Properties

Label 273.2.bt.a.136.8
Level $273$
Weight $2$
Character 273.136
Analytic conductor $2.180$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(136,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 2, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.136");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bt (of order \(12\), degree \(4\), 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: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 136.8
Character \(\chi\) \(=\) 273.136
Dual form 273.2.bt.a.271.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.12005 - 1.12005i) q^{2} +(0.866025 - 0.500000i) q^{3} -0.509024i q^{4} +(-0.973479 + 3.63307i) q^{5} +(0.409967 - 1.53002i) q^{6} +(2.28455 - 1.33448i) q^{7} +(1.66997 + 1.66997i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(1.12005 - 1.12005i) q^{2} +(0.866025 - 0.500000i) q^{3} -0.509024i q^{4} +(-0.973479 + 3.63307i) q^{5} +(0.409967 - 1.53002i) q^{6} +(2.28455 - 1.33448i) q^{7} +(1.66997 + 1.66997i) q^{8} +(0.500000 - 0.866025i) q^{9} +(2.97888 + 5.15957i) q^{10} +(0.872699 - 3.25696i) q^{11} +(-0.254512 - 0.440828i) q^{12} +(-3.03769 - 1.94228i) q^{13} +(1.06413 - 4.05349i) q^{14} +(0.973479 + 3.63307i) q^{15} +4.75894 q^{16} -3.33792 q^{17} +(-0.409967 - 1.53002i) q^{18} +(0.733837 - 0.196631i) q^{19} +(1.84932 + 0.495525i) q^{20} +(1.31124 - 2.29797i) q^{21} +(-2.67049 - 4.62542i) q^{22} +3.56245i q^{23} +(2.28122 + 0.611250i) q^{24} +(-7.92144 - 4.57345i) q^{25} +(-5.57781 + 1.22692i) q^{26} -1.00000i q^{27} +(-0.679283 - 1.16289i) q^{28} +(-1.42199 + 2.46295i) q^{29} +(5.15957 + 2.97888i) q^{30} +(-8.90596 + 2.38635i) q^{31} +(1.99032 - 1.99032i) q^{32} +(-0.872699 - 3.25696i) q^{33} +(-3.73864 + 3.73864i) q^{34} +(2.62430 + 9.59903i) q^{35} +(-0.440828 - 0.254512i) q^{36} +(-8.01070 - 8.01070i) q^{37} +(0.601698 - 1.04217i) q^{38} +(-3.60186 - 0.163214i) q^{39} +(-7.69280 + 4.44144i) q^{40} +(6.84386 - 1.83381i) q^{41} +(-1.10519 - 4.04249i) q^{42} +(10.9295 - 6.31017i) q^{43} +(-1.65787 - 0.444225i) q^{44} +(2.65960 + 2.65960i) q^{45} +(3.99012 + 3.99012i) q^{46} +(1.32905 + 0.356118i) q^{47} +(4.12137 - 2.37947i) q^{48} +(3.43833 - 6.09737i) q^{49} +(-13.9949 + 3.74992i) q^{50} +(-2.89072 + 1.66896i) q^{51} +(-0.988666 + 1.54626i) q^{52} +(-3.59290 + 6.22308i) q^{53} +(-1.12005 - 1.12005i) q^{54} +(10.9832 + 6.34116i) q^{55} +(6.04366 + 1.58659i) q^{56} +(0.537206 - 0.537206i) q^{57} +(1.16593 + 4.35132i) q^{58} +(-2.23105 + 2.23105i) q^{59} +(1.84932 - 0.495525i) q^{60} +(0.902515 + 0.521067i) q^{61} +(-7.30230 + 12.6480i) q^{62} +(-0.0134184 - 2.64572i) q^{63} +5.05937i q^{64} +(10.0136 - 9.14539i) q^{65} +(-4.62542 - 2.67049i) q^{66} +(2.85760 + 0.765690i) q^{67} +1.69908i q^{68} +(1.78122 + 3.08517i) q^{69} +(13.6907 + 7.81204i) q^{70} +(-7.00412 - 1.87675i) q^{71} +(2.28122 - 0.611250i) q^{72} +(0.559835 + 2.08933i) q^{73} -17.9448 q^{74} -9.14690 q^{75} +(-0.100090 - 0.373541i) q^{76} +(-2.35262 - 8.60528i) q^{77} +(-4.21707 + 3.85145i) q^{78} +(-5.54357 - 9.60175i) q^{79} +(-4.63273 + 17.2896i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.61151 - 9.71942i) q^{82} +(-1.51210 - 1.51210i) q^{83} +(-1.16972 - 0.667452i) q^{84} +(3.24940 - 12.1269i) q^{85} +(5.17392 - 19.3093i) q^{86} +2.84397i q^{87} +(6.89639 - 3.98163i) q^{88} +(-2.23766 + 2.23766i) q^{89} +5.95776 q^{90} +(-9.53168 - 0.383488i) q^{91} +1.81337 q^{92} +(-6.51962 + 6.51962i) q^{93} +(1.88747 - 1.08973i) q^{94} +2.85750i q^{95} +(0.728508 - 2.71883i) q^{96} +(-3.23001 + 12.0545i) q^{97} +(-2.97826 - 10.6805i) q^{98} +(-2.38426 - 2.38426i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 6 q^{7} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 6 q^{7} + 18 q^{9} - 8 q^{11} - 16 q^{12} + 42 q^{14} - 24 q^{16} - 8 q^{17} - 18 q^{19} + 14 q^{20} - 4 q^{21} + 4 q^{22} + 18 q^{24} + 24 q^{25} - 50 q^{26} + 34 q^{28} + 8 q^{29} + 6 q^{31} - 50 q^{32} + 8 q^{33} - 24 q^{34} + 14 q^{35} - 14 q^{37} - 8 q^{38} - 2 q^{39} - 30 q^{40} + 34 q^{41} - 18 q^{42} + 30 q^{43} + 28 q^{44} - 32 q^{46} - 10 q^{47} + 24 q^{48} + 6 q^{49} - 20 q^{50} - 24 q^{51} + 4 q^{52} - 8 q^{53} - 30 q^{55} - 92 q^{56} - 24 q^{57} + 72 q^{58} - 70 q^{59} + 14 q^{60} - 60 q^{61} - 48 q^{62} + 6 q^{63} - 44 q^{65} + 18 q^{66} - 46 q^{67} + 4 q^{69} + 80 q^{70} + 42 q^{71} + 18 q^{72} - 56 q^{73} + 40 q^{74} - 20 q^{75} + 12 q^{76} + 24 q^{77} - 16 q^{78} + 170 q^{80} - 18 q^{81} + 24 q^{82} - 60 q^{83} + 2 q^{85} + 12 q^{86} + 84 q^{88} + 64 q^{89} - 86 q^{91} - 100 q^{92} + 12 q^{93} - 66 q^{94} + 46 q^{96} + 36 q^{97} - 22 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.12005 1.12005i 0.791995 0.791995i −0.189823 0.981818i \(-0.560792\pi\)
0.981818 + 0.189823i \(0.0607915\pi\)
\(3\) 0.866025 0.500000i 0.500000 0.288675i
\(4\) 0.509024i 0.254512i
\(5\) −0.973479 + 3.63307i −0.435353 + 1.62476i 0.304866 + 0.952395i \(0.401388\pi\)
−0.740219 + 0.672365i \(0.765278\pi\)
\(6\) 0.409967 1.53002i 0.167368 0.624627i
\(7\) 2.28455 1.33448i 0.863478 0.504386i
\(8\) 1.66997 + 1.66997i 0.590423 + 0.590423i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 2.97888 + 5.15957i 0.942005 + 1.63160i
\(11\) 0.872699 3.25696i 0.263129 0.982010i −0.700257 0.713891i \(-0.746931\pi\)
0.963386 0.268119i \(-0.0864020\pi\)
\(12\) −0.254512 0.440828i −0.0734713 0.127256i
\(13\) −3.03769 1.94228i −0.842504 0.538690i
\(14\) 1.06413 4.05349i 0.284400 1.08334i
\(15\) 0.973479 + 3.63307i 0.251351 + 0.938056i
\(16\) 4.75894 1.18974
\(17\) −3.33792 −0.809565 −0.404782 0.914413i \(-0.632653\pi\)
−0.404782 + 0.914413i \(0.632653\pi\)
\(18\) −0.409967 1.53002i −0.0966301 0.360628i
\(19\) 0.733837 0.196631i 0.168354 0.0451103i −0.173657 0.984806i \(-0.555559\pi\)
0.342011 + 0.939696i \(0.388892\pi\)
\(20\) 1.84932 + 0.495525i 0.413521 + 0.110803i
\(21\) 1.31124 2.29797i 0.286136 0.501458i
\(22\) −2.67049 4.62542i −0.569350 0.986143i
\(23\) 3.56245i 0.742822i 0.928469 + 0.371411i \(0.121126\pi\)
−0.928469 + 0.371411i \(0.878874\pi\)
\(24\) 2.28122 + 0.611250i 0.465652 + 0.124771i
\(25\) −7.92144 4.57345i −1.58429 0.914690i
\(26\) −5.57781 + 1.22692i −1.09390 + 0.240619i
\(27\) 1.00000i 0.192450i
\(28\) −0.679283 1.16289i −0.128372 0.219766i
\(29\) −1.42199 + 2.46295i −0.264056 + 0.457358i −0.967316 0.253574i \(-0.918394\pi\)
0.703260 + 0.710933i \(0.251727\pi\)
\(30\) 5.15957 + 2.97888i 0.942005 + 0.543867i
\(31\) −8.90596 + 2.38635i −1.59956 + 0.428600i −0.944909 0.327332i \(-0.893850\pi\)
−0.654649 + 0.755933i \(0.727184\pi\)
\(32\) 1.99032 1.99032i 0.351842 0.351842i
\(33\) −0.872699 3.25696i −0.151917 0.566964i
\(34\) −3.73864 + 3.73864i −0.641171 + 0.641171i
\(35\) 2.62430 + 9.59903i 0.443588 + 1.62253i
\(36\) −0.440828 0.254512i −0.0734713 0.0424187i
\(37\) −8.01070 8.01070i −1.31695 1.31695i −0.916177 0.400775i \(-0.868741\pi\)
−0.400775 0.916177i \(-0.631259\pi\)
\(38\) 0.601698 1.04217i 0.0976083 0.169063i
\(39\) −3.60186 0.163214i −0.576758 0.0261352i
\(40\) −7.69280 + 4.44144i −1.21634 + 0.702253i
\(41\) 6.84386 1.83381i 1.06883 0.286393i 0.318819 0.947816i \(-0.396714\pi\)
0.750013 + 0.661423i \(0.230047\pi\)
\(42\) −1.10519 4.04249i −0.170534 0.623770i
\(43\) 10.9295 6.31017i 1.66674 0.962291i 0.697358 0.716723i \(-0.254359\pi\)
0.969379 0.245568i \(-0.0789746\pi\)
\(44\) −1.65787 0.444225i −0.249933 0.0669695i
\(45\) 2.65960 + 2.65960i 0.396469 + 0.396469i
\(46\) 3.99012 + 3.99012i 0.588311 + 0.588311i
\(47\) 1.32905 + 0.356118i 0.193862 + 0.0519452i 0.354444 0.935077i \(-0.384670\pi\)
−0.160582 + 0.987023i \(0.551337\pi\)
\(48\) 4.12137 2.37947i 0.594868 0.343447i
\(49\) 3.43833 6.09737i 0.491190 0.871052i
\(50\) −13.9949 + 3.74992i −1.97918 + 0.530319i
\(51\) −2.89072 + 1.66896i −0.404782 + 0.233701i
\(52\) −0.988666 + 1.54626i −0.137103 + 0.214427i
\(53\) −3.59290 + 6.22308i −0.493523 + 0.854806i −0.999972 0.00746338i \(-0.997624\pi\)
0.506450 + 0.862270i \(0.330958\pi\)
\(54\) −1.12005 1.12005i −0.152420 0.152420i
\(55\) 10.9832 + 6.34116i 1.48098 + 0.855042i
\(56\) 6.04366 + 1.58659i 0.807618 + 0.212016i
\(57\) 0.537206 0.537206i 0.0711547 0.0711547i
\(58\) 1.16593 + 4.35132i 0.153095 + 0.571357i
\(59\) −2.23105 + 2.23105i −0.290458 + 0.290458i −0.837261 0.546803i \(-0.815844\pi\)
0.546803 + 0.837261i \(0.315844\pi\)
\(60\) 1.84932 0.495525i 0.238747 0.0639720i
\(61\) 0.902515 + 0.521067i 0.115555 + 0.0667158i 0.556664 0.830738i \(-0.312081\pi\)
−0.441108 + 0.897454i \(0.645415\pi\)
\(62\) −7.30230 + 12.6480i −0.927393 + 1.60629i
\(63\) −0.0134184 2.64572i −0.00169056 0.333329i
\(64\) 5.05937i 0.632421i
\(65\) 10.0136 9.14539i 1.24203 1.13435i
\(66\) −4.62542 2.67049i −0.569350 0.328714i
\(67\) 2.85760 + 0.765690i 0.349111 + 0.0935440i 0.429113 0.903251i \(-0.358826\pi\)
−0.0800024 + 0.996795i \(0.525493\pi\)
\(68\) 1.69908i 0.206044i
\(69\) 1.78122 + 3.08517i 0.214434 + 0.371411i
\(70\) 13.6907 + 7.81204i 1.63636 + 0.933717i
\(71\) −7.00412 1.87675i −0.831236 0.222729i −0.181983 0.983302i \(-0.558252\pi\)
−0.649253 + 0.760573i \(0.724918\pi\)
\(72\) 2.28122 0.611250i 0.268844 0.0720366i
\(73\) 0.559835 + 2.08933i 0.0655238 + 0.244538i 0.990918 0.134468i \(-0.0429326\pi\)
−0.925394 + 0.379006i \(0.876266\pi\)
\(74\) −17.9448 −2.08604
\(75\) −9.14690 −1.05619
\(76\) −0.100090 0.373541i −0.0114811 0.0428481i
\(77\) −2.35262 8.60528i −0.268106 0.980663i
\(78\) −4.21707 + 3.85145i −0.477489 + 0.436091i
\(79\) −5.54357 9.60175i −0.623700 1.08028i −0.988791 0.149309i \(-0.952295\pi\)
0.365090 0.930972i \(-0.381038\pi\)
\(80\) −4.63273 + 17.2896i −0.517955 + 1.93304i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 5.61151 9.71942i 0.619688 1.07333i
\(83\) −1.51210 1.51210i −0.165975 0.165975i 0.619233 0.785208i \(-0.287444\pi\)
−0.785208 + 0.619233i \(0.787444\pi\)
\(84\) −1.16972 0.667452i −0.127627 0.0728250i
\(85\) 3.24940 12.1269i 0.352447 1.31535i
\(86\) 5.17392 19.3093i 0.557918 2.08218i
\(87\) 2.84397i 0.304906i
\(88\) 6.89639 3.98163i 0.735158 0.424444i
\(89\) −2.23766 + 2.23766i −0.237192 + 0.237192i −0.815686 0.578494i \(-0.803640\pi\)
0.578494 + 0.815686i \(0.303640\pi\)
\(90\) 5.95776 0.628003
\(91\) −9.53168 0.383488i −0.999192 0.0402005i
\(92\) 1.81337 0.189057
\(93\) −6.51962 + 6.51962i −0.676053 + 0.676053i
\(94\) 1.88747 1.08973i 0.194678 0.112397i
\(95\) 2.85750i 0.293174i
\(96\) 0.728508 2.71883i 0.0743530 0.277489i
\(97\) −3.23001 + 12.0545i −0.327957 + 1.22395i 0.583348 + 0.812222i \(0.301742\pi\)
−0.911305 + 0.411731i \(0.864924\pi\)
\(98\) −2.97826 10.6805i −0.300849 1.07889i
\(99\) −2.38426 2.38426i −0.239627 0.239627i
\(100\) −2.32800 + 4.03221i −0.232800 + 0.403221i
\(101\) −2.19617 3.80388i −0.218527 0.378500i 0.735831 0.677165i \(-0.236792\pi\)
−0.954358 + 0.298665i \(0.903459\pi\)
\(102\) −1.36844 + 5.10707i −0.135495 + 0.505676i
\(103\) 6.67838 + 11.5673i 0.658040 + 1.13976i 0.981122 + 0.193389i \(0.0619478\pi\)
−0.323082 + 0.946371i \(0.604719\pi\)
\(104\) −1.82931 8.31638i −0.179378 0.815488i
\(105\) 7.07223 + 7.00085i 0.690179 + 0.683213i
\(106\) 2.94594 + 10.9944i 0.286135 + 1.06787i
\(107\) 0.177558 0.0171652 0.00858260 0.999963i \(-0.497268\pi\)
0.00858260 + 0.999963i \(0.497268\pi\)
\(108\) −0.509024 −0.0489809
\(109\) −1.34434 5.01713i −0.128764 0.480554i 0.871182 0.490960i \(-0.163354\pi\)
−0.999946 + 0.0104068i \(0.996687\pi\)
\(110\) 19.4042 5.19933i 1.85012 0.495737i
\(111\) −10.9428 2.93212i −1.03865 0.278305i
\(112\) 10.8720 6.35071i 1.02731 0.600086i
\(113\) 10.0079 + 17.3342i 0.941462 + 1.63066i 0.762684 + 0.646771i \(0.223881\pi\)
0.178778 + 0.983889i \(0.442785\pi\)
\(114\) 1.20340i 0.112708i
\(115\) −12.9426 3.46797i −1.20691 0.323390i
\(116\) 1.25370 + 0.723825i 0.116403 + 0.0672055i
\(117\) −3.20091 + 1.65958i −0.295924 + 0.153428i
\(118\) 4.99777i 0.460082i
\(119\) −7.62564 + 4.45439i −0.699042 + 0.408333i
\(120\) −4.44144 + 7.69280i −0.405446 + 0.702253i
\(121\) −0.319891 0.184689i −0.0290810 0.0167899i
\(122\) 1.59448 0.427240i 0.144358 0.0386805i
\(123\) 5.01005 5.01005i 0.451741 0.451741i
\(124\) 1.21471 + 4.53335i 0.109084 + 0.407107i
\(125\) 11.0291 11.0291i 0.986469 0.986469i
\(126\) −2.97837 2.94831i −0.265334 0.262656i
\(127\) 6.74547 + 3.89450i 0.598564 + 0.345581i 0.768476 0.639878i \(-0.221015\pi\)
−0.169913 + 0.985459i \(0.554349\pi\)
\(128\) 9.64739 + 9.64739i 0.852717 + 0.852717i
\(129\) 6.31017 10.9295i 0.555579 0.962291i
\(130\) 0.972393 21.4590i 0.0852845 1.88208i
\(131\) 8.40782 4.85426i 0.734595 0.424118i −0.0855060 0.996338i \(-0.527251\pi\)
0.820101 + 0.572219i \(0.193917\pi\)
\(132\) −1.65787 + 0.444225i −0.144299 + 0.0386648i
\(133\) 1.41409 1.42850i 0.122617 0.123867i
\(134\) 4.05826 2.34304i 0.350580 0.202408i
\(135\) 3.63307 + 0.973479i 0.312685 + 0.0837838i
\(136\) −5.57422 5.57422i −0.477985 0.477985i
\(137\) −6.42607 6.42607i −0.549017 0.549017i 0.377140 0.926156i \(-0.376908\pi\)
−0.926156 + 0.377140i \(0.876908\pi\)
\(138\) 5.45060 + 1.46048i 0.463986 + 0.124325i
\(139\) 8.85473 5.11228i 0.751048 0.433618i −0.0750244 0.997182i \(-0.523903\pi\)
0.826073 + 0.563564i \(0.190570\pi\)
\(140\) 4.88614 1.33583i 0.412954 0.112899i
\(141\) 1.32905 0.356118i 0.111926 0.0299906i
\(142\) −9.94701 + 5.74291i −0.834735 + 0.481934i
\(143\) −8.97690 + 8.19861i −0.750686 + 0.685602i
\(144\) 2.37947 4.12137i 0.198289 0.343447i
\(145\) −7.56381 7.56381i −0.628140 0.628140i
\(146\) 2.96720 + 1.71311i 0.245567 + 0.141778i
\(147\) −0.0710028 6.99964i −0.00585621 0.577321i
\(148\) −4.07764 + 4.07764i −0.335180 + 0.335180i
\(149\) 3.88850 + 14.5121i 0.318559 + 1.18888i 0.920630 + 0.390435i \(0.127675\pi\)
−0.602072 + 0.798442i \(0.705658\pi\)
\(150\) −10.2450 + 10.2450i −0.836499 + 0.836499i
\(151\) −0.268230 + 0.0718719i −0.0218282 + 0.00584885i −0.269717 0.962940i \(-0.586930\pi\)
0.247888 + 0.968789i \(0.420263\pi\)
\(152\) 1.55385 + 0.897117i 0.126034 + 0.0727658i
\(153\) −1.66896 + 2.89072i −0.134927 + 0.233701i
\(154\) −12.2734 7.00329i −0.989018 0.564341i
\(155\) 34.6791i 2.78549i
\(156\) −0.0830802 + 1.83343i −0.00665174 + 0.146792i
\(157\) 0.272321 + 0.157225i 0.0217336 + 0.0125479i 0.510827 0.859683i \(-0.329339\pi\)
−0.489094 + 0.872231i \(0.662672\pi\)
\(158\) −16.9635 4.54536i −1.34954 0.361609i
\(159\) 7.18580i 0.569871i
\(160\) 5.29344 + 9.16852i 0.418484 + 0.724835i
\(161\) 4.75401 + 8.13859i 0.374669 + 0.641410i
\(162\) −1.53002 0.409967i −0.120209 0.0322100i
\(163\) −0.911958 + 0.244358i −0.0714300 + 0.0191396i −0.294357 0.955696i \(-0.595105\pi\)
0.222927 + 0.974835i \(0.428439\pi\)
\(164\) −0.933452 3.48369i −0.0728904 0.272031i
\(165\) 12.6823 0.987318
\(166\) −3.38726 −0.262903
\(167\) 0.626601 + 2.33851i 0.0484878 + 0.180959i 0.985923 0.167202i \(-0.0534731\pi\)
−0.937435 + 0.348161i \(0.886806\pi\)
\(168\) 6.02726 1.64781i 0.465013 0.127131i
\(169\) 5.45513 + 11.8001i 0.419626 + 0.907697i
\(170\) −9.94326 17.2222i −0.762614 1.32089i
\(171\) 0.196631 0.733837i 0.0150368 0.0561180i
\(172\) −3.21203 5.56340i −0.244915 0.424205i
\(173\) 8.61076 14.9143i 0.654664 1.13391i −0.327314 0.944916i \(-0.606143\pi\)
0.981978 0.188996i \(-0.0605233\pi\)
\(174\) 3.18539 + 3.18539i 0.241484 + 0.241484i
\(175\) −24.2001 + 0.122737i −1.82936 + 0.00927805i
\(176\) 4.15313 15.4997i 0.313054 1.16833i
\(177\) −0.816620 + 3.04767i −0.0613809 + 0.229077i
\(178\) 5.01259i 0.375710i
\(179\) 2.98125 1.72123i 0.222829 0.128651i −0.384430 0.923154i \(-0.625602\pi\)
0.607260 + 0.794503i \(0.292269\pi\)
\(180\) 1.35380 1.35380i 0.100906 0.100906i
\(181\) 25.9767 1.93084 0.965418 0.260708i \(-0.0839561\pi\)
0.965418 + 0.260708i \(0.0839561\pi\)
\(182\) −11.1055 + 10.2464i −0.823193 + 0.759516i
\(183\) 1.04213 0.0770368
\(184\) −5.94917 + 5.94917i −0.438579 + 0.438579i
\(185\) 36.9017 21.3052i 2.71307 1.56639i
\(186\) 14.6046i 1.07086i
\(187\) −2.91300 + 10.8715i −0.213020 + 0.795000i
\(188\) 0.181273 0.676520i 0.0132207 0.0493403i
\(189\) −1.33448 2.28455i −0.0970691 0.166176i
\(190\) 3.20055 + 3.20055i 0.232192 + 0.232192i
\(191\) −1.49154 + 2.58342i −0.107924 + 0.186930i −0.914929 0.403615i \(-0.867754\pi\)
0.807005 + 0.590544i \(0.201087\pi\)
\(192\) 2.52969 + 4.38154i 0.182564 + 0.316211i
\(193\) 0.676598 2.52510i 0.0487026 0.181761i −0.937290 0.348551i \(-0.886674\pi\)
0.985992 + 0.166791i \(0.0533404\pi\)
\(194\) 9.88393 + 17.1195i 0.709624 + 1.22911i
\(195\) 4.09930 12.9269i 0.293557 0.925716i
\(196\) −3.10371 1.75019i −0.221693 0.125014i
\(197\) 0.213689 + 0.797498i 0.0152247 + 0.0568194i 0.973120 0.230297i \(-0.0739699\pi\)
−0.957896 + 0.287117i \(0.907303\pi\)
\(198\) −5.34098 −0.379567
\(199\) −8.20173 −0.581405 −0.290703 0.956813i \(-0.593889\pi\)
−0.290703 + 0.956813i \(0.593889\pi\)
\(200\) −5.59104 20.8661i −0.395347 1.47545i
\(201\) 2.85760 0.765690i 0.201559 0.0540076i
\(202\) −6.72036 1.80071i −0.472843 0.126698i
\(203\) 0.0381616 + 7.52434i 0.00267842 + 0.528105i
\(204\) 0.849541 + 1.47145i 0.0594798 + 0.103022i
\(205\) 26.6494i 1.86128i
\(206\) 20.4361 + 5.47583i 1.42385 + 0.381519i
\(207\) 3.08517 + 1.78122i 0.214434 + 0.123804i
\(208\) −14.4562 9.24318i −1.00236 0.640899i
\(209\) 2.56168i 0.177195i
\(210\) 15.7625 0.0799438i 1.08772 0.00551665i
\(211\) 5.37441 9.30875i 0.369989 0.640841i −0.619574 0.784938i \(-0.712695\pi\)
0.989563 + 0.144098i \(0.0460280\pi\)
\(212\) 3.16770 + 1.82887i 0.217559 + 0.125608i
\(213\) −7.00412 + 1.87675i −0.479914 + 0.128593i
\(214\) 0.198874 0.198874i 0.0135947 0.0135947i
\(215\) 12.2856 + 45.8506i 0.837873 + 3.12699i
\(216\) 1.66997 1.66997i 0.113627 0.113627i
\(217\) −17.1616 + 17.3365i −1.16500 + 1.17688i
\(218\) −7.12516 4.11371i −0.482576 0.278616i
\(219\) 1.52950 + 1.52950i 0.103354 + 0.103354i
\(220\) 3.22781 5.59072i 0.217619 0.376927i
\(221\) 10.1396 + 6.48316i 0.682061 + 0.436105i
\(222\) −15.5406 + 8.97239i −1.04302 + 0.602187i
\(223\) 5.74055 1.53818i 0.384416 0.103004i −0.0614354 0.998111i \(-0.519568\pi\)
0.445851 + 0.895107i \(0.352901\pi\)
\(224\) 1.89094 7.20302i 0.126344 0.481272i
\(225\) −7.92144 + 4.57345i −0.528096 + 0.304897i
\(226\) 30.6245 + 8.20580i 2.03711 + 0.545842i
\(227\) −14.4159 14.4159i −0.956815 0.956815i 0.0422908 0.999105i \(-0.486534\pi\)
−0.999105 + 0.0422908i \(0.986534\pi\)
\(228\) −0.273451 0.273451i −0.0181097 0.0181097i
\(229\) −8.29019 2.22135i −0.547831 0.146791i −0.0257212 0.999669i \(-0.508188\pi\)
−0.522110 + 0.852878i \(0.674855\pi\)
\(230\) −18.3807 + 10.6121i −1.21199 + 0.699741i
\(231\) −6.34007 6.27608i −0.417146 0.412936i
\(232\) −6.48772 + 1.73838i −0.425939 + 0.114130i
\(233\) 4.35471 2.51419i 0.285286 0.164710i −0.350528 0.936552i \(-0.613998\pi\)
0.635814 + 0.771842i \(0.280664\pi\)
\(234\) −1.72636 + 5.44399i −0.112856 + 0.355885i
\(235\) −2.58761 + 4.48187i −0.168797 + 0.292365i
\(236\) 1.13566 + 1.13566i 0.0739250 + 0.0739250i
\(237\) −9.60175 5.54357i −0.623700 0.360094i
\(238\) −3.55197 + 13.5302i −0.230240 + 0.877035i
\(239\) −11.6568 + 11.6568i −0.754018 + 0.754018i −0.975227 0.221208i \(-0.929000\pi\)
0.221208 + 0.975227i \(0.429000\pi\)
\(240\) 4.63273 + 17.2896i 0.299042 + 1.11604i
\(241\) 3.99187 3.99187i 0.257139 0.257139i −0.566751 0.823889i \(-0.691800\pi\)
0.823889 + 0.566751i \(0.191800\pi\)
\(242\) −0.565154 + 0.151433i −0.0363295 + 0.00973446i
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) 0.265236 0.459402i 0.0169800 0.0294102i
\(245\) 18.8050 + 18.4274i 1.20141 + 1.17728i
\(246\) 11.2230i 0.715554i
\(247\) −2.61108 0.828010i −0.166139 0.0526850i
\(248\) −18.8578 10.8875i −1.19747 0.691360i
\(249\) −2.06557 0.553469i −0.130900 0.0350746i
\(250\) 24.7062i 1.56256i
\(251\) −5.54226 9.59948i −0.349825 0.605914i 0.636394 0.771365i \(-0.280425\pi\)
−0.986218 + 0.165451i \(0.947092\pi\)
\(252\) −1.34673 + 0.00683031i −0.0848363 + 0.000430269i
\(253\) 11.6027 + 3.10894i 0.729458 + 0.195458i
\(254\) 11.9173 3.19323i 0.747758 0.200361i
\(255\) −3.24940 12.1269i −0.203485 0.759417i
\(256\) 11.4924 0.718273
\(257\) −2.40321 −0.149908 −0.0749540 0.997187i \(-0.523881\pi\)
−0.0749540 + 0.997187i \(0.523881\pi\)
\(258\) −5.17392 19.3093i −0.322114 1.20215i
\(259\) −28.9910 7.61073i −1.80141 0.472908i
\(260\) −4.65523 5.09715i −0.288705 0.316112i
\(261\) 1.42199 + 2.46295i 0.0880187 + 0.152453i
\(262\) 3.98017 14.8542i 0.245896 0.917695i
\(263\) 13.0623 + 22.6246i 0.805456 + 1.39509i 0.915983 + 0.401218i \(0.131413\pi\)
−0.110527 + 0.993873i \(0.535254\pi\)
\(264\) 3.98163 6.89639i 0.245053 0.424444i
\(265\) −19.1113 19.1113i −1.17400 1.17400i
\(266\) −0.0161477 3.18385i −0.000990079 0.195214i
\(267\) −0.819042 + 3.05671i −0.0501246 + 0.187067i
\(268\) 0.389755 1.45459i 0.0238081 0.0888530i
\(269\) 26.4202i 1.61087i −0.592684 0.805435i \(-0.701932\pi\)
0.592684 0.805435i \(-0.298068\pi\)
\(270\) 5.15957 2.97888i 0.314002 0.181289i
\(271\) −5.35562 + 5.35562i −0.325330 + 0.325330i −0.850808 0.525477i \(-0.823887\pi\)
0.525477 + 0.850808i \(0.323887\pi\)
\(272\) −15.8850 −0.963168
\(273\) −8.44642 + 4.43373i −0.511201 + 0.268342i
\(274\) −14.3950 −0.869637
\(275\) −21.8086 + 21.8086i −1.31511 + 1.31511i
\(276\) 1.57043 0.906686i 0.0945286 0.0545761i
\(277\) 22.5430i 1.35448i 0.735764 + 0.677238i \(0.236823\pi\)
−0.735764 + 0.677238i \(0.763177\pi\)
\(278\) 4.19173 15.6437i 0.251403 0.938250i
\(279\) −2.38635 + 8.90596i −0.142867 + 0.533186i
\(280\) −11.6476 + 20.4126i −0.696075 + 1.21988i
\(281\) −7.73479 7.73479i −0.461419 0.461419i 0.437701 0.899120i \(-0.355793\pi\)
−0.899120 + 0.437701i \(0.855793\pi\)
\(282\) 1.08973 1.88747i 0.0648927 0.112397i
\(283\) 8.86524 + 15.3550i 0.526984 + 0.912763i 0.999506 + 0.0314437i \(0.0100105\pi\)
−0.472522 + 0.881319i \(0.656656\pi\)
\(284\) −0.955310 + 3.56527i −0.0566872 + 0.211560i
\(285\) 1.42875 + 2.47467i 0.0846319 + 0.146587i
\(286\) −0.871725 + 19.2374i −0.0515462 + 1.13753i
\(287\) 13.1880 13.3224i 0.778461 0.786397i
\(288\) −0.728508 2.71883i −0.0429277 0.160208i
\(289\) −5.85829 −0.344605
\(290\) −16.9437 −0.994968
\(291\) 3.23001 + 12.0545i 0.189346 + 0.706650i
\(292\) 1.06352 0.284970i 0.0622379 0.0166766i
\(293\) −12.4507 3.33616i −0.727379 0.194901i −0.123917 0.992293i \(-0.539546\pi\)
−0.603462 + 0.797392i \(0.706212\pi\)
\(294\) −7.91947 7.76042i −0.461873 0.452597i
\(295\) −5.93368 10.2774i −0.345472 0.598376i
\(296\) 26.7552i 1.55512i
\(297\) −3.25696 0.872699i −0.188988 0.0506391i
\(298\) 20.6096 + 11.8990i 1.19388 + 0.689288i
\(299\) 6.91925 10.8216i 0.400151 0.625830i
\(300\) 4.65599i 0.268814i
\(301\) 16.5483 29.0011i 0.953826 1.67160i
\(302\) −0.219930 + 0.380931i −0.0126556 + 0.0219201i
\(303\) −3.80388 2.19617i −0.218527 0.126167i
\(304\) 3.49229 0.935756i 0.200297 0.0536693i
\(305\) −2.77166 + 2.77166i −0.158705 + 0.158705i
\(306\) 1.36844 + 5.10707i 0.0782283 + 0.291952i
\(307\) −5.82305 + 5.82305i −0.332339 + 0.332339i −0.853474 0.521135i \(-0.825509\pi\)
0.521135 + 0.853474i \(0.325509\pi\)
\(308\) −4.38030 + 1.19754i −0.249591 + 0.0682362i
\(309\) 11.5673 + 6.67838i 0.658040 + 0.379920i
\(310\) −38.8423 38.8423i −2.20610 2.20610i
\(311\) −13.5284 + 23.4318i −0.767124 + 1.32870i 0.171992 + 0.985098i \(0.444980\pi\)
−0.939116 + 0.343600i \(0.888354\pi\)
\(312\) −5.74242 6.28754i −0.325100 0.355962i
\(313\) 11.8883 6.86374i 0.671969 0.387962i −0.124853 0.992175i \(-0.539846\pi\)
0.796822 + 0.604214i \(0.206513\pi\)
\(314\) 0.481113 0.128914i 0.0271508 0.00727502i
\(315\) 9.62515 + 2.52680i 0.542316 + 0.142369i
\(316\) −4.88752 + 2.82181i −0.274945 + 0.158739i
\(317\) 2.23807 + 0.599689i 0.125702 + 0.0336819i 0.321122 0.947038i \(-0.395940\pi\)
−0.195419 + 0.980720i \(0.562607\pi\)
\(318\) 8.04845 + 8.04845i 0.451335 + 0.451335i
\(319\) 6.78076 + 6.78076i 0.379650 + 0.379650i
\(320\) −18.3811 4.92519i −1.02753 0.275327i
\(321\) 0.153770 0.0887791i 0.00858260 0.00495516i
\(322\) 14.4404 + 3.79089i 0.804730 + 0.211258i
\(323\) −2.44949 + 0.656339i −0.136293 + 0.0365197i
\(324\) −0.440828 + 0.254512i −0.0244904 + 0.0141396i
\(325\) 15.1800 + 29.2783i 0.842035 + 1.62407i
\(326\) −0.747745 + 1.29513i −0.0414138 + 0.0717307i
\(327\) −3.67279 3.67279i −0.203106 0.203106i
\(328\) 14.4914 + 8.36663i 0.800155 + 0.461970i
\(329\) 3.51152 0.960022i 0.193596 0.0529277i
\(330\) 14.2048 14.2048i 0.781951 0.781951i
\(331\) 6.68605 + 24.9527i 0.367498 + 1.37152i 0.864002 + 0.503488i \(0.167950\pi\)
−0.496504 + 0.868035i \(0.665383\pi\)
\(332\) −0.769698 + 0.769698i −0.0422427 + 0.0422427i
\(333\) −10.9428 + 2.93212i −0.599663 + 0.160679i
\(334\) 3.32107 + 1.91742i 0.181721 + 0.104917i
\(335\) −5.56362 + 9.63647i −0.303973 + 0.526497i
\(336\) 6.24011 10.9359i 0.340426 0.596602i
\(337\) 32.4074i 1.76534i 0.469990 + 0.882672i \(0.344257\pi\)
−0.469990 + 0.882672i \(0.655743\pi\)
\(338\) 19.3267 + 7.10664i 1.05123 + 0.386550i
\(339\) 17.3342 + 10.0079i 0.941462 + 0.543554i
\(340\) −6.17289 1.65402i −0.334772 0.0897019i
\(341\) 31.0889i 1.68356i
\(342\) −0.601698 1.04217i −0.0325361 0.0563542i
\(343\) −0.281778 18.5181i −0.0152146 0.999884i
\(344\) 28.7897 + 7.71418i 1.55224 + 0.415921i
\(345\) −12.9426 + 3.46797i −0.696808 + 0.186709i
\(346\) −7.06025 26.3492i −0.379562 1.41654i
\(347\) −31.0215 −1.66532 −0.832660 0.553784i \(-0.813183\pi\)
−0.832660 + 0.553784i \(0.813183\pi\)
\(348\) 1.44765 0.0776022
\(349\) 0.142223 + 0.530784i 0.00761303 + 0.0284122i 0.969628 0.244585i \(-0.0786517\pi\)
−0.962015 + 0.272997i \(0.911985\pi\)
\(350\) −26.9679 + 27.2428i −1.44149 + 1.45619i
\(351\) −1.94228 + 3.03769i −0.103671 + 0.162140i
\(352\) −4.74544 8.21934i −0.252933 0.438092i
\(353\) 3.20193 11.9498i 0.170422 0.636022i −0.826865 0.562401i \(-0.809878\pi\)
0.997286 0.0736213i \(-0.0234556\pi\)
\(354\) 2.49888 + 4.32819i 0.132814 + 0.230041i
\(355\) 13.6367 23.6195i 0.723762 1.25359i
\(356\) 1.13903 + 1.13903i 0.0603682 + 0.0603682i
\(357\) −4.37681 + 7.67043i −0.231645 + 0.405962i
\(358\) 1.41129 5.26701i 0.0745891 0.278370i
\(359\) 1.88465 7.03362i 0.0994682 0.371220i −0.898191 0.439606i \(-0.855118\pi\)
0.997659 + 0.0683856i \(0.0217848\pi\)
\(360\) 8.88288i 0.468169i
\(361\) −15.9546 + 9.21141i −0.839717 + 0.484811i
\(362\) 29.0952 29.0952i 1.52921 1.52921i
\(363\) −0.369378 −0.0193873
\(364\) −0.195205 + 4.85186i −0.0102315 + 0.254306i
\(365\) −8.13569 −0.425842
\(366\) 1.16724 1.16724i 0.0610128 0.0610128i
\(367\) 3.73411 2.15589i 0.194919 0.112536i −0.399364 0.916792i \(-0.630769\pi\)
0.594283 + 0.804256i \(0.297436\pi\)
\(368\) 16.9535i 0.883761i
\(369\) 1.83381 6.84386i 0.0954642 0.356277i
\(370\) 17.4689 65.1947i 0.908163 3.38931i
\(371\) 0.0964222 + 19.0116i 0.00500599 + 0.987032i
\(372\) 3.31864 + 3.31864i 0.172064 + 0.172064i
\(373\) 8.58752 14.8740i 0.444645 0.770147i −0.553383 0.832927i \(-0.686663\pi\)
0.998027 + 0.0627799i \(0.0199966\pi\)
\(374\) 8.91388 + 15.4393i 0.460926 + 0.798347i
\(375\) 4.03692 15.0660i 0.208466 0.778004i
\(376\) 1.62477 + 2.81418i 0.0837909 + 0.145130i
\(377\) 9.10328 4.71980i 0.468843 0.243082i
\(378\) −4.05349 1.06413i −0.208489 0.0547327i
\(379\) 0.602843 + 2.24984i 0.0309659 + 0.115566i 0.979679 0.200572i \(-0.0642801\pi\)
−0.948713 + 0.316139i \(0.897613\pi\)
\(380\) 1.45454 0.0746163
\(381\) 7.78900 0.399042
\(382\) 1.22296 + 4.56415i 0.0625721 + 0.233522i
\(383\) −26.6204 + 7.13293i −1.36024 + 0.364476i −0.863905 0.503655i \(-0.831988\pi\)
−0.496336 + 0.868130i \(0.665322\pi\)
\(384\) 13.1786 + 3.53119i 0.672516 + 0.180200i
\(385\) 33.5538 0.170177i 1.71006 0.00867302i
\(386\) −2.07041 3.58606i −0.105381 0.182526i
\(387\) 12.6203i 0.641528i
\(388\) 6.13606 + 1.64415i 0.311511 + 0.0834691i
\(389\) −10.7596 6.21203i −0.545531 0.314962i 0.201787 0.979430i \(-0.435325\pi\)
−0.747318 + 0.664467i \(0.768659\pi\)
\(390\) −9.88738 19.0702i −0.500667 0.965658i
\(391\) 11.8912i 0.601362i
\(392\) 15.9243 4.44051i 0.804299 0.224279i
\(393\) 4.85426 8.40782i 0.244865 0.424118i
\(394\) 1.13258 + 0.653895i 0.0570585 + 0.0329428i
\(395\) 40.2804 10.7931i 2.02673 0.543060i
\(396\) −1.21365 + 1.21365i −0.0609880 + 0.0609880i
\(397\) −8.36351 31.2130i −0.419752 1.56654i −0.775122 0.631812i \(-0.782312\pi\)
0.355369 0.934726i \(-0.384355\pi\)
\(398\) −9.18635 + 9.18635i −0.460470 + 0.460470i
\(399\) 0.510383 1.94416i 0.0255511 0.0973300i
\(400\) −37.6977 21.7648i −1.88488 1.08824i
\(401\) −9.95929 9.95929i −0.497343 0.497343i 0.413267 0.910610i \(-0.364388\pi\)
−0.910610 + 0.413267i \(0.864388\pi\)
\(402\) 2.34304 4.05826i 0.116860 0.202408i
\(403\) 31.6885 + 10.0489i 1.57852 + 0.500569i
\(404\) −1.93627 + 1.11790i −0.0963329 + 0.0556178i
\(405\) 3.63307 0.973479i 0.180529 0.0483726i
\(406\) 8.47038 + 8.38490i 0.420378 + 0.416135i
\(407\) −33.0815 + 19.0996i −1.63979 + 0.946731i
\(408\) −7.61452 2.04031i −0.376975 0.101010i
\(409\) −20.8373 20.8373i −1.03034 1.03034i −0.999525 0.0308137i \(-0.990190\pi\)
−0.0308137 0.999525i \(-0.509810\pi\)
\(410\) 29.8487 + 29.8487i 1.47412 + 1.47412i
\(411\) −8.77818 2.35211i −0.432996 0.116021i
\(412\) 5.88804 3.39946i 0.290083 0.167479i
\(413\) −2.11965 + 8.07422i −0.104301 + 0.397307i
\(414\) 5.45060 1.46048i 0.267883 0.0717789i
\(415\) 6.96559 4.02159i 0.341927 0.197412i
\(416\) −9.91172 + 2.18023i −0.485962 + 0.106894i
\(417\) 5.11228 8.85473i 0.250349 0.433618i
\(418\) −2.86921 2.86921i −0.140338 0.140338i
\(419\) −10.6429 6.14470i −0.519941 0.300188i 0.216970 0.976178i \(-0.430383\pi\)
−0.736911 + 0.675990i \(0.763716\pi\)
\(420\) 3.56360 3.59993i 0.173886 0.175659i
\(421\) 6.08177 6.08177i 0.296407 0.296407i −0.543197 0.839605i \(-0.682787\pi\)
0.839605 + 0.543197i \(0.182787\pi\)
\(422\) −4.40666 16.4459i −0.214513 0.800572i
\(423\) 0.972933 0.972933i 0.0473056 0.0473056i
\(424\) −16.3924 + 4.39232i −0.796084 + 0.213310i
\(425\) 26.4411 + 15.2658i 1.28258 + 0.740500i
\(426\) −5.74291 + 9.94701i −0.278245 + 0.481934i
\(427\) 2.75719 0.0139838i 0.133430 0.000676724i
\(428\) 0.0903814i 0.00436875i
\(429\) −3.67492 + 11.5887i −0.177427 + 0.559505i
\(430\) 65.1155 + 37.5945i 3.14015 + 1.81297i
\(431\) 32.9505 + 8.82906i 1.58717 + 0.425281i 0.941136 0.338029i \(-0.109760\pi\)
0.646033 + 0.763309i \(0.276427\pi\)
\(432\) 4.75894i 0.228965i
\(433\) 14.7993 + 25.6331i 0.711209 + 1.23185i 0.964403 + 0.264435i \(0.0851855\pi\)
−0.253194 + 0.967415i \(0.581481\pi\)
\(434\) 0.195971 + 38.6396i 0.00940690 + 1.85476i
\(435\) −10.3324 2.76855i −0.495399 0.132742i
\(436\) −2.55384 + 0.684299i −0.122307 + 0.0327720i
\(437\) 0.700488 + 2.61426i 0.0335089 + 0.125057i
\(438\) 3.42623 0.163712
\(439\) 18.4285 0.879545 0.439772 0.898109i \(-0.355059\pi\)
0.439772 + 0.898109i \(0.355059\pi\)
\(440\) 7.75208 + 28.9311i 0.369566 + 1.37924i
\(441\) −3.56131 6.02636i −0.169586 0.286970i
\(442\) 18.6183 4.09536i 0.885582 0.194796i
\(443\) −2.87530 4.98017i −0.136610 0.236615i 0.789601 0.613620i \(-0.210287\pi\)
−0.926211 + 0.377005i \(0.876954\pi\)
\(444\) −1.49252 + 5.57016i −0.0708319 + 0.264348i
\(445\) −5.95128 10.3079i −0.282118 0.488642i
\(446\) 4.70687 8.15254i 0.222877 0.386034i
\(447\) 10.6236 + 10.6236i 0.502478 + 0.502478i
\(448\) 6.75163 + 11.5584i 0.318984 + 0.546082i
\(449\) 5.09748 19.0241i 0.240565 0.897801i −0.734996 0.678072i \(-0.762816\pi\)
0.975561 0.219729i \(-0.0705174\pi\)
\(450\) −3.74992 + 13.9949i −0.176773 + 0.659726i
\(451\) 23.8905i 1.12496i
\(452\) 8.82351 5.09426i 0.415023 0.239614i
\(453\) −0.196358 + 0.196358i −0.00922569 + 0.00922569i
\(454\) −32.2930 −1.51558
\(455\) 10.6721 34.2560i 0.500317 1.60595i
\(456\) 1.79423 0.0840227
\(457\) 2.19914 2.19914i 0.102871 0.102871i −0.653798 0.756669i \(-0.726825\pi\)
0.756669 + 0.653798i \(0.226825\pi\)
\(458\) −11.7734 + 6.79740i −0.550137 + 0.317622i
\(459\) 3.33792i 0.155801i
\(460\) −1.76528 + 6.58812i −0.0823066 + 0.307173i
\(461\) 8.13643 30.3656i 0.378951 1.41427i −0.468533 0.883446i \(-0.655217\pi\)
0.847485 0.530820i \(-0.178116\pi\)
\(462\) −14.1307 + 0.0716676i −0.657420 + 0.00333428i
\(463\) 10.2951 + 10.2951i 0.478455 + 0.478455i 0.904637 0.426182i \(-0.140142\pi\)
−0.426182 + 0.904637i \(0.640142\pi\)
\(464\) −6.76715 + 11.7210i −0.314157 + 0.544136i
\(465\) −17.3395 30.0330i −0.804102 1.39275i
\(466\) 2.06147 7.69351i 0.0954958 0.356395i
\(467\) −6.26532 10.8518i −0.289924 0.502164i 0.683867 0.729607i \(-0.260297\pi\)
−0.973791 + 0.227443i \(0.926963\pi\)
\(468\) 0.844767 + 1.62934i 0.0390493 + 0.0753162i
\(469\) 7.55012 2.06414i 0.348632 0.0953133i
\(470\) 2.12167 + 7.91817i 0.0978652 + 0.365238i
\(471\) 0.314449 0.0144891
\(472\) −7.45155 −0.342985
\(473\) −11.0138 41.1039i −0.506413 1.88996i
\(474\) −16.9635 + 4.54536i −0.779160 + 0.208775i
\(475\) −6.71233 1.79856i −0.307983 0.0825238i
\(476\) 2.26739 + 3.88164i 0.103926 + 0.177915i
\(477\) 3.59290 + 6.22308i 0.164508 + 0.284935i
\(478\) 26.1125i 1.19436i
\(479\) 20.2529 + 5.42675i 0.925379 + 0.247954i 0.689883 0.723921i \(-0.257662\pi\)
0.235496 + 0.971875i \(0.424329\pi\)
\(480\) 9.16852 + 5.29344i 0.418484 + 0.241612i
\(481\) 8.77505 + 39.8930i 0.400108 + 1.81897i
\(482\) 8.94218i 0.407305i
\(483\) 8.18639 + 4.67122i 0.372494 + 0.212548i
\(484\) −0.0940112 + 0.162832i −0.00427324 + 0.00740146i
\(485\) −40.6507 23.4697i −1.84585 1.06570i
\(486\) −1.53002 + 0.409967i −0.0694030 + 0.0185965i
\(487\) 7.62705 7.62705i 0.345615 0.345615i −0.512858 0.858473i \(-0.671413\pi\)
0.858473 + 0.512858i \(0.171413\pi\)
\(488\) 0.637005 + 2.37734i 0.0288359 + 0.107617i
\(489\) −0.667599 + 0.667599i −0.0301899 + 0.0301899i
\(490\) 41.7022 0.423018i 1.88391 0.0191100i
\(491\) 30.7318 + 17.7430i 1.38691 + 0.800730i 0.992965 0.118406i \(-0.0377785\pi\)
0.393940 + 0.919136i \(0.371112\pi\)
\(492\) −2.55024 2.55024i −0.114974 0.114974i
\(493\) 4.74647 8.22113i 0.213770 0.370261i
\(494\) −3.85196 + 1.99713i −0.173308 + 0.0898552i
\(495\) 10.9832 6.34116i 0.493659 0.285014i
\(496\) −42.3830 + 11.3565i −1.90305 + 0.509921i
\(497\) −18.5057 + 5.05933i −0.830096 + 0.226942i
\(498\) −2.93346 + 1.69363i −0.131451 + 0.0758935i
\(499\) −4.95983 1.32898i −0.222033 0.0594935i 0.146088 0.989272i \(-0.453332\pi\)
−0.368120 + 0.929778i \(0.619999\pi\)
\(500\) −5.61406 5.61406i −0.251069 0.251069i
\(501\) 1.71190 + 1.71190i 0.0764823 + 0.0764823i
\(502\) −16.9595 4.54429i −0.756940 0.202821i
\(503\) −31.3005 + 18.0713i −1.39562 + 0.805761i −0.993930 0.110015i \(-0.964910\pi\)
−0.401690 + 0.915776i \(0.631577\pi\)
\(504\) 4.39585 4.44067i 0.195807 0.197803i
\(505\) 15.9577 4.27585i 0.710108 0.190273i
\(506\) 16.4778 9.51348i 0.732529 0.422926i
\(507\) 10.6243 + 7.49159i 0.471842 + 0.332713i
\(508\) 1.98239 3.43361i 0.0879546 0.152342i
\(509\) −20.3768 20.3768i −0.903184 0.903184i 0.0925266 0.995710i \(-0.470506\pi\)
−0.995710 + 0.0925266i \(0.970506\pi\)
\(510\) −17.2222 9.94326i −0.762614 0.440295i
\(511\) 4.06714 + 4.02610i 0.179920 + 0.178104i
\(512\) −6.42274 + 6.42274i −0.283848 + 0.283848i
\(513\) −0.196631 0.733837i −0.00868148 0.0323997i
\(514\) −2.69171 + 2.69171i −0.118726 + 0.118726i
\(515\) −48.5261 + 13.0025i −2.13832 + 0.572960i
\(516\) −5.56340 3.21203i −0.244915 0.141402i
\(517\) 2.31972 4.01788i 0.102021 0.176706i
\(518\) −40.9957 + 23.9469i −1.80125 + 1.05217i
\(519\) 17.2215i 0.755941i
\(520\) 31.9948 + 1.44981i 1.40307 + 0.0635785i
\(521\) 15.6852 + 9.05586i 0.687182 + 0.396745i 0.802555 0.596578i \(-0.203473\pi\)
−0.115374 + 0.993322i \(0.536807\pi\)
\(522\) 4.35132 + 1.16593i 0.190452 + 0.0510315i
\(523\) 1.70402i 0.0745115i −0.999306 0.0372557i \(-0.988138\pi\)
0.999306 0.0372557i \(-0.0118616\pi\)
\(524\) −2.47094 4.27979i −0.107943 0.186963i
\(525\) −20.8965 + 12.2063i −0.911999 + 0.532728i
\(526\) 39.9711 + 10.7102i 1.74282 + 0.466988i
\(527\) 29.7274 7.96543i 1.29495 0.346980i
\(528\) −4.15313 15.4997i −0.180742 0.674537i
\(529\) 10.3090 0.448216
\(530\) −42.8113 −1.85960
\(531\) 0.816620 + 3.04767i 0.0354383 + 0.132257i
\(532\) −0.727144 0.719805i −0.0315257 0.0312075i
\(533\) −24.3513 7.72212i −1.05477 0.334482i
\(534\) 2.50630 + 4.34103i 0.108458 + 0.187855i
\(535\) −0.172849 + 0.645082i −0.00747292 + 0.0278893i
\(536\) 3.49341 + 6.05077i 0.150892 + 0.261353i
\(537\) 1.72123 2.98125i 0.0742764 0.128651i
\(538\) −29.5920 29.5920i −1.27580 1.27580i
\(539\) −16.8582 16.5197i −0.726136 0.711552i
\(540\) 0.495525 1.84932i 0.0213240 0.0795822i
\(541\) −2.05747 + 7.67860i −0.0884577 + 0.330129i −0.995946 0.0899476i \(-0.971330\pi\)
0.907489 + 0.420076i \(0.137997\pi\)
\(542\) 11.9971i 0.515320i
\(543\) 22.4965 12.9884i 0.965418 0.557384i
\(544\) −6.64353 + 6.64353i −0.284839 + 0.284839i
\(545\) 19.5363 0.836842
\(546\) −4.49442 + 14.4264i −0.192343 + 0.617394i
\(547\) −45.6503 −1.95187 −0.975933 0.218072i \(-0.930023\pi\)
−0.975933 + 0.218072i \(0.930023\pi\)
\(548\) −3.27103 + 3.27103i −0.139731 + 0.139731i
\(549\) 0.902515 0.521067i 0.0385184 0.0222386i
\(550\) 48.8534i 2.08311i
\(551\) −0.559213 + 2.08701i −0.0238233 + 0.0889097i
\(552\) −2.17755 + 8.12672i −0.0926826 + 0.345896i
\(553\) −25.4779 14.5379i −1.08343 0.618214i
\(554\) 25.2493 + 25.2493i 1.07274 + 1.07274i
\(555\) 21.3052 36.9017i 0.904357 1.56639i
\(556\) −2.60227 4.50727i −0.110361 0.191151i
\(557\) −3.24461 + 12.1091i −0.137479 + 0.513077i 0.862497 + 0.506063i \(0.168900\pi\)
−0.999975 + 0.00701474i \(0.997767\pi\)
\(558\) 7.30230 + 12.6480i 0.309131 + 0.535431i
\(559\) −45.4566 2.05982i −1.92261 0.0871211i
\(560\) 12.4889 + 45.6812i 0.527752 + 1.93038i
\(561\) 2.91300 + 10.8715i 0.122987 + 0.458994i
\(562\) −17.3267 −0.730883
\(563\) −14.7021 −0.619621 −0.309810 0.950798i \(-0.600266\pi\)
−0.309810 + 0.950798i \(0.600266\pi\)
\(564\) −0.181273 0.676520i −0.00763297 0.0284866i
\(565\) −72.7188 + 19.4849i −3.05930 + 0.819737i
\(566\) 27.1279 + 7.26891i 1.14027 + 0.305535i
\(567\) −2.29797 1.31124i −0.0965056 0.0550668i
\(568\) −8.56254 14.8308i −0.359276 0.622285i
\(569\) 21.1424i 0.886335i −0.896439 0.443167i \(-0.853855\pi\)
0.896439 0.443167i \(-0.146145\pi\)
\(570\) 4.37203 + 1.17148i 0.183124 + 0.0490679i
\(571\) −2.38493 1.37694i −0.0998064 0.0576232i 0.449266 0.893398i \(-0.351686\pi\)
−0.549072 + 0.835775i \(0.685019\pi\)
\(572\) 4.17329 + 4.56946i 0.174494 + 0.191059i
\(573\) 2.98307i 0.124620i
\(574\) −0.150595 29.6929i −0.00628573 1.23936i
\(575\) 16.2927 28.2197i 0.679451 1.17684i
\(576\) 4.38154 + 2.52969i 0.182564 + 0.105404i
\(577\) −6.04026 + 1.61848i −0.251459 + 0.0673783i −0.382347 0.924019i \(-0.624884\pi\)
0.130888 + 0.991397i \(0.458217\pi\)
\(578\) −6.56158 + 6.56158i −0.272926 + 0.272926i
\(579\) −0.676598 2.52510i −0.0281185 0.104940i
\(580\) −3.85016 + 3.85016i −0.159869 + 0.159869i
\(581\) −5.47235 1.43660i −0.227031 0.0596004i
\(582\) 17.1195 + 9.88393i 0.709624 + 0.409702i
\(583\) 17.1328 + 17.1328i 0.709568 + 0.709568i
\(584\) −2.55421 + 4.42403i −0.105694 + 0.183067i
\(585\) −2.91336 13.2447i −0.120453 0.547601i
\(586\) −17.6821 + 10.2088i −0.730441 + 0.421720i
\(587\) −15.8338 + 4.24265i −0.653530 + 0.175113i −0.570324 0.821420i \(-0.693183\pi\)
−0.0832057 + 0.996532i \(0.526516\pi\)
\(588\) −3.56299 + 0.0361421i −0.146935 + 0.00149048i
\(589\) −6.06630 + 3.50238i −0.249958 + 0.144313i
\(590\) −18.1573 4.86523i −0.747523 0.200298i
\(591\) 0.583809 + 0.583809i 0.0240147 + 0.0240147i
\(592\) −38.1225 38.1225i −1.56682 1.56682i
\(593\) 14.8765 + 3.98614i 0.610904 + 0.163691i 0.550989 0.834512i \(-0.314250\pi\)
0.0599148 + 0.998203i \(0.480917\pi\)
\(594\) −4.62542 + 2.67049i −0.189783 + 0.109571i
\(595\) −8.75971 32.0408i −0.359113 1.31354i
\(596\) 7.38701 1.97934i 0.302584 0.0810770i
\(597\) −7.10291 + 4.10087i −0.290703 + 0.167837i
\(598\) −4.37084 19.8707i −0.178737 0.812572i
\(599\) 13.0357 22.5784i 0.532623 0.922530i −0.466651 0.884441i \(-0.654540\pi\)
0.999274 0.0380886i \(-0.0121269\pi\)
\(600\) −15.2750 15.2750i −0.623600 0.623600i
\(601\) −36.7529 21.2193i −1.49918 0.865554i −0.499183 0.866496i \(-0.666367\pi\)
−1.00000 0.000942846i \(0.999700\pi\)
\(602\) −13.9478 51.0176i −0.568471 2.07932i
\(603\) 2.09191 2.09191i 0.0851890 0.0851890i
\(604\) 0.0365845 + 0.136535i 0.00148860 + 0.00555555i
\(605\) 0.982396 0.982396i 0.0399401 0.0399401i
\(606\) −6.72036 + 1.80071i −0.272996 + 0.0731490i
\(607\) −5.87620 3.39263i −0.238508 0.137702i 0.375983 0.926627i \(-0.377305\pi\)
−0.614491 + 0.788924i \(0.710638\pi\)
\(608\) 1.06921 1.85193i 0.0433623 0.0751057i
\(609\) 3.79522 + 6.49719i 0.153790 + 0.263279i
\(610\) 6.20879i 0.251386i
\(611\) −3.34557 3.66316i −0.135347 0.148196i
\(612\) 1.47145 + 0.849541i 0.0594798 + 0.0343407i
\(613\) 32.8333 + 8.79765i 1.32612 + 0.355334i 0.851269 0.524730i \(-0.175834\pi\)
0.474855 + 0.880064i \(0.342501\pi\)
\(614\) 13.0442i 0.526422i
\(615\) 13.3247 + 23.0791i 0.537304 + 0.930638i
\(616\) 10.4417 18.2993i 0.420710 0.737301i
\(617\) −7.13892 1.91287i −0.287402 0.0770091i 0.112238 0.993681i \(-0.464198\pi\)
−0.399640 + 0.916672i \(0.630865\pi\)
\(618\) 20.4361 5.47583i 0.822059 0.220270i
\(619\) 0.183786 + 0.685897i 0.00738697 + 0.0275685i 0.969521 0.245008i \(-0.0787907\pi\)
−0.962134 + 0.272577i \(0.912124\pi\)
\(620\) −17.6525 −0.708942
\(621\) 3.56245 0.142956
\(622\) 11.0924 + 41.3973i 0.444764 + 1.65988i
\(623\) −2.12594 + 8.09817i −0.0851739 + 0.324446i
\(624\) −17.1410 0.776728i −0.686190 0.0310940i
\(625\) 6.46561 + 11.1988i 0.258624 + 0.447951i
\(626\) 5.62781 21.0033i 0.224933 0.839460i
\(627\) −1.28084 2.21848i −0.0511518 0.0885975i
\(628\) 0.0800312 0.138618i 0.00319359 0.00553146i
\(629\) 26.7391 + 26.7391i 1.06616 + 1.06616i
\(630\) 13.6108 7.95051i 0.542267 0.316756i
\(631\) 7.80744 29.1378i 0.310809 1.15996i −0.617019 0.786948i \(-0.711660\pi\)
0.927828 0.373008i \(-0.121674\pi\)
\(632\) 6.77702 25.2922i 0.269575 1.00607i
\(633\) 10.7488i 0.427227i
\(634\) 3.17843 1.83507i 0.126232 0.0728798i
\(635\) −20.7156 + 20.7156i −0.822073 + 0.822073i
\(636\) 3.65775 0.145039
\(637\) −22.2874 + 11.8437i −0.883057 + 0.469266i
\(638\) 15.1896 0.601361
\(639\) −5.12737 + 5.12737i −0.202836 + 0.202836i
\(640\) −44.4412 + 25.6581i −1.75669 + 1.01423i
\(641\) 14.4376i 0.570251i 0.958490 + 0.285126i \(0.0920353\pi\)
−0.958490 + 0.285126i \(0.907965\pi\)
\(642\) 0.0727929 0.271667i 0.00287291 0.0107218i
\(643\) −4.71705 + 17.6043i −0.186022 + 0.694244i 0.808387 + 0.588651i \(0.200341\pi\)
−0.994409 + 0.105593i \(0.966326\pi\)
\(644\) 4.14274 2.41991i 0.163247 0.0953577i
\(645\) 33.5650 + 33.5650i 1.32162 + 1.32162i
\(646\) −2.00842 + 3.47868i −0.0790202 + 0.136867i
\(647\) 18.8833 + 32.7068i 0.742379 + 1.28584i 0.951409 + 0.307929i \(0.0996359\pi\)
−0.209031 + 0.977909i \(0.567031\pi\)
\(648\) 0.611250 2.28122i 0.0240122 0.0896147i
\(649\) 5.31939 + 9.21346i 0.208804 + 0.361660i
\(650\) 49.7956 + 15.7909i 1.95314 + 0.619368i
\(651\) −6.19409 + 23.5947i −0.242766 + 0.924749i
\(652\) 0.124384 + 0.464209i 0.00487127 + 0.0181798i
\(653\) −26.5542 −1.03915 −0.519573 0.854426i \(-0.673909\pi\)
−0.519573 + 0.854426i \(0.673909\pi\)
\(654\) −8.22742 −0.321718
\(655\) 9.45104 + 35.2718i 0.369283 + 1.37818i
\(656\) 32.5695 8.72698i 1.27163 0.340731i
\(657\) 2.08933 + 0.559835i 0.0815127 + 0.0218413i
\(658\) 2.85780 5.00835i 0.111409 0.195246i
\(659\) 2.28186 + 3.95230i 0.0888888 + 0.153960i 0.907042 0.421041i \(-0.138335\pi\)
−0.818153 + 0.575001i \(0.805002\pi\)
\(660\) 6.45561i 0.251284i
\(661\) 40.6603 + 10.8949i 1.58150 + 0.423762i 0.939390 0.342850i \(-0.111392\pi\)
0.642111 + 0.766612i \(0.278059\pi\)
\(662\) 35.4369 + 20.4595i 1.37730 + 0.795182i
\(663\) 12.0227 + 0.544797i 0.466923 + 0.0211582i
\(664\) 5.05033i 0.195991i
\(665\) 3.81328 + 6.52811i 0.147873 + 0.253149i
\(666\) −8.97239 + 15.5406i −0.347673 + 0.602187i
\(667\) −8.77413 5.06575i −0.339736 0.196146i
\(668\) 1.19036 0.318955i 0.0460563 0.0123407i
\(669\) 4.20237 4.20237i 0.162473 0.162473i
\(670\) 4.56180 + 17.0249i 0.176238 + 0.657728i
\(671\) 2.48472 2.48472i 0.0959215 0.0959215i
\(672\) −1.96391 7.18347i −0.0757594 0.277108i
\(673\) −22.4576 12.9659i −0.865675 0.499798i 0.000233516 1.00000i \(-0.499926\pi\)
−0.865909 + 0.500202i \(0.833259\pi\)
\(674\) 36.2979 + 36.2979i 1.39814 + 1.39814i
\(675\) −4.57345 + 7.92144i −0.176032 + 0.304897i
\(676\) 6.00652 2.77679i 0.231020 0.106800i
\(677\) 15.4910 8.94374i 0.595368 0.343736i −0.171849 0.985123i \(-0.554974\pi\)
0.767217 + 0.641387i \(0.221641\pi\)
\(678\) 30.6245 8.20580i 1.17613 0.315142i
\(679\) 8.70743 + 31.8496i 0.334161 + 1.22227i
\(680\) 25.6779 14.8252i 0.984704 0.568519i
\(681\) −19.6924 5.27657i −0.754616 0.202199i
\(682\) 34.8211 + 34.8211i 1.33337 + 1.33337i
\(683\) −22.6009 22.6009i −0.864799 0.864799i 0.127092 0.991891i \(-0.459436\pi\)
−0.991891 + 0.127092i \(0.959436\pi\)
\(684\) −0.373541 0.100090i −0.0142827 0.00382704i
\(685\) 29.6021 17.0908i 1.13104 0.653004i
\(686\) −21.0568 20.4256i −0.803953 0.779853i
\(687\) −8.29019 + 2.22135i −0.316290 + 0.0847497i
\(688\) 52.0130 30.0297i 1.98298 1.14487i
\(689\) 23.0011 11.9254i 0.876271 0.454322i
\(690\) −10.6121 + 18.3807i −0.403996 + 0.699741i
\(691\) 10.6170 + 10.6170i 0.403889 + 0.403889i 0.879601 0.475712i \(-0.157809\pi\)
−0.475712 + 0.879601i \(0.657809\pi\)
\(692\) −7.59173 4.38309i −0.288594 0.166620i
\(693\) −8.62870 2.26521i −0.327777 0.0860483i
\(694\) −34.7456 + 34.7456i −1.31893 + 1.31893i
\(695\) 9.95340 + 37.1466i 0.377554 + 1.40905i
\(696\) −4.74934 + 4.74934i −0.180023 + 0.180023i
\(697\) −22.8443 + 6.12110i −0.865288 + 0.231853i
\(698\) 0.753802 + 0.435208i 0.0285318 + 0.0164729i
\(699\) 2.51419 4.35471i 0.0950955 0.164710i
\(700\) 0.0624761 + 12.3184i 0.00236138 + 0.465593i
\(701\) 17.3022i 0.653495i −0.945112 0.326747i \(-0.894047\pi\)
0.945112 0.326747i \(-0.105953\pi\)
\(702\) 1.22692 + 5.57781i 0.0463071 + 0.210521i
\(703\) −7.45371 4.30340i −0.281122 0.162306i
\(704\) 16.4782 + 4.41531i 0.621044 + 0.166408i
\(705\) 5.17522i 0.194910i
\(706\) −9.79802 16.9707i −0.368753 0.638700i
\(707\) −10.0935 5.75940i −0.379604 0.216605i
\(708\) 1.55134 + 0.415679i 0.0583028 + 0.0156222i
\(709\) −13.4262 + 3.59754i −0.504231 + 0.135108i −0.501963 0.864889i \(-0.667389\pi\)
−0.00226813 + 0.999997i \(0.500722\pi\)
\(710\) −11.1812 41.7289i −0.419623 1.56606i
\(711\) −11.0871 −0.415800
\(712\) −7.47365 −0.280087
\(713\) −8.50123 31.7270i −0.318374 1.18819i
\(714\) 3.68902 + 13.4935i 0.138058 + 0.504982i
\(715\) −21.0473 40.5949i −0.787126 1.51816i
\(716\) −0.876146 1.51753i −0.0327431 0.0567128i
\(717\) −4.26670 + 15.9235i −0.159343 + 0.594675i
\(718\) −5.76710 9.98891i −0.215226 0.372783i
\(719\) 24.5650 42.5477i 0.916118 1.58676i 0.110862 0.993836i \(-0.464639\pi\)
0.805256 0.592927i \(-0.202028\pi\)
\(720\) 12.6569 + 12.6569i 0.471693 + 0.471693i
\(721\) 30.6934 + 17.5139i 1.14308 + 0.652252i
\(722\) −7.55274 + 28.1872i −0.281084 + 1.04902i
\(723\) 1.46113 5.45299i 0.0543398 0.202799i
\(724\) 13.2228i 0.491421i
\(725\) 22.5283 13.0067i 0.836682 0.483059i
\(726\) −0.413722 + 0.413722i −0.0153547 + 0.0153547i
\(727\) 19.4676 0.722014 0.361007 0.932563i \(-0.382433\pi\)
0.361007 + 0.932563i \(0.382433\pi\)
\(728\) −15.2772 16.5580i −0.566210 0.613681i
\(729\) −1.00000 −0.0370370
\(730\) −9.11238 + 9.11238i −0.337264 + 0.337264i
\(731\) −36.4819 + 21.0628i −1.34933 + 0.779037i
\(732\) 0.530472i 0.0196068i
\(733\) 1.81677 6.78026i 0.0671038 0.250435i −0.924223 0.381852i \(-0.875286\pi\)
0.991327 + 0.131418i \(0.0419529\pi\)
\(734\) 1.76768 6.59709i 0.0652464 0.243503i
\(735\) 25.4993 + 6.55605i 0.940557 + 0.241823i
\(736\) 7.09041 + 7.09041i 0.261356 + 0.261356i
\(737\) 4.98764 8.63885i 0.183722 0.318216i
\(738\) −5.61151 9.71942i −0.206563 0.357777i
\(739\) 10.3392 38.5863i 0.380332 1.41942i −0.465063 0.885278i \(-0.653968\pi\)
0.845395 0.534142i \(-0.179365\pi\)
\(740\) −10.8449 18.7839i −0.398666 0.690509i
\(741\) −2.67527 + 0.588464i −0.0982785 + 0.0216178i
\(742\) 21.4019 + 21.1859i 0.785690 + 0.777760i
\(743\) −9.49010 35.4175i −0.348158 1.29934i −0.888879 0.458141i \(-0.848515\pi\)
0.540721 0.841202i \(-0.318151\pi\)
\(744\) −21.7751 −0.798314
\(745\) −56.5089 −2.07033
\(746\) −7.04119 26.2781i −0.257796 0.962109i
\(747\) −2.06557 + 0.553469i −0.0755754 + 0.0202504i
\(748\) 5.53384 + 1.48279i 0.202337 + 0.0542161i
\(749\) 0.405640 0.236948i 0.0148218 0.00865788i
\(750\) −12.3531 21.3962i −0.451072 0.781279i
\(751\) 19.4504i 0.709755i 0.934913 + 0.354877i \(0.115477\pi\)
−0.934913 + 0.354877i \(0.884523\pi\)
\(752\) 6.32488 + 1.69475i 0.230645 + 0.0618010i
\(753\) −9.59948 5.54226i −0.349825 0.201971i
\(754\) 4.90972 15.4825i 0.178802 0.563841i
\(755\) 1.04446i 0.0380119i
\(756\) −1.16289 + 0.679283i −0.0422939 + 0.0247053i
\(757\) 3.02968 5.24756i 0.110116 0.190726i −0.805701 0.592322i \(-0.798211\pi\)
0.915817 + 0.401597i \(0.131545\pi\)
\(758\) 3.19515 + 1.84472i 0.116053 + 0.0670032i
\(759\) 11.6027 3.10894i 0.421153 0.112848i
\(760\) −4.77194 + 4.77194i −0.173096 + 0.173096i
\(761\) −7.80535 29.1300i −0.282944 1.05596i −0.950329 0.311247i \(-0.899253\pi\)
0.667385 0.744713i \(-0.267413\pi\)
\(762\) 8.72407 8.72407i 0.316040 0.316040i
\(763\) −9.76645 9.66789i −0.353569 0.350001i
\(764\) 1.31502 + 0.759229i 0.0475759 + 0.0274679i
\(765\) −8.87752 8.87752i −0.320967 0.320967i
\(766\) −21.8270 + 37.8055i −0.788641 + 1.36597i
\(767\) 11.1105 2.44392i 0.401178 0.0882450i
\(768\) 9.95269 5.74619i 0.359137 0.207348i
\(769\) 22.1109 5.92460i 0.797339 0.213646i 0.162924 0.986639i \(-0.447908\pi\)
0.634415 + 0.772992i \(0.281241\pi\)
\(770\) 37.3914 37.7726i 1.34749 1.36123i
\(771\) −2.08124 + 1.20160i −0.0749540 + 0.0432747i
\(772\) −1.28534 0.344405i −0.0462603 0.0123954i
\(773\) 10.6208 + 10.6208i 0.382004 + 0.382004i 0.871824 0.489820i \(-0.162937\pi\)
−0.489820 + 0.871824i \(0.662937\pi\)
\(774\) −14.1354 14.1354i −0.508087 0.508087i
\(775\) 81.4619 + 21.8277i 2.92620 + 0.784073i
\(776\) −25.5247 + 14.7367i −0.916283 + 0.529016i
\(777\) −28.9123 + 7.90440i −1.03722 + 0.283569i
\(778\) −19.0090 + 5.09345i −0.681506 + 0.182609i
\(779\) 4.66170 2.69143i 0.167023 0.0964306i
\(780\) −6.58012 2.08664i −0.235606 0.0747139i
\(781\) −12.2250 + 21.1743i −0.437444 + 0.757675i
\(782\) −13.3187 13.3187i −0.476276 0.476276i
\(783\) 2.46295 + 1.42199i 0.0880187 + 0.0508176i
\(784\) 16.3628 29.0170i 0.584386 1.03632i
\(785\) −0.836308 + 0.836308i −0.0298491 + 0.0298491i
\(786\) −3.98017 14.8542i −0.141968 0.529831i
\(787\) −6.19869 + 6.19869i −0.220959 + 0.220959i −0.808902 0.587943i \(-0.799938\pi\)
0.587943 + 0.808902i \(0.299938\pi\)
\(788\) 0.405946 0.108773i 0.0144612 0.00387487i
\(789\) 22.6246 + 13.0623i 0.805456 + 0.465030i
\(790\) 33.0273 57.2049i 1.17506 2.03526i
\(791\) 45.9956 + 26.2454i 1.63541 + 0.933180i
\(792\) 7.96327i 0.282962i
\(793\) −1.72951 3.33577i −0.0614165 0.118457i
\(794\) −44.3277 25.5926i −1.57313 0.908248i
\(795\) −26.1065 6.99523i −0.925904 0.248095i
\(796\) 4.17488i 0.147975i
\(797\) 21.7995 + 37.7578i 0.772177 + 1.33745i 0.936367 + 0.351021i \(0.114166\pi\)
−0.164190 + 0.986429i \(0.552501\pi\)
\(798\) −1.60591 2.74922i −0.0568485 0.0973212i
\(799\) −4.43627 1.18869i −0.156944 0.0420530i
\(800\) −24.8688 + 6.66358i −0.879246 + 0.235593i
\(801\) 0.819042 + 3.05671i 0.0289394 + 0.108003i
\(802\) −22.3098 −0.787787
\(803\) 7.29344 0.257380
\(804\) −0.389755 1.45459i −0.0137456 0.0512993i
\(805\) −34.1960 + 9.34894i −1.20525 + 0.329507i
\(806\) 46.7479 24.2375i 1.64663 0.853729i
\(807\) −13.2101 22.8806i −0.465018 0.805435i
\(808\) 2.68482 10.0199i 0.0944517 0.352498i
\(809\) −6.30114 10.9139i −0.221536 0.383712i 0.733738 0.679432i \(-0.237774\pi\)
−0.955275 + 0.295720i \(0.904440\pi\)
\(810\) 2.97888 5.15957i 0.104667 0.181289i
\(811\) −13.6469 13.6469i −0.479208 0.479208i 0.425670 0.904878i \(-0.360038\pi\)
−0.904878 + 0.425670i \(0.860038\pi\)
\(812\) 3.83007 0.0194252i 0.134409 0.000681691i
\(813\) −1.96029 + 7.31591i −0.0687504 + 0.256580i
\(814\) −15.6604 + 58.4454i −0.548896 + 2.04851i
\(815\) 3.55109i 0.124389i
\(816\) −13.7568 + 7.94249i −0.481584 + 0.278043i
\(817\) 6.77972 6.77972i 0.237192 0.237192i
\(818\) −46.6777 −1.63205
\(819\) −5.09795 + 8.06293i −0.178137 + 0.281742i
\(820\) 13.5652 0.473718
\(821\) −19.5518 + 19.5518i −0.682363 + 0.682363i −0.960532 0.278169i \(-0.910272\pi\)
0.278169 + 0.960532i \(0.410272\pi\)
\(822\) −12.4665 + 7.19752i −0.434818 + 0.251042i
\(823\) 14.0080i 0.488288i −0.969739 0.244144i \(-0.921493\pi\)
0.969739 0.244144i \(-0.0785070\pi\)
\(824\) −8.16433 + 30.4697i −0.284418 + 1.06146i
\(825\) −7.98249 + 29.7911i −0.277915 + 1.03719i
\(826\) 6.66942 + 11.4176i 0.232059 + 0.397271i
\(827\) 25.9908 + 25.9908i 0.903790 + 0.903790i 0.995762 0.0919718i \(-0.0293170\pi\)
−0.0919718 + 0.995762i \(0.529317\pi\)
\(828\) 0.906686 1.57043i 0.0315095 0.0545761i
\(829\) −1.59143 2.75645i −0.0552728 0.0957353i 0.837065 0.547103i \(-0.184270\pi\)
−0.892338 + 0.451368i \(0.850936\pi\)
\(830\) 3.29743 12.3062i 0.114456 0.427154i
\(831\) 11.2715 + 19.5228i 0.391004 + 0.677238i
\(832\) 9.82669 15.3688i 0.340679 0.532817i
\(833\) −11.4769 + 20.3525i −0.397650 + 0.705173i
\(834\) −4.19173 15.6437i −0.145148 0.541699i
\(835\) −9.10595 −0.315124
\(836\) −1.30396 −0.0450983
\(837\) 2.38635 + 8.90596i 0.0824842 + 0.307835i
\(838\) −18.8030 + 5.03824i −0.649538 + 0.174043i
\(839\) 15.7489 + 4.21991i 0.543713 + 0.145687i 0.520213 0.854036i \(-0.325852\pi\)
0.0234997 + 0.999724i \(0.492519\pi\)
\(840\) 0.119194 + 23.5016i 0.00411259 + 0.810881i
\(841\) 10.4559 + 18.1102i 0.360549 + 0.624489i
\(842\) 13.6238i 0.469506i
\(843\) −10.5659 2.83113i −0.363910 0.0975093i
\(844\) −4.73838 2.73570i −0.163102 0.0941668i
\(845\) −48.1810 + 8.33178i −1.65748 + 0.286622i
\(846\) 2.17947i 0.0749316i
\(847\) −0.977270 + 0.00495647i −0.0335794 + 0.000170306i
\(848\) −17.0984 + 29.6153i −0.587161 + 1.01699i
\(849\) 15.3550 + 8.86524i 0.526984 + 0.304254i
\(850\) 46.7139 12.5169i 1.60227 0.429328i
\(851\) 28.5377 28.5377i 0.978260 0.978260i
\(852\) 0.955310 + 3.56527i 0.0327284 + 0.122144i
\(853\) 1.18686 1.18686i 0.0406374 0.0406374i −0.686496 0.727133i \(-0.740852\pi\)
0.727133 + 0.686496i \(0.240852\pi\)
\(854\) 3.07253 3.10386i 0.105140 0.106212i
\(855\) 2.47467 + 1.42875i 0.0846319 + 0.0488623i
\(856\) 0.296516 + 0.296516i 0.0101347 + 0.0101347i
\(857\) −13.8735 + 24.0297i −0.473911 + 0.820838i −0.999554 0.0298676i \(-0.990491\pi\)
0.525643 + 0.850705i \(0.323825\pi\)
\(858\) 8.86378 + 17.0960i 0.302604 + 0.583647i
\(859\) 33.2801 19.2142i 1.13550 0.655582i 0.190188 0.981748i \(-0.439090\pi\)
0.945313 + 0.326166i \(0.105757\pi\)
\(860\) 23.3391 6.25369i 0.795856 0.213249i
\(861\) 4.75990 18.1315i 0.162217 0.617921i
\(862\) 46.7952 27.0172i 1.59385 0.920210i
\(863\) −35.6421 9.55027i −1.21327 0.325095i −0.405226 0.914216i \(-0.632807\pi\)
−0.808044 + 0.589122i \(0.799474\pi\)
\(864\) −1.99032 1.99032i −0.0677120 0.0677120i
\(865\) 45.8023 + 45.8023i 1.55732 + 1.55732i
\(866\) 45.2864 + 12.1344i 1.53889 + 0.412345i
\(867\) −5.07343 + 2.92914i −0.172303 + 0.0994790i
\(868\) 8.82473 + 8.73566i 0.299531 + 0.296508i
\(869\) −36.1104 + 9.67574i −1.22496 + 0.328227i
\(870\) −14.6737 + 8.47185i −0.497484 + 0.287222i
\(871\) −7.19331 7.87617i −0.243736 0.266874i
\(872\) 6.13344 10.6234i 0.207705 0.359755i
\(873\) 8.82454 + 8.82454i 0.298665 + 0.298665i
\(874\) 3.71268 + 2.14352i 0.125583 + 0.0725055i
\(875\) 10.4784 39.9145i 0.354234 1.34936i
\(876\) 0.778552 0.778552i 0.0263048 0.0263048i
\(877\) −12.2105 45.5701i −0.412318 1.53879i −0.790148 0.612916i \(-0.789996\pi\)
0.377830 0.925875i \(-0.376670\pi\)
\(878\) 20.6409 20.6409i 0.696595 0.696595i
\(879\) −12.4507 + 3.33616i −0.419953 + 0.112526i
\(880\) 52.2685 + 30.1772i 1.76197 + 1.01727i
\(881\) 6.77602 11.7364i 0.228290 0.395410i −0.729011 0.684501i \(-0.760020\pi\)
0.957301 + 0.289092i \(0.0933533\pi\)
\(882\) −10.7387 2.76098i −0.361590 0.0929672i
\(883\) 35.2962i 1.18781i −0.804534 0.593907i \(-0.797585\pi\)
0.804534 0.593907i \(-0.202415\pi\)
\(884\) 3.30009 5.16129i 0.110994 0.173593i
\(885\) −10.2774 5.93368i −0.345472 0.199459i
\(886\) −8.79853 2.35756i −0.295592 0.0792037i
\(887\) 12.5265i 0.420599i −0.977637 0.210300i \(-0.932556\pi\)
0.977637 0.210300i \(-0.0674440\pi\)
\(888\) −13.3776 23.1707i −0.448923 0.777558i
\(889\) 20.6075 0.104516i 0.691153 0.00350536i
\(890\) −18.2111 4.87966i −0.610438 0.163566i
\(891\) −3.25696 + 0.872699i −0.109112 + 0.0292365i
\(892\) −0.782969 2.92208i −0.0262157 0.0978384i
\(893\) 1.04533 0.0349807
\(894\) 23.7979 0.795921
\(895\) 3.35116 + 12.5067i 0.112017 + 0.418053i
\(896\) 34.9142 + 9.16569i 1.16640 + 0.306204i
\(897\) 0.581443 12.8314i 0.0194138 0.428429i
\(898\) −15.5985 27.0173i −0.520528 0.901580i
\(899\) 6.78670 25.3283i 0.226349 0.844746i
\(900\) 2.32800 + 4.03221i 0.0775999 + 0.134407i
\(901\) 11.9928 20.7722i 0.399538 0.692021i
\(902\) −26.7586 26.7586i −0.890963 0.890963i
\(903\) −0.169345 33.3898i −0.00563545 1.11114i
\(904\) −12.2346 + 45.6603i −0.406918 + 1.51864i
\(905\) −25.2878 + 94.3754i −0.840595 + 3.13714i
\(906\) 0.439861i 0.0146134i
\(907\) 32.7297 18.8965i 1.08677 0.627447i 0.154056 0.988062i \(-0.450767\pi\)
0.932715 + 0.360615i \(0.117433\pi\)
\(908\) −7.33803 + 7.33803i −0.243521 + 0.243521i
\(909\) −4.39234 −0.145685
\(910\) −26.4151 50.3218i −0.875652 1.66815i
\(911\) −15.1976 −0.503520 −0.251760 0.967790i \(-0.581009\pi\)
−0.251760 + 0.967790i \(0.581009\pi\)
\(912\) 2.55653 2.55653i 0.0846553 0.0846553i
\(913\) −6.24447 + 3.60525i −0.206662 + 0.119316i
\(914\) 4.92629i 0.162947i
\(915\) −1.01450 + 3.78615i −0.0335382 + 0.125166i
\(916\) −1.13072 + 4.21991i −0.0373601 + 0.139430i
\(917\) 12.7302 22.3099i 0.420387 0.736736i
\(918\) 3.73864 + 3.73864i 0.123393 + 0.123393i
\(919\) 9.49306 16.4425i 0.313147 0.542387i −0.665895 0.746046i \(-0.731950\pi\)
0.979042 + 0.203659i \(0.0652834\pi\)
\(920\) −15.8224 27.4052i −0.521649 0.903522i
\(921\) −2.13138 + 7.95443i −0.0702315 + 0.262108i
\(922\) −24.8978 43.1242i −0.819964 1.42022i
\(923\) 17.6312 + 19.3049i 0.580337 + 0.635429i
\(924\) −3.19468 + 3.22725i −0.105097 + 0.106169i
\(925\) 26.8198 + 100.093i 0.881830 + 3.29103i
\(926\) 23.0621 0.757868
\(927\) 13.3568 0.438694
\(928\) 2.07185 + 7.73226i 0.0680119 + 0.253824i
\(929\) 25.9735 6.95959i 0.852164 0.228337i 0.193804 0.981040i \(-0.437917\pi\)
0.658360 + 0.752704i \(0.271251\pi\)
\(930\) −53.0596 14.2173i −1.73989 0.466203i
\(931\) 1.32424 5.15056i 0.0434003 0.168803i
\(932\) −1.27978 2.21665i −0.0419207 0.0726089i
\(933\) 27.0568i 0.885799i
\(934\) −19.1721 5.13714i −0.627330 0.168092i
\(935\) −36.6611 21.1663i −1.19895 0.692212i
\(936\) −8.11685 2.57396i −0.265308 0.0841326i
\(937\) 55.8288i 1.82385i 0.410358 + 0.911924i \(0.365404\pi\)
−0.410358 + 0.911924i \(0.634596\pi\)
\(938\) 6.14456 10.7685i 0.200627 0.351602i
\(939\) 6.86374 11.8883i 0.223990 0.387962i
\(940\) 2.28138 + 1.31716i 0.0744104 + 0.0429609i
\(941\) −48.0434 + 12.8732i −1.56617 + 0.419654i −0.934610 0.355675i \(-0.884251\pi\)
−0.631559 + 0.775328i \(0.717584\pi\)
\(942\) 0.352199 0.352199i 0.0114753 0.0114753i
\(943\) 6.53284 + 24.3809i 0.212739 + 0.793951i
\(944\) −10.6174 + 10.6174i −0.345568 + 0.345568i
\(945\) 9.59903 2.62430i 0.312256 0.0853685i
\(946\) −58.3744 33.7025i −1.89791 1.09576i
\(947\) 22.6510 + 22.6510i 0.736057 + 0.736057i 0.971812 0.235755i \(-0.0757564\pi\)
−0.235755 + 0.971812i \(0.575756\pi\)
\(948\) −2.82181 + 4.88752i −0.0916482 + 0.158739i
\(949\) 2.35746 7.43410i 0.0765262 0.241321i
\(950\) −9.53263 + 5.50367i −0.309279 + 0.178563i
\(951\) 2.23807 0.599689i 0.0725743 0.0194462i
\(952\) −20.1733 5.29590i −0.653819 0.171641i
\(953\) −25.2887 + 14.6005i −0.819182 + 0.472955i −0.850134 0.526566i \(-0.823479\pi\)
0.0309522 + 0.999521i \(0.490146\pi\)
\(954\) 10.9944 + 2.94594i 0.355957 + 0.0953783i
\(955\) −7.93377 7.93377i −0.256731 0.256731i
\(956\) 5.93361 + 5.93361i 0.191907 + 0.191907i
\(957\) 9.26269 + 2.48193i 0.299420 + 0.0802294i
\(958\) 28.7625 16.6060i 0.929274 0.536517i
\(959\) −23.2561 6.10522i −0.750980 0.197148i
\(960\) −18.3811 + 4.92519i −0.593247 + 0.158960i
\(961\) 46.7748 27.0054i 1.50886 0.871143i
\(962\) 54.5107 + 34.8537i 1.75749 + 1.12373i
\(963\) 0.0887791 0.153770i 0.00286087 0.00495516i
\(964\) −2.03196 2.03196i −0.0654450 0.0654450i
\(965\) 8.51522 + 4.91627i 0.274115 + 0.158260i
\(966\) 14.4012 3.93717i 0.463350 0.126676i
\(967\) −28.2620 + 28.2620i −0.908844 + 0.908844i −0.996179 0.0873352i \(-0.972165\pi\)
0.0873352 + 0.996179i \(0.472165\pi\)
\(968\) −0.225782 0.842631i −0.00725692 0.0270832i
\(969\) −1.79315 + 1.79315i −0.0576043 + 0.0576043i
\(970\) −71.8181 + 19.2436i −2.30594 + 0.617875i
\(971\) −12.1286 7.00245i −0.389225 0.224719i 0.292599 0.956235i \(-0.405480\pi\)
−0.681824 + 0.731516i \(0.738813\pi\)
\(972\) −0.254512 + 0.440828i −0.00816348 + 0.0141396i
\(973\) 13.4068 23.4957i 0.429803 0.753238i
\(974\) 17.0854i 0.547450i
\(975\) 27.7854 + 17.7658i 0.889846 + 0.568961i
\(976\) 4.29502 + 2.47973i 0.137480 + 0.0793742i
\(977\) −20.3161 5.44369i −0.649970 0.174159i −0.0812550 0.996693i \(-0.525893\pi\)
−0.568716 + 0.822534i \(0.692559\pi\)
\(978\) 1.49549i 0.0478205i
\(979\) 5.33517 + 9.24079i 0.170513 + 0.295337i
\(980\) 9.37998 9.57223i 0.299633 0.305774i
\(981\) −5.01713 1.34434i −0.160185 0.0429213i
\(982\) 54.2942 14.5481i 1.73260 0.464248i
\(983\) 1.96757 + 7.34307i 0.0627558 + 0.234208i 0.990179 0.139806i \(-0.0446479\pi\)
−0.927423 + 0.374014i \(0.877981\pi\)
\(984\) 16.7333 0.533437
\(985\) −3.10539 −0.0989460
\(986\) −3.89179 14.5244i −0.123940 0.462550i
\(987\) 2.56105 2.58716i 0.0815192 0.0823503i
\(988\) −0.421477 + 1.32910i −0.0134090 + 0.0422845i
\(989\) 22.4796 + 38.9359i 0.714811 + 1.23809i
\(990\) 5.19933 19.4042i 0.165246 0.616705i
\(991\) −12.3131 21.3269i −0.391138 0.677470i 0.601462 0.798901i \(-0.294585\pi\)
−0.992600 + 0.121431i \(0.961252\pi\)
\(992\) −12.9761 + 22.4753i −0.411992 + 0.713592i
\(993\) 18.2666 + 18.2666i 0.579674 + 0.579674i
\(994\) −15.0606 + 26.3940i −0.477695 + 0.837168i
\(995\) 7.98422 29.7975i 0.253117 0.944645i
\(996\) −0.281729 + 1.05143i −0.00892692 + 0.0333157i
\(997\) 16.4760i 0.521801i −0.965366 0.260901i \(-0.915980\pi\)
0.965366 0.260901i \(-0.0840195\pi\)
\(998\) −7.04379 + 4.06674i −0.222967 + 0.128730i
\(999\) −8.01070 + 8.01070i −0.253447 + 0.253447i
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 273.2.bt.a.136.8 36
3.2 odd 2 819.2.et.c.136.2 36
7.5 odd 6 273.2.cg.a.19.2 yes 36
13.11 odd 12 273.2.cg.a.115.2 yes 36
21.5 even 6 819.2.gh.c.19.8 36
39.11 even 12 819.2.gh.c.388.8 36
91.89 even 12 inner 273.2.bt.a.271.8 yes 36
273.89 odd 12 819.2.et.c.271.2 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.bt.a.136.8 36 1.1 even 1 trivial
273.2.bt.a.271.8 yes 36 91.89 even 12 inner
273.2.cg.a.19.2 yes 36 7.5 odd 6
273.2.cg.a.115.2 yes 36 13.11 odd 12
819.2.et.c.136.2 36 3.2 odd 2
819.2.et.c.271.2 36 273.89 odd 12
819.2.gh.c.19.8 36 21.5 even 6
819.2.gh.c.388.8 36 39.11 even 12