Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1567,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1567");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.p (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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 1344) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1567.7 | ||
Root | \(-2.23871 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.1567 |
Dual form | 4032.2.p.k.1567.8 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.11575 | 0.498978 | 0.249489 | − | 0.968378i | \(-0.419737\pi\) | ||||
0.249489 | + | 0.968378i | \(0.419737\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.37268 | − | 2.26180i | 0.518824 | − | 0.854881i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.812826 | 0.245076 | 0.122538 | − | 0.992464i | \(-0.460897\pi\) | ||||
0.122538 | + | 0.992464i | \(0.460897\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.55819i | 0.862987i | 0.902116 | + | 0.431493i | \(0.142013\pi\) | ||||
−0.902116 | + | 0.431493i | \(0.857987\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.52360i | 1.03779i | 0.854839 | + | 0.518893i | \(0.173656\pi\) | ||||
−0.854839 | + | 0.518893i | \(0.826344\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.63935i | 0.758858i | 0.925221 | + | 0.379429i | \(0.123880\pi\) | ||||
−0.925221 | + | 0.379429i | \(0.876120\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.75510 | −0.751021 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.95482i | 1.66287i | 0.555623 | + | 0.831434i | \(0.312480\pi\) | ||||
−0.555623 | + | 0.831434i | \(0.687520\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.08975 | 0.914147 | 0.457073 | − | 0.889429i | \(-0.348898\pi\) | ||||
0.457073 | + | 0.889429i | \(0.348898\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.53157 | − | 2.52360i | 0.258882 | − | 0.426567i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.718741i | 0.118160i | 0.998253 | + | 0.0590802i | \(0.0188168\pi\) | ||||
−0.998253 | + | 0.0590802i | \(0.981183\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.4864i | 1.63770i | 0.574008 | + | 0.818849i | \(0.305388\pi\) | ||||
−0.574008 | + | 0.818849i | \(0.694612\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.11971 | −0.170754 | −0.0853770 | − | 0.996349i | \(-0.527209\pi\) | ||||
−0.0853770 | + | 0.996349i | \(0.527209\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.55385 | −1.24771 | −0.623854 | − | 0.781541i | \(-0.714434\pi\) | ||||
−0.623854 | + | 0.781541i | \(0.714434\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.23150 | − | 6.20946i | −0.461643 | − | 0.887066i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.08975i | 0.699131i | 0.936912 | + | 0.349566i | \(0.113671\pi\) | ||||
−0.936912 | + | 0.349566i | \(0.886329\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.906910 | 0.122288 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 2.23150i | − | 0.290516i | −0.989394 | − | 0.145258i | \(-0.953599\pi\) | ||
0.989394 | − | 0.145258i | \(-0.0464013\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.27871 | 0.675869 | 0.337935 | − | 0.941170i | \(-0.390272\pi\) | ||||
0.337935 | + | 0.941170i | \(0.390272\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.23150 | 0.276783 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.1643 | 1.85261 | 0.926306 | − | 0.376772i | \(-0.122966\pi\) | ||||
0.926306 | + | 0.376772i | \(0.122966\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.87085i | 0.696742i | 0.937357 | + | 0.348371i | \(0.113265\pi\) | ||||
−0.937357 | + | 0.348371i | \(0.886735\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.86507i | 0.452372i | 0.974084 | + | 0.226186i | \(0.0726257\pi\) | ||||
−0.974084 | + | 0.226186i | \(0.927374\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.11575 | − | 1.83845i | 0.127151 | − | 0.209511i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.70789i | − | 0.192153i | −0.995374 | − | 0.0960766i | \(-0.969371\pi\) | ||
0.995374 | − | 0.0960766i | \(-0.0306294\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.27871i | − | 0.798942i | −0.916746 | − | 0.399471i | \(-0.869194\pi\) | ||
0.916746 | − | 0.399471i | \(-0.130806\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.97004i | 0.430612i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3.37002i | − | 0.357221i | −0.983920 | − | 0.178611i | \(-0.942840\pi\) | ||
0.983920 | − | 0.178611i | \(-0.0571602\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.74536 | − | 4.52360i | 0.287792 | − | 0.474203i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.04721i | 0.517833i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.55385i | − | 0.868512i | −0.900789 | − | 0.434256i | \(-0.857011\pi\) | ||
0.900789 | − | 0.434256i | \(-0.142989\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.11575 | 0.111021 | 0.0555106 | − | 0.998458i | \(-0.482321\pi\) | ||||
0.0555106 | + | 0.998458i | \(0.482321\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.2574 | 1.40482 | 0.702410 | − | 0.711772i | \(-0.252107\pi\) | ||||
0.702410 | + | 0.711772i | \(0.252107\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.2317 | 1.27916 | 0.639581 | − | 0.768724i | \(-0.279108\pi\) | ||||
0.639581 | + | 0.768724i | \(0.279108\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.43748i | − | 0.137686i | −0.997628 | − | 0.0688429i | \(-0.978069\pi\) | ||
0.997628 | − | 0.0688429i | \(-0.0219307\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.23150 | −0.774354 | −0.387177 | − | 0.922005i | \(-0.626550\pi\) | ||||
−0.387177 | + | 0.922005i | \(0.626550\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.06061i | 0.378654i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.04791 | + | 4.88425i | 0.737751 | + | 0.447739i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3393 | −0.939938 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.76850 | −0.873721 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.75510i | − | 0.244476i | −0.992501 | − | 0.122238i | \(-0.960993\pi\) | ||
0.992501 | − | 0.122238i | \(-0.0390071\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 19.2787i | − | 1.68439i | −0.539174 | − | 0.842194i | \(-0.681264\pi\) | ||
0.539174 | − | 0.842194i | \(-0.318736\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.2315 | + | 6.20946i | 0.887183 | + | 0.538429i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.58421 | −0.562527 | −0.281264 | − | 0.959631i | \(-0.590754\pi\) | ||||
−0.281264 | + | 0.959631i | \(0.590754\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 17.5102i | − | 1.48520i | −0.669737 | − | 0.742598i | \(-0.733593\pi\) | ||
0.669737 | − | 0.742598i | \(-0.266407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.62565 | 0.135944 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.99134i | 0.829735i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.5805i | 0.866786i | 0.901205 | + | 0.433393i | \(0.142684\pi\) | ||||
−0.901205 | + | 0.433393i | \(0.857316\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.5236i | 1.01916i | 0.860424 | + | 0.509578i | \(0.170199\pi\) | ||||
−0.860424 | + | 0.509578i | \(0.829801\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.67889 | 0.456139 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.815710 | 0.0651008 | 0.0325504 | − | 0.999470i | \(-0.489637\pi\) | ||||
0.0325504 | + | 0.999470i | \(0.489637\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.23150 | + | 4.99567i | 0.648733 | + | 0.393714i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.18284 | −0.327626 | −0.163813 | − | 0.986491i | \(-0.552379\pi\) | ||||
−0.163813 | + | 0.986491i | \(0.552379\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.4189 | 0.961005 | 0.480503 | − | 0.876993i | \(-0.340454\pi\) | ||||
0.480503 | + | 0.876993i | \(0.340454\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 25.4417 | 1.93429 | 0.967147 | − | 0.254218i | \(-0.0818180\pi\) | ||||
0.967147 | + | 0.254218i | \(0.0818180\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.15456 | + | 8.49330i | −0.389648 | + | 0.642033i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.36668 | 0.700099 | 0.350049 | − | 0.936731i | \(-0.386165\pi\) | ||||
0.350049 | + | 0.936731i | \(0.386165\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.801935i | 0.0589595i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.89218i | 0.211497i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.1764i | 0.808693i | 0.914606 | + | 0.404346i | \(0.132501\pi\) | ||||
−0.914606 | + | 0.404346i | \(0.867499\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.2181 | 0.951460 | 0.475730 | − | 0.879591i | \(-0.342184\pi\) | ||||
0.475730 | + | 0.879591i | \(0.342184\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.5718i | 1.46568i | 0.680401 | + | 0.732840i | \(0.261806\pi\) | ||||
−0.680401 | + | 0.732840i | \(0.738194\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.7268 | −0.973067 | −0.486534 | − | 0.873662i | \(-0.661739\pi\) | ||||
−0.486534 | + | 0.873662i | \(0.661739\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.2540 | + | 12.2921i | 1.42155 | + | 0.862737i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.7002i | 0.817176i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.67690i | 0.254337i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.86173 | 0.678910 | 0.339455 | − | 0.940622i | \(-0.389757\pi\) | ||||
0.339455 | + | 0.940622i | \(0.389757\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.24931 | −0.0852026 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.98660 | − | 11.5120i | 0.474281 | − | 0.781486i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.11637i | 0.478699i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.3438 | −1.69715 | −0.848573 | − | 0.529079i | \(-0.822538\pi\) | ||||
−0.848573 | + | 0.529079i | \(0.822538\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 14.5574i | − | 0.966210i | −0.875563 | − | 0.483105i | \(-0.839509\pi\) | ||
0.875563 | − | 0.483105i | \(-0.160491\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.5842 | −0.963752 | −0.481876 | − | 0.876239i | \(-0.660044\pi\) | ||||
−0.481876 | + | 0.876239i | \(0.660044\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −27.8361 | −1.82361 | −0.911803 | − | 0.410629i | \(-0.865309\pi\) | ||||
−0.911803 | + | 0.410629i | \(0.865309\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.54396 | −0.622579 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 20.1024i | − | 1.30031i | −0.759800 | − | 0.650157i | \(-0.774703\pi\) | ||
0.759800 | − | 0.650157i | \(-0.225297\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.2840i | 1.04894i | 0.851428 | + | 0.524472i | \(0.175737\pi\) | ||||
−0.851428 | + | 0.524472i | \(0.824263\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.60554 | − | 6.92820i | −0.230350 | − | 0.442627i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.04721i | 0.575660i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.5842i | 0.794308i | 0.917752 | + | 0.397154i | \(0.130002\pi\) | ||||
−0.917752 | + | 0.397154i | \(0.869998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.95816i | 0.185978i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 28.2079i | − | 1.75956i | −0.475383 | − | 0.879779i | \(-0.657690\pi\) | ||
0.475383 | − | 0.879779i | \(-0.342310\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.62565 | + | 0.986602i | 0.101013 | + | 0.0613045i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.12915i | 0.377939i | 0.981983 | + | 0.188970i | \(0.0605148\pi\) | ||||
−0.981983 | + | 0.188970i | \(0.939485\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.67889i | 0.348851i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.2102 | 1.41515 | 0.707574 | − | 0.706639i | \(-0.249789\pi\) | ||||
0.707574 | + | 0.706639i | \(0.249789\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.1856 | 1.28693 | 0.643466 | − | 0.765475i | \(-0.277496\pi\) | ||||
0.643466 | + | 0.765475i | \(0.277496\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.05224 | −0.184057 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 6.20946i | − | 0.373090i | −0.982446 | − | 0.186545i | \(-0.940271\pi\) | ||
0.982446 | − | 0.186545i | \(-0.0597291\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.8629 | −1.54285 | −0.771426 | − | 0.636319i | \(-0.780456\pi\) | ||||
−0.771426 | + | 0.636319i | \(0.780456\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 27.0810i | − | 1.60980i | −0.593411 | − | 0.804900i | \(-0.702219\pi\) | ||
0.593411 | − | 0.804900i | \(-0.297781\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.7181 | + | 14.3945i | 1.40004 | + | 0.849678i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.33931 | 0.255254 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.4417 | 1.48632 | 0.743159 | − | 0.669115i | \(-0.233327\pi\) | ||||
0.743159 | + | 0.669115i | \(0.233327\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2.48979i | − | 0.144961i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.27871i | 0.420939i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.53700 | + | 2.53256i | −0.0885913 | + | 0.145974i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.88972 | 0.337244 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0338i | 0.572660i | 0.958131 | + | 0.286330i | \(0.0924353\pi\) | ||||
−0.958131 | + | 0.286330i | \(0.907565\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.7933 | −0.612030 | −0.306015 | − | 0.952027i | \(-0.598996\pi\) | ||||
−0.306015 | + | 0.952027i | \(0.598996\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.9641i | 1.75020i | 0.483946 | + | 0.875098i | \(0.339203\pi\) | ||||
−0.483946 | + | 0.875098i | \(0.660797\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.5805i | 0.594259i | 0.954837 | + | 0.297129i | \(0.0960292\pi\) | ||||
−0.954837 | + | 0.297129i | \(0.903971\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.27871i | 0.407529i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.0958 | −0.895596 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.51021 | −0.416591 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.7417 | + | 19.3471i | −0.647341 | + | 1.06664i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.80849 | 0.319264 | 0.159632 | − | 0.987177i | \(-0.448969\pi\) | ||||
0.159632 | + | 0.987177i | \(0.448969\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.9195 | 0.924413 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.13708 | 0.224035 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4804 | − | 1.21459i | −0.997847 | − | 0.0655819i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.0250 | 1.28973 | 0.644865 | − | 0.764296i | \(-0.276913\pi\) | ||||
0.644865 | + | 0.764296i | \(0.276913\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.2787 | 1.78137 | 0.890684 | − | 0.454623i | \(-0.150226\pi\) | ||||
0.890684 | + | 0.454623i | \(0.150226\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 24.7191i | − | 1.31567i | −0.753164 | − | 0.657833i | \(-0.771473\pi\) | ||
0.753164 | − | 0.657833i | \(-0.228527\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.55040i | 0.347659i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 29.8709i | − | 1.57652i | −0.615340 | − | 0.788262i | \(-0.710981\pi\) | ||
0.615340 | − | 0.788262i | \(-0.289019\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.46300 | −0.0769999 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.31245i | 0.225724i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.505942 | 0.0264100 | 0.0132050 | − | 0.999913i | \(-0.495797\pi\) | ||||
0.0132050 | + | 0.999913i | \(0.495797\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.5120 | + | 6.98660i | 0.597674 | + | 0.362726i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.1609i | 1.09567i | 0.836586 | + | 0.547836i | \(0.184548\pi\) | ||||
−0.836586 | + | 0.547836i | \(0.815452\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.9096i | 0.922394i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.4787 | −1.10329 | −0.551644 | − | 0.834080i | \(-0.685999\pi\) | ||||
−0.551644 | + | 0.834080i | \(0.685999\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.24931 | −0.0638370 | −0.0319185 | − | 0.999490i | \(-0.510162\pi\) | ||||
−0.0319185 | + | 0.999490i | \(0.510162\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.24490 | − | 2.05125i | 0.0634458 | − | 0.104541i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 20.5718i | − | 1.04303i | −0.853241 | − | 0.521516i | \(-0.825367\pi\) | ||
0.853241 | − | 0.521516i | \(-0.174633\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.9495 | −0.654884 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 1.90558i | − | 0.0958802i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.3259 | −1.12051 | −0.560253 | − | 0.828322i | \(-0.689296\pi\) | ||||
−0.560253 | + | 0.828322i | \(0.689296\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.6046 | 1.27863 | 0.639317 | − | 0.768943i | \(-0.279217\pi\) | ||||
0.639317 | + | 0.768943i | \(0.279217\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.1795 | 0.507077 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.584211i | 0.0289583i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.2840i | 0.805192i | 0.915378 | + | 0.402596i | \(0.131892\pi\) | ||||
−0.915378 | + | 0.402596i | \(0.868108\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.04721 | − | 3.06313i | −0.248357 | − | 0.150727i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 8.12121i | − | 0.398655i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.6945i | 0.913286i | 0.889650 | + | 0.456643i | \(0.150948\pi\) | ||||
−0.889650 | + | 0.456643i | \(0.849052\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.0473i | 1.51315i | 0.653905 | + | 0.756577i | \(0.273130\pi\) | ||||
−0.653905 | + | 0.756577i | \(0.726870\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 13.3614i | − | 0.648121i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.24598 | − | 11.9394i | 0.350657 | − | 0.577788i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 1.99207i | − | 0.0959545i | −0.998848 | − | 0.0479772i | \(-0.984723\pi\) | ||
0.998848 | − | 0.0479772i | \(-0.0152775\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10.6051i | − | 0.509649i | −0.966987 | − | 0.254824i | \(-0.917982\pi\) | ||
0.966987 | − | 0.254824i | \(-0.0820177\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.4630 | −0.787532 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.0925 | 1.05442 | 0.527208 | − | 0.849736i | \(-0.323239\pi\) | ||||
0.527208 | + | 0.849736i | \(0.323239\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.55286 | −0.358847 | −0.179424 | − | 0.983772i | \(-0.557423\pi\) | ||||
−0.179424 | + | 0.983772i | \(0.557423\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 3.76010i | − | 0.178246i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.3259 | 0.864853 | 0.432427 | − | 0.901669i | \(-0.357657\pi\) | ||||
0.432427 | + | 0.901669i | \(0.357657\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.52360i | 0.401361i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.06313 | − | 5.04721i | 0.143602 | − | 0.236617i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.00000 | 0.0935561 | 0.0467780 | − | 0.998905i | \(-0.485105\pi\) | ||||
0.0467780 | + | 0.998905i | \(0.485105\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.5787 | −1.37762 | −0.688810 | − | 0.724942i | \(-0.741866\pi\) | ||||
−0.688810 | + | 0.724942i | \(0.741866\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.2653i | 0.755913i | 0.925823 | + | 0.377957i | \(0.123373\pi\) | ||||
−0.925823 | + | 0.377957i | \(0.876627\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 21.5102i | − | 0.995374i | −0.867357 | − | 0.497687i | \(-0.834183\pi\) | ||
0.867357 | − | 0.497687i | \(-0.165817\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.8157 | − | 34.2986i | 0.961180 | − | 1.58376i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.910128 | −0.0418477 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 16.9866i | − | 0.779399i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.99134 | −0.456516 | −0.228258 | − | 0.973601i | \(-0.573303\pi\) | ||||
−0.228258 | + | 0.973601i | \(0.573303\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.43748i | 0.0655436i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 9.54396i | − | 0.433369i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 19.0810i | − | 0.864644i | −0.901719 | − | 0.432322i | \(-0.857694\pi\) | ||
0.901719 | − | 0.432322i | \(-0.142306\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.0696 | −1.71806 | −0.859028 | − | 0.511928i | \(-0.828931\pi\) | ||||
−0.859028 | + | 0.511928i | \(0.828931\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31.8629 | −1.43503 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.2787 | + | 8.05880i | 0.595631 | + | 0.361487i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.2992 | 0.505822 | 0.252911 | − | 0.967490i | \(-0.418612\pi\) | ||||
0.252911 | + | 0.967490i | \(0.418612\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.4103 | 0.999224 | 0.499612 | − | 0.866249i | \(-0.333476\pi\) | ||||
0.499612 | + | 0.866249i | \(0.333476\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.24490 | 0.0553972 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.2102 | −0.496882 | −0.248441 | − | 0.968647i | \(-0.579918\pi\) | ||||
−0.248441 | + | 0.968647i | \(0.579918\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.74202 | + | 5.30550i | 0.386724 | + | 0.234702i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.9077 | 0.700975 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.95279 | −0.305783 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.7909i | 0.779435i | 0.920935 | + | 0.389717i | \(0.127427\pi\) | ||||
−0.920935 | + | 0.389717i | \(0.872573\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.4362i | 1.15597i | 0.816046 | + | 0.577987i | \(0.196162\pi\) | ||||
−0.816046 | + | 0.577987i | \(0.803838\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.1103i | 0.788896i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.75510 | 0.424135 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.9728i | 0.908432i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.7633 | 0.638274 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.62664 | − | 5.04721i | −0.113138 | − | 0.217399i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 31.4236i | − | 1.35101i | −0.737356 | − | 0.675504i | \(-0.763926\pi\) | ||
0.737356 | − | 0.675504i | \(-0.236074\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1.60387i | − | 0.0687023i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.2906 | −0.910318 | −0.455159 | − | 0.890410i | \(-0.650418\pi\) | ||||
−0.455159 | + | 0.890410i | \(0.650418\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −40.5081 | −1.72570 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.86292 | − | 2.34439i | −0.164268 | − | 0.0996937i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 35.0420i | − | 1.48478i | −0.669970 | − | 0.742388i | \(-0.733693\pi\) | ||
0.669970 | − | 0.742388i | \(-0.266307\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.23942 | −0.0947173 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.81571i | 0.118668i | 0.998238 | + | 0.0593340i | \(0.0188977\pi\) | ||||
−0.998238 | + | 0.0593340i | \(0.981102\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.18429 | −0.386386 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.7213 | −0.449460 | −0.224730 | − | 0.974421i | \(-0.572150\pi\) | ||||
−0.224730 | + | 0.974421i | \(0.572150\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.4688 | 0.940291 | 0.470145 | − | 0.882589i | \(-0.344201\pi\) | ||||
0.470145 | + | 0.882589i | \(0.344201\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 13.6661i | − | 0.569918i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 25.2142i | − | 1.04968i | −0.851201 | − | 0.524840i | \(-0.824125\pi\) | ||
0.851201 | − | 0.524840i | \(-0.175875\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.4630 | − | 9.99134i | −0.683000 | − | 0.414511i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.13708i | 0.171340i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 9.51021i | − | 0.392528i | −0.980551 | − | 0.196264i | \(-0.937119\pi\) | ||
0.980551 | − | 0.196264i | \(-0.0628810\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.0240i | 0.948689i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 28.3960i | − | 1.16609i | −0.812442 | − | 0.583043i | \(-0.801862\pi\) | ||
0.812442 | − | 0.583043i | \(-0.198138\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.97945 | + | 5.44960i | 0.368122 | + | 0.223412i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.9653i | 1.63294i | 0.577390 | + | 0.816468i | \(0.304071\pi\) | ||||
−0.577390 | + | 0.816468i | \(0.695929\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 46.6343i | − | 1.90225i | −0.308799 | − | 0.951127i | \(-0.599927\pi\) | ||
0.308799 | − | 0.951127i | \(-0.400073\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.5361 | −0.469009 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.4582 | 1.23626 | 0.618130 | − | 0.786076i | \(-0.287891\pi\) | ||||
0.618130 | + | 0.786076i | \(0.287891\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.1077 | −0.692104 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 14.8683i | − | 0.600525i | −0.953857 | − | 0.300262i | \(-0.902926\pi\) | ||
0.953857 | − | 0.300262i | \(-0.0970742\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.5842 | −0.748172 | −0.374086 | − | 0.927394i | \(-0.622044\pi\) | ||||
−0.374086 | + | 0.927394i | \(0.622044\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.6046i | 1.43107i | 0.698577 | + | 0.715535i | \(0.253817\pi\) | ||||
−0.698577 | + | 0.715535i | \(0.746183\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.62231 | − | 4.62596i | −0.305382 | − | 0.185335i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.87632 | 0.315053 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.55742 | −0.101971 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 24.2653i | − | 0.965987i | −0.875624 | − | 0.482993i | \(-0.839550\pi\) | ||
0.875624 | − | 0.482993i | \(-0.160450\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 3.07400i | − | 0.121988i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.46300 | − | 12.4189i | −0.256073 | − | 0.492056i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.6518 | 1.68465 | 0.842323 | − | 0.538973i | \(-0.181188\pi\) | ||||
0.842323 | + | 0.538973i | \(0.181188\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 8.06061i | − | 0.317879i | −0.987288 | − | 0.158940i | \(-0.949192\pi\) | ||
0.987288 | − | 0.158940i | \(-0.0508075\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.1609 | −0.831923 | −0.415961 | − | 0.909382i | \(-0.636555\pi\) | ||||
−0.415961 | + | 0.909382i | \(0.636555\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.81382i | − | 0.0711986i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.71342i | 0.184450i | 0.995738 | + | 0.0922251i | \(0.0293979\pi\) | ||||
−0.995738 | + | 0.0922251i | \(0.970602\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 21.5102i | − | 0.840473i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −44.1959 | −1.72163 | −0.860813 | − | 0.508921i | \(-0.830045\pi\) | ||||
−0.860813 | + | 0.508921i | \(0.830045\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.3731 | 1.68702 | 0.843510 | − | 0.537114i | \(-0.180486\pi\) | ||||
0.843510 | + | 0.537114i | \(0.180486\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.4158 | + | 6.92820i | 0.442685 | + | 0.268664i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −32.5898 | −1.26188 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.29067 | 0.165639 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.2449 | −0.433459 | −0.216729 | − | 0.976232i | \(-0.569539\pi\) | ||||
−0.216729 | + | 0.976232i | \(0.569539\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.5157 | 0.634749 | 0.317374 | − | 0.948300i | \(-0.397199\pi\) | ||||
0.317374 | + | 0.948300i | \(0.397199\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.3471 | − | 11.7417i | −0.742475 | − | 0.450605i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.0349 | 0.881407 | 0.440703 | − | 0.897653i | \(-0.354729\pi\) | ||||
0.440703 | + | 0.897653i | \(0.354729\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.34633 | −0.280689 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.1795i | 0.387808i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 11.8788i | − | 0.451890i | −0.974140 | − | 0.225945i | \(-0.927453\pi\) | ||
0.974140 | − | 0.225945i | \(-0.0725470\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 19.5370i | − | 0.741081i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37.3125 | −1.41331 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.9157i | 1.09213i | 0.837742 | + | 0.546066i | \(0.183875\pi\) | ||||
−0.837742 | + | 0.546066i | \(0.816125\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.25130 | −0.122625 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.53157 | − | 2.52360i | 0.0576005 | − | 0.0949099i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 38.6943i | − | 1.45319i | −0.687064 | − | 0.726597i | \(-0.741101\pi\) | ||
0.687064 | − | 0.726597i | \(-0.258899\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.5234i | 0.693707i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.81382 | 0.0678330 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.9542 | −1.19169 | −0.595846 | − | 0.803099i | \(-0.703183\pi\) | ||||
−0.595846 | + | 0.803099i | \(0.703183\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.5708 | − | 32.2474i | 0.728855 | − | 1.20095i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 33.6263i | − | 1.24885i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.32917 | 0.271824 | 0.135912 | − | 0.990721i | \(-0.456604\pi\) | ||||
0.135912 | + | 0.990721i | \(0.456604\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 3.98413i | − | 0.147358i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.6046 | 1.24122 | 0.620608 | − | 0.784121i | \(-0.286886\pi\) | ||||
0.620608 | + | 0.784121i | \(0.286886\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.3259 | 0.454031 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.2653 | −1.62833 | −0.814163 | − | 0.580636i | \(-0.802804\pi\) | ||||
−0.814163 | + | 0.580636i | \(0.802804\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 25.7338i | − | 0.944081i | −0.881577 | − | 0.472040i | \(-0.843518\pi\) | ||
0.881577 | − | 0.472040i | \(-0.156482\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.8052i | 0.432507i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.1630 | − | 29.9276i | 0.663660 | − | 1.09353i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 18.9598i | − | 0.691853i | −0.938262 | − | 0.345927i | \(-0.887565\pi\) | ||
0.938262 | − | 0.345927i | \(-0.112435\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.9732i | 0.508537i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 39.0706i | − | 1.42004i | −0.704179 | − | 0.710022i | \(-0.748685\pi\) | ||
0.704179 | − | 0.710022i | \(-0.251315\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.6746i | 0.386952i | 0.981105 | + | 0.193476i | \(0.0619762\pi\) | ||||
−0.981105 | + | 0.193476i | \(0.938024\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.25130 | − | 1.97320i | −0.117705 | − | 0.0714348i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 4.46300i | − | 0.161150i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 12.7953i | − | 0.461409i | −0.973024 | − | 0.230704i | \(-0.925897\pi\) | ||
0.973024 | − | 0.230704i | \(-0.0741030\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.6528 | −0.742828 | −0.371414 | − | 0.928467i | \(-0.621127\pi\) | ||||
−0.371414 | + | 0.928467i | \(0.621127\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.1125 | −0.686543 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −47.4363 | −1.69958 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.77198i | 0.170755i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.910128 | 0.0324839 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.00000i | 0.142585i | 0.997455 | + | 0.0712923i | \(0.0227123\pi\) | ||||
−0.997455 | + | 0.0712923i | \(0.977288\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.2992 | + | 18.6180i | −0.401754 | + | 0.661981i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.5574 | 0.374905 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −50.6101 | −1.79270 | −0.896351 | − | 0.443346i | \(-0.853791\pi\) | ||||
−0.896351 | + | 0.443346i | \(0.853791\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 30.4362i | − | 1.07676i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.14163i | 0.110866i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.18429 | + | 5.57391i | 0.323704 | + | 0.196455i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.8361 | 0.978666 | 0.489333 | − | 0.872097i | \(-0.337240\pi\) | ||||
0.489333 | + | 0.872097i | \(0.337240\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.1416i | 0.812612i | 0.913737 | + | 0.406306i | \(0.133183\pi\) | ||||
−0.913737 | + | 0.406306i | \(0.866817\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.66700 | −0.163478 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 5.06512i | − | 0.177206i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.56859i | 0.333946i | 0.985961 | + | 0.166973i | \(0.0533993\pi\) | ||||
−0.985961 | + | 0.166973i | \(0.946601\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.3597i | 1.75543i | 0.479183 | + | 0.877715i | \(0.340933\pi\) | ||||
−0.479183 | + | 0.877715i | \(0.659067\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.3308 | −1.40244 | −0.701220 | − | 0.712945i | \(-0.747361\pi\) | ||||
−0.701220 | + | 0.712945i | \(0.747361\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.8788 | −0.620956 | −0.310478 | − | 0.950581i | \(-0.600489\pi\) | ||||
−0.310478 | + | 0.950581i | \(0.600489\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22.0944 | − | 11.4983i | 0.765526 | − | 0.398392i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.8564 | 0.479521 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −38.0587 | −1.31393 | −0.656966 | − | 0.753920i | \(-0.728161\pi\) | ||||
−0.656966 | + | 0.753920i | \(0.728161\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −51.1888 | −1.76513 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.0417 | −0.345447 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.1926 | + | 23.3855i | −0.487663 | + | 0.803535i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.61575 | −0.0896669 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.7213 | −0.641005 | −0.320502 | − | 0.947248i | \(-0.603852\pi\) | ||||
−0.320502 | + | 0.947248i | \(0.603852\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.81938i | 0.198786i | 0.995048 | + | 0.0993932i | \(0.0316902\pi\) | ||||
−0.995048 | + | 0.0993932i | \(0.968310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.4968i | 1.31349i | 0.754111 | + | 0.656747i | \(0.228068\pi\) | ||||
−0.754111 | + | 0.656747i | \(0.771932\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.25036i | 0.0766032i | 0.999266 | + | 0.0383016i | \(0.0121948\pi\) | ||||
−0.999266 | + | 0.0383016i | \(0.987805\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.3865 | 0.965171 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.38822i | − | 0.0470921i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.3286 | 1.02764 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.4090 | + | 22.0944i | −0.453308 | + | 0.746928i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.5799i | 1.13391i | 0.823748 | + | 0.566956i | \(0.191879\pi\) | ||||
−0.823748 | + | 0.566956i | \(0.808121\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.43315i | 0.216738i | 0.994111 | + | 0.108369i | \(0.0345629\pi\) | ||||
−0.994111 | + | 0.108369i | \(0.965437\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.1185 | −1.58566 | −0.792832 | − | 0.609440i | \(-0.791394\pi\) | ||||
−0.792832 | + | 0.609440i | \(0.791394\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.9215 | −0.635323 | −0.317661 | − | 0.948204i | \(-0.602898\pi\) | ||||
−0.317661 | + | 0.948204i | \(0.602898\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.23150 | − | 3.78188i | −0.208998 | − | 0.126840i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 38.6943i | − | 1.29485i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.4509 | 0.349334 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 45.5778i | 1.52011i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.1103 | −0.603341 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.23150 | −0.0741775 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.1970 | 0.936265 | 0.468133 | − | 0.883658i | \(-0.344927\pi\) | ||||
0.468133 | + | 0.883658i | \(0.344927\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 30.1291i | − | 0.998223i | −0.866538 | − | 0.499112i | \(-0.833660\pi\) | ||
0.866538 | − | 0.499112i | \(-0.166340\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 5.91632i | − | 0.195802i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −43.6046 | − | 26.4635i | −1.43995 | − | 0.873902i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 30.4968i | − | 1.00600i | −0.864287 | − | 0.502998i | \(-0.832230\pi\) | ||
0.864287 | − | 0.502998i | \(-0.167770\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.7417i | 0.386483i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.69895i | − | 0.0887409i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.62132i | 0.217238i | 0.994083 | + | 0.108619i | \(0.0346429\pi\) | ||||
−0.994083 | + | 0.108619i | \(0.965357\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.0891 | − | 14.6180i | 0.920585 | − | 0.479086i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.22695i | 0.105533i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.5452i | 0.605845i | 0.953015 | + | 0.302922i | \(0.0979623\pi\) | ||||
−0.953015 | + | 0.302922i | \(0.902038\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.6528 | 1.06445 | 0.532225 | − | 0.846603i | \(-0.321356\pi\) | ||||
0.532225 | + | 0.846603i | \(0.321356\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −38.1637 | −1.24278 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.9923 | −0.357203 | −0.178601 | − | 0.983922i | \(-0.557157\pi\) | ||||
−0.178601 | + | 0.983922i | \(0.557157\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.73014i | 0.250931i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43.9732 | −1.42443 | −0.712216 | − | 0.701960i | \(-0.752308\pi\) | ||||
−0.712216 | + | 0.701960i | \(0.752308\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.4700i | 0.403520i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.03802 | + | 14.8922i | −0.291853 | + | 0.480894i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.09442 | −0.164336 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.7481 | 0.474758 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 27.6811i | − | 0.890164i | −0.895490 | − | 0.445082i | \(-0.853175\pi\) | ||
0.895490 | − | 0.445082i | \(-0.146825\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.16842i | − | 0.0374965i | −0.999824 | − | 0.0187482i | \(-0.994032\pi\) | ||
0.999824 | − | 0.0187482i | \(-0.00596810\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −39.6046 | − | 24.0359i | −1.26967 | − | 0.770556i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.6945 | 1.17396 | 0.586980 | − | 0.809601i | \(-0.300317\pi\) | ||||
0.586980 | + | 0.809601i | \(0.300317\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.73924i | − | 0.0875464i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 59.2197 | 1.88881 | 0.944407 | − | 0.328779i | \(-0.106637\pi\) | ||||
0.944407 | + | 0.328779i | \(0.106637\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.9530i | 0.731343i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 4.07502i | − | 0.129578i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 18.1550i | − | 0.576713i | −0.957523 | − | 0.288357i | \(-0.906891\pi\) | ||
0.957523 | − | 0.288357i | \(-0.0931089\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.3157 | −0.485539 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.6473 | 0.748917 | 0.374459 | − | 0.927244i | \(-0.377829\pi\) | ||||
0.374459 | + | 0.927244i | \(0.377829\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4032.2.p.k.1567.7 | 12 | ||
3.2 | odd | 2 | 1344.2.p.d.223.10 | yes | 12 | ||
4.3 | odd | 2 | inner | 4032.2.p.k.1567.6 | 12 | ||
7.6 | odd | 2 | 4032.2.p.j.1567.5 | 12 | |||
8.3 | odd | 2 | 4032.2.p.j.1567.6 | 12 | |||
8.5 | even | 2 | 4032.2.p.j.1567.7 | 12 | |||
12.11 | even | 2 | 1344.2.p.d.223.3 | yes | 12 | ||
21.20 | even | 2 | 1344.2.p.c.223.3 | ✓ | 12 | ||
24.5 | odd | 2 | 1344.2.p.c.223.4 | yes | 12 | ||
24.11 | even | 2 | 1344.2.p.c.223.9 | yes | 12 | ||
28.27 | even | 2 | 4032.2.p.j.1567.8 | 12 | |||
56.13 | odd | 2 | inner | 4032.2.p.k.1567.5 | 12 | ||
56.27 | even | 2 | inner | 4032.2.p.k.1567.8 | 12 | ||
84.83 | odd | 2 | 1344.2.p.c.223.10 | yes | 12 | ||
168.83 | odd | 2 | 1344.2.p.d.223.4 | yes | 12 | ||
168.125 | even | 2 | 1344.2.p.d.223.9 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.2.p.c.223.3 | ✓ | 12 | 21.20 | even | 2 | ||
1344.2.p.c.223.4 | yes | 12 | 24.5 | odd | 2 | ||
1344.2.p.c.223.9 | yes | 12 | 24.11 | even | 2 | ||
1344.2.p.c.223.10 | yes | 12 | 84.83 | odd | 2 | ||
1344.2.p.d.223.3 | yes | 12 | 12.11 | even | 2 | ||
1344.2.p.d.223.4 | yes | 12 | 168.83 | odd | 2 | ||
1344.2.p.d.223.9 | yes | 12 | 168.125 | even | 2 | ||
1344.2.p.d.223.10 | yes | 12 | 3.2 | odd | 2 | ||
4032.2.p.j.1567.5 | 12 | 7.6 | odd | 2 | |||
4032.2.p.j.1567.6 | 12 | 8.3 | odd | 2 | |||
4032.2.p.j.1567.7 | 12 | 8.5 | even | 2 | |||
4032.2.p.j.1567.8 | 12 | 28.27 | even | 2 | |||
4032.2.p.k.1567.5 | 12 | 56.13 | odd | 2 | inner | ||
4032.2.p.k.1567.6 | 12 | 4.3 | odd | 2 | inner | ||
4032.2.p.k.1567.7 | 12 | 1.1 | even | 1 | trivial | ||
4032.2.p.k.1567.8 | 12 | 56.27 | even | 2 | inner |