Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [880,2,Mod(81,880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(880, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("880.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 880 = 2^{4} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 880.bo (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.02683537787\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.26265625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 220) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 641.1 | ||
Root | \(-1.21700 - 0.720348i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 880.641 |
Dual form | 880.2.bo.f.81.1 |
$q$-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 \(\left(\mathbb{Z}/880\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(177\) | \(321\) | \(661\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.655837 | − | 2.01846i | −0.378648 | − | 1.16536i | −0.940985 | − | 0.338450i | \(-0.890098\pi\) |
0.562337 | − | 0.826908i | \(-0.309902\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.809017 | + | 0.587785i | 0.361803 | + | 0.262866i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0946704 | + | 0.291365i | −0.0357820 | + | 0.110126i | −0.967352 | − | 0.253436i | \(-0.918439\pi\) |
0.931570 | + | 0.363562i | \(0.118439\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.21700 | + | 0.884205i | −0.405668 | + | 0.294735i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.72130 | − | 1.89592i | −0.820504 | − | 0.571641i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.68616 | + | 1.95161i | −0.745006 | + | 0.541279i | −0.894275 | − | 0.447518i | \(-0.852308\pi\) |
0.149269 | + | 0.988797i | \(0.452308\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.655837 | − | 2.01846i | 0.169336 | − | 0.521164i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.58719 | − | 3.33279i | −1.11256 | − | 0.808320i | −0.129492 | − | 0.991580i | \(-0.541335\pi\) |
−0.983064 | + | 0.183261i | \(0.941335\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.464854 | − | 1.43067i | −0.106645 | − | 0.328219i | 0.883468 | − | 0.468491i | \(-0.155202\pi\) |
−0.990113 | + | 0.140272i | \(0.955202\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.650198 | 0.141885 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.343838 | 0.0716951 | 0.0358476 | − | 0.999357i | \(-0.488587\pi\) | ||||
0.0358476 | + | 0.999357i | \(0.488587\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.309017 | + | 0.951057i | 0.0618034 | + | 0.190211i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.56812 | − | 1.86585i | −0.494236 | − | 0.359083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.15849 | − | 6.64316i | 0.400822 | − | 1.23360i | −0.523511 | − | 0.852019i | \(-0.675378\pi\) |
0.924334 | − | 0.381586i | \(-0.124622\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.80849 | + | 3.49357i | −0.863630 | + | 0.627464i | −0.928870 | − | 0.370405i | \(-0.879219\pi\) |
0.0652397 | + | 0.997870i | \(0.479219\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.04210 | + | 6.73625i | −0.355484 | + | 1.17263i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.247850 | + | 0.180074i | −0.0418943 | + | 0.0304380i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.63842 | − | 5.04252i | 0.269354 | − | 0.828986i | −0.721304 | − | 0.692618i | \(-0.756457\pi\) |
0.990658 | − | 0.136368i | \(-0.0435429\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.70092 | + | 4.14196i | 0.912878 | + | 0.663245i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.25645 | − | 6.94464i | −0.352398 | − | 1.08457i | −0.957503 | − | 0.288424i | \(-0.906869\pi\) |
0.605105 | − | 0.796146i | \(-0.293131\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.16046 | −0.634464 | −0.317232 | − | 0.948348i | \(-0.602753\pi\) | ||||
−0.317232 | + | 0.948348i | \(0.602753\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.50430 | −0.224248 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.94313 | + | 5.98035i | 0.283435 | + | 0.872323i | 0.986863 | + | 0.161557i | \(0.0516516\pi\) |
−0.703428 | + | 0.710766i | \(0.748348\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.58719 | + | 4.05933i | 0.798170 | + | 0.579904i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.71865 | + | 11.4448i | −0.520715 | + | 1.60259i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.63227 | + | 6.27171i | −1.18573 | + | 0.861486i | −0.992807 | − | 0.119727i | \(-0.961798\pi\) |
−0.192927 | + | 0.981213i | \(0.561798\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.08719 | − | 3.13337i | −0.146596 | − | 0.422504i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.58289 | + | 1.87658i | −0.342112 | + | 0.248559i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.590371 | − | 1.81697i | 0.0768597 | − | 0.236550i | −0.905244 | − | 0.424893i | \(-0.860312\pi\) |
0.982103 | + | 0.188343i | \(0.0603117\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.27850 | − | 6.01468i | −1.05995 | − | 0.770101i | −0.0858731 | − | 0.996306i | \(-0.527368\pi\) |
−0.974080 | + | 0.226205i | \(0.927368\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.142413 | − | 0.438301i | −0.0179423 | − | 0.0552207i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.32027 | −0.411829 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.4137 | −1.27224 | −0.636120 | − | 0.771590i | \(-0.719462\pi\) | ||||
−0.636120 | + | 0.771590i | \(0.719462\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.225502 | − | 0.694023i | −0.0271472 | − | 0.0835505i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.03760 | + | 6.56620i | 1.07257 | + | 0.779265i | 0.976372 | − | 0.216098i | \(-0.0693330\pi\) |
0.0961943 | + | 0.995363i | \(0.469333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.792610 | + | 2.43940i | −0.0927680 | + | 0.285511i | −0.986666 | − | 0.162761i | \(-0.947960\pi\) |
0.893898 | + | 0.448271i | \(0.147960\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.71700 | − | 1.24748i | 0.198263 | − | 0.144046i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.810032 | − | 0.613406i | 0.0923117 | − | 0.0699041i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.95737 | − | 1.42211i | 0.220221 | − | 0.160000i | −0.472205 | − | 0.881489i | \(-0.656542\pi\) |
0.692426 | + | 0.721489i | \(0.256542\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.47644 | + | 10.6994i | −0.386271 | + | 1.18882i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.66709 | + | 2.66430i | 0.402516 | + | 0.292445i | 0.770565 | − | 0.637361i | \(-0.219974\pi\) |
−0.368049 | + | 0.929806i | \(0.619974\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.75215 | − | 5.39256i | −0.190047 | − | 0.584906i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.8246 | −1.58936 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.46354 | 0.261134 | 0.130567 | − | 0.991439i | \(-0.458320\pi\) | ||||
0.130567 | + | 0.991439i | \(0.458320\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.314331 | − | 0.967413i | −0.0329509 | − | 0.101412i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.2052 | + | 7.41453i | 1.05823 | + | 0.768851i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.464854 | − | 1.43067i | 0.0476930 | − | 0.146784i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.1057 | + | 8.06878i | −1.12762 | + | 0.819261i | −0.985346 | − | 0.170567i | \(-0.945440\pi\) |
−0.142270 | + | 0.989828i | \(0.545440\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.98822 | − | 0.0988498i | 0.501335 | − | 0.00993478i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.79208 | − | 4.20820i | 0.576334 | − | 0.418731i | −0.261067 | − | 0.965321i | \(-0.584074\pi\) |
0.837401 | + | 0.546590i | \(0.184074\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.24201 | − | 9.97788i | 0.319445 | − | 0.983150i | −0.654441 | − | 0.756113i | \(-0.727096\pi\) |
0.973886 | − | 0.227037i | \(-0.0729038\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.526021 | + | 0.382177i | 0.0513344 | + | 0.0372966i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.27981 | − | 16.2496i | −0.510419 | − | 1.57091i | −0.791466 | − | 0.611213i | \(-0.790682\pi\) |
0.281047 | − | 0.959694i | \(-0.409318\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.9436 | 1.81447 | 0.907235 | − | 0.420624i | \(-0.138189\pi\) | ||||
0.907235 | + | 0.420624i | \(0.138189\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.2527 | −1.06806 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.10359 | − | 3.39651i | −0.103817 | − | 0.319517i | 0.885634 | − | 0.464385i | \(-0.153724\pi\) |
−0.989451 | + | 0.144867i | \(0.953724\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.278171 | + | 0.202103i | 0.0259395 | + | 0.0188462i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.54344 | − | 4.75023i | 0.142691 | − | 0.439159i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.40533 | − | 1.02103i | 0.128826 | − | 0.0935978i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.81098 | + | 10.3187i | 0.346453 | + | 0.938067i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.5376 | + | 9.10910i | −1.13048 | + | 0.821340i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.309017 | + | 0.951057i | −0.0276393 | + | 0.0850651i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.86887 | + | 4.26398i | 0.520778 | + | 0.378367i | 0.816897 | − | 0.576784i | \(-0.195693\pi\) |
−0.296119 | + | 0.955151i | \(0.595693\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.72859 | + | 8.39772i | 0.240239 | + | 0.739378i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.7731 | 1.90233 | 0.951163 | − | 0.308690i | \(-0.0998907\pi\) | ||||
0.951163 | + | 0.308690i | \(0.0998907\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.460857 | 0.0399614 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.980936 | − | 3.01901i | −0.0844255 | − | 0.259835i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.44579 | − | 1.05043i | −0.123522 | − | 0.0897441i | 0.524309 | − | 0.851528i | \(-0.324324\pi\) |
−0.647831 | + | 0.761784i | \(0.724324\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.99416 | − | 12.2928i | 0.338780 | − | 1.04266i | −0.626050 | − | 0.779783i | \(-0.715329\pi\) |
0.964830 | − | 0.262875i | \(-0.0846707\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.7967 | − | 7.84427i | 0.909247 | − | 0.660607i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.0099 | − | 0.218180i | 0.920697 | − | 0.0182451i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.65101 | − | 4.10570i | 0.469291 | − | 0.340960i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.52931 | − | 13.9398i | 0.373571 | − | 1.14973i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.69449 | − | 1.23112i | −0.138818 | − | 0.100857i | 0.516209 | − | 0.856463i | \(-0.327343\pi\) |
−0.655027 | + | 0.755605i | \(0.727343\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.46384 | − | 16.8160i | −0.444641 | − | 1.36846i | −0.882877 | − | 0.469604i | \(-0.844397\pi\) |
0.438236 | − | 0.898860i | \(-0.355603\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.52949 | 0.689569 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.94362 | −0.477403 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.29957 | − | 19.3881i | −0.502760 | − | 1.54734i | −0.804504 | − | 0.593948i | \(-0.797569\pi\) |
0.301744 | − | 0.953389i | \(-0.402431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 18.3206 | + | 13.3107i | 1.45292 | + | 1.05560i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.0325513 | + | 0.100182i | −0.00256540 | + | 0.00789548i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.4842 | − | 7.61725i | 0.821189 | − | 0.596629i | −0.0958636 | − | 0.995394i | \(-0.530561\pi\) |
0.917053 | + | 0.398766i | \(0.130561\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.61157 | + | 4.24943i | −0.436860 | + | 0.330817i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.00909 | − | 2.91277i | 0.310233 | − | 0.225397i | −0.421764 | − | 0.906706i | \(-0.638589\pi\) |
0.731996 | + | 0.681309i | \(0.238589\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.610551 | + | 1.87908i | −0.0469655 | + | 0.144545i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.83074 | + | 1.33011i | 0.140000 | + | 0.101716i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.59834 | − | 20.3076i | −0.501663 | − | 1.54396i | −0.806310 | − | 0.591494i | \(-0.798538\pi\) |
0.304647 | − | 0.952465i | \(-0.401462\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.306360 | −0.0231586 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.05468 | −0.304768 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.94425 | + | 21.3722i | 0.519038 | + | 1.59743i | 0.775813 | + | 0.630962i | \(0.217340\pi\) |
−0.256776 | + | 0.966471i | \(0.582660\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.44149 | − | 1.04730i | −0.107145 | − | 0.0778455i | 0.532923 | − | 0.846164i | \(-0.321094\pi\) |
−0.640068 | + | 0.768319i | \(0.721094\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.71104 | + | 20.6545i | −0.496094 | + | 1.52682i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.28943 | − | 3.11645i | 0.315365 | − | 0.229126i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.16444 | + | 17.7665i | 0.450788 | + | 1.29921i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.786770 | − | 0.571622i | 0.0572291 | − | 0.0415794i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.09897 | − | 24.9261i | 0.586021 | − | 1.80359i | −0.00911057 | − | 0.999958i | \(-0.502900\pi\) |
0.595131 | − | 0.803628i | \(-0.297100\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.15314 | + | 5.92361i | 0.586876 | + | 0.426390i | 0.841196 | − | 0.540730i | \(-0.181852\pi\) |
−0.254320 | + | 0.967120i | \(0.581852\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.17756 | + | 6.70184i | 0.155938 | + | 0.479928i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.84912 | 0.487979 | 0.243990 | − | 0.969778i | \(-0.421544\pi\) | ||||
0.243990 | + | 0.969778i | \(0.421544\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.7018 | −1.18396 | −0.591981 | − | 0.805952i | \(-0.701654\pi\) | ||||
−0.591981 | + | 0.805952i | \(0.701654\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.82971 | + | 21.0197i | 0.481731 | + | 1.48261i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.73124 | + | 1.25782i | 0.121509 | + | 0.0882817i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.25645 | − | 6.94464i | 0.157597 | − | 0.485034i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.418452 | + | 0.304023i | −0.0290844 | + | 0.0211311i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.44743 | + | 4.77462i | −0.100121 | + | 0.330268i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.62282 | + | 4.81176i | −0.455934 | + | 0.331255i | −0.791934 | − | 0.610607i | \(-0.790926\pi\) |
0.336000 | + | 0.941862i | \(0.390926\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.32642 | − | 22.5484i | 0.501998 | − | 1.54499i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.36588 | − | 2.44546i | −0.229551 | − | 0.166779i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.562685 | − | 1.73177i | −0.0381975 | − | 0.117560i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.44366 | 0.367848 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.8262 | 1.26639 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.07192 | + | 15.6098i | 0.339641 | + | 1.04531i | 0.964391 | + | 0.264482i | \(0.0852010\pi\) |
−0.624750 | + | 0.780825i | \(0.714799\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.21700 | − | 0.884205i | −0.0811336 | − | 0.0589470i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.56261 | − | 17.1199i | 0.369203 | − | 1.13629i | −0.578104 | − | 0.815963i | \(-0.696207\pi\) |
0.947307 | − | 0.320327i | \(-0.103793\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.9638 | + | 8.69221i | −0.790590 | + | 0.574397i | −0.908139 | − | 0.418670i | \(-0.862497\pi\) |
0.117548 | + | 0.993067i | \(0.462497\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.76938 | − | 1.23272i | −0.116417 | − | 0.0811071i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.8466 | − | 15.1459i | 1.36571 | − | 0.992243i | 0.367646 | − | 0.929966i | \(-0.380164\pi\) |
0.998059 | − | 0.0622770i | \(-0.0198362\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.94313 | + | 5.98035i | −0.126756 | + | 0.390115i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.15419 | − | 3.01820i | −0.269844 | − | 0.196053i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.42324 | + | 7.45797i | 0.156746 | + | 0.482416i | 0.998334 | − | 0.0577054i | \(-0.0183784\pi\) |
−0.841587 | + | 0.540121i | \(0.818378\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.1921 | −1.49394 | −0.746969 | − | 0.664859i | \(-0.768492\pi\) | ||||
−0.746969 | + | 0.664859i | \(0.768492\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.3531 | 0.920751 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.13412 | + | 6.56813i | 0.136344 | + | 0.419623i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.04079 | + | 2.93580i | 0.257109 | + | 0.186801i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.97276 | − | 9.14922i | 0.188391 | − | 0.579809i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.28896 | + | 6.74883i | −0.586314 | + | 0.425982i | −0.840995 | − | 0.541043i | \(-0.818030\pi\) |
0.254681 | + | 0.967025i | \(0.418030\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.935687 | − | 0.651889i | −0.0588261 | − | 0.0409839i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.73554 | + | 7.07329i | −0.609663 | + | 0.442946i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.40071 | + | 4.31093i | −0.0873736 | + | 0.268908i | −0.985191 | − | 0.171459i | \(-0.945152\pi\) |
0.897818 | + | 0.440367i | \(0.145152\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.31411 | + | 0.954755i | 0.0816547 | + | 0.0593256i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.24702 | + | 9.99331i | 0.200986 | + | 0.618570i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.80101 | −0.234380 | −0.117190 | − | 0.993110i | \(-0.537389\pi\) | ||||
−0.117190 | + | 0.993110i | \(0.537389\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.6701 | −0.655458 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.61568 | − | 4.97255i | −0.0988779 | − | 0.304315i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.6148 | + | 11.3448i | 0.952052 | + | 0.691706i | 0.951291 | − | 0.308293i | \(-0.0997579\pi\) |
0.000760692 | 1.00000i | \(0.499758\pi\) | ||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.27539 | − | 13.1583i | 0.259711 | − | 0.799309i | −0.733153 | − | 0.680063i | \(-0.761952\pi\) |
0.992865 | − | 0.119246i | \(-0.0380478\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.74653 | + | 1.26893i | −0.105705 | + | 0.0767992i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.962197 | − | 3.17398i | 0.0580227 | − | 0.191398i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.3219 | + | 11.8586i | −0.980690 | + | 0.712513i | −0.957863 | − | 0.287226i | \(-0.907267\pi\) |
−0.0228275 | + | 0.999739i | \(0.507267\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.76292 | − | 8.50338i | 0.165412 | − | 0.509084i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.19508 | − | 5.95408i | −0.488878 | − | 0.355190i | 0.315875 | − | 0.948801i | \(-0.397702\pi\) |
−0.804753 | + | 0.593610i | \(0.797702\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.50842 | + | 20.0309i | 0.386885 | + | 1.19071i | 0.935103 | + | 0.354375i | \(0.115306\pi\) |
−0.548218 | + | 0.836336i | \(0.684694\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.19263 | −0.189115 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.23705 | 0.132049 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.68153 | + | 14.4083i | 0.275384 | + | 0.847546i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.5701 | + | 17.1246i | 1.38170 | + | 1.00386i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.66886 | + | 17.4470i | −0.331178 | + | 1.01926i | 0.637396 | + | 0.770537i | \(0.280012\pi\) |
−0.968574 | + | 0.248725i | \(0.919988\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.54561 | − | 1.12295i | 0.0899889 | − | 0.0653808i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.45114 | + | 9.94650i | 0.200256 | + | 0.577154i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.923603 | + | 0.671037i | −0.0534133 | + | 0.0388070i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.393872 | − | 1.21221i | 0.0227024 | − | 0.0698709i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.2927 | − | 8.93119i | −0.706199 | − | 0.513084i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.16210 | − | 9.73196i | −0.181062 | − | 0.557250i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.3397 | −1.21792 | −0.608962 | − | 0.793199i | \(-0.708414\pi\) | ||||
−0.608962 | + | 0.793199i | \(0.708414\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.2662 | −1.26668 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.25441 | − | 13.0937i | −0.241245 | − | 0.742476i | −0.996231 | − | 0.0867356i | \(-0.972356\pi\) |
0.754986 | − | 0.655741i | \(-0.227644\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.2820 | + | 15.4623i | 1.20293 | + | 0.873978i | 0.994570 | − | 0.104074i | \(-0.0331880\pi\) |
0.208358 | + | 0.978053i | \(0.433188\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.142413 | − | 0.438301i | 0.00802404 | − | 0.0246955i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.43968 | − | 6.13179i | 0.474020 | − | 0.344396i | −0.324986 | − | 0.945719i | \(-0.605360\pi\) |
0.799006 | + | 0.601323i | \(0.205360\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.4688 | + | 13.9857i | −1.03406 | + | 0.783051i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −29.3364 | + | 21.3142i | −1.63740 | + | 1.18964i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.63576 | + | 8.11203i | −0.146658 | + | 0.451365i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.68616 | − | 1.95161i | −0.149001 | − | 0.108256i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.4239 | − | 38.2369i | −0.687045 | − | 2.11451i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.92642 | −0.106207 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.45080 | 0.519463 | 0.259732 | − | 0.965681i | \(-0.416366\pi\) | ||||
0.259732 | + | 0.965681i | \(0.416366\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.46467 | + | 7.58547i | 0.135063 | + | 0.415681i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.42488 | − | 6.12104i | −0.460301 | − | 0.334428i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.95717 | − | 15.2566i | 0.270034 | − | 0.831080i | −0.720456 | − | 0.693500i | \(-0.756068\pi\) |
0.990491 | − | 0.137580i | \(-0.0439324\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.13195 | + | 4.45512i | −0.333042 | + | 0.241969i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.7089 | − | 0.390564i | 1.06730 | − | 0.0211503i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.44664 | + | 2.50413i | −0.186101 | + | 0.135210i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.225502 | − | 0.694023i | 0.0121406 | − | 0.0373649i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.2833 | − | 14.0101i | −1.03518 | − | 0.752103i | −0.0658419 | − | 0.997830i | \(-0.520973\pi\) |
−0.969339 | + | 0.245727i | \(0.920973\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.22068 | + | 22.2230i | 0.386514 | + | 1.18957i | 0.935376 | + | 0.353655i | \(0.115061\pi\) |
−0.548862 | + | 0.835913i | \(0.684939\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.5398 | 0.562573 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.502597 | 0.0267506 | 0.0133753 | − | 0.999911i | \(-0.495742\pi\) | ||||
0.0133753 | + | 0.999911i | \(0.495742\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.45206 | + | 10.6243i | 0.183216 | + | 0.563881i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.98258 | − | 2.16697i | −0.157855 | − | 0.114688i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.52152 | − | 7.76044i | 0.133081 | − | 0.409580i | −0.862206 | − | 0.506558i | \(-0.830918\pi\) |
0.995287 | + | 0.0969777i | \(0.0309176\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.5406 | − | 9.83781i | 0.712662 | − | 0.517780i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.3286 | − | 14.4597i | 0.962000 | − | 0.758939i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.07508 | + | 1.50763i | −0.108615 | + | 0.0789132i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.57222 | + | 23.3049i | −0.395267 | + | 1.21651i | 0.533487 | + | 0.845808i | \(0.320881\pi\) |
−0.928754 | + | 0.370698i | \(0.879119\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.88659 | + | 6.45649i | 0.462617 | + | 0.336111i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.01014 | − | 3.10889i | −0.0524439 | − | 0.161406i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.9745 | 0.568236 | 0.284118 | − | 0.958789i | \(-0.408299\pi\) | ||||
0.284118 | + | 0.958789i | \(0.408299\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.12233 | 0.109597 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.16679 | + | 22.0571i | 0.369109 | + | 1.13600i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.7307 | − | 15.0617i | −1.06486 | − | 0.773669i | −0.0898815 | − | 0.995952i | \(-0.528649\pi\) |
−0.974982 | + | 0.222284i | \(0.928649\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.75765 | − | 14.6425i | 0.243742 | − | 0.750160i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.97611 | − | 2.16227i | 0.152072 | − | 0.110487i | −0.509147 | − | 0.860679i | \(-0.670039\pi\) |
0.661220 | + | 0.750192i | \(0.270039\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.01588 | − | 0.0201314i | 0.0517741 | − | 0.00102599i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.06330 | − | 3.67870i | 0.257382 | − | 0.186999i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.57725 | − | 20.2427i | 0.333480 | − | 1.02635i | −0.633986 | − | 0.773344i | \(-0.718582\pi\) |
0.967466 | − | 0.253001i | \(-0.0814175\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.57725 | − | 1.14594i | −0.0797649 | − | 0.0579526i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.2796 | − | 43.9481i | −0.720311 | − | 2.21689i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.41944 | 0.121735 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.44962 | −0.173132 | −0.0865658 | − | 0.996246i | \(-0.527589\pi\) | ||||
−0.0865658 | + | 0.996246i | \(0.527589\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.302247 | − | 0.930221i | −0.0151313 | − | 0.0465693i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.95524 | − | 5.05328i | −0.347328 | − | 0.252349i | 0.400419 | − | 0.916332i | \(-0.368865\pi\) |
−0.747747 | + | 0.663983i | \(0.768865\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.09828 | − | 18.7686i | 0.303777 | − | 0.934929i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.10143 | + | 6.61257i | −0.452254 | + | 0.328581i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.0188 | + | 10.6159i | −0.694888 | + | 0.526212i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.4094 | + | 22.8203i | −1.55310 | + | 1.12839i | −0.611698 | + | 0.791092i | \(0.709513\pi\) |
−0.941398 | + | 0.337298i | \(0.890487\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.17204 | + | 3.60718i | −0.0578126 | + | 0.177929i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.473513 | + | 0.344027i | 0.0233001 | + | 0.0169285i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.40071 | + | 4.31093i | 0.0687579 | + | 0.211615i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −27.4319 | −1.34335 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.62952 | −0.275020 | −0.137510 | − | 0.990500i | \(-0.543910\pi\) | ||||
−0.137510 | + | 0.990500i | \(0.543910\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.67683 | − | 23.6269i | −0.374146 | − | 1.15150i | −0.944053 | − | 0.329794i | \(-0.893021\pi\) |
0.569907 | − | 0.821709i | \(-0.306979\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.65265 | − | 5.55998i | −0.372085 | − | 0.270335i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.75215 | − | 5.39256i | 0.0849917 | − | 0.261578i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.53620 | − | 1.84266i | 0.122735 | − | 0.0891724i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.66111 | − | 22.0800i | −0.369882 | − | 1.06603i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.6940 | − | 8.49616i | 0.563278 | − | 0.409246i | −0.269379 | − | 0.963034i | \(-0.586818\pi\) |
0.832657 | + | 0.553788i | \(0.186818\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.59542 | − | 29.5317i | 0.461127 | − | 1.41920i | −0.402663 | − | 0.915348i | \(-0.631915\pi\) |
0.863789 | − | 0.503853i | \(-0.168085\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.9933 | − | 8.71367i | −0.575036 | − | 0.417788i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.159834 | − | 0.491920i | −0.00764592 | − | 0.0235317i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.3444 | 1.25735 | 0.628675 | − | 0.777668i | \(-0.283598\pi\) | ||||
0.628675 | + | 0.777668i | \(0.283598\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.3889 | −0.494710 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.72725 | − | 26.8597i | −0.414644 | − | 1.27614i | −0.912569 | − | 0.408923i | \(-0.865905\pi\) |
0.497925 | − | 0.867220i | \(-0.334095\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.99304 | + | 1.44803i | 0.0944793 | + | 0.0686432i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.37366 | + | 4.22768i | −0.0649717 | + | 0.199962i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.8303 | − | 13.6810i | 0.888656 | − | 0.645646i | −0.0468715 | − | 0.998901i | \(-0.514925\pi\) |
0.935527 | + | 0.353255i | \(0.114925\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.02598 | + | 23.1765i | −0.330841 | + | 1.09134i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −30.3590 | + | 22.0571i | −1.42639 | + | 1.03633i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.314331 | − | 0.967413i | 0.0147361 | − | 0.0453530i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.2045 | − | 17.5856i | −1.13224 | − | 0.822618i | −0.146218 | − | 0.989252i | \(-0.546710\pi\) |
−0.986019 | + | 0.166634i | \(0.946710\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.56198 | + | 17.1180i | 0.259611 | + | 0.799001i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.7270 | 0.685904 | 0.342952 | − | 0.939353i | \(-0.388573\pi\) | ||||
0.342952 | + | 0.939353i | \(0.388573\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.4047 | 0.901814 | 0.450907 | − | 0.892571i | \(-0.351101\pi\) | ||||
0.450907 | + | 0.892571i | \(0.351101\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.89805 | + | 11.9970i | 0.180768 | + | 0.556346i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.682974 | − | 0.496210i | −0.0316043 | − | 0.0229619i | 0.571871 | − | 0.820344i | \(-0.306218\pi\) |
−0.603475 | + | 0.797382i | \(0.706218\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.985871 | − | 3.03420i | 0.0455233 | − | 0.140106i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −35.0025 | + | 25.4308i | −1.61283 | + | 1.17179i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.3219 | + | 7.88790i | 0.520581 | + | 0.362686i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.21700 | − | 0.884205i | 0.0558400 | − | 0.0405701i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.96003 | − | 15.2654i | 0.227104 | − | 0.698955i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.82920 | + | 3.50862i | 0.220652 | + | 0.160313i | 0.692620 | − | 0.721303i | \(-0.256456\pi\) |
−0.471968 | + | 0.881616i | \(0.656456\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.43999 | + | 16.7426i | 0.248042 | + | 0.763395i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.223563 | 0.0101724 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.7274 | −0.623331 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.87468 | + | 24.2358i | 0.356836 | + | 1.09823i | 0.954937 | + | 0.296808i | \(0.0959221\pi\) |
−0.598101 | + | 0.801421i | \(0.704078\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22.2511 | − | 16.1663i | −1.00623 | − | 0.731067i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.615555 | + | 1.89448i | −0.0277796 | + | 0.0854968i | −0.963985 | − | 0.265956i | \(-0.914312\pi\) |
0.936205 | + | 0.351453i | \(0.114312\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.0417 | + | 23.2796i | −1.44308 | + | 1.04846i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.09366 | + | 2.85203i | 0.183996 | + | 0.128189i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.76876 | + | 2.01162i | −0.124196 | + | 0.0902335i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.60074 | + | 17.2373i | −0.250723 | + | 0.771647i | 0.743919 | + | 0.668270i | \(0.232965\pi\) |
−0.994642 | + | 0.103377i | \(0.967035\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.50862 | − | 6.18188i | −0.380137 | − | 0.276186i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.958726 | + | 2.95065i | 0.0427475 | + | 0.131563i | 0.970153 | − | 0.242495i | \(-0.0779659\pi\) |
−0.927405 | + | 0.374059i | \(0.877966\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.15941 | 0.318590 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.19328 | 0.186230 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.02172 | + | 6.22222i | 0.0896112 | + | 0.275795i | 0.985812 | − | 0.167854i | \(-0.0536837\pi\) |
−0.896201 | + | 0.443649i | \(0.853684\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.635721 | − | 0.461878i | −0.0281226 | − | 0.0204323i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.47562 | + | 4.54150i | −0.0651503 | + | 0.200512i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.48769 | − | 6.16667i | 0.374012 | − | 0.271736i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.05040 | − | 19.9584i | 0.266096 | − | 0.877768i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −36.6626 | + | 26.6370i | −1.60931 | + | 1.16923i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.20838 | − | 19.1074i | 0.271994 | − | 0.837112i | −0.718005 | − | 0.696038i | \(-0.754944\pi\) |
0.989999 | − | 0.141074i | \(-0.0450555\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.9613 | − | 26.8540i | −1.61620 | − | 1.17424i | −0.836046 | − | 0.548659i | \(-0.815139\pi\) |
−0.780158 | − | 0.625582i | \(-0.784861\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.200922 | + | 0.618375i | 0.00876896 | + | 0.0269881i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.7008 | 1.46803 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8818 | −0.994860 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.888095 | + | 2.73327i | 0.0385400 | + | 0.118614i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.6144 | + | 14.2507i | 0.849593 | + | 0.617266i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.27981 | − | 16.2496i | 0.228266 | − | 0.702531i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 38.5846 | − | 28.0334i | 1.66505 | − | 1.20973i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.50827 | − | 21.6395i | −0.323404 | − | 0.932080i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.9314 | + | 11.5748i | −0.684943 | + | 0.497640i | −0.874994 | − | 0.484134i | \(-0.839135\pi\) |
0.190051 | + | 0.981774i | \(0.439135\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.16856 | + | 3.59645i | −0.0501476 | + | 0.154338i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.3257 | + | 11.1348i | 0.656481 | + | 0.476962i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.28840 | + | 25.5091i | 0.354386 | + | 1.09069i | 0.956364 | + | 0.292176i | \(0.0943794\pi\) |
−0.601978 | + | 0.798513i | \(0.705621\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.3932 | 0.656965 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.5076 | −0.447638 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.229050 | + | 0.704942i | 0.00974018 | + | 0.0299772i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.10359 | − | 6.61415i | −0.386426 | − | 0.280755i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.68924 | + | 20.5874i | −0.283432 | + | 0.872315i | 0.703432 | + | 0.710763i | \(0.251650\pi\) |
−0.986864 | + | 0.161552i | \(0.948350\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.1757 | − | 8.11959i | 0.472680 | − | 0.343422i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 31.8180 | − | 24.0946i | 1.34336 | − | 1.01727i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.1055 | + | 23.3260i | −1.35309 | + | 0.983076i | −0.354236 | + | 0.935156i | \(0.615259\pi\) |
−0.998851 | + | 0.0479197i | \(0.984741\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.10359 | − | 3.39651i | 0.0464286 | − | 0.142892i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.78831 | − | 2.02583i | −0.117098 | − | 0.0850767i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.845992 | + | 2.60370i | 0.0354658 | + | 0.109153i | 0.967222 | − | 0.253931i | \(-0.0817238\pi\) |
−0.931756 | + | 0.363084i | \(0.881724\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.0562 | −1.59260 | −0.796302 | − | 0.604899i | \(-0.793213\pi\) | ||||
−0.796302 | + | 0.604899i | \(0.793213\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −55.6239 | −2.32372 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.106252 | + | 0.327009i | 0.00443100 | + | 0.0136372i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.82060 | − | 4.95545i | −0.283945 | − | 0.206298i | 0.436691 | − | 0.899611i | \(-0.356150\pi\) |
−0.720636 | + | 0.693313i | \(0.756150\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.60942 | − | 20.3417i | 0.274678 | − | 0.845372i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.12345 | + | 0.816234i | −0.0466086 | + | 0.0338631i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.3817 | − | 0.701147i | 1.46536 | − | 0.0290385i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.04079 | − | 2.93580i | 0.167066 | − | 0.121380i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.99868 | + | 9.22900i | −0.123769 | + | 0.380921i | −0.993675 | − | 0.112296i | \(-0.964179\pi\) |
0.869906 | + | 0.493218i | \(0.164179\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.23341 | + | 5.25538i | 0.298047 | + | 0.216544i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.49190 | − | 13.8247i | −0.184772 | − | 0.568670i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.3047 | −0.915943 | −0.457971 | − | 0.888967i | \(-0.651424\pi\) | ||||
−0.457971 | + | 0.888967i | \(0.651424\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.73708 | 0.0712135 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.9537 | + | 33.7120i | 0.448304 | + | 1.37974i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.0325 | + | 11.6483i | 0.655071 | + | 0.475937i | 0.864995 | − | 0.501781i | \(-0.167322\pi\) |
−0.209924 | + | 0.977718i | \(0.567322\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.98586 | + | 18.4226i | −0.244168 | + | 0.751473i | 0.751604 | + | 0.659615i | \(0.229281\pi\) |
−0.995772 | + | 0.0918582i | \(0.970719\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.6735 | − | 9.20787i | 0.516107 | − | 0.374973i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.98205 | + | 10.5881i | −0.121238 | + | 0.430467i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.465809 | + | 0.338430i | −0.0189066 | + | 0.0137365i | −0.597198 | − | 0.802094i | \(-0.703720\pi\) |
0.578292 | + | 0.815830i | \(0.303720\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.40345 | − | 4.31937i | 0.0568706 | − | 0.175030i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.8909 | − | 12.2719i | −0.683331 | − | 0.496469i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.61609 | + | 29.5953i | 0.388390 | + | 1.19534i | 0.933991 | + | 0.357297i | \(0.116302\pi\) |
−0.545601 | + | 0.838045i | \(0.683698\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.4973 | −0.624913 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.4917 | 0.744447 | 0.372224 | − | 0.928143i | \(-0.378595\pi\) | ||||
0.372224 | + | 0.928143i | \(0.378595\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.98840 | − | 9.19734i | −0.120114 | − | 0.369672i | 0.872865 | − | 0.487961i | \(-0.162259\pi\) |
−0.992979 | + | 0.118289i | \(0.962259\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.883018 | − | 0.641550i | −0.0354343 | − | 0.0257445i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.233224 | + | 0.717789i | −0.00934392 | + | 0.0287576i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.809017 | + | 0.587785i | −0.0323607 | + | 0.0235114i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.5867 | − | 0.209792i | 0.422791 | − | 0.00837830i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.3214 | + | 17.6705i | −0.969757 | + | 0.704570i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.381339 | + | 1.17364i | −0.0151809 | + | 0.0467219i | −0.958360 | − | 0.285563i | \(-0.907819\pi\) |
0.943179 | + | 0.332285i | \(0.107819\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.0558 | + | 10.2122i | 0.558669 | + | 0.405897i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.24171 | + | 6.89927i | 0.0889595 | + | 0.273789i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.9303 | −0.908531 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.8047 | −0.664782 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.92312 | − | 15.1518i | −0.194451 | − | 0.598460i | −0.999983 | − | 0.00590646i | \(-0.998120\pi\) |
0.805531 | − | 0.592553i | \(-0.201880\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.9209 | − | 8.66107i | −0.470116 | − | 0.341559i | 0.327370 | − | 0.944896i | \(-0.393838\pi\) |
−0.797487 | + | 0.603337i | \(0.793838\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.72859 | + | 8.39772i | −0.107438 | + | 0.330660i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.02156 | + | 2.19529i | −0.118790 | + | 0.0863058i | −0.645594 | − | 0.763681i | \(-0.723390\pi\) |
0.526804 | + | 0.849987i | \(0.323390\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.05141 | + | 3.82524i | −0.198285 | + | 0.150154i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.12647 | + | 2.27151i | −0.122536 | + | 0.0890276i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.9132 | + | 33.5874i | −0.427067 | + | 1.31438i | 0.473935 | + | 0.880560i | \(0.342833\pi\) |
−0.901002 | + | 0.433816i | \(0.857167\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.6148 | + | 12.7979i | 0.688268 | + | 0.500056i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.19232 | − | 3.66959i | −0.0465170 | − | 0.143164i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.5715 | 1.58044 | 0.790220 | − | 0.612823i | \(-0.209966\pi\) | ||||
0.790220 | + | 0.612823i | \(0.209966\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0301 | 0.856870 | 0.428435 | − | 0.903573i | \(-0.359065\pi\) | ||||
0.428435 | + | 0.903573i | \(0.359065\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.3469 | − | 37.9999i | −0.479515 | − | 1.47579i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.372841 | + | 0.270885i | 0.0144582 | + | 0.0105045i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.742172 | − | 2.28417i | 0.0287370 | − | 0.0884434i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.1813 | − | 20.4749i | 1.08955 | − | 0.791606i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.1250 | + | 32.0631i | 0.429474 | + | 1.23778i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.9208 | − | 13.7468i | 0.729345 | − | 0.529900i | −0.160011 | − | 0.987115i | \(-0.551153\pi\) |
0.889356 | + | 0.457215i | \(0.151153\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.980936 | − | 3.01901i | 0.0377562 | − | 0.116202i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.6959 | + | 17.9426i | 0.949139 | + | 0.689590i | 0.950603 | − | 0.310409i | \(-0.100466\pi\) |
−0.00146411 | + | 0.999999i | \(0.500466\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.29958 | − | 3.99970i | −0.0498733 | − | 0.153494i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −38.2041 | −1.46398 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.0885 | 0.845192 | 0.422596 | − | 0.906318i | \(-0.361119\pi\) | ||||
0.422596 | + | 0.906318i | \(0.361119\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.552243 | − | 1.69963i | −0.0211001 | − | 0.0649395i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.3912 | + | 18.4478i | 0.968734 | + | 0.703826i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.9477 | − | 33.6936i | 0.417075 | − | 1.28362i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.9069 | − | 10.1040i | 0.529045 | − | 0.384374i | −0.290956 | − | 0.956737i | \(-0.593973\pi\) |
0.820000 | + | 0.572363i | \(0.193973\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.443435 | + | 1.46275i | −0.0168447 | + | 0.0555654i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.4568 | − | 7.59734i | 0.396651 | − | 0.288184i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.7942 | + | 39.3766i | −0.484616 | + | 1.49150i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −44.2434 | − | 32.1447i | −1.67344 | − | 1.21582i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.6808 | + | 32.8721i | 0.403408 | + | 1.24156i | 0.922217 | + | 0.386673i | \(0.126376\pi\) |
−0.518808 | + | 0.854891i | \(0.673624\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.97583 | −0.300814 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.3455 | 0.502619 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.677784 | + | 2.08600i | 0.0254907 | + | 0.0784523i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.3833 | − | 12.6297i | −0.652844 | − | 0.474319i | 0.211395 | − | 0.977401i | \(-0.432199\pi\) |
−0.864239 | + | 0.503082i | \(0.832199\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.12469 | + | 3.46144i | −0.0421791 | + | 0.129814i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.65334 | + | 1.20122i | −0.0619181 | + | 0.0449861i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.03547 | + | 6.29497i | 0.337907 | + | 0.235418i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.4644 | − | 9.78242i | 0.502835 | − | 0.365331i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.06421 | − | 24.8191i | 0.300744 | − | 0.925596i | −0.680487 | − | 0.732760i | \(-0.738232\pi\) |
0.981231 | − | 0.192836i | \(-0.0617684\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.60029 | + | 1.88922i | 0.0968398 | + | 0.0703582i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.2103 | + | 46.8124i | 0.565676 | + | 1.74097i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.98503 | 0.259418 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.7639 | −0.436300 | −0.218150 | − | 0.975915i | \(-0.570002\pi\) | ||||
−0.218150 | + | 0.975915i | \(0.570002\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.01602 | + | 3.12699i | 0.0376303 | + | 0.115814i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.0848 | + | 13.8659i | 0.705878 | + | 0.512850i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.1366 | + | 31.1974i | −0.374405 | + | 1.15230i | 0.569474 | + | 0.822009i | \(0.307147\pi\) |
−0.943879 | + | 0.330291i | \(0.892853\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.8579 | − | 8.61525i | 0.437384 | − | 0.317778i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.3389 | + | 19.7436i | 1.04388 | + | 0.727264i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.288938 | − | 0.209926i | 0.0106288 | − | 0.00772224i | −0.582458 | − | 0.812861i | \(-0.697909\pi\) |
0.593087 | + | 0.805138i | \(0.297909\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.27570 | − | 10.0816i | 0.120336 | − | 0.370356i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.6594 | − | 21.5488i | −1.08810 | − | 0.790549i | −0.109020 | − | 0.994040i | \(-0.534771\pi\) |
−0.979077 | + | 0.203491i | \(0.934771\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.647238 | − | 1.99199i | −0.0237130 | − | 0.0729810i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.81865 | −0.249481 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.23441 | 0.191261 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.6834 | + | 42.1131i | 0.499313 | + | 1.53673i | 0.810125 | + | 0.586257i | \(0.199399\pi\) |
−0.310811 | + | 0.950472i | \(0.600601\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.7143 | + | 14.3233i | 0.718428 | + | 0.521969i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.46384 | − | 16.8160i | 0.198849 | − | 0.611996i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.7688 | − | 25.2610i | 1.26369 | − | 0.918126i | 0.264760 | − | 0.964314i | \(-0.414707\pi\) |
0.998933 | + | 0.0461881i | \(0.0147074\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.702152 | + | 2.31618i | −0.0254865 | + | 0.0840720i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.846857 | + | 0.615278i | −0.0306985 | + | 0.0223038i | −0.603029 | − | 0.797719i | \(-0.706040\pi\) |
0.572330 | + | 0.820023i | \(0.306040\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.79340 | + | 5.51952i | −0.0649254 | + | 0.199820i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.90050 | + | 5.01351i | 0.249488 | + | 0.181264i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.96019 | + | 6.03285i | 0.0707785 | + | 0.217834i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 52.9156 | 1.90818 | 0.954092 | − | 0.299513i | \(-0.0968243\pi\) | ||||
0.954092 | + | 0.299513i | \(0.0968243\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.62006 | 0.346458 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.4526 | − | 35.2476i | −0.411923 | − | 1.26777i | −0.914974 | − | 0.403512i | \(-0.867789\pi\) |
0.503051 | − | 0.864257i | \(-0.332211\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.80849 | − | 3.49357i | −0.172726 | − | 0.125493i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.06529 | − | 3.27864i | 0.0382172 | − | 0.117620i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.88659 | + | 6.45649i | −0.318395 | + | 0.231328i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.1451 | − | 35.0032i | −0.434585 | − | 1.25251i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.9384 | + | 13.0330i | −0.641067 | + | 0.465763i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.29957 | − | 19.3881i | 0.224841 | − | 0.691990i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.50000 | + | 1.08981i | 0.0534692 | + | 0.0388477i | 0.614199 | − | 0.789151i | \(-0.289479\pi\) |
−0.560730 | + | 0.827999i | \(0.689479\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.49284 | + | 7.67218i | 0.0887475 | + | 0.273137i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.09410 | 0.0389019 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 33.9756 | 1.20651 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.99783 | + | 21.5371i | 0.248188 | + | 0.763843i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.0383291 | − | 0.0278477i | −0.00135769 | − | 0.000986417i | 0.587106 | − | 0.809510i | \(-0.300267\pi\) |
−0.588464 | + | 0.808524i | \(0.700267\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.0177 | − | 33.9090i | 0.389779 | − | 1.19962i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.99813 | + | 2.17827i | −0.105934 | + | 0.0769655i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.78184 | − | 5.13563i | 0.239326 | − | 0.181233i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.0852203 | + | 0.0619162i | −0.00300362 | + | 0.00218226i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.6583 | − | 38.9582i | 0.445593 | − | 1.37139i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −44.2731 | − | 32.1663i | −1.55656 | − | 1.13091i | −0.938760 | − | 0.344573i | \(-0.888024\pi\) |
−0.617801 | − | 0.786335i | \(-0.711976\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.1648 | − | 40.5172i | −0.462280 | − | 1.42275i | −0.862371 | − | 0.506277i | \(-0.831021\pi\) |
0.400091 | − | 0.916476i | \(-0.368979\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.3634 | −1.02982 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.9592 | 0.453942 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.93401 | + | 5.95226i | 0.0676624 | + | 0.208243i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.23793 | + | 0.899412i | 0.0432569 | + | 0.0314280i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.51704 | − | 4.66898i | 0.0529452 | − | 0.162948i | −0.921088 | − | 0.389355i | \(-0.872698\pi\) |
0.974033 | + | 0.226407i | \(0.0726979\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.51286 | + | 5.45841i | −0.261882 | + | 0.190268i | −0.710976 | − | 0.703216i | \(-0.751747\pi\) |
0.449094 | + | 0.893484i | \(0.351747\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.03760 | + | 0.139462i | −0.245018 | + | 0.00485544i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.5271 | + | 19.2730i | −0.922436 | + | 0.670189i | −0.944129 | − | 0.329575i | \(-0.893094\pi\) |
0.0216929 | + | 0.999765i | \(0.493094\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.36118 | − | 10.3447i | 0.116739 | − | 0.359285i | −0.875567 | − | 0.483097i | \(-0.839512\pi\) |
0.992306 | + | 0.123812i | \(0.0395119\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 34.6406 | + | 25.1679i | 1.20167 | + | 0.873064i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.1006 | − | 37.2418i | −0.419261 | − | 1.29035i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.95551 | 0.171492 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.8673 | 0.652149 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.82985 | − | 14.8647i | −0.166745 | − | 0.513188i | 0.832416 | − | 0.554152i | \(-0.186957\pi\) |
−0.999161 | + | 0.0409637i | \(0.986957\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.0110 | − | 11.6327i | −0.552104 | − | 0.401127i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.64342 | + | 20.4463i | −0.228811 | + | 0.704209i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.59844 | + | 1.16134i | −0.0549881 | + | 0.0399512i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.36731 | + | 0.133510i | −0.115702 | + | 0.00458746i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 36.1630 | − | 26.2740i | 1.24111 | − | 0.901720i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.563349 | − | 1.73381i | 0.0193114 | − | 0.0594343i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.15097 | − | 5.19549i | −0.244845 | − | 0.177890i | 0.458594 | − | 0.888646i | \(-0.348353\pi\) |
−0.703439 | + | 0.710756i | \(0.748353\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.699280 | + | 2.15216i | 0.0239149 | + | 0.0736024i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −51.6469 | −1.76422 | −0.882112 | − | 0.471040i | \(-0.843879\pi\) | ||||
−0.882112 | + | 0.471040i | \(0.843879\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.0705 | 0.480078 | 0.240039 | − | 0.970763i | \(-0.422840\pi\) | ||||
0.240039 | + | 0.970763i | \(0.422840\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.46714 | − | 4.51539i | −0.0499999 | − | 0.153884i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.2045 | + | 24.8510i | 1.16433 | + | 0.845938i | 0.990320 | − | 0.138806i | \(-0.0443263\pi\) |
0.174014 | + | 0.984743i | \(0.444326\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.59834 | − | 20.3076i | 0.224350 | − | 0.690479i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.0122 | − | 18.8990i | 0.883420 | − | 0.641843i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.02281 | + | 0.158985i | −0.272155 | + | 0.00539321i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.9729 | − | 20.3235i | 0.947826 | − | 0.688636i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.38125 | − | 19.6395i | 0.215973 | − | 0.664696i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.247850 | − | 0.180074i | −0.00837887 | − | 0.00608760i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.06926 | + | 15.6016i | 0.171177 | + | 0.526828i | 0.999438 | − | 0.0335137i | \(-0.0106698\pi\) |
−0.828261 | + | 0.560342i | \(0.810670\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 38.9338 | 1.31321 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.6436 | −0.527045 | −0.263522 | − | 0.964653i | \(-0.584884\pi\) | ||||
−0.263522 | + | 0.964653i | \(0.584884\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.34202 | + | 7.20799i | 0.0788152 | + | 0.242568i | 0.982699 | − | 0.185210i | \(-0.0592965\pi\) |
−0.903884 | + | 0.427778i | \(0.859296\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.28030 | − | 2.38328i | −0.110266 | − | 0.0801130i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.63187 | + | 5.02238i | −0.0547929 | + | 0.168635i | −0.974708 | − | 0.223483i | \(-0.928257\pi\) |
0.919915 | + | 0.392118i | \(0.128257\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.79798 | + | 1.30631i | −0.0603025 | + | 0.0438123i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 29.7456 | − | 22.5252i | 0.996514 | − | 0.754622i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.65265 | − | 5.55998i | 0.256086 | − | 0.186058i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.94425 | + | 21.3722i | −0.232121 | + | 0.714394i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.96019 | + | 1.42416i | 0.0654489 | + | 0.0475514i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.8293 | + | 39.4844i | 0.427880 | + | 1.31688i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 60.5001 | 2.01555 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.70512 | −0.0900208 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.550600 | − | 1.69457i | −0.0183026 | − | 0.0563295i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.3680 | + | 13.3452i | 0.609901 | + | 0.443119i | 0.849379 | − | 0.527783i | \(-0.176976\pi\) |
−0.239479 | + | 0.970902i | \(0.576976\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.32808 | + | 10.2428i | −0.110385 | + | 0.339732i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.03484 | + | 5.83766i | −0.266206 | + | 0.193410i | −0.712879 | − | 0.701287i | \(-0.752609\pi\) |
0.446672 | + | 0.894698i | \(0.352609\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.92798 | − | 14.2029i | −0.163092 | − | 0.470047i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.5697 | + | 12.7652i | −0.580837 | + | 0.422003i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.06127 | + | 6.34393i | −0.0680691 | + | 0.209495i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.49295 | − | 6.89703i | −0.313143 | − | 0.227512i | 0.420101 | − | 0.907477i | \(-0.361995\pi\) |
−0.733244 | + | 0.679965i | \(0.761995\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.9954 | + | 43.0734i | 0.461164 | + | 1.41932i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −37.0911 | −1.22087 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.30202 | 0.174329 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.87695 | + | 15.0097i | 0.160180 | + | 0.492984i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.86447 | − | 6.44041i | −0.290834 | − | 0.211303i | 0.432795 | − | 0.901492i | \(-0.357527\pi\) |
−0.723629 | + | 0.690189i | \(0.757527\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.21035 | − | 9.88044i | 0.105215 | − | 0.323818i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.6389 | + | 17.1747i | −0.773904 | + | 0.562274i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.45573 | + | 17.9967i | −0.178421 | + | 0.588556i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.69826 | − | 6.31966i | 0.284160 | − | 0.206454i | −0.436570 | − | 0.899670i | \(-0.643807\pi\) |
0.720730 | + | 0.693216i | \(0.243807\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.2524 | − | 53.0975i | 0.563012 | − | 1.73277i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.7229 | − | 20.8684i | −0.936339 | − | 0.680290i | 0.0111977 | − | 0.999937i | \(-0.496436\pi\) |
−0.947537 | + | 0.319647i | \(0.896436\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.775853 | − | 2.38783i | −0.0252652 | − | 0.0777584i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.972501 | 0.0316355 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.7444 | 1.51899 | 0.759495 | − | 0.650513i | \(-0.225446\pi\) | ||||
0.759495 | + | 0.650513i | \(0.225446\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.63168 | − | 8.09949i | −0.0854280 | − | 0.262920i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.9118 | − | 13.0137i | −0.580831 | − | 0.421998i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.5357 | − | 32.4257i | 0.341286 | − | 1.05037i | −0.622256 | − | 0.782814i | \(-0.713784\pi\) |
0.963542 | − | 0.267557i | \(-0.0862162\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.2034 | − | 15.4052i | 0.686125 | − | 0.498499i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 40.3422 | + | 28.1062i | 1.30408 | + | 0.908544i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.442932 | − | 0.321809i | 0.0143030 | − | 0.0103917i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.33701 | − | 4.11488i | 0.0431292 | − | 0.132738i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.7935 | + | 15.1074i | 0.670062 | + | 0.486829i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.11422 | + | 9.58459i | 0.100250 | + | 0.308539i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.9490 | −0.673675 | −0.336837 | − | 0.941563i | \(-0.609357\pi\) | ||||
−0.336837 | + | 0.941563i | \(0.609357\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.1024 | 0.581534 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.76006 | − | 20.8053i | −0.216941 | − | 0.667675i | −0.999010 | − | 0.0444834i | \(-0.985836\pi\) |
0.782070 | − | 0.623191i | \(-0.214164\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.20356 | + | 2.32752i | 0.102701 | + | 0.0746169i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.17756 | + | 6.70184i | −0.0697377 | + | 0.214631i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.3733 | − | 14.8021i | 0.651799 | − | 0.473560i | −0.212084 | − | 0.977251i | \(-0.568025\pi\) |
0.863884 | + | 0.503691i | \(0.168025\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.70403 | − | 4.67067i | −0.214262 | − | 0.149275i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.0545 | + | 16.7500i | −0.736072 | + | 0.534788i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.46922 | + | 13.7548i | −0.142546 | + | 0.438711i | −0.996687 | − | 0.0813298i | \(-0.974083\pi\) |
0.854141 | + | 0.520041i | \(0.174083\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.54105 | + | 4.02581i | 0.176553 | + | 0.128273i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.26342 | + | 3.88841i | 0.0402151 | + | 0.123769i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.43052 | −0.0454880 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.2980 | −0.994214 | −0.497107 | − | 0.867689i | \(-0.665604\pi\) | ||||
−0.497107 | + | 0.867689i | \(0.665604\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.19819 | − | 19.0761i | −0.196694 | − | 0.605361i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.5121 | − | 9.81709i | −0.428361 | − | 0.311223i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.13608 | − | 9.65187i | 0.0993207 | − | 0.305678i | −0.889035 | − | 0.457839i | \(-0.848623\pi\) |
0.988356 | + | 0.152162i | \(0.0486234\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.6163 | + | 9.89279i | −0.430799 | + | 0.312994i |
(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 | 880.2.bo.f.641.1 | 8 | ||
4.3 | odd | 2 | 220.2.m.a.201.2 | yes | 8 | ||
11.2 | odd | 10 | 9680.2.a.cl.1.2 | 4 | |||
11.4 | even | 5 | inner | 880.2.bo.f.81.1 | 8 | ||
11.9 | even | 5 | 9680.2.a.ck.1.2 | 4 | |||
12.11 | even | 2 | 1980.2.z.c.1081.1 | 8 | |||
20.3 | even | 4 | 1100.2.cb.c.949.1 | 16 | |||
20.7 | even | 4 | 1100.2.cb.c.949.4 | 16 | |||
20.19 | odd | 2 | 1100.2.n.c.201.1 | 8 | |||
44.15 | odd | 10 | 220.2.m.a.81.2 | ✓ | 8 | ||
44.31 | odd | 10 | 2420.2.a.n.1.3 | 4 | |||
44.35 | even | 10 | 2420.2.a.m.1.3 | 4 | |||
132.59 | even | 10 | 1980.2.z.c.1621.1 | 8 | |||
220.59 | odd | 10 | 1100.2.n.c.301.1 | 8 | |||
220.103 | even | 20 | 1100.2.cb.c.1049.4 | 16 | |||
220.147 | even | 20 | 1100.2.cb.c.1049.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
220.2.m.a.81.2 | ✓ | 8 | 44.15 | odd | 10 | ||
220.2.m.a.201.2 | yes | 8 | 4.3 | odd | 2 | ||
880.2.bo.f.81.1 | 8 | 11.4 | even | 5 | inner | ||
880.2.bo.f.641.1 | 8 | 1.1 | even | 1 | trivial | ||
1100.2.n.c.201.1 | 8 | 20.19 | odd | 2 | |||
1100.2.n.c.301.1 | 8 | 220.59 | odd | 10 | |||
1100.2.cb.c.949.1 | 16 | 20.3 | even | 4 | |||
1100.2.cb.c.949.4 | 16 | 20.7 | even | 4 | |||
1100.2.cb.c.1049.1 | 16 | 220.147 | even | 20 | |||
1100.2.cb.c.1049.4 | 16 | 220.103 | even | 20 | |||
1980.2.z.c.1081.1 | 8 | 12.11 | even | 2 | |||
1980.2.z.c.1621.1 | 8 | 132.59 | even | 10 | |||
2420.2.a.m.1.3 | 4 | 44.35 | even | 10 | |||
2420.2.a.n.1.3 | 4 | 44.31 | odd | 10 | |||
9680.2.a.ck.1.2 | 4 | 11.9 | even | 5 | |||
9680.2.a.cl.1.2 | 4 | 11.2 | odd | 10 |