Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(109,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.m (of order \(4\), 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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 307.4 | ||
Character | \(\chi\) | \(=\) | 429.307 |
Dual form | 429.2.m.b.109.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.20600 | + | 1.20600i | −0.852774 | + | 0.852774i | −0.990474 | − | 0.137700i | \(-0.956029\pi\) |
0.137700 | + | 0.990474i | \(0.456029\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | − | 0.908895i | − | 0.454448i | ||||||
\(5\) | −0.200991 | − | 0.200991i | −0.0898857 | − | 0.0898857i | 0.660734 | − | 0.750620i | \(-0.270245\pi\) |
−0.750620 | + | 0.660734i | \(0.770245\pi\) | |||||||
\(6\) | −1.20600 | + | 1.20600i | −0.492349 | + | 0.492349i | ||||
\(7\) | −3.33407 | − | 3.33407i | −1.26016 | − | 1.26016i | −0.951014 | − | 0.309147i | \(-0.899956\pi\) |
−0.309147 | − | 0.951014i | \(-0.600044\pi\) | |||||||
\(8\) | −1.31588 | − | 1.31588i | −0.465233 | − | 0.465233i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.484791 | 0.153304 | ||||||||
\(11\) | 2.95091 | + | 1.51398i | 0.889733 | + | 0.456481i | ||||
\(12\) | − | 0.908895i | − | 0.262375i | ||||||
\(13\) | 2.46083 | − | 2.63521i | 0.682512 | − | 0.730875i | ||||
\(14\) | 8.04182 | 2.14927 | ||||||||
\(15\) | −0.200991 | − | 0.200991i | −0.0518956 | − | 0.0518956i | ||||
\(16\) | 4.99170 | 1.24792 | ||||||||
\(17\) | 7.25513 | 1.75963 | 0.879814 | − | 0.475319i | \(-0.157667\pi\) | ||||
0.879814 | + | 0.475319i | \(0.157667\pi\) | |||||||
\(18\) | −1.20600 | + | 1.20600i | −0.284258 | + | 0.284258i | ||||
\(19\) | −1.18165 | + | 1.18165i | −0.271089 | + | 0.271089i | −0.829538 | − | 0.558450i | \(-0.811396\pi\) |
0.558450 | + | 0.829538i | \(0.311396\pi\) | |||||||
\(20\) | −0.182679 | + | 0.182679i | −0.0408484 | + | 0.0408484i | ||||
\(21\) | −3.33407 | − | 3.33407i | −0.727554 | − | 0.727554i | ||||
\(22\) | −5.38468 | + | 1.73295i | −1.14802 | + | 0.369466i | ||||
\(23\) | − | 3.26417i | − | 0.680626i | −0.940312 | − | 0.340313i | \(-0.889467\pi\) | ||
0.940312 | − | 0.340313i | \(-0.110533\pi\) | |||||||
\(24\) | −1.31588 | − | 1.31588i | −0.268602 | − | 0.268602i | ||||
\(25\) | − | 4.91921i | − | 0.983841i | ||||||
\(26\) | 0.210296 | + | 6.14585i | 0.0412424 | + | 1.20530i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.03032 | + | 3.03032i | −0.572677 | + | 0.572677i | ||||
\(29\) | 5.67492i | 1.05381i | 0.849926 | + | 0.526903i | \(0.176647\pi\) | ||||
−0.849926 | + | 0.526903i | \(0.823353\pi\) | |||||||
\(30\) | 0.484791 | 0.0885104 | ||||||||
\(31\) | −3.86547 | − | 3.86547i | −0.694259 | − | 0.694259i | 0.268907 | − | 0.963166i | \(-0.413338\pi\) |
−0.963166 | + | 0.268907i | \(0.913338\pi\) | |||||||
\(32\) | −3.38826 | + | 3.38826i | −0.598965 | + | 0.598965i | ||||
\(33\) | 2.95091 | + | 1.51398i | 0.513688 | + | 0.263549i | ||||
\(34\) | −8.74972 | + | 8.74972i | −1.50056 | + | 1.50056i | ||||
\(35\) | 1.34024i | 0.226541i | ||||||||
\(36\) | − | 0.908895i | − | 0.151483i | ||||||
\(37\) | 2.95704 | − | 2.95704i | 0.486135 | − | 0.486135i | −0.420949 | − | 0.907084i | \(-0.638303\pi\) |
0.907084 | + | 0.420949i | \(0.138303\pi\) | |||||||
\(38\) | − | 2.85014i | − | 0.462355i | ||||||
\(39\) | 2.46083 | − | 2.63521i | 0.394048 | − | 0.421971i | ||||
\(40\) | 0.528958i | 0.0836356i | ||||||||
\(41\) | 4.75377 | − | 4.75377i | 0.742413 | − | 0.742413i | −0.230628 | − | 0.973042i | \(-0.574078\pi\) |
0.973042 | + | 0.230628i | \(0.0740782\pi\) | |||||||
\(42\) | 8.04182 | 1.24088 | ||||||||
\(43\) | −2.81887 | −0.429873 | −0.214937 | − | 0.976628i | \(-0.568954\pi\) | ||||
−0.214937 | + | 0.976628i | \(0.568954\pi\) | |||||||
\(44\) | 1.37605 | − | 2.68207i | 0.207447 | − | 0.404337i | ||||
\(45\) | −0.200991 | − | 0.200991i | −0.0299619 | − | 0.0299619i | ||||
\(46\) | 3.93660 | + | 3.93660i | 0.580420 | + | 0.580420i | ||||
\(47\) | 3.39398 | − | 3.39398i | 0.495063 | − | 0.495063i | −0.414834 | − | 0.909897i | \(-0.636160\pi\) |
0.909897 | + | 0.414834i | \(0.136160\pi\) | |||||||
\(48\) | 4.99170 | 0.720490 | ||||||||
\(49\) | 15.2321i | 2.17601i | ||||||||
\(50\) | 5.93259 | + | 5.93259i | 0.838994 | + | 0.838994i | ||||
\(51\) | 7.25513 | 1.01592 | ||||||||
\(52\) | −2.39513 | − | 2.23664i | −0.332144 | − | 0.310166i | ||||
\(53\) | −5.44413 | −0.747809 | −0.373904 | − | 0.927467i | \(-0.621981\pi\) | ||||
−0.373904 | + | 0.927467i | \(0.621981\pi\) | |||||||
\(54\) | −1.20600 | + | 1.20600i | −0.164116 | + | 0.164116i | ||||
\(55\) | −0.288811 | − | 0.897400i | −0.0389432 | − | 0.121005i | ||||
\(56\) | 8.77447i | 1.17254i | ||||||||
\(57\) | −1.18165 | + | 1.18165i | −0.156513 | + | 0.156513i | ||||
\(58\) | −6.84397 | − | 6.84397i | −0.898658 | − | 0.898658i | ||||
\(59\) | −5.68655 | + | 5.68655i | −0.740325 | + | 0.740325i | −0.972641 | − | 0.232315i | \(-0.925370\pi\) |
0.232315 | + | 0.972641i | \(0.425370\pi\) | |||||||
\(60\) | −0.182679 | + | 0.182679i | −0.0235838 | + | 0.0235838i | ||||
\(61\) | − | 14.3278i | − | 1.83448i | −0.398330 | − | 0.917242i | \(-0.630410\pi\) | ||
0.398330 | − | 0.917242i | \(-0.369590\pi\) | |||||||
\(62\) | 9.32355 | 1.18409 | ||||||||
\(63\) | −3.33407 | − | 3.33407i | −0.420054 | − | 0.420054i | ||||
\(64\) | 1.81089i | 0.226361i | ||||||||
\(65\) | −1.02426 | + | 0.0350475i | −0.127043 | + | 0.00434711i | ||||
\(66\) | −5.38468 | + | 1.73295i | −0.662808 | + | 0.213312i | ||||
\(67\) | −0.748559 | − | 0.748559i | −0.0914511 | − | 0.0914511i | 0.659901 | − | 0.751352i | \(-0.270598\pi\) |
−0.751352 | + | 0.659901i | \(0.770598\pi\) | |||||||
\(68\) | − | 6.59415i | − | 0.799658i | ||||||
\(69\) | − | 3.26417i | − | 0.392960i | ||||||
\(70\) | −1.61633 | − | 1.61633i | −0.193188 | − | 0.193188i | ||||
\(71\) | 6.94874 | + | 6.94874i | 0.824664 | + | 0.824664i | 0.986773 | − | 0.162109i | \(-0.0518295\pi\) |
−0.162109 | + | 0.986773i | \(0.551829\pi\) | |||||||
\(72\) | −1.31588 | − | 1.31588i | −0.155078 | − | 0.155078i | ||||
\(73\) | 2.84928 | + | 2.84928i | 0.333483 | + | 0.333483i | 0.853908 | − | 0.520424i | \(-0.174226\pi\) |
−0.520424 | + | 0.853908i | \(0.674226\pi\) | |||||||
\(74\) | 7.13242i | 0.829127i | ||||||||
\(75\) | − | 4.91921i | − | 0.568021i | ||||||
\(76\) | 1.07399 | + | 1.07399i | 0.123196 | + | 0.123196i | ||||
\(77\) | −4.79085 | − | 14.8863i | −0.545968 | − | 1.69645i | ||||
\(78\) | 0.210296 | + | 6.14585i | 0.0238113 | + | 0.695880i | ||||
\(79\) | 3.04264i | 0.342323i | 0.985243 | + | 0.171162i | \(0.0547520\pi\) | ||||
−0.985243 | + | 0.171162i | \(0.945248\pi\) | |||||||
\(80\) | −1.00328 | − | 1.00328i | −0.112171 | − | 0.112171i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.4661i | 1.26622i | ||||||||
\(83\) | −4.10311 | + | 4.10311i | −0.450375 | + | 0.450375i | −0.895479 | − | 0.445104i | \(-0.853167\pi\) |
0.445104 | + | 0.895479i | \(0.353167\pi\) | |||||||
\(84\) | −3.03032 | + | 3.03032i | −0.330635 | + | 0.330635i | ||||
\(85\) | −1.45821 | − | 1.45821i | −0.158165 | − | 0.158165i | ||||
\(86\) | 3.39957 | − | 3.39957i | 0.366585 | − | 0.366585i | ||||
\(87\) | 5.67492i | 0.608415i | ||||||||
\(88\) | −1.89083 | − | 5.87525i | −0.201563 | − | 0.626303i | ||||
\(89\) | 6.08327 | − | 6.08327i | 0.644826 | − | 0.644826i | −0.306912 | − | 0.951738i | \(-0.599296\pi\) |
0.951738 | + | 0.306912i | \(0.0992958\pi\) | |||||||
\(90\) | 0.484791 | 0.0511015 | ||||||||
\(91\) | −16.9906 | + | 0.581376i | −1.78109 | + | 0.0609447i | ||||
\(92\) | −2.96679 | −0.309309 | ||||||||
\(93\) | −3.86547 | − | 3.86547i | −0.400831 | − | 0.400831i | ||||
\(94\) | 8.18631i | 0.844354i | ||||||||
\(95\) | 0.475000 | 0.0487340 | ||||||||
\(96\) | −3.38826 | + | 3.38826i | −0.345813 | + | 0.345813i | ||||
\(97\) | −1.76445 | − | 1.76445i | −0.179153 | − | 0.179153i | 0.611833 | − | 0.790987i | \(-0.290432\pi\) |
−0.790987 | + | 0.611833i | \(0.790432\pi\) | |||||||
\(98\) | −18.3700 | − | 18.3700i | −1.85565 | − | 1.85565i | ||||
\(99\) | 2.95091 | + | 1.51398i | 0.296578 | + | 0.152160i | ||||
\(100\) | −4.47104 | −0.447104 | ||||||||
\(101\) | −17.5489 | −1.74618 | −0.873089 | − | 0.487561i | \(-0.837887\pi\) | ||||
−0.873089 | + | 0.487561i | \(0.837887\pi\) | |||||||
\(102\) | −8.74972 | + | 8.74972i | −0.866352 | + | 0.866352i | ||||
\(103\) | 3.92179i | 0.386426i | 0.981157 | + | 0.193213i | \(0.0618908\pi\) | ||||
−0.981157 | + | 0.193213i | \(0.938109\pi\) | |||||||
\(104\) | −6.70576 | + | 0.229455i | −0.657554 | + | 0.0224999i | ||||
\(105\) | 1.34024i | 0.130794i | ||||||||
\(106\) | 6.56565 | − | 6.56565i | 0.637712 | − | 0.637712i | ||||
\(107\) | − | 0.546231i | − | 0.0528062i | −0.999651 | − | 0.0264031i | \(-0.991595\pi\) | ||
0.999651 | − | 0.0264031i | \(-0.00840534\pi\) | |||||||
\(108\) | − | 0.908895i | − | 0.0874585i | ||||||
\(109\) | 4.52795 | − | 4.52795i | 0.433699 | − | 0.433699i | −0.456186 | − | 0.889885i | \(-0.650785\pi\) |
0.889885 | + | 0.456186i | \(0.150785\pi\) | |||||||
\(110\) | 1.43058 | + | 0.733962i | 0.136400 | + | 0.0699806i | ||||
\(111\) | 2.95704 | − | 2.95704i | 0.280670 | − | 0.280670i | ||||
\(112\) | −16.6427 | − | 16.6427i | −1.57259 | − | 1.57259i | ||||
\(113\) | 5.58972 | 0.525836 | 0.262918 | − | 0.964818i | \(-0.415315\pi\) | ||||
0.262918 | + | 0.964818i | \(0.415315\pi\) | |||||||
\(114\) | − | 2.85014i | − | 0.266941i | ||||||
\(115\) | −0.656067 | + | 0.656067i | −0.0611786 | + | 0.0611786i | ||||
\(116\) | 5.15790 | 0.478899 | ||||||||
\(117\) | 2.46083 | − | 2.63521i | 0.227504 | − | 0.243625i | ||||
\(118\) | − | 13.7160i | − | 1.26266i | ||||||
\(119\) | −24.1891 | − | 24.1891i | −2.21741 | − | 2.21741i | ||||
\(120\) | 0.528958i | 0.0482871i | ||||||||
\(121\) | 6.41575 | + | 8.93522i | 0.583250 | + | 0.812292i | ||||
\(122\) | 17.2794 | + | 17.2794i | 1.56440 | + | 1.56440i | ||||
\(123\) | 4.75377 | − | 4.75377i | 0.428633 | − | 0.428633i | ||||
\(124\) | −3.51331 | + | 3.51331i | −0.315504 | + | 0.315504i | ||||
\(125\) | −1.99367 | + | 1.99367i | −0.178319 | + | 0.178319i | ||||
\(126\) | 8.04182 | 0.716422 | ||||||||
\(127\) | 10.9493 | 0.971598 | 0.485799 | − | 0.874071i | \(-0.338529\pi\) | ||||
0.485799 | + | 0.874071i | \(0.338529\pi\) | |||||||
\(128\) | −8.96046 | − | 8.96046i | −0.792000 | − | 0.792000i | ||||
\(129\) | −2.81887 | −0.248187 | ||||||||
\(130\) | 1.19299 | − | 1.27752i | 0.104632 | − | 0.112046i | ||||
\(131\) | − | 13.8031i | − | 1.20598i | −0.797747 | − | 0.602992i | \(-0.793975\pi\) | ||
0.797747 | − | 0.602992i | \(-0.206025\pi\) | |||||||
\(132\) | 1.37605 | − | 2.68207i | 0.119769 | − | 0.233444i | ||||
\(133\) | 7.87940 | 0.683231 | ||||||||
\(134\) | 1.80553 | 0.155974 | ||||||||
\(135\) | −0.200991 | − | 0.200991i | −0.0172985 | − | 0.0172985i | ||||
\(136\) | −9.54686 | − | 9.54686i | −0.818637 | − | 0.818637i | ||||
\(137\) | −12.6531 | + | 12.6531i | −1.08103 | + | 1.08103i | −0.0846164 | + | 0.996414i | \(0.526966\pi\) |
−0.996414 | + | 0.0846164i | \(0.973034\pi\) | |||||||
\(138\) | 3.93660 | + | 3.93660i | 0.335106 | + | 0.335106i | ||||
\(139\) | 16.0680i | 1.36287i | 0.731880 | + | 0.681433i | \(0.238643\pi\) | ||||
−0.731880 | + | 0.681433i | \(0.761357\pi\) | |||||||
\(140\) | 1.21813 | 0.102951 | ||||||||
\(141\) | 3.39398 | − | 3.39398i | 0.285825 | − | 0.285825i | ||||
\(142\) | −16.7604 | −1.40650 | ||||||||
\(143\) | 11.2513 | − | 4.05062i | 0.940884 | − | 0.338730i | ||||
\(144\) | 4.99170 | 0.415975 | ||||||||
\(145\) | 1.14060 | − | 1.14060i | 0.0947221 | − | 0.0947221i | ||||
\(146\) | −6.87250 | −0.568772 | ||||||||
\(147\) | 15.2321i | 1.25632i | ||||||||
\(148\) | −2.68764 | − | 2.68764i | −0.220923 | − | 0.220923i | ||||
\(149\) | −10.6538 | + | 10.6538i | −0.872794 | + | 0.872794i | −0.992776 | − | 0.119982i | \(-0.961716\pi\) |
0.119982 | + | 0.992776i | \(0.461716\pi\) | |||||||
\(150\) | 5.93259 | + | 5.93259i | 0.484394 | + | 0.484394i | ||||
\(151\) | −2.70436 | − | 2.70436i | −0.220078 | − | 0.220078i | 0.588453 | − | 0.808531i | \(-0.299737\pi\) |
−0.808531 | + | 0.588453i | \(0.799737\pi\) | |||||||
\(152\) | 3.10981 | 0.252239 | ||||||||
\(153\) | 7.25513 | 0.586543 | ||||||||
\(154\) | 23.7307 | + | 12.1751i | 1.91227 | + | 0.981099i | ||||
\(155\) | 1.55385i | 0.124808i | ||||||||
\(156\) | −2.39513 | − | 2.23664i | −0.191764 | − | 0.179074i | ||||
\(157\) | 13.0749 | 1.04349 | 0.521746 | − | 0.853101i | \(-0.325281\pi\) | ||||
0.521746 | + | 0.853101i | \(0.325281\pi\) | |||||||
\(158\) | −3.66943 | − | 3.66943i | −0.291924 | − | 0.291924i | ||||
\(159\) | −5.44413 | −0.431748 | ||||||||
\(160\) | 1.36202 | 0.107677 | ||||||||
\(161\) | −10.8830 | + | 10.8830i | −0.857698 | + | 0.857698i | ||||
\(162\) | −1.20600 | + | 1.20600i | −0.0947527 | + | 0.0947527i | ||||
\(163\) | −3.24947 | + | 3.24947i | −0.254518 | + | 0.254518i | −0.822820 | − | 0.568302i | \(-0.807601\pi\) |
0.568302 | + | 0.822820i | \(0.307601\pi\) | |||||||
\(164\) | −4.32067 | − | 4.32067i | −0.337388 | − | 0.337388i | ||||
\(165\) | −0.288811 | − | 0.897400i | −0.0224839 | − | 0.0698625i | ||||
\(166\) | − | 9.89674i | − | 0.768136i | ||||||
\(167\) | 3.87790 | + | 3.87790i | 0.300081 | + | 0.300081i | 0.841046 | − | 0.540964i | \(-0.181941\pi\) |
−0.540964 | + | 0.841046i | \(0.681941\pi\) | |||||||
\(168\) | 8.77447i | 0.676965i | ||||||||
\(169\) | −0.888616 | − | 12.9696i | −0.0683551 | − | 0.997661i | ||||
\(170\) | 3.51722 | 0.269759 | ||||||||
\(171\) | −1.18165 | + | 1.18165i | −0.0903628 | + | 0.0903628i | ||||
\(172\) | 2.56205i | 0.195355i | ||||||||
\(173\) | 8.75558 | 0.665675 | 0.332837 | − | 0.942984i | \(-0.391994\pi\) | ||||
0.332837 | + | 0.942984i | \(0.391994\pi\) | |||||||
\(174\) | −6.84397 | − | 6.84397i | −0.518840 | − | 0.518840i | ||||
\(175\) | −16.4010 | + | 16.4010i | −1.23980 | + | 1.23980i | ||||
\(176\) | 14.7301 | + | 7.55731i | 1.11032 | + | 0.569654i | ||||
\(177\) | −5.68655 | + | 5.68655i | −0.427427 | + | 0.427427i | ||||
\(178\) | 14.6729i | 1.09978i | ||||||||
\(179\) | 8.37650i | 0.626089i | 0.949738 | + | 0.313044i | \(0.101349\pi\) | ||||
−0.949738 | + | 0.313044i | \(0.898651\pi\) | |||||||
\(180\) | −0.182679 | + | 0.182679i | −0.0136161 | + | 0.0136161i | ||||
\(181\) | 8.13564i | 0.604717i | 0.953194 | + | 0.302359i | \(0.0977740\pi\) | ||||
−0.953194 | + | 0.302359i | \(0.902226\pi\) | |||||||
\(182\) | 19.7896 | − | 21.1918i | 1.46690 | − | 1.57084i | ||||
\(183\) | − | 14.3278i | − | 1.05914i | ||||||
\(184\) | −4.29524 | + | 4.29524i | −0.316650 | + | 0.316650i | ||||
\(185\) | −1.18868 | −0.0873932 | ||||||||
\(186\) | 9.32355 | 0.683636 | ||||||||
\(187\) | 21.4092 | + | 10.9841i | 1.56560 | + | 0.803236i | ||||
\(188\) | −3.08477 | − | 3.08477i | −0.224980 | − | 0.224980i | ||||
\(189\) | −3.33407 | − | 3.33407i | −0.242518 | − | 0.242518i | ||||
\(190\) | −0.572852 | + | 0.572852i | −0.0415591 | + | 0.0415591i | ||||
\(191\) | −1.28415 | −0.0929180 | −0.0464590 | − | 0.998920i | \(-0.514794\pi\) | ||||
−0.0464590 | + | 0.998920i | \(0.514794\pi\) | |||||||
\(192\) | 1.81089i | 0.130690i | ||||||||
\(193\) | 18.7908 | + | 18.7908i | 1.35259 | + | 1.35259i | 0.882753 | + | 0.469838i | \(0.155688\pi\) |
0.469838 | + | 0.882753i | \(0.344312\pi\) | |||||||
\(194\) | 4.25588 | 0.305555 | ||||||||
\(195\) | −1.02426 | + | 0.0350475i | −0.0733485 | + | 0.00250981i | ||||
\(196\) | 13.8444 | 0.988884 | ||||||||
\(197\) | −12.3045 | + | 12.3045i | −0.876663 | + | 0.876663i | −0.993188 | − | 0.116525i | \(-0.962824\pi\) |
0.116525 | + | 0.993188i | \(0.462824\pi\) | |||||||
\(198\) | −5.38468 | + | 1.73295i | −0.382672 | + | 0.123155i | ||||
\(199\) | 20.0985i | 1.42475i | 0.701801 | + | 0.712373i | \(0.252379\pi\) | ||||
−0.701801 | + | 0.712373i | \(0.747621\pi\) | |||||||
\(200\) | −6.47307 | + | 6.47307i | −0.457715 | + | 0.457715i | ||||
\(201\) | −0.748559 | − | 0.748559i | −0.0527993 | − | 0.0527993i | ||||
\(202\) | 21.1640 | − | 21.1640i | 1.48910 | − | 1.48910i | ||||
\(203\) | 18.9206 | − | 18.9206i | 1.32796 | − | 1.32796i | ||||
\(204\) | − | 6.59415i | − | 0.461683i | ||||||
\(205\) | −1.91092 | −0.133465 | ||||||||
\(206\) | −4.72970 | − | 4.72970i | −0.329534 | − | 0.329534i | ||||
\(207\) | − | 3.26417i | − | 0.226875i | ||||||
\(208\) | 12.2837 | − | 13.1542i | 0.851724 | − | 0.912077i | ||||
\(209\) | −5.27592 | + | 1.69795i | −0.364943 | + | 0.117450i | ||||
\(210\) | −1.61633 | − | 1.61633i | −0.111537 | − | 0.111537i | ||||
\(211\) | − | 21.6318i | − | 1.48919i | −0.667515 | − | 0.744597i | \(-0.732642\pi\) | ||
0.667515 | − | 0.744597i | \(-0.267358\pi\) | |||||||
\(212\) | 4.94814i | 0.339840i | ||||||||
\(213\) | 6.94874 | + | 6.94874i | 0.476120 | + | 0.476120i | ||||
\(214\) | 0.658758 | + | 0.658758i | 0.0450317 | + | 0.0450317i | ||||
\(215\) | 0.566566 | + | 0.566566i | 0.0386395 | + | 0.0386395i | ||||
\(216\) | −1.31588 | − | 1.31588i | −0.0895341 | − | 0.0895341i | ||||
\(217\) | 25.7755i | 1.74976i | ||||||||
\(218\) | 10.9215i | 0.739695i | ||||||||
\(219\) | 2.84928 | + | 2.84928i | 0.192537 | + | 0.192537i | ||||
\(220\) | −0.815643 | + | 0.262499i | −0.0549906 | + | 0.0176976i | ||||
\(221\) | 17.8537 | − | 19.1188i | 1.20097 | − | 1.28607i | ||||
\(222\) | 7.13242i | 0.478697i | ||||||||
\(223\) | −18.0992 | − | 18.0992i | −1.21201 | − | 1.21201i | −0.970363 | − | 0.241651i | \(-0.922311\pi\) |
−0.241651 | − | 0.970363i | \(-0.577689\pi\) | |||||||
\(224\) | 22.5934 | 1.50959 | ||||||||
\(225\) | − | 4.91921i | − | 0.327947i | ||||||
\(226\) | −6.74123 | + | 6.74123i | −0.448420 | + | 0.448420i | ||||
\(227\) | −0.513536 | + | 0.513536i | −0.0340846 | + | 0.0340846i | −0.723944 | − | 0.689859i | \(-0.757672\pi\) |
0.689859 | + | 0.723944i | \(0.257672\pi\) | |||||||
\(228\) | 1.07399 | + | 1.07399i | 0.0711270 | + | 0.0711270i | ||||
\(229\) | 12.6249 | − | 12.6249i | 0.834274 | − | 0.834274i | −0.153824 | − | 0.988098i | \(-0.549159\pi\) |
0.988098 | + | 0.153824i | \(0.0491589\pi\) | |||||||
\(230\) | − | 1.58244i | − | 0.104343i | ||||||
\(231\) | −4.79085 | − | 14.8863i | −0.315215 | − | 0.979444i | ||||
\(232\) | 7.46749 | − | 7.46749i | 0.490265 | − | 0.490265i | ||||
\(233\) | 22.5952 | 1.48026 | 0.740130 | − | 0.672464i | \(-0.234764\pi\) | ||||
0.740130 | + | 0.672464i | \(0.234764\pi\) | |||||||
\(234\) | 0.210296 | + | 6.14585i | 0.0137475 | + | 0.401766i | ||||
\(235\) | −1.36432 | −0.0889982 | ||||||||
\(236\) | 5.16847 | + | 5.16847i | 0.336439 | + | 0.336439i | ||||
\(237\) | 3.04264i | 0.197640i | ||||||||
\(238\) | 58.3444 | 3.78191 | ||||||||
\(239\) | −3.72061 | + | 3.72061i | −0.240666 | + | 0.240666i | −0.817126 | − | 0.576459i | \(-0.804434\pi\) |
0.576459 | + | 0.817126i | \(0.304434\pi\) | |||||||
\(240\) | −1.00328 | − | 1.00328i | −0.0647618 | − | 0.0647618i | ||||
\(241\) | −7.81915 | − | 7.81915i | −0.503676 | − | 0.503676i | 0.408902 | − | 0.912578i | \(-0.365912\pi\) |
−0.912578 | + | 0.408902i | \(0.865912\pi\) | |||||||
\(242\) | −18.5133 | − | 3.03848i | −1.19008 | − | 0.195321i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −13.0225 | −0.833677 | ||||||||
\(245\) | 3.06151 | − | 3.06151i | 0.195593 | − | 0.195593i | ||||
\(246\) | 11.4661i | 0.731054i | ||||||||
\(247\) | 0.206049 | + | 6.02172i | 0.0131106 | + | 0.383153i | ||||
\(248\) | 10.1730i | 0.645984i | ||||||||
\(249\) | −4.10311 | + | 4.10311i | −0.260024 | + | 0.260024i | ||||
\(250\) | − | 4.80874i | − | 0.304132i | ||||||
\(251\) | 14.5266i | 0.916911i | 0.888717 | + | 0.458456i | \(0.151597\pi\) | ||||
−0.888717 | + | 0.458456i | \(0.848403\pi\) | |||||||
\(252\) | −3.03032 | + | 3.03032i | −0.190892 | + | 0.190892i | ||||
\(253\) | 4.94187 | − | 9.63227i | 0.310693 | − | 0.605575i | ||||
\(254\) | −13.2050 | + | 13.2050i | −0.828553 | + | 0.828553i | ||||
\(255\) | −1.45821 | − | 1.45821i | −0.0913169 | − | 0.0913169i | ||||
\(256\) | 17.9909 | 1.12443 | ||||||||
\(257\) | 2.83504i | 0.176845i | 0.996083 | + | 0.0884226i | \(0.0281826\pi\) | ||||
−0.996083 | + | 0.0884226i | \(0.971817\pi\) | |||||||
\(258\) | 3.39957 | − | 3.39957i | 0.211648 | − | 0.211648i | ||||
\(259\) | −19.7180 | −1.22522 | ||||||||
\(260\) | 0.0318545 | + | 0.930941i | 0.00197553 | + | 0.0577345i | ||||
\(261\) | 5.67492i | 0.351268i | ||||||||
\(262\) | 16.6466 | + | 16.6466i | 1.02843 | + | 1.02843i | ||||
\(263\) | − | 14.5178i | − | 0.895209i | −0.894232 | − | 0.447604i | \(-0.852277\pi\) | ||
0.894232 | − | 0.447604i | \(-0.147723\pi\) | |||||||
\(264\) | −1.89083 | − | 5.87525i | −0.116373 | − | 0.361596i | ||||
\(265\) | 1.09422 | + | 1.09422i | 0.0672174 | + | 0.0672174i | ||||
\(266\) | −9.50259 | + | 9.50259i | −0.582641 | + | 0.582641i | ||||
\(267\) | 6.08327 | − | 6.08327i | 0.372290 | − | 0.372290i | ||||
\(268\) | −0.680362 | + | 0.680362i | −0.0415597 | + | 0.0415597i | ||||
\(269\) | −23.0188 | −1.40348 | −0.701740 | − | 0.712433i | \(-0.747593\pi\) | ||||
−0.701740 | + | 0.712433i | \(0.747593\pi\) | |||||||
\(270\) | 0.484791 | 0.0295035 | ||||||||
\(271\) | 17.0008 | + | 17.0008i | 1.03272 | + | 1.03272i | 0.999446 | + | 0.0332760i | \(0.0105940\pi\) |
0.0332760 | + | 0.999446i | \(0.489406\pi\) | |||||||
\(272\) | 36.2154 | 2.19588 | ||||||||
\(273\) | −16.9906 | + | 0.581376i | −1.02832 | + | 0.0351865i | ||||
\(274\) | − | 30.5195i | − | 1.84375i | ||||||
\(275\) | 7.44756 | − | 14.5161i | 0.449105 | − | 0.875356i | ||||
\(276\) | −2.96679 | −0.178579 | ||||||||
\(277\) | −27.4149 | −1.64720 | −0.823601 | − | 0.567169i | \(-0.808038\pi\) | ||||
−0.823601 | + | 0.567169i | \(0.808038\pi\) | |||||||
\(278\) | −19.3780 | − | 19.3780i | −1.16222 | − | 1.16222i | ||||
\(279\) | −3.86547 | − | 3.86547i | −0.231420 | − | 0.231420i | ||||
\(280\) | 1.76359 | − | 1.76359i | 0.105394 | − | 0.105394i | ||||
\(281\) | 3.55759 | + | 3.55759i | 0.212228 | + | 0.212228i | 0.805213 | − | 0.592985i | \(-0.202051\pi\) |
−0.592985 | + | 0.805213i | \(0.702051\pi\) | |||||||
\(282\) | 8.18631i | 0.487488i | ||||||||
\(283\) | −25.2088 | −1.49851 | −0.749253 | − | 0.662284i | \(-0.769587\pi\) | ||||
−0.749253 | + | 0.662284i | \(0.769587\pi\) | |||||||
\(284\) | 6.31568 | − | 6.31568i | 0.374767 | − | 0.374767i | ||||
\(285\) | 0.475000 | 0.0281366 | ||||||||
\(286\) | −8.68410 | + | 18.4542i | −0.513501 | + | 1.09122i | ||||
\(287\) | −31.6988 | −1.87112 | ||||||||
\(288\) | −3.38826 | + | 3.38826i | −0.199655 | + | 0.199655i | ||||
\(289\) | 35.6369 | 2.09629 | ||||||||
\(290\) | 2.75115i | 0.161553i | ||||||||
\(291\) | −1.76445 | − | 1.76445i | −0.103434 | − | 0.103434i | ||||
\(292\) | 2.58970 | − | 2.58970i | 0.151551 | − | 0.151551i | ||||
\(293\) | 14.1743 | + | 14.1743i | 0.828069 | + | 0.828069i | 0.987250 | − | 0.159180i | \(-0.0508851\pi\) |
−0.159180 | + | 0.987250i | \(0.550885\pi\) | |||||||
\(294\) | −18.3700 | − | 18.3700i | −1.07136 | − | 1.07136i | ||||
\(295\) | 2.28588 | 0.133089 | ||||||||
\(296\) | −7.78222 | −0.452332 | ||||||||
\(297\) | 2.95091 | + | 1.51398i | 0.171229 | + | 0.0878498i | ||||
\(298\) | − | 25.6971i | − | 1.48859i | ||||||
\(299\) | −8.60175 | − | 8.03256i | −0.497452 | − | 0.464535i | ||||
\(300\) | −4.47104 | −0.258136 | ||||||||
\(301\) | 9.39831 | + | 9.39831i | 0.541709 | + | 0.541709i | ||||
\(302\) | 6.52295 | 0.375353 | ||||||||
\(303\) | −17.5489 | −1.00816 | ||||||||
\(304\) | −5.89843 | + | 5.89843i | −0.338298 | + | 0.338298i | ||||
\(305\) | −2.87975 | + | 2.87975i | −0.164894 | + | 0.164894i | ||||
\(306\) | −8.74972 | + | 8.74972i | −0.500188 | + | 0.500188i | ||||
\(307\) | −8.82445 | − | 8.82445i | −0.503638 | − | 0.503638i | 0.408929 | − | 0.912566i | \(-0.365903\pi\) |
−0.912566 | + | 0.408929i | \(0.865903\pi\) | |||||||
\(308\) | −13.5301 | + | 4.35438i | −0.770946 | + | 0.248114i | ||||
\(309\) | 3.92179i | 0.223103i | ||||||||
\(310\) | −1.87395 | − | 1.87395i | −0.106433 | − | 0.106433i | ||||
\(311\) | 15.5102i | 0.879502i | 0.898120 | + | 0.439751i | \(0.144933\pi\) | ||||
−0.898120 | + | 0.439751i | \(0.855067\pi\) | |||||||
\(312\) | −6.70576 | + | 0.229455i | −0.379639 | + | 0.0129903i | ||||
\(313\) | 28.7631 | 1.62579 | 0.812895 | − | 0.582411i | \(-0.197891\pi\) | ||||
0.812895 | + | 0.582411i | \(0.197891\pi\) | |||||||
\(314\) | −15.7684 | + | 15.7684i | −0.889863 | + | 0.889863i | ||||
\(315\) | 1.34024i | 0.0755137i | ||||||||
\(316\) | 2.76544 | 0.155568 | ||||||||
\(317\) | 11.7770 | + | 11.7770i | 0.661463 | + | 0.661463i | 0.955725 | − | 0.294262i | \(-0.0950737\pi\) |
−0.294262 | + | 0.955725i | \(0.595074\pi\) | |||||||
\(318\) | 6.56565 | − | 6.56565i | 0.368183 | − | 0.368183i | ||||
\(319\) | −8.59168 | + | 16.7462i | −0.481042 | + | 0.937606i | ||||
\(320\) | 0.363971 | − | 0.363971i | 0.0203466 | − | 0.0203466i | ||||
\(321\) | − | 0.546231i | − | 0.0304877i | ||||||
\(322\) | − | 26.2498i | − | 1.46285i | ||||||
\(323\) | −8.57301 | + | 8.57301i | −0.477015 | + | 0.477015i | ||||
\(324\) | − | 0.908895i | − | 0.0504942i | ||||||
\(325\) | −12.9631 | − | 12.1053i | −0.719064 | − | 0.671483i | ||||
\(326\) | − | 7.83776i | − | 0.434093i | ||||||
\(327\) | 4.52795 | − | 4.52795i | 0.250396 | − | 0.250396i | ||||
\(328\) | −12.5107 | −0.690790 | ||||||||
\(329\) | −22.6316 | −1.24772 | ||||||||
\(330\) | 1.43058 | + | 0.733962i | 0.0787506 | + | 0.0404033i | ||||
\(331\) | 0.0573492 | + | 0.0573492i | 0.00315220 | + | 0.00315220i | 0.708681 | − | 0.705529i | \(-0.249291\pi\) |
−0.705529 | + | 0.708681i | \(0.749291\pi\) | |||||||
\(332\) | 3.72930 | + | 3.72930i | 0.204672 | + | 0.204672i | ||||
\(333\) | 2.95704 | − | 2.95704i | 0.162045 | − | 0.162045i | ||||
\(334\) | −9.35354 | −0.511803 | ||||||||
\(335\) | 0.300907i | 0.0164403i | ||||||||
\(336\) | −16.6427 | − | 16.6427i | −0.907933 | − | 0.907933i | ||||
\(337\) | −3.94748 | −0.215033 | −0.107516 | − | 0.994203i | \(-0.534290\pi\) | ||||
−0.107516 | + | 0.994203i | \(0.534290\pi\) | |||||||
\(338\) | 16.7131 | + | 14.5697i | 0.909071 | + | 0.792488i | ||||
\(339\) | 5.58972 | 0.303592 | ||||||||
\(340\) | −1.32536 | + | 1.32536i | −0.0718779 | + | 0.0718779i | ||||
\(341\) | −5.55443 | − | 17.2589i | −0.300789 | − | 0.934621i | ||||
\(342\) | − | 2.85014i | − | 0.154118i | ||||||
\(343\) | 27.4464 | − | 27.4464i | 1.48197 | − | 1.48197i | ||||
\(344\) | 3.70928 | + | 3.70928i | 0.199991 | + | 0.199991i | ||||
\(345\) | −0.656067 | + | 0.656067i | −0.0353215 | + | 0.0353215i | ||||
\(346\) | −10.5593 | + | 10.5593i | −0.567670 | + | 0.567670i | ||||
\(347\) | − | 3.45221i | − | 0.185324i | −0.995698 | − | 0.0926622i | \(-0.970462\pi\) | ||
0.995698 | − | 0.0926622i | \(-0.0295377\pi\) | |||||||
\(348\) | 5.15790 | 0.276493 | ||||||||
\(349\) | −5.50942 | − | 5.50942i | −0.294912 | − | 0.294912i | 0.544105 | − | 0.839017i | \(-0.316869\pi\) |
−0.839017 | + | 0.544105i | \(0.816869\pi\) | |||||||
\(350\) | − | 39.5594i | − | 2.11454i | ||||||
\(351\) | 2.46083 | − | 2.63521i | 0.131349 | − | 0.140657i | ||||
\(352\) | −15.1282 | + | 4.86871i | −0.806335 | + | 0.259503i | ||||
\(353\) | 7.13058 | + | 7.13058i | 0.379522 | + | 0.379522i | 0.870930 | − | 0.491407i | \(-0.163517\pi\) |
−0.491407 | + | 0.870930i | \(0.663517\pi\) | |||||||
\(354\) | − | 13.7160i | − | 0.728997i | ||||||
\(355\) | − | 2.79327i | − | 0.148251i | ||||||
\(356\) | −5.52906 | − | 5.52906i | −0.293040 | − | 0.293040i | ||||
\(357\) | −24.1891 | − | 24.1891i | −1.28022 | − | 1.28022i | ||||
\(358\) | −10.1021 | − | 10.1021i | −0.533912 | − | 0.533912i | ||||
\(359\) | 16.0603 | + | 16.0603i | 0.847632 | + | 0.847632i | 0.989837 | − | 0.142205i | \(-0.0454192\pi\) |
−0.142205 | + | 0.989837i | \(0.545419\pi\) | |||||||
\(360\) | 0.528958i | 0.0278785i | ||||||||
\(361\) | 16.2074i | 0.853022i | ||||||||
\(362\) | −9.81162 | − | 9.81162i | −0.515687 | − | 0.515687i | ||||
\(363\) | 6.41575 | + | 8.93522i | 0.336740 | + | 0.468977i | ||||
\(364\) | 0.528410 | + | 15.4426i | 0.0276962 | + | 0.809414i | ||||
\(365\) | − | 1.14536i | − | 0.0599508i | ||||||
\(366\) | 17.2794 | + | 17.2794i | 0.903207 | + | 0.903207i | ||||
\(367\) | −35.5649 | −1.85647 | −0.928236 | − | 0.371993i | \(-0.878675\pi\) | ||||
−0.928236 | + | 0.371993i | \(0.878675\pi\) | |||||||
\(368\) | − | 16.2937i | − | 0.849370i | ||||||
\(369\) | 4.75377 | − | 4.75377i | 0.247471 | − | 0.247471i | ||||
\(370\) | 1.43355 | − | 1.43355i | 0.0745267 | − | 0.0745267i | ||||
\(371\) | 18.1511 | + | 18.1511i | 0.942360 | + | 0.942360i | ||||
\(372\) | −3.51331 | + | 3.51331i | −0.182156 | + | 0.182156i | ||||
\(373\) | 21.1566i | 1.09545i | 0.836659 | + | 0.547724i | \(0.184506\pi\) | ||||
−0.836659 | + | 0.547724i | \(0.815494\pi\) | |||||||
\(374\) | −39.0665 | + | 12.5728i | −2.02008 | + | 0.650123i | ||||
\(375\) | −1.99367 | + | 1.99367i | −0.102953 | + | 0.102953i | ||||
\(376\) | −8.93213 | −0.460639 | ||||||||
\(377\) | 14.9546 | + | 13.9650i | 0.770199 | + | 0.719235i | ||||
\(378\) | 8.04182 | 0.413626 | ||||||||
\(379\) | 12.9964 | + | 12.9964i | 0.667579 | + | 0.667579i | 0.957155 | − | 0.289576i | \(-0.0935143\pi\) |
−0.289576 | + | 0.957155i | \(0.593514\pi\) | |||||||
\(380\) | − | 0.431725i | − | 0.0221470i | ||||||
\(381\) | 10.9493 | 0.560952 | ||||||||
\(382\) | 1.54869 | − | 1.54869i | 0.0792381 | − | 0.0792381i | ||||
\(383\) | 15.7374 | + | 15.7374i | 0.804144 | + | 0.804144i | 0.983740 | − | 0.179596i | \(-0.0574792\pi\) |
−0.179596 | + | 0.983740i | \(0.557479\pi\) | |||||||
\(384\) | −8.96046 | − | 8.96046i | −0.457261 | − | 0.457261i | ||||
\(385\) | −2.02908 | + | 3.95491i | −0.103412 | + | 0.201561i | ||||
\(386\) | −45.3236 | −2.30691 | ||||||||
\(387\) | −2.81887 | −0.143291 | ||||||||
\(388\) | −1.60370 | + | 1.60370i | −0.0814158 | + | 0.0814158i | ||||
\(389\) | − | 6.41847i | − | 0.325429i | −0.986673 | − | 0.162715i | \(-0.947975\pi\) | ||
0.986673 | − | 0.162715i | \(-0.0520250\pi\) | |||||||
\(390\) | 1.19299 | − | 1.27752i | 0.0604094 | − | 0.0646900i | ||||
\(391\) | − | 23.6820i | − | 1.19765i | ||||||
\(392\) | 20.0436 | − | 20.0436i | 1.01235 | − | 1.01235i | ||||
\(393\) | − | 13.8031i | − | 0.696275i | ||||||
\(394\) | − | 29.6787i | − | 1.49519i | ||||||
\(395\) | 0.611541 | − | 0.611541i | 0.0307700 | − | 0.0307700i | ||||
\(396\) | 1.37605 | − | 2.68207i | 0.0691489 | − | 0.134779i | ||||
\(397\) | 13.2341 | − | 13.2341i | 0.664198 | − | 0.664198i | −0.292168 | − | 0.956367i | \(-0.594377\pi\) |
0.956367 | + | 0.292168i | \(0.0943768\pi\) | |||||||
\(398\) | −24.2389 | − | 24.2389i | −1.21499 | − | 1.21499i | ||||
\(399\) | 7.87940 | 0.394463 | ||||||||
\(400\) | − | 24.5552i | − | 1.22776i | ||||||
\(401\) | 2.12792 | − | 2.12792i | 0.106263 | − | 0.106263i | −0.651976 | − | 0.758239i | \(-0.726060\pi\) |
0.758239 | + | 0.651976i | \(0.226060\pi\) | |||||||
\(402\) | 1.80553 | 0.0900517 | ||||||||
\(403\) | −19.6986 | + | 0.674038i | −0.981256 | + | 0.0335762i | ||||
\(404\) | 15.9501i | 0.793546i | ||||||||
\(405\) | −0.200991 | − | 0.200991i | −0.00998730 | − | 0.00998730i | ||||
\(406\) | 45.6366i | 2.26491i | ||||||||
\(407\) | 13.2029 | − | 4.24908i | 0.654442 | − | 0.210619i | ||||
\(408\) | −9.54686 | − | 9.54686i | −0.472640 | − | 0.472640i | ||||
\(409\) | −5.55755 | + | 5.55755i | −0.274803 | + | 0.274803i | −0.831030 | − | 0.556227i | \(-0.812248\pi\) |
0.556227 | + | 0.831030i | \(0.312248\pi\) | |||||||
\(410\) | 2.30458 | − | 2.30458i | 0.113815 | − | 0.113815i | ||||
\(411\) | −12.6531 | + | 12.6531i | −0.624133 | + | 0.624133i | ||||
\(412\) | 3.56450 | 0.175610 | ||||||||
\(413\) | 37.9187 | 1.86586 | ||||||||
\(414\) | 3.93660 | + | 3.93660i | 0.193473 | + | 0.193473i | ||||
\(415\) | 1.64937 | 0.0809646 | ||||||||
\(416\) | 0.590824 | + | 17.2667i | 0.0289675 | + | 0.846569i | ||||
\(417\) | 16.0680i | 0.786852i | ||||||||
\(418\) | 4.31505 | − | 8.41052i | 0.211056 | − | 0.411372i | ||||
\(419\) | −11.0697 | −0.540791 | −0.270396 | − | 0.962749i | \(-0.587155\pi\) | ||||
−0.270396 | + | 0.962749i | \(0.587155\pi\) | |||||||
\(420\) | 1.21813 | 0.0594388 | ||||||||
\(421\) | 3.62745 | + | 3.62745i | 0.176791 | + | 0.176791i | 0.789955 | − | 0.613164i | \(-0.210104\pi\) |
−0.613164 | + | 0.789955i | \(0.710104\pi\) | |||||||
\(422\) | 26.0880 | + | 26.0880i | 1.26995 | + | 1.26995i | ||||
\(423\) | 3.39398 | − | 3.39398i | 0.165021 | − | 0.165021i | ||||
\(424\) | 7.16381 | + | 7.16381i | 0.347905 | + | 0.347905i | ||||
\(425\) | − | 35.6895i | − | 1.73119i | ||||||
\(426\) | −16.7604 | −0.812046 | ||||||||
\(427\) | −47.7699 | + | 47.7699i | −2.31175 | + | 2.31175i | ||||
\(428\) | −0.496467 | −0.0239976 | ||||||||
\(429\) | 11.2513 | − | 4.05062i | 0.543219 | − | 0.195566i | ||||
\(430\) | −1.36656 | −0.0659015 | ||||||||
\(431\) | −5.17800 | + | 5.17800i | −0.249415 | + | 0.249415i | −0.820731 | − | 0.571315i | \(-0.806433\pi\) |
0.571315 | + | 0.820731i | \(0.306433\pi\) | |||||||
\(432\) | 4.99170 | 0.240163 | ||||||||
\(433\) | − | 29.3459i | − | 1.41027i | −0.709072 | − | 0.705137i | \(-0.750886\pi\) | ||
0.709072 | − | 0.705137i | \(-0.249114\pi\) | |||||||
\(434\) | −31.0854 | − | 31.0854i | −1.49215 | − | 1.49215i | ||||
\(435\) | 1.14060 | − | 1.14060i | 0.0546878 | − | 0.0546878i | ||||
\(436\) | −4.11543 | − | 4.11543i | −0.197093 | − | 0.197093i | ||||
\(437\) | 3.85709 | + | 3.85709i | 0.184510 | + | 0.184510i | ||||
\(438\) | −6.87250 | −0.328381 | ||||||||
\(439\) | 28.6462 | 1.36721 | 0.683604 | − | 0.729854i | \(-0.260412\pi\) | ||||
0.683604 | + | 0.729854i | \(0.260412\pi\) | |||||||
\(440\) | −0.800830 | + | 1.56091i | −0.0381781 | + | 0.0744134i | ||||
\(441\) | 15.2321i | 0.725338i | ||||||||
\(442\) | 1.52572 | + | 44.5889i | 0.0725713 | + | 2.12088i | ||||
\(443\) | −16.3682 | −0.777679 | −0.388839 | − | 0.921306i | \(-0.627124\pi\) | ||||
−0.388839 | + | 0.921306i | \(0.627124\pi\) | |||||||
\(444\) | −2.68764 | − | 2.68764i | −0.127550 | − | 0.127550i | ||||
\(445\) | −2.44536 | −0.115921 | ||||||||
\(446\) | 43.6555 | 2.06715 | ||||||||
\(447\) | −10.6538 | + | 10.6538i | −0.503908 | + | 0.503908i | ||||
\(448\) | 6.03763 | − | 6.03763i | 0.285251 | − | 0.285251i | ||||
\(449\) | −5.62755 | + | 5.62755i | −0.265580 | + | 0.265580i | −0.827316 | − | 0.561736i | \(-0.810134\pi\) |
0.561736 | + | 0.827316i | \(0.310134\pi\) | |||||||
\(450\) | 5.93259 | + | 5.93259i | 0.279665 | + | 0.279665i | ||||
\(451\) | 21.2250 | − | 6.83085i | 0.999447 | − | 0.321652i | ||||
\(452\) | − | 5.08047i | − | 0.238965i | ||||||
\(453\) | −2.70436 | − | 2.70436i | −0.127062 | − | 0.127062i | ||||
\(454\) | − | 1.23865i | − | 0.0581329i | ||||||
\(455\) | 3.53179 | + | 3.29809i | 0.165573 | + | 0.154617i | ||||
\(456\) | 3.10981 | 0.145630 | ||||||||
\(457\) | −17.4431 | + | 17.4431i | −0.815955 | + | 0.815955i | −0.985519 | − | 0.169564i | \(-0.945764\pi\) |
0.169564 | + | 0.985519i | \(0.445764\pi\) | |||||||
\(458\) | 30.4513i | 1.42290i | ||||||||
\(459\) | 7.25513 | 0.338640 | ||||||||
\(460\) | 0.596296 | + | 0.596296i | 0.0278024 | + | 0.0278024i | ||||
\(461\) | 12.6607 | − | 12.6607i | 0.589669 | − | 0.589669i | −0.347873 | − | 0.937542i | \(-0.613096\pi\) |
0.937542 | + | 0.347873i | \(0.113096\pi\) | |||||||
\(462\) | 23.7307 | + | 12.1751i | 1.10405 | + | 0.566438i | ||||
\(463\) | 14.2561 | − | 14.2561i | 0.662535 | − | 0.662535i | −0.293442 | − | 0.955977i | \(-0.594801\pi\) |
0.955977 | + | 0.293442i | \(0.0948007\pi\) | |||||||
\(464\) | 28.3275i | 1.31507i | ||||||||
\(465\) | 1.55385i | 0.0720579i | ||||||||
\(466\) | −27.2499 | + | 27.2499i | −1.26233 | + | 1.26233i | ||||
\(467\) | − | 3.80081i | − | 0.175880i | −0.996126 | − | 0.0879402i | \(-0.971972\pi\) | ||
0.996126 | − | 0.0879402i | \(-0.0280285\pi\) | |||||||
\(468\) | −2.39513 | − | 2.23664i | −0.110715 | − | 0.103389i | ||||
\(469\) | 4.99150i | 0.230486i | ||||||||
\(470\) | 1.64537 | − | 1.64537i | 0.0758954 | − | 0.0758954i | ||||
\(471\) | 13.0749 | 0.602461 | ||||||||
\(472\) | 14.9656 | 0.688847 | ||||||||
\(473\) | −8.31822 | − | 4.26769i | −0.382472 | − | 0.196229i | ||||
\(474\) | −3.66943 | − | 3.66943i | −0.168543 | − | 0.168543i | ||||
\(475\) | 5.81277 | + | 5.81277i | 0.266708 | + | 0.266708i | ||||
\(476\) | −21.9854 | + | 21.9854i | −1.00770 | + | 1.00770i | ||||
\(477\) | −5.44413 | −0.249270 | ||||||||
\(478\) | − | 8.97415i | − | 0.410468i | ||||||
\(479\) | 15.4257 | + | 15.4257i | 0.704818 | + | 0.704818i | 0.965441 | − | 0.260623i | \(-0.0839279\pi\) |
−0.260623 | + | 0.965441i | \(0.583928\pi\) | |||||||
\(480\) | 1.36202 | 0.0621673 | ||||||||
\(481\) | −0.515632 | − | 15.0692i | −0.0235108 | − | 0.687097i | ||||
\(482\) | 18.8599 | 0.859044 | ||||||||
\(483\) | −10.8830 | + | 10.8830i | −0.495192 | + | 0.495192i | ||||
\(484\) | 8.12117 | − | 5.83125i | 0.369144 | − | 0.265057i | ||||
\(485\) | 0.709278i | 0.0322066i | ||||||||
\(486\) | −1.20600 | + | 1.20600i | −0.0547055 | + | 0.0547055i | ||||
\(487\) | −7.87086 | − | 7.87086i | −0.356663 | − | 0.356663i | 0.505918 | − | 0.862581i | \(-0.331154\pi\) |
−0.862581 | + | 0.505918i | \(0.831154\pi\) | |||||||
\(488\) | −18.8536 | + | 18.8536i | −0.853463 | + | 0.853463i | ||||
\(489\) | −3.24947 | + | 3.24947i | −0.146946 | + | 0.146946i | ||||
\(490\) | 7.38439i | 0.333593i | ||||||||
\(491\) | −33.4183 | −1.50815 | −0.754074 | − | 0.656789i | \(-0.771914\pi\) | ||||
−0.754074 | + | 0.656789i | \(0.771914\pi\) | |||||||
\(492\) | −4.32067 | − | 4.32067i | −0.194791 | − | 0.194791i | ||||
\(493\) | 41.1722i | 1.85430i | ||||||||
\(494\) | −7.51072 | − | 7.01373i | −0.337923 | − | 0.315562i | ||||
\(495\) | −0.288811 | − | 0.897400i | −0.0129811 | − | 0.0403352i | ||||
\(496\) | −19.2953 | − | 19.2953i | −0.866383 | − | 0.866383i | ||||
\(497\) | − | 46.3353i | − | 2.07842i | ||||||
\(498\) | − | 9.89674i | − | 0.443484i | ||||||
\(499\) | −13.6017 | − | 13.6017i | −0.608896 | − | 0.608896i | 0.333761 | − | 0.942658i | \(-0.391682\pi\) |
−0.942658 | + | 0.333761i | \(0.891682\pi\) | |||||||
\(500\) | 1.81203 | + | 1.81203i | 0.0810367 | + | 0.0810367i | ||||
\(501\) | 3.87790 | + | 3.87790i | 0.173252 | + | 0.173252i | ||||
\(502\) | −17.5192 | − | 17.5192i | −0.781918 | − | 0.781918i | ||||
\(503\) | − | 12.4724i | − | 0.556117i | −0.960564 | − | 0.278058i | \(-0.910309\pi\) | ||
0.960564 | − | 0.278058i | \(-0.0896909\pi\) | |||||||
\(504\) | 8.77447i | 0.390846i | ||||||||
\(505\) | 3.52716 | + | 3.52716i | 0.156957 | + | 0.156957i | ||||
\(506\) | 5.65664 | + | 17.5765i | 0.251468 | + | 0.781370i | ||||
\(507\) | −0.888616 | − | 12.9696i | −0.0394648 | − | 0.576000i | ||||
\(508\) | − | 9.95181i | − | 0.441540i | ||||||
\(509\) | 22.4584 | + | 22.4584i | 0.995450 | + | 0.995450i | 0.999990 | − | 0.00454003i | \(-0.00144514\pi\) |
−0.00454003 | + | 0.999990i | \(0.501445\pi\) | |||||||
\(510\) | 3.51722 | 0.155745 | ||||||||
\(511\) | − | 18.9994i | − | 0.840485i | ||||||
\(512\) | −3.77624 | + | 3.77624i | −0.166888 | + | 0.166888i | ||||
\(513\) | −1.18165 | + | 1.18165i | −0.0521710 | + | 0.0521710i | ||||
\(514\) | −3.41908 | − | 3.41908i | −0.150809 | − | 0.150809i | ||||
\(515\) | 0.788243 | − | 0.788243i | 0.0347342 | − | 0.0347342i | ||||
\(516\) | 2.56205i | 0.112788i | ||||||||
\(517\) | 15.1537 | − | 4.87693i | 0.666461 | − | 0.214487i | ||||
\(518\) | 23.7800 | − | 23.7800i | 1.04483 | − | 1.04483i | ||||
\(519\) | 8.75558 | 0.384327 | ||||||||
\(520\) | 1.39391 | + | 1.30168i | 0.0611272 | + | 0.0570823i | ||||
\(521\) | 40.1278 | 1.75803 | 0.879014 | − | 0.476795i | \(-0.158202\pi\) | ||||
0.879014 | + | 0.476795i | \(0.158202\pi\) | |||||||
\(522\) | −6.84397 | − | 6.84397i | −0.299553 | − | 0.299553i | ||||
\(523\) | − | 22.0859i | − | 0.965747i | −0.875690 | − | 0.482874i | \(-0.839593\pi\) | ||
0.875690 | − | 0.482874i | \(-0.160407\pi\) | |||||||
\(524\) | −12.5456 | −0.548057 | ||||||||
\(525\) | −16.4010 | + | 16.4010i | −0.715798 | + | 0.715798i | ||||
\(526\) | 17.5086 | + | 17.5086i | 0.763411 | + | 0.763411i | ||||
\(527\) | −28.0445 | − | 28.0445i | −1.22164 | − | 1.22164i | ||||
\(528\) | 14.7301 | + | 7.55731i | 0.641044 | + | 0.328890i | ||||
\(529\) | 12.3452 | 0.536748 | ||||||||
\(530\) | −2.63927 | −0.114642 | ||||||||
\(531\) | −5.68655 | + | 5.68655i | −0.246775 | + | 0.246775i | ||||
\(532\) | − | 7.16155i | − | 0.310492i | ||||||
\(533\) | −0.828933 | − | 24.2254i | −0.0359051 | − | 1.04932i | ||||
\(534\) | 14.6729i | 0.634959i | ||||||||
\(535\) | −0.109787 | + | 0.109787i | −0.00474652 | + | 0.00474652i | ||||
\(536\) | 1.97002i | 0.0850921i | ||||||||
\(537\) | 8.37650i | 0.361473i | ||||||||
\(538\) | 27.7608 | − | 27.7608i | 1.19685 | − | 1.19685i | ||||
\(539\) | −23.0610 | + | 44.9486i | −0.993308 | + | 1.93607i | ||||
\(540\) | −0.182679 | + | 0.182679i | −0.00786127 | + | 0.00786127i | ||||
\(541\) | 8.27698 | + | 8.27698i | 0.355855 | + | 0.355855i | 0.862283 | − | 0.506427i | \(-0.169034\pi\) |
−0.506427 | + | 0.862283i | \(0.669034\pi\) | |||||||
\(542\) | −41.0060 | −1.76136 | ||||||||
\(543\) | 8.13564i | 0.349134i | ||||||||
\(544\) | −24.5823 | + | 24.5823i | −1.05396 | + | 1.05396i | ||||
\(545\) | −1.82015 | −0.0779667 | ||||||||
\(546\) | 19.7896 | − | 21.1918i | 0.846915 | − | 0.906927i | ||||
\(547\) | − | 13.3885i | − | 0.572451i | −0.958162 | − | 0.286225i | \(-0.907599\pi\) | ||
0.958162 | − | 0.286225i | \(-0.0924006\pi\) | |||||||
\(548\) | 11.5004 | + | 11.5004i | 0.491271 | + | 0.491271i | ||||
\(549\) | − | 14.3278i | − | 0.611495i | ||||||
\(550\) | 8.52474 | + | 26.4883i | 0.363496 | + | 1.12947i | ||||
\(551\) | −6.70575 | − | 6.70575i | −0.285674 | − | 0.285674i | ||||
\(552\) | −4.29524 | + | 4.29524i | −0.182818 | + | 0.182818i | ||||
\(553\) | 10.1444 | − | 10.1444i | 0.431383 | − | 0.431383i | ||||
\(554\) | 33.0625 | − | 33.0625i | 1.40469 | − | 1.40469i | ||||
\(555\) | −1.18868 | −0.0504565 | ||||||||
\(556\) | 14.6041 | 0.619351 | ||||||||
\(557\) | 1.84660 | + | 1.84660i | 0.0782429 | + | 0.0782429i | 0.745145 | − | 0.666902i | \(-0.232380\pi\) |
−0.666902 | + | 0.745145i | \(0.732380\pi\) | |||||||
\(558\) | 9.32355 | 0.394697 | ||||||||
\(559\) | −6.93675 | + | 7.42829i | −0.293393 | + | 0.314183i | ||||
\(560\) | 6.69005i | 0.282706i | ||||||||
\(561\) | 21.4092 | + | 10.9841i | 0.903899 | + | 0.463749i | ||||
\(562\) | −8.58094 | −0.361965 | ||||||||
\(563\) | 13.1782 | 0.555396 | 0.277698 | − | 0.960668i | \(-0.410429\pi\) | ||||
0.277698 | + | 0.960668i | \(0.410429\pi\) | |||||||
\(564\) | −3.08477 | − | 3.08477i | −0.129892 | − | 0.129892i | ||||
\(565\) | −1.12348 | − | 1.12348i | −0.0472652 | − | 0.0472652i | ||||
\(566\) | 30.4019 | − | 30.4019i | 1.27789 | − | 1.27789i | ||||
\(567\) | −3.33407 | − | 3.33407i | −0.140018 | − | 0.140018i | ||||
\(568\) | − | 18.2874i | − | 0.767322i | ||||||
\(569\) | 4.97172 | 0.208426 | 0.104213 | − | 0.994555i | \(-0.466768\pi\) | ||||
0.104213 | + | 0.994555i | \(0.466768\pi\) | |||||||
\(570\) | −0.572852 | + | 0.572852i | −0.0239941 | + | 0.0239941i | ||||
\(571\) | −17.0888 | −0.715145 | −0.357572 | − | 0.933885i | \(-0.616395\pi\) | ||||
−0.357572 | + | 0.933885i | \(0.616395\pi\) | |||||||
\(572\) | −3.68159 | − | 10.2263i | −0.153935 | − | 0.427582i | ||||
\(573\) | −1.28415 | −0.0536462 | ||||||||
\(574\) | 38.2289 | − | 38.2289i | 1.59564 | − | 1.59564i | ||||
\(575\) | −16.0571 | −0.669628 | ||||||||
\(576\) | 1.81089i | 0.0754536i | ||||||||
\(577\) | 4.06432 | + | 4.06432i | 0.169200 | + | 0.169200i | 0.786628 | − | 0.617428i | \(-0.211825\pi\) |
−0.617428 | + | 0.786628i | \(0.711825\pi\) | |||||||
\(578\) | −42.9783 | + | 42.9783i | −1.78766 | + | 1.78766i | ||||
\(579\) | 18.7908 | + | 18.7908i | 0.780919 | + | 0.780919i | ||||
\(580\) | −1.03669 | − | 1.03669i | −0.0430462 | − | 0.0430462i | ||||
\(581\) | 27.3602 | 1.13509 | ||||||||
\(582\) | 4.25588 | 0.176412 | ||||||||
\(583\) | −16.0651 | − | 8.24228i | −0.665350 | − | 0.341360i | ||||
\(584\) | − | 7.49861i | − | 0.310295i | ||||||
\(585\) | −1.02426 | + | 0.0350475i | −0.0423478 | + | 0.00144904i | ||||
\(586\) | −34.1885 | −1.41231 | ||||||||
\(587\) | −4.92139 | − | 4.92139i | −0.203127 | − | 0.203127i | 0.598211 | − | 0.801339i | \(-0.295878\pi\) |
−0.801339 | + | 0.598211i | \(0.795878\pi\) | |||||||
\(588\) | 13.8444 | 0.570932 | ||||||||
\(589\) | 9.13525 | 0.376411 | ||||||||
\(590\) | −2.75679 | + | 2.75679i | −0.113495 | + | 0.113495i | ||||
\(591\) | −12.3045 | + | 12.3045i | −0.506141 | + | 0.506141i | ||||
\(592\) | 14.7607 | − | 14.7607i | 0.606660 | − | 0.606660i | ||||
\(593\) | −8.10376 | − | 8.10376i | −0.332781 | − | 0.332781i | 0.520860 | − | 0.853642i | \(-0.325611\pi\) |
−0.853642 | + | 0.520860i | \(0.825611\pi\) | |||||||
\(594\) | −5.38468 | + | 1.73295i | −0.220936 | + | 0.0711038i | ||||
\(595\) | 9.72358i | 0.398628i | ||||||||
\(596\) | 9.68319 | + | 9.68319i | 0.396639 | + | 0.396639i | ||||
\(597\) | 20.0985i | 0.822577i | ||||||||
\(598\) | 20.0611 | − | 0.686441i | 0.820358 | − | 0.0280707i | ||||
\(599\) | −8.72506 | −0.356496 | −0.178248 | − | 0.983986i | \(-0.557043\pi\) | ||||
−0.178248 | + | 0.983986i | \(0.557043\pi\) | |||||||
\(600\) | −6.47307 | + | 6.47307i | −0.264262 | + | 0.264262i | ||||
\(601\) | 13.9440i | 0.568786i | 0.958708 | + | 0.284393i | \(0.0917921\pi\) | ||||
−0.958708 | + | 0.284393i | \(0.908208\pi\) | |||||||
\(602\) | −22.6688 | −0.923911 | ||||||||
\(603\) | −0.748559 | − | 0.748559i | −0.0304837 | − | 0.0304837i | ||||
\(604\) | −2.45798 | + | 2.45798i | −0.100014 | + | 0.100014i | ||||
\(605\) | 0.506388 | − | 3.08540i | 0.0205876 | − | 0.125439i | ||||
\(606\) | 21.1640 | − | 21.1640i | 0.859730 | − | 0.859730i | ||||
\(607\) | 45.9267i | 1.86411i | 0.362323 | + | 0.932053i | \(0.381984\pi\) | ||||
−0.362323 | + | 0.932053i | \(0.618016\pi\) | |||||||
\(608\) | − | 8.00745i | − | 0.324745i | ||||||
\(609\) | 18.9206 | − | 18.9206i | 0.766701 | − | 0.766701i | ||||
\(610\) | − | 6.94598i | − | 0.281235i | ||||||
\(611\) | −0.591822 | − | 17.2959i | −0.0239426 | − | 0.699715i | ||||
\(612\) | − | 6.59415i | − | 0.266553i | ||||||
\(613\) | −3.85718 | + | 3.85718i | −0.155790 | + | 0.155790i | −0.780698 | − | 0.624908i | \(-0.785136\pi\) |
0.624908 | + | 0.780698i | \(0.285136\pi\) | |||||||
\(614\) | 21.2847 | 0.858979 | ||||||||
\(615\) | −1.91092 | −0.0770559 | ||||||||
\(616\) | −13.2843 | + | 25.8927i | −0.535241 | + | 1.04325i | ||||
\(617\) | 3.08121 | + | 3.08121i | 0.124045 | + | 0.124045i | 0.766404 | − | 0.642359i | \(-0.222044\pi\) |
−0.642359 | + | 0.766404i | \(0.722044\pi\) | |||||||
\(618\) | −4.72970 | − | 4.72970i | −0.190256 | − | 0.190256i | ||||
\(619\) | −18.4046 | + | 18.4046i | −0.739743 | + | 0.739743i | −0.972528 | − | 0.232785i | \(-0.925216\pi\) |
0.232785 | + | 0.972528i | \(0.425216\pi\) | |||||||
\(620\) | 1.41228 | 0.0567187 | ||||||||
\(621\) | − | 3.26417i | − | 0.130987i | ||||||
\(622\) | −18.7054 | − | 18.7054i | −0.750017 | − | 0.750017i | ||||
\(623\) | −40.5642 | −1.62517 | ||||||||
\(624\) | 12.2837 | − | 13.1542i | 0.491743 | − | 0.526588i | ||||
\(625\) | −23.7946 | −0.951784 | ||||||||
\(626\) | −34.6885 | + | 34.6885i | −1.38643 | + | 1.38643i | ||||
\(627\) | −5.27592 | + | 1.69795i | −0.210700 | + | 0.0678096i | ||||
\(628\) | − | 11.8837i | − | 0.474213i | ||||||
\(629\) | 21.4537 | − | 21.4537i | 0.855417 | − | 0.855417i | ||||
\(630\) | −1.61633 | − | 1.61633i | −0.0643961 | − | 0.0643961i | ||||
\(631\) | −17.6559 | + | 17.6559i | −0.702872 | + | 0.702872i | −0.965026 | − | 0.262154i | \(-0.915567\pi\) |
0.262154 | + | 0.965026i | \(0.415567\pi\) | |||||||
\(632\) | 4.00374 | − | 4.00374i | 0.159260 | − | 0.159260i | ||||
\(633\) | − | 21.6318i | − | 0.859786i | ||||||
\(634\) | −28.4063 | −1.12816 | ||||||||
\(635\) | −2.20072 | − | 2.20072i | −0.0873328 | − | 0.0873328i | ||||
\(636\) | 4.94814i | 0.196207i | ||||||||
\(637\) | 40.1397 | + | 37.4836i | 1.59039 | + | 1.48515i | ||||
\(638\) | −9.83435 | − | 30.5576i | −0.389346 | − | 1.20979i | ||||
\(639\) | 6.94874 | + | 6.94874i | 0.274888 | + | 0.274888i | ||||
\(640\) | 3.60194i | 0.142379i | ||||||||
\(641\) | − | 7.41695i | − | 0.292952i | −0.989214 | − | 0.146476i | \(-0.953207\pi\) | ||
0.989214 | − | 0.146476i | \(-0.0467931\pi\) | |||||||
\(642\) | 0.658758 | + | 0.658758i | 0.0259991 | + | 0.0259991i | ||||
\(643\) | −23.3090 | − | 23.3090i | −0.919217 | − | 0.919217i | 0.0777551 | − | 0.996972i | \(-0.475225\pi\) |
−0.996972 | + | 0.0777551i | \(0.975225\pi\) | |||||||
\(644\) | 9.89148 | + | 9.89148i | 0.389779 | + | 0.389779i | ||||
\(645\) | 0.566566 | + | 0.566566i | 0.0223085 | + | 0.0223085i | ||||
\(646\) | − | 20.6782i | − | 0.813572i | ||||||
\(647\) | − | 23.8718i | − | 0.938499i | −0.883066 | − | 0.469249i | \(-0.844525\pi\) | ||
0.883066 | − | 0.469249i | \(-0.155475\pi\) | |||||||
\(648\) | −1.31588 | − | 1.31588i | −0.0516926 | − | 0.0516926i | ||||
\(649\) | −25.3898 | + | 8.17120i | −0.996636 | + | 0.320748i | ||||
\(650\) | 30.2327 | − | 1.03449i | 1.18582 | − | 0.0405760i | ||||
\(651\) | 25.7755i | 1.01022i | ||||||||
\(652\) | 2.95343 | + | 2.95343i | 0.115665 | + | 0.115665i | ||||
\(653\) | −31.2998 | −1.22486 | −0.612429 | − | 0.790526i | \(-0.709807\pi\) | ||||
−0.612429 | + | 0.790526i | \(0.709807\pi\) | |||||||
\(654\) | 10.9215i | 0.427063i | ||||||||
\(655\) | −2.77430 | + | 2.77430i | −0.108401 | + | 0.108401i | ||||
\(656\) | 23.7294 | − | 23.7294i | 0.926476 | − | 0.926476i | ||||
\(657\) | 2.84928 | + | 2.84928i | 0.111161 | + | 0.111161i | ||||
\(658\) | 27.2938 | − | 27.2938i | 1.06402 | − | 1.06402i | ||||
\(659\) | 33.7688i | 1.31544i | 0.753261 | + | 0.657722i | \(0.228480\pi\) | ||||
−0.753261 | + | 0.657722i | \(0.771520\pi\) | |||||||
\(660\) | −0.815643 | + | 0.262499i | −0.0317489 | + | 0.0102177i | ||||
\(661\) | 4.49941 | − | 4.49941i | 0.175007 | − | 0.175007i | −0.614168 | − | 0.789175i | \(-0.710508\pi\) |
0.789175 | + | 0.614168i | \(0.210508\pi\) | |||||||
\(662\) | −0.138327 | −0.00537623 | ||||||||
\(663\) | 17.8537 | − | 19.1188i | 0.693378 | − | 0.742511i | ||||
\(664\) | 10.7984 | 0.419059 | ||||||||
\(665\) | −1.58369 | − | 1.58369i | −0.0614127 | − | 0.0614127i | ||||
\(666\) | 7.13242i | 0.276376i | ||||||||
\(667\) | 18.5239 | 0.717247 | ||||||||
\(668\) | 3.52461 | − | 3.52461i | 0.136371 | − | 0.136371i | ||||
\(669\) | −18.0992 | − | 18.0992i | −0.699757 | − | 0.699757i | ||||
\(670\) | −0.362895 | − | 0.362895i | −0.0140199 | − | 0.0140199i | ||||
\(671\) | 21.6919 | − | 42.2800i | 0.837407 | − | 1.63220i | ||||
\(672\) | 22.5934 | 0.871560 | ||||||||
\(673\) | −26.4783 | −1.02066 | −0.510332 | − | 0.859977i | \(-0.670478\pi\) | ||||
−0.510332 | + | 0.859977i | \(0.670478\pi\) | |||||||
\(674\) | 4.76068 | − | 4.76068i | 0.183374 | − | 0.183374i | ||||
\(675\) | − | 4.91921i | − | 0.189340i | ||||||
\(676\) | −11.7880 | + | 0.807659i | −0.453385 | + | 0.0310638i | ||||
\(677\) | − | 45.1205i | − | 1.73412i | −0.498201 | − | 0.867062i | \(-0.666006\pi\) | ||
0.498201 | − | 0.867062i | \(-0.333994\pi\) | |||||||
\(678\) | −6.74123 | + | 6.74123i | −0.258895 | + | 0.258895i | ||||
\(679\) | 11.7656i | 0.451524i | ||||||||
\(680\) | 3.83766i | 0.147168i | ||||||||
\(681\) | −0.513536 | + | 0.513536i | −0.0196787 | + | 0.0196787i | ||||
\(682\) | 27.5130 | + | 14.1156i | 1.05353 | + | 0.540515i | ||||
\(683\) | 18.7464 | − | 18.7464i | 0.717310 | − | 0.717310i | −0.250744 | − | 0.968053i | \(-0.580675\pi\) |
0.968053 | + | 0.250744i | \(0.0806752\pi\) | |||||||
\(684\) | 1.07399 | + | 1.07399i | 0.0410652 | + | 0.0410652i | ||||
\(685\) | 5.08632 | 0.194338 | ||||||||
\(686\) | 66.2010i | 2.52757i | ||||||||
\(687\) | 12.6249 | − | 12.6249i | 0.481668 | − | 0.481668i | ||||
\(688\) | −14.0709 | −0.536449 | ||||||||
\(689\) | −13.3971 | + | 14.3464i | −0.510388 | + | 0.546555i | ||||
\(690\) | − | 1.58244i | − | 0.0602425i | ||||||
\(691\) | 24.0218 | + | 24.0218i | 0.913834 | + | 0.913834i | 0.996571 | − | 0.0827376i | \(-0.0263663\pi\) |
−0.0827376 | + | 0.996571i | \(0.526366\pi\) | |||||||
\(692\) | − | 7.95791i | − | 0.302514i | ||||||
\(693\) | −4.79085 | − | 14.8863i | −0.181989 | − | 0.565482i | ||||
\(694\) | 4.16338 | + | 4.16338i | 0.158040 | + | 0.158040i | ||||
\(695\) | 3.22951 | − | 3.22951i | 0.122502 | − | 0.122502i | ||||
\(696\) | 7.46749 | − | 7.46749i | 0.283055 | − | 0.283055i | ||||
\(697\) | 34.4892 | − | 34.4892i | 1.30637 | − | 1.30637i | ||||
\(698\) | 13.2888 | 0.502987 | ||||||||
\(699\) | 22.5952 | 0.854629 | ||||||||
\(700\) | 14.9068 | + | 14.9068i | 0.563423 | + | 0.563423i | ||||
\(701\) | 3.82750 | 0.144563 | 0.0722814 | − | 0.997384i | \(-0.476972\pi\) | ||||
0.0722814 | + | 0.997384i | \(0.476972\pi\) | |||||||
\(702\) | 0.210296 | + | 6.14585i | 0.00793711 | + | 0.231960i | ||||
\(703\) | 6.98837i | 0.263571i | ||||||||
\(704\) | −2.74164 | + | 5.34377i | −0.103329 | + | 0.201401i | ||||
\(705\) | −1.36432 | −0.0513831 | ||||||||
\(706\) | −17.1990 | −0.647294 | ||||||||
\(707\) | 58.5092 | + | 58.5092i | 2.20047 | + | 2.20047i | ||||
\(708\) | 5.16847 | + | 5.16847i | 0.194243 | + | 0.194243i | ||||
\(709\) | 17.0851 | − | 17.0851i | 0.641643 | − | 0.641643i | −0.309317 | − | 0.950959i | \(-0.600100\pi\) |
0.950959 | + | 0.309317i | \(0.100100\pi\) | |||||||
\(710\) | 3.36869 | + | 3.36869i | 0.126425 | + | 0.126425i | ||||
\(711\) | 3.04264i | 0.114108i | ||||||||
\(712\) | −16.0097 | −0.599989 | ||||||||
\(713\) | −12.6175 | + | 12.6175i | −0.472531 | + | 0.472531i | ||||
\(714\) | 58.3444 | 2.18349 | ||||||||
\(715\) | −3.07555 | − | 1.44728i | −0.115019 | − | 0.0541251i | ||||
\(716\) | 7.61336 | 0.284525 | ||||||||
\(717\) | −3.72061 | + | 3.72061i | −0.138949 | + | 0.138949i | ||||
\(718\) | −38.7377 | −1.44568 | ||||||||
\(719\) | − | 50.3816i | − | 1.87892i | −0.342663 | − | 0.939459i | \(-0.611329\pi\) | ||
0.342663 | − | 0.939459i | \(-0.388671\pi\) | |||||||
\(720\) | −1.00328 | − | 1.00328i | −0.0373902 | − | 0.0373902i | ||||
\(721\) | 13.0755 | − | 13.0755i | 0.486959 | − | 0.486959i | ||||
\(722\) | −19.5462 | − | 19.5462i | −0.727435 | − | 0.727435i | ||||
\(723\) | −7.81915 | − | 7.81915i | −0.290797 | − | 0.290797i | ||||
\(724\) | 7.39444 | 0.274812 | ||||||||
\(725\) | 27.9161 | 1.03678 | ||||||||
\(726\) | −18.5133 | − | 3.03848i | −0.687095 | − | 0.112769i | ||||
\(727\) | 14.1485i | 0.524740i | 0.964967 | + | 0.262370i | \(0.0845041\pi\) | ||||
−0.964967 | + | 0.262370i | \(0.915496\pi\) | |||||||
\(728\) | 23.1225 | + | 21.5925i | 0.856978 | + | 0.800271i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.38131 | + | 1.38131i | 0.0511245 | + | 0.0511245i | ||||
\(731\) | −20.4512 | −0.756416 | ||||||||
\(732\) | −13.0225 | −0.481324 | ||||||||
\(733\) | −7.13792 | + | 7.13792i | −0.263645 | + | 0.263645i | −0.826533 | − | 0.562888i | \(-0.809690\pi\) |
0.562888 | + | 0.826533i | \(0.309690\pi\) | |||||||
\(734\) | 42.8914 | − | 42.8914i | 1.58315 | − | 1.58315i | ||||
\(735\) | 3.06151 | − | 3.06151i | 0.112925 | − | 0.112925i | ||||
\(736\) | 11.0598 | + | 11.0598i | 0.407671 | + | 0.407671i | ||||
\(737\) | −1.07563 | − | 3.34223i | −0.0396214 | − | 0.123113i | ||||
\(738\) | 11.4661i | 0.422074i | ||||||||
\(739\) | 6.21124 | + | 6.21124i | 0.228484 | + | 0.228484i | 0.812059 | − | 0.583575i | \(-0.198347\pi\) |
−0.583575 | + | 0.812059i | \(0.698347\pi\) | |||||||
\(740\) | 1.08038i | 0.0397156i | ||||||||
\(741\) | 0.206049 | + | 6.02172i | 0.00756938 | + | 0.221213i | ||||
\(742\) | −43.7807 | −1.60724 | ||||||||
\(743\) | 22.0058 | − | 22.0058i | 0.807314 | − | 0.807314i | −0.176913 | − | 0.984227i | \(-0.556611\pi\) |
0.984227 | + | 0.176913i | \(0.0566111\pi\) | |||||||
\(744\) | 10.1730i | 0.372959i | ||||||||
\(745\) | 4.28263 | 0.156903 | ||||||||
\(746\) | −25.5150 | − | 25.5150i | −0.934170 | − | 0.934170i | ||||
\(747\) | −4.10311 | + | 4.10311i | −0.150125 | + | 0.150125i | ||||
\(748\) | 9.98339 | − | 19.4588i | 0.365029 | − | 0.711483i | ||||
\(749\) | −1.82118 | + | 1.82118i | −0.0665443 | + | 0.0665443i | ||||
\(750\) | − | 4.80874i | − | 0.175591i | ||||||
\(751\) | − | 30.0145i | − | 1.09525i | −0.836725 | − | 0.547623i | \(-0.815533\pi\) | ||
0.836725 | − | 0.547623i | \(-0.184467\pi\) | |||||||
\(752\) | 16.9417 | − | 16.9417i | 0.617801 | − | 0.617801i | ||||
\(753\) | 14.5266i | 0.529379i | ||||||||
\(754\) | −34.8771 | + | 1.19341i | −1.27015 | + | 0.0434615i | ||||
\(755\) | 1.08710i | 0.0395637i | ||||||||
\(756\) | −3.03032 | + | 3.03032i | −0.110212 | + | 0.110212i | ||||
\(757\) | −42.5187 | −1.54537 | −0.772684 | − | 0.634790i | \(-0.781086\pi\) | ||||
−0.772684 | + | 0.634790i | \(0.781086\pi\) | |||||||
\(758\) | −31.3474 | −1.13859 | ||||||||
\(759\) | 4.94187 | − | 9.63227i | 0.179378 | − | 0.349629i | ||||
\(760\) | −0.625042 | − | 0.625042i | −0.0226727 | − | 0.0226727i | ||||
\(761\) | −5.20061 | − | 5.20061i | −0.188522 | − | 0.188522i | 0.606535 | − | 0.795057i | \(-0.292559\pi\) |
−0.795057 | + | 0.606535i | \(0.792559\pi\) | |||||||
\(762\) | −13.2050 | + | 13.2050i | −0.478366 | + | 0.478366i | ||||
\(763\) | −30.1930 | −1.09306 | ||||||||
\(764\) | 1.16716i | 0.0422264i | ||||||||
\(765\) | −1.45821 | − | 1.45821i | −0.0527218 | − | 0.0527218i | ||||
\(766\) | −37.9588 | −1.37151 | ||||||||
\(767\) | 0.991586 | + | 28.9788i | 0.0358041 | + | 1.04637i | ||||
\(768\) | 17.9909 | 0.649192 | ||||||||
\(769\) | 4.65425 | − | 4.65425i | 0.167836 | − | 0.167836i | −0.618191 | − | 0.786028i | \(-0.712134\pi\) |
0.786028 | + | 0.618191i | \(0.212134\pi\) | |||||||
\(770\) | −2.32256 | − | 7.21673i | −0.0836993 | − | 0.260073i | ||||
\(771\) | 2.83504i | 0.102102i | ||||||||
\(772\) | 17.0789 | − | 17.0789i | 0.614682 | − | 0.614682i | ||||
\(773\) | −13.3308 | − | 13.3308i | −0.479476 | − | 0.479476i | 0.425488 | − | 0.904964i | \(-0.360102\pi\) |
−0.904964 | + | 0.425488i | \(0.860102\pi\) | |||||||
\(774\) | 3.39957 | − | 3.39957i | 0.122195 | − | 0.122195i | ||||
\(775\) | −19.0150 | + | 19.0150i | −0.683041 | + | 0.683041i | ||||
\(776\) | 4.64361i | 0.166696i | ||||||||
\(777\) | −19.7180 | −0.707380 | ||||||||
\(778\) | 7.74070 | + | 7.74070i | 0.277518 | + | 0.277518i | ||||
\(779\) | 11.2345i | 0.402519i | ||||||||
\(780\) | 0.0318545 | + | 0.930941i | 0.00114058 | + | 0.0333330i | ||||
\(781\) | 9.98490 | + | 31.0254i | 0.357288 | + | 1.11017i | ||||
\(782\) | 28.5606 | + | 28.5606i | 1.02132 | + | 1.02132i | ||||
\(783\) | 5.67492i | 0.202805i | ||||||||
\(784\) | 76.0340i | 2.71550i | ||||||||
\(785\) | −2.62794 | − | 2.62794i | −0.0937951 | − | 0.0937951i | ||||
\(786\) | 16.6466 | + | 16.6466i | 0.593766 | + | 0.593766i | ||||
\(787\) | −11.1342 | − | 11.1342i | −0.396890 | − | 0.396890i | 0.480244 | − | 0.877135i | \(-0.340548\pi\) |
−0.877135 | + | 0.480244i | \(0.840548\pi\) | |||||||
\(788\) | 11.1835 | + | 11.1835i | 0.398397 | + | 0.398397i | ||||
\(789\) | − | 14.5178i | − | 0.516849i | ||||||
\(790\) | 1.47504i | 0.0524797i | ||||||||
\(791\) | −18.6365 | − | 18.6365i | −0.662639 | − | 0.662639i | ||||
\(792\) | −1.89083 | − | 5.87525i | −0.0671878 | − | 0.208768i | ||||
\(793\) | −37.7566 | − | 35.2583i | −1.34078 | − | 1.25206i | ||||
\(794\) | 31.9207i | 1.13282i | ||||||||
\(795\) | 1.09422 | + | 1.09422i | 0.0388080 | + | 0.0388080i | ||||
\(796\) | 18.2674 | 0.647472 | ||||||||
\(797\) | 19.7275i | 0.698784i | 0.936977 | + | 0.349392i | \(0.113612\pi\) | ||||
−0.936977 | + | 0.349392i | \(0.886388\pi\) | |||||||
\(798\) | −9.50259 | + | 9.50259i | −0.336388 | + | 0.336388i | ||||
\(799\) | 24.6238 | − | 24.6238i | 0.871126 | − | 0.871126i | ||||
\(800\) | 16.6675 | + | 16.6675i | 0.589287 | + | 0.589287i | ||||
\(801\) | 6.08327 | − | 6.08327i | 0.214942 | − | 0.214942i | ||||
\(802\) | 5.13256i | 0.181237i | ||||||||
\(803\) | 4.09423 | + | 12.7217i | 0.144482 | + | 0.448940i | ||||
\(804\) | −0.680362 | + | 0.680362i | −0.0239945 | + | 0.0239945i | ||||
\(805\) | 4.37475 | 0.154190 | ||||||||
\(806\) | 22.9437 | − | 24.5695i | 0.808157 | − | 0.865423i | ||||
\(807\) | −23.0188 | −0.810300 | ||||||||
\(808\) | 23.0922 | + | 23.0922i | 0.812380 | + | 0.812380i | ||||
\(809\) | 3.53428i | 0.124259i | 0.998068 | + | 0.0621294i | \(0.0197891\pi\) | ||||
−0.998068 | + | 0.0621294i | \(0.980211\pi\) | |||||||
\(810\) | 0.484791 | 0.0170338 | ||||||||
\(811\) | 11.8959 | − | 11.8959i | 0.417723 | − | 0.417723i | −0.466695 | − | 0.884418i | \(-0.654556\pi\) |
0.884418 | + | 0.466695i | \(0.154556\pi\) | |||||||
\(812\) | −17.1968 | − | 17.1968i | −0.603490 | − | 0.603490i | ||||
\(813\) | 17.0008 | + | 17.0008i | 0.596242 | + | 0.596242i | ||||
\(814\) | −10.7983 | + | 21.0471i | −0.378481 | + | 0.737702i | ||||
\(815\) | 1.30623 | 0.0457552 | ||||||||
\(816\) | 36.2154 | 1.26779 | ||||||||
\(817\) | 3.33091 | − | 3.33091i | 0.116534 | − | 0.116534i | ||||
\(818\) | − | 13.4049i | − | 0.468690i | ||||||
\(819\) | −16.9906 | + | 0.581376i | −0.593698 | + | 0.0203149i | ||||
\(820\) | 1.73683i | 0.0606527i | ||||||||
\(821\) | −21.4198 | + | 21.4198i | −0.747556 | + | 0.747556i | −0.974020 | − | 0.226464i | \(-0.927284\pi\) |
0.226464 | + | 0.974020i | \(0.427284\pi\) | |||||||
\(822\) | − | 30.5195i | − | 1.06449i | ||||||
\(823\) | − | 43.7848i | − | 1.52624i | −0.646255 | − | 0.763122i | \(-0.723666\pi\) | ||
0.646255 | − | 0.763122i | \(-0.276334\pi\) | |||||||
\(824\) | 5.16060 | − | 5.16060i | 0.179778 | − | 0.179778i | ||||
\(825\) | 7.44756 | − | 14.5161i | 0.259291 | − | 0.505387i | ||||
\(826\) | −45.7302 | + | 45.7302i | −1.59116 | + | 1.59116i | ||||
\(827\) | 16.0478 | + | 16.0478i | 0.558036 | + | 0.558036i | 0.928748 | − | 0.370712i | \(-0.120886\pi\) |
−0.370712 | + | 0.928748i | \(0.620886\pi\) | |||||||
\(828\) | −2.96679 | −0.103103 | ||||||||
\(829\) | 42.1586i | 1.46423i | 0.681182 | + | 0.732114i | \(0.261466\pi\) | ||||
−0.681182 | + | 0.732114i | \(0.738534\pi\) | |||||||
\(830\) | −1.98915 | + | 1.98915i | −0.0690445 | + | 0.0690445i | ||||
\(831\) | −27.4149 | −0.951013 | ||||||||
\(832\) | 4.77206 | + | 4.45629i | 0.165441 | + | 0.154494i | ||||
\(833\) | 110.511i | 3.82897i | ||||||||
\(834\) | −19.3780 | − | 19.3780i | −0.671007 | − | 0.671007i | ||||
\(835\) | − | 1.55884i | − | 0.0539460i | ||||||
\(836\) | 1.54326 | + | 4.79526i | 0.0533747 | + | 0.165848i | ||||
\(837\) | −3.86547 | − | 3.86547i | −0.133610 | − | 0.133610i | ||||
\(838\) | 13.3501 | − | 13.3501i | 0.461173 | − | 0.461173i | ||||
\(839\) | 13.9581 | − | 13.9581i | 0.481887 | − | 0.481887i | −0.423847 | − | 0.905734i | \(-0.639321\pi\) |
0.905734 | + | 0.423847i | \(0.139321\pi\) | |||||||
\(840\) | 1.76359 | − | 1.76359i | 0.0608495 | − | 0.0608495i | ||||
\(841\) | −3.20466 | −0.110506 | ||||||||
\(842\) | −8.74943 | −0.301525 | ||||||||
\(843\) | 3.55759 | + | 3.55759i | 0.122530 | + | 0.122530i | ||||
\(844\) | −19.6610 | −0.676760 | ||||||||
\(845\) | −2.42816 | + | 2.78537i | −0.0835314 | + | 0.0958197i | ||||
\(846\) | 8.18631i | 0.281451i | ||||||||
\(847\) | 8.40007 | − | 51.1813i | 0.288630 | − | 1.75861i | ||||
\(848\) | −27.1755 | −0.933209 | ||||||||
\(849\) | −25.2088 | −0.865163 | ||||||||
\(850\) | 43.0417 | + | 43.0417i | 1.47632 | + | 1.47632i | ||||
\(851\) | −9.65229 | − | 9.65229i | −0.330876 | − | 0.330876i | ||||
\(852\) | 6.31568 | − | 6.31568i | 0.216372 | − | 0.216372i | ||||
\(853\) | 40.7704 | + | 40.7704i | 1.39595 | + | 1.39595i | 0.811248 | + | 0.584702i | \(0.198789\pi\) |
0.584702 | + | 0.811248i | \(0.301211\pi\) | |||||||
\(854\) | − | 115.221i | − | 3.94280i | ||||||
\(855\) | 0.475000 | 0.0162447 | ||||||||
\(856\) | −0.718774 | + | 0.718774i | −0.0245672 | + | 0.0245672i | ||||
\(857\) | 31.5605 | 1.07809 | 0.539043 | − | 0.842278i | \(-0.318786\pi\) | ||||
0.539043 | + | 0.842278i | \(0.318786\pi\) | |||||||
\(858\) | −8.68410 | + | 18.4542i | −0.296470 | + | 0.630017i | ||||
\(859\) | 31.4713 | 1.07379 | 0.536894 | − | 0.843650i | \(-0.319598\pi\) | ||||
0.536894 | + | 0.843650i | \(0.319598\pi\) | |||||||
\(860\) | 0.514949 | − | 0.514949i | 0.0175596 | − | 0.0175596i | ||||
\(861\) | −31.6988 | −1.08029 | ||||||||
\(862\) | − | 12.4894i | − | 0.425390i | ||||||
\(863\) | 16.5706 | + | 16.5706i | 0.564070 | + | 0.564070i | 0.930461 | − | 0.366391i | \(-0.119407\pi\) |
−0.366391 | + | 0.930461i | \(0.619407\pi\) | |||||||
\(864\) | −3.38826 | + | 3.38826i | −0.115271 | + | 0.115271i | ||||
\(865\) | −1.75979 | − | 1.75979i | −0.0598347 | − | 0.0598347i | ||||
\(866\) | 35.3913 | + | 35.3913i | 1.20264 | + | 1.20264i | ||||
\(867\) | 35.6369 | 1.21029 | ||||||||
\(868\) | 23.4272 | 0.795173 | ||||||||
\(869\) | −4.60648 | + | 8.97855i | −0.156264 | + | 0.304576i | ||||
\(870\) | 2.75115i | 0.0932727i | ||||||||
\(871\) | −3.81469 | + | 0.130529i | −0.129256 | + | 0.00442282i | ||||
\(872\) | −11.9165 | −0.403542 | ||||||||
\(873\) | −1.76445 | − | 1.76445i | −0.0597177 | − | 0.0597177i | ||||
\(874\) | −9.30335 | −0.314690 | ||||||||
\(875\) | 13.2941 | 0.449422 | ||||||||
\(876\) | 2.58970 | − | 2.58970i | 0.0874978 | − | 0.0874978i | ||||
\(877\) | −14.7471 | + | 14.7471i | −0.497973 | + | 0.497973i | −0.910807 | − | 0.412833i | \(-0.864539\pi\) |
0.412833 | + | 0.910807i | \(0.364539\pi\) | |||||||
\(878\) | −34.5474 | + | 34.5474i | −1.16592 | + | 1.16592i | ||||
\(879\) | 14.1743 | + | 14.1743i | 0.478086 | + | 0.478086i | ||||
\(880\) | −1.44166 | − | 4.47955i | −0.0485982 | − | 0.151006i | ||||
\(881\) | 25.4247i | 0.856579i | 0.903642 | + | 0.428289i | \(0.140884\pi\) | ||||
−0.903642 | + | 0.428289i | \(0.859116\pi\) | |||||||
\(882\) | −18.3700 | − | 18.3700i | −0.618549 | − | 0.618549i | ||||
\(883\) | − | 16.4770i | − | 0.554494i | −0.960799 | − | 0.277247i | \(-0.910578\pi\) | ||
0.960799 | − | 0.277247i | \(-0.0894221\pi\) | |||||||
\(884\) | −17.3769 | − | 16.2271i | −0.584450 | − | 0.545776i | ||||
\(885\) | 2.28588 | 0.0768392 | ||||||||
\(886\) | 19.7402 | − | 19.7402i | 0.663184 | − | 0.663184i | ||||
\(887\) | 4.46850i | 0.150037i | 0.997182 | + | 0.0750187i | \(0.0239017\pi\) | ||||
−0.997182 | + | 0.0750187i | \(0.976098\pi\) | |||||||
\(888\) | −7.78222 | −0.261154 | ||||||||
\(889\) | −36.5059 | − | 36.5059i | −1.22437 | − | 1.22437i | ||||
\(890\) | 2.94912 | − | 2.94912i | 0.0988547 | − | 0.0988547i | ||||
\(891\) | 2.95091 | + | 1.51398i | 0.0988592 | + | 0.0507201i | ||||
\(892\) | −16.4503 | + | 16.4503i | −0.550797 | + | 0.550797i | ||||
\(893\) | 8.02098i | 0.268412i | ||||||||
\(894\) | − | 25.6971i | − | 0.859439i | ||||||
\(895\) | 1.68360 | − | 1.68360i | 0.0562765 | − | 0.0562765i | ||||
\(896\) | 59.7496i | 1.99610i | ||||||||
\(897\) | −8.60175 | − | 8.03256i | −0.287204 | − | 0.268200i | ||||
\(898\) | − | 13.5737i | − | 0.452960i | ||||||
\(899\) | 21.9362 | − | 21.9362i | 0.731614 | − | 0.731614i | ||||
\(900\) | −4.47104 | −0.149035 | ||||||||
\(901\) | −39.4979 | −1.31587 | ||||||||
\(902\) | −17.3594 | + | 33.8355i | −0.578006 | + | 1.12660i | ||||
\(903\) | 9.39831 | + | 9.39831i | 0.312756 | + | 0.312756i | ||||
\(904\) | −7.35539 | − | 7.35539i | −0.244637 | − | 0.244637i | ||||
\(905\) | 1.63519 | − | 1.63519i | 0.0543555 | − | 0.0543555i | ||||
\(906\) | 6.52295 | 0.216710 | ||||||||
\(907\) | − | 26.6927i | − | 0.886316i | −0.896443 | − | 0.443158i | \(-0.853858\pi\) | ||
0.896443 | − | 0.443158i | \(-0.146142\pi\) | |||||||
\(908\) | 0.466751 | + | 0.466751i | 0.0154897 | + | 0.0154897i | ||||
\(909\) | −17.5489 | −0.582059 | ||||||||
\(910\) | −8.23688 | + | 0.281846i | −0.273050 | + | 0.00934310i | ||||
\(911\) | −24.1348 | −0.799622 | −0.399811 | − | 0.916598i | \(-0.630924\pi\) | ||||
−0.399811 | + | 0.916598i | \(0.630924\pi\) | |||||||
\(912\) | −5.89843 | + | 5.89843i | −0.195317 | + | 0.195317i | ||||
\(913\) | −18.3199 | + | 5.89591i | −0.606301 | + | 0.195126i | ||||
\(914\) | − | 42.0730i | − | 1.39165i | ||||||
\(915\) | −2.87975 | + | 2.87975i | −0.0952016 | + | 0.0952016i | ||||
\(916\) | −11.4747 | − | 11.4747i | −0.379134 | − | 0.379134i | ||||
\(917\) | −46.0206 | + | 46.0206i | −1.51973 | + | 1.51973i | ||||
\(918\) | −8.74972 | + | 8.74972i | −0.288784 | + | 0.288784i | ||||
\(919\) | − | 41.7170i | − | 1.37612i | −0.725655 | − | 0.688059i | \(-0.758463\pi\) | ||
0.725655 | − | 0.688059i | \(-0.241537\pi\) | |||||||
\(920\) | 1.72661 | 0.0569246 | ||||||||
\(921\) | −8.82445 | − | 8.82445i | −0.290775 | − | 0.290775i | ||||
\(922\) | 30.5378i | 1.00571i | ||||||||
\(923\) | 35.4111 | − | 1.21168i | 1.16557 | − | 0.0398829i | ||||
\(924\) | −13.5301 | + | 4.35438i | −0.445106 | + | 0.143249i | ||||
\(925\) | −14.5463 | − | 14.5463i | −0.478280 | − | 0.478280i | ||||
\(926\) | 34.3857i | 1.12999i | ||||||||
\(927\) | 3.92179i | 0.128809i | ||||||||
\(928\) | −19.2281 | − | 19.2281i | −0.631193 | − | 0.631193i | ||||
\(929\) | −26.8941 | − | 26.8941i | −0.882367 | − | 0.882367i | 0.111408 | − | 0.993775i | \(-0.464464\pi\) |
−0.993775 | + | 0.111408i | \(0.964464\pi\) | |||||||
\(930\) | −1.87395 | − | 1.87395i | −0.0614491 | − | 0.0614491i | ||||
\(931\) | −17.9990 | − | 17.9990i | −0.589892 | − | 0.589892i | ||||
\(932\) | − | 20.5367i | − | 0.672701i | ||||||
\(933\) | 15.5102i | 0.507781i | ||||||||
\(934\) | 4.58379 | + | 4.58379i | 0.149986 | + | 0.149986i | ||||
\(935\) | −2.09536 | − | 6.51076i | −0.0685255 | − | 0.212925i | ||||
\(936\) | −6.70576 | + | 0.229455i | −0.219185 | + | 0.00749997i | ||||
\(937\) | − | 36.3852i | − | 1.18865i | −0.804224 | − | 0.594326i | \(-0.797419\pi\) | ||
0.804224 | − | 0.594326i | \(-0.202581\pi\) | |||||||
\(938\) | −6.01978 | − | 6.01978i | −0.196553 | − | 0.196553i | ||||
\(939\) | 28.7631 | 0.938650 | ||||||||
\(940\) | 1.24002i | 0.0404450i | ||||||||
\(941\) | −35.8119 | + | 35.8119i | −1.16743 | + | 1.16743i | −0.184626 | + | 0.982809i | \(0.559107\pi\) |
−0.982809 | + | 0.184626i | \(0.940893\pi\) | |||||||
\(942\) | −15.7684 | + | 15.7684i | −0.513763 | + | 0.513763i | ||||
\(943\) | −15.5171 | − | 15.5171i | −0.505306 | − | 0.505306i | ||||
\(944\) | −28.3855 | + | 28.3855i | −0.923870 | + | 0.923870i | ||||
\(945\) | 1.34024i | 0.0435979i | ||||||||
\(946\) | 15.1787 | − | 4.88496i | 0.493501 | − | 0.158824i | ||||
\(947\) | −35.8340 | + | 35.8340i | −1.16445 | + | 1.16445i | −0.180956 | + | 0.983491i | \(0.557919\pi\) |
−0.983491 | + | 0.180956i | \(0.942081\pi\) | |||||||
\(948\) | 2.76544 | 0.0898172 | ||||||||
\(949\) | 14.5200 | − | 0.496841i | 0.471341 | − | 0.0161281i | ||||
\(950\) | −14.0204 | −0.454883 | ||||||||
\(951\) | 11.7770 | + | 11.7770i | 0.381896 | + | 0.381896i | ||||
\(952\) | 63.6599i | 2.06323i | ||||||||
\(953\) | −56.4922 | −1.82996 | −0.914981 | − | 0.403497i | \(-0.867794\pi\) | ||||
−0.914981 | + | 0.403497i | \(0.867794\pi\) | |||||||
\(954\) | 6.56565 | − | 6.56565i | 0.212571 | − | 0.212571i | ||||
\(955\) | 0.258103 | + | 0.258103i | 0.00835200 | + | 0.00835200i | ||||
\(956\) | 3.38165 | + | 3.38165i | 0.109370 | + | 0.109370i | ||||
\(957\) | −8.59168 | + | 16.7462i | −0.277730 | + | 0.541327i | ||||
\(958\) | −37.2069 | −1.20210 | ||||||||
\(959\) | 84.3729 | 2.72454 | ||||||||
\(960\) | 0.363971 | − | 0.363971i | 0.0117471 | − | 0.0117471i | ||||
\(961\) | − | 1.11628i | − | 0.0360089i | ||||||
\(962\) | 18.7954 | + | 17.5517i | 0.605988 | + | 0.565889i | ||||
\(963\) | − | 0.546231i | − | 0.0176021i | ||||||
\(964\) | −7.10679 | + | 7.10679i | −0.228894 | + | 0.228894i | ||||
\(965\) | − | 7.55355i | − | 0.243157i | ||||||
\(966\) | − | 26.2498i | − | 0.844575i | ||||||
\(967\) | 41.1339 | − | 41.1339i | 1.32278 | − | 1.32278i | 0.411257 | − | 0.911520i | \(-0.365090\pi\) |
0.911520 | − | 0.411257i | \(-0.134910\pi\) | |||||||
\(968\) | 3.31530 | − | 20.2000i | 0.106558 | − | 0.649253i | ||||
\(969\) | −8.57301 | + | 8.57301i | −0.275405 | + | 0.275405i | ||||
\(970\) | −0.855392 | − | 0.855392i | −0.0274650 | − | 0.0274650i | ||||
\(971\) | 28.2094 | 0.905281 | 0.452641 | − | 0.891693i | \(-0.350482\pi\) | ||||
0.452641 | + | 0.891693i | \(0.350482\pi\) | |||||||
\(972\) | − | 0.908895i | − | 0.0291528i | ||||||
\(973\) | 53.5718 | − | 53.5718i | 1.71743 | − | 1.71743i | ||||
\(974\) | 18.9846 | 0.608306 | ||||||||
\(975\) | −12.9631 | − | 12.1053i | −0.415152 | − | 0.387681i | ||||
\(976\) | − | 71.5200i | − | 2.28930i | ||||||
\(977\) | −35.5051 | − | 35.5051i | −1.13591 | − | 1.13591i | −0.989176 | − | 0.146732i | \(-0.953124\pi\) |
−0.146732 | − | 0.989176i | \(-0.546876\pi\) | |||||||
\(978\) | − | 7.83776i | − | 0.250624i | ||||||
\(979\) | 27.1611 | − | 8.74127i | 0.868074 | − | 0.279372i | ||||
\(980\) | −2.78259 | − | 2.78259i | −0.0888866 | − | 0.0888866i | ||||
\(981\) | 4.52795 | − | 4.52795i | 0.144566 | − | 0.144566i | ||||
\(982\) | 40.3027 | − | 40.3027i | 1.28611 | − | 1.28611i | ||||
\(983\) | 0.418033 | − | 0.418033i | 0.0133332 | − | 0.0133332i | −0.700409 | − | 0.713742i | \(-0.746999\pi\) |
0.713742 | + | 0.700409i | \(0.246999\pi\) | |||||||
\(984\) | −12.5107 | −0.398828 | ||||||||
\(985\) | 4.94620 | 0.157599 | ||||||||
\(986\) | −49.6539 | − | 49.6539i | −1.58130 | − | 1.58130i | ||||
\(987\) | −22.6316 | −0.720371 | ||||||||
\(988\) | 5.47311 | − | 0.187277i | 0.174123 | − | 0.00595806i | ||||
\(989\) | 9.20125i | 0.292583i | ||||||||
\(990\) | 1.43058 | + | 0.733962i | 0.0454667 | + | 0.0233269i | ||||
\(991\) | 18.9713 | 0.602644 | 0.301322 | − | 0.953522i | \(-0.402572\pi\) | ||||
0.301322 | + | 0.953522i | \(0.402572\pi\) | |||||||
\(992\) | 26.1944 | 0.831674 | ||||||||
\(993\) | 0.0573492 | + | 0.0573492i | 0.00181992 | + | 0.00181992i | ||||
\(994\) | 55.8805 | + | 55.8805i | 1.77242 | + | 1.77242i | ||||
\(995\) | 4.03961 | − | 4.03961i | 0.128064 | − | 0.128064i | ||||
\(996\) | 3.72930 | + | 3.72930i | 0.118167 | + | 0.118167i | ||||
\(997\) | − | 14.2729i | − | 0.452029i | −0.974124 | − | 0.226014i | \(-0.927430\pi\) | ||
0.974124 | − | 0.226014i | \(-0.0725696\pi\) | |||||||
\(998\) | 32.8075 | 1.03850 | ||||||||
\(999\) | 2.95704 | − | 2.95704i | 0.0935568 | − | 0.0935568i |
(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 | 429.2.m.b.307.4 | yes | 28 | |
11.10 | odd | 2 | inner | 429.2.m.b.307.11 | yes | 28 | |
13.5 | odd | 4 | inner | 429.2.m.b.109.11 | yes | 28 | |
143.109 | even | 4 | inner | 429.2.m.b.109.4 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.m.b.109.4 | ✓ | 28 | 143.109 | even | 4 | inner | |
429.2.m.b.109.11 | yes | 28 | 13.5 | odd | 4 | inner | |
429.2.m.b.307.4 | yes | 28 | 1.1 | even | 1 | trivial | |
429.2.m.b.307.11 | yes | 28 | 11.10 | odd | 2 | inner |