Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1119,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.1119");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.n (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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1731891456.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1119.2 | ||
Root | \(-2.21837 + 1.28078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1119 |
Dual form | 2240.2.n.b.1119.3 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.56155 | −1.47891 | −0.739457 | − | 0.673204i | \(-0.764917\pi\) | ||||
−0.739457 | + | 0.673204i | \(0.764917\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | − | 1.00000i | 0.894427 | − | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | + | 1.73205i | −0.755929 | + | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.56155 | 1.18718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.972638 | 0.293261 | 0.146631 | − | 0.989191i | \(-0.453157\pi\) | ||||
0.146631 | + | 0.989191i | \(0.453157\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.561553i | 0.155747i | 0.996963 | + | 0.0778734i | \(0.0248130\pi\) | ||||
−0.996963 | + | 0.0778734i | \(0.975187\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.12311 | + | 2.56155i | −1.32278 | + | 0.661390i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.43674 | −1.07607 | −0.538034 | − | 0.842923i | \(-0.680833\pi\) | ||||
−0.538034 | + | 0.842923i | \(0.680833\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.12311i | 0.257658i | 0.991667 | + | 0.128829i | \(0.0411218\pi\) | ||||
−0.991667 | + | 0.128829i | \(0.958878\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.12311 | − | 4.43674i | 1.11795 | − | 0.968176i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.12311 | 0.234184 | 0.117092 | − | 0.993121i | \(-0.462643\pi\) | ||||
0.117092 | + | 0.993121i | \(0.462643\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.43845 | −0.276829 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.43674i | − | 0.823882i | −0.911211 | − | 0.411941i | \(-0.864851\pi\) | ||
0.911211 | − | 0.411941i | \(-0.135149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.87348 | −1.59372 | −0.796862 | − | 0.604161i | \(-0.793508\pi\) | ||||
−0.796862 | + | 0.604161i | \(0.793508\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.49146 | −0.433708 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.26795 | + | 5.46410i | −0.383353 | + | 0.923602i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.87348 | 1.45879 | 0.729396 | − | 0.684092i | \(-0.239801\pi\) | ||||
0.729396 | + | 0.684092i | \(0.239801\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.43845i | − | 0.230336i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.87348i | 1.38580i | 0.721031 | + | 0.692902i | \(0.243668\pi\) | ||||
−0.721031 | + | 0.692902i | \(0.756332\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.94528i | 0.296652i | 0.988939 | + | 0.148326i | \(0.0473885\pi\) | ||||
−0.988939 | + | 0.148326i | \(0.952612\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.12311 | − | 3.56155i | 1.06185 | − | 0.530925i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.972638i | − | 0.141874i | −0.997481 | − | 0.0709369i | \(-0.977401\pi\) | ||
0.997481 | − | 0.0709369i | \(-0.0225989\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.3649 | 1.59141 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.94528 | − | 0.972638i | 0.262301 | − | 0.131150i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.87689i | − | 0.381054i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 4.00000i | − | 0.520756i | −0.965507 | − | 0.260378i | \(-0.916153\pi\) | ||
0.965507 | − | 0.260378i | \(-0.0838471\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.12311 | −0.143799 | −0.0718995 | − | 0.997412i | \(-0.522906\pi\) | ||||
−0.0718995 | + | 0.997412i | \(0.522906\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.12311 | + | 6.16879i | −0.897427 | + | 0.777195i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.561553 | + | 1.12311i | 0.0696521 | + | 0.139304i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6.92820i | − | 0.846415i | −0.906033 | − | 0.423207i | \(-0.860904\pi\) | ||
0.906033 | − | 0.423207i | \(-0.139096\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.87689 | −0.346337 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.2462i | − | 1.69071i | −0.534202 | − | 0.845357i | \(-0.679388\pi\) | ||
0.534202 | − | 0.845357i | \(-0.320612\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.92820 | −0.810885 | −0.405442 | − | 0.914121i | \(-0.632883\pi\) | ||||
−0.405442 | + | 0.914121i | \(0.632883\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.68466 | + | 10.2462i | −0.887348 | + | 1.18313i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.94528 | + | 1.68466i | −0.221685 | + | 0.191985i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.68466i | 0.864592i | 0.901732 | + | 0.432296i | \(0.142296\pi\) | ||||
−0.901732 | + | 0.432296i | \(0.857704\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.87348 | + | 4.43674i | −0.962464 | + | 0.481232i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.3649i | 1.21845i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 8.87348i | − | 0.940587i | −0.882510 | − | 0.470293i | \(-0.844148\pi\) | ||
0.882510 | − | 0.470293i | \(-0.155852\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.972638 | − | 1.12311i | −0.101960 | − | 0.117733i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 22.7299 | 2.35698 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.12311 | + | 2.24621i | 0.115228 | + | 0.230456i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.41967 | −0.956422 | −0.478211 | − | 0.878245i | \(-0.658715\pi\) | ||||
−0.478211 | + | 0.878245i | \(0.658715\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.46410 | 0.348155 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.3693 | −1.13129 | −0.565645 | − | 0.824649i | \(-0.691373\pi\) | ||||
−0.565645 | + | 0.824649i | \(0.691373\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.8290i | 1.46115i | 0.682833 | + | 0.730575i | \(0.260748\pi\) | ||||
−0.682833 | + | 0.730575i | \(0.739252\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.80947 | − | 13.9966i | 0.566946 | − | 1.36593i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 10.8188i | − | 1.04589i | −0.852367 | − | 0.522944i | \(-0.824834\pi\) | ||
0.852367 | − | 0.522944i | \(-0.175166\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.2931i | 1.75217i | 0.482161 | + | 0.876083i | \(0.339852\pi\) | ||||
−0.482161 | + | 0.876083i | \(0.660148\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −22.7299 | −2.15743 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 15.3693i | − | 1.44582i | −0.690940 | − | 0.722912i | \(-0.742803\pi\) | ||
0.690940 | − | 0.722912i | \(-0.257197\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.24621 | − | 1.12311i | 0.209460 | − | 0.104730i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000i | 0.184900i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.87348 | − | 7.68466i | 0.813431 | − | 0.704451i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0540 | −0.913998 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 22.7299i | − | 2.04948i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.00000 | − | 11.0000i | 0.178885 | − | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 4.98293i | − | 0.438722i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 19.3693i | − | 1.69231i | −0.532941 | − | 0.846153i | \(-0.678913\pi\) | ||
0.532941 | − | 0.846153i | \(-0.321087\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.94528 | − | 2.24621i | −0.168677 | − | 0.194771i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.87689 | + | 1.43845i | −0.247604 | + | 0.123802i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 13.1231i | − | 1.12118i | −0.828093 | − | 0.560591i | \(-0.810574\pi\) | ||
0.828093 | − | 0.560591i | \(-0.189426\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 14.2462i | − | 1.20835i | −0.796852 | − | 0.604174i | \(-0.793503\pi\) | ||
0.796852 | − | 0.604174i | \(-0.206497\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.49146i | 0.209819i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.546188i | 0.0456745i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.43674 | − | 8.87348i | −0.368451 | − | 0.736902i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.56155 | + | 17.7470i | −0.211273 | + | 1.46374i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.8188i | 0.886307i | 0.896446 | + | 0.443153i | \(0.146140\pi\) | ||||
−0.896446 | + | 0.443153i | \(0.853860\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 15.0540i | − | 1.22508i | −0.790441 | − | 0.612538i | \(-0.790149\pi\) | ||
0.790441 | − | 0.612538i | \(-0.209851\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.8017 | −1.27749 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.7470 | + | 8.87348i | −1.42547 | + | 0.712735i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 20.2462i | − | 1.61582i | −0.589303 | − | 0.807912i | \(-0.700598\pi\) | ||
0.589303 | − | 0.807912i | \(-0.299402\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.24621 | + | 1.94528i | −0.177026 | + | 0.153309i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 24.6752i | − | 1.93271i | −0.257216 | − | 0.966354i | \(-0.582805\pi\) | ||
0.257216 | − | 0.966354i | \(-0.417195\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.98293 | + | 2.49146i | −0.387920 | + | 0.193960i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.91791i | 0.225795i | 0.993607 | + | 0.112897i | \(0.0360132\pi\) | ||||
−0.993607 | + | 0.112897i | \(0.963987\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6847 | 0.975743 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000i | 0.305888i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 9.68466i | − | 0.736311i | −0.929764 | − | 0.368155i | \(-0.879989\pi\) | ||
0.929764 | − | 0.368155i | \(-0.120011\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.928203 | + | 13.1962i | 0.0701656 | + | 0.997535i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.2462i | 0.770152i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.2111 | −1.58539 | −0.792695 | − | 0.609619i | \(-0.791322\pi\) | ||||
−0.792695 | + | 0.609619i | \(0.791322\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.2462 | −1.05891 | −0.529456 | − | 0.848337i | \(-0.677604\pi\) | ||||
−0.529456 | + | 0.848337i | \(0.677604\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.87689 | 0.212666 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.7470 | − | 8.87348i | 1.30478 | − | 0.652391i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.31534 | −0.315569 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.87689 | − | 2.49146i | 0.209263 | − | 0.181227i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 5.43845i | − | 0.393512i | −0.980452 | − | 0.196756i | \(-0.936959\pi\) | ||
0.980452 | − | 0.196756i | \(-0.0630407\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.36932i | 0.530455i | 0.964186 | + | 0.265228i | \(0.0854471\pi\) | ||||
−0.964186 | + | 0.265228i | \(0.914553\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.43845 | − | 2.87689i | −0.103009 | − | 0.206019i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.7299 | −1.61944 | −0.809719 | − | 0.586818i | \(-0.800380\pi\) | ||||
−0.809719 | + | 0.586818i | \(0.800380\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.7470 | 1.25805 | 0.629024 | − | 0.777386i | \(-0.283455\pi\) | ||||
0.629024 | + | 0.777386i | \(0.283455\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.7470i | 1.25177i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.68466 | + | 8.87348i | 0.539357 | + | 0.622796i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.87348 | + | 17.7470i | 0.619751 | + | 1.23950i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.09238i | 0.0755612i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.8290 | −1.02087 | −0.510437 | − | 0.859915i | \(-0.670516\pi\) | ||||
−0.510437 | + | 0.859915i | \(0.670516\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 36.4924i | 2.50042i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.94528 | + | 3.89055i | 0.132667 | + | 0.265333i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.7470 | − | 15.3693i | 1.20474 | − | 1.04334i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.7470 | 1.19923 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.49146i | − | 0.167594i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 0.972638i | − | 0.0651327i | −0.999470 | − | 0.0325663i | \(-0.989632\pi\) | ||
0.999470 | − | 0.0325663i | \(-0.0103680\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.6847 | − | 14.2462i | 0.712311 | − | 0.949747i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.6847 | −1.04103 | −0.520514 | − | 0.853853i | \(-0.674260\pi\) | ||||
−0.520514 | + | 0.853853i | \(0.674260\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.12311 | 0.0742169 | 0.0371085 | − | 0.999311i | \(-0.488185\pi\) | ||||
0.0371085 | + | 0.999311i | \(0.488185\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.98293 | − | 4.31534i | 0.327853 | − | 0.283929i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.4924i | 1.86660i | 0.359097 | + | 0.933300i | \(0.383085\pi\) | ||||
−0.359097 | + | 0.933300i | \(0.616915\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.972638 | − | 1.94528i | −0.0634479 | − | 0.126896i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 19.6847i | − | 1.27866i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.68466i | 0.497079i | 0.968622 | + | 0.248540i | \(0.0799506\pi\) | ||||
−0.968622 | + | 0.248540i | \(0.920049\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.98293i | − | 0.320979i | −0.987038 | − | 0.160489i | \(-0.948693\pi\) | ||
0.987038 | − | 0.160489i | \(-0.0513072\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.2462 | 1.42710 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.92820 | − | 14.8564i | −0.314851 | − | 0.949141i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.630683 | −0.0401294 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.2462 | −0.649327 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 20.0000i | − | 1.26239i | −0.775625 | − | 0.631194i | \(-0.782565\pi\) | ||
0.775625 | − | 0.631194i | \(-0.217435\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.09238 | 0.0686770 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 22.7299 | − | 11.3649i | 1.42340 | − | 0.711700i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.92820 | 0.432169 | 0.216085 | − | 0.976375i | \(-0.430671\pi\) | ||||
0.216085 | + | 0.976375i | \(0.430671\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.7470 | + | 15.3693i | −1.10274 | + | 0.955003i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 15.8017i | − | 0.978100i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0000 | 0.739952 | 0.369976 | − | 0.929041i | \(-0.379366\pi\) | ||||
0.369976 | + | 0.929041i | \(0.379366\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.7299i | 1.39105i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.0000 | 1.21942 | 0.609711 | − | 0.792624i | \(-0.291286\pi\) | ||||
0.609711 | + | 0.792624i | \(0.291286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.7299 | −1.38074 | −0.690371 | − | 0.723455i | \(-0.742553\pi\) | ||||
−0.690371 | + | 0.723455i | \(0.742553\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.49146 | + | 2.87689i | 0.150790 | + | 0.174118i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.91791 | − | 3.89055i | 0.175957 | − | 0.234609i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.8564 | −0.832551 | −0.416275 | − | 0.909239i | \(-0.636665\pi\) | ||||
−0.416275 | + | 0.909239i | \(0.636665\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −31.6034 | −1.89204 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.6847 | −1.53222 | −0.766109 | − | 0.642711i | \(-0.777810\pi\) | ||||
−0.766109 | + | 0.642711i | \(0.777810\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.43845 | 0.323282 | 0.161641 | − | 0.986850i | \(-0.448321\pi\) | ||||
0.161641 | + | 0.986850i | \(0.448321\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.87689 | − | 5.75379i | −0.170413 | − | 0.340825i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.3693 | − | 17.7470i | −0.907222 | − | 1.04757i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.68466 | 0.157921 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.1290 | 1.41447 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.3153i | 0.836311i | 0.908375 | + | 0.418156i | \(0.137323\pi\) | ||||
−0.908375 | + | 0.418156i | \(0.862677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | − | 8.00000i | −0.232889 | − | 0.465778i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.39909 | −0.0811833 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.630683i | 0.0364733i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.36932 | − | 3.89055i | −0.194204 | − | 0.224248i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 29.1231 | 1.67308 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.24621 | + | 1.12311i | −0.128618 | + | 0.0643088i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.93087 | −0.566785 | −0.283392 | − | 0.959004i | \(-0.591460\pi\) | ||||
−0.283392 | + | 0.959004i | \(0.591460\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 37.9854i | − | 2.16091i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.8393 | 1.06828 | 0.534140 | − | 0.845396i | \(-0.320635\pi\) | ||||
0.534140 | + | 0.845396i | \(0.320635\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.2931 | −1.03399 | −0.516995 | − | 0.855988i | \(-0.672949\pi\) | ||||
−0.516995 | + | 0.855988i | \(0.672949\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.07742 | + | 19.4607i | −0.455111 | + | 1.09649i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.7470 | 0.996768 | 0.498384 | − | 0.866956i | \(-0.333927\pi\) | ||||
0.498384 | + | 0.866956i | \(0.333927\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.31534i | − | 0.241613i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 27.7128i | 1.54678i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.98293i | − | 0.277257i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.24621 | + | 1.68466i | 0.124597 | + | 0.0934480i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 46.8589i | − | 2.59130i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.68466 | + | 1.94528i | 0.0928782 | + | 0.107247i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.3205 | 0.952021 | 0.476011 | − | 0.879440i | \(-0.342082\pi\) | ||||
0.476011 | + | 0.879440i | \(0.342082\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 31.6034 | 1.73185 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.92820 | − | 13.8564i | −0.378528 | − | 0.757056i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 22.7386i | − | 1.23865i | −0.785134 | − | 0.619326i | \(-0.787406\pi\) | ||
0.785134 | − | 0.619326i | \(-0.212594\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 39.3693i | 2.13825i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.63068 | −0.467378 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.75379 | + | 2.87689i | −0.309774 | + | 0.154887i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.8017i | 0.848279i | 0.905597 | + | 0.424139i | \(0.139423\pi\) | ||||
−0.905597 | + | 0.424139i | \(0.860577\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.12311 | 0.0601185 | 0.0300592 | − | 0.999548i | \(-0.490430\pi\) | ||||
0.0300592 | + | 0.999548i | \(0.490430\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 0.807764i | − | 0.0431153i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.2931 | 0.973646 | 0.486823 | − | 0.873501i | \(-0.338156\pi\) | ||||
0.486823 | + | 0.873501i | \(0.338156\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.2462 | − | 28.4924i | −0.756110 | − | 1.51222i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −22.7299 | + | 19.6847i | −1.20299 | + | 1.04182i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.0000i | 0.633336i | 0.948536 | + | 0.316668i | \(0.102564\pi\) | ||||
−0.948536 | + | 0.316668i | \(0.897436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.7386 | 0.933612 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 25.7538 | 1.35172 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.8564 | + | 6.92820i | −0.725277 | + | 0.362639i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 36.4666i | 1.90354i | 0.306814 | + | 0.951769i | \(0.400737\pi\) | ||||
−0.306814 | + | 0.951769i | \(0.599263\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 31.6034i | 1.64521i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.6204 | 1.37835 | 0.689177 | − | 0.724593i | \(-0.257972\pi\) | ||||
0.689177 | + | 0.724593i | \(0.257972\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.12311 | + | 28.1771i | −0.264556 | + | 1.45506i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.49146 | 0.128317 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.1393 | 1.44542 | 0.722708 | − | 0.691153i | \(-0.242897\pi\) | ||||
0.722708 | + | 0.691153i | \(0.242897\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 30.7386 | 1.57479 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.426450i | 0.0217906i | 0.999941 | + | 0.0108953i | \(0.00346815\pi\) | ||||
−0.999941 | + | 0.0108953i | \(0.996532\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.20589 | + | 5.31459i | −0.112423 | + | 0.270857i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.92820i | 0.352180i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 0.546188i | − | 0.0276928i | −0.999904 | − | 0.0138464i | \(-0.995592\pi\) | ||
0.999904 | − | 0.0138464i | \(-0.00440759\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.98293 | −0.251997 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 49.6155i | 2.50277i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.68466 | + | 15.3693i | 0.386657 | + | 0.773314i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.93087i | 0.197285i | 0.995123 | + | 0.0986423i | \(0.0314500\pi\) | ||||
−0.995123 | + | 0.0986423i | \(0.968550\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.98293 | + | 5.75379i | 0.249458 | + | 0.288050i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.80776 | −0.140213 | −0.0701065 | − | 0.997540i | \(-0.522334\pi\) | ||||
−0.0701065 | + | 0.997540i | \(0.522334\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 4.98293i | − | 0.248217i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −14.0000 | + | 7.00000i | −0.695666 | + | 0.347833i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.63068 | 0.427807 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 31.6034i | − | 1.56269i | −0.624102 | − | 0.781343i | \(-0.714535\pi\) | ||
0.624102 | − | 0.781343i | \(-0.285465\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 33.6155i | 1.65813i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.92820 | + | 8.00000i | 0.340915 | + | 0.393654i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.00000 | − | 4.00000i | 0.392705 | − | 0.196352i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 36.4924i | 1.78704i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.7386i | 1.30627i | 0.757242 | + | 0.653134i | \(0.226546\pi\) | ||||
−0.757242 | + | 0.653134i | \(0.773454\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.43674i | 0.216233i | 0.994138 | + | 0.108117i | \(0.0344820\pi\) | ||||
−0.994138 | + | 0.108117i | \(0.965518\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 3.46410i | − | 0.168430i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.3102 | + | 17.7470i | −0.645640 | + | 0.860854i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.24621 | − | 1.94528i | 0.108702 | − | 0.0941385i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 1.39909i | − | 0.0675486i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.3153i | 0.785882i | 0.919564 | + | 0.392941i | \(0.128542\pi\) | ||||
−0.919564 | + | 0.392941i | \(0.871458\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.03765 | −0.145980 | −0.0729901 | − | 0.997333i | \(-0.523254\pi\) | ||||
−0.0729901 | + | 0.997333i | \(0.523254\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.3649 | + | 22.7299i | 0.544907 | + | 1.08981i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.26137i | 0.0603393i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.8564 | −0.661330 | −0.330665 | − | 0.943748i | \(-0.607273\pi\) | ||||
−0.330665 | + | 0.943748i | \(0.607273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.56155 | − | 24.6752i | 0.169598 | − | 1.17501i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 29.6581i | − | 1.40910i | −0.709655 | − | 0.704549i | \(-0.751149\pi\) | ||
0.709655 | − | 0.704549i | \(-0.248851\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.87348 | − | 17.7470i | −0.420643 | − | 0.841287i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 27.7128i | − | 1.31077i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.0540 | 1.37114 | 0.685571 | − | 0.728006i | \(-0.259553\pi\) | ||||
0.685571 | + | 0.728006i | \(0.259553\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.63068i | 0.406403i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 38.5616i | 1.81178i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.06838 | − | 1.27357i | −0.143848 | − | 0.0597060i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 0.630683i | − | 0.0295021i | −0.999891 | − | 0.0147511i | \(-0.995304\pi\) | ||
0.999891 | − | 0.0147511i | \(-0.00469558\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.38202 | 0.297887 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.0000 | −0.931493 | −0.465746 | − | 0.884918i | \(-0.654214\pi\) | ||||
−0.465746 | + | 0.884918i | \(0.654214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.3693 | −0.528377 | −0.264188 | − | 0.964471i | \(-0.585104\pi\) | ||||
−0.264188 | + | 0.964471i | \(0.585104\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 45.4598 | − | 22.7299i | 2.10815 | − | 1.05407i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.0540 | 1.43701 | 0.718503 | − | 0.695524i | \(-0.244828\pi\) | ||||
0.718503 | + | 0.695524i | \(0.244828\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.0000 | + | 13.8564i | 0.554109 | + | 0.639829i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 51.8617i | 2.38966i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.89205i | 0.0869965i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.49242 | + | 3.36932i | 0.206126 | + | 0.154595i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.8393 | 0.860791 | 0.430396 | − | 0.902640i | \(-0.358374\pi\) | ||||
0.430396 | + | 0.902640i | \(0.358374\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.98293i | 0.227202i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.75379 | − | 4.98293i | 0.261806 | − | 0.226731i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.8393 | + | 9.41967i | −0.855450 | + | 0.427725i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.0000 | −0.543772 | −0.271886 | − | 0.962329i | \(-0.587647\pi\) | ||||
−0.271886 | + | 0.962329i | \(0.587647\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 63.2067i | 2.85831i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.6855 | −1.29456 | −0.647278 | − | 0.762254i | \(-0.724093\pi\) | ||||
−0.647278 | + | 0.762254i | \(0.724093\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.6847i | 0.886552i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.92820 | − | 3.46410i | 0.311400 | − | 0.155700i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.6752 | + | 28.4924i | 1.10683 | + | 1.27806i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.8290 | −0.663839 | −0.331920 | − | 0.943308i | \(-0.607696\pi\) | ||||
−0.331920 | + | 0.943308i | \(0.607696\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 7.47439i | − | 0.333931i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 30.6307i | − | 1.36576i | −0.730532 | − | 0.682878i | \(-0.760728\pi\) | ||
0.730532 | − | 0.682878i | \(-0.239272\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.7386 | + | 11.3693i | −1.01186 | + | 0.505928i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −32.4924 | −1.44304 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.00000 | −0.177297 | −0.0886484 | − | 0.996063i | \(-0.528255\pi\) | ||||
−0.0886484 | + | 0.996063i | \(0.528255\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.8564 | − | 12.0000i | 0.612971 | − | 0.530849i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 1.61553i | − | 0.0713273i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.8290 | + | 29.6581i | 0.653446 | + | 1.30689i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.946025i | − | 0.0416061i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.8078i | 1.08894i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 22.7299i | − | 0.995814i | −0.867230 | − | 0.497907i | \(-0.834102\pi\) | ||
0.867230 | − | 0.497907i | \(-0.165898\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.50758 | 0.328283 | 0.164142 | − | 0.986437i | \(-0.447515\pi\) | ||||
0.164142 | + | 0.986437i | \(0.447515\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.37764 | − | 33.8026i | −0.103769 | − | 1.47527i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39.3693 | 1.71495 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.7386 | −0.945158 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 14.2462i | − | 0.618233i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.98293 | −0.215835 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.8188 | − | 21.6375i | −0.467736 | − | 0.935471i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 54.3333 | 2.34465 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.972638 | − | 6.73863i | 0.0418945 | − | 0.290254i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.32729i | 0.358018i | 0.983847 | + | 0.179009i | \(0.0572892\pi\) | ||||
−0.983847 | + | 0.179009i | \(0.942711\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 36.4924 | 1.56604 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.2931 | + | 36.5863i | 0.783592 | + | 1.56718i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.8017i | 0.675631i | 0.941212 | + | 0.337816i | \(0.109688\pi\) | ||||
−0.941212 | + | 0.337816i | \(0.890312\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.00000 | −0.170716 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.98293 | 0.212280 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.3102 | − | 15.3693i | −0.566008 | − | 0.653570i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −45.4598 | + | 22.7299i | −1.92966 | + | 0.964830i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.8564 | 0.587115 | 0.293557 | − | 0.955941i | \(-0.405161\pi\) | ||||
0.293557 | + | 0.955941i | \(0.405161\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.09238 | −0.0462025 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.0540 | 0.466699 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.0000 | 0.842900 | 0.421450 | − | 0.906852i | \(-0.361521\pi\) | ||||
0.421450 | + | 0.906852i | \(0.361521\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.3693 | − | 30.7386i | −0.646592 | − | 1.29318i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.0000 | − | 12.1244i | 0.587945 | − | 0.509175i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.2462 | −1.35183 | −0.675916 | − | 0.736979i | \(-0.736252\pi\) | ||||
−0.675916 | + | 0.736979i | \(0.736252\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.35465 | −0.307783 | −0.153891 | − | 0.988088i | \(-0.549181\pi\) | ||||
−0.153891 | + | 0.988088i | \(0.549181\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.9309i | 0.581970i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.36932 | − | 4.49242i | 0.140510 | − | 0.187347i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.9307 | −1.66233 | −0.831167 | − | 0.556022i | \(-0.812327\pi\) | ||||
−0.831167 | + | 0.556022i | \(0.812327\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 18.8769i | − | 0.784497i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.00000 | + | 6.92820i | −0.331896 | + | 0.287430i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.00000 | + | 4.00000i | 0.0826898 | + | 0.165380i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.0000 | 1.15568 | 0.577842 | − | 0.816149i | \(-0.303895\pi\) | ||||
0.577842 | + | 0.816149i | \(0.303895\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 9.96585i | − | 0.410636i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 58.2238 | 2.39501 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.546188 | 0.0224292 | 0.0112146 | − | 0.999937i | \(-0.496430\pi\) | ||||
0.0112146 | + | 0.999937i | \(0.496430\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.0623 | − | 24.2428i | 0.412514 | − | 0.993858i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −45.4598 | −1.86054 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.43845i | 0.222209i | 0.993809 | + | 0.111104i | \(0.0354388\pi\) | ||||
−0.993809 | + | 0.111104i | \(0.964561\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.96585i | 0.406516i | 0.979125 | + | 0.203258i | \(0.0651530\pi\) | ||||
−0.979125 | + | 0.203258i | \(0.934847\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 24.6752i | − | 1.00485i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20.1080 | + | 10.0540i | −0.817504 | + | 0.408752i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 16.7743i | − | 0.680849i | −0.940272 | − | 0.340424i | \(-0.889429\pi\) | ||
0.940272 | − | 0.340424i | \(-0.110571\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −19.6847 | − | 22.7299i | −0.797663 | − | 0.921061i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.546188 | 0.0220964 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.96585 | 0.402517 | 0.201259 | − | 0.979538i | \(-0.435497\pi\) | ||||
0.201259 | + | 0.979538i | \(0.435497\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −22.7299 | − | 45.4598i | −0.916557 | − | 1.83311i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.7386i | 1.23749i | 0.785592 | + | 0.618745i | \(0.212359\pi\) | ||||
−0.785592 | + | 0.618745i | \(0.787641\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 29.6155i | − | 1.19035i | −0.803597 | − | 0.595174i | \(-0.797083\pi\) | ||
0.803597 | − | 0.595174i | \(-0.202917\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.61553 | −0.0648289 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.3693 | + | 17.7470i | 0.615759 | + | 0.711017i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 2.79818i | − | 0.111748i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −39.3693 | −1.56976 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 16.3153i | − | 0.649503i | −0.945799 | − | 0.324752i | \(-0.894719\pi\) | ||
0.945799 | − | 0.324752i | \(-0.105281\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 37.9854 | 1.50978 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.0000 | + | 12.0000i | −0.952411 | + | 0.476205i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.89055 | + | 0.561553i | 0.154149 | + | 0.0222495i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 50.7386i | − | 2.00719i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.24621 | 0.325706 | 0.162853 | − | 0.986650i | \(-0.447930\pi\) | ||||
0.162853 | + | 0.986650i | \(0.447930\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.3002 | 0.997742 | 0.498871 | − | 0.866676i | \(-0.333748\pi\) | ||||
0.498871 | + | 0.866676i | \(0.333748\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.98293 | − | 9.96585i | −0.196203 | − | 0.392405i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.0298i | 1.25922i | 0.776911 | + | 0.629611i | \(0.216786\pi\) | ||||
−0.776911 | + | 0.629611i | \(0.783214\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 3.89055i | − | 0.152718i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −45.4598 | + | 39.3693i | −1.78171 | + | 1.54301i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.7640 | −0.499495 | −0.249748 | − | 0.968311i | \(-0.580348\pi\) | ||||
−0.249748 | + | 0.968311i | \(0.580348\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.3693 | − | 38.7386i | −0.756822 | − | 1.51364i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −24.6752 | −0.962670 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.91791 | −0.113666 | −0.0568329 | − | 0.998384i | \(-0.518100\pi\) | ||||
−0.0568329 | + | 0.998384i | \(0.518100\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.2462 | 1.48761 | 0.743803 | − | 0.668399i | \(-0.233020\pi\) | ||||
0.743803 | + | 0.668399i | \(0.233020\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.38202i | 0.247857i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.13676 | − | 2.54715i | −0.237973 | − | 0.0987741i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 4.98293i | − | 0.192940i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.49146i | 0.0963255i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.09238 | −0.0421707 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 15.3693i | − | 0.592444i | −0.955119 | − | 0.296222i | \(-0.904273\pi\) | ||
0.955119 | − | 0.296222i | \(-0.0957268\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.31534 | + | 5.75379i | −0.166098 | + | 0.221463i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.6847i | 0.679677i | 0.940484 | + | 0.339838i | \(0.110372\pi\) | ||||
−0.940484 | + | 0.339838i | \(0.889628\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.8393 | − | 16.3153i | 0.722987 | − | 0.626125i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 40.1771 | 1.53959 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.6581i | 1.13484i | 0.823430 | + | 0.567418i | \(0.192057\pi\) | ||||
−0.823430 | + | 0.567418i | \(0.807943\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.1231 | − | 26.2462i | −0.501408 | − | 1.00282i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.87689 | −0.109760 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 7.50758i | − | 0.285602i | −0.989751 | − | 0.142801i | \(-0.954389\pi\) | ||
0.989751 | − | 0.142801i | \(-0.0456108\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.92820 | + | 6.00000i | −0.263181 | + | 0.227921i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.2462 | − | 28.4924i | −0.540390 | − | 1.08078i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 39.3693i | − | 1.49122i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 72.9848i | − | 2.76054i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.0230i | 1.54942i | 0.632318 | + | 0.774709i | \(0.282104\pi\) | ||||
−0.632318 | + | 0.774709i | \(0.717896\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.96585i | 0.375869i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.49146 | + | 4.98293i | 0.0938339 | + | 0.187668i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.7386 | − | 19.6922i | 0.855174 | − | 0.740603i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 0.546188i | − | 0.0205125i | −0.999947 | − | 0.0102563i | \(-0.996735\pi\) | ||
0.999947 | − | 0.0102563i | \(-0.00326472\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.3693i | 1.02643i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.96585 | −0.373224 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.546188 | + | 1.09238i | 0.0204263 | + | 0.0408525i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 19.6847i | − | 0.735137i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.87348 | 0.330925 | 0.165462 | − | 0.986216i | \(-0.447088\pi\) | ||||
0.165462 | + | 0.986216i | \(0.447088\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.6847 | − | 29.6581i | −0.956547 | − | 1.10452i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.7640i | 0.474699i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.7470 | − | 13.3102i | −0.659105 | − | 0.494329i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.2829i | 0.529722i | 0.964287 | + | 0.264861i | \(0.0853260\pi\) | ||||
−0.964287 | + | 0.264861i | \(0.914674\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −35.9848 | −1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 8.63068i | − | 0.319217i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 31.3002i | − | 1.15610i | −0.816002 | − | 0.578049i | \(-0.803814\pi\) | ||
0.816002 | − | 0.578049i | \(-0.196186\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.6239 | + | 38.0555i | 0.465638 | + | 1.40370i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 6.73863i | − | 0.248221i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.6649 | −0.760170 | −0.380085 | − | 0.924952i | \(-0.624105\pi\) | ||||
−0.380085 | + | 0.924952i | \(0.624105\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.61553 | 0.0593479 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.2462 | 1.40312 | 0.701559 | − | 0.712612i | \(-0.252488\pi\) | ||||
0.701559 | + | 0.712612i | \(0.252488\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.8188 | + | 21.6375i | 0.396369 | + | 0.792737i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.2462 | 0.521242 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.7386 | + | 21.6375i | 0.684695 | + | 0.790617i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 15.6847i | − | 0.572341i | −0.958179 | − | 0.286171i | \(-0.907618\pi\) | ||
0.958179 | − | 0.286171i | \(-0.0923824\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 51.2311i | 1.86696i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.0540 | − | 30.1080i | −0.547870 | − | 1.09574i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.8564 | 0.503620 | 0.251810 | − | 0.967777i | \(-0.418974\pi\) | ||||
0.251810 | + | 0.967777i | \(0.418974\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.79818 | −0.101567 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 30.5110i | − | 1.10602i | −0.833174 | − | 0.553011i | \(-0.813479\pi\) | ||
0.833174 | − | 0.553011i | \(-0.186521\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −31.6847 | − | 36.5863i | −1.14706 | − | 1.32451i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −31.6034 | + | 15.8017i | −1.14262 | + | 0.571311i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.24621 | 0.0811060 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.89055i | 0.140297i | 0.997537 | + | 0.0701484i | \(0.0223473\pi\) | ||||
−0.997537 | + | 0.0701484i | \(0.977653\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.7470 | −0.639141 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.94602i | 0.105961i | 0.998596 | + | 0.0529806i | \(0.0168721\pi\) | ||||
−0.998596 | + | 0.0529806i | \(0.983128\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.6204 | + | 35.4939i | −0.956234 | + | 1.27498i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 45.4598 | − | 39.3693i | 1.63086 | − | 1.41237i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.96585 | −0.357064 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 13.8564i | − | 0.495821i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.38202i | 0.228075i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.2462 | − | 40.4924i | −0.722618 | − | 1.44524i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.8078 | −1.59722 | −0.798612 | − | 0.601846i | \(-0.794432\pi\) | ||||
−0.798612 | + | 0.601846i | \(0.794432\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −30.7386 | −1.09432 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.6204 | + | 30.7386i | 0.946514 | + | 1.09294i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.630683i | − | 0.0223962i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 21.0540i | − | 0.745770i | −0.927878 | − | 0.372885i | \(-0.878369\pi\) | ||
0.927878 | − | 0.372885i | \(-0.121631\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.31534i | 0.152666i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 31.6034i | − | 1.11665i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.73863 | −0.237801 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.54715 | + | 6.13676i | −0.0897751 | + | 0.216292i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −51.2311 | −1.80342 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.3002 | 1.10046 | 0.550228 | − | 0.835014i | \(-0.314541\pi\) | ||||
0.550228 | + | 0.835014i | \(0.314541\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.2462i | 0.500252i | 0.968213 | + | 0.250126i | \(0.0804721\pi\) | ||||
−0.968213 | + | 0.250126i | \(0.919528\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 58.2238 | 2.04200 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.6752 | − | 49.3503i | −0.864333 | − | 1.72867i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.18475 | −0.0764347 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.46410 | − | 4.00000i | −0.121046 | − | 0.139771i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 18.2931i | − | 0.638435i | −0.947681 | − | 0.319218i | \(-0.896580\pi\) | ||
0.947681 | − | 0.319218i | \(-0.103420\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.3693 | −1.23290 | −0.616448 | − | 0.787395i | \(-0.711429\pi\) | ||||
−0.616448 | + | 0.787395i | \(0.711429\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.47439 | + | 9.96585i | −0.260225 | + | 0.346967i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 34.6410i | − | 1.20459i | −0.798275 | − | 0.602293i | \(-0.794254\pi\) | ||
0.798275 | − | 0.602293i | \(-0.205746\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.6155 | −1.02859 | −0.514295 | − | 0.857613i | \(-0.671946\pi\) | ||||
−0.514295 | + | 0.857613i | \(0.671946\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 35.4939 | 1.23127 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.43674 | + | 30.7386i | −0.153724 | + | 1.06503i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.91791 | + | 5.83583i | 0.100979 | + | 0.201957i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.7640 | 0.441189 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.6957 | −1.12878 | −0.564391 | − | 0.825507i | \(-0.690889\pi\) | ||||
−0.564391 | + | 0.825507i | \(0.690889\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.31534 | 0.321219 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 65.7926 | 2.26602 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.3693 | − | 12.6847i | 0.872731 | − | 0.436366i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.1080 | − | 17.4140i | 0.690917 | − | 0.598352i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.9309 | −0.478106 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.96585 | 0.341625 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 22.4924i | − | 0.770126i | −0.922890 | − | 0.385063i | \(-0.874180\pi\) | ||
0.922890 | − | 0.385063i | \(-0.125820\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000 | + | 8.00000i | 0.136797 | + | 0.273594i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.4563 | −1.10868 | −0.554342 | − | 0.832289i | \(-0.687030\pi\) | ||||
−0.554342 | + | 0.832289i | \(0.687030\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 9.75379i | − | 0.332795i | −0.986059 | − | 0.166397i | \(-0.946787\pi\) | ||
0.986059 | − | 0.166397i | \(-0.0532135\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 39.3693 | + | 45.4598i | 1.34170 | + | 1.54926i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.36932 | −0.114693 | −0.0573464 | − | 0.998354i | \(-0.518264\pi\) | ||||
−0.0573464 | + | 0.998354i | \(0.518264\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.68466 | − | 19.3693i | −0.329288 | − | 0.658577i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.87689 | −0.233552 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.47439i | 0.253551i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.89055 | 0.131826 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −33.5486 | −1.13545 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.0526 | + | 25.4641i | 0.508869 | + | 0.860844i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.6204 | −0.898908 | −0.449454 | − | 0.893303i | \(-0.648381\pi\) | ||||
−0.449454 | + | 0.893303i | \(0.648381\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 36.6695i | − | 1.23683i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.8564i | 0.466834i | 0.972377 | + | 0.233417i | \(0.0749907\pi\) | ||||
−0.972377 | + | 0.233417i | \(0.925009\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 15.8017i | − | 0.531769i | −0.964005 | − | 0.265884i | \(-0.914336\pi\) | ||
0.964005 | − | 0.265884i | \(-0.0856640\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.2462 | + | 20.4924i | 0.344423 | + | 0.688845i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 32.0298i | − | 1.07546i | −0.843118 | − | 0.537728i | \(-0.819283\pi\) | ||
0.843118 | − | 0.537728i | \(-0.180717\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.0000 | − | 20.7846i | 0.804934 | − | 0.697093i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.80847 | −0.228092 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.09238 | 0.0365549 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −42.4221 | + | 21.2111i | −1.41802 | + | 0.709008i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 1.61553i | − | 0.0539409i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 39.3693i | 1.31304i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.63068 | + | 9.96585i | 0.287211 | + | 0.331643i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28.4924 | + | 14.2462i | −0.947120 | + | 0.473560i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.5486i | 1.11396i | 0.830524 | + | 0.556982i | \(0.188041\pi\) | ||||
−0.830524 | + | 0.556982i | \(0.811959\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −40.4924 | −1.34305 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.7386i | 0.620839i | 0.950600 | + | 0.310419i | \(0.100469\pi\) | ||||
−0.950600 | + | 0.310419i | \(0.899531\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.89055 | 0.128758 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.75379 | − | 2.87689i | 0.190214 | − | 0.0951072i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 33.5486 | + | 38.7386i | 1.10787 | + | 1.27926i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 7.68466i | − | 0.253493i | −0.991935 | − | 0.126747i | \(-0.959546\pi\) | ||
0.991935 | − | 0.126747i | \(-0.0404536\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.4384 | 0.838225 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.00000 | 0.263323 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26.6204 | − | 35.4939i | 0.875275 | − | 1.16703i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 52.8144i | 1.73465i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 9.96585i | − | 0.326969i | −0.986546 | − | 0.163485i | \(-0.947727\pi\) | ||
0.986546 | − | 0.163485i | \(-0.0522734\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.78110 | + | 1.12311i | 0.255015 | + | 0.0368083i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −48.2579 | −1.57989 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.63068 | + | 4.31534i | −0.282254 | + | 0.141127i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.0572 | −1.01459 | −0.507297 | − | 0.861771i | \(-0.669355\pi\) | ||||
−0.507297 | + | 0.861771i | \(0.669355\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 46.8589 | 1.52918 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.3693 | −0.631422 | −0.315711 | − | 0.948855i | \(-0.602243\pi\) | ||||
−0.315711 | + | 0.948855i | \(0.602243\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.96585i | 0.324533i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.26233 | − | 7.85982i | 0.106123 | − | 0.255680i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.6922i | 0.639912i | 0.947432 | + | 0.319956i | \(0.103668\pi\) | ||||
−0.947432 | + | 0.319956i | \(0.896332\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 3.89055i | − | 0.126293i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −45.4598 | −1.47413 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.6155i | 0.570623i | 0.958435 | + | 0.285311i | \(0.0920970\pi\) | ||||
−0.958435 | + | 0.285311i | \(0.907903\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.43845 | − | 10.8769i | −0.175984 | − | 0.351968i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.0540i | 0.357324i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.7299 | + | 26.2462i | 0.733986 | + | 0.847534i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 47.7386 | 1.53996 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 38.5316i | − | 1.24166i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.36932 | + | 14.7386i | 0.237227 | + | 0.474453i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.26137 | −0.169194 | −0.0845971 | − | 0.996415i | \(-0.526960\pi\) | ||||
−0.0845971 | + | 0.996415i | \(0.526960\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.7640i | 0.410040i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.6307i | 0.405338i | 0.979247 | + | 0.202669i | \(0.0649615\pi\) | ||||
−0.979247 | + | 0.202669i | \(0.935038\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.6752 | + | 28.4924i | 0.791049 | + | 0.913425i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.75379 | − | 4.31534i | −0.184269 | − | 0.138202i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.1231i | 1.18767i | 0.804586 | + | 0.593837i | \(0.202387\pi\) | ||||
−0.804586 | + | 0.593837i | \(0.797613\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 8.63068i | − | 0.275838i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 65.1520i | 2.08014i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 4.86319i | − | 0.155112i | −0.996988 | − | 0.0775558i | \(-0.975288\pi\) | ||
0.996988 | − | 0.0775558i | \(-0.0247116\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −45.4598 | + | 22.7299i | −1.44847 | + | 0.724234i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.31534 | − | 4.98293i | −0.137359 | − | 0.158608i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.18475i | 0.0694710i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49.4773i | 1.57170i | 0.618419 | + | 0.785849i | \(0.287774\pi\) | ||||
−0.618419 | + | 0.785849i | \(0.712226\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −44.3674 | −1.40796 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 35.4939 | − | 17.7470i | 1.12523 | − | 0.562616i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 54.1771i | − | 1.71581i | −0.513812 | − | 0.857903i | \(-0.671767\pi\) | ||
0.513812 | − | 0.857903i | \(-0.328233\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.7640 | −0.403836 |
(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 | 2240.2.n.b.1119.2 | yes | 8 | |
4.3 | odd | 2 | 2240.2.n.h.1119.5 | yes | 8 | ||
5.4 | even | 2 | 2240.2.n.h.1119.7 | yes | 8 | ||
7.6 | odd | 2 | 2240.2.n.g.1119.7 | yes | 8 | ||
8.3 | odd | 2 | 2240.2.n.a.1119.3 | yes | 8 | ||
8.5 | even | 2 | 2240.2.n.g.1119.8 | yes | 8 | ||
20.19 | odd | 2 | inner | 2240.2.n.b.1119.4 | yes | 8 | |
28.27 | even | 2 | 2240.2.n.a.1119.4 | yes | 8 | ||
35.34 | odd | 2 | 2240.2.n.a.1119.2 | yes | 8 | ||
40.19 | odd | 2 | 2240.2.n.g.1119.6 | yes | 8 | ||
40.29 | even | 2 | 2240.2.n.a.1119.1 | ✓ | 8 | ||
56.13 | odd | 2 | inner | 2240.2.n.b.1119.1 | yes | 8 | |
56.27 | even | 2 | 2240.2.n.h.1119.6 | yes | 8 | ||
140.139 | even | 2 | 2240.2.n.g.1119.5 | yes | 8 | ||
280.69 | odd | 2 | 2240.2.n.h.1119.8 | yes | 8 | ||
280.139 | even | 2 | inner | 2240.2.n.b.1119.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.n.a.1119.1 | ✓ | 8 | 40.29 | even | 2 | ||
2240.2.n.a.1119.2 | yes | 8 | 35.34 | odd | 2 | ||
2240.2.n.a.1119.3 | yes | 8 | 8.3 | odd | 2 | ||
2240.2.n.a.1119.4 | yes | 8 | 28.27 | even | 2 | ||
2240.2.n.b.1119.1 | yes | 8 | 56.13 | odd | 2 | inner | |
2240.2.n.b.1119.2 | yes | 8 | 1.1 | even | 1 | trivial | |
2240.2.n.b.1119.3 | yes | 8 | 280.139 | even | 2 | inner | |
2240.2.n.b.1119.4 | yes | 8 | 20.19 | odd | 2 | inner | |
2240.2.n.g.1119.5 | yes | 8 | 140.139 | even | 2 | ||
2240.2.n.g.1119.6 | yes | 8 | 40.19 | odd | 2 | ||
2240.2.n.g.1119.7 | yes | 8 | 7.6 | odd | 2 | ||
2240.2.n.g.1119.8 | yes | 8 | 8.5 | even | 2 | ||
2240.2.n.h.1119.5 | yes | 8 | 4.3 | odd | 2 | ||
2240.2.n.h.1119.6 | yes | 8 | 56.27 | even | 2 | ||
2240.2.n.h.1119.7 | yes | 8 | 5.4 | even | 2 | ||
2240.2.n.h.1119.8 | yes | 8 | 280.69 | odd | 2 |