Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(23,76)]
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([9, 2]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.23");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.l (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: | \(228\) |
Relative dimension: | \(38\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 23.5 | ||
Character | \(\chi\) | \(=\) | 76.23 |
Dual form | 76.5.l.a.43.5 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{9}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.62639 | − | 1.68799i | −0.906597 | − | 0.421998i | ||||
\(3\) | −13.6381 | + | 2.40477i | −1.51535 | + | 0.267196i | −0.868602 | − | 0.495511i | \(-0.834981\pi\) |
−0.646744 | + | 0.762707i | \(0.723870\pi\) | |||||||
\(4\) | 10.3014 | + | 12.2426i | 0.643835 | + | 0.765164i | ||||
\(5\) | 29.8632 | − | 25.0582i | 1.19453 | − | 1.00233i | 0.194759 | − | 0.980851i | \(-0.437608\pi\) |
0.999769 | − | 0.0214769i | \(-0.00683685\pi\) | |||||||
\(6\) | 53.5163 | + | 14.3004i | 1.48656 | + | 0.397234i | ||||
\(7\) | −54.4581 | − | 31.4414i | −1.11139 | − | 0.641661i | −0.172201 | − | 0.985062i | \(-0.555088\pi\) |
−0.939189 | + | 0.343400i | \(0.888421\pi\) | |||||||
\(8\) | −16.6913 | − | 61.7851i | −0.260801 | − | 0.965393i | ||||
\(9\) | 104.100 | − | 37.8894i | 1.28519 | − | 0.467770i | ||||
\(10\) | −150.594 | + | 40.4619i | −1.50594 | + | 0.404619i | ||||
\(11\) | 116.509 | − | 67.2664i | 0.962883 | − | 0.555920i | 0.0658235 | − | 0.997831i | \(-0.479033\pi\) |
0.897059 | + | 0.441911i | \(0.145699\pi\) | |||||||
\(12\) | −169.932 | − | 142.194i | −1.18008 | − | 0.987458i | ||||
\(13\) | −36.2645 | + | 205.666i | −0.214583 | + | 1.21696i | 0.667046 | + | 0.745016i | \(0.267558\pi\) |
−0.881629 | + | 0.471943i | \(0.843553\pi\) | |||||||
\(14\) | 144.413 | + | 205.944i | 0.736803 | + | 1.05073i | ||||
\(15\) | −347.019 | + | 413.561i | −1.54230 | + | 1.83805i | ||||
\(16\) | −43.7638 | + | 252.232i | −0.170952 | + | 0.985279i | ||||
\(17\) | −331.637 | − | 120.706i | −1.14753 | − | 0.417667i | −0.302904 | − | 0.953021i | \(-0.597956\pi\) |
−0.844628 | + | 0.535354i | \(0.820178\pi\) | |||||||
\(18\) | −441.464 | − | 38.3188i | −1.36254 | − | 0.118268i | ||||
\(19\) | −248.486 | + | 261.870i | −0.688327 | + | 0.725401i | ||||
\(20\) | 614.410 | + | 107.470i | 1.53602 | + | 0.268676i | ||||
\(21\) | 818.315 | + | 297.842i | 1.85559 | + | 0.675380i | ||||
\(22\) | −536.051 | + | 47.2680i | −1.10754 | + | 0.0976611i | ||||
\(23\) | −246.839 | + | 294.172i | −0.466615 | + | 0.556090i | −0.947111 | − | 0.320907i | \(-0.896012\pi\) |
0.480496 | + | 0.876997i | \(0.340457\pi\) | |||||||
\(24\) | 376.216 | + | 802.494i | 0.653153 | + | 1.39322i | ||||
\(25\) | 155.367 | − | 881.132i | 0.248588 | − | 1.40981i | ||||
\(26\) | 478.672 | − | 684.611i | 0.708095 | − | 1.01274i | ||||
\(27\) | −357.169 | + | 206.212i | −0.489944 | + | 0.282869i | ||||
\(28\) | −176.067 | − | 990.600i | −0.224576 | − | 1.26352i | ||||
\(29\) | −739.926 | + | 269.311i | −0.879817 | + | 0.320227i | −0.742136 | − | 0.670250i | \(-0.766187\pi\) |
−0.137681 | + | 0.990477i | \(0.543965\pi\) | |||||||
\(30\) | 1956.51 | − | 913.966i | 2.17390 | − | 1.01552i | ||||
\(31\) | 149.916 | + | 86.5541i | 0.156000 | + | 0.0900667i | 0.575968 | − | 0.817472i | \(-0.304625\pi\) |
−0.419968 | + | 0.907539i | \(0.637959\pi\) | |||||||
\(32\) | 584.469 | − | 840.816i | 0.570771 | − | 0.821109i | ||||
\(33\) | −1427.20 | + | 1197.56i | −1.31056 | + | 1.09969i | ||||
\(34\) | 998.892 | + | 997.526i | 0.864094 | + | 0.862912i | ||||
\(35\) | −2414.16 | + | 425.681i | −1.97074 | + | 0.347495i | ||||
\(36\) | 1536.24 | + | 884.147i | 1.18537 | + | 0.682212i | ||||
\(37\) | −1117.67 | −0.816417 | −0.408208 | − | 0.912889i | \(-0.633846\pi\) | ||||
−0.408208 | + | 0.912889i | \(0.633846\pi\) | |||||||
\(38\) | 1343.14 | − | 530.198i | 0.930153 | − | 0.367173i | ||||
\(39\) | − | 2892.11i | − | 1.90145i | ||||||
\(40\) | −2046.68 | − | 1426.85i | −1.27917 | − | 0.891780i | ||||
\(41\) | 308.470 | + | 1749.42i | 0.183504 | + | 1.04070i | 0.927863 | + | 0.372921i | \(0.121644\pi\) |
−0.744359 | + | 0.667779i | \(0.767245\pi\) | |||||||
\(42\) | −2464.77 | − | 2461.40i | −1.39726 | − | 1.39535i | ||||
\(43\) | −547.604 | − | 652.609i | −0.296162 | − | 0.352952i | 0.597359 | − | 0.801974i | \(-0.296217\pi\) |
−0.893521 | + | 0.449022i | \(0.851772\pi\) | |||||||
\(44\) | 2023.72 | + | 733.438i | 1.04531 | + | 0.378842i | ||||
\(45\) | 2159.32 | − | 3740.06i | 1.06633 | − | 1.84694i | ||||
\(46\) | 1391.70 | − | 650.118i | 0.657701 | − | 0.307239i | ||||
\(47\) | 1405.80 | + | 3862.39i | 0.636394 | + | 1.74848i | 0.662766 | + | 0.748827i | \(0.269383\pi\) |
−0.0263711 | + | 0.999652i | \(0.508395\pi\) | |||||||
\(48\) | −9.70262 | − | 3545.20i | −0.00421121 | − | 1.53872i | ||||
\(49\) | 776.624 | + | 1345.15i | 0.323459 | + | 0.560247i | ||||
\(50\) | −2050.77 | + | 2933.07i | −0.820306 | + | 1.17323i | ||||
\(51\) | 4813.17 | + | 848.691i | 1.85051 | + | 0.326294i | ||||
\(52\) | −2891.47 | + | 1674.67i | −1.06933 | + | 0.619330i | ||||
\(53\) | 361.256 | + | 303.130i | 0.128607 | + | 0.107914i | 0.704822 | − | 0.709384i | \(-0.251027\pi\) |
−0.576216 | + | 0.817298i | \(0.695471\pi\) | |||||||
\(54\) | 1643.32 | − | 144.905i | 0.563551 | − | 0.0496929i | ||||
\(55\) | 1793.75 | − | 4928.29i | 0.592976 | − | 1.62919i | ||||
\(56\) | −1033.64 | + | 3889.50i | −0.329603 | + | 1.24027i | ||||
\(57\) | 2759.14 | − | 4168.96i | 0.849229 | − | 1.28315i | ||||
\(58\) | 3137.85 | + | 272.363i | 0.932774 | + | 0.0809641i | ||||
\(59\) | −818.004 | + | 2247.45i | −0.234991 | + | 0.645633i | 0.765008 | + | 0.644021i | \(0.222735\pi\) |
−0.999999 | + | 0.00161161i | \(0.999487\pi\) | |||||||
\(60\) | −8637.83 | + | 11.8201i | −2.39940 | + | 0.00328337i | ||||
\(61\) | −2124.12 | − | 1782.35i | −0.570847 | − | 0.478998i | 0.311080 | − | 0.950384i | \(-0.399309\pi\) |
−0.881927 | + | 0.471386i | \(0.843754\pi\) | |||||||
\(62\) | −397.551 | − | 566.936i | −0.103421 | − | 0.147486i | ||||
\(63\) | −6860.39 | − | 1209.67i | −1.72849 | − | 0.304780i | ||||
\(64\) | −3538.80 | + | 2062.54i | −0.863965 | + | 0.503551i | ||||
\(65\) | 4070.65 | + | 7050.57i | 0.963467 | + | 1.66877i | ||||
\(66\) | 7197.06 | − | 1933.72i | 1.65222 | − | 0.443922i | ||||
\(67\) | 411.697 | + | 1131.13i | 0.0917123 | + | 0.251977i | 0.977065 | − | 0.212943i | \(-0.0683050\pi\) |
−0.885352 | + | 0.464921i | \(0.846083\pi\) | |||||||
\(68\) | −1938.55 | − | 5303.54i | −0.419237 | − | 1.14696i | ||||
\(69\) | 2659.01 | − | 4605.54i | 0.558498 | − | 0.967347i | ||||
\(70\) | 9473.22 | + | 2531.40i | 1.93331 | + | 0.516611i | ||||
\(71\) | −4312.08 | − | 5138.94i | −0.855402 | − | 1.01943i | −0.999554 | − | 0.0298724i | \(-0.990490\pi\) |
0.144152 | − | 0.989556i | \(-0.453955\pi\) | |||||||
\(72\) | −4078.56 | − | 5799.42i | −0.786760 | − | 1.11871i | ||||
\(73\) | 562.530 | + | 3190.27i | 0.105560 | + | 0.598662i | 0.990995 | + | 0.133898i | \(0.0427495\pi\) |
−0.885435 | + | 0.464763i | \(0.846139\pi\) | |||||||
\(74\) | 4053.12 | + | 1886.63i | 0.740161 | + | 0.344526i | ||||
\(75\) | 12390.6i | 2.20277i | ||||||||
\(76\) | −5765.72 | − | 344.507i | −0.998220 | − | 0.0596445i | ||||
\(77\) | −8459.80 | −1.42685 | ||||||||
\(78\) | −4881.85 | + | 10487.9i | −0.802408 | + | 1.72385i | ||||
\(79\) | 3478.29 | − | 613.316i | 0.557329 | − | 0.0982721i | 0.112113 | − | 0.993695i | \(-0.464238\pi\) |
0.445216 | + | 0.895423i | \(0.353127\pi\) | |||||||
\(80\) | 5013.54 | + | 8629.08i | 0.783366 | + | 1.34829i | ||||
\(81\) | −2498.70 | + | 2096.66i | −0.380842 | + | 0.319564i | ||||
\(82\) | 1834.37 | − | 6864.76i | 0.272810 | − | 1.02093i | ||||
\(83\) | −147.417 | − | 85.1113i | −0.0213989 | − | 0.0123547i | 0.489262 | − | 0.872137i | \(-0.337266\pi\) |
−0.510661 | + | 0.859782i | \(0.670599\pi\) | |||||||
\(84\) | 4783.39 | + | 13086.5i | 0.677918 | + | 1.85466i | ||||
\(85\) | −12928.4 | + | 4705.55i | −1.78940 | + | 0.651288i | ||||
\(86\) | 884.224 | + | 3290.96i | 0.119554 | + | 0.444965i | ||||
\(87\) | 9443.56 | − | 5452.24i | 1.24766 | − | 0.720339i | ||||
\(88\) | −6100.74 | − | 6075.75i | −0.787802 | − | 0.784575i | ||||
\(89\) | −243.708 | + | 1382.14i | −0.0307673 | + | 0.174490i | −0.996319 | − | 0.0857203i | \(-0.972681\pi\) |
0.965552 | + | 0.260210i | \(0.0837920\pi\) | |||||||
\(90\) | −14143.7 | + | 9917.98i | −1.74614 | + | 1.22444i | ||||
\(91\) | 8441.33 | − | 10060.0i | 1.01936 | − | 1.21483i | ||||
\(92\) | −6144.22 | + | 8.40783i | −0.725924 | + | 0.000993363i | ||||
\(93\) | −2252.71 | − | 819.921i | −0.260460 | − | 0.0947995i | ||||
\(94\) | 1421.73 | − | 16379.5i | 0.160902 | − | 1.85372i | ||||
\(95\) | −858.605 | + | 14046.9i | −0.0951363 | + | 1.55644i | ||||
\(96\) | −5949.09 | + | 12872.7i | −0.645518 | + | 1.39677i | ||||
\(97\) | 352.351 | + | 128.245i | 0.0374483 | + | 0.0136301i | 0.360676 | − | 0.932691i | \(-0.382546\pi\) |
−0.323228 | + | 0.946321i | \(0.604768\pi\) | |||||||
\(98\) | −545.733 | − | 6188.98i | −0.0568235 | − | 0.644417i | ||||
\(99\) | 9579.90 | − | 11416.9i | 0.977441 | − | 1.16487i | ||||
\(100\) | 12387.9 | − | 7174.75i | 1.23879 | − | 0.717475i | ||||
\(101\) | 2528.45 | − | 14339.6i | 0.247863 | − | 1.40570i | −0.565885 | − | 0.824484i | \(-0.691465\pi\) |
0.813748 | − | 0.581218i | \(-0.197424\pi\) | |||||||
\(102\) | −16021.8 | − | 11202.3i | −1.53997 | − | 1.07673i | ||||
\(103\) | 1609.74 | − | 929.382i | 0.151733 | − | 0.0876032i | −0.422211 | − | 0.906498i | \(-0.638746\pi\) |
0.573944 | + | 0.818894i | \(0.305413\pi\) | |||||||
\(104\) | 13312.4 | − | 1192.22i | 1.23081 | − | 0.110228i | ||||
\(105\) | 31900.9 | − | 11611.0i | 2.89351 | − | 1.05315i | ||||
\(106\) | −798.374 | − | 1709.07i | −0.0710550 | − | 0.152106i | ||||
\(107\) | −17669.4 | − | 10201.4i | −1.54331 | − | 0.891032i | −0.998627 | − | 0.0523917i | \(-0.983316\pi\) |
−0.544686 | − | 0.838640i | \(-0.683351\pi\) | |||||||
\(108\) | −6203.90 | − | 2248.42i | −0.531884 | − | 0.192766i | ||||
\(109\) | −5923.73 | + | 4970.60i | −0.498588 | + | 0.418365i | −0.857092 | − | 0.515163i | \(-0.827731\pi\) |
0.358504 | + | 0.933528i | \(0.383287\pi\) | |||||||
\(110\) | −14823.8 | + | 14844.1i | −1.22510 | + | 1.22678i | ||||
\(111\) | 15243.0 | − | 2687.75i | 1.23715 | − | 0.218144i | ||||
\(112\) | 10313.8 | − | 12360.1i | 0.822210 | − | 0.985336i | ||||
\(113\) | −13452.2 | −1.05350 | −0.526752 | − | 0.850019i | \(-0.676590\pi\) | ||||
−0.526752 | + | 0.850019i | \(0.676590\pi\) | |||||||
\(114\) | −17042.9 | + | 10460.8i | −1.31140 | + | 0.804928i | ||||
\(115\) | 14970.3i | 1.13197i | ||||||||
\(116\) | −10919.3 | − | 6284.36i | −0.811483 | − | 0.467031i | ||||
\(117\) | 4017.42 | + | 22783.9i | 0.293478 | + | 1.66440i | ||||
\(118\) | 6760.08 | − | 6769.33i | 0.485498 | − | 0.486163i | ||||
\(119\) | 14265.1 | + | 17000.5i | 1.00735 | + | 1.20052i | ||||
\(120\) | 31344.1 | + | 14537.7i | 2.17667 | + | 1.00956i | ||||
\(121\) | 1729.03 | − | 2994.77i | 0.118095 | − | 0.204547i | ||||
\(122\) | 4694.29 | + | 10049.0i | 0.315392 | + | 0.675154i | ||||
\(123\) | −8413.88 | − | 23117.0i | −0.556143 | − | 1.52799i | ||||
\(124\) | 484.691 | + | 2726.99i | 0.0315226 | + | 0.177354i | ||||
\(125\) | −5257.42 | − | 9106.12i | −0.336475 | − | 0.582792i | ||||
\(126\) | 22836.5 | + | 15967.0i | 1.43843 | + | 1.00573i | ||||
\(127\) | −8901.16 | − | 1569.52i | −0.551873 | − | 0.0973101i | −0.109244 | − | 0.994015i | \(-0.534843\pi\) |
−0.442629 | + | 0.896705i | \(0.645954\pi\) | |||||||
\(128\) | 16314.6 | − | 1506.11i | 0.995766 | − | 0.0919259i | ||||
\(129\) | 9037.65 | + | 7583.49i | 0.543096 | + | 0.455711i | ||||
\(130\) | −2860.44 | − | 32439.3i | −0.169257 | − | 1.91949i | ||||
\(131\) | 5742.38 | − | 15777.1i | 0.334618 | − | 0.919356i | −0.652275 | − | 0.757982i | \(-0.726185\pi\) |
0.986893 | − | 0.161374i | \(-0.0515925\pi\) | |||||||
\(132\) | −29363.4 | − | 5136.14i | −1.68523 | − | 0.294774i | ||||
\(133\) | 21765.6 | − | 6448.18i | 1.23046 | − | 0.364530i | ||||
\(134\) | 416.363 | − | 4796.84i | 0.0231879 | − | 0.267144i | ||||
\(135\) | −5498.92 | + | 15108.1i | −0.301724 | + | 0.828979i | ||||
\(136\) | −1922.39 | + | 22504.9i | −0.103935 | + | 1.21675i | ||||
\(137\) | 19517.7 | + | 16377.3i | 1.03989 | + | 0.872573i | 0.991995 | − | 0.126279i | \(-0.0403034\pi\) |
0.0478977 | + | 0.998852i | \(0.484748\pi\) | |||||||
\(138\) | −17416.7 | + | 12213.1i | −0.914551 | + | 0.641309i | ||||
\(139\) | −26673.7 | − | 4703.29i | −1.38055 | − | 0.243429i | −0.566425 | − | 0.824113i | \(-0.691674\pi\) |
−0.814129 | + | 0.580685i | \(0.802785\pi\) | |||||||
\(140\) | −30080.6 | − | 25170.5i | −1.53472 | − | 1.28421i | ||||
\(141\) | −28460.5 | − | 49295.1i | −1.43155 | − | 2.47951i | ||||
\(142\) | 6962.78 | + | 25914.5i | 0.345308 | + | 1.28519i | ||||
\(143\) | 9609.28 | + | 26401.3i | 0.469915 | + | 1.29108i | ||||
\(144\) | 5001.07 | + | 27915.5i | 0.241178 | + | 1.34623i | ||||
\(145\) | −15348.1 | + | 26583.7i | −0.729993 | + | 1.26439i | ||||
\(146\) | 3345.19 | − | 12518.7i | 0.156934 | − | 0.587291i | ||||
\(147\) | −13826.5 | − | 16477.7i | −0.639848 | − | 0.762541i | ||||
\(148\) | −11513.6 | − | 13683.3i | −0.525638 | − | 0.624693i | ||||
\(149\) | 110.516 | + | 626.766i | 0.00497797 | + | 0.0282314i | 0.987196 | − | 0.159515i | \(-0.0509929\pi\) |
−0.982218 | + | 0.187746i | \(0.939882\pi\) | |||||||
\(150\) | 20915.2 | − | 44933.1i | 0.929566 | − | 1.99703i | ||||
\(151\) | 1937.68i | 0.0849823i | 0.999097 | + | 0.0424911i | \(0.0135294\pi\) | ||||
−0.999097 | + | 0.0424911i | \(0.986471\pi\) | |||||||
\(152\) | 20327.2 | + | 10981.8i | 0.879813 | + | 0.475320i | ||||
\(153\) | −39096.9 | −1.67016 | ||||||||
\(154\) | 30678.5 | + | 14280.1i | 1.29358 | + | 0.602128i | ||||
\(155\) | 6645.86 | − | 1171.84i | 0.276623 | − | 0.0487761i | ||||
\(156\) | 35407.0 | − | 29792.6i | 1.45492 | − | 1.22422i | ||||
\(157\) | 19013.5 | − | 15954.2i | 0.771370 | − | 0.647256i | −0.169690 | − | 0.985498i | \(-0.554277\pi\) |
0.941059 | + | 0.338242i | \(0.109832\pi\) | |||||||
\(158\) | −13648.9 | − | 3647.20i | −0.546743 | − | 0.146098i | ||||
\(159\) | −5655.81 | − | 3265.39i | −0.223718 | − | 0.129164i | ||||
\(160\) | −3615.22 | − | 39755.2i | −0.141219 | − | 1.55294i | ||||
\(161\) | 22691.6 | − | 8259.06i | 0.875413 | − | 0.318624i | ||||
\(162\) | 12600.4 | − | 3385.51i | 0.480125 | − | 0.129001i | ||||
\(163\) | −4469.60 | + | 2580.52i | −0.168226 | + | 0.0971254i | −0.581749 | − | 0.813368i | \(-0.697631\pi\) |
0.413523 | + | 0.910494i | \(0.364298\pi\) | |||||||
\(164\) | −18239.8 | + | 21797.9i | −0.678161 | + | 0.810450i | ||||
\(165\) | −12612.0 | + | 71526.1i | −0.463250 | + | 2.62722i | ||||
\(166\) | 390.924 | + | 557.485i | 0.0141865 | + | 0.0202310i | ||||
\(167\) | 32744.4 | − | 39023.2i | 1.17410 | − | 1.39923i | 0.275023 | − | 0.961438i | \(-0.411315\pi\) |
0.899074 | − | 0.437797i | \(-0.144241\pi\) | |||||||
\(168\) | 4743.50 | − | 55531.1i | 0.168066 | − | 1.96751i | ||||
\(169\) | −14144.9 | − | 5148.32i | −0.495252 | − | 0.180257i | ||||
\(170\) | 54826.3 | + | 4758.89i | 1.89711 | + | 0.164667i | ||||
\(171\) | −15945.4 | + | 36675.6i | −0.545308 | + | 1.25425i | ||||
\(172\) | 2348.58 | − | 13426.9i | 0.0793868 | − | 0.453856i | ||||
\(173\) | −6448.58 | − | 2347.09i | −0.215462 | − | 0.0784219i | 0.232034 | − | 0.972708i | \(-0.425462\pi\) |
−0.447496 | + | 0.894286i | \(0.647684\pi\) | |||||||
\(174\) | −43449.4 | + | 3831.28i | −1.43511 | + | 0.126545i | ||||
\(175\) | −36165.0 | + | 43099.8i | −1.18090 | + | 1.40734i | ||||
\(176\) | 11867.8 | + | 32331.0i | 0.383130 | + | 1.04374i | ||||
\(177\) | 5751.45 | − | 32618.1i | 0.183582 | − | 1.04115i | ||||
\(178\) | 3216.82 | − | 4600.78i | 0.101528 | − | 0.145208i | ||||
\(179\) | −21371.9 | + | 12339.1i | −0.667018 | + | 0.385103i | −0.794946 | − | 0.606680i | \(-0.792501\pi\) |
0.127928 | + | 0.991784i | \(0.459167\pi\) | |||||||
\(180\) | 68032.1 | − | 12091.9i | 2.09976 | − | 0.373207i | ||||
\(181\) | −3633.72 | + | 1322.56i | −0.110916 | + | 0.0403701i | −0.396882 | − | 0.917870i | \(-0.629908\pi\) |
0.285966 | + | 0.958240i | \(0.407686\pi\) | |||||||
\(182\) | −47592.7 | + | 22232.5i | −1.43680 | + | 0.671190i | ||||
\(183\) | 33255.2 | + | 19199.9i | 0.993017 | + | 0.573319i | ||||
\(184\) | 22295.5 | + | 10340.9i | 0.658539 | + | 0.305438i | ||||
\(185\) | −33377.3 | + | 28006.9i | −0.975233 | + | 0.818317i | ||||
\(186\) | 6785.19 | + | 6775.92i | 0.196127 | + | 0.195858i | ||||
\(187\) | −46758.0 | + | 8244.70i | −1.33713 | + | 0.235772i | ||||
\(188\) | −32804.2 | + | 56998.5i | −0.928140 | + | 1.61268i | ||||
\(189\) | 25934.3 | 0.726025 | ||||||||
\(190\) | 26824.7 | − | 49490.1i | 0.743065 | − | 1.37092i | ||||
\(191\) | 59073.7i | 1.61930i | 0.586913 | + | 0.809650i | \(0.300343\pi\) | ||||
−0.586913 | + | 0.809650i | \(0.699657\pi\) | |||||||
\(192\) | 43302.7 | − | 36639.2i | 1.17466 | − | 0.993902i | ||||
\(193\) | −7473.92 | − | 42386.7i | −0.200647 | − | 1.13793i | −0.904143 | − | 0.427229i | \(-0.859490\pi\) |
0.703496 | − | 0.710699i | \(-0.251621\pi\) | |||||||
\(194\) | −1061.28 | − | 1059.83i | −0.0281987 | − | 0.0281601i | ||||
\(195\) | −72471.0 | − | 86367.5i | −1.90588 | − | 2.27134i | ||||
\(196\) | −8467.91 | + | 23364.8i | −0.220427 | + | 0.608205i | ||||
\(197\) | 4693.55 | − | 8129.46i | 0.120940 | − | 0.209474i | −0.799199 | − | 0.601067i | \(-0.794743\pi\) |
0.920138 | + | 0.391593i | \(0.128076\pi\) | |||||||
\(198\) | −54012.0 | + | 25231.2i | −1.37772 | + | 0.643588i | ||||
\(199\) | −3518.55 | − | 9667.13i | −0.0888500 | − | 0.244113i | 0.887307 | − | 0.461179i | \(-0.152574\pi\) |
−0.976157 | + | 0.217066i | \(0.930351\pi\) | |||||||
\(200\) | −57034.1 | + | 5107.82i | −1.42585 | + | 0.127696i | ||||
\(201\) | −8334.86 | − | 14436.4i | −0.206303 | − | 0.357328i | ||||
\(202\) | −33374.2 | + | 47732.8i | −0.817916 | + | 1.16981i | ||||
\(203\) | 48762.5 | + | 8598.14i | 1.18330 | + | 0.208647i | ||||
\(204\) | 39192.0 | + | 67668.5i | 0.941753 | + | 1.62602i | ||||
\(205\) | 53049.1 | + | 44513.5i | 1.26232 | + | 1.05922i | ||||
\(206\) | −7406.32 | + | 653.076i | −0.174529 | + | 0.0153897i | ||||
\(207\) | −14550.0 | + | 39975.9i | −0.339565 | + | 0.932949i | ||||
\(208\) | −50288.4 | − | 18147.8i | −1.16236 | − | 0.419466i | ||||
\(209\) | −11335.8 | + | 47224.9i | −0.259513 | + | 1.08113i | ||||
\(210\) | −135284. | − | 11742.6i | −3.06767 | − | 0.266272i | ||||
\(211\) | −11768.4 | + | 32333.3i | −0.264333 | + | 0.726248i | 0.734530 | + | 0.678576i | \(0.237403\pi\) |
−0.998863 | + | 0.0476722i | \(0.984820\pi\) | |||||||
\(212\) | 10.3252 | + | 7545.38i | 0.000229735 | + | 0.167884i | ||||
\(213\) | 71166.6 | + | 59715.8i | 1.56862 | + | 1.31623i | ||||
\(214\) | 46856.1 | + | 66820.1i | 1.02315 | + | 1.45908i | ||||
\(215\) | −32706.4 | − | 5767.02i | −0.707548 | − | 0.124760i | ||||
\(216\) | 18702.4 | + | 18625.8i | 0.400858 | + | 0.399215i | ||||
\(217\) | −5442.76 | − | 9427.14i | −0.115585 | − | 0.200198i | ||||
\(218\) | 29872.1 | − | 8026.11i | 0.628568 | − | 0.168885i | ||||
\(219\) | −15343.7 | − | 42156.5i | −0.319920 | − | 0.878974i | ||||
\(220\) | 78813.3 | − | 28807.9i | 1.62837 | − | 0.595204i | ||||
\(221\) | 36851.7 | − | 63829.1i | 0.754525 | − | 1.30688i | ||||
\(222\) | −59813.8 | − | 15983.2i | −1.21366 | − | 0.324308i | ||||
\(223\) | −23847.4 | − | 28420.2i | −0.479547 | − | 0.571502i | 0.470980 | − | 0.882144i | \(-0.343901\pi\) |
−0.950527 | + | 0.310642i | \(0.899456\pi\) | |||||||
\(224\) | −58265.5 | + | 27412.7i | −1.16122 | + | 0.546331i | ||||
\(225\) | −17211.8 | − | 97612.7i | −0.339985 | − | 1.92815i | ||||
\(226\) | 48782.9 | + | 22707.2i | 0.955104 | + | 0.444577i | ||||
\(227\) | − | 40697.7i | − | 0.789802i | −0.918724 | − | 0.394901i | \(-0.870779\pi\) | ||
0.918724 | − | 0.394901i | \(-0.129221\pi\) | |||||||
\(228\) | 79462.0 | − | 9166.79i | 1.52858 | − | 0.176339i | ||||
\(229\) | −33392.4 | −0.636761 | −0.318381 | − | 0.947963i | \(-0.603139\pi\) | ||||
−0.318381 | + | 0.947963i | \(0.603139\pi\) | |||||||
\(230\) | 25269.7 | − | 54288.0i | 0.477688 | − | 1.02624i | ||||
\(231\) | 115376. | − | 20343.8i | 2.16217 | − | 0.381249i | ||||
\(232\) | 28989.7 | + | 41221.3i | 0.538602 | + | 0.765853i | ||||
\(233\) | 8646.76 | − | 7255.49i | 0.159273 | − | 0.133646i | −0.559668 | − | 0.828717i | \(-0.689071\pi\) |
0.718941 | + | 0.695071i | \(0.244627\pi\) | |||||||
\(234\) | 23890.4 | − | 89404.6i | 0.436306 | − | 1.63278i | ||||
\(235\) | 138766. | + | 80116.7i | 2.51274 | + | 1.45073i | ||||
\(236\) | −35941.2 | + | 13137.3i | −0.645311 | + | 0.235874i | ||||
\(237\) | −45962.4 | + | 16728.9i | −0.818288 | + | 0.297832i | ||||
\(238\) | −23034.2 | − | 85730.0i | −0.406648 | − | 1.51349i | ||||
\(239\) | 76797.1 | − | 44338.8i | 1.34446 | − | 0.776226i | 0.357004 | − | 0.934103i | \(-0.383798\pi\) |
0.987459 | + | 0.157877i | \(0.0504649\pi\) | |||||||
\(240\) | −89126.2 | − | 105628.i | −1.54733 | − | 1.83382i | ||||
\(241\) | 9526.77 | − | 54029.0i | 0.164026 | − | 0.930235i | −0.786038 | − | 0.618178i | \(-0.787871\pi\) |
0.950063 | − | 0.312057i | \(-0.101018\pi\) | |||||||
\(242\) | −11325.3 | + | 7941.61i | −0.193383 | + | 0.135606i | ||||
\(243\) | 50508.7 | − | 60194.0i | 0.855370 | − | 1.01939i | ||||
\(244\) | −60.7103 | − | 44365.5i | −0.00101972 | − | 0.745187i | ||||
\(245\) | 56899.6 | + | 20709.8i | 0.947931 | + | 0.345019i | ||||
\(246\) | −8509.24 | + | 98033.6i | −0.140611 | + | 1.61996i | ||||
\(247\) | −44846.5 | − | 60601.7i | −0.735080 | − | 0.993324i | ||||
\(248\) | 2845.46 | − | 10707.3i | 0.0462647 | − | 0.174091i | ||||
\(249\) | 2215.16 | + | 806.253i | 0.0357279 | + | 0.0130039i | ||||
\(250\) | 3694.38 | + | 41896.8i | 0.0591101 | + | 0.670349i | ||||
\(251\) | −57179.2 | + | 68143.5i | −0.907591 | + | 1.08163i | 0.0887408 | + | 0.996055i | \(0.471716\pi\) |
−0.996332 | + | 0.0855705i | \(0.972729\pi\) | |||||||
\(252\) | −55861.8 | − | 96450.5i | −0.879658 | − | 1.51881i | ||||
\(253\) | −8971.09 | + | 50877.6i | −0.140154 | + | 0.794851i | ||||
\(254\) | 29629.7 | + | 20716.8i | 0.459262 | + | 0.321110i | ||||
\(255\) | 165003. | − | 95264.7i | 2.53754 | − | 1.46505i | ||||
\(256\) | −61705.5 | − | 22077.2i | −0.941551 | − | 0.336871i | ||||
\(257\) | −4463.28 | + | 1624.50i | −0.0675752 | + | 0.0245954i | −0.375587 | − | 0.926787i | \(-0.622559\pi\) |
0.308011 | + | 0.951383i | \(0.400337\pi\) | |||||||
\(258\) | −19973.2 | − | 42756.2i | −0.300059 | − | 0.642332i | ||||
\(259\) | 60866.4 | + | 35141.3i | 0.907357 | + | 0.523863i | ||||
\(260\) | −44384.3 | + | 122466.i | −0.656572 | + | 1.81163i | ||||
\(261\) | −66822.4 | + | 56070.6i | −0.980936 | + | 0.823103i | ||||
\(262\) | −47455.7 | + | 47520.7i | −0.691330 | + | 0.692277i | ||||
\(263\) | −90848.0 | + | 16018.9i | −1.31342 | + | 0.231591i | −0.786113 | − | 0.618083i | \(-0.787909\pi\) |
−0.527307 | + | 0.849675i | \(0.676798\pi\) | |||||||
\(264\) | 97813.4 | + | 68190.9i | 1.40343 | + | 0.978404i | ||||
\(265\) | 18384.2 | 0.261790 | ||||||||
\(266\) | −89815.1 | − | 13356.6i | −1.26936 | − | 0.188770i | ||||
\(267\) | − | 19435.8i | − | 0.272634i | ||||||
\(268\) | −9606.93 | + | 16692.4i | −0.133757 | + | 0.232407i | ||||
\(269\) | −3712.24 | − | 21053.1i | −0.0513016 | − | 0.290946i | 0.948353 | − | 0.317216i | \(-0.102748\pi\) |
−0.999655 | + | 0.0262702i | \(0.991637\pi\) | |||||||
\(270\) | 45443.6 | − | 45505.9i | 0.623369 | − | 0.624223i | ||||
\(271\) | 2219.81 | + | 2645.47i | 0.0302258 | + | 0.0360217i | 0.780946 | − | 0.624599i | \(-0.214738\pi\) |
−0.750720 | + | 0.660621i | \(0.770293\pi\) | |||||||
\(272\) | 44959.5 | − | 78366.7i | 0.607692 | − | 1.05924i | ||||
\(273\) | −90931.9 | + | 157499.i | −1.22009 | + | 2.11325i | ||||
\(274\) | −43134.1 | − | 92336.3i | −0.574539 | − | 1.22990i | ||||
\(275\) | −41168.9 | − | 113111.i | −0.544382 | − | 1.49568i | ||||
\(276\) | 83775.3 | − | 14890.1i | 1.09976 | − | 0.195469i | ||||
\(277\) | −49146.9 | − | 85124.9i | −0.640525 | − | 1.10942i | −0.985316 | − | 0.170743i | \(-0.945383\pi\) |
0.344790 | − | 0.938680i | \(-0.387950\pi\) | |||||||
\(278\) | 88789.9 | + | 62080.9i | 1.14888 | + | 0.803283i | ||||
\(279\) | 18885.8 | + | 3330.07i | 0.242620 | + | 0.0427804i | ||||
\(280\) | 66596.2 | + | 142054.i | 0.849441 | + | 1.81191i | ||||
\(281\) | −97936.0 | − | 82178.1i | −1.24031 | − | 1.04074i | −0.997500 | − | 0.0706687i | \(-0.977487\pi\) |
−0.242809 | − | 0.970074i | \(-0.578069\pi\) | |||||||
\(282\) | 19999.2 | + | 226804.i | 0.251486 | + | 2.85202i | ||||
\(283\) | −13024.0 | + | 35783.2i | −0.162619 | + | 0.446793i | −0.994062 | − | 0.108818i | \(-0.965293\pi\) |
0.831442 | + | 0.555611i | \(0.187516\pi\) | |||||||
\(284\) | 18493.8 | − | 105729.i | 0.229292 | − | 1.31087i | ||||
\(285\) | −22069.7 | − | 193638.i | −0.271711 | − | 2.38397i | ||||
\(286\) | 9718.19 | − | 111962.i | 0.118810 | − | 1.36879i | ||||
\(287\) | 38205.5 | − | 104969.i | 0.463833 | − | 1.27437i | ||||
\(288\) | 28985.4 | − | 109674.i | 0.349457 | − | 1.32227i | ||||
\(289\) | 31432.2 | + | 26374.7i | 0.376338 | + | 0.315785i | ||||
\(290\) | 100531. | − | 70495.3i | 1.19538 | − | 0.838232i | ||||
\(291\) | −5113.81 | − | 901.702i | −0.0603891 | − | 0.0106482i | ||||
\(292\) | −33262.4 | + | 39751.0i | −0.390111 | + | 0.466210i | ||||
\(293\) | 68682.7 | + | 118962.i | 0.800040 | + | 1.38571i | 0.919589 | + | 0.392882i | \(0.128522\pi\) |
−0.119548 | + | 0.992828i | \(0.538145\pi\) | |||||||
\(294\) | 22325.8 | + | 83093.6i | 0.258293 | + | 0.961331i | ||||
\(295\) | 31888.8 | + | 87613.7i | 0.366432 | + | 1.00676i | ||||
\(296\) | 18655.4 | + | 69055.7i | 0.212922 | + | 0.788163i | ||||
\(297\) | −27742.2 | + | 48050.9i | −0.314505 | + | 0.544739i | ||||
\(298\) | 657.204 | − | 2459.45i | 0.00740061 | − | 0.0276952i | ||||
\(299\) | −51549.7 | − | 61434.5i | −0.576612 | − | 0.687179i | ||||
\(300\) | −151693. | + | 127640.i | −1.68548 | + | 1.41822i | ||||
\(301\) | 9302.53 | + | 52757.3i | 0.102676 | + | 0.582303i | ||||
\(302\) | 3270.79 | − | 7026.78i | 0.0358624 | − | 0.0770446i | ||||
\(303\) | 201645.i | 2.19635i | ||||||||
\(304\) | −55177.1 | − | 74136.4i | −0.597051 | − | 0.802203i | ||||
\(305\) | −108096. | −1.16201 | ||||||||
\(306\) | 141780. | + | 65995.2i | 1.51417 | + | 0.704806i | ||||
\(307\) | −142674. | + | 25157.3i | −1.51380 | + | 0.266924i | −0.867994 | − | 0.496575i | \(-0.834591\pi\) |
−0.645809 | + | 0.763499i | \(0.723480\pi\) | |||||||
\(308\) | −87147.5 | − | 103570.i | −0.918657 | − | 1.09178i | ||||
\(309\) | −19718.8 | + | 16546.1i | −0.206521 | + | 0.173292i | ||||
\(310\) | −26078.5 | − | 6968.60i | −0.271369 | − | 0.0725141i | ||||
\(311\) | 61794.5 | + | 35677.1i | 0.638895 | + | 0.368866i | 0.784189 | − | 0.620523i | \(-0.213079\pi\) |
−0.145294 | + | 0.989389i | \(0.546413\pi\) | |||||||
\(312\) | −178689. | + | 48272.9i | −1.83565 | + | 0.495900i | ||||
\(313\) | 179210. | − | 65227.0i | 1.82925 | − | 0.665792i | 0.836151 | − | 0.548500i | \(-0.184801\pi\) |
0.993097 | − | 0.117292i | \(-0.0374214\pi\) | |||||||
\(314\) | −95880.9 | + | 25761.5i | −0.972462 | + | 0.261284i | ||||
\(315\) | −235185. | + | 135784.i | −2.37022 | + | 1.36845i | ||||
\(316\) | 43339.7 | + | 36265.4i | 0.434022 | + | 0.363177i | ||||
\(317\) | −6372.12 | + | 36138.1i | −0.0634111 | + | 0.359622i | 0.936548 | + | 0.350540i | \(0.114002\pi\) |
−0.999959 | + | 0.00908204i | \(0.997109\pi\) | |||||||
\(318\) | 14998.2 | + | 21388.5i | 0.148315 | + | 0.211508i | ||||
\(319\) | −68092.3 | + | 81149.2i | −0.669139 | + | 0.797449i | ||||
\(320\) | −53996.3 | + | 150270.i | −0.527308 | + | 1.46748i | ||||
\(321\) | 265509. | + | 96637.4i | 2.57673 | + | 0.937854i | ||||
\(322\) | −96229.7 | − | 8352.67i | −0.928106 | − | 0.0805589i | ||||
\(323\) | 114016. | − | 56851.8i | 1.09285 | − | 0.544929i | ||||
\(324\) | −51408.7 | − | 8992.21i | −0.489718 | − | 0.0856597i | ||||
\(325\) | 175585. | + | 63907.6i | 1.66234 | + | 0.605042i | ||||
\(326\) | 20564.4 | − | 1813.33i | 0.193500 | − | 0.0170625i | ||||
\(327\) | 68835.4 | − | 82034.8i | 0.643748 | − | 0.767189i | ||||
\(328\) | 102939. | − | 48258.8i | 0.956827 | − | 0.448569i | ||||
\(329\) | 44882.0 | − | 254539.i | 0.414649 | − | 2.35159i | ||||
\(330\) | 166472. | − | 238093.i | 1.52866 | − | 2.18634i | ||||
\(331\) | −34332.8 | + | 19822.1i | −0.313367 | + | 0.180923i | −0.648432 | − | 0.761272i | \(-0.724575\pi\) |
0.335065 | + | 0.942195i | \(0.391242\pi\) | |||||||
\(332\) | −476.611 | − | 2681.53i | −0.00432402 | − | 0.0243280i | ||||
\(333\) | −116350. | + | 42348.0i | −1.04925 | + | 0.381895i | ||||
\(334\) | −184615. | + | 86241.1i | −1.65491 | + | 0.773075i | ||||
\(335\) | 40638.6 | + | 23462.7i | 0.362117 | + | 0.209068i | ||||
\(336\) | −110938. | + | 193370.i | −0.982655 | + | 1.71282i | ||||
\(337\) | −77702.7 | + | 65200.3i | −0.684189 | + | 0.574103i | −0.917227 | − | 0.398365i | \(-0.869578\pi\) |
0.233038 | + | 0.972468i | \(0.425133\pi\) | |||||||
\(338\) | 42604.5 | + | 42546.2i | 0.372926 | + | 0.372416i | ||||
\(339\) | 183463. | − | 32349.4i | 1.59642 | − | 0.281493i | ||||
\(340\) | −190789. | − | 109804.i | −1.65042 | − | 0.949862i | ||||
\(341\) | 23288.7 | 0.200280 | ||||||||
\(342\) | 119732. | − | 106084.i | 1.02367 | − | 0.906984i | ||||
\(343\) | 53309.0i | 0.453119i | ||||||||
\(344\) | −31181.3 | + | 44726.6i | −0.263498 | + | 0.377963i | ||||
\(345\) | −36000.0 | − | 204166.i | −0.302458 | − | 1.71532i | ||||
\(346\) | 19423.2 | + | 19396.6i | 0.162244 | + | 0.162022i | ||||
\(347\) | −62559.9 | − | 74556.0i | −0.519562 | − | 0.619190i | 0.440915 | − | 0.897549i | \(-0.354654\pi\) |
−0.960477 | + | 0.278359i | \(0.910210\pi\) | |||||||
\(348\) | 164031. | + | 59448.5i | 1.35447 | + | 0.490888i | ||||
\(349\) | 153.229 | − | 265.400i | 0.00125802 | − | 0.00217896i | −0.865396 | − | 0.501089i | \(-0.832933\pi\) |
0.866654 | + | 0.498910i | \(0.166266\pi\) | |||||||
\(350\) | 203900. | − | 95250.3i | 1.66449 | − | 0.777553i | ||||
\(351\) | −29458.2 | − | 80935.7i | −0.239107 | − | 0.656940i | ||||
\(352\) | 11537.1 | − | 137278.i | 0.0931136 | − | 1.10794i | ||||
\(353\) | 108398. | + | 187752.i | 0.869909 | + | 1.50673i | 0.862089 | + | 0.506757i | \(0.169156\pi\) |
0.00781947 | + | 0.999969i | \(0.497511\pi\) | |||||||
\(354\) | −75916.0 | + | 108577.i | −0.605797 | + | 0.866428i | ||||
\(355\) | −257545. | − | 45412.1i | −2.04360 | − | 0.360342i | ||||
\(356\) | −19431.5 | + | 11254.3i | −0.153323 | + | 0.0888009i | ||||
\(357\) | −235432. | − | 197551.i | −1.84726 | − | 1.55004i | ||||
\(358\) | 98331.2 | − | 8670.66i | 0.767229 | − | 0.0676529i | ||||
\(359\) | −61851.0 | + | 169934.i | −0.479908 | + | 1.31854i | 0.429664 | + | 0.902989i | \(0.358632\pi\) |
−0.909572 | + | 0.415547i | \(0.863590\pi\) | |||||||
\(360\) | −267122. | − | 70987.8i | −2.06113 | − | 0.547745i | ||||
\(361\) | −6830.42 | − | 130142.i | −0.0524122 | − | 0.998626i | ||||
\(362\) | 15409.7 | + | 1337.55i | 0.117592 | + | 0.0102069i | ||||
\(363\) | −16379.0 | + | 45000.9i | −0.124301 | + | 0.341514i | ||||
\(364\) | 210118. | − | 287.528i | 1.58584 | − | 0.00217009i | ||||
\(365\) | 96741.3 | + | 81175.6i | 0.726150 | + | 0.609312i | ||||
\(366\) | −88186.8 | − | 125761.i | −0.658327 | − | 0.938820i | ||||
\(367\) | −156323. | − | 27563.9i | −1.16062 | − | 0.204648i | −0.440012 | − | 0.897992i | \(-0.645026\pi\) |
−0.720607 | + | 0.693344i | \(0.756137\pi\) | |||||||
\(368\) | −63396.8 | − | 75134.8i | −0.468135 | − | 0.554811i | ||||
\(369\) | 98396.0 | + | 170427.i | 0.722645 | + | 1.25166i | ||||
\(370\) | 168315. | − | 45223.2i | 1.22947 | − | 0.330338i | ||||
\(371\) | −10142.5 | − | 27866.3i | −0.0736881 | − | 0.202456i | ||||
\(372\) | −13168.0 | − | 36025.4i | −0.0951558 | − | 0.260330i | ||||
\(373\) | −50457.5 | + | 87394.9i | −0.362667 | + | 0.628157i | −0.988399 | − | 0.151881i | \(-0.951467\pi\) |
0.625732 | + | 0.780038i | \(0.284800\pi\) | |||||||
\(374\) | 183480. | + | 49028.7i | 1.31173 | + | 0.350516i | ||||
\(375\) | 93599.4 | + | 111547.i | 0.665596 | + | 0.793226i | ||||
\(376\) | 215174. | − | 151325.i | 1.52200 | − | 1.07038i | ||||
\(377\) | −28555.1 | − | 161944.i | −0.200910 | − | 1.13942i | ||||
\(378\) | −94047.9 | − | 43776.9i | −0.658211 | − | 0.306381i | ||||
\(379\) | − | 79968.8i | − | 0.556727i | −0.960476 | − | 0.278363i | \(-0.910208\pi\) | ||
0.960476 | − | 0.278363i | \(-0.0897920\pi\) | |||||||
\(380\) | −180815. | + | 134190.i | −1.25218 | + | 0.929297i | ||||
\(381\) | 125169. | 0.862280 | ||||||||
\(382\) | 99715.9 | − | 214224.i | 0.683341 | − | 1.46805i | ||||
\(383\) | 153869. | − | 27131.3i | 1.04895 | − | 0.184958i | 0.377501 | − | 0.926009i | \(-0.376783\pi\) |
0.671449 | + | 0.741051i | \(0.265672\pi\) | |||||||
\(384\) | −218879. | + | 59773.4i | −1.48437 | + | 0.405365i | ||||
\(385\) | −252637. | + | 211987.i | −1.70441 | + | 1.43017i | ||||
\(386\) | −44445.1 | + | 166326.i | −0.298297 | + | 1.11631i | ||||
\(387\) | −81732.5 | − | 47188.3i | −0.545724 | − | 0.315074i | ||||
\(388\) | 2059.64 | + | 5634.81i | 0.0136813 | + | 0.0374296i | ||||
\(389\) | 95890.0 | − | 34901.1i | 0.633686 | − | 0.230643i | −0.00514887 | − | 0.999987i | \(-0.501639\pi\) |
0.638835 | + | 0.769344i | \(0.279417\pi\) | |||||||
\(390\) | 117020. | + | 435533.i | 0.769363 | + | 2.86346i | ||||
\(391\) | 117369. | − | 67763.2i | 0.767716 | − | 0.443241i | ||||
\(392\) | 70147.6 | − | 70436.1i | 0.456500 | − | 0.458377i | ||||
\(393\) | −40375.1 | + | 228979.i | −0.261414 | + | 1.48255i | ||||
\(394\) | −30743.1 | + | 21557.9i | −0.198041 | + | 0.138872i | ||||
\(395\) | 88504.2 | − | 105475.i | 0.567244 | − | 0.676015i | ||||
\(396\) | 238459. | − | 326.310i | 1.52063 | − | 0.00208085i | ||||
\(397\) | −233633. | − | 85035.4i | −1.48236 | − | 0.539534i | −0.530932 | − | 0.847415i | \(-0.678158\pi\) |
−0.951425 | + | 0.307881i | \(0.900380\pi\) | |||||||
\(398\) | −3558.43 | + | 40996.0i | −0.0224642 | + | 0.258807i | ||||
\(399\) | −281336. | + | 140282.i | −1.76717 | + | 0.881164i | ||||
\(400\) | 215450. | + | 77750.2i | 1.34656 | + | 0.485939i | ||||
\(401\) | −249294. | − | 90735.8i | −1.55033 | − | 0.564274i | −0.581834 | − | 0.813307i | \(-0.697665\pi\) |
−0.968495 | + | 0.249034i | \(0.919887\pi\) | |||||||
\(402\) | 5856.90 | + | 66421.2i | 0.0362423 | + | 0.411012i | ||||
\(403\) | −23237.9 | + | 27693.8i | −0.143082 | + | 0.170519i | ||||
\(404\) | 201600. | − | 116762.i | 1.23518 | − | 0.715385i | ||||
\(405\) | −22080.7 | + | 125226.i | −0.134618 | + | 0.763456i | ||||
\(406\) | −162318. | − | 113491.i | −0.984724 | − | 0.688508i | ||||
\(407\) | −130219. | + | 75181.9i | −0.786113 | + | 0.453863i | ||||
\(408\) | −27901.4 | − | 311548.i | −0.167612 | − | 1.87156i | ||||
\(409\) | −76696.1 | + | 27915.1i | −0.458487 | + | 0.166875i | −0.560930 | − | 0.827863i | \(-0.689556\pi\) |
0.102443 | + | 0.994739i | \(0.467334\pi\) | |||||||
\(410\) | −117238. | − | 250970.i | −0.697432 | − | 1.49298i | ||||
\(411\) | −305569. | − | 176420.i | −1.80895 | − | 1.04440i | ||||
\(412\) | 27960.6 | + | 10133.5i | 0.164722 | + | 0.0596988i | ||||
\(413\) | 115210. | − | 96672.6i | 0.675445 | − | 0.566765i | ||||
\(414\) | 120243. | − | 120408.i | 0.701551 | − | 0.702512i | ||||
\(415\) | −6535.08 | + | 1152.31i | −0.0379450 | + | 0.00669073i | ||||
\(416\) | 151732. | + | 150697.i | 0.876779 | + | 0.870801i | ||||
\(417\) | 375089. | 2.15706 | ||||||||
\(418\) | 120823. | − | 152121.i | 0.691509 | − | 0.870636i | ||||
\(419\) | − | 16458.1i | − | 0.0937459i | −0.998901 | − | 0.0468730i | \(-0.985074\pi\) | ||
0.998901 | − | 0.0468730i | \(-0.0149256\pi\) | |||||||
\(420\) | 470772. | + | 270942.i | 2.66877 | + | 1.53595i | ||||
\(421\) | −39272.7 | − | 222727.i | −0.221578 | − | 1.25663i | −0.869120 | − | 0.494602i | \(-0.835314\pi\) |
0.647542 | − | 0.762030i | \(-0.275797\pi\) | |||||||
\(422\) | 97254.9 | − | 97388.1i | 0.546118 | − | 0.546866i | ||||
\(423\) | 292687. | + | 348811.i | 1.63577 | + | 1.94944i | ||||
\(424\) | 12699.1 | − | 27379.9i | 0.0706385 | − | 0.152300i | ||||
\(425\) | −157883. | + | 273462.i | −0.874094 | + | 1.51398i | ||||
\(426\) | −157278. | − | 336681.i | −0.866658 | − | 1.85524i | ||||
\(427\) | 59636.1 | + | 163849.i | 0.327080 | + | 0.898644i | ||||
\(428\) | −57126.5 | − | 321408.i | −0.311853 | − | 1.75457i | ||||
\(429\) | −194541. | − | 336956.i | −1.05706 | − | 1.83087i | ||||
\(430\) | 108871. | + | 76121.6i | 0.588812 | + | 0.411691i | ||||
\(431\) | 231676. | + | 40850.8i | 1.24717 | + | 0.219910i | 0.757988 | − | 0.652269i | \(-0.226183\pi\) |
0.489186 | + | 0.872179i | \(0.337294\pi\) | |||||||
\(432\) | −36382.0 | − | 99113.8i | −0.194948 | − | 0.531088i | ||||
\(433\) | 176919. | + | 148453.i | 0.943622 | + | 0.791793i | 0.978212 | − | 0.207608i | \(-0.0665680\pi\) |
−0.0345896 | + | 0.999402i | \(0.511012\pi\) | |||||||
\(434\) | 3824.62 | + | 43373.8i | 0.0203053 | + | 0.230276i | ||||
\(435\) | 145392. | − | 399460.i | 0.768353 | − | 2.11103i | ||||
\(436\) | −121876. | − | 21318.0i | −0.641127 | − | 0.112144i | ||||
\(437\) | −15698.5 | − | 137737.i | −0.0822045 | − | 0.721255i | ||||
\(438\) | −15517.6 | + | 178776.i | −0.0808866 | + | 0.931881i | ||||
\(439\) | 5032.55 | − | 13826.8i | 0.0261131 | − | 0.0717452i | −0.925951 | − | 0.377643i | \(-0.876735\pi\) |
0.952064 | + | 0.305898i | \(0.0989567\pi\) | |||||||
\(440\) | −334435. | − | 28567.7i | −1.72745 | − | 0.147560i | ||||
\(441\) | 131814. | + | 110605.i | 0.677771 | + | 0.568718i | ||||
\(442\) | −241382. | + | 169264.i | −1.23555 | + | 0.866401i | ||||
\(443\) | 162062. | + | 28575.9i | 0.825799 | + | 0.145611i | 0.570548 | − | 0.821264i | \(-0.306731\pi\) |
0.255251 | + | 0.966875i | \(0.417842\pi\) | |||||||
\(444\) | 189928. | + | 158927.i | 0.963439 | + | 0.806177i | ||||
\(445\) | 27356.0 | + | 47381.9i | 0.138144 | + | 0.239272i | ||||
\(446\) | 38506.8 | + | 143317.i | 0.193583 | + | 0.720490i | ||||
\(447\) | −3014.45 | − | 8282.15i | −0.0150867 | − | 0.0414503i | ||||
\(448\) | 257566. | − | 1057.37i | 1.28331 | − | 0.00526833i | ||||
\(449\) | 53477.6 | − | 92625.9i | 0.265264 | − | 0.459451i | −0.702368 | − | 0.711814i | \(-0.747874\pi\) |
0.967633 | + | 0.252362i | \(0.0812074\pi\) | |||||||
\(450\) | −102353. | + | 383035.i | −0.505447 | + | 1.89153i | ||||
\(451\) | 153616. | + | 183073.i | 0.755239 | + | 0.900059i | ||||
\(452\) | −138576. | − | 164690.i | −0.678283 | − | 0.806104i | ||||
\(453\) | −4659.67 | − | 26426.3i | −0.0227070 | − | 0.128778i | ||||
\(454\) | −68697.4 | + | 147586.i | −0.333295 | + | 0.716031i | ||||
\(455\) | − | 511948.i | − | 2.47288i | ||||||
\(456\) | −303633. | − | 100889.i | −1.46022 | − | 0.485192i | ||||
\(457\) | 241889. | 1.15820 | 0.579100 | − | 0.815257i | \(-0.303404\pi\) | ||||
0.579100 | + | 0.815257i | \(0.303404\pi\) | |||||||
\(458\) | 121094. | + | 56366.1i | 0.577286 | + | 0.268712i | ||||
\(459\) | 143341. | − | 25274.9i | 0.680371 | − | 0.119968i | ||||
\(460\) | −183275. | + | 154214.i | −0.866141 | + | 0.728800i | ||||
\(461\) | −45648.5 | + | 38303.7i | −0.214795 | + | 0.180235i | −0.743837 | − | 0.668361i | \(-0.766996\pi\) |
0.529041 | + | 0.848596i | \(0.322552\pi\) | |||||||
\(462\) | −452737. | − | 120979.i | −2.12111 | − | 0.566793i | ||||
\(463\) | −254391. | − | 146873.i | −1.18670 | − | 0.685140i | −0.229144 | − | 0.973393i | \(-0.573593\pi\) |
−0.957555 | + | 0.288252i | \(0.906926\pi\) | |||||||
\(464\) | −35546.8 | − | 198419.i | −0.165106 | − | 0.921609i | ||||
\(465\) | −87819.0 | + | 31963.5i | −0.406146 | + | 0.147825i | ||||
\(466\) | −43603.7 | + | 11715.6i | −0.200794 | + | 0.0539500i | ||||
\(467\) | 61317.9 | − | 35401.9i | 0.281160 | − | 0.162328i | −0.352789 | − | 0.935703i | \(-0.614767\pi\) |
0.633948 | + | 0.773375i | \(0.281433\pi\) | |||||||
\(468\) | −237550. | + | 283889.i | −1.08458 | + | 1.29616i | ||||
\(469\) | 13144.0 | − | 74543.4i | 0.0597561 | − | 0.338894i | ||||
\(470\) | −367983. | − | 524770.i | −1.66584 | − | 2.37560i | ||||
\(471\) | −220942. | + | 263308.i | −0.995947 | + | 1.18692i | ||||
\(472\) | 152512. | + | 13027.7i | 0.684575 | + | 0.0584769i | ||||
\(473\) | −107699. | − | 39199.3i | −0.481383 | − | 0.175209i | ||||
\(474\) | 194916. | + | 16918.5i | 0.867542 | + | 0.0753020i | ||||
\(475\) | 192135. | + | 259635.i | 0.851568 | + | 1.15074i | ||||
\(476\) | −61180.8 | + | 349772.i | −0.270023 | + | 1.54373i | ||||
\(477\) | 49092.3 | + | 17868.1i | 0.215763 | + | 0.0785312i | ||||
\(478\) | −353339. | + | 31156.8i | −1.54645 | + | 0.136363i | ||||
\(479\) | 119603. | − | 142537.i | 0.521280 | − | 0.621237i | −0.439603 | − | 0.898192i | \(-0.644881\pi\) |
0.960883 | + | 0.276955i | \(0.0893253\pi\) | |||||||
\(480\) | 144907. | + | 533492.i | 0.628936 | + | 2.31550i | ||||
\(481\) | 40531.9 | − | 229868.i | 0.175189 | − | 0.993546i | ||||
\(482\) | −125748. | + | 179849.i | −0.541263 | + | 0.774130i | ||||
\(483\) | −289609. | + | 167206.i | −1.24142 | + | 0.716733i | ||||
\(484\) | 54475.2 | − | 9682.34i | 0.232546 | − | 0.0413323i | ||||
\(485\) | 13735.9 | − | 4999.47i | 0.0583949 | − | 0.0212540i | ||||
\(486\) | −284771. | + | 133028.i | −1.20566 | + | 0.563211i | ||||
\(487\) | 209716. | + | 121080.i | 0.884249 | + | 0.510521i | 0.872057 | − | 0.489405i | \(-0.162786\pi\) |
0.0121916 | + | 0.999926i | \(0.496119\pi\) | |||||||
\(488\) | −74668.4 | + | 160989.i | −0.313543 | + | 0.676015i | ||||
\(489\) | 54751.3 | − | 45941.8i | 0.228969 | − | 0.192128i | ||||
\(490\) | −171382. | − | 171148.i | −0.713794 | − | 0.712818i | ||||
\(491\) | −70159.0 | + | 12370.9i | −0.291018 | + | 0.0513144i | −0.317251 | − | 0.948341i | \(-0.602760\pi\) |
0.0262331 | + | 0.999656i | \(0.491649\pi\) | |||||||
\(492\) | 196338. | − | 341144.i | 0.811099 | − | 1.40931i | ||||
\(493\) | 277894. | 1.14337 | ||||||||
\(494\) | 60335.5 | + | 295466.i | 0.247240 | + | 1.21075i | ||||
\(495\) | − | 581000.i | − | 2.37119i | ||||||
\(496\) | −28392.6 | + | 34025.6i | −0.115409 | + | 0.138307i | ||||
\(497\) | 73252.3 | + | 415435.i | 0.296557 | + | 1.68186i | ||||
\(498\) | −6672.09 | − | 6662.97i | −0.0269032 | − | 0.0268664i | ||||
\(499\) | −123008. | − | 146595.i | −0.494005 | − | 0.588733i | 0.460226 | − | 0.887802i | \(-0.347768\pi\) |
−0.954231 | + | 0.299069i | \(0.903324\pi\) | |||||||
\(500\) | 57324.2 | − | 158170.i | 0.229297 | − | 0.632680i | ||||
\(501\) | −352730. | + | 610946.i | −1.40529 | + | 2.43404i | ||||
\(502\) | 322379. | − | 150597.i | 1.27926 | − | 0.597596i | ||||
\(503\) | 133759. | + | 367499.i | 0.528671 | + | 1.45251i | 0.860636 | + | 0.509220i | \(0.170066\pi\) |
−0.331965 | + | 0.943292i | \(0.607712\pi\) | |||||||
\(504\) | 39768.9 | + | 444061.i | 0.156561 | + | 1.74816i | ||||
\(505\) | −283816. | − | 491584.i | −1.11290 | − | 1.92759i | ||||
\(506\) | 118414. | − | 169359.i | 0.462488 | − | 0.661464i | ||||
\(507\) | 205290. | + | 36198.2i | 0.798642 | + | 0.140822i | ||||
\(508\) | −72479.1 | − | 125142.i | −0.280857 | − | 0.484925i | ||||
\(509\) | 105828. | + | 88800.6i | 0.408476 | + | 0.342752i | 0.823759 | − | 0.566940i | \(-0.191873\pi\) |
−0.415283 | + | 0.909692i | \(0.636317\pi\) | |||||||
\(510\) | −759172. | + | 66942.4i | −2.91877 | + | 0.257372i | ||||
\(511\) | 69672.2 | − | 191423.i | 0.266819 | − | 0.733080i | ||||
\(512\) | 186502. | + | 184219.i | 0.711448 | + | 0.702739i | ||||
\(513\) | 34750.9 | − | 144772.i | 0.132048 | − | 0.550112i | ||||
\(514\) | 18927.7 | + | 1642.91i | 0.0716427 | + | 0.00621853i | ||||
\(515\) | 24783.3 | − | 68091.4i | 0.0934424 | − | 0.256731i | ||||
\(516\) | 258.308 | + | 188765.i | 0.000970150 | + | 0.708960i | ||||
\(517\) | 423597. | + | 355440.i | 1.58479 | + | 1.32980i | ||||
\(518\) | −161407. | − | 230178.i | −0.601538 | − | 0.857836i | ||||
\(519\) | 93590.6 | + | 16502.6i | 0.347454 | + | 0.0612656i | ||||
\(520\) | 367676. | − | 369189.i | 1.35975 | − | 1.36534i | ||||
\(521\) | −97256.3 | − | 168453.i | −0.358296 | − | 0.620587i | 0.629380 | − | 0.777098i | \(-0.283309\pi\) |
−0.987676 | + | 0.156510i | \(0.949976\pi\) | |||||||
\(522\) | 336971. | − | 90538.1i | 1.23666 | − | 0.332270i | ||||
\(523\) | −29739.6 | − | 81709.0i | −0.108726 | − | 0.298722i | 0.873384 | − | 0.487033i | \(-0.161921\pi\) |
−0.982109 | + | 0.188311i | \(0.939699\pi\) | |||||||
\(524\) | 252307. | − | 92223.5i | 0.918897 | − | 0.335876i | ||||
\(525\) | 389578. | − | 674768.i | 1.41343 | − | 2.44814i | ||||
\(526\) | 356490. | + | 95259.8i | 1.28847 | + | 0.344301i | ||||
\(527\) | −39270.1 | − | 46800.2i | −0.141397 | − | 0.168510i | ||||
\(528\) | −239603. | − | 412395.i | −0.859459 | − | 1.47926i | ||||
\(529\) | 22986.5 | + | 130363.i | 0.0821415 | + | 0.465847i | ||||
\(530\) | −66668.1 | − | 31032.3i | −0.237338 | − | 0.110475i | ||||
\(531\) | 264953.i | 0.939681i | ||||||||
\(532\) | 303158. | + | 200043.i | 1.07114 | + | 0.706807i | ||||
\(533\) | −370982. | −1.30587 | ||||||||
\(534\) | −32807.5 | + | 70481.7i | −0.115051 | + | 0.247169i | ||||
\(535\) | −783294. | + | 138116.i | −2.73664 | + | 0.482543i | ||||
\(536\) | 63015.1 | − | 44316.7i | 0.219339 | − | 0.154254i | ||||
\(537\) | 261800. | − | 219676.i | 0.907865 | − | 0.761789i | ||||
\(538\) | −22075.5 | + | 82613.1i | −0.0762688 | + | 0.285420i | ||||
\(539\) | 180967. | + | 104481.i | 0.622905 | + | 0.359634i | ||||
\(540\) | −241610. | + | 88313.4i | −0.828566 | + | 0.302858i | ||||
\(541\) | −425227. | + | 154770.i | −1.45287 | + | 0.528801i | −0.943391 | − | 0.331683i | \(-0.892384\pi\) |
−0.509478 | + | 0.860484i | \(0.670161\pi\) | |||||||
\(542\) | −3584.37 | − | 13340.5i | −0.0122015 | − | 0.0454124i | ||||
\(543\) | 46376.6 | − | 26775.5i | 0.157289 | − | 0.0908110i | ||||
\(544\) | −295323. | + | 208297.i | −0.997928 | + | 0.703857i | ||||
\(545\) | −52347.2 | + | 296876.i | −0.176239 | + | 0.999498i | ||||
\(546\) | 595611. | − | 417659.i | 1.99792 | − | 1.40099i | ||||
\(547\) | −275593. | + | 328439.i | −0.921073 | + | 1.09769i | 0.0738717 | + | 0.997268i | \(0.476464\pi\) |
−0.994945 | + | 0.100424i | \(0.967980\pi\) | |||||||
\(548\) | 557.843 | + | 407657.i | 0.00185760 | + | 1.35748i | ||||
\(549\) | −288653. | − | 105061.i | −0.957706 | − | 0.348576i | ||||
\(550\) | −41635.5 | + | 479675.i | −0.137638 | + | 1.58570i | ||||
\(551\) | 113337. | − | 260684.i | 0.373309 | − | 0.858640i | ||||
\(552\) | −328936. | − | 87414.9i | −1.07953 | − | 0.286885i | ||||
\(553\) | −208705. | − | 75962.2i | −0.682467 | − | 0.248398i | ||||
\(554\) | 34535.4 | + | 391655.i | 0.112524 | + | 1.27610i | ||||
\(555\) | 387854. | − | 462226.i | 1.25916 | − | 1.50061i | ||||
\(556\) | −217195. | − | 375006.i | −0.702586 | − | 1.21308i | ||||
\(557\) | −67133.8 | + | 380735.i | −0.216387 | + | 1.22719i | 0.662097 | + | 0.749418i | \(0.269667\pi\) |
−0.878484 | + | 0.477772i | \(0.841444\pi\) | |||||||
\(558\) | −62865.9 | − | 43955.1i | −0.201905 | − | 0.141170i | ||||
\(559\) | 154078. | − | 88957.0i | 0.493080 | − | 0.284680i | ||||
\(560\) | −1717.52 | − | 627556.i | −0.00547677 | − | 2.00114i | ||||
\(561\) | 617865. | − | 224884.i | 1.96321 | − | 0.714552i | ||||
\(562\) | 216438. | + | 463325.i | 0.685269 | + | 1.46694i | ||||
\(563\) | −180614. | − | 104277.i | −0.569815 | − | 0.328983i | 0.187260 | − | 0.982310i | \(-0.440039\pi\) |
−0.757076 | + | 0.653327i | \(0.773373\pi\) | |||||||
\(564\) | 310319. | − | 856239.i | 0.975552 | − | 2.69176i | ||||
\(565\) | −401726. | + | 337088.i | −1.25844 | + | 1.05596i | ||||
\(566\) | 107632. | − | 107779.i | 0.335976 | − | 0.336436i | ||||
\(567\) | 201996. | − | 35617.4i | 0.628315 | − | 0.110789i | ||||
\(568\) | −245536. | + | 352198.i | −0.761058 | + | 1.09167i | ||||
\(569\) | −165446. | −0.511013 | −0.255507 | − | 0.966807i | \(-0.582242\pi\) | ||||
−0.255507 | + | 0.966807i | \(0.582242\pi\) | |||||||
\(570\) | −246826. | + | 739459.i | −0.759697 | + | 2.27596i | ||||
\(571\) | 196250.i | 0.601918i | 0.953637 | + | 0.300959i | \(0.0973068\pi\) | ||||
−0.953637 | + | 0.300959i | \(0.902693\pi\) | |||||||
\(572\) | −224232. | + | 389612.i | −0.685340 | + | 1.19080i | ||||
\(573\) | −142058. | − | 805654.i | −0.432671 | − | 2.45380i | ||||
\(574\) | −315734. | + | 316167.i | −0.958292 | + | 0.959604i | ||||
\(575\) | 220853. | + | 263203.i | 0.667987 | + | 0.796076i | ||||
\(576\) | −290241. | + | 348794.i | −0.874811 | + | 1.05129i | ||||
\(577\) | −24477.4 | + | 42396.0i | −0.0735212 | + | 0.127343i | −0.900442 | − | 0.434976i | \(-0.856757\pi\) |
0.826921 | + | 0.562318i | \(0.190090\pi\) | |||||||
\(578\) | −69464.9 | − | 148702.i | −0.207926 | − | 0.445104i | ||||
\(579\) | 203860. | + | 560101.i | 0.608101 | + | 1.67074i | ||||
\(580\) | −483561. | + | 85947.2i | −1.43746 | + | 0.255491i | ||||
\(581\) | 5352.04 | + | 9270.00i | 0.0158550 | + | 0.0274617i | ||||
\(582\) | 17022.6 | + | 11902.0i | 0.0502550 | + | 0.0351377i | ||||
\(583\) | 62480.0 | + | 11016.9i | 0.183825 | + | 0.0324133i | ||||
\(584\) | 187722. | − | 88005.6i | 0.550413 | − | 0.258039i | ||||
\(585\) | 690897. | + | 579731.i | 2.01884 | + | 1.69401i | ||||
\(586\) | −48263.2 | − | 547338.i | −0.140547 | − | 1.59390i | ||||
\(587\) | 61565.6 | − | 169150.i | 0.178674 | − | 0.490903i | −0.817733 | − | 0.575598i | \(-0.804769\pi\) |
0.996407 | + | 0.0846947i | \(0.0269915\pi\) | |||||||
\(588\) | 59299.3 | − | 339015.i | 0.171512 | − | 0.980539i | ||||
\(589\) | −59917.9 | + | 17751.0i | −0.172713 | + | 0.0511672i | ||||
\(590\) | 32250.2 | − | 371549.i | 0.0926464 | − | 1.06736i | ||||
\(591\) | −44461.7 | + | 122157.i | −0.127295 | + | 0.349740i | ||||
\(592\) | 48913.7 | − | 281913.i | 0.139568 | − | 0.804398i | ||||
\(593\) | −198342. | − | 166429.i | −0.564035 | − | 0.473282i | 0.315625 | − | 0.948884i | \(-0.397786\pi\) |
−0.879660 | + | 0.475602i | \(0.842230\pi\) | |||||||
\(594\) | 181714. | − | 127423.i | 0.515009 | − | 0.361138i | ||||
\(595\) | 852006. | + | 150232.i | 2.40663 | + | 0.424353i | ||||
\(596\) | −6534.80 | + | 7809.55i | −0.0183967 | + | 0.0219854i | ||||
\(597\) | 71233.6 | + | 123380.i | 0.199865 | + | 0.346176i | ||||
\(598\) | 83238.1 | + | 309801.i | 0.232766 | + | 0.866323i | ||||
\(599\) | −110959. | − | 304858.i | −0.309250 | − | 0.849658i | −0.992803 | − | 0.119757i | \(-0.961788\pi\) |
0.683553 | − | 0.729901i | \(-0.260434\pi\) | |||||||
\(600\) | 765554. | − | 206815.i | 2.12654 | − | 0.574486i | ||||
\(601\) | −260677. | + | 451507.i | −0.721696 | + | 1.25001i | 0.238623 | + | 0.971112i | \(0.423304\pi\) |
−0.960319 | + | 0.278902i | \(0.910029\pi\) | |||||||
\(602\) | 55319.3 | − | 207021.i | 0.152645 | − | 0.571243i | ||||
\(603\) | 85715.3 | + | 102152.i | 0.235735 | + | 0.280938i | ||||
\(604\) | −23722.3 | + | 19960.8i | −0.0650254 | + | 0.0547146i | ||||
\(605\) | −23409.1 | − | 132760.i | −0.0639551 | − | 0.362707i | ||||
\(606\) | 340375. | − | 731243.i | 0.926857 | − | 1.99121i | ||||
\(607\) | 128136.i | 0.347770i | 0.984766 | + | 0.173885i | \(0.0556321\pi\) | ||||
−0.984766 | + | 0.173885i | \(0.944368\pi\) | |||||||
\(608\) | 74951.8 | + | 361986.i | 0.202757 | + | 0.979229i | ||||
\(609\) | −685705. | −1.84885 | ||||||||
\(610\) | 391996. | + | 182464.i | 1.05347 | + | 0.490364i | ||||
\(611\) | −845343. | + | 149057.i | −2.26439 | + | 0.399273i | ||||
\(612\) | −402751. | − | 478649.i | −1.07531 | − | 1.27795i | ||||
\(613\) | 227539. | − | 190928.i | 0.605530 | − | 0.508100i | −0.287688 | − | 0.957724i | \(-0.592887\pi\) |
0.893218 | + | 0.449624i | \(0.148442\pi\) | |||||||
\(614\) | 559858. | + | 149603.i | 1.48505 | + | 0.396829i | ||||
\(615\) | −830535. | − | 479510.i | −2.19588 | − | 1.26779i | ||||
\(616\) | 141205. | + | 522690.i | 0.372124 | + | 1.37747i | ||||
\(617\) | −508551. | + | 185098.i | −1.33587 | + | 0.486217i | −0.908510 | − | 0.417864i | \(-0.862779\pi\) |
−0.427361 | + | 0.904081i | \(0.640557\pi\) | |||||||
\(618\) | 99437.7 | − | 26717.2i | 0.260360 | − | 0.0699542i | ||||
\(619\) | 184164. | − | 106327.i | 0.480645 | − | 0.277500i | −0.240040 | − | 0.970763i | \(-0.577161\pi\) |
0.720685 | + | 0.693263i | \(0.243827\pi\) | |||||||
\(620\) | 82807.9 | + | 69291.2i | 0.215421 | + | 0.180258i | ||||
\(621\) | 27501.7 | − | 155970.i | 0.0713144 | − | 0.404444i | ||||
\(622\) | −163868. | − | 233688.i | −0.423559 | − | 0.604025i | ||||
\(623\) | 56728.2 | − | 67606.0i | 0.146158 | − | 0.174184i | ||||
\(624\) | 729480. | + | 126569.i | 1.87346 | + | 0.325057i | ||||
\(625\) | 140292. | + | 51062.2i | 0.359148 | + | 0.130719i | ||||
\(626\) | −759986. | − | 65966.2i | −1.93935 | − | 0.168334i | ||||
\(627\) | 41033.8 | − | 671318.i | 0.104378 | − | 1.70763i | ||||
\(628\) | 391186. | + | 68424.9i | 0.991892 | + | 0.173498i | ||||
\(629\) | 370662. | + | 134910.i | 0.936864 | + | 0.340991i | ||||
\(630\) | 1.08208e6 | − | 95415.5i | 2.72632 | − | 0.240402i | ||||
\(631\) | 187868. | − | 223892.i | 0.471839 | − | 0.562316i | −0.476663 | − | 0.879086i | \(-0.658154\pi\) |
0.948502 | + | 0.316770i | \(0.102598\pi\) | |||||||
\(632\) | −95950.9 | − | 204669.i | −0.240223 | − | 0.512411i | ||||
\(633\) | 82744.1 | − | 469265.i | 0.206505 | − | 1.17115i | ||||
\(634\) | 84108.6 | − | 120295.i | 0.209248 | − | 0.299273i | ||||
\(635\) | −305146. | + | 176176.i | −0.756765 | + | 0.436918i | ||||
\(636\) | −18285.7 | − | 102880.i | −0.0452061 | − | 0.254341i | ||||
\(637\) | −304816. | + | 110944.i | −0.751206 | + | 0.273417i | ||||
\(638\) | 383908. | − | 179339.i | 0.943162 | − | 0.440589i | ||||
\(639\) | −643599. | − | 371582.i | −1.57621 | − | 0.910024i | ||||
\(640\) | 449467. | − | 453793.i | 1.09733 | − | 1.10789i | ||||
\(641\) | 486043. | − | 407838.i | 1.18293 | − | 0.992595i | 0.182973 | − | 0.983118i | \(-0.441428\pi\) |
0.999955 | − | 0.00947679i | \(-0.00301660\pi\) | |||||||
\(642\) | −799716. | − | 798622.i | −1.94028 | − | 1.93763i | ||||
\(643\) | −150280. | + | 26498.4i | −0.363478 | + | 0.0640910i | −0.352405 | − | 0.935848i | \(-0.614636\pi\) |
−0.0110735 | + | 0.999939i | \(0.503525\pi\) | |||||||
\(644\) | 334867. | + | 192725.i | 0.807422 | + | 0.464693i | ||||
\(645\) | 459922. | 1.10552 | ||||||||
\(646\) | −509433. | + | 13708.2i | −1.22074 | + | 0.0328486i | ||||
\(647\) | 331762.i | 0.792535i | 0.918135 | + | 0.396267i | \(0.129695\pi\) | ||||
−0.918135 | + | 0.396267i | \(0.870305\pi\) | |||||||
\(648\) | 171249. | + | 119387.i | 0.407829 | + | 0.284319i | ||||
\(649\) | 55873.0 | + | 316872.i | 0.132652 | + | 0.752305i | ||||
\(650\) | −528862. | − | 528139.i | −1.25174 | − | 1.25003i | ||||
\(651\) | 96899.1 | + | 115480.i | 0.228643 | + | 0.272486i | ||||
\(652\) | −77635.4 | − | 28136.7i | −0.182627 | − | 0.0661878i | ||||
\(653\) | 98871.1 | − | 171250.i | 0.231869 | − | 0.401609i | −0.726489 | − | 0.687178i | \(-0.758849\pi\) |
0.958358 | + | 0.285569i | \(0.0921825\pi\) | |||||||
\(654\) | −388098. | + | 181296.i | −0.907372 | + | 0.423871i | ||||
\(655\) | −223859. | − | 615048.i | −0.521786 | − | 1.43359i | ||||
\(656\) | −454758. | + | 1244.60i | −1.05675 | + | 0.00289215i | ||||
\(657\) | 179437. | + | 310793.i | 0.415700 | + | 0.720014i | ||||
\(658\) | −592419. | + | 847295.i | −1.36829 | + | 1.95696i | ||||
\(659\) | 35676.2 | + | 6290.67i | 0.0821500 | + | 0.0144853i | 0.214572 | − | 0.976708i | \(-0.431164\pi\) |
−0.132422 | + | 0.991193i | \(0.542275\pi\) | |||||||
\(660\) | −1.00559e6 | + | 582413.i | −2.30851 | + | 1.33704i | ||||
\(661\) | 291515. | + | 244611.i | 0.667204 | + | 0.559851i | 0.912236 | − | 0.409664i | \(-0.134354\pi\) |
−0.245032 | + | 0.969515i | \(0.578799\pi\) | |||||||
\(662\) | 157964. | − | 13928.9i | 0.360447 | − | 0.0317835i | ||||
\(663\) | −349094. | + | 959128.i | −0.794174 | + | 2.18197i | ||||
\(664\) | −2798.03 | + | 10528.8i | −0.00634624 | + | 0.0238805i | ||||
\(665\) | 488412. | − | 737971.i | 1.10444 | − | 1.66877i | ||||
\(666\) | 493413. | + | 42827.9i | 1.11240 | + | 0.0965558i | ||||
\(667\) | 103419. | − | 284142.i | 0.232461 | − | 0.638680i | ||||
\(668\) | 815059. | − | 1115.34i | 1.82657 | − | 0.00249950i | ||||
\(669\) | 393578. | + | 330251.i | 0.879384 | + | 0.737890i | ||||
\(670\) | −107766. | − | 153682.i | −0.240068 | − | 0.342353i | ||||
\(671\) | −367371. | − | 64777.4i | −0.815943 | − | 0.143873i | ||||
\(672\) | 728711. | − | 513973.i | 1.61368 | − | 1.13816i | ||||
\(673\) | −171479. | − | 297010.i | −0.378600 | − | 0.655754i | 0.612259 | − | 0.790657i | \(-0.290261\pi\) |
−0.990859 | + | 0.134903i | \(0.956928\pi\) | |||||||
\(674\) | 391838. | − | 105280.i | 0.862554 | − | 0.231753i | ||||
\(675\) | 126207. | + | 346751.i | 0.276998 | + | 0.761045i | ||||
\(676\) | −82682.7 | − | 226205.i | −0.180934 | − | 0.495005i | ||||
\(677\) | 268329. | − | 464759.i | 0.585450 | − | 1.01403i | −0.409369 | − | 0.912369i | \(-0.634251\pi\) |
0.994819 | − | 0.101660i | \(-0.0324154\pi\) | |||||||
\(678\) | −719912. | − | 192372.i | −1.56610 | − | 0.418487i | ||||
\(679\) | −15156.2 | − | 18062.4i | −0.0328738 | − | 0.0391775i | ||||
\(680\) | 506525. | + | 720241.i | 1.09543 | + | 1.55762i | ||||
\(681\) | 97868.5 | + | 555040.i | 0.211032 | + | 1.19682i | ||||
\(682\) | −84453.9 | − | 39311.2i | −0.181573 | − | 0.0845176i | ||||
\(683\) | 284151.i | 0.609128i | 0.952492 | + | 0.304564i | \(0.0985107\pi\) | ||||
−0.952492 | + | 0.304564i | \(0.901489\pi\) | |||||||
\(684\) | −613265. | + | 182596.i | −1.31080 | + | 0.390283i | ||||
\(685\) | 993249. | 2.11679 | ||||||||
\(686\) | 89985.2 | − | 193319.i | 0.191215 | − | 0.410796i | ||||
\(687\) | 455409. | − | 80301.0i | 0.964914 | − | 0.170140i | ||||
\(688\) | 188574. | − | 109562.i | 0.398386 | − | 0.231464i | ||||
\(689\) | −75444.4 | + | 63305.4i | −0.158924 | + | 0.133353i | ||||
\(690\) | −214081. | + | 801153.i | −0.449655 | + | 1.68274i | ||||
\(691\) | 275109. | + | 158834.i | 0.576168 | + | 0.332651i | 0.759609 | − | 0.650380i | \(-0.225390\pi\) |
−0.183441 | + | 0.983031i | \(0.558724\pi\) | |||||||
\(692\) | −37694.6 | − | 103126.i | −0.0787167 | − | 0.215355i | ||||
\(693\) | −880666. | + | 320536.i | −1.83377 | + | 0.667438i | ||||
\(694\) | 101017. | + | 375970.i | 0.209736 | + | 0.780610i | ||||
\(695\) | −914417. | + | 527939.i | −1.89311 | + | 1.09298i | ||||
\(696\) | −494493. | − | 492467.i | −1.02080 | − | 1.01662i | ||||
\(697\) | 108865. | − | 617405.i | 0.224090 | − | 1.27088i | ||||
\(698\) | −1003.66 | + | 703.793i | −0.00206004 | + | 0.00144456i | ||||
\(699\) | −100478. | + | 119745.i | −0.205644 | + | 0.245077i | ||||
\(700\) | −900204. | + | 1231.85i | −1.83715 | + | 0.00251398i | ||||
\(701\) | 137074. | + | 49890.9i | 0.278946 | + | 0.101528i | 0.477705 | − | 0.878520i | \(-0.341469\pi\) |
−0.198759 | + | 0.980048i | \(0.563691\pi\) | |||||||
\(702\) | −29792.1 | + | 343229.i | −0.0604542 | + | 0.696482i | ||||
\(703\) | 277726. | − | 292685.i | 0.561962 | − | 0.592229i | ||||
\(704\) | −273562. | + | 478347.i | −0.551963 | + | 0.965157i | ||||
\(705\) | −2.08517e6 | − | 758940.i | −4.19530 | − | 1.52697i | ||||
\(706\) | −76171.4 | − | 863836.i | −0.152821 | − | 1.73309i | ||||
\(707\) | −588551. | + | 701408.i | −1.17746 | + | 1.40324i | ||||
\(708\) | 458579. | − | 265598.i | 0.914844 | − | 0.529856i | ||||
\(709\) | 100600. | − | 570530.i | 0.200126 | − | 1.13497i | −0.704800 | − | 0.709406i | \(-0.748963\pi\) |
0.904927 | − | 0.425568i | \(-0.139926\pi\) | |||||||
\(710\) | 857303. | + | 599416.i | 1.70066 | + | 1.18908i | ||||
\(711\) | 338852. | − | 195636.i | 0.670303 | − | 0.386999i | ||||
\(712\) | 89463.3 | − | 8012.10i | 0.176476 | − | 0.0158047i | ||||
\(713\) | −62467.0 | + | 22736.1i | −0.122877 | + | 0.0447236i | ||||
\(714\) | 520303. | + | 1.11380e6i | 1.02061 | + | 2.18480i | ||||
\(715\) | 948533. | + | 547636.i | 1.85541 | + | 1.07122i | ||||
\(716\) | −371223. | − | 134539.i | −0.724117 | − | 0.262435i | ||||
\(717\) | −940742. | + | 789377.i | −1.82992 | + | 1.53549i | ||||
\(718\) | 511143. | − | 511843.i | 0.991502 | − | 0.992860i | ||||
\(719\) | 180904. | − | 31898.2i | 0.349937 | − | 0.0617033i | 0.00408298 | − | 0.999992i | \(-0.498700\pi\) |
0.345854 | + | 0.938288i | \(0.387589\pi\) | |||||||
\(720\) | 848861. | + | 708329.i | 1.63746 | + | 1.36638i | ||||
\(721\) | −116884. | −0.224846 | ||||||||
\(722\) | −194909. | + | 483474.i | −0.373901 | + | 0.927469i | ||||
\(723\) | 759763.i | 1.45346i | ||||||||
\(724\) | −53623.9 | − | 30862.0i | −0.102301 | − | 0.0588772i | ||||
\(725\) | 122338. | + | 693814.i | 0.232748 | + | 1.31998i | ||||
\(726\) | 135358. | − | 135543.i | 0.256809 | − | 0.257161i | ||||
\(727\) | −324694. | − | 386956.i | −0.614336 | − | 0.732137i | 0.365749 | − | 0.930713i | \(-0.380813\pi\) |
−0.980085 | + | 0.198576i | \(0.936368\pi\) | |||||||
\(728\) | −762454. | − | 353635.i | −1.43864 | − | 0.667255i | ||||
\(729\) | −411988. | + | 713583.i | −0.775227 | + | 1.34273i | ||||
\(730\) | −213798. | − | 457673.i | −0.401197 | − | 0.858834i | ||||
\(731\) | 102832. | + | 282528.i | 0.192439 | + | 0.528721i | ||||
\(732\) | 107517. | + | 604915.i | 0.200657 | + | 1.12894i | ||||
\(733\) | 286125. | + | 495582.i | 0.532534 | + | 0.922376i | 0.999278 | + | 0.0379836i | \(0.0120935\pi\) |
−0.466744 | + | 0.884392i | \(0.654573\pi\) | |||||||
\(734\) | 520359. | + | 363829.i | 0.965852 | + | 0.675312i | ||||
\(735\) | −825805. | − | 145612.i | −1.52863 | − | 0.269539i | ||||
\(736\) | 103074. | + | 379481.i | 0.190281 | + | 0.700542i | ||||
\(737\) | 124053. | + | 104093.i | 0.228388 | + | 0.191640i | ||||
\(738\) | −69142.7 | − | 784126.i | −0.126950 | − | 1.43970i | ||||
\(739\) | 177299. | − | 487126.i | 0.324652 | − | 0.891975i | −0.664788 | − | 0.747032i | \(-0.731478\pi\) |
0.989440 | − | 0.144943i | \(-0.0462998\pi\) | |||||||
\(740\) | −686710. | − | 120117.i | −1.25404 | − | 0.219351i | ||||
\(741\) | 757355. | + | 718648.i | 1.37931 | + | 1.30882i | ||||
\(742\) | −10257.5 | + | 118174.i | −0.0186308 | + | 0.214643i | ||||
\(743\) | −321373. | + | 882966.i | −0.582146 | + | 1.59943i | 0.202359 | + | 0.979311i | \(0.435139\pi\) |
−0.784505 | + | 0.620123i | \(0.787083\pi\) | |||||||
\(744\) | −13058.2 | + | 152870.i | −0.0235906 | + | 0.276170i | ||||
\(745\) | 19006.0 | + | 15947.9i | 0.0342435 | + | 0.0287337i | ||||
\(746\) | 330500. | − | 231756.i | 0.593874 | − | 0.416441i | ||||
\(747\) | −18570.9 | − | 3274.56i | −0.0332807 | − | 0.00586829i | ||||
\(748\) | −582608. | − | 487509.i | −1.04129 | − | 0.871324i | ||||
\(749\) | 641494. | + | 1.11110e6i | 1.14348 | + | 1.98057i | ||||
\(750\) | −151136. | − | 562509.i | −0.268687 | − | 1.00002i | ||||
\(751\) | −63578.9 | − | 174682.i | −0.112728 | − | 0.309719i | 0.870480 | − | 0.492203i | \(-0.163808\pi\) |
−0.983209 | + | 0.182485i | \(0.941586\pi\) | |||||||
\(752\) | −1.03574e6 | + | 185553.i | −1.83153 | + | 0.328120i | ||||
\(753\) | 615947. | − | 1.06685e6i | 1.08631 | − | 1.88154i | ||||
\(754\) | −169808. | + | 635473.i | −0.298687 | + | 1.11777i | ||||
\(755\) | 48554.8 | + | 57865.4i | 0.0851801 | + | 0.101514i | ||||
\(756\) | 267159. | + | 317504.i | 0.467440 | + | 0.555528i | ||||
\(757\) | −155855. | − | 883899.i | −0.271975 | − | 1.54245i | −0.748408 | − | 0.663239i | \(-0.769181\pi\) |
0.476433 | − | 0.879211i | \(-0.341930\pi\) | |||||||
\(758\) | −134987. | + | 289998.i | −0.234938 | + | 0.504727i | ||||
\(759\) | − | 715448.i | − | 1.24192i | ||||||
\(760\) | 882219. | − | 181411.i | 1.52739 | − | 0.314078i | ||||
\(761\) | −406897. | −0.702611 | −0.351306 | − | 0.936261i | \(-0.614262\pi\) | ||||
−0.351306 | + | 0.936261i | \(0.614262\pi\) | |||||||
\(762\) | −453913. | − | 211285.i | −0.781740 | − | 0.363880i | ||||
\(763\) | 478878. | − | 84439.1i | 0.822575 | − | 0.145042i | ||||
\(764\) | −723217. | + | 608539.i | −1.23903 | + | 1.04256i | ||||
\(765\) | −1.16756e6 | + | 979698.i | −1.99506 | + | 1.67405i | ||||
\(766\) | −603788. | − | 161342.i | −1.02903 | − | 0.274972i | ||||
\(767\) | −432559. | − | 249738.i | −0.735284 | − | 0.424516i | ||||
\(768\) | 894637. | + | 152704.i | 1.51679 | + | 0.258898i | ||||
\(769\) | −750250. | + | 273069.i | −1.26868 | + | 0.461763i | −0.886674 | − | 0.462395i | \(-0.846990\pi\) |
−0.382010 | + | 0.924158i | \(0.624768\pi\) | |||||||
\(770\) | 1.27399e6 | − | 342299.i | 2.14875 | − | 0.577331i | ||||
\(771\) | 56964.1 | − | 32888.3i | 0.0958281 | − | 0.0553264i | ||||
\(772\) | 441933. | − | 528141.i | 0.741518 | − | 0.886166i | ||||
\(773\) | 134823. | − | 764620.i | 0.225634 | − | 1.27964i | −0.635834 | − | 0.771826i | \(-0.719344\pi\) |
0.861469 | − | 0.507811i | \(-0.169545\pi\) | |||||||
\(774\) | 216740. | + | 309087.i | 0.361791 | + | 0.515939i | ||||
\(775\) | 99557.6 | − | 118648.i | 0.165757 | − | 0.197541i | ||||
\(776\) | 2042.46 | − | 23910.6i | 0.00339181 | − | 0.0397071i | ||||
\(777\) | −914610. | − | 332891.i | −1.51493 | − | 0.551391i | ||||
\(778\) | −406647. | − | 35296.7i | −0.671828 | − | 0.0583142i | ||||
\(779\) | −534770. | − | 353927.i | −0.881235 | − | 0.583228i | ||||
\(780\) | 310816. | − | 1.77694e6i | 0.510874 | − | 2.92067i | ||||
\(781\) | −848073. | − | 308673.i | −1.39037 | − | 0.506054i | ||||
\(782\) | −540010. | + | 47617.1i | −0.883056 | + | 0.0778663i | ||||
\(783\) | 208743. | − | 248771.i | 0.340478 | − | 0.405766i | ||||
\(784\) | −373278. | + | 137020.i | −0.607295 | + | 0.222922i | ||||
\(785\) | 168020. | − | 952888.i | 0.272660 | − | 1.54633i | ||||
\(786\) | 532930. | − | 762212.i | 0.862631 | − | 1.23376i | ||||
\(787\) | 965470. | − | 557414.i | 1.55880 | − | 0.899971i | 0.561424 | − | 0.827529i | \(-0.310254\pi\) |
0.997373 | − | 0.0724427i | \(-0.0230794\pi\) | |||||||
\(788\) | 147876. | − | 26283.2i | 0.238147 | − | 0.0423278i | ||||
\(789\) | 1.20047e6 | − | 436936.i | 1.92841 | − | 0.701882i | ||||
\(790\) | −498992. | + | 233100.i | −0.799538 | + | 0.373497i | ||||
\(791\) | 732581. | + | 422956.i | 1.17085 | + | 0.675993i | ||||
\(792\) | −865294. | − | 401333.i | −1.37947 | − | 0.639815i | ||||
\(793\) | 443599. | − | 372224.i | 0.705414 | − | 0.591913i | ||||
\(794\) | 703704. | + | 702741.i | 1.11622 | + | 1.11469i | ||||
\(795\) | −250725. | + | 44209.7i | −0.396702 | + | 0.0699492i | ||||
\(796\) | 82105.2 | − | 142661.i | 0.129582 | − | 0.225154i | ||||
\(797\) | 820150. | 1.29115 | 0.645575 | − | 0.763697i | \(-0.276618\pi\) | ||||
0.645575 | + | 0.763697i | \(0.276618\pi\) | |||||||
\(798\) | 1.25703e6 | − | 33825.1i | 1.97396 | − | 0.0531170i | ||||
\(799\) | − | 1.45060e6i | − | 2.27224i | ||||||
\(800\) | −650062. | − | 645630.i | −1.01572 | − | 1.00880i | ||||
\(801\) | 26998.2 | + | 153115.i | 0.0420795 | + | 0.238645i | ||||
\(802\) | 750877. | + | 749850.i | 1.16740 | + | 1.16580i | ||||
\(803\) | 280137. | + | 333855.i | 0.434450 | + | 0.517758i | ||||
\(804\) | 90879.0 | − | 250755.i | 0.140589 | − | 0.387916i | ||||
\(805\) | 470686. | − | 815252.i | 0.726340 | − | 1.25806i | ||||
\(806\) | 131016. | − | 61203.1i | 0.201677 | − | 0.0942114i | ||||
\(807\) | 101256. | + | 278198.i | 0.155479 | + | 0.427176i | ||||
\(808\) | −928175. | + | 83124.9i | −1.42170 | + | 0.127323i | ||||
\(809\) | 273925. | + | 474452.i | 0.418538 | + | 0.724928i | 0.995793 | − | 0.0916356i | \(-0.0292095\pi\) |
−0.577255 | + | 0.816564i | \(0.695876\pi\) | |||||||
\(810\) | 291454. | − | 416846.i | 0.444221 | − | 0.635339i | ||||
\(811\) | −545008. | − | 96099.7i | −0.828632 | − | 0.146110i | −0.256783 | − | 0.966469i | \(-0.582662\pi\) |
−0.571849 | + | 0.820359i | \(0.693774\pi\) | |||||||
\(812\) | 397056. | + | 685553.i | 0.602199 | + | 1.03975i | ||||
\(813\) | −36635.8 | − | 30741.1i | −0.0554275 | − | 0.0465092i | ||||
\(814\) | 599131. | − | 52830.2i | 0.904217 | − | 0.0797322i | ||||
\(815\) | −68813.2 | + | 189063.i | −0.103599 | + | 0.284637i | ||||
\(816\) | −424709. | + | 1.17689e6i | −0.637839 | + | 1.76749i | ||||
\(817\) | 306970. | + | 18763.3i | 0.459888 | + | 0.0281103i | ||||
\(818\) | 325250. | + | 28231.5i | 0.486084 | + | 0.0421917i | ||||
\(819\) | 497577. | − | 1.36708e6i | 0.741810 | − | 2.03811i | ||||
\(820\) | 1516.22 | + | 1.10801e6i | 0.00225493 | + | 1.64784i | ||||
\(821\) | −491866. | − | 412725.i | −0.729727 | − | 0.612314i | 0.200330 | − | 0.979728i | \(-0.435799\pi\) |
−0.930057 | + | 0.367415i | \(0.880243\pi\) | |||||||
\(822\) | 810315. | + | 1.15557e6i | 1.19925 | + | 1.71022i | ||||
\(823\) | 506938. | + | 89386.8i | 0.748437 | + | 0.131970i | 0.534841 | − | 0.844953i | \(-0.320371\pi\) |
0.213595 | + | 0.976922i | \(0.431483\pi\) | |||||||
\(824\) | −84290.6 | − | 83945.2i | −0.124144 | − | 0.123635i | ||||
\(825\) | 833470. | + | 1.44361e6i | 1.22457 | + | 2.12101i | ||||
\(826\) | −580978. | + | 156099.i | −0.851530 | + | 0.228791i | ||||
\(827\) | −114256. | − | 313917.i | −0.167059 | − | 0.458991i | 0.827708 | − | 0.561159i | \(-0.189644\pi\) |
−0.994767 | + | 0.102168i | \(0.967422\pi\) | |||||||
\(828\) | −639295. | + | 233676.i | −0.932483 | + | 0.340842i | ||||
\(829\) | 77098.2 | − | 133538.i | 0.112185 | − | 0.194310i | −0.804466 | − | 0.593999i | \(-0.797548\pi\) |
0.916651 | + | 0.399689i | \(0.130882\pi\) | |||||||
\(830\) | 25643.8 | + | 6852.44i | 0.0372243 | + | 0.00994693i | ||||
\(831\) | 874976. | + | 1.04276e6i | 1.26705 | + | 1.51001i | ||||
\(832\) | −295863. | − | 802609.i | −0.427409 | − | 1.15946i | ||||
\(833\) | −95189.2 | − | 539845.i | −0.137182 | − | 0.777999i | ||||
\(834\) | −1.36022e6 | − | 633147.i | −1.95558 | − | 0.910275i | ||||
\(835\) | − | 1.98587e6i | − | 2.84825i | ||||||
\(836\) | −694930. | + | 347701.i | −0.994326 | + | 0.497500i | ||||
\(837\) | −71393.8 | −0.101908 | ||||||||
\(838\) | −27781.2 | + | 59683.5i | −0.0395606 | + | 0.0849898i | ||||
\(839\) | 811371. | − | 143067.i | 1.15265 | − | 0.203242i | 0.435515 | − | 0.900181i | \(-0.356566\pi\) |
0.717130 | + | 0.696939i | \(0.245455\pi\) | |||||||
\(840\) | −1.24985e6 | − | 1.77720e6i | −1.77133 | − | 2.51871i | ||||
\(841\) | −66846.9 | + | 56091.2i | −0.0945125 | + | 0.0793054i | ||||
\(842\) | −233543. | + | 873985.i | −0.329414 | + | 1.23276i | ||||
\(843\) | 1.53328e6 | + | 885241.i | 2.15758 | + | 1.24568i | ||||
\(844\) | −517074. | + | 189001.i | −0.725886 | + | 0.265326i | ||||
\(845\) | −551419. | + | 200700.i | −0.772269 | + | 0.281083i | ||||
\(846\) | −472606. | − | 1.75898e6i | −0.660327 | − | 2.45765i | ||||
\(847\) | −188320. | + | 108726.i | −0.262500 | + | 0.151554i | ||||
\(848\) | −92268.9 | + | 77854.1i | −0.128311 | + | 0.108265i | ||||
\(849\) | 91572.7 | − | 519335.i | 0.127043 | − | 0.720497i | ||||
\(850\) | 1.03415e6 | − | 725173.i | 1.43135 | − | 1.00370i | ||||
\(851\) | 275886. | − | 328788.i | 0.380952 | − | 0.454001i | ||||
\(852\) | 2034.04 | + | 1.48642e6i | 0.00280207 | + | 2.04768i | ||||
\(853\) | 713521. | + | 259700.i | 0.980638 | + | 0.356923i | 0.782088 | − | 0.623168i | \(-0.214155\pi\) |
0.198550 | + | 0.980091i | \(0.436377\pi\) | |||||||
\(854\) | 60312.0 | − | 694844.i | 0.0826966 | − | 0.952734i | ||||
\(855\) | 442846. | + | 1.49481e6i | 0.605788 | + | 2.04482i | ||||
\(856\) | −335372. | + | 1.26198e6i | −0.457698 | + | 1.72228i | ||||
\(857\) | 520759. | + | 189541.i | 0.709048 | + | 0.258072i | 0.671269 | − | 0.741214i | \(-0.265750\pi\) |
0.0377787 | + | 0.999286i | \(0.487972\pi\) | |||||||
\(858\) | 136704. | + | 1.55032e6i | 0.185698 | + | 2.10594i | ||||
\(859\) | −355835. | + | 424068.i | −0.482239 | + | 0.574710i | −0.951226 | − | 0.308495i | \(-0.900175\pi\) |
0.468987 | + | 0.883205i | \(0.344619\pi\) | |||||||
\(860\) | −266317. | − | 459820.i | −0.360083 | − | 0.621715i | ||||
\(861\) | −268625. | + | 1.52345e6i | −0.362360 | + | 2.05505i | ||||
\(862\) | −771192. | − | 539208.i | −1.03788 | − | 0.725675i | ||||
\(863\) | 146660. | − | 84674.0i | 0.196920 | − | 0.113692i | −0.398298 | − | 0.917256i | \(-0.630399\pi\) |
0.595218 | + | 0.803564i | \(0.297066\pi\) | |||||||
\(864\) | −35368.2 | + | 420838.i | −0.0473790 | + | 0.563751i | ||||
\(865\) | −251389. | + | 91498.1i | −0.335980 | + | 0.122287i | ||||
\(866\) | −390989. | − | 836984.i | −0.521350 | − | 1.11604i | ||||
\(867\) | −492100. | − | 284114.i | −0.654660 | − | 0.377968i | ||||
\(868\) | 59345.1 | − | 163746.i | 0.0787672 | − | 0.217336i | ||||
\(869\) | 363996. | − | 305429.i | 0.482011 | − | 0.404455i | ||||
\(870\) | −1.20153e6 | + | 1.20318e6i | −1.58744 | + | 1.58961i | ||||
\(871\) | −247564. | + | 43652.3i | −0.326326 | + | 0.0575401i | ||||
\(872\) | 405984. | + | 283033.i | 0.533919 | + | 0.372223i | ||||
\(873\) | 41539.0 | 0.0545038 | ||||||||
\(874\) | −175571. | + | 525988.i | −0.229842 | + | 0.688577i | ||||
\(875\) | 661203.i | 0.863612i | ||||||||
\(876\) | 358045. | − | 622117.i | 0.466583 | − | 0.810706i | ||||
\(877\) | −184462. | − | 1.04614e6i | −0.239832 | − | 1.36016i | −0.832194 | − | 0.554484i | \(-0.812915\pi\) |
0.592362 | − | 0.805672i | \(-0.298196\pi\) | |||||||
\(878\) | −41589.5 | + | 41646.4i | −0.0539504 | + | 0.0540243i | ||||
\(879\) | −1.22278e6 | − | 1.45725e6i | −1.58259 | − | 1.88606i | ||||
\(880\) | 1.16457e6 | + | 668121.i | 1.50383 | + | 0.862760i | ||||
\(881\) | −657002. | + | 1.13796e6i | −0.846477 | + | 1.46614i | 0.0378553 | + | 0.999283i | \(0.487947\pi\) |
−0.884332 | + | 0.466858i | \(0.845386\pi\) | |||||||
\(882\) | −291307. | − | 623596.i | −0.374467 | − | 0.801616i | ||||
\(883\) | −252526. | − | 693809.i | −0.323880 | − | 0.889853i | −0.989625 | − | 0.143674i | \(-0.954108\pi\) |
0.665745 | − | 0.746179i | \(-0.268114\pi\) | |||||||
\(884\) | 1.16106e6 | − | 206365.i | 1.48576 | − | 0.264077i | ||||
\(885\) | −645594. | − | 1.11820e6i | −0.824276 | − | 1.42769i | ||||
\(886\) | −539464. | − | 377187.i | −0.687219 | − | 0.480496i | ||||
\(887\) | 1.38249e6 | + | 243770.i | 1.75717 | + | 0.309837i | 0.957033 | − | 0.289978i | \(-0.0936480\pi\) |
0.800139 | + | 0.599815i | \(0.204759\pi\) | |||||||
\(888\) | −420487. | − | 896927.i | −0.533245 | − | 1.13745i | ||||
\(889\) | 435393. | + | 365338.i | 0.550906 | + | 0.462265i | ||||
\(890\) | −19223.0 | − | 218002.i | −0.0242684 | − | 0.275220i | ||||
\(891\) | −150086. | + | 412358.i | −0.189054 | + | 0.519420i | ||||
\(892\) | 102277. | − | 584722.i | 0.128544 | − | 0.734886i | ||||
\(893\) | −1.36076e6 | − | 591615.i | −1.70640 | − | 0.741884i | ||||
\(894\) | −3048.62 | + | 35122.6i | −0.00381442 | + | 0.0439453i | ||||
\(895\) | −329039. | + | 904027.i | −0.410772 | + | 1.12859i | ||||
\(896\) | −935818. | − | 430935.i | −1.16567 | − | 0.536779i | ||||
\(897\) | 850776. | + | 713886.i | 1.05738 | + | 0.887246i | ||||
\(898\) | −350282. | + | 245628.i | −0.434375 | + | 0.304596i | ||||
\(899\) | −134237. | − | 23669.6i | −0.166093 | − | 0.0292867i | ||||
\(900\) | 1.01773e6 | − | 1.21626e6i | 1.25646 | − | 1.50156i | ||||
\(901\) | −83216.3 | − | 144135.i | −0.102508 | − | 0.177549i | ||||
\(902\) | −248047. | − | 923196.i | −0.304874 | − | 1.13470i | ||||
\(903\) | −253738. | − | 697139.i | −0.311179 | − | 0.854956i | ||||
\(904\) | 224534. | + | 831146.i | 0.274755 | + | 1.01705i | ||||
\(905\) | −75373.3 | + | 130550.i | −0.0920281 | + | 0.159397i | ||||
\(906\) | −27709.6 | + | 103698.i | −0.0337578 | + | 0.126332i | ||||
\(907\) | −254808. | − | 303668.i | −0.309741 | − | 0.369135i | 0.588607 | − | 0.808419i | \(-0.299676\pi\) |
−0.898348 | + | 0.439285i | \(0.855232\pi\) | |||||||
\(908\) | 498247. | − | 419242.i | 0.604328 | − | 0.508502i | ||||
\(909\) | −280105. | − | 1.58855e6i | −0.338994 | − | 1.92253i | ||||
\(910\) | −864164. | + | 1.85652e6i | −1.04355 | + | 2.24190i | ||||
\(911\) | 612066.i | 0.737499i | 0.929529 | + | 0.368749i | \(0.120214\pi\) | ||||
−0.929529 | + | 0.368749i | \(0.879786\pi\) | |||||||
\(912\) | 930792. | + | 878393.i | 1.11908 | + | 1.05609i | ||||
\(913\) | −22900.5 | −0.0274728 | ||||||||
\(914\) | −877182. | − | 408306.i | −1.05002 | − | 0.488758i | ||||
\(915\) | 1.47422e6 | − | 259945.i | 1.76084 | − | 0.310484i | ||||
\(916\) | −343987. | − | 408811.i | −0.409969 | − | 0.487227i | ||||
\(917\) | −808773. | + | 678641.i | −0.961807 | + | 0.807052i | ||||
\(918\) | −562475. | − | 150302.i | −0.667448 | − | 0.178353i | ||||
\(919\) | 314159. | + | 181380.i | 0.371979 | + | 0.214762i | 0.674323 | − | 0.738437i | \(-0.264436\pi\) |
−0.302344 | + | 0.953199i | \(0.597769\pi\) | |||||||
\(920\) | 924940. | − | 249873.i | 1.09279 | − | 0.295218i | ||||
\(921\) | 1.88531e6 | − | 686197.i | 2.22261 | − | 0.808965i | ||||
\(922\) | 230196. | − | 61849.5i | 0.270792 | − | 0.0727570i | ||||
\(923\) | 1.21328e6 | − | 700488.i | 1.42416 | − | 0.822237i | ||||
\(924\) | 1.43759e6 | + | 1.20293e6i | 1.68380 | + | 1.40896i | ||||
\(925\) | −173650. | + | 984818.i | −0.202951 | + | 1.15099i | ||||
\(926\) | 674601. | + | 962028.i | 0.786729 | + | 1.12193i | ||||
\(927\) | 132360. | − | 157741.i | 0.154027 | − | 0.183563i | ||||
\(928\) | −206023. | + | 779545.i | −0.239232 | + | 0.905202i | ||||
\(929\) | 529033. | + | 192552.i | 0.612987 | + | 0.223109i | 0.629810 | − | 0.776749i | \(-0.283133\pi\) |
−0.0168224 | + | 0.999858i | \(0.505355\pi\) | |||||||
\(930\) | 372420. | + | 32325.8i | 0.430593 | + | 0.0373752i | ||||
\(931\) | −545235. | − | 130877.i | −0.629049 | − | 0.150996i | ||||
\(932\) | 177900. | + | 31117.6i | 0.204806 | + | 0.0358240i | ||||
\(933\) | −928556. | − | 337967.i | −1.06671 | − | 0.388249i | ||||
\(934\) | −282120. | + | 24876.9i | −0.323401 | + | 0.0285169i | ||||
\(935\) | −1.18975e6 | + | 1.41789e6i | −1.36092 | + | 1.62188i | ||||
\(936\) | 1.34065e6 | − | 628509.i | 1.53026 | − | 0.717398i | ||||
\(937\) | −239883. | + | 1.36044e6i | −0.273225 | + | 1.54954i | 0.471319 | + | 0.881963i | \(0.343778\pi\) |
−0.744544 | + | 0.667573i | \(0.767333\pi\) | |||||||
\(938\) | −173494. | + | 248136.i | −0.197187 | + | 0.282023i | ||||
\(939\) | −2.28723e6 | + | 1.32053e6i | −2.59405 | + | 1.49767i | ||||
\(940\) | 448642. | + | 2.52417e6i | 0.507743 | + | 2.85669i | ||||
\(941\) | 621529. | − | 226218.i | 0.701911 | − | 0.255475i | 0.0336843 | − | 0.999433i | \(-0.489276\pi\) |
0.668227 | + | 0.743958i | \(0.267054\pi\) | |||||||
\(942\) | 1.24568e6 | − | 581910.i | 1.40380 | − | 0.655774i | ||||
\(943\) | −590772. | − | 341082.i | −0.664349 | − | 0.383562i | ||||
\(944\) | −531078. | − | 304683.i | −0.595957 | − | 0.341904i | ||||
\(945\) | 774482. | − | 649868.i | 0.867257 | − | 0.727715i | ||||
\(946\) | 324391. | + | 323947.i | 0.362482 | + | 0.361986i | ||||
\(947\) | 29499.2 | − | 5201.50i | 0.0328935 | − | 0.00580001i | −0.157177 | − | 0.987570i | \(-0.550239\pi\) |
0.190071 | + | 0.981770i | \(0.439128\pi\) | |||||||
\(948\) | −678282. | − | 390370.i | −0.754733 | − | 0.434369i | ||||
\(949\) | −676530. | −0.751198 | ||||||||
\(950\) | −258494. | − | 1.26586e6i | −0.286420 | − | 1.40261i | ||||
\(951\) | − | 508179.i | − | 0.561896i | ||||||
\(952\) | 812277. | − | 1.16513e6i | 0.896252 | − | 1.28559i | ||||
\(953\) | 228263. | + | 1.29454e6i | 0.251333 | + | 1.42538i | 0.805313 | + | 0.592849i | \(0.201997\pi\) |
−0.553981 | + | 0.832530i | \(0.686892\pi\) | |||||||
\(954\) | −147866. | − | 147664.i | −0.162470 | − | 0.162248i | ||||
\(955\) | 1.48028e6 | + | 1.76413e6i | 1.62307 | + | 1.93430i | ||||
\(956\) | 1.33394e6 | + | 483447.i | 1.45955 | + | 0.528973i | ||||
\(957\) | 733505. | − | 1.27047e6i | 0.800902 | − | 1.38720i | ||||
\(958\) | −674328. | + | 315006.i | −0.734752 | + | 0.343232i | ||||
\(959\) | −547973. | − | 1.50554e6i | −0.595830 | − | 1.63703i | ||||
\(960\) | 375043. | − | 2.17925e6i | 0.406948 | − | 2.36464i | ||||
\(961\) | −446777. | − | 773841.i | −0.483776 | − | 0.837925i | ||||
\(962\) | −534999. | + | 765172.i | −0.578100 | + | 0.826816i | ||||
\(963\) | −2.22591e6 | − | 392488.i | −2.40024 | − | 0.423228i | ||||
\(964\) | 759596. | − | 439940.i | 0.817388 | − | 0.473412i | ||||
\(965\) | −1.28533e6 | − | 1.07852e6i | −1.38026 | − | 1.15817i | ||||
\(966\) | 1.33248e6 | − | 117495.i | 1.42793 | − | 0.125912i | ||||
\(967\) | −337875. | + | 928305.i | −0.361330 | + | 0.992745i | 0.617230 | + | 0.786783i | \(0.288255\pi\) |
−0.978560 | + | 0.205962i | \(0.933968\pi\) | |||||||
\(968\) | −213892. | − | 56841.9i | −0.228267 | − | 0.0606622i | ||||
\(969\) | −1.41825e6 | + | 1.04953e6i | −1.51045 | + | 1.11776i | ||||
\(970\) | −58250.9 | − | 5056.13i | −0.0619098 | − | 0.00537372i | ||||
\(971\) | −53889.8 | + | 148061.i | −0.0571568 | + | 0.157037i | −0.964985 | − | 0.262306i | \(-0.915517\pi\) |
0.907828 | + | 0.419343i | \(0.137739\pi\) | |||||||
\(972\) | 1.25724e6 | − | 1720.42i | 1.33072 | − | 0.00182097i | ||||
\(973\) | 1.30472e6 | + | 1.09479e6i | 1.37813 | + | 1.15639i | ||||
\(974\) | −556131. | − | 793082.i | −0.586218 | − | 0.835988i | ||||
\(975\) | −2.54833e6 | − | 449339.i | −2.68068 | − | 0.472677i | ||||
\(976\) | 542524. | − | 457768.i | 0.569534 | − | 0.480558i | ||||
\(977\) | 222534. | + | 385440.i | 0.233135 | + | 0.403801i | 0.958729 | − | 0.284322i | \(-0.0917683\pi\) |
−0.725594 | + | 0.688123i | \(0.758435\pi\) | |||||||
\(978\) | −276099. | + | 74183.0i | −0.288660 | + | 0.0775580i | ||||
\(979\) | 64577.2 | + | 177424.i | 0.0673773 | + | 0.185118i | ||||
\(980\) | 332602. | + | 909939.i | 0.346316 | + | 0.947458i | ||||
\(981\) | −428328. | + | 741886.i | −0.445081 | + | 0.770902i | ||||
\(982\) | 275306. | + | 73566.1i | 0.285491 | + | 0.0762877i | ||||
\(983\) | −764456. | − | 911043.i | −0.791125 | − | 0.942827i | 0.208253 | − | 0.978075i | \(-0.433222\pi\) |
−0.999379 | + | 0.0352484i | \(0.988778\pi\) | |||||||
\(984\) | −1.28785e6 | + | 905704.i | −1.33007 | + | 0.935398i | ||||
\(985\) | −63545.4 | − | 360384.i | −0.0654955 | − | 0.371443i | ||||
\(986\) | −1.00775e6 | − | 469083.i | −1.03657 | − | 0.482498i | ||||
\(987\) | 3.57936e6i | 3.67427i | ||||||||
\(988\) | 279944. | − | 1.17332e6i | 0.286786 | − | 1.20199i | ||||
\(989\) | 327149. | 0.334467 | ||||||||
\(990\) | −980723. | + | 2.10693e6i | −1.00064 | + | 2.14971i | ||||
\(991\) | −613671. | + | 108207.i | −0.624868 | + | 0.110181i | −0.477111 | − | 0.878843i | \(-0.658316\pi\) |
−0.147756 | + | 0.989024i | \(0.547205\pi\) | |||||||
\(992\) | 160397. | − | 75463.6i | 0.162995 | − | 0.0766857i | ||||
\(993\) | 420568. | − | 352898.i | 0.426518 | − | 0.357891i | ||||
\(994\) | 435609. | − | 1.63018e6i | 0.440884 | − | 1.64992i | ||||
\(995\) | −347316. | − | 200523.i | −0.350816 | − | 0.202543i | ||||
\(996\) | 12948.5 | + | 35424.9i | 0.0130528 | + | 0.0357100i | ||||
\(997\) | −630545. | + | 229500.i | −0.634345 | + | 0.230883i | −0.639121 | − | 0.769106i | \(-0.720702\pi\) |
0.00477622 | + | 0.999989i | \(0.498480\pi\) | |||||||
\(998\) | 198623. | + | 739246.i | 0.199420 | + | 0.742212i | ||||
\(999\) | 399199. | − | 230477.i | 0.399998 | − | 0.230939i |
(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.l.a.23.5 | yes | 228 | |
4.3 | odd | 2 | inner | 76.5.l.a.23.4 | ✓ | 228 | |
19.5 | even | 9 | inner | 76.5.l.a.43.4 | yes | 228 | |
76.43 | odd | 18 | inner | 76.5.l.a.43.5 | yes | 228 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.l.a.23.4 | ✓ | 228 | 4.3 | odd | 2 | inner | |
76.5.l.a.23.5 | yes | 228 | 1.1 | even | 1 | trivial | |
76.5.l.a.43.4 | yes | 228 | 19.5 | even | 9 | inner | |
76.5.l.a.43.5 | yes | 228 | 76.43 | odd | 18 | inner |