Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(25,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.q (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 25.3 | ||
Character | \(\chi\) | \(=\) | 504.25 |
Dual form | 504.2.q.c.121.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.46869 | − | 0.918117i | −0.847951 | − | 0.530075i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.89970 | − | 3.29038i | 0.849572 | − | 1.47150i | −0.0320189 | − | 0.999487i | \(-0.510194\pi\) |
0.881591 | − | 0.472014i | \(-0.156473\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.841809 | − | 2.50826i | −0.318174 | − | 0.948032i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.31412 | + | 2.69686i | 0.438041 | + | 0.898955i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.25706 | − | 3.90934i | −0.680529 | − | 1.17871i | −0.974820 | − | 0.222995i | \(-0.928417\pi\) |
0.294290 | − | 0.955716i | \(-0.404917\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.588451 | + | 1.01923i | 0.163207 | + | 0.282683i | 0.936017 | − | 0.351955i | \(-0.114483\pi\) |
−0.772810 | + | 0.634637i | \(0.781150\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.81103 | + | 3.08841i | −1.50040 | + | 0.797424i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.95973 | + | 5.12641i | −0.717841 | + | 1.24334i | 0.244012 | + | 0.969772i | \(0.421536\pi\) |
−0.961853 | + | 0.273565i | \(0.911797\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.55676 | + | 4.42844i | 0.586562 | + | 1.01595i | 0.994679 | + | 0.103025i | \(0.0328521\pi\) |
−0.408117 | + | 0.912930i | \(0.633815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.06651 | + | 4.45674i | −0.232733 | + | 0.972541i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.09082 | − | 3.62140i | 0.435966 | − | 0.755115i | −0.561408 | − | 0.827539i | \(-0.689740\pi\) |
0.997374 | + | 0.0724243i | \(0.0230736\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.71772 | − | 8.17134i | −0.943545 | − | 1.63427i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.545992 | − | 5.16739i | 0.105076 | − | 0.994464i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.11164 | − | 3.65747i | 0.392122 | − | 0.679175i | −0.600607 | − | 0.799544i | \(-0.705075\pi\) |
0.992729 | + | 0.120369i | \(0.0384078\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.24283 | −1.12124 | −0.560622 | − | 0.828072i | \(-0.689438\pi\) | ||||
−0.560622 | + | 0.828072i | \(0.689438\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.274303 | + | 7.81387i | −0.0477500 | + | 1.36022i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.85230 | − | 1.99507i | −1.66534 | − | 0.337229i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.87179 | − | 6.70614i | −0.636519 | − | 1.10248i | −0.986191 | − | 0.165611i | \(-0.947040\pi\) |
0.349672 | − | 0.936872i | \(-0.386293\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0715150 | − | 2.03720i | 0.0114516 | − | 0.326213i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.754693 | + | 1.30717i | 0.117863 | + | 0.204145i | 0.918921 | − | 0.394442i | \(-0.129062\pi\) |
−0.801057 | + | 0.598587i | \(0.795729\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.01709 | + | 8.68986i | −0.765099 | + | 1.32519i | 0.175095 | + | 0.984552i | \(0.443977\pi\) |
−0.940194 | + | 0.340639i | \(0.889357\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.3701 | + | 0.799273i | 1.69496 | + | 0.119149i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.23665 | −0.326248 | −0.163124 | − | 0.986606i | \(-0.552157\pi\) | ||||
−0.163124 | + | 0.986606i | \(0.552157\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.58272 | + | 4.22295i | −0.797531 | + | 0.603278i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.05359 | − | 4.81175i | 1.26776 | − | 0.673779i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.49368 | − | 11.2474i | 0.891975 | − | 1.54495i | 0.0544716 | − | 0.998515i | \(-0.482653\pi\) |
0.837504 | − | 0.546431i | \(-0.184014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17.1510 | −2.31263 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.310726 | − | 8.85143i | 0.0411566 | − | 1.17240i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.3922 | 1.61332 | 0.806662 | − | 0.591013i | \(-0.201272\pi\) | ||||
0.806662 | + | 0.591013i | \(0.201272\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.45834 | 0.186722 | 0.0933608 | − | 0.995632i | \(-0.470239\pi\) | ||||
0.0933608 | + | 0.995632i | \(0.470239\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.65819 | − | 5.56640i | 0.712865 | − | 0.701301i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.47152 | 0.554624 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.62638 | 0.198694 | 0.0993472 | − | 0.995053i | \(-0.468325\pi\) | ||||
0.0993472 | + | 0.995053i | \(0.468325\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.39564 | + | 3.39912i | −0.769945 | + | 0.409206i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.48517 | 1.00700 | 0.503502 | − | 0.863994i | \(-0.332045\pi\) | ||||
0.503502 | + | 0.863994i | \(0.332045\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.72984 | − | 6.46027i | 0.436544 | − | 0.756117i | −0.560876 | − | 0.827900i | \(-0.689535\pi\) |
0.997420 | + | 0.0717827i | \(0.0228688\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.573349 | + | 16.3326i | −0.0662047 | + | 1.88593i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.90563 | + | 8.95221i | −0.900930 | + | 1.02020i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.84185 | −0.207224 | −0.103612 | − | 0.994618i | \(-0.533040\pi\) | ||||
−0.103612 | + | 0.994618i | \(0.533040\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.54616 | + | 7.08803i | −0.616240 | + | 0.787558i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.307606 | + | 0.532789i | −0.0337641 | + | 0.0584812i | −0.882414 | − | 0.470474i | \(-0.844083\pi\) |
0.848650 | + | 0.528956i | \(0.177416\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.2452 | + | 19.4773i | 1.21972 | + | 2.11261i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.45934 | + | 3.43297i | −0.692514 | + | 0.368053i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.25572 | − | 2.17496i | −0.133106 | − | 0.230546i | 0.791767 | − | 0.610824i | \(-0.209162\pi\) |
−0.924872 | + | 0.380278i | \(0.875828\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.06112 | − | 2.33398i | 0.216064 | − | 0.244668i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.16880 | + | 5.73164i | 0.950761 | + | 0.594344i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 19.4283 | 1.99330 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.36751 | − | 4.10064i | 0.240384 | − | 0.416357i | −0.720440 | − | 0.693517i | \(-0.756060\pi\) |
0.960824 | + | 0.277160i | \(0.0893934\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.57691 | − | 11.2243i | 0.761508 | − | 1.12809i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.71081 | + | 9.89141i | 0.568247 | + | 0.984232i | 0.996739 | + | 0.0806872i | \(0.0257115\pi\) |
−0.428493 | + | 0.903545i | \(0.640955\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.18752 | − | 5.52095i | 0.314076 | − | 0.543996i | −0.665165 | − | 0.746697i | \(-0.731639\pi\) |
0.979241 | + | 0.202701i | \(0.0649720\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.6383 | + | 11.9757i | 1.23337 | + | 1.16871i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.11999 | + | 1.93988i | 0.108274 | + | 0.187536i | 0.915071 | − | 0.403293i | \(-0.132134\pi\) |
−0.806797 | + | 0.590828i | \(0.798801\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.73089 | + | 4.73005i | −0.261572 | + | 0.453056i | −0.966660 | − | 0.256064i | \(-0.917574\pi\) |
0.705088 | + | 0.709120i | \(0.250908\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.470543 | + | 13.4040i | −0.0446619 | + | 1.27225i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.45456 | − | 7.71553i | −0.419050 | − | 0.725816i | 0.576794 | − | 0.816890i | \(-0.304304\pi\) |
−0.995844 | + | 0.0910734i | \(0.970970\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.94386 | − | 13.7592i | −0.740768 | − | 1.28305i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.97542 | + | 2.92636i | −0.182628 | + | 0.270542i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.3499 | + | 3.10832i | 1.40712 | + | 0.284939i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.68864 | + | 8.12096i | −0.426240 | + | 0.738269i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.0917185 | − | 2.61272i | 0.00826998 | − | 0.235581i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −16.8520 | −1.50729 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.434918 | 0.0385927 | 0.0192964 | − | 0.999814i | \(-0.493857\pi\) | ||||
0.0192964 | + | 0.999814i | \(0.493857\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.3469 | − | 8.15646i | 1.35122 | − | 0.718136i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.67633 | − | 4.63553i | 0.233832 | − | 0.405009i | −0.725101 | − | 0.688643i | \(-0.758207\pi\) |
0.958933 | + | 0.283634i | \(0.0915402\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.95537 | − | 10.1409i | 0.776529 | − | 0.879329i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15.9654 | − | 11.6130i | −1.37409 | − | 0.999489i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.95121 | − | 5.11165i | −0.252139 | − | 0.436718i | 0.711976 | − | 0.702204i | \(-0.247801\pi\) |
−0.964115 | + | 0.265487i | \(0.914467\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.33649 | + | 7.51102i | 0.367816 | + | 0.637077i | 0.989224 | − | 0.146411i | \(-0.0467721\pi\) |
−0.621407 | + | 0.783488i | \(0.713439\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.28495 | + | 2.05350i | 0.276643 | + | 0.172936i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.65634 | − | 4.60091i | 0.222134 | − | 0.384747i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.02297 | − | 13.8962i | −0.666271 | − | 1.15402i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.0765 | − | 1.07663i | 0.996050 | − | 0.0887989i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.38860 | − | 9.33333i | 0.441451 | − | 0.764616i | −0.556346 | − | 0.830951i | \(-0.687797\pi\) |
0.997797 | + | 0.0663346i | \(0.0211305\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.41310 | + | 14.5719i | 0.684648 | + | 1.18585i | 0.973547 | + | 0.228486i | \(0.0733776\pi\) |
−0.288899 | + | 0.957360i | \(0.593289\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.7147 | − | 1.24527i | −1.43215 | − | 0.100674i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.8595 | + | 20.5413i | −0.952578 | + | 1.64991i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.96136 | 0.715194 | 0.357597 | − | 0.933876i | \(-0.383596\pi\) | ||||
0.357597 | + | 0.933876i | \(0.383596\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −19.8636 | + | 10.5570i | −1.57529 | + | 0.837225i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.8435 | − | 2.19578i | −0.854586 | − | 0.173052i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.71319 | − | 6.43144i | −0.290840 | − | 0.503749i | 0.683169 | − | 0.730261i | \(-0.260601\pi\) |
−0.974009 | + | 0.226511i | \(0.927268\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 25.1895 | + | 15.7466i | 1.96100 | + | 1.22587i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.13764 | − | 8.89866i | −0.397563 | − | 0.688599i | 0.595862 | − | 0.803087i | \(-0.296811\pi\) |
−0.993425 | + | 0.114488i | \(0.963477\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.80745 | − | 10.0588i | 0.446727 | − | 0.773754i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.58301 | + | 12.7148i | −0.656359 | + | 0.972322i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.2099 | −0.776246 | −0.388123 | − | 0.921608i | \(-0.626876\pi\) | ||||
−0.388123 | + | 0.921608i | \(0.626876\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.5244 | + | 18.7120i | −1.24913 | + | 1.41449i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18.2003 | − | 11.3775i | −1.36802 | − | 0.855183i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.62985 | − | 16.6794i | 0.719769 | − | 1.24668i | −0.241323 | − | 0.970445i | \(-0.577581\pi\) |
0.961091 | − | 0.276231i | \(-0.0890854\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.39163 | −0.103439 | −0.0517195 | − | 0.998662i | \(-0.516470\pi\) | ||||
−0.0517195 | + | 0.998662i | \(0.516470\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.14186 | − | 1.33893i | −0.158331 | − | 0.0989764i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −29.4210 | −2.16307 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 26.7212 | 1.95405 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.4208 | + | 2.98046i | −0.976217 | + | 0.216797i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.71483 | −0.196438 | −0.0982190 | − | 0.995165i | \(-0.531315\pi\) | ||||
−0.0982190 | + | 0.995165i | \(0.531315\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.84169 | 0.132568 | 0.0662839 | − | 0.997801i | \(-0.478886\pi\) | ||||
0.0662839 | + | 0.997801i | \(0.478886\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.56729 | − | 4.10538i | −0.470294 | − | 0.293992i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.9198 | 1.56172 | 0.780860 | − | 0.624706i | \(-0.214781\pi\) | ||||
0.780860 | + | 0.624706i | \(0.214781\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.726101 | + | 1.25764i | −0.0514719 | + | 0.0891520i | −0.890613 | − | 0.454761i | \(-0.849725\pi\) |
0.839141 | + | 0.543913i | \(0.183058\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.38866 | − | 1.49321i | −0.168483 | − | 0.105323i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.9515 | − | 2.21765i | −0.768643 | − | 0.155649i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.73476 | 0.400533 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.5140 | + | 0.879683i | 0.869785 | + | 0.0611422i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.5415 | − | 19.9905i | 0.798344 | − | 1.38277i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.771347 | + | 1.33601i | 0.0531017 | + | 0.0919749i | 0.891354 | − | 0.453307i | \(-0.149756\pi\) |
−0.838253 | + | 0.545282i | \(0.816423\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.4621 | − | 7.79037i | −0.853890 | − | 0.533788i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.0619 | + | 33.0162i | 1.30001 | + | 2.25169i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.25527 | + | 15.6586i | 0.356751 | + | 1.06298i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.4093 | + | 6.06373i | −0.770967 | + | 0.409749i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.96663 | −0.468626 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.346045 | + | 0.599368i | −0.0231729 | + | 0.0401366i | −0.877379 | − | 0.479797i | \(-0.840710\pi\) |
0.854206 | + | 0.519934i | \(0.174043\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.8373 | − | 23.4612i | 1.05582 | − | 1.56408i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.20797 | − | 15.9487i | −0.611155 | − | 1.05855i | −0.991046 | − | 0.133520i | \(-0.957372\pi\) |
0.379892 | − | 0.925031i | \(-0.375961\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.69696 | − | 4.67127i | 0.178220 | − | 0.308686i | −0.763051 | − | 0.646338i | \(-0.776299\pi\) |
0.941271 | + | 0.337652i | \(0.109633\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.8301 | − | 5.88976i | 1.30473 | − | 0.387518i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.27352 | − | 14.3302i | −0.542016 | − | 0.938800i | −0.998788 | − | 0.0492161i | \(-0.984328\pi\) |
0.456772 | − | 0.889584i | \(-0.349006\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.24896 | + | 7.35941i | −0.277171 | + | 0.480075i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.70512 | + | 1.69103i | 0.175716 | + | 0.109844i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.56724 | − | 2.71454i | −0.101376 | − | 0.175589i | 0.810876 | − | 0.585219i | \(-0.198991\pi\) |
−0.912252 | + | 0.409630i | \(0.865658\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.23730 | + | 14.2674i | 0.530611 | + | 0.919046i | 0.999362 | + | 0.0357151i | \(0.0113709\pi\) |
−0.468751 | + | 0.883330i | \(0.655296\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.6532 | − | 5.31812i | 0.940006 | − | 0.341157i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.28960 | + | 26.3916i | 0.210165 | + | 1.68610i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.00906 | + | 5.21184i | −0.191462 | + | 0.331621i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.940942 | − | 0.500086i | 0.0596298 | − | 0.0316917i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.8939 | 0.813858 | 0.406929 | − | 0.913460i | \(-0.366600\pi\) | ||||
0.406929 | + | 0.913460i | \(0.366600\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.8764 | −1.18675 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.36664 | − | 38.9306i | 0.0855824 | − | 2.43793i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.3045 | + | 17.8478i | −0.642774 | + | 1.11332i | 0.342036 | + | 0.939687i | \(0.388883\pi\) |
−0.984811 | + | 0.173631i | \(0.944450\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.5614 | + | 15.3567i | −0.842666 | + | 0.954222i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.6387 | + | 0.888444i | 0.782313 | + | 0.0549933i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.56616 | − | 7.90883i | −0.281562 | − | 0.487679i | 0.690208 | − | 0.723611i | \(-0.257519\pi\) |
−0.971770 | + | 0.235932i | \(0.924186\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.6721 | − | 42.7333i | −1.51559 | − | 2.62509i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.152608 | + | 4.34725i | −0.00933948 | + | 0.266047i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.4387 | + | 21.5445i | −0.758401 | + | 1.31359i | 0.185265 | + | 0.982689i | \(0.440686\pi\) |
−0.943666 | + | 0.330900i | \(0.892648\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.70814 | + | 9.88679i | 0.346745 | + | 0.600580i | 0.985669 | − | 0.168690i | \(-0.0539536\pi\) |
−0.638924 | + | 0.769270i | \(0.720620\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.17002 | + | 1.53555i | −0.312904 | + | 0.0929359i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.2964 | + | 36.8864i | −1.28422 | + | 2.22433i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.4938 | − | 26.8360i | −0.930932 | − | 1.61242i | −0.781732 | − | 0.623615i | \(-0.785663\pi\) |
−0.149200 | − | 0.988807i | \(-0.547670\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.20385 | − | 16.8361i | −0.491151 | − | 1.00795i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.40910 | + | 12.8329i | −0.441990 | + | 0.765549i | −0.997837 | − | 0.0657354i | \(-0.979061\pi\) |
0.555847 | + | 0.831285i | \(0.312394\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.7431 | 1.53027 | 0.765134 | − | 0.643872i | \(-0.222673\pi\) | ||||
0.765134 | + | 0.643872i | \(0.222673\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −28.5343 | − | 17.8375i | −1.69022 | − | 1.05660i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.64340 | − | 2.99335i | 0.156035 | − | 0.176692i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.02006 | − | 15.6232i | −0.530592 | − | 0.919012i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.24201 | + | 3.84894i | −0.424534 | + | 0.225629i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.41185 | + | 14.5697i | 0.491425 | + | 0.851174i | 0.999951 | − | 0.00987288i | \(-0.00314269\pi\) |
−0.508526 | + | 0.861047i | \(0.669809\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.5414 | − | 40.7749i | 1.37063 | − | 2.37401i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21.4334 | + | 9.52863i | −1.24369 | + | 0.552907i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.92137 | 0.284610 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.0198 | + | 5.26896i | 1.49976 | + | 0.303698i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.694040 | − | 19.7706i | 0.0398716 | − | 1.13579i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.77041 | − | 4.79849i | 0.158633 | − | 0.274761i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.2972 | −1.61501 | −0.807504 | − | 0.589862i | \(-0.799182\pi\) | ||||
−0.807504 | + | 0.589862i | \(0.799182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.75037 | + | 5.18207i | −0.554679 | + | 0.294798i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.8695 | 1.12670 | 0.563349 | − | 0.826219i | \(-0.309513\pi\) | ||||
0.563349 | + | 0.826219i | \(0.309513\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.2859 | −1.03358 | −0.516789 | − | 0.856113i | \(-0.672873\pi\) | ||||
−0.516789 | + | 0.856113i | \(0.672873\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.56670 | − | 29.1921i | −0.426335 | − | 1.64479i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.9480 | 0.783399 | 0.391700 | − | 0.920093i | \(-0.371887\pi\) | ||||
0.391700 | + | 0.920093i | \(0.371887\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.0644 | −1.06740 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.136114 | − | 3.87738i | 0.00759713 | − | 0.216414i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −30.2694 | −1.68423 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.55230 | − | 9.61686i | 0.307986 | − | 0.533447i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.35358 | − | 4.43971i | 0.461954 | − | 0.245517i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.88283 | + | 5.61009i | 0.103804 | + | 0.309294i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.8399 | 1.14547 | 0.572733 | − | 0.819742i | \(-0.305883\pi\) | ||||
0.572733 | + | 0.819742i | \(0.305883\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.9975 | − | 19.2544i | 0.712261 | − | 1.05513i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.08964 | − | 5.35142i | 0.168805 | − | 0.292379i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.4376 | + | 26.7387i | 0.840939 | + | 1.45655i | 0.889101 | + | 0.457710i | \(0.151330\pi\) |
−0.0481619 | + | 0.998840i | \(0.515336\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.541367 | + | 15.4216i | −0.0294030 | + | 0.837584i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.0904 | + | 24.4054i | 0.763040 | + | 1.32162i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.2918 | + | 10.4480i | 0.825681 | + | 0.564138i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.965424 | + | 27.5014i | −0.0519767 | + | 1.48062i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.2685 | −0.551244 | −0.275622 | − | 0.961266i | \(-0.588884\pi\) | ||||
−0.275622 | + | 0.961266i | \(0.588884\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.61262 | − | 7.98930i | 0.246908 | − | 0.427657i | −0.715758 | − | 0.698348i | \(-0.753919\pi\) |
0.962666 | + | 0.270691i | \(0.0872521\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.58803 | − | 2.48426i | 0.298267 | − | 0.132600i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.08660 | − | 7.07820i | −0.217508 | − | 0.376735i | 0.736538 | − | 0.676397i | \(-0.236459\pi\) |
−0.954045 | + | 0.299662i | \(0.903126\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.1193 | − | 27.9194i | 0.855522 | − | 1.48181i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.6905 | − | 18.6582i | −1.04213 | − | 0.987495i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.35957 | + | 11.0151i | 0.335645 | + | 0.581355i | 0.983609 | − | 0.180317i | \(-0.0577123\pi\) |
−0.647963 | + | 0.761672i | \(0.724379\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.57407 | + | 6.19047i | −0.188109 | + | 0.325814i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.3422 | − | 7.62249i | 0.752769 | − | 0.400077i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.1711 | − | 24.5452i | −0.741752 | − | 1.28475i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.9431 | + | 18.9540i | 0.571224 | + | 0.989388i | 0.996441 | + | 0.0842970i | \(0.0268644\pi\) |
−0.425217 | + | 0.905091i | \(0.639802\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.53349 | + | 3.75308i | −0.131888 | + | 0.195378i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −33.6778 | − | 6.81968i | −1.74846 | − | 0.354060i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.73126 | − | 11.6589i | 0.348531 | − | 0.603674i | −0.637457 | − | 0.770486i | \(-0.720014\pi\) |
0.985989 | + | 0.166811i | \(0.0533471\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.7505 | + | 15.4721i | 1.27811 | + | 0.798978i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.97038 | 0.255988 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.2180 | −0.576231 | −0.288115 | − | 0.957596i | \(-0.593029\pi\) | ||||
−0.288115 | + | 0.957596i | \(0.593029\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.638761 | − | 0.399306i | −0.0327247 | − | 0.0204570i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.00330 | − | 6.93392i | 0.204559 | − | 0.354307i | −0.745433 | − | 0.666581i | \(-0.767757\pi\) |
0.949992 | + | 0.312274i | \(0.101091\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.4378 | + | 43.0190i | 0.735819 | + | 2.19245i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −30.0284 | − | 2.11087i | −1.52643 | − | 0.107302i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.3931 | − | 24.9296i | −0.729759 | − | 1.26398i | −0.956985 | − | 0.290137i | \(-0.906299\pi\) |
0.227226 | − | 0.973842i | \(-0.427034\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.3765 | + | 21.4368i | 0.625908 | + | 1.08410i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.18667 | + | 4.35100i | −0.412963 | + | 0.219479i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.49897 | + | 6.06039i | −0.176052 | + | 0.304931i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.8138 | + | 18.7301i | 0.542731 | + | 0.940037i | 0.998746 | + | 0.0500651i | \(0.0159429\pi\) |
−0.456015 | + | 0.889972i | \(0.650724\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −22.4632 | + | 6.67183i | −1.12457 | + | 0.334009i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.4966 | + | 23.3768i | −0.673987 | + | 1.16738i | 0.302777 | + | 0.953062i | \(0.402086\pi\) |
−0.976764 | + | 0.214318i | \(0.931247\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.67360 | − | 6.36285i | −0.182995 | − | 0.316956i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.7862 | + | 31.7141i | 0.635353 | + | 1.57589i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.4777 | + | 30.2723i | −0.866339 | + | 1.50054i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.9473 | −1.03578 | −0.517889 | − | 0.855448i | \(-0.673282\pi\) | ||||
−0.517889 | + | 0.855448i | \(0.673282\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.358663 | + | 10.2170i | −0.0176916 | + | 0.503968i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.4318 | − | 31.0828i | −0.513317 | − | 1.52948i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.16872 | + | 2.02428i | 0.0573701 | + | 0.0993680i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.527018 | − | 15.0128i | 0.0258082 | − | 0.735180i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.91450 | + | 11.9763i | 0.337795 | + | 0.585079i | 0.984018 | − | 0.178070i | \(-0.0569855\pi\) |
−0.646222 | + | 0.763149i | \(0.723652\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.86872 | + | 11.8970i | −0.334761 | + | 0.579823i | −0.983439 | − | 0.181240i | \(-0.941989\pi\) |
0.648678 | + | 0.761063i | \(0.275322\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.93923 | − | 6.03193i | −0.142910 | − | 0.293283i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 55.8529 | 2.70926 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.22764 | − | 3.65790i | −0.0594099 | − | 0.177018i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.12552 | + | 4.31850i | −0.392304 | + | 0.208499i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.20392 | + | 15.9417i | −0.443337 | + | 0.767882i | −0.997935 | − | 0.0642362i | \(-0.979539\pi\) |
0.554598 | + | 0.832119i | \(0.312872\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.3558 | 1.17047 | 0.585233 | − | 0.810865i | \(-0.301003\pi\) | ||||
0.585233 | + | 0.810865i | \(0.301003\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.975039 | + | 27.7753i | −0.0467495 | + | 1.33172i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.3829 | 1.02288 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.83655 | −0.278564 | −0.139282 | − | 0.990253i | \(-0.544479\pi\) | ||||
−0.139282 | + | 0.990253i | \(0.544479\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.7251 | − | 9.50636i | −0.891671 | − | 0.452684i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.8400 | 0.705071 | 0.352536 | − | 0.935798i | \(-0.385320\pi\) | ||||
0.352536 | + | 0.935798i | \(0.385320\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.54194 | −0.452331 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.4833 | + | 8.76044i | −0.779633 | + | 0.414355i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.26289 | −0.201178 | −0.100589 | − | 0.994928i | \(-0.532073\pi\) | ||||
−0.100589 | + | 0.994928i | \(0.532073\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.40677 | − | 5.90070i | 0.160419 | − | 0.277853i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.02245 | − | 29.1259i | 0.0480390 | − | 1.36845i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.76416 | − | 11.2157i | −0.176467 | − | 0.525801i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 39.7459 | 1.85924 | 0.929618 | − | 0.368525i | \(-0.120137\pi\) | ||||
0.929618 | + | 0.368525i | \(0.120137\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 24.8742 | + | 18.0931i | 1.16103 | + | 0.844512i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.68671 | + | 4.65353i | −0.125133 | + | 0.216736i | −0.921785 | − | 0.387702i | \(-0.873269\pi\) |
0.796652 | + | 0.604438i | \(0.206602\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.8205 | + | 34.3301i | 0.921136 | + | 1.59545i | 0.797661 | + | 0.603106i | \(0.206070\pi\) |
0.123474 | + | 0.992348i | \(0.460596\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 36.2773 | − | 19.2804i | 1.68232 | − | 0.894108i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.43069 | + | 16.3344i | 0.436400 | + | 0.755867i | 0.997409 | − | 0.0719427i | \(-0.0229199\pi\) |
−0.561009 | + | 0.827810i | \(0.689587\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.36910 | − | 4.07939i | −0.0632193 | − | 0.188369i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.1615 | − | 8.22757i | −0.606449 | − | 0.379106i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 45.2955 | 2.08269 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.1242 | − | 41.7843i | 1.10689 | − | 1.91720i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 38.8662 | + | 2.73213i | 1.77956 | + | 0.125095i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.50287 | − | 16.4595i | −0.434197 | − | 0.752052i | 0.563032 | − | 0.826435i | \(-0.309635\pi\) |
−0.997230 | + | 0.0743830i | \(0.976301\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.55672 | − | 7.89247i | 0.207768 | − | 0.359866i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.9098 | + | 13.1805i | 0.632916 | + | 0.599734i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.99511 | − | 15.5800i | −0.408447 | − | 0.707451i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.21626 | + | 9.03482i | −0.236371 | + | 0.409407i | −0.959670 | − | 0.281128i | \(-0.909291\pi\) |
0.723299 | + | 0.690535i | \(0.242625\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.451268 | + | 12.8550i | −0.0204070 | + | 0.581322i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.3311 | − | 24.8221i | −0.646752 | − | 1.12021i | −0.983894 | − | 0.178753i | \(-0.942794\pi\) |
0.337142 | − | 0.941454i | \(-0.390540\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.4998 | + | 21.6503i | 0.562962 | + | 0.975079i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −22.5385 | − | 46.2538i | −1.01303 | − | 2.07895i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.14289 | − | 21.2830i | −0.320402 | − | 0.954673i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.5396 | − | 28.6475i | 0.740416 | − | 1.28244i | −0.211890 | − | 0.977294i | \(-0.567962\pi\) |
0.952306 | − | 0.305145i | \(-0.0987049\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.624383 | + | 17.7864i | −0.0278954 | + | 0.794636i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.9523 | −1.29092 | −0.645460 | − | 0.763794i | \(-0.723334\pi\) | ||||
−0.645460 | + | 0.763794i | \(0.723334\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 43.3953 | 1.93107 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.7645 | + | 9.44138i | −0.788950 | + | 0.419306i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.8820 | + | 27.5085i | −0.703959 | + | 1.21929i | 0.263107 | + | 0.964767i | \(0.415253\pi\) |
−0.967066 | + | 0.254526i | \(0.918081\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.3438 | − | 3.91709i | −0.855721 | − | 0.173282i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 24.2794 | − | 10.7939i | 1.07196 | − | 0.476562i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.1107 | − | 20.9763i | −0.533660 | − | 0.924327i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.04825 | + | 8.74382i | 0.222022 | + | 0.384553i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.9952 | + | 9.37390i | 0.658218 | + | 0.411469i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.87897 | + | 4.98652i | −0.126130 | + | 0.218463i | −0.922174 | − | 0.386775i | \(-0.873589\pi\) |
0.796044 | + | 0.605239i | \(0.206922\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.3123 | − | 38.6461i | −0.975650 | − | 1.68987i | −0.677774 | − | 0.735270i | \(-0.737055\pi\) |
−0.297875 | − | 0.954605i | \(-0.596278\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 41.4491 | − | 12.3108i | 1.80899 | − | 0.537289i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.4771 | − | 32.0033i | 0.804876 | − | 1.39409i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.75696 | + | 4.77520i | 0.119868 | + | 0.207617i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.2848 | + | 33.4200i | 0.706702 | + | 1.45031i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.888199 | + | 1.53841i | −0.0384722 | + | 0.0666357i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.51060 | 0.367945 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −29.4569 | + | 15.6556i | −1.27116 | + | 0.675588i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 29.1095 | + | 12.2933i | 1.25383 | + | 0.529510i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.6719 | + | 27.1445i | 0.673786 | + | 1.16703i | 0.976822 | + | 0.214053i | \(0.0686665\pi\) |
−0.303036 | + | 0.952979i | \(0.598000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.04388 | + | 1.27768i | 0.0877112 | + | 0.0548304i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.3758 | + | 17.9713i | 0.444449 | + | 0.769808i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.37567 | − | 2.38273i | 0.0588195 | − | 0.101878i | −0.835116 | − | 0.550073i | \(-0.814600\pi\) |
0.893936 | + | 0.448195i | \(0.147933\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.91644 | + | 3.93295i | 0.0817917 | + | 0.167854i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.5959 | 0.920014 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.55049 | + | 4.61984i | 0.0659334 | + | 0.196455i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 43.2104 | + | 27.0119i | 1.83418 | + | 1.14659i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.42197 | − | 5.92703i | 0.144994 | − | 0.251136i | −0.784377 | − | 0.620284i | \(-0.787017\pi\) |
0.929371 | + | 0.369148i | \(0.120350\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.8092 | −0.499478 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −39.2453 | − | 24.5332i | −1.65694 | − | 1.03579i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.1001 | 0.636395 | 0.318197 | − | 0.948025i | \(-0.396923\pi\) | ||||
0.318197 | + | 0.948025i | \(0.396923\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33.8494 | −1.42405 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.4474 | + | 7.94444i | 0.942702 | + | 0.333635i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.5276 | −1.15402 | −0.577008 | − | 0.816738i | \(-0.695780\pi\) | ||||
−0.577008 | + | 0.816738i | \(0.695780\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.8755 | −1.62689 | −0.813444 | − | 0.581643i | \(-0.802410\pi\) | ||||
−0.813444 | + | 0.581643i | \(0.802410\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.98725 | + | 2.49253i | 0.166570 | + | 0.104127i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −39.4556 | −1.64541 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.84330 | + | 17.0491i | −0.409782 | + | 0.709763i | −0.994865 | − | 0.101210i | \(-0.967729\pi\) |
0.585083 | + | 0.810973i | \(0.301062\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.70488 | − | 1.69089i | −0.112411 | − | 0.0702709i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.59532 | + | 0.323049i | 0.0661849 | + | 0.0134023i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −58.6265 | −2.42806 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.87613 | + | 12.0591i | 0.242948 | + | 0.498582i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.14068 | − | 5.43982i | 0.129630 | − | 0.224525i | −0.793903 | − | 0.608044i | \(-0.791954\pi\) |
0.923533 | + | 0.383519i | \(0.125288\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.9614 | − | 27.6460i | −0.657679 | − | 1.13913i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −32.1935 | − | 20.1249i | −1.32426 | − | 0.827829i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.79280 | + | 13.4975i | 0.320012 | + | 0.554277i | 0.980490 | − | 0.196568i | \(-0.0629798\pi\) |
−0.660478 | + | 0.750845i | \(0.729646\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 39.3877 | − | 44.6021i | 1.61474 | − | 1.82851i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.22108 | − | 1.18045i | 0.0909029 | − | 0.0483125i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.05557 | 0.0431292 | 0.0215646 | − | 0.999767i | \(-0.493135\pi\) | ||||
0.0215646 | + | 0.999767i | \(0.493135\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.1622 | + | 21.0656i | −0.496107 | + | 0.859283i | −0.999990 | − | 0.00448941i | \(-0.998571\pi\) |
0.503883 | + | 0.863772i | \(0.331904\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.13727 | + | 4.38614i | 0.0870363 | + | 0.178617i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.8140 | + | 30.8548i | 0.724243 | + | 1.25443i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.16502 | + | 3.74993i | −0.0878756 | + | 0.152205i | −0.906613 | − | 0.421963i | \(-0.861341\pi\) |
0.818737 | + | 0.574168i | \(0.194674\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14.0483 | + | 13.3118i | 0.569266 | + | 0.539421i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.31616 | − | 2.27965i | −0.0532460 | − | 0.0922247i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.3556 | + | 42.1852i | −0.983714 | + | 1.70384i | −0.336196 | + | 0.941792i | \(0.609140\pi\) |
−0.647518 | + | 0.762050i | \(0.724193\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.42261 | − | 5.26518i | −0.339632 | − | 0.212313i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.6366 | + | 25.3514i | 0.589249 | + | 1.02061i | 0.994331 | + | 0.106329i | \(0.0339096\pi\) |
−0.405082 | + | 0.914280i | \(0.632757\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.2381 | + | 31.5893i | 0.733050 | + | 1.26968i | 0.955573 | + | 0.294753i | \(0.0952374\pi\) |
−0.222523 | + | 0.974927i | \(0.571429\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.5716 | − | 12.7813i | −0.705125 | − | 0.512897i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.39830 | + | 4.98056i | −0.176214 | + | 0.199542i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.42523 | + | 14.5929i | −0.337009 | + | 0.583717i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −35.3046 | + | 18.7635i | −1.40993 | + | 0.749341i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 45.8379 | 1.82768 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.501625 | 0.0199694 | 0.00998468 | − | 0.999950i | \(-0.496822\pi\) | ||||
0.00998468 | + | 0.999950i | \(0.496822\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.0937425 | − | 2.67038i | 0.00372593 | − | 0.106138i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.826214 | − | 1.43104i | 0.0327873 | − | 0.0567893i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.58929 | − | 3.20506i | −0.300699 | − | 0.126989i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.1506 | + | 22.8834i | 0.441109 | + | 0.905251i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.5112 | + | 30.3303i | 0.691651 | + | 1.19797i | 0.971297 | + | 0.237871i | \(0.0764495\pi\) |
−0.279646 | + | 0.960103i | \(0.590217\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.29049 | + | 12.6275i | 0.287509 | + | 0.497980i | 0.973215 | − | 0.229899i | \(-0.0738396\pi\) |
−0.685706 | + | 0.727879i | \(0.740506\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.31662 | − | 65.9918i | 0.0912166 | − | 2.59843i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.6503 | + | 20.1790i | −0.458022 | + | 0.793318i | −0.998856 | − | 0.0478116i | \(-0.984775\pi\) |
0.540834 | + | 0.841129i | \(0.318109\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.9699 | − | 48.4453i | −1.09791 | − | 1.90164i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.65807 | − | 27.8227i | 0.260950 | − | 1.09046i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.26780 | − | 7.39204i | 0.167012 | − | 0.289273i | −0.770356 | − | 0.637614i | \(-0.779922\pi\) |
0.937368 | + | 0.348341i | \(0.113255\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.1684 | − | 17.6123i | −0.397314 | − | 0.688168i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.3239 | + | 1.56928i | 0.870940 | + | 0.0612234i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.81616 | + | 3.14568i | −0.0707476 | + | 0.122538i | −0.899229 | − | 0.437478i | \(-0.855872\pi\) |
0.828482 | + | 0.560016i | \(0.189205\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.0231 | −1.20666 | −0.603330 | − | 0.797492i | \(-0.706160\pi\) | ||||
−0.603330 | + | 0.797492i | \(0.706160\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.2318 | + | 6.39618i | 0.397372 | + | 0.248407i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.3549 | − | 48.7313i | −0.634217 | − | 1.88972i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.83011 | − | 15.2942i | −0.341903 | − | 0.592194i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.05852 | − | 0.562578i | 0.0409249 | − | 0.0217505i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.29156 | − | 5.70116i | −0.127069 | − | 0.220091i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.291838 | − | 0.505478i | 0.0112495 | − | 0.0194848i | −0.860346 | − | 0.509711i | \(-0.829752\pi\) |
0.871595 | + | 0.490226i | \(0.163086\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −44.8003 | + | 19.9168i | −1.72436 | + | 0.766599i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.7332 | −1.29647 | −0.648237 | − | 0.761439i | \(-0.724493\pi\) | ||||
−0.648237 | + | 0.761439i | \(0.724493\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.2785 | − | 2.48636i | −0.471204 | − | 0.0954178i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.11905 | + | 31.8777i | −0.0428822 | + | 1.22156i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.60312 | + | 2.77668i | −0.0613417 | + | 0.106247i | −0.895065 | − | 0.445935i | \(-0.852871\pi\) |
0.833724 | + | 0.552182i | \(0.186205\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.4257 | −0.856841 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.24978 | + | 4.38454i | −0.314749 | + | 0.167281i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.2848 | 0.582306 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.3674 | −1.23131 | −0.615657 | − | 0.788014i | \(-0.711109\pi\) | ||||
−0.615657 | + | 0.788014i | \(0.711109\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −34.5319 | − | 9.55610i | −1.31176 | − | 0.363006i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32.9521 | 1.24995 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.93476 | −0.338428 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.00549 | + | 28.6427i | −0.0380311 | + | 1.08337i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.2591 | 0.802943 | 0.401472 | − | 0.915871i | \(-0.368499\pi\) | ||||
0.401472 | + | 0.915871i | \(0.368499\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.7985 | − | 34.2920i | 0.746715 | − | 1.29335i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.9972 | − | 6.90768i | 0.489504 | − | 0.260158i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.0028 | − | 22.6509i | 0.752283 | − | 0.851873i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.6544 | 1.18880 | 0.594402 | − | 0.804168i | \(-0.297389\pi\) | ||||
0.594402 | + | 0.804168i | \(0.297389\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.42042 | − | 4.96722i | −0.0907728 | − | 0.186285i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.0526 | + | 22.6078i | −0.488824 | + | 0.846669i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.0925 | − | 17.4807i | −0.377438 | − | 0.653741i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.190468 | + | 5.42574i | −0.00711316 | + | 0.202628i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.9776 | − | 25.9420i | −0.558571 | − | 0.967473i | −0.997616 | − | 0.0690079i | \(-0.978017\pi\) |
0.439045 | − | 0.898465i | \(-0.355317\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.5313 | − | 3.34755i | −0.615656 | − | 0.124669i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.00109 | − | 28.5173i | 0.0372308 | − | 1.06057i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −39.8486 | −1.47994 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.6310 | + | 23.6095i | −0.505544 | + | 0.875629i | 0.494435 | + | 0.869215i | \(0.335375\pi\) |
−0.999979 | + | 0.00641398i | \(0.997958\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.4038 | − | 5.64270i | −0.977918 | − | 0.208989i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29.6985 | − | 51.4393i | −1.09844 | − | 1.90255i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.2717 | − | 19.5232i | 0.416330 | − | 0.721105i | −0.579237 | − | 0.815159i | \(-0.696649\pi\) |
0.995567 | + | 0.0940545i | \(0.0299828\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 19.3991 | − | 41.7814i | 0.715548 | − | 1.54113i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.67085 | − | 6.35809i | −0.135217 | − | 0.234203i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.82742 | + | 15.2895i | −0.324722 | + | 0.562435i | −0.981456 | − | 0.191687i | \(-0.938604\pi\) |
0.656734 | + | 0.754122i | \(0.271937\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.20446 | − | 4.89193i | 0.338134 | − | 0.179710i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.31474 | − | 5.74130i | −0.121606 | − | 0.210628i | 0.798795 | − | 0.601603i | \(-0.205471\pi\) |
−0.920401 | + | 0.390975i | \(0.872138\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.4735 | − | 35.4611i | −0.750089 | − | 1.29919i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.84109 | − | 0.129421i | −0.0673621 | − | 0.00473527i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.92291 | − | 4.44224i | 0.143340 | − | 0.162316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.93721 | + | 6.81944i | −0.143671 | + | 0.248845i | −0.928876 | − | 0.370390i | \(-0.879224\pi\) |
0.785206 | + | 0.619235i | \(0.212557\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.9372 | − | 11.8381i | −0.690111 | − | 0.431406i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 63.9295 | 2.32663 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.1503 | −1.35025 | −0.675125 | − | 0.737703i | \(-0.735910\pi\) | ||||
−0.675125 | + | 0.737703i | \(0.735910\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 27.7237 | + | 17.3307i | 1.00631 | + | 0.629066i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.2273 | − | 28.1065i | 0.588238 | − | 1.01886i | −0.406225 | − | 0.913773i | \(-0.633155\pi\) |
0.994463 | − | 0.105085i | \(-0.0335115\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.1631 | + | 2.86799i | 0.512737 | + | 0.103828i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −37.7500 | + | 55.9224i | −1.36485 | + | 2.02188i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.29218 | + | 12.6304i | 0.263305 | + | 0.456058i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.4992 | + | 19.9172i | 0.414671 | + | 0.718232i | 0.995394 | − | 0.0958699i | \(-0.0305633\pi\) |
−0.580723 | + | 0.814101i | \(0.697230\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.5205 | − | 16.7523i | 1.13518 | − | 0.603320i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.2117 | − | 22.8834i | 0.475194 | − | 0.823059i | −0.524403 | − | 0.851470i | \(-0.675711\pi\) |
0.999596 | + | 0.0284109i | \(0.00904469\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.4519 | + | 51.0123i | 1.05794 | + | 1.83241i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 34.0169 | − | 10.1034i | 1.22035 | − | 0.362457i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.85914 | + | 6.68423i | −0.138268 | + | 0.239487i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.1515 | − | 33.1714i | −0.685296 | − | 1.18697i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.7466 | − | 12.9086i | −0.634212 | − | 0.461316i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.0239 | − | 29.4862i | 0.607609 | − | 1.05241i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.11300 | −0.324843 | −0.162422 | − | 0.986721i | \(-0.551931\pi\) | ||||
−0.162422 | + | 0.986721i | \(0.551931\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.554930 | + | 15.8079i | −0.0197560 | + | 0.562777i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.6027 | + | 17.6682i | −0.554767 | + | 0.628209i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.858162 | + | 1.48638i | 0.0304742 | + | 0.0527829i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.99842 | + | 85.4140i | −0.106343 | + | 3.02932i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.5330 | − | 47.6886i | −0.975270 | − | 1.68922i | −0.679042 | − | 0.734099i | \(-0.737605\pi\) |
−0.296228 | − | 0.955117i | \(-0.595729\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.61988 | − | 11.4660i | 0.234195 | − | 0.405637i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.21542 | − | 6.24467i | 0.148944 | − | 0.220644i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −33.6739 | −1.18833 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.8243 | + | 31.5078i | −0.980679 | + | 1.11050i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 38.0490 | − | 20.2220i | 1.33939 | − | 0.711849i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.0961 | − | 19.2191i | 0.390119 | − | 0.675707i | −0.602346 | − | 0.798235i | \(-0.705767\pi\) |
0.992465 | + | 0.122529i | \(0.0391004\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.0941 | 1.82927 | 0.914636 | − | 0.404279i | \(-0.132478\pi\) | ||||
0.914636 | + | 0.404279i | \(0.132478\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.693716 | − | 19.7614i | 0.0243297 | − | 0.693063i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.2158 | −0.988357 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −51.3100 | −1.79511 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.00299 | + | 2.49142i | 0.314590 | + | 0.0870574i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.6107 | 1.38242 | 0.691212 | − | 0.722652i | \(-0.257077\pi\) | ||||
0.691212 | + | 0.722652i | \(0.257077\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.3470 | −1.12755 | −0.563773 | − | 0.825930i | \(-0.690651\pi\) | ||||
−0.563773 | + | 0.825930i | \(0.690651\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 65.1439 | − | 34.6223i | 2.26802 | − | 1.20539i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.1724 | −1.32738 | −0.663692 | − | 0.748006i | \(-0.731012\pi\) | ||||
−0.663692 | + | 0.748006i | \(0.731012\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.7372 | − | 48.0422i | 0.963353 | − | 1.66858i | 0.249375 | − | 0.968407i | \(-0.419775\pi\) |
0.713977 | − | 0.700169i | \(-0.246892\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.88298 | + | 53.6390i | −0.0653197 | + | 1.86072i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.12520 | − | 41.1181i | −0.177578 | − | 1.42466i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −39.0399 | −1.35103 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.40853 | + | 32.2591i | −0.117816 | + | 1.11504i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.35256 | − | 4.07475i | 0.0812193 | − | 0.140676i | −0.822555 | − | 0.568686i | \(-0.807452\pi\) |
0.903774 | + | 0.428010i | \(0.140785\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.58195 | + | 9.66822i | 0.192481 | + | 0.333387i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.6638 | − | 12.0452i | 0.780584 | − | 0.414860i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.0648 | − | 38.2174i | −0.759054 | − | 1.31472i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.3164 | + | 4.92402i | 0.835522 | + | 0.169191i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −37.8087 | − | 23.6351i | −1.29759 | − | 0.811156i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.3809 | −1.11000 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.87889 | − | 3.25434i | 0.0643321 | − | 0.111426i | −0.832065 | − | 0.554678i | \(-0.812842\pi\) |
0.896398 | + | 0.443251i | \(0.146175\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 25.5312 | + | 52.3956i | 0.873149 | + | 1.79189i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.5780 | + | 46.0345i | 0.907888 | + | 1.57251i | 0.816993 | + | 0.576648i | \(0.195640\pi\) |
0.0908957 | + | 0.995860i | \(0.471027\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.4888 | − | 45.8799i | 0.903786 | − | 1.56540i | 0.0812476 | − | 0.996694i | \(-0.474110\pi\) |
0.822538 | − | 0.568709i | \(-0.192557\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.63059 | + | 1.96936i | −0.225970 | + | 0.0671156i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.57834 | + | 16.5902i | 0.326051 | + | 0.564736i | 0.981724 | − | 0.190308i | \(-0.0609487\pi\) |
−0.655674 | + | 0.755044i | \(0.727615\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.3958 | + | 33.5945i | −0.659477 | + | 1.14225i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.09622 | + | 31.2272i | −0.0372295 | + | 1.06053i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.15717 | + | 7.20043i | 0.141022 | + | 0.244258i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.957046 | + | 1.65765i | 0.0324283 | + | 0.0561674i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.1701 | + | 0.996096i | 0.479584 | + | 0.0337127i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14.1862 | + | 42.2693i | 0.479581 | + | 1.42896i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.83865 | + | 3.18463i | −0.0620868 | + | 0.107537i | −0.895398 | − | 0.445267i | \(-0.853109\pi\) |
0.833311 | + | 0.552804i | \(0.186442\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.02230 | − | 29.1216i | 0.0344813 | − | 0.982246i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.8862 | −0.501529 | −0.250765 | − | 0.968048i | \(-0.580682\pi\) | ||||
−0.250765 | + | 0.968048i | \(0.580682\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.9262 | 1.34362 | 0.671811 | − | 0.740722i | \(-0.265517\pi\) | ||||
0.671811 | + | 0.740722i | \(0.265517\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −72.0113 | + | 38.2721i | −2.42063 | + | 1.28650i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.25124 | − | 7.36336i | 0.142743 | − | 0.247237i | −0.785786 | − | 0.618499i | \(-0.787741\pi\) |
0.928528 | + | 0.371261i | \(0.121075\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.366118 | − | 1.09089i | −0.0122792 | − | 0.0365872i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 40.2275 | + | 5.68374i | 1.34767 | + | 0.190412i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.71857 | − | 9.90486i | −0.191365 | − | 0.331453i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.5877 | − | 63.3717i | −1.22299 | − | 2.11828i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.22799 | − | 4.51839i | −0.241336 | − | 0.150865i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.1826 | + | 22.8329i | −0.439665 | + | 0.761521i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.4391 | + | 66.5785i | 1.28059 | + | 2.21805i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −33.3776 | − | 31.6277i | −1.11074 | − | 1.05251i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.64368 | + | 4.57899i | −0.0878789 | + | 0.152211i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.59544 | + | 2.76339i | 0.0529758 | + | 0.0917568i | 0.891297 | − | 0.453419i | \(-0.149796\pi\) |
−0.838321 | + | 0.545176i | \(0.816463\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.1711 | + | 28.3998i | −0.635865 | + | 0.941963i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.63889 | − | 13.2309i | 0.253088 | − | 0.438361i | −0.711287 | − | 0.702902i | \(-0.751887\pi\) |
0.964374 | + | 0.264541i | \(0.0852206\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.77714 | 0.0919099 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.47447 | + | 4.50396i | −0.280157 | + | 0.148896i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.8801 | − | 2.81069i | −0.458360 | − | 0.0928170i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.2681 | + | 43.7656i | 0.833516 | + | 1.44369i | 0.895233 | + | 0.445599i | \(0.147009\pi\) |
−0.0617164 | + | 0.998094i | \(0.519657\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 41.5600 | + | 25.9801i | 1.36945 | + | 0.856075i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.99310 | + | 8.64831i | 0.164350 | + | 0.284662i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.5321 | + | 63.2755i | −1.20117 | + | 2.08048i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.0781 | + | 1.34111i | 0.626606 | + | 0.0440477i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47.9781 | 1.57411 | 0.787055 | − | 0.616883i | \(-0.211605\pi\) | ||||
0.787055 | + | 0.616883i | \(0.211605\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.9748 | − | 13.9257i | −1.08070 | − | 0.456395i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −29.1823 | − | 18.2426i | −0.955385 | − | 0.597235i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 50.7623 | − | 87.9228i | 1.66010 | − | 2.87538i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.5226 | 0.670443 | 0.335222 | − | 0.942139i | \(-0.391189\pi\) | ||||
0.335222 | + | 0.942139i | \(0.391189\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.8563 | + | 16.7886i | 0.876423 | + | 0.547874i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.95586 | −0.324552 | −0.162276 | − | 0.986745i | \(-0.551883\pi\) | ||||
−0.162276 | + | 0.986745i | \(0.551883\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.31170 | 0.205537 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −15.6886 | + | 49.8214i | −0.510350 | + | 1.62069i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.2213 | −0.689601 | −0.344800 | − | 0.938676i | \(-0.612053\pi\) | ||||
−0.344800 | + | 0.938676i | \(0.612053\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.77930 | 0.284988 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.4854 | − | 12.8059i | −0.664284 | − | 0.415260i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.9191 | −1.16353 | −0.581767 | − | 0.813355i | \(-0.697639\pi\) | ||||
−0.581767 | + | 0.813355i | \(0.697639\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.15736 | + | 8.93281i | −0.166888 | + | 0.289059i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27.9998 | + | 17.5033i | 0.905104 | + | 0.565803i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.3370 | + | 11.7054i | −0.333798 | + | 0.377988i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.97290 | 0.257190 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.75980 | + | 5.56972i | −0.121158 | + | 0.179482i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.49866 | − | 6.05986i | 0.112626 | − | 0.195074i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.9559 | + | 27.6365i | 0.513108 | + | 0.888729i | 0.999884 | + | 0.0152023i | \(0.00483924\pi\) |
−0.486777 | + | 0.873526i | \(0.661827\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 44.4564 | + | 27.7908i | 1.42815 | + | 0.892769i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.6645 | − | 49.6483i | −0.919886 | − | 1.59329i | −0.799585 | − | 0.600553i | \(-0.794947\pi\) |
−0.120301 | − | 0.992737i | \(-0.538386\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.1891 | − | 17.1999i | 0.486940 | − | 0.551403i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.9840 | + | 9.02657i | −0.543924 | + | 0.289081i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.58455 | 0.274644 | 0.137322 | − | 0.990526i | \(-0.456150\pi\) | ||||
0.137322 | + | 0.990526i | \(0.456150\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.66845 | + | 9.81805i | −0.181164 | + | 0.313786i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.3450 | − | 1.14899i | −0.521856 | − | 0.0366843i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.2504 | + | 19.4863i | 0.358834 | + | 0.621518i | 0.987766 | − | 0.155942i | \(-0.0498412\pi\) |
−0.628933 | + | 0.777460i | \(0.716508\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.6411 | − | 72.1244i | 1.32679 | − | 2.29807i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.38542 | − | 9.96816i | 0.0759286 | − | 0.317290i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.9796 | + | 36.3378i | 0.667114 | + | 1.15548i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.3652 | − | 33.5415i | 0.615156 | − | 1.06548i | −0.375201 | − | 0.926944i | \(-0.622426\pi\) |
0.990357 | − | 0.138538i | \(-0.0442405\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −30.6075 | − | 19.1335i | −0.971299 | − | 0.607183i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.75875 | + | 4.77829i | 0.0874582 | + | 0.151482i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.3955 | − | 31.8619i | −0.582590 | − | 1.00908i | −0.995171 | − | 0.0981549i | \(-0.968706\pi\) |
0.412581 | − | 0.910921i | \(-0.364627\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −36.7672 | + | 16.3456i | −1.16326 | + | 0.517151i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 504.2.q.c.25.3 | ✓ | 22 | |
3.2 | odd | 2 | 1512.2.q.d.1369.2 | 22 | |||
4.3 | odd | 2 | 1008.2.q.l.529.9 | 22 | |||
7.2 | even | 3 | 504.2.t.c.457.10 | yes | 22 | ||
9.4 | even | 3 | 504.2.t.c.193.10 | yes | 22 | ||
9.5 | odd | 6 | 1512.2.t.c.361.10 | 22 | |||
12.11 | even | 2 | 3024.2.q.l.2881.2 | 22 | |||
21.2 | odd | 6 | 1512.2.t.c.289.10 | 22 | |||
28.23 | odd | 6 | 1008.2.t.l.961.2 | 22 | |||
36.23 | even | 6 | 3024.2.t.k.1873.10 | 22 | |||
36.31 | odd | 6 | 1008.2.t.l.193.2 | 22 | |||
63.23 | odd | 6 | 1512.2.q.d.793.2 | 22 | |||
63.58 | even | 3 | inner | 504.2.q.c.121.3 | yes | 22 | |
84.23 | even | 6 | 3024.2.t.k.289.10 | 22 | |||
252.23 | even | 6 | 3024.2.q.l.2305.2 | 22 | |||
252.247 | odd | 6 | 1008.2.q.l.625.9 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.3 | ✓ | 22 | 1.1 | even | 1 | trivial | |
504.2.q.c.121.3 | yes | 22 | 63.58 | even | 3 | inner | |
504.2.t.c.193.10 | yes | 22 | 9.4 | even | 3 | ||
504.2.t.c.457.10 | yes | 22 | 7.2 | even | 3 | ||
1008.2.q.l.529.9 | 22 | 4.3 | odd | 2 | |||
1008.2.q.l.625.9 | 22 | 252.247 | odd | 6 | |||
1008.2.t.l.193.2 | 22 | 36.31 | odd | 6 | |||
1008.2.t.l.961.2 | 22 | 28.23 | odd | 6 | |||
1512.2.q.d.793.2 | 22 | 63.23 | odd | 6 | |||
1512.2.q.d.1369.2 | 22 | 3.2 | odd | 2 | |||
1512.2.t.c.289.10 | 22 | 21.2 | odd | 6 | |||
1512.2.t.c.361.10 | 22 | 9.5 | odd | 6 | |||
3024.2.q.l.2305.2 | 22 | 252.23 | even | 6 | |||
3024.2.q.l.2881.2 | 22 | 12.11 | even | 2 | |||
3024.2.t.k.289.10 | 22 | 84.23 | even | 6 | |||
3024.2.t.k.1873.10 | 22 | 36.23 | even | 6 |