Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(379,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, 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("630.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.03057532734\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 379.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.379 |
Dual form | 630.2.g.b.379.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | − | 2.00000i | −0.447214 | − | 0.894427i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.00000 | + | 1.00000i | −0.632456 | + | 0.316228i | ||||
\(11\) | −6.00000 | −1.80907 | −0.904534 | − | 0.426401i | \(-0.859781\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.00000i | 0.485071i | 0.970143 | + | 0.242536i | \(0.0779791\pi\) | ||||
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | 1.00000 | + | 2.00000i | 0.223607 | + | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.00000i | 1.27920i | ||||||||
\(23\) | − | 4.00000i | − | 0.834058i | −0.908893 | − | 0.417029i | \(-0.863071\pi\) | ||
0.908893 | − | 0.417029i | \(-0.136929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | + | 4.00000i | −0.600000 | + | 0.800000i | ||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 1.00000i | − | 0.188982i | ||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 2.00000 | − | 1.00000i | 0.338062 | − | 0.169031i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.0000i | 1.64399i | 0.569495 | + | 0.821995i | \(0.307139\pi\) | ||||
−0.569495 | + | 0.821995i | \(0.692861\pi\) | |||||||
\(38\) | 4.00000i | 0.648886i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.00000 | − | 1.00000i | 0.316228 | − | 0.158114i | ||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.00000i | − | 0.304997i | −0.988304 | − | 0.152499i | \(-0.951268\pi\) | ||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | 6.00000 | 0.904534 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | − | 2.00000i | − | 0.291730i | −0.989305 | − | 0.145865i | \(-0.953403\pi\) | ||
0.989305 | − | 0.145865i | \(-0.0465965\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 4.00000 | + | 3.00000i | 0.565685 | + | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 2.00000i | − | 0.277350i | ||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00000 | + | 12.0000i | 0.809040 | + | 1.61808i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 2.00000i | − | 0.262613i | ||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0000 | −1.53644 | −0.768221 | − | 0.640184i | \(-0.778858\pi\) | ||||
−0.768221 | + | 0.640184i | \(0.778858\pi\) | |||||||
\(62\) | 2.00000i | 0.254000i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 4.00000 | − | 2.00000i | 0.496139 | − | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 10.0000i | − | 1.22169i | −0.791748 | − | 0.610847i | \(-0.790829\pi\) | ||
0.791748 | − | 0.610847i | \(-0.209171\pi\) | |||||||
\(68\) | − | 2.00000i | − | 0.242536i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.00000 | − | 2.00000i | −0.119523 | − | 0.239046i | ||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.00000i | − | 0.234082i | −0.993127 | − | 0.117041i | \(-0.962659\pi\) | ||
0.993127 | − | 0.117041i | \(-0.0373409\pi\) | |||||||
\(74\) | 10.0000 | 1.16248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | − | 6.00000i | − | 0.683763i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.0000 | 1.80014 | 0.900070 | − | 0.435745i | \(-0.143515\pi\) | ||||
0.900070 | + | 0.435745i | \(0.143515\pi\) | |||||||
\(80\) | −1.00000 | − | 2.00000i | −0.111803 | − | 0.223607i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.00000i | 0.662589i | ||||||||
\(83\) | − | 12.0000i | − | 1.31717i | −0.752506 | − | 0.658586i | \(-0.771155\pi\) | ||
0.752506 | − | 0.658586i | \(-0.228845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | − | 2.00000i | 0.433861 | − | 0.216930i | ||||
\(86\) | −2.00000 | −0.215666 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 6.00000i | − | 0.639602i | ||||||
\(89\) | 14.0000 | 1.48400 | 0.741999 | − | 0.670402i | \(-0.233878\pi\) | ||||
0.741999 | + | 0.670402i | \(0.233878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | 4.00000i | 0.417029i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.00000 | −0.206284 | ||||||||
\(95\) | 4.00000 | + | 8.00000i | 0.410391 | + | 0.820783i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 18.0000i | − | 1.82762i | −0.406138 | − | 0.913812i | \(-0.633125\pi\) | ||
0.406138 | − | 0.913812i | \(-0.366875\pi\) | |||||||
\(98\) | 1.00000i | 0.101015i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.00000 | − | 4.00000i | 0.300000 | − | 0.400000i | ||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.0000i | − | 1.57653i | −0.615338 | − | 0.788263i | \(-0.710980\pi\) | ||
0.615338 | − | 0.788263i | \(-0.289020\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 4.00000i | 0.386695i | 0.981130 | + | 0.193347i | \(0.0619344\pi\) | ||||
−0.981130 | + | 0.193347i | \(0.938066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | 12.0000 | − | 6.00000i | 1.14416 | − | 0.572078i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | 14.0000i | 1.31701i | 0.752577 | + | 0.658505i | \(0.228811\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.00000 | + | 4.00000i | −0.746004 | + | 0.373002i | ||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.00000i | 0.368230i | ||||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 25.0000 | 2.27273 | ||||||||
\(122\) | 12.0000i | 1.08643i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.00000 | 0.179605 | ||||||||
\(125\) | 11.0000 | + | 2.00000i | 0.983870 | + | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000i | 0.354943i | 0.984126 | + | 0.177471i | \(0.0567917\pi\) | ||||
−0.984126 | + | 0.177471i | \(0.943208\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.00000 | − | 4.00000i | −0.175412 | − | 0.350823i | ||||
\(131\) | −20.0000 | −1.74741 | −0.873704 | − | 0.486458i | \(-0.838289\pi\) | ||||
−0.873704 | + | 0.486458i | \(0.838289\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 4.00000i | − | 0.346844i | ||||||
\(134\) | −10.0000 | −0.863868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.00000 | −0.171499 | ||||||||
\(137\) | 2.00000i | 0.170872i | 0.996344 | + | 0.0854358i | \(0.0272282\pi\) | ||||
−0.996344 | + | 0.0854358i | \(0.972772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | 0.678551 | 0.339276 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339276 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(140\) | −2.00000 | + | 1.00000i | −0.169031 | + | 0.0845154i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.0000i | 1.00702i | ||||||||
\(143\) | − | 12.0000i | − | 1.00349i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | − | 4.00000i | −0.166091 | − | 0.332182i | ||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 10.0000i | − | 0.821995i | ||||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(152\) | − | 4.00000i | − | 0.324443i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.00000 | −0.483494 | ||||||||
\(155\) | 2.00000 | + | 4.00000i | 0.160644 | + | 0.321288i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 18.0000i | − | 1.43656i | −0.695756 | − | 0.718278i | \(-0.744931\pi\) | ||
0.695756 | − | 0.718278i | \(-0.255069\pi\) | |||||||
\(158\) | − | 16.0000i | − | 1.27289i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.00000 | + | 1.00000i | −0.158114 | + | 0.0790569i | ||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000i | 0.469956i | 0.972001 | + | 0.234978i | \(0.0755019\pi\) | ||||
−0.972001 | + | 0.234978i | \(0.924498\pi\) | |||||||
\(164\) | 6.00000 | 0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.0000 | −0.931381 | ||||||||
\(167\) | − | 18.0000i | − | 1.39288i | −0.717614 | − | 0.696441i | \(-0.754766\pi\) | ||
0.717614 | − | 0.696441i | \(-0.245234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | −2.00000 | − | 4.00000i | −0.153393 | − | 0.306786i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000i | 0.152499i | ||||||||
\(173\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.00000 | − | 3.00000i | −0.302372 | − | 0.226779i | ||||
\(176\) | −6.00000 | −0.452267 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 14.0000i | − | 1.04934i | ||||||
\(179\) | −14.0000 | −1.04641 | −0.523205 | − | 0.852207i | \(-0.675264\pi\) | ||||
−0.523205 | + | 0.852207i | \(0.675264\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | 2.00000i | 0.148250i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.00000 | 0.294884 | ||||||||
\(185\) | 20.0000 | − | 10.0000i | 1.47043 | − | 0.735215i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 12.0000i | − | 0.877527i | ||||||
\(188\) | 2.00000i | 0.145865i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.00000 | − | 4.00000i | 0.580381 | − | 0.290191i | ||||
\(191\) | −16.0000 | −1.15772 | −0.578860 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578860 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.00000i | 0.287926i | 0.989583 | + | 0.143963i | \(0.0459847\pi\) | ||||
−0.989583 | + | 0.143963i | \(0.954015\pi\) | |||||||
\(194\) | −18.0000 | −1.29232 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | − | 10.0000i | − | 0.712470i | −0.934396 | − | 0.356235i | \(-0.884060\pi\) | ||
0.934396 | − | 0.356235i | \(-0.115940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.0000 | −1.27599 | −0.637993 | − | 0.770042i | \(-0.720235\pi\) | ||||
−0.637993 | + | 0.770042i | \(0.720235\pi\) | |||||||
\(200\) | −4.00000 | − | 3.00000i | −0.282843 | − | 0.212132i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.00000i | 0.422159i | ||||||||
\(203\) | 2.00000i | 0.140372i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | + | 12.0000i | 0.419058 | + | 0.838116i | ||||
\(206\) | −16.0000 | −1.11477 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.00000i | 0.138675i | ||||||||
\(209\) | 24.0000 | 1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | − | 6.00000i | − | 0.412082i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.00000 | 0.273434 | ||||||||
\(215\) | −4.00000 | + | 2.00000i | −0.272798 | + | 0.136399i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.00000i | − | 0.135769i | ||||||
\(218\) | 14.0000i | 0.948200i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.00000 | − | 12.0000i | −0.404520 | − | 0.809040i | ||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000i | 0.535720i | 0.963458 | + | 0.267860i | \(0.0863164\pi\) | ||||
−0.963458 | + | 0.267860i | \(0.913684\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.0000 | 0.931266 | ||||||||
\(227\) | 24.0000i | 1.59294i | 0.604681 | + | 0.796468i | \(0.293301\pi\) | ||||
−0.604681 | + | 0.796468i | \(0.706699\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.00000 | 0.528655 | 0.264327 | − | 0.964433i | \(-0.414850\pi\) | ||||
0.264327 | + | 0.964433i | \(0.414850\pi\) | |||||||
\(230\) | 4.00000 | + | 8.00000i | 0.263752 | + | 0.527504i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.00000i | 0.131306i | ||||||||
\(233\) | 22.0000i | 1.44127i | 0.693316 | + | 0.720634i | \(0.256149\pi\) | ||||
−0.693316 | + | 0.720634i | \(0.743851\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | + | 2.00000i | −0.260931 | + | 0.130466i | ||||
\(236\) | 4.00000 | 0.260378 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.00000i | 0.129641i | ||||||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.0000 | −1.15948 | −0.579741 | − | 0.814801i | \(-0.696846\pi\) | ||||
−0.579741 | + | 0.814801i | \(0.696846\pi\) | |||||||
\(242\) | − | 25.0000i | − | 1.60706i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.0000 | 0.768221 | ||||||||
\(245\) | 1.00000 | + | 2.00000i | 0.0638877 | + | 0.127775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 8.00000i | − | 0.509028i | ||||||
\(248\) | − | 2.00000i | − | 0.127000i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.00000 | − | 11.0000i | 0.126491 | − | 0.695701i | ||||
\(251\) | 16.0000 | 1.00991 | 0.504956 | − | 0.863145i | \(-0.331509\pi\) | ||||
0.504956 | + | 0.863145i | \(0.331509\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.0000i | 1.50887i | ||||||||
\(254\) | 4.00000 | 0.250982 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.0000i | 1.12281i | 0.827541 | + | 0.561405i | \(0.189739\pi\) | ||||
−0.827541 | + | 0.561405i | \(0.810261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.0000 | −0.621370 | ||||||||
\(260\) | −4.00000 | + | 2.00000i | −0.248069 | + | 0.124035i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 20.0000i | 1.23560i | ||||||||
\(263\) | 12.0000i | 0.739952i | 0.929041 | + | 0.369976i | \(0.120634\pi\) | ||||
−0.929041 | + | 0.369976i | \(0.879366\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.0000 | − | 6.00000i | 0.737154 | − | 0.368577i | ||||
\(266\) | −4.00000 | −0.245256 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.0000i | 0.610847i | ||||||||
\(269\) | 14.0000 | 0.853595 | 0.426798 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.0000 | −1.82237 | −0.911185 | − | 0.411997i | \(-0.864831\pi\) | ||||
−0.911185 | + | 0.411997i | \(0.864831\pi\) | |||||||
\(272\) | 2.00000i | 0.121268i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.00000 | 0.120824 | ||||||||
\(275\) | 18.0000 | − | 24.0000i | 1.08544 | − | 1.44725i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.00000i | − | 0.120168i | −0.998193 | − | 0.0600842i | \(-0.980863\pi\) | ||
0.998193 | − | 0.0600842i | \(-0.0191369\pi\) | |||||||
\(278\) | − | 8.00000i | − | 0.479808i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.00000 | + | 2.00000i | 0.0597614 | + | 0.119523i | ||||
\(281\) | 12.0000 | 0.715860 | 0.357930 | − | 0.933748i | \(-0.383483\pi\) | ||||
0.357930 | + | 0.933748i | \(0.383483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000i | 0.237775i | 0.992908 | + | 0.118888i | \(0.0379328\pi\) | ||||
−0.992908 | + | 0.118888i | \(0.962067\pi\) | |||||||
\(284\) | 12.0000 | 0.712069 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.0000 | −0.709575 | ||||||||
\(287\) | − | 6.00000i | − | 0.354169i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | −4.00000 | + | 2.00000i | −0.234888 | + | 0.117444i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.00000i | 0.117041i | ||||||||
\(293\) | − | 12.0000i | − | 0.701047i | −0.936554 | − | 0.350524i | \(-0.886004\pi\) | ||
0.936554 | − | 0.350524i | \(-0.113996\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | + | 8.00000i | 0.232889 | + | 0.465778i | ||||
\(296\) | −10.0000 | −0.581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000i | 0.347571i | ||||||||
\(299\) | 8.00000 | 0.462652 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | 0.115278 | ||||||||
\(302\) | − | 12.0000i | − | 0.690522i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.00000 | −0.229416 | ||||||||
\(305\) | 12.0000 | + | 24.0000i | 0.687118 | + | 1.37424i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.0000i | 1.82634i | 0.407583 | + | 0.913168i | \(0.366372\pi\) | ||||
−0.407583 | + | 0.913168i | \(0.633628\pi\) | |||||||
\(308\) | 6.00000i | 0.341882i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.00000 | − | 2.00000i | 0.227185 | − | 0.113592i | ||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 34.0000i | 1.92179i | 0.276907 | + | 0.960897i | \(0.410691\pi\) | ||||
−0.276907 | + | 0.960897i | \(0.589309\pi\) | |||||||
\(314\) | −18.0000 | −1.01580 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.0000 | −0.900070 | ||||||||
\(317\) | 26.0000i | 1.46031i | 0.683284 | + | 0.730153i | \(0.260551\pi\) | ||||
−0.683284 | + | 0.730153i | \(0.739449\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.0000 | −0.671871 | ||||||||
\(320\) | 1.00000 | + | 2.00000i | 0.0559017 | + | 0.111803i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 4.00000i | − | 0.222911i | ||||||
\(323\) | − | 8.00000i | − | 0.445132i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.00000 | − | 6.00000i | −0.443760 | − | 0.332820i | ||||
\(326\) | 6.00000 | 0.332309 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 6.00000i | − | 0.331295i | ||||||
\(329\) | 2.00000 | 0.110264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0000 | 1.09930 | 0.549650 | − | 0.835395i | \(-0.314761\pi\) | ||||
0.549650 | + | 0.835395i | \(0.314761\pi\) | |||||||
\(332\) | 12.0000i | 0.658586i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −18.0000 | −0.984916 | ||||||||
\(335\) | −20.0000 | + | 10.0000i | −1.09272 | + | 0.546358i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 20.0000i | − | 1.08947i | −0.838608 | − | 0.544735i | \(-0.816630\pi\) | ||
0.838608 | − | 0.544735i | \(-0.183370\pi\) | |||||||
\(338\) | − | 9.00000i | − | 0.489535i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.00000 | + | 2.00000i | −0.216930 | + | 0.108465i | ||||
\(341\) | 12.0000 | 0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 2.00000 | 0.107833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.0000i | 0.644194i | 0.946707 | + | 0.322097i | \(0.104388\pi\) | ||||
−0.946707 | + | 0.322097i | \(0.895612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.0000 | −1.28469 | −0.642345 | − | 0.766415i | \(-0.722038\pi\) | ||||
−0.642345 | + | 0.766415i | \(0.722038\pi\) | |||||||
\(350\) | −3.00000 | + | 4.00000i | −0.160357 | + | 0.213809i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.00000i | 0.319801i | ||||||||
\(353\) | − | 30.0000i | − | 1.59674i | −0.602168 | − | 0.798369i | \(-0.705696\pi\) | ||
0.602168 | − | 0.798369i | \(-0.294304\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.0000 | + | 24.0000i | 0.636894 | + | 1.27379i | ||||
\(356\) | −14.0000 | −0.741999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.0000i | 0.739923i | ||||||||
\(359\) | 4.00000 | 0.211112 | 0.105556 | − | 0.994413i | \(-0.466338\pi\) | ||||
0.105556 | + | 0.994413i | \(0.466338\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | − | 8.00000i | − | 0.420471i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | −4.00000 | + | 2.00000i | −0.209370 | + | 0.104685i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 8.00000i | − | 0.417597i | −0.977959 | − | 0.208798i | \(-0.933045\pi\) | ||
0.977959 | − | 0.208798i | \(-0.0669552\pi\) | |||||||
\(368\) | − | 4.00000i | − | 0.208514i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.0000 | − | 20.0000i | −0.519875 | − | 1.03975i | ||||
\(371\) | −6.00000 | −0.311504 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.0000i | 1.76045i | 0.474554 | + | 0.880227i | \(0.342610\pi\) | ||||
−0.474554 | + | 0.880227i | \(0.657390\pi\) | |||||||
\(374\) | −12.0000 | −0.620505 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.00000 | 0.103142 | ||||||||
\(377\) | 4.00000i | 0.206010i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | −4.00000 | − | 8.00000i | −0.205196 | − | 0.410391i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.0000i | 0.818631i | ||||||||
\(383\) | 30.0000i | 1.53293i | 0.642287 | + | 0.766464i | \(0.277986\pi\) | ||||
−0.642287 | + | 0.766464i | \(0.722014\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.0000 | + | 6.00000i | −0.611577 | + | 0.305788i | ||||
\(386\) | 4.00000 | 0.203595 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 18.0000i | 0.913812i | ||||||||
\(389\) | −6.00000 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | − | 1.00000i | − | 0.0505076i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.0000 | −0.503793 | ||||||||
\(395\) | −16.0000 | − | 32.0000i | −0.805047 | − | 1.61009i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 14.0000i | − | 0.702640i | −0.936255 | − | 0.351320i | \(-0.885733\pi\) | ||
0.936255 | − | 0.351320i | \(-0.114267\pi\) | |||||||
\(398\) | 18.0000i | 0.902258i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | + | 4.00000i | −0.150000 | + | 0.200000i | ||||
\(401\) | 24.0000 | 1.19850 | 0.599251 | − | 0.800561i | \(-0.295465\pi\) | ||||
0.599251 | + | 0.800561i | \(0.295465\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 4.00000i | − | 0.199254i | ||||||
\(404\) | 6.00000 | 0.298511 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.00000 | 0.0992583 | ||||||||
\(407\) | − | 60.0000i | − | 2.97409i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0000 | −0.494468 | −0.247234 | − | 0.968956i | \(-0.579522\pi\) | ||||
−0.247234 | + | 0.968956i | \(0.579522\pi\) | |||||||
\(410\) | 12.0000 | − | 6.00000i | 0.592638 | − | 0.296319i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.0000i | 0.788263i | ||||||||
\(413\) | − | 4.00000i | − | 0.196827i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.0000 | + | 12.0000i | −1.17811 | + | 0.589057i | ||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 24.0000i | − | 1.17388i | ||||||
\(419\) | −16.0000 | −0.781651 | −0.390826 | − | 0.920465i | \(-0.627810\pi\) | ||||
−0.390826 | + | 0.920465i | \(0.627810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 12.0000i | 0.584151i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | −8.00000 | − | 6.00000i | −0.388057 | − | 0.291043i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 12.0000i | − | 0.580721i | ||||||
\(428\) | − | 4.00000i | − | 0.193347i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.00000 | + | 4.00000i | 0.0964486 | + | 0.192897i | ||||
\(431\) | 4.00000 | 0.192673 | 0.0963366 | − | 0.995349i | \(-0.469287\pi\) | ||||
0.0963366 | + | 0.995349i | \(0.469287\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000i | 0.0961139i | 0.998845 | + | 0.0480569i | \(0.0153029\pi\) | ||||
−0.998845 | + | 0.0480569i | \(0.984697\pi\) | |||||||
\(434\) | −2.00000 | −0.0960031 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.0000 | 0.670478 | ||||||||
\(437\) | 16.0000i | 0.765384i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.0000 | 0.477274 | 0.238637 | − | 0.971109i | \(-0.423299\pi\) | ||||
0.238637 | + | 0.971109i | \(0.423299\pi\) | |||||||
\(440\) | −12.0000 | + | 6.00000i | −0.572078 | + | 0.286039i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.00000i | 0.190261i | ||||||||
\(443\) | − | 12.0000i | − | 0.570137i | −0.958507 | − | 0.285069i | \(-0.907984\pi\) | ||
0.958507 | − | 0.285069i | \(-0.0920164\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.0000 | − | 28.0000i | −0.663664 | − | 1.32733i | ||||
\(446\) | 8.00000 | 0.378811 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 1.00000i | − | 0.0472456i | ||||||
\(449\) | 20.0000 | 0.943858 | 0.471929 | − | 0.881636i | \(-0.343558\pi\) | ||||
0.471929 | + | 0.881636i | \(0.343558\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.0000 | 1.69517 | ||||||||
\(452\) | − | 14.0000i | − | 0.658505i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 24.0000 | 1.12638 | ||||||||
\(455\) | 2.00000 | + | 4.00000i | 0.0937614 | + | 0.187523i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 28.0000i | − | 1.30978i | −0.755722 | − | 0.654892i | \(-0.772714\pi\) | ||
0.755722 | − | 0.654892i | \(-0.227286\pi\) | |||||||
\(458\) | − | 8.00000i | − | 0.373815i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.00000 | − | 4.00000i | 0.373002 | − | 0.186501i | ||||
\(461\) | −34.0000 | −1.58354 | −0.791769 | − | 0.610821i | \(-0.790840\pi\) | ||||
−0.791769 | + | 0.610821i | \(0.790840\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.0000i | − | 0.743583i | −0.928316 | − | 0.371792i | \(-0.878744\pi\) | ||
0.928316 | − | 0.371792i | \(-0.121256\pi\) | |||||||
\(464\) | 2.00000 | 0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.0000 | 1.01913 | ||||||||
\(467\) | 20.0000i | 0.925490i | 0.886492 | + | 0.462745i | \(0.153135\pi\) | ||||
−0.886492 | + | 0.462745i | \(0.846865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.0000 | 0.461757 | ||||||||
\(470\) | 2.00000 | + | 4.00000i | 0.0922531 | + | 0.184506i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 4.00000i | − | 0.184115i | ||||||
\(473\) | 12.0000i | 0.551761i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.0000 | − | 16.0000i | 0.550598 | − | 0.734130i | ||||
\(476\) | 2.00000 | 0.0916698 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 8.00000i | − | 0.365911i | ||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0000 | −0.911922 | ||||||||
\(482\) | 18.0000i | 0.819878i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −25.0000 | −1.13636 | ||||||||
\(485\) | −36.0000 | + | 18.0000i | −1.63468 | + | 0.817338i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.00000i | 0.181257i | 0.995885 | + | 0.0906287i | \(0.0288876\pi\) | ||||
−0.995885 | + | 0.0906287i | \(0.971112\pi\) | |||||||
\(488\) | − | 12.0000i | − | 0.543214i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.00000 | − | 1.00000i | 0.0903508 | − | 0.0451754i | ||||
\(491\) | 6.00000 | 0.270776 | 0.135388 | − | 0.990793i | \(-0.456772\pi\) | ||||
0.135388 | + | 0.990793i | \(0.456772\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.00000i | 0.180151i | ||||||||
\(494\) | −8.00000 | −0.359937 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | − | 12.0000i | − | 0.538274i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.00000 | −0.179065 | −0.0895323 | − | 0.995984i | \(-0.528537\pi\) | ||||
−0.0895323 | + | 0.995984i | \(0.528537\pi\) | |||||||
\(500\) | −11.0000 | − | 2.00000i | −0.491935 | − | 0.0894427i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 16.0000i | − | 0.714115i | ||||||
\(503\) | 10.0000i | 0.445878i | 0.974832 | + | 0.222939i | \(0.0715651\pi\) | ||||
−0.974832 | + | 0.222939i | \(0.928435\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | + | 12.0000i | 0.266996 | + | 0.533993i | ||||
\(506\) | 24.0000 | 1.06693 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 4.00000i | − | 0.177471i | ||||||
\(509\) | −34.0000 | −1.50702 | −0.753512 | − | 0.657434i | \(-0.771642\pi\) | ||||
−0.753512 | + | 0.657434i | \(0.771642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | 0.0884748 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.0000 | 0.793946 | ||||||||
\(515\) | −32.0000 | + | 16.0000i | −1.41009 | + | 0.705044i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.0000i | 0.527759i | ||||||||
\(518\) | 10.0000i | 0.439375i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.00000 | + | 4.00000i | 0.0877058 | + | 0.175412i | ||||
\(521\) | 42.0000 | 1.84005 | 0.920027 | − | 0.391856i | \(-0.128167\pi\) | ||||
0.920027 | + | 0.391856i | \(0.128167\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 4.00000i | − | 0.174908i | −0.996169 | − | 0.0874539i | \(-0.972127\pi\) | ||
0.996169 | − | 0.0874539i | \(-0.0278730\pi\) | |||||||
\(524\) | 20.0000 | 0.873704 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.0000 | 0.523225 | ||||||||
\(527\) | − | 4.00000i | − | 0.174243i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | −6.00000 | − | 12.0000i | −0.260623 | − | 0.521247i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.00000i | 0.173422i | ||||||||
\(533\) | − | 12.0000i | − | 0.519778i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.00000 | − | 4.00000i | 0.345870 | − | 0.172935i | ||||
\(536\) | 10.0000 | 0.431934 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 14.0000i | − | 0.603583i | ||||||
\(539\) | 6.00000 | 0.258438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.0000 | −0.945854 | −0.472927 | − | 0.881102i | \(-0.656803\pi\) | ||||
−0.472927 | + | 0.881102i | \(0.656803\pi\) | |||||||
\(542\) | 30.0000i | 1.28861i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.00000 | 0.0857493 | ||||||||
\(545\) | 14.0000 | + | 28.0000i | 0.599694 | + | 1.19939i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 26.0000i | − | 1.11168i | −0.831289 | − | 0.555840i | \(-0.812397\pi\) | ||
0.831289 | − | 0.555840i | \(-0.187603\pi\) | |||||||
\(548\) | − | 2.00000i | − | 0.0854358i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −24.0000 | − | 18.0000i | −1.02336 | − | 0.767523i | ||||
\(551\) | −8.00000 | −0.340811 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.0000i | 0.680389i | ||||||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.00000 | −0.339276 | ||||||||
\(557\) | − | 38.0000i | − | 1.61011i | −0.593199 | − | 0.805056i | \(-0.702135\pi\) | ||
0.593199 | − | 0.805056i | \(-0.297865\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 2.00000 | − | 1.00000i | 0.0845154 | − | 0.0422577i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 12.0000i | − | 0.506189i | ||||||
\(563\) | − | 4.00000i | − | 0.168580i | −0.996441 | − | 0.0842900i | \(-0.973138\pi\) | ||
0.996441 | − | 0.0842900i | \(-0.0268622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.0000 | − | 14.0000i | 1.17797 | − | 0.588984i | ||||
\(566\) | 4.00000 | 0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 12.0000i | − | 0.503509i | ||||||
\(569\) | −24.0000 | −1.00613 | −0.503066 | − | 0.864248i | \(-0.667795\pi\) | ||||
−0.503066 | + | 0.864248i | \(0.667795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | 12.0000i | 0.501745i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.00000 | −0.250435 | ||||||||
\(575\) | 16.0000 | + | 12.0000i | 0.667246 | + | 0.500435i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0000i | 0.582828i | 0.956597 | + | 0.291414i | \(0.0941257\pi\) | ||||
−0.956597 | + | 0.291414i | \(0.905874\pi\) | |||||||
\(578\) | − | 13.0000i | − | 0.540729i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.00000 | + | 4.00000i | 0.0830455 | + | 0.166091i | ||||
\(581\) | 12.0000 | 0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 36.0000i | − | 1.49097i | ||||||
\(584\) | 2.00000 | 0.0827606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.0000 | −0.495715 | ||||||||
\(587\) | − | 28.0000i | − | 1.15568i | −0.816149 | − | 0.577842i | \(-0.803895\pi\) | ||
0.816149 | − | 0.577842i | \(-0.196105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.00000 | 0.329634 | ||||||||
\(590\) | 8.00000 | − | 4.00000i | 0.329355 | − | 0.164677i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.0000i | 0.410997i | ||||||||
\(593\) | − | 18.0000i | − | 0.739171i | −0.929197 | − | 0.369586i | \(-0.879500\pi\) | ||
0.929197 | − | 0.369586i | \(-0.120500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.00000 | + | 4.00000i | 0.0819920 | + | 0.163984i | ||||
\(596\) | 6.00000 | 0.245770 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 8.00000i | − | 0.327144i | ||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | − | 2.00000i | − | 0.0815139i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12.0000 | −0.488273 | ||||||||
\(605\) | −25.0000 | − | 50.0000i | −1.01639 | − | 2.03279i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.00000i | 0.324710i | 0.986732 | + | 0.162355i | \(0.0519090\pi\) | ||||
−0.986732 | + | 0.162355i | \(0.948091\pi\) | |||||||
\(608\) | 4.00000i | 0.162221i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 24.0000 | − | 12.0000i | 0.971732 | − | 0.485866i | ||||
\(611\) | 4.00000 | 0.161823 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 18.0000i | − | 0.727013i | −0.931592 | − | 0.363507i | \(-0.881579\pi\) | ||
0.931592 | − | 0.363507i | \(-0.118421\pi\) | |||||||
\(614\) | 32.0000 | 1.29141 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.00000 | 0.241747 | ||||||||
\(617\) | − | 26.0000i | − | 1.04672i | −0.852111 | − | 0.523360i | \(-0.824678\pi\) | ||
0.852111 | − | 0.523360i | \(-0.175322\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | −2.00000 | − | 4.00000i | −0.0803219 | − | 0.160644i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.0000i | 0.560898i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 34.0000 | 1.35891 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.0000i | 0.718278i | ||||||||
\(629\) | −20.0000 | −0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.0000 | −0.477712 | −0.238856 | − | 0.971055i | \(-0.576772\pi\) | ||||
−0.238856 | + | 0.971055i | \(0.576772\pi\) | |||||||
\(632\) | 16.0000i | 0.636446i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 26.0000 | 1.03259 | ||||||||
\(635\) | 8.00000 | − | 4.00000i | 0.317470 | − | 0.158735i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.00000i | − | 0.0792429i | ||||||
\(638\) | 12.0000i | 0.475085i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.00000 | − | 1.00000i | 0.0790569 | − | 0.0395285i | ||||
\(641\) | −16.0000 | −0.631962 | −0.315981 | − | 0.948766i | \(-0.602334\pi\) | ||||
−0.315981 | + | 0.948766i | \(0.602334\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 28.0000i | − | 1.10421i | −0.833774 | − | 0.552106i | \(-0.813824\pi\) | ||
0.833774 | − | 0.552106i | \(-0.186176\pi\) | |||||||
\(644\) | −4.00000 | −0.157622 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.00000 | −0.314756 | ||||||||
\(647\) | 42.0000i | 1.65119i | 0.564263 | + | 0.825595i | \(0.309160\pi\) | ||||
−0.564263 | + | 0.825595i | \(0.690840\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.0000 | 0.942082 | ||||||||
\(650\) | −6.00000 | + | 8.00000i | −0.235339 | + | 0.313786i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 6.00000i | − | 0.234978i | ||||||
\(653\) | − | 6.00000i | − | 0.234798i | −0.993085 | − | 0.117399i | \(-0.962544\pi\) | ||
0.993085 | − | 0.117399i | \(-0.0374557\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.0000 | + | 40.0000i | 0.781465 | + | 1.56293i | ||||
\(656\) | −6.00000 | −0.234261 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 2.00000i | − | 0.0779681i | ||||||
\(659\) | −6.00000 | −0.233727 | −0.116863 | − | 0.993148i | \(-0.537284\pi\) | ||||
−0.116863 | + | 0.993148i | \(0.537284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.0000 | 1.08907 | 0.544537 | − | 0.838737i | \(-0.316705\pi\) | ||||
0.544537 | + | 0.838737i | \(0.316705\pi\) | |||||||
\(662\) | − | 20.0000i | − | 0.777322i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.0000 | 0.465690 | ||||||||
\(665\) | −8.00000 | + | 4.00000i | −0.310227 | + | 0.155113i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 8.00000i | − | 0.309761i | ||||||
\(668\) | 18.0000i | 0.696441i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.0000 | + | 20.0000i | 0.386334 | + | 0.772667i | ||||
\(671\) | 72.0000 | 2.77953 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.0000i | 0.616755i | 0.951264 | + | 0.308377i | \(0.0997859\pi\) | ||||
−0.951264 | + | 0.308377i | \(0.900214\pi\) | |||||||
\(674\) | −20.0000 | −0.770371 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 8.00000i | 0.307465i | 0.988113 | + | 0.153732i | \(0.0491294\pi\) | ||||
−0.988113 | + | 0.153732i | \(0.950871\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.0000 | 0.690777 | ||||||||
\(680\) | 2.00000 | + | 4.00000i | 0.0766965 | + | 0.153393i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 12.0000i | − | 0.459504i | ||||||
\(683\) | 28.0000i | 1.07139i | 0.844411 | + | 0.535695i | \(0.179950\pi\) | ||||
−0.844411 | + | 0.535695i | \(0.820050\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.00000 | − | 2.00000i | 0.152832 | − | 0.0764161i | ||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 2.00000i | − | 0.0762493i | ||||||
\(689\) | −12.0000 | −0.457164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.00000 | −0.304334 | −0.152167 | − | 0.988355i | \(-0.548625\pi\) | ||||
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | −8.00000 | − | 16.0000i | −0.303457 | − | 0.606915i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 12.0000i | − | 0.454532i | ||||||
\(698\) | 24.0000i | 0.908413i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.00000 | + | 3.00000i | 0.151186 | + | 0.113389i | ||||
\(701\) | 22.0000 | 0.830929 | 0.415464 | − | 0.909610i | \(-0.363619\pi\) | ||||
0.415464 | + | 0.909610i | \(0.363619\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 40.0000i | − | 1.50863i | ||||||
\(704\) | 6.00000 | 0.226134 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −30.0000 | −1.12906 | ||||||||
\(707\) | − | 6.00000i | − | 0.225653i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.0000 | −0.676004 | −0.338002 | − | 0.941145i | \(-0.609751\pi\) | ||||
−0.338002 | + | 0.941145i | \(0.609751\pi\) | |||||||
\(710\) | 24.0000 | − | 12.0000i | 0.900704 | − | 0.450352i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.0000i | 0.524672i | ||||||||
\(713\) | 8.00000i | 0.299602i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.0000 | + | 12.0000i | −0.897549 | + | 0.448775i | ||||
\(716\) | 14.0000 | 0.523205 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 4.00000i | − | 0.149279i | ||||||
\(719\) | −40.0000 | −1.49175 | −0.745874 | − | 0.666087i | \(-0.767968\pi\) | ||||
−0.745874 | + | 0.666087i | \(0.767968\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | 0.595871 | ||||||||
\(722\) | 3.00000i | 0.111648i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.00000 | −0.297318 | ||||||||
\(725\) | −6.00000 | + | 8.00000i | −0.222834 | + | 0.297113i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 32.0000i | − | 1.18681i | −0.804902 | − | 0.593407i | \(-0.797782\pi\) | ||
0.804902 | − | 0.593407i | \(-0.202218\pi\) | |||||||
\(728\) | − | 2.00000i | − | 0.0741249i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.00000 | + | 4.00000i | 0.0740233 | + | 0.148047i | ||||
\(731\) | 4.00000 | 0.147945 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 26.0000i | − | 0.960332i | −0.877178 | − | 0.480166i | \(-0.840576\pi\) | ||
0.877178 | − | 0.480166i | \(-0.159424\pi\) | |||||||
\(734\) | −8.00000 | −0.295285 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | 60.0000i | 2.21013i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.0000 | −1.03000 | −0.514998 | − | 0.857191i | \(-0.672207\pi\) | ||||
−0.514998 | + | 0.857191i | \(0.672207\pi\) | |||||||
\(740\) | −20.0000 | + | 10.0000i | −0.735215 | + | 0.367607i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.00000i | 0.220267i | ||||||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00000 | + | 12.0000i | 0.219823 | + | 0.439646i | ||||
\(746\) | 34.0000 | 1.24483 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.0000i | 0.438763i | ||||||||
\(749\) | −4.00000 | −0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.0000 | −0.729810 | −0.364905 | − | 0.931045i | \(-0.618899\pi\) | ||||
−0.364905 | + | 0.931045i | \(0.618899\pi\) | |||||||
\(752\) | − | 2.00000i | − | 0.0729325i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.00000 | 0.145671 | ||||||||
\(755\) | −12.0000 | − | 24.0000i | −0.436725 | − | 0.873449i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.0000i | 1.09037i | 0.838316 | + | 0.545184i | \(0.183540\pi\) | ||||
−0.838316 | + | 0.545184i | \(0.816460\pi\) | |||||||
\(758\) | − | 20.0000i | − | 0.726433i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.00000 | + | 4.00000i | −0.290191 | + | 0.145095i | ||||
\(761\) | 38.0000 | 1.37750 | 0.688749 | − | 0.724999i | \(-0.258160\pi\) | ||||
0.688749 | + | 0.724999i | \(0.258160\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 14.0000i | − | 0.506834i | ||||||
\(764\) | 16.0000 | 0.578860 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30.0000 | 1.08394 | ||||||||
\(767\) | − | 8.00000i | − | 0.288863i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.0000 | −1.22607 | −0.613036 | − | 0.790055i | \(-0.710052\pi\) | ||||
−0.613036 | + | 0.790055i | \(0.710052\pi\) | |||||||
\(770\) | 6.00000 | + | 12.0000i | 0.216225 | + | 0.432450i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 4.00000i | − | 0.143963i | ||||||
\(773\) | − | 36.0000i | − | 1.29483i | −0.762138 | − | 0.647415i | \(-0.775850\pi\) | ||
0.762138 | − | 0.647415i | \(-0.224150\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.00000 | − | 8.00000i | 0.215526 | − | 0.287368i | ||||
\(776\) | 18.0000 | 0.646162 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.00000i | 0.215110i | ||||||||
\(779\) | 24.0000 | 0.859889 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 72.0000 | 2.57636 | ||||||||
\(782\) | − | 8.00000i | − | 0.286079i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | −36.0000 | + | 18.0000i | −1.28490 | + | 0.642448i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.0000i | 1.71102i | 0.517790 | + | 0.855508i | \(0.326755\pi\) | ||||
−0.517790 | + | 0.855508i | \(0.673245\pi\) | |||||||
\(788\) | 10.0000i | 0.356235i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −32.0000 | + | 16.0000i | −1.13851 | + | 0.569254i | ||||
\(791\) | −14.0000 | −0.497783 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 24.0000i | − | 0.852265i | ||||||
\(794\) | −14.0000 | −0.496841 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.0000 | 0.637993 | ||||||||
\(797\) | − | 40.0000i | − | 1.41687i | −0.705775 | − | 0.708436i | \(-0.749401\pi\) | ||
0.705775 | − | 0.708436i | \(-0.250599\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.00000 | 0.141510 | ||||||||
\(800\) | 4.00000 | + | 3.00000i | 0.141421 | + | 0.106066i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 24.0000i | − | 0.847469i | ||||||
\(803\) | 12.0000i | 0.423471i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.00000 | − | 8.00000i | −0.140981 | − | 0.281963i | ||||
\(806\) | −4.00000 | −0.140894 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 6.00000i | − | 0.211079i | ||||||
\(809\) | 52.0000 | 1.82822 | 0.914111 | − | 0.405463i | \(-0.132890\pi\) | ||||
0.914111 | + | 0.405463i | \(0.132890\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | − | 2.00000i | − | 0.0701862i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −60.0000 | −2.10300 | ||||||||
\(815\) | 12.0000 | − | 6.00000i | 0.420342 | − | 0.210171i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.00000i | 0.279885i | ||||||||
\(818\) | 10.0000i | 0.349642i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.00000 | − | 12.0000i | −0.209529 | − | 0.419058i | ||||
\(821\) | −18.0000 | −0.628204 | −0.314102 | − | 0.949389i | \(-0.601703\pi\) | ||||
−0.314102 | + | 0.949389i | \(0.601703\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0000i | 0.836587i | 0.908312 | + | 0.418294i | \(0.137372\pi\) | ||||
−0.908312 | + | 0.418294i | \(0.862628\pi\) | |||||||
\(824\) | 16.0000 | 0.557386 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.00000 | −0.139178 | ||||||||
\(827\) | 4.00000i | 0.139094i | 0.997579 | + | 0.0695468i | \(0.0221553\pi\) | ||||
−0.997579 | + | 0.0695468i | \(0.977845\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.0000 | 0.694629 | 0.347314 | − | 0.937749i | \(-0.387094\pi\) | ||||
0.347314 | + | 0.937749i | \(0.387094\pi\) | |||||||
\(830\) | 12.0000 | + | 24.0000i | 0.416526 | + | 0.833052i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 2.00000i | − | 0.0693375i | ||||||
\(833\) | − | 2.00000i | − | 0.0692959i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −36.0000 | + | 18.0000i | −1.24583 | + | 0.622916i | ||||
\(836\) | −24.0000 | −0.830057 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.0000i | 0.552711i | ||||||||
\(839\) | 8.00000 | 0.276191 | 0.138095 | − | 0.990419i | \(-0.455902\pi\) | ||||
0.138095 | + | 0.990419i | \(0.455902\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 2.00000i | 0.0689246i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.0000 | 0.413057 | ||||||||
\(845\) | −9.00000 | − | 18.0000i | −0.309609 | − | 0.619219i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.0000i | 0.859010i | ||||||||
\(848\) | 6.00000i | 0.206041i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.00000 | + | 8.00000i | −0.205798 | + | 0.274398i | ||||
\(851\) | 40.0000 | 1.37118 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.0000i | 0.753266i | 0.926363 | + | 0.376633i | \(0.122918\pi\) | ||||
−0.926363 | + | 0.376633i | \(0.877082\pi\) | |||||||
\(854\) | −12.0000 | −0.410632 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.00000 | −0.136717 | ||||||||
\(857\) | 34.0000i | 1.16142i | 0.814111 | + | 0.580709i | \(0.197225\pi\) | ||||
−0.814111 | + | 0.580709i | \(0.802775\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.0000 | 0.818869 | 0.409435 | − | 0.912339i | \(-0.365726\pi\) | ||||
0.409435 | + | 0.912339i | \(0.365726\pi\) | |||||||
\(860\) | 4.00000 | − | 2.00000i | 0.136399 | − | 0.0681994i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 4.00000i | − | 0.136241i | ||||||
\(863\) | − | 32.0000i | − | 1.08929i | −0.838666 | − | 0.544646i | \(-0.816664\pi\) | ||
0.838666 | − | 0.544646i | \(-0.183336\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.00000 | 0.0679628 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.00000i | 0.0678844i | ||||||||
\(869\) | −96.0000 | −3.25658 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.0000 | 0.677674 | ||||||||
\(872\) | − | 14.0000i | − | 0.474100i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 16.0000 | 0.541208 | ||||||||
\(875\) | −2.00000 | + | 11.0000i | −0.0676123 | + | 0.371868i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.0000i | 0.742887i | 0.928456 | + | 0.371444i | \(0.121137\pi\) | ||||
−0.928456 | + | 0.371444i | \(0.878863\pi\) | |||||||
\(878\) | − | 10.0000i | − | 0.337484i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.00000 | + | 12.0000i | 0.202260 | + | 0.404520i | ||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 46.0000i | − | 1.54802i | −0.633171 | − | 0.774012i | \(-0.718247\pi\) | ||
0.633171 | − | 0.774012i | \(-0.281753\pi\) | |||||||
\(884\) | 4.00000 | 0.134535 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.0000 | −0.403148 | ||||||||
\(887\) | 42.0000i | 1.41022i | 0.709097 | + | 0.705111i | \(0.249103\pi\) | ||||
−0.709097 | + | 0.705111i | \(0.750897\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.00000 | −0.134156 | ||||||||
\(890\) | −28.0000 | + | 14.0000i | −0.938562 | + | 0.469281i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 8.00000i | − | 0.267860i | ||||||
\(893\) | 8.00000i | 0.267710i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.0000 | + | 28.0000i | 0.467968 | + | 0.935937i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 20.0000i | − | 0.667409i | ||||||
\(899\) | −4.00000 | −0.133407 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0000 | −0.399778 | ||||||||
\(902\) | − | 36.0000i | − | 1.19867i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.0000 | −0.465633 | ||||||||
\(905\) | −8.00000 | − | 16.0000i | −0.265929 | − | 0.531858i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.0000i | 1.26177i | 0.775877 | + | 0.630885i | \(0.217308\pi\) | ||||
−0.775877 | + | 0.630885i | \(0.782692\pi\) | |||||||
\(908\) | − | 24.0000i | − | 0.796468i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.00000 | − | 2.00000i | 0.132599 | − | 0.0662994i | ||||
\(911\) | 16.0000 | 0.530104 | 0.265052 | − | 0.964234i | \(-0.414611\pi\) | ||||
0.265052 | + | 0.964234i | \(0.414611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 72.0000i | 2.38285i | ||||||||
\(914\) | −28.0000 | −0.926158 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.00000 | −0.264327 | ||||||||
\(917\) | − | 20.0000i | − | 0.660458i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.0000 | −0.659739 | −0.329870 | − | 0.944027i | \(-0.607005\pi\) | ||||
−0.329870 | + | 0.944027i | \(0.607005\pi\) | |||||||
\(920\) | −4.00000 | − | 8.00000i | −0.131876 | − | 0.263752i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 34.0000i | 1.11973i | ||||||||
\(923\) | − | 24.0000i | − | 0.789970i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.0000 | − | 30.0000i | −1.31519 | − | 0.986394i | ||||
\(926\) | −16.0000 | −0.525793 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 2.00000i | − | 0.0656532i | ||||||
\(929\) | −6.00000 | −0.196854 | −0.0984268 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984268 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00000 | 0.131095 | ||||||||
\(932\) | − | 22.0000i | − | 0.720634i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20.0000 | 0.654420 | ||||||||
\(935\) | −24.0000 | + | 12.0000i | −0.784884 | + | 0.392442i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 38.0000i | − | 1.24141i | −0.784046 | − | 0.620703i | \(-0.786847\pi\) | ||
0.784046 | − | 0.620703i | \(-0.213153\pi\) | |||||||
\(938\) | − | 10.0000i | − | 0.326512i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.00000 | − | 2.00000i | 0.130466 | − | 0.0652328i | ||||
\(941\) | −50.0000 | −1.62995 | −0.814977 | − | 0.579494i | \(-0.803250\pi\) | ||||
−0.814977 | + | 0.579494i | \(0.803250\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0000i | 0.781548i | ||||||||
\(944\) | −4.00000 | −0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.0000 | 0.390154 | ||||||||
\(947\) | − | 12.0000i | − | 0.389948i | −0.980808 | − | 0.194974i | \(-0.937538\pi\) | ||
0.980808 | − | 0.194974i | \(-0.0624622\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | −16.0000 | − | 12.0000i | −0.519109 | − | 0.389331i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 2.00000i | − | 0.0648204i | ||||||
\(953\) | 42.0000i | 1.36051i | 0.732974 | + | 0.680257i | \(0.238132\pi\) | ||||
−0.732974 | + | 0.680257i | \(0.761868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.0000 | + | 32.0000i | 0.517748 | + | 1.03550i | ||||
\(956\) | −8.00000 | −0.258738 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.00000 | −0.0645834 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 20.0000i | 0.644826i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 18.0000 | 0.579741 | ||||||||
\(965\) | 8.00000 | − | 4.00000i | 0.257529 | − | 0.128765i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.0000i | 1.80084i | 0.435023 | + | 0.900419i | \(0.356740\pi\) | ||||
−0.435023 | + | 0.900419i | \(0.643260\pi\) | |||||||
\(968\) | 25.0000i | 0.803530i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 18.0000 | + | 36.0000i | 0.577945 | + | 1.15589i | ||||
\(971\) | 24.0000 | 0.770197 | 0.385098 | − | 0.922876i | \(-0.374168\pi\) | ||||
0.385098 | + | 0.922876i | \(0.374168\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.00000i | 0.256468i | ||||||||
\(974\) | 4.00000 | 0.128168 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.0000 | −0.384111 | ||||||||
\(977\) | − | 30.0000i | − | 0.959785i | −0.877327 | − | 0.479893i | \(-0.840676\pi\) | ||
0.877327 | − | 0.479893i | \(-0.159324\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −84.0000 | −2.68465 | ||||||||
\(980\) | −1.00000 | − | 2.00000i | −0.0319438 | − | 0.0638877i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 6.00000i | − | 0.191468i | ||||||
\(983\) | − | 14.0000i | − | 0.446531i | −0.974758 | − | 0.223265i | \(-0.928328\pi\) | ||
0.974758 | − | 0.223265i | \(-0.0716716\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.0000 | + | 10.0000i | −0.637253 | + | 0.318626i | ||||
\(986\) | 4.00000 | 0.127386 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.00000i | 0.254514i | ||||||||
\(989\) | −8.00000 | −0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.00000 | 0.127064 | 0.0635321 | − | 0.997980i | \(-0.479763\pi\) | ||||
0.0635321 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(992\) | 2.00000i | 0.0635001i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.0000 | −0.380617 | ||||||||
\(995\) | 18.0000 | + | 36.0000i | 0.570638 | + | 1.14128i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 14.0000i | − | 0.443384i | −0.975117 | − | 0.221692i | \(-0.928842\pi\) | ||
0.975117 | − | 0.221692i | \(-0.0711580\pi\) | |||||||
\(998\) | 4.00000i | 0.126618i | ||||||||
\(999\) | 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 | 630.2.g.b.379.1 | ✓ | 2 | |
3.2 | odd | 2 | 630.2.g.e.379.2 | yes | 2 | ||
4.3 | odd | 2 | 5040.2.t.i.1009.1 | 2 | |||
5.2 | odd | 4 | 3150.2.a.v.1.1 | 1 | |||
5.3 | odd | 4 | 3150.2.a.l.1.1 | 1 | |||
5.4 | even | 2 | inner | 630.2.g.b.379.2 | yes | 2 | |
12.11 | even | 2 | 5040.2.t.j.1009.2 | 2 | |||
15.2 | even | 4 | 3150.2.a.k.1.1 | 1 | |||
15.8 | even | 4 | 3150.2.a.br.1.1 | 1 | |||
15.14 | odd | 2 | 630.2.g.e.379.1 | yes | 2 | ||
20.19 | odd | 2 | 5040.2.t.i.1009.2 | 2 | |||
60.59 | even | 2 | 5040.2.t.j.1009.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.g.b.379.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
630.2.g.b.379.2 | yes | 2 | 5.4 | even | 2 | inner | |
630.2.g.e.379.1 | yes | 2 | 15.14 | odd | 2 | ||
630.2.g.e.379.2 | yes | 2 | 3.2 | odd | 2 | ||
3150.2.a.k.1.1 | 1 | 15.2 | even | 4 | |||
3150.2.a.l.1.1 | 1 | 5.3 | odd | 4 | |||
3150.2.a.v.1.1 | 1 | 5.2 | odd | 4 | |||
3150.2.a.br.1.1 | 1 | 15.8 | even | 4 | |||
5040.2.t.i.1009.1 | 2 | 4.3 | odd | 2 | |||
5040.2.t.i.1009.2 | 2 | 20.19 | odd | 2 | |||
5040.2.t.j.1009.1 | 2 | 60.59 | even | 2 | |||
5040.2.t.j.1009.2 | 2 | 12.11 | even | 2 |