Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(91,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.h (of order \(5\), degree \(4\), 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: | \(3.59326809096\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 50) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.361 |
Dual form | 450.2.h.a.91.1 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | + | 0.587785i | −0.572061 | + | 0.415627i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | −0.690983 | + | 2.12663i | −0.309017 | + | 0.951057i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.00000 | −1.13389 | −0.566947 | − | 0.823754i | \(-0.691875\pi\) | ||||
−0.566947 | + | 0.823754i | \(0.691875\pi\) | |||||||
\(8\) | 0.309017 | + | 0.951057i | 0.109254 | + | 0.336249i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.690983 | − | 2.12663i | −0.218508 | − | 0.672499i | ||||
\(11\) | −0.190983 | + | 0.138757i | −0.0575835 | + | 0.0418369i | −0.616205 | − | 0.787586i | \(-0.711331\pi\) |
0.558621 | + | 0.829423i | \(0.311331\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.809017 | − | 0.587785i | −0.224381 | − | 0.163022i | 0.469916 | − | 0.882711i | \(-0.344284\pi\) |
−0.694297 | + | 0.719689i | \(0.744284\pi\) | |||||||
\(14\) | 2.42705 | − | 1.76336i | 0.648657 | − | 0.471277i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | −2.42705 | − | 7.46969i | −0.588646 | − | 1.81167i | −0.584106 | − | 0.811677i | \(-0.698555\pi\) |
−0.00454037 | − | 0.999990i | \(-0.501445\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.263932 | − | 0.812299i | −0.0605502 | − | 0.186354i | 0.916206 | − | 0.400707i | \(-0.131236\pi\) |
−0.976756 | + | 0.214353i | \(0.931236\pi\) | |||||||
\(20\) | 1.80902 | + | 1.31433i | 0.404508 | + | 0.293893i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0729490 | − | 0.224514i | 0.0155528 | − | 0.0478665i | ||||
\(23\) | −5.04508 | + | 3.66547i | −1.05197 | + | 0.764303i | −0.972587 | − | 0.232541i | \(-0.925296\pi\) |
−0.0793863 | + | 0.996844i | \(0.525296\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.04508 | − | 2.93893i | −0.809017 | − | 0.587785i | ||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.927051 | + | 2.85317i | −0.175196 | + | 0.539198i | ||||
\(29\) | 0.163119 | − | 0.502029i | 0.0302904 | − | 0.0932244i | −0.934768 | − | 0.355258i | \(-0.884393\pi\) |
0.965059 | + | 0.262033i | \(0.0843931\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.30902 | + | 4.02874i | 0.235106 | + | 0.723583i | 0.997107 | + | 0.0760071i | \(0.0242172\pi\) |
−0.762001 | + | 0.647576i | \(0.775783\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.35410 | + | 4.61653i | 1.08972 | + | 0.791728i | ||||
\(35\) | 2.07295 | − | 6.37988i | 0.350392 | − | 1.07840i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.92705 | − | 4.30625i | −0.974401 | − | 0.707944i | −0.0179508 | − | 0.999839i | \(-0.505714\pi\) |
−0.956450 | + | 0.291895i | \(0.905714\pi\) | |||||||
\(38\) | 0.690983 | + | 0.502029i | 0.112092 | + | 0.0814398i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.23607 | −0.353553 | ||||||||
\(41\) | −6.04508 | − | 4.39201i | −0.944084 | − | 0.685917i | 0.00531652 | − | 0.999986i | \(-0.498308\pi\) |
−0.949400 | + | 0.314069i | \(0.898308\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.76393 | −0.268997 | −0.134499 | − | 0.990914i | \(-0.542942\pi\) | ||||
−0.134499 | + | 0.990914i | \(0.542942\pi\) | |||||||
\(44\) | 0.0729490 | + | 0.224514i | 0.0109975 | + | 0.0338468i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.92705 | − | 5.93085i | 0.284128 | − | 0.874457i | ||||
\(47\) | −1.83688 | + | 5.65334i | −0.267937 | + | 0.824624i | 0.723066 | + | 0.690779i | \(0.242732\pi\) |
−0.991002 | + | 0.133845i | \(0.957268\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 5.00000 | 0.707107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.809017 | + | 0.587785i | −0.112190 | + | 0.0815111i | ||||
\(53\) | −0.472136 | + | 1.45309i | −0.0648529 | + | 0.199597i | −0.978232 | − | 0.207513i | \(-0.933463\pi\) |
0.913379 | + | 0.407109i | \(0.133463\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.163119 | − | 0.502029i | −0.0219950 | − | 0.0676935i | ||||
\(56\) | −0.927051 | − | 2.85317i | −0.123882 | − | 0.381271i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.163119 | + | 0.502029i | 0.0214186 | + | 0.0659196i | ||||
\(59\) | 3.61803 | + | 2.62866i | 0.471028 | + | 0.342222i | 0.797842 | − | 0.602867i | \(-0.205975\pi\) |
−0.326814 | + | 0.945089i | \(0.605975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.73607 | − | 1.26133i | 0.222281 | − | 0.161496i | −0.471072 | − | 0.882095i | \(-0.656133\pi\) |
0.693353 | + | 0.720598i | \(0.256133\pi\) | |||||||
\(62\) | −3.42705 | − | 2.48990i | −0.435236 | − | 0.316217i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 1.80902 | − | 1.31433i | 0.224381 | − | 0.163022i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.78115 | − | 5.48183i | −0.217602 | − | 0.669712i | −0.998959 | − | 0.0456261i | \(-0.985472\pi\) |
0.781356 | − | 0.624085i | \(-0.214528\pi\) | |||||||
\(68\) | −7.85410 | −0.952450 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.07295 | + | 6.37988i | 0.247765 | + | 0.762542i | ||||
\(71\) | 0.927051 | − | 2.85317i | 0.110021 | − | 0.338609i | −0.880855 | − | 0.473386i | \(-0.843032\pi\) |
0.990876 | + | 0.134777i | \(0.0430317\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.61803 | − | 3.35520i | 0.540500 | − | 0.392696i | −0.283771 | − | 0.958892i | \(-0.591585\pi\) |
0.824271 | + | 0.566196i | \(0.191585\pi\) | |||||||
\(74\) | 7.32624 | 0.851658 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.854102 | −0.0979722 | ||||||||
\(77\) | 0.572949 | − | 0.416272i | 0.0652936 | − | 0.0474386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.854102 | + | 2.62866i | −0.0960940 | + | 0.295747i | −0.987537 | − | 0.157385i | \(-0.949693\pi\) |
0.891443 | + | 0.453132i | \(0.149693\pi\) | |||||||
\(80\) | 1.80902 | − | 1.31433i | 0.202254 | − | 0.146946i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.47214 | 0.825159 | ||||||||
\(83\) | 4.16312 | + | 12.8128i | 0.456962 | + | 1.40638i | 0.868817 | + | 0.495134i | \(0.164881\pi\) |
−0.411855 | + | 0.911249i | \(0.635119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.5623 | 1.90490 | ||||||||
\(86\) | 1.42705 | − | 1.03681i | 0.153883 | − | 0.111802i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.190983 | − | 0.138757i | −0.0203589 | − | 0.0147916i | ||||
\(89\) | −3.61803 | + | 2.62866i | −0.383511 | + | 0.278637i | −0.762791 | − | 0.646645i | \(-0.776172\pi\) |
0.379280 | + | 0.925282i | \(0.376172\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.42705 | + | 1.76336i | 0.254424 | + | 0.184850i | ||||
\(92\) | 1.92705 | + | 5.93085i | 0.200909 | + | 0.618334i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.83688 | − | 5.65334i | −0.189460 | − | 0.583097i | ||||
\(95\) | 1.90983 | 0.195944 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.26393 | + | 10.0453i | −0.331402 | + | 1.01995i | 0.637065 | + | 0.770810i | \(0.280148\pi\) |
−0.968467 | + | 0.249141i | \(0.919852\pi\) | |||||||
\(98\) | −1.61803 | + | 1.17557i | −0.163446 | + | 0.118751i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.04508 | + | 2.93893i | −0.404508 | + | 0.293893i | ||||
\(101\) | 1.61803 | 0.161000 | 0.0805002 | − | 0.996755i | \(-0.474348\pi\) | ||||
0.0805002 | + | 0.996755i | \(0.474348\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.13525 | + | 18.8824i | −0.604525 | + | 1.86054i | −0.104499 | + | 0.994525i | \(0.533324\pi\) |
−0.500026 | + | 0.866010i | \(0.666676\pi\) | |||||||
\(104\) | 0.309017 | − | 0.951057i | 0.0303016 | − | 0.0932588i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.472136 | − | 1.45309i | −0.0458579 | − | 0.141136i | ||||
\(107\) | −10.0902 | −0.975454 | −0.487727 | − | 0.872996i | \(-0.662174\pi\) | ||||
−0.487727 | + | 0.872996i | \(0.662174\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.1353 | + | 8.81678i | 1.16235 | + | 0.844494i | 0.990073 | − | 0.140555i | \(-0.0448886\pi\) |
0.172274 | + | 0.985049i | \(0.444889\pi\) | |||||||
\(110\) | 0.427051 | + | 0.310271i | 0.0407177 | + | 0.0295832i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.42705 | + | 1.76336i | 0.229335 | + | 0.166621i | ||||
\(113\) | 6.66312 | + | 4.84104i | 0.626814 | + | 0.455407i | 0.855295 | − | 0.518142i | \(-0.173376\pi\) |
−0.228481 | + | 0.973548i | \(0.573376\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.30902 | − | 13.2618i | −0.401818 | − | 1.23667i | ||||
\(116\) | −0.427051 | − | 0.310271i | −0.0396507 | − | 0.0288079i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.47214 | −0.411693 | ||||||||
\(119\) | 7.28115 | + | 22.4091i | 0.667462 | + | 2.05424i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.38197 | + | 10.4086i | −0.307451 | + | 0.946238i | ||||
\(122\) | −0.663119 | + | 2.04087i | −0.0600360 | + | 0.184772i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.23607 | 0.380410 | ||||||||
\(125\) | 9.04508 | − | 6.57164i | 0.809017 | − | 0.587785i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.0902 | − | 7.33094i | 0.895358 | − | 0.650516i | −0.0419116 | − | 0.999121i | \(-0.513345\pi\) |
0.937269 | + | 0.348606i | \(0.113345\pi\) | |||||||
\(128\) | 0.309017 | − | 0.951057i | 0.0273135 | − | 0.0840623i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.690983 | + | 2.12663i | −0.0606032 | + | 0.186518i | ||||
\(131\) | −3.21885 | − | 9.90659i | −0.281232 | − | 0.865543i | −0.987503 | − | 0.157601i | \(-0.949624\pi\) |
0.706271 | − | 0.707942i | \(-0.250376\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.791796 | + | 2.43690i | 0.0686574 | + | 0.211306i | ||||
\(134\) | 4.66312 | + | 3.38795i | 0.402832 | + | 0.292675i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.35410 | − | 4.61653i | 0.544860 | − | 0.395864i | ||||
\(137\) | −4.92705 | − | 3.57971i | −0.420946 | − | 0.305835i | 0.357072 | − | 0.934077i | \(-0.383775\pi\) |
−0.778018 | + | 0.628241i | \(0.783775\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.35410 | + | 6.06961i | −0.708586 | + | 0.514818i | −0.882717 | − | 0.469905i | \(-0.844288\pi\) |
0.174131 | + | 0.984722i | \(0.444288\pi\) | |||||||
\(140\) | −5.42705 | − | 3.94298i | −0.458670 | − | 0.333243i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.927051 | + | 2.85317i | 0.0777964 | + | 0.239433i | ||||
\(143\) | 0.236068 | 0.0197410 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.954915 | + | 0.693786i | 0.0793014 | + | 0.0576158i | ||||
\(146\) | −1.76393 | + | 5.42882i | −0.145984 | + | 0.449293i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.92705 | + | 4.30625i | −0.487201 | + | 0.353972i | ||||
\(149\) | 2.23607 | 0.183186 | 0.0915929 | − | 0.995797i | \(-0.470804\pi\) | ||||
0.0915929 | + | 0.995797i | \(0.470804\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.70820 | 0.301769 | 0.150885 | − | 0.988551i | \(-0.451788\pi\) | ||||
0.150885 | + | 0.988551i | \(0.451788\pi\) | |||||||
\(152\) | 0.690983 | − | 0.502029i | 0.0560461 | − | 0.0407199i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.218847 | + | 0.673542i | −0.0176352 | + | 0.0542756i | ||||
\(155\) | −9.47214 | −0.760820 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.5623 | −1.24201 | −0.621004 | − | 0.783808i | \(-0.713275\pi\) | ||||
−0.621004 | + | 0.783808i | \(0.713275\pi\) | |||||||
\(158\) | −0.854102 | − | 2.62866i | −0.0679487 | − | 0.209125i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.690983 | + | 2.12663i | −0.0546270 | + | 0.168125i | ||||
\(161\) | 15.1353 | − | 10.9964i | 1.19283 | − | 0.866638i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.92705 | + | 2.85317i | 0.307590 | + | 0.223477i | 0.730862 | − | 0.682525i | \(-0.239118\pi\) |
−0.423271 | + | 0.906003i | \(0.639118\pi\) | |||||||
\(164\) | −6.04508 | + | 4.39201i | −0.472042 | + | 0.342958i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.8992 | − | 7.91872i | −0.845941 | − | 0.614612i | ||||
\(167\) | −4.82624 | − | 14.8536i | −0.373466 | − | 1.14941i | −0.944508 | − | 0.328488i | \(-0.893461\pi\) |
0.571043 | − | 0.820920i | \(-0.306539\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.70820 | − | 11.4127i | −0.285246 | − | 0.877898i | ||||
\(170\) | −14.2082 | + | 10.3229i | −1.08972 | + | 0.791728i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.545085 | + | 1.67760i | −0.0415623 | + | 0.127916i | ||||
\(173\) | 2.61803 | − | 1.90211i | 0.199045 | − | 0.144615i | −0.483798 | − | 0.875180i | \(-0.660743\pi\) |
0.682843 | + | 0.730565i | \(0.260743\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.1353 | + | 8.81678i | 0.917339 | + | 0.666486i | ||||
\(176\) | 0.236068 | 0.0177943 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.38197 | − | 4.25325i | 0.103583 | − | 0.318795i | ||||
\(179\) | 3.45492 | − | 10.6331i | 0.258232 | − | 0.794758i | −0.734943 | − | 0.678129i | \(-0.762791\pi\) |
0.993176 | − | 0.116629i | \(-0.0372089\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.61803 | − | 20.3682i | −0.491915 | − | 1.51396i | −0.821710 | − | 0.569905i | \(-0.806980\pi\) |
0.329796 | − | 0.944052i | \(-0.393020\pi\) | |||||||
\(182\) | −3.00000 | −0.222375 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.04508 | − | 3.66547i | −0.371929 | − | 0.270222i | ||||
\(185\) | 13.2533 | − | 9.62908i | 0.974401 | − | 0.707944i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.50000 | + | 1.08981i | 0.109691 | + | 0.0796951i | ||||
\(188\) | 4.80902 | + | 3.49396i | 0.350734 | + | 0.254823i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.54508 | + | 1.12257i | −0.112092 | + | 0.0814398i | ||||
\(191\) | 14.2812 | + | 10.3759i | 1.03335 | + | 0.750771i | 0.968976 | − | 0.247155i | \(-0.0794956\pi\) |
0.0643719 | + | 0.997926i | \(0.479496\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.6525 | 1.19867 | 0.599336 | − | 0.800498i | \(-0.295431\pi\) | ||||
0.599336 | + | 0.800498i | \(0.295431\pi\) | |||||||
\(194\) | −3.26393 | − | 10.0453i | −0.234337 | − | 0.721214i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.618034 | − | 1.90211i | 0.0441453 | − | 0.135865i | ||||
\(197\) | −3.70820 | + | 11.4127i | −0.264199 | + | 0.813120i | 0.727678 | + | 0.685919i | \(0.240599\pi\) |
−0.991877 | + | 0.127201i | \(0.959401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.5623 | −1.24496 | −0.622479 | − | 0.782636i | \(-0.713875\pi\) | ||||
−0.622479 | + | 0.782636i | \(0.713875\pi\) | |||||||
\(200\) | 1.54508 | − | 4.75528i | 0.109254 | − | 0.336249i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.30902 | + | 0.951057i | −0.0921021 | + | 0.0669161i | ||||
\(203\) | −0.489357 | + | 1.50609i | −0.0343461 | + | 0.105706i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.5172 | − | 9.82084i | 0.944084 | − | 0.685917i | ||||
\(206\) | −6.13525 | − | 18.8824i | −0.427463 | − | 1.31560i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.309017 | + | 0.951057i | 0.0214265 | + | 0.0659439i | ||||
\(209\) | 0.163119 | + | 0.118513i | 0.0112832 | + | 0.00819771i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.11803 | + | 6.62464i | −0.627711 | + | 0.456059i | −0.855607 | − | 0.517627i | \(-0.826816\pi\) |
0.227895 | + | 0.973686i | \(0.426816\pi\) | |||||||
\(212\) | 1.23607 | + | 0.898056i | 0.0848935 | + | 0.0616787i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.16312 | − | 5.93085i | 0.558019 | − | 0.405425i | ||||
\(215\) | 1.21885 | − | 3.75123i | 0.0831247 | − | 0.255831i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.92705 | − | 12.0862i | −0.266586 | − | 0.820466i | ||||
\(218\) | −15.0000 | −1.01593 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.527864 | −0.0355886 | ||||||||
\(221\) | −2.42705 | + | 7.46969i | −0.163261 | + | 0.502466i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.28115 | − | 5.29007i | 0.487582 | − | 0.354249i | −0.316672 | − | 0.948535i | \(-0.602565\pi\) |
0.804254 | + | 0.594286i | \(0.202565\pi\) | |||||||
\(224\) | −3.00000 | −0.200446 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.23607 | −0.547855 | ||||||||
\(227\) | −12.4271 | + | 9.02878i | −0.824812 | + | 0.599261i | −0.918087 | − | 0.396379i | \(-0.870267\pi\) |
0.0932746 | + | 0.995640i | \(0.470267\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.42705 | − | 16.7027i | 0.358630 | − | 1.10375i | −0.595245 | − | 0.803544i | \(-0.702945\pi\) |
0.953875 | − | 0.300204i | \(-0.0970549\pi\) | |||||||
\(230\) | 11.2812 | + | 8.19624i | 0.743857 | + | 0.540444i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.527864 | 0.0346560 | ||||||||
\(233\) | −8.56231 | − | 26.3521i | −0.560935 | − | 1.72638i | −0.679730 | − | 0.733463i | \(-0.737903\pi\) |
0.118795 | − | 0.992919i | \(-0.462097\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.7533 | − | 7.81272i | −0.701467 | − | 0.509646i | ||||
\(236\) | 3.61803 | − | 2.62866i | 0.235514 | − | 0.171111i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −19.0623 | − | 13.8496i | −1.23563 | − | 0.897735i | ||||
\(239\) | −14.6353 | + | 10.6331i | −0.946676 | + | 0.687800i | −0.950018 | − | 0.312194i | \(-0.898936\pi\) |
0.00334240 | + | 0.999994i | \(0.498936\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.8262 | − | 7.86572i | −0.697379 | − | 0.506676i | 0.181698 | − | 0.983354i | \(-0.441841\pi\) |
−0.879078 | + | 0.476679i | \(0.841841\pi\) | |||||||
\(242\) | −3.38197 | − | 10.4086i | −0.217401 | − | 0.669092i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.663119 | − | 2.04087i | −0.0424518 | − | 0.130653i | ||||
\(245\) | −1.38197 | + | 4.25325i | −0.0882906 | + | 0.271730i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.263932 | + | 0.812299i | −0.0167936 | + | 0.0516854i | ||||
\(248\) | −3.42705 | + | 2.48990i | −0.217618 | + | 0.158109i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.45492 | + | 10.6331i | −0.218508 | + | 0.672499i | ||||
\(251\) | −23.1803 | −1.46313 | −0.731565 | − | 0.681772i | \(-0.761210\pi\) | ||||
−0.731565 | + | 0.681772i | \(0.761210\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.454915 | − | 1.40008i | 0.0286003 | − | 0.0880226i | ||||
\(254\) | −3.85410 | + | 11.8617i | −0.241828 | + | 0.744270i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | 16.7426 | 1.04438 | 0.522189 | − | 0.852830i | \(-0.325116\pi\) | ||||
0.522189 | + | 0.852830i | \(0.325116\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.7812 | + | 12.9188i | 1.10487 | + | 0.802733i | ||||
\(260\) | −0.690983 | − | 2.12663i | −0.0428529 | − | 0.131888i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.42705 | + | 6.12261i | 0.520625 | + | 0.378256i | ||||
\(263\) | 1.92705 | + | 1.40008i | 0.118827 | + | 0.0863329i | 0.645612 | − | 0.763666i | \(-0.276603\pi\) |
−0.526785 | + | 0.849999i | \(0.676603\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.76393 | − | 2.00811i | −0.169787 | − | 0.123357i | ||||
\(266\) | −2.07295 | − | 1.50609i | −0.127101 | − | 0.0923440i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.76393 | −0.352088 | ||||||||
\(269\) | −4.04508 | − | 12.4495i | −0.246633 | − | 0.759059i | −0.995364 | − | 0.0961842i | \(-0.969336\pi\) |
0.748730 | − | 0.662875i | \(-0.230664\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.93769 | + | 9.04129i | −0.178452 | + | 0.549219i | −0.999774 | − | 0.0212453i | \(-0.993237\pi\) |
0.821322 | + | 0.570465i | \(0.193237\pi\) | |||||||
\(272\) | −2.42705 | + | 7.46969i | −0.147162 | + | 0.452917i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.09017 | 0.367921 | ||||||||
\(275\) | 1.18034 | 0.0711772 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.0902 | + | 8.05748i | −0.666344 | + | 0.484127i | −0.868799 | − | 0.495164i | \(-0.835108\pi\) |
0.202456 | + | 0.979291i | \(0.435108\pi\) | |||||||
\(278\) | 3.19098 | − | 9.82084i | 0.191382 | − | 0.589015i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.70820 | 0.400892 | ||||||||
\(281\) | 5.92705 | + | 18.2416i | 0.353578 | + | 1.08820i | 0.956829 | + | 0.290651i | \(0.0938717\pi\) |
−0.603251 | + | 0.797551i | \(0.706128\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.94427 | − | 24.4500i | −0.472238 | − | 1.45340i | −0.849647 | − | 0.527352i | \(-0.823185\pi\) |
0.377409 | − | 0.926047i | \(-0.376815\pi\) | |||||||
\(284\) | −2.42705 | − | 1.76336i | −0.144019 | − | 0.104636i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.190983 | + | 0.138757i | −0.0112931 | + | 0.00820489i | ||||
\(287\) | 18.1353 | + | 13.1760i | 1.07049 | + | 0.777757i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −36.1525 | + | 26.2663i | −2.12662 | + | 1.54508i | ||||
\(290\) | −1.18034 | −0.0693119 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.76393 | − | 5.42882i | −0.103226 | − | 0.317698i | ||||
\(293\) | 11.5623 | 0.675477 | 0.337739 | − | 0.941240i | \(-0.390338\pi\) | ||||
0.337739 | + | 0.941240i | \(0.390338\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.09017 | + | 5.87785i | −0.471028 | + | 0.342222i | ||||
\(296\) | 2.26393 | − | 6.96767i | 0.131588 | − | 0.404987i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.80902 | + | 1.31433i | −0.104794 | + | 0.0761370i | ||||
\(299\) | 6.23607 | 0.360641 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.29180 | 0.305014 | ||||||||
\(302\) | −3.00000 | + | 2.17963i | −0.172631 | + | 0.125423i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.263932 | + | 0.812299i | −0.0151375 | + | 0.0465886i | ||||
\(305\) | 1.48278 | + | 4.56352i | 0.0849037 | + | 0.261307i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.1246 | 0.977353 | 0.488677 | − | 0.872465i | \(-0.337480\pi\) | ||||
0.488677 | + | 0.872465i | \(0.337480\pi\) | |||||||
\(308\) | −0.218847 | − | 0.673542i | −0.0124700 | − | 0.0383786i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.66312 | − | 5.56758i | 0.435236 | − | 0.316217i | ||||
\(311\) | −17.0623 | + | 12.3965i | −0.967515 | + | 0.702941i | −0.954884 | − | 0.296980i | \(-0.904021\pi\) |
−0.0126308 | + | 0.999920i | \(0.504021\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.88197 | − | 2.09387i | −0.162898 | − | 0.118353i | 0.503350 | − | 0.864083i | \(-0.332101\pi\) |
−0.666248 | + | 0.745730i | \(0.732101\pi\) | |||||||
\(314\) | 12.5902 | − | 9.14729i | 0.710504 | − | 0.516212i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.23607 | + | 1.62460i | 0.125789 | + | 0.0913908i | ||||
\(317\) | −3.28115 | − | 10.0984i | −0.184288 | − | 0.567180i | 0.815647 | − | 0.578549i | \(-0.196381\pi\) |
−0.999935 | + | 0.0113694i | \(0.996381\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0385072 | + | 0.118513i | 0.00215599 | + | 0.00663545i | ||||
\(320\) | −0.690983 | − | 2.12663i | −0.0386271 | − | 0.118882i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.78115 | + | 17.7926i | −0.322171 | + | 0.991541i | ||||
\(323\) | −5.42705 | + | 3.94298i | −0.301969 | + | 0.219393i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.54508 | + | 4.75528i | 0.0857059 | + | 0.263776i | ||||
\(326\) | −4.85410 | −0.268844 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.30902 | − | 7.10642i | 0.127494 | − | 0.392387i | ||||
\(329\) | 5.51064 | − | 16.9600i | 0.303812 | − | 0.935036i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.40983 | + | 4.33901i | 0.0774913 | + | 0.238494i | 0.982297 | − | 0.187332i | \(-0.0599839\pi\) |
−0.904805 | + | 0.425825i | \(0.859984\pi\) | |||||||
\(332\) | 13.4721 | 0.739380 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.6353 | + | 9.18005i | 0.691370 | + | 0.502310i | ||||
\(335\) | 12.8885 | 0.704176 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.4164 | + | 18.4661i | 1.38452 | + | 1.00591i | 0.996442 | + | 0.0842863i | \(0.0268610\pi\) |
0.388078 | + | 0.921626i | \(0.373139\pi\) | |||||||
\(338\) | 9.70820 | + | 7.05342i | 0.528057 | + | 0.383656i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.42705 | − | 16.7027i | 0.294323 | − | 0.905834i | ||||
\(341\) | −0.809017 | − | 0.587785i | −0.0438107 | − | 0.0318304i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | −0.545085 | − | 1.67760i | −0.0293890 | − | 0.0904501i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.00000 | + | 3.07768i | −0.0537603 | + | 0.165457i | ||||
\(347\) | 3.06231 | − | 9.42481i | 0.164393 | − | 0.505950i | −0.834598 | − | 0.550860i | \(-0.814300\pi\) |
0.998991 | + | 0.0449095i | \(0.0142999\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.2361 | −1.19027 | −0.595135 | − | 0.803626i | \(-0.702901\pi\) | ||||
−0.595135 | + | 0.803626i | \(0.702901\pi\) | |||||||
\(350\) | −15.0000 | −0.801784 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.190983 | + | 0.138757i | −0.0101794 | + | 0.00739579i | ||||
\(353\) | 5.18034 | − | 15.9434i | 0.275722 | − | 0.848584i | −0.713306 | − | 0.700853i | \(-0.752803\pi\) |
0.989028 | − | 0.147731i | \(-0.0471970\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.42705 | + | 3.94298i | 0.288038 | + | 0.209272i | ||||
\(356\) | 1.38197 | + | 4.25325i | 0.0732441 | + | 0.225422i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.45492 | + | 10.6331i | 0.182598 | + | 0.561979i | ||||
\(359\) | 2.50000 | + | 1.81636i | 0.131945 | + | 0.0958636i | 0.651800 | − | 0.758391i | \(-0.274014\pi\) |
−0.519855 | + | 0.854254i | \(0.674014\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.7812 | − | 10.7391i | 0.777955 | − | 0.565218i | ||||
\(362\) | 17.3262 | + | 12.5882i | 0.910647 | + | 0.661624i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.42705 | − | 1.76336i | 0.127212 | − | 0.0924250i | ||||
\(365\) | 3.94427 | + | 12.1392i | 0.206453 | + | 0.635396i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.74671 | − | 29.9973i | −0.508774 | − | 1.56585i | −0.794332 | − | 0.607484i | \(-0.792179\pi\) |
0.285557 | − | 0.958362i | \(-0.407821\pi\) | |||||||
\(368\) | 6.23607 | 0.325078 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.06231 | + | 15.5802i | −0.263177 | + | 0.809975i | ||||
\(371\) | 1.41641 | − | 4.35926i | 0.0735362 | − | 0.226321i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.1353 | − | 9.54332i | 0.680118 | − | 0.494134i | −0.193279 | − | 0.981144i | \(-0.561912\pi\) |
0.873397 | + | 0.487009i | \(0.161912\pi\) | |||||||
\(374\) | −1.85410 | −0.0958733 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.94427 | −0.306552 | ||||||||
\(377\) | −0.427051 | + | 0.310271i | −0.0219942 | + | 0.0159798i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.163119 | − | 0.502029i | 0.00837886 | − | 0.0257875i | −0.946780 | − | 0.321882i | \(-0.895684\pi\) |
0.955159 | + | 0.296095i | \(0.0956845\pi\) | |||||||
\(380\) | 0.590170 | − | 1.81636i | 0.0302751 | − | 0.0931771i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17.6525 | −0.903179 | ||||||||
\(383\) | 1.33688 | + | 4.11450i | 0.0683114 | + | 0.210241i | 0.979385 | − | 0.202003i | \(-0.0647451\pi\) |
−0.911073 | + | 0.412244i | \(0.864745\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.489357 | + | 1.50609i | 0.0249399 | + | 0.0767572i | ||||
\(386\) | −13.4721 | + | 9.78808i | −0.685714 | + | 0.498200i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.54508 | + | 6.20837i | 0.433811 | + | 0.315182i | ||||
\(389\) | −26.8713 | + | 19.5232i | −1.36243 | + | 0.989863i | −0.364144 | + | 0.931343i | \(0.618638\pi\) |
−0.998286 | + | 0.0585208i | \(0.981362\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 39.6246 | + | 28.7890i | 2.00390 | + | 1.45592i | ||||
\(392\) | 0.618034 | + | 1.90211i | 0.0312154 | + | 0.0960712i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.70820 | − | 11.4127i | −0.186817 | − | 0.574962i | ||||
\(395\) | −5.00000 | − | 3.63271i | −0.251577 | − | 0.182782i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.78115 | + | 5.48183i | −0.0893935 | + | 0.275125i | −0.985752 | − | 0.168205i | \(-0.946203\pi\) |
0.896359 | + | 0.443330i | \(0.146203\pi\) | |||||||
\(398\) | 14.2082 | − | 10.3229i | 0.712193 | − | 0.517438i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.54508 | + | 4.75528i | 0.0772542 | + | 0.237764i | ||||
\(401\) | −8.18034 | −0.408507 | −0.204253 | − | 0.978918i | \(-0.565477\pi\) | ||||
−0.204253 | + | 0.978918i | \(0.565477\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.30902 | − | 4.02874i | 0.0652068 | − | 0.200686i | ||||
\(404\) | 0.500000 | − | 1.53884i | 0.0248759 | − | 0.0765602i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.489357 | − | 1.50609i | −0.0242864 | − | 0.0747458i | ||||
\(407\) | 1.72949 | 0.0857276 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.42705 | − | 3.94298i | −0.268350 | − | 0.194968i | 0.445470 | − | 0.895297i | \(-0.353037\pi\) |
−0.713820 | + | 0.700329i | \(0.753037\pi\) | |||||||
\(410\) | −5.16312 | + | 15.8904i | −0.254988 | + | 0.784773i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.0623 | + | 11.6699i | 0.791333 | + | 0.574937i | ||||
\(413\) | −10.8541 | − | 7.88597i | −0.534095 | − | 0.388043i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −30.1246 | −1.47876 | ||||||||
\(416\) | −0.809017 | − | 0.587785i | −0.0396653 | − | 0.0288185i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.201626 | −0.00986186 | ||||||||
\(419\) | −8.41641 | − | 25.9030i | −0.411168 | − | 1.26545i | −0.915633 | − | 0.402014i | \(-0.868310\pi\) |
0.504465 | − | 0.863432i | \(-0.331690\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.79180 | + | 11.6699i | −0.184801 | + | 0.568758i | −0.999945 | − | 0.0104998i | \(-0.996658\pi\) |
0.815144 | + | 0.579258i | \(0.196658\pi\) | |||||||
\(422\) | 3.48278 | − | 10.7189i | 0.169539 | − | 0.521787i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.52786 | −0.0741996 | ||||||||
\(425\) | −12.1353 | + | 37.3485i | −0.588646 | + | 1.81167i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.20820 | + | 3.78398i | −0.252043 | + | 0.183120i | ||||
\(428\) | −3.11803 | + | 9.59632i | −0.150716 | + | 0.463856i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.21885 | + | 3.75123i | 0.0587780 | + | 0.180900i | ||||
\(431\) | 9.90983 | + | 30.4993i | 0.477340 | + | 1.46910i | 0.842776 | + | 0.538264i | \(0.180920\pi\) |
−0.365436 | + | 0.930836i | \(0.619080\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.21885 | + | 22.2173i | 0.346916 | + | 1.06770i | 0.960550 | + | 0.278106i | \(0.0897068\pi\) |
−0.613635 | + | 0.789590i | \(0.710293\pi\) | |||||||
\(434\) | 10.2812 | + | 7.46969i | 0.493511 | + | 0.358557i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.1353 | − | 8.81678i | 0.581173 | − | 0.422247i | ||||
\(437\) | 4.30902 | + | 3.13068i | 0.206128 | + | 0.149761i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.57295 | − | 3.32244i | 0.218255 | − | 0.158572i | −0.473286 | − | 0.880909i | \(-0.656932\pi\) |
0.691541 | + | 0.722337i | \(0.256932\pi\) | |||||||
\(440\) | 0.427051 | − | 0.310271i | 0.0203589 | − | 0.0147916i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.42705 | − | 7.46969i | −0.115443 | − | 0.355297i | ||||
\(443\) | 7.41641 | 0.352364 | 0.176182 | − | 0.984358i | \(-0.443625\pi\) | ||||
0.176182 | + | 0.984358i | \(0.443625\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.09017 | − | 9.51057i | −0.146488 | − | 0.450844i | ||||
\(446\) | −2.78115 | + | 8.55951i | −0.131691 | + | 0.405304i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.42705 | − | 1.76336i | 0.114667 | − | 0.0833107i | ||||
\(449\) | −13.9443 | −0.658071 | −0.329035 | − | 0.944318i | \(-0.606724\pi\) | ||||
−0.329035 | + | 0.944318i | \(0.606724\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.76393 | 0.0830603 | ||||||||
\(452\) | 6.66312 | − | 4.84104i | 0.313407 | − | 0.227703i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.74671 | − | 14.6089i | 0.222774 | − | 0.685628i | ||||
\(455\) | −5.42705 | + | 3.94298i | −0.254424 | + | 0.184850i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.2148 | −0.524605 | −0.262303 | − | 0.964986i | \(-0.584482\pi\) | ||||
−0.262303 | + | 0.964986i | \(0.584482\pi\) | |||||||
\(458\) | 5.42705 | + | 16.7027i | 0.253589 | + | 0.780468i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −13.9443 | −0.650155 | ||||||||
\(461\) | 22.7984 | − | 16.5640i | 1.06183 | − | 0.771462i | 0.0874008 | − | 0.996173i | \(-0.472144\pi\) |
0.974425 | + | 0.224711i | \(0.0721439\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.69098 | − | 7.04091i | −0.450378 | − | 0.327219i | 0.339367 | − | 0.940654i | \(-0.389787\pi\) |
−0.789745 | + | 0.613435i | \(0.789787\pi\) | |||||||
\(464\) | −0.427051 | + | 0.310271i | −0.0198253 | + | 0.0144040i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.4164 | + | 16.2865i | 1.03842 | + | 0.754456i | ||||
\(467\) | −0.982779 | − | 3.02468i | −0.0454776 | − | 0.139966i | 0.925739 | − | 0.378162i | \(-0.123444\pi\) |
−0.971217 | + | 0.238196i | \(0.923444\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.34346 | + | 16.4455i | 0.246738 | + | 0.759381i | ||||
\(470\) | 13.2918 | 0.613105 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.38197 | + | 4.25325i | −0.0636101 | + | 0.195772i | ||||
\(473\) | 0.336881 | − | 0.244758i | 0.0154898 | − | 0.0112540i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.31966 | + | 4.06150i | −0.0605502 | + | 0.186354i | ||||
\(476\) | 23.5623 | 1.07998 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.59017 | − | 17.2048i | 0.255688 | − | 0.786928i | ||||
\(479\) | 12.2984 | − | 37.8505i | 0.561927 | − | 1.72943i | −0.114983 | − | 0.993368i | \(-0.536681\pi\) |
0.676910 | − | 0.736066i | \(-0.263319\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.26393 | + | 6.96767i | 0.103226 | + | 0.317698i | ||||
\(482\) | 13.3820 | 0.609532 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.85410 | + | 6.43288i | 0.402459 | + | 0.292404i | ||||
\(485\) | −19.1074 | − | 13.8823i | −0.867622 | − | 0.630364i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.6631 | + | 10.6534i | 0.664449 | + | 0.482751i | 0.868163 | − | 0.496280i | \(-0.165301\pi\) |
−0.203713 | + | 0.979031i | \(0.565301\pi\) | |||||||
\(488\) | 1.73607 | + | 1.26133i | 0.0785881 | + | 0.0570976i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.38197 | − | 4.25325i | −0.0624309 | − | 0.192142i | ||||
\(491\) | 11.9443 | + | 8.67802i | 0.539037 | + | 0.391634i | 0.823727 | − | 0.566986i | \(-0.191891\pi\) |
−0.284690 | + | 0.958620i | \(0.591891\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.14590 | −0.186722 | ||||||||
\(494\) | −0.263932 | − | 0.812299i | −0.0118749 | − | 0.0365471i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.30902 | − | 4.02874i | 0.0587766 | − | 0.180896i | ||||
\(497\) | −2.78115 | + | 8.55951i | −0.124752 | + | 0.383946i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 40.8541 | 1.82888 | 0.914440 | − | 0.404721i | \(-0.132631\pi\) | ||||
0.914440 | + | 0.404721i | \(0.132631\pi\) | |||||||
\(500\) | −3.45492 | − | 10.6331i | −0.154508 | − | 0.475528i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.7533 | − | 13.6251i | 0.837000 | − | 0.608116i | ||||
\(503\) | −2.31966 | + | 7.13918i | −0.103429 | + | 0.318320i | −0.989358 | − | 0.145499i | \(-0.953521\pi\) |
0.885930 | + | 0.463819i | \(0.153521\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.11803 | + | 3.44095i | −0.0497519 | + | 0.153120i | ||||
\(506\) | 0.454915 | + | 1.40008i | 0.0202234 | + | 0.0622413i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.85410 | − | 11.8617i | −0.170998 | − | 0.526278i | ||||
\(509\) | −10.5902 | − | 7.69421i | −0.469401 | − | 0.341040i | 0.327807 | − | 0.944745i | \(-0.393690\pi\) |
−0.797208 | + | 0.603705i | \(0.793690\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.8541 | + | 10.0656i | −0.612869 | + | 0.445276i | ||||
\(512\) | −0.809017 | − | 0.587785i | −0.0357538 | − | 0.0259767i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.5451 | + | 9.84108i | −0.597448 | + | 0.434071i | ||||
\(515\) | −35.9164 | − | 26.0948i | −1.58267 | − | 1.14987i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.433629 | − | 1.33457i | −0.0190710 | − | 0.0586944i | ||||
\(518\) | −21.9787 | −0.965689 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.80902 | + | 1.31433i | 0.0793306 | + | 0.0576371i | ||||
\(521\) | −10.0279 | + | 30.8626i | −0.439329 | + | 1.35211i | 0.449256 | + | 0.893403i | \(0.351689\pi\) |
−0.888585 | + | 0.458712i | \(0.848311\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.5623 | + | 15.6659i | −0.942854 | + | 0.685023i | −0.949106 | − | 0.314957i | \(-0.898010\pi\) |
0.00625211 | + | 0.999980i | \(0.498010\pi\) | |||||||
\(524\) | −10.4164 | −0.455043 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.38197 | −0.103859 | ||||||||
\(527\) | 26.9164 | − | 19.5559i | 1.17250 | − | 0.851869i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.90983 | − | 15.1109i | 0.213471 | − | 0.656996i | ||||
\(530\) | 3.41641 | 0.148399 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.56231 | 0.111090 | ||||||||
\(533\) | 2.30902 | + | 7.10642i | 0.100015 | + | 0.307813i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.97214 | − | 21.4580i | 0.301432 | − | 0.927711i | ||||
\(536\) | 4.66312 | − | 3.38795i | 0.201416 | − | 0.146337i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.5902 | + | 7.69421i | 0.456575 | + | 0.331721i | ||||
\(539\) | −0.381966 | + | 0.277515i | −0.0164524 | + | 0.0119534i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.2254 | − | 16.8743i | −0.998539 | − | 0.725481i | −0.0367646 | − | 0.999324i | \(-0.511705\pi\) |
−0.961774 | + | 0.273843i | \(0.911705\pi\) | |||||||
\(542\) | −2.93769 | − | 9.04129i | −0.126185 | − | 0.388357i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.42705 | − | 7.46969i | −0.104059 | − | 0.320261i | ||||
\(545\) | −27.1353 | + | 19.7149i | −1.16235 | + | 0.844494i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.28115 | − | 10.0984i | 0.140292 | − | 0.431774i | −0.856084 | − | 0.516837i | \(-0.827109\pi\) |
0.996376 | + | 0.0850631i | \(0.0271092\pi\) | |||||||
\(548\) | −4.92705 | + | 3.57971i | −0.210473 | + | 0.152918i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.954915 | + | 0.693786i | −0.0407177 | + | 0.0295832i | ||||
\(551\) | −0.450850 | −0.0192068 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.56231 | − | 7.88597i | 0.108960 | − | 0.335345i | ||||
\(554\) | 4.23607 | − | 13.0373i | 0.179973 | − | 0.553901i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.19098 | + | 9.82084i | 0.135328 | + | 0.416496i | ||||
\(557\) | 10.8885 | 0.461362 | 0.230681 | − | 0.973029i | \(-0.425905\pi\) | ||||
0.230681 | + | 0.973029i | \(0.425905\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.42705 | + | 1.03681i | 0.0603578 | + | 0.0438525i | ||||
\(560\) | −5.42705 | + | 3.94298i | −0.229335 | + | 0.166621i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.5172 | − | 11.2739i | −0.654554 | − | 0.475562i | ||||
\(563\) | −28.1976 | − | 20.4867i | −1.18839 | − | 0.863413i | −0.195293 | − | 0.980745i | \(-0.562566\pi\) |
−0.993093 | + | 0.117332i | \(0.962566\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.8992 | + | 10.8249i | −0.626814 | + | 0.455407i | ||||
\(566\) | 20.7984 | + | 15.1109i | 0.874221 | + | 0.635159i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.00000 | 0.125877 | ||||||||
\(569\) | −6.87132 | − | 21.1478i | −0.288061 | − | 0.886560i | −0.985464 | − | 0.169882i | \(-0.945661\pi\) |
0.697404 | − | 0.716679i | \(-0.254339\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.517221 | − | 1.59184i | 0.0216450 | − | 0.0666165i | −0.939651 | − | 0.342136i | \(-0.888850\pi\) |
0.961296 | + | 0.275519i | \(0.0888497\pi\) | |||||||
\(572\) | 0.0729490 | − | 0.224514i | 0.00305015 | − | 0.00938740i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −22.4164 | −0.935643 | ||||||||
\(575\) | 31.1803 | 1.30031 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.7877 | − | 25.2748i | 1.44823 | − | 1.05220i | 0.461992 | − | 0.886884i | \(-0.347135\pi\) |
0.986240 | − | 0.165318i | \(-0.0528651\pi\) | |||||||
\(578\) | 13.8090 | − | 42.4998i | 0.574379 | − | 1.76776i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.954915 | − | 0.693786i | 0.0396507 | − | 0.0288079i | ||||
\(581\) | −12.4894 | − | 38.4383i | −0.518146 | − | 1.59469i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.111456 | − | 0.343027i | −0.00461604 | − | 0.0142067i | ||||
\(584\) | 4.61803 | + | 3.35520i | 0.191096 | + | 0.138839i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.35410 | + | 6.79615i | −0.386414 | + | 0.280746i | ||||
\(587\) | −9.56231 | − | 6.94742i | −0.394679 | − | 0.286751i | 0.372691 | − | 0.927955i | \(-0.378435\pi\) |
−0.767370 | + | 0.641205i | \(0.778435\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.92705 | − | 2.12663i | 0.120607 | − | 0.0876261i | ||||
\(590\) | 3.09017 | − | 9.51057i | 0.127220 | − | 0.391544i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.26393 | + | 6.96767i | 0.0930470 | + | 0.286369i | ||||
\(593\) | 47.0132 | 1.93060 | 0.965299 | − | 0.261145i | \(-0.0841002\pi\) | ||||
0.965299 | + | 0.261145i | \(0.0841002\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −52.6869 | −2.15995 | ||||||||
\(596\) | 0.690983 | − | 2.12663i | 0.0283038 | − | 0.0871100i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.04508 | + | 3.66547i | −0.206309 | + | 0.149892i | ||||
\(599\) | 8.94427 | 0.365453 | 0.182727 | − | 0.983164i | \(-0.441508\pi\) | ||||
0.182727 | + | 0.983164i | \(0.441508\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.8328 | −0.605043 | −0.302522 | − | 0.953143i | \(-0.597828\pi\) | ||||
−0.302522 | + | 0.953143i | \(0.597828\pi\) | |||||||
\(602\) | −4.28115 | + | 3.11044i | −0.174487 | + | 0.126772i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.14590 | − | 3.52671i | 0.0466259 | − | 0.143500i | ||||
\(605\) | −19.7984 | − | 14.3844i | −0.804918 | − | 0.584807i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.1459 | −1.10182 | −0.550909 | − | 0.834565i | \(-0.685719\pi\) | ||||
−0.550909 | + | 0.834565i | \(0.685719\pi\) | |||||||
\(608\) | −0.263932 | − | 0.812299i | −0.0107039 | − | 0.0329431i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.88197 | − | 2.82041i | −0.157176 | − | 0.114195i | ||||
\(611\) | 4.80902 | − | 3.49396i | 0.194552 | − | 0.141350i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.6246 | + | 24.4297i | 1.35809 | + | 0.986707i | 0.998564 | + | 0.0535698i | \(0.0170600\pi\) |
0.359521 | + | 0.933137i | \(0.382940\pi\) | |||||||
\(614\) | −13.8541 | + | 10.0656i | −0.559106 | + | 0.406214i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.572949 | + | 0.416272i | 0.0230848 | + | 0.0167721i | ||||
\(617\) | 9.38197 | + | 28.8747i | 0.377704 | + | 1.16245i | 0.941636 | + | 0.336632i | \(0.109288\pi\) |
−0.563933 | + | 0.825821i | \(0.690712\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.5106 | − | 44.6592i | −0.583232 | − | 1.79500i | −0.606257 | − | 0.795269i | \(-0.707330\pi\) |
0.0230252 | − | 0.999735i | \(-0.492670\pi\) | |||||||
\(620\) | −2.92705 | + | 9.00854i | −0.117553 | + | 0.361792i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.51722 | − | 20.0579i | 0.261317 | − | 0.804250i | ||||
\(623\) | 10.8541 | − | 7.88597i | 0.434860 | − | 0.315945i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.72542 | + | 23.7764i | 0.309017 | + | 0.951057i | ||||
\(626\) | 3.56231 | 0.142378 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.80902 | + | 14.8006i | −0.191901 | + | 0.590610i | ||||
\(629\) | −17.7812 | + | 54.7248i | −0.708981 | + | 2.18202i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.72949 | + | 8.40051i | 0.108659 | + | 0.334419i | 0.990572 | − | 0.136994i | \(-0.0437441\pi\) |
−0.881913 | + | 0.471413i | \(0.843744\pi\) | |||||||
\(632\) | −2.76393 | −0.109943 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.59017 | + | 6.24112i | 0.341159 | + | 0.247867i | ||||
\(635\) | 8.61803 | + | 26.5236i | 0.341996 | + | 1.05256i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.61803 | − | 1.17557i | −0.0641088 | − | 0.0465778i | ||||
\(638\) | −0.100813 | − | 0.0732450i | −0.00399123 | − | 0.00289980i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.80902 | + | 1.31433i | 0.0715077 | + | 0.0519534i | ||||
\(641\) | 11.6180 | + | 8.44100i | 0.458885 | + | 0.333399i | 0.793094 | − | 0.609100i | \(-0.208469\pi\) |
−0.334209 | + | 0.942499i | \(0.608469\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.2361 | −1.42901 | −0.714506 | − | 0.699630i | \(-0.753348\pi\) | ||||
−0.714506 | + | 0.699630i | \(0.753348\pi\) | |||||||
\(644\) | −5.78115 | − | 17.7926i | −0.227809 | − | 0.701125i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.07295 | − | 6.37988i | 0.0815591 | − | 0.251013i | ||||
\(647\) | −2.36475 | + | 7.27794i | −0.0929677 | + | 0.286125i | −0.986719 | − | 0.162438i | \(-0.948064\pi\) |
0.893751 | + | 0.448563i | \(0.148064\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.05573 | −0.0414410 | ||||||||
\(650\) | −4.04508 | − | 2.93893i | −0.158661 | − | 0.115274i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.92705 | − | 2.85317i | 0.153795 | − | 0.111739i | ||||
\(653\) | −12.5451 | + | 38.6098i | −0.490927 | + | 1.51092i | 0.332282 | + | 0.943180i | \(0.392181\pi\) |
−0.823209 | + | 0.567738i | \(0.807819\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.2918 | 0.910086 | ||||||||
\(656\) | 2.30902 | + | 7.10642i | 0.0901520 | + | 0.277459i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.51064 | + | 16.9600i | 0.214827 | + | 0.661170i | ||||
\(659\) | 4.57295 | + | 3.32244i | 0.178137 | + | 0.129424i | 0.673281 | − | 0.739387i | \(-0.264885\pi\) |
−0.495144 | + | 0.868811i | \(0.664885\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.07295 | + | 3.68571i | −0.197315 | + | 0.143358i | −0.682056 | − | 0.731300i | \(-0.738914\pi\) |
0.484741 | + | 0.874658i | \(0.338914\pi\) | |||||||
\(662\) | −3.69098 | − | 2.68166i | −0.143454 | − | 0.104226i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.8992 | + | 7.91872i | −0.422970 | + | 0.307306i | ||||
\(665\) | −5.72949 | −0.222180 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.01722 | + | 3.13068i | 0.0393870 | + | 0.121221i | ||||
\(668\) | −15.6180 | −0.604280 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.4271 | + | 7.57570i | −0.402832 | + | 0.292675i | ||||
\(671\) | −0.156541 | + | 0.481784i | −0.00604320 | + | 0.0185991i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.00000 | − | 0.726543i | 0.0385472 | − | 0.0280062i | −0.568345 | − | 0.822790i | \(-0.692416\pi\) |
0.606892 | + | 0.794784i | \(0.292416\pi\) | |||||||
\(674\) | −31.4164 | −1.21011 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | 8.59017 | − | 6.24112i | 0.330147 | − | 0.239866i | −0.410346 | − | 0.911930i | \(-0.634592\pi\) |
0.740493 | + | 0.672064i | \(0.234592\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.79180 | − | 30.1360i | 0.375775 | − | 1.15652i | ||||
\(680\) | 5.42705 | + | 16.7027i | 0.208118 | + | 0.640521i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.00000 | 0.0382920 | ||||||||
\(683\) | −10.3090 | − | 31.7279i | −0.394464 | − | 1.21403i | −0.929379 | − | 0.369128i | \(-0.879656\pi\) |
0.534915 | − | 0.844906i | \(-0.320344\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.0172 | − | 8.00448i | 0.420946 | − | 0.305835i | ||||
\(686\) | −12.1353 | + | 8.81678i | −0.463326 | + | 0.336626i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.42705 | + | 1.03681i | 0.0544058 | + | 0.0395281i | ||||
\(689\) | 1.23607 | − | 0.898056i | 0.0470904 | − | 0.0342132i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.02786 | − | 0.746787i | −0.0391018 | − | 0.0284091i | 0.568063 | − | 0.822985i | \(-0.307693\pi\) |
−0.607164 | + | 0.794576i | \(0.707693\pi\) | |||||||
\(692\) | −1.00000 | − | 3.07768i | −0.0380143 | − | 0.116996i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.06231 | + | 9.42481i | 0.116244 | + | 0.357761i | ||||
\(695\) | −7.13525 | − | 21.9601i | −0.270656 | − | 0.832992i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.1353 | + | 55.8146i | −0.686922 | + | 2.11413i | ||||
\(698\) | 17.9894 | − | 13.0700i | 0.680907 | − | 0.494708i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 12.1353 | − | 8.81678i | 0.458670 | − | 0.333243i | ||||
\(701\) | 4.18034 | 0.157889 | 0.0789446 | − | 0.996879i | \(-0.474845\pi\) | ||||
0.0789446 | + | 0.996879i | \(0.474845\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.93363 | + | 5.95110i | −0.0729282 | + | 0.224450i | ||||
\(704\) | 0.0729490 | − | 0.224514i | 0.00274937 | − | 0.00846169i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.18034 | + | 15.9434i | 0.194965 | + | 0.600040i | ||||
\(707\) | −4.85410 | −0.182557 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.28115 | − | 4.56352i | −0.235894 | − | 0.171387i | 0.463558 | − | 0.886066i | \(-0.346572\pi\) |
−0.699452 | + | 0.714680i | \(0.746572\pi\) | |||||||
\(710\) | −6.70820 | −0.251754 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.61803 | − | 2.62866i | −0.135592 | − | 0.0985130i | ||||
\(713\) | −21.3713 | − | 15.5272i | −0.800362 | − | 0.581497i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.163119 | + | 0.502029i | −0.00610030 | + | 0.0187748i | ||||
\(716\) | −9.04508 | − | 6.57164i | −0.338031 | − | 0.245594i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.09017 | −0.115324 | ||||||||
\(719\) | 8.19098 | + | 25.2093i | 0.305472 | + | 0.940147i | 0.979501 | + | 0.201441i | \(0.0645625\pi\) |
−0.674028 | + | 0.738705i | \(0.735438\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.4058 | − | 56.6471i | 0.685466 | − | 2.10965i | ||||
\(722\) | −5.64590 | + | 17.3763i | −0.210119 | + | 0.646678i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −21.4164 | −0.795935 | ||||||||
\(725\) | −2.13525 | + | 1.55135i | −0.0793014 | + | 0.0576158i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.1803 | − | 16.8415i | 0.859711 | − | 0.624617i | −0.0680952 | − | 0.997679i | \(-0.521692\pi\) |
0.927806 | + | 0.373062i | \(0.121692\pi\) | |||||||
\(728\) | −0.927051 | + | 2.85317i | −0.0343588 | + | 0.105745i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.3262 | − | 7.50245i | −0.382191 | − | 0.277678i | ||||
\(731\) | 4.28115 | + | 13.1760i | 0.158344 | + | 0.487333i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.2918 | − | 37.8303i | −0.454008 | − | 1.39729i | −0.872296 | − | 0.488978i | \(-0.837370\pi\) |
0.418288 | − | 0.908314i | \(-0.362630\pi\) | |||||||
\(734\) | 25.5172 | + | 18.5393i | 0.941858 | + | 0.684300i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.04508 | + | 3.66547i | −0.185964 | + | 0.135111i | ||||
\(737\) | 1.10081 | + | 0.799788i | 0.0405490 | + | 0.0294606i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.2705 | + | 17.6336i | −0.892805 | + | 0.648661i | −0.936608 | − | 0.350379i | \(-0.886053\pi\) |
0.0438028 | + | 0.999040i | \(0.486053\pi\) | |||||||
\(740\) | −5.06231 | − | 15.5802i | −0.186094 | − | 0.572739i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.41641 | + | 4.35926i | 0.0519980 | + | 0.160033i | ||||
\(743\) | 18.2705 | 0.670280 | 0.335140 | − | 0.942168i | \(-0.391216\pi\) | ||||
0.335140 | + | 0.942168i | \(0.391216\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.54508 | + | 4.75528i | −0.0566075 | + | 0.174220i | ||||
\(746\) | −5.01722 | + | 15.4414i | −0.183694 | + | 0.565350i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.50000 | − | 1.08981i | 0.0548454 | − | 0.0398475i | ||||
\(749\) | 30.2705 | 1.10606 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.14590 | 0.0418144 | 0.0209072 | − | 0.999781i | \(-0.493345\pi\) | ||||
0.0209072 | + | 0.999781i | \(0.493345\pi\) | |||||||
\(752\) | 4.80902 | − | 3.49396i | 0.175367 | − | 0.127411i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.163119 | − | 0.502029i | 0.00594044 | − | 0.0182828i | ||||
\(755\) | −2.56231 | + | 7.88597i | −0.0932519 | + | 0.287000i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.4164 | 0.378591 | 0.189295 | − | 0.981920i | \(-0.439380\pi\) | ||||
0.189295 | + | 0.981920i | \(0.439380\pi\) | |||||||
\(758\) | 0.163119 | + | 0.502029i | 0.00592475 | + | 0.0182345i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.590170 | + | 1.81636i | 0.0214077 | + | 0.0658862i | ||||
\(761\) | −30.6803 | + | 22.2906i | −1.11216 | + | 0.808033i | −0.983003 | − | 0.183591i | \(-0.941228\pi\) |
−0.129159 | + | 0.991624i | \(0.541228\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −36.4058 | − | 26.4503i | −1.31798 | − | 0.957566i | ||||
\(764\) | 14.2812 | − | 10.3759i | 0.516674 | − | 0.375386i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.50000 | − | 2.54290i | −0.126460 | − | 0.0918787i | ||||
\(767\) | −1.38197 | − | 4.25325i | −0.0498999 | − | 0.153576i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.23607 | − | 22.2703i | −0.260939 | − | 0.803089i | −0.992601 | − | 0.121421i | \(-0.961255\pi\) |
0.731662 | − | 0.681668i | \(-0.238745\pi\) | |||||||
\(770\) | −1.28115 | − | 0.930812i | −0.0461695 | − | 0.0335441i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.14590 | − | 15.8374i | 0.185205 | − | 0.570002i | ||||
\(773\) | 5.01722 | − | 3.64522i | 0.180457 | − | 0.131110i | −0.493890 | − | 0.869525i | \(-0.664425\pi\) |
0.674347 | + | 0.738415i | \(0.264425\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.54508 | − | 20.1437i | 0.235106 | − | 0.723583i | ||||
\(776\) | −10.5623 | −0.379165 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.2639 | − | 31.5891i | 0.367980 | − | 1.13253i | ||||
\(779\) | −1.97214 | + | 6.06961i | −0.0706591 | + | 0.217466i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.218847 | + | 0.673542i | 0.00783096 | + | 0.0241012i | ||||
\(782\) | −48.9787 | −1.75148 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.61803 | − | 1.17557i | −0.0577869 | − | 0.0419847i | ||||
\(785\) | 10.7533 | − | 33.0952i | 0.383801 | − | 1.18122i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.4721 | − | 9.06154i | −0.444584 | − | 0.323009i | 0.342870 | − | 0.939383i | \(-0.388601\pi\) |
−0.787454 | + | 0.616374i | \(0.788601\pi\) | |||||||
\(788\) | 9.70820 | + | 7.05342i | 0.345840 | + | 0.251268i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.18034 | 0.219887 | ||||||||
\(791\) | −19.9894 | − | 14.5231i | −0.710740 | − | 0.516383i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.14590 | −0.0762031 | ||||||||
\(794\) | −1.78115 | − | 5.48183i | −0.0632108 | − | 0.194543i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.42705 | + | 16.7027i | −0.192357 | + | 0.592013i | ||||
\(797\) | −1.04508 | + | 3.21644i | −0.0370188 | + | 0.113932i | −0.967858 | − | 0.251496i | \(-0.919077\pi\) |
0.930840 | + | 0.365428i | \(0.119077\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 46.6869 | 1.65166 | ||||||||
\(800\) | −4.04508 | − | 2.93893i | −0.143015 | − | 0.103907i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.61803 | − | 4.80828i | 0.233691 | − | 0.169786i | ||||
\(803\) | −0.416408 | + | 1.28157i | −0.0146947 | + | 0.0452257i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.9271 | + | 39.7854i | 0.455619 | + | 1.40225i | ||||
\(806\) | 1.30902 | + | 4.02874i | 0.0461082 | + | 0.141906i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.500000 | + | 1.53884i | 0.0175899 | + | 0.0541363i | ||||
\(809\) | 1.80902 | + | 1.31433i | 0.0636017 | + | 0.0462093i | 0.619132 | − | 0.785287i | \(-0.287485\pi\) |
−0.555530 | + | 0.831496i | \(0.687485\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.6525 | + | 13.5518i | −0.654977 | + | 0.475869i | −0.864963 | − | 0.501836i | \(-0.832658\pi\) |
0.209986 | + | 0.977704i | \(0.432658\pi\) | |||||||
\(812\) | 1.28115 | + | 0.930812i | 0.0449597 | + | 0.0326651i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.39919 | + | 1.01657i | −0.0490415 | + | 0.0356307i | ||||
\(815\) | −8.78115 | + | 6.37988i | −0.307590 | + | 0.223477i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.465558 | + | 1.43284i | 0.0162878 | + | 0.0501287i | ||||
\(818\) | 6.70820 | 0.234547 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.16312 | − | 15.8904i | −0.180304 | − | 0.554918i | ||||
\(821\) | 9.31966 | − | 28.6830i | 0.325258 | − | 1.00104i | −0.646065 | − | 0.763282i | \(-0.723587\pi\) |
0.971324 | − | 0.237760i | \(-0.0764133\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.5623 | + | 19.2986i | −0.925904 | + | 0.672708i | −0.944986 | − | 0.327109i | \(-0.893925\pi\) |
0.0190827 | + | 0.999818i | \(0.493925\pi\) | |||||||
\(824\) | −19.8541 | −0.691650 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.4164 | 0.466817 | ||||||||
\(827\) | 19.4443 | − | 14.1271i | 0.676144 | − | 0.491247i | −0.195932 | − | 0.980617i | \(-0.562773\pi\) |
0.872076 | + | 0.489370i | \(0.162773\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.21478 | − | 25.2825i | 0.285311 | − | 0.878097i | −0.700994 | − | 0.713167i | \(-0.747260\pi\) |
0.986305 | − | 0.164930i | \(-0.0527399\pi\) | |||||||
\(830\) | 24.3713 | − | 17.7068i | 0.845941 | − | 0.614612i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −4.85410 | − | 14.9394i | −0.168185 | − | 0.517619i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34.9230 | 1.20856 | ||||||||
\(836\) | 0.163119 | − | 0.118513i | 0.00564159 | − | 0.00409885i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 22.0344 | + | 16.0090i | 0.761167 | + | 0.553020i | ||||
\(839\) | 20.4271 | − | 14.8411i | 0.705220 | − | 0.512372i | −0.176408 | − | 0.984317i | \(-0.556448\pi\) |
0.881628 | + | 0.471945i | \(0.156448\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.2361 | + | 16.8820i | 0.801244 | + | 0.582138i | ||||
\(842\) | −3.79180 | − | 11.6699i | −0.130674 | − | 0.402173i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.48278 | + | 10.7189i | 0.119882 | + | 0.368959i | ||||
\(845\) | 26.8328 | 0.923077 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.1459 | − | 31.2259i | 0.348617 | − | 1.07293i | ||||
\(848\) | 1.23607 | − | 0.898056i | 0.0424467 | − | 0.0308394i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.1353 | − | 37.3485i | −0.416236 | − | 1.28104i | ||||
\(851\) | 45.6869 | 1.56613 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.68034 | + | 23.6377i | −0.262970 | + | 0.809338i | 0.729184 | + | 0.684317i | \(0.239900\pi\) |
−0.992154 | + | 0.125021i | \(0.960100\pi\) | |||||||
\(854\) | 1.98936 | − | 6.12261i | 0.0680744 | − | 0.209511i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.11803 | − | 9.59632i | −0.106572 | − | 0.327996i | ||||
\(857\) | −35.3394 | −1.20717 | −0.603585 | − | 0.797298i | \(-0.706262\pi\) | ||||
−0.603585 | + | 0.797298i | \(0.706262\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.8713 | + | 23.1559i | 1.08744 | + | 0.790068i | 0.978964 | − | 0.204031i | \(-0.0654045\pi\) |
0.108471 | + | 0.994100i | \(0.465404\pi\) | |||||||
\(860\) | −3.19098 | − | 2.31838i | −0.108812 | − | 0.0790563i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −25.9443 | − | 18.8496i | −0.883665 | − | 0.642020i | ||||
\(863\) | −5.47214 | − | 3.97574i | −0.186274 | − | 0.135336i | 0.490740 | − | 0.871306i | \(-0.336726\pi\) |
−0.677014 | + | 0.735970i | \(0.736726\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.23607 | + | 6.88191i | 0.0760286 | + | 0.233992i | ||||
\(866\) | −18.8992 | − | 13.7311i | −0.642221 | − | 0.466601i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.7082 | −0.431345 | ||||||||
\(869\) | −0.201626 | − | 0.620541i | −0.00683970 | − | 0.0210504i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.78115 | + | 5.48183i | −0.0603521 | + | 0.185745i | ||||
\(872\) | −4.63525 | + | 14.2658i | −0.156970 | + | 0.483103i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.32624 | −0.180163 | ||||||||
\(875\) | −27.1353 | + | 19.7149i | −0.917339 | + | 0.666486i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.8713 | + | 14.4374i | −0.671007 | + | 0.487515i | −0.870362 | − | 0.492412i | \(-0.836115\pi\) |
0.199355 | + | 0.979927i | \(0.436115\pi\) | |||||||
\(878\) | −1.74671 | + | 5.37582i | −0.0589486 | + | 0.181425i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.163119 | + | 0.502029i | −0.00549874 | + | 0.0169234i | ||||
\(881\) | −4.88854 | − | 15.0454i | −0.164699 | − | 0.506892i | 0.834315 | − | 0.551288i | \(-0.185864\pi\) |
−0.999014 | + | 0.0443963i | \(0.985864\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.77458 | + | 17.7723i | 0.194330 | + | 0.598086i | 0.999984 | + | 0.00569940i | \(0.00181418\pi\) |
−0.805654 | + | 0.592387i | \(0.798186\pi\) | |||||||
\(884\) | 6.35410 | + | 4.61653i | 0.213712 | + | 0.155271i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.00000 | + | 4.35926i | −0.201574 | + | 0.146452i | ||||
\(887\) | 8.75329 | + | 6.35964i | 0.293907 | + | 0.213536i | 0.724960 | − | 0.688791i | \(-0.241858\pi\) |
−0.431054 | + | 0.902326i | \(0.641858\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.2705 | + | 21.9928i | −1.01524 | + | 0.737615i | ||||
\(890\) | 8.09017 | + | 5.87785i | 0.271183 | + | 0.197026i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.78115 | − | 8.55951i | −0.0931199 | − | 0.286594i | ||||
\(893\) | 5.07701 | 0.169896 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.2254 | + | 14.6946i | 0.676061 | + | 0.491187i | ||||
\(896\) | −0.927051 | + | 2.85317i | −0.0309706 | + | 0.0953177i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.2812 | − | 8.19624i | 0.376457 | − | 0.273512i | ||||
\(899\) | 2.23607 | 0.0745770 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | −1.42705 | + | 1.03681i | −0.0475156 | + | 0.0345221i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.54508 | + | 7.83297i | −0.0846483 | + | 0.260521i | ||||
\(905\) | 47.8885 | 1.59187 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.3820 | 0.776385 | 0.388193 | − | 0.921578i | \(-0.373099\pi\) | ||||
0.388193 | + | 0.921578i | \(0.373099\pi\) | |||||||
\(908\) | 4.74671 | + | 14.6089i | 0.157525 | + | 0.484813i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.07295 | − | 6.37988i | 0.0687176 | − | 0.211491i | ||||
\(911\) | 8.42705 | − | 6.12261i | 0.279201 | − | 0.202851i | −0.439368 | − | 0.898307i | \(-0.644798\pi\) |
0.718569 | + | 0.695456i | \(0.244798\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.57295 | − | 1.86936i | −0.0851522 | − | 0.0618667i | ||||
\(914\) | 9.07295 | − | 6.59188i | 0.300106 | − | 0.218040i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.2082 | − | 10.3229i | −0.469452 | − | 0.341077i | ||||
\(917\) | 9.65654 | + | 29.7198i | 0.318887 | + | 0.981434i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.92705 | + | 24.3970i | 0.261489 | + | 0.804781i | 0.992481 | + | 0.122395i | \(0.0390576\pi\) |
−0.730992 | + | 0.682386i | \(0.760942\pi\) | |||||||
\(920\) | 11.2812 | − | 8.19624i | 0.371929 | − | 0.270222i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.70820 | + | 26.8011i | −0.286789 | + | 0.882647i | ||||
\(923\) | −2.42705 | + | 1.76336i | −0.0798874 | + | 0.0580416i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.3197 | + | 34.8383i | 0.372188 | + | 1.14548i | ||||
\(926\) | 11.9787 | 0.393645 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.163119 | − | 0.502029i | 0.00535464 | − | 0.0164799i | ||||
\(929\) | 5.28773 | − | 16.2740i | 0.173485 | − | 0.533931i | −0.826076 | − | 0.563558i | \(-0.809432\pi\) |
0.999561 | + | 0.0296271i | \(0.00943197\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.527864 | − | 1.62460i | −0.0173000 | − | 0.0532441i | ||||
\(932\) | −27.7082 | −0.907612 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.57295 | + | 1.86936i | 0.0841895 | + | 0.0611672i | ||||
\(935\) | −3.35410 | + | 2.43690i | −0.109691 | + | 0.0796951i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.5451 | + | 13.4738i | 0.605842 | + | 0.440170i | 0.847948 | − | 0.530080i | \(-0.177838\pi\) |
−0.242106 | + | 0.970250i | \(0.577838\pi\) | |||||||
\(938\) | −13.9894 | − | 10.1639i | −0.456769 | − | 0.331862i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.7533 | + | 7.81272i | −0.350734 | + | 0.254823i | ||||
\(941\) | −9.39919 | − | 6.82891i | −0.306405 | − | 0.222616i | 0.423948 | − | 0.905687i | \(-0.360644\pi\) |
−0.730352 | + | 0.683071i | \(0.760644\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46.5967 | 1.51740 | ||||||||
\(944\) | −1.38197 | − | 4.25325i | −0.0449792 | − | 0.138432i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.128677 | + | 0.396027i | −0.00418365 | + | 0.0128760i | ||||
\(947\) | 12.8607 | − | 39.5811i | 0.417916 | − | 1.28621i | −0.491701 | − | 0.870764i | \(-0.663625\pi\) |
0.909617 | − | 0.415449i | \(-0.136375\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.70820 | −0.185296 | ||||||||
\(950\) | −1.31966 | − | 4.06150i | −0.0428154 | − | 0.131772i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −19.0623 | + | 13.8496i | −0.617813 | + | 0.448867i | ||||
\(953\) | −13.0967 | + | 40.3076i | −0.424245 | + | 1.30569i | 0.479470 | + | 0.877558i | \(0.340829\pi\) |
−0.903715 | + | 0.428134i | \(0.859171\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −31.9336 | + | 23.2011i | −1.03335 | + | 0.750771i | ||||
\(956\) | 5.59017 | + | 17.2048i | 0.180799 | + | 0.556442i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.2984 | + | 37.8505i | 0.397342 | + | 1.22289i | ||||
\(959\) | 14.7812 | + | 10.7391i | 0.477308 | + | 0.346785i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.5623 | − | 7.67396i | 0.340720 | − | 0.247547i | ||||
\(962\) | −5.92705 | − | 4.30625i | −0.191096 | − | 0.138839i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.8262 | + | 7.86572i | −0.348690 | + | 0.253338i | ||||
\(965\) | −11.5066 | + | 35.4136i | −0.370410 | + | 1.14000i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.38197 | + | 25.7970i | 0.269546 | + | 0.829577i | 0.990611 | + | 0.136710i | \(0.0436528\pi\) |
−0.721065 | + | 0.692867i | \(0.756347\pi\) | |||||||
\(968\) | −10.9443 | −0.351762 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 23.6180 | 0.758329 | ||||||||
\(971\) | 16.0902 | − | 49.5205i | 0.516358 | − | 1.58919i | −0.264439 | − | 0.964402i | \(-0.585187\pi\) |
0.780797 | − | 0.624785i | \(-0.214813\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.0623 | − | 18.2088i | 0.803461 | − | 0.583748i | ||||
\(974\) | −18.1246 | −0.580750 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.14590 | −0.0686885 | ||||||||
\(977\) | −21.0451 | + | 15.2901i | −0.673292 | + | 0.489175i | −0.871126 | − | 0.491060i | \(-0.836609\pi\) |
0.197834 | + | 0.980236i | \(0.436609\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.326238 | − | 1.00406i | 0.0104266 | − | 0.0320898i | ||||
\(980\) | 3.61803 | + | 2.62866i | 0.115574 | + | 0.0839693i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −14.7639 | −0.471136 | ||||||||
\(983\) | 14.3647 | + | 44.2101i | 0.458164 | + | 1.41008i | 0.867380 | + | 0.497647i | \(0.165802\pi\) |
−0.409216 | + | 0.912438i | \(0.634198\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.7082 | − | 15.7719i | −0.691681 | − | 0.502536i | ||||
\(986\) | 3.35410 | − | 2.43690i | 0.106816 | − | 0.0776066i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.690983 | + | 0.502029i | 0.0219831 | + | 0.0159717i | ||||
\(989\) | 8.89919 | − | 6.46564i | 0.282978 | − | 0.205595i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.4336 | − | 30.8298i | −1.34795 | − | 0.979342i | −0.999111 | − | 0.0421589i | \(-0.986576\pi\) |
−0.348838 | − | 0.937183i | \(-0.613424\pi\) | |||||||
\(992\) | 1.30902 | + | 4.02874i | 0.0415613 | + | 0.127913i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.78115 | − | 8.55951i | −0.0882128 | − | 0.271491i | ||||
\(995\) | 12.1353 | − | 37.3485i | 0.384713 | − | 1.18403i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.4549 | + | 50.6430i | −0.521132 | + | 1.60388i | 0.250707 | + | 0.968063i | \(0.419337\pi\) |
−0.771839 | + | 0.635818i | \(0.780663\pi\) | |||||||
\(998\) | −33.0517 | + | 24.0134i | −1.04623 | + | 0.760132i | ||||
\(999\) | 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 | 450.2.h.a.361.1 | 4 | ||
3.2 | odd | 2 | 50.2.d.a.11.1 | ✓ | 4 | ||
12.11 | even | 2 | 400.2.u.c.161.1 | 4 | |||
15.2 | even | 4 | 250.2.e.b.199.2 | 8 | |||
15.8 | even | 4 | 250.2.e.b.199.1 | 8 | |||
15.14 | odd | 2 | 250.2.d.a.51.1 | 4 | |||
25.16 | even | 5 | inner | 450.2.h.a.91.1 | 4 | ||
75.29 | odd | 10 | 1250.2.a.d.1.2 | 2 | |||
75.38 | even | 20 | 250.2.e.b.49.2 | 8 | |||
75.41 | odd | 10 | 50.2.d.a.41.1 | yes | 4 | ||
75.47 | even | 20 | 1250.2.b.b.1249.2 | 4 | |||
75.53 | even | 20 | 1250.2.b.b.1249.3 | 4 | |||
75.59 | odd | 10 | 250.2.d.a.201.1 | 4 | |||
75.62 | even | 20 | 250.2.e.b.49.1 | 8 | |||
75.71 | odd | 10 | 1250.2.a.a.1.1 | 2 | |||
300.71 | even | 10 | 10000.2.a.n.1.2 | 2 | |||
300.179 | even | 10 | 10000.2.a.a.1.1 | 2 | |||
300.191 | even | 10 | 400.2.u.c.241.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.2.d.a.11.1 | ✓ | 4 | 3.2 | odd | 2 | ||
50.2.d.a.41.1 | yes | 4 | 75.41 | odd | 10 | ||
250.2.d.a.51.1 | 4 | 15.14 | odd | 2 | |||
250.2.d.a.201.1 | 4 | 75.59 | odd | 10 | |||
250.2.e.b.49.1 | 8 | 75.62 | even | 20 | |||
250.2.e.b.49.2 | 8 | 75.38 | even | 20 | |||
250.2.e.b.199.1 | 8 | 15.8 | even | 4 | |||
250.2.e.b.199.2 | 8 | 15.2 | even | 4 | |||
400.2.u.c.161.1 | 4 | 12.11 | even | 2 | |||
400.2.u.c.241.1 | 4 | 300.191 | even | 10 | |||
450.2.h.a.91.1 | 4 | 25.16 | even | 5 | inner | ||
450.2.h.a.361.1 | 4 | 1.1 | even | 1 | trivial | ||
1250.2.a.a.1.1 | 2 | 75.71 | odd | 10 | |||
1250.2.a.d.1.2 | 2 | 75.29 | odd | 10 | |||
1250.2.b.b.1249.2 | 4 | 75.47 | even | 20 | |||
1250.2.b.b.1249.3 | 4 | 75.53 | even | 20 | |||
10000.2.a.a.1.1 | 2 | 300.179 | even | 10 | |||
10000.2.a.n.1.2 | 2 | 300.71 | even | 10 |