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 | 229.10 | ||
Character | \(\chi\) | \(=\) | 230.229 |
Dual form | 230.3.c.a.229.16 |
$q$-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 | \(0.167050\pi\) | ||||
−0.865423 | + | 0.501042i | \(0.832950\pi\) | |||||||
\(4\) | −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 | \(-0.680954\pi\) | ||||
−0.538355 | + | 0.842718i | \(0.680954\pi\) | |||||||
\(8\) | 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 | \(0.270933\pi\) | ||||
−0.659110 | + | 0.752047i | \(0.729067\pi\) | |||||||
\(14\) | 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 | \(-0.729345\pi\) | ||||
−0.659767 | + | 0.751470i | \(0.729345\pi\) | |||||||
\(18\) | 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 | \(-0.464380\pi\) | ||||
0.111671 | + | 0.993745i | \(0.464380\pi\) | |||||||
\(38\) | 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 | \(-0.308960\pi\) | ||||
0.564784 | + | 0.825239i | \(0.308960\pi\) | |||||||
\(44\) | 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 | \(-0.691160\pi\) | ||
0.565094 | − | 0.825027i | \(-0.308840\pi\) | |||||||
\(48\) | 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 | \(-0.378508\pi\) | ||||
0.372478 | + | 0.928041i | \(0.378508\pi\) | |||||||
\(54\) | 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 | \(-0.555628\pi\) | ||||
−0.173874 | + | 0.984768i | \(0.555628\pi\) | |||||||
\(68\) | 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 | \(-0.937669\pi\) | ||
0.980889 | − | 0.194570i | \(-0.0623312\pi\) | |||||||
\(74\) | − | 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 | \(-0.359679\pi\) | ||||
0.426692 | + | 0.904397i | \(0.359679\pi\) | |||||||
\(84\) | 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 | \(-0.162604\pi\) | ||||
0.872336 | + | 0.488907i | \(0.162604\pi\) | |||||||
\(98\) | − | 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 | \(-0.728503\pi\) | ||||
−0.657778 | + | 0.753212i | \(0.728503\pi\) | |||||||
\(104\) | −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 | \(-0.324215\pi\) | ||||
0.524599 | + | 0.851349i | \(0.324215\pi\) | |||||||
\(108\) | − | 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 | \(-0.784405\pi\) | ||||
−0.779260 | + | 0.626701i | \(0.784405\pi\) | |||||||
\(114\) | 32.5322i | 0.285370i | ||||||||
\(115\) | −114.962 | − | 2.95741i | −0.999669 | − | 0.0257166i | ||||
\(116\) | −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 | \(0.0525260\pi\) | ||||
−0.986416 | + | 0.164268i | \(0.947474\pi\) | |||||||
\(128\) | 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 | \(-0.181721\pi\) | ||||
0.841418 | + | 0.540385i | \(0.181721\pi\) | |||||||
\(138\) | −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 | \(-0.599079\pi\) | ||||
−0.306264 | + | 0.951947i | \(0.599079\pi\) | |||||||
\(158\) | −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 | \(-0.829296\pi\) | ||
0.859614 | − | 0.510943i | \(-0.170704\pi\) | |||||||
\(164\) | −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 | \(0.196987\pi\) | ||||
−0.814545 | + | 0.580100i | \(0.803013\pi\) | |||||||
\(168\) | 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 | \(-0.994211\pi\) | ||
0.999835 | − | 0.0181860i | \(-0.00578910\pi\) | |||||||
\(174\) | 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 | \(-0.699423\pi\) | ||
0.586318 | − | 0.810081i | \(-0.300577\pi\) | |||||||
\(194\) | − | 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 | \(0.210470\pi\) | ||||
−0.789249 | + | 0.614073i | \(0.789530\pi\) | |||||||
\(198\) | 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 | \(0.229878\pi\) | ||||
−0.750364 | + | 0.661025i | \(0.770122\pi\) | |||||||
\(224\) | 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 | \(-0.288986\pi\) | ||||
0.615421 | + | 0.788198i | \(0.288986\pi\) | |||||||
\(228\) | 46.0075 | 0.201787 | ||||||||
\(229\) | 19.5785i | 0.0854956i | 0.999086 | + | 0.0427478i | \(0.0136112\pi\) | ||||
−0.999086 | + | 0.0427478i | \(0.986389\pi\) | |||||||
\(230\) | −4.18240 | + | 162.581i | −0.0181844 | + | 0.706873i | ||||
\(231\) | −47.1111 | −0.203944 | ||||||||
\(232\) | 103.867i | 0.447704i | ||||||||
\(233\) | − | 202.249i | − | 0.868022i | −0.900908 | − | 0.434011i | \(-0.857098\pi\) | ||
0.900908 | − | 0.434011i | \(-0.142902\pi\) | |||||||
\(234\) | −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 | \(-0.669839\pi\) | ||
0.508605 | − | 0.861000i | \(-0.330161\pi\) | |||||||
\(258\) | 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 | \(-0.563913\pi\) | ||||
−0.199443 | + | 0.979910i | \(0.563913\pi\) | |||||||
\(264\) | 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 | \(0.0149088\pi\) | ||||
−0.998903 | + | 0.0468203i | \(0.985091\pi\) | |||||||
\(278\) | − | 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 | \(-0.268944\pi\) | ||||
0.663797 | + | 0.747913i | \(0.268944\pi\) | |||||||
\(284\) | 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 | \(-0.722271\pi\) | ||||
−0.642906 | + | 0.765945i | \(0.722271\pi\) | |||||||
\(294\) | 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 | \(-0.793376\pi\) | ||
0.796612 | − | 0.604491i | \(-0.206624\pi\) | |||||||
\(308\) | − | 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 | \(-0.748371\pi\) | ||||
−0.703478 | + | 0.710717i | \(0.748371\pi\) | |||||||
\(314\) | 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 | \(-0.956605\pi\) | ||
0.990722 | − | 0.135907i | \(-0.0433947\pi\) | |||||||
\(318\) | 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 | \(-0.654629\pi\) | ||||
−0.466900 | + | 0.884310i | \(0.654629\pi\) | |||||||
\(338\) | 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 | ||||||||
\(345\) | 8.89072 | − | 345.605i | 0.0257702 | − | 1.00175i | ||||
\(346\) | −8.89874 | −0.0257189 | ||||||||
\(347\) | 318.146i | 0.916847i | 0.888734 | + | 0.458424i | \(0.151586\pi\) | ||||
−0.888734 | + | 0.458424i | \(0.848414\pi\) | |||||||
\(348\) | − | 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 | \(-0.995140\pi\) | ||
0.999883 | − | 0.0152675i | \(-0.00485998\pi\) | |||||||
\(354\) | −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 | \(-0.442338\pi\) | ||||
0.180162 | + | 0.983637i | \(0.442338\pi\) | |||||||
\(368\) | −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 | \(-0.643150\pi\) | ||||
−0.434713 | + | 0.900569i | \(0.643150\pi\) | |||||||
\(374\) | 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 | \(-0.355413\pi\) | ||||
0.438772 | + | 0.898598i | \(0.355413\pi\) | |||||||
\(384\) | −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 | \(-0.914583\pi\) | ||
0.964211 | − | 0.265137i | \(-0.0854171\pi\) | |||||||
\(398\) | 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 | \(-0.439887\pi\) | ||||
0.187730 | + | 0.982221i | \(0.439887\pi\) | |||||||
\(434\) | − | 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 | \(-0.890140\pi\) | ||
0.941029 | − | 0.338325i | \(-0.109860\pi\) | |||||||
\(444\) | − | 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 | \(-0.256537\pi\) | ||||
0.692438 | + | 0.721477i | \(0.256537\pi\) | |||||||
\(458\) | 27.6882 | 0.0604545 | ||||||||
\(459\) | − | 604.395i | − | 1.31677i | ||||||
\(460\) | 229.924 | + | 5.91481i | 0.499835 | + | 0.0128583i | ||||
\(461\) | −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 | \(-0.949406\pi\) | ||
0.987395 | − | 0.158277i | \(-0.0505939\pi\) | |||||||
\(464\) | 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 | \(-0.460872\pi\) | ||||
0.122614 | + | 0.992454i | \(0.460872\pi\) | |||||||
\(468\) | 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 | \(-0.904228\pi\) | ||
0.955077 | − | 0.296358i | \(-0.0957722\pi\) | |||||||
\(488\) | −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 | \(-0.199674\pi\) | ||||
0.809618 | + | 0.586957i | \(0.199674\pi\) | |||||||
\(504\) | 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 | \(-0.518878\pi\) | ||||
−0.0592736 | + | 0.998242i | \(0.518878\pi\) | |||||||
\(524\) | −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 | \(0.239647\pi\) | ||||
−0.729726 | + | 0.683739i | \(0.760353\pi\) | |||||||
\(548\) | −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 | \(-0.622222\pi\) | ||||
−0.374605 | + | 0.927185i | \(0.622222\pi\) | |||||||
\(558\) | − | 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 | \(-0.190025\pi\) | ||||
0.827037 | + | 0.562147i | \(0.190025\pi\) | |||||||
\(564\) | −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 | ||||||||
\(575\) | −446.089 | − | 362.808i | −0.775807 | − | 0.630971i | ||||
\(576\) | 0.300538 | 0.000521767 | ||||||||
\(577\) | − | 7.96828i | − | 0.0138099i | −0.999976 | − | 0.00690493i | \(-0.997802\pi\) | ||
0.999976 | − | 0.00690493i | \(-0.00219792\pi\) | |||||||
\(578\) | − | 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 | \(-0.679256\pi\) | ||
0.533853 | − | 0.845577i | \(-0.320744\pi\) | |||||||
\(588\) | − | 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 | \(-0.659288\pi\) | ||
0.479792 | − | 0.877383i | \(-0.340712\pi\) | |||||||
\(594\) | − | 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 | \(-0.838421\pi\) | ||
0.873905 | − | 0.486096i | \(-0.161579\pi\) | |||||||
\(608\) | 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 | \(-0.717389\pi\) | ||||
−0.631081 | + | 0.775717i | \(0.717389\pi\) | |||||||
\(614\) | −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 | \(-0.325779\pi\) | ||||
0.520411 | + | 0.853916i | \(0.325779\pi\) | |||||||
\(618\) | −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 | \(-0.588674\pi\) | ||||
−0.274990 | + | 0.961447i | \(0.588674\pi\) | |||||||
\(644\) | −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 | \(-0.868048\pi\) | ||
0.915302 | − | 0.402768i | \(-0.131952\pi\) | |||||||
\(648\) | − | 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 | \(0.233927\pi\) | ||||
−0.741896 | + | 0.670515i | \(0.766073\pi\) | |||||||
\(654\) | − | 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 | \(-0.869000\pi\) | ||
0.916503 | − | 0.400029i | \(-0.131000\pi\) | |||||||
\(674\) | 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 | \(-0.467203\pi\) | ||||
0.102852 | + | 0.994697i | \(0.467203\pi\) | |||||||
\(678\) | −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 | \(0.277567\pi\) | ||||
−0.643294 | + | 0.765619i | \(0.722433\pi\) | |||||||
\(684\) | 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 | ||||||||
\(690\) | −488.759 | − | 12.5734i | −0.708347 | − | 0.0182223i | ||||
\(691\) | −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 | \(-0.769289\pi\) | ||||
−0.748631 | + | 0.662986i | \(0.769289\pi\) | |||||||
\(728\) | 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 | \(-0.206452\pi\) | ||||
0.796938 | + | 0.604061i | \(0.206452\pi\) | |||||||
\(734\) | − | 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 | \(-0.700320\pi\) | ||||
−0.588599 | + | 0.808425i | \(0.700320\pi\) | |||||||
\(744\) | 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 | \(-0.574972\pi\) | ||||
−0.233360 | + | 0.972390i | \(0.574972\pi\) | |||||||
\(758\) | −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 | \(-0.713356\pi\) | ||||
−0.621203 | + | 0.783650i | \(0.713356\pi\) | |||||||
\(774\) | 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 | \(-0.615338\pi\) | ||||
−0.354468 | + | 0.935068i | \(0.615338\pi\) | |||||||
\(788\) | − | 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 | \(-0.522727\pi\) | ||||
−0.0713377 | + | 0.997452i | \(0.522727\pi\) | |||||||
\(798\) | − | 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 | ||||||||
\(805\) | 866.466 | + | 22.2899i | 1.07635 | + | 0.0276893i | ||||
\(806\) | −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 | \(-0.953441\pi\) | ||
0.989322 | − | 0.145749i | \(-0.0465593\pi\) | |||||||
\(824\) | − | 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 | \(-0.205836\pi\) | ||||
0.798105 | + | 0.602519i | \(0.205836\pi\) | |||||||
\(828\) | −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 | \(0.0251973\pi\) | ||||
−0.996869 | + | 0.0790771i | \(0.974803\pi\) | |||||||
\(854\) | −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 | \(0.0902242\pi\) | ||||
−0.960097 | + | 0.279667i | \(0.909776\pi\) | |||||||
\(858\) | 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 | \(0.174176\pi\) | ||||
−0.853991 | + | 0.520288i | \(0.825824\pi\) | |||||||
\(864\) | 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 | \(0.271140\pi\) | ||||
−0.658621 | + | 0.752474i | \(0.728860\pi\) | |||||||
\(878\) | − | 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 | \(0.160410\pi\) | ||||
−0.875685 | + | 0.482883i | \(0.839590\pi\) | |||||||
\(884\) | 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 | \(0.0815823\pi\) | ||||
−0.967335 | + | 0.253502i | \(0.918418\pi\) | |||||||
\(888\) | −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 | \(-0.388909\pi\) | ||||
0.341961 | + | 0.939714i | \(0.388909\pi\) | |||||||
\(908\) | −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 | \(-0.0333550\pi\) | |||||||
\(920\) | 8.36481 | − | 325.162i | 0.00909218 | − | 0.353436i | ||||
\(921\) | 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 | \(-0.559037\pi\) | ||||
−0.184408 | + | 0.982850i | \(0.559037\pi\) | |||||||
\(938\) | − | 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 | \(-0.753282\pi\) | ||
0.714361 | − | 0.699778i | \(-0.246718\pi\) | |||||||
\(948\) | −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 | \(-0.638526\pi\) | ||||
−0.421585 | + | 0.906789i | \(0.638526\pi\) | |||||||
\(954\) | 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 | \(-0.872683\pi\) | ||
0.921070 | − | 0.389397i | \(-0.127317\pi\) | |||||||
\(968\) | 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 | \(-0.335245\pi\) | ||||
0.494790 | + | 0.869013i | \(0.335245\pi\) | |||||||
\(978\) | − | 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 | \(-0.158799\pi\) | ||||
0.878118 | + | 0.478444i | \(0.158799\pi\) | |||||||
\(984\) | −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 | \(-0.950810\pi\) | ||
0.988083 | − | 0.153922i | \(-0.0491904\pi\) | |||||||
\(998\) | 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.229.10 | yes | 24 | |
5.2 | odd | 4 | 1150.3.d.e.551.23 | 24 | |||
5.3 | odd | 4 | 1150.3.d.e.551.2 | 24 | |||
5.4 | even | 2 | inner | 230.3.c.a.229.15 | yes | 24 | |
23.22 | odd | 2 | inner | 230.3.c.a.229.9 | ✓ | 24 | |
115.22 | even | 4 | 1150.3.d.e.551.14 | 24 | |||
115.68 | even | 4 | 1150.3.d.e.551.11 | 24 | |||
115.114 | odd | 2 | inner | 230.3.c.a.229.16 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.c.a.229.9 | ✓ | 24 | 23.22 | odd | 2 | inner | |
230.3.c.a.229.10 | yes | 24 | 1.1 | even | 1 | trivial | |
230.3.c.a.229.15 | yes | 24 | 5.4 | even | 2 | inner | |
230.3.c.a.229.16 | yes | 24 | 115.114 | odd | 2 | inner | |
1150.3.d.e.551.2 | 24 | 5.3 | odd | 4 | |||
1150.3.d.e.551.11 | 24 | 115.68 | even | 4 | |||
1150.3.d.e.551.14 | 24 | 115.22 | even | 4 | |||
1150.3.d.e.551.23 | 24 | 5.2 | odd | 4 |