Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(337,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.r (of order \(3\), degree \(2\), not 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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.508277025.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 15x^{5} + 21x^{4} + 3x^{3} - 22x^{2} + 3x + 19 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 337.2 | ||
Root | \(-0.734668 + 0.348716i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.337 |
Dual form | 1008.2.r.m.673.2 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.434663 | + | 1.67662i | 0.250953 | + | 0.967999i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.21814 | + | 2.10988i | −0.544768 | + | 0.943566i | 0.453853 | + | 0.891076i | \(0.350049\pi\) |
−0.998621 | + | 0.0524895i | \(0.983284\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.62214 | + | 1.45753i | −0.874045 | + | 0.485844i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.379477 | + | 0.657274i | 0.114417 | + | 0.198176i | 0.917546 | − | 0.397629i | \(-0.130167\pi\) |
−0.803130 | + | 0.595804i | \(0.796833\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.11414 | + | 1.92976i | −0.309008 | + | 0.535218i | −0.978146 | − | 0.207921i | \(-0.933330\pi\) |
0.669138 | + | 0.743139i | \(0.266664\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.06695 | − | 1.12527i | −1.05008 | − | 0.290545i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.04904 | −1.70964 | −0.854822 | − | 0.518922i | \(-0.826334\pi\) | ||||
−0.854822 | + | 0.518922i | \(0.826334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.37172 | 0.314694 | 0.157347 | − | 0.987543i | \(-0.449706\pi\) | ||||
0.157347 | + | 0.987543i | \(0.449706\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.23467 | + | 1.21474i | −0.269427 | + | 0.265078i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.51814 | − | 6.09360i | 0.733583 | − | 1.27060i | −0.221759 | − | 0.975102i | \(-0.571180\pi\) |
0.955342 | − | 0.295502i | \(-0.0954870\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.467722 | − | 0.810117i | −0.0935443 | − | 0.162023i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.58348 | − | 3.76280i | −0.689641 | − | 0.724151i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.418134 | − | 0.724229i | −0.0776455 | − | 0.134486i | 0.824588 | − | 0.565733i | \(-0.191407\pi\) |
−0.902234 | + | 0.431248i | \(0.858074\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.265332 | + | 0.459569i | −0.0476551 | + | 0.0825411i | −0.888869 | − | 0.458161i | \(-0.848508\pi\) |
0.841214 | + | 0.540702i | \(0.181842\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.937057 | + | 0.921933i | −0.163121 | + | 0.160488i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.43628 | −0.411806 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.53066 | 0.744837 | 0.372418 | − | 0.928065i | \(-0.378529\pi\) | ||||
0.372418 | + | 0.928065i | \(0.378529\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.71975 | − | 1.02921i | −0.595637 | − | 0.164805i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.42852 | + | 7.67042i | −0.691618 | + | 1.19792i | 0.279689 | + | 0.960091i | \(0.409769\pi\) |
−0.971307 | + | 0.237828i | \(0.923565\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.70161 | + | 6.41137i | 0.564490 | + | 0.977725i | 0.997097 | + | 0.0761428i | \(0.0242605\pi\) |
−0.432607 | + | 0.901583i | \(0.642406\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.118909 | − | 7.30786i | 0.0177259 | − | 1.08939i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.39762 | − | 5.88485i | −0.495594 | − | 0.858394i | 0.504393 | − | 0.863474i | \(-0.331716\pi\) |
−0.999987 | + | 0.00508036i | \(0.998383\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.06396 | − | 11.8186i | −0.429040 | − | 1.65493i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.607978 | −0.0835122 | −0.0417561 | − | 0.999128i | \(-0.513295\pi\) | ||||
−0.0417561 | + | 0.999128i | \(0.513295\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.84902 | −0.249322 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.596236 | + | 2.29986i | 0.0789733 | + | 0.304624i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.581866 | + | 1.00782i | −0.0757525 | + | 0.131207i | −0.901413 | − | 0.432960i | \(-0.857469\pi\) |
0.825661 | + | 0.564167i | \(0.190803\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.85680 | − | 10.1443i | −0.749887 | − | 1.29884i | −0.947876 | − | 0.318638i | \(-0.896775\pi\) |
0.197990 | − | 0.980204i | \(-0.436559\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.57333 | − | 1.54207i | −0.324209 | − | 0.194283i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.71436 | − | 4.70142i | −0.336676 | − | 0.583139i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.152801 | + | 0.264659i | −0.0186676 | + | 0.0323333i | −0.875208 | − | 0.483746i | \(-0.839276\pi\) |
0.856541 | + | 0.516080i | \(0.172609\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.7459 | + | 3.24994i | 1.41404 | + | 0.391247i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.6192 | −1.49763 | −0.748813 | − | 0.662781i | \(-0.769376\pi\) | ||||
−0.748813 | + | 0.662781i | \(0.769376\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.1499 | −1.18795 | −0.593977 | − | 0.804482i | \(-0.702443\pi\) | ||||
−0.593977 | + | 0.804482i | \(0.702443\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.15496 | − | 1.13632i | 0.133363 | − | 0.131211i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.379477 | + | 0.657274i | −0.0432455 | + | 0.0749033i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.62453 | + | 13.2061i | 0.857827 | + | 1.48580i | 0.873998 | + | 0.485930i | \(0.161519\pi\) |
−0.0161711 | + | 0.999869i | \(0.505148\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.75120 | − | 7.64370i | 0.527911 | − | 0.849300i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.18909 | + | 14.1839i | 0.898869 | + | 1.55689i | 0.828942 | + | 0.559335i | \(0.188943\pi\) |
0.0699272 | + | 0.997552i | \(0.477723\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.58671 | − | 14.8726i | 0.931359 | − | 1.61316i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.03251 | − | 1.01585i | 0.110697 | − | 0.108910i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.63151 | −1.02094 | −0.510469 | − | 0.859896i | \(-0.670528\pi\) | ||||
−0.510469 | + | 0.859896i | \(0.670528\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.22829 | −0.233588 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.885855 | − | 0.245105i | −0.0918589 | − | 0.0254162i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.67094 | + | 2.89416i | −0.171435 | + | 0.296935i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.46718 | + | 9.46943i | 0.555108 | + | 0.961474i | 0.997895 | + | 0.0648479i | \(0.0206562\pi\) |
−0.442788 | + | 0.896627i | \(0.646010\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.95304 | − | 1.17036i | −0.196288 | − | 0.117626i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.750417 | − | 1.29976i | −0.0746693 | − | 0.129331i | 0.826273 | − | 0.563270i | \(-0.190457\pi\) |
−0.900942 | + | 0.433939i | \(0.857123\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.13229 | − | 8.88938i | 0.505699 | − | 0.875897i | −0.494279 | − | 0.869303i | \(-0.664568\pi\) |
0.999978 | − | 0.00659356i | \(-0.00209881\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.05896 | − | 4.08472i | −0.103344 | − | 0.398628i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.84428 | 0.758335 | 0.379168 | − | 0.925328i | \(-0.376210\pi\) | ||||
0.379168 | + | 0.925328i | \(0.376210\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.1754 | 1.16619 | 0.583096 | − | 0.812403i | \(-0.301841\pi\) | ||||
0.583096 | + | 0.812403i | \(0.301841\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.96931 | + | 7.59622i | 0.186919 | + | 0.721001i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.98586 | + | 3.43962i | −0.186814 | + | 0.323572i | −0.944186 | − | 0.329412i | \(-0.893150\pi\) |
0.757372 | + | 0.652984i | \(0.226483\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.57117 | + | 14.8457i | 0.799266 | + | 1.38437i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.108758 | − | 6.68398i | 0.0100547 | − | 0.617935i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.52452 | − | 6.10465i | −0.323092 | − | 0.559612i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.21199 | − | 9.02744i | 0.473818 | − | 0.820676i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.7853 | − | 4.09091i | −1.33315 | − | 0.368865i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.90238 | −0.885696 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.7579 | −1.39828 | −0.699142 | − | 0.714983i | \(-0.746435\pi\) | ||||
−0.699142 | + | 0.714983i | \(0.746435\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.14051 | + | 8.99299i | −0.804777 | + | 0.791789i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.93789 | + | 10.2847i | −0.518796 | + | 0.898581i | 0.480966 | + | 0.876739i | \(0.340286\pi\) |
−0.999761 | + | 0.0218413i | \(0.993047\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.685860 | + | 1.18794i | 0.0594716 | + | 0.103008i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 12.3042 | − | 2.97709i | 1.05898 | − | 0.256227i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.1869 | + | 17.6443i | 0.870328 | + | 1.50745i | 0.861658 | + | 0.507490i | \(0.169426\pi\) |
0.00867008 | + | 0.999962i | \(0.497240\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.13489 | + | 5.42979i | −0.265898 | + | 0.460549i | −0.967799 | − | 0.251726i | \(-0.919002\pi\) |
0.701900 | + | 0.712275i | \(0.252335\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.38986 | − | 8.25446i | 0.706554 | − | 0.695151i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.69117 | −0.141423 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.03738 | 0.169195 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.66933 | − | 0.461883i | −0.137684 | − | 0.0380955i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.45679 | − | 4.25529i | 0.201268 | − | 0.348607i | −0.747669 | − | 0.664071i | \(-0.768827\pi\) |
0.948937 | + | 0.315465i | \(0.102160\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.80878 | − | 4.86494i | −0.228575 | − | 0.395903i | 0.728811 | − | 0.684715i | \(-0.240073\pi\) |
−0.957386 | + | 0.288811i | \(0.906740\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.4835 | − | 10.2742i | 1.49431 | − | 0.830621i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.646423 | − | 1.11964i | −0.0519220 | − | 0.0899315i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.3174 | + | 17.8702i | −0.823416 | + | 1.42620i | 0.0797087 | + | 0.996818i | \(0.474601\pi\) |
−0.903124 | + | 0.429379i | \(0.858732\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.264265 | − | 1.01935i | −0.0209576 | − | 0.0808397i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.03629 | 0.554537 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.95096 | −0.387789 | −0.193895 | − | 0.981022i | \(-0.562112\pi\) | ||||
−0.193895 | + | 0.981022i | \(0.562112\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.803702 | − | 3.10012i | −0.0625681 | − | 0.241344i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.485864 | + | 0.841542i | −0.0375973 | + | 0.0651205i | −0.884212 | − | 0.467086i | \(-0.845304\pi\) |
0.846614 | + | 0.532207i | \(0.178637\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.01736 | + | 6.95828i | 0.309028 | + | 0.535252i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.59684 | + | 1.99933i | −0.275057 | + | 0.152892i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.90960 | + | 15.4319i | 0.677384 | + | 1.17326i | 0.975766 | + | 0.218817i | \(0.0702198\pi\) |
−0.298382 | + | 0.954447i | \(0.596447\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.467722 | − | 0.810117i | 0.0353564 | − | 0.0612391i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.94265 | − | 0.537508i | −0.146019 | − | 0.0404016i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.6065 | 0.792764 | 0.396382 | − | 0.918086i | \(-0.370266\pi\) | ||||
0.396382 | + | 0.918086i | \(0.370266\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.7360 | 1.83862 | 0.919308 | − | 0.393539i | \(-0.128749\pi\) | ||||
0.919308 | + | 0.393539i | \(0.128749\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.4624 | − | 14.2290i | 1.06909 | − | 1.05184i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.51898 | + | 9.55915i | −0.405763 | + | 0.702802i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.67495 | − | 4.63315i | −0.195612 | − | 0.338810i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.46694 | − | 4.98479i | 0.106704 | − | 0.362590i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.25120 | + | 16.0235i | 0.669393 | + | 1.15942i | 0.978074 | + | 0.208257i | \(0.0667791\pi\) |
−0.308681 | + | 0.951166i | \(0.599888\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.24505 | + | 14.2808i | −0.593492 | + | 1.02796i | 0.400266 | + | 0.916399i | \(0.368918\pi\) |
−0.993758 | + | 0.111559i | \(0.964416\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.70268 | − | 6.59450i | 0.479989 | − | 0.472242i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.68164 | −0.618541 | −0.309271 | − | 0.950974i | \(-0.600085\pi\) | ||||
−0.309271 | + | 0.950974i | \(0.600085\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.2352 | 1.36355 | 0.681774 | − | 0.731563i | \(-0.261209\pi\) | ||||
0.681774 | + | 0.731563i | \(0.261209\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.510151 | − | 0.141152i | −0.0359833 | − | 0.00995613i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.418134 | − | 0.724229i | 0.0293472 | − | 0.0508309i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.7891 | − | 18.6873i | −0.753543 | − | 1.30518i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.343425 | + | 21.1061i | −0.0238697 | + | 1.46697i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.520536 | + | 0.901595i | 0.0360063 | + | 0.0623647i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.3584 | − | 19.6734i | 0.781946 | − | 1.35437i | −0.148861 | − | 0.988858i | \(-0.547561\pi\) |
0.930807 | − | 0.365512i | \(-0.119106\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.48511 | − | 21.1577i | −0.375833 | − | 1.44970i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.0363 | −1.23006 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.530665 | −0.0360239 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.41178 | − | 17.0175i | −0.298120 | − | 1.14994i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.85365 | − | 13.6029i | 0.528294 | − | 0.915032i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.76320 | + | 13.4462i | 0.519862 | + | 0.900427i | 0.999733 | + | 0.0230886i | \(0.00734998\pi\) |
−0.479871 | + | 0.877339i | \(0.659317\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.40720 | + | 1.44252i | 0.160480 | + | 0.0961679i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.13468 | + | 1.96533i | 0.0753114 | + | 0.130443i | 0.901222 | − | 0.433358i | \(-0.142672\pi\) |
−0.825910 | + | 0.563802i | \(0.809338\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.61037 | + | 7.98540i | −0.304662 | + | 0.527690i | −0.977186 | − | 0.212385i | \(-0.931877\pi\) |
0.672524 | + | 0.740075i | \(0.265210\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.26695 | − | 0.350548i | −0.0833589 | − | 0.0230644i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.0842 | −1.57781 | −0.788905 | − | 0.614515i | \(-0.789352\pi\) | ||||
−0.788905 | + | 0.614515i | \(0.789352\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.5551 | 1.07993 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −18.8275 | + | 18.5237i | −1.22298 | + | 1.20324i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.50000 | − | 4.33013i | 0.161712 | − | 0.280093i | −0.773771 | − | 0.633465i | \(-0.781632\pi\) |
0.935483 | + | 0.353373i | \(0.114965\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.61761 | + | 14.9261i | 0.555109 | + | 0.961477i | 0.997895 | + | 0.0648494i | \(0.0206567\pi\) |
−0.442786 | + | 0.896627i | \(0.646010\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.8808 | + | 4.64354i | 0.954602 | + | 0.297883i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.21814 | − | 2.10988i | −0.0778240 | − | 0.134795i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.52829 | + | 2.64708i | −0.0972430 | + | 0.168430i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −20.2216 | + | 19.8952i | −1.28149 | + | 1.26081i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.2725 | −0.963994 | −0.481997 | − | 0.876173i | \(-0.660088\pi\) | ||||
−0.481997 | + | 0.876173i | \(0.660088\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.34022 | 0.335737 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 28.6681 | + | 7.93211i | 1.79527 | + | 0.496728i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.79524 | − | 10.0377i | 0.361497 | − | 0.626131i | −0.626710 | − | 0.779252i | \(-0.715599\pi\) |
0.988207 | + | 0.153121i | \(0.0489324\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.26533 | + | 3.92367i | 0.140761 | + | 0.243805i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.15199 | + | 1.28958i | 0.133205 | + | 0.0798232i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.05602 | − | 7.02523i | −0.250105 | − | 0.433194i | 0.713450 | − | 0.700707i | \(-0.247132\pi\) |
−0.963554 | + | 0.267512i | \(0.913798\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.740601 | − | 1.28276i | 0.0454948 | − | 0.0787992i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.18646 | − | 16.1484i | −0.256207 | − | 0.988267i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.4598 | 0.698717 | 0.349358 | − | 0.936989i | \(-0.386400\pi\) | ||||
0.349358 | + | 0.936989i | \(0.386400\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.30404 | 0.200706 | 0.100353 | − | 0.994952i | \(-0.468003\pi\) | ||||
0.100353 | + | 0.994952i | \(0.468003\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.968555 | − | 3.73600i | −0.0586196 | − | 0.226113i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.354979 | − | 0.614842i | 0.0214061 | − | 0.0370764i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.12453 | + | 8.87595i | 0.307903 | + | 0.533304i | 0.977903 | − | 0.209057i | \(-0.0670394\pi\) |
−0.670000 | + | 0.742361i | \(0.733706\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.0259006 | − | 1.59178i | 0.00155063 | − | 0.0952976i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.861334 | + | 1.49188i | 0.0513829 | + | 0.0889978i | 0.890573 | − | 0.454841i | \(-0.150304\pi\) |
−0.839190 | + | 0.543838i | \(0.816970\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.0752 | − | 20.9148i | 0.717795 | − | 1.24326i | −0.244077 | − | 0.969756i | \(-0.578485\pi\) |
0.961872 | − | 0.273501i | \(-0.0881817\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.57872 | − | 1.54356i | −0.330455 | − | 0.0914326i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.85704 | −0.522814 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.6890 | 1.92288 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.5003 | + | 13.2824i | −0.791401 | + | 0.778628i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.46533 | − | 12.9303i | 0.436129 | − | 0.755398i | −0.561258 | − | 0.827641i | \(-0.689682\pi\) |
0.997387 | + | 0.0722432i | \(0.0230158\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.41759 | − | 2.45533i | −0.0825351 | − | 0.142955i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.11334 | − | 3.78323i | 0.0646026 | − | 0.219525i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.83944 | + | 13.5783i | 0.453367 | + | 0.785254i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.70161 | + | 6.41137i | −0.213357 | + | 0.369545i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.85303 | − | 1.82312i | 0.106454 | − | 0.104736i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 28.5376 | 1.63406 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.9563 | 1.02482 | 0.512411 | − | 0.858741i | \(-0.328753\pi\) | ||||
0.512411 | + | 0.858741i | \(0.328753\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.1350 | + | 4.74103i | 0.974774 | + | 0.269708i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.8931 | − | 18.8673i | 0.617689 | − | 1.06987i | −0.372217 | − | 0.928146i | \(-0.621402\pi\) |
0.989906 | − | 0.141723i | \(-0.0452643\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.0624 | − | 19.1606i | −0.625284 | − | 1.08302i | −0.988486 | − | 0.151313i | \(-0.951650\pi\) |
0.363202 | − | 0.931710i | \(-0.381683\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.38825 | − | 3.55095i | 0.359937 | − | 0.200074i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.86480 | − | 4.96197i | −0.160903 | − | 0.278692i | 0.774290 | − | 0.632831i | \(-0.218107\pi\) |
−0.935193 | + | 0.354139i | \(0.884774\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.317344 | − | 0.549657i | 0.0177679 | − | 0.0307749i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.40962 | + | 13.1519i | 0.190306 | + | 0.734068i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.66931 | −0.538015 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.08444 | 0.115624 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.29219 | + | 20.4136i | 0.292659 | + | 1.12887i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.39762 | − | 5.88485i | 0.187317 | − | 0.324442i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.8178 | − | 27.3973i | −0.869427 | − | 1.50589i | −0.862583 | − | 0.505915i | \(-0.831155\pi\) |
−0.00684339 | − | 0.999977i | \(-0.502178\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.8800 | + | 6.60359i | −0.651021 | + | 0.361875i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.372266 | − | 0.644784i | −0.0203391 | − | 0.0352283i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.7771 | + | 20.3985i | −0.641539 | + | 1.11118i | 0.343550 | + | 0.939134i | \(0.388371\pi\) |
−0.985089 | + | 0.172044i | \(0.944963\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.63013 | − | 1.83447i | −0.360099 | − | 0.0996349i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.402751 | −0.0218102 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −21.1651 | + | 20.8235i | −1.13949 | + | 1.12110i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.81359 | + | 16.9976i | −0.526821 | + | 0.912481i | 0.472690 | + | 0.881229i | \(0.343283\pi\) |
−0.999512 | + | 0.0312526i | \(0.990050\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.0363 | + | 22.5795i | 0.697816 | + | 1.20865i | 0.969222 | + | 0.246188i | \(0.0791782\pi\) |
−0.271406 | + | 0.962465i | \(0.587488\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.2538 | − | 2.72293i | 0.600683 | − | 0.145339i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.30878 | − | 5.73097i | −0.176108 | − | 0.305029i | 0.764436 | − | 0.644700i | \(-0.223018\pi\) |
−0.940544 | + | 0.339671i | \(0.889684\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.3720 | − | 26.6250i | 0.815859 | − | 1.41311i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.70322 | − | 8.56276i | 0.460623 | − | 0.453189i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.0527 | 1.21668 | 0.608338 | − | 0.793678i | \(-0.291836\pi\) | ||||
0.608338 | + | 0.793678i | \(0.291836\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1184 | −0.900968 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.4011 | + | 4.81466i | 0.913320 | + | 0.252704i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.3640 | − | 21.4150i | 0.647159 | − | 1.12091i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.08931 | + | 7.08289i | 0.213460 | + | 0.369724i | 0.952795 | − | 0.303614i | \(-0.0981933\pi\) |
−0.739335 | + | 0.673338i | \(0.764860\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.432292 | − | 26.5676i | 0.0225042 | − | 1.38305i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.303989 | − | 0.526524i | −0.0157823 | − | 0.0273358i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.75341 | + | 13.4293i | −0.401456 | + | 0.695343i | −0.993902 | − | 0.110268i | \(-0.964829\pi\) |
0.592446 | + | 0.805610i | \(0.298163\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.30420 | − | 16.6026i | −0.222268 | − | 0.857353i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.86345 | 0.0959723 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.5814 | −0.954461 | −0.477231 | − | 0.878778i | \(-0.658359\pi\) | ||||
−0.477231 | + | 0.878778i | \(0.658359\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.84936 | − | 26.4200i | −0.350903 | − | 1.35354i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.30959 | − | 14.3926i | 0.424600 | − | 0.735429i | −0.571783 | − | 0.820405i | \(-0.693748\pi\) |
0.996383 | + | 0.0849761i | \(0.0270814\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.924512 | − | 1.60130i | −0.0471175 | − | 0.0816099i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −19.0509 | − | 11.4163i | −0.968412 | − | 0.580322i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.9112 | + | 22.3629i | 0.654624 | + | 1.13384i | 0.981988 | + | 0.188944i | \(0.0605065\pi\) |
−0.327364 | + | 0.944898i | \(0.606160\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.7995 | + | 42.9541i | −1.25417 | + | 2.17228i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.8246 | − | 5.48522i | −1.00002 | − | 0.276693i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −37.1509 | −1.86927 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.729016 | −0.0365883 | −0.0182941 | − | 0.999833i | \(-0.505824\pi\) | ||||
−0.0182941 | + | 0.999833i | \(0.505824\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.69362 | + | 1.66628i | −0.0847869 | + | 0.0834185i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.67094 | − | 15.0185i | 0.433006 | − | 0.749989i | −0.564124 | − | 0.825690i | \(-0.690786\pi\) |
0.997131 | + | 0.0757010i | \(0.0241195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.591238 | − | 1.02405i | −0.0294516 | − | 0.0510117i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.3397 | + | 19.3355i | 0.513781 | + | 0.960790i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.71928 | + | 2.97789i | 0.0852218 | + | 0.147608i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.82351 | − | 3.15841i | 0.0901668 | − | 0.156174i | −0.817414 | − | 0.576050i | \(-0.804593\pi\) |
0.907581 | + | 0.419877i | \(0.137927\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −25.1549 | + | 24.7490i | −1.24080 | + | 1.22078i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.16373 | −0.0572635 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −39.9018 | −1.95870 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.4663 | − | 2.89591i | −0.512539 | − | 0.141813i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.117685 | − | 0.203836i | 0.00574927 | − | 0.00995803i | −0.863136 | − | 0.504971i | \(-0.831503\pi\) |
0.868886 | + | 0.495013i | \(0.164837\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.8985 | − | 18.8767i | −0.531158 | − | 0.919993i | −0.999339 | − | 0.0363601i | \(-0.988424\pi\) |
0.468181 | − | 0.883633i | \(-0.344910\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.4864 | + | 10.4787i | 0.850217 | + | 0.509494i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.29699 | + | 5.71055i | 0.159927 | + | 0.277002i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.85680 | − | 10.1443i | 0.283431 | − | 0.490916i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.735089 | − | 2.83546i | −0.0354904 | − | 0.136897i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.28806 | 0.206549 | 0.103274 | − | 0.994653i | \(-0.467068\pi\) | ||||
0.103274 | + | 0.994653i | \(0.467068\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.9263 | −0.669257 | −0.334628 | − | 0.942350i | \(-0.608611\pi\) | ||||
−0.334628 | + | 0.942350i | \(0.608611\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.885573 | + | 3.41592i | 0.0424600 | + | 0.163781i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.82591 | − | 8.35871i | 0.230854 | − | 0.399851i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.9397 | − | 27.6084i | −0.760762 | − | 1.31768i | −0.942458 | − | 0.334324i | \(-0.891492\pi\) |
0.181696 | − | 0.983355i | \(-0.441841\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0488078 | − | 2.99960i | 0.00232418 | − | 0.142838i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.56216 | + | 4.43780i | 0.121732 | + | 0.210846i | 0.920451 | − | 0.390858i | \(-0.127822\pi\) |
−0.798719 | + | 0.601705i | \(0.794488\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.7325 | − | 20.3213i | 0.556174 | − | 0.963322i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.20239 | + | 2.26950i | 0.387960 | + | 0.107344i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.9914 | −1.60415 | −0.802077 | − | 0.597221i | \(-0.796272\pi\) | ||||
−0.802077 | + | 0.597221i | \(0.796272\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.72209 | −0.316531 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.93581 | − | 6.82387i | 0.325873 | − | 0.320613i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.71436 | − | 4.70142i | 0.127251 | − | 0.220406i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.78826 | − | 4.82941i | −0.130429 | − | 0.225910i | 0.793413 | − | 0.608684i | \(-0.208302\pi\) |
−0.923842 | + | 0.382774i | \(0.874969\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.2601 | + | 26.5241i | 1.17904 | + | 1.23804i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.24904 | − | 2.16340i | −0.0581734 | − | 0.100759i | 0.835472 | − | 0.549533i | \(-0.185194\pi\) |
−0.893646 | + | 0.448774i | \(0.851861\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.77517 | + | 8.27084i | −0.221921 | + | 0.384378i | −0.955391 | − | 0.295343i | \(-0.904566\pi\) |
0.733470 | + | 0.679722i | \(0.237899\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.59624 | − | 1.57047i | 0.0740237 | − | 0.0728290i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.2128 | −0.842787 | −0.421393 | − | 0.906878i | \(-0.638459\pi\) | ||||
−0.421393 | + | 0.906878i | \(0.638459\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.305602 | −0.0141114 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −34.4462 | − | 9.53083i | −1.58720 | − | 0.439157i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.80935 | + | 4.86594i | −0.129174 | + | 0.223736i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.641583 | − | 1.11125i | −0.0294378 | − | 0.0509878i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.59420 | − | 0.886147i | 0.0729934 | − | 0.0405739i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.87648 | − | 4.98222i | −0.131430 | − | 0.227643i | 0.792798 | − | 0.609484i | \(-0.208623\pi\) |
−0.924228 | + | 0.381841i | \(0.875290\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.04782 | + | 8.74308i | −0.230161 | + | 0.398650i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.05841 | + | 11.7972i | 0.139163 | + | 0.536791i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.6391 | −1.20962 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.8918 | −1.08264 | −0.541321 | − | 0.840816i | \(-0.682075\pi\) | ||||
−0.541321 | + | 0.840816i | \(0.682075\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.15200 | − | 8.30090i | −0.0973167 | − | 0.375379i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.31437 | − | 12.6689i | 0.330093 | − | 0.571738i | −0.652437 | − | 0.757843i | \(-0.726253\pi\) |
0.982530 | + | 0.186105i | \(0.0595865\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.94744 | + | 5.10512i | 0.132746 | + | 0.229923i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.84839 | − | 2.69501i | 0.217919 | − | 0.121132i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.30961 | − | 10.9286i | −0.283025 | − | 0.490213i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.9579 | + | 20.7117i | −0.535308 | + | 0.927181i | 0.463840 | + | 0.885919i | \(0.346471\pi\) |
−0.999148 | + | 0.0412621i | \(0.986862\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.62214 | − | 0.448825i | −0.0724717 | − | 0.0200520i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.57496 | −0.337751 | −0.168875 | − | 0.985637i | \(-0.554014\pi\) | ||||
−0.168875 | + | 0.985637i | \(0.554014\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.65645 | 0.162710 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.92021 | + | 9.76011i | −0.440572 | + | 0.433462i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.50078 | − | 6.06353i | 0.155169 | − | 0.268761i | −0.777951 | − | 0.628325i | \(-0.783741\pi\) |
0.933121 | + | 0.359563i | \(0.117074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.07494 | − | 8.79006i | −0.224502 | − | 0.388849i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.91553 | − | 5.16151i | −0.217026 | − | 0.227886i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.5037 | + | 21.6570i | 0.550978 | + | 0.954321i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.57864 | − | 4.46633i | 0.113408 | − | 0.196429i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.0008 | + | 21.6457i | −0.965727 | + | 0.950141i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 42.4564 | 1.86005 | 0.930025 | − | 0.367497i | \(-0.119785\pi\) | ||||
0.930025 | + | 0.367497i | \(0.119785\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.6096 | 0.813743 | 0.406871 | − | 0.913485i | \(-0.366620\pi\) | ||||
0.406871 | + | 0.913485i | \(0.366620\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.56156 | + | 0.432065i | 0.0681522 | + | 0.0188569i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.87034 | − | 3.23952i | 0.0814733 | − | 0.141116i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.2547 | − | 22.9577i | −0.576289 | − | 0.998163i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.0567992 | − | 3.49074i | 0.00246487 | − | 0.151485i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.86802 | − | 17.0919i | −0.427431 | − | 0.740333i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.55542 | + | 16.5505i | −0.413117 | + | 0.715539i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.61024 | + | 17.7831i | 0.198946 | + | 0.767395i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.758955 | −0.0326905 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.694443 | −0.0298564 | −0.0149282 | − | 0.999889i | \(-0.504752\pi\) | ||||
−0.0149282 | + | 0.999889i | \(0.504752\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.7518 | + | 41.4730i | 0.461406 | + | 1.77978i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.8313 | + | 25.6886i | −0.635304 | + | 1.10038i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.77655 | + | 15.2014i | 0.375258 | + | 0.649966i | 0.990366 | − | 0.138477i | \(-0.0442207\pi\) |
−0.615107 | + | 0.788443i | \(0.710887\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.1430 | + | 18.0632i | 1.28647 | + | 0.770919i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.573562 | − | 0.993439i | −0.0244346 | − | 0.0423219i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.62453 | + | 13.2061i | −0.324228 | + | 0.561579i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −18.4260 | − | 5.09824i | −0.782140 | − | 0.216408i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.2666 | 0.604495 | 0.302248 | − | 0.953229i | \(-0.402263\pi\) | ||||
0.302248 | + | 0.953229i | \(0.402263\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.4965 | −0.697728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.60535 | − | 6.49875i | 0.278878 | − | 0.274377i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.8742 | + | 29.2270i | −0.711162 | + | 1.23177i | 0.253259 | + | 0.967399i | \(0.418498\pi\) |
−0.964421 | + | 0.264371i | \(0.914836\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.83811 | − | 8.37986i | −0.203541 | − | 0.352543i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.99524 | + | 0.292808i | 0.377764 | + | 0.0122968i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.9867 | − | 34.6180i | −0.837886 | − | 1.45126i | −0.891659 | − | 0.452708i | \(-0.850458\pi\) |
0.0537729 | − | 0.998553i | \(-0.482875\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.2266 | − | 35.0335i | 0.846457 | − | 1.46611i | −0.0378934 | − | 0.999282i | \(-0.512065\pi\) |
0.884350 | − | 0.466824i | \(-0.154602\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.8443 | + | 22.4756i | −0.954335 | + | 0.938932i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.58204 | −0.274490 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.6758 | −1.31868 | −0.659340 | − | 0.751845i | \(-0.729164\pi\) | ||||
−0.659340 | + | 0.751845i | \(0.729164\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27.5274 | − | 7.61650i | −1.14400 | − | 0.316531i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.18909 | + | 14.1839i | −0.339741 | + | 0.588448i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.230714 | − | 0.399608i | −0.00955519 | − | 0.0165501i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.9699 | + | 8.37148i | 0.577584 | + | 0.346118i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.65220 | + | 13.2540i | 0.315840 | + | 0.547051i | 0.979616 | − | 0.200881i | \(-0.0643803\pi\) |
−0.663776 | + | 0.747932i | \(0.731047\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.363962 | + | 0.630400i | −0.0149968 | + | 0.0259752i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.77359 | − | 14.5558i | −0.155225 | − | 0.598748i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.2583 | 1.61214 | 0.806072 | − | 0.591817i | \(-0.201589\pi\) | ||||
0.806072 | + | 0.591817i | \(0.201589\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.1734 | 0.704041 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.36083 | + | 32.2502i | 0.342186 | + | 1.31991i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.77972 | − | 15.2069i | 0.358730 | − | 0.621338i | −0.629019 | − | 0.777390i | \(-0.716543\pi\) |
0.987749 | + | 0.156052i | \(0.0498766\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.12937 | − | 15.8125i | −0.372395 | − | 0.645007i | 0.617539 | − | 0.786541i | \(-0.288130\pi\) |
−0.989933 | + | 0.141534i | \(0.954797\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.0149158 | − | 0.916686i | 0.000607417 | − | 0.0373303i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.6979 | + | 21.9933i | 0.516241 | + | 0.894156i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.71415 | + | 6.43310i | −0.150753 | + | 0.261112i | −0.931504 | − | 0.363730i | \(-0.881503\pi\) |
0.780752 | + | 0.624842i | \(0.214836\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.39601 | + | 0.386258i | 0.0565690 | + | 0.0156519i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.1418 | 0.612570 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.8772 | −1.61062 | −0.805312 | − | 0.592851i | \(-0.798002\pi\) | ||||
−0.805312 | + | 0.592851i | \(0.798002\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 26.6419 | − | 26.2119i | 1.07430 | − | 1.05697i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.187473 | + | 0.324713i | −0.00754739 | + | 0.0130725i | −0.869774 | − | 0.493450i | \(-0.835736\pi\) |
0.862227 | + | 0.506522i | \(0.169069\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.95166 | − | 12.0406i | −0.279411 | − | 0.483954i | 0.691828 | − | 0.722063i | \(-0.256806\pi\) |
−0.971238 | + | 0.238109i | \(0.923472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −35.5362 | + | 8.59823i | −1.42602 | + | 0.345035i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.81575 | − | 8.34113i | −0.192939 | − | 0.334180i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.4011 | − | 24.9434i | 0.576043 | − | 0.997736i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.28538 | + | 1.26463i | −0.0513331 | + | 0.0505046i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −31.9368 | −1.27341 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.6049 | −1.13874 | −0.569372 | − | 0.822080i | \(-0.692813\pi\) | ||||
−0.569372 | + | 0.822080i | \(0.692813\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 37.9219 | + | 10.4925i | 1.50726 | + | 0.417040i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.1953 | − | 33.2472i | 0.761740 | − | 1.31937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.11414 | − | 1.92976i | −0.0441440 | − | 0.0764597i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 33.0893 | − | 18.3929i | 1.30899 | − | 0.727613i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.9011 | + | 18.8812i | 0.430566 | + | 0.745762i | 0.996922 | − | 0.0783986i | \(-0.0249807\pi\) |
−0.566356 | + | 0.824161i | \(0.691647\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.9205 | + | 36.2354i | −0.825025 | + | 1.42899i | 0.0768751 | + | 0.997041i | \(0.475506\pi\) |
−0.901900 | + | 0.431945i | \(0.857828\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.83971 | − | 30.2401i | −0.308688 | − | 1.19070i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.2614 | −0.678615 | −0.339308 | − | 0.940675i | \(-0.610193\pi\) | ||||
−0.339308 | + | 0.940675i | \(0.610193\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.883220 | −0.0346694 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.230660 | − | 0.889726i | −0.00904029 | − | 0.0348711i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.237661 | + | 0.411641i | −0.00930039 | + | 0.0161087i | −0.870638 | − | 0.491924i | \(-0.836294\pi\) |
0.861338 | + | 0.508033i | \(0.169627\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.4663 | − | 25.0564i | −0.565247 | − | 0.979036i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 26.6144 | − | 14.7938i | 1.03833 | − | 0.577161i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.2344 | + | 31.5828i | 0.710310 | + | 1.23029i | 0.964741 | + | 0.263201i | \(0.0847784\pi\) |
−0.254431 | + | 0.967091i | \(0.581888\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.04982 | + | 8.74655i | −0.196415 | + | 0.340201i | −0.947364 | − | 0.320160i | \(-0.896263\pi\) |
0.750948 | + | 0.660361i | \(0.229597\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 26.2207 | + | 7.25494i | 1.01833 | + | 0.281758i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.34189 | −0.129593 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.88422 | −0.227838 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.1699 | + | 18.8605i | −0.741152 | + | 0.729191i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.44505 | − | 7.69905i | 0.171599 | − | 0.297218i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.51044 | + | 16.4726i | 0.366600 | + | 0.634971i | 0.989032 | − | 0.147704i | \(-0.0471883\pi\) |
−0.622431 | + | 0.782675i | \(0.713855\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.37224 | + | 4.66298i | −0.0528175 | + | 0.179478i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.6374 | + | 39.2091i | 0.870024 | + | 1.50693i | 0.861970 | + | 0.506959i | \(0.169230\pi\) |
0.00805435 | + | 0.999968i | \(0.497436\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.46718 | + | 9.46943i | −0.209811 | + | 0.363403i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.80191 | + | 2.75669i | −0.107369 | + | 0.105637i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 45.5318 | 1.74222 | 0.871112 | − | 0.491084i | \(-0.163399\pi\) | ||||
0.871112 | + | 0.491084i | \(0.163399\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −49.6363 | −1.89651 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.3925 | − | 4.25890i | −0.587259 | − | 0.162487i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.677375 | − | 1.17325i | 0.0258059 | − | 0.0446972i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.09446 | − | 14.0200i | −0.307928 | − | 0.533347i | 0.669981 | − | 0.742378i | \(-0.266302\pi\) |
−0.977909 | + | 0.209031i | \(0.932969\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.0370429 | − | 2.27656i | 0.00140714 | − | 0.0864795i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.63746 | − | 13.2285i | −0.289706 | − | 0.501785i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.2168 | − | 54.0691i | 1.18242 | − | 2.04801i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.4685 | − | 40.3802i | −0.395956 | − | 1.52732i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.61120 | −0.0986238 | −0.0493119 | − | 0.998783i | \(-0.515703\pi\) | ||||
−0.0493119 | + | 0.998783i | \(0.515703\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.21480 | 0.234396 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.19588 | + | 27.7567i | 0.271013 | + | 1.04538i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.750417 | − | 1.29976i | 0.0282223 | − | 0.0488825i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.1702 | − | 40.1319i | −0.870175 | − | 1.50719i | −0.861816 | − | 0.507222i | \(-0.830673\pi\) |
−0.00835896 | − | 0.999965i | \(-0.502661\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −39.2408 | − | 23.5151i | −1.47165 | − | 0.881886i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.86696 | + | 3.23366i | 0.0699180 | + | 0.121102i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.06008 | − | 3.56816i | 0.0770426 | − | 0.133442i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.34665 | + | 2.30941i | 0.311711 | + | 0.0862467i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 46.2069 | 1.72323 | 0.861614 | − | 0.507564i | \(-0.169454\pi\) | ||||
0.861614 | + | 0.507564i | \(0.169454\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.2646 | 0.382273 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.2798 | + | 20.9363i | −0.791403 | + | 0.778630i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.391140 | + | 0.677475i | −0.0145266 | + | 0.0251608i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.72988 | − | 16.8526i | −0.360861 | − | 0.625030i | 0.627242 | − | 0.778825i | \(-0.284184\pi\) |
−0.988103 | + | 0.153795i | \(0.950851\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.31734 | + | 26.9678i | −0.0487905 | + | 0.998809i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.0928 | − | 45.1940i | −0.965077 | − | 1.67156i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.68617 | + | 13.3128i | −0.283895 | + | 0.491721i | −0.972341 | − | 0.233567i | \(-0.924960\pi\) |
0.688445 | + | 0.725288i | \(0.258293\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.00799 | − | 2.95945i | 0.110951 | − | 0.109161i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.231938 | −0.00854356 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.4962 | 1.19539 | 0.597696 | − | 0.801723i | \(-0.296083\pi\) | ||||
0.597696 | + | 0.801723i | \(0.296083\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.10246 | − | 1.41179i | −0.187443 | − | 0.0518632i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.8664 | − | 36.1417i | 0.765514 | − | 1.32591i | −0.174460 | − | 0.984664i | \(-0.555818\pi\) |
0.939974 | − | 0.341245i | \(-0.110849\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.98542 | + | 10.3671i | 0.219289 | + | 0.379819i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −42.1464 | − | 25.2563i | −1.54206 | − | 0.924079i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.92214 | + | 6.79335i | 0.143312 | + | 0.248224i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.02452 | − | 8.70273i | 0.183347 | − | 0.317567i | −0.759671 | − | 0.650308i | \(-0.774640\pi\) |
0.943018 | + | 0.332741i | \(0.107973\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.63841 | − | 25.6063i | −0.241917 | − | 0.933146i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.6859 | 0.498081 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.7989 | −1.15575 | −0.577876 | − | 0.816125i | \(-0.696118\pi\) | ||||
−0.577876 | + | 0.816125i | \(0.696118\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.32120 | + | 8.95354i | 0.0842541 | + | 0.324993i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.4352 | − | 47.5192i | 0.994526 | − | 1.72257i | 0.406775 | − | 0.913528i | \(-0.366653\pi\) |
0.587751 | − | 0.809042i | \(-0.300013\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.08770 | + | 10.5442i | 0.220389 | + | 0.381726i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.838196 | + | 51.5134i | −0.0303050 | + | 1.86247i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.29657 | − | 2.24572i | −0.0468163 | − | 0.0810882i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.39041 | − | 9.33646i | 0.194383 | − | 0.336681i | −0.752315 | − | 0.658804i | \(-0.771063\pi\) |
0.946698 | + | 0.322122i | \(0.104396\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.3483 | + | 5.35344i | 0.696814 | + | 0.192800i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −47.4885 | −1.70804 | −0.854022 | − | 0.520237i | \(-0.825844\pi\) | ||||
−0.854022 | + | 0.520237i | \(0.825844\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.496407 | 0.0178315 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.59386 | + | 5.50359i | −0.200679 | + | 0.197440i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.07469 | + | 10.5217i | −0.217648 | + | 0.376978i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.78871 | − | 8.29428i | −0.171353 | − | 0.296793i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.22676 | + | 4.16861i | −0.0438407 | + | 0.148974i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.1360 | − | 43.5368i | −0.897141 | − | 1.55389i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.0563 | + | 20.8820i | −0.429759 | + | 0.744364i | −0.996852 | − | 0.0792896i | \(-0.974735\pi\) |
0.567093 | + | 0.823654i | \(0.308068\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.0157 | − | 9.85403i | 0.356567 | − | 0.350813i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.97173 | −0.141218 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.1013 | 0.926885 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.47262 | + | 0.684142i | 0.0876946 | + | 0.0242640i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.54620 | − | 13.0704i | 0.267300 | − | 0.462978i | −0.700863 | − | 0.713295i | \(-0.747202\pi\) |
0.968164 | + | 0.250318i | \(0.0805351\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.9500 | + | 41.4826i | 0.847289 | + | 1.46755i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.2551 | − | 14.0382i | 0.892346 | − | 0.496017i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.85165 | − | 6.67125i | −0.135922 | − | 0.235423i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.57117 | + | 14.8457i | −0.302094 | + | 0.523242i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.98115 | + | 19.2138i | 0.175345 | + | 0.676357i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.1104 | 0.707043 | 0.353522 | − | 0.935426i | \(-0.384984\pi\) | ||||
0.353522 | + | 0.935426i | \(0.384984\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.9770 | 1.43890 | 0.719448 | − | 0.694546i | \(-0.244395\pi\) | ||||
0.719448 | + | 0.694546i | \(0.244395\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.43614 | + | 5.53964i | 0.0503678 | + | 0.194284i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.03095 | − | 10.4459i | 0.211255 | − | 0.365904i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.07757 | + | 8.79461i | 0.177642 | + | 0.307684i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.84288 | − | 3.24780i | 0.204167 | − | 0.113487i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.9427 | + | 20.6854i | 0.416803 | + | 0.721925i | 0.995616 | − | 0.0935360i | \(-0.0298170\pi\) |
−0.578813 | + | 0.815461i | \(0.696484\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.9451 | − | 25.8857i | 0.520954 | − | 0.902319i | −0.478749 | − | 0.877952i | \(-0.658910\pi\) |
0.999703 | − | 0.0243673i | \(-0.00775714\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.18516 | + | 0.327918i | 0.0412618 | + | 0.0114166i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44.7265 | 1.55529 | 0.777647 | − | 0.628702i | \(-0.216413\pi\) | ||||
0.777647 | + | 0.628702i | \(0.216413\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.8943 | 1.28139 | 0.640695 | − | 0.767795i | \(-0.278646\pi\) | ||||
0.640695 | + | 0.767795i | \(0.278646\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.6542 | + | 12.4500i | −0.438969 | + | 0.431884i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.52452 | − | 6.10465i | 0.122117 | − | 0.211514i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.18370 | − | 2.05023i | −0.0409636 | − | 0.0709511i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.68008 | − | 0.648464i | 0.0926372 | − | 0.0224142i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.918446 | + | 1.59080i | 0.0317083 | + | 0.0549204i | 0.881444 | − | 0.472288i | \(-0.156572\pi\) |
−0.849736 | + | 0.527209i | \(0.823239\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.1503 | − | 24.5091i | 0.487942 | − | 0.845141i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.12692 | + | 2.09260i | −0.0732551 | + | 0.0720729i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.5748 | −0.673394 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.4240 | 0.358172 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 40.3149 | + | 11.1546i | 1.38360 | + | 0.382826i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.9395 | − | 27.6081i | 0.546400 | − | 0.946392i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.0385 | + | 45.1000i | 0.891542 | + | 1.54420i | 0.838027 | + | 0.545629i | \(0.183709\pi\) |
0.0535152 | + | 0.998567i | \(0.482957\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.163110 | − | 10.0243i | 0.00557825 | − | 0.342825i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.46663 | + | 16.3967i | 0.323374 | + | 0.560100i | 0.981182 | − | 0.193086i | \(-0.0618495\pi\) |
−0.657808 | + | 0.753186i | \(0.728516\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00700 | + | 6.94033i | −0.136717 | + | 0.236801i | −0.926252 | − | 0.376905i | \(-0.876988\pi\) |
0.789535 | + | 0.613706i | \(0.210322\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.84983 | − | 14.8499i | −0.131202 | − | 0.506084i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.8647 | 0.812364 | 0.406182 | − | 0.913792i | \(-0.366860\pi\) | ||||
0.406182 | + | 0.913792i | \(0.366860\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43.4125 | −1.47607 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.2087 | + | 54.8071i | 0.482552 | + | 1.86135i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.78667 | + | 10.0228i | −0.196299 | + | 0.340001i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.340485 | − | 0.589738i | −0.0115369 | − | 0.0199825i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −28.1377 | − | 16.8615i | −0.952316 | − | 0.570677i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.95119 | − | 8.57572i | −0.167381 | − | 0.289912i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.0238 | − | 29.4861i | 0.574853 | − | 0.995674i | −0.421205 | − | 0.906965i | \(-0.638393\pi\) |
0.996058 | − | 0.0887086i | \(-0.0282740\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.9242 | + | 6.89621i | 0.840672 | + | 0.232604i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.8018 | −1.30727 | −0.653633 | − | 0.756812i | \(-0.726756\pi\) | ||||
−0.653633 | + | 0.756812i | \(0.726756\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.0944 | 1.41659 | 0.708294 | − | 0.705917i | \(-0.249465\pi\) | ||||
0.708294 | + | 0.705917i | \(0.249465\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.50050 | − | 3.44400i | 0.117668 | − | 0.115769i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.1168 | − | 20.9869i | 0.406841 | − | 0.704670i | −0.587692 | − | 0.809084i | \(-0.699964\pi\) |
0.994534 | + | 0.104414i | \(0.0332968\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.87893 | − | 13.6467i | −0.264251 | − | 0.457696i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.82698 | + | 0.222228i | 0.228712 | + | 0.00744491i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.66058 | − | 8.07236i | −0.155960 | − | 0.270131i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.9201 | + | 22.3783i | −0.431873 | + | 0.748025i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.3582 | + | 19.0458i | −0.646352 | + | 0.635920i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.443778 | 0.0148008 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.28566 | 0.142776 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.3584 | − | 3.41942i | −0.411262 | − | 0.113791i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30.1319 | + | 52.1900i | −1.00162 | + | 1.73485i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.9424 | − | 22.4170i | −0.429747 | − | 0.744343i | 0.567104 | − | 0.823646i | \(-0.308064\pi\) |
−0.996851 | + | 0.0793031i | \(0.974731\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.86214 | + | 2.31439i | 0.128099 | + | 0.0767635i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.9571 | − | 38.0308i | −0.727471 | − | 1.26002i | −0.957949 | − | 0.286939i | \(-0.907362\pi\) |
0.230478 | − | 0.973078i | \(-0.425971\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.21514 | + | 10.7649i | −0.205691 | + | 0.356268i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.4042 | + | 47.8468i | 0.410071 | + | 1.58177i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.8758 | −0.392173 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.4335 | −1.36677 | −0.683383 | − | 0.730060i | \(-0.739492\pi\) | ||||
−0.683383 | + | 0.730060i | \(0.739492\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.80495 | + | 30.1060i | 0.257182 | + | 0.992026i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.0596 | − | 24.3520i | 0.462779 | − | 0.801556i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.11909 | − | 3.67037i | −0.0696752 | − | 0.120681i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.500991 | + | 30.7896i | −0.0164547 | + | 1.01126i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.56911 | + | 2.71778i | 0.0514808 | + | 0.0891674i | 0.890617 | − | 0.454753i | \(-0.150273\pi\) |
−0.839137 | + | 0.543921i | \(0.816939\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.685860 | + | 1.18794i | −0.0224781 | + | 0.0389333i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 36.3683 | + | 10.0626i | 1.19064 | + | 0.329436i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.0338 | 0.426252 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.2810 | 0.335866 | 0.167933 | − | 0.985798i | \(-0.446291\pi\) | ||||
0.167933 | + | 0.985798i | \(0.446291\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.3168 | − | 26.8759i | 0.891449 | − | 0.877062i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.23844 | − | 12.5373i | 0.235966 | − | 0.408706i | −0.723587 | − | 0.690234i | \(-0.757508\pi\) |
0.959553 | + | 0.281528i | \(0.0908411\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.1603 | + | 53.9713i | 1.01472 | + | 1.75755i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.73035 | + | 9.16722i | 0.283998 | + | 0.298210i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.8714 | + | 25.7580i | 0.483256 | + | 0.837024i | 0.999815 | − | 0.0192278i | \(-0.00612078\pi\) |
−0.516559 | + | 0.856251i | \(0.672787\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.3084 | − | 19.5868i | 0.367088 | − | 0.635814i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.07414 | − | 6.95997i | 0.229395 | − | 0.225692i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.4869 | 0.631242 | 0.315621 | − | 0.948885i | \(-0.397787\pi\) | ||||
0.315621 | + | 0.948885i | \(0.397787\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −45.0769 | −1.45866 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.05951 | + | 0.293152i | 0.0342490 | + | 0.00947626i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.1869 | + | 17.6443i | −0.328953 | + | 0.569763i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3592 | + | 26.6029i | 0.495458 | + | 0.858158i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.5688 | + | 11.4333i | −0.662820 | + | 0.368433i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.0872 | − | 34.7921i | −0.646631 | − | 1.12000i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.94942 | + | 12.0368i | −0.223478 | + | 0.387076i | −0.955862 | − | 0.293817i | \(-0.905075\pi\) |
0.732384 | + | 0.680892i | \(0.238408\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.20289 | − | 16.2118i | −0.135016 | − | 0.520798i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.2406 | −0.617460 | −0.308730 | − | 0.951150i | \(-0.599904\pi\) | ||||
−0.308730 | + | 0.951150i | \(0.599904\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.26978 | −0.201000 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.906028 | + | 3.49482i | 0.0290161 | + | 0.111924i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.44479 | + | 4.23450i | −0.0782158 | + | 0.135474i | −0.902480 | − | 0.430731i | \(-0.858256\pi\) |
0.824264 | + | 0.566205i | \(0.191589\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.65494 | − | 6.33054i | −0.116812 | − | 0.202325i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −31.9255 | + | 17.7460i | −1.01930 | + | 0.566587i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.9670 | − | 25.9236i | −0.477373 | − | 0.826834i | 0.522291 | − | 0.852768i | \(-0.325078\pi\) |
−0.999664 | + | 0.0259332i | \(0.991744\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.5754 | − | 18.3172i | 0.336962 | − | 0.583634i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.3435 | + | 3.13860i | 0.361068 | + | 0.0999029i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 52.0912 | 1.65640 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.36157 | 0.297380 | 0.148690 | − | 0.988884i | \(-0.452494\pi\) | ||||
0.148690 | + | 0.988884i | \(0.452494\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 39.0595 | − | 38.4291i | 1.23952 | − | 1.21951i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.4311 | + | 40.5839i | −0.742817 | + | 1.28660i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.8210 | + | 41.2592i | 0.754420 | + | 1.30669i | 0.945662 | + | 0.325151i | \(0.105415\pi\) |
−0.191242 | + | 0.981543i | \(0.561252\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.2355 | − | 17.0480i | −0.513670 | − | 0.539375i |
(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 | 1008.2.r.m.337.2 | 8 | ||
3.2 | odd | 2 | 3024.2.r.l.1009.4 | 8 | |||
4.3 | odd | 2 | 504.2.r.d.337.3 | yes | 8 | ||
9.2 | odd | 6 | 3024.2.r.l.2017.4 | 8 | |||
9.4 | even | 3 | 9072.2.a.ce.1.4 | 4 | |||
9.5 | odd | 6 | 9072.2.a.cl.1.1 | 4 | |||
9.7 | even | 3 | inner | 1008.2.r.m.673.2 | 8 | ||
12.11 | even | 2 | 1512.2.r.d.1009.4 | 8 | |||
36.7 | odd | 6 | 504.2.r.d.169.3 | ✓ | 8 | ||
36.11 | even | 6 | 1512.2.r.d.505.4 | 8 | |||
36.23 | even | 6 | 4536.2.a.ba.1.1 | 4 | |||
36.31 | odd | 6 | 4536.2.a.x.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.d.169.3 | ✓ | 8 | 36.7 | odd | 6 | ||
504.2.r.d.337.3 | yes | 8 | 4.3 | odd | 2 | ||
1008.2.r.m.337.2 | 8 | 1.1 | even | 1 | trivial | ||
1008.2.r.m.673.2 | 8 | 9.7 | even | 3 | inner | ||
1512.2.r.d.505.4 | 8 | 36.11 | even | 6 | |||
1512.2.r.d.1009.4 | 8 | 12.11 | even | 2 | |||
3024.2.r.l.1009.4 | 8 | 3.2 | odd | 2 | |||
3024.2.r.l.2017.4 | 8 | 9.2 | odd | 6 | |||
4536.2.a.x.1.4 | 4 | 36.31 | odd | 6 | |||
4536.2.a.ba.1.1 | 4 | 36.23 | even | 6 | |||
9072.2.a.ce.1.4 | 4 | 9.4 | even | 3 | |||
9072.2.a.cl.1.1 | 4 | 9.5 | odd | 6 |