Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1710,2,Mod(919,1710)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1710.919");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1710.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.6544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 49 x^{16} - 8 x^{15} + 72 x^{13} + 2145 x^{12} - 648 x^{11} + 32 x^{10} - 7056 x^{9} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 570) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 919.6 | ||
Root | \(-0.372041 + 0.0996880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1710.919 |
Dual form | 1710.2.t.c.1189.6 |
$q$-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 \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(1027\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −2.05825 | + | 0.873846i | −0.920477 | + | 0.390796i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.32136i | − | 0.877391i | −0.898636 | − | 0.438696i | \(-0.855441\pi\) | ||
0.898636 | − | 0.438696i | \(-0.144559\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.34557 | + | 1.78590i | −0.425508 | + | 0.564750i | ||||
\(11\) | 2.85165 | 0.859804 | 0.429902 | − | 0.902875i | \(-0.358548\pi\) | ||||
0.429902 | + | 0.902875i | \(0.358548\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.20277 | + | 3.00382i | 1.44299 | + | 0.833110i | 0.998048 | − | 0.0624492i | \(-0.0198911\pi\) |
0.444941 | + | 0.895560i | \(0.353224\pi\) | |||||||
\(14\) | −1.16068 | − | 2.01036i | −0.310205 | − | 0.537290i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.79487 | + | 2.19097i | −0.920391 | + | 0.531388i | −0.883760 | − | 0.467941i | \(-0.844996\pi\) |
−0.0366311 | + | 0.999329i | \(0.511663\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.63121 | − | 3.47516i | −0.603641 | − | 0.797256i | ||||
\(20\) | −0.272353 | + | 2.21942i | −0.0608999 | + | 0.496277i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.46960 | − | 1.42582i | 0.526520 | − | 0.303987i | ||||
\(23\) | 4.36172 | + | 2.51824i | 0.909481 | + | 0.525089i | 0.880264 | − | 0.474484i | \(-0.157365\pi\) |
0.0292169 | + | 0.999573i | \(0.490699\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.47279 | − | 3.59719i | 0.694558 | − | 0.719437i | ||||
\(26\) | 6.00764 | 1.17820 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.01036 | − | 1.16068i | −0.379922 | − | 0.219348i | ||||
\(29\) | 4.41039 | − | 7.63902i | 0.818989 | − | 1.41853i | −0.0874397 | − | 0.996170i | \(-0.527869\pi\) |
0.906428 | − | 0.422360i | \(-0.138798\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.685205 | −0.123066 | −0.0615332 | − | 0.998105i | \(-0.519599\pi\) | ||||
−0.0615332 | + | 0.998105i | \(0.519599\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.19097 | + | 3.79487i | −0.375748 | + | 0.650815i | ||||
\(35\) | 2.02851 | + | 4.77794i | 0.342881 | + | 0.807619i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.79872i | − | 1.28210i | −0.767499 | − | 0.641050i | \(-0.778499\pi\) | ||
0.767499 | − | 0.641050i | \(-0.221501\pi\) | |||||||
\(38\) | −4.01627 | − | 1.69397i | −0.651526 | − | 0.274799i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.873846 | + | 2.05825i | 0.138167 | + | 0.325438i | ||||
\(41\) | −2.58128 | − | 4.47091i | −0.403128 | − | 0.698239i | 0.590973 | − | 0.806691i | \(-0.298744\pi\) |
−0.994102 | + | 0.108452i | \(0.965410\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.24057 | − | 1.29360i | 0.341684 | − | 0.197271i | −0.319332 | − | 0.947643i | \(-0.603459\pi\) |
0.661017 | + | 0.750371i | \(0.270125\pi\) | |||||||
\(44\) | 1.42582 | − | 2.46960i | 0.214951 | − | 0.372306i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.03648 | 0.742588 | ||||||||
\(47\) | −6.83132 | − | 3.94406i | −0.996450 | − | 0.575301i | −0.0892540 | − | 0.996009i | \(-0.528448\pi\) |
−0.907196 | + | 0.420708i | \(0.861782\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.61129 | 0.230184 | ||||||||
\(50\) | 1.20893 | − | 4.85165i | 0.170968 | − | 0.686127i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.20277 | − | 3.00382i | 0.721495 | − | 0.416555i | ||||
\(53\) | 4.86905 | + | 2.81115i | 0.668815 | + | 0.386141i | 0.795628 | − | 0.605786i | \(-0.207141\pi\) |
−0.126812 | + | 0.991927i | \(0.540475\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.86941 | + | 2.49190i | −0.791430 | + | 0.336008i | ||||
\(56\) | −2.32136 | −0.310205 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 8.82078i | − | 1.15822i | ||||||
\(59\) | 0.724643 | + | 1.25512i | 0.0943405 | + | 0.163403i | 0.909333 | − | 0.416069i | \(-0.136592\pi\) |
−0.814993 | + | 0.579471i | \(0.803259\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.40264 | − | 9.35765i | 0.691737 | − | 1.19812i | −0.279531 | − | 0.960137i | \(-0.590179\pi\) |
0.971268 | − | 0.237987i | \(-0.0764876\pi\) | |||||||
\(62\) | −0.593405 | + | 0.342602i | −0.0753625 | + | 0.0435105i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −13.3335 | − | 1.63620i | −1.65382 | − | 0.202945i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.89514 | + | 3.40356i | 0.720206 | + | 0.415811i | 0.814829 | − | 0.579702i | \(-0.196831\pi\) |
−0.0946224 | + | 0.995513i | \(0.530164\pi\) | |||||||
\(68\) | 4.38194i | 0.531388i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.14571 | + | 3.12356i | 0.495507 | + | 0.373337i | ||||
\(71\) | −1.15149 | − | 1.99443i | −0.136656 | − | 0.236696i | 0.789573 | − | 0.613657i | \(-0.210302\pi\) |
−0.926229 | + | 0.376961i | \(0.876969\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.38195 | + | 3.10727i | −0.629909 | + | 0.363678i | −0.780717 | − | 0.624885i | \(-0.785146\pi\) |
0.150808 | + | 0.988563i | \(0.451813\pi\) | |||||||
\(74\) | −3.89936 | − | 6.75389i | −0.453291 | − | 0.785123i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.32518 | + | 0.541114i | −0.496132 | + | 0.0620700i | ||||
\(77\) | − | 6.61970i | − | 0.754385i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00683 | + | 3.47593i | 0.225786 | + | 0.391072i | 0.956555 | − | 0.291552i | \(-0.0941718\pi\) |
−0.730769 | + | 0.682625i | \(0.760838\pi\) | |||||||
\(80\) | 1.78590 | + | 1.34557i | 0.199669 | + | 0.150440i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.47091 | − | 2.58128i | −0.493729 | − | 0.285055i | ||||
\(83\) | − | 12.2192i | − | 1.34123i | −0.741806 | − | 0.670614i | \(-0.766031\pi\) | ||
0.741806 | − | 0.670614i | \(-0.233969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.89622 | − | 7.82569i | 0.639535 | − | 0.848815i | ||||
\(86\) | 1.29360 | − | 2.24057i | 0.139492 | − | 0.241607i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 2.85165i | − | 0.303987i | ||||||
\(89\) | 4.34444 | − | 7.52479i | 0.460510 | − | 0.797626i | −0.538477 | − | 0.842640i | \(-0.681000\pi\) |
0.998986 | + | 0.0450142i | \(0.0143333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.97295 | − | 12.0775i | 0.730964 | − | 1.26607i | ||||
\(92\) | 4.36172 | − | 2.51824i | 0.454740 | − | 0.262545i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.88813 | −0.813598 | ||||||||
\(95\) | 8.45244 | + | 4.85348i | 0.867202 | + | 0.497956i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.79684 | − | 3.34681i | 0.588580 | − | 0.339817i | −0.175956 | − | 0.984398i | \(-0.556302\pi\) |
0.764536 | + | 0.644581i | \(0.222968\pi\) | |||||||
\(98\) | 1.39542 | − | 0.805646i | 0.140959 | − | 0.0813825i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.37886 | − | 4.80612i | −0.137886 | − | 0.480612i | ||||
\(101\) | 7.02206 | − | 12.1626i | 0.698721 | − | 1.21022i | −0.270189 | − | 0.962807i | \(-0.587086\pi\) |
0.968910 | − | 0.247413i | \(-0.0795805\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.0958i | 1.38890i | 0.719542 | + | 0.694449i | \(0.244352\pi\) | ||||
−0.719542 | + | 0.694449i | \(0.755648\pi\) | |||||||
\(104\) | 3.00382 | − | 5.20277i | 0.294549 | − | 0.510174i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.62229 | 0.546085 | ||||||||
\(107\) | 16.7729i | 1.62150i | 0.585395 | + | 0.810748i | \(0.300940\pi\) | ||||
−0.585395 | + | 0.810748i | \(0.699060\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.45191 | + | 7.71093i | 0.426416 | + | 0.738573i | 0.996551 | − | 0.0829770i | \(-0.0264428\pi\) |
−0.570136 | + | 0.821550i | \(0.693109\pi\) | |||||||
\(110\) | −3.83710 | + | 5.09275i | −0.365854 | + | 0.485575i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.01036 | + | 1.16068i | −0.189961 | + | 0.109674i | ||||
\(113\) | − | 11.8870i | − | 1.11824i | −0.829087 | − | 0.559120i | \(-0.811139\pi\) | ||
0.829087 | − | 0.559120i | \(-0.188861\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.1781 | − | 1.37170i | −1.04236 | − | 0.127912i | ||||
\(116\) | −4.41039 | − | 7.63902i | −0.409494 | − | 0.709265i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.25512 | + | 0.724643i | 0.115543 | + | 0.0667088i | ||||
\(119\) | 5.08602 | + | 8.80925i | 0.466235 | + | 0.807543i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.86810 | −0.260737 | ||||||||
\(122\) | − | 10.8053i | − | 0.978264i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.342602 | + | 0.593405i | −0.0307666 | + | 0.0532893i | ||||
\(125\) | −4.00448 | + | 10.4386i | −0.358172 | + | 0.933656i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.72660 | − | 4.46095i | −0.685625 | − | 0.395846i | 0.116346 | − | 0.993209i | \(-0.462882\pi\) |
−0.801971 | + | 0.597363i | \(0.796215\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.3652 | + | 5.24975i | −1.08450 | + | 0.460434i | ||||
\(131\) | −0.0274319 | − | 0.0475134i | −0.00239673 | − | 0.00415127i | 0.864825 | − | 0.502074i | \(-0.167430\pi\) |
−0.867221 | + | 0.497923i | \(0.834096\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.06710 | + | 6.10798i | −0.699506 | + | 0.529629i | ||||
\(134\) | 6.80712 | 0.588046 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.19097 | + | 3.79487i | 0.187874 | + | 0.325407i | ||||
\(137\) | 15.5732 | + | 8.99119i | 1.33051 | + | 0.768169i | 0.985377 | − | 0.170386i | \(-0.0545013\pi\) |
0.345131 | + | 0.938555i | \(0.387835\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.3327 | + | 17.8967i | −0.876405 | + | 1.51798i | −0.0211474 | + | 0.999776i | \(0.506732\pi\) |
−0.855258 | + | 0.518202i | \(0.826601\pi\) | |||||||
\(140\) | 5.15207 | + | 0.632228i | 0.435429 | + | 0.0534330i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.99443 | − | 1.15149i | −0.167369 | − | 0.0966306i | ||||
\(143\) | 14.8365 | + | 8.56584i | 1.24069 | + | 0.716312i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.40236 | + | 19.5770i | −0.199505 | + | 1.62578i | ||||
\(146\) | −3.10727 | + | 5.38195i | −0.257159 | + | 0.445413i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.75389 | − | 3.89936i | −0.555166 | − | 0.320525i | ||||
\(149\) | 1.92651 | + | 3.33682i | 0.157826 | + | 0.273363i | 0.934084 | − | 0.357052i | \(-0.116218\pi\) |
−0.776258 | + | 0.630415i | \(0.782885\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.77324 | 0.632577 | 0.316289 | − | 0.948663i | \(-0.397563\pi\) | ||||
0.316289 | + | 0.948663i | \(0.397563\pi\) | |||||||
\(152\) | −3.47516 | + | 2.63121i | −0.281873 | + | 0.213419i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.30985 | − | 5.73283i | −0.266715 | − | 0.461964i | ||||
\(155\) | 1.41032 | − | 0.598763i | 0.113280 | − | 0.0480938i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.6929 | + | 9.63765i | −1.33224 | + | 0.769169i | −0.985642 | − | 0.168846i | \(-0.945996\pi\) |
−0.346596 | + | 0.938014i | \(0.612663\pi\) | |||||||
\(158\) | 3.47593 | + | 2.00683i | 0.276530 | + | 0.159655i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.21942 | + | 0.272353i | 0.175461 | + | 0.0215314i | ||||
\(161\) | 5.84574 | − | 10.1251i | 0.460709 | − | 0.797971i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.9168i | 1.24670i | 0.781944 | + | 0.623348i | \(0.214228\pi\) | ||||
−0.781944 | + | 0.623348i | \(0.785772\pi\) | |||||||
\(164\) | −5.16256 | −0.403128 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.10958 | − | 10.5821i | −0.474196 | − | 0.821331i | ||||
\(167\) | −16.4675 | − | 9.50754i | −1.27430 | − | 0.735716i | −0.298503 | − | 0.954409i | \(-0.596487\pi\) |
−0.975794 | + | 0.218693i | \(0.929821\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5459 | + | 19.9981i | 0.888146 | + | 1.53831i | ||||
\(170\) | 1.19343 | − | 9.72536i | 0.0915321 | − | 0.745901i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 2.58719i | − | 0.197271i | ||||||
\(173\) | −12.3792 | + | 7.14712i | −0.941172 | + | 0.543386i | −0.890327 | − | 0.455321i | \(-0.849525\pi\) |
−0.0508444 | + | 0.998707i | \(0.516191\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.35036 | − | 8.06159i | −0.631228 | − | 0.609399i | ||||
\(176\) | −1.42582 | − | 2.46960i | −0.107476 | − | 0.186153i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 8.68888i | − | 0.651259i | ||||||
\(179\) | 6.66682 | 0.498301 | 0.249151 | − | 0.968465i | \(-0.419849\pi\) | ||||
0.249151 | + | 0.968465i | \(0.419849\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.06793 | + | 5.31382i | −0.228038 | + | 0.394973i | −0.957226 | − | 0.289340i | \(-0.906564\pi\) |
0.729189 | + | 0.684313i | \(0.239898\pi\) | |||||||
\(182\) | − | 13.9459i | − | 1.03374i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.51824 | − | 4.36172i | 0.185647 | − | 0.321550i | ||||
\(185\) | 6.81487 | + | 16.0517i | 0.501039 | + | 1.18014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.8216 | + | 6.24787i | −0.791356 | + | 0.456890i | ||||
\(188\) | −6.83132 | + | 3.94406i | −0.498225 | + | 0.287650i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.74677 | − | 0.0229835i | 0.707105 | − | 0.00166740i | ||||
\(191\) | 18.8448 | 1.36356 | 0.681780 | − | 0.731557i | \(-0.261206\pi\) | ||||
0.681780 | + | 0.731557i | \(0.261206\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.3105 | − | 8.26218i | 1.03009 | − | 0.594725i | 0.113082 | − | 0.993586i | \(-0.463928\pi\) |
0.917012 | + | 0.398861i | \(0.130594\pi\) | |||||||
\(194\) | 3.34681 | − | 5.79684i | 0.240287 | − | 0.416189i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.805646 | − | 1.39542i | 0.0575461 | − | 0.0996728i | ||||
\(197\) | 6.90254i | 0.491786i | 0.969297 | + | 0.245893i | \(0.0790811\pi\) | ||||
−0.969297 | + | 0.245893i | \(0.920919\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.26514 | − | 5.65540i | 0.231460 | − | 0.400900i | −0.726778 | − | 0.686872i | \(-0.758983\pi\) |
0.958238 | + | 0.285972i | \(0.0923164\pi\) | |||||||
\(200\) | −3.59719 | − | 3.47279i | −0.254359 | − | 0.245563i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 14.0441i | − | 0.988141i | ||||||
\(203\) | −17.7329 | − | 10.2381i | −1.24461 | − | 0.718573i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.21980 | + | 6.94661i | 0.643939 | + | 0.485172i | ||||
\(206\) | 7.04788 | + | 12.2073i | 0.491049 | + | 0.850522i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 6.00764i | − | 0.416555i | ||||||
\(209\) | −7.50328 | − | 9.90993i | −0.519013 | − | 0.685484i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.1943 | − | 19.3891i | −0.770648 | − | 1.33480i | −0.937208 | − | 0.348771i | \(-0.886599\pi\) |
0.166560 | − | 0.986031i | \(-0.446734\pi\) | |||||||
\(212\) | 4.86905 | − | 2.81115i | 0.334408 | − | 0.193070i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.38645 | + | 14.5258i | 0.573286 | + | 0.992960i | ||||
\(215\) | −3.48126 | + | 4.62046i | −0.237420 | + | 0.315113i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.59061i | 0.107977i | ||||||||
\(218\) | 7.71093 | + | 4.45191i | 0.522250 | + | 0.301521i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.776654 | + | 6.32900i | −0.0523620 | + | 0.426701i | ||||
\(221\) | −26.3251 | −1.77082 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.62511 | + | 0.938256i | −0.108825 | + | 0.0628302i | −0.553425 | − | 0.832899i | \(-0.686679\pi\) |
0.444600 | + | 0.895729i | \(0.353346\pi\) | |||||||
\(224\) | −1.16068 | + | 2.01036i | −0.0775512 | + | 0.134323i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.94352 | − | 10.2945i | −0.395357 | − | 0.684779i | ||||
\(227\) | − | 20.3703i | − | 1.35203i | −0.736890 | − | 0.676013i | \(-0.763706\pi\) | ||
0.736890 | − | 0.676013i | \(-0.236294\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.7813 | −0.712449 | −0.356224 | − | 0.934400i | \(-0.615936\pi\) | ||||
−0.356224 | + | 0.934400i | \(0.615936\pi\) | |||||||
\(230\) | −10.3663 | + | 4.40110i | −0.683536 | + | 0.290200i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.63902 | − | 4.41039i | −0.501526 | − | 0.289556i | ||||
\(233\) | −11.7576 | + | 6.78823i | −0.770263 | + | 0.444711i | −0.832968 | − | 0.553321i | \(-0.813360\pi\) |
0.0627056 | + | 0.998032i | \(0.480027\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.5071 | + | 2.14835i | 1.14203 | + | 0.140143i | ||||
\(236\) | 1.44929 | 0.0943405 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.80925 | + | 5.08602i | 0.571019 | + | 0.329678i | ||||
\(239\) | −2.08081 | −0.134596 | −0.0672981 | − | 0.997733i | \(-0.521438\pi\) | ||||
−0.0672981 | + | 0.997733i | \(0.521438\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.51317 | + | 14.7453i | −0.548382 | + | 0.949825i | 0.450004 | + | 0.893027i | \(0.351423\pi\) |
−0.998386 | + | 0.0567985i | \(0.981911\pi\) | |||||||
\(242\) | −2.48385 | + | 1.43405i | −0.159668 | + | 0.0921843i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.40264 | − | 9.35765i | −0.345869 | − | 0.599062i | ||||
\(245\) | −3.31644 | + | 1.40802i | −0.211880 | + | 0.0899551i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.25082 | − | 25.9842i | −0.206845 | − | 1.65333i | ||||
\(248\) | 0.685205i | 0.0435105i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.75131 | + | 11.0423i | 0.110763 | + | 0.698378i | ||||
\(251\) | −9.62571 | + | 16.6722i | −0.607569 | + | 1.05234i | 0.384070 | + | 0.923304i | \(0.374522\pi\) |
−0.991640 | + | 0.129037i | \(0.958811\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.4381 | + | 7.18113i | 0.781976 | + | 0.451474i | ||||
\(254\) | −8.92191 | −0.559810 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 15.3212 | + | 8.84568i | 0.955708 | + | 0.551779i | 0.894850 | − | 0.446368i | \(-0.147283\pi\) |
0.0608589 | + | 0.998146i | \(0.480616\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.1036 | −1.12490 | ||||||||
\(260\) | −8.08373 | + | 10.7290i | −0.501332 | + | 0.665387i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.0475134 | − | 0.0274319i | −0.00293539 | − | 0.00169475i | ||||
\(263\) | −9.98291 | + | 5.76364i | −0.615573 | + | 0.355401i | −0.775143 | − | 0.631785i | \(-0.782322\pi\) |
0.159570 | + | 0.987187i | \(0.448989\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.4782 | − | 1.53125i | −0.766532 | − | 0.0940637i | ||||
\(266\) | −3.93232 | + | 9.32321i | −0.241106 | + | 0.571643i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.89514 | − | 3.40356i | 0.360103 | − | 0.207906i | ||||
\(269\) | −10.2776 | − | 17.8013i | −0.626635 | − | 1.08536i | −0.988222 | − | 0.153025i | \(-0.951098\pi\) |
0.361587 | − | 0.932338i | \(-0.382235\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.9912 | + | 22.5014i | 0.789159 | + | 1.36686i | 0.926483 | + | 0.376337i | \(0.122816\pi\) |
−0.137324 | + | 0.990526i | \(0.543850\pi\) | |||||||
\(272\) | 3.79487 | + | 2.19097i | 0.230098 | + | 0.132847i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.9824 | 1.08636 | ||||||||
\(275\) | 9.90317 | − | 10.2579i | 0.597184 | − | 0.618575i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.14296i | 0.248926i | 0.992224 | + | 0.124463i | \(0.0397208\pi\) | ||||
−0.992224 | + | 0.124463i | \(0.960279\pi\) | |||||||
\(278\) | 20.6653i | 1.23942i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.77794 | − | 2.02851i | 0.285536 | − | 0.121227i | ||||
\(281\) | 4.29844 | − | 7.44511i | 0.256423 | − | 0.444138i | −0.708858 | − | 0.705351i | \(-0.750789\pi\) |
0.965281 | + | 0.261213i | \(0.0841226\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.4490 | + | 7.18742i | −0.740015 | + | 0.427248i | −0.822075 | − | 0.569379i | \(-0.807184\pi\) |
0.0820596 | + | 0.996627i | \(0.473850\pi\) | |||||||
\(284\) | −2.30297 | −0.136656 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 17.1317 | 1.01302 | ||||||||
\(287\) | −10.3786 | + | 5.99208i | −0.612628 | + | 0.353701i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.10069 | − | 1.90644i | 0.0647462 | − | 0.112144i | ||||
\(290\) | 7.70800 | + | 18.1554i | 0.452629 | + | 1.06612i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.21454i | 0.363678i | ||||||||
\(293\) | 8.47490i | 0.495109i | 0.968874 | + | 0.247554i | \(0.0796269\pi\) | ||||
−0.968874 | + | 0.247554i | \(0.920373\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.58828 | − | 1.95012i | −0.150695 | − | 0.113541i | ||||
\(296\) | −7.79872 | −0.453291 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.33682 | + | 1.92651i | 0.193297 | + | 0.111600i | ||||
\(299\) | 15.1287 | + | 26.2037i | 0.874914 | + | 1.51540i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00290 | − | 5.20118i | −0.173084 | − | 0.299791i | ||||
\(302\) | 6.73182 | − | 3.88662i | 0.387373 | − | 0.223650i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.69397 | + | 4.01627i | −0.0971560 | + | 0.230349i | ||||
\(305\) | −2.94285 | + | 23.9814i | −0.168507 | + | 1.37317i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.6780 | − | 10.7838i | 1.06601 | − | 0.615462i | 0.138922 | − | 0.990303i | \(-0.455636\pi\) |
0.927089 | + | 0.374841i | \(0.122303\pi\) | |||||||
\(308\) | −5.73283 | − | 3.30985i | −0.326658 | − | 0.188596i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.921994 | − | 1.22371i | 0.0523657 | − | 0.0695018i | ||||
\(311\) | −6.25433 | −0.354650 | −0.177325 | − | 0.984152i | \(-0.556744\pi\) | ||||
−0.177325 | + | 0.984152i | \(0.556744\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.3732 | + | 8.87575i | 0.868947 | + | 0.501687i | 0.866998 | − | 0.498311i | \(-0.166046\pi\) |
0.00194901 | + | 0.999998i | \(0.499380\pi\) | |||||||
\(314\) | −9.63765 | + | 16.6929i | −0.543884 | + | 0.942035i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.01365 | 0.225786 | ||||||||
\(317\) | −0.640437 | − | 0.369757i | −0.0359705 | − | 0.0207676i | 0.481907 | − | 0.876222i | \(-0.339944\pi\) |
−0.517877 | + | 0.855455i | \(0.673278\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.5769 | − | 21.7838i | 0.704170 | − | 1.21966i | ||||
\(320\) | 2.05825 | − | 0.873846i | 0.115060 | − | 0.0488495i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 11.6915i | − | 0.651540i | ||||||
\(323\) | 17.5991 | + | 7.42288i | 0.979238 | + | 0.413020i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.8734 | − | 8.28370i | 1.60161 | − | 0.459497i | ||||
\(326\) | 7.95838 | + | 13.7843i | 0.440774 | + | 0.763442i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.47091 | + | 2.58128i | −0.246865 | + | 0.142527i | ||||
\(329\) | −9.15559 | + | 15.8579i | −0.504764 | + | 0.874277i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.54461 | −0.249794 | −0.124897 | − | 0.992170i | \(-0.539860\pi\) | ||||
−0.124897 | + | 0.992170i | \(0.539860\pi\) | |||||||
\(332\) | −10.5821 | − | 6.10958i | −0.580769 | − | 0.335307i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.0151 | −1.04046 | ||||||||
\(335\) | −15.1079 | − | 1.85394i | −0.825431 | − | 0.101291i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.9486 | − | 10.3626i | 0.977722 | − | 0.564488i | 0.0761405 | − | 0.997097i | \(-0.475740\pi\) |
0.901582 | + | 0.432609i | \(0.142407\pi\) | |||||||
\(338\) | 19.9981 | + | 11.5459i | 1.08775 | + | 0.628014i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.82914 | − | 9.01912i | −0.207664 | − | 0.489131i | ||||
\(341\) | −1.95396 | −0.105813 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.9899i | − | 1.07935i | ||||||
\(344\) | −1.29360 | − | 2.24057i | −0.0697460 | − | 0.120804i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.14712 | + | 12.3792i | −0.384232 | + | 0.665509i | ||||
\(347\) | −10.7406 | + | 6.20108i | −0.576585 | + | 0.332891i | −0.759775 | − | 0.650186i | \(-0.774691\pi\) |
0.183190 | + | 0.983077i | \(0.441358\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.4163 | 0.771684 | 0.385842 | − | 0.922565i | \(-0.373911\pi\) | ||||
0.385842 | + | 0.922565i | \(0.373911\pi\) | |||||||
\(350\) | −11.2624 | − | 2.80636i | −0.602002 | − | 0.150006i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.46960 | − | 1.42582i | −0.131630 | − | 0.0759967i | ||||
\(353\) | − | 35.6707i | − | 1.89856i | −0.314430 | − | 0.949281i | \(-0.601813\pi\) | ||
0.314430 | − | 0.949281i | \(-0.398187\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.11287 | + | 3.09882i | 0.218289 | + | 0.164468i | ||||
\(356\) | −4.34444 | − | 7.52479i | −0.230255 | − | 0.398813i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.77363 | − | 3.33341i | 0.305146 | − | 0.176176i | ||||
\(359\) | −1.15286 | − | 1.99682i | −0.0608457 | − | 0.105388i | 0.833998 | − | 0.551768i | \(-0.186046\pi\) |
−0.894844 | + | 0.446380i | \(0.852713\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.15348 | + | 18.2877i | −0.271236 | + | 0.962513i | ||||
\(362\) | 6.13587i | 0.322494i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.97295 | − | 12.0775i | −0.365482 | − | 0.633033i | ||||
\(365\) | 8.36212 | − | 11.0985i | 0.437693 | − | 0.580923i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.47038 | − | 5.46773i | −0.494350 | − | 0.285413i | 0.232027 | − | 0.972709i | \(-0.425464\pi\) |
−0.726377 | + | 0.687296i | \(0.758797\pi\) | |||||||
\(368\) | − | 5.03648i | − | 0.262545i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 13.9277 | + | 10.4937i | 0.724067 | + | 0.545544i | ||||
\(371\) | 6.52568 | − | 11.3028i | 0.338796 | − | 0.586813i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.3847i | 1.21082i | 0.795915 | + | 0.605408i | \(0.206990\pi\) | ||||
−0.795915 | + | 0.605408i | \(0.793010\pi\) | |||||||
\(374\) | −6.24787 | + | 10.8216i | −0.323070 | + | 0.559573i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.94406 | + | 6.83132i | −0.203400 | + | 0.352298i | ||||
\(377\) | 45.8925 | − | 26.4960i | 2.36358 | − | 1.36462i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.2493 | −1.19424 | −0.597118 | − | 0.802154i | \(-0.703687\pi\) | ||||
−0.597118 | + | 0.802154i | \(0.703687\pi\) | |||||||
\(380\) | 8.42946 | − | 4.89329i | 0.432422 | − | 0.251020i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.3200 | − | 9.42238i | 0.835006 | − | 0.482091i | ||||
\(383\) | −17.9351 | + | 10.3548i | −0.916441 | + | 0.529107i | −0.882498 | − | 0.470317i | \(-0.844140\pi\) |
−0.0339428 | + | 0.999424i | \(0.510806\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.78460 | + | 13.6250i | 0.294810 | + | 0.694394i | ||||
\(386\) | 8.26218 | − | 14.3105i | 0.420534 | − | 0.728386i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 6.69361i | − | 0.339817i | ||||||
\(389\) | −18.1887 | + | 31.5037i | −0.922203 | + | 1.59730i | −0.126203 | + | 0.992004i | \(0.540279\pi\) |
−0.795999 | + | 0.605297i | \(0.793054\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.0695 | −1.11610 | ||||||||
\(392\) | − | 1.61129i | − | 0.0813825i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.45127 | + | 5.97778i | 0.173873 | + | 0.301156i | ||||
\(395\) | −7.16797 | − | 5.40067i | −0.360660 | − | 0.271737i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.6128 | − | 16.5196i | 1.43604 | − | 0.829096i | 0.438464 | − | 0.898749i | \(-0.355523\pi\) |
0.997571 | + | 0.0696530i | \(0.0221892\pi\) | |||||||
\(398\) | − | 6.53029i | − | 0.327334i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.85165 | − | 1.20893i | −0.242582 | − | 0.0604465i | ||||
\(401\) | 10.5982 | + | 18.3566i | 0.529249 | + | 0.916685i | 0.999418 | + | 0.0341092i | \(0.0108594\pi\) |
−0.470170 | + | 0.882576i | \(0.655807\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.56496 | − | 2.05823i | −0.177583 | − | 0.102528i | ||||
\(404\) | −7.02206 | − | 12.1626i | −0.349361 | − | 0.605110i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.4762 | −1.01622 | ||||||||
\(407\) | − | 22.2392i | − | 1.10236i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.26086 | + | 9.11207i | −0.260133 | + | 0.450563i | −0.966277 | − | 0.257505i | \(-0.917100\pi\) |
0.706144 | + | 0.708068i | \(0.250433\pi\) | |||||||
\(410\) | 11.4579 | + | 1.40604i | 0.565865 | + | 0.0694392i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.2073 | + | 7.04788i | 0.601410 | + | 0.347224i | ||||
\(413\) | 2.91358 | − | 1.68216i | 0.143368 | − | 0.0827735i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.6777 | + | 25.1501i | 0.524146 | + | 1.23457i | ||||
\(416\) | −3.00382 | − | 5.20277i | −0.147275 | − | 0.255087i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.4530 | − | 4.83061i | −0.560185 | − | 0.236273i | ||||
\(419\) | 26.3874 | 1.28911 | 0.644555 | − | 0.764558i | \(-0.277043\pi\) | ||||
0.644555 | + | 0.764558i | \(0.277043\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.24202 | − | 7.34740i | −0.206743 | − | 0.358090i | 0.743943 | − | 0.668243i | \(-0.232953\pi\) |
−0.950687 | + | 0.310152i | \(0.899620\pi\) | |||||||
\(422\) | −19.3891 | − | 11.1943i | −0.943847 | − | 0.544931i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.81115 | − | 4.86905i | 0.136521 | − | 0.236462i | ||||
\(425\) | −5.29745 | + | 21.2596i | −0.256964 | + | 1.03124i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.7225 | − | 12.5415i | −1.05122 | − | 0.606924i | ||||
\(428\) | 14.5258 | + | 8.38645i | 0.702129 | + | 0.405374i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.704628 | + | 5.74206i | −0.0339802 | + | 0.276907i | ||||
\(431\) | −9.83833 | + | 17.0405i | −0.473896 | + | 0.820811i | −0.999553 | − | 0.0298849i | \(-0.990486\pi\) |
0.525658 | + | 0.850696i | \(0.323819\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.0899 | − | 6.98010i | −0.581003 | − | 0.335442i | 0.180529 | − | 0.983570i | \(-0.442219\pi\) |
−0.761532 | + | 0.648127i | \(0.775552\pi\) | |||||||
\(434\) | 0.795303 | + | 1.37751i | 0.0381758 | + | 0.0661224i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.90382 | 0.426416 | ||||||||
\(437\) | −2.72531 | − | 21.7837i | −0.130369 | − | 1.04205i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.2610 | + | 17.7725i | 0.489729 | + | 0.848236i | 0.999930 | − | 0.0118193i | \(-0.00376230\pi\) |
−0.510201 | + | 0.860055i | \(0.670429\pi\) | |||||||
\(440\) | 2.49190 | + | 5.86941i | 0.118797 | + | 0.279813i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −22.7982 | + | 13.1626i | −1.08440 | + | 0.626079i | ||||
\(443\) | 20.4256 | + | 11.7927i | 0.970450 | + | 0.560290i | 0.899374 | − | 0.437181i | \(-0.144023\pi\) |
0.0710768 | + | 0.997471i | \(0.477356\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.36644 | + | 19.2843i | −0.112180 | + | 0.914162i | ||||
\(446\) | −0.938256 | + | 1.62511i | −0.0444277 | + | 0.0769510i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.32136i | 0.109674i | ||||||||
\(449\) | 28.2500 | 1.33320 | 0.666601 | − | 0.745415i | \(-0.267749\pi\) | ||||
0.666601 | + | 0.745415i | \(0.267749\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.36090 | − | 12.7495i | −0.346611 | − | 0.600349i | ||||
\(452\) | −10.2945 | − | 5.94352i | −0.484212 | − | 0.279560i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.1852 | − | 17.6412i | −0.478013 | − | 0.827943i | ||||
\(455\) | −3.79820 | + | 30.9518i | −0.178063 | + | 1.45104i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 31.6784i | − | 1.48185i | −0.671587 | − | 0.740926i | \(-0.734387\pi\) | ||
0.671587 | − | 0.740926i | \(-0.265613\pi\) | |||||||
\(458\) | −9.33688 | + | 5.39065i | −0.436284 | + | 0.251889i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.77695 | + | 8.99463i | −0.315977 | + | 0.419377i | ||||
\(461\) | −0.595751 | − | 1.03187i | −0.0277469 | − | 0.0480590i | 0.851819 | − | 0.523837i | \(-0.175500\pi\) |
−0.879565 | + | 0.475778i | \(0.842167\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.8469i | 0.922366i | 0.887305 | + | 0.461183i | \(0.152575\pi\) | ||||
−0.887305 | + | 0.461183i | \(0.847425\pi\) | |||||||
\(464\) | −8.82078 | −0.409494 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.78823 | + | 11.7576i | −0.314458 | + | 0.544658i | ||||
\(467\) | − | 14.2451i | − | 0.659184i | −0.944123 | − | 0.329592i | \(-0.893089\pi\) | ||
0.944123 | − | 0.329592i | \(-0.106911\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.90089 | − | 13.6847i | 0.364829 | − | 0.631903i | ||||
\(470\) | 16.2357 | − | 6.89300i | 0.748899 | − | 0.317951i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.25512 | − | 0.724643i | 0.0577715 | − | 0.0333544i | ||||
\(473\) | 6.38933 | − | 3.68888i | 0.293782 | − | 0.169615i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.6384 | − | 2.60355i | −0.992839 | − | 0.119459i | ||||
\(476\) | 10.1720 | 0.466235 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.80203 | + | 1.04040i | −0.0824231 | + | 0.0475870i | ||||
\(479\) | −14.3482 | + | 24.8519i | −0.655588 | + | 1.13551i | 0.326159 | + | 0.945315i | \(0.394246\pi\) |
−0.981746 | + | 0.190196i | \(0.939088\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.4260 | − | 40.5749i | 1.06813 | − | 1.85006i | ||||
\(482\) | 17.0263i | 0.775529i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.43405 | + | 2.48385i | −0.0651842 | + | 0.112902i | ||||
\(485\) | −9.00675 | + | 11.9541i | −0.408976 | + | 0.542808i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.6433i | 0.890122i | 0.895500 | + | 0.445061i | \(0.146818\pi\) | ||||
−0.895500 | + | 0.445061i | \(0.853182\pi\) | |||||||
\(488\) | −9.35765 | − | 5.40264i | −0.423601 | − | 0.244566i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.16811 | + | 2.87760i | −0.0979453 | + | 0.129997i | ||||
\(491\) | −4.99544 | − | 8.65235i | −0.225441 | − | 0.390475i | 0.731011 | − | 0.682366i | \(-0.239049\pi\) |
−0.956452 | + | 0.291891i | \(0.905716\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 38.6521i | 1.74080i | ||||||||
\(494\) | −15.8074 | − | 20.8775i | −0.711207 | − | 0.939324i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.342602 | + | 0.593405i | 0.0153833 | + | 0.0266446i | ||||
\(497\) | −4.62980 | + | 2.67301i | −0.207675 | + | 0.119901i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.18085 | − | 12.4376i | −0.321459 | − | 0.556784i | 0.659330 | − | 0.751854i | \(-0.270840\pi\) |
−0.980789 | + | 0.195070i | \(0.937507\pi\) | |||||||
\(500\) | 7.03784 | + | 8.68728i | 0.314742 | + | 0.388507i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 19.2514i | 0.859233i | ||||||||
\(503\) | 7.26003 | + | 4.19158i | 0.323709 | + | 0.186893i | 0.653044 | − | 0.757320i | \(-0.273491\pi\) |
−0.329336 | + | 0.944213i | \(0.606825\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.82495 | + | 31.1698i | −0.170208 | + | 1.38704i | ||||
\(506\) | 14.3623 | 0.638480 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.72660 | + | 4.46095i | −0.342812 | + | 0.197923i | ||||
\(509\) | −5.67635 | + | 9.83173i | −0.251600 | + | 0.435784i | −0.963966 | − | 0.266024i | \(-0.914290\pi\) |
0.712367 | + | 0.701808i | \(0.247623\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.21308 | + | 12.4934i | 0.319088 | + | 0.552677i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.6914 | 0.780333 | ||||||||
\(515\) | −12.3175 | − | 29.0126i | −0.542775 | − | 1.27845i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.4805 | − | 11.2471i | −0.856752 | − | 0.494646i | ||||
\(518\) | −15.6782 | + | 9.05181i | −0.688860 | + | 0.397714i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.63620 | + | 13.3335i | −0.0717520 | + | 0.584712i | ||||
\(521\) | 29.3742 | 1.28691 | 0.643453 | − | 0.765485i | \(-0.277501\pi\) | ||||
0.643453 | + | 0.765485i | \(0.277501\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.2243 | − | 20.3368i | −1.54025 | − | 0.889265i | −0.998822 | − | 0.0485186i | \(-0.984550\pi\) |
−0.541429 | − | 0.840746i | \(-0.682117\pi\) | |||||||
\(524\) | −0.0548638 | −0.00239673 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.76364 | + | 9.98291i | −0.251307 | + | 0.435276i | ||||
\(527\) | 2.60026 | − | 1.50126i | 0.113269 | − | 0.0653960i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.18305 | + | 2.04911i | 0.0514371 | + | 0.0890917i | ||||
\(530\) | −11.5721 | + | 4.91302i | −0.502659 | + | 0.213408i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.25612 | + | 10.0403i | 0.0544597 | + | 0.435302i | ||||
\(533\) | − | 31.0148i | − | 1.34340i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.6569 | − | 34.5228i | −0.633674 | − | 1.49255i | ||||
\(536\) | 3.40356 | − | 5.89514i | 0.147011 | − | 0.254631i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −17.8013 | − | 10.2776i | −0.767468 | − | 0.443098i | ||||
\(539\) | 4.59484 | 0.197914 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.6792 | + | 21.9610i | −0.545122 | + | 0.944179i | 0.453478 | + | 0.891268i | \(0.350183\pi\) |
−0.998599 | + | 0.0529108i | \(0.983150\pi\) | |||||||
\(542\) | 22.5014 | + | 12.9912i | 0.966518 | + | 0.558019i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.38194 | 0.187874 | ||||||||
\(545\) | −15.9013 | − | 11.9807i | −0.681137 | − | 0.513199i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.8110 | − | 16.0567i | −1.18911 | − | 0.686535i | −0.231009 | − | 0.972952i | \(-0.574203\pi\) |
−0.958105 | + | 0.286417i | \(0.907536\pi\) | |||||||
\(548\) | 15.5732 | − | 8.99119i | 0.665254 | − | 0.384085i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.44744 | − | 13.8352i | 0.146999 | − | 0.589935i | ||||
\(551\) | −38.1515 | + | 4.77304i | −1.62531 | + | 0.203338i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.06887 | − | 4.65857i | 0.343123 | − | 0.198102i | ||||
\(554\) | 2.07148 | + | 3.58791i | 0.0880087 | + | 0.152435i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.3327 | + | 17.8967i | 0.438203 | + | 0.758989i | ||||
\(557\) | −6.90306 | − | 3.98549i | −0.292492 | − | 0.168870i | 0.346573 | − | 0.938023i | \(-0.387345\pi\) |
−0.639065 | + | 0.769153i | \(0.720679\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.5429 | 0.657396 | ||||||||
\(560\) | 3.12356 | − | 4.14571i | 0.131995 | − | 0.175188i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 8.59688i | − | 0.362637i | ||||||
\(563\) | 13.8459i | 0.583537i | 0.956489 | + | 0.291768i | \(0.0942436\pi\) | ||||
−0.956489 | + | 0.291768i | \(0.905756\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.3874 | + | 24.4665i | 0.437003 | + | 1.02931i | ||||
\(566\) | −7.18742 | + | 12.4490i | −0.302110 | + | 0.523270i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.99443 | + | 1.15149i | −0.0836846 | + | 0.0483153i | ||||
\(569\) | −28.6171 | −1.19969 | −0.599845 | − | 0.800117i | \(-0.704771\pi\) | ||||
−0.599845 | + | 0.800117i | \(0.704771\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.2331 | 0.763033 | 0.381517 | − | 0.924362i | \(-0.375402\pi\) | ||||
0.381517 | + | 0.924362i | \(0.375402\pi\) | |||||||
\(572\) | 14.8365 | − | 8.56584i | 0.620344 | − | 0.358156i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.99208 | + | 10.3786i | −0.250105 | + | 0.433194i | ||||
\(575\) | 24.2059 | − | 6.94460i | 1.00946 | − | 0.289610i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 37.3878i | − | 1.55647i | −0.627970 | − | 0.778237i | \(-0.716114\pi\) | ||
0.627970 | − | 0.778237i | \(-0.283886\pi\) | |||||||
\(578\) | − | 2.20137i | − | 0.0915650i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 15.7530 | + | 11.8690i | 0.654108 | + | 0.492834i | ||||
\(581\) | −28.3651 | −1.17678 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.8848 | + | 8.01640i | 0.575050 | + | 0.332005i | ||||
\(584\) | 3.10727 | + | 5.38195i | 0.128580 | + | 0.222707i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.23745 | + | 7.33948i | 0.175047 | + | 0.303191i | ||||
\(587\) | 1.52408 | − | 0.879926i | 0.0629053 | − | 0.0363184i | −0.468217 | − | 0.883613i | \(-0.655104\pi\) |
0.531123 | + | 0.847295i | \(0.321770\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.80292 | + | 2.38120i | 0.0742879 | + | 0.0981155i | ||||
\(590\) | −3.21657 | − | 0.394717i | −0.132424 | − | 0.0162502i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.75389 | + | 3.89936i | −0.277583 | + | 0.160263i | ||||
\(593\) | 9.65263 | + | 5.57295i | 0.396386 | + | 0.228854i | 0.684923 | − | 0.728615i | \(-0.259836\pi\) |
−0.288537 | + | 0.957469i | \(0.593169\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.1662 | − | 13.6872i | −0.744743 | − | 0.561122i | ||||
\(596\) | 3.85302 | 0.157826 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 26.2037 | + | 15.1287i | 1.07155 | + | 0.618658i | ||||
\(599\) | −19.0286 | + | 32.9586i | −0.777489 | + | 1.34665i | 0.155896 | + | 0.987774i | \(0.450174\pi\) |
−0.933385 | + | 0.358877i | \(0.883160\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.4084 | 1.40355 | 0.701775 | − | 0.712399i | \(-0.252391\pi\) | ||||
0.701775 | + | 0.712399i | \(0.252391\pi\) | |||||||
\(602\) | −5.20118 | − | 3.00290i | −0.211984 | − | 0.122389i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.88662 | − | 6.73182i | 0.158144 | − | 0.273914i | ||||
\(605\) | 5.90327 | − | 2.50628i | 0.240002 | − | 0.101895i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 16.1885i | − | 0.657071i | −0.944492 | − | 0.328536i | \(-0.893445\pi\) | ||
0.944492 | − | 0.328536i | \(-0.106555\pi\) | |||||||
\(608\) | 0.541114 | + | 4.32518i | 0.0219451 | + | 0.175409i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.44215 | + | 22.2400i | 0.382301 | + | 0.900470i | ||||
\(611\) | −23.6945 | − | 41.0401i | −0.958578 | − | 1.66031i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.7637 | + | 9.67851i | −0.677078 | + | 0.390911i | −0.798753 | − | 0.601659i | \(-0.794507\pi\) |
0.121675 | + | 0.992570i | \(0.461173\pi\) | |||||||
\(614\) | 10.7838 | − | 18.6780i | 0.435197 | − | 0.753784i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.61970 | −0.266715 | ||||||||
\(617\) | 7.58517 | + | 4.37930i | 0.305367 | + | 0.176304i | 0.644852 | − | 0.764308i | \(-0.276919\pi\) |
−0.339484 | + | 0.940612i | \(0.610253\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.5640 | 1.46963 | 0.734815 | − | 0.678268i | \(-0.237269\pi\) | ||||
0.734815 | + | 0.678268i | \(0.237269\pi\) | |||||||
\(620\) | 0.186617 | − | 1.52076i | 0.00749473 | − | 0.0610750i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.41641 | + | 3.12716i | −0.217178 | + | 0.125388i | ||||
\(623\) | −17.4677 | − | 10.0850i | −0.699830 | − | 0.404047i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.879489 | − | 24.9845i | −0.0351796 | − | 0.999381i | ||||
\(626\) | 17.7515 | 0.709492 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19.2753i | 0.769169i | ||||||||
\(629\) | 17.0867 | + | 29.5951i | 0.681293 | + | 1.18003i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.0437 | − | 20.8604i | 0.479453 | − | 0.830437i | −0.520269 | − | 0.854002i | \(-0.674168\pi\) |
0.999722 | + | 0.0235650i | \(0.00750166\pi\) | |||||||
\(632\) | 3.47593 | − | 2.00683i | 0.138265 | − | 0.0798273i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.739513 | −0.0293698 | ||||||||
\(635\) | 19.8015 | + | 2.42991i | 0.785797 | + | 0.0964279i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.38318 | + | 4.84003i | 0.332154 | + | 0.191769i | ||||
\(638\) | − | 25.1538i | − | 0.995847i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.34557 | − | 1.78590i | 0.0531885 | − | 0.0705938i | ||||
\(641\) | 12.7503 | + | 22.0841i | 0.503605 | + | 0.872270i | 0.999991 | + | 0.00416788i | \(0.00132668\pi\) |
−0.496386 | + | 0.868102i | \(0.665340\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.09885 | − | 4.67587i | 0.319387 | − | 0.184398i | −0.331732 | − | 0.943374i | \(-0.607633\pi\) |
0.651119 | + | 0.758975i | \(0.274300\pi\) | |||||||
\(644\) | −5.84574 | − | 10.1251i | −0.230354 | − | 0.398985i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 18.9527 | − | 2.37113i | 0.745683 | − | 0.0932907i | ||||
\(647\) | 2.93501i | 0.115387i | 0.998334 | + | 0.0576935i | \(0.0183746\pi\) | ||||
−0.998334 | + | 0.0576935i | \(0.981625\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.06643 | + | 3.57916i | 0.0811144 | + | 0.140494i | ||||
\(650\) | 20.8633 | − | 21.6106i | 0.818325 | − | 0.847638i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.7843 | + | 7.95838i | 0.539835 | + | 0.311674i | ||||
\(653\) | 13.5336i | 0.529613i | 0.964302 | + | 0.264806i | \(0.0853080\pi\) | ||||
−0.964302 | + | 0.264806i | \(0.914692\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.0979811 | + | 0.0738233i | 0.00382844 | + | 0.00288451i | ||||
\(656\) | −2.58128 | + | 4.47091i | −0.100782 | + | 0.174560i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 18.3112i | 0.713844i | ||||||||
\(659\) | 11.2236 | − | 19.4399i | 0.437210 | − | 0.757270i | −0.560263 | − | 0.828315i | \(-0.689300\pi\) |
0.997473 | + | 0.0710447i | \(0.0226333\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.81389 | + | 8.33791i | −0.187239 | + | 0.324307i | −0.944329 | − | 0.329004i | \(-0.893287\pi\) |
0.757090 | + | 0.653311i | \(0.226620\pi\) | |||||||
\(662\) | −3.93574 | + | 2.27230i | −0.152967 | + | 0.0883156i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.2192 | −0.474196 | ||||||||
\(665\) | 11.2667 | − | 19.6211i | 0.436903 | − | 0.760876i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 38.4737 | − | 22.2128i | 1.48971 | − | 0.860084i | ||||
\(668\) | −16.4675 | + | 9.50754i | −0.637148 | + | 0.367858i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14.0108 | + | 5.94837i | −0.541283 | + | 0.229806i | ||||
\(671\) | 15.4064 | − | 26.6847i | 0.594758 | − | 1.03015i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.35484i | 0.129320i | 0.997907 | + | 0.0646598i | \(0.0205962\pi\) | ||||
−0.997907 | + | 0.0646598i | \(0.979404\pi\) | |||||||
\(674\) | 10.3626 | − | 17.9486i | 0.399153 | − | 0.691354i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.0918 | 0.888146 | ||||||||
\(677\) | 18.6287i | 0.715958i | 0.933730 | + | 0.357979i | \(0.116534\pi\) | ||||
−0.933730 | + | 0.357979i | \(0.883466\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.76914 | − | 13.4565i | −0.298152 | − | 0.516415i | ||||
\(680\) | −7.82569 | − | 5.89622i | −0.300102 | − | 0.226110i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.69218 | + | 0.976981i | −0.0647970 | + | 0.0374105i | ||||
\(683\) | − | 22.3842i | − | 0.856506i | −0.903659 | − | 0.428253i | \(-0.859129\pi\) | ||
0.903659 | − | 0.428253i | \(-0.140871\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −39.9104 | − | 4.89755i | −1.52490 | − | 0.187126i | ||||
\(686\) | −9.99495 | − | 17.3118i | −0.381609 | − | 0.660966i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.24057 | − | 1.29360i | −0.0854211 | − | 0.0493179i | ||||
\(689\) | 16.8884 | + | 29.2515i | 0.643396 | + | 1.11439i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.1700 | −1.64226 | −0.821132 | − | 0.570738i | \(-0.806657\pi\) | ||||
−0.821132 | + | 0.570738i | \(0.806657\pi\) | |||||||
\(692\) | 14.2942i | 0.543386i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.20108 | + | 10.7406i | −0.235390 | + | 0.407707i | ||||
\(695\) | 5.62826 | − | 45.8651i | 0.213492 | − | 1.73976i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.5912 | + | 11.3110i | 0.742071 | + | 0.428435i | ||||
\(698\) | 12.4848 | − | 7.20813i | 0.472558 | − | 0.272832i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11.1567 | + | 3.20083i | −0.421684 | + | 0.120980i | ||||
\(701\) | 14.1571 | + | 24.5208i | 0.534705 | + | 0.926137i | 0.999178 | + | 0.0405493i | \(0.0129108\pi\) |
−0.464472 | + | 0.885588i | \(0.653756\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.1018 | + | 20.5200i | −1.02216 | + | 0.773928i | ||||
\(704\) | −2.85165 | −0.107476 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.8354 | − | 30.8918i | −0.671243 | − | 1.16263i | ||||
\(707\) | −28.2337 | − | 16.3007i | −1.06184 | − | 0.613052i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.52409 | − | 14.7642i | 0.320129 | − | 0.554480i | −0.660385 | − | 0.750927i | \(-0.729607\pi\) |
0.980514 | + | 0.196447i | \(0.0629404\pi\) | |||||||
\(710\) | 5.11126 | + | 0.627221i | 0.191822 | + | 0.0235392i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.52479 | − | 4.34444i | −0.282003 | − | 0.162815i | ||||
\(713\) | −2.98867 | − | 1.72551i | −0.111927 | − | 0.0646208i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −38.0224 | − | 4.66586i | −1.42196 | − | 0.174493i | ||||
\(716\) | 3.33341 | − | 5.77363i | 0.124575 | − | 0.215771i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.99682 | − | 1.15286i | −0.0745205 | − | 0.0430244i | ||||
\(719\) | 1.65729 | + | 2.87050i | 0.0618063 | + | 0.107052i | 0.895273 | − | 0.445518i | \(-0.146981\pi\) |
−0.833467 | + | 0.552570i | \(0.813647\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.7213 | 1.21861 | ||||||||
\(722\) | 4.68083 | + | 18.4144i | 0.174202 | + | 0.685313i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.06793 | + | 5.31382i | 0.114019 | + | 0.197486i | ||||
\(725\) | −12.1626 | − | 42.3937i | −0.451708 | − | 1.57446i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.7663 | − | 17.1856i | 1.10397 | − | 0.637379i | 0.166711 | − | 0.986006i | \(-0.446685\pi\) |
0.937261 | + | 0.348627i | \(0.113352\pi\) | |||||||
\(728\) | −12.0775 | − | 6.97295i | −0.447622 | − | 0.258435i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.69255 | − | 13.7927i | 0.0626439 | − | 0.510489i | ||||
\(731\) | −5.66845 | + | 9.81805i | −0.209655 | + | 0.363134i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 39.0068i | − | 1.44075i | −0.693585 | − | 0.720375i | \(-0.743970\pi\) | ||
0.693585 | − | 0.720375i | \(-0.256030\pi\) | |||||||
\(734\) | −10.9355 | −0.403635 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.51824 | − | 4.36172i | −0.0928235 | − | 0.160775i | ||||
\(737\) | 16.8109 | + | 9.70576i | 0.619236 | + | 0.357516i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.19339 | − | 7.26316i | −0.154256 | − | 0.267180i | 0.778532 | − | 0.627605i | \(-0.215965\pi\) |
−0.932788 | + | 0.360426i | \(0.882631\pi\) | |||||||
\(740\) | 17.3086 | + | 2.12400i | 0.636278 | + | 0.0780798i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 13.0514i | − | 0.479131i | ||||||
\(743\) | −1.64985 | + | 0.952540i | −0.0605270 | + | 0.0349453i | −0.529958 | − | 0.848024i | \(-0.677792\pi\) |
0.469431 | + | 0.882969i | \(0.344459\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.88111 | − | 5.18453i | −0.252104 | − | 0.189946i | ||||
\(746\) | 11.6924 | + | 20.2518i | 0.428088 | + | 0.741470i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.4957i | 0.456890i | ||||||||
\(749\) | 38.9359 | 1.42269 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.63534 | + | 9.76069i | −0.205636 | + | 0.356173i | −0.950335 | − | 0.311228i | \(-0.899260\pi\) |
0.744699 | + | 0.667401i | \(0.232593\pi\) | |||||||
\(752\) | 7.88813i | 0.287650i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 26.4960 | − | 45.8925i | 0.964929 | − | 1.67131i | ||||
\(755\) | −15.9993 | + | 6.79261i | −0.582273 | + | 0.247208i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.7692 | + | 22.3834i | −1.40909 | + | 0.813540i | −0.995301 | − | 0.0968318i | \(-0.969129\pi\) |
−0.413792 | + | 0.910372i | \(0.635796\pi\) | |||||||
\(758\) | −20.1345 | + | 11.6246i | −0.731317 | + | 0.422226i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.85348 | − | 8.45244i | 0.176054 | − | 0.306602i | ||||
\(761\) | 33.7181 | 1.22228 | 0.611139 | − | 0.791523i | \(-0.290711\pi\) | ||||
0.611139 | + | 0.791523i | \(0.290711\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.8998 | − | 10.3345i | 0.648018 | − | 0.374133i | ||||
\(764\) | 9.42238 | − | 16.3200i | 0.340890 | − | 0.590439i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.3548 | + | 17.9351i | −0.374135 | + | 0.648021i | ||||
\(767\) | 8.70680i | 0.314384i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.2178 | − | 28.0901i | 0.584830 | − | 1.01296i | −0.410066 | − | 0.912056i | \(-0.634494\pi\) |
0.994897 | − | 0.100900i | \(-0.0321723\pi\) | |||||||
\(770\) | 11.8221 | + | 8.90730i | 0.426039 | + | 0.320997i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 16.5244i | − | 0.594725i | ||||||
\(773\) | 35.2122 | + | 20.3298i | 1.26649 | + | 0.731211i | 0.974323 | − | 0.225155i | \(-0.0722888\pi\) |
0.292172 | + | 0.956366i | \(0.405622\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.37957 | + | 2.46481i | −0.0854767 | + | 0.0885385i | ||||
\(776\) | −3.34681 | − | 5.79684i | −0.120143 | − | 0.208094i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 36.3774i | 1.30419i | ||||||||
\(779\) | −8.74524 | + | 20.7343i | −0.313331 | + | 0.742882i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.28363 | − | 5.68742i | −0.117498 | − | 0.203512i | ||||
\(782\) | −19.1128 | + | 11.0348i | −0.683471 | + | 0.394602i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.805646 | − | 1.39542i | −0.0287731 | − | 0.0498364i | ||||
\(785\) | 25.9364 | − | 34.4237i | 0.925708 | − | 1.22864i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.0432i | 1.17786i | 0.808183 | + | 0.588931i | \(0.200451\pi\) | ||||
−0.808183 | + | 0.588931i | \(0.799549\pi\) | |||||||
\(788\) | 5.97778 | + | 3.45127i | 0.212949 | + | 0.122946i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.90798 | − | 1.09313i | −0.316932 | − | 0.0388918i | ||||
\(791\) | −27.5941 | −0.981133 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 56.2174 | − | 32.4571i | 1.99634 | − | 1.15259i | ||||
\(794\) | 16.5196 | − | 28.6128i | 0.586259 | − | 1.01543i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.26514 | − | 5.65540i | −0.115730 | − | 0.200450i | ||||
\(797\) | 25.1288i | 0.890109i | 0.895504 | + | 0.445054i | \(0.146816\pi\) | ||||
−0.895504 | + | 0.445054i | \(0.853184\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.5653 | 1.22283 | ||||||||
\(800\) | −4.80612 | + | 1.37886i | −0.169922 | + | 0.0487501i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.3566 | + | 10.5982i | 0.648194 | + | 0.374235i | ||||
\(803\) | −15.3474 | + | 8.86083i | −0.541599 | + | 0.312692i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.18420 | + | 25.9483i | −0.112228 | + | 0.914557i | ||||
\(806\) | −4.11647 | −0.144996 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.1626 | − | 7.02206i | −0.427878 | − | 0.247035i | ||||
\(809\) | −22.9578 | −0.807152 | −0.403576 | − | 0.914946i | \(-0.632233\pi\) | ||||
−0.403576 | + | 0.914946i | \(0.632233\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.0425 | + | 46.8390i | −0.949590 | + | 1.64474i | −0.203301 | + | 0.979116i | \(0.565167\pi\) |
−0.746289 | + | 0.665622i | \(0.768166\pi\) | |||||||
\(812\) | −17.7329 | + | 10.2381i | −0.622303 | + | 0.359287i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11.1196 | − | 19.2597i | −0.389742 | − | 0.675052i | ||||
\(815\) | −13.9088 | − | 32.7607i | −0.487203 | − | 1.14756i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.3909 | − | 4.38263i | −0.363531 | − | 0.153329i | ||||
\(818\) | 10.5217i | 0.367883i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.6258 | − | 4.51128i | 0.371070 | − | 0.157541i | ||||
\(821\) | −5.40068 | + | 9.35426i | −0.188485 | + | 0.326466i | −0.944745 | − | 0.327805i | \(-0.893691\pi\) |
0.756260 | + | 0.654271i | \(0.227024\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.3326 | − | 16.9352i | −1.02247 | − | 0.590324i | −0.107652 | − | 0.994189i | \(-0.534333\pi\) |
−0.914819 | + | 0.403865i | \(0.867667\pi\) | |||||||
\(824\) | 14.0958 | 0.491049 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.68216 | − | 2.91358i | 0.0585297 | − | 0.101376i | ||||
\(827\) | −14.8973 | − | 8.60097i | −0.518030 | − | 0.299085i | 0.218098 | − | 0.975927i | \(-0.430015\pi\) |
−0.736128 | + | 0.676842i | \(0.763348\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.3463 | −0.532998 | −0.266499 | − | 0.963835i | \(-0.585867\pi\) | ||||
−0.266499 | + | 0.963835i | \(0.585867\pi\) | |||||||
\(830\) | 21.8222 | + | 16.4418i | 0.757459 | + | 0.570703i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.20277 | − | 3.00382i | −0.180374 | − | 0.104139i | ||||
\(833\) | −6.11464 | + | 3.53029i | −0.211860 | + | 0.122317i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 42.2024 | + | 5.17881i | 1.46048 | + | 0.179220i | ||||
\(836\) | −12.3339 | + | 1.54307i | −0.426577 | + | 0.0533680i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 22.8522 | − | 13.1937i | 0.789415 | − | 0.455769i | ||||
\(839\) | −22.5501 | − | 39.0579i | −0.778516 | − | 1.34843i | −0.932797 | − | 0.360402i | \(-0.882639\pi\) |
0.154281 | − | 0.988027i | \(-0.450694\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.4030 | − | 42.2673i | −0.841484 | − | 1.45749i | ||||
\(842\) | −7.34740 | − | 4.24202i | −0.253208 | − | 0.146190i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −22.3886 | −0.770648 | ||||||||
\(845\) | −41.2396 | − | 31.0717i | −1.41868 | − | 1.06890i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.65790i | 0.228768i | ||||||||
\(848\) | − | 5.62229i | − | 0.193070i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.04208 | + | 21.0601i | 0.207242 | + | 0.722355i | ||||
\(851\) | 19.6390 | − | 34.0158i | 0.673217 | − | 1.16605i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.3790 | − | 6.56967i | 0.389609 | − | 0.224941i | −0.292381 | − | 0.956302i | \(-0.594448\pi\) |
0.681991 | + | 0.731361i | \(0.261114\pi\) | |||||||
\(854\) | −25.0829 | −0.858320 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.7729 | 0.573286 | ||||||||
\(857\) | −19.8940 | + | 11.4858i | −0.679566 | + | 0.392348i | −0.799692 | − | 0.600411i | \(-0.795004\pi\) |
0.120125 | + | 0.992759i | \(0.461670\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.2488 | + | 19.4834i | −0.383803 | + | 0.664766i | −0.991602 | − | 0.129325i | \(-0.958719\pi\) |
0.607800 | + | 0.794090i | \(0.292052\pi\) | |||||||
\(860\) | 2.26081 | + | 5.32509i | 0.0770928 | + | 0.181584i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.6767i | 0.670190i | ||||||||
\(863\) | 24.1235i | 0.821175i | 0.911821 | + | 0.410587i | \(0.134676\pi\) | ||||
−0.911821 | + | 0.410587i | \(0.865324\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.2340 | − | 25.5281i | 0.653975 | − | 0.867980i | ||||
\(866\) | −13.9602 | −0.474387 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.37751 | + | 0.795303i | 0.0467556 | + | 0.0269943i | ||||
\(869\) | 5.72276 | + | 9.91212i | 0.194131 | + | 0.336246i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.4474 | + | 35.4159i | 0.692833 | + | 1.20002i | ||||
\(872\) | 7.71093 | − | 4.45191i | 0.261125 | − | 0.150761i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −13.2520 | − | 17.5026i | −0.448256 | − | 0.592033i | ||||
\(875\) | 24.2317 | + | 9.29584i | 0.819181 | + | 0.314257i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.11105 | − | 0.641465i | 0.0375175 | − | 0.0216607i | −0.481124 | − | 0.876653i | \(-0.659771\pi\) |
0.518641 | + | 0.854992i | \(0.326438\pi\) | |||||||
\(878\) | 17.7725 | + | 10.2610i | 0.599793 | + | 0.346291i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.09275 | + | 3.83710i | 0.171677 | + | 0.129349i | ||||
\(881\) | 18.1444 | 0.611301 | 0.305650 | − | 0.952144i | \(-0.401126\pi\) | ||||
0.305650 | + | 0.952144i | \(0.401126\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.6706 | − | 22.9039i | −1.33502 | − | 0.770776i | −0.348958 | − | 0.937138i | \(-0.613465\pi\) |
−0.986065 | + | 0.166362i | \(0.946798\pi\) | |||||||
\(884\) | −13.1626 | + | 22.7982i | −0.442705 | + | 0.766787i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.5855 | 0.792369 | ||||||||
\(887\) | −50.4856 | − | 29.1479i | −1.69514 | − | 0.978689i | −0.950243 | − | 0.311509i | \(-0.899166\pi\) |
−0.744896 | − | 0.667180i | \(-0.767501\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.3555 | + | 17.9362i | −0.347312 | + | 0.601561i | ||||
\(890\) | 7.59274 | + | 17.8839i | 0.254509 | + | 0.599469i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.87651i | 0.0628302i | ||||||||
\(893\) | 4.26837 | + | 34.1176i | 0.142836 | + | 1.14170i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.7220 | + | 5.82577i | −0.458675 | + | 0.194734i | ||||
\(896\) | 1.16068 | + | 2.01036i | 0.0387756 | + | 0.0671613i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24.4653 | − | 14.1250i | 0.816416 | − | 0.471358i | ||||
\(899\) | −3.02202 | + | 5.23429i | −0.100790 | + | 0.174573i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.6365 | −0.820762 | ||||||||
\(902\) | −12.7495 | − | 7.36090i | −0.424511 | − | 0.245091i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.8870 | −0.395357 | ||||||||
\(905\) | 1.67112 | − | 13.6181i | 0.0555499 | − | 0.452680i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.2008 | − | 15.7044i | 0.903187 | − | 0.521455i | 0.0249542 | − | 0.999689i | \(-0.492056\pi\) |
0.878233 | + | 0.478233i | \(0.158723\pi\) | |||||||
\(908\) | −17.6412 | − | 10.1852i | −0.585444 | − | 0.338006i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 12.1866 | + | 28.7042i | 0.403981 | + | 0.951533i | ||||
\(911\) | −19.8665 | −0.658206 | −0.329103 | − | 0.944294i | \(-0.606746\pi\) | ||||
−0.329103 | + | 0.944294i | \(0.606746\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 34.8448i | − | 1.15319i | ||||||
\(914\) | −15.8392 | − | 27.4343i | −0.523914 | − | 0.907445i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.39065 | + | 9.33688i | −0.178112 | + | 0.308499i | ||||
\(917\) | −0.110296 | + | 0.0636793i | −0.00364228 | + | 0.00210287i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.8314 | 1.34690 | 0.673451 | − | 0.739231i | \(-0.264811\pi\) | ||||
0.673451 | + | 0.739231i | \(0.264811\pi\) | |||||||
\(920\) | −1.37170 | + | 11.1781i | −0.0452235 | + | 0.368530i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.03187 | − | 0.595751i | −0.0339828 | − | 0.0196200i | ||||
\(923\) | − | 13.8354i | − | 0.455399i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.0534 | − | 27.0833i | −0.922391 | − | 0.890493i | ||||
\(926\) | 9.92347 | + | 17.1880i | 0.326106 | + | 0.564831i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.63902 | + | 4.41039i | −0.250763 | + | 0.144778i | ||||
\(929\) | −10.3109 | − | 17.8591i | −0.338291 | − | 0.585937i | 0.645821 | − | 0.763489i | \(-0.276515\pi\) |
−0.984111 | + | 0.177553i | \(0.943182\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.23964 | − | 5.59950i | −0.138949 | − | 0.183516i | ||||
\(932\) | 13.5765i | 0.444711i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.12255 | − | 12.3366i | −0.233057 | − | 0.403666i | ||||
\(935\) | 16.8139 | − | 22.3161i | 0.549875 | − | 0.729815i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.5342 | + | 6.65926i | 0.376805 | + | 0.217548i | 0.676427 | − | 0.736509i | \(-0.263527\pi\) |
−0.299622 | + | 0.954058i | \(0.596861\pi\) | |||||||
\(938\) | − | 15.8018i | − | 0.515946i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10.6141 | − | 14.0874i | 0.346192 | − | 0.459480i | ||||
\(941\) | −2.77725 | + | 4.81033i | −0.0905356 | + | 0.156812i | −0.907737 | − | 0.419540i | \(-0.862191\pi\) |
0.817201 | + | 0.576353i | \(0.195525\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 26.0011i | − | 0.846713i | ||||||
\(944\) | 0.724643 | − | 1.25512i | 0.0235851 | − | 0.0408506i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.68888 | − | 6.38933i | 0.119936 | − | 0.207735i | ||||
\(947\) | 1.05045 | − | 0.606477i | 0.0341350 | − | 0.0197079i | −0.482835 | − | 0.875711i | \(-0.660393\pi\) |
0.516970 | + | 0.856003i | \(0.327060\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37.3347 | −1.21194 | ||||||||
\(950\) | −20.0412 | + | 8.56448i | −0.650222 | + | 0.277868i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.80925 | − | 5.08602i | 0.285510 | − | 0.164839i | ||||
\(953\) | 5.12855 | − | 2.96097i | 0.166130 | − | 0.0959153i | −0.414630 | − | 0.909990i | \(-0.636089\pi\) |
0.580760 | + | 0.814075i | \(0.302756\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −38.7872 | + | 16.4674i | −1.25513 | + | 0.532873i | ||||
\(956\) | −1.04040 | + | 1.80203i | −0.0336491 | + | 0.0582819i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.6965i | 0.927141i | ||||||||
\(959\) | 20.8718 | − | 36.1510i | 0.673985 | − | 1.16738i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5305 | −0.984855 | ||||||||
\(962\) | − | 46.8519i | − | 1.51057i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.51317 | + | 14.7453i | 0.274191 | + | 0.474913i | ||||
\(965\) | −22.2348 | + | 29.5108i | −0.715762 | + | 0.949987i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.8853 | + | 22.4505i | −1.25047 | + | 0.721958i | −0.971202 | − | 0.238256i | \(-0.923424\pi\) |
−0.279265 | + | 0.960214i | \(0.590091\pi\) | |||||||
\(968\) | 2.86810i | 0.0921843i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.82302 | + | 14.8559i | −0.0585337 | + | 0.476995i | ||||
\(971\) | 3.97050 | + | 6.87710i | 0.127419 | + | 0.220697i | 0.922676 | − | 0.385576i | \(-0.125997\pi\) |
−0.795257 | + | 0.606273i | \(0.792664\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 41.5447 | + | 23.9858i | 1.33186 | + | 0.768950i | ||||
\(974\) | 9.82164 | + | 17.0116i | 0.314706 | + | 0.545086i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.8053 | −0.345869 | ||||||||
\(977\) | − | 25.2607i | − | 0.808162i | −0.914723 | − | 0.404081i | \(-0.867591\pi\) | ||
0.914723 | − | 0.404081i | \(-0.132409\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.3888 | − | 21.4581i | 0.395948 | − | 0.685802i | ||||
\(980\) | −0.438840 | + | 3.57613i | −0.0140182 | + | 0.114235i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.65235 | − | 4.99544i | −0.276108 | − | 0.159411i | ||||
\(983\) | −9.18945 | + | 5.30553i | −0.293098 | + | 0.169220i | −0.639338 | − | 0.768926i | \(-0.720792\pi\) |
0.346240 | + | 0.938146i | \(0.387458\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.03176 | − | 14.2072i | −0.192188 | − | 0.452678i | ||||
\(986\) | 19.3260 | + | 33.4737i | 0.615467 | + | 1.06602i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24.1283 | − | 10.1768i | −0.767625 | − | 0.323767i | ||||
\(989\) | 13.0303 | 0.414340 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.6138 | + | 18.3837i | 0.337159 | + | 0.583976i | 0.983897 | − | 0.178736i | \(-0.0572007\pi\) |
−0.646738 | + | 0.762712i | \(0.723867\pi\) | |||||||
\(992\) | 0.593405 | + | 0.342602i | 0.0188406 | + | 0.0108776i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.67301 | + | 4.62980i | −0.0847829 | + | 0.146848i | ||||
\(995\) | −1.77854 | + | 14.4935i | −0.0563836 | + | 0.459473i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.4427 | − | 19.8855i | −1.09081 | − | 0.629780i | −0.157019 | − | 0.987596i | \(-0.550188\pi\) |
−0.933792 | + | 0.357816i | \(0.883522\pi\) | |||||||
\(998\) | −12.4376 | − | 7.18085i | −0.393705 | − | 0.227306i | ||||
\(999\) | 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 | 1710.2.t.c.919.6 | 20 | ||
3.2 | odd | 2 | 570.2.q.c.349.5 | yes | 20 | ||
5.4 | even | 2 | inner | 1710.2.t.c.919.4 | 20 | ||
15.14 | odd | 2 | 570.2.q.c.349.7 | yes | 20 | ||
19.11 | even | 3 | inner | 1710.2.t.c.1189.4 | 20 | ||
57.11 | odd | 6 | 570.2.q.c.49.7 | yes | 20 | ||
95.49 | even | 6 | inner | 1710.2.t.c.1189.6 | 20 | ||
285.239 | odd | 6 | 570.2.q.c.49.5 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.q.c.49.5 | ✓ | 20 | 285.239 | odd | 6 | ||
570.2.q.c.49.7 | yes | 20 | 57.11 | odd | 6 | ||
570.2.q.c.349.5 | yes | 20 | 3.2 | odd | 2 | ||
570.2.q.c.349.7 | yes | 20 | 15.14 | odd | 2 | ||
1710.2.t.c.919.4 | 20 | 5.4 | even | 2 | inner | ||
1710.2.t.c.919.6 | 20 | 1.1 | even | 1 | trivial | ||
1710.2.t.c.1189.4 | 20 | 19.11 | even | 3 | inner | ||
1710.2.t.c.1189.6 | 20 | 95.49 | even | 6 | inner |