Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(193,504)]
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, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.t (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 | 193.10 | ||
Character | \(\chi\) | \(=\) | 504.193 |
Dual form | 504.2.t.c.457.10 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.52946 | + | 0.812868i | 0.883034 | + | 0.469309i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.79940 | −1.69914 | −0.849572 | − | 0.527473i | \(-0.823140\pi\) | ||||
−0.849572 | + | 0.527473i | \(0.823140\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.59312 | + | 0.525101i | 0.980107 | + | 0.198470i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.67849 | + | 2.48650i | 0.559497 | + | 0.828832i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.51412 | 1.36106 | 0.680529 | − | 0.732721i | \(-0.261750\pi\) | ||||
0.680529 | + | 0.732721i | \(0.261750\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.588451 | − | 1.01923i | 0.163207 | − | 0.282683i | −0.772810 | − | 0.634637i | \(-0.781150\pi\) |
0.936017 | + | 0.351955i | \(0.114483\pi\) | |||||||
\(14\) | 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 | ||||||||
\(21\) | 3.53923 | + | 2.91098i | 0.772324 | + | 0.635229i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.18164 | −0.871931 | −0.435966 | − | 0.899963i | \(-0.643593\pi\) | ||||
−0.435966 | + | 0.899963i | \(0.643593\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.43545 | 1.88709 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.545992 | + | 5.16739i | 0.105076 | + | 0.994464i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.11164 | + | 3.65747i | 0.392122 | + | 0.679175i | 0.992729 | − | 0.120369i | \(-0.0384078\pi\) |
−0.600607 | + | 0.799544i | \(0.705075\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.12141 | + | 5.40645i | 0.560622 | + | 0.971027i | 0.997442 | + | 0.0714776i | \(0.0227714\pi\) |
−0.436820 | + | 0.899549i | \(0.643895\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.90416 | + | 3.66938i | 1.20186 | + | 0.638758i | ||||
\(34\) | 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 | ||||||||
\(39\) | 1.72851 | − | 1.08053i | 0.276783 | − | 0.173024i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.754693 | − | 1.30717i | 0.117863 | − | 0.204145i | −0.801057 | − | 0.598587i | \(-0.795729\pi\) |
0.918921 | + | 0.394442i | \(0.129062\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.01709 | − | 8.68986i | −0.765099 | − | 1.32519i | −0.940194 | − | 0.340639i | \(-0.889357\pi\) |
0.175095 | − | 0.984552i | \(-0.443977\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.37726 | − | 9.44720i | −0.950666 | − | 1.40831i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.11832 | − | 1.93699i | 0.163124 | − | 0.282539i | −0.772863 | − | 0.634572i | \(-0.781176\pi\) |
0.935988 | + | 0.352033i | \(0.114510\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.44854 | + | 2.72330i | 0.921220 | + | 0.389043i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.69389 | + | 5.43476i | −1.21739 | + | 0.761019i | ||||
\(52\) | 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 | ||||||||
\(59\) | −6.19609 | − | 10.7319i | −0.806662 | − | 1.39718i | −0.915163 | − | 0.403083i | \(-0.867939\pi\) |
0.108501 | − | 0.994096i | \(-0.465395\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.729171 | + | 1.26296i | −0.0933608 | + | 0.161706i | −0.908923 | − | 0.416963i | \(-0.863094\pi\) |
0.815563 | + | 0.578669i | \(0.196428\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.04687 | + | 7.32916i | 0.383869 | + | 0.923388i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.23576 | + | 3.87245i | −0.277312 | + | 0.480318i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.813192 | − | 1.40849i | −0.0993472 | − | 0.172074i | 0.812067 | − | 0.583564i | \(-0.198342\pi\) |
−0.911415 | + | 0.411489i | \(0.865009\pi\) | |||||||
\(68\) | 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 | ||||||||
\(75\) | 14.4311 | + | 7.66977i | 1.66636 | + | 0.885629i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.7057 | + | 2.37037i | 1.33398 | + | 0.270129i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.920926 | − | 1.59509i | 0.103612 | − | 0.179462i | −0.809558 | − | 0.587040i | \(-0.800293\pi\) |
0.913170 | + | 0.407578i | \(0.133627\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.36533 | + | 8.34713i | −0.373926 | + | 0.927459i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.307606 | − | 0.532789i | −0.0337641 | − | 0.0584812i | 0.848650 | − | 0.528956i | \(-0.177416\pi\) |
−0.882414 | + | 0.470474i | \(0.844083\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.2452 | − | 19.4773i | 1.21972 | − | 2.11261i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.256630 | + | 7.31043i | 0.0275136 | + | 0.783761i | ||||
\(88\) | 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 | ||||||||
\(93\) | 0.379348 | + | 10.8062i | 0.0393366 | + | 1.12055i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.71417 | − | 16.8254i | −0.996652 | − | 1.72625i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.36751 | + | 4.10064i | 0.240384 | + | 0.416357i | 0.960824 | − | 0.277160i | \(-0.0893934\pi\) |
−0.720440 | + | 0.693517i | \(0.756060\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.57691 | + | 11.2243i | 0.761508 | + | 1.12809i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.4216 | −1.13649 | −0.568247 | − | 0.822858i | \(-0.692378\pi\) | ||||
−0.568247 | + | 0.822858i | \(0.692378\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.37505 | −0.628152 | −0.314076 | − | 0.949398i | \(-0.601695\pi\) | ||||
−0.314076 | + | 0.949398i | \(0.601695\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13.4470 | − | 11.0600i | −1.31229 | − | 1.07935i | ||||
\(106\) | 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 | −0.995844 | − | 0.0910734i | \(-0.970970\pi\) |
0.576794 | + | 0.816890i | \(0.304304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.8877 | 1.48154 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.52201 | − | 0.247583i | 0.325610 | − | 0.0228890i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.3668 | + | 11.7392i | −0.950326 | + | 1.07613i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.37728 | 0.852480 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.21683 | − | 1.38579i | 0.199884 | − | 0.124953i | ||||
\(124\) | 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 | ||||||||
\(129\) | −0.609732 | − | 17.3690i | −0.0536839 | − | 1.52926i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.35265 | −0.467664 | −0.233832 | − | 0.972277i | \(-0.575126\pi\) | ||||
−0.233832 | + | 0.972277i | \(0.575126\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.30461 | + | 12.8260i | 0.373257 | + | 1.11216i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.07444 | − | 19.6330i | −0.178539 | − | 1.68974i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.90242 | 0.504278 | 0.252139 | − | 0.967691i | \(-0.418866\pi\) | ||||
0.252139 | + | 0.967691i | \(0.418866\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.33649 | − | 7.51102i | 0.367816 | − | 0.637077i | −0.621407 | − | 0.783488i | \(-0.713439\pi\) |
0.989224 | + | 0.146411i | \(0.0467721\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | 7.64909 | + | 9.40699i | 0.630886 | + | 0.775875i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.7772 | −0.882903 | −0.441451 | − | 0.897285i | \(-0.645536\pi\) | ||||
−0.441451 | + | 0.897285i | \(0.645536\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.8262 | −1.36930 | −0.684648 | − | 0.728873i | \(-0.740044\pi\) | ||||
−0.684648 | + | 0.728873i | \(0.740044\pi\) | |||||||
\(152\) | 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 | ||||||||
\(157\) | −4.48068 | − | 7.76076i | −0.357597 | − | 0.619376i | 0.629962 | − | 0.776626i | \(-0.283071\pi\) |
−0.987559 | + | 0.157250i | \(0.949737\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.0745 | − | 11.9239i | 1.51270 | − | 0.945628i | ||||
\(160\) | 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 | ||||||||
\(165\) | −26.2317 | − | 13.9415i | −2.04213 | − | 1.08534i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.13764 | + | 8.89866i | −0.397563 | + | 0.688599i | −0.993425 | − | 0.114488i | \(-0.963477\pi\) |
0.595862 | + | 0.803087i | \(0.296811\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.80745 | + | 10.0588i | 0.446727 | + | 0.773754i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.71980 | + | 13.7905i | −0.513876 | + | 1.05458i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.10496 | − | 8.84205i | 0.388123 | − | 0.672249i | −0.604074 | − | 0.796928i | \(-0.706457\pi\) |
0.992197 | + | 0.124679i | \(0.0397903\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 24.4672 | + | 4.95457i | 1.84955 | + | 0.374530i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.753016 | − | 21.4507i | −0.0566002 | − | 1.61233i | ||||
\(178\) | 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 | ||||||||
\(185\) | 14.7105 | + | 25.4793i | 1.08154 | + | 1.87328i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.3606 | + | 23.1412i | −0.977024 | + | 1.69225i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.29758 | + | 13.6864i | −0.0943851 | + | 0.995536i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.35741 | − | 2.35111i | 0.0982190 | − | 0.170120i | −0.812728 | − | 0.582643i | \(-0.802019\pi\) |
0.910948 | + | 0.412522i | \(0.135352\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.920846 | − | 1.59495i | −0.0662839 | − | 0.114807i | 0.830979 | − | 0.556304i | \(-0.187781\pi\) |
−0.897263 | + | 0.441497i | \(0.854448\pi\) | |||||||
\(194\) | 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 | ||||||||
\(201\) | −0.0988280 | − | 2.81524i | −0.00697079 | − | 0.198572i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.55519 | + | 10.5931i | 0.249526 | + | 0.743488i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.86738 | + | 4.96645i | −0.200267 | + | 0.346872i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.01884 | − | 10.3976i | −0.487843 | − | 0.722685i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.5415 | + | 19.9905i | 0.798344 | + | 1.38277i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.771347 | − | 1.33601i | 0.0531017 | − | 0.0919749i | −0.838253 | − | 0.545282i | \(-0.816423\pi\) |
0.891354 | + | 0.453307i | \(0.149756\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.9777 | + | 6.89732i | 0.889219 | + | 0.472597i | ||||
\(214\) | 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 | ||||||||
\(219\) | 10.9560 | − | 6.84885i | 0.740336 | − | 0.462803i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.48332 | + | 6.03328i | 0.234313 | + | 0.405842i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.346045 | − | 0.599368i | −0.0231729 | − | 0.0401366i | 0.854206 | − | 0.519934i | \(-0.174043\pi\) |
−0.877379 | + | 0.479797i | \(0.840710\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.8373 | + | 23.4612i | 1.05582 | + | 1.56408i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.4159 | 1.22231 | 0.611155 | − | 0.791511i | \(-0.290705\pi\) | ||||
0.611155 | + | 0.791511i | \(0.290705\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.39392 | −0.356440 | −0.178220 | − | 0.983991i | \(-0.557034\pi\) | ||||
−0.178220 | + | 0.983991i | \(0.557034\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.9765 | + | 13.1405i | 1.05118 | + | 0.864584i | ||||
\(232\) | 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 | −0.912252 | − | 0.409630i | \(-0.865658\pi\) |
0.810876 | + | 0.585219i | \(0.198991\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.4746 | −1.06122 | −0.530611 | − | 0.847615i | \(-0.678038\pi\) | ||||
−0.530611 | + | 0.847615i | \(0.678038\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.9322 | + | 10.0310i | −0.765454 | + | 0.643490i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24.5006 | − | 10.3469i | −1.56528 | − | 0.661040i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.01811 | 0.382923 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.0373836 | − | 1.06492i | −0.00236909 | − | 0.0674867i | ||||
\(250\) | 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 | ||||||||
\(255\) | 33.0316 | − | 20.6488i | 2.06852 | − | 1.29308i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.6089 | 1.28555 | 0.642774 | − | 0.766055i | \(-0.277783\pi\) | ||||
0.642774 | + | 0.766055i | \(0.277783\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.51862 | − | 19.4229i | −0.405047 | − | 1.20688i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.54991 | + | 11.3896i | −0.343531 | + | 0.705000i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.13233 | 0.563123 | 0.281562 | − | 0.959543i | \(-0.409148\pi\) | ||||
0.281562 | + | 0.959543i | \(0.409148\pi\) | |||||||
\(264\) | 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 | ||||||||
\(273\) | 5.04962 | − | 1.89431i | 0.305617 | − | 0.114649i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 42.5927 | 2.56844 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.9876 | 1.86186 | 0.930932 | − | 0.365192i | \(-0.118997\pi\) | ||||
0.930932 | + | 0.365192i | \(0.118997\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.20385 | + | 16.8361i | −0.491151 | + | 1.00795i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.40910 | − | 12.8329i | −0.441990 | − | 0.765549i | 0.555847 | − | 0.831285i | \(-0.312394\pi\) |
−0.997837 | + | 0.0657354i | \(0.979061\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.8715 | − | 22.2942i | −0.765134 | − | 1.32525i | −0.940176 | − | 0.340689i | \(-0.889340\pi\) |
0.175042 | − | 0.984561i | \(-0.443994\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.18057 | − | 33.6301i | −0.0699310 | − | 1.99208i | ||||
\(286\) | 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 | ||||||||
\(291\) | 0.287725 | + | 8.19623i | 0.0168668 | + | 0.480472i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.41185 | − | 14.5697i | 0.491425 | − | 0.851174i | −0.508526 | − | 0.861047i | \(-0.669809\pi\) |
0.999951 | + | 0.00987288i | \(0.00314269\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.5414 | + | 40.7749i | 1.37063 | + | 2.37401i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.46467 | + | 23.3262i | 0.143015 | + | 1.35352i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.46069 | + | 4.26203i | −0.142305 | + | 0.246480i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.44686 | − | 25.1683i | −0.486869 | − | 1.45068i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.4689 | − | 9.28427i | −1.00356 | − | 0.533367i | ||||
\(304\) | 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 | ||||||||
\(311\) | −9.93477 | − | 17.2075i | −0.563349 | − | 0.975750i | −0.997201 | − | 0.0747654i | \(-0.976179\pi\) |
0.433852 | − | 0.900984i | \(-0.357154\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.14293 | − | 15.8360i | 0.516789 | − | 0.895105i | −0.483021 | − | 0.875609i | \(-0.660460\pi\) |
0.999810 | − | 0.0194961i | \(-0.00620619\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.5763 | − | 27.8464i | −0.652249 | − | 1.56897i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.97401 | + | 12.0793i | −0.391700 | + | 0.678444i | −0.992674 | − | 0.120825i | \(-0.961446\pi\) |
0.600974 | + | 0.799268i | \(0.294779\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.53220 | + | 16.5103i | 0.533701 | + | 0.924397i | ||||
\(320\) | 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 | ||||||||
\(327\) | −8.02169 | + | 5.01456i | −0.443601 | + | 0.277306i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.91706 | − | 4.43562i | 0.215955 | − | 0.244544i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.4200 | + | 18.0479i | −0.572733 | + | 0.992003i | 0.423551 | + | 0.905872i | \(0.360783\pi\) |
−0.996284 | + | 0.0861302i | \(0.972550\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.1760 | − | 20.8834i | 0.557643 | − | 1.14440i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.08964 | + | 5.35142i | 0.168805 | + | 0.292379i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.4376 | − | 26.7387i | 0.840939 | − | 1.45655i | −0.0481619 | − | 0.998840i | \(-0.515336\pi\) |
0.889101 | − | 0.457710i | \(-0.151330\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.0848 | + | 8.17962i | −0.710668 | + | 0.444256i | ||||
\(340\) | 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 | ||||||||
\(345\) | 24.2996 | + | 12.9146i | 1.30825 | + | 0.695299i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.13427 | + | 8.89281i | 0.275622 | + | 0.477391i | 0.970292 | − | 0.241938i | \(-0.0777829\pi\) |
−0.694670 | + | 0.719329i | \(0.744450\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.61262 | + | 7.98930i | 0.246908 | + | 0.427657i | 0.962666 | − | 0.270691i | \(-0.0872521\pi\) |
−0.715758 | + | 0.698348i | \(0.753919\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.58803 | + | 2.48426i | 0.298267 | + | 0.132600i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.17321 | 0.435016 | 0.217508 | − | 0.976059i | \(-0.430207\pi\) | ||||
0.217508 | + | 0.976059i | \(0.430207\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −32.2386 | −1.71104 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −25.3981 | + | 9.52782i | −1.34421 | + | 0.504266i | ||||
\(358\) | 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 | ||||||||
\(367\) | −21.8861 | −1.14245 | −0.571224 | − | 0.820794i | \(-0.693531\pi\) | ||||
−0.571224 | + | 0.820794i | \(0.693531\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.51701 | − | 0.317527i | 0.235146 | − | 0.0165298i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.7449 | − | 25.7560i | 1.18086 | − | 1.33718i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.4625 | −0.697063 | −0.348531 | − | 0.937297i | \(-0.613320\pi\) | ||||
−0.348531 | + | 0.937297i | \(0.613320\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −25.7745 | − | 13.6985i | −1.33099 | − | 0.707387i | ||||
\(376\) | 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 | ||||||||
\(381\) | 0.665189 | + | 0.353531i | 0.0340787 | + | 0.0181119i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.00660 | −0.409118 | −0.204559 | − | 0.978854i | \(-0.565576\pi\) | ||||
−0.204559 | + | 0.978854i | \(0.565576\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −44.4745 | − | 9.00599i | −2.26663 | − | 0.458988i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.1862 | − | 27.0608i | 0.670290 | − | 1.37558i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.7862 | 1.45952 | 0.729759 | − | 0.683705i | \(-0.239632\pi\) | ||||
0.729759 | + | 0.683705i | \(0.239632\pi\) | |||||||
\(390\) | 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 | ||||||||
\(399\) | −3.84215 | + | 23.1160i | −0.192348 | + | 1.15725i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.9932 | 1.34797 | 0.673987 | − | 0.738743i | \(-0.264580\pi\) | ||||
0.673987 | + | 0.738743i | \(0.264580\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.34719 | 0.365990 | ||||||||
\(404\) | 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 | ||||||||
\(409\) | 10.4737 | + | 18.1409i | 0.517889 | + | 0.897010i | 0.999784 | + | 0.0207814i | \(0.00661539\pi\) |
−0.481895 | + | 0.876229i | \(0.660051\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.02752 | + | 4.79789i | 0.445295 | + | 0.236662i | ||||
\(412\) | 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 | ||||||||
\(417\) | 12.7380 | − | 7.96281i | 0.623781 | − | 0.389941i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.91450 | − | 11.9763i | 0.337795 | − | 0.585079i | −0.646222 | − | 0.763149i | \(-0.723652\pi\) |
0.984018 | + | 0.178070i | \(0.0569855\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.86872 | − | 11.8970i | −0.334761 | − | 0.579823i | 0.648678 | − | 0.761063i | \(-0.275322\pi\) |
−0.983439 | + | 0.181240i | \(0.941989\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.69342 | − | 0.470519i | 0.325445 | − | 0.0228774i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −27.9264 | + | 48.3700i | −1.35463 | + | 2.34629i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.55401 | + | 2.89212i | −0.123597 | + | 0.139959i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.80269 | − | 4.87765i | 0.376717 | − | 0.235495i | ||||
\(430\) | 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 | ||||||||
\(437\) | −10.6914 | − | 18.5181i | −0.511441 | − | 0.885842i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.91828 | − | 5.05460i | 0.139282 | − | 0.241243i | −0.787943 | − | 0.615748i | \(-0.788854\pi\) |
0.927225 | + | 0.374505i | \(0.122187\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.05234 | + | 20.6053i | 0.192968 | + | 0.981205i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.42002 | + | 12.8518i | −0.352536 | + | 0.610610i | −0.986693 | − | 0.162594i | \(-0.948014\pi\) |
0.634157 | + | 0.773204i | \(0.281347\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.77097 | + | 8.26356i | 0.226166 | + | 0.391730i | ||||
\(446\) | 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 | ||||||||
\(453\) | −25.7350 | − | 13.6775i | −1.20914 | − | 0.642624i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.83102 | + | 8.86772i | −0.367124 | + | 0.415725i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.8730 | + | 34.4210i | −0.929618 | + | 1.61015i | −0.145657 | + | 0.989335i | \(0.546530\pi\) |
−0.783961 | + | 0.620810i | \(0.786804\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −28.1061 | − | 12.4951i | −1.31188 | − | 0.583222i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.68671 | − | 4.65353i | −0.125133 | − | 0.216736i | 0.796652 | − | 0.604438i | \(-0.206602\pi\) |
−0.921785 | + | 0.387702i | \(0.873269\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.8205 | − | 34.3301i | 0.921136 | − | 1.59545i | 0.123474 | − | 0.992348i | \(-0.460596\pi\) |
0.797661 | − | 0.603106i | \(-0.206070\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.44130 | − | 41.0572i | −0.0668385 | − | 1.90398i | ||||
\(466\) | 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 | ||||||||
\(471\) | −0.544541 | − | 15.5120i | −0.0250911 | − | 0.714754i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.6477 | − | 39.2270i | −1.04134 | − | 1.80366i | ||||
\(474\) | 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 | ||||||||
\(479\) | 19.0057 | 0.868395 | 0.434197 | − | 0.900818i | \(-0.357032\pi\) | ||||
0.434197 | + | 0.900818i | \(0.357032\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.11344 | −0.415537 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.7998 | − | 12.1727i | −0.673413 | − | 0.553876i | ||||
\(484\) | 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 | 0.337142 | + | 0.941454i | \(0.390540\pi\) |
−0.983894 | + | 0.178753i | \(0.942794\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.9996 | −1.12592 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −28.7877 | − | 42.6458i | −1.29391 | − | 1.91679i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.0031 | + | 4.45557i | 0.986972 | + | 0.199860i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.0793 | −1.48083 | −0.740416 | − | 0.672149i | \(-0.765372\pi\) | ||||
−0.740416 | + | 0.672149i | \(0.765372\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.0913 | + | 9.43391i | −0.674227 | + | 0.421476i | ||||
\(502\) | 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 | ||||||||
\(507\) | 0.705785 | + | 20.1052i | 0.0313450 | + | 0.892904i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.7641 | 1.40792 | 0.703959 | − | 0.710241i | \(-0.251414\pi\) | ||||
0.703959 | + | 0.710241i | \(0.251414\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.0642 | − | 14.7937i | 0.577927 | − | 0.654435i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −21.4875 | + | 15.6297i | −0.948697 | + | 0.690067i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.2214 | 1.06732 | ||||||||
\(516\) | 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 | ||||||||
\(525\) | 33.3942 | + | 27.4664i | 1.45744 | + | 1.19873i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −36.9542 | −1.60975 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.51392 | −0.239736 | ||||||||
\(530\) | 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 | ||||||||
\(535\) | −4.25530 | − | 7.37040i | −0.183973 | − | 0.318650i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 28.2866 | − | 17.6826i | 1.22066 | − | 0.763063i | ||||
\(538\) | 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 | ||||||||
\(543\) | −2.12844 | − | 1.13121i | −0.0913401 | − | 0.0485449i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.3758 | − | 17.9713i | 0.444449 | − | 0.769808i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.37567 | + | 2.38273i | 0.0588195 | + | 0.101878i | 0.893936 | − | 0.448195i | \(-0.147933\pi\) |
−0.835116 | + | 0.550073i | \(0.814600\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.36426 | + | 0.306789i | −0.186262 | + | 0.0130934i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.7979 | + | 18.7026i | −0.460007 | + | 0.796756i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.22565 | − | 3.65268i | 0.137169 | − | 0.155328i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.78778 | + | 50.9273i | 0.0758870 | + | 2.16174i | ||||
\(556\) | 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 | ||||||||
\(563\) | −7.55007 | − | 13.0771i | −0.318197 | − | 0.551134i | 0.661915 | − | 0.749579i | \(-0.269744\pi\) |
−0.980112 | + | 0.198445i | \(0.936411\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.9247 | − | 29.3144i | 0.712027 | − | 1.23327i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.1098 | + | 19.8780i | −0.550560 | + | 0.834796i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.7638 | − | 23.8396i | 0.577008 | − | 0.999408i | −0.418812 | − | 0.908073i | \(-0.637553\pi\) |
0.995820 | − | 0.0913346i | \(-0.0291133\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.4377 | + | 33.6672i | 0.813444 | + | 1.40893i | 0.910439 | + | 0.413642i | \(0.135744\pi\) |
−0.0969950 | + | 0.995285i | \(0.530923\pi\) | |||||||
\(572\) | 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 | ||||||||
\(579\) | −0.111911 | − | 3.18794i | −0.00465087 | − | 0.132486i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.517891 | − | 1.54311i | −0.0214857 | − | 0.0640190i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29.3132 | − | 50.7720i | 1.21403 | − | 2.10276i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.3815 | + | 0.940665i | −0.553259 | + | 0.0388917i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.14068 | + | 5.43982i | 0.129630 | + | 0.224525i | 0.923533 | − | 0.383519i | \(-0.125288\pi\) |
−0.793903 | + | 0.608044i | \(0.791954\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.9614 | + | 27.6460i | −0.657679 | + | 1.13913i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 33.5254 | + | 17.8179i | 1.37905 | + | 0.732930i | ||||
\(592\) | 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 | ||||||||
\(597\) | −2.13284 | + | 1.33329i | −0.0872913 | + | 0.0545679i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.527783 | − | 0.914146i | −0.0215646 | − | 0.0373510i | 0.855042 | − | 0.518559i | \(-0.173531\pi\) |
−0.876606 | + | 0.481208i | \(0.840198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.1622 | − | 21.0656i | −0.496107 | − | 0.859283i | 0.503883 | − | 0.863772i | \(-0.331904\pi\) |
−0.999990 | + | 0.00448941i | \(0.998571\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.13727 | − | 4.38614i | 0.0870363 | − | 0.178617i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −35.6280 | −1.44849 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.33005 | 0.175751 | 0.0878756 | − | 0.996131i | \(-0.471992\pi\) | ||||
0.0878756 | + | 0.996131i | \(0.471992\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.17325 | + | 19.0916i | −0.128587 | + | 0.773630i | ||||
\(610\) | 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 | −0.405082 | − | 0.914280i | \(-0.632757\pi\) |
0.994331 | − | 0.106329i | \(-0.0339096\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.4762 | −1.46610 | −0.733050 | − | 0.680174i | \(-0.761904\pi\) | ||||
−0.733050 | + | 0.680174i | \(0.761904\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.28314 | − | 21.6081i | −0.0916192 | − | 0.867105i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.11414 | − | 6.29932i | −0.0847014 | − | 0.252377i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.8505 | 0.674018 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.40265 | + | 39.9564i | 0.0560166 | + | 1.59571i | ||||
\(628\) | 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 | ||||||||
\(633\) | 2.26575 | − | 1.41637i | 0.0900553 | − | 0.0562958i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.65243 | −0.0655746 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.57031 | − | 4.96999i | 0.260325 | − | 0.196918i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.2423 | + | 21.0983i | 0.563416 | + | 0.834637i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.0224 | −1.38330 | −0.691651 | − | 0.722232i | \(-0.743116\pi\) | ||||
−0.691651 | + | 0.722232i | \(0.743116\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.29049 | − | 12.6275i | 0.287509 | − | 0.497980i | −0.685706 | − | 0.727879i | \(-0.740506\pi\) |
0.973215 | + | 0.229899i | \(0.0738396\pi\) | |||||||
\(644\) | 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 | ||||||||
\(651\) | −4.69068 | + | 28.2211i | −0.183842 | + | 1.10607i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.53559 | −0.334023 | −0.167012 | − | 0.985955i | \(-0.553412\pi\) | ||||
−0.167012 | + | 0.985955i | \(0.553412\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.3369 | 0.794628 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.3239 | − | 1.56928i | 0.870940 | − | 0.0612234i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.81616 | − | 3.14568i | −0.0707476 | − | 0.122538i | 0.828482 | − | 0.560016i | \(-0.189205\pi\) |
−0.899229 | + | 0.437478i | \(0.855872\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.5116 | + | 26.8668i | 0.603330 | + | 1.04500i | 0.992313 | + | 0.123753i | \(0.0394932\pi\) |
−0.388983 | + | 0.921245i | \(0.627173\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.423331 | + | 12.0591i | 0.0164408 | + | 0.468338i | ||||
\(664\) | 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 | ||||||||
\(669\) | −0.0420552 | − | 1.19800i | −0.00162595 | − | 0.0463173i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.29156 | + | 5.70116i | −0.127069 | + | 0.220091i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.291838 | + | 0.505478i | 0.0112495 | + | 0.0194848i | 0.871595 | − | 0.490226i | \(-0.163086\pi\) |
−0.860346 | + | 0.509711i | \(0.829752\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.15168 | + | 48.7566i | 0.198288 | + | 1.87664i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.8666 | − | 29.2138i | 0.648237 | − | 1.12278i | −0.335307 | − | 0.942109i | \(-0.608840\pi\) |
0.983544 | − | 0.180670i | \(-0.0578265\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.98597 | + | 11.8766i | 0.152968 | + | 0.455783i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.1664 | + | 14.9697i | 1.07934 | + | 0.573641i | ||||
\(682\) | 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 | ||||||||
\(689\) | −7.64242 | − | 13.2371i | −0.291153 | − | 0.504292i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.1837 | − | 28.0310i | 0.615657 | − | 1.06635i | −0.374611 | − | 0.927182i | \(-0.622224\pi\) |
0.990269 | − | 0.139168i | \(-0.0444428\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.7539 | + | 33.0847i | 0.522468 | + | 1.25678i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.4761 | + | 28.5374i | −0.624973 | + | 1.08249i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.46738 | + | 7.73773i | 0.169214 | + | 0.293087i | ||||
\(698\) | 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 | ||||||||
\(705\) | −12.4808 | + | 7.80208i | −0.470056 | + | 0.293843i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.6176 | − | 5.99751i | −1.11389 | − | 0.225560i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.8272 | + | 27.4135i | −0.594402 | + | 1.02953i | 0.399229 | + | 0.916851i | \(0.369278\pi\) |
−0.993631 | + | 0.112684i | \(0.964055\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.51195 | − | 0.387467i | 0.206714 | − | 0.0145311i | ||||
\(712\) | 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 | ||||||||
\(717\) | −4.60359 | + | 2.87782i | −0.171924 | + | 0.107474i | ||||
\(718\) | 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 | ||||||||
\(723\) | −25.1972 | − | 13.3917i | −0.937095 | − | 0.498042i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.9243 | + | 34.5099i | 0.739969 | + | 1.28166i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.6310 | − | 23.6095i | −0.505544 | − | 0.875629i | −0.999979 | − | 0.00641398i | \(-0.997958\pi\) |
0.494435 | − | 0.869215i | \(-0.335375\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.4038 | + | 5.64270i | −0.977918 | + | 0.208989i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 59.3970 | 2.19688 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.5434 | −0.832660 | −0.416330 | − | 0.909214i | \(-0.636684\pi\) | ||||
−0.416330 | + | 0.909214i | \(0.636684\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −29.0620 | − | 35.7409i | −1.07197 | − | 1.31832i | ||||
\(736\) | 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 | −0.920401 | − | 0.390975i | \(-0.872138\pi\) |
0.798795 | + | 0.601603i | \(0.205471\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40.9469 | 1.50018 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.808464 | − | 1.65914i | 0.0295802 | − | 0.0607049i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.88564 | + | 5.61846i | 0.0688997 | + | 0.205294i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.87441 | 0.287341 | 0.143671 | − | 0.989626i | \(-0.454109\pi\) | ||||
0.143671 | + | 0.989626i | \(0.454109\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.7207 | + | 10.4811i | 0.718664 | + | 0.381951i | ||||
\(754\) | 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 | ||||||||
\(759\) | −28.8707 | − | 15.3440i | −1.04794 | − | 0.556953i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.4545 | −1.17648 | −0.588238 | − | 0.808688i | \(-0.700178\pi\) | ||||
−0.588238 | + | 0.808688i | \(0.700178\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.56529 | + | 10.8316i | −0.346287 | + | 0.392129i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 67.3052 | − | 4.73127i | 2.43343 | − | 0.171060i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.5844 | −0.526611 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.4992 | − | 19.9172i | 0.414671 | − | 0.718232i | −0.580723 | − | 0.814101i | \(-0.697230\pi\) |
0.995394 | + | 0.0958699i | \(0.0305633\pi\) | |||||||
\(770\) | 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 | ||||||||
\(777\) | 5.81830 | − | 35.0053i | 0.208730 | − | 1.25581i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.71828 | 0.276536 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.3031 | 1.37059 | ||||||||
\(782\) | 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 | ||||||||
\(787\) | 4.55650 | + | 7.89209i | 0.162422 | + | 0.281323i | 0.935737 | − | 0.352699i | \(-0.114736\pi\) |
−0.773315 | + | 0.634022i | \(0.781403\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.9675 | + | 7.42337i | 0.497257 | + | 0.264279i | ||||
\(790\) | 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 | ||||||||
\(795\) | −72.4715 | + | 45.3037i | −2.57030 | + | 1.60676i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.5330 | + | 47.6886i | −0.975270 | + | 1.68922i | −0.296228 | + | 0.955117i | \(0.595729\pi\) |
−0.679042 | + | 0.734099i | \(0.737605\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.61988 | + | 11.4660i | 0.234195 | + | 0.405637i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.30033 | − | 6.77299i | 0.116611 | − | 0.239312i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.8369 | − | 29.1624i | 0.594163 | − | 1.02912i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 41.1987 | + | 8.34266i | 1.45206 | + | 0.294040i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −36.5373 | + | 22.8404i | −1.28617 | + | 0.804019i | ||||
\(808\) | 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 | ||||||||
\(815\) | 14.1079 | + | 24.4356i | 0.494179 | + | 0.855943i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.6550 | − | 44.4358i | 0.897555 | − | 1.55461i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.26301 | + | 1.20740i | 0.323676 | + | 0.0421901i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.8054 | + | 34.3039i | −0.691212 | + | 1.19721i | 0.280229 | + | 0.959933i | \(0.409590\pi\) |
−0.971441 | + | 0.237282i | \(0.923744\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.1735 | + | 28.0134i | 0.563773 | + | 0.976484i | 0.997163 | + | 0.0752773i | \(0.0239842\pi\) |
−0.433389 | + | 0.901207i | \(0.642682\pi\) | |||||||
\(824\) | 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 | ||||||||
\(831\) | 47.3943 | + | 25.1888i | 1.64409 | + | 0.873790i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33.0467 | + | 24.9976i | −1.14500 | + | 0.866116i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.5200 | − | 33.8096i | 0.675516 | − | 1.17003i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −26.2329 | + | 19.0814i | −0.906743 | + | 0.659551i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.35256 | + | 4.07475i | 0.0812193 | + | 0.140676i | 0.903774 | − | 0.428010i | \(-0.140785\pi\) |
−0.822555 | + | 0.568686i | \(0.807452\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.58195 | − | 9.66822i | 0.192481 | − | 0.333387i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.900435 | − | 25.6501i | −0.0310126 | − | 0.883436i | ||||
\(844\) | 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 | ||||||||
\(849\) | −1.56429 | − | 44.5609i | −0.0536863 | − | 1.52933i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.1904 | + | 28.0426i | 0.555001 | + | 0.961289i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.87889 | + | 3.25434i | 0.0643321 | + | 0.111426i | 0.896398 | − | 0.443251i | \(-0.146175\pi\) |
−0.832065 | + | 0.554678i | \(0.812842\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 25.5312 | − | 52.3956i | 0.873149 | − | 1.79189i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −53.1561 | −1.81578 | −0.907888 | − | 0.419212i | \(-0.862306\pi\) | ||||
−0.907888 | + | 0.419212i | \(0.862306\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −52.9776 | −1.80757 | −0.903786 | − | 0.427985i | \(-0.859224\pi\) | ||||
−0.903786 | + | 0.427985i | \(0.859224\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.47617 | − | 2.42947i | 0.220707 | − | 0.0827960i | ||||
\(862\) | 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 | ||||||||
\(871\) | −1.91409 | −0.0648566 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.22239 | + | 12.7697i | −0.210596 | + | 0.432189i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −43.6994 | − | 8.84904i | −1.47731 | − | 0.299152i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.67730 | 0.124174 | 0.0620868 | − | 0.998071i | \(-0.480224\pi\) | ||||
0.0620868 | + | 0.998071i | \(0.480224\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.7089 | − | 15.4461i | 0.833409 | − | 0.520985i | ||||
\(880\) | 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 | ||||||||
\(885\) | 2.86101 | + | 81.4997i | 0.0961718 | + | 2.73958i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.50247 | −0.285485 | −0.142743 | − | 0.989760i | \(-0.545592\pi\) | ||||
−0.142743 | + | 0.989760i | \(0.545592\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.12779 | + | 0.228376i | 0.0378250 | + | 0.00765949i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.1915 | + | 37.6799i | −0.508935 | + | 1.26233i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.4371 | 0.382730 | ||||||||
\(894\) | 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 | ||||||||
\(903\) | 7.53939 | − | 45.3601i | 0.250895 | − | 1.50949i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.28736 | 0.175758 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.19089 | −0.105952 | −0.0529758 | − | 0.998596i | \(-0.516871\pi\) | ||||
−0.0529758 | + | 0.998596i | \(0.516871\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.1711 | − | 28.3998i | −0.635865 | − | 0.941963i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.63889 | + | 13.2309i | 0.253088 | + | 0.438361i | 0.964374 | − | 0.264541i | \(-0.0852206\pi\) |
−0.711287 | + | 0.702902i | \(0.751887\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.38857 | − | 2.40507i | −0.0459550 | − | 0.0795963i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.13778 | − | 5.08712i | 0.269027 | − | 0.168175i | ||||
\(916\) | 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 | ||||||||
\(921\) | −43.2794 | − | 23.0019i | −1.42611 | − | 0.757938i | ||||
\(922\) | 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 | ||||||||
\(927\) | −10.7005 | − | 15.8515i | −0.351449 | − | 0.520633i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.9890 | + | 41.5502i | −0.787055 | + | 1.36322i | 0.140709 | + | 0.990051i | \(0.455062\pi\) |
−0.927764 | + | 0.373168i | \(0.878271\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.42739 | + | 35.5198i | 0.145102 | + | 1.16411i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.20738 | − | 34.3939i | −0.0395279 | − | 1.12601i | ||||
\(934\) | 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 | ||||||||
\(941\) | 4.97793 | + | 8.62203i | 0.162276 | + | 0.281070i | 0.935685 | − | 0.352838i | \(-0.114783\pi\) |
−0.773409 | + | 0.633908i | \(0.781450\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.15585 | + | 5.46609i | −0.102769 | + | 0.178000i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.93003 | − | 51.9999i | 0.160374 | − | 1.69156i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.6107 | − | 18.3782i | 0.344800 | − | 0.597212i | −0.640517 | − | 0.767944i | \(-0.721280\pi\) |
0.985317 | + | 0.170732i | \(0.0546133\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.38965 | − | 7.60310i | −0.142494 | − | 0.246807i | ||||
\(950\) | 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 | ||||||||
\(957\) | 1.15846 | + | 33.0002i | 0.0374476 | + | 1.06674i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.3057 | + | 3.09937i | 0.494246 | + | 0.100084i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.98645 | + | 6.90473i | −0.128595 | + | 0.222733i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.94362 | + | 6.04094i | −0.0948567 | + | 0.194666i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.49866 | + | 6.05986i | 0.112626 | + | 0.195074i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.9559 | − | 27.6365i | 0.513108 | − | 0.888729i | −0.486777 | − | 0.873526i | \(-0.661827\pi\) |
0.999884 | − | 0.0152023i | \(-0.00483924\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −46.2957 | − | 24.6050i | −1.48723 | − | 0.790426i | ||||
\(970\) | 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 | ||||||||
\(975\) | 16.3092 | − | 10.1953i | 0.522314 | − | 0.326511i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.29227 | − | 7.43444i | −0.137322 | − | 0.237849i | 0.789160 | − | 0.614188i | \(-0.210516\pi\) |
−0.926482 | + | 0.376339i | \(0.877183\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | −22.5009 | −0.717667 | −0.358834 | − | 0.933402i | \(-0.616825\pi\) | ||||
−0.358834 | + | 0.933402i | \(0.616825\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −83.2821 | −2.65359 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.59656 | − | 3.60005i | 0.305462 | − | 0.114591i | ||||
\(988\) | 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 | ||||||||
\(997\) | 36.7909 | 1.16518 | 0.582590 | − | 0.812766i | \(-0.302039\pi\) | ||||
0.582590 | + | 0.812766i | \(0.302039\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 32.5393 | − | 23.6686i | 1.02950 | − | 0.748840i |
(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.t.c.193.10 | yes | 22 | |
3.2 | odd | 2 | 1512.2.t.c.361.10 | 22 | |||
4.3 | odd | 2 | 1008.2.t.l.193.2 | 22 | |||
7.2 | even | 3 | 504.2.q.c.121.3 | yes | 22 | ||
9.2 | odd | 6 | 1512.2.q.d.1369.2 | 22 | |||
9.7 | even | 3 | 504.2.q.c.25.3 | ✓ | 22 | ||
12.11 | even | 2 | 3024.2.t.k.1873.10 | 22 | |||
21.2 | odd | 6 | 1512.2.q.d.793.2 | 22 | |||
28.23 | odd | 6 | 1008.2.q.l.625.9 | 22 | |||
36.7 | odd | 6 | 1008.2.q.l.529.9 | 22 | |||
36.11 | even | 6 | 3024.2.q.l.2881.2 | 22 | |||
63.2 | odd | 6 | 1512.2.t.c.289.10 | 22 | |||
63.16 | even | 3 | inner | 504.2.t.c.457.10 | yes | 22 | |
84.23 | even | 6 | 3024.2.q.l.2305.2 | 22 | |||
252.79 | odd | 6 | 1008.2.t.l.961.2 | 22 | |||
252.191 | even | 6 | 3024.2.t.k.289.10 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.3 | ✓ | 22 | 9.7 | even | 3 | ||
504.2.q.c.121.3 | yes | 22 | 7.2 | even | 3 | ||
504.2.t.c.193.10 | yes | 22 | 1.1 | even | 1 | trivial | |
504.2.t.c.457.10 | yes | 22 | 63.16 | even | 3 | inner | |
1008.2.q.l.529.9 | 22 | 36.7 | odd | 6 | |||
1008.2.q.l.625.9 | 22 | 28.23 | odd | 6 | |||
1008.2.t.l.193.2 | 22 | 4.3 | odd | 2 | |||
1008.2.t.l.961.2 | 22 | 252.79 | odd | 6 | |||
1512.2.q.d.793.2 | 22 | 21.2 | odd | 6 | |||
1512.2.q.d.1369.2 | 22 | 9.2 | odd | 6 | |||
1512.2.t.c.289.10 | 22 | 63.2 | odd | 6 | |||
1512.2.t.c.361.10 | 22 | 3.2 | odd | 2 | |||
3024.2.q.l.2305.2 | 22 | 84.23 | even | 6 | |||
3024.2.q.l.2881.2 | 22 | 36.11 | even | 6 | |||
3024.2.t.k.289.10 | 22 | 252.191 | even | 6 | |||
3024.2.t.k.1873.10 | 22 | 12.11 | even | 2 |