Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(323,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.j (of order \(2\), degree \(1\), 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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.56070144.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.4 | ||
Root | \(0.500000 + 1.19293i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.323 |
Dual form | 1512.2.j.b.323.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.366025 | + | 1.36603i | −0.258819 | + | 0.965926i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.73205 | − | 1.00000i | −0.866025 | − | 0.500000i | ||||
\(5\) | 4.38587 | 1.96142 | 0.980710 | − | 0.195469i | \(-0.0626229\pi\) | ||||
0.980710 | + | 0.195469i | \(0.0626229\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.60534 | + | 5.99121i | −0.507653 | + | 1.89459i | ||||
\(11\) | 5.11792i | 1.54311i | 0.636162 | + | 0.771555i | \(0.280521\pi\) | ||||
−0.636162 | + | 0.771555i | \(0.719479\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.21068i | 1.44518i | 0.691276 | + | 0.722591i | \(0.257049\pi\) | ||||
−0.691276 | + | 0.722591i | \(0.742951\pi\) | |||||||
\(14\) | −1.36603 | − | 0.366025i | −0.365086 | − | 0.0978244i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | − | 2.00000i | − | 0.485071i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.50379 | −1.49207 | −0.746035 | − | 0.665906i | \(-0.768045\pi\) | ||||
−0.746035 | + | 0.665906i | \(0.768045\pi\) | |||||||
\(20\) | −7.59655 | − | 4.38587i | −1.69864 | − | 0.980710i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.99121 | − | 1.87329i | −1.49053 | − | 0.399386i | ||||
\(23\) | −4.63929 | −0.967359 | −0.483680 | − | 0.875245i | \(-0.660700\pi\) | ||||
−0.483680 | + | 0.875245i | \(0.660700\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.2358 | 2.84717 | ||||||||
\(26\) | −7.11792 | − | 1.90724i | −1.39594 | − | 0.374041i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | − | 1.73205i | 0.188982 | − | 0.327327i | ||||
\(29\) | 1.26795 | 0.235452 | 0.117726 | − | 0.993046i | \(-0.462440\pi\) | ||||
0.117726 | + | 0.993046i | \(0.462440\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.21068i | − | 0.756260i | −0.925752 | − | 0.378130i | \(-0.876567\pi\) | ||
0.925752 | − | 0.378130i | \(-0.123433\pi\) | |||||||
\(32\) | −5.46410 | + | 1.46410i | −0.965926 | + | 0.258819i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.73205 | + | 0.732051i | 0.468543 | + | 0.125546i | ||||
\(35\) | 4.38587i | 0.741347i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.98547i | 0.326410i | 0.986592 | + | 0.163205i | \(0.0521832\pi\) | ||||
−0.986592 | + | 0.163205i | \(0.947817\pi\) | |||||||
\(38\) | 2.38055 | − | 8.88434i | 0.386176 | − | 1.44123i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.77174 | − | 8.77174i | 1.38693 | − | 1.38693i | ||||
\(41\) | 7.37134i | 1.15121i | 0.817728 | + | 0.575605i | \(0.195233\pi\) | ||||
−0.817728 | + | 0.575605i | \(0.804767\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.71753 | 0.566917 | 0.283459 | − | 0.958984i | \(-0.408518\pi\) | ||||
0.283459 | + | 0.958984i | \(0.408518\pi\) | |||||||
\(44\) | 5.11792 | − | 8.86450i | 0.771555 | − | 1.33637i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.69810 | − | 6.33739i | 0.250371 | − | 0.934397i | ||||
\(47\) | 2.57558 | 0.375687 | 0.187844 | − | 0.982199i | \(-0.439850\pi\) | ||||
0.187844 | + | 0.982199i | \(0.439850\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −5.21068 | + | 19.4465i | −0.736901 | + | 2.75015i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.21068 | − | 9.02516i | 0.722591 | − | 1.25156i | ||||
\(53\) | −10.2358 | −1.40600 | −0.703000 | − | 0.711190i | \(-0.748157\pi\) | ||||
−0.703000 | + | 0.711190i | \(0.748157\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 22.4465i | 3.02669i | ||||||||
\(56\) | 2.00000 | + | 2.00000i | 0.267261 | + | 0.267261i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.464102 | + | 1.73205i | −0.0609395 | + | 0.227429i | ||||
\(59\) | − | 3.50379i | − | 0.456154i | −0.973643 | − | 0.228077i | \(-0.926756\pi\) | ||
0.973643 | − | 0.228077i | \(-0.0732438\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.53590i | 0.580762i | 0.956911 | + | 0.290381i | \(0.0937821\pi\) | ||||
−0.956911 | + | 0.290381i | \(0.906218\pi\) | |||||||
\(62\) | 5.75189 | + | 1.54122i | 0.730491 | + | 0.195735i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 22.8533i | 2.83461i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.21068 | 0.636586 | 0.318293 | − | 0.947992i | \(-0.396890\pi\) | ||||
0.318293 | + | 0.947992i | \(0.396890\pi\) | |||||||
\(68\) | −2.00000 | + | 3.46410i | −0.242536 | + | 0.420084i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.99121 | − | 1.60534i | −0.716086 | − | 0.191875i | ||||
\(71\) | −1.36071 | −0.161486 | −0.0807432 | − | 0.996735i | \(-0.525729\pi\) | ||||
−0.0807432 | + | 0.996735i | \(0.525729\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.4465 | 1.80788 | 0.903939 | − | 0.427662i | \(-0.140662\pi\) | ||||
0.903939 | + | 0.427662i | \(0.140662\pi\) | |||||||
\(74\) | −2.71221 | − | 0.726734i | −0.315288 | − | 0.0844811i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.2649 | + | 6.50379i | 1.29217 | + | 0.746035i | ||||
\(77\) | −5.11792 | −0.583241 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.98241i | − | 0.448057i | −0.974583 | − | 0.224028i | \(-0.928079\pi\) | ||
0.974583 | − | 0.224028i | \(-0.0719208\pi\) | |||||||
\(80\) | 8.77174 | + | 15.1931i | 0.980710 | + | 1.69864i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.0694 | − | 2.69810i | −1.11198 | − | 0.297955i | ||||
\(83\) | 11.6893i | 1.28307i | 0.767095 | + | 0.641534i | \(0.221702\pi\) | ||||
−0.767095 | + | 0.641534i | \(0.778298\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 8.77174i | − | 0.951428i | ||||||
\(86\) | −1.36071 | + | 5.07823i | −0.146729 | + | 0.547600i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.2358 | + | 10.2358i | 1.09114 | + | 1.09114i | ||||
\(89\) | − | 14.8645i | − | 1.57563i | −0.615910 | − | 0.787817i | \(-0.711211\pi\) | ||
0.615910 | − | 0.787817i | \(-0.288789\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.21068 | −0.546227 | ||||||||
\(92\) | 8.03549 | + | 4.63929i | 0.837758 | + | 0.483680i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.942729 | + | 3.51831i | −0.0972351 | + | 0.362886i | ||||
\(95\) | −28.5247 | −2.92658 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.42136 | 0.448921 | 0.224460 | − | 0.974483i | \(-0.427938\pi\) | ||||
0.224460 | + | 0.974483i | \(0.427938\pi\) | |||||||
\(98\) | 0.366025 | − | 1.36603i | 0.0369741 | − | 0.137989i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −24.6572 | − | 14.2358i | −2.46572 | − | 1.42358i | ||||
\(101\) | 2.00000 | 0.199007 | 0.0995037 | − | 0.995037i | \(-0.468274\pi\) | ||||
0.0995037 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.67478i | − | 0.165021i | −0.996590 | − | 0.0825105i | \(-0.973706\pi\) | ||
0.996590 | − | 0.0825105i | \(-0.0262938\pi\) | |||||||
\(104\) | 10.4214 | + | 10.4214i | 1.02190 | + | 1.02190i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.74658 | − | 13.9824i | 0.363900 | − | 1.35809i | ||||
\(107\) | − | 10.2649i | − | 0.992344i | −0.868224 | − | 0.496172i | \(-0.834738\pi\) | ||
0.868224 | − | 0.496172i | \(-0.165262\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.29311i | − | 0.123857i | −0.998081 | − | 0.0619287i | \(-0.980275\pi\) | ||
0.998081 | − | 0.0619287i | \(-0.0197251\pi\) | |||||||
\(110\) | −30.6625 | − | 8.21599i | −2.92356 | − | 0.783364i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.46410 | + | 2.00000i | −0.327327 | + | 0.188982i | ||||
\(113\) | − | 8.07937i | − | 0.760043i | −0.924978 | − | 0.380022i | \(-0.875917\pi\) | ||
0.924978 | − | 0.380022i | \(-0.124083\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20.3473 | −1.89740 | ||||||||
\(116\) | −2.19615 | − | 1.26795i | −0.203908 | − | 0.117726i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.78626 | + | 1.28247i | 0.440611 | + | 0.118061i | ||||
\(119\) | 2.00000 | 0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.1931 | −1.38119 | ||||||||
\(122\) | −6.19615 | − | 1.66025i | −0.560973 | − | 0.150312i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.21068 | + | 7.29311i | −0.378130 | + | 0.654940i | ||||
\(125\) | 40.5072 | 3.62307 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.4465i | 1.19319i | 0.802544 | + | 0.596593i | \(0.203479\pi\) | ||||
−0.802544 | + | 0.596593i | \(0.796521\pi\) | |||||||
\(128\) | 10.9282 | + | 2.92820i | 0.965926 | + | 0.258819i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −31.2183 | − | 8.36491i | −2.73802 | − | 0.733651i | ||||
\(131\) | 1.77480i | 0.155065i | 0.996990 | + | 0.0775323i | \(0.0247041\pi\) | ||||
−0.996990 | + | 0.0775323i | \(0.975296\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 6.50379i | − | 0.563950i | ||||||
\(134\) | −1.90724 | + | 7.11792i | −0.164760 | + | 0.614895i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.00000 | − | 4.00000i | −0.342997 | − | 0.342997i | ||||
\(137\) | − | 14.5756i | − | 1.24528i | −0.782510 | − | 0.622638i | \(-0.786061\pi\) | ||
0.782510 | − | 0.622638i | \(-0.213939\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.0076 | 1.27293 | 0.636463 | − | 0.771307i | \(-0.280397\pi\) | ||||
0.636463 | + | 0.771307i | \(0.280397\pi\) | |||||||
\(140\) | 4.38587 | − | 7.59655i | 0.370673 | − | 0.642025i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.498054 | − | 1.85876i | 0.0417958 | − | 0.155984i | ||||
\(143\) | −26.6678 | −2.23008 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.56106 | 0.461821 | ||||||||
\(146\) | −5.65382 | + | 21.1003i | −0.467913 | + | 1.74628i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.98547 | − | 3.43894i | 0.163205 | − | 0.282679i | ||||
\(149\) | −5.33669 | −0.437198 | −0.218599 | − | 0.975815i | \(-0.570149\pi\) | ||||
−0.218599 | + | 0.975815i | \(0.570149\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.5725i | 1.43003i | 0.699108 | + | 0.715016i | \(0.253581\pi\) | ||||
−0.699108 | + | 0.715016i | \(0.746419\pi\) | |||||||
\(152\) | −13.0076 | + | 13.0076i | −1.05505 | + | 1.05505i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.87329 | − | 6.99121i | 0.150954 | − | 0.563368i | ||||
\(155\) | − | 18.4675i | − | 1.48334i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.8259i | 1.10343i | 0.834032 | + | 0.551715i | \(0.186027\pi\) | ||||
−0.834032 | + | 0.551715i | \(0.813973\pi\) | |||||||
\(158\) | 5.44008 | + | 1.45766i | 0.432789 | + | 0.115966i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −23.9648 | + | 6.42136i | −1.89459 | + | 0.507653i | ||||
\(161\) | − | 4.63929i | − | 0.365627i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.67478 | 0.679461 | 0.339731 | − | 0.940523i | \(-0.389664\pi\) | ||||
0.339731 | + | 0.940523i | \(0.389664\pi\) | |||||||
\(164\) | 7.37134 | − | 12.7675i | 0.575605 | − | 0.996977i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.9679 | − | 4.27858i | −1.23935 | − | 0.332082i | ||||
\(167\) | −15.8855 | −1.22925 | −0.614627 | − | 0.788818i | \(-0.710693\pi\) | ||||
−0.614627 | + | 0.788818i | \(0.710693\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.1512 | −1.08855 | ||||||||
\(170\) | 11.9824 | + | 3.21068i | 0.919009 | + | 0.246248i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.43894 | − | 3.71753i | −0.490965 | − | 0.283459i | ||||
\(173\) | 4.22940 | 0.321555 | 0.160778 | − | 0.986991i | \(-0.448600\pi\) | ||||
0.160778 | + | 0.986991i | \(0.448600\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.2358i | 1.07613i | ||||||||
\(176\) | −17.7290 | + | 10.2358i | −1.33637 | + | 0.771555i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 20.3053 | + | 5.44078i | 1.52194 | + | 0.407804i | ||||
\(179\) | 6.45041i | 0.482126i | 0.970509 | + | 0.241063i | \(0.0774961\pi\) | ||||
−0.970509 | + | 0.241063i | \(0.922504\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5068i | 0.780968i | 0.920610 | + | 0.390484i | \(0.127692\pi\) | ||||
−0.920610 | + | 0.390484i | \(0.872308\pi\) | |||||||
\(182\) | 1.90724 | − | 7.11792i | 0.141374 | − | 0.527615i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.27858 | + | 9.27858i | −0.684026 | + | 0.684026i | ||||
\(185\) | 8.70803i | 0.640227i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.2358 | 0.748519 | ||||||||
\(188\) | −4.46104 | − | 2.57558i | −0.325355 | − | 0.187844i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.4408 | − | 38.9655i | 0.757454 | − | 2.82686i | ||||
\(191\) | 8.25986 | 0.597663 | 0.298831 | − | 0.954306i | \(-0.403403\pi\) | ||||
0.298831 | + | 0.954306i | \(0.403403\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.07937 | −0.581566 | −0.290783 | − | 0.956789i | \(-0.593916\pi\) | ||||
−0.290783 | + | 0.956789i | \(0.593916\pi\) | |||||||
\(194\) | −1.61833 | + | 6.03969i | −0.116189 | + | 0.433624i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.73205 | + | 1.00000i | 0.123718 | + | 0.0714286i | ||||
\(197\) | 7.04275 | 0.501775 | 0.250887 | − | 0.968016i | \(-0.419278\pi\) | ||||
0.250887 | + | 0.968016i | \(0.419278\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 20.1336i | − | 1.42723i | −0.700537 | − | 0.713616i | \(-0.747056\pi\) | ||
0.700537 | − | 0.713616i | \(-0.252944\pi\) | |||||||
\(200\) | 28.4717 | − | 28.4717i | 2.01325 | − | 2.01325i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.732051 | + | 2.73205i | −0.0515069 | + | 0.192226i | ||||
\(203\) | 1.26795i | 0.0889926i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 32.3297i | 2.25801i | ||||||||
\(206\) | 2.28779 | + | 0.613012i | 0.159398 | + | 0.0427106i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −18.0503 | + | 10.4214i | −1.25156 | + | 0.722591i | ||||
\(209\) | − | 33.2859i | − | 2.30243i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.54347 | 0.519314 | 0.259657 | − | 0.965701i | \(-0.416390\pi\) | ||||
0.259657 | + | 0.965701i | \(0.416390\pi\) | |||||||
\(212\) | 17.7290 | + | 10.2358i | 1.21763 | + | 0.703000i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.0221 | + | 3.75721i | 0.958531 | + | 0.256838i | ||||
\(215\) | 16.3046 | 1.11196 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.21068 | 0.285839 | ||||||||
\(218\) | 1.76642 | + | 0.473311i | 0.119637 | + | 0.0320566i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 22.4465 | − | 38.8785i | 1.51334 | − | 2.62119i | ||||
\(221\) | 10.4214 | 0.701016 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 5.48926i | − | 0.367588i | −0.982965 | − | 0.183794i | \(-0.941162\pi\) | ||
0.982965 | − | 0.183794i | \(-0.0588380\pi\) | |||||||
\(224\) | −1.46410 | − | 5.46410i | −0.0978244 | − | 0.365086i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.0366 | + | 2.95725i | 0.734145 | + | 0.196714i | ||||
\(227\) | − | 0.127416i | − | 0.00845689i | −0.999991 | − | 0.00422845i | \(-0.998654\pi\) | ||
0.999991 | − | 0.00422845i | \(-0.00134596\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.53590i | 0.431904i | 0.976404 | + | 0.215952i | \(0.0692855\pi\) | ||||
−0.976404 | + | 0.215952i | \(0.930714\pi\) | |||||||
\(230\) | 7.44764 | − | 27.7950i | 0.491083 | − | 1.83275i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.53590 | − | 2.53590i | 0.166490 | − | 0.166490i | ||||
\(233\) | − | 10.5359i | − | 0.690230i | −0.938560 | − | 0.345115i | \(-0.887840\pi\) | ||
0.938560 | − | 0.345115i | \(-0.112160\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.2962 | 0.736881 | ||||||||
\(236\) | −3.50379 | + | 6.06874i | −0.228077 | + | 0.395041i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.732051 | + | 2.73205i | −0.0474518 | + | 0.177093i | ||||
\(239\) | 24.3862 | 1.57741 | 0.788706 | − | 0.614771i | \(-0.210752\pi\) | ||||
0.788706 | + | 0.614771i | \(0.210752\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.8603 | −0.699573 | −0.349787 | − | 0.936829i | \(-0.613746\pi\) | ||||
−0.349787 | + | 0.936829i | \(0.613746\pi\) | |||||||
\(242\) | 5.56106 | − | 20.7541i | 0.357478 | − | 1.33413i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.53590 | − | 7.85641i | 0.290381 | − | 0.502955i | ||||
\(245\) | −4.38587 | −0.280203 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 33.8891i | − | 2.15631i | ||||||
\(248\) | −8.42136 | − | 8.42136i | −0.534757 | − | 0.534757i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.8267 | + | 55.3338i | −0.937720 | + | 3.49962i | ||||
\(251\) | 3.73511i | 0.235758i | 0.993028 | + | 0.117879i | \(0.0376095\pi\) | ||||
−0.993028 | + | 0.117879i | \(0.962390\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 23.7435i | − | 1.49274i | ||||||
\(254\) | −18.3683 | − | 4.92177i | −1.15253 | − | 0.308819i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | − | 7.52781i | − | 0.469572i | −0.972047 | − | 0.234786i | \(-0.924561\pi\) | ||
0.972047 | − | 0.234786i | \(-0.0754389\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.98547 | −0.123371 | ||||||||
\(260\) | 22.8533 | − | 39.5832i | 1.41730 | − | 2.45484i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.42442 | − | 0.649620i | −0.149781 | − | 0.0401337i | ||||
\(263\) | −16.7187 | −1.03092 | −0.515458 | − | 0.856915i | \(-0.672378\pi\) | ||||
−0.515458 | + | 0.856915i | \(0.672378\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −44.8930 | −2.75776 | ||||||||
\(266\) | 8.88434 | + | 2.38055i | 0.544734 | + | 0.145961i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.02516 | − | 5.21068i | −0.551299 | − | 0.318293i | ||||
\(269\) | −4.11486 | −0.250887 | −0.125444 | − | 0.992101i | \(-0.540035\pi\) | ||||
−0.125444 | + | 0.992101i | \(0.540035\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.31293i | 0.261992i | 0.991383 | + | 0.130996i | \(0.0418175\pi\) | ||||
−0.991383 | + | 0.130996i | \(0.958182\pi\) | |||||||
\(272\) | 6.92820 | − | 4.00000i | 0.420084 | − | 0.242536i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.9106 | + | 5.33503i | 1.20284 | + | 0.322301i | ||||
\(275\) | 72.8579i | 4.39349i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 27.7564i | − | 1.66772i | −0.551976 | − | 0.833860i | \(-0.686126\pi\) | ||
0.551976 | − | 0.833860i | \(-0.313874\pi\) | |||||||
\(278\) | −5.49315 | + | 20.5007i | −0.329457 | + | 1.22955i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.77174 | + | 8.77174i | 0.524211 | + | 0.524211i | ||||
\(281\) | 21.8961i | 1.30621i | 0.757267 | + | 0.653106i | \(0.226534\pi\) | ||||
−0.757267 | + | 0.653106i | \(0.773466\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.3786 | 0.914164 | 0.457082 | − | 0.889425i | \(-0.348895\pi\) | ||||
0.457082 | + | 0.889425i | \(0.348895\pi\) | |||||||
\(284\) | 2.35682 | + | 1.36071i | 0.139851 | + | 0.0807432i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.76110 | − | 36.4289i | 0.577186 | − | 2.15409i | ||||
\(287\) | −7.37134 | −0.435117 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | −2.03549 | + | 7.59655i | −0.119528 | + | 0.446085i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −26.7541 | − | 15.4465i | −1.56567 | − | 0.903939i | ||||
\(293\) | −0.408482 | −0.0238638 | −0.0119319 | − | 0.999929i | \(-0.503798\pi\) | ||||
−0.0119319 | + | 0.999929i | \(0.503798\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 15.3671i | − | 0.894710i | ||||||
\(296\) | 3.97095 | + | 3.97095i | 0.230807 | + | 0.230807i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.95336 | − | 7.29005i | 0.113155 | − | 0.422301i | ||||
\(299\) | − | 24.1739i | − | 1.39801i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.71753i | 0.214275i | ||||||||
\(302\) | −24.0045 | − | 6.43199i | −1.38130 | − | 0.370119i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −13.0076 | − | 22.5298i | −0.746035 | − | 1.29217i | ||||
\(305\) | 19.8939i | 1.13912i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.99694 | 0.570555 | 0.285278 | − | 0.958445i | \(-0.407914\pi\) | ||||
0.285278 | + | 0.958445i | \(0.407914\pi\) | |||||||
\(308\) | 8.86450 | + | 5.11792i | 0.505101 | + | 0.291620i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 25.2270 | + | 6.75957i | 1.43280 | + | 0.383918i | ||||
\(311\) | −19.9603 | −1.13185 | −0.565923 | − | 0.824458i | \(-0.691480\pi\) | ||||
−0.565923 | + | 0.824458i | \(0.691480\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.4465 | 1.32528 | 0.662638 | − | 0.748940i | \(-0.269437\pi\) | ||||
0.662638 | + | 0.748940i | \(0.269437\pi\) | |||||||
\(314\) | −18.8866 | − | 5.06065i | −1.06583 | − | 0.285589i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.98241 | + | 6.89774i | −0.224028 | + | 0.388028i | ||||
\(317\) | 20.7740 | 1.16678 | 0.583391 | − | 0.812191i | \(-0.301725\pi\) | ||||
0.583391 | + | 0.812191i | \(0.301725\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.48926i | 0.363329i | ||||||||
\(320\) | − | 35.0869i | − | 1.96142i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.33739 | + | 1.69810i | 0.353169 | + | 0.0946313i | ||||
\(323\) | 13.0076i | 0.723761i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 74.1784i | 4.11468i | ||||||||
\(326\) | −3.17519 | + | 11.8500i | −0.175857 | + | 0.656309i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 14.7427 | + | 14.7427i | 0.814029 | + | 0.814029i | ||||
\(329\) | 2.57558i | 0.141997i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.0366 | 1.04635 | 0.523174 | − | 0.852226i | \(-0.324748\pi\) | ||||
0.523174 | + | 0.852226i | \(0.324748\pi\) | |||||||
\(332\) | 11.6893 | − | 20.2465i | 0.641534 | − | 1.11117i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.81448 | − | 21.6999i | 0.318154 | − | 1.18737i | ||||
\(335\) | 22.8533 | 1.24861 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.88546 | 0.157181 | 0.0785905 | − | 0.996907i | \(-0.474958\pi\) | ||||
0.0785905 | + | 0.996907i | \(0.474958\pi\) | |||||||
\(338\) | 5.17969 | − | 19.3309i | 0.281738 | − | 1.05146i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.77174 | + | 15.1931i | −0.475714 | + | 0.823961i | ||||
\(341\) | 21.5499 | 1.16699 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 7.43505 | − | 7.43505i | 0.400871 | − | 0.400871i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.54807 | + | 5.77747i | −0.0832247 | + | 0.310599i | ||||
\(347\) | − | 30.7033i | − | 1.64824i | −0.566415 | − | 0.824120i | \(-0.691670\pi\) | ||
0.566415 | − | 0.824120i | \(-0.308330\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 26.5007i | − | 1.41855i | −0.704931 | − | 0.709276i | \(-0.749022\pi\) | ||
0.704931 | − | 0.709276i | \(-0.250978\pi\) | |||||||
\(350\) | −19.4465 | − | 5.21068i | −1.03946 | − | 0.278522i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.49315 | − | 27.9648i | −0.399386 | − | 1.49053i | ||||
\(353\) | 6.29955i | 0.335291i | 0.985847 | + | 0.167645i | \(0.0536164\pi\) | ||||
−0.985847 | + | 0.167645i | \(0.946384\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.96789 | −0.316743 | ||||||||
\(356\) | −14.8645 | + | 25.7461i | −0.787817 | + | 1.36454i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.81142 | − | 2.36101i | −0.465698 | − | 0.124783i | ||||
\(359\) | −1.60770 | −0.0848509 | −0.0424255 | − | 0.999100i | \(-0.513508\pi\) | ||||
−0.0424255 | + | 0.999100i | \(0.513508\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.2992 | 1.22628 | ||||||||
\(362\) | −14.3526 | − | 3.84577i | −0.754357 | − | 0.202129i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.02516 | + | 5.21068i | 0.473047 | + | 0.273114i | ||||
\(365\) | 67.7464 | 3.54601 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 17.1763i | − | 0.896597i | −0.893884 | − | 0.448298i | \(-0.852030\pi\) | ||
0.893884 | − | 0.448298i | \(-0.147970\pi\) | |||||||
\(368\) | −9.27858 | − | 16.0710i | −0.483680 | − | 0.837758i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.8954 | − | 3.18736i | −0.618412 | − | 0.165703i | ||||
\(371\) | − | 10.2358i | − | 0.531418i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.27941i | 0.118024i | 0.998257 | + | 0.0590118i | \(0.0187950\pi\) | ||||
−0.998257 | + | 0.0590118i | \(0.981205\pi\) | |||||||
\(374\) | −3.74658 | + | 13.9824i | −0.193731 | + | 0.723013i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.15117 | − | 5.15117i | 0.265651 | − | 0.265651i | ||||
\(377\) | 6.60688i | 0.340271i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.1389 | 1.03446 | 0.517232 | − | 0.855845i | \(-0.326962\pi\) | ||||
0.517232 | + | 0.855845i | \(0.326962\pi\) | |||||||
\(380\) | 49.4063 | + | 28.5247i | 2.53449 | + | 1.46329i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.02332 | + | 11.2832i | −0.154686 | + | 0.577298i | ||||
\(383\) | −22.3068 | −1.13982 | −0.569912 | − | 0.821705i | \(-0.693023\pi\) | ||||
−0.569912 | + | 0.821705i | \(0.693023\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −22.4465 | −1.14398 | ||||||||
\(386\) | 2.95725 | − | 11.0366i | 0.150520 | − | 0.561749i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.65801 | − | 4.42136i | −0.388777 | − | 0.224460i | ||||
\(389\) | 1.57864 | 0.0800404 | 0.0400202 | − | 0.999199i | \(-0.487258\pi\) | ||||
0.0400202 | + | 0.999199i | \(0.487258\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.27858i | 0.469238i | ||||||||
\(392\) | −2.00000 | + | 2.00000i | −0.101015 | + | 0.101015i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.57782 | + | 9.62057i | −0.129869 | + | 0.484677i | ||||
\(395\) | − | 17.4663i | − | 0.878827i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.4289i | 1.57737i | 0.614796 | + | 0.788686i | \(0.289238\pi\) | ||||
−0.614796 | + | 0.788686i | \(0.710762\pi\) | |||||||
\(398\) | 27.5030 | + | 7.36940i | 1.37860 | + | 0.369395i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 28.4717 | + | 49.3144i | 1.42358 | + | 2.46572i | ||||
\(401\) | − | 26.5404i | − | 1.32536i | −0.748901 | − | 0.662682i | \(-0.769418\pi\) | ||
0.748901 | − | 0.662682i | \(-0.230582\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.9405 | 1.09293 | ||||||||
\(404\) | −3.46410 | − | 2.00000i | −0.172345 | − | 0.0995037i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.73205 | − | 0.464102i | −0.0859602 | − | 0.0230330i | ||||
\(407\) | −10.1615 | −0.503687 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.0037 | 1.58248 | 0.791240 | − | 0.611506i | \(-0.209436\pi\) | ||||
0.791240 | + | 0.611506i | \(0.209436\pi\) | |||||||
\(410\) | −44.1632 | − | 11.8335i | −2.18107 | − | 0.584415i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.67478 | + | 2.90080i | −0.0825105 | + | 0.142912i | ||||
\(413\) | 3.50379 | 0.172410 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 51.2678i | 2.51663i | ||||||||
\(416\) | −7.62896 | − | 28.4717i | −0.374041 | − | 1.39594i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 45.4693 | + | 12.1835i | 2.22398 | + | 0.595913i | ||||
\(419\) | 20.6572i | 1.00917i | 0.863362 | + | 0.504585i | \(0.168354\pi\) | ||||
−0.863362 | + | 0.504585i | \(0.831646\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 32.9930i | − | 1.60798i | −0.594641 | − | 0.803991i | \(-0.702706\pi\) | ||
0.594641 | − | 0.803991i | \(-0.297294\pi\) | |||||||
\(422\) | −2.76110 | + | 10.3046i | −0.134408 | + | 0.501619i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −20.4717 | + | 20.4717i | −0.994192 | + | 0.994192i | ||||
\(425\) | − | 28.4717i | − | 1.38108i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.53590 | −0.219508 | ||||||||
\(428\) | −10.2649 | + | 17.7793i | −0.496172 | + | 0.859395i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.96789 | + | 22.2725i | −0.287797 | + | 1.07407i | ||||
\(431\) | 6.48282 | 0.312267 | 0.156133 | − | 0.987736i | \(-0.450097\pi\) | ||||
0.156133 | + | 0.987736i | \(0.450097\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.4038 | −0.884429 | −0.442214 | − | 0.896909i | \(-0.645807\pi\) | ||||
−0.442214 | + | 0.896909i | \(0.645807\pi\) | |||||||
\(434\) | −1.54122 | + | 5.75189i | −0.0739807 | + | 0.276100i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.29311 | + | 2.23973i | −0.0619287 | + | 0.107264i | ||||
\(437\) | 30.1730 | 1.44337 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.31293i | − | 0.205845i | −0.994689 | − | 0.102923i | \(-0.967181\pi\) | ||
0.994689 | − | 0.102923i | \(-0.0328194\pi\) | |||||||
\(440\) | 44.8930 | + | 44.8930i | 2.14019 | + | 2.14019i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.81448 | + | 14.2358i | −0.181436 | + | 0.677130i | ||||
\(443\) | 5.54540i | 0.263470i | 0.991285 | + | 0.131735i | \(0.0420547\pi\) | ||||
−0.991285 | + | 0.131735i | \(0.957945\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 65.1937i | − | 3.09048i | ||||||
\(446\) | 7.49847 | + | 2.00921i | 0.355063 | + | 0.0951388i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.00000 | 0.377964 | ||||||||
\(449\) | 30.2007i | 1.42526i | 0.701541 | + | 0.712629i | \(0.252496\pi\) | ||||
−0.701541 | + | 0.712629i | \(0.747504\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37.7259 | −1.77644 | ||||||||
\(452\) | −8.07937 | + | 13.9939i | −0.380022 | + | 0.658217i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.174053 | + | 0.0466375i | 0.00816873 | + | 0.00218880i | ||||
\(455\) | −22.8533 | −1.07138 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.3205 | −1.13767 | −0.568833 | − | 0.822453i | \(-0.692605\pi\) | ||||
−0.568833 | + | 0.822453i | \(0.692605\pi\) | |||||||
\(458\) | −8.92820 | − | 2.39230i | −0.417188 | − | 0.111785i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 35.2426 | + | 20.3473i | 1.64319 | + | 0.948699i | ||||
\(461\) | −37.3141 | −1.73789 | −0.868945 | − | 0.494909i | \(-0.835201\pi\) | ||||
−0.868945 | + | 0.494909i | \(0.835201\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.2853i | 1.63985i | 0.572472 | + | 0.819924i | \(0.305985\pi\) | ||||
−0.572472 | + | 0.819924i | \(0.694015\pi\) | |||||||
\(464\) | 2.53590 | + | 4.39230i | 0.117726 | + | 0.203908i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.3923 | + | 3.85641i | 0.666711 | + | 0.178645i | ||||
\(467\) | − | 20.7824i | − | 0.961693i | −0.876805 | − | 0.480847i | \(-0.840329\pi\) | ||
0.876805 | − | 0.480847i | \(-0.159671\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.21068i | 0.240607i | ||||||||
\(470\) | −4.13468 | + | 15.4309i | −0.190719 | + | 0.711772i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.00757 | − | 7.00757i | −0.322550 | − | 0.322550i | ||||
\(473\) | 19.0260i | 0.874816i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −92.5868 | −4.24818 | ||||||||
\(476\) | −3.46410 | − | 2.00000i | −0.158777 | − | 0.0916698i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.92596 | + | 33.3121i | −0.408264 | + | 1.52366i | ||||
\(479\) | 17.1640 | 0.784245 | 0.392123 | − | 0.919913i | \(-0.371741\pi\) | ||||
0.392123 | + | 0.919913i | \(0.371741\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.3457 | −0.471722 | ||||||||
\(482\) | 3.97515 | − | 14.8354i | 0.181063 | − | 0.675736i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 26.3152 | + | 15.1931i | 1.19615 | + | 0.690595i | ||||
\(485\) | 19.3915 | 0.880522 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 38.7961i | − | 1.75802i | −0.476805 | − | 0.879009i | \(-0.658205\pi\) | ||
0.476805 | − | 0.879009i | \(-0.341795\pi\) | |||||||
\(488\) | 9.07180 | + | 9.07180i | 0.410661 | + | 0.410661i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.60534 | − | 5.99121i | 0.0725218 | − | 0.270655i | ||||
\(491\) | − | 31.1973i | − | 1.40791i | −0.710243 | − | 0.703957i | \(-0.751415\pi\) | ||
0.710243 | − | 0.703957i | \(-0.248585\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2.53590i | − | 0.114211i | ||||||
\(494\) | 46.2934 | + | 12.4043i | 2.08284 | + | 0.558095i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.5862 | − | 8.42136i | 0.654940 | − | 0.378130i | ||||
\(497\) | − | 1.36071i | − | 0.0610361i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.78320 | −0.393190 | −0.196595 | − | 0.980485i | \(-0.562988\pi\) | ||||
−0.196595 | + | 0.980485i | \(0.562988\pi\) | |||||||
\(500\) | −70.1605 | − | 40.5072i | −3.13767 | − | 1.81154i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.10226 | − | 1.36715i | −0.227725 | − | 0.0610187i | ||||
\(503\) | 11.2679 | 0.502413 | 0.251207 | − | 0.967934i | \(-0.419173\pi\) | ||||
0.251207 | + | 0.967934i | \(0.419173\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.77174 | 0.390337 | ||||||||
\(506\) | 32.4342 | + | 8.69073i | 1.44188 | + | 0.386350i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.4465 | − | 23.2900i | 0.596593 | − | 1.03333i | ||||
\(509\) | −7.99388 | −0.354322 | −0.177161 | − | 0.984182i | \(-0.556691\pi\) | ||||
−0.177161 | + | 0.984182i | \(0.556691\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.4465i | 0.683314i | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.2832 | + | 2.75537i | 0.453572 | + | 0.121534i | ||||
\(515\) | − | 7.34536i | − | 0.323675i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.1816i | 0.579727i | ||||||||
\(518\) | 0.726734 | − | 2.71221i | 0.0319309 | − | 0.119168i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 45.7067 | + | 45.7067i | 2.00437 | + | 2.00437i | ||||
\(521\) | − | 15.1797i | − | 0.665035i | −0.943097 | − | 0.332517i | \(-0.892102\pi\) | ||
0.943097 | − | 0.332517i | \(-0.107898\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.58846 | −0.244366 | −0.122183 | − | 0.992508i | \(-0.538990\pi\) | ||||
−0.122183 | + | 0.992508i | \(0.538990\pi\) | |||||||
\(524\) | 1.77480 | − | 3.07404i | 0.0775323 | − | 0.134290i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.11945 | − | 22.8381i | 0.266821 | − | 0.995789i | ||||
\(527\) | −8.42136 | −0.366840 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.47698 | −0.0642163 | ||||||||
\(530\) | 16.4320 | − | 61.3250i | 0.713760 | − | 2.66379i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.50379 | + | 11.2649i | −0.281975 | + | 0.488395i | ||||
\(533\) | −38.4097 | −1.66371 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 45.0204i | − | 1.94640i | ||||||
\(536\) | 10.4214 | − | 10.4214i | 0.450134 | − | 0.450134i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.50614 | − | 5.62100i | 0.0649344 | − | 0.242339i | ||||
\(539\) | − | 5.11792i | − | 0.220444i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 10.1229i | − | 0.435219i | −0.976036 | − | 0.217610i | \(-0.930174\pi\) | ||
0.976036 | − | 0.217610i | \(-0.0698260\pi\) | |||||||
\(542\) | −5.89158 | − | 1.57864i | −0.253065 | − | 0.0678086i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.92820 | + | 10.9282i | 0.125546 | + | 0.468543i | ||||
\(545\) | − | 5.67140i | − | 0.242936i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.03662 | 0.300864 | 0.150432 | − | 0.988620i | \(-0.451933\pi\) | ||||
0.150432 | + | 0.988620i | \(0.451933\pi\) | |||||||
\(548\) | −14.5756 | + | 25.2457i | −0.622638 | + | 1.07844i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −99.5257 | − | 26.6678i | −4.24379 | − | 1.13712i | ||||
\(551\) | −8.24647 | −0.351311 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.98241 | 0.169349 | ||||||||
\(554\) | 37.9159 | + | 10.1595i | 1.61089 | + | 0.431638i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −25.9939 | − | 15.0076i | −1.10239 | − | 0.636463i | ||||
\(557\) | 11.0427 | 0.467896 | 0.233948 | − | 0.972249i | \(-0.424835\pi\) | ||||
0.233948 | + | 0.972249i | \(0.424835\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.3708i | 0.819299i | ||||||||
\(560\) | −15.1931 | + | 8.77174i | −0.642025 | + | 0.370673i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −29.9106 | − | 8.01453i | −1.26170 | − | 0.338072i | ||||
\(563\) | − | 19.1115i | − | 0.805453i | −0.915320 | − | 0.402726i | \(-0.868063\pi\) | ||
0.915320 | − | 0.402726i | \(-0.131937\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 35.4351i | − | 1.49076i | ||||||
\(566\) | −5.62896 | + | 21.0076i | −0.236603 | + | 0.883014i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.72142 | + | 2.72142i | −0.114188 | + | 0.114188i | ||||
\(569\) | − | 12.6443i | − | 0.530077i | −0.964238 | − | 0.265039i | \(-0.914615\pi\) | ||
0.964238 | − | 0.265039i | \(-0.0853847\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.4351 | 0.813332 | 0.406666 | − | 0.913577i | \(-0.366691\pi\) | ||||
0.406666 | + | 0.913577i | \(0.366691\pi\) | |||||||
\(572\) | 46.1900 | + | 26.6678i | 1.93130 | + | 1.11504i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.69810 | − | 10.0694i | 0.112616 | − | 0.420290i | ||||
\(575\) | −66.0442 | −2.75423 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −42.8137 | −1.78236 | −0.891178 | − | 0.453654i | \(-0.850120\pi\) | ||||
−0.891178 | + | 0.453654i | \(0.850120\pi\) | |||||||
\(578\) | −4.75833 | + | 17.7583i | −0.197920 | + | 0.738649i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.63203 | − | 5.56106i | −0.399948 | − | 0.230910i | ||||
\(581\) | −11.6893 | −0.484954 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 52.3862i | − | 2.16961i | ||||||
\(584\) | 30.8930 | − | 30.8930i | 1.27836 | − | 1.27836i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.149515 | − | 0.557997i | 0.00617641 | − | 0.0230507i | ||||
\(587\) | − | 28.9221i | − | 1.19374i | −0.802337 | − | 0.596871i | \(-0.796410\pi\) | ||
0.802337 | − | 0.596871i | \(-0.203590\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.3854i | 1.12839i | ||||||||
\(590\) | 20.9919 | + | 5.62477i | 0.864223 | + | 0.231568i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.87788 | + | 3.97095i | −0.282679 | + | 0.163205i | ||||
\(593\) | − | 41.9140i | − | 1.72120i | −0.509280 | − | 0.860601i | \(-0.670088\pi\) | ||
0.509280 | − | 0.860601i | \(-0.329912\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.77174 | 0.359606 | ||||||||
\(596\) | 9.24341 | + | 5.33669i | 0.378625 | + | 0.218599i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 33.0221 | + | 8.84824i | 1.35037 | + | 0.361832i | ||||
\(599\) | 20.5829 | 0.840993 | 0.420496 | − | 0.907294i | \(-0.361856\pi\) | ||||
0.420496 | + | 0.907294i | \(0.361856\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.44652 | 0.222168 | 0.111084 | − | 0.993811i | \(-0.464568\pi\) | ||||
0.111084 | + | 0.993811i | \(0.464568\pi\) | |||||||
\(602\) | −5.07823 | − | 1.36071i | −0.206973 | − | 0.0554583i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.5725 | − | 30.4365i | 0.715016 | − | 1.23844i | ||||
\(605\) | −66.6349 | −2.70909 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 3.40600i | − | 0.138245i | −0.997608 | − | 0.0691226i | \(-0.977980\pi\) | ||
0.997608 | − | 0.0691226i | \(-0.0220200\pi\) | |||||||
\(608\) | 35.5374 | − | 9.52220i | 1.44123 | − | 0.386176i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −27.1755 | − | 7.28165i | −1.10030 | − | 0.294826i | ||||
\(611\) | 13.4205i | 0.542937i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 23.0992i | − | 0.932968i | −0.884530 | − | 0.466484i | \(-0.845521\pi\) | ||
0.884530 | − | 0.466484i | \(-0.154479\pi\) | |||||||
\(614\) | −3.65913 | + | 13.6561i | −0.147671 | + | 0.551114i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.2358 | + | 10.2358i | −0.412414 | + | 0.412414i | ||||
\(617\) | 25.4457i | 1.02440i | 0.858865 | + | 0.512202i | \(0.171170\pi\) | ||||
−0.858865 | + | 0.512202i | \(0.828830\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.7167 | −0.752287 | −0.376144 | − | 0.926561i | \(-0.622750\pi\) | ||||
−0.376144 | + | 0.926561i | \(0.622750\pi\) | |||||||
\(620\) | −18.4675 | + | 31.9866i | −0.741672 | + | 1.28461i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.30598 | − | 27.2663i | 0.292943 | − | 1.09328i | ||||
\(623\) | 14.8645 | 0.595533 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 106.480 | 4.25920 | ||||||||
\(626\) | −8.58202 | + | 32.0285i | −0.343007 | + | 1.28012i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.8259 | − | 23.9472i | 0.551715 | − | 0.955599i | ||||
\(629\) | 3.97095 | 0.158332 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.5549i | 1.25618i | 0.778140 | + | 0.628091i | \(0.216163\pi\) | ||||
−0.778140 | + | 0.628091i | \(0.783837\pi\) | |||||||
\(632\) | −7.96483 | − | 7.96483i | −0.316824 | − | 0.316824i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.60380 | + | 28.3778i | −0.301986 | + | 1.12703i | ||||
\(635\) | 58.9746i | 2.34034i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 5.21068i | − | 0.206455i | ||||||
\(638\) | −8.86450 | − | 2.37523i | −0.350949 | − | 0.0940364i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 47.9297 | + | 12.8427i | 1.89459 | + | 0.507653i | ||||
\(641\) | 9.53508i | 0.376613i | 0.982110 | + | 0.188306i | \(0.0602998\pi\) | ||||
−0.982110 | + | 0.188306i | \(0.939700\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.8243 | −1.49164 | −0.745822 | − | 0.666145i | \(-0.767943\pi\) | ||||
−0.745822 | + | 0.666145i | \(0.767943\pi\) | |||||||
\(644\) | −4.63929 | + | 8.03549i | −0.182814 | + | 0.316643i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.7687 | − | 4.76110i | −0.699099 | − | 0.187323i | ||||
\(647\) | −19.4663 | −0.765301 | −0.382650 | − | 0.923893i | \(-0.624989\pi\) | ||||
−0.382650 | + | 0.923893i | \(0.624989\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.9321 | 0.703896 | ||||||||
\(650\) | −101.330 | − | 27.1512i | −3.97447 | − | 1.06496i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.0252 | − | 8.67478i | −0.588431 | − | 0.339731i | ||||
\(653\) | 9.58928 | 0.375257 | 0.187629 | − | 0.982240i | \(-0.439920\pi\) | ||||
0.187629 | + | 0.982240i | \(0.439920\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.78402i | 0.304147i | ||||||||
\(656\) | −25.5351 | + | 14.7427i | −0.996977 | + | 0.575605i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.51831 | − | 0.942729i | −0.137158 | − | 0.0367514i | ||||
\(659\) | 13.0615i | 0.508803i | 0.967099 | + | 0.254402i | \(0.0818785\pi\) | ||||
−0.967099 | + | 0.254402i | \(0.918122\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 39.8807i | − | 1.55118i | −0.631236 | − | 0.775591i | \(-0.717452\pi\) | ||
0.631236 | − | 0.775591i | \(-0.282548\pi\) | |||||||
\(662\) | −6.96789 | + | 26.0045i | −0.270815 | + | 1.01069i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 23.3786 | + | 23.3786i | 0.907266 | + | 0.907266i | ||||
\(665\) | − | 28.5247i | − | 1.10614i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.88239 | −0.227767 | ||||||||
\(668\) | 27.5144 | + | 15.8855i | 1.06456 | + | 0.614627i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.36491 | + | 31.2183i | −0.323164 | + | 1.20607i | ||||
\(671\) | −23.2144 | −0.896180 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.8992 | −0.497226 | −0.248613 | − | 0.968603i | \(-0.579975\pi\) | ||||
−0.248613 | + | 0.968603i | \(0.579975\pi\) | |||||||
\(674\) | −1.05615 | + | 3.94161i | −0.0406814 | + | 0.151825i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 24.5105 | + | 14.1512i | 0.942713 | + | 0.544276i | ||||
\(677\) | −30.1713 | −1.15958 | −0.579789 | − | 0.814767i | \(-0.696865\pi\) | ||||
−0.579789 | + | 0.814767i | \(0.696865\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.42136i | 0.169676i | ||||||||
\(680\) | −17.5435 | − | 17.5435i | −0.672761 | − | 0.672761i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.88781 | + | 29.4377i | −0.302040 | + | 1.12723i | ||||
\(683\) | 6.61719i | 0.253200i | 0.991954 | + | 0.126600i | \(0.0404064\pi\) | ||||
−0.991954 | + | 0.126600i | \(0.959594\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 63.9266i | − | 2.44251i | ||||||
\(686\) | 1.36603 | + | 0.366025i | 0.0521551 | + | 0.0139749i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.43505 | + | 12.8779i | 0.283459 | + | 0.490965i | ||||
\(689\) | − | 53.3357i | − | 2.03193i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.6701 | 1.54716 | 0.773581 | − | 0.633697i | \(-0.218463\pi\) | ||||
0.773581 | + | 0.633697i | \(0.218463\pi\) | |||||||
\(692\) | −7.32554 | − | 4.22940i | −0.278475 | − | 0.160778i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 41.9415 | + | 11.2382i | 1.59208 | + | 0.426596i | ||||
\(695\) | 65.8212 | 2.49674 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.7427 | 0.558419 | ||||||||
\(698\) | 36.2007 | + | 9.69994i | 1.37022 | + | 0.367148i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 14.2358 | − | 24.6572i | 0.538064 | − | 0.931954i | ||||
\(701\) | −18.4320 | −0.696167 | −0.348083 | − | 0.937464i | \(-0.613167\pi\) | ||||
−0.348083 | + | 0.937464i | \(0.613167\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 12.9131i | − | 0.487027i | ||||||
\(704\) | 40.9433 | 1.54311 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.60534 | − | 2.30579i | −0.323866 | − | 0.0867797i | ||||
\(707\) | 2.00000i | 0.0752177i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.1221i | 0.793258i | 0.917979 | + | 0.396629i | \(0.129820\pi\) | ||||
−0.917979 | + | 0.396629i | \(0.870180\pi\) | |||||||
\(710\) | 2.18440 | − | 8.15229i | 0.0819790 | − | 0.305950i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −29.7290 | − | 29.7290i | −1.11414 | − | 1.11414i | ||||
\(713\) | 19.5346i | 0.731575i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −116.962 | −4.37411 | ||||||||
\(716\) | 6.45041 | − | 11.1724i | 0.241063 | − | 0.417533i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.588457 | − | 2.19615i | 0.0219610 | − | 0.0819597i | ||||
\(719\) | −24.1319 | −0.899969 | −0.449985 | − | 0.893036i | \(-0.648571\pi\) | ||||
−0.449985 | + | 0.893036i | \(0.648571\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.67478 | 0.0623721 | ||||||||
\(722\) | −8.52811 | + | 31.8274i | −0.317384 | + | 1.18449i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.5068 | − | 18.1984i | 0.390484 | − | 0.676338i | ||||
\(725\) | 18.0503 | 0.670372 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 18.3923i | − | 0.682133i | −0.940039 | − | 0.341066i | \(-0.889212\pi\) | ||
0.940039 | − | 0.341066i | \(-0.110788\pi\) | |||||||
\(728\) | −10.4214 | + | 10.4214i | −0.386241 | + | 0.386241i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −24.7969 | + | 92.5433i | −0.917774 | + | 3.42518i | ||||
\(731\) | − | 7.43505i | − | 0.274995i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 34.5602i | − | 1.27651i | −0.769824 | − | 0.638256i | \(-0.779656\pi\) | ||
0.769824 | − | 0.638256i | \(-0.220344\pi\) | |||||||
\(734\) | 23.4633 | + | 6.28697i | 0.866046 | + | 0.232056i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 25.3496 | − | 6.79239i | 0.934397 | − | 0.250371i | ||||
\(737\) | 26.6678i | 0.982322i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.0366 | 1.65670 | 0.828350 | − | 0.560212i | \(-0.189280\pi\) | ||||
0.828350 | + | 0.560212i | \(0.189280\pi\) | |||||||
\(740\) | 8.70803 | − | 15.0827i | 0.320113 | − | 0.554453i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.9824 | + | 3.74658i | 0.513311 | + | 0.137541i | ||||
\(743\) | −7.83850 | −0.287567 | −0.143783 | − | 0.989609i | \(-0.545927\pi\) | ||||
−0.143783 | + | 0.989609i | \(0.545927\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.4060 | −0.857529 | ||||||||
\(746\) | −3.11374 | − | 0.834324i | −0.114002 | − | 0.0305468i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −17.7290 | − | 10.2358i | −0.648236 | − | 0.374259i | ||||
\(749\) | 10.2649 | 0.375071 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 38.4328i | − | 1.40243i | −0.712948 | − | 0.701217i | \(-0.752641\pi\) | ||
0.712948 | − | 0.701217i | \(-0.247359\pi\) | |||||||
\(752\) | 5.15117 | + | 8.92208i | 0.187844 | + | 0.325355i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.02516 | − | 2.41828i | −0.328677 | − | 0.0880687i | ||||
\(755\) | 77.0708i | 2.80489i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.24423i | − | 0.0815680i | −0.999168 | − | 0.0407840i | \(-0.987014\pi\) | ||
0.999168 | − | 0.0407840i | \(-0.0129855\pi\) | |||||||
\(758\) | −7.37134 | + | 27.5102i | −0.267739 | + | 0.999216i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −57.0495 | + | 57.0495i | −2.06940 | + | 2.06940i | ||||
\(761\) | 28.3946i | 1.02930i | 0.857400 | + | 0.514651i | \(0.172079\pi\) | ||||
−0.857400 | + | 0.514651i | \(0.827921\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.29311 | 0.0468137 | ||||||||
\(764\) | −14.3065 | − | 8.25986i | −0.517591 | − | 0.298831i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.16486 | − | 30.4717i | 0.295008 | − | 1.10099i | ||||
\(767\) | 18.2571 | 0.659226 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.2968 | 0.984348 | 0.492174 | − | 0.870497i | \(-0.336202\pi\) | ||||
0.492174 | + | 0.870497i | \(0.336202\pi\) | |||||||
\(770\) | 8.21599 | − | 30.6625i | 0.296084 | − | 1.10500i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.9939 | + | 8.07937i | 0.503651 | + | 0.290783i | ||||
\(773\) | 31.6583 | 1.13867 | 0.569335 | − | 0.822105i | \(-0.307201\pi\) | ||||
0.569335 | + | 0.822105i | \(0.307201\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 59.9425i | − | 2.15320i | ||||||
\(776\) | 8.84271 | − | 8.84271i | 0.317435 | − | 0.317435i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.577824 | + | 2.15647i | −0.0207160 | + | 0.0773131i | ||||
\(779\) | − | 47.9416i | − | 1.71769i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 6.96400i | − | 0.249191i | ||||||
\(782\) | −12.6748 | − | 3.39620i | −0.453249 | − | 0.121448i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.00000 | − | 3.46410i | −0.0714286 | − | 0.123718i | ||||
\(785\) | 60.6388i | 2.16429i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.1375 | −0.860408 | −0.430204 | − | 0.902732i | \(-0.641558\pi\) | ||||
−0.430204 | + | 0.902732i | \(0.641558\pi\) | |||||||
\(788\) | −12.1984 | − | 7.04275i | −0.434550 | − | 0.250887i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 23.8595 | + | 6.39312i | 0.848882 | + | 0.227457i | ||||
\(791\) | 8.07937 | 0.287269 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.6351 | −0.839307 | ||||||||
\(794\) | −42.9327 | − | 11.5038i | −1.52363 | − | 0.408254i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.1336 | + | 34.8724i | −0.713616 | + | 1.23602i | ||||
\(797\) | −23.1867 | −0.821313 | −0.410657 | − | 0.911790i | \(-0.634701\pi\) | ||||
−0.410657 | + | 0.911790i | \(0.634701\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.15117i | − | 0.182235i | ||||||
\(800\) | −77.7861 | + | 20.8427i | −2.75015 | + | 0.736901i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 36.2549 | + | 9.71446i | 1.28020 | + | 0.343030i | ||||
\(803\) | 79.0540i | 2.78976i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 20.3473i | − | 0.717149i | ||||||
\(806\) | −8.03078 | + | 29.9713i | −0.282872 | + | 1.05569i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.00000 | − | 4.00000i | 0.140720 | − | 0.140720i | ||||
\(809\) | − | 24.2823i | − | 0.853719i | −0.904318 | − | 0.426860i | \(-0.859620\pi\) | ||
0.904318 | − | 0.426860i | \(-0.140380\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.1610 | 1.02398 | 0.511990 | − | 0.858991i | \(-0.328908\pi\) | ||||
0.511990 | + | 0.858991i | \(0.328908\pi\) | |||||||
\(812\) | 1.26795 | − | 2.19615i | 0.0444963 | − | 0.0770698i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.71937 | − | 13.8809i | 0.130364 | − | 0.486524i | ||||
\(815\) | 38.0464 | 1.33271 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.1780 | −0.845881 | ||||||||
\(818\) | −11.7142 | + | 43.7178i | −0.409576 | + | 1.52856i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 32.3297 | − | 55.9967i | 1.12900 | − | 1.95549i | ||||
\(821\) | 42.6701 | 1.48920 | 0.744598 | − | 0.667513i | \(-0.232641\pi\) | ||||
0.744598 | + | 0.667513i | \(0.232641\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 18.4487i | − | 0.643083i | −0.946896 | − | 0.321541i | \(-0.895799\pi\) | ||
0.946896 | − | 0.321541i | \(-0.104201\pi\) | |||||||
\(824\) | −3.34956 | − | 3.34956i | −0.116687 | − | 0.116687i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.28247 | + | 4.78626i | −0.0446230 | + | 0.166535i | ||||
\(827\) | − | 37.8393i | − | 1.31580i | −0.753104 | − | 0.657901i | \(-0.771444\pi\) | ||
0.753104 | − | 0.657901i | \(-0.228556\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.5463i | 1.61662i | 0.588756 | + | 0.808310i | \(0.299618\pi\) | ||||
−0.588756 | + | 0.808310i | \(0.700382\pi\) | |||||||
\(830\) | −70.0330 | − | 18.7653i | −2.43088 | − | 0.651353i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 41.6854 | 1.44518 | ||||||||
\(833\) | 2.00000i | 0.0692959i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −69.6715 | −2.41108 | ||||||||
\(836\) | −33.2859 | + | 57.6528i | −1.15122 | + | 1.99396i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −28.2183 | − | 7.56106i | −0.974783 | − | 0.261192i | ||||
\(839\) | 12.9388 | 0.446698 | 0.223349 | − | 0.974739i | \(-0.428301\pi\) | ||||
0.223349 | + | 0.974739i | \(0.428301\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3923 | −0.944562 | ||||||||
\(842\) | 45.0693 | + | 12.0763i | 1.55319 | + | 0.416177i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.0657 | − | 7.54347i | −0.449739 | − | 0.259657i | ||||
\(845\) | −62.0651 | −2.13511 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 15.1931i | − | 0.522041i | ||||||
\(848\) | −20.4717 | − | 35.4580i | −0.703000 | − | 1.21763i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 38.8930 | + | 10.4214i | 1.33402 | + | 0.357450i | ||||
\(851\) | − | 9.21119i | − | 0.315756i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.9509i | 1.71029i | 0.518391 | + | 0.855144i | \(0.326531\pi\) | ||||
−0.518391 | + | 0.855144i | \(0.673469\pi\) | |||||||
\(854\) | 1.66025 | − | 6.19615i | 0.0568127 | − | 0.212028i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20.5298 | − | 20.5298i | −0.701693 | − | 0.701693i | ||||
\(857\) | 32.4208i | 1.10747i | 0.832691 | + | 0.553737i | \(0.186799\pi\) | ||||
−0.832691 | + | 0.553737i | \(0.813201\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.3311 | −0.625450 | −0.312725 | − | 0.949844i | \(-0.601242\pi\) | ||||
−0.312725 | + | 0.949844i | \(0.601242\pi\) | |||||||
\(860\) | −28.2404 | − | 16.3046i | −0.962988 | − | 0.555981i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.37288 | + | 8.85570i | −0.0808206 | + | 0.301626i | ||||
\(863\) | −3.77704 | −0.128572 | −0.0642859 | − | 0.997932i | \(-0.520477\pi\) | ||||
−0.0642859 | + | 0.997932i | \(0.520477\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.5496 | 0.630705 | ||||||||
\(866\) | 6.73625 | − | 25.1400i | 0.228907 | − | 0.854293i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.29311 | − | 4.21068i | −0.247544 | − | 0.142920i | ||||
\(869\) | 20.3817 | 0.691401 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.1512i | 0.919982i | ||||||||
\(872\) | −2.58622 | − | 2.58622i | −0.0875804 | − | 0.0875804i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.0441 | + | 41.2170i | −0.373571 | + | 1.39419i | ||||
\(875\) | 40.5072i | 1.36939i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 9.61218i | − | 0.324580i | −0.986743 | − | 0.162290i | \(-0.948112\pi\) | ||
0.986743 | − | 0.162290i | \(-0.0518880\pi\) | |||||||
\(878\) | 5.89158 | + | 1.57864i | 0.198831 | + | 0.0532766i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −77.7570 | + | 44.8930i | −2.62119 | + | 1.51334i | ||||
\(881\) | 22.4722i | 0.757107i | 0.925579 | + | 0.378554i | \(0.123578\pi\) | ||||
−0.925579 | + | 0.378554i | \(0.876422\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.77704 | −0.329023 | −0.164512 | − | 0.986375i | \(-0.552605\pi\) | ||||
−0.164512 | + | 0.986375i | \(0.552605\pi\) | |||||||
\(884\) | −18.0503 | − | 10.4214i | −0.607098 | − | 0.350508i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.57515 | − | 2.02976i | −0.254492 | − | 0.0681910i | ||||
\(887\) | −59.1043 | −1.98453 | −0.992265 | − | 0.124141i | \(-0.960383\pi\) | ||||
−0.992265 | + | 0.124141i | \(0.960383\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.4465 | −0.450982 | ||||||||
\(890\) | 89.0563 | + | 23.8626i | 2.98517 | + | 0.799875i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.48926 | + | 9.50768i | −0.183794 | + | 0.318341i | ||||
\(893\) | −16.7510 | −0.560552 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.2906i | 0.945652i | ||||||||
\(896\) | −2.92820 | + | 10.9282i | −0.0978244 | + | 0.365086i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −41.2549 | − | 11.0542i | −1.37669 | − | 0.368884i | ||||
\(899\) | − | 5.33893i | − | 0.178063i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.4717i | 0.682010i | ||||||||
\(902\) | 13.8086 | − | 51.5346i | 0.459778 | − | 1.71591i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.1587 | − | 16.1587i | −0.537432 | − | 0.537432i | ||||
\(905\) | 46.0816i | 1.53181i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.9861 | −1.06208 | −0.531040 | − | 0.847346i | \(-0.678199\pi\) | ||||
−0.531040 | + | 0.847346i | \(0.678199\pi\) | |||||||
\(908\) | −0.127416 | + | 0.220691i | −0.00422845 | + | 0.00732388i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.36491 | − | 31.2183i | 0.277294 | − | 1.03487i | ||||
\(911\) | 26.4052 | 0.874843 | 0.437421 | − | 0.899257i | \(-0.355892\pi\) | ||||
0.437421 | + | 0.899257i | \(0.355892\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −59.8249 | −1.97992 | ||||||||
\(914\) | 8.90192 | − | 33.2224i | 0.294449 | − | 1.09890i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.53590 | − | 11.3205i | 0.215952 | − | 0.374040i | ||||
\(917\) | −1.77480 | −0.0586089 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.4656i | 1.53276i | 0.642389 | + | 0.766379i | \(0.277943\pi\) | ||||
−0.642389 | + | 0.766379i | \(0.722057\pi\) | |||||||
\(920\) | −40.6946 | + | 40.6946i | −1.34166 | + | 1.34166i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.6579 | − | 50.9720i | 0.449799 | − | 1.67867i | ||||
\(923\) | − | 7.09021i | − | 0.233377i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.2649i | 0.929344i | ||||||||
\(926\) | −48.2007 | − | 12.9153i | −1.58397 | − | 0.424424i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.92820 | + | 1.85641i | −0.227429 | + | 0.0609395i | ||||
\(929\) | 16.7656i | 0.550062i | 0.961435 | + | 0.275031i | \(0.0886881\pi\) | ||||
−0.961435 | + | 0.275031i | \(0.911312\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.50379 | 0.213153 | ||||||||
\(932\) | −10.5359 | + | 18.2487i | −0.345115 | + | 0.597756i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28.3892 | + | 7.60688i | 0.928924 | + | 0.248905i | ||||
\(935\) | 44.8930 | 1.46816 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.3923 | −1.05821 | −0.529105 | − | 0.848556i | \(-0.677472\pi\) | ||||
−0.529105 | + | 0.848556i | \(0.677472\pi\) | |||||||
\(938\) | −7.11792 | − | 1.90724i | −0.232408 | − | 0.0622736i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −19.5655 | − | 11.2962i | −0.638157 | − | 0.368440i | ||||
\(941\) | −40.1216 | −1.30793 | −0.653964 | − | 0.756526i | \(-0.726895\pi\) | ||||
−0.653964 | + | 0.756526i | \(0.726895\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 34.1978i | − | 1.11363i | ||||||
\(944\) | 12.1375 | − | 7.00757i | 0.395041 | − | 0.228077i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −25.9900 | − | 6.96400i | −0.845007 | − | 0.226419i | ||||
\(947\) | 38.9905i | 1.26702i | 0.773734 | + | 0.633511i | \(0.218387\pi\) | ||||
−0.773734 | + | 0.633511i | \(0.781613\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 80.4868i | 2.61271i | ||||||||
\(950\) | 33.8891 | − | 126.476i | 1.09951 | − | 4.10342i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.00000 | − | 4.00000i | 0.129641 | − | 0.129641i | ||||
\(953\) | − | 1.39764i | − | 0.0452739i | −0.999744 | − | 0.0226370i | \(-0.992794\pi\) | ||
0.999744 | − | 0.0226370i | \(-0.00720619\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36.2267 | 1.17227 | ||||||||
\(956\) | −42.2381 | − | 24.3862i | −1.36608 | − | 0.788706i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.28247 | + | 23.4465i | −0.202978 | + | 0.757523i | ||||
\(959\) | 14.5756 | 0.470670 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.2702 | 0.428071 | ||||||||
\(962\) | 3.78678 | − | 14.1324i | 0.122091 | − | 0.455648i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 18.8106 | + | 10.8603i | 0.605848 | + | 0.349787i | ||||
\(965\) | −35.4351 | −1.14069 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.9709i | 0.706538i | 0.935522 | + | 0.353269i | \(0.114930\pi\) | ||||
−0.935522 | + | 0.353269i | \(0.885070\pi\) | |||||||
\(968\) | −30.3862 | + | 30.3862i | −0.976649 | + | 0.976649i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.09778 | + | 26.4893i | −0.227896 | + | 0.850519i | ||||
\(971\) | 42.7098i | 1.37062i | 0.728251 | + | 0.685311i | \(0.240334\pi\) | ||||
−0.728251 | + | 0.685311i | \(0.759666\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.0076i | 0.481121i | ||||||||
\(974\) | 52.9964 | + | 14.2003i | 1.69811 | + | 0.455009i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15.7128 | + | 9.07180i | −0.502955 | + | 0.290381i | ||||
\(977\) | − | 60.3885i | − | 1.93200i | −0.258546 | − | 0.965999i | \(-0.583243\pi\) | ||
0.258546 | − | 0.965999i | \(-0.416757\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 76.0753 | 2.43138 | ||||||||
\(980\) | 7.59655 | + | 4.38587i | 0.242663 | + | 0.140101i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 42.6163 | + | 11.4190i | 1.35994 | + | 0.364395i | ||||
\(983\) | −19.6251 | −0.625943 | −0.312971 | − | 0.949763i | \(-0.601324\pi\) | ||||
−0.312971 | + | 0.949763i | \(0.601324\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30.8886 | 0.984191 | ||||||||
\(986\) | 3.46410 | + | 0.928203i | 0.110319 | + | 0.0295600i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −33.8891 | + | 58.6977i | −1.07816 | + | 1.86742i | ||||
\(989\) | −17.2467 | −0.548413 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.84660i | 0.249256i | 0.992204 | + | 0.124628i | \(0.0397737\pi\) | ||||
−0.992204 | + | 0.124628i | \(0.960226\pi\) | |||||||
\(992\) | 6.16486 | + | 23.0076i | 0.195735 | + | 0.730491i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.85876 | + | 0.498054i | 0.0589564 | + | 0.0157973i | ||||
\(995\) | − | 88.3032i | − | 2.79940i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.9128i | 0.630646i | 0.948984 | + | 0.315323i | \(0.102113\pi\) | ||||
−0.948984 | + | 0.315323i | \(0.897887\pi\) | |||||||
\(998\) | 3.21487 | − | 11.9981i | 0.101765 | − | 0.379792i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1512.2.j.b.323.4 | yes | 8 | |
3.2 | odd | 2 | 1512.2.j.a.323.5 | ✓ | 8 | ||
4.3 | odd | 2 | 6048.2.j.b.5615.7 | 8 | |||
8.3 | odd | 2 | 1512.2.j.a.323.7 | yes | 8 | ||
8.5 | even | 2 | 6048.2.j.a.5615.2 | 8 | |||
12.11 | even | 2 | 6048.2.j.a.5615.1 | 8 | |||
24.5 | odd | 2 | 6048.2.j.b.5615.8 | 8 | |||
24.11 | even | 2 | inner | 1512.2.j.b.323.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.a.323.5 | ✓ | 8 | 3.2 | odd | 2 | ||
1512.2.j.a.323.7 | yes | 8 | 8.3 | odd | 2 | ||
1512.2.j.b.323.2 | yes | 8 | 24.11 | even | 2 | inner | |
1512.2.j.b.323.4 | yes | 8 | 1.1 | even | 1 | trivial | |
6048.2.j.a.5615.1 | 8 | 12.11 | even | 2 | |||
6048.2.j.a.5615.2 | 8 | 8.5 | even | 2 | |||
6048.2.j.b.5615.7 | 8 | 4.3 | odd | 2 | |||
6048.2.j.b.5615.8 | 8 | 24.5 | odd | 2 |