Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2475,2,Mod(199,2475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2475.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2475.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.7629745003\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 55) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2475.199 |
Dual form | 2475.2.c.l.199.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2475\mathbb{Z}\right)^\times\).
\(n\) | \(551\) | \(2026\) | \(2377\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.41421i | − 1.70711i | −0.521005 | − | 0.853553i | \(-0.674443\pi\) | ||||
0.521005 | − | 0.853553i | \(-0.325557\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.82843 | −1.91421 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.00000i | − 0.755929i | −0.925820 | − | 0.377964i | \(-0.876624\pi\) | ||||
0.925820 | − | 0.377964i | \(-0.123376\pi\) | |||||||
\(8\) | 4.41421i | 1.56066i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.17157i | 0.324936i | 0.986714 | + | 0.162468i | \(0.0519454\pi\) | ||||
−0.986714 | + | 0.162468i | \(0.948055\pi\) | |||||||
\(14\) | −4.82843 | −1.29045 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | − 6.82843i | − 1.65614i | −0.560627 | − | 0.828068i | \(-0.689440\pi\) | ||||
0.560627 | − | 0.828068i | \(-0.310560\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.41421i | 0.514712i | ||||||||
\(23\) | − 2.82843i | − 0.589768i | −0.955533 | − | 0.294884i | \(-0.904719\pi\) | ||||
0.955533 | − | 0.294884i | \(-0.0952810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.82843 | 0.554700 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.65685i | 1.44701i | ||||||||
\(29\) | −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 | \(0.5\pi\) | |||||||||
\(32\) | 1.58579i | 0.280330i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −16.4853 | −2.82720 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 7.65685i | − 1.25878i | −0.777090 | − | 0.629390i | \(-0.783305\pi\) | ||||
0.777090 | − | 0.629390i | \(-0.216695\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00000i | 0.914991i | 0.889212 | + | 0.457496i | \(0.151253\pi\) | ||||
−0.889212 | + | 0.457496i | \(0.848747\pi\) | |||||||
\(44\) | 3.82843 | 0.577157 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.82843 | −1.00680 | ||||||||
\(47\) | − 2.82843i | − 0.412568i | −0.978492 | − | 0.206284i | \(-0.933863\pi\) | ||||
0.978492 | − | 0.206284i | \(-0.0661372\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 4.48528i | − 0.621997i | ||||||||
\(53\) | 11.6569i | 1.60119i | 0.599204 | + | 0.800596i | \(0.295484\pi\) | ||||
−0.599204 | + | 0.800596i | \(0.704516\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.82843 | 1.17975 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.82843i | 1.15923i | ||||||||
\(59\) | 1.65685 | 0.215704 | 0.107852 | − | 0.994167i | \(-0.465603\pi\) | ||||
0.107852 | + | 0.994167i | \(0.465603\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.31371 | −1.19250 | −0.596249 | − | 0.802799i | \(-0.703343\pi\) | ||||
−0.596249 | + | 0.802799i | \(0.703343\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 9.82843 | 1.22855 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4853i | 1.52532i | 0.646800 | + | 0.762660i | \(0.276107\pi\) | ||||
−0.646800 | + | 0.762660i | \(0.723893\pi\) | |||||||
\(68\) | 26.1421i | 3.17020i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3137 | −1.34269 | −0.671345 | − | 0.741145i | \(-0.734283\pi\) | ||||
−0.671345 | + | 0.741145i | \(0.734283\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.17157i | 0.137122i | 0.997647 | + | 0.0685611i | \(0.0218408\pi\) | ||||
−0.997647 | + | 0.0685611i | \(0.978159\pi\) | |||||||
\(74\) | −18.4853 | −2.14887 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00000i | 0.227921i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 14.4853i | 1.59963i | ||||||||
\(83\) | − 6.00000i | − 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14.4853 | 1.56199 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 4.41421i | − 0.470557i | ||||||||
\(89\) | −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 | ||||||||
\(92\) | 10.8284i | 1.12894i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.82843 | −0.704298 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.65685i | 0.371297i | 0.982616 | + | 0.185649i | \(0.0594386\pi\) | ||||
−0.982616 | + | 0.185649i | \(0.940561\pi\) | |||||||
\(98\) | − 7.24264i | − 0.731617i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.31371 | −0.926749 | −0.463374 | − | 0.886163i | \(-0.653361\pi\) | ||||
−0.463374 | + | 0.886163i | \(0.653361\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 6.82843i | − 0.672825i | −0.941715 | − | 0.336412i | \(-0.890786\pi\) | ||||
0.941715 | − | 0.336412i | \(-0.109214\pi\) | |||||||
\(104\) | −5.17157 | −0.507114 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 28.1421 | 2.73341 | ||||||||
\(107\) | − 7.65685i | − 0.740216i | −0.928989 | − | 0.370108i | \(-0.879321\pi\) | ||||
0.928989 | − | 0.370108i | \(-0.120679\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.65685 | 0.733394 | 0.366697 | − | 0.930341i | \(-0.380489\pi\) | ||||
0.366697 | + | 0.930341i | \(0.380489\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 6.00000i | − 0.566947i | ||||||||
\(113\) | 19.6569i | 1.84916i | 0.380986 | + | 0.924581i | \(0.375584\pi\) | ||||
−0.380986 | + | 0.924581i | \(0.624416\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 14.0000 | 1.29987 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 4.00000i | − 0.368230i | ||||||||
\(119\) | −13.6569 | −1.25192 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 22.4853i | 2.03572i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.34315i | 0.385392i | 0.981259 | + | 0.192696i | \(0.0617231\pi\) | ||||
−0.981259 | + | 0.192696i | \(0.938277\pi\) | |||||||
\(128\) | − 20.5563i | − 1.81694i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | ||||||||
\(134\) | 30.1421 | 2.60388 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 30.1421 | 2.58467 | ||||||||
\(137\) | 10.9706i | 0.937278i | 0.883390 | + | 0.468639i | \(0.155256\pi\) | ||||
−0.883390 | + | 0.468639i | \(0.844744\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 27.3137i | 2.29212i | ||||||||
\(143\) | − 1.17157i | − 0.0979718i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.82843 | 0.234082 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 29.3137i | 2.40957i | ||||||||
\(149\) | 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 | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.82843 | 0.389086 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 14.0000i | − 1.11732i | −0.829396 | − | 0.558661i | \(-0.811315\pi\) | ||||
0.829396 | − | 0.558661i | \(-0.188685\pi\) | |||||||
\(158\) | 9.65685i | 0.768258i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.65685 | −0.445823 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 16.4853i | − 1.29123i | −0.763664 | − | 0.645613i | \(-0.776602\pi\) | ||||
0.763664 | − | 0.645613i | \(-0.223398\pi\) | |||||||
\(164\) | 22.9706 | 1.79370 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.4853 | −1.12428 | ||||||||
\(167\) | 22.9706i | 1.77752i | 0.458377 | + | 0.888758i | \(0.348431\pi\) | ||||
−0.458377 | + | 0.888758i | \(0.651569\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.6274 | 0.894417 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 22.9706i | − 1.75149i | ||||||||
\(173\) | − 22.1421i | − 1.68344i | −0.539918 | − | 0.841718i | \(-0.681545\pi\) | ||||
0.539918 | − | 0.841718i | \(-0.318455\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 32.1421i | 2.40915i | ||||||||
\(179\) | 9.65685 | 0.721787 | 0.360894 | − | 0.932607i | \(-0.382472\pi\) | ||||
0.360894 | + | 0.932607i | \(0.382472\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.3137 | 1.58424 | 0.792118 | − | 0.610368i | \(-0.208979\pi\) | ||||
0.792118 | + | 0.610368i | \(0.208979\pi\) | |||||||
\(182\) | − 5.65685i | − 0.419314i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.4853 | 0.920427 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.82843i | 0.499344i | ||||||||
\(188\) | 10.8284i | 0.789744i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.31371 | −0.239772 | −0.119886 | − | 0.992788i | \(-0.538253\pi\) | ||||
−0.119886 | + | 0.992788i | \(0.538253\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.17157i | 0.0843317i | 0.999111 | + | 0.0421658i | \(0.0134258\pi\) | ||||
−0.999111 | + | 0.0421658i | \(0.986574\pi\) | |||||||
\(194\) | 8.82843 | 0.633844 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.4853 | −0.820377 | ||||||||
\(197\) | 10.8284i | 0.771493i | 0.922605 | + | 0.385747i | \(0.126056\pi\) | ||||
−0.922605 | + | 0.385747i | \(0.873944\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.3431 | −0.733206 | −0.366603 | − | 0.930377i | \(-0.619479\pi\) | ||||
−0.366603 | + | 0.930377i | \(0.619479\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 22.4853i | 1.58206i | ||||||||
\(203\) | 7.31371i | 0.513322i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −16.4853 | −1.14858 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.51472i | 0.243702i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | − 44.6274i | − 3.06502i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.4853 | −1.26363 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 18.4853i | − 1.25198i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.00000 | 0.538138 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.8284i | 0.725125i | 0.931959 | + | 0.362563i | \(0.118098\pi\) | ||||
−0.931959 | + | 0.362563i | \(0.881902\pi\) | |||||||
\(224\) | 3.17157 | 0.211910 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 47.4558 | 3.15672 | ||||||||
\(227\) | − 25.3137i | − 1.68013i | −0.542486 | − | 0.840065i | \(-0.682517\pi\) | ||||
0.542486 | − | 0.840065i | \(-0.317483\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.31371 | −0.0868123 | −0.0434062 | − | 0.999058i | \(-0.513821\pi\) | ||||
−0.0434062 | + | 0.999058i | \(0.513821\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 16.1421i | − 1.05978i | ||||||||
\(233\) | − 6.14214i | − 0.402385i | −0.979552 | − | 0.201192i | \(-0.935518\pi\) | ||||
0.979552 | − | 0.201192i | \(-0.0644816\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.34315 | −0.412904 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 32.9706i | 2.13716i | ||||||||
\(239\) | −23.3137 | −1.50804 | −0.754019 | − | 0.656852i | \(-0.771887\pi\) | ||||
−0.754019 | + | 0.656852i | \(0.771887\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | − 2.41421i | − 0.155192i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 35.6569 | 2.28270 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.82843i | 0.177822i | ||||||||
\(254\) | 10.4853 | 0.657905 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 9.31371i | 0.580973i | 0.956879 | + | 0.290487i | \(0.0938172\pi\) | ||||
−0.956879 | + | 0.290487i | \(0.906183\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.3137 | −0.951548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 27.3137i | − 1.68745i | ||||||||
\(263\) | − 10.9706i | − 0.676474i | −0.941061 | − | 0.338237i | \(-0.890169\pi\) | ||||
0.941061 | − | 0.338237i | \(-0.109831\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 47.7990i | − 2.91979i | ||||||||
\(269\) | 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 | \(-0.428696\pi\) | ||||
0.222138 | + | 0.975015i | \(0.428696\pi\) | |||||||
\(272\) | − 20.4853i | − 1.24210i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 26.4853 | 1.60003 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.82843i | 0.410280i | 0.978733 | + | 0.205140i | \(0.0657650\pi\) | ||||
−0.978733 | + | 0.205140i | \(0.934235\pi\) | |||||||
\(278\) | − 9.65685i | − 0.579180i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.3137 | −1.03285 | −0.516425 | − | 0.856333i | \(-0.672737\pi\) | ||||
−0.516425 | + | 0.856333i | \(0.672737\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 32.6274i | − 1.93950i | −0.244103 | − | 0.969749i | \(-0.578493\pi\) | ||||
0.244103 | − | 0.969749i | \(-0.421507\pi\) | |||||||
\(284\) | 43.3137 | 2.57020 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.82843 | −0.167248 | ||||||||
\(287\) | 12.0000i | 0.708338i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −29.6274 | −1.74279 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 4.48528i | − 0.262481i | ||||||||
\(293\) | − 9.17157i | − 0.535809i | −0.963445 | − | 0.267905i | \(-0.913669\pi\) | ||||
0.963445 | − | 0.267905i | \(-0.0863312\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 33.7990 | 1.96453 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 0.828427i | − 0.0479895i | ||||||||
\(299\) | 3.31371 | 0.191637 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0000 | 0.691669 | ||||||||
\(302\) | 28.9706i | 1.66707i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 16.3431i | − 0.932753i | −0.884586 | − | 0.466376i | \(-0.845559\pi\) | ||||
0.884586 | − | 0.466376i | \(-0.154441\pi\) | |||||||
\(308\) | − 7.65685i | − 0.436290i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.68629 | −0.265735 | −0.132868 | − | 0.991134i | \(-0.542419\pi\) | ||||
−0.132868 | + | 0.991134i | \(0.542419\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.31371i | 0.0742552i | 0.999311 | + | 0.0371276i | \(0.0118208\pi\) | ||||
−0.999311 | + | 0.0371276i | \(0.988179\pi\) | |||||||
\(314\) | −33.7990 | −1.90739 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.3137 | 0.861463 | ||||||||
\(317\) | 1.31371i | 0.0737852i | 0.999319 | + | 0.0368926i | \(0.0117459\pi\) | ||||
−0.999319 | + | 0.0368926i | \(0.988254\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.65685 | 0.204745 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 13.6569i | 0.761067i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −39.7990 | −2.20426 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 26.4853i | − 1.46241i | ||||||||
\(329\) | −5.65685 | −0.311872 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.31371 | −0.401998 | −0.200999 | − | 0.979591i | \(-0.564419\pi\) | ||||
−0.200999 | + | 0.979591i | \(0.564419\pi\) | |||||||
\(332\) | 22.9706i | 1.26067i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 55.4558 | 3.03441 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 20.4853i | − 1.11590i | −0.829873 | − | 0.557952i | \(-0.811587\pi\) | ||||
0.829873 | − | 0.557952i | \(-0.188413\pi\) | |||||||
\(338\) | − 28.0711i | − 1.52686i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 20.0000i | − 1.07990i | ||||||||
\(344\) | −26.4853 | −1.42799 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −53.4558 | −2.87380 | ||||||||
\(347\) | − 10.9706i | − 0.588931i | −0.955662 | − | 0.294465i | \(-0.904858\pi\) | ||||
0.955662 | − | 0.294465i | \(-0.0951416\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.9706 | −1.44370 | −0.721851 | − | 0.692049i | \(-0.756708\pi\) | ||||
−0.721851 | + | 0.692049i | \(0.756708\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 1.58579i | − 0.0845227i | ||||||||
\(353\) | 21.3137i | 1.13441i | 0.823575 | + | 0.567207i | \(0.191976\pi\) | ||||
−0.823575 | + | 0.567207i | \(0.808024\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 50.9706 | 2.70143 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 23.3137i | − 1.23217i | ||||||||
\(359\) | 0.686292 | 0.0362211 | 0.0181105 | − | 0.999836i | \(-0.494235\pi\) | ||||
0.0181105 | + | 0.999836i | \(0.494235\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | − 51.4558i | − 2.70446i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.97056 | −0.470185 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 8.48528i | − 0.442928i | −0.975169 | − | 0.221464i | \(-0.928916\pi\) | ||||
0.975169 | − | 0.221464i | \(-0.0710835\pi\) | |||||||
\(368\) | − 8.48528i | − 0.442326i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.3137 | 1.21039 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 35.7990i | − 1.85360i | −0.375554 | − | 0.926801i | \(-0.622547\pi\) | ||||
0.375554 | − | 0.926801i | \(-0.377453\pi\) | |||||||
\(374\) | 16.4853 | 0.852434 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.4853 | 0.643879 | ||||||||
\(377\) | − 4.28427i | − 0.220651i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.6569 | −1.72884 | −0.864418 | − | 0.502773i | \(-0.832313\pi\) | ||||
−0.864418 | + | 0.502773i | \(0.832313\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.00000i | 0.409316i | ||||||||
\(383\) | − 5.85786i | − 0.299323i | −0.988737 | − | 0.149661i | \(-0.952182\pi\) | ||||
0.988737 | − | 0.149661i | \(-0.0478184\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.82843 | 0.143963 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 14.0000i | − 0.710742i | ||||||||
\(389\) | 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 | ||||||||
\(392\) | 13.2426i | 0.668854i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 26.1421 | 1.31702 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 9.31371i | − 0.467442i | −0.972304 | − | 0.233721i | \(-0.924910\pi\) | ||||
0.972304 | − | 0.233721i | \(-0.0750902\pi\) | |||||||
\(398\) | 24.9706i | 1.25166i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.31371 | 0.265354 | 0.132677 | − | 0.991159i | \(-0.457643\pi\) | ||||
0.132677 | + | 0.991159i | \(0.457643\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 35.6569 | 1.77399 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.6569 | 0.876295 | ||||||||
\(407\) | 7.65685i | 0.379536i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.02944 | −0.0509024 | −0.0254512 | − | 0.999676i | \(-0.508102\pi\) | ||||
−0.0254512 | + | 0.999676i | \(0.508102\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 26.1421i | 1.28793i | ||||||||
\(413\) | − 3.31371i | − 0.163057i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.85786 | −0.0910893 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.6569 | −1.25342 | −0.626710 | − | 0.779253i | \(-0.715599\pi\) | ||||
−0.626710 | + | 0.779253i | \(0.715599\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | 38.6274i | 1.88035i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −51.4558 | −2.49892 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.6274i | 0.901444i | ||||||||
\(428\) | 29.3137i | 1.41693i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.3137 | 0.544962 | 0.272481 | − | 0.962161i | \(-0.412156\pi\) | ||||
0.272481 | + | 0.962161i | \(0.412156\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.65685i | 0.367965i | 0.982930 | + | 0.183982i | \(0.0588990\pi\) | ||||
−0.982930 | + | 0.183982i | \(0.941101\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −29.3137 | −1.40387 | ||||||||
\(437\) | 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 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 19.3137i | − 0.918659i | ||||||||
\(443\) | − 26.8284i | − 1.27466i | −0.770592 | − | 0.637329i | \(-0.780039\pi\) | ||||
0.770592 | − | 0.637329i | \(-0.219961\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 26.1421 | 1.23787 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 19.6569i | − 0.928699i | ||||||||
\(449\) | 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 | ||||||||
\(452\) | − 75.2548i | − 3.53969i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −61.1127 | −2.86816 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.485281i | 0.0227005i | 0.999936 | + | 0.0113503i | \(0.00361298\pi\) | ||||
−0.999936 | + | 0.0113503i | \(0.996387\pi\) | |||||||
\(458\) | 3.17157i | 0.148198i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.6274 | −0.588117 | −0.294059 | − | 0.955787i | \(-0.595006\pi\) | ||||
−0.294059 | + | 0.955787i | \(0.595006\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.14214i | 0.285449i | 0.989762 | + | 0.142725i | \(0.0455863\pi\) | ||||
−0.989762 | + | 0.142725i | \(0.954414\pi\) | |||||||
\(464\) | −10.9706 | −0.509296 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.8284 | −0.686914 | ||||||||
\(467\) | 14.8284i | 0.686178i | 0.939303 | + | 0.343089i | \(0.111473\pi\) | ||||
−0.939303 | + | 0.343089i | \(0.888527\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.9706 | 1.15303 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.31371i | 0.336641i | ||||||||
\(473\) | − 6.00000i | − 0.275880i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 52.2843 | 2.39645 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 56.2843i | 2.57438i | ||||||||
\(479\) | −36.0000 | −1.64488 | −0.822441 | − | 0.568850i | \(-0.807388\pi\) | ||||
−0.822441 | + | 0.568850i | \(0.807388\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.97056 | 0.409022 | ||||||||
\(482\) | − 14.4853i | − 0.659786i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.82843 | −0.174019 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 24.4853i | − 1.10953i | −0.832006 | − | 0.554767i | \(-0.812807\pi\) | ||||
0.832006 | − | 0.554767i | \(-0.187193\pi\) | |||||||
\(488\) | − 41.1127i | − 1.86108i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.686292 | 0.0309719 | 0.0154860 | − | 0.999880i | \(-0.495070\pi\) | ||||
0.0154860 | + | 0.999880i | \(0.495070\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.9706i | 1.12462i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.6274i | 1.01498i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.65685 | −0.432300 | −0.216150 | − | 0.976360i | \(-0.569350\pi\) | ||||
−0.216150 | + | 0.976360i | \(0.569350\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.9706i | 1.29302i | ||||||||
\(503\) | 16.6274i | 0.741380i | 0.928757 | + | 0.370690i | \(0.120879\pi\) | ||||
−0.928757 | + | 0.370690i | \(0.879121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.82843 | 0.303561 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 16.6274i | − 0.737722i | ||||||||
\(509\) | −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 | ||||||||
\(512\) | 31.2426i | 1.38074i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.4853 | 0.991783 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.82843i | 0.124394i | ||||||||
\(518\) | 36.9706i | 1.62439i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.3137 | −1.10901 | −0.554507 | − | 0.832179i | \(-0.687093\pi\) | ||||
−0.554507 | + | 0.832179i | \(0.687093\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.5980i | 1.81895i | 0.415756 | + | 0.909476i | \(0.363517\pi\) | ||||
−0.415756 | + | 0.909476i | \(0.636483\pi\) | |||||||
\(524\) | −43.3137 | −1.89217 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −26.4853 | −1.15481 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 7.02944i | − 0.304479i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −55.1127 | −2.38051 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 41.7990i | − 1.80208i | ||||||||
\(539\) | −3.00000 | −0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.00000 | 0.257960 | 0.128980 | − | 0.991647i | \(-0.458830\pi\) | ||||
0.128980 | + | 0.991647i | \(0.458830\pi\) | |||||||
\(542\) | − 17.6569i | − 0.758427i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.8284 | 0.464265 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 34.0000i | − 1.45374i | −0.686778 | − | 0.726868i | \(-0.740975\pi\) | ||||
0.686778 | − | 0.726868i | \(-0.259025\pi\) | |||||||
\(548\) | − 42.0000i | − 1.79415i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000i | 0.340195i | ||||||||
\(554\) | 16.4853 | 0.700392 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.3137 | −0.649446 | ||||||||
\(557\) | − 9.85786i | − 0.417691i | −0.977949 | − | 0.208846i | \(-0.933029\pi\) | ||||
0.977949 | − | 0.208846i | \(-0.0669706\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.02944 | −0.297314 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 41.7990i | 1.76318i | ||||||||
\(563\) | 0.343146i | 0.0144619i | 0.999974 | + | 0.00723093i | \(0.00230170\pi\) | ||||
−0.999974 | + | 0.00723093i | \(0.997698\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −78.7696 | −3.31093 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 49.9411i | − 2.09548i | ||||||||
\(569\) | 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 | \(-0.651829\pi\) | ||||
−0.459104 | + | 0.888383i | \(0.651829\pi\) | |||||||
\(572\) | 4.48528i | 0.187539i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 28.9706 | 1.20921 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 26.9706i | − 1.12280i | −0.827545 | − | 0.561400i | \(-0.810263\pi\) | ||||
0.827545 | − | 0.561400i | \(-0.189737\pi\) | |||||||
\(578\) | 71.5269i | 2.97513i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0000 | −0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 11.6569i | − 0.482778i | ||||||||
\(584\) | −5.17157 | −0.214001 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.1421 | −0.914683 | ||||||||
\(587\) | 2.14214i | 0.0884154i | 0.999022 | + | 0.0442077i | \(0.0140763\pi\) | ||||
−0.999022 | + | 0.0442077i | \(0.985924\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 22.9706i | − 0.944084i | ||||||||
\(593\) | 3.51472i | 0.144332i | 0.997393 | + | 0.0721661i | \(0.0229912\pi\) | ||||
−0.997393 | + | 0.0721661i | \(0.977009\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.31371 | −0.0538116 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 8.00000i | − 0.327144i | ||||||||
\(599\) | −5.65685 | −0.231133 | −0.115566 | − | 0.993300i | \(-0.536868\pi\) | ||||
−0.115566 | + | 0.993300i | \(0.536868\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.9411 | 0.976579 | 0.488289 | − | 0.872682i | \(-0.337621\pi\) | ||||
0.488289 | + | 0.872682i | \(0.337621\pi\) | |||||||
\(602\) | − 28.9706i | − 1.18075i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 45.9411 | 1.86932 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.2843i | 1.55391i | 0.629556 | + | 0.776955i | \(0.283237\pi\) | ||||
−0.629556 | + | 0.776955i | \(0.716763\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.31371 | 0.134058 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.4558i | 1.02815i | 0.857745 | + | 0.514076i | \(0.171865\pi\) | ||||
−0.857745 | + | 0.514076i | \(0.828135\pi\) | |||||||
\(614\) | −39.4558 | −1.59231 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.82843 | −0.355707 | ||||||||
\(617\) | − 0.343146i | − 0.0138145i | −0.999976 | − | 0.00690726i | \(-0.997801\pi\) | ||||
0.999976 | − | 0.00690726i | \(-0.00219867\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.3431 | 0.576500 | 0.288250 | − | 0.957555i | \(-0.406927\pi\) | ||||
0.288250 | + | 0.957555i | \(0.406927\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.3137i | 0.453638i | ||||||||
\(623\) | 26.6274i | 1.06680i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.17157 | 0.126762 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 53.5980i | 2.13879i | ||||||||
\(629\) | −52.2843 | −2.08471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | − 17.6569i | − 0.702352i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.17157 | 0.125959 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.51472i | 0.139258i | ||||||||
\(638\) | − 8.82843i | − 0.349521i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.0000 | −1.18493 | −0.592464 | − | 0.805597i | \(-0.701845\pi\) | ||||
−0.592464 | + | 0.805597i | \(0.701845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.45584i | 0.0574129i | 0.999588 | + | 0.0287064i | \(0.00913880\pi\) | ||||
−0.999588 | + | 0.0287064i | \(0.990861\pi\) | |||||||
\(644\) | 21.6569 | 0.853400 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 27.1127i | − 1.06591i | −0.846144 | − | 0.532955i | \(-0.821081\pi\) | ||||
0.846144 | − | 0.532955i | \(-0.178919\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.65685 | −0.0650372 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 63.1127i | 2.47168i | ||||||||
\(653\) | 11.6569i | 0.456168i | 0.973641 | + | 0.228084i | \(0.0732461\pi\) | ||||
−0.973641 | + | 0.228084i | \(0.926754\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −18.0000 | −0.702782 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 13.6569i | 0.532400i | ||||||||
\(659\) | 45.9411 | 1.78961 | 0.894806 | − | 0.446455i | \(-0.147314\pi\) | ||||
0.894806 | + | 0.446455i | \(0.147314\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.6274 | 1.73581 | 0.867903 | − | 0.496734i | \(-0.165468\pi\) | ||||
0.867903 | + | 0.496734i | \(0.165468\pi\) | |||||||
\(662\) | 17.6569i | 0.686253i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 26.4853 | 1.02783 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.3431i | 0.400488i | ||||||||
\(668\) | − 87.9411i | − 3.40254i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.31371 | 0.359552 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.4853i | 0.481272i | 0.970615 | + | 0.240636i | \(0.0773560\pi\) | ||||
−0.970615 | + | 0.240636i | \(0.922644\pi\) | |||||||
\(674\) | −49.4558 | −1.90497 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −44.5147 | −1.71210 | ||||||||
\(677\) | − 22.8284i | − 0.877368i | −0.898641 | − | 0.438684i | \(-0.855445\pi\) | ||||
0.898641 | − | 0.438684i | \(-0.144555\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.31371 | 0.280674 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 7.79899i | − 0.298420i | −0.988806 | − | 0.149210i | \(-0.952327\pi\) | ||||
0.988806 | − | 0.149210i | \(-0.0476731\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −48.2843 | −1.84350 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 18.0000i | 0.686244i | ||||||||
\(689\) | −13.6569 | −0.520285 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.3137 | −1.49556 | −0.747782 | − | 0.663944i | \(-0.768881\pi\) | ||||
−0.747782 | + | 0.663944i | \(0.768881\pi\) | |||||||
\(692\) | 84.7696i | 3.22245i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26.4853 | −1.00537 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.9706i | 1.55187i | ||||||||
\(698\) | 65.1127i | 2.46455i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.6274 | 0.476931 | 0.238465 | − | 0.971151i | \(-0.423356\pi\) | ||||
0.238465 | + | 0.971151i | \(0.423356\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −9.82843 | −0.370423 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 51.4558 | 1.93657 | ||||||||
\(707\) | 18.6274i | 0.700556i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.6274 | −0.924902 | −0.462451 | − | 0.886645i | \(-0.653030\pi\) | ||||
−0.462451 | + | 0.886645i | \(0.653030\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 58.7696i | − 2.20248i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −36.9706 | −1.38165 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 1.65685i | − 0.0618333i | ||||||||
\(719\) | 18.3431 | 0.684084 | 0.342042 | − | 0.939685i | \(-0.388882\pi\) | ||||
0.342042 | + | 0.939685i | \(0.388882\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.6569 | −0.508608 | ||||||||
\(722\) | 45.8701i | 1.70711i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −81.5980 | −3.03257 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 19.5147i | − 0.723761i | −0.932225 | − | 0.361880i | \(-0.882135\pi\) | ||||
0.932225 | − | 0.361880i | \(-0.117865\pi\) | |||||||
\(728\) | 10.3431i | 0.383342i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 40.9706 | 1.51535 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.4558i | 0.644746i | 0.946613 | + | 0.322373i | \(0.104481\pi\) | ||||
−0.946613 | + | 0.322373i | \(0.895519\pi\) | |||||||
\(734\) | −20.4853 | −0.756126 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.48528 | 0.165330 | ||||||||
\(737\) | − 12.4853i | − 0.459901i | ||||||||
\(738\) | 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 | ||||||||
\(742\) | − 56.2843i | − 2.06626i | ||||||||
\(743\) | − 49.5980i | − 1.81957i | −0.415076 | − | 0.909787i | \(-0.636245\pi\) | ||||
0.415076 | − | 0.909787i | \(-0.363755\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −86.4264 | −3.16430 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 26.1421i | − 0.955851i | ||||||||
\(749\) | −15.3137 | −0.559551 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.0000 | −0.583848 | −0.291924 | − | 0.956441i | \(-0.594295\pi\) | ||||
−0.291924 | + | 0.956441i | \(0.594295\pi\) | |||||||
\(752\) | − 8.48528i | − 0.309426i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.3431 | −0.376675 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.3137i | 0.483895i | 0.970289 | + | 0.241947i | \(0.0777862\pi\) | ||||
−0.970289 | + | 0.241947i | \(0.922214\pi\) | |||||||
\(758\) | 81.2548i | 2.95131i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.0000 | 1.08750 | 0.543750 | − | 0.839248i | \(-0.317004\pi\) | ||||
0.543750 | + | 0.839248i | \(0.317004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 15.3137i | − 0.554393i | ||||||||
\(764\) | 12.6863 | 0.458974 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.1421 | −0.510976 | ||||||||
\(767\) | 1.94113i | 0.0700900i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.9706 | 0.684096 | 0.342048 | − | 0.939682i | \(-0.388879\pi\) | ||||
0.342048 | + | 0.939682i | \(0.388879\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 4.48528i | − 0.161429i | ||||||||
\(773\) | 26.2843i | 0.945380i | 0.881229 | + | 0.472690i | \(0.156717\pi\) | ||||
−0.881229 | + | 0.472690i | \(0.843283\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16.1421 | −0.579469 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 49.7990i | − 1.78538i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.3137 | 0.404836 | ||||||||
\(782\) | 46.6274i | 1.66739i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.00000 | 0.321429 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 14.9706i | − 0.533643i | −0.963746 | − | 0.266821i | \(-0.914027\pi\) | ||||
0.963746 | − | 0.266821i | \(-0.0859734\pi\) | |||||||
\(788\) | − 41.4558i | − 1.47680i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 39.3137 | 1.39783 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 10.9117i | − 0.387485i | ||||||||
\(794\) | −22.4853 | −0.797973 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 39.5980 | 1.40351 | ||||||||
\(797\) | − 32.6274i | − 1.15572i | −0.816135 | − | 0.577861i | \(-0.803887\pi\) | ||||
0.816135 | − | 0.577861i | \(-0.196113\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.3137 | −0.683270 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 12.8284i | − 0.452988i | ||||||||
\(803\) | − 1.17157i | − 0.0413439i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 41.1127i | − 1.44634i | ||||||||
\(809\) | −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 | \(-0.104033\pi\) | ||||
0.947065 | + | 0.321043i | \(0.104033\pi\) | |||||||
\(812\) | − 28.0000i | − 0.982607i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 18.4853 | 0.647909 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 2.48528i | 0.0868958i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.3137 | 1.44186 | 0.720929 | − | 0.693009i | \(-0.243715\pi\) | ||||
0.720929 | + | 0.693009i | \(0.243715\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 19.5147i | − 0.680240i | −0.940382 | − | 0.340120i | \(-0.889532\pi\) | ||||
0.940382 | − | 0.340120i | \(-0.110468\pi\) | |||||||
\(824\) | 30.1421 | 1.05005 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | −0.278356 | ||||||||
\(827\) | − 22.2843i | − 0.774900i | −0.921891 | − | 0.387450i | \(-0.873356\pi\) | ||||
0.921891 | − | 0.387450i | \(-0.126644\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.0000 | −0.625166 | −0.312583 | − | 0.949890i | \(-0.601194\pi\) | ||||
−0.312583 | + | 0.949890i | \(0.601194\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.5147i | 0.399201i | ||||||||
\(833\) | − 20.4853i | − 0.709773i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 61.9411i | 2.13972i | ||||||||
\(839\) | 26.3431 | 0.909466 | 0.454733 | − | 0.890628i | \(-0.349735\pi\) | ||||
0.454733 | + | 0.890628i | \(0.349735\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.6274 | −0.538876 | ||||||||
\(842\) | 14.4853i | 0.499196i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 61.2548 | 2.10848 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 2.00000i | − 0.0687208i | ||||||||
\(848\) | 34.9706i | 1.20089i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.6569 | −0.742387 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.5147i | 0.531214i | 0.964081 | + | 0.265607i | \(0.0855723\pi\) | ||||
−0.964081 | + | 0.265607i | \(0.914428\pi\) | |||||||
\(854\) | 44.9706 | 1.53886 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 33.7990 | 1.15523 | ||||||||
\(857\) | − 24.7696i | − 0.846112i | −0.906104 | − | 0.423056i | \(-0.860957\pi\) | ||||
0.906104 | − | 0.423056i | \(-0.139043\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.2843 | −0.828569 | −0.414284 | − | 0.910148i | \(-0.635968\pi\) | ||||
−0.414284 | + | 0.910148i | \(0.635968\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 27.3137i | − 0.930309i | ||||||||
\(863\) | − 9.17157i | − 0.312204i | −0.987741 | − | 0.156102i | \(-0.950107\pi\) | ||||
0.987741 | − | 0.156102i | \(-0.0498929\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 18.4853 | 0.628155 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.00000 | 0.135691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.6274 | −0.495631 | ||||||||
\(872\) | 33.7990i | 1.14458i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 49.4558i | − 1.67001i | −0.550246 | − | 0.835003i | \(-0.685466\pi\) | ||||
0.550246 | − | 0.835003i | \(-0.314534\pi\) | |||||||
\(878\) | − 38.6274i | − 1.30361i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.37258 | 0.248389 | 0.124194 | − | 0.992258i | \(-0.460365\pi\) | ||||
0.124194 | + | 0.992258i | \(0.460365\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 37.1716i | − 1.25092i | −0.780255 | − | 0.625462i | \(-0.784911\pi\) | ||||
0.780255 | − | 0.625462i | \(-0.215089\pi\) | |||||||
\(884\) | −30.6274 | −1.03011 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −64.7696 | −2.17598 | ||||||||
\(887\) | − 38.2843i | − 1.28546i | −0.766093 | − | 0.642730i | \(-0.777802\pi\) | ||||
0.766093 | − | 0.642730i | \(-0.222198\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.68629 | 0.291329 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 41.4558i | − 1.38804i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −41.1127 | −1.37348 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 69.1127i | − 2.30632i | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 79.5980 | 2.65179 | ||||||||
\(902\) | − 14.4853i | − 0.482307i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −86.7696 | −2.88591 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 27.5147i | − 0.913611i | −0.889567 | − | 0.456806i | \(-0.848993\pi\) | ||||
0.889567 | − | 0.456806i | \(-0.151007\pi\) | |||||||
\(908\) | 96.9117i | 3.21613i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.94113 | 0.329364 | 0.164682 | − | 0.986347i | \(-0.447340\pi\) | ||||
0.164682 | + | 0.986347i | \(0.447340\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.00000i | 0.198571i | ||||||||
\(914\) | 1.17157 | 0.0387522 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.02944 | 0.166177 | ||||||||
\(917\) | − 22.6274i | − 0.747223i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.0000 | 1.05558 | 0.527791 | − | 0.849374i | \(-0.323020\pi\) | ||||
0.527791 | + | 0.849374i | \(0.323020\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 30.4853i | 1.00398i | ||||||||
\(923\) | − 13.2548i | − 0.436288i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 14.8284 | 0.487292 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 5.79899i | − 0.190361i | ||||||||
\(929\) | 5.31371 | 0.174337 | 0.0871686 | − | 0.996194i | \(-0.472218\pi\) | ||||
0.0871686 | + | 0.996194i | \(0.472218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 23.5147i | 0.770250i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 35.7990 | 1.17138 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1.45584i | − 0.0475604i | −0.999717 | − | 0.0237802i | \(-0.992430\pi\) | ||||
0.999717 | − | 0.0237802i | \(-0.00757018\pi\) | |||||||
\(938\) | − 60.2843i | − 1.96835i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.68629 | 0.217967 | 0.108983 | − | 0.994044i | \(-0.465240\pi\) | ||||
0.108983 | + | 0.994044i | \(0.465240\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.9706i | 0.552638i | ||||||||
\(944\) | 4.97056 | 0.161778 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.4853 | −0.470957 | ||||||||
\(947\) | − 41.1716i | − 1.33790i | −0.743309 | − | 0.668948i | \(-0.766745\pi\) | ||||
0.743309 | − | 0.668948i | \(-0.233255\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.37258 | −0.0445559 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 60.2843i | − 1.95382i | ||||||||
\(953\) | 53.1716i | 1.72240i | 0.508269 | + | 0.861198i | \(0.330285\pi\) | ||||
−0.508269 | + | 0.861198i | \(0.669715\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 89.2548 | 2.88671 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 86.9117i | 2.80799i | ||||||||
\(959\) | 21.9411 | 0.708516 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | − 21.6569i | − 0.698245i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.9706 | −0.739832 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 14.9706i | − 0.481421i | −0.970597 | − | 0.240710i | \(-0.922620\pi\) | ||||
0.970597 | − | 0.240710i | \(-0.0773804\pi\) | |||||||
\(968\) | 4.41421i | 0.141878i | ||||||||
\(969\) | 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 | ||||||||
\(973\) | − 8.00000i | − 0.256468i | ||||||||
\(974\) | −59.1127 | −1.89409 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27.9411 | −0.894374 | ||||||||
\(977\) | − 32.3431i | − 1.03475i | −0.855759 | − | 0.517374i | \(-0.826909\pi\) | ||||
0.855759 | − | 0.517374i | \(-0.173091\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.3137 | 0.425508 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 1.65685i | − 0.0528723i | ||||||||
\(983\) | − 21.8579i | − 0.697158i | −0.937279 | − | 0.348579i | \(-0.886664\pi\) | ||||
0.937279 | − | 0.348579i | \(-0.113336\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 60.2843 | 1.91984 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.9706 | 0.539633 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.9411 | −1.84056 | −0.920280 | − | 0.391260i | \(-0.872039\pi\) | ||||
−0.920280 | + | 0.391260i | \(0.872039\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 54.6274 | 1.73268 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 41.4558i | − 1.31292i | −0.754361 | − | 0.656460i | \(-0.772053\pi\) | ||||
0.754361 | − | 0.656460i | \(-0.227947\pi\) | |||||||
\(998\) | 23.3137i | 0.737983i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2475.2.c.l.199.1 | 4 | ||
3.2 | odd | 2 | 275.2.b.d.199.4 | 4 | |||
5.2 | odd | 4 | 2475.2.a.x.1.2 | 2 | |||
5.3 | odd | 4 | 495.2.a.b.1.1 | 2 | |||
5.4 | even | 2 | inner | 2475.2.c.l.199.4 | 4 | ||
12.11 | even | 2 | 4400.2.b.q.4049.2 | 4 | |||
15.2 | even | 4 | 275.2.a.c.1.1 | 2 | |||
15.8 | even | 4 | 55.2.a.b.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 275.2.b.d.199.1 | 4 | |||
20.3 | even | 4 | 7920.2.a.ch.1.2 | 2 | |||
55.43 | even | 4 | 5445.2.a.y.1.2 | 2 | |||
60.23 | odd | 4 | 880.2.a.m.1.2 | 2 | |||
60.47 | odd | 4 | 4400.2.a.bn.1.1 | 2 | |||
60.59 | even | 2 | 4400.2.b.q.4049.3 | 4 | |||
105.83 | odd | 4 | 2695.2.a.f.1.2 | 2 | |||
120.53 | even | 4 | 3520.2.a.bn.1.2 | 2 | |||
120.83 | odd | 4 | 3520.2.a.bo.1.1 | 2 | |||
165.8 | odd | 20 | 605.2.g.l.251.1 | 8 | |||
165.32 | odd | 4 | 3025.2.a.o.1.2 | 2 | |||
165.38 | even | 20 | 605.2.g.f.366.1 | 8 | |||
165.53 | even | 20 | 605.2.g.f.81.1 | 8 | |||
165.68 | odd | 20 | 605.2.g.l.81.2 | 8 | |||
165.83 | odd | 20 | 605.2.g.l.366.2 | 8 | |||
165.98 | odd | 4 | 605.2.a.d.1.1 | 2 | |||
165.113 | even | 20 | 605.2.g.f.251.2 | 8 | |||
165.128 | odd | 20 | 605.2.g.l.511.1 | 8 | |||
165.158 | even | 20 | 605.2.g.f.511.2 | 8 | |||
195.38 | even | 4 | 9295.2.a.g.1.1 | 2 | |||
660.263 | even | 4 | 9680.2.a.bn.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.a.b.1.2 | ✓ | 2 | 15.8 | even | 4 | ||
275.2.a.c.1.1 | 2 | 15.2 | even | 4 | |||
275.2.b.d.199.1 | 4 | 15.14 | odd | 2 | |||
275.2.b.d.199.4 | 4 | 3.2 | odd | 2 | |||
495.2.a.b.1.1 | 2 | 5.3 | odd | 4 | |||
605.2.a.d.1.1 | 2 | 165.98 | odd | 4 | |||
605.2.g.f.81.1 | 8 | 165.53 | even | 20 | |||
605.2.g.f.251.2 | 8 | 165.113 | even | 20 | |||
605.2.g.f.366.1 | 8 | 165.38 | even | 20 | |||
605.2.g.f.511.2 | 8 | 165.158 | even | 20 | |||
605.2.g.l.81.2 | 8 | 165.68 | odd | 20 | |||
605.2.g.l.251.1 | 8 | 165.8 | odd | 20 | |||
605.2.g.l.366.2 | 8 | 165.83 | odd | 20 | |||
605.2.g.l.511.1 | 8 | 165.128 | odd | 20 | |||
880.2.a.m.1.2 | 2 | 60.23 | odd | 4 | |||
2475.2.a.x.1.2 | 2 | 5.2 | odd | 4 | |||
2475.2.c.l.199.1 | 4 | 1.1 | even | 1 | trivial | ||
2475.2.c.l.199.4 | 4 | 5.4 | even | 2 | inner | ||
2695.2.a.f.1.2 | 2 | 105.83 | odd | 4 | |||
3025.2.a.o.1.2 | 2 | 165.32 | odd | 4 | |||
3520.2.a.bn.1.2 | 2 | 120.53 | even | 4 | |||
3520.2.a.bo.1.1 | 2 | 120.83 | odd | 4 | |||
4400.2.a.bn.1.1 | 2 | 60.47 | odd | 4 | |||
4400.2.b.q.4049.2 | 4 | 12.11 | even | 2 | |||
4400.2.b.q.4049.3 | 4 | 60.59 | even | 2 | |||
5445.2.a.y.1.2 | 2 | 55.43 | even | 4 | |||
7920.2.a.ch.1.2 | 2 | 20.3 | even | 4 | |||
9295.2.a.g.1.1 | 2 | 195.38 | even | 4 | |||
9680.2.a.bn.1.2 | 2 | 660.263 | even | 4 |