Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 29.1 | ||
Character | \(\chi\) | \(=\) | 76.29 |
Dual form | 76.5.j.a.21.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{17}{18}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −8.26669 | − | 9.85185i | −0.918521 | − | 1.09465i | −0.995226 | − | 0.0975965i | \(-0.968885\pi\) |
0.0767054 | − | 0.997054i | \(-0.475560\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −19.2135 | − | 6.99315i | −0.768541 | − | 0.279726i | −0.0721550 | − | 0.997393i | \(-0.522988\pi\) |
−0.696386 | + | 0.717667i | \(0.745210\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.56085 | − | 2.70347i | 0.0318540 | − | 0.0551728i | −0.849659 | − | 0.527333i | \(-0.823192\pi\) |
0.881513 | + | 0.472160i | \(0.156525\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −14.6554 | + | 83.1149i | −0.180931 | + | 1.02611i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 57.2296 | + | 99.1246i | 0.472972 | + | 0.819212i | 0.999521 | − | 0.0309329i | \(-0.00984782\pi\) |
−0.526549 | + | 0.850145i | \(0.676514\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −73.1984 | + | 87.2344i | −0.433127 | + | 0.516180i | −0.937822 | − | 0.347118i | \(-0.887160\pi\) |
0.504695 | + | 0.863298i | \(0.331605\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 89.9367 | + | 247.099i | 0.399719 | + | 1.09822i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.6409 | + | 66.0190i | 0.0402800 | + | 0.228439i | 0.998302 | − | 0.0582566i | \(-0.0185541\pi\) |
−0.958022 | + | 0.286696i | \(0.907443\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 113.685 | + | 342.632i | 0.314916 | + | 0.949119i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −39.5372 | + | 6.97148i | −0.0896536 | + | 0.0158083i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −229.764 | + | 83.6274i | −0.434337 | + | 0.158086i | −0.549930 | − | 0.835211i | \(-0.685346\pi\) |
0.115593 | + | 0.993297i | \(0.463123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −158.522 | − | 133.016i | −0.253636 | − | 0.212826i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 37.8358 | − | 21.8445i | 0.0519010 | − | 0.0299651i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1363.50 | − | 240.421i | −1.62128 | − | 0.285875i | −0.712037 | − | 0.702142i | \(-0.752227\pi\) |
−0.909243 | + | 0.416266i | \(0.863338\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 708.058 | + | 408.797i | 0.736793 | + | 0.425387i | 0.820902 | − | 0.571069i | \(-0.193471\pi\) |
−0.0841094 | + | 0.996457i | \(0.526805\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 503.462 | − | 1383.25i | 0.462316 | − | 1.27020i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −48.8952 | + | 41.0279i | −0.0399144 | + | 0.0334922i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1099.85i | − | 0.803397i | −0.915772 | − | 0.401699i | \(-0.868420\pi\) | ||
0.915772 | − | 0.401699i | \(-0.131580\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1464.53 | 0.962872 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −51.0022 | − | 60.7821i | −0.0303404 | − | 0.0361583i | 0.750661 | − | 0.660688i | \(-0.229735\pi\) |
−0.781001 | + | 0.624529i | \(0.785291\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −317.379 | − | 115.516i | −0.171649 | − | 0.0624751i | 0.254766 | − | 0.967003i | \(-0.418001\pi\) |
−0.426415 | + | 0.904528i | \(0.640224\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 862.817 | − | 1494.44i | 0.426083 | − | 0.737997i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −275.570 | + | 1562.84i | −0.124749 | + | 0.707486i | 0.856708 | + | 0.515802i | \(0.172506\pi\) |
−0.981457 | + | 0.191684i | \(0.938605\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1195.63 | + | 2070.89i | 0.497971 | + | 0.862510i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 554.178 | − | 660.443i | 0.213063 | − | 0.253919i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −876.707 | − | 2408.73i | −0.312106 | − | 0.857505i | −0.992231 | − | 0.124409i | \(-0.960297\pi\) |
0.680125 | − | 0.733097i | \(-0.261926\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −406.389 | − | 2304.75i | −0.134344 | − | 0.761900i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2435.76 | − | 3952.44i | 0.749697 | − | 1.21651i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4803.44 | + | 846.977i | −1.37990 | + | 0.243314i | −0.813860 | − | 0.581061i | \(-0.802638\pi\) |
−0.566044 | + | 0.824375i | \(0.691527\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1504.98 | + | 547.766i | −0.404455 | + | 0.147209i | −0.536234 | − | 0.844070i | \(-0.680153\pi\) |
0.131779 | + | 0.991279i | \(0.457931\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 201.824 | + | 169.350i | 0.0508500 | + | 0.0426682i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2016.44 | − | 1164.19i | 0.477264 | − | 0.275549i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4753.54 | − | 838.177i | −1.05893 | − | 0.186718i | −0.383048 | − | 0.923728i | \(-0.625126\pi\) |
−0.675881 | + | 0.737010i | \(0.736237\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2723.28 | + | 1572.28i | 0.571997 | + | 0.330242i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 183.202 | − | 503.344i | 0.0363425 | − | 0.0998501i | −0.920194 | − | 0.391462i | \(-0.871969\pi\) |
0.956537 | + | 0.291612i | \(0.0941916\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5428.81 | + | 4555.31i | −1.01873 | + | 0.854816i | −0.989467 | − | 0.144756i | \(-0.953760\pi\) |
−0.0292626 | + | 0.999572i | \(0.509316\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2661.34i | 0.473127i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 357.307 | 0.0602643 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7499.16 | + | 8937.15i | 1.20160 | + | 1.43201i | 0.873127 | + | 0.487492i | \(0.162088\pi\) |
0.328469 | + | 0.944515i | \(0.393467\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5895.91 | + | 2145.94i | 0.898629 | + | 0.327074i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3230.90 | + | 5596.08i | −0.468994 | + | 0.812321i | −0.999372 | − | 0.0354403i | \(-0.988717\pi\) |
0.530378 | + | 0.847761i | \(0.322050\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 238.018 | − | 1349.86i | 0.0329436 | − | 0.186832i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8903.00 | + | 15420.5i | 1.17625 | + | 2.03732i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6885.48 | + | 8205.80i | −0.869269 | + | 1.03595i | 0.129745 | + | 0.991547i | \(0.458584\pi\) |
−0.999014 | + | 0.0444070i | \(0.985860\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 121.584 | + | 334.049i | 0.0146823 | + | 0.0403392i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1825.88 | − | 10355.1i | −0.211109 | − | 1.19726i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 211.792 | − | 7378.19i | 0.0234672 | − | 0.817528i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4876.88 | + | 859.926i | −0.518321 | + | 0.0913940i | −0.426688 | − | 0.904399i | \(-0.640320\pi\) |
−0.0916331 | + | 0.995793i | \(0.529209\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9077.46 | + | 3303.92i | −0.926177 | + | 0.337101i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10204.2 | − | 8562.37i | −1.00032 | − | 0.839366i | −0.0132891 | − | 0.999912i | \(-0.504230\pi\) |
−0.987028 | + | 0.160546i | \(0.948675\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17592.0 | − | 10156.8i | 1.65822 | − | 0.957372i | 0.684680 | − | 0.728844i | \(-0.259942\pi\) |
0.973537 | − | 0.228529i | \(-0.0733914\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 808.402 | + | 142.543i | 0.0733244 | + | 0.0129291i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −446.474 | − | 257.772i | −0.0389968 | − | 0.0225148i | 0.480375 | − | 0.877063i | \(-0.340501\pi\) |
−0.519372 | + | 0.854548i | \(0.673834\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1442.56 | − | 3963.39i | 0.121417 | − | 0.333591i | −0.864062 | − | 0.503385i | \(-0.832088\pi\) |
0.985480 | + | 0.169794i | \(0.0543101\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10835.6 | + | 9092.12i | −0.879439 | + | 0.737937i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 21932.9i | − | 1.71767i | −0.512251 | − | 0.858836i | \(-0.671188\pi\) | ||
0.512251 | − | 0.858836i | \(-0.328812\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4999.40 | 0.378027 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6177.73 | − | 7362.33i | −0.451292 | − | 0.537828i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 196.650 | + | 71.5748i | 0.0138867 | + | 0.00505436i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 770.041 | − | 1333.75i | 0.0525949 | − | 0.0910970i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −177.197 | + | 1004.93i | −0.0117124 | + | 0.0664243i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8505.14 | + | 14731.3i | 0.544329 | + | 0.942805i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8629.27 | − | 10284.0i | 0.535016 | − | 0.637607i | −0.429047 | − | 0.903282i | \(-0.641151\pi\) |
0.964063 | + | 0.265675i | \(0.0855949\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1485.62 | + | 4081.71i | 0.0892747 | + | 0.245280i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3972.35 | − | 22528.3i | −0.231476 | − | 1.31276i | −0.849910 | − | 0.526927i | \(-0.823344\pi\) |
0.618435 | − | 0.785836i | \(-0.287767\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1103.74 | + | 227.453i | 0.0623970 | + | 0.0128585i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −879.722 | + | 155.119i | −0.0482701 | + | 0.00851132i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3938.12 | + | 1433.36i | −0.209820 | + | 0.0763684i | −0.444792 | − | 0.895634i | \(-0.646722\pi\) |
0.234972 | + | 0.972002i | \(0.424500\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17460.2 | + | 14650.9i | 0.903691 | + | 0.758287i | 0.970908 | − | 0.239451i | \(-0.0769675\pi\) |
−0.0672169 | + | 0.997738i | \(0.521412\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17674.9 | − | 10204.6i | 0.889034 | − | 0.513284i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12836.2 | − | 2263.37i | −0.627717 | − | 0.110684i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24516.3 | + | 14154.5i | 1.16605 | + | 0.673221i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10518.2 | − | 28898.5i | 0.486751 | − | 1.33734i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −24075.2 | + | 20201.5i | −1.08442 | + | 0.909937i | −0.996280 | − | 0.0861711i | \(-0.972537\pi\) |
−0.0881403 | + | 0.996108i | \(0.528092\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 24250.1i | − | 1.06355i | −0.846885 | − | 0.531776i | \(-0.821525\pi\) | ||
0.846885 | − | 0.531776i | \(-0.178475\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5657.77 | −0.241692 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10745.5 | − | 12806.0i | −0.447263 | − | 0.533028i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4379.41 | + | 1593.98i | 0.177671 | + | 0.0646669i | 0.429324 | − | 0.903151i | \(-0.358752\pi\) |
−0.251653 | + | 0.967818i | \(0.580974\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16483.0 | + | 28549.4i | −0.651992 | + | 1.12928i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −132.543 | + | 751.691i | −0.00511336 | + | 0.0289993i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1164.96 | + | 2017.78i | 0.0438467 | + | 0.0759448i | 0.887116 | − | 0.461547i | \(-0.152705\pi\) |
−0.843269 | + | 0.537492i | \(0.819372\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −19346.6 | + | 23056.3i | −0.710617 | + | 0.846880i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16240.9 | − | 44621.6i | −0.582341 | − | 1.59997i | −0.784168 | − | 0.620549i | \(-0.786910\pi\) |
0.201826 | − | 0.979421i | \(-0.435312\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2707.72 | + | 15356.3i | 0.0948049 | + | 0.537665i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −30143.9 | + | 4427.49i | −1.03088 | + | 0.151414i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7189.27 | − | 1267.66i | 0.240211 | − | 0.0423557i | −0.0522465 | − | 0.998634i | \(-0.516638\pi\) |
0.292457 | + | 0.956279i | \(0.405527\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −607.034 | + | 220.942i | −0.0198215 | + | 0.00721445i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 48052.9 | + | 40321.1i | 1.53381 | + | 1.28702i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14758.6 | + | 8520.88i | −0.460616 | + | 0.265937i | −0.712303 | − | 0.701872i | \(-0.752348\pi\) |
0.251687 | + | 0.967809i | \(0.419015\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8504.11 | + | 1499.50i | 0.259580 | + | 0.0457710i | 0.301924 | − | 0.953332i | \(-0.402371\pi\) |
−0.0423434 | + | 0.999103i | \(0.513482\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17837.7 | + | 10298.6i | 0.532643 | + | 0.307522i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7691.42 | + | 21132.0i | −0.224731 | + | 0.617444i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5877.90 | + | 4932.15i | −0.168089 | + | 0.141043i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 136.384i | − | 0.00381803i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12103.5 | −0.331776 | −0.165888 | − | 0.986145i | \(-0.553049\pi\) | ||||
−0.165888 | + | 0.986145i | \(0.553049\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1445.25 | + | 1722.38i | 0.0387996 | + | 0.0462396i | 0.785095 | − | 0.619375i | \(-0.212614\pi\) |
−0.746296 | + | 0.665615i | \(0.768169\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −28138.8 | − | 10241.7i | −0.740007 | − | 0.269340i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11434.8 | − | 19805.6i | 0.294642 | − | 0.510335i | −0.680260 | − | 0.732971i | \(-0.738133\pi\) |
0.974902 | + | 0.222637i | \(0.0714663\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8358.98 | + | 47406.2i | −0.211080 | + | 1.19709i | 0.676500 | + | 0.736442i | \(0.263496\pi\) |
−0.887580 | + | 0.460653i | \(0.847615\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 31038.4 | + | 53760.1i | 0.768258 | + | 1.33066i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2778.18 | + | 3310.91i | −0.0674169 | + | 0.0803443i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 554.874 | + | 1524.50i | 0.0132034 | + | 0.0362761i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3583.40 | − | 20322.4i | −0.0836285 | − | 0.474281i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27457.1 | + | 30877.7i | −0.628583 | + | 0.706890i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 48912.2 | − | 8624.53i | 1.09863 | − | 0.193718i | 0.405191 | − | 0.914232i | \(-0.367205\pi\) |
0.693440 | + | 0.720514i | \(0.256094\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6473.35 | + | 2356.11i | −0.142682 | + | 0.0519321i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5290.14 | + | 4438.96i | 0.114443 | + | 0.0960293i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2210.34 | − | 1276.14i | 0.0469397 | − | 0.0271006i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 89756.6 | + | 15826.5i | 1.87145 | + | 0.329987i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6611.23 | − | 3816.99i | −0.135362 | − | 0.0781514i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22601.8 | − | 62097.9i | 0.454499 | − | 1.24873i | −0.475027 | − | 0.879971i | \(-0.657562\pi\) |
0.929527 | − | 0.368755i | \(-0.120216\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13378.8 | − | 11226.2i | 0.264273 | − | 0.221752i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 66333.9i | 1.28731i | 0.765315 | + | 0.643656i | \(0.222583\pi\) | ||||
−0.765315 | + | 0.643656i | \(0.777417\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −92938.4 | −1.77225 | −0.886124 | − | 0.463449i | \(-0.846612\pi\) | ||||
−0.886124 | + | 0.463449i | \(0.846612\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2953.75 | − | 3520.14i | −0.0553540 | − | 0.0659683i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −84238.9 | − | 30660.5i | −1.55168 | − | 0.564764i | −0.582866 | − | 0.812569i | \(-0.698069\pi\) |
−0.968810 | + | 0.247805i | \(0.920291\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16223.8 | − | 28100.5i | 0.293777 | − | 0.508836i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 26054.3 | − | 147761.i | 0.463856 | − | 2.63066i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24727.5 | − | 42829.3i | −0.432897 | − | 0.749800i | 0.564224 | − | 0.825622i | \(-0.309175\pi\) |
−0.997121 | + | 0.0758216i | \(0.975842\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −58976.1 | + | 70284.9i | −1.01541 | + | 1.21012i | −0.0378895 | + | 0.999282i | \(0.512063\pi\) |
−0.977521 | + | 0.210837i | \(0.932381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −28808.5 | − | 79150.8i | −0.487875 | − | 1.34043i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8490.19 | − | 48150.3i | −0.141444 | − | 0.802170i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −38210.9 | − | 15162.9i | −0.626315 | − | 0.248535i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 81840.6 | − | 14430.7i | 1.31999 | − | 0.232749i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 42840.7 | − | 15592.7i | 0.680000 | − | 0.247500i | 0.0211523 | − | 0.999776i | \(-0.493267\pi\) |
0.658847 | + | 0.752277i | \(0.271044\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21438.9 | − | 17989.3i | −0.334935 | − | 0.281044i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15266.3 | + | 8813.99i | −0.234776 | + | 0.135548i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 101228. | + | 17849.2i | 1.53262 | + | 0.270242i | 0.875378 | − | 0.483439i | \(-0.160612\pi\) |
0.657240 | + | 0.753681i | \(0.271724\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2973.41 | − | 1716.70i | −0.0443257 | − | 0.0255914i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 39965.2 | − | 109803.i | 0.586679 | − | 1.61189i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −55109.3 | + | 46242.2i | −0.796735 | + | 0.668540i | −0.947402 | − | 0.320045i | \(-0.896302\pi\) |
0.150668 | + | 0.988584i | \(0.451858\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 52411.2i | 0.746332i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 137762. | 1.93245 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3420.43 | − | 4076.32i | −0.0472690 | − | 0.0563330i | 0.741892 | − | 0.670519i | \(-0.233929\pi\) |
−0.789161 | + | 0.614186i | \(0.789484\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −85921.4 | − | 31272.8i | −1.16994 | − | 0.425822i | −0.317300 | − | 0.948325i | \(-0.602776\pi\) |
−0.852638 | + | 0.522503i | \(0.824998\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2285.91 | − | 3959.31i | 0.0306714 | − | 0.0531244i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4112.99 | − | 23325.9i | 0.0543867 | − | 0.308442i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4412.53 | − | 7642.73i | −0.0575080 | − | 0.0996068i | 0.835838 | − | 0.548976i | \(-0.184982\pi\) |
−0.893346 | + | 0.449369i | \(0.851649\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −44354.0 | + | 52859.1i | −0.569803 | + | 0.679065i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12846.7 | + | 35295.9i | 0.162696 | + | 0.447005i | 0.994074 | − | 0.108703i | \(-0.0346697\pi\) |
−0.831378 | + | 0.555707i | \(0.812447\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21836.2 | + | 123839.i | 0.272649 | + | 1.54627i | 0.746332 | + | 0.665574i | \(0.231813\pi\) |
−0.473683 | + | 0.880696i | \(0.657076\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −74439.6 | + | 58906.6i | −0.916462 | + | 0.725228i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −243.929 | + | 43.0113i | −0.00296142 | + | 0.000522178i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 74261.1 | − | 27028.8i | 0.889131 | − | 0.323617i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 48787.5 | + | 40937.6i | 0.576133 | + | 0.483433i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9067.24 | + | 5234.97i | −0.105618 | + | 0.0609788i | −0.551879 | − | 0.833924i | \(-0.686089\pi\) |
0.446260 | + | 0.894903i | \(0.352756\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 98214.1 | + | 17317.8i | 1.12857 | + | 0.198998i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4330.66 | + | 2500.31i | 0.0490955 | + | 0.0283453i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9523.19 | − | 26164.8i | 0.106522 | − | 0.292667i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −807.675 | + | 677.720i | −0.00891464 | + | 0.00748027i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 171313.i | 1.86597i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 32746.5 | 0.352018 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2931.65 | − | 3493.80i | −0.0311053 | − | 0.0370699i | 0.750268 | − | 0.661134i | \(-0.229925\pi\) |
−0.781373 | + | 0.624064i | \(0.785480\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −245491. | − | 89351.3i | −2.57109 | − | 0.935802i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10594.0 | − | 18349.3i | 0.109531 | − | 0.189714i | −0.806049 | − | 0.591848i | \(-0.798398\pi\) |
0.915580 | + | 0.402135i | \(0.131732\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4983.07 | + | 28260.4i | −0.0508637 | + | 0.288463i | −0.999621 | − | 0.0275445i | \(-0.991231\pi\) |
0.948757 | + | 0.316007i | \(0.102342\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2693.45 | − | 4665.20i | −0.0271449 | − | 0.0470164i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8523.70 | + | 10158.2i | −0.0848222 | + | 0.101087i | −0.806786 | − | 0.590843i | \(-0.798795\pi\) |
0.721964 | + | 0.691931i | \(0.243240\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −54200.7 | − | 148915.i | −0.532628 | − | 1.46338i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1151.33 | + | 6529.52i | 0.0111735 | + | 0.0633681i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21296.8 | + | 11493.9i | −0.204131 | + | 0.110170i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23207.2 | − | 4092.05i | 0.219713 | − | 0.0387413i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −50971.9 | + | 18552.3i | −0.476689 | + | 0.173501i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3794.95 | + | 3184.34i | 0.0350602 | + | 0.0294190i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −99006.8 | + | 57161.6i | −0.903669 | + | 0.521733i | −0.878389 | − | 0.477947i | \(-0.841381\pi\) |
−0.0252800 | + | 0.999680i | \(0.508048\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 91414.0 | + | 16118.8i | 0.824374 | + | 0.145359i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 85470.7 | + | 49346.5i | 0.761601 | + | 0.439711i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 49309.4 | − | 135477.i | 0.434180 | − | 1.19290i | −0.509043 | − | 0.860741i | \(-0.670001\pi\) |
0.943223 | − | 0.332160i | \(-0.107777\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −216080. | + | 181313.i | −1.88025 | + | 1.57772i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 93581.3i | 0.804785i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14960.0 | 0.127158 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −41328.5 | − | 49253.4i | −0.347225 | − | 0.413807i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −44410.2 | − | 16164.0i | −0.368828 | − | 0.134243i | 0.150955 | − | 0.988541i | \(-0.451765\pi\) |
−0.519783 | + | 0.854298i | \(0.673987\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 55218.0 | − | 95640.3i | 0.453346 | − | 0.785218i | −0.545246 | − | 0.838276i | \(-0.683564\pi\) |
0.998591 | + | 0.0530586i | \(0.0168970\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −863.927 | + | 4899.57i | −0.00701234 | + | 0.0397689i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 102767. | + | 177998.i | 0.824717 | + | 1.42845i | 0.902136 | + | 0.431453i | \(0.141999\pi\) |
−0.0774187 | + | 0.996999i | \(0.524668\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7039.93 | + | 8389.86i | −0.0558613 | + | 0.0665730i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −920.500 | − | 2529.05i | −0.00722250 | − | 0.0198436i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22847.0 | + | 129572.i | 0.177272 | + | 1.00536i | 0.935488 | + | 0.353357i | \(0.114960\pi\) |
−0.758216 | + | 0.652003i | \(0.773929\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −104473. | + | 77904.2i | −0.801655 | + | 0.597787i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −19505.6 | + | 3439.36i | −0.148029 | + | 0.0261015i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 136163. | − | 49559.1i | 1.02205 | − | 0.371996i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 190217. | + | 159611.i | 1.41227 | + | 1.18504i | 0.955331 | + | 0.295539i | \(0.0954991\pi\) |
0.456940 | + | 0.889497i | \(0.348945\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5799.36 | − | 3348.26i | 0.0425919 | − | 0.0245905i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7880.34 | − | 1389.52i | −0.0572529 | − | 0.0100952i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 65920.1 | + | 38059.0i | 0.473805 | + | 0.273552i | 0.717831 | − | 0.696217i | \(-0.245135\pi\) |
−0.244026 | + | 0.969769i | \(0.578468\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 74821.6 | − | 205571.i | 0.532065 | − | 1.46184i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 120779. | − | 101345.i | 0.849783 | − | 0.713052i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 45055.4i | − | 0.313667i | −0.987625 | − | 0.156834i | \(-0.949871\pi\) | ||
0.987625 | − | 0.156834i | \(-0.0501286\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −172651. | −1.18938 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 34187.5 | + | 40743.1i | 0.233061 | + | 0.277752i | 0.869882 | − | 0.493261i | \(-0.164195\pi\) |
−0.636820 | + | 0.771012i | \(0.719751\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6865.13 | − | 2498.70i | −0.0463156 | − | 0.0168575i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14252.5 | − | 24686.0i | 0.0951629 | − | 0.164827i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19761.0 | − | 112070.i | 0.130590 | − | 0.740611i | −0.847240 | − | 0.531210i | \(-0.821738\pi\) |
0.977830 | − | 0.209401i | \(-0.0671514\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8195.67 | − | 14195.3i | −0.0536082 | − | 0.0928521i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −189108. | + | 225370.i | −1.22440 | + | 1.45919i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −81586.5 | − | 224157.i | −0.522906 | − | 1.43667i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −39544.9 | − | 224270.i | −0.250905 | − | 1.42295i | −0.806369 | − | 0.591413i | \(-0.798570\pi\) |
0.555464 | − | 0.831541i | \(-0.312541\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6883.43 | − | 12754.2i | −0.0432374 | − | 0.0801136i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 302245. | − | 53294.0i | 1.87962 | − | 0.331428i | 0.887922 | − | 0.459993i | \(-0.152148\pi\) |
0.991701 | + | 0.128565i | \(0.0410370\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −87489.9 | + | 31843.7i | −0.538701 | + | 0.196071i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −98274.3 | − | 82462.0i | −0.599142 | − | 0.502740i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 109022. | − | 62944.0i | 0.658152 | − | 0.379984i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −262236. | − | 46239.3i | −1.56764 | − | 0.276417i | −0.678690 | − | 0.734425i | \(-0.737452\pi\) |
−0.888948 | + | 0.458008i | \(0.848563\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 46676.4 | + | 26948.6i | 0.276321 | + | 0.159534i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5207.67 | + | 14308.0i | −0.0305312 | + | 0.0838837i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 101211. | − | 84926.2i | 0.587668 | − | 0.493112i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 293130.i | − | 1.68573i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 115258. | 0.656514 | 0.328257 | − | 0.944588i | \(-0.393539\pi\) | ||||
0.328257 | + | 0.944588i | \(0.393539\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22344.9 | − | 26629.6i | −0.126071 | − | 0.150245i | 0.699317 | − | 0.714812i | \(-0.253488\pi\) |
−0.825387 | + | 0.564567i | \(0.809043\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −125856. | − | 45808.0i | −0.703387 | − | 0.256012i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6936.24 | − | 12013.9i | 0.0384013 | − | 0.0665131i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −868.170 | + | 4923.64i | −0.00476156 | + | 0.0270041i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 83814.4 | + | 145171.i | 0.455412 | + | 0.788796i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9788.89 | + | 11665.9i | −0.0526962 | + | 0.0628008i | −0.791749 | − | 0.610847i | \(-0.790829\pi\) |
0.739053 | + | 0.673648i | \(0.235274\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1615.17 | + | 4437.64i | 0.00861474 | + | 0.0236688i | 0.943925 | − | 0.330159i | \(-0.107102\pi\) |
−0.935311 | + | 0.353827i | \(0.884880\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −63220.5 | − | 358541.i | −0.334102 | − | 1.89479i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −54774.2 | − | 69217.5i | −0.286822 | − | 0.362454i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −256793. | + | 45279.5i | −1.33246 | + | 0.234949i | −0.794111 | − | 0.607773i | \(-0.792063\pi\) |
−0.538349 | + | 0.842722i | \(0.680952\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −189644. | + | 69024.8i | −0.975129 | + | 0.354918i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 128893. | + | 108154.i | 0.656783 | + | 0.551106i | 0.909121 | − | 0.416533i | \(-0.136755\pi\) |
−0.252338 | + | 0.967639i | \(0.581199\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 189679. | − | 109511.i | 0.957852 | − | 0.553016i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 398045. | + | 70186.0i | 1.99213 | + | 0.351265i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 44967.9 | + | 25962.2i | 0.223054 | + | 0.128780i | 0.607364 | − | 0.794424i | \(-0.292227\pi\) |
−0.384310 | + | 0.923204i | \(0.625560\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3106.16 | − | 8534.11i | 0.0152711 | − | 0.0419571i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −238908. | + | 200468.i | −1.16422 | + | 0.976895i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 7268.52i | − | 0.0351094i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −313833. | −1.50268 | −0.751341 | − | 0.659915i | \(-0.770592\pi\) | ||||
−0.751341 | + | 0.659915i | \(0.770592\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1882.60 | + | 2243.59i | 0.00893578 | + | 0.0106492i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 285937. | + | 104073.i | 1.34545 | + | 0.489705i | 0.911526 | − | 0.411242i | \(-0.134905\pi\) |
0.433928 | + | 0.900947i | \(0.357127\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38084.9 | + | 65964.9i | −0.177660 | + | 0.307717i | −0.941079 | − | 0.338188i | \(-0.890186\pi\) |
0.763418 | + | 0.645904i | \(0.223520\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −37333.0 | + | 211726.i | −0.172658 | + | 0.979194i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 107590. | + | 186351.i | 0.493330 | + | 0.854473i | 0.999970 | − | 0.00768464i | \(-0.00244612\pi\) |
−0.506640 | + | 0.862158i | \(0.669113\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9685.53 | + | 11542.8i | −0.0440330 | + | 0.0524764i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20499.6 | − | 56322.2i | −0.0924068 | − | 0.253886i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6712.95 | − | 38071.0i | −0.0300048 | − | 0.170166i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27554.0 | − | 69436.8i | 0.122123 | − | 0.307753i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 213050. | − | 37566.5i | 0.936365 | − | 0.165106i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −115062. | + | 41879.2i | −0.501490 | + | 0.182527i | −0.580364 | − | 0.814357i | \(-0.697090\pi\) |
0.0788742 | + | 0.996885i | \(0.474867\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 95944.8 | + | 80507.3i | 0.414698 | + | 0.347973i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8501.24 | − | 4908.19i | 0.0364408 | − | 0.0210391i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 99715.7 | + | 17582.6i | 0.423916 | + | 0.0747479i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 143586. | + | 82899.5i | 0.605417 | + | 0.349538i | 0.771170 | − | 0.636630i | \(-0.219672\pi\) |
−0.165752 | + | 0.986167i | \(0.553005\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10248.4 | − | 28157.4i | 0.0428588 | − | 0.117754i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −341110. | + | 286226.i | −1.41492 | + | 1.18726i | −0.460924 | + | 0.887440i | \(0.652482\pi\) |
−0.953996 | + | 0.299819i | \(0.903074\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 92815.4i | − | 0.381879i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 197515. | 0.806101 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1074.82 | − | 1280.93i | −0.00435136 | − | 0.00518575i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30922.7 | + | 11254.9i | 0.124187 | + | 0.0452003i | 0.403366 | − | 0.915039i | \(-0.367840\pi\) |
−0.279179 | + | 0.960239i | \(0.590062\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −305346. | + | 528876.i | −1.21651 | + | 2.10707i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9171.59 | − | 52014.6i | 0.0362500 | − | 0.205584i | −0.961303 | − | 0.275492i | \(-0.911159\pi\) |
0.997553 | + | 0.0699076i | \(0.0222704\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 136181. | + | 235873.i | 0.533992 | + | 0.924902i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 128904. | − | 153621.i | 0.501475 | − | 0.597635i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 97679.4 | + | 268372.i | 0.377023 | + | 1.03586i | 0.972584 | + | 0.232552i | \(0.0747074\pi\) |
−0.595561 | + | 0.803310i | \(0.703070\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3841.60 | + | 21786.8i | 0.0147119 | + | 0.0834356i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11786.0 | + | 10480.4i | 0.0447849 | + | 0.0398238i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −409033. | + | 72123.5i | −1.54221 | + | 0.271933i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −170686. | + | 62124.7i | −0.638583 | + | 0.232425i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −71920.3 | − | 60348.3i | −0.267003 | − | 0.224042i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 319762. | − | 184615.i | 1.17802 | − | 0.680128i | 0.222461 | − | 0.974942i | \(-0.428591\pi\) |
0.955555 | + | 0.294814i | \(0.0952577\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −450051. | − | 79356.1i | −1.64535 | − | 0.290119i | −0.727221 | − | 0.686403i | \(-0.759188\pi\) |
−0.918128 | + | 0.396284i | \(0.870300\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7194.85 | + | 4153.95i | 0.0261038 | + | 0.0150710i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18745.9 | + | 51504.0i | −0.0674972 | + | 0.185447i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −168572. | + | 141449.i | −0.602387 | + | 0.505462i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 411651.i | − | 1.45996i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9035.57 | 0.0318054 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6775.70 | + | 8074.97i | 0.0236726 | + | 0.0282120i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 205951. | + | 74960.1i | 0.714193 | + | 0.259945i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −136851. | + | 237032.i | −0.471052 | + | 0.815887i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8700.04 | − | 49340.4i | 0.0297253 | − | 0.168581i | −0.966331 | − | 0.257301i | \(-0.917167\pi\) |
0.996057 | + | 0.0887206i | \(0.0282778\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −55527.9 | − | 96177.1i | −0.188327 | − | 0.326191i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −55433.2 | + | 66062.7i | −0.186628 | + | 0.222415i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −66561.1 | − | 182875.i | −0.222457 | − | 0.611195i | 0.777384 | − | 0.629026i | \(-0.216546\pi\) |
−0.999841 | + | 0.0178308i | \(0.994324\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23471.5 | − | 133114.i | −0.0778748 | − | 0.441650i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −72632.9 | − | 494510.i | −0.239238 | − | 1.62882i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35866.4 | − | 6324.21i | 0.117284 | − | 0.0206803i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 271772. | − | 98916.9i | 0.882305 | − | 0.321133i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10023.2 | − | 8410.44i | −0.0323069 | − | 0.0271087i | 0.626491 | − | 0.779428i | \(-0.284490\pi\) |
−0.658798 | + | 0.752320i | \(0.728935\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33308.6 | − | 19230.7i | 0.106594 | − | 0.0615421i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 97181.5 | + | 17135.7i | 0.308786 | + | 0.0544474i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −133471. | − | 77059.4i | −0.421085 | − | 0.243113i | 0.274456 | − | 0.961600i | \(-0.411502\pi\) |
−0.695541 | + | 0.718486i | \(0.744835\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −153380. | + | 421409.i | −0.480477 | + | 1.32010i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15004.1 | − | 12589.9i | 0.0466706 | − | 0.0391613i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 80777.1i | − | 0.249496i | −0.992188 | − | 0.124748i | \(-0.960188\pi\) | ||
0.992188 | − | 0.124748i | \(-0.0398122\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 296393. | 0.909065 | 0.454533 | − | 0.890730i | \(-0.349806\pi\) | ||||
0.454533 | + | 0.890730i | \(0.349806\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 100056. | + | 119242.i | 0.304743 | + | 0.363179i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 47546.6 | + | 17305.5i | 0.143808 | + | 0.0523419i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 185757. | − | 321741.i | 0.557949 | − | 0.966396i | −0.439718 | − | 0.898136i | \(-0.644922\pi\) |
0.997668 | − | 0.0682605i | \(-0.0217449\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5021.21 | − | 28476.7i | 0.0149779 | − | 0.0849440i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10085.9 | + | 17469.3i | 0.0298787 | + | 0.0517514i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 188591. | − | 224754.i | 0.554861 | − | 0.661257i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 67210.1 | + | 184658.i | 0.196392 | + | 0.539581i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4885.12 | + | 27704.9i | 0.0141775 | + | 0.0804045i | 0.991076 | − | 0.133301i | \(-0.0425578\pi\) |
−0.976898 | + | 0.213706i | \(0.931447\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −59571.7 | + | 289077.i | −0.171715 | + | 0.833266i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −289649. | + | 51073.0i | −0.829273 | + | 0.146223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16303.7 | + | 5934.06i | −0.0463635 | + | 0.0168749i | −0.365098 | − | 0.930969i | \(-0.618964\pi\) |
0.318734 | + | 0.947844i | \(0.396742\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3277.81 | − | 2750.41i | −0.00925869 | − | 0.00776896i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 536140. | − | 309540.i | 1.50428 | − | 0.868498i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −464365. | − | 81880.1i | −1.29421 | − | 0.228205i | −0.516209 | − | 0.856463i | \(-0.672657\pi\) |
−0.778005 | + | 0.628258i | \(0.783768\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29997.0 | + | 17318.8i | 0.0830478 | + | 0.0479477i | 0.540949 | − | 0.841055i | \(-0.318065\pi\) |
−0.457901 | + | 0.889003i | \(0.651399\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 139330. | − | 382806.i | 0.383186 | − | 1.05280i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24122.3 | + | 20241.0i | −0.0659035 | + | 0.0552996i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 65.3741i | − | 0.000177431i | −1.00000 | 8.87153e-5i | \(-0.999972\pi\) | |||
1.00000 | 8.87153e-5i | \(-2.82389e-5\pi\) | ||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 55585.0 | 0.149873 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −116162. | − | 138436.i | −0.311158 | − | 0.370824i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 189683. | + | 69038.8i | 0.504785 | + | 0.183727i | 0.581845 | − | 0.813300i | \(-0.302331\pi\) |
−0.0770598 | + | 0.997026i | \(0.524553\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10432.2 | − | 18069.1i | 0.0275821 | − | 0.0477735i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13154.6 | − | 74603.7i | 0.0345548 | − | 0.195970i | −0.962644 | − | 0.270772i | \(-0.912721\pi\) |
0.997198 | + | 0.0748014i | \(0.0238323\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 291209. | + | 504389.i | 0.760017 | + | 1.31639i | 0.942841 | + | 0.333243i | \(0.108143\pi\) |
−0.182824 | + | 0.983146i | \(0.558524\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6866.53 | + | 8183.21i | −0.0178055 | + | 0.0212198i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11436.9 | + | 31422.7i | 0.0294668 | + | 0.0809594i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −37936.4 | − | 215148.i | −0.0971173 | − | 0.550779i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 531182. | + | 15247.6i | 1.35116 | + | 0.0387853i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 72611.0 | − | 12803.3i | 0.183528 | − | 0.0323609i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 322731. | − | 117464.i | 0.810553 | − | 0.295017i | 0.0967008 | − | 0.995313i | \(-0.469171\pi\) |
0.713852 | + | 0.700296i | \(0.246949\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −489309. | − | 410579.i | −1.22117 | − | 1.02468i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −237716. | + | 137245.i | −0.589537 | + | 0.340369i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −268171. | − | 47285.7i | −0.660895 | − | 0.116534i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 39150.5 | + | 22603.6i | 0.0958817 | + | 0.0553573i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22622.2 | + | 62153.9i | −0.0550577 | + | 0.151270i | −0.964173 | − | 0.265276i | \(-0.914537\pi\) |
0.909115 | + | 0.416545i | \(0.136759\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 323935. | − | 271814.i | 0.783496 | − | 0.657431i | −0.160631 | − | 0.987015i | \(-0.551353\pi\) |
0.944126 | + | 0.329584i | \(0.106908\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 88813.1i | − | 0.213480i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −748603. | −1.78831 | −0.894156 | − | 0.447757i | \(-0.852223\pi\) | ||||
−0.894156 | + | 0.447757i | \(0.852223\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −358856. | − | 427667.i | −0.851982 | − | 1.01535i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −30844.6 | − | 11226.5i | −0.0727807 | − | 0.0264900i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 395000. | − | 684159.i | 0.926340 | − | 1.60447i | 0.136947 | − | 0.990578i | \(-0.456271\pi\) |
0.789392 | − | 0.613889i | \(-0.210396\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −81221.1 | + | 460628.i | −0.189316 | + | 1.07366i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −299053. | − | 517975.i | −0.692816 | − | 1.19999i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 75605.7 | − | 90103.4i | 0.174094 | − | 0.207477i | −0.671941 | − | 0.740605i | \(-0.734539\pi\) |
0.846035 | + | 0.533128i | \(0.178983\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −107073. | − | 294181.i | −0.245063 | − | 0.673304i | −0.999850 | − | 0.0173341i | \(-0.994482\pi\) |
0.754787 | − | 0.655970i | \(-0.227740\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17048.5 | + | 96686.7i | 0.0387845 | + | 0.219958i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19616.1 | − | 12088.8i | −0.0443578 | − | 0.0273363i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 333389. | − | 58785.5i | 0.749375 | − | 0.132135i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −798621. | + | 290674.i | −1.78439 | + | 0.649463i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −140426. | − | 117832.i | −0.311891 | − | 0.261708i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −596200. | + | 344216.i | −1.31632 | + | 0.759978i | −0.983135 | − | 0.182883i | \(-0.941457\pi\) |
−0.333186 | + | 0.942861i | \(0.608124\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8903.50 | − | 1569.93i | −0.0195413 | − | 0.00344566i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −272892. | − | 157554.i | −0.595406 | − | 0.343758i | 0.171826 | − | 0.985127i | \(-0.445033\pi\) |
−0.767232 | + | 0.641369i | \(0.778367\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5287.29 | + | 14526.7i | −0.0114682 | + | 0.0315085i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 653512. | − | 548361.i | 1.40916 | − | 1.18242i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 732776.i | 1.57083i | 0.618968 | + | 0.785416i | \(0.287551\pi\) | ||||
−0.618968 | + | 0.785416i | \(0.712449\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 85688.8 | 0.182618 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 768293. | + | 915616.i | 1.62785 | + | 1.93999i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 274298. | + | 99836.3i | 0.577809 | + | 0.210305i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10550.9 | − | 18274.7i | 0.0220970 | − | 0.0382732i | −0.854765 | − | 0.519014i | \(-0.826299\pi\) |
0.876862 | + | 0.480741i | \(0.159632\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5236.48 | + | 29697.5i | −0.0109037 | + | 0.0618378i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −233017. | − | 403597.i | −0.482411 | − | 0.835561i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3419.06 | − | 4074.68i | 0.00703787 | − | 0.00838740i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 394314. | + | 1.08337e6i | 0.807027 | + | 2.21729i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 93054.4 | + | 527738.i | 0.189366 | + | 1.07395i | 0.920217 | + | 0.391409i | \(0.128012\pi\) |
−0.730851 | + | 0.682537i | \(0.760877\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 376844. | − | 125036.i | 0.762520 | − | 0.253003i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −410959. | + | 72463.2i | −0.826838 | + | 0.145794i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −39075.4 | + | 14222.3i | −0.0781744 | + | 0.0284531i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 483631. | + | 405815.i | 0.962103 | + | 0.807300i | 0.981294 | − | 0.192515i | \(-0.0616645\pi\) |
−0.0191907 | + | 0.999816i | \(0.506109\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −852714. | + | 492315.i | −1.68680 | + | 0.973876i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −196873. | − | 34714.0i | −0.387264 | − | 0.0682851i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 230800. | + | 133253.i | 0.451466 | + | 0.260654i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −217534. | + | 597669.i | −0.423144 | + | 1.16258i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 198461. | − | 166529.i | 0.383899 | − | 0.322130i | −0.430332 | − | 0.902671i | \(-0.641603\pi\) |
0.814231 | + | 0.580541i | \(0.197159\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 63412.7i | − | 0.121985i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.17997e6 | 2.25733 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 184165. | + | 219479.i | 0.350373 | + | 0.417558i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −182622. | − | 66469.1i | −0.345529 | − | 0.125762i | 0.163425 | − | 0.986556i | \(-0.447746\pi\) |
−0.508955 | + | 0.860793i | \(0.669968\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −287522. | + | 498003.i | −0.541023 | + | 0.937080i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3931.69 | − | 22297.7i | 0.00735775 | − | 0.0417279i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −96413.3 | − | 166993.i | −0.179444 | − | 0.310806i | 0.762246 | − | 0.647287i | \(-0.224097\pi\) |
−0.941690 | + | 0.336481i | \(0.890763\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −404183. | + | 481687.i | −0.748176 | + | 0.891642i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −188959. | − | 519161.i | −0.347883 | − | 0.955800i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 139019. | + | 788416.i | 0.254557 | + | 1.44367i | 0.797207 | + | 0.603706i | \(0.206310\pi\) |
−0.542650 | + | 0.839959i | \(0.682579\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 166495. | + | 501795.i | 0.303224 | + | 0.913881i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −329829. | + | 58157.8i | −0.597463 | + | 0.105349i | −0.464198 | − | 0.885731i | \(-0.653657\pi\) |
−0.133265 | + | 0.991080i | \(0.542546\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 603842. | − | 219781.i | 1.08795 | − | 0.395983i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −417768. | − | 350549.i | −0.748675 | − | 0.628213i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1393.76 | + | 804.686i | −0.00248441 | + | 0.00143438i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16726.8 | − | 2949.38i | −0.0296574 | − | 0.00522939i | 0.158800 | − | 0.987311i | \(-0.449238\pi\) |
−0.188457 | + | 0.982081i | \(0.560349\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −507768. | − | 293160.i | −0.895519 | − | 0.517028i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −169584. | + | 465929.i | −0.297503 | + | 0.817383i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 483204. | − | 405457.i | 0.843216 | − | 0.707543i | −0.115068 | − | 0.993358i | \(-0.536709\pi\) |
0.958285 | + | 0.285815i | \(0.0922643\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 359925.i | 0.624782i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −411928. | −0.711299 | −0.355650 | − | 0.934619i | \(-0.615740\pi\) | ||||
−0.355650 | + | 0.934619i | \(0.615740\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8463.30 | − | 10086.2i | −0.0145375 | − | 0.0173251i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 108706. | + | 39565.6i | 0.185750 | + | 0.0676075i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 277719. | − | 481023.i | 0.472079 | − | 0.817665i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14069.9 | + | 79794.5i | −0.0237924 | + | 0.134934i | −0.994390 | − | 0.105773i | \(-0.966268\pi\) |
0.970598 | + | 0.240707i | \(0.0773793\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −660972. | − | 1.14484e6i | −1.11192 | − | 1.92590i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 533118. | − | 635345.i | 0.892204 | − | 1.06329i | −0.105422 | − | 0.994428i | \(-0.533619\pi\) |
0.997626 | − | 0.0688597i | \(-0.0219361\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −57866.4 | − | 158987.i | −0.0963436 | − | 0.264702i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7667.58 | + | 43485.0i | 0.0127004 | + | 0.0720274i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15027.7 | − | 24385.0i | 0.0247638 | − | 0.0401835i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 60378.4 | − | 10646.3i | 0.0989873 | − | 0.0174541i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −56840.9 | + | 20688.4i | −0.0927124 | + | 0.0337445i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −72997.0 | − | 61251.8i | −0.118458 | − | 0.0993984i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −743260. | + | 429121.i | −1.20003 | + | 0.692836i | −0.960561 | − | 0.278069i | \(-0.910306\pi\) |
−0.239466 | + | 0.970905i | \(0.576972\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 911143. | + | 160659.i | 1.46363 | + | 0.258078i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −59295.0 | − | 34234.0i | −0.0947688 | − | 0.0547148i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 62377.7 | − | 171381.i | 0.0991935 | − | 0.272532i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 516347. | − | 433267.i | 0.816973 | − | 0.685522i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 275787.i | 0.434167i | 0.976153 | + | 0.217083i | \(0.0696544\pi\) | ||||
−0.976153 | + | 0.217083i | \(0.930346\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −106385. | −0.166643 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −581115. | − | 692545.i | −0.905726 | − | 1.07940i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −762233. | − | 277430.i | −1.18211 | − | 0.430251i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7803.31 | − | 13515.7i | 0.0120417 | − | 0.0208568i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11883.6 | + | 67395.2i | −0.0182474 | + | 0.103486i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −564969. | − | 978555.i | −0.863233 | − | 1.49516i | −0.868792 | − | 0.495178i | \(-0.835103\pi\) |
0.00555901 | − | 0.999985i | \(-0.498231\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 432761. | − | 515745.i | 0.657971 | − | 0.784139i | −0.329122 | − | 0.944287i | \(-0.606753\pi\) |
0.987093 | + | 0.160148i | \(0.0511972\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 402190. | + | 1.10501e6i | 0.608485 | + | 1.67180i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8272.44 | − | 46915.4i | −0.0124543 | − | 0.0706317i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3498.48 | − | 121877.i | 0.00524126 | − | 0.182590i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −29546.3 | + | 5209.82i | −0.0440490 | + | 0.00776702i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 644340. | − | 234521.i | 0.955937 | − | 0.347932i | 0.183497 | − | 0.983020i | \(-0.441258\pi\) |
0.772440 | + | 0.635088i | \(0.219036\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −522167. | − | 438150.i | −0.770921 | − | 0.646879i | 0.170024 | − | 0.985440i | \(-0.445615\pi\) |
−0.940945 | + | 0.338561i | \(0.890060\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −263804. | + | 152308.i | −0.387591 | + | 0.223776i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −177534. | − | 31304.0i | −0.259579 | − | 0.0457708i | 0.0423440 | − | 0.999103i | \(-0.486517\pi\) |
−0.301923 | + | 0.953332i | \(0.597629\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −928800. | − | 536243.i | −1.35149 | − | 0.780283i | −0.363032 | − | 0.931777i | \(-0.618258\pi\) |
−0.988458 | + | 0.151493i | \(0.951592\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −38818.0 | + | 106652.i | −0.0562123 | + | 0.154442i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −122800. | + | 103041.i | −0.176973 | + | 0.148498i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 970913.i | 1.39254i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 35719.9 | 0.0509870 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −146454. | − | 174538.i | −0.208055 | − | 0.247950i | 0.651918 | − | 0.758289i | \(-0.273964\pi\) |
−0.859973 | + | 0.510339i | \(0.829520\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.13669e6 | + | 413723.i | 1.60713 | + | 0.584948i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 241531. | − | 418344.i | 0.339874 | − | 0.588679i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 55363.7 | − | 313983.i | 0.0775375 | − | 0.439737i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2403.84 | − | 4163.56i | −0.00335072 | − | 0.00580361i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.03953e6 | − | 1.23887e6i | 1.44219 | − | 1.71874i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 91977.7 | + | 252707.i | 0.127006 | + | 0.348945i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 160381. | + | 909569.i | 0.220423 | + | 1.25008i | 0.871245 | + | 0.490849i | \(0.163313\pi\) |
−0.650822 | + | 0.759230i | \(0.725576\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 610133. | + | 125733.i | 0.834627 | + | 0.171996i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 727876. | − | 128344.i | 0.991051 | − | 0.174749i | 0.345461 | − | 0.938433i | \(-0.387723\pi\) |
0.645590 | + | 0.763684i | \(0.276612\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 990958. | − | 360679.i | 1.34298 | − | 0.488804i | 0.432229 | − | 0.901764i | \(-0.357727\pi\) |
0.910749 | + | 0.412960i | \(0.135505\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2440.23 | + | 2047.59i | 0.00329173 | + | 0.00276209i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 529157. | − | 305509.i | 0.710498 | − | 0.410206i | −0.100747 | − | 0.994912i | \(-0.532123\pi\) |
0.811245 | + | 0.584706i | \(0.198790\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −146996. | − | 25919.4i | −0.196460 | − | 0.0346412i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −880177. | − | 508170.i | −1.17093 | − | 0.676038i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −456718. | + | 1.25482e6i | −0.604795 | + | 1.66166i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 421069. | − | 353319.i | 0.555031 | − | 0.465726i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 417944.i | − | 0.548391i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 53100.9 | 0.0693563 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 141645. | + | 168806.i | 0.184163 | + | 0.219477i | 0.850225 | − | 0.526420i | \(-0.176466\pi\) |
−0.666062 | + | 0.745896i | \(0.732021\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 126530. | + | 46053.2i | 0.163763 | + | 0.0596049i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −445430. | + | 771508.i | −0.573889 | + | 0.994005i | 0.422272 | + | 0.906469i | \(0.361233\pi\) |
−0.996161 | + | 0.0875361i | \(0.972101\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 157356. | − | 892408.i | 0.201818 | − | 1.14457i | −0.700550 | − | 0.713603i | \(-0.747062\pi\) |
0.902368 | − | 0.430966i | \(-0.141827\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −641293. | − | 1.11075e6i | −0.818785 | − | 1.41818i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −236211. | + | 281505.i | −0.300229 | + | 0.357799i | −0.894976 | − | 0.446114i | \(-0.852808\pi\) |
0.594747 | + | 0.803913i | \(0.297252\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14333.4 | − | 39380.7i | −0.0181362 | − | 0.0498287i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 124706. | + | 707241.i | 0.157083 | + | 0.890865i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −566806. | + | 83251.6i | −0.710774 | + | 0.104397i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 343152. | − | 60507.0i | 0.428392 | − | 0.0755370i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −336497. | + | 122475.i | −0.418211 | + | 0.152216i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −867151. | − | 727626.i | −1.07294 | − | 0.900303i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 148816. | − | 85919.2i | 0.183316 | − | 0.105838i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13353.6 | + | 2354.60i | 0.0163766 | + | 0.00288763i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −152908. | − | 88281.2i | −0.186695 | − | 0.107788i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −459883. | + | 1.26352e6i | −0.559027 | + | 1.53592i | 0.262024 | + | 0.965061i | \(0.415610\pi\) |
−0.821052 | + | 0.570854i | \(0.806612\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 861208. | − | 722639.i | 1.04227 | − | 0.874569i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33412.4i | 0.0402597i | 0.999797 | + | 0.0201299i | \(0.00640797\pi\) | ||||
−0.999797 | + | 0.0201299i | \(0.993592\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −739612. | −0.887284 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −270705. | − | 322614.i | −0.323336 | − | 0.385337i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −67104.9 | − | 24424.2i | −0.0798023 | − | 0.0290457i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 642264. | − | 1.11243e6i | 0.760471 | − | 1.31717i | −0.182137 | − | 0.983273i | \(-0.558301\pi\) |
0.942608 | − | 0.333902i | \(-0.108365\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10185.4 | + | 57764.3i | −0.0120077 | + | 0.0680989i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30498.8 | + | 52825.5i | 0.0357997 | + | 0.0620070i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −146298. | + | 174351.i | −0.170984 | + | 0.203770i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 586360. | + | 1.61101e6i | 0.682347 | + | 1.87473i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 144556. | + | 819819.i | 0.167496 | + | 0.949919i | 0.946453 | + | 0.322842i | \(0.104638\pi\) |
−0.778957 | + | 0.627078i | \(0.784251\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −573628. | + | 645089.i | −0.661806 | + | 0.744252i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −268351. | + | 47317.6i | −0.308277 | + | 0.0543575i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 147426. | − | 53658.8i | 0.168637 | − | 0.0613788i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 243893. | + | 204651.i | 0.277792 | + | 0.233096i | 0.771030 | − | 0.636799i | \(-0.219742\pi\) |
−0.493237 | + | 0.869895i | \(0.664186\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 319611. | − | 184527.i | 0.362485 | − | 0.209281i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −341216. | − | 60165.7i | −0.385346 | − | 0.0679469i | −0.0223805 | − | 0.999750i | \(-0.507125\pi\) |
−0.362965 | + | 0.931803i | \(0.618236\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16801.5 | + | 9700.38i | 0.0188941 | + | 0.0109085i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −953.754 | + | 2620.42i | −0.00106800 | + | 0.00293432i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14070.7 | − | 11806.7i | 0.0156898 | − | 0.0131653i | −0.634909 | − | 0.772587i | \(-0.718962\pi\) |
0.650599 | + | 0.759422i | \(0.274518\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 807021.i | − | 0.896092i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 170539. | 0.188566 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −335588. | − | 399938.i | −0.369505 | − | 0.440359i | 0.548967 | − | 0.835844i | \(-0.315021\pi\) |
−0.918473 | + | 0.395484i | \(0.870577\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 232551. | + | 84641.8i | 0.254984 | + | 0.0928064i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.01903e6 | + | 1.76501e6i | −1.11266 | + | 1.92719i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2271.77 | + | 12883.8i | −0.00247017 | + | 0.0140090i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −127530. | − | 220888.i | −0.138091 | − | 0.239181i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 27968.0 | − | 33330.9i | 0.0301584 | − | 0.0359414i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15723.4 | − | 43199.8i | −0.0168847 | − | 0.0463903i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −90193.0 | − | 511510.i | −0.0964539 | − | 0.547017i | −0.994292 | − | 0.106692i | \(-0.965974\pi\) |
0.897838 | − | 0.440325i | \(-0.145137\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 289291. | + | 114797.i | 0.308097 | + | 0.122259i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 183235. | − | 32309.3i | 0.194344 | − | 0.0342680i | −0.0756290 | − | 0.997136i | \(-0.524096\pi\) |
0.269973 | + | 0.962868i | \(0.412985\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 66860.9 | − | 24335.4i | 0.0706231 | − | 0.0257047i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −232161. | − | 194806.i | −0.244219 | − | 0.204924i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.31897e6 | + | 761510.i | −1.38181 | + | 0.797786i | −0.992373 | − | 0.123269i | \(-0.960662\pi\) |
−0.389433 | + | 0.921055i | \(0.627329\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.20745e6 | − | 212906.i | −1.25981 | − | 0.222138i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 308276. | + | 177983.i | 0.320333 | + | 0.184944i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −309658. | + | 850779.i | −0.320461 | + | 0.880460i | 0.669962 | + | 0.742395i | \(0.266310\pi\) |
−0.990423 | + | 0.138064i | \(0.955912\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −358205. | + | 300570.i | −0.369198 | + | 0.309794i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 63711.3i | − | 0.0654007i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 82582.7 | 0.0844299 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 862721. | + | 1.02815e6i | 0.878463 | + | 1.04691i | 0.998533 | + | 0.0541456i | \(0.0172435\pi\) |
−0.120070 | + | 0.992765i | \(0.538312\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.38161e6 | + | 502864.i | 1.40115 | + | 0.509978i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 492124. | − | 852384.i | 0.497082 | − | 0.860972i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −270146. | + | 1.53207e6i | −0.271774 | + | 1.54131i | 0.477251 | + | 0.878767i | \(0.341633\pi\) |
−0.749025 | + | 0.662542i | \(0.769478\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −24025.7 | − | 41613.8i | −0.0240738 | − | 0.0416971i |
(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 | 76.5.j.a.29.1 | yes | 42 | |
19.2 | odd | 18 | inner | 76.5.j.a.21.1 | ✓ | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.j.a.21.1 | ✓ | 42 | 19.2 | odd | 18 | inner | |
76.5.j.a.29.1 | yes | 42 | 1.1 | even | 1 | trivial |