Properties

Label 124.2.j.a.27.2
Level $124$
Weight $2$
Character 124.27
Analytic conductor $0.990$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [124,2,Mod(15,124)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(124, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("124.15");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 124.j (of order \(10\), 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: \(0.990144985064\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 27.2
Root \(0.587785 + 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 124.27
Dual form 124.2.j.a.23.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.26007 + 0.642040i) q^{2} +(-0.224514 + 0.690983i) q^{3} +(1.17557 + 1.61803i) q^{4} +0.618034 q^{5} +(-0.726543 + 0.726543i) q^{6} +(-2.48990 - 3.42705i) q^{7} +(0.442463 + 2.79360i) q^{8} +(2.00000 + 1.45309i) q^{9} +O(q^{10})\) \(q+(1.26007 + 0.642040i) q^{2} +(-0.224514 + 0.690983i) q^{3} +(1.17557 + 1.61803i) q^{4} +0.618034 q^{5} +(-0.726543 + 0.726543i) q^{6} +(-2.48990 - 3.42705i) q^{7} +(0.442463 + 2.79360i) q^{8} +(2.00000 + 1.45309i) q^{9} +(0.778768 + 0.396802i) q^{10} +(-1.17557 + 0.854102i) q^{11} +(-1.38197 + 0.449028i) q^{12} +(-4.73607 - 1.53884i) q^{13} +(-0.937153 - 5.91695i) q^{14} +(-0.138757 + 0.427051i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(4.04508 - 5.56758i) q^{17} +(1.58721 + 3.11507i) q^{18} +(4.75528 - 1.54508i) q^{19} +(0.726543 + 1.00000i) q^{20} +(2.92705 - 0.951057i) q^{21} +(-2.02967 + 0.321469i) q^{22} +(-2.48990 - 1.80902i) q^{23} +(-2.02967 - 0.321469i) q^{24} -4.61803 q^{25} +(-4.97980 - 4.97980i) q^{26} +(-3.21644 + 2.33688i) q^{27} +(2.61803 - 8.05748i) q^{28} +(-3.19098 + 1.03681i) q^{29} +(-0.449028 + 0.449028i) q^{30} +(2.85317 + 4.78115i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-0.326238 - 1.00406i) q^{33} +(8.67171 - 4.41846i) q^{34} +(-1.53884 - 2.11803i) q^{35} +4.94427i q^{36} +2.17963i q^{37} +(6.98401 + 1.10616i) q^{38} +(2.12663 - 2.92705i) q^{39} +(0.273457 + 1.72654i) q^{40} +(-0.236068 - 0.726543i) q^{41} +(4.29892 + 0.680881i) q^{42} +(1.31433 + 4.04508i) q^{43} +(-2.76393 - 0.898056i) q^{44} +(1.23607 + 0.898056i) q^{45} +(-1.97599 - 3.87811i) q^{46} +(3.21644 + 1.04508i) q^{47} +(-2.35114 - 1.70820i) q^{48} +(-3.38197 + 10.4086i) q^{49} +(-5.81906 - 2.96496i) q^{50} +(2.93893 + 4.04508i) q^{51} +(-3.07768 - 9.47214i) q^{52} +(1.28115 - 1.76336i) q^{53} +(-5.55332 + 0.879560i) q^{54} +(-0.726543 + 0.527864i) q^{55} +(8.47214 - 8.47214i) q^{56} +3.63271i q^{57} +(-4.68655 - 0.742276i) q^{58} +(3.30220 + 1.07295i) q^{59} +(-0.854102 + 0.277515i) q^{60} +9.95959i q^{61} +(0.525514 + 7.85645i) q^{62} -10.4721i q^{63} +(-7.60845 + 2.47214i) q^{64} +(-2.92705 - 0.951057i) q^{65} +(0.233561 - 1.47464i) q^{66} +10.2361i q^{67} +13.7638 q^{68} +(1.80902 - 1.31433i) q^{69} +(-0.579192 - 3.65688i) q^{70} +(2.57565 - 3.54508i) q^{71} +(-3.17442 + 6.23015i) q^{72} +(-0.690983 - 0.951057i) q^{73} +(-1.39941 + 2.74649i) q^{74} +(1.03681 - 3.19098i) q^{75} +(8.09017 + 5.87785i) q^{76} +(5.85410 + 1.90211i) q^{77} +(4.55899 - 2.32292i) q^{78} +(-11.8617 - 8.61803i) q^{79} +(-0.763932 + 2.35114i) q^{80} +(1.39919 + 4.30625i) q^{81} +(0.169006 - 1.06706i) q^{82} +(1.98787 + 6.11803i) q^{83} +(4.97980 + 3.61803i) q^{84} +(2.50000 - 3.44095i) q^{85} +(-0.940955 + 5.94095i) q^{86} -2.43769i q^{87} +(-2.90617 - 2.90617i) q^{88} +(-10.1631 - 13.9883i) q^{89} +(0.980949 + 1.92522i) q^{90} +(6.51864 + 20.0623i) q^{91} -6.15537i q^{92} +(-3.94427 + 0.898056i) q^{93} +(3.38197 + 3.38197i) q^{94} +(2.93893 - 0.954915i) q^{95} +(-1.86588 - 3.66199i) q^{96} +(6.04508 - 4.39201i) q^{97} +(-10.9443 + 10.9443i) q^{98} -3.59222 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + 16 q^{9} + 6 q^{10} - 20 q^{12} - 20 q^{13} - 14 q^{14} + 8 q^{16} + 10 q^{17} - 24 q^{18} + 10 q^{21} + 20 q^{22} + 20 q^{24} - 28 q^{25} + 12 q^{28} - 30 q^{29} - 32 q^{32} + 60 q^{33} + 30 q^{34} + 10 q^{38} + 8 q^{40} + 16 q^{41} + 10 q^{42} - 40 q^{44} - 8 q^{45} - 10 q^{46} - 36 q^{49} + 2 q^{50} - 30 q^{53} - 50 q^{54} + 32 q^{56} + 20 q^{58} + 20 q^{60} + 38 q^{62} - 10 q^{65} - 20 q^{66} + 10 q^{69} - 8 q^{70} + 48 q^{72} - 10 q^{73} - 30 q^{74} + 20 q^{76} + 20 q^{77} - 24 q^{80} - 38 q^{81} - 4 q^{82} + 20 q^{85} + 20 q^{86} - 50 q^{89} + 32 q^{90} + 40 q^{93} + 36 q^{94} - 40 q^{96} + 26 q^{97} - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).

\(n\) \(63\) \(65\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.26007 + 0.642040i 0.891007 + 0.453990i
\(3\) −0.224514 + 0.690983i −0.129623 + 0.398939i −0.994715 0.102674i \(-0.967260\pi\)
0.865092 + 0.501614i \(0.167260\pi\)
\(4\) 1.17557 + 1.61803i 0.587785 + 0.809017i
\(5\) 0.618034 0.276393 0.138197 0.990405i \(-0.455869\pi\)
0.138197 + 0.990405i \(0.455869\pi\)
\(6\) −0.726543 + 0.726543i −0.296610 + 0.296610i
\(7\) −2.48990 3.42705i −0.941093 1.29530i −0.955372 0.295405i \(-0.904545\pi\)
0.0142789 0.999898i \(-0.495455\pi\)
\(8\) 0.442463 + 2.79360i 0.156434 + 0.987688i
\(9\) 2.00000 + 1.45309i 0.666667 + 0.484362i
\(10\) 0.778768 + 0.396802i 0.246268 + 0.125480i
\(11\) −1.17557 + 0.854102i −0.354448 + 0.257521i −0.750733 0.660606i \(-0.770299\pi\)
0.396285 + 0.918128i \(0.370299\pi\)
\(12\) −1.38197 + 0.449028i −0.398939 + 0.129623i
\(13\) −4.73607 1.53884i −1.31355 0.426798i −0.433274 0.901262i \(-0.642642\pi\)
−0.880275 + 0.474464i \(0.842642\pi\)
\(14\) −0.937153 5.91695i −0.250465 1.58137i
\(15\) −0.138757 + 0.427051i −0.0358270 + 0.110264i
\(16\) −1.23607 + 3.80423i −0.309017 + 0.951057i
\(17\) 4.04508 5.56758i 0.981077 1.35034i 0.0448301 0.998995i \(-0.485725\pi\)
0.936247 0.351342i \(-0.114275\pi\)
\(18\) 1.58721 + 3.11507i 0.374109 + 0.734230i
\(19\) 4.75528 1.54508i 1.09094 0.354467i 0.292328 0.956318i \(-0.405570\pi\)
0.798608 + 0.601851i \(0.205570\pi\)
\(20\) 0.726543 + 1.00000i 0.162460 + 0.223607i
\(21\) 2.92705 0.951057i 0.638735 0.207538i
\(22\) −2.02967 + 0.321469i −0.432728 + 0.0685373i
\(23\) −2.48990 1.80902i −0.519180 0.377206i 0.297115 0.954842i \(-0.403975\pi\)
−0.816295 + 0.577636i \(0.803975\pi\)
\(24\) −2.02967 0.321469i −0.414305 0.0656195i
\(25\) −4.61803 −0.923607
\(26\) −4.97980 4.97980i −0.976618 0.976618i
\(27\) −3.21644 + 2.33688i −0.619004 + 0.449733i
\(28\) 2.61803 8.05748i 0.494762 1.52272i
\(29\) −3.19098 + 1.03681i −0.592551 + 0.192531i −0.589915 0.807465i \(-0.700839\pi\)
−0.00263539 + 0.999997i \(0.500839\pi\)
\(30\) −0.449028 + 0.449028i −0.0819809 + 0.0819809i
\(31\) 2.85317 + 4.78115i 0.512444 + 0.858720i
\(32\) −4.00000 + 4.00000i −0.707107 + 0.707107i
\(33\) −0.326238 1.00406i −0.0567907 0.174784i
\(34\) 8.67171 4.41846i 1.48719 0.757759i
\(35\) −1.53884 2.11803i −0.260112 0.358013i
\(36\) 4.94427i 0.824045i
\(37\) 2.17963i 0.358329i 0.983819 + 0.179164i \(0.0573394\pi\)
−0.983819 + 0.179164i \(0.942661\pi\)
\(38\) 6.98401 + 1.10616i 1.13296 + 0.179443i
\(39\) 2.12663 2.92705i 0.340533 0.468703i
\(40\) 0.273457 + 1.72654i 0.0432374 + 0.272990i
\(41\) −0.236068 0.726543i −0.0368676 0.113467i 0.930929 0.365200i \(-0.118999\pi\)
−0.967797 + 0.251733i \(0.918999\pi\)
\(42\) 4.29892 + 0.680881i 0.663337 + 0.105062i
\(43\) 1.31433 + 4.04508i 0.200433 + 0.616870i 0.999870 + 0.0161197i \(0.00513128\pi\)
−0.799437 + 0.600750i \(0.794869\pi\)
\(44\) −2.76393 0.898056i −0.416678 0.135387i
\(45\) 1.23607 + 0.898056i 0.184262 + 0.133874i
\(46\) −1.97599 3.87811i −0.291344 0.571796i
\(47\) 3.21644 + 1.04508i 0.469166 + 0.152441i 0.534052 0.845451i \(-0.320668\pi\)
−0.0648863 + 0.997893i \(0.520668\pi\)
\(48\) −2.35114 1.70820i −0.339358 0.246558i
\(49\) −3.38197 + 10.4086i −0.483138 + 1.48695i
\(50\) −5.81906 2.96496i −0.822940 0.419309i
\(51\) 2.93893 + 4.04508i 0.411532 + 0.566425i
\(52\) −3.07768 9.47214i −0.426798 1.31355i
\(53\) 1.28115 1.76336i 0.175980 0.242216i −0.711911 0.702270i \(-0.752170\pi\)
0.887891 + 0.460054i \(0.152170\pi\)
\(54\) −5.55332 + 0.879560i −0.755711 + 0.119693i
\(55\) −0.726543 + 0.527864i −0.0979670 + 0.0711772i
\(56\) 8.47214 8.47214i 1.13214 1.13214i
\(57\) 3.63271i 0.481165i
\(58\) −4.68655 0.742276i −0.615374 0.0974657i
\(59\) 3.30220 + 1.07295i 0.429909 + 0.139686i 0.515975 0.856603i \(-0.327430\pi\)
−0.0860659 + 0.996289i \(0.527430\pi\)
\(60\) −0.854102 + 0.277515i −0.110264 + 0.0358270i
\(61\) 9.95959i 1.27520i 0.770370 + 0.637598i \(0.220072\pi\)
−0.770370 + 0.637598i \(0.779928\pi\)
\(62\) 0.525514 + 7.85645i 0.0667404 + 0.997770i
\(63\) 10.4721i 1.31937i
\(64\) −7.60845 + 2.47214i −0.951057 + 0.309017i
\(65\) −2.92705 0.951057i −0.363056 0.117964i
\(66\) 0.233561 1.47464i 0.0287493 0.181516i
\(67\) 10.2361i 1.25053i 0.780411 + 0.625267i \(0.215010\pi\)
−0.780411 + 0.625267i \(0.784990\pi\)
\(68\) 13.7638 1.66911
\(69\) 1.80902 1.31433i 0.217780 0.158226i
\(70\) −0.579192 3.65688i −0.0692267 0.437080i
\(71\) 2.57565 3.54508i 0.305674 0.420724i −0.628352 0.777929i \(-0.716270\pi\)
0.934026 + 0.357205i \(0.116270\pi\)
\(72\) −3.17442 + 6.23015i −0.374109 + 0.734230i
\(73\) −0.690983 0.951057i −0.0808734 0.111313i 0.766664 0.642049i \(-0.221915\pi\)
−0.847537 + 0.530736i \(0.821915\pi\)
\(74\) −1.39941 + 2.74649i −0.162678 + 0.319273i
\(75\) 1.03681 3.19098i 0.119721 0.368463i
\(76\) 8.09017 + 5.87785i 0.928006 + 0.674236i
\(77\) 5.85410 + 1.90211i 0.667137 + 0.216766i
\(78\) 4.55899 2.32292i 0.516204 0.263019i
\(79\) −11.8617 8.61803i −1.33455 0.969605i −0.999626 0.0273582i \(-0.991291\pi\)
−0.334921 0.942246i \(-0.608709\pi\)
\(80\) −0.763932 + 2.35114i −0.0854102 + 0.262866i
\(81\) 1.39919 + 4.30625i 0.155465 + 0.478473i
\(82\) 0.169006 1.06706i 0.0186636 0.117837i
\(83\) 1.98787 + 6.11803i 0.218197 + 0.671541i 0.998911 + 0.0466531i \(0.0148555\pi\)
−0.780714 + 0.624888i \(0.785144\pi\)
\(84\) 4.97980 + 3.61803i 0.543340 + 0.394760i
\(85\) 2.50000 3.44095i 0.271163 0.373224i
\(86\) −0.940955 + 5.94095i −0.101466 + 0.640630i
\(87\) 2.43769i 0.261348i
\(88\) −2.90617 2.90617i −0.309799 0.309799i
\(89\) −10.1631 13.9883i −1.07729 1.48276i −0.862471 0.506106i \(-0.831084\pi\)
−0.214817 0.976654i \(-0.568916\pi\)
\(90\) 0.980949 + 1.92522i 0.103401 + 0.202936i
\(91\) 6.51864 + 20.0623i 0.683339 + 2.10310i
\(92\) 6.15537i 0.641741i
\(93\) −3.94427 + 0.898056i −0.409002 + 0.0931241i
\(94\) 3.38197 + 3.38197i 0.348823 + 0.348823i
\(95\) 2.93893 0.954915i 0.301527 0.0979722i
\(96\) −1.86588 3.66199i −0.190435 0.373750i
\(97\) 6.04508 4.39201i 0.613785 0.445941i −0.236960 0.971519i \(-0.576151\pi\)
0.850745 + 0.525578i \(0.176151\pi\)
\(98\) −10.9443 + 10.9443i −1.10554 + 1.10554i
\(99\) −3.59222 −0.361032
\(100\) −5.42882 7.47214i −0.542882 0.747214i
\(101\) 7.23607 + 5.25731i 0.720016 + 0.523122i 0.886389 0.462941i \(-0.153206\pi\)
−0.166374 + 0.986063i \(0.553206\pi\)
\(102\) 1.10616 + 6.98401i 0.109526 + 0.691520i
\(103\) 0.865300 0.281153i 0.0852605 0.0277028i −0.266076 0.963952i \(-0.585727\pi\)
0.351337 + 0.936249i \(0.385727\pi\)
\(104\) 2.20338 13.9116i 0.216059 1.36414i
\(105\) 1.80902 0.587785i 0.176542 0.0573620i
\(106\) 2.74649 1.39941i 0.266763 0.135922i
\(107\) 8.14324 11.2082i 0.787236 1.08354i −0.207210 0.978296i \(-0.566438\pi\)
0.994447 0.105242i \(-0.0335616\pi\)
\(108\) −7.56231 2.45714i −0.727683 0.236439i
\(109\) 2.21885 6.82891i 0.212527 0.654091i −0.786793 0.617217i \(-0.788260\pi\)
0.999320 0.0368738i \(-0.0117400\pi\)
\(110\) −1.25441 + 0.198678i −0.119603 + 0.0189433i
\(111\) −1.50609 0.489357i −0.142951 0.0464477i
\(112\) 16.1150 5.23607i 1.52272 0.494762i
\(113\) 9.35410 6.79615i 0.879960 0.639328i −0.0532810 0.998580i \(-0.516968\pi\)
0.933241 + 0.359251i \(0.116968\pi\)
\(114\) −2.33235 + 4.57748i −0.218444 + 0.428721i
\(115\) −1.53884 1.11803i −0.143498 0.104257i
\(116\) −5.42882 3.94427i −0.504054 0.366216i
\(117\) −7.23607 9.95959i −0.668975 0.920765i
\(118\) 3.47214 + 3.47214i 0.319636 + 0.319636i
\(119\) −29.1522 −2.67238
\(120\) −1.25441 0.198678i −0.114511 0.0181368i
\(121\) −2.74671 + 8.45351i −0.249701 + 0.768501i
\(122\) −6.39445 + 12.5498i −0.578927 + 1.13621i
\(123\) 0.555029 0.0500453
\(124\) −4.38197 + 10.2371i −0.393512 + 0.919319i
\(125\) −5.94427 −0.531672
\(126\) 6.72353 13.1957i 0.598979 1.17556i
\(127\) 1.22857 3.78115i 0.109018 0.335523i −0.881634 0.471933i \(-0.843556\pi\)
0.990652 + 0.136410i \(0.0435564\pi\)
\(128\) −11.1744 1.76985i −0.987688 0.156434i
\(129\) −3.09017 −0.272074
\(130\) −3.07768 3.07768i −0.269931 0.269931i
\(131\) −11.0822 15.2533i −0.968253 1.33269i −0.942924 0.333007i \(-0.891937\pi\)
−0.0253287 0.999679i \(-0.508063\pi\)
\(132\) 1.24108 1.70820i 0.108022 0.148680i
\(133\) −17.1353 12.4495i −1.48582 1.07951i
\(134\) −6.57196 + 12.8982i −0.567731 + 1.11423i
\(135\) −1.98787 + 1.44427i −0.171089 + 0.124303i
\(136\) 17.3434 + 8.83692i 1.48719 + 0.757759i
\(137\) 0.854102 + 0.277515i 0.0729709 + 0.0237097i 0.345275 0.938502i \(-0.387786\pi\)
−0.272304 + 0.962211i \(0.587786\pi\)
\(138\) 3.12334 0.494689i 0.265877 0.0421107i
\(139\) −0.138757 + 0.427051i −0.0117692 + 0.0362220i −0.956769 0.290850i \(-0.906062\pi\)
0.944999 + 0.327072i \(0.106062\pi\)
\(140\) 1.61803 4.97980i 0.136749 0.420870i
\(141\) −1.44427 + 1.98787i −0.121630 + 0.167409i
\(142\) 5.52160 2.81340i 0.463362 0.236095i
\(143\) 6.88191 2.23607i 0.575494 0.186989i
\(144\) −8.00000 + 5.81234i −0.666667 + 0.484362i
\(145\) −1.97214 + 0.640786i −0.163777 + 0.0532144i
\(146\) −0.260074 1.64204i −0.0215238 0.135896i
\(147\) −6.43288 4.67376i −0.530575 0.385485i
\(148\) −3.52671 + 2.56231i −0.289894 + 0.210620i
\(149\) 10.8541 0.889203 0.444601 0.895729i \(-0.353345\pi\)
0.444601 + 0.895729i \(0.353345\pi\)
\(150\) 3.35520 3.35520i 0.273951 0.273951i
\(151\) 12.8128 9.30902i 1.04269 0.757557i 0.0718794 0.997413i \(-0.477100\pi\)
0.970808 + 0.239856i \(0.0771003\pi\)
\(152\) 6.42040 + 12.6007i 0.520763 + 1.02205i
\(153\) 16.1803 5.25731i 1.30810 0.425028i
\(154\) 6.15537 + 6.15537i 0.496014 + 0.496014i
\(155\) 1.76336 + 2.95492i 0.141636 + 0.237344i
\(156\) 7.23607 0.579349
\(157\) −0.291796 0.898056i −0.0232879 0.0716727i 0.938737 0.344634i \(-0.111997\pi\)
−0.962025 + 0.272961i \(0.911997\pi\)
\(158\) −9.41350 18.4750i −0.748898 1.46980i
\(159\) 0.930812 + 1.28115i 0.0738182 + 0.101602i
\(160\) −2.47214 + 2.47214i −0.195440 + 0.195440i
\(161\) 13.0373i 1.02748i
\(162\) −1.00171 + 6.32453i −0.0787016 + 0.496902i
\(163\) −11.7229 + 16.1353i −0.918212 + 1.26381i 0.0460712 + 0.998938i \(0.485330\pi\)
−0.964283 + 0.264873i \(0.914670\pi\)
\(164\) 0.898056 1.23607i 0.0701264 0.0965207i
\(165\) −0.201626 0.620541i −0.0156966 0.0483091i
\(166\) −1.42316 + 8.98546i −0.110458 + 0.697407i
\(167\) −2.52265 7.76393i −0.195209 0.600791i −0.999974 0.00719787i \(-0.997709\pi\)
0.804765 0.593593i \(-0.202291\pi\)
\(168\) 3.95199 + 7.75621i 0.304903 + 0.598405i
\(169\) 9.54508 + 6.93491i 0.734237 + 0.533455i
\(170\) 5.35941 2.73076i 0.411048 0.209440i
\(171\) 11.7557 + 3.81966i 0.898981 + 0.292097i
\(172\) −5.00000 + 6.88191i −0.381246 + 0.524741i
\(173\) 4.95492 15.2497i 0.376715 1.15941i −0.565599 0.824680i \(-0.691355\pi\)
0.942314 0.334730i \(-0.108645\pi\)
\(174\) 1.56510 3.07167i 0.118650 0.232863i
\(175\) 11.4984 + 15.8262i 0.869200 + 1.19635i
\(176\) −1.79611 5.52786i −0.135387 0.416678i
\(177\) −1.48278 + 2.04087i −0.111453 + 0.153401i
\(178\) −3.82521 24.1515i −0.286712 1.81023i
\(179\) −2.12663 + 1.54508i −0.158952 + 0.115485i −0.664418 0.747361i \(-0.731320\pi\)
0.505466 + 0.862846i \(0.331320\pi\)
\(180\) 3.05573i 0.227761i
\(181\) 3.07768i 0.228762i 0.993437 + 0.114381i \(0.0364885\pi\)
−0.993437 + 0.114381i \(0.963511\pi\)
\(182\) −4.66683 + 29.4652i −0.345928 + 2.18411i
\(183\) −6.88191 2.23607i −0.508725 0.165295i
\(184\) 3.95199 7.75621i 0.291344 0.571796i
\(185\) 1.34708i 0.0990396i
\(186\) −5.54666 1.40076i −0.406701 0.102709i
\(187\) 10.0000i 0.731272i
\(188\) 2.09017 + 6.43288i 0.152441 + 0.469166i
\(189\) 16.0172 + 5.20431i 1.16508 + 0.378558i
\(190\) 4.31636 + 0.683644i 0.313141 + 0.0495967i
\(191\) 15.3262i 1.10897i 0.832194 + 0.554484i \(0.187084\pi\)
−0.832194 + 0.554484i \(0.812916\pi\)
\(192\) 5.81234i 0.419470i
\(193\) −12.0172 + 8.73102i −0.865018 + 0.628473i −0.929246 0.369463i \(-0.879542\pi\)
0.0642271 + 0.997935i \(0.479542\pi\)
\(194\) 10.4371 1.65307i 0.749340 0.118684i
\(195\) 1.31433 1.80902i 0.0941210 0.129546i
\(196\) −20.8172 + 6.76393i −1.48695 + 0.483138i
\(197\) 10.9549 + 15.0781i 0.780505 + 1.07427i 0.995226 + 0.0975980i \(0.0311159\pi\)
−0.214721 + 0.976676i \(0.568884\pi\)
\(198\) −4.52647 2.30635i −0.321682 0.163905i
\(199\) 4.75528 14.6353i 0.337093 1.03747i −0.628589 0.777738i \(-0.716367\pi\)
0.965682 0.259728i \(-0.0836329\pi\)
\(200\) −2.04331 12.9010i −0.144484 0.912236i
\(201\) −7.07295 2.29814i −0.498887 0.162098i
\(202\) 5.74258 + 11.2704i 0.404046 + 0.792985i
\(203\) 11.4984 + 8.35410i 0.807032 + 0.586343i
\(204\) −3.09017 + 9.51057i −0.216355 + 0.665873i
\(205\) −0.145898 0.449028i −0.0101900 0.0313615i
\(206\) 1.27085 + 0.201283i 0.0885445 + 0.0140241i
\(207\) −2.35114 7.23607i −0.163416 0.502941i
\(208\) 11.7082 16.1150i 0.811818 1.11737i
\(209\) −4.27051 + 5.87785i −0.295397 + 0.406580i
\(210\) 2.65688 + 0.420808i 0.183342 + 0.0290385i
\(211\) 21.4164i 1.47437i −0.675693 0.737183i \(-0.736155\pi\)
0.675693 0.737183i \(-0.263845\pi\)
\(212\) 4.35926 0.299395
\(213\) 1.87132 + 2.57565i 0.128221 + 0.176481i
\(214\) 17.4572 8.89488i 1.19335 0.608042i
\(215\) 0.812299 + 2.50000i 0.0553983 + 0.170499i
\(216\) −7.95148 7.95148i −0.541030 0.541030i
\(217\) 9.28115 21.6825i 0.630046 1.47191i
\(218\) 7.18034 7.18034i 0.486314 0.486314i
\(219\) 0.812299 0.263932i 0.0548901 0.0178349i
\(220\) −1.70820 0.555029i −0.115167 0.0374201i
\(221\) −27.7254 + 20.1437i −1.86501 + 1.35501i
\(222\) −1.58359 1.58359i −0.106284 0.106284i
\(223\) 9.23305 0.618291 0.309145 0.951015i \(-0.399957\pi\)
0.309145 + 0.951015i \(0.399957\pi\)
\(224\) 23.6678 + 3.74861i 1.58137 + 0.250465i
\(225\) −9.23607 6.71040i −0.615738 0.447360i
\(226\) 16.1503 2.55795i 1.07430 0.170152i
\(227\) 1.71036 0.555728i 0.113520 0.0368850i −0.251706 0.967804i \(-0.580992\pi\)
0.365226 + 0.930919i \(0.380992\pi\)
\(228\) −5.87785 + 4.27051i −0.389270 + 0.282821i
\(229\) −18.0902 + 5.87785i −1.19543 + 0.388419i −0.838078 0.545550i \(-0.816321\pi\)
−0.357354 + 0.933969i \(0.616321\pi\)
\(230\) −1.22123 2.39680i −0.0805256 0.158040i
\(231\) −2.62866 + 3.61803i −0.172953 + 0.238049i
\(232\) −4.30834 8.45559i −0.282856 0.555137i
\(233\) −4.42705 + 13.6251i −0.290026 + 0.892607i 0.694821 + 0.719182i \(0.255483\pi\)
−0.984847 + 0.173425i \(0.944517\pi\)
\(234\) −2.72353 17.1957i −0.178042 1.12412i
\(235\) 1.98787 + 0.645898i 0.129674 + 0.0421337i
\(236\) 2.14590 + 6.60440i 0.139686 + 0.429909i
\(237\) 8.61803 6.26137i 0.559801 0.406720i
\(238\) −36.7340 18.7169i −2.38111 1.21324i
\(239\) 21.3723 + 15.5279i 1.38246 + 1.00441i 0.996646 + 0.0818364i \(0.0260785\pi\)
0.385812 + 0.922578i \(0.373921\pi\)
\(240\) −1.45309 1.05573i −0.0937962 0.0681470i
\(241\) 1.80902 + 2.48990i 0.116529 + 0.160388i 0.863297 0.504696i \(-0.168395\pi\)
−0.746768 + 0.665085i \(0.768395\pi\)
\(242\) −8.88854 + 8.88854i −0.571377 + 0.571377i
\(243\) −15.2169 −0.976165
\(244\) −16.1150 + 11.7082i −1.03165 + 0.749541i
\(245\) −2.09017 + 6.43288i −0.133536 + 0.410982i
\(246\) 0.699377 + 0.356351i 0.0445907 + 0.0227201i
\(247\) −24.8990 −1.58428
\(248\) −12.0942 + 10.0861i −0.767984 + 0.640469i
\(249\) −4.67376 −0.296188
\(250\) −7.49022 3.81646i −0.473723 0.241374i
\(251\) 0.726543 2.23607i 0.0458590 0.141139i −0.925505 0.378735i \(-0.876359\pi\)
0.971364 + 0.237595i \(0.0763592\pi\)
\(252\) 16.9443 12.3107i 1.06739 0.775503i
\(253\) 4.47214 0.281161
\(254\) 3.97574 3.97574i 0.249460 0.249460i
\(255\) 1.81636 + 2.50000i 0.113745 + 0.156556i
\(256\) −12.9443 9.40456i −0.809017 0.587785i
\(257\) −5.61803 4.08174i −0.350443 0.254612i 0.398612 0.917120i \(-0.369492\pi\)
−0.749055 + 0.662508i \(0.769492\pi\)
\(258\) −3.89384 1.98401i −0.242420 0.123519i
\(259\) 7.46969 5.42705i 0.464144 0.337221i
\(260\) −1.90211 5.85410i −0.117964 0.363056i
\(261\) −7.88854 2.56314i −0.488289 0.158655i
\(262\) −4.17113 26.3355i −0.257693 1.62701i
\(263\) −2.59590 + 7.98936i −0.160070 + 0.492645i −0.998639 0.0521502i \(-0.983393\pi\)
0.838569 + 0.544795i \(0.183393\pi\)
\(264\) 2.66059 1.35564i 0.163748 0.0834338i
\(265\) 0.791796 1.08981i 0.0486396 0.0669467i
\(266\) −13.5986 26.6888i −0.833785 1.63639i
\(267\) 11.9475 3.88197i 0.731173 0.237572i
\(268\) −16.5623 + 12.0332i −1.01170 + 0.735046i
\(269\) 26.9336 8.75127i 1.64217 0.533574i 0.665150 0.746710i \(-0.268368\pi\)
0.977023 + 0.213136i \(0.0683677\pi\)
\(270\) −3.43214 + 0.543598i −0.208873 + 0.0330823i
\(271\) 7.69421 + 5.59017i 0.467390 + 0.339579i 0.796423 0.604740i \(-0.206723\pi\)
−0.329033 + 0.944318i \(0.606723\pi\)
\(272\) 16.1803 + 22.2703i 0.981077 + 1.35034i
\(273\) −15.3262 −0.927586
\(274\) 0.898056 + 0.898056i 0.0542535 + 0.0542535i
\(275\) 5.42882 3.94427i 0.327370 0.237849i
\(276\) 4.25325 + 1.38197i 0.256016 + 0.0831846i
\(277\) −4.73607 + 1.53884i −0.284563 + 0.0924600i −0.447821 0.894123i \(-0.647800\pi\)
0.163258 + 0.986583i \(0.447800\pi\)
\(278\) −0.449028 + 0.449028i −0.0269309 + 0.0269309i
\(279\) −1.24108 + 13.7082i −0.0743017 + 0.820689i
\(280\) 5.23607 5.23607i 0.312915 0.312915i
\(281\) 2.82624 + 8.69827i 0.168599 + 0.518895i 0.999283 0.0378488i \(-0.0120505\pi\)
−0.830684 + 0.556744i \(0.812051\pi\)
\(282\) −3.09618 + 1.57758i −0.184375 + 0.0939437i
\(283\) −8.28199 11.3992i −0.492313 0.677611i 0.488499 0.872564i \(-0.337545\pi\)
−0.980813 + 0.194953i \(0.937545\pi\)
\(284\) 8.76393 0.520044
\(285\) 2.24514i 0.132991i
\(286\) 10.1074 + 1.60085i 0.597660 + 0.0946601i
\(287\) −1.90211 + 2.61803i −0.112278 + 0.154538i
\(288\) −13.8123 + 2.18766i −0.813900 + 0.128909i
\(289\) −9.38197 28.8747i −0.551880 1.69851i
\(290\) −2.89645 0.458752i −0.170085 0.0269388i
\(291\) 1.67760 + 5.16312i 0.0983426 + 0.302667i
\(292\) 0.726543 2.23607i 0.0425177 0.130856i
\(293\) −9.51722 6.91467i −0.556002 0.403959i 0.273992 0.961732i \(-0.411656\pi\)
−0.829994 + 0.557773i \(0.811656\pi\)
\(294\) −5.10516 10.0194i −0.297739 0.584346i
\(295\) 2.04087 + 0.663119i 0.118824 + 0.0386083i
\(296\) −6.08902 + 0.964406i −0.353917 + 0.0560549i
\(297\) 1.78522 5.49434i 0.103589 0.318814i
\(298\) 13.6770 + 6.96876i 0.792285 + 0.403690i
\(299\) 9.00854 + 12.3992i 0.520977 + 0.717063i
\(300\) 6.38197 2.07363i 0.368463 0.119721i
\(301\) 10.5902 14.5761i 0.610407 0.840153i
\(302\) 22.1218 3.50375i 1.27297 0.201618i
\(303\) −5.25731 + 3.81966i −0.302025 + 0.219434i
\(304\) 20.0000i 1.14708i
\(305\) 6.15537i 0.352455i
\(306\) 23.7638 + 3.76382i 1.35849 + 0.215163i
\(307\) −29.6870 9.64590i −1.69433 0.550520i −0.706724 0.707489i \(-0.749828\pi\)
−0.987604 + 0.156969i \(0.949828\pi\)
\(308\) 3.80423 + 11.7082i 0.216766 + 0.667137i
\(309\) 0.661030i 0.0376047i
\(310\) 0.324786 + 4.85555i 0.0184466 + 0.275777i
\(311\) 12.7639i 0.723776i −0.932222 0.361888i \(-0.882132\pi\)
0.932222 0.361888i \(-0.117868\pi\)
\(312\) 9.11798 + 4.64584i 0.516204 + 0.263019i
\(313\) 7.76393 + 2.52265i 0.438843 + 0.142589i 0.520102 0.854104i \(-0.325894\pi\)
−0.0812585 + 0.996693i \(0.525894\pi\)
\(314\) 0.208903 1.31896i 0.0117891 0.0744333i
\(315\) 6.47214i 0.364664i
\(316\) 29.3238i 1.64959i
\(317\) −10.2361 + 7.43694i −0.574915 + 0.417700i −0.836887 0.547375i \(-0.815627\pi\)
0.261972 + 0.965075i \(0.415627\pi\)
\(318\) 0.350341 + 2.21197i 0.0196461 + 0.124041i
\(319\) 2.86568 3.94427i 0.160447 0.220837i
\(320\) −4.70228 + 1.52786i −0.262866 + 0.0854102i
\(321\) 5.91641 + 8.14324i 0.330222 + 0.454511i
\(322\) −8.37045 + 16.4279i −0.466467 + 0.915493i
\(323\) 10.6331 32.7254i 0.591643 1.82089i
\(324\) −5.32282 + 7.32624i −0.295712 + 0.407013i
\(325\) 21.8713 + 7.10642i 1.21320 + 0.394193i
\(326\) −25.1312 + 12.8050i −1.39189 + 0.709204i
\(327\) 4.22050 + 3.06637i 0.233394 + 0.169571i
\(328\) 1.92522 0.980949i 0.106303 0.0541639i
\(329\) −4.42705 13.6251i −0.244071 0.751174i
\(330\) 0.144348 0.911380i 0.00794612 0.0501698i
\(331\) 8.92278 + 27.4615i 0.490440 + 1.50942i 0.823944 + 0.566671i \(0.191769\pi\)
−0.333504 + 0.942749i \(0.608231\pi\)
\(332\) −7.56231 + 10.4086i −0.415035 + 0.571247i
\(333\) −3.16718 + 4.35926i −0.173561 + 0.238886i
\(334\) 1.80602 11.4028i 0.0988211 0.623932i
\(335\) 6.32624i 0.345639i
\(336\) 12.3107i 0.671606i
\(337\) 9.40983 + 12.9515i 0.512586 + 0.705514i 0.984353 0.176209i \(-0.0563835\pi\)
−0.471767 + 0.881723i \(0.656384\pi\)
\(338\) 7.57502 + 14.8668i 0.412027 + 0.808648i
\(339\) 2.59590 + 7.98936i 0.140990 + 0.433922i
\(340\) 8.50651 0.461330
\(341\) −7.43769 3.18368i −0.402774 0.172406i
\(342\) 12.3607 + 12.3607i 0.668389 + 0.668389i
\(343\) 15.8904 5.16312i 0.858003 0.278782i
\(344\) −10.7188 + 5.46151i −0.577920 + 0.294465i
\(345\) 1.11803 0.812299i 0.0601929 0.0437327i
\(346\) 16.0344 16.0344i 0.862017 0.862017i
\(347\) −30.0503 −1.61318 −0.806592 0.591108i \(-0.798691\pi\)
−0.806592 + 0.591108i \(0.798691\pi\)
\(348\) 3.94427 2.86568i 0.211435 0.153617i
\(349\) 11.2812 + 8.19624i 0.603866 + 0.438735i 0.847249 0.531196i \(-0.178257\pi\)
−0.243383 + 0.969930i \(0.578257\pi\)
\(350\) 4.32780 + 27.3247i 0.231331 + 1.46057i
\(351\) 18.8294 6.11803i 1.00504 0.326556i
\(352\) 1.28587 8.11869i 0.0685373 0.432728i
\(353\) 13.3541 4.33901i 0.710767 0.230942i 0.0687515 0.997634i \(-0.478098\pi\)
0.642016 + 0.766692i \(0.278098\pi\)
\(354\) −3.17873 + 1.61964i −0.168948 + 0.0860831i
\(355\) 1.59184 2.19098i 0.0844862 0.116285i
\(356\) 10.6861 32.8885i 0.566364 1.74309i
\(357\) 6.54508 20.1437i 0.346403 1.06612i
\(358\) −3.67171 + 0.581542i −0.194056 + 0.0307355i
\(359\) −18.8294 6.11803i −0.993776 0.322897i −0.233400 0.972381i \(-0.574985\pi\)
−0.760376 + 0.649483i \(0.774985\pi\)
\(360\) −1.96190 + 3.85044i −0.103401 + 0.202936i
\(361\) 4.85410 3.52671i 0.255479 0.185616i
\(362\) −1.97599 + 3.87811i −0.103856 + 0.203829i
\(363\) −5.22455 3.79586i −0.274218 0.199231i
\(364\) −24.7984 + 34.1320i −1.29979 + 1.78900i
\(365\) −0.427051 0.587785i −0.0223529 0.0307661i
\(366\) −7.23607 7.23607i −0.378235 0.378235i
\(367\) −4.08174 −0.213065 −0.106533 0.994309i \(-0.533975\pi\)
−0.106533 + 0.994309i \(0.533975\pi\)
\(368\) 9.95959 7.23607i 0.519180 0.377206i
\(369\) 0.583592 1.79611i 0.0303806 0.0935019i
\(370\) −0.864881 + 1.69742i −0.0449630 + 0.0882449i
\(371\) −9.23305 −0.479356
\(372\) −6.08985 5.32624i −0.315744 0.276153i
\(373\) −12.4164 −0.642897 −0.321449 0.946927i \(-0.604170\pi\)
−0.321449 + 0.946927i \(0.604170\pi\)
\(374\) −6.42040 + 12.6007i −0.331991 + 0.651569i
\(375\) 1.33457 4.10739i 0.0689170 0.212105i
\(376\) −1.49640 + 9.44788i −0.0771708 + 0.487237i
\(377\) 16.7082 0.860516
\(378\) 16.8415 + 16.8415i 0.866233 + 0.866233i
\(379\) −16.3597 22.5172i −0.840342 1.15663i −0.985909 0.167283i \(-0.946500\pi\)
0.145567 0.989348i \(-0.453500\pi\)
\(380\) 5.00000 + 3.63271i 0.256495 + 0.186354i
\(381\) 2.33688 + 1.69784i 0.119722 + 0.0869832i
\(382\) −9.84005 + 19.3122i −0.503461 + 0.988097i
\(383\) −28.2012 + 20.4894i −1.44101 + 1.04696i −0.453183 + 0.891417i \(0.649712\pi\)
−0.987830 + 0.155540i \(0.950288\pi\)
\(384\) 3.73175 7.32398i 0.190435 0.373750i
\(385\) 3.61803 + 1.17557i 0.184392 + 0.0599126i
\(386\) −20.7482 + 3.28620i −1.05606 + 0.167263i
\(387\) −3.24920 + 10.0000i −0.165166 + 0.508329i
\(388\) 14.2128 + 4.61803i 0.721548 + 0.234445i
\(389\) −5.62868 + 7.74721i −0.285385 + 0.392799i −0.927508 0.373802i \(-0.878054\pi\)
0.642123 + 0.766602i \(0.278054\pi\)
\(390\) 2.81761 1.43564i 0.142675 0.0726967i
\(391\) −20.1437 + 6.54508i −1.01871 + 0.330999i
\(392\) −30.5740 4.84244i −1.54422 0.244580i
\(393\) 13.0279 4.23301i 0.657169 0.213527i
\(394\) 4.12323 + 26.0331i 0.207725 + 1.31153i
\(395\) −7.33094 5.32624i −0.368860 0.267992i
\(396\) −4.22291 5.81234i −0.212209 0.292081i
\(397\) −12.0000 −0.602263 −0.301131 0.953583i \(-0.597364\pi\)
−0.301131 + 0.953583i \(0.597364\pi\)
\(398\) 15.3884 15.3884i 0.771352 0.771352i
\(399\) 12.4495 9.04508i 0.623254 0.452821i
\(400\) 5.70820 17.5680i 0.285410 0.878402i
\(401\) 13.2533 4.30625i 0.661838 0.215044i 0.0412112 0.999150i \(-0.486878\pi\)
0.620626 + 0.784106i \(0.286878\pi\)
\(402\) −7.43694 7.43694i −0.370921 0.370921i
\(403\) −6.15537 27.0344i −0.306621 1.34668i
\(404\) 17.8885i 0.889988i
\(405\) 0.864745 + 2.66141i 0.0429695 + 0.132247i
\(406\) 9.12521 + 17.9092i 0.452877 + 0.888820i
\(407\) −1.86162 2.56231i −0.0922773 0.127009i
\(408\) −10.0000 + 10.0000i −0.495074 + 0.495074i
\(409\) 1.24108i 0.0613676i 0.999529 + 0.0306838i \(0.00976849\pi\)
−0.999529 + 0.0306838i \(0.990232\pi\)
\(410\) 0.104451 0.659481i 0.00515849 0.0325694i
\(411\) −0.383516 + 0.527864i −0.0189174 + 0.0260376i
\(412\) 1.47214 + 1.06957i 0.0725269 + 0.0526939i
\(413\) −4.54508 13.9883i −0.223649 0.688321i
\(414\) 1.68323 10.6275i 0.0827263 0.522313i
\(415\) 1.22857 + 3.78115i 0.0603082 + 0.185609i
\(416\) 25.0996 12.7889i 1.23061 0.627028i
\(417\) −0.263932 0.191758i −0.0129248 0.00939042i
\(418\) −9.15497 + 4.66469i −0.447784 + 0.228157i
\(419\) 2.07363 + 0.673762i 0.101303 + 0.0329154i 0.359230 0.933249i \(-0.383039\pi\)
−0.257927 + 0.966164i \(0.583039\pi\)
\(420\) 3.07768 + 2.23607i 0.150176 + 0.109109i
\(421\) −6.67376 + 20.5397i −0.325259 + 1.00105i 0.646064 + 0.763283i \(0.276414\pi\)
−0.971323 + 0.237762i \(0.923586\pi\)
\(422\) 13.7502 26.9862i 0.669348 1.31367i
\(423\) 4.91428 + 6.76393i 0.238941 + 0.328874i
\(424\) 5.49298 + 2.79881i 0.266763 + 0.135922i
\(425\) −18.6803 + 25.7113i −0.906130 + 1.24718i
\(426\) 0.704332 + 4.44698i 0.0341250 + 0.215457i
\(427\) 34.1320 24.7984i 1.65176 1.20008i
\(428\) 27.7082 1.33933
\(429\) 5.25731i 0.253825i
\(430\) −0.581542 + 3.67171i −0.0280444 + 0.177066i
\(431\) 25.7970 + 8.38197i 1.24260 + 0.403745i 0.855263 0.518193i \(-0.173395\pi\)
0.387336 + 0.921939i \(0.373395\pi\)
\(432\) −4.91428 15.1246i −0.236439 0.727683i
\(433\) 22.6134i 1.08673i −0.839497 0.543364i \(-0.817150\pi\)
0.839497 0.543364i \(-0.182850\pi\)
\(434\) 25.6160 21.3627i 1.22961 1.02544i
\(435\) 1.50658i 0.0722349i
\(436\) 13.6578 4.43769i 0.654091 0.212527i
\(437\) −14.6353 4.75528i −0.700099 0.227476i
\(438\) 1.19301 + 0.188954i 0.0570043 + 0.00902859i
\(439\) 13.4721i 0.642990i 0.946911 + 0.321495i \(0.104185\pi\)
−0.946911 + 0.321495i \(0.895815\pi\)
\(440\) −1.79611 1.79611i −0.0856263 0.0856263i
\(441\) −21.8885 + 15.9030i −1.04231 + 0.757284i
\(442\) −47.8691 + 7.58172i −2.27690 + 0.360626i
\(443\) 18.2946 25.1803i 0.869202 1.19635i −0.110094 0.993921i \(-0.535115\pi\)
0.979296 0.202433i \(-0.0648848\pi\)
\(444\) −0.978714 3.01217i −0.0464477 0.142951i
\(445\) −6.28115 8.64527i −0.297755 0.409825i
\(446\) 11.6343 + 5.92798i 0.550901 + 0.280698i
\(447\) −2.43690 + 7.50000i −0.115261 + 0.354738i
\(448\) 27.4164 + 19.9192i 1.29530 + 0.941093i
\(449\) 34.5967 + 11.2412i 1.63272 + 0.530503i 0.974895 0.222666i \(-0.0714759\pi\)
0.657827 + 0.753169i \(0.271476\pi\)
\(450\) −7.32979 14.3855i −0.345529 0.678140i
\(451\) 0.898056 + 0.652476i 0.0422878 + 0.0307239i
\(452\) 21.9928 + 7.14590i 1.03445 + 0.336115i
\(453\) 3.55573 + 10.9434i 0.167063 + 0.514166i
\(454\) 2.51197 + 0.397857i 0.117893 + 0.0186724i
\(455\) 4.02874 + 12.3992i 0.188870 + 0.581283i
\(456\) −10.1484 + 1.60734i −0.475241 + 0.0752707i
\(457\) 7.17376 9.87384i 0.335574 0.461879i −0.607568 0.794268i \(-0.707855\pi\)
0.943142 + 0.332389i \(0.107855\pi\)
\(458\) −26.5688 4.20808i −1.24148 0.196631i
\(459\) 27.3607i 1.27709i
\(460\) 3.80423i 0.177373i
\(461\) −23.9058 32.9035i −1.11340 1.53247i −0.816306 0.577620i \(-0.803982\pi\)
−0.297096 0.954848i \(-0.596018\pi\)
\(462\) −5.63522 + 2.87129i −0.262174 + 0.133584i
\(463\) −1.79611 5.52786i −0.0834724 0.256902i 0.900606 0.434636i \(-0.143123\pi\)
−0.984078 + 0.177735i \(0.943123\pi\)
\(464\) 13.4208i 0.623045i
\(465\) −2.43769 + 0.555029i −0.113045 + 0.0257389i
\(466\) −14.3262 + 14.3262i −0.663650 + 0.663650i
\(467\) −24.1194 + 7.83688i −1.11611 + 0.362648i −0.808284 0.588793i \(-0.799603\pi\)
−0.307831 + 0.951441i \(0.599603\pi\)
\(468\) 7.60845 23.4164i 0.351701 1.08242i
\(469\) 35.0795 25.4868i 1.61982 1.17687i
\(470\) 2.09017 + 2.09017i 0.0964124 + 0.0964124i
\(471\) 0.686054 0.0316117
\(472\) −1.53629 + 9.69977i −0.0707136 + 0.446468i
\(473\) −5.00000 3.63271i −0.229900 0.167032i
\(474\) 14.8794 2.35667i 0.683434 0.108245i
\(475\) −21.9601 + 7.13525i −1.00760 + 0.327388i
\(476\) −34.2705 47.1693i −1.57079 2.16200i
\(477\) 5.12461 1.66509i 0.234640 0.0762391i
\(478\) 16.9611 + 33.2881i 0.775784 + 1.52256i
\(479\) −10.4741 + 14.4164i −0.478575 + 0.658702i −0.978230 0.207522i \(-0.933460\pi\)
0.499655 + 0.866225i \(0.333460\pi\)
\(480\) −1.15317 2.26323i −0.0526350 0.103302i
\(481\) 3.35410 10.3229i 0.152934 0.470682i
\(482\) 0.680881 + 4.29892i 0.0310133 + 0.195810i
\(483\) −9.00854 2.92705i −0.409903 0.133185i
\(484\) −16.9070 + 5.49342i −0.768501 + 0.249701i
\(485\) 3.73607 2.71441i 0.169646 0.123255i
\(486\) −19.1744 9.76985i −0.869769 0.443170i
\(487\) −5.48183 3.98278i −0.248405 0.180477i 0.456615 0.889665i \(-0.349062\pi\)
−0.705020 + 0.709188i \(0.749062\pi\)
\(488\) −27.8232 + 4.40676i −1.25950 + 0.199484i
\(489\) −8.51722 11.7229i −0.385162 0.530130i
\(490\) −6.76393 + 6.76393i −0.305563 + 0.305563i
\(491\) 33.1280 1.49504 0.747522 0.664237i \(-0.231243\pi\)
0.747522 + 0.664237i \(0.231243\pi\)
\(492\) 0.652476 + 0.898056i 0.0294159 + 0.0404875i
\(493\) −7.13525 + 21.9601i −0.321356 + 0.989031i
\(494\) −31.3745 15.9861i −1.41161 0.719250i
\(495\) −2.22012 −0.0997868
\(496\) −21.7153 + 4.94427i −0.975046 + 0.222004i
\(497\) −18.5623 −0.832633
\(498\) −5.88928 3.00074i −0.263905 0.134466i
\(499\) 0.930812 2.86475i 0.0416689 0.128244i −0.928058 0.372436i \(-0.878523\pi\)
0.969727 + 0.244192i \(0.0785227\pi\)
\(500\) −6.98791 9.61803i −0.312509 0.430132i
\(501\) 5.93112 0.264983
\(502\) 2.35114 2.35114i 0.104937 0.104937i
\(503\) 18.4131 + 25.3435i 0.821000 + 1.13001i 0.989532 + 0.144313i \(0.0460972\pi\)
−0.168533 + 0.985696i \(0.553903\pi\)
\(504\) 29.2550 4.63354i 1.30312 0.206394i
\(505\) 4.47214 + 3.24920i 0.199007 + 0.144587i
\(506\) 5.63522 + 2.87129i 0.250516 + 0.127644i
\(507\) −6.93491 + 5.03851i −0.307990 + 0.223768i
\(508\) 7.56231 2.45714i 0.335523 0.109018i
\(509\) −13.8820 4.51052i −0.615307 0.199925i −0.0152516 0.999884i \(-0.504855\pi\)
−0.600056 + 0.799958i \(0.704855\pi\)
\(510\) 0.683644 + 4.31636i 0.0302723 + 0.191131i
\(511\) −1.53884 + 4.73607i −0.0680744 + 0.209511i
\(512\) −10.2726 20.1612i −0.453990 0.891007i
\(513\) −11.6844 + 16.0822i −0.515879 + 0.710047i
\(514\) −4.45850 8.75029i −0.196656 0.385959i
\(515\) 0.534785 0.173762i 0.0235654 0.00765687i
\(516\) −3.63271 5.00000i −0.159921 0.220113i
\(517\) −4.67376 + 1.51860i −0.205552 + 0.0667878i
\(518\) 12.8967 2.04264i 0.566650 0.0897486i
\(519\) 9.42481 + 6.84752i 0.413703 + 0.300573i
\(520\) 1.36176 8.59783i 0.0597172 0.377040i
\(521\) −4.34752 −0.190468 −0.0952342 0.995455i \(-0.530360\pi\)
−0.0952342 + 0.995455i \(0.530360\pi\)
\(522\) −8.29451 8.29451i −0.363041 0.363041i
\(523\) 17.7068 12.8647i 0.774264 0.562536i −0.128988 0.991646i \(-0.541173\pi\)
0.903252 + 0.429110i \(0.141173\pi\)
\(524\) 11.6525 35.8626i 0.509041 1.56667i
\(525\) −13.5172 + 4.39201i −0.589940 + 0.191683i
\(526\) −8.40051 + 8.40051i −0.366280 + 0.366280i
\(527\) 38.1608 + 3.45492i 1.66231 + 0.150498i
\(528\) 4.22291 0.183779
\(529\) −4.18034 12.8658i −0.181754 0.559381i
\(530\) 1.69742 0.864881i 0.0737314 0.0375680i
\(531\) 5.04531 + 6.94427i 0.218948 + 0.301356i
\(532\) 42.3607i 1.83657i
\(533\) 3.80423i 0.164779i
\(534\) 17.5471 + 2.77918i 0.759335 + 0.120267i
\(535\) 5.03280 6.92705i 0.217587 0.299483i
\(536\) −28.5955 + 4.52909i −1.23514 + 0.195627i
\(537\) −0.590170 1.81636i −0.0254677 0.0783816i
\(538\) 39.5570 + 6.26522i 1.70542 + 0.270113i
\(539\) −4.91428 15.1246i −0.211673 0.651463i
\(540\) −4.67376 1.51860i −0.201127 0.0653500i
\(541\) 8.61803 + 6.26137i 0.370518 + 0.269197i 0.757426 0.652921i \(-0.226457\pi\)
−0.386908 + 0.922119i \(0.626457\pi\)
\(542\) 6.10616 + 11.9840i 0.262282 + 0.514757i
\(543\) −2.12663 0.690983i −0.0912623 0.0296529i
\(544\) 6.08999 + 38.4507i 0.261106 + 1.64856i
\(545\) 1.37132 4.22050i 0.0587410 0.180786i
\(546\) −19.3122 9.84005i −0.826485 0.421115i
\(547\) 0.171513 + 0.236068i 0.00733338 + 0.0100935i 0.812668 0.582727i \(-0.198014\pi\)
−0.805335 + 0.592821i \(0.798014\pi\)
\(548\) 0.555029 + 1.70820i 0.0237097 + 0.0729709i
\(549\) −14.4721 + 19.9192i −0.617656 + 0.850130i
\(550\) 9.37310 1.48455i 0.399670 0.0633015i
\(551\) −13.5721 + 9.86068i −0.578189 + 0.420079i
\(552\) 4.47214 + 4.47214i 0.190347 + 0.190347i
\(553\) 62.1087i 2.64113i
\(554\) −6.95579 1.10169i −0.295523 0.0468063i
\(555\) −0.930812 0.302439i −0.0395108 0.0128378i
\(556\) −0.854102 + 0.277515i −0.0362220 + 0.0117692i
\(557\) 24.9645i 1.05778i 0.848691 + 0.528890i \(0.177392\pi\)
−0.848691 + 0.528890i \(0.822608\pi\)
\(558\) −10.3651 + 16.4765i −0.438788 + 0.697507i
\(559\) 21.1803i 0.895833i
\(560\) 9.95959 3.23607i 0.420870 0.136749i
\(561\) −6.90983 2.24514i −0.291733 0.0947899i
\(562\) −2.02336 + 12.7750i −0.0853504 + 0.538881i
\(563\) 33.6869i 1.41973i −0.704336 0.709867i \(-0.748755\pi\)
0.704336 0.709867i \(-0.251245\pi\)
\(564\) −4.91428 −0.206929
\(565\) 5.78115 4.20025i 0.243215 0.176706i
\(566\) −3.11719 19.6812i −0.131025 0.827262i
\(567\) 11.2739 15.5172i 0.473460 0.651662i
\(568\) 11.0432 + 5.62679i 0.463362 + 0.236095i
\(569\) −21.3820 29.4298i −0.896379 1.23376i −0.971609 0.236593i \(-0.923969\pi\)
0.0752302 0.997166i \(-0.476031\pi\)
\(570\) −1.44147 + 2.82904i −0.0603765 + 0.118496i
\(571\) −7.44945 + 22.9271i −0.311750 + 0.959467i 0.665322 + 0.746557i \(0.268294\pi\)
−0.977072 + 0.212911i \(0.931706\pi\)
\(572\) 11.7082 + 8.50651i 0.489545 + 0.355675i
\(573\) −10.5902 3.44095i −0.442411 0.143748i
\(574\) −4.07768 + 2.07768i −0.170199 + 0.0867208i
\(575\) 11.4984 + 8.35410i 0.479518 + 0.348390i
\(576\) −18.8091 6.11146i −0.783714 0.254644i
\(577\) 3.10081 + 9.54332i 0.129089 + 0.397294i 0.994624 0.103554i \(-0.0330216\pi\)
−0.865535 + 0.500848i \(0.833022\pi\)
\(578\) 6.71675 42.4079i 0.279380 1.76393i
\(579\) −3.33495 10.2639i −0.138596 0.426554i
\(580\) −3.35520 2.43769i −0.139317 0.101220i
\(581\) 16.0172 22.0458i 0.664506 0.914614i
\(582\) −1.20103 + 7.58299i −0.0497842 + 0.314325i
\(583\) 3.16718i 0.131171i
\(584\) 2.35114 2.35114i 0.0972909 0.0972909i
\(585\) −4.47214 6.15537i −0.184900 0.254493i
\(586\) −7.55291 14.8234i −0.312008 0.612350i
\(587\) −0.0530006 0.163119i −0.00218757 0.00673264i 0.949957 0.312381i \(-0.101127\pi\)
−0.952144 + 0.305649i \(0.901127\pi\)
\(588\) 15.9030i 0.655827i
\(589\) 20.9549 + 18.3273i 0.863432 + 0.755165i
\(590\) 2.14590 + 2.14590i 0.0883452 + 0.0883452i
\(591\) −12.8783 + 4.18441i −0.529741 + 0.172123i
\(592\) −8.29180 2.69417i −0.340791 0.110730i
\(593\) 4.85410 3.52671i 0.199334 0.144825i −0.483641 0.875267i \(-0.660686\pi\)
0.682975 + 0.730442i \(0.260686\pi\)
\(594\) 5.77709 5.77709i 0.237037 0.237037i
\(595\) −18.0171 −0.738628
\(596\) 12.7598 + 17.5623i 0.522660 + 0.719380i
\(597\) 9.04508 + 6.57164i 0.370191 + 0.268959i
\(598\) 3.39065 + 21.4077i 0.138654 + 0.875427i
\(599\) 30.5851 9.93769i 1.24967 0.406043i 0.391869 0.920021i \(-0.371829\pi\)
0.857803 + 0.513978i \(0.171829\pi\)
\(600\) 9.37310 + 1.48455i 0.382655 + 0.0606066i
\(601\) −30.8541 + 10.0251i −1.25857 + 0.408933i −0.860983 0.508634i \(-0.830151\pi\)
−0.397582 + 0.917567i \(0.630151\pi\)
\(602\) 22.7028 11.5677i 0.925299 0.471463i
\(603\) −14.8739 + 20.4721i −0.605711 + 0.833690i
\(604\) 30.1246 + 9.78808i 1.22575 + 0.398271i
\(605\) −1.69756 + 5.22455i −0.0690157 + 0.212408i
\(606\) −9.07697 + 1.43765i −0.368727 + 0.0584006i
\(607\) 6.15537 + 2.00000i 0.249839 + 0.0811775i 0.431259 0.902228i \(-0.358069\pi\)
−0.181420 + 0.983406i \(0.558069\pi\)
\(608\) −12.8408 + 25.2015i −0.520763 + 1.02205i
\(609\) −8.35410 + 6.06961i −0.338525 + 0.245953i
\(610\) −3.95199 + 7.75621i −0.160011 + 0.314040i
\(611\) −13.6251 9.89919i −0.551211 0.400478i
\(612\) 27.5276 + 20.0000i 1.11274 + 0.808452i
\(613\) 23.2918 + 32.0584i 0.940747 + 1.29483i 0.955517 + 0.294936i \(0.0952983\pi\)
−0.0147702 + 0.999891i \(0.504702\pi\)
\(614\) −31.2148 31.2148i −1.25973 1.25973i
\(615\) 0.343027 0.0138322
\(616\) −2.72353 + 17.1957i −0.109734 + 0.692833i
\(617\) −4.39919 + 13.5393i −0.177105 + 0.545072i −0.999723 0.0235215i \(-0.992512\pi\)
0.822619 + 0.568593i \(0.192512\pi\)
\(618\) −0.424408 + 0.832947i −0.0170722 + 0.0335060i
\(619\) 10.1716 0.408831 0.204415 0.978884i \(-0.434471\pi\)
0.204415 + 0.978884i \(0.434471\pi\)
\(620\) −2.70820 + 6.32688i −0.108764 + 0.254094i
\(621\) 12.2361 0.491016
\(622\) 8.19495 16.0835i 0.328588 0.644889i
\(623\) −22.6336 + 69.6591i −0.906796 + 2.79083i
\(624\) 8.50651 + 11.7082i 0.340533 + 0.468703i
\(625\) 19.4164 0.776656
\(626\) 8.16348 + 8.16348i 0.326278 + 0.326278i
\(627\) −3.10271 4.27051i −0.123910 0.170548i
\(628\) 1.11006 1.52786i 0.0442961 0.0609684i
\(629\) 12.1353 + 8.81678i 0.483864 + 0.351548i
\(630\) 4.15537 8.15537i 0.165554 0.324918i
\(631\) 2.26538 1.64590i 0.0901835 0.0655222i −0.541780 0.840520i \(-0.682249\pi\)
0.631963 + 0.774998i \(0.282249\pi\)
\(632\) 18.8270 36.9501i 0.748898 1.46980i
\(633\) 14.7984 + 4.80828i 0.588183 + 0.191112i
\(634\) −17.6730 + 2.79913i −0.701885 + 0.111168i
\(635\) 0.759299 2.33688i 0.0301318 0.0927363i
\(636\) −0.978714 + 3.01217i −0.0388085 + 0.119440i
\(637\) 32.0344 44.0916i 1.26925 1.74697i
\(638\) 6.14335 3.13019i 0.243217 0.123925i
\(639\) 10.3026 3.34752i 0.407565 0.132426i
\(640\) −6.90617 1.09383i −0.272990 0.0432374i
\(641\) 9.57295 3.11044i 0.378109 0.122855i −0.113796 0.993504i \(-0.536301\pi\)
0.491904 + 0.870649i \(0.336301\pi\)
\(642\) 2.22683 + 14.0596i 0.0878859 + 0.554890i
\(643\) 18.8294 + 13.6803i 0.742558 + 0.539500i 0.893511 0.449041i \(-0.148234\pi\)
−0.150953 + 0.988541i \(0.548234\pi\)
\(644\) −21.0948 + 15.3262i −0.831250 + 0.603938i
\(645\) −1.90983 −0.0751995
\(646\) 34.4095 34.4095i 1.35383 1.35383i
\(647\) −14.9394 + 10.8541i −0.587328 + 0.426719i −0.841359 0.540477i \(-0.818244\pi\)
0.254031 + 0.967196i \(0.418244\pi\)
\(648\) −11.4109 + 5.81414i −0.448262 + 0.228401i
\(649\) −4.79837 + 1.55909i −0.188353 + 0.0611995i
\(650\) 22.9969 + 22.9969i 0.902011 + 0.902011i
\(651\) 12.8985 + 11.2812i 0.505533 + 0.442143i
\(652\) −39.8885 −1.56216
\(653\) −1.27458 3.92274i −0.0498780 0.153509i 0.923015 0.384763i \(-0.125717\pi\)
−0.972893 + 0.231255i \(0.925717\pi\)
\(654\) 3.34941 + 6.57358i 0.130972 + 0.257047i
\(655\) −6.84915 9.42705i −0.267619 0.368345i
\(656\) 3.05573 0.119306
\(657\) 2.90617i 0.113380i
\(658\) 3.16942 20.0109i 0.123557 0.780107i
\(659\) −5.06555 + 6.97214i −0.197326 + 0.271596i −0.896201 0.443648i \(-0.853684\pi\)
0.698875 + 0.715243i \(0.253684\pi\)
\(660\) 0.767031 1.05573i 0.0298567 0.0410942i
\(661\) 0.628677 + 1.93487i 0.0244527 + 0.0752577i 0.962538 0.271146i \(-0.0874027\pi\)
−0.938085 + 0.346404i \(0.887403\pi\)
\(662\) −6.38801 + 40.3323i −0.248277 + 1.56756i
\(663\) −7.69421 23.6803i −0.298818 0.919668i
\(664\) −16.2118 + 8.26033i −0.629140 + 0.320563i
\(665\) −10.5902 7.69421i −0.410669 0.298369i
\(666\) −6.78970 + 3.45952i −0.263095 + 0.134054i
\(667\) 9.82084 + 3.19098i 0.380264 + 0.123555i
\(668\) 9.59675 13.2088i 0.371309 0.511063i
\(669\) −2.07295 + 6.37988i −0.0801448 + 0.246660i
\(670\) −4.06169 + 7.97152i −0.156917 + 0.307967i
\(671\) −8.50651 11.7082i −0.328390 0.451990i
\(672\) −7.90398 + 15.5124i −0.304903 + 0.598405i
\(673\) 16.0795 22.1316i 0.619820 0.853109i −0.377520 0.926002i \(-0.623223\pi\)
0.997340 + 0.0728923i \(0.0232229\pi\)
\(674\) 3.54169 + 22.3614i 0.136421 + 0.861327i
\(675\) 14.8536 10.7918i 0.571717 0.415376i
\(676\) 23.5967i 0.907567i
\(677\) 21.3723i 0.821403i −0.911770 0.410702i \(-0.865284\pi\)
0.911770 0.410702i \(-0.134716\pi\)
\(678\) −1.85846 + 11.7338i −0.0713737 + 0.450636i
\(679\) −30.1033 9.78115i −1.15526 0.375366i
\(680\) 10.7188 + 5.46151i 0.411048 + 0.209440i
\(681\) 1.30660i 0.0500688i
\(682\) −7.32799 8.78697i −0.280603 0.336470i
\(683\) 14.1246i 0.540463i −0.962795 0.270232i \(-0.912900\pi\)
0.962795 0.270232i \(-0.0871003\pi\)
\(684\) 7.63932 + 23.5114i 0.292097 + 0.898981i
\(685\) 0.527864 + 0.171513i 0.0201686 + 0.00655319i
\(686\) 23.3381 + 3.69639i 0.891051 + 0.141129i
\(687\) 13.8197i 0.527253i
\(688\) −17.0130 −0.648615
\(689\) −8.78115 + 6.37988i −0.334535 + 0.243054i
\(690\) 1.93033 0.305735i 0.0734865 0.0116391i
\(691\) −13.6906 + 18.8435i −0.520814 + 0.716839i −0.985696 0.168534i \(-0.946097\pi\)
0.464882 + 0.885373i \(0.346097\pi\)
\(692\) 30.4993 9.90983i 1.15941 0.376715i
\(693\) 8.94427 + 12.3107i 0.339765 + 0.467646i
\(694\) −37.8656 19.2935i −1.43736 0.732370i
\(695\) −0.0857567 + 0.263932i −0.00325294 + 0.0100115i
\(696\) 6.80995 1.07859i 0.258131 0.0408839i
\(697\) −5.00000 1.62460i −0.189389 0.0615361i
\(698\) 8.95277 + 17.5708i 0.338867 + 0.665065i
\(699\) −8.42075 6.11803i −0.318502 0.231405i
\(700\) −12.0902 + 37.2097i −0.456965 + 1.40640i
\(701\) −2.24671 6.91467i −0.0848571 0.261163i 0.899621 0.436672i \(-0.143843\pi\)
−0.984478 + 0.175509i \(0.943843\pi\)
\(702\) 27.6544 + 4.38003i 1.04375 + 0.165314i
\(703\) 3.36771 + 10.3647i 0.127016 + 0.390914i
\(704\) 6.83282 9.40456i 0.257521 0.354448i
\(705\) −0.892609 + 1.22857i −0.0336176 + 0.0462707i
\(706\) 19.6130 + 3.10639i 0.738144 + 0.116910i
\(707\) 37.8885i 1.42495i
\(708\) −5.04531 −0.189614
\(709\) −23.8050 32.7647i −0.894014 1.23050i −0.972338 0.233576i \(-0.924957\pi\)
0.0783247 0.996928i \(-0.475043\pi\)
\(710\) 3.41254 1.73877i 0.128070 0.0652550i
\(711\) −11.2007 34.4721i −0.420058 1.29281i
\(712\) 34.5811 34.5811i 1.29598 1.29598i
\(713\) 1.54508 17.0660i 0.0578639 0.639127i
\(714\) 21.1803 21.1803i 0.792654 0.792654i
\(715\) 4.25325 1.38197i 0.159063 0.0516826i
\(716\) −5.00000 1.62460i −0.186859 0.0607141i
\(717\) −15.5279 + 11.2817i −0.579899 + 0.421321i
\(718\) −19.7984 19.7984i −0.738869 0.738869i
\(719\) −5.15131 −0.192111 −0.0960557 0.995376i \(-0.530623\pi\)
−0.0960557 + 0.995376i \(0.530623\pi\)
\(720\) −4.94427 + 3.59222i −0.184262 + 0.133874i
\(721\) −3.11803 2.26538i −0.116122 0.0843673i
\(722\) 8.38081 1.32739i 0.311902 0.0494004i
\(723\) −2.12663 + 0.690983i −0.0790901 + 0.0256979i
\(724\) −4.97980 + 3.61803i −0.185073 + 0.134463i
\(725\) 14.7361 4.78804i 0.547284 0.177823i
\(726\) −4.14623 8.13744i −0.153881 0.302009i
\(727\) −4.49801 + 6.19098i −0.166822 + 0.229611i −0.884241 0.467031i \(-0.845323\pi\)
0.717419 + 0.696642i \(0.245323\pi\)
\(728\) −53.1619 + 27.0873i −1.97031 + 1.00392i
\(729\) −0.781153 + 2.40414i −0.0289316 + 0.0890423i
\(730\) −0.160734 1.01484i −0.00594904 0.0375608i
\(731\) 27.8379 + 9.04508i 1.02962 + 0.334545i
\(732\) −4.47214 13.7638i −0.165295 0.508725i
\(733\) 16.9894 12.3435i 0.627516 0.455917i −0.228023 0.973656i \(-0.573226\pi\)
0.855539 + 0.517739i \(0.173226\pi\)
\(734\) −5.14329 2.62064i −0.189842 0.0967295i
\(735\) −3.97574 2.88854i −0.146647 0.106546i
\(736\) 17.1957 2.72353i 0.633840 0.100390i
\(737\) −8.74265 12.0332i −0.322039 0.443249i
\(738\) 1.88854 1.88854i 0.0695183 0.0695183i
\(739\) 0.343027 0.0126184 0.00630922 0.999980i \(-0.497992\pi\)
0.00630922 + 0.999980i \(0.497992\pi\)
\(740\) −2.17963 + 1.58359i −0.0801247 + 0.0582140i
\(741\) 5.59017 17.2048i 0.205360 0.632033i
\(742\) −11.6343 5.92798i −0.427109 0.217623i
\(743\) 6.43288 0.236000 0.118000 0.993014i \(-0.462352\pi\)
0.118000 + 0.993014i \(0.462352\pi\)
\(744\) −4.25401 10.6214i −0.155960 0.389399i
\(745\) 6.70820 0.245770
\(746\) −15.6456 7.97182i −0.572826 0.291869i
\(747\) −4.91428 + 15.1246i −0.179804 + 0.553381i
\(748\) −16.1803 + 11.7557i −0.591612 + 0.429831i
\(749\) −58.6869 −2.14437
\(750\) 4.31877 4.31877i 0.157699 0.157699i
\(751\) −9.75532 13.4271i −0.355977 0.489960i 0.593046 0.805169i \(-0.297925\pi\)
−0.949022 + 0.315209i \(0.897925\pi\)
\(752\) −7.95148 + 10.9443i −0.289961 + 0.399097i
\(753\) 1.38197 + 1.00406i 0.0503616 + 0.0365899i
\(754\) 21.0536 + 10.7273i 0.766726 + 0.390666i
\(755\) 7.91872 5.75329i 0.288192 0.209384i
\(756\) 10.4086 + 32.0344i 0.378558 + 1.16508i
\(757\) −24.4721 7.95148i −0.889455 0.289001i −0.171577 0.985171i \(-0.554886\pi\)
−0.717878 + 0.696169i \(0.754886\pi\)
\(758\) −6.15750 38.8769i −0.223651 1.41207i
\(759\) −1.00406 + 3.09017i −0.0364450 + 0.112166i
\(760\) 3.96802 + 7.78768i 0.143935 + 0.282489i
\(761\) −2.72542 + 3.75123i −0.0987966 + 0.135982i −0.855553 0.517715i \(-0.826783\pi\)
0.756757 + 0.653697i \(0.226783\pi\)
\(762\) 1.85456 + 3.63978i 0.0671836 + 0.131855i
\(763\) −28.9277 + 9.39919i −1.04725 + 0.340273i
\(764\) −24.7984 + 18.0171i −0.897174 + 0.651835i
\(765\) 10.0000 3.24920i 0.361551 0.117475i
\(766\) −48.6905 + 7.71182i −1.75926 + 0.278640i
\(767\) −13.9883 10.1631i −0.505089 0.366969i
\(768\) 9.40456 6.83282i 0.339358 0.246558i
\(769\) −23.0902 −0.832653 −0.416326 0.909215i \(-0.636683\pi\)
−0.416326 + 0.909215i \(0.636683\pi\)
\(770\) 3.80423 + 3.80423i 0.137095 + 0.137095i
\(771\) 4.08174 2.96556i 0.147000 0.106802i
\(772\) −28.2542 9.18034i −1.01689 0.330408i
\(773\) 41.7320 13.5595i 1.50100 0.487703i 0.560688 0.828027i \(-0.310537\pi\)
0.940308 + 0.340324i \(0.110537\pi\)
\(774\) −10.5146 + 10.5146i −0.377940 + 0.377940i
\(775\) −13.1760 22.0795i −0.473297 0.793120i
\(776\) 14.9443 + 14.9443i 0.536468 + 0.536468i
\(777\) 2.07295 + 6.37988i 0.0743666 + 0.228877i
\(778\) −12.0666 + 6.14822i −0.432607 + 0.220424i
\(779\) −2.24514 3.09017i −0.0804405 0.110717i
\(780\) 4.47214 0.160128
\(781\) 6.36737i 0.227842i
\(782\) −29.5847 4.68576i −1.05795 0.167563i
\(783\) 7.84070 10.7918i 0.280204 0.385667i
\(784\) −35.4164 25.7315i −1.26487 0.918983i
\(785\) −0.180340 0.555029i −0.00643661 0.0198098i
\(786\) 19.1338 + 3.03050i 0.682481 + 0.108094i
\(787\) 6.76340 + 20.8156i 0.241089 + 0.741996i 0.996255 + 0.0864623i \(0.0275562\pi\)
−0.755166 + 0.655534i \(0.772444\pi\)
\(788\) −11.5187 + 35.4508i −0.410336 + 1.26288i
\(789\) −4.93769 3.58744i −0.175787 0.127716i
\(790\) −5.81787 11.4182i −0.206990 0.406241i
\(791\) −46.5815 15.1353i −1.65625 0.538148i
\(792\) −1.58943 10.0353i −0.0564779 0.356587i
\(793\) 15.3262 47.1693i 0.544251 1.67503i
\(794\) −15.1209 7.70447i −0.536620 0.273422i
\(795\) 0.575274 + 0.791796i 0.0204028 + 0.0280821i
\(796\) 29.2705 9.51057i 1.03747 0.337093i
\(797\) 20.0000 27.5276i 0.708436 0.975079i −0.291393 0.956603i \(-0.594119\pi\)
0.999829 0.0184755i \(-0.00588128\pi\)
\(798\) 21.4946 3.40441i 0.760900 0.120515i
\(799\) 18.8294 13.6803i 0.666135 0.483976i
\(800\) 18.4721 18.4721i 0.653089 0.653089i
\(801\) 42.7445i 1.51030i
\(802\) 19.4649 + 3.08294i 0.687330 + 0.108862i
\(803\) 1.62460 + 0.527864i 0.0573308 + 0.0186279i
\(804\) −4.59628 14.1459i −0.162098 0.498887i
\(805\) 8.05748i 0.283989i
\(806\) 9.60097 38.0174i 0.338180 1.33910i
\(807\) 20.5755i 0.724291i
\(808\) −11.4852 + 22.5409i −0.404046 + 0.792985i
\(809\) 45.8779 + 14.9066i 1.61298 + 0.524089i 0.970271 0.242020i \(-0.0778101\pi\)
0.642710 + 0.766110i \(0.277810\pi\)
\(810\) −0.619089 + 3.90877i −0.0217526 + 0.137340i
\(811\) 7.36068i 0.258468i −0.991614 0.129234i \(-0.958748\pi\)
0.991614 0.129234i \(-0.0412519\pi\)
\(812\) 28.4257i 0.997546i
\(813\) −5.59017 + 4.06150i −0.196056 + 0.142443i
\(814\) −0.700682 4.42393i −0.0245589 0.155059i
\(815\) −7.24518 + 9.97214i −0.253788 + 0.349309i
\(816\) −19.0211 + 6.18034i −0.665873 + 0.216355i
\(817\) 12.5000 + 17.2048i 0.437320 + 0.601919i
\(818\) −0.796824 + 1.56386i −0.0278603 + 0.0546789i
\(819\) −16.1150 + 49.5967i −0.563102 + 1.73305i
\(820\) 0.555029 0.763932i 0.0193825 0.0266777i
\(821\) −45.4508 14.7679i −1.58625 0.515402i −0.622590 0.782549i \(-0.713919\pi\)
−0.963656 + 0.267146i \(0.913919\pi\)
\(822\) −0.822168 + 0.418915i −0.0286764 + 0.0146113i
\(823\) 25.7643 + 18.7188i 0.898086 + 0.652498i 0.937974 0.346706i \(-0.112700\pi\)
−0.0398873 + 0.999204i \(0.512700\pi\)
\(824\) 1.16829 + 2.29291i 0.0406994 + 0.0798771i
\(825\) 1.50658 + 4.63677i 0.0524523 + 0.161432i
\(826\) 3.25392 20.5445i 0.113218 0.714833i
\(827\) 6.69015 + 20.5902i 0.232639 + 0.715990i 0.997426 + 0.0717065i \(0.0228445\pi\)
−0.764786 + 0.644284i \(0.777156\pi\)
\(828\) 8.94427 12.3107i 0.310835 0.427828i
\(829\) −16.8328 + 23.1684i −0.584628 + 0.804671i −0.994193 0.107610i \(-0.965680\pi\)
0.409565 + 0.912281i \(0.365680\pi\)
\(830\) −0.879560 + 5.55332i −0.0305300 + 0.192759i
\(831\) 3.61803i 0.125508i
\(832\) 39.8384 1.38115
\(833\) 44.2705 + 60.9331i 1.53388 + 2.11121i
\(834\) −0.209458 0.411084i −0.00725292 0.0142347i
\(835\) −1.55909 4.79837i −0.0539544 0.166055i
\(836\) −14.5309 −0.502560
\(837\) −20.3500 8.71078i −0.703400 0.301089i
\(838\) 2.18034 + 2.18034i 0.0753186 + 0.0753186i
\(839\) 4.75528 1.54508i 0.164171 0.0533423i −0.225779 0.974179i \(-0.572493\pi\)
0.389949 + 0.920836i \(0.372493\pi\)
\(840\) 2.44246 + 4.79360i 0.0842730 + 0.165395i
\(841\) −14.3541 + 10.4289i −0.494969 + 0.359616i
\(842\) −21.5967 + 21.5967i −0.744273 + 0.744273i
\(843\) −6.64488 −0.228862
\(844\) 34.6525 25.1765i 1.19279 0.866611i
\(845\) 5.89919 + 4.28601i 0.202938 + 0.147443i
\(846\) 1.84965 + 11.6782i 0.0635922 + 0.401505i
\(847\) 35.8096 11.6353i 1.23043 0.399792i
\(848\) 5.12461 + 7.05342i 0.175980 + 0.242216i
\(849\) 9.73607 3.16344i 0.334141 0.108569i
\(850\) −40.0463 + 20.4046i −1.37358 + 0.699872i
\(851\) 3.94298 5.42705i 0.135164 0.186037i
\(852\) −1.96763 + 6.05573i −0.0674097 + 0.207466i
\(853\) −13.4377 + 41.3570i −0.460098 + 1.41604i 0.404947 + 0.914340i \(0.367290\pi\)
−0.865044 + 0.501695i \(0.832710\pi\)
\(854\) 58.9304 9.33366i 2.01656 0.319391i
\(855\) 7.26543 + 2.36068i 0.248472 + 0.0807335i
\(856\) 34.9144 + 17.7898i 1.19335 + 0.608042i
\(857\) −15.0344 + 10.9232i −0.513567 + 0.373128i −0.814175 0.580620i \(-0.802810\pi\)
0.300608 + 0.953748i \(0.402810\pi\)
\(858\) −3.37540 + 6.62460i −0.115234 + 0.226160i
\(859\) −24.3112 17.6631i −0.829487 0.602658i 0.0899269 0.995948i \(-0.471337\pi\)
−0.919414 + 0.393291i \(0.871337\pi\)
\(860\) −3.09017 + 4.25325i −0.105374 + 0.145035i
\(861\) −1.38197 1.90211i −0.0470973 0.0648238i
\(862\) 27.1246 + 27.1246i 0.923868 + 0.923868i
\(863\) 32.7194 1.11378 0.556891 0.830585i \(-0.311994\pi\)
0.556891 + 0.830585i \(0.311994\pi\)
\(864\) 3.51824 22.2133i 0.119693 0.755711i
\(865\) 3.06231 9.42481i 0.104122 0.320453i
\(866\) 14.5187 28.4945i 0.493364 0.968282i
\(867\) 22.0583 0.749140
\(868\) 45.9937 10.4721i 1.56113 0.355447i
\(869\) 21.3050 0.722721
\(870\) 0.967282 1.89840i 0.0327939 0.0643617i
\(871\) 15.7517 48.4787i 0.533726 1.64264i
\(872\) 20.0590 + 3.17704i 0.679284 + 0.107588i
\(873\) 18.4721 0.625187
\(874\) −15.3884 15.3884i −0.520521 0.520521i
\(875\) 14.8006 + 20.3713i 0.500353 + 0.688676i
\(876\) 1.38197 + 1.00406i 0.0466923 + 0.0339239i
\(877\) −17.4721 12.6942i −0.589992 0.428654i 0.252320 0.967644i \(-0.418806\pi\)
−0.842313 + 0.538989i \(0.818806\pi\)
\(878\) −8.64964 + 16.9759i −0.291911 + 0.572908i
\(879\) 6.91467 5.02380i 0.233226 0.169449i
\(880\) −1.11006 3.41641i −0.0374201 0.115167i
\(881\) 4.30902 + 1.40008i 0.145174 + 0.0471700i 0.380703 0.924697i \(-0.375682\pi\)
−0.235528 + 0.971867i \(0.575682\pi\)
\(882\) −37.7915 + 5.98559i −1.27251 + 0.201545i
\(883\) −11.1477 + 34.3090i −0.375149 + 1.15459i 0.568229 + 0.822871i \(0.307629\pi\)
−0.943378 + 0.331720i \(0.892371\pi\)
\(884\) −65.1864 21.1803i −2.19246 0.712372i
\(885\) −0.916408 + 1.26133i −0.0308047 + 0.0423991i
\(886\) 39.2193 19.9832i 1.31760 0.671350i
\(887\) −53.3449 + 17.3328i −1.79115 + 0.581979i −0.999577 0.0290987i \(-0.990736\pi\)
−0.791571 + 0.611078i \(0.790736\pi\)
\(888\) 0.700682 4.42393i 0.0235133 0.148457i
\(889\) −16.0172 + 5.20431i −0.537200 + 0.174547i
\(890\) −2.36411 14.9264i −0.0792452 0.500335i
\(891\) −5.32282 3.86726i −0.178321 0.129558i
\(892\) 10.8541 + 14.9394i 0.363422 + 0.500208i
\(893\) 16.9098 0.565866
\(894\) −7.88597 + 7.88597i −0.263746 + 0.263746i
\(895\) −1.31433 + 0.954915i −0.0439331 + 0.0319193i
\(896\) 21.7578 + 42.7021i 0.726877 + 1.42658i
\(897\) −10.5902 + 3.44095i −0.353595 + 0.114890i
\(898\) 36.3772 + 36.3772i 1.21392 + 1.21392i
\(899\) −14.0616 12.2984i −0.468980 0.410174i
\(900\) 22.8328i 0.761094i
\(901\) −4.63525 14.2658i −0.154423 0.475264i
\(902\) 0.712701 + 1.39875i 0.0237304 + 0.0465734i
\(903\) 7.69421 + 10.5902i 0.256047 + 0.352419i
\(904\) 23.1246 + 23.1246i 0.769113 + 0.769113i
\(905\) 1.90211i 0.0632284i
\(906\) −2.54562 + 16.0724i −0.0845726 + 0.533970i
\(907\) 15.0579 20.7254i 0.499989 0.688176i −0.482202 0.876060i \(-0.660163\pi\)
0.982191 + 0.187884i \(0.0601628\pi\)
\(908\) 2.90983 + 2.11412i 0.0965661 + 0.0701594i
\(909\) 6.83282 + 21.0292i 0.226630 + 0.697496i
\(910\) −2.88426 + 18.2105i −0.0956123 + 0.603672i
\(911\) −4.14725 12.7639i −0.137405 0.422888i 0.858552 0.512727i \(-0.171365\pi\)
−0.995956 + 0.0898391i \(0.971365\pi\)
\(912\) −13.8197 4.49028i −0.457615 0.148688i
\(913\) −7.56231 5.49434i −0.250276 0.181836i
\(914\) 15.3789 7.83592i 0.508688 0.259189i
\(915\) −4.25325 1.38197i −0.140608 0.0456864i
\(916\) −30.7768 22.3607i −1.01690 0.738818i
\(917\) −24.6803 + 75.9583i −0.815017 + 2.50836i
\(918\) −17.5666 + 34.4765i −0.579785 + 1.13789i
\(919\) −17.3233 23.8435i −0.571443 0.786523i 0.421282 0.906930i \(-0.361580\pi\)
−0.992725 + 0.120406i \(0.961580\pi\)
\(920\) 2.44246 4.79360i 0.0805256 0.158040i
\(921\) 13.3303 18.3476i 0.439248 0.604574i
\(922\) −8.99770 56.8092i −0.296323 1.87091i
\(923\) −17.6538 + 12.8262i −0.581082 + 0.422181i
\(924\) −8.94427 −0.294245
\(925\) 10.0656i 0.330955i
\(926\) 1.28587 8.11869i 0.0422564 0.266797i
\(927\) 2.13914 + 0.695048i 0.0702585 + 0.0228284i
\(928\) 8.61668 16.9112i 0.282856 0.555137i
\(929\) 6.11488i 0.200623i −0.994956 0.100311i \(-0.968016\pi\)
0.994956 0.100311i \(-0.0319839\pi\)
\(930\) −3.42802 0.865718i −0.112409 0.0283880i
\(931\) 54.7214i 1.79342i
\(932\) −27.2501 + 8.85410i −0.892607 + 0.290026i
\(933\) 8.81966 + 2.86568i 0.288743 + 0.0938182i
\(934\) −35.4239 5.61059i −1.15910 0.183584i
\(935\) 6.18034i 0.202119i
\(936\) 24.6215 24.6215i 0.804778 0.804778i
\(937\) 15.8435 11.5109i 0.517583 0.376046i −0.298109 0.954532i \(-0.596356\pi\)
0.815693 + 0.578485i \(0.196356\pi\)
\(938\) 60.5663 9.59276i 1.97756 0.313215i
\(939\) −3.48622 + 4.79837i −0.113769 + 0.156589i
\(940\) 1.29180 + 3.97574i 0.0421337 + 0.129674i
\(941\) 15.8541 + 21.8213i 0.516829 + 0.711354i 0.985052 0.172256i \(-0.0551057\pi\)
−0.468223 + 0.883610i \(0.655106\pi\)
\(942\) 0.864478 + 0.440474i 0.0281662 + 0.0143514i
\(943\) −0.726543 + 2.23607i −0.0236595 + 0.0728164i
\(944\) −8.16348 + 11.2361i −0.265699 + 0.365703i
\(945\) 9.89919 + 3.21644i 0.322021 + 0.104631i
\(946\) −3.96802 7.78768i −0.129012 0.253199i
\(947\) 9.40456 + 6.83282i 0.305607 + 0.222037i 0.730009 0.683437i \(-0.239516\pi\)
−0.424402 + 0.905474i \(0.639516\pi\)
\(948\) 20.2622 + 6.58359i 0.658086 + 0.213825i
\(949\) 1.80902 + 5.56758i 0.0587232 + 0.180731i
\(950\) −32.2524 5.10828i −1.04641 0.165734i
\(951\) −2.84066 8.74265i −0.0921146 0.283500i
\(952\) −12.8988 81.4398i −0.418053 2.63948i
\(953\) −9.73607 + 13.4005i −0.315382 + 0.434086i −0.937050 0.349194i \(-0.886455\pi\)
0.621668 + 0.783281i \(0.286455\pi\)
\(954\) 7.52644 + 1.19207i 0.243677 + 0.0385947i
\(955\) 9.47214i 0.306511i
\(956\) 52.8352i 1.70881i
\(957\) 2.08204 + 2.86568i 0.0673028 + 0.0926343i
\(958\) −22.4541 + 11.4409i −0.725458 + 0.369640i
\(959\) −1.17557 3.61803i −0.0379612 0.116832i
\(960\) 3.59222i 0.115939i
\(961\) −14.7188 + 27.2829i −0.474802 + 0.880093i
\(962\) 10.8541 10.8541i 0.349950 0.349950i
\(963\) 32.5729 10.5836i 1.04965 0.341051i
\(964\) −1.90211 + 5.85410i −0.0612629 + 0.188548i
\(965\) −7.42705 + 5.39607i −0.239085 + 0.173706i
\(966\) −9.47214 9.47214i −0.304761 0.304761i
\(967\) 18.0826 0.581497 0.290748 0.956800i \(-0.406096\pi\)
0.290748 + 0.956800i \(0.406096\pi\)
\(968\) −24.8311 3.93286i −0.798101 0.126407i
\(969\) 20.2254 + 14.6946i 0.649734 + 0.472060i
\(970\) 6.45048 1.02166i 0.207112 0.0328034i
\(971\) 40.4792 13.1525i 1.29904 0.422083i 0.423791 0.905760i \(-0.360699\pi\)
0.875247 + 0.483677i \(0.160699\pi\)
\(972\) −17.8885 24.6215i −0.573775 0.789734i
\(973\) 1.80902 0.587785i 0.0579944 0.0188435i
\(974\) −4.35040 8.53814i −0.139396 0.273580i
\(975\) −9.82084 + 13.5172i −0.314518 + 0.432898i
\(976\) −37.8885 12.3107i −1.21278 0.394057i
\(977\) 2.47214 7.60845i 0.0790906 0.243416i −0.903691 0.428184i \(-0.859153\pi\)
0.982782 + 0.184768i \(0.0591534\pi\)
\(978\) −3.20573 20.2402i −0.102508 0.647209i
\(979\) 23.8949 + 7.76393i 0.763685 + 0.248136i
\(980\) −12.8658 + 4.18034i −0.410982 + 0.133536i
\(981\) 14.3607 10.4336i 0.458501 0.333121i
\(982\) 41.7437 + 21.2695i 1.33209 + 0.678736i
\(983\) 25.1235 + 18.2533i 0.801315 + 0.582190i 0.911300 0.411744i \(-0.135080\pi\)
−0.109985 + 0.993933i \(0.535080\pi\)
\(984\) 0.245580 + 1.55053i 0.00782881 + 0.0494291i
\(985\) 6.77051 + 9.31881i 0.215726 + 0.296922i
\(986\) −23.0902 + 23.0902i −0.735341 + 0.735341i
\(987\) 10.4086 0.331310
\(988\) −29.2705 40.2874i −0.931219 1.28171i
\(989\) 4.04508 12.4495i 0.128626 0.395871i
\(990\) −2.79751 1.42540i −0.0889107 0.0453023i
\(991\) 20.9232 0.664649 0.332324 0.943165i \(-0.392167\pi\)
0.332324 + 0.943165i \(0.392167\pi\)
\(992\) −30.5373 7.71193i −0.969560 0.244854i
\(993\) −20.9787 −0.665739
\(994\) −23.3899 11.9177i −0.741882 0.378008i
\(995\) 2.93893 9.04508i 0.0931702 0.286748i
\(996\) −5.49434 7.56231i −0.174095 0.239621i
\(997\) −48.5279 −1.53689 −0.768446 0.639914i \(-0.778970\pi\)
−0.768446 + 0.639914i \(0.778970\pi\)
\(998\) 3.01217 3.01217i 0.0953486 0.0953486i
\(999\) −5.09353 7.01064i −0.161152 0.221807i
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 124.2.j.a.27.2 yes 8
4.3 odd 2 inner 124.2.j.a.27.1 yes 8
31.23 odd 10 inner 124.2.j.a.23.1 8
124.23 even 10 inner 124.2.j.a.23.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
124.2.j.a.23.1 8 31.23 odd 10 inner
124.2.j.a.23.2 yes 8 124.23 even 10 inner
124.2.j.a.27.1 yes 8 4.3 odd 2 inner
124.2.j.a.27.2 yes 8 1.1 even 1 trivial