Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,2,Mod(97,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.i (of order \(3\), 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: | \(2.29969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.170772624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.4 | ||
Root | \(-1.02187 - 0.977642i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 288.193 |
Dual form | 288.2.i.f.97.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 1.35760 | + | 1.07561i | 0.783809 | + | 0.621002i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.18614 | + | 2.05446i | −0.530458 | + | 0.918781i | 0.468910 | + | 0.883246i | \(0.344647\pi\) |
−0.999368 | + | 0.0355348i | \(0.988687\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.10489 | + | 1.91373i | 0.417610 | + | 0.723322i | 0.995699 | − | 0.0926519i | \(-0.0295344\pi\) |
−0.578088 | + | 0.815974i | \(0.696201\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.686141 | + | 2.92048i | 0.228714 | + | 0.973494i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.96790 | − | 5.14055i | −0.894855 | − | 1.54993i | −0.833984 | − | 0.551789i | \(-0.813945\pi\) |
−0.0608712 | − | 0.998146i | \(-0.519388\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.18614 | + | 3.78651i | −0.606326 | + | 1.05019i | 0.385514 | + | 0.922702i | \(0.374024\pi\) |
−0.991840 | + | 0.127486i | \(0.959309\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.82009 | + | 1.51330i | −0.986342 | + | 0.390733i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.37228 | 0.817898 | 0.408949 | − | 0.912557i | \(-0.365895\pi\) | ||||
0.408949 | + | 0.912557i | \(0.365895\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.72601 | 0.854805 | 0.427403 | − | 0.904061i | \(-0.359429\pi\) | ||||
0.427403 | + | 0.904061i | \(0.359429\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.558422 | + | 3.78651i | −0.121858 | + | 0.826284i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.10489 | − | 1.91373i | 0.230386 | − | 0.399041i | −0.727536 | − | 0.686070i | \(-0.759334\pi\) |
0.957922 | + | 0.287029i | \(0.0926677\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.313859 | − | 0.543620i | −0.0627719 | − | 0.108724i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.20979 | + | 4.70285i | −0.425274 | + | 0.905065i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.186141 | − | 0.322405i | −0.0345655 | − | 0.0598691i | 0.848225 | − | 0.529636i | \(-0.177671\pi\) |
−0.882791 | + | 0.469767i | \(0.844338\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.83090 | − | 8.36737i | 0.867656 | − | 1.50282i | 0.00327038 | − | 0.999995i | \(-0.498959\pi\) |
0.864386 | − | 0.502830i | \(-0.167708\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.50000 | − | 10.1711i | 0.261116 | − | 1.77056i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.24224 | −0.886099 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.04069 | + | 2.78912i | −1.12741 | + | 0.446617i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.500000 | + | 0.866025i | −0.0780869 | + | 0.135250i | −0.902424 | − | 0.430848i | \(-0.858214\pi\) |
0.824338 | + | 0.566099i | \(0.191548\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.96790 | + | 5.14055i | 0.452600 | + | 0.783927i | 0.998547 | − | 0.0538934i | \(-0.0171631\pi\) |
−0.545946 | + | 0.837820i | \(0.683830\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.81386 | − | 2.05446i | −1.01575 | − | 0.306260i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.10489 | + | 1.91373i | 0.161165 | + | 0.279146i | 0.935287 | − | 0.353891i | \(-0.115141\pi\) |
−0.774122 | + | 0.633037i | \(0.781808\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.05842 | − | 1.83324i | 0.151203 | − | 0.261892i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.57820 | + | 3.62725i | 0.641076 | + | 0.507916i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.00000 | −0.549442 | −0.274721 | − | 0.961524i | \(-0.588586\pi\) | ||||
−0.274721 | + | 0.961524i | \(0.588586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.0814 | 1.89873 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.05842 | + | 4.00772i | 0.670004 | + | 0.530836i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.17769 | − | 8.96801i | 0.674077 | − | 1.16754i | −0.302661 | − | 0.953098i | \(-0.597875\pi\) |
0.976738 | − | 0.214437i | \(-0.0687918\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.55842 | − | 13.0916i | −0.967757 | − | 1.67620i | −0.702019 | − | 0.712159i | \(-0.747718\pi\) |
−0.265738 | − | 0.964045i | \(-0.585616\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.83090 | + | 4.53991i | −0.608637 | + | 0.571975i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.18614 | − | 8.98266i | −0.643262 | − | 1.11416i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.17769 | + | 8.96801i | −0.632555 | + | 1.09562i | 0.354473 | + | 0.935066i | \(0.384660\pi\) |
−0.987028 | + | 0.160551i | \(0.948673\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.55842 | − | 1.40965i | 0.428384 | − | 0.169701i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.41957 | −0.524507 | −0.262253 | − | 0.964999i | \(-0.584466\pi\) | ||||
−0.262253 | + | 0.964999i | \(0.584466\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.62772 | 0.541634 | 0.270817 | − | 0.962631i | \(-0.412706\pi\) | ||||
0.270817 | + | 0.962631i | \(0.412706\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.158627 | − | 1.07561i | 0.0183167 | − | 0.124200i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.55842 | − | 11.3595i | 0.747402 | − | 1.29454i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.83090 | − | 8.36737i | −0.543519 | − | 0.941403i | −0.998698 | − | 0.0510030i | \(-0.983758\pi\) |
0.455179 | − | 0.890400i | \(-0.349575\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.05842 | + | 4.00772i | −0.895380 | + | 0.445302i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.04069 | − | 12.1948i | −0.772816 | − | 1.33856i | −0.936014 | − | 0.351963i | \(-0.885514\pi\) |
0.163198 | − | 0.986593i | \(-0.447819\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | + | 6.92820i | −0.433861 | + | 0.751469i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.0940770 | − | 0.637910i | 0.0100861 | − | 0.0683912i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.25544 | 0.133076 | 0.0665380 | − | 0.997784i | \(-0.478805\pi\) | ||||
0.0665380 | + | 0.997784i | \(0.478805\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.66181 | −1.01283 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.5584 | − | 6.16337i | 1.61333 | − | 0.639111i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.41957 | + | 7.65492i | −0.453439 | + | 0.785379i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.50000 | − | 7.79423i | −0.456906 | − | 0.791384i | 0.541890 | − | 0.840450i | \(-0.317709\pi\) |
−0.998796 | + | 0.0490655i | \(0.984376\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.9765 | − | 12.1948i | 1.30419 | − | 1.22563i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.55842 | + | 13.0916i | 0.752091 | + | 1.30266i | 0.946808 | + | 0.321800i | \(0.104288\pi\) |
−0.194716 | + | 0.980860i | \(0.562379\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.10489 | + | 1.91373i | −0.108868 | + | 0.188566i | −0.915312 | − | 0.402745i | \(-0.868056\pi\) |
0.806444 | + | 0.591311i | \(0.201389\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.11684 | − | 5.63858i | −0.694533 | − | 0.550269i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.72601 | 0.360207 | 0.180104 | − | 0.983648i | \(-0.442357\pi\) | ||||
0.180104 | + | 0.983648i | \(0.442357\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.4891 | 1.67515 | 0.837577 | − | 0.546319i | \(-0.183971\pi\) | ||||
0.837577 | + | 0.546319i | \(0.183971\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.43039 | + | 4.30243i | 0.515430 | + | 0.408368i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.81386 | + | 10.0699i | −0.546922 | + | 0.947296i | 0.451561 | + | 0.892240i | \(0.350867\pi\) |
−0.998483 | + | 0.0550564i | \(0.982466\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.62112 | + | 4.53991i | 0.244420 | + | 0.423349i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.5584 | − | 3.78651i | −1.16103 | − | 0.350063i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.72601 | + | 6.45364i | 0.341563 | + | 0.591604i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.1168 | + | 20.9870i | −1.10153 | + | 1.90791i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.61030 | + | 0.637910i | −0.145196 | + | 0.0575184i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.3723 | −0.927725 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.45202 | −0.661260 | −0.330630 | − | 0.943760i | \(-0.607261\pi\) | ||||
−0.330630 | + | 0.943760i | \(0.607261\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.50000 | + | 10.1711i | −0.132068 | + | 0.895515i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.83090 | + | 8.36737i | −0.422078 | + | 0.731061i | −0.996143 | − | 0.0877494i | \(-0.972033\pi\) |
0.574065 | + | 0.818810i | \(0.305366\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.11684 | + | 7.13058i | 0.356976 | + | 0.618300i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.04069 | − | 10.1182i | −0.605966 | − | 0.870832i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.24456 | + | 10.8159i | 0.533509 | + | 0.924065i | 0.999234 | + | 0.0391351i | \(0.0124603\pi\) |
−0.465725 | + | 0.884930i | \(0.654206\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.45167 | − | 2.51437i | 0.123129 | − | 0.213266i | −0.797871 | − | 0.602829i | \(-0.794040\pi\) |
0.921000 | + | 0.389562i | \(0.127374\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.558422 | + | 3.78651i | −0.0470276 | + | 0.318881i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 25.9530 | 2.17030 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.883156 | 0.0733421 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.40876 | − | 1.35036i | 0.281150 | − | 0.111376i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.81386 | − | 10.0699i | 0.476290 | − | 0.824958i | −0.523341 | − | 0.852123i | \(-0.675315\pi\) |
0.999631 | + | 0.0271650i | \(0.00864795\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.10489 | − | 1.91373i | −0.0899149 | − | 0.155737i | 0.817560 | − | 0.575843i | \(-0.195326\pi\) |
−0.907475 | + | 0.420106i | \(0.861993\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.31386 | + | 9.84868i | 0.187064 | + | 0.796219i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.4603 | + | 19.8498i | 0.920510 | + | 1.59437i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.55842 | − | 2.69927i | 0.124376 | − | 0.215425i | −0.797113 | − | 0.603830i | \(-0.793641\pi\) |
0.921489 | + | 0.388405i | \(0.126974\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.43039 | − | 4.30243i | −0.430658 | − | 0.341205i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.88316 | 0.384847 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.83915 | −0.692335 | −0.346168 | − | 0.938173i | \(-0.612517\pi\) | ||||
−0.346168 | + | 0.938173i | \(0.612517\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 19.1168 | + | 15.1460i | 1.48824 | + | 1.17912i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.83090 | + | 8.36737i | −0.373827 | + | 0.647487i | −0.990151 | − | 0.140006i | \(-0.955288\pi\) |
0.616324 | + | 0.787493i | \(0.288621\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.05842 | − | 5.29734i | −0.235263 | − | 0.407488i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.55657 | + | 10.8817i | 0.195506 | + | 0.832148i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.186141 | + | 0.322405i | 0.0141520 | + | 0.0245120i | 0.873015 | − | 0.487694i | \(-0.162162\pi\) |
−0.858863 | + | 0.512206i | \(0.828828\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.693562 | − | 1.20128i | 0.0524284 | − | 0.0908086i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.6753 | − | 6.60580i | 1.25339 | − | 0.496522i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.83915 | −0.660669 | −0.330334 | − | 0.943864i | \(-0.607162\pi\) | ||||
−0.330334 | + | 0.943864i | \(0.607162\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.23369 | −0.612005 | −0.306003 | − | 0.952031i | \(-0.598992\pi\) | ||||
−0.306003 | + | 0.952031i | \(0.598992\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.82009 | − | 25.9030i | 0.282389 | − | 1.91480i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.74456 | + | 8.21782i | −0.348827 | + | 0.604186i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.0086 | − | 17.3354i | −0.731901 | − | 1.26769i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.4416 | + | 0.967215i | −0.832252 | + | 0.0703546i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.55691 | + | 14.8210i | 0.619157 | + | 1.07241i | 0.989640 | + | 0.143572i | \(0.0458587\pi\) |
−0.370483 | + | 0.928839i | \(0.620808\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.500000 | + | 0.866025i | −0.0359908 | + | 0.0623379i | −0.883460 | − | 0.468507i | \(-0.844792\pi\) |
0.847469 | + | 0.530845i | \(0.178125\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.62112 | − | 17.7731i | 0.187702 | − | 1.27276i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.744563 | 0.0530479 | 0.0265239 | − | 0.999648i | \(-0.491556\pi\) | ||||
0.0265239 | + | 0.999648i | \(0.491556\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.7107 | −1.46815 | −0.734073 | − | 0.679071i | \(-0.762383\pi\) | ||||
−0.734073 | + | 0.679071i | \(0.762383\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.6753 | + | 6.60580i | −1.17618 | + | 0.465937i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.411331 | − | 0.712446i | 0.0288698 | − | 0.0500039i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.18614 | − | 2.05446i | −0.0828437 | − | 0.143489i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.34713 | + | 1.91373i | 0.441156 | + | 0.133014i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.0584 | − | 19.1537i | −0.764927 | − | 1.32489i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.62112 | + | 4.53991i | −0.180445 | + | 0.312540i | −0.942032 | − | 0.335522i | \(-0.891087\pi\) |
0.761587 | + | 0.648063i | \(0.224421\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.00000 | − | 4.75372i | −0.411113 | − | 0.325720i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.0814 | −0.960342 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.3505 | 1.44937 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.28258 | + | 4.97760i | 0.424537 | + | 0.336355i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.37228 | + | 12.7692i | −0.495913 | + | 0.858947i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.10489 | + | 1.91373i | 0.0739891 | + | 0.128153i | 0.900646 | − | 0.434553i | \(-0.143094\pi\) |
−0.826657 | + | 0.562706i | \(0.809760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.37228 | − | 1.28962i | 0.0914854 | − | 0.0859747i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.48412 | + | 7.76673i | 0.297622 | + | 0.515496i | 0.975591 | − | 0.219594i | \(-0.0704733\pi\) |
−0.677970 | + | 0.735090i | \(0.737140\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.18614 | − | 3.78651i | 0.144464 | − | 0.250219i | −0.784709 | − | 0.619865i | \(-0.787187\pi\) |
0.929173 | + | 0.369645i | \(0.120521\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 21.1221 | − | 8.36737i | 1.38973 | − | 0.550533i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.86141 | 0.187457 | 0.0937285 | − | 0.995598i | \(-0.470121\pi\) | ||||
0.0937285 | + | 0.995598i | \(0.470121\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.24224 | −0.341966 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.44158 | − | 16.5557i | 0.158598 | − | 1.07541i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.55691 | − | 14.8210i | 0.553501 | − | 0.958692i | −0.444518 | − | 0.895770i | \(-0.646625\pi\) |
0.998018 | − | 0.0629214i | \(-0.0200418\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.127719 | − | 0.221215i | −0.00822708 | − | 0.0142497i | 0.861883 | − | 0.507108i | \(-0.169285\pi\) |
−0.870110 | + | 0.492858i | \(0.835952\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.2508 | − | 3.22682i | −0.978341 | − | 0.207001i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.51087 | + | 4.34896i | 0.160414 | + | 0.277845i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.14558 | + | 14.1086i | −0.518291 | + | 0.897706i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.55842 | − | 24.1287i | 0.225506 | − | 1.52909i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.1780 | 0.705551 | 0.352776 | − | 0.935708i | \(-0.385238\pi\) | ||||
0.352776 | + | 0.935708i | \(0.385238\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.1168 | −0.824649 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.8824 | + | 5.10328i | −0.806728 | + | 0.319580i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.24456 | − | 5.61975i | 0.202390 | − | 0.350550i | −0.746908 | − | 0.664928i | \(-0.768462\pi\) |
0.949298 | + | 0.314377i | \(0.101796\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.41957 | + | 7.65492i | 0.274619 | + | 0.475654i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.813859 | − | 0.764836i | 0.0503766 | − | 0.0473421i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.55691 | − | 14.8210i | −0.527642 | − | 0.913903i | −0.999481 | − | 0.0322179i | \(-0.989743\pi\) |
0.471839 | − | 0.881685i | \(-0.343590\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.74456 | − | 8.21782i | 0.291456 | − | 0.504817i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.70438 | + | 1.35036i | 0.104306 | + | 0.0826405i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.48913 | 0.578562 | 0.289281 | − | 0.957244i | \(-0.406584\pi\) | ||||
0.289281 | + | 0.957244i | \(0.406584\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.9040 | −0.905356 | −0.452678 | − | 0.891674i | \(-0.649531\pi\) | ||||
−0.452678 | + | 0.891674i | \(0.649531\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.1168 | − | 10.3923i | −0.793868 | − | 0.628971i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.86301 | + | 3.22682i | −0.112343 | + | 0.194585i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.55842 | − | 11.3595i | −0.394057 | − | 0.682527i | 0.598923 | − | 0.800807i | \(-0.295596\pi\) |
−0.992980 | + | 0.118279i | \(0.962262\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 27.7514 | + | 8.36737i | 1.66143 | + | 0.500941i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.9307 | − | 22.3966i | −0.771381 | − | 1.33607i | −0.936806 | − | 0.349849i | \(-0.886233\pi\) |
0.165425 | − | 0.986222i | \(-0.447100\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.62112 | − | 4.53991i | 0.155809 | − | 0.269870i | −0.777544 | − | 0.628828i | \(-0.783535\pi\) |
0.933353 | + | 0.358959i | \(0.116868\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14.2337 | + | 5.63858i | −0.843131 | + | 0.334001i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.20979 | −0.130440 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.62772 | −0.331042 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.27434 | − | 15.4217i | 0.133324 | − | 0.904033i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.1861 | − | 17.6429i | 0.595081 | − | 1.03071i | −0.398455 | − | 0.917188i | \(-0.630453\pi\) |
0.993535 | − | 0.113522i | \(-0.0362132\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.2829 | + | 21.2747i | 0.715140 | + | 1.23866i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 30.7337 | − | 2.59808i | 1.78335 | − | 0.150756i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.83090 | + | 8.36737i | 0.279378 | + | 0.483898i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.55842 | + | 11.3595i | −0.378021 | + | 0.654752i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.82009 | + | 25.9030i | −0.219458 | + | 1.48809i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 35.8614 | 2.05342 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.8563 | 1.64692 | 0.823459 | − | 0.567376i | \(-0.192041\pi\) | ||||
0.823459 | + | 0.567376i | \(0.192041\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.55842 | + | 1.40965i | −0.202432 | + | 0.0801919i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.34713 | + | 10.9935i | −0.359913 | + | 0.623387i | −0.987946 | − | 0.154800i | \(-0.950527\pi\) |
0.628033 | + | 0.778186i | \(0.283860\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.61684 | − | 16.6569i | −0.543576 | − | 0.941502i | −0.998695 | − | 0.0510708i | \(-0.983737\pi\) |
0.455119 | − | 0.890431i | \(-0.349597\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.59691 | − | 15.3098i | −0.202663 | − | 0.862612i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.18614 | − | 7.25061i | −0.235117 | − | 0.407235i | 0.724190 | − | 0.689601i | \(-0.242214\pi\) |
−0.959307 | + | 0.282366i | \(0.908881\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.10489 | + | 1.91373i | −0.0618621 | + | 0.107148i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.05842 | + | 4.00772i | 0.282334 | + | 0.223689i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.5652 | 0.699144 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.74456 | 0.152241 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 23.7432 | + | 18.8114i | 1.31300 | + | 1.04027i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.44158 | + | 4.22894i | −0.134609 | + | 0.233149i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.7025 | − | 28.9296i | −0.918052 | − | 1.59011i | −0.802370 | − | 0.596827i | \(-0.796428\pi\) |
−0.115682 | − | 0.993286i | \(-0.536905\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.74456 | + | 11.6819i | 0.150401 | + | 0.640166i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.2829 | − | 21.2747i | −0.671088 | − | 1.16236i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.50000 | − | 7.79423i | 0.245131 | − | 0.424579i | −0.717038 | − | 0.697034i | \(-0.754502\pi\) |
0.962168 | + | 0.272456i | \(0.0878358\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.7241 | + | 7.41744i | −1.01696 | + | 0.402860i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −57.3505 | −3.10571 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1463 | 1.08780 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.32473 | + | 8.98266i | −0.0713213 | + | 0.483610i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.17769 | + | 8.96801i | −0.277953 | + | 0.481428i | −0.970876 | − | 0.239583i | \(-0.922989\pi\) |
0.692923 | + | 0.721011i | \(0.256323\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.5584 | + | 20.0198i | 0.618708 | + | 1.07163i | 0.989722 | + | 0.143007i | \(0.0456770\pi\) |
−0.371014 | + | 0.928627i | \(0.620990\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.9765 | − | 18.6485i | −0.692634 | − | 0.995382i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.61684 | + | 16.6569i | 0.511853 | + | 0.886555i | 0.999906 | + | 0.0137411i | \(0.00437407\pi\) |
−0.488053 | + | 0.872814i | \(0.662293\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.24224 | − | 9.07982i | 0.278229 | − | 0.481907i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.88316 | + | 12.7692i | −0.0996672 | + | 0.675816i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.3561 | −1.17991 | −0.589954 | − | 0.807437i | \(-0.700854\pi\) | ||||
−0.589954 | + | 0.807437i | \(0.700854\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.11684 | −0.269308 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −39.0235 | + | 15.4589i | −2.04820 | + | 0.811383i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.48913 | + | 9.50744i | −0.287314 | + | 0.497642i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.6700 | − | 23.6772i | −0.713571 | − | 1.23594i | −0.963508 | − | 0.267679i | \(-0.913743\pi\) |
0.249937 | − | 0.968262i | \(-0.419590\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.87228 | − | 0.866025i | −0.149525 | − | 0.0450835i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.41957 | − | 7.65492i | −0.229453 | − | 0.397424i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.55842 | − | 14.8236i | 0.443138 | − | 0.767538i | −0.554782 | − | 0.831996i | \(-0.687198\pi\) |
0.997920 | + | 0.0644576i | \(0.0205317\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.0814 | − | 11.1565i | −0.727159 | − | 0.576119i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.62772 | 0.0838318 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.14558 | 0.418411 | 0.209205 | − | 0.977872i | \(-0.432912\pi\) | ||||
0.209205 | + | 0.977872i | \(0.432912\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.1168 | − | 8.01544i | −0.518302 | − | 0.410644i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.4603 | − | 19.8498i | 0.585592 | − | 1.01428i | −0.409209 | − | 0.912441i | \(-0.634195\pi\) |
0.994801 | − | 0.101835i | \(-0.0324713\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.5584 | + | 26.9480i | 0.792931 | + | 1.37340i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.9765 | + | 12.1948i | −0.659632 | + | 0.619898i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.67527 | + | 16.7581i | 0.490555 | + | 0.849667i | 0.999941 | − | 0.0108715i | \(-0.00346057\pi\) |
−0.509385 | + | 0.860538i | \(0.670127\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.72601 | − | 6.45364i | 0.188432 | − | 0.326375i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.5584 | + | 6.16337i | −0.784819 | + | 0.310901i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.9205 | 1.15326 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.00000 | −0.200754 | −0.100377 | − | 0.994949i | \(-0.532005\pi\) | ||||
−0.100377 | + | 0.994949i | \(0.532005\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.08069 | + | 14.1086i | −0.104165 | + | 0.706312i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.9891 | + | 24.2299i | −0.698584 | + | 1.20998i | 0.270374 | + | 0.962755i | \(0.412853\pi\) |
−0.968958 | + | 0.247227i | \(0.920481\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.1221 | + | 36.5845i | 1.05217 | + | 1.82240i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.32473 | − | 21.3094i | 0.0658266 | − | 1.05887i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.8716 | − | 20.5622i | −0.588453 | − | 1.01923i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.12772 | − | 15.8097i | 0.451337 | − | 0.781738i | −0.547133 | − | 0.837046i | \(-0.684281\pi\) |
0.998469 | + | 0.0553079i | \(0.0176140\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.15605 | + | 21.4003i | −0.155677 | + | 1.05560i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.8832 | 1.12601 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 33.4050 | 1.63979 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.67527 | − | 1.85208i | 0.228949 | − | 0.0906966i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.62112 | + | 4.53991i | −0.128050 | + | 0.221789i | −0.922921 | − | 0.384989i | \(-0.874205\pi\) |
0.794871 | + | 0.606778i | \(0.207538\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.1861 | + | 19.3750i | 0.545179 | + | 0.944278i | 0.998596 | + | 0.0529792i | \(0.0168717\pi\) |
−0.453416 | + | 0.891299i | \(0.649795\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.83090 | + | 4.53991i | −0.234887 | + | 0.220738i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.05842 | − | 1.83324i | −0.0513410 | − | 0.0889252i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.7025 | − | 28.9296i | 0.808291 | − | 1.40000i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 35.2337 | + | 27.9152i | 1.70110 | + | 1.34776i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.45202 | −0.358951 | −0.179476 | − | 0.983762i | \(-0.557440\pi\) | ||||
−0.179476 | + | 0.983762i | \(0.557440\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.1168 | −0.870640 | −0.435320 | − | 0.900276i | \(-0.643365\pi\) | ||||
−0.435320 | + | 0.900276i | \(0.643365\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.19897 | + | 0.949929i | 0.0574862 | + | 0.0455456i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.11684 | − | 7.13058i | 0.196935 | − | 0.341102i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.4603 | + | 19.8498i | 0.546969 | + | 0.947377i | 0.998480 | + | 0.0551120i | \(0.0175516\pi\) |
−0.451512 | + | 0.892265i | \(0.649115\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.08017 | + | 1.83324i | 0.289532 | + | 0.0872972i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.48412 | − | 7.76673i | −0.213047 | − | 0.369008i | 0.739620 | − | 0.673025i | \(-0.235005\pi\) |
−0.952667 | + | 0.304017i | \(0.901672\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.48913 | + | 2.57924i | −0.0705913 | + | 0.122268i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.7241 | − | 7.41744i | 0.885621 | − | 0.350833i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.1168 | −0.854987 | −0.427493 | − | 0.904018i | \(-0.640603\pi\) | ||||
−0.427493 | + | 0.904018i | \(0.640603\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.93580 | 0.279506 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.558422 | − | 3.78651i | 0.0262370 | − | 0.177906i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.4603 | − | 19.8498i | 0.537265 | − | 0.930571i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.9891 | + | 22.4978i | 0.607606 | + | 1.05240i | 0.991634 | + | 0.129083i | \(0.0412032\pi\) |
−0.384028 | + | 0.923321i | \(0.625463\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.45202 | + | 15.8593i | −0.347831 | + | 0.740251i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.5584 | + | 25.2159i | 0.678053 | + | 1.17442i | 0.975566 | + | 0.219705i | \(0.0705095\pi\) |
−0.297513 | + | 0.954718i | \(0.596157\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.9123 | + | 32.7570i | −0.878928 | + | 1.52235i | −0.0264102 | + | 0.999651i | \(0.508408\pi\) |
−0.852518 | + | 0.522697i | \(0.824926\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.79211 | + | 39.2747i | −0.268603 | + | 1.82132i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.3083 | −1.68015 | −0.840075 | − | 0.542470i | \(-0.817489\pi\) | ||||
−0.840075 | + | 0.542470i | \(0.817489\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.8832 | −1.05665 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.01906 | − | 1.98827i | 0.231266 | − | 0.0916145i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.6168 | − | 30.5133i | 0.810023 | − | 1.40300i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.16944 | − | 2.02554i | −0.0536577 | − | 0.0929379i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.74456 | − | 11.6819i | −0.125665 | − | 0.534879i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.10489 | − | 1.91373i | −0.0504839 | − | 0.0874406i | 0.839679 | − | 0.543083i | \(-0.182743\pi\) |
−0.890163 | + | 0.455642i | \(0.849410\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.74456 | + | 15.1460i | −0.398718 | + | 0.690599i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.62936 | + | 5.25236i | 0.301646 | + | 0.238990i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.3505 | 0.969478 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.45202 | −0.337683 | −0.168842 | − | 0.985643i | \(-0.554003\pi\) | ||||
−0.168842 | + | 0.985643i | \(0.554003\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.0000 | − | 9.50744i | −0.542659 | − | 0.429941i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.0645501 | − | 0.111804i | 0.00291310 | − | 0.00504564i | −0.864565 | − | 0.502521i | \(-0.832406\pi\) |
0.867478 | + | 0.497475i | \(0.165739\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.627719 | − | 1.08724i | −0.0282710 | − | 0.0489669i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.66181 | + | 41.1244i | 0.434266 | + | 1.84840i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.88316 | − | 8.45787i | −0.219039 | − | 0.379388i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.6297 | − | 21.8753i | 0.565383 | − | 0.979273i | −0.431631 | − | 0.902050i | \(-0.642062\pi\) |
0.997014 | − | 0.0772222i | \(-0.0246051\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.5584 | + | 6.16337i | −0.695099 | + | 0.275359i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.4845 | −0.467479 | −0.233740 | − | 0.972299i | \(-0.575096\pi\) | ||||
−0.233740 | + | 0.972299i | \(0.575096\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −35.8614 | −1.59581 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.54575 | − | 10.4813i | 0.0686492 | − | 0.465492i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.67527 | − | 11.5619i | 0.295876 | − | 0.512472i | −0.679312 | − | 0.733849i | \(-0.737722\pi\) |
0.975188 | + | 0.221377i | \(0.0710552\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.11313 | + | 8.85621i | 0.226192 | + | 0.391776i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.23369 | + | 17.5229i | −0.363526 | + | 0.773654i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.62112 | − | 4.53991i | −0.115500 | − | 0.200052i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.55842 | − | 11.3595i | 0.288439 | − | 0.499591i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.0940770 | + | 0.637910i | −0.00412952 | + | 0.0280012i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.3505 | −0.716330 | −0.358165 | − | 0.933658i | \(-0.616597\pi\) | ||||
−0.358165 | + | 0.933658i | \(0.616597\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.3236 | 0.844963 | 0.422481 | − | 0.906372i | \(-0.361159\pi\) | ||||
0.422481 | + | 0.906372i | \(0.361159\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.23369 | − | 0.884861i | 0.0974861 | − | 0.0386185i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.2912 | − | 28.2171i | 0.709654 | − | 1.22916i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.05842 | + | 15.6896i | 0.393844 | + | 0.682159i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 29.7435 | + | 8.96801i | 1.29076 | + | 0.389179i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.18614 | − | 3.78651i | −0.0946923 | − | 0.164012i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.41957 | + | 7.65492i | −0.191075 | + | 0.330951i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0000 | − | 9.50744i | −0.517838 | − | 0.410276i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.5652 | −0.541220 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.74456 | 0.375958 | 0.187979 | − | 0.982173i | \(-0.439806\pi\) | ||||
0.187979 | + | 0.982173i | \(0.439806\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.1780 | − | 8.85621i | −0.479695 | − | 0.380056i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.7446 | + | 35.9306i | −0.888599 | + | 1.53910i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.758112 | + | 1.31309i | 0.0324145 | + | 0.0561436i | 0.881778 | − | 0.471665i | \(-0.156347\pi\) |
−0.849363 | + | 0.527809i | \(0.823014\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 33.0475 | − | 31.0569i | 1.41043 | − | 1.32548i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.693562 | − | 1.20128i | −0.0295467 | − | 0.0511765i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.6753 | − | 18.4901i | 0.453958 | − | 0.786279i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.2804 | + | 6.05321i | −0.648615 | + | 0.256945i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.7446 | −0.794233 | −0.397116 | − | 0.917768i | \(-0.629989\pi\) | ||||
−0.397116 | + | 0.917768i | \(0.629989\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.9530 | −1.09769 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.05842 | − | 34.2998i | 0.213567 | − | 1.44814i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.1135 | − | 19.2491i | 0.468377 | − | 0.811254i | −0.530969 | − | 0.847391i | \(-0.678172\pi\) |
0.999347 | + | 0.0361375i | \(0.0115054\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.7921 | − | 23.8886i | −0.580238 | − | 1.00500i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.5734 | − | 10.9935i | −0.696017 | − | 0.461686i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.8723 | + | 34.4198i | 0.833089 | + | 1.44295i | 0.895577 | + | 0.444907i | \(0.146763\pi\) |
−0.0624872 | + | 0.998046i | \(0.519903\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.0645501 | + | 0.111804i | −0.00270134 | + | 0.00467885i | −0.867373 | − | 0.497659i | \(-0.834193\pi\) |
0.864672 | + | 0.502338i | \(0.167527\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.32473 | + | 29.3248i | −0.180668 | + | 1.22506i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.38712 | −0.0578471 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.1168 | 0.754214 | 0.377107 | − | 0.926170i | \(-0.376919\pi\) | ||||
0.377107 | + | 0.926170i | \(0.376919\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.61030 | + | 0.637910i | −0.0669218 | + | 0.0265107i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.5584 | − | 26.9480i | 0.645472 | − | 1.11799i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.8716 | + | 20.5622i | 0.491671 | + | 0.851599i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 22.6753 | − | 21.3094i | 0.937507 | − | 0.881035i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.87125 | − | 10.1693i | −0.242332 | − | 0.419732i | 0.719046 | − | 0.694963i | \(-0.244579\pi\) |
−0.961378 | + | 0.275231i | \(0.911246\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.0000 | − | 31.1769i | 0.741677 | − | 1.28462i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.01082 | + | 0.800857i | 0.0415794 | + | 0.0329428i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.7228 | −0.727789 | −0.363894 | − | 0.931440i | \(-0.618553\pi\) | ||||
−0.363894 | + | 0.931440i | \(0.618553\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.6783 | −0.724739 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −28.1168 | − | 22.2766i | −1.15075 | − | 0.911721i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.6700 | + | 23.6772i | −0.558543 | + | 0.967425i | 0.439075 | + | 0.898450i | \(0.355306\pi\) |
−0.997618 | + | 0.0689747i | \(0.978027\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.38316 | + | 2.39570i | 0.0564201 | + | 0.0977225i | 0.892856 | − | 0.450342i | \(-0.148698\pi\) |
−0.836436 | + | 0.548065i | \(0.815365\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −29.7435 | − | 8.96801i | −1.21125 | − | 0.365206i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −28.7446 | − | 49.7870i | −1.16863 | − | 2.02413i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.9123 | − | 32.7570i | 0.767626 | − | 1.32957i | −0.171221 | − | 0.985233i | \(-0.554771\pi\) |
0.938847 | − | 0.344335i | \(-0.111895\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.32473 | − | 0.524785i | 0.0536809 | − | 0.0212654i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.66181 | −0.390875 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.4674 | 1.47290 | 0.736452 | − | 0.676490i | \(-0.236500\pi\) | ||||
0.736452 | + | 0.676490i | \(0.236500\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.599485 | − | 4.06494i | 0.0241736 | − | 0.163914i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.8723 | − | 32.6878i | 0.759769 | − | 1.31596i | −0.183199 | − | 0.983076i | \(-0.558645\pi\) |
0.942968 | − | 0.332883i | \(-0.108022\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.758112 | + | 1.31309i | 0.0304711 | + | 0.0527775i | 0.880859 | − | 0.473379i | \(-0.156966\pi\) |
−0.850388 | + | 0.526157i | \(0.823633\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.55842 | + | 9.42509i | 0.263180 | + | 0.378216i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.38712 | + | 2.40257i | 0.0555740 | + | 0.0962569i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.8723 | − | 24.0275i | 0.554891 | − | 0.961100i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.58902 | − | 37.8976i | 0.223204 | − | 1.51348i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.4891 | 0.537847 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.44158 | + | 3.34408i | −0.335523 | + | 0.132915i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.83915 | − | 15.3098i | 0.350771 | − | 0.607553i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.62772 | + | 8.01544i | 0.183357 | + | 0.317583i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.03245 | − | 12.9073i | −0.119962 | − | 0.510604i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.87228 | − | 11.9031i | −0.271439 | − | 0.470146i | 0.697792 | − | 0.716301i | \(-0.254166\pi\) |
−0.969230 | + | 0.246155i | \(0.920833\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.90370 | + | 15.4217i | −0.351127 | + | 0.608171i | −0.986447 | − | 0.164079i | \(-0.947535\pi\) |
0.635320 | + | 0.772249i | \(0.280868\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.1168 | − | 15.1460i | −0.752725 | − | 0.596374i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.0344 | 1.57391 | 0.786956 | − | 0.617009i | \(-0.211656\pi\) | ||||
0.786956 | + | 0.617009i | \(0.211656\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −61.4674 | −2.41281 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 28.9854 | + | 22.9648i | 1.13603 | + | 0.900060i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.5584 | + | 35.6082i | −0.804513 | + | 1.39346i | 0.112106 | + | 0.993696i | \(0.464240\pi\) |
−0.916619 | + | 0.399762i | \(0.869093\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.4603 | − | 19.8498i | −0.447790 | − | 0.775594i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.17527 | + | 13.5152i | 0.123879 | + | 0.527277i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.8798 | + | 27.5047i | 0.618591 | + | 1.07143i | 0.989743 | + | 0.142858i | \(0.0456294\pi\) |
−0.371153 | + | 0.928572i | \(0.621037\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.55842 | − | 2.69927i | 0.0606156 | − | 0.104989i | −0.834125 | − | 0.551575i | \(-0.814027\pi\) |
0.894741 | + | 0.446586i | \(0.147360\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −23.7432 | + | 9.40571i | −0.922109 | + | 0.365287i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.5326 | −0.757443 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.822662 | −0.0318536 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.558422 | + | 3.78651i | −0.0215898 | + | 0.146395i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −44.8653 | + | 77.7089i | −1.73200 | + | 2.99992i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.6753 | − | 20.2222i | −0.450048 | − | 0.779507i | 0.548340 | − | 0.836255i | \(-0.315260\pi\) |
−0.998388 | + | 0.0567487i | \(0.981927\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.25013 | − | 0.274750i | 0.125098 | − | 0.0105751i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.675266 | − | 1.16959i | −0.0259526 | − | 0.0449512i | 0.852757 | − | 0.522307i | \(-0.174929\pi\) |
−0.878710 | + | 0.477356i | \(0.841595\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.94404 | − | 17.2236i | 0.381617 | − | 0.660980i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.26631 | + | 15.3672i | −0.0868453 | + | 0.588874i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.3083 | 1.38930 | 0.694650 | − | 0.719348i | \(-0.255559\pi\) | ||||
0.694650 | + | 0.719348i | \(0.255559\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.6277 | −1.13202 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.04069 | − | 2.78912i | 0.268619 | − | 0.106412i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.74456 | − | 15.1460i | 0.333141 | − | 0.577018i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.3319 | − | 40.4120i | −0.887586 | − | 1.53734i | −0.842721 | − | 0.538350i | \(-0.819048\pi\) |
−0.0448646 | − | 0.998993i | \(-0.514286\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 37.6753 | + | 11.3595i | 1.43117 | + | 0.431512i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.44378 | + | 5.96480i | 0.130630 | + | 0.226258i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.68614 | + | 2.92048i | −0.0638671 | + | 0.110621i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.88464 | + | 3.07775i | 0.146930 | + | 0.116411i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.7446 | 1.31228 | 0.656142 | − | 0.754637i | \(-0.272187\pi\) | ||||
0.656142 | + | 0.754637i | \(0.272187\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.9040 | 0.562117 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.11684 | − | 5.63858i | −0.268036 | − | 0.212361i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.7025 | + | 28.9296i | −0.628162 | + | 1.08801i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.30298 | + | 10.9171i | 0.236714 | + | 0.410000i | 0.959769 | − | 0.280790i | \(-0.0905964\pi\) |
−0.723056 | + | 0.690790i | \(0.757263\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.1221 | − | 19.8498i | 0.792140 | − | 0.744424i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.6753 | − | 18.4901i | −0.399792 | − | 0.692460i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −30.7839 | + | 53.3192i | −1.15125 | + | 1.99403i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 27.5584 | − | 10.9171i | 1.02919 | − | 0.407706i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.5823 | 1.21512 | 0.607558 | − | 0.794275i | \(-0.292149\pi\) | ||||
0.607558 | + | 0.794275i | \(0.292149\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.88316 | −0.181858 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.0645501 | − | 0.437696i | 0.00240064 | − | 0.0162781i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.116844 | + | 0.202380i | −0.00433948 | + | 0.00751619i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.3961 | − | 30.1309i | −0.645184 | − | 1.11749i | −0.984259 | − | 0.176732i | \(-0.943447\pi\) |
0.339075 | − | 0.940759i | \(-0.389886\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.2337 | − | 20.7846i | −0.638285 | − | 0.769800i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.0086 | + | 17.3354i | 0.370181 | + | 0.641172i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.4416 | + | 19.8174i | −0.422604 | + | 0.731972i | −0.996193 | − | 0.0871711i | \(-0.972217\pi\) |
0.573589 | + | 0.819143i | \(0.305551\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.26902 | + | 8.60485i | −0.0468084 | + | 0.317395i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 61.4674 | 2.26418 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.5976 | −0.573767 | −0.286884 | − | 0.957965i | \(-0.592619\pi\) | ||||
−0.286884 | + | 0.957965i | \(0.592619\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −26.2337 | + | 10.3923i | −0.963719 | + | 0.381771i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.7991 | − | 23.9008i | 0.506242 | − | 0.876836i | −0.493732 | − | 0.869614i | \(-0.664368\pi\) |
0.999974 | − | 0.00722236i | \(-0.00229897\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.7921 | + | 23.8886i | 0.505304 | + | 0.875212i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.7839 | − | 28.9296i | 1.12632 | − | 1.05848i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.11684 | + | 7.13058i | 0.150426 | + | 0.260546i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.4603 | − | 19.8498i | 0.418191 | − | 0.724328i | −0.577567 | − | 0.816344i | \(-0.695998\pi\) |
0.995758 | + | 0.0920156i | \(0.0293310\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.1753 | + | 12.0232i | 0.553017 | + | 0.438149i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.24224 | 0.190784 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.4674 | −1.25274 | −0.626369 | − | 0.779527i | \(-0.715460\pi\) | ||||
−0.626369 | + | 0.779527i | \(0.715460\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17.8074 | − | 14.1086i | −0.646367 | − | 0.512108i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.1861 | + | 17.6429i | −0.369247 | + | 0.639555i | −0.989448 | − | 0.144888i | \(-0.953718\pi\) |
0.620201 | + | 0.784443i | \(0.287051\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.3236 | + | 33.4695i | 0.699562 | + | 1.21168i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −22.9783 | − | 6.92820i | −0.830780 | − | 0.250490i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.6383 | + | 39.2107i | 0.817421 | + | 1.41582i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.44158 | − | 12.8892i | 0.268350 | − | 0.464796i | −0.700086 | − | 0.714059i | \(-0.746855\pi\) |
0.968436 | + | 0.249263i | \(0.0801882\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.4494 | − | 4.13948i | 0.376328 | − | 0.149080i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.7446 | −0.674195 | −0.337098 | − | 0.941470i | \(-0.609445\pi\) | ||||
−0.337098 | + | 0.941470i | \(0.609445\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.06490 | −0.217858 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.23369 | + | 15.1460i | −0.0801331 | + | 0.543361i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.86301 | + | 3.22682i | −0.0667491 | + | 0.115613i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.1168 | + | 22.7190i | 0.469358 | + | 0.812951i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.92756 | − | 0.162946i | 0.0688852 | − | 0.00582322i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.69702 | + | 6.40342i | 0.131952 | + | 0.228548i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.1221 | + | 36.5845i | −0.752921 | + | 1.30410i | 0.193481 | + | 0.981104i | \(0.438022\pi\) |
−0.946402 | + | 0.322993i | \(0.895311\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.32473 | − | 29.3248i | 0.153965 | − | 1.04399i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.6948 | −0.913601 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 66.0951 | 2.34711 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.2804 | − | 6.05321i | 0.541938 | − | 0.214685i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.0475 | + | 39.9195i | −0.816386 | + | 1.41402i | 0.0919424 | + | 0.995764i | \(0.470692\pi\) |
−0.908328 | + | 0.418258i | \(0.862641\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.72601 | + | 6.45364i | 0.131817 | + | 0.228313i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.861407 | + | 3.66648i | 0.0304363 | + | 0.129549i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.7346 | − | 23.7890i | −0.484683 | − | 0.839496i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.79211 | + | 10.0322i | −0.204145 | + | 0.353590i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.8824 | + | 10.2066i | 0.453482 | + | 0.359288i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.6277 | −0.443967 | −0.221983 | − | 0.975050i | \(-0.571253\pi\) | ||||
−0.221983 | + | 0.975050i | \(0.571253\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.5341 | −1.17754 | −0.588771 | − | 0.808300i | \(-0.700388\pi\) | ||||
−0.588771 | + | 0.808300i | \(0.700388\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.2337 | − | 16.0309i | −0.709626 | − | 0.562228i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.4845 | − | 18.1596i | 0.367255 | − | 0.636104i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.0584 | + | 19.1537i | 0.386885 | + | 0.670105i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.62936 | − | 28.2171i | −0.231649 | − | 0.985986i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.18614 | − | 7.25061i | −0.146097 | − | 0.253048i | 0.783684 | − | 0.621159i | \(-0.213338\pi\) |
−0.929782 | + | 0.368111i | \(0.880005\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.4603 | + | 19.8498i | −0.399480 | + | 0.691919i | −0.993662 | − | 0.112411i | \(-0.964143\pi\) |
0.594182 | + | 0.804331i | \(0.297476\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.00000 | + | 2.37686i | −0.208893 | + | 0.0827517i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.83915 | −0.307367 | −0.153684 | − | 0.988120i | \(-0.549114\pi\) | ||||
−0.153684 | + | 0.988120i | \(0.549114\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.23369 | −0.285968 | −0.142984 | − | 0.989725i | \(-0.545670\pi\) | ||||
−0.142984 | + | 0.989725i | \(0.545670\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.31468 | − | 22.4759i | 0.114985 | − | 0.779682i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.56930 | − | 6.18220i | 0.123669 | − | 0.214201i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.4603 | − | 19.8498i | −0.396599 | − | 0.686929i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 28.6753 | + | 41.2091i | 0.991162 | + | 1.42440i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.83090 | + | 8.36737i | 0.166781 | + | 0.288874i | 0.937286 | − | 0.348560i | \(-0.113329\pi\) |
−0.770505 | + | 0.637434i | \(0.779996\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4307 | − | 24.9947i | 0.497610 | − | 0.861887i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.53528 | − | 44.3140i | 0.225087 | − | 1.52625i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.5109 | 0.499189 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −53.5513 | −1.84004 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.44158 | − | 3.34408i | 0.289714 | − | 0.114768i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.41957 | − | 7.65492i | 0.151501 | − | 0.262407i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.5584 | + | 18.2877i | 0.361513 | + | 0.626160i | 0.988210 | − | 0.153104i | \(-0.0489268\pi\) |
−0.626697 | + | 0.779263i | \(0.715593\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −25.3885 | − | 7.65492i | −0.868269 | − | 0.261793i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.0475 | + | 38.1875i | 0.753130 | + | 1.30446i | 0.946299 | + | 0.323294i | \(0.104790\pi\) |
−0.193169 | + | 0.981166i | \(0.561877\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.90370 | + | 15.4217i | −0.303790 | + | 0.526180i | −0.976991 | − | 0.213279i | \(-0.931586\pi\) |
0.673201 | + | 0.739459i | \(0.264919\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.00000 | − | 2.37686i | −0.102240 | − | 0.0810032i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.6783 | −0.601776 | −0.300888 | − | 0.953659i | \(-0.597283\pi\) | ||||
−0.300888 | + | 0.953659i | \(0.597283\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.883156 | −0.0300282 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.64018 | − | 6.05321i | −0.259474 | − | 0.205578i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.6753 | + | 49.6670i | −0.972742 | + | 1.68484i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.6383 | − | 39.2107i | −0.767069 | − | 1.32860i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 19.6753 | − | 18.4901i | 0.665907 | − | 0.625795i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.4603 | − | 19.8498i | −0.387428 | − | 0.671044i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.67527 | − | 11.5619i | 0.225408 | − | 0.390418i | −0.731034 | − | 0.682341i | \(-0.760962\pi\) |
0.956442 | + | 0.291923i | \(0.0942953\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 32.8055 | − | 12.9957i | 1.10650 | − | 0.438334i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.23369 | 0.142637 | 0.0713183 | − | 0.997454i | \(-0.477279\pi\) | ||||
0.0713183 | + | 0.997454i | \(0.477279\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.4043 | −0.720312 | −0.360156 | − | 0.932892i | \(-0.617277\pi\) | ||||
−0.360156 | + | 0.932892i | \(0.617277\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.20789 | + | 42.0940i | −0.208676 | + | 1.41497i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.4603 | + | 19.8498i | −0.384798 | + | 0.666490i | −0.991741 | − | 0.128256i | \(-0.959062\pi\) |
0.606943 | + | 0.794745i | \(0.292396\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.23369 | − | 14.2612i | −0.276149 | − | 0.478304i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 44.5185 | + | 29.5302i | 1.49143 | + | 0.989300i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.11684 | + | 7.13058i | 0.137765 | + | 0.238616i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.4845 | − | 18.1596i | 0.350457 | − | 0.607010i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.44158 | + | 16.5557i | −0.0815219 | + | 0.552778i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.59691 | −0.119964 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.4891 | −0.449388 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −21.1221 | + | 8.36737i | −0.702899 | + | 0.278449i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.76631 | − | 16.9157i | 0.324643 | − | 0.562299i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.1459 | + | 24.5015i | 0.469708 | + | 0.813558i | 0.999400 | − | 0.0346319i | \(-0.0110259\pi\) |
−0.529692 | + | 0.848190i | \(0.677693\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −33.0475 | + | 31.0569i | −1.09612 | + | 1.03009i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.3643 | + | 45.6643i | 0.873488 | + | 1.51293i | 0.858364 | + | 0.513041i | \(0.171481\pi\) |
0.0151242 | + | 0.999886i | \(0.495186\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −41.7921 | + | 72.3861i | −1.38312 | + | 2.39563i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 48.6853 | + | 38.5728i | 1.60949 | + | 1.27518i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21.3505 | −0.705057 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.1303 | 0.828973 | 0.414486 | − | 0.910056i | \(-0.363961\pi\) | ||||
0.414486 | + | 0.910056i | \(0.363961\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.1753 | + | 31.0381i | 1.29087 | + | 1.02274i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.66181 | − | 16.7347i | 0.318022 | − | 0.550831i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.25544 | − | 2.17448i | −0.0412785 | − | 0.0714965i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.34713 | − | 1.91373i | −0.208467 | − | 0.0628552i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.1861 | − | 31.4993i | −0.596668 | − | 1.03346i | −0.993309 | − | 0.115485i | \(-0.963158\pi\) |
0.396641 | − | 0.917974i | \(-0.370176\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.94369 | − | 6.83067i | 0.129249 | − | 0.223866i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.4416 | + | 8.09780i | −0.669227 | + | 0.265110i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 47.4864 | 1.55297 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.2337 | 0.399657 | 0.199829 | − | 0.979831i | \(-0.435961\pi\) | ||||
0.199829 | + | 0.979831i | \(0.435961\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.86043 | − | 32.9573i | 0.158614 | − | 1.07552i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.0475 | − | 39.9195i | 0.751329 | − | 1.30134i | −0.195850 | − | 0.980634i | \(-0.562747\pi\) |
0.947179 | − | 0.320705i | \(-0.103920\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.10489 | + | 1.91373i | 0.0359803 | + | 0.0623197i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.5842 | − | 24.6535i | 0.376835 | − | 0.801977i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.0493 | + | 29.5302i | 0.554027 | + | 0.959603i | 0.997979 | + | 0.0635523i | \(0.0202430\pi\) |
−0.443951 | + | 0.896051i | \(0.646424\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.1168 | + | 17.5229i | −0.328407 | + | 0.568817i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.11571 | − | 14.3460i | 0.0686066 | − | 0.465202i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31.6060 | −1.02382 | −0.511909 | − | 0.859040i | \(-0.671061\pi\) | ||||
−0.511909 | + | 0.859040i | \(0.671061\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.5988 | −1.31375 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.55842 | + | 1.40965i | −0.115027 | + | 0.0455674i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.7991 | + | 23.9008i | −0.445598 | + | 0.771798i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.1753 | − | 53.9971i | −1.00565 | − | 1.74184i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.55657 | + | 10.8817i | 0.0823842 | + | 0.350659i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.18614 | − | 2.05446i | −0.0381832 | − | 0.0661353i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.7991 | + | 23.9008i | −0.443751 | + | 0.768599i | −0.997964 | − | 0.0637757i | \(-0.979686\pi\) |
0.554214 | + | 0.832375i | \(0.313019\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.0584 | + | 13.5152i | 0.547995 | + | 0.434170i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.1317 | −1.57671 | −0.788356 | − | 0.615220i | \(-0.789067\pi\) | ||||
−0.788356 | + | 0.615220i | \(0.789067\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.41578 | 0.205680 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.72601 | + | 2.95207i | 0.119328 | + | 0.0945419i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.38316 | + | 9.32390i | −0.172222 | + | 0.298298i | −0.939197 | − | 0.343380i | \(-0.888428\pi\) |
0.766974 | + | 0.641678i | \(0.221761\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.72601 | − | 6.45364i | −0.119084 | − | 0.206259i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.0000 | + | 51.0767i | 0.383131 | + | 1.63075i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.2994 | + | 35.1596i | 0.647451 | + | 1.12142i | 0.983730 | + | 0.179655i | \(0.0574981\pi\) |
−0.336279 | + | 0.941762i | \(0.609169\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.883156 | + | 1.52967i | −0.0281397 | + | 0.0487394i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.86335 | + | 3.11502i | −0.250293 | + | 0.0991521i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.1168 | 0.417091 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.4864 | 1.50845 | 0.754227 | − | 0.656613i | \(-0.228012\pi\) | ||||
0.754227 | + | 0.656613i | \(0.228012\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.44158 | − | 57.2400i | 0.267885 | − | 1.81646i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.5659 | − | 42.5493i | 0.778790 | − | 1.34890i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.6753 | − | 35.8106i | −0.654792 | − | 1.13413i | −0.981946 | − | 0.189162i | \(-0.939423\pi\) |
0.327154 | − | 0.944971i | \(-0.393911\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.83915 | + | 18.8114i | −0.279658 | + | 0.595167i |
(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 | 288.2.i.f.193.4 | yes | 8 | |
3.2 | odd | 2 | 864.2.i.f.577.4 | 8 | |||
4.3 | odd | 2 | inner | 288.2.i.f.193.1 | yes | 8 | |
8.3 | odd | 2 | 576.2.i.n.193.4 | 8 | |||
8.5 | even | 2 | 576.2.i.n.193.1 | 8 | |||
9.2 | odd | 6 | 864.2.i.f.289.4 | 8 | |||
9.4 | even | 3 | 2592.2.a.u.1.3 | 4 | |||
9.5 | odd | 6 | 2592.2.a.x.1.1 | 4 | |||
9.7 | even | 3 | inner | 288.2.i.f.97.4 | yes | 8 | |
12.11 | even | 2 | 864.2.i.f.577.3 | 8 | |||
24.5 | odd | 2 | 1728.2.i.n.577.2 | 8 | |||
24.11 | even | 2 | 1728.2.i.n.577.1 | 8 | |||
36.7 | odd | 6 | inner | 288.2.i.f.97.1 | ✓ | 8 | |
36.11 | even | 6 | 864.2.i.f.289.3 | 8 | |||
36.23 | even | 6 | 2592.2.a.x.1.2 | 4 | |||
36.31 | odd | 6 | 2592.2.a.u.1.4 | 4 | |||
72.5 | odd | 6 | 5184.2.a.cc.1.3 | 4 | |||
72.11 | even | 6 | 1728.2.i.n.1153.1 | 8 | |||
72.13 | even | 6 | 5184.2.a.cf.1.1 | 4 | |||
72.29 | odd | 6 | 1728.2.i.n.1153.2 | 8 | |||
72.43 | odd | 6 | 576.2.i.n.385.4 | 8 | |||
72.59 | even | 6 | 5184.2.a.cc.1.4 | 4 | |||
72.61 | even | 6 | 576.2.i.n.385.1 | 8 | |||
72.67 | odd | 6 | 5184.2.a.cf.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.i.f.97.1 | ✓ | 8 | 36.7 | odd | 6 | inner | |
288.2.i.f.97.4 | yes | 8 | 9.7 | even | 3 | inner | |
288.2.i.f.193.1 | yes | 8 | 4.3 | odd | 2 | inner | |
288.2.i.f.193.4 | yes | 8 | 1.1 | even | 1 | trivial | |
576.2.i.n.193.1 | 8 | 8.5 | even | 2 | |||
576.2.i.n.193.4 | 8 | 8.3 | odd | 2 | |||
576.2.i.n.385.1 | 8 | 72.61 | even | 6 | |||
576.2.i.n.385.4 | 8 | 72.43 | odd | 6 | |||
864.2.i.f.289.3 | 8 | 36.11 | even | 6 | |||
864.2.i.f.289.4 | 8 | 9.2 | odd | 6 | |||
864.2.i.f.577.3 | 8 | 12.11 | even | 2 | |||
864.2.i.f.577.4 | 8 | 3.2 | odd | 2 | |||
1728.2.i.n.577.1 | 8 | 24.11 | even | 2 | |||
1728.2.i.n.577.2 | 8 | 24.5 | odd | 2 | |||
1728.2.i.n.1153.1 | 8 | 72.11 | even | 6 | |||
1728.2.i.n.1153.2 | 8 | 72.29 | odd | 6 | |||
2592.2.a.u.1.3 | 4 | 9.4 | even | 3 | |||
2592.2.a.u.1.4 | 4 | 36.31 | odd | 6 | |||
2592.2.a.x.1.1 | 4 | 9.5 | odd | 6 | |||
2592.2.a.x.1.2 | 4 | 36.23 | even | 6 | |||
5184.2.a.cc.1.3 | 4 | 72.5 | odd | 6 | |||
5184.2.a.cc.1.4 | 4 | 72.59 | even | 6 | |||
5184.2.a.cf.1.1 | 4 | 72.13 | even | 6 | |||
5184.2.a.cf.1.2 | 4 | 72.67 | odd | 6 |