Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(5615,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 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("6048.5615");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.j (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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.56070144.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5615.4 | ||
Root | \(0.500000 + 0.564882i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.5615 |
Dual form | 6048.2.j.a.5615.3 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.12976 | −1.39967 | −0.699837 | − | 0.714303i | \(-0.746744\pi\) | ||||
−0.699837 | + | 0.714303i | \(0.746744\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 0.397714i | − 0.119915i | −0.998201 | − | 0.0599577i | \(-0.980903\pi\) | ||||
0.998201 | − | 0.0599577i | \(-0.0190966\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.55068i | 1.81683i | 0.418069 | + | 0.908415i | \(0.362707\pi\) | ||||
−0.418069 | + | 0.908415i | \(0.637293\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 2.00000i | − 0.485071i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.527479 | 0.121012 | 0.0605060 | − | 0.998168i | \(-0.480729\pi\) | ||||
0.0605060 | + | 0.998168i | \(0.480729\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.21634 | −1.71323 | −0.856613 | − | 0.515960i | \(-0.827435\pi\) | ||||
−0.856613 | + | 0.515960i | \(0.827435\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.79543 | 0.959086 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.73205 | −0.878720 | −0.439360 | − | 0.898311i | \(-0.644795\pi\) | ||||
−0.439360 | + | 0.898311i | \(0.644795\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.55068i | 1.35614i | 0.734997 | + | 0.678071i | \(0.237184\pi\) | ||||
−0.734997 | + | 0.678071i | \(0.762816\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 3.12976i | − 0.529027i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 3.35452i | − 0.551480i | −0.961232 | − | 0.275740i | \(-0.911077\pi\) | ||||
0.961232 | − | 0.275740i | \(-0.0889229\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.48429i | 1.16885i | 0.811448 | + | 0.584425i | \(0.198680\pi\) | ||||
−0.811448 | + | 0.584425i | \(0.801320\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.62247 | −0.247425 | −0.123712 | − | 0.992318i | \(-0.539480\pi\) | ||||
−0.123712 | + | 0.992318i | \(0.539480\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.4557 | 1.52512 | 0.762559 | − | 0.646919i | \(-0.223943\pi\) | ||||
0.762559 | + | 0.646919i | \(0.223943\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.795428 | 0.109260 | 0.0546302 | − | 0.998507i | \(-0.482602\pi\) | ||||
0.0546302 | + | 0.998507i | \(0.482602\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.24475i | 0.167842i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 2.47252i | − 0.321895i | −0.986963 | − | 0.160947i | \(-0.948545\pi\) | ||||
0.986963 | − | 0.160947i | \(-0.0514550\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 11.4641i | − 1.46783i | −0.679243 | − | 0.733914i | \(-0.737692\pi\) | ||||
0.679243 | − | 0.733914i | \(-0.262308\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 20.5021i | − 2.54297i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.55068 | 0.800293 | 0.400146 | − | 0.916451i | \(-0.368959\pi\) | ||||
0.400146 | + | 0.916451i | \(0.368959\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.21634 | 0.263031 | 0.131516 | − | 0.991314i | \(-0.458016\pi\) | ||||
0.131516 | + | 0.991314i | \(0.458016\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.75525 | −0.673601 | −0.336800 | − | 0.941576i | \(-0.609345\pi\) | ||||
−0.336800 | + | 0.941576i | \(0.609345\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.397714 | 0.0453237 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.2911i | 1.15784i | 0.815383 | + | 0.578922i | \(0.196527\pi\) | ||||
−0.815383 | + | 0.578922i | \(0.803473\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.36930i | 0.918650i | 0.888268 | + | 0.459325i | \(0.151909\pi\) | ||||
−0.888268 | + | 0.459325i | \(0.848091\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.25953i | 0.678941i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 5.31114i | − 0.562980i | −0.959564 | − | 0.281490i | \(-0.909171\pi\) | ||||
0.959564 | − | 0.281490i | \(-0.0908286\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.55068 | −0.686697 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.65089 | −0.169377 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −19.1014 | −1.93945 | −0.969724 | − | 0.244202i | \(-0.921474\pi\) | ||||
−0.969724 | + | 0.244202i | \(0.921474\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.00000 | −0.199007 | −0.0995037 | − | 0.995037i | \(-0.531726\pi\) | ||||
−0.0995037 | + | 0.995037i | \(0.531726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.0148i | 1.67652i | 0.545274 | + | 0.838258i | \(0.316426\pi\) | ||||
−0.545274 | + | 0.838258i | \(0.683574\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1.91362i | − 0.184997i | −0.995713 | − | 0.0924983i | \(-0.970515\pi\) | ||||
0.995713 | − | 0.0924983i | \(-0.0294853\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.07816i | 0.677964i | 0.940793 | + | 0.338982i | \(0.110083\pi\) | ||||
−0.940793 | + | 0.338982i | \(0.889917\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 9.98316i | − 0.939137i | −0.882896 | − | 0.469568i | \(-0.844410\pi\) | ||||
0.882896 | − | 0.469568i | \(-0.155590\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 25.7152 | 2.39796 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00000 | 0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.8418 | 0.985620 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.640262 | 0.0572668 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 7.75525i | − 0.688167i | −0.938939 | − | 0.344084i | \(-0.888190\pi\) | ||||
0.938939 | − | 0.344084i | \(-0.111810\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 14.9052i | − 1.30227i | −0.758960 | − | 0.651137i | \(-0.774292\pi\) | ||||
0.758960 | − | 0.651137i | \(-0.225708\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.527479i | 0.0457382i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 22.4557i | − 1.91852i | −0.282527 | − | 0.959259i | \(-0.591173\pi\) | ||||
0.282527 | − | 0.959259i | \(-0.408827\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.05496 | −0.259118 | −0.129559 | − | 0.991572i | \(-0.541356\pi\) | ||||
−0.129559 | + | 0.991572i | \(0.541356\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.60530 | 0.217866 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.8102 | 1.22992 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.01458 | 0.574657 | 0.287329 | − | 0.957832i | \(-0.407233\pi\) | ||||
0.287329 | + | 0.957832i | \(0.407233\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.81001i | 0.798327i | 0.916880 | + | 0.399164i | \(0.130699\pi\) | ||||
−0.916880 | + | 0.399164i | \(0.869301\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 23.6318i | − 1.89816i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 10.8966i | − 0.869642i | −0.900517 | − | 0.434821i | \(-0.856812\pi\) | ||||
0.900517 | − | 0.434821i | \(-0.143188\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 8.21634i | − 0.647538i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0148 | 0.784418 | 0.392209 | − | 0.919876i | \(-0.371711\pi\) | ||||
0.392209 | + | 0.919876i | \(0.371711\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.5655 | 1.12711 | 0.563554 | − | 0.826079i | \(-0.309434\pi\) | ||||
0.563554 | + | 0.826079i | \(0.309434\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −29.9114 | −2.30087 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.3175 | −1.08854 | −0.544270 | − | 0.838910i | \(-0.683193\pi\) | ||||
−0.544270 | + | 0.838910i | \(0.683193\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.79543i | 0.362500i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.8104i | 1.48070i | 0.672222 | + | 0.740349i | \(0.265340\pi\) | ||||
−0.672222 | + | 0.740349i | \(0.734660\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 20.1732i | − 1.49946i | −0.661745 | − | 0.749729i | \(-0.730184\pi\) | ||||
0.661745 | − | 0.749729i | \(-0.269816\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.4989i | 0.771892i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.795428 | −0.0581675 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.43549 | −0.465656 | −0.232828 | − | 0.972518i | \(-0.574798\pi\) | ||||
−0.232828 | + | 0.972518i | \(0.574798\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.98316 | −0.718604 | −0.359302 | − | 0.933221i | \(-0.616985\pi\) | ||||
−0.359302 | + | 0.933221i | \(0.616985\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.6373 | −1.68408 | −0.842042 | − | 0.539412i | \(-0.818647\pi\) | ||||
−0.842042 | + | 0.539412i | \(0.818647\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 21.6202i | − 1.53262i | −0.642473 | − | 0.766308i | \(-0.722092\pi\) | ||||
0.642473 | − | 0.766308i | \(-0.277908\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4.73205i | − 0.332125i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 23.4241i | − 1.63601i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 0.209786i | − 0.0145112i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.51906 | −0.173419 | −0.0867096 | − | 0.996234i | \(-0.527635\pi\) | ||||
−0.0867096 | + | 0.996234i | \(0.527635\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.07796 | 0.346314 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.55068 | −0.512573 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.1014 | 0.881292 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 0.882003i | − 0.0590633i | −0.999564 | − | 0.0295316i | \(-0.990598\pi\) | ||||
0.999564 | − | 0.0295316i | \(-0.00940158\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 8.47868i | − 0.562750i | −0.959598 | − | 0.281375i | \(-0.909210\pi\) | ||||
0.959598 | − | 0.281375i | \(-0.0907905\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 13.4641i | − 0.889733i | −0.895597 | − | 0.444866i | \(-0.853251\pi\) | ||||
0.895597 | − | 0.444866i | \(-0.146749\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 17.4641i | − 1.14411i | −0.820215 | − | 0.572056i | \(-0.806146\pi\) | ||||
0.820215 | − | 0.572056i | \(-0.193854\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −32.7238 | −2.13467 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.6836 | −1.79071 | −0.895353 | − | 0.445357i | \(-0.853077\pi\) | ||||
−0.895353 | + | 0.445357i | \(0.853077\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.9116 | 1.41145 | 0.705724 | − | 0.708487i | \(-0.250622\pi\) | ||||
0.705724 | + | 0.708487i | \(0.250622\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.12976 | 0.199953 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.45534i | 0.219858i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 15.9136i | − 1.00446i | −0.864734 | − | 0.502229i | \(-0.832513\pi\) | ||||
0.864734 | − | 0.502229i | \(-0.167487\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.26775i | 0.205442i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.70344i | 0.231014i | 0.993307 | + | 0.115507i | \(0.0368493\pi\) | ||||
−0.993307 | + | 0.115507i | \(0.963151\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.35452 | 0.208440 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.1995 | −1.36888 | −0.684440 | − | 0.729069i | \(-0.739953\pi\) | ||||
−0.684440 | + | 0.729069i | \(0.739953\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.48950 | −0.152929 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.2480 | −0.990655 | −0.495328 | − | 0.868706i | \(-0.664952\pi\) | ||||
−0.495328 | + | 0.868706i | \(0.664952\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 18.3755i | − 1.11623i | −0.829764 | − | 0.558115i | \(-0.811525\pi\) | ||||
0.829764 | − | 0.558115i | \(-0.188475\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1.90721i | − 0.115009i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 31.7764i | − 1.90926i | −0.297798 | − | 0.954629i | \(-0.596252\pi\) | ||||
0.297798 | − | 0.954629i | \(-0.403748\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 4.86483i | − 0.290211i | −0.989416 | − | 0.145106i | \(-0.953648\pi\) | ||||
0.989416 | − | 0.145106i | \(-0.0463522\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.7386 | 1.47056 | 0.735279 | − | 0.677765i | \(-0.237051\pi\) | ||||
0.735279 | + | 0.677765i | \(0.237051\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.48429 | −0.441784 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.9428 | 0.931388 | 0.465694 | − | 0.884946i | \(-0.345805\pi\) | ||||
0.465694 | + | 0.884946i | \(0.345805\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.73841i | 0.450548i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 53.8226i | − 3.11264i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.62247i | − 0.0935178i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 35.8799i | 2.05448i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.64567 | 0.322215 | 0.161108 | − | 0.986937i | \(-0.448493\pi\) | ||||
0.161108 | + | 0.986937i | \(0.448493\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.0084 | −1.07787 | −0.538934 | − | 0.842348i | \(-0.681173\pi\) | ||||
−0.538934 | + | 0.842348i | \(0.681173\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.24475 | 0.126881 | 0.0634404 | − | 0.997986i | \(-0.479793\pi\) | ||||
0.0634404 | + | 0.997986i | \(0.479793\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.4852 | 1.37523 | 0.687614 | − | 0.726076i | \(-0.258658\pi\) | ||||
0.687614 | + | 0.726076i | \(0.258658\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.88200i | 0.105372i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.05496i | − 0.0586994i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 31.4133i | 1.74250i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.4557i | 0.576440i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.34591 | −0.238873 | −0.119436 | − | 0.992842i | \(-0.538109\pi\) | ||||
−0.119436 | + | 0.992842i | \(0.538109\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −20.5021 | −1.12015 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.5655 | −1.50159 | −0.750793 | − | 0.660538i | \(-0.770328\pi\) | ||||
−0.750793 | + | 0.660538i | \(0.770328\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.00301 | 0.162622 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 20.8364i | − 1.11856i | −0.828980 | − | 0.559279i | \(-0.811078\pi\) | ||||
0.828980 | − | 0.559279i | \(-0.188922\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.88181i | 0.261317i | 0.991427 | + | 0.130659i | \(0.0417092\pi\) | ||||
−0.991427 | + | 0.130659i | \(0.958291\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 7.44391i | − 0.396200i | −0.980182 | − | 0.198100i | \(-0.936523\pi\) | ||||
0.980182 | − | 0.198100i | \(-0.0634770\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.93662 | −0.368158 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.3923 | −1.18182 | −0.590910 | − | 0.806737i | \(-0.701231\pi\) | ||||
−0.590910 | + | 0.806737i | \(0.701231\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7218 | −0.985356 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.0126 | 0.942821 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 35.2575i | − 1.84042i | −0.391419 | − | 0.920212i | \(-0.628016\pi\) | ||||
0.391419 | − | 0.920212i | \(-0.371984\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.795428i | 0.0412966i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.2681i | 0.583442i | 0.956503 | + | 0.291721i | \(0.0942279\pi\) | ||||
−0.956503 | + | 0.291721i | \(0.905772\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 30.9981i | − 1.59649i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.47888 | 0.281431 | 0.140716 | − | 0.990050i | \(-0.455060\pi\) | ||||
0.140716 | + | 0.990050i | \(0.455060\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.6668 | 1.61810 | 0.809049 | − | 0.587741i | \(-0.199983\pi\) | ||||
0.809049 | + | 0.587741i | \(0.199983\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.24475 | −0.0634384 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.1014 | −1.27269 | −0.636345 | − | 0.771405i | \(-0.719554\pi\) | ||||
−0.636345 | + | 0.771405i | \(0.719554\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.4327i | 0.831036i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 32.2089i | − 1.62060i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.04640i | 0.203083i | 0.994831 | + | 0.101541i | \(0.0323774\pi\) | ||||
−0.994831 | + | 0.101541i | \(0.967623\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 5.87339i | − 0.293303i | −0.989188 | − | 0.146652i | \(-0.953150\pi\) | ||||
0.989188 | − | 0.146652i | \(-0.0468496\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −49.4620 | −2.46388 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.33414 | −0.0661309 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.1101 | 1.24162 | 0.620808 | − | 0.783963i | \(-0.286805\pi\) | ||||
0.620808 | + | 0.783963i | \(0.286805\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.47252 | 0.121665 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 26.1939i | − 1.28581i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.3059i | 0.601184i | 0.953753 | + | 0.300592i | \(0.0971842\pi\) | ||||
−0.953753 | + | 0.300592i | \(0.902816\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.4095i | 1.09217i | 0.837729 | + | 0.546086i | \(0.183883\pi\) | ||||
−0.837729 | + | 0.546086i | \(0.816117\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 9.59086i | − 0.465225i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.4641 | 0.554787 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.4041 | 1.03100 | 0.515499 | − | 0.856890i | \(-0.327607\pi\) | ||||
0.515499 | + | 0.856890i | \(0.327607\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.3925 | 0.931944 | 0.465972 | − | 0.884799i | \(-0.345705\pi\) | ||||
0.465972 | + | 0.884799i | \(0.345705\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.33395 | −0.207321 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.3755i | 0.877013i | 0.898728 | + | 0.438507i | \(0.144492\pi\) | ||||
−0.898728 | + | 0.438507i | \(0.855508\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 8.58770i | − 0.408014i | −0.978969 | − | 0.204007i | \(-0.934603\pi\) | ||||
0.978969 | − | 0.204007i | \(-0.0653965\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.6226i | 0.787988i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 7.78687i | − 0.367485i | −0.982974 | − | 0.183742i | \(-0.941179\pi\) | ||||
0.982974 | − | 0.183742i | \(-0.0588212\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.97661 | 0.140163 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 20.5021 | 0.961152 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.3205 | 0.482773 | 0.241387 | − | 0.970429i | \(-0.422398\pi\) | ||||
0.241387 | + | 0.970429i | \(0.422398\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.2016 | 1.03403 | 0.517015 | − | 0.855976i | \(-0.327043\pi\) | ||||
0.517015 | + | 0.855976i | \(0.327043\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 27.9028i | − 1.29675i | −0.761320 | − | 0.648377i | \(-0.775448\pi\) | ||||
0.761320 | − | 0.648377i | \(-0.224552\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.9602i | 1.01619i | 0.861300 | + | 0.508097i | \(0.169651\pi\) | ||||
−0.861300 | + | 0.508097i | \(0.830349\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.55068i | 0.302482i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.645280i | 0.0296700i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.52949 | 0.116061 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.13278 | −0.280214 | −0.140107 | − | 0.990136i | \(-0.544745\pi\) | ||||
−0.140107 | + | 0.990136i | \(0.544745\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.9744 | 1.00195 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 59.7827 | 2.71459 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.7848i | 0.896535i | 0.893899 | + | 0.448268i | \(0.147959\pi\) | ||||
−0.893899 | + | 0.448268i | \(0.852041\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.3809i | 1.28081i | 0.768037 | + | 0.640405i | \(0.221234\pi\) | ||||
−0.768037 | + | 0.640405i | \(0.778766\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.46410i | 0.426242i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.21634i | 0.0994164i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.7407 | −0.480818 | −0.240409 | − | 0.970672i | \(-0.577282\pi\) | ||||
−0.240409 | + | 0.970672i | \(0.577282\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.7321 | 0.656870 | 0.328435 | − | 0.944527i | \(-0.393479\pi\) | ||||
0.328435 | + | 0.944527i | \(0.393479\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.25953 | 0.278545 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.2913 | −1.03237 | −0.516185 | − | 0.856477i | \(-0.672648\pi\) | ||||
−0.516185 | + | 0.856477i | \(0.672648\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 5.75525i | − 0.254597i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 53.2523i | − 2.34657i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 4.15837i | − 0.182885i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.91027i | 0.0836905i | 0.999124 | + | 0.0418453i | \(0.0133237\pi\) | ||||
−0.999124 | + | 0.0418453i | \(0.986676\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.5885 | −1.11891 | −0.559453 | − | 0.828862i | \(-0.688989\pi\) | ||||
−0.559453 | + | 0.828862i | \(0.688989\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.1014 | 0.657825 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.5082 | 1.93514 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −49.0272 | −2.12360 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.98918i | 0.258935i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.397714i | 0.0171308i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.91959i | 0.340490i | 0.985402 | + | 0.170245i | \(0.0544559\pi\) | ||||
−0.985402 | + | 0.170245i | \(0.945544\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 22.1530i | − 0.948929i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.65409 | 0.327265 | 0.163633 | − | 0.986521i | \(-0.447679\pi\) | ||||
0.163633 | + | 0.986521i | \(0.447679\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.49606 | −0.106336 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.2911 | −0.437624 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.6373 | −1.17103 | −0.585514 | − | 0.810662i | \(-0.699107\pi\) | ||||
−0.585514 | + | 0.810662i | \(0.699107\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 10.6283i | − 0.449529i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.9198i | 1.42955i | 0.699355 | + | 0.714774i | \(0.253471\pi\) | ||||
−0.699355 | + | 0.714774i | \(0.746529\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.2449i | 1.31448i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 18.7382i | − 0.785547i | −0.919635 | − | 0.392773i | \(-0.871516\pi\) | ||||
0.919635 | − | 0.392773i | \(-0.128484\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.2449 | −0.637981 | −0.318991 | − | 0.947758i | \(-0.603344\pi\) | ||||
−0.318991 | + | 0.947758i | \(0.603344\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −39.4009 | −1.64313 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.49366 | 0.0621818 | 0.0310909 | − | 0.999517i | \(-0.490102\pi\) | ||||
0.0310909 | + | 0.999517i | \(0.490102\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.36930 | −0.347217 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 0.316353i | − 0.0131020i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 16.2195i | − 0.669452i | −0.942315 | − | 0.334726i | \(-0.891356\pi\) | ||||
0.942315 | − | 0.334726i | \(-0.108644\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.98282i | 0.164109i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.3871i | 0.878263i | 0.898423 | + | 0.439131i | \(0.144714\pi\) | ||||
−0.898423 | + | 0.439131i | \(0.855286\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.25953 | −0.256616 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.7672 | −0.480795 | −0.240398 | − | 0.970674i | \(-0.577278\pi\) | ||||
−0.240398 | + | 0.970674i | \(0.577278\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.7552 | −0.642670 | −0.321335 | − | 0.946966i | \(-0.604132\pi\) | ||||
−0.321335 | + | 0.946966i | \(0.604132\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −33.9324 | −1.37955 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 1.95400i | − 0.0793102i | −0.999213 | − | 0.0396551i | \(-0.987374\pi\) | ||||
0.999213 | − | 0.0396551i | \(-0.0126259\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 68.4918i | 2.77088i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 3.47046i | − 0.140171i | −0.997541 | − | 0.0700853i | \(-0.977673\pi\) | ||||
0.997541 | − | 0.0700853i | \(-0.0223271\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.9456i | 1.00427i | 0.864789 | + | 0.502136i | \(0.167452\pi\) | ||||
−0.864789 | + | 0.502136i | \(0.832548\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.3233 | 1.50015 | 0.750075 | − | 0.661353i | \(-0.230017\pi\) | ||||
0.750075 | + | 0.661353i | \(0.230017\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.31114 | 0.212786 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.9810 | −1.03924 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.70905 | −0.267507 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.51886i | 0.378940i | 0.981887 | + | 0.189470i | \(0.0606770\pi\) | ||||
−0.981887 | + | 0.189470i | \(0.939323\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.2721i | 0.963209i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 6.55068i | − 0.259547i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 41.9263i | − 1.65599i | −0.560735 | − | 0.827995i | \(-0.689481\pi\) | ||||
0.560735 | − | 0.827995i | \(-0.310519\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.79303 | −0.110146 | −0.0550732 | − | 0.998482i | \(-0.517539\pi\) | ||||
−0.0550732 | + | 0.998482i | \(0.517539\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.2089 | 1.18763 | 0.593817 | − | 0.804600i | \(-0.297620\pi\) | ||||
0.593817 | + | 0.804600i | \(0.297620\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.983356 | −0.0386001 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −36.8020 | −1.44017 | −0.720086 | − | 0.693884i | \(-0.755898\pi\) | ||||
−0.720086 | + | 0.693884i | \(0.755898\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 46.6498i | 1.82276i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.5858i | 1.07459i | 0.843394 | + | 0.537296i | \(0.180554\pi\) | ||||
−0.843394 | + | 0.537296i | \(0.819446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 43.9007i | − 1.70754i | −0.520650 | − | 0.853770i | \(-0.674310\pi\) | ||||
0.520650 | − | 0.853770i | \(-0.325690\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 1.65089i | − 0.0640186i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 38.8801 | 1.50544 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.55943 | −0.176015 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.78085 | −0.0686465 | −0.0343233 | − | 0.999411i | \(-0.510928\pi\) | ||||
−0.0343233 | + | 0.999411i | \(0.510928\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.7356 | 1.75776 | 0.878881 | − | 0.477041i | \(-0.158291\pi\) | ||||
0.878881 | + | 0.477041i | \(0.158291\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 19.1014i | − 0.733043i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 23.5159i | − 0.899811i | −0.893076 | − | 0.449906i | \(-0.851458\pi\) | ||||
0.893076 | − | 0.449906i | \(-0.148542\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 70.2810i | 2.68530i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.21059i | 0.198508i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.3501 | 1.19261 | 0.596306 | − | 0.802757i | \(-0.296634\pi\) | ||||
0.596306 | + | 0.802757i | \(0.296634\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.56130 | 0.362681 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.9686 | 0.566975 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.40072 | −0.0529046 | −0.0264523 | − | 0.999650i | \(-0.508421\pi\) | ||||
−0.0264523 | + | 0.999650i | \(0.508421\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1.76944i | − 0.0667357i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2.00000i | − 0.0752177i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.4709i | 1.48236i | 0.671307 | + | 0.741179i | \(0.265733\pi\) | ||||
−0.671307 | + | 0.741179i | \(0.734267\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 62.0389i | − 2.32338i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.15396 | −0.304941 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.0694 | 0.450113 | 0.225056 | − | 0.974346i | \(-0.427743\pi\) | ||||
0.225056 | + | 0.974346i | \(0.427743\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.0148 | −0.633663 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22.6922 | −0.842768 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.39230i | 0.0887257i | 0.999015 | + | 0.0443628i | \(0.0141258\pi\) | ||||
−0.999015 | + | 0.0443628i | \(0.985874\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.24495i | 0.120019i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 14.5802i | − 0.538533i | −0.963066 | − | 0.269267i | \(-0.913219\pi\) | ||||
0.963066 | − | 0.269267i | \(-0.0867813\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 2.60530i | − 0.0959673i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.3459 | −1.11629 | −0.558146 | − | 0.829743i | \(-0.688487\pi\) | ||||
−0.558146 | + | 0.829743i | \(0.688487\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.6659 | −0.611411 | −0.305706 | − | 0.952126i | \(-0.598892\pi\) | ||||
−0.305706 | + | 0.952126i | \(0.598892\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.9540 | −0.804332 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.91362 | 0.0699222 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.10155i | 0.0766866i | 0.999265 | + | 0.0383433i | \(0.0122080\pi\) | ||||
−0.999265 | + | 0.0383433i | \(0.987792\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 30.7030i | − 1.11740i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.2408i | 1.42623i | 0.701046 | + | 0.713116i | \(0.252717\pi\) | ||||
−0.701046 | + | 0.713116i | \(0.747283\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.7618i | 0.825113i | 0.910932 | + | 0.412556i | \(0.135364\pi\) | ||||
−0.910932 | + | 0.412556i | \(0.864636\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.07816 | −0.256246 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.1967 | 0.584828 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.9030 | −1.90773 | −0.953865 | − | 0.300234i | \(-0.902935\pi\) | ||||
−0.953865 | + | 0.300234i | \(0.902935\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.27110 | −0.225556 | −0.112778 | − | 0.993620i | \(-0.535975\pi\) | ||||
−0.112778 | + | 0.993620i | \(0.535975\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.2087i | 1.30066i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.94780i | 0.141445i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 0.881470i | − 0.0315415i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 34.1038i | 1.21722i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.5651 | 0.733065 | 0.366533 | − | 0.930405i | \(-0.380545\pi\) | ||||
0.366533 | + | 0.930405i | \(0.380545\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.98316 | 0.354960 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 75.0976 | 2.66679 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.6802 | 0.590845 | 0.295422 | − | 0.955367i | \(-0.404540\pi\) | ||||
0.295422 | + | 0.955367i | \(0.404540\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 20.9114i | − 0.739791i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.28894i | 0.0807751i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.7152i | 0.906342i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 54.5485i | 1.91782i | 0.283707 | + | 0.958911i | \(0.408436\pi\) | ||||
−0.283707 | + | 0.958911i | \(0.591564\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.77845 | 0.343368 | 0.171684 | − | 0.985152i | \(-0.445079\pi\) | ||||
0.171684 | + | 0.985152i | \(0.445079\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −31.3439 | −1.09793 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.855821 | −0.0299414 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.5488 | −0.996359 | −0.498179 | − | 0.867074i | \(-0.665998\pi\) | ||||
−0.498179 | + | 0.867074i | \(0.665998\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 33.5912i | − 1.17092i | −0.810702 | − | 0.585459i | \(-0.800914\pi\) | ||||
0.810702 | − | 0.585459i | \(-0.199086\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.9650i | 0.902893i | 0.892298 | + | 0.451446i | \(0.149092\pi\) | ||||
−0.892298 | + | 0.451446i | \(0.850908\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.7613i | 0.825263i | 0.910898 | + | 0.412631i | \(0.135390\pi\) | ||||
−0.910898 | + | 0.412631i | \(0.864610\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.00000i | 0.0692959i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −45.5864 | −1.57758 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.77243 | 0.0957148 | 0.0478574 | − | 0.998854i | \(-0.484761\pi\) | ||||
0.0478574 | + | 0.998854i | \(0.484761\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.60770 | −0.227852 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 93.6155 | 3.22047 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.8418i | 0.372529i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.5619i | 0.944810i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 0.236670i | − 0.00810344i | −0.999992 | − | 0.00405172i | \(-0.998710\pi\) | ||||
0.999992 | − | 0.00405172i | \(-0.00128971\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 21.2139i | − 0.724654i | −0.932051 | − | 0.362327i | \(-0.881982\pi\) | ||||
0.932051 | − | 0.362327i | \(-0.118018\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.6199 | −0.430585 | −0.215292 | − | 0.976550i | \(-0.569070\pi\) | ||||
−0.215292 | + | 0.976550i | \(0.569070\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.8396 | 0.879589 | 0.439795 | − | 0.898098i | \(-0.355051\pi\) | ||||
0.439795 | + | 0.898098i | \(0.355051\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 44.8104 | 1.52360 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.09293 | 0.138843 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42.9114i | 1.45400i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.640262i | 0.0216448i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 55.0972i | − 1.86050i | −0.366925 | − | 0.930251i | \(-0.619589\pi\) | ||||
0.366925 | − | 0.930251i | \(-0.380411\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.7034i | 1.13550i | 0.823202 | + | 0.567749i | \(0.192186\pi\) | ||||
−0.823202 | + | 0.567749i | \(0.807814\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.8396 | −0.667655 | −0.333827 | − | 0.942634i | \(-0.608340\pi\) | ||||
−0.333827 | + | 0.942634i | \(0.608340\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.5967 | 0.590840 | 0.295420 | − | 0.955367i | \(-0.404540\pi\) | ||||
0.295420 | + | 0.955367i | \(0.404540\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.75525 | 0.260103 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.51515 | 0.184558 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 62.0019i | − 2.07249i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 35.7302i | − 1.19167i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1.59086i | − 0.0529991i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 63.1372i | 2.09875i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.8190 | 0.359238 | 0.179619 | − | 0.983736i | \(-0.442514\pi\) | ||||
0.179619 | + | 0.983736i | \(0.442514\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.4364 | −1.10780 | −0.553899 | − | 0.832584i | \(-0.686861\pi\) | ||||
−0.553899 | + | 0.832584i | \(0.686861\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.32859 | 0.110160 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.9052 | 0.492213 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 3.70049i | − 0.122068i | −0.998136 | − | 0.0610339i | \(-0.980560\pi\) | ||||
0.998136 | − | 0.0610339i | \(-0.0194398\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.5185i | 0.477883i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 16.0864i | − 0.528917i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 17.0318i | − 0.558796i | −0.960175 | − | 0.279398i | \(-0.909865\pi\) | ||||
0.960175 | − | 0.279398i | \(-0.0901348\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.527479 | −0.0172874 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.48950 | 0.0814155 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.6077 | −0.379207 | −0.189603 | − | 0.981861i | \(-0.560720\pi\) | ||||
−0.189603 | + | 0.981861i | \(0.560720\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −50.5834 | −1.64897 | −0.824486 | − | 0.565882i | \(-0.808536\pi\) | ||||
−0.824486 | + | 0.565882i | \(0.808536\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 61.4935i | − 2.00250i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 42.8764i | − 1.39330i | −0.717413 | − | 0.696648i | \(-0.754674\pi\) | ||||
0.717413 | − | 0.696648i | \(-0.245326\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 37.7008i | − 1.22382i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 11.4074i | − 0.369523i | −0.982783 | − | 0.184761i | \(-0.940849\pi\) | ||||
0.982783 | − | 0.184761i | \(-0.0591512\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.1416 | 0.651766 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.4557 | 0.725132 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.0127 | −0.839120 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 31.2449 | 1.00581 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.7090i | 0.794589i | 0.917691 | + | 0.397295i | \(0.130051\pi\) | ||||
−0.917691 | + | 0.397295i | \(0.869949\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.3585i | 0.910067i | 0.890474 | + | 0.455034i | \(0.150373\pi\) | ||||
−0.890474 | + | 0.455034i | \(0.849627\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 3.05496i | − 0.0979375i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 23.4704i | − 0.750885i | −0.926846 | − | 0.375442i | \(-0.877491\pi\) | ||||
0.926846 | − | 0.375442i | \(-0.122509\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.11231 | −0.0675099 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.2425 | 0.837007 | 0.418504 | − | 0.908215i | \(-0.362555\pi\) | ||||
0.418504 | + | 0.908215i | \(0.362555\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 73.9790 | 2.35717 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.3308 | 0.423895 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 44.2579i | − 1.40590i | −0.711241 | − | 0.702949i | \(-0.751866\pi\) | ||||
0.711241 | − | 0.702949i | \(-0.248134\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 67.6662i | 2.14516i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 28.1271i | − 0.890796i | −0.895333 | − | 0.445398i | \(-0.853062\pi\) | ||||
0.895333 | − | 0.445398i | \(-0.146938\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6048.2.j.a.5615.4 | 8 | ||
3.2 | odd | 2 | 6048.2.j.b.5615.6 | 8 | |||
4.3 | odd | 2 | 1512.2.j.a.323.1 | ✓ | 8 | ||
8.3 | odd | 2 | 6048.2.j.b.5615.5 | 8 | |||
8.5 | even | 2 | 1512.2.j.b.323.6 | yes | 8 | ||
12.11 | even | 2 | 1512.2.j.b.323.8 | yes | 8 | ||
24.5 | odd | 2 | 1512.2.j.a.323.3 | yes | 8 | ||
24.11 | even | 2 | inner | 6048.2.j.a.5615.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.a.323.1 | ✓ | 8 | 4.3 | odd | 2 | ||
1512.2.j.a.323.3 | yes | 8 | 24.5 | odd | 2 | ||
1512.2.j.b.323.6 | yes | 8 | 8.5 | even | 2 | ||
1512.2.j.b.323.8 | yes | 8 | 12.11 | even | 2 | ||
6048.2.j.a.5615.3 | 8 | 24.11 | even | 2 | inner | ||
6048.2.j.a.5615.4 | 8 | 1.1 | even | 1 | trivial | ||
6048.2.j.b.5615.5 | 8 | 8.3 | odd | 2 | |||
6048.2.j.b.5615.6 | 8 | 3.2 | odd | 2 |