Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(193,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.t (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.4 | ||
Character | \(\chi\) | \(=\) | 1008.193 |
Dual form | 1008.2.t.l.961.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.677409 | + | 1.59409i | −0.391102 | + | 0.920347i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.66851 | −1.19339 | −0.596696 | − | 0.802467i | \(-0.703520\pi\) | ||||
−0.596696 | + | 0.802467i | \(0.703520\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.654882 | − | 2.56342i | 0.247522 | − | 0.968882i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.08224 | − | 2.15970i | −0.694078 | − | 0.719899i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.98378 | 1.20115 | 0.600577 | − | 0.799567i | \(-0.294938\pi\) | ||||
0.600577 | + | 0.799567i | \(0.294938\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00103 | − | 1.73384i | 0.277636 | − | 0.480880i | −0.693161 | − | 0.720783i | \(-0.743782\pi\) |
0.970797 | + | 0.239903i | \(0.0771156\pi\) | |||||||
\(14\) | 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 | \(0.206903\pi\) |
0.126068 | + | 0.992022i | \(0.459764\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.64270 | + | 2.78042i | 0.794902 | + | 0.606738i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.887818 | 0.185123 | 0.0925614 | − | 0.995707i | \(-0.470495\pi\) | ||||
0.0925614 | + | 0.995707i | \(0.470495\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.12092 | 0.424185 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.85327 | − | 1.85627i | 0.934013 | − | 0.357239i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.35035 | − | 2.33887i | −0.250753 | − | 0.434317i | 0.712980 | − | 0.701184i | \(-0.247345\pi\) |
−0.963733 | + | 0.266867i | \(0.914012\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.614943 | − | 1.06511i | −0.110447 | − | 0.191300i | 0.805504 | − | 0.592591i | \(-0.201895\pi\) |
−0.915951 | + | 0.401291i | \(0.868562\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.69864 | + | 6.35049i | −0.469774 | + | 1.10548i | ||||
\(34\) | 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 | ||||||||
\(39\) | 2.08578 | + | 2.77025i | 0.333993 | + | 0.443595i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.43477 | + | 2.48509i | −0.224073 | + | 0.388105i | −0.956041 | − | 0.293234i | \(-0.905269\pi\) |
0.731968 | + | 0.681339i | \(0.238602\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.40053 | − | 5.88989i | −0.518576 | − | 0.898200i | −0.999767 | − | 0.0215840i | \(-0.993129\pi\) |
0.481191 | − | 0.876616i | \(-0.340204\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.55646 | + | 5.76317i | 0.828308 | + | 0.859122i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.06845 | + | 10.5109i | −0.885175 | + | 1.53317i | −0.0396620 | + | 0.999213i | \(0.512628\pi\) |
−0.845513 | + | 0.533955i | \(0.820705\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.14226 | − | 3.35748i | −0.877466 | − | 0.479639i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.44223 | − | 9.88445i | −1.04212 | − | 1.38410i | ||||
\(52\) | 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 | ||||||||
\(59\) | 4.79029 | + | 8.29703i | 0.623643 | + | 1.08018i | 0.988802 | + | 0.149236i | \(0.0476813\pi\) |
−0.365159 | + | 0.930945i | \(0.618985\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.74981 | − | 8.22692i | 0.608151 | − | 1.05335i | −0.383394 | − | 0.923585i | \(-0.625245\pi\) |
0.991545 | − | 0.129764i | \(-0.0414218\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.89983 | + | 3.92330i | −0.869297 | + | 0.494289i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.67126 | + | 4.62676i | −0.331329 | + | 0.573879i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.49446 | + | 9.51668i | 0.671255 | + | 1.16265i | 0.977549 | + | 0.210710i | \(0.0675777\pi\) |
−0.306294 | + | 0.951937i | \(0.599089\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.601415 | + | 1.41526i | −0.0724019 | + | 0.170377i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.62888 | 0.549347 | 0.274673 | − | 0.961538i | \(-0.411430\pi\) | ||||
0.274673 | + | 0.961538i | \(0.411430\pi\) | |||||||
\(72\) | 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 | ||||||||
\(75\) | −1.43673 | + | 3.38094i | −0.165900 | + | 0.390398i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.60890 | − | 10.2121i | 0.297312 | − | 1.16378i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.514987 | + | 0.891984i | −0.0579406 | + | 0.100356i | −0.893541 | − | 0.448982i | \(-0.851787\pi\) |
0.835600 | + | 0.549338i | \(0.185120\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.328592 | + | 8.99400i | −0.0365102 | + | 0.999333i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.26656 | + | 9.12195i | 0.578080 | + | 1.00126i | 0.995699 | + | 0.0926419i | \(0.0295312\pi\) |
−0.417620 | + | 0.908622i | \(0.637135\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.53125 | − | 16.5086i | 1.03381 | − | 1.79061i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.64310 | − | 0.568202i | 0.497792 | − | 0.0609176i | ||||
\(88\) | 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 | ||||||||
\(93\) | 2.11445 | − | 0.258757i | 0.219258 | − | 0.0268319i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.7262 | − | 18.5784i | −1.10049 | − | 1.90610i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.12061 | − | 1.94096i | −0.113781 | − | 0.197075i | 0.803511 | − | 0.595290i | \(-0.202963\pi\) |
−0.917292 | + | 0.398216i | \(0.869630\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.29516 | − | 8.60376i | −0.833695 | − | 0.864710i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.56830 | −0.454562 | −0.227281 | − | 0.973829i | \(-0.572984\pi\) | ||||
−0.227281 | + | 0.973829i | \(0.572984\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.7502 | 1.25631 | 0.628156 | − | 0.778088i | \(-0.283810\pi\) | ||||
0.628156 | + | 0.778088i | \(0.283810\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.72056 | − | 7.41958i | −0.948630 | − | 0.724076i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.659761 | + | 1.14274i | 0.0637815 | + | 0.110473i | 0.896153 | − | 0.443746i | \(-0.146351\pi\) |
−0.832371 | + | 0.554218i | \(0.813017\pi\) | |||||||
\(108\) | 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 | −0.888723 | − | 0.458444i | \(-0.848407\pi\) |
0.841386 | + | 0.540435i | \(0.181740\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.36915 | −0.220924 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.82895 | + | 1.44833i | −0.538887 | + | 0.133898i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.5194 | + | 13.2073i | 1.23932 | + | 1.21071i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.87048 | 0.442771 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.98953 | − | 3.97056i | −0.269556 | − | 0.358014i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.68283 | 0.687173 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.38400 | −0.122810 | −0.0614051 | − | 0.998113i | \(-0.519558\pi\) | ||||
−0.0614051 | + | 0.998113i | \(0.519558\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.6926 | − | 1.43088i | 1.02947 | − | 0.125982i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.329724 | 0.0288081 | 0.0144041 | − | 0.999896i | \(-0.495415\pi\) | ||||
0.0144041 | + | 0.999896i | \(0.495415\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.4791 | − | 5.74448i | 1.77576 | − | 0.498110i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.9510 | + | 4.95347i | −1.11464 | + | 0.426326i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.94189 | 0.763958 | 0.381979 | − | 0.924171i | \(-0.375243\pi\) | ||||
0.381979 | + | 0.924171i | \(0.375243\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.92869 | + | 6.80470i | −0.333227 | + | 0.577167i | −0.983143 | − | 0.182840i | \(-0.941471\pi\) |
0.649915 | + | 0.760007i | \(0.274804\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | 9.51293 | − | 7.51692i | 0.784613 | − | 0.619985i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.3215 | 1.33711 | 0.668554 | − | 0.743663i | \(-0.266913\pi\) | ||||
0.668554 | + | 0.743663i | \(0.266913\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.63354 | 0.377072 | 0.188536 | − | 0.982066i | \(-0.439626\pi\) | ||||
0.188536 | + | 0.982066i | \(0.439626\pi\) | |||||||
\(152\) | 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 | ||||||||
\(157\) | 4.25926 | + | 7.37725i | 0.339926 | + | 0.588769i | 0.984418 | − | 0.175842i | \(-0.0562647\pi\) |
−0.644493 | + | 0.764611i | \(0.722931\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.97291 | − | 6.60481i | −0.394377 | − | 0.523795i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.581416 | − | 2.27585i | 0.0458220 | − | 0.179362i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.22354 | − | 2.11923i | −0.0958350 | − | 0.165991i | 0.814122 | − | 0.580694i | \(-0.197219\pi\) |
−0.909957 | + | 0.414703i | \(0.863885\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.20135 | − | 16.9463i | 0.560624 | − | 1.31927i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.0713948 | − | 0.123659i | 0.00552470 | − | 0.00956906i | −0.863250 | − | 0.504777i | \(-0.831575\pi\) |
0.868775 | + | 0.495208i | \(0.164908\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.49587 | + | 7.78708i | 0.345836 | + | 0.599006i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.66632 | − | 23.1777i | 0.509787 | − | 1.77244i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.99834 | + | 15.5856i | −0.684131 | + | 1.18495i | 0.289578 | + | 0.957154i | \(0.406485\pi\) |
−0.973709 | + | 0.227795i | \(0.926848\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.38896 | − | 5.43682i | 0.104995 | − | 0.410985i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.4712 | + | 2.01567i | −1.23805 | + | 0.151507i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.02413 | − | 1.77384i | 0.0765468 | − | 0.132583i | −0.825211 | − | 0.564824i | \(-0.808944\pi\) |
0.901758 | + | 0.432242i | \(0.142277\pi\) | |||||||
\(180\) | 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 | ||||||||
\(185\) | −14.0504 | − | 24.3361i | −1.03301 | − | 1.78922i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.2291 | + | 24.6455i | −1.04053 | + | 1.80226i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.58008 | − | 13.6566i | −0.114934 | − | 0.993373i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.40457 | − | 16.2892i | 0.680491 | − | 1.17864i | −0.294341 | − | 0.955701i | \(-0.595100\pi\) |
0.974831 | − | 0.222944i | \(-0.0715667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.24357 | − | 5.61803i | −0.233477 | − | 0.404394i | 0.725352 | − | 0.688378i | \(-0.241677\pi\) |
−0.958829 | + | 0.283984i | \(0.908344\pi\) | |||||||
\(194\) | 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 | \(-0.600016\pi\) |
0.978158 | − | 0.207863i | \(-0.0666508\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.8924 | + | 2.31197i | −1.33257 | + | 0.163074i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.87982 | + | 1.92982i | −0.482869 | + | 0.135447i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.82868 | − | 6.63147i | 0.267407 | − | 0.463162i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.84865 | − | 1.91742i | −0.128490 | − | 0.133270i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0130 | + | 27.7354i | 1.10764 | + | 1.91850i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.9133 | − | 20.6344i | 0.820145 | − | 1.42053i | −0.0854297 | − | 0.996344i | \(-0.527226\pi\) |
0.905574 | − | 0.424188i | \(-0.139440\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.13564 | + | 7.37884i | −0.214851 | + | 0.505590i | ||||
\(214\) | 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 | ||||||||
\(219\) | 4.18819 | + | 5.56258i | 0.283012 | + | 0.375884i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.15088 | + | 12.3857i | 0.481020 | + | 0.833152i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.53734 | − | 11.3230i | −0.437773 | − | 0.758245i | 0.559745 | − | 0.828665i | \(-0.310899\pi\) |
−0.997517 | + | 0.0704203i | \(0.977566\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.41626 | − | 4.58056i | −0.294418 | − | 0.305371i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.1690 | −1.53778 | −0.768890 | − | 0.639381i | \(-0.779191\pi\) | ||||
−0.768890 | + | 0.639381i | \(0.779191\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.5588 | −1.42465 | −0.712323 | − | 0.701851i | \(-0.752357\pi\) | ||||
−0.712323 | + | 0.701851i | \(0.752357\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.5117 | + | 11.0766i | 0.954800 | + | 0.728786i | ||||
\(232\) | 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 | \(-0.837782\pi\) |
0.858953 | + | 0.512054i | \(0.171115\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.05674 | 0.196902 | 0.0984509 | − | 0.995142i | \(-0.468611\pi\) | ||||
0.0984509 | + | 0.995142i | \(0.468611\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.1146 | − | 6.61642i | −0.905455 | − | 0.424443i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 16.3907 | + | 8.95945i | 1.04716 | + | 0.572398i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.0948 | 1.02409 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.1088 | + | 2.21608i | −1.14760 | + | 0.140438i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.9066 | −0.751541 | −0.375770 | − | 0.926713i | \(-0.622622\pi\) | ||||
−0.375770 | + | 0.926713i | \(0.622622\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.53687 | 0.222361 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 19.8596 | + | 26.3767i | 1.24366 | + | 1.65177i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −31.9453 | −1.99269 | −0.996346 | − | 0.0854116i | \(-0.972779\pi\) | ||||
−0.996346 | + | 0.0854116i | \(0.972779\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.8259 | − | 7.52479i | 1.66688 | − | 0.467567i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.23951 | + | 7.78641i | −0.138622 | + | 0.481967i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.70989 | −0.413750 | −0.206875 | − | 0.978367i | \(-0.566329\pi\) | ||||
−0.206875 | + | 0.978367i | \(0.566329\pi\) | |||||||
\(264\) | 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 | 0.977900 | − | 0.209073i | \(-0.0670447\pi\) |
−0.670013 | + | 0.742350i | \(0.733711\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.46726 | − | 3.53256i | 0.512462 | − | 0.213800i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.44929 | 0.509512 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.2865 | −1.27898 | −0.639492 | − | 0.768798i | \(-0.720855\pi\) | ||||
−0.639492 | + | 0.768798i | \(0.720855\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.01987 | + | 3.54591i | −0.0610578 | + | 0.212288i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.26945 | − | 10.8590i | −0.374004 | − | 0.647794i | 0.616174 | − | 0.787610i | \(-0.288682\pi\) |
−0.990177 | + | 0.139817i | \(0.955349\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.4749 | + | 21.6071i | 0.741554 | + | 1.28441i | 0.951788 | + | 0.306758i | \(0.0992441\pi\) |
−0.210234 | + | 0.977651i | \(0.567423\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 36.8816 | − | 4.51340i | 2.18468 | − | 0.267351i | ||||
\(286\) | 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 | ||||||||
\(291\) | 3.85317 | − | 0.471534i | 0.225877 | − | 0.0276418i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.42625 | − | 12.8626i | 0.433846 | − | 0.751443i | −0.563355 | − | 0.826215i | \(-0.690490\pi\) |
0.997201 | + | 0.0747718i | \(0.0238228\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.7829 | − | 22.1407i | −0.744250 | − | 1.28908i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 19.3344 | − | 7.39496i | 1.12189 | − | 0.429099i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.888734 | − | 1.53933i | 0.0513968 | − | 0.0890219i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.3252 | + | 4.85981i | −0.998609 | + | 0.280115i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.09460 | − | 7.28227i | 0.177780 | − | 0.418355i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.6749 | + | 21.9536i | −0.725763 | + | 1.25706i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.9045 | 1.25016 | 0.625079 | − | 0.780561i | \(-0.285067\pi\) | ||||
0.625079 | + | 0.780561i | \(0.285067\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.63707 | + | 20.3249i | −0.491346 | + | 1.15624i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.78359 | − | 15.2136i | −0.498072 | − | 0.862686i | 0.501926 | − | 0.864911i | \(-0.332625\pi\) |
−0.999998 | + | 0.00222515i | \(0.999292\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.98820 | − | 10.3719i | 0.338473 | − | 0.586252i | −0.645673 | − | 0.763614i | \(-0.723423\pi\) |
0.984146 | + | 0.177362i | \(0.0567563\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 18.4123 | − | 10.4693i | 1.03741 | − | 0.589881i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.866633 | − | 1.50105i | 0.0486750 | − | 0.0843075i | −0.840661 | − | 0.541561i | \(-0.817833\pi\) |
0.889336 | + | 0.457254i | \(0.151167\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.37948 | − | 9.31753i | −0.301193 | − | 0.521681i | ||||
\(320\) | 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 | ||||||||
\(327\) | −13.1684 | − | 17.4897i | −0.728212 | − | 0.967180i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.9697 | + | 22.4394i | 1.26636 | + | 1.23712i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.363127 | + | 0.628954i | −0.0199593 | + | 0.0345705i | −0.875833 | − | 0.482615i | \(-0.839687\pi\) |
0.855873 | + | 0.517186i | \(0.173020\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.73232 | − | 30.3609i | 0.478528 | − | 1.66376i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.6620 | − | 25.3953i | −0.801070 | − | 1.38749i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.84810 | + | 11.8613i | −0.373040 | + | 0.646124i | −0.990032 | − | 0.140846i | \(-0.955018\pi\) |
0.616992 | + | 0.786970i | \(0.288351\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.04848 | − | 1.39255i | −0.0569459 | − | 0.0756331i | ||||
\(340\) | 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 | ||||||||
\(345\) | 1.60488 | − | 3.77663i | 0.0864039 | − | 0.203327i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.10709 | − | 3.64958i | −0.113114 | − | 0.195920i | 0.803910 | − | 0.594751i | \(-0.202749\pi\) |
−0.917024 | + | 0.398831i | \(0.869416\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.8070 | − | 18.7183i | −0.578486 | − | 1.00197i | −0.995653 | − | 0.0931372i | \(-0.970310\pi\) |
0.417167 | − | 0.908830i | \(-0.363023\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.63981 | − | 10.2730i | 0.0875267 | − | 0.548331i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.85115 | 0.258201 | 0.129100 | − | 0.991632i | \(-0.458791\pi\) | ||||
0.129100 | + | 0.991632i | \(0.458791\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.3522 | −0.655586 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −30.2118 | + | 12.6044i | −1.59898 | + | 0.667097i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.90433 | − | 5.03045i | −0.153285 | − | 0.265497i | 0.779148 | − | 0.626839i | \(-0.215652\pi\) |
−0.932433 | + | 0.361343i | \(0.882318\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | −21.6890 | −1.13216 | −0.566078 | − | 0.824352i | \(-0.691540\pi\) | ||||
−0.566078 | + | 0.824352i | \(0.691540\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.35456 | − | 2.07588i | 0.434921 | − | 0.108066i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.03370 | + | 8.82515i | 0.469006 | + | 0.458179i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.7104 | 1.27946 | 0.639729 | − | 0.768601i | \(-0.279047\pi\) | ||||
0.639729 | + | 0.768601i | \(0.279047\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.20441 | + | 12.2471i | −0.268755 | + | 0.632438i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.40696 | −0.278473 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.9950 | 1.43801 | 0.719005 | − | 0.695005i | \(-0.244598\pi\) | ||||
0.719005 | + | 0.695005i | \(0.244598\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.937534 | − | 2.20622i | 0.0480313 | − | 0.113028i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.6227 | 1.05377 | 0.526884 | − | 0.849937i | \(-0.323360\pi\) | ||||
0.526884 | + | 0.849937i | \(0.323360\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.96187 | + | 27.2511i | −0.354810 | + | 1.38884i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.63968 | + | 19.6083i | −0.286681 | + | 0.996743i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.4007 | 0.882250 | 0.441125 | − | 0.897446i | \(-0.354580\pi\) | ||||
0.441125 | + | 0.897446i | \(0.354580\pi\) | |||||||
\(390\) | 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 | ||||||||
\(399\) | −4.71549 | + | 36.5368i | −0.236070 | + | 1.82913i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.70529 | 0.384784 | 0.192392 | − | 0.981318i | \(-0.438376\pi\) | ||||
0.192392 | + | 0.981318i | \(0.438376\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.46231 | −0.122656 | ||||||||
\(404\) | 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 | ||||||||
\(409\) | 7.86755 | + | 13.6270i | 0.389025 | + | 0.673811i | 0.992319 | − | 0.123708i | \(-0.0394786\pi\) |
−0.603294 | + | 0.797519i | \(0.706145\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.05732 | + | 14.2542i | −0.298785 | + | 0.703106i | ||||
\(412\) | 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 | ||||||||
\(417\) | −8.18596 | − | 10.8722i | −0.400868 | − | 0.532416i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.3452 | − | 30.0428i | 0.847369 | − | 1.46769i | −0.0361784 | − | 0.999345i | \(-0.511518\pi\) |
0.883548 | − | 0.468341i | \(-0.155148\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.607053 | − | 1.05145i | −0.0295860 | − | 0.0512444i | 0.850853 | − | 0.525403i | \(-0.176086\pi\) |
−0.880439 | + | 0.474159i | \(0.842752\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 35.3363 | − | 8.78008i | 1.71811 | − | 0.426902i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.57542 | + | 13.1210i | −0.367462 | + | 0.636463i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.9785 | − | 17.5634i | −0.870040 | − | 0.849954i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.30930 | + | 11.0361i | 0.401177 | + | 0.532826i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.68495 | + | 2.91841i | −0.0811610 | + | 0.140575i | −0.903749 | − | 0.428063i | \(-0.859196\pi\) |
0.822588 | + | 0.568638i | \(0.192529\pi\) | |||||||
\(432\) | 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 | ||||||||
\(437\) | 3.56864 | + | 6.18106i | 0.170711 | + | 0.295680i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.5395 | + | 28.6472i | −0.789385 | + | 1.36725i | 0.136959 | + | 0.990577i | \(0.456267\pi\) |
−0.926344 | + | 0.376678i | \(0.877066\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.53849 | + | 20.2565i | 0.263738 | + | 0.964594i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.36682 | − | 2.36740i | 0.0649397 | − | 0.112479i | −0.831728 | − | 0.555184i | \(-0.812648\pi\) |
0.896667 | + | 0.442705i | \(0.145981\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.61086 | − | 7.98625i | −0.218576 | − | 0.378584i | ||||
\(446\) | 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 | ||||||||
\(453\) | −3.13880 | + | 7.38627i | −0.147474 | + | 0.347037i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.1110 | + | 9.87754i | 0.474010 | + | 0.463066i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.68162 | + | 2.91265i | −0.0786628 | + | 0.136248i | −0.902673 | − | 0.430327i | \(-0.858398\pi\) |
0.824010 | + | 0.566575i | \(0.191732\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.85097 | + | 36.6547i | −0.273100 | + | 1.71090i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.0040 | − | 17.3275i | −0.465934 | − | 0.807021i | 0.533309 | − | 0.845920i | \(-0.320948\pi\) |
−0.999243 | + | 0.0388994i | \(0.987615\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.29434 | + | 12.6342i | −0.338997 | + | 0.587160i | −0.984244 | − | 0.176814i | \(-0.943421\pi\) |
0.645247 | + | 0.763974i | \(0.276754\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.64243 | + | 0.690495i | −0.261661 | + | 0.0320210i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.26334 | − | 12.5805i | −0.336107 | − | 0.582155i | 0.647590 | − | 0.761989i | \(-0.275777\pi\) |
−0.983697 | + | 0.179834i | \(0.942444\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.9935 | − | 7.85231i | 1.29262 | − | 0.362586i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.6453 | + | 1.79222i | −0.674818 | + | 0.0825812i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.5470 | − | 23.4640i | −0.622889 | − | 1.07888i | ||||
\(474\) | 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 | ||||||||
\(479\) | 11.3243 | 0.517421 | 0.258710 | − | 0.965955i | \(-0.416702\pi\) | ||||
0.258710 | + | 0.965955i | \(0.416702\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.0829 | 0.961296 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.23405 | + | 2.46851i | 0.147154 | + | 0.112321i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.99036 | + | 5.17946i | 0.135785 | + | 0.235187i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.93684 | + | 10.2829i | −0.269024 | + | 0.465963i | −0.968610 | − | 0.248585i | \(-0.920034\pi\) |
0.699586 | + | 0.714548i | \(0.253368\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.20708 | − | 0.514844i | 0.190251 | − | 0.0232820i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.9598 | + | 20.7150i | −0.539738 | + | 0.934853i | 0.459180 | + | 0.888343i | \(0.348143\pi\) |
−0.998918 | + | 0.0465101i | \(0.985190\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.2924 | 0.868887 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 22.1357 | + | 22.9592i | 0.994925 | + | 1.03194i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.03137 | − | 11.8658i | 0.135975 | − | 0.532252i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.451968 | 0.0202329 | 0.0101164 | − | 0.999949i | \(-0.496780\pi\) | ||||
0.0101164 | + | 0.999949i | \(0.496780\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.148761 | + | 0.197578i | 0.00664614 | + | 0.00882712i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.6077 | 0.651326 | 0.325663 | − | 0.945486i | \(-0.394413\pi\) | ||||
0.325663 | + | 0.945486i | \(0.394413\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.1905 | 0.542471 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.4588 | + | 1.89178i | −0.686551 | + | 0.0840170i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.493171 | −0.0218594 | −0.0109297 | − | 0.999940i | \(-0.503479\pi\) | ||||
−0.0109297 | + | 0.999940i | \(0.503479\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.60819 | − | 7.43255i | −0.336567 | − | 0.328797i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 32.4315 | + | 26.3275i | 1.43189 | + | 1.16239i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −34.0239 | −1.49927 | ||||||||
\(516\) | 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 | 0.835227 | − | 0.549906i | \(-0.185336\pi\) |
−0.893846 | + | 0.448374i | \(0.852003\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.72589 | + | 5.89707i | 0.337185 | + | 0.257369i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.78571 | 0.382711 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.2118 | −0.965730 | ||||||||
\(530\) | 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 | ||||||||
\(535\) | −1.76058 | − | 3.04941i | −0.0761163 | − | 0.131837i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.13390 | + | 2.83416i | 0.0920848 | + | 0.122303i | ||||
\(538\) | 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 | ||||||||
\(543\) | −1.22723 | + | 2.88793i | −0.0526653 | + | 0.123933i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.8647 | − | 29.2105i | 0.722404 | − | 1.25124i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.2496 | + | 26.4132i | 0.652028 | + | 1.12935i | 0.982630 | + | 0.185575i | \(0.0594149\pi\) |
−0.330602 | + | 0.943770i | \(0.607252\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −27.6579 | + | 6.87221i | −1.18041 | + | 0.293299i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.8556 | − | 18.8024i | 0.462464 | − | 0.801011i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.94928 | + | 1.90427i | 0.0828916 | + | 0.0809779i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 48.3117 | − | 5.91217i | 2.05072 | − | 0.250958i | ||||
\(556\) | 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 | ||||||||
\(563\) | 1.31411 | + | 2.27611i | 0.0553831 | + | 0.0959264i | 0.892388 | − | 0.451269i | \(-0.149029\pi\) |
−0.837005 | + | 0.547196i | \(0.815695\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.34279 | − | 2.32579i | 0.0564917 | − | 0.0978465i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.8402 | + | 6.73233i | 0.959199 | + | 0.282731i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.0581 | − | 27.8134i | 0.673191 | − | 1.16600i | −0.303804 | − | 0.952735i | \(-0.598257\pi\) |
0.976994 | − | 0.213266i | \(-0.0684100\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.5907 | + | 35.6642i | 0.861696 | + | 1.49250i | 0.870291 | + | 0.492538i | \(0.163931\pi\) |
−0.00859553 | + | 0.999963i | \(0.502736\pi\) | |||||||
\(572\) | 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 | ||||||||
\(579\) | 11.1529 | − | 1.36484i | 0.463497 | − | 0.0567207i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.8324 | − | 7.52661i | 1.11319 | − | 0.312257i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.50789 | + | 16.4681i | −0.393777 | + | 0.682041i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.5546 | − | 3.86488i | 0.643103 | − | 0.159793i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.98618 | + | 6.90426i | 0.164527 | + | 0.284969i | 0.936487 | − | 0.350702i | \(-0.114057\pi\) |
−0.771960 | + | 0.635671i | \(0.780723\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.94360 | − | 8.56257i | 0.203698 | − | 0.352815i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.34015 | − | 17.2730i | 0.301933 | − | 0.710514i | ||||
\(592\) | 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 | ||||||||
\(597\) | 19.6668 | + | 26.1207i | 0.804910 | + | 1.06905i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.6886 | − | 32.3696i | −0.763594 | − | 1.32258i | −0.940987 | − | 0.338444i | \(-0.890099\pi\) |
0.177392 | − | 0.984140i | \(-0.443234\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.81596 | + | 11.8056i | 0.278029 | + | 0.481560i | 0.970895 | − | 0.239506i | \(-0.0769856\pi\) |
−0.692866 | + | 0.721066i | \(0.743652\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.11240 | − | 31.6823i | 0.371086 | − | 1.29020i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.9969 | −0.528400 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.74228 | −0.111306 | −0.0556529 | − | 0.998450i | \(-0.517724\pi\) | ||||
−0.0556529 | + | 0.998450i | \(0.517724\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.58414 | − | 12.2743i | 0.0641926 | − | 0.497381i | ||||
\(610\) | 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 | −0.490467 | − | 0.871460i | \(-0.663174\pi\) |
0.999940 | − | 0.0109734i | \(-0.00349302\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.1616 | 1.09172 | 0.545859 | − | 0.837877i | \(-0.316204\pi\) | ||||
0.545859 | + | 0.837877i | \(0.316204\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.30882 | − | 1.64803i | 0.172907 | − | 0.0661331i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.80331 | − | 2.46937i | 0.352697 | − | 0.0989333i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1063 | −1.24425 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −55.0600 | + | 6.73800i | −2.19888 | + | 0.269090i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −75.2252 | −2.99942 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.6597 | 1.18073 | 0.590366 | − | 0.807136i | \(-0.298983\pi\) | ||||
0.590366 | + | 0.807136i | \(0.298983\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.8229 | + | 32.9688i | 0.986623 | + | 1.31039i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.69321 | 0.146561 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.9699 | + | 7.28874i | −0.474265 | + | 0.288791i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.63841 | − | 9.99698i | −0.381290 | − | 0.395474i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.1975 | 1.66670 | 0.833350 | − | 0.552746i | \(-0.186420\pi\) | ||||
0.833350 | + | 0.552746i | \(0.186420\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.1099 | + | 17.5109i | −0.398696 | + | 0.690562i | −0.993565 | − | 0.113260i | \(-0.963871\pi\) |
0.594869 | + | 0.803823i | \(0.297204\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −31.2016 | + | 3.81832i | −1.22856 | + | 0.150346i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.08988 | − | 1.88772i | 0.0428475 | − | 0.0742141i | −0.843806 | − | 0.536648i | \(-0.819690\pi\) |
0.886654 | + | 0.462434i | \(0.153024\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.0834 | + | 33.0535i | 0.749091 | + | 1.29746i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.721412 | − | 5.58969i | 0.0282744 | − | 0.219077i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −34.1069 | −1.33471 | −0.667354 | − | 0.744741i | \(-0.732573\pi\) | ||||
−0.667354 | + | 0.744741i | \(0.732573\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.879871 | −0.0343794 | ||||||||
\(656\) | 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 | \(-0.154336\pi\) |
−0.846011 | + | 0.533165i | \(0.821002\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.24205 | + | 7.34744i | 0.164997 | + | 0.285782i | 0.936654 | − | 0.350256i | \(-0.113905\pi\) |
−0.771658 | + | 0.636038i | \(0.780572\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −24.5880 | + | 3.00896i | −0.954917 | + | 0.116859i | ||||
\(664\) | 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 | ||||||||
\(669\) | 22.4783 | − | 2.75080i | 0.869063 | − | 0.106352i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.9222 | − | 32.7742i | 0.730483 | − | 1.26523i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.4056 | + | 38.8077i | 0.863674 | + | 1.49593i | 0.868358 | + | 0.495938i | \(0.165176\pi\) |
−0.00468438 | + | 0.999989i | \(0.501491\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.2934 | − | 3.93701i | 0.396194 | − | 0.151535i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.02684 | + | 6.97469i | −0.154764 | + | 0.268059i | −0.932973 | − | 0.359946i | \(-0.882795\pi\) |
0.778209 | + | 0.628005i | \(0.216128\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.70937 | + | 1.60151i | −0.219105 | + | 0.0614602i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.6949 | − | 36.9334i | 0.601429 | − | 1.41529i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.8446 | + | 36.1039i | −0.797597 | + | 1.38148i | 0.123580 | + | 0.992335i | \(0.460562\pi\) |
−0.921177 | + | 0.389144i | \(0.872771\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.8615 | −0.911701 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.6041 | − | 34.3667i | 0.557182 | − | 1.31117i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.77823 | + | 8.27614i | 0.182036 | + | 0.315296i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.66345 | − | 9.80938i | 0.215448 | − | 0.373166i | −0.737963 | − | 0.674841i | \(-0.764212\pi\) |
0.953411 | + | 0.301674i | \(0.0975456\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −27.4874 | + | 15.6296i | −1.04416 | + | 0.593718i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.4837 | − | 18.1584i | 0.397671 | − | 0.688786i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.2493 | − | 17.7522i | −0.388218 | − | 0.672414i | ||||
\(698\) | 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 | ||||||||
\(705\) | 33.7417 | + | 44.8144i | 1.27079 | + | 1.68781i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.99169 | + | 11.7105i | −0.112514 | + | 0.440418i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.6074 | + | 39.1571i | −0.849037 | + | 1.47058i | 0.0330317 | + | 0.999454i | \(0.489484\pi\) |
−0.882069 | + | 0.471121i | \(0.843850\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.99874 | − | 0.745104i | 0.112462 | − | 0.0279436i | ||||
\(712\) | 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 | ||||||||
\(717\) | −0.450188 | − | 0.597921i | −0.0168126 | − | 0.0223298i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.3171 | − | 19.6018i | −0.422057 | − | 0.731024i | 0.574084 | − | 0.818797i | \(-0.305358\pi\) |
−0.996141 | + | 0.0877727i | \(0.972025\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.34986 | − | 32.6841i | 0.310965 | − | 1.21722i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.07066 | + | 4.87271i | −0.0770087 | + | 0.181218i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.86398 | − | 4.96056i | −0.106366 | − | 0.184231i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.04956 | − | 1.81789i | −0.0389259 | − | 0.0674217i | 0.845906 | − | 0.533332i | \(-0.179060\pi\) |
−0.884832 | + | 0.465910i | \(0.845727\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.1085 | − | 18.0180i | 0.744760 | − | 0.667332i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 48.5834 | 1.79692 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.2906 | −1.15574 | −0.577872 | − | 0.816127i | \(-0.696117\pi\) | ||||
−0.577872 | + | 0.816127i | \(0.696117\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −25.3853 | + | 20.0590i | −0.936352 | + | 0.739886i | ||||
\(736\) | 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 | \(0.449935\pi\) |
−0.933654 | + | 0.358177i | \(0.883399\pi\) | |||||||
\(740\) | 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 | \(-0.909794\pi\) |
0.722208 | + | 0.691676i | \(0.243127\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −43.5540 | −1.59570 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.73444 | − | 30.3682i | 0.319576 | − | 1.11112i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.36139 | − | 0.942886i | 0.122822 | − | 0.0344523i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.7298 | −1.19433 | −0.597164 | − | 0.802119i | \(-0.703706\pi\) | ||||
−0.597164 | + | 0.802119i | \(0.703706\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.06566 | − | 18.9802i | 0.293929 | − | 0.691679i | ||||
\(754\) | 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 | ||||||||
\(759\) | −2.39591 | + | 5.63808i | −0.0869658 | + | 0.204649i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.2936 | −1.38814 | −0.694070 | − | 0.719907i | \(-0.744184\pi\) | ||||
−0.694070 | + | 0.719907i | \(0.744184\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.9214 | + | 23.3692i | 0.866014 | + | 0.846020i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −55.4999 | + | 13.7902i | −2.00660 | + | 0.498585i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.1809 | 0.692583 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.0674 | − | 19.1693i | 0.399100 | − | 0.691262i | −0.594515 | − | 0.804085i | \(-0.702656\pi\) |
0.993615 | + | 0.112823i | \(0.0359892\pi\) | |||||||
\(770\) | 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 | ||||||||
\(777\) | −6.17689 | + | 47.8601i | −0.221595 | + | 1.71697i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.0685 | −0.826515 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.4404 | 0.659850 | ||||||||
\(782\) | 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 | ||||||||
\(787\) | −16.1523 | − | 27.9766i | −0.575767 | − | 0.997257i | −0.995958 | − | 0.0898216i | \(-0.971370\pi\) |
0.420191 | − | 0.907436i | \(-0.361963\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.54534 | − | 10.6962i | 0.161818 | − | 0.380793i | ||||
\(790\) | 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 | ||||||||
\(795\) | 13.2702 | + | 17.6250i | 0.470647 | + | 0.625093i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.6877 | + | 20.2438i | −0.414001 | + | 0.717071i | −0.995323 | − | 0.0966026i | \(-0.969202\pi\) |
0.581322 | + | 0.813674i | \(0.302536\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43.3501 | − | 75.0845i | −1.53361 | − | 2.65630i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.86564 | − | 9.96337i | 0.101252 | − | 0.352038i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.00755 | − | 13.8695i | 0.282580 | − | 0.489444i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.55151 | + | 6.07312i | −0.0546836 | + | 0.214049i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.8040 | + | 15.6776i | 0.415521 | + | 0.551877i | ||||
\(808\) | 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 | \(-0.138550\pi\) | ||||
0.906758 | + | 0.421652i | \(0.138550\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.4277 | + | 2.13272i | −0.611215 | + | 0.0747978i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.26502 | + | 5.65518i | 0.114369 | + | 0.198092i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.3373 | − | 47.3495i | 0.956409 | − | 1.65655i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.104588 | + | 15.8905i | −0.00365459 | + | 0.555261i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.3787 | − | 23.1727i | 0.466921 | − | 0.808731i | −0.532365 | − | 0.846515i | \(-0.678696\pi\) |
0.999286 | + | 0.0377837i | \(0.0120298\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.2449 | − | 35.0652i | −0.705693 | − | 1.22230i | −0.966441 | − | 0.256890i | \(-0.917302\pi\) |
0.260747 | − | 0.965407i | \(-0.416031\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.72362 | + | 13.4689i | −0.199271 | + | 0.468928i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.9452 | 0.971749 | 0.485875 | − | 0.874029i | \(-0.338501\pi\) | ||||
0.485875 | + | 0.874029i | \(0.338501\pi\) | |||||||
\(828\) | 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 | ||||||||
\(831\) | 14.4197 | − | 33.9326i | 0.500213 | − | 1.17711i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 42.7095 | − | 26.0068i | 1.47980 | − | 0.901081i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.190518 | + | 0.329986i | −0.00659313 | + | 0.0114196i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.96162 | − | 4.02778i | −0.171499 | − | 0.139221i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.6312 | + | 28.8061i | 0.574174 | + | 0.994499i | 0.996131 | + | 0.0878827i | \(0.0280101\pi\) |
−0.421957 | + | 0.906616i | \(0.638657\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.8531 | − | 18.7982i | 0.374246 | − | 0.648213i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.5572 | − | 2.63807i | 0.742469 | − | 0.0908601i | ||||
\(844\) | 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 | ||||||||
\(849\) | −42.8942 | + | 5.24920i | −1.47213 | + | 0.180152i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.67461 | + | 8.09666i | 0.160244 | + | 0.277550i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.38730 | − | 7.59902i | −0.150218 | − | 0.260186i | 0.781089 | − | 0.624419i | \(-0.214664\pi\) |
−0.931308 | + | 0.364234i | \(0.881331\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −17.7891 | + | 61.8499i | −0.608375 | + | 2.11522i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.35440 | −0.0462653 | −0.0231327 | − | 0.999732i | \(-0.507364\pi\) | ||||
−0.0231327 | + | 0.999732i | \(0.507364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.0387 | 0.615472 | 0.307736 | − | 0.951472i | \(-0.400429\pi\) | ||||
0.307736 | + | 0.951472i | \(0.400429\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.1360 | + | 5.06317i | −0.413594 | + | 0.172552i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.37624 | + | 11.0440i | 0.217050 | + | 0.375941i | 0.953905 | − | 0.300110i | \(-0.0970233\pi\) |
−0.736855 | + | 0.676051i | \(0.763690\pi\) | |||||||
\(864\) | 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 | ||||||||
\(871\) | 22.0005 | 0.745459 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.85851 | + | 6.46172i | −0.0629009 | + | 0.218696i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.03135 | − | 19.6943i | 0.170091 | − | 0.665790i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.5807 | −0.593657 | −0.296829 | − | 0.954931i | \(-0.595929\pi\) | ||||
−0.296829 | + | 0.954931i | \(0.595929\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.4736 | + | 20.5514i | 0.521911 | + | 0.693180i | ||||
\(880\) | 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 | \(-0.739334\pi\) | ||||
−0.683020 | + | 0.730400i | \(0.739334\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 43.9534 | − | 5.37883i | 1.47748 | − | 0.180807i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.93571 | 0.0985715 | 0.0492858 | − | 0.998785i | \(-0.484305\pi\) | ||||
0.0492858 | + | 0.998785i | \(0.484305\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.906357 | + | 3.54778i | −0.0303982 | + | 0.118989i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.30904 | + | 35.8301i | −0.0438544 | + | 1.20035i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −97.5700 | −3.26506 | ||||||||
\(894\) | 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 | ||||||||
\(903\) | 3.98928 | − | 30.9100i | 0.132755 | − | 1.02862i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.83439 | −0.160701 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.2790 | 1.13822 | 0.569108 | − | 0.822263i | \(-0.307289\pi\) | ||||
0.569108 | + | 0.822263i | \(0.307289\pi\) | |||||||
\(908\) | 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 | \(-0.113870\pi\) |
−0.771586 | + | 0.636124i | \(0.780536\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.9808 | + | 36.3398i | 0.694363 | + | 1.20267i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −26.4098 | − | 35.0765i | −0.873083 | − | 1.15959i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.215930 | − | 0.845222i | 0.00713065 | − | 0.0279117i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.9444 | − | 24.1524i | −0.459983 | − | 0.796714i | 0.538976 | − | 0.842321i | \(-0.318811\pi\) |
−0.998959 | + | 0.0456069i | \(0.985478\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.8383 | + | 34.9178i | −0.488940 | + | 1.15058i | ||||
\(922\) | 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 | ||||||||
\(927\) | −26.5489 | − | 27.5365i | −0.871979 | − | 0.904418i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.15294 | − | 15.8534i | 0.300298 | − | 0.520132i | −0.675905 | − | 0.736989i | \(-0.736247\pi\) |
0.976203 | + | 0.216857i | \(0.0695804\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.31415 | − | 56.2585i | −0.0430697 | − | 1.84380i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 30.2019 | − | 3.69598i | 0.988767 | − | 0.121001i | ||||
\(934\) | 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 | ||||||||
\(941\) | −18.2251 | − | 31.5668i | −0.594120 | − | 1.02905i | −0.993670 | − | 0.112335i | \(-0.964167\pi\) |
0.399550 | − | 0.916711i | \(-0.369166\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.27381 | + | 2.20630i | −0.0414810 | + | 0.0718472i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.21645 | + | 36.4428i | 0.137161 | + | 1.18548i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.7202 | − | 41.0846i | 0.770803 | − | 1.33507i | −0.166321 | − | 0.986072i | \(-0.553189\pi\) |
0.937124 | − | 0.348998i | \(-0.113478\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.02423 | − | 6.97017i | −0.130632 | − | 0.226261i | ||||
\(950\) | 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 | ||||||||
\(957\) | 18.4971 | − | 2.26359i | 0.597925 | − | 0.0731715i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.85588 | − | 22.9218i | 0.189096 | − | 0.740185i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.7437 | − | 25.5368i | 0.475603 | − | 0.823768i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.09419 | − | 3.80434i | 0.0352599 | − | 0.122593i | ||||
\(964\) | 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 | \(-0.911943\pi\) |
0.717522 | + | 0.696536i | \(0.245276\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 38.9019 | − | 91.5445i | 1.24971 | − | 2.94083i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.363057 | − | 0.628834i | −0.0116511 | − | 0.0201802i | 0.860141 | − | 0.510056i | \(-0.170375\pi\) |
−0.871792 | + | 0.489876i | \(0.837042\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.8705 | + | 14.5272i | 0.476726 | + | 0.465720i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.42379 | + | 5.87549i | 0.141675 | + | 0.188166i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.5203 | + | 37.2742i | 0.688494 | + | 1.19251i | 0.972325 | + | 0.233633i | \(0.0750613\pi\) |
−0.283831 | + | 0.958874i | \(0.591605\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | −43.0382 | −1.37271 | −0.686353 | − | 0.727269i | \(-0.740789\pi\) | ||||
−0.686353 | + | 0.727269i | \(0.740789\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.9149 | 0.921307 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −51.3302 | + | 21.4151i | −1.63386 | + | 0.681649i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.01905 | − | 5.22915i | −0.0960002 | − | 0.166277i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.2758 | − | 19.5302i | 0.358187 | − | 0.620398i | −0.629471 | − | 0.777024i | \(-0.716728\pi\) |
0.987658 | + | 0.156626i | \(0.0500618\pi\) | |||||||
\(992\) | 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 | ||||||||
\(997\) | −28.3341 | −0.897350 | −0.448675 | − | 0.893695i | \(-0.648104\pi\) | ||||
−0.448675 | + | 0.893695i | \(0.648104\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 42.4825 | + | 34.4868i | 1.34409 | + | 1.09111i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1008.2.t.l.193.4 | 22 | ||
3.2 | odd | 2 | 3024.2.t.k.1873.9 | 22 | |||
4.3 | odd | 2 | 504.2.t.c.193.8 | yes | 22 | ||
7.2 | even | 3 | 1008.2.q.l.625.3 | 22 | |||
9.2 | odd | 6 | 3024.2.q.l.2881.3 | 22 | |||
9.7 | even | 3 | 1008.2.q.l.529.3 | 22 | |||
12.11 | even | 2 | 1512.2.t.c.361.9 | 22 | |||
21.2 | odd | 6 | 3024.2.q.l.2305.3 | 22 | |||
28.23 | odd | 6 | 504.2.q.c.121.9 | yes | 22 | ||
36.7 | odd | 6 | 504.2.q.c.25.9 | ✓ | 22 | ||
36.11 | even | 6 | 1512.2.q.d.1369.3 | 22 | |||
63.2 | odd | 6 | 3024.2.t.k.289.9 | 22 | |||
63.16 | even | 3 | inner | 1008.2.t.l.961.4 | 22 | ||
84.23 | even | 6 | 1512.2.q.d.793.3 | 22 | |||
252.79 | odd | 6 | 504.2.t.c.457.8 | yes | 22 | ||
252.191 | even | 6 | 1512.2.t.c.289.9 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.9 | ✓ | 22 | 36.7 | odd | 6 | ||
504.2.q.c.121.9 | yes | 22 | 28.23 | odd | 6 | ||
504.2.t.c.193.8 | yes | 22 | 4.3 | odd | 2 | ||
504.2.t.c.457.8 | yes | 22 | 252.79 | odd | 6 | ||
1008.2.q.l.529.3 | 22 | 9.7 | even | 3 | |||
1008.2.q.l.625.3 | 22 | 7.2 | even | 3 | |||
1008.2.t.l.193.4 | 22 | 1.1 | even | 1 | trivial | ||
1008.2.t.l.961.4 | 22 | 63.16 | even | 3 | inner | ||
1512.2.q.d.793.3 | 22 | 84.23 | even | 6 | |||
1512.2.q.d.1369.3 | 22 | 36.11 | even | 6 | |||
1512.2.t.c.289.9 | 22 | 252.191 | even | 6 | |||
1512.2.t.c.361.9 | 22 | 12.11 | even | 2 | |||
3024.2.q.l.2305.3 | 22 | 21.2 | odd | 6 | |||
3024.2.q.l.2881.3 | 22 | 9.2 | odd | 6 | |||
3024.2.t.k.289.9 | 22 | 63.2 | odd | 6 | |||
3024.2.t.k.1873.9 | 22 | 3.2 | odd | 2 |