Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(109,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.k (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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 109.11 | ||
Character | \(\chi\) | \(=\) | 432.109 |
Dual form | 432.2.k.d.325.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.524142 | − | 1.31350i | 0.370625 | − | 0.928783i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.45055 | − | 1.37692i | −0.725275 | − | 0.688459i | ||||
\(5\) | −1.14284 | + | 1.14284i | −0.511094 | + | 0.511094i | −0.914861 | − | 0.403768i | \(-0.867700\pi\) |
0.403768 | + | 0.914861i | \(0.367700\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.40079i | 1.66334i | 0.555269 | + | 0.831671i | \(0.312615\pi\) | ||||
−0.555269 | + | 0.831671i | \(0.687385\pi\) | |||||||
\(8\) | −2.56887 | + | 1.18359i | −0.908234 | + | 0.418463i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.902107 | + | 2.10013i | 0.285271 | + | 0.664119i | ||||
\(11\) | −4.02070 | + | 4.02070i | −1.21229 | + | 1.21229i | −0.242014 | + | 0.970273i | \(0.577808\pi\) |
−0.970273 | + | 0.242014i | \(0.922192\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.98322 | − | 1.98322i | −0.550046 | − | 0.550046i | 0.376408 | − | 0.926454i | \(-0.377159\pi\) |
−0.926454 | + | 0.376408i | \(0.877159\pi\) | |||||||
\(14\) | 5.78043 | + | 2.30664i | 1.54488 | + | 0.616475i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.208190 | + | 3.99458i | 0.0520475 | + | 0.998645i | ||||
\(17\) | −3.27591 | −0.794524 | −0.397262 | − | 0.917705i | \(-0.630040\pi\) | ||||
−0.397262 | + | 0.917705i | \(0.630040\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.53770 | + | 1.53770i | 0.352773 | + | 0.352773i | 0.861140 | − | 0.508368i | \(-0.169751\pi\) |
−0.508368 | + | 0.861140i | \(0.669751\pi\) | |||||||
\(20\) | 3.23134 | − | 0.0841487i | 0.722551 | − | 0.0188162i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.17376 | + | 7.38860i | 0.676648 | + | 1.57525i | ||||
\(23\) | − | 8.02513i | − | 1.67336i | −0.547695 | − | 0.836678i | \(-0.684495\pi\) | ||
0.547695 | − | 0.836678i | \(-0.315505\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.38783i | 0.477567i | ||||||||
\(26\) | −3.64444 | + | 1.56546i | −0.714734 | + | 0.307013i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.05953 | − | 6.38357i | 1.14514 | − | 1.20638i | ||||
\(29\) | −0.520201 | − | 0.520201i | −0.0965989 | − | 0.0965989i | 0.657156 | − | 0.753755i | \(-0.271759\pi\) |
−0.753755 | + | 0.657156i | \(0.771759\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.97091 | 1.79083 | 0.895414 | − | 0.445235i | \(-0.146880\pi\) | ||||
0.895414 | + | 0.445235i | \(0.146880\pi\) | |||||||
\(32\) | 5.35599 | + | 1.82027i | 0.946814 | + | 0.321781i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.71704 | + | 4.30290i | −0.294470 | + | 0.737941i | ||||
\(35\) | −5.02940 | − | 5.02940i | −0.850124 | − | 0.850124i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.92995 | + | 1.92995i | −0.317282 | + | 0.317282i | −0.847722 | − | 0.530441i | \(-0.822027\pi\) |
0.530441 | + | 0.847722i | \(0.322027\pi\) | |||||||
\(38\) | 2.82574 | − | 1.21379i | 0.458395 | − | 0.196903i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.58315 | − | 4.28847i | 0.250319 | − | 0.678066i | ||||
\(41\) | 1.02135i | 0.159508i | 0.996815 | + | 0.0797541i | \(0.0254135\pi\) | ||||
−0.996815 | + | 0.0797541i | \(0.974587\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.20053 | + | 1.20053i | −0.183080 | + | 0.183080i | −0.792696 | − | 0.609617i | \(-0.791323\pi\) |
0.609617 | + | 0.792696i | \(0.291323\pi\) | |||||||
\(44\) | 11.3684 | − | 0.296049i | 1.71385 | − | 0.0446311i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.5410 | − | 4.20631i | −1.55418 | − | 0.620187i | ||||
\(47\) | 4.16250 | 0.607164 | 0.303582 | − | 0.952805i | \(-0.401817\pi\) | ||||
0.303582 | + | 0.952805i | \(0.401817\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12.3670 | −1.76671 | ||||||||
\(50\) | 3.13641 | + | 1.25156i | 0.443556 | + | 0.176998i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.146027 | + | 5.60749i | 0.0202503 | + | 0.777619i | ||||
\(53\) | −1.08787 | + | 1.08787i | −0.149430 | + | 0.149430i | −0.777864 | − | 0.628433i | \(-0.783697\pi\) |
0.628433 | + | 0.777864i | \(0.283697\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 9.19003i | − | 1.23918i | ||||||
\(56\) | −5.20874 | − | 11.3051i | −0.696047 | − | 1.51070i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.955942 | + | 0.410623i | −0.125521 | + | 0.0539175i | ||||
\(59\) | −7.31146 | + | 7.31146i | −0.951871 | + | 0.951871i | −0.998894 | − | 0.0470224i | \(-0.985027\pi\) |
0.0470224 | + | 0.998894i | \(0.485027\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.59986 | − | 5.59986i | −0.716988 | − | 0.716988i | 0.250999 | − | 0.967987i | \(-0.419241\pi\) |
−0.967987 | + | 0.250999i | \(0.919241\pi\) | |||||||
\(62\) | 5.22617 | − | 13.0968i | 0.663725 | − | 1.66329i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.19822 | − | 6.08100i | 0.649777 | − | 0.760124i | ||||
\(65\) | 4.53301 | 0.562250 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.24116 | + | 4.24116i | 0.518140 | + | 0.518140i | 0.917008 | − | 0.398868i | \(-0.130597\pi\) |
−0.398868 | + | 0.917008i | \(0.630597\pi\) | |||||||
\(68\) | 4.75187 | + | 4.51066i | 0.576249 | + | 0.546998i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9.24222 | + | 3.96998i | −1.10466 | + | 0.474504i | ||||
\(71\) | 9.01840i | 1.07029i | 0.844761 | + | 0.535143i | \(0.179742\pi\) | ||||
−0.844761 | + | 0.535143i | \(0.820258\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.45814i | − | 0.287704i | −0.989599 | − | 0.143852i | \(-0.954051\pi\) | ||
0.989599 | − | 0.143852i | \(-0.0459489\pi\) | |||||||
\(74\) | 1.52341 | + | 3.54655i | 0.177093 | + | 0.412278i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.113223 | − | 4.34780i | −0.0129875 | − | 0.498727i | ||||
\(77\) | −17.6943 | − | 17.6943i | −2.01645 | − | 2.01645i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.0383076 | −0.00430994 | −0.00215497 | − | 0.999998i | \(-0.500686\pi\) | ||||
−0.00215497 | + | 0.999998i | \(0.500686\pi\) | |||||||
\(80\) | −4.80309 | − | 4.32724i | −0.537002 | − | 0.483800i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.34154 | + | 0.535333i | 0.148148 | + | 0.0591176i | ||||
\(83\) | 8.61127 | + | 8.61127i | 0.945210 | + | 0.945210i | 0.998575 | − | 0.0533652i | \(-0.0169948\pi\) |
−0.0533652 | + | 0.998575i | \(0.516995\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.74384 | − | 3.74384i | 0.406076 | − | 0.406076i | ||||
\(86\) | 0.947647 | + | 2.20615i | 0.102187 | + | 0.237895i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.56980 | − | 15.0875i | 0.593743 | − | 1.60834i | ||||
\(89\) | 10.6312i | 1.12690i | 0.826150 | + | 0.563450i | \(0.190526\pi\) | ||||
−0.826150 | + | 0.563450i | \(0.809474\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.72773 | − | 8.72773i | 0.914915 | − | 0.914915i | ||||
\(92\) | −11.0500 | + | 11.6409i | −1.15204 | + | 1.21364i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.18174 | − | 5.46744i | 0.225030 | − | 0.563923i | ||||
\(95\) | −3.51469 | −0.360600 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.18703 | −0.526663 | −0.263332 | − | 0.964705i | \(-0.584821\pi\) | ||||
−0.263332 | + | 0.964705i | \(0.584821\pi\) | |||||||
\(98\) | −6.48204 | + | 16.2440i | −0.654785 | + | 1.64089i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.28785 | − | 3.46367i | 0.328785 | − | 0.346367i | ||||
\(101\) | 3.60642 | − | 3.60642i | 0.358852 | − | 0.358852i | −0.504538 | − | 0.863390i | \(-0.668337\pi\) |
0.863390 | + | 0.504538i | \(0.168337\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.3856i | 1.02332i | 0.859188 | + | 0.511659i | \(0.170969\pi\) | ||||
−0.859188 | + | 0.511659i | \(0.829031\pi\) | |||||||
\(104\) | 7.44196 | + | 2.74732i | 0.729745 | + | 0.269397i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.858715 | + | 1.99911i | 0.0834058 | + | 0.194171i | ||||
\(107\) | 3.98900 | − | 3.98900i | 0.385631 | − | 0.385631i | −0.487495 | − | 0.873126i | \(-0.662089\pi\) |
0.873126 | + | 0.487495i | \(0.162089\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.40487 | − | 1.40487i | −0.134562 | − | 0.134562i | 0.636617 | − | 0.771180i | \(-0.280333\pi\) |
−0.771180 | + | 0.636617i | \(0.780333\pi\) | |||||||
\(110\) | −12.0711 | − | 4.81688i | −1.15093 | − | 0.459272i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −17.5793 | + | 0.916200i | −1.66109 | + | 0.0865728i | ||||
\(113\) | 12.8259 | 1.20656 | 0.603282 | − | 0.797528i | \(-0.293860\pi\) | ||||
0.603282 | + | 0.797528i | \(0.293860\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.17144 | + | 9.17144i | 0.855241 | + | 0.855241i | ||||
\(116\) | 0.0383031 | + | 1.47085i | 0.00355635 | + | 0.136565i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.77134 | + | 13.4358i | 0.531295 | + | 1.23687i | ||||
\(119\) | − | 14.4166i | − | 1.32157i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 21.3320i | − | 1.93928i | ||||||
\(122\) | −10.2905 | + | 4.42027i | −0.931659 | + | 0.400193i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −14.4633 | − | 13.7291i | −1.29884 | − | 1.23291i | ||||
\(125\) | −8.44311 | − | 8.44311i | −0.755175 | − | 0.755175i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.36993 | 0.121561 | 0.0607806 | − | 0.998151i | \(-0.480641\pi\) | ||||
0.0607806 | + | 0.998151i | \(0.480641\pi\) | |||||||
\(128\) | −5.26276 | − | 10.0152i | −0.465167 | − | 0.885223i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.37594 | − | 5.95409i | 0.208384 | − | 0.522208i | ||||
\(131\) | −6.72910 | − | 6.72910i | −0.587924 | − | 0.587924i | 0.349145 | − | 0.937069i | \(-0.386472\pi\) |
−0.937069 | + | 0.349145i | \(0.886472\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.76710 | + | 6.76710i | −0.586782 | + | 0.586782i | ||||
\(134\) | 7.79373 | − | 3.34778i | 0.673275 | − | 0.289204i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.41539 | − | 3.87734i | 0.721614 | − | 0.332479i | ||||
\(137\) | 22.2550i | 1.90137i | 0.310156 | + | 0.950686i | \(0.399619\pi\) | ||||
−0.310156 | + | 0.950686i | \(0.600381\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.77425 | + | 7.77425i | −0.659403 | + | 0.659403i | −0.955239 | − | 0.295836i | \(-0.904402\pi\) |
0.295836 | + | 0.955239i | \(0.404402\pi\) | |||||||
\(140\) | 0.370321 | + | 14.2205i | 0.0312978 | + | 1.20185i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.8456 | + | 4.72692i | 0.994064 | + | 0.396674i | ||||
\(143\) | 15.9479 | 1.33363 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.18901 | 0.0987422 | ||||||||
\(146\) | −3.22877 | − | 1.28842i | −0.267215 | − | 0.106630i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.45687 | − | 0.142104i | 0.448552 | − | 0.0116809i | ||||
\(149\) | −3.84216 | + | 3.84216i | −0.314762 | + | 0.314762i | −0.846751 | − | 0.531989i | \(-0.821445\pi\) |
0.531989 | + | 0.846751i | \(0.321445\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.96169i | 0.322398i | 0.986922 | + | 0.161199i | \(0.0515361\pi\) | ||||
−0.986922 | + | 0.161199i | \(0.948464\pi\) | |||||||
\(152\) | −5.77017 | − | 2.13015i | −0.468022 | − | 0.172778i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −32.5157 | + | 13.9670i | −2.62019 | + | 1.12550i | ||||
\(155\) | −11.3952 | + | 11.3952i | −0.915281 | + | 0.915281i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.00887 | − | 4.00887i | −0.319943 | − | 0.319943i | 0.528802 | − | 0.848745i | \(-0.322641\pi\) |
−0.848745 | + | 0.528802i | \(0.822641\pi\) | |||||||
\(158\) | −0.0200786 | + | 0.0503170i | −0.00159737 | + | 0.00400300i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.20132 | + | 4.04076i | −0.648371 | + | 0.319450i | ||||
\(161\) | 35.3169 | 2.78336 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.8476 | − | 14.8476i | −1.16295 | − | 1.16295i | −0.983826 | − | 0.179126i | \(-0.942673\pi\) |
−0.179126 | − | 0.983826i | \(-0.557327\pi\) | |||||||
\(164\) | 1.40632 | − | 1.48152i | 0.109815 | − | 0.115687i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.8244 | − | 6.79735i | 1.22821 | − | 0.527577i | ||||
\(167\) | − | 10.5791i | − | 0.818635i | −0.912392 | − | 0.409317i | \(-0.865767\pi\) | ||
0.912392 | − | 0.409317i | \(-0.134233\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.13368i | − | 0.394898i | ||||||
\(170\) | −2.95522 | − | 6.87983i | −0.226655 | − | 0.527659i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.39447 | − | 0.0883968i | 0.258826 | − | 0.00674019i | ||||
\(173\) | 8.39876 | + | 8.39876i | 0.638546 | + | 0.638546i | 0.950197 | − | 0.311651i | \(-0.100882\pi\) |
−0.311651 | + | 0.950197i | \(0.600882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.5084 | −0.794357 | ||||||||
\(176\) | −16.8981 | − | 15.2239i | −1.27374 | − | 1.14755i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.9640 | + | 5.57223i | 1.04665 | + | 0.417657i | ||||
\(179\) | 2.96025 | + | 2.96025i | 0.221260 | + | 0.221260i | 0.809029 | − | 0.587769i | \(-0.199994\pi\) |
−0.587769 | + | 0.809029i | \(0.699994\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.76128 | + | 3.76128i | −0.279574 | + | 0.279574i | −0.832939 | − | 0.553365i | \(-0.813343\pi\) |
0.553365 | + | 0.832939i | \(0.313343\pi\) | |||||||
\(182\) | −6.88928 | − | 16.0384i | −0.510667 | − | 1.18885i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.49848 | + | 20.6155i | 0.700237 | + | 1.51980i | ||||
\(185\) | − | 4.41124i | − | 0.324321i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.1714 | − | 13.1714i | 0.963191 | − | 0.963191i | ||||
\(188\) | −6.03792 | − | 5.73143i | −0.440361 | − | 0.418007i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.84220 | + | 4.61654i | −0.133647 | + | 0.334919i | ||||
\(191\) | 19.1339 | 1.38448 | 0.692242 | − | 0.721666i | \(-0.256623\pi\) | ||||
0.692242 | + | 0.721666i | \(0.256623\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.8020 | 1.35340 | 0.676698 | − | 0.736261i | \(-0.263410\pi\) | ||||
0.676698 | + | 0.736261i | \(0.263410\pi\) | |||||||
\(194\) | −2.71874 | + | 6.81315i | −0.195194 | + | 0.489156i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 17.9389 | + | 17.0283i | 1.28135 | + | 1.21631i | ||||
\(197\) | 3.32506 | − | 3.32506i | 0.236901 | − | 0.236901i | −0.578665 | − | 0.815565i | \(-0.696426\pi\) |
0.815565 | + | 0.578665i | \(0.196426\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.94198i | 0.350328i | 0.984539 | + | 0.175164i | \(0.0560455\pi\) | ||||
−0.984539 | + | 0.175164i | \(0.943954\pi\) | |||||||
\(200\) | −2.82622 | − | 6.13404i | −0.199844 | − | 0.433742i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.84674 | − | 6.62730i | −0.200296 | − | 0.466295i | ||||
\(203\) | 2.28930 | − | 2.28930i | 0.160677 | − | 0.160677i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.16724 | − | 1.16724i | −0.0815236 | − | 0.0815236i | ||||
\(206\) | 13.6414 | + | 5.44351i | 0.950441 | + | 0.379267i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.50924 | − | 8.33501i | 0.520672 | − | 0.577929i | ||||
\(209\) | −12.3653 | −0.855323 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.6698 | + | 16.6698i | 1.14759 | + | 1.14759i | 0.987025 | + | 0.160569i | \(0.0513329\pi\) |
0.160569 | + | 0.987025i | \(0.448667\pi\) | |||||||
\(212\) | 3.07592 | − | 0.0801011i | 0.211255 | − | 0.00550137i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.14873 | − | 7.33034i | −0.215243 | − | 0.501092i | ||||
\(215\) | − | 2.74404i | − | 0.187142i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 43.8799i | 2.97876i | ||||||||
\(218\) | −2.58165 | + | 1.10894i | −0.174851 | + | 0.0751072i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12.6539 | + | 13.3306i | −0.853128 | + | 0.898749i | ||||
\(221\) | 6.49685 | + | 6.49685i | 0.437025 | + | 0.437025i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.43910 | 0.565124 | 0.282562 | − | 0.959249i | \(-0.408816\pi\) | ||||
0.282562 | + | 0.959249i | \(0.408816\pi\) | |||||||
\(224\) | −8.01063 | + | 23.5706i | −0.535233 | + | 1.57488i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.72262 | − | 16.8468i | 0.447182 | − | 1.12064i | ||||
\(227\) | 13.7762 | + | 13.7762i | 0.914356 | + | 0.914356i | 0.996611 | − | 0.0822551i | \(-0.0262122\pi\) |
−0.0822551 | + | 0.996611i | \(0.526212\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.24202 | + | 8.24202i | −0.544648 | + | 0.544648i | −0.924888 | − | 0.380240i | \(-0.875841\pi\) |
0.380240 | + | 0.924888i | \(0.375841\pi\) | |||||||
\(230\) | 16.8538 | − | 7.23952i | 1.11131 | − | 0.477360i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.95204 | + | 0.720625i | 0.128158 | + | 0.0473113i | ||||
\(233\) | − | 5.50905i | − | 0.360910i | −0.983583 | − | 0.180455i | \(-0.942243\pi\) | ||
0.983583 | − | 0.180455i | \(-0.0577570\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.75708 | + | 4.75708i | −0.310317 | + | 0.310317i | ||||
\(236\) | 20.6729 | − | 0.538352i | 1.34569 | − | 0.0350437i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −18.9361 | − | 7.55634i | −1.22745 | − | 0.489805i | ||||
\(239\) | 22.6716 | 1.46650 | 0.733251 | − | 0.679959i | \(-0.238002\pi\) | ||||
0.733251 | + | 0.679959i | \(0.238002\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0533528 | 0.00343676 | 0.00171838 | − | 0.999999i | \(-0.499453\pi\) | ||||
0.00171838 | + | 0.999999i | \(0.499453\pi\) | |||||||
\(242\) | −28.0196 | − | 11.1810i | −1.80117 | − | 0.718744i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.412324 | + | 15.8334i | 0.0263964 | + | 1.01363i | ||||
\(245\) | 14.1334 | − | 14.1334i | 0.902953 | − | 0.902953i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6.09919i | − | 0.388082i | ||||||
\(248\) | −25.6140 | + | 11.8015i | −1.62649 | + | 0.749395i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −15.5154 | + | 6.66461i | −0.981280 | + | 0.421507i | ||||
\(251\) | −11.4159 | + | 11.4159i | −0.720566 | + | 0.720566i | −0.968720 | − | 0.248154i | \(-0.920176\pi\) |
0.248154 | + | 0.968720i | \(0.420176\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 32.2666 | + | 32.2666i | 2.02859 | + | 2.02859i | ||||
\(254\) | 0.718036 | − | 1.79939i | 0.0450536 | − | 0.112904i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.9133 | + | 1.66326i | −0.994582 | + | 0.103954i | ||||
\(257\) | −12.8857 | −0.803788 | −0.401894 | − | 0.915686i | \(-0.631648\pi\) | ||||
−0.401894 | + | 0.915686i | \(0.631648\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.49330 | − | 8.49330i | −0.527748 | − | 0.527748i | ||||
\(260\) | −6.57535 | − | 6.24158i | −0.407786 | − | 0.387086i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.3657 | + | 5.31165i | −0.763953 | + | 0.328155i | ||||
\(263\) | − | 26.2126i | − | 1.61634i | −0.588953 | − | 0.808168i | \(-0.700460\pi\) | ||
0.588953 | − | 0.808168i | \(-0.299540\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.48652i | − | 0.152746i | ||||||
\(266\) | 5.34164 | + | 12.4355i | 0.327517 | + | 0.762468i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.312282 | − | 11.9918i | −0.0190757 | − | 0.732513i | ||||
\(269\) | −13.1408 | − | 13.1408i | −0.801208 | − | 0.801208i | 0.182077 | − | 0.983284i | \(-0.441718\pi\) |
−0.983284 | + | 0.182077i | \(0.941718\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.2489 | −0.622576 | −0.311288 | − | 0.950316i | \(-0.600760\pi\) | ||||
−0.311288 | + | 0.950316i | \(0.600760\pi\) | |||||||
\(272\) | −0.682011 | − | 13.0859i | −0.0413530 | − | 0.793448i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 29.2319 | + | 11.6648i | 1.76596 | + | 0.704695i | ||||
\(275\) | −9.60076 | − | 9.60076i | −0.578948 | − | 0.578948i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.2698 | − | 17.2698i | 1.03764 | − | 1.03764i | 0.0383797 | − | 0.999263i | \(-0.487780\pi\) |
0.999263 | − | 0.0383797i | \(-0.0122197\pi\) | |||||||
\(278\) | 6.13664 | + | 14.2863i | 0.368051 | + | 0.856833i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 18.8726 | + | 6.96713i | 1.12786 | + | 0.416366i | ||||
\(281\) | − | 13.0834i | − | 0.780487i | −0.920712 | − | 0.390244i | \(-0.872391\pi\) | ||
0.920712 | − | 0.390244i | \(-0.127609\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.95147 | + | 5.95147i | −0.353778 | + | 0.353778i | −0.861513 | − | 0.507735i | \(-0.830483\pi\) |
0.507735 | + | 0.861513i | \(0.330483\pi\) | |||||||
\(284\) | 12.4176 | − | 13.0816i | 0.736849 | − | 0.776252i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.35895 | − | 20.9475i | 0.494275 | − | 1.23865i | ||||
\(287\) | −4.49475 | −0.265317 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.26843 | −0.368731 | ||||||||
\(290\) | 0.623212 | − | 1.56177i | 0.0365963 | − | 0.0917101i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.38467 | + | 3.56566i | −0.198073 | + | 0.208665i | ||||
\(293\) | 8.16327 | − | 8.16327i | 0.476903 | − | 0.476903i | −0.427236 | − | 0.904140i | \(-0.640513\pi\) |
0.904140 | + | 0.427236i | \(0.140513\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 16.7117i | − | 0.972991i | ||||||
\(296\) | 2.67352 | − | 7.24206i | 0.155395 | − | 0.420936i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.03283 | + | 7.06051i | 0.175687 | + | 0.409005i | ||||
\(299\) | −15.9156 | + | 15.9156i | −0.920423 | + | 0.920423i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.28330 | − | 5.28330i | −0.304524 | − | 0.304524i | ||||
\(302\) | 5.20367 | + | 2.07649i | 0.299438 | + | 0.119489i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.82233 | + | 6.46260i | −0.333934 | + | 0.370655i | ||||
\(305\) | 12.7995 | 0.732896 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.89022 | − | 8.89022i | −0.507391 | − | 0.507391i | 0.406333 | − | 0.913725i | \(-0.366807\pi\) |
−0.913725 | + | 0.406333i | \(0.866807\pi\) | |||||||
\(308\) | 1.30285 | + | 50.0299i | 0.0742367 | + | 2.85072i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.99482 | + | 20.9402i | 0.510872 | + | 1.18932i | ||||
\(311\) | 26.1862i | 1.48489i | 0.669909 | + | 0.742443i | \(0.266333\pi\) | ||||
−0.669909 | + | 0.742443i | \(0.733667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 8.60708i | − | 0.486501i | −0.969963 | − | 0.243251i | \(-0.921786\pi\) | ||
0.969963 | − | 0.243251i | \(-0.0782137\pi\) | |||||||
\(314\) | −7.36686 | + | 3.16442i | −0.415736 | + | 0.178579i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.0555671 | + | 0.0527465i | 0.00312590 | + | 0.00296722i | ||||
\(317\) | 11.0091 | + | 11.0091i | 0.618334 | + | 0.618334i | 0.945104 | − | 0.326770i | \(-0.105960\pi\) |
−0.326770 | + | 0.945104i | \(0.605960\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.18315 | 0.234211 | ||||||||
\(320\) | 1.00887 | + | 12.8903i | 0.0563977 | + | 0.720592i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 18.5111 | − | 46.3887i | 1.03158 | − | 2.58514i | ||||
\(323\) | −5.03736 | − | 5.03736i | −0.280286 | − | 0.280286i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.73560 | − | 4.73560i | 0.262684 | − | 0.262684i | ||||
\(326\) | −27.2845 | + | 11.7200i | −1.51115 | + | 0.649111i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.20886 | − | 2.62372i | −0.0667482 | − | 0.144871i | ||||
\(329\) | 18.3183i | 1.00992i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.4754 | + | 20.4754i | −1.12543 | + | 1.12543i | −0.134518 | + | 0.990911i | \(0.542949\pi\) |
−0.990911 | + | 0.134518i | \(0.957051\pi\) | |||||||
\(332\) | −0.634058 | − | 24.3481i | −0.0347985 | − | 1.33628i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.8956 | − | 5.54495i | −0.760334 | − | 0.303406i | ||||
\(335\) | −9.69394 | −0.529636 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.2159 | −0.992281 | −0.496141 | − | 0.868242i | \(-0.665250\pi\) | ||||
−0.496141 | + | 0.868242i | \(0.665250\pi\) | |||||||
\(338\) | −6.74307 | − | 2.69078i | −0.366775 | − | 0.146359i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.5856 | + | 0.275663i | −0.574084 | + | 0.0149499i | ||||
\(341\) | −40.0900 | + | 40.0900i | −2.17100 | + | 2.17100i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 23.6188i | − | 1.27530i | ||||||
\(344\) | 1.66308 | − | 4.50496i | 0.0896671 | − | 0.242891i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.4339 | − | 6.62960i | 0.829731 | − | 0.356410i | ||||
\(347\) | 4.43980 | − | 4.43980i | 0.238341 | − | 0.238341i | −0.577822 | − | 0.816163i | \(-0.696097\pi\) |
0.816163 | + | 0.577822i | \(0.196097\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.3495 | + | 10.3495i | 0.553996 | + | 0.553996i | 0.927592 | − | 0.373595i | \(-0.121875\pi\) |
−0.373595 | + | 0.927592i | \(0.621875\pi\) | |||||||
\(350\) | −5.50787 | + | 13.8027i | −0.294408 | + | 0.737785i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −28.8536 | + | 14.2161i | −1.53790 | + | 0.757719i | ||||
\(353\) | −25.5873 | −1.36188 | −0.680938 | − | 0.732341i | \(-0.738428\pi\) | ||||
−0.680938 | + | 0.732341i | \(0.738428\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.3066 | − | 10.3066i | −0.547017 | − | 0.547017i | ||||
\(356\) | 14.6382 | − | 15.4210i | 0.775825 | − | 0.817312i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.43988 | − | 2.33669i | 0.287507 | − | 0.123498i | ||||
\(359\) | 4.65858i | 0.245871i | 0.992415 | + | 0.122935i | \(0.0392308\pi\) | ||||
−0.992415 | + | 0.122935i | \(0.960769\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 14.2710i | − | 0.751103i | ||||||
\(362\) | 2.96899 | + | 6.91188i | 0.156047 | + | 0.363280i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −24.6774 | + | 0.642634i | −1.29345 | + | 0.0336832i | ||||
\(365\) | 2.80927 | + | 2.80927i | 0.147044 | + | 0.147044i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.8994 | −1.09094 | −0.545469 | − | 0.838131i | \(-0.683648\pi\) | ||||
−0.545469 | + | 0.838131i | \(0.683648\pi\) | |||||||
\(368\) | 32.0570 | − | 1.67075i | 1.67109 | − | 0.0870940i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.79416 | − | 2.31212i | −0.301224 | − | 0.120201i | ||||
\(371\) | −4.78748 | − | 4.78748i | −0.248554 | − | 0.248554i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.2131 | − | 22.2131i | 1.15015 | − | 1.15015i | 0.163627 | − | 0.986522i | \(-0.447681\pi\) |
0.986522 | − | 0.163627i | \(-0.0523193\pi\) | |||||||
\(374\) | −10.3969 | − | 24.2044i | −0.537613 | − | 1.25158i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.6929 | + | 4.92671i | −0.551446 | + | 0.254075i | ||||
\(377\) | 2.06335i | 0.106268i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.2327 | + | 13.2327i | −0.679717 | + | 0.679717i | −0.959936 | − | 0.280219i | \(-0.909593\pi\) |
0.280219 | + | 0.959936i | \(0.409593\pi\) | |||||||
\(380\) | 5.09823 | + | 4.83944i | 0.261534 | + | 0.248258i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.0289 | − | 25.1324i | 0.513123 | − | 1.28588i | ||||
\(383\) | −13.6857 | −0.699306 | −0.349653 | − | 0.936879i | \(-0.613701\pi\) | ||||
−0.349653 | + | 0.936879i | \(0.613701\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 40.4434 | 2.06119 | ||||||||
\(386\) | 9.85491 | − | 24.6963i | 0.501602 | − | 1.25701i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.52405 | + | 7.14212i | 0.381976 | + | 0.362586i | ||||
\(389\) | 2.59662 | − | 2.59662i | 0.131654 | − | 0.131654i | −0.638209 | − | 0.769863i | \(-0.720325\pi\) |
0.769863 | + | 0.638209i | \(0.220325\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.2896i | 1.32952i | ||||||||
\(392\) | 31.7691 | − | 14.6374i | 1.60458 | − | 0.739302i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.62465 | − | 6.11026i | −0.132228 | − | 0.307830i | ||||
\(395\) | 0.0437795 | − | 0.0437795i | 0.00220279 | − | 0.00220279i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.6682 | − | 17.6682i | −0.886742 | − | 0.886742i | 0.107466 | − | 0.994209i | \(-0.465726\pi\) |
−0.994209 | + | 0.107466i | \(0.965726\pi\) | |||||||
\(398\) | 6.49128 | + | 2.59030i | 0.325378 | + | 0.129840i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.53839 | + | 0.497123i | −0.476919 | + | 0.0248561i | ||||
\(401\) | 5.27444 | 0.263393 | 0.131696 | − | 0.991290i | \(-0.457958\pi\) | ||||
0.131696 | + | 0.991290i | \(0.457958\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.7745 | − | 19.7745i | −0.985038 | − | 0.985038i | ||||
\(404\) | −10.1970 | + | 0.265545i | −0.507321 | + | 0.0132114i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.80707 | − | 4.20690i | −0.0896833 | − | 0.208785i | ||||
\(407\) | − | 15.5195i | − | 0.769272i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.5988i | 1.31523i | 0.753356 | + | 0.657613i | \(0.228434\pi\) | ||||
−0.753356 | + | 0.657613i | \(0.771566\pi\) | |||||||
\(410\) | −2.14497 | + | 0.921367i | −0.105932 | + | 0.0455031i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.3001 | − | 15.0648i | 0.704513 | − | 0.742188i | ||||
\(413\) | −32.1762 | − | 32.1762i | −1.58329 | − | 1.58329i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.6826 | −0.966181 | ||||||||
\(416\) | −7.01211 | − | 14.2321i | −0.343797 | − | 0.697786i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.48116 | + | 16.2417i | −0.317004 | + | 0.794409i | ||||
\(419\) | 19.8536 | + | 19.8536i | 0.969911 | + | 0.969911i | 0.999560 | − | 0.0296493i | \(-0.00943905\pi\) |
−0.0296493 | + | 0.999560i | \(0.509439\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.81162 | − | 5.81162i | 0.283241 | − | 0.283241i | −0.551159 | − | 0.834400i | \(-0.685814\pi\) |
0.834400 | + | 0.551159i | \(0.185814\pi\) | |||||||
\(422\) | 30.6330 | − | 13.1584i | 1.49119 | − | 0.640539i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.50700 | − | 4.08219i | 0.0731866 | − | 0.198249i | ||||
\(425\) | − | 7.82232i | − | 0.379438i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.6438 | − | 24.6438i | 1.19260 | − | 1.19260i | ||||
\(428\) | −11.2788 | + | 0.293715i | −0.545180 | + | 0.0141972i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.60428 | − | 1.43827i | −0.173814 | − | 0.0693593i | ||||
\(431\) | −26.1479 | −1.25950 | −0.629750 | − | 0.776798i | \(-0.716843\pi\) | ||||
−0.629750 | + | 0.776798i | \(0.716843\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 39.2763 | 1.88750 | 0.943748 | − | 0.330665i | \(-0.107273\pi\) | ||||
0.943748 | + | 0.330665i | \(0.107273\pi\) | |||||||
\(434\) | 57.6361 | + | 22.9993i | 2.76662 | + | 1.10400i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.103443 | + | 3.97224i | 0.00495400 | + | 0.190236i | ||||
\(437\) | 12.3402 | − | 12.3402i | 0.590314 | − | 0.590314i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.25236i | 0.202954i | 0.994838 | + | 0.101477i | \(0.0323568\pi\) | ||||
−0.994838 | + | 0.101477i | \(0.967643\pi\) | |||||||
\(440\) | 10.8772 | + | 23.6080i | 0.518553 | + | 1.12547i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.9389 | − | 5.12832i | 0.567874 | − | 0.243929i | ||||
\(443\) | 14.2988 | − | 14.2988i | 0.679357 | − | 0.679357i | −0.280497 | − | 0.959855i | \(-0.590499\pi\) |
0.959855 | + | 0.280497i | \(0.0904994\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.1497 | − | 12.1497i | −0.575951 | − | 0.575951i | ||||
\(446\) | 4.42329 | − | 11.0847i | 0.209449 | − | 0.524877i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 26.7612 | + | 22.8763i | 1.26435 | + | 1.08080i | ||||
\(449\) | 20.7419 | 0.978869 | 0.489434 | − | 0.872040i | \(-0.337203\pi\) | ||||
0.489434 | + | 0.872040i | \(0.337203\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.10654 | − | 4.10654i | −0.193370 | − | 0.193370i | ||||
\(452\) | −18.6047 | − | 17.6603i | −0.875090 | − | 0.830670i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 25.3156 | − | 10.8743i | 1.18812 | − | 0.510356i | ||||
\(455\) | 19.9488i | 0.935214i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3.83369i | − | 0.179333i | −0.995972 | − | 0.0896663i | \(-0.971420\pi\) | ||
0.995972 | − | 0.0896663i | \(-0.0285801\pi\) | |||||||
\(458\) | 6.50588 | + | 15.1459i | 0.304000 | + | 0.707720i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.675304 | − | 25.9320i | −0.0314862 | − | 1.20908i | ||||
\(461\) | −11.8553 | − | 11.8553i | −0.552155 | − | 0.552155i | 0.374908 | − | 0.927062i | \(-0.377674\pi\) |
−0.927062 | + | 0.374908i | \(0.877674\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.91516 | 0.321375 | 0.160687 | − | 0.987005i | \(-0.448629\pi\) | ||||
0.160687 | + | 0.987005i | \(0.448629\pi\) | |||||||
\(464\) | 1.96968 | − | 2.18629i | 0.0914403 | − | 0.101496i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.23613 | − | 2.88753i | −0.335207 | − | 0.133762i | ||||
\(467\) | −18.7210 | − | 18.7210i | −0.866304 | − | 0.866304i | 0.125757 | − | 0.992061i | \(-0.459864\pi\) |
−0.992061 | + | 0.125757i | \(0.959864\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.6645 | + | 18.6645i | −0.861845 | + | 0.861845i | ||||
\(470\) | 3.75502 | + | 8.74179i | 0.173206 | + | 0.403229i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.1284 | − | 27.4360i | 0.466199 | − | 1.26284i | ||||
\(473\) | − | 9.65397i | − | 0.443890i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.67177 | + | 3.67177i | −0.168472 | + | 0.168472i | ||||
\(476\) | −19.8505 | + | 20.9120i | −0.909844 | + | 0.958499i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.8831 | − | 29.7790i | 0.543521 | − | 1.36206i | ||||
\(479\) | −18.0704 | −0.825657 | −0.412829 | − | 0.910809i | \(-0.635459\pi\) | ||||
−0.412829 | + | 0.910809i | \(0.635459\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.65502 | 0.349039 | ||||||||
\(482\) | 0.0279645 | − | 0.0700788i | 0.00127375 | − | 0.00319200i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −29.3725 | + | 30.9432i | −1.33511 | + | 1.40651i | ||||
\(485\) | 5.92795 | − | 5.92795i | 0.269174 | − | 0.269174i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 20.2269i | − | 0.916569i | −0.888806 | − | 0.458284i | \(-0.848464\pi\) | ||
0.888806 | − | 0.458284i | \(-0.151536\pi\) | |||||||
\(488\) | 21.0133 | + | 7.75737i | 0.951226 | + | 0.351160i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −11.1563 | − | 25.9722i | −0.503991 | − | 1.17330i | ||||
\(491\) | 13.1245 | − | 13.1245i | 0.592300 | − | 0.592300i | −0.345952 | − | 0.938252i | \(-0.612444\pi\) |
0.938252 | + | 0.345952i | \(0.112444\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.70413 | + | 1.70413i | 0.0767502 | + | 0.0767502i | ||||
\(494\) | −8.01128 | − | 3.19685i | −0.360444 | − | 0.143833i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.07584 | + | 39.8296i | 0.0932081 | + | 1.78840i | ||||
\(497\) | −39.6881 | −1.78025 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.4295 | − | 25.4295i | −1.13838 | − | 1.13838i | −0.988741 | − | 0.149640i | \(-0.952189\pi\) |
−0.149640 | − | 0.988741i | \(-0.547811\pi\) | |||||||
\(500\) | 0.621677 | + | 23.8726i | 0.0278022 | + | 1.06762i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.01121 | + | 20.9783i | 0.402190 | + | 0.936309i | ||||
\(503\) | 24.5234i | 1.09344i | 0.837314 | + | 0.546722i | \(0.184125\pi\) | ||||
−0.837314 | + | 0.546722i | \(0.815875\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.24312i | 0.366814i | ||||||||
\(506\) | 59.2945 | − | 25.4698i | 2.63596 | − | 1.13227i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.98715 | − | 1.88628i | −0.0881653 | − | 0.0836900i | ||||
\(509\) | 12.2303 | + | 12.2303i | 0.542099 | + | 0.542099i | 0.924144 | − | 0.382045i | \(-0.124780\pi\) |
−0.382045 | + | 0.924144i | \(0.624780\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.8178 | 0.478550 | ||||||||
\(512\) | −6.15615 | + | 21.7739i | −0.272066 | + | 0.962279i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.75394 | + | 16.9253i | −0.297904 | + | 0.746545i | ||||
\(515\) | −11.8690 | − | 11.8690i | −0.523012 | − | 0.523012i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.7362 | + | 16.7362i | −0.736056 | + | 0.736056i | ||||
\(518\) | −15.6076 | + | 6.70423i | −0.685759 | + | 0.294567i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −11.6447 | + | 5.36523i | −0.510655 | + | 0.235281i | ||||
\(521\) | 2.65067i | 0.116128i | 0.998313 | + | 0.0580640i | \(0.0184927\pi\) | ||||
−0.998313 | + | 0.0580640i | \(0.981507\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.6853 | − | 22.6853i | 0.991961 | − | 0.991961i | −0.00800717 | − | 0.999968i | \(-0.502549\pi\) |
0.999968 | + | 0.00800717i | \(0.00254879\pi\) | |||||||
\(524\) | 0.495472 | + | 19.0263i | 0.0216448 | + | 0.831169i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −34.4301 | − | 13.7391i | −1.50122 | − | 0.599053i | ||||
\(527\) | −32.6638 | −1.42286 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −41.4027 | −1.80012 | ||||||||
\(530\) | −3.26604 | − | 1.30329i | −0.141868 | − | 0.0566113i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 19.1338 | − | 0.498270i | 0.829553 | − | 0.0216027i | ||||
\(533\) | 2.02556 | − | 2.02556i | 0.0877368 | − | 0.0877368i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.11757i | 0.394187i | ||||||||
\(536\) | −15.9148 | − | 5.87520i | −0.687415 | − | 0.253770i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −24.1480 | + | 10.3727i | −1.04110 | + | 0.447201i | ||||
\(539\) | 49.7238 | − | 49.7238i | 2.14176 | − | 2.14176i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.2345 | + | 23.2345i | 0.998930 | + | 0.998930i | 0.999999 | − | 0.00106969i | \(-0.000340495\pi\) |
−0.00106969 | + | 0.999999i | \(0.500340\pi\) | |||||||
\(542\) | −5.37188 | + | 13.4619i | −0.230742 | + | 0.578238i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17.5457 | − | 5.96304i | −0.752267 | − | 0.255663i | ||||
\(545\) | 3.21109 | 0.137548 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.8516 | + | 20.8516i | 0.891551 | + | 0.891551i | 0.994669 | − | 0.103118i | \(-0.0328819\pi\) |
−0.103118 | + | 0.994669i | \(0.532882\pi\) | |||||||
\(548\) | 30.6433 | − | 32.2820i | 1.30902 | − | 1.37902i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −17.6427 | + | 7.57841i | −0.752289 | + | 0.323144i | ||||
\(551\) | − | 1.59983i | − | 0.0681549i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 0.168584i | − | 0.00716891i | ||||||
\(554\) | −13.6320 | − | 31.7357i | −0.579169 | − | 1.34832i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 21.9814 | − | 0.572428i | 0.932221 | − | 0.0242763i | ||||
\(557\) | 25.1470 | + | 25.1470i | 1.06551 | + | 1.06551i | 0.997698 | + | 0.0678126i | \(0.0216020\pi\) |
0.0678126 | + | 0.997698i | \(0.478398\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.76184 | 0.201405 | ||||||||
\(560\) | 19.0433 | − | 21.1374i | 0.804725 | − | 0.893218i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.1849 | − | 6.85754i | −0.724903 | − | 0.289268i | ||||
\(563\) | −8.46453 | − | 8.46453i | −0.356737 | − | 0.356737i | 0.505871 | − | 0.862609i | \(-0.331171\pi\) |
−0.862609 | + | 0.505871i | \(0.831171\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.6580 | + | 14.6580i | −0.616667 | + | 0.616667i | ||||
\(566\) | 4.69782 | + | 10.9367i | 0.197464 | + | 0.459702i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.6741 | − | 23.1671i | −0.447875 | − | 0.972071i | ||||
\(569\) | − | 0.889656i | − | 0.0372963i | −0.999826 | − | 0.0186482i | \(-0.994064\pi\) | ||
0.999826 | − | 0.0186482i | \(-0.00593624\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.51710 | + | 8.51710i | −0.356429 | + | 0.356429i | −0.862495 | − | 0.506066i | \(-0.831099\pi\) |
0.506066 | + | 0.862495i | \(0.331099\pi\) | |||||||
\(572\) | −23.1332 | − | 21.9589i | −0.967246 | − | 0.918148i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.35589 | + | 5.90384i | −0.0983328 | + | 0.246422i | ||||
\(575\) | 19.1627 | 0.799139 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.88759 | 0.203473 | 0.101736 | − | 0.994811i | \(-0.467560\pi\) | ||||
0.101736 | + | 0.994811i | \(0.467560\pi\) | |||||||
\(578\) | −3.28555 | + | 8.23356i | −0.136661 | + | 0.342471i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.72472 | − | 1.63718i | −0.0716152 | − | 0.0679800i | ||||
\(581\) | −37.8964 | + | 37.8964i | −1.57221 | + | 1.57221i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 8.74799i | − | 0.362305i | ||||||
\(584\) | 2.90944 | + | 6.31466i | 0.120394 | + | 0.261303i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.44372 | − | 15.0012i | −0.266188 | − | 0.619692i | ||||
\(587\) | −28.4721 | + | 28.4721i | −1.17517 | + | 1.17517i | −0.194209 | + | 0.980960i | \(0.562214\pi\) |
−0.980960 | + | 0.194209i | \(0.937786\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.3323 | + | 15.3323i | 0.631755 | + | 0.631755i | ||||
\(590\) | −21.9507 | − | 8.75929i | −0.903697 | − | 0.360614i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.11113 | − | 7.30753i | −0.333365 | − | 0.300338i | ||||
\(593\) | −11.7815 | −0.483808 | −0.241904 | − | 0.970300i | \(-0.577772\pi\) | ||||
−0.241904 | + | 0.970300i | \(0.577772\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.4758 | + | 16.4758i | 0.675444 | + | 0.675444i | ||||
\(596\) | 10.8636 | − | 0.282903i | 0.444990 | − | 0.0115882i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.5631 | + | 29.2471i | 0.513742 | + | 1.19600i | ||||
\(599\) | 15.9520i | 0.651780i | 0.945408 | + | 0.325890i | \(0.105664\pi\) | ||||
−0.945408 | + | 0.325890i | \(0.894336\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.0500i | 1.02181i | 0.859637 | + | 0.510905i | \(0.170690\pi\) | ||||
−0.859637 | + | 0.510905i | \(0.829310\pi\) | |||||||
\(602\) | −9.70880 | + | 4.17040i | −0.395701 | + | 0.169973i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.45493 | − | 5.74663i | 0.221958 | − | 0.233827i | ||||
\(605\) | 24.3791 | + | 24.3791i | 0.991152 | + | 0.991152i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.5877 | −1.07916 | −0.539580 | − | 0.841934i | \(-0.681417\pi\) | ||||
−0.539580 | + | 0.841934i | \(0.681417\pi\) | |||||||
\(608\) | 5.43688 | + | 11.0349i | 0.220494 | + | 0.447526i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.70875 | − | 16.8121i | 0.271629 | − | 0.680701i | ||||
\(611\) | −8.25516 | − | 8.25516i | −0.333968 | − | 0.333968i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.29751 | − | 6.29751i | 0.254354 | − | 0.254354i | −0.568399 | − | 0.822753i | \(-0.692437\pi\) |
0.822753 | + | 0.568399i | \(0.192437\pi\) | |||||||
\(614\) | −16.3370 | + | 7.01754i | −0.659308 | + | 0.283205i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 66.3971 | + | 24.5115i | 2.67521 | + | 0.987597i | ||||
\(617\) | 14.0208i | 0.564456i | 0.959347 | + | 0.282228i | \(0.0910735\pi\) | ||||
−0.959347 | + | 0.282228i | \(0.908927\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.36830 | + | 3.36830i | −0.135383 | + | 0.135383i | −0.771551 | − | 0.636168i | \(-0.780519\pi\) |
0.636168 | + | 0.771551i | \(0.280519\pi\) | |||||||
\(620\) | 32.2194 | − | 0.839039i | 1.29396 | − | 0.0336966i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 34.3956 | + | 13.7253i | 1.37914 | + | 0.550335i | ||||
\(623\) | −46.7855 | −1.87442 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.35909 | 0.294363 | ||||||||
\(626\) | −11.3054 | − | 4.51134i | −0.451854 | − | 0.180309i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.295178 | + | 11.3350i | 0.0117789 | + | 0.452314i | ||||
\(629\) | 6.32233 | − | 6.32233i | 0.252088 | − | 0.252088i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.7665i | 0.627655i | 0.949480 | + | 0.313827i | \(0.101611\pi\) | ||||
−0.949480 | + | 0.313827i | \(0.898389\pi\) | |||||||
\(632\) | 0.0984074 | − | 0.0453406i | 0.00391444 | − | 0.00180355i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20.2308 | − | 8.69011i | 0.803468 | − | 0.345128i | ||||
\(635\) | −1.56561 | + | 1.56561i | −0.0621292 | + | 0.0621292i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.5264 | + | 24.5264i | 0.971771 | + | 0.971771i | ||||
\(638\) | 2.19256 | − | 5.49455i | 0.0868044 | − | 0.217531i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 17.4602 | + | 5.43122i | 0.690176 | + | 0.214688i | ||||
\(641\) | −36.9165 | −1.45811 | −0.729057 | − | 0.684453i | \(-0.760041\pi\) | ||||
−0.729057 | + | 0.684453i | \(0.760041\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.1072 | + | 29.1072i | 1.14787 | + | 1.14787i | 0.986970 | + | 0.160904i | \(0.0514410\pi\) |
0.160904 | + | 0.986970i | \(0.448559\pi\) | |||||||
\(644\) | −51.2290 | − | 48.6285i | −2.01870 | − | 1.91623i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.25686 | + | 3.97627i | −0.364206 | + | 0.156444i | ||||
\(647\) | 24.5298i | 0.964364i | 0.876071 | + | 0.482182i | \(0.160156\pi\) | ||||
−0.876071 | + | 0.482182i | \(0.839844\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 58.7944i | − | 2.30788i | ||||||
\(650\) | −3.73807 | − | 8.70232i | −0.146619 | − | 0.341333i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.09325 | + | 41.9811i | 0.0428148 | + | 1.64410i | ||||
\(653\) | 12.2674 | + | 12.2674i | 0.480060 | + | 0.480060i | 0.905151 | − | 0.425091i | \(-0.139758\pi\) |
−0.425091 | + | 0.905151i | \(0.639758\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.3806 | 0.600969 | ||||||||
\(656\) | −4.07986 | + | 0.212635i | −0.159292 | + | 0.00830200i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24.0610 | + | 9.60140i | 0.937997 | + | 0.374301i | ||||
\(659\) | 28.8769 | + | 28.8769i | 1.12488 | + | 1.12488i | 0.990997 | + | 0.133886i | \(0.0427455\pi\) |
0.133886 | + | 0.990997i | \(0.457254\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.5186 | − | 29.5186i | 1.14814 | − | 1.14814i | 0.161222 | − | 0.986918i | \(-0.448456\pi\) |
0.986918 | − | 0.161222i | \(-0.0515435\pi\) | |||||||
\(662\) | 16.1624 | + | 37.6264i | 0.628168 | + | 1.46239i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −32.3135 | − | 11.9290i | −1.25401 | − | 0.462936i | ||||
\(665\) | − | 15.4674i | − | 0.599801i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.17468 | + | 4.17468i | −0.161644 | + | 0.161644i | ||||
\(668\) | −14.5666 | + | 15.3455i | −0.563597 | + | 0.593735i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.08100 | + | 12.7330i | −0.196296 | + | 0.491917i | ||||
\(671\) | 45.0307 | 1.73839 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.9500 | −1.15449 | −0.577243 | − | 0.816572i | \(-0.695872\pi\) | ||||
−0.577243 | + | 0.816572i | \(0.695872\pi\) | |||||||
\(674\) | −9.54770 | + | 23.9265i | −0.367764 | + | 0.921614i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.06866 | + | 7.44666i | −0.271872 | + | 0.286410i | ||||
\(677\) | 30.3970 | − | 30.3970i | 1.16825 | − | 1.16825i | 0.185633 | − | 0.982619i | \(-0.440566\pi\) |
0.982619 | − | 0.185633i | \(-0.0594337\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 22.8270i | − | 0.876021i | ||||||
\(680\) | −5.18627 | + | 14.0486i | −0.198884 | + | 0.538740i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 31.6453 | + | 73.6710i | 1.21176 | + | 2.82101i | ||||
\(683\) | 14.1557 | − | 14.1557i | 0.541653 | − | 0.541653i | −0.382360 | − | 0.924013i | \(-0.624889\pi\) |
0.924013 | + | 0.382360i | \(0.124889\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.4339 | − | 25.4339i | −0.971779 | − | 0.971779i | ||||
\(686\) | −31.0233 | − | 12.3796i | −1.18447 | − | 0.472656i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.04557 | − | 4.54569i | −0.192360 | − | 0.173303i | ||||
\(689\) | 4.31497 | 0.164387 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.52007 | + | 9.52007i | 0.362161 | + | 0.362161i | 0.864608 | − | 0.502447i | \(-0.167567\pi\) |
−0.502447 | + | 0.864608i | \(0.667567\pi\) | |||||||
\(692\) | −0.618411 | − | 23.7472i | −0.0235085 | − | 0.902734i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.50458 | − | 8.15876i | −0.133032 | − | 0.309702i | ||||
\(695\) | − | 17.7694i | − | 0.674034i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.34585i | − | 0.126733i | ||||||
\(698\) | 19.0187 | − | 8.16944i | 0.719867 | − | 0.309218i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 15.2429 | + | 14.4691i | 0.576127 | + | 0.546882i | ||||
\(701\) | 28.7521 | + | 28.7521i | 1.08595 | + | 1.08595i | 0.995941 | + | 0.0900099i | \(0.0286899\pi\) |
0.0900099 | + | 0.995941i | \(0.471310\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.93536 | −0.223856 | ||||||||
\(704\) | 3.54938 | + | 45.3503i | 0.133772 | + | 1.70921i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.4114 | + | 33.6089i | −0.504744 | + | 1.26489i | ||||
\(707\) | 15.8711 | + | 15.8711i | 0.596894 | + | 0.596894i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.2256 | + | 19.2256i | −0.722034 | + | 0.722034i | −0.969019 | − | 0.246985i | \(-0.920560\pi\) |
0.246985 | + | 0.969019i | \(0.420560\pi\) | |||||||
\(710\) | −18.9398 | + | 8.13555i | −0.710797 | + | 0.305322i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.5829 | − | 27.3101i | −0.471566 | − | 1.02349i | ||||
\(713\) | − | 80.0179i | − | 2.99669i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.2259 | + | 18.2259i | −0.681608 | + | 0.681608i | ||||
\(716\) | −0.217967 | − | 8.37003i | −0.00814581 | − | 0.312803i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.11904 | + | 2.44176i | 0.228360 | + | 0.0911257i | ||||
\(719\) | −15.5795 | −0.581017 | −0.290508 | − | 0.956872i | \(-0.593824\pi\) | ||||
−0.290508 | + | 0.956872i | \(0.593824\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −45.7046 | −1.70213 | ||||||||
\(722\) | −18.7449 | − | 7.48001i | −0.697611 | − | 0.278377i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.6349 | − | 0.276948i | 0.395243 | − | 0.0102927i | ||||
\(725\) | 1.24215 | − | 1.24215i | 0.0461324 | − | 0.0461324i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.2519i | 1.34451i | 0.740320 | + | 0.672255i | \(0.234674\pi\) | ||||
−0.740320 | + | 0.672255i | \(0.765326\pi\) | |||||||
\(728\) | −12.0904 | + | 32.7505i | −0.448099 | + | 1.21381i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.16242 | − | 2.21751i | 0.191070 | − | 0.0820737i | ||||
\(731\) | 3.93284 | − | 3.93284i | 0.145461 | − | 0.145461i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.83390 | + | 2.83390i | 0.104673 | + | 0.104673i | 0.757504 | − | 0.652831i | \(-0.226419\pi\) |
−0.652831 | + | 0.757504i | \(0.726419\pi\) | |||||||
\(734\) | −10.9542 | + | 27.4513i | −0.404328 | + | 1.01324i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 14.6079 | − | 42.9825i | 0.538455 | − | 1.58436i | ||||
\(737\) | −34.1049 | −1.25627 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.1067 | + | 10.1067i | 0.371782 | + | 0.371782i | 0.868126 | − | 0.496344i | \(-0.165325\pi\) |
−0.496344 | + | 0.868126i | \(0.665325\pi\) | |||||||
\(740\) | −6.07392 | + | 6.39873i | −0.223282 | + | 0.235222i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.79767 | + | 3.77902i | −0.322973 | + | 0.138732i | ||||
\(743\) | − | 29.6504i | − | 1.08777i | −0.839161 | − | 0.543884i | \(-0.816953\pi\) | ||
0.839161 | − | 0.543884i | \(-0.183047\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 8.78196i | − | 0.321746i | ||||||
\(746\) | −17.5340 | − | 40.8196i | −0.641965 | − | 1.49451i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −37.2418 | + | 0.969829i | −1.36170 | + | 0.0354605i | ||||
\(749\) | 17.5547 | + | 17.5547i | 0.641436 | + | 0.641436i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.55537 | 0.129737 | 0.0648687 | − | 0.997894i | \(-0.479337\pi\) | ||||
0.0648687 | + | 0.997894i | \(0.479337\pi\) | |||||||
\(752\) | 0.866591 | + | 16.6274i | 0.0316013 | + | 0.606341i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.71020 | + | 1.08149i | 0.0986997 | + | 0.0393854i | ||||
\(755\) | −4.52758 | − | 4.52758i | −0.164776 | − | 0.164776i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.4898 | − | 22.4898i | 0.817407 | − | 0.817407i | −0.168325 | − | 0.985732i | \(-0.553836\pi\) |
0.985732 | + | 0.168325i | \(0.0538358\pi\) | |||||||
\(758\) | 10.4453 | + | 24.3169i | 0.379390 | + | 0.883229i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.02880 | − | 4.15996i | 0.327509 | − | 0.150898i | ||||
\(761\) | − | 25.4350i | − | 0.922017i | −0.887396 | − | 0.461009i | \(-0.847488\pi\) | ||
0.887396 | − | 0.461009i | \(-0.152512\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.18255 | − | 6.18255i | 0.223823 | − | 0.223823i | ||||
\(764\) | −27.7547 | − | 26.3459i | −1.00413 | − | 0.953161i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.17325 | + | 17.9761i | −0.259180 | + | 0.649504i | ||||
\(767\) | 29.0005 | 1.04715 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 47.4685 | 1.71176 | 0.855879 | − | 0.517176i | \(-0.173017\pi\) | ||||
0.855879 | + | 0.517176i | \(0.173017\pi\) | |||||||
\(770\) | 21.1981 | − | 53.1223i | 0.763926 | − | 1.91439i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −27.2732 | − | 25.8888i | −0.981584 | − | 0.931758i | ||||
\(773\) | −2.12004 | + | 2.12004i | −0.0762527 | + | 0.0762527i | −0.744205 | − | 0.667952i | \(-0.767171\pi\) |
0.667952 | + | 0.744205i | \(0.267171\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.8089i | 0.855240i | ||||||||
\(776\) | 13.3248 | − | 6.13933i | 0.478333 | − | 0.220389i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.04965 | − | 4.77164i | −0.0734836 | − | 0.171072i | ||||
\(779\) | −1.57053 | + | 1.57053i | −0.0562701 | + | 0.0562701i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.2603 | − | 36.2603i | −1.29749 | − | 1.29749i | ||||
\(782\) | 34.5313 | + | 13.7795i | 1.23484 | + | 0.492753i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.57468 | − | 49.4008i | −0.0919527 | − | 1.76431i | ||||
\(785\) | 9.16300 | 0.327042 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.616222 | + | 0.616222i | 0.0219659 | + | 0.0219659i | 0.718004 | − | 0.696039i | \(-0.245056\pi\) |
−0.696039 | + | 0.718004i | \(0.745056\pi\) | |||||||
\(788\) | −9.40150 | + | 0.244828i | −0.334915 | + | 0.00872164i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.0345576 | − | 0.0804509i | −0.00122950 | − | 0.00286232i | ||||
\(791\) | 56.4443i | 2.00693i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.2115i | 0.788753i | ||||||||
\(794\) | −32.4678 | + | 13.9465i | −1.15224 | + | 0.494943i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.80471 | − | 7.16859i | 0.241186 | − | 0.254084i | ||||
\(797\) | 7.38372 | + | 7.38372i | 0.261545 | + | 0.261545i | 0.825681 | − | 0.564137i | \(-0.190791\pi\) |
−0.564137 | + | 0.825681i | \(0.690791\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.6360 | −0.482406 | ||||||||
\(800\) | −4.34650 | + | 12.7892i | −0.153672 | + | 0.452167i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.76456 | − | 6.92796i | 0.0976198 | − | 0.244635i | ||||
\(803\) | 9.88346 | + | 9.88346i | 0.348780 | + | 0.348780i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −40.3616 | + | 40.3616i | −1.42256 | + | 1.42256i | ||||
\(806\) | −36.3384 | + | 15.6091i | −1.27997 | + | 0.549807i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.99590 | + | 13.5330i | −0.175755 | + | 0.476088i | ||||
\(809\) | − | 41.6071i | − | 1.46283i | −0.681934 | − | 0.731413i | \(-0.738861\pi\) | ||
0.681934 | − | 0.731413i | \(-0.261139\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.26526 | − | 4.26526i | 0.149773 | − | 0.149773i | −0.628243 | − | 0.778017i | \(-0.716226\pi\) |
0.778017 | + | 0.628243i | \(0.216226\pi\) | |||||||
\(812\) | −6.47291 | + | 0.168564i | −0.227155 | + | 0.00591543i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20.3848 | − | 8.13442i | −0.714487 | − | 0.285111i | ||||
\(815\) | 33.9368 | 1.18875 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.69212 | −0.129171 | ||||||||
\(818\) | 34.9374 | + | 13.9415i | 1.22156 | + | 0.487455i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0859453 | + | 3.30033i | 0.00300134 | + | 0.115253i | ||||
\(821\) | 5.03247 | − | 5.03247i | 0.175634 | − | 0.175634i | −0.613815 | − | 0.789450i | \(-0.710366\pi\) |
0.789450 | + | 0.613815i | \(0.210366\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 15.8921i | − | 0.553964i | −0.960875 | − | 0.276982i | \(-0.910666\pi\) | ||
0.960875 | − | 0.276982i | \(-0.0893343\pi\) | |||||||
\(824\) | −12.2923 | − | 26.6792i | −0.428221 | − | 0.929413i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −59.1283 | + | 25.3985i | −2.05734 | + | 0.883725i | ||||
\(827\) | 4.30482 | − | 4.30482i | 0.149693 | − | 0.149693i | −0.628288 | − | 0.777981i | \(-0.716244\pi\) |
0.777981 | + | 0.628288i | \(0.216244\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.3218 | − | 20.3218i | −0.705804 | − | 0.705804i | 0.259846 | − | 0.965650i | \(-0.416328\pi\) |
−0.965650 | + | 0.259846i | \(0.916328\pi\) | |||||||
\(830\) | −10.3165 | + | 25.8531i | −0.358091 | + | 0.897373i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −22.3692 | + | 1.75074i | −0.775511 | + | 0.0606960i | ||||
\(833\) | 40.5130 | 1.40369 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.0902 | + | 12.0902i | 0.418399 | + | 0.418399i | ||||
\(836\) | 17.9364 | + | 17.0260i | 0.620344 | + | 0.588855i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 36.4837 | − | 15.6715i | 1.26031 | − | 0.541364i | ||||
\(839\) | − | 18.4813i | − | 0.638046i | −0.947747 | − | 0.319023i | \(-0.896645\pi\) | ||
0.947747 | − | 0.319023i | \(-0.103355\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 28.4588i | − | 0.981337i | ||||||
\(842\) | −4.58743 | − | 10.6797i | −0.158093 | − | 0.368045i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.22741 | − | 47.1332i | −0.0422494 | − | 1.62239i | ||||
\(845\) | 5.86697 | + | 5.86697i | 0.201830 | + | 0.201830i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 93.8779 | 3.22568 | ||||||||
\(848\) | −4.57206 | − | 4.11910i | −0.157005 | − | 0.141450i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10.2746 | − | 4.10001i | −0.352416 | − | 0.140629i | ||||
\(851\) | 15.4881 | + | 15.4881i | 0.530925 | + | 0.530925i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.16310 | − | 8.16310i | 0.279499 | − | 0.279499i | −0.553410 | − | 0.832909i | \(-0.686674\pi\) |
0.832909 | + | 0.553410i | \(0.186674\pi\) | |||||||
\(854\) | −19.4527 | − | 45.2864i | −0.665658 | − | 1.54967i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.52588 | + | 14.9686i | −0.188871 | + | 0.511615i | ||||
\(857\) | 33.5755i | 1.14692i | 0.819234 | + | 0.573459i | \(0.194399\pi\) | ||||
−0.819234 | + | 0.573459i | \(0.805601\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.3288 | − | 20.3288i | 0.693609 | − | 0.693609i | −0.269415 | − | 0.963024i | \(-0.586830\pi\) |
0.963024 | + | 0.269415i | \(0.0868305\pi\) | |||||||
\(860\) | −3.77832 | + | 3.98036i | −0.128839 | + | 0.135729i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.7052 | + | 34.3452i | −0.466802 | + | 1.16980i | ||||
\(863\) | −14.3176 | −0.487375 | −0.243688 | − | 0.969854i | \(-0.578357\pi\) | ||||
−0.243688 | + | 0.969854i | \(0.578357\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.1969 | −0.652713 | ||||||||
\(866\) | 20.5863 | − | 51.5893i | 0.699553 | − | 1.75307i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 60.4190 | − | 63.6499i | 2.05076 | − | 2.16042i | ||||
\(869\) | 0.154023 | − | 0.154023i | 0.00522489 | − | 0.00522489i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 16.8223i | − | 0.570002i | ||||||
\(872\) | 5.27174 | + | 1.94614i | 0.178524 | + | 0.0659048i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.74084 | − | 22.6769i | −0.329489 | − | 0.767058i | ||||
\(875\) | 37.1564 | − | 37.1564i | 1.25611 | − | 1.25611i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.60409 | − | 3.60409i | −0.121702 | − | 0.121702i | 0.643633 | − | 0.765334i | \(-0.277426\pi\) |
−0.765334 | + | 0.643633i | \(0.777426\pi\) | |||||||
\(878\) | 5.58546 | + | 2.22884i | 0.188500 | + | 0.0752197i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 36.7103 | − | 1.91327i | 1.23750 | − | 0.0644964i | ||||
\(881\) | −6.93242 | −0.233559 | −0.116780 | − | 0.993158i | \(-0.537257\pi\) | ||||
−0.116780 | + | 0.993158i | \(0.537257\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.50145 | + | 9.50145i | 0.319749 | + | 0.319749i | 0.848671 | − | 0.528922i | \(-0.177403\pi\) |
−0.528922 | + | 0.848671i | \(0.677403\pi\) | |||||||
\(884\) | −0.478371 | − | 18.3696i | −0.0160893 | − | 0.617837i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.2868 | − | 26.2761i | −0.379189 | − | 0.882762i | ||||
\(887\) | 16.8549i | 0.565933i | 0.959130 | + | 0.282967i | \(0.0913186\pi\) | ||||
−0.959130 | + | 0.282967i | \(0.908681\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.02875i | 0.202198i | ||||||||
\(890\) | −22.3268 | + | 9.59043i | −0.748395 | + | 0.321472i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.2413 | − | 11.6200i | −0.409870 | − | 0.389065i | ||||
\(893\) | 6.40068 | + | 6.40068i | 0.214191 | + | 0.214191i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.76619 | −0.226169 | ||||||||
\(896\) | 44.0746 | − | 23.1603i | 1.47243 | − | 0.773732i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.8717 | − | 27.2444i | 0.362793 | − | 0.909156i | ||||
\(899\) | −5.18688 | − | 5.18688i | −0.172992 | − | 0.172992i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.56376 | − | 3.56376i | 0.118726 | − | 0.118726i | ||||
\(902\) | −7.54635 | + | 3.24152i | −0.251266 | + | 0.107931i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −32.9482 | + | 15.1807i | −1.09584 | + | 0.504902i | ||||
\(905\) | − | 8.59709i | − | 0.285777i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.0494 | − | 28.0494i | 0.931367 | − | 0.931367i | −0.0664249 | − | 0.997791i | \(-0.521159\pi\) |
0.997791 | + | 0.0664249i | \(0.0211593\pi\) | |||||||
\(908\) | −1.01436 | − | 38.9517i | −0.0336626 | − | 1.29266i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 26.2027 | + | 10.4560i | 0.868611 | + | 0.346613i | ||||
\(911\) | 26.0100 | 0.861748 | 0.430874 | − | 0.902412i | \(-0.358205\pi\) | ||||
0.430874 | + | 0.902412i | \(0.358205\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −69.2467 | −2.29173 | ||||||||
\(914\) | −5.03555 | − | 2.00940i | −0.166561 | − | 0.0664651i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 23.3041 | − | 0.606870i | 0.769988 | − | 0.0200516i | ||||
\(917\) | 29.6134 | − | 29.6134i | 0.977919 | − | 0.977919i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.5283i | 1.46885i | 0.678688 | + | 0.734426i | \(0.262549\pi\) | ||||
−0.678688 | + | 0.734426i | \(0.737451\pi\) | |||||||
\(920\) | −34.4155 | − | 12.7050i | −1.13465 | − | 0.418872i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −21.7857 | + | 9.35801i | −0.717474 | + | 0.308190i | ||||
\(923\) | 17.8855 | − | 17.8855i | 0.588707 | − | 0.588707i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.60839 | − | 4.60839i | −0.151523 | − | 0.151523i | ||||
\(926\) | 3.62453 | − | 9.08305i | 0.119109 | − | 0.298487i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.83929 | − | 3.73310i | −0.0603775 | − | 0.122545i | ||||
\(929\) | −5.00362 | −0.164163 | −0.0820817 | − | 0.996626i | \(-0.526157\pi\) | ||||
−0.0820817 | + | 0.996626i | \(0.526157\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.0167 | − | 19.0167i | −0.623246 | − | 0.623246i | ||||
\(932\) | −7.58552 | + | 7.99116i | −0.248472 | + | 0.261759i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −34.4024 | + | 14.7775i | −1.12568 | + | 0.483535i | ||||
\(935\) | 30.1057i | 0.984562i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 0.197040i | − | 0.00643700i | −0.999995 | − | 0.00321850i | \(-0.998976\pi\) | ||
0.999995 | − | 0.00321850i | \(-0.00102448\pi\) | |||||||
\(938\) | 14.7329 | + | 34.2986i | 0.481046 | + | 1.11989i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 13.4505 | − | 0.350269i | 0.438706 | − | 0.0114245i | ||||
\(941\) | 21.0406 | + | 21.0406i | 0.685902 | + | 0.685902i | 0.961324 | − | 0.275421i | \(-0.0888173\pi\) |
−0.275421 | + | 0.961324i | \(0.588817\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.19647 | 0.266914 | ||||||||
\(944\) | −30.7284 | − | 27.6840i | −1.00012 | − | 0.901039i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.6805 | − | 5.06005i | −0.412277 | − | 0.164517i | ||||
\(947\) | 1.19798 | + | 1.19798i | 0.0389291 | + | 0.0389291i | 0.726303 | − | 0.687374i | \(-0.241237\pi\) |
−0.687374 | + | 0.726303i | \(0.741237\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.87504 | + | 4.87504i | −0.158251 | + | 0.158251i | ||||
\(950\) | 2.89833 | + | 6.74739i | 0.0940343 | + | 0.218914i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 17.0634 | + | 37.0344i | 0.553026 | + | 1.20029i | ||||
\(953\) | 22.4857i | 0.728383i | 0.931324 | + | 0.364191i | \(0.118655\pi\) | ||||
−0.931324 | + | 0.364191i | \(0.881345\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.8670 | + | 21.8670i | −0.707601 | + | 0.707601i | ||||
\(956\) | −32.8862 | − | 31.2169i | −1.06362 | − | 1.00963i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.47145 | + | 23.7354i | −0.306009 | + | 0.766856i | ||||
\(959\) | −97.9395 | −3.16263 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 68.4190 | 2.20706 | ||||||||
\(962\) | 4.01232 | − | 10.0549i | 0.129362 | − | 0.324181i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.0773909 | − | 0.0734625i | −0.00249259 | − | 0.00236607i | ||||
\(965\) | −21.4877 | + | 21.4877i | −0.691712 | + | 0.691712i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 53.3321i | − | 1.71504i | −0.514447 | − | 0.857522i | \(-0.672003\pi\) | ||
0.514447 | − | 0.857522i | \(-0.327997\pi\) | |||||||
\(968\) | 25.2484 | + | 54.7993i | 0.811516 | + | 1.76132i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.67926 | − | 10.8934i | −0.150242 | − | 0.349767i | ||||
\(971\) | 21.5658 | − | 21.5658i | 0.692079 | − | 0.692079i | −0.270610 | − | 0.962689i | \(-0.587225\pi\) |
0.962689 | + | 0.270610i | \(0.0872254\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −34.2128 | − | 34.2128i | −1.09681 | − | 1.09681i | ||||
\(974\) | −26.5680 | − | 10.6018i | −0.851293 | − | 0.339703i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 21.2032 | − | 23.5349i | 0.678699 | − | 0.753334i | ||||
\(977\) | −5.49655 | −0.175850 | −0.0879251 | − | 0.996127i | \(-0.528024\pi\) | ||||
−0.0879251 | + | 0.996127i | \(0.528024\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −42.7447 | − | 42.7447i | −1.36613 | − | 1.36613i | ||||
\(980\) | −39.9619 | + | 1.04066i | −1.27654 | + | 0.0332428i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.3599 | − | 24.1181i | −0.330597 | − | 0.769639i | ||||
\(983\) | − | 25.3192i | − | 0.807556i | −0.914857 | − | 0.403778i | \(-0.867697\pi\) | ||
0.914857 | − | 0.403778i | \(-0.132303\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.60002i | 0.242157i | ||||||||
\(986\) | 3.13158 | − | 1.34516i | 0.0997298 | − | 0.0428388i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.39810 | + | 8.84719i | −0.267179 | + | 0.281466i | ||||
\(989\) | 9.63444 | + | 9.63444i | 0.306357 | + | 0.306357i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.4022 | −0.362203 | −0.181102 | − | 0.983464i | \(-0.557966\pi\) | ||||
−0.181102 | + | 0.983464i | \(0.557966\pi\) | |||||||
\(992\) | 53.4041 | + | 18.1497i | 1.69558 | + | 0.576255i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −20.8022 | + | 52.1302i | −0.659805 | + | 1.65347i | ||||
\(995\) | −5.64790 | − | 5.64790i | −0.179050 | − | 0.179050i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.2501 | + | 34.2501i | −1.08471 | + | 1.08471i | −0.0886501 | + | 0.996063i | \(0.528255\pi\) |
−0.996063 | + | 0.0886501i | \(0.971745\pi\) | |||||||
\(998\) | −46.7302 | + | 20.0729i | −1.47922 | + | 0.635397i | ||||
\(999\) | 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 | 432.2.k.d.109.11 | yes | 32 | |
3.2 | odd | 2 | inner | 432.2.k.d.109.6 | ✓ | 32 | |
4.3 | odd | 2 | 1728.2.k.d.1297.6 | 32 | |||
12.11 | even | 2 | 1728.2.k.d.1297.11 | 32 | |||
16.5 | even | 4 | inner | 432.2.k.d.325.11 | yes | 32 | |
16.11 | odd | 4 | 1728.2.k.d.433.6 | 32 | |||
48.5 | odd | 4 | inner | 432.2.k.d.325.6 | yes | 32 | |
48.11 | even | 4 | 1728.2.k.d.433.11 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.k.d.109.6 | ✓ | 32 | 3.2 | odd | 2 | inner | |
432.2.k.d.109.11 | yes | 32 | 1.1 | even | 1 | trivial | |
432.2.k.d.325.6 | yes | 32 | 48.5 | odd | 4 | inner | |
432.2.k.d.325.11 | yes | 32 | 16.5 | even | 4 | inner | |
1728.2.k.d.433.6 | 32 | 16.11 | odd | 4 | |||
1728.2.k.d.433.11 | 32 | 48.11 | even | 4 | |||
1728.2.k.d.1297.6 | 32 | 4.3 | odd | 2 | |||
1728.2.k.d.1297.11 | 32 | 12.11 | even | 2 |