Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4680,2,Mod(2809,4680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4680.2809");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4680 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4680.l (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: | \(37.3699881460\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.57815240704.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 89x^{4} - 170x^{3} + 162x^{2} - 72x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1560) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2809.6 | ||
Root | \(0.594137 + 0.594137i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4680.2809 |
Dual form | 4680.2.l.g.2809.5 |
$q$-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 \(\left(\mathbb{Z}/4680\mathbb{Z}\right)^\times\).
\(n\) | \(937\) | \(1081\) | \(2081\) | \(2341\) | \(3511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 0.594137 | + | 2.15569i | 0.265706 | + | 0.964054i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.92778i | − | 1.86252i | −0.364349 | − | 0.931262i | \(-0.618709\pi\) | ||
0.364349 | − | 0.931262i | \(-0.381291\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.38360 | 0.417172 | 0.208586 | − | 0.978004i | \(-0.433114\pi\) | ||||
0.208586 | + | 0.978004i | \(0.433114\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.00000i | − | 0.277350i | ||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.195329i | − | 0.0473741i | −0.999719 | − | 0.0236871i | \(-0.992459\pi\) | ||
0.999719 | − | 0.0236871i | \(-0.00754053\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.19533i | − | 0.457758i | −0.973455 | − | 0.228879i | \(-0.926494\pi\) | ||
0.973455 | − | 0.228879i | \(-0.0735060\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.29400 | + | 2.56155i | −0.858800 | + | 0.512311i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.49966 | 1.39265 | 0.696326 | − | 0.717726i | \(-0.254817\pi\) | ||||
0.696326 | + | 0.717726i | \(0.254817\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.6228 | − | 2.92778i | 1.79557 | − | 0.494885i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.05088i | 0.994759i | 0.867533 | + | 0.497379i | \(0.165704\pi\) | ||||
−0.867533 | + | 0.497379i | \(0.834296\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.11605 | 0.330472 | 0.165236 | − | 0.986254i | \(-0.447161\pi\) | ||||
0.165236 | + | 0.986254i | \(0.447161\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.49966i | − | 0.533692i | −0.963739 | − | 0.266846i | \(-0.914018\pi\) | ||
0.963739 | − | 0.266846i | \(-0.0859816\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 2.31138i | − | 0.337150i | −0.985689 | − | 0.168575i | \(-0.946084\pi\) | ||
0.985689 | − | 0.168575i | \(-0.0539165\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −17.2830 | −2.46900 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.05088i | − | 0.831153i | −0.909558 | − | 0.415576i | \(-0.863580\pi\) | ||
0.909558 | − | 0.415576i | \(-0.136420\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.822051 | + | 2.98262i | 0.110845 | + | 0.402176i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.43449 | 1.22827 | 0.614133 | − | 0.789203i | \(-0.289506\pi\) | ||||
0.614133 | + | 0.789203i | \(0.289506\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.69498 | −0.473094 | −0.236547 | − | 0.971620i | \(-0.576016\pi\) | ||||
−0.236547 | + | 0.971620i | \(0.576016\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.15569 | − | 0.594137i | 0.267380 | − | 0.0736937i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.6228i | − | 1.54212i | −0.636765 | − | 0.771058i | \(-0.719728\pi\) | ||
0.636765 | − | 0.771058i | \(-0.280272\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.9716 | −1.65812 | −0.829062 | − | 0.559156i | \(-0.811125\pi\) | ||||
−0.829062 | + | 0.559156i | \(0.811125\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.73245i | − | 0.553891i | −0.960886 | − | 0.276946i | \(-0.910678\pi\) | ||
0.960886 | − | 0.276946i | \(-0.0893222\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 6.81809i | − | 0.776993i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.07153 | 0.908119 | 0.454059 | − | 0.890971i | \(-0.349975\pi\) | ||||
0.454059 | + | 0.890971i | \(0.349975\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 13.3997i | − | 1.47081i | −0.677627 | − | 0.735406i | \(-0.736992\pi\) | ||
0.677627 | − | 0.735406i | \(-0.263008\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.421068 | − | 0.116052i | 0.0456712 | − | 0.0125876i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.02770 | 0.320936 | 0.160468 | − | 0.987041i | \(-0.448700\pi\) | ||||
0.160468 | + | 0.987041i | \(0.448700\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.92778 | −0.516571 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.01612i | 0.610845i | 0.952217 | + | 0.305422i | \(0.0987977\pi\) | ||||
−0.952217 | + | 0.305422i | \(0.901202\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.10900 | 0.309357 | 0.154678 | − | 0.987965i | \(-0.450566\pi\) | ||||
0.154678 | + | 0.987965i | \(0.450566\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.8690i | − | 1.66215i | −0.556161 | − | 0.831075i | \(-0.687726\pi\) | ||
0.556161 | − | 0.831075i | \(-0.312274\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.1946i | 1.66227i | 0.556072 | + | 0.831134i | \(0.312308\pi\) | ||||
−0.556072 | + | 0.831134i | \(0.687692\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.76721 | −0.839746 | −0.419873 | − | 0.907583i | \(-0.637925\pi\) | ||||
−0.419873 | + | 0.907583i | \(0.637925\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.46490i | 0.702238i | 0.936331 | + | 0.351119i | \(0.114199\pi\) | ||||
−0.936331 | + | 0.351119i | \(0.885801\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.73245 | − | 1.30433i | 0.441303 | − | 0.121629i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.962536 | −0.0882355 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.08564 | −0.825967 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.07314 | − | 7.73462i | −0.722084 | − | 0.691806i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.1231i | − | 0.987016i | −0.869741 | − | 0.493508i | \(-0.835714\pi\) | ||
0.869741 | − | 0.493508i | \(-0.164286\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.82080 | 0.159084 | 0.0795418 | − | 0.996832i | \(-0.474654\pi\) | ||||
0.0795418 | + | 0.996832i | \(0.474654\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.70204i | 0.743465i | 0.928340 | + | 0.371733i | \(0.121236\pi\) | ||||
−0.928340 | + | 0.371733i | \(0.878764\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.81809 | −0.578303 | −0.289151 | − | 0.957283i | \(-0.593373\pi\) | ||||
−0.289151 | + | 0.957283i | \(0.593373\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1.38360i | − | 0.115703i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.45583 | + | 16.1669i | 0.370036 | + | 1.34259i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.48537 | −0.613225 | −0.306613 | − | 0.951834i | \(-0.599196\pi\) | ||||
−0.306613 | + | 0.951834i | \(0.599196\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.8549 | 1.04611 | 0.523057 | − | 0.852298i | \(-0.324791\pi\) | ||||
0.523057 | + | 0.852298i | \(0.324791\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.7318i | − | 1.41515i | −0.706639 | − | 0.707574i | \(-0.749790\pi\) | ||
0.706639 | − | 0.707574i | \(-0.250210\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.8181 | −0.852585 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 18.1385i | − | 1.42072i | −0.703838 | − | 0.710360i | \(-0.748532\pi\) | ||
0.703838 | − | 0.710360i | \(-0.251468\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.06517i | 0.314572i | 0.987553 | + | 0.157286i | \(0.0502745\pi\) | ||||
−0.987553 | + | 0.157286i | \(0.949726\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 23.2455i | − | 1.76732i | −0.468125 | − | 0.883662i | \(-0.655070\pi\) | ||
0.468125 | − | 0.883662i | \(-0.344930\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.6228 | + | 21.1599i | 0.954191 | + | 1.59954i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.1224 | 1.05556 | 0.527779 | − | 0.849381i | \(-0.323025\pi\) | ||||
0.527779 | + | 0.849381i | \(0.323025\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.67433 | 0.273111 | 0.136556 | − | 0.990632i | \(-0.456397\pi\) | ||||
0.136556 | + | 0.990632i | \(0.456397\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.0438 | + | 3.59506i | −0.959001 | + | 0.264314i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.270257i | − | 0.0197632i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.8549 | 1.21958 | 0.609788 | − | 0.792565i | \(-0.291255\pi\) | ||||
0.609788 | + | 0.792565i | \(0.291255\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 6.53712i | − | 0.470552i | −0.971929 | − | 0.235276i | \(-0.924401\pi\) | ||
0.971929 | − | 0.235276i | \(-0.0755994\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 25.7890i | − | 1.83739i | −0.394967 | − | 0.918695i | \(-0.629244\pi\) | ||
0.394967 | − | 0.918695i | \(-0.370756\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.9646 | 1.20259 | 0.601293 | − | 0.799029i | \(-0.294653\pi\) | ||||
0.601293 | + | 0.799029i | \(0.294653\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 36.9566i | − | 2.59385i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.25723 | + | 4.56155i | 0.0878085 | + | 0.318593i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.4577 | −1.82142 | −0.910710 | − | 0.413046i | \(-0.864465\pi\) | ||||
−0.910710 | + | 0.413046i | \(0.864465\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.54417 | − | 2.07928i | 0.514508 | − | 0.141805i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.195329 | −0.0131392 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.02065i | 0.135313i | 0.997709 | + | 0.0676564i | \(0.0215522\pi\) | ||||
−0.997709 | + | 0.0676564i | \(0.978448\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.7904i | 1.18079i | 0.807115 | + | 0.590395i | \(0.201028\pi\) | ||||
−0.807115 | + | 0.590395i | \(0.798972\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.3339 | 1.21154 | 0.605768 | − | 0.795641i | \(-0.292866\pi\) | ||||
0.605768 | + | 0.795641i | \(0.292866\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 23.0361i | − | 1.50914i | −0.656217 | − | 0.754572i | \(-0.727844\pi\) | ||
0.656217 | − | 0.754572i | \(-0.272156\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.98262 | − | 1.37328i | 0.325030 | − | 0.0895828i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.986402 | −0.0638051 | −0.0319025 | − | 0.999491i | \(-0.510157\pi\) | ||||
−0.0319025 | + | 0.999491i | \(0.510157\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.52031 | 0.0979316 | 0.0489658 | − | 0.998800i | \(-0.484407\pi\) | ||||
0.0489658 | + | 0.998800i | \(0.484407\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.2685 | − | 37.2568i | −0.656028 | − | 2.38025i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.6763 | −0.737005 | −0.368502 | − | 0.929627i | \(-0.620129\pi\) | ||||
−0.368502 | + | 0.929627i | \(0.620129\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.03746i | − | 0.190964i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.00069i | 0.187178i | 0.995611 | + | 0.0935889i | \(0.0298339\pi\) | ||||
−0.995611 | + | 0.0935889i | \(0.970166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29.8174 | 1.85276 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.8683i | 1.59511i | 0.603248 | + | 0.797553i | \(0.293873\pi\) | ||||
−0.603248 | + | 0.797553i | \(0.706127\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.0438 | − | 3.59506i | 0.801276 | − | 0.220843i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.1090 | 0.677328 | 0.338664 | − | 0.940907i | \(-0.390025\pi\) | ||||
0.338664 | + | 0.940907i | \(0.390025\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.9859 | −0.849582 | −0.424791 | − | 0.905291i | \(-0.639653\pi\) | ||||
−0.424791 | + | 0.905291i | \(0.639653\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.94120 | + | 3.54417i | −0.358268 | + | 0.213722i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.0529i | 0.604020i | 0.953305 | + | 0.302010i | \(0.0976576\pi\) | ||||
−0.953305 | + | 0.302010i | \(0.902342\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.6318 | 1.17114 | 0.585568 | − | 0.810623i | \(-0.300871\pi\) | ||||
0.585568 | + | 0.810623i | \(0.300871\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.5667i | 1.51978i | 0.650051 | + | 0.759890i | \(0.274747\pi\) | ||||
−0.650051 | + | 0.759890i | \(0.725253\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 10.4274i | − | 0.615512i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9618 | 0.997756 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.71614i | 0.392361i | 0.980568 | + | 0.196181i | \(0.0628539\pi\) | ||||
−0.980568 | + | 0.196181i | \(0.937146\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.60538 | + | 20.3378i | 0.326358 | + | 1.18411i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.19533 | −0.126959 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.2455 | −0.994015 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.19533 | − | 7.96524i | −0.125704 | − | 0.456088i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.2689i | 0.814368i | 0.913346 | + | 0.407184i | \(0.133489\pi\) | ||||
−0.913346 | + | 0.407184i | \(0.866511\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.15786 | 0.405885 | 0.202943 | − | 0.979191i | \(-0.434950\pi\) | ||||
0.202943 | + | 0.979191i | \(0.434950\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 21.6568i | − | 1.22412i | −0.790813 | − | 0.612058i | \(-0.790342\pi\) | ||
0.790813 | − | 0.612058i | \(-0.209658\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.0232i | 1.63010i | 0.579388 | + | 0.815052i | \(0.303292\pi\) | ||||
−0.579388 | + | 0.815052i | \(0.696708\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.3765 | 0.580975 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.56155 | + | 4.29400i | 0.142089 | + | 0.238188i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.3900 | −0.627949 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.8683 | 1.20199 | 0.600995 | − | 0.799253i | \(-0.294771\pi\) | ||||
0.600995 | + | 0.799253i | \(0.294771\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 27.2108 | − | 7.49966i | 1.48668 | − | 0.409750i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 22.2991i | − | 1.21471i | −0.794431 | − | 0.607355i | \(-0.792231\pi\) | ||
0.794431 | − | 0.607355i | \(-0.207769\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 50.6723i | 2.73605i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 22.9199i | − | 1.23040i | −0.788370 | − | 0.615201i | \(-0.789075\pi\) | ||
0.788370 | − | 0.615201i | \(-0.210925\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.75310 | −0.361485 | −0.180743 | − | 0.983530i | \(-0.557850\pi\) | ||||
−0.180743 | + | 0.983530i | \(0.557850\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.07859i | 0.163857i | 0.996638 | + | 0.0819283i | \(0.0261079\pi\) | ||||
−0.996638 | + | 0.0819283i | \(0.973892\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.30105 | − | 30.1185i | −0.440574 | − | 1.59852i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.0091 | −0.686592 | −0.343296 | − | 0.939227i | \(-0.611543\pi\) | ||||
−0.343296 | + | 0.939227i | \(0.611543\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.2017 | − | 2.81173i | 0.533981 | − | 0.147172i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 27.4041i | − | 1.43048i | −0.698878 | − | 0.715241i | \(-0.746317\pi\) | ||
0.698878 | − | 0.715241i | \(-0.253683\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −29.8174 | −1.54804 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 19.9573i | − | 1.03335i | −0.856181 | − | 0.516675i | \(-0.827169\pi\) | ||
0.856181 | − | 0.516675i | \(-0.172831\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7.49966i | − | 0.386252i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.2042 | 1.50012 | 0.750060 | − | 0.661370i | \(-0.230025\pi\) | ||||
0.750060 | + | 0.661370i | \(0.230025\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.5764i | 0.795918i | 0.917403 | + | 0.397959i | \(0.130281\pi\) | ||||
−0.917403 | + | 0.397959i | \(0.869719\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.6977 | − | 4.05088i | 0.749064 | − | 0.206452i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.0529 | 1.01672 | 0.508361 | − | 0.861144i | \(-0.330251\pi\) | ||||
0.508361 | + | 0.861144i | \(0.330251\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.428810 | −0.0216859 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.79560 | + | 17.3997i | 0.241293 | + | 0.875475i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 30.9057i | − | 1.55112i | −0.631277 | − | 0.775558i | \(-0.717469\pi\) | ||
0.631277 | − | 0.775558i | \(-0.282531\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.9902 | 0.598764 | 0.299382 | − | 0.954133i | \(-0.403220\pi\) | ||||
0.299382 | + | 0.954133i | \(0.403220\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.37202i | 0.414986i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −39.2169 | −1.93915 | −0.969577 | − | 0.244788i | \(-0.921282\pi\) | ||||
−0.969577 | + | 0.244788i | \(0.921282\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 46.4910i | − | 2.28767i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.8857 | − | 7.96128i | 1.41794 | − | 0.390804i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.8621 | −0.872621 | −0.436310 | − | 0.899796i | \(-0.643715\pi\) | ||||
−0.436310 | + | 0.899796i | \(0.643715\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.8690 | 1.40699 | 0.703494 | − | 0.710701i | \(-0.251622\pi\) | ||||
0.703494 | + | 0.710701i | \(0.251622\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.500344 | + | 0.838741i | 0.0242703 | + | 0.0406849i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.2081i | 0.881150i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.0373 | −0.820657 | −0.410329 | − | 0.911938i | \(-0.634586\pi\) | ||||
−0.410329 | + | 0.911938i | \(0.634586\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.1554i | 1.40112i | 0.713595 | + | 0.700558i | \(0.247066\pi\) | ||||
−0.713595 | + | 0.700558i | \(0.752934\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.2087 | 1.10769 | 0.553847 | − | 0.832619i | \(-0.313159\pi\) | ||||
0.553847 | + | 0.832619i | \(0.313159\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 14.9484i | − | 0.710221i | −0.934824 | − | 0.355111i | \(-0.884443\pi\) | ||
0.934824 | − | 0.355111i | \(-0.115557\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.79887 | + | 6.52679i | 0.0852748 | + | 0.309400i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −42.2023 | −1.99165 | −0.995826 | − | 0.0912763i | \(-0.970905\pi\) | ||||
−0.995826 | + | 0.0912763i | \(0.970905\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.92778 | 0.137864 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.92778 | − | 10.6228i | −0.137256 | − | 0.498003i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 15.1599i | − | 0.709149i | −0.935028 | − | 0.354575i | \(-0.884626\pi\) | ||
0.935028 | − | 0.354575i | \(-0.115374\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.848501 | 0.0395186 | 0.0197593 | − | 0.999805i | \(-0.493710\pi\) | ||||
0.0197593 | + | 0.999805i | \(0.493710\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13.8109i | − | 0.641845i | −0.947105 | − | 0.320922i | \(-0.896007\pi\) | ||
0.947105 | − | 0.320922i | \(-0.103993\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 10.5165i | − | 0.486644i | −0.969946 | − | 0.243322i | \(-0.921763\pi\) | ||
0.969946 | − | 0.243322i | \(-0.0782372\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −62.2022 | −2.87223 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 4.84214i | − | 0.222642i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.41905 | −0.293294 | −0.146647 | − | 0.989189i | \(-0.546848\pi\) | ||||
−0.146647 | + | 0.989189i | \(0.546848\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.05088 | 0.275897 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.9689 | + | 3.57440i | −0.588887 | + | 0.162305i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.5492i | 1.06711i | 0.845764 | + | 0.533557i | \(0.179145\pi\) | ||||
−0.845764 | + | 0.533557i | \(0.820855\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.99346 | −0.180222 | −0.0901111 | − | 0.995932i | \(-0.528722\pi\) | ||||
−0.0901111 | + | 0.995932i | \(0.528722\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.46490i | − | 0.0659756i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 68.8490i | 3.08830i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.30231 | 0.237364 | 0.118682 | − | 0.992932i | \(-0.462133\pi\) | ||||
0.118682 | + | 0.992932i | \(0.462133\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.8408i | 1.55347i | 0.629826 | + | 0.776736i | \(0.283126\pi\) | ||||
−0.629826 | + | 0.776736i | \(0.716874\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.84717 | + | 6.70204i | 0.0821981 | + | 0.298237i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 42.2526 | 1.87281 | 0.936406 | − | 0.350918i | \(-0.114130\pi\) | ||||
0.936406 | + | 0.350918i | \(0.114130\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.3205 | −1.03164 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 36.3643 | − | 10.0225i | 1.60240 | − | 0.441644i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 3.19803i | − | 0.140649i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.65098 | 0.116141 | 0.0580707 | − | 0.998312i | \(-0.481505\pi\) | ||||
0.0580707 | + | 0.998312i | \(0.481505\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.6014i | 1.38183i | 0.722934 | + | 0.690917i | \(0.242793\pi\) | ||||
−0.722934 | + | 0.690917i | \(0.757207\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.1805 | 0.790458 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.11605i | − | 0.0916564i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −37.0663 | + | 10.2160i | −1.60252 | + | 0.441675i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.9128 | −1.03000 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.54852 | 0.0665761 | 0.0332881 | − | 0.999446i | \(-0.489402\pi\) | ||||
0.0332881 | + | 0.999446i | \(0.489402\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.20893 | − | 18.8994i | −0.223126 | − | 0.809561i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 33.2376i | − | 1.42114i | −0.703628 | − | 0.710569i | \(-0.748438\pi\) | ||
0.703628 | − | 0.710569i | \(-0.251562\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 39.7747i | − | 1.69139i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1.64594i | − | 0.0697407i | −0.999392 | − | 0.0348703i | \(-0.988898\pi\) | ||
0.999392 | − | 0.0348703i | \(-0.0111018\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.49966 | −0.148020 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 18.7486i | − | 0.790158i | −0.918647 | − | 0.395079i | \(-0.870717\pi\) | ||
0.918647 | − | 0.395079i | \(-0.129283\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.0920 | + | 4.43518i | −0.676996 | + | 0.186589i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.6543 | −1.74624 | −0.873120 | − | 0.487505i | \(-0.837907\pi\) | ||||
−0.873120 | + | 0.487505i | \(0.837907\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.3184 | −1.14324 | −0.571620 | − | 0.820518i | \(-0.693685\pi\) | ||||
−0.571620 | + | 0.820518i | \(0.693685\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.62345 | + | 9.42674i | 0.234514 | + | 0.393122i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 24.0715i | − | 1.00211i | −0.865415 | − | 0.501056i | \(-0.832945\pi\) | ||
0.865415 | − | 0.501056i | \(-0.167055\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −66.0309 | −2.73942 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 8.37202i | − | 0.346734i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 23.6872i | − | 0.977677i | −0.872374 | − | 0.488839i | \(-0.837421\pi\) | ||
0.872374 | − | 0.488839i | \(-0.162579\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 38.8632i | 1.59592i | 0.602709 | + | 0.797961i | \(0.294088\pi\) | ||||
−0.602709 | + | 0.797961i | \(0.705912\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.571878 | − | 2.07493i | −0.0234447 | − | 0.0850638i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.4783 | 0.755003 | 0.377502 | − | 0.926009i | \(-0.376783\pi\) | ||||
0.377502 | + | 0.926009i | \(0.376783\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.08702 | −0.0851313 | −0.0425656 | − | 0.999094i | \(-0.513553\pi\) | ||||
−0.0425656 | + | 0.999094i | \(0.513553\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.39812 | − | 19.5858i | −0.219465 | − | 0.796277i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 3.59120i | − | 0.145762i | −0.997341 | − | 0.0728812i | \(-0.976781\pi\) | ||
0.997341 | − | 0.0728812i | \(-0.0232194\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.31138 | −0.0935084 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.7895i | 1.00124i | 0.865667 | + | 0.500620i | \(0.166894\pi\) | ||||
−0.865667 | + | 0.500620i | \(0.833106\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.7574i | 0.594112i | 0.954860 | + | 0.297056i | \(0.0960049\pi\) | ||||
−0.954860 | + | 0.297056i | \(0.903995\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.4081 | −1.02124 | −0.510619 | − | 0.859807i | \(-0.670584\pi\) | ||||
−0.510619 | + | 0.859807i | \(0.670584\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 14.9199i | − | 0.597751i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.8769 | − | 21.9986i | 0.475076 | − | 0.879945i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.18191 | 0.0471258 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.46490 | 0.376792 | 0.188396 | − | 0.982093i | \(-0.439671\pi\) | ||||
0.188396 | + | 0.982093i | \(0.439671\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 23.9780 | − | 6.60865i | 0.951537 | − | 0.262256i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.2830i | 0.684777i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.89686 | −0.311907 | −0.155954 | − | 0.987764i | \(-0.549845\pi\) | ||||
−0.155954 | + | 0.987764i | \(0.549845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 16.1204i | − | 0.635727i | −0.948137 | − | 0.317863i | \(-0.897035\pi\) | ||
0.948137 | − | 0.317863i | \(-0.102965\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 2.99616i | − | 0.117791i | −0.998264 | − | 0.0588956i | \(-0.981242\pi\) | ||
0.998264 | − | 0.0588956i | \(-0.0187579\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.0536 | 0.512398 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.5330i | 0.842653i | 0.906909 | + | 0.421326i | \(0.138435\pi\) | ||||
−0.906909 | + | 0.421326i | \(0.861565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.08180 | + | 3.92507i | 0.0422695 | + | 0.153365i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.4429 | 0.679478 | 0.339739 | − | 0.940520i | \(-0.389661\pi\) | ||||
0.339739 | + | 0.940520i | \(0.389661\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.4642 | −0.873756 | −0.436878 | − | 0.899521i | \(-0.643916\pi\) | ||||
−0.436878 | + | 0.899521i | \(0.643916\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 16.4642i | − | 0.637497i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.11239 | −0.197362 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.8122i | 1.80448i | 0.431237 | + | 0.902239i | \(0.358077\pi\) | ||||
−0.431237 | + | 0.902239i | \(0.641923\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.2682i | 1.20173i | 0.799349 | + | 0.600867i | \(0.205178\pi\) | ||||
−0.799349 | + | 0.600867i | \(0.794822\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.6461 | 1.13771 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.1797i | 1.69049i | 0.534381 | + | 0.845244i | \(0.320545\pi\) | ||||
−0.534381 | + | 0.845244i | \(0.679455\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.7589 | + | 5.17021i | −0.716741 | + | 0.197543i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.05088 | −0.230520 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.8360 | −0.982849 | −0.491425 | − | 0.870920i | \(-0.663524\pi\) | ||||
−0.491425 | + | 0.870920i | \(0.663524\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.05088 | − | 14.6977i | −0.153659 | − | 0.557515i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 0.413325i | − | 0.0156558i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.5887 | −0.588777 | −0.294388 | − | 0.955686i | \(-0.595116\pi\) | ||||
−0.294388 | + | 0.955686i | \(0.595116\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 15.3205i | − | 0.576185i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.05541 | 0.152304 | 0.0761521 | − | 0.997096i | \(-0.475737\pi\) | ||||
0.0761521 | + | 0.997096i | \(0.475737\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.98262 | − | 0.822051i | 0.111544 | − | 0.0307430i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.4081 | 0.500038 | 0.250019 | − | 0.968241i | \(-0.419563\pi\) | ||||
0.250019 | + | 0.968241i | \(0.419563\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −83.1265 | −3.09579 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −32.2035 | + | 19.2108i | −1.19601 | + | 0.713470i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 12.9787i | − | 0.481352i | −0.970606 | − | 0.240676i | \(-0.922631\pi\) | ||
0.970606 | − | 0.240676i | \(-0.0773691\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.683583 | −0.0252832 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 49.2410i | 1.81876i | 0.415969 | + | 0.909379i | \(0.363443\pi\) | ||||
−0.415969 | + | 0.909379i | \(0.636557\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 17.4649i | − | 0.643328i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.3359 | 0.416999 | 0.208500 | − | 0.978022i | \(-0.433142\pi\) | ||||
0.208500 | + | 0.978022i | \(0.433142\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 8.07790i | − | 0.296349i | −0.988961 | − | 0.148175i | \(-0.952660\pi\) | ||
0.988961 | − | 0.148175i | \(-0.0473398\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.44734 | − | 16.1361i | −0.162938 | − | 0.591182i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 84.7314 | 3.09602 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.2403 | 0.665598 | 0.332799 | − | 0.942998i | \(-0.392007\pi\) | ||||
0.332799 | + | 0.942998i | \(0.392007\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.63756 | + | 27.7111i | 0.277959 | + | 1.00851i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.71111i | 0.207574i | 0.994600 | + | 0.103787i | \(0.0330960\pi\) | ||||
−0.994600 | + | 0.103787i | \(0.966904\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.6543 | −0.458718 | −0.229359 | − | 0.973342i | \(-0.573663\pi\) | ||||
−0.229359 | + | 0.973342i | \(0.573663\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.2028i | 1.56405i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 9.43449i | − | 0.340660i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.4222 | 0.772505 | 0.386252 | − | 0.922393i | \(-0.373769\pi\) | ||||
0.386252 | + | 0.922393i | \(0.373769\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.0547i | 1.29680i | 0.761300 | + | 0.648399i | \(0.224561\pi\) | ||||
−0.761300 | + | 0.648399i | \(0.775439\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.3312 | −0.691723 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 38.2242 | − | 10.5351i | 1.36428 | − | 0.376014i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 40.8394i | − | 1.45577i | −0.685701 | − | 0.727883i | \(-0.740504\pi\) | ||
0.685701 | − | 0.727883i | \(-0.259496\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36.7853 | 1.30794 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.69498i | 0.131213i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.4691i | 0.902161i | 0.892483 | + | 0.451080i | \(0.148961\pi\) | ||||
−0.892483 | + | 0.451080i | \(0.851039\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.451479 | −0.0159722 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 6.54783i | − | 0.231068i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.42743 | − | 23.3205i | −0.226537 | − | 0.821938i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.7252 | 0.552869 | 0.276435 | − | 0.961033i | \(-0.410847\pi\) | ||||
0.276435 | + | 0.961033i | \(0.410847\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.6815 | −1.74455 | −0.872277 | − | 0.489012i | \(-0.837357\pi\) | ||||
−0.872277 | + | 0.489012i | \(0.837357\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 39.1011 | − | 10.7768i | 1.36965 | − | 0.377494i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.9936 | −0.837384 | −0.418692 | − | 0.908128i | \(-0.637511\pi\) | ||||
−0.418692 | + | 0.908128i | \(0.637511\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.0457i | 0.803321i | 0.915789 | + | 0.401661i | \(0.131567\pi\) | ||||
−0.915789 | + | 0.401661i | \(0.868433\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 49.1195i | − | 1.70805i | −0.520229 | − | 0.854027i | \(-0.674153\pi\) | ||
0.520229 | − | 0.854027i | \(-0.325847\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.54739 | 0.192669 | 0.0963344 | − | 0.995349i | \(-0.469288\pi\) | ||||
0.0963344 | + | 0.995349i | \(0.469288\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.37586i | 0.116967i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.76325 | + | 2.41527i | −0.303265 | + | 0.0835838i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.7106 | −0.991200 | −0.495600 | − | 0.868551i | \(-0.665052\pi\) | ||||
−0.495600 | + | 0.868551i | \(0.665052\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.2448 | 0.939477 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.594137 | − | 2.15569i | −0.0204390 | − | 0.0741580i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 44.7720i | 1.53838i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.2837 | 0.455359 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.7606i | 0.950505i | 0.879849 | + | 0.475253i | \(0.157643\pi\) | ||||
−0.879849 | + | 0.475253i | \(0.842357\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.8869i | 1.22587i | 0.790132 | + | 0.612937i | \(0.210012\pi\) | ||||
−0.790132 | + | 0.612937i | \(0.789988\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.6107 | 0.907944 | 0.453972 | − | 0.891016i | \(-0.350007\pi\) | ||||
0.453972 | + | 0.891016i | \(0.350007\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 20.0366i | − | 0.682054i | −0.940054 | − | 0.341027i | \(-0.889225\pi\) | ||
0.940054 | − | 0.341027i | \(-0.110775\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 50.1101 | − | 13.8110i | 1.70380 | − | 0.469589i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.1678 | 0.378842 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.6228 | −0.427706 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −38.1145 | + | 39.7826i | −1.28851 | + | 1.34490i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.15855i | 0.0728892i | 0.999336 | + | 0.0364446i | \(0.0116032\pi\) | ||||
−0.999336 | + | 0.0364446i | \(0.988397\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.8421 | 0.500044 | 0.250022 | − | 0.968240i | \(-0.419562\pi\) | ||||
0.250022 | + | 0.968240i | \(0.419562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 13.0742i | − | 0.439983i | −0.975502 | − | 0.219992i | \(-0.929397\pi\) | ||
0.975502 | − | 0.219992i | \(-0.0706030\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39.4254i | 1.32377i | 0.749604 | + | 0.661887i | \(0.230244\pi\) | ||||
−0.749604 | + | 0.661887i | \(0.769756\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −54.8122 | −1.83834 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.39066 | + | 30.4436i | 0.280469 | + | 1.01762i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.18191 | −0.0393751 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.18306 | + | 7.92072i | 0.0725673 | + | 0.263294i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.8397i | 1.65490i | 0.561539 | + | 0.827450i | \(0.310209\pi\) | ||||
−0.561539 | + | 0.827450i | \(0.689791\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.92438 | −0.295678 | −0.147839 | − | 0.989011i | \(-0.547232\pi\) | ||||
−0.147839 | + | 0.989011i | \(0.547232\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 18.5399i | − | 0.613581i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 8.97247i | − | 0.296297i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.9876 | 0.725302 | 0.362651 | − | 0.931925i | \(-0.381872\pi\) | ||||
0.362651 | + | 0.931925i | \(0.381872\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.9716i | 0.459881i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.4997 | − | 25.9825i | −0.509626 | − | 0.854299i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.14289 | 0.135924 | 0.0679619 | − | 0.997688i | \(-0.478350\pi\) | ||||
0.0679619 | + | 0.997688i | \(0.478350\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.582591 | − | 0.160570i | 0.0190528 | − | 0.00525120i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 59.2235i | 1.93475i | 0.253354 | + | 0.967374i | \(0.418466\pi\) | ||||
−0.253354 | + | 0.967374i | \(0.581534\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.7615 | −0.383415 | −0.191707 | − | 0.981452i | \(-0.561402\pi\) | ||||
−0.191707 | + | 0.981452i | \(0.561402\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.64543i | − | 0.151276i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.51629i | 0.276742i | 0.990380 | + | 0.138371i | \(0.0441867\pi\) | ||||
−0.990380 | + | 0.138371i | \(0.955813\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.73245 | −0.153622 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.4872i | 1.14954i | 0.818314 | + | 0.574772i | \(0.194909\pi\) | ||||
−0.818314 | + | 0.574772i | \(0.805091\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.0141 | + | 36.3339i | 0.324049 | + | 1.17574i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 42.8817 | 1.38472 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.0920 | − | 3.88395i | 0.453638 | − | 0.125029i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 8.51445i | − | 0.273806i | −0.990584 | − | 0.136903i | \(-0.956285\pi\) | ||
0.990584 | − | 0.136903i | \(-0.0437149\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.5013 | 1.62066 | 0.810331 | − | 0.585972i | \(-0.199287\pi\) | ||||
0.810331 | + | 0.585972i | \(0.199287\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33.5980i | 1.07710i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.0540i | 1.24945i | 0.780845 | + | 0.624725i | \(0.214789\pi\) | ||||
−0.780845 | + | 0.624725i | \(0.785211\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.18914 | 0.133886 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 54.9882i | 1.75385i | 0.480627 | + | 0.876925i | \(0.340409\pi\) | ||||
−0.480627 | + | 0.876925i | \(0.659591\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 55.5931 | − | 15.3222i | 1.77134 | − | 0.488206i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.68289 | −0.244302 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.0052 | −0.476656 | −0.238328 | − | 0.971185i | \(-0.576599\pi\) | ||||
−0.238328 | + | 0.971185i | \(0.576599\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.0793 | + | 36.5703i | 0.319535 | + | 1.15936i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.4113i | 0.709773i | 0.934909 | + | 0.354887i | \(0.115481\pi\) | ||||
−0.934909 | + | 0.354887i | \(0.884519\pi\) | |||||||
\(998\) | 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 | 4680.2.l.g.2809.6 | 8 | ||
3.2 | odd | 2 | 1560.2.l.d.1249.6 | yes | 8 | ||
5.4 | even | 2 | inner | 4680.2.l.g.2809.5 | 8 | ||
12.11 | even | 2 | 3120.2.l.n.1249.2 | 8 | |||
15.2 | even | 4 | 7800.2.a.by.1.4 | 4 | |||
15.8 | even | 4 | 7800.2.a.bt.1.1 | 4 | |||
15.14 | odd | 2 | 1560.2.l.d.1249.2 | ✓ | 8 | ||
60.59 | even | 2 | 3120.2.l.n.1249.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.l.d.1249.2 | ✓ | 8 | 15.14 | odd | 2 | ||
1560.2.l.d.1249.6 | yes | 8 | 3.2 | odd | 2 | ||
3120.2.l.n.1249.2 | 8 | 12.11 | even | 2 | |||
3120.2.l.n.1249.6 | 8 | 60.59 | even | 2 | |||
4680.2.l.g.2809.5 | 8 | 5.4 | even | 2 | inner | ||
4680.2.l.g.2809.6 | 8 | 1.1 | even | 1 | trivial | ||
7800.2.a.bt.1.1 | 4 | 15.8 | even | 4 | |||
7800.2.a.by.1.4 | 4 | 15.2 | even | 4 |