Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(49,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.bi (of order \(6\), 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: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Character | \(\chi\) | \(=\) | 360.49 |
Dual form | 360.2.bi.b.169.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | −1.27766 | + | 1.16944i | −0.737655 | + | 0.675177i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.307984 | + | 2.21476i | 0.137734 | + | 0.990469i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.28422 | + | 1.89614i | −1.24132 | + | 0.716675i | −0.969362 | − | 0.245635i | \(-0.921003\pi\) |
−0.271955 | + | 0.962310i | \(0.587670\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.264813 | − | 2.98829i | 0.0882709 | − | 0.996097i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.86561 | − | 3.23134i | −0.562504 | − | 0.974285i | −0.997277 | − | 0.0737451i | \(-0.976505\pi\) |
0.434773 | − | 0.900540i | \(-0.356828\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.09954 | − | 0.634820i | −0.304958 | − | 0.176067i | 0.339710 | − | 0.940530i | \(-0.389671\pi\) |
−0.644668 | + | 0.764463i | \(0.723004\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.98353 | − | 2.46953i | −0.770343 | − | 0.637630i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.973091i | 0.236009i | 0.993013 | + | 0.118005i | \(0.0376498\pi\) | ||||
−0.993013 | + | 0.118005i | \(0.962350\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.74455 | 0.629642 | 0.314821 | − | 0.949151i | \(-0.398055\pi\) | ||||
0.314821 | + | 0.949151i | \(0.398055\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.97867 | − | 6.26332i | 0.431782 | − | 1.36677i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.83699 | − | 3.36999i | −1.21710 | − | 0.702691i | −0.252800 | − | 0.967518i | \(-0.581352\pi\) |
−0.964296 | + | 0.264828i | \(0.914685\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.81029 | + | 1.36422i | −0.962058 | + | 0.272843i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.15629 | + | 4.12769i | 0.607428 | + | 0.794374i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.99547 | − | 3.45625i | −0.370549 | − | 0.641809i | 0.619101 | − | 0.785311i | \(-0.287497\pi\) |
−0.989650 | + | 0.143502i | \(0.954164\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.36108 | + | 9.28566i | −0.962878 | + | 1.66775i | −0.247668 | + | 0.968845i | \(0.579664\pi\) |
−0.715211 | + | 0.698909i | \(0.753669\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.16247 | + | 1.94681i | 1.07275 | + | 0.338897i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.21098 | − | 6.68976i | −0.880816 | − | 1.13078i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.59511i | 1.24863i | 0.781173 | + | 0.624314i | \(0.214621\pi\) | ||||
−0.781173 | + | 0.624314i | \(0.785379\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.14722 | − | 0.474767i | 0.343830 | − | 0.0760235i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.92955 | + | 5.07413i | −0.457519 | + | 0.792446i | −0.998829 | − | 0.0483769i | \(-0.984595\pi\) |
0.541310 | + | 0.840823i | \(0.317928\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.95478 | − | 2.86065i | 0.755597 | − | 0.436244i | −0.0721154 | − | 0.997396i | \(-0.522975\pi\) |
0.827713 | + | 0.561152i | \(0.189642\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.69989 | − | 0.333848i | 0.998761 | − | 0.0497672i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.18344 | + | 2.41531i | −0.610217 | + | 0.352309i | −0.773051 | − | 0.634344i | \(-0.781270\pi\) |
0.162833 | + | 0.986654i | \(0.447937\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.69072 | − | 6.39251i | 0.527245 | − | 0.913215i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.13797 | − | 1.24328i | −0.159348 | − | 0.174094i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 10.1260i | − | 1.39091i | −0.718570 | − | 0.695455i | \(-0.755203\pi\) | ||
0.718570 | − | 0.695455i | \(-0.244797\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.58205 | − | 5.12708i | 0.887523 | − | 0.691335i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.50659 | + | 3.20959i | −0.464459 | + | 0.425120i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.98987 | + | 6.91066i | −0.519437 | + | 0.899691i | 0.480308 | + | 0.877100i | \(0.340525\pi\) |
−0.999745 | + | 0.0225909i | \(0.992808\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.29821 | + | 7.44471i | 0.550329 | + | 0.953198i | 0.998251 | + | 0.0591248i | \(0.0188310\pi\) |
−0.447922 | + | 0.894073i | \(0.647836\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.79652 | + | 10.3163i | 0.604305 | + | 1.29973i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.06733 | − | 2.63073i | 0.132386 | − | 0.326302i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.993211 | + | 0.573431i | 0.121340 | + | 0.0700557i | 0.559442 | − | 0.828870i | \(-0.311016\pi\) |
−0.438102 | + | 0.898926i | \(0.644349\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.3987 | − | 2.52033i | 1.37224 | − | 0.303412i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.20350 | 1.09225 | 0.546127 | − | 0.837702i | \(-0.316101\pi\) | ||||
0.546127 | + | 0.837702i | \(0.316101\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.990931i | − | 0.115980i | −0.998317 | − | 0.0579899i | \(-0.981531\pi\) | ||
0.998317 | − | 0.0579899i | \(-0.0184691\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.55053 | − | 7.36836i | 0.525450 | − | 0.850825i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.2542 | + | 7.07494i | 1.39649 | + | 0.806264i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.83472 | + | 13.5701i | 0.881474 | + | 1.52676i | 0.849702 | + | 0.527263i | \(0.176782\pi\) |
0.0317725 | + | 0.999495i | \(0.489885\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.85975 | − | 1.58267i | −0.984417 | − | 0.175853i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.08329 | − | 0.625439i | 0.118907 | − | 0.0686509i | −0.439367 | − | 0.898308i | \(-0.644797\pi\) |
0.558274 | + | 0.829657i | \(0.311464\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.15516 | + | 0.299696i | −0.233760 | + | 0.0325066i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.59140 | + | 2.08232i | 0.706672 | + | 0.223248i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.97031 | −0.950851 | −0.475425 | − | 0.879756i | \(-0.657706\pi\) | ||||
−0.475425 | + | 0.879756i | \(0.657706\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.81484 | 0.504732 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.00942 | − | 18.1334i | −0.415758 | − | 1.88034i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.845275 | + | 6.07851i | 0.0867234 | + | 0.623641i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.56207 | + | 3.21126i | −0.564743 | + | 0.326054i | −0.755047 | − | 0.655671i | \(-0.772386\pi\) |
0.190304 | + | 0.981725i | \(0.439053\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.1502 | + | 4.71929i | −1.02013 | + | 0.474307i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.57733 | + | 7.92817i | 0.455462 | + | 0.788883i | 0.998715 | − | 0.0506864i | \(-0.0161409\pi\) |
−0.543253 | + | 0.839569i | \(0.682808\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.09661 | − | 2.36518i | −0.403651 | − | 0.233048i | 0.284407 | − | 0.958704i | \(-0.408203\pi\) |
−0.688058 | + | 0.725656i | \(0.741537\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14.4811 | + | 2.45328i | 1.41321 | + | 0.239415i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 9.92233i | − | 0.959228i | −0.877480 | − | 0.479614i | \(-0.840777\pi\) | ||
0.877480 | − | 0.479614i | \(-0.159223\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.8233 | −1.61138 | −0.805688 | − | 0.592340i | \(-0.798204\pi\) | ||||
−0.805688 | + | 0.592340i | \(0.798204\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.88204 | − | 9.70394i | −0.843045 | − | 0.921057i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.1494 | + | 6.43709i | 1.04884 | + | 0.605550i | 0.922326 | − | 0.386414i | \(-0.126286\pi\) |
0.126519 | + | 0.991964i | \(0.459620\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.66600 | − | 13.9654i | 0.528358 | − | 1.30228i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.18820 | + | 3.11764i | −0.202299 | + | 0.288226i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.84512 | − | 3.19584i | −0.169142 | − | 0.292962i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.46103 | + | 2.53058i | −0.132821 | + | 0.230052i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.19094 | − | 9.90893i | −0.197550 | − | 0.893458i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.50290 | − | 10.2335i | −0.402752 | − | 0.915309i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.91379i | 0.702235i | 0.936331 | + | 0.351118i | \(0.114198\pi\) | ||||
−0.936331 | + | 0.351118i | \(0.885802\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.98515 | + | 9.44925i | −0.262828 | + | 0.831960i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7079 | − | 18.5466i | 0.935554 | − | 1.62043i | 0.161911 | − | 0.986805i | \(-0.448234\pi\) |
0.773643 | − | 0.633622i | \(-0.218432\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.01369 | + | 5.20405i | −0.781586 | + | 0.451249i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.16974 | + | 8.26168i | −0.703140 | + | 0.711052i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.2066 | + | 8.20220i | −1.21375 | + | 0.700761i | −0.963575 | − | 0.267439i | \(-0.913823\pi\) |
−0.250179 | + | 0.968200i | \(0.580489\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.66492 | − | 4.61578i | 0.226036 | − | 0.391505i | −0.730594 | − | 0.682812i | \(-0.760757\pi\) |
0.956630 | + | 0.291307i | \(0.0940901\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.52044 | − | 7.97823i | 0.212259 | − | 0.671888i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.73732i | 0.396154i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.04018 | − | 5.48394i | 0.584655 | − | 0.455416i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.76020 | + | 12.4835i | 0.227657 | + | 1.02962i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.81487 | + | 6.60754i | −0.312526 | + | 0.541311i | −0.978909 | − | 0.204299i | \(-0.934509\pi\) |
0.666382 | + | 0.745610i | \(0.267842\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.99814 | − | 5.19292i | −0.243985 | − | 0.422594i | 0.717861 | − | 0.696187i | \(-0.245121\pi\) |
−0.961846 | + | 0.273592i | \(0.911788\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.90788 | + | 0.257687i | 0.235088 | + | 0.0208328i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.2166 | − | 9.01365i | −1.78448 | − | 0.723994i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.2887 | + | 5.94016i | 0.821125 | + | 0.474077i | 0.850804 | − | 0.525483i | \(-0.176115\pi\) |
−0.0296795 | + | 0.999559i | \(0.509449\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.8417 | + | 12.9375i | 0.939111 | + | 1.02601i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 25.5599 | 2.01440 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.45806i | 0.662487i | 0.943545 | + | 0.331243i | \(0.107468\pi\) | ||||
−0.943545 | + | 0.331243i | \(0.892532\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.41378 | + | 14.2480i | −0.187912 | + | 1.10920i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.48250 | − | 2.01062i | −0.269484 | − | 0.155587i | 0.359169 | − | 0.933272i | \(-0.383060\pi\) |
−0.628653 | + | 0.777686i | \(0.716393\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.69401 | − | 9.86231i | −0.438001 | − | 0.758639i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.726791 | − | 8.20150i | 0.0555791 | − | 0.627185i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.15204 | + | 2.39718i | −0.315674 | + | 0.182254i | −0.649463 | − | 0.760393i | \(-0.725006\pi\) |
0.333789 | + | 0.942648i | \(0.391673\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.2113 | − | 13.6014i | 0.998679 | − | 1.02817i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.98393 | − | 13.4954i | −0.224286 | − | 1.01437i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.2763 | 0.842828 | 0.421414 | − | 0.906868i | \(-0.361534\pi\) | ||||
0.421414 | + | 0.906868i | \(0.361534\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.2372 | −1.57855 | −0.789275 | − | 0.614040i | \(-0.789543\pi\) | ||||
−0.789275 | + | 0.614040i | \(0.789543\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.1978 | − | 4.48528i | −1.04953 | − | 0.331562i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.8213 | + | 2.33917i | −1.23673 | + | 0.171979i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.14439 | − | 1.81541i | 0.229940 | − | 0.132756i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −18.1926 | − | 7.57145i | −1.32332 | − | 0.550742i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.33607 | + | 4.04618i | 0.169032 | + | 0.292772i | 0.938080 | − | 0.346420i | \(-0.112603\pi\) |
−0.769048 | + | 0.639191i | \(0.779269\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.20871 | − | 5.31665i | −0.662857 | − | 0.382701i | 0.130508 | − | 0.991447i | \(-0.458339\pi\) |
−0.793365 | + | 0.608746i | \(0.791673\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.71280 | + | 4.60935i | 0.122656 | + | 0.330082i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.4334i | 1.38457i | 0.721622 | + | 0.692287i | \(0.243397\pi\) | ||||
−0.721622 | + | 0.692287i | \(0.756603\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.778360 | 0.0551765 | 0.0275882 | − | 0.999619i | \(-0.491217\pi\) | ||||
0.0275882 | + | 0.999619i | \(0.491217\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.93958 | + | 0.428855i | −0.136807 | + | 0.0302491i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.1071 | + | 7.56738i | 0.919937 | + | 0.531126i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.1402 | − | 4.92549i | −0.847909 | − | 0.344011i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.6162 | + | 16.5502i | −0.807382 | + | 1.15032i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.12027 | − | 8.86856i | −0.354176 | − | 0.613451i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.6242 | + | 18.4017i | −0.731403 | + | 1.26683i | 0.224881 | + | 0.974386i | \(0.427801\pi\) |
−0.956284 | + | 0.292441i | \(0.905533\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.7589 | + | 10.7630i | −0.805708 | + | 0.737466i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.86162 | + | 10.0926i | 0.536158 | + | 0.688310i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 40.6615i | − | 2.76028i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.15884 | + | 1.26607i | 0.0783069 | + | 0.0855531i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.617738 | − | 1.06995i | 0.0415536 | − | 0.0719729i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0876 | − | 13.9070i | 1.61303 | − | 0.931281i | 0.624363 | − | 0.781135i | \(-0.285359\pi\) |
0.988664 | − | 0.150147i | \(-0.0479746\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.80285 | + | 14.7358i | 0.186857 | + | 0.982387i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.48981 | + | 2.59220i | −0.297999 | + | 0.172050i | −0.641544 | − | 0.767086i | \(-0.721706\pi\) |
0.343544 | + | 0.939136i | \(0.388372\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.5022 | − | 21.6545i | 0.826170 | − | 1.43097i | −0.0748511 | − | 0.997195i | \(-0.523848\pi\) |
0.901022 | − | 0.433774i | \(-0.142819\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −23.9303 | + | 5.29118i | −1.57450 | + | 0.348134i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.61032i | 0.105496i | 0.998608 | + | 0.0527479i | \(0.0167980\pi\) | ||||
−0.998608 | + | 0.0527479i | \(0.983202\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.63775 | − | 8.52142i | −0.432999 | − | 0.555876i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −25.8795 | − | 8.17572i | −1.68106 | − | 0.531070i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.27688 | + | 2.21162i | −0.0825944 | + | 0.143058i | −0.904364 | − | 0.426763i | \(-0.859654\pi\) |
0.821769 | + | 0.569821i | \(0.192987\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.11330 | + | 14.0527i | 0.522624 | + | 0.905211i | 0.999653 | + | 0.0263238i | \(0.00838010\pi\) |
−0.477030 | + | 0.878887i | \(0.658287\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.1706 | − | 8.33884i | 0.844892 | − | 0.534937i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.2945 | + | 6.20525i | 0.977131 | + | 0.396439i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.01774 | − | 1.74229i | −0.192014 | − | 0.110860i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.652661 | + | 2.06594i | −0.0413607 | + | 0.130924i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.7288 | 0.992791 | 0.496395 | − | 0.868096i | \(-0.334657\pi\) | ||||
0.496395 | + | 0.868096i | \(0.334657\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.1484i | 1.58106i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.40308 | − | 2.90324i | 0.150487 | − | 0.181808i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.09479 | + | 0.632077i | 0.0682911 | + | 0.0394279i | 0.533757 | − | 0.845638i | \(-0.320780\pi\) |
−0.465466 | + | 0.885066i | \(0.654113\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.4014 | − | 24.9440i | −0.894860 | − | 1.54994i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.8567 | + | 5.04777i | −0.672012 | + | 0.312449i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.32659 | + | 3.65266i | −0.390114 | + | 0.225233i | −0.682210 | − | 0.731157i | \(-0.738981\pi\) |
0.292095 | + | 0.956389i | \(0.405648\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.4266 | − | 3.11863i | 1.37765 | − | 0.191576i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.4610 | − | 10.4903i | 0.701400 | − | 0.641993i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.85871 | 0.601096 | 0.300548 | − | 0.953767i | \(-0.402830\pi\) | ||||
0.300548 | + | 0.953767i | \(0.402830\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.99866 | −0.485884 | −0.242942 | − | 0.970041i | \(-0.578112\pi\) | ||||
−0.242942 | + | 0.970041i | \(0.578112\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.15171 | + | 5.63067i | −0.372318 | + | 0.340784i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.3824 | + | 12.9986i | 0.806989 | + | 0.783844i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.3068 | − | 8.26005i | 0.859614 | − | 0.496298i | −0.00426933 | − | 0.999991i | \(-0.501359\pi\) |
0.863883 | + | 0.503693i | \(0.168026\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 26.3286 | + | 18.4794i | 1.57625 | + | 1.10633i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.6622 | − | 20.1996i | −0.695711 | − | 1.20501i | −0.969940 | − | 0.243342i | \(-0.921756\pi\) |
0.274230 | − | 0.961664i | \(-0.411577\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.4247 | − | 10.6375i | −1.09524 | − | 0.632335i | −0.160271 | − | 0.987073i | \(-0.551237\pi\) |
−0.934966 | + | 0.354738i | \(0.884570\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.18843 | − | 6.77774i | −0.485041 | − | 0.401479i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 22.2194i | − | 1.31157i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.0531 | 0.944300 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.35103 | − | 10.6074i | 0.196441 | − | 0.621817i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.15049 | + | 1.24158i | 0.125633 | + | 0.0725342i | 0.561499 | − | 0.827477i | \(-0.310225\pi\) |
−0.435867 | + | 0.900011i | \(0.643558\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.5342 | − | 6.70822i | −0.962660 | − | 0.390568i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.44954 | − | 17.8997i | 0.432266 | − | 1.03865i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.27867 | + | 7.41088i | 0.247442 | + | 0.428582i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.8484 | + | 18.7900i | −0.625291 | + | 1.08303i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.1198 | − | 4.77656i | −0.868609 | − | 0.274406i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.1644 | + | 11.8123i | −0.868314 | + | 0.676372i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.7398i | 0.612955i | 0.951878 | + | 0.306478i | \(0.0991504\pi\) | ||||
−0.951878 | + | 0.306478i | \(0.900850\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | − | 1.76886i | 0.455104 | − | 0.100627i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.41774 | + | 4.18764i | −0.137097 | + | 0.237460i | −0.926397 | − | 0.376549i | \(-0.877111\pi\) |
0.789299 | + | 0.614009i | \(0.210444\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.2023 | − | 9.35443i | 0.915811 | − | 0.528744i | 0.0335146 | − | 0.999438i | \(-0.489330\pi\) |
0.882296 | + | 0.470695i | \(0.155997\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −21.3709 | + | 13.8004i | −1.20411 | + | 0.777563i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.2517 | − | 15.1564i | 1.47444 | − | 0.851270i | 0.474858 | − | 0.880062i | \(-0.342499\pi\) |
0.999585 | + | 0.0287919i | \(0.00916602\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.44554 | + | 12.8960i | −0.416870 | + | 0.722040i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.6036 | + | 12.6773i | 0.647649 | + | 0.707580i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.67070i | 0.148601i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.15514 | + | 1.55366i | 0.341426 | + | 0.0861815i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.4944 | − | 19.6738i | 1.18864 | − | 1.08796i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.15955 | − | 15.8648i | 0.504982 | − | 0.874655i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.17353 | + | 7.22877i | 0.229398 | + | 0.397329i | 0.957630 | − | 0.288002i | \(-0.0929909\pi\) |
−0.728232 | + | 0.685331i | \(0.759658\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 22.6964 | + | 2.01128i | 1.24375 | + | 0.110218i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.964117 | + | 2.37633i | −0.0526753 | + | 0.129833i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.8323 | + | 6.83137i | 0.644546 | + | 0.372129i | 0.786363 | − | 0.617764i | \(-0.211961\pi\) |
−0.141818 | + | 0.989893i | \(0.545295\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.7729 | + | 4.81414i | −1.18254 | + | 0.261468i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 40.0068 | 2.16649 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.44650i | 0.0781035i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.09252 | + | 24.4691i | 0.489525 | + | 1.31737i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.31113 | + | 0.756981i | 0.0703851 | + | 0.0406368i | 0.534780 | − | 0.844992i | \(-0.320395\pi\) |
−0.464394 | + | 0.885628i | \(0.653728\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.48031 | + | 2.56397i | 0.0792392 | + | 0.137246i | 0.902922 | − | 0.429805i | \(-0.141418\pi\) |
−0.823683 | + | 0.567051i | \(0.808084\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.850129 | − | 6.54224i | −0.0453765 | − | 0.349199i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.7247 | + | 11.9654i | −1.10307 | + | 0.636855i | −0.937025 | − | 0.349263i | \(-0.886432\pi\) |
−0.166041 | + | 0.986119i | \(0.553098\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.83453 | + | 20.3835i | 0.150441 | + | 1.08184i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.09478 | + | 1.92543i | 0.322570 | + | 0.101904i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.76880 | −0.462800 | −0.231400 | − | 0.972859i | \(-0.574331\pi\) | ||||
−0.231400 | + | 0.972859i | \(0.574331\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.4675 | −0.603550 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.09267 | − | 4.94180i | −0.0573502 | − | 0.259377i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.19467 | − | 0.305190i | 0.114874 | − | 0.0159744i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.9301 | + | 13.2387i | −1.19694 | + | 0.691055i | −0.959872 | − | 0.280438i | \(-0.909520\pi\) |
−0.237070 | + | 0.971493i | \(0.576187\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.3872 | + | 10.0980i | 0.748967 | + | 0.525683i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.2003 | + | 33.2559i | 0.996830 | + | 1.72656i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.0449 | + | 9.26355i | 0.830776 | + | 0.479648i | 0.854118 | − | 0.520079i | \(-0.174098\pi\) |
−0.0233426 | + | 0.999728i | \(0.507431\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.7206 | + | 7.80898i | 0.915088 | + | 0.403254i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.06705i | 0.260966i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.5529 | 1.20983 | 0.604917 | − | 0.796289i | \(-0.293206\pi\) | ||||
0.604917 | + | 0.796289i | \(0.293206\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.25472 | − | 10.1111i | −0.474133 | − | 0.518008i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.456831 | + | 0.263751i | 0.0233430 | + | 0.0134771i | 0.511626 | − | 0.859208i | \(-0.329043\pi\) |
−0.488283 | + | 0.872685i | \(0.662377\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.8952 | + | 29.3189i | −0.606235 | + | 1.49423i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.23635 | − | 15.5639i | −0.367844 | − | 0.791156i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.21656 | + | 5.57125i | 0.163086 | + | 0.282473i | 0.935974 | − | 0.352069i | \(-0.114522\pi\) |
−0.772888 | + | 0.634543i | \(0.781188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.27931 | − | 5.67992i | 0.165842 | − | 0.287246i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.00818 | + | 36.2185i | 0.403959 | + | 1.82698i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −27.6416 | + | 21.5314i | −1.39080 | + | 1.08336i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 17.9480i | − | 0.900782i | −0.892831 | − | 0.450391i | \(-0.851285\pi\) | ||
0.892831 | − | 0.450391i | \(-0.148715\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.43056 | − | 17.1900i | 0.271868 | − | 0.860575i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.3216 | − | 21.3416i | 0.615310 | − | 1.06575i | −0.375020 | − | 0.927017i | \(-0.622364\pi\) |
0.990330 | − | 0.138732i | \(-0.0443026\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.7894 | − | 6.80664i | 0.587274 | − | 0.339063i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.776581 | − | 20.1096i | 0.0385886 | − | 0.999255i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.5424 | − | 14.1695i | 1.21652 | − | 0.702358i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.99246 | + | 8.64719i | −0.246861 | + | 0.427576i | −0.962653 | − | 0.270737i | \(-0.912732\pi\) |
0.715792 | + | 0.698313i | \(0.246066\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.55919 | − | 27.0934i | 0.422194 | − | 1.33642i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 30.2614i | − | 1.48907i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.71883 | + | 2.20660i | 0.0843741 | + | 0.108318i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.99303 | + | 9.01385i | 0.0975991 | + | 0.441410i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.35550 | + | 9.27599i | −0.261633 | + | 0.453162i | −0.966676 | − | 0.256003i | \(-0.917594\pi\) |
0.705043 | + | 0.709165i | \(0.250928\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.204268 | − | 0.353803i | −0.00995543 | − | 0.0172433i | 0.861005 | − | 0.508597i | \(-0.169836\pi\) |
−0.870960 | + | 0.491354i | \(0.836502\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.10982 | + | 13.1409i | 0.297070 | + | 0.638934i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.32751 | − | 4.68085i | −0.0643936 | − | 0.227055i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.2325 | − | 16.3000i | −1.36627 | − | 0.788814i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.54001 | − | 6.05266i | −0.267474 | − | 0.292225i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.2522 | −1.50536 | −0.752682 | − | 0.658384i | \(-0.771240\pi\) | ||||
−0.752682 | + | 0.658384i | \(0.771240\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 17.0844i | − | 0.821023i | −0.911855 | − | 0.410512i | \(-0.865350\pi\) | ||
0.911855 | − | 0.410512i | \(-0.134650\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.58178 | + | 15.2397i | −0.123787 | + | 0.730686i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.0199 | − | 9.24909i | −0.766335 | − | 0.442444i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.78572 | − | 8.28910i | −0.228410 | − | 0.395617i | 0.728927 | − | 0.684591i | \(-0.240019\pi\) |
−0.957337 | + | 0.288974i | \(0.906686\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.1253 | − | 12.7217i | −0.863110 | − | 0.605797i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.803150 | − | 0.463699i | 0.0381588 | − | 0.0220310i | −0.480799 | − | 0.876831i | \(-0.659653\pi\) |
0.518958 | + | 0.854800i | \(0.326320\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.76271 | − | 19.8670i | −0.130965 | − | 0.941788i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.85305 | − | 12.9034i | −0.134944 | − | 0.610312i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.0869 | −1.23112 | −0.615558 | − | 0.788092i | \(-0.711069\pi\) | ||||
−0.615558 | + | 0.788092i | \(0.711069\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.8616 | 1.02942 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.90341 | + | 3.12863i | 0.465303 | + | 0.146996i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.48289 | + | 10.6637i | 0.0695190 | + | 0.499922i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.9713 | − | 13.2625i | 1.07455 | − | 0.620392i | 0.145129 | − | 0.989413i | \(-0.453640\pi\) |
0.929421 | + | 0.369021i | \(0.120307\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.01662 | + | 3.07136i | −0.187480 | + | 0.143359i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.04128 | + | 3.53560i | 0.0950718 | + | 0.164669i | 0.909639 | − | 0.415401i | \(-0.136359\pi\) |
−0.814567 | + | 0.580070i | \(0.803025\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.74462 | + | 3.89401i | 0.313449 | + | 0.180970i | 0.648469 | − | 0.761241i | \(-0.275410\pi\) |
−0.335020 | + | 0.942211i | \(0.608743\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 38.9261 | − | 14.4647i | 1.80516 | − | 0.670783i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 30.1413i | − | 1.39477i | −0.716695 | − | 0.697387i | \(-0.754346\pi\) | ||
0.716695 | − | 0.697387i | \(-0.245654\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.34923 | −0.200829 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.0921 | + | 4.44250i | −0.925793 | + | 0.204700i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.4874 | − | 10.6737i | −0.850053 | − | 0.490778i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.2021 | + | 3.74416i | −0.605753 | + | 0.171794i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −30.2594 | − | 2.68149i | −1.38548 | − | 0.122777i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.64266 | − | 8.04133i | −0.212129 | − | 0.367418i | 0.740252 | − | 0.672330i | \(-0.234706\pi\) |
−0.952381 | + | 0.304912i | \(0.901373\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.82153 | − | 8.35113i | 0.219843 | − | 0.380779i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −32.6568 | + | 29.8908i | −1.48594 | + | 1.36008i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.82519 | − | 11.3296i | −0.400731 | − | 0.514452i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 11.7910i | − | 0.534300i | −0.963655 | − | 0.267150i | \(-0.913918\pi\) | ||
0.963655 | − | 0.267150i | \(-0.0860818\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.89121 | − | 10.8065i | −0.447296 | − | 0.488687i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.74759 | + | 9.95512i | −0.259385 | + | 0.449268i | −0.966077 | − | 0.258253i | \(-0.916853\pi\) |
0.706692 | + | 0.707521i | \(0.250187\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.36324 | − | 1.94177i | 0.151473 | − | 0.0874529i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.5782 | − | 21.0268i | −0.610294 | − | 0.945083i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −30.2263 | + | 17.4512i | −1.35583 | + | 0.782791i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.00545 | + | 12.1338i | −0.313607 | + | 0.543183i | −0.979140 | − | 0.203185i | \(-0.934871\pi\) |
0.665533 | + | 0.746368i | \(0.268204\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.80074 | − | 1.50370i | 0.303835 | − | 0.0671802i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.3416i | 0.817811i | 0.912577 | + | 0.408905i | \(0.134089\pi\) | ||||
−0.912577 | + | 0.408905i | \(0.865911\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.1492 | + | 12.5794i | −0.718631 | + | 0.559777i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.8084 | + | 5.94184i | 0.835309 | + | 0.263886i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.88475 | + | 8.46063i | −0.216513 | + | 0.375011i | −0.953739 | − | 0.300634i | \(-0.902802\pi\) |
0.737227 | + | 0.675645i | \(0.236135\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.87895 | + | 3.25443i | 0.0831197 | + | 0.143968i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.66259 | + | 11.3286i | 0.382463 | + | 0.500172i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.97661 | − | 9.80143i | 0.175230 | − | 0.431903i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.6094 | + | 9.01207i | 0.686499 | + | 0.396350i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.50152 | − | 7.91835i | 0.109804 | − | 0.347577i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.0391 | −1.35985 | −0.679923 | − | 0.733284i | \(-0.737987\pi\) | ||||
−0.679923 | + | 0.733284i | \(0.737987\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.8139i | 1.65349i | 0.562579 | + | 0.826744i | \(0.309809\pi\) | ||||
−0.562579 | + | 0.826744i | \(0.690191\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.973464 | + | 32.8277i | −0.0424854 | + | 1.43272i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.03580 | − | 5.21682i | −0.393606 | − | 0.227248i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2136 | + | 19.4226i | 0.487549 | + | 0.844459i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.5945 | + | 13.7529i | 0.850328 | + | 0.596826i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.44232 | − | 3.71948i | 0.279048 | − | 0.161108i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.9755 | − | 3.05591i | 0.950086 | − | 0.132119i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.4072 | + | 13.1869i | −0.621716 | + | 0.569058i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −27.5418 | −1.18631 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.5060 | 0.666656 | 0.333328 | − | 0.942811i | \(-0.391828\pi\) | ||||
0.333328 | + | 0.942811i | \(0.391828\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.1339 | − | 24.8357i | 1.16443 | − | 1.06580i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.18129 | − | 37.2594i | −0.221942 | − | 1.59602i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.2535 | + | 18.6215i | −1.37906 | + | 0.796200i | −0.992046 | − | 0.125875i | \(-0.959826\pi\) |
−0.387012 | + | 0.922075i | \(0.626493\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 23.3852 | − | 10.8728i | 0.998055 | − | 0.464041i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.47665 | − | 9.48584i | −0.233313 | − | 0.404110i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −51.4618 | − | 29.7115i | −2.18838 | − | 1.26346i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.7563 | − | 22.6602i | 0.796162 | − | 0.961872i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.54570i | 0.192608i | 0.995352 | + | 0.0963038i | \(0.0307020\pi\) | ||||
−0.995352 | + | 0.0963038i | \(0.969298\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.26398 | −0.307234 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.89443 | + | 5.99665i | −0.0799828 | + | 0.253179i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.0016 | − | 10.9706i | −0.800820 | − | 0.462354i | 0.0429376 | − | 0.999078i | \(-0.486328\pi\) |
−0.843758 | + | 0.536724i | \(0.819662\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.8228 | + | 26.6756i | −0.455317 | + | 1.12225i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 32.0983 | − | 11.6015i | 1.34800 | − | 0.487217i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.06022 | + | 1.83635i | 0.0444466 | + | 0.0769838i | 0.887393 | − | 0.461014i | \(-0.152514\pi\) |
−0.842946 | + | 0.537998i | \(0.819181\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.0869292 | + | 0.150566i | −0.00363788 | + | 0.00630099i | −0.867839 | − | 0.496846i | \(-0.834491\pi\) |
0.864201 | + | 0.503147i | \(0.167825\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.71646 | − | 2.43774i | −0.322360 | − | 0.101838i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 32.6750 | + | 8.24770i | 1.36264 | + | 0.343953i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.84498i | 0.326591i | 0.986577 | + | 0.163295i | \(0.0522123\pi\) | ||||
−0.986577 | + | 0.163295i | \(0.947788\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.9831 | − | 3.97619i | 0.747351 | − | 0.165245i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.37184 | + | 4.10815i | −0.0984007 | + | 0.170435i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −32.7205 | + | 18.8912i | −1.35514 | + | 0.782392i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.57874 | − | 3.88615i | −0.313342 | − | 0.160672i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.8070 | − | 7.97146i | 0.569874 | − | 0.329017i | −0.187225 | − | 0.982317i | \(-0.559949\pi\) |
0.757099 | + | 0.653300i | \(0.226616\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.7137 | + | 25.4849i | −0.606269 | + | 1.05009i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.7263 | − | 24.8293i | −0.934834 | − | 1.02134i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.7893i | 0.730517i | 0.930906 | + | 0.365259i | \(0.119019\pi\) | ||||
−0.930906 | + | 0.365259i | \(0.880981\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.50975 | − | 5.07076i | 0.266874 | − | 0.207881i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.994477 | + | 0.910247i | −0.0407012 | + | 0.0372539i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.73972 | − | 8.20944i | 0.193660 | − | 0.335429i | −0.752801 | − | 0.658249i | \(-0.771298\pi\) |
0.946460 | + | 0.322820i | \(0.104631\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.2642 | + | 28.1705i | 0.663431 | + | 1.14910i | 0.979708 | + | 0.200430i | \(0.0642338\pi\) |
−0.316277 | + | 0.948667i | \(0.602433\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.97659 | − | 2.81615i | 0.0804930 | − | 0.114683i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.05458 | − | 2.45645i | −0.246154 | − | 0.0998688i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.65327 | − | 1.53187i | −0.107693 | − | 0.0621766i | 0.445186 | − | 0.895438i | \(-0.353138\pi\) |
−0.552879 | + | 0.833261i | \(0.686471\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −25.5959 | + | 5.65946i | −1.03720 | + | 0.229333i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.13315 | 0.248121 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 48.3053i | 1.95103i | 0.219930 | + | 0.975516i | \(0.429417\pi\) | ||||
−0.219930 | + | 0.975516i | \(0.570583\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 21.2711 | − | 7.90419i | 0.857734 | − | 0.318728i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.43835 | + | 1.40778i | 0.0981641 | + | 0.0566751i | 0.548278 | − | 0.836296i | \(-0.315283\pi\) |
−0.450114 | + | 0.892971i | \(0.648617\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.63476 | − | 16.6879i | −0.387254 | − | 0.670743i | 0.604825 | − | 0.796358i | \(-0.293243\pi\) |
−0.992079 | + | 0.125615i | \(0.959910\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.51297 | − | 34.7299i | −0.181099 | − | 1.39366i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 29.4604 | − | 17.0090i | 1.18031 | − | 0.681451i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.2778 | − | 13.1246i | 0.851113 | − | 0.524983i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.9132 | + | 5.34312i | 0.675448 | + | 0.213384i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.39073 | −0.294688 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −47.6172 | −1.89561 | −0.947805 | − | 0.318851i | \(-0.896703\pi\) | ||||
−0.947805 | + | 0.318851i | \(0.896703\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.94561 | − | 35.9355i | −0.315810 | − | 1.42831i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.5271 | + | 2.43732i | −0.695542 | + | 0.0967220i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.11618 | + | 4.68588i | −0.321575 | + | 0.185661i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.43720 | − | 27.5027i | 0.0964143 | − | 1.08799i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.339505 | + | 0.588039i | 0.0134096 | + | 0.0232262i | 0.872652 | − | 0.488342i | \(-0.162398\pi\) |
−0.859243 | + | 0.511568i | \(0.829065\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.4381 | − | 11.2226i | −0.766563 | − | 0.442575i | 0.0650844 | − | 0.997880i | \(-0.479268\pi\) |
−0.831647 | + | 0.555305i | \(0.812602\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −21.8472 | − | 3.70117i | −0.860231 | − | 0.145734i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.0230i | 0.865815i | 0.901438 | + | 0.432907i | \(0.142512\pi\) | ||||
−0.901438 | + | 0.432907i | \(0.857488\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.7742 | 1.16874 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 47.5512 | + | 51.9514i | 1.86368 | + | 2.03614i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.3221 | − | 15.1971i | −1.03006 | − | 0.594708i | −0.113062 | − | 0.993588i | \(-0.536066\pi\) |
−0.917003 | + | 0.398880i | \(0.869399\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 44.3741 | + | 18.0033i | 1.73384 | + | 0.703449i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.96119 | − | 0.262411i | −0.115527 | − | 0.0102376i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.95605 | − | 10.3162i | −0.232015 | − | 0.401862i | 0.726386 | − | 0.687287i | \(-0.241198\pi\) |
−0.958401 | + | 0.285425i | \(0.907865\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.76736 | − | 6.52526i | 0.146533 | − | 0.253803i | −0.783411 | − | 0.621505i | \(-0.786522\pi\) |
0.929944 | + | 0.367701i | \(0.119855\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.461991 | + | 2.08944i | 0.0179423 | + | 0.0811472i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.3018 | − | 18.3604i | −0.554599 | − | 0.711984i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.8988i | 1.04152i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.5123 | + | 45.9374i | −0.561078 | + | 1.77604i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.0376 | − | 27.7779i | 0.619124 | − | 1.07235i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.3568 | − | 9.44361i | 0.630509 | − | 0.364025i | −0.150440 | − | 0.988619i | \(-0.548069\pi\) |
0.780949 | + | 0.624595i | \(0.214736\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20.8137 | − | 15.5495i | −0.801121 | − | 0.598502i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.1944 | − | 9.34982i | 0.622400 | − | 0.359343i | −0.155403 | − | 0.987851i | \(-0.549668\pi\) |
0.777803 | + | 0.628508i | \(0.216334\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.1780 | − | 21.0930i | 0.467350 | − | 0.809474i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.70502 | − | 8.56251i | 0.103657 | − | 0.328116i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.6717i | 1.44147i | 0.693212 | + | 0.720734i | \(0.256195\pi\) | ||||
−0.693212 | + | 0.720734i | \(0.743805\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.5413 | − | 28.9381i | −0.861258 | − | 1.10567i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.35011 | + | 42.2876i | 0.356729 | + | 1.61337i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.42818 | + | 11.1339i | −0.244894 | + | 0.424169i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.67544 | + | 6.36605i | 0.139820 | + | 0.242176i | 0.927429 | − | 0.374000i | \(-0.122014\pi\) |
−0.787608 | + | 0.616176i | \(0.788681\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 24.3870 | − | 34.7454i | 0.926387 | − | 1.31987i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.0436 | + | 4.48057i | 0.418907 | + | 0.169958i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.93759 | − | 2.85072i | −0.187025 | − | 0.107979i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.88318 | − | 2.05744i | −0.0712283 | − | 0.0778195i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.4837 | −1.18912 | −0.594561 | − | 0.804051i | \(-0.702674\pi\) | ||||
−0.594561 | + | 0.804051i | \(0.702674\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.8451i | 0.786189i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.4461 | + | 3.12499i | 0.694720 | + | 0.117694i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −30.0659 | − | 17.3586i | −1.13074 | − | 0.652836i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.9738 | + | 25.9353i | 0.562351 | + | 0.974021i | 0.997291 | + | 0.0735610i | \(0.0234363\pi\) |
−0.434940 | + | 0.900460i | \(0.643230\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 42.6262 | − | 19.8189i | 1.59861 | − | 0.743265i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 62.5851 | − | 36.1335i | 2.34383 | − | 1.35321i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.4920 | + | 1.45902i | −0.392379 | + | 0.0545641i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.954947 | − | 4.31893i | −0.0356631 | − | 0.161293i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.61533 | 0.209416 | 0.104708 | − | 0.994503i | \(-0.466609\pi\) | ||||
0.104708 | + | 0.994503i | \(0.466609\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.9389 | 0.668079 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26.7998 | − | 8.46643i | −0.996694 | − | 0.314870i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.3138 | + | 13.9033i | 0.531603 | + | 0.516356i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.38153 | + | 1.95233i | −0.125414 | + | 0.0724078i | −0.561395 | − | 0.827548i | \(-0.689735\pi\) |
0.435981 | + | 0.899956i | \(0.356402\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.07566 | + | 26.0564i | −0.262062 | + | 0.965051i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.78367 | + | 4.82146i | 0.102958 | + | 0.178328i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.31071 | + | 1.33409i | 0.0853480 | + | 0.0492757i | 0.542067 | − | 0.840336i | \(-0.317642\pi\) |
−0.456719 | + | 0.889611i | \(0.650975\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −26.7978 | + | 9.95788i | −0.988453 | + | 0.367302i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 4.27920i | − | 0.157626i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.48405 | −0.348876 | −0.174438 | − | 0.984668i | \(-0.555811\pi\) | ||||
−0.174438 | + | 0.984668i | \(0.555811\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.89315 | − | 1.30302i | 0.216490 | − | 0.0478676i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.5459 | + | 18.7904i | 1.19399 | + | 0.689353i | 0.959210 | − | 0.282694i | \(-0.0912282\pi\) |
0.234784 | + | 0.972047i | \(0.424562\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.8090 | − | 6.41399i | −0.579198 | − | 0.234990i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.58212 | − | 3.40282i | −0.0578869 | − | 0.124502i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.8142 | + | 32.5871i | 0.687454 | + | 1.19071i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.53509 | − | 9.58706i | 0.201978 | − | 0.349837i | −0.747187 | − | 0.664613i | \(-0.768596\pi\) |
0.949166 | + | 0.314777i | \(0.101930\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.0960 | + | 18.3939i | −0.732338 | + | 0.670310i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.5777 | − | 8.23948i | 0.384961 | − | 0.299865i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 37.8369i | − | 1.37521i | −0.726087 | − | 0.687603i | \(-0.758663\pi\) | ||
0.726087 | − | 0.687603i | \(-0.241337\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −29.4096 | − | 32.1310i | −1.06750 | − | 1.16628i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.4427 | + | 42.3361i | −0.886049 | + | 1.53468i | −0.0415422 | + | 0.999137i | \(0.513227\pi\) |
−0.844507 | + | 0.535545i | \(0.820106\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 55.2512 | − | 31.8993i | 2.00023 | − | 1.15483i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.324865 | + | 6.51961i | 0.0117455 | + | 0.235717i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.77405 | − | 5.06570i | 0.316812 | − | 0.182912i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.59389 | + | 7.95684i | −0.165660 | + | 0.286931i | −0.936889 | − | 0.349626i | \(-0.886309\pi\) |
0.771230 | + | 0.636557i | \(0.219642\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.13794 | + | 0.472715i | −0.0769961 | + | 0.0170244i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 0.238387i | − | 0.00857419i | −0.999991 | − | 0.00428710i | \(-0.998635\pi\) | ||
0.999991 | − | 0.00428710i | \(-0.00136463\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.1207 | − | 51.9804i | 0.471310 | − | 1.86719i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 47.5706 | + | 15.0282i | 1.70658 | + | 0.539135i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.04029 | + | 13.9262i | −0.288073 | + | 0.498958i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.1702 | − | 29.7396i | −0.614397 | − | 1.06417i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.96805 | − | 19.1456i | 0.284755 | − | 0.684207i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.98727 | + | 24.6164i | −0.356461 | + | 0.878595i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.6401 | + | 25.7730i | 1.59125 | + | 0.918707i | 0.993094 | + | 0.117326i | \(0.0374321\pi\) |
0.598154 | + | 0.801381i | \(0.295901\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.81164 | − | 12.0654i | 0.135698 | − | 0.429541i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −48.8226 | −1.73593 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 10.9144i | − | 0.387580i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −25.0064 | + | 30.2111i | −0.886886 | + | 1.07148i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.00605 | + | 4.62229i | 0.283589 | + | 0.163730i | 0.635047 | − | 0.772474i | \(-0.280981\pi\) |
−0.351458 | + | 0.936204i | \(0.614314\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.35032 | − | 4.07087i | −0.0831483 | − | 0.144017i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.37545 | + | 26.8059i | −0.0839324 | + | 0.947139i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.20203 | + | 1.84869i | −0.112997 | + | 0.0652390i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.87203 | + | 56.6090i | 0.277453 | + | 1.99520i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.5960 | + | 11.5292i | −0.443402 | + | 0.405847i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.3473 | 1.45369 | 0.726847 | − | 0.686799i | \(-0.240985\pi\) | ||||
0.726847 | + | 0.686799i | \(0.240985\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.5079 | 1.42242 | 0.711212 | − | 0.702977i | \(-0.248146\pi\) | ||||
0.711212 | + | 0.702977i | \(0.248146\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.2195 | − | 9.35396i | 0.358415 | − | 0.328058i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.7326 | + | 2.60494i | −0.656173 | + | 0.0912472i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.5986 | − | 7.85118i | 0.475756 | − | 0.274678i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.27503 | − | 14.3881i | 0.0445532 | − | 0.502762i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.0294 | − | 22.5676i | −0.454729 | − | 0.787615i | 0.543943 | − | 0.839122i | \(-0.316931\pi\) |
−0.998673 | + | 0.0515075i | \(0.983597\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.5143 | − | 15.8854i | −0.959089 | − | 0.553730i | −0.0631963 | − | 0.998001i | \(-0.520129\pi\) |
−0.895892 | + | 0.444271i | \(0.853463\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −32.2992 | − | 0.957791i | −1.12451 | − | 0.0333460i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.9806i | 1.00776i | 0.863775 | + | 0.503878i | \(0.168094\pi\) | ||||
−0.863775 | + | 0.503878i | \(0.831906\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.2492 | −0.460165 | −0.230082 | − | 0.973171i | \(-0.573900\pi\) | ||||
−0.230082 | + | 0.973171i | \(0.573900\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.61956 | + | 27.2845i | −0.299009 | + | 0.946489i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.22049 | + | 3.59140i | 0.215527 | + | 0.124435i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.38049 | − | 8.33213i | 0.116987 | − | 0.288345i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −55.2495 | + | 7.17937i | −1.90970 | + | 0.248155i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.720616 | + | 1.24814i | 0.0248784 | + | 0.0430907i | 0.878197 | − | 0.478300i | \(-0.158747\pi\) |
−0.853318 | + | 0.521391i | \(0.825413\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.53623 | − | 11.3211i | 0.225387 | − | 0.390382i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 38.5226 | + | 12.1698i | 1.32679 | + | 0.419151i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.0890 | − | 15.6483i | 0.691081 | − | 0.538317i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 11.0813i | − | 0.380757i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 35.9805 | − | 7.95555i | 1.23485 | − | 0.273034i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.5954 | − | 44.3326i | 0.877399 | − | 1.51970i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.2785 | + | 9.39837i | −0.557364 | + | 0.321794i | −0.752087 | − | 0.659064i | \(-0.770953\pi\) |
0.194723 | + | 0.980858i | \(0.437619\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.3882 | − | 0.916263i | 0.628862 | − | 0.0313355i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.0576 | + | 15.0444i | −0.890111 | + | 0.513906i | −0.873979 | − | 0.485964i | \(-0.838469\pi\) |
−0.0161324 | + | 0.999870i | \(0.505135\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.39690 | + | 9.34770i | −0.184140 | + | 0.318940i | −0.943286 | − | 0.331980i | \(-0.892283\pi\) |
0.759146 | + | 0.650920i | \(0.225617\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 25.9843 | + | 28.3887i | 0.885542 | + | 0.967486i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 28.5284i | − | 0.971117i | −0.874204 | − | 0.485559i | \(-0.838616\pi\) | ||
0.874204 | − | 0.485559i | \(-0.161384\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.58794 | − | 8.45747i | −0.223997 | − | 0.287563i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.5103 | + | 18.7732i | −0.696568 | + | 0.637570i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29.2331 | − | 50.6332i | 0.991665 | − | 1.71761i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.728051 | − | 1.26102i | −0.0246691 | − | 0.0427281i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.12328 | + | 17.4715i | 0.274931 | + | 0.591320i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 34.1926 | + | 25.0708i | 1.15592 | + | 0.847547i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.43095 | + | 1.98086i | 0.115855 | + | 0.0668889i | 0.556808 | − | 0.830641i | \(-0.312026\pi\) |
−0.440953 | + | 0.897530i | \(0.645359\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.19955 | + | 0.928551i | −0.141647 | + | 0.0313193i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.2264 | 0.614062 | 0.307031 | − | 0.951700i | \(-0.400665\pi\) | ||||
0.307031 | + | 0.951700i | \(0.400665\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 5.15578i | − | 0.173506i | −0.996230 | − | 0.0867529i | \(-0.972351\pi\) | ||
0.996230 | − | 0.0867529i | \(-0.0276491\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28.9699 | − | 10.7650i | 0.973814 | − | 0.361862i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.4111 | − | 6.01083i | −0.349570 | − | 0.201824i | 0.314926 | − | 0.949116i | \(-0.398020\pi\) |
−0.664496 | + | 0.747292i | \(0.731354\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.0057 | − | 25.9906i | −0.503274 | − | 0.871697i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.4147 | + | 31.5815i | 0.382407 | + | 1.05802i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.4817 | + | 6.62893i | −0.384219 | + | 0.221829i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.47290 | + | 24.9742i | 0.116086 | + | 0.834795i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.1333 | − | 4.46490i | −0.471896 | − | 0.149079i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 42.7914 | 1.42717 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.85350 | 0.328268 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.11324 | − | 36.6937i | −0.269992 | − | 1.22109i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.54071 | − | 47.0353i | −0.217421 | − | 1.56351i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.7789 | + | 9.10998i | −0.523931 | + | 0.302492i | −0.738542 | − | 0.674208i | \(-0.764485\pi\) |
0.214610 | + | 0.976700i | \(0.431152\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 24.9038 | − | 11.5789i | 0.826007 | − | 0.384048i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.6827 | + | 30.6273i | 0.585853 | + | 1.01473i | 0.994768 | + | 0.102155i | \(0.0325738\pi\) |
−0.408915 | + | 0.912572i | \(0.634093\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.04201 | − | 2.33366i | −0.133771 | − | 0.0772327i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.56113 | − | 32.8260i | 0.183845 | − | 1.08520i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 81.2149i | 2.68195i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.7063 | 0.452129 | 0.226065 | − | 0.974112i | \(-0.427414\pi\) | ||||
0.226065 | + | 0.974112i | \(0.427414\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.5596 | − | 13.7218i | −0.413853 | − | 0.452150i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.1196 | − | 5.84257i | −0.333092 | − | 0.192310i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.3614 | − | 36.5347i | −0.340680 | − | 1.20125i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.15268 | + | 11.6155i | −0.267769 | + | 0.381504i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.0101 | + | 36.3906i | 0.689319 | + | 1.19394i | 0.972059 | + | 0.234739i | \(0.0754234\pi\) |
−0.282740 | + | 0.959197i | \(0.591243\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.1293 | − | 17.5445i | 0.331976 | − | 0.574999i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.80817 | − | 8.17777i | −0.0591967 | − | 0.267728i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.98912 | + | 6.40493i | 0.163162 | + | 0.209464i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.2829i | 1.34865i | 0.738433 | + | 0.674326i | \(0.235566\pi\) | ||||
−0.738433 | + | 0.674326i | \(0.764434\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.76158 | + | 30.8994i | −0.318557 | + | 1.00837i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.2029 | + | 31.5283i | −0.593397 | + | 1.02779i | 0.400374 | + | 0.916352i | \(0.368880\pi\) |
−0.993771 | + | 0.111442i | \(0.964453\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.1995 | − | 19.7451i | 1.11369 | − | 0.642989i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.1659 | − | 42.6241i | 0.363226 | − | 1.38656i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.39203 | + | 0.803687i | −0.0452348 | + | 0.0261163i | −0.522447 | − | 0.852672i | \(-0.674981\pi\) |
0.477212 | + | 0.878788i | \(0.341647\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.629063 | + | 1.08957i | −0.0204202 | + | 0.0353689i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.8161 | + | 50.0646i | −0.512873 | + | 1.62346i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46.0152i | 1.49058i | 0.666742 | + | 0.745289i | \(0.267688\pi\) | ||||
−0.666742 | + | 0.745289i | \(0.732312\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.24184 | + | 6.41997i | −0.266700 | + | 0.207745i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.56834 | − | 25.1838i | −0.179999 | − | 0.814078i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 31.1051 | − | 53.8756i | 1.00444 | − | 1.73973i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −41.9823 | − | 72.7155i | −1.35427 | − | 2.34566i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −29.6508 | − | 2.62756i | −0.955484 | − | 0.0846719i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.93895 | − | 22.0325i | 0.287755 | − | 0.709251i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.8357 | + | 24.7312i | 1.37750 | + | 0.795301i | 0.991858 | − | 0.127347i | \(-0.0406461\pi\) |
0.385644 | + | 0.922648i | \(0.373979\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.12322 | − | 3.41223i | −0.100332 | − | 0.109617i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.3398 | −1.16620 | −0.583100 | − | 0.812401i | \(-0.698160\pi\) | ||||
−0.583100 | + | 0.812401i | \(0.698160\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.2123i | 0.647976i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.68107 | + | 5.21304i | −0.310042 | + | 0.166951i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 49.4177 | + | 28.5313i | 1.58101 | + | 0.912797i | 0.994712 | + | 0.102702i | \(0.0327488\pi\) |
0.586299 | + | 0.810095i | \(0.300584\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.7351 | + | 28.9861i | 0.534857 | + | 0.926400i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.45501 | + | 50.2728i | −0.142238 | + | 1.60509i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41.1642 | + | 23.7662i | −1.31293 | + | 0.758023i | −0.982581 | − | 0.185835i | \(-0.940501\pi\) |
−0.330353 | + | 0.943858i | \(0.607168\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −43.0403 | + | 5.98518i | −1.37138 | + | 0.190704i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.85020 | + | 30.9813i | 0.218044 | + | 0.986146i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −38.5614 | −1.22618 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.2512 | −1.50098 | −0.750492 | − | 0.660879i | \(-0.770184\pi\) | ||||
−0.750492 | + | 0.660879i | \(0.770184\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.7860 | − | 4.35519i | −0.437485 | − | 0.138208i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.239722 | + | 1.72388i | 0.00759970 | + | 0.0546506i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.3221 | + | 14.0423i | −0.770287 | + | 0.444726i | −0.832977 | − | 0.553307i | \(-0.813365\pi\) |
0.0626897 | + | 0.998033i | \(0.480032\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −31.3503 | + | 23.9724i | −0.991878 | + | 0.758452i |
(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 | 360.2.bi.b.49.4 | ✓ | 32 | |
3.2 | odd | 2 | 1080.2.bi.b.1009.9 | 32 | |||
4.3 | odd | 2 | 720.2.by.f.49.13 | 32 | |||
5.4 | even | 2 | inner | 360.2.bi.b.49.13 | yes | 32 | |
9.2 | odd | 6 | 1080.2.bi.b.289.13 | 32 | |||
9.4 | even | 3 | 3240.2.f.k.649.13 | 16 | |||
9.5 | odd | 6 | 3240.2.f.i.649.4 | 16 | |||
9.7 | even | 3 | inner | 360.2.bi.b.169.13 | yes | 32 | |
12.11 | even | 2 | 2160.2.by.f.1009.9 | 32 | |||
15.14 | odd | 2 | 1080.2.bi.b.1009.13 | 32 | |||
20.19 | odd | 2 | 720.2.by.f.49.4 | 32 | |||
36.7 | odd | 6 | 720.2.by.f.529.4 | 32 | |||
36.11 | even | 6 | 2160.2.by.f.289.13 | 32 | |||
45.4 | even | 6 | 3240.2.f.k.649.14 | 16 | |||
45.14 | odd | 6 | 3240.2.f.i.649.3 | 16 | |||
45.29 | odd | 6 | 1080.2.bi.b.289.9 | 32 | |||
45.34 | even | 6 | inner | 360.2.bi.b.169.4 | yes | 32 | |
60.59 | even | 2 | 2160.2.by.f.1009.13 | 32 | |||
180.79 | odd | 6 | 720.2.by.f.529.13 | 32 | |||
180.119 | even | 6 | 2160.2.by.f.289.9 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.bi.b.49.4 | ✓ | 32 | 1.1 | even | 1 | trivial | |
360.2.bi.b.49.13 | yes | 32 | 5.4 | even | 2 | inner | |
360.2.bi.b.169.4 | yes | 32 | 45.34 | even | 6 | inner | |
360.2.bi.b.169.13 | yes | 32 | 9.7 | even | 3 | inner | |
720.2.by.f.49.4 | 32 | 20.19 | odd | 2 | |||
720.2.by.f.49.13 | 32 | 4.3 | odd | 2 | |||
720.2.by.f.529.4 | 32 | 36.7 | odd | 6 | |||
720.2.by.f.529.13 | 32 | 180.79 | odd | 6 | |||
1080.2.bi.b.289.9 | 32 | 45.29 | odd | 6 | |||
1080.2.bi.b.289.13 | 32 | 9.2 | odd | 6 | |||
1080.2.bi.b.1009.9 | 32 | 3.2 | odd | 2 | |||
1080.2.bi.b.1009.13 | 32 | 15.14 | odd | 2 | |||
2160.2.by.f.289.9 | 32 | 180.119 | even | 6 | |||
2160.2.by.f.289.13 | 32 | 36.11 | even | 6 | |||
2160.2.by.f.1009.9 | 32 | 12.11 | even | 2 | |||
2160.2.by.f.1009.13 | 32 | 60.59 | even | 2 | |||
3240.2.f.i.649.3 | 16 | 45.14 | odd | 6 | |||
3240.2.f.i.649.4 | 16 | 9.5 | odd | 6 | |||
3240.2.f.k.649.13 | 16 | 9.4 | even | 3 | |||
3240.2.f.k.649.14 | 16 | 45.4 | even | 6 |