Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1151,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bf (of order \(6\), degree \(2\), 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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1601.2 | ||
Character | \(\chi\) | \(=\) | 3150.1601 |
Dual form | 3150.2.bf.f.1151.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.54232 | − | 0.732536i | 0.960907 | − | 0.276872i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.07577 | − | 1.19845i | 0.625869 | − | 0.361346i | −0.153282 | − | 0.988183i | \(-0.548984\pi\) |
0.779150 | + | 0.626837i | \(0.215651\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.67714i | 1.57455i | 0.616599 | + | 0.787277i | \(0.288510\pi\) | ||||
−0.616599 | + | 0.787277i | \(0.711490\pi\) | |||||||
\(14\) | −2.56798 | − | 0.636766i | −0.686322 | − | 0.170183i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.03596 | − | 1.79434i | −0.251258 | − | 0.435191i | 0.712615 | − | 0.701556i | \(-0.247511\pi\) |
−0.963872 | + | 0.266365i | \(0.914177\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.12164 | + | 2.95698i | 1.17499 | + | 0.678378i | 0.954849 | − | 0.297091i | \(-0.0960164\pi\) |
0.220136 | + | 0.975469i | \(0.429350\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.39690 | −0.511020 | ||||||||
\(23\) | 1.61233 | + | 0.930877i | 0.336193 | + | 0.194101i | 0.658587 | − | 0.752504i | \(-0.271154\pi\) |
−0.322394 | + | 0.946606i | \(0.604488\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.83857 | − | 4.91654i | 0.556689 | − | 0.964214i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.90555 | + | 1.83545i | 0.360116 | + | 0.346867i | ||||
\(29\) | 4.88913i | 0.907889i | 0.891030 | + | 0.453944i | \(0.149984\pi\) | ||||
−0.891030 | + | 0.453944i | \(0.850016\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.92008 | + | 2.26326i | −0.704067 | + | 0.406493i | −0.808860 | − | 0.588001i | \(-0.799915\pi\) |
0.104794 | + | 0.994494i | \(0.466582\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.07192i | 0.355332i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.48455 | + | 2.57132i | −0.244059 | + | 0.422723i | −0.961867 | − | 0.273519i | \(-0.911812\pi\) |
0.717807 | + | 0.696242i | \(0.245146\pi\) | |||||||
\(38\) | −2.95698 | − | 5.12164i | −0.479686 | − | 0.830840i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.04428 | 1.10013 | 0.550066 | − | 0.835121i | \(-0.314603\pi\) | ||||
0.550066 | + | 0.835121i | \(0.314603\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.55956 | −1.30532 | −0.652660 | − | 0.757651i | \(-0.726347\pi\) | ||||
−0.652660 | + | 0.757651i | \(0.726347\pi\) | |||||||
\(44\) | 2.07577 | + | 1.19845i | 0.312934 | + | 0.180673i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.930877 | − | 1.61233i | −0.137250 | − | 0.237725i | ||||
\(47\) | −2.78941 | + | 4.83140i | −0.406877 | + | 0.704732i | −0.994538 | − | 0.104375i | \(-0.966716\pi\) |
0.587661 | + | 0.809107i | \(0.300049\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.92678 | − | 3.72468i | 0.846683 | − | 0.532097i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.91654 | + | 2.83857i | −0.681802 | + | 0.393639i | ||||
\(53\) | −3.62931 | + | 2.09538i | −0.498524 | + | 0.287823i | −0.728104 | − | 0.685467i | \(-0.759598\pi\) |
0.229580 | + | 0.973290i | \(0.426265\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.732536 | − | 2.54232i | −0.0978892 | − | 0.339732i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.44457 | − | 4.23411i | 0.320987 | − | 0.555966i | ||||
\(59\) | −1.00312 | − | 1.73746i | −0.130595 | − | 0.226198i | 0.793311 | − | 0.608817i | \(-0.208356\pi\) |
−0.923906 | + | 0.382619i | \(0.875022\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.7862 | + | 6.22739i | 1.38103 | + | 0.797335i | 0.992281 | − | 0.124011i | \(-0.0395757\pi\) |
0.388744 | + | 0.921346i | \(0.372909\pi\) | |||||||
\(62\) | 4.52651 | 0.574868 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.81111 | + | 6.60103i | 0.465601 | + | 0.806445i | 0.999228 | − | 0.0392750i | \(-0.0125048\pi\) |
−0.533627 | + | 0.845720i | \(0.679171\pi\) | |||||||
\(68\) | 1.03596 | − | 1.79434i | 0.125629 | − | 0.217596i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.14126i | − | 1.08487i | −0.840099 | − | 0.542434i | \(-0.817503\pi\) | ||
0.840099 | − | 0.542434i | \(-0.182497\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.937339 | − | 0.541173i | 0.109707 | − | 0.0633395i | −0.444142 | − | 0.895956i | \(-0.646492\pi\) |
0.553850 | + | 0.832617i | \(0.313158\pi\) | |||||||
\(74\) | 2.57132 | − | 1.48455i | 0.298910 | − | 0.172576i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.91397i | 0.678378i | ||||||||
\(77\) | 4.39937 | − | 4.56742i | 0.501355 | − | 0.520505i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.38392 | + | 14.5214i | −0.943265 | + | 1.63378i | −0.184076 | + | 0.982912i | \(0.558929\pi\) |
−0.759189 | + | 0.650870i | \(0.774404\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.10053 | − | 3.52214i | −0.673690 | − | 0.388955i | ||||
\(83\) | −13.6122 | −1.49414 | −0.747068 | − | 0.664747i | \(-0.768539\pi\) | ||||
−0.747068 | + | 0.664747i | \(0.768539\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.41279 | + | 4.27978i | 0.799342 | + | 0.461500i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.19845 | − | 2.07577i | −0.127755 | − | 0.221278i | ||||
\(89\) | 6.63129 | − | 11.4857i | 0.702916 | − | 1.21749i | −0.264523 | − | 0.964379i | \(-0.585214\pi\) |
0.967438 | − | 0.253106i | \(-0.0814523\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.15870 | + | 14.4331i | 0.435951 | + | 1.51300i | ||||
\(92\) | 1.86175i | 0.194101i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.83140 | − | 2.78941i | 0.498321 | − | 0.287706i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.8260i | − | 1.30229i | −0.758955 | − | 0.651143i | \(-0.774290\pi\) | ||
0.758955 | − | 0.651143i | \(-0.225710\pi\) | |||||||
\(98\) | −6.99508 | + | 0.262276i | −0.706610 | + | 0.0264939i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.45573 | + | 7.71756i | 0.443362 | + | 0.767926i | 0.997937 | − | 0.0642084i | \(-0.0204523\pi\) |
−0.554574 | + | 0.832134i | \(0.687119\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.37021 | − | 5.40989i | −0.923274 | − | 0.533053i | −0.0385960 | − | 0.999255i | \(-0.512289\pi\) |
−0.884678 | + | 0.466202i | \(0.845622\pi\) | |||||||
\(104\) | 5.67714 | 0.556689 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.19077 | 0.407043 | ||||||||
\(107\) | −4.82989 | − | 2.78854i | −0.466923 | − | 0.269578i | 0.248028 | − | 0.968753i | \(-0.420218\pi\) |
−0.714951 | + | 0.699175i | \(0.753551\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | + | 1.73205i | 0.0957826 | + | 0.165900i | 0.909935 | − | 0.414751i | \(-0.136131\pi\) |
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.636766 | + | 2.56798i | −0.0601687 | + | 0.242651i | ||||
\(113\) | − | 14.5030i | − | 1.36432i | −0.731202 | − | 0.682161i | \(-0.761040\pi\) | ||
0.731202 | − | 0.682161i | \(-0.238960\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.23411 | + | 2.44457i | −0.393127 | + | 0.226972i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.00624i | 0.184690i | ||||||||
\(119\) | −3.94816 | − | 3.80290i | −0.361928 | − | 0.348612i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.62745 | + | 4.55087i | −0.238859 | + | 0.413715i | ||||
\(122\) | −6.22739 | − | 10.7862i | −0.563801 | − | 0.976532i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.92008 | − | 2.26326i | −0.352033 | − | 0.203247i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.2462 | 1.70783 | 0.853913 | − | 0.520416i | \(-0.174223\pi\) | ||||
0.853913 | + | 0.520416i | \(0.174223\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.34970 | + | 4.06980i | −0.205294 | + | 0.355580i | −0.950226 | − | 0.311560i | \(-0.899149\pi\) |
0.744932 | + | 0.667140i | \(0.232482\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.1870 | + | 3.76581i | 1.31688 | + | 0.326537i | ||||
\(134\) | − | 7.62222i | − | 0.658459i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.79434 | + | 1.03596i | −0.153863 | + | 0.0888330i | ||||
\(137\) | −19.8185 | + | 11.4422i | −1.69321 | + | 0.977577i | −0.741317 | + | 0.671155i | \(0.765798\pi\) |
−0.951896 | + | 0.306421i | \(0.900868\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.13862i | − | 0.775127i | −0.921843 | − | 0.387564i | \(-0.873317\pi\) | ||
0.921843 | − | 0.387564i | \(-0.126683\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.57063 | + | 7.91656i | −0.383559 | + | 0.664343i | ||||
\(143\) | 6.80375 | + | 11.7844i | 0.568958 | + | 0.985465i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.08235 | −0.0895756 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.96911 | −0.244059 | ||||||||
\(149\) | 9.05052 | + | 5.22532i | 0.741448 | + | 0.428075i | 0.822596 | − | 0.568627i | \(-0.192525\pi\) |
−0.0811477 | + | 0.996702i | \(0.525859\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.85937 | + | 15.3449i | 0.720965 | + | 1.24875i | 0.960613 | + | 0.277888i | \(0.0896346\pi\) |
−0.239648 | + | 0.970860i | \(0.577032\pi\) | |||||||
\(152\) | 2.95698 | − | 5.12164i | 0.239843 | − | 0.415420i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.09368 | + | 1.75581i | −0.491042 | + | 0.141487i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.26801 | − | 3.04149i | 0.420433 | − | 0.242737i | −0.274830 | − | 0.961493i | \(-0.588621\pi\) |
0.695263 | + | 0.718756i | \(0.255288\pi\) | |||||||
\(158\) | 14.5214 | − | 8.38392i | 1.15526 | − | 0.666989i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.78095 | + | 1.18550i | 0.376792 | + | 0.0934305i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.468670 | + | 0.811759i | −0.0367090 | + | 0.0635819i | −0.883796 | − | 0.467872i | \(-0.845021\pi\) |
0.847087 | + | 0.531454i | \(0.178354\pi\) | |||||||
\(164\) | 3.52214 | + | 6.10053i | 0.275033 | + | 0.476371i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.7885 | + | 6.80611i | 0.914968 | + | 0.528257i | ||||
\(167\) | 17.2101 | 1.33176 | 0.665879 | − | 0.746060i | \(-0.268057\pi\) | ||||
0.665879 | + | 0.746060i | \(0.268057\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −19.2299 | −1.47922 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.27978 | − | 7.41279i | −0.326330 | − | 0.565220i | ||||
\(173\) | −0.988114 | + | 1.71146i | −0.0751249 | + | 0.130120i | −0.901141 | − | 0.433527i | \(-0.857269\pi\) |
0.826016 | + | 0.563647i | \(0.190602\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.39690i | 0.180673i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.4857 | + | 6.63129i | −0.860893 | + | 0.497037i | ||||
\(179\) | 0.768461 | − | 0.443671i | 0.0574375 | − | 0.0331615i | −0.471006 | − | 0.882130i | \(-0.656109\pi\) |
0.528444 | + | 0.848968i | \(0.322776\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.89973i | 0.364194i | 0.983281 | + | 0.182097i | \(0.0582885\pi\) | ||||
−0.983281 | + | 0.182097i | \(0.941712\pi\) | |||||||
\(182\) | 3.61500 | − | 14.5788i | 0.267962 | − | 1.08065i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.930877 | − | 1.61233i | 0.0686252 | − | 0.118862i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.30084 | − | 2.48309i | −0.314509 | − | 0.181582i | ||||
\(188\) | −5.57882 | −0.406877 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.44949 | − | 1.41421i | −0.177239 | − | 0.102329i | 0.408756 | − | 0.912644i | \(-0.365963\pi\) |
−0.585995 | + | 0.810315i | \(0.699296\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.74828 | + | 16.8845i | 0.701697 | + | 1.21537i | 0.967871 | + | 0.251449i | \(0.0809071\pi\) |
−0.266174 | + | 0.963925i | \(0.585760\pi\) | |||||||
\(194\) | −6.41301 | + | 11.1077i | −0.460428 | + | 0.797484i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.18906 | + | 3.27040i | 0.442076 | + | 0.233600i | ||||
\(197\) | 27.1576i | 1.93490i | 0.253069 | + | 0.967448i | \(0.418560\pi\) | ||||
−0.253069 | + | 0.967448i | \(0.581440\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.00000 | − | 1.73205i | 0.212664 | − | 0.122782i | −0.389885 | − | 0.920864i | \(-0.627485\pi\) |
0.602549 | + | 0.798082i | \(0.294152\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 8.91147i | − | 0.627009i | ||||||
\(203\) | 3.58146 | + | 12.4297i | 0.251369 | + | 0.872396i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.40989 | + | 9.37021i | 0.376925 | + | 0.652853i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.91654 | − | 2.83857i | −0.340901 | − | 0.196819i | ||||
\(209\) | 14.1752 | 0.980516 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.06071 | −0.279551 | −0.139775 | − | 0.990183i | \(-0.544638\pi\) | ||||
−0.139775 | + | 0.990183i | \(0.544638\pi\) | |||||||
\(212\) | −3.62931 | − | 2.09538i | −0.249262 | − | 0.143912i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.78854 | + | 4.82989i | 0.190620 | + | 0.330164i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.30817 | + | 8.62552i | −0.563996 | + | 0.585538i | ||||
\(218\) | − | 2.00000i | − | 0.135457i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.1867 | − | 5.88130i | 0.685232 | − | 0.395619i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 16.1486i | − | 1.08139i | −0.841218 | − | 0.540696i | \(-0.818161\pi\) | ||
0.841218 | − | 0.540696i | \(-0.181839\pi\) | |||||||
\(224\) | 1.83545 | − | 1.90555i | 0.122636 | − | 0.127320i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.25148 | + | 12.5599i | −0.482361 | + | 0.835474i | ||||
\(227\) | 0.839901 | + | 1.45475i | 0.0557462 | + | 0.0965552i | 0.892552 | − | 0.450945i | \(-0.148913\pi\) |
−0.836806 | + | 0.547500i | \(0.815580\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.9143 | + | 6.30136i | 0.721236 | + | 0.416406i | 0.815207 | − | 0.579169i | \(-0.196623\pi\) |
−0.0939717 | + | 0.995575i | \(0.529956\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.88913 | 0.320987 | ||||||||
\(233\) | 12.5715 | + | 7.25818i | 0.823589 | + | 0.475499i | 0.851653 | − | 0.524107i | \(-0.175601\pi\) |
−0.0280635 | + | 0.999606i | \(0.508934\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.00312 | − | 1.73746i | 0.0652977 | − | 0.113099i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.51776 | + | 5.26749i | 0.0983816 | + | 0.341441i | ||||
\(239\) | − | 0.207089i | − | 0.0133955i | −0.999978 | − | 0.00669774i | \(-0.997868\pi\) | ||
0.999978 | − | 0.00669774i | \(-0.00213197\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.04172 | − | 5.22024i | 0.582428 | − | 0.336265i | −0.179669 | − | 0.983727i | \(-0.557503\pi\) |
0.762098 | + | 0.647462i | \(0.224169\pi\) | |||||||
\(242\) | 4.55087 | − | 2.62745i | 0.292541 | − | 0.168899i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.4548i | 0.797335i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.7872 | + | 29.0763i | −1.06814 | + | 1.85008i | ||||
\(248\) | 2.26326 | + | 3.92008i | 0.143717 | + | 0.248925i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.6464 | 1.80815 | 0.904074 | − | 0.427377i | \(-0.140562\pi\) | ||||
0.904074 | + | 0.427377i | \(0.140562\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.46243 | 0.280551 | ||||||||
\(254\) | −16.6677 | − | 9.62311i | −1.04583 | − | 0.603808i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −12.4595 | + | 21.5805i | −0.777202 | + | 1.34615i | 0.156346 | + | 0.987702i | \(0.450029\pi\) |
−0.933548 | + | 0.358452i | \(0.883305\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.89063 | + | 7.62462i | −0.117478 | + | 0.473771i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.06980 | − | 2.34970i | 0.251433 | − | 0.145165i | ||||
\(263\) | 16.6197 | − | 9.59538i | 1.02481 | − | 0.591677i | 0.109319 | − | 0.994007i | \(-0.465133\pi\) |
0.915495 | + | 0.402330i | \(0.131800\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −11.2694 | − | 10.8548i | −0.690970 | − | 0.665548i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.81111 | + | 6.60103i | −0.232801 | + | 0.403222i | ||||
\(269\) | −2.42744 | − | 4.20446i | −0.148004 | − | 0.256350i | 0.782486 | − | 0.622668i | \(-0.213951\pi\) |
−0.930490 | + | 0.366318i | \(0.880618\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.8344 | − | 6.83257i | −0.718886 | − | 0.415049i | 0.0954567 | − | 0.995434i | \(-0.469569\pi\) |
−0.814342 | + | 0.580385i | \(0.802902\pi\) | |||||||
\(272\) | 2.07192 | 0.125629 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.8845 | 1.38250 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.06491 | + | 10.5047i | 0.364405 | + | 0.631168i | 0.988680 | − | 0.150036i | \(-0.0479391\pi\) |
−0.624276 | + | 0.781204i | \(0.714606\pi\) | |||||||
\(278\) | −4.56931 | + | 7.91427i | −0.274049 | + | 0.474667i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 32.6206i | − | 1.94598i | −0.230839 | − | 0.972992i | \(-0.574147\pi\) | ||
0.230839 | − | 0.972992i | \(-0.425853\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.9647 | − | 6.33045i | 0.651781 | − | 0.376306i | −0.137357 | − | 0.990522i | \(-0.543861\pi\) |
0.789138 | + | 0.614216i | \(0.210527\pi\) | |||||||
\(284\) | 7.91656 | − | 4.57063i | 0.469761 | − | 0.271217i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 13.6075i | − | 0.804628i | ||||||
\(287\) | 17.9088 | − | 5.16019i | 1.05712 | − | 0.304596i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.35357 | − | 11.0047i | 0.373739 | − | 0.647335i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.937339 | + | 0.541173i | 0.0548536 | + | 0.0316698i | ||||
\(293\) | −25.1151 | −1.46724 | −0.733621 | − | 0.679559i | \(-0.762171\pi\) | ||||
−0.733621 | + | 0.679559i | \(0.762171\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.57132 | + | 1.48455i | 0.149455 | + | 0.0862880i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.22532 | − | 9.05052i | −0.302695 | − | 0.524283i | ||||
\(299\) | −5.28472 | + | 9.15340i | −0.305623 | + | 0.529355i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.7611 | + | 6.27018i | −1.25429 | + | 0.361407i | ||||
\(302\) | − | 17.7187i | − | 1.01960i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.12164 | + | 2.95698i | −0.293746 | + | 0.169595i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 18.5674i | − | 1.05970i | −0.848092 | − | 0.529849i | \(-0.822249\pi\) | ||
0.848092 | − | 0.529849i | \(-0.177751\pi\) | |||||||
\(308\) | 6.15518 | + | 1.52626i | 0.350724 | + | 0.0869668i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.21831 | − | 10.7704i | −0.352608 | − | 0.610735i | 0.634098 | − | 0.773253i | \(-0.281372\pi\) |
−0.986706 | + | 0.162518i | \(0.948038\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.7504 | + | 6.20675i | 0.607649 | + | 0.350826i | 0.772045 | − | 0.635568i | \(-0.219234\pi\) |
−0.164396 | + | 0.986394i | \(0.552567\pi\) | |||||||
\(314\) | −6.08297 | −0.343282 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.7678 | −0.943265 | ||||||||
\(317\) | 21.3444 | + | 12.3232i | 1.19882 | + | 0.692141i | 0.960293 | − | 0.278995i | \(-0.0900012\pi\) |
0.238530 | + | 0.971135i | \(0.423335\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.85937 | + | 10.1487i | 0.328062 | + | 0.568219i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.54767 | − | 3.41715i | −0.197704 | − | 0.190430i | ||||
\(323\) | − | 12.2533i | − | 0.681791i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.811759 | − | 0.468670i | 0.0449592 | − | 0.0259572i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 7.04428i | − | 0.388955i | ||||||
\(329\) | −3.55240 | + | 14.3263i | −0.195850 | + | 0.789835i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.5788 | − | 21.7871i | 0.691392 | − | 1.19753i | −0.279989 | − | 0.960003i | \(-0.590331\pi\) |
0.971382 | − | 0.237524i | \(-0.0763357\pi\) | |||||||
\(332\) | −6.80611 | − | 11.7885i | −0.373534 | − | 0.646980i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14.9044 | − | 8.60505i | −0.815531 | − | 0.470847i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.4214 | 0.785584 | 0.392792 | − | 0.919627i | \(-0.371509\pi\) | ||||
0.392792 | + | 0.919627i | \(0.371509\pi\) | |||||||
\(338\) | 16.6536 | + | 9.61494i | 0.905834 | + | 0.522984i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.42479 | + | 9.39601i | −0.293769 | + | 0.508823i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.3393 | − | 13.8109i | 0.666261 | − | 0.745719i | ||||
\(344\) | 8.55956i | 0.461500i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.71146 | − | 0.988114i | 0.0920088 | − | 0.0531213i | ||||
\(347\) | 12.5457 | − | 7.24329i | 0.673491 | − | 0.388840i | −0.123907 | − | 0.992294i | \(-0.539543\pi\) |
0.797398 | + | 0.603454i | \(0.206209\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.12483i | 0.113739i | 0.998382 | + | 0.0568697i | \(0.0181119\pi\) | ||||
−0.998382 | + | 0.0568697i | \(0.981888\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.19845 | − | 2.07577i | 0.0638775 | − | 0.110639i | ||||
\(353\) | 7.26335 | + | 12.5805i | 0.386589 | + | 0.669592i | 0.991988 | − | 0.126330i | \(-0.0403199\pi\) |
−0.605399 | + | 0.795922i | \(0.706987\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.2626 | 0.702916 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.887342 | −0.0468975 | ||||||||
\(359\) | −3.42054 | − | 1.97485i | −0.180529 | − | 0.104228i | 0.407012 | − | 0.913423i | \(-0.366571\pi\) |
−0.587541 | + | 0.809194i | \(0.699904\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.98749 | + | 13.8347i | 0.420394 | + | 0.728144i | ||||
\(362\) | 2.44986 | − | 4.24329i | 0.128762 | − | 0.223022i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.4201 | + | 10.8181i | −0.546160 | + | 0.567022i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.9826 | − | 13.8464i | 1.25188 | − | 0.722775i | 0.280400 | − | 0.959883i | \(-0.409533\pi\) |
0.971483 | + | 0.237109i | \(0.0761997\pi\) | |||||||
\(368\) | −1.61233 | + | 0.930877i | −0.0840483 | + | 0.0485253i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.69193 | + | 7.98574i | −0.399345 | + | 0.414599i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.06491 | − | 10.5047i | 0.314029 | − | 0.543914i | −0.665202 | − | 0.746664i | \(-0.731654\pi\) |
0.979231 | + | 0.202750i | \(0.0649878\pi\) | |||||||
\(374\) | 2.48309 | + | 4.30084i | 0.128398 | + | 0.222391i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.83140 | + | 2.78941i | 0.249160 | + | 0.143853i | ||||
\(377\) | −27.7563 | −1.42952 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.6821 | 0.959636 | 0.479818 | − | 0.877368i | \(-0.340703\pi\) | ||||
0.479818 | + | 0.877368i | \(0.340703\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.41421 | + | 2.44949i | 0.0723575 | + | 0.125327i | ||||
\(383\) | −5.51463 | + | 9.55162i | −0.281784 | + | 0.488065i | −0.971824 | − | 0.235706i | \(-0.924260\pi\) |
0.690040 | + | 0.723771i | \(0.257593\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 19.4966i | − | 0.992349i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.1077 | − | 6.41301i | 0.563906 | − | 0.325571i | ||||
\(389\) | −29.7662 | + | 17.1855i | −1.50921 | + | 0.871341i | −0.509264 | + | 0.860611i | \(0.670082\pi\) |
−0.999942 | + | 0.0107299i | \(0.996584\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.85741i | − | 0.195078i | ||||||
\(392\) | −3.72468 | − | 5.92678i | −0.188125 | − | 0.299348i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13.5788 | − | 23.5191i | 0.684089 | − | 1.18488i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.8561 | − | 15.5054i | −1.34787 | − | 0.778191i | −0.359920 | − | 0.932983i | \(-0.617196\pi\) |
−0.987947 | + | 0.154792i | \(0.950529\pi\) | |||||||
\(398\) | −3.46410 | −0.173640 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.20771 | + | 4.73872i | 0.409873 | + | 0.236641i | 0.690735 | − | 0.723108i | \(-0.257287\pi\) |
−0.280862 | + | 0.959748i | \(0.590620\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.8488 | − | 22.2548i | −0.640045 | − | 1.10859i | ||||
\(404\) | −4.45573 | + | 7.71756i | −0.221681 | + | 0.383963i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.11323 | − | 12.5552i | 0.154507 | − | 0.623104i | ||||
\(407\) | 7.11665i | 0.352759i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.20805 | + | 4.73892i | −0.405862 | + | 0.234324i | −0.689010 | − | 0.724752i | \(-0.741954\pi\) |
0.283148 | + | 0.959076i | \(0.408621\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 10.8198i | − | 0.533053i | ||||||
\(413\) | −3.82301 | − | 3.68235i | −0.188118 | − | 0.181197i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.83857 | + | 4.91654i | 0.139172 | + | 0.241053i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −12.2760 | − | 7.08758i | −0.600441 | − | 0.346665i | ||||
\(419\) | 2.54445 | 0.124305 | 0.0621523 | − | 0.998067i | \(-0.480204\pi\) | ||||
0.0621523 | + | 0.998067i | \(0.480204\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.08573 | −0.247863 | −0.123932 | − | 0.992291i | \(-0.539550\pi\) | ||||
−0.123932 | + | 0.992291i | \(0.539550\pi\) | |||||||
\(422\) | 3.51668 | + | 2.03035i | 0.171189 | + | 0.0988361i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.09538 | + | 3.62931i | 0.101761 | + | 0.176255i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.9836 | + | 7.93077i | 1.54780 | + | 0.383797i | ||||
\(428\) | − | 5.57707i | − | 0.269578i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.5164 | + | 6.64902i | −0.554727 | + | 0.320272i | −0.751027 | − | 0.660272i | \(-0.770441\pi\) |
0.196299 | + | 0.980544i | \(0.437108\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.7895i | 0.614626i | 0.951608 | + | 0.307313i | \(0.0994299\pi\) | ||||
−0.951608 | + | 0.307313i | \(0.900570\pi\) | |||||||
\(434\) | 11.5078 | − | 3.31583i | 0.552394 | − | 0.159165i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | + | 1.73205i | −0.0478913 | + | 0.0829502i | ||||
\(437\) | 5.50517 | + | 9.53524i | 0.263348 | + | 0.456132i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.323211 | − | 0.186606i | −0.0154260 | − | 0.00890623i | 0.492267 | − | 0.870444i | \(-0.336168\pi\) |
−0.507693 | + | 0.861538i | \(0.669502\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.7626 | −0.559490 | ||||||||
\(443\) | 21.3328 | + | 12.3165i | 1.01355 | + | 0.585175i | 0.912230 | − | 0.409679i | \(-0.134359\pi\) |
0.101323 | + | 0.994854i | \(0.467693\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.07432 | + | 13.9851i | −0.382330 | + | 0.662215i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.54232 | + | 0.732536i | −0.120113 | + | 0.0346091i | ||||
\(449\) | − | 40.6223i | − | 1.91708i | −0.284950 | − | 0.958542i | \(-0.591977\pi\) | ||
0.284950 | − | 0.958542i | \(-0.408023\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.6223 | − | 8.44220i | 0.688538 | − | 0.397528i | ||||
\(452\) | 12.5599 | − | 7.25148i | 0.590769 | − | 0.341081i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 1.67980i | − | 0.0788370i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.495276 | − | 0.857843i | 0.0231680 | − | 0.0401282i | −0.854209 | − | 0.519930i | \(-0.825958\pi\) |
0.877377 | + | 0.479802i | \(0.159291\pi\) | |||||||
\(458\) | −6.30136 | − | 10.9143i | −0.294443 | − | 0.509991i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.7397 | −0.965945 | −0.482972 | − | 0.875636i | \(-0.660443\pi\) | ||||
−0.482972 | + | 0.875636i | \(0.660443\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.46421 | 0.0680476 | 0.0340238 | − | 0.999421i | \(-0.489168\pi\) | ||||
0.0340238 | + | 0.999421i | \(0.489168\pi\) | |||||||
\(464\) | −4.23411 | − | 2.44457i | −0.196564 | − | 0.113486i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.25818 | − | 12.5715i | −0.336229 | − | 0.582365i | ||||
\(467\) | −18.1340 | + | 31.4090i | −0.839142 | + | 1.45344i | 0.0514705 | + | 0.998675i | \(0.483609\pi\) |
−0.890613 | + | 0.454762i | \(0.849724\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.5246 | + | 13.9902i | 0.670682 | + | 0.646006i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.73746 | + | 1.00312i | −0.0799730 | + | 0.0461724i | ||||
\(473\) | −17.7677 | + | 10.2582i | −0.816959 | + | 0.471672i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.31933 | − | 5.32066i | 0.0604714 | − | 0.243872i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.103545 | + | 0.179344i | −0.00473602 | + | 0.00820302i | ||||
\(479\) | 5.16288 | + | 8.94237i | 0.235898 | + | 0.408587i | 0.959533 | − | 0.281595i | \(-0.0908635\pi\) |
−0.723635 | + | 0.690183i | \(0.757530\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.5978 | − | 8.42802i | −0.665600 | − | 0.384285i | ||||
\(482\) | −10.4405 | −0.475551 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.25489 | −0.238859 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.1645 | − | 17.6055i | −0.460599 | − | 0.797781i | 0.538392 | − | 0.842695i | \(-0.319032\pi\) |
−0.998991 | + | 0.0449135i | \(0.985699\pi\) | |||||||
\(488\) | 6.22739 | − | 10.7862i | 0.281901 | − | 0.488266i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.6034i | 1.56163i | 0.624764 | + | 0.780814i | \(0.285195\pi\) | ||||
−0.624764 | + | 0.780814i | \(0.714805\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.77276 | − | 5.06495i | 0.395105 | − | 0.228114i | ||||
\(494\) | 29.0763 | − | 16.7872i | 1.30820 | − | 0.755292i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 4.52651i | − | 0.203247i | ||||||
\(497\) | −6.69630 | − | 23.2400i | −0.300370 | − | 1.04246i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.47545 | − | 2.55555i | 0.0660501 | − | 0.114402i | −0.831109 | − | 0.556109i | \(-0.812294\pi\) |
0.897159 | + | 0.441707i | \(0.145627\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −24.8085 | − | 14.3232i | −1.10726 | − | 0.639277i | ||||
\(503\) | 31.8907 | 1.42193 | 0.710967 | − | 0.703225i | \(-0.248258\pi\) | ||||
0.710967 | + | 0.703225i | \(0.248258\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.86458 | − | 2.23121i | −0.171801 | − | 0.0991896i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.62311 | + | 16.6677i | 0.426957 | + | 0.739510i | ||||
\(509\) | −0.421199 | + | 0.729538i | −0.0186693 | + | 0.0323362i | −0.875209 | − | 0.483745i | \(-0.839276\pi\) |
0.856540 | + | 0.516081i | \(0.172610\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.98659 | − | 2.06247i | 0.0878815 | − | 0.0912383i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.5805 | − | 12.4595i | 0.951875 | − | 0.549565i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.3718i | 0.588093i | ||||||||
\(518\) | 5.44964 | − | 5.65780i | 0.239443 | − | 0.248589i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.81499 | − | 4.87571i | −0.123327 | − | 0.213609i | 0.797751 | − | 0.602987i | \(-0.206023\pi\) |
−0.921078 | + | 0.389379i | \(0.872690\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.4482 | − | 8.91899i | −0.675500 | − | 0.390000i | 0.122657 | − | 0.992449i | \(-0.460858\pi\) |
−0.798158 | + | 0.602449i | \(0.794192\pi\) | |||||||
\(524\) | −4.69940 | −0.205294 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.1908 | −0.836757 | ||||||||
\(527\) | 8.12210 | + | 4.68930i | 0.353804 | + | 0.204269i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.76694 | − | 16.9168i | −0.424649 | − | 0.735514i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.33219 | + | 15.0352i | 0.187824 | + | 0.651858i | ||||
\(533\) | 39.9913i | 1.73222i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.60103 | − | 3.81111i | 0.285121 | − | 0.164615i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.85489i | 0.209309i | ||||||||
\(539\) | 7.83882 | − | 14.8345i | 0.337642 | − | 0.638968i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.7120 | − | 22.0179i | 0.546533 | − | 0.946623i | −0.451976 | − | 0.892030i | \(-0.649281\pi\) |
0.998509 | − | 0.0545925i | \(-0.0173860\pi\) | |||||||
\(542\) | 6.83257 | + | 11.8344i | 0.293484 | + | 0.508329i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.79434 | − | 1.03596i | −0.0769316 | − | 0.0444165i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.1182 | −0.518138 | −0.259069 | − | 0.965859i | \(-0.583416\pi\) | ||||
−0.259069 | + | 0.965859i | \(0.583416\pi\) | |||||||
\(548\) | −19.8185 | − | 11.4422i | −0.846606 | − | 0.488788i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.4571 | + | 25.0404i | −0.615892 | + | 1.06676i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.6772 | + | 43.0595i | −0.454040 | + | 1.83108i | ||||
\(554\) | − | 12.1298i | − | 0.515346i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.91427 | − | 4.56931i | 0.335640 | − | 0.193782i | ||||
\(557\) | −1.33331 | + | 0.769786i | −0.0564941 | + | 0.0326169i | −0.527981 | − | 0.849256i | \(-0.677051\pi\) |
0.471487 | + | 0.881873i | \(0.343717\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 48.5938i | − | 2.05530i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.3103 | + | 28.2503i | −0.688009 | + | 1.19167i | ||||
\(563\) | −11.2322 | − | 19.4548i | −0.473381 | − | 0.819920i | 0.526155 | − | 0.850389i | \(-0.323633\pi\) |
−0.999536 | + | 0.0304689i | \(0.990300\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −12.6609 | −0.532177 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.14126 | −0.383559 | ||||||||
\(569\) | 9.35810 | + | 5.40290i | 0.392312 | + | 0.226501i | 0.683161 | − | 0.730267i | \(-0.260605\pi\) |
−0.290849 | + | 0.956769i | \(0.593938\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.98169 | + | 6.89649i | 0.166629 | + | 0.288609i | 0.937232 | − | 0.348705i | \(-0.113379\pi\) |
−0.770604 | + | 0.637314i | \(0.780045\pi\) | |||||||
\(572\) | −6.80375 | + | 11.7844i | −0.284479 | + | 0.492732i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −18.0896 | − | 4.48555i | −0.755045 | − | 0.187223i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.2980 | − | 12.2964i | 0.886648 | − | 0.511906i | 0.0138033 | − | 0.999905i | \(-0.495606\pi\) |
0.872845 | + | 0.487998i | \(0.162273\pi\) | |||||||
\(578\) | −11.0047 | + | 6.35357i | −0.457735 | + | 0.264274i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −34.6066 | + | 9.97144i | −1.43573 | + | 0.413685i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.02242 | + | 8.69908i | −0.208007 | + | 0.360279i | ||||
\(584\) | −0.541173 | − | 0.937339i | −0.0223939 | − | 0.0387874i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.7503 | + | 12.5576i | 0.898498 | + | 0.518748i | ||||
\(587\) | −12.8469 | −0.530248 | −0.265124 | − | 0.964214i | \(-0.585413\pi\) | ||||
−0.265124 | + | 0.964214i | \(0.585413\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.7696 | −1.10302 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.48455 | − | 2.57132i | −0.0610148 | − | 0.105681i | ||||
\(593\) | −8.58155 | + | 14.8637i | −0.352402 | + | 0.610379i | −0.986670 | − | 0.162735i | \(-0.947968\pi\) |
0.634268 | + | 0.773114i | \(0.281302\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.4506i | 0.428075i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.15340 | − | 5.28472i | 0.374310 | − | 0.216108i | ||||
\(599\) | −16.9813 | + | 9.80416i | −0.693837 | + | 0.400587i | −0.805048 | − | 0.593210i | \(-0.797860\pi\) |
0.111211 | + | 0.993797i | \(0.464527\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 28.2340i | − | 1.15169i | −0.817560 | − | 0.575844i | \(-0.804674\pi\) | ||
0.817560 | − | 0.575844i | \(-0.195326\pi\) | |||||||
\(602\) | 21.9808 | + | 5.45043i | 0.895870 | + | 0.222143i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.85937 | + | 15.3449i | −0.360483 | + | 0.624374i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.35987 | + | 4.82657i | 0.339316 | + | 0.195904i | 0.659970 | − | 0.751292i | \(-0.270569\pi\) |
−0.320653 | + | 0.947197i | \(0.603902\pi\) | |||||||
\(608\) | 5.91397 | 0.239843 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.4285 | − | 15.8359i | −1.10964 | − | 0.640650i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.52794 | − | 7.84262i | −0.182882 | − | 0.316761i | 0.759979 | − | 0.649948i | \(-0.225209\pi\) |
−0.942861 | + | 0.333187i | \(0.891876\pi\) | |||||||
\(614\) | −9.28370 | + | 16.0798i | −0.374660 | + | 0.648930i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.56742 | − | 4.39937i | −0.184026 | − | 0.177256i | ||||
\(617\) | − | 25.3122i | − | 1.01903i | −0.860462 | − | 0.509515i | \(-0.829825\pi\) | ||
0.860462 | − | 0.509515i | \(-0.170175\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.6634 | + | 19.4356i | −1.35304 | + | 0.781181i | −0.988675 | − | 0.150073i | \(-0.952049\pi\) |
−0.364370 | + | 0.931254i | \(0.618716\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.4366i | 0.498663i | ||||||||
\(623\) | 8.44516 | − | 34.0581i | 0.338348 | − | 1.36451i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.20675 | − | 10.7504i | −0.248072 | − | 0.429673i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.26801 | + | 3.04149i | 0.210216 | + | 0.121369i | ||||
\(629\) | 6.15177 | 0.245287 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.8670 | −0.950129 | −0.475065 | − | 0.879951i | \(-0.657575\pi\) | ||||
−0.475065 | + | 0.879951i | \(0.657575\pi\) | |||||||
\(632\) | 14.5214 | + | 8.38392i | 0.577629 | + | 0.333494i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.3232 | − | 21.3444i | −0.489417 | − | 0.847696i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.1455 | + | 33.6472i | 0.837816 | + | 1.33315i | ||||
\(638\) | − | 11.7187i | − | 0.463949i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.2066 | + | 17.4398i | −1.19309 | + | 0.688830i | −0.959006 | − | 0.283386i | \(-0.908542\pi\) |
−0.234083 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.25944i | 0.246848i | 0.992354 | + | 0.123424i | \(0.0393875\pi\) | ||||
−0.992354 | + | 0.123424i | \(0.960612\pi\) | |||||||
\(644\) | 1.36380 | + | 4.73317i | 0.0537413 | + | 0.186513i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.12664 | + | 10.6117i | −0.241050 | + | 0.417510i | ||||
\(647\) | −18.7511 | − | 32.4778i | −0.737181 | − | 1.27683i | −0.953760 | − | 0.300570i | \(-0.902823\pi\) |
0.216579 | − | 0.976265i | \(-0.430510\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.16451 | − | 2.40438i | −0.163471 | − | 0.0943801i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.937339 | −0.0367090 | ||||||||
\(653\) | −22.9077 | − | 13.2258i | −0.896449 | − | 0.517565i | −0.0204023 | − | 0.999792i | \(-0.506495\pi\) |
−0.876046 | + | 0.482227i | \(0.839828\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.52214 | + | 6.10053i | −0.137516 | + | 0.238186i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 10.2396 | − | 10.6307i | 0.399182 | − | 0.414430i | ||||
\(659\) | 19.9524i | 0.777234i | 0.921399 | + | 0.388617i | \(0.127047\pi\) | ||||
−0.921399 | + | 0.388617i | \(0.872953\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.71203 | − | 2.72049i | 0.183277 | − | 0.105815i | −0.405555 | − | 0.914071i | \(-0.632922\pi\) |
0.588831 | + | 0.808256i | \(0.299588\pi\) | |||||||
\(662\) | −21.7871 | + | 12.5788i | −0.846779 | + | 0.488888i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.6122i | 0.528257i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.55118 | + | 7.88287i | −0.176222 | + | 0.305226i | ||||
\(668\) | 8.60505 | + | 14.9044i | 0.332939 | + | 0.576668i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.8528 | 1.15245 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.50635 | 0.327896 | 0.163948 | − | 0.986469i | \(-0.447577\pi\) | ||||
0.163948 | + | 0.986469i | \(0.447577\pi\) | |||||||
\(674\) | −12.4893 | − | 7.21070i | −0.481070 | − | 0.277746i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.61494 | − | 16.6536i | −0.369805 | − | 0.640522i | ||||
\(677\) | 2.54320 | − | 4.40495i | 0.0977430 | − | 0.169296i | −0.813007 | − | 0.582254i | \(-0.802171\pi\) |
0.910750 | + | 0.412958i | \(0.135504\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.39552 | − | 32.6079i | −0.360567 | − | 1.25138i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.39601 | − | 5.42479i | 0.359792 | − | 0.207726i | ||||
\(683\) | 18.1991 | − | 10.5073i | 0.696370 | − | 0.402050i | −0.109624 | − | 0.993973i | \(-0.534965\pi\) |
0.805994 | + | 0.591924i | \(0.201631\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −17.5916 | + | 5.79094i | −0.671651 | + | 0.221099i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.27978 | − | 7.41279i | 0.163165 | − | 0.282610i | ||||
\(689\) | −11.8958 | − | 20.6041i | −0.453193 | − | 0.784953i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.5723 | − | 12.4548i | −0.820649 | − | 0.473802i | 0.0299912 | − | 0.999550i | \(-0.490452\pi\) |
−0.850640 | + | 0.525748i | \(0.823785\pi\) | |||||||
\(692\) | −1.97623 | −0.0751249 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.4866 | −0.549903 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.29761 | − | 12.6398i | −0.276417 | − | 0.478767i | ||||
\(698\) | 1.06241 | − | 1.84015i | 0.0402129 | − | 0.0696508i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 22.5321i | − | 0.851025i | −0.904953 | − | 0.425512i | \(-0.860094\pi\) | ||
0.904953 | − | 0.425512i | \(-0.139906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.2067 | + | 8.77961i | −0.573532 | + | 0.331129i | ||||
\(704\) | −2.07577 | + | 1.19845i | −0.0782336 | + | 0.0451682i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 14.5267i | − | 0.546719i | ||||||
\(707\) | 16.9813 | + | 16.3565i | 0.638647 | + | 0.615150i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.4504 | − | 21.5648i | 0.467586 | − | 0.809882i | −0.531728 | − | 0.846915i | \(-0.678457\pi\) |
0.999314 | + | 0.0370327i | \(0.0117906\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.4857 | − | 6.63129i | −0.430446 | − | 0.248518i | ||||
\(713\) | −8.42726 | −0.315603 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.768461 | + | 0.443671i | 0.0287187 | + | 0.0165808i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.97485 | + | 3.42054i | 0.0737007 | + | 0.127653i | ||||
\(719\) | 19.9241 | − | 34.5096i | 0.743045 | − | 1.28699i | −0.208057 | − | 0.978117i | \(-0.566714\pi\) |
0.951103 | − | 0.308875i | \(-0.0999526\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.7850 | − | 6.88967i | −1.03477 | − | 0.256585i | ||||
\(722\) | − | 15.9750i | − | 0.594527i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.24329 | + | 2.44986i | −0.157701 | + | 0.0910485i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.124004i | 0.00459906i | 0.999997 | + | 0.00229953i | \(0.000731964\pi\) | ||||
−0.999997 | + | 0.00229953i | \(0.999268\pi\) | |||||||
\(728\) | 14.4331 | − | 4.15870i | 0.534926 | − | 0.154132i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.86738 | + | 15.3587i | 0.327972 | + | 0.568064i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.7231 | − | 14.2739i | −0.913168 | − | 0.527218i | −0.0317189 | − | 0.999497i | \(-0.510098\pi\) |
−0.881449 | + | 0.472279i | \(0.843431\pi\) | |||||||
\(734\) | −27.6927 | −1.02216 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.86175 | 0.0686252 | ||||||||
\(737\) | 15.8220 | + | 9.13483i | 0.582811 | + | 0.336486i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.51807 | − | 16.4858i | −0.350128 | − | 0.606439i | 0.636144 | − | 0.771571i | \(-0.280529\pi\) |
−0.986272 | + | 0.165131i | \(0.947195\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.6543 | − | 3.06989i | 0.391131 | − | 0.112699i | ||||
\(743\) | 17.0800i | 0.626605i | 0.949653 | + | 0.313303i | \(0.101435\pi\) | ||||
−0.949653 | + | 0.313303i | \(0.898565\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10.5047 | + | 6.06491i | −0.384605 | + | 0.222052i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 4.96618i | − | 0.181582i | ||||||
\(749\) | −14.3218 | − | 3.55129i | −0.523308 | − | 0.129761i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.44463 | − | 14.6265i | 0.308149 | − | 0.533730i | −0.669809 | − | 0.742534i | \(-0.733624\pi\) |
0.977957 | + | 0.208804i | \(0.0669572\pi\) | |||||||
\(752\) | −2.78941 | − | 4.83140i | −0.101719 | − | 0.176183i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 24.0376 | + | 13.8781i | 0.875399 | + | 0.505412i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.4057 | 1.21415 | 0.607076 | − | 0.794644i | \(-0.292342\pi\) | ||||
0.607076 | + | 0.794644i | \(0.292342\pi\) | |||||||
\(758\) | −16.1792 | − | 9.34106i | −0.587655 | − | 0.339282i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.3074 | + | 28.2453i | −0.591143 | + | 1.02389i | 0.402935 | + | 0.915228i | \(0.367990\pi\) |
−0.994079 | + | 0.108662i | \(0.965343\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.81111 | + | 3.67089i | 0.137971 | + | 0.132895i | ||||
\(764\) | − | 2.82843i | − | 0.102329i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.55162 | − | 5.51463i | 0.345114 | − | 0.199252i | ||||
\(767\) | 9.86379 | − | 5.69486i | 0.356161 | − | 0.205630i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.4396i | 0.809192i | 0.914495 | + | 0.404596i | \(0.132588\pi\) | ||||
−0.914495 | + | 0.404596i | \(0.867412\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.74828 | + | 16.8845i | −0.350848 | + | 0.607687i | ||||
\(773\) | −19.9165 | − | 34.4965i | −0.716348 | − | 1.24075i | −0.962437 | − | 0.271505i | \(-0.912479\pi\) |
0.246089 | − | 0.969247i | \(-0.420855\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12.8260 | −0.460428 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34.3710 | 1.23226 | ||||||||
\(779\) | 36.0783 | + | 20.8298i | 1.29264 | + | 0.746306i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.9553 | − | 18.9752i | −0.392012 | − | 0.678985i | ||||
\(782\) | −1.92871 | + | 3.34062i | −0.0689704 | + | 0.119460i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.262276 | + | 6.99508i | 0.00936701 | + | 0.249824i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.4912 | − | 8.36649i | 0.516555 | − | 0.298233i | −0.218969 | − | 0.975732i | \(-0.570269\pi\) |
0.735524 | + | 0.677499i | \(0.236936\pi\) | |||||||
\(788\) | −23.5191 | + | 13.5788i | −0.837835 | + | 0.483724i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.6239 | − | 36.8711i | −0.377743 | − | 1.31099i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.3537 | + | 61.2344i | −1.25545 | + | 2.17450i | ||||
\(794\) | 15.5054 | + | 26.8561i | 0.550264 | + | 0.953086i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.00000 | + | 1.73205i | 0.106332 | + | 0.0613909i | ||||
\(797\) | −2.68812 | −0.0952182 | −0.0476091 | − | 0.998866i | \(-0.515160\pi\) | ||||
−0.0476091 | + | 0.998866i | \(0.515160\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.5589 | 0.408924 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.73872 | − | 8.20771i | −0.167330 | − | 0.289824i | ||||
\(803\) | 1.29714 | − | 2.24670i | 0.0457749 | − | 0.0792845i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 25.6976i | 0.905161i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.71756 | − | 4.45573i | 0.271503 | − | 0.156752i | ||||
\(809\) | −27.2213 | + | 15.7162i | −0.957051 | + | 0.552554i | −0.895264 | − | 0.445536i | \(-0.853013\pi\) |
−0.0617867 | + | 0.998089i | \(0.519680\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 49.3830i | − | 1.73407i | −0.498246 | − | 0.867036i | \(-0.666022\pi\) | ||
0.498246 | − | 0.867036i | \(-0.333978\pi\) | |||||||
\(812\) | −8.97374 | + | 9.31651i | −0.314916 | + | 0.326945i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.55832 | − | 6.16320i | 0.124719 | − | 0.216020i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −43.8390 | − | 25.3105i | −1.53373 | − | 0.885501i | ||||
\(818\) | 9.47784 | 0.331385 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.7342 | + | 22.3632i | 1.35183 | + | 0.780480i | 0.988506 | − | 0.151182i | \(-0.0483080\pi\) |
0.363325 | + | 0.931662i | \(0.381641\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.57071 | + | 11.3808i | 0.229041 | + | 0.396710i | 0.957524 | − | 0.288353i | \(-0.0931078\pi\) |
−0.728483 | + | 0.685063i | \(0.759774\pi\) | |||||||
\(824\) | −5.40989 | + | 9.37021i | −0.188463 | + | 0.326427i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.46965 | + | 5.10052i | 0.0511355 | + | 0.177470i | ||||
\(827\) | − | 47.4125i | − | 1.64869i | −0.566086 | − | 0.824346i | \(-0.691543\pi\) | ||
0.566086 | − | 0.824346i | \(-0.308457\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.11516 | + | 4.10794i | −0.247120 | + | 0.142675i | −0.618445 | − | 0.785828i | \(-0.712237\pi\) |
0.371325 | + | 0.928503i | \(0.378904\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 5.67714i | − | 0.196819i | ||||||
\(833\) | −12.8233 | − | 6.77603i | −0.444300 | − | 0.234775i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.08758 | + | 12.2760i | 0.245129 | + | 0.424576i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.20356 | − | 1.27223i | −0.0761208 | − | 0.0439483i | ||||
\(839\) | 17.6943 | 0.610875 | 0.305437 | − | 0.952212i | \(-0.401197\pi\) | ||||
0.305437 | + | 0.952212i | \(0.401197\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.09640 | 0.175738 | ||||||||
\(842\) | 4.40437 | + | 2.54286i | 0.151785 | + | 0.0876328i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.03035 | − | 3.51668i | −0.0698877 | − | 0.121049i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.34613 | + | 13.4945i | −0.114975 | + | 0.463675i | ||||
\(848\) | − | 4.19077i | − | 0.143912i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.78717 | + | 2.76388i | −0.164102 | + | 0.0947444i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 40.1129i | − | 1.37344i | −0.726922 | − | 0.686720i | \(-0.759050\pi\) | ||
0.726922 | − | 0.686720i | \(-0.240950\pi\) | |||||||
\(854\) | −23.7333 | − | 22.8601i | −0.812135 | − | 0.782255i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.78854 | + | 4.82989i | −0.0953102 | + | 0.165082i | ||||
\(857\) | −22.0654 | − | 38.2184i | −0.753740 | − | 1.30552i | −0.945998 | − | 0.324171i | \(-0.894915\pi\) |
0.192259 | − | 0.981344i | \(-0.438419\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.4339 | + | 7.17873i | 0.424240 | + | 0.244935i | 0.696890 | − | 0.717178i | \(-0.254567\pi\) |
−0.272650 | + | 0.962113i | \(0.587900\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.2980 | 0.452933 | ||||||||
\(863\) | −11.0876 | − | 6.40143i | −0.377426 | − | 0.217907i | 0.299272 | − | 0.954168i | \(-0.403256\pi\) |
−0.676698 | + | 0.736261i | \(0.736590\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.39477 | − | 11.0761i | 0.217303 | − | 0.376380i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.6240 | − | 2.88233i | −0.394544 | − | 0.0978326i | ||||
\(869\) | 40.1908i | 1.36338i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.4750 | + | 21.6362i | −1.26979 | + | 0.733114i | ||||
\(872\) | 1.73205 | − | 1.00000i | 0.0586546 | − | 0.0338643i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 11.0103i | − | 0.372431i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.1360 | + | 50.4650i | −0.983853 | + | 1.70408i | −0.336925 | + | 0.941532i | \(0.609387\pi\) |
−0.646928 | + | 0.762551i | \(0.723947\pi\) | |||||||
\(878\) | 0.186606 | + | 0.323211i | 0.00629765 | + | 0.0109079i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.80667 | 0.0608682 | 0.0304341 | − | 0.999537i | \(-0.490311\pi\) | ||||
0.0304341 | + | 0.999537i | \(0.490311\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.8997 | 0.467761 | 0.233881 | − | 0.972265i | \(-0.424858\pi\) | ||||
0.233881 | + | 0.972265i | \(0.424858\pi\) | |||||||
\(884\) | 10.1867 | + | 5.88130i | 0.342616 | + | 0.197809i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.3165 | − | 21.3328i | −0.413781 | − | 0.716690i | ||||
\(887\) | −13.2459 | + | 22.9426i | −0.444754 | + | 0.770337i | −0.998035 | − | 0.0626581i | \(-0.980042\pi\) |
0.553281 | + | 0.832995i | \(0.313376\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 48.9301 | − | 14.0985i | 1.64106 | − | 0.472850i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.9851 | − | 8.07432i | 0.468257 | − | 0.270348i | ||||
\(893\) | −28.5727 | + | 16.4965i | −0.956150 | + | 0.552033i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.56798 | + | 0.636766i | 0.0857902 | + | 0.0212728i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.3111 | + | 35.1799i | −0.677792 | + | 1.17397i | ||||
\(899\) | −11.0654 | − | 19.1658i | −0.369050 | − | 0.639214i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.51966 | + | 4.34148i | 0.250516 | + | 0.144636i | ||||
\(902\) | −16.8844 | −0.562189 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.5030 | −0.482361 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.3650 | − | 31.8091i | −0.609800 | − | 1.05620i | −0.991273 | − | 0.131824i | \(-0.957917\pi\) |
0.381474 | − | 0.924380i | \(-0.375417\pi\) | |||||||
\(908\) | −0.839901 | + | 1.45475i | −0.0278731 | + | 0.0482776i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 39.8018i | − | 1.31869i | −0.751839 | − | 0.659347i | \(-0.770833\pi\) | ||
0.751839 | − | 0.659347i | \(-0.229167\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.2559 | + | 16.3135i | −0.935134 | + | 0.539900i | ||||
\(914\) | −0.857843 | + | 0.495276i | −0.0283749 | + | 0.0163823i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.6027i | 0.416406i | ||||||||
\(917\) | −2.99242 | + | 12.0680i | −0.0988184 | + | 0.398520i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.1692 | + | 52.2545i | −0.995189 | + | 1.72372i | −0.412747 | + | 0.910846i | \(0.635430\pi\) |
−0.582442 | + | 0.812872i | \(0.697903\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17.9611 | + | 10.3699i | 0.591518 | + | 0.341513i | ||||
\(923\) | 51.8962 | 1.70818 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.26804 | − | 0.732105i | −0.0416705 | − | 0.0240585i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.44457 | + | 4.23411i | 0.0802468 | + | 0.138992i | ||||
\(929\) | −22.1749 | + | 38.4080i | −0.727533 | + | 1.26012i | 0.230389 | + | 0.973099i | \(0.426000\pi\) |
−0.957923 | + | 0.287026i | \(0.907333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 41.3687 | − | 1.55109i | 1.35580 | − | 0.0508350i | ||||
\(932\) | 14.5164i | 0.475499i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 31.4090 | − | 18.1340i | 1.02774 | − | 0.593363i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.54073i | − | 0.0830021i | −0.999138 | − | 0.0415010i | \(-0.986786\pi\) | ||
0.999138 | − | 0.0415010i | \(-0.0132140\pi\) | |||||||
\(938\) | −5.58355 | − | 19.3781i | −0.182309 | − | 0.632718i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.9488 | − | 29.3563i | −0.552516 | − | 0.956987i | −0.998092 | − | 0.0617423i | \(-0.980334\pi\) |
0.445576 | − | 0.895244i | \(-0.352999\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.3577 | + | 6.55736i | 0.369857 | + | 0.213537i | ||||
\(944\) | 2.00624 | 0.0652977 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.5164 | 0.667045 | ||||||||
\(947\) | 42.8759 | + | 24.7544i | 1.39328 | + | 0.804411i | 0.993677 | − | 0.112277i | \(-0.0358145\pi\) |
0.399604 | + | 0.916688i | \(0.369148\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.07231 | + | 5.32140i | 0.0997315 | + | 0.172740i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.80290 | + | 3.94816i | −0.123253 | + | 0.127961i | ||||
\(953\) | 17.0625i | 0.552709i | 0.961056 | + | 0.276355i | \(0.0891264\pi\) | ||||
−0.961056 | + | 0.276355i | \(0.910874\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.179344 | − | 0.103545i | 0.00580041 | − | 0.00334887i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 10.3258i | − | 0.333610i | ||||||
\(959\) | −42.0032 | + | 43.6076i | −1.35636 | + | 1.40816i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.25533 | + | 9.10250i | −0.169527 | + | 0.293629i | ||||
\(962\) | 8.42802 | + | 14.5978i | 0.271730 | + | 0.470651i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.04172 | + | 5.22024i | 0.291214 | + | 0.168133i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.6639 | −1.59708 | −0.798541 | − | 0.601940i | \(-0.794394\pi\) | ||||
−0.798541 | + | 0.601940i | \(0.794394\pi\) | |||||||
\(968\) | 4.55087 | + | 2.62745i | 0.146270 | + | 0.0844493i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.2930 | − | 24.7561i | 0.458683 | − | 0.794462i | −0.540209 | − | 0.841531i | \(-0.681655\pi\) |
0.998892 | + | 0.0470689i | \(0.0149880\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.69436 | − | 23.2333i | −0.214611 | − | 0.744825i | ||||
\(974\) | 20.3291i | 0.651386i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.7862 | + | 6.22739i | −0.345256 | + | 0.199334i | ||||
\(977\) | −24.0067 | + | 13.8603i | −0.768042 | + | 0.443429i | −0.832176 | − | 0.554512i | \(-0.812905\pi\) |
0.0641335 | + | 0.997941i | \(0.479572\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 31.7890i | − | 1.01598i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.3017 | − | 29.9674i | 0.552119 | − | 0.956298i | ||||
\(983\) | −21.4134 | − | 37.0891i | −0.682982 | − | 1.18296i | −0.974067 | − | 0.226262i | \(-0.927350\pi\) |
0.291085 | − | 0.956697i | \(-0.405984\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −10.1299 | −0.322602 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −33.5744 | −1.06814 | ||||||||
\(989\) | −13.8008 | − | 7.96789i | −0.438840 | − | 0.253364i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.3723 | − | 37.0179i | −0.678914 | − | 1.17591i | −0.975308 | − | 0.220848i | \(-0.929118\pi\) |
0.296394 | − | 0.955066i | \(-0.404216\pi\) | |||||||
\(992\) | −2.26326 | + | 3.92008i | −0.0718585 | + | 0.124463i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.82084 | + | 23.4746i | −0.184626 | + | 0.744568i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.4679 | − | 16.4359i | 0.901587 | − | 0.520531i | 0.0238722 | − | 0.999715i | \(-0.492401\pi\) |
0.877715 | + | 0.479184i | \(0.159067\pi\) | |||||||
\(998\) | −2.55555 | + | 1.47545i | −0.0808945 | + | 0.0467045i | ||||
\(999\) | 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 | 3150.2.bf.f.1601.2 | 32 | ||
3.2 | odd | 2 | inner | 3150.2.bf.f.1601.12 | 32 | ||
5.2 | odd | 4 | 630.2.bo.b.89.5 | yes | 16 | ||
5.3 | odd | 4 | 630.2.bo.a.89.7 | yes | 16 | ||
5.4 | even | 2 | inner | 3150.2.bf.f.1601.11 | 32 | ||
7.3 | odd | 6 | inner | 3150.2.bf.f.1151.12 | 32 | ||
15.2 | even | 4 | 630.2.bo.a.89.4 | ✓ | 16 | ||
15.8 | even | 4 | 630.2.bo.b.89.2 | yes | 16 | ||
15.14 | odd | 2 | inner | 3150.2.bf.f.1601.1 | 32 | ||
21.17 | even | 6 | inner | 3150.2.bf.f.1151.2 | 32 | ||
35.2 | odd | 12 | 4410.2.d.a.4409.2 | 16 | |||
35.3 | even | 12 | 630.2.bo.a.269.4 | yes | 16 | ||
35.12 | even | 12 | 4410.2.d.a.4409.15 | 16 | |||
35.17 | even | 12 | 630.2.bo.b.269.2 | yes | 16 | ||
35.23 | odd | 12 | 4410.2.d.b.4409.1 | 16 | |||
35.24 | odd | 6 | inner | 3150.2.bf.f.1151.1 | 32 | ||
35.33 | even | 12 | 4410.2.d.b.4409.16 | 16 | |||
105.2 | even | 12 | 4410.2.d.b.4409.15 | 16 | |||
105.17 | odd | 12 | 630.2.bo.a.269.7 | yes | 16 | ||
105.23 | even | 12 | 4410.2.d.a.4409.16 | 16 | |||
105.38 | odd | 12 | 630.2.bo.b.269.5 | yes | 16 | ||
105.47 | odd | 12 | 4410.2.d.b.4409.2 | 16 | |||
105.59 | even | 6 | inner | 3150.2.bf.f.1151.11 | 32 | ||
105.68 | odd | 12 | 4410.2.d.a.4409.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.bo.a.89.4 | ✓ | 16 | 15.2 | even | 4 | ||
630.2.bo.a.89.7 | yes | 16 | 5.3 | odd | 4 | ||
630.2.bo.a.269.4 | yes | 16 | 35.3 | even | 12 | ||
630.2.bo.a.269.7 | yes | 16 | 105.17 | odd | 12 | ||
630.2.bo.b.89.2 | yes | 16 | 15.8 | even | 4 | ||
630.2.bo.b.89.5 | yes | 16 | 5.2 | odd | 4 | ||
630.2.bo.b.269.2 | yes | 16 | 35.17 | even | 12 | ||
630.2.bo.b.269.5 | yes | 16 | 105.38 | odd | 12 | ||
3150.2.bf.f.1151.1 | 32 | 35.24 | odd | 6 | inner | ||
3150.2.bf.f.1151.2 | 32 | 21.17 | even | 6 | inner | ||
3150.2.bf.f.1151.11 | 32 | 105.59 | even | 6 | inner | ||
3150.2.bf.f.1151.12 | 32 | 7.3 | odd | 6 | inner | ||
3150.2.bf.f.1601.1 | 32 | 15.14 | odd | 2 | inner | ||
3150.2.bf.f.1601.2 | 32 | 1.1 | even | 1 | trivial | ||
3150.2.bf.f.1601.11 | 32 | 5.4 | even | 2 | inner | ||
3150.2.bf.f.1601.12 | 32 | 3.2 | odd | 2 | inner | ||
4410.2.d.a.4409.1 | 16 | 105.68 | odd | 12 | |||
4410.2.d.a.4409.2 | 16 | 35.2 | odd | 12 | |||
4410.2.d.a.4409.15 | 16 | 35.12 | even | 12 | |||
4410.2.d.a.4409.16 | 16 | 105.23 | even | 12 | |||
4410.2.d.b.4409.1 | 16 | 35.23 | odd | 12 | |||
4410.2.d.b.4409.2 | 16 | 105.47 | odd | 12 | |||
4410.2.d.b.4409.15 | 16 | 105.2 | even | 12 | |||
4410.2.d.b.4409.16 | 16 | 35.33 | even | 12 |