Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(1025,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, 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("1152.1025");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.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: | \(31.3897264543\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} + 11x^{2} - 10x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1025.3 | ||
Root | \(0.500000 - 0.244099i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.1025 |
Dual form | 1152.3.e.c.1025.2 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.21904i | 1.04381i | 0.853004 | + | 0.521904i | \(0.174778\pi\) | ||||
−0.853004 | + | 0.521904i | \(0.825222\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | −0.285714 | −0.142857 | − | 0.989743i | \(-0.545629\pi\) | ||||
−0.142857 | + | 0.989743i | \(0.545629\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.78122i | 0.434656i | 0.976099 | + | 0.217328i | \(0.0697341\pi\) | ||||
−0.976099 | + | 0.217328i | \(0.930266\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.38083 | −0.106218 | −0.0531089 | − | 0.998589i | \(-0.516913\pi\) | ||||
−0.0531089 | + | 0.998589i | \(0.516913\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 14.6807i | − 0.863571i | −0.901976 | − | 0.431786i | \(-0.857884\pi\) | ||||
0.901976 | − | 0.431786i | \(-0.142116\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −26.7617 | −1.40851 | −0.704254 | − | 0.709948i | \(-0.748719\pi\) | ||||
−0.704254 | + | 0.709948i | \(0.748719\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 18.0477i | 0.784683i | 0.919820 | + | 0.392342i | \(0.128335\pi\) | ||||
−0.919820 | + | 0.392342i | \(0.871665\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.23834 | −0.0895335 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 25.0180i | 0.862691i | 0.902187 | + | 0.431345i | \(0.141961\pi\) | ||||
−0.902187 | + | 0.431345i | \(0.858039\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −39.5233 | −1.27495 | −0.637473 | − | 0.770473i | \(-0.720020\pi\) | ||||
−0.637473 | + | 0.770473i | \(0.720020\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 10.4381i | − 0.298231i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 26.0000 | 0.702703 | 0.351351 | − | 0.936244i | \(-0.385722\pi\) | ||||
0.351351 | + | 0.936244i | \(0.385722\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 28.8228i | − 0.702996i | −0.936189 | − | 0.351498i | \(-0.885672\pi\) | ||||
0.936189 | − | 0.351498i | \(-0.114328\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.52333 | 0.221473 | 0.110736 | − | 0.993850i | \(-0.464679\pi\) | ||||
0.110736 | + | 0.993850i | \(0.464679\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 80.2731i | − 1.70794i | −0.520323 | − | 0.853969i | \(-0.674189\pi\) | ||||
0.520323 | − | 0.853969i | \(-0.325811\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −45.0000 | −0.918367 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.79874i | 0.184882i | 0.995718 | + | 0.0924409i | \(0.0294669\pi\) | ||||
−0.995718 | + | 0.0924409i | \(0.970533\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −24.9533 | −0.453697 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 73.5391i | − 1.24643i | −0.782052 | − | 0.623213i | \(-0.785827\pi\) | ||||
0.782052 | − | 0.623213i | \(-0.214173\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 67.5233 | 1.10694 | 0.553470 | − | 0.832869i | \(-0.313303\pi\) | ||||
0.553470 | + | 0.832869i | \(0.313303\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 7.20661i | − 0.110871i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −102.762 | −1.53376 | −0.766878 | − | 0.641793i | \(-0.778191\pi\) | ||||
−0.766878 | + | 0.641793i | \(0.778191\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 21.9533i | − 0.309201i | −0.987977 | − | 0.154601i | \(-0.950591\pi\) | ||||
0.987977 | − | 0.154601i | \(-0.0494091\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −140.570 | −1.92562 | −0.962808 | − | 0.270186i | \(-0.912915\pi\) | ||||
−0.962808 | + | 0.270186i | \(0.912915\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 9.56244i | − 0.124187i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.476674 | −0.00603385 | −0.00301692 | − | 0.999995i | \(-0.500960\pi\) | ||||
−0.00301692 | + | 0.999995i | \(0.500960\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 31.3142i | − 0.377280i | −0.982046 | − | 0.188640i | \(-0.939592\pi\) | ||||
0.982046 | − | 0.188640i | \(-0.0604079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 76.6192 | 0.901402 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.1310i | 0.147539i | 0.997275 | + | 0.0737694i | \(0.0235029\pi\) | ||||
−0.997275 | + | 0.0737694i | \(0.976497\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.76166 | 0.0303479 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 139.670i | − 1.47021i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −69.2383 | −0.713797 | −0.356899 | − | 0.934143i | \(-0.616166\pi\) | ||||
−0.356899 | + | 0.934143i | \(0.616166\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 78.5566i | 0.777788i | 0.921282 | + | 0.388894i | \(0.127143\pi\) | ||||
−0.921282 | + | 0.388894i | \(0.872857\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −198.570 | −1.92786 | −0.963932 | − | 0.266149i | \(-0.914249\pi\) | ||||
−0.963932 | + | 0.266149i | \(0.914249\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 177.517i | − 1.65904i | −0.558480 | − | 0.829518i | \(-0.688615\pi\) | ||||
0.558480 | − | 0.829518i | \(-0.311385\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 137.381 | 1.26037 | 0.630187 | − | 0.776443i | \(-0.282978\pi\) | ||||
0.630187 | + | 0.776443i | \(0.282978\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 72.5279i | − 0.641840i | −0.947106 | − | 0.320920i | \(-0.896008\pi\) | ||||
0.947106 | − | 0.320920i | \(-0.103992\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −94.1917 | −0.819058 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 29.3614i | 0.246735i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 98.1400 | 0.811074 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 118.794i | 0.950352i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 81.0467 | 0.638163 | 0.319081 | − | 0.947727i | \(-0.396626\pi\) | ||||
0.319081 | + | 0.947727i | \(0.396626\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 164.452i | 1.25536i | 0.778473 | + | 0.627679i | \(0.215995\pi\) | ||||
−0.778473 | + | 0.627679i | \(0.784005\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 53.5233 | 0.402431 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 224.790i | − 1.64081i | −0.571786 | − | 0.820403i | \(-0.693749\pi\) | ||||
0.571786 | − | 0.820403i | \(-0.306251\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −170.378 | −1.22574 | −0.612872 | − | 0.790183i | \(-0.709986\pi\) | ||||
−0.612872 | + | 0.790183i | \(0.709986\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 6.60206i | − 0.0461682i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −130.570 | −0.900483 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 59.5637i | 0.399756i | 0.979821 | + | 0.199878i | \(0.0640546\pi\) | ||||
−0.979821 | + | 0.199878i | \(0.935945\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −242.570 | −1.60642 | −0.803212 | − | 0.595693i | \(-0.796877\pi\) | ||||
−0.803212 | + | 0.595693i | \(0.796877\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 206.274i | − 1.33080i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −161.617 | −1.02941 | −0.514703 | − | 0.857369i | \(-0.672098\pi\) | ||||
−0.514703 | + | 0.857369i | \(0.672098\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 36.0954i | − 0.224195i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −80.9533 | −0.496646 | −0.248323 | − | 0.968677i | \(-0.579879\pi\) | ||||
−0.248323 | + | 0.968677i | \(0.579879\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 179.268i | 1.07346i | 0.843754 | + | 0.536731i | \(0.180341\pi\) | ||||
−0.843754 | + | 0.536731i | \(0.819659\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −167.093 | −0.988718 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 26.4982i | 0.153169i | 0.997063 | + | 0.0765844i | \(0.0244015\pi\) | ||||
−0.997063 | + | 0.0765844i | \(0.975599\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.47667 | 0.0255810 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 306.679i | 1.71329i | 0.515905 | + | 0.856646i | \(0.327456\pi\) | ||||
−0.515905 | + | 0.856646i | \(0.672544\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 57.3808 | 0.317021 | 0.158511 | − | 0.987357i | \(-0.449331\pi\) | ||||
0.158511 | + | 0.987357i | \(0.449331\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 135.695i | 0.733486i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 70.1917 | 0.375357 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 216.712i | − 1.13462i | −0.823506 | − | 0.567308i | \(-0.807985\pi\) | ||||
0.823506 | − | 0.567308i | \(-0.192015\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 187.140 | 0.969637 | 0.484819 | − | 0.874615i | \(-0.338886\pi\) | ||||
0.484819 | + | 0.874615i | \(0.338886\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 65.8947i | 0.334491i | 0.985915 | + | 0.167245i | \(0.0534872\pi\) | ||||
−0.985915 | + | 0.167245i | \(0.946513\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −114.953 | −0.577655 | −0.288828 | − | 0.957381i | \(-0.593265\pi\) | ||||
−0.288828 | + | 0.957381i | \(0.593265\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 50.0361i | − 0.246483i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 150.427 | 0.733793 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 127.953i | − 0.612217i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −103.332 | −0.489723 | −0.244862 | − | 0.969558i | \(-0.578743\pi\) | ||||
−0.244862 | + | 0.969558i | \(0.578743\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 49.7026i | 0.231175i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 79.0467 | 0.364270 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.2716i | 0.0917267i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 241.047 | 1.08093 | 0.540463 | − | 0.841368i | \(-0.318249\pi\) | ||||
0.540463 | + | 0.841368i | \(0.318249\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 22.5579i | − 0.0993738i | −0.998765 | − | 0.0496869i | \(-0.984178\pi\) | ||||
0.998765 | − | 0.0496869i | \(-0.0158223\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −212.997 | −0.930120 | −0.465060 | − | 0.885279i | \(-0.653967\pi\) | ||||
−0.465060 | + | 0.885279i | \(0.653967\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 63.9107i | 0.274295i | 0.990551 | + | 0.137147i | \(0.0437934\pi\) | ||||
−0.990551 | + | 0.137147i | \(0.956207\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 418.948 | 1.78276 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 174.417i | − 0.729779i | −0.931051 | − | 0.364890i | \(-0.881107\pi\) | ||||
0.931051 | − | 0.364890i | \(-0.118893\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −47.3316 | −0.196397 | −0.0981984 | − | 0.995167i | \(-0.531308\pi\) | ||||
−0.0981984 | + | 0.995167i | \(0.531308\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 234.857i | − 0.958598i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 36.9533 | 0.149609 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 205.731i | − 0.819647i | −0.912165 | − | 0.409824i | \(-0.865590\pi\) | ||||
0.912165 | − | 0.409824i | \(-0.134410\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −86.2901 | −0.341067 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 251.796i | 0.979751i | 0.871792 | + | 0.489875i | \(0.162958\pi\) | ||||
−0.871792 | + | 0.489875i | \(0.837042\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −52.0000 | −0.200772 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 206.607i | 0.785578i | 0.919629 | + | 0.392789i | \(0.128490\pi\) | ||||
−0.919629 | + | 0.392789i | \(0.871510\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −51.1400 | −0.192981 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 430.963i | − 1.60209i | −0.598601 | − | 0.801047i | \(-0.704277\pi\) | ||||
0.598601 | − | 0.801047i | \(-0.295723\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 290.953 | 1.07363 | 0.536814 | − | 0.843700i | \(-0.319628\pi\) | ||||
0.536814 | + | 0.843700i | \(0.319628\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 10.7020i | − 0.0389163i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 57.9508 | 0.209209 | 0.104604 | − | 0.994514i | \(-0.466642\pi\) | ||||
0.104604 | + | 0.994514i | \(0.466642\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 124.517i | 0.443120i | 0.975147 | + | 0.221560i | \(0.0711149\pi\) | ||||
−0.975147 | + | 0.221560i | \(0.928885\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 254.093 | 0.897856 | 0.448928 | − | 0.893568i | \(-0.351806\pi\) | ||||
0.448928 | + | 0.893568i | \(0.351806\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 57.6457i | 0.200856i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 73.4767 | 0.254245 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 239.909i | − 0.818802i | −0.912355 | − | 0.409401i | \(-0.865738\pi\) | ||||
0.912355 | − | 0.409401i | \(-0.134262\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 383.803 | 1.30103 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 24.9209i | − 0.0833473i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.0467 | −0.0632779 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 352.407i | 1.15543i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.71501 | −0.0121010 | −0.00605051 | − | 0.999982i | \(-0.501926\pi\) | ||||
−0.00605051 | + | 0.999982i | \(0.501926\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 473.828i | 1.52356i | 0.647835 | + | 0.761781i | \(0.275675\pi\) | ||||
−0.647835 | + | 0.761781i | \(0.724325\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 310.000 | 0.990415 | 0.495208 | − | 0.868775i | \(-0.335092\pi\) | ||||
0.495208 | + | 0.868775i | \(0.335092\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 475.342i | 1.49950i | 0.661719 | + | 0.749752i | \(0.269827\pi\) | ||||
−0.661719 | + | 0.749752i | \(0.730173\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −119.617 | −0.374974 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 392.880i | 1.21635i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.09077 | 0.00951005 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 160.546i | 0.487982i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 390.762 | 1.18055 | 0.590274 | − | 0.807203i | \(-0.299020\pi\) | ||||
0.590274 | + | 0.807203i | \(0.299020\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 536.317i | − 1.60095i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 316.000 | 0.937685 | 0.468843 | − | 0.883282i | \(-0.344671\pi\) | ||||
0.468843 | + | 0.883282i | \(0.344671\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 188.970i | − 0.554163i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 188.000 | 0.548105 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 485.475i | 1.39906i | 0.714602 | + | 0.699531i | \(0.246608\pi\) | ||||
−0.714602 | + | 0.699531i | \(0.753392\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −561.233 | −1.60812 | −0.804059 | − | 0.594549i | \(-0.797330\pi\) | ||||
−0.804059 | + | 0.594549i | \(0.797330\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 114.280i | − 0.323740i | −0.986812 | − | 0.161870i | \(-0.948247\pi\) | ||||
0.986812 | − | 0.161870i | \(-0.0517525\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 114.575 | 0.322747 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 217.789i | 0.606654i | 0.952886 | + | 0.303327i | \(0.0980975\pi\) | ||||
−0.952886 | + | 0.303327i | \(0.901903\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 355.187 | 0.983896 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 733.640i | − 2.00997i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 143.907 | 0.392116 | 0.196058 | − | 0.980592i | \(-0.437186\pi\) | ||||
0.196058 | + | 0.980592i | \(0.437186\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 19.5975i | − 0.0528234i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −400.663 | −1.07416 | −0.537082 | − | 0.843530i | \(-0.680473\pi\) | ||||
−0.537082 | + | 0.843530i | \(0.680473\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 34.5457i | − 0.0916331i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 156.668 | 0.413373 | 0.206686 | − | 0.978407i | \(-0.433732\pi\) | ||||
0.206686 | + | 0.978407i | \(0.433732\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 483.390i | 1.26211i | 0.775736 | + | 0.631057i | \(0.217379\pi\) | ||||
−0.775736 | + | 0.631057i | \(0.782621\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 49.9067 | 0.129628 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 726.933i | 1.86872i | 0.356326 | + | 0.934362i | \(0.384029\pi\) | ||||
−0.356326 | + | 0.934362i | \(0.615971\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 264.953 | 0.677630 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 2.48778i | − 0.00629817i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −94.1866 | −0.237246 | −0.118623 | − | 0.992939i | \(-0.537848\pi\) | ||||
−0.118623 | + | 0.992939i | \(0.537848\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.42898i | 0.00605731i | 0.999995 | + | 0.00302865i | \(0.000964052\pi\) | ||||
−0.999995 | + | 0.00302865i | \(0.999036\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 54.5751 | 0.135422 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 124.312i | 0.305434i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −66.7617 | −0.163231 | −0.0816157 | − | 0.996664i | \(-0.526008\pi\) | ||||
−0.0816157 | + | 0.996664i | \(0.526008\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 147.078i | 0.356122i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 163.430 | 0.393807 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 241.021i | 0.575229i | 0.957746 | + | 0.287614i | \(0.0928621\pi\) | ||||
−0.957746 | + | 0.287614i | \(0.907138\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −698.806 | −1.65987 | −0.829936 | − | 0.557859i | \(-0.811623\pi\) | ||||
−0.829936 | + | 0.557859i | \(0.811623\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 32.8604i | 0.0773185i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −135.047 | −0.316269 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 783.599i | 1.81810i | 0.416692 | + | 0.909048i | \(0.363189\pi\) | ||||
−0.416692 | + | 0.909048i | \(0.636811\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 317.233 | 0.732640 | 0.366320 | − | 0.930489i | \(-0.380617\pi\) | ||||
0.366320 | + | 0.930489i | \(0.380617\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 482.987i | − 1.10523i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −219.140 | −0.499180 | −0.249590 | − | 0.968352i | \(-0.580296\pi\) | ||||
−0.249590 | + | 0.968352i | \(0.580296\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 229.707i | 0.518526i | 0.965807 | + | 0.259263i | \(0.0834797\pi\) | ||||
−0.965807 | + | 0.259263i | \(0.916520\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −68.5309 | −0.154002 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 107.074i | − 0.238471i | −0.992866 | − | 0.119236i | \(-0.961956\pi\) | ||||
0.992866 | − | 0.119236i | \(-0.0380444\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 137.808 | 0.305562 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.4132i | 0.0316774i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 605.042 | 1.32394 | 0.661971 | − | 0.749529i | \(-0.269720\pi\) | ||||
0.661971 | + | 0.749529i | \(0.269720\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 305.435i | − 0.662550i | −0.943534 | − | 0.331275i | \(-0.892521\pi\) | ||||
0.943534 | − | 0.331275i | \(-0.107479\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 59.1400 | 0.127732 | 0.0638660 | − | 0.997958i | \(-0.479657\pi\) | ||||
0.0638660 | + | 0.997958i | \(0.479657\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 565.477i | 1.21087i | 0.795894 | + | 0.605435i | \(0.207001\pi\) | ||||
−0.795894 | + | 0.605435i | \(0.792999\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 205.523 | 0.438216 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 45.5331i | 0.0962645i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 59.9016 | 0.126109 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 249.576i | − 0.521035i | −0.965469 | − | 0.260517i | \(-0.916107\pi\) | ||||
0.965469 | − | 0.260517i | \(-0.0838932\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −35.9016 | −0.0746395 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 361.357i | − 0.745067i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −435.897 | −0.895065 | −0.447532 | − | 0.894268i | \(-0.647697\pi\) | ||||
−0.447532 | + | 0.894268i | \(0.647697\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 335.506i | 0.683311i | 0.939825 | + | 0.341655i | \(0.110988\pi\) | ||||
−0.939825 | + | 0.341655i | \(0.889012\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 367.282 | 0.744995 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 43.9066i | 0.0883433i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 712.373 | 1.42760 | 0.713801 | − | 0.700349i | \(-0.246972\pi\) | ||||
0.713801 | + | 0.700349i | \(0.246972\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 527.832i | − 1.04937i | −0.851297 | − | 0.524683i | \(-0.824184\pi\) | ||||
0.851297 | − | 0.524683i | \(-0.175816\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −409.990 | −0.811861 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 736.294i | 1.44655i | 0.690560 | + | 0.723275i | \(0.257364\pi\) | ||||
−0.690560 | + | 0.723275i | \(0.742636\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 281.140 | 0.550176 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 1036.34i | − 2.01232i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 383.803 | 0.742366 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 372.001i | 0.714013i | 0.934102 | + | 0.357006i | \(0.116203\pi\) | ||||
−0.934102 | + | 0.357006i | \(0.883797\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −251.135 | −0.480181 | −0.240091 | − | 0.970750i | \(-0.577177\pi\) | ||||
−0.240091 | + | 0.970750i | \(0.577177\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 580.231i | 1.10101i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 203.280 | 0.384272 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 39.7995i | 0.0746707i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 926.467 | 1.73171 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 215.155i | − 0.399174i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −966.992 | −1.78742 | −0.893708 | − | 0.448648i | \(-0.851906\pi\) | ||||
−0.893708 | + | 0.448648i | \(0.851906\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 716.996i | 1.31559i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 293.710 | 0.536947 | 0.268473 | − | 0.963287i | \(-0.413481\pi\) | ||||
0.268473 | + | 0.963287i | \(0.413481\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 669.524i | − 1.21511i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.953348 | 0.00172396 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 566.193i | − 1.01650i | −0.861208 | − | 0.508252i | \(-0.830292\pi\) | ||||
0.861208 | − | 0.508252i | \(-0.169708\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.1501 | −0.0235243 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 150.108i | − 0.266622i | −0.991074 | − | 0.133311i | \(-0.957439\pi\) | ||||
0.991074 | − | 0.133311i | \(-0.0425609\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 378.526 | 0.669957 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 899.707i | − 1.58121i | −0.612328 | − | 0.790604i | \(-0.709767\pi\) | ||||
0.612328 | − | 0.790604i | \(-0.290233\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −680.570 | −1.19189 | −0.595946 | − | 0.803025i | \(-0.703223\pi\) | ||||
−0.595946 | + | 0.803025i | \(0.703223\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 40.3969i | − 0.0702554i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −249.233 | −0.431947 | −0.215973 | − | 0.976399i | \(-0.569292\pi\) | ||||
−0.215973 | + | 0.976399i | \(0.569292\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 62.6284i | 0.107794i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −46.8499 | −0.0803600 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 602.587i | − 1.02655i | −0.858223 | − | 0.513277i | \(-0.828431\pi\) | ||||
0.858223 | − | 0.513277i | \(-0.171569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1057.71 | 1.79577 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 154.142i | 0.259936i | 0.991518 | + | 0.129968i | \(0.0414875\pi\) | ||||
−0.991518 | + | 0.129968i | \(0.958513\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −153.238 | −0.257543 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 309.244i | − 0.516267i | −0.966109 | − | 0.258133i | \(-0.916893\pi\) | ||||
0.966109 | − | 0.258133i | \(-0.0831074\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −811.327 | −1.34996 | −0.674981 | − | 0.737836i | \(-0.735848\pi\) | ||||
−0.674981 | + | 0.737836i | \(0.735848\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 512.196i | 0.846605i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −202.197 | −0.333108 | −0.166554 | − | 0.986032i | \(-0.553264\pi\) | ||||
−0.166554 | + | 0.986032i | \(0.553264\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 110.844i | 0.181413i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −694.560 | −1.13305 | −0.566525 | − | 0.824044i | \(-0.691713\pi\) | ||||
−0.566525 | + | 0.824044i | \(0.691713\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 896.267i | 1.45262i | 0.687367 | + | 0.726311i | \(0.258767\pi\) | ||||
−0.687367 | + | 0.726311i | \(0.741233\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −672.570 | −1.08654 | −0.543271 | − | 0.839557i | \(-0.682815\pi\) | ||||
−0.543271 | + | 0.839557i | \(0.682815\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 26.2619i | − 0.0421540i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −675.948 | −1.08152 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 381.699i | − 0.606834i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −218.953 | −0.346994 | −0.173497 | − | 0.984834i | \(-0.555507\pi\) | ||||
−0.173497 | + | 0.984834i | \(0.555507\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 422.985i | 0.666119i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 62.1374 | 0.0975470 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 1193.18i | − 1.86144i | −0.365734 | − | 0.930720i | \(-0.619182\pi\) | ||||
0.365734 | − | 0.930720i | \(-0.380818\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1009.33 | 1.56971 | 0.784857 | − | 0.619676i | \(-0.212736\pi\) | ||||
0.784857 | + | 0.619676i | \(0.212736\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 637.605i | − 0.985479i | −0.870177 | − | 0.492740i | \(-0.835995\pi\) | ||||
0.870177 | − | 0.492740i | \(-0.164005\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 351.606 | 0.541767 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 939.073i | − 1.43809i | −0.694964 | − | 0.719045i | \(-0.744580\pi\) | ||||
0.694964 | − | 0.719045i | \(-0.255420\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −858.280 | −1.31035 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1224.84i | − 1.85864i | −0.369281 | − | 0.929318i | \(-0.620396\pi\) | ||||
0.369281 | − | 0.929318i | \(-0.379604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1034.18 | 1.56456 | 0.782282 | − | 0.622925i | \(-0.214056\pi\) | ||||
0.782282 | + | 0.622925i | \(0.214056\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 279.340i | 0.420060i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −451.518 | −0.676939 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 322.844i | 0.481138i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.9533 | −0.0281625 | −0.0140812 | − | 0.999901i | \(-0.504482\pi\) | ||||
−0.0140812 | + | 0.999901i | \(0.504482\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1024.66i | 1.51353i | 0.653685 | + | 0.756767i | \(0.273222\pi\) | ||||
−0.653685 | + | 0.756767i | \(0.726778\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 138.477 | 0.203942 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 965.904i | 1.41421i | 0.707109 | + | 0.707104i | \(0.249999\pi\) | ||||
−0.707109 | + | 0.707104i | \(0.750001\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1173.19 | 1.71268 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 13.5304i | − 0.0196377i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −419.233 | −0.606705 | −0.303353 | − | 0.952878i | \(-0.598106\pi\) | ||||
−0.303353 | + | 0.952878i | \(0.598106\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 889.210i | − 1.27944i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −423.140 | −0.607087 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1085.27i | 1.54817i | 0.633081 | + | 0.774086i | \(0.281790\pi\) | ||||
−0.633081 | + | 0.774086i | \(0.718210\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −695.803 | −0.989763 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 157.113i | − 0.222225i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 369.469 | 0.521113 | 0.260556 | − | 0.965459i | \(-0.416094\pi\) | ||||
0.260556 | + | 0.965459i | \(0.416094\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 713.306i | − 1.00043i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 34.4564 | 0.0481907 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 468.567i | 0.651692i | 0.945423 | + | 0.325846i | \(0.105649\pi\) | ||||
−0.945423 | + | 0.325846i | \(0.894351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 397.140 | 0.550818 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 55.9988i | − 0.0772397i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −502.570 | −0.691293 | −0.345646 | − | 0.938365i | \(-0.612340\pi\) | ||||
−0.345646 | + | 0.938365i | \(0.612340\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 139.809i | − 0.191257i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1189.37 | −1.62261 | −0.811303 | − | 0.584625i | \(-0.801241\pi\) | ||||
−0.811303 | + | 0.584625i | \(0.801241\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 491.326i | − 0.666657i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1431.04 | −1.93645 | −0.968225 | − | 0.250081i | \(-0.919543\pi\) | ||||
−0.968225 | + | 0.250081i | \(0.919543\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 203.508i | 0.273900i | 0.990578 | + | 0.136950i | \(0.0437300\pi\) | ||||
−0.990578 | + | 0.136950i | \(0.956270\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −310.865 | −0.417269 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 355.034i | 0.474010i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −930.570 | −1.23911 | −0.619554 | − | 0.784954i | \(-0.712686\pi\) | ||||
−0.619554 | + | 0.784954i | \(0.712686\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 1265.98i | − 1.67680i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −306.894 | −0.405408 | −0.202704 | − | 0.979240i | \(-0.564973\pi\) | ||||
−0.202704 | + | 0.979240i | \(0.564973\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 939.701i | − 1.23482i | −0.786640 | − | 0.617412i | \(-0.788181\pi\) | ||||
0.786640 | − | 0.617412i | \(-0.211819\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −274.762 | −0.360107 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 101.545i | 0.132393i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1238.19 | −1.61013 | −0.805063 | − | 0.593190i | \(-0.797868\pi\) | ||||
−0.805063 | + | 0.593190i | \(0.797868\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 697.502i | 0.902332i | 0.892440 | + | 0.451166i | \(0.148992\pi\) | ||||
−0.892440 | + | 0.451166i | \(0.851008\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 88.4665 | 0.114150 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 771.347i | 0.990176i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 104.964 | 0.134396 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 843.483i | − 1.07450i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 206.575 | 0.262484 | 0.131242 | − | 0.991350i | \(-0.458103\pi\) | ||||
0.131242 | + | 0.991350i | \(0.458103\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 145.056i | 0.183383i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −93.2383 | −0.117577 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 566.596i | 0.710911i | 0.934693 | + | 0.355455i | \(0.115674\pi\) | ||||
−0.934693 | + | 0.355455i | \(0.884326\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1178.47 | −1.47493 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 672.096i | − 0.836981i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 188.383 | 0.234017 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 806.091i | − 0.996404i | −0.867061 | − | 0.498202i | \(-0.833994\pi\) | ||||
0.867061 | − | 0.498202i | \(-0.166006\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −420.472 | −0.518461 | −0.259230 | − | 0.965816i | \(-0.583469\pi\) | ||||
−0.259230 | + | 0.965816i | \(0.583469\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 422.498i | − 0.518403i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −254.860 | −0.311946 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 386.042i | 0.470209i | 0.971970 | + | 0.235105i | \(0.0755433\pi\) | ||||
−0.971970 | + | 0.235105i | \(0.924457\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 998.570 | 1.21333 | 0.606665 | − | 0.794958i | \(-0.292507\pi\) | ||||
0.606665 | + | 0.794958i | \(0.292507\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 684.604i | 0.827816i | 0.910319 | + | 0.413908i | \(0.135837\pi\) | ||||
−0.910319 | + | 0.413908i | \(0.864163\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 533.567 | 0.643628 | 0.321814 | − | 0.946803i | \(-0.395707\pi\) | ||||
0.321814 | + | 0.946803i | \(0.395707\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 660.632i | 0.793076i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −935.606 | −1.12049 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1441.02i | − 1.71754i | −0.512360 | − | 0.858771i | \(-0.671229\pi\) | ||||
0.512360 | − | 0.858771i | \(-0.328771\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 215.098 | 0.255765 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 872.066i | − 1.03203i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −196.280 | −0.231735 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 469.241i | 0.551399i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 670.383 | 0.785913 | 0.392956 | − | 0.919557i | \(-0.371452\pi\) | ||||
0.392956 | + | 0.919557i | \(0.371452\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 223.046i | − 0.260264i | −0.991497 | − | 0.130132i | \(-0.958460\pi\) | ||||
0.991497 | − | 0.130132i | \(-0.0415401\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1174.48 | −1.36726 | −0.683630 | − | 0.729829i | \(-0.739600\pi\) | ||||
−0.683630 | + | 0.729829i | \(0.739600\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 780.785i | 0.904734i | 0.891832 | + | 0.452367i | \(0.149420\pi\) | ||||
−0.891832 | + | 0.452367i | \(0.850580\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −138.295 | −0.159879 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 2.27908i | − 0.00262265i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 141.897 | 0.162912 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 237.588i | − 0.271529i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1096.28 | 1.25003 | 0.625017 | − | 0.780611i | \(-0.285092\pi\) | ||||
0.625017 | + | 0.780611i | \(0.285092\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1164.43i | 1.32171i | 0.750514 | + | 0.660854i | \(0.229806\pi\) | ||||
−0.750514 | + | 0.660854i | \(0.770194\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.8032 | −0.0133672 | −0.00668360 | − | 0.999978i | \(-0.502127\pi\) | ||||
−0.00668360 | + | 0.999978i | \(0.502127\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 295.505i | 0.333151i | 0.986029 | + | 0.166575i | \(0.0532709\pi\) | ||||
−0.986029 | + | 0.166575i | \(0.946729\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −162.093 | −0.182332 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2148.24i | 2.40565i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1600.57 | −1.78835 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 988.796i | − 1.09988i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 143.852 | 0.159659 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 299.473i | 0.330909i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −423.617 | −0.467053 | −0.233526 | − | 0.972350i | \(-0.575026\pi\) | ||||
−0.233526 | + | 0.972350i | \(0.575026\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1008.39i | − 1.10691i | −0.832880 | − | 0.553454i | \(-0.813309\pi\) | ||||
0.832880 | − | 0.553454i | \(-0.186691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 149.720 | 0.163987 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 328.904i | − 0.358674i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1067.51 | −1.16160 | −0.580802 | − | 0.814045i | \(-0.697261\pi\) | ||||
−0.580802 | + | 0.814045i | \(0.697261\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.3138i | 0.0328427i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −58.1968 | −0.0629154 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 720.842i | − 0.775934i | −0.921673 | − | 0.387967i | \(-0.873178\pi\) | ||||
0.921673 | − | 0.387967i | \(-0.126822\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1204.27 | 1.29353 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 366.333i | 0.391800i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1032.47 | −1.10189 | −0.550943 | − | 0.834543i | \(-0.685732\pi\) | ||||
−0.550943 | + | 0.834543i | \(0.685732\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1597.62i | − 1.69779i | −0.528565 | − | 0.848893i | \(-0.677270\pi\) | ||||
0.528565 | − | 0.848893i | \(-0.322730\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 520.187 | 0.551629 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 625.214i | − 0.660205i | −0.943945 | − | 0.330103i | \(-0.892917\pi\) | ||||
0.943945 | − | 0.330103i | \(-0.107083\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 194.103 | 0.204535 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 807.036i | 0.846838i | 0.905934 | + | 0.423419i | \(0.139170\pi\) | ||||
−0.905934 | + | 0.423419i | \(0.860830\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1131.03 | 1.18432 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 449.581i | 0.468802i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 601.093 | 0.625487 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 976.690i | 1.01211i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1296.47 | 1.34071 | 0.670355 | − | 0.742041i | \(-0.266142\pi\) | ||||
0.670355 | + | 0.742041i | \(0.266142\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 200.075i | 0.206050i | 0.994679 | + | 0.103025i | \(0.0328522\pi\) | ||||
−0.994679 | + | 0.103025i | \(0.967148\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 340.757 | 0.350212 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 1309.95i | − 1.34079i | −0.742003 | − | 0.670396i | \(-0.766124\pi\) | ||||
0.742003 | − | 0.670396i | \(-0.233876\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −62.7820 | −0.0641287 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1553.47i | − 1.58033i | −0.612893 | − | 0.790166i | \(-0.709994\pi\) | ||||
0.612893 | − | 0.790166i | \(-0.290006\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −343.907 | −0.349144 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 171.874i | 0.173786i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 922.757 | 0.931137 | 0.465568 | − | 0.885012i | \(-0.345850\pi\) | ||||
0.465568 | + | 0.885012i | \(0.345850\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 599.946i | − 0.602960i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −787.710 | −0.790080 | −0.395040 | − | 0.918664i | \(-0.629269\pi\) | ||||
−0.395040 | + | 0.918664i | \(0.629269\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1152.3.e.c.1025.3 | yes | 4 | |
3.2 | odd | 2 | inner | 1152.3.e.c.1025.2 | yes | 4 | |
4.3 | odd | 2 | 1152.3.e.g.1025.3 | yes | 4 | ||
8.3 | odd | 2 | 1152.3.e.e.1025.2 | yes | 4 | ||
8.5 | even | 2 | 1152.3.e.a.1025.2 | ✓ | 4 | ||
12.11 | even | 2 | 1152.3.e.g.1025.2 | yes | 4 | ||
16.3 | odd | 4 | 2304.3.h.j.2177.5 | 8 | |||
16.5 | even | 4 | 2304.3.h.l.2177.4 | 8 | |||
16.11 | odd | 4 | 2304.3.h.j.2177.4 | 8 | |||
16.13 | even | 4 | 2304.3.h.l.2177.5 | 8 | |||
24.5 | odd | 2 | 1152.3.e.a.1025.3 | yes | 4 | ||
24.11 | even | 2 | 1152.3.e.e.1025.3 | yes | 4 | ||
48.5 | odd | 4 | 2304.3.h.l.2177.6 | 8 | |||
48.11 | even | 4 | 2304.3.h.j.2177.6 | 8 | |||
48.29 | odd | 4 | 2304.3.h.l.2177.3 | 8 | |||
48.35 | even | 4 | 2304.3.h.j.2177.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.3.e.a.1025.2 | ✓ | 4 | 8.5 | even | 2 | ||
1152.3.e.a.1025.3 | yes | 4 | 24.5 | odd | 2 | ||
1152.3.e.c.1025.2 | yes | 4 | 3.2 | odd | 2 | inner | |
1152.3.e.c.1025.3 | yes | 4 | 1.1 | even | 1 | trivial | |
1152.3.e.e.1025.2 | yes | 4 | 8.3 | odd | 2 | ||
1152.3.e.e.1025.3 | yes | 4 | 24.11 | even | 2 | ||
1152.3.e.g.1025.2 | yes | 4 | 12.11 | even | 2 | ||
1152.3.e.g.1025.3 | yes | 4 | 4.3 | odd | 2 | ||
2304.3.h.j.2177.3 | 8 | 48.35 | even | 4 | |||
2304.3.h.j.2177.4 | 8 | 16.11 | odd | 4 | |||
2304.3.h.j.2177.5 | 8 | 16.3 | odd | 4 | |||
2304.3.h.j.2177.6 | 8 | 48.11 | even | 4 | |||
2304.3.h.l.2177.3 | 8 | 48.29 | odd | 4 | |||
2304.3.h.l.2177.4 | 8 | 16.5 | even | 4 | |||
2304.3.h.l.2177.5 | 8 | 16.13 | even | 4 | |||
2304.3.h.l.2177.6 | 8 | 48.5 | odd | 4 |