Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,5,Mod(307,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([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("450.307");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.g (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(46.5164833877\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 30) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 343.1 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.343 |
Dual form | 450.5.g.f.307.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | + | 2.00000i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 8.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −44.4393 | + | 44.4393i | −0.906924 | + | 0.906924i | −0.996023 | − | 0.0890986i | \(-0.971601\pi\) |
0.0890986 | + | 0.996023i | \(0.471601\pi\) | |||||||
\(8\) | 16.0000 | + | 16.0000i | 0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | 0.911170 | + | 0.412031i | \(0.135180\pi\) |
0.412031 | + | 0.911170i | \(0.364820\pi\) | |||||||
\(14\) | − | 177.757i | − | 0.906924i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −64.0000 | −0.250000 | ||||||||
\(17\) | −71.0148 | + | 71.0148i | −0.245726 | + | 0.245726i | −0.819214 | − | 0.573488i | \(-0.805590\pi\) |
0.573488 | + | 0.819214i | \(0.305590\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 272.211i | 0.754048i | 0.926204 | + | 0.377024i | \(0.123053\pi\) | ||||
−0.926204 | + | 0.377024i | \(0.876947\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 334.879 | − | 334.879i | 0.691898 | − | 0.691898i | ||||
\(23\) | 87.6821 | + | 87.6821i | 0.165751 | + | 0.165751i | 0.785109 | − | 0.619358i | \(-0.212607\pi\) |
−0.619358 | + | 0.785109i | \(0.712607\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −894.484 | −1.32320 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 355.514 | + | 355.514i | 0.453462 | + | 0.453462i | ||||
\(29\) | − | 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 | \(-0.432625\pi\) | ||||
0.210087 | + | 0.977683i | \(0.432625\pi\) | |||||||
\(32\) | 128.000 | − | 128.000i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 284.059i | − | 0.245726i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 207.589 | − | 207.589i | 0.151636 | − | 0.151636i | −0.627212 | − | 0.778848i | \(-0.715804\pi\) |
0.778848 | + | 0.627212i | \(0.215804\pi\) | |||||||
\(38\) | −544.422 | − | 544.422i | −0.377024 | − | 0.377024i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1386.39 | 0.824742 | 0.412371 | − | 0.911016i | \(-0.364701\pi\) | ||||
0.412371 | + | 0.911016i | \(0.364701\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −568.393 | − | 568.393i | −0.307406 | − | 0.307406i | 0.536497 | − | 0.843902i | \(-0.319747\pi\) |
−0.843902 | + | 0.536497i | \(0.819747\pi\) | |||||||
\(44\) | 1339.51i | 0.691898i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −350.729 | −0.165751 | ||||||||
\(47\) | −2642.77 | + | 2642.77i | −1.19637 | + | 1.19637i | −0.221119 | + | 0.975247i | \(0.570971\pi\) |
−0.975247 | + | 0.221119i | \(0.929029\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1548.70i | − | 0.645023i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1788.97 | − | 1788.97i | 0.661600 | − | 0.661600i | ||||
\(53\) | −1378.64 | − | 1378.64i | −0.490792 | − | 0.490792i | 0.417763 | − | 0.908556i | \(-0.362814\pi\) |
−0.908556 | + | 0.417763i | \(0.862814\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1422.06 | −0.453462 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1679.66 | + | 1679.66i | 0.499306 | + | 0.499306i | ||||
\(59\) | − | 327.503i | − | 0.0940829i | −0.998893 | − | 0.0470415i | \(-0.985021\pi\) | ||
0.998893 | − | 0.0470415i | \(-0.0149793\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4205.66 | −1.13025 | −0.565125 | − | 0.825005i | \(-0.691172\pi\) | ||||
−0.565125 | + | 0.825005i | \(0.691172\pi\) | |||||||
\(62\) | −807.573 | + | 807.573i | −0.210087 | + | 0.210087i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 512.000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2832.99 | + | 2832.99i | −0.631097 | + | 0.631097i | −0.948343 | − | 0.317246i | \(-0.897242\pi\) |
0.317246 | + | 0.948343i | \(0.397242\pi\) | |||||||
\(68\) | 568.118 | + | 568.118i | 0.122863 | + | 0.122863i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | −0.935832 | − | 0.352447i | \(-0.885350\pi\) |
−0.352447 | − | 0.935832i | \(-0.614650\pi\) | |||||||
\(74\) | 830.357i | 0.151636i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2177.69 | 0.377024 | ||||||||
\(77\) | 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 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2772.78 | + | 2772.78i | −0.412371 | + | 0.412371i | ||||
\(83\) | 4111.98 | + | 4111.98i | 0.596890 | + | 0.596890i | 0.939484 | − | 0.342594i | \(-0.111305\pi\) |
−0.342594 | + | 0.939484i | \(0.611305\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2273.57 | 0.307406 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2679.03 | − | 2679.03i | −0.345949 | − | 0.345949i | ||||
\(89\) | − | 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 | ||||||||
\(92\) | 701.457 | − | 701.457i | 0.0828754 | − | 0.0828754i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 10571.1i | − | 1.19637i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10688.9 | − | 10688.9i | 1.13603 | − | 1.13603i | 0.146871 | − | 0.989156i | \(-0.453080\pi\) |
0.989156 | − | 0.146871i | \(-0.0469203\pi\) | |||||||
\(98\) | 3097.40 | + | 3097.40i | 0.322511 | + | 0.322511i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1763.09 | 0.172835 | 0.0864177 | − | 0.996259i | \(-0.472458\pi\) | ||||
0.0864177 | + | 0.996259i | \(0.472458\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2414.27 | + | 2414.27i | 0.227568 | + | 0.227568i | 0.811676 | − | 0.584108i | \(-0.198556\pi\) |
−0.584108 | + | 0.811676i | \(0.698556\pi\) | |||||||
\(104\) | 7155.87i | 0.661600i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5514.54 | 0.490792 | ||||||||
\(107\) | 4279.03 | − | 4279.03i | 0.373747 | − | 0.373747i | −0.495093 | − | 0.868840i | \(-0.664866\pi\) |
0.868840 | + | 0.495093i | \(0.164866\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11819.5i | − | 0.994827i | −0.867514 | − | 0.497413i | \(-0.834283\pi\) | ||
0.867514 | − | 0.497413i | \(-0.165717\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2844.11 | − | 2844.11i | 0.226731 | − | 0.226731i | ||||
\(113\) | 1620.60 | + | 1620.60i | 0.126917 | + | 0.126917i | 0.767712 | − | 0.640795i | \(-0.221395\pi\) |
−0.640795 | + | 0.767712i | \(0.721395\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6718.66 | −0.499306 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 655.005 | + | 655.005i | 0.0470415 | + | 0.0470415i | ||||
\(119\) | − | 6311.69i | − | 0.445710i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13394.9 | 0.914891 | ||||||||
\(122\) | 8411.32 | − | 8411.32i | 0.565125 | − | 0.565125i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 3230.29i | − | 0.210087i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11572.5 | − | 11572.5i | 0.717494 | − | 0.717494i | −0.250597 | − | 0.968091i | \(-0.580627\pi\) |
0.968091 | + | 0.250597i | \(0.0806270\pi\) | |||||||
\(128\) | −1024.00 | − | 1024.00i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | ||||
\(134\) | − | 11332.0i | − | 0.631097i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2272.47 | −0.122863 | ||||||||
\(137\) | 579.439 | − | 579.439i | 0.0308721 | − | 0.0308721i | −0.691502 | − | 0.722374i | \(-0.743051\pi\) |
0.722374 | + | 0.691502i | \(0.243051\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 36158.2i | − | 1.87145i | −0.352734 | − | 0.935724i | \(-0.614748\pi\) | ||
0.352734 | − | 0.935724i | \(-0.385252\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10678.1 | − | 10678.1i | 0.529560 | − | 0.529560i | ||||
\(143\) | −37442.9 | − | 37442.9i | −1.83104 | − | 1.83104i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 27461.0 | 1.28828 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1660.71 | − | 1660.71i | −0.0758178 | − | 0.0758178i | ||||
\(149\) | − | 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 | \(-0.562814\pi\) | ||||
−0.196057 | + | 0.980593i | \(0.562814\pi\) | |||||||
\(152\) | −4355.38 | + | 4355.38i | −0.188512 | + | 0.188512i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 29763.5i | 1.25500i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18032.9 | + | 18032.9i | −0.731586 | + | 0.731586i | −0.970934 | − | 0.239348i | \(-0.923066\pi\) |
0.239348 | + | 0.970934i | \(0.423066\pi\) | |||||||
\(158\) | 9333.39 | + | 9333.39i | 0.373874 | + | 0.373874i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7793.06 | −0.300647 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6859.00 | + | 6859.00i | 0.258158 | + | 0.258158i | 0.824305 | − | 0.566147i | \(-0.191566\pi\) |
−0.566147 | + | 0.824305i | \(0.691566\pi\) | |||||||
\(164\) | − | 11091.1i | − | 0.412371i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16447.9 | −0.596890 | ||||||||
\(167\) | −37439.2 | + | 37439.2i | −1.34244 | + | 1.34244i | −0.448811 | + | 0.893627i | \(0.648152\pi\) |
−0.893627 | + | 0.448811i | \(0.851848\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 71451.6i | 2.50172i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4547.14 | + | 4547.14i | −0.153703 | + | 0.153703i | ||||
\(173\) | −32638.2 | − | 32638.2i | −1.09052 | − | 1.09052i | −0.995472 | − | 0.0950500i | \(-0.969699\pi\) |
−0.0950500 | − | 0.995472i | \(-0.530301\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10716.1 | 0.345949 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 19823.2 | + | 19823.2i | 0.625654 | + | 0.625654i | ||||
\(179\) | − | 6396.19i | − | 0.199625i | −0.995006 | − | 0.0998126i | \(-0.968176\pi\) | ||
0.995006 | − | 0.0998126i | \(-0.0318243\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 49025.9 | 1.49647 | 0.748236 | − | 0.663432i | \(-0.230901\pi\) | ||||
0.748236 | + | 0.663432i | \(0.230901\pi\) | |||||||
\(182\) | 39750.2 | − | 39750.2i | 1.20004 | − | 1.20004i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2805.83i | 0.0828754i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11890.7 | − | 11890.7i | 0.340034 | − | 0.340034i | ||||
\(188\) | 21142.2 | + | 21142.2i | 0.598183 | + | 0.598183i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | \(-0.101126\pi\) |
−0.312380 | + | 0.949957i | \(0.601126\pi\) | |||||||
\(194\) | 42755.5i | 1.13603i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −12389.6 | −0.322511 | ||||||||
\(197\) | −2725.09 | + | 2725.09i | −0.0702181 | + | 0.0702181i | −0.741344 | − | 0.671126i | \(-0.765811\pi\) |
0.671126 | + | 0.741344i | \(0.265811\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 63212.5i | − | 1.59624i | −0.602502 | − | 0.798118i | \(-0.705829\pi\) | ||
0.602502 | − | 0.798118i | \(-0.294171\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3526.19 | + | 3526.19i | −0.0864177 | + | 0.0864177i | ||||
\(203\) | 37321.5 | + | 37321.5i | 0.905665 | + | 0.905665i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9657.07 | −0.227568 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14311.7 | − | 14311.7i | −0.330800 | − | 0.330800i | ||||
\(209\) | − | 45578.9i | − | 1.04345i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15470.2 | 0.347480 | 0.173740 | − | 0.984792i | \(-0.444415\pi\) | ||||
0.173740 | + | 0.984792i | \(0.444415\pi\) | |||||||
\(212\) | −11029.1 | + | 11029.1i | −0.245396 | + | 0.245396i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 17116.1i | 0.373747i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17944.0 | + | 17944.0i | −0.381065 | + | 0.381065i | ||||
\(218\) | 23639.1 | + | 23639.1i | 0.497413 | + | 0.497413i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −31760.8 | −0.650289 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28817.8 | − | 28817.8i | −0.579496 | − | 0.579496i | 0.355268 | − | 0.934764i | \(-0.384389\pi\) |
−0.934764 | + | 0.355268i | \(0.884389\pi\) | |||||||
\(224\) | 11376.5i | 0.226731i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6482.41 | −0.126917 | ||||||||
\(227\) | 884.237 | − | 884.237i | 0.0171600 | − | 0.0171600i | −0.698475 | − | 0.715635i | \(-0.746138\pi\) |
0.715635 | + | 0.698475i | \(0.246138\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12076.4i | 0.230285i | 0.993349 | + | 0.115143i | \(0.0367325\pi\) | ||||
−0.993349 | + | 0.115143i | \(0.963268\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13437.3 | − | 13437.3i | 0.249653 | − | 0.249653i | ||||
\(233\) | −24695.8 | − | 24695.8i | −0.454894 | − | 0.454894i | 0.442081 | − | 0.896975i | \(-0.354240\pi\) |
−0.896975 | + | 0.442081i | \(0.854240\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2620.02 | −0.0470415 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 12623.4 | + | 12623.4i | 0.222855 | + | 0.222855i | ||||
\(239\) | 48187.8i | 0.843608i | 0.906687 | + | 0.421804i | \(0.138603\pi\) | ||||
−0.906687 | + | 0.421804i | \(0.861397\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −55184.2 | −0.950125 | −0.475062 | − | 0.879952i | \(-0.657574\pi\) | ||||
−0.475062 | + | 0.879952i | \(0.657574\pi\) | |||||||
\(242\) | −26789.8 | + | 26789.8i | −0.457445 | + | 0.457445i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 33645.3i | 0.565125i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −60872.1 | + | 60872.1i | −0.997756 | + | 0.997756i | ||||
\(248\) | 6460.59 | + | 6460.59i | 0.105043 | + | 0.105043i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | ||||
\(254\) | 46289.8i | 0.717494i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | −11614.4 | + | 11614.4i | −0.175846 | + | 0.175846i | −0.789542 | − | 0.613696i | \(-0.789682\pi\) |
0.613696 | + | 0.789542i | \(0.289682\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18450.2i | 0.275044i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 131.246 | − | 131.246i | 0.00191198 | − | 0.00191198i | ||||
\(263\) | 86811.6 | + | 86811.6i | 1.25507 | + | 1.25507i | 0.953420 | + | 0.301646i | \(0.0975360\pi\) |
0.301646 | + | 0.953420i | \(0.402464\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 48387.5 | 0.683864 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 22663.9 | + | 22663.9i | 0.315548 | + | 0.315548i | ||||
\(269\) | 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 | \(-0.523549\pi\) | ||||
−0.0739131 | + | 0.997265i | \(0.523549\pi\) | |||||||
\(272\) | 4544.95 | − | 4544.95i | 0.0614315 | − | 0.0614315i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2317.76i | 0.0308721i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −65214.7 | + | 65214.7i | −0.849935 | + | 0.849935i | −0.990125 | − | 0.140189i | \(-0.955229\pi\) |
0.140189 | + | 0.990125i | \(0.455229\pi\) | |||||||
\(278\) | 72316.5 | + | 72316.5i | 0.935724 | + | 0.935724i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8669.34 | 0.109793 | 0.0548963 | − | 0.998492i | \(-0.482517\pi\) | ||||
0.0548963 | + | 0.998492i | \(0.482517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23747.0 | + | 23747.0i | 0.296508 | + | 0.296508i | 0.839645 | − | 0.543136i | \(-0.182763\pi\) |
−0.543136 | + | 0.839645i | \(0.682763\pi\) | |||||||
\(284\) | 42712.2i | 0.529560i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 149772. | 1.83104 | ||||||||
\(287\) | −61610.2 | + | 61610.2i | −0.747978 | + | 0.747978i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 73434.8i | 0.879238i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −54921.9 | + | 54921.9i | −0.644139 | + | 0.644139i | ||||
\(293\) | −55077.2 | − | 55077.2i | −0.641559 | − | 0.641559i | 0.309380 | − | 0.950939i | \(-0.399879\pi\) |
−0.950939 | + | 0.309380i | \(0.899879\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6642.86 | 0.0758178 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4287.88 | + | 4287.88i | 0.0482847 | + | 0.0482847i | ||||
\(299\) | 39215.1i | 0.438643i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 50517.9 | 0.557587 | ||||||||
\(302\) | 17881.2 | − | 17881.2i | 0.196057 | − | 0.196057i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 17421.5i | − | 0.188512i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11961.1 | + | 11961.1i | −0.126910 | + | 0.126910i | −0.767709 | − | 0.640799i | \(-0.778603\pi\) |
0.640799 | + | 0.767709i | \(0.278603\pi\) | |||||||
\(308\) | −59527.1 | − | 59527.1i | −0.627499 | − | 0.627499i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | \(-0.235249\pi\) |
−0.673590 | + | 0.739105i | \(0.735249\pi\) | |||||||
\(314\) | − | 72131.4i | − | 0.731586i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −37333.5 | −0.373874 | ||||||||
\(317\) | 22100.1 | − | 22100.1i | 0.219926 | − | 0.219926i | −0.588541 | − | 0.808467i | \(-0.700298\pi\) |
0.808467 | + | 0.588541i | \(0.200298\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 140621.i | 1.38187i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 15586.1 | − | 15586.1i | 0.150323 | − | 0.150323i | ||||
\(323\) | −19331.0 | − | 19331.0i | −0.185289 | − | 0.185289i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −27436.0 | −0.258158 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 22182.3 | + | 22182.3i | 0.206185 | + | 0.206185i | ||||
\(329\) | − | 234886.i | − | 2.17003i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −49108.7 | −0.448231 | −0.224116 | − | 0.974563i | \(-0.571949\pi\) | ||||
−0.224116 | + | 0.974563i | \(0.571949\pi\) | |||||||
\(332\) | 32895.8 | − | 32895.8i | 0.298445 | − | 0.298445i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 149757.i | − | 1.34244i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 142816. | − | 142816.i | 1.25753 | − | 1.25753i | 0.305260 | − | 0.952269i | \(-0.401257\pi\) |
0.952269 | − | 0.305260i | \(-0.0987434\pi\) | |||||||
\(338\) | −142903. | − | 142903.i | −1.25086 | − | 1.25086i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −67609.8 | −0.581434 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −37875.6 | − | 37875.6i | −0.321937 | − | 0.321937i | ||||
\(344\) | − | 18188.6i | − | 0.153703i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 130553. | 1.09052 | ||||||||
\(347\) | −21400.3 | + | 21400.3i | −0.177730 | + | 0.177730i | −0.790366 | − | 0.612635i | \(-0.790109\pi\) |
0.612635 | + | 0.790366i | \(0.290109\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34091.2i | 0.279893i | 0.990159 | + | 0.139946i | \(0.0446930\pi\) | ||||
−0.990159 | + | 0.139946i | \(0.955307\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −21432.2 | + | 21432.2i | −0.172974 | + | 0.172974i | ||||
\(353\) | 28.7539 | + | 28.7539i | 0.000230753 | + | 0.000230753i | 0.707222 | − | 0.706991i | \(-0.249948\pi\) |
−0.706991 | + | 0.707222i | \(0.749948\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −79292.9 | −0.625654 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12792.4 | + | 12792.4i | 0.0998126 | + | 0.0998126i | ||||
\(359\) | 173943.i | 1.34964i | 0.737984 | + | 0.674818i | \(0.235778\pi\) | ||||
−0.737984 | + | 0.674818i | \(0.764222\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 56222.1 | 0.431412 | ||||||||
\(362\) | −98051.9 | + | 98051.9i | −0.748236 | + | 0.748236i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 159001.i | 1.20004i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 41954.1 | − | 41954.1i | 0.311489 | − | 0.311489i | −0.533997 | − | 0.845486i | \(-0.679311\pi\) |
0.845486 | + | 0.533997i | \(0.179311\pi\) | |||||||
\(368\) | −5611.66 | − | 5611.66i | −0.0414377 | − | 0.0414377i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 122531. | 0.890223 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 65875.2 | + | 65875.2i | 0.473483 | + | 0.473483i | 0.903040 | − | 0.429557i | \(-0.141330\pi\) |
−0.429557 | + | 0.903040i | \(0.641330\pi\) | |||||||
\(374\) | 47562.7i | 0.340034i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −84568.7 | −0.598183 | ||||||||
\(377\) | 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 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 79898.0 | − | 79898.0i | 0.547531 | − | 0.547531i | ||||
\(383\) | 22327.5 | + | 22327.5i | 0.152210 | + | 0.152210i | 0.779104 | − | 0.626894i | \(-0.215674\pi\) |
−0.626894 | + | 0.779104i | \(0.715674\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −94996.5 | −0.637577 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −85511.0 | − | 85511.0i | −0.568013 | − | 0.568013i | ||||
\(389\) | − | 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 | ||||||||
\(392\) | 24779.2 | − | 24779.2i | 0.161256 | − | 0.161256i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 10900.4i | − | 0.0702181i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −117299. | + | 117299.i | −0.744238 | + | 0.744238i | −0.973390 | − | 0.229153i | \(-0.926404\pi\) |
0.229153 | + | 0.973390i | \(0.426404\pi\) | |||||||
\(398\) | 126425. | + | 126425.i | 0.798118 | + | 0.798118i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −43093.1 | −0.267990 | −0.133995 | − | 0.990982i | \(-0.542781\pi\) | ||||
−0.133995 | + | 0.990982i | \(0.542781\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 90295.2 | + | 90295.2i | 0.555974 | + | 0.555974i | ||||
\(404\) | − | 14104.7i | − | 0.0864177i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −149286. | −0.905665 | ||||||||
\(407\) | −34758.6 | + | 34758.6i | −0.209833 | + | 0.209833i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 186090.i | − | 1.11244i | −0.831036 | − | 0.556219i | \(-0.812252\pi\) | ||
0.831036 | − | 0.556219i | \(-0.187748\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 19314.1 | − | 19314.1i | 0.113784 | − | 0.113784i | ||||
\(413\) | 14554.0 | + | 14554.0i | 0.0853261 | + | 0.0853261i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 57247.0 | 0.330800 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 91157.7 | + | 91157.7i | 0.521724 | + | 0.521724i | ||||
\(419\) | − | 101699.i | − | 0.579278i | −0.957136 | − | 0.289639i | \(-0.906465\pi\) | ||
0.957136 | − | 0.289639i | \(-0.0935352\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22533.0 | −0.127132 | −0.0635659 | − | 0.997978i | \(-0.520247\pi\) | ||||
−0.0635659 | + | 0.997978i | \(0.520247\pi\) | |||||||
\(422\) | −30940.3 | + | 30940.3i | −0.173740 | + | 0.173740i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 44116.3i | − | 0.245396i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 186897. | − | 186897.i | 1.02505 | − | 1.02505i | ||||
\(428\) | −34232.2 | − | 34232.2i | −0.186873 | − | 0.186873i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | \(-0.404096\pi\) |
−0.954954 | + | 0.296754i | \(0.904096\pi\) | |||||||
\(434\) | − | 71776.0i | − | 0.381065i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −94556.3 | −0.497413 | ||||||||
\(437\) | −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 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 63521.6 | − | 63521.6i | 0.325145 | − | 0.325145i | ||||
\(443\) | −99815.9 | − | 99815.9i | −0.508619 | − | 0.508619i | 0.405484 | − | 0.914102i | \(-0.367103\pi\) |
−0.914102 | + | 0.405484i | \(0.867103\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 115271. | 0.579496 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −22752.9 | − | 22752.9i | −0.113366 | − | 0.113366i | ||||
\(449\) | 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 | ||||||||
\(452\) | 12964.8 | − | 12964.8i | 0.0634585 | − | 0.0634585i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3536.95i | 0.0171600i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −147497. | + | 147497.i | −0.706239 | + | 0.706239i | −0.965742 | − | 0.259503i | \(-0.916441\pi\) |
0.259503 | + | 0.965742i | \(0.416441\pi\) | |||||||
\(458\) | −24152.8 | − | 24152.8i | −0.115143 | − | 0.115143i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 354912. | 1.67001 | 0.835006 | − | 0.550241i | \(-0.185464\pi\) | ||||
0.835006 | + | 0.550241i | \(0.185464\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −182475. | − | 182475.i | −0.851221 | − | 0.851221i | 0.139063 | − | 0.990284i | \(-0.455591\pi\) |
−0.990284 | + | 0.139063i | \(0.955591\pi\) | |||||||
\(464\) | 53749.3i | 0.249653i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 98783.0 | 0.454894 | ||||||||
\(467\) | 4348.30 | − | 4348.30i | 0.0199382 | − | 0.0199382i | −0.697067 | − | 0.717006i | \(-0.745512\pi\) |
0.717006 | + | 0.697067i | \(0.245512\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 251792.i | − | 1.14471i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5240.04 | − | 5240.04i | 0.0235207 | − | 0.0235207i | ||||
\(473\) | 95171.3 | + | 95171.3i | 0.425386 | + | 0.425386i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −50493.5 | −0.222855 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −96375.5 | − | 96375.5i | −0.421804 | − | 0.421804i | ||||
\(479\) | − | 77346.0i | − | 0.337106i | −0.985693 | − | 0.168553i | \(-0.946091\pi\) | ||
0.985693 | − | 0.168553i | \(-0.0539095\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 92842.6 | 0.401289 | ||||||||
\(482\) | 110368. | − | 110368.i | 0.475062 | − | 0.475062i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 107159.i | − | 0.457445i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −77225.6 | + | 77225.6i | −0.325614 | + | 0.325614i | −0.850916 | − | 0.525302i | \(-0.823952\pi\) |
0.525302 | + | 0.850916i | \(0.323952\pi\) | |||||||
\(488\) | −67290.6 | − | 67290.6i | −0.282562 | − | 0.282562i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | ||||
\(494\) | − | 243488.i | − | 0.997756i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −25842.4 | −0.105043 | ||||||||
\(497\) | 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 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −139336. | + | 139336.i | −0.552910 | + | 0.552910i | ||||
\(503\) | −123301. | − | 123301.i | −0.487338 | − | 0.487338i | 0.420127 | − | 0.907465i | \(-0.361985\pi\) |
−0.907465 | + | 0.420127i | \(0.861985\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 58725.7 | 0.229365 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −92579.7 | − | 92579.7i | −0.358747 | − | 0.358747i | ||||
\(509\) | 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 | ||||||||
\(512\) | −8192.00 | + | 8192.00i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 46457.8i | − | 0.175846i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 442504. | − | 442504.i | 1.65553 | − | 1.65553i | ||||
\(518\) | −36900.5 | − | 36900.5i | −0.137522 | − | 0.137522i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 203461. | 0.749560 | 0.374780 | − | 0.927114i | \(-0.377718\pi\) | ||||
0.374780 | + | 0.927114i | \(0.377718\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −72655.5 | − | 72655.5i | −0.265623 | − | 0.265623i | 0.561711 | − | 0.827334i | \(-0.310143\pi\) |
−0.827334 | + | 0.561711i | \(0.810143\pi\) | |||||||
\(524\) | 524.984i | 0.00191198i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −347247. | −1.25507 | ||||||||
\(527\) | −28674.8 | + | 28674.8i | −0.103248 | + | 0.103248i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 264465.i | − | 0.945053i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −96775.0 | + | 96775.0i | −0.341932 | + | 0.341932i | ||||
\(533\) | 310026. | + | 310026.i | 1.09130 | + | 1.09130i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −90655.8 | −0.315548 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −186879. | − | 186879.i | −0.645647 | − | 0.645647i | ||||
\(539\) | 259313.i | 0.892580i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −91367.2 | −0.312173 | −0.156087 | − | 0.987743i | \(-0.549888\pi\) | ||||
−0.156087 | + | 0.987743i | \(0.549888\pi\) | |||||||
\(542\) | 21713.0 | − | 21713.0i | 0.0739131 | − | 0.0739131i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18179.8i | 0.0614315i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9895.50 | − | 9895.50i | 0.0330722 | − | 0.0330722i | −0.690377 | − | 0.723450i | \(-0.742555\pi\) |
0.723450 | + | 0.690377i | \(0.242555\pi\) | |||||||
\(548\) | −4635.51 | − | 4635.51i | −0.0154361 | − | 0.0154361i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 228612. | 0.753001 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 207384. | + | 207384.i | 0.678150 | + | 0.678150i | ||||
\(554\) | − | 260859.i | − | 0.849935i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −289266. | −0.935724 | ||||||||
\(557\) | −306800. | + | 306800.i | −0.988883 | + | 0.988883i | −0.999939 | − | 0.0110558i | \(-0.996481\pi\) |
0.0110558 | + | 0.999939i | \(0.496481\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 254209.i | − | 0.813518i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17338.7 | + | 17338.7i | −0.0548963 | + | 0.0548963i | ||||
\(563\) | 331132. | + | 331132.i | 1.04468 | + | 1.04468i | 0.998954 | + | 0.0457279i | \(0.0145607\pi\) |
0.0457279 | + | 0.998954i | \(0.485439\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −94988.2 | −0.296508 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −85424.5 | − | 85424.5i | −0.264780 | − | 0.264780i | ||||
\(569\) | − | 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 | \(-0.903745\pi\) | ||||
−0.954626 | + | 0.297807i | \(0.903745\pi\) | |||||||
\(572\) | −299543. | + | 299543.i | −0.915520 | + | 0.915520i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 246441.i | − | 0.747978i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23928.8 | − | 23928.8i | 0.0718736 | − | 0.0718736i | −0.670256 | − | 0.742130i | \(-0.733816\pi\) |
0.742130 | + | 0.670256i | \(0.233816\pi\) | |||||||
\(578\) | −146870. | − | 146870.i | −0.439619 | − | 0.439619i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −365467. | −1.08267 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 230838. | + | 230838.i | 0.679156 | + | 0.679156i | ||||
\(584\) | − | 219688.i | − | 0.644139i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 220309. | 0.641559 | ||||||||
\(587\) | 181136. | − | 181136.i | 0.525690 | − | 0.525690i | −0.393595 | − | 0.919284i | \(-0.628769\pi\) |
0.919284 | + | 0.393595i | \(0.128769\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 109915.i | 0.316831i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −13285.7 | + | 13285.7i | −0.0379089 | + | 0.0379089i | ||||
\(593\) | −235890. | − | 235890.i | −0.670812 | − | 0.670812i | 0.287091 | − | 0.957903i | \(-0.407312\pi\) |
−0.957903 | + | 0.287091i | \(0.907312\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17151.5 | −0.0482847 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −78430.2 | − | 78430.2i | −0.219322 | − | 0.219322i | ||||
\(599\) | 141629.i | 0.394728i | 0.980330 | + | 0.197364i | \(0.0632381\pi\) | ||||
−0.980330 | + | 0.197364i | \(0.936762\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −564417. | −1.56261 | −0.781306 | − | 0.624148i | \(-0.785446\pi\) | ||||
−0.781306 | + | 0.624148i | \(0.785446\pi\) | |||||||
\(602\) | −101036. | + | 101036.i | −0.278794 | + | 0.278794i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 71524.7i | 0.196057i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −247253. | + | 247253.i | −0.671064 | + | 0.671064i | −0.957961 | − | 0.286898i | \(-0.907376\pi\) |
0.286898 | + | 0.957961i | \(0.407376\pi\) | |||||||
\(608\) | 34843.0 | + | 34843.0i | 0.0942560 | + | 0.0942560i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.18196e6 | −3.16606 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 163758. | + | 163758.i | 0.435794 | + | 0.435794i | 0.890594 | − | 0.454800i | \(-0.150289\pi\) |
−0.454800 | + | 0.890594i | \(0.650289\pi\) | |||||||
\(614\) | − | 47844.5i | − | 0.126910i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 238108. | 0.627499 | ||||||||
\(617\) | 273782. | − | 273782.i | 0.719176 | − | 0.719176i | −0.249260 | − | 0.968437i | \(-0.580188\pi\) |
0.968437 | + | 0.249260i | \(0.0801875\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 428345.i | 1.11792i | 0.829194 | + | 0.558962i | \(0.188800\pi\) | ||||
−0.829194 | + | 0.558962i | \(0.811200\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −130569. | + | 130569.i | −0.337489 | + | 0.337489i | ||||
\(623\) | 440465. | + | 440465.i | 1.13484 | + | 1.13484i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −25673.8 | −0.0655151 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 144263. | + | 144263.i | 0.365793 | + | 0.365793i | ||||
\(629\) | 29483.8i | 0.0745216i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 108870. | 0.273432 | 0.136716 | − | 0.990610i | \(-0.456345\pi\) | ||||
0.136716 | + | 0.990610i | \(0.456345\pi\) | |||||||
\(632\) | 74667.1 | − | 74667.1i | 0.186937 | − | 0.186937i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 88400.5i | 0.219926i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 346322. | − | 346322.i | 0.853495 | − | 0.853495i | ||||
\(638\) | −281242. | − | 281242.i | −0.690937 | − | 0.690937i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 501643. | 1.22090 | 0.610448 | − | 0.792056i | \(-0.290989\pi\) | ||||
0.610448 | + | 0.792056i | \(0.290989\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 117251. | + | 117251.i | 0.283592 | + | 0.283592i | 0.834540 | − | 0.550948i | \(-0.185734\pi\) |
−0.550948 | + | 0.834540i | \(0.685734\pi\) | |||||||
\(644\) | 62344.5i | 0.150323i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 77324.1 | 0.185289 | ||||||||
\(647\) | −362031. | + | 362031.i | −0.864843 | + | 0.864843i | −0.991896 | − | 0.127053i | \(-0.959448\pi\) |
0.127053 | + | 0.991896i | \(0.459448\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 54836.8i | 0.130192i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 54872.0 | − | 54872.0i | 0.129079 | − | 0.129079i | ||||
\(653\) | −411293. | − | 411293.i | −0.964552 | − | 0.964552i | 0.0348413 | − | 0.999393i | \(-0.488907\pi\) |
−0.999393 | + | 0.0348413i | \(0.988907\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −88729.0 | −0.206185 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 469772. | + | 469772.i | 1.08501 | + | 1.08501i | ||||
\(659\) | 291952.i | 0.672265i | 0.941815 | + | 0.336133i | \(0.109119\pi\) | ||||
−0.941815 | + | 0.336133i | \(0.890881\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 757270. | 1.73320 | 0.866599 | − | 0.499006i | \(-0.166301\pi\) | ||||
0.866599 | + | 0.499006i | \(0.166301\pi\) | |||||||
\(662\) | 98217.4 | − | 98217.4i | 0.224116 | − | 0.224116i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 131583.i | 0.298445i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 73638.3 | − | 73638.3i | 0.165521 | − | 0.165521i | ||||
\(668\) | 299514. | + | 299514.i | 0.671219 | + | 0.671219i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 704193. | 1.56404 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −310335. | − | 310335.i | −0.685173 | − | 0.685173i | 0.275988 | − | 0.961161i | \(-0.410995\pi\) |
−0.961161 | + | 0.275988i | \(0.910995\pi\) | |||||||
\(674\) | 571265.i | 1.25753i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 571613. | 1.25086 | ||||||||
\(677\) | 9203.97 | − | 9203.97i | 0.0200816 | − | 0.0200816i | −0.696995 | − | 0.717076i | \(-0.745480\pi\) |
0.717076 | + | 0.696995i | \(0.245480\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 950012.i | 2.06058i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 135220. | − | 135220.i | 0.290717 | − | 0.290717i | ||||
\(683\) | −421590. | − | 421590.i | −0.903750 | − | 0.903750i | 0.0920080 | − | 0.995758i | \(-0.470671\pi\) |
−0.995758 | + | 0.0920080i | \(0.970671\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 151502. | 0.321937 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 36377.1 | + | 36377.1i | 0.0768514 | + | 0.0768514i | ||||
\(689\) | − | 616584.i | − | 1.29883i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 102275. | 0.214197 | 0.107098 | − | 0.994248i | \(-0.465844\pi\) | ||||
0.107098 | + | 0.994248i | \(0.465844\pi\) | |||||||
\(692\) | −261106. | + | 261106.i | −0.545261 | + | 0.545261i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 85601.3i | − | 0.177730i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −98454.3 | + | 98454.3i | −0.202660 | + | 0.202660i | ||||
\(698\) | −68182.4 | − | 68182.4i | −0.139946 | − | 0.139946i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 685359. | 1.39471 | 0.697353 | − | 0.716728i | \(-0.254361\pi\) | ||||
0.697353 | + | 0.716728i | \(0.254361\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 56508.1 | + | 56508.1i | 0.114341 | + | 0.114341i | ||||
\(704\) | − | 85728.9i | − | 0.172974i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −115.016 | −0.000230753 | ||||||||
\(707\) | −78350.6 | + | 78350.6i | −0.156749 | + | 0.156749i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 164715.i | 0.327673i | 0.986487 | + | 0.163837i | \(0.0523870\pi\) | ||||
−0.986487 | + | 0.163837i | \(0.947613\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 158586. | − | 158586.i | 0.312827 | − | 0.312827i | ||||
\(713\) | 35404.9 | + | 35404.9i | 0.0696441 | + | 0.0696441i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −51169.5 | −0.0998126 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −347885. | − | 347885.i | −0.674818 | − | 0.674818i | ||||
\(719\) | − | 782798.i | − | 1.51423i | −0.653282 | − | 0.757115i | \(-0.726608\pi\) | ||
0.653282 | − | 0.757115i | \(-0.273392\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −214577. | −0.412774 | ||||||||
\(722\) | −112444. | + | 112444.i | −0.215706 | + | 0.215706i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 392208.i | − | 0.748236i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −659110. | + | 659110.i | −1.24706 | + | 1.24706i | −0.290054 | + | 0.957010i | \(0.593673\pi\) |
−0.957010 | + | 0.290054i | \(0.906327\pi\) | |||||||
\(728\) | −318002. | − | 318002.i | −0.600021 | − | 0.600021i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 80728.6 | 0.151075 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −356952. | − | 356952.i | −0.664358 | − | 0.664358i | 0.292046 | − | 0.956404i | \(-0.405664\pi\) |
−0.956404 | + | 0.292046i | \(0.905664\pi\) | |||||||
\(734\) | 167816.i | 0.311489i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22446.6 | 0.0414377 | ||||||||
\(737\) | 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 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −245062. | + | 245062.i | −0.445111 | + | 0.445111i | ||||
\(743\) | −35964.9 | − | 35964.9i | −0.0651480 | − | 0.0651480i | 0.673782 | − | 0.738930i | \(-0.264669\pi\) |
−0.738930 | + | 0.673782i | \(0.764669\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −263501. | −0.473483 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −95125.3 | − | 95125.3i | −0.170017 | − | 0.170017i | ||||
\(749\) | 380314.i | 0.677920i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 702045. | 1.24476 | 0.622379 | − | 0.782716i | \(-0.286166\pi\) | ||||
0.622379 | + | 0.782716i | \(0.286166\pi\) | |||||||
\(752\) | 169137. | − | 169137.i | 0.299091 | − | 0.299091i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 751216.i | 1.32136i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 111880. | − | 111880.i | 0.195236 | − | 0.195236i | −0.602718 | − | 0.797954i | \(-0.705916\pi\) |
0.797954 | + | 0.602718i | \(0.205916\pi\) | |||||||
\(758\) | −21673.9 | − | 21673.9i | −0.0377224 | − | 0.0377224i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 579015. | 0.999817 | 0.499908 | − | 0.866078i | \(-0.333367\pi\) | ||||
0.499908 | + | 0.866078i | \(0.333367\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 525252. | + | 525252.i | 0.902232 | + | 0.902232i | ||||
\(764\) | 319592.i | 0.547531i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −89310.0 | −0.152210 | ||||||||
\(767\) | 73236.4 | − | 73236.4i | 0.124491 | − | 0.124491i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 472110.i | − | 0.798344i | −0.916876 | − | 0.399172i | \(-0.869298\pi\) | ||
0.916876 | − | 0.399172i | \(-0.130702\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 189993. | − | 189993.i | 0.318789 | − | 0.318789i | ||||
\(773\) | −20353.7 | − | 20353.7i | −0.0340631 | − | 0.0340631i | 0.689870 | − | 0.723933i | \(-0.257668\pi\) |
−0.723933 | + | 0.689870i | \(0.757668\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 342044. | 0.568013 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 407768. | + | 407768.i | 0.673680 | + | 0.673680i | ||||
\(779\) | 377391.i | 0.621895i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 893963. | 1.46561 | ||||||||
\(782\) | 24906.9 | − | 24906.9i | 0.0407293 | − | 0.0407293i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 99116.8i | 0.161256i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −640630. | + | 640630.i | −1.03433 | + | 1.03433i | −0.0349373 | + | 0.999390i | \(0.511123\pi\) |
−0.999390 | + | 0.0349373i | \(0.988877\pi\) | |||||||
\(788\) | 21800.7 | + | 21800.7i | 0.0351090 | + | 0.0351090i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −144037. | −0.230208 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −940474. | − | 940474.i | −1.49555 | − | 1.49555i | ||||
\(794\) | − | 469194.i | − | 0.744238i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −505700. | −0.798118 | ||||||||
\(797\) | 542782. | − | 542782.i | 0.854494 | − | 0.854494i | −0.136189 | − | 0.990683i | \(-0.543485\pi\) |
0.990683 | + | 0.136189i | \(0.0434854\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 375352.i | − | 0.587956i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 86186.2 | − | 86186.2i | 0.133995 | − | 0.133995i | ||||
\(803\) | 1.14951e6 | + | 1.14951e6i | 1.78271 | + | 1.78271i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −361181. | −0.555974 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 28209.5 | + | 28209.5i | 0.0432088 | + | 0.0432088i | ||||
\(809\) | 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 | \(-0.681880\pi\) | ||||
−0.540805 | + | 0.841148i | \(0.681880\pi\) | |||||||
\(812\) | 298572. | − | 298572.i | 0.452832 | − | 0.452832i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 139034.i | − | 0.209833i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 154723. | − | 154723.i | 0.231798 | − | 0.231798i | ||||
\(818\) | 372179. | + | 372179.i | 0.556219 | + | 0.556219i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 566243. | 0.840071 | 0.420036 | − | 0.907508i | \(-0.362018\pi\) | ||||
0.420036 | + | 0.907508i | \(0.362018\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 678523. | + | 678523.i | 1.00176 | + | 1.00176i | 0.999998 | + | 0.00176504i | \(0.000561830\pi\) |
0.00176504 | + | 0.999998i | \(0.499438\pi\) | |||||||
\(824\) | 77256.6i | 0.113784i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −58215.9 | −0.0853261 | ||||||||
\(827\) | −822466. | + | 822466.i | −1.20256 | + | 1.20256i | −0.229174 | + | 0.973385i | \(0.573603\pi\) |
−0.973385 | + | 0.229174i | \(0.926397\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.26805e6i | 1.84514i | 0.385832 | + | 0.922569i | \(0.373914\pi\) | ||||
−0.385832 | + | 0.922569i | \(0.626086\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −114494. | + | 114494.i | −0.165400 | + | 0.165400i | ||||
\(833\) | 109981. | + | 109981.i | 0.158499 | + | 0.158499i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −364631. | −0.521724 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 203397. | + | 203397.i | 0.289639 | + | 0.289639i | ||||
\(839\) | − | 487091.i | − | 0.691968i | −0.938240 | − | 0.345984i | \(-0.887545\pi\) | ||
0.938240 | − | 0.345984i | \(-0.112455\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1962.99 | 0.00277541 | ||||||||
\(842\) | 45065.9 | − | 45065.9i | 0.0635659 | − | 0.0635659i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 123761.i | − | 0.173740i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −595260. | + | 595260.i | −0.829736 | + | 0.829736i | ||||
\(848\) | 88232.7 | + | 88232.7i | 0.122698 | + | 0.122698i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36403.7 | 0.0502675 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10645.4 | − | 10645.4i | −0.0146307 | − | 0.0146307i | 0.699754 | − | 0.714384i | \(-0.253293\pi\) |
−0.714384 | + | 0.699754i | \(0.753293\pi\) | |||||||
\(854\) | 747586.i | 1.02505i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 136929. | 0.186873 | ||||||||
\(857\) | −692563. | + | 692563.i | −0.942970 | + | 0.942970i | −0.998459 | − | 0.0554896i | \(-0.982328\pi\) |
0.0554896 | + | 0.998459i | \(0.482328\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 745974.i | − | 1.01097i | −0.862836 | − | 0.505484i | \(-0.831314\pi\) | ||
0.862836 | − | 0.505484i | \(-0.168686\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 421196. | − | 421196.i | 0.566852 | − | 0.566852i | ||||
\(863\) | 259362. | + | 259362.i | 0.348245 | + | 0.348245i | 0.859456 | − | 0.511211i | \(-0.170803\pi\) |
−0.511211 | + | 0.859456i | \(0.670803\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 493621. | 0.658201 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 143552. | + | 143552.i | 0.190533 | + | 0.190533i | ||||
\(869\) | 781388.i | 1.03473i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.26703e6 | −1.67013 | ||||||||
\(872\) | 189113. | − | 189113.i | 0.248707 | − | 0.248707i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 95472.3i | − | 0.124984i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 191986. | − | 191986.i | 0.249615 | − | 0.249615i | −0.571197 | − | 0.820813i | \(-0.693521\pi\) |
0.820813 | + | 0.571197i | \(0.193521\pi\) | |||||||
\(878\) | 530360. | + | 530360.i | 0.687989 | + | 0.687989i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.08074e6 | −1.39241 | −0.696207 | − | 0.717841i | \(-0.745130\pi\) | ||||
−0.696207 | + | 0.717841i | \(0.745130\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −294604. | − | 294604.i | −0.377848 | − | 0.377848i | 0.492477 | − | 0.870325i | \(-0.336091\pi\) |
−0.870325 | + | 0.492477i | \(0.836091\pi\) | |||||||
\(884\) | 254086.i | 0.325145i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 399264. | 0.508619 | ||||||||
\(887\) | −373328. | + | 373328.i | −0.474507 | + | 0.474507i | −0.903370 | − | 0.428862i | \(-0.858915\pi\) |
0.428862 | + | 0.903370i | \(0.358915\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.02854e6i | 1.30143i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −230542. | + | 230542.i | −0.289748 | + | 0.289748i | ||||
\(893\) | −719392. | − | 719392.i | −0.902117 | − | 0.902117i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 91011.7 | 0.113366 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −365869. | − | 365869.i | −0.453704 | − | 0.453704i | ||||
\(899\) | − | 339113.i | − | 0.419590i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 195807. | 0.241201 | ||||||||
\(902\) | 464273. | − | 464273.i | 0.570637 | − | 0.570637i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 51859.3i | 0.0634585i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 342694. | − | 342694.i | 0.416574 | − | 0.416574i | −0.467447 | − | 0.884021i | \(-0.654826\pi\) |
0.884021 | + | 0.467447i | \(0.154826\pi\) | |||||||
\(908\) | −7073.89 | − | 7073.89i | −0.00857999 | − | 0.00857999i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | ||||
\(914\) | − | 589989.i | − | 0.706239i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 96611.0 | 0.115143 | ||||||||
\(917\) | 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 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −709825. | + | 709825.i | −0.835006 | + | 0.835006i | ||||
\(923\) | −1.19392e6 | − | 1.19392e6i | −1.40143 | − | 1.40143i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 729901. | 0.851221 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −107499. | − | 107499.i | −0.124826 | − | 0.124826i | ||||
\(929\) | − | 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 | ||||||||
\(932\) | −197566. | + | 197566.i | −0.227447 | + | 0.227447i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17393.2i | 0.0199382i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −81884.2 | + | 81884.2i | −0.0932655 | + | 0.0932655i | −0.752200 | − | 0.658935i | \(-0.771007\pi\) |
0.658935 | + | 0.752200i | \(0.271007\pi\) | |||||||
\(938\) | 503585. | + | 503585.i | 0.572357 | + | 0.572357i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.67094e6 | −1.88705 | −0.943524 | − | 0.331305i | \(-0.892511\pi\) | ||||
−0.943524 | + | 0.331305i | \(0.892511\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 121562. | + | 121562.i | 0.136702 | + | 0.136702i | ||||
\(944\) | 20960.2i | 0.0235207i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −380685. | −0.425386 | ||||||||
\(947\) | 689602. | − | 689602.i | 0.768950 | − | 0.768950i | −0.208971 | − | 0.977922i | \(-0.567012\pi\) |
0.977922 | + | 0.208971i | \(0.0670116\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 3.07042e6i | − | 3.40930i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 100987. | − | 100987.i | 0.111427 | − | 0.111427i | ||||
\(953\) | 150337. | + | 150337.i | 0.165532 | + | 0.165532i | 0.785012 | − | 0.619480i | \(-0.212657\pi\) |
−0.619480 | + | 0.785012i | \(0.712657\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 385502. | 0.421804 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 154692. | + | 154692.i | 0.168553 | + | 0.168553i | ||||
\(959\) | 51499.7i | 0.0559974i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −760477. | −0.823454 | ||||||||
\(962\) | −185685. | + | 185685.i | −0.200644 | + | 0.200644i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 441473.i | 0.475062i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 312723. | − | 312723.i | 0.334432 | − | 0.334432i | −0.519835 | − | 0.854267i | \(-0.674007\pi\) |
0.854267 | + | 0.519835i | \(0.174007\pi\) | |||||||
\(968\) | 214319. | + | 214319.i | 0.228723 | + | 0.228723i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | ||||
\(974\) | − | 308903.i | − | 0.325614i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 269162. | 0.282562 | ||||||||
\(977\) | −748461. | + | 748461.i | −0.784115 | + | 0.784115i | −0.980522 | − | 0.196407i | \(-0.937073\pi\) |
0.196407 | + | 0.980522i | \(0.437073\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.65959e6i | 1.73156i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 680434. | − | 680434.i | 0.705607 | − | 0.705607i | ||||
\(983\) | −542812. | − | 542812.i | −0.561749 | − | 0.561749i | 0.368055 | − | 0.929804i | \(-0.380024\pi\) |
−0.929804 | + | 0.368055i | \(0.880024\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −238562. | −0.245385 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 486977. | + | 486977.i | 0.498878 | + | 0.498878i | ||||
\(989\) | − | 99675.8i | − | 0.101905i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.08269e6 | 1.10245 | 0.551224 | − | 0.834357i | \(-0.314161\pi\) | ||||
0.551224 | + | 0.834357i | \(0.314161\pi\) | |||||||
\(992\) | 51684.7 | − | 51684.7i | 0.0525217 | − | 0.0525217i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 949050.i | 0.960542i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25593.2 | + | 25593.2i | −0.0257475 | + | 0.0257475i | −0.719863 | − | 0.694116i | \(-0.755796\pi\) |
0.694116 | + | 0.719863i | \(0.255796\pi\) | |||||||
\(998\) | −662047. | − | 662047.i | −0.664703 | − | 0.664703i | ||||
\(999\) | 0 | 0 |
(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 | 450.5.g.f.343.1 | 4 | ||
3.2 | odd | 2 | 150.5.f.e.43.2 | 4 | |||
5.2 | odd | 4 | inner | 450.5.g.f.307.1 | 4 | ||
5.3 | odd | 4 | 90.5.g.e.37.1 | 4 | |||
5.4 | even | 2 | 90.5.g.e.73.1 | 4 | |||
15.2 | even | 4 | 150.5.f.e.7.2 | 4 | |||
15.8 | even | 4 | 30.5.f.a.7.1 | ✓ | 4 | ||
15.14 | odd | 2 | 30.5.f.a.13.1 | yes | 4 | ||
60.23 | odd | 4 | 240.5.bg.b.97.2 | 4 | |||
60.59 | even | 2 | 240.5.bg.b.193.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
30.5.f.a.7.1 | ✓ | 4 | 15.8 | even | 4 | ||
30.5.f.a.13.1 | yes | 4 | 15.14 | odd | 2 | ||
90.5.g.e.37.1 | 4 | 5.3 | odd | 4 | |||
90.5.g.e.73.1 | 4 | 5.4 | even | 2 | |||
150.5.f.e.7.2 | 4 | 15.2 | even | 4 | |||
150.5.f.e.43.2 | 4 | 3.2 | odd | 2 | |||
240.5.bg.b.97.2 | 4 | 60.23 | odd | 4 | |||
240.5.bg.b.193.2 | 4 | 60.59 | even | 2 | |||
450.5.g.f.307.1 | 4 | 5.2 | odd | 4 | inner | ||
450.5.g.f.343.1 | 4 | 1.1 | even | 1 | trivial |