Properties

Label 187.2.p.a.38.1
Level $187$
Weight $2$
Character 187.38
Analytic conductor $1.493$
Analytic rank $0$
Dimension $128$
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] = [187,2,Mod(4,187)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(187, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([4, 15]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("187.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 187 = 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 187.p (of order \(20\), degree \(8\), 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: \(1.49320251780\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(16\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 38.1
Character \(\chi\) \(=\) 187.38
Dual form 187.2.p.a.64.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.30228 + 0.748055i) q^{2} +(1.85991 - 0.294580i) q^{3} +(3.12286 - 2.26889i) q^{4} +(1.21515 + 2.38487i) q^{5} +(-4.06166 + 2.06952i) q^{6} +(0.345011 + 0.0546444i) q^{7} +(-2.64667 + 3.64282i) q^{8} +(0.519302 - 0.168732i) q^{9} +O(q^{10})\) \(q+(-2.30228 + 0.748055i) q^{2} +(1.85991 - 0.294580i) q^{3} +(3.12286 - 2.26889i) q^{4} +(1.21515 + 2.38487i) q^{5} +(-4.06166 + 2.06952i) q^{6} +(0.345011 + 0.0546444i) q^{7} +(-2.64667 + 3.64282i) q^{8} +(0.519302 - 0.168732i) q^{9} +(-4.58163 - 4.58163i) q^{10} +(3.29872 - 0.344184i) q^{11} +(5.13986 - 5.13986i) q^{12} +(-1.26183 - 3.88353i) q^{13} +(-0.835189 + 0.132281i) q^{14} +(2.96260 + 4.07767i) q^{15} +(0.982673 - 3.02436i) q^{16} +(0.915773 + 4.02012i) q^{17} +(-1.06936 + 0.776934i) q^{18} +(-0.944299 + 1.29972i) q^{19} +(9.20575 + 4.69056i) q^{20} +0.657785 q^{21} +(-7.33710 + 3.26003i) q^{22} +(0.895855 + 0.895855i) q^{23} +(-3.84945 + 7.55496i) q^{24} +(-1.27207 + 1.75086i) q^{25} +(5.81019 + 7.99704i) q^{26} +(-4.11739 + 2.09791i) q^{27} +(1.20140 - 0.612146i) q^{28} +(-0.540052 + 3.40976i) q^{29} +(-9.87105 - 7.17174i) q^{30} +(6.19275 + 3.15536i) q^{31} -1.30755i q^{32} +(6.03391 - 1.61189i) q^{33} +(-5.11564 - 8.57038i) q^{34} +(0.288921 + 0.889207i) q^{35} +(1.23888 - 1.70517i) q^{36} +(1.86952 - 11.8037i) q^{37} +(1.20178 - 3.69869i) q^{38} +(-3.49090 - 6.85128i) q^{39} +(-11.9037 - 1.88537i) q^{40} +(-0.288382 - 1.82078i) q^{41} +(-1.51440 + 0.492060i) q^{42} +3.79501i q^{43} +(9.52052 - 8.55927i) q^{44} +(1.03343 + 1.03343i) q^{45} +(-2.73266 - 1.39236i) q^{46} +(-7.76702 - 5.64307i) q^{47} +(0.936764 - 5.91450i) q^{48} +(-6.54135 - 2.12541i) q^{49} +(1.61893 - 4.98254i) q^{50} +(2.88750 + 7.20727i) q^{51} +(-12.7518 - 9.26475i) q^{52} +(-1.41331 + 0.459213i) q^{53} +(7.91001 - 7.91001i) q^{54} +(4.82927 + 7.44877i) q^{55} +(-1.11219 + 1.11219i) q^{56} +(-1.37344 + 2.69552i) q^{57} +(-1.30734 - 8.25419i) q^{58} +(-7.24584 - 9.97304i) q^{59} +(18.5036 + 6.01218i) q^{60} +(4.92519 - 2.50951i) q^{61} +(-16.6178 - 2.63200i) q^{62} +(0.188385 - 0.0298373i) q^{63} +(2.94347 + 9.05906i) q^{64} +(7.72838 - 7.72838i) q^{65} +(-12.6860 + 8.22471i) q^{66} -7.27578 q^{67} +(11.9810 + 10.4765i) q^{68} +(1.93011 + 1.40231i) q^{69} +(-1.33035 - 1.83107i) q^{70} +(4.52616 + 8.88308i) q^{71} +(-0.759761 + 2.33830i) q^{72} +(0.687332 - 4.33964i) q^{73} +(4.52565 + 28.5739i) q^{74} +(-1.85017 + 3.63116i) q^{75} +6.20134i q^{76} +(1.15690 + 0.0615092i) q^{77} +(13.1622 + 13.1622i) q^{78} +(5.26610 - 10.3353i) q^{79} +(8.40678 - 1.33150i) q^{80} +(-8.36518 + 6.07766i) q^{81} +(2.02598 + 3.97620i) q^{82} +(-12.1731 - 3.95528i) q^{83} +(2.05417 - 1.49244i) q^{84} +(-8.47465 + 7.06905i) q^{85} +(-2.83888 - 8.73718i) q^{86} +6.50091i q^{87} +(-7.47680 + 12.9276i) q^{88} +0.411806 q^{89} +(-3.15231 - 1.60618i) q^{90} +(-0.223134 - 1.40881i) q^{91} +(4.83023 + 0.765033i) q^{92} +(12.4474 + 4.04442i) q^{93} +(22.1032 + 7.18175i) q^{94} +(-4.24711 - 0.672677i) q^{95} +(-0.385179 - 2.43192i) q^{96} +(-14.0408 - 7.15416i) q^{97} +16.6499 q^{98} +(1.65496 - 0.735333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q - 10 q^{3} + 16 q^{4} - 2 q^{5} - 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 128 q - 10 q^{3} + 16 q^{4} - 2 q^{5} - 8 q^{6} - 24 q^{10} - 40 q^{13} + 2 q^{14} - 48 q^{16} - 18 q^{17} - 2 q^{20} + 16 q^{21} - 70 q^{22} - 16 q^{23} + 28 q^{24} - 22 q^{27} + 42 q^{28} - 2 q^{29} - 44 q^{30} - 6 q^{31} + 32 q^{33} + 44 q^{34} + 12 q^{35} + 30 q^{37} - 80 q^{38} + 78 q^{39} - 100 q^{40} - 56 q^{41} + 52 q^{44} - 68 q^{45} + 14 q^{46} - 16 q^{47} - 110 q^{48} + 84 q^{50} + 14 q^{51} - 100 q^{52} - 20 q^{54} - 84 q^{55} + 36 q^{56} - 48 q^{57} - 26 q^{58} + 28 q^{61} + 108 q^{62} - 40 q^{63} + 120 q^{64} + 28 q^{65} - 48 q^{67} + 102 q^{68} + 24 q^{69} + 2 q^{71} + 80 q^{72} - 30 q^{73} - 28 q^{74} - 80 q^{75} - 104 q^{78} + 44 q^{79} - 92 q^{80} + 140 q^{81} - 28 q^{82} - 52 q^{84} + 76 q^{85} + 12 q^{86} + 50 q^{88} - 32 q^{89} + 204 q^{90} + 42 q^{91} + 2 q^{92} + 16 q^{95} + 240 q^{96} - 34 q^{97} + 24 q^{98} - 90 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).

\(n\) \(35\) \(122\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.30228 + 0.748055i −1.62796 + 0.528955i −0.973800 0.227405i \(-0.926976\pi\)
−0.654156 + 0.756360i \(0.726976\pi\)
\(3\) 1.85991 0.294580i 1.07382 0.170076i 0.405606 0.914048i \(-0.367060\pi\)
0.668211 + 0.743972i \(0.267060\pi\)
\(4\) 3.12286 2.26889i 1.56143 1.13445i
\(5\) 1.21515 + 2.38487i 0.543432 + 1.06654i 0.985518 + 0.169572i \(0.0542386\pi\)
−0.442086 + 0.896973i \(0.645761\pi\)
\(6\) −4.06166 + 2.06952i −1.65816 + 0.844877i
\(7\) 0.345011 + 0.0546444i 0.130402 + 0.0206536i 0.221294 0.975207i \(-0.428972\pi\)
−0.0908923 + 0.995861i \(0.528972\pi\)
\(8\) −2.64667 + 3.64282i −0.935738 + 1.28793i
\(9\) 0.519302 0.168732i 0.173101 0.0562439i
\(10\) −4.58163 4.58163i −1.44884 1.44884i
\(11\) 3.29872 0.344184i 0.994601 0.103775i
\(12\) 5.13986 5.13986i 1.48375 1.48375i
\(13\) −1.26183 3.88353i −0.349970 1.07710i −0.958869 0.283849i \(-0.908389\pi\)
0.608899 0.793248i \(-0.291611\pi\)
\(14\) −0.835189 + 0.132281i −0.223214 + 0.0353535i
\(15\) 2.96260 + 4.07767i 0.764940 + 1.05285i
\(16\) 0.982673 3.02436i 0.245668 0.756089i
\(17\) 0.915773 + 4.02012i 0.222108 + 0.975022i
\(18\) −1.06936 + 0.776934i −0.252050 + 0.183125i
\(19\) −0.944299 + 1.29972i −0.216637 + 0.298175i −0.903480 0.428631i \(-0.858996\pi\)
0.686843 + 0.726806i \(0.258996\pi\)
\(20\) 9.20575 + 4.69056i 2.05847 + 1.04884i
\(21\) 0.657785 0.143541
\(22\) −7.33710 + 3.26003i −1.56427 + 0.695041i
\(23\) 0.895855 + 0.895855i 0.186799 + 0.186799i 0.794311 0.607512i \(-0.207832\pi\)
−0.607512 + 0.794311i \(0.707832\pi\)
\(24\) −3.84945 + 7.55496i −0.785765 + 1.54215i
\(25\) −1.27207 + 1.75086i −0.254415 + 0.350172i
\(26\) 5.81019 + 7.99704i 1.13947 + 1.56835i
\(27\) −4.11739 + 2.09791i −0.792392 + 0.403744i
\(28\) 1.20140 0.612146i 0.227044 0.115685i
\(29\) −0.540052 + 3.40976i −0.100285 + 0.633176i 0.885432 + 0.464768i \(0.153862\pi\)
−0.985717 + 0.168407i \(0.946138\pi\)
\(30\) −9.87105 7.17174i −1.80220 1.30937i
\(31\) 6.19275 + 3.15536i 1.11225 + 0.566720i 0.910829 0.412785i \(-0.135444\pi\)
0.201422 + 0.979505i \(0.435444\pi\)
\(32\) 1.30755i 0.231145i
\(33\) 6.03391 1.61189i 1.05037 0.280593i
\(34\) −5.11564 8.57038i −0.877324 1.46981i
\(35\) 0.288921 + 0.889207i 0.0488365 + 0.150303i
\(36\) 1.23888 1.70517i 0.206479 0.284194i
\(37\) 1.86952 11.8037i 0.307347 1.94051i −0.0310701 0.999517i \(-0.509892\pi\)
0.338417 0.940996i \(-0.390108\pi\)
\(38\) 1.20178 3.69869i 0.194954 0.600007i
\(39\) −3.49090 6.85128i −0.558992 1.09708i
\(40\) −11.9037 1.88537i −1.88215 0.298103i
\(41\) −0.288382 1.82078i −0.0450378 0.284357i 0.954883 0.296984i \(-0.0959808\pi\)
−0.999920 + 0.0126265i \(0.995981\pi\)
\(42\) −1.51440 + 0.492060i −0.233678 + 0.0759265i
\(43\) 3.79501i 0.578734i 0.957218 + 0.289367i \(0.0934448\pi\)
−0.957218 + 0.289367i \(0.906555\pi\)
\(44\) 9.52052 8.55927i 1.43527 1.29036i
\(45\) 1.03343 + 1.03343i 0.154055 + 0.154055i
\(46\) −2.73266 1.39236i −0.402908 0.205292i
\(47\) −7.76702 5.64307i −1.13294 0.823126i −0.146817 0.989164i \(-0.546903\pi\)
−0.986119 + 0.166037i \(0.946903\pi\)
\(48\) 0.936764 5.91450i 0.135210 0.853684i
\(49\) −6.54135 2.12541i −0.934478 0.303630i
\(50\) 1.61893 4.98254i 0.228951 0.704638i
\(51\) 2.88750 + 7.20727i 0.404331 + 1.00922i
\(52\) −12.7518 9.26475i −1.76836 1.28479i
\(53\) −1.41331 + 0.459213i −0.194133 + 0.0630777i −0.404470 0.914551i \(-0.632544\pi\)
0.210337 + 0.977629i \(0.432544\pi\)
\(54\) 7.91001 7.91001i 1.07642 1.07642i
\(55\) 4.82927 + 7.44877i 0.651179 + 1.00439i
\(56\) −1.11219 + 1.11219i −0.148623 + 0.148623i
\(57\) −1.37344 + 2.69552i −0.181916 + 0.357030i
\(58\) −1.30734 8.25419i −0.171662 1.08383i
\(59\) −7.24584 9.97304i −0.943328 1.29838i −0.954428 0.298441i \(-0.903534\pi\)
0.0111006 0.999938i \(-0.496466\pi\)
\(60\) 18.5036 + 6.01218i 2.38880 + 0.776169i
\(61\) 4.92519 2.50951i 0.630606 0.321310i −0.109311 0.994008i \(-0.534865\pi\)
0.739917 + 0.672698i \(0.234865\pi\)
\(62\) −16.6178 2.63200i −2.11046 0.334265i
\(63\) 0.188385 0.0298373i 0.0237343 0.00375915i
\(64\) 2.94347 + 9.05906i 0.367933 + 1.13238i
\(65\) 7.72838 7.72838i 0.958587 0.958587i
\(66\) −12.6860 + 8.22471i −1.56153 + 1.01239i
\(67\) −7.27578 −0.888878 −0.444439 0.895809i \(-0.646597\pi\)
−0.444439 + 0.895809i \(0.646597\pi\)
\(68\) 11.9810 + 10.4765i 1.45292 + 1.27046i
\(69\) 1.93011 + 1.40231i 0.232358 + 0.168818i
\(70\) −1.33035 1.83107i −0.159007 0.218855i
\(71\) 4.52616 + 8.88308i 0.537156 + 1.05423i 0.986940 + 0.161090i \(0.0515011\pi\)
−0.449784 + 0.893138i \(0.648499\pi\)
\(72\) −0.759761 + 2.33830i −0.0895387 + 0.275572i
\(73\) 0.687332 4.33964i 0.0804461 0.507917i −0.914258 0.405133i \(-0.867225\pi\)
0.994704 0.102783i \(-0.0327749\pi\)
\(74\) 4.52565 + 28.5739i 0.526097 + 3.32164i
\(75\) −1.85017 + 3.63116i −0.213639 + 0.419290i
\(76\) 6.20134i 0.711343i
\(77\) 1.15690 + 0.0615092i 0.131841 + 0.00700962i
\(78\) 13.1622 + 13.1622i 1.49032 + 1.49032i
\(79\) 5.26610 10.3353i 0.592483 1.16281i −0.378932 0.925424i \(-0.623709\pi\)
0.971415 0.237388i \(-0.0762914\pi\)
\(80\) 8.40678 1.33150i 0.939907 0.148867i
\(81\) −8.36518 + 6.07766i −0.929465 + 0.675296i
\(82\) 2.02598 + 3.97620i 0.223732 + 0.439098i
\(83\) −12.1731 3.95528i −1.33617 0.434148i −0.448153 0.893957i \(-0.647918\pi\)
−0.888018 + 0.459808i \(0.847918\pi\)
\(84\) 2.05417 1.49244i 0.224129 0.162839i
\(85\) −8.47465 + 7.06905i −0.919205 + 0.766746i
\(86\) −2.83888 8.73718i −0.306124 0.942154i
\(87\) 6.50091i 0.696971i
\(88\) −7.47680 + 12.9276i −0.797030 + 1.37809i
\(89\) 0.411806 0.0436514 0.0218257 0.999762i \(-0.493052\pi\)
0.0218257 + 0.999762i \(0.493052\pi\)
\(90\) −3.15231 1.60618i −0.332283 0.169307i
\(91\) −0.223134 1.40881i −0.0233908 0.147684i
\(92\) 4.83023 + 0.765033i 0.503586 + 0.0797603i
\(93\) 12.4474 + 4.04442i 1.29074 + 0.419387i
\(94\) 22.1032 + 7.18175i 2.27977 + 0.740741i
\(95\) −4.24711 0.672677i −0.435745 0.0690152i
\(96\) −0.385179 2.43192i −0.0393122 0.248207i
\(97\) −14.0408 7.15416i −1.42563 0.726395i −0.440427 0.897788i \(-0.645173\pi\)
−0.985203 + 0.171393i \(0.945173\pi\)
\(98\) 16.6499 1.68190
\(99\) 1.65496 0.735333i 0.166329 0.0739038i
\(100\) 8.35388i 0.835388i
\(101\) −2.73230 8.40917i −0.271874 0.836743i −0.990029 0.140860i \(-0.955013\pi\)
0.718155 0.695883i \(-0.244987\pi\)
\(102\) −12.0393 14.4331i −1.19206 1.42909i
\(103\) 5.35825 3.89300i 0.527964 0.383588i −0.291632 0.956531i \(-0.594198\pi\)
0.819596 + 0.572942i \(0.194198\pi\)
\(104\) 17.4867 + 5.68176i 1.71471 + 0.557143i
\(105\) 0.799308 + 1.56873i 0.0780045 + 0.153092i
\(106\) 2.91032 2.11447i 0.282675 0.205375i
\(107\) −1.08133 + 0.171265i −0.104536 + 0.0165568i −0.208483 0.978026i \(-0.566853\pi\)
0.103947 + 0.994583i \(0.466853\pi\)
\(108\) −8.09809 + 15.8934i −0.779239 + 1.52934i
\(109\) 12.7693 + 12.7693i 1.22308 + 1.22308i 0.966531 + 0.256548i \(0.0825852\pi\)
0.256548 + 0.966531i \(0.417415\pi\)
\(110\) −16.6904 13.5366i −1.59137 1.29066i
\(111\) 22.5045i 2.13603i
\(112\) 0.504297 0.989739i 0.0476516 0.0935216i
\(113\) −0.318486 2.01084i −0.0299606 0.189164i 0.968169 0.250298i \(-0.0805285\pi\)
−0.998130 + 0.0611335i \(0.980528\pi\)
\(114\) 1.14563 7.23324i 0.107298 0.677455i
\(115\) −1.04790 + 3.22509i −0.0977169 + 0.300742i
\(116\) 6.04986 + 11.8735i 0.561715 + 1.10243i
\(117\) −1.31055 1.80381i −0.121160 0.166763i
\(118\) 24.1423 + 17.5404i 2.22248 + 1.61473i
\(119\) 0.0962749 + 1.43703i 0.00882550 + 0.131732i
\(120\) −22.6952 −2.07178
\(121\) 10.7631 2.27073i 0.978461 0.206430i
\(122\) −9.46191 + 9.46191i −0.856641 + 0.856641i
\(123\) −1.07273 3.30152i −0.0967247 0.297688i
\(124\) 26.4983 4.19692i 2.37962 0.376894i
\(125\) 7.49690 + 1.18739i 0.670543 + 0.106204i
\(126\) −0.411395 + 0.209616i −0.0366500 + 0.0186741i
\(127\) −11.5650 3.75770i −1.02623 0.333442i −0.252930 0.967485i \(-0.581394\pi\)
−0.773298 + 0.634043i \(0.781394\pi\)
\(128\) −12.0162 16.5389i −1.06210 1.46185i
\(129\) 1.11794 + 7.05837i 0.0984288 + 0.621455i
\(130\) −12.0116 + 23.5741i −1.05349 + 2.06759i
\(131\) 0.0239106 0.0239106i 0.00208908 0.00208908i −0.706061 0.708151i \(-0.749530\pi\)
0.708151 + 0.706061i \(0.249530\pi\)
\(132\) 15.1859 18.7240i 1.32176 1.62971i
\(133\) −0.396816 + 0.396816i −0.0344083 + 0.0344083i
\(134\) 16.7509 5.44269i 1.44705 0.470177i
\(135\) −10.0065 7.27014i −0.861221 0.625714i
\(136\) −17.0683 7.30392i −1.46360 0.626306i
\(137\) −2.62205 + 8.06985i −0.224017 + 0.689454i 0.774373 + 0.632730i \(0.218066\pi\)
−0.998390 + 0.0567242i \(0.981934\pi\)
\(138\) −5.49265 1.78467i −0.467565 0.151921i
\(139\) −2.83653 + 17.9091i −0.240591 + 1.51903i 0.511102 + 0.859520i \(0.329237\pi\)
−0.751693 + 0.659513i \(0.770763\pi\)
\(140\) 2.91977 + 2.12134i 0.246766 + 0.179286i
\(141\) −16.1083 8.20757i −1.35656 0.691202i
\(142\) −17.0655 17.0655i −1.43211 1.43211i
\(143\) −5.49908 12.3764i −0.459856 1.03496i
\(144\) 1.73636i 0.144697i
\(145\) −8.78806 + 2.85541i −0.729809 + 0.237129i
\(146\) 1.66386 + 10.5052i 0.137702 + 0.869418i
\(147\) −12.7924 2.02612i −1.05510 0.167111i
\(148\) −20.9430 41.1030i −1.72151 3.37865i
\(149\) 1.04563 3.21812i 0.0856614 0.263639i −0.899046 0.437854i \(-0.855739\pi\)
0.984708 + 0.174215i \(0.0557388\pi\)
\(150\) 1.54329 9.74396i 0.126009 0.795591i
\(151\) 7.51279 10.3405i 0.611382 0.841495i −0.385308 0.922788i \(-0.625905\pi\)
0.996690 + 0.0812927i \(0.0259049\pi\)
\(152\) −2.23539 6.87983i −0.181314 0.558028i
\(153\) 1.15388 + 1.93314i 0.0932860 + 0.156285i
\(154\) −2.70952 + 0.723816i −0.218340 + 0.0583267i
\(155\) 18.6031i 1.49424i
\(156\) −26.4464 13.4751i −2.11741 1.07887i
\(157\) 15.4977 + 11.2598i 1.23685 + 0.898628i 0.997385 0.0722761i \(-0.0230263\pi\)
0.239470 + 0.970904i \(0.423026\pi\)
\(158\) −4.39265 + 27.7341i −0.349460 + 2.20640i
\(159\) −2.49335 + 1.27043i −0.197736 + 0.100751i
\(160\) 3.11834 1.58887i 0.246526 0.125611i
\(161\) 0.260127 + 0.358034i 0.0205008 + 0.0282170i
\(162\) 14.7125 20.2501i 1.15593 1.59100i
\(163\) −0.712156 + 1.39769i −0.0557804 + 0.109475i −0.917214 0.398395i \(-0.869567\pi\)
0.861433 + 0.507871i \(0.169567\pi\)
\(164\) −5.03172 5.03172i −0.392911 0.392911i
\(165\) 11.1762 + 12.4314i 0.870070 + 0.967783i
\(166\) 30.9846 2.40487
\(167\) 13.4220 + 6.83884i 1.03862 + 0.529205i 0.888219 0.459420i \(-0.151943\pi\)
0.150404 + 0.988625i \(0.451943\pi\)
\(168\) −1.74094 + 2.39620i −0.134316 + 0.184871i
\(169\) −2.97234 + 2.15953i −0.228641 + 0.166118i
\(170\) 14.2230 22.6144i 1.09085 1.73445i
\(171\) −0.271073 + 0.834278i −0.0207295 + 0.0637989i
\(172\) 8.61048 + 11.8513i 0.656543 + 0.903654i
\(173\) −7.79857 + 1.23517i −0.592914 + 0.0939084i −0.445679 0.895193i \(-0.647038\pi\)
−0.147236 + 0.989101i \(0.547038\pi\)
\(174\) −4.86304 14.9669i −0.368666 1.13464i
\(175\) −0.534554 + 0.534554i −0.0404085 + 0.0404085i
\(176\) 2.20063 10.3147i 0.165878 0.777501i
\(177\) −16.4144 16.4144i −1.23378 1.23378i
\(178\) −0.948092 + 0.308054i −0.0710625 + 0.0230896i
\(179\) −2.25007 + 3.09696i −0.168178 + 0.231477i −0.884784 0.466000i \(-0.845694\pi\)
0.716606 + 0.697478i \(0.245694\pi\)
\(180\) 5.57201 + 0.882520i 0.415313 + 0.0657792i
\(181\) 16.5981 8.45717i 1.23373 0.628617i 0.289271 0.957247i \(-0.406587\pi\)
0.944459 + 0.328631i \(0.106587\pi\)
\(182\) 1.56759 + 3.07656i 0.116197 + 0.228050i
\(183\) 8.42114 6.11832i 0.622509 0.452279i
\(184\) −5.63447 + 0.892413i −0.415379 + 0.0657896i
\(185\) 30.4220 9.88469i 2.23667 0.726737i
\(186\) −31.6829 −2.32310
\(187\) 4.40454 + 12.9460i 0.322092 + 0.946709i
\(188\) −37.0588 −2.70279
\(189\) −1.53518 + 0.498811i −0.111668 + 0.0362832i
\(190\) 10.2812 1.62839i 0.745879 0.118136i
\(191\) −18.4098 + 13.3755i −1.33209 + 0.967818i −0.332392 + 0.943141i \(0.607856\pi\)
−0.999695 + 0.0246768i \(0.992144\pi\)
\(192\) 8.14319 + 15.9819i 0.587684 + 1.15340i
\(193\) 1.89245 0.964249i 0.136221 0.0694082i −0.384552 0.923104i \(-0.625644\pi\)
0.520773 + 0.853695i \(0.325644\pi\)
\(194\) 37.6776 + 5.96754i 2.70509 + 0.428445i
\(195\) 12.0974 16.6507i 0.866315 1.19238i
\(196\) −25.2501 + 8.20424i −1.80358 + 0.586017i
\(197\) −0.264021 0.264021i −0.0188107 0.0188107i 0.697639 0.716450i \(-0.254234\pi\)
−0.716450 + 0.697639i \(0.754234\pi\)
\(198\) −3.26010 + 2.93094i −0.231685 + 0.208293i
\(199\) −13.3186 + 13.3186i −0.944130 + 0.944130i −0.998520 0.0543901i \(-0.982679\pi\)
0.0543901 + 0.998520i \(0.482679\pi\)
\(200\) −3.01131 9.26787i −0.212932 0.655338i
\(201\) −13.5323 + 2.14330i −0.954493 + 0.151177i
\(202\) 12.5810 + 17.3163i 0.885199 + 1.21837i
\(203\) −0.372648 + 1.14689i −0.0261548 + 0.0804961i
\(204\) 25.3698 + 15.9559i 1.77624 + 1.11714i
\(205\) 3.99188 2.90027i 0.278805 0.202564i
\(206\) −9.42400 + 12.9710i −0.656601 + 0.903734i
\(207\) 0.616379 + 0.314061i 0.0428413 + 0.0218287i
\(208\) −12.9851 −0.900358
\(209\) −2.66763 + 4.61241i −0.184524 + 0.319047i
\(210\) −3.01373 3.01373i −0.207967 0.207967i
\(211\) −11.5750 + 22.7173i −0.796859 + 1.56392i 0.0286863 + 0.999588i \(0.490868\pi\)
−0.825545 + 0.564336i \(0.809132\pi\)
\(212\) −3.37167 + 4.64071i −0.231567 + 0.318725i
\(213\) 11.0350 + 15.1884i 0.756106 + 1.04069i
\(214\) 2.36140 1.20319i 0.161422 0.0822485i
\(215\) −9.05060 + 4.61151i −0.617246 + 0.314503i
\(216\) 3.25502 20.5514i 0.221476 1.39835i
\(217\) 1.96414 + 1.42703i 0.133335 + 0.0968734i
\(218\) −38.9507 19.8464i −2.63807 1.34417i
\(219\) 8.27380i 0.559092i
\(220\) 31.9816 + 12.3044i 2.15620 + 0.829561i
\(221\) 14.4567 8.62916i 0.972462 0.580460i
\(222\) 16.8346 + 51.8115i 1.12986 + 3.47736i
\(223\) −2.88450 + 3.97017i −0.193160 + 0.265862i −0.894601 0.446865i \(-0.852540\pi\)
0.701441 + 0.712728i \(0.252540\pi\)
\(224\) 0.0714504 0.451120i 0.00477398 0.0301417i
\(225\) −0.365165 + 1.12386i −0.0243444 + 0.0749242i
\(226\) 2.23746 + 4.39127i 0.148834 + 0.292103i
\(227\) −7.61599 1.20625i −0.505491 0.0800619i −0.101520 0.994834i \(-0.532371\pi\)
−0.403971 + 0.914772i \(0.632371\pi\)
\(228\) 1.82679 + 11.5339i 0.120982 + 0.763852i
\(229\) 18.9165 6.14634i 1.25004 0.406161i 0.392102 0.919922i \(-0.371748\pi\)
0.857934 + 0.513760i \(0.171748\pi\)
\(230\) 8.20895i 0.541282i
\(231\) 2.16985 0.226399i 0.142766 0.0148960i
\(232\) −10.9918 10.9918i −0.721647 0.721647i
\(233\) 12.8575 + 6.55121i 0.842321 + 0.429184i 0.821233 0.570593i \(-0.193287\pi\)
0.0210887 + 0.999778i \(0.493287\pi\)
\(234\) 4.36660 + 3.17252i 0.285453 + 0.207394i
\(235\) 4.01987 25.3805i 0.262228 1.65564i
\(236\) −45.2555 14.7044i −2.94588 0.957175i
\(237\) 6.74988 20.7740i 0.438452 1.34942i
\(238\) −1.29663 3.23642i −0.0840479 0.209786i
\(239\) −0.964590 0.700815i −0.0623941 0.0453320i 0.556151 0.831081i \(-0.312278\pi\)
−0.618545 + 0.785749i \(0.712278\pi\)
\(240\) 15.2436 4.95294i 0.983970 0.319711i
\(241\) 17.8222 17.8222i 1.14803 1.14803i 0.161091 0.986940i \(-0.448499\pi\)
0.986940 0.161091i \(-0.0515013\pi\)
\(242\) −23.0810 + 13.2792i −1.48370 + 0.853621i
\(243\) −3.96536 + 3.96536i −0.254378 + 0.254378i
\(244\) 9.68688 19.0116i 0.620139 1.21709i
\(245\) −2.87989 18.1829i −0.183990 1.16167i
\(246\) 4.93944 + 6.79855i 0.314927 + 0.433460i
\(247\) 6.23903 + 2.02718i 0.396980 + 0.128987i
\(248\) −27.8846 + 14.2079i −1.77067 + 0.902203i
\(249\) −23.8060 3.77050i −1.50864 0.238945i
\(250\) −18.1482 + 2.87439i −1.14779 + 0.181792i
\(251\) −5.70141 17.5471i −0.359870 1.10757i −0.953132 0.302556i \(-0.902160\pi\)
0.593262 0.805010i \(-0.297840\pi\)
\(252\) 0.520604 0.520604i 0.0327950 0.0327950i
\(253\) 3.26351 + 2.64683i 0.205175 + 0.166405i
\(254\) 29.4368 1.84703
\(255\) −13.6796 + 15.6442i −0.856653 + 0.979679i
\(256\) 24.6246 + 17.8908i 1.53904 + 1.11817i
\(257\) 13.1877 + 18.1512i 0.822623 + 1.13224i 0.989252 + 0.146224i \(0.0467119\pi\)
−0.166628 + 0.986020i \(0.553288\pi\)
\(258\) −7.85385 15.4140i −0.488959 0.959637i
\(259\) 1.29001 3.97024i 0.0801573 0.246699i
\(260\) 6.59980 41.6695i 0.409302 2.58423i
\(261\) 0.294883 + 1.86182i 0.0182528 + 0.115244i
\(262\) −0.0371624 + 0.0729353i −0.00229590 + 0.00450596i
\(263\) 10.1248i 0.624324i 0.950029 + 0.312162i \(0.101053\pi\)
−0.950029 + 0.312162i \(0.898947\pi\)
\(264\) −10.0979 + 26.2466i −0.621485 + 1.61537i
\(265\) −2.81255 2.81255i −0.172773 0.172773i
\(266\) 0.616740 1.21042i 0.0378148 0.0742156i
\(267\) 0.765921 0.121310i 0.0468736 0.00742405i
\(268\) −22.7213 + 16.5080i −1.38792 + 1.00838i
\(269\) −2.52921 4.96386i −0.154209 0.302652i 0.800958 0.598721i \(-0.204324\pi\)
−0.955166 + 0.296069i \(0.904324\pi\)
\(270\) 28.4762 + 9.25247i 1.73301 + 0.563088i
\(271\) −14.9663 + 10.8736i −0.909136 + 0.660526i −0.940796 0.338972i \(-0.889921\pi\)
0.0316599 + 0.999499i \(0.489921\pi\)
\(272\) 13.0582 + 1.18084i 0.791769 + 0.0715989i
\(273\) −0.830016 2.55453i −0.0502349 0.154607i
\(274\) 20.5405i 1.24090i
\(275\) −3.59359 + 6.21341i −0.216702 + 0.374683i
\(276\) 9.20914 0.554325
\(277\) −24.0608 12.2596i −1.44567 0.736608i −0.457395 0.889264i \(-0.651218\pi\)
−0.988279 + 0.152655i \(0.951218\pi\)
\(278\) −6.86655 43.3537i −0.411828 2.60018i
\(279\) 3.74832 + 0.593675i 0.224406 + 0.0355424i
\(280\) −4.00390 1.30095i −0.239279 0.0777464i
\(281\) −15.3470 4.98656i −0.915528 0.297473i −0.186897 0.982380i \(-0.559843\pi\)
−0.728631 + 0.684907i \(0.759843\pi\)
\(282\) 43.2254 + 6.84623i 2.57404 + 0.407687i
\(283\) 2.04503 + 12.9118i 0.121564 + 0.767526i 0.970867 + 0.239620i \(0.0770228\pi\)
−0.849303 + 0.527906i \(0.822977\pi\)
\(284\) 34.2893 + 17.4713i 2.03470 + 1.03673i
\(285\) −8.09739 −0.479648
\(286\) 21.9186 + 24.3802i 1.29608 + 1.44163i
\(287\) 0.643946i 0.0380109i
\(288\) −0.220625 0.679015i −0.0130005 0.0400113i
\(289\) −15.3227 + 7.36303i −0.901336 + 0.433120i
\(290\) 18.0965 13.1479i 1.06267 0.772072i
\(291\) −28.2221 9.16991i −1.65441 0.537550i
\(292\) −7.69974 15.1116i −0.450593 0.884339i
\(293\) −4.34105 + 3.15396i −0.253607 + 0.184256i −0.707324 0.706890i \(-0.750098\pi\)
0.453717 + 0.891146i \(0.350098\pi\)
\(294\) 30.9673 4.90474i 1.80605 0.286050i
\(295\) 14.9796 29.3991i 0.872145 1.71168i
\(296\) 38.0507 + 38.0507i 2.21165 + 2.21165i
\(297\) −12.8600 + 8.33756i −0.746215 + 0.483794i
\(298\) 8.19120i 0.474503i
\(299\) 2.34866 4.60950i 0.135826 0.266574i
\(300\) 2.46089 + 15.5374i 0.142079 + 0.897054i
\(301\) −0.207376 + 1.30932i −0.0119530 + 0.0754681i
\(302\) −9.56128 + 29.4266i −0.550190 + 1.69331i
\(303\) −7.55900 14.8354i −0.434253 0.852270i
\(304\) 3.00287 + 4.13309i 0.172226 + 0.237049i
\(305\) 11.9697 + 8.69649i 0.685383 + 0.497960i
\(306\) −4.10266 3.58745i −0.234533 0.205081i
\(307\) 8.31334 0.474467 0.237234 0.971453i \(-0.423759\pi\)
0.237234 + 0.971453i \(0.423759\pi\)
\(308\) 3.75240 2.43280i 0.213813 0.138622i
\(309\) 8.81904 8.81904i 0.501698 0.501698i
\(310\) −13.9162 42.8296i −0.790385 2.43256i
\(311\) 2.99160 0.473823i 0.169638 0.0268681i −0.0710375 0.997474i \(-0.522631\pi\)
0.240676 + 0.970606i \(0.422631\pi\)
\(312\) 34.1973 + 5.41632i 1.93604 + 0.306639i
\(313\) −1.45015 + 0.738890i −0.0819675 + 0.0417645i −0.494494 0.869181i \(-0.664647\pi\)
0.412526 + 0.910946i \(0.364647\pi\)
\(314\) −44.1031 14.3299i −2.48888 0.808686i
\(315\) 0.300074 + 0.413017i 0.0169073 + 0.0232709i
\(316\) −7.00438 44.2239i −0.394027 2.48779i
\(317\) 2.02966 3.98344i 0.113997 0.223732i −0.826958 0.562264i \(-0.809930\pi\)
0.940955 + 0.338532i \(0.109930\pi\)
\(318\) 4.79004 4.79004i 0.268612 0.268612i
\(319\) −0.607897 + 11.4337i −0.0340357 + 0.640164i
\(320\) −18.0279 + 18.0279i −1.00779 + 1.00779i
\(321\) −1.96071 + 0.637074i −0.109436 + 0.0355580i
\(322\) −0.866713 0.629704i −0.0483000 0.0350920i
\(323\) −6.08978 2.60595i −0.338844 0.144999i
\(324\) −12.3338 + 37.9594i −0.685209 + 2.10886i
\(325\) 8.40465 + 2.73084i 0.466206 + 0.151480i
\(326\) 0.594035 3.75059i 0.0329006 0.207726i
\(327\) 27.5113 + 19.9882i 1.52138 + 1.10535i
\(328\) 7.39602 + 3.76846i 0.408377 + 0.208078i
\(329\) −2.37135 2.37135i −0.130737 0.130737i
\(330\) −35.0302 20.2601i −1.92835 1.11528i
\(331\) 10.9402i 0.601327i 0.953730 + 0.300664i \(0.0972081\pi\)
−0.953730 + 0.300664i \(0.902792\pi\)
\(332\) −46.9890 + 15.2677i −2.57886 + 0.837922i
\(333\) −1.02081 6.44513i −0.0559399 0.353191i
\(334\) −36.0169 5.70452i −1.97076 0.312138i
\(335\) −8.84117 17.3518i −0.483045 0.948028i
\(336\) 0.646388 1.98938i 0.0352634 0.108529i
\(337\) 0.298083 1.88202i 0.0162376 0.102520i −0.978238 0.207484i \(-0.933473\pi\)
0.994476 + 0.104964i \(0.0334726\pi\)
\(338\) 5.22770 7.19531i 0.284349 0.391373i
\(339\) −1.18471 3.64616i −0.0643445 0.198032i
\(340\) −10.4263 + 41.3037i −0.565443 + 2.24001i
\(341\) 21.5142 + 8.27721i 1.16506 + 0.448236i
\(342\) 2.12352i 0.114827i
\(343\) −4.31937 2.20083i −0.233224 0.118834i
\(344\) −13.8246 10.0441i −0.745371 0.541544i
\(345\) −0.998940 + 6.30706i −0.0537811 + 0.339561i
\(346\) 17.0305 8.67747i 0.915565 0.466504i
\(347\) 6.71892 3.42346i 0.360690 0.183781i −0.264248 0.964455i \(-0.585124\pi\)
0.624939 + 0.780674i \(0.285124\pi\)
\(348\) 14.7499 + 20.3015i 0.790676 + 1.08827i
\(349\) −7.29114 + 10.0354i −0.390286 + 0.537183i −0.958273 0.285855i \(-0.907722\pi\)
0.567987 + 0.823038i \(0.307722\pi\)
\(350\) 0.830816 1.63057i 0.0444090 0.0871575i
\(351\) 13.3428 + 13.3428i 0.712184 + 0.712184i
\(352\) −0.450038 4.31325i −0.0239871 0.229897i
\(353\) 30.5926 1.62828 0.814141 0.580667i \(-0.197208\pi\)
0.814141 + 0.580667i \(0.197208\pi\)
\(354\) 50.0695 + 25.5117i 2.66116 + 1.35593i
\(355\) −15.6850 + 21.5886i −0.832474 + 1.14580i
\(356\) 1.28601 0.934344i 0.0681586 0.0495201i
\(357\) 0.602382 + 2.64438i 0.0318814 + 0.139955i
\(358\) 2.86359 8.81323i 0.151346 0.465794i
\(359\) 11.6727 + 16.0660i 0.616059 + 0.847933i 0.997059 0.0766424i \(-0.0244200\pi\)
−0.380999 + 0.924575i \(0.624420\pi\)
\(360\) −6.49976 + 1.02946i −0.342568 + 0.0542574i
\(361\) 5.07376 + 15.6154i 0.267040 + 0.821865i
\(362\) −31.8871 + 31.8871i −1.67595 + 1.67595i
\(363\) 19.3494 7.39393i 1.01558 0.388081i
\(364\) −3.89326 3.89326i −0.204062 0.204062i
\(365\) 11.1847 3.63412i 0.585433 0.190219i
\(366\) −14.8110 + 20.3855i −0.774181 + 1.06557i
\(367\) −4.98970 0.790291i −0.260460 0.0412529i 0.0248385 0.999691i \(-0.492093\pi\)
−0.285299 + 0.958439i \(0.592093\pi\)
\(368\) 3.58972 1.82905i 0.187127 0.0953460i
\(369\) −0.456980 0.896874i −0.0237894 0.0466894i
\(370\) −62.6455 + 45.5146i −3.25678 + 2.36619i
\(371\) −0.512701 + 0.0812039i −0.0266181 + 0.00421590i
\(372\) 48.0480 15.6117i 2.49117 0.809431i
\(373\) −15.9946 −0.828167 −0.414084 0.910239i \(-0.635898\pi\)
−0.414084 + 0.910239i \(0.635898\pi\)
\(374\) −19.8248 26.5106i −1.02512 1.37083i
\(375\) 14.2933 0.738104
\(376\) 41.1134 13.3586i 2.12026 0.688915i
\(377\) 13.9233 2.20524i 0.717088 0.113576i
\(378\) 3.16128 2.29680i 0.162599 0.118135i
\(379\) 13.3801 + 26.2598i 0.687287 + 1.34888i 0.925902 + 0.377763i \(0.123307\pi\)
−0.238615 + 0.971114i \(0.576693\pi\)
\(380\) −14.7894 + 7.53557i −0.758679 + 0.386566i
\(381\) −22.6167 3.58214i −1.15869 0.183519i
\(382\) 32.3789 44.5657i 1.65665 2.28018i
\(383\) 10.9436 3.55578i 0.559189 0.181692i −0.0157670 0.999876i \(-0.505019\pi\)
0.574956 + 0.818184i \(0.305019\pi\)
\(384\) −27.2211 27.2211i −1.38912 1.38912i
\(385\) 1.25912 + 2.83380i 0.0641706 + 0.144424i
\(386\) −3.63562 + 3.63562i −0.185048 + 0.185048i
\(387\) 0.640339 + 1.97076i 0.0325502 + 0.100179i
\(388\) −60.0796 + 9.51567i −3.05008 + 0.483085i
\(389\) −7.79451 10.7282i −0.395198 0.543943i 0.564333 0.825547i \(-0.309133\pi\)
−0.959531 + 0.281604i \(0.909133\pi\)
\(390\) −15.3960 + 47.3840i −0.779607 + 2.39938i
\(391\) −2.78105 + 4.42185i −0.140644 + 0.223622i
\(392\) 25.0553 18.2037i 1.26548 0.919427i
\(393\) 0.0374279 0.0515150i 0.00188799 0.00259859i
\(394\) 0.805352 + 0.410347i 0.0405731 + 0.0206730i
\(395\) 31.0474 1.56217
\(396\) 3.49981 6.05126i 0.175872 0.304087i
\(397\) −5.84008 5.84008i −0.293105 0.293105i 0.545201 0.838306i \(-0.316453\pi\)
−0.838306 + 0.545201i \(0.816453\pi\)
\(398\) 20.7000 40.6261i 1.03760 2.03640i
\(399\) −0.621146 + 0.854934i −0.0310962 + 0.0428002i
\(400\) 4.04519 + 5.56772i 0.202259 + 0.278386i
\(401\) −12.4825 + 6.36013i −0.623344 + 0.317610i −0.736982 0.675913i \(-0.763750\pi\)
0.113638 + 0.993522i \(0.463750\pi\)
\(402\) 29.5517 15.0574i 1.47391 0.750993i
\(403\) 4.43972 28.0313i 0.221158 1.39634i
\(404\) −27.6121 20.0614i −1.37375 0.998090i
\(405\) −24.6594 12.5646i −1.22533 0.624339i
\(406\) 2.91923i 0.144879i
\(407\) 2.10438 39.5805i 0.104310 1.96193i
\(408\) −33.8971 8.55660i −1.67816 0.423615i
\(409\) −1.48754 4.57817i −0.0735540 0.226376i 0.907520 0.420009i \(-0.137973\pi\)
−0.981074 + 0.193633i \(0.937973\pi\)
\(410\) −7.02085 + 9.66337i −0.346735 + 0.477240i
\(411\) −2.49955 + 15.7816i −0.123294 + 0.778447i
\(412\) 7.90028 24.3146i 0.389219 1.19789i
\(413\) −1.95492 3.83675i −0.0961955 0.188794i
\(414\) −1.65401 0.261969i −0.0812902 0.0128751i
\(415\) −5.35933 33.8375i −0.263079 1.66102i
\(416\) −5.07791 + 1.64991i −0.248965 + 0.0808937i
\(417\) 34.1449i 1.67208i
\(418\) 2.69130 12.6146i 0.131636 0.616999i
\(419\) 2.59405 + 2.59405i 0.126728 + 0.126728i 0.767626 0.640898i \(-0.221438\pi\)
−0.640898 + 0.767626i \(0.721438\pi\)
\(420\) 6.05541 + 3.08538i 0.295474 + 0.150551i
\(421\) 15.2833 + 11.1039i 0.744861 + 0.541173i 0.894230 0.447609i \(-0.147724\pi\)
−0.149369 + 0.988782i \(0.547724\pi\)
\(422\) 9.65517 60.9603i 0.470006 2.96750i
\(423\) −4.98559 1.61992i −0.242408 0.0787631i
\(424\) 2.06773 6.36383i 0.100418 0.309055i
\(425\) −8.20359 3.51050i −0.397932 0.170284i
\(426\) −36.7674 26.7131i −1.78139 1.29425i
\(427\) 1.83638 0.596675i 0.0888685 0.0288751i
\(428\) −2.98825 + 2.98825i −0.144442 + 0.144442i
\(429\) −13.8736 21.3989i −0.669824 1.03315i
\(430\) 17.3873 17.3873i 0.838492 0.838492i
\(431\) 8.93245 17.5309i 0.430261 0.844435i −0.569487 0.822000i \(-0.692858\pi\)
0.999748 0.0224348i \(-0.00714181\pi\)
\(432\) 2.29879 + 14.5140i 0.110601 + 0.698306i
\(433\) 16.8209 + 23.1520i 0.808361 + 1.11261i 0.991574 + 0.129540i \(0.0413502\pi\)
−0.183213 + 0.983073i \(0.558650\pi\)
\(434\) −5.58951 1.81614i −0.268305 0.0871776i
\(435\) −15.5038 + 7.89959i −0.743351 + 0.378756i
\(436\) 68.8491 + 10.9046i 3.29727 + 0.522237i
\(437\) −2.01031 + 0.318402i −0.0961663 + 0.0152312i
\(438\) 6.18926 + 19.0486i 0.295734 + 0.910177i
\(439\) −10.2214 + 10.2214i −0.487841 + 0.487841i −0.907624 0.419784i \(-0.862106\pi\)
0.419784 + 0.907624i \(0.362106\pi\)
\(440\) −39.9160 2.12222i −1.90292 0.101173i
\(441\) −3.75556 −0.178836
\(442\) −26.8282 + 30.6811i −1.27609 + 1.45935i
\(443\) 4.93539 + 3.58577i 0.234488 + 0.170365i 0.698824 0.715294i \(-0.253707\pi\)
−0.464336 + 0.885659i \(0.653707\pi\)
\(444\) −51.0602 70.2783i −2.42321 3.33526i
\(445\) 0.500406 + 0.982103i 0.0237215 + 0.0465561i
\(446\) 3.67101 11.2982i 0.173827 0.534985i
\(447\) 0.996781 6.29342i 0.0471461 0.297669i
\(448\) 0.520502 + 3.28632i 0.0245914 + 0.155264i
\(449\) −8.88037 + 17.4287i −0.419091 + 0.822512i 0.580873 + 0.813994i \(0.302711\pi\)
−0.999964 + 0.00851750i \(0.997289\pi\)
\(450\) 2.86061i 0.134850i
\(451\) −1.57797 5.90697i −0.0743039 0.278148i
\(452\) −5.55697 5.55697i −0.261378 0.261378i
\(453\) 10.9270 21.4454i 0.513394 1.00759i
\(454\) 18.4365 2.92005i 0.865267 0.137045i
\(455\) 3.08869 2.24406i 0.144800 0.105203i
\(456\) −6.18428 12.1373i −0.289605 0.568383i
\(457\) −4.51695 1.46765i −0.211294 0.0686536i 0.201457 0.979497i \(-0.435432\pi\)
−0.412752 + 0.910844i \(0.635432\pi\)
\(458\) −38.9532 + 28.3011i −1.82016 + 1.32243i
\(459\) −12.2045 14.6312i −0.569655 0.682925i
\(460\) 4.04495 + 12.4491i 0.188597 + 0.580442i
\(461\) 33.2493i 1.54857i −0.632834 0.774287i \(-0.718108\pi\)
0.632834 0.774287i \(-0.281892\pi\)
\(462\) −4.82623 + 2.14440i −0.224537 + 0.0997665i
\(463\) 15.8346 0.735895 0.367948 0.929847i \(-0.380061\pi\)
0.367948 + 0.929847i \(0.380061\pi\)
\(464\) 9.78163 + 4.98399i 0.454101 + 0.231376i
\(465\) 5.48011 + 34.6001i 0.254134 + 1.60454i
\(466\) −34.5022 5.46460i −1.59828 0.253143i
\(467\) 15.9510 + 5.18278i 0.738122 + 0.239830i 0.653862 0.756613i \(-0.273147\pi\)
0.0842596 + 0.996444i \(0.473147\pi\)
\(468\) −8.18532 2.65957i −0.378366 0.122939i
\(469\) −2.51023 0.397581i −0.115911 0.0183586i
\(470\) 9.73114 + 61.4400i 0.448864 + 2.83402i
\(471\) 32.1413 + 16.3768i 1.48099 + 0.754603i
\(472\) 55.5073 2.55493
\(473\) 1.30618 + 12.5187i 0.0600584 + 0.575610i
\(474\) 52.8768i 2.42871i
\(475\) −1.07440 3.30667i −0.0492969 0.151720i
\(476\) 3.56111 + 4.26920i 0.163223 + 0.195679i
\(477\) −0.656452 + 0.476940i −0.0300569 + 0.0218376i
\(478\) 2.74500 + 0.891905i 0.125553 + 0.0407948i
\(479\) −1.83186 3.59523i −0.0837000 0.164270i 0.845363 0.534193i \(-0.179384\pi\)
−0.929063 + 0.369922i \(0.879384\pi\)
\(480\) 5.33176 3.87375i 0.243361 0.176812i
\(481\) −48.1989 + 7.63396i −2.19768 + 0.348079i
\(482\) −27.6997 + 54.3637i −1.26169 + 2.47620i
\(483\) 0.589281 + 0.589281i 0.0268132 + 0.0268132i
\(484\) 28.4596 31.5114i 1.29362 1.43234i
\(485\) 42.1789i 1.91524i
\(486\) 6.16306 12.0957i 0.279562 0.548671i
\(487\) −0.431500 2.72438i −0.0195531 0.123454i 0.975981 0.217855i \(-0.0699061\pi\)
−0.995534 + 0.0944019i \(0.969906\pi\)
\(488\) −3.89363 + 24.5834i −0.176257 + 1.11284i
\(489\) −0.912813 + 2.80935i −0.0412788 + 0.127043i
\(490\) 20.2322 + 39.7079i 0.913996 + 1.79382i
\(491\) 13.7564 + 18.9340i 0.620817 + 0.854482i 0.997412 0.0718965i \(-0.0229051\pi\)
−0.376595 + 0.926378i \(0.622905\pi\)
\(492\) −10.8408 7.87628i −0.488740 0.355090i
\(493\) −14.2022 + 0.951487i −0.639635 + 0.0428528i
\(494\) −15.8804 −0.714494
\(495\) 3.76469 + 3.05331i 0.169210 + 0.137236i
\(496\) 15.6284 15.6284i 0.701736 0.701736i
\(497\) 1.07616 + 3.31209i 0.0482725 + 0.148568i
\(498\) 57.6285 9.12746i 2.58239 0.409011i
\(499\) −16.3303 2.58646i −0.731042 0.115786i −0.220193 0.975456i \(-0.570669\pi\)
−0.510849 + 0.859670i \(0.670669\pi\)
\(500\) 26.1059 13.3016i 1.16749 0.594866i
\(501\) 26.9782 + 8.76574i 1.20530 + 0.391625i
\(502\) 26.2525 + 36.1334i 1.17170 + 1.61271i
\(503\) 6.39126 + 40.3529i 0.284972 + 1.79925i 0.550172 + 0.835051i \(0.314562\pi\)
−0.265199 + 0.964194i \(0.585438\pi\)
\(504\) −0.389901 + 0.765224i −0.0173676 + 0.0340858i
\(505\) 16.7346 16.7346i 0.744679 0.744679i
\(506\) −9.49349 3.65246i −0.422037 0.162372i
\(507\) −4.89212 + 4.89212i −0.217266 + 0.217266i
\(508\) −44.6417 + 14.5050i −1.98065 + 0.643554i
\(509\) −0.954656 0.693598i −0.0423144 0.0307432i 0.566427 0.824112i \(-0.308325\pi\)
−0.608741 + 0.793369i \(0.708325\pi\)
\(510\) 19.7916 46.2505i 0.876387 2.04801i
\(511\) 0.474274 1.45967i 0.0209807 0.0645718i
\(512\) −31.1905 10.1344i −1.37844 0.447882i
\(513\) 1.16135 7.33249i 0.0512750 0.323737i
\(514\) −43.9398 31.9241i −1.93810 1.40811i
\(515\) 15.7954 + 8.04813i 0.696026 + 0.354643i
\(516\) 19.5058 + 19.5058i 0.858697 + 0.858697i
\(517\) −27.5635 15.9416i −1.21224 0.701111i
\(518\) 10.1056i 0.444015i
\(519\) −14.1407 + 4.59461i −0.620710 + 0.201681i
\(520\) 7.69868 + 48.6076i 0.337609 + 2.13158i
\(521\) −27.8031 4.40357i −1.21807 0.192924i −0.485884 0.874024i \(-0.661502\pi\)
−0.732191 + 0.681099i \(0.761502\pi\)
\(522\) −2.07165 4.06583i −0.0906735 0.177957i
\(523\) 8.28224 25.4901i 0.362157 1.11460i −0.589585 0.807706i \(-0.700709\pi\)
0.951742 0.306899i \(-0.0992912\pi\)
\(524\) 0.0204189 0.128920i 0.000892005 0.00563190i
\(525\) −0.836751 + 1.15169i −0.0365188 + 0.0502638i
\(526\) −7.57393 23.3102i −0.330239 1.01637i
\(527\) −7.01379 + 27.7852i −0.305525 + 1.21034i
\(528\) 1.05445 19.8327i 0.0458889 0.863106i
\(529\) 21.3949i 0.930212i
\(530\) 8.57920 + 4.37132i 0.372657 + 0.189878i
\(531\) −5.44555 3.95642i −0.236317 0.171694i
\(532\) −0.338869 + 2.13953i −0.0146918 + 0.0927605i
\(533\) −6.70714 + 3.41746i −0.290519 + 0.148027i
\(534\) −1.67262 + 0.852240i −0.0723811 + 0.0368800i
\(535\) −1.72242 2.37070i −0.0744666 0.102494i
\(536\) 19.2566 26.5044i 0.831757 1.14482i
\(537\) −3.27262 + 6.42287i −0.141224 + 0.277168i
\(538\) 9.53618 + 9.53618i 0.411134 + 0.411134i
\(539\) −22.3096 4.75971i −0.960942 0.205015i
\(540\) −47.7440 −2.05458
\(541\) 16.6866 + 8.50225i 0.717413 + 0.365540i 0.774281 0.632841i \(-0.218112\pi\)
−0.0568683 + 0.998382i \(0.518112\pi\)
\(542\) 26.3224 36.2297i 1.13065 1.55620i
\(543\) 28.3796 20.6190i 1.21789 0.884847i
\(544\) 5.25652 1.19742i 0.225371 0.0513390i
\(545\) −14.9365 + 45.9698i −0.639809 + 1.96913i
\(546\) 3.82186 + 5.26033i 0.163560 + 0.225122i
\(547\) 31.0332 4.91517i 1.32688 0.210157i 0.547552 0.836771i \(-0.315560\pi\)
0.779330 + 0.626614i \(0.215560\pi\)
\(548\) 10.1213 + 31.1502i 0.432361 + 1.33067i
\(549\) 2.13423 2.13423i 0.0910867 0.0910867i
\(550\) 3.62547 16.9932i 0.154591 0.724593i
\(551\) −3.92174 3.92174i −0.167072 0.167072i
\(552\) −10.2167 + 3.31961i −0.434852 + 0.141292i
\(553\) 2.38163 3.27803i 0.101277 0.139396i
\(554\) 64.5656 + 10.2262i 2.74313 + 0.434469i
\(555\) 53.6701 27.3463i 2.27817 1.16079i
\(556\) 31.7758 + 62.3635i 1.34759 + 2.64480i
\(557\) 29.4302 21.3823i 1.24700 0.905997i 0.248954 0.968515i \(-0.419913\pi\)
0.998044 + 0.0625186i \(0.0199133\pi\)
\(558\) −9.07377 + 1.43714i −0.384123 + 0.0608392i
\(559\) 14.7380 4.78868i 0.623353 0.202540i
\(560\) 2.97319 0.125640
\(561\) 12.0057 + 22.7809i 0.506880 + 0.961812i
\(562\) 39.0634 1.64779
\(563\) 30.4929 9.90775i 1.28512 0.417562i 0.414741 0.909939i \(-0.363872\pi\)
0.870382 + 0.492378i \(0.163872\pi\)
\(564\) −68.9259 + 10.9168i −2.90231 + 0.459680i
\(565\) 4.40858 3.20302i 0.185470 0.134752i
\(566\) −14.3670 28.1967i −0.603888 1.18520i
\(567\) −3.21819 + 1.63975i −0.135151 + 0.0688631i
\(568\) −44.3387 7.02257i −1.86041 0.294660i
\(569\) −15.5057 + 21.3418i −0.650032 + 0.894693i −0.999101 0.0424046i \(-0.986498\pi\)
0.349068 + 0.937097i \(0.386498\pi\)
\(570\) 18.6424 6.05729i 0.780846 0.253712i
\(571\) −30.0857 30.0857i −1.25905 1.25905i −0.951549 0.307498i \(-0.900508\pi\)
−0.307498 0.951549i \(-0.599492\pi\)
\(572\) −45.2535 26.1728i −1.89214 1.09434i
\(573\) −30.3004 + 30.3004i −1.26582 + 1.26582i
\(574\) 0.481707 + 1.48254i 0.0201061 + 0.0618802i
\(575\) −2.70811 + 0.428922i −0.112936 + 0.0178873i
\(576\) 3.05710 + 4.20774i 0.127379 + 0.175322i
\(577\) −5.38135 + 16.5621i −0.224029 + 0.689489i 0.774360 + 0.632745i \(0.218072\pi\)
−0.998389 + 0.0567441i \(0.981928\pi\)
\(578\) 29.7692 28.4140i 1.23824 1.18187i
\(579\) 3.23572 2.35089i 0.134472 0.0976996i
\(580\) −20.9653 + 28.8562i −0.870535 + 1.19819i
\(581\) −3.98372 2.02981i −0.165273 0.0842106i
\(582\) 71.8347 2.97764
\(583\) −4.50406 + 2.00125i −0.186539 + 0.0828834i
\(584\) 13.9894 + 13.9894i 0.578886 + 0.578886i
\(585\) 2.70934 5.31739i 0.112018 0.219847i
\(586\) 7.63497 10.5086i 0.315398 0.434107i
\(587\) −2.00908 2.76526i −0.0829235 0.114134i 0.765540 0.643388i \(-0.222472\pi\)
−0.848463 + 0.529254i \(0.822472\pi\)
\(588\) −44.5459 + 22.6973i −1.83704 + 0.936020i
\(589\) −9.94888 + 5.06921i −0.409937 + 0.208873i
\(590\) −12.4950 + 78.8904i −0.514412 + 3.24787i
\(591\) −0.568830 0.413279i −0.0233985 0.0170000i
\(592\) −33.8614 17.2533i −1.39170 0.709104i
\(593\) 2.37083i 0.0973582i −0.998814 0.0486791i \(-0.984499\pi\)
0.998814 0.0486791i \(-0.0155012\pi\)
\(594\) 23.3704 28.8154i 0.958899 1.18231i
\(595\) −3.31013 + 1.97581i −0.135702 + 0.0810002i
\(596\) −4.03621 12.4222i −0.165330 0.508832i
\(597\) −20.8479 + 28.6947i −0.853249 + 1.17440i
\(598\) −1.95910 + 12.3693i −0.0801136 + 0.505817i
\(599\) −8.34021 + 25.6685i −0.340772 + 1.04879i 0.623037 + 0.782193i \(0.285899\pi\)
−0.963809 + 0.266595i \(0.914101\pi\)
\(600\) −8.33089 16.3503i −0.340107 0.667498i
\(601\) −3.19472 0.505994i −0.130315 0.0206399i 0.0909360 0.995857i \(-0.471014\pi\)
−0.221251 + 0.975217i \(0.571014\pi\)
\(602\) −0.502008 3.16955i −0.0204603 0.129181i
\(603\) −3.77833 + 1.22765i −0.153866 + 0.0499939i
\(604\) 49.3376i 2.00752i
\(605\) 18.4941 + 22.9092i 0.751894 + 0.931392i
\(606\) 28.5006 + 28.5006i 1.15776 + 1.15776i
\(607\) 11.4772 + 5.84793i 0.465846 + 0.237360i 0.671126 0.741343i \(-0.265811\pi\)
−0.205281 + 0.978703i \(0.565811\pi\)
\(608\) 1.69945 + 1.23472i 0.0689216 + 0.0500745i
\(609\) −0.355239 + 2.24289i −0.0143950 + 0.0908864i
\(610\) −34.0630 11.0677i −1.37917 0.448120i
\(611\) −12.1143 + 37.2841i −0.490093 + 1.50835i
\(612\) 7.98950 + 3.41888i 0.322956 + 0.138200i
\(613\) −26.7659 19.4466i −1.08106 0.785439i −0.103196 0.994661i \(-0.532907\pi\)
−0.977868 + 0.209222i \(0.932907\pi\)
\(614\) −19.1396 + 6.21884i −0.772412 + 0.250972i
\(615\) 6.57016 6.57016i 0.264934 0.264934i
\(616\) −3.28600 + 4.05160i −0.132397 + 0.163243i
\(617\) −2.36030 + 2.36030i −0.0950222 + 0.0950222i −0.753020 0.657998i \(-0.771404\pi\)
0.657998 + 0.753020i \(0.271404\pi\)
\(618\) −13.7067 + 26.9010i −0.551366 + 1.08212i
\(619\) −0.551193 3.48009i −0.0221543 0.139877i 0.974132 0.225980i \(-0.0725585\pi\)
−0.996286 + 0.0861034i \(0.972558\pi\)
\(620\) 42.2085 + 58.0950i 1.69513 + 2.33315i
\(621\) −5.56801 1.80916i −0.223437 0.0725989i
\(622\) −6.53305 + 3.32876i −0.261952 + 0.133471i
\(623\) 0.142078 + 0.0225029i 0.00569222 + 0.000901560i
\(624\) −24.1511 + 3.82517i −0.966820 + 0.153129i
\(625\) 9.62193 + 29.6133i 0.384877 + 1.18453i
\(626\) 2.78592 2.78592i 0.111348 0.111348i
\(627\) −3.60282 + 9.36448i −0.143883 + 0.373981i
\(628\) 73.9445 2.95071
\(629\) 49.1643 3.29380i 1.96031 0.131332i
\(630\) −0.999814 0.726408i −0.0398336 0.0289408i
\(631\) −6.98018 9.60739i −0.277876 0.382464i 0.647153 0.762361i \(-0.275960\pi\)
−0.925029 + 0.379896i \(0.875960\pi\)
\(632\) 23.7121 + 46.5376i 0.943216 + 1.85117i
\(633\) −14.8364 + 45.6618i −0.589695 + 1.81489i
\(634\) −1.69302 + 10.6893i −0.0672382 + 0.424525i
\(635\) −5.09161 32.1471i −0.202054 1.27572i
\(636\) −4.90393 + 9.62451i −0.194453 + 0.381636i
\(637\) 28.0854i 1.11279i
\(638\) −7.15349 26.7783i −0.283209 1.06016i
\(639\) 3.84930 + 3.84930i 0.152276 + 0.152276i
\(640\) 24.8416 48.7544i 0.981951 1.92719i
\(641\) −16.6941 + 2.64408i −0.659376 + 0.104435i −0.477150 0.878822i \(-0.658330\pi\)
−0.182226 + 0.983257i \(0.558330\pi\)
\(642\) 4.03754 2.93344i 0.159349 0.115774i
\(643\) −10.5987 20.8010i −0.417970 0.820313i −0.999975 0.00712696i \(-0.997731\pi\)
0.582004 0.813186i \(-0.302269\pi\)
\(644\) 1.62468 + 0.527890i 0.0640213 + 0.0208018i
\(645\) −15.4748 + 11.2431i −0.609320 + 0.442697i
\(646\) 15.9697 + 1.44413i 0.628321 + 0.0568185i
\(647\) 0.581475 + 1.78960i 0.0228602 + 0.0703563i 0.961836 0.273627i \(-0.0882235\pi\)
−0.938976 + 0.343984i \(0.888224\pi\)
\(648\) 46.5584i 1.82899i
\(649\) −27.3345 30.4043i −1.07297 1.19347i
\(650\) −21.3927 −0.839089
\(651\) 4.07350 + 2.07555i 0.159653 + 0.0813473i
\(652\) 0.947231 + 5.98058i 0.0370964 + 0.234218i
\(653\) 22.1620 + 3.51011i 0.867264 + 0.137361i 0.574184 0.818727i \(-0.305320\pi\)
0.293081 + 0.956088i \(0.405320\pi\)
\(654\) −78.2910 25.4383i −3.06142 0.994715i
\(655\) 0.0860785 + 0.0279686i 0.00336337 + 0.00109282i
\(656\) −5.79006 0.917056i −0.226064 0.0358050i
\(657\) −0.375302 2.36956i −0.0146419 0.0924454i
\(658\) 7.23340 + 3.68560i 0.281987 + 0.143680i
\(659\) 2.54108 0.0989865 0.0494932 0.998774i \(-0.484239\pi\)
0.0494932 + 0.998774i \(0.484239\pi\)
\(660\) 63.1074 + 13.4638i 2.45645 + 0.524079i
\(661\) 47.1927i 1.83558i −0.397062 0.917792i \(-0.629970\pi\)
0.397062 0.917792i \(-0.370030\pi\)
\(662\) −8.18387 25.1873i −0.318075 0.978934i
\(663\) 24.3461 20.3081i 0.945524 0.788700i
\(664\) 46.6265 33.8762i 1.80946 1.31465i
\(665\) −1.42854 0.464162i −0.0553965 0.0179994i
\(666\) 7.17149 + 14.0749i 0.277890 + 0.545389i
\(667\) −3.53846 + 2.57084i −0.137010 + 0.0995433i
\(668\) 57.4315 9.09626i 2.22209 0.351945i
\(669\) −4.19536 + 8.23386i −0.162202 + 0.318340i
\(670\) 33.3349 + 33.3349i 1.28784 + 1.28784i
\(671\) 15.3831 9.97334i 0.593857 0.385016i
\(672\) 0.860089i 0.0331786i
\(673\) −13.9548 + 27.3878i −0.537918 + 1.05572i 0.448853 + 0.893606i \(0.351833\pi\)
−0.986771 + 0.162118i \(0.948167\pi\)
\(674\) 0.721586 + 4.55591i 0.0277945 + 0.175487i
\(675\) 1.56447 9.87766i 0.0602164 0.380191i
\(676\) −4.38246 + 13.4878i −0.168556 + 0.518763i
\(677\) −8.88055 17.4291i −0.341307 0.669853i 0.655008 0.755622i \(-0.272665\pi\)
−0.996315 + 0.0857691i \(0.972665\pi\)
\(678\) 5.45505 + 7.50824i 0.209500 + 0.288352i
\(679\) −4.45331 3.23552i −0.170902 0.124168i
\(680\) −3.32172 49.5811i −0.127382 1.90135i
\(681\) −14.5204 −0.556422
\(682\) −55.7234 2.96265i −2.13376 0.113446i
\(683\) −21.7997 + 21.7997i −0.834142 + 0.834142i −0.988080 0.153938i \(-0.950804\pi\)
0.153938 + 0.988080i \(0.450804\pi\)
\(684\) 1.04636 + 3.22037i 0.0400087 + 0.123134i
\(685\) −22.4317 + 3.55283i −0.857072 + 0.135747i
\(686\) 11.5907 + 1.83579i 0.442536 + 0.0700908i
\(687\) 33.3723 17.0040i 1.27323 0.648744i
\(688\) 11.4775 + 3.72926i 0.437575 + 0.142177i
\(689\) 3.56673 + 4.90918i 0.135882 + 0.187025i
\(690\) −2.41819 15.2679i −0.0920590 0.581238i
\(691\) 6.07743 11.9276i 0.231196 0.453749i −0.746040 0.665901i \(-0.768047\pi\)
0.977237 + 0.212152i \(0.0680473\pi\)
\(692\) −21.5514 + 21.5514i −0.819260 + 0.819260i
\(693\) 0.611160 0.163264i 0.0232161 0.00620189i
\(694\) −12.9079 + 12.9079i −0.489976 + 0.489976i
\(695\) −46.1577 + 14.9975i −1.75086 + 0.568889i
\(696\) −23.6817 17.2058i −0.897652 0.652182i
\(697\) 7.05564 2.82675i 0.267251 0.107071i
\(698\) 9.27920 28.5585i 0.351223 1.08095i
\(699\) 25.8436 + 8.39708i 0.977493 + 0.317607i
\(700\) −0.456493 + 2.88218i −0.0172538 + 0.108936i
\(701\) −3.67652 2.67114i −0.138860 0.100888i 0.516187 0.856476i \(-0.327351\pi\)
−0.655047 + 0.755588i \(0.727351\pi\)
\(702\) −40.6999 20.7376i −1.53612 0.782691i
\(703\) 13.5760 + 13.5760i 0.512030 + 0.512030i
\(704\) 12.8277 + 28.8702i 0.483460 + 1.08809i
\(705\) 48.3895i 1.82245i
\(706\) −70.4328 + 22.8850i −2.65077 + 0.861288i
\(707\) −0.483161 3.05056i −0.0181712 0.114728i
\(708\) −88.5026 14.0174i −3.32613 0.526807i
\(709\) 1.14587 + 2.24889i 0.0430339 + 0.0844588i 0.911522 0.411251i \(-0.134908\pi\)
−0.868488 + 0.495710i \(0.834908\pi\)
\(710\) 19.9618 61.4361i 0.749153 2.30566i
\(711\) 0.990806 6.25571i 0.0371581 0.234607i
\(712\) −1.08991 + 1.50014i −0.0408462 + 0.0562200i
\(713\) 2.72106 + 8.37456i 0.101904 + 0.313630i
\(714\) −3.36499 5.63747i −0.125932 0.210977i
\(715\) 22.8337 28.1537i 0.853934 1.05289i
\(716\) 14.7765i 0.552225i
\(717\) −2.00049 1.01930i −0.0747097 0.0380665i
\(718\) −38.8920 28.2567i −1.45144 1.05453i
\(719\) 0.143387 0.905311i 0.00534744 0.0337624i −0.984870 0.173293i \(-0.944559\pi\)
0.990218 + 0.139530i \(0.0445593\pi\)
\(720\) 4.14100 2.10994i 0.154326 0.0786329i
\(721\) 2.06139 1.05033i 0.0767700 0.0391163i
\(722\) −23.3624 32.1556i −0.869459 1.19671i
\(723\) 27.8976 38.3977i 1.03752 1.42803i
\(724\) 32.6453 64.0699i 1.21325 2.38114i
\(725\) −5.28301 5.28301i −0.196206 0.196206i
\(726\) −39.0166 + 31.4973i −1.44804 + 1.16897i
\(727\) −38.7836 −1.43841 −0.719203 0.694800i \(-0.755493\pi\)
−0.719203 + 0.694800i \(0.755493\pi\)
\(728\) 5.72262 + 2.91582i 0.212094 + 0.108067i
\(729\) 12.0259 16.5522i 0.445404 0.613046i
\(730\) −23.0317 + 16.7335i −0.852442 + 0.619335i
\(731\) −15.2564 + 3.47537i −0.564279 + 0.128541i
\(732\) 12.4163 38.2133i 0.458918 1.41240i
\(733\) −4.72314 6.50085i −0.174453 0.240114i 0.712833 0.701334i \(-0.247412\pi\)
−0.887286 + 0.461220i \(0.847412\pi\)
\(734\) 12.0789 1.91310i 0.445839 0.0706139i
\(735\) −10.7127 32.9702i −0.395143 1.21612i
\(736\) 1.17138 1.17138i 0.0431775 0.0431775i
\(737\) −24.0007 + 2.50421i −0.884079 + 0.0922436i
\(738\) 1.72301 + 1.72301i 0.0634247 + 0.0634247i
\(739\) −18.4823 + 6.00527i −0.679883 + 0.220907i −0.628544 0.777774i \(-0.716349\pi\)
−0.0513387 + 0.998681i \(0.516349\pi\)
\(740\) 72.5763 99.8927i 2.66796 3.67213i
\(741\) 12.2012 + 1.93248i 0.448221 + 0.0709913i
\(742\) 1.11964 0.570483i 0.0411031 0.0209431i
\(743\) −15.4078 30.2396i −0.565259 1.10938i −0.979917 0.199406i \(-0.936099\pi\)
0.414658 0.909977i \(-0.363901\pi\)
\(744\) −47.6773 + 34.6396i −1.74794 + 1.26995i
\(745\) 8.94539 1.41681i 0.327734 0.0519079i
\(746\) 36.8239 11.9648i 1.34822 0.438063i
\(747\) −6.98890 −0.255711
\(748\) 43.1279 + 30.4353i 1.57691 + 1.11282i
\(749\) −0.382428 −0.0139736
\(750\) −32.9072 + 10.6922i −1.20160 + 0.390424i
\(751\) 4.44916 0.704678i 0.162352 0.0257141i −0.0747291 0.997204i \(-0.523809\pi\)
0.237081 + 0.971490i \(0.423809\pi\)
\(752\) −24.6991 + 17.9449i −0.900683 + 0.654385i
\(753\) −15.7731 30.9565i −0.574805 1.12812i
\(754\) −30.4058 + 15.4925i −1.10731 + 0.564204i
\(755\) 33.7898 + 5.35178i 1.22974 + 0.194771i
\(756\) −3.66242 + 5.04089i −0.133201 + 0.183335i
\(757\) 39.0036 12.6730i 1.41761 0.460609i 0.502768 0.864422i \(-0.332315\pi\)
0.914842 + 0.403812i \(0.132315\pi\)
\(758\) −50.4484 50.4484i −1.83237 1.83237i
\(759\) 6.84953 + 3.96150i 0.248622 + 0.143793i
\(760\) 13.6911 13.6911i 0.496630 0.496630i
\(761\) −15.1530 46.6362i −0.549296 1.69056i −0.710550 0.703646i \(-0.751554\pi\)
0.161254 0.986913i \(-0.448446\pi\)
\(762\) 54.7497 8.67150i 1.98337 0.314135i
\(763\) 3.70779 + 5.10333i 0.134231 + 0.184753i
\(764\) −27.1437 + 83.5398i −0.982025 + 3.02236i
\(765\) −3.20813 + 5.10091i −0.115990 + 0.184424i
\(766\) −22.5352 + 16.3728i −0.814229 + 0.591572i
\(767\) −29.5875 + 40.7237i −1.06834 + 1.47045i
\(768\) 51.0696 + 26.0213i 1.84282 + 0.938962i
\(769\) −44.5217 −1.60549 −0.802747 0.596320i \(-0.796629\pi\)
−0.802747 + 0.596320i \(0.796629\pi\)
\(770\) −5.01868 5.58230i −0.180861 0.201172i
\(771\) 29.8748 + 29.8748i 1.07591 + 1.07591i
\(772\) 3.72207 7.30497i 0.133960 0.262912i
\(773\) 3.05504 4.20490i 0.109882 0.151240i −0.750534 0.660832i \(-0.770204\pi\)
0.860416 + 0.509592i \(0.170204\pi\)
\(774\) −2.94847 4.05823i −0.105981 0.145870i
\(775\) −13.4022 + 6.82877i −0.481422 + 0.245297i
\(776\) 63.2227 32.2136i 2.26956 1.15640i
\(777\) 1.22974 7.76429i 0.0441168 0.278542i
\(778\) 25.9704 + 18.8686i 0.931086 + 0.676473i
\(779\) 2.63881 + 1.34454i 0.0945452 + 0.0481732i
\(780\) 79.4455i 2.84461i
\(781\) 17.9879 + 27.7450i 0.643659 + 0.992792i
\(782\) 3.09495 12.2607i 0.110675 0.438441i
\(783\) −4.92977 15.1723i −0.176176 0.542213i
\(784\) −12.8560 + 17.6948i −0.459143 + 0.631957i
\(785\) −8.02096 + 50.6424i −0.286280 + 1.80750i
\(786\) −0.0476332 + 0.146600i −0.00169902 + 0.00522905i
\(787\) 16.0440 + 31.4882i 0.571909 + 1.12243i 0.978001 + 0.208602i \(0.0668912\pi\)
−0.406092 + 0.913832i \(0.633109\pi\)
\(788\) −1.42354 0.225466i −0.0507114 0.00803189i
\(789\) 2.98257 + 18.8312i 0.106182 + 0.670410i
\(790\) −71.4798 + 23.2252i −2.54314 + 0.826315i
\(791\) 0.711166i 0.0252862i
\(792\) −1.70143 + 7.97490i −0.0604577 + 0.283376i
\(793\) −15.9605 15.9605i −0.566775 0.566775i
\(794\) 17.8142 + 9.07678i 0.632202 + 0.322123i
\(795\) −6.05959 4.40255i −0.214912 0.156142i
\(796\) −11.3737 + 71.8105i −0.403129 + 2.54526i
\(797\) −37.4467 12.1672i −1.32643 0.430983i −0.441731 0.897147i \(-0.645636\pi\)
−0.884698 + 0.466164i \(0.845636\pi\)
\(798\) 0.790512 2.43295i 0.0279838 0.0861254i
\(799\) 15.5730 36.3921i 0.550933 1.28746i
\(800\) 2.28934 + 1.66330i 0.0809403 + 0.0588066i
\(801\) 0.213852 0.0694847i 0.00755609 0.00245512i
\(802\) 23.9803 23.9803i 0.846776 0.846776i
\(803\) 0.773678 14.5518i 0.0273025 0.513523i
\(804\) −37.3965 + 37.3965i −1.31887 + 1.31887i
\(805\) −0.537769 + 1.05543i −0.0189539 + 0.0371991i
\(806\) 10.7475 + 67.8569i 0.378564 + 2.39016i
\(807\) −6.16635 8.48725i −0.217066 0.298765i
\(808\) 37.8646 + 12.3030i 1.33207 + 0.432817i
\(809\) 42.5450 21.6777i 1.49580 0.762149i 0.501143 0.865365i \(-0.332913\pi\)
0.994659 + 0.103216i \(0.0329132\pi\)
\(810\) 66.1717 + 10.4806i 2.32504 + 0.368250i
\(811\) 18.5835 2.94333i 0.652554 0.103354i 0.178625 0.983917i \(-0.442835\pi\)
0.473929 + 0.880563i \(0.342835\pi\)
\(812\) 1.43845 + 4.42709i 0.0504796 + 0.155360i
\(813\) −24.6327 + 24.6327i −0.863907 + 0.863907i
\(814\) 24.7635 + 92.6994i 0.867961 + 3.24911i
\(815\) −4.19867 −0.147073
\(816\) 24.6348 1.65043i 0.862392 0.0577766i
\(817\) −4.93244 3.58363i −0.172564 0.125375i
\(818\) 6.84945 + 9.42746i 0.239486 + 0.329624i
\(819\) −0.353585 0.693950i −0.0123553 0.0242486i
\(820\) 5.88569 18.1143i 0.205537 0.632578i
\(821\) 3.15042 19.8910i 0.109950 0.694200i −0.869714 0.493556i \(-0.835697\pi\)
0.979664 0.200643i \(-0.0643033\pi\)
\(822\) −6.05082 38.2034i −0.211046 1.33250i
\(823\) −19.8026 + 38.8647i −0.690274 + 1.35474i 0.233710 + 0.972306i \(0.424913\pi\)
−0.923984 + 0.382432i \(0.875087\pi\)
\(824\) 29.8226i 1.03892i
\(825\) −4.85339 + 12.6150i −0.168973 + 0.439197i
\(826\) 7.37088 + 7.37088i 0.256466 + 0.256466i
\(827\) −10.1139 + 19.8496i −0.351693 + 0.690237i −0.997300 0.0734329i \(-0.976605\pi\)
0.645607 + 0.763670i \(0.276605\pi\)
\(828\) 2.63744 0.417729i 0.0916572 0.0145171i
\(829\) 20.9739 15.2384i 0.728455 0.529253i −0.160620 0.987016i \(-0.551349\pi\)
0.889074 + 0.457763i \(0.151349\pi\)
\(830\) 37.6510 + 73.8942i 1.30688 + 2.56491i
\(831\) −48.3623 15.7139i −1.67767 0.545108i
\(832\) 31.4669 22.8621i 1.09092 0.792600i
\(833\) 2.55402 28.2434i 0.0884917 0.978576i
\(834\) −25.5423 78.6110i −0.884456 2.72208i
\(835\) 40.3198i 1.39533i
\(836\) 2.13440 + 20.4565i 0.0738199 + 0.707502i
\(837\) −32.1176 −1.11015
\(838\) −7.91273 4.03174i −0.273341 0.139274i
\(839\) −0.566286 3.57539i −0.0195504 0.123436i 0.975983 0.217847i \(-0.0699033\pi\)
−0.995533 + 0.0944107i \(0.969903\pi\)
\(840\) −7.83011 1.24017i −0.270164 0.0427899i
\(841\) 16.2459 + 5.27860i 0.560202 + 0.182021i
\(842\) −43.4927 14.1316i −1.49886 0.487008i
\(843\) −30.0130 4.75359i −1.03370 0.163722i
\(844\) 15.3958 + 97.2056i 0.529947 + 3.34595i
\(845\) −8.76203 4.46448i −0.301423 0.153583i
\(846\) 12.6900 0.436292
\(847\) 3.83746 0.195286i 0.131857 0.00671010i
\(848\) 4.72561i 0.162278i
\(849\) 7.60711 + 23.4123i 0.261075 + 0.803507i
\(850\) 21.5130 + 1.94540i 0.737889 + 0.0667266i
\(851\) 12.2492 8.89957i 0.419898 0.305073i
\(852\) 68.9216 + 22.3940i 2.36121 + 0.767205i
\(853\) 16.3222 + 32.0342i 0.558862 + 1.09683i 0.981666 + 0.190608i \(0.0610459\pi\)
−0.422804 + 0.906221i \(0.638954\pi\)
\(854\) −3.78150 + 2.74742i −0.129400 + 0.0940149i
\(855\) −2.31904 + 0.367300i −0.0793094 + 0.0125614i
\(856\) 2.23802 4.39236i 0.0764939 0.150128i
\(857\) −5.23850 5.23850i −0.178944 0.178944i 0.611952 0.790895i \(-0.290385\pi\)
−0.790895 + 0.611952i \(0.790385\pi\)
\(858\) 47.9485 + 38.8881i 1.63693 + 1.32762i
\(859\) 4.18510i 0.142794i 0.997448 + 0.0713970i \(0.0227457\pi\)
−0.997448 + 0.0713970i \(0.977254\pi\)
\(860\) −17.8008 + 34.9360i −0.607001 + 1.19131i
\(861\) −0.189694 1.19768i −0.00646475 0.0408168i
\(862\) −7.45088 + 47.0430i −0.253778 + 1.60229i
\(863\) −5.19632 + 15.9926i −0.176885 + 0.544395i −0.999715 0.0238927i \(-0.992394\pi\)
0.822830 + 0.568288i \(0.192394\pi\)
\(864\) 2.74313 + 5.38370i 0.0933232 + 0.183157i
\(865\) −12.4222 17.0976i −0.422366 0.581337i
\(866\) −56.0454 40.7193i −1.90450 1.38370i
\(867\) −26.3298 + 18.2083i −0.894207 + 0.618387i
\(868\) 9.37154 0.318091
\(869\) 13.8141 35.9058i 0.468612 1.21802i
\(870\) 29.7848 29.7848i 1.00980 1.00980i
\(871\) 9.18083 + 28.2557i 0.311081 + 0.957408i
\(872\) −80.3126 + 12.7203i −2.71973 + 0.430762i
\(873\) −8.49857 1.34604i −0.287633 0.0455566i
\(874\) 4.39011 2.23688i 0.148498 0.0756634i
\(875\) 2.52163 + 0.819328i 0.0852467 + 0.0276983i
\(876\) −18.7724 25.8379i −0.634259 0.872983i
\(877\) −2.97086 18.7573i −0.100319 0.633388i −0.985698 0.168519i \(-0.946102\pi\)
0.885380 0.464869i \(-0.153898\pi\)
\(878\) 15.8863 31.1787i 0.536137 1.05223i
\(879\) −7.14485 + 7.14485i −0.240990 + 0.240990i
\(880\) 27.2733 7.28573i 0.919384 0.245602i
\(881\) 0.497790 0.497790i 0.0167710 0.0167710i −0.698672 0.715443i \(-0.746225\pi\)
0.715443 + 0.698672i \(0.246225\pi\)
\(882\) 8.64635 2.80937i 0.291138 0.0945964i
\(883\) 0.707262 + 0.513856i 0.0238012 + 0.0172926i 0.599622 0.800283i \(-0.295317\pi\)
−0.575821 + 0.817576i \(0.695317\pi\)
\(884\) 25.5676 59.7483i 0.859932 2.00955i
\(885\) 19.2002 59.0922i 0.645409 1.98636i
\(886\) −14.0450 4.56350i −0.471851 0.153314i
\(887\) 2.38533 15.0604i 0.0800917 0.505679i −0.914732 0.404061i \(-0.867598\pi\)
0.994824 0.101617i \(-0.0324018\pi\)
\(888\) 81.9798 + 59.5618i 2.75106 + 1.99876i
\(889\) −3.78472 1.92841i −0.126935 0.0646768i
\(890\) −1.88674 1.88674i −0.0632437 0.0632437i
\(891\) −25.5025 + 22.9276i −0.854367 + 0.768105i
\(892\) 18.9429i 0.634256i
\(893\) 14.6688 4.76617i 0.490872 0.159494i
\(894\) 2.41296 + 15.2349i 0.0807016 + 0.509530i
\(895\) −10.1200 1.60285i −0.338274 0.0535774i
\(896\) −3.24198 6.36274i −0.108307 0.212564i
\(897\) 3.01041 9.26510i 0.100515 0.309353i
\(898\) 7.40744 46.7687i 0.247189 1.56069i
\(899\) −14.1034 + 19.4117i −0.470376 + 0.647417i
\(900\) 1.40956 + 4.33819i 0.0469855 + 0.144606i
\(901\) −3.14036 5.26114i −0.104621 0.175274i
\(902\) 8.05167 + 12.4191i 0.268091 + 0.413510i
\(903\) 2.49631i 0.0830718i
\(904\) 8.16807 + 4.16184i 0.271666 + 0.138421i
\(905\) 40.3385 + 29.3076i 1.34090 + 0.974218i
\(906\) −9.11459 + 57.5473i −0.302812 + 1.91188i
\(907\) 28.6022 14.5735i 0.949719 0.483906i 0.0907161 0.995877i \(-0.471084\pi\)
0.859003 + 0.511971i \(0.171084\pi\)
\(908\) −26.5206 + 13.5129i −0.880116 + 0.448441i
\(909\) −2.83778 3.90587i −0.0941233 0.129550i
\(910\) −5.43234 + 7.47697i −0.180080 + 0.247859i
\(911\) −3.94558 + 7.74365i −0.130723 + 0.256558i −0.947085 0.320982i \(-0.895987\pi\)
0.816362 + 0.577540i \(0.195987\pi\)
\(912\) 6.80258 + 6.80258i 0.225256 + 0.225256i
\(913\) −41.5170 8.85757i −1.37401 0.293143i
\(914\) 11.4972 0.380292
\(915\) 24.8243 + 12.6486i 0.820667 + 0.418151i
\(916\) 45.1282 62.1136i 1.49108 2.05229i
\(917\) 0.00955600 0.00694284i 0.000315567 0.000229273i
\(918\) 39.0430 + 24.5554i 1.28861 + 0.810450i
\(919\) −11.7873 + 36.2776i −0.388827 + 1.19669i 0.544838 + 0.838541i \(0.316591\pi\)
−0.933665 + 0.358146i \(0.883409\pi\)
\(920\) −8.97502 12.3531i −0.295898 0.407268i
\(921\) 15.4620 2.44894i 0.509491 0.0806955i
\(922\) 24.8723 + 76.5492i 0.819126 + 2.52101i
\(923\) 28.7864 28.7864i 0.947517 0.947517i
\(924\) 6.26246 5.63016i 0.206020 0.185219i
\(925\) 18.2884 + 18.2884i 0.601319 + 0.601319i
\(926\) −36.4556 + 11.8451i −1.19800 + 0.389255i
\(927\) 2.12568 2.92575i 0.0698165 0.0960942i
\(928\) 4.45843 + 0.706147i 0.146355 + 0.0231804i
\(929\) −0.694737 + 0.353986i −0.0227936 + 0.0116139i −0.465350 0.885127i \(-0.654072\pi\)
0.442557 + 0.896741i \(0.354072\pi\)
\(930\) −38.4995 75.5595i −1.26245 2.47769i
\(931\) 8.93942 6.49487i 0.292978 0.212861i
\(932\) 55.0161 8.71370i 1.80211 0.285427i
\(933\) 5.42452 1.76253i 0.177591 0.0577028i
\(934\) −40.6005 −1.32849
\(935\) −25.5224 + 26.2356i −0.834672 + 0.857997i
\(936\) 10.0396 0.328153
\(937\) 13.7443 4.46581i 0.449008 0.145892i −0.0757798 0.997125i \(-0.524145\pi\)
0.524788 + 0.851233i \(0.324145\pi\)
\(938\) 6.07665 0.962447i 0.198410 0.0314250i
\(939\) −2.47949 + 1.80145i −0.0809150 + 0.0587882i
\(940\) −45.0321 88.3804i −1.46878 2.88265i
\(941\) −19.5183 + 9.94508i −0.636279 + 0.324200i −0.742204 0.670174i \(-0.766220\pi\)
0.105925 + 0.994374i \(0.466220\pi\)
\(942\) −86.2488 13.6605i −2.81014 0.445082i
\(943\) 1.37280 1.88950i 0.0447046 0.0615306i
\(944\) −37.2823 + 12.1138i −1.21344 + 0.394269i
\(945\) −3.05508 3.05508i −0.0993817 0.0993817i
\(946\) −12.3719 27.8444i −0.402244 0.905299i
\(947\) −11.8689 + 11.8689i −0.385687 + 0.385687i −0.873146 0.487459i \(-0.837924\pi\)
0.487459 + 0.873146i \(0.337924\pi\)
\(948\) −26.0550 80.1890i −0.846227 2.60442i
\(949\) −17.7204 + 2.80664i −0.575229 + 0.0911073i
\(950\) 4.94714 + 6.80915i 0.160506 + 0.220918i
\(951\) 2.60154 8.00671i 0.0843607 0.259636i
\(952\) −5.48965 3.45262i −0.177920 0.111900i
\(953\) −6.43653 + 4.67641i −0.208500 + 0.151484i −0.687135 0.726530i \(-0.741132\pi\)
0.478635 + 0.878014i \(0.341132\pi\)
\(954\) 1.15456 1.58911i 0.0373802 0.0514494i
\(955\) −54.2695 27.6517i −1.75612 0.894788i
\(956\) −4.60235 −0.148851
\(957\) 2.23751 + 21.4447i 0.0723284 + 0.693208i
\(958\) 6.90689 + 6.90689i 0.223152 + 0.223152i
\(959\) −1.34561 + 2.64091i −0.0434520 + 0.0852794i
\(960\) −28.2195 + 38.8409i −0.910782 + 1.25358i
\(961\) 10.1725 + 14.0012i 0.328145 + 0.451653i
\(962\) 105.257 53.6310i 3.39361 1.72913i
\(963\) −0.532637 + 0.271392i −0.0171640 + 0.00874549i
\(964\) 15.2196 96.0931i 0.490192 3.09495i
\(965\) 4.59921 + 3.34152i 0.148054 + 0.107567i
\(966\) −1.79750 0.915873i −0.0578337 0.0294677i
\(967\) 30.9834i 0.996359i 0.867074 + 0.498180i \(0.165998\pi\)
−0.867074 + 0.498180i \(0.834002\pi\)
\(968\) −20.2144 + 45.2179i −0.649715 + 1.45336i
\(969\) −12.0941 3.05289i −0.388517 0.0980731i
\(970\) 31.5521 + 97.1075i 1.01308 + 3.11793i
\(971\) 19.8312 27.2953i 0.636414 0.875948i −0.362004 0.932176i \(-0.617907\pi\)
0.998418 + 0.0562281i \(0.0179074\pi\)
\(972\) −3.38630 + 21.3803i −0.108616 + 0.685772i
\(973\) −1.95727 + 6.02385i −0.0627471 + 0.193116i
\(974\) 3.03142 + 5.94950i 0.0971331 + 0.190634i
\(975\) 16.4363 + 2.60326i 0.526383 + 0.0833709i
\(976\) −2.74980 17.3616i −0.0880190 0.555730i
\(977\) 36.8466 11.9722i 1.17883 0.383024i 0.346896 0.937904i \(-0.387236\pi\)
0.831930 + 0.554880i \(0.187236\pi\)
\(978\) 7.15074i 0.228655i
\(979\) 1.35843 0.141737i 0.0434157 0.00452994i
\(980\) −50.2486 50.2486i −1.60513 1.60513i
\(981\) 8.78573 + 4.47655i 0.280507 + 0.142925i
\(982\) −45.8347 33.3009i −1.46265 1.06267i
\(983\) 5.77184 36.4420i 0.184093 1.16232i −0.706566 0.707647i \(-0.749757\pi\)
0.890659 0.454672i \(-0.150243\pi\)
\(984\) 14.8660 + 4.83026i 0.473911 + 0.153983i
\(985\) 0.308830 0.950480i 0.00984013 0.0302848i
\(986\) 31.9856 12.8146i 1.01863 0.408100i
\(987\) −5.10903 3.71193i −0.162622 0.118152i
\(988\) 24.0831 7.82507i 0.766185 0.248949i
\(989\) −3.39978 + 3.39978i −0.108107 + 0.108107i
\(990\) −10.9514 4.21337i −0.348059 0.133910i
\(991\) 29.6655 29.6655i 0.942356 0.942356i −0.0560709 0.998427i \(-0.517857\pi\)
0.998427 + 0.0560709i \(0.0178573\pi\)
\(992\) 4.12580 8.09734i 0.130994 0.257091i
\(993\) 3.22276 + 20.3477i 0.102271 + 0.645715i
\(994\) −4.95526 6.82032i −0.157171 0.216328i
\(995\) −47.9471 15.5790i −1.52003 0.493887i
\(996\) −82.8976 + 42.2384i −2.62671 + 1.33838i
\(997\) 20.1139 + 3.18573i 0.637013 + 0.100893i 0.466584 0.884477i \(-0.345485\pi\)
0.170429 + 0.985370i \(0.445485\pi\)
\(998\) 39.5316 6.26119i 1.25135 0.198194i
\(999\) 17.0656 + 52.5224i 0.539931 + 1.66174i
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 187.2.p.a.38.1 128
11.9 even 5 inner 187.2.p.a.174.16 yes 128
17.13 even 4 inner 187.2.p.a.115.16 yes 128
187.64 even 20 inner 187.2.p.a.64.1 yes 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
187.2.p.a.38.1 128 1.1 even 1 trivial
187.2.p.a.64.1 yes 128 187.64 even 20 inner
187.2.p.a.115.16 yes 128 17.13 even 4 inner
187.2.p.a.174.16 yes 128 11.9 even 5 inner