Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [156,3,Mod(77,156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(156, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("156.77");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 156 = 2^{2} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 156.g (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: | \(4.25069212402\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 77.4 | ||
Root | \(-1.65831 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 156.77 |
Dual form | 156.3.g.b.77.2 |
$q$-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 \(\left(\mathbb{Z}/156\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(79\) | \(145\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −2.50000 | + | 1.65831i | −0.833333 | + | 0.552771i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.31662 | 0.663325 | 0.331662 | − | 0.943398i | \(-0.392390\pi\) | ||||
0.331662 | + | 0.943398i | \(0.392390\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.50000 | − | 8.29156i | 0.388889 | − | 0.921285i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −19.8997 | −1.80907 | −0.904534 | − | 0.426401i | \(-0.859781\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0000i | 1.00000i | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.29156 | + | 5.50000i | −0.552771 | + | 0.366667i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 23.2164i | 1.36567i | 0.730573 | + | 0.682835i | \(0.239253\pi\) | ||||
−0.730573 | + | 0.682835i | \(0.760747\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 30.0000i | 1.57895i | 0.613784 | + | 0.789474i | \(0.289646\pi\) | ||||
−0.613784 | + | 0.789474i | \(0.710354\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.6082 | − | 17.5000i | −0.552771 | − | 0.833333i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 26.5330i | − | 1.15361i | −0.816882 | − | 0.576804i | \(-0.804300\pi\) | ||
0.816882 | − | 0.576804i | \(-0.195700\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −14.0000 | −0.560000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | + | 26.5330i | 0.185185 | + | 0.982704i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 33.1662i | − | 1.14366i | −0.820371 | − | 0.571832i | \(-0.806233\pi\) | ||
0.820371 | − | 0.571832i | \(-0.193767\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.0000i | 0.322581i | 0.986907 | + | 0.161290i | \(0.0515656\pi\) | ||||
−0.986907 | + | 0.161290i | \(0.948434\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 49.7494 | − | 33.0000i | 1.50756 | − | 1.00000i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 23.2164i | 0.663325i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 13.0000i | − | 0.351351i | −0.984448 | − | 0.175676i | \(-0.943789\pi\) | ||
0.984448 | − | 0.175676i | \(-0.0562110\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −21.5581 | − | 32.5000i | −0.552771 | − | 0.833333i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 46.4327 | 1.13251 | 0.566253 | − | 0.824231i | \(-0.308393\pi\) | ||||
0.566253 | + | 0.824231i | \(0.308393\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 55.0000 | 1.27907 | 0.639535 | − | 0.768762i | \(-0.279127\pi\) | ||||
0.639535 | + | 0.768762i | \(0.279127\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.6082 | − | 27.5000i | 0.257960 | − | 0.611111i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 49.7494 | 1.05850 | 0.529249 | − | 0.848467i | \(-0.322474\pi\) | ||||
0.529249 | + | 0.848467i | \(0.322474\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −38.5000 | − | 58.0409i | −0.754902 | − | 1.13806i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 39.7995i | 0.750934i | 0.926836 | + | 0.375467i | \(0.122518\pi\) | ||||
−0.926836 | + | 0.375467i | \(0.877482\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −66.0000 | −1.20000 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −49.7494 | − | 75.0000i | −0.872796 | − | 1.31579i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −92.8655 | −1.57399 | −0.786996 | − | 0.616958i | \(-0.788365\pi\) | ||||
−0.786996 | + | 0.616958i | \(0.788365\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.0000 | 0.229508 | 0.114754 | − | 0.993394i | \(-0.463392\pi\) | ||||
0.114754 | + | 0.993394i | \(0.463392\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 58.0409 | + | 24.5000i | 0.921285 | + | 0.388889i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 43.1161i | 0.663325i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 16.0000i | 0.238806i | 0.992846 | + | 0.119403i | \(0.0380980\pi\) | ||||
−0.992846 | + | 0.119403i | \(0.961902\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 44.0000 | + | 66.3325i | 0.637681 | + | 0.961341i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 29.8496 | 0.420417 | 0.210209 | − | 0.977657i | \(-0.432586\pi\) | ||||
0.210209 | + | 0.977657i | \(0.432586\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.00000i | − | 0.0547945i | −0.999625 | − | 0.0273973i | \(-0.991278\pi\) | ||
0.999625 | − | 0.0273973i | \(-0.00872191\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 35.0000 | − | 23.2164i | 0.466667 | − | 0.309552i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 139.298i | − | 1.80907i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 54.0000 | 0.683544 | 0.341772 | − | 0.939783i | \(-0.388973\pi\) | ||||
0.341772 | + | 0.939783i | \(0.388973\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −56.5000 | − | 58.0409i | −0.697531 | − | 0.716555i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 33.1662 | 0.399593 | 0.199797 | − | 0.979837i | \(-0.435972\pi\) | ||||
0.199797 | + | 0.979837i | \(0.435972\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 77.0000i | 0.905882i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 55.0000 | + | 82.9156i | 0.632184 | + | 0.953053i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −19.8997 | −0.223593 | −0.111796 | − | 0.993731i | \(-0.535660\pi\) | ||||
−0.111796 | + | 0.993731i | \(0.535660\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −91.0000 | −1.00000 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.5831 | − | 25.0000i | −0.178313 | − | 0.268817i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 99.4987i | 1.04736i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 78.0000i | − | 0.804124i | −0.915613 | − | 0.402062i | \(-0.868294\pi\) | ||
0.915613 | − | 0.402062i | \(-0.131706\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −69.6491 | + | 165.000i | −0.703526 | + | 1.66667i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 66.3325i | 0.656757i | 0.944546 | + | 0.328379i | \(0.106502\pi\) | ||||
−0.944546 | + | 0.328379i | \(0.893498\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −70.0000 | −0.679612 | −0.339806 | − | 0.940496i | \(-0.610361\pi\) | ||||
−0.339806 | + | 0.940496i | \(0.610361\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −38.5000 | − | 58.0409i | −0.366667 | − | 0.552771i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 92.8655i | − | 0.867902i | −0.900937 | − | 0.433951i | \(-0.857119\pi\) | ||
0.900937 | − | 0.433951i | \(-0.142881\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 175.000i | 1.60550i | 0.596313 | + | 0.802752i | \(0.296632\pi\) | ||||
−0.596313 | + | 0.802752i | \(0.703368\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21.5581 | + | 32.5000i | 0.194217 | + | 0.292793i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 13.2665i | − | 0.117403i | −0.998276 | − | 0.0587013i | \(-0.981304\pi\) | ||
0.998276 | − | 0.0587013i | \(-0.0186960\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 88.0000i | − | 0.765217i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 107.790 | + | 45.5000i | 0.921285 | + | 0.388889i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −162.515 | −1.36567 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 275.000 | 2.27273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −116.082 | + | 77.0000i | −0.943755 | + | 0.626016i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −129.348 | −1.03479 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 140.000 | 1.10236 | 0.551181 | − | 0.834386i | \(-0.314177\pi\) | ||||
0.551181 | + | 0.834386i | \(0.314177\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −137.500 | + | 91.2072i | −1.06589 | + | 0.707032i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 82.9156i | 0.632944i | 0.948602 | + | 0.316472i | \(0.102498\pi\) | ||||
−0.948602 | + | 0.316472i | \(0.897502\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −210.000 | −1.57895 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16.5831 | + | 88.0000i | 0.122838 | + | 0.651852i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 66.3325 | 0.484179 | 0.242089 | − | 0.970254i | \(-0.422167\pi\) | ||||
0.242089 | + | 0.970254i | \(0.422167\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.0000 | −0.0791367 | −0.0395683 | − | 0.999217i | \(-0.512598\pi\) | ||||
−0.0395683 | + | 0.999217i | \(0.512598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −124.373 | + | 82.5000i | −0.882081 | + | 0.585106i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 258.697i | − | 1.80907i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 110.000i | − | 0.758621i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.2665 | 0.0890369 | 0.0445185 | − | 0.999009i | \(-0.485825\pi\) | ||||
0.0445185 | + | 0.999009i | \(0.485825\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 215.000i | − | 1.42384i | −0.702260 | − | 0.711921i | \(-0.747826\pi\) | ||
0.702260 | − | 0.711921i | \(-0.252174\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 192.500 | + | 81.2573i | 1.25817 | + | 0.531094i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 33.1662i | 0.213976i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −140.000 | −0.891720 | −0.445860 | − | 0.895103i | \(-0.647102\pi\) | ||||
−0.445860 | + | 0.895103i | \(0.647102\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −66.0000 | − | 99.4987i | −0.415094 | − | 0.625778i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 185.731 | 1.15361 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 188.000i | − | 1.15337i | −0.816965 | − | 0.576687i | \(-0.804345\pi\) | ||
0.816965 | − | 0.576687i | \(-0.195655\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 165.000 | − | 109.449i | 1.00000 | − | 0.663325i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 198.997 | 1.19160 | 0.595801 | − | 0.803132i | \(-0.296835\pi\) | ||||
0.595801 | + | 0.803132i | \(0.296835\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −169.000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 248.747 | + | 105.000i | 1.45466 | + | 0.614035i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 218.897i | 1.26530i | 0.774437 | + | 0.632651i | \(0.218033\pi\) | ||||
−0.774437 | + | 0.632651i | \(0.781967\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 98.0000i | − | 0.560000i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 232.164 | − | 154.000i | 1.31166 | − | 0.870056i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 248.747i | 1.38965i | 0.719180 | + | 0.694824i | \(0.244518\pi\) | ||||
−0.719180 | + | 0.694824i | \(0.755482\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 94.0000 | 0.519337 | 0.259669 | − | 0.965698i | \(-0.416387\pi\) | ||||
0.259669 | + | 0.965698i | \(0.416387\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −35.0000 | + | 23.2164i | −0.191257 | + | 0.126865i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 43.1161i | − | 0.233060i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 462.000i | − | 2.47059i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −185.731 | + | 35.0000i | −0.982704 | + | 0.185185i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 99.4987i | 0.520936i | 0.965483 | + | 0.260468i | \(0.0838768\pi\) | ||||
−0.965483 | + | 0.260468i | \(0.916123\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 82.0000i | 0.424870i | 0.977175 | + | 0.212435i | \(0.0681395\pi\) | ||||
−0.977175 | + | 0.212435i | \(0.931861\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −71.5000 | − | 107.790i | −0.366667 | − | 0.552771i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −116.082 | −0.589248 | −0.294624 | − | 0.955613i | \(-0.595194\pi\) | ||||
−0.294624 | + | 0.955613i | \(0.595194\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 252.000 | 1.26633 | 0.633166 | − | 0.774016i | \(-0.281755\pi\) | ||||
0.633166 | + | 0.774016i | \(0.281755\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −26.5330 | − | 40.0000i | −0.132005 | − | 0.199005i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 232.164 | 1.14366 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 154.000 | 0.751220 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −220.000 | − | 92.8655i | −1.06280 | − | 0.448626i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 596.992i | − | 2.85642i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −153.000 | −0.725118 | −0.362559 | − | 0.931961i | \(-0.618097\pi\) | ||||
−0.362559 | + | 0.931961i | \(0.618097\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −74.6241 | + | 49.5000i | −0.350348 | + | 0.232394i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 182.414 | 0.848439 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −70.0000 | −0.322581 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.63325 | + | 10.0000i | 0.0302888 | + | 0.0456621i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −301.813 | −1.36567 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 29.0000i | − | 0.130045i | −0.997884 | − | 0.0650224i | \(-0.979288\pi\) | ||
0.997884 | − | 0.0650224i | \(-0.0207119\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −49.0000 | + | 116.082i | −0.217778 | + | 0.515919i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 33.1662 | 0.146107 | 0.0730534 | − | 0.997328i | \(-0.476726\pi\) | ||||
0.0730534 | + | 0.997328i | \(0.476726\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 385.000i | 1.68122i | 0.541639 | + | 0.840611i | \(0.317804\pi\) | ||||
−0.541639 | + | 0.840611i | \(0.682196\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 231.000 | + | 348.246i | 1.00000 | + | 1.50756i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 189.048i | 0.811363i | 0.914014 | + | 0.405682i | \(0.132966\pi\) | ||||
−0.914014 | + | 0.405682i | \(0.867034\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 165.000 | 0.702128 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −135.000 | + | 89.5489i | −0.569620 | + | 0.377843i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −434.478 | −1.81790 | −0.908949 | − | 0.416906i | \(-0.863114\pi\) | ||||
−0.908949 | + | 0.416906i | \(0.863114\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 130.000i | − | 0.539419i | −0.962942 | − | 0.269710i | \(-0.913072\pi\) | ||
0.962942 | − | 0.269710i | \(-0.0869277\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 237.500 | + | 51.4077i | 0.977366 | + | 0.211554i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −390.000 | −1.57895 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −82.9156 | + | 55.0000i | −0.332994 | + | 0.220884i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 331.662i | − | 1.32136i | −0.750666 | − | 0.660682i | \(-0.770267\pi\) | ||
0.750666 | − | 0.660682i | \(-0.229733\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 528.000i | 2.08696i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −127.690 | − | 192.500i | −0.500745 | − | 0.754902i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 268.647i | 1.04532i | 0.852542 | + | 0.522659i | \(0.175060\pi\) | ||||
−0.852542 | + | 0.522659i | \(0.824940\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 91.0000 | 0.351351 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −275.000 | − | 116.082i | −1.05364 | − | 0.444758i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 179.098i | − | 0.680980i | −0.940248 | − | 0.340490i | \(-0.889407\pi\) | ||
0.940248 | − | 0.340490i | \(-0.110593\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 132.000i | 0.498113i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 49.7494 | − | 33.0000i | 0.186327 | − | 0.123596i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 165.831i | 0.616473i | 0.951310 | + | 0.308237i | \(0.0997388\pi\) | ||||
−0.951310 | + | 0.308237i | \(0.900261\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 245.000i | 0.904059i | 0.892003 | + | 0.452030i | \(0.149300\pi\) | ||||
−0.892003 | + | 0.452030i | \(0.850700\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 227.500 | − | 150.906i | 0.833333 | − | 0.552771i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 278.596 | 1.01308 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 430.000 | 1.55235 | 0.776173 | − | 0.630520i | \(-0.217158\pi\) | ||||
0.776173 | + | 0.630520i | \(0.217158\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 82.9156 | + | 35.0000i | 0.297189 | + | 0.125448i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −325.029 | −1.15669 | −0.578344 | − | 0.815793i | \(-0.696301\pi\) | ||||
−0.578344 | + | 0.815793i | \(0.696301\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 70.0000 | 0.247350 | 0.123675 | − | 0.992323i | \(-0.460532\pi\) | ||||
0.123675 | + | 0.992323i | \(0.460532\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −165.000 | − | 248.747i | −0.578947 | − | 0.872796i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 325.029i | 1.13251i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −250.000 | −0.865052 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 129.348 | + | 195.000i | 0.444496 | + | 0.670103i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −82.9156 | −0.282988 | −0.141494 | − | 0.989939i | \(-0.545191\pi\) | ||||
−0.141494 | + | 0.989939i | \(0.545191\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −308.000 | −1.04407 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −99.4987 | − | 528.000i | −0.335013 | − | 1.77778i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 344.929 | 1.15361 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 385.000i | 1.27907i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −110.000 | − | 165.831i | −0.363036 | − | 0.547298i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 46.4327 | 0.152239 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 232.000i | 0.755700i | 0.925867 | + | 0.377850i | \(0.123337\pi\) | ||||
−0.925867 | + | 0.377850i | \(0.876663\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 175.000 | − | 116.082i | 0.566343 | − | 0.375669i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 232.164i | − | 0.746507i | −0.927729 | − | 0.373254i | \(-0.878242\pi\) | ||
0.927729 | − | 0.373254i | \(-0.121758\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −155.000 | −0.495208 | −0.247604 | − | 0.968861i | \(-0.579643\pi\) | ||||
−0.247604 | + | 0.968861i | \(0.579643\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 192.500 | + | 81.2573i | 0.611111 | + | 0.257960i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 198.997 | 0.627752 | 0.313876 | − | 0.949464i | \(-0.398372\pi\) | ||||
0.313876 | + | 0.949464i | \(0.398372\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 660.000i | 2.06897i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 154.000 | + | 232.164i | 0.479751 | + | 0.723252i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −696.491 | −2.15632 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 182.000i | − | 0.560000i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −290.205 | − | 437.500i | −0.887476 | − | 1.33792i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 348.246i | 1.05850i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 490.000i | − | 1.48036i | −0.672407 | − | 0.740181i | \(-0.734740\pi\) | ||
0.672407 | − | 0.740181i | \(-0.265260\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −107.790 | − | 45.5000i | −0.323695 | − | 0.136637i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 53.0660i | 0.158406i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 475.000 | 1.40950 | 0.704748 | − | 0.709458i | \(-0.251060\pi\) | ||||
0.704748 | + | 0.709458i | \(0.251060\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 22.0000 | + | 33.1662i | 0.0648968 | + | 0.0978355i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 198.997i | − | 0.583570i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000i | 1.00000i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 145.931 | + | 220.000i | 0.422990 | + | 0.637681i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 208.947i | − | 0.602154i | −0.953600 | − | 0.301077i | \(-0.902654\pi\) | ||
0.953600 | − | 0.301077i | \(-0.0973461\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 85.0000i | − | 0.243553i | −0.992558 | − | 0.121777i | \(-0.961141\pi\) | ||
0.992558 | − | 0.121777i | \(-0.0388591\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −344.929 | + | 65.0000i | −0.982704 | + | 0.185185i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 232.164 | 0.657688 | 0.328844 | − | 0.944384i | \(-0.393341\pi\) | ||||
0.328844 | + | 0.944384i | \(0.393341\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 99.0000 | 0.278873 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 406.287 | − | 269.500i | 1.13806 | − | 0.754902i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −92.8655 | −0.258678 | −0.129339 | − | 0.991600i | \(-0.541286\pi\) | ||||
−0.129339 | + | 0.991600i | \(0.541286\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −539.000 | −1.49307 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −687.500 | + | 456.036i | −1.89394 | + | 1.25630i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 13.2665i | − | 0.0363466i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 140.000 | 0.381471 | 0.190736 | − | 0.981641i | \(-0.438913\pi\) | ||||
0.190736 | + | 0.981641i | \(0.438913\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 162.515 | − | 385.000i | 0.440419 | − | 1.04336i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −278.596 | −0.750934 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −60.0000 | −0.160858 | −0.0804290 | − | 0.996760i | \(-0.525629\pi\) | ||||
−0.0804290 | + | 0.996760i | \(0.525629\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 323.371 | − | 214.500i | 0.862322 | − | 0.572000i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 431.161 | 1.14366 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 220.000i | 0.580475i | 0.956955 | + | 0.290237i | \(0.0937343\pi\) | ||||
−0.956955 | + | 0.290237i | \(0.906266\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −350.000 | + | 232.164i | −0.918635 | + | 0.609354i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −116.082 | −0.303086 | −0.151543 | − | 0.988451i | \(-0.548424\pi\) | ||||
−0.151543 | + | 0.988451i | \(0.548424\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 462.000i | − | 1.20000i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 192.500 | − | 456.036i | 0.497416 | − | 1.17839i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 616.000 | 1.57545 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −137.500 | − | 207.289i | −0.349873 | − | 0.527453i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 179.098 | 0.453412 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 478.000i | − | 1.20403i | −0.798485 | − | 0.602015i | \(-0.794365\pi\) | ||
0.798485 | − | 0.602015i | \(-0.205635\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 525.000 | − | 348.246i | 1.31579 | − | 0.872796i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 636.792 | 1.58801 | 0.794005 | − | 0.607911i | \(-0.207992\pi\) | ||||
0.794005 | + | 0.607911i | \(0.207992\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −130.000 | −0.322581 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −187.389 | − | 192.500i | −0.462690 | − | 0.475309i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 258.697i | 0.635619i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 200.000i | − | 0.488998i | −0.969650 | − | 0.244499i | \(-0.921377\pi\) | ||
0.969650 | − | 0.244499i | \(-0.0786234\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −165.831 | + | 110.000i | −0.403482 | + | 0.267640i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 650.058i | − | 1.57399i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 110.000 | 0.265060 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.5000 | − | 18.2414i | 0.0659472 | − | 0.0437445i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 480.911i | 1.14776i | 0.818940 | + | 0.573879i | \(0.194562\pi\) | ||||
−0.818940 | + | 0.573879i | \(0.805438\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 385.000i | − | 0.914489i | −0.889341 | − | 0.457245i | \(-0.848836\pi\) | ||
0.889341 | − | 0.457245i | \(-0.151164\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 174.123 | − | 412.500i | 0.411638 | − | 0.975177i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 325.029i | − | 0.764775i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 98.0000i | 0.229508i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 429.000 | + | 646.742i | 1.00000 | + | 1.50756i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 255.380 | 0.592529 | 0.296265 | − | 0.955106i | \(-0.404259\pi\) | ||||
0.296265 | + | 0.955106i | \(0.404259\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 235.000 | 0.542725 | 0.271363 | − | 0.962477i | \(-0.412526\pi\) | ||||
0.271363 | + | 0.962477i | \(0.412526\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 182.414 | + | 275.000i | 0.419343 | + | 0.632184i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 795.990 | 1.82149 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −336.000 | −0.765376 | −0.382688 | − | 0.923878i | \(-0.625002\pi\) | ||||
−0.382688 | + | 0.923878i | \(0.625002\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 653.375i | 1.47489i | 0.675409 | + | 0.737444i | \(0.263967\pi\) | ||||
−0.675409 | + | 0.737444i | \(0.736033\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −66.0000 | −0.148315 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −33.1662 | + | 22.0000i | −0.0741974 | + | 0.0492170i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 179.098 | 0.398881 | 0.199441 | − | 0.979910i | \(-0.436087\pi\) | ||||
0.199441 | + | 0.979910i | \(0.436087\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −924.000 | −2.04878 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 356.537 | + | 537.500i | 0.787058 | + | 1.18653i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −301.813 | −0.663325 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 518.000i | − | 1.13348i | −0.823897 | − | 0.566740i | \(-0.808205\pi\) | ||
0.823897 | − | 0.566740i | \(-0.191795\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −616.000 | + | 116.082i | −1.34205 | + | 0.252902i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −766.140 | −1.66191 | −0.830955 | − | 0.556340i | \(-0.812205\pi\) | ||||
−0.830955 | + | 0.556340i | \(0.812205\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 462.000i | 0.997840i | 0.866648 | + | 0.498920i | \(0.166270\pi\) | ||||
−0.866648 | + | 0.498920i | \(0.833730\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −55.0000 | − | 82.9156i | −0.118280 | − | 0.178313i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 557.193i | − | 1.19313i | −0.802564 | − | 0.596566i | \(-0.796531\pi\) | ||
0.802564 | − | 0.596566i | \(-0.203469\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −112.000 | −0.238806 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 350.000 | − | 232.164i | 0.743100 | − | 0.492917i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1094.49 | −2.31392 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 420.000i | − | 0.884211i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 330.000 | + | 139.298i | 0.691824 | + | 0.292030i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.8496 | 0.0623165 | 0.0311583 | − | 0.999514i | \(-0.490080\pi\) | ||||
0.0311583 | + | 0.999514i | \(0.490080\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 169.000 | 0.351351 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −464.327 | + | 308.000i | −0.961341 | + | 0.637681i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 258.697i | − | 0.533395i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 462.000i | 0.948665i | 0.880346 | + | 0.474333i | \(0.157311\pi\) | ||||
−0.880346 | + | 0.474333i | \(0.842689\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 311.763 | + | 470.000i | 0.637552 | + | 0.961145i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 580.409i | − | 1.18210i | −0.806636 | − | 0.591048i | \(-0.798714\pi\) | ||
0.806636 | − | 0.591048i | \(-0.201286\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 770.000 | 1.56187 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −231.000 | + | 547.243i | −0.466667 | + | 1.10554i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 208.947i | 0.420417i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 350.000i | 0.701403i | 0.936487 | + | 0.350701i | \(0.114057\pi\) | ||||
−0.936487 | + | 0.350701i | \(0.885943\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −497.494 | + | 330.000i | −0.993001 | + | 0.658683i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 417.895i | 0.830805i | 0.909638 | + | 0.415402i | \(0.136359\pi\) | ||||
−0.909638 | + | 0.415402i | \(0.863641\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 220.000i | 0.435644i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 422.500 | − | 280.255i | 0.833333 | − | 0.552771i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −119.398 | −0.234575 | −0.117287 | − | 0.993098i | \(-0.537420\pi\) | ||||
−0.117287 | + | 0.993098i | \(0.537420\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.0000 | 0.0547945 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −795.990 | + | 150.000i | −1.55164 | + | 0.292398i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −232.164 | −0.450803 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −990.000 | −1.91489 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −363.000 | − | 547.243i | −0.699422 | − | 1.05442i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 348.246i | 0.668418i | 0.942499 | + | 0.334209i | \(0.108469\pi\) | ||||
−0.942499 | + | 0.334209i | \(0.891531\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 910.000 | 1.73996 | 0.869981 | − | 0.493085i | \(-0.164131\pi\) | ||||
0.869981 | + | 0.493085i | \(0.164131\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 162.515 | + | 245.000i | 0.309552 | + | 0.466667i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −232.164 | −0.440538 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −175.000 | −0.330813 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −325.029 | + | 770.000i | −0.612108 | + | 1.45009i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 603.626i | 1.13251i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 308.000i | − | 0.575701i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −412.500 | − | 621.867i | −0.768156 | − | 1.15804i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 755.000i | − | 1.39556i | −0.716310 | − | 0.697782i | \(-0.754170\pi\) | ||
0.716310 | − | 0.697782i | \(-0.245830\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −235.000 | + | 155.881i | −0.432781 | + | 0.287074i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 580.409i | 1.06497i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 715.000 | 1.30713 | 0.653565 | − | 0.756870i | \(-0.273273\pi\) | ||||
0.653565 | + | 0.756870i | \(0.273273\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 49.0000 | − | 116.082i | 0.0892532 | − | 0.211442i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 994.987 | 1.80578 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 378.000i | 0.683544i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 71.5000 | + | 107.790i | 0.128829 | + | 0.194217i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −348.246 | −0.625217 | −0.312608 | − | 0.949882i | \(-0.601203\pi\) | ||||
−0.312608 | + | 0.949882i | \(0.601203\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 715.000i | 1.27907i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 766.140 | + | 1155.00i | 1.36567 | + | 2.05882i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 739.607i | − | 1.31369i | −0.754026 | − | 0.656845i | \(-0.771891\pi\) | ||
0.754026 | − | 0.656845i | \(-0.228109\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 44.0000i | − | 0.0778761i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 406.287 | − | 395.500i | 0.716555 | − | 0.697531i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 514.077i | − | 0.903474i | −0.892151 | − | 0.451737i | \(-0.850804\pi\) | ||
0.892151 | − | 0.451737i | \(-0.149196\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 479.000 | 0.838879 | 0.419440 | − | 0.907783i | \(-0.362227\pi\) | ||||
0.419440 | + | 0.907783i | \(0.362227\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −165.000 | − | 248.747i | −0.287958 | − | 0.434113i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 371.462i | 0.646021i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 448.000i | − | 0.776430i | −0.921569 | − | 0.388215i | \(-0.873092\pi\) | ||
0.921569 | − | 0.388215i | \(-0.126908\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −135.982 | − | 205.000i | −0.234856 | − | 0.354059i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 232.164i | 0.399593i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 792.000i | − | 1.35849i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 357.500 | + | 150.906i | 0.611111 | + | 0.257960i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −729.657 | −1.24303 | −0.621514 | − | 0.783403i | \(-0.713482\pi\) | ||||
−0.621514 | + | 0.783403i | \(0.713482\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −300.000 | −0.509338 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 290.205 | − | 192.500i | 0.491040 | − | 0.325719i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −762.824 | −1.28638 | −0.643190 | − | 0.765706i | \(-0.722390\pi\) | ||||
−0.643190 | + | 0.765706i | \(0.722390\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −539.000 | −0.905882 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −630.000 | + | 417.895i | −1.05528 | + | 0.699991i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 795.990i | − | 1.32886i | −0.747348 | − | 0.664432i | \(-0.768673\pi\) | ||
0.747348 | − | 0.664432i | \(-0.231327\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −101.000 | −0.168053 | −0.0840266 | − | 0.996464i | \(-0.526778\pi\) | ||||
−0.0840266 | + | 0.996464i | \(0.526778\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 132.665 | + | 56.0000i | 0.220008 | + | 0.0928690i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 912.072 | 1.50756 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1100.00 | −1.81219 | −0.906096 | − | 0.423073i | \(-0.860951\pi\) | ||||
−0.906096 | + | 0.423073i | \(0.860951\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −580.409 | + | 385.000i | −0.953053 | + | 0.632184i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 646.742i | 1.05850i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 338.000i | − | 0.551387i | −0.961246 | − | 0.275693i | \(-0.911093\pi\) | ||
0.961246 | − | 0.275693i | \(-0.0889074\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −385.000 | + | 255.380i | −0.626016 | + | 0.415252i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 928.655 | 1.50511 | 0.752557 | − | 0.658527i | \(-0.228820\pi\) | ||||
0.752557 | + | 0.658527i | \(0.228820\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 770.000i | − | 1.24394i | −0.783040 | − | 0.621971i | \(-0.786332\pi\) | ||
0.783040 | − | 0.621971i | \(-0.213668\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 704.000 | − | 132.665i | 1.13366 | − | 0.213631i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 139.298i | − | 0.223593i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −79.0000 | −0.126400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 990.000 | + | 1492.48i | 1.57895 | + | 2.38035i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 301.813 | 0.479830 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 385.000i | 0.610143i | 0.952330 | + | 0.305071i | \(0.0986803\pi\) | ||||
−0.952330 | + | 0.305071i | \(0.901320\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 382.500 | − | 253.722i | 0.604265 | − | 0.400824i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 464.327 | 0.731224 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 104.474 | − | 247.500i | 0.163496 | − | 0.387324i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 596.992i | − | 0.931345i | −0.884957 | − | 0.465673i | \(-0.845812\pi\) | ||
0.884957 | − | 0.465673i | \(-0.154188\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 168.000i | − | 0.261275i | −0.991430 | − | 0.130638i | \(-0.958298\pi\) | ||
0.991430 | − | 0.130638i | \(-0.0417024\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −456.036 | + | 302.500i | −0.707032 | + | 0.468992i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 371.462i | 0.574130i | 0.957911 | + | 0.287065i | \(0.0926795\pi\) | ||||
−0.957911 | + | 0.287065i | \(0.907320\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1848.00 | 2.84746 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 175.000 | − | 116.082i | 0.268817 | − | 0.178313i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 742.924i | − | 1.13771i | −0.822438 | − | 0.568854i | \(-0.807387\pi\) | ||
0.822438 | − | 0.568854i | \(-0.192613\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 275.000i | 0.419847i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −33.1662 | − | 14.0000i | −0.0504814 | − | 0.0213090i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 729.657i | − | 1.10722i | −0.832776 | − | 0.553610i | \(-0.813250\pi\) | ||
0.832776 | − | 0.553610i | \(-0.186750\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1270.00i | − | 1.92133i | −0.277708 | − | 0.960666i | \(-0.589575\pi\) | ||
0.277708 | − | 0.960666i | \(-0.410425\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 754.532 | − | 500.500i | 1.13806 | − | 0.754902i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −696.491 | −1.04736 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −880.000 | −1.31934 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 48.0911 | + | 72.5000i | 0.0718850 | + | 0.108371i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −278.596 | −0.415196 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1035.00 | −1.53789 | −0.768945 | − | 0.639315i | \(-0.779218\pi\) | ||||
−0.768945 | + | 0.639315i | \(0.779218\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −70.0000 | − | 371.462i | −0.103704 | − | 0.550314i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 139.298i | 0.205758i | 0.994694 | + | 0.102879i | \(0.0328055\pi\) | ||||
−0.994694 | + | 0.102879i | \(0.967195\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 546.000 | 0.804124 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −82.9156 | + | 55.0000i | −0.121756 | + | 0.0807636i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 696.491 | 1.01975 | 0.509876 | − | 0.860248i | \(-0.329691\pi\) | ||||
0.509876 | + | 0.860248i | \(0.329691\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 220.000 | 0.321168 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −638.450 | − | 962.500i | −0.929331 | − | 1.40102i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −517.393 | −0.750934 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 100.000i | − | 0.144718i | −0.997379 | − | 0.0723589i | \(-0.976947\pi\) | ||
0.997379 | − | 0.0723589i | \(-0.0230527\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1155.00 | − | 487.544i | −1.66667 | − | 0.703526i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −36.4829 | −0.0524933 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1078.00i | 1.54663i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −313.500 | − | 472.619i | −0.448498 | − | 0.676136i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1127.65i | 1.60863i | 0.594200 | + | 0.804317i | \(0.297469\pi\) | ||||
−0.594200 | + | 0.804317i | \(0.702531\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 390.000 | 0.554765 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −412.500 | + | 273.622i | −0.585106 | + | 0.388116i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −464.327 | −0.656757 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 330.000i | − | 0.465444i | −0.972543 | − | 0.232722i | \(-0.925237\pi\) | ||
0.972543 | − | 0.232722i | \(-0.0747633\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 189.000 | − | 447.744i | 0.265823 | − | 0.629739i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 265.330 | 0.372132 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 858.000i | − | 1.20000i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1086.19 | − | 720.500i | 1.51492 | − | 1.00488i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 464.327i | 0.645796i | 0.946434 | + | 0.322898i | \(0.104657\pi\) | ||||
−0.946434 | + | 0.322898i | \(0.895343\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 490.000i | − | 0.679612i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 215.581 | + | 325.000i | 0.298175 | + | 0.449516i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 464.327i | 0.640452i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −130.000 | −0.178817 | −0.0894085 | − | 0.995995i | \(-0.528498\pi\) | ||||
−0.0894085 | + | 0.995995i | \(0.528498\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −679.000 | + | 265.330i | −0.931413 | + | 0.363964i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1276.90i | 1.74679i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 817.000i | 1.11460i | 0.830312 | + | 0.557299i | \(0.188162\pi\) | ||||
−0.830312 | + | 0.557299i | \(0.811838\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 318.396i | − | 0.432016i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 310.000i | 0.419486i | 0.977757 | + | 0.209743i | \(0.0672627\pi\) | ||||
−0.977757 | + | 0.209743i | \(0.932737\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 975.000 | − | 646.742i | 1.31579 | − | 0.872796i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1409.57 | 1.89713 | 0.948564 | − | 0.316587i | \(-0.102537\pi\) | ||||
0.948564 | + | 0.316587i | \(0.102537\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 44.0000 | 0.0590604 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 116.082 | − | 275.000i | 0.155397 | − | 0.368139i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 650.058 | 0.867902 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 674.000 | 0.897470 | 0.448735 | − | 0.893665i | \(-0.351875\pi\) | ||||
0.448735 | + | 0.893665i | \(0.351875\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 550.000 | + | 829.156i | 0.730412 | + | 1.10114i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 713.074i | − | 0.944469i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 860.000 | 1.13606 | 0.568032 | − | 0.823007i | \(-0.307705\pi\) | ||||
0.568032 | + | 0.823007i | \(0.307705\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −875.589 | − | 1320.00i | −1.15361 | − | 1.73913i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −955.188 | −1.25517 | −0.627587 | − | 0.778546i | \(-0.715957\pi\) | ||||
−0.627587 | + | 0.778546i | \(0.715957\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1225.00 | −1.60550 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 638.450 | + | 269.500i | 0.834576 | + | 0.352288i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1207.25i | − | 1.57399i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 540.000i | 0.702211i | 0.936336 | + | 0.351105i | \(0.114194\pi\) | ||||
−0.936336 | + | 0.351105i | \(0.885806\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −445.500 | − | 671.617i | −0.577821 | − | 0.871098i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1243.73 | 1.60897 | 0.804485 | − | 0.593973i | \(-0.202441\pi\) | ||||
0.804485 | + | 0.593973i | \(0.202441\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 140.000i | − | 0.180645i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −227.500 | + | 150.906i | −0.292793 | + | 0.194217i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1392.98i | 1.78817i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −594.000 | −0.760563 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 880.000 | − | 165.831i | 1.12388 | − | 0.211790i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −464.327 | −0.591500 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 626.000i | 0.795426i | 0.917510 | + | 0.397713i | \(0.130196\pi\) | ||||
−0.917510 | + | 0.397713i | \(0.869804\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 297.000 | + | 447.744i | 0.376426 | + | 0.567483i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 92.8655 | 0.117403 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 182.000i | 0.229508i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −218.897 | − | 330.000i | −0.275342 | − | 0.415094i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1121.02i | − | 1.40655i | −0.710919 | − | 0.703274i | \(-0.751721\pi\) | ||
0.710919 | − | 0.703274i | \(-0.248279\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1155.00i | 1.44556i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −69.6491 | + | 165.000i | −0.0869527 | + | 0.205993i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 79.5990i | 0.0991270i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 616.000 | 0.765217 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −275.000 | − | 414.578i | −0.340768 | − | 0.513728i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 16.5831i | − | 0.0204983i | −0.999947 | − | 0.0102491i | \(-0.996738\pi\) | ||
0.999947 | − | 0.0102491i | \(-0.00326246\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 740.000i | − | 0.912454i | −0.889863 | − | 0.456227i | \(-0.849201\pi\) | ||
0.889863 | − | 0.456227i | \(-0.150799\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −406.287 | − | 612.500i | −0.499737 | − | 0.753383i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 623.525i | − | 0.765062i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1650.00i | 2.01958i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −318.500 | + | 754.532i | −0.388889 | + | 0.921285i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −965.138 | −1.17556 | −0.587782 | − | 0.809019i | \(-0.699999\pi\) | ||||
−0.587782 | + | 0.809019i | \(0.699999\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 420.000 | 0.510328 | 0.255164 | − | 0.966898i | \(-0.417871\pi\) | ||||
0.255164 | + | 0.966898i | \(0.417871\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −696.491 | + | 462.000i | −0.844232 | + | 0.560000i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −99.4987 | −0.120313 | −0.0601564 | − | 0.998189i | \(-0.519160\pi\) | ||||
−0.0601564 | + | 0.998189i | \(0.519160\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1008.00 | −1.21592 | −0.607961 | − | 0.793967i | \(-0.708012\pi\) | ||||
−0.607961 | + | 0.793967i | \(0.708012\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1075.00 | + | 713.074i | −1.29362 | + | 0.858092i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 660.000 | 0.790419 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −265.330 | + | 50.0000i | −0.317001 | + | 0.0597372i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1180.72 | −1.40729 | −0.703646 | − | 0.710550i | \(-0.748446\pi\) | ||||
−0.703646 | + | 0.710550i | \(0.748446\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −259.000 | −0.307967 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 812.573 | − | 539.000i | 0.963906 | − | 0.639383i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −560.510 | −0.663325 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1925.00i | 2.27273i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −175.000 | + | 116.082i | −0.206125 | + | 0.136728i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −344.929 | −0.405322 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 797.000i | 0.934349i | 0.884165 | + | 0.467175i | \(0.154728\pi\) | ||||
−0.884165 | + | 0.467175i | \(0.845272\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 825.000 | + | 348.246i | 0.964912 | + | 0.407305i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 92.8655i | − | 0.108361i | −0.998531 | − | 0.0541806i | \(-0.982745\pi\) | ||
0.998531 | − | 0.0541806i | \(-0.0172547\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.0000 | 0.0395809 | 0.0197905 | − | 0.999804i | \(-0.493700\pi\) | ||||
0.0197905 | + | 0.999804i | \(0.493700\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −539.000 | − | 812.573i | −0.626016 | − | 0.943755i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 116.082 | 0.134510 | 0.0672548 | − | 0.997736i | \(-0.478576\pi\) | ||||
0.0672548 | + | 0.997736i | \(0.478576\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 726.000i | 0.839306i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 625.000 | − | 414.578i | 0.720877 | − | 0.478175i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1074.59 | −1.23658 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −208.000 | −0.238806 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −646.742 | − | 273.000i | −0.740827 | − | 0.312715i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 905.439i | − | 1.03479i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 679.000i | − | 0.774230i | −0.922031 | − | 0.387115i | \(-0.873472\pi\) | ||
0.922031 | − | 0.387115i | \(-0.126528\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 207.289 | − | 137.500i | 0.235824 | − | 0.156428i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 447.744i | − | 0.508223i | −0.967175 | − | 0.254111i | \(-0.918217\pi\) | ||
0.967175 | − | 0.254111i | \(-0.0817830\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 525.000 | 0.594564 | 0.297282 | − | 0.954790i | \(-0.403920\pi\) | ||||
0.297282 | + | 0.954790i | \(0.403920\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 770.000 | − | 510.760i | 0.870056 | − | 0.577130i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1333.28i | 1.50314i | 0.659655 | + | 0.751569i | \(0.270703\pi\) | ||||
−0.659655 | + | 0.751569i | \(0.729297\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 980.000i | 1.10236i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1124.34 | + | 1155.00i | 1.26188 | + | 1.29630i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1492.48i | 1.67131i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 825.000i | 0.921788i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −862.322 | + | 572.000i | −0.961341 | + | 0.637681i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 331.662 | 0.368924 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −924.000 | −1.02553 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −638.450 | − | 962.500i | −0.707032 | − | 1.06589i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 311.763 | 0.344489 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 445.000 | 0.490628 | 0.245314 | − | 0.969444i | \(-0.421109\pi\) | ||||
0.245314 | + | 0.969444i | \(0.421109\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 550.000 | + | 232.164i | 0.605061 | + | 0.255406i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 497.494i | 0.546096i | 0.962000 | + | 0.273048i | \(0.0880318\pi\) | ||||
−0.962000 | + | 0.273048i | \(0.911968\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −660.000 | −0.722892 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −116.082 | + | 77.0000i | −0.126865 | + | 0.0841530i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −580.409 | −0.632944 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −756.000 | −0.822633 | −0.411317 | − | 0.911493i | \(-0.634931\pi\) | ||||
−0.411317 | + | 0.911493i | \(0.634931\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −384.728 | − | 580.000i | −0.417729 | − | 0.629750i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 388.045i | 0.420417i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 182.000i | 0.196757i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −245.000 | + | 580.409i | −0.264293 | + | 0.626116i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −716.391 | −0.771142 | −0.385571 | − | 0.922678i | \(-0.625996\pi\) | ||||
−0.385571 | + | 0.922678i | \(0.625996\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 385.000 | + | 580.409i | 0.412647 | + | 0.622089i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 1532.28i | − | 1.63880i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.0000 | 0.0106724 | 0.00533618 | − | 0.999986i | \(-0.498301\pi\) | ||||
0.00533618 | + | 0.999986i | \(0.498301\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 387.500 | − | 257.038i | 0.412673 | − | 0.273736i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1456.00 | 1.54729 | 0.773644 | − | 0.633620i | \(-0.218432\pi\) | ||||
0.773644 | + | 0.633620i | \(0.218432\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1232.00i | − | 1.30647i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −616.000 | + | 116.082i | −0.651852 | + | 0.122838i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 431.161 | 0.455292 | 0.227646 | − | 0.973744i | \(-0.426897\pi\) | ||||
0.227646 | + | 0.973744i | \(0.426897\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 52.0000 | 0.0547945 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −497.494 | + | 330.000i | −0.523127 | + | 0.347003i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 288.546i | 0.302777i | 0.988474 | + | 0.151388i | \(0.0483744\pi\) | ||||
−0.988474 | + | 0.151388i | \(0.951626\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 330.000i | 0.345550i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1094.49 | − | 1650.00i | −1.14366 | − | 1.72414i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 464.327i | 0.484179i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 861.000 | 0.895942 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −770.000 | − | 325.029i | −0.799585 | − | 0.337517i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 271.963i | 0.281827i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 109.000i | − | 0.112720i | −0.998411 | − | 0.0563599i | \(-0.982051\pi\) | ||
0.998411 | − | 0.0563599i | \(-0.0179494\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1741.23 | − | 1155.00i | 1.79693 | − | 1.19195i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1741.23i | − | 1.79323i | −0.442809 | − | 0.896616i | \(-0.646018\pi\) | ||
0.442809 | − | 0.896616i | \(-0.353982\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 77.0000i | − | 0.0791367i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 301.813 | + | 455.000i | 0.309552 | + | 0.466667i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 397.995 | 0.407364 | 0.203682 | − | 0.979037i | \(-0.434709\pi\) | ||||
0.203682 | + | 0.979037i | \(0.434709\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 396.000 | 0.404494 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1451.02 | + | 612.500i | 1.47913 | + | 0.624363i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 447.744 | 0.455488 | 0.227744 | − | 0.973721i | \(-0.426865\pi\) | ||||
0.227744 | + | 0.973721i | \(0.426865\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −385.000 | −0.390863 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −577.500 | − | 870.614i | −0.585106 | − | 0.882081i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1459.31i | − | 1.47555i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −266.000 | −0.268416 | −0.134208 | − | 0.990953i | \(-0.542849\pi\) | ||||
−0.134208 | + | 0.990953i | \(0.542849\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 812.573 | + | 1225.00i | 0.818301 | + | 1.23364i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 835.789 | 0.839989 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1890.00 | 1.89569 | 0.947844 | − | 0.318736i | \(-0.103258\pi\) | ||||
0.947844 | + | 0.318736i | \(0.103258\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 344.929 | − | 65.0000i | 0.345274 | − | 0.0650651i |
(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 | 156.3.g.b.77.4 | yes | 4 | |
3.2 | odd | 2 | inner | 156.3.g.b.77.1 | ✓ | 4 | |
4.3 | odd | 2 | 624.3.l.h.545.2 | 4 | |||
12.11 | even | 2 | 624.3.l.h.545.3 | 4 | |||
13.12 | even | 2 | inner | 156.3.g.b.77.3 | yes | 4 | |
39.38 | odd | 2 | inner | 156.3.g.b.77.2 | yes | 4 | |
52.51 | odd | 2 | 624.3.l.h.545.1 | 4 | |||
156.155 | even | 2 | 624.3.l.h.545.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
156.3.g.b.77.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
156.3.g.b.77.2 | yes | 4 | 39.38 | odd | 2 | inner | |
156.3.g.b.77.3 | yes | 4 | 13.12 | even | 2 | inner | |
156.3.g.b.77.4 | yes | 4 | 1.1 | even | 1 | trivial | |
624.3.l.h.545.1 | 4 | 52.51 | odd | 2 | |||
624.3.l.h.545.2 | 4 | 4.3 | odd | 2 | |||
624.3.l.h.545.3 | 4 | 12.11 | even | 2 | |||
624.3.l.h.545.4 | 4 | 156.155 | even | 2 |