Properties

Label 162.3.f.a.89.4
Level $162$
Weight $3$
Character 162.89
Analytic conductor $4.414$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,3,Mod(17,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([11]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.17");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 162.f (of order \(18\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.41418028264\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 89.4
Character \(\chi\) \(=\) 162.89
Dual form 162.3.f.a.71.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.39273 + 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(-5.54906 - 6.61311i) q^{5} +(7.83131 - 2.85036i) q^{7} +(2.44949 + 1.41421i) q^{8} +O(q^{10})\) \(q+(1.39273 + 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(-5.54906 - 6.61311i) q^{5} +(7.83131 - 2.85036i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-6.10431 - 10.5730i) q^{10} +(10.8191 - 12.8937i) q^{11} +(0.524960 + 2.97720i) q^{13} +(11.6069 - 2.04660i) q^{14} +(3.06418 + 2.57115i) q^{16} +(-8.43596 + 4.87051i) q^{17} +(3.84677 - 6.66281i) q^{19} +(-5.90519 - 16.2244i) q^{20} +(18.2344 - 15.3005i) q^{22} +(-10.1434 + 27.8689i) q^{23} +(-8.59998 + 48.7729i) q^{25} +4.27534i q^{26} +16.6678 q^{28} +(10.5809 + 1.86569i) q^{29} +(-10.8017 - 3.93149i) q^{31} +(3.63616 + 4.33340i) q^{32} +(-12.9451 + 4.71163i) q^{34} +(-62.3062 - 35.9725i) q^{35} +(-11.5925 - 20.0787i) q^{37} +(6.99373 - 8.33481i) q^{38} +(-4.24001 - 24.0463i) q^{40} +(16.7264 - 2.94931i) q^{41} +(18.0881 + 15.1778i) q^{43} +(29.1530 - 16.8315i) q^{44} +(-20.9710 + 36.3228i) q^{46} +(5.67901 + 15.6029i) q^{47} +(15.6687 - 13.1476i) q^{49} +(-23.9549 + 65.8155i) q^{50} +(-1.04992 + 5.95439i) q^{52} +75.3383i q^{53} -145.303 q^{55} +(23.2137 + 4.09321i) q^{56} +(14.2781 + 5.19681i) q^{58} +(38.6968 + 46.1170i) q^{59} +(32.1023 - 11.6843i) q^{61} +(-14.0783 - 8.12813i) q^{62} +(4.00000 + 6.92820i) q^{64} +(16.7755 - 19.9923i) q^{65} +(6.53483 + 37.0609i) q^{67} +(-19.1860 + 3.38302i) q^{68} +(-77.9416 - 65.4008i) q^{70} +(-44.0325 + 25.4222i) q^{71} +(49.2453 - 85.2954i) q^{73} +(-11.2143 - 30.8110i) q^{74} +(11.7872 - 9.89063i) q^{76} +(47.9758 - 131.813i) q^{77} +(-14.0913 + 79.9158i) q^{79} -34.5312i q^{80} +24.0196 q^{82} +(15.8868 + 2.80127i) q^{83} +(79.0209 + 28.7612i) q^{85} +(21.4646 + 25.5805i) q^{86} +(44.7356 - 16.2824i) q^{88} +(-14.0161 - 8.09222i) q^{89} +(12.5972 + 21.8190i) q^{91} +(-38.1269 + 45.4378i) q^{92} +(4.07761 + 23.1253i) q^{94} +(-65.4078 + 11.5332i) q^{95} +(-101.648 - 85.2929i) q^{97} +(25.0509 - 14.4632i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 18 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.39273 + 0.245576i 0.696364 + 0.122788i
\(3\) 0 0
\(4\) 1.87939 + 0.684040i 0.469846 + 0.171010i
\(5\) −5.54906 6.61311i −1.10981 1.32262i −0.941547 0.336880i \(-0.890628\pi\)
−0.168264 0.985742i \(-0.553816\pi\)
\(6\) 0 0
\(7\) 7.83131 2.85036i 1.11876 0.407195i 0.284560 0.958658i \(-0.408153\pi\)
0.834199 + 0.551463i \(0.185930\pi\)
\(8\) 2.44949 + 1.41421i 0.306186 + 0.176777i
\(9\) 0 0
\(10\) −6.10431 10.5730i −0.610431 1.05730i
\(11\) 10.8191 12.8937i 0.983551 1.17215i −0.00151930 0.999999i \(-0.500484\pi\)
0.985070 0.172152i \(-0.0550719\pi\)
\(12\) 0 0
\(13\) 0.524960 + 2.97720i 0.0403815 + 0.229015i 0.998319 0.0579628i \(-0.0184605\pi\)
−0.957937 + 0.286978i \(0.907349\pi\)
\(14\) 11.6069 2.04660i 0.829062 0.146186i
\(15\) 0 0
\(16\) 3.06418 + 2.57115i 0.191511 + 0.160697i
\(17\) −8.43596 + 4.87051i −0.496233 + 0.286500i −0.727157 0.686472i \(-0.759159\pi\)
0.230924 + 0.972972i \(0.425825\pi\)
\(18\) 0 0
\(19\) 3.84677 6.66281i 0.202462 0.350674i −0.746859 0.664982i \(-0.768439\pi\)
0.949321 + 0.314308i \(0.101772\pi\)
\(20\) −5.90519 16.2244i −0.295259 0.811218i
\(21\) 0 0
\(22\) 18.2344 15.3005i 0.828836 0.695476i
\(23\) −10.1434 + 27.8689i −0.441019 + 1.21169i 0.497804 + 0.867290i \(0.334140\pi\)
−0.938823 + 0.344400i \(0.888082\pi\)
\(24\) 0 0
\(25\) −8.59998 + 48.7729i −0.343999 + 1.95092i
\(26\) 4.27534i 0.164436i
\(27\) 0 0
\(28\) 16.6678 0.595279
\(29\) 10.5809 + 1.86569i 0.364858 + 0.0643342i 0.353072 0.935596i \(-0.385137\pi\)
0.0117860 + 0.999931i \(0.496248\pi\)
\(30\) 0 0
\(31\) −10.8017 3.93149i −0.348441 0.126822i 0.161870 0.986812i \(-0.448248\pi\)
−0.510311 + 0.859990i \(0.670470\pi\)
\(32\) 3.63616 + 4.33340i 0.113630 + 0.135419i
\(33\) 0 0
\(34\) −12.9451 + 4.71163i −0.380738 + 0.138577i
\(35\) −62.3062 35.9725i −1.78018 1.02779i
\(36\) 0 0
\(37\) −11.5925 20.0787i −0.313309 0.542668i 0.665767 0.746160i \(-0.268104\pi\)
−0.979077 + 0.203492i \(0.934771\pi\)
\(38\) 6.99373 8.33481i 0.184046 0.219337i
\(39\) 0 0
\(40\) −4.24001 24.0463i −0.106000 0.601158i
\(41\) 16.7264 2.94931i 0.407960 0.0719344i 0.0340976 0.999419i \(-0.489144\pi\)
0.373863 + 0.927484i \(0.378033\pi\)
\(42\) 0 0
\(43\) 18.0881 + 15.1778i 0.420655 + 0.352971i 0.828412 0.560119i \(-0.189245\pi\)
−0.407757 + 0.913090i \(0.633689\pi\)
\(44\) 29.1530 16.8315i 0.662567 0.382533i
\(45\) 0 0
\(46\) −20.9710 + 36.3228i −0.455891 + 0.789626i
\(47\) 5.67901 + 15.6029i 0.120830 + 0.331977i 0.985331 0.170653i \(-0.0545878\pi\)
−0.864501 + 0.502631i \(0.832366\pi\)
\(48\) 0 0
\(49\) 15.6687 13.1476i 0.319769 0.268318i
\(50\) −23.9549 + 65.8155i −0.479097 + 1.31631i
\(51\) 0 0
\(52\) −1.04992 + 5.95439i −0.0201908 + 0.114508i
\(53\) 75.3383i 1.42148i 0.703456 + 0.710739i \(0.251639\pi\)
−0.703456 + 0.710739i \(0.748361\pi\)
\(54\) 0 0
\(55\) −145.303 −2.64187
\(56\) 23.2137 + 4.09321i 0.414531 + 0.0730930i
\(57\) 0 0
\(58\) 14.2781 + 5.19681i 0.246174 + 0.0896001i
\(59\) 38.6968 + 46.1170i 0.655878 + 0.781645i 0.986788 0.162017i \(-0.0518001\pi\)
−0.330910 + 0.943662i \(0.607356\pi\)
\(60\) 0 0
\(61\) 32.1023 11.6843i 0.526267 0.191546i −0.0652037 0.997872i \(-0.520770\pi\)
0.591471 + 0.806326i \(0.298547\pi\)
\(62\) −14.0783 8.12813i −0.227070 0.131099i
\(63\) 0 0
\(64\) 4.00000 + 6.92820i 0.0625000 + 0.108253i
\(65\) 16.7755 19.9923i 0.258085 0.307573i
\(66\) 0 0
\(67\) 6.53483 + 37.0609i 0.0975348 + 0.553147i 0.993941 + 0.109914i \(0.0350575\pi\)
−0.896406 + 0.443233i \(0.853831\pi\)
\(68\) −19.1860 + 3.38302i −0.282148 + 0.0497503i
\(69\) 0 0
\(70\) −77.9416 65.4008i −1.11345 0.934297i
\(71\) −44.0325 + 25.4222i −0.620175 + 0.358058i −0.776937 0.629578i \(-0.783228\pi\)
0.156762 + 0.987636i \(0.449894\pi\)
\(72\) 0 0
\(73\) 49.2453 85.2954i 0.674593 1.16843i −0.301994 0.953310i \(-0.597652\pi\)
0.976588 0.215120i \(-0.0690144\pi\)
\(74\) −11.2143 30.8110i −0.151545 0.416365i
\(75\) 0 0
\(76\) 11.7872 9.89063i 0.155095 0.130140i
\(77\) 47.9758 131.813i 0.623063 1.71185i
\(78\) 0 0
\(79\) −14.0913 + 79.9158i −0.178371 + 1.01159i 0.755809 + 0.654792i \(0.227244\pi\)
−0.934180 + 0.356801i \(0.883867\pi\)
\(80\) 34.5312i 0.431640i
\(81\) 0 0
\(82\) 24.0196 0.292921
\(83\) 15.8868 + 2.80127i 0.191407 + 0.0337503i 0.268530 0.963271i \(-0.413462\pi\)
−0.0771226 + 0.997022i \(0.524573\pi\)
\(84\) 0 0
\(85\) 79.0209 + 28.7612i 0.929657 + 0.338368i
\(86\) 21.4646 + 25.5805i 0.249588 + 0.297448i
\(87\) 0 0
\(88\) 44.7356 16.2824i 0.508359 0.185027i
\(89\) −14.0161 8.09222i −0.157485 0.0909238i 0.419187 0.907900i \(-0.362315\pi\)
−0.576671 + 0.816976i \(0.695649\pi\)
\(90\) 0 0
\(91\) 12.5972 + 21.8190i 0.138431 + 0.239769i
\(92\) −38.1269 + 45.4378i −0.414422 + 0.493889i
\(93\) 0 0
\(94\) 4.07761 + 23.1253i 0.0433788 + 0.246014i
\(95\) −65.4078 + 11.5332i −0.688504 + 0.121402i
\(96\) 0 0
\(97\) −101.648 85.2929i −1.04792 0.879308i −0.0550452 0.998484i \(-0.517530\pi\)
−0.992873 + 0.119176i \(0.961975\pi\)
\(98\) 25.0509 14.4632i 0.255622 0.147583i
\(99\) 0 0
\(100\) −49.5253 + 85.7803i −0.495253 + 0.857803i
\(101\) 5.20626 + 14.3041i 0.0515471 + 0.141625i 0.962794 0.270235i \(-0.0871015\pi\)
−0.911247 + 0.411860i \(0.864879\pi\)
\(102\) 0 0
\(103\) −28.9968 + 24.3312i −0.281522 + 0.236225i −0.772604 0.634889i \(-0.781046\pi\)
0.491082 + 0.871113i \(0.336602\pi\)
\(104\) −2.92451 + 8.03502i −0.0281203 + 0.0772598i
\(105\) 0 0
\(106\) −18.5013 + 104.926i −0.174540 + 0.989866i
\(107\) 118.659i 1.10897i −0.832195 0.554483i \(-0.812916\pi\)
0.832195 0.554483i \(-0.187084\pi\)
\(108\) 0 0
\(109\) 206.055 1.89042 0.945208 0.326468i \(-0.105859\pi\)
0.945208 + 0.326468i \(0.105859\pi\)
\(110\) −202.367 35.6828i −1.83970 0.324389i
\(111\) 0 0
\(112\) 31.3252 + 11.4015i 0.279690 + 0.101799i
\(113\) 45.6567 + 54.4116i 0.404042 + 0.481519i 0.929248 0.369457i \(-0.120456\pi\)
−0.525206 + 0.850975i \(0.676012\pi\)
\(114\) 0 0
\(115\) 240.586 87.5663i 2.09206 0.761446i
\(116\) 18.6093 + 10.7441i 0.160425 + 0.0926215i
\(117\) 0 0
\(118\) 42.5689 + 73.7315i 0.360753 + 0.624843i
\(119\) −52.1819 + 62.1880i −0.438504 + 0.522588i
\(120\) 0 0
\(121\) −28.1828 159.833i −0.232916 1.32093i
\(122\) 47.5792 8.38949i 0.389993 0.0687663i
\(123\) 0 0
\(124\) −17.6112 14.7776i −0.142026 0.119174i
\(125\) 183.357 105.861i 1.46685 0.846888i
\(126\) 0 0
\(127\) −19.1347 + 33.1422i −0.150667 + 0.260963i −0.931473 0.363811i \(-0.881475\pi\)
0.780806 + 0.624774i \(0.214809\pi\)
\(128\) 3.86952 + 10.6314i 0.0302306 + 0.0830579i
\(129\) 0 0
\(130\) 28.2733 23.7241i 0.217487 0.182493i
\(131\) 74.5355 204.785i 0.568973 1.56324i −0.237137 0.971476i \(-0.576209\pi\)
0.806110 0.591765i \(-0.201569\pi\)
\(132\) 0 0
\(133\) 11.1339 63.1432i 0.0837132 0.474761i
\(134\) 53.2205i 0.397168i
\(135\) 0 0
\(136\) −27.5517 −0.202586
\(137\) 181.295 + 31.9672i 1.32332 + 0.233337i 0.790277 0.612749i \(-0.209936\pi\)
0.533045 + 0.846087i \(0.321048\pi\)
\(138\) 0 0
\(139\) −228.486 83.1623i −1.64379 0.598290i −0.656092 0.754681i \(-0.727792\pi\)
−0.987695 + 0.156391i \(0.950014\pi\)
\(140\) −92.4907 110.226i −0.660648 0.787329i
\(141\) 0 0
\(142\) −67.5683 + 24.5929i −0.475833 + 0.173189i
\(143\) 44.0665 + 25.4418i 0.308157 + 0.177915i
\(144\) 0 0
\(145\) −46.3758 80.3253i −0.319833 0.553968i
\(146\) 89.5318 106.700i 0.613232 0.730821i
\(147\) 0 0
\(148\) −8.05203 45.6653i −0.0544056 0.308550i
\(149\) −141.886 + 25.0183i −0.952255 + 0.167908i −0.628132 0.778107i \(-0.716180\pi\)
−0.324123 + 0.946015i \(0.605069\pi\)
\(150\) 0 0
\(151\) −77.8368 65.3129i −0.515476 0.432535i 0.347575 0.937652i \(-0.387005\pi\)
−0.863051 + 0.505117i \(0.831449\pi\)
\(152\) 18.8453 10.8803i 0.123982 0.0715810i
\(153\) 0 0
\(154\) 99.1872 171.797i 0.644073 1.11557i
\(155\) 33.9398 + 93.2488i 0.218966 + 0.601605i
\(156\) 0 0
\(157\) −237.118 + 198.965i −1.51030 + 1.26730i −0.647143 + 0.762369i \(0.724036\pi\)
−0.863162 + 0.504927i \(0.831519\pi\)
\(158\) −39.2508 + 107.841i −0.248423 + 0.682535i
\(159\) 0 0
\(160\) 8.48002 48.0926i 0.0530001 0.300579i
\(161\) 247.162i 1.53517i
\(162\) 0 0
\(163\) 160.056 0.981937 0.490969 0.871177i \(-0.336643\pi\)
0.490969 + 0.871177i \(0.336643\pi\)
\(164\) 33.4527 + 5.89862i 0.203980 + 0.0359672i
\(165\) 0 0
\(166\) 21.4381 + 7.80282i 0.129145 + 0.0470050i
\(167\) −160.019 190.703i −0.958197 1.14193i −0.989804 0.142434i \(-0.954507\pi\)
0.0316076 0.999500i \(-0.489937\pi\)
\(168\) 0 0
\(169\) 150.220 54.6756i 0.888875 0.323524i
\(170\) 102.992 + 59.4622i 0.605833 + 0.349778i
\(171\) 0 0
\(172\) 23.6124 + 40.8979i 0.137281 + 0.237778i
\(173\) −43.4383 + 51.7678i −0.251088 + 0.299236i −0.876836 0.480790i \(-0.840350\pi\)
0.625747 + 0.780026i \(0.284794\pi\)
\(174\) 0 0
\(175\) 71.6714 + 406.469i 0.409551 + 2.32268i
\(176\) 66.3031 11.6910i 0.376722 0.0664262i
\(177\) 0 0
\(178\) −17.5334 14.7123i −0.0985024 0.0826533i
\(179\) −203.717 + 117.616i −1.13808 + 0.657073i −0.945955 0.324297i \(-0.894872\pi\)
−0.192128 + 0.981370i \(0.561539\pi\)
\(180\) 0 0
\(181\) −108.916 + 188.647i −0.601744 + 1.04225i 0.390813 + 0.920470i \(0.372194\pi\)
−0.992557 + 0.121781i \(0.961140\pi\)
\(182\) 12.1863 + 33.4815i 0.0669576 + 0.183965i
\(183\) 0 0
\(184\) −64.2588 + 53.9195i −0.349233 + 0.293041i
\(185\) −68.4556 + 188.080i −0.370030 + 1.01665i
\(186\) 0 0
\(187\) −28.4706 + 161.465i −0.152249 + 0.863448i
\(188\) 33.2086i 0.176642i
\(189\) 0 0
\(190\) −93.9276 −0.494356
\(191\) −253.418 44.6844i −1.32679 0.233950i −0.535060 0.844814i \(-0.679711\pi\)
−0.791735 + 0.610864i \(0.790822\pi\)
\(192\) 0 0
\(193\) 72.0472 + 26.2230i 0.373302 + 0.135871i 0.521856 0.853034i \(-0.325240\pi\)
−0.148554 + 0.988904i \(0.547462\pi\)
\(194\) −120.622 143.752i −0.621765 0.740990i
\(195\) 0 0
\(196\) 38.4410 13.9914i 0.196127 0.0713845i
\(197\) 211.300 + 121.994i 1.07259 + 0.619260i 0.928888 0.370361i \(-0.120766\pi\)
0.143702 + 0.989621i \(0.454099\pi\)
\(198\) 0 0
\(199\) −41.0539 71.1075i −0.206301 0.357324i 0.744245 0.667906i \(-0.232809\pi\)
−0.950547 + 0.310582i \(0.899476\pi\)
\(200\) −90.0408 + 107.307i −0.450204 + 0.536533i
\(201\) 0 0
\(202\) 3.73817 + 21.2002i 0.0185058 + 0.104952i
\(203\) 88.1800 15.5485i 0.434384 0.0765936i
\(204\) 0 0
\(205\) −112.320 94.2474i −0.547901 0.459743i
\(206\) −46.3597 + 26.7658i −0.225047 + 0.129931i
\(207\) 0 0
\(208\) −6.04625 + 10.4724i −0.0290685 + 0.0503481i
\(209\) −44.2895 121.684i −0.211911 0.582221i
\(210\) 0 0
\(211\) 44.0427 36.9562i 0.208733 0.175148i −0.532427 0.846476i \(-0.678720\pi\)
0.741161 + 0.671328i \(0.234276\pi\)
\(212\) −51.5344 + 141.590i −0.243087 + 0.667876i
\(213\) 0 0
\(214\) 29.1399 165.260i 0.136168 0.772245i
\(215\) 203.841i 0.948098i
\(216\) 0 0
\(217\) −95.7975 −0.441463
\(218\) 286.979 + 50.6022i 1.31642 + 0.232120i
\(219\) 0 0
\(220\) −273.080 99.3930i −1.24127 0.451786i
\(221\) −18.9290 22.5587i −0.0856516 0.102076i
\(222\) 0 0
\(223\) −217.997 + 79.3444i −0.977565 + 0.355805i −0.780893 0.624665i \(-0.785236\pi\)
−0.196672 + 0.980469i \(0.563013\pi\)
\(224\) 40.8276 + 23.5718i 0.182266 + 0.105231i
\(225\) 0 0
\(226\) 50.2253 + 86.9928i 0.222236 + 0.384924i
\(227\) −137.899 + 164.342i −0.607485 + 0.723973i −0.978865 0.204508i \(-0.934440\pi\)
0.371379 + 0.928481i \(0.378885\pi\)
\(228\) 0 0
\(229\) −68.6623 389.403i −0.299835 1.70045i −0.646871 0.762599i \(-0.723923\pi\)
0.347036 0.937852i \(-0.387188\pi\)
\(230\) 356.576 62.8739i 1.55033 0.273365i
\(231\) 0 0
\(232\) 23.2792 + 19.5336i 0.100342 + 0.0841966i
\(233\) −82.9298 + 47.8796i −0.355922 + 0.205492i −0.667290 0.744798i \(-0.732546\pi\)
0.311368 + 0.950289i \(0.399213\pi\)
\(234\) 0 0
\(235\) 71.6708 124.138i 0.304982 0.528245i
\(236\) 41.1803 + 113.142i 0.174493 + 0.479415i
\(237\) 0 0
\(238\) −87.9471 + 73.7964i −0.369526 + 0.310069i
\(239\) 30.1617 82.8687i 0.126200 0.346731i −0.860462 0.509514i \(-0.829825\pi\)
0.986662 + 0.162784i \(0.0520473\pi\)
\(240\) 0 0
\(241\) −66.8780 + 379.284i −0.277502 + 1.57379i 0.453399 + 0.891308i \(0.350211\pi\)
−0.730901 + 0.682484i \(0.760900\pi\)
\(242\) 229.525i 0.948449i
\(243\) 0 0
\(244\) 68.3251 0.280021
\(245\) −173.893 30.6620i −0.709767 0.125151i
\(246\) 0 0
\(247\) 21.8559 + 7.95489i 0.0884854 + 0.0322060i
\(248\) −20.8986 24.9060i −0.0842687 0.100428i
\(249\) 0 0
\(250\) 281.363 102.408i 1.12545 0.409631i
\(251\) 126.850 + 73.2368i 0.505378 + 0.291780i 0.730932 0.682451i \(-0.239086\pi\)
−0.225554 + 0.974231i \(0.572419\pi\)
\(252\) 0 0
\(253\) 249.589 + 432.301i 0.986518 + 1.70870i
\(254\) −34.7883 + 41.4591i −0.136962 + 0.163225i
\(255\) 0 0
\(256\) 2.77837 + 15.7569i 0.0108530 + 0.0615505i
\(257\) −204.456 + 36.0511i −0.795548 + 0.140277i −0.556627 0.830762i \(-0.687905\pi\)
−0.238921 + 0.971039i \(0.576794\pi\)
\(258\) 0 0
\(259\) −148.016 124.200i −0.571489 0.479536i
\(260\) 45.2031 26.0980i 0.173858 0.100377i
\(261\) 0 0
\(262\) 154.098 266.905i 0.588160 1.01872i
\(263\) 11.3833 + 31.2753i 0.0432825 + 0.118918i 0.959451 0.281876i \(-0.0909567\pi\)
−0.916168 + 0.400794i \(0.868734\pi\)
\(264\) 0 0
\(265\) 498.221 418.057i 1.88008 1.57757i
\(266\) 31.0129 85.2071i 0.116590 0.320328i
\(267\) 0 0
\(268\) −13.0697 + 74.1217i −0.0487674 + 0.276574i
\(269\) 399.099i 1.48364i −0.670599 0.741820i \(-0.733963\pi\)
0.670599 0.741820i \(-0.266037\pi\)
\(270\) 0 0
\(271\) −83.9974 −0.309954 −0.154977 0.987918i \(-0.549530\pi\)
−0.154977 + 0.987918i \(0.549530\pi\)
\(272\) −38.3721 6.76604i −0.141074 0.0248751i
\(273\) 0 0
\(274\) 244.645 + 89.0434i 0.892864 + 0.324976i
\(275\) 535.817 + 638.562i 1.94843 + 2.32204i
\(276\) 0 0
\(277\) −168.403 + 61.2936i −0.607953 + 0.221277i −0.627607 0.778530i \(-0.715966\pi\)
0.0196546 + 0.999807i \(0.493743\pi\)
\(278\) −297.797 171.933i −1.07121 0.618465i
\(279\) 0 0
\(280\) −101.746 176.228i −0.363377 0.629387i
\(281\) 298.873 356.183i 1.06361 1.26756i 0.101513 0.994834i \(-0.467632\pi\)
0.962093 0.272722i \(-0.0879239\pi\)
\(282\) 0 0
\(283\) 45.4847 + 257.956i 0.160723 + 0.911507i 0.953365 + 0.301819i \(0.0975939\pi\)
−0.792642 + 0.609687i \(0.791295\pi\)
\(284\) −100.144 + 17.6580i −0.352619 + 0.0621762i
\(285\) 0 0
\(286\) 55.1248 + 46.2552i 0.192744 + 0.161731i
\(287\) 122.583 70.7732i 0.427118 0.246596i
\(288\) 0 0
\(289\) −97.0563 + 168.107i −0.335835 + 0.581683i
\(290\) −44.8630 123.260i −0.154700 0.425035i
\(291\) 0 0
\(292\) 150.896 126.617i 0.516769 0.433620i
\(293\) 33.5970 92.3071i 0.114666 0.315041i −0.869063 0.494701i \(-0.835278\pi\)
0.983729 + 0.179660i \(0.0574997\pi\)
\(294\) 0 0
\(295\) 90.2463 511.812i 0.305920 1.73496i
\(296\) 65.5768i 0.221543i
\(297\) 0 0
\(298\) −203.753 −0.683733
\(299\) −88.2960 15.5690i −0.295304 0.0520701i
\(300\) 0 0
\(301\) 184.916 + 67.3039i 0.614339 + 0.223601i
\(302\) −92.3663 110.078i −0.305849 0.364496i
\(303\) 0 0
\(304\) 28.9183 10.5254i 0.0951259 0.0346230i
\(305\) −255.407 147.459i −0.837400 0.483473i
\(306\) 0 0
\(307\) −246.426 426.822i −0.802690 1.39030i −0.917840 0.396952i \(-0.870068\pi\)
0.115150 0.993348i \(-0.463265\pi\)
\(308\) 180.330 214.909i 0.585487 0.697757i
\(309\) 0 0
\(310\) 24.3693 + 138.205i 0.0786106 + 0.445823i
\(311\) 16.6486 2.93559i 0.0535324 0.00943921i −0.146818 0.989164i \(-0.546903\pi\)
0.200350 + 0.979724i \(0.435792\pi\)
\(312\) 0 0
\(313\) 319.525 + 268.113i 1.02085 + 0.856591i 0.989734 0.142925i \(-0.0456507\pi\)
0.0311120 + 0.999516i \(0.490095\pi\)
\(314\) −379.102 + 218.875i −1.20733 + 0.697053i
\(315\) 0 0
\(316\) −81.1487 + 140.554i −0.256800 + 0.444790i
\(317\) −155.193 426.388i −0.489567 1.34507i −0.901074 0.433666i \(-0.857220\pi\)
0.411507 0.911407i \(-0.365003\pi\)
\(318\) 0 0
\(319\) 138.531 116.241i 0.434265 0.364392i
\(320\) 23.6207 64.8975i 0.0738148 0.202805i
\(321\) 0 0
\(322\) −60.6970 + 344.230i −0.188500 + 1.06904i
\(323\) 74.9429i 0.232021i
\(324\) 0 0
\(325\) −149.721 −0.460680
\(326\) 222.914 + 39.3058i 0.683786 + 0.120570i
\(327\) 0 0
\(328\) 45.1420 + 16.4303i 0.137628 + 0.0500925i
\(329\) 88.9481 + 106.004i 0.270359 + 0.322201i
\(330\) 0 0
\(331\) 220.616 80.2978i 0.666515 0.242591i 0.0134681 0.999909i \(-0.495713\pi\)
0.653046 + 0.757318i \(0.273491\pi\)
\(332\) 27.9412 + 16.1319i 0.0841604 + 0.0485900i
\(333\) 0 0
\(334\) −176.031 304.894i −0.527038 0.912857i
\(335\) 208.825 248.868i 0.623360 0.742891i
\(336\) 0 0
\(337\) −55.0894 312.428i −0.163470 0.927085i −0.950628 0.310333i \(-0.899559\pi\)
0.787158 0.616752i \(-0.211552\pi\)
\(338\) 222.643 39.2579i 0.658706 0.116148i
\(339\) 0 0
\(340\) 128.837 + 108.107i 0.378932 + 0.317961i
\(341\) −167.555 + 96.7381i −0.491365 + 0.283689i
\(342\) 0 0
\(343\) −118.950 + 206.027i −0.346793 + 0.600662i
\(344\) 22.8421 + 62.7583i 0.0664016 + 0.182437i
\(345\) 0 0
\(346\) −73.2107 + 61.4310i −0.211592 + 0.177546i
\(347\) 15.0965 41.4774i 0.0435059 0.119531i −0.916037 0.401093i \(-0.868630\pi\)
0.959543 + 0.281562i \(0.0908525\pi\)
\(348\) 0 0
\(349\) 57.3986 325.523i 0.164466 0.932732i −0.785148 0.619309i \(-0.787413\pi\)
0.949614 0.313423i \(-0.101476\pi\)
\(350\) 583.701i 1.66772i
\(351\) 0 0
\(352\) 95.2132 0.270492
\(353\) 466.298 + 82.2209i 1.32096 + 0.232920i 0.789283 0.614029i \(-0.210452\pi\)
0.531673 + 0.846949i \(0.321563\pi\)
\(354\) 0 0
\(355\) 412.458 + 150.123i 1.16185 + 0.422880i
\(356\) −20.8063 24.7960i −0.0584447 0.0696517i
\(357\) 0 0
\(358\) −312.606 + 113.779i −0.873201 + 0.317819i
\(359\) −378.055 218.270i −1.05308 0.607994i −0.129568 0.991571i \(-0.541359\pi\)
−0.923509 + 0.383576i \(0.874692\pi\)
\(360\) 0 0
\(361\) 150.905 + 261.375i 0.418018 + 0.724029i
\(362\) −198.017 + 235.988i −0.547009 + 0.651899i
\(363\) 0 0
\(364\) 8.74994 + 49.6234i 0.0240383 + 0.136328i
\(365\) −837.333 + 147.644i −2.29406 + 0.404505i
\(366\) 0 0
\(367\) 365.154 + 306.401i 0.994970 + 0.834879i 0.986280 0.165083i \(-0.0527893\pi\)
0.00869048 + 0.999962i \(0.497234\pi\)
\(368\) −102.736 + 59.3149i −0.279175 + 0.161182i
\(369\) 0 0
\(370\) −141.528 + 245.134i −0.382508 + 0.662523i
\(371\) 214.742 + 589.998i 0.578818 + 1.59029i
\(372\) 0 0
\(373\) −282.763 + 237.266i −0.758077 + 0.636102i −0.937625 0.347647i \(-0.886981\pi\)
0.179549 + 0.983749i \(0.442536\pi\)
\(374\) −79.3036 + 217.885i −0.212042 + 0.582580i
\(375\) 0 0
\(376\) −8.15522 + 46.2506i −0.0216894 + 0.123007i
\(377\) 32.4807i 0.0861558i
\(378\) 0 0
\(379\) −216.903 −0.572304 −0.286152 0.958184i \(-0.592376\pi\)
−0.286152 + 0.958184i \(0.592376\pi\)
\(380\) −130.816 23.0663i −0.344252 0.0607009i
\(381\) 0 0
\(382\) −341.969 124.466i −0.895206 0.325828i
\(383\) 346.686 + 413.164i 0.905185 + 1.07876i 0.996555 + 0.0829400i \(0.0264310\pi\)
−0.0913699 + 0.995817i \(0.529125\pi\)
\(384\) 0 0
\(385\) −1137.91 + 414.166i −2.95561 + 1.07576i
\(386\) 93.9025 + 54.2146i 0.243271 + 0.140452i
\(387\) 0 0
\(388\) −132.692 229.830i −0.341990 0.592344i
\(389\) −94.9161 + 113.117i −0.244000 + 0.290788i −0.874120 0.485710i \(-0.838561\pi\)
0.630120 + 0.776498i \(0.283006\pi\)
\(390\) 0 0
\(391\) −50.1658 284.504i −0.128301 0.727633i
\(392\) 56.9738 10.0460i 0.145341 0.0256276i
\(393\) 0 0
\(394\) 264.325 + 221.795i 0.670875 + 0.562931i
\(395\) 606.686 350.270i 1.53591 0.886760i
\(396\) 0 0
\(397\) 251.308 435.278i 0.633017 1.09642i −0.353915 0.935278i \(-0.615150\pi\)
0.986932 0.161139i \(-0.0515169\pi\)
\(398\) −39.7147 109.115i −0.0997857 0.274159i
\(399\) 0 0
\(400\) −151.754 + 127.337i −0.379386 + 0.318342i
\(401\) −79.1589 + 217.487i −0.197404 + 0.542362i −0.998415 0.0562876i \(-0.982074\pi\)
0.801011 + 0.598650i \(0.204296\pi\)
\(402\) 0 0
\(403\) 6.03437 34.2226i 0.0149736 0.0849196i
\(404\) 30.4442i 0.0753569i
\(405\) 0 0
\(406\) 126.629 0.311894
\(407\) −384.307 67.7638i −0.944244 0.166496i
\(408\) 0 0
\(409\) −423.279 154.061i −1.03491 0.376677i −0.231963 0.972725i \(-0.574515\pi\)
−0.802949 + 0.596048i \(0.796737\pi\)
\(410\) −133.286 158.844i −0.325088 0.387424i
\(411\) 0 0
\(412\) −71.1396 + 25.8927i −0.172669 + 0.0628463i
\(413\) 434.497 + 250.857i 1.05205 + 0.607402i
\(414\) 0 0
\(415\) −69.6317 120.606i −0.167787 0.290616i
\(416\) −10.9926 + 13.1004i −0.0264244 + 0.0314914i
\(417\) 0 0
\(418\) −31.8005 180.350i −0.0760777 0.431458i
\(419\) 324.142 57.1549i 0.773608 0.136408i 0.227111 0.973869i \(-0.427072\pi\)
0.546497 + 0.837461i \(0.315961\pi\)
\(420\) 0 0
\(421\) −156.740 131.520i −0.372303 0.312399i 0.437369 0.899282i \(-0.355910\pi\)
−0.809672 + 0.586883i \(0.800355\pi\)
\(422\) 70.4151 40.6542i 0.166860 0.0963369i
\(423\) 0 0
\(424\) −106.544 + 184.540i −0.251284 + 0.435237i
\(425\) −165.000 453.333i −0.388234 1.06666i
\(426\) 0 0
\(427\) 218.099 183.006i 0.510770 0.428587i
\(428\) 81.1678 223.007i 0.189645 0.521044i
\(429\) 0 0
\(430\) 50.0584 283.895i 0.116415 0.660222i
\(431\) 5.85402i 0.0135824i 0.999977 + 0.00679120i \(0.00216172\pi\)
−0.999977 + 0.00679120i \(0.997838\pi\)
\(432\) 0 0
\(433\) 233.310 0.538821 0.269411 0.963025i \(-0.413171\pi\)
0.269411 + 0.963025i \(0.413171\pi\)
\(434\) −133.420 23.5255i −0.307419 0.0542063i
\(435\) 0 0
\(436\) 387.257 + 140.950i 0.888205 + 0.323280i
\(437\) 146.665 + 174.789i 0.335619 + 0.399975i
\(438\) 0 0
\(439\) 126.662 46.1012i 0.288524 0.105014i −0.193704 0.981060i \(-0.562050\pi\)
0.482227 + 0.876046i \(0.339828\pi\)
\(440\) −355.918 205.489i −0.808904 0.467021i
\(441\) 0 0
\(442\) −20.8231 36.0666i −0.0471110 0.0815987i
\(443\) −18.4121 + 21.9426i −0.0415622 + 0.0495319i −0.786425 0.617686i \(-0.788070\pi\)
0.744863 + 0.667218i \(0.232515\pi\)
\(444\) 0 0
\(445\) 24.2616 + 137.594i 0.0545205 + 0.309201i
\(446\) −323.096 + 56.9705i −0.724430 + 0.127737i
\(447\) 0 0
\(448\) 51.0731 + 42.8555i 0.114003 + 0.0956595i
\(449\) −430.226 + 248.391i −0.958188 + 0.553210i −0.895615 0.444831i \(-0.853264\pi\)
−0.0625728 + 0.998040i \(0.519931\pi\)
\(450\) 0 0
\(451\) 142.936 247.573i 0.316932 0.548942i
\(452\) 48.5869 + 133.491i 0.107493 + 0.295335i
\(453\) 0 0
\(454\) −232.414 + 195.019i −0.511926 + 0.429557i
\(455\) 74.3889 204.382i 0.163492 0.449191i
\(456\) 0 0
\(457\) −80.5387 + 456.758i −0.176234 + 0.999470i 0.760477 + 0.649365i \(0.224965\pi\)
−0.936710 + 0.350105i \(0.886146\pi\)
\(458\) 559.195i 1.22095i
\(459\) 0 0
\(460\) 512.054 1.11316
\(461\) 262.335 + 46.2568i 0.569057 + 0.100340i 0.450771 0.892640i \(-0.351149\pi\)
0.118286 + 0.992980i \(0.462260\pi\)
\(462\) 0 0
\(463\) −224.935 81.8697i −0.485821 0.176824i 0.0874848 0.996166i \(-0.472117\pi\)
−0.573306 + 0.819341i \(0.694339\pi\)
\(464\) 27.6247 + 32.9218i 0.0595360 + 0.0709522i
\(465\) 0 0
\(466\) −127.257 + 46.3177i −0.273083 + 0.0993942i
\(467\) 184.565 + 106.559i 0.395215 + 0.228177i 0.684417 0.729091i \(-0.260057\pi\)
−0.289202 + 0.957268i \(0.593390\pi\)
\(468\) 0 0
\(469\) 156.813 + 271.609i 0.334357 + 0.579123i
\(470\) 130.303 155.289i 0.277241 0.330403i
\(471\) 0 0
\(472\) 29.5681 + 167.689i 0.0626442 + 0.355273i
\(473\) 391.394 69.0132i 0.827470 0.145905i
\(474\) 0 0
\(475\) 291.882 + 244.918i 0.614489 + 0.515617i
\(476\) −140.609 + 81.1807i −0.295397 + 0.170548i
\(477\) 0 0
\(478\) 62.3576 108.007i 0.130455 0.225955i
\(479\) −136.882 376.079i −0.285765 0.785134i −0.996647 0.0818220i \(-0.973926\pi\)
0.710882 0.703312i \(-0.248296\pi\)
\(480\) 0 0
\(481\) 53.6927 45.0535i 0.111627 0.0936664i
\(482\) −186.286 + 511.816i −0.386485 + 1.06186i
\(483\) 0 0
\(484\) 56.3657 319.666i 0.116458 0.660466i
\(485\) 1145.51i 2.36187i
\(486\) 0 0
\(487\) −323.676 −0.664632 −0.332316 0.943168i \(-0.607830\pi\)
−0.332316 + 0.943168i \(0.607830\pi\)
\(488\) 95.1583 + 16.7790i 0.194997 + 0.0343832i
\(489\) 0 0
\(490\) −234.656 85.4077i −0.478889 0.174301i
\(491\) −589.862 702.970i −1.20135 1.43171i −0.873392 0.487018i \(-0.838085\pi\)
−0.327956 0.944693i \(-0.606360\pi\)
\(492\) 0 0
\(493\) −98.3467 + 35.7953i −0.199486 + 0.0726070i
\(494\) 28.4858 + 16.4463i 0.0576635 + 0.0332921i
\(495\) 0 0
\(496\) −22.9898 39.8195i −0.0463504 0.0802813i
\(497\) −272.369 + 324.597i −0.548027 + 0.653113i
\(498\) 0 0
\(499\) −37.5201 212.787i −0.0751906 0.426427i −0.999045 0.0436840i \(-0.986091\pi\)
0.923855 0.382743i \(-0.125021\pi\)
\(500\) 417.011 73.5303i 0.834022 0.147061i
\(501\) 0 0
\(502\) 158.682 + 133.150i 0.316100 + 0.265240i
\(503\) −31.3557 + 18.1032i −0.0623373 + 0.0359905i −0.530845 0.847469i \(-0.678125\pi\)
0.468507 + 0.883460i \(0.344792\pi\)
\(504\) 0 0
\(505\) 65.7046 113.804i 0.130108 0.225354i
\(506\) 241.447 + 663.371i 0.477169 + 1.31101i
\(507\) 0 0
\(508\) −58.6321 + 49.1982i −0.115417 + 0.0968468i
\(509\) 79.8138 219.287i 0.156805 0.430818i −0.836267 0.548322i \(-0.815267\pi\)
0.993072 + 0.117503i \(0.0374891\pi\)
\(510\) 0 0
\(511\) 142.532 808.342i 0.278929 1.58188i
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) −293.605 −0.571216
\(515\) 321.809 + 56.7437i 0.624873 + 0.110182i
\(516\) 0 0
\(517\) 262.620 + 95.5860i 0.507970 + 0.184886i
\(518\) −175.645 209.326i −0.339083 0.404104i
\(519\) 0 0
\(520\) 69.3647 25.2467i 0.133394 0.0485513i
\(521\) 119.806 + 69.1700i 0.229954 + 0.132764i 0.610551 0.791977i \(-0.290948\pi\)
−0.380597 + 0.924741i \(0.624281\pi\)
\(522\) 0 0
\(523\) 98.4346 + 170.494i 0.188212 + 0.325992i 0.944654 0.328068i \(-0.106398\pi\)
−0.756442 + 0.654060i \(0.773064\pi\)
\(524\) 280.162 333.884i 0.534660 0.637183i
\(525\) 0 0
\(526\) 8.17338 + 46.3535i 0.0155387 + 0.0881246i
\(527\) 110.271 19.4437i 0.209243 0.0368951i
\(528\) 0 0
\(529\) −268.547 225.338i −0.507651 0.425969i
\(530\) 796.551 459.889i 1.50293 0.867715i
\(531\) 0 0
\(532\) 64.1173 111.054i 0.120521 0.208749i
\(533\) 17.5613 + 48.2494i 0.0329481 + 0.0905242i
\(534\) 0 0
\(535\) −784.708 + 658.448i −1.46674 + 1.23074i
\(536\) −36.4050 + 100.022i −0.0679197 + 0.186608i
\(537\) 0 0
\(538\) 98.0090 555.837i 0.182173 1.03315i
\(539\) 344.271i 0.638722i
\(540\) 0 0
\(541\) −136.735 −0.252745 −0.126373 0.991983i \(-0.540334\pi\)
−0.126373 + 0.991983i \(0.540334\pi\)
\(542\) −116.986 20.6277i −0.215841 0.0380585i
\(543\) 0 0
\(544\) −51.7803 18.8465i −0.0951844 0.0346443i
\(545\) −1143.41 1362.67i −2.09801 2.50031i
\(546\) 0 0
\(547\) 625.697 227.735i 1.14387 0.416335i 0.300561 0.953763i \(-0.402826\pi\)
0.843310 + 0.537428i \(0.180604\pi\)
\(548\) 318.857 + 184.092i 0.581855 + 0.335934i
\(549\) 0 0
\(550\) 589.433 + 1020.93i 1.07170 + 1.85623i
\(551\) 53.1330 63.3214i 0.0964300 0.114921i
\(552\) 0 0
\(553\) 117.436 + 666.011i 0.212361 + 1.20436i
\(554\) −249.592 + 44.0098i −0.450527 + 0.0794400i
\(555\) 0 0
\(556\) −372.528 312.588i −0.670014 0.562208i
\(557\) 943.861 544.939i 1.69454 0.978346i 0.743784 0.668420i \(-0.233029\pi\)
0.950761 0.309926i \(-0.100304\pi\)
\(558\) 0 0
\(559\) −35.6916 + 61.8197i −0.0638490 + 0.110590i
\(560\) −98.4265 270.425i −0.175762 0.482901i
\(561\) 0 0
\(562\) 503.719 422.671i 0.896298 0.752083i
\(563\) −209.400 + 575.323i −0.371937 + 1.02189i 0.602675 + 0.797987i \(0.294102\pi\)
−0.974612 + 0.223901i \(0.928121\pi\)
\(564\) 0 0
\(565\) 106.478 603.866i 0.188457 1.06879i
\(566\) 370.433i 0.654475i
\(567\) 0 0
\(568\) −143.809 −0.253186
\(569\) −491.784 86.7148i −0.864295 0.152399i −0.276111 0.961126i \(-0.589046\pi\)
−0.588184 + 0.808727i \(0.700157\pi\)
\(570\) 0 0
\(571\) 284.552 + 103.569i 0.498341 + 0.181381i 0.578947 0.815365i \(-0.303464\pi\)
−0.0806069 + 0.996746i \(0.525686\pi\)
\(572\) 65.4147 + 77.9582i 0.114361 + 0.136291i
\(573\) 0 0
\(574\) 188.105 68.4645i 0.327708 0.119276i
\(575\) −1272.01 734.397i −2.21220 1.27721i
\(576\) 0 0
\(577\) −18.5614 32.1493i −0.0321688 0.0557181i 0.849493 0.527600i \(-0.176908\pi\)
−0.881662 + 0.471882i \(0.843575\pi\)
\(578\) −176.456 + 210.292i −0.305287 + 0.363827i
\(579\) 0 0
\(580\) −32.2123 182.685i −0.0555385 0.314974i
\(581\) 132.399 23.3455i 0.227881 0.0401817i
\(582\) 0 0
\(583\) 971.386 + 815.090i 1.66619 + 1.39810i
\(584\) 241.252 139.287i 0.413102 0.238505i
\(585\) 0 0
\(586\) 69.4599 120.308i 0.118532 0.205304i
\(587\) 299.988 + 824.210i 0.511053 + 1.40411i 0.880141 + 0.474712i \(0.157448\pi\)
−0.369088 + 0.929394i \(0.620330\pi\)
\(588\) 0 0
\(589\) −67.7464 + 56.8459i −0.115019 + 0.0965126i
\(590\) 251.377 690.653i 0.426063 1.17060i
\(591\) 0 0
\(592\) 16.1041 91.3307i 0.0272028 0.154275i
\(593\) 284.591i 0.479917i −0.970783 0.239958i \(-0.922866\pi\)
0.970783 0.239958i \(-0.0771338\pi\)
\(594\) 0 0
\(595\) 700.817 1.17784
\(596\) −283.772 50.0367i −0.476127 0.0839541i
\(597\) 0 0
\(598\) −119.149 43.3667i −0.199246 0.0725195i
\(599\) 211.516 + 252.075i 0.353115 + 0.420827i 0.913138 0.407651i \(-0.133652\pi\)
−0.560022 + 0.828477i \(0.689207\pi\)
\(600\) 0 0
\(601\) −6.64685 + 2.41926i −0.0110597 + 0.00402538i −0.347544 0.937664i \(-0.612984\pi\)
0.336484 + 0.941689i \(0.390762\pi\)
\(602\) 241.010 + 139.147i 0.400348 + 0.231141i
\(603\) 0 0
\(604\) −101.609 175.992i −0.168226 0.291377i
\(605\) −900.604 + 1073.30i −1.48860 + 1.77405i
\(606\) 0 0
\(607\) 83.8924 + 475.778i 0.138208 + 0.783818i 0.972572 + 0.232603i \(0.0747244\pi\)
−0.834363 + 0.551215i \(0.814165\pi\)
\(608\) 42.8601 7.55739i 0.0704936 0.0124299i
\(609\) 0 0
\(610\) −319.500 268.092i −0.523771 0.439496i
\(611\) −43.4718 + 25.0984i −0.0711485 + 0.0410776i
\(612\) 0 0
\(613\) −287.932 + 498.713i −0.469710 + 0.813562i −0.999400 0.0346296i \(-0.988975\pi\)
0.529690 + 0.848191i \(0.322308\pi\)
\(614\) −238.387 654.963i −0.388253 1.06672i
\(615\) 0 0
\(616\) 303.927 255.025i 0.493389 0.414002i
\(617\) 239.991 659.369i 0.388964 1.06867i −0.578505 0.815679i \(-0.696364\pi\)
0.967469 0.252991i \(-0.0814143\pi\)
\(618\) 0 0
\(619\) 78.3389 444.282i 0.126557 0.717741i −0.853814 0.520579i \(-0.825716\pi\)
0.980371 0.197162i \(-0.0631726\pi\)
\(620\) 198.467i 0.320107i
\(621\) 0 0
\(622\) 23.9079 0.0384371
\(623\) −132.830 23.4216i −0.213211 0.0375949i
\(624\) 0 0
\(625\) −554.064 201.663i −0.886502 0.322660i
\(626\) 379.169 + 451.876i 0.605701 + 0.721847i
\(627\) 0 0
\(628\) −581.736 + 211.735i −0.926331 + 0.337157i
\(629\) 195.587 + 112.922i 0.310949 + 0.179527i
\(630\) 0 0
\(631\) 283.716 + 491.411i 0.449630 + 0.778782i 0.998362 0.0572166i \(-0.0182226\pi\)
−0.548732 + 0.835998i \(0.684889\pi\)
\(632\) −147.535 + 175.825i −0.233441 + 0.278204i
\(633\) 0 0
\(634\) −111.431 631.954i −0.175758 0.996773i
\(635\) 325.353 57.3685i 0.512367 0.0903441i
\(636\) 0 0
\(637\) 47.3684 + 39.7468i 0.0743616 + 0.0623968i
\(638\) 221.482 127.872i 0.347150 0.200427i
\(639\) 0 0
\(640\) 48.8345 84.5839i 0.0763039 0.132162i
\(641\) −50.9735 140.049i −0.0795219 0.218485i 0.893560 0.448943i \(-0.148200\pi\)
−0.973082 + 0.230459i \(0.925977\pi\)
\(642\) 0 0
\(643\) −20.8996 + 17.5368i −0.0325032 + 0.0272734i −0.658895 0.752235i \(-0.728976\pi\)
0.626391 + 0.779509i \(0.284531\pi\)
\(644\) −169.069 + 464.513i −0.262529 + 0.721294i
\(645\) 0 0
\(646\) −18.4042 + 104.375i −0.0284894 + 0.161571i
\(647\) 263.970i 0.407991i 0.978972 + 0.203996i \(0.0653929\pi\)
−0.978972 + 0.203996i \(0.934607\pi\)
\(648\) 0 0
\(649\) 1013.28 1.56129
\(650\) −208.521 36.7679i −0.320801 0.0565659i
\(651\) 0 0
\(652\) 300.806 + 109.485i 0.461360 + 0.167921i
\(653\) 538.345 + 641.575i 0.824418 + 0.982503i 0.999998 0.00196193i \(-0.000624502\pi\)
−0.175580 + 0.984465i \(0.556180\pi\)
\(654\) 0 0
\(655\) −1767.87 + 643.450i −2.69903 + 0.982367i
\(656\) 58.8357 + 33.9688i 0.0896885 + 0.0517817i
\(657\) 0 0
\(658\) 97.8485 + 169.479i 0.148706 + 0.257566i
\(659\) 477.726 569.332i 0.724926 0.863933i −0.270173 0.962812i \(-0.587081\pi\)
0.995100 + 0.0988784i \(0.0315255\pi\)
\(660\) 0 0
\(661\) 46.6386 + 264.501i 0.0705577 + 0.400152i 0.999548 + 0.0300495i \(0.00956649\pi\)
−0.928991 + 0.370103i \(0.879322\pi\)
\(662\) 326.978 57.6550i 0.493924 0.0870922i
\(663\) 0 0
\(664\) 34.9530 + 29.3290i 0.0526400 + 0.0441702i
\(665\) −479.355 + 276.756i −0.720835 + 0.416174i
\(666\) 0 0
\(667\) −159.321 + 275.952i −0.238862 + 0.413722i
\(668\) −170.289 467.864i −0.254923 0.700395i
\(669\) 0 0
\(670\) 351.953 295.324i 0.525303 0.440782i
\(671\) 196.664 540.329i 0.293090 0.805259i
\(672\) 0 0
\(673\) 114.573 649.776i 0.170242 0.965492i −0.773251 0.634100i \(-0.781371\pi\)
0.943493 0.331392i \(-0.107518\pi\)
\(674\) 448.656i 0.665661i
\(675\) 0 0
\(676\) 319.721 0.472961
\(677\) −251.116 44.2786i −0.370925 0.0654041i −0.0149216 0.999889i \(-0.504750\pi\)
−0.356004 + 0.934485i \(0.615861\pi\)
\(678\) 0 0
\(679\) −1039.15 378.221i −1.53042 0.557026i
\(680\) 152.886 + 182.203i 0.224833 + 0.267945i
\(681\) 0 0
\(682\) −257.116 + 93.5824i −0.377002 + 0.137218i
\(683\) 376.413 + 217.322i 0.551117 + 0.318187i 0.749572 0.661923i \(-0.230259\pi\)
−0.198456 + 0.980110i \(0.563593\pi\)
\(684\) 0 0
\(685\) −794.615 1376.31i −1.16002 2.00922i
\(686\) −216.260 + 257.729i −0.315248 + 0.375698i
\(687\) 0 0
\(688\) 16.4010 + 93.0147i 0.0238387 + 0.135196i
\(689\) −224.297 + 39.5496i −0.325540 + 0.0574015i
\(690\) 0 0
\(691\) −1022.63 858.086i −1.47992 1.24180i −0.906266 0.422707i \(-0.861080\pi\)
−0.573657 0.819096i \(-0.694476\pi\)
\(692\) −117.049 + 67.5780i −0.169145 + 0.0976561i
\(693\) 0 0
\(694\) 31.2112 54.0594i 0.0449729 0.0778954i
\(695\) 717.924 + 1972.48i 1.03298 + 2.83810i
\(696\) 0 0
\(697\) −126.738 + 106.346i −0.181834 + 0.152577i
\(698\) 159.881 439.270i 0.229056 0.629327i
\(699\) 0 0
\(700\) −143.343 + 812.938i −0.204775 + 1.16134i
\(701\) 1001.61i 1.42883i −0.699722 0.714415i \(-0.746693\pi\)
0.699722 0.714415i \(-0.253307\pi\)
\(702\) 0 0
\(703\) −178.374 −0.253733
\(704\) 132.606 + 23.3820i 0.188361 + 0.0332131i
\(705\) 0 0
\(706\) 629.235 + 229.023i 0.891267 + 0.324395i
\(707\) 81.5437 + 97.1800i 0.115338 + 0.137454i
\(708\) 0 0
\(709\) 720.055 262.078i 1.01559 0.369645i 0.220014 0.975497i \(-0.429390\pi\)
0.795578 + 0.605852i \(0.207167\pi\)
\(710\) 537.576 + 310.370i 0.757149 + 0.437140i
\(711\) 0 0
\(712\) −22.8883 39.6436i −0.0321464 0.0556792i
\(713\) 219.132 261.152i 0.307339 0.366272i
\(714\) 0 0
\(715\) −76.2782 432.595i −0.106683 0.605028i
\(716\) −463.317 + 81.6953i −0.647090 + 0.114100i
\(717\) 0 0
\(718\) −472.926 396.832i −0.658671 0.552691i
\(719\) −544.595 + 314.422i −0.757434 + 0.437305i −0.828374 0.560176i \(-0.810733\pi\)
0.0709399 + 0.997481i \(0.477400\pi\)
\(720\) 0 0
\(721\) −157.730 + 273.196i −0.218765 + 0.378913i
\(722\) 145.982 + 401.082i 0.202191 + 0.555516i
\(723\) 0 0
\(724\) −333.737 + 280.038i −0.460962 + 0.386793i
\(725\) −181.990 + 500.015i −0.251021 + 0.689675i
\(726\) 0 0
\(727\) −116.145 + 658.690i −0.159759 + 0.906039i 0.794546 + 0.607204i \(0.207709\pi\)
−0.954305 + 0.298835i \(0.903402\pi\)
\(728\) 71.2606i 0.0978855i
\(729\) 0 0
\(730\) −1202.44 −1.64717
\(731\) −226.514 39.9406i −0.309869 0.0546383i
\(732\) 0 0
\(733\) −104.288 37.9578i −0.142276 0.0517842i 0.269901 0.962888i \(-0.413009\pi\)
−0.412177 + 0.911104i \(0.635231\pi\)
\(734\) 433.316 + 516.406i 0.590349 + 0.703550i
\(735\) 0 0
\(736\) −157.650 + 57.3800i −0.214199 + 0.0779619i
\(737\) 548.551 + 316.706i 0.744302 + 0.429723i
\(738\) 0 0
\(739\) −231.298 400.619i −0.312987 0.542110i 0.666020 0.745934i \(-0.267996\pi\)
−0.979008 + 0.203824i \(0.934663\pi\)
\(740\) −257.309 + 306.649i −0.347715 + 0.414390i
\(741\) 0 0
\(742\) 154.188 + 874.442i 0.207800 + 1.17849i
\(743\) −952.218 + 167.902i −1.28159 + 0.225978i −0.772653 0.634829i \(-0.781071\pi\)
−0.508932 + 0.860807i \(0.669960\pi\)
\(744\) 0 0
\(745\) 952.783 + 799.480i 1.27890 + 1.07313i
\(746\) −452.078 + 261.007i −0.606003 + 0.349876i
\(747\) 0 0
\(748\) −163.956 + 283.979i −0.219192 + 0.379652i
\(749\) −338.223 929.259i −0.451566 1.24067i
\(750\) 0 0
\(751\) −805.112 + 675.569i −1.07205 + 0.899560i −0.995237 0.0974855i \(-0.968920\pi\)
−0.0768166 + 0.997045i \(0.524476\pi\)
\(752\) −22.7160 + 62.4118i −0.0302075 + 0.0829944i
\(753\) 0 0
\(754\) −7.97648 + 45.2368i −0.0105789 + 0.0599958i
\(755\) 877.168i 1.16181i
\(756\) 0 0
\(757\) −266.724 −0.352343 −0.176172 0.984359i \(-0.556371\pi\)
−0.176172 + 0.984359i \(0.556371\pi\)
\(758\) −302.087 53.2662i −0.398532 0.0702720i
\(759\) 0 0
\(760\) −176.526 64.2503i −0.232271 0.0845399i
\(761\) 0.229396 + 0.273383i 0.000301440 + 0.000359242i 0.766195 0.642608i \(-0.222148\pi\)
−0.765894 + 0.642967i \(0.777703\pi\)
\(762\) 0 0
\(763\) 1613.68 587.333i 2.11492 0.769768i
\(764\) −445.704 257.327i −0.583382 0.336816i
\(765\) 0 0
\(766\) 381.376 + 660.563i 0.497880 + 0.862353i
\(767\) −116.985 + 139.418i −0.152523 + 0.181770i
\(768\) 0 0
\(769\) 77.8630 + 441.583i 0.101252 + 0.574230i 0.992651 + 0.121011i \(0.0386136\pi\)
−0.891399 + 0.453220i \(0.850275\pi\)
\(770\) −1686.51 + 297.377i −2.19027 + 0.386204i
\(771\) 0 0
\(772\) 117.467 + 98.5664i 0.152159 + 0.127677i
\(773\) −580.814 + 335.333i −0.751376 + 0.433807i −0.826191 0.563390i \(-0.809497\pi\)
0.0748149 + 0.997197i \(0.476163\pi\)
\(774\) 0 0
\(775\) 284.644 493.018i 0.367283 0.636153i
\(776\) −128.364 352.676i −0.165417 0.454479i
\(777\) 0 0
\(778\) −159.971 + 134.232i −0.205618 + 0.172534i
\(779\) 44.6918 122.790i 0.0573708 0.157625i
\(780\) 0 0
\(781\) −148.605 + 842.783i −0.190276 + 1.07911i
\(782\) 408.557i 0.522451i
\(783\) 0 0
\(784\) 81.8160 0.104357
\(785\) 2631.56 + 464.015i 3.35231 + 0.591102i
\(786\) 0 0
\(787\) 1152.23 + 419.377i 1.46408 + 0.532881i 0.946485 0.322747i \(-0.104606\pi\)
0.517592 + 0.855627i \(0.326828\pi\)
\(788\) 313.665 + 373.812i 0.398053 + 0.474381i
\(789\) 0 0
\(790\) 930.967 338.844i 1.17844 0.428917i
\(791\) 512.645 + 295.976i 0.648097 + 0.374179i
\(792\) 0 0
\(793\) 51.6388 + 89.4411i 0.0651183 + 0.112788i
\(794\) 456.897 544.508i 0.575437 0.685779i
\(795\) 0 0
\(796\) −28.5158 161.721i −0.0358238 0.203167i
\(797\) 391.758 69.0776i 0.491541 0.0866720i 0.0776168 0.996983i \(-0.475269\pi\)
0.413924 + 0.910311i \(0.364158\pi\)
\(798\) 0 0
\(799\) −123.902 103.966i −0.155071 0.130120i
\(800\) −242.623 + 140.079i −0.303279 + 0.175098i
\(801\) 0 0
\(802\) −163.656 + 283.461i −0.204060 + 0.353443i
\(803\) −566.981 1557.77i −0.706079 1.93994i
\(804\) 0 0
\(805\) 1634.51 1371.52i 2.03045 1.70375i
\(806\) 16.8085 46.1809i 0.0208542 0.0572964i
\(807\) 0 0
\(808\) −7.47635 + 42.4005i −0.00925290 + 0.0524758i
\(809\) 438.654i 0.542218i 0.962549 + 0.271109i \(0.0873903\pi\)
−0.962549 + 0.271109i \(0.912610\pi\)
\(810\) 0 0
\(811\) −1037.62 −1.27943 −0.639716 0.768611i \(-0.720948\pi\)
−0.639716 + 0.768611i \(0.720948\pi\)
\(812\) 176.360 + 31.0970i 0.217192 + 0.0382968i
\(813\) 0 0
\(814\) −518.595 188.753i −0.637094 0.231883i
\(815\) −888.159 1058.47i −1.08977 1.29873i
\(816\) 0 0
\(817\) 170.707 62.1324i 0.208944 0.0760495i
\(818\) −551.679 318.512i −0.674424 0.389379i
\(819\) 0 0
\(820\) −146.623 253.958i −0.178808 0.309705i
\(821\) 919.156 1095.41i 1.11956 1.33424i 0.183245 0.983067i \(-0.441340\pi\)
0.936312 0.351168i \(-0.114216\pi\)
\(822\) 0 0
\(823\) −245.722 1393.56i −0.298568 1.69327i −0.652334 0.757932i \(-0.726210\pi\)
0.353765 0.935334i \(-0.384901\pi\)
\(824\) −105.437 + 18.5913i −0.127957 + 0.0225623i
\(825\) 0 0
\(826\) 543.532 + 456.078i 0.658029 + 0.552152i
\(827\) −609.863 + 352.105i −0.737440 + 0.425761i −0.821138 0.570730i \(-0.806660\pi\)
0.0836977 + 0.996491i \(0.473327\pi\)
\(828\) 0 0
\(829\) −145.579 + 252.151i −0.175608 + 0.304162i −0.940372 0.340149i \(-0.889523\pi\)
0.764763 + 0.644311i \(0.222856\pi\)
\(830\) −67.3602 185.071i −0.0811569 0.222977i
\(831\) 0 0
\(832\) −18.5268 + 15.5458i −0.0222678 + 0.0186849i
\(833\) −68.1450 + 187.227i −0.0818067 + 0.224762i
\(834\) 0 0
\(835\) −373.186 + 2116.44i −0.446930 + 2.53466i
\(836\) 258.987i 0.309794i
\(837\) 0 0
\(838\) 465.477 0.555462
\(839\) −852.208 150.267i −1.01574 0.179103i −0.359096 0.933301i \(-0.616915\pi\)
−0.656647 + 0.754198i \(0.728026\pi\)
\(840\) 0 0
\(841\) −681.808 248.158i −0.810710 0.295074i
\(842\) −185.997 221.663i −0.220900 0.263258i
\(843\) 0 0
\(844\) 108.053 39.3280i 0.128025 0.0465971i
\(845\) −1195.16 690.023i −1.41438 0.816595i
\(846\) 0 0
\(847\) −676.290 1171.37i −0.798454 1.38296i
\(848\) −193.706 + 230.850i −0.228427 + 0.272229i
\(849\) 0 0
\(850\) −118.472 671.889i −0.139379 0.790458i
\(851\) 677.158 119.401i 0.795721 0.140307i
\(852\) 0 0
\(853\) −83.2215 69.8311i −0.0975633 0.0818653i 0.592701 0.805422i \(-0.298061\pi\)
−0.690265 + 0.723557i \(0.742506\pi\)
\(854\) 348.694 201.319i 0.408307 0.235736i
\(855\) 0 0
\(856\) 167.810 290.655i 0.196039 0.339550i
\(857\) 364.690 + 1001.98i 0.425543 + 1.16917i 0.948491 + 0.316804i \(0.102610\pi\)
−0.522948 + 0.852364i \(0.675168\pi\)
\(858\) 0 0
\(859\) −42.4891 + 35.6526i −0.0494635 + 0.0415048i −0.667184 0.744893i \(-0.732501\pi\)
0.617721 + 0.786398i \(0.288056\pi\)
\(860\) 139.436 383.096i 0.162134 0.445461i
\(861\) 0 0
\(862\) −1.43760 + 8.15306i −0.00166775 + 0.00945830i
\(863\) 75.8244i 0.0878614i −0.999035 0.0439307i \(-0.986012\pi\)
0.999035 0.0439307i \(-0.0139881\pi\)
\(864\) 0 0
\(865\) 583.388 0.674437
\(866\) 324.937 + 57.2952i 0.375216 + 0.0661607i
\(867\) 0 0
\(868\) −180.040 65.5293i −0.207420 0.0754946i
\(869\) 877.953 + 1046.30i 1.01030 + 1.20403i
\(870\) 0 0
\(871\) −106.907 + 38.9109i −0.122740 + 0.0446739i
\(872\) 504.731 + 291.406i 0.578820 + 0.334182i
\(873\) 0 0
\(874\) 161.341 + 279.451i 0.184601 + 0.319738i
\(875\) 1134.18 1351.66i 1.29621 1.54476i
\(876\) 0 0
\(877\) 100.329 + 568.994i 0.114400 + 0.648796i 0.987045 + 0.160441i \(0.0512918\pi\)
−0.872645 + 0.488355i \(0.837597\pi\)
\(878\) 187.727 33.1013i 0.213812 0.0377008i
\(879\) 0 0
\(880\) −445.234 373.595i −0.505947 0.424540i
\(881\) −118.578 + 68.4609i −0.134594 + 0.0777082i −0.565785 0.824553i \(-0.691427\pi\)
0.431191 + 0.902261i \(0.358094\pi\)
\(882\) 0 0
\(883\) 634.745 1099.41i 0.718851 1.24509i −0.242605 0.970125i \(-0.578002\pi\)
0.961455 0.274961i \(-0.0886648\pi\)
\(884\) −20.1438 55.3447i −0.0227871 0.0626071i
\(885\) 0 0
\(886\) −31.0316 + 26.0386i −0.0350244 + 0.0293889i
\(887\) −220.369 + 605.458i −0.248443 + 0.682591i 0.751301 + 0.659960i \(0.229427\pi\)
−0.999744 + 0.0226314i \(0.992796\pi\)
\(888\) 0 0
\(889\) −55.3822 + 314.088i −0.0622972 + 0.353305i
\(890\) 197.590i 0.222011i
\(891\) 0 0
\(892\) −463.975 −0.520152
\(893\) 125.805 + 22.1829i 0.140879 + 0.0248408i
\(894\) 0 0
\(895\) 1908.25 + 694.545i 2.13212 + 0.776027i
\(896\) 60.6068 + 72.2283i 0.0676415 + 0.0806120i
\(897\) 0 0
\(898\) −660.187 + 240.288i −0.735175 + 0.267582i
\(899\) −106.956 61.7512i −0.118972 0.0686888i
\(900\) 0 0
\(901\) −366.936 635.551i −0.407254 0.705384i
\(902\) 259.869 309.700i 0.288103 0.343348i
\(903\) 0 0
\(904\) 34.8861 + 197.849i 0.0385908 + 0.218860i
\(905\) 1851.93 326.544i 2.04633 0.360823i
\(906\) 0 0
\(907\) −468.430 393.059i −0.516461 0.433362i 0.346935 0.937889i \(-0.387222\pi\)
−0.863396 + 0.504527i \(0.831667\pi\)
\(908\) −371.582 + 214.533i −0.409231 + 0.236270i
\(909\) 0 0
\(910\) 153.795 266.380i 0.169005 0.292726i
\(911\) −359.212 986.926i −0.394305 1.08334i −0.965016 0.262193i \(-0.915554\pi\)
0.570711 0.821151i \(-0.306668\pi\)
\(912\) 0 0
\(913\) 207.999 174.532i 0.227819 0.191163i
\(914\) −224.337 + 616.361i −0.245445 + 0.674356i
\(915\) 0 0
\(916\) 137.325 778.806i 0.149918 0.850225i
\(917\) 1816.19i 1.98057i
\(918\) 0 0
\(919\) 133.483 0.145248 0.0726238 0.997359i \(-0.476863\pi\)
0.0726238 + 0.997359i \(0.476863\pi\)
\(920\) 713.152 + 125.748i 0.775165 + 0.136682i
\(921\) 0 0
\(922\) 354.002 + 128.846i 0.383950 + 0.139747i
\(923\) −98.8020 117.748i −0.107044 0.127571i
\(924\) 0 0
\(925\) 1078.99 392.721i 1.16648 0.424563i
\(926\) −293.168 169.261i −0.316597 0.182787i
\(927\) 0 0
\(928\) 30.3889 + 52.6351i 0.0327467 + 0.0567189i
\(929\) −714.192 + 851.141i −0.768775 + 0.916190i −0.998369 0.0570965i \(-0.981816\pi\)
0.229594 + 0.973287i \(0.426260\pi\)
\(930\) 0 0
\(931\) −27.3259 154.973i −0.0293512 0.166459i
\(932\) −188.609 + 33.2568i −0.202370 + 0.0356833i
\(933\) 0 0
\(934\) 230.881 + 193.732i 0.247196 + 0.207422i
\(935\) 1225.77 707.698i 1.31098 0.756896i
\(936\) 0 0
\(937\) 862.772 1494.36i 0.920781 1.59484i 0.122572 0.992460i \(-0.460886\pi\)
0.798209 0.602380i \(-0.205781\pi\)
\(938\) 151.698 + 416.786i 0.161725 + 0.444335i
\(939\) 0 0
\(940\) 219.612 184.277i 0.233630 0.196039i
\(941\) −465.200 + 1278.13i −0.494368 + 1.35827i 0.402278 + 0.915517i \(0.368218\pi\)
−0.896646 + 0.442748i \(0.854004\pi\)
\(942\) 0 0
\(943\) −87.4689 + 496.061i −0.0927560 + 0.526046i
\(944\) 240.806i 0.255091i
\(945\) 0 0
\(946\) 562.053 0.594136
\(947\) −1590.14 280.385i −1.67914 0.296077i −0.748804 0.662792i \(-0.769372\pi\)
−0.930334 + 0.366714i \(0.880483\pi\)
\(948\) 0 0
\(949\) 279.793 + 101.836i 0.294829 + 0.107309i
\(950\) 346.367 + 412.784i 0.364597 + 0.434509i
\(951\) 0 0
\(952\) −215.766 + 78.5325i −0.226645 + 0.0824921i
\(953\) 181.146 + 104.585i 0.190080 + 0.109743i 0.592020 0.805923i \(-0.298331\pi\)
−0.401940 + 0.915666i \(0.631664\pi\)
\(954\) 0 0
\(955\) 1110.73 + 1923.84i 1.16307 + 2.01449i
\(956\) 113.371 135.110i 0.118589 0.141329i
\(957\) 0 0
\(958\) −98.2830 557.391i −0.102592 0.581827i
\(959\) 1510.90 266.412i 1.57549 0.277802i
\(960\) 0 0
\(961\) −634.949 532.786i −0.660717 0.554407i
\(962\) 85.8434 49.5617i 0.0892343 0.0515194i
\(963\) 0 0
\(964\) −385.135 + 667.073i −0.399518 + 0.691985i
\(965\) −226.378 621.969i −0.234589 0.644528i
\(966\) 0 0
\(967\) 672.104 563.962i 0.695041 0.583208i −0.225317 0.974285i \(-0.572342\pi\)
0.920358 + 0.391077i \(0.127897\pi\)
\(968\) 157.004 431.365i 0.162194 0.445625i
\(969\) 0 0
\(970\) −281.308 + 1595.38i −0.290008 + 1.64472i
\(971\) 686.372i 0.706871i −0.935459 0.353435i \(-0.885013\pi\)
0.935459 0.353435i \(-0.114987\pi\)
\(972\) 0 0
\(973\) −2026.39 −2.08262
\(974\) −450.793 79.4869i −0.462826 0.0816087i
\(975\) 0 0
\(976\) 128.409 + 46.7371i 0.131567 + 0.0478864i
\(977\) −905.640 1079.30i −0.926960 1.10471i −0.994262 0.106975i \(-0.965883\pi\)
0.0673015 0.997733i \(-0.478561\pi\)
\(978\) 0 0
\(979\) −255.980 + 93.1690i −0.261471 + 0.0951675i
\(980\) −305.838 176.575i −0.312079 0.180179i
\(981\) 0 0
\(982\) −648.885 1123.90i −0.660779 1.14450i
\(983\) −606.673 + 723.005i −0.617165 + 0.735508i −0.980580 0.196119i \(-0.937166\pi\)
0.363415 + 0.931627i \(0.381611\pi\)
\(984\) 0 0
\(985\) −365.756 2074.30i −0.371326 2.10589i
\(986\) −145.761 + 25.7015i −0.147830 + 0.0260665i
\(987\) 0 0
\(988\) 35.6342 + 29.9006i 0.0360670 + 0.0302638i
\(989\) −606.463 + 350.142i −0.613208 + 0.354036i
\(990\) 0 0
\(991\) −424.153 + 734.654i −0.428005 + 0.741326i −0.996696 0.0812254i \(-0.974117\pi\)
0.568691 + 0.822551i \(0.307450\pi\)
\(992\) −22.2399 61.1035i −0.0224192 0.0615963i
\(993\) 0 0
\(994\) −459.050 + 385.189i −0.461821 + 0.387514i
\(995\) −242.431 + 666.074i −0.243649 + 0.669421i
\(996\) 0 0
\(997\) −29.2963 + 166.148i −0.0293845 + 0.166648i −0.995969 0.0897017i \(-0.971409\pi\)
0.966584 + 0.256349i \(0.0825198\pi\)
\(998\) 305.569i 0.306181i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 162.3.f.a.89.4 36
3.2 odd 2 54.3.f.a.29.1 36
12.11 even 2 432.3.bc.c.353.6 36
27.11 odd 18 1458.3.b.c.1457.18 36
27.13 even 9 54.3.f.a.41.1 yes 36
27.14 odd 18 inner 162.3.f.a.71.4 36
27.16 even 9 1458.3.b.c.1457.19 36
108.67 odd 18 432.3.bc.c.257.6 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.3.f.a.29.1 36 3.2 odd 2
54.3.f.a.41.1 yes 36 27.13 even 9
162.3.f.a.71.4 36 27.14 odd 18 inner
162.3.f.a.89.4 36 1.1 even 1 trivial
432.3.bc.c.257.6 36 108.67 odd 18
432.3.bc.c.353.6 36 12.11 even 2
1458.3.b.c.1457.18 36 27.11 odd 18
1458.3.b.c.1457.19 36 27.16 even 9