Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,2,Mod(26,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1575.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.bk (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: | \(12.5764383184\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 315) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 26.11 | ||
Character | \(\chi\) | \(=\) | 1575.26 |
Dual form | 1575.2.bk.i.1151.11 |
$q$-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 \(\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(1226\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.22514 | + | 1.28469i | 1.57341 | + | 0.908411i | 0.995746 | + | 0.0921382i | \(0.0293702\pi\) |
0.577667 | + | 0.816272i | \(0.303963\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.30084 | + | 3.98517i | 1.15042 | + | 1.99259i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.151755 | − | 2.64140i | −0.0573579 | − | 0.998354i | ||||
\(8\) | 6.68468i | 2.36339i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.88189 | − | 2.81856i | 1.47195 | − | 0.849828i | 0.472442 | − | 0.881362i | \(-0.343372\pi\) |
0.999503 | + | 0.0315336i | \(0.0100391\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.53537i | 0.980535i | 0.871572 | + | 0.490267i | \(0.163101\pi\) | ||||
−0.871572 | + | 0.490267i | \(0.836899\pi\) | |||||||
\(14\) | 3.05569 | − | 6.07244i | 0.816667 | − | 1.62293i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.98605 | + | 6.90403i | −0.996512 | + | 1.72601i | ||||
\(17\) | 2.67142 | + | 4.62703i | 0.647914 | + | 1.12222i | 0.983620 | + | 0.180253i | \(0.0576916\pi\) |
−0.335707 | + | 0.941967i | \(0.608975\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.24942 | + | 0.721351i | 0.286636 | + | 0.165489i | 0.636424 | − | 0.771340i | \(-0.280413\pi\) |
−0.349788 | + | 0.936829i | \(0.613746\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 14.4839 | 3.08797 | ||||||||
\(23\) | −2.59686 | − | 1.49930i | −0.541484 | − | 0.312626i | 0.204196 | − | 0.978930i | \(-0.434542\pi\) |
−0.745680 | + | 0.666304i | \(0.767875\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.54184 | + | 7.86670i | −0.890728 | + | 1.54279i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 10.1772 | − | 6.68220i | 1.92332 | − | 1.26282i | ||||
\(29\) | 2.19404i | 0.407423i | 0.979031 | + | 0.203712i | \(0.0653005\pi\) | ||||
−0.979031 | + | 0.203712i | \(0.934699\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.31899 | − | 0.761520i | 0.236898 | − | 0.136773i | −0.376852 | − | 0.926273i | \(-0.622994\pi\) |
0.613750 | + | 0.789500i | \(0.289660\pi\) | |||||||
\(32\) | −6.16083 | + | 3.55696i | −1.08909 | + | 0.628787i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13.7277i | 2.35429i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.546572 | + | 0.946690i | −0.0898558 | + | 0.155635i | −0.907450 | − | 0.420160i | \(-0.861974\pi\) |
0.817594 | + | 0.575795i | \(0.195307\pi\) | |||||||
\(38\) | 1.85342 | + | 3.21022i | 0.300665 | + | 0.520766i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.52058 | −1.01834 | −0.509172 | − | 0.860665i | \(-0.670048\pi\) | ||||
−0.509172 | + | 0.860665i | \(0.670048\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.486125 | 0.0741333 | 0.0370667 | − | 0.999313i | \(-0.488199\pi\) | ||||
0.0370667 | + | 0.999313i | \(0.488199\pi\) | |||||||
\(44\) | 22.4649 | + | 12.9701i | 3.38671 | + | 1.95532i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.85226 | − | 6.67231i | −0.567985 | − | 0.983779i | ||||
\(47\) | −2.12816 | + | 3.68608i | −0.310424 | + | 0.537671i | −0.978454 | − | 0.206464i | \(-0.933804\pi\) |
0.668030 | + | 0.744134i | \(0.267138\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.95394 | + | 0.801688i | −0.993420 | + | 0.114527i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −14.0891 | + | 8.13432i | −1.95380 | + | 1.12803i | ||||
\(53\) | 3.48318 | − | 2.01102i | 0.478452 | − | 0.276235i | −0.241319 | − | 0.970446i | \(-0.577580\pi\) |
0.719771 | + | 0.694211i | \(0.244247\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 17.6569 | − | 1.01443i | 2.35950 | − | 0.135559i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.81866 | + | 4.88206i | −0.370108 | + | 0.641046i | ||||
\(59\) | −5.70978 | − | 9.88963i | −0.743350 | − | 1.28752i | −0.950962 | − | 0.309309i | \(-0.899902\pi\) |
0.207612 | − | 0.978211i | \(-0.433431\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.06957 | + | 3.50427i | 0.777129 | + | 0.448676i | 0.835412 | − | 0.549624i | \(-0.185229\pi\) |
−0.0582826 | + | 0.998300i | \(0.518562\pi\) | |||||||
\(62\) | 3.91326 | 0.496984 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.33411 | −0.291764 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.24490 | − | 2.15623i | −0.152089 | − | 0.263425i | 0.779907 | − | 0.625896i | \(-0.215267\pi\) |
−0.931995 | + | 0.362471i | \(0.881933\pi\) | |||||||
\(68\) | −12.2930 | + | 21.2921i | −1.49075 | + | 2.58205i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.13849i | − | 0.965861i | −0.875659 | − | 0.482930i | \(-0.839572\pi\) | ||
0.875659 | − | 0.482930i | \(-0.160428\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.71761 | + | 1.56901i | −0.318072 | + | 0.183639i | −0.650533 | − | 0.759478i | \(-0.725454\pi\) |
0.332461 | + | 0.943117i | \(0.392121\pi\) | |||||||
\(74\) | −2.43240 | + | 1.40435i | −0.282761 | + | 0.163252i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.63886i | 0.761529i | ||||||||
\(77\) | −8.18578 | − | 12.4673i | −0.932856 | − | 1.42078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.40252 | − | 11.0895i | 0.720340 | − | 1.24766i | −0.240524 | − | 0.970643i | \(-0.577319\pi\) |
0.960864 | − | 0.277022i | \(-0.0893474\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −14.5092 | − | 8.37690i | −1.60228 | − | 0.925074i | ||||
\(83\) | −6.77241 | −0.743368 | −0.371684 | − | 0.928359i | \(-0.621220\pi\) | ||||
−0.371684 | + | 0.928359i | \(0.621220\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.08170 | + | 0.624518i | 0.116642 | + | 0.0673435i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 18.8412 | + | 32.6339i | 2.00848 | + | 3.47878i | ||||
\(89\) | −5.16513 | + | 8.94627i | −0.547503 | + | 0.948303i | 0.450942 | + | 0.892553i | \(0.351088\pi\) |
−0.998445 | + | 0.0557494i | \(0.982245\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.33831 | − | 0.536509i | 0.978921 | − | 0.0562414i | ||||
\(92\) | − | 13.7986i | − | 1.43860i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.47093 | + | 5.46804i | −0.976852 | + | 0.563985i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.7321i | 1.49582i | 0.663802 | + | 0.747908i | \(0.268942\pi\) | ||||
−0.663802 | + | 0.747908i | \(0.731058\pi\) | |||||||
\(98\) | −16.5034 | − | 7.14976i | −1.66710 | − | 0.722235i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.46683 | − | 12.9329i | −0.742977 | − | 1.28687i | −0.951134 | − | 0.308779i | \(-0.900080\pi\) |
0.208157 | − | 0.978095i | \(-0.433254\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.39058 | − | 1.95755i | −0.334084 | − | 0.192883i | 0.323569 | − | 0.946205i | \(-0.395117\pi\) |
−0.657653 | + | 0.753321i | \(0.728451\pi\) | |||||||
\(104\) | −23.6328 | −2.31739 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.3341 | 1.00374 | ||||||||
\(107\) | −12.8363 | − | 7.41102i | −1.24093 | − | 0.716450i | −0.271645 | − | 0.962398i | \(-0.587568\pi\) |
−0.969283 | + | 0.245948i | \(0.920901\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.51932 | + | 9.55974i | 0.528655 | + | 0.915657i | 0.999442 | + | 0.0334099i | \(0.0106367\pi\) |
−0.470787 | + | 0.882247i | \(0.656030\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 18.8412 | + | 9.48101i | 1.78032 | + | 0.895871i | ||||
\(113\) | − | 7.54314i | − | 0.709599i | −0.934942 | − | 0.354799i | \(-0.884549\pi\) | ||
0.934942 | − | 0.354799i | \(-0.115451\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.74363 | + | 5.04814i | −0.811826 | + | 0.468708i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 29.3411i | − | 2.70107i | ||||||
\(119\) | 11.8164 | − | 7.75844i | 1.08321 | − | 0.711215i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3886 | − | 17.9935i | 0.944415 | − | 1.63577i | ||||
\(122\) | 9.00378 | + | 15.5950i | 0.815164 | + | 1.41191i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.06957 | + | 3.50427i | 0.545064 | + | 0.314693i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.93715 | −0.349366 | −0.174683 | − | 0.984625i | \(-0.555890\pi\) | ||||
−0.174683 | + | 0.984625i | \(0.555890\pi\) | |||||||
\(128\) | 7.12793 | + | 4.11531i | 0.630026 | + | 0.363746i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.97399 | − | 3.41906i | 0.172469 | − | 0.298724i | −0.766814 | − | 0.641870i | \(-0.778159\pi\) |
0.939282 | + | 0.343145i | \(0.111492\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.71577 | − | 3.40967i | 0.148776 | − | 0.295656i | ||||
\(134\) | − | 6.39722i | − | 0.552635i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −30.9302 | + | 17.8576i | −2.65225 | + | 1.53127i | ||||
\(137\) | −4.90279 | + | 2.83062i | −0.418873 | + | 0.241837i | −0.694595 | − | 0.719401i | \(-0.744416\pi\) |
0.275722 | + | 0.961237i | \(0.411083\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 23.3015i | − | 1.97640i | −0.153158 | − | 0.988202i | \(-0.548944\pi\) | ||
0.153158 | − | 0.988202i | \(-0.451056\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.4554 | − | 18.1093i | 0.877398 | − | 1.51970i | ||||
\(143\) | 9.96465 | + | 17.2593i | 0.833286 | + | 1.44329i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.06275 | −0.667278 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.03030 | −0.413488 | ||||||||
\(149\) | −4.04926 | − | 2.33784i | −0.331728 | − | 0.191523i | 0.324880 | − | 0.945755i | \(-0.394676\pi\) |
−0.656608 | + | 0.754232i | \(0.728009\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.930426 | − | 1.61155i | −0.0757170 | − | 0.131146i | 0.825681 | − | 0.564138i | \(-0.190791\pi\) |
−0.901398 | + | 0.432992i | \(0.857458\pi\) | |||||||
\(152\) | −4.82201 | + | 8.35196i | −0.391116 | + | 0.677433i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.19799 | − | 38.2576i | −0.177119 | − | 3.08289i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.68802 | + | 3.28398i | −0.453953 | + | 0.262090i | −0.709498 | − | 0.704707i | \(-0.751078\pi\) |
0.255545 | + | 0.966797i | \(0.417745\pi\) | |||||||
\(158\) | 28.4930 | − | 16.4505i | 2.26678 | − | 1.30873i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.56616 | + | 7.08687i | −0.281053 | + | 0.558524i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.38762 | − | 16.2598i | 0.735295 | − | 1.27357i | −0.219299 | − | 0.975658i | \(-0.570377\pi\) |
0.954594 | − | 0.297910i | \(-0.0962896\pi\) | |||||||
\(164\) | −15.0028 | − | 25.9856i | −1.17152 | − | 2.02914i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.0696 | − | 8.70042i | −1.16963 | − | 0.675284i | ||||
\(167\) | −4.80581 | −0.371884 | −0.185942 | − | 0.982561i | \(-0.559534\pi\) | ||||
−0.185942 | + | 0.982561i | \(0.559534\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.501166 | 0.0385512 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.11849 | + | 1.93729i | 0.0852844 | + | 0.147717i | ||||
\(173\) | −1.68189 | + | 2.91312i | −0.127872 | + | 0.221480i | −0.922852 | − | 0.385155i | \(-0.874148\pi\) |
0.794980 | + | 0.606635i | \(0.207481\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 44.9396i | 3.38745i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −22.9863 | + | 13.2712i | −1.72290 | + | 0.994715i | ||||
\(179\) | −9.63782 | + | 5.56440i | −0.720365 | + | 0.415903i | −0.814887 | − | 0.579620i | \(-0.803201\pi\) |
0.0945223 | + | 0.995523i | \(0.469868\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.19549i | − | 0.163190i | −0.996666 | − | 0.0815949i | \(-0.973999\pi\) | ||
0.996666 | − | 0.0815949i | \(-0.0260014\pi\) | |||||||
\(182\) | 21.4683 | + | 10.8030i | 1.59134 | + | 0.800771i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 10.0223 | − | 17.3592i | 0.738857 | − | 1.27974i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 26.0831 | + | 15.0591i | 1.90739 | + | 1.10123i | ||||
\(188\) | −19.5862 | −1.42847 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.62053 | + | 4.97707i | 0.623760 | + | 0.360128i | 0.778331 | − | 0.627854i | \(-0.216066\pi\) |
−0.154572 | + | 0.987982i | \(0.549400\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.4747 | + | 21.6068i | 0.897948 | + | 1.55529i | 0.830114 | + | 0.557594i | \(0.188275\pi\) |
0.0678339 | + | 0.997697i | \(0.478391\pi\) | |||||||
\(194\) | −18.9261 | + | 32.7810i | −1.35882 | + | 2.35354i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −19.1948 | − | 25.8681i | −1.37105 | − | 1.84772i | ||||
\(197\) | 19.1023i | 1.36098i | 0.732755 | + | 0.680492i | \(0.238234\pi\) | ||||
−0.732755 | + | 0.680492i | \(0.761766\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.59632 | + | 0.921633i | −0.113160 | + | 0.0653329i | −0.555512 | − | 0.831509i | \(-0.687478\pi\) |
0.442352 | + | 0.896842i | \(0.354144\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 38.3701i | − | 2.69971i | ||||||
\(203\) | 5.79533 | − | 0.332956i | 0.406753 | − | 0.0233689i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.02968 | − | 8.71167i | −0.350435 | − | 0.606971i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −24.4083 | − | 14.0921i | −1.69241 | − | 0.977114i | ||||
\(209\) | 8.13269 | 0.562550 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.77713 | −0.673085 | −0.336543 | − | 0.941668i | \(-0.609258\pi\) | ||||
−0.336543 | + | 0.941668i | \(0.609258\pi\) | |||||||
\(212\) | 16.0285 | + | 9.25406i | 1.10084 | + | 0.635571i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −19.0417 | − | 32.9811i | −1.30166 | − | 2.25454i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.21164 | − | 3.36841i | −0.150136 | − | 0.228663i | ||||
\(218\) | 28.3624i | 1.92094i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.3583 | + | 9.44444i | −1.10038 | + | 0.635302i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.84782i | 0.525529i | 0.964860 | + | 0.262765i | \(0.0846342\pi\) | ||||
−0.964860 | + | 0.262765i | \(0.915366\pi\) | |||||||
\(224\) | 10.3303 | + | 15.7334i | 0.690220 | + | 1.05123i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.69057 | − | 16.7846i | 0.644607 | − | 1.11649i | ||||
\(227\) | −0.274741 | − | 0.475865i | −0.0182352 | − | 0.0315843i | 0.856764 | − | 0.515709i | \(-0.172471\pi\) |
−0.874999 | + | 0.484125i | \(0.839138\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.5833 | + | 10.7291i | 1.22802 | + | 0.708998i | 0.966616 | − | 0.256231i | \(-0.0824807\pi\) |
0.261406 | + | 0.965229i | \(0.415814\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.6665 | −0.962902 | ||||||||
\(233\) | −16.2522 | − | 9.38319i | −1.06471 | − | 0.614713i | −0.137982 | − | 0.990435i | \(-0.544061\pi\) |
−0.926733 | + | 0.375722i | \(0.877395\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 26.2746 | − | 45.5089i | 1.71033 | − | 2.96238i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 36.2604 | − | 2.08325i | 2.35041 | − | 0.135037i | ||||
\(239\) | 7.35866i | 0.475992i | 0.971266 | + | 0.237996i | \(0.0764905\pi\) | ||||
−0.971266 | + | 0.237996i | \(0.923509\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.8467 | − | 13.7679i | 1.53610 | − | 0.886868i | 0.537040 | − | 0.843557i | \(-0.319543\pi\) |
0.999062 | − | 0.0433114i | \(-0.0137908\pi\) | |||||||
\(242\) | 46.2321 | − | 26.6921i | 2.97191 | − | 1.71583i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 32.2511i | 2.06466i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.55024 | + | 4.41715i | −0.162268 | + | 0.281057i | ||||
\(248\) | 5.09052 | + | 8.81704i | 0.323248 | + | 0.559883i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.4204 | −1.41516 | −0.707582 | − | 0.706631i | \(-0.750214\pi\) | ||||
−0.707582 | + | 0.706631i | \(0.750214\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.9035 | −1.06271 | ||||||||
\(254\) | −8.76072 | − | 5.05801i | −0.549697 | − | 0.317368i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.9079 | + | 22.3571i | 0.806743 | + | 1.39732i | ||||
\(257\) | 8.56373 | − | 14.8328i | 0.534191 | − | 0.925246i | −0.465011 | − | 0.885305i | \(-0.653950\pi\) |
0.999202 | − | 0.0399409i | \(-0.0127170\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.58353 | + | 1.30005i | 0.160533 | + | 0.0807810i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.78483 | − | 5.07193i | 0.542729 | − | 0.313345i | ||||
\(263\) | 1.40092 | − | 0.808821i | 0.0863844 | − | 0.0498741i | −0.456186 | − | 0.889885i | \(-0.650785\pi\) |
0.542570 | + | 0.840011i | \(0.317451\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.19819 | − | 5.38278i | 0.502664 | − | 0.330040i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.72862 | − | 9.92226i | 0.349931 | − | 0.606099i | ||||
\(269\) | −5.84048 | − | 10.1160i | −0.356101 | − | 0.616784i | 0.631205 | − | 0.775616i | \(-0.282561\pi\) |
−0.987306 | + | 0.158832i | \(0.949227\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.05562 | + | 2.91886i | 0.307107 | + | 0.177308i | 0.645631 | − | 0.763649i | \(-0.276594\pi\) |
−0.338524 | + | 0.940958i | \(0.609928\pi\) | |||||||
\(272\) | −42.5936 | −2.58261 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.5459 | −0.878748 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.29998 | + | 14.3760i | 0.498698 | + | 0.863770i | 0.999999 | − | 0.00150328i | \(-0.000478509\pi\) |
−0.501301 | + | 0.865273i | \(0.667145\pi\) | |||||||
\(278\) | 29.9351 | − | 51.8491i | 1.79539 | − | 3.10970i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.4255i | − | 1.21848i | −0.792984 | − | 0.609242i | \(-0.791474\pi\) | ||
0.792984 | − | 0.609242i | \(-0.208526\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.74423 | + | 3.31643i | −0.341459 | + | 0.197141i | −0.660917 | − | 0.750459i | \(-0.729832\pi\) |
0.319458 | + | 0.947600i | \(0.396499\pi\) | |||||||
\(284\) | 32.4333 | − | 18.7254i | 1.92456 | − | 1.11115i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 51.2058i | 3.02786i | ||||||||
\(287\) | 0.989529 | + | 17.2234i | 0.0584100 | + | 1.01667i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.77293 | + | 9.99901i | −0.339584 | + | 0.588177i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12.5055 | − | 7.22008i | −0.731832 | − | 0.422523i | ||||
\(293\) | −16.3716 | −0.956437 | −0.478219 | − | 0.878241i | \(-0.658717\pi\) | ||||
−0.478219 | + | 0.878241i | \(0.658717\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.32832 | − | 3.65366i | −0.367826 | − | 0.212365i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.00678 | − | 10.4040i | −0.347963 | − | 0.602690i | ||||
\(299\) | 5.30058 | − | 9.18087i | 0.306540 | − | 0.530944i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0737717 | − | 1.28405i | −0.00425213 | − | 0.0740113i | ||||
\(302\) | − | 4.78122i | − | 0.275129i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.96047 | + | 5.75068i | −0.571272 | + | 0.329824i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 25.5071i | − | 1.45576i | −0.685702 | − | 0.727882i | \(-0.740505\pi\) | ||
0.685702 | − | 0.727882i | \(-0.259495\pi\) | |||||||
\(308\) | 30.8500 | − | 61.3069i | 1.75784 | − | 3.49329i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.5180 | + | 26.8780i | 0.879946 | + | 1.52411i | 0.851399 | + | 0.524519i | \(0.175755\pi\) |
0.0285476 | + | 0.999592i | \(0.490912\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.0310 | − | 7.52345i | −0.736556 | − | 0.425251i | 0.0842599 | − | 0.996444i | \(-0.473147\pi\) |
−0.820816 | + | 0.571193i | \(0.806481\pi\) | |||||||
\(314\) | −16.8755 | −0.952341 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 58.9247 | 3.31477 | ||||||||
\(317\) | −13.4937 | − | 7.79061i | −0.757884 | − | 0.437564i | 0.0706518 | − | 0.997501i | \(-0.477492\pi\) |
−0.828535 | + | 0.559937i | \(0.810825\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.18404 | + | 10.7111i | 0.346240 | + | 0.599705i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −17.0396 | + | 11.1879i | −0.949581 | + | 0.623477i | ||||
\(323\) | 7.70812i | 0.428891i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 41.7776 | − | 24.1203i | 2.31385 | − | 1.33590i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 43.5880i | − | 2.40675i | ||||||
\(329\) | 10.0594 | + | 5.06194i | 0.554591 | + | 0.279074i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.83411 | + | 11.8370i | −0.375637 | + | 0.650622i | −0.990422 | − | 0.138073i | \(-0.955909\pi\) |
0.614785 | + | 0.788694i | \(0.289243\pi\) | |||||||
\(332\) | −15.5822 | − | 26.9892i | −0.855186 | − | 1.48123i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.6936 | − | 6.17395i | −0.585128 | − | 0.337824i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.8443 | −1.24441 | −0.622204 | − | 0.782855i | \(-0.713763\pi\) | ||||
−0.622204 | + | 0.782855i | \(0.713763\pi\) | |||||||
\(338\) | 1.11516 | + | 0.643841i | 0.0606570 | + | 0.0350203i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.29278 | − | 7.43531i | 0.232467 | − | 0.402645i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.17287 | + | 18.2464i | 0.171319 | + | 0.985216i | ||||
\(344\) | 3.24959i | 0.175206i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.48488 | + | 4.32140i | −0.402390 | + | 0.232320i | ||||
\(347\) | −16.9956 | + | 9.81241i | −0.912372 | + | 0.526758i | −0.881193 | − | 0.472756i | \(-0.843259\pi\) |
−0.0311781 | + | 0.999514i | \(0.509926\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.14050i | 0.328693i | 0.986403 | + | 0.164347i | \(0.0525516\pi\) | ||||
−0.986403 | + | 0.164347i | \(0.947448\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −20.0510 | + | 34.7293i | −1.06872 | + | 1.85108i | ||||
\(353\) | −12.0021 | − | 20.7882i | −0.638805 | − | 1.10644i | −0.985695 | − | 0.168537i | \(-0.946096\pi\) |
0.346890 | − | 0.937906i | \(-0.387238\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −47.5366 | −2.51943 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −28.5940 | −1.51124 | ||||||||
\(359\) | −14.6798 | − | 8.47541i | −0.774773 | − | 0.447315i | 0.0598018 | − | 0.998210i | \(-0.480953\pi\) |
−0.834575 | + | 0.550895i | \(0.814286\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.45930 | − | 14.6519i | −0.445227 | − | 0.771155i | ||||
\(362\) | 2.82052 | − | 4.88529i | 0.148243 | − | 0.256765i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 23.6240 | + | 35.9803i | 1.23824 | + | 1.88588i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.3140 | + | 17.5018i | −1.58238 | + | 0.913587i | −0.587869 | + | 0.808956i | \(0.700033\pi\) |
−0.994511 | + | 0.104631i | \(0.966634\pi\) | |||||||
\(368\) | 20.7024 | − | 11.9526i | 1.07919 | − | 0.623070i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.84048 | − | 8.89529i | −0.303223 | − | 0.461820i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.99576 | − | 5.18881i | 0.155115 | − | 0.268667i | −0.777986 | − | 0.628282i | \(-0.783759\pi\) |
0.933101 | + | 0.359615i | \(0.117092\pi\) | |||||||
\(374\) | 38.6924 | + | 67.0173i | 2.00074 | + | 3.46538i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.6403 | − | 14.2261i | −1.27073 | − | 0.733655i | ||||
\(377\) | −7.75675 | −0.399493 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.12842 | 0.160696 | 0.0803481 | − | 0.996767i | \(-0.474397\pi\) | ||||
0.0803481 | + | 0.996767i | \(0.474397\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.7879 | + | 22.1494i | 0.654288 | + | 1.13326i | ||||
\(383\) | −8.48295 | + | 14.6929i | −0.433459 | + | 0.750772i | −0.997168 | − | 0.0752006i | \(-0.976040\pi\) |
0.563710 | + | 0.825973i | \(0.309374\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 64.1043i | 3.26282i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −58.7099 | + | 33.8961i | −2.98054 | + | 1.72082i | ||||
\(389\) | 0.389255 | − | 0.224737i | 0.0197360 | − | 0.0113946i | −0.490100 | − | 0.871666i | \(-0.663040\pi\) |
0.509836 | + | 0.860272i | \(0.329706\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 16.0210i | − | 0.810218i | ||||||
\(392\) | −5.35903 | − | 46.4849i | −0.270672 | − | 2.34784i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −24.5405 | + | 42.5054i | −1.23633 | + | 2.14139i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.6870 | + | 11.3663i | 0.988064 | + | 0.570459i | 0.904695 | − | 0.426060i | \(-0.140099\pi\) |
0.0833689 | + | 0.996519i | \(0.473432\pi\) | |||||||
\(398\) | −4.73604 | −0.237396 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.41308 | + | 4.85729i | 0.420129 | + | 0.242562i | 0.695132 | − | 0.718882i | \(-0.255346\pi\) |
−0.275004 | + | 0.961443i | \(0.588679\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.69225 | + | 4.66312i | 0.134111 | + | 0.232287i | ||||
\(404\) | 34.3599 | − | 59.5132i | 1.70947 | − | 2.96089i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.3232 | + | 6.70431i | 0.661219 | + | 0.332729i | ||||
\(407\) | 6.16218i | 0.305448i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.51628 | + | 2.03013i | −0.173869 | + | 0.100383i | −0.584409 | − | 0.811459i | \(-0.698674\pi\) |
0.410540 | + | 0.911843i | \(0.365340\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 18.0161i | − | 0.887587i | ||||||
\(413\) | −25.2559 | + | 16.5826i | −1.24276 | + | 0.815976i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −12.5752 | − | 21.7808i | −0.616548 | − | 1.06789i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.0964 | + | 10.4480i | 0.885124 | + | 0.511026i | ||||
\(419\) | 20.9314 | 1.02257 | 0.511283 | − | 0.859412i | \(-0.329170\pi\) | ||||
0.511283 | + | 0.859412i | \(0.329170\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.7795 | −0.963992 | −0.481996 | − | 0.876173i | \(-0.660088\pi\) | ||||
−0.481996 | + | 0.876173i | \(0.660088\pi\) | |||||||
\(422\) | −21.7555 | − | 12.5605i | −1.05904 | − | 0.611438i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.4430 | + | 23.2840i | 0.652851 | + | 1.13077i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.33508 | − | 16.5639i | 0.403363 | − | 0.801585i | ||||
\(428\) | − | 68.2062i | − | 3.29687i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.23148 | − | 5.32980i | 0.444665 | − | 0.256727i | −0.260910 | − | 0.965363i | \(-0.584022\pi\) |
0.705574 | + | 0.708636i | \(0.250689\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 21.2351i | − | 1.02050i | −0.860028 | − | 0.510248i | \(-0.829554\pi\) | ||
0.860028 | − | 0.510248i | \(-0.170446\pi\) | |||||||
\(434\) | −0.593855 | − | 10.3365i | −0.0285060 | − | 0.496166i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −25.3981 | + | 43.9908i | −1.21635 | + | 2.10678i | ||||
\(437\) | −2.16304 | − | 3.74650i | −0.103472 | − | 0.179220i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.5707 | − | 10.7218i | −0.886333 | − | 0.511725i | −0.0135918 | − | 0.999908i | \(-0.504327\pi\) |
−0.872741 | + | 0.488183i | \(0.837660\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −48.5326 | −2.30846 | ||||||||
\(443\) | −0.148064 | − | 0.0854851i | −0.00703475 | − | 0.00406152i | 0.496478 | − | 0.868049i | \(-0.334626\pi\) |
−0.503513 | + | 0.863988i | \(0.667959\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.0820 | + | 17.4625i | −0.477396 | + | 0.826874i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.354212 | + | 6.16531i | 0.0167350 | + | 0.291283i | ||||
\(449\) | 9.38752i | 0.443025i | 0.975158 | + | 0.221512i | \(0.0710993\pi\) | ||||
−0.975158 | + | 0.221512i | \(0.928901\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.8328 | + | 18.3786i | −1.49895 | + | 0.865417i | ||||
\(452\) | 30.0607 | − | 17.3556i | 1.41394 | − | 0.816337i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 1.41182i | − | 0.0662602i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.44623 | − | 14.6293i | 0.395098 | − | 0.684330i | −0.598016 | − | 0.801484i | \(-0.704044\pi\) |
0.993114 | + | 0.117155i | \(0.0373774\pi\) | |||||||
\(458\) | 27.5670 | + | 47.7475i | 1.28812 | + | 2.23110i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.0360 | 1.44549 | 0.722746 | − | 0.691113i | \(-0.242880\pi\) | ||||
0.722746 | + | 0.691113i | \(0.242880\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.9434 | 0.555055 | 0.277528 | − | 0.960718i | \(-0.410485\pi\) | ||||
0.277528 | + | 0.960718i | \(0.410485\pi\) | |||||||
\(464\) | −15.1477 | − | 8.74555i | −0.703216 | − | 0.406002i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.1089 | − | 41.7579i | −1.11682 | − | 1.93440i | ||||
\(467\) | 17.2803 | − | 29.9304i | 0.799638 | − | 1.38501i | −0.120215 | − | 0.992748i | \(-0.538358\pi\) |
0.919852 | − | 0.392265i | \(-0.128308\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.50653 | + | 3.61549i | −0.254268 | + | 0.166948i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 66.1090 | − | 38.1681i | 3.04292 | − | 1.75683i | ||||
\(473\) | 2.37321 | − | 1.37017i | 0.109120 | − | 0.0630006i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 58.1064 | + | 29.2395i | 2.66330 | + | 1.34019i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.45357 | + | 16.3741i | −0.432396 | + | 0.748932i | ||||
\(479\) | 1.48615 | + | 2.57409i | 0.0679040 | + | 0.117613i | 0.897978 | − | 0.440039i | \(-0.145036\pi\) |
−0.830074 | + | 0.557653i | \(0.811702\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.34690 | − | 1.93233i | −0.152605 | − | 0.0881068i | ||||
\(482\) | 70.7498 | 3.22256 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 95.6097 | 4.34589 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.3562 | + | 19.6695i | 0.514598 | + | 0.891310i | 0.999857 | + | 0.0169394i | \(0.00539222\pi\) |
−0.485258 | + | 0.874371i | \(0.661274\pi\) | |||||||
\(488\) | −23.4249 | + | 40.5732i | −1.06040 | + | 1.83666i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.0036i | 0.586846i | 0.955983 | + | 0.293423i | \(0.0947944\pi\) | ||||
−0.955983 | + | 0.293423i | \(0.905206\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.1519 | + | 5.86120i | −0.457219 | + | 0.263975i | ||||
\(494\) | −11.3493 | + | 6.55253i | −0.510630 | + | 0.294812i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.1418i | 0.545184i | ||||||||
\(497\) | −21.4970 | + | 1.23505i | −0.964271 | + | 0.0553997i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.8039 | + | 18.7129i | −0.483648 | + | 0.837702i | −0.999824 | − | 0.0187802i | \(-0.994022\pi\) |
0.516176 | + | 0.856483i | \(0.327355\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −49.8886 | − | 28.8032i | −2.22664 | − | 1.28555i | ||||
\(503\) | 32.4125 | 1.44520 | 0.722601 | − | 0.691265i | \(-0.242946\pi\) | ||||
0.722601 | + | 0.691265i | \(0.242946\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −37.6126 | − | 21.7157i | −1.67209 | − | 0.965379i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.05875 | − | 15.6902i | −0.401917 | − | 0.696141i | ||||
\(509\) | 18.2802 | − | 31.6622i | 0.810255 | − | 1.40340i | −0.102430 | − | 0.994740i | \(-0.532662\pi\) |
0.912685 | − | 0.408663i | \(-0.134005\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.55679 | + | 6.94017i | 0.201580 | + | 0.307015i | ||||
\(512\) | 49.8691i | 2.20392i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 38.1110 | − | 22.0034i | 1.68101 | − | 0.970529i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.9934i | 1.05523i | ||||||||
\(518\) | 4.07856 | + | 6.21181i | 0.179202 | + | 0.272931i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.43608 | − | 16.3438i | −0.413402 | − | 0.716033i | 0.581857 | − | 0.813291i | \(-0.302326\pi\) |
−0.995259 | + | 0.0972577i | \(0.968993\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.4434 | + | 14.1124i | 1.06884 | + | 0.617092i | 0.927863 | − | 0.372921i | \(-0.121644\pi\) |
0.140972 | + | 0.990014i | \(0.454977\pi\) | |||||||
\(524\) | 18.1674 | 0.793645 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.15633 | 0.181225 | ||||||||
\(527\) | 7.04715 | + | 4.06867i | 0.306979 | + | 0.177234i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00420 | − | 12.1316i | −0.304530 | − | 0.527462i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 17.5358 | − | 1.00748i | 0.760275 | − | 0.0436797i | ||||
\(533\) | − | 23.0527i | − | 0.998521i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 14.4137 | − | 8.32175i | 0.622577 | − | 0.359445i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 30.0128i | − | 1.29394i | ||||||
\(539\) | −31.6888 | + | 23.5139i | −1.36493 | + | 1.01281i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.2269 | + | 24.6417i | −0.611661 | + | 1.05943i | 0.379299 | + | 0.925274i | \(0.376165\pi\) |
−0.990960 | + | 0.134154i | \(0.957168\pi\) | |||||||
\(542\) | 7.49965 | + | 12.9898i | 0.322138 | + | 0.557959i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −32.9163 | − | 19.0042i | −1.41127 | − | 0.814799i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.9338 | 0.937820 | 0.468910 | − | 0.883246i | \(-0.344647\pi\) | ||||
0.468910 | + | 0.883246i | \(0.344647\pi\) | |||||||
\(548\) | −22.5610 | − | 13.0256i | −0.963760 | − | 0.556427i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.58268 | + | 2.74127i | −0.0674242 | + | 0.116782i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.2633 | − | 15.2287i | −1.28693 | − | 0.647590i | ||||
\(554\) | 42.6515i | 1.81209i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 92.8603 | − | 53.6129i | 3.93815 | − | 2.27369i | ||||
\(557\) | −21.1601 | + | 12.2168i | −0.896583 | + | 0.517643i | −0.876090 | − | 0.482147i | \(-0.839857\pi\) |
−0.0204933 | + | 0.999790i | \(0.506524\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.71863i | 0.0726903i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 26.2404 | − | 45.4497i | 1.10688 | − | 1.91718i | ||||
\(563\) | 10.6570 | + | 18.4585i | 0.449139 | + | 0.777932i | 0.998330 | − | 0.0577647i | \(-0.0183973\pi\) |
−0.549191 | + | 0.835697i | \(0.685064\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −17.0423 | −0.716341 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 54.4032 | 2.28271 | ||||||||
\(569\) | 24.1707 | + | 13.9549i | 1.01329 | + | 0.585022i | 0.912152 | − | 0.409851i | \(-0.134419\pi\) |
0.101135 | + | 0.994873i | \(0.467753\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.1936 | + | 40.1725i | 0.970622 | + | 1.68117i | 0.693685 | + | 0.720279i | \(0.255986\pi\) |
0.276937 | + | 0.960888i | \(0.410681\pi\) | |||||||
\(572\) | −45.8541 | + | 79.4217i | −1.91726 | + | 3.32079i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −19.9249 | + | 39.5958i | −0.831648 | + | 1.65270i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.0881 | + | 16.2167i | −1.16932 | + | 0.675108i | −0.953520 | − | 0.301329i | \(-0.902570\pi\) |
−0.215801 | + | 0.976437i | \(0.569236\pi\) | |||||||
\(578\) | −25.6912 | + | 14.8328i | −1.06861 | + | 0.616964i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.02774 | + | 17.8886i | 0.0426380 | + | 0.742145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.3363 | − | 19.6351i | 0.469504 | − | 0.813204i | ||||
\(584\) | −10.4883 | − | 18.1663i | −0.434011 | − | 0.751728i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −36.4291 | − | 21.0323i | −1.50487 | − | 0.868838i | ||||
\(587\) | 0.790380 | 0.0326225 | 0.0163112 | − | 0.999867i | \(-0.494808\pi\) | ||||
0.0163112 | + | 0.999867i | \(0.494808\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.19729 | 0.0905379 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.35732 | − | 7.54710i | −0.179085 | − | 0.310184i | ||||
\(593\) | 10.1424 | − | 17.5672i | 0.416499 | − | 0.721397i | −0.579086 | − | 0.815267i | \(-0.696590\pi\) |
0.995585 | + | 0.0938695i | \(0.0299236\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 21.5160i | − | 0.881328i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 23.5891 | − | 13.6192i | 0.964630 | − | 0.556929i | ||||
\(599\) | −8.77781 | + | 5.06787i | −0.358652 | + | 0.207068i | −0.668489 | − | 0.743722i | \(-0.733059\pi\) |
0.309837 | + | 0.950790i | \(0.399725\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.6657i | 1.45483i | 0.686196 | + | 0.727417i | \(0.259279\pi\) | ||||
−0.686196 | + | 0.727417i | \(0.740721\pi\) | |||||||
\(602\) | 1.48545 | − | 2.95196i | 0.0605423 | − | 0.120313i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.28152 | − | 7.41581i | 0.174213 | − | 0.301745i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.7475 | + | 13.1333i | 0.923292 | + | 0.533063i | 0.884684 | − | 0.466192i | \(-0.154374\pi\) |
0.0386080 | + | 0.999254i | \(0.487708\pi\) | |||||||
\(608\) | −10.2633 | −0.416230 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.0317 | − | 7.52384i | −0.527205 | − | 0.304382i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.9410 | + | 22.4144i | 0.522681 | + | 0.905310i | 0.999652 | + | 0.0263906i | \(0.00840138\pi\) |
−0.476971 | + | 0.878919i | \(0.658265\pi\) | |||||||
\(614\) | 32.7686 | − | 56.7568i | 1.32243 | − | 2.29052i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 83.3398 | − | 54.7194i | 3.35786 | − | 2.20471i | ||||
\(617\) | − | 16.1754i | − | 0.651198i | −0.945508 | − | 0.325599i | \(-0.894434\pi\) | ||
0.945508 | − | 0.325599i | \(-0.105566\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.29108 | + | 3.05481i | −0.212667 | + | 0.122783i | −0.602550 | − | 0.798081i | \(-0.705849\pi\) |
0.389883 | + | 0.920864i | \(0.372515\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 79.7432i | 3.19741i | ||||||||
\(623\) | 24.4145 | + | 12.2855i | 0.978145 | + | 0.492209i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −19.3306 | − | 33.4815i | −0.772605 | − | 1.33819i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −26.1744 | − | 15.1118i | −1.04447 | − | 0.603027i | ||||
\(629\) | −5.84048 | −0.232875 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.89949 | 0.0756174 | 0.0378087 | − | 0.999285i | \(-0.487962\pi\) | ||||
0.0378087 | + | 0.999285i | \(0.487962\pi\) | |||||||
\(632\) | 74.1297 | + | 42.7988i | 2.94872 | + | 1.70245i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −20.0170 | − | 34.6704i | −0.794976 | − | 1.37694i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.83426 | − | 24.5847i | −0.112298 | − | 0.974083i | ||||
\(638\) | 31.7782i | 1.25811i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.82533 | + | 5.67266i | −0.388077 | + | 0.224057i | −0.681327 | − | 0.731979i | \(-0.738597\pi\) |
0.293249 | + | 0.956036i | \(0.405263\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.2255i | 0.718742i | 0.933195 | + | 0.359371i | \(0.117009\pi\) | ||||
−0.933195 | + | 0.359371i | \(0.882991\pi\) | |||||||
\(644\) | −36.4476 | + | 2.09400i | −1.43623 | + | 0.0825152i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.90252 | + | 17.1517i | −0.389609 | + | 0.674823i | ||||
\(647\) | 12.2706 | + | 21.2533i | 0.482406 | + | 0.835552i | 0.999796 | − | 0.0201980i | \(-0.00642966\pi\) |
−0.517390 | + | 0.855750i | \(0.673096\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −55.7490 | − | 32.1867i | −2.18834 | − | 1.26344i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 86.3976 | 3.38359 | ||||||||
\(653\) | 7.58043 | + | 4.37656i | 0.296645 | + | 0.171268i | 0.640935 | − | 0.767595i | \(-0.278547\pi\) |
−0.344290 | + | 0.938863i | \(0.611880\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 25.9913 | − | 45.0183i | 1.01479 | − | 1.75767i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15.8805 | + | 24.1867i | 0.619087 | + | 0.942894i | ||||
\(659\) | − | 2.51324i | − | 0.0979020i | −0.998801 | − | 0.0489510i | \(-0.984412\pi\) | ||
0.998801 | − | 0.0489510i | \(-0.0155878\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.5393 | + | 19.9413i | −1.34342 | + | 0.775626i | −0.987308 | − | 0.158815i | \(-0.949233\pi\) |
−0.356116 | + | 0.934442i | \(0.615899\pi\) | |||||||
\(662\) | −30.4137 | + | 17.5594i | −1.18206 | + | 0.682465i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 45.2714i | − | 1.75687i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.28953 | − | 5.69763i | 0.127371 | − | 0.220613i | ||||
\(668\) | −11.0574 | − | 19.1520i | −0.427823 | − | 0.741011i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.5080 | 1.52519 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.0634 | 1.39014 | 0.695071 | − | 0.718941i | \(-0.255373\pi\) | ||||
0.695071 | + | 0.718941i | \(0.255373\pi\) | |||||||
\(674\) | −50.8318 | − | 29.3478i | −1.95797 | − | 1.13043i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.15310 | + | 1.99723i | 0.0443501 | + | 0.0768166i | ||||
\(677\) | 3.95189 | − | 6.84487i | 0.151883 | − | 0.263070i | −0.780036 | − | 0.625734i | \(-0.784800\pi\) |
0.931920 | + | 0.362664i | \(0.118133\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.9132 | − | 2.23566i | 1.49335 | − | 0.0857968i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 19.1041 | − | 11.0298i | 0.731534 | − | 0.422351i | ||||
\(683\) | 21.8984 | − | 12.6430i | 0.837918 | − | 0.483772i | −0.0186377 | − | 0.999826i | \(-0.505933\pi\) |
0.856556 | + | 0.516054i | \(0.172600\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −16.3809 | + | 44.6771i | −0.625425 | + | 1.70578i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.93772 | + | 3.35622i | −0.0738747 | + | 0.127955i | ||||
\(689\) | 7.10969 | + | 12.3143i | 0.270858 | + | 0.469139i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.1380 | − | 7.58522i | −0.499792 | − | 0.288555i | 0.228835 | − | 0.973465i | \(-0.426508\pi\) |
−0.728628 | + | 0.684910i | \(0.759842\pi\) | |||||||
\(692\) | −15.4790 | −0.588424 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −50.4235 | −1.91405 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.4192 | − | 30.1709i | −0.659799 | − | 1.14280i | ||||
\(698\) | −7.88861 | + | 13.6635i | −0.298588 | + | 0.517170i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.6815i | 1.30990i | 0.755671 | + | 0.654951i | \(0.227311\pi\) | ||||
−0.755671 | + | 0.654951i | \(0.772689\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.36579 | + | 0.788541i | −0.0515118 | + | 0.0297404i | ||||
\(704\) | −11.3949 | + | 6.57883i | −0.429460 | + | 0.247949i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 61.6755i | − | 2.32119i | ||||||
\(707\) | −33.0278 | + | 21.6855i | −1.24214 | + | 0.815566i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.2311 | − | 29.8451i | 0.647126 | − | 1.12086i | −0.336680 | − | 0.941619i | \(-0.609304\pi\) |
0.983806 | − | 0.179237i | \(-0.0573628\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −59.8030 | − | 34.5273i | −2.24121 | − | 1.29396i | ||||
\(713\) | −4.56699 | −0.171035 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −44.3502 | − | 25.6056i | −1.65744 | − | 0.956925i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −21.7765 | − | 37.7180i | −0.812692 | − | 1.40762i | ||||
\(719\) | −13.4825 | + | 23.3523i | −0.502812 | + | 0.870895i | 0.497183 | + | 0.867646i | \(0.334368\pi\) |
−0.999995 | + | 0.00324951i | \(0.998966\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.65613 | + | 9.25293i | −0.173403 | + | 0.344597i | ||||
\(722\) | − | 43.4702i | − | 1.61779i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.74942 | − | 5.05148i | 0.325170 | − | 0.187737i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.4196i | 0.386442i | 0.981155 | + | 0.193221i | \(0.0618935\pi\) | ||||
−0.981155 | + | 0.193221i | \(0.938106\pi\) | |||||||
\(728\) | 3.58639 | + | 62.4236i | 0.132921 | + | 2.31357i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.29864 | + | 2.24931i | 0.0480320 | + | 0.0831938i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.6659 | − | 11.3541i | −0.726377 | − | 0.419374i | 0.0907181 | − | 0.995877i | \(-0.471084\pi\) |
−0.817095 | + | 0.576503i | \(0.804417\pi\) | |||||||
\(734\) | −89.9374 | −3.31965 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.3318 | 0.786300 | ||||||||
\(737\) | −12.1549 | − | 7.01764i | −0.447732 | − | 0.258498i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.8897 | + | 25.7898i | 0.547728 | + | 0.948692i | 0.998430 | + | 0.0560176i | \(0.0178403\pi\) |
−0.450702 | + | 0.892674i | \(0.648826\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.56825 | − | 27.2965i | −0.0575723 | − | 1.00209i | ||||
\(743\) | 34.8044i | 1.27685i | 0.769684 | + | 0.638424i | \(0.220414\pi\) | ||||
−0.769684 | + | 0.638424i | \(0.779586\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 13.3320 | − | 7.69723i | 0.488119 | − | 0.281816i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 138.594i | 5.06751i | ||||||||
\(749\) | −17.6275 | + | 35.0303i | −0.644093 | + | 1.27998i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.74522 | + | 6.48691i | −0.136665 | + | 0.236711i | −0.926232 | − | 0.376953i | \(-0.876972\pi\) |
0.789567 | + | 0.613664i | \(0.210305\pi\) | |||||||
\(752\) | −16.9659 | − | 29.3858i | −0.618683 | − | 1.07159i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −17.2599 | − | 9.96499i | −0.628568 | − | 0.362904i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.66139 | −0.0967300 | −0.0483650 | − | 0.998830i | \(-0.515401\pi\) | ||||
−0.0483650 | + | 0.998830i | \(0.515401\pi\) | |||||||
\(758\) | 6.96118 | + | 4.01904i | 0.252842 | + | 0.145978i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.78479 | + | 4.82340i | −0.100949 | + | 0.174848i | −0.912076 | − | 0.410022i | \(-0.865521\pi\) |
0.811127 | + | 0.584870i | \(0.198854\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.4135 | − | 16.0294i | 0.883827 | − | 0.580304i | ||||
\(764\) | 45.8057i | 1.65719i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −37.7516 | + | 21.7959i | −1.36402 | + | 0.787517i | ||||
\(767\) | 34.9635 | − | 20.1862i | 1.26246 | − | 0.728881i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 11.5002i | − | 0.414709i | −0.978266 | − | 0.207355i | \(-0.933515\pi\) | ||
0.978266 | − | 0.207355i | \(-0.0664854\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −57.4045 | + | 99.4275i | −2.06603 | + | 3.57847i | ||||
\(773\) | −12.6872 | − | 21.9748i | −0.456325 | − | 0.790378i | 0.542438 | − | 0.840096i | \(-0.317501\pi\) |
−0.998763 | + | 0.0497174i | \(0.984168\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −98.4793 | −3.53520 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.15486 | 0.0414039 | ||||||||
\(779\) | −8.14692 | − | 4.70363i | −0.291894 | − | 0.168525i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.9388 | − | 39.7312i | −0.820816 | − | 1.42169i | ||||
\(782\) | 20.5820 | − | 35.6491i | 0.736011 | − | 1.27481i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 22.1838 | − | 51.2058i | 0.792280 | − | 1.82878i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.7789 | + | 11.9967i | −0.740688 | + | 0.427636i | −0.822319 | − | 0.569026i | \(-0.807320\pi\) |
0.0816315 | + | 0.996663i | \(0.473987\pi\) | |||||||
\(788\) | −76.1260 | + | 43.9514i | −2.71188 | + | 1.56570i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.9244 | + | 1.14471i | −0.708431 | + | 0.0407011i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.3889 | + | 21.4582i | −0.439942 | + | 0.762002i | ||||
\(794\) | 29.2043 | + | 50.5833i | 1.03642 | + | 1.79514i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.34573 | − | 4.24106i | −0.260363 | − | 0.150320i | ||||
\(797\) | 28.1188 | 0.996020 | 0.498010 | − | 0.867171i | \(-0.334064\pi\) | ||||
0.498010 | + | 0.867171i | \(0.334064\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.7408 | −0.804513 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.4802 | + | 21.6163i | 0.440691 | + | 0.763299i | ||||
\(803\) | −8.84470 | + | 15.3195i | −0.312123 | + | 0.540612i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.8348i | 0.487310i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 86.4525 | − | 49.9134i | 3.04139 | − | 1.75595i | ||||
\(809\) | −24.2977 | + | 14.0283i | −0.854263 | + | 0.493209i | −0.862087 | − | 0.506761i | \(-0.830843\pi\) |
0.00782425 | + | 0.999969i | \(0.497509\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 43.4980i | − | 1.52742i | −0.645559 | − | 0.763710i | \(-0.723376\pi\) | ||
0.645559 | − | 0.763710i | \(-0.276624\pi\) | |||||||
\(812\) | 14.6610 | + | 22.3293i | 0.514501 | + | 0.783605i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.91647 | + | 13.7117i | −0.277472 | + | 0.480596i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.607373 | + | 0.350667i | 0.0212493 | + | 0.0122683i | ||||
\(818\) | −10.4323 | −0.364757 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.5875 | + | 18.2371i | 1.10241 | + | 0.636477i | 0.936853 | − | 0.349723i | \(-0.113724\pi\) |
0.165558 | + | 0.986200i | \(0.447058\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.0523 | − | 39.9277i | −0.803551 | − | 1.39179i | −0.917265 | − | 0.398278i | \(-0.869608\pi\) |
0.113713 | − | 0.993514i | \(-0.463725\pi\) | |||||||
\(824\) | 13.0856 | − | 22.6650i | 0.455859 | − | 0.789571i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −77.5015 | + | 4.45265i | −2.69662 | + | 0.154928i | ||||
\(827\) | − | 20.1533i | − | 0.700800i | −0.936600 | − | 0.350400i | \(-0.886046\pi\) | ||
0.936600 | − | 0.350400i | \(-0.113954\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.13818 | + | 3.54388i | −0.213188 | + | 0.123084i | −0.602792 | − | 0.797898i | \(-0.705945\pi\) |
0.389604 | + | 0.920982i | \(0.372612\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 8.25194i | − | 0.286085i | ||||||
\(833\) | −22.2863 | − | 30.0344i | −0.772175 | − | 1.04063i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 18.7120 | + | 32.4102i | 0.647169 | + | 1.12093i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 46.5754 | + | 26.8903i | 1.60892 | + | 0.928911i | ||||
\(839\) | 33.0805 | 1.14206 | 0.571032 | − | 0.820928i | \(-0.306543\pi\) | ||||
0.571032 | + | 0.820928i | \(0.306543\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.1862 | 0.834006 | ||||||||
\(842\) | −44.0121 | − | 25.4104i | −1.51676 | − | 0.875701i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −22.4956 | − | 38.9635i | −0.774331 | − | 1.34118i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −49.1045 | − | 24.7097i | −1.68725 | − | 0.849036i | ||||
\(848\) | 32.0640i | 1.10108i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.83875 | − | 1.63895i | 0.0973109 | − | 0.0561825i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.1187i | 1.30516i | 0.757719 | + | 0.652580i | \(0.226314\pi\) | ||||
−0.757719 | + | 0.652580i | \(0.773686\pi\) | |||||||
\(854\) | 39.8262 | − | 26.1492i | 1.36282 | − | 0.894806i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 49.5403 | − | 85.8063i | 1.69325 | − | 2.93280i | ||||
\(857\) | 3.51807 | + | 6.09347i | 0.120175 | + | 0.208149i | 0.919837 | − | 0.392302i | \(-0.128321\pi\) |
−0.799662 | + | 0.600451i | \(0.794988\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.2343 | − | 12.8370i | −0.758624 | − | 0.437992i | 0.0701772 | − | 0.997535i | \(-0.477644\pi\) |
−0.828802 | + | 0.559543i | \(0.810977\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.3885 | 0.932855 | ||||||||
\(863\) | −44.1550 | − | 25.4929i | −1.50305 | − | 0.867788i | −0.999994 | − | 0.00353683i | \(-0.998874\pi\) |
−0.503060 | − | 0.864252i | \(-0.667792\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 27.2805 | − | 47.2512i | 0.927029 | − | 1.60566i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.33508 | − | 16.5639i | 0.282911 | − | 0.562217i | ||||
\(869\) | − | 72.1835i | − | 2.44866i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.62306 | − | 4.40117i | 0.258297 | − | 0.149128i | ||||
\(872\) | −63.9038 | + | 36.8949i | −2.16406 | + | 1.24942i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 11.1153i | − | 0.375982i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.2766 | − | 33.3881i | 0.650925 | − | 1.12743i | −0.331974 | − | 0.943289i | \(-0.607715\pi\) |
0.982899 | − | 0.184146i | \(-0.0589520\pi\) | |||||||
\(878\) | −27.5484 | − | 47.7152i | −0.929712 | − | 1.61031i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.4764 | 1.16154 | 0.580770 | − | 0.814068i | \(-0.302752\pi\) | ||||
0.580770 | + | 0.814068i | \(0.302752\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.5869 | −0.861068 | −0.430534 | − | 0.902574i | \(-0.641675\pi\) | ||||
−0.430534 | + | 0.902574i | \(0.641675\pi\) | |||||||
\(884\) | −75.2754 | − | 43.4603i | −2.53179 | − | 1.46173i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.219643 | − | 0.380433i | −0.00737905 | − | 0.0127809i | ||||
\(887\) | −11.8978 | + | 20.6076i | −0.399489 | + | 0.691936i | −0.993663 | − | 0.112401i | \(-0.964146\pi\) |
0.594174 | + | 0.804337i | \(0.297479\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.597481 | + | 10.3996i | 0.0200389 | + | 0.348791i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −31.2749 | + | 18.0566i | −1.04716 | + | 0.604579i | ||||
\(893\) | −5.31792 | + | 3.07031i | −0.177958 | + | 0.102744i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 9.78847 | − | 19.4522i | 0.327010 | − | 0.649852i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.0600 | + | 20.8886i | −0.402448 | + | 0.697061i | ||||
\(899\) | 1.67081 | + | 2.89392i | 0.0557245 | + | 0.0965177i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.6101 | + | 10.7445i | 0.619991 | + | 0.357952i | ||||
\(902\) | −94.4432 | −3.14461 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 50.4235 | 1.67706 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.3878 | − | 33.5806i | −0.643760 | − | 1.11503i | −0.984586 | − | 0.174899i | \(-0.944040\pi\) |
0.340826 | − | 0.940126i | \(-0.389293\pi\) | |||||||
\(908\) | 1.26427 | − | 2.18978i | 0.0419563 | − | 0.0726704i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.4438i | 1.04178i | 0.853624 | + | 0.520889i | \(0.174400\pi\) | ||||
−0.853624 | + | 0.520889i | \(0.825600\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.0622 | + | 19.0884i | −1.09420 | + | 0.631735i | ||||
\(914\) | 37.5881 | − | 21.7015i | 1.24330 | − | 0.717822i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 98.7437i | 3.26258i | ||||||||
\(917\) | −9.33064 | − | 4.69524i | −0.308125 | − | 0.155050i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.9872 | − | 24.2266i | 0.461396 | − | 0.799161i | −0.537635 | − | 0.843178i | \(-0.680682\pi\) |
0.999031 | + | 0.0440170i | \(0.0140156\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 69.0596 | + | 39.8716i | 2.27436 | + | 1.31310i | ||||
\(923\) | 28.7726 | 0.947060 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 26.5757 | + | 15.3435i | 0.873332 | + | 0.504218i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.80411 | − | 13.5171i | −0.256183 | − | 0.443721i | ||||
\(929\) | −11.2452 | + | 19.4772i | −0.368943 | + | 0.639027i | −0.989400 | − | 0.145212i | \(-0.953613\pi\) |
0.620458 | + | 0.784240i | \(0.286947\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.26667 | − | 4.01459i | −0.303703 | − | 0.131573i | ||||
\(932\) | − | 86.3568i | − | 2.82871i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 76.9023 | − | 44.3996i | 2.51632 | − | 1.45280i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.0994i | 1.04864i | 0.851521 | + | 0.524321i | \(0.175681\pi\) | ||||
−0.851521 | + | 0.524321i | \(0.824319\pi\) | |||||||
\(938\) | −16.8976 | + | 0.970808i | −0.551725 | + | 0.0316980i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.10912 | + | 8.84925i | 0.166552 | + | 0.288477i | 0.937206 | − | 0.348778i | \(-0.113403\pi\) |
−0.770653 | + | 0.637255i | \(0.780070\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.9331 | + | 9.77631i | 0.551416 | + | 0.318360i | ||||
\(944\) | 91.0378 | 2.96303 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.04097 | 0.228922 | ||||||||
\(947\) | 8.91925 | + | 5.14953i | 0.289837 | + | 0.167337i | 0.637868 | − | 0.770146i | \(-0.279816\pi\) |
−0.348031 | + | 0.937483i | \(0.613150\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.54703 | − | 9.60774i | −0.180064 | − | 0.311880i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 51.8627 | + | 78.9890i | 1.68088 | + | 2.56005i | ||||
\(953\) | 0.930159i | 0.0301308i | 0.999887 | + | 0.0150654i | \(0.00479565\pi\) | ||||
−0.999887 | + | 0.0150654i | \(0.995204\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −29.3255 | + | 16.9311i | −0.948455 | + | 0.547591i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.63696i | 0.246739i | ||||||||
\(959\) | 8.22082 | + | 12.5206i | 0.265464 | + | 0.404312i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.3402 | + | 24.8379i | −0.462586 | + | 0.801223i | ||||
\(962\) | −4.96488 | − | 8.59943i | −0.160074 | − | 0.277257i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 109.735 | + | 63.3555i | 3.53432 | + | 2.04054i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.22117 | −0.135744 | −0.0678719 | − | 0.997694i | \(-0.521621\pi\) | ||||
−0.0678719 | + | 0.997694i | \(0.521621\pi\) | |||||||
\(968\) | 120.281 | + | 69.4443i | 3.86598 | + | 2.23202i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.28935 | + | 3.96527i | −0.0734688 | + | 0.127252i | −0.900419 | − | 0.435023i | \(-0.856740\pi\) |
0.826951 | + | 0.562275i | \(0.190074\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −61.5483 | + | 3.53610i | −1.97315 | + | 0.113362i | ||||
\(974\) | 58.3566i | 1.86987i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −48.3872 | + | 27.9364i | −1.54884 | + | 0.894221i | ||||
\(977\) | 39.4138 | − | 22.7556i | 1.26096 | − | 0.728015i | 0.287698 | − | 0.957721i | \(-0.407110\pi\) |
0.973260 | + | 0.229707i | \(0.0737766\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58.2329i | 1.86113i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −16.7056 | + | 28.9350i | −0.533097 | + | 0.923351i | ||||
\(983\) | 5.25831 | + | 9.10765i | 0.167714 | + | 0.290489i | 0.937616 | − | 0.347673i | \(-0.113028\pi\) |
−0.769902 | + | 0.638162i | \(0.779695\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −30.1192 | −0.959192 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −23.4708 | −0.746706 | ||||||||
\(989\) | −1.26240 | − | 0.728847i | −0.0401420 | − | 0.0231760i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.9539 | + | 24.1689i | 0.443262 | + | 0.767752i | 0.997929 | − | 0.0643204i | \(-0.0204880\pi\) |
−0.554668 | + | 0.832072i | \(0.687155\pi\) | |||||||
\(992\) | −5.41739 | + | 9.38319i | −0.172002 | + | 0.297916i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −49.4205 | − | 24.8687i | −1.56752 | − | 0.788787i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.7000 | − | 19.4567i | 1.06729 | − | 0.616201i | 0.139851 | − | 0.990173i | \(-0.455338\pi\) |
0.927440 | + | 0.373972i | \(0.122004\pi\) | |||||||
\(998\) | −48.0803 | + | 27.7592i | −1.52196 | + | 0.878701i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1575.2.bk.i.26.11 | 24 | ||
3.2 | odd | 2 | inner | 1575.2.bk.i.26.2 | 24 | ||
5.2 | odd | 4 | 315.2.bb.b.89.1 | ✓ | 24 | ||
5.3 | odd | 4 | 315.2.bb.b.89.11 | yes | 24 | ||
5.4 | even | 2 | inner | 1575.2.bk.i.26.1 | 24 | ||
7.3 | odd | 6 | inner | 1575.2.bk.i.1151.2 | 24 | ||
15.2 | even | 4 | 315.2.bb.b.89.12 | yes | 24 | ||
15.8 | even | 4 | 315.2.bb.b.89.2 | yes | 24 | ||
15.14 | odd | 2 | inner | 1575.2.bk.i.26.12 | 24 | ||
21.17 | even | 6 | inner | 1575.2.bk.i.1151.11 | 24 | ||
35.2 | odd | 12 | 2205.2.g.b.2204.22 | 24 | |||
35.3 | even | 12 | 315.2.bb.b.269.12 | yes | 24 | ||
35.12 | even | 12 | 2205.2.g.b.2204.21 | 24 | |||
35.17 | even | 12 | 315.2.bb.b.269.2 | yes | 24 | ||
35.23 | odd | 12 | 2205.2.g.b.2204.2 | 24 | |||
35.24 | odd | 6 | inner | 1575.2.bk.i.1151.12 | 24 | ||
35.33 | even | 12 | 2205.2.g.b.2204.1 | 24 | |||
105.2 | even | 12 | 2205.2.g.b.2204.4 | 24 | |||
105.17 | odd | 12 | 315.2.bb.b.269.11 | yes | 24 | ||
105.23 | even | 12 | 2205.2.g.b.2204.24 | 24 | |||
105.38 | odd | 12 | 315.2.bb.b.269.1 | yes | 24 | ||
105.47 | odd | 12 | 2205.2.g.b.2204.3 | 24 | |||
105.59 | even | 6 | inner | 1575.2.bk.i.1151.1 | 24 | ||
105.68 | odd | 12 | 2205.2.g.b.2204.23 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bb.b.89.1 | ✓ | 24 | 5.2 | odd | 4 | ||
315.2.bb.b.89.2 | yes | 24 | 15.8 | even | 4 | ||
315.2.bb.b.89.11 | yes | 24 | 5.3 | odd | 4 | ||
315.2.bb.b.89.12 | yes | 24 | 15.2 | even | 4 | ||
315.2.bb.b.269.1 | yes | 24 | 105.38 | odd | 12 | ||
315.2.bb.b.269.2 | yes | 24 | 35.17 | even | 12 | ||
315.2.bb.b.269.11 | yes | 24 | 105.17 | odd | 12 | ||
315.2.bb.b.269.12 | yes | 24 | 35.3 | even | 12 | ||
1575.2.bk.i.26.1 | 24 | 5.4 | even | 2 | inner | ||
1575.2.bk.i.26.2 | 24 | 3.2 | odd | 2 | inner | ||
1575.2.bk.i.26.11 | 24 | 1.1 | even | 1 | trivial | ||
1575.2.bk.i.26.12 | 24 | 15.14 | odd | 2 | inner | ||
1575.2.bk.i.1151.1 | 24 | 105.59 | even | 6 | inner | ||
1575.2.bk.i.1151.2 | 24 | 7.3 | odd | 6 | inner | ||
1575.2.bk.i.1151.11 | 24 | 21.17 | even | 6 | inner | ||
1575.2.bk.i.1151.12 | 24 | 35.24 | odd | 6 | inner | ||
2205.2.g.b.2204.1 | 24 | 35.33 | even | 12 | |||
2205.2.g.b.2204.2 | 24 | 35.23 | odd | 12 | |||
2205.2.g.b.2204.3 | 24 | 105.47 | odd | 12 | |||
2205.2.g.b.2204.4 | 24 | 105.2 | even | 12 | |||
2205.2.g.b.2204.21 | 24 | 35.12 | even | 12 | |||
2205.2.g.b.2204.22 | 24 | 35.2 | odd | 12 | |||
2205.2.g.b.2204.23 | 24 | 105.68 | odd | 12 | |||
2205.2.g.b.2204.24 | 24 | 105.23 | even | 12 |