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 | 673.3 | ||
Root | \(1.86526 - 0.199842i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.673 |
Dual form | 1008.2.r.m.337.3 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 1.60570 | + | 0.649414i | 0.927049 | + | 0.374939i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.468293 | − | 0.811107i | −0.209427 | − | 0.362738i | 0.742107 | − | 0.670281i | \(-0.233827\pi\) |
−0.951534 | + | 0.307543i | \(0.900493\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.15652 | + | 2.08552i | 0.718841 | + | 0.695174i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.48741 | − | 4.30833i | 0.749983 | − | 1.29901i | −0.197847 | − | 0.980233i | \(-0.563395\pi\) |
0.947830 | − | 0.318776i | \(-0.103272\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.622156 | − | 1.07761i | −0.172555 | − | 0.298874i | 0.766757 | − | 0.641937i | \(-0.221869\pi\) |
−0.939312 | + | 0.343063i | \(0.888536\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.225193 | − | 1.60651i | −0.0581445 | − | 0.414799i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.22446 | 1.26712 | 0.633559 | − | 0.773694i | \(-0.281593\pi\) | ||||
0.633559 | + | 0.773694i | \(0.281593\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.18622 | −1.18980 | −0.594900 | − | 0.803800i | \(-0.702808\pi\) | ||||
−0.594900 | + | 0.803800i | \(0.702808\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.36526 | − | 1.06587i | 0.297923 | − | 0.232591i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00266 | − | 1.73666i | −0.209069 | − | 0.362118i | 0.742352 | − | 0.670010i | \(-0.233710\pi\) |
−0.951422 | + | 0.307891i | \(0.900377\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.06140 | − | 3.57046i | 0.412281 | − | 0.714091i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.10836 | + | 4.74919i | 0.405754 | + | 0.913983i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.43925 | + | 5.95695i | −0.638652 | + | 1.10618i | 0.347077 | + | 0.937837i | \(0.387174\pi\) |
−0.985729 | + | 0.168341i | \(0.946159\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.86526 | − | 4.96277i | −0.514615 | − | 0.891340i | −0.999856 | − | 0.0169594i | \(-0.994601\pi\) |
0.485241 | − | 0.874381i | \(-0.338732\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.79192 | − | 5.30251i | 1.18232 | − | 0.923048i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.936586 | −0.158312 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.73051 | 1.59969 | 0.799843 | − | 0.600209i | \(-0.204916\pi\) | ||||
0.799843 | + | 0.600209i | \(0.204916\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.299182 | − | 2.13435i | −0.0479075 | − | 0.341769i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.73705 | + | 9.93686i | 0.895976 | + | 1.55188i | 0.832592 | + | 0.553887i | \(0.186856\pi\) |
0.0633848 | + | 0.997989i | \(0.479810\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.80184 | − | 8.31704i | 0.732274 | − | 1.26834i | −0.223635 | − | 0.974673i | \(-0.571792\pi\) |
0.955909 | − | 0.293663i | \(-0.0948744\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.681697 | − | 2.72581i | 0.101621 | − | 0.406339i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.984753 | + | 1.70564i | −0.143641 | + | 0.248793i | −0.928865 | − | 0.370418i | \(-0.879214\pi\) |
0.785224 | + | 0.619212i | \(0.212548\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.38890 | + | 3.39284i | 1.17468 | + | 0.475092i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.63418 | −1.04864 | −0.524318 | − | 0.851523i | \(-0.675680\pi\) | ||||
−0.524318 | + | 0.851523i | \(0.675680\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.65935 | −0.628267 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.32750 | − | 3.36800i | −1.10300 | − | 0.446103i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.43925 | + | 4.22490i | 0.317563 | + | 0.550035i | 0.979979 | − | 0.199101i | \(-0.0638022\pi\) |
−0.662416 | + | 0.749136i | \(0.730469\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.52178 | − | 2.63580i | 0.194844 | − | 0.337480i | −0.752005 | − | 0.659157i | \(-0.770913\pi\) |
0.946849 | + | 0.321677i | \(0.104247\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.88438 | − | 0.824844i | 0.363397 | − | 0.103921i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.582703 | + | 1.00927i | −0.0722754 | + | 0.125185i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.573990 | − | 0.994179i | −0.0701240 | − | 0.121458i | 0.828831 | − | 0.559498i | \(-0.189006\pi\) |
−0.898955 | + | 0.438040i | \(0.855673\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.482159 | − | 3.43969i | −0.0580451 | − | 0.414090i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.83749 | 1.04882 | 0.524409 | − | 0.851467i | \(-0.324286\pi\) | ||||
0.524409 | + | 0.851467i | \(0.324286\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.10698 | 0.714768 | 0.357384 | − | 0.933958i | \(-0.383669\pi\) | ||||
0.357384 | + | 0.933958i | \(0.383669\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.62869 | − | 4.39437i | 0.649945 | − | 0.507418i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.48741 | − | 4.30833i | −0.283467 | − | 0.490979i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.05414 | + | 10.4861i | −0.681144 | + | 1.17978i | 0.293488 | + | 0.955963i | \(0.405184\pi\) |
−0.974632 | + | 0.223813i | \(0.928150\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.301193 | + | 8.99496i | 0.0334659 | + | 0.999440i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.431332 | + | 0.747088i | −0.0473448 | + | 0.0820036i | −0.888727 | − | 0.458438i | \(-0.848409\pi\) |
0.841382 | + | 0.540441i | \(0.181743\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.44658 | − | 4.23760i | −0.265369 | − | 0.459632i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.39091 | + | 7.33156i | −1.00681 | + | 0.786026i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.8480 | −1.14989 | −0.574943 | − | 0.818194i | \(-0.694976\pi\) | ||||
−0.574943 | + | 0.818194i | \(0.694976\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.24431 | −0.130439 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.37784 | − | 9.82944i | −0.142876 | − | 1.01927i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.42867 | + | 4.20658i | 0.249176 | + | 0.431586i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.78521 | + | 6.55618i | −0.384330 | + | 0.665680i | −0.991676 | − | 0.128758i | \(-0.958901\pi\) |
0.607346 | + | 0.794438i | \(0.292234\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.3493 | − | 4.10345i | 1.44216 | − | 0.412413i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.52970 | + | 4.38156i | −0.251714 | + | 0.435982i | −0.963998 | − | 0.265910i | \(-0.914328\pi\) |
0.712284 | + | 0.701892i | \(0.247661\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.119496 | + | 0.206973i | 0.0117743 | + | 0.0203936i | 0.871853 | − | 0.489769i | \(-0.162919\pi\) |
−0.860078 | + | 0.510162i | \(0.829585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.50387 | − | 0.608232i | −0.146763 | − | 0.0593573i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.25496 | −0.894710 | −0.447355 | − | 0.894356i | \(-0.647634\pi\) | ||||
−0.447355 | + | 0.894356i | \(0.647634\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.5453 | −1.01005 | −0.505026 | − | 0.863104i | \(-0.668517\pi\) | ||||
−0.505026 | + | 0.863104i | \(0.668517\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.6243 | + | 6.31913i | 1.48299 | + | 0.599785i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.06406 | + | 8.77122i | 0.476387 | + | 0.825127i | 0.999634 | − | 0.0270545i | \(-0.00861278\pi\) |
−0.523247 | + | 0.852181i | \(0.675279\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.939078 | + | 1.62653i | −0.0875695 | + | 0.151675i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.905677 | − | 3.62141i | 0.0837299 | − | 0.334799i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.61223 | − | 4.52452i | 0.239463 | − | 0.414762i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.87445 | − | 11.9069i | −0.624950 | − | 1.08245i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.75883 | + | 19.6813i | 0.248755 | + | 1.77460i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.54429 | −0.764225 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.52720 | −0.579196 | −0.289598 | − | 0.957148i | \(-0.593522\pi\) | ||||
−0.289598 | + | 0.957148i | \(0.593522\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.1115 | − | 10.2363i | 1.15440 | − | 0.901252i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.76748 | − | 3.06136i | −0.154425 | − | 0.267472i | 0.778424 | − | 0.627738i | \(-0.216019\pi\) |
−0.932850 | + | 0.360266i | \(0.882686\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.59311 | + | 4.49140i | −0.224851 | + | 0.389454i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.86478 | − | 3.93412i | 0.246561 | − | 0.338595i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.48603 | + | 4.30593i | −0.212396 | + | 0.367881i | −0.952464 | − | 0.304651i | \(-0.901460\pi\) |
0.740068 | + | 0.672532i | \(0.234793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.87566 | + | 8.44490i | 0.413548 | + | 0.716287i | 0.995275 | − | 0.0970976i | \(-0.0309559\pi\) |
−0.581726 | + | 0.813385i | \(0.697623\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.68888 | + | 2.09923i | −0.226445 | + | 0.176787i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.19024 | −0.517654 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.44230 | 0.535004 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.240440 | − | 1.71528i | −0.0198311 | − | 0.141474i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.39108 | + | 11.0697i | 0.523578 | + | 0.906863i | 0.999623 | + | 0.0274426i | \(0.00873635\pi\) |
−0.476046 | + | 0.879421i | \(0.657930\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.4781 | − | 19.8807i | 0.934078 | − | 1.61787i | 0.157807 | − | 0.987470i | \(-0.449558\pi\) |
0.776271 | − | 0.630400i | \(-0.217109\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.2667 | + | 10.8957i | 0.910857 | + | 0.880868i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.68356 | + | 4.64806i | −0.215549 | + | 0.373341i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.25489 | − | 14.2979i | −0.658812 | − | 1.14110i | −0.980924 | − | 0.194394i | \(-0.937726\pi\) |
0.322112 | − | 0.946702i | \(-0.395607\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.2582 | − | 4.95774i | −0.972137 | − | 0.393174i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.00532 | −0.158041 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.2245 | −1.34912 | −0.674562 | − | 0.738218i | \(-0.735667\pi\) | ||||
−0.674562 | + | 0.738218i | \(0.735667\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.48151 | − | 3.02585i | −0.582435 | − | 0.235562i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.56406 | + | 11.3693i | 0.507943 | + | 0.879782i | 0.999958 | + | 0.00919564i | \(0.00292711\pi\) |
−0.492015 | + | 0.870587i | \(0.663740\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.72584 | − | 9.91745i | 0.440449 | − | 0.762881i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.1842 | − | 10.8160i | −0.855278 | − | 0.827119i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.49412 | − | 16.4443i | 0.721824 | − | 1.25024i | −0.238444 | − | 0.971156i | \(-0.576637\pi\) |
0.960268 | − | 0.279080i | \(-0.0900295\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.06140 | − | 3.57046i | −0.155827 | − | 0.269901i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.17298 | + | 8.36799i | 0.0881669 | + | 0.628976i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.61835 | −0.569422 | −0.284711 | − | 0.958613i | \(-0.591898\pi\) | ||||
−0.284711 | + | 0.958613i | \(0.591898\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.27737 | −0.689581 | −0.344791 | − | 0.938680i | \(-0.612050\pi\) | ||||
−0.344791 | + | 0.938680i | \(0.612050\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.15524 | − | 3.24403i | 0.307165 | − | 0.239806i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.55673 | − | 7.89249i | −0.335018 | − | 0.580267i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.9954 | − | 22.5087i | 0.950317 | − | 1.64600i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.16710 | + | 0.548705i | 0.375851 | + | 0.0399124i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.80119 | − | 8.31591i | 0.347402 | − | 0.601718i | −0.638385 | − | 0.769717i | \(-0.720397\pi\) |
0.985787 | + | 0.167999i | \(0.0537306\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.54155 | + | 13.0624i | 0.542853 | + | 0.940249i | 0.998739 | + | 0.0502103i | \(0.0159892\pi\) |
−0.455886 | + | 0.890038i | \(0.650677\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.59108 | + | 1.24217i | −0.113940 | + | 0.0889535i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.0712 | −0.788788 | −0.394394 | − | 0.918942i | \(-0.629045\pi\) | ||||
−0.394394 | + | 0.918942i | \(0.629045\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.3368 | −1.29986 | −0.649929 | − | 0.759995i | \(-0.725201\pi\) | ||||
−0.649929 | + | 0.759995i | \(0.725201\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.276020 | − | 1.96911i | −0.0194689 | − | 0.138890i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.43925 | + | 5.95695i | 0.241388 | + | 0.418096i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.37324 | − | 9.30672i | 0.375283 | − | 0.650010i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.45958 | − | 5.83622i | 0.101448 | − | 0.405645i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.9003 | + | 22.3439i | −0.892331 | + | 1.54556i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.30911 | + | 2.26744i | 0.0901227 | + | 0.156097i | 0.907563 | − | 0.419917i | \(-0.137941\pi\) |
−0.817440 | + | 0.576014i | \(0.804607\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.1903 | + | 5.73919i | 0.972305 | + | 0.393243i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.99468 | −0.613432 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.73051 | −0.389013 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.80595 | + | 3.96595i | 0.662625 | + | 0.267994i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.25043 | − | 5.62991i | −0.218648 | − | 0.378709i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.5442 | + | 21.7272i | −0.840023 | + | 1.45496i | 0.0498520 | + | 0.998757i | \(0.484125\pi\) |
−0.889875 | + | 0.456205i | \(0.849208\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.8917 | − | 3.40067i | 0.792782 | − | 0.226711i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.7781 | + | 22.1323i | −0.848113 | + | 1.46898i | 0.0347761 | + | 0.999395i | \(0.488928\pi\) |
−0.882890 | + | 0.469581i | \(0.844405\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.73657 | − | 4.73987i | −0.180837 | − | 0.313220i | 0.761329 | − | 0.648366i | \(-0.224547\pi\) |
−0.942166 | + | 0.335147i | \(0.891214\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.19615 | − | 8.53323i | −0.0787006 | − | 0.561445i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.6774 | 0.699500 | 0.349750 | − | 0.936843i | \(-0.386267\pi\) | ||||
0.349750 | + | 0.936843i | \(0.386267\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.84461 | 0.120329 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.5309 | + | 12.9058i | −1.07380 | + | 0.838323i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.50000 | + | 4.33013i | 0.161712 | + | 0.280093i | 0.935483 | − | 0.353373i | \(-0.114965\pi\) |
−0.773771 | + | 0.633465i | \(0.781632\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.1684 | + | 17.6121i | −0.655003 | + | 1.13450i | 0.326890 | + | 0.945062i | \(0.393999\pi\) |
−0.981893 | + | 0.189436i | \(0.939334\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.35782 | + | 14.6388i | −0.343705 | + | 0.939078i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.468293 | + | 0.811107i | −0.0299181 | + | 0.0518197i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.22664 | + | 5.58871i | 0.205306 | + | 0.355601i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.17776 | + | 0.919485i | −0.0746373 | + | 0.0582700i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.8151 | −1.25072 | −0.625358 | − | 0.780338i | \(-0.715047\pi\) | ||||
−0.625358 | + | 0.780338i | \(0.715047\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.97613 | −0.627194 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.17651 | − | 8.39314i | −0.0736759 | − | 0.525599i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.969506 | + | 1.67923i | 0.0604761 | + | 0.104748i | 0.894678 | − | 0.446711i | \(-0.147405\pi\) |
−0.834202 | + | 0.551459i | \(0.814071\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.86526 | − | 8.42687i | 0.302312 | − | 0.523620i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.8402 | + | 5.67368i | −1.22808 | + | 0.351192i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.67768 | + | 11.5661i | −0.411763 | + | 0.713195i | −0.995083 | − | 0.0990481i | \(-0.968420\pi\) |
0.583320 | + | 0.812243i | \(0.301754\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.57503 | + | 6.19214i | 0.219613 | + | 0.380380i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.4186 | − | 7.04484i | −1.06600 | − | 0.431137i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.15040 | 0.253055 | 0.126527 | − | 0.991963i | \(-0.459617\pi\) | ||||
0.126527 | + | 0.991963i | \(0.459617\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.6050 | 1.00868 | 0.504341 | − | 0.863505i | \(-0.331736\pi\) | ||||
0.504341 | + | 0.863505i | \(0.331736\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.99799 | − | 0.808074i | −0.120924 | − | 0.0489068i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.2551 | − | 17.7624i | −0.618407 | − | 1.07111i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.55414 | + | 14.8162i | −0.513968 | + | 0.890219i | 0.485900 | + | 0.874014i | \(0.338492\pi\) |
−0.999869 | + | 0.0162051i | \(0.994842\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.17097 | − | 16.6779i | 0.249710 | − | 0.998479i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.49007 | − | 12.9732i | 0.446820 | − | 0.773916i | −0.551357 | − | 0.834270i | \(-0.685890\pi\) |
0.998177 | + | 0.0603541i | \(0.0192230\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.00580 | − | 15.5985i | −0.535339 | − | 0.927235i | −0.999147 | − | 0.0412990i | \(-0.986850\pi\) |
0.463807 | − | 0.885936i | \(-0.346483\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.16790 | + | 8.33171i | 0.0691803 | + | 0.493528i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.4741 | 0.677294 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.2950 | 0.605588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.3356 | + | 8.06907i | −0.605883 | + | 0.473017i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.8362 | + | 23.9650i | 0.808320 | + | 1.40005i | 0.914027 | + | 0.405654i | \(0.132956\pi\) |
−0.105707 | + | 0.994397i | \(0.533710\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.28456 | − | 3.95698i | 0.133012 | − | 0.230384i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 25.7054 | + | 2.72971i | 1.49158 | + | 0.158394i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.24762 | + | 2.16095i | −0.0721519 | + | 0.124971i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.80184 | − | 8.31704i | −0.276774 | − | 0.479386i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.90737 | + | 5.39264i | −0.396818 | + | 0.309799i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.85056 | −0.163222 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.10040 | 0.348168 | 0.174084 | − | 0.984731i | \(-0.444304\pi\) | ||||
0.174084 | + | 0.984731i | \(0.444304\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0574631 | + | 0.409938i | 0.00326896 | + | 0.0233205i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.3277 | + | 23.0842i | 0.755743 | + | 1.30898i | 0.945004 | + | 0.327058i | \(0.106057\pi\) |
−0.189262 | + | 0.981927i | \(0.560609\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.0681 | + | 20.9026i | −0.682130 | + | 1.18148i | 0.292200 | + | 0.956357i | \(0.405613\pi\) |
−0.974330 | + | 0.225126i | \(0.927721\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.01977 | − | 1.95327i | −0.113801 | − | 0.110054i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.80046 | − | 15.2428i | 0.494283 | − | 0.856124i | −0.505695 | − | 0.862712i | \(-0.668764\pi\) |
0.999978 | + | 0.00658868i | \(0.00209726\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.1097 | + | 29.6348i | 0.957957 | + | 1.65923i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.8607 | − | 6.01029i | −0.829441 | − | 0.335462i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −27.0952 | −1.50762 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.13006 | −0.284565 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.9325 | − | 6.84823i | −0.936368 | − | 0.378708i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.984753 | + | 1.70564i | 0.0542912 | + | 0.0940351i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.1497 | − | 21.0440i | 0.667810 | − | 1.15668i | −0.310705 | − | 0.950506i | \(-0.600565\pi\) |
0.978515 | − | 0.206175i | \(-0.0661015\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.9841 | + | 20.2932i | 1.14992 | + | 1.11206i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.537591 | + | 0.931135i | −0.0293717 | + | 0.0508733i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.4722 | − | 19.8704i | −0.624929 | − | 1.08241i | −0.988555 | − | 0.150863i | \(-0.951795\pi\) |
0.363626 | − | 0.931545i | \(-0.381539\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.43520 | + | 17.3726i | 0.132262 | + | 0.943549i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −28.5083 | −1.54381 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.56417 | + | 2.00187i | −0.138050 | + | 0.107777i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.36930 | − | 11.0319i | −0.341922 | − | 0.592226i | 0.642868 | − | 0.765977i | \(-0.277744\pi\) |
−0.984790 | + | 0.173751i | \(0.944411\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.99468 | − | 6.91899i | 0.213830 | − | 0.370365i | −0.739080 | − | 0.673618i | \(-0.764739\pi\) |
0.952910 | + | 0.303253i | \(0.0980727\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.80603 | − | 5.22672i | 0.203151 | − | 0.278982i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.9781 | − | 19.0147i | 0.584307 | − | 1.01205i | −0.410654 | − | 0.911791i | \(-0.634700\pi\) |
0.994961 | − | 0.100259i | \(-0.0319671\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.13854 | − | 7.16815i | −0.219651 | − | 0.380446i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.13273 | − | 5.56858i | 0.377504 | − | 0.294721i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.4673 | −1.08022 | −0.540112 | − | 0.841593i | \(-0.681618\pi\) | ||||
−0.540112 | + | 0.841593i | \(0.681618\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.89688 | 0.415625 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.30578 | − | 23.5832i | −0.173509 | − | 1.23780i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.85985 | − | 4.95341i | −0.149692 | − | 0.259273i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.94174 | + | 17.2196i | −0.518955 | + | 0.898856i | 0.480803 | + | 0.876829i | \(0.340345\pi\) |
−0.999757 | + | 0.0220269i | \(0.992988\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.35146 | + | 33.3938i | −0.434760 | + | 1.73841i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.81709 | + | 6.61139i | −0.198173 | + | 0.343246i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.1438 | − | 29.6939i | −0.887672 | − | 1.53749i | −0.842620 | − | 0.538508i | \(-0.818988\pi\) |
−0.0450513 | − | 0.998985i | \(-0.514345\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.7195 | − | 5.54878i | −0.708474 | − | 0.286538i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.55900 | 0.440811 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.6248 | −0.956694 | −0.478347 | − | 0.878171i | \(-0.658764\pi\) | ||||
−0.478347 | + | 0.878171i | \(0.658764\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.4807 | − | 4.23885i | −0.536943 | − | 0.217163i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.4360 | + | 28.4680i | 0.839842 | + | 1.45465i | 0.890027 | + | 0.455908i | \(0.150686\pi\) |
−0.0501852 | + | 0.998740i | \(0.515981\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.32968 | + | 4.03512i | −0.118731 | + | 0.205649i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 27.7007 | − | 7.92154i | 1.40810 | − | 0.402674i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.8250 | − | 18.7495i | 0.548850 | − | 0.950635i | −0.449504 | − | 0.893278i | \(-0.648399\pi\) |
0.998354 | − | 0.0573571i | \(-0.0182674\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.23836 | − | 9.07311i | −0.264915 | − | 0.458847i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.849943 | − | 6.06343i | −0.0428739 | − | 0.305860i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.3404 | 0.570600 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.2721 | 0.816673 | 0.408336 | − | 0.912832i | \(-0.366109\pi\) | ||||
0.408336 | + | 0.912832i | \(0.366109\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.08052 | + | 5.52782i | −0.354470 | + | 0.276737i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.57133 | + | 7.91777i | 0.228281 | + | 0.395395i | 0.957299 | − | 0.289100i | \(-0.0933561\pi\) |
−0.729018 | + | 0.684495i | \(0.760023\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.56528 | + | 6.17524i | −0.177599 | + | 0.307611i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.15483 | − | 4.45658i | 0.355526 | − | 0.221449i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.2038 | − | 41.9222i | 1.19974 | − | 2.07801i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.0976 | + | 19.2217i | 0.548743 | + | 0.950450i | 0.998361 | + | 0.0572294i | \(0.0182266\pi\) |
−0.449618 | + | 0.893221i | \(0.648440\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.78815 | + | 5.29956i | −0.334835 | + | 0.261408i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.87849 | 0.240055 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.807958 | 0.0396611 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.34461 | + | 16.7263i | 0.114816 | + | 0.819089i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.9601 | + | 24.1795i | 0.681994 | + | 1.18125i | 0.974372 | + | 0.224945i | \(0.0722202\pi\) |
−0.292378 | + | 0.956303i | \(0.594447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.0441 | + | 20.8611i | −0.586996 | + | 1.01671i | 0.407628 | + | 0.913148i | \(0.366356\pi\) |
−0.994623 | + | 0.103558i | \(0.966977\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.68080 | + | 1.62453i | −0.276210 | + | 0.0789875i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.7697 | − | 18.6537i | 0.522408 | − | 0.904838i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.52178 | − | 2.63580i | −0.0736442 | − | 0.127555i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.93965 | − | 4.02003i | −0.479891 | − | 0.194089i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.1623 | 1.26020 | 0.630098 | − | 0.776516i | \(-0.283015\pi\) | ||||
0.630098 | + | 0.776516i | \(0.283015\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.5630 | −0.892082 | −0.446041 | − | 0.895013i | \(-0.647166\pi\) | ||||
−0.446041 | + | 0.895013i | \(0.647166\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.3444 | + | 4.18372i | 0.495975 | + | 0.200594i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.20002 | + | 9.00670i | 0.248751 | + | 0.430849i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.85395 | − | 6.67524i | 0.183939 | − | 0.318592i | −0.759279 | − | 0.650765i | \(-0.774448\pi\) |
0.943218 | + | 0.332173i | \(0.107782\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.727853 | − | 2.91037i | 0.0346597 | − | 0.138589i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.5204 | − | 28.6142i | 0.784909 | − | 1.35950i | −0.144145 | − | 0.989557i | \(-0.546043\pi\) |
0.929053 | − | 0.369945i | \(-0.120624\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.08004 | + | 8.79889i | 0.240817 | + | 0.417107i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.07334 | + | 21.9250i | 0.145364 | + | 1.03702i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.9283 | 0.940477 | 0.470238 | − | 0.882540i | \(-0.344168\pi\) | ||||
0.470238 | + | 0.882540i | \(0.344168\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 57.0816 | 2.68787 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 31.3412 | − | 24.4683i | 1.47254 | − | 1.14962i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.582703 | + | 1.00927i | 0.0273175 | + | 0.0473154i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.9326 | − | 29.3282i | 0.792075 | − | 1.37191i | −0.132605 | − | 0.991169i | \(-0.542334\pi\) |
0.924680 | − | 0.380745i | \(-0.124333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.0150 | + | 24.8120i | 0.514138 | + | 1.15812i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.25351 | − | 12.5634i | 0.337830 | − | 0.585138i | −0.646195 | − | 0.763173i | \(-0.723641\pi\) |
0.984024 | + | 0.178035i | \(0.0569739\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.5348 | + | 21.7110i | 0.582544 | + | 1.00900i | 0.995177 | + | 0.0980981i | \(0.0312759\pi\) |
−0.412633 | + | 0.910897i | \(0.635391\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.32750 | + | 5.72064i | −0.339805 | + | 0.265288i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.102955 | 0.00476419 | 0.00238209 | − | 0.999997i | \(-0.499242\pi\) | ||||
0.00238209 | + | 0.999997i | \(0.499242\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.14798 | −0.0530088 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.96961 | − | 28.3189i | −0.182910 | − | 1.30487i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.8883 | − | 41.3758i | −1.09839 | − | 1.90246i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.6909 | + | 18.5172i | −0.490532 | + | 0.849626i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.4633 | − | 15.9213i | −0.753802 | − | 0.728984i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.62668 | − | 4.54954i | 0.120016 | − | 0.207874i | −0.799758 | − | 0.600323i | \(-0.795039\pi\) |
0.919774 | + | 0.392449i | \(0.128372\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.05390 | − | 10.4857i | −0.276034 | − | 0.478105i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.21994 | − | 1.30228i | −0.146512 | − | 0.0592559i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.09036 | 0.321957 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.7319 | 1.39260 | 0.696299 | − | 0.717752i | \(-0.254829\pi\) | ||||
0.696299 | + | 0.717752i | \(0.254829\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −27.6573 | − | 11.1858i | −1.25070 | − | 0.505839i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.35920 | − | 4.08626i | −0.106469 | − | 0.184410i | 0.807868 | − | 0.589363i | \(-0.200621\pi\) |
−0.914338 | + | 0.404953i | \(0.867288\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.9682 | + | 31.1219i | −0.809248 | + | 1.40166i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.0480 | − | 9.71719i | −0.451624 | − | 0.436755i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.41875 | − | 7.65349i | 0.198208 | − | 0.343306i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.3566 | + | 21.4023i | 0.553158 | + | 0.958098i | 0.998044 | + | 0.0625105i | \(0.0199107\pi\) |
−0.444886 | + | 0.895587i | \(0.646756\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.15652 | + | 22.5184i | 0.141023 | + | 1.00605i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.4083 | 0.865371 | 0.432686 | − | 0.901545i | \(-0.357566\pi\) | ||||
0.432686 | + | 0.901545i | \(0.357566\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.73856 | 0.210863 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.6345 | − | 12.2060i | 0.694352 | − | 0.542087i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.72850 | − | 4.72591i | −0.120939 | − | 0.209472i | 0.799199 | − | 0.601066i | \(-0.205257\pi\) |
−0.920138 | + | 0.391594i | \(0.871924\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.05349 | − | 5.28880i | 0.135078 | − | 0.233963i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.9344 | − | 24.6304i | −0.482766 | − | 1.08746i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.111918 | − | 0.193848i | 0.00493170 | − | 0.00854196i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.89897 | + | 8.48527i | 0.215457 | + | 0.373182i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.9238 | − | 20.2389i | 1.13793 | − | 0.888391i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.7683 | −1.08512 | −0.542558 | − | 0.840018i | \(-0.682544\pi\) | ||||
−0.542558 | + | 0.840018i | \(0.682544\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.7530 | 1.43219 | 0.716094 | − | 0.698004i | \(-0.245928\pi\) | ||||
0.716094 | + | 0.698004i | \(0.245928\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.991287 | − | 7.07177i | −0.0432633 | − | 0.308637i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.9694 | − | 25.9278i | −0.652078 | − | 1.12943i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.48934 | − | 16.4360i | 0.412580 | − | 0.714610i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.55083 | + | 14.1982i | −0.154093 | + | 0.616149i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.13868 | − | 12.3646i | 0.309211 | − | 0.535569i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.33403 | + | 7.50676i | 0.187377 | + | 0.324546i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.2328 | − | 4.94746i | −0.527883 | − | 0.213499i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.97483 | −0.214281 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.8575 | 1.62762 | 0.813811 | − | 0.581130i | \(-0.197389\pi\) | ||||
0.813811 | + | 0.581130i | \(0.197389\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.8966 | − | 6.02485i | −0.639276 | − | 0.258551i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.93827 | + | 8.55333i | 0.211532 | + | 0.366385i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.74835 | − | 3.02824i | 0.0747543 | − | 0.129478i | −0.826225 | − | 0.563340i | \(-0.809516\pi\) |
0.900979 | + | 0.433862i | \(0.142849\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.77878 | − | 2.51046i | 0.374669 | − | 0.107144i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.8367 | − | 30.8941i | 0.759869 | − | 1.31613i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.05414 | + | 10.4861i | 0.257448 | + | 0.445913i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.19124 | − | 15.6322i | −0.0930129 | − | 0.663548i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.1226 | −1.44582 | −0.722911 | − | 0.690941i | \(-0.757197\pi\) | ||||
−0.722911 | + | 0.690941i | \(0.757197\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.9500 | −0.505431 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 35.4841 | − | 27.7027i | 1.49814 | − | 1.16961i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.65071 | + | 13.2514i | 0.322439 | + | 0.558481i | 0.980991 | − | 0.194055i | \(-0.0621640\pi\) |
−0.658552 | + | 0.752535i | \(0.728831\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.74293 | − | 8.21500i | 0.199537 | − | 0.345608i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.94046 | + | 4.23664i | 0.333468 | + | 0.177922i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.4953 | + | 28.5707i | −0.691520 | + | 1.19775i | 0.279820 | + | 0.960053i | \(0.409725\pi\) |
−0.971340 | + | 0.237695i | \(0.923608\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.7150 | − | 18.5590i | −0.448410 | − | 0.776668i | 0.549873 | − | 0.835248i | \(-0.314676\pi\) |
−0.998283 | + | 0.0585801i | \(0.981343\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.1097 | − | 10.2349i | 0.547667 | − | 0.427568i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.26755 | −0.344781 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.4188 | −1.59939 | −0.799697 | − | 0.600404i | \(-0.795007\pi\) | ||||
−0.799697 | + | 0.600404i | \(0.795007\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.62658 | + | 25.8718i | 0.150715 | + | 1.07519i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.431332 | + | 0.747088i | 0.0178947 | + | 0.0309944i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.9894 | + | 32.8905i | −0.786459 | + | 1.36219i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.36147 | + | 0.961278i | −0.138980 | + | 0.0397439i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.43772 | + | 14.6146i | −0.348262 | + | 0.603207i | −0.985941 | − | 0.167095i | \(-0.946561\pi\) |
0.637679 | + | 0.770302i | \(0.279895\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.8599 | + | 25.7380i | 0.612290 | + | 1.06052i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.7769 | − | 7.18976i | −0.731245 | − | 0.295747i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.7817 | 0.894467 | 0.447233 | − | 0.894417i | \(-0.352409\pi\) | ||||
0.447233 | + | 0.894417i | \(0.352409\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.89316 | −0.200600 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −29.4433 | − | 11.9081i | −1.20503 | − | 0.487368i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.3778 | − | 23.1710i | −0.546601 | − | 0.946740i | −0.998504 | − | 0.0546732i | \(-0.982588\pi\) |
0.451904 | − | 0.892067i | \(-0.350745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.5615 | − | 21.7571i | 0.512393 | − | 0.887491i | −0.487504 | − | 0.873121i | \(-0.662092\pi\) |
0.999897 | − | 0.0143699i | \(-0.00457423\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.835561 | − | 3.34104i | 0.0340267 | − | 0.136058i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.43852 | + | 11.1518i | −0.261763 | + | 0.453387i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.31975 | + | 7.48203i | 0.175333 | + | 0.303686i | 0.940277 | − | 0.340411i | \(-0.110566\pi\) |
−0.764943 | + | 0.644098i | \(0.777233\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.65386 | + | 11.7985i | 0.0670179 | + | 0.478101i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.45068 | 0.0991440 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.1789 | 1.86515 | 0.932575 | − | 0.360977i | \(-0.117557\pi\) | ||||
0.932575 | + | 0.360977i | \(0.117557\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14.6717 | − | 11.4543i | 0.591620 | − | 0.461883i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.76222 | + | 9.98046i | 0.231978 | + | 0.401798i | 0.958390 | − | 0.285461i | \(-0.0921468\pi\) |
−0.726412 | + | 0.687260i | \(0.758814\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.6325 | − | 34.0045i | 0.789096 | − | 1.36675i | −0.137425 | − | 0.990512i | \(-0.543883\pi\) |
0.926521 | − | 0.376242i | \(-0.122784\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.13376 | − | 8.42333i | 0.246139 | − | 0.338016i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.42400 | + | 9.39464i | −0.217308 | + | 0.376388i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.30578 | − | 10.9219i | −0.252231 | − | 0.436877i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −35.2244 | + | 27.5000i | −1.40673 | + | 1.09824i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 50.8367 | 2.02699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.8387 | −0.909193 | −0.454596 | − | 0.890698i | \(-0.650216\pi\) | ||||
−0.454596 | + | 0.890698i | \(0.650216\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.629523 | + | 4.49098i | 0.0250213 | + | 0.178500i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.05664 | + | 5.29426i | 0.121299 | + | 0.210096i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.622156 | + | 1.07761i | −0.0246507 | + | 0.0426963i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.0583 | + | 18.4308i | 0.753933 | + | 0.729111i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.04899 | − | 15.6733i | 0.357413 | − | 0.619058i | −0.630114 | − | 0.776502i | \(-0.716992\pi\) |
0.987528 | + | 0.157444i | \(0.0503254\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.0416 | − | 26.0529i | −0.593184 | − | 1.02742i | −0.993800 | − | 0.111179i | \(-0.964537\pi\) |
0.400616 | − | 0.916246i | \(-0.368796\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.4427 | − | 5.84127i | −0.568682 | − | 0.230000i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.1323 | 0.988054 | 0.494027 | − | 0.869447i | \(-0.335524\pi\) | ||||
0.494027 | + | 0.869447i | \(0.335524\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.2697 | 0.952668 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.20147 | − | 3.72147i | −0.360634 | − | 0.145856i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.24884 | − | 9.09125i | −0.205403 | − | 0.355768i | 0.744858 | − | 0.667223i | \(-0.232517\pi\) |
−0.950261 | + | 0.311455i | \(0.899184\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.65539 | + | 2.86722i | −0.0646815 | + | 0.112032i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.1698 | + | 12.7362i | 0.513804 | + | 0.496888i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.04138 | + | 6.99988i | −0.157430 | + | 0.272677i | −0.933941 | − | 0.357427i | \(-0.883654\pi\) |
0.776511 | + | 0.630103i | \(0.216988\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.4530 | + | 23.3012i | 0.523260 | + | 0.906312i | 0.999634 | + | 0.0270695i | \(0.00861755\pi\) |
−0.476374 | + | 0.879243i | \(0.658049\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.56307 | − | 11.1508i | −0.0607045 | − | 0.433062i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.85734 | 0.188360 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.7936 | 0.534090 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −34.2521 | + | 26.7409i | −1.32426 | + | 1.03386i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.57060 | − | 13.1127i | −0.292260 | − | 0.506209i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.11160 | − | 10.5856i | 0.235585 | − | 0.408045i | −0.723858 | − | 0.689949i | \(-0.757633\pi\) |
0.959443 | + | 0.281904i | \(0.0909661\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 21.3030 | + | 2.26220i | 0.819951 | + | 0.0870723i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.34015 | + | 5.78531i | −0.128372 | + | 0.222348i | −0.923046 | − | 0.384689i | \(-0.874309\pi\) |
0.794674 | + | 0.607037i | \(0.207642\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.78521 | + | 6.55618i | 0.145263 | + | 0.251603i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −34.8908 | + | 27.2396i | −1.33702 | + | 1.04382i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.2125 | −0.735146 | −0.367573 | − | 0.929995i | \(-0.619811\pi\) | ||||
−0.367573 | + | 0.929995i | \(0.619811\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.65677 | 0.177926 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.31596 | − | 9.38796i | −0.0502070 | − | 0.358173i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.74966 | + | 8.22664i | 0.180947 | + | 0.313410i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.72706 | + | 9.91955i | −0.217867 | + | 0.377357i | −0.954156 | − | 0.299310i | \(-0.903243\pi\) |
0.736288 | + | 0.676668i | \(0.236577\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.62094 | − | 14.4786i | 0.137548 | − | 0.549995i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.56648 | − | 7.90937i | 0.173216 | − | 0.300020i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.9730 | + | 51.9147i | 1.13531 | + | 1.96641i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.1447 | + | 6.93405i | 0.648471 | + | 0.262270i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.29596 | −0.162256 | −0.0811281 | − | 0.996704i | \(-0.525852\pi\) | ||||
−0.0811281 | + | 0.996704i | \(0.525852\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −50.4646 | −1.90331 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.96189 | + | 1.19792i | 0.111551 | + | 0.0451161i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.52970 | + | 4.38156i | 0.0951390 | + | 0.164786i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.44506 | + | 11.1632i | −0.242049 | + | 0.419242i | −0.961298 | − | 0.275511i | \(-0.911153\pi\) |
0.719248 | + | 0.694753i | \(0.244486\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −34.9248 | + | 9.98743i | −1.30978 | + | 0.374558i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.74576 | + | 9.95195i | −0.215180 | + | 0.372703i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.89885 | + | 5.02095i | 0.108411 | + | 0.187773i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.20220 | + | 8.57640i | 0.0448969 | + | 0.320292i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.46489 | −0.203806 | −0.101903 | − | 0.994794i | \(-0.532493\pi\) | ||||
−0.101903 | + | 0.994794i | \(0.532493\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.238992 | 0.00890051 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −27.7649 | + | 21.6763i | −1.03259 | + | 0.806150i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.1793 | + | 24.5594i | 0.526608 | + | 0.912111i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.9300 | + | 43.1800i | −0.924601 | + | 1.60146i | −0.132401 | + | 0.991196i | \(0.542269\pi\) |
−0.792201 | + | 0.610260i | \(0.791065\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1097 | + | 20.0260i | −0.670728 | + | 0.741703i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.0870 | − | 43.4520i | 0.927878 | − | 1.60713i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.6123 | + | 30.5054i | 0.650525 | + | 1.12674i | 0.982996 | + | 0.183629i | \(0.0587844\pi\) |
−0.332471 | + | 0.943114i | \(0.607882\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.27868 | + | 0.998277i | −0.0471648 | + | 0.0368220i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.71100 | −0.210367 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.7209 | 1.31401 | 0.657007 | − | 0.753885i | \(-0.271822\pi\) | ||||
0.657007 | + | 0.753885i | \(0.271822\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.55163 | + | 11.0692i | 0.0570004 | + | 0.406637i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.53043 | + | 11.3110i | 0.239578 | + | 0.414962i | 0.960593 | − | 0.277958i | \(-0.0896575\pi\) |
−0.721015 | + | 0.692919i | \(0.756324\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.98580 | − | 10.3677i | 0.219303 | − | 0.379843i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.48825 | + | 0.711562i | −0.0910402 | + | 0.0260347i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.62748 | + | 8.01503i | −0.169084 | + | 0.292863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.11223 | − | 1.92644i | −0.0405859 | − | 0.0702968i | 0.845019 | − | 0.534736i | \(-0.179589\pi\) |
−0.885605 | + | 0.464440i | \(0.846256\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31.8170 | − | 12.8682i | −1.15948 | − | 0.468943i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.5005 | −0.782484 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.27335 | 0.155317 | 0.0776587 | − | 0.996980i | \(-0.475256\pi\) | ||||
0.0776587 | + | 0.996980i | \(0.475256\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.0186 | − | 6.47863i | −0.581440 | − | 0.235159i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.2206 | − | 43.6833i | −0.914245 | − | 1.58352i | −0.808003 | − | 0.589179i | \(-0.799451\pi\) |
−0.106242 | − | 0.994340i | \(-0.533882\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.27263 | + | 9.13246i | −0.190882 | + | 0.330617i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.56150 | − | 14.2409i | 0.128766 | − | 0.514880i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.03519 | − | 5.25710i | 0.109594 | − | 0.189823i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.03493 | + | 1.79255i | 0.0373205 | + | 0.0646411i | 0.884082 | − | 0.467331i | \(-0.154784\pi\) |
−0.846762 | + | 0.531972i | \(0.821451\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.466215 | + | 3.32595i | 0.0167903 | + | 0.119781i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.3739 | −1.02054 | −0.510269 | − | 0.860015i | \(-0.670454\pi\) | ||||
−0.510269 | + | 0.860015i | \(0.670454\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23.6258 | −0.848664 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.2847 | − | 10.3714i | 0.476584 | − | 0.372073i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29.7536 | − | 51.5347i | −1.06603 | − | 1.84642i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.9825 | − | 38.0748i | 0.786595 | − | 1.36242i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −35.5419 | − | 3.77426i | −1.27016 | − | 0.134881i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.73141 | + | 13.3912i | −0.275946 | + | 0.477952i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.72536 | − | 2.98841i | −0.0615025 | − | 0.106525i | 0.833635 | − | 0.552316i | \(-0.186256\pi\) |
−0.895137 | + | 0.445791i | \(0.852923\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.2335 | + | 14.2350i | −0.649129 | + | 0.506781i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.1281 | 0.360115 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.78714 | −0.134485 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.71916 | + | 12.2644i | 0.0609723 | + | 0.434973i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.2230 | + | 19.4388i | 0.397540 | + | 0.688559i | 0.993422 | − | 0.114513i | \(-0.0365308\pi\) |
−0.595882 | + | 0.803072i | \(0.703197\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.14480 | + | 8.91106i | −0.182010 | + | 0.315251i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −23.3940 | − | 22.6237i | −0.826585 | − | 0.799371i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.1906 | − | 26.3108i | 0.536064 | − | 0.928490i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.939078 | + | 1.62653i | 0.0330982 | + | 0.0573277i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.66429 | + | 2.69533i | 0.234594 | + | 0.0948801i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.2366 | 0.641164 | 0.320582 | − | 0.947221i | \(-0.396122\pi\) | ||||
0.320582 | + | 0.947221i | \(0.396122\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.8280 | −0.590910 | −0.295455 | − | 0.955357i | \(-0.595471\pi\) | ||||
−0.295455 | + | 0.955357i | \(0.595471\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.6626 | + | 10.7835i | 0.935097 | + | 0.378194i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.06610 | + | 13.9709i | 0.282543 | + | 0.489379i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.9034 | + | 43.1340i | −0.871260 | + | 1.50907i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.68339 | − | 2.59504i | −0.0937653 | − | 0.0906781i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.6149 | − | 32.2420i | 0.649665 | − | 1.12525i | −0.333538 | − | 0.942737i | \(-0.608243\pi\) |
0.983203 | − | 0.182516i | \(-0.0584241\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.13747 | − | 10.6304i | −0.213939 | − | 0.370553i | 0.739005 | − | 0.673700i | \(-0.235296\pi\) |
−0.952944 | + | 0.303147i | \(0.901963\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.93148 | − | 35.1808i | −0.171692 | − | 1.22484i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.60355 | 0.299175 | 0.149587 | − | 0.988749i | \(-0.452205\pi\) | ||||
0.149587 | + | 0.988749i | \(0.452205\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.2887 | −1.53821 | −0.769105 | − | 0.639123i | \(-0.779298\pi\) | ||||
−0.769105 | + | 0.639123i | \(0.779298\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.3572 | + | 18.2352i | −0.810252 | + | 0.632571i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.61223 | − | 4.52452i | −0.0905084 | − | 0.156765i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.14781 | − | 10.6483i | 0.212754 | − | 0.368500i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.5282 | − | 24.0710i | 0.605862 | − | 0.832014i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.6154 | − | 40.9030i | 0.815293 | − | 1.41213i | −0.0938240 | − | 0.995589i | \(-0.529909\pi\) |
0.909117 | − | 0.416540i | \(-0.136758\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.15684 | − | 15.8601i | −0.315753 | − | 0.546900i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.4518 | − | 15.9669i | 0.704396 | − | 0.549928i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.7255 | −0.368968 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.7489 | −0.472418 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.33071 | − | 30.8950i | −0.148629 | − | 1.06031i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.75640 | − | 16.8986i | −0.334445 | − | 0.579276i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.9825 | − | 20.7543i | 0.410273 | − | 0.710614i | −0.584646 | − | 0.811288i | \(-0.698767\pi\) |
0.994919 | + | 0.100674i | \(0.0321000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.53543 | + | 14.1366i | −0.120909 | + | 0.483463i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.50903 | + | 11.2740i | −0.222344 | + | 0.385111i | −0.955519 | − | 0.294928i | \(-0.904704\pi\) |
0.733175 | + | 0.680040i | \(0.238038\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.0473685 | − | 0.0820447i | −0.00161619 | − | 0.00279933i | 0.865216 | − | 0.501399i | \(-0.167181\pi\) |
−0.866832 | + | 0.498600i | \(0.833848\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.4239 | + | 7.45143i | 0.627885 | + | 0.253944i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.8729 | 0.880723 | 0.440361 | − | 0.897821i | \(-0.354850\pi\) | ||||
0.440361 | + | 0.897821i | \(0.354850\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.7841 | −0.604678 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.5306 | + | 6.68571i | 0.561410 | + | 0.227059i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30.1183 | + | 52.1664i | 1.02169 | + | 1.76962i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.714223 | + | 1.23707i | −0.0242005 | + | 0.0419165i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.8360 | + | 6.24442i | −0.739036 | + | 0.211342i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.27215 | + | 7.39958i | −0.144425 | + | 0.250151i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.9042 | + | 46.5994i | 0.908489 | + | 1.57355i | 0.816164 | + | 0.577821i | \(0.196097\pi\) |
0.0923254 | + | 0.995729i | \(0.470570\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.65355 | + | 47.4660i | 0.224419 | + | 1.60099i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.8689 | −1.44429 | −0.722144 | − | 0.691743i | \(-0.756843\pi\) | ||||
−0.722144 | + | 0.691743i | \(0.756843\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.5967 | −1.16427 | −0.582136 | − | 0.813092i | \(-0.697783\pi\) | ||||
−0.582136 | + | 0.813092i | \(0.697783\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.23804 | − | 4.87009i | 0.209689 | − | 0.163706i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.2278 | − | 17.7150i | −0.343415 | − | 0.594812i | 0.641650 | − | 0.766998i | \(-0.278250\pi\) |
−0.985064 | + | 0.172186i | \(0.944917\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.26360 | + | 5.65272i | −0.109458 | + | 0.189586i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 39.5024 | + | 21.0765i | 1.32338 | + | 0.706091i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.10714 | − | 8.84583i | 0.170904 | − | 0.296015i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.56762 | + | 6.17930i | 0.119252 | + | 0.206551i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.40665 | + | 2.65960i | −0.113745 | + | 0.0888016i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 39.4173 | 1.31464 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.8845 | −1.32874 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.30911 | − | 16.4730i | −0.0768423 | − | 0.548188i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.34453 | + | 7.52494i | 0.144417 | + | 0.250137i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.92456 | + | 6.79754i | −0.130313 | + | 0.225709i | −0.923797 | − | 0.382882i | \(-0.874932\pi\) |
0.793484 | + | 0.608591i | \(0.208265\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.5932 | + | 4.17321i | −0.484026 | + | 0.138417i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.87189 | + | 6.70631i | −0.128282 | + | 0.222190i | −0.923011 | − | 0.384774i | \(-0.874279\pi\) |
0.794729 | + | 0.606964i | \(0.207613\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.14580 | + | 3.71663i | 0.0710156 | + | 0.123003i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.57713 | − | 1.85119i | −0.151315 | − | 0.0611985i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.53495 | −0.116734 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.3702 | −0.638963 | −0.319482 | − | 0.947592i | \(-0.603509\pi\) | ||||
−0.319482 | + | 0.947592i | \(0.603509\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.79539 | + | 3.96168i | 0.322769 | + | 0.130542i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.49830 | − | 9.52334i | −0.180979 | − | 0.313464i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.0585 | − | 34.7424i | 0.659520 | − | 1.14232i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.173951 | + | 0.695553i | −0.00571329 | + | 0.0228450i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.77989 | − | 3.08287i | 0.0583964 | − | 0.101146i | −0.835349 | − | 0.549720i | \(-0.814735\pi\) |
0.893746 | + | 0.448574i | \(0.148068\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.59311 | + | 4.49140i | 0.0849858 | + | 0.147200i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.40900 | + | 45.7214i | 0.209821 | + | 1.49685i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −24.3426 | −0.796089 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.2230 | −1.11802 | −0.559008 | − | 0.829162i | \(-0.688818\pi\) | ||||
−0.559008 | + | 0.829162i | \(0.688818\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.9521 | + | 25.7260i | −1.07535 | + | 0.839536i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.02033 | + | 10.4275i | 0.196257 | + | 0.339928i | 0.947312 | − | 0.320312i | \(-0.103788\pi\) |
−0.751055 | + | 0.660240i | \(0.770455\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.5046 | − | 19.9266i | 0.374642 | − | 0.648899i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.97466 | − | 4.44803i | −0.0642356 | − | 0.144694i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.3623 | + | 19.6802i | −0.369227 | + | 0.639519i | −0.989445 | − | 0.144910i | \(-0.953711\pi\) |
0.620218 | + | 0.784429i | \(0.287044\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.79949 | − | 6.58092i | −0.123337 | − | 0.213626i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.0298 | − | 18.7603i | 0.779219 | − | 0.608343i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.74488 | −0.218488 | −0.109244 | − | 0.994015i | \(-0.534843\pi\) | ||||
−0.109244 | + | 0.994015i | \(0.534843\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.99346 | −0.291022 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.22768 | + | 58.6957i | 0.265963 | + | 1.89736i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.48603 | + | 4.30593i | 0.0802782 | + | 0.139046i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.919395 | + | 1.59244i | −0.0296579 | + | 0.0513690i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.9585 | − | 19.3014i | −0.643155 | − | 0.621979i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.06331 | − | 12.2340i | 0.227376 | − | 0.393827i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.8267 | − | 22.2165i | −0.412479 | − | 0.714434i | 0.582681 | − | 0.812701i | \(-0.302004\pi\) |
−0.995160 | + | 0.0982664i | \(0.968670\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −43.5067 | − | 17.5960i | −1.39764 | − | 0.565265i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.9298 | −1.31350 | −0.656750 | − | 0.754108i | \(-0.728069\pi\) | ||||
−0.656750 | + | 0.754108i | \(0.728069\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.75133 | 0.312613 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.23732 | − | 3.33153i | −0.263805 | − | 0.106694i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.2365 | − | 38.5147i | −0.711408 | − | 1.23220i | −0.964329 | − | 0.264708i | \(-0.914724\pi\) |
0.252920 | − | 0.967487i | \(-0.418609\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.9835 | + | 46.7367i | −0.862395 | + | 1.49371i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −22.7411 | − | 21.9924i | −0.726067 | − | 0.702162i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.4550 | + | 49.2855i | −0.907573 | + | 1.57196i | −0.0901483 | + | 0.995928i | \(0.528734\pi\) |
−0.817425 | + | 0.576035i | \(0.804599\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.18455 | + | 8.97990i | 0.165193 | + | 0.286123i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.473547 | + | 3.37826i | 0.0150732 | + | 0.107531i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.2585 | −0.612384 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.7331 | 1.42099 | 0.710496 | − | 0.703701i | \(-0.248470\pi\) | ||||
0.710496 | + | 0.703701i | \(0.248470\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.1750 | − | 25.9000i | 1.05278 | − | 0.821912i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.58698 | + | 14.8731i | 0.272225 | + | 0.471508i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.36681 | − | 16.2238i | 0.296650 | − | 0.513812i | −0.678718 | − | 0.734399i | \(-0.737464\pi\) |
0.975367 | + | 0.220587i | \(0.0707973\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.5154 | + | 46.2121i | 0.649079 | + | 1.46209i |
(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.673.3 | 8 | ||
3.2 | odd | 2 | 3024.2.r.l.2017.3 | 8 | |||
4.3 | odd | 2 | 504.2.r.d.169.2 | ✓ | 8 | ||
9.2 | odd | 6 | 9072.2.a.cl.1.2 | 4 | |||
9.4 | even | 3 | inner | 1008.2.r.m.337.3 | 8 | ||
9.5 | odd | 6 | 3024.2.r.l.1009.3 | 8 | |||
9.7 | even | 3 | 9072.2.a.ce.1.3 | 4 | |||
12.11 | even | 2 | 1512.2.r.d.505.3 | 8 | |||
36.7 | odd | 6 | 4536.2.a.x.1.3 | 4 | |||
36.11 | even | 6 | 4536.2.a.ba.1.2 | 4 | |||
36.23 | even | 6 | 1512.2.r.d.1009.3 | 8 | |||
36.31 | odd | 6 | 504.2.r.d.337.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.d.169.2 | ✓ | 8 | 4.3 | odd | 2 | ||
504.2.r.d.337.2 | yes | 8 | 36.31 | odd | 6 | ||
1008.2.r.m.337.3 | 8 | 9.4 | even | 3 | inner | ||
1008.2.r.m.673.3 | 8 | 1.1 | even | 1 | trivial | ||
1512.2.r.d.505.3 | 8 | 12.11 | even | 2 | |||
1512.2.r.d.1009.3 | 8 | 36.23 | even | 6 | |||
3024.2.r.l.1009.3 | 8 | 9.5 | odd | 6 | |||
3024.2.r.l.2017.3 | 8 | 3.2 | odd | 2 | |||
4536.2.a.x.1.3 | 4 | 36.7 | odd | 6 | |||
4536.2.a.ba.1.2 | 4 | 36.11 | even | 6 | |||
9072.2.a.ce.1.3 | 4 | 9.7 | even | 3 | |||
9072.2.a.cl.1.2 | 4 | 9.2 | odd | 6 |