Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [120,3,Mod(89,120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("120.89");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 120 = 2^{3} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 120.c (of order \(2\), degree \(1\), 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: | \(3.26976317232\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 34x^{10} + 305x^{8} + 616x^{6} + 305x^{4} + 34x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 89.1 | ||
Root | \(-0.220185i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 120.89 |
Dual form | 120.3.c.a.89.2 |
$q$-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 \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(41\) | \(61\) | \(97\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.72256 | − | 1.26002i | −0.907521 | − | 0.420007i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.689011 | + | 4.95230i | 0.137802 | + | 0.990460i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.735748i | − | 0.105107i | −0.998618 | − | 0.0525534i | \(-0.983264\pi\) | ||
0.998618 | − | 0.0525534i | \(-0.0167360\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.82469 | + | 6.86097i | 0.647188 | + | 0.762330i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.9451i | 0.995009i | 0.867461 | + | 0.497505i | \(0.165750\pi\) | ||||
−0.867461 | + | 0.497505i | \(0.834250\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 21.1901i | 1.63000i | 0.579458 | + | 0.815002i | \(0.303264\pi\) | ||||
−0.579458 | + | 0.815002i | \(0.696736\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.36412 | − | 14.3511i | 0.290942 | − | 0.956741i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.03488 | 0.413816 | 0.206908 | − | 0.978360i | \(-0.433660\pi\) | ||||
0.206908 | + | 0.978360i | \(0.433660\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 23.1529 | 1.21857 | 0.609287 | − | 0.792950i | \(-0.291456\pi\) | ||||
0.609287 | + | 0.792950i | \(0.291456\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.927058 | + | 2.00312i | −0.0441456 | + | 0.0953867i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −24.7483 | −1.07601 | −0.538006 | − | 0.842941i | \(-0.680822\pi\) | ||||
−0.538006 | + | 0.842941i | \(0.680822\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.0505 | + | 6.82438i | −0.962021 | + | 0.272975i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.21312 | − | 26.0187i | −0.267153 | − | 0.963654i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 32.3284i | − | 1.11477i | −0.830254 | − | 0.557386i | \(-0.811804\pi\) | ||
0.830254 | − | 0.557386i | \(-0.188196\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −34.9482 | −1.12736 | −0.563680 | − | 0.825993i | \(-0.690615\pi\) | ||||
−0.563680 | + | 0.825993i | \(0.690615\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13.7911 | − | 29.7987i | 0.417911 | − | 0.902992i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.64364 | − | 0.506939i | 0.104104 | − | 0.0144840i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 37.7818i | 1.02113i | 0.859839 | + | 0.510565i | \(0.170564\pi\) | ||||
−0.859839 | + | 0.510565i | \(0.829436\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 26.6999 | − | 57.6912i | 0.684613 | − | 1.47926i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 39.0848i | − | 0.953288i | −0.879096 | − | 0.476644i | \(-0.841853\pi\) | ||
0.879096 | − | 0.476644i | \(-0.158147\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 22.6804i | 0.527451i | 0.964598 | + | 0.263725i | \(0.0849513\pi\) | ||||
−0.964598 | + | 0.263725i | \(0.915049\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −29.9643 | + | 33.5729i | −0.665873 | + | 0.746065i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 39.1076 | 0.832076 | 0.416038 | − | 0.909347i | \(-0.363418\pi\) | ||||
0.416038 | + | 0.909347i | \(0.363418\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.4587 | 0.988953 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −19.1529 | − | 8.86409i | −0.375547 | − | 0.173806i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 60.9179 | 1.14939 | 0.574697 | − | 0.818366i | \(-0.305120\pi\) | ||||
0.574697 | + | 0.818366i | \(0.305120\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −54.2034 | + | 7.54130i | −0.985517 | + | 0.137115i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −63.0352 | − | 29.1731i | −1.10588 | − | 0.511809i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.79696i | 0.132152i | 0.997815 | + | 0.0660759i | \(0.0210480\pi\) | ||||
−0.997815 | + | 0.0660759i | \(0.978952\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.1529 | −0.182834 | −0.0914171 | − | 0.995813i | \(-0.529140\pi\) | ||||
−0.0914171 | + | 0.995813i | \(0.529140\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.04795 | − | 4.28551i | 0.0801262 | − | 0.0680239i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −104.939 | + | 14.6002i | −1.61445 | + | 0.224618i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 33.3485i | 0.497739i | 0.968537 | + | 0.248869i | \(0.0800590\pi\) | ||||
−0.968537 | + | 0.248869i | \(0.919941\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 67.3787 | + | 31.1833i | 0.976503 | + | 0.451933i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 96.9650i | 1.36570i | 0.730557 | + | 0.682852i | \(0.239261\pi\) | ||||
−0.730557 | + | 0.682852i | \(0.760739\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 134.535i | − | 1.84295i | −0.388436 | − | 0.921476i | \(-0.626984\pi\) | ||
0.388436 | − | 0.921476i | \(-0.373016\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 74.0779 | + | 11.7244i | 0.987706 | + | 0.156325i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.05284 | 0.104582 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 121.049 | 1.53227 | 0.766134 | − | 0.642681i | \(-0.222178\pi\) | ||||
0.766134 | + | 0.642681i | \(0.222178\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −13.1459 | + | 79.9261i | −0.162295 | + | 0.986742i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −90.2345 | −1.08716 | −0.543582 | − | 0.839356i | \(-0.682932\pi\) | ||||
−0.543582 | + | 0.839356i | \(0.682932\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.84711 | + | 34.8388i | 0.0570248 | + | 0.409868i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −40.7344 | + | 88.0160i | −0.468212 | + | 1.01168i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 53.1846i | − | 0.597579i | −0.954319 | − | 0.298790i | \(-0.903417\pi\) | ||
0.954319 | − | 0.298790i | \(-0.0965829\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.5905 | 0.171325 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 95.1486 | + | 44.0354i | 1.02310 | + | 0.473499i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.9526 | + | 114.660i | 0.167922 | + | 1.20695i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 115.001i | − | 1.18557i | −0.805359 | − | 0.592787i | \(-0.798028\pi\) | ||
0.805359 | − | 0.592787i | \(-0.201972\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −75.0940 | + | 63.7519i | −0.758526 | + | 0.643958i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 29.1802i | 0.288913i | 0.989511 | + | 0.144457i | \(0.0461434\pi\) | ||||
−0.989511 | + | 0.144457i | \(0.953857\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 89.9481i | 0.873283i | 0.899636 | + | 0.436641i | \(0.143832\pi\) | ||||
−0.899636 | + | 0.436641i | \(0.856168\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.5588 | − | 3.21090i | −0.100560 | − | 0.0305800i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 153.586 | 1.43538 | 0.717689 | − | 0.696363i | \(-0.245200\pi\) | ||||
0.717689 | + | 0.696363i | \(0.245200\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −59.5623 | −0.546444 | −0.273222 | − | 0.961951i | \(-0.588089\pi\) | ||||
−0.273222 | + | 0.961951i | \(0.588089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 47.6059 | − | 102.863i | 0.428882 | − | 0.926697i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.01796 | −0.00900851 | −0.00450426 | − | 0.999990i | \(-0.501434\pi\) | ||||
−0.00450426 | + | 0.999990i | \(0.501434\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.0518 | − | 122.561i | −0.148277 | − | 1.06575i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −145.384 | + | 123.426i | −1.24260 | + | 1.05492i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 5.17590i | − | 0.0434949i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.20473 | 0.00995643 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −49.2477 | + | 106.411i | −0.400388 | + | 0.865129i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −50.3674 | − | 114.403i | −0.402940 | − | 0.915227i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 209.731i | − | 1.65142i | −0.564091 | − | 0.825712i | \(-0.690773\pi\) | ||
0.564091 | − | 0.825712i | \(-0.309227\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 28.5778 | − | 61.7488i | 0.221533 | − | 0.478672i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 210.051i | − | 1.60344i | −0.597698 | − | 0.801721i | \(-0.703918\pi\) | ||
0.597698 | − | 0.801721i | \(-0.296082\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 17.0347i | − | 0.128080i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 123.882 | − | 53.6487i | 0.917646 | − | 0.397398i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 168.688 | 1.23130 | 0.615648 | − | 0.788021i | \(-0.288894\pi\) | ||||
0.615648 | + | 0.788021i | \(0.288894\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −129.251 | −0.929866 | −0.464933 | − | 0.885346i | \(-0.653922\pi\) | ||||
−0.464933 | + | 0.885346i | \(0.653922\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −106.473 | − | 49.2763i | −0.755126 | − | 0.349478i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −231.927 | −1.62187 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 160.100 | − | 22.2746i | 1.10414 | − | 0.153618i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −131.932 | − | 61.0590i | −0.897495 | − | 0.415367i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 83.9655i | 0.563527i | 0.959484 | + | 0.281763i | \(0.0909193\pi\) | ||||
−0.959484 | + | 0.281763i | \(0.909081\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.04922 | 0.0599286 | 0.0299643 | − | 0.999551i | \(-0.490461\pi\) | ||||
0.0299643 | + | 0.999551i | \(0.490461\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 40.9760 | + | 48.2661i | 0.267817 | + | 0.315465i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −24.0797 | − | 173.074i | −0.155353 | − | 1.11660i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 162.054i | 1.03219i | 0.856530 | + | 0.516097i | \(0.172616\pi\) | ||||
−0.856530 | + | 0.516097i | \(0.827384\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −165.853 | − | 76.7578i | −1.04310 | − | 0.482754i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.2085i | 0.113096i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 136.172i | − | 0.835411i | −0.908583 | − | 0.417705i | \(-0.862834\pi\) | ||
0.908583 | − | 0.417705i | \(-0.137166\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 157.074 | + | 47.7658i | 0.951966 | + | 0.289490i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 140.931 | 0.843898 | 0.421949 | − | 0.906620i | \(-0.361346\pi\) | ||||
0.421949 | + | 0.906620i | \(0.361346\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −280.018 | −1.65691 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 134.859 | + | 158.851i | 0.788646 | + | 0.928955i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 132.351 | 0.765032 | 0.382516 | − | 0.923949i | \(-0.375058\pi\) | ||||
0.382516 | + | 0.923949i | \(0.375058\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.02102 | + | 17.6951i | 0.0286916 | + | 0.101115i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.82433 | − | 21.2277i | 0.0555047 | − | 0.119931i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 92.2499i | 0.515363i | 0.966230 | + | 0.257681i | \(0.0829585\pi\) | ||||
−0.966230 | + | 0.257681i | \(0.917042\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 115.896 | 0.640311 | 0.320156 | − | 0.947365i | \(-0.396265\pi\) | ||||
0.320156 | + | 0.947365i | \(0.396265\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 30.3644 | + | 14.0529i | 0.165926 | + | 0.0767917i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −187.107 | + | 26.0321i | −1.01139 | + | 0.140714i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 76.9974i | 0.411751i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −19.1432 | + | 5.30704i | −0.101287 | + | 0.0280796i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 53.1183i | 0.278106i | 0.990285 | + | 0.139053i | \(0.0444059\pi\) | ||||
−0.990285 | + | 0.139053i | \(0.955594\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 271.315i | 1.40578i | 0.711299 | + | 0.702890i | \(0.248107\pi\) | ||||
−0.711299 | + | 0.702890i | \(0.751893\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 304.101 | + | 92.4760i | 1.55949 | + | 0.474236i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −64.3941 | −0.326873 | −0.163437 | − | 0.986554i | \(-0.552258\pi\) | ||||
−0.163437 | + | 0.986554i | \(0.552258\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 72.0308 | 0.361964 | 0.180982 | − | 0.983486i | \(-0.442072\pi\) | ||||
0.180982 | + | 0.983486i | \(0.442072\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 42.0198 | − | 90.7933i | 0.209054 | − | 0.451708i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −23.7855 | −0.117170 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 193.560 | − | 26.9299i | 0.944194 | − | 0.131365i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −144.151 | − | 169.797i | −0.696382 | − | 0.820276i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 253.411i | 1.21249i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 108.583 | 0.514613 | 0.257307 | − | 0.966330i | \(-0.417165\pi\) | ||||
0.257307 | + | 0.966330i | \(0.417165\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 122.178 | − | 263.993i | 0.573605 | − | 1.23940i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −112.320 | + | 15.6270i | −0.522419 | + | 0.0726839i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.7130i | 0.118493i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −169.518 | + | 366.281i | −0.774053 | + | 1.67252i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 149.069i | 0.674522i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 83.6192i | − | 0.374974i | −0.982267 | − | 0.187487i | \(-0.939966\pi\) | ||
0.982267 | − | 0.187487i | \(-0.0600342\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −186.909 | − | 125.260i | −0.830706 | − | 0.556712i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 51.6591 | 0.227573 | 0.113787 | − | 0.993505i | \(-0.463702\pi\) | ||||
0.113787 | + | 0.993505i | \(0.463702\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −280.974 | −1.22696 | −0.613480 | − | 0.789710i | \(-0.710231\pi\) | ||||
−0.613480 | + | 0.789710i | \(0.710231\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −21.9244 | − | 10.1467i | −0.0949106 | − | 0.0439253i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −169.192 | −0.726148 | −0.363074 | − | 0.931760i | \(-0.618273\pi\) | ||||
−0.363074 | + | 0.931760i | \(0.618273\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 26.9455 | + | 193.672i | 0.114662 | + | 0.824137i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −329.564 | − | 152.525i | −1.39057 | − | 0.643564i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.12039i | 0.00468782i | 0.999997 | + | 0.00234391i | \(0.000746090\pi\) | ||||
−0.999997 | + | 0.00234391i | \(0.999254\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 153.254 | 0.635908 | 0.317954 | − | 0.948106i | \(-0.397004\pi\) | ||||
0.317954 | + | 0.948106i | \(0.397004\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 136.499 | − | 201.040i | 0.561725 | − | 0.827324i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 33.3886 | + | 239.982i | 0.136280 | + | 0.979518i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 490.611i | 1.98628i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 245.669 | + | 113.697i | 0.986623 | + | 0.456616i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 126.692i | − | 0.504751i | −0.967629 | − | 0.252375i | \(-0.918788\pi\) | ||
0.967629 | − | 0.252375i | \(-0.0812118\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 270.872i | − | 1.07064i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 30.7011 | − | 100.958i | 0.120396 | − | 0.395915i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 396.692 | 1.54355 | 0.771774 | − | 0.635897i | \(-0.219370\pi\) | ||||
0.771774 | + | 0.635897i | \(0.219370\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27.7979 | 0.107328 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 221.804 | − | 188.303i | 0.849824 | − | 0.721467i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 394.431 | 1.49974 | 0.749868 | − | 0.661587i | \(-0.230117\pi\) | ||||
0.749868 | + | 0.661587i | \(0.230117\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 41.9731 | + | 301.684i | 0.158389 | + | 1.13843i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −67.0137 | + | 144.798i | −0.250987 | + | 0.542316i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 104.802i | − | 0.389597i | −0.980843 | − | 0.194798i | \(-0.937595\pi\) | ||
0.980843 | − | 0.194798i | \(-0.0624053\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −335.355 | −1.23747 | −0.618736 | − | 0.785599i | \(-0.712355\pi\) | ||||
−0.618736 | + | 0.785599i | \(0.712355\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −42.4462 | − | 19.6444i | −0.155481 | − | 0.0719576i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −74.6935 | − | 263.235i | −0.271613 | − | 0.957220i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 167.790i | − | 0.605739i | −0.953032 | − | 0.302870i | \(-0.902055\pi\) | ||
0.953032 | − | 0.302870i | \(-0.0979447\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −203.562 | − | 239.778i | −0.729614 | − | 0.859421i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 99.4601i | − | 0.353950i | −0.984215 | − | 0.176975i | \(-0.943369\pi\) | ||
0.984215 | − | 0.176975i | \(-0.0566312\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 487.022i | 1.72093i | 0.509512 | + | 0.860464i | \(0.329826\pi\) | ||||
−0.509512 | + | 0.860464i | \(0.670174\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 101.042 | − | 332.270i | 0.354534 | − | 1.16586i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −28.7566 | −0.100197 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −239.511 | −0.828756 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −144.903 | + | 313.097i | −0.497950 | + | 1.07593i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −343.107 | −1.17101 | −0.585507 | − | 0.810667i | \(-0.699105\pi\) | ||||
−0.585507 | + | 0.810667i | \(0.699105\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −38.6129 | + | 5.37219i | −0.130891 | + | 0.0182108i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 284.777 | − | 78.9484i | 0.958845 | − | 0.265819i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 524.417i | − | 1.75390i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.6870 | 0.0554387 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 36.7677 | − | 79.4450i | 0.121346 | − | 0.262195i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.68447 | − | 55.2325i | −0.0251950 | − | 0.181090i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 364.627i | − | 1.18771i | −0.804573 | − | 0.593854i | \(-0.797606\pi\) | ||
0.804573 | − | 0.593854i | \(-0.202394\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 113.337 | − | 244.889i | 0.366785 | − | 0.792522i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 121.963i | 0.392164i | 0.980587 | + | 0.196082i | \(0.0628219\pi\) | ||||
−0.980587 | + | 0.196082i | \(0.937178\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 94.8060i | 0.302895i | 0.988465 | + | 0.151447i | \(0.0483934\pi\) | ||||
−0.988465 | + | 0.151447i | \(0.951607\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 24.7012 | + | 22.0462i | 0.0784165 | + | 0.0699879i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −511.282 | −1.61288 | −0.806438 | − | 0.591318i | \(-0.798608\pi\) | ||||
−0.806438 | + | 0.591318i | \(0.798608\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 353.837 | 1.10921 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −418.146 | − | 193.521i | −1.30264 | − | 0.602869i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 162.878 | 0.504265 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −144.609 | − | 509.632i | −0.444951 | − | 1.56810i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 162.162 | + | 75.0498i | 0.495909 | + | 0.229510i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 28.7733i | − | 0.0874569i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −182.682 | −0.551909 | −0.275954 | − | 0.961171i | \(-0.588994\pi\) | ||||
−0.275954 | + | 0.961171i | \(0.588994\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −259.220 | + | 220.067i | −0.778438 | + | 0.660863i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −165.152 | + | 22.9775i | −0.492990 | + | 0.0685895i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 89.0617i | 0.264278i | 0.991231 | + | 0.132139i | \(0.0421845\pi\) | ||||
−0.991231 | + | 0.132139i | \(0.957815\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.77147 | + | 1.28265i | 0.00817541 | + | 0.00378364i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 382.511i | − | 1.12173i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 71.7050i | − | 0.209053i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −108.005 | + | 355.165i | −0.313057 | + | 1.02946i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.7180 | 0.0510605 | 0.0255303 | − | 0.999674i | \(-0.491873\pi\) | ||||
0.0255303 | + | 0.999674i | \(0.491873\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 229.114 | 0.656488 | 0.328244 | − | 0.944593i | \(-0.393543\pi\) | ||||
0.328244 | + | 0.944593i | \(0.393543\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 551.337 | − | 152.846i | 1.57076 | − | 0.435460i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −183.760 | −0.520566 | −0.260283 | − | 0.965532i | \(-0.583816\pi\) | ||||
−0.260283 | + | 0.965532i | \(0.583816\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −480.199 | + | 66.8099i | −1.35267 | + | 0.188197i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.52174 | + | 14.0917i | −0.0182682 | + | 0.0394726i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 537.837i | 1.49815i | 0.662484 | + | 0.749076i | \(0.269502\pi\) | ||||
−0.662484 | + | 0.749076i | \(0.730498\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 175.056 | 0.484921 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.27995 | − | 1.51798i | −0.00903567 | − | 0.00418177i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 666.260 | − | 92.6964i | 1.82537 | − | 0.253963i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 153.740i | − | 0.418909i | −0.977818 | − | 0.209455i | \(-0.932831\pi\) | ||
0.977818 | − | 0.209455i | \(-0.0671689\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 268.160 | − | 227.657i | 0.726721 | − | 0.616957i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 44.8202i | − | 0.120809i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 211.056i | 0.565833i | 0.959145 | + | 0.282917i | \(0.0913020\pi\) | ||||
−0.959145 | + | 0.282917i | \(0.908698\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.02209 | + | 374.934i | −0.0187256 | + | 0.999825i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 685.040 | 1.81708 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 699.345 | 1.84524 | 0.922618 | − | 0.385715i | \(-0.126045\pi\) | ||||
0.922618 | + | 0.385715i | \(0.126045\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −264.265 | + | 571.006i | −0.693610 | + | 1.49870i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −186.008 | −0.485662 | −0.242831 | − | 0.970069i | \(-0.578076\pi\) | ||||
−0.242831 | + | 0.970069i | \(0.578076\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.54850 | + | 39.8801i | 0.0144117 | + | 0.103585i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −155.609 | + | 132.106i | −0.402092 | + | 0.341360i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 288.194i | 0.740858i | 0.928861 | + | 0.370429i | \(0.120789\pi\) | ||||
−0.928861 | + | 0.370429i | \(0.879211\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −174.101 | −0.445271 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −264.669 | + | 571.877i | −0.673457 | + | 1.45516i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 83.4043 | + | 599.472i | 0.211150 | + | 1.51765i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 64.3054i | − | 0.161978i | −0.996715 | − | 0.0809892i | \(-0.974192\pi\) | ||
0.996715 | − | 0.0809892i | \(-0.0258079\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −21.4641 | + | 46.3780i | −0.0537947 | + | 0.116236i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 659.774i | 1.64532i | 0.568533 | + | 0.822661i | \(0.307511\pi\) | ||||
−0.568533 | + | 0.822661i | \(0.692489\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 740.553i | − | 1.83760i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −404.876 | − | 10.0324i | −0.999693 | − | 0.0247712i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −413.526 | −1.01603 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 217.863 | 0.532672 | 0.266336 | − | 0.963880i | \(-0.414187\pi\) | ||||
0.266336 | + | 0.963880i | \(0.414187\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −459.263 | − | 212.550i | −1.11743 | − | 0.517153i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.73660 | 0.0138901 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −62.1726 | − | 446.868i | −0.149814 | − | 1.07679i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 351.895 | + | 162.859i | 0.843872 | + | 0.390550i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 407.129i | − | 0.971668i | −0.874051 | − | 0.485834i | \(-0.838516\pi\) | ||
0.874051 | − | 0.485834i | \(-0.161484\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −69.1949 | −0.164359 | −0.0821793 | − | 0.996618i | \(-0.526188\pi\) | ||||
−0.0821793 | + | 0.996618i | \(0.526188\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 227.790 | + | 268.316i | 0.538510 | + | 0.634316i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −169.192 | + | 48.0087i | −0.398100 | + | 0.112962i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.20572i | 0.0192171i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 631.437 | + | 292.233i | 1.47188 | + | 0.681197i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 452.663i | 1.05026i | 0.851021 | + | 0.525132i | \(0.175984\pi\) | ||||
−0.851021 | + | 0.525132i | \(0.824016\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 226.323i | 0.522686i | 0.965246 | + | 0.261343i | \(0.0841654\pi\) | ||||
−0.965246 | + | 0.261343i | \(0.915835\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −463.948 | − | 141.085i | −1.06655 | − | 0.324333i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −572.994 | −1.31120 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 188.642 | 0.429709 | 0.214855 | − | 0.976646i | \(-0.431072\pi\) | ||||
0.214855 | + | 0.976646i | \(0.431072\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 282.257 | + | 332.474i | 0.640038 | + | 0.753908i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 499.705 | 1.12800 | 0.564001 | − | 0.825774i | \(-0.309261\pi\) | ||||
0.564001 | + | 0.825774i | \(0.309261\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 263.386 | − | 36.6448i | 0.591878 | − | 0.0823478i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 105.798 | − | 228.601i | 0.236685 | − | 0.511412i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 818.928i | − | 1.82389i | −0.410310 | − | 0.911946i | \(-0.634579\pi\) | ||
0.410310 | − | 0.911946i | \(-0.365421\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 427.787 | 0.948531 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.6371 | − | 11.4022i | −0.0543864 | − | 0.0251704i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.7421 | + | 77.2090i | 0.0236089 | + | 0.169690i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 311.602i | − | 0.681842i | −0.940092 | − | 0.340921i | \(-0.889261\pi\) | ||
0.940092 | − | 0.340921i | \(-0.110739\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −50.7434 | − | 183.038i | −0.110552 | − | 0.398776i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.18351i | 0.0155825i | 0.999970 | + | 0.00779123i | \(0.00248005\pi\) | ||||
−0.999970 | + | 0.00779123i | \(0.997520\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 557.563i | − | 1.20424i | −0.798406 | − | 0.602120i | \(-0.794323\pi\) | ||
0.798406 | − | 0.602120i | \(-0.205677\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −152.518 | + | 501.545i | −0.327996 | + | 1.07859i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −659.257 | −1.41168 | −0.705842 | − | 0.708369i | \(-0.749431\pi\) | ||||
−0.705842 | + | 0.708369i | \(0.749431\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.5361 | 0.0523157 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 204.192 | − | 441.203i | 0.433529 | − | 0.936738i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −248.239 | −0.524818 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −556.839 | + | 158.004i | −1.17229 | + | 0.332640i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 354.828 | + | 417.956i | 0.743875 | + | 0.876218i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 30.3870i | − | 0.0634384i | −0.999497 | − | 0.0317192i | \(-0.989902\pi\) | ||
0.999497 | − | 0.0317192i | \(-0.0100982\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −800.598 | −1.66445 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 22.9431 | − | 49.5738i | 0.0475012 | − | 0.102637i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 569.518 | − | 79.2368i | 1.17426 | − | 0.163375i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 26.5618i | − | 0.0545416i | −0.999628 | − | 0.0272708i | \(-0.991318\pi\) | ||
0.999628 | − | 0.0272708i | \(-0.00868164\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −171.580 | + | 370.737i | −0.350878 | + | 0.758153i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19.3354i | − | 0.0393796i | −0.999806 | − | 0.0196898i | \(-0.993732\pi\) | ||
0.999806 | − | 0.0196898i | \(-0.00626786\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 227.426i | − | 0.461311i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −367.459 | − | 327.962i | −0.742341 | − | 0.662550i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 71.3418 | 0.143545 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 313.190 | 0.627635 | 0.313817 | − | 0.949483i | \(-0.398392\pi\) | ||||
0.313817 | + | 0.949483i | \(0.398392\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −383.693 | − | 177.576i | −0.765855 | − | 0.354443i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 551.684 | 1.09679 | 0.548394 | − | 0.836220i | \(-0.315240\pi\) | ||||
0.548394 | + | 0.836220i | \(0.315240\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −144.509 | + | 20.1055i | −0.286157 | + | 0.0398129i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 762.368 | + | 352.829i | 1.50368 | + | 0.695915i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 567.057i | − | 1.11406i | −0.830492 | − | 0.557031i | \(-0.811941\pi\) | ||
0.830492 | − | 0.557031i | \(-0.188059\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −98.9842 | −0.193707 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −167.005 | − | 602.407i | −0.325545 | − | 1.17428i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −445.450 | + | 61.9753i | −0.864951 | + | 0.120340i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 428.036i | 0.827923i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −360.333 | − | 166.764i | −0.694283 | − | 0.321319i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 740.223i | − | 1.42077i | −0.703811 | − | 0.710387i | \(-0.748520\pi\) | ||
0.703811 | − | 0.710387i | \(-0.251480\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.11805i | 0.00404981i | 0.999998 | + | 0.00202491i | \(0.000644548\pi\) | ||||
−0.999998 | + | 0.00202491i | \(0.999355\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.62619 | − | 54.5027i | 0.0164308 | − | 0.103815i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −245.856 | −0.466520 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 83.4771 | 0.157802 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −53.4947 | + | 45.4149i | −0.100743 | + | 0.0855271i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 828.210 | 1.55386 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 105.822 | + | 760.602i | 0.197798 | + | 1.42169i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 116.237 | − | 251.156i | 0.216456 | − | 0.467702i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 530.385i | 0.984017i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.61681 | 0.0122307 | 0.00611535 | − | 0.999981i | \(-0.498053\pi\) | ||||
0.00611535 | + | 0.999981i | \(0.498053\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −315.535 | − | 146.032i | −0.581096 | − | 0.268935i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −41.0391 | − | 294.971i | −0.0753011 | − | 0.541230i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 230.092i | 0.420644i | 0.977632 | + | 0.210322i | \(0.0674512\pi\) | ||||
−0.977632 | + | 0.210322i | \(0.932549\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −64.9622 | − | 76.5197i | −0.118328 | − | 0.139380i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 748.495i | − | 1.35843i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 89.0617i | − | 0.161052i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 542.211 | + | 164.885i | 0.976957 | + | 0.297089i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −529.620 | −0.950844 | −0.475422 | − | 0.879758i | \(-0.657705\pi\) | ||||
−0.475422 | + | 0.879758i | \(0.657705\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −480.598 | −0.859747 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 97.0184 | − | 209.630i | 0.172938 | − | 0.373673i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 131.530 | 0.233623 | 0.116812 | − | 0.993154i | \(-0.462733\pi\) | ||||
0.116812 | + | 0.993154i | \(0.462733\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.701387 | − | 5.04125i | −0.00124139 | − | 0.00892257i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 58.8055 | + | 9.67206i | 0.103713 | + | 0.0170583i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 172.534i | 0.303224i | 0.988440 | + | 0.151612i | \(0.0484464\pi\) | ||||
−0.988440 | + | 0.151612i | \(0.951554\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 197.935 | 0.346646 | 0.173323 | − | 0.984865i | \(-0.444550\pi\) | ||||
0.173323 | + | 0.984865i | \(0.444550\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 66.9302 | − | 144.618i | 0.116807 | − | 0.252387i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 595.209 | − | 168.892i | 1.03515 | − | 0.293724i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 865.374i | − | 1.49978i | −0.661562 | − | 0.749891i | \(-0.730106\pi\) | ||
0.661562 | − | 0.749891i | \(-0.269894\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 341.863 | − | 738.673i | 0.590437 | − | 1.27577i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 66.3899i | 0.114268i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 666.753i | 1.14366i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −711.412 | − | 634.945i | −1.21609 | − | 1.08538i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.8886 | −0.0526211 | −0.0263105 | − | 0.999654i | \(-0.508376\pi\) | ||||
−0.0263105 | + | 0.999654i | \(0.508376\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −809.151 | −1.37377 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 175.317 | + | 81.1379i | 0.296644 | + | 0.137289i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −511.286 | −0.862202 | −0.431101 | − | 0.902304i | \(-0.641875\pi\) | ||||
−0.431101 | + | 0.902304i | \(0.641875\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 25.6326 | − | 3.56625i | 0.0430800 | − | 0.00599370i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −196.108 | − | 90.7603i | −0.328490 | − | 0.152027i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 514.866i | 0.859543i | 0.902938 | + | 0.429772i | \(0.141406\pi\) | ||||
−0.902938 | + | 0.429772i | \(0.858594\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 853.532 | 1.42019 | 0.710093 | − | 0.704107i | \(-0.248653\pi\) | ||||
0.710093 | + | 0.704107i | \(0.248653\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −228.803 | + | 194.245i | −0.379441 | + | 0.322131i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.830071 | + | 5.96618i | 0.00137202 | + | 0.00986145i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 88.0713i | 0.145093i | 0.997365 | + | 0.0725464i | \(0.0231125\pi\) | ||||
−0.997365 | + | 0.0725464i | \(0.976887\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 64.7576 | + | 29.9703i | 0.106334 | + | 0.0492123i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 828.691i | 1.35629i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 403.346i | 0.657987i | 0.944332 | + | 0.328994i | \(0.106709\pi\) | ||||
−0.944332 | + | 0.328994i | \(0.893291\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −560.911 | − | 170.571i | −0.912050 | − | 0.277351i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −365.738 | −0.592769 | −0.296384 | − | 0.955069i | \(-0.595781\pi\) | ||||
−0.296384 | + | 0.955069i | \(0.595781\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −399.495 | −0.645389 | −0.322694 | − | 0.946503i | \(-0.604589\pi\) | ||||
−0.322694 | + | 0.946503i | \(0.604589\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 178.512 | + | 643.917i | 0.287460 | + | 1.03690i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −39.1304 | −0.0628097 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 531.856 | − | 328.260i | 0.850969 | − | 0.525216i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 319.303 | − | 689.927i | 0.509255 | − | 1.10036i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 265.790i | 0.422560i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −715.762 | −1.13433 | −0.567165 | − | 0.823604i | \(-0.691960\pi\) | ||||
−0.567165 | + | 0.823604i | \(0.691960\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −295.625 | − | 136.817i | −0.467022 | − | 0.216141i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1038.65 | − | 144.507i | 1.63567 | − | 0.227570i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1026.84i | 1.61200i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −665.274 | + | 564.791i | −1.04112 | + | 0.883867i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 627.158i | 0.978406i | 0.872170 | + | 0.489203i | \(0.162712\pi\) | ||||
−0.872170 | + | 0.489203i | \(0.837288\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 802.039i | 1.24734i | 0.781688 | + | 0.623669i | \(0.214359\pi\) | ||||
−0.781688 | + | 0.623669i | \(0.785641\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 325.489 | + | 98.9800i | 0.504634 | + | 0.153457i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.9275 | 0.0307998 | 0.0153999 | − | 0.999881i | \(-0.495098\pi\) | ||||
0.0153999 | + | 0.999881i | \(0.495098\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −85.3385 | −0.131492 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32.3990 | − | 70.0054i | 0.0497680 | − | 0.107535i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 78.4638 | 0.120159 | 0.0600795 | − | 0.998194i | \(-0.480865\pi\) | ||||
0.0600795 | + | 0.998194i | \(0.480865\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1040.23 | − | 144.727i | 1.58815 | − | 0.220958i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 923.044 | − | 783.628i | 1.40494 | − | 1.19274i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 371.793i | 0.564178i | 0.959388 | + | 0.282089i | \(0.0910274\pi\) | ||||
−0.959388 | + | 0.282089i | \(0.908973\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 782.868 | 1.18437 | 0.592185 | − | 0.805802i | \(-0.298266\pi\) | ||||
0.592185 | + | 0.805802i | \(0.298266\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 187.831 | − | 405.851i | 0.283304 | − | 0.612143i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 84.3609 | − | 11.7371i | 0.126859 | − | 0.0176498i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 800.071i | 1.19951i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −105.362 | + | 227.658i | −0.157492 | + | 0.340297i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 122.070i | − | 0.181922i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 221.323i | − | 0.328860i | −0.986389 | − | 0.164430i | \(-0.947421\pi\) | ||
0.986389 | − | 0.164430i | \(-0.0525785\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 351.041 | + | 576.537i | 0.520060 | + | 0.854130i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −576.855 | −0.852076 | −0.426038 | − | 0.904705i | \(-0.640091\pi\) | ||||
−0.426038 | + | 0.904705i | \(0.640091\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −84.6116 | −0.124612 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −140.645 | − | 65.0916i | −0.206527 | − | 0.0955824i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1272.02 | −1.86239 | −0.931197 | − | 0.364516i | \(-0.881234\pi\) | ||||
−0.931197 | + | 0.364516i | \(0.881234\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 116.228 | + | 835.392i | 0.169675 | + | 1.21955i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 764.969 | + | 354.033i | 1.11349 | + | 0.515332i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1290.85i | 1.87352i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.61487 | 0.00233701 | 0.00116851 | − | 0.999999i | \(-0.499628\pi\) | ||||
0.00116851 | + | 0.999999i | \(0.499628\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 46.9053 | + | 55.2503i | 0.0676844 | + | 0.0797263i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −89.0556 | − | 640.091i | −0.128138 | − | 0.920995i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 274.957i | − | 0.394486i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 460.637 | + | 213.186i | 0.658994 | + | 0.304987i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 550.235i | − | 0.784929i | −0.919767 | − | 0.392465i | \(-0.871623\pi\) | ||
0.919767 | − | 0.392465i | \(-0.128377\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 874.758i | 1.24432i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 170.670 | − | 561.237i | 0.242085 | − | 0.796081i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21.4693 | 0.0303668 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −430.539 | −0.607249 | −0.303624 | − | 0.952792i | \(-0.598197\pi\) | ||||
−0.303624 | + | 0.952792i | \(0.598197\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 705.075 | + | 830.515i | 0.991666 | + | 1.16809i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 864.907 | 1.21305 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −159.801 | − | 1148.57i | −0.223497 | − | 1.60640i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.41171 | − | 3.05033i | 0.00196892 | − | 0.00425429i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 460.561i | − | 0.640558i | −0.947323 | − | 0.320279i | \(-0.896223\pi\) | ||
0.947323 | − | 0.320279i | \(-0.103777\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 66.1792 | 0.0917880 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −417.243 | − | 193.103i | −0.577100 | − | 0.267086i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 220.621 | + | 777.514i | 0.304305 | + | 1.07243i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 413.275i | − | 0.568467i | −0.958755 | − | 0.284233i | \(-0.908261\pi\) | ||
0.958755 | − | 0.284233i | \(-0.0917390\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −624.942 | + | 375.352i | −0.857259 | + | 0.514886i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 159.554i | 0.218268i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 307.003i | − | 0.418831i | −0.977827 | − | 0.209416i | \(-0.932844\pi\) | ||
0.977827 | − | 0.209416i | \(-0.0671562\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 211.480 | − | 695.436i | 0.287727 | − | 0.946171i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −365.003 | −0.495255 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −988.511 | −1.33763 | −0.668817 | − | 0.743427i | \(-0.733199\pi\) | ||||
−0.668817 | + | 0.743427i | \(0.733199\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 618.180 | − | 1335.72i | 0.834251 | − | 1.80259i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −652.187 | −0.877775 | −0.438887 | − | 0.898542i | \(-0.644627\pi\) | ||||
−0.438887 | + | 0.898542i | \(0.644627\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −415.822 | + | 57.8532i | −0.558151 | + | 0.0776552i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −525.589 | − | 619.097i | −0.703599 | − | 0.828777i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 113.000i | − | 0.150868i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 554.876 | 0.738850 | 0.369425 | − | 0.929261i | \(-0.379555\pi\) | ||||
0.369425 | + | 0.929261i | \(0.379555\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −159.635 | + | 344.928i | −0.211999 | + | 0.458072i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.23501 | + | 44.8144i | 0.00825829 | + | 0.0593569i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 547.156i | 0.722795i | 0.932412 | + | 0.361397i | \(0.117700\pi\) | ||||
−0.932412 | + | 0.361397i | \(0.882300\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −341.305 | + | 737.467i | −0.449677 | + | 0.971630i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1361.34i | − | 1.78888i | −0.447184 | − | 0.894442i | \(-0.647573\pi\) | ||
0.447184 | − | 0.894442i | \(-0.352427\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.8229i | 0.0574350i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −210.795 | + | 236.181i | −0.275549 | + | 0.308734i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −165.218 | −0.215408 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −396.180 | −0.515188 | −0.257594 | − | 0.966253i | \(-0.582930\pi\) | ||||
−0.257594 | + | 0.966253i | \(0.582930\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1080.02 | − | 499.840i | −1.40080 | − | 0.648301i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 664.286 | 0.859361 | 0.429681 | − | 0.902981i | \(-0.358626\pi\) | ||||
0.429681 | + | 0.902981i | \(0.358626\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 840.522 | − | 238.499i | 1.08454 | − | 0.307741i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −75.6815 | − | 35.0259i | −0.0974022 | − | 0.0450784i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 904.927i | − | 1.16165i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1061.29 | −1.35889 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −841.141 | + | 233.189i | −1.07425 | + | 0.297814i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −802.542 | + | 111.657i | −1.02235 | + | 0.142239i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 957.551i | − | 1.21671i | −0.793665 | − | 0.608355i | \(-0.791830\pi\) | ||
0.793665 | − | 0.608355i | \(-0.208170\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1073.86 | − | 496.991i | −1.36104 | − | 0.629900i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.748964i | 0.000946857i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 236.330i | − | 0.298021i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 265.853 | − | 874.240i | 0.334407 | − | 1.09967i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 643.860 | 0.807854 | 0.403927 | − | 0.914791i | \(-0.367645\pi\) | ||||
0.403927 | + | 0.914791i | \(0.367645\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 275.117 | 0.344326 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 364.898 | − | 309.784i | 0.455553 | − | 0.386746i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1472.50 | 1.83375 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −90.1739 | + | 12.5459i | −0.112017 | + | 0.0155849i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −132.052 | + | 285.329i | −0.163633 | + | 0.353567i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 675.342i | − | 0.834786i | −0.908726 | − | 0.417393i | \(-0.862944\pi\) | ||
0.908726 | − | 0.417393i | \(-0.137056\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 808.662 | 0.997117 | 0.498559 | − | 0.866856i | \(-0.333863\pi\) | ||||
0.498559 | + | 0.866856i | \(0.333863\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 913.025 | + | 422.554i | 1.12303 | + | 0.519747i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 674.364 | − | 93.8240i | 0.827441 | − | 0.115121i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 525.116i | 0.642737i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 90.8101 | + | 106.966i | 0.110879 | + | 0.130606i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1348.63i | 1.64267i | 0.570445 | + | 0.821336i | \(0.306771\pi\) | ||||
−0.570445 | + | 0.821336i | \(0.693229\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1433.75i | − | 1.74211i | −0.491188 | − | 0.871053i | \(-0.663437\pi\) | ||
0.491188 | − | 0.871053i | \(-0.336563\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −128.324 | + | 810.790i | −0.155545 | + | 0.982776i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.5276 | 0.0332861 | 0.0166431 | − | 0.999861i | \(-0.494702\pi\) | ||||
0.0166431 | + | 0.999861i | \(0.494702\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 374.884 | 0.452212 | 0.226106 | − | 0.974103i | \(-0.427400\pi\) | ||||
0.226106 | + | 0.974103i | \(0.427400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −211.419 | + | 456.818i | −0.254415 | + | 0.549721i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 340.901 | 0.409245 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 97.1030 | + | 697.932i | 0.116291 | + | 0.835847i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 252.085 | + | 909.304i | 0.301177 | + | 1.08639i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1173.68i | − | 1.39890i | −0.714681 | − | 0.699451i | \(-0.753428\pi\) | ||
0.714681 | − | 0.699451i | \(-0.246572\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −204.123 | −0.242715 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −125.322 | + | 270.786i | −0.148662 | + | 0.321217i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −192.936 | − | 1386.73i | −0.228326 | − | 1.64111i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 0.886377i | − | 0.00104649i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 613.659 | − | 1325.95i | 0.722802 | − | 1.56178i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 935.034i | − | 1.09875i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 112.279i | 0.131629i | 0.997832 | + | 0.0658143i | \(0.0209645\pi\) | ||||
−0.997832 | + | 0.0658143i | \(0.979036\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −693.760 | + | 777.310i | −0.811416 | + | 0.909134i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −619.631 | −0.723023 | −0.361511 | − | 0.932368i | \(-0.617739\pi\) | ||||
−0.361511 | + | 0.932368i | \(0.617739\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1227.29 | −1.42875 | −0.714373 | − | 0.699765i | \(-0.753288\pi\) | ||||
−0.714373 | + | 0.699765i | \(0.753288\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 78.2916 | + | 36.2339i | 0.0909310 | + | 0.0420835i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −975.318 | −1.13015 | −0.565074 | − | 0.825040i | \(-0.691152\pi\) | ||||
−0.565074 | + | 0.825040i | \(0.691152\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 91.1910 | + | 655.439i | 0.105423 | + | 0.757734i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 652.082 | + | 301.788i | 0.752113 | + | 0.348083i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1324.90i | 1.52462i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −706.656 | −0.811316 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 789.017 | − | 669.844i | 0.903799 | − | 0.767290i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −84.1720 | + | 37.0578i | −0.0961966 | + | 0.0423517i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 991.857i | − | 1.13097i | −0.824760 | − | 0.565483i | \(-0.808690\pi\) | ||
0.824760 | − | 0.565483i | \(-0.191310\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 934.131 | + | 432.322i | 1.06272 | + | 0.491834i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1024.25i | 1.16260i | 0.813690 | + | 0.581299i | \(0.197455\pi\) | ||||
−0.813690 | + | 0.581299i | \(0.802545\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1170.22i | − | 1.32527i | −0.748941 | − | 0.662637i | \(-0.769437\pi\) | ||
0.748941 | − | 0.662637i | \(-0.230563\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 111.895 | + | 34.0269i | 0.126435 | + | 0.0384485i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 540.358 | 0.609197 | 0.304599 | − | 0.952481i | \(-0.401478\pi\) | ||||
0.304599 | + | 0.952481i | \(0.401478\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −154.309 | −0.173576 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −874.800 | − | 143.883i | −0.981818 | − | 0.161485i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 905.453 | 1.01395 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −456.849 | + | 63.5612i | −0.510446 | + | 0.0710181i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −660.777 | + | 1427.76i | −0.736652 | + | 1.59170i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1129.82i | 1.25675i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 428.550 | 0.475638 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −45.4315 | − | 21.0260i | −0.0503118 | − | 0.0232846i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 79.8539 | + | 573.953i | 0.0882363 | + | 0.634202i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 682.738i | − | 0.752744i | −0.926469 | − | 0.376372i | \(-0.877172\pi\) | ||
0.926469 | − | 0.376372i | \(-0.122828\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −200.205 | + | 169.966i | −0.220247 | + | 0.186981i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1326.30i | − | 1.45587i | −0.685647 | − | 0.727934i | \(-0.740481\pi\) | ||
0.685647 | − | 0.727934i | \(-0.259519\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 987.626i | − | 1.08174i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −48.6726 | + | 160.056i | −0.0531941 | + | 0.174925i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −154.545 | −0.168533 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 688.107 | 0.748756 | 0.374378 | − | 0.927276i | \(-0.377856\pi\) | ||||
0.374378 | + | 0.927276i | \(0.377856\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −459.437 | + | 992.719i | −0.498846 | + | 1.07787i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2054.69 | −2.22610 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −257.837 | − | 908.672i | −0.278743 | − | 0.982348i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −617.132 | + | 523.920i | −0.665730 | + | 0.565178i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 637.084i | 0.685774i | 0.939377 | + | 0.342887i | \(0.111405\pi\) | ||||
−0.939377 | + | 0.342887i | \(0.888595\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1121.96 | 1.20511 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 153.676 | − | 332.052i | 0.164712 | − | 0.355897i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −381.314 | + | 53.0521i | −0.407823 | + | 0.0567402i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 358.254i | 0.382341i | 0.981557 | + | 0.191171i | \(0.0612284\pi\) | ||||
−0.981557 | + | 0.191171i | \(0.938772\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 119.458 | − | 258.115i | 0.127218 | − | 0.274883i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 124.973i | 0.132809i | 0.997793 | + | 0.0664043i | \(0.0211527\pi\) | ||||
−0.997793 | + | 0.0664043i | \(0.978847\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 967.282i | 1.02575i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −39.4719 | − | 91.1462i | −0.0417692 | − | 0.0964510i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −378.826 | −0.400027 | −0.200014 | − | 0.979793i | \(-0.564099\pi\) | ||||
−0.200014 | + | 0.979793i | \(0.564099\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2850.81 | 3.00402 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1392.00 | + | 644.226i | 1.46372 | + | 0.677419i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.82139 | 0.00715780 | 0.00357890 | − | 0.999994i | \(-0.498861\pi\) | ||||
0.00357890 | + | 0.999994i | \(0.498861\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −263.058 | + | 36.5991i | −0.275453 | + | 0.0383237i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −963.344 | − | 445.842i | −1.00663 | − | 0.465875i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 124.112i | − | 0.129418i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 260.374 | 0.270941 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 894.589 | + | 1053.75i | 0.928960 | + | 1.09423i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1343.63 | + | 186.939i | −1.39237 | + | 0.193719i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1193.53i | − | 1.23426i | −0.786861 | − | 0.617130i | \(-0.788295\pi\) | ||
0.786861 | − | 0.617130i | \(-0.211705\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −443.445 | − | 205.229i | −0.457631 | − | 0.211795i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1256.06i | 1.29357i | 0.762672 | + | 0.646785i | \(0.223887\pi\) | ||||
−0.762672 | + | 0.646785i | \(0.776113\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 95.0964i | 0.0977353i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −248.440 | + | 1569.72i | −0.254810 | + | 1.60996i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 551.251 | 0.564228 | 0.282114 | − | 0.959381i | \(-0.408964\pi\) | ||||
0.282114 | + | 0.959381i | \(0.408964\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 582.110 | 0.594597 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −346.932 | − | 408.656i | −0.353652 | − | 0.416570i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1598.65 | 1.62630 | 0.813151 | − | 0.582053i | \(-0.197750\pi\) | ||||
0.813151 | + | 0.582053i | \(0.197750\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −44.3682 | − | 318.899i | −0.0450439 | − | 0.323755i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −36.2550 | + | 78.3371i | −0.0367325 | + | 0.0793689i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 561.300i | − | 0.567543i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1734.40 | −1.75015 | −0.875077 | − | 0.483984i | \(-0.839189\pi\) | ||||
−0.875077 | + | 0.483984i | \(0.839189\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 497.363 | + | 230.183i | 0.500869 | + | 0.231806i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 49.6300 | + | 356.718i | 0.0498794 | + | 0.358511i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1118.15i | − | 1.12151i | −0.827980 | − | 0.560757i | \(-0.810510\pi\) | ||
0.827980 | − | 0.560757i | \(-0.189490\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 983.032 | − | 272.525i | 0.984016 | − | 0.272798i |
(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 | 120.3.c.a.89.1 | ✓ | 12 | |
3.2 | odd | 2 | inner | 120.3.c.a.89.11 | yes | 12 | |
4.3 | odd | 2 | 240.3.c.e.209.12 | 12 | |||
5.2 | odd | 4 | 600.3.l.g.401.6 | 12 | |||
5.3 | odd | 4 | 600.3.l.g.401.7 | 12 | |||
5.4 | even | 2 | inner | 120.3.c.a.89.12 | yes | 12 | |
8.3 | odd | 2 | 960.3.c.j.449.1 | 12 | |||
8.5 | even | 2 | 960.3.c.k.449.12 | 12 | |||
12.11 | even | 2 | 240.3.c.e.209.2 | 12 | |||
15.2 | even | 4 | 600.3.l.g.401.5 | 12 | |||
15.8 | even | 4 | 600.3.l.g.401.8 | 12 | |||
15.14 | odd | 2 | inner | 120.3.c.a.89.2 | yes | 12 | |
20.3 | even | 4 | 1200.3.l.y.401.6 | 12 | |||
20.7 | even | 4 | 1200.3.l.y.401.7 | 12 | |||
20.19 | odd | 2 | 240.3.c.e.209.1 | 12 | |||
24.5 | odd | 2 | 960.3.c.k.449.2 | 12 | |||
24.11 | even | 2 | 960.3.c.j.449.11 | 12 | |||
40.19 | odd | 2 | 960.3.c.j.449.12 | 12 | |||
40.29 | even | 2 | 960.3.c.k.449.1 | 12 | |||
60.23 | odd | 4 | 1200.3.l.y.401.5 | 12 | |||
60.47 | odd | 4 | 1200.3.l.y.401.8 | 12 | |||
60.59 | even | 2 | 240.3.c.e.209.11 | 12 | |||
120.29 | odd | 2 | 960.3.c.k.449.11 | 12 | |||
120.59 | even | 2 | 960.3.c.j.449.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.3.c.a.89.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
120.3.c.a.89.2 | yes | 12 | 15.14 | odd | 2 | inner | |
120.3.c.a.89.11 | yes | 12 | 3.2 | odd | 2 | inner | |
120.3.c.a.89.12 | yes | 12 | 5.4 | even | 2 | inner | |
240.3.c.e.209.1 | 12 | 20.19 | odd | 2 | |||
240.3.c.e.209.2 | 12 | 12.11 | even | 2 | |||
240.3.c.e.209.11 | 12 | 60.59 | even | 2 | |||
240.3.c.e.209.12 | 12 | 4.3 | odd | 2 | |||
600.3.l.g.401.5 | 12 | 15.2 | even | 4 | |||
600.3.l.g.401.6 | 12 | 5.2 | odd | 4 | |||
600.3.l.g.401.7 | 12 | 5.3 | odd | 4 | |||
600.3.l.g.401.8 | 12 | 15.8 | even | 4 | |||
960.3.c.j.449.1 | 12 | 8.3 | odd | 2 | |||
960.3.c.j.449.2 | 12 | 120.59 | even | 2 | |||
960.3.c.j.449.11 | 12 | 24.11 | even | 2 | |||
960.3.c.j.449.12 | 12 | 40.19 | odd | 2 | |||
960.3.c.k.449.1 | 12 | 40.29 | even | 2 | |||
960.3.c.k.449.2 | 12 | 24.5 | odd | 2 | |||
960.3.c.k.449.11 | 12 | 120.29 | odd | 2 | |||
960.3.c.k.449.12 | 12 | 8.5 | even | 2 | |||
1200.3.l.y.401.5 | 12 | 60.23 | odd | 4 | |||
1200.3.l.y.401.6 | 12 | 20.3 | even | 4 | |||
1200.3.l.y.401.7 | 12 | 20.7 | even | 4 | |||
1200.3.l.y.401.8 | 12 | 60.47 | odd | 4 |