.303310\pi\) |
−0.0103977 | + | 0.999946i | \(0.503310\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 832.940 | − | 2563.53i | 0.0276139 | − | 0.0849869i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7140.12 | − | 21975.0i | −0.235981 | − | 0.726274i | −0.996990 | − | 0.0775329i | \(-0.975296\pi\) |
0.761009 | − | 0.648741i | \(-0.224704\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −739.084 | + | 1017.26i | −0.0243514 | + | 0.0335169i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5872.39 | + | 804.227i | −0.192889 | + | 0.0264163i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12740.7 | − | 17536.0i | 0.417206 | − | 0.574235i | −0.547751 | − | 0.836641i | \(-0.684516\pi\) |
0.964958 | + | 0.262406i | \(0.0845160\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2586.50 | + | 7960.44i | 0.0844382 | + | 0.259874i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1710.06 | + | 5263.02i | −0.0556554 | + | 0.171290i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20330.0 | + | 6605.62i | 0.659641 | + | 0.214330i | 0.619660 | − | 0.784870i | \(-0.287270\pi\) |
0.0399806 | + | 0.999200i | \(0.487270\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35569.1 | + | 42541.5i | 1.15058 | + | 1.37613i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −141.758 | − | 195.113i | −0.00457164 | − | 0.00629232i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16408.4 | + | 11921.4i | 0.527559 | + | 0.383294i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21169.5 | − | 15380.5i | 0.678578 | − | 0.493016i | −0.194308 | − | 0.980941i | \(-0.562246\pi\) |
0.872886 | + | 0.487925i | \(0.162246\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7780.12i | 0.248635i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10518.5 | + | 26166.9i | 0.335136 | + | 0.833714i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31795.7 | − | 10331.1i | 1.01001 | − | 0.328173i | 0.243152 | − | 0.969988i | \(-0.421819\pi\) |
0.766859 | + | 0.641816i | \(0.221819\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18255.7 | 0.578164 |
(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 | 100.4.i.a.9.4 | ✓ | 32 | |
5.2 | odd | 4 | 500.4.g.b.201.9 | 64 | |||
5.3 | odd | 4 | 500.4.g.b.201.8 | 64 | |||
5.4 | even | 2 | 500.4.i.a.49.5 | 32 | |||
25.2 | odd | 20 | 500.4.g.b.301.9 | 64 | |||
25.8 | odd | 20 | 2500.4.a.g.1.16 | 32 | |||
25.11 | even | 5 | 500.4.i.a.449.5 | 32 | |||
25.14 | even | 10 | inner | 100.4.i.a.89.4 | yes | 32 | |
25.17 | odd | 20 | 2500.4.a.g.1.17 | 32 | |||
25.23 | odd | 20 | 500.4.g.b.301.8 | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
100.4.i.a.9.4 | ✓ | 32 | 1.1 | even | 1 | trivial | |
100.4.i.a.89.4 | yes | 32 | 25.14 | even | 10 | inner | |
500.4.g.b.201.8 | 64 | 5.3 | odd | 4 | |||
500.4.g.b.201.9 | 64 | 5.2 | odd | 4 | |||
500.4.g.b.301.8 | 64 | 25.23 | odd | 20 | |||
500.4.g.b.301.9 | 64 | 25.2 | odd | 20 | |||
500.4.i.a.49.5 | 32 | 5.4 | even | 2 | |||
500.4.i.a.449.5 | 32 | 25.11 | even | 5 | |||
2500.4.a.g.1.16 | 32 | 25.8 | odd | 20 | |||
2500.4.a.g.1.17 | 32 | 25.17 | odd | 20 |