Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [240,5,Mod(97,240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("240.97");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.bg (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.8087911401\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 30) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 97.2 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 240.97 |
Dual form | 240.5.bg.b.193.2 |
$q$-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 \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(181\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.67423 | − | 3.67423i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 24.6742 | + | 4.02270i | 0.986969 | + | 0.160908i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −44.4393 | − | 44.4393i | −0.906924 | − | 0.906924i | 0.0890986 | − | 0.996023i | \(-0.471601\pi\) |
−0.996023 | + | 0.0890986i | \(0.971601\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 27.0000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −167.439 | −1.38380 | −0.691898 | − | 0.721995i | \(-0.743225\pi\) | ||||
−0.691898 | + | 0.721995i | \(0.743225\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −223.621 | + | 223.621i | −1.32320 | + | 1.32320i | −0.412031 | + | 0.911170i | \(0.635180\pi\) |
−0.911170 | + | 0.412031i | \(0.864820\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 105.439 | − | 75.8786i | 0.468619 | − | 0.337238i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −71.0148 | − | 71.0148i | −0.245726 | − | 0.245726i | 0.573488 | − | 0.819214i | \(-0.305590\pi\) |
−0.819214 | + | 0.573488i | \(0.805590\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 272.211i | 0.754048i | 0.926204 | + | 0.377024i | \(0.123053\pi\) | ||||
−0.926204 | + | 0.377024i | \(0.876947\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −326.561 | −0.740500 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −87.6821 | + | 87.6821i | −0.165751 | + | 0.165751i | −0.785109 | − | 0.619358i | \(-0.787393\pi\) |
0.619358 | + | 0.785109i | \(0.287393\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 592.636 | + | 198.514i | 0.948217 | + | 0.317623i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −99.2043 | − | 99.2043i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 839.832i | − | 0.998611i | −0.866426 | − | 0.499306i | \(-0.833588\pi\) | ||
0.866426 | − | 0.499306i | \(-0.166412\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −403.787 | −0.420173 | −0.210087 | − | 0.977683i | \(-0.567375\pi\) | ||||
−0.210087 | + | 0.977683i | \(0.567375\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −615.211 | + | 615.211i | −0.564932 | + | 0.564932i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −917.739 | − | 1275.27i | −0.749175 | − | 1.04104i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −207.589 | − | 207.589i | −0.151636 | − | 0.151636i | 0.627212 | − | 0.778848i | \(-0.284196\pi\) |
−0.778848 | + | 0.627212i | \(0.784196\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1643.27i | 1.08039i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1386.39 | −0.824742 | −0.412371 | − | 0.911016i | \(-0.635299\pi\) | ||||
−0.412371 | + | 0.911016i | \(0.635299\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −568.393 | + | 568.393i | −0.307406 | + | 0.307406i | −0.843902 | − | 0.536497i | \(-0.819747\pi\) |
0.536497 | + | 0.843902i | \(0.319747\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 108.613 | − | 666.204i | 0.0536361 | − | 0.328990i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2642.77 | + | 2642.77i | 1.19637 | + | 1.19637i | 0.975247 | + | 0.221119i | \(0.0709709\pi\) |
0.221119 | + | 0.975247i | \(0.429029\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1548.70i | 0.645023i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −521.850 | −0.200634 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1378.64 | + | 1378.64i | −0.490792 | + | 0.490792i | −0.908556 | − | 0.417763i | \(-0.862814\pi\) |
0.417763 | + | 0.908556i | \(0.362814\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4131.44 | − | 673.559i | −1.36576 | − | 0.222664i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1000.17 | + | 1000.17i | 0.307839 | + | 0.307839i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 327.503i | 0.0940829i | 0.998893 | + | 0.0470415i | \(0.0149793\pi\) | ||||
−0.998893 | + | 0.0470415i | \(0.985021\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4205.66 | −1.13025 | −0.565125 | − | 0.825005i | \(-0.691172\pi\) | ||||
−0.565125 | + | 0.825005i | \(0.691172\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1199.86 | + | 1199.86i | −0.302308 | + | 0.302308i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6417.24 | + | 4618.11i | −1.51887 | + | 1.09304i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2832.99 | − | 2832.99i | −0.631097 | − | 0.631097i | 0.317246 | − | 0.948343i | \(-0.397242\pi\) |
−0.948343 | + | 0.317246i | \(0.897242\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 644.330i | 0.135335i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5339.03 | −1.05912 | −0.529560 | − | 0.848272i | \(-0.677643\pi\) | ||||
−0.529560 | + | 0.848272i | \(0.677643\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6865.24 | − | 6865.24i | 1.28828 | − | 1.28828i | 0.352447 | − | 0.935832i | \(-0.385350\pi\) |
0.935832 | − | 0.352447i | \(-0.114650\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2906.87 | − | 1448.09i | 0.516777 | − | 0.257439i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7440.88 | + | 7440.88i | 1.25500 | + | 1.25500i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4666.69i | − | 0.747748i | −0.927480 | − | 0.373874i | \(-0.878029\pi\) | ||
0.927480 | − | 0.373874i | \(-0.121971\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −729.000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4111.98 | + | 4111.98i | −0.596890 | + | 0.596890i | −0.939484 | − | 0.342594i | \(-0.888695\pi\) |
0.342594 | + | 0.939484i | \(0.388695\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1466.56 | − | 2037.91i | −0.202985 | − | 0.282063i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3085.74 | − | 3085.74i | −0.407681 | − | 0.407681i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9911.62i | − | 1.25131i | −0.780100 | − | 0.625654i | \(-0.784832\pi\) | ||
0.780100 | − | 0.625654i | \(-0.215168\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19875.1 | 2.40009 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1483.61 | + | 1483.61i | −0.171535 | + | 0.171535i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1095.03 | + | 6716.60i | −0.121332 | + | 0.744222i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10688.9 | − | 10688.9i | −1.13603 | − | 1.13603i | −0.989156 | − | 0.146871i | \(-0.953080\pi\) |
−0.146871 | − | 0.989156i | \(-0.546920\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4520.86i | 0.461265i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1763.09 | −0.172835 | −0.0864177 | − | 0.996259i | \(-0.527542\pi\) | ||||
−0.0864177 | + | 0.996259i | \(0.527542\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2414.27 | − | 2414.27i | 0.227568 | − | 0.227568i | −0.584108 | − | 0.811676i | \(-0.698556\pi\) |
0.811676 | + | 0.584108i | \(0.198556\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8057.64 | − | 1313.66i | −0.730851 | − | 0.119153i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4279.03 | − | 4279.03i | −0.373747 | − | 0.373747i | 0.495093 | − | 0.868840i | \(-0.335134\pi\) |
−0.868840 | + | 0.495093i | \(0.835134\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11819.5i | 0.994827i | 0.867514 | + | 0.497413i | \(0.165717\pi\) | ||||
−0.867514 | + | 0.497413i | \(0.834283\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1525.46 | −0.123810 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1620.60 | − | 1620.60i | 0.126917 | − | 0.126917i | −0.640795 | − | 0.767712i | \(-0.721395\pi\) |
0.767712 | + | 0.640795i | \(0.221395\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2516.21 | + | 1810.77i | −0.190262 | + | 0.136920i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6037.76 | + | 6037.76i | 0.441067 | + | 0.441067i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6311.69i | 0.445710i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13394.9 | 0.914891 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5093.93 | + | 5093.93i | −0.336699 | + | 0.336699i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 13824.3 | + | 7282.19i | 0.884753 | + | 0.466060i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11572.5 | + | 11572.5i | 0.717494 | + | 0.717494i | 0.968091 | − | 0.250597i | \(-0.0806270\pi\) |
−0.250597 | + | 0.968091i | \(0.580627\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4176.82i | 0.250996i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −65.6230 | −0.00382396 | −0.00191198 | − | 0.999998i | \(-0.500609\pi\) | ||||
−0.00191198 | + | 0.999998i | \(0.500609\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12096.9 | − | 12096.9i | 0.683864 | − | 0.683864i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2048.72 | − | 2846.86i | −0.112413 | − | 0.156206i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 579.439 | + | 579.439i | 0.0308721 | + | 0.0308721i | 0.722374 | − | 0.691502i | \(-0.243051\pi\) |
−0.691502 | + | 0.722374i | \(0.743051\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 36158.2i | − | 1.87145i | −0.352734 | − | 0.935724i | \(-0.614748\pi\) | ||
0.352734 | − | 0.935724i | \(-0.385252\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19420.3 | 0.976829 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 37442.9 | − | 37442.9i | 1.83104 | − | 1.83104i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3378.40 | − | 20722.2i | 0.160685 | − | 0.985599i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5690.29 | + | 5690.29i | 0.263330 | + | 0.263330i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2143.94i | − | 0.0965695i | −0.998834 | − | 0.0482847i | \(-0.984625\pi\) | ||
0.998834 | − | 0.0482847i | \(-0.0153755\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8940.59 | 0.392114 | 0.196057 | − | 0.980593i | \(-0.437186\pi\) | ||||
0.196057 | + | 0.980593i | \(0.437186\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1917.40 | + | 1917.40i | −0.0819086 | + | 0.0819086i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9963.13 | − | 1624.31i | −0.414698 | − | 0.0676093i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18032.9 | + | 18032.9i | 0.731586 | + | 0.731586i | 0.970934 | − | 0.239348i | \(-0.0769337\pi\) |
−0.239348 | + | 0.970934i | \(0.576934\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10130.9i | 0.400730i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7793.06 | 0.300647 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6859.00 | − | 6859.00i | 0.258158 | − | 0.258158i | −0.566147 | − | 0.824305i | \(-0.691566\pi\) |
0.824305 | + | 0.566147i | \(0.191566\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −17654.7 | + | 12705.1i | −0.648473 | + | 0.466669i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 37439.2 | + | 37439.2i | 1.34244 | + | 1.34244i | 0.893627 | + | 0.448811i | \(0.148152\pi\) |
0.448811 | + | 0.893627i | \(0.351848\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 71451.6i | − | 2.50172i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7349.70 | 0.251349 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −32638.2 | + | 32638.2i | −1.09052 | + | 1.09052i | −0.0950500 | + | 0.995472i | \(0.530301\pi\) |
−0.995472 | + | 0.0950500i | \(0.969699\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17514.5 | − | 35158.1i | −0.571901 | − | 1.14802i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1203.32 | + | 1203.32i | 0.0384092 | + | 0.0384092i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6396.19i | 0.199625i | 0.995006 | + | 0.0998126i | \(0.0318243\pi\) | ||||
−0.995006 | + | 0.0998126i | \(0.968176\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 49025.9 | 1.49647 | 0.748236 | − | 0.663432i | \(-0.230901\pi\) | ||||
0.748236 | + | 0.663432i | \(0.230901\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15452.6 | + | 15452.6i | −0.461423 | + | 0.461423i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4287.04 | − | 5957.18i | −0.125260 | − | 0.174059i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11890.7 | + | 11890.7i | 0.340034 | + | 0.340034i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8817.14i | 0.246833i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −39949.0 | −1.09506 | −0.547531 | − | 0.836785i | \(-0.684432\pi\) | ||||
−0.547531 | + | 0.836785i | \(0.684432\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23749.1 | + | 23749.1i | −0.637577 | + | 0.637577i | −0.949957 | − | 0.312380i | \(-0.898874\pi\) |
0.312380 | + | 0.949957i | \(0.398874\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6610.39 | + | 40546.5i | −0.173843 | + | 1.06631i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2725.09 | − | 2725.09i | −0.0702181 | − | 0.0702181i | 0.671126 | − | 0.741344i | \(-0.265811\pi\) |
−0.741344 | + | 0.671126i | \(0.765811\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 63212.5i | − | 1.59624i | −0.602502 | − | 0.798118i | \(-0.705829\pi\) | ||
0.602502 | − | 0.798118i | \(-0.294171\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20818.2 | −0.515288 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −37321.5 | + | 37321.5i | −0.905665 | + | 0.905665i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −34208.1 | − | 5577.04i | −0.813995 | − | 0.132708i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2367.42 | + | 2367.42i | 0.0552502 | + | 0.0552502i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 45578.9i | − | 1.04345i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15470.2 | −0.347480 | −0.173740 | − | 0.984792i | \(-0.555585\pi\) | ||||
−0.173740 | + | 0.984792i | \(0.555585\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −19616.8 | + | 19616.8i | −0.432384 | + | 0.432384i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16311.1 | + | 11738.2i | −0.352864 | + | 0.253936i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17944.0 | + | 17944.0i | 0.381065 | + | 0.381065i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 50449.0i | − | 1.05188i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 31760.8 | 0.650289 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28817.8 | + | 28817.8i | −0.579496 | + | 0.579496i | −0.934764 | − | 0.355268i | \(-0.884389\pi\) |
0.355268 | + | 0.934764i | \(0.384389\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5359.89 | − | 16001.2i | 0.105874 | − | 0.316072i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −884.237 | − | 884.237i | −0.0171600 | − | 0.0171600i | 0.698475 | − | 0.715635i | \(-0.253862\pi\) |
−0.715635 | + | 0.698475i | \(0.753862\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 12076.4i | − | 0.230285i | −0.993349 | − | 0.115143i | \(-0.963268\pi\) | ||
0.993349 | − | 0.115143i | \(-0.0367325\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 54679.1 | 1.02470 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24695.8 | + | 24695.8i | −0.454894 | + | 0.454894i | −0.896975 | − | 0.442081i | \(-0.854240\pi\) |
0.442081 | + | 0.896975i | \(0.354240\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 54577.3 | + | 75839.5i | 0.988271 | + | 1.37328i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −17146.5 | − | 17146.5i | −0.305267 | − | 0.305267i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 48187.8i | − | 0.843608i | −0.906687 | − | 0.421804i | \(-0.861397\pi\) | ||
0.906687 | − | 0.421804i | \(-0.138603\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −55184.2 | −0.950125 | −0.475062 | − | 0.879952i | \(-0.657574\pi\) | ||||
−0.475062 | + | 0.879952i | \(0.657574\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2678.52 | + | 2678.52i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6229.96 | + | 38213.0i | −0.103789 | + | 0.636618i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −60872.1 | − | 60872.1i | −0.997756 | − | 0.997756i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 30216.7i | 0.487359i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 69667.8 | 1.10582 | 0.552910 | − | 0.833241i | \(-0.313517\pi\) | ||||
0.552910 | + | 0.833241i | \(0.313517\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14681.4 | − | 14681.4i | 0.229365 | − | 0.229365i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12876.2 | − | 2099.25i | −0.198020 | − | 0.0322837i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11614.4 | − | 11614.4i | −0.175846 | − | 0.175846i | 0.613696 | − | 0.789542i | \(-0.289682\pi\) |
−0.789542 | + | 0.613696i | \(0.789682\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18450.2i | 0.275044i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22675.5 | −0.332870 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −86811.6 | + | 86811.6i | −1.25507 | + | 1.25507i | −0.301646 | + | 0.953420i | \(0.597536\pi\) |
−0.953420 | + | 0.301646i | \(0.902464\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −39562.6 | + | 28470.9i | −0.563370 | + | 0.405425i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −36417.6 | − | 36417.6i | −0.510845 | − | 0.510845i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 93439.3i | 1.29129i | 0.763636 | + | 0.645647i | \(0.223412\pi\) | ||||
−0.763636 | + | 0.645647i | \(0.776588\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10856.5 | 0.147826 | 0.0739131 | − | 0.997265i | \(-0.476451\pi\) | ||||
0.0739131 | + | 0.997265i | \(0.476451\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 73025.8 | − | 73025.8i | 0.979831 | − | 0.979831i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −99230.5 | − | 33239.1i | −1.31214 | − | 0.439525i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 65214.7 | + | 65214.7i | 0.849935 | + | 0.849935i | 0.990125 | − | 0.140189i | \(-0.0447711\pi\) |
−0.140189 | + | 0.990125i | \(0.544771\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10902.2i | 0.140058i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8669.34 | −0.109793 | −0.0548963 | − | 0.998492i | \(-0.517483\pi\) | ||||
−0.0548963 | + | 0.998492i | \(0.517483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23747.0 | − | 23747.0i | 0.296508 | − | 0.296508i | −0.543136 | − | 0.839645i | \(-0.682763\pi\) |
0.839645 | + | 0.543136i | \(0.182763\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 20655.0 | + | 28701.8i | 0.254294 | + | 0.353361i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 61610.2 | + | 61610.2i | 0.747978 | + | 0.747978i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 73434.8i | − | 0.879238i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −78546.9 | −0.927562 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −55077.2 | + | 55077.2i | −0.641559 | + | 0.641559i | −0.950939 | − | 0.309380i | \(-0.899879\pi\) |
0.309380 | + | 0.950939i | \(0.399879\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1317.45 | + | 8080.88i | −0.0151387 | + | 0.0928569i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16610.7 | + | 16610.7i | 0.188311 | + | 0.188311i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 39215.1i | − | 0.438643i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 50517.9 | 0.557587 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6478.02 | + | 6478.02i | −0.0705597 | + | 0.0705597i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −103771. | − | 16918.1i | −1.11552 | − | 0.181866i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11961.1 | − | 11961.1i | −0.126910 | − | 0.126910i | 0.640799 | − | 0.767709i | \(-0.278603\pi\) |
−0.767709 | + | 0.640799i | \(0.778603\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 17741.2i | − | 0.185808i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 65284.5 | 0.674977 | 0.337489 | − | 0.941330i | \(-0.390423\pi\) | ||||
0.337489 | + | 0.941330i | \(0.390423\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6418.45 | + | 6418.45i | −0.0655151 | + | 0.0655151i | −0.739105 | − | 0.673590i | \(-0.764751\pi\) |
0.673590 | + | 0.739105i | \(0.264751\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −34432.3 | + | 24779.0i | −0.347013 | + | 0.249725i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22100.1 | + | 22100.1i | 0.219926 | + | 0.219926i | 0.808467 | − | 0.588541i | \(-0.200298\pi\) |
−0.588541 | + | 0.808467i | \(0.700298\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 140621.i | 1.38187i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −31444.3 | −0.305163 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19331.0 | − | 19331.0i | 0.185289 | − | 0.185289i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −176918. | + | 88133.8i | −1.67496 | + | 0.834403i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 43427.7 | + | 43427.7i | 0.406136 | + | 0.406136i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 234886.i | − | 2.17003i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 49108.7 | 0.448231 | 0.224116 | − | 0.974563i | \(-0.428051\pi\) | ||||
0.224116 | + | 0.974563i | \(0.428051\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5604.91 | + | 5604.91i | −0.0505452 | + | 0.0505452i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −58505.6 | − | 81298.2i | −0.521324 | − | 0.724422i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −142816. | − | 142816.i | −1.25753 | − | 1.25753i | −0.952269 | − | 0.305260i | \(-0.901257\pi\) |
−0.305260 | − | 0.952269i | \(-0.598743\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 11909.0i | − | 0.103627i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 67609.8 | 0.581434 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −37875.6 | + | 37875.6i | −0.321937 | + | 0.321937i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2591.95 | + | 15898.3i | −0.0217765 | + | 0.133571i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21400.3 | + | 21400.3i | 0.177730 | + | 0.177730i | 0.790366 | − | 0.612635i | \(-0.209891\pi\) |
−0.612635 | + | 0.790366i | \(0.709891\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 34091.2i | − | 0.279893i | −0.990159 | − | 0.139946i | \(-0.955307\pi\) | ||
0.990159 | − | 0.139946i | \(-0.0446930\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 44368.3 | 0.360130 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.7539 | − | 28.7539i | 0.000230753 | − | 0.000230753i | −0.706991 | − | 0.707222i | \(-0.749948\pi\) |
0.707222 | + | 0.706991i | \(0.249948\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −131736. | − | 21477.3i | −1.04532 | − | 0.170421i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 23190.6 | + | 23190.6i | 0.181960 | + | 0.181960i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 173943.i | − | 1.34964i | −0.737984 | − | 0.674818i | \(-0.764222\pi\) | ||
0.737984 | − | 0.674818i | \(-0.235778\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 56222.1 | 0.431412 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 49216.1 | − | 49216.1i | 0.373503 | − | 0.373503i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 197011. | − | 141778.i | 1.47879 | − | 1.06420i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 41954.1 | + | 41954.1i | 0.311489 | + | 0.311489i | 0.845486 | − | 0.533997i | \(-0.179311\pi\) |
−0.533997 | + | 0.845486i | \(0.679311\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 37432.6i | 0.274914i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 122531. | 0.890223 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −65875.2 | + | 65875.2i | −0.473483 | + | 0.473483i | −0.903040 | − | 0.429557i | \(-0.858670\pi\) |
0.429557 | + | 0.903040i | \(0.358670\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 77550.1 | − | 24037.1i | 0.551467 | − | 0.170931i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 187804. | + | 187804.i | 1.32136 | + | 1.32136i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10837.0i | 0.0754448i | 0.999288 | + | 0.0377224i | \(0.0120103\pi\) | ||||
−0.999288 | + | 0.0377224i | \(0.987990\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 85039.9 | 0.585831 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22327.5 | + | 22327.5i | −0.152210 | + | 0.152210i | −0.779104 | − | 0.626894i | \(-0.784326\pi\) |
0.626894 | + | 0.779104i | \(0.284326\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 153666. | + | 213531.i | 1.03671 | + | 1.44058i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15346.6 | + | 15346.6i | 0.102469 | + | 0.102469i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 203884.i | − | 1.34736i | −0.739023 | − | 0.673680i | \(-0.764713\pi\) | ||
0.739023 | − | 0.673680i | \(-0.235287\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12453.5 | 0.0814585 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −241.114 | + | 241.114i | −0.00156113 | + | 0.00156113i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18772.7 | − | 115147.i | 0.120319 | − | 0.738004i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 117299. | + | 117299.i | 0.744238 | + | 0.744238i | 0.973390 | − | 0.229153i | \(-0.0735955\pi\) |
−0.229153 | + | 0.973390i | \(0.573596\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 88893.5i | − | 0.558373i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 43093.1 | 0.267990 | 0.133995 | − | 0.990982i | \(-0.457219\pi\) | ||||
0.133995 | + | 0.990982i | \(0.457219\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 90295.2 | − | 90295.2i | 0.555974 | − | 0.555974i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17987.5 | − | 2932.55i | −0.109663 | − | 0.0178787i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 34758.6 | + | 34758.6i | 0.209833 | + | 0.209833i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 186090.i | 1.11244i | 0.831036 | + | 0.556219i | \(0.187748\pi\) | ||||
−0.831036 | + | 0.556219i | \(0.812252\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4257.99 | 0.0252070 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14554.0 | − | 14554.0i | 0.0853261 | − | 0.0853261i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −118001. | + | 84918.6i | −0.685157 | + | 0.493068i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −132854. | − | 132854.i | −0.764015 | − | 0.764015i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 101699.i | 0.579278i | 0.957136 | + | 0.289639i | \(0.0935352\pi\) | ||||
−0.957136 | + | 0.289639i | \(0.906465\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22533.0 | −0.127132 | −0.0635659 | − | 0.997978i | \(-0.520247\pi\) | ||||
−0.0635659 | + | 0.997978i | \(0.520247\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 71354.8 | − | 71354.8i | 0.398789 | − | 0.398789i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −27988.5 | − | 56183.4i | −0.154953 | − | 0.311050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 186897. | + | 186897.i | 1.02505 | + | 1.02505i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 275148.i | − | 1.49504i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −210598. | −1.13370 | −0.566852 | − | 0.823820i | \(-0.691839\pi\) | ||||
−0.566852 | + | 0.823820i | \(0.691839\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 123405. | − | 123405.i | 0.658201 | − | 0.658201i | −0.296754 | − | 0.954954i | \(-0.595904\pi\) |
0.954954 | + | 0.296754i | \(0.0959040\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −63725.3 | − | 88551.3i | −0.336770 | − | 0.467968i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −23868.1 | − | 23868.1i | −0.124984 | − | 0.124984i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 265180.i | − | 1.37598i | −0.725721 | − | 0.687989i | \(-0.758494\pi\) | ||
0.725721 | − | 0.687989i | \(-0.241506\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 41814.9 | 0.215008 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 99815.9 | − | 99815.9i | 0.508619 | − | 0.508619i | −0.405484 | − | 0.914102i | \(-0.632897\pi\) |
0.914102 | + | 0.405484i | \(0.132897\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 39871.5 | − | 244562.i | 0.201346 | − | 1.23500i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7877.34 | − | 7877.34i | −0.0394243 | − | 0.0394243i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 182934.i | 0.907408i | 0.891152 | + | 0.453704i | \(0.149898\pi\) | ||||
−0.891152 | + | 0.453704i | \(0.850102\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 232136. | 1.14127 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 32849.8 | − | 32849.8i | 0.160080 | − | 0.160080i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 490403. | + | 79951.7i | 2.36881 | + | 0.386193i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 147497. | + | 147497.i | 0.706239 | + | 0.706239i | 0.965742 | − | 0.259503i | \(-0.0835588\pi\) |
−0.259503 | + | 0.965742i | \(0.583559\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14090.0i | 0.0668781i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −354912. | −1.67001 | −0.835006 | − | 0.550241i | \(-0.814536\pi\) | ||||
−0.835006 | + | 0.550241i | \(0.814536\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −182475. | + | 182475.i | −0.851221 | + | 0.851221i | −0.990284 | − | 0.139063i | \(-0.955591\pi\) |
0.139063 | + | 0.990284i | \(0.455591\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −42575.0 | + | 30638.8i | −0.196901 | + | 0.141699i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4348.30 | − | 4348.30i | −0.0199382 | − | 0.0199382i | 0.697067 | − | 0.717006i | \(-0.254488\pi\) |
−0.717006 | + | 0.697067i | \(0.754488\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 251792.i | 1.14471i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 132514. | 0.597337 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 95171.3 | − | 95171.3i | 0.425386 | − | 0.425386i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −54037.8 | + | 161322.i | −0.239503 | + | 0.715001i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 37223.2 | + | 37223.2i | 0.163597 | + | 0.163597i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 77346.0i | 0.337106i | 0.985693 | + | 0.168553i | \(0.0539095\pi\) | ||||
−0.985693 | + | 0.168553i | \(0.946091\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 92842.6 | 0.401289 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 28633.5 | − | 28633.5i | 0.122739 | − | 0.122739i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −220742. | − | 306738.i | −0.938428 | − | 1.30402i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −77225.6 | − | 77225.6i | −0.325614 | − | 0.325614i | 0.525302 | − | 0.850916i | \(-0.323952\pi\) |
−0.850916 | + | 0.525302i | \(0.823952\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 50403.1i | − | 0.210785i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −340217. | −1.41121 | −0.705607 | − | 0.708603i | \(-0.749326\pi\) | ||||
−0.705607 | + | 0.708603i | \(0.749326\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −59640.5 | + | 59640.5i | −0.245385 | + | 0.245385i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −18186.1 | + | 111549.i | −0.0742213 | + | 0.455255i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 237263. | + | 237263.i | 0.960542 | + | 0.960542i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 331024.i | 1.32941i | 0.747108 | + | 0.664703i | \(0.231442\pi\) | ||||
−0.747108 | + | 0.664703i | \(0.768558\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 275121. | 1.09610 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 123301. | − | 123301.i | 0.487338 | − | 0.487338i | −0.420127 | − | 0.907465i | \(-0.638015\pi\) |
0.907465 | + | 0.420127i | \(0.138015\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −43503.0 | − | 7092.40i | −0.170583 | − | 0.0278106i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −262530. | − | 262530.i | −1.02132 | − | 1.02132i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 364729.i | 1.40778i | 0.710309 | + | 0.703890i | \(0.248555\pi\) | ||||
−0.710309 | + | 0.703890i | \(0.751445\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −610173. | −2.33674 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 27004.5 | − | 27004.5i | 0.102613 | − | 0.102613i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 69282.1 | − | 49858.3i | 0.261220 | − | 0.187985i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −442504. | − | 442504.i | −1.65553 | − | 1.65553i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 239841.i | 0.890408i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −203461. | −0.749560 | −0.374780 | − | 0.927114i | \(-0.622282\pi\) | ||||
−0.374780 | + | 0.927114i | \(0.622282\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −72655.5 | + | 72655.5i | −0.265623 | + | 0.265623i | −0.827334 | − | 0.561711i | \(-0.810143\pi\) |
0.561711 | + | 0.827334i | \(0.310143\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −193532. | − | 64827.0i | −0.702155 | − | 0.235200i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28674.8 | + | 28674.8i | 0.103248 | + | 0.103248i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 264465.i | 0.945053i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8842.57 | 0.0313610 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 310026. | − | 310026.i | 1.09130 | − | 1.09130i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −88368.4 | − | 122795.i | −0.308738 | − | 0.429015i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23501.1 | + | 23501.1i | 0.0814966 | + | 0.0814966i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 259313.i | − | 0.892580i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −91367.2 | −0.312173 | −0.156087 | − | 0.987743i | \(-0.549888\pi\) | ||||
−0.156087 | + | 0.987743i | \(0.549888\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 180133. | − | 180133.i | 0.610932 | − | 0.610932i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −47546.5 | + | 291638.i | −0.160076 | + | 0.981863i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9895.50 | + | 9895.50i | 0.0330722 | + | 0.0330722i | 0.723450 | − | 0.690377i | \(-0.242555\pi\) |
−0.690377 | + | 0.723450i | \(0.742555\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 113553.i | 0.376750i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 228612. | 0.753001 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −207384. | + | 207384.i | −0.678150 | + | 0.678150i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −37639.6 | − | 6136.49i | −0.122197 | − | 0.0199220i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −306800. | − | 306800.i | −0.988883 | − | 0.988883i | 0.0110558 | − | 0.999939i | \(-0.496481\pi\) |
−0.999939 | + | 0.0110558i | \(0.996481\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 254209.i | − | 0.813518i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 87378.2 | 0.277637 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −331132. | + | 331132.i | −1.04468 | + | 1.04468i | −0.0457279 | + | 0.998954i | \(0.514561\pi\) |
−0.998954 | + | 0.0457279i | \(0.985439\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 46506.4 | − | 33467.9i | 0.145685 | − | 0.104841i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 32396.2 | + | 32396.2i | 0.100769 | + | 0.100769i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 257399.i | − | 0.795028i | −0.917596 | − | 0.397514i | \(-0.869873\pi\) | ||
0.917596 | − | 0.397514i | \(-0.130127\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 622495. | 1.90925 | 0.954626 | − | 0.297807i | \(-0.0962552\pi\) | ||||
0.954626 | + | 0.297807i | \(0.0962552\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −146782. | + | 146782.i | −0.447057 | + | 0.447057i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −69369.7 | + | 34557.4i | −0.209814 | + | 0.104521i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23928.8 | − | 23928.8i | −0.0718736 | − | 0.0718736i | 0.670256 | − | 0.742130i | \(-0.266184\pi\) |
−0.742130 | + | 0.670256i | \(0.766184\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 174520.i | 0.520580i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 365467. | 1.08267 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 230838. | − | 230838.i | 0.679156 | − | 0.679156i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 124689. | + | 173265.i | 0.364348 | + | 0.506291i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −181136. | − | 181136.i | −0.525690 | − | 0.525690i | 0.393595 | − | 0.919284i | \(-0.371231\pi\) |
−0.919284 | + | 0.393595i | \(0.871231\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 109915.i | − | 0.316831i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20025.3 | −0.0573328 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −235890. | + | 235890.i | −0.670812 | + | 0.670812i | −0.957903 | − | 0.287091i | \(-0.907312\pi\) |
0.287091 | + | 0.957903i | \(0.407312\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25390.1 | + | 155736.i | −0.0717183 | + | 0.439902i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −232258. | − | 232258.i | −0.651660 | − | 0.651660i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 141629.i | − | 0.394728i | −0.980330 | − | 0.197364i | \(-0.936762\pi\) | ||
0.980330 | − | 0.197364i | \(-0.0632381\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −564417. | −1.56261 | −0.781306 | − | 0.624148i | \(-0.785446\pi\) | ||||
−0.781306 | + | 0.624148i | \(0.785446\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −76490.8 | + | 76490.8i | −0.210366 | + | 0.210366i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 330509. | + | 53883.8i | 0.902969 | + | 0.147213i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −247253. | − | 247253.i | −0.671064 | − | 0.671064i | 0.286898 | − | 0.957961i | \(-0.407376\pi\) |
−0.957961 | + | 0.286898i | \(0.907376\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 274256.i | 0.739472i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.18196e6 | −3.16606 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −163758. | + | 163758.i | −0.435794 | + | 0.435794i | −0.890594 | − | 0.454800i | \(-0.849711\pi\) |
0.454800 | + | 0.890594i | \(0.349711\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −146180. | + | 105197.i | −0.386490 | + | 0.278134i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 273782. | + | 273782.i | 0.719176 | + | 0.719176i | 0.968437 | − | 0.249260i | \(-0.0801875\pi\) |
−0.249260 | + | 0.968437i | \(0.580188\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 428345.i | 1.11792i | 0.829194 | + | 0.558962i | \(0.188800\pi\) | ||||
−0.829194 | + | 0.558962i | \(0.811200\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17396.9 | 0.0451116 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −440465. | + | 440465.i | −1.13484 | + | 1.13484i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 311809. | + | 235293.i | 0.798231 | + | 0.602351i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −167467. | − | 167467.i | −0.425986 | − | 0.425986i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29483.8i | 0.0745216i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −108870. | −0.273432 | −0.136716 | − | 0.990610i | \(-0.543655\pi\) | ||||
−0.136716 | + | 0.990610i | \(0.543655\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −56841.0 | + | 56841.0i | −0.141858 | + | 0.141858i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 238989. | + | 332094.i | 0.592694 | + | 0.823595i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −346322. | − | 346322.i | −0.853495 | − | 0.853495i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 144154.i | 0.353040i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −501643. | −1.22090 | −0.610448 | − | 0.792056i | \(-0.709011\pi\) | ||||
−0.610448 | + | 0.792056i | \(0.709011\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 117251. | − | 117251.i | 0.283592 | − | 0.283592i | −0.550948 | − | 0.834540i | \(-0.685734\pi\) |
0.834540 | + | 0.550948i | \(0.185734\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16802.1 | + | 103060.i | −0.0403872 | + | 0.247725i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 362031. | + | 362031.i | 0.864843 | + | 0.864843i | 0.991896 | − | 0.127053i | \(-0.0405519\pi\) |
−0.127053 | + | 0.991896i | \(0.540552\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 54836.8i | − | 0.130192i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 131861. | 0.311139 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −411293. | + | 411293.i | −0.964552 | + | 0.964552i | −0.999393 | − | 0.0348413i | \(-0.988907\pi\) |
0.0348413 | + | 0.999393i | \(0.488907\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1619.20 | − | 263.982i | −0.00377413 | − | 0.000615306i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −185361. | − | 185361.i | −0.429426 | − | 0.429426i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 291952.i | − | 0.672265i | −0.941815 | − | 0.336133i | \(-0.890881\pi\) | ||
0.941815 | − | 0.336133i | \(-0.109119\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 757270. | 1.73320 | 0.866599 | − | 0.499006i | \(-0.166301\pi\) | ||||
0.866599 | + | 0.499006i | \(0.166301\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 116697. | − | 116697.i | 0.265480 | − | 0.265480i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 347143. | − | 249819.i | 0.784992 | − | 0.564914i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 73638.3 | + | 73638.3i | 0.165521 | + | 0.165521i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 211766.i | 0.473156i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 704193. | 1.56404 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 310335. | − | 310335.i | 0.685173 | − | 0.685173i | −0.275988 | − | 0.961161i | \(-0.589005\pi\) |
0.961161 | + | 0.275988i | \(0.0890050\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −39098.6 | − | 78485.5i | −0.0858130 | − | 0.172259i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9203.97 | + | 9203.97i | 0.0200816 | + | 0.0200816i | 0.717076 | − | 0.696995i | \(-0.245480\pi\) |
−0.696995 | + | 0.717076i | \(0.745480\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 950012.i | 2.06058i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6497.79 | −0.0140111 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 421590. | − | 421590.i | 0.903750 | − | 0.903750i | −0.0920080 | − | 0.995758i | \(-0.529329\pi\) |
0.995758 | + | 0.0920080i | \(0.0293285\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11966.3 | + | 16628.1i | 0.0255023 | + | 0.0354374i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −44371.4 | − | 44371.4i | −0.0940135 | − | 0.0940135i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 616584.i | − | 1.29883i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −102275. | −0.214197 | −0.107098 | − | 0.994248i | \(-0.534156\pi\) | ||||
−0.107098 | + | 0.994248i | \(0.534156\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 200904. | − | 200904.i | 0.418333 | − | 0.418333i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 145454. | − | 892177.i | 0.301131 | − | 1.84706i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 98454.3 | + | 98454.3i | 0.202660 | + | 0.202660i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 181476.i | 0.371420i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −685359. | −1.39471 | −0.697353 | − | 0.716728i | \(-0.745639\pi\) | ||||
−0.697353 | + | 0.716728i | \(0.745639\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 56508.1 | − | 56508.1i | 0.114341 | − | 0.114341i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 479182. | + | 78122.2i | 0.964100 | + | 0.157180i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 78350.6 | + | 78350.6i | 0.156749 | + | 0.156749i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 164715.i | − | 0.327673i | −0.986487 | − | 0.163837i | \(-0.947613\pi\) | ||
0.986487 | − | 0.163837i | \(-0.0523870\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −126001. | −0.249249 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 35404.9 | − | 35404.9i | 0.0696441 | − | 0.0696441i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.07450e6 | − | 773254.i | 2.10181 | − | 1.51255i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −177053. | − | 177053.i | −0.344402 | − | 0.344402i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 782798.i | 1.51423i | 0.653282 | + | 0.757115i | \(0.273392\pi\) | ||||
−0.653282 | + | 0.757115i | \(0.726608\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −214577. | −0.412774 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −202760. | + | 202760.i | −0.387887 | + | 0.387887i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 166719. | − | 497715.i | 0.317182 | − | 0.946900i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −659110. | − | 659110.i | −1.24706 | − | 1.24706i | −0.957010 | − | 0.290054i | \(-0.906327\pi\) |
−0.290054 | − | 0.957010i | \(-0.593673\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19683.0i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 80728.6 | 0.151075 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 356952. | − | 356952.i | 0.664358 | − | 0.664358i | −0.292046 | − | 0.956404i | \(-0.594336\pi\) |
0.956404 | + | 0.292046i | \(0.0943361\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 117513. | + | 163294.i | 0.217526 | + | 0.302270i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 474354. | + | 474354.i | 0.873309 | + | 0.873309i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 231725.i | − | 0.424311i | −0.977236 | − | 0.212156i | \(-0.931952\pi\) | ||
0.977236 | − | 0.212156i | \(-0.0680483\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −447317. | −0.814665 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35964.9 | − | 35964.9i | 0.0651480 | − | 0.0651480i | −0.673782 | − | 0.738930i | \(-0.735331\pi\) |
0.738930 | + | 0.673782i | \(0.235331\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8624.43 | − | 52900.1i | 0.0155388 | − | 0.0953111i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 111023. | + | 111023.i | 0.198963 | + | 0.198963i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 380314.i | 0.677920i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −702045. | −1.24476 | −0.622379 | − | 0.782716i | \(-0.713834\pi\) | ||||
−0.622379 | + | 0.782716i | \(0.713834\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 255976. | − | 255976.i | 0.451449 | − | 0.451449i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 220602. | + | 35965.3i | 0.387004 | + | 0.0630943i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −111880. | − | 111880.i | −0.195236 | − | 0.195236i | 0.602718 | − | 0.797954i | \(-0.294084\pi\) |
−0.797954 | + | 0.602718i | \(0.794084\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 107886.i | − | 0.187276i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −579015. | −0.999817 | −0.499908 | − | 0.866078i | \(-0.666633\pi\) | ||||
−0.499908 | + | 0.866078i | \(0.666633\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 525252. | − | 525252.i | 0.902232 | − | 0.902232i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −55023.5 | + | 39597.2i | −0.0940211 | + | 0.0676616i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −73236.4 | − | 73236.4i | −0.124491 | − | 0.124491i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 472110.i | 0.798344i | 0.916876 | + | 0.399172i | \(0.130702\pi\) | ||||
−0.916876 | + | 0.399172i | \(0.869298\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −85348.4 | −0.143578 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20353.7 | + | 20353.7i | −0.0340631 | + | 0.0340631i | −0.723933 | − | 0.689870i | \(-0.757668\pi\) |
0.689870 | + | 0.723933i | \(0.257668\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −239298. | − | 80157.4i | −0.398416 | − | 0.133457i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 67790.5 | + | 67790.5i | 0.112286 | + | 0.112286i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 377391.i | − | 0.621895i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 893963. | 1.46561 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −83315.0 | + | 83315.0i | −0.135894 | + | 0.135894i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 372406. | + | 517488.i | 0.604335 | + | 0.839771i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −640630. | − | 640630.i | −1.03433 | − | 1.03433i | −0.999390 | − | 0.0349373i | \(-0.988877\pi\) |
−0.0349373 | − | 0.999390i | \(-0.511123\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 637933.i | 1.02476i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −144037. | −0.230208 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 940474. | − | 940474.i | 1.49555 | − | 1.49555i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −40753.5 | + | 249971.i | −0.0644808 | + | 0.395509i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 542782. | + | 542782.i | 0.854494 | + | 0.854494i | 0.990683 | − | 0.136189i | \(-0.0434854\pi\) |
−0.136189 | + | 0.990683i | \(0.543485\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 375352.i | − | 0.587956i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −267614. | −0.417103 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.14951e6 | + | 1.14951e6i | −1.78271 | + | 1.78271i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 192288. | + | 31349.2i | 0.296729 | + | 0.0483765i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 343318. | + | 343318.i | 0.527168 | + | 0.527168i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.09699e6i | 1.67613i | 0.545571 | + | 0.838065i | \(0.316313\pi\) | ||||
−0.545571 | + | 0.838065i | \(0.683687\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 711398. | 1.08161 | 0.540805 | − | 0.841148i | \(-0.318120\pi\) | ||||
0.540805 | + | 0.841148i | \(0.318120\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 39889.3 | − | 39889.3i | 0.0603498 | − | 0.0603498i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 196832. | − | 141649.i | 0.296334 | − | 0.213254i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −154723. | − | 154723.i | −0.231798 | − | 0.231798i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 536628.i | − | 0.800028i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −566243. | −0.840071 | −0.420036 | − | 0.907508i | \(-0.637982\pi\) | ||||
−0.420036 | + | 0.907508i | \(0.637982\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 678523. | − | 678523.i | 1.00176 | − | 1.00176i | 0.00176504 | − | 0.999998i | \(-0.499438\pi\) |
0.999998 | − | 0.00176504i | \(-0.000561830\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −486724. | + | 242468.i | −0.715114 | + | 0.356243i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 822466. | + | 822466.i | 1.20256 | + | 1.20256i | 0.973385 | + | 0.229174i | \(0.0736026\pi\) |
0.229174 | + | 0.973385i | \(0.426397\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1.26805e6i | − | 1.84514i | −0.385832 | − | 0.922569i | \(-0.626086\pi\) | ||
0.385832 | − | 0.922569i | \(-0.373914\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 479228. | 0.693969 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 109981. | − | 109981.i | 0.158499 | − | 0.158499i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 773178. | + | 1.07439e6i | 1.10894 | + | 1.54095i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 40057.4 | + | 40057.4i | 0.0571784 | + | 0.0571784i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 487091.i | 0.691968i | 0.938240 | + | 0.345984i | \(0.112455\pi\) | ||||
−0.938240 | + | 0.345984i | \(0.887545\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1962.99 | 0.00277541 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −31853.2 | + | 31853.2i | −0.0448227 | + | 0.0448227i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 287429. | − | 1.76301e6i | 0.402547 | − | 2.46912i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −595260. | − | 595260.i | −0.829736 | − | 0.829736i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 174504.i | − | 0.242098i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36403.7 | 0.0502675 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10645.4 | − | 10645.4i | 0.0146307 | − | 0.0146307i | −0.699754 | − | 0.714384i | \(-0.746707\pi\) |
0.714384 | + | 0.699754i | \(0.246707\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 181348. | + | 29565.7i | 0.248074 | + | 0.0404441i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −692563. | − | 692563.i | −0.942970 | − | 0.942970i | 0.0554896 | − | 0.998459i | \(-0.482328\pi\) |
−0.998459 | + | 0.0554896i | \(0.982328\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 745974.i | − | 1.01097i | −0.862836 | − | 0.505484i | \(-0.831314\pi\) | ||
0.862836 | − | 0.505484i | \(-0.168686\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 452741. | 0.610722 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −259362. | + | 259362.i | −0.348245 | + | 0.348245i | −0.859456 | − | 0.511211i | \(-0.829197\pi\) |
0.511211 | + | 0.859456i | \(0.329197\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −936618. | + | 674030.i | −1.25179 | + | 0.900838i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −269817. | − | 269817.i | −0.358947 | − | 0.358947i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 781388.i | 1.03473i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.26703e6 | 1.67013 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −288600. | + | 288600.i | −0.378676 | + | 0.378676i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −290725. | − | 937956.i | −0.379723 | − | 1.22509i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −191986. | − | 191986.i | −0.249615 | − | 0.249615i | 0.571197 | − | 0.820813i | \(-0.306479\pi\) |
−0.820813 | + | 0.571197i | \(0.806479\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 404733.i | 0.523830i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.08074e6 | 1.39241 | 0.696207 | − | 0.717841i | \(-0.254870\pi\) | ||||
0.696207 | + | 0.717841i | \(0.254870\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −294604. | + | 294604.i | −0.377848 | + | 0.377848i | −0.870325 | − | 0.492477i | \(-0.836091\pi\) |
0.492477 | + | 0.870325i | \(0.336091\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 24850.4 | + | 34531.6i | 0.0317283 | + | 0.0440890i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 373328. | + | 373328.i | 0.474507 | + | 0.474507i | 0.903370 | − | 0.428862i | \(-0.141085\pi\) |
−0.428862 | + | 0.903370i | \(0.641085\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.02854e6i | − | 1.30143i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 122063. | 0.153755 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −719392. | + | 719392.i | −0.902117 | + | 0.902117i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25730.0 | + | 157821.i | −0.0321213 | + | 0.197024i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −144086. | − | 144086.i | −0.179075 | − | 0.179075i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 339113.i | 0.419590i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 195807. | 0.241201 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 185615. | − | 185615.i | 0.227634 | − | 0.227634i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.20968e6 | + | 197217.i | 1.47697 | + | 0.240795i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 342694. | + | 342694.i | 0.416574 | + | 0.416574i | 0.884021 | − | 0.467447i | \(-0.154826\pi\) |
−0.467447 | + | 0.884021i | \(0.654826\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 47603.5i | 0.0576118i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −653388. | −0.787290 | −0.393645 | − | 0.919263i | \(-0.628786\pi\) | ||||
−0.393645 | + | 0.919263i | \(0.628786\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 688506. | − | 688506.i | 0.825974 | − | 0.825974i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −443442. | + | 319119.i | −0.529657 | + | 0.381163i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2916.24 | + | 2916.24i | 0.00346804 | + | 0.00346804i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 316752.i | 0.375050i | 0.982260 | + | 0.187525i | \(0.0600465\pi\) | ||||
−0.982260 | + | 0.187525i | \(0.939953\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −87896.0 | −0.103621 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.19392e6 | − | 1.19392e6i | 1.40143 | − | 1.40143i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −81815.4 | − | 164234.i | −0.0956206 | − | 0.191947i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −65185.2 | − | 65185.2i | −0.0758560 | − | 0.0758560i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1.39646e6i | − | 1.61807i | −0.587759 | − | 0.809036i | \(-0.699990\pi\) | ||
0.587759 | − | 0.809036i | \(-0.300010\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −421574. | −0.486378 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 239870. | − | 239870.i | 0.275558 | − | 0.275558i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 245560. | + | 341226.i | 0.280889 | + | 0.390318i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 81884.2 | + | 81884.2i | 0.0932655 | + | 0.0932655i | 0.752200 | − | 0.658935i | \(-0.228993\pi\) |
−0.658935 | + | 0.752200i | \(0.728993\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 47165.7i | 0.0534928i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.67094e6 | 1.88705 | 0.943524 | − | 0.331305i | \(-0.107489\pi\) | ||||
0.943524 | + | 0.331305i | \(0.107489\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 121562. | − | 121562.i | 0.136702 | − | 0.136702i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −35468.7 | + | 217556.i | −0.0397175 | + | 0.243617i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −689602. | − | 689602.i | −0.768950 | − | 0.768950i | 0.208971 | − | 0.977922i | \(-0.432988\pi\) |
−0.977922 | + | 0.208971i | \(0.932988\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.07042e6i | 3.40930i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 162402. | 0.179569 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 150337. | − | 150337.i | 0.165532 | − | 0.165532i | −0.619480 | − | 0.785012i | \(-0.712657\pi\) |
0.785012 | + | 0.619480i | \(0.212657\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −985710. | − | 160703.i | −1.08079 | − | 0.176204i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 516674. | + | 516674.i | 0.564148 | + | 0.564148i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 51499.7i | − | 0.0559974i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −760477. | −0.823454 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −115534. | + | 115534.i | −0.124582 | + | 0.124582i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −681527. | + | 490456.i | −0.731861 | + | 0.526678i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 312723. | + | 312723.i | 0.334432 | + | 0.334432i | 0.854267 | − | 0.519835i | \(-0.174007\pi\) |
−0.519835 | + | 0.854267i | \(0.674007\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 142053.i | − | 0.151288i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.16534e6 | −1.23598 | −0.617992 | − | 0.786185i | \(-0.712054\pi\) | ||||
−0.617992 | + | 0.786185i | \(0.712054\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.60685e6 | + | 1.60685e6i | −1.69726 | + | 1.69726i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −326213. | + | 973861.i | −0.343156 | + | 1.02444i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −748461. | − | 748461.i | −0.784115 | − | 0.784115i | 0.196407 | − | 0.980522i | \(-0.437073\pi\) |
−0.980522 | + | 0.196407i | \(0.937073\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.65959e6i | 1.73156i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 319127. | 0.331609 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 542812. | − | 542812.i | 0.561749 | − | 0.561749i | −0.368055 | − | 0.929804i | \(-0.619976\pi\) |
0.929804 | + | 0.368055i | \(0.119976\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −56277.3 | − | 78201.8i | −0.0580044 | − | 0.0806017i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −863025. | − | 863025.i | −0.885909 | − | 0.885909i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 99675.8i | − | 0.101905i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.08269e6 | −1.10245 | −0.551224 | − | 0.834357i | \(-0.685839\pi\) | ||||
−0.551224 | + | 0.834357i | \(0.685839\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 180437. | − | 180437.i | 0.182990 | − | 0.182990i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 254285. | − | 1.55972e6i | 0.256847 | − | 1.57544i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25593.2 | + | 25593.2i | 0.0257475 | + | 0.0257475i | 0.719863 | − | 0.694116i | \(-0.244204\pi\) |
−0.694116 | + | 0.719863i | \(0.744204\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 41187.5i | 0.0412700i |
(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 | 240.5.bg.b.97.2 | 4 | ||
4.3 | odd | 2 | 30.5.f.a.7.1 | ✓ | 4 | ||
5.3 | odd | 4 | inner | 240.5.bg.b.193.2 | 4 | ||
12.11 | even | 2 | 90.5.g.e.37.1 | 4 | |||
20.3 | even | 4 | 30.5.f.a.13.1 | yes | 4 | ||
20.7 | even | 4 | 150.5.f.e.43.2 | 4 | |||
20.19 | odd | 2 | 150.5.f.e.7.2 | 4 | |||
60.23 | odd | 4 | 90.5.g.e.73.1 | 4 | |||
60.47 | odd | 4 | 450.5.g.f.343.1 | 4 | |||
60.59 | even | 2 | 450.5.g.f.307.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
30.5.f.a.7.1 | ✓ | 4 | 4.3 | odd | 2 | ||
30.5.f.a.13.1 | yes | 4 | 20.3 | even | 4 | ||
90.5.g.e.37.1 | 4 | 12.11 | even | 2 | |||
90.5.g.e.73.1 | 4 | 60.23 | odd | 4 | |||
150.5.f.e.7.2 | 4 | 20.19 | odd | 2 | |||
150.5.f.e.43.2 | 4 | 20.7 | even | 4 | |||
240.5.bg.b.97.2 | 4 | 1.1 | even | 1 | trivial | ||
240.5.bg.b.193.2 | 4 | 5.3 | odd | 4 | inner | ||
450.5.g.f.307.1 | 4 | 60.59 | even | 2 | |||
450.5.g.f.343.1 | 4 | 60.47 | odd | 4 |