Properties

Label 280.2.l.a.29.5
Level $280$
Weight $2$
Character 280.29
Analytic conductor $2.236$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [280,2,Mod(29,280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(280, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("280.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.l (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: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(36\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 29.5
Character \(\chi\) \(=\) 280.29
Dual form 280.2.l.a.29.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.36669 - 0.363546i) q^{2} +0.460762 q^{3} +(1.73567 + 0.993708i) q^{4} +(-2.19557 + 0.423658i) q^{5} +(-0.629718 - 0.167508i) q^{6} -1.00000i q^{7} +(-2.01086 - 1.98908i) q^{8} -2.78770 q^{9} +O(q^{10})\) \(q+(-1.36669 - 0.363546i) q^{2} +0.460762 q^{3} +(1.73567 + 0.993708i) q^{4} +(-2.19557 + 0.423658i) q^{5} +(-0.629718 - 0.167508i) q^{6} -1.00000i q^{7} +(-2.01086 - 1.98908i) q^{8} -2.78770 q^{9} +(3.15467 + 0.219182i) q^{10} -4.70105i q^{11} +(0.799730 + 0.457863i) q^{12} +0.906993 q^{13} +(-0.363546 + 1.36669i) q^{14} +(-1.01163 + 0.195206i) q^{15} +(2.02509 + 3.44949i) q^{16} -7.25402i q^{17} +(3.80991 + 1.01346i) q^{18} -2.15170i q^{19} +(-4.23177 - 1.44642i) q^{20} -0.460762i q^{21} +(-1.70905 + 6.42487i) q^{22} +5.89989i q^{23} +(-0.926527 - 0.916494i) q^{24} +(4.64103 - 1.86034i) q^{25} +(-1.23958 - 0.329734i) q^{26} -2.66675 q^{27} +(0.993708 - 1.73567i) q^{28} -6.91659i q^{29} +(1.45355 + 0.100991i) q^{30} -8.02835 q^{31} +(-1.51362 - 5.45059i) q^{32} -2.16607i q^{33} +(-2.63717 + 9.91398i) q^{34} +(0.423658 + 2.19557i) q^{35} +(-4.83852 - 2.77016i) q^{36} -6.21426 q^{37} +(-0.782242 + 2.94070i) q^{38} +0.417908 q^{39} +(5.25766 + 3.51525i) q^{40} -6.21775 q^{41} +(-0.167508 + 0.629718i) q^{42} +9.32915 q^{43} +(4.67147 - 8.15947i) q^{44} +(6.12058 - 1.18103i) q^{45} +(2.14488 - 8.06330i) q^{46} +3.80960i q^{47} +(0.933085 + 1.58940i) q^{48} -1.00000 q^{49} +(-7.01915 + 0.855274i) q^{50} -3.34238i q^{51} +(1.57424 + 0.901285i) q^{52} +4.96064 q^{53} +(3.64462 + 0.969487i) q^{54} +(1.99164 + 10.3215i) q^{55} +(-1.98908 + 2.01086i) q^{56} -0.991422i q^{57} +(-2.51450 + 9.45282i) q^{58} +11.7227i q^{59} +(-1.94984 - 0.666456i) q^{60} -6.20163i q^{61} +(10.9722 + 2.91867i) q^{62} +2.78770i q^{63} +(0.0870983 + 7.99953i) q^{64} +(-1.99136 + 0.384255i) q^{65} +(-0.787465 + 2.96034i) q^{66} +5.42728 q^{67} +(7.20838 - 12.5906i) q^{68} +2.71844i q^{69} +(0.219182 - 3.15467i) q^{70} +1.74762 q^{71} +(5.60566 + 5.54496i) q^{72} +5.82777i q^{73} +(8.49296 + 2.25917i) q^{74} +(2.13841 - 0.857174i) q^{75} +(2.13816 - 3.73464i) q^{76} -4.70105 q^{77} +(-0.571149 - 0.151929i) q^{78} +8.05583 q^{79} +(-5.90763 - 6.71565i) q^{80} +7.13436 q^{81} +(8.49771 + 2.26044i) q^{82} -10.5144 q^{83} +(0.457863 - 0.799730i) q^{84} +(3.07322 + 15.9267i) q^{85} +(-12.7500 - 3.39157i) q^{86} -3.18690i q^{87} +(-9.35078 + 9.45315i) q^{88} +11.5168 q^{89} +(-8.79428 - 0.611012i) q^{90} -0.906993i q^{91} +(-5.86276 + 10.2402i) q^{92} -3.69916 q^{93} +(1.38496 - 5.20653i) q^{94} +(0.911585 + 4.72420i) q^{95} +(-0.697417 - 2.51143i) q^{96} -11.6450i q^{97} +(1.36669 + 0.363546i) q^{98} +13.1051i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9} - 8 q^{10} + 20 q^{16} - 24 q^{20} - 48 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{30} - 16 q^{31} + 12 q^{34} - 20 q^{36} - 32 q^{39} + 16 q^{40} - 8 q^{41} + 56 q^{44} - 36 q^{49} - 12 q^{50} - 52 q^{54} - 32 q^{55} + 12 q^{56} - 20 q^{60} - 20 q^{64} - 24 q^{65} - 28 q^{66} - 12 q^{70} + 56 q^{71} - 24 q^{74} + 48 q^{76} + 24 q^{79} + 64 q^{80} + 36 q^{81} + 24 q^{86} - 40 q^{89} - 52 q^{90} - 92 q^{94} + 40 q^{95} + 48 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36669 0.363546i −0.966394 0.257066i
\(3\) 0.460762 0.266021 0.133011 0.991115i \(-0.457536\pi\)
0.133011 + 0.991115i \(0.457536\pi\)
\(4\) 1.73567 + 0.993708i 0.867834 + 0.496854i
\(5\) −2.19557 + 0.423658i −0.981887 + 0.189466i
\(6\) −0.629718 0.167508i −0.257081 0.0683850i
\(7\) 1.00000i 0.377964i
\(8\) −2.01086 1.98908i −0.710946 0.703247i
\(9\) −2.78770 −0.929233
\(10\) 3.15467 + 0.219182i 0.997595 + 0.0693113i
\(11\) 4.70105i 1.41742i −0.705500 0.708710i \(-0.749277\pi\)
0.705500 0.708710i \(-0.250723\pi\)
\(12\) 0.799730 + 0.457863i 0.230862 + 0.132174i
\(13\) 0.906993 0.251554 0.125777 0.992059i \(-0.459858\pi\)
0.125777 + 0.992059i \(0.459858\pi\)
\(14\) −0.363546 + 1.36669i −0.0971618 + 0.365263i
\(15\) −1.01163 + 0.195206i −0.261203 + 0.0504018i
\(16\) 2.02509 + 3.44949i 0.506273 + 0.862373i
\(17\) 7.25402i 1.75936i −0.475567 0.879679i \(-0.657757\pi\)
0.475567 0.879679i \(-0.342243\pi\)
\(18\) 3.80991 + 1.01346i 0.898005 + 0.238874i
\(19\) 2.15170i 0.493634i −0.969062 0.246817i \(-0.920615\pi\)
0.969062 0.246817i \(-0.0793846\pi\)
\(20\) −4.23177 1.44642i −0.946252 0.323430i
\(21\) 0.460762i 0.100547i
\(22\) −1.70905 + 6.42487i −0.364370 + 1.36979i
\(23\) 5.89989i 1.23021i 0.788445 + 0.615106i \(0.210887\pi\)
−0.788445 + 0.615106i \(0.789113\pi\)
\(24\) −0.926527 0.916494i −0.189127 0.187079i
\(25\) 4.64103 1.86034i 0.928206 0.372068i
\(26\) −1.23958 0.329734i −0.243101 0.0646661i
\(27\) −2.66675 −0.513217
\(28\) 0.993708 1.73567i 0.187793 0.328011i
\(29\) 6.91659i 1.28438i −0.766546 0.642189i \(-0.778026\pi\)
0.766546 0.642189i \(-0.221974\pi\)
\(30\) 1.45355 + 0.100991i 0.265381 + 0.0184383i
\(31\) −8.02835 −1.44193 −0.720967 0.692970i \(-0.756302\pi\)
−0.720967 + 0.692970i \(0.756302\pi\)
\(32\) −1.51362 5.45059i −0.267572 0.963538i
\(33\) 2.16607i 0.377064i
\(34\) −2.63717 + 9.91398i −0.452271 + 1.70023i
\(35\) 0.423658 + 2.19557i 0.0716113 + 0.371119i
\(36\) −4.83852 2.77016i −0.806420 0.461693i
\(37\) −6.21426 −1.02162 −0.510809 0.859694i \(-0.670654\pi\)
−0.510809 + 0.859694i \(0.670654\pi\)
\(38\) −0.782242 + 2.94070i −0.126896 + 0.477045i
\(39\) 0.417908 0.0669188
\(40\) 5.25766 + 3.51525i 0.831310 + 0.555810i
\(41\) −6.21775 −0.971049 −0.485524 0.874223i \(-0.661371\pi\)
−0.485524 + 0.874223i \(0.661371\pi\)
\(42\) −0.167508 + 0.629718i −0.0258471 + 0.0971676i
\(43\) 9.32915 1.42268 0.711341 0.702847i \(-0.248088\pi\)
0.711341 + 0.702847i \(0.248088\pi\)
\(44\) 4.67147 8.15947i 0.704251 1.23009i
\(45\) 6.12058 1.18103i 0.912402 0.176058i
\(46\) 2.14488 8.06330i 0.316245 1.18887i
\(47\) 3.80960i 0.555687i 0.960626 + 0.277844i \(0.0896197\pi\)
−0.960626 + 0.277844i \(0.910380\pi\)
\(48\) 0.933085 + 1.58940i 0.134679 + 0.229410i
\(49\) −1.00000 −0.142857
\(50\) −7.01915 + 0.855274i −0.992658 + 0.120954i
\(51\) 3.34238i 0.468027i
\(52\) 1.57424 + 0.901285i 0.218308 + 0.124986i
\(53\) 4.96064 0.681396 0.340698 0.940173i \(-0.389337\pi\)
0.340698 + 0.940173i \(0.389337\pi\)
\(54\) 3.64462 + 0.969487i 0.495969 + 0.131930i
\(55\) 1.99164 + 10.3215i 0.268552 + 1.39175i
\(56\) −1.98908 + 2.01086i −0.265802 + 0.268712i
\(57\) 0.991422i 0.131317i
\(58\) −2.51450 + 9.45282i −0.330170 + 1.24122i
\(59\) 11.7227i 1.52616i 0.646303 + 0.763081i \(0.276314\pi\)
−0.646303 + 0.763081i \(0.723686\pi\)
\(60\) −1.94984 0.666456i −0.251723 0.0860391i
\(61\) 6.20163i 0.794038i −0.917810 0.397019i \(-0.870045\pi\)
0.917810 0.397019i \(-0.129955\pi\)
\(62\) 10.9722 + 2.91867i 1.39348 + 0.370672i
\(63\) 2.78770i 0.351217i
\(64\) 0.0870983 + 7.99953i 0.0108873 + 0.999941i
\(65\) −1.99136 + 0.384255i −0.246998 + 0.0476609i
\(66\) −0.787465 + 2.96034i −0.0969302 + 0.364392i
\(67\) 5.42728 0.663047 0.331524 0.943447i \(-0.392437\pi\)
0.331524 + 0.943447i \(0.392437\pi\)
\(68\) 7.20838 12.5906i 0.874144 1.52683i
\(69\) 2.71844i 0.327262i
\(70\) 0.219182 3.15467i 0.0261972 0.377055i
\(71\) 1.74762 0.207405 0.103702 0.994608i \(-0.466931\pi\)
0.103702 + 0.994608i \(0.466931\pi\)
\(72\) 5.60566 + 5.54496i 0.660634 + 0.653480i
\(73\) 5.82777i 0.682089i 0.940047 + 0.341045i \(0.110781\pi\)
−0.940047 + 0.341045i \(0.889219\pi\)
\(74\) 8.49296 + 2.25917i 0.987286 + 0.262623i
\(75\) 2.13841 0.857174i 0.246922 0.0989779i
\(76\) 2.13816 3.73464i 0.245264 0.428392i
\(77\) −4.70105 −0.535735
\(78\) −0.571149 0.151929i −0.0646699 0.0172025i
\(79\) 8.05583 0.906352 0.453176 0.891421i \(-0.350291\pi\)
0.453176 + 0.891421i \(0.350291\pi\)
\(80\) −5.90763 6.71565i −0.660493 0.750832i
\(81\) 7.13436 0.792706
\(82\) 8.49771 + 2.26044i 0.938416 + 0.249623i
\(83\) −10.5144 −1.15410 −0.577052 0.816707i \(-0.695797\pi\)
−0.577052 + 0.816707i \(0.695797\pi\)
\(84\) 0.457863 0.799730i 0.0499569 0.0872577i
\(85\) 3.07322 + 15.9267i 0.333338 + 1.72749i
\(86\) −12.7500 3.39157i −1.37487 0.365723i
\(87\) 3.18690i 0.341672i
\(88\) −9.35078 + 9.45315i −0.996797 + 1.00771i
\(89\) 11.5168 1.22078 0.610391 0.792100i \(-0.291012\pi\)
0.610391 + 0.792100i \(0.291012\pi\)
\(90\) −8.79428 0.611012i −0.926998 0.0644064i
\(91\) 0.906993i 0.0950787i
\(92\) −5.86276 + 10.2402i −0.611235 + 1.06762i
\(93\) −3.69916 −0.383585
\(94\) 1.38496 5.20653i 0.142848 0.537013i
\(95\) 0.911585 + 4.72420i 0.0935266 + 0.484693i
\(96\) −0.697417 2.51143i −0.0711798 0.256321i
\(97\) 11.6450i 1.18237i −0.806536 0.591184i \(-0.798661\pi\)
0.806536 0.591184i \(-0.201339\pi\)
\(98\) 1.36669 + 0.363546i 0.138056 + 0.0367237i
\(99\) 13.1051i 1.31711i
\(100\) 9.90392 + 1.38289i 0.990392 + 0.138289i
\(101\) 10.4414i 1.03896i 0.854482 + 0.519481i \(0.173875\pi\)
−0.854482 + 0.519481i \(0.826125\pi\)
\(102\) −1.21511 + 4.56799i −0.120314 + 0.452298i
\(103\) 0.974021i 0.0959731i −0.998848 0.0479866i \(-0.984720\pi\)
0.998848 0.0479866i \(-0.0152805\pi\)
\(104\) −1.82383 1.80408i −0.178842 0.176905i
\(105\) 0.195206 + 1.01163i 0.0190501 + 0.0987254i
\(106\) −6.77964 1.80342i −0.658497 0.175164i
\(107\) −3.56456 −0.344599 −0.172300 0.985045i \(-0.555120\pi\)
−0.172300 + 0.985045i \(0.555120\pi\)
\(108\) −4.62860 2.64997i −0.445387 0.254994i
\(109\) 10.9852i 1.05219i −0.850426 0.526095i \(-0.823656\pi\)
0.850426 0.526095i \(-0.176344\pi\)
\(110\) 1.03038 14.8303i 0.0982433 1.41401i
\(111\) −2.86330 −0.271772
\(112\) 3.44949 2.02509i 0.325947 0.191353i
\(113\) 13.6270i 1.28192i −0.767574 0.640961i \(-0.778536\pi\)
0.767574 0.640961i \(-0.221464\pi\)
\(114\) −0.360427 + 1.35496i −0.0337571 + 0.126904i
\(115\) −2.49953 12.9536i −0.233083 1.20793i
\(116\) 6.87307 12.0049i 0.638148 1.11463i
\(117\) −2.52842 −0.233753
\(118\) 4.26173 16.0212i 0.392324 1.47487i
\(119\) −7.25402 −0.664975
\(120\) 2.42253 + 1.61969i 0.221146 + 0.147857i
\(121\) −11.0999 −1.00908
\(122\) −2.25458 + 8.47569i −0.204120 + 0.767353i
\(123\) −2.86490 −0.258319
\(124\) −13.9345 7.97783i −1.25136 0.716430i
\(125\) −9.40154 + 6.05071i −0.840899 + 0.541192i
\(126\) 1.01346 3.80991i 0.0902859 0.339414i
\(127\) 9.10398i 0.807847i −0.914793 0.403924i \(-0.867646\pi\)
0.914793 0.403924i \(-0.132354\pi\)
\(128\) 2.78916 10.9645i 0.246529 0.969135i
\(129\) 4.29852 0.378463
\(130\) 2.86126 + 0.198796i 0.250950 + 0.0174356i
\(131\) 3.54709i 0.309911i 0.987921 + 0.154955i \(0.0495234\pi\)
−0.987921 + 0.154955i \(0.950477\pi\)
\(132\) 2.15244 3.75957i 0.187346 0.327229i
\(133\) −2.15170 −0.186576
\(134\) −7.41739 1.97306i −0.640765 0.170447i
\(135\) 5.85503 1.12979i 0.503921 0.0972369i
\(136\) −14.4289 + 14.5868i −1.23726 + 1.25081i
\(137\) 8.61460i 0.735995i −0.929827 0.367998i \(-0.880043\pi\)
0.929827 0.367998i \(-0.119957\pi\)
\(138\) 0.988280 3.71526i 0.0841280 0.316264i
\(139\) 2.63222i 0.223262i −0.993750 0.111631i \(-0.964393\pi\)
0.993750 0.111631i \(-0.0356075\pi\)
\(140\) −1.44642 + 4.23177i −0.122245 + 0.357650i
\(141\) 1.75532i 0.147824i
\(142\) −2.38845 0.635341i −0.200435 0.0533166i
\(143\) 4.26382i 0.356559i
\(144\) −5.64534 9.61615i −0.470445 0.801346i
\(145\) 2.93027 + 15.1858i 0.243346 + 1.26112i
\(146\) 2.11866 7.96475i 0.175342 0.659167i
\(147\) −0.460762 −0.0380030
\(148\) −10.7859 6.17516i −0.886596 0.507595i
\(149\) 1.34906i 0.110519i −0.998472 0.0552597i \(-0.982401\pi\)
0.998472 0.0552597i \(-0.0175987\pi\)
\(150\) −3.23416 + 0.394078i −0.264068 + 0.0321763i
\(151\) 1.05365 0.0857447 0.0428723 0.999081i \(-0.486349\pi\)
0.0428723 + 0.999081i \(0.486349\pi\)
\(152\) −4.27991 + 4.32676i −0.347146 + 0.350947i
\(153\) 20.2220i 1.63485i
\(154\) 6.42487 + 1.70905i 0.517731 + 0.137719i
\(155\) 17.6268 3.40127i 1.41582 0.273197i
\(156\) 0.725349 + 0.415278i 0.0580744 + 0.0332489i
\(157\) 6.90765 0.551291 0.275645 0.961259i \(-0.411108\pi\)
0.275645 + 0.961259i \(0.411108\pi\)
\(158\) −11.0098 2.92867i −0.875893 0.232992i
\(159\) 2.28567 0.181266
\(160\) 5.63243 + 11.3259i 0.445283 + 0.895390i
\(161\) 5.89989 0.464976
\(162\) −9.75043 2.59367i −0.766066 0.203778i
\(163\) 3.81159 0.298547 0.149273 0.988796i \(-0.452307\pi\)
0.149273 + 0.988796i \(0.452307\pi\)
\(164\) −10.7919 6.17862i −0.842709 0.482469i
\(165\) 0.917671 + 4.75575i 0.0714406 + 0.370234i
\(166\) 14.3699 + 3.82246i 1.11532 + 0.296681i
\(167\) 5.96816i 0.461830i −0.972974 0.230915i \(-0.925828\pi\)
0.972974 0.230915i \(-0.0741719\pi\)
\(168\) −0.916494 + 0.926527i −0.0707091 + 0.0714831i
\(169\) −12.1774 −0.936720
\(170\) 1.58995 22.8841i 0.121944 1.75513i
\(171\) 5.99829i 0.458701i
\(172\) 16.1923 + 9.27044i 1.23465 + 0.706865i
\(173\) −9.53599 −0.725008 −0.362504 0.931982i \(-0.618078\pi\)
−0.362504 + 0.931982i \(0.618078\pi\)
\(174\) −1.15859 + 4.35550i −0.0878322 + 0.330190i
\(175\) −1.86034 4.64103i −0.140628 0.350829i
\(176\) 16.2163 9.52006i 1.22235 0.717601i
\(177\) 5.40136i 0.405991i
\(178\) −15.7399 4.18690i −1.17976 0.313821i
\(179\) 16.7514i 1.25206i 0.779800 + 0.626028i \(0.215321\pi\)
−0.779800 + 0.626028i \(0.784679\pi\)
\(180\) 11.7969 + 4.03219i 0.879289 + 0.300541i
\(181\) 4.40466i 0.327396i 0.986511 + 0.163698i \(0.0523422\pi\)
−0.986511 + 0.163698i \(0.947658\pi\)
\(182\) −0.329734 + 1.23958i −0.0244415 + 0.0918834i
\(183\) 2.85748i 0.211231i
\(184\) 11.7354 11.8638i 0.865143 0.874613i
\(185\) 13.6438 2.63272i 1.00311 0.193562i
\(186\) 5.05559 + 1.34481i 0.370694 + 0.0986066i
\(187\) −34.1015 −2.49375
\(188\) −3.78563 + 6.61220i −0.276095 + 0.482244i
\(189\) 2.66675i 0.193978i
\(190\) 0.471613 6.78791i 0.0342144 0.492447i
\(191\) 23.6219 1.70922 0.854609 0.519272i \(-0.173797\pi\)
0.854609 + 0.519272i \(0.173797\pi\)
\(192\) 0.0401316 + 3.68588i 0.00289625 + 0.266005i
\(193\) 16.9843i 1.22255i 0.791417 + 0.611277i \(0.209344\pi\)
−0.791417 + 0.611277i \(0.790656\pi\)
\(194\) −4.23349 + 15.9151i −0.303947 + 1.14263i
\(195\) −0.917545 + 0.177050i −0.0657067 + 0.0126788i
\(196\) −1.73567 0.993708i −0.123976 0.0709791i
\(197\) 7.12840 0.507877 0.253939 0.967220i \(-0.418274\pi\)
0.253939 + 0.967220i \(0.418274\pi\)
\(198\) 4.76431 17.9106i 0.338585 1.27285i
\(199\) −7.59968 −0.538727 −0.269363 0.963039i \(-0.586813\pi\)
−0.269363 + 0.963039i \(0.586813\pi\)
\(200\) −13.0328 5.49051i −0.921559 0.388238i
\(201\) 2.50068 0.176385
\(202\) 3.79594 14.2702i 0.267081 1.00405i
\(203\) −6.91659 −0.485449
\(204\) 3.32135 5.80126i 0.232541 0.406170i
\(205\) 13.6515 2.63420i 0.953460 0.183980i
\(206\) −0.354101 + 1.33118i −0.0246714 + 0.0927479i
\(207\) 16.4471i 1.14315i
\(208\) 1.83674 + 3.12867i 0.127355 + 0.216934i
\(209\) −10.1153 −0.699687
\(210\) 0.100991 1.45355i 0.00696902 0.100305i
\(211\) 12.5535i 0.864220i −0.901821 0.432110i \(-0.857769\pi\)
0.901821 0.432110i \(-0.142231\pi\)
\(212\) 8.61002 + 4.92942i 0.591338 + 0.338554i
\(213\) 0.805238 0.0551740
\(214\) 4.87164 + 1.29588i 0.333019 + 0.0885847i
\(215\) −20.4828 + 3.95237i −1.39691 + 0.269549i
\(216\) 5.36246 + 5.30439i 0.364869 + 0.360918i
\(217\) 8.02835i 0.545000i
\(218\) −3.99362 + 15.0133i −0.270482 + 1.01683i
\(219\) 2.68522i 0.181450i
\(220\) −6.79970 + 19.8938i −0.458436 + 1.34124i
\(221\) 6.57934i 0.442575i
\(222\) 3.91323 + 1.04094i 0.262639 + 0.0698633i
\(223\) 7.22407i 0.483760i −0.970306 0.241880i \(-0.922236\pi\)
0.970306 0.241880i \(-0.0777640\pi\)
\(224\) −5.45059 + 1.51362i −0.364183 + 0.101133i
\(225\) −12.9378 + 5.18606i −0.862519 + 0.345738i
\(226\) −4.95405 + 18.6239i −0.329538 + 1.23884i
\(227\) 6.31624 0.419224 0.209612 0.977785i \(-0.432780\pi\)
0.209612 + 0.977785i \(0.432780\pi\)
\(228\) 0.985183 1.72078i 0.0652454 0.113961i
\(229\) 20.4708i 1.35275i −0.736559 0.676373i \(-0.763551\pi\)
0.736559 0.676373i \(-0.236449\pi\)
\(230\) −1.29315 + 18.6122i −0.0852676 + 1.22725i
\(231\) −2.16607 −0.142517
\(232\) −13.7577 + 13.9083i −0.903235 + 0.913123i
\(233\) 12.6153i 0.826458i −0.910627 0.413229i \(-0.864401\pi\)
0.910627 0.413229i \(-0.135599\pi\)
\(234\) 3.45556 + 0.919198i 0.225897 + 0.0600898i
\(235\) −1.61397 8.36423i −0.105284 0.545622i
\(236\) −11.6489 + 20.3467i −0.758279 + 1.32446i
\(237\) 3.71182 0.241109
\(238\) 9.91398 + 2.63717i 0.642628 + 0.170942i
\(239\) 24.7537 1.60119 0.800593 0.599209i \(-0.204518\pi\)
0.800593 + 0.599209i \(0.204518\pi\)
\(240\) −2.72201 3.09432i −0.175705 0.199737i
\(241\) 9.84368 0.634087 0.317043 0.948411i \(-0.397310\pi\)
0.317043 + 0.948411i \(0.397310\pi\)
\(242\) 15.1701 + 4.03532i 0.975170 + 0.259400i
\(243\) 11.2875 0.724093
\(244\) 6.16261 10.7640i 0.394521 0.689093i
\(245\) 2.19557 0.423658i 0.140270 0.0270665i
\(246\) 3.91542 + 1.04152i 0.249638 + 0.0664051i
\(247\) 1.95158i 0.124176i
\(248\) 16.1439 + 15.9690i 1.02514 + 1.01404i
\(249\) −4.84463 −0.307016
\(250\) 15.0487 4.85153i 0.951762 0.306838i
\(251\) 5.68663i 0.358937i −0.983764 0.179469i \(-0.942562\pi\)
0.983764 0.179469i \(-0.0574378\pi\)
\(252\) −2.77016 + 4.83852i −0.174503 + 0.304798i
\(253\) 27.7357 1.74373
\(254\) −3.30971 + 12.4423i −0.207670 + 0.780699i
\(255\) 1.41603 + 7.33842i 0.0886749 + 0.459549i
\(256\) −7.79802 + 13.9711i −0.487376 + 0.873192i
\(257\) 9.85759i 0.614899i 0.951564 + 0.307450i \(0.0994756\pi\)
−0.951564 + 0.307450i \(0.900524\pi\)
\(258\) −5.87473 1.56271i −0.365745 0.0972900i
\(259\) 6.21426i 0.386136i
\(260\) −3.83818 1.31189i −0.238034 0.0813602i
\(261\) 19.2814i 1.19349i
\(262\) 1.28953 4.84776i 0.0796675 0.299496i
\(263\) 4.80107i 0.296047i −0.988984 0.148023i \(-0.952709\pi\)
0.988984 0.148023i \(-0.0472911\pi\)
\(264\) −4.30849 + 4.35565i −0.265169 + 0.268072i
\(265\) −10.8914 + 2.10161i −0.669054 + 0.129101i
\(266\) 2.94070 + 0.782242i 0.180306 + 0.0479623i
\(267\) 5.30652 0.324754
\(268\) 9.41995 + 5.39312i 0.575415 + 0.329438i
\(269\) 24.3324i 1.48358i −0.670635 0.741788i \(-0.733978\pi\)
0.670635 0.741788i \(-0.266022\pi\)
\(270\) −8.41273 0.584503i −0.511982 0.0355717i
\(271\) −21.7578 −1.32169 −0.660846 0.750521i \(-0.729802\pi\)
−0.660846 + 0.750521i \(0.729802\pi\)
\(272\) 25.0227 14.6901i 1.51722 0.890715i
\(273\) 0.417908i 0.0252929i
\(274\) −3.13181 + 11.7735i −0.189199 + 0.711261i
\(275\) −8.74555 21.8177i −0.527377 1.31566i
\(276\) −2.70134 + 4.71832i −0.162601 + 0.284009i
\(277\) −11.0672 −0.664966 −0.332483 0.943109i \(-0.607886\pi\)
−0.332483 + 0.943109i \(0.607886\pi\)
\(278\) −0.956934 + 3.59742i −0.0573931 + 0.215759i
\(279\) 22.3806 1.33989
\(280\) 3.51525 5.25766i 0.210076 0.314205i
\(281\) 7.46541 0.445349 0.222675 0.974893i \(-0.428521\pi\)
0.222675 + 0.974893i \(0.428521\pi\)
\(282\) 0.638139 2.39897i 0.0380006 0.142857i
\(283\) 12.9066 0.767215 0.383608 0.923496i \(-0.374682\pi\)
0.383608 + 0.923496i \(0.374682\pi\)
\(284\) 3.03329 + 1.73663i 0.179993 + 0.103050i
\(285\) 0.420024 + 2.17673i 0.0248801 + 0.128939i
\(286\) −1.55009 + 5.82731i −0.0916590 + 0.344576i
\(287\) 6.21775i 0.367022i
\(288\) 4.21950 + 15.1946i 0.248637 + 0.895351i
\(289\) −35.6208 −2.09534
\(290\) 1.51599 21.8196i 0.0890220 1.28129i
\(291\) 5.36557i 0.314535i
\(292\) −5.79110 + 10.1151i −0.338899 + 0.591941i
\(293\) −16.5980 −0.969668 −0.484834 0.874606i \(-0.661120\pi\)
−0.484834 + 0.874606i \(0.661120\pi\)
\(294\) 0.629718 + 0.167508i 0.0367259 + 0.00976928i
\(295\) −4.96640 25.7379i −0.289155 1.49852i
\(296\) 12.4960 + 12.3607i 0.726315 + 0.718450i
\(297\) 12.5365i 0.727444i
\(298\) −0.490446 + 1.84374i −0.0284107 + 0.106805i
\(299\) 5.35115i 0.309465i
\(300\) 4.56335 + 0.637185i 0.263465 + 0.0367879i
\(301\) 9.32915i 0.537723i
\(302\) −1.44001 0.383050i −0.0828631 0.0220420i
\(303\) 4.81102i 0.276386i
\(304\) 7.42227 4.35739i 0.425697 0.249913i
\(305\) 2.62737 + 13.6161i 0.150443 + 0.779655i
\(306\) 7.35164 27.6372i 0.420265 1.57991i
\(307\) 22.4910 1.28363 0.641815 0.766860i \(-0.278182\pi\)
0.641815 + 0.766860i \(0.278182\pi\)
\(308\) −8.15947 4.67147i −0.464929 0.266182i
\(309\) 0.448792i 0.0255309i
\(310\) −25.3268 1.75967i −1.43847 0.0999424i
\(311\) −13.5423 −0.767911 −0.383955 0.923352i \(-0.625438\pi\)
−0.383955 + 0.923352i \(0.625438\pi\)
\(312\) −0.840353 0.831253i −0.0475756 0.0470605i
\(313\) 8.36225i 0.472662i 0.971673 + 0.236331i \(0.0759450\pi\)
−0.971673 + 0.236331i \(0.924055\pi\)
\(314\) −9.44060 2.51125i −0.532764 0.141718i
\(315\) −1.18103 6.12058i −0.0665435 0.344856i
\(316\) 13.9823 + 8.00514i 0.786563 + 0.450324i
\(317\) −9.55188 −0.536487 −0.268244 0.963351i \(-0.586443\pi\)
−0.268244 + 0.963351i \(0.586443\pi\)
\(318\) −3.12380 0.830947i −0.175174 0.0465972i
\(319\) −32.5153 −1.82050
\(320\) −3.58029 17.5266i −0.200144 0.979766i
\(321\) −1.64242 −0.0916707
\(322\) −8.06330 2.14488i −0.449350 0.119530i
\(323\) −15.6085 −0.868479
\(324\) 12.3829 + 7.08946i 0.687938 + 0.393859i
\(325\) 4.20938 1.68731i 0.233494 0.0935953i
\(326\) −5.20925 1.38569i −0.288514 0.0767462i
\(327\) 5.06156i 0.279905i
\(328\) 12.5030 + 12.3676i 0.690363 + 0.682887i
\(329\) 3.80960 0.210030
\(330\) 0.474762 6.83323i 0.0261348 0.376157i
\(331\) 4.02356i 0.221155i −0.993868 0.110577i \(-0.964730\pi\)
0.993868 0.110577i \(-0.0352700\pi\)
\(332\) −18.2495 10.4482i −1.00157 0.573421i
\(333\) 17.3235 0.949322
\(334\) −2.16970 + 8.15661i −0.118721 + 0.446310i
\(335\) −11.9159 + 2.29931i −0.651038 + 0.125625i
\(336\) 1.58940 0.933085i 0.0867087 0.0509040i
\(337\) 2.35080i 0.128056i −0.997948 0.0640282i \(-0.979605\pi\)
0.997948 0.0640282i \(-0.0203947\pi\)
\(338\) 16.6426 + 4.42703i 0.905241 + 0.240799i
\(339\) 6.27881i 0.341018i
\(340\) −10.4924 + 30.6973i −0.569029 + 1.66480i
\(341\) 37.7417i 2.04383i
\(342\) 2.18065 8.19779i 0.117916 0.443286i
\(343\) 1.00000i 0.0539949i
\(344\) −18.7596 18.5564i −1.01145 1.00050i
\(345\) −1.15169 5.96853i −0.0620049 0.321335i
\(346\) 13.0327 + 3.46677i 0.700643 + 0.186375i
\(347\) 18.8580 1.01235 0.506175 0.862431i \(-0.331059\pi\)
0.506175 + 0.862431i \(0.331059\pi\)
\(348\) 3.16685 5.53141i 0.169761 0.296515i
\(349\) 36.6217i 1.96032i −0.198215 0.980159i \(-0.563514\pi\)
0.198215 0.980159i \(-0.436486\pi\)
\(350\) 0.855274 + 7.01915i 0.0457163 + 0.375190i
\(351\) −2.41872 −0.129102
\(352\) −25.6235 + 7.11559i −1.36574 + 0.379262i
\(353\) 4.26233i 0.226861i 0.993546 + 0.113430i \(0.0361839\pi\)
−0.993546 + 0.113430i \(0.963816\pi\)
\(354\) 1.96364 7.38197i 0.104367 0.392348i
\(355\) −3.83702 + 0.740394i −0.203648 + 0.0392960i
\(356\) 19.9894 + 11.4444i 1.05944 + 0.606550i
\(357\) −3.34238 −0.176897
\(358\) 6.08990 22.8939i 0.321861 1.20998i
\(359\) 10.2985 0.543532 0.271766 0.962363i \(-0.412392\pi\)
0.271766 + 0.962363i \(0.412392\pi\)
\(360\) −14.6568 9.79945i −0.772480 0.516477i
\(361\) 14.3702 0.756326
\(362\) 1.60130 6.01979i 0.0841623 0.316393i
\(363\) −5.11441 −0.268437
\(364\) 0.901285 1.57424i 0.0472402 0.0825125i
\(365\) −2.46898 12.7953i −0.129232 0.669735i
\(366\) −1.03882 + 3.90528i −0.0543002 + 0.204132i
\(367\) 21.6339i 1.12928i −0.825337 0.564640i \(-0.809015\pi\)
0.825337 0.564640i \(-0.190985\pi\)
\(368\) −20.3516 + 11.9478i −1.06090 + 0.622822i
\(369\) 17.3332 0.902330
\(370\) −19.6040 1.36205i −1.01916 0.0708098i
\(371\) 4.96064i 0.257543i
\(372\) −6.42051 3.67588i −0.332888 0.190586i
\(373\) −1.59921 −0.0828039 −0.0414020 0.999143i \(-0.513182\pi\)
−0.0414020 + 0.999143i \(0.513182\pi\)
\(374\) 46.6061 + 12.3975i 2.40995 + 0.641058i
\(375\) −4.33187 + 2.78794i −0.223697 + 0.143968i
\(376\) 7.57761 7.66056i 0.390785 0.395063i
\(377\) 6.27330i 0.323091i
\(378\) 0.969487 3.64462i 0.0498650 0.187459i
\(379\) 9.67642i 0.497044i −0.968626 0.248522i \(-0.920055\pi\)
0.968626 0.248522i \(-0.0799449\pi\)
\(380\) −3.11226 + 9.10549i −0.159656 + 0.467102i
\(381\) 4.19477i 0.214904i
\(382\) −32.2837 8.58764i −1.65178 0.439382i
\(383\) 0.198092i 0.0101220i 0.999987 + 0.00506102i \(0.00161098\pi\)
−0.999987 + 0.00506102i \(0.998389\pi\)
\(384\) 1.28514 5.05203i 0.0655820 0.257810i
\(385\) 10.3215 1.99164i 0.526031 0.101503i
\(386\) 6.17456 23.2122i 0.314277 1.18147i
\(387\) −26.0068 −1.32200
\(388\) 11.5717 20.2118i 0.587464 1.02610i
\(389\) 27.9997i 1.41964i 0.704382 + 0.709821i \(0.251224\pi\)
−0.704382 + 0.709821i \(0.748776\pi\)
\(390\) 1.31836 + 0.0915977i 0.0667579 + 0.00463823i
\(391\) 42.7979 2.16438
\(392\) 2.01086 + 1.98908i 0.101564 + 0.100464i
\(393\) 1.63437i 0.0824428i
\(394\) −9.74229 2.59150i −0.490810 0.130558i
\(395\) −17.6871 + 3.41292i −0.889935 + 0.171722i
\(396\) −13.0227 + 22.7461i −0.654413 + 1.14304i
\(397\) 9.16728 0.460093 0.230046 0.973180i \(-0.426112\pi\)
0.230046 + 0.973180i \(0.426112\pi\)
\(398\) 10.3864 + 2.76283i 0.520622 + 0.138488i
\(399\) −0.991422 −0.0496332
\(400\) 15.8157 + 12.2418i 0.790786 + 0.612092i
\(401\) −25.8889 −1.29283 −0.646416 0.762986i \(-0.723733\pi\)
−0.646416 + 0.762986i \(0.723733\pi\)
\(402\) −3.41765 0.909113i −0.170457 0.0453425i
\(403\) −7.28165 −0.362725
\(404\) −10.3757 + 18.1229i −0.516212 + 0.901646i
\(405\) −15.6640 + 3.02253i −0.778348 + 0.150191i
\(406\) 9.45282 + 2.51450i 0.469135 + 0.124792i
\(407\) 29.2136i 1.44806i
\(408\) −6.64827 + 6.72105i −0.329138 + 0.332741i
\(409\) −2.34443 −0.115924 −0.0579622 0.998319i \(-0.518460\pi\)
−0.0579622 + 0.998319i \(0.518460\pi\)
\(410\) −19.6150 1.36282i −0.968713 0.0673047i
\(411\) 3.96928i 0.195790i
\(412\) 0.967892 1.69058i 0.0476846 0.0832888i
\(413\) 11.7227 0.576835
\(414\) −5.97928 + 22.4781i −0.293866 + 1.10474i
\(415\) 23.0850 4.45450i 1.13320 0.218663i
\(416\) −1.37284 4.94365i −0.0673089 0.242382i
\(417\) 1.21283i 0.0593924i
\(418\) 13.8244 + 3.67736i 0.676173 + 0.179866i
\(419\) 20.5898i 1.00588i 0.864323 + 0.502938i \(0.167747\pi\)
−0.864323 + 0.502938i \(0.832253\pi\)
\(420\) −0.666456 + 1.94984i −0.0325197 + 0.0951424i
\(421\) 2.24931i 0.109625i 0.998497 + 0.0548123i \(0.0174560\pi\)
−0.998497 + 0.0548123i \(0.982544\pi\)
\(422\) −4.56378 + 17.1567i −0.222161 + 0.835177i
\(423\) 10.6200i 0.516363i
\(424\) −9.97513 9.86711i −0.484435 0.479189i
\(425\) −13.4949 33.6661i −0.654601 1.63305i
\(426\) −1.10051 0.292741i −0.0533198 0.0141834i
\(427\) −6.20163 −0.300118
\(428\) −6.18690 3.54213i −0.299055 0.171215i
\(429\) 1.96461i 0.0948521i
\(430\) 29.4304 + 2.04478i 1.41926 + 0.0986080i
\(431\) −2.18110 −0.105060 −0.0525299 0.998619i \(-0.516728\pi\)
−0.0525299 + 0.998619i \(0.516728\pi\)
\(432\) −5.40041 9.19894i −0.259828 0.442584i
\(433\) 7.03200i 0.337936i −0.985622 0.168968i \(-0.945956\pi\)
0.985622 0.168968i \(-0.0540435\pi\)
\(434\) 2.91867 10.9722i 0.140101 0.526684i
\(435\) 1.35016 + 6.99706i 0.0647351 + 0.335483i
\(436\) 10.9161 19.0667i 0.522785 0.913127i
\(437\) 12.6948 0.607274
\(438\) 0.976200 3.66985i 0.0466447 0.175352i
\(439\) 5.52633 0.263757 0.131879 0.991266i \(-0.457899\pi\)
0.131879 + 0.991266i \(0.457899\pi\)
\(440\) 16.5254 24.7166i 0.787816 1.17832i
\(441\) 2.78770 0.132748
\(442\) −2.39189 + 8.99191i −0.113771 + 0.427701i
\(443\) 16.0527 0.762685 0.381342 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(444\) −4.96974 2.84528i −0.235853 0.135031i
\(445\) −25.2860 + 4.87920i −1.19867 + 0.231296i
\(446\) −2.62628 + 9.87305i −0.124358 + 0.467502i
\(447\) 0.621596i 0.0294005i
\(448\) 7.99953 0.0870983i 0.377942 0.00411501i
\(449\) 35.7937 1.68921 0.844606 0.535389i \(-0.179835\pi\)
0.844606 + 0.535389i \(0.179835\pi\)
\(450\) 19.5673 2.38425i 0.922410 0.112394i
\(451\) 29.2300i 1.37638i
\(452\) 13.5413 23.6520i 0.636927 1.11250i
\(453\) 0.485481 0.0228099
\(454\) −8.63233 2.29625i −0.405135 0.107768i
\(455\) 0.384255 + 1.99136i 0.0180141 + 0.0933565i
\(456\) −1.97202 + 1.99361i −0.0923483 + 0.0933593i
\(457\) 10.5179i 0.492007i 0.969269 + 0.246004i \(0.0791175\pi\)
−0.969269 + 0.246004i \(0.920882\pi\)
\(458\) −7.44206 + 27.9771i −0.347745 + 1.30729i
\(459\) 19.3447i 0.902932i
\(460\) 8.53372 24.9670i 0.397887 1.16409i
\(461\) 3.48563i 0.162342i −0.996700 0.0811711i \(-0.974134\pi\)
0.996700 0.0811711i \(-0.0258660\pi\)
\(462\) 2.96034 + 0.787465i 0.137727 + 0.0366362i
\(463\) 17.0646i 0.793060i 0.918022 + 0.396530i \(0.129786\pi\)
−0.918022 + 0.396530i \(0.870214\pi\)
\(464\) 23.8587 14.0067i 1.10761 0.650246i
\(465\) 8.12175 1.56718i 0.376637 0.0726761i
\(466\) −4.58626 + 17.2412i −0.212454 + 0.798684i
\(467\) 20.2827 0.938572 0.469286 0.883046i \(-0.344511\pi\)
0.469286 + 0.883046i \(0.344511\pi\)
\(468\) −4.38850 2.51251i −0.202859 0.116141i
\(469\) 5.42728i 0.250608i
\(470\) −0.834994 + 12.0180i −0.0385154 + 0.554351i
\(471\) 3.18278 0.146655
\(472\) 23.3174 23.5726i 1.07327 1.08502i
\(473\) 43.8568i 2.01654i
\(474\) −5.07290 1.34942i −0.233006 0.0619808i
\(475\) −4.00289 9.98610i −0.183665 0.458194i
\(476\) −12.5906 7.20838i −0.577088 0.330395i
\(477\) −13.8288 −0.633175
\(478\) −33.8306 8.99912i −1.54738 0.411610i
\(479\) −29.4100 −1.34378 −0.671889 0.740652i \(-0.734517\pi\)
−0.671889 + 0.740652i \(0.734517\pi\)
\(480\) 2.59521 + 5.21854i 0.118455 + 0.238193i
\(481\) −5.63629 −0.256993
\(482\) −13.4532 3.57863i −0.612778 0.163002i
\(483\) 2.71844 0.123694
\(484\) −19.2657 11.0301i −0.875716 0.501366i
\(485\) 4.93349 + 25.5673i 0.224018 + 1.16095i
\(486\) −15.4265 4.10352i −0.699759 0.186140i
\(487\) 8.24187i 0.373475i 0.982410 + 0.186737i \(0.0597914\pi\)
−0.982410 + 0.186737i \(0.940209\pi\)
\(488\) −12.3356 + 12.4706i −0.558405 + 0.564518i
\(489\) 1.75624 0.0794198
\(490\) −3.15467 0.219182i −0.142514 0.00990162i
\(491\) 13.7812i 0.621937i 0.950420 + 0.310969i \(0.100653\pi\)
−0.950420 + 0.310969i \(0.899347\pi\)
\(492\) −4.97252 2.84687i −0.224179 0.128347i
\(493\) −50.1731 −2.25968
\(494\) −0.709488 + 2.66719i −0.0319214 + 0.120003i
\(495\) −5.55209 28.7732i −0.249548 1.29326i
\(496\) −16.2581 27.6937i −0.730012 1.24349i
\(497\) 1.74762i 0.0783916i
\(498\) 6.62110 + 1.76125i 0.296699 + 0.0789234i
\(499\) 9.19790i 0.411755i 0.978578 + 0.205877i \(0.0660048\pi\)
−0.978578 + 0.205877i \(0.933995\pi\)
\(500\) −22.3306 + 1.15964i −0.998654 + 0.0518607i
\(501\) 2.74990i 0.122857i
\(502\) −2.06735 + 7.77185i −0.0922705 + 0.346875i
\(503\) 37.3905i 1.66716i 0.552400 + 0.833579i \(0.313712\pi\)
−0.552400 + 0.833579i \(0.686288\pi\)
\(504\) 5.54496 5.60566i 0.246992 0.249696i
\(505\) −4.42359 22.9249i −0.196847 1.02014i
\(506\) −37.9060 10.0832i −1.68513 0.448253i
\(507\) −5.61087 −0.249187
\(508\) 9.04669 15.8015i 0.401382 0.701077i
\(509\) 34.5582i 1.53177i −0.642980 0.765883i \(-0.722302\pi\)
0.642980 0.765883i \(-0.277698\pi\)
\(510\) 0.732588 10.5441i 0.0324396 0.466901i
\(511\) 5.82777 0.257806
\(512\) 15.7366 16.2592i 0.695465 0.718560i
\(513\) 5.73805i 0.253341i
\(514\) 3.58369 13.4722i 0.158070 0.594235i
\(515\) 0.412652 + 2.13853i 0.0181836 + 0.0942348i
\(516\) 7.46080 + 4.27147i 0.328443 + 0.188041i
\(517\) 17.9091 0.787642
\(518\) 2.25917 8.49296i 0.0992623 0.373159i
\(519\) −4.39382 −0.192867
\(520\) 4.76866 + 3.18830i 0.209120 + 0.139816i
\(521\) 39.5046 1.73073 0.865363 0.501146i \(-0.167088\pi\)
0.865363 + 0.501146i \(0.167088\pi\)
\(522\) 7.00966 26.3516i 0.306805 1.15338i
\(523\) −10.0402 −0.439026 −0.219513 0.975610i \(-0.570447\pi\)
−0.219513 + 0.975610i \(0.570447\pi\)
\(524\) −3.52477 + 6.15658i −0.153980 + 0.268951i
\(525\) −0.857174 2.13841i −0.0374101 0.0933279i
\(526\) −1.74541 + 6.56156i −0.0761035 + 0.286098i
\(527\) 58.2378i 2.53688i
\(528\) 7.47183 4.38648i 0.325170 0.190897i
\(529\) −11.8087 −0.513420
\(530\) 15.6492 + 1.08728i 0.679757 + 0.0472284i
\(531\) 32.6793i 1.41816i
\(532\) −3.73464 2.13816i −0.161917 0.0927010i
\(533\) −5.63945 −0.244272
\(534\) −7.25236 1.92917i −0.313840 0.0834831i
\(535\) 7.82624 1.51016i 0.338358 0.0652897i
\(536\) −10.9135 10.7953i −0.471390 0.466286i
\(537\) 7.71840i 0.333074i
\(538\) −8.84596 + 33.2548i −0.381377 + 1.43372i
\(539\) 4.70105i 0.202489i
\(540\) 11.2851 + 3.85725i 0.485632 + 0.165990i
\(541\) 2.72177i 0.117018i −0.998287 0.0585090i \(-0.981365\pi\)
0.998287 0.0585090i \(-0.0186346\pi\)
\(542\) 29.7361 + 7.90996i 1.27728 + 0.339762i
\(543\) 2.02950i 0.0870942i
\(544\) −39.5387 + 10.9798i −1.69521 + 0.470755i
\(545\) 4.65396 + 24.1187i 0.199354 + 1.03313i
\(546\) −0.151929 + 0.571149i −0.00650195 + 0.0244429i
\(547\) −16.6603 −0.712342 −0.356171 0.934421i \(-0.615918\pi\)
−0.356171 + 0.934421i \(0.615918\pi\)
\(548\) 8.56040 14.9521i 0.365682 0.638722i
\(549\) 17.2883i 0.737846i
\(550\) 4.02069 + 32.9974i 0.171443 + 1.40701i
\(551\) −14.8824 −0.634013
\(552\) 5.40721 5.46641i 0.230146 0.232666i
\(553\) 8.05583i 0.342569i
\(554\) 15.1255 + 4.02345i 0.642619 + 0.170940i
\(555\) 6.28656 1.21306i 0.266850 0.0514915i
\(556\) 2.61566 4.56866i 0.110929 0.193754i
\(557\) 18.4977 0.783774 0.391887 0.920013i \(-0.371822\pi\)
0.391887 + 0.920013i \(0.371822\pi\)
\(558\) −30.5873 8.13638i −1.29486 0.344441i
\(559\) 8.46147 0.357882
\(560\) −6.71565 + 5.90763i −0.283788 + 0.249643i
\(561\) −15.7127 −0.663391
\(562\) −10.2029 2.71402i −0.430383 0.114484i
\(563\) 38.2569 1.61234 0.806169 0.591685i \(-0.201537\pi\)
0.806169 + 0.591685i \(0.201537\pi\)
\(564\) −1.74427 + 3.04665i −0.0734472 + 0.128287i
\(565\) 5.77319 + 29.9190i 0.242880 + 1.25870i
\(566\) −17.6392 4.69213i −0.741432 0.197225i
\(567\) 7.13436i 0.299615i
\(568\) −3.51422 3.47617i −0.147453 0.145857i
\(569\) −29.2380 −1.22572 −0.612859 0.790192i \(-0.709981\pi\)
−0.612859 + 0.790192i \(0.709981\pi\)
\(570\) 0.217302 3.12761i 0.00910176 0.131001i
\(571\) 23.5861i 0.987046i 0.869733 + 0.493523i \(0.164291\pi\)
−0.869733 + 0.493523i \(0.835709\pi\)
\(572\) 4.23699 7.40058i 0.177157 0.309434i
\(573\) 10.8841 0.454688
\(574\) 2.26044 8.49771i 0.0943488 0.354688i
\(575\) 10.9758 + 27.3815i 0.457722 + 1.14189i
\(576\) −0.242804 22.3003i −0.0101168 0.929178i
\(577\) 19.5025i 0.811898i −0.913896 0.405949i \(-0.866941\pi\)
0.913896 0.405949i \(-0.133059\pi\)
\(578\) 48.6825 + 12.9498i 2.02493 + 0.538641i
\(579\) 7.82570i 0.325225i
\(580\) −10.0043 + 29.2694i −0.415406 + 1.21535i
\(581\) 10.5144i 0.436210i
\(582\) −1.95063 + 7.33305i −0.0808562 + 0.303965i
\(583\) 23.3202i 0.965824i
\(584\) 11.5919 11.7188i 0.479677 0.484928i
\(585\) 5.55132 1.07119i 0.229519 0.0442881i
\(586\) 22.6843 + 6.03415i 0.937081 + 0.249269i
\(587\) 26.1827 1.08067 0.540337 0.841449i \(-0.318297\pi\)
0.540337 + 0.841449i \(0.318297\pi\)
\(588\) −0.799730 0.457863i −0.0329803 0.0188819i
\(589\) 17.2746i 0.711787i
\(590\) −2.56940 + 36.9812i −0.105780 + 1.52249i
\(591\) 3.28450 0.135106
\(592\) −12.5844 21.4361i −0.517218 0.881017i
\(593\) 12.4309i 0.510474i −0.966878 0.255237i \(-0.917846\pi\)
0.966878 0.255237i \(-0.0821536\pi\)
\(594\) 4.55761 17.1335i 0.187001 0.702997i
\(595\) 15.9267 3.07322i 0.652931 0.125990i
\(596\) 1.34057 2.34152i 0.0549119 0.0959125i
\(597\) −3.50164 −0.143313
\(598\) 1.94539 7.31335i 0.0795529 0.299065i
\(599\) −2.39815 −0.0979859 −0.0489929 0.998799i \(-0.515601\pi\)
−0.0489929 + 0.998799i \(0.515601\pi\)
\(600\) −6.00503 2.52982i −0.245154 0.103279i
\(601\) −9.37275 −0.382322 −0.191161 0.981559i \(-0.561225\pi\)
−0.191161 + 0.981559i \(0.561225\pi\)
\(602\) −3.39157 + 12.7500i −0.138230 + 0.519652i
\(603\) −15.1296 −0.616125
\(604\) 1.82878 + 1.04702i 0.0744122 + 0.0426026i
\(605\) 24.3706 4.70256i 0.990804 0.191186i
\(606\) 1.74903 6.57515i 0.0710493 0.267097i
\(607\) 34.0497i 1.38203i 0.722839 + 0.691017i \(0.242837\pi\)
−0.722839 + 0.691017i \(0.757163\pi\)
\(608\) −11.7280 + 3.25685i −0.475635 + 0.132083i
\(609\) −3.18690 −0.129140
\(610\) 1.35928 19.5641i 0.0550358 0.792128i
\(611\) 3.45528i 0.139786i
\(612\) −20.0948 + 35.0987i −0.812283 + 1.41878i
\(613\) −2.83753 −0.114607 −0.0573035 0.998357i \(-0.518250\pi\)
−0.0573035 + 0.998357i \(0.518250\pi\)
\(614\) −30.7382 8.17651i −1.24049 0.329977i
\(615\) 6.29008 1.21374i 0.253641 0.0489427i
\(616\) 9.45315 + 9.35078i 0.380878 + 0.376754i
\(617\) 32.4594i 1.30677i 0.757027 + 0.653384i \(0.226651\pi\)
−0.757027 + 0.653384i \(0.773349\pi\)
\(618\) −0.163157 + 0.613358i −0.00656312 + 0.0246729i
\(619\) 10.5243i 0.423006i −0.977377 0.211503i \(-0.932164\pi\)
0.977377 0.211503i \(-0.0678359\pi\)
\(620\) 33.9741 + 11.6124i 1.36443 + 0.466364i
\(621\) 15.7335i 0.631365i
\(622\) 18.5080 + 4.92323i 0.742104 + 0.197404i
\(623\) 11.5168i 0.461412i
\(624\) 0.846301 + 1.44157i 0.0338792 + 0.0577090i
\(625\) 18.0783 17.2678i 0.723131 0.690711i
\(626\) 3.04006 11.4286i 0.121505 0.456778i
\(627\) −4.66073 −0.186131
\(628\) 11.9894 + 6.86419i 0.478429 + 0.273911i
\(629\) 45.0784i 1.79739i
\(630\) −0.611012 + 8.79428i −0.0243433 + 0.350372i
\(631\) −8.92822 −0.355427 −0.177713 0.984082i \(-0.556870\pi\)
−0.177713 + 0.984082i \(0.556870\pi\)
\(632\) −16.1991 16.0237i −0.644367 0.637389i
\(633\) 5.78419i 0.229901i
\(634\) 13.0544 + 3.47255i 0.518458 + 0.137913i
\(635\) 3.85697 + 19.9884i 0.153059 + 0.793215i
\(636\) 3.96717 + 2.27129i 0.157309 + 0.0900625i
\(637\) −0.906993 −0.0359364
\(638\) 44.4382 + 11.8208i 1.75932 + 0.467990i
\(639\) −4.87184 −0.192727
\(640\) −1.47858 + 25.2550i −0.0584461 + 0.998291i
\(641\) 3.21151 0.126847 0.0634235 0.997987i \(-0.479798\pi\)
0.0634235 + 0.997987i \(0.479798\pi\)
\(642\) 2.24467 + 0.597094i 0.0885900 + 0.0235654i
\(643\) −19.3330 −0.762418 −0.381209 0.924489i \(-0.624492\pi\)
−0.381209 + 0.924489i \(0.624492\pi\)
\(644\) 10.2402 + 5.86276i 0.403522 + 0.231025i
\(645\) −9.43768 + 1.82110i −0.371608 + 0.0717058i
\(646\) 21.3319 + 5.67440i 0.839293 + 0.223256i
\(647\) 44.1500i 1.73571i 0.496814 + 0.867857i \(0.334503\pi\)
−0.496814 + 0.867857i \(0.665497\pi\)
\(648\) −14.3462 14.1908i −0.563571 0.557468i
\(649\) 55.1089 2.16321
\(650\) −6.36632 + 0.775727i −0.249708 + 0.0304265i
\(651\) 3.69916i 0.144981i
\(652\) 6.61566 + 3.78761i 0.259089 + 0.148334i
\(653\) −15.5908 −0.610114 −0.305057 0.952334i \(-0.598676\pi\)
−0.305057 + 0.952334i \(0.598676\pi\)
\(654\) −1.84011 + 6.91757i −0.0719540 + 0.270498i
\(655\) −1.50275 7.78788i −0.0587174 0.304298i
\(656\) −12.5915 21.4481i −0.491615 0.837407i
\(657\) 16.2461i 0.633820i
\(658\) −5.20653 1.38496i −0.202972 0.0539915i
\(659\) 46.2070i 1.79997i −0.435923 0.899984i \(-0.643578\pi\)
0.435923 0.899984i \(-0.356422\pi\)
\(660\) −3.13305 + 9.16629i −0.121954 + 0.356798i
\(661\) 20.3644i 0.792082i −0.918233 0.396041i \(-0.870384\pi\)
0.918233 0.396041i \(-0.129616\pi\)
\(662\) −1.46275 + 5.49894i −0.0568513 + 0.213723i
\(663\) 3.03151i 0.117734i
\(664\) 21.1429 + 20.9140i 0.820505 + 0.811620i
\(665\) 4.72420 0.911585i 0.183197 0.0353497i
\(666\) −23.6758 6.29789i −0.917419 0.244038i
\(667\) 40.8071 1.58006
\(668\) 5.93060 10.3587i 0.229462 0.400792i
\(669\) 3.32858i 0.128690i
\(670\) 17.1213 + 1.18956i 0.661453 + 0.0459567i
\(671\) −29.1542 −1.12549
\(672\) −2.51143 + 0.697417i −0.0968804 + 0.0269034i
\(673\) 7.07374i 0.272673i 0.990663 + 0.136336i \(0.0435328\pi\)
−0.990663 + 0.136336i \(0.956467\pi\)
\(674\) −0.854624 + 3.21281i −0.0329189 + 0.123753i
\(675\) −12.3765 + 4.96106i −0.476371 + 0.190951i
\(676\) −21.1359 12.1007i −0.812918 0.465413i
\(677\) −6.92717 −0.266233 −0.133116 0.991100i \(-0.542498\pi\)
−0.133116 + 0.991100i \(0.542498\pi\)
\(678\) −2.28264 + 8.58117i −0.0876641 + 0.329558i
\(679\) −11.6450 −0.446893
\(680\) 25.4997 38.1392i 0.977869 1.46257i
\(681\) 2.91029 0.111522
\(682\) 13.7208 51.5811i 0.525398 1.97514i
\(683\) −34.8750 −1.33445 −0.667227 0.744855i \(-0.732519\pi\)
−0.667227 + 0.744855i \(0.732519\pi\)
\(684\) −5.96055 + 10.4110i −0.227907 + 0.398076i
\(685\) 3.64965 + 18.9139i 0.139446 + 0.722664i
\(686\) 0.363546 1.36669i 0.0138803 0.0521804i
\(687\) 9.43215i 0.359859i
\(688\) 18.8924 + 32.1808i 0.720265 + 1.22688i
\(689\) 4.49926 0.171408
\(690\) −0.595833 + 8.57580i −0.0226830 + 0.326475i
\(691\) 16.0227i 0.609534i 0.952427 + 0.304767i \(0.0985785\pi\)
−0.952427 + 0.304767i \(0.901421\pi\)
\(692\) −16.5513 9.47599i −0.629187 0.360223i
\(693\) 13.1051 0.497822
\(694\) −25.7730 6.85575i −0.978329 0.260241i
\(695\) 1.11516 + 5.77922i 0.0423005 + 0.219218i
\(696\) −6.33901 + 6.40841i −0.240280 + 0.242910i
\(697\) 45.1037i 1.70842i
\(698\) −13.3137 + 50.0505i −0.503931 + 1.89444i
\(699\) 5.81267i 0.219855i
\(700\) 1.38289 9.90392i 0.0522684 0.374333i
\(701\) 18.2912i 0.690848i −0.938447 0.345424i \(-0.887735\pi\)
0.938447 0.345424i \(-0.112265\pi\)
\(702\) 3.30564 + 0.879318i 0.124763 + 0.0331877i
\(703\) 13.3712i 0.504306i
\(704\) 37.6062 0.409454i 1.41734 0.0154319i
\(705\) −0.743655 3.85392i −0.0280077 0.145147i
\(706\) 1.54955 5.82527i 0.0583181 0.219237i
\(707\) 10.4414 0.392690
\(708\) −5.36738 + 9.37498i −0.201718 + 0.352333i
\(709\) 14.3639i 0.539446i 0.962938 + 0.269723i \(0.0869321\pi\)
−0.962938 + 0.269723i \(0.913068\pi\)
\(710\) 5.51318 + 0.383047i 0.206906 + 0.0143755i
\(711\) −22.4572 −0.842212
\(712\) −23.1587 22.9079i −0.867910 0.858512i
\(713\) 47.3663i 1.77388i
\(714\) 4.56799 + 1.21511i 0.170953 + 0.0454743i
\(715\) 1.80640 + 9.36150i 0.0675556 + 0.350100i
\(716\) −16.6460 + 29.0748i −0.622089 + 1.08658i
\(717\) 11.4056 0.425949
\(718\) −14.0748 3.74396i −0.525266 0.139723i
\(719\) 45.5549 1.69891 0.849456 0.527659i \(-0.176930\pi\)
0.849456 + 0.527659i \(0.176930\pi\)
\(720\) 16.4687 + 18.7212i 0.613752 + 0.697698i
\(721\) −0.974021 −0.0362744
\(722\) −19.6396 5.22423i −0.730909 0.194426i
\(723\) 4.53559 0.168681
\(724\) −4.37694 + 7.64503i −0.162668 + 0.284125i
\(725\) −12.8672 32.1001i −0.477876 1.19217i
\(726\) 6.98980 + 1.85932i 0.259416 + 0.0690060i
\(727\) 36.7749i 1.36390i −0.731397 0.681952i \(-0.761131\pi\)
0.731397 0.681952i \(-0.238869\pi\)
\(728\) −1.80408 + 1.82383i −0.0668638 + 0.0675958i
\(729\) −16.2022 −0.600082
\(730\) −1.27734 + 18.3847i −0.0472765 + 0.680449i
\(731\) 67.6738i 2.50301i
\(732\) 2.83950 4.95963i 0.104951 0.183313i
\(733\) 10.0181 0.370028 0.185014 0.982736i \(-0.440767\pi\)
0.185014 + 0.982736i \(0.440767\pi\)
\(734\) −7.86492 + 29.5668i −0.290299 + 1.09133i
\(735\) 1.01163 0.195206i 0.0373147 0.00720026i
\(736\) 32.1579 8.93016i 1.18536 0.329170i
\(737\) 25.5139i 0.939817i
\(738\) −23.6891 6.30142i −0.872006 0.231958i
\(739\) 6.41780i 0.236082i −0.993009 0.118041i \(-0.962339\pi\)
0.993009 0.118041i \(-0.0376615\pi\)
\(740\) 26.2973 + 8.98845i 0.966709 + 0.330422i
\(741\) 0.899212i 0.0330334i
\(742\) −1.80342 + 6.77964i −0.0662056 + 0.248888i
\(743\) 19.0455i 0.698712i −0.936990 0.349356i \(-0.886400\pi\)
0.936990 0.349356i \(-0.113600\pi\)
\(744\) 7.43848 + 7.35793i 0.272708 + 0.269755i
\(745\) 0.571540 + 2.96195i 0.0209396 + 0.108518i
\(746\) 2.18562 + 0.581386i 0.0800212 + 0.0212861i
\(747\) 29.3109 1.07243
\(748\) −59.1890 33.8870i −2.16416 1.23903i
\(749\) 3.56456i 0.130246i
\(750\) 6.93386 2.23540i 0.253189 0.0816253i
\(751\) 27.9139 1.01859 0.509296 0.860591i \(-0.329906\pi\)
0.509296 + 0.860591i \(0.329906\pi\)
\(752\) −13.1412 + 7.71478i −0.479210 + 0.281329i
\(753\) 2.62019i 0.0954849i
\(754\) −2.28063 + 8.57363i −0.0830557 + 0.312233i
\(755\) −2.31335 + 0.446386i −0.0841916 + 0.0162457i
\(756\) −2.64997 + 4.62860i −0.0963785 + 0.168340i
\(757\) −39.2145 −1.42528 −0.712638 0.701532i \(-0.752500\pi\)
−0.712638 + 0.701532i \(0.752500\pi\)
\(758\) −3.51782 + 13.2246i −0.127773 + 0.480341i
\(759\) 12.7796 0.463868
\(760\) 7.56376 11.3129i 0.274366 0.410362i
\(761\) −19.8361 −0.719057 −0.359529 0.933134i \(-0.617063\pi\)
−0.359529 + 0.933134i \(0.617063\pi\)
\(762\) −1.52499 + 5.73294i −0.0552446 + 0.207682i
\(763\) −10.9852 −0.397691
\(764\) 40.9997 + 23.4732i 1.48332 + 0.849231i
\(765\) −8.56722 44.3988i −0.309749 1.60524i
\(766\) 0.0720156 0.270730i 0.00260203 0.00978187i
\(767\) 10.6324i 0.383913i
\(768\) −3.59303 + 6.43734i −0.129652 + 0.232288i
\(769\) 11.4291 0.412144 0.206072 0.978537i \(-0.433932\pi\)
0.206072 + 0.978537i \(0.433932\pi\)
\(770\) −14.8303 1.03038i −0.534446 0.0371325i
\(771\) 4.54200i 0.163576i
\(772\) −16.8774 + 29.4791i −0.607431 + 1.06097i
\(773\) −49.5840 −1.78341 −0.891707 0.452614i \(-0.850492\pi\)
−0.891707 + 0.452614i \(0.850492\pi\)
\(774\) 35.5432 + 9.45469i 1.27757 + 0.339842i
\(775\) −37.2598 + 14.9354i −1.33841 + 0.536497i
\(776\) −23.1628 + 23.4164i −0.831497 + 0.840600i
\(777\) 2.86330i 0.102720i
\(778\) 10.1792 38.2669i 0.364941 1.37193i
\(779\) 13.3787i 0.479342i
\(780\) −1.76849 0.604471i −0.0633221 0.0216435i
\(781\) 8.21566i 0.293980i
\(782\) −58.4914 15.5590i −2.09165 0.556389i
\(783\) 18.4448i 0.659164i
\(784\) −2.02509 3.44949i −0.0723247 0.123196i
\(785\) −15.1662 + 2.92648i −0.541305 + 0.104451i
\(786\) 0.594167 2.23367i 0.0211932 0.0796722i
\(787\) −21.3743 −0.761911 −0.380955 0.924593i \(-0.624405\pi\)
−0.380955 + 0.924593i \(0.624405\pi\)
\(788\) 12.3725 + 7.08354i 0.440753 + 0.252341i
\(789\) 2.21215i 0.0787547i
\(790\) 25.4135 + 1.76569i 0.904172 + 0.0628205i
\(791\) −13.6270 −0.484521
\(792\) 26.0672 26.3525i 0.926256 0.936396i
\(793\) 5.62483i 0.199744i
\(794\) −12.5288 3.33273i −0.444631 0.118274i
\(795\) −5.01835 + 0.968343i −0.177982 + 0.0343436i
\(796\) −13.1905 7.55185i −0.467526 0.267668i
\(797\) 20.4572 0.724630 0.362315 0.932056i \(-0.381986\pi\)
0.362315 + 0.932056i \(0.381986\pi\)
\(798\) 1.35496 + 0.360427i 0.0479652 + 0.0127590i
\(799\) 27.6349 0.977653
\(800\) −17.1647 22.4805i −0.606863 0.794806i
\(801\) −32.1055 −1.13439
\(802\) 35.3821 + 9.41182i 1.24938 + 0.332343i
\(803\) 27.3967 0.966808
\(804\) 4.34036 + 2.48495i 0.153073 + 0.0876373i
\(805\) −12.9536 + 2.49953i −0.456554 + 0.0880970i
\(806\) 9.95174 + 2.64722i 0.350535 + 0.0932442i
\(807\) 11.2115i 0.394662i
\(808\) 20.7689 20.9962i 0.730646 0.738645i
\(809\) −34.2917 −1.20563 −0.602816 0.797881i \(-0.705955\pi\)
−0.602816 + 0.797881i \(0.705955\pi\)
\(810\) 22.5066 + 1.56372i 0.790800 + 0.0549435i
\(811\) 36.9434i 1.29726i 0.761104 + 0.648630i \(0.224658\pi\)
−0.761104 + 0.648630i \(0.775342\pi\)
\(812\) −12.0049 6.87307i −0.421290 0.241197i
\(813\) −10.0252 −0.351598
\(814\) 10.6205 39.9258i 0.372248 1.39940i
\(815\) −8.36860 + 1.61481i −0.293139 + 0.0565644i
\(816\) 11.5295 6.76862i 0.403614 0.236949i
\(817\) 20.0735i 0.702284i
\(818\) 3.20410 + 0.852307i 0.112029 + 0.0298002i
\(819\) 2.52842i 0.0883502i
\(820\) 26.3121 + 8.99348i 0.918857 + 0.314066i
\(821\) 25.4645i 0.888718i −0.895849 0.444359i \(-0.853432\pi\)
0.895849 0.444359i \(-0.146568\pi\)
\(822\) −1.44302 + 5.42477i −0.0503310 + 0.189211i
\(823\) 24.8734i 0.867032i 0.901146 + 0.433516i \(0.142727\pi\)
−0.901146 + 0.433516i \(0.857273\pi\)
\(824\) −1.93741 + 1.95862i −0.0674928 + 0.0682317i
\(825\) −4.02962 10.0528i −0.140293 0.349993i
\(826\) −16.0212 4.26173i −0.557450 0.148285i
\(827\) 4.26715 0.148383 0.0741917 0.997244i \(-0.476362\pi\)
0.0741917 + 0.997244i \(0.476362\pi\)
\(828\) 16.3436 28.5467i 0.567980 0.992067i
\(829\) 30.6203i 1.06349i 0.846906 + 0.531743i \(0.178463\pi\)
−0.846906 + 0.531743i \(0.821537\pi\)
\(830\) −33.1695 2.30456i −1.15133 0.0799925i
\(831\) −5.09937 −0.176895
\(832\) 0.0789975 + 7.25551i 0.00273875 + 0.251540i
\(833\) 7.25402i 0.251337i
\(834\) −0.440919 + 1.65756i −0.0152678 + 0.0573965i
\(835\) 2.52846 + 13.1035i 0.0875009 + 0.453465i
\(836\) −17.5567 10.0516i −0.607212 0.347642i
\(837\) 21.4096 0.740024
\(838\) 7.48532 28.1398i 0.258576 0.972072i
\(839\) −18.2282 −0.629308 −0.314654 0.949206i \(-0.601888\pi\)
−0.314654 + 0.949206i \(0.601888\pi\)
\(840\) 1.61969 2.42253i 0.0558847 0.0835853i
\(841\) −18.8392 −0.649628
\(842\) 0.817727 3.07410i 0.0281807 0.105940i
\(843\) 3.43978 0.118472
\(844\) 12.4745 21.7888i 0.429391 0.750000i
\(845\) 26.7362 5.15904i 0.919754 0.177476i
\(846\) −3.86086 + 14.5142i −0.132739 + 0.499010i
\(847\) 11.0999i 0.381397i
\(848\) 10.0457 + 17.1117i 0.344972 + 0.587618i
\(849\) 5.94685 0.204095
\(850\) 6.20418 + 50.9171i 0.212801 + 1.74644i
\(851\) 36.6635i 1.25681i
\(852\) 1.39763 + 0.800171i 0.0478819 + 0.0274134i
\(853\) 55.5473 1.90190 0.950951 0.309340i \(-0.100108\pi\)
0.950951 + 0.309340i \(0.100108\pi\)
\(854\) 8.47569 + 2.25458i 0.290032 + 0.0771501i
\(855\) −2.54122 13.1696i −0.0869080 0.450392i
\(856\) 7.16783 + 7.09021i 0.244991 + 0.242338i
\(857\) 18.4129i 0.628974i 0.949262 + 0.314487i \(0.101832\pi\)
−0.949262 + 0.314487i \(0.898168\pi\)
\(858\) −0.714225 + 2.68500i −0.0243832 + 0.0916645i
\(859\) 54.3135i 1.85315i −0.376108 0.926576i \(-0.622738\pi\)
0.376108 0.926576i \(-0.377262\pi\)
\(860\) −39.4788 13.4939i −1.34622 0.460137i
\(861\) 2.86490i 0.0976356i
\(862\) 2.98088 + 0.792930i 0.101529 + 0.0270073i
\(863\) 54.3942i 1.85160i −0.378012 0.925801i \(-0.623392\pi\)
0.378012 0.925801i \(-0.376608\pi\)
\(864\) 4.03644 + 14.5354i 0.137322 + 0.494504i
\(865\) 20.9369 4.04000i 0.711876 0.137364i
\(866\) −2.55646 + 9.61054i −0.0868719 + 0.326580i
\(867\) −16.4127 −0.557406
\(868\) −7.97783 + 13.9345i −0.270785 + 0.472969i
\(869\) 37.8709i 1.28468i
\(870\) 0.698511 10.0536i 0.0236817 0.340850i
\(871\) 4.92250 0.166792
\(872\) −21.8505 + 22.0897i −0.739950 + 0.748050i
\(873\) 32.4627i 1.09870i
\(874\) −17.3498 4.61514i −0.586866 0.156109i
\(875\) 6.05071 + 9.40154i 0.204551 + 0.317830i
\(876\) −2.66832 + 4.66065i −0.0901542 + 0.157469i
\(877\) 42.2117 1.42539 0.712694 0.701475i \(-0.247475\pi\)
0.712694 + 0.701475i \(0.247475\pi\)
\(878\) −7.55277 2.00908i −0.254894 0.0678030i
\(879\) −7.64775 −0.257952
\(880\) −31.5706 + 27.7721i −1.06425 + 0.936196i
\(881\) −11.6420 −0.392230 −0.196115 0.980581i \(-0.562833\pi\)
−0.196115 + 0.980581i \(0.562833\pi\)
\(882\) −3.80991 1.01346i −0.128286 0.0341249i
\(883\) −47.4507 −1.59684 −0.798421 0.602099i \(-0.794331\pi\)
−0.798421 + 0.602099i \(0.794331\pi\)
\(884\) 6.53794 11.4196i 0.219895 0.384081i
\(885\) −2.28833 11.8591i −0.0769214 0.398638i
\(886\) −21.9390 5.83588i −0.737054 0.196060i
\(887\) 48.2129i 1.61883i −0.587236 0.809416i \(-0.699784\pi\)
0.587236 0.809416i \(-0.300216\pi\)
\(888\) 5.75768 + 5.69534i 0.193215 + 0.191123i
\(889\) −9.10398 −0.305338
\(890\) 36.3319 + 2.52428i 1.21785 + 0.0846141i
\(891\) 33.5390i 1.12360i
\(892\) 7.17861 12.5386i 0.240358 0.419823i
\(893\) 8.19711 0.274306
\(894\) −0.225979 + 0.849527i −0.00755786 + 0.0284124i
\(895\) −7.09685 36.7788i −0.237222 1.22938i
\(896\) −10.9645 2.78916i −0.366299 0.0931793i
\(897\) 2.46561i 0.0823243i
\(898\) −48.9189 13.0127i −1.63244 0.434239i
\(899\) 55.5288i 1.85199i
\(900\) −27.6091 3.85509i −0.920305 0.128503i
\(901\) 35.9846i 1.19882i
\(902\) 10.6264 39.9482i 0.353821 1.33013i
\(903\) 4.29852i 0.143046i
\(904\) −27.1053 + 27.4020i −0.901507 + 0.911376i
\(905\) −1.86607 9.67073i −0.0620302 0.321466i
\(906\) −0.663501 0.176495i −0.0220433 0.00586364i
\(907\) −20.0205 −0.664770 −0.332385 0.943144i \(-0.607853\pi\)
−0.332385 + 0.943144i \(0.607853\pi\)
\(908\) 10.9629 + 6.27650i 0.363817 + 0.208293i
\(909\) 29.1076i 0.965437i
\(910\) 0.198796 2.86126i 0.00659003 0.0948500i
\(911\) −27.8697 −0.923365 −0.461682 0.887045i \(-0.652754\pi\)
−0.461682 + 0.887045i \(0.652754\pi\)
\(912\) 3.41990 2.00772i 0.113244 0.0664822i
\(913\) 49.4287i 1.63585i
\(914\) 3.82375 14.3747i 0.126478 0.475473i
\(915\) 1.21059 + 6.27378i 0.0400210 + 0.207405i
\(916\) 20.3420 35.5305i 0.672117 1.17396i
\(917\) 3.54709 0.117135
\(918\) 7.03268 26.4381i 0.232113 0.872588i
\(919\) −30.5251 −1.00693 −0.503465 0.864016i \(-0.667942\pi\)
−0.503465 + 0.864016i \(0.667942\pi\)
\(920\) −20.7396 + 31.0196i −0.683763 + 1.02269i
\(921\) 10.3630 0.341472
\(922\) −1.26719 + 4.76377i −0.0417326 + 0.156886i
\(923\) 1.58508 0.0521736
\(924\) −3.75957 2.15244i −0.123681 0.0708100i
\(925\) −28.8406 + 11.5606i −0.948272 + 0.380111i
\(926\) 6.20378 23.3220i 0.203869 0.766409i
\(927\) 2.71528i 0.0891814i
\(928\) −37.6995 + 10.4691i −1.23755 + 0.343664i
\(929\) 9.09643 0.298444 0.149222 0.988804i \(-0.452323\pi\)
0.149222 + 0.988804i \(0.452323\pi\)
\(930\) −11.6696 0.810788i −0.382662 0.0265868i
\(931\) 2.15170i 0.0705191i
\(932\) 12.5360 21.8960i 0.410629 0.717229i
\(933\) −6.23976 −0.204281
\(934\) −27.7201 7.37370i −0.907030 0.241275i
\(935\) 74.8722 14.4474i 2.44858 0.472480i
\(936\) 5.08430 + 5.02924i 0.166185 + 0.164386i
\(937\) 23.6954i 0.774095i 0.922060 + 0.387047i \(0.126505\pi\)
−0.922060 + 0.387047i \(0.873495\pi\)
\(938\) −1.97306 + 7.41739i −0.0644228 + 0.242186i
\(939\) 3.85301i 0.125738i
\(940\) 5.51029 16.1213i 0.179726 0.525820i
\(941\) 21.8195i 0.711294i −0.934620 0.355647i \(-0.884261\pi\)
0.934620 0.355647i \(-0.115739\pi\)
\(942\) −4.34987 1.15709i −0.141726 0.0377000i
\(943\) 36.6840i 1.19460i
\(944\) −40.4373 + 23.7395i −1.31612 + 0.772654i
\(945\) −1.12979 5.85503i −0.0367521 0.190464i
\(946\) −15.9440 + 59.9385i −0.518383 + 1.94877i
\(947\) −48.8564 −1.58762 −0.793809 0.608167i \(-0.791905\pi\)
−0.793809 + 0.608167i \(0.791905\pi\)
\(948\) 6.44249 + 3.68846i 0.209242 + 0.119796i
\(949\) 5.28575i 0.171583i
\(950\) 1.84029 + 15.1031i 0.0597070 + 0.490010i
\(951\) −4.40115 −0.142717
\(952\) 14.5868 + 14.4289i 0.472761 + 0.467642i
\(953\) 9.57502i 0.310165i 0.987901 + 0.155083i \(0.0495644\pi\)
−0.987901 + 0.155083i \(0.950436\pi\)
\(954\) 18.8996 + 5.02739i 0.611897 + 0.162768i
\(955\) −51.8634 + 10.0076i −1.67826 + 0.323838i
\(956\) 42.9643 + 24.5980i 1.38956 + 0.795555i
\(957\) −14.9818 −0.484293
\(958\) 40.1943 + 10.6919i 1.29862 + 0.345439i
\(959\) −8.61460 −0.278180
\(960\) −1.64966 8.07559i −0.0532427 0.260639i
\(961\) 33.4544 1.07917
\(962\) 7.70305 + 2.04905i 0.248356 + 0.0660641i
\(963\) 9.93693 0.320213
\(964\) 17.0854 + 9.78174i 0.550282 + 0.315048i
\(965\) −7.19552 37.2901i −0.231632 1.20041i
\(966\) −3.71526 0.988280i −0.119537 0.0317974i
\(967\) 47.6790i 1.53325i 0.642094 + 0.766626i \(0.278066\pi\)
−0.642094 + 0.766626i \(0.721934\pi\)
\(968\) 22.3203 + 22.0786i 0.717402 + 0.709634i
\(969\) −7.19179 −0.231034
\(970\) 2.55237 36.7361i 0.0819516 1.17953i
\(971\) 10.4524i 0.335435i 0.985835 + 0.167717i \(0.0536396\pi\)
−0.985835 + 0.167717i \(0.946360\pi\)
\(972\) 19.5914 + 11.2165i 0.628393 + 0.359768i
\(973\) −2.63222 −0.0843851
\(974\) 2.99630 11.2641i 0.0960077 0.360924i
\(975\) 1.93952 0.777450i 0.0621144 0.0248983i
\(976\) 21.3925 12.5589i 0.684757 0.402000i
\(977\) 51.6435i 1.65222i −0.563507 0.826111i \(-0.690548\pi\)
0.563507 0.826111i \(-0.309452\pi\)
\(978\) −2.40023 0.638473i −0.0767508 0.0204161i
\(979\) 54.1413i 1.73036i
\(980\) 4.23177 + 1.44642i 0.135179 + 0.0462042i
\(981\) 30.6234i 0.977730i
\(982\) 5.01010 18.8346i 0.159879 0.601036i
\(983\) 32.3755i 1.03262i −0.856403 0.516308i \(-0.827306\pi\)
0.856403 0.516308i \(-0.172694\pi\)
\(984\) 5.76091 + 5.69853i 0.183651 + 0.181662i
\(985\) −15.6509 + 3.02000i −0.498678 + 0.0962253i
\(986\) 68.5709 + 18.2402i 2.18374 + 0.580887i
\(987\) 1.75532 0.0558724
\(988\) 1.93930 3.38729i 0.0616972 0.107764i
\(989\) 55.0409i 1.75020i
\(990\) −2.87240 + 41.3424i −0.0912909 + 1.31395i
\(991\) 19.5212 0.620110 0.310055 0.950719i \(-0.399653\pi\)
0.310055 + 0.950719i \(0.399653\pi\)
\(992\) 12.1518 + 43.7593i 0.385821 + 1.38936i
\(993\) 1.85390i 0.0588318i
\(994\) −0.635341 + 2.38845i −0.0201518 + 0.0757571i
\(995\) 16.6856 3.21966i 0.528969 0.102070i
\(996\) −8.40868 4.81415i −0.266439 0.152542i
\(997\) 9.19720 0.291278 0.145639 0.989338i \(-0.453476\pi\)
0.145639 + 0.989338i \(0.453476\pi\)
\(998\) 3.34386 12.5707i 0.105848 0.397917i
\(999\) 16.5719 0.524312
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 280.2.l.a.29.5 36
4.3 odd 2 1120.2.l.a.1009.13 36
5.4 even 2 inner 280.2.l.a.29.32 yes 36
8.3 odd 2 1120.2.l.a.1009.24 36
8.5 even 2 inner 280.2.l.a.29.31 yes 36
20.19 odd 2 1120.2.l.a.1009.23 36
40.19 odd 2 1120.2.l.a.1009.14 36
40.29 even 2 inner 280.2.l.a.29.6 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.l.a.29.5 36 1.1 even 1 trivial
280.2.l.a.29.6 yes 36 40.29 even 2 inner
280.2.l.a.29.31 yes 36 8.5 even 2 inner
280.2.l.a.29.32 yes 36 5.4 even 2 inner
1120.2.l.a.1009.13 36 4.3 odd 2
1120.2.l.a.1009.14 36 40.19 odd 2
1120.2.l.a.1009.23 36 20.19 odd 2
1120.2.l.a.1009.24 36 8.3 odd 2