Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(757,1512)]
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([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.757");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.c (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: | 8.0.3317760000.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 7x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 757.2 | ||
Root | \(0.178197 - 1.40294i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.757 |
Dual form | 1512.2.c.c.757.1 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.40294 | + | 0.178197i | −0.992030 | + | 0.126004i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.93649 | − | 0.500000i | 0.968246 | − | 0.250000i | ||||
\(5\) | − | 0.356394i | − | 0.159384i | −0.996820 | − | 0.0796921i | \(-0.974606\pi\) | ||
0.996820 | − | 0.0796921i | \(-0.0253937\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.62769 | + | 1.04655i | −0.929028 | + | 0.370011i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.0635083 | + | 0.500000i | 0.0200831 | + | 0.158114i | ||||
\(11\) | 5.96816i | 1.79947i | 0.436438 | + | 0.899734i | \(0.356240\pi\) | ||||
−0.436438 | + | 0.899734i | \(0.643760\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.87298i | − | 0.796822i | −0.917207 | − | 0.398411i | \(-0.869562\pi\) | ||
0.917207 | − | 0.398411i | \(-0.130438\pi\) | |||||||
\(14\) | 1.40294 | − | 0.178197i | 0.374952 | − | 0.0476251i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.50000 | − | 1.93649i | 0.875000 | − | 0.484123i | ||||
\(17\) | 3.16228 | 0.766965 | 0.383482 | − | 0.923548i | \(-0.374725\pi\) | ||||
0.383482 | + | 0.923548i | \(0.374725\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.127017i | − | 0.0291396i | −0.999894 | − | 0.0145698i | \(-0.995362\pi\) | ||
0.999894 | − | 0.0145698i | \(-0.00463788\pi\) | |||||||
\(20\) | −0.178197 | − | 0.690154i | −0.0398461 | − | 0.154323i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.06351 | − | 8.37298i | −0.226741 | − | 1.78513i | ||||
\(23\) | −2.80588 | −0.585067 | −0.292534 | − | 0.956255i | \(-0.594498\pi\) | ||||
−0.292534 | + | 0.956255i | \(0.594498\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.87298 | 0.974597 | ||||||||
\(26\) | 0.511957 | + | 4.03063i | 0.100403 | + | 0.790471i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.93649 | + | 0.500000i | −0.365963 | + | 0.0944911i | ||||
\(29\) | 2.44949i | 0.454859i | 0.973795 | + | 0.227429i | \(0.0730321\pi\) | ||||
−0.973795 | + | 0.227429i | \(0.926968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.00000 | −1.25724 | −0.628619 | − | 0.777714i | \(-0.716379\pi\) | ||||
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | −4.56522 | + | 3.34047i | −0.807024 | + | 0.590518i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.43649 | + | 0.563508i | −0.760852 | + | 0.0966409i | ||||
\(35\) | 0.356394i | 0.0602416i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.87298i | 0.307917i | 0.988077 | + | 0.153958i | \(0.0492021\pi\) | ||||
−0.988077 | + | 0.153958i | \(0.950798\pi\) | |||||||
\(38\) | 0.0226340 | + | 0.178197i | 0.00367172 | + | 0.0289074i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.372983 | + | 0.936492i | 0.0589738 | + | 0.148072i | ||||
\(41\) | −6.99208 | −1.09198 | −0.545989 | − | 0.837792i | \(-0.683846\pi\) | ||||
−0.545989 | + | 0.837792i | \(0.683846\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.12702i | − | 0.171868i | −0.996301 | − | 0.0859342i | \(-0.972613\pi\) | ||
0.996301 | − | 0.0859342i | \(-0.0273875\pi\) | |||||||
\(44\) | 2.98408 | + | 11.5573i | 0.449867 | + | 1.74233i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.93649 | − | 0.500000i | 0.580404 | − | 0.0737210i | ||||
\(47\) | −7.34847 | −1.07188 | −0.535942 | − | 0.844255i | \(-0.680044\pi\) | ||||
−0.535942 | + | 0.844255i | \(0.680044\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −6.83651 | + | 0.868351i | −0.966829 | + | 0.122803i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.43649 | − | 5.56351i | −0.199206 | − | 0.771520i | ||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.12702 | 0.286807 | ||||||||
\(56\) | 2.62769 | − | 1.04655i | 0.351139 | − | 0.139851i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.436492 | − | 3.43649i | −0.0573142 | − | 0.451233i | ||||
\(59\) | 6.63568i | 0.863892i | 0.901899 | + | 0.431946i | \(0.142173\pi\) | ||||
−0.901899 | + | 0.431946i | \(0.857827\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.7460i | 1.75999i | 0.474982 | + | 0.879995i | \(0.342454\pi\) | ||||
−0.474982 | + | 0.879995i | \(0.657546\pi\) | |||||||
\(62\) | 9.82059 | − | 1.24738i | 1.24722 | − | 0.158417i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.80948 | − | 5.50000i | 0.726184 | − | 0.687500i | ||||
\(65\) | −1.02391 | −0.127001 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.61895i | 1.05297i | 0.850184 | + | 0.526486i | \(0.176491\pi\) | ||||
−0.850184 | + | 0.526486i | \(0.823509\pi\) | |||||||
\(68\) | 6.12372 | − | 1.58114i | 0.742611 | − | 0.191741i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.0635083 | − | 0.500000i | −0.00759070 | − | 0.0597614i | ||||
\(71\) | 5.96816 | 0.708290 | 0.354145 | − | 0.935190i | \(-0.384772\pi\) | ||||
0.354145 | + | 0.935190i | \(0.384772\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.872983 | 0.102175 | 0.0510875 | − | 0.998694i | \(-0.483731\pi\) | ||||
0.0510875 | + | 0.998694i | \(0.483731\pi\) | |||||||
\(74\) | −0.333760 | − | 2.62769i | −0.0387988 | − | 0.305462i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0635083 | − | 0.245967i | −0.00728490 | − | 0.0282143i | ||||
\(77\) | − | 5.96816i | − | 0.680135i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.6190 | 1.41974 | 0.709871 | − | 0.704331i | \(-0.248753\pi\) | ||||
0.709871 | + | 0.704331i | \(0.248753\pi\) | |||||||
\(80\) | −0.690154 | − | 1.24738i | −0.0771616 | − | 0.139461i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.80948 | − | 1.24597i | 1.08328 | − | 0.137594i | ||||
\(83\) | 6.63568i | 0.728361i | 0.931328 | + | 0.364180i | \(0.118651\pi\) | ||||
−0.931328 | + | 0.364180i | \(0.881349\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1.12702i | − | 0.122242i | ||||||
\(86\) | 0.200831 | + | 1.58114i | 0.0216562 | + | 0.170499i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.24597 | − | 15.6825i | −0.665822 | − | 1.67176i | ||||
\(89\) | −6.99208 | −0.741158 | −0.370579 | − | 0.928801i | \(-0.620841\pi\) | ||||
−0.370579 | + | 0.928801i | \(0.620841\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.87298i | 0.301170i | ||||||||
\(92\) | −5.43357 | + | 1.40294i | −0.566489 | + | 0.146267i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.3095 | − | 1.30948i | 1.06334 | − | 0.135062i | ||||
\(95\) | −0.0452680 | −0.00464440 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.74597 | −0.989553 | −0.494776 | − | 0.869020i | \(-0.664750\pi\) | ||||
−0.494776 | + | 0.869020i | \(0.664750\pi\) | |||||||
\(98\) | −1.40294 | + | 0.178197i | −0.141719 | + | 0.0180006i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.43649 | − | 2.43649i | 0.943649 | − | 0.243649i | ||||
\(101\) | − | 11.5347i | − | 1.14774i | −0.818946 | − | 0.573871i | \(-0.805441\pi\) | ||
0.818946 | − | 0.573871i | \(-0.194559\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.7460 | −1.05883 | −0.529416 | − | 0.848363i | \(-0.677589\pi\) | ||||
−0.529416 | + | 0.848363i | \(0.677589\pi\) | |||||||
\(104\) | 3.00671 | + | 7.54930i | 0.294833 | + | 0.740270i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.3858i | 1.39073i | 0.718657 | + | 0.695364i | \(0.244757\pi\) | ||||
−0.718657 | + | 0.695364i | \(0.755243\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.7460i | 1.22084i | 0.792077 | + | 0.610421i | \(0.209000\pi\) | ||||
−0.792077 | + | 0.610421i | \(0.791000\pi\) | |||||||
\(110\) | −2.98408 | + | 0.379028i | −0.284521 | + | 0.0361389i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.50000 | + | 1.93649i | −0.330719 | + | 0.182981i | ||||
\(113\) | 16.8353 | 1.58373 | 0.791866 | − | 0.610695i | \(-0.209110\pi\) | ||||
0.791866 | + | 0.610695i | \(0.209110\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000i | 0.0932505i | ||||||||
\(116\) | 1.22474 | + | 4.74342i | 0.113715 | + | 0.440415i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.18246 | − | 9.30948i | −0.108854 | − | 0.857007i | ||||
\(119\) | −3.16228 | −0.289886 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −24.6190 | −2.23809 | ||||||||
\(122\) | −2.44949 | − | 19.2848i | −0.221766 | − | 1.74596i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −13.5554 | + | 3.50000i | −1.21731 | + | 0.314309i | ||||
\(125\) | − | 3.51867i | − | 0.314720i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.8730 | 0.964821 | 0.482411 | − | 0.875945i | \(-0.339761\pi\) | ||||
0.482411 | + | 0.875945i | \(0.339761\pi\) | |||||||
\(128\) | −7.17027 | + | 8.75141i | −0.633769 | + | 0.773523i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.43649 | − | 0.182458i | 0.125989 | − | 0.0160027i | ||||
\(131\) | 8.77405i | 0.766592i | 0.923626 | + | 0.383296i | \(0.125211\pi\) | ||||
−0.923626 | + | 0.383296i | \(0.874789\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.127017i | 0.0110137i | ||||||||
\(134\) | −1.53587 | − | 12.0919i | −0.132679 | − | 1.04458i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.30948 | + | 3.30948i | −0.712532 | + | 0.283785i | ||||
\(137\) | −4.58785 | −0.391967 | −0.195983 | − | 0.980607i | \(-0.562790\pi\) | ||||
−0.195983 | + | 0.980607i | \(0.562790\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.0000i | 1.18746i | 0.804663 | + | 0.593732i | \(0.202346\pi\) | ||||
−0.804663 | + | 0.593732i | \(0.797654\pi\) | |||||||
\(140\) | 0.178197 | + | 0.690154i | 0.0150604 | + | 0.0583287i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.37298 | + | 1.06351i | −0.702645 | + | 0.0892476i | ||||
\(143\) | 17.1464 | 1.43386 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.872983 | 0.0724973 | ||||||||
\(146\) | −1.22474 | + | 0.155563i | −0.101361 | + | 0.0128745i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.936492 | + | 3.62702i | 0.0769791 | + | 0.298139i | ||||
\(149\) | 9.79796i | 0.802680i | 0.915929 | + | 0.401340i | \(0.131455\pi\) | ||||
−0.915929 | + | 0.401340i | \(0.868545\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 0.132929 | + | 0.333760i | 0.0107820 | + | 0.0270715i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.06351 | + | 8.37298i | 0.0856999 | + | 0.674714i | ||||
\(155\) | 2.49476i | 0.200384i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 7.12702i | − | 0.568798i | −0.958706 | − | 0.284399i | \(-0.908206\pi\) | ||
0.958706 | − | 0.284399i | \(-0.0917940\pi\) | |||||||
\(158\) | −17.7037 | + | 2.24866i | −1.40843 | + | 0.178894i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.19052 | + | 1.62702i | 0.0941193 | + | 0.128627i | ||||
\(161\) | 2.80588 | 0.221135 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.8730i | 1.79155i | 0.444507 | + | 0.895775i | \(0.353379\pi\) | ||||
−0.444507 | + | 0.895775i | \(0.646621\pi\) | |||||||
\(164\) | −13.5401 | + | 3.49604i | −1.05730 | + | 0.272995i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.18246 | − | 9.30948i | −0.0917766 | − | 0.722555i | ||||
\(167\) | 1.42558 | 0.110314 | 0.0551572 | − | 0.998478i | \(-0.482434\pi\) | ||||
0.0551572 | + | 0.998478i | \(0.482434\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.74597 | 0.365074 | ||||||||
\(170\) | 0.200831 | + | 1.58114i | 0.0154030 | + | 0.121268i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.563508 | − | 2.18246i | −0.0429671 | − | 0.166411i | ||||
\(173\) | − | 18.2156i | − | 1.38491i | −0.721462 | − | 0.692454i | \(-0.756530\pi\) | ||
0.721462 | − | 0.692454i | \(-0.243470\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.87298 | −0.368363 | ||||||||
\(176\) | 11.5573 | + | 20.8886i | 0.871164 | + | 1.57453i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.80948 | − | 1.24597i | 0.735251 | − | 0.0933892i | ||||
\(179\) | 8.77405i | 0.655803i | 0.944712 | + | 0.327901i | \(0.106341\pi\) | ||||
−0.944712 | + | 0.327901i | \(0.893659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.7460i | 1.61636i | 0.588932 | + | 0.808182i | \(0.299549\pi\) | ||||
−0.588932 | + | 0.808182i | \(0.700451\pi\) | |||||||
\(182\) | −0.511957 | − | 4.03063i | −0.0379488 | − | 0.298770i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.37298 | − | 2.93649i | 0.543544 | − | 0.216481i | ||||
\(185\) | 0.667520 | 0.0490770 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.8730i | 1.38013i | ||||||||
\(188\) | −14.2302 | + | 3.67423i | −1.03785 | + | 0.267971i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.0635083 | − | 0.00806662i | 0.00460738 | − | 0.000585214i | ||||
\(191\) | −21.7795 | −1.57591 | −0.787956 | − | 0.615731i | \(-0.788861\pi\) | ||||
−0.787956 | + | 0.615731i | \(0.788861\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.49193 | −0.683244 | −0.341622 | − | 0.939837i | \(-0.610976\pi\) | ||||
−0.341622 | + | 0.939837i | \(0.610976\pi\) | |||||||
\(194\) | 13.6730 | − | 1.73670i | 0.981666 | − | 0.124688i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.93649 | − | 0.500000i | 0.138321 | − | 0.0357143i | ||||
\(197\) | 2.04783i | 0.145902i | 0.997336 | + | 0.0729508i | \(0.0232416\pi\) | ||||
−0.997336 | + | 0.0729508i | \(0.976758\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.127017 | 0.00900397 | 0.00450199 | − | 0.999990i | \(-0.498567\pi\) | ||||
0.00450199 | + | 0.999990i | \(0.498567\pi\) | |||||||
\(200\) | −12.8047 | + | 5.09981i | −0.905427 | + | 0.360611i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.05544 | + | 16.1825i | 0.144620 | + | 1.13859i | ||||
\(203\) | − | 2.44949i | − | 0.171920i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.49193i | 0.174044i | ||||||||
\(206\) | 15.0760 | − | 1.91490i | 1.05039 | − | 0.133417i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.56351 | − | 10.0554i | −0.385760 | − | 0.697219i | ||||
\(209\) | 0.758056 | 0.0524358 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 20.0000i | − | 1.37686i | −0.725304 | − | 0.688428i | \(-0.758301\pi\) | ||
0.725304 | − | 0.688428i | \(-0.241699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.56351 | − | 20.1825i | −0.175238 | − | 1.37964i | ||||
\(215\) | −0.401662 | −0.0273931 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.00000 | 0.475191 | ||||||||
\(218\) | −2.27129 | − | 17.8819i | −0.153831 | − | 1.21111i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.11895 | − | 1.06351i | 0.277700 | − | 0.0717017i | ||||
\(221\) | − | 9.08517i | − | 0.611135i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.61895 | 0.510203 | 0.255101 | − | 0.966914i | \(-0.417891\pi\) | ||||
0.255101 | + | 0.966914i | \(0.417891\pi\) | |||||||
\(224\) | 4.56522 | − | 3.34047i | 0.305027 | − | 0.223195i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −23.6190 | + | 3.00000i | −1.57111 | + | 0.199557i | ||||
\(227\) | − | 25.9205i | − | 1.72040i | −0.509955 | − | 0.860201i | \(-0.670338\pi\) | ||
0.509955 | − | 0.860201i | \(-0.329662\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.7460i | 1.04052i | 0.854007 | + | 0.520261i | \(0.174165\pi\) | ||||
−0.854007 | + | 0.520261i | \(0.825835\pi\) | |||||||
\(230\) | −0.178197 | − | 1.40294i | −0.0117500 | − | 0.0925072i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.56351 | − | 6.43649i | −0.168303 | − | 0.422576i | ||||
\(233\) | −5.61177 | −0.367639 | −0.183820 | − | 0.982960i | \(-0.558846\pi\) | ||||
−0.183820 | + | 0.982960i | \(0.558846\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.61895i | 0.170841i | ||||||||
\(236\) | 3.31784 | + | 12.8499i | 0.215973 | + | 0.836460i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.43649 | − | 0.563508i | 0.287575 | − | 0.0365268i | ||||
\(239\) | −12.2474 | −0.792222 | −0.396111 | − | 0.918203i | \(-0.629640\pi\) | ||||
−0.396111 | + | 0.918203i | \(0.629640\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.6190 | 1.84351 | 0.921754 | − | 0.387774i | \(-0.126756\pi\) | ||||
0.921754 | + | 0.387774i | \(0.126756\pi\) | |||||||
\(242\) | 34.5390 | − | 4.38702i | 2.22025 | − | 0.282008i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.87298 | + | 26.6190i | 0.439998 | + | 1.70410i | ||||
\(245\) | − | 0.356394i | − | 0.0227692i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.364917 | −0.0232191 | ||||||||
\(248\) | 18.3938 | − | 7.32584i | 1.16801 | − | 0.465191i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.627017 | + | 4.93649i | 0.0396560 | + | 0.312211i | ||||
\(251\) | 16.8353i | 1.06263i | 0.847173 | + | 0.531317i | \(0.178303\pi\) | ||||
−0.847173 | + | 0.531317i | \(0.821697\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 16.7460i | − | 1.05281i | ||||||
\(254\) | −15.2542 | + | 1.93753i | −0.957131 | + | 0.121572i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.50000 | − | 13.5554i | 0.531250 | − | 0.847215i | ||||
\(257\) | 20.0428 | 1.25024 | 0.625119 | − | 0.780529i | \(-0.285050\pi\) | ||||
0.625119 | + | 0.780529i | \(0.285050\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.87298i | − | 0.116382i | ||||||
\(260\) | −1.98280 | + | 0.511957i | −0.122968 | + | 0.0317502i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.56351 | − | 12.3095i | −0.0965939 | − | 0.760482i | ||||
\(263\) | 2.80588 | 0.173018 | 0.0865091 | − | 0.996251i | \(-0.472429\pi\) | ||||
0.0865091 | + | 0.996251i | \(0.472429\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.0226340 | − | 0.178197i | −0.00138778 | − | 0.0109260i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.30948 | + | 16.6905i | 0.263243 | + | 1.01954i | ||||
\(269\) | − | 10.5560i | − | 0.643612i | −0.946806 | − | 0.321806i | \(-0.895710\pi\) | ||
0.946806 | − | 0.321806i | \(-0.104290\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.7460 | −1.19948 | −0.599741 | − | 0.800194i | \(-0.704730\pi\) | ||||
−0.599741 | + | 0.800194i | \(0.704730\pi\) | |||||||
\(272\) | 11.0680 | − | 6.12372i | 0.671094 | − | 0.371305i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.43649 | − | 0.817542i | 0.388843 | − | 0.0493895i | ||||
\(275\) | 29.0828i | 1.75376i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.87298i | 0.352873i | 0.984312 | + | 0.176437i | \(0.0564571\pi\) | ||||
−0.984312 | + | 0.176437i | \(0.943543\pi\) | |||||||
\(278\) | −2.49476 | − | 19.6412i | −0.149626 | − | 1.17800i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.372983 | − | 0.936492i | −0.0222900 | − | 0.0559661i | ||||
\(281\) | −22.0454 | −1.31512 | −0.657559 | − | 0.753403i | \(-0.728411\pi\) | ||||
−0.657559 | + | 0.753403i | \(0.728411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 11.4919i | − | 0.683125i | −0.939859 | − | 0.341562i | \(-0.889044\pi\) | ||
0.939859 | − | 0.341562i | \(-0.110956\pi\) | |||||||
\(284\) | 11.5573 | − | 2.98408i | 0.685799 | − | 0.177073i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −24.0554 | + | 3.05544i | −1.42243 | + | 0.180672i | ||||
\(287\) | 6.99208 | 0.412729 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | −1.22474 | + | 0.155563i | −0.0719195 | + | 0.00913497i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.69052 | − | 0.436492i | 0.0989305 | − | 0.0255437i | ||||
\(293\) | − | 31.8434i | − | 1.86031i | −0.367168 | − | 0.930155i | \(-0.619673\pi\) | ||
0.367168 | − | 0.930155i | \(-0.380327\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.36492 | 0.137691 | ||||||||
\(296\) | −1.96017 | − | 4.92161i | −0.113932 | − | 0.286063i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.74597 | − | 13.7460i | −0.101141 | − | 0.796282i | ||||
\(299\) | 8.06126i | 0.466195i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.12702i | 0.0649602i | ||||||||
\(302\) | 16.8353 | − | 2.13836i | 0.968763 | − | 0.123049i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.245967 | − | 0.444558i | −0.0141072 | − | 0.0254972i | ||||
\(305\) | 4.89898 | 0.280515 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 29.6190i | − | 1.69044i | −0.534416 | − | 0.845221i | \(-0.679469\pi\) | ||
0.534416 | − | 0.845221i | \(-0.320531\pi\) | |||||||
\(308\) | −2.98408 | − | 11.5573i | −0.170034 | − | 0.658538i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.444558 | − | 3.50000i | −0.0252492 | − | 0.198787i | ||||
\(311\) | −20.7104 | −1.17438 | −0.587189 | − | 0.809450i | \(-0.699765\pi\) | ||||
−0.587189 | + | 0.809450i | \(0.699765\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.87298 | 0.162391 | 0.0811953 | − | 0.996698i | \(-0.474126\pi\) | ||||
0.0811953 | + | 0.996698i | \(0.474126\pi\) | |||||||
\(314\) | 1.27001 | + | 9.99879i | 0.0716710 | + | 0.564264i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.4365 | − | 6.30948i | 1.37466 | − | 0.354936i | ||||
\(317\) | − | 13.6730i | − | 0.767954i | −0.923343 | − | 0.383977i | \(-0.874554\pi\) | ||
0.923343 | − | 0.383977i | \(-0.125446\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.6190 | −0.818504 | ||||||||
\(320\) | −1.96017 | − | 2.07046i | −0.109577 | − | 0.115742i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.93649 | + | 0.500000i | −0.219372 | + | 0.0278639i | ||||
\(323\) | − | 0.401662i | − | 0.0223491i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 14.0000i | − | 0.776580i | ||||||
\(326\) | −4.07590 | − | 32.0895i | −0.225743 | − | 1.77727i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 18.3730 | − | 7.31754i | 1.01448 | − | 0.404044i | ||||
\(329\) | 7.34847 | 0.405134 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000i | 0.549650i | 0.961494 | + | 0.274825i | \(0.0886199\pi\) | ||||
−0.961494 | + | 0.274825i | \(0.911380\pi\) | |||||||
\(332\) | 3.31784 | + | 12.8499i | 0.182090 | + | 0.705232i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.00000 | + | 0.254033i | −0.109435 | + | 0.0139001i | ||||
\(335\) | 3.07174 | 0.167827 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.25403 | −0.177258 | −0.0886292 | − | 0.996065i | \(-0.528249\pi\) | ||||
−0.0886292 | + | 0.996065i | \(0.528249\pi\) | |||||||
\(338\) | −6.65832 | + | 0.845717i | −0.362165 | + | 0.0460009i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.563508 | − | 2.18246i | −0.0305605 | − | 0.118360i | ||||
\(341\) | − | 41.7771i | − | 2.26236i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 1.17948 | + | 2.96145i | 0.0635931 | + | 0.159671i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.24597 | + | 25.5554i | 0.174504 | + | 1.37387i | ||||
\(347\) | − | 36.4765i | − | 1.95816i | −0.203475 | − | 0.979080i | \(-0.565223\pi\) | ||
0.203475 | − | 0.979080i | \(-0.434777\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 23.4919i | − | 1.25749i | −0.777610 | − | 0.628747i | \(-0.783568\pi\) | ||
0.777610 | − | 0.628747i | \(-0.216432\pi\) | |||||||
\(350\) | 6.83651 | − | 0.868351i | 0.365427 | − | 0.0464153i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −19.9365 | − | 27.2460i | −1.06262 | − | 1.45221i | ||||
\(353\) | 13.3166 | 0.708773 | 0.354386 | − | 0.935099i | \(-0.384690\pi\) | ||||
0.354386 | + | 0.935099i | \(0.384690\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 2.12702i | − | 0.112890i | ||||||
\(356\) | −13.5401 | + | 3.49604i | −0.717624 | + | 0.185290i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.56351 | − | 12.3095i | −0.0826340 | − | 0.650576i | ||||
\(359\) | 29.1733 | 1.53971 | 0.769854 | − | 0.638221i | \(-0.220329\pi\) | ||||
0.769854 | + | 0.638221i | \(0.220329\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9839 | 0.999151 | ||||||||
\(362\) | −3.87507 | − | 30.5083i | −0.203669 | − | 1.60348i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.43649 | + | 5.56351i | 0.0752926 | + | 0.291607i | ||||
\(365\) | − | 0.311126i | − | 0.0162851i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.8730 | 1.14176 | 0.570880 | − | 0.821033i | \(-0.306602\pi\) | ||||
0.570880 | + | 0.821033i | \(0.306602\pi\) | |||||||
\(368\) | −9.82059 | + | 5.43357i | −0.511934 | + | 0.283244i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.936492 | + | 0.118950i | −0.0486859 | + | 0.00618392i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.2379i | 1.46210i | 0.682322 | + | 0.731052i | \(0.260970\pi\) | ||||
−0.682322 | + | 0.731052i | \(0.739030\pi\) | |||||||
\(374\) | −3.36311 | − | 26.4777i | −0.173902 | − | 1.36913i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 19.3095 | − | 7.69052i | 0.995810 | − | 0.396609i | ||||
\(377\) | 7.03734 | 0.362442 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.87298i | 0.455775i | 0.973688 | + | 0.227887i | \(0.0731818\pi\) | ||||
−0.973688 | + | 0.227887i | \(0.926818\pi\) | |||||||
\(380\) | −0.0876610 | + | 0.0226340i | −0.00449692 | + | 0.00116110i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 30.5554 | − | 3.88105i | 1.56335 | − | 0.198572i | ||||
\(383\) | 17.4576 | 0.892039 | 0.446020 | − | 0.895023i | \(-0.352841\pi\) | ||||
0.446020 | + | 0.895023i | \(0.352841\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.12702 | −0.108403 | ||||||||
\(386\) | 13.3166 | − | 1.69143i | 0.677799 | − | 0.0860917i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.8730 | + | 4.87298i | −0.958131 | + | 0.247388i | ||||
\(389\) | − | 15.4097i | − | 0.781304i | −0.920538 | − | 0.390652i | \(-0.872250\pi\) | ||
0.920538 | − | 0.390652i | \(-0.127750\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.87298 | −0.448726 | ||||||||
\(392\) | −2.62769 | + | 1.04655i | −0.132718 | + | 0.0528587i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.364917 | − | 2.87298i | −0.0183842 | − | 0.144739i | ||||
\(395\) | − | 4.49732i | − | 0.226285i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 10.0000i | − | 0.501886i | −0.968002 | − | 0.250943i | \(-0.919259\pi\) | ||
0.968002 | − | 0.250943i | \(-0.0807406\pi\) | |||||||
\(398\) | −0.178197 | + | 0.0226340i | −0.00893221 | + | 0.00113454i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.0554 | − | 9.43649i | 0.852772 | − | 0.471825i | ||||
\(401\) | 16.5242 | 0.825178 | 0.412589 | − | 0.910917i | \(-0.364625\pi\) | ||||
0.412589 | + | 0.910917i | \(0.364625\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.1109i | 1.00179i | ||||||||
\(404\) | −5.76733 | − | 22.3368i | −0.286935 | − | 1.11130i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.436492 | + | 3.43649i | 0.0216627 | + | 0.170550i | ||||
\(407\) | −11.1783 | −0.554086 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.3649 | −0.611406 | −0.305703 | − | 0.952127i | \(-0.598891\pi\) | ||||
−0.305703 | + | 0.952127i | \(0.598891\pi\) | |||||||
\(410\) | −0.444055 | − | 3.49604i | −0.0219303 | − | 0.172657i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −20.8095 | + | 5.37298i | −1.02521 | + | 0.264708i | ||||
\(413\) | − | 6.63568i | − | 0.326521i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.36492 | 0.116089 | ||||||||
\(416\) | 9.59713 | + | 13.1158i | 0.470538 | + | 0.643055i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.06351 | + | 0.135083i | −0.0520179 | + | 0.00660714i | ||||
\(419\) | 28.7716i | 1.40559i | 0.711394 | + | 0.702793i | \(0.248064\pi\) | ||||
−0.711394 | + | 0.702793i | \(0.751936\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 19.1109i | − | 0.931407i | −0.884941 | − | 0.465704i | \(-0.845801\pi\) | ||
0.884941 | − | 0.465704i | \(-0.154199\pi\) | |||||||
\(422\) | 3.56394 | + | 28.0588i | 0.173490 | + | 1.36588i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.4097 | 0.747482 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 13.7460i | − | 0.665214i | ||||||
\(428\) | 7.19291 | + | 27.8580i | 0.347682 | + | 1.34657i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.563508 | − | 0.0715749i | 0.0271748 | − | 0.00345165i | ||||
\(431\) | 23.1146 | 1.11339 | 0.556695 | − | 0.830717i | \(-0.312069\pi\) | ||||
0.556695 | + | 0.830717i | \(0.312069\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.87298 | −0.234181 | −0.117090 | − | 0.993121i | \(-0.537357\pi\) | ||||
−0.117090 | + | 0.993121i | \(0.537357\pi\) | |||||||
\(434\) | −9.82059 | + | 1.24738i | −0.471404 | + | 0.0598761i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.37298 | + | 24.6825i | 0.305211 | + | 1.18208i | ||||
\(437\) | 0.356394i | 0.0170486i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.7460 | 1.22879 | 0.614394 | − | 0.788999i | \(-0.289401\pi\) | ||||
0.614394 | + | 0.788999i | \(0.289401\pi\) | |||||||
\(440\) | −5.58913 | + | 2.22602i | −0.266451 | + | 0.106122i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.61895 | + | 12.7460i | 0.0770056 | + | 0.606264i | ||||
\(443\) | 27.7024i | 1.31618i | 0.752938 | + | 0.658091i | \(0.228636\pi\) | ||||
−0.752938 | + | 0.658091i | \(0.771364\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.49193i | 0.118129i | ||||||||
\(446\) | −10.6889 | + | 1.35767i | −0.506136 | + | 0.0642877i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.80948 | + | 5.50000i | −0.274472 | + | 0.259851i | ||||
\(449\) | −30.9100 | −1.45873 | −0.729366 | − | 0.684123i | \(-0.760185\pi\) | ||||
−0.729366 | + | 0.684123i | \(0.760185\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 41.7298i | − | 1.96498i | ||||||
\(452\) | 32.6014 | − | 8.41765i | 1.53344 | − | 0.395933i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.61895 | + | 36.3649i | 0.216778 | + | 1.70669i | ||||
\(455\) | 1.02391 | 0.0480018 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.25403 | 0.432885 | 0.216443 | − | 0.976295i | \(-0.430555\pi\) | ||||
0.216443 | + | 0.976295i | \(0.430555\pi\) | |||||||
\(458\) | −2.80588 | − | 22.0907i | −0.131110 | − | 1.03223i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.500000 | + | 1.93649i | 0.0233126 | + | 0.0902894i | ||||
\(461\) | 13.9389i | 0.649198i | 0.945852 | + | 0.324599i | \(0.105229\pi\) | ||||
−0.945852 | + | 0.324599i | \(0.894771\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.508067 | 0.0236119 | 0.0118059 | − | 0.999930i | \(-0.496242\pi\) | ||||
0.0118059 | + | 0.999930i | \(0.496242\pi\) | |||||||
\(464\) | 4.74342 | + | 8.57321i | 0.220208 | + | 0.398001i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.87298 | − | 1.00000i | 0.364709 | − | 0.0463241i | ||||
\(467\) | 0.401662i | 0.0185867i | 0.999957 | + | 0.00929335i | \(0.00295821\pi\) | ||||
−0.999957 | + | 0.00929335i | \(0.997042\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 8.61895i | − | 0.397986i | ||||||
\(470\) | −0.466689 | − | 3.67423i | −0.0215268 | − | 0.169480i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.94456 | − | 17.4365i | −0.319649 | − | 0.802580i | ||||
\(473\) | 6.72622 | 0.309272 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 0.618950i | − | 0.0283994i | ||||||
\(476\) | −6.12372 | + | 1.58114i | −0.280680 | + | 0.0724714i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 17.1825 | − | 2.18246i | 0.785907 | − | 0.0998233i | ||||
\(479\) | −0.712788 | −0.0325681 | −0.0162841 | − | 0.999867i | \(-0.505184\pi\) | ||||
−0.0162841 | + | 0.999867i | \(0.505184\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.38105 | 0.245355 | ||||||||
\(482\) | −40.1507 | + | 5.09981i | −1.82882 | + | 0.232290i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −47.6744 | + | 12.3095i | −2.16702 | + | 0.559522i | ||||
\(485\) | 3.47340i | 0.157719i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.1109 | 1.18320 | 0.591599 | − | 0.806233i | \(-0.298497\pi\) | ||||
0.591599 | + | 0.806233i | \(0.298497\pi\) | |||||||
\(488\) | −14.3858 | − | 36.1201i | −0.651215 | − | 1.63508i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.0635083 | + | 0.500000i | 0.00286901 | + | 0.0225877i | ||||
\(491\) | − | 13.4072i | − | 0.605057i | −0.953140 | − | 0.302528i | \(-0.902169\pi\) | ||
0.953140 | − | 0.302528i | \(-0.0978307\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.74597i | 0.348861i | ||||||||
\(494\) | 0.511957 | − | 0.0650271i | 0.0230340 | − | 0.00292571i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24.5000 | + | 13.5554i | −1.10008 | + | 0.608657i | ||||
\(497\) | −5.96816 | −0.267709 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 34.3649i | − | 1.53838i | −0.639017 | − | 0.769192i | \(-0.720659\pi\) | ||
0.639017 | − | 0.769192i | \(-0.279341\pi\) | |||||||
\(500\) | −1.75934 | − | 6.81388i | −0.0786799 | − | 0.304726i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.00000 | − | 23.6190i | −0.133897 | − | 1.05417i | ||||
\(503\) | 7.34847 | 0.327652 | 0.163826 | − | 0.986489i | \(-0.447616\pi\) | ||||
0.163826 | + | 0.986489i | \(0.447616\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.11088 | −0.182932 | ||||||||
\(506\) | 2.98408 | + | 23.4936i | 0.132659 | + | 1.04442i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 21.0554 | − | 5.43649i | 0.934184 | − | 0.241205i | ||||
\(509\) | − | 0.311126i | − | 0.0137904i | −0.999976 | − | 0.00689521i | \(-0.997805\pi\) | ||
0.999976 | − | 0.00689521i | \(-0.00219483\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.872983 | −0.0386185 | ||||||||
\(512\) | −9.50947 | + | 20.5322i | −0.420263 | + | 0.907402i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −28.1190 | + | 3.57157i | −1.24027 | + | 0.157535i | ||||
\(515\) | 3.82980i | 0.168761i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 43.8569i | − | 1.92882i | ||||||
\(518\) | 0.333760 | + | 2.62769i | 0.0146646 | + | 0.115454i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.69052 | − | 1.07157i | 0.117987 | − | 0.0469917i | ||||
\(521\) | −29.8408 | −1.30735 | −0.653675 | − | 0.756776i | \(-0.726774\pi\) | ||||
−0.653675 | + | 0.756776i | \(0.726774\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.7460i | 1.51934i | 0.650312 | + | 0.759668i | \(0.274638\pi\) | ||||
−0.650312 | + | 0.759668i | \(0.725362\pi\) | |||||||
\(524\) | 4.38702 | + | 16.9909i | 0.191648 | + | 0.742249i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.93649 | + | 0.500000i | −0.171639 | + | 0.0218010i | ||||
\(527\) | −22.1359 | −0.964257 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.1270 | −0.657696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.0635083 | + | 0.245967i | 0.00275344 | + | 0.0106640i | ||||
\(533\) | 20.0881i | 0.870113i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.12702 | 0.221660 | ||||||||
\(536\) | −9.02014 | − | 22.6479i | −0.389611 | − | 0.978240i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.88105 | + | 14.8095i | 0.0810978 | + | 0.638482i | ||||
\(539\) | 5.96816i | 0.257067i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 30.8569i | − | 1.32664i | −0.748336 | − | 0.663320i | \(-0.769147\pi\) | ||
0.748336 | − | 0.663320i | \(-0.230853\pi\) | |||||||
\(542\) | 27.7024 | − | 3.51867i | 1.18992 | − | 0.151140i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −14.4365 | + | 10.5635i | −0.618959 | + | 0.452907i | ||||
\(545\) | 4.54259 | 0.194583 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 39.2379i | − | 1.67769i | −0.544369 | − | 0.838846i | \(-0.683231\pi\) | ||
0.544369 | − | 0.838846i | \(-0.316769\pi\) | |||||||
\(548\) | −8.88434 | + | 2.29393i | −0.379520 | + | 0.0979917i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.18246 | − | 40.8014i | −0.220981 | − | 1.73978i | ||||
\(551\) | 0.311126 | 0.0132544 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.6190 | −0.536612 | ||||||||
\(554\) | −1.04655 | − | 8.23945i | −0.0444636 | − | 0.350061i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.00000 | + | 27.1109i | 0.296866 | + | 1.14976i | ||||
\(557\) | − | 9.17571i | − | 0.388787i | −0.980924 | − | 0.194394i | \(-0.937726\pi\) | ||
0.980924 | − | 0.194394i | \(-0.0622739\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.23790 | −0.136949 | ||||||||
\(560\) | 0.690154 | + | 1.24738i | 0.0291643 | + | 0.0527114i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 30.9284 | − | 3.92843i | 1.30464 | − | 0.165711i | ||||
\(563\) | − | 7.34847i | − | 0.309701i | −0.987938 | − | 0.154851i | \(-0.950510\pi\) | ||
0.987938 | − | 0.154851i | \(-0.0494896\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 6.00000i | − | 0.252422i | ||||||
\(566\) | 2.04783 | + | 16.1225i | 0.0860766 | + | 0.677680i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15.6825 | + | 6.24597i | −0.658021 | + | 0.262075i | ||||
\(569\) | −5.52123 | −0.231462 | −0.115731 | − | 0.993281i | \(-0.536921\pi\) | ||||
−0.115731 | + | 0.993281i | \(0.536921\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.9839i | 1.38033i | 0.723651 | + | 0.690166i | \(0.242462\pi\) | ||||
−0.723651 | + | 0.690166i | \(0.757538\pi\) | |||||||
\(572\) | 33.2039 | − | 8.57321i | 1.38833 | − | 0.358464i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.80948 | + | 1.24597i | −0.409440 | + | 0.0520056i | ||||
\(575\) | −13.6730 | −0.570205 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.2540 | −0.926448 | −0.463224 | − | 0.886241i | \(-0.653307\pi\) | ||||
−0.463224 | + | 0.886241i | \(0.653307\pi\) | |||||||
\(578\) | 9.82059 | − | 1.24738i | 0.408483 | − | 0.0518841i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.69052 | − | 0.436492i | 0.0701952 | − | 0.0181243i | ||||
\(581\) | − | 6.63568i | − | 0.275294i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.29393 | + | 0.913619i | −0.0949234 | + | 0.0378058i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.67439 | + | 44.6744i | 0.234407 | + | 1.84548i | ||||
\(587\) | 37.8568i | 1.56252i | 0.624208 | + | 0.781259i | \(0.285422\pi\) | ||||
−0.624208 | + | 0.781259i | \(0.714578\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.889117i | 0.0366354i | ||||||||
\(590\) | −3.31784 | + | 0.421421i | −0.136593 | + | 0.0173496i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.62702 | + | 6.55544i | 0.149069 | + | 0.269427i | ||||
\(593\) | −22.8035 | −0.936426 | −0.468213 | − | 0.883616i | \(-0.655102\pi\) | ||||
−0.468213 | + | 0.883616i | \(0.655102\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.12702i | 0.0462032i | ||||||||
\(596\) | 4.89898 | + | 18.9737i | 0.200670 | + | 0.777192i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.43649 | − | 11.3095i | −0.0587425 | − | 0.462479i | ||||
\(599\) | −41.3755 | −1.69056 | −0.845278 | − | 0.534327i | \(-0.820565\pi\) | ||||
−0.845278 | + | 0.534327i | \(0.820565\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.1109 | 1.30983 | 0.654915 | − | 0.755702i | \(-0.272704\pi\) | ||||
0.654915 | + | 0.755702i | \(0.272704\pi\) | |||||||
\(602\) | −0.200831 | − | 1.58114i | −0.00818526 | − | 0.0644424i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −23.2379 | + | 6.00000i | −0.945537 | + | 0.244137i | ||||
\(605\) | 8.77405i | 0.356716i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.2379 | 0.618487 | 0.309244 | − | 0.950983i | \(-0.399924\pi\) | ||||
0.309244 | + | 0.950983i | \(0.399924\pi\) | |||||||
\(608\) | 0.424296 | + | 0.579859i | 0.0172075 | + | 0.0235164i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.87298 | + | 0.872983i | −0.278279 | + | 0.0353461i | ||||
\(611\) | 21.1120i | 0.854101i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.2379i | 1.62519i | 0.582826 | + | 0.812597i | \(0.301947\pi\) | ||||
−0.582826 | + | 0.812597i | \(0.698053\pi\) | |||||||
\(614\) | 5.27801 | + | 41.5537i | 0.213003 | + | 1.67697i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.24597 | + | 15.6825i | 0.251657 | + | 0.631864i | ||||
\(617\) | 15.7209 | 0.632898 | 0.316449 | − | 0.948610i | \(-0.397509\pi\) | ||||
0.316449 | + | 0.948610i | \(0.397509\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 0.491933i | − | 0.0197725i | −0.999951 | − | 0.00988624i | \(-0.996853\pi\) | ||
0.999951 | − | 0.00988624i | \(-0.00314694\pi\) | |||||||
\(620\) | 1.24738 | + | 4.83108i | 0.0500959 | + | 0.194021i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 29.0554 | − | 3.69052i | 1.16502 | − | 0.147977i | ||||
\(623\) | 6.99208 | 0.280132 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.1109 | 0.924435 | ||||||||
\(626\) | −4.03063 | + | 0.511957i | −0.161096 | + | 0.0204619i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.56351 | − | 13.8014i | −0.142199 | − | 0.550736i | ||||
\(629\) | 5.92289i | 0.236161i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.87298 | −0.353228 | −0.176614 | − | 0.984280i | \(-0.556514\pi\) | ||||
−0.176614 | + | 0.984280i | \(0.556514\pi\) | |||||||
\(632\) | −33.1586 | + | 13.2063i | −1.31898 | + | 0.525320i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.43649 | + | 19.1825i | 0.0967654 | + | 0.761833i | ||||
\(635\) | − | 3.87507i | − | 0.153777i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.87298i | − | 0.113832i | ||||||
\(638\) | 20.5095 | − | 2.60505i | 0.811980 | − | 0.103135i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.11895 | + | 2.55544i | 0.123287 | + | 0.101013i | ||||
\(641\) | 18.1703 | 0.717685 | 0.358843 | − | 0.933398i | \(-0.383171\pi\) | ||||
0.358843 | + | 0.933398i | \(0.383171\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 8.38105i | − | 0.330516i | −0.986250 | − | 0.165258i | \(-0.947154\pi\) | ||
0.986250 | − | 0.165258i | \(-0.0528457\pi\) | |||||||
\(644\) | 5.43357 | − | 1.40294i | 0.214113 | − | 0.0552837i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.0715749 | + | 0.563508i | 0.00281608 | + | 0.0221709i | ||||
\(647\) | 21.4232 | 0.842231 | 0.421116 | − | 0.907007i | \(-0.361639\pi\) | ||||
0.421116 | + | 0.907007i | \(0.361639\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39.6028 | −1.55455 | ||||||||
\(650\) | 2.49476 | + | 19.6412i | 0.0978524 | + | 0.770391i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.4365 | + | 44.2933i | 0.447888 | + | 1.73466i | ||||
\(653\) | 0.311126i | 0.0121753i | 0.999981 | + | 0.00608765i | \(0.00193777\pi\) | ||||
−0.999981 | + | 0.00608765i | \(0.998062\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.12702 | 0.122183 | ||||||||
\(656\) | −24.4723 | + | 13.5401i | −0.955481 | + | 0.528652i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.3095 | + | 1.30948i | −0.401905 | + | 0.0510487i | ||||
\(659\) | − | 35.3620i | − | 1.37751i | −0.724994 | − | 0.688755i | \(-0.758158\pi\) | ||
0.724994 | − | 0.688755i | \(-0.241842\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 45.8569i | − | 1.78362i | −0.452405 | − | 0.891812i | \(-0.649434\pi\) | ||
0.452405 | − | 0.891812i | \(-0.350566\pi\) | |||||||
\(662\) | −1.78197 | − | 14.0294i | −0.0692582 | − | 0.545269i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.94456 | − | 17.4365i | −0.269501 | − | 0.676667i | ||||
\(665\) | 0.0452680 | 0.00175542 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 6.87298i | − | 0.266123i | ||||||
\(668\) | 2.76062 | − | 0.712788i | 0.106811 | − | 0.0275786i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.30948 | + | 0.547375i | −0.166490 | + | 0.0211469i | ||||
\(671\) | −82.0381 | −3.16705 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.4919 | 1.13683 | 0.568415 | − | 0.822742i | \(-0.307557\pi\) | ||||
0.568415 | + | 0.822742i | \(0.307557\pi\) | |||||||
\(674\) | 4.56522 | − | 0.579859i | 0.175846 | − | 0.0223353i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.19052 | − | 2.37298i | 0.353482 | − | 0.0912686i | ||||
\(677\) | − | 17.9045i | − | 0.688125i | −0.938947 | − | 0.344063i | \(-0.888197\pi\) | ||
0.938947 | − | 0.344063i | \(-0.111803\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.74597 | 0.374016 | ||||||||
\(680\) | 1.17948 | + | 2.96145i | 0.0452309 | + | 0.113566i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.44456 | + | 58.6109i | 0.285067 | + | 2.24433i | ||||
\(683\) | − | 9.44157i | − | 0.361271i | −0.983550 | − | 0.180636i | \(-0.942184\pi\) | ||
0.983550 | − | 0.180636i | \(-0.0578155\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.63508i | 0.0624733i | ||||||||
\(686\) | 1.40294 | − | 0.178197i | 0.0535646 | − | 0.00680359i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.18246 | − | 3.94456i | −0.0832054 | − | 0.150385i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 22.0000i | − | 0.836919i | −0.908235 | − | 0.418460i | \(-0.862570\pi\) | ||
0.908235 | − | 0.418460i | \(-0.137430\pi\) | |||||||
\(692\) | −9.10781 | − | 35.2744i | −0.346227 | − | 1.34093i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.50000 | + | 51.1744i | 0.246737 | + | 1.94255i | ||||
\(695\) | 4.98952 | 0.189263 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.1109 | −0.837509 | ||||||||
\(698\) | 4.18619 | + | 32.9578i | 0.158450 | + | 1.24747i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.43649 | + | 2.43649i | −0.356666 | + | 0.0920907i | ||||
\(701\) | 48.7692i | 1.84199i | 0.389577 | + | 0.920994i | \(0.372621\pi\) | ||||
−0.389577 | + | 0.920994i | \(0.627379\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.237900 | 0.00897257 | ||||||||
\(704\) | 32.8249 | + | 34.6719i | 1.23713 | + | 1.30675i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.6825 | + | 2.37298i | −0.703124 | + | 0.0893084i | ||||
\(707\) | 11.5347i | 0.433806i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.2540i | 0.798212i | 0.916905 | + | 0.399106i | \(0.130679\pi\) | ||||
−0.916905 | + | 0.399106i | \(0.869321\pi\) | |||||||
\(710\) | 0.379028 | + | 2.98408i | 0.0142247 | + | 0.111991i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 18.3730 | − | 7.31754i | 0.688557 | − | 0.274236i | ||||
\(713\) | 19.6412 | 0.735568 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 6.11088i | − | 0.228534i | ||||||
\(716\) | 4.38702 | + | 16.9909i | 0.163951 | + | 0.634978i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −40.9284 | + | 5.19859i | −1.52744 | + | 0.194010i | ||||
\(719\) | 36.8329 | 1.37363 | 0.686817 | − | 0.726830i | \(-0.259007\pi\) | ||||
0.686817 | + | 0.726830i | \(0.259007\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.7460 | 0.400201 | ||||||||
\(722\) | −26.6333 | + | 3.38287i | −0.991187 | + | 0.125897i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.8730 | + | 42.1109i | 0.404091 | + | 1.56504i | ||||
\(725\) | 11.9363i | 0.443304i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.49193 | 0.129509 | 0.0647543 | − | 0.997901i | \(-0.479374\pi\) | ||||
0.0647543 | + | 0.997901i | \(0.479374\pi\) | |||||||
\(728\) | −3.00671 | − | 7.54930i | −0.111436 | − | 0.279796i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.0554417 | + | 0.436492i | 0.00205199 | + | 0.0161553i | ||||
\(731\) | − | 3.56394i | − | 0.131817i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.36492i | 0.308965i | 0.987996 | + | 0.154483i | \(0.0493711\pi\) | ||||
−0.987996 | + | 0.154483i | \(0.950629\pi\) | |||||||
\(734\) | −30.6865 | + | 3.89770i | −1.13266 | + | 0.143867i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.8095 | − | 9.37298i | 0.472164 | − | 0.345493i | ||||
\(737\) | −51.4393 | −1.89479 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 0.254033i | − | 0.00934477i | −0.999989 | − | 0.00467238i | \(-0.998513\pi\) | ||
0.999989 | − | 0.00467238i | \(-0.00148727\pi\) | |||||||
\(740\) | 1.29265 | − | 0.333760i | 0.0475186 | − | 0.0122693i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.3037 | 1.40523 | 0.702614 | − | 0.711571i | \(-0.252016\pi\) | ||||
0.702614 | + | 0.711571i | \(0.252016\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.49193 | 0.127935 | ||||||||
\(746\) | −5.03191 | − | 39.6161i | −0.184231 | − | 1.45045i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.43649 | + | 36.5474i | 0.345032 | + | 1.33630i | ||||
\(749\) | − | 14.3858i | − | 0.525646i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −51.3488 | −1.87374 | −0.936872 | − | 0.349673i | \(-0.886293\pi\) | ||||
−0.936872 | + | 0.349673i | \(0.886293\pi\) | |||||||
\(752\) | −25.7196 | + | 14.2302i | −0.937899 | + | 0.518924i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.87298 | + | 1.25403i | −0.359553 | + | 0.0456692i | ||||
\(755\) | 4.27673i | 0.155646i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 25.7460i | − | 0.935753i | −0.883794 | − | 0.467877i | \(-0.845019\pi\) | ||
0.883794 | − | 0.467877i | \(-0.154981\pi\) | |||||||
\(758\) | −1.58114 | − | 12.4483i | −0.0574295 | − | 0.452142i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.118950 | − | 0.0473751i | 0.00431477 | − | 0.00171848i | ||||
\(761\) | 34.6945 | 1.25768 | 0.628838 | − | 0.777537i | \(-0.283531\pi\) | ||||
0.628838 | + | 0.777537i | \(0.283531\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 12.7460i | − | 0.461435i | ||||||
\(764\) | −42.1759 | + | 10.8898i | −1.52587 | + | 0.393978i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.4919 | + | 3.11088i | −0.884930 | + | 0.112401i | ||||
\(767\) | 19.0642 | 0.688368 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.6351 | 0.419572 | 0.209786 | − | 0.977747i | \(-0.432723\pi\) | ||||
0.209786 | + | 0.977747i | \(0.432723\pi\) | |||||||
\(770\) | 2.98408 | − | 0.379028i | 0.107539 | − | 0.0136592i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −18.3810 | + | 4.74597i | −0.661548 | + | 0.170811i | ||||
\(773\) | 22.0001i | 0.791290i | 0.918404 | + | 0.395645i | \(0.129479\pi\) | ||||
−0.918404 | + | 0.395645i | \(0.870521\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34.1109 | −1.22530 | ||||||||
\(776\) | 25.6093 | − | 10.1996i | 0.919322 | − | 0.366145i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.74597 | + | 21.6190i | 0.0984477 | + | 0.775077i | ||||
\(779\) | 0.888110i | 0.0318198i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.6190i | 1.27455i | ||||||||
\(782\) | 12.4483 | − | 1.58114i | 0.445150 | − | 0.0565414i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.50000 | − | 1.93649i | 0.125000 | − | 0.0691604i | ||||
\(785\) | −2.54003 | −0.0906574 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.25403i | 0.151640i | 0.997122 | + | 0.0758200i | \(0.0241574\pi\) | ||||
−0.997122 | + | 0.0758200i | \(0.975843\pi\) | |||||||
\(788\) | 1.02391 | + | 3.96560i | 0.0364754 | + | 0.141269i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.801408 | + | 6.30948i | 0.0285128 | + | 0.224481i | ||||
\(791\) | −16.8353 | −0.598594 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 39.4919 | 1.40240 | ||||||||
\(794\) | 1.78197 | + | 14.0294i | 0.0632397 | + | 0.497885i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.245967 | − | 0.0635083i | 0.00871806 | − | 0.00225099i | ||||
\(797\) | 31.2664i | 1.10751i | 0.832679 | + | 0.553756i | \(0.186806\pi\) | ||||
−0.832679 | + | 0.553756i | \(0.813194\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.2379 | −0.822098 | ||||||||
\(800\) | −22.2462 | + | 16.2781i | −0.786523 | + | 0.575517i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −23.1825 | + | 2.94456i | −0.818601 | + | 0.103976i | ||||
\(803\) | 5.21011i | 0.183861i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 1.00000i | − | 0.0352454i | ||||||
\(806\) | −3.58370 | − | 28.2144i | −0.126230 | − | 0.993810i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.0716 | + | 30.3095i | 0.424677 | + | 1.06628i | ||||
\(809\) | 4.58785 | 0.161300 | 0.0806502 | − | 0.996742i | \(-0.474300\pi\) | ||||
0.0806502 | + | 0.996742i | \(0.474300\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 41.9839i | − | 1.47425i | −0.675755 | − | 0.737126i | \(-0.736182\pi\) | ||
0.675755 | − | 0.737126i | \(-0.263818\pi\) | |||||||
\(812\) | −1.22474 | − | 4.74342i | −0.0429801 | − | 0.166461i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15.6825 | − | 1.99193i | 0.549670 | − | 0.0698172i | ||||
\(815\) | 8.15179 | 0.285545 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.143150 | −0.00500818 | ||||||||
\(818\) | 17.3473 | − | 2.20339i | 0.606533 | − | 0.0770398i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.24597 | + | 4.82561i | 0.0435110 | + | 0.168518i | ||||
\(821\) | 22.1359i | 0.772550i | 0.922384 | + | 0.386275i | \(0.126238\pi\) | ||||
−0.922384 | + | 0.386275i | \(0.873762\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.4919 | −1.30689 | −0.653443 | − | 0.756975i | \(-0.726676\pi\) | ||||
−0.653443 | + | 0.756975i | \(0.726676\pi\) | |||||||
\(824\) | 28.2370 | − | 11.2462i | 0.983684 | − | 0.391779i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.18246 | + | 9.30948i | 0.0411430 | + | 0.323918i | ||||
\(827\) | − | 30.1519i | − | 1.04849i | −0.851569 | − | 0.524243i | \(-0.824348\pi\) | ||
0.851569 | − | 0.524243i | \(-0.175652\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 2.36492i | − | 0.0821370i | −0.999156 | − | 0.0410685i | \(-0.986924\pi\) | ||
0.999156 | − | 0.0410685i | \(-0.0130762\pi\) | |||||||
\(830\) | −3.31784 | + | 0.421421i | −0.115164 | + | 0.0146277i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −15.8014 | − | 16.6905i | −0.547815 | − | 0.578640i | ||||
\(833\) | 3.16228 | 0.109566 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 0.508067i | − | 0.0175824i | ||||||
\(836\) | 1.46797 | − | 0.379028i | 0.0507708 | − | 0.0131090i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.12702 | − | 40.3649i | −0.177110 | − | 1.39438i | ||||
\(839\) | 37.5457 | 1.29622 | 0.648110 | − | 0.761547i | \(-0.275560\pi\) | ||||
0.648110 | + | 0.761547i | \(0.275560\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.0000 | 0.793103 | ||||||||
\(842\) | 3.40550 | + | 26.8115i | 0.117361 | + | 0.923984i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.0000 | − | 38.7298i | −0.344214 | − | 1.33314i | ||||
\(845\) | − | 1.69143i | − | 0.0581871i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.6190 | 0.845917 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −21.6190 | + | 2.74597i | −0.741524 | + | 0.0941859i | ||||
\(851\) | − | 5.25537i | − | 0.180152i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 5.23790i | − | 0.179342i | −0.995971 | − | 0.0896711i | \(-0.971418\pi\) | ||
0.995971 | − | 0.0896711i | \(-0.0285816\pi\) | |||||||
\(854\) | 2.44949 | + | 19.2848i | 0.0838198 | + | 0.659912i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.0554 | − | 37.8014i | −0.514584 | − | 1.29203i | ||||
\(857\) | 47.6095 | 1.62631 | 0.813155 | − | 0.582048i | \(-0.197748\pi\) | ||||
0.813155 | + | 0.582048i | \(0.197748\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.8730i | 1.08749i | 0.839250 | + | 0.543746i | \(0.182995\pi\) | ||||
−0.839250 | + | 0.543746i | \(0.817005\pi\) | |||||||
\(860\) | −0.777815 | + | 0.200831i | −0.0265233 | + | 0.00684828i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −32.4284 | + | 4.11895i | −1.10452 | + | 0.140292i | ||||
\(863\) | −26.3221 | −0.896016 | −0.448008 | − | 0.894030i | \(-0.647866\pi\) | ||||
−0.448008 | + | 0.894030i | \(0.647866\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.49193 | −0.220732 | ||||||||
\(866\) | 6.83651 | − | 0.868351i | 0.232314 | − | 0.0295078i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13.5554 | − | 3.50000i | 0.460102 | − | 0.118798i | ||||
\(869\) | 75.3119i | 2.55478i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.7621 | 0.839032 | ||||||||
\(872\) | −13.3393 | − | 33.4924i | −0.451724 | − | 1.13420i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.0635083 | − | 0.500000i | −0.00214820 | − | 0.0169128i | ||||
\(875\) | 3.51867i | 0.118953i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 13.4919i | − | 0.455590i | −0.973709 | − | 0.227795i | \(-0.926848\pi\) | ||
0.973709 | − | 0.227795i | \(-0.0731516\pi\) | |||||||
\(878\) | −36.1201 | + | 4.58785i | −1.21899 | + | 0.154833i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.44456 | − | 4.11895i | 0.250956 | − | 0.138850i | ||||
\(881\) | −43.4233 | −1.46297 | −0.731484 | − | 0.681859i | \(-0.761172\pi\) | ||||
−0.731484 | + | 0.681859i | \(0.761172\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.2379i | 0.512796i | 0.966571 | + | 0.256398i | \(0.0825358\pi\) | ||||
−0.966571 | + | 0.256398i | \(0.917464\pi\) | |||||||
\(884\) | −4.54259 | − | 17.5934i | −0.152784 | − | 0.591729i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.93649 | − | 38.8649i | −0.165845 | − | 1.30569i | ||||
\(887\) | −48.0564 | −1.61358 | −0.806788 | − | 0.590841i | \(-0.798796\pi\) | ||||
−0.806788 | + | 0.590841i | \(0.798796\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.8730 | −0.364668 | ||||||||
\(890\) | −0.444055 | − | 3.49604i | −0.0148848 | − | 0.117187i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.7540 | − | 3.80948i | 0.494002 | − | 0.127551i | ||||
\(893\) | 0.933378i | 0.0312343i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.12702 | 0.104525 | ||||||||
\(896\) | 7.17027 | − | 8.75141i | 0.239542 | − | 0.292364i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 43.3649 | − | 5.50807i | 1.44711 | − | 0.183807i | ||||
\(899\) | − | 17.1464i | − | 0.571865i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 7.43613 | + | 58.5445i | 0.247596 | + | 1.94932i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −44.2379 | + | 17.6190i | −1.47133 | + | 0.585998i | ||||
\(905\) | 7.75013 | 0.257623 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.00000i | 0.265636i | 0.991140 | + | 0.132818i | \(0.0424025\pi\) | ||||
−0.991140 | + | 0.132818i | \(0.957597\pi\) | |||||||
\(908\) | −12.9602 | − | 50.1948i | −0.430101 | − | 1.66577i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.43649 | + | 0.182458i | −0.0476192 | + | 0.00604844i | ||||
\(911\) | 33.3595 | 1.10525 | 0.552624 | − | 0.833430i | \(-0.313626\pi\) | ||||
0.552624 | + | 0.833430i | \(0.313626\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39.6028 | −1.31066 | ||||||||
\(914\) | −12.9829 | + | 1.64904i | −0.429435 | + | 0.0545454i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.87298 | + | 30.4919i | 0.260131 | + | 1.00748i | ||||
\(917\) | − | 8.77405i | − | 0.289744i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.5081 | −0.478577 | −0.239288 | − | 0.970949i | \(-0.576914\pi\) | ||||
−0.239288 | + | 0.970949i | \(0.576914\pi\) | |||||||
\(920\) | −1.04655 | − | 2.62769i | −0.0345037 | − | 0.0866323i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.48387 | − | 19.5554i | −0.0818018 | − | 0.644024i | ||||
\(923\) | − | 17.1464i | − | 0.564382i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.12702i | 0.300094i | ||||||||
\(926\) | −0.712788 | + | 0.0905359i | −0.0234237 | + | 0.00297520i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.18246 | − | 11.1825i | −0.268602 | − | 0.367082i | ||||
\(929\) | −23.4710 | −0.770058 | −0.385029 | − | 0.922904i | \(-0.625809\pi\) | ||||
−0.385029 | + | 0.922904i | \(0.625809\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 0.127017i | − | 0.00416280i | ||||||
\(932\) | −10.8671 | + | 2.80588i | −0.355965 | + | 0.0919098i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.0715749 | − | 0.563508i | −0.00234200 | − | 0.0184386i | ||||
\(935\) | 6.72622 | 0.219971 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.4919 | 1.35548 | 0.677741 | − | 0.735301i | \(-0.262959\pi\) | ||||
0.677741 | + | 0.735301i | \(0.262959\pi\) | |||||||
\(938\) | 1.53587 | + | 12.0919i | 0.0501480 | + | 0.394814i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.30948 | + | 5.07157i | 0.0427104 | + | 0.165417i | ||||
\(941\) | − | 11.4894i | − | 0.374544i | −0.982308 | − | 0.187272i | \(-0.940036\pi\) | ||
0.982308 | − | 0.187272i | \(-0.0599645\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.6190 | 0.638881 | ||||||||
\(944\) | 12.8499 | + | 23.2249i | 0.418230 | + | 0.755906i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.43649 | + | 1.19859i | −0.306807 | + | 0.0389696i | ||||
\(947\) | 2.00256i | 0.0650745i | 0.999471 | + | 0.0325372i | \(0.0103587\pi\) | ||||
−0.999471 | + | 0.0325372i | \(0.989641\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 2.50807i | − | 0.0814153i | ||||||
\(950\) | 0.110295 | + | 0.868351i | 0.00357844 | + | 0.0281730i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.30948 | − | 3.30948i | 0.269312 | − | 0.107261i | ||||
\(953\) | 0.311126 | 0.0100784 | 0.00503918 | − | 0.999987i | \(-0.498396\pi\) | ||||
0.00503918 | + | 0.999987i | \(0.498396\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.76210i | 0.251176i | ||||||||
\(956\) | −23.7171 | + | 6.12372i | −0.767065 | + | 0.198055i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.00000 | − | 0.127017i | 0.0323085 | − | 0.00410372i | ||||
\(959\) | 4.58785 | 0.148150 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0000 | 0.580645 | ||||||||
\(962\) | −7.54930 | + | 0.958887i | −0.243399 | + | 0.0309158i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 55.4204 | − | 14.3095i | 1.78497 | − | 0.460877i | ||||
\(965\) | 3.38287i | 0.108898i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.2379 | 0.811596 | 0.405798 | − | 0.913963i | \(-0.366994\pi\) | ||||
0.405798 | + | 0.913963i | \(0.366994\pi\) | |||||||
\(968\) | 64.6909 | − | 25.7649i | 2.07924 | − | 0.828116i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.618950 | − | 4.87298i | −0.0198733 | − | 0.156462i | ||||
\(971\) | 13.7636i | 0.441694i | 0.975309 | + | 0.220847i | \(0.0708821\pi\) | ||||
−0.975309 | + | 0.220847i | \(0.929118\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 14.0000i | − | 0.448819i | ||||||
\(974\) | −36.6321 | + | 4.65288i | −1.17377 | + | 0.149088i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 26.6190 | + | 48.1109i | 0.852052 | + | 1.53999i | ||||
\(977\) | −23.1599 | −0.740949 | −0.370475 | − | 0.928843i | \(-0.620805\pi\) | ||||
−0.370475 | + | 0.928843i | \(0.620805\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 41.7298i | − | 1.33369i | ||||||
\(980\) | −0.178197 | − | 0.690154i | −0.00569229 | − | 0.0220462i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.38912 | + | 18.8095i | 0.0762398 | + | 0.600234i | ||||
\(983\) | −53.6682 | −1.71175 | −0.855875 | − | 0.517183i | \(-0.826981\pi\) | ||||
−0.855875 | + | 0.517183i | \(0.826981\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.729833 | 0.0232544 | ||||||||
\(986\) | −1.38031 | − | 10.8671i | −0.0439580 | − | 0.346080i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.706658 | + | 0.182458i | −0.0224818 | + | 0.00580477i | ||||
\(989\) | 3.16228i | 0.100555i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.3810 | 0.552127 | 0.276064 | − | 0.961139i | \(-0.410970\pi\) | ||||
0.276064 | + | 0.961139i | \(0.410970\pi\) | |||||||
\(992\) | 31.9565 | − | 23.3833i | 1.01462 | − | 0.742421i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.37298 | − | 1.06351i | 0.265575 | − | 0.0337324i | ||||
\(995\) | − | 0.0452680i | − | 0.00143509i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 18.0000i | − | 0.570066i | −0.958518 | − | 0.285033i | \(-0.907995\pi\) | ||
0.958518 | − | 0.285033i | \(-0.0920045\pi\) | |||||||
\(998\) | 6.12372 | + | 48.2120i | 0.193843 | + | 1.52612i | ||||
\(999\) | 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.c.c.757.2 | yes | 8 | |
3.2 | odd | 2 | inner | 1512.2.c.c.757.7 | yes | 8 | |
4.3 | odd | 2 | 6048.2.c.c.3025.3 | 8 | |||
8.3 | odd | 2 | 6048.2.c.c.3025.6 | 8 | |||
8.5 | even | 2 | inner | 1512.2.c.c.757.1 | ✓ | 8 | |
12.11 | even | 2 | 6048.2.c.c.3025.5 | 8 | |||
24.5 | odd | 2 | inner | 1512.2.c.c.757.8 | yes | 8 | |
24.11 | even | 2 | 6048.2.c.c.3025.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.c.757.1 | ✓ | 8 | 8.5 | even | 2 | inner | |
1512.2.c.c.757.2 | yes | 8 | 1.1 | even | 1 | trivial | |
1512.2.c.c.757.7 | yes | 8 | 3.2 | odd | 2 | inner | |
1512.2.c.c.757.8 | yes | 8 | 24.5 | odd | 2 | inner | |
6048.2.c.c.3025.3 | 8 | 4.3 | odd | 2 | |||
6048.2.c.c.3025.4 | 8 | 24.11 | even | 2 | |||
6048.2.c.c.3025.5 | 8 | 12.11 | even | 2 | |||
6048.2.c.c.3025.6 | 8 | 8.3 | odd | 2 |