Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(226,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("675.226");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.e (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: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.1223810289.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 8x^{6} - 2x^{5} + 23x^{4} - 8x^{3} + 37x^{2} + 15x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 225) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 451.2 | ||
Root | \(0.736627 - 1.27588i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.451 |
Dual form | 675.2.e.c.226.2 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.736627 | + | 1.27588i | −0.520874 | + | 0.902180i | 0.478831 | + | 0.877907i | \(0.341061\pi\) |
−0.999705 | + | 0.0242735i | \(0.992273\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.0852394 | − | 0.147639i | −0.0426197 | − | 0.0738195i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.93291 | − | 3.34791i | 0.730573 | − | 1.26539i | −0.226066 | − | 0.974112i | \(-0.572586\pi\) |
0.956639 | − | 0.291278i | \(-0.0940803\pi\) | |||||||
\(8\) | −2.69535 | −0.952950 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.130139 | − | 0.225407i | 0.0392384 | − | 0.0679628i | −0.845739 | − | 0.533596i | \(-0.820840\pi\) |
0.884978 | + | 0.465634i | \(0.154174\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.03940 | − | 3.53235i | −0.565629 | − | 0.979697i | −0.996991 | − | 0.0775187i | \(-0.975300\pi\) |
0.431362 | − | 0.902179i | \(-0.358033\pi\) | |||||||
\(14\) | 2.84768 | + | 4.93232i | 0.761073 | + | 1.31822i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.15595 | − | 3.73421i | 0.538987 | − | 0.933553i | ||||
\(17\) | 3.26028 | 0.790734 | 0.395367 | − | 0.918523i | \(-0.370617\pi\) | ||||
0.395367 | + | 0.918523i | \(0.370617\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.24928 | 0.974853 | 0.487426 | − | 0.873164i | \(-0.337936\pi\) | ||||
0.487426 | + | 0.873164i | \(0.337936\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.191728 | + | 0.332082i | 0.0408765 | + | 0.0708002i | ||||
\(23\) | −4.34768 | − | 7.53039i | −0.906553 | − | 1.57020i | −0.818819 | − | 0.574052i | \(-0.805371\pi\) |
−0.0877339 | − | 0.996144i | \(-0.527963\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.00912 | 1.17849 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.659042 | −0.124547 | ||||||||
\(29\) | 2.11105 | − | 3.65644i | 0.392012 | − | 0.678984i | −0.600703 | − | 0.799472i | \(-0.705113\pi\) |
0.992715 | + | 0.120488i | \(0.0384459\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.32643 | − | 2.29744i | −0.238233 | − | 0.412632i | 0.721974 | − | 0.691920i | \(-0.243235\pi\) |
−0.960207 | + | 0.279288i | \(0.909902\pi\) | |||||||
\(32\) | 0.480909 | + | 0.832959i | 0.0850135 | + | 0.147248i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.40161 | + | 4.15971i | −0.411873 | + | 0.713384i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.27559 | 0.374104 | 0.187052 | − | 0.982350i | \(-0.440107\pi\) | ||||
0.187052 | + | 0.982350i | \(0.440107\pi\) | |||||||
\(38\) | −3.13014 | + | 5.42156i | −0.507776 | + | 0.879493i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.82093 | + | 4.88599i | 0.440555 | + | 0.763064i | 0.997731 | − | 0.0673308i | \(-0.0214483\pi\) |
−0.557176 | + | 0.830395i | \(0.688115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.53631 | + | 7.85712i | −0.691780 | + | 1.19820i | 0.279474 | + | 0.960153i | \(0.409840\pi\) |
−0.971254 | + | 0.238046i | \(0.923493\pi\) | |||||||
\(44\) | −0.0443719 | −0.00668931 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12.8105 | 1.88880 | ||||||||
\(47\) | 0.714441 | − | 1.23745i | 0.104212 | − | 0.180500i | −0.809204 | − | 0.587528i | \(-0.800101\pi\) |
0.913416 | + | 0.407027i | \(0.133435\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.97232 | − | 6.88026i | −0.567474 | − | 0.982894i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.347675 | + | 0.602191i | −0.0482139 | + | 0.0835089i | ||||
\(53\) | 11.3816 | 1.56338 | 0.781690 | − | 0.623667i | \(-0.214358\pi\) | ||||
0.781690 | + | 0.623667i | \(0.214358\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.20988 | + | 9.02378i | −0.696200 | + | 1.20585i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.11011 | + | 5.38687i | 0.408378 | + | 0.707331i | ||||
\(59\) | −3.56212 | − | 6.16977i | −0.463748 | − | 0.803235i | 0.535396 | − | 0.844601i | \(-0.320162\pi\) |
−0.999144 | + | 0.0413660i | \(0.986829\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.26244 | + | 2.18660i | −0.161638 | + | 0.279966i | −0.935456 | − | 0.353442i | \(-0.885011\pi\) |
0.773818 | + | 0.633408i | \(0.218344\pi\) | |||||||
\(62\) | 3.90833 | 0.496358 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.20679 | 0.900848 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.64280 | + | 9.77361i | 0.689377 | + | 1.19404i | 0.972040 | + | 0.234817i | \(0.0754491\pi\) |
−0.282662 | + | 0.959219i | \(0.591218\pi\) | |||||||
\(68\) | −0.277904 | − | 0.481344i | −0.0337008 | − | 0.0583716i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.38158 | 0.994711 | 0.497355 | − | 0.867547i | \(-0.334305\pi\) | ||||
0.497355 | + | 0.867547i | \(0.334305\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.403568 | −0.0472340 | −0.0236170 | − | 0.999721i | \(-0.507518\pi\) | ||||
−0.0236170 | + | 0.999721i | \(0.507518\pi\) | |||||||
\(74\) | −1.67626 | + | 2.90337i | −0.194861 | + | 0.337509i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.362207 | − | 0.627360i | −0.0415480 | − | 0.0719632i | ||||
\(77\) | −0.503095 | − | 0.871386i | −0.0573330 | − | 0.0993036i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.52125 | − | 2.63488i | 0.171154 | − | 0.296447i | −0.767670 | − | 0.640846i | \(-0.778584\pi\) |
0.938824 | + | 0.344399i | \(0.111917\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.31189 | −0.917895 | ||||||||
\(83\) | −2.29012 | + | 3.96660i | −0.251373 | + | 0.435391i | −0.963904 | − | 0.266250i | \(-0.914215\pi\) |
0.712531 | + | 0.701641i | \(0.247549\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.68314 | − | 11.5755i | −0.720661 | − | 1.24822i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.350770 | + | 0.607551i | −0.0373922 | + | 0.0647652i | ||||
\(89\) | −7.17772 | −0.760837 | −0.380419 | − | 0.924814i | \(-0.624220\pi\) | ||||
−0.380419 | + | 0.924814i | \(0.624220\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.7680 | −1.65293 | ||||||||
\(92\) | −0.741187 | + | 1.28377i | −0.0772741 | + | 0.133843i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.05255 | + | 1.82308i | 0.108563 | + | 0.188036i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.55756 | − | 2.69777i | 0.158146 | − | 0.273917i | −0.776054 | − | 0.630666i | \(-0.782782\pi\) |
0.934200 | + | 0.356749i | \(0.116115\pi\) | |||||||
\(98\) | 11.7045 | 1.18233 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.92286 | − | 3.33049i | 0.191332 | − | 0.331396i | −0.754360 | − | 0.656461i | \(-0.772053\pi\) |
0.945692 | + | 0.325065i | \(0.105386\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.10339 | − | 3.64318i | −0.207254 | − | 0.358974i | 0.743595 | − | 0.668630i | \(-0.233119\pi\) |
−0.950848 | + | 0.309657i | \(0.899786\pi\) | |||||||
\(104\) | 5.49691 | + | 9.52092i | 0.539016 | + | 0.933603i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.38398 | + | 14.5215i | −0.814324 | + | 1.41045i | ||||
\(107\) | −1.62655 | −0.157245 | −0.0786223 | − | 0.996904i | \(-0.525052\pi\) | ||||
−0.0786223 | + | 0.996904i | \(0.525052\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.9021 | −1.23580 | −0.617900 | − | 0.786256i | \(-0.712016\pi\) | ||||
−0.617900 | + | 0.786256i | \(0.712016\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.33452 | − | 14.4358i | −0.787539 | − | 1.36406i | ||||
\(113\) | −0.664539 | − | 1.15102i | −0.0625146 | − | 0.108278i | 0.833074 | − | 0.553161i | \(-0.186579\pi\) |
−0.895589 | + | 0.444883i | \(0.853245\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.719778 | −0.0668297 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.4958 | 0.966217 | ||||||||
\(119\) | 6.30184 | − | 10.9151i | 0.577689 | − | 1.00059i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.46613 | + | 9.46761i | 0.496921 | + | 0.860692i | ||||
\(122\) | −1.85989 | − | 3.22142i | −0.168386 | − | 0.291654i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.226128 | + | 0.391665i | −0.0203069 | + | 0.0351725i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.65285 | 0.146667 | 0.0733335 | − | 0.997307i | \(-0.476636\pi\) | ||||
0.0733335 | + | 0.997307i | \(0.476636\pi\) | |||||||
\(128\) | −6.27053 | + | 10.8609i | −0.554242 | + | 0.959975i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.58886 | − | 11.4122i | −0.575672 | − | 0.997092i | −0.995968 | − | 0.0897057i | \(-0.971407\pi\) |
0.420297 | − | 0.907387i | \(-0.361926\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.21350 | − | 14.2262i | 0.712201 | − | 1.23357i | ||||
\(134\) | −16.6266 | −1.43632 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.78759 | −0.753530 | ||||||||
\(137\) | −10.1464 | + | 17.5741i | −0.866867 | + | 1.50146i | −0.00168578 | + | 0.999999i | \(0.500537\pi\) |
−0.865181 | + | 0.501459i | \(0.832797\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.53440 | − | 2.65766i | −0.130146 | − | 0.225420i | 0.793587 | − | 0.608457i | \(-0.208211\pi\) |
−0.923733 | + | 0.383038i | \(0.874878\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.17410 | + | 10.6939i | −0.518119 | + | 0.897409i | ||||
\(143\) | −1.06162 | −0.0887774 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.297279 | − | 0.514902i | 0.0246030 | − | 0.0426136i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.193970 | − | 0.335965i | −0.0159442 | − | 0.0276162i | ||||
\(149\) | 2.03081 | + | 3.51747i | 0.166371 | + | 0.288162i | 0.937141 | − | 0.348951i | \(-0.113462\pi\) |
−0.770771 | + | 0.637113i | \(0.780129\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.80994 | − | 11.7952i | 0.554185 | − | 0.959876i | −0.443782 | − | 0.896135i | \(-0.646363\pi\) |
0.997966 | − | 0.0637412i | \(-0.0203032\pi\) | |||||||
\(152\) | −11.4533 | −0.928986 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.48237 | 0.119453 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.03131 | + | 1.78627i | 0.0823071 | + | 0.142560i | 0.904241 | − | 0.427023i | \(-0.140438\pi\) |
−0.821933 | + | 0.569584i | \(0.807104\pi\) | |||||||
\(158\) | 2.24119 | + | 3.88185i | 0.178299 | + | 0.308823i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −33.6147 | −2.64921 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.50525 | 0.274552 | 0.137276 | − | 0.990533i | \(-0.456165\pi\) | ||||
0.137276 | + | 0.990533i | \(0.456165\pi\) | |||||||
\(164\) | 0.480909 | − | 0.832959i | 0.0375527 | − | 0.0650431i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.37393 | − | 5.84381i | −0.261868 | − | 0.453568i | ||||
\(167\) | −10.2674 | − | 17.7837i | −0.794518 | − | 1.37615i | −0.923145 | − | 0.384453i | \(-0.874390\pi\) |
0.128626 | − | 0.991693i | \(-0.458943\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.81833 | + | 3.14944i | −0.139871 | + | 0.242264i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.54669 | 0.117934 | ||||||||
\(173\) | 3.87589 | − | 6.71323i | 0.294678 | − | 0.510397i | −0.680232 | − | 0.732997i | \(-0.738121\pi\) |
0.974910 | + | 0.222600i | \(0.0714542\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.561145 | − | 0.971932i | −0.0422979 | − | 0.0732622i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.28731 | − | 9.15788i | 0.396300 | − | 0.686412i | ||||
\(179\) | 10.7632 | 0.804477 | 0.402238 | − | 0.915535i | \(-0.368232\pi\) | ||||
0.402238 | + | 0.915535i | \(0.368232\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.84572 | −0.583168 | −0.291584 | − | 0.956545i | \(-0.594182\pi\) | ||||
−0.291584 | + | 0.956545i | \(0.594182\pi\) | |||||||
\(182\) | 11.6151 | − | 20.1180i | 0.860970 | − | 1.49124i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 11.7185 | + | 20.2970i | 0.863900 | + | 1.49632i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.424289 | − | 0.734890i | 0.0310271 | − | 0.0537405i | ||||
\(188\) | −0.243594 | −0.0177659 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.86627 | + | 4.96453i | −0.207396 | + | 0.359221i | −0.950894 | − | 0.309518i | \(-0.899832\pi\) |
0.743497 | + | 0.668739i | \(0.233166\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.24119 | − | 7.34595i | −0.305287 | − | 0.528773i | 0.672038 | − | 0.740517i | \(-0.265419\pi\) |
−0.977325 | + | 0.211744i | \(0.932086\pi\) | |||||||
\(194\) | 2.29468 | + | 3.97450i | 0.164748 | + | 0.285352i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.677196 | + | 1.17294i | −0.0483712 | + | 0.0837813i | ||||
\(197\) | 10.6266 | 0.757110 | 0.378555 | − | 0.925579i | \(-0.376421\pi\) | ||||
0.378555 | + | 0.925579i | \(0.376421\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.5784 | −1.31699 | −0.658495 | − | 0.752585i | \(-0.728807\pi\) | ||||
−0.658495 | + | 0.752585i | \(0.728807\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.83286 | + | 4.90666i | 0.199319 | + | 0.345231i | ||||
\(203\) | −8.16095 | − | 14.1352i | −0.572786 | − | 0.992095i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.19767 | 0.431812 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −17.5874 | −1.21947 | ||||||||
\(209\) | 0.552997 | − | 0.957820i | 0.0382516 | − | 0.0662538i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.22666 | − | 9.05283i | −0.359818 | − | 0.623223i | 0.628112 | − | 0.778123i | \(-0.283828\pi\) |
−0.987930 | + | 0.154900i | \(0.950494\pi\) | |||||||
\(212\) | −0.970160 | − | 1.68037i | −0.0666308 | − | 0.115408i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.19816 | − | 2.07528i | 0.0819046 | − | 0.141863i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.2555 | −0.696187 | ||||||||
\(218\) | 9.50407 | − | 16.4615i | 0.643697 | − | 1.11492i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.64902 | − | 11.5164i | −0.447261 | − | 0.774680i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.96560 | − | 3.40452i | 0.131626 | − | 0.227983i | −0.792677 | − | 0.609641i | \(-0.791313\pi\) |
0.924304 | + | 0.381658i | \(0.124647\pi\) | |||||||
\(224\) | 3.71822 | 0.248434 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.95807 | 0.130249 | ||||||||
\(227\) | −2.41570 | + | 4.18411i | −0.160335 | + | 0.277709i | −0.934989 | − | 0.354677i | \(-0.884591\pi\) |
0.774654 | + | 0.632386i | \(0.217924\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.42648 | + | 16.3271i | 0.622919 | + | 1.07893i | 0.988939 | + | 0.148321i | \(0.0473869\pi\) |
−0.366020 | + | 0.930607i | \(0.619280\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.69001 | + | 9.85539i | −0.373568 | + | 0.647038i | ||||
\(233\) | −11.9021 | −0.779735 | −0.389867 | − | 0.920871i | \(-0.627479\pi\) | ||||
−0.389867 | + | 0.920871i | \(0.627479\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.607266 | + | 1.05181i | −0.0395296 | + | 0.0684673i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.28421 | + | 16.0807i | 0.601806 | + | 1.04236i | ||||
\(239\) | −10.8147 | − | 18.7317i | −0.699547 | − | 1.21165i | −0.968624 | − | 0.248533i | \(-0.920052\pi\) |
0.269076 | − | 0.963119i | \(-0.413282\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.94916 | + | 3.37604i | −0.125556 | + | 0.217470i | −0.921950 | − | 0.387308i | \(-0.873405\pi\) |
0.796394 | + | 0.604778i | \(0.206738\pi\) | |||||||
\(242\) | −16.1060 | −1.03533 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.430437 | 0.0275559 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.66600 | − | 15.0100i | −0.551405 | − | 0.955061i | ||||
\(248\) | 3.57518 | + | 6.19240i | 0.227024 | + | 0.393218i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.1033 | 1.90010 | 0.950052 | − | 0.312092i | \(-0.101030\pi\) | ||||
0.950052 | + | 0.312092i | \(0.101030\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.26321 | −0.142287 | ||||||||
\(254\) | −1.21754 | + | 2.10883i | −0.0763950 | + | 0.132320i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.03131 | − | 3.51832i | −0.126957 | − | 0.219895i | ||||
\(257\) | 8.20707 | + | 14.2151i | 0.511943 | + | 0.886711i | 0.999904 | + | 0.0138459i | \(0.00440744\pi\) |
−0.487961 | + | 0.872865i | \(0.662259\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.39851 | − | 7.61845i | 0.273310 | − | 0.473388i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 19.4141 | 1.19941 | ||||||||
\(263\) | −12.9036 | + | 22.3497i | −0.795670 | + | 1.37814i | 0.126743 | + | 0.991936i | \(0.459548\pi\) |
−0.922413 | + | 0.386206i | \(0.873786\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 12.1006 | + | 20.9588i | 0.741934 | + | 1.28507i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.961978 | − | 1.66619i | 0.0587621 | − | 0.101779i | ||||
\(269\) | 12.5206 | 0.763392 | 0.381696 | − | 0.924288i | \(-0.375340\pi\) | ||||
0.381696 | + | 0.924288i | \(0.375340\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.6462 | 1.19342 | 0.596710 | − | 0.802457i | \(-0.296474\pi\) | ||||
0.596710 | + | 0.802457i | \(0.296474\pi\) | |||||||
\(272\) | 7.02899 | − | 12.1746i | 0.426195 | − | 0.738191i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.9483 | − | 25.8911i | −0.903057 | − | 1.56414i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.4150 | + | 18.0394i | −0.625779 | + | 1.08388i | 0.362610 | + | 0.931941i | \(0.381886\pi\) |
−0.988390 | + | 0.151941i | \(0.951448\pi\) | |||||||
\(278\) | 4.52112 | 0.271159 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.36221 | − | 4.09146i | 0.140917 | − | 0.244076i | −0.786925 | − | 0.617049i | \(-0.788328\pi\) |
0.927842 | + | 0.372973i | \(0.121661\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.5762 | + | 20.0506i | 0.688136 | + | 1.19189i | 0.972440 | + | 0.233152i | \(0.0749041\pi\) |
−0.284304 | + | 0.958734i | \(0.591763\pi\) | |||||||
\(284\) | −0.714441 | − | 1.23745i | −0.0423943 | − | 0.0734291i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.782020 | − | 1.35450i | 0.0462418 | − | 0.0800932i | ||||
\(287\) | 21.8105 | 1.28743 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.37059 | −0.374740 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.0343999 | + | 0.0595824i | 0.00201310 | + | 0.00348679i | ||||
\(293\) | 8.43963 | + | 14.6179i | 0.493049 | + | 0.853985i | 0.999968 | − | 0.00800832i | \(-0.00254915\pi\) |
−0.506919 | + | 0.861993i | \(0.669216\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.13350 | −0.356503 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.98380 | −0.346632 | ||||||||
\(299\) | −17.7333 | + | 30.7150i | −1.02554 | + | 1.77630i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.5366 | + | 30.3743i | 1.01079 | + | 1.75074i | ||||
\(302\) | 10.0328 | + | 17.3773i | 0.577321 | + | 0.999949i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.16123 | − | 15.8677i | 0.525433 | − | 0.910076i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.7177 | 1.29657 | 0.648285 | − | 0.761398i | \(-0.275487\pi\) | ||||
0.648285 | + | 0.761398i | \(0.275487\pi\) | |||||||
\(308\) | −0.0857671 | + | 0.148553i | −0.00488703 | + | 0.00846459i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.7968 | + | 27.3608i | 0.895754 | + | 1.55149i | 0.832869 | + | 0.553470i | \(0.186697\pi\) |
0.0628843 | + | 0.998021i | \(0.479970\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.2498 | + | 26.4134i | −0.861970 | + | 1.49298i | 0.00805392 | + | 0.999968i | \(0.497436\pi\) |
−0.870024 | + | 0.493009i | \(0.835897\pi\) | |||||||
\(314\) | −3.03875 | −0.171487 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.518682 | −0.0291781 | ||||||||
\(317\) | −11.0445 | + | 19.1296i | −0.620320 | + | 1.07443i | 0.369106 | + | 0.929387i | \(0.379664\pi\) |
−0.989426 | + | 0.145039i | \(0.953669\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.549459 | − | 0.951691i | −0.0307638 | − | 0.0532845i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 24.7615 | − | 42.8882i | 1.37991 | − | 2.39007i | ||||
\(323\) | 13.8538 | 0.770849 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.58206 | + | 4.47226i | −0.143007 | + | 0.247696i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.60339 | − | 13.1695i | −0.419827 | − | 0.727162i | ||||
\(329\) | −2.76191 | − | 4.78377i | −0.152269 | − | 0.263738i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.8024 | − | 25.6385i | 0.813612 | − | 1.40922i | −0.0967089 | − | 0.995313i | \(-0.530832\pi\) |
0.910321 | − | 0.413904i | \(-0.135835\pi\) | |||||||
\(332\) | 0.780834 | 0.0428538 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 30.2531 | 1.65538 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.26553 | + | 10.8522i | 0.341305 | + | 0.591158i | 0.984675 | − | 0.174397i | \(-0.0557977\pi\) |
−0.643370 | + | 0.765555i | \(0.722464\pi\) | |||||||
\(338\) | −2.67886 | − | 4.63992i | −0.145711 | − | 0.252379i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.690479 | −0.0373915 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.65180 | −0.197179 | ||||||||
\(344\) | 12.2269 | − | 21.1777i | 0.659232 | − | 1.14182i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.71017 | + | 9.89030i | 0.306980 | + | 0.531706i | ||||
\(347\) | 8.54872 | + | 14.8068i | 0.458919 | + | 0.794872i | 0.998904 | − | 0.0468031i | \(-0.0149033\pi\) |
−0.539985 | + | 0.841675i | \(0.681570\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.20231 | − | 15.9389i | 0.492588 | − | 0.853188i | −0.507375 | − | 0.861725i | \(-0.669384\pi\) |
0.999964 | + | 0.00853709i | \(0.00271747\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.250340 | 0.0133432 | ||||||||
\(353\) | 15.8594 | − | 27.4693i | 0.844110 | − | 1.46204i | −0.0422810 | − | 0.999106i | \(-0.513462\pi\) |
0.886391 | − | 0.462936i | \(-0.153204\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.611825 | + | 1.05971i | 0.0324267 | + | 0.0561646i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.92844 | + | 13.7325i | −0.419031 | + | 0.725783i | ||||
\(359\) | 11.4533 | 0.604483 | 0.302241 | − | 0.953231i | \(-0.402265\pi\) | ||||
0.302241 | + | 0.953231i | \(0.402265\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.943580 | −0.0496621 | ||||||||
\(362\) | 5.77937 | − | 10.0102i | 0.303757 | − | 0.526122i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.34405 | + | 2.32797i | 0.0704475 | + | 0.122019i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.24619 | − | 2.15846i | 0.0650506 | − | 0.112671i | −0.831666 | − | 0.555276i | \(-0.812612\pi\) |
0.896716 | + | 0.442606i | \(0.145946\pi\) | |||||||
\(368\) | −37.4934 | −1.95448 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.9996 | − | 38.1045i | 1.14216 | − | 1.97829i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.51868 | − | 13.0227i | −0.389303 | − | 0.674292i | 0.603053 | − | 0.797701i | \(-0.293951\pi\) |
−0.992356 | + | 0.123409i | \(0.960617\pi\) | |||||||
\(374\) | 0.625086 | + | 1.08268i | 0.0323224 | + | 0.0559841i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.92567 | + | 3.33536i | −0.0993088 | + | 0.172008i | ||||
\(377\) | −17.2211 | −0.886932 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.27273 | 0.322208 | 0.161104 | − | 0.986937i | \(-0.448495\pi\) | ||||
0.161104 | + | 0.986937i | \(0.448495\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.22275 | − | 7.31402i | −0.216055 | − | 0.374218i | ||||
\(383\) | 11.0944 | + | 19.2161i | 0.566897 | + | 0.981894i | 0.996870 | + | 0.0790528i | \(0.0251896\pi\) |
−0.429973 | + | 0.902842i | \(0.641477\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.4967 | 0.636065 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.531061 | −0.0269605 | ||||||||
\(389\) | −15.0461 | + | 26.0606i | −0.762869 | + | 1.32133i | 0.178498 | + | 0.983940i | \(0.442876\pi\) |
−0.941366 | + | 0.337387i | \(0.890457\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.1746 | − | 24.5512i | −0.716842 | − | 1.24161i | ||||
\(392\) | 10.7068 | + | 18.5447i | 0.540774 | + | 0.936649i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.82781 | + | 13.5582i | −0.394359 | + | 0.683050i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.2313 | −1.46708 | −0.733538 | − | 0.679648i | \(-0.762132\pi\) | ||||
−0.733538 | + | 0.679648i | \(0.762132\pi\) | |||||||
\(398\) | 13.6854 | − | 23.7038i | 0.685986 | − | 1.18816i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.1171 | + | 20.9874i | 0.605098 | + | 1.04806i | 0.992036 | + | 0.125954i | \(0.0401993\pi\) |
−0.386938 | + | 0.922106i | \(0.626467\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.41024 | + | 9.37080i | −0.269503 | + | 0.466793i | ||||
\(404\) | −0.655614 | −0.0326180 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 24.0463 | 1.19340 | ||||||||
\(407\) | 0.296142 | − | 0.512934i | 0.0146792 | − | 0.0254252i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.16995 | − | 2.02642i | −0.0578504 | − | 0.100200i | 0.835650 | − | 0.549263i | \(-0.185091\pi\) |
−0.893500 | + | 0.449063i | \(0.851758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.358584 | + | 0.621086i | −0.0176662 | + | 0.0305987i | ||||
\(413\) | −27.5411 | −1.35521 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.96153 | − | 3.39748i | 0.0961721 | − | 0.166575i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.814706 | + | 1.41111i | 0.0398486 | + | 0.0690197i | ||||
\(419\) | 11.4212 | + | 19.7821i | 0.557964 | + | 0.966421i | 0.997666 | + | 0.0682778i | \(0.0217504\pi\) |
−0.439703 | + | 0.898143i | \(0.644916\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.93792 | + | 10.2848i | −0.289396 | + | 0.501249i | −0.973666 | − | 0.227980i | \(-0.926788\pi\) |
0.684269 | + | 0.729229i | \(0.260121\pi\) | |||||||
\(422\) | 15.4004 | 0.749679 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −30.6773 | −1.48982 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.88036 | + | 8.45303i | 0.236177 | + | 0.409071i | ||||
\(428\) | 0.138646 | + | 0.240142i | 0.00670172 | + | 0.0116077i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.86916 | −0.427212 | −0.213606 | − | 0.976920i | \(-0.568521\pi\) | ||||
−0.213606 | + | 0.976920i | \(0.568521\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.37059 | −0.450322 | −0.225161 | − | 0.974322i | \(-0.572291\pi\) | ||||
−0.225161 | + | 0.974322i | \(0.572291\pi\) | |||||||
\(434\) | 7.55446 | − | 13.0847i | 0.362626 | − | 0.628086i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.09977 | + | 1.90486i | 0.0526695 | + | 0.0912262i | ||||
\(437\) | −18.4745 | − | 31.9988i | −0.883756 | − | 1.53071i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.71155 | + | 16.8209i | −0.463507 | + | 0.802817i | −0.999133 | − | 0.0416380i | \(-0.986742\pi\) |
0.535626 | + | 0.844455i | \(0.320076\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19.5914 | 0.931868 | ||||||||
\(443\) | −5.43963 | + | 9.42172i | −0.258445 | + | 0.447639i | −0.965825 | − | 0.259193i | \(-0.916543\pi\) |
0.707381 | + | 0.706833i | \(0.249877\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.89583 | + | 5.01572i | 0.137121 | + | 0.237501i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 13.9301 | − | 24.1276i | 0.658136 | − | 1.13992i | ||||
\(449\) | −1.34014 | −0.0632451 | −0.0316225 | − | 0.999500i | \(-0.510067\pi\) | ||||
−0.0316225 | + | 0.999500i | \(0.510067\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.46845 | 0.0691467 | ||||||||
\(452\) | −0.113290 | + | 0.196224i | −0.00532871 | + | 0.00922959i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.55894 | − | 6.16426i | −0.167029 | − | 0.289303i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.0556 | − | 17.4169i | 0.470383 | − | 0.814728i | −0.529043 | − | 0.848595i | \(-0.677449\pi\) |
0.999426 | + | 0.0338671i | \(0.0107823\pi\) | |||||||
\(458\) | −27.7752 | −1.29785 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.8766 | + | 29.2312i | −0.786024 | + | 1.36143i | 0.142362 | + | 0.989815i | \(0.454530\pi\) |
−0.928386 | + | 0.371618i | \(0.878803\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.62268 | − | 4.54262i | −0.121886 | − | 0.211114i | 0.798625 | − | 0.601829i | \(-0.205561\pi\) |
−0.920512 | + | 0.390715i | \(0.872228\pi\) | |||||||
\(464\) | −9.10262 | − | 15.7662i | −0.422578 | − | 0.731927i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.76744 | − | 15.1856i | 0.406144 | − | 0.703462i | ||||
\(467\) | 14.2120 | 0.657652 | 0.328826 | − | 0.944390i | \(-0.393347\pi\) | ||||
0.328826 | + | 0.944390i | \(0.393347\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 43.6282 | 2.01456 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.60115 | + | 16.6297i | 0.441929 | + | 0.765443i | ||||
\(473\) | 1.18070 | + | 2.04503i | 0.0542887 | + | 0.0940307i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.14866 | −0.0984837 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 31.8657 | 1.45750 | ||||||||
\(479\) | 10.2417 | − | 17.7391i | 0.467954 | − | 0.810519i | −0.531376 | − | 0.847136i | \(-0.678325\pi\) |
0.999329 | + | 0.0366168i | \(0.0116581\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.64084 | − | 8.03817i | −0.211604 | − | 0.366509i | ||||
\(482\) | −2.87161 | − | 4.97377i | −0.130798 | − | 0.226549i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.931859 | − | 1.61403i | 0.0423572 | − | 0.0733649i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.3554 | −1.42085 | −0.710425 | − | 0.703772i | \(-0.751497\pi\) | ||||
−0.710425 | + | 0.703772i | \(0.751497\pi\) | |||||||
\(488\) | 3.40271 | − | 5.89366i | 0.154033 | − | 0.266793i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.19604 | − | 8.99980i | −0.234494 | − | 0.406155i | 0.724632 | − | 0.689136i | \(-0.242010\pi\) |
−0.959125 | + | 0.282981i | \(0.908677\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.88260 | − | 11.9210i | 0.309977 | − | 0.536896i | ||||
\(494\) | 25.5345 | 1.14885 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.4388 | −0.513618 | ||||||||
\(497\) | 16.2009 | − | 28.0607i | 0.726709 | − | 1.25870i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.91285 | + | 3.31316i | 0.0856310 | + | 0.148317i | 0.905660 | − | 0.424005i | \(-0.139376\pi\) |
−0.820029 | + | 0.572322i | \(0.806043\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −22.1749 | + | 38.4081i | −0.989715 | + | 1.71424i | ||||
\(503\) | 1.00236 | 0.0446931 | 0.0223466 | − | 0.999750i | \(-0.492886\pi\) | ||||
0.0223466 | + | 0.999750i | \(0.492886\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.66714 | − | 2.88757i | 0.0741134 | − | 0.128368i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.140888 | − | 0.244026i | −0.00625090 | − | 0.0108269i | ||||
\(509\) | 2.28161 | + | 3.95187i | 0.101131 | + | 0.175163i | 0.912151 | − | 0.409855i | \(-0.134421\pi\) |
−0.811020 | + | 0.585018i | \(0.801087\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.780062 | + | 1.35111i | −0.0345079 | + | 0.0597695i | ||||
\(512\) | −19.0969 | −0.843971 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −24.1822 | −1.06663 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.185953 | − | 0.322080i | −0.00817822 | − | 0.0141651i | ||||
\(518\) | 6.48013 | + | 11.2239i | 0.284721 | + | 0.493151i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.3708 | −1.72486 | −0.862432 | − | 0.506173i | \(-0.831060\pi\) | ||||
−0.862432 | + | 0.506173i | \(0.831060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.3998 | 0.454749 | 0.227375 | − | 0.973807i | \(-0.426986\pi\) | ||||
0.227375 | + | 0.973807i | \(0.426986\pi\) | |||||||
\(524\) | −1.12326 | + | 1.94555i | −0.0490699 | + | 0.0849916i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.0103 | − | 32.9268i | −0.828888 | − | 1.43568i | ||||
\(527\) | −4.32452 | − | 7.49029i | −0.188379 | − | 0.326282i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −26.3046 | + | 45.5608i | −1.14368 | + | 1.98091i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.80046 | −0.121415 | ||||||||
\(533\) | 11.5060 | − | 19.9290i | 0.498381 | − | 0.863222i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −15.2093 | − | 26.3433i | −0.656942 | − | 1.13786i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.22298 | + | 15.9747i | −0.397631 | + | 0.688717i | ||||
\(539\) | −2.06781 | −0.0890670 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.7093 | 0.589408 | 0.294704 | − | 0.955589i | \(-0.404779\pi\) | ||||
0.294704 | + | 0.955589i | \(0.404779\pi\) | |||||||
\(542\) | −14.4719 | + | 25.0661i | −0.621622 | + | 1.07668i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.56790 | + | 2.71568i | 0.0672230 | + | 0.116434i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.3924 | − | 19.7322i | 0.487102 | − | 0.843686i | −0.512788 | − | 0.858515i | \(-0.671387\pi\) |
0.999890 | + | 0.0148294i | \(0.00472053\pi\) | |||||||
\(548\) | 3.45950 | 0.147783 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.97044 | − | 15.5373i | 0.382154 | − | 0.661910i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.88089 | − | 10.1860i | −0.250081 | − | 0.433153i | ||||
\(554\) | −15.3440 | − | 26.5766i | −0.651905 | − | 1.12913i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.261583 | + | 0.453075i | −0.0110936 | + | 0.0192146i | ||||
\(557\) | −18.2341 | −0.772605 | −0.386303 | − | 0.922372i | \(-0.626248\pi\) | ||||
−0.386303 | + | 0.922372i | \(0.626248\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.0054 | 1.56516 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.48013 | + | 6.02776i | 0.146800 | + | 0.254266i | ||||
\(563\) | −12.0556 | − | 20.8809i | −0.508083 | − | 0.880025i | −0.999956 | − | 0.00935862i | \(-0.997021\pi\) |
0.491873 | − | 0.870667i | \(-0.336312\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −34.1095 | −1.43373 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −22.5913 | −0.947910 | ||||||||
\(569\) | −16.0024 | + | 27.7170i | −0.670857 | + | 1.16196i | 0.306804 | + | 0.951773i | \(0.400740\pi\) |
−0.977661 | + | 0.210186i | \(0.932593\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.89042 | + | 17.1307i | 0.413901 | + | 0.716898i | 0.995312 | − | 0.0967121i | \(-0.0308326\pi\) |
−0.581411 | + | 0.813610i | \(0.697499\pi\) | |||||||
\(572\) | 0.0904921 | + | 0.156737i | 0.00378367 | + | 0.00655350i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16.0662 | + | 27.8274i | −0.670589 | + | 1.16150i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.4119 | 1.47422 | 0.737108 | − | 0.675775i | \(-0.236191\pi\) | ||||
0.737108 | + | 0.675775i | \(0.236191\pi\) | |||||||
\(578\) | 4.69275 | − | 8.12808i | 0.195193 | − | 0.338084i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.85321 | + | 15.3342i | 0.367293 | + | 0.636170i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.48119 | − | 2.56549i | 0.0613445 | − | 0.106252i | ||||
\(584\) | 1.08776 | 0.0450117 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.8675 | −1.02726 | ||||||||
\(587\) | 16.1925 | − | 28.0463i | 0.668338 | − | 1.15759i | −0.310031 | − | 0.950726i | \(-0.600339\pi\) |
0.978369 | − | 0.206868i | \(-0.0663272\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.63636 | − | 9.76247i | −0.232242 | − | 0.402255i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.90605 | − | 8.49752i | 0.201637 | − | 0.349246i | ||||
\(593\) | 29.2504 | 1.20117 | 0.600585 | − | 0.799561i | \(-0.294934\pi\) | ||||
0.600585 | + | 0.799561i | \(0.294934\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.346210 | − | 0.599654i | 0.0141813 | − | 0.0245628i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −26.1257 | − | 45.2510i | −1.06836 | − | 1.85045i | ||||
\(599\) | 2.03081 | + | 3.51747i | 0.0829767 | + | 0.143720i | 0.904527 | − | 0.426416i | \(-0.140224\pi\) |
−0.821551 | + | 0.570136i | \(0.806891\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.4538 | + | 40.6232i | −0.956700 | + | 1.65705i | −0.226271 | + | 0.974064i | \(0.572653\pi\) |
−0.730429 | + | 0.682989i | \(0.760680\pi\) | |||||||
\(602\) | −51.6717 | −2.10598 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.32190 | −0.0944768 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.4733 | − | 35.4608i | −0.830987 | − | 1.43931i | −0.897257 | − | 0.441509i | \(-0.854443\pi\) |
0.0662702 | − | 0.997802i | \(-0.478890\pi\) | |||||||
\(608\) | 2.04352 | + | 3.53948i | 0.0828756 | + | 0.143545i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.82813 | −0.235781 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.3827 | 1.34831 | 0.674157 | − | 0.738588i | \(-0.264507\pi\) | ||||
0.674157 | + | 0.738588i | \(0.264507\pi\) | |||||||
\(614\) | −16.7345 | + | 28.9850i | −0.675350 | + | 1.16974i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.35602 | + | 2.34869i | 0.0546355 | + | 0.0946314i | ||||
\(617\) | −1.12440 | − | 1.94752i | −0.0452666 | − | 0.0784040i | 0.842504 | − | 0.538689i | \(-0.181080\pi\) |
−0.887771 | + | 0.460285i | \(0.847747\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.1467 | − | 29.6990i | 0.689184 | − | 1.19370i | −0.282918 | − | 0.959144i | \(-0.591302\pi\) |
0.972102 | − | 0.234558i | \(-0.0753642\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −46.5454 | −1.86630 | ||||||||
\(623\) | −13.8739 | + | 24.0303i | −0.555847 | + | 0.962756i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −22.4669 | − | 38.9137i | −0.897956 | − | 1.55531i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.175816 | − | 0.304522i | 0.00701581 | − | 0.0121517i | ||||
\(629\) | 7.41904 | 0.295817 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.7552 | −0.746633 | −0.373316 | − | 0.927704i | \(-0.621779\pi\) | ||||
−0.373316 | + | 0.927704i | \(0.621779\pi\) | |||||||
\(632\) | −4.10030 | + | 7.10193i | −0.163101 | + | 0.282499i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16.2713 | − | 28.1828i | −0.646218 | − | 1.11928i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.2023 | + | 28.0632i | −0.641959 | + | 1.11191i | ||||
\(638\) | 1.61899 | 0.0640963 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.3175 | − | 17.8704i | 0.407517 | − | 0.705840i | −0.587094 | − | 0.809519i | \(-0.699728\pi\) |
0.994611 | + | 0.103679i | \(0.0330614\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.5970 | + | 23.5506i | 0.536212 | + | 0.928746i | 0.999104 | + | 0.0423312i | \(0.0134785\pi\) |
−0.462892 | + | 0.886415i | \(0.653188\pi\) | |||||||
\(644\) | 2.86530 | + | 4.96285i | 0.112909 | + | 0.195564i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.2051 | + | 17.6758i | −0.401515 | + | 0.695445i | ||||
\(647\) | 16.7316 | 0.657787 | 0.328893 | − | 0.944367i | \(-0.393324\pi\) | ||||
0.328893 | + | 0.944367i | \(0.393324\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.85428 | −0.0727869 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.298785 | − | 0.517511i | −0.0117013 | − | 0.0202673i | ||||
\(653\) | 22.8666 | + | 39.6060i | 0.894837 | + | 1.54990i | 0.834006 | + | 0.551756i | \(0.186042\pi\) |
0.0608319 | + | 0.998148i | \(0.480625\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 24.3271 | 0.949814 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.13799 | 0.317252 | ||||||||
\(659\) | 9.30543 | − | 16.1175i | 0.362488 | − | 0.627848i | −0.625882 | − | 0.779918i | \(-0.715261\pi\) |
0.988370 | + | 0.152070i | \(0.0485941\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.39799 | − | 14.5457i | −0.326644 | − | 0.565764i | 0.655200 | − | 0.755456i | \(-0.272584\pi\) |
−0.981844 | + | 0.189692i | \(0.939251\pi\) | |||||||
\(662\) | 21.8077 | + | 37.7720i | 0.847579 | + | 1.46805i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.17267 | − | 10.6914i | 0.239546 | − | 0.414906i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −36.7126 | −1.42152 | ||||||||
\(668\) | −1.75038 | + | 3.03175i | −0.0677243 | + | 0.117302i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.328584 | + | 0.569124i | 0.0126848 | + | 0.0219708i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.9740 | − | 43.2562i | 0.962676 | − | 1.66740i | 0.246944 | − | 0.969030i | \(-0.420574\pi\) |
0.715733 | − | 0.698374i | \(-0.246093\pi\) | |||||||
\(674\) | −18.4614 | −0.711108 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.619973 | 0.0238451 | ||||||||
\(677\) | −5.41553 | + | 9.37998i | −0.208136 | + | 0.360502i | −0.951127 | − | 0.308799i | \(-0.900073\pi\) |
0.742991 | + | 0.669301i | \(0.233406\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.02125 | − | 10.4291i | −0.231074 | − | 0.400232i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.508625 | − | 0.880965i | 0.0194763 | − | 0.0337339i | ||||
\(683\) | 0.429870 | 0.0164485 | 0.00822426 | − | 0.999966i | \(-0.497382\pi\) | ||||
0.00822426 | + | 0.999966i | \(0.497382\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.69001 | − | 4.65924i | 0.102705 | − | 0.177891i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 19.5601 | + | 33.8791i | 0.745721 | + | 1.29163i | ||||
\(689\) | −23.2116 | − | 40.2037i | −0.884293 | − | 1.53164i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.3518 | + | 30.0542i | −0.660093 | + | 1.14331i | 0.320498 | + | 0.947249i | \(0.396150\pi\) |
−0.980591 | + | 0.196065i | \(0.937184\pi\) | |||||||
\(692\) | −1.32151 | −0.0502364 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25.1889 | −0.956157 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.19701 | + | 15.9297i | 0.348362 | + | 0.603380i | ||||
\(698\) | 13.5573 | + | 23.4820i | 0.513153 | + | 0.888807i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.84808 | −0.0698010 | −0.0349005 | − | 0.999391i | \(-0.511111\pi\) | ||||
−0.0349005 | + | 0.999391i | \(0.511111\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.66962 | 0.364696 | ||||||||
\(704\) | 0.937884 | − | 1.62446i | 0.0353478 | − | 0.0612242i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.3649 | + | 40.4692i | 0.879351 | + | 1.52308i | ||||
\(707\) | −7.43344 | − | 12.8751i | −0.279563 | − | 0.484218i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.15338 | − | 5.46181i | 0.118428 | − | 0.205123i | −0.800717 | − | 0.599043i | \(-0.795548\pi\) |
0.919145 | + | 0.393920i | \(0.128881\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 19.3465 | 0.725040 | ||||||||
\(713\) | −11.5337 | + | 19.9770i | −0.431942 | + | 0.748145i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.917446 | − | 1.58906i | −0.0342866 | − | 0.0593861i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.43682 | + | 14.6130i | −0.314859 | + | 0.545352i | ||||
\(719\) | −18.0129 | −0.671770 | −0.335885 | − | 0.941903i | \(-0.609035\pi\) | ||||
−0.335885 | + | 0.941903i | \(0.609035\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.2627 | −0.605655 | ||||||||
\(722\) | 0.695067 | − | 1.20389i | 0.0258677 | − | 0.0448042i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.668765 | + | 1.15833i | 0.0248544 | + | 0.0430491i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.1412 | − | 22.7612i | 0.487379 | − | 0.844165i | −0.512516 | − | 0.858678i | \(-0.671286\pi\) |
0.999895 | + | 0.0145126i | \(0.00461966\pi\) | |||||||
\(728\) | 42.5002 | 1.57516 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.7896 | + | 25.6164i | −0.547014 | + | 0.947456i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.8317 | + | 41.2777i | 0.880243 | + | 1.52462i | 0.851071 | + | 0.525050i | \(0.175954\pi\) |
0.0291714 | + | 0.999574i | \(0.490713\pi\) | |||||||
\(734\) | 1.83595 | + | 3.17997i | 0.0677663 | + | 0.117375i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.18167 | − | 7.24287i | 0.154138 | − | 0.266976i | ||||
\(737\) | 2.93739 | 0.108200 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.0273 | −0.368859 | −0.184429 | − | 0.982846i | \(-0.559044\pi\) | ||||
−0.184429 | + | 0.982846i | \(0.559044\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 32.4110 | + | 56.1376i | 1.18985 | + | 2.06088i | ||||
\(743\) | −4.13633 | − | 7.16433i | −0.151747 | − | 0.262834i | 0.780123 | − | 0.625627i | \(-0.215157\pi\) |
−0.931870 | + | 0.362793i | \(0.881823\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 22.1539 | 0.811111 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.144665 | −0.00528946 | ||||||||
\(749\) | −3.14398 | + | 5.44554i | −0.114879 | + | 0.198976i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.89880 | + | 5.02087i | 0.105779 | + | 0.183214i | 0.914056 | − | 0.405588i | \(-0.132933\pi\) |
−0.808277 | + | 0.588802i | \(0.799600\pi\) | |||||||
\(752\) | −3.08060 | − | 5.33575i | −0.112338 | − | 0.194575i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.6855 | − | 21.9720i | 0.461980 | − | 0.800173i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.2804 | 0.918830 | 0.459415 | − | 0.888222i | \(-0.348059\pi\) | ||||
0.459415 | + | 0.888222i | \(0.348059\pi\) | |||||||
\(758\) | −4.62066 | + | 8.00322i | −0.167830 | + | 0.290690i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.73190 | + | 16.8561i | 0.352781 | + | 0.611035i | 0.986736 | − | 0.162335i | \(-0.0519027\pi\) |
−0.633954 | + | 0.773370i | \(0.718569\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.9387 | + | 43.1951i | −0.902843 | + | 1.56377i | ||||
\(764\) | 0.977278 | 0.0353567 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.6897 | −1.18113 | ||||||||
\(767\) | −14.5292 | + | 25.1653i | −0.524618 | + | 0.908666i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.6715 | + | 42.7324i | 0.889678 | + | 1.54097i | 0.840256 | + | 0.542190i | \(0.182405\pi\) |
0.0494224 | + | 0.998778i | \(0.484262\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.723033 | + | 1.25233i | −0.0260225 | + | 0.0450723i | ||||
\(773\) | 20.8502 | 0.749930 | 0.374965 | − | 0.927039i | \(-0.377655\pi\) | ||||
0.374965 | + | 0.927039i | \(0.377655\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.19816 | + | 7.27143i | −0.150705 | + | 0.261029i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −22.1668 | − | 38.3940i | −0.794717 | − | 1.37649i | ||||
\(779\) | 11.9869 | + | 20.7620i | 0.429476 | + | 0.743875i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.09077 | − | 1.88927i | 0.0390308 | − | 0.0676034i | ||||
\(782\) | 41.7657 | 1.49354 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −34.2564 | −1.22344 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.0941 | − | 38.2682i | −0.787571 | − | 1.36411i | −0.927451 | − | 0.373945i | \(-0.878005\pi\) |
0.139880 | − | 0.990169i | \(-0.455328\pi\) | |||||||
\(788\) | −0.905801 | − | 1.56889i | −0.0322678 | − | 0.0558895i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.13799 | −0.182686 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.2985 | 0.365709 | ||||||||
\(794\) | 21.5326 | − | 37.2955i | 0.764162 | − | 1.32357i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.58362 | + | 2.74290i | 0.0561297 | + | 0.0972196i | ||||
\(797\) | −15.5187 | − | 26.8792i | −0.549701 | − | 0.952110i | −0.998295 | − | 0.0583744i | \(-0.981408\pi\) |
0.448594 | − | 0.893736i | \(-0.351925\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.32928 | − | 4.03443i | 0.0824039 | − | 0.142728i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −35.7031 | −1.26072 | ||||||||
\(803\) | −0.0525199 | + | 0.0909671i | −0.00185339 | + | 0.00321016i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.97065 | − | 13.8056i | −0.280754 | − | 0.486281i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.18278 | + | 8.97683i | −0.182329 | + | 0.315804i | ||||
\(809\) | −14.6229 | −0.514114 | −0.257057 | − | 0.966396i | \(-0.582753\pi\) | ||||
−0.257057 | + | 0.966396i | \(0.582753\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.7177 | 0.938187 | 0.469093 | − | 0.883149i | \(-0.344581\pi\) | ||||
0.469093 | + | 0.883149i | \(0.344581\pi\) | |||||||
\(812\) | −1.39127 | + | 2.40975i | −0.0488240 | + | 0.0845656i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.436293 | + | 0.755682i | 0.0152921 | + | 0.0264866i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.2761 | + | 33.3871i | −0.674384 | + | 1.16807i | ||||
\(818\) | 3.44727 | 0.120531 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.29903 | + | 16.1064i | −0.324538 | + | 0.562117i | −0.981419 | − | 0.191878i | \(-0.938542\pi\) |
0.656881 | + | 0.753995i | \(0.271876\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.53102 | − | 2.65181i | −0.0533680 | − | 0.0924362i | 0.838107 | − | 0.545506i | \(-0.183662\pi\) |
−0.891475 | + | 0.453069i | \(0.850329\pi\) | |||||||
\(824\) | 5.66938 | + | 9.81966i | 0.197502 | + | 0.342084i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 20.2875 | − | 35.1390i | 0.705892 | − | 1.22264i | ||||
\(827\) | 7.27526 | 0.252985 | 0.126493 | − | 0.991968i | \(-0.459628\pi\) | ||||
0.126493 | + | 0.991968i | \(0.459628\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.5211 | 0.365411 | 0.182706 | − | 0.983168i | \(-0.441514\pi\) | ||||
0.182706 | + | 0.983168i | \(0.441514\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −14.6975 | − | 25.4569i | −0.509546 | − | 0.882559i | ||||
\(833\) | −12.9509 | − | 22.4315i | −0.448721 | − | 0.777207i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.188549 | −0.00652109 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −33.6528 | −1.16252 | ||||||||
\(839\) | 7.59033 | − | 13.1468i | 0.262047 | − | 0.453879i | −0.704739 | − | 0.709467i | \(-0.748936\pi\) |
0.966786 | + | 0.255588i | \(0.0822691\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.58695 | + | 9.67689i | 0.192654 | + | 0.333686i | ||||
\(842\) | −8.74806 | − | 15.1521i | −0.301478 | − | 0.522176i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.891034 | + | 1.54332i | −0.0306707 | + | 0.0531232i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 42.2622 | 1.45215 | ||||||||
\(848\) | 24.5381 | − | 42.5012i | 0.842641 | − | 1.45950i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.89351 | − | 17.1361i | −0.339145 | − | 0.587417i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.24309 | − | 9.08131i | 0.179520 | − | 0.310938i | −0.762196 | − | 0.647346i | \(-0.775879\pi\) |
0.941716 | + | 0.336408i | \(0.109212\pi\) | |||||||
\(854\) | −14.3800 | −0.492074 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.38412 | 0.149846 | ||||||||
\(857\) | 4.42038 | − | 7.65631i | 0.150997 | − | 0.261535i | −0.780597 | − | 0.625034i | \(-0.785085\pi\) |
0.931594 | + | 0.363500i | \(0.118418\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.03416 | + | 1.79121i | 0.0352849 | + | 0.0611153i | 0.883129 | − | 0.469131i | \(-0.155433\pi\) |
−0.847844 | + | 0.530246i | \(0.822099\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.53326 | − | 11.3159i | 0.222524 | − | 0.385423i | ||||
\(863\) | −22.4434 | −0.763984 | −0.381992 | − | 0.924166i | \(-0.624762\pi\) | ||||
−0.381992 | + | 0.924166i | \(0.624762\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.90263 | − | 11.9557i | 0.234561 | − | 0.406271i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.874171 | + | 1.51411i | 0.0296713 | + | 0.0513922i | ||||
\(869\) | −0.395947 | − | 0.685801i | −0.0134316 | − | 0.0232642i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.0159 | − | 39.8647i | 0.779863 | − | 1.35076i | ||||
\(872\) | 34.7758 | 1.17766 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 54.4353 | 1.84130 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.9466 | + | 24.1562i | 0.470943 | + | 0.815697i | 0.999448 | − | 0.0332332i | \(-0.0105804\pi\) |
−0.528505 | + | 0.848930i | \(0.677247\pi\) | |||||||
\(878\) | −14.3076 | − | 24.7815i | −0.482857 | − | 0.836334i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.22153 | 0.310681 | 0.155341 | − | 0.987861i | \(-0.450353\pi\) | ||||
0.155341 | + | 0.987861i | \(0.450353\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.2436 | −1.65718 | −0.828589 | − | 0.559858i | \(-0.810856\pi\) | ||||
−0.828589 | + | 0.559858i | \(0.810856\pi\) | |||||||
\(884\) | −1.13352 | + | 1.96331i | −0.0381243 | + | 0.0660333i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.01396 | − | 13.8806i | −0.269234 | − | 0.466328i | ||||
\(887\) | −5.38403 | − | 9.32542i | −0.180778 | − | 0.313117i | 0.761368 | − | 0.648320i | \(-0.224528\pi\) |
−0.942146 | + | 0.335203i | \(0.891195\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.19482 | − | 5.53360i | 0.107151 | − | 0.185591i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.670187 | −0.0224395 | ||||||||
\(893\) | 3.03586 | − | 5.25827i | 0.101591 | − | 0.175961i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 24.2408 | + | 41.9863i | 0.809829 | + | 1.40266i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.987183 | − | 1.70985i | 0.0329427 | − | 0.0570585i | ||||
\(899\) | −11.2006 | −0.373561 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.1071 | 1.23622 | ||||||||
\(902\) | −1.08170 | + | 1.87356i | −0.0360167 | + | 0.0623828i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.79116 | + | 3.10239i | 0.0595733 | + | 0.103184i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.9852 | + | 27.6871i | −0.530779 | + | 0.919336i | 0.468576 | + | 0.883423i | \(0.344767\pi\) |
−0.999355 | + | 0.0359130i | \(0.988566\pi\) | |||||||
\(908\) | 0.823651 | 0.0273338 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.04010 | + | 8.72970i | −0.166986 | + | 0.289228i | −0.937359 | − | 0.348366i | \(-0.886737\pi\) |
0.770373 | + | 0.637594i | \(0.220070\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.596067 | + | 1.03242i | 0.0197269 | + | 0.0341681i | ||||
\(914\) | 14.8145 | + | 25.6595i | 0.490021 | + | 0.848741i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.60702 | − | 2.78343i | 0.0530973 | − | 0.0919672i | ||||
\(917\) | −50.9428 | −1.68228 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.7976 | −0.982932 | −0.491466 | − | 0.870897i | \(-0.663539\pi\) | ||||
−0.491466 | + | 0.870897i | \(0.663539\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −24.8636 | − | 43.0650i | −0.818839 | − | 1.41827i | ||||
\(923\) | −17.0934 | − | 29.6067i | −0.562637 | − | 0.974516i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.72776 | 0.253950 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.06089 | 0.133305 | ||||||||
\(929\) | −6.19275 | + | 10.7262i | −0.203178 | + | 0.351914i | −0.949551 | − | 0.313614i | \(-0.898460\pi\) |
0.746373 | + | 0.665528i | \(0.231794\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.8795 | − | 29.2362i | −0.553204 | − | 0.958177i | ||||
\(932\) | 1.01453 | + | 1.75722i | 0.0332321 | + | 0.0575597i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.4689 | + | 18.1327i | −0.342554 | + | 0.593321i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.4280 | 1.45140 | 0.725699 | − | 0.688012i | \(-0.241516\pi\) | ||||
0.725699 | + | 0.688012i | \(0.241516\pi\) | |||||||
\(938\) | −32.1377 | + | 55.6641i | −1.04933 | + | 1.81750i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.66617 | + | 13.2782i | 0.249910 | + | 0.432857i | 0.963501 | − | 0.267706i | \(-0.0862656\pi\) |
−0.713591 | + | 0.700563i | \(0.752932\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.5290 | − | 42.4854i | 0.798773 | − | 1.38352i | ||||
\(944\) | −30.7189 | −0.999816 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.47894 | −0.113110 | ||||||||
\(947\) | 10.8498 | − | 18.7925i | 0.352572 | − | 0.610673i | −0.634127 | − | 0.773229i | \(-0.718640\pi\) |
0.986699 | + | 0.162556i | \(0.0519738\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.823037 | + | 1.42554i | 0.0267169 | + | 0.0462751i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −16.9857 | + | 29.4200i | −0.550508 | + | 0.953509i | ||||
\(953\) | −36.9099 | −1.19563 | −0.597815 | − | 0.801634i | \(-0.703964\pi\) | ||||
−0.597815 | + | 0.801634i | \(0.703964\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.84368 | + | 3.19336i | −0.0596290 | + | 0.103281i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.0886 | + | 26.1342i | 0.487490 | + | 0.844357i | ||||
\(959\) | 39.2243 | + | 67.9385i | 1.26662 | + | 2.19385i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.9812 | − | 20.7520i | 0.386490 | − | 0.669420i | ||||
\(962\) | 13.6743 | 0.440876 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.664581 | 0.0214047 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.6691 | + | 18.4794i | 0.343095 | + | 0.594258i | 0.985006 | − | 0.172521i | \(-0.0551914\pi\) |
−0.641911 | + | 0.766779i | \(0.721858\pi\) | |||||||
\(968\) | −14.7331 | − | 25.5185i | −0.473541 | − | 0.820197i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.5851 | 1.36662 | 0.683311 | − | 0.730128i | \(-0.260540\pi\) | ||||
0.683311 | + | 0.730128i | \(0.260540\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.8635 | −0.380325 | ||||||||
\(974\) | 23.0973 | − | 40.0057i | 0.740085 | − | 1.28186i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.44349 | + | 9.42840i | 0.174242 | + | 0.301796i | ||||
\(977\) | 24.4696 | + | 42.3826i | 0.782852 | + | 1.35594i | 0.930274 | + | 0.366865i | \(0.119569\pi\) |
−0.147423 | + | 0.989074i | \(0.547098\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.934101 | + | 1.61791i | −0.0298540 | + | 0.0517087i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.3102 | 0.488567 | ||||||||
\(983\) | −18.0545 | + | 31.2712i | −0.575848 | + | 0.997398i | 0.420101 | + | 0.907477i | \(0.361995\pi\) |
−0.995949 | + | 0.0899205i | \(0.971339\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10.1398 | + | 17.5627i | 0.322918 | + | 0.559310i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.47737 | + | 2.55888i | −0.0470014 | + | 0.0814088i | ||||
\(989\) | 78.8896 | 2.50854 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.0054 | 1.01669 | 0.508343 | − | 0.861155i | \(-0.330258\pi\) | ||||
0.508343 | + | 0.861155i | \(0.330258\pi\) | |||||||
\(992\) | 1.27578 | − | 2.20972i | 0.0405061 | − | 0.0701586i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 23.8680 | + | 41.3406i | 0.757048 | + | 1.31125i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.8840 | − | 44.8324i | 0.819754 | − | 1.41986i | −0.0861095 | − | 0.996286i | \(-0.527443\pi\) |
0.905863 | − | 0.423570i | \(-0.139223\pi\) | |||||||
\(998\) | −5.63624 | −0.178412 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 675.2.e.c.451.2 | 8 | ||
3.2 | odd | 2 | 225.2.e.e.151.3 | yes | 8 | ||
5.2 | odd | 4 | 675.2.k.c.424.3 | 16 | |||
5.3 | odd | 4 | 675.2.k.c.424.6 | 16 | |||
5.4 | even | 2 | 675.2.e.e.451.3 | 8 | |||
9.2 | odd | 6 | 2025.2.a.q.1.2 | 4 | |||
9.4 | even | 3 | inner | 675.2.e.c.226.2 | 8 | ||
9.5 | odd | 6 | 225.2.e.e.76.3 | yes | 8 | ||
9.7 | even | 3 | 2025.2.a.z.1.3 | 4 | |||
15.2 | even | 4 | 225.2.k.c.124.6 | 16 | |||
15.8 | even | 4 | 225.2.k.c.124.3 | 16 | |||
15.14 | odd | 2 | 225.2.e.c.151.2 | yes | 8 | ||
45.2 | even | 12 | 2025.2.b.n.649.3 | 8 | |||
45.4 | even | 6 | 675.2.e.e.226.3 | 8 | |||
45.7 | odd | 12 | 2025.2.b.o.649.6 | 8 | |||
45.13 | odd | 12 | 675.2.k.c.199.3 | 16 | |||
45.14 | odd | 6 | 225.2.e.c.76.2 | ✓ | 8 | ||
45.22 | odd | 12 | 675.2.k.c.199.6 | 16 | |||
45.23 | even | 12 | 225.2.k.c.49.6 | 16 | |||
45.29 | odd | 6 | 2025.2.a.y.1.3 | 4 | |||
45.32 | even | 12 | 225.2.k.c.49.3 | 16 | |||
45.34 | even | 6 | 2025.2.a.p.1.2 | 4 | |||
45.38 | even | 12 | 2025.2.b.n.649.6 | 8 | |||
45.43 | odd | 12 | 2025.2.b.o.649.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.e.c.76.2 | ✓ | 8 | 45.14 | odd | 6 | ||
225.2.e.c.151.2 | yes | 8 | 15.14 | odd | 2 | ||
225.2.e.e.76.3 | yes | 8 | 9.5 | odd | 6 | ||
225.2.e.e.151.3 | yes | 8 | 3.2 | odd | 2 | ||
225.2.k.c.49.3 | 16 | 45.32 | even | 12 | |||
225.2.k.c.49.6 | 16 | 45.23 | even | 12 | |||
225.2.k.c.124.3 | 16 | 15.8 | even | 4 | |||
225.2.k.c.124.6 | 16 | 15.2 | even | 4 | |||
675.2.e.c.226.2 | 8 | 9.4 | even | 3 | inner | ||
675.2.e.c.451.2 | 8 | 1.1 | even | 1 | trivial | ||
675.2.e.e.226.3 | 8 | 45.4 | even | 6 | |||
675.2.e.e.451.3 | 8 | 5.4 | even | 2 | |||
675.2.k.c.199.3 | 16 | 45.13 | odd | 12 | |||
675.2.k.c.199.6 | 16 | 45.22 | odd | 12 | |||
675.2.k.c.424.3 | 16 | 5.2 | odd | 4 | |||
675.2.k.c.424.6 | 16 | 5.3 | odd | 4 | |||
2025.2.a.p.1.2 | 4 | 45.34 | even | 6 | |||
2025.2.a.q.1.2 | 4 | 9.2 | odd | 6 | |||
2025.2.a.y.1.3 | 4 | 45.29 | odd | 6 | |||
2025.2.a.z.1.3 | 4 | 9.7 | even | 3 | |||
2025.2.b.n.649.3 | 8 | 45.2 | even | 12 | |||
2025.2.b.n.649.6 | 8 | 45.38 | even | 12 | |||
2025.2.b.o.649.3 | 8 | 45.43 | odd | 12 | |||
2025.2.b.o.649.6 | 8 | 45.7 | odd | 12 |