Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,3,Mod(229,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("230.229");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.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: | \(6.26704608029\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 229.15 | ||
Character | \(\chi\) | \(=\) | 230.229 |
Dual form | 230.3.c.a.229.9 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | − | 3.00625i | − | 1.00208i | −0.865423 | − | 0.501042i | \(-0.832950\pi\) | ||
0.865423 | − | 0.501042i | \(-0.167050\pi\) | |||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | −3.95888 | + | 3.05405i | −0.791777 | + | 0.610811i | ||||
\(6\) | 4.25149 | 0.708581 | ||||||||
\(7\) | 7.53698 | 1.07671 | 0.538355 | − | 0.842718i | \(-0.319046\pi\) | ||||
0.538355 | + | 0.842718i | \(0.319046\pi\) | |||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | −0.0375672 | −0.00417413 | ||||||||
\(10\) | −4.31908 | − | 5.59871i | −0.431908 | − | 0.559871i | ||||
\(11\) | − | 2.07922i | − | 0.189020i | −0.995524 | − | 0.0945099i | \(-0.969872\pi\) | ||
0.995524 | − | 0.0945099i | \(-0.0301284\pi\) | |||||||
\(12\) | 6.01251i | 0.501042i | ||||||||
\(13\) | − | 19.5532i | − | 1.50409i | −0.659110 | − | 0.752047i | \(-0.729067\pi\) | ||
0.659110 | − | 0.752047i | \(-0.270933\pi\) | |||||||
\(14\) | 10.6589i | 0.761350i | ||||||||
\(15\) | 9.18126 | + | 11.9014i | 0.612084 | + | 0.793427i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 22.4321 | 1.31953 | 0.659767 | − | 0.751470i | \(-0.270655\pi\) | ||||
0.659767 | + | 0.751470i | \(0.270655\pi\) | |||||||
\(18\) | − | 0.0531281i | − | 0.00295156i | ||||||
\(19\) | 7.65196i | 0.402735i | 0.979516 | + | 0.201367i | \(0.0645385\pi\) | ||||
−0.979516 | + | 0.201367i | \(0.935461\pi\) | |||||||
\(20\) | 7.91777 | − | 6.10811i | 0.395888 | − | 0.305405i | ||||
\(21\) | − | 22.6581i | − | 1.07896i | ||||||
\(22\) | 2.94046 | 0.133657 | ||||||||
\(23\) | 18.5661 | − | 13.5757i | 0.807223 | − | 0.590247i | ||||
\(24\) | −8.50297 | −0.354291 | ||||||||
\(25\) | 6.34551 | − | 24.1813i | 0.253820 | − | 0.967251i | ||||
\(26\) | 27.6524 | 1.06355 | ||||||||
\(27\) | − | 26.9434i | − | 0.997902i | ||||||
\(28\) | −15.0740 | −0.538355 | ||||||||
\(29\) | 36.7226 | 1.26630 | 0.633149 | − | 0.774030i | \(-0.281762\pi\) | ||||
0.633149 | + | 0.774030i | \(0.281762\pi\) | |||||||
\(30\) | −16.8311 | + | 12.9843i | −0.561038 | + | 0.432809i | ||||
\(31\) | −9.27717 | −0.299263 | −0.149632 | − | 0.988742i | \(-0.547809\pi\) | ||||
−0.149632 | + | 0.988742i | \(0.547809\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | −6.25066 | −0.189414 | ||||||||
\(34\) | 31.7237i | 0.933051i | ||||||||
\(35\) | −29.8380 | + | 23.0183i | −0.852514 | + | 0.657667i | ||||
\(36\) | 0.0751344 | 0.00208707 | ||||||||
\(37\) | −8.26365 | −0.223342 | −0.111671 | − | 0.993745i | \(-0.535620\pi\) | ||||
−0.111671 | + | 0.993745i | \(0.535620\pi\) | |||||||
\(38\) | −10.8215 | −0.284777 | ||||||||
\(39\) | −58.7820 | −1.50723 | ||||||||
\(40\) | 8.63817 | + | 11.1974i | 0.215954 | + | 0.279935i | ||||
\(41\) | 29.3484 | 0.715814 | 0.357907 | − | 0.933757i | \(-0.383491\pi\) | ||||
0.357907 | + | 0.933757i | \(0.383491\pi\) | |||||||
\(42\) | 32.0433 | 0.762937 | ||||||||
\(43\) | −48.5714 | −1.12957 | −0.564784 | − | 0.825239i | \(-0.691040\pi\) | ||||
−0.564784 | + | 0.825239i | \(0.691040\pi\) | |||||||
\(44\) | 4.15843i | 0.0945099i | ||||||||
\(45\) | 0.148724 | − | 0.114732i | 0.00330498 | − | 0.00254961i | ||||
\(46\) | 19.1989 | + | 26.2565i | 0.417368 | + | 0.570793i | ||||
\(47\) | 77.5525i | 1.65005i | 0.565094 | + | 0.825027i | \(0.308840\pi\) | ||||
−0.565094 | + | 0.825027i | \(0.691160\pi\) | |||||||
\(48\) | − | 12.0250i | − | 0.250521i | ||||||
\(49\) | 7.80601 | 0.159306 | ||||||||
\(50\) | 34.1975 | + | 8.97391i | 0.683950 | + | 0.179478i | ||||
\(51\) | − | 67.4365i | − | 1.32228i | ||||||
\(52\) | 39.1064i | 0.752047i | ||||||||
\(53\) | −39.4826 | −0.744955 | −0.372478 | − | 0.928041i | \(-0.621492\pi\) | ||||
−0.372478 | + | 0.928041i | \(0.621492\pi\) | |||||||
\(54\) | 38.1037 | 0.705623 | ||||||||
\(55\) | 6.35004 | + | 8.23138i | 0.115455 | + | 0.149661i | ||||
\(56\) | − | 21.3178i | − | 0.380675i | ||||||
\(57\) | 23.0038 | 0.403575 | ||||||||
\(58\) | 51.9337i | 0.895408i | ||||||||
\(59\) | −19.3611 | −0.328154 | −0.164077 | − | 0.986448i | \(-0.552465\pi\) | ||||
−0.164077 | + | 0.986448i | \(0.552465\pi\) | |||||||
\(60\) | −18.3625 | − | 23.8028i | −0.306042 | − | 0.396714i | ||||
\(61\) | 11.9413i | 0.195760i | 0.995198 | + | 0.0978798i | \(0.0312061\pi\) | ||||
−0.995198 | + | 0.0978798i | \(0.968794\pi\) | |||||||
\(62\) | − | 13.1199i | − | 0.211611i | ||||||
\(63\) | −0.283143 | −0.00449434 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 59.7166 | + | 77.4089i | 0.918717 | + | 1.19091i | ||||
\(66\) | − | 8.83976i | − | 0.133936i | ||||||
\(67\) | 23.2991 | 0.347748 | 0.173874 | − | 0.984768i | \(-0.444372\pi\) | ||||
0.173874 | + | 0.984768i | \(0.444372\pi\) | |||||||
\(68\) | −44.8641 | −0.659767 | ||||||||
\(69\) | −40.8120 | − | 55.8145i | −0.591478 | − | 0.808906i | ||||
\(70\) | −32.5528 | − | 42.1973i | −0.465041 | − | 0.602819i | ||||
\(71\) | −9.60115 | −0.135228 | −0.0676138 | − | 0.997712i | \(-0.521539\pi\) | ||||
−0.0676138 | + | 0.997712i | \(0.521539\pi\) | |||||||
\(72\) | 0.106256i | 0.00147578i | ||||||||
\(73\) | 28.4073i | 0.389140i | 0.980889 | + | 0.194570i | \(0.0623312\pi\) | ||||
−0.980889 | + | 0.194570i | \(0.937669\pi\) | |||||||
\(74\) | − | 11.6866i | − | 0.157927i | ||||||
\(75\) | −72.6951 | − | 19.0762i | −0.969268 | − | 0.254350i | ||||
\(76\) | − | 15.3039i | − | 0.201367i | ||||||
\(77\) | − | 15.6710i | − | 0.203520i | ||||||
\(78\) | − | 83.1302i | − | 1.06577i | ||||||
\(79\) | − | 88.7761i | − | 1.12375i | −0.827223 | − | 0.561874i | \(-0.810081\pi\) | ||
0.827223 | − | 0.561874i | \(-0.189919\pi\) | |||||||
\(80\) | −15.8355 | + | 12.2162i | −0.197944 | + | 0.152703i | ||||
\(81\) | −81.3367 | −1.00416 | ||||||||
\(82\) | 41.5049i | 0.506157i | ||||||||
\(83\) | −70.8309 | −0.853385 | −0.426692 | − | 0.904397i | \(-0.640321\pi\) | ||||
−0.426692 | + | 0.904397i | \(0.640321\pi\) | |||||||
\(84\) | 45.3161i | 0.539478i | ||||||||
\(85\) | −88.8060 | + | 68.5088i | −1.04478 | + | 0.805985i | ||||
\(86\) | − | 68.6903i | − | 0.798725i | ||||||
\(87\) | − | 110.398i | − | 1.26894i | ||||||
\(88\) | −5.88092 | −0.0668286 | ||||||||
\(89\) | 130.974i | 1.47162i | 0.677189 | + | 0.735809i | \(0.263198\pi\) | ||||
−0.677189 | + | 0.735809i | \(0.736802\pi\) | |||||||
\(90\) | 0.162256 | + | 0.210328i | 0.00180284 | + | 0.00233698i | ||||
\(91\) | − | 147.372i | − | 1.61947i | ||||||
\(92\) | −37.1322 | + | 27.1514i | −0.403611 | + | 0.295123i | ||||
\(93\) | 27.8895i | 0.299887i | ||||||||
\(94\) | −109.676 | −1.16676 | ||||||||
\(95\) | −23.3695 | − | 30.2932i | −0.245995 | − | 0.318876i | ||||
\(96\) | 17.0059 | 0.177145 | ||||||||
\(97\) | −169.233 | −1.74467 | −0.872336 | − | 0.488907i | \(-0.837396\pi\) | ||||
−0.872336 | + | 0.488907i | \(0.837396\pi\) | |||||||
\(98\) | 11.0394i | 0.112647i | ||||||||
\(99\) | 0.0781104i | 0.000788994i | ||||||||
\(100\) | −12.6910 | + | 48.3626i | −0.126910 | + | 0.483626i | ||||
\(101\) | 146.128 | 1.44681 | 0.723406 | − | 0.690423i | \(-0.242575\pi\) | ||||
0.723406 | + | 0.690423i | \(0.242575\pi\) | |||||||
\(102\) | 95.3697 | 0.934997 | ||||||||
\(103\) | 135.502 | 1.31556 | 0.657778 | − | 0.753212i | \(-0.271497\pi\) | ||||
0.657778 | + | 0.753212i | \(0.271497\pi\) | |||||||
\(104\) | −55.3049 | −0.531777 | ||||||||
\(105\) | 69.1990 | + | 89.7006i | 0.659038 | + | 0.854292i | ||||
\(106\) | − | 55.8369i | − | 0.526763i | ||||||
\(107\) | −112.264 | −1.04920 | −0.524599 | − | 0.851349i | \(-0.675785\pi\) | ||||
−0.524599 | + | 0.851349i | \(0.675785\pi\) | |||||||
\(108\) | 53.8867i | 0.498951i | ||||||||
\(109\) | − | 155.964i | − | 1.43086i | −0.698685 | − | 0.715429i | \(-0.746231\pi\) | ||
0.698685 | − | 0.715429i | \(-0.253769\pi\) | |||||||
\(110\) | −11.6409 | + | 8.98032i | −0.105827 | + | 0.0816392i | ||||
\(111\) | 24.8426i | 0.223808i | ||||||||
\(112\) | 30.1479 | 0.269178 | ||||||||
\(113\) | 176.113 | 1.55852 | 0.779260 | − | 0.626701i | \(-0.215595\pi\) | ||||
0.779260 | + | 0.626701i | \(0.215595\pi\) | |||||||
\(114\) | 32.5322i | 0.285370i | ||||||||
\(115\) | −32.0402 | + | 110.446i | −0.278611 | + | 0.960404i | ||||
\(116\) | −73.4453 | −0.633149 | ||||||||
\(117\) | 0.734560i | 0.00627829i | ||||||||
\(118\) | − | 27.3807i | − | 0.232040i | ||||||
\(119\) | 169.070 | 1.42076 | ||||||||
\(120\) | 33.6623 | − | 25.9685i | 0.280519 | − | 0.216404i | ||||
\(121\) | 116.677 | 0.964272 | ||||||||
\(122\) | −16.8876 | −0.138423 | ||||||||
\(123\) | − | 88.2287i | − | 0.717306i | ||||||
\(124\) | 18.5543 | 0.149632 | ||||||||
\(125\) | 48.7298 | + | 115.110i | 0.389838 | + | 0.920883i | ||||
\(126\) | − | 0.400425i | − | 0.00317798i | ||||||
\(127\) | − | 41.7240i | − | 0.328535i | −0.986416 | − | 0.164268i | \(-0.947474\pi\) | ||
0.986416 | − | 0.164268i | \(-0.0525260\pi\) | |||||||
\(128\) | − | 11.3137i | − | 0.0883883i | ||||||
\(129\) | 146.018i | 1.13192i | ||||||||
\(130\) | −109.473 | + | 84.4520i | −0.842098 | + | 0.649631i | ||||
\(131\) | 119.975 | 0.915840 | 0.457920 | − | 0.888993i | \(-0.348595\pi\) | ||||
0.457920 | + | 0.888993i | \(0.348595\pi\) | |||||||
\(132\) | 12.5013 | 0.0947069 | ||||||||
\(133\) | 57.6727i | 0.433629i | ||||||||
\(134\) | 32.9499i | 0.245895i | ||||||||
\(135\) | 82.2865 | + | 106.666i | 0.609529 | + | 0.790116i | ||||
\(136\) | − | 63.4475i | − | 0.466526i | ||||||
\(137\) | −230.549 | −1.68284 | −0.841418 | − | 0.540385i | \(-0.818279\pi\) | ||||
−0.841418 | + | 0.540385i | \(0.818279\pi\) | |||||||
\(138\) | 78.9336 | − | 57.7168i | 0.571983 | − | 0.418238i | ||||
\(139\) | 91.6204 | 0.659139 | 0.329570 | − | 0.944131i | \(-0.393096\pi\) | ||||
0.329570 | + | 0.944131i | \(0.393096\pi\) | |||||||
\(140\) | 59.6760 | − | 46.0367i | 0.426257 | − | 0.328833i | ||||
\(141\) | 233.143 | 1.65349 | ||||||||
\(142\) | − | 13.5781i | − | 0.0956203i | ||||||
\(143\) | −40.6554 | −0.284303 | ||||||||
\(144\) | −0.150269 | −0.00104353 | ||||||||
\(145\) | −145.381 | + | 112.153i | −1.00263 | + | 0.773468i | ||||
\(146\) | −40.1739 | −0.275164 | ||||||||
\(147\) | − | 23.4668i | − | 0.159638i | ||||||
\(148\) | 16.5273 | 0.111671 | ||||||||
\(149\) | 202.520i | 1.35920i | 0.733584 | + | 0.679599i | \(0.237846\pi\) | ||||
−0.733584 | + | 0.679599i | \(0.762154\pi\) | |||||||
\(150\) | 26.9778 | − | 102.806i | 0.179852 | − | 0.685376i | ||||
\(151\) | −130.456 | −0.863944 | −0.431972 | − | 0.901887i | \(-0.642182\pi\) | ||||
−0.431972 | + | 0.901887i | \(0.642182\pi\) | |||||||
\(152\) | 21.6430 | 0.142388 | ||||||||
\(153\) | −0.842711 | −0.00550791 | ||||||||
\(154\) | 22.1622 | 0.143910 | ||||||||
\(155\) | 36.7272 | − | 28.3330i | 0.236950 | − | 0.182793i | ||||
\(156\) | 117.564 | 0.753615 | ||||||||
\(157\) | 96.1669 | 0.612528 | 0.306264 | − | 0.951947i | \(-0.400921\pi\) | ||||
0.306264 | + | 0.951947i | \(0.400921\pi\) | |||||||
\(158\) | 125.548 | 0.794610 | ||||||||
\(159\) | 118.695i | 0.746508i | ||||||||
\(160\) | −17.2763 | − | 22.3948i | −0.107977 | − | 0.139968i | ||||
\(161\) | 139.932 | − | 102.320i | 0.869145 | − | 0.635525i | ||||
\(162\) | − | 115.027i | − | 0.710046i | ||||||
\(163\) | 166.567i | 1.02189i | 0.859614 | + | 0.510943i | \(0.170704\pi\) | ||||
−0.859614 | + | 0.510943i | \(0.829296\pi\) | |||||||
\(164\) | −58.6967 | −0.357907 | ||||||||
\(165\) | 24.7456 | − | 19.0898i | 0.149973 | − | 0.115696i | ||||
\(166\) | − | 100.170i | − | 0.603434i | ||||||
\(167\) | − | 193.754i | − | 1.16020i | −0.814545 | − | 0.580100i | \(-0.803013\pi\) | ||
0.814545 | − | 0.580100i | \(-0.196987\pi\) | |||||||
\(168\) | −64.0867 | −0.381468 | ||||||||
\(169\) | −213.328 | −1.26230 | ||||||||
\(170\) | −96.8860 | − | 125.591i | −0.569918 | − | 0.738768i | ||||
\(171\) | − | 0.287463i | − | 0.00168107i | ||||||
\(172\) | 97.1428 | 0.564784 | ||||||||
\(173\) | 6.29236i | 0.0363720i | 0.999835 | + | 0.0181860i | \(0.00578910\pi\) | ||||
−0.999835 | + | 0.0181860i | \(0.994211\pi\) | |||||||
\(174\) | 156.126 | 0.897275 | ||||||||
\(175\) | 47.8260 | − | 182.254i | 0.273291 | − | 1.04145i | ||||
\(176\) | − | 8.31687i | − | 0.0472549i | ||||||
\(177\) | 58.2044i | 0.328838i | ||||||||
\(178\) | −185.225 | −1.04059 | ||||||||
\(179\) | −127.641 | −0.713077 | −0.356539 | − | 0.934281i | \(-0.616043\pi\) | ||||
−0.356539 | + | 0.934281i | \(0.616043\pi\) | |||||||
\(180\) | −0.297448 | + | 0.229465i | −0.00165249 | + | 0.00127480i | ||||
\(181\) | 175.172i | 0.967799i | 0.875124 | + | 0.483899i | \(0.160780\pi\) | ||||
−0.875124 | + | 0.483899i | \(0.839220\pi\) | |||||||
\(182\) | 208.416 | 1.14514 | ||||||||
\(183\) | 35.8987 | 0.196168 | ||||||||
\(184\) | −38.3978 | − | 52.5129i | −0.208684 | − | 0.285396i | ||||
\(185\) | 32.7148 | − | 25.2376i | 0.176837 | − | 0.136420i | ||||
\(186\) | −39.4417 | −0.212052 | ||||||||
\(187\) | − | 46.6412i | − | 0.249418i | ||||||
\(188\) | − | 155.105i | − | 0.825027i | ||||||
\(189\) | − | 203.071i | − | 1.07445i | ||||||
\(190\) | 42.8411 | − | 33.0495i | 0.225479 | − | 0.173945i | ||||
\(191\) | 33.1238i | 0.173423i | 0.996233 | + | 0.0867116i | \(0.0276359\pi\) | ||||
−0.996233 | + | 0.0867116i | \(0.972364\pi\) | |||||||
\(192\) | 24.0500i | 0.125261i | ||||||||
\(193\) | 312.691i | 1.62016i | 0.586318 | + | 0.810081i | \(0.300577\pi\) | ||||
−0.586318 | + | 0.810081i | \(0.699423\pi\) | |||||||
\(194\) | − | 239.332i | − | 1.23367i | ||||||
\(195\) | 232.711 | − | 179.523i | 1.19339 | − | 0.920632i | ||||
\(196\) | −15.6120 | −0.0796531 | ||||||||
\(197\) | − | 241.945i | − | 1.22815i | −0.789249 | − | 0.614073i | \(-0.789530\pi\) | ||
0.789249 | − | 0.614073i | \(-0.210470\pi\) | |||||||
\(198\) | −0.110465 | −0.000557903 | ||||||||
\(199\) | 194.994i | 0.979870i | 0.871759 | + | 0.489935i | \(0.162980\pi\) | ||||
−0.871759 | + | 0.489935i | \(0.837020\pi\) | |||||||
\(200\) | −68.3950 | − | 17.9478i | −0.341975 | − | 0.0897391i | ||||
\(201\) | − | 70.0430i | − | 0.348473i | ||||||
\(202\) | 206.656i | 1.02305i | ||||||||
\(203\) | 276.778 | 1.36344 | ||||||||
\(204\) | 134.873i | 0.661142i | ||||||||
\(205\) | −116.187 | + | 89.6315i | −0.566765 | + | 0.437227i | ||||
\(206\) | 191.629i | 0.930238i | ||||||||
\(207\) | −0.697477 | + | 0.510000i | −0.00336946 | + | 0.00246377i | ||||
\(208\) | − | 78.2129i | − | 0.376023i | ||||||
\(209\) | 15.9101 | 0.0761249 | ||||||||
\(210\) | −126.856 | + | 97.8621i | −0.604076 | + | 0.466010i | ||||
\(211\) | −392.823 | −1.86172 | −0.930861 | − | 0.365375i | \(-0.880941\pi\) | ||||
−0.930861 | + | 0.365375i | \(0.880941\pi\) | |||||||
\(212\) | 78.9652 | 0.372478 | ||||||||
\(213\) | 28.8635i | 0.135509i | ||||||||
\(214\) | − | 158.766i | − | 0.741895i | ||||||
\(215\) | 192.288 | − | 148.340i | 0.894365 | − | 0.689952i | ||||
\(216\) | −76.2073 | −0.352812 | ||||||||
\(217\) | −69.9218 | −0.322220 | ||||||||
\(218\) | 220.566 | 1.01177 | ||||||||
\(219\) | 85.3994 | 0.389952 | ||||||||
\(220\) | −12.7001 | − | 16.4628i | −0.0577277 | − | 0.0748307i | ||||
\(221\) | − | 438.619i | − | 1.98470i | ||||||
\(222\) | −35.1328 | −0.158256 | ||||||||
\(223\) | − | 294.817i | − | 1.32205i | −0.750364 | − | 0.661025i | \(-0.770122\pi\) | ||
0.750364 | − | 0.661025i | \(-0.229878\pi\) | |||||||
\(224\) | 42.6356i | 0.190337i | ||||||||
\(225\) | −0.238383 | + | 0.908423i | −0.00105948 | + | 0.00403744i | ||||
\(226\) | 249.061i | 1.10204i | ||||||||
\(227\) | −279.401 | −1.23084 | −0.615421 | − | 0.788198i | \(-0.711014\pi\) | ||||
−0.615421 | + | 0.788198i | \(0.711014\pi\) | |||||||
\(228\) | −46.0075 | −0.201787 | ||||||||
\(229\) | 19.5785i | 0.0854956i | 0.999086 | + | 0.0427478i | \(0.0136112\pi\) | ||||
−0.999086 | + | 0.0427478i | \(0.986389\pi\) | |||||||
\(230\) | −156.195 | − | 45.3118i | −0.679108 | − | 0.197008i | ||||
\(231\) | −47.1111 | −0.203944 | ||||||||
\(232\) | − | 103.867i | − | 0.447704i | ||||||
\(233\) | 202.249i | 0.868022i | 0.900908 | + | 0.434011i | \(0.142902\pi\) | ||||
−0.900908 | + | 0.434011i | \(0.857098\pi\) | |||||||
\(234\) | −1.03882 | −0.00443942 | ||||||||
\(235\) | −236.850 | − | 307.021i | −1.00787 | − | 1.30647i | ||||
\(236\) | 38.7222 | 0.164077 | ||||||||
\(237\) | −266.884 | −1.12609 | ||||||||
\(238\) | 239.101i | 1.00463i | ||||||||
\(239\) | −116.074 | −0.485667 | −0.242834 | − | 0.970068i | \(-0.578077\pi\) | ||||
−0.242834 | + | 0.970068i | \(0.578077\pi\) | |||||||
\(240\) | 36.7251 | + | 47.6056i | 0.153021 | + | 0.198357i | ||||
\(241\) | − | 127.761i | − | 0.530130i | −0.964231 | − | 0.265065i | \(-0.914607\pi\) | ||
0.964231 | − | 0.265065i | \(-0.0853935\pi\) | |||||||
\(242\) | 165.006i | 0.681843i | ||||||||
\(243\) | 2.02862i | 0.00834822i | ||||||||
\(244\) | − | 23.8827i | − | 0.0978798i | ||||||
\(245\) | −30.9031 | + | 23.8400i | −0.126135 | + | 0.0973060i | ||||
\(246\) | 124.774 | 0.507212 | ||||||||
\(247\) | 149.621 | 0.605751 | ||||||||
\(248\) | 26.2398i | 0.105806i | ||||||||
\(249\) | 212.936i | 0.855164i | ||||||||
\(250\) | −162.791 | + | 68.9144i | −0.651163 | + | 0.275657i | ||||
\(251\) | 391.496i | 1.55975i | 0.625937 | + | 0.779873i | \(0.284717\pi\) | ||||
−0.625937 | + | 0.779873i | \(0.715283\pi\) | |||||||
\(252\) | 0.566286 | 0.00224717 | ||||||||
\(253\) | −28.2268 | − | 38.6030i | −0.111568 | − | 0.152581i | ||||
\(254\) | 59.0066 | 0.232309 | ||||||||
\(255\) | 205.955 | + | 266.973i | 0.807666 | + | 1.04695i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 442.554i | 1.72200i | 0.508605 | + | 0.861000i | \(0.330161\pi\) | ||||
−0.508605 | + | 0.861000i | \(0.669839\pi\) | |||||||
\(258\) | −206.501 | −0.800390 | ||||||||
\(259\) | −62.2829 | −0.240475 | ||||||||
\(260\) | −119.433 | − | 154.818i | −0.459358 | − | 0.595453i | ||||
\(261\) | −1.37957 | −0.00528570 | ||||||||
\(262\) | 169.670i | 0.647597i | ||||||||
\(263\) | 104.907 | 0.398885 | 0.199443 | − | 0.979910i | \(-0.436087\pi\) | ||||
0.199443 | + | 0.979910i | \(0.436087\pi\) | |||||||
\(264\) | 17.6795i | 0.0669679i | ||||||||
\(265\) | 156.307 | − | 120.582i | 0.589838 | − | 0.455027i | ||||
\(266\) | −81.5615 | −0.306622 | ||||||||
\(267\) | 393.741 | 1.47469 | ||||||||
\(268\) | −46.5982 | −0.173874 | ||||||||
\(269\) | 38.9402 | 0.144759 | 0.0723795 | − | 0.997377i | \(-0.476941\pi\) | ||||
0.0723795 | + | 0.997377i | \(0.476941\pi\) | |||||||
\(270\) | −150.848 | + | 116.371i | −0.558696 | + | 0.431002i | ||||
\(271\) | −275.239 | −1.01564 | −0.507822 | − | 0.861462i | \(-0.669549\pi\) | ||||
−0.507822 | + | 0.861462i | \(0.669549\pi\) | |||||||
\(272\) | 89.7283 | 0.329883 | ||||||||
\(273\) | −443.038 | −1.62285 | ||||||||
\(274\) | − | 326.045i | − | 1.18994i | ||||||
\(275\) | −50.2781 | − | 13.1937i | −0.182830 | − | 0.0479771i | ||||
\(276\) | 81.6239 | + | 111.629i | 0.295739 | + | 0.404453i | ||||
\(277\) | − | 25.9384i | − | 0.0936406i | −0.998903 | − | 0.0468203i | \(-0.985091\pi\) | ||
0.998903 | − | 0.0468203i | \(-0.0149088\pi\) | |||||||
\(278\) | 129.571i | 0.466082i | ||||||||
\(279\) | 0.348517 | 0.00124917 | ||||||||
\(280\) | 65.1057 | + | 84.3946i | 0.232520 | + | 0.301409i | ||||
\(281\) | − | 235.636i | − | 0.838563i | −0.907856 | − | 0.419281i | \(-0.862282\pi\) | ||
0.907856 | − | 0.419281i | \(-0.137718\pi\) | |||||||
\(282\) | 329.713i | 1.16920i | ||||||||
\(283\) | −375.709 | −1.32759 | −0.663797 | − | 0.747913i | \(-0.731056\pi\) | ||||
−0.663797 | + | 0.747913i | \(0.731056\pi\) | |||||||
\(284\) | 19.2023 | 0.0676138 | ||||||||
\(285\) | −91.0692 | + | 70.2547i | −0.319541 | + | 0.246508i | ||||
\(286\) | − | 57.4954i | − | 0.201033i | ||||||
\(287\) | 221.198 | 0.770725 | ||||||||
\(288\) | − | 0.212512i | − | 0.000737890i | ||||||
\(289\) | 214.198 | 0.741169 | ||||||||
\(290\) | −158.608 | − | 205.599i | −0.546925 | − | 0.708963i | ||||
\(291\) | 508.758i | 1.74831i | ||||||||
\(292\) | − | 56.8145i | − | 0.194570i | ||||||
\(293\) | 376.743 | 1.28581 | 0.642906 | − | 0.765945i | \(-0.277729\pi\) | ||||
0.642906 | + | 0.765945i | \(0.277729\pi\) | |||||||
\(294\) | 33.1871 | 0.112881 | ||||||||
\(295\) | 76.6483 | − | 59.1298i | 0.259825 | − | 0.200440i | ||||
\(296\) | 23.3731i | 0.0789633i | ||||||||
\(297\) | −56.0211 | −0.188623 | ||||||||
\(298\) | −286.407 | −0.961098 | ||||||||
\(299\) | −265.448 | − | 363.027i | −0.887787 | − | 1.21414i | ||||
\(300\) | 145.390 | + | 38.1524i | 0.484634 | + | 0.127175i | ||||
\(301\) | −366.081 | −1.21622 | ||||||||
\(302\) | − | 184.492i | − | 0.610901i | ||||||
\(303\) | − | 439.298i | − | 1.44983i | ||||||
\(304\) | 30.6079i | 0.100684i | ||||||||
\(305\) | −36.4695 | − | 47.2743i | −0.119572 | − | 0.154998i | ||||
\(306\) | − | 1.19177i | − | 0.00389468i | ||||||
\(307\) | 371.158i | 1.20898i | 0.796612 | + | 0.604491i | \(0.206624\pi\) | ||||
−0.796612 | + | 0.604491i | \(0.793376\pi\) | |||||||
\(308\) | 31.3420i | 0.101760i | ||||||||
\(309\) | − | 407.354i | − | 1.31830i | ||||||
\(310\) | 40.0689 | + | 51.9401i | 0.129254 | + | 0.167549i | ||||
\(311\) | 304.788 | 0.980025 | 0.490013 | − | 0.871715i | \(-0.336992\pi\) | ||||
0.490013 | + | 0.871715i | \(0.336992\pi\) | |||||||
\(312\) | 166.260i | 0.532886i | ||||||||
\(313\) | 440.377 | 1.40696 | 0.703478 | − | 0.710717i | \(-0.251629\pi\) | ||||
0.703478 | + | 0.710717i | \(0.251629\pi\) | |||||||
\(314\) | 136.001i | 0.433123i | ||||||||
\(315\) | 1.12093 | − | 0.864735i | 0.00355851 | − | 0.00274519i | ||||
\(316\) | 177.552i | 0.561874i | ||||||||
\(317\) | 86.1647i | 0.271813i | 0.990722 | + | 0.135907i | \(0.0433947\pi\) | ||||
−0.990722 | + | 0.135907i | \(0.956605\pi\) | |||||||
\(318\) | −167.860 | −0.527861 | ||||||||
\(319\) | − | 76.3544i | − | 0.239355i | ||||||
\(320\) | 31.6711 | − | 24.4324i | 0.0989721 | − | 0.0763513i | ||||
\(321\) | 337.495i | 1.05139i | ||||||||
\(322\) | 144.702 | + | 197.894i | 0.449384 | + | 0.614579i | ||||
\(323\) | 171.649i | 0.531422i | ||||||||
\(324\) | 162.673 | 0.502078 | ||||||||
\(325\) | −472.822 | − | 124.075i | −1.45484 | − | 0.381770i | ||||
\(326\) | −235.562 | −0.722583 | ||||||||
\(327\) | −468.866 | −1.43384 | ||||||||
\(328\) | − | 83.0097i | − | 0.253078i | ||||||
\(329\) | 584.511i | 1.77663i | ||||||||
\(330\) | 26.9971 | + | 34.9956i | 0.0818094 | + | 0.106047i | ||||
\(331\) | −28.8280 | −0.0870936 | −0.0435468 | − | 0.999051i | \(-0.513866\pi\) | ||||
−0.0435468 | + | 0.999051i | \(0.513866\pi\) | |||||||
\(332\) | 141.662 | 0.426692 | ||||||||
\(333\) | 0.310442 | 0.000932259 | ||||||||
\(334\) | 274.009 | 0.820386 | ||||||||
\(335\) | −92.2383 | + | 71.1567i | −0.275338 | + | 0.212408i | ||||
\(336\) | − | 90.6323i | − | 0.269739i | ||||||
\(337\) | 314.690 | 0.933799 | 0.466900 | − | 0.884310i | \(-0.345371\pi\) | ||||
0.466900 | + | 0.884310i | \(0.345371\pi\) | |||||||
\(338\) | − | 301.692i | − | 0.892580i | ||||||
\(339\) | − | 529.440i | − | 1.56177i | ||||||
\(340\) | 177.612 | − | 137.018i | 0.522388 | − | 0.402993i | ||||
\(341\) | 19.2892i | 0.0565667i | ||||||||
\(342\) | 0.406534 | 0.00118870 | ||||||||
\(343\) | −310.478 | −0.905184 | ||||||||
\(344\) | 137.381i | 0.399362i | ||||||||
\(345\) | 332.030 | + | 96.3211i | 0.962406 | + | 0.279192i | ||||
\(346\) | −8.89874 | −0.0257189 | ||||||||
\(347\) | − | 318.146i | − | 0.916847i | −0.888734 | − | 0.458424i | \(-0.848414\pi\) | ||
0.888734 | − | 0.458424i | \(-0.151586\pi\) | |||||||
\(348\) | 220.795i | 0.634469i | ||||||||
\(349\) | −161.289 | −0.462147 | −0.231074 | − | 0.972936i | \(-0.574224\pi\) | ||||
−0.231074 | + | 0.972936i | \(0.574224\pi\) | |||||||
\(350\) | 257.746 | + | 67.6361i | 0.736416 | + | 0.193246i | ||||
\(351\) | −526.829 | −1.50094 | ||||||||
\(352\) | 11.7618 | 0.0334143 | ||||||||
\(353\) | 10.7788i | 0.0305349i | 0.999883 | + | 0.0152675i | \(0.00485998\pi\) | ||||
−0.999883 | + | 0.0152675i | \(0.995140\pi\) | |||||||
\(354\) | −82.3134 | −0.232524 | ||||||||
\(355\) | 38.0098 | − | 29.3224i | 0.107070 | − | 0.0825984i | ||||
\(356\) | − | 261.948i | − | 0.735809i | ||||||
\(357\) | − | 508.268i | − | 1.42372i | ||||||
\(358\) | − | 180.511i | − | 0.504222i | ||||||
\(359\) | − | 310.640i | − | 0.865292i | −0.901564 | − | 0.432646i | \(-0.857580\pi\) | ||
0.901564 | − | 0.432646i | \(-0.142420\pi\) | |||||||
\(360\) | −0.324512 | − | 0.420656i | −0.000901422 | − | 0.00116849i | ||||
\(361\) | 302.447 | 0.837805 | ||||||||
\(362\) | −247.730 | −0.684337 | ||||||||
\(363\) | − | 350.760i | − | 0.966282i | ||||||
\(364\) | 294.744i | 0.809737i | ||||||||
\(365\) | −86.7573 | − | 112.461i | −0.237691 | − | 0.308112i | ||||
\(366\) | 50.7684i | 0.138711i | ||||||||
\(367\) | −132.239 | −0.360324 | −0.180162 | − | 0.983637i | \(-0.557662\pi\) | ||||
−0.180162 | + | 0.983637i | \(0.557662\pi\) | |||||||
\(368\) | 74.2645 | − | 54.3027i | 0.201806 | − | 0.147562i | ||||
\(369\) | −1.10254 | −0.00298790 | ||||||||
\(370\) | 35.6914 | + | 46.2658i | 0.0964633 | + | 0.125043i | ||||
\(371\) | −297.580 | −0.802101 | ||||||||
\(372\) | − | 55.7790i | − | 0.149944i | ||||||
\(373\) | 324.296 | 0.869426 | 0.434713 | − | 0.900569i | \(-0.356850\pi\) | ||||
0.434713 | + | 0.900569i | \(0.356850\pi\) | |||||||
\(374\) | 65.9606 | 0.176365 | ||||||||
\(375\) | 346.051 | − | 146.494i | 0.922803 | − | 0.390651i | ||||
\(376\) | 219.352 | 0.583382 | ||||||||
\(377\) | − | 718.046i | − | 1.90463i | ||||||
\(378\) | 287.186 | 0.759752 | ||||||||
\(379\) | − | 274.491i | − | 0.724252i | −0.932129 | − | 0.362126i | \(-0.882051\pi\) | ||
0.932129 | − | 0.362126i | \(-0.117949\pi\) | |||||||
\(380\) | 46.7390 | + | 60.5865i | 0.122997 | + | 0.159438i | ||||
\(381\) | −125.433 | −0.329220 | ||||||||
\(382\) | −46.8442 | −0.122629 | ||||||||
\(383\) | −336.100 | −0.877545 | −0.438772 | − | 0.898598i | \(-0.644587\pi\) | ||||
−0.438772 | + | 0.898598i | \(0.644587\pi\) | |||||||
\(384\) | −34.0119 | −0.0885726 | ||||||||
\(385\) | 47.8601 | + | 62.0397i | 0.124312 | + | 0.161142i | ||||
\(386\) | −442.212 | −1.14563 | ||||||||
\(387\) | 1.82469 | 0.00471497 | ||||||||
\(388\) | 338.466 | 0.872336 | ||||||||
\(389\) | 46.7493i | 0.120178i | 0.998193 | + | 0.0600891i | \(0.0191385\pi\) | ||||
−0.998193 | + | 0.0600891i | \(0.980862\pi\) | |||||||
\(390\) | 253.884 | + | 329.103i | 0.650985 | + | 0.843854i | ||||
\(391\) | 416.477 | − | 304.531i | 1.06516 | − | 0.778851i | ||||
\(392\) | − | 22.0787i | − | 0.0563233i | ||||||
\(393\) | − | 360.676i | − | 0.917750i | ||||||
\(394\) | 342.161 | 0.868430 | ||||||||
\(395\) | 271.127 | + | 351.454i | 0.686397 | + | 0.889758i | ||||
\(396\) | − | 0.156221i | − | 0.000394497i | ||||||
\(397\) | 210.518i | 0.530273i | 0.964211 | + | 0.265137i | \(0.0854171\pi\) | ||||
−0.964211 | + | 0.265137i | \(0.914583\pi\) | |||||||
\(398\) | −275.763 | −0.692873 | ||||||||
\(399\) | 173.379 | 0.434533 | ||||||||
\(400\) | 25.3820 | − | 96.7251i | 0.0634551 | − | 0.241813i | ||||
\(401\) | 263.085i | 0.656073i | 0.944665 | + | 0.328036i | \(0.106387\pi\) | ||||
−0.944665 | + | 0.328036i | \(0.893613\pi\) | |||||||
\(402\) | 99.0557 | 0.246407 | ||||||||
\(403\) | 181.398i | 0.450120i | ||||||||
\(404\) | −292.256 | −0.723406 | ||||||||
\(405\) | 322.002 | − | 248.407i | 0.795068 | − | 0.613350i | ||||
\(406\) | 391.423i | 0.964095i | ||||||||
\(407\) | 17.1819i | 0.0422160i | ||||||||
\(408\) | −190.739 | −0.467498 | ||||||||
\(409\) | 719.544 | 1.75928 | 0.879638 | − | 0.475644i | \(-0.157785\pi\) | ||||
0.879638 | + | 0.475644i | \(0.157785\pi\) | |||||||
\(410\) | −126.758 | − | 164.313i | −0.309166 | − | 0.400763i | ||||
\(411\) | 693.088i | 1.68634i | ||||||||
\(412\) | −271.004 | −0.657778 | ||||||||
\(413\) | −145.924 | −0.353327 | ||||||||
\(414\) | −0.721250 | − | 0.986382i | −0.00174215 | − | 0.00238257i | ||||
\(415\) | 280.411 | − | 216.321i | 0.675690 | − | 0.521256i | ||||
\(416\) | 110.610 | 0.265889 | ||||||||
\(417\) | − | 275.434i | − | 0.660514i | ||||||
\(418\) | 22.5003i | 0.0538284i | ||||||||
\(419\) | 566.267i | 1.35147i | 0.737143 | + | 0.675737i | \(0.236174\pi\) | ||||
−0.737143 | + | 0.675737i | \(0.763826\pi\) | |||||||
\(420\) | −138.398 | − | 179.401i | −0.329519 | − | 0.427146i | ||||
\(421\) | 506.544i | 1.20319i | 0.798800 | + | 0.601596i | \(0.205468\pi\) | ||||
−0.798800 | + | 0.601596i | \(0.794532\pi\) | |||||||
\(422\) | − | 555.536i | − | 1.31644i | ||||||
\(423\) | − | 2.91343i | − | 0.00688755i | ||||||
\(424\) | 111.674i | 0.263381i | ||||||||
\(425\) | 142.343 | − | 542.436i | 0.334925 | − | 1.27632i | ||||
\(426\) | −40.8192 | −0.0958197 | ||||||||
\(427\) | 90.0015i | 0.210776i | ||||||||
\(428\) | 224.528 | 0.524599 | ||||||||
\(429\) | 122.220i | 0.284896i | ||||||||
\(430\) | 209.784 | + | 271.937i | 0.487870 | + | 0.632411i | ||||
\(431\) | 174.935i | 0.405883i | 0.979191 | + | 0.202941i | \(0.0650501\pi\) | ||||
−0.979191 | + | 0.202941i | \(0.934950\pi\) | |||||||
\(432\) | − | 107.773i | − | 0.249476i | ||||||
\(433\) | −162.574 | −0.375460 | −0.187730 | − | 0.982221i | \(-0.560113\pi\) | ||||
−0.187730 | + | 0.982221i | \(0.560113\pi\) | |||||||
\(434\) | − | 98.8843i | − | 0.227844i | ||||||
\(435\) | 337.160 | + | 437.051i | 0.775081 | + | 1.00472i | ||||
\(436\) | 311.927i | 0.715429i | ||||||||
\(437\) | 103.881 | + | 142.067i | 0.237713 | + | 0.325097i | ||||
\(438\) | 120.773i | 0.275738i | ||||||||
\(439\) | 88.5661 | 0.201745 | 0.100873 | − | 0.994899i | \(-0.467837\pi\) | ||||
0.100873 | + | 0.994899i | \(0.467837\pi\) | |||||||
\(440\) | 23.2819 | − | 17.9606i | 0.0529133 | − | 0.0408196i | ||||
\(441\) | −0.293250 | −0.000664966 | ||||||||
\(442\) | 620.301 | 1.40340 | ||||||||
\(443\) | 299.756i | 0.676650i | 0.941029 | + | 0.338325i | \(0.109860\pi\) | ||||
−0.941029 | + | 0.338325i | \(0.890140\pi\) | |||||||
\(444\) | − | 49.6853i | − | 0.111904i | ||||||
\(445\) | −400.001 | − | 518.511i | −0.898880 | − | 1.16519i | ||||
\(446\) | 416.934 | 0.934830 | ||||||||
\(447\) | 608.828 | 1.36203 | ||||||||
\(448\) | −60.2958 | −0.134589 | ||||||||
\(449\) | −475.804 | −1.05970 | −0.529849 | − | 0.848092i | \(-0.677751\pi\) | ||||
−0.529849 | + | 0.848092i | \(0.677751\pi\) | |||||||
\(450\) | −1.28470 | − | 0.337125i | −0.00285490 | − | 0.000749166i | ||||
\(451\) | − | 61.0216i | − | 0.135303i | ||||||
\(452\) | −352.225 | −0.779260 | ||||||||
\(453\) | 392.183i | 0.865746i | ||||||||
\(454\) | − | 395.133i | − | 0.870337i | ||||||
\(455\) | 450.082 | + | 583.429i | 0.989192 | + | 1.28226i | ||||
\(456\) | − | 65.0644i | − | 0.142685i | ||||||
\(457\) | −632.889 | −1.38488 | −0.692438 | − | 0.721477i | \(-0.743463\pi\) | ||||
−0.692438 | + | 0.721477i | \(0.743463\pi\) | |||||||
\(458\) | −27.6882 | −0.0604545 | ||||||||
\(459\) | − | 604.395i | − | 1.31677i | ||||||
\(460\) | 64.0805 | − | 220.893i | 0.139305 | − | 0.480202i | ||||
\(461\) | −389.815 | −0.845587 | −0.422793 | − | 0.906226i | \(-0.638950\pi\) | ||||
−0.422793 | + | 0.906226i | \(0.638950\pi\) | |||||||
\(462\) | − | 66.6251i | − | 0.144210i | ||||||
\(463\) | 146.564i | 0.316554i | 0.987395 | + | 0.158277i | \(0.0505939\pi\) | ||||
−0.987395 | + | 0.158277i | \(0.949406\pi\) | |||||||
\(464\) | 146.891 | 0.316575 | ||||||||
\(465\) | −85.1761 | − | 110.411i | −0.183174 | − | 0.237444i | ||||
\(466\) | −286.023 | −0.613784 | ||||||||
\(467\) | −114.522 | −0.245228 | −0.122614 | − | 0.992454i | \(-0.539128\pi\) | ||||
−0.122614 | + | 0.992454i | \(0.539128\pi\) | |||||||
\(468\) | − | 1.46912i | − | 0.00313915i | ||||||
\(469\) | 175.605 | 0.374424 | ||||||||
\(470\) | 434.194 | − | 334.956i | 0.923817 | − | 0.712672i | ||||
\(471\) | − | 289.102i | − | 0.613805i | ||||||
\(472\) | 54.7614i | 0.116020i | ||||||||
\(473\) | 100.990i | 0.213511i | ||||||||
\(474\) | − | 377.430i | − | 0.796267i | ||||||
\(475\) | 185.034 | + | 48.5556i | 0.389546 | + | 0.102222i | ||||
\(476\) | −338.140 | −0.710378 | ||||||||
\(477\) | 1.48325 | 0.00310954 | ||||||||
\(478\) | − | 164.154i | − | 0.343419i | ||||||
\(479\) | 572.110i | 1.19438i | 0.802098 | + | 0.597192i | \(0.203717\pi\) | ||||
−0.802098 | + | 0.597192i | \(0.796283\pi\) | |||||||
\(480\) | −67.3245 | + | 51.9371i | −0.140259 | + | 0.108202i | ||||
\(481\) | 161.581i | 0.335927i | ||||||||
\(482\) | 180.682 | 0.374859 | ||||||||
\(483\) | −307.599 | − | 420.672i | −0.636850 | − | 0.870958i | ||||
\(484\) | −233.354 | −0.482136 | ||||||||
\(485\) | 669.974 | − | 516.847i | 1.38139 | − | 1.06566i | ||||
\(486\) | −2.86890 | −0.00590308 | ||||||||
\(487\) | 288.653i | 0.592716i | 0.955077 | + | 0.296358i | \(0.0957722\pi\) | ||||
−0.955077 | + | 0.296358i | \(0.904228\pi\) | |||||||
\(488\) | 33.7752 | 0.0692114 | ||||||||
\(489\) | 500.744 | 1.02402 | ||||||||
\(490\) | −33.7148 | − | 43.7035i | −0.0688057 | − | 0.0891909i | ||||
\(491\) | 665.833 | 1.35608 | 0.678038 | − | 0.735027i | \(-0.262830\pi\) | ||||
0.678038 | + | 0.735027i | \(0.262830\pi\) | |||||||
\(492\) | 176.457i | 0.358653i | ||||||||
\(493\) | 823.765 | 1.67092 | ||||||||
\(494\) | 211.595i | 0.428331i | ||||||||
\(495\) | −0.238553 | − | 0.309230i | −0.000481926 | − | 0.000624707i | ||||
\(496\) | −37.1087 | −0.0748158 | ||||||||
\(497\) | −72.3637 | −0.145601 | ||||||||
\(498\) | −301.137 | −0.604692 | ||||||||
\(499\) | −118.165 | −0.236805 | −0.118402 | − | 0.992966i | \(-0.537777\pi\) | ||||
−0.118402 | + | 0.992966i | \(0.537777\pi\) | |||||||
\(500\) | −97.4596 | − | 230.221i | −0.194919 | − | 0.460442i | ||||
\(501\) | −582.472 | −1.16262 | ||||||||
\(502\) | −553.660 | −1.10291 | ||||||||
\(503\) | −814.476 | −1.61924 | −0.809618 | − | 0.586957i | \(-0.800326\pi\) | ||||
−0.809618 | + | 0.586957i | \(0.800326\pi\) | |||||||
\(504\) | 0.800850i | 0.00158899i | ||||||||
\(505\) | −578.504 | + | 446.283i | −1.14555 | + | 0.883728i | ||||
\(506\) | 54.5929 | − | 39.9187i | 0.107891 | − | 0.0788907i | ||||
\(507\) | 641.320i | 1.26493i | ||||||||
\(508\) | 83.4479i | 0.164268i | ||||||||
\(509\) | −221.229 | −0.434635 | −0.217318 | − | 0.976101i | \(-0.569731\pi\) | ||||
−0.217318 | + | 0.976101i | \(0.569731\pi\) | |||||||
\(510\) | −377.557 | + | 291.264i | −0.740308 | + | 0.571106i | ||||
\(511\) | 214.105i | 0.418992i | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 206.170 | 0.401890 | ||||||||
\(514\) | −625.866 | −1.21764 | ||||||||
\(515\) | −536.437 | + | 413.831i | −1.04163 | + | 0.803555i | ||||
\(516\) | − | 292.036i | − | 0.565961i | ||||||
\(517\) | 161.249 | 0.311893 | ||||||||
\(518\) | − | 88.0814i | − | 0.170041i | ||||||
\(519\) | 18.9164 | 0.0364478 | ||||||||
\(520\) | 218.945 | − | 168.904i | 0.421049 | − | 0.324815i | ||||
\(521\) | 92.1604i | 0.176891i | 0.996081 | + | 0.0884457i | \(0.0281900\pi\) | ||||
−0.996081 | + | 0.0884457i | \(0.971810\pi\) | |||||||
\(522\) | − | 1.95100i | − | 0.00373755i | ||||||
\(523\) | 62.0002 | 0.118547 | 0.0592736 | − | 0.998242i | \(-0.481122\pi\) | ||||
0.0592736 | + | 0.998242i | \(0.481122\pi\) | |||||||
\(524\) | −239.950 | −0.457920 | ||||||||
\(525\) | −547.901 | − | 143.777i | −1.04362 | − | 0.273861i | ||||
\(526\) | 148.361i | 0.282054i | ||||||||
\(527\) | −208.106 | −0.394888 | ||||||||
\(528\) | −25.0026 | −0.0473535 | ||||||||
\(529\) | 160.402 | − | 504.095i | 0.303217 | − | 0.952922i | ||||
\(530\) | 170.529 | + | 221.052i | 0.321752 | + | 0.417078i | ||||
\(531\) | 0.727342 | 0.00136976 | ||||||||
\(532\) | − | 115.345i | − | 0.216815i | ||||||
\(533\) | − | 573.855i | − | 1.07665i | ||||||
\(534\) | 556.834i | 1.04276i | ||||||||
\(535\) | 444.441 | − | 342.861i | 0.830730 | − | 0.640861i | ||||
\(536\) | − | 65.8998i | − | 0.122947i | ||||||
\(537\) | 383.721i | 0.714564i | ||||||||
\(538\) | 55.0697i | 0.102360i | ||||||||
\(539\) | − | 16.2304i | − | 0.0301120i | ||||||
\(540\) | −164.573 | − | 213.331i | −0.304765 | − | 0.395058i | ||||
\(541\) | −93.7470 | −0.173285 | −0.0866424 | − | 0.996239i | \(-0.527614\pi\) | ||||
−0.0866424 | + | 0.996239i | \(0.527614\pi\) | |||||||
\(542\) | − | 389.247i | − | 0.718168i | ||||||
\(543\) | 526.610 | 0.969817 | ||||||||
\(544\) | 126.895i | 0.233263i | ||||||||
\(545\) | 476.321 | + | 617.442i | 0.873984 | + | 1.13292i | ||||
\(546\) | − | 626.551i | − | 1.14753i | ||||||
\(547\) | − | 748.011i | − | 1.36748i | −0.729726 | − | 0.683739i | \(-0.760353\pi\) | ||
0.729726 | − | 0.683739i | \(-0.239647\pi\) | |||||||
\(548\) | 461.097 | 0.841418 | ||||||||
\(549\) | − | 0.448602i | − | 0.000817127i | ||||||
\(550\) | 18.6587 | − | 71.1040i | 0.0339249 | − | 0.129280i | ||||
\(551\) | 281.000i | 0.509982i | ||||||||
\(552\) | −157.867 | + | 115.434i | −0.285991 | + | 0.209119i | ||||
\(553\) | − | 669.103i | − | 1.20995i | ||||||
\(554\) | 36.6825 | 0.0662139 | ||||||||
\(555\) | −75.8708 | − | 98.3491i | −0.136704 | − | 0.177206i | ||||
\(556\) | −183.241 | −0.329570 | ||||||||
\(557\) | 417.310 | 0.749209 | 0.374605 | − | 0.927185i | \(-0.377778\pi\) | ||||
0.374605 | + | 0.927185i | \(0.377778\pi\) | |||||||
\(558\) | 0.492878i | 0.000883294i | ||||||||
\(559\) | 949.727i | 1.69897i | ||||||||
\(560\) | −119.352 | + | 92.0733i | −0.213129 | + | 0.164417i | ||||
\(561\) | −140.215 | −0.249938 | ||||||||
\(562\) | 333.240 | 0.592953 | ||||||||
\(563\) | −931.244 | −1.65407 | −0.827037 | − | 0.562147i | \(-0.809975\pi\) | ||||
−0.827037 | + | 0.562147i | \(0.809975\pi\) | |||||||
\(564\) | −466.285 | −0.826747 | ||||||||
\(565\) | −697.209 | + | 537.858i | −1.23400 | + | 0.951960i | ||||
\(566\) | − | 531.333i | − | 0.938751i | ||||||
\(567\) | −613.033 | −1.08119 | ||||||||
\(568\) | 27.1562i | 0.0478101i | ||||||||
\(569\) | − | 342.848i | − | 0.602546i | −0.953538 | − | 0.301273i | \(-0.902589\pi\) | ||
0.953538 | − | 0.301273i | \(-0.0974115\pi\) | |||||||
\(570\) | −99.3552 | − | 128.791i | −0.174307 | − | 0.225950i | ||||
\(571\) | − | 50.5137i | − | 0.0884653i | −0.999021 | − | 0.0442327i | \(-0.985916\pi\) | ||
0.999021 | − | 0.0442327i | \(-0.0140843\pi\) | |||||||
\(572\) | 81.3108 | 0.142152 | ||||||||
\(573\) | 99.5786 | 0.173785 | ||||||||
\(574\) | 312.821i | 0.544985i | ||||||||
\(575\) | −210.466 | − | 535.097i | −0.366028 | − | 0.930604i | ||||
\(576\) | 0.300538 | 0.000521767 | ||||||||
\(577\) | 7.96828i | 0.0138099i | 0.999976 | + | 0.00690493i | \(0.00219792\pi\) | ||||
−0.999976 | + | 0.00690493i | \(0.997802\pi\) | |||||||
\(578\) | 302.922i | 0.524086i | ||||||||
\(579\) | 940.030 | 1.62354 | ||||||||
\(580\) | 290.761 | − | 224.306i | 0.501313 | − | 0.386734i | ||||
\(581\) | −533.851 | −0.918848 | ||||||||
\(582\) | −719.492 | −1.23624 | ||||||||
\(583\) | 82.0929i | 0.140811i | ||||||||
\(584\) | 80.3478 | 0.137582 | ||||||||
\(585\) | −2.24339 | − | 2.90804i | −0.00383485 | − | 0.00497100i | ||||
\(586\) | 532.795i | 0.909206i | ||||||||
\(587\) | 992.708i | 1.69115i | 0.533853 | + | 0.845577i | \(0.320744\pi\) | ||||
−0.533853 | + | 0.845577i | \(0.679256\pi\) | |||||||
\(588\) | 46.9337i | 0.0798192i | ||||||||
\(589\) | − | 70.9885i | − | 0.120524i | ||||||
\(590\) | 83.6222 | + | 108.397i | 0.141732 | + | 0.183724i | ||||
\(591\) | −727.347 | −1.23071 | ||||||||
\(592\) | −33.0546 | −0.0558355 | ||||||||
\(593\) | 1040.58i | 1.75477i | 0.479792 | + | 0.877383i | \(0.340712\pi\) | ||||
−0.479792 | + | 0.877383i | \(0.659288\pi\) | |||||||
\(594\) | − | 79.2258i | − | 0.133377i | ||||||
\(595\) | −669.328 | + | 516.349i | −1.12492 | + | 0.867813i | ||||
\(596\) | − | 405.041i | − | 0.679599i | ||||||
\(597\) | 586.202 | 0.981913 | ||||||||
\(598\) | 513.398 | − | 375.401i | 0.858526 | − | 0.627760i | ||||
\(599\) | −194.575 | −0.324832 | −0.162416 | − | 0.986722i | \(-0.551929\pi\) | ||||
−0.162416 | + | 0.986722i | \(0.551929\pi\) | |||||||
\(600\) | −53.9557 | + | 205.613i | −0.0899262 | + | 0.342688i | ||||
\(601\) | 841.243 | 1.39974 | 0.699869 | − | 0.714271i | \(-0.253242\pi\) | ||||
0.699869 | + | 0.714271i | \(0.253242\pi\) | |||||||
\(602\) | − | 517.717i | − | 0.859995i | ||||||
\(603\) | −0.875282 | −0.00145155 | ||||||||
\(604\) | 260.911 | 0.431972 | ||||||||
\(605\) | −461.910 | + | 356.337i | −0.763488 | + | 0.588987i | ||||
\(606\) | 621.261 | 1.02518 | ||||||||
\(607\) | 590.121i | 0.972192i | 0.873905 | + | 0.486096i | \(0.161579\pi\) | ||||
−0.873905 | + | 0.486096i | \(0.838421\pi\) | |||||||
\(608\) | −43.2860 | −0.0711942 | ||||||||
\(609\) | − | 832.064i | − | 1.36628i | ||||||
\(610\) | 66.8560 | − | 51.5756i | 0.109600 | − | 0.0845502i | ||||
\(611\) | 1516.40 | 2.48184 | ||||||||
\(612\) | 1.68542 | 0.00275396 | ||||||||
\(613\) | 773.706 | 1.26216 | 0.631081 | − | 0.775717i | \(-0.282611\pi\) | ||||
0.631081 | + | 0.775717i | \(0.282611\pi\) | |||||||
\(614\) | −524.896 | −0.854880 | ||||||||
\(615\) | 269.455 | + | 349.287i | 0.438138 | + | 0.567946i | ||||
\(616\) | −44.3243 | −0.0719551 | ||||||||
\(617\) | −642.187 | −1.04082 | −0.520411 | − | 0.853916i | \(-0.674221\pi\) | ||||
−0.520411 | + | 0.853916i | \(0.674221\pi\) | |||||||
\(618\) | 576.086 | 0.932177 | ||||||||
\(619\) | − | 1036.23i | − | 1.67405i | −0.547168 | − | 0.837023i | \(-0.684294\pi\) | ||
0.547168 | − | 0.837023i | \(-0.315706\pi\) | |||||||
\(620\) | −73.4544 | + | 56.6659i | −0.118475 | + | 0.0913967i | ||||
\(621\) | −365.774 | − | 500.234i | −0.589009 | − | 0.805529i | ||||
\(622\) | 431.035i | 0.692982i | ||||||||
\(623\) | 987.148i | 1.58451i | ||||||||
\(624\) | −235.128 | −0.376807 | ||||||||
\(625\) | −544.469 | − | 306.885i | −0.871150 | − | 0.491016i | ||||
\(626\) | 622.788i | 0.994868i | ||||||||
\(627\) | − | 47.8298i | − | 0.0762836i | ||||||
\(628\) | −192.334 | −0.306264 | ||||||||
\(629\) | −185.371 | −0.294707 | ||||||||
\(630\) | 1.22292 | + | 1.58524i | 0.00194114 | + | 0.00251625i | ||||
\(631\) | − | 1106.65i | − | 1.75381i | −0.480668 | − | 0.876903i | \(-0.659606\pi\) | ||
0.480668 | − | 0.876903i | \(-0.340394\pi\) | |||||||
\(632\) | −251.097 | −0.397305 | ||||||||
\(633\) | 1180.93i | 1.86560i | ||||||||
\(634\) | −121.855 | −0.192201 | ||||||||
\(635\) | 127.427 | + | 165.180i | 0.200673 | + | 0.260126i | ||||
\(636\) | − | 237.390i | − | 0.373254i | ||||||
\(637\) | − | 152.633i | − | 0.239612i | ||||||
\(638\) | 107.981 | 0.169250 | ||||||||
\(639\) | 0.360689 | 0.000564458 | ||||||||
\(640\) | 34.5527 | + | 44.7896i | 0.0539886 | + | 0.0699838i | ||||
\(641\) | − | 862.461i | − | 1.34549i | −0.739873 | − | 0.672746i | \(-0.765115\pi\) | ||
0.739873 | − | 0.672746i | \(-0.234885\pi\) | |||||||
\(642\) | −477.290 | −0.743442 | ||||||||
\(643\) | 353.637 | 0.549980 | 0.274990 | − | 0.961447i | \(-0.411326\pi\) | ||||
0.274990 | + | 0.961447i | \(0.411326\pi\) | |||||||
\(644\) | −279.865 | + | 204.639i | −0.434573 | + | 0.317763i | ||||
\(645\) | −445.947 | − | 578.068i | −0.691390 | − | 0.896230i | ||||
\(646\) | −242.749 | −0.375772 | ||||||||
\(647\) | 521.182i | 0.805536i | 0.915302 | + | 0.402768i | \(0.131952\pi\) | ||||
−0.915302 | + | 0.402768i | \(0.868048\pi\) | |||||||
\(648\) | 230.055i | 0.355023i | ||||||||
\(649\) | 40.2559i | 0.0620276i | ||||||||
\(650\) | 175.469 | − | 668.671i | 0.269952 | − | 1.02872i | ||||
\(651\) | 210.203i | 0.322892i | ||||||||
\(652\) | − | 333.135i | − | 0.510943i | ||||||
\(653\) | − | 875.693i | − | 1.34103i | −0.741896 | − | 0.670515i | \(-0.766073\pi\) | ||
0.741896 | − | 0.670515i | \(-0.233927\pi\) | |||||||
\(654\) | − | 663.077i | − | 1.01388i | ||||||
\(655\) | −474.967 | + | 366.410i | −0.725141 | + | 0.559405i | ||||
\(656\) | 117.393 | 0.178953 | ||||||||
\(657\) | − | 1.06718i | − | 0.00162432i | ||||||
\(658\) | −826.624 | −1.25627 | ||||||||
\(659\) | 1148.81i | 1.74326i | 0.490165 | + | 0.871630i | \(0.336937\pi\) | ||||
−0.490165 | + | 0.871630i | \(0.663063\pi\) | |||||||
\(660\) | −49.4912 | + | 38.1797i | −0.0749867 | + | 0.0578480i | ||||
\(661\) | − | 231.297i | − | 0.349920i | −0.984576 | − | 0.174960i | \(-0.944020\pi\) | ||
0.984576 | − | 0.174960i | \(-0.0559796\pi\) | |||||||
\(662\) | − | 40.7689i | − | 0.0615845i | ||||||
\(663\) | −1318.60 | −1.98884 | ||||||||
\(664\) | 200.340i | 0.301717i | ||||||||
\(665\) | −176.135 | − | 228.319i | −0.264865 | − | 0.343337i | ||||
\(666\) | 0.439032i | 0.000659207i | ||||||||
\(667\) | 681.797 | − | 498.535i | 1.02218 | − | 0.747429i | ||||
\(668\) | 387.507i | 0.580100i | ||||||||
\(669\) | −886.295 | −1.32481 | ||||||||
\(670\) | −100.631 | − | 130.445i | −0.150195 | − | 0.194694i | ||||
\(671\) | 24.8286 | 0.0370024 | ||||||||
\(672\) | 128.173 | 0.190734 | ||||||||
\(673\) | 538.439i | 0.800058i | 0.916503 | + | 0.400029i | \(0.131000\pi\) | ||||
−0.916503 | + | 0.400029i | \(0.869000\pi\) | |||||||
\(674\) | 445.039i | 0.660296i | ||||||||
\(675\) | −651.525 | − | 170.969i | −0.965222 | − | 0.253288i | ||||
\(676\) | 426.657 | 0.631149 | ||||||||
\(677\) | −139.261 | −0.205703 | −0.102852 | − | 0.994697i | \(-0.532797\pi\) | ||||
−0.102852 | + | 0.994697i | \(0.532797\pi\) | |||||||
\(678\) | 748.741 | 1.10434 | ||||||||
\(679\) | −1275.51 | −1.87851 | ||||||||
\(680\) | 193.772 | + | 251.181i | 0.284959 | + | 0.369384i | ||||
\(681\) | 839.951i | 1.23341i | ||||||||
\(682\) | −27.2791 | −0.0399987 | ||||||||
\(683\) | − | 1045.84i | − | 1.53124i | −0.643294 | − | 0.765619i | \(-0.722433\pi\) | ||
0.643294 | − | 0.765619i | \(-0.277567\pi\) | |||||||
\(684\) | 0.574926i | 0.000840535i | ||||||||
\(685\) | 912.715 | − | 704.108i | 1.33243 | − | 1.02789i | ||||
\(686\) | − | 439.082i | − | 0.640062i | ||||||
\(687\) | 58.8579 | 0.0856738 | ||||||||
\(688\) | −194.286 | −0.282392 | ||||||||
\(689\) | 772.012i | 1.12048i | ||||||||
\(690\) | −136.219 | + | 469.562i | −0.197418 | + | 0.680524i | ||||
\(691\) | −38.1323 | −0.0551842 | −0.0275921 | − | 0.999619i | \(-0.508784\pi\) | ||||
−0.0275921 | + | 0.999619i | \(0.508784\pi\) | |||||||
\(692\) | − | 12.5847i | − | 0.0181860i | ||||||
\(693\) | 0.588716i | 0.000849518i | ||||||||
\(694\) | 449.926 | 0.648309 | ||||||||
\(695\) | −362.714 | + | 279.814i | −0.521891 | + | 0.402609i | ||||
\(696\) | −312.252 | −0.448637 | ||||||||
\(697\) | 658.345 | 0.944541 | ||||||||
\(698\) | − | 228.098i | − | 0.326787i | ||||||
\(699\) | 608.012 | 0.869832 | ||||||||
\(700\) | −95.6519 | + | 364.508i | −0.136646 | + | 0.520725i | ||||
\(701\) | − | 1257.67i | − | 1.79410i | −0.441925 | − | 0.897052i | \(-0.645704\pi\) | ||
0.441925 | − | 0.897052i | \(-0.354296\pi\) | |||||||
\(702\) | − | 745.049i | − | 1.06132i | ||||||
\(703\) | − | 63.2332i | − | 0.0899476i | ||||||
\(704\) | 16.6337i | 0.0236275i | ||||||||
\(705\) | −922.984 | + | 712.030i | −1.30920 | + | 1.00997i | ||||
\(706\) | −15.2436 | −0.0215915 | ||||||||
\(707\) | 1101.36 | 1.55780 | ||||||||
\(708\) | − | 116.409i | − | 0.164419i | ||||||
\(709\) | − | 109.672i | − | 0.154685i | −0.997005 | − | 0.0773426i | \(-0.975356\pi\) | ||
0.997005 | − | 0.0773426i | \(-0.0246435\pi\) | |||||||
\(710\) | 41.4682 | + | 53.7540i | 0.0584059 | + | 0.0757099i | ||||
\(711\) | 3.33507i | 0.00469068i | ||||||||
\(712\) | 370.450 | 0.520295 | ||||||||
\(713\) | −172.241 | + | 125.944i | −0.241572 | + | 0.176639i | ||||
\(714\) | 718.799 | 1.00672 | ||||||||
\(715\) | 160.950 | − | 124.164i | 0.225105 | − | 0.173656i | ||||
\(716\) | 255.282 | 0.356539 | ||||||||
\(717\) | 348.949i | 0.486680i | ||||||||
\(718\) | 439.311 | 0.611854 | ||||||||
\(719\) | 805.978 | 1.12097 | 0.560485 | − | 0.828164i | \(-0.310615\pi\) | ||||
0.560485 | + | 0.828164i | \(0.310615\pi\) | |||||||
\(720\) | 0.594897 | − | 0.458929i | 0.000826246 | − | 0.000637402i | ||||
\(721\) | 1021.28 | 1.41647 | ||||||||
\(722\) | 427.725i | 0.592417i | ||||||||
\(723\) | −384.083 | −0.531236 | ||||||||
\(724\) | − | 350.343i | − | 0.483899i | ||||||
\(725\) | 233.024 | − | 888.001i | 0.321412 | − | 1.22483i | ||||
\(726\) | 496.050 | 0.683265 | ||||||||
\(727\) | 1088.51 | 1.49726 | 0.748631 | − | 0.662986i | \(-0.230711\pi\) | ||||
0.748631 | + | 0.662986i | \(0.230711\pi\) | |||||||
\(728\) | −416.831 | −0.572571 | ||||||||
\(729\) | −725.932 | −0.995791 | ||||||||
\(730\) | 159.044 | − | 122.693i | 0.217868 | − | 0.168073i | ||||
\(731\) | −1089.56 | −1.49050 | ||||||||
\(732\) | −71.7974 | −0.0980838 | ||||||||
\(733\) | −1168.31 | −1.59388 | −0.796938 | − | 0.604061i | \(-0.793548\pi\) | ||||
−0.796938 | + | 0.604061i | \(0.793548\pi\) | |||||||
\(734\) | − | 187.014i | − | 0.254788i | ||||||
\(735\) | 71.6690 | + | 92.9025i | 0.0975089 | + | 0.126398i | ||||
\(736\) | 76.7956 | + | 105.026i | 0.104342 | + | 0.142698i | ||||
\(737\) | − | 48.4439i | − | 0.0657312i | ||||||
\(738\) | − | 1.55922i | − | 0.00211277i | ||||||
\(739\) | 1476.43 | 1.99788 | 0.998941 | − | 0.0460187i | \(-0.0146534\pi\) | ||||
0.998941 | + | 0.0460187i | \(0.0146534\pi\) | |||||||
\(740\) | −65.4297 | + | 50.4753i | −0.0884185 | + | 0.0682098i | ||||
\(741\) | − | 449.797i | − | 0.607014i | ||||||
\(742\) | − | 420.841i | − | 0.567171i | ||||||
\(743\) | 874.658 | 1.17720 | 0.588599 | − | 0.808425i | \(-0.299680\pi\) | ||||
0.588599 | + | 0.808425i | \(0.299680\pi\) | |||||||
\(744\) | 78.8835 | 0.106026 | ||||||||
\(745\) | −618.508 | − | 801.754i | −0.830212 | − | 1.07618i | ||||
\(746\) | 458.624i | 0.614777i | ||||||||
\(747\) | 2.66092 | 0.00356214 | ||||||||
\(748\) | 93.2823i | 0.124709i | ||||||||
\(749\) | −846.132 | −1.12968 | ||||||||
\(750\) | 207.174 | + | 489.390i | 0.276232 | + | 0.652520i | ||||
\(751\) | − | 23.7157i | − | 0.0315788i | −0.999875 | − | 0.0157894i | \(-0.994974\pi\) | ||
0.999875 | − | 0.0157894i | \(-0.00502613\pi\) | |||||||
\(752\) | 310.210i | 0.412513i | ||||||||
\(753\) | 1176.94 | 1.56300 | ||||||||
\(754\) | 1015.47 | 1.34678 | ||||||||
\(755\) | 516.458 | − | 398.418i | 0.684051 | − | 0.527707i | ||||
\(756\) | 406.143i | 0.537226i | ||||||||
\(757\) | 353.307 | 0.466720 | 0.233360 | − | 0.972390i | \(-0.425028\pi\) | ||||
0.233360 | + | 0.972390i | \(0.425028\pi\) | |||||||
\(758\) | 388.190 | 0.512123 | ||||||||
\(759\) | −116.050 | + | 84.8569i | −0.152899 | + | 0.111801i | ||||
\(760\) | −85.6822 | + | 66.0990i | −0.112740 | + | 0.0869723i | ||||
\(761\) | −984.853 | −1.29416 | −0.647078 | − | 0.762423i | \(-0.724009\pi\) | ||||
−0.647078 | + | 0.762423i | \(0.724009\pi\) | |||||||
\(762\) | − | 177.389i | − | 0.232794i | ||||||
\(763\) | − | 1175.49i | − | 1.54062i | ||||||
\(764\) | − | 66.2476i | − | 0.0867116i | ||||||
\(765\) | 3.33619 | − | 2.57368i | 0.00436104 | − | 0.00336429i | ||||
\(766\) | − | 475.317i | − | 0.620518i | ||||||
\(767\) | 378.572i | 0.493574i | ||||||||
\(768\) | − | 48.1001i | − | 0.0626303i | ||||||
\(769\) | − | 590.079i | − | 0.767333i | −0.923472 | − | 0.383666i | \(-0.874661\pi\) | ||
0.923472 | − | 0.383666i | \(-0.125339\pi\) | |||||||
\(770\) | −87.7374 | + | 67.6844i | −0.113945 | + | 0.0879018i | ||||
\(771\) | 1330.43 | 1.72559 | ||||||||
\(772\) | − | 625.383i | − | 0.810081i | ||||||
\(773\) | 960.379 | 1.24241 | 0.621203 | − | 0.783650i | \(-0.286644\pi\) | ||||
0.621203 | + | 0.783650i | \(0.286644\pi\) | |||||||
\(774\) | 2.58050i | 0.00333398i | ||||||||
\(775\) | −58.8683 | + | 224.334i | −0.0759592 | + | 0.289463i | ||||
\(776\) | 478.664i | 0.616835i | ||||||||
\(777\) | 187.238i | 0.240976i | ||||||||
\(778\) | −66.1135 | −0.0849788 | ||||||||
\(779\) | 224.573i | 0.288283i | ||||||||
\(780\) | −465.422 | + | 359.047i | −0.596695 | + | 0.460316i | ||||
\(781\) | 19.9629i | 0.0255607i | ||||||||
\(782\) | 430.671 | + | 588.987i | 0.550731 | + | 0.753180i | ||||
\(783\) | − | 989.431i | − | 1.26364i | ||||||
\(784\) | 31.2240 | 0.0398266 | ||||||||
\(785\) | −380.714 | + | 293.699i | −0.484985 | + | 0.374139i | ||||
\(786\) | 510.072 | 0.648947 | ||||||||
\(787\) | 557.933 | 0.708937 | 0.354468 | − | 0.935068i | \(-0.384662\pi\) | ||||
0.354468 | + | 0.935068i | \(0.384662\pi\) | |||||||
\(788\) | 483.889i | 0.614073i | ||||||||
\(789\) | − | 315.376i | − | 0.399717i | ||||||
\(790\) | −497.031 | + | 383.431i | −0.629154 | + | 0.485356i | ||||
\(791\) | 1327.36 | 1.67807 | ||||||||
\(792\) | 0.220930 | 0.000278952 | ||||||||
\(793\) | 233.491 | 0.294441 | ||||||||
\(794\) | −297.718 | −0.374960 | ||||||||
\(795\) | −362.500 | − | 469.899i | −0.455975 | − | 0.591068i | ||||
\(796\) | − | 389.988i | − | 0.489935i | ||||||
\(797\) | 113.712 | 0.142675 | 0.0713377 | − | 0.997452i | \(-0.477273\pi\) | ||||
0.0713377 | + | 0.997452i | \(0.477273\pi\) | |||||||
\(798\) | 245.195i | 0.307261i | ||||||||
\(799\) | 1739.66i | 2.17730i | ||||||||
\(800\) | 136.790 | + | 35.8956i | 0.170987 | + | 0.0448695i | ||||
\(801\) | − | 4.92033i | − | 0.00614273i | ||||||
\(802\) | −372.059 | −0.463913 | ||||||||
\(803\) | 59.0649 | 0.0735552 | ||||||||
\(804\) | 140.086i | 0.174236i | ||||||||
\(805\) | −241.487 | + | 832.432i | −0.299983 | + | 1.03408i | ||||
\(806\) | −256.536 | −0.318283 | ||||||||
\(807\) | − | 117.064i | − | 0.145061i | ||||||
\(808\) | − | 413.312i | − | 0.511525i | ||||||
\(809\) | 638.881 | 0.789716 | 0.394858 | − | 0.918742i | \(-0.370794\pi\) | ||||
0.394858 | + | 0.918742i | \(0.370794\pi\) | |||||||
\(810\) | 351.300 | + | 455.380i | 0.433704 | + | 0.562198i | ||||
\(811\) | 109.715 | 0.135284 | 0.0676421 | − | 0.997710i | \(-0.478452\pi\) | ||||
0.0676421 | + | 0.997710i | \(0.478452\pi\) | |||||||
\(812\) | −553.555 | −0.681718 | ||||||||
\(813\) | 827.440i | 1.01776i | ||||||||
\(814\) | −24.2989 | −0.0298512 | ||||||||
\(815\) | −508.706 | − | 659.421i | −0.624179 | − | 0.809106i | ||||
\(816\) | − | 269.746i | − | 0.330571i | ||||||
\(817\) | − | 371.667i | − | 0.454916i | ||||||
\(818\) | 1017.59i | 1.24400i | ||||||||
\(819\) | 5.53636i | 0.00675990i | ||||||||
\(820\) | 232.374 | − | 179.263i | 0.283382 | − | 0.218613i | ||||
\(821\) | 1159.45 | 1.41224 | 0.706119 | − | 0.708093i | \(-0.250444\pi\) | ||||
0.706119 | + | 0.708093i | \(0.250444\pi\) | |||||||
\(822\) | −980.174 | −1.19243 | ||||||||
\(823\) | 239.903i | 0.291498i | 0.989322 | + | 0.145749i | \(0.0465593\pi\) | ||||
−0.989322 | + | 0.145749i | \(0.953441\pi\) | |||||||
\(824\) | − | 383.258i | − | 0.465119i | ||||||
\(825\) | −39.6636 | + | 151.149i | −0.0480771 | + | 0.183211i | ||||
\(826\) | − | 206.368i | − | 0.249840i | ||||||
\(827\) | −1320.07 | −1.59621 | −0.798105 | − | 0.602519i | \(-0.794164\pi\) | ||||
−0.798105 | + | 0.602519i | \(0.794164\pi\) | |||||||
\(828\) | 1.39495 | − | 1.02000i | 0.00168473 | − | 0.00123189i | ||||
\(829\) | −637.640 | −0.769168 | −0.384584 | − | 0.923090i | \(-0.625655\pi\) | ||||
−0.384584 | + | 0.923090i | \(0.625655\pi\) | |||||||
\(830\) | 305.925 | + | 396.562i | 0.368584 | + | 0.477785i | ||||
\(831\) | −77.9775 | −0.0938358 | ||||||||
\(832\) | 156.426i | 0.188012i | ||||||||
\(833\) | 175.105 | 0.210210 | ||||||||
\(834\) | 389.523 | 0.467054 | ||||||||
\(835\) | 591.734 | + | 767.048i | 0.708663 | + | 0.918620i | ||||
\(836\) | −31.8202 | −0.0380624 | ||||||||
\(837\) | 249.958i | 0.298636i | ||||||||
\(838\) | −800.823 | −0.955636 | ||||||||
\(839\) | 641.702i | 0.764841i | 0.923988 | + | 0.382421i | \(0.124909\pi\) | ||||
−0.923988 | + | 0.382421i | \(0.875091\pi\) | |||||||
\(840\) | 253.712 | − | 195.724i | 0.302038 | − | 0.233005i | ||||
\(841\) | 507.553 | 0.603511 | ||||||||
\(842\) | −716.361 | −0.850785 | ||||||||
\(843\) | −708.382 | −0.840311 | ||||||||
\(844\) | 785.646 | 0.930861 | ||||||||
\(845\) | 844.542 | − | 651.516i | 0.999458 | − | 0.771025i | ||||
\(846\) | 4.12022 | 0.00487023 | ||||||||
\(847\) | 879.391 | 1.03824 | ||||||||
\(848\) | −157.930 | −0.186239 | ||||||||
\(849\) | 1129.48i | 1.33036i | ||||||||
\(850\) | 767.121 | + | 201.303i | 0.902495 | + | 0.236827i | ||||
\(851\) | −153.424 | + | 112.185i | −0.180287 | + | 0.131827i | ||||
\(852\) | − | 57.7270i | − | 0.0677547i | ||||||
\(853\) | − | 134.906i | − | 0.158154i | −0.996869 | − | 0.0790771i | \(-0.974803\pi\) | ||
0.996869 | − | 0.0790771i | \(-0.0251973\pi\) | |||||||
\(854\) | −127.281 | −0.149041 | ||||||||
\(855\) | 0.877927 | + | 1.13803i | 0.00102682 | + | 0.00133103i | ||||
\(856\) | 317.531i | 0.370947i | ||||||||
\(857\) | − | 479.350i | − | 0.559335i | −0.960097 | − | 0.279667i | \(-0.909776\pi\) | ||
0.960097 | − | 0.279667i | \(-0.0902242\pi\) | |||||||
\(858\) | −172.846 | −0.201452 | ||||||||
\(859\) | −1325.07 | −1.54258 | −0.771289 | − | 0.636485i | \(-0.780388\pi\) | ||||
−0.771289 | + | 0.636485i | \(0.780388\pi\) | |||||||
\(860\) | −384.577 | + | 296.679i | −0.447182 | + | 0.344976i | ||||
\(861\) | − | 664.977i | − | 0.772331i | ||||||
\(862\) | −247.396 | −0.287002 | ||||||||
\(863\) | − | 898.018i | − | 1.04058i | −0.853991 | − | 0.520288i | \(-0.825824\pi\) | ||
0.853991 | − | 0.520288i | \(-0.174176\pi\) | |||||||
\(864\) | 152.415 | 0.176406 | ||||||||
\(865\) | −19.2172 | − | 24.9107i | −0.0222164 | − | 0.0287985i | ||||
\(866\) | − | 229.914i | − | 0.265490i | ||||||
\(867\) | − | 643.934i | − | 0.742715i | ||||||
\(868\) | 139.844 | 0.161110 | ||||||||
\(869\) | −184.585 | −0.212411 | ||||||||
\(870\) | −618.084 | + | 476.817i | −0.710441 | + | 0.548065i | ||||
\(871\) | − | 455.572i | − | 0.523045i | ||||||
\(872\) | −441.132 | −0.505885 | ||||||||
\(873\) | 6.35762 | 0.00728249 | ||||||||
\(874\) | −200.914 | + | 146.909i | −0.229878 | + | 0.168089i | ||||
\(875\) | 367.275 | + | 867.584i | 0.419743 | + | 0.991525i | ||||
\(876\) | −170.799 | −0.194976 | ||||||||
\(877\) | − | 1319.84i | − | 1.50495i | −0.658621 | − | 0.752474i | \(-0.728860\pi\) | ||
0.658621 | − | 0.752474i | \(-0.271140\pi\) | |||||||
\(878\) | 125.251i | 0.142655i | ||||||||
\(879\) | − | 1132.58i | − | 1.28849i | ||||||
\(880\) | 25.4002 | + | 32.9255i | 0.0288638 | + | 0.0374154i | ||||
\(881\) | 1258.50i | 1.42849i | 0.699893 | + | 0.714247i | \(0.253231\pi\) | ||||
−0.699893 | + | 0.714247i | \(0.746769\pi\) | |||||||
\(882\) | − | 0.414718i | − | 0.000470202i | ||||||
\(883\) | − | 852.771i | − | 0.965765i | −0.875685 | − | 0.482883i | \(-0.839590\pi\) | ||
0.875685 | − | 0.482883i | \(-0.160410\pi\) | |||||||
\(884\) | 877.239i | 0.992351i | ||||||||
\(885\) | −177.759 | − | 230.424i | −0.200858 | − | 0.260366i | ||||
\(886\) | −423.919 | −0.478464 | ||||||||
\(887\) | − | 449.712i | − | 0.507003i | −0.967335 | − | 0.253502i | \(-0.918418\pi\) | ||
0.967335 | − | 0.253502i | \(-0.0815823\pi\) | |||||||
\(888\) | 70.2656 | 0.0791279 | ||||||||
\(889\) | − | 314.472i | − | 0.353737i | ||||||
\(890\) | 733.285 | − | 565.688i | 0.823915 | − | 0.635604i | ||||
\(891\) | 169.117i | 0.189805i | ||||||||
\(892\) | 589.634i | 0.661025i | ||||||||
\(893\) | −593.429 | −0.664534 | ||||||||
\(894\) | 861.013i | 0.963101i | ||||||||
\(895\) | 505.315 | − | 389.822i | 0.564598 | − | 0.435555i | ||||
\(896\) | − | 85.2712i | − | 0.0951687i | ||||||
\(897\) | −1091.35 | + | 798.005i | −1.21667 | + | 0.889638i | ||||
\(898\) | − | 672.889i | − | 0.749319i | ||||||
\(899\) | −340.682 | −0.378957 | ||||||||
\(900\) | 0.476766 | − | 1.81685i | 0.000529740 | − | 0.00201872i | ||||
\(901\) | −885.677 | −0.982993 | ||||||||
\(902\) | 86.2976 | 0.0956736 | ||||||||
\(903\) | 1100.53i | 1.21875i | ||||||||
\(904\) | − | 498.122i | − | 0.551020i | ||||||
\(905\) | −534.984 | − | 693.484i | −0.591142 | − | 0.766281i | ||||
\(906\) | −554.630 | −0.612175 | ||||||||
\(907\) | −620.317 | −0.683922 | −0.341961 | − | 0.939714i | \(-0.611091\pi\) | ||||
−0.341961 | + | 0.939714i | \(0.611091\pi\) | |||||||
\(908\) | 558.802 | 0.615421 | ||||||||
\(909\) | −5.48962 | −0.00603919 | ||||||||
\(910\) | −825.093 | + | 636.513i | −0.906696 | + | 0.699465i | ||||
\(911\) | − | 1122.03i | − | 1.23164i | −0.787886 | − | 0.615821i | \(-0.788825\pi\) | ||
0.787886 | − | 0.615821i | \(-0.211175\pi\) | |||||||
\(912\) | 92.0150 | 0.100894 | ||||||||
\(913\) | 147.273i | 0.161307i | ||||||||
\(914\) | − | 895.040i | − | 0.979256i | ||||||
\(915\) | −142.119 | + | 109.637i | −0.155321 | + | 0.119821i | ||||
\(916\) | − | 39.1570i | − | 0.0427478i | ||||||
\(917\) | 904.249 | 0.986095 | ||||||||
\(918\) | 854.744 | 0.931094 | ||||||||
\(919\) | − | 192.248i | − | 0.209192i | −0.994515 | − | 0.104596i | \(-0.966645\pi\) | ||
0.994515 | − | 0.104596i | \(-0.0333550\pi\) | |||||||
\(920\) | 312.390 | + | 90.6235i | 0.339554 | + | 0.0985038i | ||||
\(921\) | 1115.79 | 1.21150 | ||||||||
\(922\) | − | 551.282i | − | 0.597920i | ||||||
\(923\) | 187.733i | 0.203395i | ||||||||
\(924\) | 94.2221 | 0.101972 | ||||||||
\(925\) | −52.4371 | + | 199.826i | −0.0566887 | + | 0.216028i | ||||
\(926\) | −207.273 | −0.223837 | ||||||||
\(927\) | −5.09044 | −0.00549130 | ||||||||
\(928\) | 207.735i | 0.223852i | ||||||||
\(929\) | −403.792 | −0.434652 | −0.217326 | − | 0.976099i | \(-0.569733\pi\) | ||||
−0.217326 | + | 0.976099i | \(0.569733\pi\) | |||||||
\(930\) | 156.145 | − | 120.457i | 0.167898 | − | 0.129524i | ||||
\(931\) | 59.7313i | 0.0641582i | ||||||||
\(932\) | − | 404.498i | − | 0.434011i | ||||||
\(933\) | − | 916.270i | − | 0.982068i | ||||||
\(934\) | − | 161.958i | − | 0.173403i | ||||||
\(935\) | 142.445 | + | 184.647i | 0.152347 | + | 0.197483i | ||||
\(936\) | 2.07765 | 0.00221971 | ||||||||
\(937\) | 345.580 | 0.368815 | 0.184408 | − | 0.982850i | \(-0.440963\pi\) | ||||
0.184408 | + | 0.982850i | \(0.440963\pi\) | |||||||
\(938\) | 248.342i | 0.264757i | ||||||||
\(939\) | − | 1323.89i | − | 1.40989i | ||||||
\(940\) | 473.699 | + | 614.043i | 0.503935 | + | 0.653237i | ||||
\(941\) | − | 536.881i | − | 0.570543i | −0.958447 | − | 0.285272i | \(-0.907916\pi\) | ||
0.958447 | − | 0.285272i | \(-0.0920838\pi\) | |||||||
\(942\) | 408.852 | 0.434026 | ||||||||
\(943\) | 544.885 | − | 398.424i | 0.577821 | − | 0.422507i | ||||
\(944\) | −77.4444 | −0.0820385 | ||||||||
\(945\) | 620.191 | + | 803.936i | 0.656287 | + | 0.850726i | ||||
\(946\) | −142.822 | −0.150975 | ||||||||
\(947\) | 1325.38i | 1.39956i | 0.714361 | + | 0.699778i | \(0.246718\pi\) | ||||
−0.714361 | + | 0.699778i | \(0.753282\pi\) | |||||||
\(948\) | 533.767 | 0.563046 | ||||||||
\(949\) | 555.453 | 0.585304 | ||||||||
\(950\) | −68.6680 | + | 261.678i | −0.0722821 | + | 0.275451i | ||||
\(951\) | 259.033 | 0.272380 | ||||||||
\(952\) | − | 478.202i | − | 0.502313i | ||||||
\(953\) | 803.540 | 0.843169 | 0.421585 | − | 0.906789i | \(-0.361474\pi\) | ||||
0.421585 | + | 0.906789i | \(0.361474\pi\) | |||||||
\(954\) | 2.09764i | 0.00219878i | ||||||||
\(955\) | −101.162 | − | 131.133i | −0.105929 | − | 0.137312i | ||||
\(956\) | 232.149 | 0.242834 | ||||||||
\(957\) | −229.541 | −0.239854 | ||||||||
\(958\) | −809.086 | −0.844557 | ||||||||
\(959\) | −1737.64 | −1.81193 | ||||||||
\(960\) | −73.4501 | − | 95.2113i | −0.0765105 | − | 0.0991784i | ||||
\(961\) | −874.934 | −0.910441 | ||||||||
\(962\) | −228.510 | −0.237536 | ||||||||
\(963\) | 4.21745 | 0.00437949 | ||||||||
\(964\) | 255.523i | 0.265065i | ||||||||
\(965\) | −954.976 | − | 1237.91i | −0.989612 | − | 1.28281i | ||||
\(966\) | 594.921 | − | 435.010i | 0.615860 | − | 0.450321i | ||||
\(967\) | 753.094i | 0.778794i | 0.921070 | + | 0.389397i | \(0.127317\pi\) | ||||
−0.921070 | + | 0.389397i | \(0.872683\pi\) | |||||||
\(968\) | − | 330.012i | − | 0.340921i | ||||||
\(969\) | 516.022 | 0.532530 | ||||||||
\(970\) | 730.932 | + | 947.487i | 0.753538 | + | 0.976790i | ||||
\(971\) | − | 1335.10i | − | 1.37498i | −0.726196 | − | 0.687488i | \(-0.758713\pi\) | ||
0.726196 | − | 0.687488i | \(-0.241287\pi\) | |||||||
\(972\) | − | 4.05723i | − | 0.00417411i | ||||||
\(973\) | 690.540 | 0.709702 | ||||||||
\(974\) | −408.217 | −0.419114 | ||||||||
\(975\) | −373.002 | + | 1421.42i | −0.382566 | + | 1.45787i | ||||
\(976\) | 47.7653i | 0.0489399i | ||||||||
\(977\) | −966.819 | −0.989579 | −0.494790 | − | 0.869013i | \(-0.664755\pi\) | ||||
−0.494790 | + | 0.869013i | \(0.664755\pi\) | |||||||
\(978\) | 708.159i | 0.724089i | ||||||||
\(979\) | 272.323 | 0.278165 | ||||||||
\(980\) | 61.8061 | − | 47.6799i | 0.0630675 | − | 0.0486530i | ||||
\(981\) | 5.85912i | 0.00597260i | ||||||||
\(982\) | 941.631i | 0.958891i | ||||||||
\(983\) | −1726.38 | −1.75624 | −0.878118 | − | 0.478444i | \(-0.841201\pi\) | ||||
−0.878118 | + | 0.478444i | \(0.841201\pi\) | |||||||
\(984\) | −249.548 | −0.253606 | ||||||||
\(985\) | 738.912 | + | 957.831i | 0.750165 | + | 0.972417i | ||||
\(986\) | 1164.98i | 1.18152i | ||||||||
\(987\) | 1757.19 | 1.78033 | ||||||||
\(988\) | −299.241 | −0.302876 | ||||||||
\(989\) | −901.782 | + | 659.390i | −0.911812 | + | 0.666724i | ||||
\(990\) | 0.437317 | − | 0.337365i | 0.000441735 | − | 0.000340773i | ||||
\(991\) | −981.652 | −0.990567 | −0.495283 | − | 0.868732i | \(-0.664936\pi\) | ||||
−0.495283 | + | 0.868732i | \(0.664936\pi\) | |||||||
\(992\) | − | 52.4796i | − | 0.0529028i | ||||||
\(993\) | 86.6642i | 0.0872752i | ||||||||
\(994\) | − | 102.338i | − | 0.102955i | ||||||
\(995\) | −595.523 | − | 771.959i | −0.598515 | − | 0.775838i | ||||
\(996\) | − | 425.872i | − | 0.427582i | ||||||
\(997\) | 306.920i | 0.307844i | 0.988083 | + | 0.153922i | \(0.0491904\pi\) | ||||
−0.988083 | + | 0.153922i | \(0.950810\pi\) | |||||||
\(998\) | − | 167.111i | − | 0.167446i | ||||||
\(999\) | 222.650i | 0.222873i |
(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 | 230.3.c.a.229.15 | yes | 24 | |
5.2 | odd | 4 | 1150.3.d.e.551.2 | 24 | |||
5.3 | odd | 4 | 1150.3.d.e.551.23 | 24 | |||
5.4 | even | 2 | inner | 230.3.c.a.229.10 | yes | 24 | |
23.22 | odd | 2 | inner | 230.3.c.a.229.16 | yes | 24 | |
115.22 | even | 4 | 1150.3.d.e.551.11 | 24 | |||
115.68 | even | 4 | 1150.3.d.e.551.14 | 24 | |||
115.114 | odd | 2 | inner | 230.3.c.a.229.9 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.c.a.229.9 | ✓ | 24 | 115.114 | odd | 2 | inner | |
230.3.c.a.229.10 | yes | 24 | 5.4 | even | 2 | inner | |
230.3.c.a.229.15 | yes | 24 | 1.1 | even | 1 | trivial | |
230.3.c.a.229.16 | yes | 24 | 23.22 | odd | 2 | inner | |
1150.3.d.e.551.2 | 24 | 5.2 | odd | 4 | |||
1150.3.d.e.551.11 | 24 | 115.22 | even | 4 | |||
1150.3.d.e.551.14 | 24 | 115.68 | even | 4 | |||
1150.3.d.e.551.23 | 24 | 5.3 | odd | 4 |