Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(80,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.80");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.p (of order \(6\), 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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} - 1762200 x^{2} + 810000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 80.2 | ||
Root | \(-3.91663 + 2.26127i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.80 |
Dual form | 441.4.p.c.215.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.91663 | + | 2.26127i | −1.38474 | + | 0.799480i | −0.992716 | − | 0.120476i | \(-0.961558\pi\) |
−0.392023 | + | 0.919955i | \(0.628225\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 6.22668 | − | 10.7849i | 0.778336 | − | 1.34812i | ||||
\(5\) | 0.632851 | + | 1.09613i | 0.0566040 | + | 0.0980409i | 0.892939 | − | 0.450178i | \(-0.148639\pi\) |
−0.836335 | + | 0.548219i | \(0.815306\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 20.1405i | 0.890094i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.95730 | − | 2.86210i | −0.156763 | − | 0.0905074i | ||||
\(11\) | 36.0248 | + | 20.7989i | 0.987443 | + | 0.570101i | 0.904509 | − | 0.426454i | \(-0.140237\pi\) |
0.0829344 | + | 0.996555i | \(0.473571\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 85.7355i | − | 1.82914i | −0.404433 | − | 0.914568i | \(-0.632531\pi\) | ||
0.404433 | − | 0.914568i | \(-0.367469\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.27028 | + | 7.39634i | 0.0667231 | + | 0.115568i | ||||
\(17\) | −38.8929 | + | 67.3645i | −0.554878 | + | 0.961076i | 0.443035 | + | 0.896504i | \(0.353902\pi\) |
−0.997913 | + | 0.0645722i | \(0.979432\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −42.1638 | + | 24.3433i | −0.509107 | + | 0.293933i | −0.732466 | − | 0.680803i | \(-0.761631\pi\) |
0.223360 | + | 0.974736i | \(0.428298\pi\) | |||||||
\(20\) | 15.7623 | 0.176227 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −188.128 | −1.82314 | ||||||||
\(23\) | 78.7639 | − | 45.4743i | 0.714061 | − | 0.412263i | −0.0985019 | − | 0.995137i | \(-0.531405\pi\) |
0.812563 | + | 0.582874i | \(0.198072\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 61.6990 | − | 106.866i | 0.493592 | − | 0.854926i | ||||
\(26\) | 193.871 | + | 335.795i | 1.46236 | + | 2.53288i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 151.196i | 0.968151i | 0.875026 | + | 0.484075i | \(0.160844\pi\) | ||||
−0.875026 | + | 0.484075i | \(0.839156\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −76.3661 | − | 44.0900i | −0.442444 | − | 0.255445i | 0.262190 | − | 0.965016i | \(-0.415555\pi\) |
−0.704634 | + | 0.709571i | \(0.748889\pi\) | |||||||
\(32\) | −172.988 | − | 99.8747i | −0.955633 | − | 0.551735i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 351.790i | − | 1.77445i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −45.2914 | − | 78.4470i | −0.201239 | − | 0.348557i | 0.747689 | − | 0.664050i | \(-0.231164\pi\) |
−0.948928 | + | 0.315493i | \(0.897830\pi\) | |||||||
\(38\) | 110.093 | − | 190.687i | 0.469987 | − | 0.814041i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −22.0767 | + | 12.7460i | −0.0872657 | + | 0.0503829i | ||||
\(41\) | −383.530 | −1.46091 | −0.730455 | − | 0.682961i | \(-0.760692\pi\) | ||||
−0.730455 | + | 0.682961i | \(0.760692\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −227.894 | −0.808222 | −0.404111 | − | 0.914710i | \(-0.632419\pi\) | ||||
−0.404111 | + | 0.914710i | \(0.632419\pi\) | |||||||
\(44\) | 448.630 | − | 259.017i | 1.53712 | − | 0.887459i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −205.660 | + | 356.213i | −0.659192 | + | 1.14175i | ||||
\(47\) | −69.5529 | − | 120.469i | −0.215858 | − | 0.373877i | 0.737680 | − | 0.675151i | \(-0.235922\pi\) |
−0.953538 | + | 0.301274i | \(0.902588\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 558.072i | 1.57847i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −924.652 | − | 533.848i | −2.46589 | − | 1.42368i | ||||
\(53\) | −289.749 | − | 167.287i | −0.750945 | − | 0.433558i | 0.0750904 | − | 0.997177i | \(-0.476075\pi\) |
−0.826035 | + | 0.563619i | \(0.809409\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 52.6505i | 0.129080i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −341.895 | − | 592.179i | −0.774017 | − | 1.34064i | ||||
\(59\) | 440.050 | − | 762.189i | 0.971010 | − | 1.68184i | 0.278493 | − | 0.960438i | \(-0.410165\pi\) |
0.692518 | − | 0.721401i | \(-0.256501\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.3944 | + | 6.57854i | −0.0239164 | + | 0.0138081i | −0.511911 | − | 0.859039i | \(-0.671062\pi\) |
0.487994 | + | 0.872847i | \(0.337729\pi\) | |||||||
\(62\) | 398.797 | 0.816892 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 835.050 | 1.63096 | ||||||||
\(65\) | 93.9774 | − | 54.2579i | 0.179330 | − | 0.103536i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 221.212 | − | 383.151i | 0.403364 | − | 0.698647i | −0.590766 | − | 0.806843i | \(-0.701174\pi\) |
0.994130 | + | 0.108197i | \(0.0345076\pi\) | |||||||
\(68\) | 484.348 | + | 838.915i | 0.863762 | + | 1.49608i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 341.552i | − | 0.570912i | −0.958392 | − | 0.285456i | \(-0.907855\pi\) | ||
0.958392 | − | 0.285456i | \(-0.0921450\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 798.218 | + | 460.851i | 1.27979 | + | 0.738885i | 0.976809 | − | 0.214113i | \(-0.0686862\pi\) |
0.302977 | + | 0.952998i | \(0.402019\pi\) | |||||||
\(74\) | 354.780 | + | 204.832i | 0.557328 | + | 0.321774i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 606.311i | 0.915114i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 206.564 | + | 357.780i | 0.294181 | + | 0.509537i | 0.974794 | − | 0.223107i | \(-0.0716198\pi\) |
−0.680613 | + | 0.732643i | \(0.738286\pi\) | |||||||
\(80\) | −5.40490 | + | 9.36157i | −0.00755358 | + | 0.0130832i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1502.15 | − | 867.265i | 2.02298 | − | 1.16797i | ||||
\(83\) | 954.307 | 1.26203 | 0.631017 | − | 0.775769i | \(-0.282638\pi\) | ||||
0.631017 | + | 0.775769i | \(0.282638\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −98.4538 | −0.125633 | ||||||||
\(86\) | 892.579 | − | 515.331i | 1.11918 | − | 0.646157i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −418.901 | + | 725.558i | −0.507444 | + | 0.878918i | ||||
\(89\) | 14.8490 | + | 25.7193i | 0.0176853 | + | 0.0306319i | 0.874733 | − | 0.484606i | \(-0.161037\pi\) |
−0.857047 | + | 0.515238i | \(0.827704\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 1132.62i | − | 1.28352i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 544.826 | + | 314.556i | 0.597814 | + | 0.345148i | ||||
\(95\) | −53.3668 | − | 30.8113i | −0.0576349 | − | 0.0332755i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1199.63i | − | 1.25572i | −0.778328 | − | 0.627858i | \(-0.783932\pi\) | ||
0.778328 | − | 0.627858i | \(-0.216068\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −768.360 | − | 1330.84i | −0.768360 | − | 1.33084i | ||||
\(101\) | −327.422 | + | 567.111i | −0.322571 | + | 0.558710i | −0.981018 | − | 0.193918i | \(-0.937881\pi\) |
0.658447 | + | 0.752628i | \(0.271214\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1186.01 | − | 684.744i | 1.13457 | − | 0.655047i | 0.189493 | − | 0.981882i | \(-0.439316\pi\) |
0.945081 | + | 0.326836i | \(0.105982\pi\) | |||||||
\(104\) | 1726.76 | 1.62810 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1513.12 | 1.38648 | ||||||||
\(107\) | −371.311 | + | 214.377i | −0.335477 | + | 0.193688i | −0.658270 | − | 0.752782i | \(-0.728711\pi\) |
0.322793 | + | 0.946470i | \(0.395378\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 334.261 | − | 578.957i | 0.293728 | − | 0.508752i | −0.680960 | − | 0.732321i | \(-0.738437\pi\) |
0.974688 | + | 0.223568i | \(0.0717706\pi\) | |||||||
\(110\) | −119.057 | − | 206.213i | −0.103197 | − | 0.178742i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 914.837i | − | 0.761598i | −0.924658 | − | 0.380799i | \(-0.875649\pi\) | ||
0.924658 | − | 0.380799i | \(-0.124351\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 99.6917 | + | 57.5570i | 0.0808374 | + | 0.0466715i | ||||
\(116\) | 1630.64 | + | 941.449i | 1.30518 | + | 0.753546i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3980.29i | 3.10521i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 199.690 | + | 345.873i | 0.150030 | + | 0.259859i | ||||
\(122\) | 29.7517 | − | 51.5314i | 0.0220786 | − | 0.0382413i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −951.015 | + | 549.069i | −0.688739 | + | 0.397644i | ||||
\(125\) | 314.398 | 0.224965 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1260.95 | 0.881034 | 0.440517 | − | 0.897744i | \(-0.354795\pi\) | ||||
0.440517 | + | 0.897744i | \(0.354795\pi\) | |||||||
\(128\) | −1886.68 | + | 1089.28i | −1.30282 | + | 0.752182i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −245.383 | + | 425.016i | −0.165550 | + | 0.286742i | ||||
\(131\) | −683.600 | − | 1184.03i | −0.455926 | − | 0.789688i | 0.542814 | − | 0.839853i | \(-0.317359\pi\) |
−0.998741 | + | 0.0501648i | \(0.984025\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2000.88i | 1.28992i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1356.76 | − | 783.325i | −0.855449 | − | 0.493894i | ||||
\(137\) | −953.631 | − | 550.579i | −0.594702 | − | 0.343351i | 0.172252 | − | 0.985053i | \(-0.444896\pi\) |
−0.766955 | + | 0.641701i | \(0.778229\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2306.56i | − | 1.40748i | −0.710458 | − | 0.703739i | \(-0.751512\pi\) | ||
0.710458 | − | 0.703739i | \(-0.248488\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 772.341 | + | 1337.73i | 0.456432 | + | 0.790564i | ||||
\(143\) | 1783.21 | − | 3088.60i | 1.04279 | − | 1.80617i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −165.730 | + | 95.6845i | −0.0949184 | + | 0.0548012i | ||||
\(146\) | −4168.44 | −2.36289 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1128.06 | −0.626527 | ||||||||
\(149\) | 1520.57 | − | 877.901i | 0.836040 | − | 0.482688i | −0.0198764 | − | 0.999802i | \(-0.506327\pi\) |
0.855916 | + | 0.517115i | \(0.172994\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 262.491 | − | 454.647i | 0.141465 | − | 0.245024i | −0.786584 | − | 0.617484i | \(-0.788152\pi\) |
0.928048 | + | 0.372460i | \(0.121485\pi\) | |||||||
\(152\) | −490.286 | − | 849.201i | −0.261628 | − | 0.453153i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 111.610i | − | 0.0578368i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1141.44 | + | 659.009i | 0.580233 | + | 0.334998i | 0.761226 | − | 0.648487i | \(-0.224598\pi\) |
−0.180993 | + | 0.983484i | \(0.557931\pi\) | |||||||
\(158\) | −1618.07 | − | 934.195i | −0.814728 | − | 0.470384i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 252.823i | − | 0.124921i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 223.916 | + | 387.834i | 0.107598 | + | 0.186365i | 0.914797 | − | 0.403915i | \(-0.132351\pi\) |
−0.807199 | + | 0.590280i | \(0.799017\pi\) | |||||||
\(164\) | −2388.12 | + | 4136.35i | −1.13708 | + | 1.96948i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3737.67 | + | 2157.95i | −1.74759 | + | 1.00897i | ||||
\(167\) | −811.124 | −0.375848 | −0.187924 | − | 0.982184i | \(-0.560176\pi\) | ||||
−0.187924 | + | 0.982184i | \(0.560176\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5153.58 | −2.34574 | ||||||||
\(170\) | 385.608 | − | 222.631i | 0.173969 | − | 0.100441i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1419.03 | + | 2457.82i | −0.629068 | + | 1.08958i | ||||
\(173\) | −1121.24 | − | 1942.04i | −0.492751 | − | 0.853470i | 0.507214 | − | 0.861820i | \(-0.330675\pi\) |
−0.999965 | + | 0.00834994i | \(0.997342\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 355.269i | 0.152156i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −116.317 | − | 67.1554i | −0.0489792 | − | 0.0282781i | ||||
\(179\) | −2531.77 | − | 1461.72i | −1.05717 | − | 0.610357i | −0.132521 | − | 0.991180i | \(-0.542307\pi\) |
−0.924648 | + | 0.380824i | \(0.875641\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 282.859i | 0.116159i | 0.998312 | + | 0.0580794i | \(0.0184977\pi\) | ||||
−0.998312 | + | 0.0580794i | \(0.981502\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 915.878 | + | 1586.35i | 0.366953 | + | 0.635582i | ||||
\(185\) | 57.3255 | − | 99.2906i | 0.0227819 | − | 0.0394594i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2802.22 | + | 1617.86i | −1.09582 | + | 0.632672i | ||||
\(188\) | −1732.34 | −0.672040 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 278.691 | 0.106412 | ||||||||
\(191\) | −3998.63 | + | 2308.61i | −1.51482 | + | 0.874582i | −0.514971 | + | 0.857208i | \(0.672197\pi\) |
−0.999849 | + | 0.0173741i | \(0.994469\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2077.73 | − | 3598.73i | 0.774912 | − | 1.34219i | −0.159933 | − | 0.987128i | \(-0.551128\pi\) |
0.934844 | − | 0.355058i | \(-0.115539\pi\) | |||||||
\(194\) | 2712.70 | + | 4698.53i | 1.00392 | + | 1.73884i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1626.36i | − | 0.588190i | −0.955776 | − | 0.294095i | \(-0.904982\pi\) | ||
0.955776 | − | 0.294095i | \(-0.0950183\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −150.861 | − | 87.0995i | −0.0537399 | − | 0.0310267i | 0.472889 | − | 0.881122i | \(-0.343211\pi\) |
−0.526629 | + | 0.850095i | \(0.676544\pi\) | |||||||
\(200\) | 2152.33 | + | 1242.65i | 0.760965 | + | 0.439344i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 2961.56i | − | 1.03156i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −242.718 | − | 420.399i | −0.0826933 | − | 0.143229i | ||||
\(206\) | −3096.78 | + | 5363.78i | −1.04739 | + | 1.81414i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 634.129 | − | 366.115i | 0.211389 | − | 0.122046i | ||||
\(209\) | −2025.25 | −0.670286 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2942.35 | −0.959999 | −0.479999 | − | 0.877269i | \(-0.659363\pi\) | ||||
−0.479999 | + | 0.877269i | \(0.659363\pi\) | |||||||
\(212\) | −3608.35 | + | 2083.28i | −1.16897 | + | 0.674907i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 969.527 | − | 1679.27i | 0.309699 | − | 0.536414i | ||||
\(215\) | −144.223 | − | 249.802i | −0.0457486 | − | 0.0792389i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3023.42i | 0.939319i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 567.832 | + | 327.838i | 0.174015 | + | 0.100467i | ||||
\(221\) | 5775.53 | + | 3334.51i | 1.75794 | + | 1.01495i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3374.75i | − | 1.01341i | −0.862120 | − | 0.506704i | \(-0.830864\pi\) | ||
0.862120 | − | 0.506704i | \(-0.169136\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2068.69 | + | 3583.08i | 0.608882 | + | 1.05461i | ||||
\(227\) | −1515.43 | + | 2624.79i | −0.443094 | + | 0.767461i | −0.997917 | − | 0.0645069i | \(-0.979453\pi\) |
0.554823 | + | 0.831968i | \(0.312786\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −960.030 | + | 554.274i | −0.277033 | + | 0.159945i | −0.632080 | − | 0.774904i | \(-0.717798\pi\) |
0.355046 | + | 0.934849i | \(0.384465\pi\) | |||||||
\(230\) | −520.608 | −0.149252 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3045.17 | −0.861746 | ||||||||
\(233\) | 2684.57 | − | 1549.94i | 0.754815 | − | 0.435793i | −0.0726160 | − | 0.997360i | \(-0.523135\pi\) |
0.827431 | + | 0.561567i | \(0.189801\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 88.0333 | − | 152.478i | 0.0244368 | − | 0.0423259i | ||||
\(236\) | −5480.10 | − | 9491.82i | −1.51154 | − | 2.61807i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1735.25i | 0.469640i | 0.972039 | + | 0.234820i | \(0.0754501\pi\) | ||||
−0.972039 | + | 0.234820i | \(0.924550\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1039.26 | + | 600.019i | 0.277779 | + | 0.160376i | 0.632418 | − | 0.774628i | \(-0.282063\pi\) |
−0.354638 | + | 0.935004i | \(0.615396\pi\) | |||||||
\(242\) | −1564.22 | − | 903.104i | −0.415504 | − | 0.239892i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 163.850i | 0.0429894i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2087.08 | + | 3614.93i | 0.537643 | + | 0.931225i | ||||
\(248\) | 887.996 | − | 1538.05i | 0.227370 | − | 0.393817i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1231.38 | + | 710.939i | −0.311518 | + | 0.179855i | ||||
\(251\) | 3712.56 | 0.933603 | 0.466802 | − | 0.884362i | \(-0.345406\pi\) | ||||
0.466802 | + | 0.884362i | \(0.345406\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3783.27 | 0.940126 | ||||||||
\(254\) | −4938.69 | + | 2851.35i | −1.22000 | + | 0.704369i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1586.09 | − | 2747.20i | 0.387230 | − | 0.670702i | ||||
\(257\) | 389.574 | + | 674.762i | 0.0945563 | + | 0.163776i | 0.909423 | − | 0.415872i | \(-0.136523\pi\) |
−0.814867 | + | 0.579648i | \(0.803190\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 1351.39i | − | 0.322344i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5354.82 | + | 3091.61i | 1.26268 | + | 0.729008i | ||||
\(263\) | 1702.07 | + | 982.690i | 0.399065 | + | 0.230400i | 0.686080 | − | 0.727526i | \(-0.259330\pi\) |
−0.287015 | + | 0.957926i | \(0.592663\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 423.470i | − | 0.0981644i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2754.84 | − | 4771.52i | −0.627905 | − | 1.08756i | ||||
\(269\) | 1236.41 | − | 2141.53i | 0.280243 | − | 0.485395i | −0.691201 | − | 0.722662i | \(-0.742918\pi\) |
0.971444 | + | 0.237267i | \(0.0762516\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4095.79 | + | 2364.71i | −0.918088 | + | 0.530058i | −0.883025 | − | 0.469327i | \(-0.844497\pi\) |
−0.0350633 | + | 0.999385i | \(0.511163\pi\) | |||||||
\(272\) | −664.334 | −0.148093 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4980.03 | 1.09801 | ||||||||
\(275\) | 4445.39 | − | 2566.54i | 0.974788 | − | 0.562794i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −586.579 | + | 1015.98i | −0.127235 | + | 0.220378i | −0.922604 | − | 0.385747i | \(-0.873944\pi\) |
0.795369 | + | 0.606125i | \(0.207277\pi\) | |||||||
\(278\) | 5215.74 | + | 9033.93i | 1.12525 | + | 1.94899i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8195.18i | − | 1.73980i | −0.493229 | − | 0.869899i | \(-0.664184\pi\) | ||
0.493229 | − | 0.869899i | \(-0.335816\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2242.44 | − | 1294.67i | −0.471021 | − | 0.271944i | 0.245646 | − | 0.969360i | \(-0.421000\pi\) |
−0.716667 | + | 0.697415i | \(0.754333\pi\) | |||||||
\(284\) | −3683.61 | − | 2126.74i | −0.769656 | − | 0.444361i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16129.2i | 3.33476i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −568.820 | − | 985.225i | −0.115779 | − | 0.200534i | ||||
\(290\) | 432.737 | − | 749.523i | 0.0876248 | − | 0.151771i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9940.50 | − | 5739.15i | 1.99221 | − | 1.15020i | ||||
\(293\) | 8871.16 | 1.76880 | 0.884400 | − | 0.466729i | \(-0.154568\pi\) | ||||
0.884400 | + | 0.466729i | \(0.154568\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1113.94 | 0.219852 | ||||||||
\(296\) | 1579.96 | − | 912.193i | 0.310249 | − | 0.179122i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3970.34 | + | 6876.84i | −0.771798 | + | 1.33679i | ||||
\(299\) | −3898.77 | − | 6752.86i | −0.754085 | − | 1.30611i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2374.25i | 0.452393i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −360.102 | − | 207.905i | −0.0679383 | − | 0.0392242i | ||||
\(305\) | −14.4219 | − | 8.32647i | −0.00270752 | − | 0.00156319i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2707.52i | 0.503344i | 0.967813 | + | 0.251672i | \(0.0809804\pi\) | ||||
−0.967813 | + | 0.251672i | \(0.919020\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 252.379 | + | 437.134i | 0.0462393 | + | 0.0800889i | ||||
\(311\) | 1080.55 | − | 1871.56i | 0.197017 | − | 0.341243i | −0.750543 | − | 0.660822i | \(-0.770208\pi\) |
0.947560 | + | 0.319579i | \(0.103541\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7300.25 | − | 4214.80i | 1.31832 | − | 0.761133i | 0.334863 | − | 0.942267i | \(-0.391310\pi\) |
0.983459 | + | 0.181133i | \(0.0579766\pi\) | |||||||
\(314\) | −5960.79 | −1.07130 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5144.84 | 0.915886 | ||||||||
\(317\) | −8310.07 | + | 4797.82i | −1.47237 | + | 0.850071i | −0.999517 | − | 0.0310734i | \(-0.990107\pi\) |
−0.472848 | + | 0.881144i | \(0.656774\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3144.71 | + | 5446.80i | −0.551943 | + | 0.955994i | ||||
\(320\) | 528.463 | + | 915.324i | 0.0923186 | + | 0.159901i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3787.12i | − | 0.652387i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9162.20 | − | 5289.80i | −1.56378 | − | 0.902847i | ||||
\(326\) | −1753.99 | − | 1012.67i | −0.297990 | − | 0.172045i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 7724.50i | − | 1.30035i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4271.96 | − | 7399.25i | −0.709390 | − | 1.22870i | −0.965084 | − | 0.261941i | \(-0.915637\pi\) |
0.255694 | − | 0.966758i | \(-0.417696\pi\) | |||||||
\(332\) | 5942.17 | − | 10292.1i | 0.982286 | − | 1.70137i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3176.88 | − | 1834.17i | 0.520452 | − | 0.300483i | ||||
\(335\) | 559.978 | 0.0913280 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 598.875 | 0.0968036 | 0.0484018 | − | 0.998828i | \(-0.484587\pi\) | ||||
0.0484018 | + | 0.998828i | \(0.484587\pi\) | |||||||
\(338\) | 20184.7 | − | 11653.6i | 3.24823 | − | 1.87537i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −613.041 | + | 1061.82i | −0.0977847 | + | 0.169368i | ||||
\(341\) | −1834.05 | − | 3176.66i | −0.291259 | − | 0.504475i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 4589.91i | − | 0.719394i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8782.94 | + | 5070.83i | 1.36466 | + | 0.787889i | ||||
\(347\) | −6149.62 | − | 3550.49i | −0.951381 | − | 0.549280i | −0.0578712 | − | 0.998324i | \(-0.518431\pi\) |
−0.893510 | + | 0.449044i | \(0.851765\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3620.71i | 0.555336i | 0.960677 | + | 0.277668i | \(0.0895616\pi\) | ||||
−0.960677 | + | 0.277668i | \(0.910438\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4154.57 | − | 7195.92i | −0.629089 | − | 1.08961i | ||||
\(353\) | −1164.89 | + | 2017.64i | −0.175639 | + | 0.304216i | −0.940382 | − | 0.340119i | \(-0.889533\pi\) |
0.764743 | + | 0.644335i | \(0.222866\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 374.386 | − | 216.152i | 0.0559727 | − | 0.0323159i | ||||
\(356\) | 369.841 | 0.0550605 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13221.3 | 1.95187 | ||||||||
\(359\) | −1522.43 | + | 878.975i | −0.223818 | + | 0.129222i | −0.607717 | − | 0.794154i | \(-0.707914\pi\) |
0.383899 | + | 0.923375i | \(0.374581\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2244.31 | + | 3887.26i | −0.327207 | + | 0.566739i | ||||
\(362\) | −639.621 | − | 1107.86i | −0.0928667 | − | 0.160850i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1166.60i | 0.167295i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1458.89 | − | 842.290i | −0.207503 | − | 0.119802i | 0.392648 | − | 0.919689i | \(-0.371559\pi\) |
−0.600150 | + | 0.799887i | \(0.704893\pi\) | |||||||
\(368\) | 672.687 | + | 388.376i | 0.0952887 | + | 0.0550150i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 518.513i | 0.0728547i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 148.646 | + | 257.462i | 0.0206343 | + | 0.0357397i | 0.876158 | − | 0.482024i | \(-0.160098\pi\) |
−0.855524 | + | 0.517763i | \(0.826765\pi\) | |||||||
\(374\) | 7316.84 | − | 12673.1i | 1.01162 | − | 1.75217i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2426.31 | − | 1400.83i | 0.332786 | − | 0.192134i | ||||
\(377\) | 12962.9 | 1.77088 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7402.78 | −1.00331 | −0.501656 | − | 0.865067i | \(-0.667276\pi\) | ||||
−0.501656 | + | 0.865067i | \(0.667276\pi\) | |||||||
\(380\) | −664.596 | + | 383.705i | −0.0897186 | + | 0.0517991i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10440.8 | − | 18084.0i | 1.39842 | − | 2.42214i | ||||
\(383\) | 6263.77 | + | 10849.2i | 0.835676 | + | 1.44743i | 0.893479 | + | 0.449105i | \(0.148257\pi\) |
−0.0578031 | + | 0.998328i | \(0.518410\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18793.2i | 2.47810i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12938.0 | − | 7469.75i | −1.69285 | − | 0.977368i | ||||
\(389\) | 6904.14 | + | 3986.11i | 0.899881 | + | 0.519547i | 0.877162 | − | 0.480195i | \(-0.159434\pi\) |
0.0227196 | + | 0.999742i | \(0.492767\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7074.52i | 0.915023i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3677.64 | + | 6369.87i | 0.470246 | + | 0.814491i | ||||
\(395\) | −261.449 | + | 452.843i | −0.0333036 | + | 0.0576836i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10832.5 | + | 6254.16i | −1.36944 | + | 0.790648i | −0.990857 | − | 0.134918i | \(-0.956923\pi\) |
−0.378586 | + | 0.925566i | \(0.623590\pi\) | |||||||
\(398\) | 787.822 | 0.0992210 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1053.89 | 0.131736 | ||||||||
\(401\) | −6943.55 | + | 4008.86i | −0.864699 | + | 0.499234i | −0.865583 | − | 0.500765i | \(-0.833052\pi\) |
0.000883860 | 1.00000i | \(0.499719\pi\) | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3780.08 | + | 6547.29i | −0.467243 | + | 0.809289i | ||||
\(404\) | 4077.51 | + | 7062.45i | 0.502137 | + | 0.869728i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3768.05i | − | 0.458907i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7566.04 | + | 4368.26i | 0.914711 | + | 0.528109i | 0.881944 | − | 0.471354i | \(-0.156235\pi\) |
0.0327670 | + | 0.999463i | \(0.489568\pi\) | |||||||
\(410\) | 1901.27 | + | 1097.70i | 0.229017 | + | 0.132223i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 17054.7i | − | 2.03938i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 603.935 | + | 1046.05i | 0.0714361 | + | 0.123731i | ||||
\(416\) | −8562.81 | + | 14831.2i | −1.00920 | + | 1.74798i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7932.18 | − | 4579.64i | 0.928171 | − | 0.535880i | ||||
\(419\) | −3926.67 | −0.457829 | −0.228914 | − | 0.973447i | \(-0.573518\pi\) | ||||
−0.228914 | + | 0.973447i | \(0.573518\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1443.44 | 0.167100 | 0.0835499 | − | 0.996504i | \(-0.473374\pi\) | ||||
0.0835499 | + | 0.996504i | \(0.473374\pi\) | |||||||
\(422\) | 11524.1 | − | 6653.45i | 1.32935 | − | 0.767500i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3369.24 | − | 5835.70i | 0.385908 | − | 0.668412i | ||||
\(425\) | 4799.31 | + | 8312.65i | 0.547766 | + | 0.948759i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5339.42i | 0.603016i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1129.74 | + | 652.255i | 0.126700 | + | 0.0731501i | ||||
\(431\) | 12820.5 | + | 7401.92i | 1.43281 | + | 0.827234i | 0.997334 | − | 0.0729655i | \(-0.0232463\pi\) |
0.435477 | + | 0.900200i | \(0.356580\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 15872.1i | − | 1.76158i | −0.473508 | − | 0.880790i | \(-0.657012\pi\) | ||
0.473508 | − | 0.880790i | \(-0.342988\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4162.67 | − | 7209.96i | −0.457238 | − | 0.791960i | ||||
\(437\) | −2213.99 | + | 3834.74i | −0.242356 | + | 0.419772i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2626.58 | − | 1516.45i | 0.285557 | − | 0.164867i | −0.350379 | − | 0.936608i | \(-0.613947\pi\) |
0.635937 | + | 0.771741i | \(0.280614\pi\) | |||||||
\(440\) | −1060.41 | −0.114893 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −30160.9 | −3.24572 | ||||||||
\(443\) | 11126.8 | − | 6424.08i | 1.19334 | − | 0.688978i | 0.234281 | − | 0.972169i | \(-0.424726\pi\) |
0.959064 | + | 0.283191i | \(0.0913930\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.7945 | + | 32.5530i | −0.00200212 | + | 0.00346777i | ||||
\(446\) | 7631.22 | + | 13217.7i | 0.810199 | + | 1.40331i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 107.668i | − | 0.0113166i | −0.999984 | − | 0.00565831i | \(-0.998199\pi\) | ||
0.999984 | − | 0.00565831i | \(-0.00180111\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13816.6 | − | 7977.01i | −1.44257 | − | 0.832866i | ||||
\(452\) | −9866.45 | − | 5696.40i | −1.02672 | − | 0.592779i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 13707.1i | − | 1.41698i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4888.53 | + | 8467.18i | 0.500385 | + | 0.866691i | 1.00000 | 0.000444115i | \(0.000141366\pi\) | |
−0.499615 | + | 0.866247i | \(0.666525\pi\) | |||||||
\(458\) | 2506.72 | − | 4341.77i | 0.255746 | − | 0.442965i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1241.50 | − | 716.779i | 0.125837 | − | 0.0726521i | ||||
\(461\) | 638.874 | 0.0645452 | 0.0322726 | − | 0.999479i | \(-0.489726\pi\) | ||||
0.0322726 | + | 0.999479i | \(0.489726\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5602.26 | −0.562331 | −0.281165 | − | 0.959659i | \(-0.590721\pi\) | ||||
−0.281165 | + | 0.959659i | \(0.590721\pi\) | |||||||
\(464\) | −1118.30 | + | 645.648i | −0.111887 | + | 0.0645980i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7009.65 | + | 12141.1i | −0.696815 | + | 1.20692i | ||||
\(467\) | −2759.44 | − | 4779.49i | −0.273430 | − | 0.473594i | 0.696308 | − | 0.717743i | \(-0.254825\pi\) |
−0.969738 | + | 0.244149i | \(0.921491\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 796.268i | 0.0781470i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 15350.9 | + | 8862.84i | 1.49700 | + | 0.864291i | ||||
\(473\) | −8209.84 | − | 4739.95i | −0.798074 | − | 0.460768i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6007.82i | 0.580332i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3923.87 | − | 6796.34i | −0.375468 | − | 0.650329i | ||||
\(479\) | −2734.40 | + | 4736.11i | −0.260830 | + | 0.451771i | −0.966463 | − | 0.256807i | \(-0.917330\pi\) |
0.705632 | + | 0.708578i | \(0.250663\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6725.70 | + | 3883.08i | −0.637558 | + | 0.368094i | ||||
\(482\) | −5427.22 | −0.512869 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4973.62 | 0.467094 | ||||||||
\(485\) | 1314.96 | − | 759.190i | 0.123112 | − | 0.0710785i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5866.72 | − | 10161.5i | 0.545886 | − | 0.945502i | −0.452665 | − | 0.891681i | \(-0.649527\pi\) |
0.998551 | − | 0.0538213i | \(-0.0171401\pi\) | |||||||
\(488\) | −132.495 | − | 229.489i | −0.0122905 | − | 0.0212878i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3514.92i | − | 0.323068i | −0.986867 | − | 0.161534i | \(-0.948356\pi\) | ||
0.986867 | − | 0.161534i | \(-0.0516441\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10185.2 | − | 5880.45i | −0.930467 | − | 0.537205i | ||||
\(494\) | −16348.7 | − | 9438.91i | −1.48899 | − | 0.859670i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 753.106i | − | 0.0681763i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4944.49 | − | 8564.11i | −0.443579 | − | 0.768301i | 0.554373 | − | 0.832268i | \(-0.312958\pi\) |
−0.997952 | + | 0.0639672i | \(0.979625\pi\) | |||||||
\(500\) | 1957.66 | − | 3390.76i | 0.175098 | − | 0.303279i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14540.7 | + | 8395.09i | −1.29280 | + | 0.746397i | ||||
\(503\) | −10172.2 | −0.901698 | −0.450849 | − | 0.892600i | \(-0.648879\pi\) | ||||
−0.450849 | + | 0.892600i | \(0.648879\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −828.838 | −0.0730353 | ||||||||
\(506\) | −14817.7 | + | 8554.99i | −1.30183 | + | 0.751612i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7851.55 | − | 13599.3i | 0.685740 | − | 1.18774i | ||||
\(509\) | −2149.56 | − | 3723.15i | −0.187186 | − | 0.324216i | 0.757125 | − | 0.653270i | \(-0.226603\pi\) |
−0.944311 | + | 0.329054i | \(0.893270\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 3082.06i | − | 0.266033i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3051.64 | − | 1761.86i | −0.261872 | − | 0.151192i | ||||
\(515\) | 1501.14 | + | 866.682i | 0.128443 | + | 0.0741565i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 5786.50i | − | 0.492243i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1092.78 | + | 1892.76i | 0.0921571 | + | 0.159621i | ||||
\(521\) | −5496.48 | + | 9520.18i | −0.462198 | + | 0.800550i | −0.999070 | − | 0.0431133i | \(-0.986272\pi\) |
0.536872 | + | 0.843664i | \(0.319606\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7386.80 | + | 4264.77i | −0.617595 | + | 0.356569i | −0.775932 | − | 0.630817i | \(-0.782720\pi\) |
0.158337 | + | 0.987385i | \(0.449387\pi\) | |||||||
\(524\) | −17026.2 | −1.41946 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8888.51 | −0.736801 | ||||||||
\(527\) | 5940.20 | − | 3429.58i | 0.491004 | − | 0.283481i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1947.67 | + | 3373.46i | −0.160078 | + | 0.277263i | ||||
\(530\) | 957.581 | + | 1658.58i | 0.0784805 | + | 0.135932i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32882.2i | 2.67220i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −469.970 | − | 271.337i | −0.0379786 | − | 0.0219270i | ||||
\(536\) | 7716.86 | + | 4455.33i | 0.621862 | + | 0.359032i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11183.4i | 0.896195i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4352.93 | + | 7539.49i | 0.345928 | + | 0.599165i | 0.985522 | − | 0.169548i | \(-0.0542308\pi\) |
−0.639594 | + | 0.768713i | \(0.720897\pi\) | |||||||
\(542\) | 10694.5 | − | 18523.4i | 0.847542 | − | 1.46799i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13456.0 | − | 7768.84i | 1.06052 | − | 0.612291i | ||||
\(545\) | 846.150 | 0.0665047 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17183.8 | 1.34319 | 0.671596 | − | 0.740917i | \(-0.265609\pi\) | ||||
0.671596 | + | 0.740917i | \(0.265609\pi\) | |||||||
\(548\) | −11875.9 | + | 6856.56i | −0.925756 | + | 0.534485i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −11607.3 | + | 20104.4i | −0.899885 | + | 1.55865i | ||||
\(551\) | −3680.60 | − | 6374.99i | −0.284571 | − | 0.492892i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 5305.66i | − | 0.406888i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −24876.0 | − | 14362.2i | −1.89744 | − | 1.09549i | ||||
\(557\) | 8989.79 | + | 5190.26i | 0.683859 | + | 0.394826i | 0.801307 | − | 0.598253i | \(-0.204138\pi\) |
−0.117448 | + | 0.993079i | \(0.537471\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19538.6i | 1.47835i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18531.5 | + | 32097.5i | 1.39093 | + | 2.40917i | ||||
\(563\) | 9248.22 | − | 16018.4i | 0.692302 | − | 1.19910i | −0.278780 | − | 0.960355i | \(-0.589930\pi\) |
0.971082 | − | 0.238747i | \(-0.0767366\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1002.78 | − | 578.956i | 0.0746678 | − | 0.0431095i | ||||
\(566\) | 11710.4 | 0.869656 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6879.04 | 0.508166 | ||||||||
\(569\) | 3493.45 | − | 2016.94i | 0.257386 | − | 0.148602i | −0.365755 | − | 0.930711i | \(-0.619189\pi\) |
0.623142 | + | 0.782109i | \(0.285856\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6430.01 | + | 11137.1i | −0.471257 | + | 0.816241i | −0.999459 | − | 0.0328777i | \(-0.989533\pi\) |
0.528203 | + | 0.849118i | \(0.322866\pi\) | |||||||
\(572\) | −22206.9 | − | 38463.5i | −1.62328 | − | 2.81161i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 11222.9i | − | 0.813959i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17669.2 | + | 10201.3i | 1.27483 | + | 0.736026i | 0.975894 | − | 0.218246i | \(-0.0700335\pi\) |
0.298940 | + | 0.954272i | \(0.403367\pi\) | |||||||
\(578\) | 4455.72 | + | 2572.51i | 0.320646 | + | 0.185125i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2383.19i | 0.170615i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6958.76 | − | 12052.9i | −0.494344 | − | 0.856228i | ||||
\(584\) | −9281.80 | + | 16076.5i | −0.657677 | + | 1.13913i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −34745.1 | + | 20060.1i | −2.44933 | + | 1.41412i | ||||
\(587\) | −16279.7 | −1.14470 | −0.572348 | − | 0.820011i | \(-0.693967\pi\) | ||||
−0.572348 | + | 0.820011i | \(0.693967\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4293.17 | 0.300335 | ||||||||
\(590\) | −4362.91 | + | 2518.93i | −0.304438 | + | 0.175767i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 386.814 | − | 669.981i | 0.0268546 | − | 0.0465136i | ||||
\(593\) | 1342.16 | + | 2324.68i | 0.0929440 | + | 0.160984i | 0.908749 | − | 0.417344i | \(-0.137039\pi\) |
−0.815805 | + | 0.578328i | \(0.803706\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 21865.7i | − | 1.50277i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 30540.1 | + | 17632.3i | 2.08842 | + | 1.20575i | ||||
\(599\) | −12224.6 | − | 7057.90i | −0.833865 | − | 0.481432i | 0.0213091 | − | 0.999773i | \(-0.493217\pi\) |
−0.855174 | + | 0.518341i | \(0.826550\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11096.1i | 0.753109i | 0.926394 | + | 0.376555i | \(0.122891\pi\) | ||||
−0.926394 | + | 0.376555i | \(0.877109\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3268.89 | − | 5661.89i | −0.220214 | − | 0.381422i | ||||
\(605\) | −252.748 | + | 437.772i | −0.0169846 | + | 0.0294181i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9592.70 | − | 5538.35i | 0.641442 | − | 0.370337i | −0.143728 | − | 0.989617i | \(-0.545909\pi\) |
0.785170 | + | 0.619280i | \(0.212576\pi\) | |||||||
\(608\) | 9725.10 | 0.648692 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 75.3136 | 0.00499895 | ||||||||
\(611\) | −10328.5 | + | 5963.15i | −0.683872 | + | 0.394834i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3801.34 | − | 6584.11i | 0.250464 | − | 0.433817i | −0.713189 | − | 0.700971i | \(-0.752750\pi\) |
0.963654 | + | 0.267154i | \(0.0860834\pi\) | |||||||
\(614\) | −6122.44 | − | 10604.4i | −0.402413 | − | 0.697000i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 11325.9i | − | 0.738998i | −0.929231 | − | 0.369499i | \(-0.879529\pi\) | ||
0.929231 | − | 0.369499i | \(-0.120471\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16595.2 | + | 9581.22i | 1.07757 | + | 0.622136i | 0.930240 | − | 0.366952i | \(-0.119599\pi\) |
0.147330 | + | 0.989087i | \(0.452932\pi\) | |||||||
\(620\) | −1203.70 | − | 694.958i | −0.0779707 | − | 0.0450164i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9773.64i | 0.630044i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7513.41 | − | 13013.6i | −0.480858 | − | 0.832871i | ||||
\(626\) | −19061.6 | + | 33015.7i | −1.21702 | + | 2.10794i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14214.7 | − | 8206.88i | 0.903232 | − | 0.521481i | ||||
\(629\) | 7046.06 | 0.446653 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10140.7 | 0.639768 | 0.319884 | − | 0.947457i | \(-0.396356\pi\) | ||||
0.319884 | + | 0.947457i | \(0.396356\pi\) | |||||||
\(632\) | −7205.88 | + | 4160.32i | −0.453536 | + | 0.261849i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 21698.3 | − | 37582.6i | 1.35923 | − | 2.35425i | ||||
\(635\) | 797.995 | + | 1382.17i | 0.0498700 | + | 0.0863774i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 28444.2i | − | 1.76507i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2387.98 | − | 1378.70i | −0.147489 | − | 0.0851530i | ||||
\(641\) | 2950.66 | + | 1703.56i | 0.181816 | + | 0.104972i | 0.588146 | − | 0.808755i | \(-0.299858\pi\) |
−0.406330 | + | 0.913727i | \(0.633192\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 659.110i | 0.0404242i | 0.999796 | + | 0.0202121i | \(0.00643415\pi\) | ||||
−0.999796 | + | 0.0202121i | \(0.993566\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8563.71 | + | 14832.8i | 0.521570 | + | 0.903386i | ||||
\(647\) | 3303.47 | − | 5721.78i | 0.200731 | − | 0.347676i | −0.748033 | − | 0.663661i | \(-0.769002\pi\) |
0.948764 | + | 0.315985i | \(0.102335\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31705.4 | − | 18305.1i | 1.91764 | − | 1.10715i | ||||
\(650\) | 47846.6 | 2.88723 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5577.01 | 0.334989 | ||||||||
\(653\) | −22417.1 | + | 12942.5i | −1.34342 | + | 0.775622i | −0.987307 | − | 0.158823i | \(-0.949230\pi\) |
−0.356109 | + | 0.934444i | \(0.615897\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 865.234 | − | 1498.63i | 0.0516145 | − | 0.0893989i | ||||
\(656\) | −1637.78 | − | 2836.72i | −0.0974764 | − | 0.168834i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7468.86i | 0.441495i | 0.975331 | + | 0.220748i | \(0.0708497\pi\) | ||||
−0.975331 | + | 0.220748i | \(0.929150\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5501.96 | + | 3176.56i | 0.323754 | + | 0.186919i | 0.653065 | − | 0.757302i | \(-0.273483\pi\) |
−0.329311 | + | 0.944222i | \(0.606816\pi\) | |||||||
\(662\) | 33463.4 | + | 19320.1i | 1.96464 | + | 1.13429i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 19220.3i | 1.12333i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6875.53 | + | 11908.8i | 0.399133 | + | 0.691319i | ||||
\(668\) | −5050.61 | + | 8747.92i | −0.292536 | + | 0.506687i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2193.23 | + | 1266.26i | −0.126465 | + | 0.0730148i | ||||
\(671\) | −547.306 | −0.0314881 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20238.2 | −1.15918 | −0.579589 | − | 0.814909i | \(-0.696787\pi\) | ||||
−0.579589 | + | 0.814909i | \(0.696787\pi\) | |||||||
\(674\) | −2345.58 | + | 1354.22i | −0.134048 | + | 0.0773925i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −32089.7 | + | 55581.1i | −1.82577 | + | 3.16233i | ||||
\(677\) | 5658.37 | + | 9800.59i | 0.321224 | + | 0.556377i | 0.980741 | − | 0.195313i | \(-0.0625723\pi\) |
−0.659516 | + | 0.751690i | \(0.729239\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 1982.91i | − | 0.111825i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 14366.6 | + | 8294.55i | 0.806635 | + | 0.465711i | ||||
\(683\) | −14869.4 | − | 8584.87i | −0.833035 | − | 0.480953i | 0.0218557 | − | 0.999761i | \(-0.493043\pi\) |
−0.854891 | + | 0.518808i | \(0.826376\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1393.74i | − | 0.0777402i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −973.172 | − | 1685.58i | −0.0539271 | − | 0.0934044i | ||||
\(689\) | −14342.4 | + | 24841.8i | −0.793037 | + | 1.37358i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7238.59 | − | 4179.20i | 0.398508 | − | 0.230079i | −0.287332 | − | 0.957831i | \(-0.592768\pi\) |
0.685840 | + | 0.727752i | \(0.259435\pi\) | |||||||
\(692\) | −27926.3 | −1.53410 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 32114.4 | 1.75655 | ||||||||
\(695\) | 2528.29 | − | 1459.71i | 0.137990 | − | 0.0796688i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14916.6 | − | 25836.3i | 0.810627 | − | 1.40405i | ||||
\(698\) | −8187.41 | − | 14181.0i | −0.443980 | − | 0.768996i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 19235.8i | − | 1.03641i | −0.855256 | − | 0.518206i | \(-0.826600\pi\) | ||
0.855256 | − | 0.518206i | \(-0.173400\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3819.31 | + | 2205.08i | 0.204905 | + | 0.118302i | ||||
\(704\) | 30082.5 | + | 17368.1i | 1.61048 | + | 0.929810i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 10536.5i | − | 0.561680i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5160.17 | + | 8937.67i | 0.273334 | + | 0.473429i | 0.969714 | − | 0.244245i | \(-0.0785401\pi\) |
−0.696379 | + | 0.717674i | \(0.745207\pi\) | |||||||
\(710\) | −977.554 | + | 1693.17i | −0.0516718 | + | 0.0894981i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −518.001 | + | 299.068i | −0.0272653 | + | 0.0157416i | ||||
\(713\) | −8019.85 | −0.421242 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4514.02 | 0.236105 | ||||||||
\(716\) | −31529.0 | + | 18203.3i | −1.64566 | + | 0.950124i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3975.20 | − | 6885.25i | 0.206620 | − | 0.357876i | ||||
\(719\) | −11679.8 | − | 20229.9i | −0.605815 | − | 1.04930i | −0.991922 | − | 0.126849i | \(-0.959514\pi\) |
0.386107 | − | 0.922454i | \(-0.373820\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 20300.0i | − | 1.04638i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3050.62 | + | 1761.28i | 0.156596 | + | 0.0904106i | ||||
\(725\) | 16157.7 | + | 9328.63i | 0.827698 | + | 0.477871i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 22260.4i | − | 1.13561i | −0.823162 | − | 0.567807i | \(-0.807792\pi\) | ||
0.823162 | − | 0.567807i | \(-0.192208\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2638.00 | − | 4569.15i | −0.133749 | − | 0.231660i | ||||
\(731\) | 8863.48 | − | 15352.0i | 0.448464 | − | 0.776763i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9047.84 | + | 5223.77i | −0.455920 | + | 0.263226i | −0.710327 | − | 0.703872i | \(-0.751453\pi\) |
0.254407 | + | 0.967097i | \(0.418120\pi\) | |||||||
\(734\) | 7618.58 | 0.383116 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18166.9 | −0.909840 | ||||||||
\(737\) | 15938.2 | − | 9201.95i | 0.796598 | − | 0.459916i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6595.44 | + | 11423.6i | −0.328304 | + | 0.568640i | −0.982176 | − | 0.187966i | \(-0.939811\pi\) |
0.653871 | + | 0.756606i | \(0.273144\pi\) | |||||||
\(740\) | −713.895 | − | 1236.50i | −0.0354639 | − | 0.0614253i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35382.2i | 1.74703i | 0.486795 | + | 0.873517i | \(0.338166\pi\) | ||||
−0.486795 | + | 0.873517i | \(0.661834\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1924.59 | + | 1111.16i | 0.0946463 | + | 0.0546441i | ||||
\(746\) | −1164.38 | − | 672.258i | −0.0571463 | − | 0.0329934i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 40295.6i | 1.96973i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14692.3 | + | 25447.8i | 0.713888 | + | 1.23649i | 0.963387 | + | 0.268116i | \(0.0864010\pi\) |
−0.249498 | + | 0.968375i | \(0.580266\pi\) | |||||||
\(752\) | 594.020 | − | 1028.87i | 0.0288054 | − | 0.0498925i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −50770.8 | + | 29312.5i | −2.45221 | + | 1.41578i | ||||
\(755\) | 664.470 | 0.0320299 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11329.1 | 0.543939 | 0.271969 | − | 0.962306i | \(-0.412325\pi\) | ||||
0.271969 | + | 0.962306i | \(0.412325\pi\) | |||||||
\(758\) | 28994.0 | − | 16739.7i | 1.38932 | − | 0.802127i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 620.557 | − | 1074.84i | 0.0296184 | − | 0.0513005i | ||||
\(761\) | 12696.5 | + | 21990.9i | 0.604792 | + | 1.04753i | 0.992084 | + | 0.125574i | \(0.0400772\pi\) |
−0.387292 | + | 0.921957i | \(0.626589\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 57499.9i | 2.72287i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −49065.8 | − | 28328.2i | −2.31439 | − | 1.33621i | ||||
\(767\) | −65346.7 | − | 37727.9i | −3.07631 | − | 1.77611i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 18120.8i | − | 0.849744i | −0.905253 | − | 0.424872i | \(-0.860319\pi\) | ||
0.905253 | − | 0.424872i | \(-0.139681\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −25874.7 | − | 44816.3i | −1.20628 | − | 2.08934i | ||||
\(773\) | 8673.05 | − | 15022.2i | 0.403555 | − | 0.698978i | −0.590597 | − | 0.806967i | \(-0.701108\pi\) |
0.994152 | + | 0.107989i | \(0.0344410\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9423.42 | + | 5440.61i | −0.436773 | + | 0.252171i | ||||
\(776\) | 24161.3 | 1.11771 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −36054.7 | −1.66147 | ||||||||
\(779\) | 16171.1 | − | 9336.37i | 0.743759 | − | 0.429410i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7103.91 | − | 12304.3i | 0.325477 | − | 0.563743i | ||||
\(782\) | −15997.4 | − | 27708.3i | −0.731542 | − | 1.26707i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1668.22i | 0.0758488i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1801.52 | − | 1040.11i | −0.0815977 | − | 0.0471104i | 0.458646 | − | 0.888619i | \(-0.348335\pi\) |
−0.540244 | + | 0.841509i | \(0.681668\pi\) | |||||||
\(788\) | −17540.2 | − | 10126.8i | −0.792949 | − | 0.457810i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 2364.83i | − | 0.106502i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 564.014 | + | 976.901i | 0.0252569 | + | 0.0437463i | ||||
\(794\) | 28284.7 | − | 48990.5i | 1.26421 | − | 2.18968i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1878.73 | + | 1084.68i | −0.0836554 | + | 0.0482984i | ||||
\(797\) | −39737.3 | −1.76608 | −0.883041 | − | 0.469297i | \(-0.844507\pi\) | ||||
−0.883041 | + | 0.469297i | \(0.844507\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10820.5 | 0.479099 | ||||||||
\(800\) | −21346.4 | + | 12324.3i | −0.943385 | + | 0.544664i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18130.2 | − | 31402.5i | 0.798255 | − | 1.38262i | ||||
\(803\) | 19170.4 | + | 33204.1i | 0.842477 | + | 1.45921i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 34191.1i | − | 1.49421i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11421.9 | − | 6594.45i | −0.497305 | − | 0.287119i | ||||
\(809\) | 9713.37 | + | 5608.02i | 0.422131 | + | 0.243717i | 0.695989 | − | 0.718053i | \(-0.254966\pi\) |
−0.273858 | + | 0.961770i | \(0.588300\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14792.0i | 0.640465i | 0.947339 | + | 0.320232i | \(0.103761\pi\) | ||||
−0.947339 | + | 0.320232i | \(0.896239\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8520.57 | + | 14758.1i | 0.366887 | + | 0.635467i | ||||
\(815\) | −283.411 | + | 490.882i | −0.0121809 | + | 0.0210980i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9608.88 | − | 5547.69i | 0.411471 | − | 0.237563i | ||||
\(818\) | −39511.2 | −1.68885 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6045.30 | −0.257453 | ||||||||
\(821\) | 28632.7 | − | 16531.1i | 1.21716 | − | 0.702726i | 0.252849 | − | 0.967506i | \(-0.418632\pi\) |
0.964309 | + | 0.264779i | \(0.0852992\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10045.4 | + | 17399.1i | −0.425467 | + | 0.736930i | −0.996464 | − | 0.0840220i | \(-0.973223\pi\) |
0.570997 | + | 0.820952i | \(0.306557\pi\) | |||||||
\(824\) | 13791.1 | + | 23886.9i | 0.583053 | + | 1.00988i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36882.5i | 1.55082i | 0.631458 | + | 0.775410i | \(0.282457\pi\) | ||||
−0.631458 | + | 0.775410i | \(0.717543\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32697.0 | + | 18877.6i | 1.36986 | + | 0.790888i | 0.990910 | − | 0.134530i | \(-0.0429524\pi\) |
0.378949 | + | 0.925418i | \(0.376286\pi\) | |||||||
\(830\) | −4730.78 | − | 2731.32i | −0.197841 | − | 0.114223i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 71593.5i | − | 2.98324i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −513.321 | − | 889.098i | −0.0212745 | − | 0.0368485i | ||||
\(836\) | −12610.6 | + | 21842.2i | −0.521707 | + | 0.903623i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15379.3 | − | 8879.25i | 0.633973 | − | 0.366025i | ||||
\(839\) | −44250.4 | −1.82085 | −0.910426 | − | 0.413672i | \(-0.864246\pi\) | ||||
−0.910426 | + | 0.413672i | \(0.864246\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1528.81 | 0.0626844 | ||||||||
\(842\) | −5653.43 | + | 3264.01i | −0.231390 | + | 0.133593i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −18321.1 | + | 31733.1i | −0.747201 | + | 1.29419i | ||||
\(845\) | −3261.45 | − | 5649.00i | −0.132778 | − | 0.229978i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 2857.44i | − | 0.115713i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −37594.3 | − | 21705.1i | −1.51703 | − | 0.875856i | ||||
\(851\) | −7134.65 | − | 4119.19i | −0.287394 | − | 0.165927i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 14952.2i | − | 0.600179i | −0.953911 | − | 0.300089i | \(-0.902983\pi\) | ||
0.953911 | − | 0.300089i | \(-0.0970165\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4317.66 | − | 7478.41i | −0.172400 | − | 0.298606i | ||||
\(857\) | −1224.76 | + | 2121.35i | −0.0488181 | + | 0.0845555i | −0.889402 | − | 0.457126i | \(-0.848879\pi\) |
0.840584 | + | 0.541682i | \(0.182212\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5751.97 | − | 3320.90i | 0.228469 | − | 0.131906i | −0.381397 | − | 0.924411i | \(-0.624557\pi\) |
0.609865 | + | 0.792505i | \(0.291223\pi\) | |||||||
\(860\) | −3592.13 | −0.142431 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −66951.0 | −2.64543 | ||||||||
\(863\) | −16339.2 | + | 9433.46i | −0.644489 | + | 0.372096i | −0.786342 | − | 0.617792i | \(-0.788027\pi\) |
0.141853 | + | 0.989888i | \(0.454694\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1419.15 | − | 2458.04i | 0.0557833 | − | 0.0966196i | ||||
\(866\) | 35891.1 | + | 62165.2i | 1.40835 | + | 2.43933i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17185.3i | 0.670851i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32849.6 | − | 18965.8i | −1.27792 | − | 0.737807i | ||||
\(872\) | 11660.5 | + | 6732.19i | 0.452837 | + | 0.261446i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 20025.7i | − | 0.775033i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5989.84 | − | 10374.7i | −0.230630 | − | 0.399463i | 0.727364 | − | 0.686252i | \(-0.240745\pi\) |
−0.957994 | + | 0.286789i | \(0.907412\pi\) | |||||||
\(878\) | −6858.23 | + | 11878.8i | −0.263615 | + | 0.456594i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −389.421 | + | 224.832i | −0.0149175 | + | 0.00861261i | ||||
\(881\) | 34504.0 | 1.31949 | 0.659743 | − | 0.751491i | \(-0.270665\pi\) | ||||
0.659743 | + | 0.751491i | \(0.270665\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8148.85 | −0.310567 | −0.155283 | − | 0.987870i | \(-0.549629\pi\) | ||||
−0.155283 | + | 0.987870i | \(0.549629\pi\) | |||||||
\(884\) | 71924.9 | − | 41525.8i | 2.73653 | − | 1.57994i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29053.2 | + | 50321.6i | −1.10165 | + | 1.90811i | ||||
\(887\) | −17477.6 | − | 30272.1i | −0.661602 | − | 1.14593i | −0.980195 | − | 0.198036i | \(-0.936544\pi\) |
0.318593 | − | 0.947892i | \(-0.396790\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 169.998i | − | 0.00640262i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −36396.4 | − | 21013.5i | −1.36619 | − | 0.788771i | ||||
\(893\) | 5865.22 | + | 3386.29i | 0.219790 | + | 0.126896i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3700.20i | − | 0.138194i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 243.466 | + | 421.696i | 0.00904741 | + | 0.0156706i | ||||
\(899\) | 6666.22 | − | 11546.2i | 0.247309 | − | 0.428352i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22538.4 | − | 13012.5i | 0.833365 | − | 0.481144i | ||||
\(902\) | 72152.7 | 2.66344 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18425.3 | 0.677894 | ||||||||
\(905\) | −310.051 | + | 179.008i | −0.0113883 | + | 0.00657505i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12494.5 | − | 21641.1i | 0.457412 | − | 0.792261i | −0.541411 | − | 0.840758i | \(-0.682110\pi\) |
0.998823 | + | 0.0484970i | \(0.0154431\pi\) | |||||||
\(908\) | 18872.2 | + | 32687.5i | 0.689752 | + | 1.19468i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41609.1i | 1.51325i | 0.653849 | + | 0.756625i | \(0.273153\pi\) | ||||
−0.653849 | + | 0.756625i | \(0.726847\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34378.7 | + | 19848.5i | 1.24619 | + | 0.719486i | ||||
\(914\) | −38293.2 | − | 22108.6i | −1.38580 | − | 0.800095i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13805.1i | 0.497964i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25496.0 | − | 44160.4i | −0.915164 | − | 1.58511i | −0.806661 | − | 0.591014i | \(-0.798728\pi\) |
−0.108502 | − | 0.994096i | \(-0.534605\pi\) | |||||||
\(920\) | −1159.23 | + | 2007.84i | −0.0415420 | + | 0.0719529i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2502.24 | + | 1444.67i | −0.0893782 | + | 0.0516025i | ||||
\(923\) | −29283.1 | −1.04428 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11177.7 | −0.397321 | ||||||||
\(926\) | 21942.0 | − | 12668.2i | 0.778682 | − | 0.449572i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 15100.6 | − | 26155.1i | 0.534162 | − | 0.925196i | ||||
\(929\) | 23746.5 | + | 41130.2i | 0.838642 | + | 1.45257i | 0.891031 | + | 0.453943i | \(0.149983\pi\) |
−0.0523888 | + | 0.998627i | \(0.516684\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 38603.9i | − | 1.35677i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21615.4 | + | 12479.7i | 0.757258 | + | 0.437203i | ||||
\(935\) | −3546.78 | − | 2047.73i | −0.124056 | − | 0.0716235i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6811.98i | 0.237500i | 0.992924 | + | 0.118750i | \(0.0378887\pi\) | ||||
−0.992924 | + | 0.118750i | \(0.962111\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1096.31 | − | 1898.87i | −0.0380401 | − | 0.0658874i | ||||
\(941\) | −16271.0 | + | 28182.2i | −0.563677 | + | 0.976318i | 0.433494 | + | 0.901156i | \(0.357280\pi\) |
−0.997171 | + | 0.0751612i | \(0.976053\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30208.3 | + | 17440.8i | −1.04318 | + | 0.602280i | ||||
\(944\) | 7516.54 | 0.259155 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 42873.3 | 1.47350 | ||||||||
\(947\) | −10119.9 | + | 5842.70i | −0.347256 | + | 0.200488i | −0.663476 | − | 0.748198i | \(-0.730920\pi\) |
0.316220 | + | 0.948686i | \(0.397586\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39511.3 | − | 68435.7i | 1.35152 | − | 2.34090i | ||||
\(950\) | −13585.3 | − | 23530.4i | −0.463963 | − | 0.803608i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 46457.5i | − | 1.57912i | −0.613671 | − | 0.789562i | \(-0.710308\pi\) | ||
0.613671 | − | 0.789562i | \(-0.289692\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5061.08 | − | 2922.01i | −0.171490 | − | 0.0990096i | ||||
\(956\) | 18714.6 | + | 10804.9i | 0.633130 | + | 0.365538i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 24732.8i | − | 0.834114i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11007.6 | − | 19065.8i | −0.369496 | − | 0.639986i | ||||
\(962\) | 17561.4 | − | 30417.2i | 0.588568 | − | 1.01943i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12942.3 | − | 7472.25i | 0.432411 | − | 0.249653i | ||||
\(965\) | 5259.57 | 0.175452 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27949.1 | −0.929455 | −0.464728 | − | 0.885454i | \(-0.653848\pi\) | ||||
−0.464728 | + | 0.885454i | \(0.653848\pi\) | |||||||
\(968\) | −6966.06 | + | 4021.86i | −0.231299 | + | 0.133541i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3433.47 | + | 5946.94i | −0.113652 | + | 0.196850i | ||||
\(971\) | 1609.85 | + | 2788.33i | 0.0532053 | + | 0.0921544i | 0.891401 | − | 0.453215i | \(-0.149723\pi\) |
−0.838196 | + | 0.545369i | \(0.816390\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 53064.9i | 1.74570i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −97.3141 | − | 56.1843i | −0.00319155 | − | 0.00184264i | ||||
\(977\) | 33258.6 | + | 19201.9i | 1.08909 | + | 0.628785i | 0.933333 | − | 0.359011i | \(-0.116886\pi\) |
0.155754 | + | 0.987796i | \(0.450219\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1235.38i | 0.0403297i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7948.19 | + | 13766.7i | 0.258286 | + | 0.447364i | ||||
\(983\) | 13709.1 | − | 23744.8i | 0.444814 | − | 0.770440i | −0.553226 | − | 0.833031i | \(-0.686603\pi\) |
0.998039 | + | 0.0625917i | \(0.0199366\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1782.71 | − | 1029.25i | 0.0576667 | − | 0.0332939i | ||||
\(986\) | 53189.1 | 1.71794 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 51982.4 | 1.67387 | ||||||||
\(989\) | −17949.8 | + | 10363.3i | −0.577120 | + | 0.333200i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21857.9 | + | 37859.1i | −0.700646 | + | 1.21355i | 0.267594 | + | 0.963532i | \(0.413771\pi\) |
−0.968240 | + | 0.250023i | \(0.919562\pi\) | |||||||
\(992\) | 8806.94 | + | 15254.1i | 0.281876 | + | 0.488223i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 220.484i | − | 0.00702495i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21930.8 | + | 12661.7i | 0.696644 | + | 0.402208i | 0.806096 | − | 0.591784i | \(-0.201576\pi\) |
−0.109452 | + | 0.993992i | \(0.534910\pi\) | |||||||
\(998\) | 38731.5 | + | 22361.7i | 1.22848 | + | 0.709264i | ||||
\(999\) | 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 | 441.4.p.c.80.2 | 16 | ||
3.2 | odd | 2 | inner | 441.4.p.c.80.7 | 16 | ||
7.2 | even | 3 | 63.4.p.a.26.7 | yes | 16 | ||
7.3 | odd | 6 | 441.4.c.a.440.4 | 16 | |||
7.4 | even | 3 | 441.4.c.a.440.3 | 16 | |||
7.5 | odd | 6 | inner | 441.4.p.c.215.7 | 16 | ||
7.6 | odd | 2 | 63.4.p.a.17.2 | ✓ | 16 | ||
21.2 | odd | 6 | 63.4.p.a.26.2 | yes | 16 | ||
21.5 | even | 6 | inner | 441.4.p.c.215.2 | 16 | ||
21.11 | odd | 6 | 441.4.c.a.440.14 | 16 | |||
21.17 | even | 6 | 441.4.c.a.440.13 | 16 | |||
21.20 | even | 2 | 63.4.p.a.17.7 | yes | 16 | ||
28.23 | odd | 6 | 1008.4.bt.a.593.5 | 16 | |||
28.27 | even | 2 | 1008.4.bt.a.17.4 | 16 | |||
84.23 | even | 6 | 1008.4.bt.a.593.4 | 16 | |||
84.83 | odd | 2 | 1008.4.bt.a.17.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.p.a.17.2 | ✓ | 16 | 7.6 | odd | 2 | ||
63.4.p.a.17.7 | yes | 16 | 21.20 | even | 2 | ||
63.4.p.a.26.2 | yes | 16 | 21.2 | odd | 6 | ||
63.4.p.a.26.7 | yes | 16 | 7.2 | even | 3 | ||
441.4.c.a.440.3 | 16 | 7.4 | even | 3 | |||
441.4.c.a.440.4 | 16 | 7.3 | odd | 6 | |||
441.4.c.a.440.13 | 16 | 21.17 | even | 6 | |||
441.4.c.a.440.14 | 16 | 21.11 | odd | 6 | |||
441.4.p.c.80.2 | 16 | 1.1 | even | 1 | trivial | ||
441.4.p.c.80.7 | 16 | 3.2 | odd | 2 | inner | ||
441.4.p.c.215.2 | 16 | 21.5 | even | 6 | inner | ||
441.4.p.c.215.7 | 16 | 7.5 | odd | 6 | inner | ||
1008.4.bt.a.17.4 | 16 | 28.27 | even | 2 | |||
1008.4.bt.a.17.5 | 16 | 84.83 | odd | 2 | |||
1008.4.bt.a.593.4 | 16 | 84.23 | even | 6 | |||
1008.4.bt.a.593.5 | 16 | 28.23 | odd | 6 |