Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(449,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.b (of order \(2\), degree \(1\), not 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.5 | ||
Root | \(1.14412 - 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.449 |
Dual form | 900.3.b.b.449.4 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.48683i | 0.783833i | 0.920001 | + | 0.391917i | \(0.128188\pi\) | ||||
−0.920001 | + | 0.391917i | \(0.871812\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 9.17377i | − 0.833979i | −0.908911 | − | 0.416989i | \(-0.863085\pi\) | ||||
0.908911 | − | 0.416989i | \(-0.136915\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 11.4868i | − 0.883603i | −0.897113 | − | 0.441801i | \(-0.854340\pi\) | ||||
0.897113 | − | 0.441801i | \(-0.145660\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 16.9706 | 0.998268 | 0.499134 | − | 0.866525i | \(-0.333651\pi\) | ||||
0.499134 | + | 0.866525i | \(0.333651\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −26.9737 | −1.41967 | −0.709833 | − | 0.704370i | \(-0.751230\pi\) | ||||
−0.709833 | + | 0.704370i | \(0.751230\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.93113 | −0.214397 | −0.107198 | − | 0.994238i | \(-0.534188\pi\) | ||||
−0.107198 | + | 0.994238i | \(0.534188\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 20.5247i | − 0.707749i | −0.935293 | − | 0.353874i | \(-0.884864\pi\) | ||||
0.935293 | − | 0.353874i | \(-0.115136\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.9737 | 0.676570 | 0.338285 | − | 0.941044i | \(-0.390153\pi\) | ||||
0.338285 | + | 0.941044i | \(0.390153\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 62.4605i | − 1.68812i | −0.536247 | − | 0.844061i | \(-0.680159\pi\) | ||||
0.536247 | − | 0.844061i | \(-0.319841\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 40.9377i | 0.998481i | 0.866464 | + | 0.499240i | \(0.166388\pi\) | ||||
−0.866464 | + | 0.499240i | \(0.833612\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.02633i | − 0.0238682i | −0.999929 | − | 0.0119341i | \(-0.996201\pi\) | ||||
0.999929 | − | 0.0119341i | \(-0.00379884\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 86.2298 | 1.83468 | 0.917338 | − | 0.398109i | \(-0.130333\pi\) | ||||
0.917338 | + | 0.398109i | \(0.130333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.8947 | 0.385605 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 96.0920 | 1.81306 | 0.906529 | − | 0.422144i | \(-0.138722\pi\) | ||||
0.906529 | + | 0.422144i | \(0.138722\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 112.374i | − 1.90465i | −0.305092 | − | 0.952323i | \(-0.598687\pi\) | ||||
0.305092 | − | 0.952323i | \(-0.401313\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −66.9210 | −1.09707 | −0.548533 | − | 0.836129i | \(-0.684813\pi\) | ||||
−0.548533 | + | 0.836129i | \(0.684813\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 76.0000i | − 1.13433i | −0.823605 | − | 0.567164i | \(-0.808040\pi\) | ||||
0.823605 | − | 0.567164i | \(-0.191960\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 24.0789i | 0.339139i | 0.985518 | + | 0.169570i | \(0.0542377\pi\) | ||||
−0.985518 | + | 0.169570i | \(0.945762\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 18.9210i | 0.259192i | 0.991567 | + | 0.129596i | \(0.0413680\pi\) | ||||
−0.991567 | + | 0.129596i | \(0.958632\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 50.3349 | 0.653700 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −106.921 | −1.35343 | −0.676715 | − | 0.736245i | \(-0.736597\pi\) | ||||
−0.676715 | + | 0.736245i | \(0.736597\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −45.1804 | −0.544342 | −0.272171 | − | 0.962249i | \(-0.587742\pi\) | ||||
−0.272171 | + | 0.962249i | \(0.587742\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 115.928i | − 1.30256i | −0.758835 | − | 0.651282i | \(-0.774231\pi\) | ||||
0.758835 | − | 0.651282i | \(-0.225769\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 63.0263 | 0.692597 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 87.0263i | − 0.897179i | −0.893738 | − | 0.448589i | \(-0.851927\pi\) | ||||
0.893738 | − | 0.448589i | \(-0.148073\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 129.233i | − 1.27953i | −0.768569 | − | 0.639767i | \(-0.779031\pi\) | ||||
0.768569 | − | 0.639767i | \(-0.220969\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 114.302i | − 1.10973i | −0.831939 | − | 0.554866i | \(-0.812769\pi\) | ||||
0.831939 | − | 0.554866i | \(-0.187231\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 93.3381 | 0.872319 | 0.436159 | − | 0.899869i | \(-0.356338\pi\) | ||||
0.436159 | + | 0.899869i | \(0.356338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −120.868 | −1.10888 | −0.554442 | − | 0.832222i | \(-0.687068\pi\) | ||||
−0.554442 | + | 0.832222i | \(0.687068\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 110.309 | 0.976183 | 0.488091 | − | 0.872793i | \(-0.337693\pi\) | ||||
0.488091 | + | 0.872793i | \(0.337693\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 93.1146i | 0.782476i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 36.8420 | 0.304479 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 105.381i | 0.829776i | 0.909873 | + | 0.414888i | \(0.136179\pi\) | ||||
−0.909873 | + | 0.414888i | \(0.863821\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 140.584i | 1.07316i | 0.843850 | + | 0.536580i | \(0.180284\pi\) | ||||
−0.843850 | + | 0.536580i | \(0.819716\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 148.000i | − 1.11278i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 266.951 | 1.94855 | 0.974274 | − | 0.225365i | \(-0.0723575\pi\) | ||||
0.974274 | + | 0.225365i | \(0.0723575\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.8420 | 0.113971 | 0.0569856 | − | 0.998375i | \(-0.481851\pi\) | ||||
0.0569856 | + | 0.998375i | \(0.481851\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −105.378 | −0.736906 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 41.6262i | − 0.279370i | −0.990196 | − | 0.139685i | \(-0.955391\pi\) | ||||
0.990196 | − | 0.139685i | \(-0.0446091\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 103.842 | 0.687695 | 0.343848 | − | 0.939025i | \(-0.388270\pi\) | ||||
0.343848 | + | 0.939025i | \(0.388270\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 12.5132i | − 0.0797017i | −0.999206 | − | 0.0398509i | \(-0.987312\pi\) | ||||
0.999206 | − | 0.0398509i | \(-0.0126883\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 27.0563i | − 0.168051i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 290.868i | 1.78447i | 0.451573 | + | 0.892234i | \(0.350863\pi\) | ||||
−0.451573 | + | 0.892234i | \(0.649137\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −174.637 | −1.04573 | −0.522865 | − | 0.852416i | \(-0.675137\pi\) | ||||
−0.522865 | + | 0.852416i | \(0.675137\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 37.0527 | 0.219247 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −43.5799 | −0.251907 | −0.125954 | − | 0.992036i | \(-0.540199\pi\) | ||||
−0.125954 | + | 0.992036i | \(0.540199\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 88.2952i | − 0.493270i | −0.969109 | − | 0.246635i | \(-0.920675\pi\) | ||||
0.969109 | − | 0.246635i | \(-0.0793248\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −56.8683 | −0.314190 | −0.157095 | − | 0.987584i | \(-0.550213\pi\) | ||||
−0.157095 | + | 0.987584i | \(0.550213\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 155.684i | − 0.832535i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 56.6430i | 0.296560i | 0.988945 | + | 0.148280i | \(0.0473737\pi\) | ||||
−0.988945 | + | 0.148280i | \(0.952626\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 110.000i | − 0.569948i | −0.958535 | − | 0.284974i | \(-0.908015\pi\) | ||||
0.958535 | − | 0.284974i | \(-0.0919850\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −245.049 | −1.24391 | −0.621953 | − | 0.783055i | \(-0.713661\pi\) | ||||
−0.621953 | + | 0.783055i | \(0.713661\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 169.895 | 0.853742 | 0.426871 | − | 0.904313i | \(-0.359616\pi\) | ||||
0.426871 | + | 0.904313i | \(0.359616\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 112.616 | 0.554757 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 247.450i | 1.18397i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −265.579 | −1.25867 | −0.629333 | − | 0.777136i | \(-0.716672\pi\) | ||||
−0.629333 | + | 0.777136i | \(0.716672\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 115.079i | 0.530318i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 194.938i | − 0.882072i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 187.329i | 0.840040i | 0.907515 | + | 0.420020i | \(0.137977\pi\) | ||||
−0.907515 | + | 0.420020i | \(0.862023\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −421.063 | −1.85490 | −0.927452 | − | 0.373942i | \(-0.878006\pi\) | ||||
−0.927452 | + | 0.373942i | \(0.878006\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 102.105 | 0.445875 | 0.222937 | − | 0.974833i | \(-0.428435\pi\) | ||||
0.222937 | + | 0.974833i | \(0.428435\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 99.0694 | 0.425191 | 0.212595 | − | 0.977140i | \(-0.431808\pi\) | ||||
0.212595 | + | 0.977140i | \(0.431808\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 77.9680i | 0.326226i | 0.986607 | + | 0.163113i | \(0.0521535\pi\) | ||||
−0.986607 | + | 0.163113i | \(0.947847\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −257.947 | −1.07032 | −0.535160 | − | 0.844750i | \(-0.679749\pi\) | ||||
−0.535160 | + | 0.844750i | \(0.679749\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 309.842i | 1.25442i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 274.971i | 1.09550i | 0.836641 | + | 0.547752i | \(0.184516\pi\) | ||||
−0.836641 | + | 0.547752i | \(0.815484\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 45.2370i | 0.178802i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −131.634 | −0.512193 | −0.256096 | − | 0.966651i | \(-0.582436\pi\) | ||||
−0.256096 | + | 0.966651i | \(0.582436\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 342.710 | 1.32321 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −458.782 | −1.74442 | −0.872209 | − | 0.489133i | \(-0.837313\pi\) | ||||
−0.872209 | + | 0.489133i | \(0.837313\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 301.916i | 1.12236i | 0.827692 | + | 0.561182i | \(0.189653\pi\) | ||||
−0.827692 | + | 0.561182i | \(0.810347\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 475.842 | 1.75587 | 0.877937 | − | 0.478776i | \(-0.158919\pi\) | ||||
0.877937 | + | 0.478776i | \(0.158919\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 322.039i | 1.16260i | 0.813691 | + | 0.581298i | \(0.197455\pi\) | ||||
−0.813691 | + | 0.581298i | \(0.802545\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 352.139i | − 1.25316i | −0.779355 | − | 0.626582i | \(-0.784453\pi\) | ||||
0.779355 | − | 0.626582i | \(-0.215547\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 281.631i | 0.995164i | 0.867417 | + | 0.497582i | \(0.165779\pi\) | ||||
−0.867417 | + | 0.497582i | \(0.834221\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −224.618 | −0.782642 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.00346021 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 64.3281 | 0.219550 | 0.109775 | − | 0.993956i | \(-0.464987\pi\) | ||||
0.109775 | + | 0.993956i | \(0.464987\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 56.6430i | 0.189442i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.63132 | 0.0187087 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 230.158i | 0.749700i | 0.927085 | + | 0.374850i | \(0.122306\pi\) | ||||
−0.927085 | + | 0.374850i | \(0.877694\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.48528i | 0.0272839i | 0.999907 | + | 0.0136419i | \(0.00434250\pi\) | ||||
−0.999907 | + | 0.0136419i | \(0.995658\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 605.579i | − 1.93476i | −0.253337 | − | 0.967378i | \(-0.581528\pi\) | ||||
0.253337 | − | 0.967378i | \(-0.418472\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 87.9601 | 0.277477 | 0.138738 | − | 0.990329i | \(-0.455695\pi\) | ||||
0.138738 | + | 0.990329i | \(0.455695\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −188.289 | −0.590248 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −457.758 | −1.41721 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 473.128i | 1.43808i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −49.2370 | −0.148752 | −0.0743761 | − | 0.997230i | \(-0.523697\pi\) | ||||
−0.0743761 | + | 0.997230i | \(0.523697\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 2.71033i | − 0.00804251i | −0.999992 | − | 0.00402125i | \(-0.998720\pi\) | ||||
0.999992 | − | 0.00402125i | \(-0.00128001\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 192.408i | − 0.564245i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 372.527i | 1.08608i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −74.9906 | −0.216111 | −0.108056 | − | 0.994145i | \(-0.534462\pi\) | ||||
−0.108056 | + | 0.994145i | \(0.534462\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 150.921 | 0.432438 | 0.216219 | − | 0.976345i | \(-0.430627\pi\) | ||||
0.216219 | + | 0.976345i | \(0.430627\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 292.407 | 0.828349 | 0.414174 | − | 0.910198i | \(-0.364070\pi\) | ||||
0.414174 | + | 0.910198i | \(0.364070\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 576.776i | 1.60662i | 0.595563 | + | 0.803309i | \(0.296929\pi\) | ||||
−0.595563 | + | 0.803309i | \(0.703071\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 366.579 | 1.01545 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 243.540i | 0.663595i | 0.943351 | + | 0.331798i | \(0.107655\pi\) | ||||
−0.943351 | + | 0.331798i | \(0.892345\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 527.241i | 1.42113i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 115.908i | − 0.310746i | −0.987856 | − | 0.155373i | \(-0.950342\pi\) | ||||
0.987856 | − | 0.155373i | \(-0.0496579\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −235.764 | −0.625369 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.2107 | −0.0797115 | −0.0398558 | − | 0.999205i | \(-0.512690\pi\) | ||||
−0.0398558 | + | 0.999205i | \(0.512690\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −651.319 | −1.70057 | −0.850286 | − | 0.526320i | \(-0.823571\pi\) | ||||
−0.850286 | + | 0.526320i | \(0.823571\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 205.600i | − 0.528536i | −0.964449 | − | 0.264268i | \(-0.914870\pi\) | ||||
0.964449 | − | 0.264268i | \(-0.0851303\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −83.6840 | −0.214026 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 118.355i | 0.298124i | 0.988828 | + | 0.149062i | \(0.0476254\pi\) | ||||
−0.988828 | + | 0.149062i | \(0.952375\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 170.971i | − 0.426361i | −0.977013 | − | 0.213181i | \(-0.931618\pi\) | ||||
0.977013 | − | 0.213181i | \(-0.0683823\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 240.921i | − 0.597819i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −572.998 | −1.40786 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 335.947 | 0.821387 | 0.410694 | − | 0.911773i | \(-0.365287\pi\) | ||||
0.410694 | + | 0.911773i | \(0.365287\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 616.578 | 1.49292 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 407.535i | − 0.972637i | −0.873781 | − | 0.486319i | \(-0.838339\pi\) | ||||
0.873781 | − | 0.486319i | \(-0.161661\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −771.210 | −1.83185 | −0.915926 | − | 0.401346i | \(-0.868542\pi\) | ||||
−0.915926 | + | 0.401346i | \(0.868542\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 367.184i | − 0.859916i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 436.210i | − 1.01209i | −0.862508 | − | 0.506044i | \(-0.831107\pi\) | ||||
0.862508 | − | 0.506044i | \(-0.168893\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 838.500i | 1.93649i | 0.250006 | + | 0.968244i | \(0.419568\pi\) | ||||
−0.250006 | + | 0.968244i | \(0.580432\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 133.011 | 0.304372 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −50.0000 | −0.113895 | −0.0569476 | − | 0.998377i | \(-0.518137\pi\) | ||||
−0.0569476 | + | 0.998377i | \(0.518137\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 492.853 | 1.11253 | 0.556267 | − | 0.831003i | \(-0.312233\pi\) | ||||
0.556267 | + | 0.831003i | \(0.312233\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 483.102i | − 1.07595i | −0.842960 | − | 0.537976i | \(-0.819189\pi\) | ||||
0.842960 | − | 0.537976i | \(-0.180811\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 375.553 | 0.832712 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 546.921i | − 1.19676i | −0.801211 | − | 0.598382i | \(-0.795811\pi\) | ||||
0.801211 | − | 0.598382i | \(-0.204189\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 130.386i | 0.282834i | 0.989950 | + | 0.141417i | \(0.0451658\pi\) | ||||
−0.989950 | + | 0.141417i | \(0.954834\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 24.7765i | − 0.0535130i | −0.999642 | − | 0.0267565i | \(-0.991482\pi\) | ||||
0.999642 | − | 0.0267565i | \(-0.00851787\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 671.491 | 1.43788 | 0.718941 | − | 0.695071i | \(-0.244627\pi\) | ||||
0.718941 | + | 0.695071i | \(0.244627\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 416.999 | 0.889124 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.41535 | −0.0199056 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 538.257i | − 1.12371i | −0.827236 | − | 0.561855i | \(-0.810088\pi\) | ||||
0.827236 | − | 0.561855i | \(-0.189912\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −717.473 | −1.49163 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 608.250i | 1.24897i | 0.781036 | + | 0.624486i | \(0.214692\pi\) | ||||
−0.781036 | + | 0.624486i | \(0.785308\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 143.561i | 0.292386i | 0.989256 | + | 0.146193i | \(0.0467020\pi\) | ||||
−0.989256 | + | 0.146193i | \(0.953298\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 348.316i | − 0.706523i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −132.117 | −0.265828 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −616.605 | −1.23568 | −0.617841 | − | 0.786303i | \(-0.711992\pi\) | ||||
−0.617841 | + | 0.786303i | \(0.711992\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −374.729 | −0.744989 | −0.372494 | − | 0.928034i | \(-0.621497\pi\) | ||||
−0.372494 | + | 0.928034i | \(0.621497\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 173.036i | 0.339953i | 0.985448 | + | 0.169977i | \(0.0543693\pi\) | ||||
−0.985448 | + | 0.169977i | \(0.945631\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −103.816 | −0.203163 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 791.052i | − 1.53008i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 455.116i | 0.873543i | 0.899572 | + | 0.436772i | \(0.143878\pi\) | ||||
−0.899572 | + | 0.436772i | \(0.856122\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 295.395i | 0.564809i | 0.959295 | + | 0.282404i | \(0.0911320\pi\) | ||||
−0.959295 | + | 0.282404i | \(0.908868\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 355.935 | 0.675398 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −504.684 | −0.954034 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 470.245 | 0.882260 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 173.335i | − 0.321587i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 906.394 | 1.67541 | 0.837703 | − | 0.546127i | \(-0.183898\pi\) | ||||
0.837703 | + | 0.546127i | \(0.183898\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 672.921i | − 1.23020i | −0.788448 | − | 0.615101i | \(-0.789115\pi\) | ||||
0.788448 | − | 0.615101i | \(-0.210885\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 553.627i | 1.00477i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 586.658i | − 1.06086i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 870.336 | 1.56254 | 0.781271 | − | 0.624192i | \(-0.214572\pi\) | ||||
0.781271 | + | 0.624192i | \(0.214572\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.7893 | −0.0210900 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.6320 | −0.0419751 | −0.0209875 | − | 0.999780i | \(-0.506681\pi\) | ||||
−0.0209875 | + | 0.999780i | \(0.506681\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 295.273i | − 0.518933i | −0.965752 | − | 0.259466i | \(-0.916453\pi\) | ||||
0.965752 | − | 0.259466i | \(-0.0835467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 893.920 | 1.56553 | 0.782767 | − | 0.622314i | \(-0.213807\pi\) | ||||
0.782767 | + | 0.622314i | \(0.213807\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 264.763i | − 0.458861i | −0.973325 | − | 0.229431i | \(-0.926314\pi\) | ||||
0.973325 | − | 0.229431i | \(-0.0736864\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 247.897i | − 0.426673i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 881.526i | − 1.51205i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 791.885 | 1.34904 | 0.674519 | − | 0.738258i | \(-0.264351\pi\) | ||||
0.674519 | + | 0.738258i | \(0.264351\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −565.737 | −0.960504 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.82388 | 0.00307567 | 0.00153784 | − | 0.999999i | \(-0.499510\pi\) | ||||
0.00153784 | + | 0.999999i | \(0.499510\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 758.204i | 1.26578i | 0.774241 | + | 0.632891i | \(0.218132\pi\) | ||||
−0.774241 | + | 0.632891i | \(0.781868\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −283.579 | −0.471845 | −0.235922 | − | 0.971772i | \(-0.575811\pi\) | ||||
−0.235922 | + | 0.971772i | \(0.575811\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 167.828i | 0.276488i | 0.990398 | + | 0.138244i | \(0.0441459\pi\) | ||||
−0.990398 | + | 0.138244i | \(0.955854\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 990.507i | − 1.62112i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 395.698i | 0.645510i | 0.946483 | + | 0.322755i | \(0.104609\pi\) | ||||
−0.946483 | + | 0.322755i | \(0.895391\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 855.190 | 1.38604 | 0.693022 | − | 0.720916i | \(-0.256279\pi\) | ||||
0.693022 | + | 0.720916i | \(0.256279\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −308.158 | −0.497832 | −0.248916 | − | 0.968525i | \(-0.580074\pi\) | ||||
−0.248916 | + | 0.968525i | \(0.580074\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 636.079 | 1.02099 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1059.99i | − 1.68520i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 344.974 | 0.546709 | 0.273355 | − | 0.961913i | \(-0.411867\pi\) | ||||
0.273355 | + | 0.961913i | \(0.411867\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 217.040i | − 0.340722i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 202.641i | − 0.316133i | −0.987428 | − | 0.158066i | \(-0.949474\pi\) | ||||
0.987428 | − | 0.158066i | \(-0.0505260\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 724.605i | − 1.12691i | −0.826146 | − | 0.563456i | \(-0.809471\pi\) | ||||
0.826146 | − | 0.563456i | \(-0.190529\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 125.679 | 0.194249 | 0.0971243 | − | 0.995272i | \(-0.469036\pi\) | ||||
0.0971243 | + | 0.995272i | \(0.469036\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1030.89 | −1.58843 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −551.226 | −0.844144 | −0.422072 | − | 0.906562i | \(-0.638697\pi\) | ||||
−0.422072 | + | 0.906562i | \(0.638697\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 801.765i | − 1.21664i | −0.793692 | − | 0.608320i | \(-0.791844\pi\) | ||||
0.793692 | − | 0.608320i | \(-0.208156\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −529.079 | −0.800422 | −0.400211 | − | 0.916423i | \(-0.631063\pi\) | ||||
−0.400211 | + | 0.916423i | \(0.631063\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 101.210i | 0.151739i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 613.918i | 0.914929i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 413.395i | − 0.614257i | −0.951668 | − | 0.307129i | \(-0.900632\pi\) | ||||
0.951668 | − | 0.307129i | \(-0.0993682\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 359.936 | 0.531663 | 0.265832 | − | 0.964019i | \(-0.414353\pi\) | ||||
0.265832 | + | 0.964019i | \(0.414353\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 477.499 | 0.703239 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.5484 | 0.0315496 | 0.0157748 | − | 0.999876i | \(-0.494979\pi\) | ||||
0.0157748 | + | 0.999876i | \(0.494979\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 1103.79i | − 1.60202i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −384.921 | −0.557049 | −0.278525 | − | 0.960429i | \(-0.589845\pi\) | ||||
−0.278525 | + | 0.960429i | \(0.589845\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 694.736i | 0.996752i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 439.057i | 0.626330i | 0.949699 | + | 0.313165i | \(0.101389\pi\) | ||||
−0.949699 | + | 0.313165i | \(0.898611\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1684.79i | 2.39657i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 709.080 | 1.00294 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 126.421 | 0.178309 | 0.0891547 | − | 0.996018i | \(-0.471583\pi\) | ||||
0.0891547 | + | 0.996018i | \(0.471583\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −103.424 | −0.145054 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 571.715i | 0.795153i | 0.917569 | + | 0.397576i | \(0.130149\pi\) | ||||
−0.917569 | + | 0.397576i | \(0.869851\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 627.159 | 0.869846 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 841.038i | − 1.15686i | −0.815731 | − | 0.578431i | \(-0.803665\pi\) | ||||
0.815731 | − | 0.578431i | \(-0.196335\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 17.4175i | − 0.0238269i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 494.749i | − 0.674965i | −0.941332 | − | 0.337483i | \(-0.890425\pi\) | ||||
0.941332 | − | 0.337483i | \(-0.109575\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −697.206 | −0.946006 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1263.97 | −1.71038 | −0.855191 | − | 0.518312i | \(-0.826561\pi\) | ||||
−0.855191 | + | 0.518312i | \(0.826561\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 956.343 | 1.28714 | 0.643568 | − | 0.765389i | \(-0.277453\pi\) | ||||
0.643568 | + | 0.765389i | \(0.277453\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 512.131i | 0.683752i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1121.66 | −1.49355 | −0.746776 | − | 0.665076i | \(-0.768399\pi\) | ||||
−0.746776 | + | 0.665076i | \(0.768399\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 466.433i | − 0.616160i | −0.951360 | − | 0.308080i | \(-0.900313\pi\) | ||||
0.951360 | − | 0.308080i | \(-0.0996865\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 1223.41i | − 1.60763i | −0.594880 | − | 0.803814i | \(-0.702801\pi\) | ||||
0.594880 | − | 0.803814i | \(-0.297199\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 663.184i | − 0.869180i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1290.82 | −1.68295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1290.63 | 1.67832 | 0.839162 | − | 0.543882i | \(-0.183046\pi\) | ||||
0.839162 | + | 0.543882i | \(0.183046\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 329.455 | 0.426204 | 0.213102 | − | 0.977030i | \(-0.431643\pi\) | ||||
0.213102 | + | 0.977030i | \(0.431643\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1104.24i | − 1.41751i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 220.894 | 0.282835 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1506.13i | − 1.91376i | −0.290480 | − | 0.956881i | \(-0.593815\pi\) | ||||
0.290480 | − | 0.956881i | \(-0.406185\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 605.245i | 0.765165i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 768.710i | 0.969370i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −250.874 | −0.314773 | −0.157387 | − | 0.987537i | \(-0.550307\pi\) | ||||
−0.157387 | + | 0.987537i | \(0.550307\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1463.37 | 1.83150 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 173.577 | 0.216160 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1097.02i | 1.35602i | 0.735053 | + | 0.678010i | \(0.237157\pi\) | ||||
−0.735053 | + | 0.678010i | \(0.762843\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −221.473 | −0.273087 | −0.136543 | − | 0.990634i | \(-0.543599\pi\) | ||||
−0.136543 | + | 0.990634i | \(0.543599\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.6840i | 0.0338849i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1003.92i | 1.22281i | 0.791319 | + | 0.611403i | \(0.209395\pi\) | ||||
−0.791319 | + | 0.611403i | \(0.790605\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 335.013i | − 0.407063i | −0.979068 | − | 0.203531i | \(-0.934758\pi\) | ||||
0.979068 | − | 0.203531i | \(-0.0652419\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1004.72 | 1.21490 | 0.607451 | − | 0.794357i | \(-0.292192\pi\) | ||||
0.607451 | + | 0.794357i | \(0.292192\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −676.763 | −0.816361 | −0.408180 | − | 0.912901i | \(-0.633837\pi\) | ||||
−0.408180 | + | 0.912901i | \(0.633837\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 320.653 | 0.384938 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 621.286i | − 0.740507i | −0.928931 | − | 0.370254i | \(-0.879271\pi\) | ||||
0.928931 | − | 0.370254i | \(-0.120729\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 419.736 | 0.499092 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 202.146i | 0.238661i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 308.001i | 0.361928i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 544.591i | 0.638443i | 0.947680 | + | 0.319221i | \(0.103421\pi\) | ||||
−0.947680 | + | 0.319221i | \(0.896579\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 362.149 | 0.422578 | 0.211289 | − | 0.977424i | \(-0.432234\pi\) | ||||
0.211289 | + | 0.977424i | \(0.432234\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.6840 | 0.0252433 | 0.0126216 | − | 0.999920i | \(-0.495982\pi\) | ||||
0.0126216 | + | 0.999920i | \(0.495982\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −220.300 | −0.255273 | −0.127636 | − | 0.991821i | \(-0.540739\pi\) | ||||
−0.127636 | + | 0.991821i | \(0.540739\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 980.868i | 1.12873i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −872.999 | −1.00230 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1136.41i | 1.29579i | 0.761730 | + | 0.647895i | \(0.224350\pi\) | ||||
−0.761730 | + | 0.647895i | \(0.775650\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 711.758i | 0.807898i | 0.914782 | + | 0.403949i | \(0.132363\pi\) | ||||
−0.914782 | + | 0.403949i | \(0.867637\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 536.394i | 0.607468i | 0.952757 | + | 0.303734i | \(0.0982334\pi\) | ||||
−0.952757 | + | 0.303734i | \(0.901767\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1463.95 | −1.65045 | −0.825227 | − | 0.564801i | \(-0.808953\pi\) | ||||
−0.825227 | + | 0.564801i | \(0.808953\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −578.211 | −0.650406 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2325.93 | −2.60463 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 430.479i | − 0.478842i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1630.74 | 1.80992 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 855.657i | 0.943392i | 0.881761 | + | 0.471696i | \(0.156358\pi\) | ||||
−0.881761 | + | 0.471696i | \(0.843642\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1581.02i | − 1.73547i | −0.497024 | − | 0.867737i | \(-0.665574\pi\) | ||||
0.497024 | − | 0.867737i | \(-0.334426\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 414.474i | 0.453969i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −771.360 | −0.841178 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1489.08 | 1.62033 | 0.810163 | − | 0.586205i | \(-0.199379\pi\) | ||||
0.810163 | + | 0.586205i | \(0.199379\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 276.590 | 0.299664 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 736.990i | 0.793316i | 0.917966 | + | 0.396658i | \(0.129830\pi\) | ||||
−0.917966 | + | 0.396658i | \(0.870170\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −509.658 | −0.547431 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1550.05i | 1.65427i | 0.562003 | + | 0.827135i | \(0.310031\pi\) | ||||
−0.562003 | + | 0.827135i | \(0.689969\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 628.711i | 0.668131i | 0.942550 | + | 0.334065i | \(0.108421\pi\) | ||||
−0.942550 | + | 0.334065i | \(0.891579\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 201.869i | − 0.214071i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1498.73 | 1.58261 | 0.791304 | − | 0.611423i | \(-0.209402\pi\) | ||||
0.791304 | + | 0.611423i | \(0.209402\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 217.342 | 0.229022 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −224.748 | −0.235832 | −0.117916 | − | 0.993024i | \(-0.537621\pi\) | ||||
−0.117916 | + | 0.993024i | \(0.537621\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1464.72i | 1.52734i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −521.105 | −0.542253 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 233.986i | 0.241972i | 0.992654 | + | 0.120986i | \(0.0386055\pi\) | ||||
−0.992654 | + | 0.120986i | \(0.961394\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 691.940i | − 0.712606i | −0.934371 | − | 0.356303i | \(-0.884037\pi\) | ||||
0.934371 | − | 0.356303i | \(-0.115963\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 86.9224i | 0.0893344i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −395.571 | −0.404883 | −0.202442 | − | 0.979294i | \(-0.564888\pi\) | ||||
−0.202442 | + | 0.979294i | \(0.564888\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1063.50 | −1.08631 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.82388 | −0.00185542 | −0.000927709 | − | 1.00000i | \(-0.500295\pi\) | ||||
−0.000927709 | 1.00000i | \(0.500295\pi\) | ||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.06098i | 0.00511727i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 506.316 | 0.510914 | 0.255457 | − | 0.966820i | \(-0.417774\pi\) | ||||
0.255457 | + | 0.966820i | \(0.417774\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 295.670i | − 0.296560i | −0.988945 | − | 0.148280i | \(-0.952626\pi\) | ||||
0.988945 | − | 0.148280i | \(-0.0473737\pi\) | |||||||
\(998\) | 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 | 900.3.b.b.449.5 | 8 | ||
3.2 | odd | 2 | inner | 900.3.b.b.449.6 | 8 | ||
4.3 | odd | 2 | 3600.3.c.k.449.4 | 8 | |||
5.2 | odd | 4 | 900.3.g.d.701.1 | 4 | |||
5.3 | odd | 4 | 180.3.g.a.161.2 | ✓ | 4 | ||
5.4 | even | 2 | inner | 900.3.b.b.449.3 | 8 | ||
12.11 | even | 2 | 3600.3.c.k.449.3 | 8 | |||
15.2 | even | 4 | 900.3.g.d.701.2 | 4 | |||
15.8 | even | 4 | 180.3.g.a.161.4 | yes | 4 | ||
15.14 | odd | 2 | inner | 900.3.b.b.449.4 | 8 | ||
20.3 | even | 4 | 720.3.l.c.161.1 | 4 | |||
20.7 | even | 4 | 3600.3.l.n.1601.4 | 4 | |||
20.19 | odd | 2 | 3600.3.c.k.449.6 | 8 | |||
40.3 | even | 4 | 2880.3.l.f.1601.3 | 4 | |||
40.13 | odd | 4 | 2880.3.l.b.1601.4 | 4 | |||
45.13 | odd | 12 | 1620.3.o.f.1241.1 | 8 | |||
45.23 | even | 12 | 1620.3.o.f.1241.3 | 8 | |||
45.38 | even | 12 | 1620.3.o.f.701.1 | 8 | |||
45.43 | odd | 12 | 1620.3.o.f.701.3 | 8 | |||
60.23 | odd | 4 | 720.3.l.c.161.3 | 4 | |||
60.47 | odd | 4 | 3600.3.l.n.1601.3 | 4 | |||
60.59 | even | 2 | 3600.3.c.k.449.5 | 8 | |||
120.53 | even | 4 | 2880.3.l.b.1601.2 | 4 | |||
120.83 | odd | 4 | 2880.3.l.f.1601.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.g.a.161.2 | ✓ | 4 | 5.3 | odd | 4 | ||
180.3.g.a.161.4 | yes | 4 | 15.8 | even | 4 | ||
720.3.l.c.161.1 | 4 | 20.3 | even | 4 | |||
720.3.l.c.161.3 | 4 | 60.23 | odd | 4 | |||
900.3.b.b.449.3 | 8 | 5.4 | even | 2 | inner | ||
900.3.b.b.449.4 | 8 | 15.14 | odd | 2 | inner | ||
900.3.b.b.449.5 | 8 | 1.1 | even | 1 | trivial | ||
900.3.b.b.449.6 | 8 | 3.2 | odd | 2 | inner | ||
900.3.g.d.701.1 | 4 | 5.2 | odd | 4 | |||
900.3.g.d.701.2 | 4 | 15.2 | even | 4 | |||
1620.3.o.f.701.1 | 8 | 45.38 | even | 12 | |||
1620.3.o.f.701.3 | 8 | 45.43 | odd | 12 | |||
1620.3.o.f.1241.1 | 8 | 45.13 | odd | 12 | |||
1620.3.o.f.1241.3 | 8 | 45.23 | even | 12 | |||
2880.3.l.b.1601.2 | 4 | 120.53 | even | 4 | |||
2880.3.l.b.1601.4 | 4 | 40.13 | odd | 4 | |||
2880.3.l.f.1601.1 | 4 | 120.83 | odd | 4 | |||
2880.3.l.f.1601.3 | 4 | 40.3 | even | 4 | |||
3600.3.c.k.449.3 | 8 | 12.11 | even | 2 | |||
3600.3.c.k.449.4 | 8 | 4.3 | odd | 2 | |||
3600.3.c.k.449.5 | 8 | 60.59 | even | 2 | |||
3600.3.c.k.449.6 | 8 | 20.19 | odd | 2 | |||
3600.3.l.n.1601.3 | 4 | 60.47 | odd | 4 | |||
3600.3.l.n.1601.4 | 4 | 20.7 | even | 4 |