Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(25,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.q (of order \(3\), degree \(2\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 25.9 | ||
Character | \(\chi\) | \(=\) | 504.25 |
Dual form | 504.2.q.c.121.9 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.04182 | − | 1.38370i | 0.601493 | − | 0.798878i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.33425 | − | 2.31099i | 0.596696 | − | 1.03351i | −0.396609 | − | 0.917988i | \(-0.629813\pi\) |
0.993305 | − | 0.115520i | \(-0.0368535\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.54743 | − | 0.714566i | 0.962838 | − | 0.270081i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.829236 | − | 2.88312i | −0.276412 | − | 0.961039i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.99189 | + | 3.45005i | 0.600577 | + | 1.04023i | 0.992734 | + | 0.120332i | \(0.0383958\pi\) |
−0.392157 | + | 0.919898i | \(0.628271\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00103 | + | 1.73384i | 0.277636 | + | 0.480880i | 0.970797 | − | 0.239903i | \(-0.0771156\pi\) |
−0.693161 | + | 0.720783i | \(0.743782\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.80767 | − | 4.25383i | −0.466738 | − | 1.09834i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.57175 | + | 6.18646i | −0.866278 | + | 1.50044i | −0.000504947 | 1.00000i | \(0.500161\pi\) | |
−0.865773 | + | 0.500437i | \(0.833173\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.01956 | − | 6.96208i | −0.922150 | − | 1.59721i | −0.796082 | − | 0.605189i | \(-0.793097\pi\) |
−0.126068 | − | 0.992022i | \(-0.540236\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.66521 | − | 4.26932i | 0.363379 | − | 0.931641i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.443909 | − | 0.768873i | 0.0925614 | − | 0.160321i | −0.816027 | − | 0.578014i | \(-0.803828\pi\) |
0.908588 | + | 0.417693i | \(0.137161\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.06046 | − | 1.83677i | −0.212092 | − | 0.367355i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.85327 | − | 1.85627i | −0.934013 | − | 0.357239i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.35035 | + | 2.33887i | −0.250753 | + | 0.434317i | −0.963733 | − | 0.266867i | \(-0.914012\pi\) |
0.712980 | + | 0.701184i | \(0.247345\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.22989 | −0.220894 | −0.110447 | − | 0.993882i | \(-0.535228\pi\) | ||||
−0.110447 | + | 0.993882i | \(0.535228\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.84901 | + | 0.838152i | 1.19226 | + | 0.145903i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.74756 | − | 6.84051i | 0.295391 | − | 1.15626i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.26528 | + | 9.11973i | 0.865607 | + | 1.49928i | 0.866443 | + | 0.499275i | \(0.166400\pi\) |
−0.000836477 | 1.00000i | \(0.500266\pi\) | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.44200 | + | 0.421217i | 0.551161 | + | 0.0674486i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.43477 | − | 2.48509i | −0.224073 | − | 0.388105i | 0.731968 | − | 0.681339i | \(-0.238602\pi\) |
−0.956041 | + | 0.293234i | \(0.905269\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.40053 | − | 5.88989i | 0.518576 | − | 0.898200i | −0.481191 | − | 0.876616i | \(-0.659796\pi\) |
0.999767 | − | 0.0215840i | \(-0.00687093\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.76928 | − | 1.93045i | −1.15818 | − | 0.287774i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.1369 | −1.77035 | −0.885175 | − | 0.465258i | \(-0.845961\pi\) | ||||
−0.885175 | + | 0.465258i | \(0.845961\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.97879 | − | 3.64061i | 0.854113 | − | 0.520088i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.83907 | + | 11.3874i | 0.677606 | + | 1.59455i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.38665 | + | 4.13380i | −0.327832 | + | 0.567821i | −0.982081 | − | 0.188457i | \(-0.939651\pi\) |
0.654250 | + | 0.756279i | \(0.272985\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.6307 | 1.43345 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13.8211 | − | 1.69136i | −1.83064 | − | 0.224026i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.58058 | 1.24729 | 0.623643 | − | 0.781710i | \(-0.285652\pi\) | ||||
0.623643 | + | 0.781710i | \(0.285652\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.49962 | −1.21630 | −0.608151 | − | 0.793821i | \(-0.708089\pi\) | ||||
−0.608151 | + | 0.793821i | \(0.708089\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.17260 | − | 6.75199i | −0.525698 | − | 0.850671i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.34252 | 0.662658 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.9889 | 1.34251 | 0.671255 | − | 0.741227i | \(-0.265756\pi\) | ||||
0.671255 | + | 0.741227i | \(0.265756\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.601415 | − | 1.41526i | −0.0724019 | − | 0.170377i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.62888 | −0.549347 | −0.274673 | − | 0.961538i | \(-0.588570\pi\) | ||||
−0.274673 | + | 0.961538i | \(0.588570\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.01004 | − | 3.48149i | 0.235257 | − | 0.407478i | −0.724090 | − | 0.689705i | \(-0.757740\pi\) |
0.959347 | + | 0.282228i | \(0.0910733\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.64635 | − | 0.446224i | −0.421044 | − | 0.0515255i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.53949 | + | 7.36543i | 0.859204 | + | 0.839368i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.02997 | −0.115881 | −0.0579406 | − | 0.998320i | \(-0.518453\pi\) | ||||
−0.0579406 | + | 0.998320i | \(0.518453\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.62474 | + | 4.78157i | −0.847193 | + | 0.531285i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.26656 | + | 9.12195i | −0.578080 | + | 1.00126i | 0.417620 | + | 0.908622i | \(0.362865\pi\) |
−0.995699 | + | 0.0926419i | \(0.970469\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.53125 | + | 16.5086i | 1.03381 | + | 1.79061i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.82947 | + | 4.30514i | 0.196140 | + | 0.461560i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.72788 | + | 2.99278i | 0.183155 | + | 0.317234i | 0.942953 | − | 0.332925i | \(-0.108036\pi\) |
−0.759798 | + | 0.650159i | \(0.774702\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.78900 | + | 3.70153i | 0.397195 | + | 0.388025i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.28132 | + | 1.70179i | −0.132866 | + | 0.176467i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −21.4524 | −2.20097 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.12061 | + | 1.94096i | −0.113781 | + | 0.197075i | −0.917292 | − | 0.398216i | \(-0.869630\pi\) |
0.803511 | + | 0.595290i | \(0.202963\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.29516 | − | 8.60376i | 0.833695 | − | 0.864710i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.28415 | + | 3.95626i | 0.227281 | + | 0.393663i | 0.957001 | − | 0.290083i | \(-0.0936830\pi\) |
−0.729720 | + | 0.683746i | \(0.760350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.37509 | − | 11.0420i | 0.628156 | − | 1.08800i | −0.359766 | − | 0.933043i | \(-0.617143\pi\) |
0.987922 | − | 0.154955i | \(-0.0495233\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.64456 | − | 9.54464i | −0.746032 | − | 0.931462i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.659761 | − | 1.14274i | −0.0637815 | − | 0.110473i | 0.832371 | − | 0.554218i | \(-0.186983\pi\) |
−0.896153 | + | 0.443746i | \(0.853649\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.31990 | + | 10.9464i | −0.605337 | + | 1.04847i | 0.386661 | + | 0.922222i | \(0.373628\pi\) |
−0.991998 | + | 0.126252i | \(0.959705\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.1044 | + | 2.21554i | 1.71839 | + | 0.210289i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.503200 | − | 0.871568i | −0.0473371 | − | 0.0819903i | 0.841386 | − | 0.540435i | \(-0.181740\pi\) |
−0.888723 | + | 0.458444i | \(0.848407\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.18457 | − | 2.05174i | −0.110462 | − | 0.191326i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.16877 | − | 4.32385i | 0.385403 | − | 0.399740i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.67815 | + | 18.3118i | −0.428846 | + | 1.67864i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.43524 | + | 4.21796i | −0.221386 | + | 0.383451i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.93337 | − | 0.603724i | −0.444827 | − | 0.0544360i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.68283 | 0.687173 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.38400 | 0.122810 | 0.0614051 | − | 0.998113i | \(-0.480442\pi\) | ||||
0.0614051 | + | 0.998113i | \(0.480442\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.60709 | − | 10.8415i | −0.405632 | − | 0.954540i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.164862 | − | 0.285550i | 0.0144041 | − | 0.0249486i | −0.858734 | − | 0.512422i | \(-0.828748\pi\) |
0.873138 | + | 0.487474i | \(0.162082\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.2144 | − | 14.8632i | −1.31926 | − | 1.28880i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.7653 | + | 8.73915i | −0.926531 | + | 0.752147i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.47095 | − | 7.74391i | −0.381979 | − | 0.661607i | 0.609366 | − | 0.792889i | \(-0.291424\pi\) |
−0.991345 | + | 0.131282i | \(0.958091\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.92869 | + | 6.80470i | 0.333227 | + | 0.577167i | 0.983143 | − | 0.182840i | \(-0.0585290\pi\) |
−0.649915 | + | 0.760007i | \(0.725196\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.6444 | + | 16.7938i | −1.06485 | + | 1.41429i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.98789 | + | 6.90723i | −0.333484 | + | 0.577611i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.60341 | + | 6.24128i | 0.299247 | + | 0.518310i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.19129 | − | 12.0657i | 0.0982563 | − | 0.995161i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.16075 | + | 14.1348i | −0.668554 | + | 1.15797i | 0.309754 | + | 0.950817i | \(0.399753\pi\) |
−0.978308 | + | 0.207153i | \(0.933580\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.31677 | + | 4.01276i | 0.188536 | + | 0.326554i | 0.944762 | − | 0.327756i | \(-0.106292\pi\) |
−0.756226 | + | 0.654310i | \(0.772959\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.7981 | + | 5.16776i | 1.68143 | + | 0.417788i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.64098 | + | 2.84226i | −0.131807 | + | 0.228296i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.51852 | −0.679852 | −0.339926 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339926 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.23348 | + | 7.60907i | 0.256431 | + | 0.603438i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.581416 | − | 2.27585i | 0.0458220 | − | 0.179362i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.22354 | + | 2.11923i | 0.0958350 | + | 0.165991i | 0.909957 | − | 0.414703i | \(-0.136115\pi\) |
−0.814122 | + | 0.580694i | \(0.802781\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.0753 | − | 14.7097i | 0.862209 | − | 1.14515i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.0713948 | − | 0.123659i | −0.00552470 | − | 0.00956906i | 0.863250 | − | 0.504777i | \(-0.168425\pi\) |
−0.868775 | + | 0.495208i | \(0.835092\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.49587 | − | 7.78708i | 0.345836 | − | 0.599006i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.7393 | + | 17.3621i | −1.28009 | + | 1.32771i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.9967 | 1.36826 | 0.684131 | − | 0.729359i | \(-0.260182\pi\) | ||||
0.684131 | + | 0.729359i | \(0.260182\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.01395 | − | 3.92128i | −0.303426 | − | 0.296421i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.98121 | − | 13.2566i | 0.750234 | − | 0.996429i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.02413 | + | 1.77384i | −0.0765468 | + | 0.132583i | −0.901758 | − | 0.432242i | \(-0.857723\pi\) |
0.825211 | + | 0.564824i | \(0.191056\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.81165 | 0.134659 | 0.0673294 | − | 0.997731i | \(-0.478552\pi\) | ||||
0.0673294 | + | 0.997731i | \(0.478552\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.89687 | + | 13.1446i | −0.731597 | + | 0.971677i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 28.1009 | 2.06602 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −28.4582 | −2.08107 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.6898 | − | 1.26073i | −0.995786 | − | 0.0917044i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.8091 | 1.36098 | 0.680491 | − | 0.732757i | \(-0.261767\pi\) | ||||
0.680491 | + | 0.732757i | \(0.261767\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.48714 | 0.466954 | 0.233477 | − | 0.972362i | \(-0.424990\pi\) | ||||
0.233477 | + | 0.972362i | \(0.424990\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.56593 | − | 7.39243i | 0.398584 | − | 0.529383i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.8356 | −0.772007 | −0.386003 | − | 0.922497i | \(-0.626145\pi\) | ||||
−0.386003 | + | 0.922497i | \(0.626145\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.43873 | + | 16.3484i | −0.669094 | + | 1.15890i | 0.309064 | + | 0.951041i | \(0.399984\pi\) |
−0.978158 | + | 0.207863i | \(0.933349\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.4484 | − | 15.2053i | 0.807510 | − | 1.07250i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.76863 | + | 6.92301i | −0.124134 | + | 0.485900i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.65736 | −0.534813 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.58486 | − | 0.642265i | −0.179660 | − | 0.0446405i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0130 | − | 27.7354i | 1.10764 | − | 1.91850i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.9133 | − | 20.6344i | −0.820145 | − | 1.42053i | −0.905574 | − | 0.424188i | \(-0.860560\pi\) |
0.0854297 | − | 0.996344i | \(-0.472774\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.82244 | + | 6.40497i | −0.330428 | + | 0.438861i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.07433 | − | 15.7172i | −0.618864 | − | 1.07190i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.13305 | + | 0.878836i | −0.212685 | + | 0.0596593i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.72324 | − | 6.40836i | −0.184019 | − | 0.433037i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.3018 | −0.962041 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.53734 | − | 11.3230i | 0.437773 | − | 0.758245i | −0.559745 | − | 0.828665i | \(-0.689101\pi\) |
0.997517 | + | 0.0704203i | \(0.0224341\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.41626 | + | 4.58056i | −0.294418 | + | 0.305371i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.5845 | − | 20.0649i | −0.768890 | − | 1.33176i | −0.938165 | − | 0.346188i | \(-0.887476\pi\) |
0.169275 | − | 0.985569i | \(-0.445858\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.7794 | − | 18.6705i | 0.712323 | − | 1.23378i | −0.251660 | − | 0.967816i | \(-0.580976\pi\) |
0.963983 | − | 0.265964i | \(-0.0856904\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.0463 | − | 2.75894i | 1.18736 | − | 0.181525i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.05558 | − | 13.9527i | −0.527739 | − | 0.914070i | −0.999477 | − | 0.0323318i | \(-0.989707\pi\) |
0.471738 | − | 0.881739i | \(-0.343627\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.1937 | + | 28.0483i | −1.05636 | + | 1.82967i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.07304 | + | 1.42517i | −0.0697017 | + | 0.0925749i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.216059 | + | 0.374225i | 0.0139757 | + | 0.0242066i | 0.872929 | − | 0.487848i | \(-0.162218\pi\) |
−0.858953 | + | 0.512054i | \(0.828885\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.52837 | − | 2.64721i | −0.0984509 | − | 0.170522i | 0.812593 | − | 0.582832i | \(-0.198055\pi\) |
−0.911044 | + | 0.412310i | \(0.864722\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.32733 | + | 15.5318i | −0.0851486 | + | 0.996368i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.436221 | − | 18.6744i | −0.0278691 | − | 1.19307i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.04741 | − | 13.9385i | 0.512045 | − | 0.886887i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.13522 | + | 16.7907i | 0.452176 | + | 1.06407i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.9066 | 0.751541 | 0.375770 | − | 0.926713i | \(-0.377378\pi\) | ||||
0.375770 | + | 0.926713i | \(0.377378\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.53687 | 0.222361 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 32.7727 | + | 4.01058i | 2.05231 | + | 0.251152i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.9726 | − | 27.6654i | 0.996346 | − | 1.72572i | 0.424204 | − | 0.905567i | \(-0.360554\pi\) |
0.572142 | − | 0.820155i | \(-0.306113\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.9296 | + | 19.4695i | 1.23836 | + | 1.20977i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.86299 | + | 1.95373i | 0.486707 | + | 0.120933i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.35495 | − | 5.81094i | −0.206875 | − | 0.358318i | 0.743854 | − | 0.668343i | \(-0.232996\pi\) |
−0.950728 | + | 0.310025i | \(0.899663\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.36879 | + | 11.0311i | 0.391232 | + | 0.677634i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.94124 | + | 0.727062i | 0.363598 | + | 0.0444955i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.66510 | − | 9.81225i | 0.345408 | − | 0.598263i | −0.640020 | − | 0.768358i | \(-0.721074\pi\) |
0.985428 | + | 0.170095i | \(0.0544074\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.06846 | − | 8.77884i | −0.307887 | − | 0.533276i | 0.670013 | − | 0.742350i | \(-0.266289\pi\) |
−0.977900 | + | 0.209073i | \(0.932955\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.06924 | − | 1.38652i | 0.548895 | − | 0.0839159i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.22465 | − | 7.31730i | 0.254756 | − | 0.441250i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.6433 | + | 18.4347i | 0.639492 | + | 1.10763i | 0.985544 | + | 0.169418i | \(0.0541886\pi\) |
−0.346052 | + | 0.938215i | \(0.612478\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.01987 | + | 3.54591i | 0.0610578 | + | 0.212288i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.26945 | + | 10.8590i | −0.374004 | + | 0.647794i | −0.990177 | − | 0.139817i | \(-0.955349\pi\) |
0.616174 | + | 0.787610i | \(0.288682\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.9497 | 1.48311 | 0.741554 | − | 0.670893i | \(-0.234089\pi\) | ||||
0.741554 | + | 0.670893i | \(0.234089\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −22.3495 | + | 29.6837i | −1.32387 | + | 1.75831i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.43072 | − | 5.30535i | −0.320565 | − | 0.313165i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0149 | − | 29.4706i | −1.00087 | − | 1.73357i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.51823 | + | 3.57271i | 0.0890000 | + | 0.209436i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.42625 | + | 12.8626i | 0.433846 | + | 0.751443i | 0.997201 | − | 0.0747718i | \(-0.0238228\pi\) |
−0.563355 | + | 0.826215i | \(0.690490\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.7829 | − | 22.1407i | 0.744250 | − | 1.28908i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.26295 | − | 20.4415i | −0.189336 | − | 1.18614i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.77747 | 0.102794 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.45389 | − | 17.4340i | 0.256718 | − | 1.00488i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.85393 | + | 0.961129i | 0.451197 | + | 0.0552154i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.6749 | + | 21.9536i | −0.725763 | + | 1.25706i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.9045 | −1.25016 | −0.625079 | − | 0.780561i | \(-0.714933\pi\) | ||||
−0.625079 | + | 0.780561i | \(0.714933\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.63707 | − | 20.3249i | −0.491346 | − | 1.15624i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.5672 | −0.996143 | −0.498072 | − | 0.867136i | \(-0.665958\pi\) | ||||
−0.498072 | + | 0.867136i | \(0.665958\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.9764 | −0.676946 | −0.338473 | − | 0.940976i | \(-0.609910\pi\) | ||||
−0.338473 | + | 0.940976i | \(0.609910\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −21.1711 | + | 0.633982i | −1.19286 | + | 0.0357208i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.73327 | −0.0973499 | −0.0486750 | − | 0.998815i | \(-0.515500\pi\) | ||||
−0.0486750 | + | 0.998815i | \(0.515500\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.7590 | −0.602386 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.26855 | − | 0.277616i | −0.126618 | − | 0.0154950i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 57.4275 | 3.19535 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.12311 | − | 3.67734i | 0.117769 | − | 0.203982i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.56231 | + | 20.1490i | 0.473497 | + | 1.11424i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −30.9179 | + | 8.67263i | −1.70456 | + | 0.478137i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.726254 | −0.0399185 | −0.0199593 | − | 0.999801i | \(-0.506354\pi\) | ||||
−0.0199593 | + | 0.999801i | \(0.506354\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21.9271 | − | 22.7428i | 1.20160 | − | 1.24630i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.6620 | − | 25.3953i | 0.801070 | − | 1.38749i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.84810 | − | 11.8613i | −0.373040 | − | 0.646124i | 0.616992 | − | 0.786970i | \(-0.288351\pi\) |
−0.990032 | + | 0.140846i | \(0.955018\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.73023 | − | 0.211738i | −0.0939732 | − | 0.0115000i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.44980 | − | 4.24317i | −0.132664 | − | 0.229781i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.6291 | − | 13.5465i | 0.681906 | − | 0.731440i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.07310 | − | 0.498448i | −0.219288 | − | 0.0268355i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.21417 | −0.226229 | −0.113114 | − | 0.993582i | \(-0.536083\pi\) | ||||
−0.113114 | + | 0.993582i | \(0.536083\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.8070 | + | 18.7183i | −0.578486 | + | 1.00197i | 0.417167 | + | 0.908830i | \(0.363023\pi\) |
−0.995653 | + | 0.0931372i | \(0.970310\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.63981 | − | 10.2730i | −0.0875267 | − | 0.548331i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.42558 | − | 4.20122i | −0.129100 | − | 0.223609i | 0.794228 | − | 0.607620i | \(-0.207876\pi\) |
−0.923328 | + | 0.384012i | \(0.874542\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.17609 | + | 10.6973i | −0.327793 | + | 0.567754i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 20.4642 | + | 25.5507i | 1.08308 | + | 1.35229i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.90433 | + | 5.03045i | 0.153285 | + | 0.265497i | 0.932433 | − | 0.361343i | \(-0.117682\pi\) |
−0.779148 | + | 0.626839i | \(0.784348\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.8137 | + | 39.5145i | −1.20072 | + | 2.07971i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.29931 | + | 7.76398i | 0.173169 | + | 0.407503i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.36381 | − | 9.29038i | −0.280754 | − | 0.486281i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.8445 | − | 18.7832i | −0.566078 | − | 0.980476i | −0.996949 | − | 0.0780619i | \(-0.975127\pi\) |
0.430871 | − | 0.902414i | \(-0.358207\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.97504 | + | 6.19732i | −0.311048 | + | 0.322620i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.12595 | + | 12.2360i | −0.162291 | + | 0.635261i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.3552 | + | 21.3999i | −0.639729 | + | 1.10804i | 0.345764 | + | 0.938322i | \(0.387620\pi\) |
−0.985492 | + | 0.169721i | \(0.945713\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.00410 | − | 10.6307i | 0.413330 | − | 0.548967i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.40696 | −0.278473 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.9950 | −1.43801 | −0.719005 | − | 0.695005i | \(-0.755402\pi\) | ||||
−0.719005 | + | 0.695005i | \(0.755402\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.44188 | − | 1.91504i | 0.0738695 | − | 0.0981104i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.3113 | − | 17.8598i | 0.526884 | − | 0.912591i | −0.472625 | − | 0.881264i | \(-0.656693\pi\) |
0.999509 | − | 0.0313269i | \(-0.00997329\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 27.0810 | − | 7.59637i | 1.38018 | − | 0.387147i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −19.8011 | − | 4.92002i | −1.00655 | − | 0.250099i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.70035 | − | 15.0694i | −0.441125 | − | 0.764051i | 0.556648 | − | 0.830748i | \(-0.312087\pi\) |
−0.997773 | + | 0.0666973i | \(0.978754\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.17107 | + | 5.49245i | 0.160368 | + | 0.277765i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.223358 | − | 0.525610i | −0.0112669 | − | 0.0265135i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.37425 | + | 2.38026i | −0.0691458 | + | 0.119764i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.74152 | + | 16.8728i | 0.488913 | + | 0.846822i | 0.999919 | − | 0.0127553i | \(-0.00406024\pi\) |
−0.511006 | + | 0.859577i | \(0.670727\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −36.4167 | + | 5.56744i | −1.82312 | + | 0.278721i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.85264 | + | 6.67297i | −0.192392 | + | 0.333232i | −0.946042 | − | 0.324043i | \(-0.894958\pi\) |
0.753651 | + | 0.657275i | \(0.228291\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.23116 | − | 2.13242i | −0.0613282 | − | 0.106224i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.876849 | + | 24.0005i | 0.0435710 | + | 1.19260i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.9757 | + | 36.3310i | −1.03973 | + | 1.80086i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.7351 | −0.778050 | −0.389025 | − | 0.921227i | \(-0.627188\pi\) | ||||
−0.389025 | + | 0.921227i | \(0.627188\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.3731 | − | 1.88130i | −0.758301 | − | 0.0927975i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.4058 | − | 6.84596i | 1.20093 | − | 0.336868i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.0538 | + | 24.3420i | 0.689876 | + | 1.19490i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.5086 | + | 1.65313i | 0.661520 | + | 0.0809539i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.3452 | − | 30.0428i | −0.847369 | − | 1.46769i | −0.883548 | − | 0.468341i | \(-0.844852\pi\) |
0.0361784 | − | 0.999345i | \(-0.488482\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.607053 | + | 1.05145i | −0.0295860 | + | 0.0512444i | −0.880439 | − | 0.474159i | \(-0.842752\pi\) |
0.850853 | + | 0.525403i | \(0.176086\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.0644 | + | 34.9921i | 0.489346 | + | 1.70138i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.1508 | 0.734924 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.1996 | + | 6.78811i | −1.17110 | + | 0.328500i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.40286 | + | 12.7141i | 0.260853 | + | 0.613842i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.68495 | − | 2.91841i | 0.0811610 | − | 0.140575i | −0.822588 | − | 0.568638i | \(-0.807471\pi\) |
0.903749 | + | 0.428063i | \(0.140804\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.8651 | −1.48328 | −0.741640 | − | 0.670798i | \(-0.765952\pi\) | ||||
−0.741640 | + | 0.670798i | \(0.765952\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.3901 | + | 1.51625i | 0.594062 | + | 0.0726986i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.13727 | −0.341422 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.0789 | −1.57877 | −0.789385 | − | 0.613898i | \(-0.789600\pi\) | ||||
−0.789385 | + | 0.613898i | \(0.789600\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.4541 | − | 14.2186i | −0.735912 | − | 0.677077i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.73364 | 0.129879 | 0.0649397 | − | 0.997889i | \(-0.479315\pi\) | ||||
0.0649397 | + | 0.997889i | \(0.479315\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.22172 | 0.437152 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.0563 | + | 26.0179i | 0.522946 | + | 1.23060i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.7472 | 1.07351 | 0.536753 | − | 0.843740i | \(-0.319651\pi\) | ||||
0.536753 | + | 0.843740i | \(0.319651\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.71579 | − | 9.90003i | 0.269146 | − | 0.466174i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.96609 | + | 0.974855i | 0.374280 | + | 0.0458027i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.6097 | − | 3.81759i | 0.638032 | − | 0.178971i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.36324 | 0.157326 | 0.0786628 | − | 0.996901i | \(-0.474935\pi\) | ||||
0.0786628 | + | 0.996901i | \(0.474935\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 28.8184 | − | 23.3944i | 1.34513 | − | 1.09196i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.0040 | + | 17.3275i | −0.465934 | + | 0.807021i | −0.999243 | − | 0.0388994i | \(-0.987615\pi\) |
0.533309 | + | 0.845920i | \(0.320948\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.29434 | + | 12.6342i | 0.338997 | + | 0.587160i | 0.984244 | − | 0.176814i | \(-0.0565791\pi\) |
−0.645247 | + | 0.763974i | \(0.723246\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.22323 | + | 5.23173i | 0.103100 | + | 0.242616i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.26334 | + | 12.5805i | 0.336107 | + | 0.582155i | 0.983697 | − | 0.179834i | \(-0.0575562\pi\) |
−0.647590 | + | 0.761989i | \(0.724223\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.9935 | − | 7.85231i | 1.29262 | − | 0.362586i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.87474 | + | 11.7871i | −0.408926 | + | 0.543119i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27.0939 | 1.24578 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.52518 | + | 14.7660i | −0.391162 | + | 0.677513i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.8973 | + | 3.45310i | 0.636315 | + | 0.158107i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.66216 | + | 9.80714i | 0.258710 | + | 0.448100i | 0.965897 | − | 0.258928i | \(-0.0833691\pi\) |
−0.707186 | + | 0.707027i | \(0.750036\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.5414 | + | 18.2583i | −0.480648 | + | 0.832506i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.54336 | − | 3.17552i | −0.115727 | − | 0.144491i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.99036 | + | 5.17946i | 0.135785 | + | 0.235187i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.93684 | − | 10.2829i | 0.269024 | − | 0.465963i | −0.699586 | − | 0.714548i | \(-0.746632\pi\) |
0.968610 | + | 0.248585i | \(0.0799657\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.20708 | + | 0.514844i | 0.190251 | + | 0.0232820i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.9598 | + | 20.7150i | 0.539738 | + | 0.934853i | 0.998918 | + | 0.0465101i | \(0.0148100\pi\) |
−0.459180 | + | 0.888343i | \(0.651857\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.64621 | − | 16.7077i | −0.434443 | − | 0.752478i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.81538 | − | 30.6497i | −0.396222 | − | 1.37760i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.7917 | + | 3.30764i | −0.528932 | + | 0.148368i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.225984 | − | 0.391416i | 0.0101164 | − | 0.0175222i | −0.860923 | − | 0.508736i | \(-0.830113\pi\) |
0.871039 | + | 0.491213i | \(0.163446\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.245488 | − | 0.0300417i | −0.0109676 | − | 0.00134216i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.6077 | −0.651326 | −0.325663 | − | 0.945486i | \(-0.605587\pi\) | ||||
−0.325663 | + | 0.945486i | \(0.605587\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.1905 | 0.542471 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.09108 | − | 14.3336i | −0.270514 | − | 0.636579i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.246585 | − | 0.427099i | 0.0109297 | − | 0.0189308i | −0.860509 | − | 0.509436i | \(-0.829854\pi\) |
0.871439 | + | 0.490505i | \(0.163188\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.63268 | − | 10.3052i | 0.116463 | − | 0.455874i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.58452 | + | 41.2503i | 0.290714 | + | 1.82124i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.0120 | − | 29.4656i | −0.749636 | − | 1.29841i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.1754 | − | 41.8730i | −1.06323 | − | 1.84157i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.7492 | − | 24.9020i | 0.823000 | − | 1.09307i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.06874 | + | 10.5114i | −0.265876 | + | 0.460511i | −0.967793 | − | 0.251748i | \(-0.918995\pi\) |
0.701917 | + | 0.712259i | \(0.252328\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.34058 | + | 2.32195i | 0.0586193 | + | 0.101532i | 0.893846 | − | 0.448374i | \(-0.147997\pi\) |
−0.835227 | + | 0.549906i | \(0.814664\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.60767 | + | 1.46883i | −0.419313 | + | 0.0641052i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.39285 | − | 7.60865i | 0.191356 | − | 0.331438i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1059 | + | 19.2360i | 0.482865 | + | 0.836346i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.94456 | − | 27.6219i | −0.344764 | − | 1.19869i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.87249 | − | 4.97530i | 0.124421 | − | 0.215504i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.52115 | −0.152233 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.38750 | + | 3.26510i | 0.0598752 | + | 0.140899i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.4694 | + | 13.3754i | 1.05397 | + | 0.576121i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.5072 | − | 23.3951i | −0.580719 | − | 1.00583i | −0.995394 | − | 0.0958650i | \(-0.969438\pi\) |
0.414676 | − | 0.909969i | \(-0.363895\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.88741 | − | 2.50677i | 0.0809963 | − | 0.107576i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.8647 | + | 29.2105i | 0.722404 | + | 1.25124i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.2496 | + | 26.4132i | −0.652028 | + | 1.12935i | 0.330602 | + | 0.943770i | \(0.392748\pi\) |
−0.982630 | + | 0.185575i | \(0.940585\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.87743 | + | 27.3885i | 0.336200 | + | 1.16891i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.7112 | 0.924927 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.62379 | + | 0.735985i | −0.111575 | + | 0.0312973i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 29.2760 | − | 38.8831i | 1.24270 | − | 1.65050i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.39250 | + | 12.8042i | −0.313230 | + | 0.542531i | −0.979060 | − | 0.203573i | \(-0.934745\pi\) |
0.665829 | + | 0.746104i | \(0.268078\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.6162 | 0.575902 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −29.6482 | + | 39.3775i | −1.25175 | + | 1.66252i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.62822 | 0.110766 | 0.0553831 | − | 0.998465i | \(-0.482362\pi\) | ||||
0.0553831 | + | 0.998465i | \(0.482362\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.68559 | −0.112983 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.0067 | + | 17.6291i | −0.672219 | + | 0.740352i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.1162 | −1.34638 | −0.673191 | − | 0.739469i | \(-0.735077\pi\) | ||||
−0.673191 | + | 0.739469i | \(0.735077\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.1815 | 1.72339 | 0.861696 | − | 0.507425i | \(-0.169403\pi\) | ||||
0.861696 | + | 0.507425i | \(0.169403\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.5957 | − | 26.0262i | 0.818621 | − | 1.08726i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.88300 | −0.0785263 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.0735 | − | 20.9119i | 0.502625 | − | 0.870573i | −0.497370 | − | 0.867539i | \(-0.665701\pi\) |
0.999995 | − | 0.00303429i | \(-0.000965847\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.75841 | − | 8.97623i | 0.280870 | − | 0.373040i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.89795 | + | 27.0008i | −0.286175 | + | 1.12018i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.0158 | −0.787553 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.43021 | − | 15.4031i | −0.183167 | − | 0.636840i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.98618 | + | 6.90426i | −0.164527 | + | 0.284969i | −0.936487 | − | 0.350702i | \(-0.885943\pi\) |
0.771960 | + | 0.635671i | \(0.219277\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.94360 | + | 8.56257i | 0.203698 | + | 0.352815i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.2887 | + | 14.9932i | −0.464357 | + | 0.616739i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.10338 | − | 3.64316i | −0.0863753 | − | 0.149606i | 0.819601 | − | 0.572935i | \(-0.194195\pi\) |
−0.905976 | + | 0.423328i | \(0.860862\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 36.0767 | + | 35.2438i | 1.47900 | + | 1.44485i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.7877 | + | 30.0923i | 0.523368 | + | 1.23160i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.3771 | −1.52719 | −0.763594 | − | 0.645696i | \(-0.776567\pi\) | ||||
−0.763594 | + | 0.645696i | \(0.776567\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.81596 | − | 11.8056i | 0.278029 | − | 0.481560i | −0.692866 | − | 0.721066i | \(-0.743652\pi\) |
0.970895 | + | 0.239506i | \(0.0769856\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.11240 | − | 31.6823i | −0.371086 | − | 1.29020i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.49846 | + | 11.2557i | 0.264200 | + | 0.457607i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.37114 | + | 2.37489i | −0.0556529 | + | 0.0963937i | −0.892510 | − | 0.451028i | \(-0.851057\pi\) |
0.836857 | + | 0.547422i | \(0.184391\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.73676 | + | 9.65976i | 0.313509 | + | 0.391433i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.1494 | − | 21.0434i | −0.491513 | − | 0.851326i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.798502 | − | 1.38305i | 0.0322512 | − | 0.0558607i | −0.849449 | − | 0.527670i | \(-0.823066\pi\) |
0.881700 | + | 0.471810i | \(0.156399\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.97757 | + | 10.5955i | −0.321687 | + | 0.427251i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.6551 | + | 21.9192i | 0.509473 | + | 0.882433i | 0.999940 | + | 0.0109734i | \(0.00349302\pi\) |
−0.490467 | + | 0.871460i | \(0.663174\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.5808 | + | 23.5226i | 0.545859 | + | 0.945455i | 0.998552 | + | 0.0537888i | \(0.0171298\pi\) |
−0.452694 | + | 0.891666i | \(0.649537\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.58165 | + | 2.90754i | −0.143727 | + | 0.116675i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.54019 | + | 6.38920i | 0.262027 | + | 0.255978i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5532 | − | 26.9388i | 0.622126 | − | 1.07755i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −21.6947 | − | 51.0524i | −0.866404 | − | 2.03883i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −75.2252 | −2.99942 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.6597 | −1.18073 | −0.590366 | − | 0.807136i | \(-0.701017\pi\) | ||||
−0.590366 | + | 0.807136i | \(0.701017\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −40.9633 | − | 5.01290i | −1.62814 | − | 0.199245i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.84661 | − | 3.19842i | 0.0732804 | − | 0.126925i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.2972 | + | 6.72188i | 0.487233 | + | 0.266331i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.83843 | + | 13.3456i | 0.151846 | + | 0.527944i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.0987 | − | 36.5441i | −0.833350 | − | 1.44340i | −0.895367 | − | 0.445329i | \(-0.853087\pi\) |
0.0620175 | − | 0.998075i | \(-0.480247\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.1099 | + | 17.5109i | 0.398696 | + | 0.690562i | 0.993565 | − | 0.113260i | \(-0.0361294\pi\) |
−0.594869 | + | 0.803823i | \(0.702796\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −31.2016 | − | 3.81832i | −1.22856 | − | 0.150346i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.08988 | + | 1.88772i | −0.0428475 | + | 0.0742141i | −0.886654 | − | 0.462434i | \(-0.846976\pi\) |
0.843806 | + | 0.536648i | \(0.180310\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.0834 | + | 33.0535i | 0.749091 | + | 1.29746i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.04802 | + | 5.25078i | −0.0802682 | + | 0.205794i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.0535 | − | 29.5375i | 0.667354 | − | 1.15589i | −0.311288 | − | 0.950316i | \(-0.600760\pi\) |
0.978641 | − | 0.205575i | \(-0.0659063\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.439936 | − | 0.761991i | −0.0171897 | − | 0.0297734i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.7044 | − | 2.90821i | −0.456630 | − | 0.113460i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.994211 | + | 1.72202i | −0.0387290 | + | 0.0670805i | −0.884740 | − | 0.466085i | \(-0.845664\pi\) |
0.846011 | + | 0.533165i | \(0.178998\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.48409 | −0.329993 | −0.164997 | − | 0.986294i | \(-0.552761\pi\) | ||||
−0.164997 | + | 0.986294i | \(0.552761\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.8998 | + | 19.7893i | −0.578661 | + | 0.768553i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −54.6486 | + | 15.3292i | −2.11918 | + | 0.594440i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.19886 | + | 2.07649i | 0.0464201 | + | 0.0804020i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.85690 | − | 20.8422i | −0.342428 | − | 0.805806i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.9222 | − | 32.7742i | −0.730483 | − | 1.26523i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.4056 | − | 38.8077i | 0.863674 | − | 1.49593i | −0.00468438 | − | 0.999989i | \(-0.501491\pi\) |
0.868358 | − | 0.495938i | \(-0.165176\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.73717 | + | 10.8829i | 0.0668635 | + | 0.418882i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.05367 | 0.309528 | 0.154764 | − | 0.987951i | \(-0.450538\pi\) | ||||
0.154764 | + | 0.987951i | \(0.450538\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.46774 | + | 5.74521i | −0.0563267 | + | 0.220481i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −39.8327 | − | 4.87455i | −1.52639 | − | 0.186793i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.8446 | − | 36.1039i | 0.797597 | − | 1.38148i | −0.123580 | − | 0.992335i | \(-0.539438\pi\) |
0.921177 | − | 0.389144i | \(-0.127229\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.8615 | −0.911701 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.6041 | − | 34.3667i | −0.557182 | − | 1.31117i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.55646 | −0.364072 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.3269 | 0.430895 | 0.215448 | − | 0.976515i | \(-0.430879\pi\) | ||||
0.215448 | + | 0.976515i | \(0.430879\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14.9834 | − | 27.8449i | 0.569172 | − | 1.05774i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.9675 | 0.795342 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.4985 | 0.776437 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −27.6987 | − | 3.38965i | −1.04766 | − | 0.128208i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.6560 | −0.855705 | −0.427853 | − | 0.903849i | \(-0.640730\pi\) | ||||
−0.427853 | + | 0.903849i | \(0.640730\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 42.3282 | − | 73.3146i | 1.59644 | − | 2.76511i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 21.9395 | + | 51.6284i | 0.826290 | + | 1.94444i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.64572 | + | 8.44612i | 0.325156 | + | 0.317649i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.2147 | 1.69807 | 0.849037 | − | 0.528333i | \(-0.177183\pi\) | ||||
0.849037 | + | 0.528333i | \(0.177183\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.854092 | + | 2.96954i | 0.0320309 | + | 0.111366i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.545958 | + | 0.945626i | −0.0204463 | + | 0.0354140i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.6417 | + | 18.4320i | 0.397977 | + | 0.689317i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.742908 | + | 0.0909139i | 0.0277444 | + | 0.00339524i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.3171 | + | 19.6018i | 0.422057 | + | 0.731024i | 0.996141 | − | 0.0877727i | \(-0.0279749\pi\) |
−0.574084 | + | 0.818797i | \(0.694642\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.34986 | − | 32.6841i | 0.310965 | − | 1.21722i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.25522 | − | 0.643111i | −0.195444 | − | 0.0239175i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.72797 | 0.212731 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.04956 | − | 1.81789i | 0.0389259 | − | 0.0674217i | −0.845906 | − | 0.533332i | \(-0.820940\pi\) |
0.884832 | + | 0.465910i | \(0.154273\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.1085 | + | 18.0180i | 0.744760 | + | 0.667332i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.2917 | + | 42.0745i | 0.898461 | + | 1.55618i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.6453 | − | 27.0985i | 0.577872 | − | 1.00090i | −0.417851 | − | 0.908516i | \(-0.637216\pi\) |
0.995723 | − | 0.0923886i | \(-0.0294502\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −26.2942 | − | 18.8518i | −0.969878 | − | 0.695357i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.8887 | + | 37.9123i | 0.806280 | + | 1.39652i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.1229 | − | 36.5859i | 0.777017 | − | 1.34583i | −0.156637 | − | 0.987656i | \(-0.550065\pi\) |
0.933654 | − | 0.358177i | \(-0.116601\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.9028 | − | 25.6566i | −0.400523 | − | 0.942518i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.48482 | + | 11.2320i | 0.237905 | + | 0.412064i | 0.960113 | − | 0.279612i | \(-0.0902060\pi\) |
−0.722208 | + | 0.691676i | \(0.756873\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.7770 | + | 37.7189i | 0.797848 | + | 1.38191i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.6669 | + | 7.61986i | 1.12204 | + | 0.278796i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.49726 | − | 2.43960i | −0.0912478 | − | 0.0891412i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.3649 | + | 28.3448i | −0.597164 | + | 1.03432i | 0.396074 | + | 0.918219i | \(0.370372\pi\) |
−0.993238 | + | 0.116099i | \(0.962961\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.4045 | − | 16.4752i | 0.452047 | − | 0.600389i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.3646 | 0.449995 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.6305 | 1.14963 | 0.574815 | − | 0.818283i | \(-0.305074\pi\) | ||||
0.574815 | + | 0.818283i | \(0.305074\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.68477 | − | 4.89396i | 0.133749 | − | 0.177639i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.1468 | − | 33.1632i | 0.694070 | − | 1.20217i | −0.276423 | − | 0.961036i | \(-0.589149\pi\) |
0.970493 | − | 0.241129i | \(-0.0775177\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.27758 | + | 32.4011i | −0.299668 | + | 1.17300i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 39.6926 | − | 41.1692i | 1.43509 | − | 1.48848i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.59047 | + | 16.6112i | 0.346292 | + | 0.599795i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.0674 | + | 19.1693i | 0.399100 | + | 0.691262i | 0.993615 | − | 0.112823i | \(-0.0359892\pi\) |
−0.594515 | + | 0.804085i | \(0.702656\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.6400 | − | 50.9236i | −0.779346 | − | 1.83397i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.8165 | − | 44.7155i | 0.928555 | − | 1.60830i | 0.142813 | − | 0.989750i | \(-0.454385\pi\) |
0.785742 | − | 0.618555i | \(-0.212281\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.30425 | + | 2.25902i | 0.0468500 | + | 0.0811466i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 47.7028 | − | 7.29288i | 1.71133 | − | 0.261631i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.5342 | + | 19.9779i | −0.413257 | + | 0.715783i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.22021 | − | 15.9699i | −0.329925 | − | 0.571447i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.8952 | − | 8.84456i | 0.389362 | − | 0.316079i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.3659 | + | 19.6862i | −0.405665 | + | 0.702632i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.3046 | −1.15153 | −0.575767 | − | 0.817614i | \(-0.695296\pi\) | ||||
−0.575767 | + | 0.817614i | \(0.695296\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.5358 | − | 1.41170i | −0.410686 | − | 0.0502579i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.90466 | − | 1.86069i | −0.0677219 | − | 0.0661585i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.50943 | − | 16.4708i | −0.337690 | − | 0.584896i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 21.8988 | + | 2.67988i | 0.776670 | + | 0.0950454i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.6877 | − | 20.2438i | −0.414001 | − | 0.717071i | 0.581322 | − | 0.813674i | \(-0.302536\pi\) |
−0.995323 | + | 0.0966026i | \(0.969202\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.3501 | − | 75.0845i | 1.53361 | − | 2.65630i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.19571 | − | 7.46340i | 0.254248 | − | 0.263706i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.0151 | 0.565161 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.48372 | − | 4.38021i | −0.158030 | − | 0.154382i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.67518 | − | 18.0614i | −0.270179 | − | 0.635790i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.2503 | − | 26.4143i | 0.536171 | − | 0.928676i | −0.462935 | − | 0.886392i | \(-0.653203\pi\) |
0.999106 | − | 0.0422832i | \(-0.0134632\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51.6454 | −1.81352 | −0.906758 | − | 0.421652i | \(-0.861450\pi\) | ||||
−0.906758 | + | 0.421652i | \(0.861450\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.4277 | − | 2.13272i | −0.611215 | − | 0.0747978i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.53004 | 0.228737 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −54.6745 | −1.91282 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.52996 | − | 13.9936i | 0.263118 | − | 0.488975i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.7575 | −0.933843 | −0.466921 | − | 0.884299i | \(-0.654637\pi\) | ||||
−0.466921 | + | 0.884299i | \(0.654637\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.4898 | −1.41139 | −0.705693 | − | 0.708517i | \(-0.749364\pi\) | ||||
−0.705693 | + | 0.708517i | \(0.749364\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.72362 | − | 13.4689i | −0.199271 | − | 0.468928i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.9452 | −0.971749 | −0.485875 | − | 0.874029i | \(-0.661499\pi\) | ||||
−0.485875 | + | 0.874029i | \(0.661499\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.0226 | + | 34.6802i | −0.695415 | + | 1.20449i | 0.274625 | + | 0.961551i | \(0.411446\pi\) |
−0.970040 | + | 0.242943i | \(0.921887\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 36.5964 | + | 4.47850i | 1.26951 | + | 0.155357i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.16775 | + | 49.9909i | 0.0404601 | + | 1.73208i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.381035 | −0.0131863 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.96898 | + | 2.28300i | 0.206318 | + | 0.0789120i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.6312 | + | 28.8061i | −0.574174 | + | 0.994499i | 0.421957 | + | 0.906616i | \(0.361343\pi\) |
−0.996131 | + | 0.0878827i | \(0.971990\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.8531 | + | 18.7982i | 0.374246 | + | 0.648213i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.49395 | + | 19.9881i | 0.292547 | + | 0.688427i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.9973 | − | 20.7799i | −0.412718 | − | 0.714849i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.18959 | + | 12.4851i | −0.109596 | + | 0.428993i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.9930 | − | 34.5229i | 0.892079 | − | 1.18482i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.34922 | 0.320487 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.38730 | + | 7.59902i | −0.150218 | + | 0.260186i | −0.931308 | − | 0.364234i | \(-0.881331\pi\) |
0.781089 | + | 0.624419i | \(0.214664\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 17.7891 | + | 61.8499i | 0.608375 | + | 2.11522i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.677198 | + | 1.17294i | 0.0231327 | + | 0.0400669i | 0.877360 | − | 0.479833i | \(-0.159303\pi\) |
−0.854227 | + | 0.519900i | \(0.825969\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.01934 | − | 15.6220i | 0.307736 | − | 0.533014i | −0.670131 | − | 0.742243i | \(-0.733762\pi\) |
0.977867 | + | 0.209229i | \(0.0670953\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.9988 | + | 1.98728i | −0.442998 | + | 0.0677262i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.37624 | − | 11.0440i | −0.217050 | − | 0.375941i | 0.736855 | − | 0.676051i | \(-0.236310\pi\) |
−0.953905 | + | 0.300110i | \(0.902977\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.0121 | − | 41.5902i | 0.816437 | − | 1.41411i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −58.5048 | − | 7.15955i | −1.98693 | − | 0.243151i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.05159 | − | 3.55347i | −0.0695956 | − | 0.120543i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.0003 | + | 19.0530i | 0.372729 | + | 0.645586i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.52527 | + | 1.62135i | 0.220847 | + | 0.0548743i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19.5715 | − | 5.48989i | 0.661636 | − | 0.185592i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.79034 | − | 15.2253i | 0.296829 | − | 0.514122i | −0.678580 | − | 0.734527i | \(-0.737404\pi\) |
0.975409 | + | 0.220404i | \(0.0707376\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.5348 | + | 3.12483i | 0.861267 | + | 0.105398i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.8682 | −0.871523 | −0.435762 | − | 0.900062i | \(-0.643521\pi\) | ||||
−0.435762 | + | 0.900062i | \(0.643521\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.5923 | 1.36604 | 0.683020 | − | 0.730400i | \(-0.260666\pi\) | ||||
0.683020 | + | 0.730400i | \(0.260666\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −17.3185 | − | 40.7542i | −0.582156 | − | 1.36994i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.46786 | − | 2.54240i | 0.0492858 | − | 0.0853655i | −0.840330 | − | 0.542075i | \(-0.817639\pi\) |
0.889616 | + | 0.456710i | \(0.150972\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.52564 | − | 0.988961i | 0.118246 | − | 0.0331687i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −31.6843 | − | 16.7814i | −1.06146 | − | 0.562198i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 48.7850 | + | 84.4981i | 1.63253 | + | 2.82762i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.73289 | + | 4.73350i | 0.0913504 | + | 0.158223i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.85180 | − | 2.45948i | 0.0618297 | − | 0.0821196i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.66077 | − | 2.87654i | 0.0553899 | − | 0.0959381i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.0491 | − | 29.5299i | −0.567987 | − | 0.983782i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −19.4832 | − | 24.3258i | −0.648361 | − | 0.809513i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.41720 | − | 4.18671i | 0.0803503 | − | 0.139171i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.1395 | + | 29.6865i | 0.569108 | + | 0.985723i | 0.996655 | + | 0.0817300i | \(0.0260445\pi\) |
−0.427547 | + | 0.903993i | \(0.640622\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.51227 | − | 9.86614i | 0.315502 | − | 0.327239i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.98338 | + | 8.63146i | −0.165107 | + | 0.285973i | −0.936693 | − | 0.350151i | \(-0.886130\pi\) |
0.771586 | + | 0.636124i | \(0.219464\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −41.9616 | −1.38873 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17.1722 | + | 40.4098i | 0.567695 | + | 1.33591i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.215930 | − | 0.845222i | 0.00713065 | − | 0.0279117i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.9444 | + | 24.1524i | 0.459983 | + | 0.796714i | 0.998959 | − | 0.0456069i | \(-0.0145222\pi\) |
−0.538976 | + | 0.842321i | \(0.681189\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.8205 | + | 30.3093i | −0.751962 | + | 0.998724i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.63365 | − | 8.02573i | −0.152519 | − | 0.264170i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.1673 | − | 19.3423i | 0.367177 | − | 0.635970i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −37.1218 | − | 9.22372i | −1.21924 | − | 0.302947i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.3059 | −0.600597 | −0.300298 | − | 0.953845i | \(-0.597086\pi\) | ||||
−0.300298 | + | 0.953845i | \(0.597086\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −49.3783 | − | 26.9911i | −1.61831 | − | 0.884599i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.3018 | + | 24.3077i | −0.599173 | + | 0.795797i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −37.9704 | + | 65.7666i | −1.24176 | + | 2.15080i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.2063 | 1.50950 | 0.754748 | − | 0.656015i | \(-0.227759\pi\) | ||||
0.754748 | + | 0.656015i | \(0.227759\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.4772 | + | 16.5717i | −0.407178 | + | 0.540797i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.4501 | 1.18824 | 0.594120 | − | 0.804376i | \(-0.297500\pi\) | ||||
0.594120 | + | 0.804376i | \(0.297500\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.54762 | −0.0829620 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −21.1792 | + | 29.9549i | −0.688959 | + | 0.974433i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.4404 | 1.54161 | 0.770803 | − | 0.637074i | \(-0.219855\pi\) | ||||
0.770803 | + | 0.637074i | \(0.219855\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.04846 | 0.261264 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.80575 | + | 2.39832i | −0.0585553 | + | 0.0777707i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.68090 | −0.216415 | −0.108208 | − | 0.994128i | \(-0.534511\pi\) | ||||
−0.108208 | + | 0.994128i | \(0.534511\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.0961 | − | 43.4678i | 0.812092 | − | 1.40659i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.2089 | + | 14.8871i | −0.362331 | + | 0.481233i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.9230 | − | 16.5323i | −0.546471 | − | 0.533855i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4874 | −0.951206 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.74755 | + | 2.84977i | −0.0885387 | + | 0.0918325i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.65548 | − | 14.9917i | 0.278630 | − | 0.482601i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.60180 | + | 13.1667i | 0.244457 | + | 0.423413i | 0.961979 | − | 0.273124i | \(-0.0880568\pi\) |
−0.717522 | + | 0.696536i | \(0.754724\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 59.8289 | − | 79.4623i | 1.92198 | − | 2.55270i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.363057 | + | 0.628834i | 0.0116511 | + | 0.0201802i | 0.871792 | − | 0.489876i | \(-0.162958\pi\) |
−0.860141 | + | 0.510056i | \(0.829625\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.8705 | + | 14.5272i | 0.476726 | + | 0.465720i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.87643 | − | 6.76886i | −0.0921195 | − | 0.216777i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.0405 | −1.37699 | −0.688494 | − | 0.725242i | \(-0.741728\pi\) | ||||
−0.688494 | + | 0.725242i | \(0.741728\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.88350 | + | 11.9226i | −0.219997 | + | 0.381047i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 36.8004 | + | 9.14388i | 1.17495 | + | 0.291942i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.5191 | − | 37.2722i | −0.686353 | − | 1.18880i | −0.973010 | − | 0.230765i | \(-0.925877\pi\) |
0.286657 | − | 0.958033i | \(-0.407456\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.4575 | + | 25.0411i | −0.460653 | + | 0.797875i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −20.2105 | + | 51.8163i | −0.643308 | + | 1.64933i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.01905 | − | 5.22915i | −0.0960002 | − | 0.166277i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.2758 | + | 19.5302i | −0.358187 | + | 0.620398i | −0.987658 | − | 0.156626i | \(-0.949938\pi\) |
0.629471 | + | 0.777024i | \(0.283272\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.756624 | + | 1.00492i | −0.0240107 | + | 0.0318900i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.1873 | + | 43.6257i | 0.798491 | + | 1.38303i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.1670 | + | 24.5380i | 0.448675 | + | 0.777128i | 0.998300 | − | 0.0582836i | \(-0.0185628\pi\) |
−0.549625 | + | 0.835411i | \(0.685229\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.62517 | − | 54.0343i | −0.272888 | − | 1.70957i |
(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 | 504.2.q.c.25.9 | ✓ | 22 | |
3.2 | odd | 2 | 1512.2.q.d.1369.3 | 22 | |||
4.3 | odd | 2 | 1008.2.q.l.529.3 | 22 | |||
7.2 | even | 3 | 504.2.t.c.457.8 | yes | 22 | ||
9.4 | even | 3 | 504.2.t.c.193.8 | yes | 22 | ||
9.5 | odd | 6 | 1512.2.t.c.361.9 | 22 | |||
12.11 | even | 2 | 3024.2.q.l.2881.3 | 22 | |||
21.2 | odd | 6 | 1512.2.t.c.289.9 | 22 | |||
28.23 | odd | 6 | 1008.2.t.l.961.4 | 22 | |||
36.23 | even | 6 | 3024.2.t.k.1873.9 | 22 | |||
36.31 | odd | 6 | 1008.2.t.l.193.4 | 22 | |||
63.23 | odd | 6 | 1512.2.q.d.793.3 | 22 | |||
63.58 | even | 3 | inner | 504.2.q.c.121.9 | yes | 22 | |
84.23 | even | 6 | 3024.2.t.k.289.9 | 22 | |||
252.23 | even | 6 | 3024.2.q.l.2305.3 | 22 | |||
252.247 | odd | 6 | 1008.2.q.l.625.3 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.9 | ✓ | 22 | 1.1 | even | 1 | trivial | |
504.2.q.c.121.9 | yes | 22 | 63.58 | even | 3 | inner | |
504.2.t.c.193.8 | yes | 22 | 9.4 | even | 3 | ||
504.2.t.c.457.8 | yes | 22 | 7.2 | even | 3 | ||
1008.2.q.l.529.3 | 22 | 4.3 | odd | 2 | |||
1008.2.q.l.625.3 | 22 | 252.247 | odd | 6 | |||
1008.2.t.l.193.4 | 22 | 36.31 | odd | 6 | |||
1008.2.t.l.961.4 | 22 | 28.23 | odd | 6 | |||
1512.2.q.d.793.3 | 22 | 63.23 | odd | 6 | |||
1512.2.q.d.1369.3 | 22 | 3.2 | odd | 2 | |||
1512.2.t.c.289.9 | 22 | 21.2 | odd | 6 | |||
1512.2.t.c.361.9 | 22 | 9.5 | odd | 6 | |||
3024.2.q.l.2305.3 | 22 | 252.23 | even | 6 | |||
3024.2.q.l.2881.3 | 22 | 12.11 | even | 2 | |||
3024.2.t.k.289.9 | 22 | 84.23 | even | 6 | |||
3024.2.t.k.1873.9 | 22 | 36.23 | even | 6 |