Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,6,Mod(47,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("160.47");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.o (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: | \(25.6614111701\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.10 | ||
Character | \(\chi\) | \(=\) | 160.47 |
Dual form | 160.6.o.a.143.10 |
$q$-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 \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(101\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −10.0657 | + | 10.0657i | −0.645715 | + | 0.645715i | −0.951954 | − | 0.306240i | \(-0.900929\pi\) |
0.306240 | + | 0.951954i | \(0.400929\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 23.9125 | − | 50.5291i | 0.427760 | − | 0.903892i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −96.6855 | + | 96.6855i | −0.745790 | + | 0.745790i | −0.973686 | − | 0.227896i | \(-0.926815\pi\) |
0.227896 | + | 0.973686i | \(0.426815\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 40.3635i | 0.166105i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 283.587 | 0.706650 | 0.353325 | − | 0.935501i | \(-0.385051\pi\) | ||||
0.353325 | + | 0.935501i | \(0.385051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −699.519 | − | 699.519i | −1.14800 | − | 1.14800i | −0.986946 | − | 0.161052i | \(-0.948511\pi\) |
−0.161052 | − | 0.986946i | \(-0.551489\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 267.915 | + | 749.307i | 0.307446 | + | 0.859868i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 399.025 | + | 399.025i | 0.334871 | + | 0.334871i | 0.854433 | − | 0.519562i | \(-0.173905\pi\) |
−0.519562 | + | 0.854433i | \(0.673905\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 338.083i | 0.214852i | 0.994213 | + | 0.107426i | \(0.0342609\pi\) | ||||
−0.994213 | + | 0.107426i | \(0.965739\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1946.41i | − | 0.963135i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −594.687 | − | 594.687i | −0.234406 | − | 0.234406i | 0.580123 | − | 0.814529i | \(-0.303005\pi\) |
−0.814529 | + | 0.580123i | \(0.803005\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1981.38 | − | 2416.56i | −0.634043 | − | 0.773298i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2852.25 | − | 2852.25i | −0.752971 | − | 0.752971i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5582.41 | 1.23261 | 0.616306 | − | 0.787507i | \(-0.288628\pi\) | ||||
0.616306 | + | 0.787507i | \(0.288628\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 144.182i | 0.0269468i | 0.999909 | + | 0.0134734i | \(0.00428884\pi\) | ||||
−0.999909 | + | 0.0134734i | \(0.995711\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2854.50 | + | 2854.50i | −0.456294 | + | 0.456294i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2573.44 | + | 7197.43i | 0.355095 | + | 0.993133i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11418.4 | − | 11418.4i | 1.37120 | − | 1.37120i | 0.512523 | − | 0.858674i | \(-0.328711\pi\) |
0.858674 | − | 0.512523i | \(-0.171289\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14082.3 | 1.48256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11892.0 | 1.10483 | 0.552413 | − | 0.833570i | \(-0.313707\pi\) | ||||
0.552413 | + | 0.833570i | \(0.313707\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8345.23 | − | 8345.23i | 0.688283 | − | 0.688283i | −0.273569 | − | 0.961852i | \(-0.588204\pi\) |
0.961852 | + | 0.273569i | \(0.0882042\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2039.53 | + | 965.191i | 0.150141 | + | 0.0710530i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 17955.5 | − | 17955.5i | 1.18564 | − | 1.18564i | 0.207383 | − | 0.978260i | \(-0.433505\pi\) |
0.978260 | − | 0.207383i | \(-0.0664946\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1889.19i | − | 0.112405i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8032.92 | −0.432462 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3977.21 | + | 3977.21i | 0.194486 | + | 0.194486i | 0.797631 | − | 0.603145i | \(-0.206086\pi\) |
−0.603145 | + | 0.797631i | \(0.706086\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6781.27 | − | 14329.4i | 0.302276 | − | 0.638735i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3403.04 | − | 3403.04i | −0.138733 | − | 0.138733i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 17288.6i | 0.646590i | 0.946298 | + | 0.323295i | \(0.104791\pi\) | ||||
−0.946298 | + | 0.323295i | \(0.895209\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6236.61i | − | 0.214597i | −0.994227 | − | 0.107299i | \(-0.965780\pi\) | ||
0.994227 | − | 0.107299i | \(-0.0342201\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3902.56 | − | 3902.56i | −0.123879 | − | 0.123879i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −52073.3 | + | 18618.8i | −1.52873 | + | 0.546599i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −39565.2 | − | 39565.2i | −1.07678 | − | 1.07678i | −0.996796 | − | 0.0799829i | \(-0.974513\pi\) |
−0.0799829 | − | 0.996796i | \(-0.525487\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11971.9 | 0.302719 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 50088.5i | − | 1.17921i | −0.807691 | − | 0.589606i | \(-0.799283\pi\) | ||
0.807691 | − | 0.589606i | \(-0.200717\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 42184.8 | − | 42184.8i | 0.926508 | − | 0.926508i | −0.0709703 | − | 0.997478i | \(-0.522610\pi\) |
0.997478 | + | 0.0709703i | \(0.0226096\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 44268.3 | + | 4380.30i | 0.908741 | + | 0.0899189i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −27418.7 | + | 27418.7i | −0.527012 | + | 0.527012i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −22093.6 | −0.398290 | −0.199145 | − | 0.979970i | \(-0.563816\pi\) | ||||
−0.199145 | + | 0.979970i | \(0.563816\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 47611.5 | 0.806304 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −51337.5 | + | 51337.5i | −0.817974 | + | 0.817974i | −0.985814 | − | 0.167840i | \(-0.946321\pi\) |
0.167840 | + | 0.985814i | \(0.446321\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 29704.0 | − | 10620.7i | 0.445932 | − | 0.159443i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −56190.8 | + | 56190.8i | −0.795916 | + | 0.795916i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 78727.1i | 1.05354i | 0.850009 | + | 0.526768i | \(0.176596\pi\) | ||||
−0.850009 | + | 0.526768i | \(0.823404\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 135267. | 1.71233 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1451.29 | − | 1451.29i | −0.0173999 | − | 0.0173999i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 17083.0 | + | 8084.41i | 0.194203 | + | 0.0919050i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9943.42 | − | 9943.42i | −0.107302 | − | 0.107302i | 0.651418 | − | 0.758719i | \(-0.274175\pi\) |
−0.758719 | + | 0.651418i | \(0.774175\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11446.5i | 0.117378i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 34886.7i | − | 0.340296i | −0.985419 | − | 0.170148i | \(-0.945575\pi\) | ||
0.985419 | − | 0.170148i | \(-0.0544246\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 74849.2 | + | 74849.2i | 0.695175 | + | 0.695175i | 0.963366 | − | 0.268191i | \(-0.0864257\pi\) |
−0.268191 | + | 0.963366i | \(0.586426\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −98350.6 | − | 46543.7i | −0.870570 | − | 0.411991i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −117317. | − | 117317.i | −0.990608 | − | 0.990608i | 0.00934815 | − | 0.999956i | \(-0.497024\pi\) |
−0.999956 | + | 0.00934815i | \(0.997024\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −111201. | −0.896486 | −0.448243 | − | 0.893912i | \(-0.647950\pi\) | ||||
−0.448243 | + | 0.893912i | \(0.647950\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 229868.i | 1.77080i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 66036.6 | − | 66036.6i | 0.486506 | − | 0.486506i | −0.420696 | − | 0.907202i | \(-0.638214\pi\) |
0.907202 | + | 0.420696i | \(0.138214\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −44269.5 | + | 15828.6i | −0.312148 | + | 0.111608i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 28235.0 | − | 28235.0i | 0.190688 | − | 0.190688i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −77159.8 | −0.499487 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −80629.6 | −0.500646 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −119701. | + | 119701.i | −0.713403 | + | 0.713403i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −169486. | + | 42331.7i | −0.970196 | + | 0.242321i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −78416.4 | + | 78416.4i | −0.431418 | + | 0.431418i | −0.889110 | − | 0.457693i | \(-0.848676\pi\) |
0.457693 | + | 0.889110i | \(0.348676\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 168001.i | 0.888870i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 309770. | 1.57711 | 0.788554 | − | 0.614966i | \(-0.210830\pi\) | ||||
0.788554 | + | 0.614966i | \(0.210830\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −32687.7 | − | 32687.7i | −0.160234 | − | 0.160234i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −212326. | + | 75917.3i | −1.00270 | + | 0.358514i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 61997.1 | + | 61997.1i | 0.282208 | + | 0.282208i | 0.833989 | − | 0.551781i | \(-0.186051\pi\) |
−0.551781 | + | 0.833989i | \(0.686051\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 114337.i | − | 0.501938i | −0.967995 | − | 0.250969i | \(-0.919251\pi\) | ||
0.967995 | − | 0.250969i | \(-0.0807492\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 361470.i | 1.53117i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −198374. | − | 198374.i | −0.811232 | − | 0.811232i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 133489. | − | 282074.i | 0.527262 | − | 1.11415i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19016.0 | + | 19016.0i | 0.0725815 | + | 0.0725815i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 63562.8 | 0.234551 | 0.117276 | − | 0.993099i | \(-0.462584\pi\) | ||||
0.117276 | + | 0.993099i | \(0.462584\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 397853.i | − | 1.41998i | −0.704214 | − | 0.709988i | \(-0.748700\pi\) | ||
0.704214 | − | 0.709988i | \(-0.251300\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16106.0 | + | 16106.0i | −0.0556237 | + | 0.0556237i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7285.39 | + | 3447.75i | 0.0243570 | + | 0.0115267i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −283821. | + | 283821.i | −0.918958 | + | 0.918958i | −0.996954 | − | 0.0779961i | \(-0.975148\pi\) |
0.0779961 | + | 0.996954i | \(0.475148\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −80066.8 | −0.251165 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 114995. | 0.349635 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −298452. | + | 298452.i | −0.879843 | + | 0.879843i | −0.993518 | − | 0.113675i | \(-0.963738\pi\) |
0.113675 | + | 0.993518i | \(0.463738\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 75977.1 | + | 212493.i | 0.217256 | + | 0.607625i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 234469. | − | 234469.i | 0.650570 | − | 0.650570i | −0.302560 | − | 0.953130i | \(-0.597841\pi\) |
0.953130 | + | 0.302560i | \(0.0978413\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 607360.i | 1.63580i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13646.2 | −0.0356879 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −131530. | − | 131530.i | −0.334126 | − | 0.334126i | 0.520025 | − | 0.854151i | \(-0.325923\pi\) |
−0.854151 | + | 0.520025i | \(0.825923\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 425217. | + | 42074.8i | 1.04958 | + | 0.103855i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −174022. | − | 174022.i | −0.417513 | − | 0.417513i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 370114.i | − | 0.863383i | −0.902021 | − | 0.431691i | \(-0.857917\pi\) | ||
0.902021 | − | 0.431691i | \(-0.142083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 473727.i | − | 1.07481i | −0.843324 | − | 0.537405i | \(-0.819405\pi\) | ||
0.843324 | − | 0.537405i | \(-0.180595\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 62775.9 | + | 62775.9i | 0.138569 | + | 0.138569i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −303918. | − | 850002.i | −0.652871 | − | 1.82596i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 113158. | + | 113158.i | 0.236636 | + | 0.236636i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 551543. | 1.12312 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 287004.i | 0.569252i | 0.958639 | + | 0.284626i | \(0.0918695\pi\) | ||||
−0.958639 | + | 0.284626i | \(0.908131\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −391702. | + | 391702.i | −0.756941 | + | 0.756941i | −0.975765 | − | 0.218823i | \(-0.929778\pi\) |
0.218823 | + | 0.975765i | \(0.429778\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 336743. | − | 711566.i | 0.634179 | − | 1.34007i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 686198. | − | 686198.i | 1.25975 | − | 1.25975i | 0.308535 | − | 0.951213i | \(-0.400161\pi\) |
0.951213 | − | 0.308535i | \(-0.0998386\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 775467. | 1.38813 | 0.694066 | − | 0.719912i | \(-0.255818\pi\) | ||||
0.694066 | + | 0.719912i | \(0.255818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 796503. | 1.39058 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −539738. | + | 539738.i | −0.919270 | + | 0.919270i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 284367. | − | 600891.i | 0.472601 | − | 0.998645i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 24003.6 | − | 24003.6i | 0.0389360 | − | 0.0389360i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 95875.8i | 0.151825i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 307476. | 0.475450 | 0.237725 | − | 0.971333i | \(-0.423598\pi\) | ||||
0.237725 | + | 0.971333i | \(0.423598\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 504176. | + | 504176.i | 0.761435 | + | 0.761435i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −222122. | − | 621233.i | −0.327714 | − | 0.916554i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13940.3 | − | 13940.3i | −0.0200966 | − | 0.0200966i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 849240.i | 1.19652i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 558251.i | − | 0.768862i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 836770. | + | 836770.i | 1.12679 | + | 1.12679i | 0.990696 | + | 0.136097i | \(0.0434557\pi\) |
0.136097 | + | 0.990696i | \(0.456544\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 97540.6 | − | 79975.5i | 0.128448 | − | 0.105318i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 79173.7 | + | 79173.7i | 0.101980 | + | 0.101980i | 0.756256 | − | 0.654276i | \(-0.227026\pi\) |
−0.654276 | + | 0.756256i | \(0.727026\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −686727. | −0.865357 | −0.432679 | − | 0.901548i | \(-0.642432\pi\) | ||||
−0.432679 | + | 0.901548i | \(0.642432\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 551977.i | − | 0.680599i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −566816. | + | 566816.i | −0.683994 | + | 0.683994i | −0.960898 | − | 0.276903i | \(-0.910692\pi\) |
0.276903 | + | 0.960898i | \(0.410692\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −477916. | − | 1.33664e6i | −0.564523 | − | 1.57886i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 222388. | − | 222388.i | 0.257182 | − | 0.257182i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −764329. | −0.865537 | −0.432769 | − | 0.901505i | \(-0.642463\pi\) | ||||
−0.432769 | + | 0.901505i | \(0.642463\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 257789. | 0.285905 | 0.142952 | − | 0.989730i | \(-0.454340\pi\) | ||||
0.142952 | + | 0.989730i | \(0.454340\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 213854. | − | 213854.i | 0.232328 | − | 0.232328i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −95459.0 | − | 45175.2i | −0.101602 | − | 0.0480823i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 236495. | − | 236495.i | 0.246650 | − | 0.246650i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 1.03350e6i | − | 1.05636i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 818014. | 0.819552 | 0.409776 | − | 0.912186i | \(-0.365607\pi\) | ||||
0.409776 | + | 0.912186i | \(0.365607\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −168645. | − | 168645.i | −0.165643 | − | 0.165643i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −192087. | + | 405897.i | −0.184990 | + | 0.390899i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 212976. | + | 212976.i | 0.201140 | + | 0.201140i | 0.800488 | − | 0.599348i | \(-0.204574\pi\) |
−0.599348 | + | 0.800488i | \(0.704574\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.20798e6i | 2.04525i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 225325.i | 0.204743i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.19052e6 | − | 1.19052e6i | −1.06132 | − | 1.06132i | −0.997993 | − | 0.0633261i | \(-0.979829\pi\) |
−0.0633261 | − | 0.997993i | \(-0.520171\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 296070. | − | 105860.i | 0.258988 | − | 0.0926012i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −792444. | − | 792444.i | −0.680284 | − | 0.680284i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 507577. | 0.427682 | 0.213841 | − | 0.976868i | \(-0.431402\pi\) | ||||
0.213841 | + | 0.976868i | \(0.431402\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 680345.i | 0.562737i | 0.959600 | + | 0.281369i | \(0.0907884\pi\) | ||||
−0.959600 | + | 0.281369i | \(0.909212\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.36155e6 | + | 1.36155e6i | −1.10568 | + | 1.10568i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −561894. | − | 685303.i | −0.448046 | − | 0.546451i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.29751e6 | + | 1.29751e6i | −1.01604 | + | 1.01604i | −0.0161744 | + | 0.999869i | \(0.505149\pi\) |
−0.999869 | + | 0.0161744i | \(0.994851\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5819.68 | −0.00447599 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.38793e6 | 1.04858 | 0.524289 | − | 0.851541i | \(-0.324331\pi\) | ||||
0.524289 | + | 0.851541i | \(0.324331\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 506188. | − | 506188.i | 0.375704 | − | 0.375704i | −0.493846 | − | 0.869550i | \(-0.664409\pi\) |
0.869550 | + | 0.493846i | \(0.164409\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −253328. | + | 90577.4i | −0.184744 | + | 0.0660553i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.14978e6 | + | 1.14978e6i | −0.823969 | + | 0.823969i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.10142e6i | − | 0.775723i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 200175. | 0.138573 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −358870. | − | 358870.i | −0.244212 | − | 0.244212i | 0.574378 | − | 0.818590i | \(-0.305244\pi\) |
−0.818590 | + | 0.574378i | \(0.805244\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 873577. | + | 413413.i | 0.584448 | + | 0.276585i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −808860. | − | 808860.i | −0.532087 | − | 0.532087i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 831990.i | 0.538196i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.61373e6i | 1.02663i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 351159. | + | 351159.i | 0.219734 | + | 0.219734i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −315131. | − | 149133.i | −0.193973 | − | 0.0917961i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −800065. | − | 800065.i | −0.484484 | − | 0.484484i | 0.422076 | − | 0.906560i | \(-0.361301\pi\) |
−0.906560 | + | 0.422076i | \(0.861301\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.50682e6 | −0.897770 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.39145e6i | − | 0.815766i | −0.913034 | − | 0.407883i | \(-0.866267\pi\) | ||
0.913034 | − | 0.407883i | \(-0.133733\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −731178. | + | 731178.i | −0.421854 | + | 0.421854i | −0.885842 | − | 0.463987i | \(-0.846418\pi\) |
0.463987 | + | 0.885842i | \(0.346418\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −290513. | + | 103873.i | −0.164964 | + | 0.0589829i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −415835. | + | 415835.i | −0.232420 | + | 0.232420i | −0.813702 | − | 0.581282i | \(-0.802551\pi\) |
0.581282 | + | 0.813702i | \(0.302551\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.58310e6 | 0.871025 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.36176e6 | 1.27930 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −134903. | + | 134903.i | −0.0719477 | + | 0.0719477i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −304411. | + | 3.07644e6i | −0.159864 | + | 1.61562i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.11932e6 | − | 1.11932e6i | 0.578874 | − | 0.578874i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.47208e6i | 1.76848i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.46277e6 | 1.23553 | 0.617765 | − | 0.786363i | \(-0.288038\pi\) | ||||
0.617765 | + | 0.786363i | \(0.288038\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 460885. | + | 460885.i | 0.227762 | + | 0.227762i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.94530e6 | + | 1.05309e6i | −1.43390 | + | 0.512690i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.44346e6 | − | 1.44346e6i | −0.692355 | − | 0.692355i | 0.270395 | − | 0.962749i | \(-0.412846\pi\) |
−0.962749 | + | 0.270395i | \(0.912846\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.32941e6i | 0.628289i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 40888.1i | 0.0190419i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.44234e6 | − | 1.44234e6i | −0.661959 | − | 0.661959i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 286278. | − | 604929.i | 0.129491 | − | 0.273625i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 966813. | + | 966813.i | 0.431041 | + | 0.431041i | 0.888982 | − | 0.457941i | \(-0.151413\pi\) |
−0.457941 | + | 0.888982i | \(0.651413\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.77134e6 | 0.778462 | 0.389231 | − | 0.921140i | \(-0.372741\pi\) | ||||
0.389231 | + | 0.921140i | \(0.372741\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.99041e6i | 1.72882i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.32730e6 | − | 1.32730e6i | 0.566932 | − | 0.566932i | −0.364336 | − | 0.931268i | \(-0.618704\pi\) |
0.931268 | + | 0.364336i | \(0.118704\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.53093e6 | − | 1.19774e6i | −1.06588 | − | 0.504420i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 776668. | − | 776668.i | 0.322526 | − | 0.322526i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.44839e6 | −1.41215 | −0.706074 | − | 0.708138i | \(-0.749535\pi\) | ||||
−0.706074 | + | 0.708138i | \(0.749535\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.36180e6 | 0.953839 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 811593. | − | 811593.i | 0.323275 | − | 0.323275i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.12282e6 | − | 3.14031e6i | −0.441141 | − | 1.23379i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.52705e6 | + | 2.52705e6i | −0.979374 | + | 0.979374i | −0.999792 | − | 0.0204173i | \(-0.993501\pi\) |
0.0204173 | + | 0.999792i | \(0.493501\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 480001.i | 0.183517i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −769077. | −0.290092 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −268402. | − | 268402.i | −0.0998882 | − | 0.0998882i | 0.655397 | − | 0.755285i | \(-0.272501\pi\) |
−0.755285 | + | 0.655397i | \(0.772501\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.27990e6 | − | 2.13210e6i | 0.470000 | − | 0.782940i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.90500e6 | − | 3.90500e6i | −1.41504 | − | 1.41504i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 847168.i | − | 0.302951i | −0.988461 | − | 0.151475i | \(-0.951598\pi\) | ||
0.988461 | − | 0.151475i | \(-0.0484024\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 1.57863e6i | − | 0.557145i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.32473e6 | + | 2.32473e6i | 0.809795 | + | 0.809795i | 0.984603 | − | 0.174807i | \(-0.0559303\pi\) |
−0.174807 | + | 0.984603i | \(0.555930\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 729794. | + | 2.04109e6i | 0.250928 | + | 0.701797i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 336842. | + | 336842.i | 0.114327 | + | 0.114327i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.52032e6 | −1.17953 | −0.589764 | − | 0.807575i | \(-0.700779\pi\) | ||||
−0.589764 | + | 0.807575i | \(0.700779\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 474590.i | − | 0.156992i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.11805e6 | + | 3.11805e6i | −1.01836 | + | 1.01836i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −528314. | + | 1.11637e6i | −0.170372 | + | 0.360011i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 239629. | − | 239629.i | 0.0763067 | − | 0.0763067i | −0.667923 | − | 0.744230i | \(-0.732817\pi\) |
0.744230 | + | 0.667923i | \(0.232817\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 658050. | 0.206931 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.56689e6 | −0.486607 | −0.243303 | − | 0.969950i | \(-0.578231\pi\) | ||||
−0.243303 | + | 0.969950i | \(0.578231\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 100858. | − | 100858.i | 0.0309348 | − | 0.0309348i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.13851e6 | − | 2.40577e6i | 0.344905 | − | 0.728812i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.23810e6 | − | 3.23810e6i | 0.968955 | − | 0.968955i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 220244.i | 0.0651022i | 0.999470 | + | 0.0325511i | \(0.0103632\pi\) | ||||
−0.999470 | + | 0.0325511i | \(0.989637\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.24809e6 | −0.364452 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.67156e6 | − | 1.67156e6i | −0.482220 | − | 0.482220i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.36643e6 | + | 3.82165e6i | 0.389464 | + | 1.08926i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.15088e6 | + | 1.15088e6i | 0.324109 | + | 0.324109i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 3.95300e6i | − | 1.10000i | −0.835165 | − | 0.549999i | \(-0.814628\pi\) | ||
0.835165 | − | 0.549999i | \(-0.185372\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 1.92105e6i | − | 0.528244i | −0.964489 | − | 0.264122i | \(-0.914918\pi\) | ||
0.964489 | − | 0.264122i | \(-0.0850821\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 724748. | + | 724748.i | 0.196941 | + | 0.196941i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 173644. | − | 1.75489e6i | 0.0466324 | − | 0.471278i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 602990. | + | 602990.i | 0.160045 | + | 0.160045i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.99355e6 | 1.04765 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 5.12491e6i | − | 1.32890i | −0.747331 | − | 0.664451i | \(-0.768665\pi\) | ||
0.747331 | − | 0.664451i | \(-0.231335\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.93044e6 | − | 4.93044e6i | 1.26376 | − | 1.26376i | 0.314510 | − | 0.949254i | \(-0.398160\pi\) |
0.949254 | − | 0.314510i | \(-0.101840\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.49561e6 | + | 4.18294e6i | 0.378962 | + | 1.05988i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 201054. | − | 201054.i | 0.0503626 | − | 0.0503626i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.70879e6 | 0.670833 | 0.335417 | − | 0.942070i | \(-0.391123\pi\) | ||||
0.335417 | + | 0.942070i | \(0.391123\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 76254.2 | 0.0186710 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −940341. | + | 940341.i | −0.227654 | + | 0.227654i | −0.811712 | − | 0.584058i | \(-0.801464\pi\) |
0.584058 | + | 0.811712i | \(0.301464\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.97801e6 | + | 1.88256e6i | 0.952283 | + | 0.450660i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −639804. | + | 639804.i | −0.151453 | + | 0.151453i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.66405e6i | 0.623630i | 0.950143 | + | 0.311815i | \(0.100937\pi\) | ||||
−0.950143 | + | 0.311815i | \(0.899063\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.37240e6 | 0.780725 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.00467e6 | + | 4.00467e6i | 0.916899 | + | 0.916899i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.23457e6 | − | 6.83491e6i | 0.732466 | − | 1.54776i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.92890e6 | + | 4.92890e6i | 1.10398 | + | 1.10398i | 0.993926 | + | 0.110049i | \(0.0351007\pi\) |
0.110049 | + | 0.993926i | \(0.464899\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 2.27624e6i | − | 0.504296i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.34239e6i | − | 0.294189i | −0.989122 | − | 0.147095i | \(-0.953008\pi\) | ||
0.989122 | − | 0.147095i | \(-0.0469922\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 66298.4 | + | 66298.4i | 0.0143731 | + | 0.0143731i | 0.714257 | − | 0.699884i | \(-0.246765\pi\) |
−0.699884 | + | 0.714257i | \(0.746765\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −108037. | + | 38628.5i | −0.0231706 | + | 0.00828467i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 493248. | + | 493248.i | 0.104658 | + | 0.104658i | 0.757497 | − | 0.652839i | \(-0.226422\pi\) |
−0.652839 | + | 0.757497i | \(0.726422\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.65077e6 | 1.60610 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 5.71371e6i | − | 1.18677i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.36660e6 | − | 2.36660e6i | 0.486375 | − | 0.486375i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 816996. | − | 669872.i | 0.166145 | − | 0.136225i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −160534. | + | 160534.i | −0.0323051 | + | 0.0323051i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.01091e6 | 0.400456 | 0.200228 | − | 0.979749i | \(-0.435832\pi\) | ||||
0.200228 | + | 0.979749i | \(0.435832\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.59747e7 | −3.14826 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.15751e6 | + | 1.15751e6i | −0.225765 | + | 0.225765i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −740204. | + | 264660.i | −0.142889 | + | 0.0510898i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.94894e6 | − | 2.94894e6i | 0.563435 | − | 0.563435i | −0.366847 | − | 0.930281i | \(-0.619563\pi\) |
0.930281 | + | 0.366847i | \(0.119563\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 6.00825e6i | − | 1.13625i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.11456e6 | −0.957425 | −0.478712 | − | 0.877972i | \(-0.658896\pi\) | ||||
−0.478712 | + | 0.877972i | \(0.658896\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.22752e6 | + | 2.22752e6i | 0.412766 | + | 0.412766i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 578384. | + | 273715.i | 0.106097 | + | 0.0502095i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.84283e6 | + | 4.84283e6i | 0.879445 | + | 0.879445i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 22809.7i | − | 0.00410079i | −0.999998 | − | 0.00205040i | \(-0.999347\pi\) | ||
0.999998 | − | 0.00205040i | \(-0.000652662\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.72019e6i | 0.840165i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.18776e6 | − | 5.18776e6i | −0.914240 | − | 0.914240i | 0.0823624 | − | 0.996602i | \(-0.473753\pi\) |
−0.996602 | + | 0.0823624i | \(0.973753\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.76280e6 | − | 834229.i | −0.307591 | − | 0.145565i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.11350e6 | − | 6.11350e6i | −1.05626 | − | 1.05626i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.15335e7 | −1.97318 | −0.986589 | − | 0.163222i | \(-0.947811\pi\) | ||||
−0.986589 | + | 0.163222i | \(0.947811\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.15733e6i | 1.38196i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 964297. | − | 964297.i | 0.161777 | − | 0.161777i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.57190e6 | − | 1.99223e6i | 0.925732 | − | 0.330995i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.09195e6 | − | 5.09195e6i | 0.837834 | − | 0.837834i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.64789e6 | 0.431500 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 736346. | 0.118847 | 0.0594234 | − | 0.998233i | \(-0.481074\pi\) | ||||
0.0594234 | + | 0.998233i | \(0.481074\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.83896e6 | + | 5.83896e6i | −0.933430 | + | 0.933430i | −0.997918 | − | 0.0644887i | \(-0.979458\pi\) |
0.0644887 | + | 0.997918i | \(0.479458\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.70362e6 | + | 3.85660e6i | −0.744790 | + | 0.610669i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −57532.1 | + | 57532.1i | −0.00902369 | + | 0.00902369i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 5.72904e6i | − | 0.890107i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −697827. | −0.107402 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.31866e6 | − | 8.31866e6i | −1.26834 | − | 1.26834i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.73328e6 | + | 3.12258e6i | −1.31915 | + | 0.471661i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.72546e6 | + | 3.72546e6i | 0.557499 | + | 0.557499i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 535749.i | − | 0.0794308i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.66802e6i | 0.832604i | 0.909226 | + | 0.416302i | \(0.136674\pi\) | ||||
−0.909226 | + | 0.416302i | \(0.863326\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.76839e6 | + | 4.76839e6i | 0.694021 | + | 0.694021i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.65910e6 | + | 5.61890e6i | −0.383481 | + | 0.810327i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.64899e6 | + | 3.64899e6i | 0.521440 | + | 0.521440i | 0.918006 | − | 0.396566i | \(-0.129798\pi\) |
−0.396566 | + | 0.918006i | \(0.629798\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 251731. | 0.0356456 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.88732e6i | 0.264829i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.13613e6 | − | 2.13613e6i | 0.297040 | − | 0.297040i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.16150e7 | + | 5.49671e6i | 1.60062 | + | 0.757479i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.61980e6 | + | 1.61980e6i | −0.221219 | + | 0.221219i | −0.809012 | − | 0.587793i | \(-0.799997\pi\) |
0.587793 | + | 0.809012i | \(0.299997\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.16753e7 | −1.58030 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.27803e6 | −0.305599 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.15791e6 | − | 6.15791e6i | 0.818771 | − | 0.818771i | −0.167159 | − | 0.985930i | \(-0.553459\pi\) |
0.985930 | + | 0.167159i | \(0.0534592\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.75767e6 | − | 4.91587e6i | −0.231641 | − | 0.647857i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.60334e6 | + | 4.60334e6i | −0.601334 | + | 0.601334i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.23310e6i | 0.548123i | 0.961712 | + | 0.274061i | \(0.0883672\pi\) | ||||
−0.961712 | + | 0.274061i | \(0.911633\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.05998e6 | −0.777823 | −0.388912 | − | 0.921275i | \(-0.627149\pi\) | ||||
−0.388912 | + | 0.921275i | \(0.627149\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.88890e6 | − | 2.88890e6i | −0.367575 | − | 0.367575i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −258791. | + | 2.61540e6i | −0.0326422 | + | 0.329889i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.43951e6 | + | 6.43951e6i | 0.805217 | + | 0.805217i | 0.983906 | − | 0.178689i | \(-0.0571855\pi\) |
−0.178689 | + | 0.983906i | \(0.557185\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 7.88550e6i | − | 0.977536i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 9.92719e6i | − | 1.22007i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.12788e6 | + | 1.12788e6i | 0.137434 | + | 0.137434i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −751520. | − | 2.10186e6i | −0.0907927 | − | 0.253930i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.09859e6 | + | 9.09859e6i | 1.08988 | + | 1.08988i | 0.995540 | + | 0.0943400i | \(0.0300741\pi\) |
0.0943400 | + | 0.995540i | \(0.469926\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −48745.5 | −0.00578956 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.38141e7i | 1.62688i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.99751e6 | − | 3.99751e6i | 0.466823 | − | 0.466823i | −0.434061 | − | 0.900884i | \(-0.642920\pi\) |
0.900884 | + | 0.434061i | \(0.142920\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.84508e6 | + | 3.89882e6i | −0.213660 | + | 0.451482i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.80561e6 | + | 7.80561e6i | −0.896337 | + | 0.896337i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −448071. | −0.0510246 | −0.0255123 | − | 0.999675i | \(-0.508122\pi\) | ||||
−0.0255123 | + | 0.999675i | \(0.508122\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.18693e6 | −0.359903 | −0.179952 | − | 0.983675i | \(-0.557594\pi\) | ||||
−0.179952 | + | 0.983675i | \(0.557594\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.59699e6 | − | 1.59699e6i | 0.178858 | − | 0.178858i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.92806e6 | + | 4.07414e6i | −0.214156 | + | 0.452531i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.74029e6 | + | 5.74029e6i | −0.632357 | + | 0.632357i | −0.948659 | − | 0.316302i | \(-0.897559\pi\) |
0.316302 | + | 0.948659i | \(0.397559\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 1.08657e7i | − | 1.18717i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.51205e7 | −2.72223 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.84512e6 | + | 4.84512e6i | 0.520779 | + | 0.520779i | 0.917807 | − | 0.397028i | \(-0.129958\pi\) |
−0.397028 | + | 0.917807i | \(0.629958\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.18604e6 | + | 8.91074e6i | 0.339674 | + | 0.950005i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.13817e6 | − | 7.13817e6i | −0.754874 | − | 0.754874i | 0.220511 | − | 0.975384i | \(-0.429228\pi\) |
−0.975384 | + | 0.220511i | \(0.929228\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 8.04378e6i | − | 0.843789i | −0.906645 | − | 0.421894i | \(-0.861365\pi\) | ||
0.906645 | − | 0.421894i | \(-0.138635\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.39239e6i | 0.353002i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.61178e6 | − | 7.61178e6i | −0.785717 | − | 0.785717i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.91386e6 | + | 9.57625e6i | −0.195979 | + | 0.980608i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −965057. | − | 965057.i | −0.0980357 | − | 0.0980357i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.11242e6 | 0.918348 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.34627e7i | − | 1.34604i | −0.739622 | − | 0.673022i | \(-0.764996\pi\) | ||
0.739622 | − | 0.673022i | \(-0.235004\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.09496e6 | + | 3.09496e6i | −0.307005 | + | 0.307005i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.08718e6 | + | 5.83745e6i | 0.205412 | + | 0.574498i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.32152e6 | + | 1.32152e6i | −0.129041 | + | 0.129041i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.02175e6 | 0.195873 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.67079e6 | −0.256741 | −0.128370 | − | 0.991726i | \(-0.540975\pi\) | ||||
−0.128370 | + | 0.991726i | \(0.540975\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.33127e6 | − | 4.33127e6i | 0.413131 | − | 0.413131i | −0.469697 | − | 0.882828i | \(-0.655637\pi\) |
0.882828 | + | 0.469697i | \(0.155637\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.48895e6 | + | 4.01733e6i | 0.803442 | + | 0.380223i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.01146e6 | + | 2.01146e6i | −0.188908 | + | 0.188908i | −0.795224 | − | 0.606316i | \(-0.792647\pi\) |
0.606316 | + | 0.795224i | \(0.292647\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.90281e6i | 0.456913i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 280638. | 0.0259534 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.78586e6 | + | 3.78586e6i | 0.347441 | + | 0.347441i | 0.859156 | − | 0.511714i | \(-0.170989\pi\) |
−0.511714 | + | 0.859156i | \(0.670989\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.40738e6 | − | 1.56524e7i | 0.674623 | − | 1.42554i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.70273e6 | + | 1.70273e6i | 0.153897 | + | 0.153897i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.51951e6i | 0.315696i | 0.987463 | + | 0.157848i | \(0.0504556\pi\) | ||||
−0.987463 | + | 0.157848i | \(0.949544\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.09747e7i | 0.976991i | 0.872566 | + | 0.488496i | \(0.162454\pi\) | ||||
−0.872566 | + | 0.488496i | \(0.837546\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.61918e6 | + | 5.61918e6i | 0.496466 | + | 0.496466i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.43333e6 | + | 870037.i | −0.213376 | + | 0.0762928i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.31979e6 | − | 3.31979e6i | −0.288932 | − | 0.288932i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.68453e7 | −1.45517 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.76862e6i | − | 0.151645i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.14860e7 | − | 1.14860e7i | 0.977532 | − | 0.977532i | −0.0222213 | − | 0.999753i | \(-0.507074\pi\) |
0.999753 | + | 0.0222213i | \(0.00707384\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.24122e6 | + | 1.25440e7i | −0.104855 | + | 1.05969i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.56904e6 | + | 1.56904e6i | −0.131571 | + | 0.131571i | −0.769826 | − | 0.638254i | \(-0.779657\pi\) |
0.638254 | + | 0.769826i | \(0.279657\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.92277e6 | 0.160049 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.59388e6 | −0.131700 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.69137e6 | − | 8.69137e6i | 0.712913 | − | 0.712913i | −0.254231 | − | 0.967144i | \(-0.581822\pi\) |
0.967144 | + | 0.254231i | \(0.0818223\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.61516e6 | − | 1.65015e6i | 0.375803 | − | 0.134369i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.91239e6 | − | 6.91239e6i | 0.558774 | − | 0.558774i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 5.56427e6i | − | 0.446539i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.40891e7 | 1.12250 | 0.561252 | − | 0.827645i | \(-0.310320\pi\) | ||||
0.561252 | + | 0.827645i | \(0.310320\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.10671e6 | − | 1.10671e6i | −0.0875392 | − | 0.0875392i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.77735e6 | − | 2.73409e6i | −0.453698 | − | 0.214709i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.74519e6 | + | 4.74519e6i | 0.369974 | + | 0.369974i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1.14108e7i | − | 0.883331i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.15723e7i | − | 0.889457i | −0.895665 | − | 0.444729i | \(-0.853300\pi\) | ||
0.895665 | − | 0.444729i | \(-0.146700\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.86035e6 | + | 3.86035e6i | 0.294604 | + | 0.294604i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.82648e7 | + | 8.64365e6i | 1.38402 | + | 0.654975i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.37304e6 | + | 3.37304e6i | 0.253789 | + | 0.253789i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.95975e6 | −0.744103 | −0.372051 | − | 0.928212i | \(-0.621345\pi\) | ||||
−0.372051 | + | 0.928212i | \(0.621345\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 891775.i | − | 0.0661578i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 85743.2 | − | 85743.2i | 0.00631649 | − | 0.00631649i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.47673e7 | + | 5.28005e6i | −1.08028 | + | 0.386254i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.69351e6 | − | 7.69351e6i | 0.558890 | − | 0.558890i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.73997e6 | −0.269803 | −0.134901 | − | 0.990859i | \(-0.543072\pi\) | ||||
−0.134901 | + | 0.990859i | \(0.543072\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.44737e7 | −1.03691 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.59482e6 | + | 2.59482e6i | −0.184613 | + | 0.184613i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.10609e7 | − | 1.34902e7i | −0.781529 | − | 0.953176i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.69069e6 | − | 4.69069e6i | 0.329155 | − | 0.329155i | −0.523110 | − | 0.852265i | \(-0.675228\pi\) |
0.852265 | + | 0.523110i | \(0.175228\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.58748e7i | 1.10634i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.65991e6 | 0.460972 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.58662e6 | + | 5.58662e6i | 0.384051 | + | 0.384051i | 0.872559 | − | 0.488508i | \(-0.162459\pi\) |
−0.488508 | + | 0.872559i | \(0.662459\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.41558e6 | − | 506142.i | 0.0966533 | − | 0.0345584i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.12202e7 | − | 1.12202e7i | −0.760905 | − | 0.760905i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.60299e7i | 1.07974i | 0.841749 | + | 0.539870i | \(0.181527\pi\) | ||||
−0.841749 | + | 0.539870i | \(0.818473\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.76098e6i | 0.318531i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 269940. | + | 269940.i | 0.0179389 | + | 0.0179389i | 0.716019 | − | 0.698080i | \(-0.245962\pi\) |
−0.698080 | + | 0.716019i | \(0.745962\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.51995e6 | − | 3.21177e6i | 0.100332 | − | 0.212009i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.07216e6 | − | 2.07216e6i | −0.135869 | − | 0.135869i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.26857e7 | 1.47757 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.18503e7i | − | 0.766707i | −0.923602 | − | 0.383353i | \(-0.874769\pi\) | ||
0.923602 | − | 0.383353i | \(-0.125231\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.23388e6 | + | 8.23388e6i | −0.529197 | + | 0.529197i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.01032e7 | − | 9.51367e6i | −1.28350 | − | 0.607408i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.72173e6 | − | 1.72173e6i | 0.109201 | − | 0.109201i | −0.650395 | − | 0.759596i | \(-0.725397\pi\) |
0.759596 | + | 0.650395i | \(0.225397\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.39507e6 | 0.213916 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.62361e7 | 1.01629 | 0.508147 | − | 0.861271i | \(-0.330331\pi\) | ||||
0.508147 | + | 0.861271i | \(0.330331\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.07516e7 | − | 1.07516e7i | 0.668590 | − | 0.668590i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 428688. | + | 1.19896e6i | 0.0264842 | + | 0.0740714i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.20937e7 | − | 1.20937e7i | 0.742284 | − | 0.742284i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.91198e7i | − | 1.16592i | −0.812502 | − | 0.582958i | \(-0.801895\pi\) | ||
0.812502 | − | 0.582958i | \(-0.198105\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.28751e6 | −0.259758 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.13423e6 | − | 1.13423e6i | −0.0682737 | − | 0.0682737i | 0.672145 | − | 0.740419i | \(-0.265373\pi\) |
−0.740419 | + | 0.672145i | \(0.765373\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 348424. | − | 285680.i | 0.0208379 | − | 0.0170854i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.22249e7 | − | 2.22249e7i | −1.32065 | − | 1.32065i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.02047e6i | 0.237374i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1.42044e7i | − | 0.833290i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.59224e7 | − | 1.59224e7i | −0.928121 | − | 0.928121i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.55436e6 | + | 2.11281e7i | 0.437546 | + | 1.22373i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.19263e6 | − | 5.19263e6i | −0.298848 | − | 0.298848i | 0.541715 | − | 0.840563i | \(-0.317775\pi\) |
−0.840563 | + | 0.541715i | \(0.817775\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.39668e7 | 1.37062 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.27696e7i | 0.725663i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.36263e6 | + | 4.36263e6i | −0.246357 | + | 0.246357i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.91460e6 | + | 4.04570e6i | −0.107438 | + | 0.227026i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.09058e7 | − | 1.09058e7i | 0.608154 | − | 0.608154i | −0.334309 | − | 0.942463i | \(-0.608503\pi\) |
0.942463 | + | 0.334309i | \(0.108503\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.43294e7 | 0.794075 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.17770e6 | −0.174997 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.19631e7 | − | 1.19631e7i | 0.654717 | − | 0.654717i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.74983e6 | − | 5.81061e6i | 0.149560 | − | 0.316033i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.10912e6 | + | 5.10912e6i | −0.276161 | + | 0.276161i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.21861e6i | − | 0.334058i | −0.985952 | − | 0.167029i | \(-0.946583\pi\) | ||
0.985952 | − | 0.167029i | \(-0.0534174\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.23689e6 | 0.386367 | 0.193183 | − | 0.981163i | \(-0.438119\pi\) | ||||
0.193183 | + | 0.981163i | \(0.438119\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.84814e6 | − | 6.84814e6i | −0.363368 | − | 0.363368i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.94378e6 | + | 2.22172e7i | 0.418922 | + | 1.17164i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.82138e6 | + | 2.82138e6i | 0.147879 | + | 0.147879i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.45983e6i | 0.284426i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.66191e6i | 0.500271i | 0.968211 | + | 0.250135i | \(0.0804751\pi\) | ||||
−0.968211 | + | 0.250135i | \(0.919525\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.66712e7 | + | 1.66712e7i | 0.857961 | + | 0.857961i | 0.991098 | − | 0.133137i | \(-0.0425050\pi\) |
−0.133137 | + | 0.991098i | \(0.542505\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.25539e7 | + | 1.24220e6i | 0.642161 | + | 0.0635411i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.31048e7 | + | 1.31048e7i | 0.666297 | + | 0.666297i | 0.956857 | − | 0.290560i | \(-0.0938415\pi\) |
−0.290560 | + | 0.956857i | \(0.593841\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.86602e6 | −0.397529 | −0.198764 | − | 0.980047i | \(-0.563693\pi\) | ||||
−0.198764 | + | 0.980047i | \(0.563693\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 2.61207e7i | − | 1.31215i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 753833. | − | 753833.i | 0.0376411 | − | 0.0376411i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.24077e6 | − | 1.74542e7i | −0.309758 | − | 0.866333i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 411243. | − | 411243.i | 0.0202901 | − | 0.0202901i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.46126e6 | 0.365938 | 0.182969 | − | 0.983119i | \(-0.441429\pi\) | ||||
0.182969 | + | 0.983119i | \(0.441429\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.06521e7 | 0.519333 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.39704e7 | + | 1.39704e7i | −0.677082 | + | 0.677082i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.06894e7 | + | 1.45235e7i | 1.47859 | + | 0.699729i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.79572e6 | − | 7.79572e6i | 0.373377 | − | 0.373377i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.01903e7i | 0.485195i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.35807e7 | −0.642834 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.59287e7 | − | 1.59287e7i | −0.749562 | − | 0.749562i | 0.224835 | − | 0.974397i | \(-0.427816\pi\) |
−0.974397 | + | 0.224835i | \(0.927816\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −326315. | + | 689530.i | −0.0152659 | + | 0.0322581i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.57402e6 | + | 4.57402e6i | 0.212738 | + | 0.212738i | 0.805430 | − | 0.592691i | \(-0.201935\pi\) |
−0.592691 | + | 0.805430i | \(0.701935\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.72334e7i | 0.796872i | 0.917196 | + | 0.398436i | \(0.130447\pi\) | ||||
−0.917196 | + | 0.398436i | \(0.869553\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 2.31467e7i | − | 1.06410i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.12321e6 | − | 1.12321e6i | −0.0513373 | − | 0.0513373i | 0.680972 | − | 0.732309i | \(-0.261557\pi\) |
−0.732309 | + | 0.680972i | \(0.761557\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.79132e6 | + | 3.50089e6i | −0.444940 | + | 0.159088i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.10865e7 | + | 1.10865e7i | 0.500896 | + | 0.500896i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.26546e6 | −0.281451 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.53532e7i | 2.47228i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 401351. | − | 401351.i | 0.0178233 | − | 0.0178233i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.22940e7 | − | 2.04797e7i | 0.542842 | − | 0.904283i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.11686e6 | − | 5.11686e6i | 0.224649 | − | 0.224649i | −0.585804 | − | 0.810453i | \(-0.699221\pi\) |
0.810453 | + | 0.585804i | \(0.199221\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.22455e6 | 0.315383 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.96052e6 | 0.171915 | 0.0859573 | − | 0.996299i | \(-0.472605\pi\) | ||||
0.0859573 | + | 0.996299i | \(0.472605\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.32476e7 | − | 1.32476e7i | 0.571790 | − | 0.571790i | −0.360838 | − | 0.932628i | \(-0.617509\pi\) |
0.932628 | + | 0.360838i | \(0.117509\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.29545e7 | + | 4.63187e6i | −0.555982 | + | 0.198792i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.58340e7 | + | 2.58340e7i | −1.10251 | + | 1.10251i | −0.108401 | + | 0.994107i | \(0.534573\pi\) |
−0.994107 | + | 0.108401i | \(0.965427\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.51635e7i | − | 0.643494i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.35020e7 | 0.569775 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.07046e6 | + | 6.07046e6i | 0.254738 | + | 0.254738i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.87016e7 | − | 8.85036e6i | −0.780405 | − | 0.369321i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.37456e6 | − | 8.37456e6i | −0.347521 | − | 0.347521i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 804882.i | 0.0332149i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.17401e6i | 0.130256i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.62433e7 | − | 1.62433e7i | −0.662910 | − | 0.662910i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.39370e7 | − | 1.13280e7i | −0.971513 | − | 0.459761i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.97512e7 | − | 1.97512e7i | −0.797214 | − | 0.797214i | 0.185441 | − | 0.982655i | \(-0.440629\pi\) |
−0.982655 | + | 0.185441i | \(0.940629\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.40815e6 | 0.0565248 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.40853e7i | − | 0.562304i | −0.959663 | − | 0.281152i | \(-0.909284\pi\) | ||
0.959663 | − | 0.281152i | \(-0.0907165\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.45586e7 | + | 1.45586e7i | −0.578021 | + | 0.578021i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.67314e6 | − | 1.67088e6i | 0.184525 | − | 0.0659771i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.99503e7 | + | 2.99503e7i | −1.17619 | + | 1.17619i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.47354e7 | −0.966116 | −0.483058 | − | 0.875588i | \(-0.660474\pi\) | ||||
−0.483058 | + | 0.875588i | \(0.660474\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.61064e7 | 0.625677 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.50378e7 | + | 3.50378e7i | −1.35373 | + | 1.35373i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.02173e7 | − | 4.96895e6i | −1.92974 | − | 0.190946i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.02117e6 | + | 3.02117e6i | −0.115472 | + | 0.115472i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.69900e7i | 0.645884i | 0.946419 | + | 0.322942i | \(0.104672\pi\) | ||||
−0.946419 | + | 0.322942i | \(0.895328\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 638702. | 0.0241504 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.40059e7 | + | 1.40059e7i | 0.526752 | + | 0.526752i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.42367e6 | − | 3.01189e6i | 0.315117 | − | 0.112670i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.16683e7 | + | 2.16683e7i | 0.806260 | + | 0.806260i | 0.984066 | − | 0.177806i | \(-0.0568998\pi\) |
−0.177806 | + | 0.984066i | \(0.556900\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 1.47196e7i | − | 0.544795i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.14995e7i | 1.89596i | 0.318331 | + | 0.947980i | \(0.396878\pi\) | ||||
−0.318331 | + | 0.947980i | \(0.603122\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.07200e6 | − | 7.07200e6i | −0.258978 | − | 0.258978i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.31888e7 | − | 2.78690e7i | 0.480424 | − | 1.01518i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.45885e7 | + | 1.45885e7i | 0.528610 | + | 0.528610i | 0.920158 | − | 0.391548i | \(-0.128060\pi\) |
−0.391548 | + | 0.920158i | \(0.628060\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.90182e7 | −2.12726 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 8.37134e6i | − | 0.300154i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.66848e7 | + | 1.66848e7i | −0.595097 | + | 0.595097i | −0.939004 | − | 0.343907i | \(-0.888250\pi\) |
0.343907 | + | 0.939004i | \(0.388250\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.45021e7 | + | 6.86299e6i | 0.514543 | + | 0.243503i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.59350e7 | + | 1.59350e7i | −0.562434 | + | 0.562434i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.19884e7 | −0.420936 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.86084e7 | 0.999274 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.73532e6 | − | 4.73532e6i | 0.164545 | − | 0.164545i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.04258e7 | + | 2.91589e7i | 0.360404 | + | 1.00798i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.09186e6 | − | 7.09186e6i | 0.243890 | − | 0.243890i | −0.574567 | − | 0.818457i | \(-0.694830\pi\) |
0.818457 | + | 0.574567i | \(0.194830\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 2.71579e6i | − | 0.0929153i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.60523e7 | −0.886742 | −0.443371 | − | 0.896338i | \(-0.646218\pi\) | ||||
−0.443371 | + | 0.896338i | \(0.646218\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.10547e7 | + | 1.10547e7i | 0.374340 | + | 0.374340i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.79024e7 | − | 3.40306e7i | −0.940006 | − | 1.14646i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.40458e6 | − | 2.40458e6i | −0.0805939 | − | 0.0805939i | 0.665661 | − | 0.746255i | \(-0.268150\pi\) |
−0.746255 | + | 0.665661i | \(0.768150\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.23260e7i | 0.744481i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 4.48847e6i | − | 0.148911i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.99200e7 | + | 2.99200e7i | 0.987591 | + | 0.987591i | 0.999924 | − | 0.0123328i | \(-0.00392576\pi\) |
−0.0123328 | + | 0.999924i | \(0.503926\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.82643e7 | − | 5.10817e7i | −0.599807 | − | 1.67755i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.49489e7 | − | 3.49489e7i | −1.14193 | − | 1.14193i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.92561e6 | −0.322676 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 3.78149e7i | − | 1.22315i | −0.791187 | − | 0.611574i | \(-0.790537\pi\) | ||
0.791187 | − | 0.611574i | \(-0.209463\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.47895e7 | + | 2.47895e7i | −0.797800 | + | 0.797800i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.85434e7 | − | 3.91837e7i | 0.593787 | − | 1.25472i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.28781e6 | + | 1.28781e6i | −0.0410312 | + | 0.0410312i | −0.727325 | − | 0.686294i | \(-0.759237\pi\) |
0.686294 | + | 0.727325i | \(0.259237\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.51361e7 | −2.06494 |
(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 | 160.6.o.a.47.10 | 56 | ||
4.3 | odd | 2 | 40.6.k.a.27.9 | yes | 56 | ||
5.3 | odd | 4 | inner | 160.6.o.a.143.9 | 56 | ||
8.3 | odd | 2 | inner | 160.6.o.a.47.9 | 56 | ||
8.5 | even | 2 | 40.6.k.a.27.7 | yes | 56 | ||
20.3 | even | 4 | 40.6.k.a.3.7 | ✓ | 56 | ||
40.3 | even | 4 | inner | 160.6.o.a.143.10 | 56 | ||
40.13 | odd | 4 | 40.6.k.a.3.9 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.k.a.3.7 | ✓ | 56 | 20.3 | even | 4 | ||
40.6.k.a.3.9 | yes | 56 | 40.13 | odd | 4 | ||
40.6.k.a.27.7 | yes | 56 | 8.5 | even | 2 | ||
40.6.k.a.27.9 | yes | 56 | 4.3 | odd | 2 | ||
160.6.o.a.47.9 | 56 | 8.3 | odd | 2 | inner | ||
160.6.o.a.47.10 | 56 | 1.1 | even | 1 | trivial | ||
160.6.o.a.143.9 | 56 | 5.3 | odd | 4 | inner | ||
160.6.o.a.143.10 | 56 | 40.3 | even | 4 | inner |