Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,2,Mod(241,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("960.241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.s (of order \(4\), degree \(2\), 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: | \(7.66563859404\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 240) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 721.3 | ||
Root | \(0.500000 + 1.44392i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.721 |
Dual form | 960.2.s.b.241.3 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.707107 | − | 0.707107i | 0.316228 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.41421i | 0.534522i | 0.963624 | + | 0.267261i | \(0.0861187\pi\) | ||||
−0.963624 | + | 0.267261i | \(0.913881\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.22274 | + | 4.22274i | −1.27321 | + | 1.27321i | −0.328808 | + | 0.944397i | \(0.606647\pi\) |
−0.944397 | + | 0.328808i | \(0.893353\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.33490 | + | 1.33490i | 0.370236 | + | 0.370236i | 0.867563 | − | 0.497327i | \(-0.165685\pi\) |
−0.497327 | + | 0.867563i | \(0.665685\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.14343 | −0.277323 | −0.138662 | − | 0.990340i | \(-0.544280\pi\) | ||||
−0.138662 | + | 0.990340i | \(0.544280\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.05941 | − | 1.05941i | −0.243046 | − | 0.243046i | 0.575063 | − | 0.818109i | \(-0.304977\pi\) |
−0.818109 | + | 0.575063i | \(0.804977\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | + | 1.00000i | −0.218218 | + | 0.218218i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.77568i | 1.62134i | 0.585503 | + | 0.810671i | \(0.300897\pi\) | ||||
−0.585503 | + | 0.810671i | \(0.699103\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.94059 | + | 2.94059i | 0.546053 | + | 0.546053i | 0.925297 | − | 0.379243i | \(-0.123816\pi\) |
−0.379243 | + | 0.925297i | \(0.623816\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.389604 | −0.0699750 | −0.0349875 | − | 0.999388i | \(-0.511139\pi\) | ||||
−0.0349875 | + | 0.999388i | \(0.511139\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.97186 | −1.03957 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | + | 1.00000i | 0.169031 | + | 0.169031i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.28216 | + | 4.28216i | −0.703982 | + | 0.703982i | −0.965263 | − | 0.261281i | \(-0.915855\pi\) |
0.261281 | + | 0.965263i | \(0.415855\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.88784i | 0.302296i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.45844i | − | 0.852465i | −0.904614 | − | 0.426233i | \(-0.859841\pi\) | ||
0.904614 | − | 0.426233i | \(-0.140159\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.91245 | − | 4.91245i | 0.749141 | − | 0.749141i | −0.225177 | − | 0.974318i | \(-0.572296\pi\) |
0.974318 | + | 0.225177i | \(0.0722959\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.707107 | + | 0.707107i | 0.105409 | + | 0.105409i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.7324 | 1.56547 | 0.782737 | − | 0.622352i | \(-0.213823\pi\) | ||||
0.782737 | + | 0.622352i | \(0.213823\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.808530 | − | 0.808530i | −0.113217 | − | 0.113217i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.863230 | + | 0.863230i | −0.118574 | + | 0.118574i | −0.763904 | − | 0.645330i | \(-0.776720\pi\) |
0.645330 | + | 0.763904i | \(0.276720\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.97186i | 0.805246i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.49824i | − | 0.198446i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.50961 | + | 8.50961i | −1.10786 | + | 1.10786i | −0.114425 | + | 0.993432i | \(0.536503\pi\) |
−0.993432 | + | 0.114425i | \(0.963497\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.22746 | + | 2.22746i | 0.285196 | + | 0.285196i | 0.835177 | − | 0.549981i | \(-0.185365\pi\) |
−0.549981 | + | 0.835177i | \(0.685365\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.41421 | −0.178174 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.88784 | 0.234158 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.94725 | − | 2.94725i | −0.360064 | − | 0.360064i | 0.503772 | − | 0.863836i | \(-0.331945\pi\) |
−0.863836 | + | 0.503772i | \(0.831945\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.49824 | + | 5.49824i | −0.661910 | + | 0.661910i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.27391i | − | 0.388542i | −0.980948 | − | 0.194271i | \(-0.937766\pi\) | ||
0.980948 | − | 0.194271i | \(-0.0622341\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.84138i | − | 0.215517i | −0.994177 | − | 0.107759i | \(-0.965633\pi\) | ||
0.994177 | − | 0.107759i | \(-0.0343674\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.707107 | − | 0.707107i | 0.0816497 | − | 0.0816497i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.97186 | − | 5.97186i | −0.680557 | − | 0.680557i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3861 | 1.28103 | 0.640517 | − | 0.767944i | \(-0.278720\pi\) | ||||
0.640517 | + | 0.767944i | \(0.278720\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.1153 | − | 11.1153i | −1.22006 | − | 1.22006i | −0.967609 | − | 0.252453i | \(-0.918763\pi\) |
−0.252453 | − | 0.967609i | \(-0.581237\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.808530 | + | 0.808530i | −0.0876974 | + | 0.0876974i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.15862i | 0.445851i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 18.6533i | 1.97725i | 0.150407 | + | 0.988624i | \(0.451942\pi\) | ||||
−0.150407 | + | 0.988624i | \(0.548058\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.88784 | + | 1.88784i | −0.197899 | + | 0.197899i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.275492 | − | 0.275492i | −0.0285672 | − | 0.0285672i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.49824 | −0.153716 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.44902 | −0.553264 | −0.276632 | − | 0.960976i | \(-0.589218\pi\) | ||||
−0.276632 | + | 0.960976i | \(0.589218\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.22274 | − | 4.22274i | −0.424402 | − | 0.424402i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.1899 | + | 11.1899i | −1.11344 | + | 1.11344i | −0.120753 | + | 0.992683i | \(0.538531\pi\) |
−0.992683 | + | 0.120753i | \(0.961469\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 18.2919i | − | 1.80235i | −0.433455 | − | 0.901175i | \(-0.642706\pi\) | ||
0.433455 | − | 0.901175i | \(-0.357294\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.41421i | 0.138013i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.99647 | + | 6.99647i | −0.676374 | + | 0.676374i | −0.959178 | − | 0.282804i | \(-0.908736\pi\) |
0.282804 | + | 0.959178i | \(0.408736\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.6729 | + | 12.6729i | 1.21385 | + | 1.21385i | 0.969751 | + | 0.244097i | \(0.0784915\pi\) |
0.244097 | + | 0.969751i | \(0.421509\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.05588 | −0.574799 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.8101 | 1.67543 | 0.837716 | − | 0.546106i | \(-0.183890\pi\) | ||||
0.837716 | + | 0.546106i | \(0.183890\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.49824 | + | 5.49824i | 0.512713 | + | 0.512713i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.33490 | + | 1.33490i | −0.123412 | + | 0.123412i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1.61706i | − | 0.148236i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 24.6631i | − | 2.24210i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.85970 | − | 3.85970i | 0.348017 | − | 0.348017i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.707107 | − | 0.707107i | −0.0632456 | − | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.0442 | 0.891281 | 0.445641 | − | 0.895212i | \(-0.352976\pi\) | ||||
0.445641 | + | 0.895212i | \(0.352976\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.94725 | 0.611671 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.60215 | − | 7.60215i | −0.664203 | − | 0.664203i | 0.292165 | − | 0.956368i | \(-0.405624\pi\) |
−0.956368 | + | 0.292165i | \(0.905624\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.49824 | − | 1.49824i | 0.129913 | − | 0.129913i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 14.8003i | − | 1.26447i | −0.774775 | − | 0.632237i | \(-0.782137\pi\) | ||
0.774775 | − | 0.632237i | \(-0.217863\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.43606 | − | 8.43606i | 0.715537 | − | 0.715537i | −0.252151 | − | 0.967688i | \(-0.581138\pi\) |
0.967688 | + | 0.252151i | \(0.0811378\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.58892 | + | 7.58892i | 0.639102 | + | 0.639102i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.2739 | −0.942772 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.15862 | 0.345355 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.53553 | + | 3.53553i | 0.291606 | + | 0.291606i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.772545 | − | 0.772545i | 0.0632893 | − | 0.0632893i | −0.674754 | − | 0.738043i | \(-0.735750\pi\) |
0.738043 | + | 0.674754i | \(0.235750\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.90079i | − | 0.236063i | −0.993010 | − | 0.118032i | \(-0.962342\pi\) | ||
0.993010 | − | 0.118032i | \(-0.0376584\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.14343i | − | 0.0924411i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.275492 | + | 0.275492i | −0.0221280 | + | 0.0221280i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.60882 | + | 2.60882i | 0.208206 | + | 0.208206i | 0.803505 | − | 0.595298i | \(-0.202966\pi\) |
−0.595298 | + | 0.803505i | \(0.702966\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.22079 | −0.0968151 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.9965 | −0.866643 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.42364 | + | 1.42364i | 0.111508 | + | 0.111508i | 0.760659 | − | 0.649151i | \(-0.224876\pi\) |
−0.649151 | + | 0.760659i | \(0.724876\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.22274 | + | 4.22274i | −0.328740 | + | 0.328740i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 4.22117i | − | 0.326644i | −0.986573 | − | 0.163322i | \(-0.947779\pi\) | ||
0.986573 | − | 0.163322i | \(-0.0522209\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 9.43606i | − | 0.725851i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.05941 | − | 1.05941i | 0.0810153 | − | 0.0810153i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.1582 | − | 14.1582i | −1.07643 | − | 1.07643i | −0.996827 | − | 0.0796031i | \(-0.974635\pi\) |
−0.0796031 | − | 0.996827i | \(-0.525365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.41421 | 0.106904 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.0344 | −0.904561 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.8796 | + | 11.8796i | 0.887923 | + | 0.887923i | 0.994323 | − | 0.106401i | \(-0.0339326\pi\) |
−0.106401 | + | 0.994323i | \(0.533933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.04646 | − | 7.04646i | 0.523759 | − | 0.523759i | −0.394945 | − | 0.918705i | \(-0.629237\pi\) |
0.918705 | + | 0.394945i | \(0.129237\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.15010i | 0.232862i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.05588i | 0.445237i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.82843 | − | 4.82843i | 0.353090 | − | 0.353090i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | − | 1.00000i | −0.0727393 | − | 0.0727393i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.3857 | 1.11327 | 0.556634 | − | 0.830758i | \(-0.312092\pi\) | ||||
0.556634 | + | 0.830758i | \(0.312092\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.52099 | 0.541372 | 0.270686 | − | 0.962668i | \(-0.412749\pi\) | ||||
0.270686 | + | 0.962668i | \(0.412749\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.33490 | + | 1.33490i | 0.0955945 | + | 0.0955945i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.66352 | − | 9.66352i | 0.688497 | − | 0.688497i | −0.273403 | − | 0.961900i | \(-0.588149\pi\) |
0.961900 | + | 0.273403i | \(0.0881491\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.35570i | 0.663208i | 0.943419 | + | 0.331604i | \(0.107590\pi\) | ||||
−0.943419 | + | 0.331604i | \(0.892410\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 4.16804i | − | 0.293991i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.15862 | + | 4.15862i | −0.291878 | + | 0.291878i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.85970 | − | 3.85970i | −0.269573 | − | 0.269573i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.77568 | −0.540447 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.94725 | 0.618894 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.0625461 | + | 0.0625461i | 0.00430585 | + | 0.00430585i | 0.709256 | − | 0.704951i | \(-0.249031\pi\) |
−0.704951 | + | 0.709256i | \(0.749031\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.31501 | − | 2.31501i | 0.158622 | − | 0.158622i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 6.94725i | − | 0.473799i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.550984i | − | 0.0374032i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.30205 | − | 1.30205i | 0.0879846 | − | 0.0879846i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.52637 | − | 1.52637i | −0.102675 | − | 0.102675i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.1203 | −0.878599 | −0.439300 | − | 0.898341i | \(-0.644773\pi\) | ||||
−0.439300 | + | 0.898341i | \(0.644773\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.76235 | − | 5.76235i | −0.382461 | − | 0.382461i | 0.489527 | − | 0.871988i | \(-0.337169\pi\) |
−0.871988 | + | 0.489527i | \(0.837169\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.12549 | − | 5.12549i | 0.338702 | − | 0.338702i | −0.517177 | − | 0.855879i | \(-0.673017\pi\) |
0.855879 | + | 0.517177i | \(0.173017\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 8.44549i | − | 0.555672i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.2552i | 0.868377i | 0.900822 | + | 0.434188i | \(0.142965\pi\) | ||||
−0.900822 | + | 0.434188i | \(0.857035\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.58892 | − | 7.58892i | 0.495047 | − | 0.495047i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.05117 | + | 8.05117i | 0.522980 | + | 0.522980i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.8119 | 1.21684 | 0.608422 | − | 0.793614i | \(-0.291803\pi\) | ||||
0.608422 | + | 0.793614i | \(0.291803\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.66665 | −0.171774 | −0.0858871 | − | 0.996305i | \(-0.527372\pi\) | ||||
−0.0858871 | + | 0.996305i | \(0.527372\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.53553 | − | 3.53553i | 0.225877 | − | 0.225877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.82843i | − | 0.179969i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 15.7194i | − | 0.996177i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.77726 | − | 7.77726i | 0.490896 | − | 0.490896i | −0.417692 | − | 0.908588i | \(-0.637161\pi\) |
0.908588 | + | 0.417692i | \(0.137161\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.8347 | − | 32.8347i | −2.06430 | − | 2.06430i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.14343 | −0.0716046 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.83971 | −0.364271 | −0.182136 | − | 0.983273i | \(-0.558301\pi\) | ||||
−0.182136 | + | 0.983273i | \(0.558301\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.05588 | − | 6.05588i | −0.376294 | − | 0.376294i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.94059 | + | 2.94059i | −0.182018 | + | 0.182018i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 10.0094i | − | 0.617208i | −0.951191 | − | 0.308604i | \(-0.900138\pi\) | ||
0.951191 | − | 0.308604i | \(-0.0998617\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.22079i | 0.0749926i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.1899 | + | 13.1899i | −0.807208 | + | 0.807208i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.82529 | + | 1.82529i | 0.111290 | + | 0.111290i | 0.760559 | − | 0.649269i | \(-0.224925\pi\) |
−0.649269 | + | 0.760559i | \(0.724925\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.44862 | 0.330980 | 0.165490 | − | 0.986211i | \(-0.447079\pi\) | ||||
0.165490 | + | 0.986211i | \(0.447079\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.66981 | −0.161584 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.22274 | + | 4.22274i | 0.254641 | + | 0.254641i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.5690 | − | 10.5690i | 0.635031 | − | 0.635031i | −0.314294 | − | 0.949326i | \(-0.601768\pi\) |
0.949326 | + | 0.314294i | \(0.101768\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 0.389604i | − | 0.0233250i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.2376i | 0.610727i | 0.952236 | + | 0.305363i | \(0.0987780\pi\) | ||||
−0.952236 | + | 0.305363i | \(0.901222\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.88744 | − | 9.88744i | 0.587748 | − | 0.587748i | −0.349273 | − | 0.937021i | \(-0.613572\pi\) |
0.937021 | + | 0.349273i | \(0.113572\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.05941 | − | 1.05941i | −0.0627542 | − | 0.0627542i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.71940 | 0.455662 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6926 | −0.923092 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.85304 | − | 3.85304i | −0.225869 | − | 0.225869i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.05235 | − | 9.05235i | 0.528844 | − | 0.528844i | −0.391384 | − | 0.920228i | \(-0.628003\pi\) |
0.920228 | + | 0.391384i | \(0.128003\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0344i | 0.700670i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 5.97186i | − | 0.346523i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.3798 | + | 10.3798i | −0.600278 | + | 0.600278i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.94725 | + | 6.94725i | 0.400433 | + | 0.400433i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.8249 | −0.909117 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.15010 | 0.180374 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.77215 | − | 2.77215i | −0.158215 | − | 0.158215i | 0.623560 | − | 0.781775i | \(-0.285686\pi\) |
−0.781775 | + | 0.623560i | \(0.785686\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.9343 | − | 12.9343i | 0.735806 | − | 0.735806i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 20.9441i | − | 1.18763i | −0.804601 | − | 0.593815i | \(-0.797621\pi\) | ||
0.804601 | − | 0.593815i | \(-0.202379\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.1814i | 0.575485i | 0.957708 | + | 0.287743i | \(0.0929047\pi\) | ||||
−0.957708 | + | 0.287743i | \(0.907095\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.00000 | + | 1.00000i | −0.0563436 | + | 0.0563436i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.7655 | − | 14.7655i | −0.829312 | − | 0.829312i | 0.158109 | − | 0.987422i | \(-0.449460\pi\) |
−0.987422 | + | 0.158109i | \(0.949460\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.8347 | −1.39048 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.89450 | −0.552257 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.21137 | + | 1.21137i | 0.0674023 | + | 0.0674023i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.33490 | − | 1.33490i | 0.0740472 | − | 0.0740472i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.9222i | 0.991102i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.1778i | 0.836781i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.8815 | + | 16.8815i | −0.927894 | + | 0.927894i | −0.997570 | − | 0.0696758i | \(-0.977804\pi\) |
0.0696758 | + | 0.997570i | \(0.477804\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.28216 | − | 4.28216i | −0.234661 | − | 0.234661i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.16804 | −0.227725 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.8343 | 1.29834 | 0.649169 | − | 0.760644i | \(-0.275117\pi\) | ||||
0.649169 | + | 0.760644i | \(0.275117\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.5936 | + | 12.5936i | 0.683992 | + | 0.683992i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.64520 | − | 1.64520i | 0.0890925 | − | 0.0890925i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706i | 0.916324i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.77568i | 0.418628i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.38294 | − | 4.38294i | 0.235289 | − | 0.235289i | −0.579607 | − | 0.814896i | \(-0.696794\pi\) |
0.814896 | + | 0.579607i | \(0.196794\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.4357 | + | 17.4357i | 0.933310 | + | 0.933310i | 0.997911 | − | 0.0646013i | \(-0.0205776\pi\) |
−0.0646013 | + | 0.997911i | \(0.520578\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.88784 | −0.100765 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.5795 | −1.68081 | −0.840403 | − | 0.541961i | \(-0.817682\pi\) | ||||
−0.840403 | + | 0.541961i | \(0.817682\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.31501 | − | 2.31501i | −0.122868 | − | 0.122868i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.14343 | − | 1.14343i | 0.0605169 | − | 0.0605169i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.5310i | 1.34747i | 0.738972 | + | 0.673737i | \(0.235312\pi\) | ||||
−0.738972 | + | 0.673737i | \(0.764688\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 16.7553i | − | 0.881857i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.4395 | − | 17.4395i | 0.915334 | − | 0.915334i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.30205 | − | 1.30205i | −0.0681526 | − | 0.0681526i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.9084 | −0.726010 | −0.363005 | − | 0.931787i | \(-0.618249\pi\) | ||||
−0.363005 | + | 0.931787i | \(0.618249\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.45844 | 0.284155 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.22079 | − | 1.22079i | −0.0633803 | − | 0.0633803i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.88942 | − | 2.88942i | 0.149608 | − | 0.149608i | −0.628335 | − | 0.777943i | \(-0.716263\pi\) |
0.777943 | + | 0.628335i | \(0.216263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1.00000i | − | 0.0516398i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.85080i | 0.404337i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.96687 | − | 5.96687i | 0.306497 | − | 0.306497i | −0.537052 | − | 0.843549i | \(-0.680462\pi\) |
0.843549 | + | 0.537052i | \(0.180462\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.10234 | + | 7.10234i | 0.363864 | + | 0.363864i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.8382 | −0.707100 | −0.353550 | − | 0.935416i | \(-0.615026\pi\) | ||||
−0.353550 | + | 0.935416i | \(0.615026\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.44549 | −0.430422 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.91245 | + | 4.91245i | 0.249714 | + | 0.249714i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.2560 | + | 20.2560i | −1.02702 | + | 1.02702i | −0.0273936 | + | 0.999625i | \(0.508721\pi\) |
−0.999625 | + | 0.0273936i | \(0.991279\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 8.89097i | − | 0.449636i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 10.7511i | − | 0.542320i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.05117 | − | 8.05117i | 0.405098 | − | 0.405098i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.0941 | + | 21.0941i | 1.05868 | + | 1.05868i | 0.998167 | + | 0.0605152i | \(0.0192744\pi\) |
0.0605152 | + | 0.998167i | \(0.480726\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.11882 | 0.106074 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.98314 | 0.248846 | 0.124423 | − | 0.992229i | \(-0.460292\pi\) | ||||
0.124423 | + | 0.992229i | \(0.460292\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.520084 | − | 0.520084i | −0.0259072 | − | 0.0259072i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.707107 | + | 0.707107i | −0.0351364 | + | 0.0351364i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 36.1649i | − | 1.79263i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.7686i | 1.66975i | 0.550439 | + | 0.834875i | \(0.314460\pi\) | ||||
−0.550439 | + | 0.834875i | \(0.685540\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.4654 | − | 10.4654i | 0.516219 | − | 0.516219i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.0344 | − | 12.0344i | −0.592174 | − | 0.592174i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.7194 | −0.771635 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.9304 | 0.584234 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.9453 | + | 15.9453i | 0.778979 | + | 0.778979i | 0.979657 | − | 0.200678i | \(-0.0643146\pi\) |
−0.200678 | + | 0.979657i | \(0.564315\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.33295 | + | 2.33295i | −0.113701 | + | 0.113701i | −0.761668 | − | 0.647967i | \(-0.775619\pi\) |
0.647967 | + | 0.761668i | \(0.275619\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.7324i | 0.521825i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.14343i | 0.0554647i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.15010 | + | 3.15010i | −0.152444 | + | 0.152444i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.97186 | − | 7.97186i | −0.384885 | − | 0.384885i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.6400 | 0.994194 | 0.497097 | − | 0.867695i | \(-0.334399\pi\) | ||||
0.497097 | + | 0.867695i | \(0.334399\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.07550 | 0.0516852 | 0.0258426 | − | 0.999666i | \(-0.491773\pi\) | ||||
0.0258426 | + | 0.999666i | \(0.491773\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.94059 | + | 2.94059i | 0.140990 | + | 0.140990i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.23765 | − | 8.23765i | 0.394060 | − | 0.394060i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.24041i | 0.202384i | 0.994867 | + | 0.101192i | \(0.0322656\pi\) | ||||
−0.994867 | + | 0.101192i | \(0.967734\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.00000i | 0.238095i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.8969 | − | 19.8969i | 0.945329 | − | 0.945329i | −0.0532524 | − | 0.998581i | \(-0.516959\pi\) |
0.998581 | + | 0.0532524i | \(0.0169588\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.1899 | + | 13.1899i | 0.625261 | + | 0.625261i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.09254 | 0.0516755 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.2441 | 0.813800 | 0.406900 | − | 0.913473i | \(-0.366610\pi\) | ||||
0.406900 | + | 0.913473i | \(0.366610\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.0496 | + | 23.0496i | 1.08536 | + | 1.08536i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.05117 | − | 2.05117i | 0.0963724 | − | 0.0963724i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.66981i | 0.125163i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.3141i | 1.51159i | 0.654809 | + | 0.755795i | \(0.272749\pi\) | ||||
−0.654809 | + | 0.755795i | \(0.727251\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.808530 | − | 0.808530i | 0.0377389 | − | 0.0377389i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.4884 | + | 15.4884i | 0.721367 | + | 0.721367i | 0.968884 | − | 0.247516i | \(-0.0796144\pi\) |
−0.247516 | + | 0.968884i | \(0.579614\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.2150 | −1.26479 | −0.632394 | − | 0.774647i | \(-0.717928\pi\) | ||||
−0.632394 | + | 0.774647i | \(0.717928\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.389604 | −0.0180675 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.60373 | − | 7.60373i | −0.351859 | − | 0.351859i | 0.508942 | − | 0.860801i | \(-0.330037\pi\) |
−0.860801 | + | 0.508942i | \(0.830037\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.16804 | − | 4.16804i | 0.192462 | − | 0.192462i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.68943i | 0.170000i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 41.4880i | 1.90762i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.05941 | + | 1.05941i | −0.0486092 | + | 0.0486092i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.863230 | − | 0.863230i | −0.0395246 | − | 0.0395246i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.515092 | −0.0235352 | −0.0117676 | − | 0.999931i | \(-0.503746\pi\) | ||||
−0.0117676 | + | 0.999931i | \(0.503746\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.4325 | −0.521279 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.77568 | − | 7.77568i | −0.353806 | − | 0.353806i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.85304 | + | 3.85304i | −0.174957 | + | 0.174957i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 18.2489i | − | 0.826937i | −0.910518 | − | 0.413468i | \(-0.864317\pi\) | ||
0.910518 | − | 0.413468i | \(-0.135683\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.01333i | 0.0910458i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.5557 | + | 26.5557i | −1.19844 | + | 1.19844i | −0.223807 | + | 0.974633i | \(0.571849\pi\) |
−0.974633 | + | 0.223807i | \(0.928151\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.36237 | − | 3.36237i | −0.151433 | − | 0.151433i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.97186 | −0.268415 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.63001 | 0.207684 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.2247 | + | 11.2247i | 0.502486 | + | 0.502486i | 0.912210 | − | 0.409723i | \(-0.134375\pi\) |
−0.409723 | + | 0.912210i | \(0.634375\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.98481 | − | 2.98481i | 0.133352 | − | 0.133352i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.3061i | 1.21752i | 0.793355 | + | 0.608759i | \(0.208332\pi\) | ||||
−0.793355 | + | 0.608759i | \(0.791668\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.8249i | 0.704199i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.67230 | − | 6.67230i | 0.296327 | − | 0.296327i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.9387 | − | 17.9387i | −0.795120 | − | 0.795120i | 0.187201 | − | 0.982322i | \(-0.440058\pi\) |
−0.982322 | + | 0.187201i | \(0.940058\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.60411 | 0.115199 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.49824 | 0.0661487 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.9343 | − | 12.9343i | −0.569953 | − | 0.569953i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −45.3200 | + | 45.3200i | −1.99317 | + | 1.99317i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 20.0228i | − | 0.878901i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.7686i | 0.515593i | 0.966199 | + | 0.257796i | \(0.0829963\pi\) | ||||
−0.966199 | + | 0.257796i | \(0.917004\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.02148 | + | 2.02148i | −0.0883929 | + | 0.0883929i | −0.749921 | − | 0.661528i | \(-0.769908\pi\) |
0.661528 | + | 0.749921i | \(0.269908\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.00000 | + | 1.00000i | 0.0436436 | + | 0.0436436i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.445487 | 0.0194057 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −37.4612 | −1.62875 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.50961 | − | 8.50961i | −0.369286 | − | 0.369286i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.28649 | − | 7.28649i | 0.315613 | − | 0.315613i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.89450i | 0.427777i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.8003i | 0.724986i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21.1137 | + | 21.1137i | −0.909432 | + | 0.909432i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.9598 | − | 28.9598i | −1.24508 | − | 1.24508i | −0.957867 | − | 0.287213i | \(-0.907271\pi\) |
−0.287213 | − | 0.957867i | \(-0.592729\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.96520 | 0.427648 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.9222 | 0.767705 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.3485 | + | 11.3485i | 0.485227 | + | 0.485227i | 0.906796 | − | 0.421569i | \(-0.138520\pi\) |
−0.421569 | + | 0.906796i | \(0.638520\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.22746 | + | 2.22746i | −0.0950655 | + | 0.0950655i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 6.23059i | − | 0.265432i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.1023i | 0.684741i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.28216 | + | 4.28216i | −0.181767 | + | 0.181767i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.8445 | + | 18.8445i | 0.798468 | + | 0.798468i | 0.982854 | − | 0.184386i | \(-0.0590297\pi\) |
−0.184386 | + | 0.982854i | \(0.559030\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.1153 | 0.554718 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.82843 | 0.288296 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.1082 | + | 33.1082i | 1.39535 | + | 1.39535i | 0.812793 | + | 0.582553i | \(0.197946\pi\) |
0.582553 | + | 0.812793i | \(0.302054\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.5936 | − | 12.5936i | 0.529818 | − | 0.529818i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1.41421i | − | 0.0593914i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.55688i | − | 0.0652677i | −0.999467 | − | 0.0326339i | \(-0.989610\pi\) | ||
0.999467 | − | 0.0326339i | \(-0.0103895\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.1614 | + | 33.1614i | −1.38776 | + | 1.38776i | −0.557752 | + | 0.830008i | \(0.688336\pi\) |
−0.830008 | + | 0.557752i | \(0.811664\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.8793 | + | 10.8793i | 0.454490 | + | 0.454490i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.77568 | 0.324268 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.5706 | −1.52245 | −0.761227 | − | 0.648486i | \(-0.775402\pi\) | ||||
−0.761227 | + | 0.648486i | \(0.775402\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.31814 | + | 5.31814i | 0.221014 | + | 0.221014i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.7194 | − | 15.7194i | 0.652151 | − | 0.652151i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 7.29040i | − | 0.301937i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.88784i | 0.0780525i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.73235 | − | 6.73235i | 0.277874 | − | 0.277874i | −0.554386 | − | 0.832260i | \(-0.687047\pi\) |
0.832260 | + | 0.554386i | \(0.187047\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.412751 | + | 0.412751i | 0.0170071 | + | 0.0170071i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.6663 | 0.562156 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.7154 | 0.481092 | 0.240546 | − | 0.970638i | \(-0.422673\pi\) | ||||
0.240546 | + | 0.970638i | \(0.422673\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.14343 | − | 1.14343i | −0.0468762 | − | 0.0468762i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.61548 | + | 6.61548i | −0.270754 | + | 0.270754i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.86233i | 0.239528i | 0.992802 | + | 0.119764i | \(0.0382138\pi\) | ||||
−0.992802 | + | 0.119764i | \(0.961786\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.00353i | 0.204098i | 0.994779 | + | 0.102049i | \(0.0325399\pi\) | ||||
−0.994779 | + | 0.102049i | \(0.967460\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.94725 | − | 2.94725i | 0.120021 | − | 0.120021i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.4395 | − | 17.4395i | −0.709015 | − | 0.709015i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.7109 | −0.921806 | −0.460903 | − | 0.887450i | \(-0.652474\pi\) | ||||
−0.460903 | + | 0.887450i | \(0.652474\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.88118 | −0.238317 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.3267 | + | 14.3267i | 0.579595 | + | 0.579595i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.25531 | + | 7.25531i | −0.293039 | + | 0.293039i | −0.838280 | − | 0.545240i | \(-0.816438\pi\) |
0.545240 | + | 0.838280i | \(0.316438\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 5.45844i | − | 0.220106i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 46.0710i | − | 1.85475i | −0.374133 | − | 0.927375i | \(-0.622060\pi\) | ||
0.374133 | − | 0.927375i | \(-0.377940\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.2931 | − | 34.2931i | 1.37836 | − | 1.37836i | 0.530962 | − | 0.847396i | \(-0.321831\pi\) |
0.847396 | − | 0.530962i | \(-0.178169\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.49824 | − | 5.49824i | −0.220637 | − | 0.220637i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −26.3798 | −1.05688 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.32666 | + | 6.32666i | 0.252663 | + | 0.252663i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.89636 | − | 4.89636i | 0.195231 | − | 0.195231i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.9017i | 1.03113i | 0.856850 | + | 0.515566i | \(0.172418\pi\) | ||||
−0.856850 | + | 0.515566i | \(0.827582\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.0884535i | 0.00351571i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.10234 | − | 7.10234i | 0.281848 | − | 0.281848i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.67452 | + | 6.67452i | 0.264454 | + | 0.264454i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.27391 | 0.129514 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.3341 | −0.605660 | −0.302830 | − | 0.953045i | \(-0.597931\pi\) | ||||
−0.302830 | + | 0.953045i | \(0.597931\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.7507 | + | 16.7507i | 0.660582 | + | 0.660582i | 0.955517 | − | 0.294935i | \(-0.0952981\pi\) |
−0.294935 | + | 0.955517i | \(0.595298\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.91245 | − | 4.91245i | 0.193427 | − | 0.193427i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 4.81900i | − | 0.189455i | −0.995503 | − | 0.0947273i | \(-0.969802\pi\) | ||
0.995503 | − | 0.0947273i | \(-0.0301979\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 71.8678i | − | 2.82106i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.389604 | − | 0.389604i | 0.0152698 | − | 0.0152698i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.7842 | + | 16.7842i | 0.656817 | + | 0.656817i | 0.954625 | − | 0.297809i | \(-0.0962558\pi\) |
−0.297809 | + | 0.954625i | \(0.596256\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.7511 | −0.420079 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.84138 | 0.0718391 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.4376 | − | 16.4376i | −0.640320 | − | 0.640320i | 0.310314 | − | 0.950634i | \(-0.399566\pi\) |
−0.950634 | + | 0.310314i | \(0.899566\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.5904 | + | 17.5904i | −0.684187 | + | 0.684187i | −0.960941 | − | 0.276754i | \(-0.910741\pi\) |
0.276754 | + | 0.960941i | \(0.410741\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 2.15862i | − | 0.0838338i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 2.11882i | − | 0.0821645i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.8651 | + | 22.8651i | −0.885339 | + | 0.885339i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.27744 | − | 9.27744i | −0.358687 | − | 0.358687i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.8119 | −0.726227 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.0762 | 1.04371 | 0.521856 | − | 0.853033i | \(-0.325240\pi\) | ||||
0.521856 | + | 0.853033i | \(0.325240\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.707107 | + | 0.707107i | 0.0272166 | + | 0.0272166i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.9093 | − | 16.9093i | 0.649877 | − | 0.649877i | −0.303086 | − | 0.952963i | \(-0.598017\pi\) |
0.952963 | + | 0.303086i | \(0.0980170\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 7.70607i | − | 0.295732i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 8.14920i | − | 0.312278i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.0531 | − | 14.0531i | 0.537728 | − | 0.537728i | −0.385133 | − | 0.922861i | \(-0.625845\pi\) |
0.922861 | + | 0.385133i | \(0.125845\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.4654 | − | 10.4654i | −0.399862 | − | 0.399862i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.24853 | 0.276549 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.30466 | −0.0878005 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.9737 | − | 25.9737i | −0.988086 | − | 0.988086i | 0.0118439 | − | 0.999930i | \(-0.496230\pi\) |
−0.999930 | + | 0.0118439i | \(0.996230\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.97186 | − | 5.97186i | 0.226852 | − | 0.226852i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 11.9304i | − | 0.452546i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.24136i | 0.236409i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.37284 | + | 9.37284i | −0.354513 | + | 0.354513i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.8789 | + | 20.8789i | 0.788586 | + | 0.788586i | 0.981262 | − | 0.192676i | \(-0.0617168\pi\) |
−0.192676 | + | 0.981262i | \(0.561717\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.07314 | 0.342200 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.7324 | 0.404204 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.8249 | − | 15.8249i | −0.595157 | − | 0.595157i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.4580 | − | 14.4580i | 0.542983 | − | 0.542983i | −0.381419 | − | 0.924402i | \(-0.624564\pi\) |
0.924402 | + | 0.381419i | \(0.124564\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.3861i | 0.427011i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 3.02944i | − | 0.113453i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.97186 | + | 7.97186i | −0.298131 | + | 0.298131i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.3021 | + | 13.3021i | 0.496774 | + | 0.496774i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.53803 | −0.131946 | −0.0659731 | − | 0.997821i | \(-0.521015\pi\) | ||||
−0.0659731 | + | 0.997821i | \(0.521015\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.8686 | 0.963397 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.88561 | − | 1.88561i | −0.0701265 | − | 0.0701265i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.94059 | − | 2.94059i | 0.109211 | − | 0.109211i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.6681i | 0.877802i | 0.898535 | + | 0.438901i | \(0.144632\pi\) | ||||
−0.898535 | + | 0.438901i | \(0.855368\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.61706 | + | 5.61706i | −0.207754 | + | 0.207754i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.3055 | − | 20.3055i | −0.750000 | − | 0.750000i | 0.224479 | − | 0.974479i | \(-0.427932\pi\) |
−0.974479 | + | 0.224479i | \(0.927932\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.00000 | 0.184428 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.8910 | 0.916871 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.63944 | − | 4.63944i | −0.170664 | − | 0.170664i | 0.616607 | − | 0.787271i | \(-0.288507\pi\) |
−0.787271 | + | 0.616607i | \(0.788507\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.00000 | − | 2.00000i | 0.0734718 | − | 0.0734718i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.3029i | 1.00165i | 0.865549 | + | 0.500824i | \(0.166970\pi\) | ||||
−0.865549 | + | 0.500824i | \(0.833030\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1.09254i | − | 0.0400277i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.1153 | − | 11.1153i | 0.406687 | − | 0.406687i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.89450 | − | 9.89450i | −0.361537 | − | 0.361537i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.1582 | 0.954527 | 0.477264 | − | 0.878760i | \(-0.341629\pi\) | ||||
0.477264 | + | 0.878760i | \(0.341629\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.9987 | 0.400815 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.05117 | − | 2.05117i | −0.0746497 | − | 0.0746497i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.8559 | + | 16.8559i | −0.612638 | + | 0.612638i | −0.943633 | − | 0.330995i | \(-0.892616\pi\) |
0.330995 | + | 0.943633i | \(0.392616\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 46.4353i | − | 1.68549i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 34.6337i | − | 1.25547i | −0.778427 | − | 0.627735i | \(-0.783982\pi\) | ||
0.778427 | − | 0.627735i | \(-0.216018\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.9222 | + | 17.9222i | −0.648829 | + | 0.648829i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.808530 | − | 0.808530i | −0.0292325 | − | 0.0292325i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22.7190 | −0.820337 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.79179 | −0.317040 | −0.158520 | − | 0.987356i | \(-0.550672\pi\) | ||||
−0.158520 | + | 0.987356i | \(0.550672\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.12930 | − | 4.12930i | −0.148713 | − | 0.148713i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.17118 | + | 7.17118i | −0.257929 | + | 0.257929i | −0.824211 | − | 0.566282i | \(-0.808381\pi\) |
0.566282 | + | 0.824211i | \(0.308381\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.389604i | 0.0139950i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 8.56431i | − | 0.307243i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.78274 | + | 5.78274i | −0.207188 | + | 0.207188i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8249 | + | 13.8249i | 0.494694 | + | 0.494694i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.15862 | −0.148617 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.68943 | 0.131681 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.9687 | − | 10.9687i | −0.390993 | − | 0.390993i | 0.484048 | − | 0.875041i | \(-0.339166\pi\) |
−0.875041 | + | 0.484048i | \(0.839166\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.07773 | − | 7.07773i | 0.251974 | − | 0.251974i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.1873i | 0.895556i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.94688i | 0.211180i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.863230 | + | 0.863230i | −0.0306156 | + | 0.0306156i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.13138 | + | 1.13138i | 0.0400756 | + | 0.0400756i | 0.726861 | − | 0.686785i | \(-0.240979\pi\) |
−0.686785 | + | 0.726861i | \(0.740979\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.2717 | −0.434143 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.6533 | −0.659083 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.77568 | + | 7.77568i | 0.274398 | + | 0.274398i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.77568 | + | 7.77568i | −0.274057 | + | 0.274057i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.58135i | 0.0908680i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 20.1610i | − | 0.708822i | −0.935090 | − | 0.354411i | \(-0.884681\pi\) | ||
0.935090 | − | 0.354411i | \(-0.115319\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.0206 | − | 28.0206i | 0.983935 | − | 0.983935i | −0.0159383 | − | 0.999873i | \(-0.505074\pi\) |
0.999873 | + | 0.0159383i | \(0.00507355\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.85276 | + | 3.85276i | 0.135122 | + | 0.135122i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.01333 | 0.0705238 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.4086 | −0.364151 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.88784 | − | 1.88784i | −0.0659664 | − | 0.0659664i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.0657 | − | 31.0657i | 1.08420 | − | 1.08420i | 0.0880869 | − | 0.996113i | \(-0.471925\pi\) |
0.996113 | − | 0.0880869i | \(-0.0280753\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 18.5484i | − | 0.646555i | −0.946304 | − | 0.323278i | \(-0.895215\pi\) | ||
0.946304 | − | 0.323278i | \(-0.104785\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.97186i | 0.207914i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.6080 | − | 16.6080i | 0.577517 | − | 0.577517i | −0.356701 | − | 0.934218i | \(-0.616099\pi\) |
0.934218 | + | 0.356701i | \(0.116099\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.0261 | − | 19.0261i | −0.660803 | − | 0.660803i | 0.294767 | − | 0.955569i | \(-0.404758\pi\) |
−0.955569 | + | 0.294767i | \(0.904758\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.9469 | 0.518501 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.71717 | −0.198088 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.98481 | − | 2.98481i | −0.103294 | − | 0.103294i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.275492 | − | 0.275492i | 0.00952239 | − | 0.00952239i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 15.5569i | − | 0.537083i | −0.963268 | − | 0.268542i | \(-0.913458\pi\) | ||
0.963268 | − | 0.268542i | \(-0.0865417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 11.7059i | − | 0.403651i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.23911 | + | 7.23911i | −0.249328 | + | 0.249328i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.67230 | − | 6.67230i | −0.229534 | − | 0.229534i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34.8789 | 1.19845 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.9830 | 0.479894 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33.2967 | − | 33.2967i | −1.14139 | − | 1.14139i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.5124 | + | 15.5124i | −0.531133 | + | 0.531133i | −0.920910 | − | 0.389776i | \(-0.872552\pi\) |
0.389776 | + | 0.920910i | \(0.372552\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1.49824i | − | 0.0512386i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 27.0005i | − | 0.922320i | −0.887317 | − | 0.461160i | \(-0.847433\pi\) | ||
0.887317 | − | 0.461160i | \(-0.152567\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.31020 | + | 1.31020i | −0.0447035 | + | 0.0447035i | −0.729105 | − | 0.684402i | \(-0.760063\pi\) |
0.684402 | + | 0.729105i | \(0.260063\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.45844 | + | 5.45844i | 0.186023 | + | 0.186023i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.1917 | 1.53834 | 0.769172 | − | 0.639042i | \(-0.220669\pi\) | ||||
0.769172 | + | 0.639042i | \(0.220669\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.0228 | −0.680794 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.0963 | − | 11.0963i | −0.376851 | − | 0.376851i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48.0805 | + | 48.0805i | −1.63102 | + | 1.63102i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 7.86860i | − | 0.266617i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 5.44902i | − | 0.184421i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | − | 1.00000i | 0.0338062 | − | 0.0338062i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.2259 | − | 10.2259i | −0.345303 | − | 0.345303i | 0.513053 | − | 0.858357i | \(-0.328514\pi\) |
−0.858357 | + | 0.513053i | \(0.828514\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.8020 | 0.431799 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.61942 | −0.256705 | −0.128352 | − | 0.991729i | \(-0.540969\pi\) | ||||
−0.128352 | + | 0.991729i | \(0.540969\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.70424 | + | 1.70424i | 0.0573521 | + | 0.0573521i | 0.735201 | − | 0.677849i | \(-0.237088\pi\) |
−0.677849 | + | 0.735201i | \(0.737088\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.50961 | + | 8.50961i | −0.286047 | + | 0.286047i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 23.9647i | − | 0.804655i | −0.915496 | − | 0.402327i | \(-0.868201\pi\) | ||
0.915496 | − | 0.402327i | \(-0.131799\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.2047i | 0.476410i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.22274 | − | 4.22274i | 0.141467 | − | 0.141467i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.3700 | − | 11.3700i | −0.380482 | − | 0.380482i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.8003 | 0.561572 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.6792 | −0.490125 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.14567 | − | 1.14567i | −0.0382101 | − | 0.0382101i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.987046 | − | 0.987046i | 0.0328833 | − | 0.0328833i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.82490i | 0.326952i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 9.96520i | − | 0.331254i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.1197 | + | 19.1197i | −0.634860 | + | 0.634860i | −0.949283 | − | 0.314423i | \(-0.898189\pi\) |
0.314423 | + | 0.949283i | \(0.398189\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.1899 | − | 11.1899i | −0.371145 | − | 0.371145i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.15918 | −0.137800 | −0.0688999 | − | 0.997624i | \(-0.521949\pi\) | ||||
−0.0688999 | + | 0.997624i | \(0.521949\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 93.8741 | 3.10678 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.22746 | + | 2.22746i | 0.0736374 | + | 0.0736374i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.7511 | − | 10.7511i | 0.355032 | − | 0.355032i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.6229i | 1.43899i | 0.694499 | + | 0.719494i | \(0.255626\pi\) | ||||
−0.694499 | + | 0.719494i | \(0.744374\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 3.92041i | − | 0.129182i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.37036 | − | 4.37036i | 0.143852 | − | 0.143852i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.28216 | + | 4.28216i | 0.140796 | + | 0.140796i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.2919 | 0.600783 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.24392 | 0.139238 | 0.0696192 | − | 0.997574i | \(-0.477822\pi\) | ||||
0.0696192 | + | 0.997574i | \(0.477822\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.29706 | − | 5.29706i | −0.173604 | − | 0.173604i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.8097 | − | 14.8097i | 0.484848 | − | 0.484848i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 6.82843i | − | 0.223313i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 9.87491i | − | 0.322599i | −0.986905 | − | 0.161300i | \(-0.948431\pi\) | ||
0.986905 | − | 0.161300i | \(-0.0515685\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.19932 | + | 7.19932i | −0.234941 | + | 0.234941i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.0675 | + | 26.0675i | 0.849777 | + | 0.849777i | 0.990105 | − | 0.140328i | \(-0.0448156\pi\) |
−0.140328 | + | 0.990105i | \(0.544816\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.4431 | 1.38214 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.41421 | −0.0460044 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.7355 | + | 10.7355i | 0.348857 | + | 0.348857i | 0.859684 | − | 0.510827i | \(-0.170661\pi\) |
−0.510827 | + | 0.859684i | \(0.670661\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.45807 | − | 2.45807i | 0.0797922 | − | 0.0797922i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 20.8815i | − | 0.677131i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 34.0844i | − | 1.10410i | −0.833811 | − | 0.552051i | \(-0.813846\pi\) | ||
0.833811 | − | 0.552051i | \(-0.186154\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.8793 | − | 10.8793i | 0.352046 | − | 0.352046i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −17.5608 | − | 17.5608i | −0.567659 | − | 0.567659i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.9308 | 0.675890 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8482 | −0.995104 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.99647 | − | 6.99647i | −0.225458 | − | 0.225458i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.31814 | − | 5.31814i | 0.171197 | − | 0.171197i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 9.41342i | − | 0.302715i | −0.988479 | − | 0.151358i | \(-0.951635\pi\) | ||
0.988479 | − | 0.151358i | \(-0.0483645\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.71313i | 0.0550337i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.84018 | − | 6.84018i | 0.219512 | − | 0.219512i | −0.588781 | − | 0.808293i | \(-0.700392\pi\) |
0.808293 | + | 0.588781i | \(0.200392\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.9304 | + | 11.9304i | 0.382471 | + | 0.382471i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.88784 | 0.0604592 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.38555 | 0.172299 | 0.0861494 | − | 0.996282i | \(-0.472544\pi\) | ||||
0.0861494 | + | 0.996282i | \(0.472544\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −78.7682 | − | 78.7682i | −2.51744 | − | 2.51744i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.6729 | + | 12.6729i | −0.404616 | + | 0.404616i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.31630i | 0.297144i | 0.988902 | + | 0.148572i | \(0.0474677\pi\) | ||||
−0.988902 | + | 0.148572i | \(0.952532\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 13.6663i | − | 0.435444i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.7324 | + | 10.7324i | −0.341615 | + | 0.341615i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.1976 | + | 38.1976i | 1.21461 | + | 1.21461i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.25727 | 0.0399384 | 0.0199692 | − | 0.999801i | \(-0.493643\pi\) | ||||
0.0199692 | + | 0.999801i | \(0.493643\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23.8741 | −0.757622 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.61548 | + | 6.61548i | 0.209725 | + | 0.209725i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.1661 | − | 25.1661i | 0.797017 | − | 0.797017i | −0.185607 | − | 0.982624i | \(-0.559425\pi\) |
0.982624 | + | 0.185607i | \(0.0594250\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 6.05588i | − | 0.191600i |
(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 | 960.2.s.b.721.3 | 8 | ||
3.2 | odd | 2 | 2880.2.t.b.721.2 | 8 | |||
4.3 | odd | 2 | 240.2.s.b.61.2 | ✓ | 8 | ||
8.3 | odd | 2 | 1920.2.s.c.1441.3 | 8 | |||
8.5 | even | 2 | 1920.2.s.d.1441.2 | 8 | |||
12.11 | even | 2 | 720.2.t.b.541.3 | 8 | |||
16.3 | odd | 4 | 1920.2.s.c.481.3 | 8 | |||
16.5 | even | 4 | inner | 960.2.s.b.241.3 | 8 | ||
16.11 | odd | 4 | 240.2.s.b.181.2 | yes | 8 | ||
16.13 | even | 4 | 1920.2.s.d.481.2 | 8 | |||
48.5 | odd | 4 | 2880.2.t.b.2161.2 | 8 | |||
48.11 | even | 4 | 720.2.t.b.181.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.s.b.61.2 | ✓ | 8 | 4.3 | odd | 2 | ||
240.2.s.b.181.2 | yes | 8 | 16.11 | odd | 4 | ||
720.2.t.b.181.3 | 8 | 48.11 | even | 4 | |||
720.2.t.b.541.3 | 8 | 12.11 | even | 2 | |||
960.2.s.b.241.3 | 8 | 16.5 | even | 4 | inner | ||
960.2.s.b.721.3 | 8 | 1.1 | even | 1 | trivial | ||
1920.2.s.c.481.3 | 8 | 16.3 | odd | 4 | |||
1920.2.s.c.1441.3 | 8 | 8.3 | odd | 2 | |||
1920.2.s.d.481.2 | 8 | 16.13 | even | 4 | |||
1920.2.s.d.1441.2 | 8 | 8.5 | even | 2 | |||
2880.2.t.b.721.2 | 8 | 3.2 | odd | 2 | |||
2880.2.t.b.2161.2 | 8 | 48.5 | odd | 4 |