Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,3,Mod(341,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.341");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.e (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: | \(10.3542500457\) |
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: | \( x^{12} + 62x^{10} + 1445x^{8} + 15924x^{6} + 83244x^{4} + 170640x^{2} + 55600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{9}\cdot 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 341.1 | ||
Root | \(-4.83157i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 380.341 |
Dual form | 380.3.e.a.341.12 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 4.83157i | − | 1.61052i | −0.592919 | − | 0.805262i | \(-0.702025\pi\) | ||
0.592919 | − | 0.805262i | \(-0.297975\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.72856 | −0.532651 | −0.266326 | − | 0.963883i | \(-0.585810\pi\) | ||||
−0.266326 | + | 0.963883i | \(0.585810\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −14.3441 | −1.59379 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −13.8938 | −1.26308 | −0.631539 | − | 0.775344i | \(-0.717576\pi\) | ||||
−0.631539 | + | 0.775344i | \(0.717576\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.10699i | 0.315922i | 0.987445 | + | 0.157961i | \(0.0504920\pi\) | ||||
−0.987445 | + | 0.157961i | \(0.949508\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 10.8037i | − | 0.720248i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −15.3087 | −0.900510 | −0.450255 | − | 0.892900i | \(-0.648667\pi\) | ||||
−0.450255 | + | 0.892900i | \(0.648667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16.4588 | − | 9.49250i | −0.866253 | − | 0.499605i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 18.0148i | 0.857847i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 17.4452 | 0.758486 | 0.379243 | − | 0.925297i | \(-0.376184\pi\) | ||||
0.379243 | + | 0.925297i | \(0.376184\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 25.8203i | 0.956307i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 16.3924i | − | 0.565254i | −0.959230 | − | 0.282627i | \(-0.908794\pi\) | ||
0.959230 | − | 0.282627i | \(-0.0912059\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 15.9121i | − | 0.513292i | −0.966505 | − | 0.256646i | \(-0.917383\pi\) | ||
0.966505 | − | 0.256646i | \(-0.0826175\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 67.1291i | 2.03422i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.33731 | −0.238209 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.14304i | 0.139001i | 0.997582 | + | 0.0695005i | \(0.0221405\pi\) | ||||
−0.997582 | + | 0.0695005i | \(0.977859\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 19.8432 | 0.508800 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 42.2785i | 1.03118i | 0.856835 | + | 0.515591i | \(0.172428\pi\) | ||||
−0.856835 | + | 0.515591i | \(0.827572\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.56664 | 0.0364334 | 0.0182167 | − | 0.999834i | \(-0.494201\pi\) | ||||
0.0182167 | + | 0.999834i | \(0.494201\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −32.0743 | −0.712763 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −54.5821 | −1.16132 | −0.580660 | − | 0.814146i | \(-0.697206\pi\) | ||||
−0.580660 | + | 0.814146i | \(0.697206\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −35.0979 | −0.716283 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 73.9649i | 1.45029i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 55.9822i | 1.05627i | 0.849161 | + | 0.528134i | \(0.177108\pi\) | ||||
−0.849161 | + | 0.528134i | \(0.822892\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −31.0676 | −0.564865 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −45.8637 | + | 79.5219i | −0.804626 | + | 1.39512i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 101.822i | − | 1.72580i | −0.505376 | − | 0.862899i | \(-0.668646\pi\) | ||
0.505376 | − | 0.862899i | \(-0.331354\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 80.5719 | 1.32085 | 0.660426 | − | 0.750892i | \(-0.270376\pi\) | ||||
0.660426 | + | 0.750892i | \(0.270376\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 53.4827 | 0.848932 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.18350i | 0.141285i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 24.8838i | 0.371400i | 0.982606 | + | 0.185700i | \(0.0594552\pi\) | ||||
−0.982606 | + | 0.185700i | \(0.940545\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 84.2876i | − | 1.22156i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 121.245i | − | 1.70767i | −0.520545 | − | 0.853835i | \(-0.674271\pi\) | ||
0.520545 | − | 0.853835i | \(-0.325729\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −33.9798 | −0.465476 | −0.232738 | − | 0.972539i | \(-0.574769\pi\) | ||||
−0.232738 | + | 0.972539i | \(0.574769\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 24.1579i | − | 0.322105i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 51.8040 | 0.672779 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 102.623i | − | 1.29902i | −0.760351 | − | 0.649512i | \(-0.774973\pi\) | ||
0.760351 | − | 0.649512i | \(-0.225027\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.34417 | −0.0536317 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 80.3324 | 0.967860 | 0.483930 | − | 0.875107i | \(-0.339209\pi\) | ||||
0.483930 | + | 0.875107i | \(0.339209\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −34.2312 | −0.402720 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −79.2009 | −0.910355 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.0884i | 0.135824i | 0.997691 | + | 0.0679121i | \(0.0216338\pi\) | ||||
−0.997691 | + | 0.0679121i | \(0.978366\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 15.3131i | − | 0.168276i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −76.8802 | −0.826669 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −36.8030 | − | 21.2259i | −0.387400 | − | 0.223430i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 161.837i | − | 1.66842i | −0.551447 | − | 0.834210i | \(-0.685924\pi\) | ||
0.551447 | − | 0.834210i | \(-0.314076\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 199.294 | 2.01308 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.07921 | −0.0601901 | −0.0300951 | − | 0.999547i | \(-0.509581\pi\) | ||||
−0.0300951 | + | 0.999547i | \(0.509581\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 27.8929i | 0.270805i | 0.990791 | + | 0.135402i | \(0.0432327\pi\) | ||||
−0.990791 | + | 0.135402i | \(0.956767\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 40.2823i | 0.383641i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 61.4652i | 0.574441i | 0.957865 | + | 0.287220i | \(0.0927312\pi\) | ||||
−0.957865 | + | 0.287220i | \(0.907269\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 30.2310i | 0.277348i | 0.990338 | + | 0.138674i | \(0.0442841\pi\) | ||||
−0.990338 | + | 0.138674i | \(0.955716\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 24.8489 | 0.223864 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 178.939i | − | 1.58353i | −0.610826 | − | 0.791765i | \(-0.709163\pi\) | ||
0.610826 | − | 0.791765i | \(-0.290837\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 39.0086 | 0.339205 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 58.9109i | − | 0.503512i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 57.0793 | 0.479658 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 72.0390 | 0.595364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 204.272 | 1.66074 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 53.4071i | 0.420528i | 0.977645 | + | 0.210264i | \(0.0674324\pi\) | ||||
−0.977645 | + | 0.210264i | \(0.932568\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 7.56932i | − | 0.0586769i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −109.035 | −0.832327 | −0.416163 | − | 0.909290i | \(-0.636626\pi\) | ||||
−0.416163 | + | 0.909290i | \(0.636626\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 61.3676 | + | 35.3933i | 0.461411 | + | 0.266115i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 57.7359i | 0.427673i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −24.9987 | −0.182472 | −0.0912362 | − | 0.995829i | \(-0.529082\pi\) | ||||
−0.0912362 | + | 0.995829i | \(0.529082\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 115.083 | 0.827936 | 0.413968 | − | 0.910291i | \(-0.364143\pi\) | ||||
0.413968 | + | 0.910291i | \(0.364143\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 263.717i | 1.87033i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 57.0619i | − | 0.399034i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 36.6545i | − | 0.252789i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 169.578i | 1.15359i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −141.364 | −0.948750 | −0.474375 | − | 0.880323i | \(-0.657326\pi\) | ||||
−0.474375 | + | 0.880323i | \(0.657326\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 250.107i | − | 1.65634i | −0.560478 | − | 0.828169i | \(-0.689383\pi\) | ||
0.560478 | − | 0.828169i | \(-0.310617\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 219.589 | 1.43522 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 35.5804i | − | 0.229551i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.5947 | −0.0929601 | −0.0464801 | − | 0.998919i | \(-0.514800\pi\) | ||||
−0.0464801 | + | 0.998919i | \(0.514800\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 270.482 | 1.70115 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −65.0454 | −0.404009 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.57924 | −0.0587684 | −0.0293842 | − | 0.999568i | \(-0.509355\pi\) | ||||
−0.0293842 | + | 0.999568i | \(0.509355\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 150.105i | 0.909729i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 302.815i | 1.81326i | 0.421923 | + | 0.906631i | \(0.361355\pi\) | ||||
−0.421923 | + | 0.906631i | \(0.638645\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 152.133 | 0.900193 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 236.086 | + | 136.161i | 1.38062 | + | 0.796264i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 111.084i | − | 0.642102i | −0.947062 | − | 0.321051i | \(-0.895964\pi\) | ||
0.947062 | − | 0.321051i | \(-0.104036\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.6428 | −0.106530 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −491.961 | −2.77944 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 247.724i | 1.38393i | 0.721929 | + | 0.691967i | \(0.243256\pi\) | ||||
−0.721929 | + | 0.691967i | \(0.756744\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 234.560i | − | 1.29591i | −0.761678 | − | 0.647956i | \(-0.775624\pi\) | ||
0.761678 | − | 0.647956i | \(-0.224376\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 389.289i | − | 2.12726i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.5002i | 0.0621631i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 212.696 | 1.13741 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 96.2724i | − | 0.509378i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −250.384 | −1.31091 | −0.655455 | − | 0.755235i | \(-0.727523\pi\) | ||||
−0.655455 | + | 0.755235i | \(0.727523\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 122.208i | − | 0.633204i | −0.948558 | − | 0.316602i | \(-0.897458\pi\) | ||
0.948558 | − | 0.316602i | \(-0.102542\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 44.3707 | 0.227542 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −343.177 | −1.74201 | −0.871007 | − | 0.491271i | \(-0.836533\pi\) | ||||
−0.871007 | + | 0.491271i | \(0.836533\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 297.583 | 1.49539 | 0.747696 | − | 0.664042i | \(-0.231160\pi\) | ||||
0.747696 | + | 0.664042i | \(0.231160\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 120.228 | 0.598148 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 61.1199i | 0.301083i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 94.5376i | 0.461159i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −250.235 | −1.20886 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 228.676 | + | 131.887i | 1.09414 | + | 0.631040i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 237.792i | − | 1.12698i | −0.826124 | − | 0.563488i | \(-0.809459\pi\) | ||
0.826124 | − | 0.563488i | \(-0.190541\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −585.801 | −2.75024 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.50311 | 0.0162935 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 59.3290i | 0.273406i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 164.176i | 0.749661i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 62.8725i | − | 0.284491i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 152.390i | − | 0.683365i | −0.939815 | − | 0.341682i | \(-0.889003\pi\) | ||
0.939815 | − | 0.341682i | \(-0.110997\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −71.7204 | −0.318757 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 205.814i | − | 0.906670i | −0.891340 | − | 0.453335i | \(-0.850234\pi\) | ||
0.891340 | − | 0.453335i | \(-0.149766\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 135.060 | 0.589783 | 0.294892 | − | 0.955531i | \(-0.404716\pi\) | ||||
0.294892 | + | 0.955531i | \(0.404716\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 250.295i | − | 1.08353i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 100.593 | 0.431728 | 0.215864 | − | 0.976423i | \(-0.430743\pi\) | ||||
0.215864 | + | 0.976423i | \(0.430743\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −122.049 | −0.519358 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −495.830 | −2.09211 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −328.565 | −1.37475 | −0.687373 | − | 0.726304i | \(-0.741236\pi\) | ||||
−0.687373 | + | 0.726304i | \(0.741236\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 144.249i | 0.598543i | 0.954168 | + | 0.299272i | \(0.0967437\pi\) | ||||
−0.954168 | + | 0.299272i | \(0.903256\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 253.372i | 1.04268i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −78.4812 | −0.320331 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 38.9856 | − | 67.5961i | 0.157836 | − | 0.273669i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 388.132i | − | 1.55876i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 66.0565 | 0.263173 | 0.131587 | − | 0.991305i | \(-0.457993\pi\) | ||||
0.131587 | + | 0.991305i | \(0.457993\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −242.381 | −0.958027 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 165.391i | 0.648591i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 268.255i | 1.04379i | 0.853009 | + | 0.521896i | \(0.174775\pi\) | ||||
−0.853009 | + | 0.521896i | \(0.825225\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 19.1761i | − | 0.0740390i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 235.133i | 0.900895i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −241.131 | −0.916848 | −0.458424 | − | 0.888734i | \(-0.651586\pi\) | ||||
−0.458424 | + | 0.888734i | \(0.651586\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 125.180i | 0.472378i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 58.4058 | 0.218748 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 270.274i | 1.00473i | 0.864654 | + | 0.502367i | \(0.167538\pi\) | ||||
−0.864654 | + | 0.502367i | \(0.832462\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 159.872 | 0.589934 | 0.294967 | − | 0.955507i | \(-0.404691\pi\) | ||||
0.294967 | + | 0.955507i | \(0.404691\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −73.9865 | −0.271013 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −69.4692 | −0.252615 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 480.862 | 1.73596 | 0.867981 | − | 0.496597i | \(-0.165417\pi\) | ||||
0.867981 | + | 0.496597i | \(0.165417\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 228.244i | 0.818078i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 125.506i | − | 0.446639i | −0.974745 | − | 0.223320i | \(-0.928311\pi\) | ||
0.974745 | − | 0.223320i | \(-0.0716894\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −169.824 | −0.600086 | −0.300043 | − | 0.953926i | \(-0.597001\pi\) | ||||
−0.300043 | + | 0.953926i | \(0.597001\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −102.554 | + | 177.816i | −0.359840 | + | 0.623917i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 157.638i | − | 0.549261i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −54.6445 | −0.189081 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −781.925 | −2.68703 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 103.213i | 0.352263i | 0.984367 | + | 0.176131i | \(0.0563583\pi\) | ||||
−0.984367 | + | 0.176131i | \(0.943642\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 227.681i | − | 0.771801i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 358.743i | − | 1.20789i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 71.6472i | 0.239623i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.84130 | −0.0194063 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 29.3721i | 0.0969377i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 180.164 | 0.590703 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 470.447i | 1.53240i | 0.642602 | + | 0.766200i | \(0.277855\pi\) | ||||
−0.642602 | + | 0.766200i | \(0.722145\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 134.767 | 0.436138 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −104.966 | −0.337511 | −0.168756 | − | 0.985658i | \(-0.553975\pi\) | ||||
−0.168756 | + | 0.985658i | \(0.553975\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 358.845 | 1.14647 | 0.573234 | − | 0.819392i | \(-0.305689\pi\) | ||||
0.573234 | + | 0.819392i | \(0.305689\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 119.591 | 0.379654 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 367.285i | 1.15863i | 0.815104 | + | 0.579314i | \(0.196680\pi\) | ||||
−0.815104 | + | 0.579314i | \(0.803320\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 227.753i | 0.713960i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 296.973 | 0.925150 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 251.963 | + | 145.318i | 0.780070 | + | 0.449900i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.5349i | 0.0631844i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 146.063 | 0.446676 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 203.512 | 0.618579 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 496.428i | 1.49978i | 0.661561 | + | 0.749892i | \(0.269894\pi\) | ||||
−0.661561 | + | 0.749892i | \(0.730106\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 73.7721i | − | 0.221538i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 55.6419i | 0.166095i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 52.5036i | 0.155797i | 0.996961 | + | 0.0778986i | \(0.0248210\pi\) | ||||
−0.996961 | + | 0.0778986i | \(0.975179\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −864.556 | −2.55031 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 221.080i | 0.648328i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 313.564 | 0.914180 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 188.473i | − | 0.546298i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 409.556 | 1.18028 | 0.590138 | − | 0.807302i | \(-0.299073\pi\) | ||||
0.590138 | + | 0.807302i | \(0.299073\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 562.063 | 1.61050 | 0.805248 | − | 0.592938i | \(-0.202032\pi\) | ||||
0.805248 | + | 0.592938i | \(0.202032\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −106.044 | −0.302118 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 252.453 | 0.715165 | 0.357583 | − | 0.933881i | \(-0.383601\pi\) | ||||
0.357583 | + | 0.933881i | \(0.383601\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 271.111i | − | 0.763693i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 275.783i | − | 0.772500i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −119.344 | −0.332433 | −0.166217 | − | 0.986089i | \(-0.553155\pi\) | ||||
−0.166217 | + | 0.986089i | \(0.553155\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 180.785 | + | 312.470i | 0.500789 | + | 0.865569i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 348.062i | − | 0.958848i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −75.9811 | −0.208167 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −690.635 | −1.88184 | −0.940920 | − | 0.338629i | \(-0.890037\pi\) | ||||
−0.940920 | + | 0.338629i | \(0.890037\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 606.446i | − | 1.64349i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 208.733i | − | 0.562623i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 491.052i | 1.31649i | 0.752803 | + | 0.658246i | \(0.228701\pi\) | ||||
−0.752803 | + | 0.658246i | \(0.771299\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 54.0186i | − | 0.144050i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 67.3233 | 0.178576 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 691.775i | − | 1.82526i | −0.408782 | − | 0.912632i | \(-0.634046\pi\) | ||
0.408782 | − | 0.912632i | \(-0.365954\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 258.040 | 0.677271 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 252.889i | − | 0.660285i | −0.943931 | − | 0.330142i | \(-0.892903\pi\) | ||
0.943931 | − | 0.330142i | \(-0.107097\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 115.837 | 0.300876 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −22.4720 | −0.0580671 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −504.764 | −1.29759 | −0.648797 | − | 0.760961i | \(-0.724728\pi\) | ||||
−0.648797 | + | 0.760961i | \(0.724728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −267.063 | −0.683025 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 526.809i | 1.34048i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 229.472i | − | 0.580941i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 313.581 | 0.789876 | 0.394938 | − | 0.918708i | \(-0.370766\pi\) | ||||
0.394938 | + | 0.918708i | \(0.370766\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 171.005 | − | 296.502i | 0.428585 | − | 0.743113i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 561.838i | 1.40109i | 0.713607 | + | 0.700546i | \(0.247060\pi\) | ||||
−0.713607 | + | 0.700546i | \(0.752940\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 65.3506 | 0.162160 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.71385 | −0.0239848 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 71.4566i | − | 0.175569i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 165.613i | − | 0.404921i | −0.979290 | − | 0.202460i | \(-0.935106\pi\) | ||
0.979290 | − | 0.202460i | \(-0.0648937\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 120.783i | 0.293876i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 379.650i | 0.919249i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 179.629 | 0.432840 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 556.032i | − | 1.33341i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −440.399 | −1.05107 | −0.525536 | − | 0.850771i | \(-0.676135\pi\) | ||||
−0.525536 | + | 0.850771i | \(0.676135\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 786.831i | − | 1.86896i | −0.356018 | − | 0.934479i | \(-0.615866\pi\) | ||
0.356018 | − | 0.934479i | \(-0.384134\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 782.929 | 1.85090 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −76.5434 | −0.180102 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −300.417 | −0.703553 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −275.698 | −0.642654 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 219.539i | − | 0.509372i | −0.967024 | − | 0.254686i | \(-0.918028\pi\) | ||
0.967024 | − | 0.254686i | \(-0.0819721\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 450.900i | − | 1.04134i | −0.853758 | − | 0.520670i | \(-0.825682\pi\) | ||
0.853758 | − | 0.520670i | \(-0.174318\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −177.099 | −0.407123 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −287.127 | − | 165.598i | −0.657041 | − | 0.378944i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 319.069i | 0.726808i | 0.931632 | + | 0.363404i | \(0.118385\pi\) | ||||
−0.931632 | + | 0.363404i | \(0.881615\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 503.446 | 1.14160 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 780.776 | 1.76247 | 0.881237 | − | 0.472674i | \(-0.156711\pi\) | ||||
0.881237 | + | 0.472674i | \(0.156711\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.0304i | 0.0607425i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 683.009i | 1.52798i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 523.244i | − | 1.16535i | −0.812704 | − | 0.582677i | \(-0.802005\pi\) | ||
0.812704 | − | 0.582677i | \(-0.197995\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 587.411i | − | 1.30246i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1208.41 | −2.66757 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 34.2412i | − | 0.0752554i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 874.643 | 1.91388 | 0.956940 | − | 0.290285i | \(-0.0937500\pi\) | ||||
0.956940 | + | 0.290285i | \(0.0937500\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 395.274i | − | 0.861164i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 120.368 | 0.261102 | 0.130551 | − | 0.991442i | \(-0.458325\pi\) | ||||
0.130551 | + | 0.991442i | \(0.458325\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 256.911 | 0.554883 | 0.277441 | − | 0.960743i | \(-0.410514\pi\) | ||||
0.277441 | + | 0.960743i | \(0.410514\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −171.909 | −0.369698 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 490.911 | 1.05120 | 0.525601 | − | 0.850731i | \(-0.323840\pi\) | ||||
0.525601 | + | 0.850731i | \(0.323840\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 92.7807i | − | 0.197827i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 70.5155i | 0.149714i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.7666 | −0.0460182 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −82.2941 | − | 47.4625i | −0.173251 | − | 0.0999210i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 803.014i | − | 1.68347i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 545.752 | 1.13936 | 0.569679 | − | 0.821868i | \(-0.307068\pi\) | ||||
0.569679 | + | 0.821868i | \(0.307068\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.1224 | −0.0439135 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 314.271i | 0.650665i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 361.878i | − | 0.746140i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 243.032i | − | 0.499039i | −0.968370 | − | 0.249519i | \(-0.919727\pi\) | ||
0.968370 | − | 0.249519i | \(-0.0802726\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 46.2828i | 0.0946479i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −555.332 | −1.13102 | −0.565511 | − | 0.824740i | \(-0.691321\pi\) | ||||
−0.565511 | + | 0.824740i | \(0.691321\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 250.946i | 0.509017i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 445.636 | 0.900275 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 452.067i | 0.909592i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −231.235 | −0.463397 | −0.231698 | − | 0.972788i | \(-0.574428\pi\) | ||||
−0.231698 | + | 0.972788i | \(0.574428\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1463.07 | 2.92030 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −206.048 | −0.409638 | −0.204819 | − | 0.978800i | \(-0.565660\pi\) | ||||
−0.204819 | + | 0.978800i | \(0.565660\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.5935 | −0.0269179 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 735.040i | − | 1.44978i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 398.832i | 0.783560i | 0.920059 | + | 0.391780i | \(0.128141\pi\) | ||||
−0.920059 | + | 0.391780i | \(0.871859\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 126.696 | 0.247936 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 245.099 | − | 424.971i | 0.477776 | − | 0.828404i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 62.3704i | 0.121108i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 758.355 | 1.46684 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −536.708 | −1.03412 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 262.617i | − | 0.504064i | −0.967719 | − | 0.252032i | \(-0.918901\pi\) | ||
0.967719 | − | 0.252032i | \(-0.0810988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 814.031i | 1.55646i | 0.627977 | + | 0.778232i | \(0.283883\pi\) | ||||
−0.627977 | + | 0.778232i | \(0.716117\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 90.0740i | 0.171569i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 243.592i | 0.462225i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −224.666 | −0.424699 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1460.54i | 2.75055i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −173.637 | −0.325773 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 137.440i | 0.256898i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1196.90 | 2.22886 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 487.644 | 0.904720 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −196.753 | −0.363684 | −0.181842 | − | 0.983328i | \(-0.558206\pi\) | ||||
−0.181842 | + | 0.983328i | \(0.558206\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1133.29 | −2.08710 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 67.5985i | 0.124034i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 759.052i | 1.38766i | 0.720137 | + | 0.693832i | \(0.244079\pi\) | ||||
−0.720137 | + | 0.693832i | \(0.755921\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1155.73 | −2.10515 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −155.605 | + | 269.799i | −0.282404 | + | 0.489653i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 382.636i | 0.691927i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 55.5639 | 0.100115 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 705.968 | 1.26745 | 0.633723 | − | 0.773560i | \(-0.281526\pi\) | ||||
0.633723 | + | 0.773560i | \(0.281526\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.43416i | 0.0115101i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 1027.66i | − | 1.83183i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 357.744i | 0.635424i | 0.948187 | + | 0.317712i | \(0.102914\pi\) | ||||
−0.948187 | + | 0.317712i | \(0.897086\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 400.119i | − | 0.708176i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.1975 | 0.0285670 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 448.411i | 0.788069i | 0.919096 | + | 0.394034i | \(0.128921\pi\) | ||||
−0.919096 | + | 0.394034i | \(0.871079\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 203.672 | 0.356694 | 0.178347 | − | 0.983968i | \(-0.442925\pi\) | ||||
0.178347 | + | 0.983968i | \(0.442925\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1209.75i | 2.11125i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 87.2259 | 0.151697 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 232.447 | 0.402854 | 0.201427 | − | 0.979504i | \(-0.435442\pi\) | ||||
0.201427 | + | 0.979504i | \(0.435442\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −590.458 | −1.01979 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −299.524 | −0.515532 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 777.809i | − | 1.33415i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 131.729i | − | 0.225178i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1101.80 | −1.87701 | −0.938503 | − | 0.345271i | \(-0.887787\pi\) | ||||
−0.938503 | + | 0.345271i | \(0.887787\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −151.045 | + | 261.894i | −0.256443 | + | 0.444641i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1658.08i | 2.80555i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −387.409 | −0.653303 | −0.326651 | − | 0.945145i | \(-0.605920\pi\) | ||||
−0.326651 | + | 0.945145i | \(0.605920\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 127.633 | 0.214509 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 1437.79i | − | 2.40836i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 649.288i | 1.08395i | 0.840393 | + | 0.541977i | \(0.182324\pi\) | ||||
−0.840393 | + | 0.541977i | \(0.817676\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 564.191i | − | 0.938754i | −0.882998 | − | 0.469377i | \(-0.844479\pi\) | ||
0.882998 | − | 0.469377i | \(-0.155521\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 356.935i | − | 0.591932i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 161.084 | 0.266255 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 431.505i | 0.710882i | 0.934699 | + | 0.355441i | \(0.115669\pi\) | ||||
−0.934699 | + | 0.355441i | \(0.884331\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 295.305 | 0.484902 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 224.168i | − | 0.366887i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 360.161 | 0.587539 | 0.293769 | − | 0.955876i | \(-0.405090\pi\) | ||||
0.293769 | + | 0.955876i | \(0.405090\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 456.765 | 0.742707 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −255.900 | −0.414749 | −0.207375 | − | 0.978262i | \(-0.566492\pi\) | ||||
−0.207375 | + | 0.978262i | \(0.566492\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −231.220 | −0.373538 | −0.186769 | − | 0.982404i | \(-0.559802\pi\) | ||||
−0.186769 | + | 0.982404i | \(0.559802\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 450.440i | 0.725346i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 45.0722i | − | 0.0723470i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 637.223 | − | 1104.87i | 1.01630 | − | 1.76215i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 78.7331i | − | 0.125172i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 55.6688 | 0.0882232 | 0.0441116 | − | 0.999027i | \(-0.485954\pi\) | ||||
0.0441116 | + | 0.999027i | \(0.485954\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1148.91 | −1.81502 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 119.422i | 0.188066i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 144.146i | − | 0.226290i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1739.14i | 2.72166i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1086.58i | − | 1.69513i | −0.530692 | − | 0.847565i | \(-0.678068\pi\) | ||
0.530692 | − | 0.847565i | \(-0.321932\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 132.021 | 0.205320 | 0.102660 | − | 0.994717i | \(-0.467265\pi\) | ||||
0.102660 | + | 0.994717i | \(0.467265\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 16.9255i | − | 0.0262411i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 139.001 | 0.214840 | 0.107420 | − | 0.994214i | \(-0.465741\pi\) | ||||
0.107420 | + | 0.994214i | \(0.465741\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1414.70i | 2.17982i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 286.652 | 0.440326 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.61433 | −0.00400356 | −0.00200178 | − | 0.999998i | \(-0.500637\pi\) | ||||
−0.00200178 | + | 0.999998i | \(0.500637\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −243.809 | −0.372228 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 487.408 | 0.741870 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1115.25i | − | 1.69234i | −0.532911 | − | 0.846171i | \(-0.678902\pi\) | ||
0.532911 | − | 0.846171i | \(-0.321098\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1032.56i | − | 1.56212i | −0.624453 | − | 0.781062i | \(-0.714678\pi\) | ||
0.624453 | − | 0.781062i | \(-0.285322\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −303.773 | −0.458180 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 137.222 | + | 79.1419i | 0.206349 | + | 0.119010i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 285.968i | − | 0.428738i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −736.285 | −1.10058 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1119.45 | −1.66834 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 923.804i | − | 1.37267i | −0.727288 | − | 0.686333i | \(-0.759219\pi\) | ||
0.727288 | − | 0.686333i | \(-0.240781\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 129.101i | 0.191261i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1144.25i | 1.69017i | 0.534631 | + | 0.845086i | \(0.320451\pi\) | ||||
−0.534631 | + | 0.845086i | \(0.679549\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 603.417i | 0.888686i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −994.406 | −1.46021 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 686.997i | − | 1.00585i | −0.864330 | − | 0.502926i | \(-0.832257\pi\) | ||
0.864330 | − | 0.502926i | \(-0.167743\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −55.8988 | −0.0816041 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 652.554i | − | 0.949860i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −229.918 | −0.333699 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1216.77 | −1.76088 | −0.880442 | − | 0.474154i | \(-0.842754\pi\) | ||||
−0.880442 | + | 0.474154i | \(0.842754\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −743.081 | −1.07227 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 257.334 | 0.370264 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 647.228i | − | 0.928591i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 486.020i | − | 0.695308i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1082.00 | −1.54351 | −0.771753 | − | 0.635922i | \(-0.780620\pi\) | ||||
−0.771753 | + | 0.635922i | \(0.780620\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 48.8203 | − | 84.6482i | 0.0694456 | − | 0.120410i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 589.690i | 0.836439i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.6667 | 0.0320604 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −639.509 | −0.901987 | −0.450994 | − | 0.892527i | \(-0.648930\pi\) | ||||
−0.450994 | + | 0.892527i | \(0.648930\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1472.03i | 2.07037i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 277.589i | − | 0.389325i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 127.594i | − | 0.178453i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1587.48i | 2.21406i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −95.9878 | −0.133502 | −0.0667509 | − | 0.997770i | \(-0.521263\pi\) | ||||
−0.0667509 | + | 0.997770i | \(0.521263\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 104.000i | − | 0.144245i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 696.949 | 0.963968 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 81.9619i | − | 0.113051i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −368.875 | −0.507394 | −0.253697 | − | 0.967284i | \(-0.581647\pi\) | ||||
−0.253697 | + | 0.967284i | \(0.581647\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1185.09 | 1.62563 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23.9831 | −0.0328087 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −865.251 | −1.18042 | −0.590212 | − | 0.807248i | \(-0.700956\pi\) | ||||
−0.590212 | + | 0.807248i | \(0.700956\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 379.187i | 0.515901i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 345.732i | − | 0.469107i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −934.331 | −1.26432 | −0.632159 | − | 0.774839i | \(-0.717831\pi\) | ||||
−0.632159 | + | 0.774839i | \(0.717831\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −326.595 | − | 188.362i | −0.440750 | − | 0.254199i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 235.551i | − | 0.317027i | −0.987357 | − | 0.158514i | \(-0.949330\pi\) | ||
0.987357 | − | 0.158514i | \(-0.0506702\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −316.099 | −0.424294 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1152.29 | −1.54256 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 229.176i | − | 0.305976i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 971.042i | − | 1.29300i | −0.762915 | − | 0.646499i | \(-0.776232\pi\) | ||
0.762915 | − | 0.646499i | \(-0.223768\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 319.156i | − | 0.423847i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 559.256i | − | 0.740737i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −177.074 | −0.233916 | −0.116958 | − | 0.993137i | \(-0.537314\pi\) | ||||
−0.116958 | + | 0.993137i | \(0.537314\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1171.08i | 1.54292i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −159.521 | −0.209621 | −0.104810 | − | 0.994492i | \(-0.533424\pi\) | ||||
−0.104810 | + | 0.994492i | \(0.533424\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 112.718i | − | 0.147730i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 491.015 | 0.641850 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 418.182 | 0.545218 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 707.134 | 0.919551 | 0.459775 | − | 0.888035i | \(-0.347930\pi\) | ||||
0.459775 | + | 0.888035i | \(0.347930\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1296.09 | 1.68105 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 799.572i | − | 1.03438i | −0.855872 | − | 0.517188i | \(-0.826979\pi\) | ||
0.855872 | − | 0.517188i | \(-0.173021\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 79.5603i | − | 0.102658i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −92.6507 | −0.119242 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 401.329 | − | 695.854i | 0.515184 | − | 0.893265i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1684.55i | 2.15692i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 423.256 | 0.540557 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −32.6348 | −0.0415730 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1366.97i | − | 1.73693i | −0.495749 | − | 0.868466i | \(-0.665107\pi\) | ||
0.495749 | − | 0.868466i | \(-0.334893\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1165.04i | 1.47661i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 667.184i | 0.843469i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 330.908i | 0.417286i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 604.817 | 0.760776 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 121.258i | − | 0.152143i | −0.997102 | − | 0.0760717i | \(-0.975762\pi\) | ||
0.997102 | − | 0.0760717i | \(-0.0242378\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 835.579 | 1.04578 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 173.396i | − | 0.216475i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 472.110 | 0.587933 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −145.446 | −0.180678 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1305.85 | 1.61815 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 820.488 | 1.01420 | 0.507100 | − | 0.861887i | \(-0.330717\pi\) | ||||
0.507100 | + | 0.861887i | \(0.330717\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 537.722i | 0.663036i | 0.943449 | + | 0.331518i | \(0.107561\pi\) | ||||
−0.943449 | + | 0.331518i | \(0.892439\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 772.434i | − | 0.950103i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.4198 | −0.0262820 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.7850 | − | 14.8713i | −0.0315606 | − | 0.0182023i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 219.653i | 0.268196i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −54.0424 | −0.0658250 | −0.0329125 | − | 0.999458i | \(-0.510478\pi\) | ||||
−0.0329125 | + | 0.999458i | \(0.510478\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −599.052 | −0.727889 | −0.363944 | − | 0.931421i | \(-0.618570\pi\) | ||||
−0.363944 | + | 0.931421i | \(0.618570\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 335.646i | 0.406843i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 620.339i | 0.750108i | 0.927003 | + | 0.375054i | \(0.122376\pi\) | ||||
−0.927003 | + | 0.375054i | \(0.877624\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.8107i | 0.0444038i | 0.999754 | + | 0.0222019i | \(0.00706766\pi\) | ||||
−0.999754 | + | 0.0222019i | \(0.992932\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 2323.32i | − | 2.79581i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 537.302 | 0.645020 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 677.115i | 0.810916i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 410.854 | 0.490865 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 531.549i | 0.633551i | 0.948501 | + | 0.316776i | \(0.102600\pi\) | ||||
−0.948501 | + | 0.316776i | \(0.897400\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 572.290 | 0.680488 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −606.389 | −0.719323 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 340.179 | 0.402579 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −268.602 | −0.317121 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 820.519i | 0.966453i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 89.7212i | 0.105430i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.6518 | 0.0195214 | 0.00976072 | − | 0.999952i | \(-0.496893\pi\) | ||||
0.00976072 | + | 0.999952i | \(0.496893\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 527.905 | + | 304.466i | 0.617433 | + | 0.356100i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 656.701i | 0.766279i | 0.923691 | + | 0.383139i | \(0.125157\pi\) | ||||
−0.923691 | + | 0.383139i | \(0.874843\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.72122 | −0.00898862 | −0.00449431 | − | 0.999990i | \(-0.501431\pi\) | ||||
−0.00449431 | + | 0.999990i | \(0.501431\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −761.638 | −0.884597 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1132.71i | − | 1.31253i | −0.754530 | − | 0.656266i | \(-0.772135\pi\) | ||
0.754530 | − | 0.656266i | \(-0.227865\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 248.390i | − | 0.287157i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 264.019i | 0.304520i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1425.83i | 1.64077i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −102.197 | −0.117333 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2321.40i | 2.65910i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −41.6865 | −0.0476418 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 826.040i | 0.941893i | 0.882162 | + | 0.470947i | \(0.156088\pi\) | ||||
−0.882162 | + | 0.470947i | \(0.843912\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 498.681 | 0.567327 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 691.162 | 0.784520 | 0.392260 | − | 0.919854i | \(-0.371693\pi\) | ||||
0.392260 | + | 0.919854i | \(0.371693\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1339.08 | −1.51651 | −0.758255 | − | 0.651958i | \(-0.773948\pi\) | ||||
−0.758255 | + | 0.651958i | \(0.773948\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1100.06 | −1.24300 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1263.16i | − | 1.42408i | −0.702139 | − | 0.712040i | \(-0.747772\pi\) | ||
0.702139 | − | 0.712040i | \(-0.252228\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 199.131i | − | 0.223995i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 60.3572 | 0.0677409 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 898.356 | + | 518.120i | 1.00600 | + | 0.580202i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 553.928i | 0.618914i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 346.168 | 0.385918 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −260.836 | −0.290141 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 857.014i | − | 0.951181i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28.2227i | 0.0312543i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 524.492i | − | 0.579549i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 531.490i | 0.585987i | 0.956114 | + | 0.292994i | \(0.0946515\pi\) | ||||
−0.956114 | + | 0.292994i | \(0.905349\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 87.2006 | 0.0959302 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 214.421i | − | 0.235368i | −0.993051 | − | 0.117684i | \(-0.962453\pi\) | ||
0.993051 | − | 0.117684i | \(-0.0375471\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1116.13 | −1.22248 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 870.476i | − | 0.951340i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 406.542 | 0.443340 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1523.80 | −1.65811 | −0.829055 | − | 0.559167i | \(-0.811121\pi\) | ||||
−0.829055 | + | 0.559167i | \(0.811121\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2273.00 | 2.46797 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 497.950 | 0.539490 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.7152i | 0.0278002i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 400.098i | − | 0.431605i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −269.533 | −0.290132 | −0.145066 | − | 0.989422i | \(-0.546339\pi\) | ||||
−0.145066 | + | 0.989422i | \(0.546339\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 577.669 | + | 333.166i | 0.620482 | + | 0.357859i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 507.151i | 0.543570i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 475.604 | 0.508667 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −492.223 | −0.525318 | −0.262659 | − | 0.964889i | \(-0.584599\pi\) | ||||
−0.262659 | + | 0.964889i | \(0.584599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 1733.78i | − | 1.84641i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1364.05i | − | 1.44958i | −0.688972 | − | 0.724788i | \(-0.741938\pi\) | ||
0.688972 | − | 0.724788i | \(-0.258062\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 737.556i | 0.782138i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 215.272i | − | 0.227801i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1082.40 | −1.14298 | −0.571490 | − | 0.820609i | \(-0.693634\pi\) | ||||
−0.571490 | + | 0.820609i | \(0.693634\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 139.554i | − | 0.147054i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1774.56 | 1.86600 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 196.828i | 0.206535i | 0.994654 | + | 0.103268i | \(0.0329298\pi\) | ||||
−0.994654 | + | 0.103268i | \(0.967070\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −559.875 | −0.586256 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1100.41 | 1.14985 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 93.2092 | 0.0971941 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 707.806 | 0.736531 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 881.661i | − | 0.915536i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 273.266i | − | 0.283177i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1381.14 | 1.42828 | 0.714138 | − | 0.700005i | \(-0.246819\pi\) | ||||
0.714138 | + | 0.700005i | \(0.246819\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 702.112 | − | 1217.37i | 0.724574 | − | 1.25632i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1116.21i | 1.14954i | 0.818314 | + | 0.574771i | \(0.194909\pi\) | ||||
−0.818314 | + | 0.574771i | \(0.805091\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −429.094 | −0.441001 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 99.2160 | 0.101760 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1784.43i | − | 1.82644i | −0.407471 | − | 0.913218i | \(-0.633589\pi\) | ||
0.407471 | − | 0.913218i | \(-0.366411\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 167.954i | − | 0.171557i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 433.635i | − | 0.442034i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 600.203i | − | 0.610583i | −0.952259 | − | 0.305291i | \(-0.901246\pi\) | ||
0.952259 | − | 0.305291i | \(-0.0987538\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −767.366 | −0.779052 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 983.285i | − | 0.996236i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.3303 | 0.0276343 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.0179i | 0.0141452i | 0.999975 | + | 0.00707259i | \(0.00225129\pi\) | ||||
−0.999975 | + | 0.00707259i | \(0.997749\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2398.53 | 2.41544 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 665.415 | 0.668759 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 137.727 | 0.138142 | 0.0690708 | − | 0.997612i | \(-0.477997\pi\) | ||||
0.0690708 | + | 0.997612i | \(0.477997\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −132.795 | −0.132928 |
(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 | 380.3.e.a.341.1 | ✓ | 12 | |
3.2 | odd | 2 | 3420.3.o.a.721.4 | 12 | |||
4.3 | odd | 2 | 1520.3.h.b.721.12 | 12 | |||
5.2 | odd | 4 | 1900.3.g.c.949.2 | 24 | |||
5.3 | odd | 4 | 1900.3.g.c.949.23 | 24 | |||
5.4 | even | 2 | 1900.3.e.f.1101.12 | 12 | |||
19.18 | odd | 2 | inner | 380.3.e.a.341.12 | yes | 12 | |
57.56 | even | 2 | 3420.3.o.a.721.3 | 12 | |||
76.75 | even | 2 | 1520.3.h.b.721.1 | 12 | |||
95.18 | even | 4 | 1900.3.g.c.949.1 | 24 | |||
95.37 | even | 4 | 1900.3.g.c.949.24 | 24 | |||
95.94 | odd | 2 | 1900.3.e.f.1101.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.3.e.a.341.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
380.3.e.a.341.12 | yes | 12 | 19.18 | odd | 2 | inner | |
1520.3.h.b.721.1 | 12 | 76.75 | even | 2 | |||
1520.3.h.b.721.12 | 12 | 4.3 | odd | 2 | |||
1900.3.e.f.1101.1 | 12 | 95.94 | odd | 2 | |||
1900.3.e.f.1101.12 | 12 | 5.4 | even | 2 | |||
1900.3.g.c.949.1 | 24 | 95.18 | even | 4 | |||
1900.3.g.c.949.2 | 24 | 5.2 | odd | 4 | |||
1900.3.g.c.949.23 | 24 | 5.3 | odd | 4 | |||
1900.3.g.c.949.24 | 24 | 95.37 | even | 4 | |||
3420.3.o.a.721.3 | 12 | 57.56 | even | 2 | |||
3420.3.o.a.721.4 | 12 | 3.2 | odd | 2 |