Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,2,Mod(143,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([2, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.q (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.7798042729\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 1043.2 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.1043 |
Dual form | 1350.2.q.g.1007.2 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.258819 | − | 0.965926i | 0.183013 | − | 0.683013i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.866025 | − | 0.500000i | −0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.05902 | + | 0.283763i | 0.400271 | + | 0.107252i | 0.453338 | − | 0.891339i | \(-0.350233\pi\) |
−0.0530669 | + | 0.998591i | \(0.516900\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.44949 | − | 3.14626i | 1.64308 | − | 0.948634i | 0.663354 | − | 0.748305i | \(-0.269132\pi\) |
0.979729 | − | 0.200329i | \(-0.0642011\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.34607 | + | 0.896575i | −0.928032 | + | 0.248665i | −0.691015 | − | 0.722840i | \(-0.742836\pi\) |
−0.237016 | + | 0.971506i | \(0.576170\pi\) | |||||||
\(14\) | 0.548188 | − | 0.949490i | 0.146509 | − | 0.253762i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 3.14626 | + | 3.14626i | 0.763081 | + | 0.763081i | 0.976878 | − | 0.213797i | \(-0.0685831\pi\) |
−0.213797 | + | 0.976878i | \(0.568583\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.55051i | − | 0.355711i | −0.984057 | − | 0.177856i | \(-0.943084\pi\) | ||
0.984057 | − | 0.177856i | \(-0.0569160\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.62863 | − | 6.07812i | −0.347224 | − | 1.29586i | ||||
\(23\) | 0.258819 | + | 0.965926i | 0.0539675 | + | 0.201409i | 0.987646 | − | 0.156704i | \(-0.0500868\pi\) |
−0.933678 | + | 0.358113i | \(0.883420\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.46410i | 0.679366i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.775255 | − | 0.775255i | −0.146509 | − | 0.146509i | ||||
\(29\) | 1.57313 | + | 2.72474i | 0.292123 | + | 0.505972i | 0.974312 | − | 0.225204i | \(-0.0723049\pi\) |
−0.682188 | + | 0.731177i | \(0.738972\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.22474 | − | 3.85337i | 0.399576 | − | 0.692086i | −0.594098 | − | 0.804393i | \(-0.702491\pi\) |
0.993674 | + | 0.112307i | \(0.0358240\pi\) | |||||||
\(32\) | 0.965926 | − | 0.258819i | 0.170753 | − | 0.0457532i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.85337 | − | 2.22474i | 0.660848 | − | 0.381541i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | − | 3.00000i | 0.493197 | − | 0.493197i | −0.416115 | − | 0.909312i | \(-0.636609\pi\) |
0.909312 | + | 0.416115i | \(0.136609\pi\) | |||||||
\(38\) | −1.49768 | − | 0.401302i | −0.242955 | − | 0.0650997i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.39898 | + | 1.96240i | 0.530831 | + | 0.306476i | 0.741355 | − | 0.671113i | \(-0.234184\pi\) |
−0.210524 | + | 0.977589i | \(0.567517\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.896575 | + | 3.34607i | −0.136726 | + | 0.510270i | 0.863258 | + | 0.504762i | \(0.168420\pi\) |
−0.999985 | + | 0.00550783i | \(0.998247\pi\) | |||||||
\(44\) | −6.29253 | −0.948634 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 2.32937 | − | 8.69333i | 0.339774 | − | 1.26805i | −0.558827 | − | 0.829285i | \(-0.688748\pi\) |
0.898600 | − | 0.438768i | \(-0.144585\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.02118 | − | 2.89898i | −0.717311 | − | 0.414140i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.34607 | + | 0.896575i | 0.464016 | + | 0.124333i | ||||
\(53\) | 6.61037 | − | 6.61037i | 0.908004 | − | 0.908004i | −0.0881074 | − | 0.996111i | \(-0.528082\pi\) |
0.996111 | + | 0.0881074i | \(0.0280819\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.949490 | + | 0.548188i | −0.126881 | + | 0.0732547i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.03906 | − | 0.814313i | 0.399048 | − | 0.106925i | ||||
\(59\) | 5.90326 | − | 10.2247i | 0.768539 | − | 1.33115i | −0.169816 | − | 0.985476i | \(-0.554317\pi\) |
0.938355 | − | 0.345673i | \(-0.112349\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.72474 | + | 4.71940i | 0.348868 | + | 0.604257i | 0.986049 | − | 0.166458i | \(-0.0532329\pi\) |
−0.637181 | + | 0.770714i | \(0.719900\pi\) | |||||||
\(62\) | −3.14626 | − | 3.14626i | −0.399576 | − | 0.399576i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.978838 | − | 3.65307i | −0.119584 | − | 0.446294i | 0.880005 | − | 0.474965i | \(-0.157539\pi\) |
−0.999589 | + | 0.0286709i | \(0.990873\pi\) | |||||||
\(68\) | −1.15161 | − | 4.29788i | −0.139654 | − | 0.521194i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.635674i | 0.0754407i | 0.999288 | + | 0.0377203i | \(0.0120096\pi\) | ||||
−0.999288 | + | 0.0377203i | \(0.987990\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.89898 | − | 2.89898i | −0.339300 | − | 0.339300i | 0.516804 | − | 0.856104i | \(-0.327122\pi\) |
−0.856104 | + | 0.516804i | \(0.827122\pi\) | |||||||
\(74\) | −2.12132 | − | 3.67423i | −0.246598 | − | 0.427121i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.775255 | + | 1.34278i | −0.0889279 | + | 0.154028i | ||||
\(77\) | 6.66390 | − | 1.78559i | 0.759422 | − | 0.203487i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.12132 | − | 1.22474i | 0.238667 | − | 0.137795i | −0.375897 | − | 0.926662i | \(-0.622665\pi\) |
0.614564 | + | 0.788867i | \(0.289332\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.77526 | − | 2.77526i | 0.306476 | − | 0.306476i | ||||
\(83\) | −0.531752 | − | 0.142483i | −0.0583674 | − | 0.0156395i | 0.229517 | − | 0.973305i | \(-0.426285\pi\) |
−0.287885 | + | 0.957665i | \(0.592952\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.00000 | + | 1.73205i | 0.323498 | + | 0.186772i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.62863 | + | 6.07812i | −0.173612 | + | 0.647929i | ||||
\(89\) | 2.36773 | 0.250978 | 0.125489 | − | 0.992095i | \(-0.459950\pi\) | ||||
0.125489 | + | 0.992095i | \(0.459950\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.79796 | −0.398134 | ||||||||
\(92\) | 0.258819 | − | 0.965926i | 0.0269838 | − | 0.100705i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.79423 | − | 4.50000i | −0.803913 | − | 0.464140i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.7902 | − | 2.89123i | −1.09558 | − | 0.293560i | −0.334616 | − | 0.942355i | \(-0.608607\pi\) |
−0.760963 | + | 0.648795i | \(0.775273\pi\) | |||||||
\(98\) | −4.09978 | + | 4.09978i | −0.414140 | + | 0.414140i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.10102 | + | 0.635674i | −0.109556 | + | 0.0632520i | −0.553777 | − | 0.832665i | \(-0.686814\pi\) |
0.444221 | + | 0.895917i | \(0.353481\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.96008 | − | 1.06110i | 0.390198 | − | 0.104553i | −0.0583855 | − | 0.998294i | \(-0.518595\pi\) |
0.448584 | + | 0.893741i | \(0.351929\pi\) | |||||||
\(104\) | 1.73205 | − | 3.00000i | 0.169842 | − | 0.294174i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.67423 | − | 8.09601i | −0.454002 | − | 0.786354i | ||||
\(107\) | 3.71051 | + | 3.71051i | 0.358708 | + | 0.358708i | 0.863337 | − | 0.504628i | \(-0.168370\pi\) |
−0.504628 | + | 0.863337i | \(0.668370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.3485i | 1.94903i | 0.224323 | + | 0.974515i | \(0.427983\pi\) | ||||
−0.224323 | + | 0.974515i | \(0.572017\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.283763 | + | 1.05902i | 0.0268131 | + | 0.100068i | ||||
\(113\) | −3.57117 | − | 13.3278i | −0.335948 | − | 1.25377i | −0.902838 | − | 0.429981i | \(-0.858520\pi\) |
0.566890 | − | 0.823793i | \(-0.308146\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 3.14626i | − | 0.292123i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.34847 | − | 8.34847i | −0.768539 | − | 0.768539i | ||||
\(119\) | 2.43916 | + | 4.22474i | 0.223597 | + | 0.387282i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.2980 | − | 24.7648i | 1.29981 | − | 2.25134i | ||||
\(122\) | 5.26380 | − | 1.41043i | 0.476562 | − | 0.127694i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.85337 | + | 2.22474i | −0.346043 | + | 0.199788i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.1237 | + | 14.1237i | −1.25328 | + | 1.25328i | −0.299036 | + | 0.954242i | \(0.596665\pi\) |
−0.954242 | + | 0.299036i | \(0.903335\pi\) | |||||||
\(128\) | −0.965926 | − | 0.258819i | −0.0853766 | − | 0.0228766i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.12372 | − | 5.26758i | −0.797143 | − | 0.460231i | 0.0453278 | − | 0.998972i | \(-0.485567\pi\) |
−0.842471 | + | 0.538741i | \(0.818900\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.439978 | − | 1.64202i | 0.0381509 | − | 0.142381i | ||||
\(134\) | −3.78194 | −0.326710 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.44949 | −0.381541 | ||||||||
\(137\) | −0.569930 | + | 2.12701i | −0.0486924 | + | 0.181723i | −0.985989 | − | 0.166810i | \(-0.946653\pi\) |
0.937297 | + | 0.348533i | \(0.113320\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.1708 | + | 6.44949i | 0.947499 | + | 0.547039i | 0.892303 | − | 0.451437i | \(-0.149088\pi\) |
0.0551956 | + | 0.998476i | \(0.482422\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.614014 | + | 0.164525i | 0.0515269 | + | 0.0138066i | ||||
\(143\) | −15.4135 | + | 15.4135i | −1.28894 | + | 1.28894i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.55051 | + | 2.04989i | −0.293842 | + | 0.169650i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.09808 | + | 1.09808i | −0.336860 | + | 0.0902613i | ||||
\(149\) | −6.45145 | + | 11.1742i | −0.528523 | + | 0.915429i | 0.470924 | + | 0.882174i | \(0.343921\pi\) |
−0.999447 | + | 0.0332550i | \(0.989413\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7980 | + | 18.7026i | 0.878725 | + | 1.52200i | 0.852741 | + | 0.522335i | \(0.174939\pi\) |
0.0259849 | + | 0.999662i | \(0.491728\pi\) | |||||||
\(152\) | 1.09638 | + | 1.09638i | 0.0889279 | + | 0.0889279i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 6.89898i | − | 0.555936i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.59165 | − | 5.94012i | −0.127028 | − | 0.474073i | 0.872876 | − | 0.487942i | \(-0.162252\pi\) |
−0.999904 | + | 0.0138684i | \(0.995585\pi\) | |||||||
\(158\) | −0.633975 | − | 2.36603i | −0.0504363 | − | 0.188231i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.09638i | 0.0864066i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.449490 | + | 0.449490i | 0.0352068 | + | 0.0352068i | 0.724491 | − | 0.689284i | \(-0.242075\pi\) |
−0.689284 | + | 0.724491i | \(0.742075\pi\) | |||||||
\(164\) | −1.96240 | − | 3.39898i | −0.153238 | − | 0.265416i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.275255 | + | 0.476756i | −0.0213639 | + | 0.0370034i | ||||
\(167\) | −10.4300 | + | 2.79472i | −0.807100 | + | 0.216262i | −0.638699 | − | 0.769457i | \(-0.720527\pi\) |
−0.168401 | + | 0.985719i | \(0.553860\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.866025 | + | 0.500000i | −0.0666173 | + | 0.0384615i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.44949 | − | 2.44949i | 0.186772 | − | 0.186772i | ||||
\(173\) | 2.99536 | + | 0.802603i | 0.227733 | + | 0.0610208i | 0.370881 | − | 0.928680i | \(-0.379056\pi\) |
−0.143148 | + | 0.989701i | \(0.545723\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.44949 | + | 3.14626i | 0.410771 | + | 0.237159i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.612812 | − | 2.28705i | 0.0459322 | − | 0.171421i | ||||
\(179\) | 17.6062 | 1.31595 | 0.657976 | − | 0.753039i | \(-0.271413\pi\) | ||||
0.657976 | + | 0.753039i | \(0.271413\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.5505 | −0.784213 | −0.392107 | − | 0.919920i | \(-0.628254\pi\) | ||||
−0.392107 | + | 0.919920i | \(0.628254\pi\) | |||||||
\(182\) | −0.982984 | + | 3.66855i | −0.0728636 | + | 0.271931i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.866025 | − | 0.500000i | −0.0638442 | − | 0.0368605i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.0445 | + | 7.24656i | 1.97769 | + | 0.529921i | ||||
\(188\) | −6.36396 | + | 6.36396i | −0.464140 | + | 0.464140i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.87628 | − | 1.66062i | 0.208120 | − | 0.120158i | −0.392317 | − | 0.919830i | \(-0.628327\pi\) |
0.600437 | + | 0.799672i | \(0.294993\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.7303 | − | 4.48288i | 1.20428 | − | 0.322685i | 0.399762 | − | 0.916619i | \(-0.369093\pi\) |
0.804513 | + | 0.593934i | \(0.202426\pi\) | |||||||
\(194\) | −5.58542 | + | 9.67423i | −0.401010 | + | 0.694570i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.89898 | + | 5.02118i | 0.207070 | + | 0.358656i | ||||
\(197\) | 6.92820 | + | 6.92820i | 0.493614 | + | 0.493614i | 0.909443 | − | 0.415829i | \(-0.136508\pi\) |
−0.415829 | + | 0.909443i | \(0.636508\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.55051i | − | 0.251689i | −0.992050 | − | 0.125844i | \(-0.959836\pi\) | ||
0.992050 | − | 0.125844i | \(-0.0401640\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.329049 | + | 1.22803i | 0.0231518 | + | 0.0864038i | ||||
\(203\) | 0.892794 | + | 3.33195i | 0.0626618 | + | 0.233857i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 4.09978i | − | 0.285645i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.44949 | − | 2.44949i | −0.169842 | − | 0.169842i | ||||
\(209\) | −4.87832 | − | 8.44949i | −0.337440 | − | 0.584463i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.44949 | + | 16.3670i | −0.650530 | + | 1.12675i | 0.332465 | + | 0.943116i | \(0.392120\pi\) |
−0.982995 | + | 0.183635i | \(0.941214\pi\) | |||||||
\(212\) | −9.02993 | + | 2.41956i | −0.620178 | + | 0.166176i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.54442 | − | 2.62372i | 0.310650 | − | 0.179354i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.44949 | − | 3.44949i | 0.234167 | − | 0.234167i | ||||
\(218\) | 19.6551 | + | 5.26657i | 1.33121 | + | 0.356697i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.3485 | − | 7.70674i | −0.897915 | − | 0.518412i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.15087 | + | 8.02714i | −0.144033 | + | 0.537537i | 0.855764 | + | 0.517367i | \(0.173088\pi\) |
−0.999797 | + | 0.0201706i | \(0.993579\pi\) | |||||||
\(224\) | 1.09638 | 0.0732547 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.7980 | −0.917827 | ||||||||
\(227\) | −3.90843 | + | 14.5865i | −0.259412 | + | 0.968138i | 0.706171 | + | 0.708041i | \(0.250421\pi\) |
−0.965583 | + | 0.260096i | \(0.916246\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.1582 | − | 8.17423i | −0.935600 | − | 0.540169i | −0.0470214 | − | 0.998894i | \(-0.514973\pi\) |
−0.888578 | + | 0.458725i | \(0.848306\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.03906 | − | 0.814313i | −0.199524 | − | 0.0534623i | ||||
\(233\) | 10.9959 | − | 10.9959i | 0.720363 | − | 0.720363i | −0.248316 | − | 0.968679i | \(-0.579877\pi\) |
0.968679 | + | 0.248316i | \(0.0798770\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.2247 | + | 5.90326i | −0.665574 | + | 0.384269i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.71209 | − | 1.26260i | 0.305439 | − | 0.0818423i | ||||
\(239\) | −8.48528 | + | 14.6969i | −0.548867 | + | 0.950666i | 0.449485 | + | 0.893288i | \(0.351607\pi\) |
−0.998353 | + | 0.0573782i | \(0.981726\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.50000 | − | 16.4545i | −0.611949 | − | 1.05993i | −0.990912 | − | 0.134515i | \(-0.957053\pi\) |
0.378963 | − | 0.925412i | \(-0.376281\pi\) | |||||||
\(242\) | −20.2204 | − | 20.2204i | −1.29981 | − | 1.29981i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 5.44949i | − | 0.348868i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.39015 | + | 5.18811i | 0.0884531 | + | 0.330111i | ||||
\(248\) | 1.15161 | + | 4.29788i | 0.0731275 | + | 0.272915i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.1708i | 0.705097i | 0.935793 | + | 0.352549i | \(0.114685\pi\) | ||||
−0.935793 | + | 0.352549i | \(0.885315\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.44949 | + | 4.44949i | 0.279737 | + | 0.279737i | ||||
\(254\) | 9.98698 | + | 17.2980i | 0.626639 | + | 1.08537i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −25.1579 | + | 6.74105i | −1.56931 | + | 0.420495i | −0.935596 | − | 0.353073i | \(-0.885137\pi\) |
−0.633713 | + | 0.773568i | \(0.718470\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.02834 | − | 2.32577i | 0.250309 | − | 0.144516i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.44949 | + | 7.44949i | −0.460231 | + | 0.460231i | ||||
\(263\) | 12.2643 | + | 3.28621i | 0.756249 | + | 0.202636i | 0.616288 | − | 0.787521i | \(-0.288636\pi\) |
0.139961 | + | 0.990157i | \(0.455302\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.47219 | − | 0.849971i | −0.0902660 | − | 0.0521151i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.978838 | + | 3.65307i | −0.0597920 | + | 0.223147i | ||||
\(269\) | −4.70334 | −0.286768 | −0.143384 | − | 0.989667i | \(-0.545798\pi\) | ||||
−0.143384 | + | 0.989667i | \(0.545798\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0454 | −0.974689 | −0.487345 | − | 0.873210i | \(-0.662034\pi\) | ||||
−0.487345 | + | 0.873210i | \(0.662034\pi\) | |||||||
\(272\) | −1.15161 | + | 4.29788i | −0.0698268 | + | 0.260597i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.90702 | + | 1.10102i | 0.115208 | + | 0.0665151i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.7983 | − | 3.69723i | −0.829057 | − | 0.222145i | −0.180754 | − | 0.983528i | \(-0.557854\pi\) |
−0.648302 | + | 0.761383i | \(0.724521\pi\) | |||||||
\(278\) | 9.12096 | − | 9.12096i | 0.547039 | − | 0.547039i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.151531 | − | 0.0874863i | 0.00903957 | − | 0.00521900i | −0.495473 | − | 0.868623i | \(-0.665005\pi\) |
0.504513 | + | 0.863404i | \(0.331672\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.66112 | − | 1.78484i | 0.395962 | − | 0.106098i | −0.0553430 | − | 0.998467i | \(-0.517625\pi\) |
0.451305 | + | 0.892370i | \(0.350959\pi\) | |||||||
\(284\) | 0.317837 | − | 0.550510i | 0.0188602 | − | 0.0326668i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.8990 | + | 18.8776i | 0.644470 | + | 1.11626i | ||||
\(287\) | 3.04272 | + | 3.04272i | 0.179606 | + | 0.179606i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.79796i | 0.164586i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.06110 | + | 3.96008i | 0.0620962 | + | 0.231746i | ||||
\(293\) | 5.70577 | + | 21.2942i | 0.333335 | + | 1.24402i | 0.905663 | + | 0.423998i | \(0.139374\pi\) |
−0.572329 | + | 0.820024i | \(0.693960\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.24264i | 0.246598i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.12372 | + | 9.12372i | 0.528523 | + | 0.528523i | ||||
\(299\) | −1.73205 | − | 3.00000i | −0.100167 | − | 0.173494i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.89898 | + | 3.28913i | −0.109455 | + | 0.189582i | ||||
\(302\) | 20.8601 | − | 5.58943i | 1.20036 | − | 0.321636i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.34278 | − | 0.775255i | 0.0770138 | − | 0.0444639i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.674235 | + | 0.674235i | −0.0384806 | + | 0.0384806i | −0.726085 | − | 0.687605i | \(-0.758662\pi\) |
0.687605 | + | 0.726085i | \(0.258662\pi\) | |||||||
\(308\) | −6.66390 | − | 1.78559i | −0.379711 | − | 0.101743i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.8207 | + | 10.2888i | 1.01052 | + | 0.583422i | 0.911343 | − | 0.411648i | \(-0.135047\pi\) |
0.0991741 | + | 0.995070i | \(0.468380\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.29958 | + | 4.85009i | −0.0734564 | + | 0.274143i | −0.992879 | − | 0.119128i | \(-0.961990\pi\) |
0.919422 | + | 0.393271i | \(0.128657\pi\) | |||||||
\(314\) | −6.14966 | −0.347046 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.44949 | −0.137795 | ||||||||
\(317\) | 0.284965 | − | 1.06350i | 0.0160052 | − | 0.0597323i | −0.957461 | − | 0.288561i | \(-0.906823\pi\) |
0.973467 | + | 0.228829i | \(0.0734897\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.1455 | + | 9.89898i | 0.959966 | + | 0.554236i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.05902 | + | 0.283763i | 0.0590168 | + | 0.0158135i | ||||
\(323\) | 4.87832 | − | 4.87832i | 0.271437 | − | 0.271437i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.550510 | − | 0.317837i | 0.0304899 | − | 0.0176034i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.79107 | + | 1.01581i | −0.209327 | + | 0.0560889i | ||||
\(329\) | 4.93369 | − | 8.54541i | 0.272003 | − | 0.471124i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.22474 | + | 3.85337i | 0.122283 | + | 0.211800i | 0.920668 | − | 0.390347i | \(-0.127645\pi\) |
−0.798385 | + | 0.602148i | \(0.794312\pi\) | |||||||
\(332\) | 0.389270 | + | 0.389270i | 0.0213639 | + | 0.0213639i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.7980i | 0.590838i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.97861 | + | 29.7766i | 0.434622 | + | 1.62203i | 0.741968 | + | 0.670435i | \(0.233892\pi\) |
−0.307346 | + | 0.951598i | \(0.599441\pi\) | |||||||
\(338\) | 0.258819 | + | 0.965926i | 0.0140779 | + | 0.0525394i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 27.9985i | − | 1.51621i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.92168 | − | 9.92168i | −0.535721 | − | 0.535721i | ||||
\(344\) | −1.73205 | − | 3.00000i | −0.0933859 | − | 0.161749i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.55051 | − | 2.68556i | 0.0833559 | − | 0.144377i | ||||
\(347\) | −4.05886 | + | 1.08757i | −0.217891 | + | 0.0583837i | −0.366113 | − | 0.930570i | \(-0.619312\pi\) |
0.148222 | + | 0.988954i | \(0.452645\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.0297 | − | 7.52270i | 0.697464 | − | 0.402681i | −0.108938 | − | 0.994049i | \(-0.534745\pi\) |
0.806402 | + | 0.591367i | \(0.201412\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.44949 | − | 4.44949i | 0.237159 | − | 0.237159i | ||||
\(353\) | −33.1244 | − | 8.87564i | −1.76303 | − | 0.472403i | −0.775704 | − | 0.631097i | \(-0.782605\pi\) |
−0.987328 | + | 0.158694i | \(0.949272\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.05051 | − | 1.18386i | −0.108677 | − | 0.0627446i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.55683 | − | 17.0063i | 0.240836 | − | 0.898812i | ||||
\(359\) | −17.4634 | −0.921682 | −0.460841 | − | 0.887483i | \(-0.652452\pi\) | ||||
−0.460841 | + | 0.887483i | \(0.652452\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.5959 | 0.873469 | ||||||||
\(362\) | −2.73067 | + | 10.1910i | −0.143521 | + | 0.535628i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.28913 | + | 1.89898i | 0.172397 | + | 0.0995336i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.42418 | + | 2.52520i | 0.491938 | + | 0.131814i | 0.496256 | − | 0.868176i | \(-0.334708\pi\) |
−0.00431778 | + | 0.999991i | \(0.501374\pi\) | |||||||
\(368\) | −0.707107 | + | 0.707107i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.87628 | − | 5.12472i | 0.460833 | − | 0.266062i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.6004 | − | 5.25190i | 1.01487 | − | 0.271933i | 0.287206 | − | 0.957869i | \(-0.407273\pi\) |
0.727662 | + | 0.685935i | \(0.240607\pi\) | |||||||
\(374\) | 13.9993 | − | 24.2474i | 0.723885 | − | 1.25381i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.50000 | + | 7.79423i | 0.232070 | + | 0.401957i | ||||
\(377\) | −7.70674 | − | 7.70674i | −0.396917 | − | 0.396917i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.65153i | 0.341666i | 0.985300 | + | 0.170833i | \(0.0546459\pi\) | ||||
−0.985300 | + | 0.170833i | \(0.945354\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.859599 | − | 3.20807i | −0.0439809 | − | 0.164139i | ||||
\(383\) | 7.19464 | + | 26.8508i | 0.367629 | + | 1.37201i | 0.863822 | + | 0.503798i | \(0.168064\pi\) |
−0.496193 | + | 0.868212i | \(0.665269\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 17.3205i | − | 0.881591i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.89898 | + | 7.89898i | 0.401010 | + | 0.401010i | ||||
\(389\) | 2.81237 | + | 4.87117i | 0.142593 | + | 0.246978i | 0.928472 | − | 0.371402i | \(-0.121123\pi\) |
−0.785879 | + | 0.618380i | \(0.787789\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.22474 | + | 3.85337i | −0.112510 | + | 0.194873i | ||||
\(392\) | 5.60040 | − | 1.50062i | 0.282863 | − | 0.0757929i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.48528 | − | 4.89898i | 0.427482 | − | 0.246807i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.4495 | + | 15.4495i | −0.775388 | + | 0.775388i | −0.979043 | − | 0.203655i | \(-0.934718\pi\) |
0.203655 | + | 0.979043i | \(0.434718\pi\) | |||||||
\(398\) | −3.42953 | − | 0.918940i | −0.171907 | − | 0.0460623i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.3485 | − | 12.9029i | −1.11603 | − | 0.644340i | −0.175645 | − | 0.984454i | \(-0.556201\pi\) |
−0.940384 | + | 0.340114i | \(0.889534\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.98930 | + | 14.8883i | −0.198721 | + | 0.741638i | ||||
\(404\) | 1.27135 | 0.0632520 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.44949 | 0.171195 | ||||||||
\(407\) | 6.90968 | − | 25.7873i | 0.342500 | − | 1.27823i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.5420 | − | 9.55051i | −0.817948 | − | 0.472242i | 0.0317605 | − | 0.999496i | \(-0.489889\pi\) |
−0.849708 | + | 0.527253i | \(0.823222\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.96008 | − | 1.06110i | −0.195099 | − | 0.0522767i | ||||
\(413\) | 9.15306 | − | 9.15306i | 0.450393 | − | 0.450393i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.00000 | + | 1.73205i | −0.147087 | + | 0.0849208i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.42418 | + | 2.52520i | −0.460952 | + | 0.123512i | ||||
\(419\) | 5.97469 | − | 10.3485i | 0.291883 | − | 0.505556i | −0.682372 | − | 0.731005i | \(-0.739052\pi\) |
0.974255 | + | 0.225449i | \(0.0723850\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.44949 | + | 12.9029i | 0.363066 | + | 0.628849i | 0.988464 | − | 0.151457i | \(-0.0483966\pi\) |
−0.625398 | + | 0.780306i | \(0.715063\pi\) | |||||||
\(422\) | 13.3636 | + | 13.3636i | 0.650530 | + | 0.650530i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.34847i | 0.454002i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.54636 | + | 5.77111i | 0.0748338 | + | 0.279284i | ||||
\(428\) | −1.35814 | − | 5.06865i | −0.0656482 | − | 0.245002i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.5563i | 0.749323i | 0.927162 | + | 0.374661i | \(0.122241\pi\) | ||||
−0.927162 | + | 0.374661i | \(0.877759\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.55051 | − | 8.55051i | −0.410911 | − | 0.410911i | 0.471145 | − | 0.882056i | \(-0.343841\pi\) |
−0.882056 | + | 0.471145i | \(0.843841\pi\) | |||||||
\(434\) | −2.43916 | − | 4.22474i | −0.117083 | − | 0.202794i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.1742 | − | 17.6223i | 0.487257 | − | 0.843955i | ||||
\(437\) | 1.49768 | − | 0.401302i | 0.0716436 | − | 0.0191969i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.83523 | + | 5.10102i | −0.421682 | + | 0.243458i | −0.695797 | − | 0.718239i | \(-0.744949\pi\) |
0.274114 | + | 0.961697i | \(0.411615\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.8990 | + | 10.8990i | −0.518412 | + | 0.518412i | ||||
\(443\) | 0.531752 | + | 0.142483i | 0.0252643 | + | 0.00676955i | 0.271429 | − | 0.962458i | \(-0.412504\pi\) |
−0.246165 | + | 0.969228i | \(0.579170\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7.19694 | + | 4.15515i | 0.340785 | + | 0.196752i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.283763 | − | 1.05902i | 0.0134065 | − | 0.0500339i | ||||
\(449\) | 21.7060 | 1.02437 | 0.512185 | − | 0.858875i | \(-0.328836\pi\) | ||||
0.512185 | + | 0.858875i | \(0.328836\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.6969 | 1.16293 | ||||||||
\(452\) | −3.57117 | + | 13.3278i | −0.167974 | + | 0.626887i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.0779 | + | 7.55051i | 0.613775 | + | 0.354363i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.94012 | + | 1.59165i | 0.277867 | + | 0.0744543i | 0.395061 | − | 0.918655i | \(-0.370723\pi\) |
−0.117194 | + | 0.993109i | \(0.537390\pi\) | |||||||
\(458\) | −11.5601 | + | 11.5601i | −0.540169 | + | 0.540169i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.3763 | + | 9.45485i | −0.762719 | + | 0.440356i | −0.830271 | − | 0.557360i | \(-0.811814\pi\) |
0.0675520 | + | 0.997716i | \(0.478481\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.8946 | + | 8.54613i | −1.48227 | + | 0.397172i | −0.907118 | − | 0.420876i | \(-0.861723\pi\) |
−0.575150 | + | 0.818048i | \(0.695056\pi\) | |||||||
\(464\) | −1.57313 | + | 2.72474i | −0.0730308 | + | 0.126493i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.77526 | − | 13.4671i | −0.360182 | − | 0.623853i | ||||
\(467\) | −2.82843 | − | 2.82843i | −0.130884 | − | 0.130884i | 0.638630 | − | 0.769514i | \(-0.279501\pi\) |
−0.769514 | + | 0.638630i | \(0.779501\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 4.14643i | − | 0.191464i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.05575 | + | 11.4042i | 0.140652 | + | 0.524922i | ||||
\(473\) | 5.64173 | + | 21.0552i | 0.259407 | + | 0.968120i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 4.87832i | − | 0.223597i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.0000 | + | 12.0000i | 0.548867 | + | 0.548867i | ||||
\(479\) | −3.53553 | − | 6.12372i | −0.161543 | − | 0.279800i | 0.773879 | − | 0.633333i | \(-0.218314\pi\) |
−0.935422 | + | 0.353533i | \(0.884980\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.34847 | + | 12.7279i | −0.335061 | + | 0.580343i | ||||
\(482\) | −18.3526 | + | 4.91756i | −0.835938 | + | 0.223989i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −24.7648 | + | 14.2980i | −1.12567 | + | 0.649907i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0000 | − | 12.0000i | 0.543772 | − | 0.543772i | −0.380861 | − | 0.924632i | \(-0.624372\pi\) |
0.924632 | + | 0.380861i | \(0.124372\pi\) | |||||||
\(488\) | −5.26380 | − | 1.41043i | −0.238281 | − | 0.0638472i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.247449 | − | 0.142865i | −0.0111672 | − | 0.00644739i | 0.494406 | − | 0.869231i | \(-0.335386\pi\) |
−0.505573 | + | 0.862784i | \(0.668719\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.62328 | + | 13.5223i | −0.163184 | + | 0.609012i | ||||
\(494\) | 5.37113 | 0.241658 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.44949 | 0.199788 | ||||||||
\(497\) | −0.180381 | + | 0.673191i | −0.00809119 | + | 0.0301967i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.70674 | − | 4.44949i | −0.345001 | − | 0.199187i | 0.317480 | − | 0.948265i | \(-0.397163\pi\) |
−0.662481 | + | 0.749078i | \(0.730497\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.7902 | + | 2.89123i | 0.481590 | + | 0.129042i | ||||
\(503\) | 16.7563 | − | 16.7563i | 0.747125 | − | 0.747125i | −0.226813 | − | 0.973938i | \(-0.572831\pi\) |
0.973938 | + | 0.226813i | \(0.0728307\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.44949 | − | 3.14626i | 0.242259 | − | 0.139869i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 19.2934 | − | 5.16964i | 0.856005 | − | 0.229366i | ||||
\(509\) | −19.8150 | + | 34.3207i | −0.878286 | + | 1.52124i | −0.0250662 | + | 0.999686i | \(0.507980\pi\) |
−0.853220 | + | 0.521551i | \(0.825354\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.24745 | − | 3.89270i | −0.0994213 | − | 0.172203i | ||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 26.0454i | 1.14881i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.6576 | − | 54.7030i | −0.644642 | − | 2.40584i | ||||
\(518\) | −1.20390 | − | 4.49303i | −0.0528965 | − | 0.197413i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.4449i | 1.29000i | 0.764181 | + | 0.645001i | \(0.223143\pi\) | ||||
−0.764181 | + | 0.645001i | \(0.776857\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.77526 | − | 1.77526i | −0.0776265 | − | 0.0776265i | 0.667228 | − | 0.744854i | \(-0.267481\pi\) |
−0.744854 | + | 0.667228i | \(0.767481\pi\) | |||||||
\(524\) | 5.26758 | + | 9.12372i | 0.230116 | + | 0.398572i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.34847 | − | 10.9959i | 0.276806 | − | 0.479443i | ||||
\(527\) | 19.1234 | − | 5.12409i | 0.833027 | − | 0.223209i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.0526 | − | 11.0000i | 0.828372 | − | 0.478261i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.20204 | + | 1.20204i | −0.0521151 | + | 0.0521151i | ||||
\(533\) | −13.1326 | − | 3.51888i | −0.568838 | − | 0.152420i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.27526 | + | 1.89097i | 0.141469 | + | 0.0816774i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.21731 | + | 4.54308i | −0.0524822 | + | 0.195866i | ||||
\(539\) | −36.4838 | −1.57147 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.9444 | −1.11544 | −0.557718 | − | 0.830030i | \(-0.688323\pi\) | ||||
−0.557718 | + | 0.830030i | \(0.688323\pi\) | |||||||
\(542\) | −4.15286 | + | 15.4987i | −0.178380 | + | 0.665725i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.85337 | + | 2.22474i | 0.165212 | + | 0.0953851i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.6594 | − | 5.53567i | −0.883332 | − | 0.236688i | −0.211488 | − | 0.977381i | \(-0.567831\pi\) |
−0.671844 | + | 0.740693i | \(0.734498\pi\) | |||||||
\(548\) | 1.55708 | − | 1.55708i | 0.0665151 | − | 0.0665151i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.22474 | − | 2.43916i | 0.179980 | − | 0.103912i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.59405 | − | 0.695075i | 0.110310 | − | 0.0295576i | ||||
\(554\) | −7.14250 | + | 12.3712i | −0.303456 | + | 0.525601i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.44949 | − | 11.1708i | −0.273519 | − | 0.473749i | ||||
\(557\) | −16.3670 | − | 16.3670i | −0.693492 | − | 0.693492i | 0.269507 | − | 0.962999i | \(-0.413139\pi\) |
−0.962999 | + | 0.269507i | \(0.913139\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 12.0000i | − | 0.507546i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.0452863 | − | 0.169011i | −0.00191029 | − | 0.00712928i | ||||
\(563\) | −8.89004 | − | 33.1781i | −0.374670 | − | 1.39829i | −0.853826 | − | 0.520559i | \(-0.825724\pi\) |
0.479155 | − | 0.877730i | \(-0.340943\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 6.89610i | − | 0.289864i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.449490 | − | 0.449490i | −0.0188602 | − | 0.0188602i | ||||
\(569\) | −13.0458 | − | 22.5959i | −0.546907 | − | 0.947270i | −0.998484 | − | 0.0550383i | \(-0.982472\pi\) |
0.451578 | − | 0.892232i | \(-0.350861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.5505 | + | 23.4702i | −0.567071 | + | 0.982196i | 0.429782 | + | 0.902932i | \(0.358590\pi\) |
−0.996854 | + | 0.0792637i | \(0.974743\pi\) | |||||||
\(572\) | 21.0552 | − | 5.64173i | 0.880363 | − | 0.235892i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.72656 | − | 2.15153i | 0.155544 | − | 0.0898032i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.0000 | − | 17.0000i | 0.707719 | − | 0.707719i | −0.258336 | − | 0.966055i | \(-0.583174\pi\) |
0.966055 | + | 0.258336i | \(0.0831741\pi\) | |||||||
\(578\) | 2.70262 | + | 0.724165i | 0.112414 | + | 0.0301213i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.522704 | − | 0.301783i | −0.0216854 | − | 0.0125201i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.2252 | − | 56.8211i | 0.630562 | − | 2.35329i | ||||
\(584\) | 4.09978 | 0.169650 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.0454 | 0.910687 | ||||||||
\(587\) | 8.03514 | − | 29.9876i | 0.331646 | − | 1.23772i | −0.575814 | − | 0.817581i | \(-0.695315\pi\) |
0.907460 | − | 0.420138i | \(-0.138019\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.97469 | − | 3.44949i | −0.246183 | − | 0.142134i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.09808 | + | 1.09808i | 0.168430 | + | 0.0451307i | ||||
\(593\) | −10.0745 | + | 10.0745i | −0.413709 | + | 0.413709i | −0.883028 | − | 0.469320i | \(-0.844499\pi\) |
0.469320 | + | 0.883028i | \(0.344499\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.1742 | − | 6.45145i | 0.457714 | − | 0.264262i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.34607 | + | 0.896575i | −0.136831 | + | 0.0366637i | ||||
\(599\) | 16.8991 | − | 29.2702i | 0.690480 | − | 1.19595i | −0.281201 | − | 0.959649i | \(-0.590733\pi\) |
0.971681 | − | 0.236297i | \(-0.0759339\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.3485 | − | 30.0484i | −0.707659 | − | 1.22570i | −0.965723 | − | 0.259573i | \(-0.916418\pi\) |
0.258065 | − | 0.966128i | \(-0.416915\pi\) | |||||||
\(602\) | 2.68556 | + | 2.68556i | 0.109455 | + | 0.109455i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 21.5959i | − | 0.878725i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.73717 | − | 21.4114i | −0.232864 | − | 0.869062i | −0.979100 | − | 0.203380i | \(-0.934807\pi\) |
0.746235 | − | 0.665682i | \(-0.231859\pi\) | |||||||
\(608\) | −0.401302 | − | 1.49768i | −0.0162749 | − | 0.0607389i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.1769i | 1.26128i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.7980 | + | 12.7980i | 0.516905 | + | 0.516905i | 0.916633 | − | 0.399729i | \(-0.130896\pi\) |
−0.399729 | + | 0.916633i | \(0.630896\pi\) | |||||||
\(614\) | 0.476756 | + | 0.825765i | 0.0192403 | + | 0.0333252i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.44949 | + | 5.97469i | −0.138984 | + | 0.240727i | ||||
\(617\) | 6.85906 | − | 1.83788i | 0.276135 | − | 0.0739902i | −0.118094 | − | 0.993002i | \(-0.537678\pi\) |
0.394229 | + | 0.919012i | \(0.371012\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.4275 | + | 12.3712i | −0.861244 | + | 0.497239i | −0.864429 | − | 0.502756i | \(-0.832320\pi\) |
0.00318471 | + | 0.999995i | \(0.498986\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.5505 | − | 14.5505i | 0.583422 | − | 0.583422i | ||||
\(623\) | 2.50746 | + | 0.671873i | 0.100459 | + | 0.0269180i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.34847 | + | 2.51059i | 0.173800 | + | 0.100343i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.59165 | + | 5.94012i | −0.0635138 | + | 0.237037i | ||||
\(629\) | 18.8776 | 0.752699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.8990 | −0.513500 | −0.256750 | − | 0.966478i | \(-0.582652\pi\) | ||||
−0.256750 | + | 0.966478i | \(0.582652\pi\) | |||||||
\(632\) | −0.633975 | + | 2.36603i | −0.0252182 | + | 0.0941154i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.953512 | − | 0.550510i | −0.0378688 | − | 0.0218636i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.4003 | + | 5.19831i | 0.768670 | + | 0.205964i | ||||
\(638\) | 13.9993 | − | 13.9993i | 0.554236 | − | 0.554236i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.74745 | − | 4.47299i | 0.306006 | − | 0.176673i | −0.339132 | − | 0.940739i | \(-0.610133\pi\) |
0.645138 | + | 0.764066i | \(0.276800\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.6976 | + | 8.22539i | −1.21059 | + | 0.324378i | −0.806995 | − | 0.590558i | \(-0.798908\pi\) |
−0.403599 | + | 0.914936i | \(0.632241\pi\) | |||||||
\(644\) | 0.548188 | − | 0.949490i | 0.0216016 | − | 0.0374151i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.44949 | − | 5.97469i | −0.135718 | − | 0.235071i | ||||
\(647\) | 24.9558 | + | 24.9558i | 0.981114 | + | 0.981114i | 0.999825 | − | 0.0187105i | \(-0.00595608\pi\) |
−0.0187105 | + | 0.999825i | \(0.505956\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 74.2929i | − | 2.91625i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.164525 | − | 0.614014i | −0.00644328 | − | 0.0240467i | ||||
\(653\) | −5.57768 | − | 20.8162i | −0.218272 | − | 0.814601i | −0.984989 | − | 0.172616i | \(-0.944778\pi\) |
0.766718 | − | 0.641985i | \(-0.221889\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.92480i | 0.153238i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.97730 | − | 6.97730i | −0.272003 | − | 0.272003i | ||||
\(659\) | 5.65685 | + | 9.79796i | 0.220360 | + | 0.381674i | 0.954917 | − | 0.296872i | \(-0.0959435\pi\) |
−0.734557 | + | 0.678546i | \(0.762610\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.3485 | − | 26.5843i | 0.596986 | − | 1.03401i | −0.396277 | − | 0.918131i | \(-0.629698\pi\) |
0.993263 | − | 0.115880i | \(-0.0369687\pi\) | |||||||
\(662\) | 4.29788 | − | 1.15161i | 0.167042 | − | 0.0447587i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.476756 | − | 0.275255i | 0.0185017 | − | 0.0106820i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.22474 | + | 2.22474i | −0.0861425 | + | 0.0861425i | ||||
\(668\) | 10.4300 | + | 2.79472i | 0.403550 | + | 0.108131i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.6969 | + | 17.1455i | 1.14644 | + | 0.661896i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.22778 | − | 15.7783i | 0.162969 | − | 0.608208i | −0.835322 | − | 0.549762i | \(-0.814719\pi\) |
0.998291 | − | 0.0584468i | \(-0.0186148\pi\) | |||||||
\(674\) | 30.8270 | 1.18741 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 1.65750 | − | 6.18587i | 0.0637028 | − | 0.237742i | −0.926732 | − | 0.375723i | \(-0.877394\pi\) |
0.990435 | + | 0.137981i | \(0.0440612\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.6066 | − | 6.12372i | −0.407044 | − | 0.235007i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −27.0445 | − | 7.24656i | −1.03559 | − | 0.277485i | ||||
\(683\) | −13.8564 | + | 13.8564i | −0.530201 | + | 0.530201i | −0.920632 | − | 0.390431i | \(-0.872326\pi\) |
0.390431 | + | 0.920632i | \(0.372326\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12.1515 | + | 7.01569i | −0.463948 | + | 0.267860i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.34607 | + | 0.896575i | −0.127568 | + | 0.0341816i | ||||
\(689\) | −16.1920 | + | 28.0454i | −0.616867 | + | 1.06844i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.4722 | − | 28.5307i | −0.626632 | − | 1.08536i | −0.988223 | − | 0.153021i | \(-0.951100\pi\) |
0.361591 | − | 0.932337i | \(-0.382234\pi\) | |||||||
\(692\) | −2.19275 | − | 2.19275i | −0.0833559 | − | 0.0833559i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.20204i | 0.159507i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.51985 | + | 16.8683i | 0.171202 | + | 0.638933i | ||||
\(698\) | −3.89404 | − | 14.5327i | −0.147392 | − | 0.550073i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 23.9309i | − | 0.903857i | −0.892054 | − | 0.451928i | \(-0.850736\pi\) | ||
0.892054 | − | 0.451928i | \(-0.149264\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.65153 | − | 4.65153i | −0.175436 | − | 0.175436i | ||||
\(704\) | −3.14626 | − | 5.44949i | −0.118579 | − | 0.205385i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.1464 | + | 29.6985i | −0.645314 | + | 1.11772i | ||||
\(707\) | −1.34638 | + | 0.360762i | −0.0506359 | + | 0.0135678i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.4069 | + | 22.1742i | −1.44240 | + | 0.832771i | −0.998010 | − | 0.0630617i | \(-0.979914\pi\) |
−0.444392 | + | 0.895833i | \(0.646580\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.67423 | + | 1.67423i | −0.0627446 | + | 0.0627446i | ||||
\(713\) | 4.29788 | + | 1.15161i | 0.160957 | + | 0.0431282i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15.2474 | − | 8.80312i | −0.569824 | − | 0.328988i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.51985 | + | 16.8683i | −0.168679 | + | 0.629520i | ||||
\(719\) | 32.5269 | 1.21305 | 0.606525 | − | 0.795065i | \(-0.292563\pi\) | ||||
0.606525 | + | 0.795065i | \(0.292563\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.49490 | 0.167399 | ||||||||
\(722\) | 4.29534 | − | 16.0304i | 0.159856 | − | 0.596591i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.13701 | + | 5.27526i | 0.339574 | + | 0.196053i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.2836 | − | 8.11447i | −1.12316 | − | 0.300949i | −0.350996 | − | 0.936377i | \(-0.614157\pi\) |
−0.772160 | + | 0.635428i | \(0.780824\pi\) | |||||||
\(728\) | 2.68556 | − | 2.68556i | 0.0995336 | − | 0.0995336i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.3485 | + | 7.70674i | −0.493711 | + | 0.285044i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.8603 | + | 3.71385i | −0.511941 | + | 0.137174i | −0.505536 | − | 0.862805i | \(-0.668705\pi\) |
−0.00640470 | + | 0.999979i | \(0.502039\pi\) | |||||||
\(734\) | 4.87832 | − | 8.44949i | 0.180062 | − | 0.311876i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.500000 | + | 0.866025i | 0.0184302 | + | 0.0319221i | ||||
\(737\) | −16.8277 | − | 16.8277i | −0.619856 | − | 0.619856i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.9444i | 0.917594i | 0.888541 | + | 0.458797i | \(0.151720\pi\) | ||||
−0.888541 | + | 0.458797i | \(0.848280\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.65275 | − | 9.90020i | −0.0973855 | − | 0.363448i | ||||
\(743\) | 0.0261460 | + | 0.0975783i | 0.000959205 | + | 0.00357980i | 0.966404 | − | 0.257029i | \(-0.0827435\pi\) |
−0.965445 | + | 0.260609i | \(0.916077\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 20.2918i | − | 0.742936i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −19.7980 | − | 19.7980i | −0.723885 | − | 0.723885i | ||||
\(749\) | 2.87659 | + | 4.98240i | 0.105108 | + | 0.182053i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.34847 | − | 7.53177i | 0.158678 | − | 0.274838i | −0.775714 | − | 0.631084i | \(-0.782610\pi\) |
0.934392 | + | 0.356246i | \(0.115944\pi\) | |||||||
\(752\) | 8.69333 | − | 2.32937i | 0.317013 | − | 0.0849434i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.43879 | + | 5.44949i | −0.343741 | + | 0.198459i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.0454 | − | 22.0454i | 0.801254 | − | 0.801254i | −0.182038 | − | 0.983292i | \(-0.558269\pi\) |
0.983292 | + | 0.182038i | \(0.0582693\pi\) | |||||||
\(758\) | 6.42489 | + | 1.72154i | 0.233362 | + | 0.0625293i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.3990 | + | 8.89060i | 0.558213 | + | 0.322284i | 0.752428 | − | 0.658675i | \(-0.228883\pi\) |
−0.194215 | + | 0.980959i | \(0.562216\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.77414 | + | 21.5494i | −0.209038 | + | 0.780141i | ||||
\(764\) | −3.32124 | −0.120158 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.7980 | 1.00438 | ||||||||
\(767\) | −10.5854 | + | 39.5054i | −0.382218 | + | 1.42646i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.0580 | + | 9.84847i | 0.615129 | + | 0.355145i | 0.774970 | − | 0.631998i | \(-0.217765\pi\) |
−0.159841 | + | 0.987143i | \(0.551098\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16.7303 | − | 4.48288i | −0.602138 | − | 0.161342i | ||||
\(773\) | −3.11416 | + | 3.11416i | −0.112008 | + | 0.112008i | −0.760890 | − | 0.648881i | \(-0.775237\pi\) |
0.648881 | + | 0.760890i | \(0.275237\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.67423 | − | 5.58542i | 0.347285 | − | 0.200505i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.43309 | − | 1.45579i | 0.194786 | − | 0.0521927i | ||||
\(779\) | 3.04272 | − | 5.27015i | 0.109017 | − | 0.188823i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00000 | + | 3.46410i | 0.0715656 | + | 0.123955i | ||||
\(782\) | 3.14626 | + | 3.14626i | 0.112510 | + | 0.112510i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 5.79796i | − | 0.207070i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.06110 | − | 3.96008i | −0.0378241 | − | 0.141162i | 0.944432 | − | 0.328708i | \(-0.106613\pi\) |
−0.982256 | + | 0.187546i | \(0.939947\pi\) | |||||||
\(788\) | −2.53590 | − | 9.46410i | −0.0903376 | − | 0.337145i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 15.1278i | − | 0.537881i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.3485 | − | 13.3485i | −0.474018 | − | 0.474018i | ||||
\(794\) | 10.9244 | + | 18.9217i | 0.387694 | + | 0.671505i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.77526 | + | 3.07483i | −0.0629222 | + | 0.108985i | ||||
\(797\) | −19.5137 | + | 5.22867i | −0.691210 | + | 0.185209i | −0.587290 | − | 0.809377i | \(-0.699805\pi\) |
−0.103920 | + | 0.994586i | \(0.533139\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.6803 | − | 20.0227i | 1.22690 | − | 0.708352i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.2474 | + | 18.2474i | −0.644340 | + | 0.644340i | ||||
\(803\) | −24.9189 | − | 6.67700i | −0.879369 | − | 0.235626i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.3485 | + | 7.70674i | 0.470180 | + | 0.271458i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.329049 | − | 1.22803i | 0.0115759 | − | 0.0432019i | ||||
\(809\) | −54.0901 | −1.90171 | −0.950853 | − | 0.309644i | \(-0.899790\pi\) | ||||
−0.950853 | + | 0.309644i | \(0.899790\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.6413 | 1.53245 | 0.766227 | − | 0.642570i | \(-0.222132\pi\) | ||||
0.766227 | + | 0.642570i | \(0.222132\pi\) | |||||||
\(812\) | 0.892794 | − | 3.33195i | 0.0313309 | − | 0.116929i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −23.1202 | − | 13.3485i | −0.810364 | − | 0.467864i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.18811 | + | 1.39015i | 0.181509 | + | 0.0486352i | ||||
\(818\) | −13.5065 | + | 13.5065i | −0.472242 | + | 0.472242i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.3207 | − | 12.8868i | 0.778997 | − | 0.449754i | −0.0570780 | − | 0.998370i | \(-0.518178\pi\) |
0.836075 | + | 0.548616i | \(0.184845\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −46.9519 | + | 12.5807i | −1.63664 | + | 0.438536i | −0.955829 | − | 0.293923i | \(-0.905039\pi\) |
−0.680811 | + | 0.732459i | \(0.738373\pi\) | |||||||
\(824\) | −2.04989 | + | 3.55051i | −0.0714112 | + | 0.123688i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.47219 | − | 11.2102i | −0.225196 | − | 0.390052i | ||||
\(827\) | 27.3235 | + | 27.3235i | 0.950133 | + | 0.950133i | 0.998814 | − | 0.0486816i | \(-0.0155020\pi\) |
−0.0486816 | + | 0.998814i | \(0.515502\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.4495i | 0.536583i | 0.963338 | + | 0.268291i | \(0.0864590\pi\) | ||||
−0.963338 | + | 0.268291i | \(0.913541\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.896575 | + | 3.34607i | 0.0310832 | + | 0.116004i | ||||
\(833\) | −6.67700 | − | 24.9189i | −0.231344 | − | 0.863389i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 9.75663i | 0.337440i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.44949 | − | 8.44949i | −0.291883 | − | 0.291883i | ||||
\(839\) | −10.1459 | − | 17.5732i | −0.350275 | − | 0.606695i | 0.636022 | − | 0.771671i | \(-0.280579\pi\) |
−0.986298 | + | 0.164976i | \(0.947245\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.55051 | − | 16.5420i | 0.329328 | − | 0.570413i | ||||
\(842\) | 14.3913 | − | 3.85614i | 0.495957 | − | 0.132891i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16.3670 | − | 9.44949i | 0.563375 | − | 0.325265i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.1691 | − | 22.1691i | 0.761740 | − | 0.761740i | ||||
\(848\) | 9.02993 | + | 2.41956i | 0.310089 | + | 0.0830881i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.67423 | + | 2.12132i | 0.125951 | + | 0.0727179i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.60723 | − | 35.8547i | 0.328945 | − | 1.22764i | −0.581340 | − | 0.813660i | \(-0.697472\pi\) |
0.910286 | − | 0.413980i | \(-0.135862\pi\) | |||||||
\(854\) | 5.97469 | 0.204450 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.24745 | −0.179354 | ||||||||
\(857\) | 0.982984 | − | 3.66855i | 0.0335781 | − | 0.125315i | −0.947102 | − | 0.320932i | \(-0.896004\pi\) |
0.980680 | + | 0.195616i | \(0.0626707\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.16064 | + | 1.24745i | 0.0737202 | + | 0.0425624i | 0.536407 | − | 0.843959i | \(-0.319781\pi\) |
−0.462687 | + | 0.886522i | \(0.653115\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.0263 | + | 4.02628i | 0.511797 | + | 0.137136i | ||||
\(863\) | −27.7842 | + | 27.7842i | −0.945787 | + | 0.945787i | −0.998604 | − | 0.0528175i | \(-0.983180\pi\) |
0.0528175 | + | 0.998604i | \(0.483180\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −10.4722 | + | 6.04612i | −0.355860 | + | 0.205456i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.71209 | + | 1.26260i | −0.159939 | + | 0.0428555i | ||||
\(869\) | 7.70674 | − | 13.3485i | 0.261433 | − | 0.452816i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.55051 | + | 11.3458i | 0.221956 | + | 0.384438i | ||||
\(872\) | −14.3885 | − | 14.3885i | −0.487257 | − | 0.487257i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 1.55051i | − | 0.0524468i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.10558 | − | 7.85813i | −0.0711004 | − | 0.265350i | 0.921220 | − | 0.389041i | \(-0.127194\pi\) |
−0.992321 | + | 0.123691i | \(0.960527\pi\) | |||||||
\(878\) | 2.64048 | + | 9.85441i | 0.0891120 | + | 0.332570i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 58.3006i | − | 1.96420i | −0.188368 | − | 0.982098i | \(-0.560320\pi\) | ||
0.188368 | − | 0.982098i | \(-0.439680\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.2702 | + | 40.2702i | 1.35520 | + | 1.35520i | 0.879736 | + | 0.475463i | \(0.157719\pi\) |
0.475463 | + | 0.879736i | \(0.342281\pi\) | |||||||
\(884\) | 7.70674 | + | 13.3485i | 0.259206 | + | 0.448958i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.275255 | − | 0.476756i | 0.00924738 | − | 0.0160169i | ||||
\(887\) | 26.8508 | − | 7.19464i | 0.901561 | − | 0.241572i | 0.221874 | − | 0.975075i | \(-0.428783\pi\) |
0.679686 | + | 0.733503i | \(0.262116\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.9651 | + | 10.9495i | −0.636068 | + | 0.367234i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.87628 | − | 5.87628i | 0.196752 | − | 0.196752i | ||||
\(893\) | −13.4791 | − | 3.61171i | −0.451061 | − | 0.120861i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.949490 | − | 0.548188i | −0.0317202 | − | 0.0183137i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.61793 | − | 20.9664i | 0.187473 | − | 0.699658i | ||||
\(899\) | 13.9993 | 0.466902 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.5959 | 1.38576 | ||||||||
\(902\) | 6.39204 | − | 23.8554i | 0.212832 | − | 0.794298i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.9494 | + | 6.89898i | 0.397431 | + | 0.229457i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.38512 | + | 1.71089i | 0.212015 | + | 0.0568091i | 0.363263 | − | 0.931687i | \(-0.381663\pi\) |
−0.151248 | + | 0.988496i | \(0.548329\pi\) | |||||||
\(908\) | 10.6780 | − | 10.6780i | 0.354363 | − | 0.354363i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.12372 | + | 3.53553i | −0.202888 | + | 0.117137i | −0.598002 | − | 0.801495i | \(-0.704038\pi\) |
0.395114 | + | 0.918632i | \(0.370705\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.34607 | + | 0.896575i | −0.110739 | + | 0.0296723i | ||||
\(914\) | 3.07483 | − | 5.32577i | 0.101706 | − | 0.176161i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.17423 | + | 14.1582i | 0.270084 | + | 0.467800i | ||||
\(917\) | −8.16744 | − | 8.16744i | −0.269713 | − | 0.269713i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 27.3485i | − | 0.902143i | −0.892488 | − | 0.451071i | \(-0.851042\pi\) | ||
0.892488 | − | 0.451071i | \(-0.148958\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.89419 | + | 18.2654i | 0.161182 | + | 0.601538i | ||||
\(923\) | −0.569930 | − | 2.12701i | −0.0187595 | − | 0.0700113i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 33.0197i | 1.08510i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.22474 | + | 2.22474i | 0.0730308 | + | 0.0730308i | ||||
\(929\) | −23.9309 | − | 41.4495i | −0.785147 | − | 1.35991i | −0.928912 | − | 0.370302i | \(-0.879254\pi\) |
0.143765 | − | 0.989612i | \(-0.454079\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.49490 | + | 7.78539i | −0.147314 | + | 0.255156i | ||||
\(932\) | −15.0206 | + | 4.02477i | −0.492017 | + | 0.131836i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.46410 | + | 2.00000i | −0.113349 | + | 0.0654420i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.8990 | − | 12.8990i | 0.421391 | − | 0.421391i | −0.464291 | − | 0.885683i | \(-0.653691\pi\) |
0.885683 | + | 0.464291i | \(0.153691\pi\) | |||||||
\(938\) | −4.00514 | − | 1.07317i | −0.130773 | − | 0.0350404i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.47730 | − | 3.16232i | −0.178555 | − | 0.103089i | 0.408059 | − | 0.912956i | \(-0.366206\pi\) |
−0.586613 | + | 0.809867i | \(0.699539\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.01581 | + | 3.79107i | −0.0330795 | + | 0.123454i | ||||
\(944\) | 11.8065 | 0.384269 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21.7980 | 0.708713 | ||||||||
\(947\) | 10.6233 | − | 39.6468i | 0.345212 | − | 1.28835i | −0.547152 | − | 0.837033i | \(-0.684288\pi\) |
0.892364 | − | 0.451316i | \(-0.149045\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.2993 | + | 7.10102i | 0.399253 | + | 0.230509i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.71209 | − | 1.26260i | −0.152720 | − | 0.0409211i | ||||
\(953\) | 19.6561 | − | 19.6561i | 0.636724 | − | 0.636724i | −0.313022 | − | 0.949746i | \(-0.601341\pi\) |
0.949746 | + | 0.313022i | \(0.101341\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14.6969 | − | 8.48528i | 0.475333 | − | 0.274434i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.83013 | + | 1.83013i | −0.220671 | + | 0.0591287i | ||||
\(959\) | −1.20713 | + | 2.09082i | −0.0389804 | + | 0.0675159i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.60102 | + | 9.70125i | 0.180678 | + | 0.312944i | ||||
\(962\) | 10.3923 | + | 10.3923i | 0.335061 | + | 0.335061i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19.0000i | 0.611949i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.0577 | + | 48.7319i | 0.419907 | + | 1.56711i | 0.774800 | + | 0.632206i | \(0.217850\pi\) |
−0.354894 | + | 0.934907i | \(0.615483\pi\) | |||||||
\(968\) | 7.40117 | + | 27.6215i | 0.237883 | + | 0.887790i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.2117i | 1.57928i | 0.613570 | + | 0.789640i | \(0.289733\pi\) | ||||
−0.613570 | + | 0.789640i | \(0.710267\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.0000 | + | 10.0000i | 0.320585 | + | 0.320585i | ||||
\(974\) | −8.48528 | − | 14.6969i | −0.271886 | − | 0.470920i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.72474 | + | 4.71940i | −0.0872170 | + | 0.151064i | ||||
\(977\) | 41.0469 | − | 10.9985i | 1.31321 | − | 0.351873i | 0.466778 | − | 0.884374i | \(-0.345415\pi\) |
0.846429 | + | 0.532502i | \(0.178748\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.9029 | − | 7.44949i | 0.412378 | − | 0.238087i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.202041 | + | 0.202041i | −0.00644739 | + | 0.00644739i | ||||
\(983\) | 45.2034 | + | 12.1122i | 1.44176 | + | 0.386319i | 0.893151 | − | 0.449757i | \(-0.148490\pi\) |
0.548612 | + | 0.836077i | \(0.315156\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 12.1237 | + | 6.99964i | 0.386098 | + | 0.222914i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.39015 | − | 5.18811i | 0.0442265 | − | 0.165056i | ||||
\(989\) | −3.46410 | −0.110152 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.7423 | −1.80248 | −0.901240 | − | 0.433320i | \(-0.857342\pi\) | ||||
−0.901240 | + | 0.433320i | \(0.857342\pi\) | |||||||
\(992\) | 1.15161 | − | 4.29788i | 0.0365637 | − | 0.136458i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.603566 | + | 0.348469i | 0.0191440 | + | 0.0110528i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.9528 | − | 10.7053i | −1.26532 | − | 0.339041i | −0.437082 | − | 0.899422i | \(-0.643988\pi\) |
−0.828235 | + | 0.560381i | \(0.810655\pi\) | |||||||
\(998\) | −6.29253 | + | 6.29253i | −0.199187 | + | 0.199187i | ||||
\(999\) | 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 | 1350.2.q.g.1043.2 | 8 | ||
3.2 | odd | 2 | 450.2.p.a.293.1 | 8 | |||
5.2 | odd | 4 | inner | 1350.2.q.g.557.2 | 8 | ||
5.3 | odd | 4 | 270.2.m.a.17.1 | 8 | |||
5.4 | even | 2 | 270.2.m.a.233.1 | 8 | |||
9.2 | odd | 6 | inner | 1350.2.q.g.143.2 | 8 | ||
9.7 | even | 3 | 450.2.p.a.443.1 | 8 | |||
15.2 | even | 4 | 450.2.p.a.257.1 | 8 | |||
15.8 | even | 4 | 90.2.l.a.77.2 | yes | 8 | ||
15.14 | odd | 2 | 90.2.l.a.23.2 | ✓ | 8 | ||
45.2 | even | 12 | inner | 1350.2.q.g.1007.2 | 8 | ||
45.4 | even | 6 | 810.2.f.b.323.2 | 8 | |||
45.7 | odd | 12 | 450.2.p.a.407.1 | 8 | |||
45.13 | odd | 12 | 810.2.f.b.647.4 | 8 | |||
45.14 | odd | 6 | 810.2.f.b.323.3 | 8 | |||
45.23 | even | 12 | 810.2.f.b.647.1 | 8 | |||
45.29 | odd | 6 | 270.2.m.a.143.1 | 8 | |||
45.34 | even | 6 | 90.2.l.a.83.2 | yes | 8 | ||
45.38 | even | 12 | 270.2.m.a.197.1 | 8 | |||
45.43 | odd | 12 | 90.2.l.a.47.2 | yes | 8 | ||
60.23 | odd | 4 | 720.2.cu.a.257.2 | 8 | |||
60.59 | even | 2 | 720.2.cu.a.113.2 | 8 | |||
180.43 | even | 12 | 720.2.cu.a.497.2 | 8 | |||
180.79 | odd | 6 | 720.2.cu.a.353.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.2.l.a.23.2 | ✓ | 8 | 15.14 | odd | 2 | ||
90.2.l.a.47.2 | yes | 8 | 45.43 | odd | 12 | ||
90.2.l.a.77.2 | yes | 8 | 15.8 | even | 4 | ||
90.2.l.a.83.2 | yes | 8 | 45.34 | even | 6 | ||
270.2.m.a.17.1 | 8 | 5.3 | odd | 4 | |||
270.2.m.a.143.1 | 8 | 45.29 | odd | 6 | |||
270.2.m.a.197.1 | 8 | 45.38 | even | 12 | |||
270.2.m.a.233.1 | 8 | 5.4 | even | 2 | |||
450.2.p.a.257.1 | 8 | 15.2 | even | 4 | |||
450.2.p.a.293.1 | 8 | 3.2 | odd | 2 | |||
450.2.p.a.407.1 | 8 | 45.7 | odd | 12 | |||
450.2.p.a.443.1 | 8 | 9.7 | even | 3 | |||
720.2.cu.a.113.2 | 8 | 60.59 | even | 2 | |||
720.2.cu.a.257.2 | 8 | 60.23 | odd | 4 | |||
720.2.cu.a.353.2 | 8 | 180.79 | odd | 6 | |||
720.2.cu.a.497.2 | 8 | 180.43 | even | 12 | |||
810.2.f.b.323.2 | 8 | 45.4 | even | 6 | |||
810.2.f.b.323.3 | 8 | 45.14 | odd | 6 | |||
810.2.f.b.647.1 | 8 | 45.23 | even | 12 | |||
810.2.f.b.647.4 | 8 | 45.13 | odd | 12 | |||
1350.2.q.g.143.2 | 8 | 9.2 | odd | 6 | inner | ||
1350.2.q.g.557.2 | 8 | 5.2 | odd | 4 | inner | ||
1350.2.q.g.1007.2 | 8 | 45.2 | even | 12 | inner | ||
1350.2.q.g.1043.2 | 8 | 1.1 | even | 1 | trivial |