Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1121,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.1121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 35 x^{10} - 120 x^{9} + 362 x^{8} - 794 x^{7} + 1463 x^{6} - 2048 x^{5} + 2258 x^{4} + \cdots + 61 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1121.11 | ||
Root | \(0.500000 + 2.14588i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1121 |
Dual form | 2240.2.b.h.1121.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 3.13466i | 1.80979i | 0.425630 | + | 0.904897i | \(0.360053\pi\) | ||||
−0.425630 | + | 0.904897i | \(0.639947\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.82607 | −2.27536 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 4.07158i | − 1.22763i | −0.789451 | − | 0.613813i | \(-0.789635\pi\) | ||||
0.789451 | − | 0.613813i | \(-0.210365\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.86968i | 0.795905i | 0.917406 | + | 0.397952i | \(0.130279\pi\) | ||||
−0.917406 | + | 0.397952i | \(0.869721\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.13466 | 0.809365 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.69437 | 1.86616 | 0.933079 | − | 0.359672i | \(-0.117111\pi\) | ||||
0.933079 | + | 0.359672i | \(0.117111\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 2.79216i | − 0.640566i | −0.947322 | − | 0.320283i | \(-0.896222\pi\) | ||||
0.947322 | − | 0.320283i | \(-0.103778\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.13466i | 0.684038i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.79136 | 1.62461 | 0.812305 | − | 0.583233i | \(-0.198212\pi\) | ||||
0.812305 | + | 0.583233i | \(0.198212\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 11.9934i | − 2.30814i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.95657i | 1.84889i | 0.381318 | + | 0.924444i | \(0.375470\pi\) | ||||
−0.381318 | + | 0.924444i | \(0.624530\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.232455 | −0.0417501 | −0.0208751 | − | 0.999782i | \(-0.506645\pi\) | ||||
−0.0208751 | + | 0.999782i | \(0.506645\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.7630 | 2.22175 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.00000i | − 0.169031i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.98614i | 0.819717i | 0.912149 | + | 0.409859i | \(0.134422\pi\) | ||||
−0.912149 | + | 0.409859i | \(0.865578\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.99545 | −1.44042 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.91752 | −0.611814 | −0.305907 | − | 0.952061i | \(-0.598960\pi\) | ||||
−0.305907 | + | 0.952061i | \(0.598960\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.54585i | 1.45573i | 0.685721 | + | 0.727865i | \(0.259487\pi\) | ||||
−0.685721 | + | 0.727865i | \(0.740513\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.82607i | 1.01757i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.90855 | −0.570121 | −0.285061 | − | 0.958509i | \(-0.592014\pi\) | ||||
−0.285061 | + | 0.958509i | \(0.592014\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 24.1192i | 3.37736i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.85958i | 0.530154i | 0.964227 | + | 0.265077i | \(0.0853973\pi\) | ||||
−0.964227 | + | 0.265077i | \(0.914603\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.07158 | −0.549011 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.75248 | 1.15929 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 7.86790i | − 1.02431i | −0.858892 | − | 0.512157i | \(-0.828847\pi\) | ||||
0.858892 | − | 0.512157i | \(-0.171153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9651i | 1.40393i | 0.712210 | + | 0.701966i | \(0.247694\pi\) | ||||
−0.712210 | + | 0.701966i | \(0.752306\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.82607 | −0.860004 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.86968 | 0.355939 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 11.5177i | − 1.40711i | −0.710643 | − | 0.703553i | \(-0.751596\pi\) | ||||
0.710643 | − | 0.703553i | \(-0.248404\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 24.4232i | 2.94021i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.0745 | 1.55166 | 0.775830 | − | 0.630942i | \(-0.217331\pi\) | ||||
0.775830 | + | 0.630942i | \(0.217331\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.99406 | 0.701552 | 0.350776 | − | 0.936459i | \(-0.385918\pi\) | ||||
0.350776 | + | 0.936459i | \(0.385918\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 3.13466i | − 0.361959i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 4.07158i | − 0.463999i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.872456 | 0.0981589 | 0.0490795 | − | 0.998795i | \(-0.484371\pi\) | ||||
0.0490795 | + | 0.998795i | \(0.484371\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 17.1171 | 1.90190 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.33875i | 0.915296i | 0.889133 | + | 0.457648i | \(0.151308\pi\) | ||||
−0.889133 | + | 0.457648i | \(0.848692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 7.69437i | − 0.834571i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −31.2104 | −3.34611 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.79136 | −0.613883 | −0.306941 | − | 0.951728i | \(-0.599306\pi\) | ||||
−0.306941 | + | 0.951728i | \(0.599306\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.86968i | 0.300824i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 0.728666i | − 0.0755592i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.79216 | −0.286470 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.6226 | −1.07856 | −0.539279 | − | 0.842127i | \(-0.681303\pi\) | ||||
−0.539279 | + | 0.842127i | \(0.681303\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 27.7929i | 2.79329i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 17.2257i | − 1.71402i | −0.515298 | − | 0.857011i | \(-0.672319\pi\) | ||||
0.515298 | − | 0.857011i | \(-0.327681\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.90855 | 0.385121 | 0.192561 | − | 0.981285i | \(-0.438321\pi\) | ||||
0.192561 | + | 0.981285i | \(0.438321\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.13466 | 0.305911 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.60452i | 0.348462i | 0.984705 | + | 0.174231i | \(0.0557440\pi\) | ||||
−0.984705 | + | 0.174231i | \(0.944256\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 8.80667i | − 0.843526i | −0.906706 | − | 0.421763i | \(-0.861411\pi\) | ||||
0.906706 | − | 0.421763i | \(-0.138589\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.6299 | −1.48352 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.43908 | 0.511665 | 0.255833 | − | 0.966721i | \(-0.417650\pi\) | ||||
0.255833 | + | 0.966721i | \(0.417650\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 7.79136i | − 0.726548i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 19.5886i | − 1.81097i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.69437 | 0.705341 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.57773 | −0.507066 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 12.2801i | − 1.10726i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.38283 | 0.477649 | 0.238825 | − | 0.971063i | \(-0.423238\pi\) | ||||
0.238825 | + | 0.971063i | \(0.423238\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −29.9230 | −2.63457 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.8008i | 0.943673i | 0.881686 | + | 0.471836i | \(0.156409\pi\) | ||||
−0.881686 | + | 0.471836i | \(0.843591\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2.79216i | − 0.242111i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.9934 | −1.03223 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.9651 | 0.936808 | 0.468404 | − | 0.883514i | \(-0.344829\pi\) | ||||
0.468404 | + | 0.883514i | \(0.344829\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2.40141i | − 0.203685i | −0.994801 | − | 0.101843i | \(-0.967526\pi\) | ||||
0.994801 | − | 0.101843i | \(-0.0324738\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 12.2520i | − 1.03180i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.6841 | 0.977073 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.95657 | 0.826848 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.13466i | 0.258542i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.46329i | 0.529494i | 0.964318 | + | 0.264747i | \(0.0852884\pi\) | ||||
−0.964318 | + | 0.264747i | \(0.914712\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.45678 | 0.525446 | 0.262723 | − | 0.964871i | \(-0.415380\pi\) | ||||
0.262723 | + | 0.964871i | \(0.415380\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −52.5223 | −4.24618 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.232455i | 0.0186712i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 5.25667i | − 0.419528i | −0.977752 | − | 0.209764i | \(-0.932730\pi\) | ||||
0.977752 | − | 0.209764i | \(-0.0672696\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.0985 | −0.959470 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.79136 | 0.614045 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1.94327i | − 0.152209i | −0.997100 | − | 0.0761044i | \(-0.975752\pi\) | ||||
0.997100 | − | 0.0761044i | \(-0.0242482\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 12.7630i | − 0.993598i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.419913 | 0.0324938 | 0.0162469 | − | 0.999868i | \(-0.494828\pi\) | ||||
0.0162469 | + | 0.999868i | \(0.494828\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.76496 | 0.366536 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 19.0595i | 1.45752i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.3128i | 1.16421i | 0.813114 | + | 0.582104i | \(0.197770\pi\) | ||||
−0.813114 | + | 0.582104i | \(0.802230\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 24.6632 | 1.85380 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.19122i | 0.462753i | 0.972864 | + | 0.231377i | \(0.0743230\pi\) | ||||
−0.972864 | + | 0.231377i | \(0.925677\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3446i | 0.768912i | 0.923143 | + | 0.384456i | \(0.125611\pi\) | ||||
−0.923143 | + | 0.384456i | \(0.874389\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −34.3717 | −2.54083 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.98614 | 0.366589 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 31.3282i | − 2.29094i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 11.9934i | − 0.872393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.3266 | −1.25371 | −0.626856 | − | 0.779135i | \(-0.715659\pi\) | ||||
−0.626856 | + | 0.779135i | \(0.715659\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.2039 | −1.81422 | −0.907108 | − | 0.420897i | \(-0.861715\pi\) | ||||
−0.907108 | + | 0.420897i | \(0.861715\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.99545i | 0.644177i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.4680i | 1.67203i | 0.548707 | + | 0.836014i | \(0.315120\pi\) | ||||
−0.548707 | + | 0.836014i | \(0.684880\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.26099 | 0.585606 | 0.292803 | − | 0.956173i | \(-0.405412\pi\) | ||||
0.292803 | + | 0.956173i | \(0.405412\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 36.1039 | 2.54657 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.95657i | 0.698814i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.91752i | 0.273611i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −53.1844 | −3.69657 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.3685 | −0.786376 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.20050i | 0.289174i | 0.989492 | + | 0.144587i | \(0.0461854\pi\) | ||||
−0.989492 | + | 0.144587i | \(0.953815\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 40.9842i | 2.80819i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.54585 | 0.651022 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.232455 | −0.0157801 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.7893i | 1.26967i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.0803i | 1.48528i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.89315 | −0.193739 | −0.0968697 | − | 0.995297i | \(-0.530883\pi\) | ||||
−0.0968697 | + | 0.995297i | \(0.530883\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.82607 | 0.455072 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.26914i | 0.216981i | 0.994098 | + | 0.108490i | \(0.0346017\pi\) | ||||
−0.994098 | + | 0.108490i | \(0.965398\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 15.7195i | − 1.03877i | −0.854540 | − | 0.519386i | \(-0.826161\pi\) | ||||
0.854540 | − | 0.519386i | \(-0.173839\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.7630 | 0.839743 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.1154 | 1.05576 | 0.527879 | − | 0.849320i | \(-0.322988\pi\) | ||||
0.527879 | + | 0.849320i | \(0.322988\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.90855i | 0.254966i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.73485i | 0.177648i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.1445 | 1.10899 | 0.554494 | − | 0.832188i | \(-0.312912\pi\) | ||||
0.554494 | + | 0.832188i | \(0.312912\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.90488 | −0.315951 | −0.157975 | − | 0.987443i | \(-0.550497\pi\) | ||||
−0.157975 | + | 0.987443i | \(0.550497\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.6758i | 1.13390i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.00000i | − 0.0638877i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.01261 | 0.509830 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −26.1391 | −1.65650 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 17.4597i | − 1.10205i | −0.834489 | − | 0.551024i | \(-0.814237\pi\) | ||||
0.834489 | − | 0.551024i | \(-0.185763\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 31.7231i | − 1.99441i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 24.1192 | 1.51040 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.622321 | −0.0388193 | −0.0194096 | − | 0.999812i | \(-0.506179\pi\) | ||||
−0.0194096 | + | 0.999812i | \(0.506179\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.98614i | 0.309824i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 67.9643i | − 4.20688i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −32.3923 | −1.99739 | −0.998696 | − | 0.0510429i | \(-0.983745\pi\) | ||||
−0.998696 | + | 0.0510429i | \(0.983745\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.85958 | 0.237092 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 18.1539i | − 1.11100i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.8298i | 0.782244i | 0.920339 | + | 0.391122i | \(0.127913\pi\) | ||||
−0.920339 | + | 0.391122i | \(0.872087\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.29751 | −0.504038 | −0.252019 | − | 0.967722i | \(-0.581095\pi\) | ||||
−0.252019 | + | 0.967722i | \(0.581095\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.99545 | −0.544429 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.07158i | 0.245525i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.3642i | 1.16348i | 0.813374 | + | 0.581741i | \(0.197628\pi\) | ||||
−0.813374 | + | 0.581741i | \(0.802372\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.58675 | 0.0949965 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.50829 | −0.149632 | −0.0748161 | − | 0.997197i | \(-0.523837\pi\) | ||||
−0.0748161 | + | 0.997197i | \(0.523837\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 9.05932i | − 0.538521i | −0.963067 | − | 0.269260i | \(-0.913221\pi\) | ||||
0.963067 | − | 0.269260i | \(-0.0867792\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 8.75248i | − 0.518452i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.91752 | −0.231244 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 42.2033 | 2.48255 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 33.2981i | − 1.95197i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.0128i | 1.11074i | 0.831603 | + | 0.555371i | \(0.187424\pi\) | ||||
−0.831603 | + | 0.555371i | \(0.812576\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.86790 | −0.458087 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −48.8321 | −2.83353 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 22.3587i | 1.29303i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.54585i | 0.550214i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 53.9967 | 3.10203 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.9651 | 0.627858 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 27.9149i | − 1.59319i | −0.604516 | − | 0.796593i | \(-0.706633\pi\) | ||||
0.604516 | − | 0.796593i | \(-0.293367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.2520i | 0.696991i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.995357 | −0.0564415 | −0.0282207 | − | 0.999602i | \(-0.508984\pi\) | ||||
−0.0282207 | + | 0.999602i | \(0.508984\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.69245 | −0.265233 | −0.132616 | − | 0.991167i | \(-0.542338\pi\) | ||||
−0.132616 | + | 0.991167i | \(0.542338\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.82607i | 0.384606i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.32928i | − 0.0746595i | −0.999303 | − | 0.0373298i | \(-0.988115\pi\) | ||||
0.999303 | − | 0.0373298i | \(-0.0118852\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 40.5389 | 2.26974 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.2989 | −0.630646 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 21.4839i | − 1.19540i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 2.86968i | − 0.159181i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 27.6059 | 1.52661 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.90855 | −0.215486 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.850445i | 0.0467447i | 0.999727 | + | 0.0233723i | \(0.00744033\pi\) | ||||
−0.999727 | + | 0.0233723i | \(0.992560\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 34.0358i | − 1.86515i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.5177 | −0.629277 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.98257 | −0.107997 | −0.0539987 | − | 0.998541i | \(-0.517197\pi\) | ||||
−0.0539987 | + | 0.998541i | \(0.517197\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.0496i | 0.926009i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.946457i | 0.0512535i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 24.4232 | 1.31490 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 15.8282i | − 0.849703i | −0.905263 | − | 0.424851i | \(-0.860326\pi\) | ||||
0.905263 | − | 0.424851i | \(-0.139674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.81595i | 0.311321i | 0.987811 | + | 0.155660i | \(0.0497505\pi\) | ||||
−0.987811 | + | 0.155660i | \(0.950249\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 34.4172 | 1.83706 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.4270 | 1.51302 | 0.756508 | − | 0.653985i | \(-0.226904\pi\) | ||||
0.756508 | + | 0.653985i | \(0.226904\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 13.0745i | − 0.693924i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 24.1192i | 1.27652i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.3907 | −1.70952 | −0.854758 | − | 0.519027i | \(-0.826294\pi\) | ||||
−0.854758 | + | 0.519027i | \(0.826294\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.2038 | 0.589675 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 17.4843i | − 0.917686i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 5.99406i | − 0.313744i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.14858 | 0.373153 | 0.186576 | − | 0.982440i | \(-0.440261\pi\) | ||||
0.186576 | + | 0.982440i | \(0.440261\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 26.7413 | 1.39209 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.85958i | 0.200379i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 34.7310i | − 1.79830i | −0.437640 | − | 0.899150i | \(-0.644186\pi\) | ||||
0.437640 | − | 0.899150i | \(-0.355814\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.13466 | −0.161873 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −28.5721 | −1.47154 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.22799i | 0.474010i | 0.971508 | + | 0.237005i | \(0.0761658\pi\) | ||||
−0.971508 | + | 0.237005i | \(0.923834\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.8733i | 0.864447i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.71562 | −0.343152 | −0.171576 | − | 0.985171i | \(-0.554886\pi\) | ||||
−0.171576 | + | 0.985171i | \(0.554886\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.07158 | −0.207507 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 65.1607i | − 3.31230i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 10.5635i | − 0.535588i | −0.963476 | − | 0.267794i | \(-0.913705\pi\) | ||||
0.963476 | − | 0.267794i | \(-0.0862947\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 59.9496 | 3.03178 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −33.8569 | −1.70785 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 0.872456i | − 0.0438980i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 16.3585i | − 0.821008i | −0.911859 | − | 0.410504i | \(-0.865353\pi\) | ||||
0.911859 | − | 0.410504i | \(-0.134647\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.75248 | 0.438172 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.2429 | 0.911008 | 0.455504 | − | 0.890234i | \(-0.349459\pi\) | ||||
0.455504 | + | 0.890234i | \(0.349459\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 0.667070i | − 0.0332291i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 17.1171i | − 0.850553i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.3015 | 1.00631 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.7302 | −1.66785 | −0.833927 | − | 0.551875i | \(-0.813912\pi\) | ||||
−0.833927 | + | 0.551875i | \(0.813912\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 34.3717i | 1.69543i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 7.86790i | − 0.387154i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.33875 | 0.409333 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.52760 | 0.368628 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 27.7029i | − 1.35338i | −0.736269 | − | 0.676689i | \(-0.763414\pi\) | ||||
0.736269 | − | 0.676689i | \(-0.236586\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.6253i | 1.29764i | 0.760943 | + | 0.648819i | \(0.224737\pi\) | ||||
−0.760943 | + | 0.648819i | \(0.775263\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 26.6801 | 1.29723 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.69437 | −0.373232 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.9651i | 0.530637i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 36.6256i | 1.76830i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.24973 | 0.301039 | 0.150519 | − | 0.988607i | \(-0.451905\pi\) | ||||
0.150519 | + | 0.988607i | \(0.451905\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.8155 | 1.43284 | 0.716420 | − | 0.697670i | \(-0.245780\pi\) | ||||
0.716420 | + | 0.697670i | \(0.245780\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 31.2104i | 1.49643i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 21.7547i | − 1.04067i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.0945 | 1.00678 | 0.503392 | − | 0.864058i | \(-0.332085\pi\) | ||||
0.503392 | + | 0.864058i | \(0.332085\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.82607 | −0.325051 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 36.5359i | − 1.73587i | −0.496675 | − | 0.867937i | \(-0.665446\pi\) | ||||
0.496675 | − | 0.867937i | \(-0.334554\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.79136i | 0.274537i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.2602 | −0.958275 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.9644 | −1.08376 | −0.541879 | − | 0.840456i | \(-0.682287\pi\) | ||||
−0.541879 | + | 0.840456i | \(0.682287\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.9505i | 0.751079i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.2398i | 0.950949i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.86968 | 0.134532 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.59652 | −0.0746822 | −0.0373411 | − | 0.999303i | \(-0.511889\pi\) | ||||
−0.0373411 | + | 0.999303i | \(0.511889\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 92.2818i | − 4.30735i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 9.34977i | − 0.435462i | −0.976009 | − | 0.217731i | \(-0.930134\pi\) | ||||
0.976009 | − | 0.217731i | \(-0.0698656\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 42.1170 | 1.95734 | 0.978670 | − | 0.205436i | \(-0.0658613\pi\) | ||||
0.978670 | + | 0.205436i | \(0.0658613\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.728666 | −0.0337911 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.5548i | 1.59901i | 0.600661 | + | 0.799503i | \(0.294904\pi\) | ||||
−0.600661 | + | 0.799503i | \(0.705096\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 11.5177i | − 0.531836i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.4779 | 0.759260 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 38.8667 | 1.78709 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.79216i | 0.128113i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 26.3458i | − 1.20629i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.5529 | 0.710630 | 0.355315 | − | 0.934747i | \(-0.384374\pi\) | ||||
0.355315 | + | 0.934747i | \(0.384374\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.3086 | −0.652417 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.4232i | 1.11130i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.6226i | 0.482346i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.0868 | 0.728961 | 0.364480 | − | 0.931211i | \(-0.381247\pi\) | ||||
0.364480 | + | 0.931211i | \(0.381247\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.09149 | 0.275467 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.4429i | 0.877445i | 0.898623 | + | 0.438722i | \(0.144569\pi\) | ||||
−0.898623 | + | 0.438722i | \(0.855431\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 76.6095i | 3.45032i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 27.7929 | 1.24920 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.0745 | 0.586473 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 6.85663i | − 0.306945i | −0.988153 | − | 0.153472i | \(-0.950954\pi\) | ||||
0.988153 | − | 0.153472i | \(-0.0490456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.31628i | 0.0588072i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.7137 | −0.923580 | −0.461790 | − | 0.886989i | \(-0.652793\pi\) | ||||
−0.461790 | + | 0.886989i | \(0.652793\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.2257 | −0.766534 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14.9365i | 0.663354i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.5146i | 0.776319i | 0.921592 | + | 0.388160i | \(0.126889\pi\) | ||||
−0.921592 | + | 0.388160i | \(0.873111\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.99406 | 0.265162 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −33.4876 | −1.47851 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 3.90855i | − 0.172231i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.9140i | 0.699896i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −48.0003 | −2.10698 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.9413 | −0.829831 | −0.414916 | − | 0.909860i | \(-0.636189\pi\) | ||||
−0.414916 | + | 0.909860i | \(0.636189\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 8.81407i | − 0.385412i | −0.981257 | − | 0.192706i | \(-0.938274\pi\) | ||||
0.981257 | − | 0.192706i | \(-0.0617264\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 3.13466i | − 0.136808i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.78859 | −0.0779123 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 37.7052 | 1.63936 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 53.7069i | 2.33068i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 11.2420i | − 0.486945i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.60452 | 0.155837 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.4073 | −0.837488 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 4.07158i | − 0.175375i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 25.1371i | − 1.08073i | −0.841431 | − | 0.540364i | \(-0.818287\pi\) | ||||
0.841431 | − | 0.540364i | \(-0.181713\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −32.4269 | −1.39157 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.80667 | −0.377236 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 18.5973i | − 0.795163i | −0.917567 | − | 0.397581i | \(-0.869850\pi\) | ||||
0.917567 | − | 0.397581i | \(-0.130150\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 74.8483i | − 3.19445i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.8004 | 1.18434 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.872456 | 0.0371006 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.6299i | 0.663450i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 24.1967i | − 1.02525i | −0.858613 | − | 0.512624i | \(-0.828674\pi\) | ||||
0.858613 | − | 0.512624i | \(-0.171326\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.3935 | −1.15862 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 98.2031 | 4.14614 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 10.1127i | − 0.426198i | −0.977031 | − | 0.213099i | \(-0.931644\pi\) | ||||
0.977031 | − | 0.213099i | \(-0.0683558\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 5.43908i | − 0.228824i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 17.1171 | 0.718849 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.63003 | −0.194101 | −0.0970505 | − | 0.995279i | \(-0.530941\pi\) | ||||
−0.0970505 | + | 0.995279i | \(0.530941\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.7318i | 1.07684i | 0.842676 | + | 0.538420i | \(0.180979\pi\) | ||||
−0.842676 | + | 0.538420i | \(0.819021\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 54.3131i | − 2.26896i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.79136 | −0.324922 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.8525 | −1.45093 | −0.725464 | − | 0.688260i | \(-0.758375\pi\) | ||||
−0.725464 | + | 0.688260i | \(0.758375\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 79.0056i | − 3.28336i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.33875i | 0.345950i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.7146 | 0.650831 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −19.5886 | −0.809889 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.5473i | 1.09572i | 0.836569 | + | 0.547862i | \(0.184558\pi\) | ||||
−0.836569 | + | 0.547862i | \(0.815442\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.649052i | 0.0267437i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −73.5643 | −3.02603 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.15928 | 0.170801 | 0.0854005 | − | 0.996347i | \(-0.472783\pi\) | ||||
0.0854005 | + | 0.996347i | \(0.472783\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 7.69437i | − 0.315438i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.8954i | 1.05983i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.0612 | 1.22827 | 0.614134 | − | 0.789202i | \(-0.289506\pi\) | ||||
0.614134 | + | 0.789202i | \(0.289506\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.60964 | 0.310404 | 0.155202 | − | 0.987883i | \(-0.450397\pi\) | ||||
0.155202 | + | 0.987883i | \(0.450397\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 78.6204i | 3.20167i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.57773i | 0.226767i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.7256 | −1.32829 | −0.664146 | − | 0.747603i | \(-0.731205\pi\) | ||||
−0.664146 | + | 0.747603i | \(0.731205\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −31.2104 | −1.26471 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 11.2163i | − 0.453762i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 30.2155i | − 1.22039i | −0.792251 | − | 0.610196i | \(-0.791091\pi\) | ||||
0.792251 | − | 0.610196i | \(-0.208909\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.2801 | −0.495181 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.5315 | −0.665531 | −0.332766 | − | 0.943010i | \(-0.607982\pi\) | ||||
−0.332766 | + | 0.943010i | \(0.607982\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 30.9167i | − 1.24265i | −0.783554 | − | 0.621324i | \(-0.786595\pi\) | ||||
0.783554 | − | 0.621324i | \(-0.213405\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 93.4451i | − 3.74982i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.79136 | −0.232026 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 35.6364i | − 1.42318i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 38.3652i | 1.52972i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.70749 | −0.187402 | −0.0937012 | − | 0.995600i | \(-0.529870\pi\) | ||||
−0.0937012 | + | 0.995600i | \(0.529870\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.1671 | −0.523347 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 5.38283i | − 0.213611i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.86968i | 0.113701i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −89.2477 | −3.53058 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.3531 | 1.19888 | 0.599438 | − | 0.800421i | \(-0.295391\pi\) | ||||
0.599438 | + | 0.800421i | \(0.295391\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 26.5539i | − 1.04718i | −0.851970 | − | 0.523591i | \(-0.824592\pi\) | ||||
0.851970 | − | 0.523591i | \(-0.175408\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 29.9230i | 1.17822i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.0929 | −0.475421 | −0.237710 | − | 0.971336i | \(-0.576397\pi\) | ||||
−0.237710 | + | 0.971336i | \(0.576397\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.0348 | −1.25747 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 0.728666i | − 0.0285587i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 31.5455i | − 1.23447i | −0.786779 | − | 0.617235i | \(-0.788253\pi\) | ||||
0.786779 | − | 0.617235i | \(-0.211747\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.8008 | 0.422023 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −40.9159 | −1.59628 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 23.3195i | − 0.908398i | −0.890900 | − | 0.454199i | \(-0.849926\pi\) | ||||
0.890900 | − | 0.454199i | \(-0.150074\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 48.3614i | − 1.88104i | −0.339740 | − | 0.940519i | \(-0.610339\pi\) | ||||
0.339740 | − | 0.940519i | \(-0.389661\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −69.2143 | −2.68806 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.79216 | −0.108275 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 77.5752i | 3.00372i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 9.06902i | − 0.350629i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 44.6451 | 1.72350 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.4774 | −0.982083 | −0.491041 | − | 0.871136i | \(-0.663384\pi\) | ||||
−0.491041 | + | 0.871136i | \(0.663384\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11.9934i | 0.461627i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.1635i | 0.736513i | 0.929724 | + | 0.368256i | \(0.120045\pi\) | ||||
−0.929724 | + | 0.368256i | \(0.879955\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.6226 | −0.407657 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.2476 | −0.392691 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.8961i | 0.531718i | 0.964012 | + | 0.265859i | \(0.0856556\pi\) | ||||
−0.964012 | + | 0.265859i | \(0.914344\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 10.9651i | − 0.418953i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 49.2752 | 1.87997 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.0757 | −0.421952 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 39.9837i | − 1.52105i | −0.649308 | − | 0.760525i | \(-0.724941\pi\) | ||||
0.649308 | − | 0.760525i | \(-0.275059\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 27.7929i | 1.05576i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.40141 | −0.0910907 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.1428 | −1.14174 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 50.5164i | 1.91070i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 10.7313i | − 0.405317i | −0.979249 | − | 0.202659i | \(-0.935042\pi\) | ||||
0.979249 | − | 0.202659i | \(-0.0649582\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.9221 | 0.525083 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.2520 | −0.461436 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 17.2257i | − 0.647840i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 23.7245i | − 0.890991i | −0.895284 | − | 0.445495i | \(-0.853028\pi\) | ||||
0.895284 | − | 0.445495i | \(-0.146972\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.95545 | −0.223347 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.81114 | −0.0678277 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 11.6841i | − 0.436961i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 53.7422i | 2.00704i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −43.5164 | −1.62289 | −0.811444 | − | 0.584430i | \(-0.801318\pi\) | ||||
−0.811444 | + | 0.584430i | \(0.801318\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.90855 | 0.145562 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 15.3751i | − 0.571806i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 9.95657i | − 0.369778i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.207057 | 0.00767931 | 0.00383966 | − | 0.999993i | \(-0.498778\pi\) | ||||
0.00383966 | + | 0.999993i | \(0.498778\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.05645 | −0.150239 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 73.4493i | 2.71662i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.739133i | 0.0273005i | 0.999907 | + | 0.0136502i | \(0.00434514\pi\) | ||||
−0.999907 | + | 0.0136502i | \(0.995655\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.13466 | 0.115624 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −46.8950 | −1.72740 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 43.7486i | − 1.60932i | −0.593738 | − | 0.804659i | \(-0.702348\pi\) | ||||
0.593738 | − | 0.804659i | \(-0.297652\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.1168i | 0.922687i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.0721 | −0.809748 | −0.404874 | − | 0.914373i | \(-0.632685\pi\) | ||||
−0.404874 | + | 0.914373i | \(0.632685\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.46329 | 0.236797 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 56.9209i | − 2.08263i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.60452i | 0.131706i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.2686 | 1.72486 | 0.862429 | − | 0.506179i | \(-0.168942\pi\) | ||||
0.862429 | + | 0.506179i | \(0.168942\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 54.7302 | 1.99448 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 6.45678i | − 0.234986i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 0.312591i | − 0.0113613i | −0.999984 | − | 0.00568066i | \(-0.998192\pi\) | ||||
0.999984 | − | 0.00568066i | \(-0.00180822\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 99.4410 | 3.60948 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.74491 | 0.208253 | 0.104126 | − | 0.994564i | \(-0.466795\pi\) | ||||
0.104126 | + | 0.994564i | \(0.466795\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 8.80667i | − 0.318823i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 52.5223i | 1.89895i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.5783 | 0.815256 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.97307 | 0.143273 | 0.0716363 | − | 0.997431i | \(-0.477178\pi\) | ||||
0.0716363 | + | 0.997431i | \(0.477178\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 1.95076i | − 0.0702550i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 24.1261i | − 0.867756i | −0.900972 | − | 0.433878i | \(-0.857145\pi\) | ||||
0.900972 | − | 0.433878i | \(-0.142855\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.232455 | 0.00835002 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.6299 | −0.560718 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.9384i | 0.391907i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 53.2339i | − 1.90486i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 119.413 | 4.26749 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.25667 | −0.187619 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.9252i | 0.532025i | 0.963970 | + | 0.266013i | \(0.0857063\pi\) | ||||
−0.963970 | + | 0.266013i | \(0.914294\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 101.539i | − 3.61487i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.43908 | 0.193391 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.4662 | −1.11740 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.0985i | 0.429088i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 7.25881i | − 0.257120i | −0.991702 | − | 0.128560i | \(-0.958964\pi\) | ||||
0.991702 | − | 0.128560i | \(-0.0410355\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.0738 | −1.06394 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 39.5322 | 1.39680 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 24.4053i | − 0.861244i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 7.79136i | − 0.274609i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −40.2169 | −1.41570 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.4223 | 0.612534 | 0.306267 | − | 0.951946i | \(-0.400920\pi\) | ||||
0.306267 | + | 0.951946i | \(0.400920\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.54412i | 0.300025i | 0.988684 | + | 0.150012i | \(0.0479313\pi\) | ||||
−0.988684 | + | 0.150012i | \(0.952069\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 26.0098i | − 0.912205i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.94327 | −0.0680698 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.6536 | 0.932491 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 19.5886i | − 0.684482i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.2641i | 0.846821i | 0.905938 | + | 0.423411i | \(0.139167\pi\) | ||||
−0.905938 | + | 0.423411i | \(0.860833\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.8067 | −1.38758 | −0.693788 | − | 0.720180i | \(-0.744059\pi\) | ||||
−0.693788 | + | 0.720180i | \(0.744059\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.7630 | −0.444350 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 6.33123i | − 0.220158i | −0.993923 | − | 0.110079i | \(-0.964890\pi\) | ||||
0.993923 | − | 0.110079i | \(-0.0351105\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 28.3161i | − 0.983460i | −0.870748 | − | 0.491730i | \(-0.836365\pi\) | ||||
0.870748 | − | 0.491730i | \(-0.163635\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −60.7001 | −2.10566 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.69437 | 0.266594 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 0.419913i | − 0.0145317i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.78793i | 0.0963649i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.0742 | −1.24542 | −0.622710 | − | 0.782453i | \(-0.713968\pi\) | ||||
−0.622710 | + | 0.782453i | \(0.713968\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −70.1332 | −2.41839 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 7.86264i | − 0.270804i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 4.76496i | − 0.163920i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.57773 | −0.191653 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.3979 | 0.974612 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.8488i | 1.33172i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 16.0460i | − 0.549405i | −0.961529 | − | 0.274702i | \(-0.911421\pi\) | ||||
0.961529 | − | 0.274702i | \(-0.0885793\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19.0595 | 0.651822 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46.0559 | 1.57324 | 0.786620 | − | 0.617437i | \(-0.211829\pi\) | ||||
0.786620 | + | 0.617437i | \(0.211829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.62040i | 0.328244i | 0.986440 | + | 0.164122i | \(0.0524790\pi\) | ||||
−0.986440 | + | 0.164122i | \(0.947521\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 12.2801i | − 0.418504i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.1023 | 1.39914 | 0.699570 | − | 0.714564i | \(-0.253375\pi\) | ||||
0.699570 | + | 0.714564i | \(0.253375\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.3128 | 0.520650 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 132.293i | 4.49290i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 3.55227i | − 0.120502i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.0519 | 1.11992 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 72.5104 | 2.45411 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000i | 0.0338062i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.23672i | 0.176831i | 0.996084 | + | 0.0884157i | \(0.0281804\pi\) | ||||
−0.996084 | + | 0.0884157i | \(0.971820\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −59.5987 | −2.01021 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.0181 | −1.44932 | −0.724659 | − | 0.689108i | \(-0.758003\pi\) | ||||
−0.724659 | + | 0.689108i | \(0.758003\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 32.8329i | − 1.10492i | −0.833541 | − | 0.552458i | \(-0.813690\pi\) | ||||
0.833541 | − | 0.552458i | \(-0.186310\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 24.6632i | − 0.829044i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.8267 | −0.699292 | −0.349646 | − | 0.936882i | \(-0.613698\pi\) | ||||
−0.349646 | + | 0.936882i | \(0.613698\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.38283 | 0.180534 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 69.6934i | − 2.33482i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.9133i | 0.365201i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.19122 | 0.206950 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −70.0867 | −2.34013 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 2.31445i | − 0.0771913i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.6970i | 0.989351i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −29.9230 | −0.995774 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.3446 | 0.343868 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.2109i | 1.63402i | 0.576622 | + | 0.817011i | \(0.304371\pi\) | ||||
−0.576622 | + | 0.817011i | \(0.695629\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 117.584i | 3.90001i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.0717 | −1.39390 | −0.696949 | − | 0.717121i | \(-0.745460\pi\) | ||||
−0.696949 | + | 0.717121i | \(0.745460\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.9518 | 1.12364 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 34.3717i | 1.13629i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.8008i | 0.356675i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.2172 | −1.19469 | −0.597347 | − | 0.801983i | \(-0.703778\pi\) | ||||
−0.597347 | + | 0.801983i | \(0.703778\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 87.5036 | 2.88334 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37.5196i | 1.23497i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 4.98614i | − 0.163943i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −26.6801 | −0.876289 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.7342 | −0.417796 | −0.208898 | − | 0.977937i | \(-0.566988\pi\) | ||||
−0.208898 | + | 0.977937i | \(0.566988\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 2.79216i | − 0.0915095i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 3.12010i | − 0.102148i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −31.3282 | −1.02454 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.2176 | −1.15051 | −0.575254 | − | 0.817975i | \(-0.695097\pi\) | ||||
−0.575254 | + | 0.817975i | \(0.695097\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 14.7092i | − 0.480017i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.2193i | 0.985121i | 0.870278 | + | 0.492561i | \(0.163939\pi\) | ||||
−0.870278 | + | 0.492561i | \(0.836061\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.5228 | −0.993959 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.9934 | −0.390146 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 7.23680i | − 0.235164i | −0.993063 | − | 0.117582i | \(-0.962486\pi\) | ||||
0.993063 | − | 0.117582i | \(-0.0375144\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.2010i | 0.558369i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.16682 | 0.135118 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.1717 | 1.43086 | 0.715431 | − | 0.698683i | \(-0.246230\pi\) | ||||
0.715431 | + | 0.698683i | \(0.246230\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.3266i | 0.560677i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 127.076i | 4.10777i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.9651 | 0.354080 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9460 | −0.998257 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 24.6047i | − 0.792877i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.2039i | 0.811342i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.4144 | 1.17101 | 0.585505 | − | 0.810669i | \(-0.300896\pi\) | ||||
0.585505 | + | 0.810669i | \(0.300896\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 67.3448 | 2.16343 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 13.8144i | − 0.443326i | −0.975123 | − | 0.221663i | \(-0.928851\pi\) | ||||
0.975123 | − | 0.221663i | \(-0.0711486\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2.40141i | − 0.0769857i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.99545 | 0.288085 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.883020 | 0.0282503 | 0.0141252 | − | 0.999900i | \(-0.495504\pi\) | ||||
0.0141252 | + | 0.999900i | \(0.495504\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.5799i | 0.753618i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 60.1150i | 1.91932i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51.6614 | −1.64774 | −0.823871 | − | 0.566777i | \(-0.808190\pi\) | ||||
−0.823871 | + | 0.566777i | \(0.808190\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.4680 | 0.747754 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 12.2520i | − 0.389985i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 74.3752i | 2.36499i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.1941 | −0.514423 | −0.257211 | − | 0.966355i | \(-0.582804\pi\) | ||||
−0.257211 | + | 0.966355i | \(0.582804\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.66585 | −0.0845983 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 8.26099i | − 0.261891i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.0128i | 0.602142i | 0.953602 | + | 0.301071i | \(0.0973442\pi\) | ||||
−0.953602 | + | 0.301071i | \(0.902656\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 59.8010 | 1.89202 |
(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 | 2240.2.b.h.1121.11 | yes | 12 | |
4.3 | odd | 2 | 2240.2.b.g.1121.2 | ✓ | 12 | ||
8.3 | odd | 2 | 2240.2.b.g.1121.11 | yes | 12 | ||
8.5 | even | 2 | inner | 2240.2.b.h.1121.2 | yes | 12 | |
16.3 | odd | 4 | 8960.2.a.cc.1.6 | 6 | |||
16.5 | even | 4 | 8960.2.a.ce.1.6 | 6 | |||
16.11 | odd | 4 | 8960.2.a.ch.1.1 | 6 | |||
16.13 | even | 4 | 8960.2.a.cb.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.b.g.1121.2 | ✓ | 12 | 4.3 | odd | 2 | ||
2240.2.b.g.1121.11 | yes | 12 | 8.3 | odd | 2 | ||
2240.2.b.h.1121.2 | yes | 12 | 8.5 | even | 2 | inner | |
2240.2.b.h.1121.11 | yes | 12 | 1.1 | even | 1 | trivial | |
8960.2.a.cb.1.1 | 6 | 16.13 | even | 4 | |||
8960.2.a.cc.1.6 | 6 | 16.3 | odd | 4 | |||
8960.2.a.ce.1.6 | 6 | 16.5 | even | 4 | |||
8960.2.a.ch.1.1 | 6 | 16.11 | odd | 4 |