Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(1567,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.1567");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.b (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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.116304318664704.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + x^{10} + 6x^{9} - 9x^{8} - 2x^{7} + 18x^{6} - 4x^{5} - 36x^{4} + 48x^{3} + 16x^{2} - 64x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1567.4 | ||
Root | \(1.33544 - 0.465413i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1567 |
Dual form | 1728.3.b.j.1567.9 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | − 3.99718i | − 0.799436i | −0.916638 | − | 0.399718i | \(-0.869108\pi\) | ||||
0.916638 | − | 0.399718i | \(-0.130892\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.74742i | 1.10677i | 0.832924 | + | 0.553387i | \(0.186665\pi\) | ||||
−0.832924 | + | 0.553387i | \(0.813335\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.68970 | −0.699063 | −0.349532 | − | 0.936925i | \(-0.613659\pi\) | ||||
−0.349532 | + | 0.936925i | \(0.613659\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.42738i | − 0.109799i | −0.998492 | − | 0.0548994i | \(-0.982516\pi\) | ||||
0.998492 | − | 0.0548994i | \(-0.0174838\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 22.3189 | 1.31288 | 0.656440 | − | 0.754379i | \(-0.272062\pi\) | ||||
0.656440 | + | 0.754379i | \(0.272062\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −21.9464 | −1.15507 | −0.577536 | − | 0.816365i | \(-0.695986\pi\) | ||||
−0.577536 | + | 0.816365i | \(0.695986\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 18.1656i | − 0.789808i | −0.918722 | − | 0.394904i | \(-0.870778\pi\) | ||||
0.918722 | − | 0.394904i | \(-0.129222\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.02254 | 0.360902 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 15.2838i | − 0.527027i | −0.964656 | − | 0.263514i | \(-0.915119\pi\) | ||||
0.964656 | − | 0.263514i | \(-0.0848814\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 10.2197i | − 0.329668i | −0.986321 | − | 0.164834i | \(-0.947291\pi\) | ||||
0.986321 | − | 0.164834i | \(-0.0527089\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 30.9678 | 0.884796 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 59.1765i | 1.59937i | 0.600423 | + | 0.799683i | \(0.294999\pi\) | ||||
−0.600423 | + | 0.799683i | \(0.705001\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 41.3743 | 1.00913 | 0.504565 | − | 0.863374i | \(-0.331653\pi\) | ||||
0.504565 | + | 0.863374i | \(0.331653\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.0016 | −0.255852 | −0.127926 | − | 0.991784i | \(-0.540832\pi\) | ||||
−0.127926 | + | 0.991784i | \(0.540832\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 63.6933i | 1.35518i | 0.735442 | + | 0.677588i | \(0.236975\pi\) | ||||
−0.735442 | + | 0.677588i | \(0.763025\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11.0225 | −0.224950 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 19.2810i | − 0.363792i | −0.983318 | − | 0.181896i | \(-0.941777\pi\) | ||||
0.983318 | − | 0.181896i | \(-0.0582234\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 30.7371i | 0.558857i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −16.1799 | −0.274236 | −0.137118 | − | 0.990555i | \(-0.543784\pi\) | ||||
−0.137118 | + | 0.990555i | \(0.543784\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 27.7128i | − 0.454308i | −0.973859 | − | 0.227154i | \(-0.927058\pi\) | ||||
0.973859 | − | 0.227154i | \(-0.0729421\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.70551 | −0.0877771 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 60.6039 | 0.904536 | 0.452268 | − | 0.891882i | \(-0.350615\pi\) | ||||
0.452268 | + | 0.891882i | \(0.350615\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 134.803i | 1.89864i | 0.314311 | + | 0.949320i | \(0.398227\pi\) | ||||
−0.314311 | + | 0.949320i | \(0.601773\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 90.0019 | 1.23290 | 0.616451 | − | 0.787393i | \(-0.288570\pi\) | ||||
0.616451 | + | 0.787393i | \(0.288570\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 59.5753i | − 0.773705i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 12.0122i | − 0.152054i | −0.997106 | − | 0.0760268i | \(-0.975777\pi\) | ||||
0.997106 | − | 0.0760268i | \(-0.0242234\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 164.757 | 1.98503 | 0.992513 | − | 0.122137i | \(-0.0389746\pi\) | ||||
0.992513 | + | 0.122137i | \(0.0389746\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 89.2129i | − 1.04956i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 35.6688 | 0.400773 | 0.200387 | − | 0.979717i | \(-0.435780\pi\) | ||||
0.200387 | + | 0.979717i | \(0.435780\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.0585 | 0.121522 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 87.7236i | 0.923407i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −147.070 | −1.51618 | −0.758090 | − | 0.652149i | \(-0.773867\pi\) | ||||
−0.758090 | + | 0.652149i | \(0.773867\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 74.2140i | 0.734793i | 0.930065 | + | 0.367396i | \(0.119751\pi\) | ||||
−0.930065 | + | 0.367396i | \(0.880249\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 55.0676i | − 0.534637i | −0.963608 | − | 0.267319i | \(-0.913862\pi\) | ||||
0.963608 | − | 0.267319i | \(-0.0861376\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 32.6046 | 0.304716 | 0.152358 | − | 0.988325i | \(-0.451313\pi\) | ||||
0.152358 | + | 0.988325i | \(0.451313\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 29.6714i | 0.272215i | 0.990694 | + | 0.136108i | \(0.0434593\pi\) | ||||
−0.990694 | + | 0.136108i | \(0.956541\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 213.399 | 1.88848 | 0.944242 | − | 0.329251i | \(-0.106796\pi\) | ||||
0.944242 | + | 0.329251i | \(0.106796\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −72.6111 | −0.631401 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 172.914i | 1.45306i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −61.8686 | −0.511311 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 135.994i | − 1.08795i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 64.2526i | − 0.505926i | −0.967476 | − | 0.252963i | \(-0.918595\pi\) | ||||
0.967476 | − | 0.252963i | \(-0.0814051\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 92.1030 | 0.703076 | 0.351538 | − | 0.936174i | \(-0.385659\pi\) | ||||
0.351538 | + | 0.936174i | \(0.385659\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 170.028i | − 1.27840i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 169.582 | 1.23783 | 0.618914 | − | 0.785459i | \(-0.287573\pi\) | ||||
0.618914 | + | 0.785459i | \(0.287573\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 71.6056 | 0.515148 | 0.257574 | − | 0.966259i | \(-0.417077\pi\) | ||||
0.257574 | + | 0.966259i | \(0.417077\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.9761i | 0.0767563i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −61.0921 | −0.421325 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 198.277i | − 1.33072i | −0.746525 | − | 0.665358i | \(-0.768279\pi\) | ||||
0.746525 | − | 0.665358i | \(-0.231721\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 72.3305i | 0.479010i | 0.970895 | + | 0.239505i | \(0.0769852\pi\) | ||||
−0.970895 | + | 0.239505i | \(0.923015\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −40.8501 | −0.263549 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 124.063i | 0.790208i | 0.918636 | + | 0.395104i | \(0.129291\pi\) | ||||
−0.918636 | + | 0.395104i | \(0.870709\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 140.736 | 0.874139 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 232.533 | 1.42659 | 0.713293 | − | 0.700866i | \(-0.247203\pi\) | ||||
0.713293 | + | 0.700866i | \(0.247203\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 43.9755i | 0.263327i | 0.991294 | + | 0.131663i | \(0.0420318\pi\) | ||||
−0.991294 | + | 0.131663i | \(0.957968\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 166.963 | 0.987944 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 305.908i | − 1.76826i | −0.467245 | − | 0.884128i | \(-0.654753\pi\) | ||||
0.467245 | − | 0.884128i | \(-0.345247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 69.9014i | 0.399437i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.19254 | −0.0122488 | −0.00612442 | − | 0.999981i | \(-0.501949\pi\) | ||||
−0.00612442 | + | 0.999981i | \(0.501949\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 132.855i | 0.734003i | 0.930220 | + | 0.367001i | \(0.119616\pi\) | ||||
−0.930220 | + | 0.367001i | \(0.880384\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 236.539 | 1.27859 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −171.626 | −0.917785 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 151.417i | 0.792759i | 0.918087 | + | 0.396379i | \(0.129733\pi\) | ||||
−0.918087 | + | 0.396379i | \(0.870267\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 229.850 | 1.19093 | 0.595466 | − | 0.803381i | \(-0.296967\pi\) | ||||
0.595466 | + | 0.803381i | \(0.296967\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 189.195i | 0.960380i | 0.877164 | + | 0.480190i | \(0.159432\pi\) | ||||
−0.877164 | + | 0.480190i | \(0.840568\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 217.686i | − 1.09390i | −0.837166 | − | 0.546949i | \(-0.815789\pi\) | ||||
0.837166 | − | 0.546949i | \(-0.184211\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 118.410 | 0.583300 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 165.381i | − 0.806735i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 168.761 | 0.807468 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −247.120 | −1.17118 | −0.585591 | − | 0.810606i | \(-0.699138\pi\) | ||||
−0.585591 | + | 0.810606i | \(0.699138\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 43.9755i | 0.204537i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 79.1765 | 0.364869 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 31.8577i | − 0.144153i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 361.006i | 1.61886i | 0.587216 | + | 0.809430i | \(0.300224\pi\) | ||||
−0.587216 | + | 0.809430i | \(0.699776\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.0546 | 0.0927515 | 0.0463758 | − | 0.998924i | \(-0.485233\pi\) | ||||
0.0463758 | + | 0.998924i | \(0.485233\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 319.313i | 1.39438i | 0.716886 | + | 0.697191i | \(0.245567\pi\) | ||||
−0.716886 | + | 0.697191i | \(0.754433\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 197.607 | 0.848098 | 0.424049 | − | 0.905639i | \(-0.360608\pi\) | ||||
0.424049 | + | 0.905639i | \(0.360608\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 254.594 | 1.08338 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 256.325i | 1.07249i | 0.844062 | + | 0.536245i | \(0.180158\pi\) | ||||
−0.844062 | + | 0.536245i | \(0.819842\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −375.717 | −1.55899 | −0.779495 | − | 0.626409i | \(-0.784524\pi\) | ||||
−0.779495 | + | 0.626409i | \(0.784524\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 44.0591i | 0.179833i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 31.3259i | 0.126825i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 423.810 | 1.68849 | 0.844243 | − | 0.535961i | \(-0.180050\pi\) | ||||
0.844243 | + | 0.535961i | \(0.180050\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 139.688i | 0.552126i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −205.754 | −0.800601 | −0.400300 | − | 0.916384i | \(-0.631094\pi\) | ||||
−0.400300 | + | 0.916384i | \(0.631094\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −458.466 | −1.77014 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 75.9941i | − 0.288951i | −0.989508 | − | 0.144476i | \(-0.953851\pi\) | ||||
0.989508 | − | 0.144476i | \(-0.0461495\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −77.0695 | −0.290828 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 327.627i | − 1.21794i | −0.793192 | − | 0.608971i | \(-0.791582\pi\) | ||||
0.793192 | − | 0.608971i | \(-0.208418\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 277.780i | − 1.02502i | −0.858681 | − | 0.512510i | \(-0.828716\pi\) | ||||
0.858681 | − | 0.512510i | \(-0.171284\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −69.3806 | −0.252293 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 92.9929i | − 0.335714i | −0.985811 | − | 0.167857i | \(-0.946315\pi\) | ||||
0.985811 | − | 0.167857i | \(-0.0536847\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −190.784 | −0.678947 | −0.339474 | − | 0.940616i | \(-0.610249\pi\) | ||||
−0.339474 | + | 0.940616i | \(0.610249\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −153.511 | −0.542441 | −0.271220 | − | 0.962517i | \(-0.587427\pi\) | ||||
−0.271220 | + | 0.962517i | \(0.587427\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 320.544i | 1.11688i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 209.135 | 0.723651 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 550.059i | 1.87733i | 0.344825 | + | 0.938667i | \(0.387938\pi\) | ||||
−0.344825 | + | 0.938667i | \(0.612062\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 64.6741i | 0.219234i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −25.9293 | −0.0867200 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 85.2343i | − 0.283171i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −110.773 | −0.363191 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 403.571 | 1.31456 | 0.657282 | − | 0.753645i | \(-0.271706\pi\) | ||||
0.657282 | + | 0.753645i | \(0.271706\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 328.988i | 1.05784i | 0.848672 | + | 0.528919i | \(0.177402\pi\) | ||||
−0.848672 | + | 0.528919i | \(0.822598\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −168.133 | −0.537167 | −0.268584 | − | 0.963256i | \(-0.586556\pi\) | ||||
−0.268584 | + | 0.963256i | \(0.586556\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 171.437i | − 0.540809i | −0.962747 | − | 0.270405i | \(-0.912843\pi\) | ||||
0.962747 | − | 0.270405i | \(-0.0871575\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 117.528i | 0.368425i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −489.820 | −1.51647 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 12.8786i | − 0.0396266i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −493.459 | −1.49987 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −520.075 | −1.57122 | −0.785612 | − | 0.618720i | \(-0.787652\pi\) | ||||
−0.785612 | + | 0.618720i | \(0.787652\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 242.245i | − 0.723119i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 411.987 | 1.22251 | 0.611257 | − | 0.791432i | \(-0.290664\pi\) | ||||
0.611257 | + | 0.791432i | \(0.290664\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 78.5866i | 0.230459i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 294.227i | 0.857806i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 309.229 | 0.891151 | 0.445575 | − | 0.895244i | \(-0.352999\pi\) | ||||
0.445575 | + | 0.895244i | \(0.352999\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 609.516i | − 1.74646i | −0.487306 | − | 0.873231i | \(-0.662020\pi\) | ||||
0.487306 | − | 0.873231i | \(-0.337980\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 376.662 | 1.06703 | 0.533515 | − | 0.845791i | \(-0.320871\pi\) | ||||
0.533515 | + | 0.845791i | \(0.320871\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 538.834 | 1.51784 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 186.196i | − 0.518652i | −0.965790 | − | 0.259326i | \(-0.916500\pi\) | ||||
0.965790 | − | 0.259326i | \(-0.0835003\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 120.643 | 0.334192 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 359.754i | − 0.985627i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 89.1514i | − 0.242919i | −0.992596 | − | 0.121460i | \(-0.961243\pi\) | ||||
0.992596 | − | 0.121460i | \(-0.0387575\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 149.378 | 0.402636 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 103.487i | 0.277444i | 0.990331 | + | 0.138722i | \(0.0442995\pi\) | ||||
−0.990331 | + | 0.138722i | \(0.955701\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.8158 | −0.0578669 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 636.105 | 1.67838 | 0.839188 | − | 0.543841i | \(-0.183031\pi\) | ||||
0.839188 | + | 0.543841i | \(0.183031\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 617.514i | − 1.61231i | −0.591707 | − | 0.806153i | \(-0.701546\pi\) | ||||
0.591707 | − | 0.806153i | \(-0.298454\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −238.133 | −0.618528 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 674.534i | 1.73402i | 0.498290 | + | 0.867010i | \(0.333961\pi\) | ||||
−0.498290 | + | 0.867010i | \(0.666039\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 405.437i | − 1.03692i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −48.0151 | −0.121557 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 758.512i | 1.91061i | 0.295622 | + | 0.955305i | \(0.404473\pi\) | ||||
−0.295622 | + | 0.955305i | \(0.595527\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −314.381 | −0.783993 | −0.391997 | − | 0.919967i | \(-0.628216\pi\) | ||||
−0.391997 | + | 0.919967i | \(0.628216\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.5875 | −0.0361972 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 455.050i | − 1.11806i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −591.015 | −1.44503 | −0.722513 | − | 0.691358i | \(-0.757013\pi\) | ||||
−0.722513 | + | 0.691358i | \(0.757013\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 125.353i | − 0.303517i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 658.564i | − 1.58690i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −371.686 | −0.887078 | −0.443539 | − | 0.896255i | \(-0.646277\pi\) | ||||
−0.443539 | + | 0.896255i | \(0.646277\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 660.963i | − 1.56998i | −0.619507 | − | 0.784991i | \(-0.712667\pi\) | ||||
0.619507 | − | 0.784991i | \(-0.287333\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 201.374 | 0.473820 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 214.703 | 0.502817 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 376.295i | − 0.873074i | −0.899686 | − | 0.436537i | \(-0.856205\pi\) | ||||
0.899686 | − | 0.436537i | \(-0.143795\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 301.156 | 0.695510 | 0.347755 | − | 0.937585i | \(-0.386944\pi\) | ||||
0.347755 | + | 0.937585i | \(0.386944\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 398.669i | 0.912285i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 463.627i | 1.05610i | 0.849214 | + | 0.528049i | \(0.177076\pi\) | ||||
−0.849214 | + | 0.528049i | \(0.822924\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −655.755 | −1.48026 | −0.740130 | − | 0.672464i | \(-0.765236\pi\) | ||||
−0.740130 | + | 0.672464i | \(0.765236\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 142.575i | − 0.320393i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −167.436 | −0.372909 | −0.186455 | − | 0.982464i | \(-0.559700\pi\) | ||||
−0.186455 | + | 0.982464i | \(0.559700\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −318.156 | −0.705446 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 44.2030i | − 0.0971495i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −527.115 | −1.15342 | −0.576712 | − | 0.816948i | \(-0.695664\pi\) | ||||
−0.576712 | + | 0.816948i | \(0.695664\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 395.196i | − 0.857259i | −0.903480 | − | 0.428629i | \(-0.858997\pi\) | ||||
0.903480 | − | 0.428629i | \(-0.141003\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 159.767i | − 0.345070i | −0.985003 | − | 0.172535i | \(-0.944804\pi\) | ||||
0.985003 | − | 0.172535i | \(-0.0551958\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −275.233 | −0.589363 | −0.294682 | − | 0.955595i | \(-0.595214\pi\) | ||||
−0.294682 | + | 0.955595i | \(0.595214\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 469.524i | 1.00112i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 84.5993 | 0.178857 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −198.012 | −0.416867 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 551.742i | − 1.15186i | −0.817498 | − | 0.575931i | \(-0.804640\pi\) | ||||
0.817498 | − | 0.575931i | \(-0.195360\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 84.4676 | 0.175608 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 587.864i | 1.21209i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 219.363i | − 0.450437i | −0.974308 | − | 0.225218i | \(-0.927690\pi\) | ||||
0.974308 | − | 0.225218i | \(-0.0723095\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −346.740 | −0.706191 | −0.353095 | − | 0.935587i | \(-0.614871\pi\) | ||||
−0.353095 | + | 0.935587i | \(0.614871\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 341.118i | − 0.691923i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1044.38 | −2.10137 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 101.861 | 0.204130 | 0.102065 | − | 0.994778i | \(-0.467455\pi\) | ||||
0.102065 | + | 0.994778i | \(0.467455\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 752.544i | − 1.49611i | −0.663635 | − | 0.748056i | \(-0.730987\pi\) | ||||
0.663635 | − | 0.748056i | \(-0.269013\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 296.647 | 0.587420 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 339.596i | − 0.667182i | −0.942718 | − | 0.333591i | \(-0.891740\pi\) | ||||
0.942718 | − | 0.333591i | \(-0.108260\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 697.283i | 1.36455i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −220.115 | −0.427408 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 489.782i | − 0.947354i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −683.717 | −1.31232 | −0.656158 | − | 0.754623i | \(-0.727820\pi\) | ||||
−0.656158 | + | 0.754623i | \(0.727820\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −112.671 | −0.215433 | −0.107716 | − | 0.994182i | \(-0.534354\pi\) | ||||
−0.107716 | + | 0.994182i | \(0.534354\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 228.093i | − 0.432815i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 199.011 | 0.376203 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 59.0571i | − 0.110801i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 130.327i | − 0.243601i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 84.7600 | 0.157254 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 752.788i | 1.39147i | 0.718296 | + | 0.695737i | \(0.244922\pi\) | ||||
−0.718296 | + | 0.695737i | \(0.755078\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 118.602 | 0.217619 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −892.328 | −1.63131 | −0.815657 | − | 0.578536i | \(-0.803624\pi\) | ||||
−0.815657 | + | 0.578536i | \(0.803624\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 335.424i | 0.608754i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 93.0638 | 0.168289 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 105.929i | 0.190177i | 0.995469 | + | 0.0950887i | \(0.0303135\pi\) | ||||
−0.995469 | + | 0.0950887i | \(0.969687\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.7036i | 0.0280922i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 221.818 | 0.393993 | 0.196997 | − | 0.980404i | \(-0.436881\pi\) | ||||
0.196997 | + | 0.980404i | \(0.436881\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 852.994i | − 1.50972i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −604.024 | −1.06155 | −0.530777 | − | 0.847511i | \(-0.678100\pi\) | ||||
−0.530777 | + | 0.847511i | \(0.678100\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 470.074 | 0.823248 | 0.411624 | − | 0.911354i | \(-0.364962\pi\) | ||||
0.411624 | + | 0.911354i | \(0.364962\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 163.900i | − 0.285043i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 484.209 | 0.839183 | 0.419592 | − | 0.907713i | \(-0.362173\pi\) | ||||
0.419592 | + | 0.907713i | \(0.362173\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1276.44i | 2.19698i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 148.265i | 0.254314i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −361.426 | −0.615717 | −0.307858 | − | 0.951432i | \(-0.599612\pi\) | ||||
−0.307858 | + | 0.951432i | \(0.599612\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 224.286i | 0.380791i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −277.115 | −0.467310 | −0.233655 | − | 0.972320i | \(-0.575069\pi\) | ||||
−0.233655 | + | 0.972320i | \(0.575069\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 691.170 | 1.16163 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 654.345i | − 1.09240i | −0.837656 | − | 0.546198i | \(-0.816075\pi\) | ||||
0.837656 | − | 0.546198i | \(-0.183925\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −138.002 | −0.229620 | −0.114810 | − | 0.993387i | \(-0.536626\pi\) | ||||
−0.114810 | + | 0.993387i | \(0.536626\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 247.300i | 0.408760i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 569.498i | 0.938217i | 0.883140 | + | 0.469109i | \(0.155425\pi\) | ||||
−0.883140 | + | 0.469109i | \(0.844575\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 90.9148 | 0.148797 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1132.55i | 1.84756i | 0.382925 | + | 0.923779i | \(0.374917\pi\) | ||||
−0.382925 | + | 0.923779i | \(0.625083\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −651.926 | −1.05661 | −0.528303 | − | 0.849056i | \(-0.677171\pi\) | ||||
−0.528303 | + | 0.849056i | \(0.677171\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −691.283 | −1.11677 | −0.558387 | − | 0.829580i | \(-0.688580\pi\) | ||||
−0.558387 | + | 0.829580i | \(0.688580\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 276.341i | 0.443566i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −318.030 | −0.508848 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1320.76i | 2.09977i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1008.39i | 1.59808i | 0.601280 | + | 0.799038i | \(0.294658\pi\) | ||||
−0.601280 | + | 0.799038i | \(0.705342\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −256.829 | −0.404455 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.7334i | 0.0246992i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −609.937 | −0.951540 | −0.475770 | − | 0.879570i | \(-0.657831\pi\) | ||||
−0.475770 | + | 0.879570i | \(0.657831\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −453.534 | −0.705341 | −0.352670 | − | 0.935748i | \(-0.614726\pi\) | ||||
−0.352670 | + | 0.935748i | \(0.614726\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 422.050i | − 0.652319i | −0.945315 | − | 0.326159i | \(-0.894245\pi\) | ||||
0.945315 | − | 0.326159i | \(-0.105755\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 124.419 | 0.191708 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 912.070i | − 1.39674i | −0.715738 | − | 0.698369i | \(-0.753909\pi\) | ||||
0.715738 | − | 0.698369i | \(-0.246091\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 368.152i | − 0.562065i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1130.79 | 1.71591 | 0.857957 | − | 0.513722i | \(-0.171734\pi\) | ||||
0.857957 | + | 0.513722i | \(0.171734\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 669.361i | 1.01265i | 0.862343 | + | 0.506324i | \(0.168996\pi\) | ||||
−0.862343 | + | 0.506324i | \(0.831004\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −679.632 | −1.02200 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −277.639 | −0.416250 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 213.103i | 0.317590i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −504.561 | −0.749719 | −0.374859 | − | 0.927082i | \(-0.622309\pi\) | ||||
−0.374859 | + | 0.927082i | \(0.622309\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 863.692i | 1.27576i | 0.770134 | + | 0.637882i | \(0.220189\pi\) | ||||
−0.770134 | + | 0.637882i | \(0.779811\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 1139.41i | − 1.67807i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −845.591 | −1.23805 | −0.619027 | − | 0.785369i | \(-0.712473\pi\) | ||||
−0.619027 | + | 0.785369i | \(0.712473\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 677.852i | − 0.989565i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27.5213 | −0.0399439 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −165.670 | −0.239753 | −0.119877 | − | 0.992789i | \(-0.538250\pi\) | ||||
−0.119877 | + | 0.992789i | \(0.538250\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 286.220i | − 0.411828i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 923.432 | 1.32487 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 947.047i | − 1.35099i | −0.737362 | − | 0.675497i | \(-0.763929\pi\) | ||||
0.737362 | − | 0.675497i | \(-0.236071\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1298.71i | − 1.84738i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −574.967 | −0.813250 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 835.746i | 1.17877i | 0.807853 | + | 0.589383i | \(0.200629\pi\) | ||||
−0.807853 | + | 0.589383i | \(0.799371\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −185.647 | −0.260375 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 43.8737 | 0.0613618 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 20.1727i | − 0.0280566i | −0.999902 | − | 0.0140283i | \(-0.995535\pi\) | ||||
0.999902 | − | 0.0140283i | \(-0.00446549\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 426.632 | 0.591723 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 137.899i | − 0.190205i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 276.178i | − 0.379887i | −0.981795 | − | 0.189943i | \(-0.939170\pi\) | ||||
0.981795 | − | 0.189943i | \(-0.0608305\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −245.545 | −0.335903 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 294.820i | 0.402210i | 0.979570 | + | 0.201105i | \(0.0644533\pi\) | ||||
−0.979570 | + | 0.201105i | \(0.935547\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −466.026 | −0.632328 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 914.711 | 1.23777 | 0.618885 | − | 0.785482i | \(-0.287585\pi\) | ||||
0.618885 | + | 0.785482i | \(0.287585\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1068.78i | − 1.43846i | −0.694772 | − | 0.719230i | \(-0.744495\pi\) | ||||
0.694772 | − | 0.719230i | \(-0.255505\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −792.548 | −1.06382 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 252.602i | 0.337252i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1147.59i | 1.52809i | 0.645164 | + | 0.764044i | \(0.276789\pi\) | ||||
−0.645164 | + | 0.764044i | \(0.723211\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 289.118 | 0.382938 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 91.4460i | − 0.120801i | −0.998174 | − | 0.0604003i | \(-0.980762\pi\) | ||||
0.998174 | − | 0.0604003i | \(-0.0192377\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 762.676 | 1.00220 | 0.501101 | − | 0.865389i | \(-0.332928\pi\) | ||||
0.501101 | + | 0.865389i | \(0.332928\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −229.877 | −0.301281 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.0950i | 0.0301108i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −214.567 | −0.279021 | −0.139511 | − | 0.990221i | \(-0.544553\pi\) | ||||
−0.139511 | + | 0.990221i | \(0.544553\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 459.360i | − 0.594257i | −0.954838 | − | 0.297128i | \(-0.903971\pi\) | ||||
0.954838 | − | 0.297128i | \(-0.0960289\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 92.2079i | − 0.118978i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −908.017 | −1.16562 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1036.60i | − 1.32727i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 495.901 | 0.631721 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 76.5940 | 0.0973241 | 0.0486620 | − | 0.998815i | \(-0.484504\pi\) | ||||
0.0486620 | + | 0.998815i | \(0.484504\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1653.29i | 2.09013i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.5568 | −0.0498825 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 273.548i | − 0.343223i | −0.985165 | − | 0.171611i | \(-0.945103\pi\) | ||||
0.985165 | − | 0.171611i | \(-0.0548973\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1421.57i | 1.77918i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −692.087 | −0.861877 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 562.549i | − 0.698819i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 999.127 | 1.23502 | 0.617508 | − | 0.786565i | \(-0.288142\pi\) | ||||
0.617508 | + | 0.786565i | \(0.288142\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1189.75 | 1.46702 | 0.733509 | − | 0.679679i | \(-0.237881\pi\) | ||||
0.733509 | + | 0.679679i | \(0.237881\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 929.478i | − 1.14046i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 241.446 | 0.295528 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 985.174i | 1.19997i | 0.800012 | + | 0.599984i | \(0.204826\pi\) | ||||
−0.800012 | + | 0.599984i | \(0.795174\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 186.578i | − 0.226705i | −0.993555 | − | 0.113352i | \(-0.963841\pi\) | ||||
0.993555 | − | 0.113352i | \(-0.0361589\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 189.836 | 0.229548 | 0.114774 | − | 0.993392i | \(-0.463386\pi\) | ||||
0.114774 | + | 0.993392i | \(0.463386\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 920.478i | − 1.11035i | −0.831735 | − | 0.555174i | \(-0.812652\pi\) | ||||
0.831735 | − | 0.555174i | \(-0.187348\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −246.011 | −0.295332 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 175.778 | 0.210513 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 584.287i | − 0.696408i | −0.937419 | − | 0.348204i | \(-0.886792\pi\) | ||||
0.937419 | − | 0.348204i | \(-0.113208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 607.406 | 0.722242 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 667.380i | − 0.789798i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 479.322i | − 0.565906i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1074.98 | 1.26319 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 767.535i | − 0.899806i | −0.893077 | − | 0.449903i | \(-0.851458\pi\) | ||||
0.893077 | − | 0.449903i | \(-0.148542\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.7621 | 0.0358951 | 0.0179476 | − | 0.999839i | \(-0.494287\pi\) | ||||
0.0179476 | + | 0.999839i | \(0.494287\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −795.268 | −0.925807 | −0.462903 | − | 0.886409i | \(-0.653192\pi\) | ||||
−0.462903 | + | 0.886409i | \(0.653192\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1107.46i | − 1.28327i | −0.767012 | − | 0.641633i | \(-0.778257\pi\) | ||||
0.767012 | − | 0.641633i | \(-0.221743\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1222.77 | −1.41361 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 92.3704i | 0.106295i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 86.5051i | − 0.0993169i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1053.60 | 1.20412 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 649.012i | 0.740037i | 0.929024 | + | 0.370018i | \(0.120649\pi\) | ||||
−0.929024 | + | 0.370018i | \(0.879351\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 951.863 | 1.08043 | 0.540217 | − | 0.841526i | \(-0.318342\pi\) | ||||
0.540217 | + | 0.841526i | \(0.318342\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −431.588 | −0.488774 | −0.244387 | − | 0.969678i | \(-0.578587\pi\) | ||||
−0.244387 | + | 0.969678i | \(0.578587\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 101.304i | − 0.114209i | −0.998368 | − | 0.0571047i | \(-0.981813\pi\) | ||||
0.998368 | − | 0.0571047i | \(-0.0181869\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 497.792 | 0.559946 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1397.84i | − 1.56533i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.76399i | 0.00979216i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −156.196 | −0.173744 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 430.331i | − 0.477615i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 531.044 | 0.586789 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 489.763 | 0.539981 | 0.269991 | − | 0.962863i | \(-0.412979\pi\) | ||||
0.269991 | + | 0.962863i | \(0.412979\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 253.105i | 0.277832i | 0.990304 | + | 0.138916i | \(0.0443617\pi\) | ||||
−0.990304 | + | 0.138916i | \(0.955638\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1266.93 | −1.38766 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 713.561i | 0.778147i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 68.3565i | 0.0743813i | 0.999308 | + | 0.0371907i | \(0.0118409\pi\) | ||||
−0.999308 | + | 0.0371907i | \(0.988159\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 192.416 | 0.208468 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 533.923i | 0.577214i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 319.311 | 0.343715 | 0.171857 | − | 0.985122i | \(-0.445023\pi\) | ||||
0.171857 | + | 0.985122i | \(0.445023\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 241.905 | 0.259833 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 686.020i | 0.733711i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −680.412 | −0.726161 | −0.363080 | − | 0.931758i | \(-0.618275\pi\) | ||||
−0.363080 | + | 0.931758i | \(0.618275\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 265.255i | − 0.281886i | −0.990018 | − | 0.140943i | \(-0.954987\pi\) | ||||
0.990018 | − | 0.140943i | \(-0.0450134\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 751.589i | − 0.797019i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −412.117 | −0.435182 | −0.217591 | − | 0.976040i | \(-0.569820\pi\) | ||||
−0.217591 | + | 0.976040i | \(0.569820\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 128.467i | − 0.135371i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 149.202 | 0.156561 | 0.0782804 | − | 0.996931i | \(-0.475057\pi\) | ||||
0.0782804 | + | 0.996931i | \(0.475057\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 605.241 | 0.633760 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1313.83i | 1.37000i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 856.557 | 0.891319 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 918.752i | − 0.952074i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 91.2392i | − 0.0943528i | −0.998887 | − | 0.0471764i | \(-0.984978\pi\) | ||||
0.998887 | − | 0.0471764i | \(-0.0150223\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 117.427 | 0.120934 | 0.0604669 | − | 0.998170i | \(-0.480741\pi\) | ||||
0.0604669 | + | 0.998170i | \(0.480741\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 554.758i | 0.570153i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 576.207 | 0.589772 | 0.294886 | − | 0.955532i | \(-0.404718\pi\) | ||||
0.294886 | + | 0.955532i | \(0.404718\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −274.282 | −0.280166 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1338.61i | 1.36176i | 0.732395 | + | 0.680880i | \(0.238403\pi\) | ||||
−0.732395 | + | 0.680880i | \(0.761597\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 756.246 | 0.767763 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 199.851i | 0.202074i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 1519.83i | − 1.53363i | −0.641867 | − | 0.766816i | \(-0.721840\pi\) | ||||
0.641867 | − | 0.766816i | \(-0.278160\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −870.129 | −0.874501 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 492.073i | − 0.493554i | −0.969072 | − | 0.246777i | \(-0.920628\pi\) | ||||
0.969072 | − | 0.246777i | \(-0.0793715\pi\) | |||||||
\(998\) | 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 | 1728.3.b.j.1567.4 | yes | 12 | |
3.2 | odd | 2 | 1728.3.b.i.1567.10 | yes | 12 | ||
4.3 | odd | 2 | inner | 1728.3.b.j.1567.3 | yes | 12 | |
8.3 | odd | 2 | inner | 1728.3.b.j.1567.9 | yes | 12 | |
8.5 | even | 2 | inner | 1728.3.b.j.1567.10 | yes | 12 | |
12.11 | even | 2 | 1728.3.b.i.1567.9 | yes | 12 | ||
24.5 | odd | 2 | 1728.3.b.i.1567.4 | yes | 12 | ||
24.11 | even | 2 | 1728.3.b.i.1567.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.3.b.i.1567.3 | ✓ | 12 | 24.11 | even | 2 | ||
1728.3.b.i.1567.4 | yes | 12 | 24.5 | odd | 2 | ||
1728.3.b.i.1567.9 | yes | 12 | 12.11 | even | 2 | ||
1728.3.b.i.1567.10 | yes | 12 | 3.2 | odd | 2 | ||
1728.3.b.j.1567.3 | yes | 12 | 4.3 | odd | 2 | inner | |
1728.3.b.j.1567.4 | yes | 12 | 1.1 | even | 1 | trivial | |
1728.3.b.j.1567.9 | yes | 12 | 8.3 | odd | 2 | inner | |
1728.3.b.j.1567.10 | yes | 12 | 8.5 | even | 2 | inner |