Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(91,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.p (of order \(2\), degree \(1\), 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: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.4 | ||
Character | \(\chi\) | \(=\) | 1380.91 |
Dual form | 1380.2.p.a.91.3 |
$q$-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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.39049 | + | 0.257970i | −0.983222 | + | 0.182412i | ||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.86690 | − | 0.717408i | 0.933451 | − | 0.358704i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | −0.257970 | − | 1.39049i | −0.105316 | − | 0.567664i | ||||
\(7\) | 2.59830 | 0.982067 | 0.491033 | − | 0.871141i | \(-0.336619\pi\) | ||||
0.491033 | + | 0.871141i | \(0.336619\pi\) | |||||||
\(8\) | −2.41083 | + | 1.47915i | −0.852358 | + | 0.522959i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −0.257970 | − | 1.39049i | −0.0815773 | − | 0.439710i | ||||
\(11\) | −1.75416 | −0.528898 | −0.264449 | − | 0.964400i | \(-0.585190\pi\) | ||||
−0.264449 | + | 0.964400i | \(0.585190\pi\) | |||||||
\(12\) | 0.717408 | + | 1.86690i | 0.207098 | + | 0.538928i | ||||
\(13\) | −2.03614 | −0.564722 | −0.282361 | − | 0.959308i | \(-0.591118\pi\) | ||||
−0.282361 | + | 0.959308i | \(0.591118\pi\) | |||||||
\(14\) | −3.61291 | + | 0.670285i | −0.965590 | + | 0.179141i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 2.97065 | − | 2.67866i | 0.742663 | − | 0.669665i | ||||
\(17\) | − | 3.95759i | − | 0.959856i | −0.877308 | − | 0.479928i | \(-0.840663\pi\) | ||
0.877308 | − | 0.479928i | \(-0.159337\pi\) | |||||||
\(18\) | 1.39049 | − | 0.257970i | 0.327741 | − | 0.0608042i | ||||
\(19\) | −5.10890 | −1.17206 | −0.586031 | − | 0.810289i | \(-0.699310\pi\) | ||||
−0.586031 | + | 0.810289i | \(0.699310\pi\) | |||||||
\(20\) | 0.717408 | + | 1.86690i | 0.160417 | + | 0.417452i | ||||
\(21\) | 2.59830i | 0.566997i | ||||||||
\(22\) | 2.43913 | − | 0.452520i | 0.520024 | − | 0.0964776i | ||||
\(23\) | −4.47835 | + | 1.71592i | −0.933800 | + | 0.357795i | ||||
\(24\) | −1.47915 | − | 2.41083i | −0.301930 | − | 0.492109i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 2.83122 | − | 0.525262i | 0.555247 | − | 0.103012i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 4.85078 | − | 1.86404i | 0.916712 | − | 0.352271i | ||||
\(29\) | −7.32394 | −1.36002 | −0.680011 | − | 0.733202i | \(-0.738025\pi\) | ||||
−0.680011 | + | 0.733202i | \(0.738025\pi\) | |||||||
\(30\) | 1.39049 | − | 0.257970i | 0.253867 | − | 0.0470987i | ||||
\(31\) | − | 4.91715i | − | 0.883147i | −0.897225 | − | 0.441573i | \(-0.854420\pi\) | ||
0.897225 | − | 0.441573i | \(-0.145580\pi\) | |||||||
\(32\) | −3.43964 | + | 4.49098i | −0.608047 | + | 0.793901i | ||||
\(33\) | − | 1.75416i | − | 0.305360i | ||||||
\(34\) | 1.02094 | + | 5.50297i | 0.175090 | + | 0.943752i | ||||
\(35\) | 2.59830i | 0.439194i | ||||||||
\(36\) | −1.86690 | + | 0.717408i | −0.311150 | + | 0.119568i | ||||
\(37\) | 0.890633i | 0.146419i | 0.997317 | + | 0.0732096i | \(0.0233242\pi\) | ||||
−0.997317 | + | 0.0732096i | \(0.976676\pi\) | |||||||
\(38\) | 7.10385 | − | 1.31794i | 1.15240 | − | 0.213799i | ||||
\(39\) | − | 2.03614i | − | 0.326043i | ||||||
\(40\) | −1.47915 | − | 2.41083i | −0.233874 | − | 0.381186i | ||||
\(41\) | −10.1575 | −1.58634 | −0.793168 | − | 0.609003i | \(-0.791570\pi\) | ||||
−0.793168 | + | 0.609003i | \(0.791570\pi\) | |||||||
\(42\) | −0.670285 | − | 3.61291i | −0.103427 | − | 0.557484i | ||||
\(43\) | 5.82796 | 0.888755 | 0.444377 | − | 0.895840i | \(-0.353425\pi\) | ||||
0.444377 | + | 0.895840i | \(0.353425\pi\) | |||||||
\(44\) | −3.27484 | + | 1.25845i | −0.493701 | + | 0.189718i | ||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 5.78443 | − | 3.54125i | 0.852867 | − | 0.522128i | ||||
\(47\) | 2.70292i | 0.394262i | 0.980377 | + | 0.197131i | \(0.0631624\pi\) | ||||
−0.980377 | + | 0.197131i | \(0.936838\pi\) | |||||||
\(48\) | 2.67866 | + | 2.97065i | 0.386631 | + | 0.428777i | ||||
\(49\) | −0.248811 | −0.0355445 | ||||||||
\(50\) | 1.39049 | − | 0.257970i | 0.196644 | − | 0.0364825i | ||||
\(51\) | 3.95759 | 0.554173 | ||||||||
\(52\) | −3.80127 | + | 1.46074i | −0.527141 | + | 0.202568i | ||||
\(53\) | − | 2.16224i | − | 0.297007i | −0.988912 | − | 0.148504i | \(-0.952554\pi\) | ||
0.988912 | − | 0.148504i | \(-0.0474456\pi\) | |||||||
\(54\) | 0.257970 | + | 1.39049i | 0.0351053 | + | 0.189221i | ||||
\(55\) | − | 1.75416i | − | 0.236531i | ||||||
\(56\) | −6.26408 | + | 3.84328i | −0.837073 | + | 0.513581i | ||||
\(57\) | − | 5.10890i | − | 0.676690i | ||||||
\(58\) | 10.1838 | − | 1.88936i | 1.33720 | − | 0.248085i | ||||
\(59\) | 10.3196i | 1.34349i | 0.740780 | + | 0.671747i | \(0.234456\pi\) | ||||
−0.740780 | + | 0.671747i | \(0.765544\pi\) | |||||||
\(60\) | −1.86690 | + | 0.717408i | −0.241016 | + | 0.0926170i | ||||
\(61\) | 7.39410i | 0.946717i | 0.880870 | + | 0.473359i | \(0.156959\pi\) | ||||
−0.880870 | + | 0.473359i | \(0.843041\pi\) | |||||||
\(62\) | 1.26848 | + | 6.83723i | 0.161097 | + | 0.868330i | ||||
\(63\) | −2.59830 | −0.327356 | ||||||||
\(64\) | 3.62423 | − | 7.13197i | 0.453028 | − | 0.891496i | ||||
\(65\) | − | 2.03614i | − | 0.252552i | ||||||
\(66\) | 0.452520 | + | 2.43913i | 0.0557014 | + | 0.300236i | ||||
\(67\) | 8.20400 | 1.00228 | 0.501139 | − | 0.865367i | \(-0.332914\pi\) | ||||
0.501139 | + | 0.865367i | \(0.332914\pi\) | |||||||
\(68\) | −2.83920 | − | 7.38843i | −0.344304 | − | 0.895979i | ||||
\(69\) | −1.71592 | − | 4.47835i | −0.206573 | − | 0.539130i | ||||
\(70\) | −0.670285 | − | 3.61291i | −0.0801144 | − | 0.431825i | ||||
\(71\) | 7.48672i | 0.888511i | 0.895900 | + | 0.444255i | \(0.146532\pi\) | ||||
−0.895900 | + | 0.444255i | \(0.853468\pi\) | |||||||
\(72\) | 2.41083 | − | 1.47915i | 0.284119 | − | 0.174320i | ||||
\(73\) | −13.8075 | −1.61605 | −0.808024 | − | 0.589150i | \(-0.799463\pi\) | ||||
−0.808024 | + | 0.589150i | \(0.799463\pi\) | |||||||
\(74\) | −0.229757 | − | 1.23841i | −0.0267087 | − | 0.143963i | ||||
\(75\) | − | 1.00000i | − | 0.115470i | ||||||
\(76\) | −9.53782 | + | 3.66516i | −1.09406 | + | 0.420423i | ||||
\(77\) | −4.55784 | −0.519414 | ||||||||
\(78\) | 0.525262 | + | 2.83122i | 0.0594742 | + | 0.320572i | ||||
\(79\) | −6.39670 | −0.719685 | −0.359843 | − | 0.933013i | \(-0.617170\pi\) | ||||
−0.359843 | + | 0.933013i | \(0.617170\pi\) | |||||||
\(80\) | 2.67866 | + | 2.97065i | 0.299483 | + | 0.332129i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 14.1239 | − | 2.62033i | 1.55972 | − | 0.289367i | ||||
\(83\) | 9.80321 | 1.07604 | 0.538021 | − | 0.842931i | \(-0.319172\pi\) | ||||
0.538021 | + | 0.842931i | \(0.319172\pi\) | |||||||
\(84\) | 1.86404 | + | 4.85078i | 0.203384 | + | 0.529264i | ||||
\(85\) | 3.95759 | 0.429261 | ||||||||
\(86\) | −8.10369 | + | 1.50344i | −0.873844 | + | 0.162120i | ||||
\(87\) | − | 7.32394i | − | 0.785209i | ||||||
\(88\) | 4.22898 | − | 2.59466i | 0.450811 | − | 0.276592i | ||||
\(89\) | − | 15.8514i | − | 1.68025i | −0.542393 | − | 0.840125i | \(-0.682482\pi\) | ||
0.542393 | − | 0.840125i | \(-0.317518\pi\) | |||||||
\(90\) | 0.257970 | + | 1.39049i | 0.0271924 | + | 0.146570i | ||||
\(91\) | −5.29050 | −0.554595 | ||||||||
\(92\) | −7.12963 | + | 6.41626i | −0.743315 | + | 0.668942i | ||||
\(93\) | 4.91715 | 0.509885 | ||||||||
\(94\) | −0.697273 | − | 3.75837i | −0.0719182 | − | 0.387647i | ||||
\(95\) | − | 5.10890i | − | 0.524162i | ||||||
\(96\) | −4.49098 | − | 3.43964i | −0.458359 | − | 0.351056i | ||||
\(97\) | 0.186909i | 0.0189777i | 0.999955 | + | 0.00948885i | \(0.00302044\pi\) | ||||
−0.999955 | + | 0.00948885i | \(0.996980\pi\) | |||||||
\(98\) | 0.345968 | − | 0.0641859i | 0.0349481 | − | 0.00648375i | ||||
\(99\) | 1.75416 | 0.176299 | ||||||||
\(100\) | −1.86690 | + | 0.717408i | −0.186690 | + | 0.0717408i | ||||
\(101\) | −9.35168 | −0.930527 | −0.465264 | − | 0.885172i | \(-0.654040\pi\) | ||||
−0.465264 | + | 0.885172i | \(0.654040\pi\) | |||||||
\(102\) | −5.50297 | + | 1.02094i | −0.544875 | + | 0.101088i | ||||
\(103\) | −1.95123 | −0.192260 | −0.0961302 | − | 0.995369i | \(-0.530647\pi\) | ||||
−0.0961302 | + | 0.995369i | \(0.530647\pi\) | |||||||
\(104\) | 4.90878 | − | 3.01175i | 0.481346 | − | 0.295327i | ||||
\(105\) | −2.59830 | −0.253569 | ||||||||
\(106\) | 0.557794 | + | 3.00657i | 0.0541778 | + | 0.292024i | ||||
\(107\) | 7.60436 | 0.735141 | 0.367570 | − | 0.929996i | \(-0.380190\pi\) | ||||
0.367570 | + | 0.929996i | \(0.380190\pi\) | |||||||
\(108\) | −0.717408 | − | 1.86690i | −0.0690326 | − | 0.179643i | ||||
\(109\) | − | 6.19075i | − | 0.592966i | −0.955038 | − | 0.296483i | \(-0.904186\pi\) | ||
0.955038 | − | 0.296483i | \(-0.0958138\pi\) | |||||||
\(110\) | 0.452520 | + | 2.43913i | 0.0431461 | + | 0.232562i | ||||
\(111\) | −0.890633 | −0.0845352 | ||||||||
\(112\) | 7.71866 | − | 6.95998i | 0.729345 | − | 0.657656i | ||||
\(113\) | 8.58491i | 0.807600i | 0.914847 | + | 0.403800i | \(0.132311\pi\) | ||||
−0.914847 | + | 0.403800i | \(0.867689\pi\) | |||||||
\(114\) | 1.31794 | + | 7.10385i | 0.123437 | + | 0.665337i | ||||
\(115\) | −1.71592 | − | 4.47835i | −0.160011 | − | 0.417608i | ||||
\(116\) | −13.6731 | + | 5.25425i | −1.26951 | + | 0.487845i | ||||
\(117\) | 2.03614 | 0.188241 | ||||||||
\(118\) | −2.66214 | − | 14.3492i | −0.245070 | − | 1.32095i | ||||
\(119\) | − | 10.2830i | − | 0.942643i | ||||||
\(120\) | 2.41083 | − | 1.47915i | 0.220078 | − | 0.135027i | ||||
\(121\) | −7.92293 | −0.720267 | ||||||||
\(122\) | −1.90746 | − | 10.2814i | −0.172693 | − | 0.930833i | ||||
\(123\) | − | 10.1575i | − | 0.915871i | ||||||
\(124\) | −3.52760 | − | 9.17985i | −0.316788 | − | 0.824375i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 3.61291 | − | 0.670285i | 0.321863 | − | 0.0597137i | ||||
\(127\) | 3.84618i | 0.341294i | 0.985332 | + | 0.170647i | \(0.0545857\pi\) | ||||
−0.985332 | + | 0.170647i | \(0.945414\pi\) | |||||||
\(128\) | −3.19960 | + | 10.8518i | −0.282807 | + | 0.959177i | ||||
\(129\) | 5.82796i | 0.513123i | ||||||||
\(130\) | 0.525262 | + | 2.83122i | 0.0460685 | + | 0.248314i | ||||
\(131\) | − | 8.85272i | − | 0.773466i | −0.922192 | − | 0.386733i | \(-0.873604\pi\) | ||
0.922192 | − | 0.386733i | \(-0.126396\pi\) | |||||||
\(132\) | −1.25845 | − | 3.27484i | −0.109534 | − | 0.285038i | ||||
\(133\) | −13.2745 | −1.15104 | ||||||||
\(134\) | −11.4076 | + | 2.11639i | −0.985462 | + | 0.182828i | ||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 5.85387 | + | 9.54108i | 0.501965 | + | 0.818141i | ||||
\(137\) | − | 17.8085i | − | 1.52148i | −0.649054 | − | 0.760742i | \(-0.724835\pi\) | ||
0.649054 | − | 0.760742i | \(-0.275165\pi\) | |||||||
\(138\) | 3.54125 | + | 5.78443i | 0.301451 | + | 0.492403i | ||||
\(139\) | 1.26954i | 0.107681i | 0.998550 | + | 0.0538403i | \(0.0171462\pi\) | ||||
−0.998550 | + | 0.0538403i | \(0.982854\pi\) | |||||||
\(140\) | 1.86404 | + | 4.85078i | 0.157540 | + | 0.409966i | ||||
\(141\) | −2.70292 | −0.227627 | ||||||||
\(142\) | −1.93135 | − | 10.4102i | −0.162075 | − | 0.873603i | ||||
\(143\) | 3.57170 | 0.298681 | ||||||||
\(144\) | −2.97065 | + | 2.67866i | −0.247554 | + | 0.223222i | ||||
\(145\) | − | 7.32394i | − | 0.608220i | ||||||
\(146\) | 19.1992 | − | 3.56193i | 1.58893 | − | 0.294787i | ||||
\(147\) | − | 0.248811i | − | 0.0205216i | ||||||
\(148\) | 0.638947 | + | 1.66273i | 0.0525211 | + | 0.136675i | ||||
\(149\) | 10.5890i | 0.867486i | 0.901037 | + | 0.433743i | \(0.142807\pi\) | ||||
−0.901037 | + | 0.433743i | \(0.857193\pi\) | |||||||
\(150\) | 0.257970 | + | 1.39049i | 0.0210632 | + | 0.113533i | ||||
\(151\) | − | 9.56575i | − | 0.778450i | −0.921143 | − | 0.389225i | \(-0.872743\pi\) | ||
0.921143 | − | 0.389225i | \(-0.127257\pi\) | |||||||
\(152\) | 12.3167 | − | 7.55683i | 0.999016 | − | 0.612940i | ||||
\(153\) | 3.95759i | 0.319952i | ||||||||
\(154\) | 6.33761 | − | 1.17579i | 0.510699 | − | 0.0947475i | ||||
\(155\) | 4.91715 | 0.394955 | ||||||||
\(156\) | −1.46074 | − | 3.80127i | −0.116953 | − | 0.304345i | ||||
\(157\) | − | 14.8452i | − | 1.18477i | −0.805653 | − | 0.592387i | \(-0.798186\pi\) | ||
0.805653 | − | 0.592387i | \(-0.201814\pi\) | |||||||
\(158\) | 8.89453 | − | 1.65016i | 0.707610 | − | 0.131280i | ||||
\(159\) | 2.16224 | 0.171477 | ||||||||
\(160\) | −4.49098 | − | 3.43964i | −0.355043 | − | 0.271927i | ||||
\(161\) | −11.6361 | + | 4.45849i | −0.917054 | + | 0.351378i | ||||
\(162\) | −1.39049 | + | 0.257970i | −0.109247 | + | 0.0202681i | ||||
\(163\) | − | 9.70954i | − | 0.760510i | −0.924882 | − | 0.380255i | \(-0.875836\pi\) | ||
0.924882 | − | 0.380255i | \(-0.124164\pi\) | |||||||
\(164\) | −18.9631 | + | 7.28707i | −1.48077 | + | 0.569025i | ||||
\(165\) | 1.75416 | 0.136561 | ||||||||
\(166\) | −13.6312 | + | 2.52894i | −1.05799 | + | 0.196283i | ||||
\(167\) | − | 17.5706i | − | 1.35966i | −0.733371 | − | 0.679829i | \(-0.762054\pi\) | ||
0.733371 | − | 0.679829i | \(-0.237946\pi\) | |||||||
\(168\) | −3.84328 | − | 6.26408i | −0.296516 | − | 0.483284i | ||||
\(169\) | −8.85415 | −0.681089 | ||||||||
\(170\) | −5.50297 | + | 1.02094i | −0.422059 | + | 0.0783025i | ||||
\(171\) | 5.10890 | 0.390687 | ||||||||
\(172\) | 10.8802 | − | 4.18102i | 0.829610 | − | 0.318800i | ||||
\(173\) | −3.61225 | −0.274635 | −0.137317 | − | 0.990527i | \(-0.543848\pi\) | ||||
−0.137317 | + | 0.990527i | \(0.543848\pi\) | |||||||
\(174\) | 1.88936 | + | 10.1838i | 0.143232 | + | 0.772035i | ||||
\(175\) | −2.59830 | −0.196413 | ||||||||
\(176\) | −5.21099 | + | 4.69879i | −0.392793 | + | 0.354185i | ||||
\(177\) | −10.3196 | −0.775667 | ||||||||
\(178\) | 4.08920 | + | 22.0412i | 0.306498 | + | 1.65206i | ||||
\(179\) | 21.6167i | 1.61571i | 0.589383 | + | 0.807854i | \(0.299371\pi\) | ||||
−0.589383 | + | 0.807854i | \(0.700629\pi\) | |||||||
\(180\) | −0.717408 | − | 1.86690i | −0.0534724 | − | 0.139151i | ||||
\(181\) | 20.6411i | 1.53424i | 0.641503 | + | 0.767121i | \(0.278311\pi\) | ||||
−0.641503 | + | 0.767121i | \(0.721689\pi\) | |||||||
\(182\) | 7.35637 | − | 1.36479i | 0.545290 | − | 0.101165i | ||||
\(183\) | −7.39410 | −0.546587 | ||||||||
\(184\) | 8.25844 | − | 10.7610i | 0.608820 | − | 0.793308i | ||||
\(185\) | −0.890633 | −0.0654807 | ||||||||
\(186\) | −6.83723 | + | 1.26848i | −0.501330 | + | 0.0930094i | ||||
\(187\) | 6.94223i | 0.507666i | ||||||||
\(188\) | 1.93910 | + | 5.04609i | 0.141423 | + | 0.368024i | ||||
\(189\) | − | 2.59830i | − | 0.188999i | ||||||
\(190\) | 1.31794 | + | 7.10385i | 0.0956137 | + | 0.515368i | ||||
\(191\) | 0.429593 | 0.0310843 | 0.0155421 | − | 0.999879i | \(-0.495053\pi\) | ||||
0.0155421 | + | 0.999879i | \(0.495053\pi\) | |||||||
\(192\) | 7.13197 | + | 3.62423i | 0.514706 | + | 0.261556i | ||||
\(193\) | 8.47229 | 0.609849 | 0.304924 | − | 0.952377i | \(-0.401369\pi\) | ||||
0.304924 | + | 0.952377i | \(0.401369\pi\) | |||||||
\(194\) | −0.0482169 | − | 0.259894i | −0.00346177 | − | 0.0186593i | ||||
\(195\) | 2.03614 | 0.145811 | ||||||||
\(196\) | −0.464506 | + | 0.178499i | −0.0331790 | + | 0.0127499i | ||||
\(197\) | −12.5408 | −0.893497 | −0.446748 | − | 0.894660i | \(-0.647418\pi\) | ||||
−0.446748 | + | 0.894660i | \(0.647418\pi\) | |||||||
\(198\) | −2.43913 | + | 0.452520i | −0.173341 | + | 0.0321592i | ||||
\(199\) | 6.94093 | 0.492029 | 0.246015 | − | 0.969266i | \(-0.420879\pi\) | ||||
0.246015 | + | 0.969266i | \(0.420879\pi\) | |||||||
\(200\) | 2.41083 | − | 1.47915i | 0.170472 | − | 0.104592i | ||||
\(201\) | 8.20400i | 0.578666i | ||||||||
\(202\) | 13.0034 | − | 2.41245i | 0.914915 | − | 0.169740i | ||||
\(203\) | −19.0298 | −1.33563 | ||||||||
\(204\) | 7.38843 | − | 2.83920i | 0.517294 | − | 0.198784i | ||||
\(205\) | − | 10.1575i | − | 0.709431i | ||||||
\(206\) | 2.71316 | − | 0.503359i | 0.189035 | − | 0.0350707i | ||||
\(207\) | 4.47835 | − | 1.71592i | 0.311267 | − | 0.119265i | ||||
\(208\) | −6.04865 | + | 5.45412i | −0.419398 | + | 0.378175i | ||||
\(209\) | 8.96181 | 0.619901 | ||||||||
\(210\) | 3.61291 | − | 0.670285i | 0.249314 | − | 0.0462541i | ||||
\(211\) | 8.77564i | 0.604140i | 0.953286 | + | 0.302070i | \(0.0976776\pi\) | ||||
−0.953286 | + | 0.302070i | \(0.902322\pi\) | |||||||
\(212\) | −1.55121 | − | 4.03670i | −0.106538 | − | 0.277242i | ||||
\(213\) | −7.48672 | −0.512982 | ||||||||
\(214\) | −10.5738 | + | 1.96170i | −0.722807 | + | 0.134099i | ||||
\(215\) | 5.82796i | 0.397463i | ||||||||
\(216\) | 1.47915 | + | 2.41083i | 0.100643 | + | 0.164036i | ||||
\(217\) | − | 12.7763i | − | 0.867309i | ||||||
\(218\) | 1.59703 | + | 8.60815i | 0.108164 | + | 0.583017i | ||||
\(219\) | − | 13.8075i | − | 0.933025i | ||||||
\(220\) | −1.25845 | − | 3.27484i | −0.0848444 | − | 0.220790i | ||||
\(221\) | 8.05818i | 0.542052i | ||||||||
\(222\) | 1.23841 | − | 0.229757i | 0.0831169 | − | 0.0154203i | ||||
\(223\) | 12.3863i | 0.829447i | 0.909948 | + | 0.414723i | \(0.136122\pi\) | ||||
−0.909948 | + | 0.414723i | \(0.863878\pi\) | |||||||
\(224\) | −8.93722 | + | 11.6689i | −0.597143 | + | 0.779664i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −2.21465 | − | 11.9372i | −0.147316 | − | 0.794050i | ||||
\(227\) | 1.51099 | 0.100288 | 0.0501438 | − | 0.998742i | \(-0.484032\pi\) | ||||
0.0501438 | + | 0.998742i | \(0.484032\pi\) | |||||||
\(228\) | −3.66516 | − | 9.53782i | −0.242731 | − | 0.631657i | ||||
\(229\) | − | 20.9819i | − | 1.38652i | −0.720687 | − | 0.693260i | \(-0.756174\pi\) | ||
0.720687 | − | 0.693260i | \(-0.243826\pi\) | |||||||
\(230\) | 3.54125 | + | 5.78443i | 0.233503 | + | 0.381414i | ||||
\(231\) | − | 4.55784i | − | 0.299884i | ||||||
\(232\) | 17.6568 | − | 10.8332i | 1.15923 | − | 0.711236i | ||||
\(233\) | −6.16707 | −0.404018 | −0.202009 | − | 0.979384i | \(-0.564747\pi\) | ||||
−0.202009 | + | 0.979384i | \(0.564747\pi\) | |||||||
\(234\) | −2.83122 | + | 0.525262i | −0.185082 | + | 0.0343375i | ||||
\(235\) | −2.70292 | −0.176319 | ||||||||
\(236\) | 7.40335 | + | 19.2656i | 0.481917 | + | 1.25409i | ||||
\(237\) | − | 6.39670i | − | 0.415510i | ||||||
\(238\) | 2.65271 | + | 14.2984i | 0.171950 | + | 0.926827i | ||||
\(239\) | − | 20.3266i | − | 1.31482i | −0.753535 | − | 0.657408i | \(-0.771653\pi\) | ||
0.753535 | − | 0.657408i | \(-0.228347\pi\) | |||||||
\(240\) | −2.97065 | + | 2.67866i | −0.191755 | + | 0.172907i | ||||
\(241\) | 0.798895i | 0.0514613i | 0.999669 | + | 0.0257307i | \(0.00819123\pi\) | ||||
−0.999669 | + | 0.0257307i | \(0.991809\pi\) | |||||||
\(242\) | 11.0167 | − | 2.04388i | 0.708182 | − | 0.131386i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 5.30458 | + | 13.8041i | 0.339591 | + | 0.883715i | ||||
\(245\) | − | 0.248811i | − | 0.0158960i | ||||||
\(246\) | 2.62033 | + | 14.1239i | 0.167066 | + | 0.900505i | ||||
\(247\) | 10.4024 | 0.661889 | ||||||||
\(248\) | 7.27321 | + | 11.8544i | 0.461849 | + | 0.752757i | ||||
\(249\) | 9.80321i | 0.621253i | ||||||||
\(250\) | 0.257970 | + | 1.39049i | 0.0163155 | + | 0.0879421i | ||||
\(251\) | −12.7763 | −0.806433 | −0.403216 | − | 0.915105i | \(-0.632108\pi\) | ||||
−0.403216 | + | 0.915105i | \(0.632108\pi\) | |||||||
\(252\) | −4.85078 | + | 1.86404i | −0.305571 | + | 0.117424i | ||||
\(253\) | 7.85573 | − | 3.01000i | 0.493885 | − | 0.189237i | ||||
\(254\) | −0.992201 | − | 5.34806i | −0.0622562 | − | 0.335567i | ||||
\(255\) | 3.95759i | 0.247834i | ||||||||
\(256\) | 1.64955 | − | 15.9147i | 0.103097 | − | 0.994671i | ||||
\(257\) | 16.6463 | 1.03837 | 0.519185 | − | 0.854662i | \(-0.326236\pi\) | ||||
0.519185 | + | 0.854662i | \(0.326236\pi\) | |||||||
\(258\) | −1.50344 | − | 8.10369i | −0.0936000 | − | 0.504514i | ||||
\(259\) | 2.31414i | 0.143793i | ||||||||
\(260\) | −1.46074 | − | 3.80127i | −0.0905912 | − | 0.235745i | ||||
\(261\) | 7.32394 | 0.453341 | ||||||||
\(262\) | 2.28374 | + | 12.3096i | 0.141090 | + | 0.760489i | ||||
\(263\) | −10.4192 | −0.642474 | −0.321237 | − | 0.946999i | \(-0.604099\pi\) | ||||
−0.321237 | + | 0.946999i | \(0.604099\pi\) | |||||||
\(264\) | 2.59466 | + | 4.22898i | 0.159690 | + | 0.260276i | ||||
\(265\) | 2.16224 | 0.132826 | ||||||||
\(266\) | 18.4580 | − | 3.42442i | 1.13173 | − | 0.209965i | ||||
\(267\) | 15.8514 | 0.970093 | ||||||||
\(268\) | 15.3161 | − | 5.88562i | 0.935578 | − | 0.359521i | ||||
\(269\) | 18.5876 | 1.13330 | 0.566652 | − | 0.823957i | \(-0.308238\pi\) | ||||
0.566652 | + | 0.823957i | \(0.308238\pi\) | |||||||
\(270\) | −1.39049 | + | 0.257970i | −0.0846223 | + | 0.0156996i | ||||
\(271\) | 17.7596i | 1.07882i | 0.842043 | + | 0.539410i | \(0.181353\pi\) | ||||
−0.842043 | + | 0.539410i | \(0.818647\pi\) | |||||||
\(272\) | −10.6010 | − | 11.7566i | −0.642782 | − | 0.712850i | ||||
\(273\) | − | 5.29050i | − | 0.320196i | ||||||
\(274\) | 4.59407 | + | 24.7625i | 0.277538 | + | 1.49596i | ||||
\(275\) | 1.75416 | 0.105780 | ||||||||
\(276\) | −6.41626 | − | 7.12963i | −0.386214 | − | 0.429153i | ||||
\(277\) | 18.4824 | 1.11050 | 0.555250 | − | 0.831683i | \(-0.312622\pi\) | ||||
0.555250 | + | 0.831683i | \(0.312622\pi\) | |||||||
\(278\) | −0.327503 | − | 1.76527i | −0.0196423 | − | 0.105874i | ||||
\(279\) | 4.91715i | 0.294382i | ||||||||
\(280\) | −3.84328 | − | 6.26408i | −0.229680 | − | 0.374350i | ||||
\(281\) | − | 7.06994i | − | 0.421758i | −0.977512 | − | 0.210879i | \(-0.932367\pi\) | ||
0.977512 | − | 0.210879i | \(-0.0676325\pi\) | |||||||
\(282\) | 3.75837 | − | 0.697273i | 0.223808 | − | 0.0415220i | ||||
\(283\) | −20.8787 | −1.24111 | −0.620554 | − | 0.784164i | \(-0.713092\pi\) | ||||
−0.620554 | + | 0.784164i | \(0.713092\pi\) | |||||||
\(284\) | 5.37103 | + | 13.9770i | 0.318712 | + | 0.829382i | ||||
\(285\) | 5.10890 | 0.302625 | ||||||||
\(286\) | −4.96640 | + | 0.921392i | −0.293669 | + | 0.0544831i | ||||
\(287\) | −26.3923 | −1.55789 | ||||||||
\(288\) | 3.43964 | − | 4.49098i | 0.202682 | − | 0.264634i | ||||
\(289\) | 1.33750 | 0.0786765 | ||||||||
\(290\) | 1.88936 | + | 10.1838i | 0.110947 | + | 0.598016i | ||||
\(291\) | −0.186909 | −0.0109568 | ||||||||
\(292\) | −25.7773 | + | 9.90562i | −1.50850 | + | 0.579683i | ||||
\(293\) | 31.0901i | 1.81630i | 0.418641 | + | 0.908152i | \(0.362507\pi\) | ||||
−0.418641 | + | 0.908152i | \(0.637493\pi\) | |||||||
\(294\) | 0.0641859 | + | 0.345968i | 0.00374340 | + | 0.0201773i | ||||
\(295\) | −10.3196 | −0.600829 | ||||||||
\(296\) | −1.31738 | − | 2.14717i | −0.0765712 | − | 0.124802i | ||||
\(297\) | 1.75416i | 0.101787i | ||||||||
\(298\) | −2.73165 | − | 14.7239i | −0.158240 | − | 0.852932i | ||||
\(299\) | 9.11852 | − | 3.49385i | 0.527338 | − | 0.202055i | ||||
\(300\) | −0.717408 | − | 1.86690i | −0.0414196 | − | 0.107786i | ||||
\(301\) | 15.1428 | 0.872817 | ||||||||
\(302\) | 2.46768 | + | 13.3010i | 0.141999 | + | 0.765389i | ||||
\(303\) | − | 9.35168i | − | 0.537240i | ||||||
\(304\) | −15.1768 | + | 13.6850i | −0.870447 | + | 0.784889i | ||||
\(305\) | −7.39410 | −0.423385 | ||||||||
\(306\) | −1.02094 | − | 5.50297i | −0.0583632 | − | 0.314584i | ||||
\(307\) | 18.6521i | 1.06453i | 0.846578 | + | 0.532265i | \(0.178659\pi\) | ||||
−0.846578 | + | 0.532265i | \(0.821341\pi\) | |||||||
\(308\) | −8.50904 | + | 3.26983i | −0.484847 | + | 0.186316i | ||||
\(309\) | − | 1.95123i | − | 0.111002i | ||||||
\(310\) | −6.83723 | + | 1.26848i | −0.388329 | + | 0.0720448i | ||||
\(311\) | − | 8.82536i | − | 0.500440i | −0.968189 | − | 0.250220i | \(-0.919497\pi\) | ||
0.968189 | − | 0.250220i | \(-0.0805030\pi\) | |||||||
\(312\) | 3.01175 | + | 4.90878i | 0.170507 | + | 0.277905i | ||||
\(313\) | 34.9736i | 1.97682i | 0.151801 | + | 0.988411i | \(0.451493\pi\) | ||||
−0.151801 | + | 0.988411i | \(0.548507\pi\) | |||||||
\(314\) | 3.82961 | + | 20.6420i | 0.216118 | + | 1.16490i | ||||
\(315\) | − | 2.59830i | − | 0.146398i | ||||||
\(316\) | −11.9420 | + | 4.58904i | −0.671791 | + | 0.258154i | ||||
\(317\) | 23.4318 | 1.31606 | 0.658032 | − | 0.752990i | \(-0.271389\pi\) | ||||
0.658032 | + | 0.752990i | \(0.271389\pi\) | |||||||
\(318\) | −3.00657 | + | 0.557794i | −0.168600 | + | 0.0312796i | ||||
\(319\) | 12.8473 | 0.719313 | ||||||||
\(320\) | 7.13197 | + | 3.62423i | 0.398689 | + | 0.202600i | ||||
\(321\) | 7.60436i | 0.424434i | ||||||||
\(322\) | 15.0297 | − | 9.20124i | 0.837572 | − | 0.512765i | ||||
\(323\) | 20.2189i | 1.12501i | ||||||||
\(324\) | 1.86690 | − | 0.717408i | 0.103717 | − | 0.0398560i | ||||
\(325\) | 2.03614 | 0.112944 | ||||||||
\(326\) | 2.50477 | + | 13.5010i | 0.138726 | + | 0.747750i | ||||
\(327\) | 6.19075 | 0.342349 | ||||||||
\(328\) | 24.4880 | − | 15.0245i | 1.35213 | − | 0.829588i | ||||
\(329\) | 7.02301i | 0.387191i | ||||||||
\(330\) | −2.43913 | + | 0.452520i | −0.134270 | + | 0.0249104i | ||||
\(331\) | 12.3559i | 0.679143i | 0.940580 | + | 0.339572i | \(0.110282\pi\) | ||||
−0.940580 | + | 0.339572i | \(0.889718\pi\) | |||||||
\(332\) | 18.3016 | − | 7.03290i | 1.00443 | − | 0.385981i | ||||
\(333\) | − | 0.890633i | − | 0.0488064i | ||||||
\(334\) | 4.53270 | + | 24.4317i | 0.248018 | + | 1.33685i | ||||
\(335\) | 8.20400i | 0.448233i | ||||||||
\(336\) | 6.95998 | + | 7.71866i | 0.379698 | + | 0.421087i | ||||
\(337\) | 7.53162i | 0.410274i | 0.978733 | + | 0.205137i | \(0.0657639\pi\) | ||||
−0.978733 | + | 0.205137i | \(0.934236\pi\) | |||||||
\(338\) | 12.3116 | − | 2.28411i | 0.669661 | − | 0.124239i | ||||
\(339\) | −8.58491 | −0.466268 | ||||||||
\(340\) | 7.38843 | − | 2.83920i | 0.400694 | − | 0.153977i | ||||
\(341\) | 8.62546i | 0.467095i | ||||||||
\(342\) | −7.10385 | + | 1.31794i | −0.384132 | + | 0.0712662i | ||||
\(343\) | −18.8346 | −1.01697 | ||||||||
\(344\) | −14.0502 | + | 8.62043i | −0.757537 | + | 0.464782i | ||||
\(345\) | 4.47835 | − | 1.71592i | 0.241106 | − | 0.0923822i | ||||
\(346\) | 5.02279 | − | 0.931854i | 0.270027 | − | 0.0500968i | ||||
\(347\) | 23.8968i | 1.28285i | 0.767187 | + | 0.641424i | \(0.221656\pi\) | ||||
−0.767187 | + | 0.641424i | \(0.778344\pi\) | |||||||
\(348\) | −5.25425 | − | 13.6731i | −0.281658 | − | 0.732955i | ||||
\(349\) | 10.0932 | 0.540275 | 0.270137 | − | 0.962822i | \(-0.412931\pi\) | ||||
0.270137 | + | 0.962822i | \(0.412931\pi\) | |||||||
\(350\) | 3.61291 | − | 0.670285i | 0.193118 | − | 0.0358282i | ||||
\(351\) | 2.03614i | 0.108681i | ||||||||
\(352\) | 6.03366 | − | 7.87789i | 0.321595 | − | 0.419893i | ||||
\(353\) | 0.820616 | 0.0436770 | 0.0218385 | − | 0.999762i | \(-0.493048\pi\) | ||||
0.0218385 | + | 0.999762i | \(0.493048\pi\) | |||||||
\(354\) | 14.3492 | − | 2.66214i | 0.762653 | − | 0.141491i | ||||
\(355\) | −7.48672 | −0.397354 | ||||||||
\(356\) | −11.3720 | − | 29.5931i | −0.602712 | − | 1.56843i | ||||
\(357\) | 10.2830 | 0.544235 | ||||||||
\(358\) | −5.57646 | − | 30.0577i | −0.294725 | − | 1.58860i | ||||
\(359\) | 23.8059 | 1.25643 | 0.628214 | − | 0.778041i | \(-0.283786\pi\) | ||||
0.628214 | + | 0.778041i | \(0.283786\pi\) | |||||||
\(360\) | 1.47915 | + | 2.41083i | 0.0779581 | + | 0.127062i | ||||
\(361\) | 7.10084 | 0.373728 | ||||||||
\(362\) | −5.32479 | − | 28.7012i | −0.279865 | − | 1.50850i | ||||
\(363\) | − | 7.92293i | − | 0.415846i | ||||||
\(364\) | −9.87685 | + | 3.79545i | −0.517688 | + | 0.198935i | ||||
\(365\) | − | 13.8075i | − | 0.722718i | ||||||
\(366\) | 10.2814 | − | 1.90746i | 0.537417 | − | 0.0997044i | ||||
\(367\) | 34.8932 | 1.82141 | 0.910704 | − | 0.413059i | \(-0.135540\pi\) | ||||
0.910704 | + | 0.413059i | \(0.135540\pi\) | |||||||
\(368\) | −8.70724 | + | 17.0934i | −0.453896 | + | 0.891054i | ||||
\(369\) | 10.1575 | 0.528778 | ||||||||
\(370\) | 1.23841 | − | 0.229757i | 0.0643820 | − | 0.0119445i | ||||
\(371\) | − | 5.61817i | − | 0.291681i | ||||||
\(372\) | 9.17985 | − | 3.52760i | 0.475953 | − | 0.182898i | ||||
\(373\) | 30.7357i | 1.59144i | 0.605667 | + | 0.795718i | \(0.292906\pi\) | ||||
−0.605667 | + | 0.795718i | \(0.707094\pi\) | |||||||
\(374\) | −1.79089 | − | 9.65307i | −0.0926046 | − | 0.499149i | ||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −3.99803 | − | 6.51629i | −0.206183 | − | 0.336052i | ||||
\(377\) | 14.9125 | 0.768035 | ||||||||
\(378\) | 0.670285 | + | 3.61291i | 0.0344757 | + | 0.185828i | ||||
\(379\) | −25.6529 | −1.31770 | −0.658850 | − | 0.752274i | \(-0.728957\pi\) | ||||
−0.658850 | + | 0.752274i | \(0.728957\pi\) | |||||||
\(380\) | −3.66516 | − | 9.53782i | −0.188019 | − | 0.489280i | ||||
\(381\) | −3.84618 | −0.197046 | ||||||||
\(382\) | −0.597343 | + | 0.110822i | −0.0305627 | + | 0.00567016i | ||||
\(383\) | 19.3975 | 0.991168 | 0.495584 | − | 0.868560i | \(-0.334954\pi\) | ||||
0.495584 | + | 0.868560i | \(0.334954\pi\) | |||||||
\(384\) | −10.8518 | − | 3.19960i | −0.553781 | − | 0.163279i | ||||
\(385\) | − | 4.55784i | − | 0.232289i | ||||||
\(386\) | −11.7806 | + | 2.18560i | −0.599617 | + | 0.111244i | ||||
\(387\) | −5.82796 | −0.296252 | ||||||||
\(388\) | 0.134090 | + | 0.348940i | 0.00680738 | + | 0.0177148i | ||||
\(389\) | 5.01904i | 0.254475i | 0.991872 | + | 0.127238i | \(0.0406111\pi\) | ||||
−0.991872 | + | 0.127238i | \(0.959389\pi\) | |||||||
\(390\) | −2.83122 | + | 0.525262i | −0.143364 | + | 0.0265977i | ||||
\(391\) | 6.79091 | + | 17.7235i | 0.343431 | + | 0.896314i | ||||
\(392\) | 0.599842 | − | 0.368029i | 0.0302966 | − | 0.0185883i | ||||
\(393\) | 8.85272 | 0.446561 | ||||||||
\(394\) | 17.4378 | − | 3.23516i | 0.878506 | − | 0.162985i | ||||
\(395\) | − | 6.39670i | − | 0.321853i | ||||||
\(396\) | 3.27484 | − | 1.25845i | 0.164567 | − | 0.0632393i | ||||
\(397\) | −19.3839 | −0.972849 | −0.486425 | − | 0.873723i | \(-0.661699\pi\) | ||||
−0.486425 | + | 0.873723i | \(0.661699\pi\) | |||||||
\(398\) | −9.65126 | + | 1.79055i | −0.483774 | + | 0.0897523i | ||||
\(399\) | − | 13.2745i | − | 0.664555i | ||||||
\(400\) | −2.97065 | + | 2.67866i | −0.148533 | + | 0.133933i | ||||
\(401\) | − | 18.9091i | − | 0.944278i | −0.881524 | − | 0.472139i | \(-0.843482\pi\) | ||
0.881524 | − | 0.472139i | \(-0.156518\pi\) | |||||||
\(402\) | −2.11639 | − | 11.4076i | −0.105556 | − | 0.568957i | ||||
\(403\) | 10.0120i | 0.498733i | ||||||||
\(404\) | −17.4587 | + | 6.70897i | −0.868602 | + | 0.333784i | ||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 26.4607 | − | 4.90913i | 1.31322 | − | 0.243636i | ||||
\(407\) | − | 1.56231i | − | 0.0774409i | ||||||
\(408\) | −9.54108 | + | 5.85387i | −0.472354 | + | 0.289810i | ||||
\(409\) | −24.6813 | −1.22041 | −0.610206 | − | 0.792242i | \(-0.708913\pi\) | ||||
−0.610206 | + | 0.792242i | \(0.708913\pi\) | |||||||
\(410\) | 2.62033 | + | 14.1239i | 0.129409 | + | 0.697528i | ||||
\(411\) | 17.8085 | 0.878429 | ||||||||
\(412\) | −3.64276 | + | 1.39983i | −0.179466 | + | 0.0689646i | ||||
\(413\) | 26.8134i | 1.31940i | ||||||||
\(414\) | −5.78443 | + | 3.54125i | −0.284289 | + | 0.174043i | ||||
\(415\) | 9.80321i | 0.481221i | ||||||||
\(416\) | 7.00356 | − | 9.14424i | 0.343378 | − | 0.448333i | ||||
\(417\) | −1.26954 | −0.0621695 | ||||||||
\(418\) | −12.4613 | + | 2.31188i | −0.609501 | + | 0.113078i | ||||
\(419\) | 24.3020 | 1.18723 | 0.593616 | − | 0.804748i | \(-0.297700\pi\) | ||||
0.593616 | + | 0.804748i | \(0.297700\pi\) | |||||||
\(420\) | −4.85078 | + | 1.86404i | −0.236694 | + | 0.0909560i | ||||
\(421\) | − | 7.78410i | − | 0.379374i | −0.981845 | − | 0.189687i | \(-0.939253\pi\) | ||
0.981845 | − | 0.189687i | \(-0.0607473\pi\) | |||||||
\(422\) | −2.26385 | − | 12.2024i | −0.110203 | − | 0.594004i | ||||
\(423\) | − | 2.70292i | − | 0.131421i | ||||||
\(424\) | 3.19828 | + | 5.21281i | 0.155322 | + | 0.253156i | ||||
\(425\) | 3.95759i | 0.191971i | ||||||||
\(426\) | 10.4102 | − | 1.93135i | 0.504375 | − | 0.0935743i | ||||
\(427\) | 19.2121i | 0.929740i | ||||||||
\(428\) | 14.1966 | − | 5.45543i | 0.686218 | − | 0.263698i | ||||
\(429\) | 3.57170i | 0.172443i | ||||||||
\(430\) | −1.50344 | − | 8.10369i | −0.0725023 | − | 0.390795i | ||||
\(431\) | −1.36631 | −0.0658129 | −0.0329065 | − | 0.999458i | \(-0.510476\pi\) | ||||
−0.0329065 | + | 0.999458i | \(0.510476\pi\) | |||||||
\(432\) | −2.67866 | − | 2.97065i | −0.128877 | − | 0.142926i | ||||
\(433\) | − | 29.1429i | − | 1.40052i | −0.713889 | − | 0.700259i | \(-0.753068\pi\) | ||
0.713889 | − | 0.700259i | \(-0.246932\pi\) | |||||||
\(434\) | 3.29590 | + | 17.7652i | 0.158208 | + | 0.852758i | ||||
\(435\) | 7.32394 | 0.351156 | ||||||||
\(436\) | −4.44129 | − | 11.5575i | −0.212699 | − | 0.553505i | ||||
\(437\) | 22.8794 | − | 8.76647i | 1.09447 | − | 0.419357i | ||||
\(438\) | 3.56193 | + | 19.1992i | 0.170195 | + | 0.917371i | ||||
\(439\) | 1.78962i | 0.0854138i | 0.999088 | + | 0.0427069i | \(0.0135982\pi\) | ||||
−0.999088 | + | 0.0427069i | \(0.986402\pi\) | |||||||
\(440\) | 2.59466 | + | 4.22898i | 0.123696 | + | 0.201609i | ||||
\(441\) | 0.248811 | 0.0118482 | ||||||||
\(442\) | −2.07877 | − | 11.2048i | −0.0988771 | − | 0.532958i | ||||
\(443\) | − | 31.5079i | − | 1.49699i | −0.663143 | − | 0.748493i | \(-0.730778\pi\) | ||
0.663143 | − | 0.748493i | \(-0.269222\pi\) | |||||||
\(444\) | −1.66273 | + | 0.638947i | −0.0789095 | + | 0.0303231i | ||||
\(445\) | 15.8514 | 0.751431 | ||||||||
\(446\) | −3.19529 | − | 17.2229i | −0.151301 | − | 0.815530i | ||||
\(447\) | −10.5890 | −0.500843 | ||||||||
\(448\) | 9.41684 | − | 18.5310i | 0.444904 | − | 0.875509i | ||||
\(449\) | −6.54651 | −0.308949 | −0.154475 | − | 0.987997i | \(-0.549368\pi\) | ||||
−0.154475 | + | 0.987997i | \(0.549368\pi\) | |||||||
\(450\) | −1.39049 | + | 0.257970i | −0.0655481 | + | 0.0121608i | ||||
\(451\) | 17.8179 | 0.839010 | ||||||||
\(452\) | 6.15888 | + | 16.0272i | 0.289689 | + | 0.753855i | ||||
\(453\) | 9.56575 | 0.449438 | ||||||||
\(454\) | −2.10100 | + | 0.389789i | −0.0986050 | + | 0.0182937i | ||||
\(455\) | − | 5.29050i | − | 0.248022i | ||||||
\(456\) | 7.55683 | + | 12.3167i | 0.353881 | + | 0.576782i | ||||
\(457\) | 8.53045i | 0.399038i | 0.979894 | + | 0.199519i | \(0.0639379\pi\) | ||||
−0.979894 | + | 0.199519i | \(0.936062\pi\) | |||||||
\(458\) | 5.41269 | + | 29.1750i | 0.252919 | + | 1.36326i | ||||
\(459\) | −3.95759 | −0.184724 | ||||||||
\(460\) | −6.41626 | − | 7.12963i | −0.299160 | − | 0.332421i | ||||
\(461\) | 28.1888 | 1.31288 | 0.656441 | − | 0.754377i | \(-0.272061\pi\) | ||||
0.656441 | + | 0.754377i | \(0.272061\pi\) | |||||||
\(462\) | 1.17579 | + | 6.33761i | 0.0547025 | + | 0.294852i | ||||
\(463\) | 2.51180i | 0.116733i | 0.998295 | + | 0.0583667i | \(0.0185892\pi\) | ||||
−0.998295 | + | 0.0583667i | \(0.981411\pi\) | |||||||
\(464\) | −21.7569 | + | 19.6184i | −1.01004 | + | 0.910760i | ||||
\(465\) | 4.91715i | 0.228028i | ||||||||
\(466\) | 8.57522 | − | 1.59092i | 0.397239 | − | 0.0736979i | ||||
\(467\) | −39.3961 | −1.82303 | −0.911516 | − | 0.411264i | \(-0.865088\pi\) | ||||
−0.911516 | + | 0.411264i | \(0.865088\pi\) | |||||||
\(468\) | 3.80127 | − | 1.46074i | 0.175714 | − | 0.0675227i | ||||
\(469\) | 21.3165 | 0.984305 | ||||||||
\(470\) | 3.75837 | − | 0.697273i | 0.173361 | − | 0.0321628i | ||||
\(471\) | 14.8452 | 0.684030 | ||||||||
\(472\) | −15.2642 | − | 24.8788i | −0.702592 | − | 1.14514i | ||||
\(473\) | −10.2232 | −0.470061 | ||||||||
\(474\) | 1.65016 | + | 8.89453i | 0.0757943 | + | 0.408539i | ||||
\(475\) | 5.10890 | 0.234412 | ||||||||
\(476\) | −7.37712 | − | 19.1974i | −0.338130 | − | 0.879911i | ||||
\(477\) | 2.16224i | 0.0990024i | ||||||||
\(478\) | 5.24364 | + | 28.2638i | 0.239839 | + | 1.29276i | ||||
\(479\) | −28.5976 | −1.30666 | −0.653329 | − | 0.757074i | \(-0.726628\pi\) | ||||
−0.653329 | + | 0.757074i | \(0.726628\pi\) | |||||||
\(480\) | 3.43964 | − | 4.49098i | 0.156997 | − | 0.204984i | ||||
\(481\) | − | 1.81345i | − | 0.0826862i | ||||||
\(482\) | −0.206091 | − | 1.11085i | −0.00938719 | − | 0.0505979i | ||||
\(483\) | −4.45849 | − | 11.6361i | −0.202868 | − | 0.529462i | ||||
\(484\) | −14.7913 | + | 5.68397i | −0.672334 | + | 0.258362i | ||||
\(485\) | −0.186909 | −0.00848709 | ||||||||
\(486\) | −0.257970 | − | 1.39049i | −0.0117018 | − | 0.0630737i | ||||
\(487\) | 23.2007i | 1.05132i | 0.850694 | + | 0.525661i | \(0.176182\pi\) | ||||
−0.850694 | + | 0.525661i | \(0.823818\pi\) | |||||||
\(488\) | −10.9370 | − | 17.8259i | −0.495094 | − | 0.806942i | ||||
\(489\) | 9.70954 | 0.439081 | ||||||||
\(490\) | 0.0641859 | + | 0.345968i | 0.00289962 | + | 0.0156293i | ||||
\(491\) | 10.7234i | 0.483941i | 0.970284 | + | 0.241970i | \(0.0777937\pi\) | ||||
−0.970284 | + | 0.241970i | \(0.922206\pi\) | |||||||
\(492\) | −7.28707 | − | 18.9631i | −0.328527 | − | 0.854921i | ||||
\(493\) | 28.9851i | 1.30543i | ||||||||
\(494\) | −14.4644 | + | 2.68351i | −0.650784 | + | 0.120737i | ||||
\(495\) | 1.75416i | 0.0788435i | ||||||||
\(496\) | −13.1714 | − | 14.6072i | −0.591413 | − | 0.655881i | ||||
\(497\) | 19.4528i | 0.872577i | ||||||||
\(498\) | −2.52894 | − | 13.6312i | −0.113324 | − | 0.610830i | ||||
\(499\) | 21.4690i | 0.961086i | 0.876971 | + | 0.480543i | \(0.159560\pi\) | ||||
−0.876971 | + | 0.480543i | \(0.840440\pi\) | |||||||
\(500\) | −0.717408 | − | 1.86690i | −0.0320835 | − | 0.0834904i | ||||
\(501\) | 17.5706 | 0.784999 | ||||||||
\(502\) | 17.7653 | − | 3.29590i | 0.792903 | − | 0.147103i | ||||
\(503\) | 37.2965 | 1.66297 | 0.831485 | − | 0.555547i | \(-0.187491\pi\) | ||||
0.831485 | + | 0.555547i | \(0.187491\pi\) | |||||||
\(504\) | 6.26408 | − | 3.84328i | 0.279024 | − | 0.171194i | ||||
\(505\) | − | 9.35168i | − | 0.416144i | ||||||
\(506\) | −10.1468 | + | 6.21190i | −0.451080 | + | 0.276153i | ||||
\(507\) | − | 8.85415i | − | 0.393227i | ||||||
\(508\) | 2.75928 | + | 7.18045i | 0.122423 | + | 0.318581i | ||||
\(509\) | −5.86771 | −0.260082 | −0.130041 | − | 0.991509i | \(-0.541511\pi\) | ||||
−0.130041 | + | 0.991509i | \(0.541511\pi\) | |||||||
\(510\) | −1.02094 | − | 5.50297i | −0.0452080 | − | 0.243676i | ||||
\(511\) | −35.8761 | −1.58707 | ||||||||
\(512\) | 1.81186 | + | 22.5548i | 0.0800735 | + | 0.996789i | ||||
\(513\) | 5.10890i | 0.225563i | ||||||||
\(514\) | −23.1465 | + | 4.29426i | −1.02095 | + | 0.189412i | ||||
\(515\) | − | 1.95123i | − | 0.0859815i | ||||||
\(516\) | 4.18102 | + | 10.8802i | 0.184059 | + | 0.478975i | ||||
\(517\) | − | 4.74135i | − | 0.208524i | ||||||
\(518\) | −0.596978 | − | 3.21778i | −0.0262297 | − | 0.141381i | ||||
\(519\) | − | 3.61225i | − | 0.158560i | ||||||
\(520\) | 3.01175 | + | 4.90878i | 0.132074 | + | 0.215264i | ||||
\(521\) | − | 25.6449i | − | 1.12352i | −0.827299 | − | 0.561762i | \(-0.810124\pi\) | ||
0.827299 | − | 0.561762i | \(-0.189876\pi\) | |||||||
\(522\) | −10.1838 | + | 1.88936i | −0.445735 | + | 0.0826950i | ||||
\(523\) | −18.7797 | −0.821178 | −0.410589 | − | 0.911821i | \(-0.634677\pi\) | ||||
−0.410589 | + | 0.911821i | \(0.634677\pi\) | |||||||
\(524\) | −6.35101 | − | 16.5272i | −0.277445 | − | 0.721993i | ||||
\(525\) | − | 2.59830i | − | 0.113399i | ||||||
\(526\) | 14.4877 | − | 2.68784i | 0.631695 | − | 0.117195i | ||||
\(527\) | −19.4601 | −0.847694 | ||||||||
\(528\) | −4.69879 | − | 5.21099i | −0.204489 | − | 0.226779i | ||||
\(529\) | 17.1112 | − | 15.3690i | 0.743966 | − | 0.668217i | ||||
\(530\) | −3.00657 | + | 0.557794i | −0.130597 | + | 0.0242290i | ||||
\(531\) | − | 10.3196i | − | 0.447832i | ||||||
\(532\) | −24.7822 | + | 9.52321i | −1.07444 | + | 0.412884i | ||||
\(533\) | 20.6821 | 0.895839 | ||||||||
\(534\) | −22.0412 | + | 4.08920i | −0.953817 | + | 0.176957i | ||||
\(535\) | 7.60436i | 0.328765i | ||||||||
\(536\) | −19.7785 | + | 12.1350i | −0.854300 | + | 0.524150i | ||||
\(537\) | −21.6167 | −0.932829 | ||||||||
\(538\) | −25.8457 | + | 4.79504i | −1.11429 | + | 0.206729i | ||||
\(539\) | 0.436454 | 0.0187994 | ||||||||
\(540\) | 1.86690 | − | 0.717408i | 0.0803387 | − | 0.0308723i | ||||
\(541\) | −29.0557 | −1.24920 | −0.624601 | − | 0.780944i | \(-0.714738\pi\) | ||||
−0.624601 | + | 0.780944i | \(0.714738\pi\) | |||||||
\(542\) | −4.58146 | − | 24.6945i | −0.196790 | − | 1.06072i | ||||
\(543\) | −20.6411 | −0.885795 | ||||||||
\(544\) | 17.7734 | + | 13.6127i | 0.762030 | + | 0.583638i | ||||
\(545\) | 6.19075 | 0.265182 | ||||||||
\(546\) | 1.36479 | + | 7.35637i | 0.0584077 | + | 0.314823i | ||||
\(547\) | − | 15.5085i | − | 0.663094i | −0.943439 | − | 0.331547i | \(-0.892429\pi\) | ||
0.943439 | − | 0.331547i | \(-0.107571\pi\) | |||||||
\(548\) | −12.7760 | − | 33.2468i | −0.545762 | − | 1.42023i | ||||
\(549\) | − | 7.39410i | − | 0.315572i | ||||||
\(550\) | −2.43913 | + | 0.452520i | −0.104005 | + | 0.0192955i | ||||
\(551\) | 37.4173 | 1.59403 | ||||||||
\(552\) | 10.7610 | + | 8.25844i | 0.458017 | + | 0.351503i | ||||
\(553\) | −16.6206 | −0.706779 | ||||||||
\(554\) | −25.6995 | + | 4.76791i | −1.09187 | + | 0.202569i | ||||
\(555\) | − | 0.890633i | − | 0.0378053i | ||||||
\(556\) | 0.910775 | + | 2.37010i | 0.0386255 | + | 0.100515i | ||||
\(557\) | − | 28.2878i | − | 1.19859i | −0.800527 | − | 0.599296i | \(-0.795447\pi\) | ||
0.800527 | − | 0.599296i | \(-0.204553\pi\) | |||||||
\(558\) | −1.26848 | − | 6.83723i | −0.0536990 | − | 0.289443i | ||||
\(559\) | −11.8665 | −0.501900 | ||||||||
\(560\) | 6.95998 | + | 7.71866i | 0.294113 | + | 0.326173i | ||||
\(561\) | −6.94223 | −0.293101 | ||||||||
\(562\) | 1.82383 | + | 9.83066i | 0.0769338 | + | 0.414681i | ||||
\(563\) | −6.04537 | −0.254782 | −0.127391 | − | 0.991853i | \(-0.540660\pi\) | ||||
−0.127391 | + | 0.991853i | \(0.540660\pi\) | |||||||
\(564\) | −5.04609 | + | 1.93910i | −0.212479 | + | 0.0816507i | ||||
\(565\) | −8.58491 | −0.361170 | ||||||||
\(566\) | 29.0315 | − | 5.38607i | 1.22028 | − | 0.226394i | ||||
\(567\) | 2.59830 | 0.109119 | ||||||||
\(568\) | −11.0740 | − | 18.0492i | −0.464654 | − | 0.757329i | ||||
\(569\) | − | 34.8074i | − | 1.45920i | −0.683872 | − | 0.729602i | \(-0.739706\pi\) | ||
0.683872 | − | 0.729602i | \(-0.260294\pi\) | |||||||
\(570\) | −7.10385 | + | 1.31794i | −0.297548 | + | 0.0552026i | ||||
\(571\) | −34.3474 | −1.43739 | −0.718697 | − | 0.695323i | \(-0.755261\pi\) | ||||
−0.718697 | + | 0.695323i | \(0.755261\pi\) | |||||||
\(572\) | 6.66802 | − | 2.56237i | 0.278804 | − | 0.107138i | ||||
\(573\) | 0.429593i | 0.0179465i | ||||||||
\(574\) | 36.6981 | − | 6.80842i | 1.53175 | − | 0.284178i | ||||
\(575\) | 4.47835 | − | 1.71592i | 0.186760 | − | 0.0715589i | ||||
\(576\) | −3.62423 | + | 7.13197i | −0.151009 | + | 0.297165i | ||||
\(577\) | −29.0033 | −1.20742 | −0.603712 | − | 0.797202i | \(-0.706312\pi\) | ||||
−0.603712 | + | 0.797202i | \(0.706312\pi\) | |||||||
\(578\) | −1.85978 | + | 0.345035i | −0.0773565 | + | 0.0143516i | ||||
\(579\) | 8.47229i | 0.352096i | ||||||||
\(580\) | −5.25425 | − | 13.6731i | −0.218171 | − | 0.567744i | ||||
\(581\) | 25.4717 | 1.05675 | ||||||||
\(582\) | 0.259894 | − | 0.0482169i | 0.0107730 | − | 0.00199865i | ||||
\(583\) | 3.79292i | 0.157087i | ||||||||
\(584\) | 33.2876 | − | 20.4234i | 1.37745 | − | 0.845126i | ||||
\(585\) | 2.03614i | 0.0841838i | ||||||||
\(586\) | −8.02032 | − | 43.2304i | −0.331316 | − | 1.78583i | ||||
\(587\) | − | 15.8918i | − | 0.655923i | −0.944691 | − | 0.327961i | \(-0.893638\pi\) | ||
0.944691 | − | 0.327961i | \(-0.106362\pi\) | |||||||
\(588\) | −0.178499 | − | 0.464506i | −0.00736118 | − | 0.0191559i | ||||
\(589\) | 25.1212i | 1.03510i | ||||||||
\(590\) | 14.3492 | − | 2.66214i | 0.590748 | − | 0.109599i | ||||
\(591\) | − | 12.5408i | − | 0.515861i | ||||||
\(592\) | 2.38571 | + | 2.64576i | 0.0980519 | + | 0.108740i | ||||
\(593\) | −30.1078 | −1.23638 | −0.618190 | − | 0.786029i | \(-0.712134\pi\) | ||||
−0.618190 | + | 0.786029i | \(0.712134\pi\) | |||||||
\(594\) | −0.452520 | − | 2.43913i | −0.0185671 | − | 0.100079i | ||||
\(595\) | 10.2830 | 0.421563 | ||||||||
\(596\) | 7.59664 | + | 19.7687i | 0.311171 | + | 0.809756i | ||||
\(597\) | 6.94093i | 0.284073i | ||||||||
\(598\) | −11.7779 | + | 7.21046i | −0.481633 | + | 0.294858i | ||||
\(599\) | − | 1.22255i | − | 0.0499519i | −0.999688 | − | 0.0249760i | \(-0.992049\pi\) | ||
0.999688 | − | 0.0249760i | \(-0.00795092\pi\) | |||||||
\(600\) | 1.47915 | + | 2.41083i | 0.0603861 | + | 0.0984218i | ||||
\(601\) | −2.02167 | −0.0824655 | −0.0412327 | − | 0.999150i | \(-0.513129\pi\) | ||||
−0.0412327 | + | 0.999150i | \(0.513129\pi\) | |||||||
\(602\) | −21.0559 | + | 3.90639i | −0.858173 | + | 0.159213i | ||||
\(603\) | −8.20400 | −0.334093 | ||||||||
\(604\) | −6.86254 | − | 17.8583i | −0.279233 | − | 0.726645i | ||||
\(605\) | − | 7.92293i | − | 0.322113i | ||||||
\(606\) | 2.41245 | + | 13.0034i | 0.0979993 | + | 0.528226i | ||||
\(607\) | 37.5362i | 1.52355i | 0.647844 | + | 0.761773i | \(0.275671\pi\) | ||||
−0.647844 | + | 0.761773i | \(0.724329\pi\) | |||||||
\(608\) | 17.5727 | − | 22.9440i | 0.712669 | − | 0.930501i | ||||
\(609\) | − | 19.0298i | − | 0.771128i | ||||||
\(610\) | 10.2814 | − | 1.90746i | 0.416281 | − | 0.0772307i | ||||
\(611\) | − | 5.50351i | − | 0.222648i | ||||||
\(612\) | 2.83920 | + | 7.38843i | 0.114768 | + | 0.298660i | ||||
\(613\) | 10.9310i | 0.441498i | 0.975331 | + | 0.220749i | \(0.0708501\pi\) | ||||
−0.975331 | + | 0.220749i | \(0.929150\pi\) | |||||||
\(614\) | −4.81167 | − | 25.9354i | −0.194183 | − | 1.04667i | ||||
\(615\) | 10.1575 | 0.409590 | ||||||||
\(616\) | 10.9882 | − | 6.74173i | 0.442726 | − | 0.271632i | ||||
\(617\) | − | 10.2444i | − | 0.412425i | −0.978507 | − | 0.206212i | \(-0.933886\pi\) | ||
0.978507 | − | 0.206212i | \(-0.0661137\pi\) | |||||||
\(618\) | 0.503359 | + | 2.71316i | 0.0202481 | + | 0.109139i | ||||
\(619\) | 12.0993 | 0.486314 | 0.243157 | − | 0.969987i | \(-0.421817\pi\) | ||||
0.243157 | + | 0.969987i | \(0.421817\pi\) | |||||||
\(620\) | 9.17985 | − | 3.52760i | 0.368672 | − | 0.141672i | ||||
\(621\) | 1.71592 | + | 4.47835i | 0.0688576 | + | 0.179710i | ||||
\(622\) | 2.27668 | + | 12.2715i | 0.0912866 | + | 0.492044i | ||||
\(623\) | − | 41.1869i | − | 1.65012i | ||||||
\(624\) | −5.45412 | − | 6.04865i | −0.218339 | − | 0.242140i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −9.02213 | − | 48.6302i | −0.360597 | − | 1.94366i | ||||
\(627\) | 8.96181i | 0.357900i | ||||||||
\(628\) | −10.6500 | − | 27.7145i | −0.424983 | − | 1.10593i | ||||
\(629\) | 3.52476 | 0.140541 | ||||||||
\(630\) | 0.670285 | + | 3.61291i | 0.0267048 | + | 0.143942i | ||||
\(631\) | −15.8148 | −0.629579 | −0.314789 | − | 0.949162i | \(-0.601934\pi\) | ||||
−0.314789 | + | 0.949162i | \(0.601934\pi\) | |||||||
\(632\) | 15.4214 | − | 9.46169i | 0.613430 | − | 0.376366i | ||||
\(633\) | −8.77564 | −0.348800 | ||||||||
\(634\) | −32.5817 | + | 6.04472i | −1.29398 | + | 0.240066i | ||||
\(635\) | −3.84618 | −0.152631 | ||||||||
\(636\) | 4.03670 | − | 1.55121i | 0.160066 | − | 0.0615095i | ||||
\(637\) | 0.506613 | 0.0200727 | ||||||||
\(638\) | −17.8641 | + | 3.31423i | −0.707245 | + | 0.131212i | ||||
\(639\) | − | 7.48672i | − | 0.296170i | ||||||
\(640\) | −10.8518 | − | 3.19960i | −0.428957 | − | 0.126475i | ||||
\(641\) | 44.2351i | 1.74718i | 0.486661 | + | 0.873591i | \(0.338215\pi\) | ||||
−0.486661 | + | 0.873591i | \(0.661785\pi\) | |||||||
\(642\) | −1.96170 | − | 10.5738i | −0.0774220 | − | 0.417313i | ||||
\(643\) | −18.6431 | −0.735211 | −0.367606 | − | 0.929982i | \(-0.619822\pi\) | ||||
−0.367606 | + | 0.929982i | \(0.619822\pi\) | |||||||
\(644\) | −18.5249 | + | 16.6714i | −0.729985 | + | 0.656946i | ||||
\(645\) | −5.82796 | −0.229476 | ||||||||
\(646\) | −5.21588 | − | 28.1141i | −0.205216 | − | 1.10614i | ||||
\(647\) | − | 19.8452i | − | 0.780194i | −0.920774 | − | 0.390097i | \(-0.872442\pi\) | ||
0.920774 | − | 0.390097i | \(-0.127558\pi\) | |||||||
\(648\) | −2.41083 | + | 1.47915i | −0.0947064 | + | 0.0581065i | ||||
\(649\) | − | 18.1022i | − | 0.710572i | ||||||
\(650\) | −2.83122 | + | 0.525262i | −0.111049 | + | 0.0206025i | ||||
\(651\) | 12.7763 | 0.500741 | ||||||||
\(652\) | −6.96570 | − | 18.1268i | −0.272798 | − | 0.709899i | ||||
\(653\) | −33.2325 | −1.30049 | −0.650243 | − | 0.759726i | \(-0.725333\pi\) | ||||
−0.650243 | + | 0.759726i | \(0.725333\pi\) | |||||||
\(654\) | −8.60815 | + | 1.59703i | −0.336605 | + | 0.0624487i | ||||
\(655\) | 8.85272 | 0.345904 | ||||||||
\(656\) | −30.1744 | + | 27.2085i | −1.17811 | + | 1.06231i | ||||
\(657\) | 13.8075 | 0.538682 | ||||||||
\(658\) | −1.81173 | − | 9.76540i | −0.0706285 | − | 0.380695i | ||||
\(659\) | −12.5073 | −0.487215 | −0.243607 | − | 0.969874i | \(-0.578331\pi\) | ||||
−0.243607 | + | 0.969874i | \(0.578331\pi\) | |||||||
\(660\) | 3.27484 | − | 1.25845i | 0.127473 | − | 0.0489849i | ||||
\(661\) | − | 19.4372i | − | 0.756020i | −0.925802 | − | 0.378010i | \(-0.876609\pi\) | ||
0.925802 | − | 0.378010i | \(-0.123391\pi\) | |||||||
\(662\) | −3.18746 | − | 17.1808i | −0.123884 | − | 0.667749i | ||||
\(663\) | −8.05818 | −0.312954 | ||||||||
\(664\) | −23.6339 | + | 14.5004i | −0.917173 | + | 0.562726i | ||||
\(665\) | − | 13.2745i | − | 0.514762i | ||||||
\(666\) | 0.229757 | + | 1.23841i | 0.00890290 | + | 0.0479875i | ||||
\(667\) | 32.7992 | − | 12.5673i | 1.26999 | − | 0.486609i | ||||
\(668\) | −12.6053 | − | 32.8027i | −0.487714 | − | 1.26917i | ||||
\(669\) | −12.3863 | −0.478881 | ||||||||
\(670\) | −2.11639 | − | 11.4076i | −0.0817632 | − | 0.440712i | ||||
\(671\) | − | 12.9704i | − | 0.500717i | ||||||
\(672\) | −11.6689 | − | 8.93722i | −0.450139 | − | 0.344761i | ||||
\(673\) | 24.8890 | 0.959401 | 0.479700 | − | 0.877432i | \(-0.340745\pi\) | ||||
0.479700 | + | 0.877432i | \(0.340745\pi\) | |||||||
\(674\) | −1.94293 | − | 10.4726i | −0.0748390 | − | 0.403390i | ||||
\(675\) | 1.00000i | 0.0384900i | ||||||||
\(676\) | −16.5298 | + | 6.35204i | −0.635763 | + | 0.244309i | ||||
\(677\) | − | 27.4911i | − | 1.05657i | −0.849067 | − | 0.528284i | \(-0.822835\pi\) | ||
0.849067 | − | 0.528284i | \(-0.177165\pi\) | |||||||
\(678\) | 11.9372 | − | 2.21465i | 0.458445 | − | 0.0850531i | ||||
\(679\) | 0.485646i | 0.0186374i | ||||||||
\(680\) | −9.54108 | + | 5.85387i | −0.365884 | + | 0.224486i | ||||
\(681\) | 1.51099i | 0.0579011i | ||||||||
\(682\) | −2.22511 | − | 11.9936i | −0.0852039 | − | 0.459258i | ||||
\(683\) | 49.4721i | 1.89300i | 0.322707 | + | 0.946499i | \(0.395407\pi\) | ||||
−0.322707 | + | 0.946499i | \(0.604593\pi\) | |||||||
\(684\) | 9.53782 | − | 3.66516i | 0.364688 | − | 0.140141i | ||||
\(685\) | 17.8085 | 0.680428 | ||||||||
\(686\) | 26.1893 | − | 4.85877i | 0.999911 | − | 0.185509i | ||||
\(687\) | 20.9819 | 0.800508 | ||||||||
\(688\) | 17.3128 | − | 15.6111i | 0.660045 | − | 0.595168i | ||||
\(689\) | 4.40262i | 0.167727i | ||||||||
\(690\) | −5.78443 | + | 3.54125i | −0.220209 | + | 0.134813i | ||||
\(691\) | − | 48.6195i | − | 1.84957i | −0.380487 | − | 0.924786i | \(-0.624244\pi\) | ||
0.380487 | − | 0.924786i | \(-0.375756\pi\) | |||||||
\(692\) | −6.74373 | + | 2.59146i | −0.256358 | + | 0.0985125i | ||||
\(693\) | 4.55784 | 0.173138 | ||||||||
\(694\) | −6.16466 | − | 33.2282i | −0.234007 | − | 1.26132i | ||||
\(695\) | −1.26954 | −0.0481563 | ||||||||
\(696\) | 10.8332 | + | 17.6568i | 0.410632 | + | 0.669279i | ||||
\(697\) | 40.1992i | 1.52265i | ||||||||
\(698\) | −14.0344 | + | 2.60374i | −0.531210 | + | 0.0985528i | ||||
\(699\) | − | 6.16707i | − | 0.233260i | ||||||
\(700\) | −4.85078 | + | 1.86404i | −0.183342 | + | 0.0704543i | ||||
\(701\) | 16.2570i | 0.614020i | 0.951706 | + | 0.307010i | \(0.0993285\pi\) | ||||
−0.951706 | + | 0.307010i | \(0.900672\pi\) | |||||||
\(702\) | −0.525262 | − | 2.83122i | −0.0198247 | − | 0.106857i | ||||
\(703\) | − | 4.55016i | − | 0.171612i | ||||||
\(704\) | −6.35746 | + | 12.5106i | −0.239606 | + | 0.471511i | ||||
\(705\) | − | 2.70292i | − | 0.101798i | ||||||
\(706\) | −1.14106 | + | 0.211695i | −0.0429442 | + | 0.00796723i | ||||
\(707\) | −24.2985 | −0.913840 | ||||||||
\(708\) | −19.2656 | + | 7.40335i | −0.724047 | + | 0.278235i | ||||
\(709\) | 18.0103i | 0.676390i | 0.941076 | + | 0.338195i | \(0.109816\pi\) | ||||
−0.941076 | + | 0.338195i | \(0.890184\pi\) | |||||||
\(710\) | 10.4102 | − | 1.93135i | 0.390687 | − | 0.0724823i | ||||
\(711\) | 6.39670 | 0.239895 | ||||||||
\(712\) | 23.4467 | + | 38.2152i | 0.878701 | + | 1.43217i | ||||
\(713\) | 8.43745 | + | 22.0207i | 0.315985 | + | 0.824683i | ||||
\(714\) | −14.2984 | + | 2.65271i | −0.535104 | + | 0.0992753i | ||||
\(715\) | 3.57170i | 0.133574i | ||||||||
\(716\) | 15.5080 | + | 40.3563i | 0.579560 | + | 1.50818i | ||||
\(717\) | 20.3266 | 0.759109 | ||||||||
\(718\) | −33.1018 | + | 6.14121i | −1.23535 | + | 0.229188i | ||||
\(719\) | 10.5365i | 0.392946i | 0.980509 | + | 0.196473i | \(0.0629488\pi\) | ||||
−0.980509 | + | 0.196473i | \(0.937051\pi\) | |||||||
\(720\) | −2.67866 | − | 2.97065i | −0.0998278 | − | 0.110710i | ||||
\(721\) | −5.06989 | −0.188813 | ||||||||
\(722\) | −9.87362 | + | 1.83180i | −0.367458 | + | 0.0681727i | ||||
\(723\) | −0.798895 | −0.0297112 | ||||||||
\(724\) | 14.8081 | + | 38.5349i | 0.550338 | + | 1.43214i | ||||
\(725\) | 7.32394 | 0.272004 | ||||||||
\(726\) | 2.04388 | + | 11.0167i | 0.0758555 | + | 0.408869i | ||||
\(727\) | 30.3679 | 1.12628 | 0.563142 | − | 0.826360i | \(-0.309592\pi\) | ||||
0.563142 | + | 0.826360i | \(0.309592\pi\) | |||||||
\(728\) | 12.7545 | − | 7.82545i | 0.472714 | − | 0.290030i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 3.56193 | + | 19.1992i | 0.131833 | + | 0.710593i | ||||
\(731\) | − | 23.0646i | − | 0.853077i | ||||||
\(732\) | −13.8041 | + | 5.30458i | −0.510213 | + | 0.196063i | ||||
\(733\) | − | 6.62522i | − | 0.244708i | −0.992487 | − | 0.122354i | \(-0.960956\pi\) | ||
0.992487 | − | 0.122354i | \(-0.0390443\pi\) | |||||||
\(734\) | −48.5185 | + | 9.00140i | −1.79085 | + | 0.332248i | ||||
\(735\) | 0.248811 | 0.00917754 | ||||||||
\(736\) | 7.69771 | − | 26.0143i | 0.283741 | − | 0.958901i | ||||
\(737\) | −14.3911 | −0.530103 | ||||||||
\(738\) | −14.1239 | + | 2.62033i | −0.519907 | + | 0.0964558i | ||||
\(739\) | 24.3361i | 0.895217i | 0.894230 | + | 0.447608i | \(0.147724\pi\) | ||||
−0.894230 | + | 0.447608i | \(0.852276\pi\) | |||||||
\(740\) | −1.66273 | + | 0.638947i | −0.0611230 | + | 0.0234882i | ||||
\(741\) | 10.4024i | 0.382142i | ||||||||
\(742\) | 1.44932 | + | 7.81199i | 0.0532062 | + | 0.286787i | ||||
\(743\) | 30.2508 | 1.10980 | 0.554898 | − | 0.831919i | \(-0.312757\pi\) | ||||
0.554898 | + | 0.831919i | \(0.312757\pi\) | |||||||
\(744\) | −11.8544 | + | 7.27321i | −0.434605 | + | 0.266649i | ||||
\(745\) | −10.5890 | −0.387952 | ||||||||
\(746\) | −7.92891 | − | 42.7376i | −0.290298 | − | 1.56474i | ||||
\(747\) | −9.80321 | −0.358681 | ||||||||
\(748\) | 4.98041 | + | 12.9605i | 0.182102 | + | 0.473882i | ||||
\(749\) | 19.7584 | 0.721958 | ||||||||
\(750\) | −1.39049 | + | 0.257970i | −0.0507734 | + | 0.00941974i | ||||
\(751\) | −34.2351 | −1.24926 | −0.624629 | − | 0.780922i | \(-0.714750\pi\) | ||||
−0.624629 | + | 0.780922i | \(0.714750\pi\) | |||||||
\(752\) | 7.24021 | + | 8.02944i | 0.264023 | + | 0.292803i | ||||
\(753\) | − | 12.7763i | − | 0.465594i | ||||||
\(754\) | −20.7357 | + | 3.84699i | −0.755149 | + | 0.140099i | ||||
\(755\) | 9.56575 | 0.348133 | ||||||||
\(756\) | −1.86404 | − | 4.85078i | −0.0677946 | − | 0.176421i | ||||
\(757\) | 22.6203i | 0.822147i | 0.911602 | + | 0.411074i | \(0.134846\pi\) | ||||
−0.911602 | + | 0.411074i | \(0.865154\pi\) | |||||||
\(758\) | 35.6700 | − | 6.61768i | 1.29559 | − | 0.240365i | ||||
\(759\) | 3.01000 | + | 7.85573i | 0.109256 | + | 0.285145i | ||||
\(760\) | 7.55683 | + | 12.3167i | 0.274115 | + | 0.446774i | ||||
\(761\) | −40.6373 | −1.47310 | −0.736551 | − | 0.676382i | \(-0.763547\pi\) | ||||
−0.736551 | + | 0.676382i | \(0.763547\pi\) | |||||||
\(762\) | 5.34806 | − | 0.992201i | 0.193740 | − | 0.0359436i | ||||
\(763\) | − | 16.0854i | − | 0.582332i | ||||||
\(764\) | 0.802009 | − | 0.308193i | 0.0290157 | − | 0.0111500i | ||||
\(765\) | −3.95759 | −0.143087 | ||||||||
\(766\) | −26.9720 | + | 5.00399i | −0.974538 | + | 0.180801i | ||||
\(767\) | − | 21.0121i | − | 0.758701i | ||||||
\(768\) | 15.9147 | + | 1.64955i | 0.574274 | + | 0.0595229i | ||||
\(769\) | − | 44.9857i | − | 1.62223i | −0.584889 | − | 0.811114i | \(-0.698862\pi\) | ||
0.584889 | − | 0.811114i | \(-0.301138\pi\) | |||||||
\(770\) | 1.17579 | + | 6.33761i | 0.0423724 | + | 0.228391i | ||||
\(771\) | 16.6463i | 0.599503i | ||||||||
\(772\) | 15.8169 | − | 6.07809i | 0.569264 | − | 0.218755i | ||||
\(773\) | 50.2656i | 1.80793i | 0.427609 | + | 0.903964i | \(0.359356\pi\) | ||||
−0.427609 | + | 0.903964i | \(0.640644\pi\) | |||||||
\(774\) | 8.10369 | − | 1.50344i | 0.291281 | − | 0.0540400i | ||||
\(775\) | 4.91715i | 0.176629i | ||||||||
\(776\) | −0.276466 | − | 0.450606i | −0.00992456 | − | 0.0161758i | ||||
\(777\) | −2.31414 | −0.0830192 | ||||||||
\(778\) | −1.29476 | − | 6.97890i | −0.0464194 | − | 0.250206i | ||||
\(779\) | 51.8936 | 1.85928 | ||||||||
\(780\) | 3.80127 | − | 1.46074i | 0.136107 | − | 0.0523029i | ||||
\(781\) | − | 13.1329i | − | 0.469932i | ||||||
\(782\) | −14.0148 | − | 22.8924i | −0.501168 | − | 0.818629i | ||||
\(783\) | 7.32394i | 0.261736i | ||||||||
\(784\) | −0.739131 | + | 0.666481i | −0.0263976 | + | 0.0238029i | ||||
\(785\) | 14.8452 | 0.529847 | ||||||||
\(786\) | −12.3096 | + | 2.28374i | −0.439068 | + | 0.0814582i | ||||
\(787\) | 13.0884 | 0.466550 | 0.233275 | − | 0.972411i | \(-0.425056\pi\) | ||||
0.233275 | + | 0.972411i | \(0.425056\pi\) | |||||||
\(788\) | −23.4125 | + | 8.99688i | −0.834036 | + | 0.320501i | ||||
\(789\) | − | 10.4192i | − | 0.370933i | ||||||
\(790\) | 1.65016 | + | 8.89453i | 0.0587100 | + | 0.316453i | ||||
\(791\) | 22.3062i | 0.793117i | ||||||||
\(792\) | −4.22898 | + | 2.59466i | −0.150270 | + | 0.0921973i | ||||
\(793\) | − | 15.0554i | − | 0.534632i | ||||||
\(794\) | 26.9530 | − | 5.00046i | 0.956527 | − | 0.177460i | ||||
\(795\) | 2.16224i | 0.0766869i | ||||||||
\(796\) | 12.9580 | − | 4.97948i | 0.459286 | − | 0.176493i | ||||
\(797\) | 28.0520i | 0.993652i | 0.867850 | + | 0.496826i | \(0.165501\pi\) | ||||
−0.867850 | + | 0.496826i | \(0.834499\pi\) | |||||||
\(798\) | 3.42442 | + | 18.4580i | 0.121223 | + | 0.653405i | ||||
\(799\) | 10.6970 | 0.378434 | ||||||||
\(800\) | 3.43964 | − | 4.49098i | 0.121609 | − | 0.158780i | ||||
\(801\) | 15.8514i | 0.560083i | ||||||||
\(802\) | 4.87800 | + | 26.2929i | 0.172248 | + | 0.928435i | ||||
\(803\) | 24.2206 | 0.854725 | ||||||||
\(804\) | 5.88562 | + | 15.3161i | 0.207570 | + | 0.540156i | ||||
\(805\) | −4.45849 | − | 11.6361i | −0.157141 | − | 0.410119i | ||||
\(806\) | −2.58279 | − | 13.9215i | −0.0909751 | − | 0.490365i | ||||
\(807\) | 18.5876i | 0.654313i | ||||||||
\(808\) | 22.5453 | − | 13.8325i | 0.793142 | − | 0.486627i | ||||
\(809\) | 18.9978 | 0.667928 | 0.333964 | − | 0.942586i | \(-0.391614\pi\) | ||||
0.333964 | + | 0.942586i | \(0.391614\pi\) | |||||||
\(810\) | −0.257970 | − | 1.39049i | −0.00906415 | − | 0.0488567i | ||||
\(811\) | 7.94646i | 0.279038i | 0.990219 | + | 0.139519i | \(0.0445556\pi\) | ||||
−0.990219 | + | 0.139519i | \(0.955444\pi\) | |||||||
\(812\) | −35.5269 | + | 13.6522i | −1.24675 | + | 0.479097i | ||||
\(813\) | −17.7596 | −0.622858 | ||||||||
\(814\) | 0.403030 | + | 2.17237i | 0.0141262 | + | 0.0761416i | ||||
\(815\) | 9.70954 | 0.340110 | ||||||||
\(816\) | 11.7566 | − | 10.6010i | 0.411564 | − | 0.371111i | ||||
\(817\) | −29.7744 | −1.04168 | ||||||||
\(818\) | 34.3190 | − | 6.36704i | 1.19994 | − | 0.222618i | ||||
\(819\) | 5.29050 | 0.184865 | ||||||||
\(820\) | −7.28707 | − | 18.9631i | −0.254476 | − | 0.662219i | ||||
\(821\) | 4.42411 | 0.154403 | 0.0772013 | − | 0.997016i | \(-0.475402\pi\) | ||||
0.0772013 | + | 0.997016i | \(0.475402\pi\) | |||||||
\(822\) | −24.7625 | + | 4.59407i | −0.863691 | + | 0.160236i | ||||
\(823\) | 32.2030i | 1.12252i | 0.827638 | + | 0.561262i | \(0.189684\pi\) | ||||
−0.827638 | + | 0.561262i | \(0.810316\pi\) | |||||||
\(824\) | 4.70409 | − | 2.88616i | 0.163875 | − | 0.100544i | ||||
\(825\) | 1.75416i | 0.0610719i | ||||||||
\(826\) | −6.91706 | − | 37.2837i | −0.240675 | − | 1.29726i | ||||
\(827\) | −49.2912 | −1.71402 | −0.857011 | − | 0.515298i | \(-0.827681\pi\) | ||||
−0.857011 | + | 0.515298i | \(0.827681\pi\) | |||||||
\(828\) | 7.12963 | − | 6.41626i | 0.247772 | − | 0.222981i | ||||
\(829\) | −3.25392 | −0.113013 | −0.0565067 | − | 0.998402i | \(-0.517996\pi\) | ||||
−0.0565067 | + | 0.998402i | \(0.517996\pi\) | |||||||
\(830\) | −2.52894 | − | 13.6312i | −0.0877806 | − | 0.473147i | ||||
\(831\) | 18.4824i | 0.641148i | ||||||||
\(832\) | −7.37941 | + | 14.5217i | −0.255835 | + | 0.503448i | ||||
\(833\) | 0.984692i | 0.0341176i | ||||||||
\(834\) | 1.76527 | − | 0.327503i | 0.0611264 | − | 0.0113405i | ||||
\(835\) | 17.5706 | 0.608057 | ||||||||
\(836\) | 16.7308 | − | 6.42927i | 0.578648 | − | 0.222361i | ||||
\(837\) | −4.91715 | −0.169962 | ||||||||
\(838\) | −33.7916 | + | 6.26920i | −1.16731 | + | 0.216566i | ||||
\(839\) | −9.24797 | −0.319275 | −0.159638 | − | 0.987176i | \(-0.551033\pi\) | ||||
−0.159638 | + | 0.987176i | \(0.551033\pi\) | |||||||
\(840\) | 6.26408 | − | 3.84328i | 0.216131 | − | 0.132606i | ||||
\(841\) | 24.6402 | 0.849660 | ||||||||
\(842\) | 2.00807 | + | 10.8237i | 0.0692025 | + | 0.373009i | ||||
\(843\) | 7.06994 | 0.243502 | ||||||||
\(844\) | 6.29571 | + | 16.3833i | 0.216707 | + | 0.563935i | ||||
\(845\) | − | 8.85415i | − | 0.304592i | ||||||
\(846\) | 0.697273 | + | 3.75837i | 0.0239727 | + | 0.129216i | ||||
\(847\) | −20.5862 | −0.707350 | ||||||||
\(848\) | −5.79192 | − | 6.42327i | −0.198895 | − | 0.220576i | ||||
\(849\) | − | 20.8787i | − | 0.716554i | ||||||
\(850\) | −1.02094 | − | 5.50297i | −0.0350179 | − | 0.188750i | ||||
\(851\) | −1.52826 | − | 3.98857i | −0.0523880 | − | 0.136726i | ||||
\(852\) | −13.9770 | + | 5.37103i | −0.478844 | + | 0.184009i | ||||
\(853\) | 30.3727 | 1.03994 | 0.519971 | − | 0.854184i | \(-0.325943\pi\) | ||||
0.519971 | + | 0.854184i | \(0.325943\pi\) | |||||||
\(854\) | −4.95615 | − | 26.7142i | −0.169596 | − | 0.914141i | ||||
\(855\) | 5.10890i | 0.174721i | ||||||||
\(856\) | −18.3328 | + | 11.2480i | −0.626603 | + | 0.384448i | ||||
\(857\) | −18.2387 | −0.623023 | −0.311511 | − | 0.950242i | \(-0.600835\pi\) | ||||
−0.311511 | + | 0.950242i | \(0.600835\pi\) | |||||||
\(858\) | −0.921392 | − | 4.96640i | −0.0314558 | − | 0.169550i | ||||
\(859\) | − | 46.4910i | − | 1.58625i | −0.609058 | − | 0.793126i | \(-0.708452\pi\) | ||
0.609058 | − | 0.793126i | \(-0.291548\pi\) | |||||||
\(860\) | 4.18102 | + | 10.8802i | 0.142572 | + | 0.371013i | ||||
\(861\) | − | 26.3923i | − | 0.899447i | ||||||
\(862\) | 1.89984 | − | 0.352468i | 0.0647087 | − | 0.0120051i | ||||
\(863\) | − | 16.0349i | − | 0.545833i | −0.962038 | − | 0.272917i | \(-0.912012\pi\) | ||
0.962038 | − | 0.272917i | \(-0.0879883\pi\) | |||||||
\(864\) | 4.49098 | + | 3.43964i | 0.152786 | + | 0.117019i | ||||
\(865\) | − | 3.61225i | − | 0.122820i | ||||||
\(866\) | 7.51800 | + | 40.5228i | 0.255472 | + | 1.37702i | ||||
\(867\) | 1.33750i | 0.0454239i | ||||||||
\(868\) | −9.16579 | − | 23.8520i | −0.311107 | − | 0.809591i | ||||
\(869\) | 11.2208 | 0.380640 | ||||||||
\(870\) | −10.1838 | + | 1.88936i | −0.345265 | + | 0.0640553i | ||||
\(871\) | −16.7045 | −0.566009 | ||||||||
\(872\) | 9.15705 | + | 14.9249i | 0.310097 | + | 0.505419i | ||||
\(873\) | − | 0.186909i | − | 0.00632590i | ||||||
\(874\) | −29.5520 | + | 18.0919i | −0.999613 | + | 0.611967i | ||||
\(875\) | − | 2.59830i | − | 0.0878387i | ||||||
\(876\) | −9.90562 | − | 25.7773i | −0.334680 | − | 0.870934i | ||||
\(877\) | 2.63429 | 0.0889535 | 0.0444768 | − | 0.999010i | \(-0.485838\pi\) | ||||
0.0444768 | + | 0.999010i | \(0.485838\pi\) | |||||||
\(878\) | −0.461668 | − | 2.48844i | −0.0155805 | − | 0.0839808i | ||||
\(879\) | −31.0901 | −1.04864 | ||||||||
\(880\) | −4.69879 | − | 5.21099i | −0.158396 | − | 0.175662i | ||||
\(881\) | 23.7900i | 0.801504i | 0.916187 | + | 0.400752i | \(0.131251\pi\) | ||||
−0.916187 | + | 0.400752i | \(0.868749\pi\) | |||||||
\(882\) | −0.345968 | + | 0.0641859i | −0.0116494 | + | 0.00216125i | ||||
\(883\) | 17.2297i | 0.579826i | 0.957053 | + | 0.289913i | \(0.0936264\pi\) | ||||
−0.957053 | + | 0.289913i | \(0.906374\pi\) | |||||||
\(884\) | 5.78100 | + | 15.0438i | 0.194436 | + | 0.505979i | ||||
\(885\) | − | 10.3196i | − | 0.346889i | ||||||
\(886\) | 8.12810 | + | 43.8113i | 0.273069 | + | 1.47187i | ||||
\(887\) | − | 39.2819i | − | 1.31896i | −0.751723 | − | 0.659479i | \(-0.770777\pi\) | ||
0.751723 | − | 0.659479i | \(-0.229223\pi\) | |||||||
\(888\) | 2.14717 | − | 1.31738i | 0.0720542 | − | 0.0442084i | ||||
\(889\) | 9.99356i | 0.335173i | ||||||||
\(890\) | −22.0412 | + | 4.08920i | −0.738823 | + | 0.137070i | ||||
\(891\) | −1.75416 | −0.0587665 | ||||||||
\(892\) | 8.88601 | + | 23.1240i | 0.297526 | + | 0.774248i | ||||
\(893\) | − | 13.8089i | − | 0.462099i | ||||||
\(894\) | 14.7239 | − | 2.73165i | 0.492440 | − | 0.0913601i | ||||
\(895\) | −21.6167 | −0.722566 | ||||||||
\(896\) | −8.31354 | + | 28.1964i | −0.277736 | + | 0.941976i | ||||
\(897\) | 3.49385 | + | 9.11852i | 0.116656 | + | 0.304459i | ||||
\(898\) | 9.10284 | − | 1.68881i | 0.303766 | − | 0.0563562i | ||||
\(899\) | 36.0130i | 1.20110i | ||||||||
\(900\) | 1.86690 | − | 0.717408i | 0.0622301 | − | 0.0239136i | ||||
\(901\) | −8.55727 | −0.285084 | ||||||||
\(902\) | −24.7755 | + | 4.59648i | −0.824933 | + | 0.153046i | ||||
\(903\) | 15.1428i | 0.503921i | ||||||||
\(904\) | −12.6984 | − | 20.6968i | −0.422341 | − | 0.688364i | ||||
\(905\) | −20.6411 | −0.686134 | ||||||||
\(906\) | −13.3010 | + | 2.46768i | −0.441897 | + | 0.0819831i | ||||
\(907\) | −33.4013 | −1.10907 | −0.554536 | − | 0.832160i | \(-0.687104\pi\) | ||||
−0.554536 | + | 0.832160i | \(0.687104\pi\) | |||||||
\(908\) | 2.82086 | − | 1.08399i | 0.0936136 | − | 0.0359736i | ||||
\(909\) | 9.35168 | 0.310176 | ||||||||
\(910\) | 1.36479 | + | 7.35637i | 0.0452424 | + | 0.243861i | ||||
\(911\) | 52.8101 | 1.74968 | 0.874838 | − | 0.484416i | \(-0.160968\pi\) | ||||
0.874838 | + | 0.484416i | \(0.160968\pi\) | |||||||
\(912\) | −13.6850 | − | 15.1768i | −0.453156 | − | 0.502553i | ||||
\(913\) | −17.1964 | −0.569117 | ||||||||
\(914\) | −2.20060 | − | 11.8615i | −0.0727894 | − | 0.392343i | ||||
\(915\) | − | 7.39410i | − | 0.244441i | ||||||
\(916\) | −15.0526 | − | 39.1711i | −0.497350 | − | 1.29425i | ||||
\(917\) | − | 23.0021i | − | 0.759595i | ||||||
\(918\) | 5.50297 | − | 1.02094i | 0.181625 | − | 0.0336960i | ||||
\(919\) | 15.4354 | 0.509168 | 0.254584 | − | 0.967051i | \(-0.418061\pi\) | ||||
0.254584 | + | 0.967051i | \(0.418061\pi\) | |||||||
\(920\) | 10.7610 | + | 8.25844i | 0.354778 | + | 0.272273i | ||||
\(921\) | −18.6521 | −0.614606 | ||||||||
\(922\) | −39.1961 | + | 7.27186i | −1.29085 | + | 0.239486i | ||||
\(923\) | − | 15.2440i | − | 0.501762i | ||||||
\(924\) | −3.26983 | − | 8.50904i | −0.107569 | − | 0.279927i | ||||
\(925\) | − | 0.890633i | − | 0.0292838i | ||||||
\(926\) | −0.647970 | − | 3.49263i | −0.0212936 | − | 0.114775i | ||||
\(927\) | 1.95123 | 0.0640868 | ||||||||
\(928\) | 25.1917 | − | 32.8917i | 0.826958 | − | 1.07972i | ||||
\(929\) | 16.3559 | 0.536619 | 0.268310 | − | 0.963333i | \(-0.413535\pi\) | ||||
0.268310 | + | 0.963333i | \(0.413535\pi\) | |||||||
\(930\) | −1.26848 | − | 6.83723i | −0.0415951 | − | 0.224202i | ||||
\(931\) | 1.27115 | 0.0416603 | ||||||||
\(932\) | −11.5133 | + | 4.42430i | −0.377131 | + | 0.144923i | ||||
\(933\) | 8.82536 | 0.288929 | ||||||||
\(934\) | 54.7797 | − | 10.1630i | 1.79245 | − | 0.332544i | ||||
\(935\) | −6.94223 | −0.227035 | ||||||||
\(936\) | −4.90878 | + | 3.01175i | −0.160449 | + | 0.0984422i | ||||
\(937\) | 50.5247i | 1.65057i | 0.564716 | + | 0.825286i | \(0.308986\pi\) | ||||
−0.564716 | + | 0.825286i | \(0.691014\pi\) | |||||||
\(938\) | −29.6403 | + | 5.49902i | −0.967790 | + | 0.179549i | ||||
\(939\) | −34.9736 | −1.14132 | ||||||||
\(940\) | −5.04609 | + | 1.93910i | −0.164585 | + | 0.0632464i | ||||
\(941\) | − | 0.921848i | − | 0.0300514i | −0.999887 | − | 0.0150257i | \(-0.995217\pi\) | ||
0.999887 | − | 0.0150257i | \(-0.00478300\pi\) | |||||||
\(942\) | −20.6420 | + | 3.82961i | −0.672553 | + | 0.124776i | ||||
\(943\) | 45.4888 | − | 17.4295i | 1.48132 | − | 0.567582i | ||||
\(944\) | 27.6427 | + | 30.6559i | 0.899692 | + | 0.997764i | ||||
\(945\) | 2.59830 | 0.0845229 | ||||||||
\(946\) | 14.2151 | − | 2.63727i | 0.462174 | − | 0.0857450i | ||||
\(947\) | − | 55.9151i | − | 1.81700i | −0.417888 | − | 0.908499i | \(-0.637229\pi\) | ||
0.417888 | − | 0.908499i | \(-0.362771\pi\) | |||||||
\(948\) | −4.58904 | − | 11.9420i | −0.149045 | − | 0.387859i | ||||
\(949\) | 28.1140 | 0.912618 | ||||||||
\(950\) | −7.10385 | + | 1.31794i | −0.230479 | + | 0.0427597i | ||||
\(951\) | 23.4318i | 0.759830i | ||||||||
\(952\) | 15.2101 | + | 24.7906i | 0.492963 | + | 0.803469i | ||||
\(953\) | − | 0.618608i | − | 0.0200387i | −0.999950 | − | 0.0100193i | \(-0.996811\pi\) | ||
0.999950 | − | 0.0100193i | \(-0.00318931\pi\) | |||||||
\(954\) | −0.557794 | − | 3.00657i | −0.0180593 | − | 0.0973413i | ||||
\(955\) | 0.429593i | 0.0139013i | ||||||||
\(956\) | −14.5824 | − | 37.9477i | −0.471629 | − | 1.22732i | ||||
\(957\) | 12.8473i | 0.415296i | ||||||||
\(958\) | 39.7645 | − | 7.37732i | 1.28473 | − | 0.238351i | ||||
\(959\) | − | 46.2720i | − | 1.49420i | ||||||
\(960\) | −3.62423 | + | 7.13197i | −0.116971 | + | 0.230183i | ||||
\(961\) | 6.82160 | 0.220052 | ||||||||
\(962\) | 0.467816 | + | 2.52158i | 0.0150830 | + | 0.0812989i | ||||
\(963\) | −7.60436 | −0.245047 | ||||||||
\(964\) | 0.573133 | + | 1.49146i | 0.0184594 | + | 0.0480366i | ||||
\(965\) | 8.47229i | 0.272733i | ||||||||
\(966\) | 9.20124 | + | 15.0297i | 0.296045 | + | 0.483573i | ||||
\(967\) | − | 44.5923i | − | 1.43399i | −0.697077 | − | 0.716996i | \(-0.745516\pi\) | ||
0.697077 | − | 0.716996i | \(-0.254484\pi\) | |||||||
\(968\) | 19.1009 | − | 11.7192i | 0.613925 | − | 0.376670i | ||||
\(969\) | −20.2189 | −0.649525 | ||||||||
\(970\) | 0.259894 | − | 0.0482169i | 0.00834469 | − | 0.00154815i | ||||
\(971\) | −9.61774 | −0.308648 | −0.154324 | − | 0.988020i | \(-0.549320\pi\) | ||||
−0.154324 | + | 0.988020i | \(0.549320\pi\) | |||||||
\(972\) | 0.717408 | + | 1.86690i | 0.0230109 | + | 0.0598809i | ||||
\(973\) | 3.29864i | 0.105750i | ||||||||
\(974\) | −5.98508 | − | 32.2602i | −0.191774 | − | 1.03368i | ||||
\(975\) | 2.03614i | 0.0652085i | ||||||||
\(976\) | 19.8063 | + | 21.9653i | 0.633984 | + | 0.703092i | ||||
\(977\) | 54.1107i | 1.73116i | 0.500775 | + | 0.865578i | \(0.333048\pi\) | ||||
−0.500775 | + | 0.865578i | \(0.666952\pi\) | |||||||
\(978\) | −13.5010 | + | 2.50477i | −0.431714 | + | 0.0800938i | ||||
\(979\) | 27.8059i | 0.888681i | ||||||||
\(980\) | −0.178499 | − | 0.464506i | −0.00570194 | − | 0.0148381i | ||||
\(981\) | 6.19075i | 0.197655i | ||||||||
\(982\) | −2.76632 | − | 14.9108i | −0.0882768 | − | 0.475821i | ||||
\(983\) | 31.0113 | 0.989108 | 0.494554 | − | 0.869147i | \(-0.335331\pi\) | ||||
0.494554 | + | 0.869147i | \(0.335331\pi\) | |||||||
\(984\) | 15.0245 | + | 24.4880i | 0.478963 | + | 0.780650i | ||||
\(985\) | − | 12.5408i | − | 0.399584i | ||||||
\(986\) | −7.47730 | − | 40.3034i | −0.238126 | − | 1.28352i | ||||
\(987\) | −7.02301 | −0.223545 | ||||||||
\(988\) | 19.4203 | − | 7.46277i | 0.617842 | − | 0.237422i | ||||
\(989\) | −26.0996 | + | 10.0003i | −0.829920 | + | 0.317992i | ||||
\(990\) | −0.452520 | − | 2.43913i | −0.0143820 | − | 0.0775207i | ||||
\(991\) | − | 21.4252i | − | 0.680593i | −0.940318 | − | 0.340297i | \(-0.889472\pi\) | ||
0.940318 | − | 0.340297i | \(-0.110528\pi\) | |||||||
\(992\) | 22.0828 | + | 16.9132i | 0.701131 | + | 0.536995i | ||||
\(993\) | −12.3559 | −0.392104 | ||||||||
\(994\) | −5.01824 | − | 27.0488i | −0.159169 | − | 0.857937i | ||||
\(995\) | 6.94093i | 0.220042i | ||||||||
\(996\) | 7.03290 | + | 18.3016i | 0.222846 | + | 0.579910i | ||||
\(997\) | 21.4409 | 0.679041 | 0.339521 | − | 0.940599i | \(-0.389735\pi\) | ||||
0.339521 | + | 0.940599i | \(0.389735\pi\) | |||||||
\(998\) | −5.53837 | − | 29.8524i | −0.175314 | − | 0.944961i | ||||
\(999\) | 0.890633 | 0.0281784 |
(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 | 1380.2.p.a.91.4 | yes | 48 | |
4.3 | odd | 2 | 1380.2.p.b.91.3 | yes | 48 | ||
23.22 | odd | 2 | 1380.2.p.b.91.4 | yes | 48 | ||
92.91 | even | 2 | inner | 1380.2.p.a.91.3 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.p.a.91.3 | ✓ | 48 | 92.91 | even | 2 | inner | |
1380.2.p.a.91.4 | yes | 48 | 1.1 | even | 1 | trivial | |
1380.2.p.b.91.3 | yes | 48 | 4.3 | odd | 2 | ||
1380.2.p.b.91.4 | yes | 48 | 23.22 | odd | 2 |