Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4400,2,Mod(1,4400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("4400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4400.a (trivial) |
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: | yes |
Analytic conductor: | \(35.1341768894\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 55) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4400.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −2.82843 | −1.63299 | −0.816497 | − | 0.577350i | \(-0.804087\pi\) | ||||
−0.816497 | + | 0.577350i | \(0.804087\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.00000 | 1.66667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.17157 | 0.324936 | 0.162468 | − | 0.986714i | \(-0.448055\pi\) | ||||
0.162468 | + | 0.986714i | \(0.448055\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.82843 | −1.65614 | −0.828068 | − | 0.560627i | \(-0.810560\pi\) | ||||
−0.828068 | + | 0.560627i | \(0.810560\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.65685 | 1.23443 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.82843 | −0.589768 | −0.294884 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294884 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65685 | −1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.65685 | −0.679061 | −0.339530 | − | 0.940595i | \(-0.610268\pi\) | ||||
−0.339530 | + | 0.940595i | \(0.610268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.82843 | 0.492366 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.65685 | 1.25878 | 0.629390 | − | 0.777090i | \(-0.283305\pi\) | ||||
0.629390 | + | 0.777090i | \(0.283305\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.31371 | −0.530618 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 19.3137 | 2.70446 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.6569 | −1.60119 | −0.800596 | − | 0.599204i | \(-0.795484\pi\) | ||||
−0.800596 | + | 0.599204i | \(0.795484\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.65685 | −0.215704 | −0.107852 | − | 0.994167i | \(-0.534397\pi\) | ||||
−0.107852 | + | 0.994167i | \(0.534397\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.31371 | −1.19250 | −0.596249 | − | 0.802799i | \(-0.703343\pi\) | ||||
−0.596249 | + | 0.802799i | \(0.703343\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.0000 | −1.25988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4853 | 1.52532 | 0.762660 | − | 0.646800i | \(-0.223893\pi\) | ||||
0.762660 | + | 0.646800i | \(0.223893\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.00000 | 0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3137 | −1.34269 | −0.671345 | − | 0.741145i | \(-0.734283\pi\) | ||||
−0.671345 | + | 0.741145i | \(0.734283\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.17157 | 0.137122 | 0.0685611 | − | 0.997647i | \(-0.478159\pi\) | ||||
0.0685611 | + | 0.997647i | \(0.478159\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.3431 | 1.10890 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.3137 | −1.41125 | −0.705625 | − | 0.708585i | \(-0.749334\pi\) | ||||
−0.705625 | + | 0.708585i | \(0.749334\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.34315 | −0.245628 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.65685 | −0.371297 | −0.185649 | − | 0.982616i | \(-0.559439\pi\) | ||||
−0.185649 | + | 0.982616i | \(0.559439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.00000 | −0.502519 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.31371 | 0.926749 | 0.463374 | − | 0.886163i | \(-0.346639\pi\) | ||||
0.463374 | + | 0.886163i | \(0.346639\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.82843 | 0.672825 | 0.336412 | − | 0.941715i | \(-0.390786\pi\) | ||||
0.336412 | + | 0.941715i | \(0.390786\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.65685 | 0.740216 | 0.370108 | − | 0.928989i | \(-0.379321\pi\) | ||||
0.370108 | + | 0.928989i | \(0.379321\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.65685 | −0.733394 | −0.366697 | − | 0.930341i | \(-0.619511\pi\) | ||||
−0.366697 | + | 0.930341i | \(0.619511\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.6569 | −2.05558 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.6569 | −1.84916 | −0.924581 | − | 0.380986i | \(-0.875584\pi\) | ||||
−0.924581 | + | 0.380986i | \(0.875584\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.85786 | 0.541560 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.6569 | 1.25192 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16.9706 | −1.53018 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.34315 | 0.385392 | 0.192696 | − | 0.981259i | \(-0.438277\pi\) | ||||
0.192696 | + | 0.981259i | \(0.438277\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.9706 | 1.49417 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.3137 | 0.988483 | 0.494242 | − | 0.869325i | \(-0.335446\pi\) | ||||
0.494242 | + | 0.869325i | \(0.335446\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.9706 | 0.937278 | 0.468639 | − | 0.883390i | \(-0.344744\pi\) | ||||
0.468639 | + | 0.883390i | \(0.344744\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.00000 | −0.673722 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.17157 | −0.0979718 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.48528 | 0.699854 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.343146 | 0.0281116 | 0.0140558 | − | 0.999901i | \(-0.495526\pi\) | ||||
0.0140558 | + | 0.999901i | \(0.495526\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −34.1421 | −2.76023 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 32.9706 | 2.61474 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.65685 | 0.445823 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.4853 | 1.29123 | 0.645613 | − | 0.763664i | \(-0.276602\pi\) | ||||
0.645613 | + | 0.763664i | \(0.276602\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.9706 | −1.77752 | −0.888758 | − | 0.458377i | \(-0.848431\pi\) | ||||
−0.888758 | + | 0.458377i | \(0.848431\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6274 | −0.894417 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.1421 | 1.68344 | 0.841718 | − | 0.539918i | \(-0.181545\pi\) | ||||
0.841718 | + | 0.539918i | \(0.181545\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.68629 | 0.352243 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.65685 | −0.721787 | −0.360894 | − | 0.932607i | \(-0.617528\pi\) | ||||
−0.360894 | + | 0.932607i | \(0.617528\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.3137 | 1.58424 | 0.792118 | − | 0.610368i | \(-0.208979\pi\) | ||||
0.792118 | + | 0.610368i | \(0.208979\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 26.3431 | 1.94734 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.82843 | 0.499344 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.3137 | 0.822951 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.31371 | −0.239772 | −0.119886 | − | 0.992788i | \(-0.538253\pi\) | ||||
−0.119886 | + | 0.992788i | \(0.538253\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.17157 | 0.0843317 | 0.0421658 | − | 0.999111i | \(-0.486574\pi\) | ||||
0.0421658 | + | 0.999111i | \(0.486574\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.8284 | 0.771493 | 0.385747 | − | 0.922605i | \(-0.373944\pi\) | ||||
0.385747 | + | 0.922605i | \(0.373944\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.3431 | −0.733206 | −0.366603 | − | 0.930377i | \(-0.619479\pi\) | ||||
−0.366603 | + | 0.930377i | \(0.619479\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −35.3137 | −2.49084 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.31371 | 0.513322 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.1421 | −0.982946 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0000 | 1.10149 | 0.550743 | − | 0.834675i | \(-0.314345\pi\) | ||||
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 32.0000 | 2.19260 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.31371 | −0.223920 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.8284 | −0.725125 | −0.362563 | − | 0.931959i | \(-0.618098\pi\) | ||||
−0.362563 | + | 0.931959i | \(0.618098\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.3137 | 1.68013 | 0.840065 | − | 0.542486i | \(-0.182517\pi\) | ||||
0.840065 | + | 0.542486i | \(0.182517\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.31371 | 0.0868123 | 0.0434062 | − | 0.999058i | \(-0.486179\pi\) | ||||
0.0434062 | + | 0.999058i | \(0.486179\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.65685 | −0.372194 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.14214 | 0.402385 | 0.201192 | − | 0.979552i | \(-0.435518\pi\) | ||||
0.201192 | + | 0.979552i | \(0.435518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.3137 | 0.734904 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.3137 | 1.50804 | 0.754019 | − | 0.656852i | \(-0.228113\pi\) | ||||
0.754019 | + | 0.656852i | \(0.228113\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.1421 | 0.907218 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.9706 | 1.07547 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.82843 | 0.177822 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.31371 | 0.580973 | 0.290487 | − | 0.956879i | \(-0.406183\pi\) | ||||
0.290487 | + | 0.956879i | \(0.406183\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.3137 | −0.951548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.2843 | −1.13177 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.9706 | −0.676474 | −0.338237 | − | 0.941061i | \(-0.609831\pi\) | ||||
−0.338237 | + | 0.941061i | \(0.609831\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 37.6569 | 2.30456 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.3137 | 1.05564 | 0.527818 | − | 0.849358i | \(-0.323010\pi\) | ||||
0.527818 | + | 0.849358i | \(0.323010\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.31371 | −0.444276 | −0.222138 | − | 0.975015i | \(-0.571304\pi\) | ||||
−0.222138 | + | 0.975015i | \(0.571304\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.62742 | 0.401110 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.82843 | −0.410280 | −0.205140 | − | 0.978733i | \(-0.565765\pi\) | ||||
−0.205140 | + | 0.978733i | \(0.565765\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.3137 | 1.03285 | 0.516425 | − | 0.856333i | \(-0.327263\pi\) | ||||
0.516425 | + | 0.856333i | \(0.327263\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 32.6274 | 1.93950 | 0.969749 | − | 0.244103i | \(-0.0784935\pi\) | ||||
0.969749 | + | 0.244103i | \(0.0784935\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | −0.708338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.6274 | 1.74279 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.3431 | 0.606326 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.17157 | 0.535809 | 0.267905 | − | 0.963445i | \(-0.413669\pi\) | ||||
0.267905 | + | 0.963445i | \(0.413669\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.65685 | 0.328244 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.31371 | −0.191637 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0000 | 0.691669 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −26.3431 | −1.51337 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.3431 | −0.932753 | −0.466376 | − | 0.884586i | \(-0.654441\pi\) | ||||
−0.466376 | + | 0.884586i | \(0.654441\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.3137 | −1.09872 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.68629 | −0.265735 | −0.132868 | − | 0.991134i | \(-0.542419\pi\) | ||||
−0.132868 | + | 0.991134i | \(0.542419\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.31371 | 0.0742552 | 0.0371276 | − | 0.999311i | \(-0.488179\pi\) | ||||
0.0371276 | + | 0.999311i | \(0.488179\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.31371 | 0.0737852 | 0.0368926 | − | 0.999319i | \(-0.488254\pi\) | ||||
0.0368926 | + | 0.999319i | \(0.488254\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.65685 | 0.204745 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.6569 | −1.20877 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.6569 | 1.19763 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.65685 | −0.311872 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.31371 | 0.401998 | 0.200999 | − | 0.979591i | \(-0.435581\pi\) | ||||
0.200999 | + | 0.979591i | \(0.435581\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 38.2843 | 2.09797 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.4853 | 1.11590 | 0.557952 | − | 0.829873i | \(-0.311587\pi\) | ||||
0.557952 | + | 0.829873i | \(0.311587\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 55.5980 | 3.01967 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.9706 | 0.588931 | 0.294465 | − | 0.955662i | \(-0.404858\pi\) | ||||
0.294465 | + | 0.955662i | \(0.404858\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.9706 | 1.44370 | 0.721851 | − | 0.692049i | \(-0.243292\pi\) | ||||
0.721851 | + | 0.692049i | \(0.243292\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.62742 | −0.353745 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.3137 | −1.13441 | −0.567207 | − | 0.823575i | \(-0.691976\pi\) | ||||
−0.567207 | + | 0.823575i | \(0.691976\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −38.6274 | −2.04438 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.686292 | −0.0362211 | −0.0181105 | − | 0.999836i | \(-0.505765\pi\) | ||||
−0.0181105 | + | 0.999836i | \(0.505765\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.82843 | −0.148454 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.48528 | −0.442928 | −0.221464 | − | 0.975169i | \(-0.571084\pi\) | ||||
−0.221464 | + | 0.975169i | \(0.571084\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 30.0000 | 1.56174 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.3137 | 1.21039 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.7990 | −1.85360 | −0.926801 | − | 0.375554i | \(-0.877453\pi\) | ||||
−0.926801 | + | 0.375554i | \(0.877453\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.28427 | −0.220651 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.6569 | −1.72884 | −0.864418 | − | 0.502773i | \(-0.832313\pi\) | ||||
−0.864418 | + | 0.502773i | \(0.832313\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.2843 | −0.629342 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.85786 | −0.299323 | −0.149661 | − | 0.988737i | \(-0.547818\pi\) | ||||
−0.149661 | + | 0.988737i | \(0.547818\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −30.0000 | −1.52499 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.6274 | 1.04585 | 0.522926 | − | 0.852378i | \(-0.324840\pi\) | ||||
0.522926 | + | 0.852378i | \(0.324840\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.3137 | 0.976736 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −32.0000 | −1.61419 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.31371 | 0.467442 | 0.233721 | − | 0.972304i | \(-0.424910\pi\) | ||||
0.233721 | + | 0.972304i | \(0.424910\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.31371 | −0.265354 | −0.132677 | − | 0.991159i | \(-0.542357\pi\) | ||||
−0.132677 | + | 0.991159i | \(0.542357\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.65685 | −0.379536 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.02944 | 0.0509024 | 0.0254512 | − | 0.999676i | \(-0.491898\pi\) | ||||
0.0254512 | + | 0.999676i | \(0.491898\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −31.0294 | −1.53057 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.31371 | 0.163057 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.3137 | −0.554035 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.6569 | 1.25342 | 0.626710 | − | 0.779253i | \(-0.284401\pi\) | ||||
0.626710 | + | 0.779253i | \(0.284401\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.1421 | 0.687614 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.6274 | 0.901444 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.31371 | 0.159987 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.3137 | 0.544962 | 0.272481 | − | 0.962161i | \(-0.412156\pi\) | ||||
0.272481 | + | 0.962161i | \(0.412156\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.65685 | 0.367965 | 0.183982 | − | 0.982930i | \(-0.441101\pi\) | ||||
0.183982 | + | 0.982930i | \(0.441101\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0000 | 0.763638 | 0.381819 | − | 0.924237i | \(-0.375298\pi\) | ||||
0.381819 | + | 0.924237i | \(0.375298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | −0.714286 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.8284 | −1.27466 | −0.637329 | − | 0.770592i | \(-0.719961\pi\) | ||||
−0.637329 | + | 0.770592i | \(0.719961\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.970563 | −0.0459060 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.6274 | 1.35101 | 0.675506 | − | 0.737355i | \(-0.263925\pi\) | ||||
0.675506 | + | 0.737355i | \(0.263925\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | −0.282529 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −33.9411 | −1.59469 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.485281 | −0.0227005 | −0.0113503 | − | 0.999936i | \(-0.503613\pi\) | ||||
−0.0113503 | + | 0.999936i | \(0.503613\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 38.6274 | 1.80297 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.6274 | 0.588117 | 0.294059 | − | 0.955787i | \(-0.404994\pi\) | ||||
0.294059 | + | 0.955787i | \(0.404994\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.14214 | −0.285449 | −0.142725 | − | 0.989762i | \(-0.545586\pi\) | ||||
−0.142725 | + | 0.989762i | \(0.545586\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.8284 | −0.686178 | −0.343089 | − | 0.939303i | \(-0.611473\pi\) | ||||
−0.343089 | + | 0.939303i | \(0.611473\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.9706 | −1.15303 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −39.5980 | −1.82458 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.00000 | 0.275880 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −58.2843 | −2.66865 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.0000 | 1.64488 | 0.822441 | − | 0.568850i | \(-0.192612\pi\) | ||||
0.822441 | + | 0.568850i | \(0.192612\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.97056 | 0.409022 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.0000 | −0.728025 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.4853 | −1.10953 | −0.554767 | − | 0.832006i | \(-0.687193\pi\) | ||||
−0.554767 | + | 0.832006i | \(0.687193\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −46.6274 | −2.10856 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.686292 | 0.0309719 | 0.0154860 | − | 0.999880i | \(-0.495070\pi\) | ||||
0.0154860 | + | 0.999880i | \(0.495070\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.9706 | 1.12462 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.6274 | 1.01498 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.65685 | −0.432300 | −0.216150 | − | 0.976360i | \(-0.569350\pi\) | ||||
−0.216150 | + | 0.976360i | \(0.569350\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 64.9706 | 2.90267 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.6274 | 0.741380 | 0.370690 | − | 0.928757i | \(-0.379121\pi\) | ||||
0.370690 | + | 0.928757i | \(0.379121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 32.8873 | 1.46058 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.3137 | −0.590120 | −0.295060 | − | 0.955479i | \(-0.595340\pi\) | ||||
−0.295060 | + | 0.955479i | \(0.595340\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.34315 | −0.103655 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.82843 | −0.124394 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −62.6274 | −2.74904 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.3137 | 1.10901 | 0.554507 | − | 0.832179i | \(-0.312907\pi\) | ||||
0.554507 | + | 0.832179i | \(0.312907\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −41.5980 | −1.81895 | −0.909476 | − | 0.415756i | \(-0.863517\pi\) | ||||
−0.909476 | + | 0.415756i | \(0.863517\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.28427 | −0.359507 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.02944 | 0.304479 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 27.3137 | 1.17867 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.00000 | 0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.00000 | 0.257960 | 0.128980 | − | 0.991647i | \(-0.458830\pi\) | ||||
0.128980 | + | 0.991647i | \(0.458830\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −60.2843 | −2.58705 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.0000 | −1.45374 | −0.726868 | − | 0.686778i | \(-0.759025\pi\) | ||||
−0.726868 | + | 0.686778i | \(0.759025\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −46.5685 | −1.98750 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000 | 0.340195 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.85786 | −0.417691 | −0.208846 | − | 0.977949i | \(-0.566971\pi\) | ||||
−0.208846 | + | 0.977949i | \(0.566971\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.02944 | −0.297314 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.3137 | −0.815425 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.343146 | 0.0144619 | 0.00723093 | − | 0.999974i | \(-0.497698\pi\) | ||||
0.00723093 | + | 0.999974i | \(0.497698\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.00000 | −0.0839921 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.6569 | 1.32712 | 0.663562 | − | 0.748121i | \(-0.269044\pi\) | ||||
0.663562 | + | 0.748121i | \(0.269044\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.9411 | 0.918208 | 0.459104 | − | 0.888383i | \(-0.348171\pi\) | ||||
0.459104 | + | 0.888383i | \(0.348171\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.37258 | 0.391545 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.9706 | 1.12280 | 0.561400 | − | 0.827545i | \(-0.310263\pi\) | ||||
0.561400 | + | 0.827545i | \(0.310263\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.31371 | −0.137713 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | 0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.6569 | 0.482778 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.14214 | −0.0884154 | −0.0442077 | − | 0.999022i | \(-0.514076\pi\) | ||||
−0.0442077 | + | 0.999022i | \(0.514076\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.6274 | −1.25984 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.51472 | −0.144332 | −0.0721661 | − | 0.997393i | \(-0.522991\pi\) | ||||
−0.0721661 | + | 0.997393i | \(0.522991\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.2548 | 1.19732 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.65685 | 0.231133 | 0.115566 | − | 0.993300i | \(-0.463132\pi\) | ||||
0.115566 | + | 0.993300i | \(0.463132\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.9411 | 0.976579 | 0.488289 | − | 0.872682i | \(-0.337621\pi\) | ||||
0.488289 | + | 0.872682i | \(0.337621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 62.4264 | 2.54220 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.2843 | 1.55391 | 0.776955 | − | 0.629556i | \(-0.216763\pi\) | ||||
0.776955 | + | 0.629556i | \(0.216763\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.6863 | −0.838251 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.31371 | 0.134058 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.4558 | 1.02815 | 0.514076 | − | 0.857745i | \(-0.328135\pi\) | ||||
0.514076 | + | 0.857745i | \(0.328135\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.343146 | −0.0138145 | −0.00690726 | − | 0.999976i | \(-0.502199\pi\) | ||||
−0.00690726 | + | 0.999976i | \(0.502199\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.3431 | 0.576500 | 0.288250 | − | 0.957555i | \(-0.406927\pi\) | ||||
0.288250 | + | 0.957555i | \(0.406927\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.0000 | 0.642058 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 26.6274 | 1.06680 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −52.2843 | −2.08471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −45.2548 | −1.79872 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.51472 | −0.139258 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −56.5685 | −2.23782 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.0000 | 1.18493 | 0.592464 | − | 0.805597i | \(-0.298155\pi\) | ||||
0.592464 | + | 0.805597i | \(0.298155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.45584 | −0.0574129 | −0.0287064 | − | 0.999588i | \(-0.509139\pi\) | ||||
−0.0287064 | + | 0.999588i | \(0.509139\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.1127 | 1.06591 | 0.532955 | − | 0.846144i | \(-0.321081\pi\) | ||||
0.532955 | + | 0.846144i | \(0.321081\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.65685 | 0.0650372 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.6569 | −0.456168 | −0.228084 | − | 0.973641i | \(-0.573246\pi\) | ||||
−0.228084 | + | 0.973641i | \(0.573246\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.85786 | 0.228537 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.9411 | −1.78961 | −0.894806 | − | 0.446455i | \(-0.852686\pi\) | ||||
−0.894806 | + | 0.446455i | \(0.852686\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.6274 | 1.73581 | 0.867903 | − | 0.496734i | \(-0.165468\pi\) | ||||
0.867903 | + | 0.496734i | \(0.165468\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 22.6274 | 0.878776 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.3431 | 0.400488 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 30.6274 | 1.18412 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.31371 | 0.359552 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.4853 | 0.481272 | 0.240636 | − | 0.970615i | \(-0.422644\pi\) | ||||
0.240636 | + | 0.970615i | \(0.422644\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.8284 | −0.877368 | −0.438684 | − | 0.898641i | \(-0.644555\pi\) | ||||
−0.438684 | + | 0.898641i | \(0.644555\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.31371 | 0.280674 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −71.5980 | −2.74364 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.79899 | −0.298420 | −0.149210 | − | 0.988806i | \(-0.547673\pi\) | ||||
−0.149210 | + | 0.988806i | \(0.547673\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.71573 | −0.141764 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.6569 | −0.520285 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.3137 | 1.49556 | 0.747782 | − | 0.663944i | \(-0.231119\pi\) | ||||
0.747782 | + | 0.663944i | \(0.231119\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.0000 | 0.379869 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −40.9706 | −1.55187 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.3726 | −0.657091 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.6274 | −0.476931 | −0.238465 | − | 0.971151i | \(-0.576644\pi\) | ||||
−0.238465 | + | 0.971151i | \(0.576644\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.6274 | −0.700556 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.6274 | 0.924902 | 0.462451 | − | 0.886645i | \(-0.346970\pi\) | ||||
0.462451 | + | 0.886645i | \(0.346970\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.0000 | −0.750059 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −65.9411 | −2.46262 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.3431 | −0.684084 | −0.342042 | − | 0.939685i | \(-0.611118\pi\) | ||||
−0.342042 | + | 0.939685i | \(0.611118\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.6569 | −0.508608 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.9706 | −0.631142 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.5147 | −0.723761 | −0.361880 | − | 0.932225i | \(-0.617865\pi\) | ||||
−0.361880 | + | 0.932225i | \(0.617865\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.0000 | −1.59259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 40.9706 | 1.51535 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.4558 | 0.644746 | 0.322373 | − | 0.946613i | \(-0.395519\pi\) | ||||
0.322373 | + | 0.946613i | \(0.395519\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.4853 | −0.459901 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.9411 | −1.10140 | −0.550701 | − | 0.834703i | \(-0.685640\pi\) | ||||
−0.550701 | + | 0.834703i | \(0.685640\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −49.5980 | −1.81957 | −0.909787 | − | 0.415076i | \(-0.863755\pi\) | ||||
−0.909787 | + | 0.415076i | \(0.863755\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −30.0000 | −1.09764 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.3137 | −0.559551 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.0000 | 0.583848 | 0.291924 | − | 0.956441i | \(-0.405705\pi\) | ||||
0.291924 | + | 0.956441i | \(0.405705\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 33.9411 | 1.23688 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.3137 | −0.483895 | −0.241947 | − | 0.970289i | \(-0.577786\pi\) | ||||
−0.241947 | + | 0.970289i | \(0.577786\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.00000 | −0.290382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.0000 | −1.08750 | −0.543750 | − | 0.839248i | \(-0.682996\pi\) | ||||
−0.543750 | + | 0.839248i | \(0.682996\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.3137 | 0.554393 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.94113 | −0.0700900 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.9706 | −0.684096 | −0.342048 | − | 0.939682i | \(-0.611121\pi\) | ||||
−0.342048 | + | 0.939682i | \(0.611121\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.3431 | −0.948725 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.2843 | −0.945380 | −0.472690 | − | 0.881229i | \(-0.656717\pi\) | ||||
−0.472690 | + | 0.881229i | \(0.656717\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 43.3137 | 1.55387 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.3137 | 0.404836 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.6863 | 0.739268 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.9706 | −0.533643 | −0.266821 | − | 0.963746i | \(-0.585973\pi\) | ||||
−0.266821 | + | 0.963746i | \(0.585973\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 31.0294 | 1.10468 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 39.3137 | 1.39783 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.9117 | −0.387485 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.6274 | −1.15572 | −0.577861 | − | 0.816135i | \(-0.696113\pi\) | ||||
−0.577861 | + | 0.816135i | \(0.696113\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.3137 | −0.683270 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −66.5685 | −2.35208 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.17157 | −0.0413439 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −48.9706 | −1.72385 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.9706 | −0.385704 | −0.192852 | − | 0.981228i | \(-0.561774\pi\) | ||||
−0.192852 | + | 0.981228i | \(0.561774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −53.9411 | −1.89413 | −0.947065 | − | 0.321043i | \(-0.895967\pi\) | ||||
−0.947065 | + | 0.321043i | \(0.895967\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.6863 | 0.725500 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11.7157 | −0.409381 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.3137 | −1.44186 | −0.720929 | − | 0.693009i | \(-0.756285\pi\) | ||||
−0.720929 | + | 0.693009i | \(0.756285\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.5147 | 0.680240 | 0.340120 | − | 0.940382i | \(-0.389532\pi\) | ||||
0.340120 | + | 0.940382i | \(0.389532\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.2843 | 0.774900 | 0.387450 | − | 0.921891i | \(-0.373356\pi\) | ||||
0.387450 | + | 0.921891i | \(0.373356\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.0000 | 0.625166 | 0.312583 | − | 0.949890i | \(-0.398806\pi\) | ||||
0.312583 | + | 0.949890i | \(0.398806\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.3137 | 0.669985 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.4853 | 0.709773 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.3431 | −0.909466 | −0.454733 | − | 0.890628i | \(-0.650265\pi\) | ||||
−0.454733 | + | 0.890628i | \(0.650265\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.6274 | −0.538876 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −48.9706 | −1.68664 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.00000 | −0.0687208 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −92.2843 | −3.16719 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.6569 | −0.742387 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.5147 | 0.531214 | 0.265607 | − | 0.964081i | \(-0.414428\pi\) | ||||
0.265607 | + | 0.964081i | \(0.414428\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.7696 | −0.846112 | −0.423056 | − | 0.906104i | \(-0.639043\pi\) | ||||
−0.423056 | + | 0.906104i | \(0.639043\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.2843 | −0.828569 | −0.414284 | − | 0.910148i | \(-0.635968\pi\) | ||||
−0.414284 | + | 0.910148i | \(0.635968\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 33.9411 | 1.15671 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.17157 | −0.312204 | −0.156102 | − | 0.987741i | \(-0.549893\pi\) | ||||
−0.156102 | + | 0.987741i | \(0.549893\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −83.7990 | −2.84596 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.00000 | 0.135691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.6274 | 0.495631 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.2843 | −0.618829 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.4558 | 1.67001 | 0.835003 | − | 0.550246i | \(-0.185466\pi\) | ||||
0.835003 | + | 0.550246i | \(0.185466\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25.9411 | −0.874972 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.37258 | −0.248389 | −0.124194 | − | 0.992258i | \(-0.539635\pi\) | ||||
−0.124194 | + | 0.992258i | \(0.539635\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.1716 | 1.25092 | 0.625462 | − | 0.780255i | \(-0.284911\pi\) | ||||
0.625462 | + | 0.780255i | \(0.284911\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38.2843 | 1.28546 | 0.642730 | − | 0.766093i | \(-0.277802\pi\) | ||||
0.642730 | + | 0.766093i | \(0.277802\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.68629 | −0.291329 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.37258 | 0.312941 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 79.5980 | 2.65179 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −33.9411 | −1.12949 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.5147 | −0.913611 | −0.456806 | − | 0.889567i | \(-0.651007\pi\) | ||||
−0.456806 | + | 0.889567i | \(0.651007\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 46.5685 | 1.54458 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.94113 | 0.329364 | 0.164682 | − | 0.986347i | \(-0.447340\pi\) | ||||
0.164682 | + | 0.986347i | \(0.447340\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.00000 | 0.198571 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.6274 | −0.747223 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.0000 | 1.05558 | 0.527791 | − | 0.849374i | \(-0.323020\pi\) | ||||
0.527791 | + | 0.849374i | \(0.323020\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 46.2254 | 1.52318 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.2548 | −0.436288 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 34.1421 | 1.12137 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.31371 | 0.174337 | 0.0871686 | − | 0.996194i | \(-0.472218\pi\) | ||||
0.0871686 | + | 0.996194i | \(0.472218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.2548 | 0.433944 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.45584 | 0.0475604 | 0.0237802 | − | 0.999717i | \(-0.492430\pi\) | ||||
0.0237802 | + | 0.999717i | \(0.492430\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.71573 | −0.121258 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.68629 | −0.217967 | −0.108983 | − | 0.994044i | \(-0.534760\pi\) | ||||
−0.108983 | + | 0.994044i | \(0.534760\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.9706 | −0.552638 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.1716 | 1.33790 | 0.668948 | − | 0.743309i | \(-0.266745\pi\) | ||||
0.668948 | + | 0.743309i | \(0.266745\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.37258 | 0.0445559 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.71573 | −0.120491 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53.1716 | −1.72240 | −0.861198 | − | 0.508269i | \(-0.830285\pi\) | ||||
−0.861198 | + | 0.508269i | \(0.830285\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.3431 | −0.334346 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −21.9411 | −0.708516 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 38.2843 | 1.23369 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.9706 | −0.481421 | −0.240710 | − | 0.970597i | \(-0.577380\pi\) | ||||
−0.240710 | + | 0.970597i | \(0.577380\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.68629 | 0.278756 | 0.139378 | − | 0.990239i | \(-0.455490\pi\) | ||||
0.139378 | + | 0.990239i | \(0.455490\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.00000 | −0.256468 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.3431 | −1.03475 | −0.517374 | − | 0.855759i | \(-0.673091\pi\) | ||||
−0.517374 | + | 0.855759i | \(0.673091\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.3137 | 0.425508 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −38.2843 | −1.22232 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.8579 | −0.697158 | −0.348579 | − | 0.937279i | \(-0.613336\pi\) | ||||
−0.348579 | + | 0.937279i | \(0.613336\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.0000 | 0.509286 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.9706 | 0.539633 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57.9411 | 1.84056 | 0.920280 | − | 0.391260i | \(-0.127961\pi\) | ||||
0.920280 | + | 0.391260i | \(0.127961\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.6863 | −0.656460 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.4558 | 1.31292 | 0.656460 | − | 0.754361i | \(-0.272053\pi\) | ||||
0.656460 | + | 0.754361i | \(0.272053\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −43.3137 | −1.37039 |
(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 | 4400.2.a.bn.1.1 | 2 | ||
4.3 | odd | 2 | 275.2.a.c.1.1 | 2 | |||
5.2 | odd | 4 | 4400.2.b.q.4049.3 | 4 | |||
5.3 | odd | 4 | 4400.2.b.q.4049.2 | 4 | |||
5.4 | even | 2 | 880.2.a.m.1.2 | 2 | |||
12.11 | even | 2 | 2475.2.a.x.1.2 | 2 | |||
15.14 | odd | 2 | 7920.2.a.ch.1.2 | 2 | |||
20.3 | even | 4 | 275.2.b.d.199.4 | 4 | |||
20.7 | even | 4 | 275.2.b.d.199.1 | 4 | |||
20.19 | odd | 2 | 55.2.a.b.1.2 | ✓ | 2 | ||
40.19 | odd | 2 | 3520.2.a.bn.1.2 | 2 | |||
40.29 | even | 2 | 3520.2.a.bo.1.1 | 2 | |||
44.43 | even | 2 | 3025.2.a.o.1.2 | 2 | |||
55.54 | odd | 2 | 9680.2.a.bn.1.2 | 2 | |||
60.23 | odd | 4 | 2475.2.c.l.199.1 | 4 | |||
60.47 | odd | 4 | 2475.2.c.l.199.4 | 4 | |||
60.59 | even | 2 | 495.2.a.b.1.1 | 2 | |||
140.139 | even | 2 | 2695.2.a.f.1.2 | 2 | |||
220.19 | even | 10 | 605.2.g.l.251.1 | 8 | |||
220.39 | even | 10 | 605.2.g.l.366.2 | 8 | |||
220.59 | odd | 10 | 605.2.g.f.511.2 | 8 | |||
220.79 | even | 10 | 605.2.g.l.81.2 | 8 | |||
220.119 | odd | 10 | 605.2.g.f.81.1 | 8 | |||
220.139 | even | 10 | 605.2.g.l.511.1 | 8 | |||
220.159 | odd | 10 | 605.2.g.f.366.1 | 8 | |||
220.179 | odd | 10 | 605.2.g.f.251.2 | 8 | |||
220.219 | even | 2 | 605.2.a.d.1.1 | 2 | |||
260.259 | odd | 2 | 9295.2.a.g.1.1 | 2 | |||
660.659 | odd | 2 | 5445.2.a.y.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.a.b.1.2 | ✓ | 2 | 20.19 | odd | 2 | ||
275.2.a.c.1.1 | 2 | 4.3 | odd | 2 | |||
275.2.b.d.199.1 | 4 | 20.7 | even | 4 | |||
275.2.b.d.199.4 | 4 | 20.3 | even | 4 | |||
495.2.a.b.1.1 | 2 | 60.59 | even | 2 | |||
605.2.a.d.1.1 | 2 | 220.219 | even | 2 | |||
605.2.g.f.81.1 | 8 | 220.119 | odd | 10 | |||
605.2.g.f.251.2 | 8 | 220.179 | odd | 10 | |||
605.2.g.f.366.1 | 8 | 220.159 | odd | 10 | |||
605.2.g.f.511.2 | 8 | 220.59 | odd | 10 | |||
605.2.g.l.81.2 | 8 | 220.79 | even | 10 | |||
605.2.g.l.251.1 | 8 | 220.19 | even | 10 | |||
605.2.g.l.366.2 | 8 | 220.39 | even | 10 | |||
605.2.g.l.511.1 | 8 | 220.139 | even | 10 | |||
880.2.a.m.1.2 | 2 | 5.4 | even | 2 | |||
2475.2.a.x.1.2 | 2 | 12.11 | even | 2 | |||
2475.2.c.l.199.1 | 4 | 60.23 | odd | 4 | |||
2475.2.c.l.199.4 | 4 | 60.47 | odd | 4 | |||
2695.2.a.f.1.2 | 2 | 140.139 | even | 2 | |||
3025.2.a.o.1.2 | 2 | 44.43 | even | 2 | |||
3520.2.a.bn.1.2 | 2 | 40.19 | odd | 2 | |||
3520.2.a.bo.1.1 | 2 | 40.29 | even | 2 | |||
4400.2.a.bn.1.1 | 2 | 1.1 | even | 1 | trivial | ||
4400.2.b.q.4049.2 | 4 | 5.3 | odd | 4 | |||
4400.2.b.q.4049.3 | 4 | 5.2 | odd | 4 | |||
5445.2.a.y.1.2 | 2 | 660.659 | odd | 2 | |||
7920.2.a.ch.1.2 | 2 | 15.14 | odd | 2 | |||
9295.2.a.g.1.1 | 2 | 260.259 | odd | 2 | |||
9680.2.a.bn.1.2 | 2 | 55.54 | odd | 2 |