Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [124,2,Mod(33,124)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(124, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("124.33");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 124 = 2^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 124.f (of order \(5\), degree \(4\), 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: | \(0.990144985064\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 124.109 |
Dual form | 124.2.f.b.33.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).
\(n\) | \(63\) | \(65\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 | ||||||||
\(3\) | 1.80902 | + | 1.31433i | 1.04444 | + | 0.758827i | 0.971147 | − | 0.238483i | \(-0.0766502\pi\) |
0.0732898 | + | 0.997311i | \(0.476650\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.381966 | −0.170820 | −0.0854102 | − | 0.996346i | \(-0.527220\pi\) | ||||
−0.0854102 | + | 0.996346i | \(0.527220\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0729490 | − | 0.224514i | 0.0275721 | − | 0.0848583i | −0.936324 | − | 0.351138i | \(-0.885795\pi\) |
0.963896 | + | 0.266280i | \(0.0857946\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.618034 | + | 1.90211i | 0.206011 | + | 0.634038i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.381966 | + | 1.17557i | −0.115167 | + | 0.354448i | −0.991982 | − | 0.126380i | \(-0.959664\pi\) |
0.876815 | + | 0.480828i | \(0.159664\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.73607 | − | 2.71441i | −1.03620 | − | 0.752843i | −0.0666589 | − | 0.997776i | \(-0.521234\pi\) |
−0.969540 | + | 0.244933i | \(0.921234\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.690983 | − | 0.502029i | −0.178411 | − | 0.129623i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.690983 | + | 2.12663i | 0.167588 | + | 0.515783i | 0.999218 | − | 0.0395478i | \(-0.0125917\pi\) |
−0.831630 | + | 0.555331i | \(0.812592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.42705 | − | 3.94298i | 1.24505 | − | 0.904582i | 0.247127 | − | 0.968983i | \(-0.420514\pi\) |
0.997924 | + | 0.0644007i | \(0.0205136\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.427051 | − | 0.310271i | 0.0931902 | − | 0.0677066i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.545085 | − | 1.67760i | −0.113658 | − | 0.349804i | 0.878007 | − | 0.478648i | \(-0.158873\pi\) |
−0.991665 | + | 0.128845i | \(0.958873\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.85410 | −0.970820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.690983 | − | 2.12663i | 0.132980 | − | 0.409270i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.54508 | + | 3.30220i | −0.844001 | + | 0.613203i | −0.923485 | − | 0.383633i | \(-0.874673\pi\) |
0.0794844 | + | 0.996836i | \(0.474673\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.19098 | − | 3.66547i | −0.752723 | − | 0.658338i | ||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.23607 | + | 1.62460i | −0.389249 | + | 0.282806i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0278640 | + | 0.0857567i | −0.00470988 | + | 0.0144955i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.70820 | 0.774024 | 0.387012 | − | 0.922075i | \(-0.373507\pi\) | ||||
0.387012 | + | 0.922075i | \(0.373507\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.19098 | − | 9.82084i | −0.510966 | − | 1.57259i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.47214 | + | 6.15537i | −1.32313 | + | 0.961307i | −0.323238 | + | 0.946318i | \(0.604771\pi\) |
−0.999888 | + | 0.0149890i | \(0.995229\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.927051 | + | 0.673542i | −0.141374 | + | 0.102714i | −0.656224 | − | 0.754566i | \(-0.727847\pi\) |
0.514850 | + | 0.857280i | \(0.327847\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.236068 | − | 0.726543i | −0.0351909 | − | 0.108307i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.92705 | + | 5.03280i | 1.01041 | + | 0.734109i | 0.964296 | − | 0.264827i | \(-0.0853149\pi\) |
0.0461183 | + | 0.998936i | \(0.485315\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.61803 | + | 4.08174i | 0.802576 | + | 0.583106i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.54508 | + | 4.75528i | −0.216355 | + | 0.665873i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.83688 | − | 8.73102i | −0.389676 | − | 1.19930i | −0.933031 | − | 0.359795i | \(-0.882846\pi\) |
0.543356 | − | 0.839503i | \(-0.317154\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.145898 | − | 0.449028i | 0.0196729 | − | 0.0605469i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15.0000 | 1.98680 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.2812 | + | 7.46969i | 1.33849 | + | 0.972471i | 0.999498 | + | 0.0316830i | \(0.0100867\pi\) |
0.338994 | + | 0.940788i | \(0.389913\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.472136 | 0.0594835 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.42705 | + | 1.03681i | 0.177004 | + | 0.128601i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.00000 | 0.366508 | 0.183254 | − | 0.983066i | \(-0.441337\pi\) | ||||
0.183254 | + | 0.983066i | \(0.441337\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.21885 | − | 3.75123i | 0.146732 | − | 0.451594i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.04508 | + | 12.4495i | 0.480063 | + | 1.47748i | 0.839005 | + | 0.544123i | \(0.183138\pi\) |
−0.358942 | + | 0.933360i | \(0.616862\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.0450850 | − | 0.138757i | 0.00527680 | − | 0.0162403i | −0.948383 | − | 0.317126i | \(-0.897282\pi\) |
0.953660 | + | 0.300886i | \(0.0972822\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.78115 | − | 6.37988i | −1.01396 | − | 0.736685i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.236068 | + | 0.171513i | 0.0269024 | + | 0.0195458i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.89919 | − | 6.46564i | 0.988799 | − | 0.718404i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.35410 | + | 4.61653i | −0.697453 | + | 0.506729i | −0.879102 | − | 0.476634i | \(-0.841857\pi\) |
0.181649 | + | 0.983364i | \(0.441857\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.263932 | − | 0.812299i | −0.0286274 | − | 0.0881062i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.5623 | −1.34682 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.95492 | + | 15.2497i | −0.525220 | + | 1.61646i | 0.238661 | + | 0.971103i | \(0.423292\pi\) |
−0.763880 | + | 0.645358i | \(0.776708\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.881966 | + | 0.640786i | −0.0924552 | + | 0.0671726i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.76393 | − | 12.1392i | −0.286606 | − | 1.25878i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.07295 | + | 1.50609i | −0.212680 | + | 0.154521i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.45492 | − | 4.47777i | 0.147724 | − | 0.454648i | −0.849627 | − | 0.527384i | \(-0.823173\pi\) |
0.997351 | + | 0.0727356i | \(0.0231729\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.47214 | −0.248459 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.85410 | − | 8.78402i | −0.283994 | − | 0.874043i | −0.986698 | − | 0.162561i | \(-0.948024\pi\) |
0.702705 | − | 0.711482i | \(-0.251976\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.78115 | + | 4.20025i | −0.569634 | + | 0.413863i | −0.834972 | − | 0.550292i | \(-0.814516\pi\) |
0.265338 | + | 0.964155i | \(0.414516\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.163119 | + | 0.118513i | −0.0159188 | + | 0.0115657i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.26393 | − | 3.88998i | −0.122189 | − | 0.376059i | 0.871190 | − | 0.490947i | \(-0.163349\pi\) |
−0.993378 | + | 0.114888i | \(0.963349\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.66312 | − | 4.11450i | −0.542428 | − | 0.394097i | 0.282558 | − | 0.959250i | \(-0.408817\pi\) |
−0.824986 | + | 0.565153i | \(0.808817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.51722 | + | 6.18812i | 0.808419 | + | 0.587351i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.44427 | − | 7.52270i | 0.229938 | − | 0.707676i | −0.767815 | − | 0.640672i | \(-0.778656\pi\) |
0.997753 | − | 0.0670040i | \(-0.0213440\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.208204 | + | 0.640786i | 0.0194151 | + | 0.0597536i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.85410 | − | 8.78402i | 0.263862 | − | 0.812083i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.527864 | 0.0483892 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.66312 | + | 5.56758i | 0.696647 | + | 0.506144i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −23.4164 | −2.11139 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.76393 | 0.336656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.28115 | + | 5.29007i | 0.646098 | + | 0.469418i | 0.861940 | − | 0.507011i | \(-0.169250\pi\) |
−0.215842 | + | 0.976428i | \(0.569250\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.56231 | −0.225598 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.33688 | − | 13.3475i | 0.378915 | − | 1.16618i | −0.561884 | − | 0.827216i | \(-0.689923\pi\) |
0.940799 | − | 0.338965i | \(-0.110077\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.489357 | − | 1.50609i | −0.0424326 | − | 0.130594i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.263932 | + | 0.812299i | −0.0227157 | + | 0.0699116i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.47214 | − | 6.15537i | −0.723823 | − | 0.525888i | 0.163780 | − | 0.986497i | \(-0.447631\pi\) |
−0.887603 | + | 0.460608i | \(0.847631\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.3992 | − | 8.28199i | −0.966866 | − | 0.702470i | −0.0121312 | − | 0.999926i | \(-0.503862\pi\) |
−0.954735 | + | 0.297457i | \(0.903862\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.91641 | + | 18.2088i | 0.498251 | + | 1.53346i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.61803 | − | 3.35520i | 0.386179 | − | 0.280576i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.73607 | − | 1.26133i | 0.144173 | − | 0.104748i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.79837 | + | 14.7679i | 0.395763 | + | 1.21803i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.56231 | 0.455682 | 0.227841 | − | 0.973698i | \(-0.426833\pi\) | ||||
0.227841 | + | 0.973698i | \(0.426833\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.66312 | − | 5.11855i | 0.135343 | − | 0.416542i | −0.860300 | − | 0.509787i | \(-0.829724\pi\) |
0.995643 | + | 0.0932453i | \(0.0297241\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.61803 | + | 2.62866i | −0.292501 | + | 0.212514i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.60081 | + | 1.40008i | 0.128580 | + | 0.112457i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.9443 | + | 11.5842i | −1.27249 | + | 0.924519i | −0.999299 | − | 0.0374402i | \(-0.988080\pi\) |
−0.273193 | + | 0.961959i | \(0.588080\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.34346 | − | 19.5232i | 0.503069 | − | 1.54829i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.416408 | −0.0328175 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.45492 | − | 7.55545i | −0.192284 | − | 0.591789i | −0.999998 | − | 0.00221381i | \(-0.999295\pi\) |
0.807714 | − | 0.589575i | \(-0.200705\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.854102 | − | 0.620541i | 0.0664917 | − | 0.0483091i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.0902 | + | 10.9637i | −1.16771 | + | 0.848393i | −0.990733 | − | 0.135822i | \(-0.956633\pi\) |
−0.176979 | + | 0.984215i | \(0.556633\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.57295 | + | 7.91872i | 0.197919 | + | 0.609133i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.8541 | + | 7.88597i | 0.830034 | + | 0.603055i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.78115 | − | 5.65334i | −0.591590 | − | 0.429815i | 0.251294 | − | 0.967911i | \(-0.419144\pi\) |
−0.842884 | + | 0.538095i | \(0.819144\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.354102 | + | 1.08981i | −0.0267676 | + | 0.0823822i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.78115 | + | 27.0256i | 0.660032 | + | 2.03137i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.28115 | − | 7.02067i | 0.170501 | − | 0.524749i | −0.828898 | − | 0.559400i | \(-0.811032\pi\) |
0.999399 | + | 0.0346503i | \(0.0110317\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.4164 | 1.22022 | 0.610111 | − | 0.792316i | \(-0.291125\pi\) | ||||
0.610111 | + | 0.792316i | \(0.291125\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.61803 | + | 2.62866i | 0.267453 | + | 0.194316i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.79837 | −0.132219 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.76393 | −0.202119 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.427051 | − | 0.310271i | −0.0310634 | − | 0.0225689i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.3820 | 1.54714 | 0.773572 | − | 0.633708i | \(-0.218468\pi\) | ||||
0.773572 | + | 0.633708i | \(0.218468\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.51722 | − | 10.8249i | 0.253175 | − | 0.779193i | −0.741009 | − | 0.671496i | \(-0.765652\pi\) |
0.994184 | − | 0.107697i | \(-0.0343477\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.21885 | + | 3.75123i | 0.0872835 | + | 0.268631i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.30902 | − | 25.5725i | 0.591993 | − | 1.82197i | 0.0228342 | − | 0.999739i | \(-0.492731\pi\) |
0.569159 | − | 0.822228i | \(-0.307269\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.7533 | + | 12.8985i | 1.25850 | + | 0.914352i | 0.998683 | − | 0.0513068i | \(-0.0163386\pi\) |
0.259814 | + | 0.965659i | \(0.416339\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.42705 | + | 3.94298i | 0.382795 | + | 0.278117i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.409830 | + | 1.26133i | 0.0287644 | + | 0.0885278i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.23607 | − | 2.35114i | 0.226017 | − | 0.164211i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.85410 | − | 2.07363i | 0.198374 | − | 0.144127i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.56231 | + | 7.88597i | 0.177238 | + | 0.545484i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.88854 | −0.680755 | −0.340378 | − | 0.940289i | \(-0.610555\pi\) | ||||
−0.340378 | + | 0.940289i | \(0.610555\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.04508 | + | 27.8379i | −0.619759 | + | 1.90742i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.354102 | − | 0.257270i | 0.0241496 | − | 0.0175457i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.12868 | + | 0.673542i | −0.0766196 | + | 0.0457230i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.263932 | − | 0.191758i | 0.0178349 | − | 0.0129578i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.19098 | − | 9.82084i | 0.214649 | − | 0.660621i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.47214 | −0.232511 | −0.116256 | − | 0.993219i | \(-0.537089\pi\) | ||||
−0.116256 | + | 0.993219i | \(0.537089\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | − | 9.23305i | −0.200000 | − | 0.615537i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.6803 | − | 14.2986i | 1.30623 | − | 0.949032i | 0.306234 | − | 0.951956i | \(-0.400931\pi\) |
0.999996 | + | 0.00292450i | \(0.000930897\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.7082 | + | 12.1392i | −1.10411 | + | 0.802182i | −0.981726 | − | 0.190301i | \(-0.939054\pi\) |
−0.122383 | + | 0.992483i | \(0.539054\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.201626 | + | 0.620541i | 0.0132660 | + | 0.0408286i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.2533 | − | 11.8087i | −1.06479 | − | 0.773614i | −0.0898201 | − | 0.995958i | \(-0.528629\pi\) |
−0.974968 | + | 0.222344i | \(0.928629\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.64590 | − | 1.92236i | −0.172599 | − | 0.125401i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.909830 | − | 2.80017i | −0.0588520 | − | 0.181128i | 0.917309 | − | 0.398177i | \(-0.130357\pi\) |
−0.976161 | + | 0.217049i | \(0.930357\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.92705 | + | 9.00854i | −0.188548 | + | 0.580291i | −0.999991 | − | 0.00414002i | \(-0.998682\pi\) |
0.811444 | + | 0.584431i | \(0.198682\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.8885 | 1.14755 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.14590 | − | 1.55909i | −0.137096 | − | 0.0996064i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.9787 | −1.97113 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.5623 | −1.11297 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.763932 | + | 0.555029i | 0.0482190 | + | 0.0350331i | 0.611634 | − | 0.791141i | \(-0.290513\pi\) |
−0.563415 | + | 0.826174i | \(0.690513\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.18034 | 0.137077 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.590170 | − | 1.81636i | 0.0369579 | − | 0.113745i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.85410 | − | 24.1724i | −0.489925 | − | 1.50784i | −0.824718 | − | 0.565544i | \(-0.808666\pi\) |
0.334793 | − | 0.942292i | \(-0.391334\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.343459 | − | 1.05706i | 0.0213415 | − | 0.0656824i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.09017 | − | 6.60440i | −0.562667 | − | 0.408802i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.2533 | − | 16.8945i | −1.43386 | − | 1.04176i | −0.989282 | − | 0.146019i | \(-0.953354\pi\) |
−0.444577 | − | 0.895740i | \(-0.646646\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.08359 | + | 3.33495i | 0.0665645 | + | 0.204865i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −29.0066 | + | 21.0745i | −1.77517 | + | 1.28974i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.0172 | + | 7.27794i | −0.610761 | + | 0.443744i | −0.849682 | − | 0.527295i | \(-0.823206\pi\) |
0.238921 | + | 0.971039i | \(0.423206\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.82624 | + | 17.9313i | 0.353919 | + | 1.08925i | 0.956634 | + | 0.291293i | \(0.0940856\pi\) |
−0.602715 | + | 0.797957i | \(0.705914\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.43769 | −0.147536 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.85410 | − | 5.70634i | 0.111807 | − | 0.344105i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.8262 | − | 7.86572i | 0.650486 | − | 0.472605i | −0.212951 | − | 0.977063i | \(-0.568307\pi\) |
0.863437 | + | 0.504457i | \(0.168307\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.38197 | − | 10.2371i | 0.262341 | − | 0.612880i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.35410 | − | 2.43690i | 0.200089 | − | 0.145373i | −0.483229 | − | 0.875494i | \(-0.660536\pi\) |
0.683318 | + | 0.730121i | \(0.260536\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.86475 | − | 18.0498i | 0.348623 | − | 1.07295i | −0.610993 | − | 0.791636i | \(-0.709230\pi\) |
0.959616 | − | 0.281315i | \(-0.0907705\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.72949 | −0.339386 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.763932 | + | 2.35114i | 0.0450935 | + | 0.138783i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.70820 | − | 7.05342i | 0.571071 | − | 0.414907i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.51722 | − | 6.18812i | 0.499288 | − | 0.362754i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.36475 | + | 25.7440i | 0.488674 | + | 1.50398i | 0.826589 | + | 0.562806i | \(0.190278\pi\) |
−0.337915 | + | 0.941177i | \(0.609722\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.92705 | − | 2.85317i | −0.228642 | − | 0.166118i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.23607 | + | 1.62460i | 0.129750 | + | 0.0942688i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.51722 | + | 7.74721i | −0.145575 | + | 0.448033i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.0835921 | + | 0.257270i | 0.00481817 | + | 0.0148288i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.38197 | − | 19.6417i | 0.366634 | − | 1.12838i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.763932 | −0.0437426 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.9164 | + | 15.1967i | 1.19376 | + | 0.867319i | 0.993657 | − | 0.112455i | \(-0.0358715\pi\) |
0.200106 | + | 0.979774i | \(0.435871\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.9787 | −0.908997 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.9443 | 1.07423 | 0.537116 | − | 0.843509i | \(-0.319514\pi\) | ||||
0.537116 | + | 0.843509i | \(0.319514\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.5623 | − | 8.40051i | −0.653540 | − | 0.474825i | 0.210935 | − | 0.977500i | \(-0.432349\pi\) |
−0.864475 | + | 0.502675i | \(0.832349\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.180340 | −0.0101610 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.52786 | − | 4.70228i | 0.0858134 | − | 0.264106i | −0.898937 | − | 0.438077i | \(-0.855660\pi\) |
0.984751 | + | 0.173970i | \(0.0556597\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.14590 | − | 6.60440i | −0.120147 | − | 0.369775i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.82624 | − | 8.69827i | 0.157745 | − | 0.485490i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.1353 | + | 8.81678i | 0.675224 | + | 0.490579i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.1353 | + | 13.1760i | 1.00596 | + | 0.730875i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.83688 | − | 14.8864i | −0.267480 | − | 0.823219i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.63525 | − | 1.18808i | 0.0901545 | − | 0.0655011i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.5451 | + | 9.11454i | −0.689540 | + | 0.500980i | −0.876509 | − | 0.481386i | \(-0.840134\pi\) |
0.186969 | + | 0.982366i | \(0.440134\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.90983 | + | 8.95554i | 0.159458 | + | 0.490760i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.14590 | −0.0626071 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.3541 | + | 31.8666i | −0.564024 | + | 1.73589i | 0.106810 | + | 0.994279i | \(0.465936\pi\) |
−0.670834 | + | 0.741608i | \(0.734064\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.3090 | − | 10.3961i | 0.777159 | − | 0.564639i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.90983 | − | 3.52671i | 0.320035 | − | 0.190982i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.66312 | − | 1.93487i | 0.143795 | − | 0.104473i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.465558 | + | 1.43284i | −0.0250648 | + | 0.0771415i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.47214 | 0.508491 | 0.254245 | − | 0.967140i | \(-0.418173\pi\) | ||||
0.254245 | + | 0.967140i | \(0.418173\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.63525 | + | 23.4989i | 0.408706 | + | 1.25787i | 0.917761 | + | 0.397133i | \(0.129995\pi\) |
−0.509055 | + | 0.860734i | \(0.670005\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.35410 | + | 6.06961i | −0.445909 | + | 0.323972i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.59017 | + | 5.51458i | −0.403984 | + | 0.293512i | −0.771162 | − | 0.636639i | \(-0.780324\pi\) |
0.367178 | + | 0.930151i | \(0.380324\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.54508 | − | 4.75528i | −0.0820046 | − | 0.252384i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.954915 | + | 0.693786i | 0.0505395 | + | 0.0367191i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.97214 | − | 5.06555i | −0.367975 | − | 0.267350i | 0.388396 | − | 0.921493i | \(-0.373029\pi\) |
−0.756371 | + | 0.654143i | \(0.773029\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.03444 | − | 24.7275i | 0.422865 | − | 1.30145i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.54508 | + | 20.1437i | 0.343528 | + | 1.05727i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.0172209 | + | 0.0530006i | −0.000901385 | + | 0.00277418i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.3820 | −0.907331 | −0.453666 | − | 0.891172i | \(-0.649884\pi\) | ||||
−0.453666 | + | 0.891172i | \(0.649884\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.9443 | − | 12.3107i | −0.882084 | − | 0.640871i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.16718 | −0.112515 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.7082 | −0.968674 | −0.484337 | − | 0.874881i | \(-0.660939\pi\) | ||||
−0.484337 | + | 0.874881i | \(0.660939\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.80902 | + | 4.94704i | 0.351616 | + | 0.255464i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.9443 | 1.33620 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.92705 | − | 12.0862i | 0.201719 | − | 0.620827i | −0.798113 | − | 0.602508i | \(-0.794168\pi\) |
0.999832 | − | 0.0183198i | \(-0.00583170\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.21885 | + | 19.1396i | 0.318601 | + | 0.980554i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.89919 | + | 8.92278i | −0.148142 | + | 0.455933i | −0.997402 | − | 0.0720420i | \(-0.977048\pi\) |
0.849260 | + | 0.527975i | \(0.177048\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0901699 | − | 0.0655123i | −0.00459549 | − | 0.00333882i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.85410 | − | 1.34708i | −0.0942493 | − | 0.0684761i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.39919 | + | 25.8500i | 0.425856 | + | 1.31065i | 0.902173 | + | 0.431375i | \(0.141972\pi\) |
−0.476317 | + | 0.879274i | \(0.658028\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.19098 | − | 2.31838i | 0.161375 | − | 0.117246i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 25.3885 | − | 18.4459i | 1.28068 | − | 0.930470i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.1803 | 1.41433 | 0.707165 | − | 0.707048i | \(-0.249974\pi\) | ||||
0.707165 | + | 0.707048i | \(0.249974\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.09424 | − | 3.36771i | 0.0547803 | − | 0.168596i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.7533 | + | 12.8985i | −0.886557 | + | 0.644121i | −0.934978 | − | 0.354706i | \(-0.884581\pi\) |
0.0484211 | + | 0.998827i | \(0.484581\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.70820 | + | 25.0705i | 0.284346 | + | 1.24885i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.39919 | + | 2.46965i | −0.168907 | + | 0.122718i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.79837 | + | 5.53483i | −0.0891421 | + | 0.274351i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.76393 | 0.235561 | 0.117781 | − | 0.993040i | \(-0.462422\pi\) | ||||
0.117781 | + | 0.993040i | \(0.462422\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.23607 | − | 22.2703i | −0.356929 | − | 1.09851i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.42705 | − | 1.76336i | 0.119427 | − | 0.0867691i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.42705 | − | 1.76336i | 0.119139 | − | 0.0865597i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.73607 | − | 29.9645i | −0.476777 | − | 1.46737i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.85410 | + | 3.52671i | 0.237138 | + | 0.172291i | 0.700007 | − | 0.714136i | \(-0.253180\pi\) |
−0.462869 | + | 0.886427i | \(0.653180\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.38197 | − | 1.00406i | −0.0673529 | − | 0.0489347i | 0.553599 | − | 0.832783i | \(-0.313254\pi\) |
−0.620952 | + | 0.783848i | \(0.713254\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.29180 | + | 16.2865i | −0.257296 | + | 0.791875i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.35410 | − | 10.3229i | −0.162698 | − | 0.500732i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.145898 | − | 0.449028i | 0.00706050 | − | 0.0217300i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.7639 | 0.616248 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.145898 | − | 0.106001i | −0.00702766 | − | 0.00510589i | 0.584266 | − | 0.811562i | \(-0.301383\pi\) |
−0.591294 | + | 0.806456i | \(0.701383\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.4164 | 0.933093 | 0.466547 | − | 0.884497i | \(-0.345498\pi\) | ||||
0.466547 | + | 0.884497i | \(0.345498\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.79837 | 0.230064 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.57295 | − | 6.95515i | −0.457936 | − | 0.332710i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.7082 | −0.606529 | −0.303265 | − | 0.952906i | \(-0.598077\pi\) | ||||
−0.303265 | + | 0.952906i | \(0.598077\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.29180 | + | 13.2088i | −0.204371 | + | 0.628990i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.14590 | − | 3.52671i | −0.0544433 | − | 0.167559i | 0.920138 | − | 0.391595i | \(-0.128077\pi\) |
−0.974581 | + | 0.224036i | \(0.928077\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.89261 | − | 5.82485i | 0.0897183 | − | 0.276124i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.0623 | + | 7.31069i | 0.475931 | + | 0.345784i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.61803 | − | 4.80828i | −0.312324 | − | 0.226917i | 0.420569 | − | 0.907261i | \(-0.361831\pi\) |
−0.732893 | + | 0.680344i | \(0.761831\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.00000 | − | 12.3107i | −0.188353 | − | 0.579690i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.73607 | − | 7.07367i | 0.457440 | − | 0.332350i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.336881 | − | 0.244758i | 0.0157932 | − | 0.0114745i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.15248 | − | 22.0131i | −0.334579 | − | 1.02973i | −0.966929 | − | 0.255045i | \(-0.917910\pi\) |
0.632350 | − | 0.774682i | \(-0.282090\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.00000 | 0.233380 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.84346 | − | 21.0620i | 0.318732 | − | 0.980955i | −0.655459 | − | 0.755230i | \(-0.727525\pi\) |
0.974191 | − | 0.225725i | \(-0.0724750\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.61803 | − | 1.90211i | 0.121670 | − | 0.0883987i | −0.525286 | − | 0.850926i | \(-0.676042\pi\) |
0.646956 | + | 0.762527i | \(0.276042\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.05573 | + | 4.63677i | 0.0489582 | + | 0.215025i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.3713 | + | 19.1599i | −1.22032 | + | 0.886614i | −0.996127 | − | 0.0879310i | \(-0.971975\pi\) |
−0.224193 | + | 0.974545i | \(0.571975\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.218847 | − | 0.673542i | 0.0101054 | − | 0.0311013i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −44.0689 | −2.03059 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.437694 | − | 1.34708i | −0.0201252 | − | 0.0619390i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26.3435 | + | 19.1396i | −1.20872 | + | 0.878187i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.8541 | − | 10.7921i | 0.680123 | − | 0.494138i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.65248 | + | 14.3188i | 0.212577 | + | 0.654245i | 0.999317 | + | 0.0369600i | \(0.0117674\pi\) |
−0.786740 | + | 0.617285i | \(0.788233\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.5902 | − | 12.7800i | −0.802043 | − | 0.582718i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.753289 | − | 0.547296i | −0.0342758 | − | 0.0249028i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.555728 | + | 1.71036i | −0.0252343 | + | 0.0776632i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.71885 | − | 14.5231i | −0.213831 | − | 0.658105i | −0.999234 | − | 0.0391207i | \(-0.987544\pi\) |
0.785403 | − | 0.618985i | \(-0.212456\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.48936 | − | 16.8945i | 0.248237 | − | 0.763996i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.0689 | −1.62777 | −0.813883 | − | 0.581029i | \(-0.802650\pi\) | ||||
−0.813883 | + | 0.581029i | \(0.802650\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.1631 | − | 7.38394i | −0.457724 | − | 0.332556i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.944272 | 0.0424419 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.09017 | 0.138613 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.0172 | + | 10.9106i | 0.672263 | + | 0.488428i | 0.870782 | − | 0.491669i | \(-0.163613\pi\) |
−0.198519 | + | 0.980097i | \(0.563613\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −41.7082 | −1.86339 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.22542 | + | 22.2376i | −0.322166 | + | 0.991524i | 0.650538 | + | 0.759474i | \(0.274543\pi\) |
−0.972704 | + | 0.232051i | \(0.925457\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.09017 | + | 3.35520i | 0.0485119 | + | 0.149304i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.75329 | + | 17.7068i | −0.255513 | + | 0.786387i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.40983 | − | 1.02430i | −0.0624896 | − | 0.0454014i | 0.556102 | − | 0.831114i | \(-0.312296\pi\) |
−0.618592 | + | 0.785713i | \(0.712296\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0278640 | − | 0.0202444i | −0.00123263 | − | 0.000895560i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.63525 | − | 14.2658i | −0.204652 | − | 0.629853i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.20820 | − | 1.60435i | 0.0973051 | − | 0.0706963i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.56231 | + | 6.22088i | −0.376570 | + | 0.273594i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.64590 | − | 20.4540i | −0.291723 | − | 0.897830i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.6525 | −1.21148 | −0.605738 | − | 0.795664i | \(-0.707122\pi\) | ||||
−0.605738 | + | 0.795664i | \(0.707122\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.7254 | − | 36.0871i | 0.512717 | − | 1.57798i | −0.274681 | − | 0.961535i | \(-0.588572\pi\) |
0.787398 | − | 0.616445i | \(-0.211428\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.07295 | + | 1.50609i | −0.0904709 | + | 0.0657310i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.89919 | − | 11.4454i | 0.213412 | − | 0.498571i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.0902 | − | 11.6902i | 0.699573 | − | 0.508269i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.85410 | + | 24.1724i | −0.340839 | + | 1.04899i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 48.3607 | 2.09473 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.482779 | + | 1.48584i | 0.0208724 | + | 0.0642385i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.3541 | − | 9.70232i | 0.576272 | − | 0.418686i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.94427 | + | 5.04531i | −0.299111 | + | 0.217317i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.96556 | − | 12.2047i | −0.170493 | − | 0.524722i | 0.828906 | − | 0.559387i | \(-0.188964\pi\) |
−0.999399 | + | 0.0346650i | \(0.988964\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 29.6976 | + | 21.5765i | 1.27444 | + | 0.925938i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.16312 | + | 1.57160i | 0.0926578 | + | 0.0673199i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.58359 | − | 4.87380i | 0.0677095 | − | 0.208388i | −0.911477 | − | 0.411351i | \(-0.865057\pi\) |
0.979186 | + | 0.202963i | \(0.0650570\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.23607 | + | 3.80423i | 0.0527541 | + | 0.162360i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.6459 | + | 35.8424i | −0.496132 | + | 1.52694i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.25329 | − | 2.36365i | −0.138094 | − | 0.100331i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.0000 | 1.27114 | 0.635570 | − | 0.772043i | \(-0.280765\pi\) | ||||
0.635570 | + | 0.772043i | \(0.280765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.29180 | 0.223819 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.00000 | − | 3.63271i | −0.211100 | − | 0.153373i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.61803 | −0.194627 | −0.0973135 | − | 0.995254i | \(-0.531025\pi\) | ||||
−0.0973135 | + | 0.995254i | \(0.531025\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.933629 | + | 2.87341i | −0.0392781 | + | 0.120885i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.802439 | − | 2.46965i | −0.0336993 | − | 0.103716i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.14590 | + | 12.7598i | −0.173805 | + | 0.534917i | −0.999577 | − | 0.0290873i | \(-0.990740\pi\) |
0.825772 | + | 0.564004i | \(0.190740\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.8435 | − | 18.0498i | −1.03967 | − | 0.755362i | −0.0694460 | − | 0.997586i | \(-0.522123\pi\) |
−0.970220 | + | 0.242224i | \(0.922123\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 38.6803 | + | 28.1029i | 1.61589 | + | 1.17402i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.64590 | + | 8.14324i | 0.110342 | + | 0.339596i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.3992 | − | 12.6412i | 0.724338 | − | 0.526262i | −0.163429 | − | 0.986555i | \(-0.552256\pi\) |
0.887767 | + | 0.460293i | \(0.152256\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.5902 | − | 14.9596i | 0.855698 | − | 0.621701i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.572949 | + | 1.76336i | 0.0237699 | + | 0.0731563i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.3475 | 0.469966 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.09017 | + | 3.35520i | −0.0450730 | + | 0.138720i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.0450850 | + | 0.0327561i | −0.00186086 | + | 0.00135199i | −0.588715 | − | 0.808340i | \(-0.700366\pi\) |
0.586854 | + | 0.809692i | \(0.300366\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −37.1976 | − | 3.36771i | −1.53270 | − | 0.138764i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 48.6418 | − | 35.3404i | 2.00086 | − | 1.45371i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.8885 | + | 42.7445i | −0.570334 | + | 1.75531i | 0.0812097 | + | 0.996697i | \(0.474122\pi\) |
−0.651544 | + | 0.758611i | \(0.725878\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.201626 | −0.00826587 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.1631 | + | 46.6673i | 0.620585 | + | 1.90996i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.3541 | − | 12.6085i | 0.709069 | − | 0.515169i | −0.173804 | − | 0.984780i | \(-0.555606\pi\) |
0.882873 | + | 0.469611i | \(0.155606\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.2705 | − | 17.6336i | 0.990015 | − | 0.719288i | 0.0300904 | − | 0.999547i | \(-0.490420\pi\) |
0.959924 | + | 0.280259i | \(0.0904205\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.85410 | + | 5.70634i | 0.0755049 | + | 0.232380i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.92705 | − | 2.12663i | −0.119002 | − | 0.0864597i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.0902 | + | 14.5964i | 0.815435 | + | 0.592448i | 0.915401 | − | 0.402543i | \(-0.131874\pi\) |
−0.0999664 | + | 0.994991i | \(0.531874\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.916408 | + | 2.82041i | −0.0371347 | + | 0.114289i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.2188 | − | 37.6057i | −0.494322 | − | 1.52137i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.85410 | + | 30.3278i | −0.398003 | + | 1.22493i | 0.528594 | + | 0.848875i | \(0.322719\pi\) |
−0.926598 | + | 0.376054i | \(0.877281\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.94427 | 0.360668 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.71885 | + | 1.24882i | 0.0691982 | + | 0.0502754i | 0.621847 | − | 0.783139i | \(-0.286383\pi\) |
−0.552648 | + | 0.833415i | \(0.686383\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.8328 | 1.56082 | 0.780411 | − | 0.625266i | \(-0.215010\pi\) | ||||
0.780411 | + | 0.625266i | \(0.215010\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.94427 | −0.158278 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.06231 | + | 2.22490i | 0.122689 | + | 0.0891386i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.8328 | 0.913313 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.72949 | + | 17.6336i | −0.228814 | + | 0.704216i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.25329 | + | 10.0126i | 0.129717 | + | 0.399228i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.68034 | + | 23.6377i | −0.305750 | + | 0.941000i | 0.673647 | + | 0.739053i | \(0.264727\pi\) |
−0.979396 | + | 0.201947i | \(0.935273\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.8885 | − | 12.9968i | −0.711006 | − | 0.516576i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.78115 | − | 2.02063i | −0.110367 | − | 0.0801861i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.90983 | − | 30.4993i | −0.392642 | − | 1.20843i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −21.1803 | + | 15.3884i | −0.837881 | + | 0.608756i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.0517 | + | 26.1931i | −1.42396 | + | 1.03456i | −0.432852 | + | 0.901465i | \(0.642493\pi\) |
−0.991103 | + | 0.133099i | \(0.957507\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.38854 | − | 25.8173i | −0.330812 | − | 1.01813i | −0.968748 | − | 0.248045i | \(-0.920212\pi\) |
0.637937 | − | 0.770089i | \(-0.279788\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.978714 | 0.0385368 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.29180 | − | 13.2088i | 0.168728 | − | 0.519291i | −0.830564 | − | 0.556924i | \(-0.811982\pi\) |
0.999292 | + | 0.0376325i | \(0.0119816\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.7082 | + | 9.23305i | −0.498841 | + | 0.362429i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.92705 | − | 0.265003i | −0.114720 | − | 0.0103863i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.89919 | − | 5.73910i | 0.309119 | − | 0.224588i | −0.422399 | − | 0.906410i | \(-0.638812\pi\) |
0.731518 | + | 0.681822i | \(0.238812\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.65654 | + | 5.09831i | −0.0647264 | + | 0.199207i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.291796 | 0.0113840 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.91641 | − | 8.97578i | −0.113607 | − | 0.349647i | 0.878047 | − | 0.478575i | \(-0.158846\pi\) |
−0.991654 | + | 0.128928i | \(0.958846\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.9615 | + | 23.2214i | −1.24316 | + | 0.903207i | −0.997805 | − | 0.0662266i | \(-0.978904\pi\) |
−0.245353 | + | 0.969434i | \(0.578904\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.6803 | − | 13.5721i | 0.725484 | − | 0.527095i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.186918 | + | 0.575274i | 0.00724836 | + | 0.0223082i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.01722 | + | 5.82485i | 0.310428 | + | 0.225539i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.28115 | − | 4.56352i | −0.242843 | − | 0.176436i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.763932 | + | 2.35114i | −0.0294913 | + | 0.0907648i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.72542 | − | 5.31031i | −0.0665102 | − | 0.204697i | 0.912278 | − | 0.409571i | \(-0.134322\pi\) |
−0.978788 | + | 0.204874i | \(0.934322\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.35410 | + | 10.3229i | −0.129099 | + | 0.397327i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.0689 | −1.15564 | −0.577821 | − | 0.816164i | \(-0.696097\pi\) | ||||
−0.577821 | + | 0.816164i | \(0.696097\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.899187 | − | 0.653298i | −0.0345076 | − | 0.0250713i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 54.3951 | 2.08443 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.5967 | 1.40034 | 0.700168 | − | 0.713978i | \(-0.253109\pi\) | ||||
0.700168 | + | 0.713978i | \(0.253109\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.23607 | + | 2.35114i | 0.123644 | + | 0.0898325i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −46.1803 | −1.76189 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.1008 | + | 40.3202i | −0.499101 | + | 1.53608i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.0385072 | + | 0.118513i | 0.00146488 | + | 0.00450844i | 0.951786 | − | 0.306762i | \(-0.0992455\pi\) |
−0.950321 | + | 0.311270i | \(0.899246\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.180340 | + | 0.555029i | −0.00685055 | + | 0.0210838i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.35410 | + | 3.16344i | 0.165161 | + | 0.119996i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.9443 | − | 13.7638i | −0.717565 | − | 0.521342i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.8820 | − | 42.7243i | −0.525064 | − | 1.61598i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.63525 | + | 1.91462i | −0.0995322 | + | 0.0723144i | −0.636438 | − | 0.771328i | \(-0.719593\pi\) |
0.536906 | + | 0.843642i | \(0.319593\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.5517 | − | 18.5644i | 0.963699 | − | 0.700168i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.25987 | − | 6.95515i | −0.0851115 | − | 0.261946i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.18034 | −0.0820001 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.7705 | − | 33.1482i | 0.404495 | − | 1.24491i | −0.516821 | − | 0.856093i | \(-0.672885\pi\) |
0.921316 | − | 0.388814i | \(-0.127115\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.86475 | + | 9.02878i | −0.144736 | + | 0.338131i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.76393 | + | 1.28157i | −0.0659673 | + | 0.0479281i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.03444 | − | 6.26137i | 0.0759776 | − | 0.233835i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.79837 | 0.365418 | 0.182709 | − | 0.983167i | \(-0.441513\pi\) | ||||
0.182709 | + | 0.983167i | \(0.441513\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.521286 | + | 1.60435i | 0.0194137 | + | 0.0597493i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.1353 | + | 12.4495i | −0.637267 | + | 0.463002i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.0623 | − | 16.0292i | 0.819373 | − | 0.595310i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.12868 | + | 9.62908i | 0.116036 | + | 0.357123i | 0.992162 | − | 0.124960i | \(-0.0398804\pi\) |
−0.876126 | + | 0.482083i | \(0.839880\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.66312 | + | 4.11450i | 0.209745 | + | 0.152389i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.07295 | − | 1.50609i | −0.0766708 | − | 0.0557046i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.9615 | + | 33.7360i | −0.404872 | + | 1.24607i | 0.516130 | + | 0.856510i | \(0.327372\pi\) |
−0.921002 | + | 0.389558i | \(0.872628\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.83282 | − | 5.64083i | −0.0676044 | − | 0.208065i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.14590 | + | 3.52671i | −0.0422097 | + | 0.129908i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.29180 | 0.157876 | 0.0789381 | − | 0.996880i | \(-0.474847\pi\) | ||||
0.0789381 | + | 0.996880i | \(0.474847\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −56.0410 | − | 40.7162i | −2.05872 | − | 1.49575i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.0344 | 0.734992 | 0.367496 | − | 0.930025i | \(-0.380215\pi\) | ||||
0.367496 | + | 0.930025i | \(0.380215\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.12461 | −0.0778398 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.7082 | − | 9.23305i | −0.464969 | − | 0.337820i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.965558 | −0.0352807 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.9615 | − | 42.9691i | 0.509462 | − | 1.56796i | −0.283675 | − | 0.958920i | \(-0.591554\pi\) |
0.793137 | − | 0.609043i | \(-0.208446\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.652476 | + | 2.00811i | 0.0237775 | + | 0.0731797i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.635255 | + | 1.95511i | −0.0231193 | + | 0.0711539i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.2705 | + | 19.8132i | 0.991164 | + | 0.720122i | 0.960176 | − | 0.279397i | \(-0.0901346\pi\) |
0.0309880 | + | 0.999520i | \(0.490135\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.94427 | + | 2.86568i | 0.143168 | + | 0.104018i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.6418 | + | 45.0629i | 0.530766 | + | 1.63353i | 0.752624 | + | 0.658451i | \(0.228788\pi\) |
−0.221858 | + | 0.975079i | \(0.571212\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.33688 | + | 0.971301i | −0.0483983 | + | 0.0351635i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.38197 | − | 1.00406i | 0.0499651 | − | 0.0363018i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.1353 | − | 55.8146i | −0.654826 | − | 2.01535i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.2016 | −0.728489 | −0.364245 | − | 0.931303i | \(-0.618673\pi\) | ||||
−0.364245 | + | 0.931303i | \(0.618673\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.5623 | − | 54.0512i | 0.632491 | − | 1.94661i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.545085 | + | 0.396027i | −0.0196053 | + | 0.0142441i | −0.597545 | − | 0.801836i | \(-0.703857\pi\) |
0.577939 | + | 0.816080i | \(0.303857\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.3435 | + | 17.7926i | 0.730759 | + | 0.639128i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.01064 | − | 1.46082i | 0.0721314 | − | 0.0524065i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.7082 | + | 66.8110i | −0.777777 | + | 2.39375i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.1803 | −0.578978 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.88197 | + | 11.9475i | 0.138730 | + | 0.426967i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.09017 | − | 4.42477i | 0.217367 | − | 0.157927i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.0451 | + | 14.5636i | −0.714530 | + | 0.519137i | −0.884632 | − | 0.466290i | \(-0.845590\pi\) |
0.170102 | + | 0.985426i | \(0.445590\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.8607 | − | 61.1249i | −0.707059 | − | 2.17610i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.51064 | − | 1.09755i | −0.0537123 | − | 0.0390243i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.47214 | − | 5.42882i | −0.265343 | − | 0.192783i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.42299 | + | 7.45718i | −0.0859344 | + | 0.264479i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.8541 | − | 42.6385i | −0.490737 | − | 1.51033i | −0.823496 | − | 0.567322i | \(-0.807979\pi\) |
0.332758 | − | 0.943012i | \(-0.392021\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.91641 | + | 18.2088i | −0.209307 | + | 0.644182i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.0689 | −1.13310 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.145898 | + | 0.106001i | 0.00514863 | + | 0.00374070i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.159054 | 0.00560590 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.6869 | −0.974626 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.7254 | − | 15.0579i | −0.728667 | − | 0.529408i | 0.160474 | − | 0.987040i | \(-0.448698\pi\) |
−0.889142 | + | 0.457632i | \(0.848698\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.2918 | −0.607197 | −0.303599 | − | 0.952800i | \(-0.598188\pi\) | ||||
−0.303599 | + | 0.952800i | \(0.598188\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.0279 | + | 40.0956i | −0.456907 | + | 1.40622i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.937694 | + | 2.88593i | 0.0328460 | + | 0.101090i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.37539 | + | 7.31069i | −0.0831043 | + | 0.255769i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.76393 | − | 1.28157i | −0.0616368 | − | 0.0447817i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.8541 | + | 13.6983i | 0.658013 | + | 0.478074i | 0.865991 | − | 0.500059i | \(-0.166688\pi\) |
−0.207979 | + | 0.978133i | \(0.566688\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.489357 | − | 1.50609i | −0.0170579 | − | 0.0524988i | 0.942165 | − | 0.335149i | \(-0.108787\pi\) |
−0.959223 | + | 0.282650i | \(0.908787\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.8541 | − | 7.88597i | 0.377891 | − | 0.274554i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.5000 | − | 11.2614i | 0.538988 | − | 0.391598i | −0.284721 | − | 0.958610i | \(-0.591901\pi\) |
0.823709 | + | 0.567013i | \(0.191901\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.56231 | + | 7.88597i | 0.0889926 | + | 0.273891i | 0.985642 | − | 0.168851i | \(-0.0540057\pi\) |
−0.896649 | + | 0.442742i | \(0.854006\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.9230 | 1.03802 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.79837 | + | 14.7679i | −0.166254 | + | 0.511677i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.76393 | − | 4.18774i | 0.199469 | − | 0.144923i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.6910 | + | 6.37988i | −0.369534 | + | 0.220521i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.3713 | + | 16.9803i | −0.806868 | + | 0.586224i | −0.912921 | − | 0.408137i | \(-0.866179\pi\) |
0.106053 | + | 0.994360i | \(0.466179\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.791796 | − | 2.43690i | 0.0273033 | − | 0.0840310i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.27051 | 0.319293 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.982779 | − | 3.02468i | −0.0338086 | − | 0.104052i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.80902 | − | 1.31433i | 0.0621586 | − | 0.0451608i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 34.3328 | − | 24.9443i | 1.17830 | − | 0.856084i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.56637 | − | 7.89848i | −0.0879741 | − | 0.270756i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.7082 | − | 9.95959i | −0.469360 | − | 0.341010i | 0.327832 | − | 0.944736i | \(-0.393682\pi\) |
−0.797192 | + | 0.603726i | \(0.793682\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.14590 | − | 3.01217i | −0.141787 | − | 0.103014i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.0902 | − | 31.0543i | 0.344674 | − | 1.06080i | −0.617085 | − | 0.786897i | \(-0.711686\pi\) |
0.961758 | − | 0.273900i | \(-0.0883136\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.07295 | + | 21.7683i | 0.241326 | + | 0.742725i | 0.996219 | + | 0.0868770i | \(0.0276887\pi\) |
−0.754893 | + | 0.655848i | \(0.772311\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.70820 | + | 5.25731i | −0.0582154 | + | 0.179169i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.6180 | −1.38265 | −0.691327 | − | 0.722542i | \(-0.742974\pi\) | ||||
−0.691327 | + | 0.722542i | \(0.742974\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.97214 | + | 2.15938i | 0.101056 | + | 0.0734212i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.8328 | 0.911290 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.2082 | − | 8.14324i | −0.379776 | − | 0.275923i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.41641 | 0.318697 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.274575 | − | 0.845055i | 0.00928233 | − | 0.0285681i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.18034 | + | 9.78808i | 0.107392 | + | 0.330520i | 0.990285 | − | 0.139056i | \(-0.0444068\pi\) |
−0.882892 | + | 0.469576i | \(0.844407\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.7041 | + | 57.5654i | −0.630875 | + | 1.94163i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.1910 | + | 9.58381i | 0.444416 | + | 0.322887i | 0.787387 | − | 0.616459i | \(-0.211433\pi\) |
−0.342971 | + | 0.939346i | \(0.611433\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.4058 | + | 27.1769i | 1.25880 | + | 0.914575i | 0.998698 | − | 0.0510053i | \(-0.0162425\pi\) |
0.260106 | + | 0.965580i | \(0.416243\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.35410 | − | 10.3229i | −0.112747 | − | 0.346999i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.59017 | − | 1.88187i | 0.0869694 | − | 0.0631870i | −0.543451 | − | 0.839441i | \(-0.682883\pi\) |
0.630420 | + | 0.776254i | \(0.282883\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.71885 | − | 1.24882i | 0.0576483 | − | 0.0418839i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.20163 | + | 12.9313i | 0.140760 | + | 0.433214i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 57.4377 | 1.92208 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.871323 | + | 2.68166i | −0.0291251 | + | 0.0896379i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.7361 | + | 10.7064i | −0.492023 | + | 0.357476i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31.1525 | + | 2.82041i | 1.03899 | + | 0.0940661i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.6074 | − | 12.0660i | 0.553272 | − | 0.401976i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.186918 | + | 0.575274i | −0.00622023 | + | 0.0191439i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.27051 | −0.208439 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.7877 | + | 48.5896i | 0.524223 | + | 1.61339i | 0.765847 | + | 0.643023i | \(0.222320\pi\) |
−0.241624 | + | 0.970370i | \(0.577680\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.9443 | − | 10.8576i | 0.495670 | − | 0.360125i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.23607 | − | 5.98385i | 0.272873 | − | 0.198254i | −0.442930 | − | 0.896556i | \(-0.646061\pi\) |
0.715803 | + | 0.698302i | \(0.246061\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.00000 | − | 9.23305i | −0.0992855 | − | 0.305569i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.38197 | − | 1.00406i | −0.0456864 | − | 0.0331931i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.68034 | − | 1.94738i | −0.0885126 | − | 0.0643082i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.16312 | − | 25.1235i | 0.269276 | − | 0.828748i | −0.721401 | − | 0.692518i | \(-0.756501\pi\) |
0.990677 | − | 0.136230i | \(-0.0434986\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.8647 | + | 54.9820i | 0.588663 | + | 1.81172i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.6803 | − | 57.4922i | 0.614871 | − | 1.89238i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.8541 | −0.751438 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.5623 | − | 8.40051i | −0.379756 | − | 0.275909i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.8197 | 0.748689 | 0.374344 | − | 0.927290i | \(-0.377868\pi\) | ||||
0.374344 | + | 0.927290i | \(0.377868\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 46.5836 | 1.52672 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 34.2705 | + | 24.8990i | 1.12197 | + | 0.815156i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.05573 | 0.0345260 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.9828 | + | 52.2676i | −0.554803 | + | 1.70751i | 0.141659 | + | 0.989915i | \(0.454756\pi\) |
−0.696462 | + | 0.717593i | \(0.745244\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.87539 | − | 30.3933i | −0.322271 | − | 0.991849i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.1246 | − | 52.7041i | 0.558246 | − | 1.71811i | −0.128966 | − | 0.991649i | \(-0.541166\pi\) |
0.687212 | − | 0.726457i | \(-0.258834\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.9443 | + | 10.8576i | 0.486652 | + | 0.353574i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.163119 | + | 0.118513i | 0.00530626 | + | 0.00385522i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.742646 | − | 2.28563i | −0.0241327 | − | 0.0742730i | 0.938265 | − | 0.345918i | \(-0.112432\pi\) |
−0.962398 | + | 0.271645i | \(0.912432\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.545085 | + | 0.396027i | −0.0176942 | + | 0.0128556i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.94427 | − | 6.49839i | 0.290038 | − | 0.210725i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.73607 | + | 5.34307i | 0.0562368 | + | 0.173079i | 0.975229 | − | 0.221196i | \(-0.0709959\pi\) |
−0.918993 | + | 0.394275i | \(0.870996\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.16718 | −0.264284 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.79837 | − | 14.7679i | 0.155109 | − | 0.477378i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.00000 | + | 1.45309i | −0.0645834 | + | 0.0469226i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.12868 | + | 30.7238i | 0.133183 | + | 0.991091i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.61803 | − | 4.80828i | 0.213263 | − | 0.154945i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.34346 | + | 4.13474i | −0.0432475 | + | 0.133102i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.1115 | −0.421636 | −0.210818 | − | 0.977525i | \(-0.567613\pi\) | ||||
−0.210818 | + | 0.977525i | \(0.567613\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.3647 | + | 31.8994i | 0.332964 | + | 1.02476i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.02786 | − | 1.47333i | 0.0650773 | − | 0.0472814i | −0.554771 | − | 0.832003i | \(-0.687194\pi\) |
0.619848 | + | 0.784722i | \(0.287194\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.69098 | + | 1.95511i | −0.0862690 | + | 0.0626781i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15.4894 | + | 47.6713i | 0.496056 | + | 1.52670i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.7082 | + | 16.4985i | 0.726500 | + | 0.527833i | 0.888454 | − | 0.458965i | \(-0.151780\pi\) |
−0.161954 | + | 0.986798i | \(0.551780\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.0344 | − | 11.6497i | −0.512463 | − | 0.372326i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.32624 | − | 13.3148i | 0.138126 | − | 0.425109i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.3713 | − | 47.3081i | −0.490269 | − | 1.50889i | −0.824202 | − | 0.566296i | \(-0.808376\pi\) |
0.333933 | − | 0.942597i | \(-0.391624\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.17376 | + | 9.76784i | −0.101124 | + | 0.311229i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.51973 | 0.143865 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.63525 | + | 1.18808i | 0.0519981 | + | 0.0377788i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.9787 | −0.507581 | −0.253790 | − | 0.967259i | \(-0.581677\pi\) | ||||
−0.253790 | + | 0.967259i | \(0.581677\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −34.6738 | −1.10034 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.78115 | − | 4.92680i | −0.214977 | − | 0.156190i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.8885 | −1.35829 | −0.679147 | − | 0.734002i | \(-0.737650\pi\) | ||||
−0.679147 | + | 0.734002i | \(0.737650\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.25329 | − | 10.0126i | 0.102930 | − | 0.316784i |
(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 | 124.2.f.b.109.1 | yes | 4 | |
3.2 | odd | 2 | 1116.2.m.c.109.1 | 4 | |||
4.3 | odd | 2 | 496.2.n.a.481.1 | 4 | |||
31.2 | even | 5 | inner | 124.2.f.b.33.1 | ✓ | 4 | |
31.8 | even | 5 | 3844.2.a.g.1.1 | 2 | |||
31.23 | odd | 10 | 3844.2.a.f.1.2 | 2 | |||
93.2 | odd | 10 | 1116.2.m.c.901.1 | 4 | |||
124.95 | odd | 10 | 496.2.n.a.33.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
124.2.f.b.33.1 | ✓ | 4 | 31.2 | even | 5 | inner | |
124.2.f.b.109.1 | yes | 4 | 1.1 | even | 1 | trivial | |
496.2.n.a.33.1 | 4 | 124.95 | odd | 10 | |||
496.2.n.a.481.1 | 4 | 4.3 | odd | 2 | |||
1116.2.m.c.109.1 | 4 | 3.2 | odd | 2 | |||
1116.2.m.c.901.1 | 4 | 93.2 | odd | 10 | |||
3844.2.a.f.1.2 | 2 | 31.23 | odd | 10 | |||
3844.2.a.g.1.1 | 2 | 31.8 | even | 5 |