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 | 193.1 | ||
Root | \(0.335728 + 1.37379i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 288.193 |
Dual form | 288.2.i.f.97.1 |
$q$-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 | 0.578088 | − | 0.815974i | \(-0.303799\pi\) |
−0.995699 | + | 0.0926519i | \(0.970466\pi\) | |||||||
\(8\) | 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 | \(0.186055\pi\) |
0.0608712 | + | 0.998146i | \(0.480612\pi\) | |||||||
\(12\) | 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 | \(-0.640571\pi\) | ||||
−0.427403 | + | 0.904061i | \(0.640571\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.558422 | + | 3.78651i | −0.121858 | + | 0.826284i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.10489 | + | 1.91373i | −0.230386 | + | 0.399041i | −0.957922 | − | 0.287029i | \(-0.907332\pi\) |
0.727536 | + | 0.686070i | \(0.240666\pi\) | |||||||
\(24\) | 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 | \(0.501041\pi\) |
−0.864386 | + | 0.502830i | \(0.832292\pi\) | |||||||
\(32\) | 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 | 0.545946 | − | 0.837820i | \(-0.316170\pi\) |
−0.998547 | + | 0.0538934i | \(0.982837\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.81386 | − | 2.05446i | −1.01575 | − | 0.306260i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.10489 | − | 1.91373i | −0.161165 | − | 0.279146i | 0.774122 | − | 0.633037i | \(-0.218192\pi\) |
−0.935287 | + | 0.353891i | \(0.884859\pi\) | |||||||
\(48\) | 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 | \(0.402125\pi\) |
−0.976738 | + | 0.214437i | \(0.931208\pi\) | |||||||
\(60\) | 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 | \(-0.615340\pi\) |
0.987028 | − | 0.160551i | \(-0.0513271\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.55842 | − | 1.40965i | 0.428384 | − | 0.169701i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.41957 | 0.524507 | 0.262253 | − | 0.964999i | \(-0.415534\pi\) | ||||
0.262253 | + | 0.964999i | \(0.415534\pi\) | |||||||
\(72\) | 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 | \(0.0162418\pi\) |
−0.455179 | + | 0.890400i | \(0.650425\pi\) | |||||||
\(80\) | 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 | \(0.114486\pi\) |
−0.163198 | + | 0.986593i | \(0.552181\pi\) | |||||||
\(84\) | 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 | −0.806444 | − | 0.591311i | \(-0.798611\pi\) |
0.915312 | + | 0.402745i | \(0.131944\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.11684 | − | 5.63858i | −0.694533 | − | 0.550269i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.72601 | −0.360207 | −0.180104 | − | 0.983648i | \(-0.557643\pi\) | ||||
−0.180104 | + | 0.983648i | \(0.557643\pi\) | |||||||
\(108\) | 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 | \(-0.392739\pi\) | ||||
0.330630 | + | 0.943760i | \(0.392739\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.50000 | + | 10.1711i | −0.132068 | + | 0.895515i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.83090 | − | 8.36737i | 0.422078 | − | 0.731061i | −0.574065 | − | 0.818810i | \(-0.694634\pi\) |
0.996143 | + | 0.0877494i | \(0.0279675\pi\) | |||||||
\(132\) | 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 | −0.921000 | − | 0.389562i | \(-0.872626\pi\) |
0.797871 | + | 0.602829i | \(0.205960\pi\) | |||||||
\(140\) | 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 | 0.907475 | − | 0.420106i | \(-0.138007\pi\) |
−0.817560 | + | 0.575843i | \(0.804674\pi\) | |||||||
\(152\) | 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 | \(-0.387483\pi\) | ||||
0.346168 | + | 0.938173i | \(0.387483\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 19.1168 | + | 15.1460i | 1.48824 | + | 1.17912i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.83090 | − | 8.36737i | 0.373827 | − | 0.647487i | −0.616324 | − | 0.787493i | \(-0.711379\pi\) |
0.990151 | + | 0.140006i | \(0.0447122\pi\) | |||||||
\(168\) | 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 | \(-0.392838\pi\) | ||||
0.330334 | + | 0.943864i | \(0.392838\pi\) | |||||||
\(180\) | 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 | \(-0.954141\pi\) |
0.370483 | − | 0.928839i | \(-0.379192\pi\) | |||||||
\(192\) | 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 | \(-0.237617\pi\) | ||||
0.734073 | + | 0.679071i | \(0.237617\pi\) | |||||||
\(200\) | 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 | −0.761587 | − | 0.648063i | \(-0.775579\pi\) |
0.942032 | + | 0.335522i | \(0.108913\pi\) | |||||||
\(212\) | 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 | 0.826657 | − | 0.562706i | \(-0.190240\pi\) |
−0.900646 | + | 0.434553i | \(0.856906\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.37228 | − | 1.28962i | 0.0914854 | − | 0.0859747i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.48412 | − | 7.76673i | −0.297622 | − | 0.515496i | 0.677970 | − | 0.735090i | \(-0.262860\pi\) |
−0.975591 | + | 0.219594i | \(0.929527\pi\) | |||||||
\(228\) | 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 | \(0.353375\pi\) |
−0.998018 | + | 0.0629214i | \(0.979958\pi\) | |||||||
\(240\) | 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 | \(-0.614762\pi\) | ||||
−0.352776 | + | 0.935708i | \(0.614762\pi\) | |||||||
\(252\) | 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 | \(0.0102571\pi\) |
−0.471839 | + | 0.881685i | \(0.656410\pi\) | |||||||
\(264\) | 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 | \(-0.350469\pi\) | ||||
0.452678 | + | 0.891674i | \(0.350469\pi\) | |||||||
\(272\) | 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 | −0.933353 | − | 0.358959i | \(-0.883132\pi\) |
0.777544 | + | 0.628828i | \(0.216465\pi\) | |||||||
\(284\) | 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 | \(-0.807959\pi\) | ||||
−0.823459 | + | 0.567376i | \(0.807959\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.55842 | + | 1.40965i | −0.202432 | + | 0.0801919i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.34713 | − | 10.9935i | 0.359913 | − | 0.623387i | −0.628033 | − | 0.778186i | \(-0.716140\pi\) |
0.987946 | + | 0.154800i | \(0.0494732\pi\) | |||||||
\(312\) | 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 | \(0.203572\pi\) |
0.115682 | + | 0.993286i | \(0.463095\pi\) | |||||||
\(332\) | 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 | −0.692923 | − | 0.721011i | \(-0.743677\pi\) |
0.970876 | + | 0.239583i | \(0.0770108\pi\) | |||||||
\(348\) | 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 | \(-0.299146\pi\) | ||||
0.589954 | + | 0.807437i | \(0.299146\pi\) | |||||||
\(360\) | 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 | \(0.0862566\pi\) |
−0.249937 | + | 0.968262i | \(0.580410\pi\) | |||||||
\(368\) | 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 | \(-0.567088\pi\) | ||||
−0.209205 | + | 0.977872i | \(0.567088\pi\) | |||||||
\(380\) | 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 | \(0.365805\pi\) |
−0.994801 | + | 0.101835i | \(0.967529\pi\) | |||||||
\(384\) | 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 | −0.794871 | − | 0.606778i | \(-0.792462\pi\) |
0.922921 | + | 0.384989i | \(0.125795\pi\) | |||||||
\(420\) | 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 | \(-0.442560\pi\) | ||||
0.179476 | + | 0.983762i | \(0.442560\pi\) | |||||||
\(432\) | 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 | \(-0.982448\pi\) |
0.451512 | − | 0.892265i | \(-0.350885\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.08017 | + | 1.83324i | 0.289532 | + | 0.0872972i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.48412 | + | 7.76673i | 0.213047 | + | 0.369008i | 0.952667 | − | 0.304017i | \(-0.0983279\pi\) |
−0.739620 | + | 0.673025i | \(0.764995\pi\) | |||||||
\(444\) | 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 | \(-0.491592\pi\) |
0.852518 | − | 0.522697i | \(-0.175074\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.79211 | + | 39.2747i | −0.268603 | + | 1.82132i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.3083 | 1.68015 | 0.840075 | − | 0.542470i | \(-0.182511\pi\) | ||||
0.840075 | + | 0.542470i | \(0.182511\pi\) | |||||||
\(468\) | 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 | 0.890163 | − | 0.455642i | \(-0.150590\pi\) |
−0.839679 | + | 0.543083i | \(0.817257\pi\) | |||||||
\(480\) | 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 | \(-0.445997\pi\) | ||||
0.168842 | + | 0.985643i | \(0.445997\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.0000 | − | 9.50744i | −0.542659 | − | 0.429941i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.0645501 | + | 0.111804i | −0.00291310 | + | 0.00504564i | −0.867478 | − | 0.497475i | \(-0.834261\pi\) |
0.864565 | + | 0.502521i | \(0.167594\pi\) | |||||||
\(492\) | 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 | \(0.357938\pi\) |
−0.997014 | + | 0.0772222i | \(0.975395\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.5584 | + | 6.16337i | −0.695099 | + | 0.275359i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.4845 | 0.467479 | 0.233740 | − | 0.972299i | \(-0.424904\pi\) | ||||
0.233740 | + | 0.972299i | \(0.424904\pi\) | |||||||
\(504\) | 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 | \(-0.638841\pi\) | ||||
−0.422481 | + | 0.906372i | \(0.638841\pi\) | |||||||
\(524\) | 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 | 0.849363 | − | 0.527809i | \(-0.176986\pi\) |
−0.881778 | + | 0.471665i | \(0.843653\pi\) | |||||||
\(548\) | 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 | −0.999347 | − | 0.0361375i | \(-0.988495\pi\) |
0.530969 | + | 0.847391i | \(0.321828\pi\) | |||||||
\(564\) | 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 | −0.864672 | − | 0.502338i | \(-0.832473\pi\) |
0.867373 | + | 0.497659i | \(0.165807\pi\) | |||||||
\(572\) | 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 | 0.961378 | − | 0.275231i | \(-0.0887542\pi\) |
−0.719046 | + | 0.694963i | \(0.755421\pi\) | |||||||
\(588\) | 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 | \(-0.644694\pi\) |
0.997618 | − | 0.0689747i | \(-0.0219728\pi\) | |||||||
\(600\) | 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 | \(0.445229\pi\) |
−0.938847 | + | 0.344335i | \(0.888105\pi\) | |||||||
\(608\) | 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 | 0.850388 | − | 0.526157i | \(-0.176367\pi\) |
−0.880859 | + | 0.473379i | \(0.843034\pi\) | |||||||
\(620\) | 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 | −0.635320 | − | 0.772249i | \(-0.719132\pi\) |
0.986447 | + | 0.164079i | \(0.0524650\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.1168 | − | 15.1460i | −0.752725 | − | 0.596374i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.0344 | −1.57391 | −0.786956 | − | 0.617009i | \(-0.788344\pi\) | ||||
−0.786956 | + | 0.617009i | \(0.788344\pi\) | |||||||
\(648\) | 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 | \(-0.954371\pi\) |
0.371153 | − | 0.928572i | \(-0.378963\pi\) | |||||||
\(660\) | 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 | \(-0.744441\pi\) | ||||
−0.694650 | + | 0.719348i | \(0.744441\pi\) | |||||||
\(684\) | 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 | \(0.180952\pi\) |
0.0448646 | + | 0.998993i | \(0.485714\pi\) | |||||||
\(692\) | 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 | \(-0.707851\pi\) | ||||
−0.607558 | + | 0.794275i | \(0.707851\pi\) | |||||||
\(720\) | 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 | \(0.0565527\pi\) |
−0.339075 | + | 0.940759i | \(0.610114\pi\) | |||||||
\(728\) | 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 | \(-0.407381\pi\) | ||||
0.286884 | + | 0.957965i | \(0.407381\pi\) | |||||||
\(740\) | 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 | \(0.335632\pi\) |
−0.999974 | + | 0.00722236i | \(0.997701\pi\) | |||||||
\(744\) | 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 | −0.995758 | − | 0.0920156i | \(-0.970669\pi\) |
0.577567 | + | 0.816344i | \(0.304002\pi\) | |||||||
\(752\) | 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 | \(-0.561978\pi\) |
0.946402 | − | 0.322993i | \(-0.104689\pi\) | |||||||
\(788\) | 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 | \(-0.299612\pi\) | ||||
0.588771 | + | 0.808300i | \(0.299612\pi\) | |||||||
\(812\) | 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 | −0.594182 | − | 0.804331i | \(-0.702524\pi\) |
0.993662 | + | 0.112411i | \(0.0358575\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.00000 | + | 2.37686i | −0.208893 | + | 0.0827517i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.83915 | 0.307367 | 0.153684 | − | 0.988120i | \(-0.450886\pi\) | ||||
0.153684 | + | 0.988120i | \(0.450886\pi\) | |||||||
\(828\) | 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 | 0.770505 | − | 0.637434i | \(-0.220004\pi\) |
−0.937286 | + | 0.348560i | \(0.886671\pi\) | |||||||
\(840\) | 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 | −0.673201 | − | 0.739459i | \(-0.735081\pi\) |
0.976991 | + | 0.213279i | \(0.0684145\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.00000 | − | 2.37686i | −0.102240 | − | 0.0810032i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.6783 | 0.601776 | 0.300888 | − | 0.953659i | \(-0.402717\pi\) | ||||
0.300888 | + | 0.953659i | \(0.402717\pi\) | |||||||
\(864\) | 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 | \(-0.382723\pi\) | ||||
0.360156 | + | 0.932892i | \(0.382723\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.20789 | + | 42.0940i | −0.208676 | + | 1.41497i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.4603 | − | 19.8498i | 0.384798 | − | 0.666490i | −0.606943 | − | 0.794745i | \(-0.707604\pi\) |
0.991741 | + | 0.128256i | \(0.0409378\pi\) | |||||||
\(888\) | 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 | 0.529692 | − | 0.848190i | \(-0.322307\pi\) |
−0.999400 | + | 0.0346319i | \(0.988974\pi\) | |||||||
\(908\) | 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 | \(-0.828519\pi\) |
−0.0151242 | − | 0.999886i | \(-0.504814\pi\) | |||||||
\(912\) | 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 | \(-0.636039\pi\) | ||||
−0.414486 | + | 0.910056i | \(0.636039\pi\) | |||||||
\(920\) | 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 | \(-0.979757\pi\) |
0.443951 | − | 0.896051i | \(-0.353576\pi\) | |||||||
\(948\) | 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 | −0.554214 | − | 0.832375i | \(-0.686981\pi\) |
0.997964 | + | 0.0637757i | \(0.0203142\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.0584 | + | 13.5152i | 0.547995 | + | 0.434170i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.1317 | 1.57671 | 0.788356 | − | 0.615220i | \(-0.210933\pi\) | ||||
0.788356 | + | 0.615220i | \(0.210933\pi\) | |||||||
\(972\) | 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 | \(-0.942502\pi\) |
0.336279 | − | 0.941762i | \(-0.390831\pi\) | |||||||
\(984\) | 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 | \(-0.771988\pi\) | ||||
−0.754227 | + | 0.656613i | \(0.771988\pi\) | |||||||
\(992\) | 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.193.1 | yes | 8 | |
3.2 | odd | 2 | 864.2.i.f.577.3 | 8 | |||
4.3 | odd | 2 | inner | 288.2.i.f.193.4 | yes | 8 | |
8.3 | odd | 2 | 576.2.i.n.193.1 | 8 | |||
8.5 | even | 2 | 576.2.i.n.193.4 | 8 | |||
9.2 | odd | 6 | 864.2.i.f.289.3 | 8 | |||
9.4 | even | 3 | 2592.2.a.u.1.4 | 4 | |||
9.5 | odd | 6 | 2592.2.a.x.1.2 | 4 | |||
9.7 | even | 3 | inner | 288.2.i.f.97.1 | ✓ | 8 | |
12.11 | even | 2 | 864.2.i.f.577.4 | 8 | |||
24.5 | odd | 2 | 1728.2.i.n.577.1 | 8 | |||
24.11 | even | 2 | 1728.2.i.n.577.2 | 8 | |||
36.7 | odd | 6 | inner | 288.2.i.f.97.4 | yes | 8 | |
36.11 | even | 6 | 864.2.i.f.289.4 | 8 | |||
36.23 | even | 6 | 2592.2.a.x.1.1 | 4 | |||
36.31 | odd | 6 | 2592.2.a.u.1.3 | 4 | |||
72.5 | odd | 6 | 5184.2.a.cc.1.4 | 4 | |||
72.11 | even | 6 | 1728.2.i.n.1153.2 | 8 | |||
72.13 | even | 6 | 5184.2.a.cf.1.2 | 4 | |||
72.29 | odd | 6 | 1728.2.i.n.1153.1 | 8 | |||
72.43 | odd | 6 | 576.2.i.n.385.1 | 8 | |||
72.59 | even | 6 | 5184.2.a.cc.1.3 | 4 | |||
72.61 | even | 6 | 576.2.i.n.385.4 | 8 | |||
72.67 | odd | 6 | 5184.2.a.cf.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.i.f.97.1 | ✓ | 8 | 9.7 | even | 3 | inner | |
288.2.i.f.97.4 | yes | 8 | 36.7 | odd | 6 | inner | |
288.2.i.f.193.1 | yes | 8 | 1.1 | even | 1 | trivial | |
288.2.i.f.193.4 | yes | 8 | 4.3 | odd | 2 | inner | |
576.2.i.n.193.1 | 8 | 8.3 | odd | 2 | |||
576.2.i.n.193.4 | 8 | 8.5 | even | 2 | |||
576.2.i.n.385.1 | 8 | 72.43 | odd | 6 | |||
576.2.i.n.385.4 | 8 | 72.61 | even | 6 | |||
864.2.i.f.289.3 | 8 | 9.2 | odd | 6 | |||
864.2.i.f.289.4 | 8 | 36.11 | even | 6 | |||
864.2.i.f.577.3 | 8 | 3.2 | odd | 2 | |||
864.2.i.f.577.4 | 8 | 12.11 | even | 2 | |||
1728.2.i.n.577.1 | 8 | 24.5 | odd | 2 | |||
1728.2.i.n.577.2 | 8 | 24.11 | even | 2 | |||
1728.2.i.n.1153.1 | 8 | 72.29 | odd | 6 | |||
1728.2.i.n.1153.2 | 8 | 72.11 | even | 6 | |||
2592.2.a.u.1.3 | 4 | 36.31 | odd | 6 | |||
2592.2.a.u.1.4 | 4 | 9.4 | even | 3 | |||
2592.2.a.x.1.1 | 4 | 36.23 | even | 6 | |||
2592.2.a.x.1.2 | 4 | 9.5 | odd | 6 | |||
5184.2.a.cc.1.3 | 4 | 72.59 | even | 6 | |||
5184.2.a.cc.1.4 | 4 | 72.5 | odd | 6 | |||
5184.2.a.cf.1.1 | 4 | 72.67 | odd | 6 | |||
5184.2.a.cf.1.2 | 4 | 72.13 | even | 6 |