Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,2,Mod(971,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.971");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.e (of order \(2\), degree \(1\), 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: | \(12.9357651274\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 971.32 | ||
Character | \(\chi\) | \(=\) | 1620.971 |
Dual form | 1620.2.e.b.971.31 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.499529 | + | 1.32305i | 0.353220 | + | 0.935540i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.50094 | + | 1.32181i | −0.750471 | + | 0.660903i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.20913i | 0.457008i | 0.973543 | + | 0.228504i | \(0.0733835\pi\) | ||||
−0.973543 | + | 0.228504i | \(0.926617\pi\) | |||||||
\(8\) | −2.49858 | − | 1.32555i | −0.883383 | − | 0.468651i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.32305 | − | 0.499529i | 0.418386 | − | 0.157965i | ||||
\(11\) | 3.04322 | 0.917564 | 0.458782 | − | 0.888549i | \(-0.348286\pi\) | ||||
0.458782 | + | 0.888549i | \(0.348286\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.07917 | −1.40871 | −0.704354 | − | 0.709849i | \(-0.748763\pi\) | ||||
−0.704354 | + | 0.709849i | \(0.748763\pi\) | |||||||
\(14\) | −1.59974 | + | 0.603996i | −0.427550 | + | 0.161425i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.505654 | − | 3.96791i | 0.126413 | − | 0.991978i | ||||
\(17\) | 2.23944i | 0.543143i | 0.962418 | + | 0.271572i | \(0.0875434\pi\) | ||||
−0.962418 | + | 0.271572i | \(0.912457\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.53835i | 0.582337i | 0.956672 | + | 0.291169i | \(0.0940441\pi\) | ||||
−0.956672 | + | 0.291169i | \(0.905956\pi\) | |||||||
\(20\) | 1.32181 | + | 1.50094i | 0.295565 | + | 0.335621i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.52017 | + | 4.02634i | 0.324102 | + | 0.858418i | ||||
\(23\) | −6.96134 | −1.45154 | −0.725770 | − | 0.687937i | \(-0.758516\pi\) | ||||
−0.725770 | + | 0.687937i | \(0.758516\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −2.53719 | − | 6.72001i | −0.497584 | − | 1.31790i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.59824 | − | 1.81484i | −0.302038 | − | 0.342972i | ||||
\(29\) | 5.59345i | 1.03868i | 0.854568 | + | 0.519339i | \(0.173822\pi\) | ||||
−0.854568 | + | 0.519339i | \(0.826178\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.27657i | − | 0.588489i | −0.955730 | − | 0.294245i | \(-0.904932\pi\) | ||
0.955730 | − | 0.294245i | \(-0.0950680\pi\) | |||||||
\(32\) | 5.50235 | − | 1.31308i | 0.972687 | − | 0.232122i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.96289 | + | 1.11866i | −0.508132 | + | 0.191849i | ||||
\(35\) | 1.20913 | 0.204380 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.3514 | −1.70176 | −0.850882 | − | 0.525356i | \(-0.823932\pi\) | ||||
−0.850882 | + | 0.525356i | \(0.823932\pi\) | |||||||
\(38\) | −3.35837 | + | 1.26798i | −0.544800 | + | 0.205693i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.32555 | + | 2.49858i | −0.209587 | + | 0.395061i | ||||
\(41\) | 4.27480i | 0.667611i | 0.942642 | + | 0.333806i | \(0.108333\pi\) | ||||
−0.942642 | + | 0.333806i | \(0.891667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.31983i | − | 0.658767i | −0.944196 | − | 0.329384i | \(-0.893159\pi\) | ||
0.944196 | − | 0.329384i | \(-0.106841\pi\) | |||||||
\(44\) | −4.56769 | + | 4.02254i | −0.688605 | + | 0.606421i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.47739 | − | 9.21023i | −0.512713 | − | 1.35797i | ||||
\(47\) | −10.3014 | −1.50262 | −0.751308 | − | 0.659951i | \(-0.770577\pi\) | ||||
−0.751308 | + | 0.659951i | \(0.770577\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.53800 | 0.791143 | ||||||||
\(50\) | −0.499529 | − | 1.32305i | −0.0706440 | − | 0.187108i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.62354 | − | 6.71368i | 1.05719 | − | 0.931020i | ||||
\(53\) | 9.42683i | 1.29487i | 0.762119 | + | 0.647437i | \(0.224159\pi\) | ||||
−0.762119 | + | 0.647437i | \(0.775841\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.04322i | − | 0.410347i | ||||||
\(56\) | 1.60276 | − | 3.02112i | 0.214178 | − | 0.403714i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.40044 | + | 2.79409i | −0.971725 | + | 0.366882i | ||||
\(59\) | −8.92669 | −1.16216 | −0.581078 | − | 0.813848i | \(-0.697369\pi\) | ||||
−0.581078 | + | 0.813848i | \(0.697369\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.65793 | −0.340313 | −0.170156 | − | 0.985417i | \(-0.554427\pi\) | ||||
−0.170156 | + | 0.985417i | \(0.554427\pi\) | |||||||
\(62\) | 4.33508 | − | 1.63674i | 0.550555 | − | 0.207866i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.48585 | + | 6.62398i | 0.560732 | + | 0.827998i | ||||
\(65\) | 5.07917i | 0.629993i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 14.4173i | − | 1.76136i | −0.473714 | − | 0.880679i | \(-0.657087\pi\) | ||
0.473714 | − | 0.880679i | \(-0.342913\pi\) | |||||||
\(68\) | −2.96010 | − | 3.36126i | −0.358965 | − | 0.407613i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.603996 | + | 1.59974i | 0.0721913 | + | 0.191206i | ||||
\(71\) | −3.49303 | −0.414546 | −0.207273 | − | 0.978283i | \(-0.566459\pi\) | ||||
−0.207273 | + | 0.978283i | \(0.566459\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.10052 | 0.596970 | 0.298485 | − | 0.954414i | \(-0.403519\pi\) | ||||
0.298485 | + | 0.954414i | \(0.403519\pi\) | |||||||
\(74\) | −5.17084 | − | 13.6955i | −0.601098 | − | 1.59207i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.35521 | − | 3.80992i | −0.384869 | − | 0.437027i | ||||
\(77\) | 3.67965i | 0.419335i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.76977i | − | 0.424132i | −0.977255 | − | 0.212066i | \(-0.931981\pi\) | ||
0.977255 | − | 0.212066i | \(-0.0680192\pi\) | |||||||
\(80\) | −3.96791 | − | 0.505654i | −0.443626 | − | 0.0565338i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.65579 | + | 2.13538i | −0.624577 | + | 0.235814i | ||||
\(83\) | −0.572344 | −0.0628230 | −0.0314115 | − | 0.999507i | \(-0.510000\pi\) | ||||
−0.0314115 | + | 0.999507i | \(0.510000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.23944 | 0.242901 | ||||||||
\(86\) | 5.71536 | − | 2.15788i | 0.616303 | − | 0.232690i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.60373 | − | 4.03392i | −0.810561 | − | 0.430018i | ||||
\(89\) | 2.40129i | 0.254536i | 0.991868 | + | 0.127268i | \(0.0406208\pi\) | ||||
−0.991868 | + | 0.127268i | \(0.959379\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6.14138i | − | 0.643791i | ||||||
\(92\) | 10.4486 | − | 9.20155i | 1.08934 | − | 0.959328i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.14586 | − | 13.6293i | −0.530755 | − | 1.40576i | ||||
\(95\) | 2.53835 | 0.260429 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.6511 | −1.18299 | −0.591496 | − | 0.806308i | \(-0.701462\pi\) | ||||
−0.591496 | + | 0.806308i | \(0.701462\pi\) | |||||||
\(98\) | 2.76639 | + | 7.32708i | 0.279448 | + | 0.740146i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.50094 | − | 1.32181i | 0.150094 | − | 0.132181i | ||||
\(101\) | 4.77766i | 0.475395i | 0.971339 | + | 0.237698i | \(0.0763927\pi\) | ||||
−0.971339 | + | 0.237698i | \(0.923607\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.45891i | − | 0.932014i | −0.884781 | − | 0.466007i | \(-0.845692\pi\) | ||
0.884781 | − | 0.466007i | \(-0.154308\pi\) | |||||||
\(104\) | 12.6907 | + | 6.73267i | 1.24443 | + | 0.660193i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.4722 | + | 4.70897i | −1.21141 | + | 0.457376i | ||||
\(107\) | 18.3014 | 1.76926 | 0.884630 | − | 0.466294i | \(-0.154411\pi\) | ||||
0.884630 | + | 0.466294i | \(0.154411\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.2589 | −0.982625 | −0.491312 | − | 0.870983i | \(-0.663483\pi\) | ||||
−0.491312 | + | 0.870983i | \(0.663483\pi\) | |||||||
\(110\) | 4.02634 | − | 1.52017i | 0.383896 | − | 0.144943i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.79772 | + | 0.611402i | 0.453342 | + | 0.0577720i | ||||
\(113\) | 6.13462i | 0.577096i | 0.957465 | + | 0.288548i | \(0.0931725\pi\) | ||||
−0.957465 | + | 0.288548i | \(0.906827\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.96134i | 0.649149i | ||||||||
\(116\) | −7.39346 | − | 8.39545i | −0.686466 | − | 0.779498i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.45914 | − | 11.8105i | −0.410497 | − | 1.08724i | ||||
\(119\) | −2.70777 | −0.248221 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.73884 | −0.158076 | ||||||||
\(122\) | −1.32771 | − | 3.51658i | −0.120205 | − | 0.318376i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.33099 | + | 4.91794i | 0.388934 | + | 0.441644i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.41213i | 0.835192i | 0.908633 | + | 0.417596i | \(0.137127\pi\) | ||||
−0.908633 | + | 0.417596i | \(0.862873\pi\) | |||||||
\(128\) | −6.52307 | + | 9.24389i | −0.576563 | + | 0.817053i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.72001 | + | 2.53719i | −0.589384 | + | 0.222526i | ||||
\(131\) | 2.13260 | 0.186327 | 0.0931633 | − | 0.995651i | \(-0.470302\pi\) | ||||
0.0931633 | + | 0.995651i | \(0.470302\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.06920 | −0.266133 | ||||||||
\(134\) | 19.0749 | − | 7.20187i | 1.64782 | − | 0.622147i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.96848 | − | 5.59542i | 0.254545 | − | 0.479803i | ||||
\(137\) | − | 16.4869i | − | 1.40857i | −0.709918 | − | 0.704285i | \(-0.751268\pi\) | ||
0.709918 | − | 0.704285i | \(-0.248732\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.1007i | 1.70492i | 0.522792 | + | 0.852460i | \(0.324890\pi\) | ||||
−0.522792 | + | 0.852460i | \(0.675110\pi\) | |||||||
\(140\) | −1.81484 | + | 1.59824i | −0.153382 | + | 0.135076i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.74487 | − | 4.62146i | −0.146426 | − | 0.387824i | ||||
\(143\) | −15.4570 | −1.29258 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.59345 | 0.464511 | ||||||||
\(146\) | 2.54785 | + | 6.74826i | 0.210862 | + | 0.558490i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 15.5369 | − | 13.6826i | 1.27713 | − | 1.12470i | ||||
\(149\) | 1.88370i | 0.154319i | 0.997019 | + | 0.0771594i | \(0.0245850\pi\) | ||||
−0.997019 | + | 0.0771594i | \(0.975415\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.18825i | 0.503593i | 0.967780 | + | 0.251796i | \(0.0810214\pi\) | ||||
−0.967780 | + | 0.251796i | \(0.918979\pi\) | |||||||
\(152\) | 3.36470 | − | 6.34228i | 0.272913 | − | 0.514427i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.86837 | + | 1.83809i | −0.392304 | + | 0.148117i | ||||
\(155\) | −3.27657 | −0.263180 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.20024 | −0.175598 | −0.0877991 | − | 0.996138i | \(-0.527983\pi\) | ||||
−0.0877991 | + | 0.996138i | \(0.527983\pi\) | |||||||
\(158\) | 4.98761 | − | 1.88311i | 0.396793 | − | 0.149812i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.31308 | − | 5.50235i | −0.103808 | − | 0.434999i | ||||
\(161\) | − | 8.41717i | − | 0.663366i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 15.3649i | − | 1.20347i | −0.798694 | − | 0.601737i | \(-0.794475\pi\) | ||
0.798694 | − | 0.601737i | \(-0.205525\pi\) | |||||||
\(164\) | −5.65046 | − | 6.41622i | −0.441227 | − | 0.501023i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.285903 | − | 0.757242i | −0.0221903 | − | 0.0587734i | ||||
\(167\) | 22.2247 | 1.71980 | 0.859901 | − | 0.510461i | \(-0.170525\pi\) | ||||
0.859901 | + | 0.510461i | \(0.170525\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.7979 | 0.984457 | ||||||||
\(170\) | 1.11866 | + | 2.96289i | 0.0857975 | + | 0.227244i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.70997 | + | 6.48381i | 0.435381 | + | 0.494386i | ||||
\(173\) | 15.4106i | 1.17165i | 0.810438 | + | 0.585825i | \(0.199229\pi\) | ||||
−0.810438 | + | 0.585825i | \(0.800771\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.20913i | − | 0.0914017i | ||||||
\(176\) | 1.53881 | − | 12.0752i | 0.115992 | − | 0.910203i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.17703 | + | 1.19951i | −0.238129 | + | 0.0899073i | ||||
\(179\) | −12.8229 | −0.958425 | −0.479212 | − | 0.877699i | \(-0.659078\pi\) | ||||
−0.479212 | + | 0.877699i | \(0.659078\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3649 | 1.29072 | 0.645360 | − | 0.763879i | \(-0.276707\pi\) | ||||
0.645360 | + | 0.763879i | \(0.276707\pi\) | |||||||
\(182\) | 8.12537 | − | 3.06779i | 0.602293 | − | 0.227400i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 17.3935 | + | 9.22758i | 1.28227 | + | 0.680266i | ||||
\(185\) | 10.3514i | 0.761052i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.81509i | 0.498369i | ||||||||
\(188\) | 15.4618 | − | 13.6165i | 1.12767 | − | 0.993085i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.26798 | + | 3.35837i | 0.0919889 | + | 0.243642i | ||||
\(191\) | 17.8286 | 1.29003 | 0.645017 | − | 0.764169i | \(-0.276850\pi\) | ||||
0.645017 | + | 0.764169i | \(0.276850\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.88362 | −0.351530 | −0.175765 | − | 0.984432i | \(-0.556240\pi\) | ||||
−0.175765 | + | 0.984432i | \(0.556240\pi\) | |||||||
\(194\) | −5.82007 | − | 15.4151i | −0.417856 | − | 1.10674i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.31222 | + | 7.32017i | −0.593730 | + | 0.522869i | ||||
\(197\) | 16.8173i | 1.19818i | 0.800682 | + | 0.599090i | \(0.204471\pi\) | ||||
−0.800682 | + | 0.599090i | \(0.795529\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.91492i | 0.419297i | 0.977777 | + | 0.209649i | \(0.0672320\pi\) | ||||
−0.977777 | + | 0.209649i | \(0.932768\pi\) | |||||||
\(200\) | 2.49858 | + | 1.32555i | 0.176677 | + | 0.0937303i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.32110 | + | 2.38658i | −0.444751 | + | 0.167919i | ||||
\(203\) | −6.76321 | −0.474685 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.27480 | 0.298565 | ||||||||
\(206\) | 12.5146 | − | 4.72500i | 0.871937 | − | 0.329206i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.56830 | + | 20.1537i | −0.178080 | + | 1.39741i | ||||
\(209\) | 7.72475i | 0.534332i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.6534i | 1.90374i | 0.306507 | + | 0.951868i | \(0.400840\pi\) | ||||
−0.306507 | + | 0.951868i | \(0.599160\pi\) | |||||||
\(212\) | −12.4604 | − | 14.1491i | −0.855787 | − | 0.971766i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.14206 | + | 24.2137i | 0.624938 | + | 1.65521i | ||||
\(215\) | −4.31983 | −0.294610 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.96180 | 0.268945 | ||||||||
\(218\) | −5.12462 | − | 13.5731i | −0.347083 | − | 0.919285i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.02254 | + | 4.56769i | 0.271200 | + | 0.307954i | ||||
\(221\) | − | 11.3745i | − | 0.765130i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 23.9473i | − | 1.60363i | −0.597572 | − | 0.801815i | \(-0.703868\pi\) | ||
0.597572 | − | 0.801815i | \(-0.296132\pi\) | |||||||
\(224\) | 1.58768 | + | 6.65306i | 0.106082 | + | 0.444526i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.11643 | + | 3.06442i | −0.539897 | + | 0.203842i | ||||
\(227\) | −6.91958 | −0.459269 | −0.229634 | − | 0.973277i | \(-0.573753\pi\) | ||||
−0.229634 | + | 0.973277i | \(0.573753\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.3167 | −1.01216 | −0.506080 | − | 0.862487i | \(-0.668906\pi\) | ||||
−0.506080 | + | 0.862487i | \(0.668906\pi\) | |||||||
\(230\) | −9.21023 | + | 3.47739i | −0.607305 | + | 0.229292i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.41438 | − | 13.9757i | 0.486778 | − | 0.917551i | ||||
\(233\) | 6.61050i | 0.433068i | 0.976275 | + | 0.216534i | \(0.0694753\pi\) | ||||
−0.976275 | + | 0.216534i | \(0.930525\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.3014i | 0.671991i | ||||||||
\(236\) | 13.3984 | − | 11.7994i | 0.872165 | − | 0.768073i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.35261 | − | 3.58253i | −0.0876767 | − | 0.232221i | ||||
\(239\) | 8.22119 | 0.531785 | 0.265892 | − | 0.964003i | \(-0.414333\pi\) | ||||
0.265892 | + | 0.964003i | \(0.414333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.6155 | 0.941470 | 0.470735 | − | 0.882275i | \(-0.343989\pi\) | ||||
0.470735 | + | 0.882275i | \(0.343989\pi\) | |||||||
\(242\) | −0.868600 | − | 2.30058i | −0.0558357 | − | 0.147887i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.98940 | − | 3.51327i | 0.255395 | − | 0.224914i | ||||
\(245\) | − | 5.53800i | − | 0.353810i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 12.8927i | − | 0.820343i | ||||||
\(248\) | −4.34324 | + | 8.18679i | −0.275796 | + | 0.519861i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.32305 | + | 0.499529i | −0.0836773 | + | 0.0315930i | ||||
\(251\) | −2.39191 | −0.150976 | −0.0754880 | − | 0.997147i | \(-0.524051\pi\) | ||||
−0.0754880 | + | 0.997147i | \(0.524051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.1849 | −1.33188 | ||||||||
\(254\) | −12.4528 | + | 4.70163i | −0.781355 | + | 0.295007i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.4886 | − | 4.01278i | −0.968039 | − | 0.250799i | ||||
\(257\) | 8.44949i | 0.527065i | 0.964651 | + | 0.263532i | \(0.0848876\pi\) | ||||
−0.964651 | + | 0.263532i | \(0.915112\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 12.5162i | − | 0.777721i | ||||||
\(260\) | −6.71368 | − | 7.62354i | −0.416365 | − | 0.472792i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.06530 | + | 2.82155i | 0.0658143 | + | 0.174316i | ||||
\(263\) | −6.46324 | −0.398540 | −0.199270 | − | 0.979945i | \(-0.563857\pi\) | ||||
−0.199270 | + | 0.979945i | \(0.563857\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.42683 | 0.579086 | ||||||||
\(266\) | −1.53315 | − | 4.06071i | −0.0940036 | − | 0.248978i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 19.0569 | + | 21.6396i | 1.16409 | + | 1.32185i | ||||
\(269\) | − | 6.14888i | − | 0.374904i | −0.982274 | − | 0.187452i | \(-0.939977\pi\) | ||
0.982274 | − | 0.187452i | \(-0.0600229\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.446839i | 0.0271436i | 0.999908 | + | 0.0135718i | \(0.00432016\pi\) | ||||
−0.999908 | + | 0.0135718i | \(0.995680\pi\) | |||||||
\(272\) | 8.88588 | + | 1.13238i | 0.538786 | + | 0.0686606i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 21.8130 | − | 8.23567i | 1.31777 | − | 0.497535i | ||||
\(275\) | −3.04322 | −0.183513 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.83247 | 0.410524 | 0.205262 | − | 0.978707i | \(-0.434195\pi\) | ||||
0.205262 | + | 0.978707i | \(0.434195\pi\) | |||||||
\(278\) | −26.5943 | + | 10.0409i | −1.59502 | + | 0.602212i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.02112 | − | 1.60276i | −0.180546 | − | 0.0957832i | ||||
\(281\) | 3.29157i | 0.196359i | 0.995169 | + | 0.0981794i | \(0.0313019\pi\) | ||||
−0.995169 | + | 0.0981794i | \(0.968698\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.4374i | 1.39321i | 0.717457 | + | 0.696603i | \(0.245306\pi\) | ||||
−0.717457 | + | 0.696603i | \(0.754694\pi\) | |||||||
\(284\) | 5.24283 | − | 4.61711i | 0.311105 | − | 0.273975i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.72122 | − | 20.4504i | −0.456565 | − | 1.20926i | ||||
\(287\) | −5.16879 | −0.305104 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.9849 | 0.704996 | ||||||||
\(290\) | 2.79409 | + | 7.40044i | 0.164075 | + | 0.434569i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.65558 | + | 6.74190i | −0.448009 | + | 0.394540i | ||||
\(293\) | 27.9131i | 1.63070i | 0.578970 | + | 0.815349i | \(0.303455\pi\) | ||||
−0.578970 | + | 0.815349i | \(0.696545\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.92669i | 0.519732i | ||||||||
\(296\) | 25.8639 | + | 13.7213i | 1.50331 | + | 0.797535i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.49224 | + | 0.940963i | −0.144371 | + | 0.0545085i | ||||
\(299\) | 35.3578 | 2.04480 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.22323 | 0.301062 | ||||||||
\(302\) | −8.18739 | + | 3.09121i | −0.471131 | + | 0.177879i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.0719 | + | 1.28353i | 0.577666 | + | 0.0736153i | ||||
\(305\) | 2.65793i | 0.152193i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 22.5939i | − | 1.28950i | −0.764393 | − | 0.644750i | \(-0.776961\pi\) | ||
0.764393 | − | 0.644750i | \(-0.223039\pi\) | |||||||
\(308\) | −4.86378 | − | 5.52293i | −0.277140 | − | 0.314698i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.63674 | − | 4.33508i | −0.0929606 | − | 0.246216i | ||||
\(311\) | 5.89086 | 0.334040 | 0.167020 | − | 0.985953i | \(-0.446586\pi\) | ||||
0.167020 | + | 0.985953i | \(0.446586\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.76738 | 0.439038 | 0.219519 | − | 0.975608i | \(-0.429551\pi\) | ||||
0.219519 | + | 0.975608i | \(0.429551\pi\) | |||||||
\(314\) | −1.09908 | − | 2.91104i | −0.0620249 | − | 0.164279i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.98291 | + | 5.65820i | 0.280310 | + | 0.318299i | ||||
\(317\) | 11.7709i | 0.661120i | 0.943785 | + | 0.330560i | \(0.107238\pi\) | ||||
−0.943785 | + | 0.330560i | \(0.892762\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.0221i | 0.953054i | ||||||||
\(320\) | 6.62398 | − | 4.48585i | 0.370292 | − | 0.250767i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.1364 | − | 4.20462i | 0.620606 | − | 0.234314i | ||||
\(323\) | −5.68447 | −0.316293 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.07917 | 0.281742 | ||||||||
\(326\) | 20.3286 | − | 7.67523i | 1.12590 | − | 0.425091i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.66644 | − | 10.6809i | 0.312877 | − | 0.589757i | ||||
\(329\) | − | 12.4558i | − | 0.686709i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 4.32394i | − | 0.237665i | −0.992914 | − | 0.118833i | \(-0.962085\pi\) | ||
0.992914 | − | 0.118833i | \(-0.0379152\pi\) | |||||||
\(332\) | 0.859056 | − | 0.756529i | 0.0471468 | − | 0.0415199i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.1019 | + | 29.4045i | 0.607469 | + | 1.60894i | ||||
\(335\) | −14.4173 | −0.787703 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.77010 | 0.423264 | 0.211632 | − | 0.977349i | \(-0.432122\pi\) | ||||
0.211632 | + | 0.977349i | \(0.432122\pi\) | |||||||
\(338\) | 6.39294 | + | 16.9324i | 0.347730 | + | 0.920999i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.36126 | + | 2.96010i | −0.182290 | + | 0.160534i | ||||
\(341\) | − | 9.97131i | − | 0.539977i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.1601i | 0.818568i | ||||||||
\(344\) | −5.72613 | + | 10.7935i | −0.308732 | + | 0.581944i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.3891 | + | 7.69806i | −1.09613 | + | 0.413850i | ||||
\(347\) | −11.2661 | −0.604798 | −0.302399 | − | 0.953181i | \(-0.597788\pi\) | ||||
−0.302399 | + | 0.953181i | \(0.597788\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.2806 | −1.19265 | −0.596326 | − | 0.802742i | \(-0.703374\pi\) | ||||
−0.596326 | + | 0.802742i | \(0.703374\pi\) | |||||||
\(350\) | 1.59974 | − | 0.603996i | 0.0855100 | − | 0.0322849i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.7448 | − | 3.99598i | 0.892502 | − | 0.212986i | ||||
\(353\) | 22.0645i | 1.17438i | 0.809451 | + | 0.587188i | \(0.199765\pi\) | ||||
−0.809451 | + | 0.587188i | \(0.800235\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.49303i | 0.185391i | ||||||||
\(356\) | −3.17404 | − | 3.60420i | −0.168224 | − | 0.191022i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.40538 | − | 16.9653i | −0.338535 | − | 0.896645i | ||||
\(359\) | 1.70332 | 0.0898978 | 0.0449489 | − | 0.998989i | \(-0.485687\pi\) | ||||
0.0449489 | + | 0.998989i | \(0.485687\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.5568 | 0.660883 | ||||||||
\(362\) | 8.67425 | + | 22.9746i | 0.455908 | + | 1.20752i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.11771 | + | 9.21785i | 0.425484 | + | 0.483147i | ||||
\(365\) | − | 5.10052i | − | 0.266973i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.42151i | 0.491799i | 0.969295 | + | 0.245900i | \(0.0790833\pi\) | ||||
−0.969295 | + | 0.245900i | \(0.920917\pi\) | |||||||
\(368\) | −3.52003 | + | 27.6220i | −0.183494 | + | 1.43990i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −13.6955 | + | 5.17084i | −0.711995 | + | 0.268819i | ||||
\(371\) | −11.3983 | −0.591769 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.5855 | 0.755210 | 0.377605 | − | 0.925967i | \(-0.376748\pi\) | ||||
0.377605 | + | 0.925967i | \(0.376748\pi\) | |||||||
\(374\) | −9.01673 | + | 3.40433i | −0.466244 | + | 0.176034i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 25.7390 | + | 13.6550i | 1.32739 | + | 0.704203i | ||||
\(377\) | − | 28.4101i | − | 1.46319i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.46065i | − | 0.485961i | −0.970031 | − | 0.242980i | \(-0.921875\pi\) | ||
0.970031 | − | 0.242980i | \(-0.0781251\pi\) | |||||||
\(380\) | −3.80992 | + | 3.35521i | −0.195445 | + | 0.172119i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.90590 | + | 23.5882i | 0.455666 | + | 1.20688i | ||||
\(383\) | 6.86013 | 0.350536 | 0.175268 | − | 0.984521i | \(-0.443921\pi\) | ||||
0.175268 | + | 0.984521i | \(0.443921\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.67965 | 0.187532 | ||||||||
\(386\) | −2.43951 | − | 6.46129i | −0.124168 | − | 0.328871i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.4876 | − | 15.4005i | 0.887801 | − | 0.781843i | ||||
\(389\) | − | 8.21735i | − | 0.416636i | −0.978061 | − | 0.208318i | \(-0.933201\pi\) | ||
0.978061 | − | 0.208318i | \(-0.0667989\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 15.5895i | − | 0.788394i | ||||||
\(392\) | −13.8372 | − | 7.34088i | −0.698883 | − | 0.370770i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −22.2501 | + | 8.40070i | −1.12095 | + | 0.423221i | ||||
\(395\) | −3.76977 | −0.189678 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.07936 | −0.355303 | −0.177651 | − | 0.984093i | \(-0.556850\pi\) | ||||
−0.177651 | + | 0.984093i | \(0.556850\pi\) | |||||||
\(398\) | −7.82575 | + | 2.95467i | −0.392269 | + | 0.148104i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.505654 | + | 3.96791i | −0.0252827 | + | 0.198396i | ||||
\(401\) | − | 17.6923i | − | 0.883511i | −0.897136 | − | 0.441755i | \(-0.854356\pi\) | ||
0.897136 | − | 0.441755i | \(-0.145644\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.6422i | 0.829009i | ||||||||
\(404\) | −6.31514 | − | 7.17099i | −0.314190 | − | 0.356770i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.37842 | − | 8.94810i | −0.167668 | − | 0.444087i | ||||
\(407\) | −31.5016 | −1.56148 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.7084 | −1.12286 | −0.561428 | − | 0.827526i | \(-0.689748\pi\) | ||||
−0.561428 | + | 0.827526i | \(0.689748\pi\) | |||||||
\(410\) | 2.13538 | + | 5.65579i | 0.105459 | + | 0.279319i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.5028 | + | 14.1973i | 0.615971 | + | 0.699449i | ||||
\(413\) | − | 10.7935i | − | 0.531115i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.572344i | 0.0280953i | ||||||||
\(416\) | −27.9473 | + | 6.66934i | −1.37023 | + | 0.326992i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.2203 | + | 3.85873i | −0.499889 | + | 0.188737i | ||||
\(419\) | −26.3609 | −1.28782 | −0.643908 | − | 0.765103i | \(-0.722688\pi\) | ||||
−0.643908 | + | 0.765103i | \(0.722688\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.1554 | 0.836101 | 0.418050 | − | 0.908424i | \(-0.362714\pi\) | ||||
0.418050 | + | 0.908424i | \(0.362714\pi\) | |||||||
\(422\) | −36.5869 | + | 13.8137i | −1.78102 | + | 0.672438i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.4957 | − | 23.5537i | 0.606845 | − | 1.14387i | ||||
\(425\) | − | 2.23944i | − | 0.108629i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3.21378i | − | 0.155526i | ||||||
\(428\) | −27.4693 | + | 24.1909i | −1.32778 | + | 1.16931i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.15788 | − | 5.71536i | −0.104062 | − | 0.275619i | ||||
\(431\) | 12.5816 | 0.606037 | 0.303018 | − | 0.952985i | \(-0.402006\pi\) | ||||
0.303018 | + | 0.952985i | \(0.402006\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.7433 | −0.564346 | −0.282173 | − | 0.959364i | \(-0.591055\pi\) | ||||
−0.282173 | + | 0.959364i | \(0.591055\pi\) | |||||||
\(434\) | 1.97903 | + | 5.24167i | 0.0949966 | + | 0.251608i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.3980 | − | 13.5603i | 0.737431 | − | 0.649420i | ||||
\(437\) | − | 17.6703i | − | 0.845286i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.68284i | − | 0.0803176i | −0.999193 | − | 0.0401588i | \(-0.987214\pi\) | ||
0.999193 | − | 0.0401588i | \(-0.0127864\pi\) | |||||||
\(440\) | −4.03392 | + | 7.60373i | −0.192310 | + | 0.362494i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.0490 | − | 5.68188i | 0.715810 | − | 0.270259i | ||||
\(443\) | 0.759020 | 0.0360621 | 0.0180311 | − | 0.999837i | \(-0.494260\pi\) | ||||
0.0180311 | + | 0.999837i | \(0.494260\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.40129 | 0.113832 | ||||||||
\(446\) | 31.6836 | − | 11.9624i | 1.50026 | − | 0.566434i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.00926 | + | 5.42398i | −0.378402 | + | 0.256259i | ||||
\(449\) | 17.4579i | 0.823887i | 0.911209 | + | 0.411943i | \(0.135150\pi\) | ||||
−0.911209 | + | 0.411943i | \(0.864850\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.0091i | 0.612576i | ||||||||
\(452\) | −8.10878 | − | 9.20770i | −0.381405 | − | 0.433094i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.45653 | − | 9.15498i | −0.162223 | − | 0.429665i | ||||
\(455\) | −6.14138 | −0.287912 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.8638 | −1.63086 | −0.815430 | − | 0.578855i | \(-0.803500\pi\) | ||||
−0.815430 | + | 0.578855i | \(0.803500\pi\) | |||||||
\(458\) | −7.65116 | − | 20.2649i | −0.357515 | − | 0.946916i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.20155 | − | 10.4486i | −0.429025 | − | 0.487167i | ||||
\(461\) | − | 31.2815i | − | 1.45692i | −0.685086 | − | 0.728462i | \(-0.740235\pi\) | ||
0.685086 | − | 0.728462i | \(-0.259765\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.2827i | − | 0.477879i | −0.971034 | − | 0.238940i | \(-0.923200\pi\) | ||
0.971034 | − | 0.238940i | \(-0.0767998\pi\) | |||||||
\(464\) | 22.1943 | + | 2.82835i | 1.03035 | + | 0.131303i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.74605 | + | 3.30214i | −0.405153 | + | 0.152968i | ||||
\(467\) | −2.90585 | −0.134467 | −0.0672333 | − | 0.997737i | \(-0.521417\pi\) | ||||
−0.0672333 | + | 0.997737i | \(0.521417\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.4324 | 0.804955 | ||||||||
\(470\) | −13.6293 | + | 5.14586i | −0.628674 | + | 0.237361i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 22.3041 | + | 11.8327i | 1.02663 | + | 0.544646i | ||||
\(473\) | − | 13.1462i | − | 0.604461i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.53835i | − | 0.116467i | ||||||
\(476\) | 4.06421 | − | 3.57915i | 0.186283 | − | 0.164050i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.10672 | + | 10.8771i | 0.187837 | + | 0.497506i | ||||
\(479\) | 18.8555 | 0.861528 | 0.430764 | − | 0.902465i | \(-0.358244\pi\) | ||||
0.430764 | + | 0.902465i | \(0.358244\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 52.5767 | 2.39729 | ||||||||
\(482\) | 7.30088 | + | 19.3371i | 0.332546 | + | 0.880783i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.60990 | − | 2.29841i | 0.118632 | − | 0.104473i | ||||
\(485\) | 11.6511i | 0.529050i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.5696i | 0.524268i | 0.965031 | + | 0.262134i | \(0.0844263\pi\) | ||||
−0.965031 | + | 0.262134i | \(0.915574\pi\) | |||||||
\(488\) | 6.64106 | + | 3.52321i | 0.300627 | + | 0.159488i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.32708 | − | 2.76639i | 0.331004 | − | 0.124973i | ||||
\(491\) | −1.49523 | −0.0674790 | −0.0337395 | − | 0.999431i | \(-0.510742\pi\) | ||||
−0.0337395 | + | 0.999431i | \(0.510742\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.5262 | −0.564151 | ||||||||
\(494\) | 17.0577 | − | 6.44028i | 0.767464 | − | 0.289762i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.0011 | − | 1.65681i | −0.583768 | − | 0.0743930i | ||||
\(497\) | − | 4.22352i | − | 0.189451i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 31.4785i | − | 1.40917i | −0.709618 | − | 0.704586i | \(-0.751133\pi\) | ||
0.709618 | − | 0.704586i | \(-0.248867\pi\) | |||||||
\(500\) | −1.32181 | − | 1.50094i | −0.0591130 | − | 0.0671242i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.19483 | − | 3.16463i | −0.0533278 | − | 0.141244i | ||||
\(503\) | 1.90449 | 0.0849171 | 0.0424585 | − | 0.999098i | \(-0.486481\pi\) | ||||
0.0424585 | + | 0.999098i | \(0.486481\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.77766 | 0.212603 | ||||||||
\(506\) | −10.5825 | − | 28.0287i | −0.470447 | − | 1.24603i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.4410 | − | 14.1271i | −0.551981 | − | 0.626787i | ||||
\(509\) | 31.4341i | 1.39329i | 0.717414 | + | 0.696647i | \(0.245326\pi\) | ||||
−0.717414 | + | 0.696647i | \(0.754674\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.16719i | 0.272820i | ||||||||
\(512\) | −2.42789 | − | 22.4968i | −0.107299 | − | 0.994227i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.1791 | + | 4.22076i | −0.493090 | + | 0.186170i | ||||
\(515\) | −9.45891 | −0.416809 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31.3494 | −1.37875 | ||||||||
\(518\) | 16.5596 | − | 6.25222i | 0.727589 | − | 0.274707i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.73267 | − | 12.6907i | 0.295247 | − | 0.556525i | ||||
\(521\) | 23.2742i | 1.01966i | 0.860275 | + | 0.509831i | \(0.170292\pi\) | ||||
−0.860275 | + | 0.509831i | \(0.829708\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.8804i | 0.475769i | 0.971293 | + | 0.237884i | \(0.0764539\pi\) | ||||
−0.971293 | + | 0.237884i | \(0.923546\pi\) | |||||||
\(524\) | −3.20092 | + | 2.81889i | −0.139833 | + | 0.123144i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.22857 | − | 8.55121i | −0.140773 | − | 0.372851i | ||||
\(527\) | 7.33767 | 0.319634 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.4603 | 1.10697 | ||||||||
\(530\) | 4.70897 | + | 12.4722i | 0.204545 | + | 0.541758i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.60669 | − | 4.05689i | 0.199725 | − | 0.175888i | ||||
\(533\) | − | 21.7124i | − | 0.940469i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 18.3014i | − | 0.791237i | ||||||
\(536\) | −19.1108 | + | 36.0229i | −0.825463 | + | 1.55595i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.13530 | − | 3.07154i | 0.350738 | − | 0.132424i | ||||
\(539\) | 16.8533 | 0.725925 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.53795 | −0.281088 | −0.140544 | − | 0.990074i | \(-0.544885\pi\) | ||||
−0.140544 | + | 0.990074i | \(0.544885\pi\) | |||||||
\(542\) | −0.591192 | + | 0.223209i | −0.0253939 | + | 0.00958765i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.94055 | + | 12.3222i | 0.126075 | + | 0.528308i | ||||
\(545\) | 10.2589i | 0.439443i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.5771i | 1.13636i | 0.822906 | + | 0.568178i | \(0.192351\pi\) | ||||
−0.822906 | + | 0.568178i | \(0.807649\pi\) | |||||||
\(548\) | 21.7925 | + | 24.7458i | 0.930928 | + | 1.05709i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.52017 | − | 4.02634i | −0.0648204 | − | 0.171684i | ||||
\(551\) | −14.1981 | −0.604861 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.55814 | 0.193832 | ||||||||
\(554\) | 3.41302 | + | 9.03973i | 0.145005 | + | 0.384061i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −26.5693 | − | 30.1700i | −1.12679 | − | 1.27949i | ||||
\(557\) | 8.68248i | 0.367889i | 0.982937 | + | 0.183944i | \(0.0588866\pi\) | ||||
−0.982937 | + | 0.183944i | \(0.941113\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.9411i | 0.928010i | ||||||||
\(560\) | 0.611402 | − | 4.79772i | 0.0258364 | − | 0.202741i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.35493 | + | 1.64424i | −0.183702 | + | 0.0693579i | ||||
\(563\) | −31.6649 | −1.33451 | −0.667257 | − | 0.744827i | \(-0.732532\pi\) | ||||
−0.667257 | + | 0.744827i | \(0.732532\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.13462 | 0.258085 | ||||||||
\(566\) | −31.0089 | + | 11.7076i | −1.30340 | + | 0.492109i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.72762 | + | 4.63017i | 0.366203 | + | 0.194278i | ||||
\(569\) | − | 32.2966i | − | 1.35395i | −0.736008 | − | 0.676973i | \(-0.763291\pi\) | ||
0.736008 | − | 0.676973i | \(-0.236709\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 14.6930i | − | 0.614884i | −0.951567 | − | 0.307442i | \(-0.900527\pi\) | ||
0.951567 | − | 0.307442i | \(-0.0994729\pi\) | |||||||
\(572\) | 23.2001 | − | 20.4312i | 0.970043 | − | 0.854270i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.58196 | − | 6.83859i | −0.107769 | − | 0.285437i | ||||
\(575\) | 6.96134 | 0.290308 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.4886 | −0.936214 | −0.468107 | − | 0.883672i | \(-0.655064\pi\) | ||||
−0.468107 | + | 0.883672i | \(0.655064\pi\) | |||||||
\(578\) | 5.98682 | + | 15.8567i | 0.249019 | + | 0.659552i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.39545 | + | 7.39346i | −0.348602 | + | 0.306997i | ||||
\(581\) | − | 0.692039i | − | 0.0287106i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.6879i | 1.18813i | ||||||||
\(584\) | −12.7441 | − | 6.76097i | −0.527354 | − | 0.279771i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −36.9305 | + | 13.9434i | −1.52558 | + | 0.575996i | ||||
\(587\) | 34.4969 | 1.42384 | 0.711919 | − | 0.702262i | \(-0.247826\pi\) | ||||
0.711919 | + | 0.702262i | \(0.247826\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.31708 | 0.342699 | ||||||||
\(590\) | −11.8105 | + | 4.45914i | −0.486230 | + | 0.183580i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.23424 | + | 41.0736i | −0.215126 | + | 1.68811i | ||||
\(593\) | 11.5133i | 0.472794i | 0.971656 | + | 0.236397i | \(0.0759667\pi\) | ||||
−0.971656 | + | 0.236397i | \(0.924033\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.70777i | 0.111008i | ||||||||
\(596\) | −2.48989 | − | 2.82733i | −0.101990 | − | 0.115812i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 17.6623 | + | 46.7803i | 0.722263 | + | 1.91299i | ||||
\(599\) | 35.6121 | 1.45507 | 0.727535 | − | 0.686071i | \(-0.240666\pi\) | ||||
0.727535 | + | 0.686071i | \(0.240666\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.8274 | 1.66539 | 0.832693 | − | 0.553735i | \(-0.186798\pi\) | ||||
0.832693 | + | 0.553735i | \(0.186798\pi\) | |||||||
\(602\) | 2.60916 | + | 6.91062i | 0.106341 | + | 0.281656i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.17968 | − | 9.28821i | −0.332826 | − | 0.377932i | ||||
\(605\) | 1.73884i | 0.0706938i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.19423i | − | 0.0890609i | −0.999008 | − | 0.0445304i | \(-0.985821\pi\) | ||
0.999008 | − | 0.0445304i | \(-0.0141792\pi\) | |||||||
\(608\) | 3.33305 | + | 13.9669i | 0.135173 | + | 0.566432i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.51658 | + | 1.32771i | −0.142382 | + | 0.0537575i | ||||
\(611\) | 52.3227 | 2.11675 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.7673 | 1.56580 | 0.782899 | − | 0.622149i | \(-0.213740\pi\) | ||||
0.782899 | + | 0.622149i | \(0.213740\pi\) | |||||||
\(614\) | 29.8929 | − | 11.2863i | 1.20638 | − | 0.455478i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.87754 | − | 9.19391i | 0.196522 | − | 0.370433i | ||||
\(617\) | − | 14.8556i | − | 0.598062i | −0.954243 | − | 0.299031i | \(-0.903337\pi\) | ||
0.954243 | − | 0.299031i | \(-0.0966634\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.2470i | 0.572637i | 0.958135 | + | 0.286318i | \(0.0924315\pi\) | ||||
−0.958135 | + | 0.286318i | \(0.907569\pi\) | |||||||
\(620\) | 4.91794 | − | 4.33099i | 0.197509 | − | 0.173937i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.94266 | + | 7.79393i | 0.117990 | + | 0.312508i | ||||
\(623\) | −2.90347 | −0.116325 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.88003 | + | 10.2767i | 0.155077 | + | 0.410738i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.30243 | − | 2.90829i | 0.131781 | − | 0.116053i | ||||
\(629\) | − | 23.1814i | − | 0.924302i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.8200i | 1.54540i | 0.634772 | + | 0.772700i | \(0.281094\pi\) | ||||
−0.634772 | + | 0.772700i | \(0.718906\pi\) | |||||||
\(632\) | −4.99700 | + | 9.41909i | −0.198770 | + | 0.374671i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.5735 | + | 5.87991i | −0.618504 | + | 0.233521i | ||||
\(635\) | 9.41213 | 0.373509 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28.1284 | −1.11449 | ||||||||
\(638\) | −22.5211 | + | 8.50302i | −0.891620 | + | 0.336638i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.24389 | + | 6.52307i | 0.365397 | + | 0.257847i | ||||
\(641\) | − | 19.1212i | − | 0.755243i | −0.925960 | − | 0.377621i | \(-0.876742\pi\) | ||
0.925960 | − | 0.377621i | \(-0.123258\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.57189i | 0.259170i | 0.991568 | + | 0.129585i | \(0.0413645\pi\) | ||||
−0.991568 | + | 0.129585i | \(0.958635\pi\) | |||||||
\(644\) | 11.1259 | + | 12.6337i | 0.438421 | + | 0.497837i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.83956 | − | 7.52086i | −0.111721 | − | 0.295904i | ||||
\(647\) | 12.7191 | 0.500040 | 0.250020 | − | 0.968241i | \(-0.419563\pi\) | ||||
0.250020 | + | 0.968241i | \(0.419563\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.1658 | −1.06635 | ||||||||
\(650\) | 2.53719 | + | 6.72001i | 0.0995168 | + | 0.263581i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.3095 | + | 23.0619i | 0.795380 | + | 0.903173i | ||||
\(653\) | − | 44.0821i | − | 1.72506i | −0.506002 | − | 0.862532i | \(-0.668877\pi\) | ||
0.506002 | − | 0.862532i | \(-0.331123\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2.13260i | − | 0.0833278i | ||||||
\(656\) | 16.9620 | + | 2.16157i | 0.662256 | + | 0.0843951i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 16.4796 | − | 6.22201i | 0.642444 | − | 0.242559i | ||||
\(659\) | −21.7858 | −0.848656 | −0.424328 | − | 0.905509i | \(-0.639490\pi\) | ||||
−0.424328 | + | 0.905509i | \(0.639490\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.5513 | 0.799353 | 0.399676 | − | 0.916656i | \(-0.369123\pi\) | ||||
0.399676 | + | 0.916656i | \(0.369123\pi\) | |||||||
\(662\) | 5.72080 | − | 2.15993i | 0.222345 | − | 0.0839481i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.43005 | + | 0.758669i | 0.0554968 | + | 0.0294421i | ||||
\(665\) | 3.06920i | 0.119018i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 38.9379i | − | 1.50768i | ||||||
\(668\) | −33.3580 | + | 29.3768i | −1.29066 | + | 1.13662i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.20187 | − | 19.0749i | −0.278233 | − | 0.736928i | ||||
\(671\) | −8.08865 | −0.312259 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.17749 | −0.0839359 | −0.0419680 | − | 0.999119i | \(-0.513363\pi\) | ||||
−0.0419680 | + | 0.999119i | \(0.513363\pi\) | |||||||
\(674\) | 3.88139 | + | 10.2803i | 0.149505 | + | 0.395981i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.2090 | + | 16.9164i | −0.738807 | + | 0.650631i | ||||
\(677\) | − | 2.22672i | − | 0.0855798i | −0.999084 | − | 0.0427899i | \(-0.986375\pi\) | ||
0.999084 | − | 0.0427899i | \(-0.0136246\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 14.0877i | − | 0.540637i | ||||||
\(680\) | −5.59542 | − | 2.96848i | −0.214575 | − | 0.113836i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 13.1926 | − | 4.98095i | 0.505170 | − | 0.190731i | ||||
\(683\) | 12.9800 | 0.496665 | 0.248333 | − | 0.968675i | \(-0.420117\pi\) | ||||
0.248333 | + | 0.968675i | \(0.420117\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.4869 | −0.629931 | ||||||||
\(686\) | −20.0576 | + | 7.57290i | −0.765803 | + | 0.289135i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −17.1407 | − | 2.18434i | −0.653482 | − | 0.0832770i | ||||
\(689\) | − | 47.8805i | − | 1.82410i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 27.9275i | − | 1.06241i | −0.847243 | − | 0.531205i | \(-0.821739\pi\) | ||
0.847243 | − | 0.531205i | \(-0.178261\pi\) | |||||||
\(692\) | −20.3699 | − | 23.1305i | −0.774347 | − | 0.879289i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.62776 | − | 14.9057i | −0.213627 | − | 0.565813i | ||||
\(695\) | 20.1007 | 0.762464 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.57314 | −0.362608 | ||||||||
\(698\) | −11.1298 | − | 29.4784i | −0.421269 | − | 1.11577i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.59824 | + | 1.81484i | 0.0604077 | + | 0.0685943i | ||||
\(701\) | − | 31.0643i | − | 1.17328i | −0.809847 | − | 0.586641i | \(-0.800450\pi\) | ||
0.809847 | − | 0.586641i | \(-0.199550\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 26.2756i | − | 0.991001i | ||||||
\(704\) | 13.6514 | + | 20.1582i | 0.514507 | + | 0.759741i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −29.1925 | + | 11.0219i | −1.09868 | + | 0.414813i | ||||
\(707\) | −5.77682 | −0.217260 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.4478 | −1.63172 | −0.815859 | − | 0.578251i | \(-0.803735\pi\) | ||||
−0.815859 | + | 0.578251i | \(0.803735\pi\) | |||||||
\(710\) | −4.62146 | + | 1.74487i | −0.173440 | + | 0.0654837i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.18302 | − | 5.99982i | 0.119289 | − | 0.224853i | ||||
\(713\) | 22.8093i | 0.854216i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.4570i | 0.578059i | ||||||||
\(716\) | 19.2464 | − | 16.9493i | 0.719270 | − | 0.633426i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.850858 | + | 2.25358i | 0.0317537 | + | 0.0841030i | ||||
\(719\) | −12.6495 | −0.471747 | −0.235874 | − | 0.971784i | \(-0.575795\pi\) | ||||
−0.235874 | + | 0.971784i | \(0.575795\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.4371 | 0.425938 | ||||||||
\(722\) | 6.27247 | + | 16.6133i | 0.233437 | + | 0.618283i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −26.0636 | + | 22.9530i | −0.968648 | + | 0.853041i | ||||
\(725\) | − | 5.59345i | − | 0.207736i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 50.1181i | − | 1.85878i | −0.369103 | − | 0.929389i | \(-0.620335\pi\) | ||
0.369103 | − | 0.929389i | \(-0.379665\pi\) | |||||||
\(728\) | −8.14068 | + | 15.3448i | −0.301714 | + | 0.568714i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.74826 | − | 2.54785i | 0.249764 | − | 0.0943003i | ||||
\(731\) | 9.67397 | 0.357805 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.4655 | −1.08833 | −0.544166 | − | 0.838978i | \(-0.683154\pi\) | ||||
−0.544166 | + | 0.838978i | \(0.683154\pi\) | |||||||
\(734\) | −12.4652 | + | 4.70632i | −0.460098 | + | 0.173713i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −38.3037 | + | 9.14079i | −1.41189 | + | 0.336934i | ||||
\(737\) | − | 43.8751i | − | 1.61616i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 45.3131i | − | 1.66687i | −0.552618 | − | 0.833435i | \(-0.686371\pi\) | ||
0.552618 | − | 0.833435i | \(-0.313629\pi\) | |||||||
\(740\) | −13.6826 | − | 15.5369i | −0.502982 | − | 0.571148i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.69376 | − | 15.0805i | −0.209025 | − | 0.553623i | ||||
\(743\) | 8.07559 | 0.296265 | 0.148132 | − | 0.988968i | \(-0.452674\pi\) | ||||
0.148132 | + | 0.988968i | \(0.452674\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.88370 | 0.0690135 | ||||||||
\(746\) | 7.28589 | + | 19.2974i | 0.266756 | + | 0.706530i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.00823 | − | 10.2291i | −0.329373 | − | 0.374011i | ||||
\(749\) | 22.1287i | 0.808567i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.2164i | 0.409291i | 0.978836 | + | 0.204646i | \(0.0656042\pi\) | ||||
−0.978836 | + | 0.204646i | \(0.934396\pi\) | |||||||
\(752\) | −5.20895 | + | 40.8751i | −0.189951 | + | 1.49056i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 37.5881 | − | 14.1917i | 1.36888 | − | 0.516829i | ||||
\(755\) | 6.18825 | 0.225214 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.9148 | −0.978236 | −0.489118 | − | 0.872218i | \(-0.662681\pi\) | ||||
−0.489118 | + | 0.872218i | \(0.662681\pi\) | |||||||
\(758\) | 12.5169 | − | 4.72587i | 0.454636 | − | 0.171651i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.34228 | − | 3.36470i | −0.230059 | − | 0.122051i | ||||
\(761\) | 7.78903i | 0.282352i | 0.989985 | + | 0.141176i | \(0.0450884\pi\) | ||||
−0.989985 | + | 0.141176i | \(0.954912\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 12.4044i | − | 0.449068i | ||||||
\(764\) | −26.7597 | + | 23.5660i | −0.968132 | + | 0.852587i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.42683 | + | 9.07632i | 0.123816 | + | 0.327941i | ||||
\(767\) | 45.3402 | 1.63714 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.72981 | 0.242683 | 0.121342 | − | 0.992611i | \(-0.461280\pi\) | ||||
0.121342 | + | 0.992611i | \(0.461280\pi\) | |||||||
\(770\) | 1.83809 | + | 4.86837i | 0.0662401 | + | 0.175444i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.33003 | − | 6.45520i | 0.263813 | − | 0.232328i | ||||
\(773\) | − | 16.5270i | − | 0.594435i | −0.954810 | − | 0.297217i | \(-0.903941\pi\) | ||
0.954810 | − | 0.297217i | \(-0.0960586\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.27657i | 0.117698i | ||||||||
\(776\) | 29.1113 | + | 15.4441i | 1.04503 | + | 0.554411i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.8720 | − | 4.10480i | 0.389780 | − | 0.147164i | ||||
\(779\) | −10.8509 | −0.388775 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.6300 | −0.380372 | ||||||||
\(782\) | 20.6257 | − | 7.78740i | 0.737574 | − | 0.278477i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.80031 | − | 21.9743i | 0.100011 | − | 0.784796i | ||||
\(785\) | 2.20024i | 0.0785299i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.75942i | 0.0983628i | 0.998790 | + | 0.0491814i | \(0.0156612\pi\) | ||||
−0.998790 | + | 0.0491814i | \(0.984339\pi\) | |||||||
\(788\) | −22.2292 | − | 25.2417i | −0.791881 | − | 0.899199i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.88311 | − | 4.98761i | −0.0669980 | − | 0.177451i | ||||
\(791\) | −7.41755 | −0.263738 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.5001 | 0.479401 | ||||||||
\(794\) | −3.53634 | − | 9.36637i | −0.125500 | − | 0.332400i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.81838 | − | 8.87795i | −0.277115 | − | 0.314670i | ||||
\(797\) | 5.24247i | 0.185698i | 0.995680 | + | 0.0928488i | \(0.0295973\pi\) | ||||
−0.995680 | + | 0.0928488i | \(0.970403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 23.0694i | − | 0.816136i | ||||||
\(800\) | −5.50235 | + | 1.31308i | −0.194537 | + | 0.0464243i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 23.4079 | − | 8.83781i | 0.826560 | − | 0.312074i | ||||
\(803\) | 15.5220 | 0.547759 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.41717 | −0.296666 | ||||||||
\(806\) | −22.0186 | + | 8.31328i | −0.775571 | + | 0.292823i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.33301 | − | 11.9374i | 0.222795 | − | 0.419956i | ||||
\(809\) | − | 47.1813i | − | 1.65881i | −0.558650 | − | 0.829403i | \(-0.688681\pi\) | ||
0.558650 | − | 0.829403i | \(-0.311319\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.8666i | 0.662495i | 0.943544 | + | 0.331247i | \(0.107469\pi\) | ||||
−0.943544 | + | 0.331247i | \(0.892531\pi\) | |||||||
\(812\) | 10.1512 | − | 8.93966i | 0.356237 | − | 0.313721i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.7360 | − | 41.6784i | −0.551546 | − | 1.46083i | ||||
\(815\) | −15.3649 | −0.538210 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.9652 | 0.383625 | ||||||||
\(818\) | −11.3435 | − | 30.0444i | −0.396615 | − | 1.05048i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.41622 | + | 5.65046i | −0.224064 | + | 0.197323i | ||||
\(821\) | − | 1.29788i | − | 0.0452962i | −0.999743 | − | 0.0226481i | \(-0.992790\pi\) | ||
0.999743 | − | 0.0226481i | \(-0.00720973\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.67062i | 0.232523i | 0.993219 | + | 0.116262i | \(0.0370911\pi\) | ||||
−0.993219 | + | 0.116262i | \(0.962909\pi\) | |||||||
\(824\) | −12.5382 | + | 23.6339i | −0.436790 | + | 0.823325i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.2804 | − | 5.39168i | 0.496880 | − | 0.187601i | ||||
\(827\) | −37.4924 | −1.30374 | −0.651869 | − | 0.758331i | \(-0.726015\pi\) | ||||
−0.651869 | + | 0.758331i | \(0.726015\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.9261 | −0.796255 | −0.398127 | − | 0.917330i | \(-0.630340\pi\) | ||||
−0.398127 | + | 0.917330i | \(0.630340\pi\) | |||||||
\(830\) | −0.757242 | + | 0.285903i | −0.0262843 | + | 0.00992382i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −22.7844 | − | 33.6443i | −0.789907 | − | 1.16641i | ||||
\(833\) | 12.4020i | 0.429704i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 22.2247i | − | 0.769119i | ||||||
\(836\) | −10.2106 | − | 11.5944i | −0.353142 | − | 0.401001i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.1680 | − | 34.8769i | −0.454882 | − | 1.20480i | ||||
\(839\) | −18.2210 | −0.629057 | −0.314529 | − | 0.949248i | \(-0.601846\pi\) | ||||
−0.314529 | + | 0.949248i | \(0.601846\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.28670 | −0.0788518 | ||||||||
\(842\) | 8.56959 | + | 22.6975i | 0.295328 | + | 0.782206i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −36.5524 | − | 41.5061i | −1.25819 | − | 1.42870i | ||||
\(845\) | − | 12.7979i | − | 0.440263i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2.10248i | − | 0.0722422i | ||||||
\(848\) | 37.4048 | + | 4.76671i | 1.28449 | + | 0.163690i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.96289 | − | 1.11866i | 0.101626 | − | 0.0383698i | ||||
\(851\) | 72.0599 | 2.47018 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.95096 | −0.0667994 | −0.0333997 | − | 0.999442i | \(-0.510633\pi\) | ||||
−0.0333997 | + | 0.999442i | \(0.510633\pi\) | |||||||
\(854\) | 4.25201 | − | 1.60538i | 0.145501 | − | 0.0549349i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −45.7275 | − | 24.2593i | −1.56293 | − | 0.829166i | ||||
\(857\) | − | 13.0233i | − | 0.444868i | −0.974948 | − | 0.222434i | \(-0.928600\pi\) | ||
0.974948 | − | 0.222434i | \(-0.0714002\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.04184i | 0.137906i | 0.997620 | + | 0.0689530i | \(0.0219658\pi\) | ||||
−0.997620 | + | 0.0689530i | \(0.978034\pi\) | |||||||
\(860\) | 6.48381 | − | 5.70997i | 0.221096 | − | 0.194709i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.28489 | + | 16.6462i | 0.214064 | + | 0.566972i | ||||
\(863\) | −10.6258 | −0.361705 | −0.180853 | − | 0.983510i | \(-0.557886\pi\) | ||||
−0.180853 | + | 0.983510i | \(0.557886\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.4106 | 0.523978 | ||||||||
\(866\) | −5.86611 | − | 15.5370i | −0.199338 | − | 0.527969i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.94643 | + | 5.23673i | −0.201835 | + | 0.177746i | ||||
\(869\) | − | 11.4722i | − | 0.389168i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 73.2281i | 2.48124i | ||||||||
\(872\) | 25.6327 | + | 13.5986i | 0.868034 | + | 0.460508i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 23.3788 | − | 8.82684i | 0.790799 | − | 0.298572i | ||||
\(875\) | −1.20913 | −0.0408761 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −53.1060 | −1.79326 | −0.896631 | − | 0.442779i | \(-0.853992\pi\) | ||||
−0.896631 | + | 0.442779i | \(0.853992\pi\) | |||||||
\(878\) | 2.22649 | − | 0.840628i | 0.0751404 | − | 0.0283698i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −12.0752 | − | 1.53881i | −0.407055 | − | 0.0518734i | ||||
\(881\) | − | 10.8244i | − | 0.364685i | −0.983235 | − | 0.182342i | \(-0.941632\pi\) | ||
0.983235 | − | 0.182342i | \(-0.0583679\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.6083i | 0.727178i | 0.931559 | + | 0.363589i | \(0.118449\pi\) | ||||
−0.931559 | + | 0.363589i | \(0.881551\pi\) | |||||||
\(884\) | 15.0349 | + | 17.0724i | 0.505677 | + | 0.574208i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.379152 | + | 1.00422i | 0.0127379 | + | 0.0337376i | ||||
\(887\) | −0.528051 | −0.0177302 | −0.00886511 | − | 0.999961i | \(-0.502822\pi\) | ||||
−0.00886511 | + | 0.999961i | \(0.502822\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.3805 | −0.381690 | ||||||||
\(890\) | 1.19951 | + | 3.17703i | 0.0402078 | + | 0.106494i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 31.6537 | + | 35.9435i | 1.05984 | + | 1.20348i | ||||
\(893\) | − | 26.1486i | − | 0.875030i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.8229i | 0.428621i | ||||||||
\(896\) | −11.1771 | − | 7.88724i | −0.373400 | − | 0.263494i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −23.0977 | + | 8.72070i | −0.770779 | + | 0.291013i | ||||
\(899\) | 18.3273 | 0.611251 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.1108 | −0.703302 | ||||||||
\(902\) | −17.2118 | + | 6.49844i | −0.573090 | + | 0.216374i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.13172 | − | 15.3279i | 0.270457 | − | 0.509797i | ||||
\(905\) | − | 17.3649i | − | 0.577227i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 47.3294i | − | 1.57155i | −0.618515 | − | 0.785773i | \(-0.712265\pi\) | ||
0.618515 | − | 0.785773i | \(-0.287735\pi\) | |||||||
\(908\) | 10.3859 | − | 9.14635i | 0.344668 | − | 0.303532i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.06779 | − | 8.12537i | −0.101696 | − | 0.269353i | ||||
\(911\) | 37.6319 | 1.24680 | 0.623401 | − | 0.781902i | \(-0.285750\pi\) | ||||
0.623401 | + | 0.781902i | \(0.285750\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.74177 | −0.0576441 | ||||||||
\(914\) | −17.4155 | − | 46.1267i | −0.576053 | − | 1.52574i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 22.9896 | − | 20.2458i | 0.759596 | − | 0.668939i | ||||
\(917\) | 2.57860i | 0.0851528i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 42.9157i | − | 1.41566i | −0.706383 | − | 0.707830i | \(-0.749674\pi\) | ||
0.706383 | − | 0.707830i | \(-0.250326\pi\) | |||||||
\(920\) | 9.22758 | − | 17.3935i | 0.304224 | − | 0.573447i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 41.3871 | − | 15.6260i | 1.36301 | − | 0.514615i | ||||
\(923\) | 17.7417 | 0.583974 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.3514 | 0.340353 | ||||||||
\(926\) | 13.6046 | − | 5.13652i | 0.447075 | − | 0.168797i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.34464 | + | 30.7771i | 0.241100 | + | 1.01031i | ||||
\(929\) | 29.0533i | 0.953209i | 0.879118 | + | 0.476605i | \(0.158133\pi\) | ||||
−0.879118 | + | 0.476605i | \(0.841867\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.0574i | 0.460712i | ||||||||
\(932\) | −8.73781 | − | 9.92198i | −0.286216 | − | 0.325005i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.45156 | − | 3.84459i | −0.0474963 | − | 0.125799i | ||||
\(935\) | 6.81509 | 0.222877 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.0143 | 1.66656 | 0.833282 | − | 0.552848i | \(-0.186459\pi\) | ||||
0.833282 | + | 0.552848i | \(0.186459\pi\) | |||||||
\(938\) | 8.70801 | + | 23.0641i | 0.284326 | + | 0.753068i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13.6165 | − | 15.4618i | −0.444121 | − | 0.504310i | ||||
\(941\) | 8.71487i | 0.284097i | 0.989860 | + | 0.142048i | \(0.0453688\pi\) | ||||
−0.989860 | + | 0.142048i | \(0.954631\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 29.7583i | − | 0.969065i | ||||||
\(944\) | −4.51382 | + | 35.4203i | −0.146912 | + | 1.15283i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.3931 | − | 6.56689i | 0.565498 | − | 0.213508i | ||||
\(947\) | 38.1607 | 1.24006 | 0.620028 | − | 0.784580i | \(-0.287121\pi\) | ||||
0.620028 | + | 0.784580i | \(0.287121\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.9064 | −0.840957 | ||||||||
\(950\) | 3.35837 | − | 1.26798i | 0.108960 | − | 0.0411387i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.76560 | + | 3.58928i | 0.219274 | + | 0.116329i | ||||
\(953\) | 40.4395i | 1.30996i | 0.755645 | + | 0.654982i | \(0.227324\pi\) | ||||
−0.755645 | + | 0.654982i | \(0.772676\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 17.8286i | − | 0.576920i | ||||||
\(956\) | −12.3395 | + | 10.8668i | −0.399089 | + | 0.351458i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.41884 | + | 24.9468i | 0.304309 | + | 0.805994i | ||||
\(959\) | 19.9348 | 0.643728 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.2641 | 0.653680 | ||||||||
\(962\) | 26.2636 | + | 69.5617i | 0.846771 | + | 2.24276i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21.9371 | + | 19.3189i | −0.706546 | + | 0.622220i | ||||
\(965\) | 4.88362i | 0.157209i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.8302i | 0.541224i | 0.962689 | + | 0.270612i | \(0.0872260\pi\) | ||||
−0.962689 | + | 0.270612i | \(0.912774\pi\) | |||||||
\(968\) | 4.34463 | + | 2.30491i | 0.139642 | + | 0.0740826i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −15.4151 | + | 5.82007i | −0.494947 | + | 0.186871i | ||||
\(971\) | −34.0951 | −1.09416 | −0.547082 | − | 0.837079i | \(-0.684262\pi\) | ||||
−0.547082 | + | 0.837079i | \(0.684262\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.3044 | −0.779163 | ||||||||
\(974\) | −15.3072 | + | 5.77934i | −0.490474 | + | 0.185182i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.34399 | + | 10.5464i | −0.0430201 | + | 0.337583i | ||||
\(977\) | 0.863887i | 0.0276382i | 0.999905 | + | 0.0138191i | \(0.00439889\pi\) | ||||
−0.999905 | + | 0.0138191i | \(0.995601\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.30764i | 0.233553i | ||||||||
\(980\) | 7.32017 | + | 8.31222i | 0.233834 | + | 0.265524i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.746913 | − | 1.97828i | −0.0238349 | − | 0.0631293i | ||||
\(983\) | −36.8214 | −1.17442 | −0.587209 | − | 0.809435i | \(-0.699774\pi\) | ||||
−0.587209 | + | 0.809435i | \(0.699774\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.8173 | 0.535842 | ||||||||
\(986\) | −6.25719 | − | 16.5728i | −0.199269 | − | 0.527786i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17.0417 | + | 19.3512i | 0.542168 | + | 0.615644i | ||||
\(989\) | 30.0718i | 0.956227i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 35.9773i | − | 1.14286i | −0.820652 | − | 0.571428i | \(-0.806390\pi\) | ||
0.820652 | − | 0.571428i | \(-0.193610\pi\) | |||||||
\(992\) | −4.30239 | − | 18.0288i | −0.136601 | − | 0.572416i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.58795 | − | 2.10977i | 0.177239 | − | 0.0669179i | ||||
\(995\) | 5.91492 | 0.187515 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.4645 | −1.05983 | −0.529915 | − | 0.848051i | \(-0.677776\pi\) | ||||
−0.529915 | + | 0.848051i | \(0.677776\pi\) | |||||||
\(998\) | 41.6478 | − | 15.7244i | 1.31834 | − | 0.497748i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1620.2.e.b.971.32 | 48 | ||
3.2 | odd | 2 | inner | 1620.2.e.b.971.17 | 48 | ||
4.3 | odd | 2 | inner | 1620.2.e.b.971.18 | 48 | ||
9.2 | odd | 6 | 180.2.q.a.131.8 | yes | 48 | ||
9.4 | even | 3 | 180.2.q.a.11.1 | ✓ | 48 | ||
9.5 | odd | 6 | 540.2.q.a.251.24 | 48 | |||
9.7 | even | 3 | 540.2.q.a.71.17 | 48 | |||
12.11 | even | 2 | inner | 1620.2.e.b.971.31 | 48 | ||
36.7 | odd | 6 | 540.2.q.a.71.24 | 48 | |||
36.11 | even | 6 | 180.2.q.a.131.1 | yes | 48 | ||
36.23 | even | 6 | 540.2.q.a.251.17 | 48 | |||
36.31 | odd | 6 | 180.2.q.a.11.8 | yes | 48 | ||
45.2 | even | 12 | 900.2.o.b.599.6 | 48 | |||
45.4 | even | 6 | 900.2.r.f.551.24 | 48 | |||
45.13 | odd | 12 | 900.2.o.b.299.11 | 48 | |||
45.22 | odd | 12 | 900.2.o.c.299.14 | 48 | |||
45.29 | odd | 6 | 900.2.r.f.851.17 | 48 | |||
45.38 | even | 12 | 900.2.o.c.599.19 | 48 | |||
180.47 | odd | 12 | 900.2.o.b.599.11 | 48 | |||
180.67 | even | 12 | 900.2.o.c.299.19 | 48 | |||
180.83 | odd | 12 | 900.2.o.c.599.14 | 48 | |||
180.103 | even | 12 | 900.2.o.b.299.6 | 48 | |||
180.119 | even | 6 | 900.2.r.f.851.24 | 48 | |||
180.139 | odd | 6 | 900.2.r.f.551.17 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.2.q.a.11.1 | ✓ | 48 | 9.4 | even | 3 | ||
180.2.q.a.11.8 | yes | 48 | 36.31 | odd | 6 | ||
180.2.q.a.131.1 | yes | 48 | 36.11 | even | 6 | ||
180.2.q.a.131.8 | yes | 48 | 9.2 | odd | 6 | ||
540.2.q.a.71.17 | 48 | 9.7 | even | 3 | |||
540.2.q.a.71.24 | 48 | 36.7 | odd | 6 | |||
540.2.q.a.251.17 | 48 | 36.23 | even | 6 | |||
540.2.q.a.251.24 | 48 | 9.5 | odd | 6 | |||
900.2.o.b.299.6 | 48 | 180.103 | even | 12 | |||
900.2.o.b.299.11 | 48 | 45.13 | odd | 12 | |||
900.2.o.b.599.6 | 48 | 45.2 | even | 12 | |||
900.2.o.b.599.11 | 48 | 180.47 | odd | 12 | |||
900.2.o.c.299.14 | 48 | 45.22 | odd | 12 | |||
900.2.o.c.299.19 | 48 | 180.67 | even | 12 | |||
900.2.o.c.599.14 | 48 | 180.83 | odd | 12 | |||
900.2.o.c.599.19 | 48 | 45.38 | even | 12 | |||
900.2.r.f.551.17 | 48 | 180.139 | odd | 6 | |||
900.2.r.f.551.24 | 48 | 45.4 | even | 6 | |||
900.2.r.f.851.17 | 48 | 45.29 | odd | 6 | |||
900.2.r.f.851.24 | 48 | 180.119 | even | 6 | |||
1620.2.e.b.971.17 | 48 | 3.2 | odd | 2 | inner | ||
1620.2.e.b.971.18 | 48 | 4.3 | odd | 2 | inner | ||
1620.2.e.b.971.31 | 48 | 12.11 | even | 2 | inner | ||
1620.2.e.b.971.32 | 48 | 1.1 | even | 1 | trivial |