Properties

Label 1380.2.p.a.91.4
Level $1380$
Weight $2$
Character 1380.91
Analytic conductor $11.019$
Analytic rank $0$
Dimension $48$
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] = [1380,2,Mod(91,1380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1380.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1380.p (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.0193554789\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.4
Character \(\chi\) \(=\) 1380.91
Dual form 1380.2.p.a.91.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39049 + 0.257970i) q^{2} +1.00000i q^{3} +(1.86690 - 0.717408i) q^{4} +1.00000i q^{5} +(-0.257970 - 1.39049i) q^{6} +2.59830 q^{7} +(-2.41083 + 1.47915i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-1.39049 + 0.257970i) q^{2} +1.00000i q^{3} +(1.86690 - 0.717408i) q^{4} +1.00000i q^{5} +(-0.257970 - 1.39049i) q^{6} +2.59830 q^{7} +(-2.41083 + 1.47915i) q^{8} -1.00000 q^{9} +(-0.257970 - 1.39049i) q^{10} -1.75416 q^{11} +(0.717408 + 1.86690i) q^{12} -2.03614 q^{13} +(-3.61291 + 0.670285i) q^{14} -1.00000 q^{15} +(2.97065 - 2.67866i) q^{16} -3.95759i q^{17} +(1.39049 - 0.257970i) q^{18} -5.10890 q^{19} +(0.717408 + 1.86690i) q^{20} +2.59830i q^{21} +(2.43913 - 0.452520i) q^{22} +(-4.47835 + 1.71592i) q^{23} +(-1.47915 - 2.41083i) q^{24} -1.00000 q^{25} +(2.83122 - 0.525262i) q^{26} -1.00000i q^{27} +(4.85078 - 1.86404i) q^{28} -7.32394 q^{29} +(1.39049 - 0.257970i) q^{30} -4.91715i q^{31} +(-3.43964 + 4.49098i) q^{32} -1.75416i q^{33} +(1.02094 + 5.50297i) q^{34} +2.59830i q^{35} +(-1.86690 + 0.717408i) q^{36} +0.890633i q^{37} +(7.10385 - 1.31794i) q^{38} -2.03614i q^{39} +(-1.47915 - 2.41083i) q^{40} -10.1575 q^{41} +(-0.670285 - 3.61291i) q^{42} +5.82796 q^{43} +(-3.27484 + 1.25845i) q^{44} -1.00000i q^{45} +(5.78443 - 3.54125i) q^{46} +2.70292i q^{47} +(2.67866 + 2.97065i) q^{48} -0.248811 q^{49} +(1.39049 - 0.257970i) q^{50} +3.95759 q^{51} +(-3.80127 + 1.46074i) q^{52} -2.16224i q^{53} +(0.257970 + 1.39049i) q^{54} -1.75416i q^{55} +(-6.26408 + 3.84328i) q^{56} -5.10890i q^{57} +(10.1838 - 1.88936i) q^{58} +10.3196i q^{59} +(-1.86690 + 0.717408i) q^{60} +7.39410i q^{61} +(1.26848 + 6.83723i) q^{62} -2.59830 q^{63} +(3.62423 - 7.13197i) q^{64} -2.03614i q^{65} +(0.452520 + 2.43913i) q^{66} +8.20400 q^{67} +(-2.83920 - 7.38843i) q^{68} +(-1.71592 - 4.47835i) q^{69} +(-0.670285 - 3.61291i) q^{70} +7.48672i q^{71} +(2.41083 - 1.47915i) q^{72} -13.8075 q^{73} +(-0.229757 - 1.23841i) q^{74} -1.00000i q^{75} +(-9.53782 + 3.66516i) q^{76} -4.55784 q^{77} +(0.525262 + 2.83122i) q^{78} -6.39670 q^{79} +(2.67866 + 2.97065i) q^{80} +1.00000 q^{81} +(14.1239 - 2.62033i) q^{82} +9.80321 q^{83} +(1.86404 + 4.85078i) q^{84} +3.95759 q^{85} +(-8.10369 + 1.50344i) q^{86} -7.32394i q^{87} +(4.22898 - 2.59466i) q^{88} -15.8514i q^{89} +(0.257970 + 1.39049i) q^{90} -5.29050 q^{91} +(-7.12963 + 6.41626i) q^{92} +4.91715 q^{93} +(-0.697273 - 3.75837i) q^{94} -5.10890i q^{95} +(-4.49098 - 3.43964i) q^{96} +0.186909i q^{97} +(0.345968 - 0.0641859i) q^{98} +1.75416 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} - 2 q^{10} + 20 q^{14} - 48 q^{15} - 6 q^{16} + 4 q^{18} + 16 q^{19} + 28 q^{22} + 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} + 4 q^{30} + 16 q^{32} - 28 q^{34} + 2 q^{36} + 2 q^{40} - 8 q^{41} + 14 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} + 16 q^{51} - 16 q^{52} + 2 q^{54} + 40 q^{56} - 8 q^{58} + 2 q^{60} + 24 q^{62} - 26 q^{64} - 48 q^{67} - 44 q^{68} - 8 q^{69} + 4 q^{72} + 20 q^{74} - 64 q^{76} + 32 q^{77} - 64 q^{79} + 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} - 40 q^{86} + 2 q^{90} - 4 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(691\) \(1201\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(-1\)

Coefficient data

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



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