LMFDB - Embedded newform 552.2.bf.a.5.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(5,552)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 11, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("552.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bf (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$920$
Relative dimension:	$92$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.14
Character	$\chi$	$=$	552.5
Dual form			552.2.bf.a.221.14

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26067 + 0.640864i) q^{2} +(0.0422748 - 1.73153i) q^{3} +(1.17859 - 1.61584i) q^{4} +(0.349508 + 0.0502517i) q^{5} +(1.05638 + 2.20999i) q^{6} +(-2.03405 + 0.928918i) q^{7} +(-0.450281 + 2.79236i) q^{8} +(-2.99643 - 0.146400i) q^{9} +O(q^{10})$	\(q+(-1.26067 + 0.640864i) q^{2} +(0.0422748 - 1.73153i) q^{3} +(1.17859 - 1.61584i) q^{4} +(0.349508 + 0.0502517i) q^{5} +(1.05638 + 2.20999i) q^{6} +(-2.03405 + 0.928918i) q^{7} +(-0.450281 + 2.79236i) q^{8} +(-2.99643 - 0.146400i) q^{9} +(-0.472820 + 0.160636i) q^{10} +(1.12602 + 3.83486i) q^{11} +(-2.74805 - 2.10907i) q^{12} +(-1.80537 - 0.824483i) q^{13} +(1.96896 - 2.47461i) q^{14} +(0.101788 - 0.603061i) q^{15} +(-1.22186 - 3.80881i) q^{16} +(-4.63384 + 2.97799i) q^{17} +(3.87133 - 1.73574i) q^{18} +(-4.29786 - 2.76207i) q^{19} +(0.493124 - 0.505522i) q^{20} +(1.52246 + 3.56129i) q^{21} +(-3.87716 - 4.11288i) q^{22} +(2.87421 + 3.83913i) q^{23} +(4.81602 + 0.897723i) q^{24} +(-4.67783 - 1.37354i) q^{25} +(2.80436 - 0.117591i) q^{26} +(-0.380171 + 5.18223i) q^{27} +(-0.896321 + 4.38150i) q^{28} +(2.50090 - 1.60723i) q^{29} +(0.258159 + 0.825494i) q^{30} +(6.12589 + 7.06965i) q^{31} +(3.98130 + 4.01862i) q^{32} +(6.68779 - 1.78762i) q^{33} +(3.93327 - 6.72393i) q^{34} +(-0.757595 + 0.222450i) q^{35} +(-3.76811 + 4.66919i) q^{36} +(0.0172901 + 0.120255i) q^{37} +(7.18830 + 0.727718i) q^{38} +(-1.50394 + 3.09120i) q^{39} +(-0.297697 + 0.953323i) q^{40} +(-7.06660 - 1.01602i) q^{41} +(-4.20163 - 3.51393i) q^{42} +(2.56719 - 2.96270i) q^{43} +(7.52362 + 2.70026i) q^{44} +(-1.03992 - 0.201744i) q^{45} +(-6.08379 - 2.99791i) q^{46} +8.82061i q^{47} +(-6.64675 + 1.95468i) q^{48} +(-1.30957 + 1.51132i) q^{49} +(6.77746 - 1.26628i) q^{50} +(4.96060 + 8.14955i) q^{51} +(-3.46001 + 1.94545i) q^{52} +(-10.1247 + 4.62381i) q^{53} +(-2.84183 - 6.77673i) q^{54} +(0.200844 + 1.39690i) q^{55} +(-1.67798 - 6.09805i) q^{56} +(-4.96431 + 7.32513i) q^{57} +(-2.12280 + 3.62893i) q^{58} +(2.81179 - 6.15696i) q^{59} +(-0.854483 - 0.875233i) q^{60} +(4.63948 + 5.35425i) q^{61} +(-12.2534 - 4.98665i) q^{62} +(6.23086 - 2.48565i) q^{63} +(-7.59449 - 2.51469i) q^{64} +(-0.589559 - 0.378886i) q^{65} +(-7.28549 + 6.53956i) q^{66} +(-0.685736 - 0.201350i) q^{67} +(-0.649442 + 10.9974i) q^{68} +(6.76909 - 4.81450i) q^{69} +(0.812519 - 0.765952i) q^{70} +(1.95249 - 6.64958i) q^{71} +(1.75804 - 8.30116i) q^{72} +(-12.4715 - 8.01497i) q^{73} +(-0.0988641 - 0.140522i) q^{74} +(-2.57608 + 8.04177i) q^{75} +(-9.52846 + 3.68931i) q^{76} +(-5.85264 - 6.75430i) q^{77} +(-0.0850590 - 4.86081i) q^{78} +(2.08355 + 0.951524i) q^{79} +(-0.235652 - 1.39261i) q^{80} +(8.95713 + 0.877356i) q^{81} +(9.55979 - 3.24785i) q^{82} +(-8.23829 + 1.18449i) q^{83} +(7.54883 + 1.73724i) q^{84} +(-1.76921 + 0.807973i) q^{85} +(-1.33770 + 5.38021i) q^{86} +(-2.67725 - 4.39834i) q^{87} +(-11.2153 + 1.41747i) q^{88} +(-5.97472 + 6.89519i) q^{89} +(1.44029 - 0.412113i) q^{90} +4.43808 q^{91} +(9.59092 - 0.119505i) q^{92} +(12.5003 - 10.3083i) q^{93} +(-5.65281 - 11.1199i) q^{94} +(-1.36334 - 1.18134i) q^{95} +(7.12668 - 6.72387i) q^{96} +(13.6045 + 1.95603i) q^{97} +(0.682385 - 2.74454i) q^{98} +(-2.81260 - 11.6557i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9}+O(q^{10}) $ 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9	$ 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9} - 22 q^{10} - 12 q^{12} - 22 q^{15} - 30 q^{16} - 10 q^{18} - 14 q^{24} + 40 q^{25} - 22 q^{28} - 11 q^{30} - 20 q^{31} - 22 q^{33} - 18 q^{36} - 42 q^{39} - 176 q^{40} - 11 q^{42} + 90 q^{46} - 64 q^{48} + 32 q^{49} - 90 q^{52} + 21 q^{54} - 76 q^{55} - 22 q^{57} + 76 q^{58} - 11 q^{60} - 22 q^{63} - 28 q^{64} - 44 q^{66} - 116 q^{70} - 79 q^{72} - 36 q^{73} - 22 q^{76} - 134 q^{78} - 44 q^{79} - 34 q^{81} - 40 q^{82} - 165 q^{84} - 18 q^{87} - 22 q^{88} - 198 q^{90} + 88 q^{94} - 231 q^{96} - 44 q^{97}+O(q^{100}) $ 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9 - 22 * q^10 - 12 * q^12 - 22 * q^15 - 30 * q^16 - 10 * q^18 - 14 * q^24 + 40 * q^25 - 22 * q^28 - 11 * q^30 - 20 * q^31 - 22 * q^33 - 18 * q^36 - 42 * q^39 - 176 * q^40 - 11 * q^42 + 90 * q^46 - 64 * q^48 + 32 * q^49 - 90 * q^52 + 21 * q^54 - 76 * q^55 - 22 * q^57 + 76 * q^58 - 11 * q^60 - 22 * q^63 - 28 * q^64 - 44 * q^66 - 116 * q^70 - 79 * q^72 - 36 * q^73 - 22 * q^76 - 134 * q^78 - 44 * q^79 - 34 * q^81 - 40 * q^82 - 165 * q^84 - 18 * q^87 - 22 * q^88 - 198 * q^90 + 88 * q^94 - 231 * q^96 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$-1$	$-1$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.26067	+	0.640864i	−0.891430	+	0.453159i
$2$	−1.26067	+	0.640864i	−0.891430	+	0.453159i
$3$	0.0422748	−	1.73153i	0.0244074	−	0.999702i
$3$	0.0422748	−	1.73153i	0.0244074	−	0.999702i
$4$	1.17859	−	1.61584i	0.589294	−	0.807919i
$5$	0.349508	+	0.0502517i	0.156305	+	0.0224732i	0.220023	−	0.975495i	$-0.429387\pi$
$5$	0.349508	+	0.0502517i	0.156305	+	0.0224732i	−0.0637182	+	0.997968i	$0.520296\pi$
$6$	1.05638	+	2.20999i	0.431267	+	0.902225i
$7$	−2.03405	+	0.928918i	−0.768797	+	0.351098i	−0.760899	−	0.648871i	$-0.775242\pi$
$7$	−2.03405	+	0.928918i	−0.768797	+	0.351098i	−0.00789867	+	0.999969i	$0.502514\pi$
$8$	−0.450281	+	2.79236i	−0.159198	+	0.987247i
$9$	−2.99643	−	0.146400i	−0.998809	−	0.0488002i
$10$	−0.472820	+	0.160636i	−0.149519	+	0.0507976i
$11$	1.12602	+	3.83486i	0.339507	+	1.15625i	0.935518	+	0.353278i	$0.114933\pi$
$11$	1.12602	+	3.83486i	0.339507	+	1.15625i	−0.596012	+	0.802976i	$0.703249\pi$
$12$	−2.74805	−	2.10907i	−0.793295	−	0.608837i
$13$	−1.80537	−	0.824483i	−0.500719	−	0.228671i	0.149011	−	0.988835i	$-0.452391\pi$
$13$	−1.80537	−	0.824483i	−0.500719	−	0.228671i	−0.649730	+	0.760165i	$0.725118\pi$
$14$	1.96896	−	2.47461i	0.526225	−	0.661366i
$15$	0.101788	−	0.603061i	0.0262815	−	0.155710i
$16$	−1.22186	−	3.80881i	−0.305466	−	0.952203i
$17$	−4.63384	+	2.97799i	−1.12387	+	0.722269i	−0.964272	−	0.264913i	$-0.914657\pi$
$17$	−4.63384	+	2.97799i	−1.12387	+	0.722269i	−0.159600	+	0.987182i	$0.551020\pi$
$18$	3.87133	−	1.73574i	0.912482	−	0.409117i
$19$	−4.29786	−	2.76207i	−0.985997	−	0.633662i	−0.0549224	−	0.998491i	$-0.517491\pi$
$19$	−4.29786	−	2.76207i	−0.985997	−	0.633662i	−0.931075	+	0.364829i	$0.881128\pi$
$20$	0.493124	−	0.505522i	0.110266	−	0.113038i
$21$	1.52246	+	3.56129i	0.332229	+	0.777138i
$22$	−3.87716	−	4.11288i	−0.826613	−	0.876868i
$23$	2.87421	+	3.83913i	0.599314	+	0.800514i
$23$	2.87421	+	3.83913i	0.599314	+	0.800514i
$24$	4.81602	+	0.897723i	0.983067	+	0.183247i
$25$	−4.67783	−	1.37354i	−0.935567	−	0.274707i
$26$	2.80436	−	0.117591i	0.549980	−	0.0230615i
$27$	−0.380171	+	5.18223i	−0.0731639	+	0.997320i
$28$	−0.896321	+	4.38150i	−0.169389	+	0.828026i
$29$	2.50090	−	1.60723i	0.464406	−	0.298455i	−0.287435	−	0.957800i	$-0.592803\pi$
$29$	2.50090	−	1.60723i	0.464406	−	0.298455i	0.751841	+	0.659345i	$0.229166\pi$
$30$	0.258159	+	0.825494i	0.0471331	+	0.150714i
$31$	6.12589	+	7.06965i	1.10024	+	1.26975i	0.960112	+	0.279614i	$0.0902065\pi$
$31$	6.12589	+	7.06965i	1.10024	+	1.26975i	0.140130	+	0.990133i	$0.455248\pi$
$32$	3.98130	+	4.01862i	0.703801	+	0.710398i
$33$	6.68779	−	1.78762i	1.16420	−	0.311184i
$34$	3.93327	−	6.72393i	0.674550	−	1.15314i
$35$	−0.757595	+	0.222450i	−0.128057	+	0.0376009i
$36$	−3.76811	+	4.66919i	−0.628018	+	0.778199i
$37$	0.0172901	+	0.120255i	0.00284247	+	0.0197698i	0.991193	−	0.132423i	$-0.0422757\pi$
$37$	0.0172901	+	0.120255i	0.00284247	+	0.0197698i	−0.988351	+	0.152193i	$0.951367\pi$
$38$	7.18830	+	0.727718i	1.16610	+	0.118052i
$39$	−1.50394	+	3.09120i	−0.240824	+	0.494988i
$40$	−0.297697	+	0.953323i	−0.0470701	+	0.150734i
$41$	−7.06660	−	1.01602i	−1.10362	−	0.158676i	−0.433660	−	0.901076i	$-0.642778\pi$
$41$	−7.06660	−	1.01602i	−1.10362	−	0.158676i	−0.669957	+	0.742400i	$0.733687\pi$
$42$	−4.20163	−	3.51393i	−0.648326	−	0.542211i
$43$	2.56719	−	2.96270i	0.391493	−	0.451808i	−0.525450	−	0.850824i	$-0.676103\pi$
$43$	2.56719	−	2.96270i	0.391493	−	0.451808i	0.916944	+	0.399017i	$0.130649\pi$
$44$	7.52362	+	2.70026i	1.13423	+	0.407079i
$45$	−1.03992	−	0.201744i	−0.155022	−	0.0300742i
$46$	−6.08379	−	2.99791i	−0.897007	−	0.442017i
$47$			8.82061i			1.28662i	0.765607	+	0.643309i	$0.222439\pi$
$47$			8.82061i			1.28662i	−0.765607	+	0.643309i	$0.777561\pi$
$48$	−6.64675	+	1.95468i	−0.959375	+	0.282134i
$49$	−1.30957	+	1.51132i	−0.187081	+	0.215903i
$50$	6.77746	−	1.26628i	0.958478	−	0.179078i
$51$	4.96060	+	8.14955i	0.694623	+	1.14117i
$52$	−3.46001	+	1.94545i	−0.479818	+	0.269786i
$53$	−10.1247	+	4.62381i	−1.39074	+	0.635129i	−0.963180	−	0.268858i	$-0.913354\pi$
$53$	−10.1247	+	4.62381i	−1.39074	+	0.635129i	−0.427560	+	0.903987i	$0.640627\pi$
$54$	−2.84183	−	6.77673i	−0.386724	−	0.922195i
$55$	0.200844	+	1.39690i	0.0270818	+	0.188358i
$56$	−1.67798	−	6.09805i	−0.224229	−	0.814887i
$57$	−4.96431	+	7.32513i	−0.657539	+	0.970237i
$58$	−2.12280	+	3.62893i	−0.278737	+	0.476502i
$59$	2.81179	−	6.15696i	0.366064	−	0.801568i	−0.633548	−	0.773703i	$-0.718402\pi$
$59$	2.81179	−	6.15696i	0.366064	−	0.801568i	0.999612	−	0.0278642i	$-0.00887060\pi$
$60$	−0.854483	−	0.875233i	−0.110313	−	0.112992i
$61$	4.63948	+	5.35425i	0.594025	+	0.685542i	0.970560	−	0.240861i	$-0.0774298\pi$
$61$	4.63948	+	5.35425i	0.594025	+	0.685542i	−0.376534	+	0.926403i	$0.622884\pi$
$62$	−12.2534	−	4.98665i	−1.55619	−	0.633306i
$63$	6.23086	−	2.48565i	0.785015	−	0.313162i
$64$	−7.59449	−	2.51469i	−0.949312	−	0.314336i
$65$	−0.589559	−	0.378886i	−0.0731258	−	0.0469951i
$66$	−7.28549	+	6.53956i	−0.896782	+	0.804965i
$67$	−0.685736	−	0.201350i	−0.0837760	−	0.0245989i	0.239576	−	0.970878i	$-0.422992\pi$
$67$	−0.685736	−	0.201350i	−0.0837760	−	0.0245989i	−0.323352	+	0.946279i	$0.604810\pi$
$68$	−0.649442	+	10.9974i	−0.0787564	+	1.33363i
$69$	6.76909	−	4.81450i	0.814903	−	0.579597i
$70$	0.812519	−	0.765952i	0.0971146	−	0.0915487i
$71$	1.95249	−	6.64958i	0.231718	−	0.789160i	−0.758745	−	0.651387i	$-0.774187\pi$
$71$	1.95249	−	6.64958i	0.231718	−	0.789160i	0.990464	−	0.137773i	$-0.0439945\pi$
$72$	1.75804	−	8.30116i	0.207186	−	0.978301i
$73$	−12.4715	−	8.01497i	−1.45968	−	0.938081i	−0.998716	−	0.0506640i	$-0.983866\pi$
$73$	−12.4715	−	8.01497i	−1.45968	−	0.938081i	−0.460967	−	0.887417i	$-0.652497\pi$
$74$	−0.0988641	−	0.140522i	−0.0114927	−	0.0163353i
$75$	−2.57608	+	8.04177i	−0.297460	+	0.928583i
$76$	−9.52846	+	3.68931i	−1.09299	+	0.423193i
$77$	−5.85264	−	6.75430i	−0.666970	−	0.769724i
$78$	−0.0850590	−	4.86081i	−0.00963104	−	0.550379i
$79$	2.08355	+	0.951524i	0.234417	+	0.107055i	0.529161	−	0.848522i	$-0.322507\pi$
$79$	2.08355	+	0.951524i	0.234417	+	0.107055i	−0.294743	+	0.955576i	$0.595234\pi$
$80$	−0.235652	−	1.39261i	−0.0263466	−	0.155699i
$81$	8.95713	+	0.877356i	0.995237	+	0.0974840i
$82$	9.55979	−	3.24785i	1.05570	−	0.358665i
$83$	−8.23829	+	1.18449i	−0.904270	+	0.130014i	−0.578735	−	0.815516i	$-0.696453\pi$
$83$	−8.23829	+	1.18449i	−0.904270	+	0.130014i	−0.325535	+	0.945530i	$0.605544\pi$
$84$	7.54883	+	1.73724i	0.823645	+	0.189548i
$85$	−1.76921	+	0.807973i	−0.191898	+	0.0876370i
$86$	−1.33770	+	5.38021i	−0.144248	+	0.580163i
$87$	−2.67725	−	4.39834i	−0.287032	−	0.471552i
$88$	−11.2153	+	1.41747i	−1.19556	+	0.151103i
$89$	−5.97472	+	6.89519i	−0.633319	+	0.730889i	−0.978179	−	0.207765i	$-0.933381\pi$
$89$	−5.97472	+	6.89519i	−0.633319	+	0.730889i	0.344860	+	0.938654i	$0.387926\pi$
$90$	1.44029	−	0.412113i	0.151819	−	0.0434405i
$91$	4.43808			0.465237
$92$	9.59092	−	0.119505i	0.999922	−	0.0124593i
$93$	12.5003	−	10.3083i	1.29622	−	1.06892i
$94$	−5.65281	−	11.1199i	−0.583042	−	1.14693i
$95$	−1.36334	−	1.18134i	−0.139876	−	0.121203i
$96$	7.12668	−	6.72387i	0.727364	−	0.686252i
$97$	13.6045	+	1.95603i	1.38133	+	0.198605i	0.792607	−	0.609732i	$-0.208723\pi$
$97$	13.6045	+	1.95603i	1.38133	+	0.198605i	0.588720	+	0.808337i	$0.299632\pi$
$98$	0.682385	−	2.74454i	0.0689313	−	0.277240i
$99$	−2.81260	−	11.6557i	−0.282677	−	1.17144i
$100$	−7.73265	+	5.93979i	−0.773265	+	0.593979i
$101$	−2.16918	−	15.0870i	−0.215842	−	1.50121i	−0.753162	−	0.657835i	$-0.771472\pi$
$101$	−2.16918	−	15.0870i	−0.215842	−	1.50121i	0.537320	−	0.843378i	$-0.319437\pi$
$102$	−11.4764	−	7.09485i	−1.13634	−	0.702494i
$103$	3.21191	+	10.9388i	0.316479	+	1.07783i	0.952090	+	0.305819i	$0.0989302\pi$
$103$	3.21191	+	10.9388i	0.316479	+	1.07783i	−0.635611	+	0.772010i	$0.719252\pi$
$104$	3.11517	−	4.66998i	0.305468	−	0.457929i
$105$	0.353153	+	1.32121i	0.0344642	+	0.128937i
$106$	9.80074	−	12.3177i	0.951932	−	1.19640i
$107$	−7.59255	+	6.57898i	−0.733999	+	0.636014i	−0.939463	−	0.342651i	$-0.888675\pi$
$107$	−7.59255	+	6.57898i	−0.733999	+	0.636014i	0.205464	+	0.978665i	$0.434130\pi$
$108$	7.92557	+	6.72200i	0.762638	+	0.646825i
$109$	10.3864	−	6.67496i	0.994841	−	0.639345i	0.0614137	−	0.998112i	$-0.480439\pi$
$109$	10.3864	−	6.67496i	0.994841	−	0.639345i	0.933427	+	0.358767i	$0.116803\pi$
$110$	−1.14842	−	1.63232i	−0.109497	−	0.155635i
$111$	0.208957	−	0.0248546i	0.0198333	−	0.00235909i
$112$	6.02340	+	6.61229i	0.569158	+	0.624803i
$113$	2.37904	+	0.698548i	0.223801	+	0.0657139i	0.391710	−	0.920089i	$-0.371883\pi$
$113$	2.37904	+	0.698548i	0.223801	+	0.0657139i	−0.167910	+	0.985802i	$0.553702\pi$
$114$	1.56395	−	12.4160i	0.146478	−	1.16287i
$115$	0.811637	+	1.48624i	0.0756855	+	0.138593i
$116$	0.350506	−	5.93531i	0.0325437	−	0.551080i
$117$	5.28894	+	2.73481i	0.488963	+	0.252833i
$118$	0.401027	+	9.56388i	0.0369176	+	0.880426i
$119$	6.65914	−	10.3618i	0.610443	−	0.949867i
$120$	1.63813	+	0.555775i	0.149540	+	0.0507351i
$121$	−4.18444	+	2.68918i	−0.380404	+	0.244471i
$122$	−9.28021	−	3.77668i	−0.840191	−	0.341924i
$123$	−2.05802	+	12.1931i	−0.185565	+	1.09942i
$124$	18.6433	−	1.56624i	1.67422	−	0.140652i
$125$	−3.17188	−	1.44855i	−0.283702	−	0.129562i
$126$	−6.26211	+	7.12672i	−0.557873	+	0.634899i
$127$	−10.5327	+	3.09267i	−0.934625	+	0.274431i	−0.713372	−	0.700786i	$-0.752833\pi$
$127$	−10.5327	+	3.09267i	−0.934625	+	0.274431i	−0.221253	+	0.975216i	$0.571015\pi$
$128$	11.1857	−	1.69684i	0.988689	−	0.149981i
$129$	−5.02149	−	4.57043i	−0.442118	−	0.402404i
$130$	0.986055	+	0.0998247i	0.0864827	+	0.00875521i
$131$	−1.44027	−	3.15375i	−0.125837	−	0.275545i	0.836219	−	0.548395i	$-0.184761\pi$
$131$	−1.44027	−	3.15375i	−0.125837	−	0.275545i	−0.962057	+	0.272850i	$0.912034\pi$
$132$	4.99365	−	12.9133i	0.434641	−	1.12395i
$133$	11.3078	+	1.62581i	0.980509	+	0.140976i
$134$	0.993527	−	0.185627i	0.0858276	−	0.0160357i
$135$	−0.393288	+	1.79213i	−0.0338489	+	0.154242i
$136$	−6.22907	−	14.2803i	−0.534139	−	1.22452i
$137$	14.2656			1.21879			0.609394	−	0.792867i	$-0.291413\pi$
$137$	14.2656			1.21879			0.609394	+	0.792867i	$0.291413\pi$
$138$	−5.44817	+	10.4076i	−0.463779	+	0.885951i
$139$		−	2.60732i		−	0.221150i	−0.993868	−	0.110575i	$-0.964731\pi$
$139$		−	2.60732i		−	0.221150i	0.993868	−	0.110575i	$-0.0352692\pi$
$140$	−0.533449	+	1.48633i	−0.0450847	+	0.125618i
$141$	15.2732	+	0.372889i	1.28623	+	0.0314029i
$142$	1.80002	+	9.63423i	0.151054	+	0.808486i
$143$	1.12891	−	7.85171i	0.0944038	−	0.656593i
$144$	3.10361	+	11.5917i	0.258634	+	0.965975i
$145$	0.954851	−	0.436066i	0.0792961	−	0.0362133i
$146$	20.8590	+	2.11169i	1.72630	+	0.174765i
$147$	2.56155	+	2.33146i	0.211273	+	0.192295i
$148$	0.214690	+	0.113793i	0.0176474	+	0.00935374i
$149$	0.261678	+	0.891192i	0.0214375	+	0.0730093i	0.969517	−	0.245024i	$-0.0787958\pi$
$149$	0.261678	+	0.891192i	0.0214375	+	0.0730093i	−0.948080	+	0.318033i	$0.896978\pi$
$150$	−1.90608	−	11.7889i	−0.155631	−	0.962563i
$151$	−1.96565	+	4.30418i	−0.159963	+	0.350269i	−0.972594	−	0.232508i	$-0.925307\pi$
$151$	−1.96565	+	4.30418i	−0.159963	+	0.350269i	0.812632	+	0.582777i	$0.198034\pi$
$152$	9.64792	−	10.7574i	0.782550	−	0.872544i
$153$	14.3209	−	8.24493i	1.15778	−	0.666563i
$154$	11.7068	+	4.76422i	0.943364	+	0.383912i
$155$	1.78579	+	2.77874i	0.143438	+	0.223194i
$156$	3.22235	+	6.07338i	0.257994	+	0.486260i
$157$	−16.4963	−	10.6015i	−1.31655	−	0.846095i	−0.321640	−	0.946862i	$-0.604234\pi$
$157$	−16.4963	−	10.6015i	−1.31655	−	0.846095i	−0.994910	+	0.100767i	$0.967870\pi$
$158$	−3.23647	+	0.135710i	−0.257479	+	0.0107965i
$159$	7.57827	+	17.7268i	0.600996	+	1.40583i
$160$	1.18955	+	1.60461i	0.0940424	+	0.126855i
$161$	−9.41251	−	5.13906i	−0.741810	−	0.405015i
$162$	−11.8543	+	4.63424i	−0.931360	+	0.364100i
$163$	2.74464	−	9.34737i	0.214977	−	0.732143i	−0.779427	−	0.626493i	$-0.784490\pi$
$163$	2.74464	−	9.34737i	0.214977	−	0.732143i	0.994403	−	0.105650i	$-0.0336922\pi$
$164$	−9.97033	+	10.2210i	−0.778552	+	0.798126i
$165$	2.42727	−	0.288714i	0.188963	−	0.0224764i
$166$	9.62669	−	6.77287i	0.747176	−	0.525677i
$167$	1.33465	+	2.07676i	0.103279	+	0.160705i	0.889047	−	0.457817i	$-0.151368\pi$
$167$	1.33465	+	2.07676i	0.103279	+	0.160705i	−0.785768	+	0.618521i	$0.787732\pi$
$168$	−10.6299	+	2.64768i	−0.820117	+	0.204273i
$169$	−5.93361	−	6.84775i	−0.456432	−	0.526750i
$170$	1.71260	−	2.15241i	0.131350	−	0.165083i
$171$	12.4739	+	8.90554i	0.953899	+	0.681024i
$172$	−1.76158	−	7.63997i	−0.134319	−	0.582542i
$173$	−15.5988	+	4.58021i	−1.18595	+	0.348227i	−0.814466	−	0.580212i	$-0.802970\pi$
$173$	−15.5988	+	4.58021i	−1.18595	+	0.348227i	−0.371486	+	0.928439i	$0.621152\pi$
$174$	6.19388	+	3.82911i	0.469556	+	0.290284i
$175$	10.7908	−	1.55149i	0.815710	−	0.117281i
$176$	13.2304	−	8.97445i	0.997280	−	0.676475i
$177$	−10.5421	−	5.12899i	−0.792394	−	0.385519i
$178$	3.11328	−	12.5216i	0.233350	−	0.938530i
$179$	−1.78059	+	12.3843i	−0.133088	+	0.925646i	0.808408	+	0.588622i	$0.200329\pi$
$179$	−1.78059	+	12.3843i	−0.133088	+	0.925646i	−0.941496	+	0.337024i	$0.890580\pi$
$180$	−1.55162	+	1.44257i	−0.115651	+	0.107523i
$181$	−11.5662	+	13.3481i	−0.859707	+	0.992155i	0.140290	+	0.990110i	$0.455196\pi$
$181$	−11.5662	+	13.3481i	−0.859707	+	0.992155i	−0.999998	+	0.00204489i	$0.999349\pi$
$182$	−5.59496	+	2.84420i	−0.414726	+	0.210826i
$183$	9.46720	−	7.80708i	0.699836	−	0.577116i
$184$	−12.0144	+	6.29713i	−0.885714	+	0.464230i
$185$			0.0428990i			0.00315399i
$186$	−9.15258	+	21.0064i	−0.671099	+	1.54027i
$187$	−16.6379	−	14.4169i	−1.21669	−	1.05427i
$188$	14.2527	+	10.3959i	1.03948	+	0.758196i
$189$	−4.04058	−	10.8940i	−0.293909	−	0.792424i
$190$	2.47580	+	0.615568i	0.179613	+	0.0446580i
$191$	−3.31255	−	7.25347i	−0.239687	−	0.524842i	0.751113	−	0.660174i	$-0.229517\pi$
$191$	−3.31255	−	7.25347i	−0.239687	−	0.524842i	−0.990800	+	0.135331i	$0.956790\pi$
$192$	−4.67533	+	13.0438i	−0.337413	+	0.941357i
$193$	−1.35583	−	9.43002i	−0.0975950	−	0.678788i	−0.978614	−	0.205707i	$-0.934051\pi$
$193$	−1.35583	−	9.43002i	−0.0975950	−	0.678788i	0.881019	−	0.473081i	$-0.156858\pi$
$194$	−18.4044	+	6.25271i	−1.32136	+	0.448919i
$195$	−0.680978	+	1.00482i	−0.0487659	+	0.0719569i
$196$	0.898611	+	3.89728i	0.0641865	+	0.278377i
$197$	7.31771	−	16.0236i	0.521366	−	1.14163i	−0.447554	−	0.894257i	$-0.647705\pi$
$197$	7.31771	−	16.0236i	0.521366	−	1.14163i	0.968920	−	0.247375i	$-0.0795678\pi$
$198$	11.0155	+	12.8915i	0.782837	+	0.916162i
$199$	10.7469	−	9.31227i	0.761830	−	0.660130i	−0.184682	−	0.982798i	$-0.559125\pi$
$199$	10.7469	−	9.31227i	0.761830	−	0.660130i	0.946512	+	0.322669i	$0.104580\pi$
$200$	5.94174	−	12.4437i	0.420144	−	0.879902i
$201$	−0.377635	+	1.17886i	−0.0266363	+	0.0831507i
$202$	12.4033	+	17.6296i	0.872696	+	1.24042i
$203$	−3.59396	+	5.59231i	−0.252247	+	0.392504i
$204$	19.0149	+	1.58944i	1.33131	+	0.111283i
$205$	−2.41878	−	0.710217i	−0.168935	−	0.0496037i
$206$	−11.0594	−	11.7318i	−0.770547	−	0.817393i
$207$	−8.05031	−	11.9245i	−0.559535	−	0.828807i
$208$	−0.934393	+	7.88371i	−0.0647885	+	0.546637i
$209$	5.75268	−	19.5918i	0.397921	−	1.35519i
$210$	−1.29192	−	1.43929i	−0.0891512	−	0.0993201i
$211$	0.898123	−	1.39751i	0.0618294	−	0.0962084i	−0.808962	−	0.587860i	$-0.799970\pi$
$211$	0.898123	−	1.39751i	0.0618294	−	0.0962084i	0.870792	+	0.491652i	$0.163607\pi$
$212$	−4.46156	+	21.8095i	−0.306421	+	1.49788i
$213$	−11.4314	−	3.66192i	−0.783270	−	0.250911i
$214$	5.35548	−	13.1597i	0.366093	−	0.899580i
$215$	1.04614	−	0.906482i	0.0713459	−	0.0618215i
$216$	−14.2994	−	3.39503i	−0.972953	−	0.231002i
$217$	−19.0275	−	8.68955i	−1.29167	−	0.589885i
$218$	−8.81616	+	15.0712i	−0.597106	+	1.02075i
$219$	−14.4054	+	21.2561i	−0.973429	+	1.43635i
$220$	2.49387	+	1.32184i	0.168137	+	0.0891182i
$221$	10.8211	−	1.55584i	0.727905	−	0.104657i
$222$	−0.247497	+	0.165246i	−0.0166109	+	0.0110906i
$223$	−7.86326	−	17.2181i	−0.526563	−	1.15301i	−0.966894	−	0.255177i	$-0.917866\pi$
$223$	−7.86326	−	17.2181i	−0.526563	−	1.15301i	0.440331	−	0.897835i	$-0.354861\pi$
$224$	−11.8311	−	4.47575i	−0.790499	−	0.299049i
$225$	13.8157	+	4.80054i	0.921046	+	0.320036i
$226$	−3.44686	+	0.643998i	−0.229282	+	0.0428381i
$227$	−13.0941	−	11.3461i	−0.869087	−	0.753068i	0.101241	−	0.994862i	$-0.467719\pi$
$227$	−13.0941	−	11.3461i	−0.869087	−	0.753068i	−0.970328	+	0.241794i	$0.922264\pi$
$228$	5.98535	+	16.6548i	0.396389	+	1.10299i
$229$	7.08734			0.468345			0.234172	−	0.972195i	$-0.424762\pi$
$229$	7.08734			0.468345			0.234172	+	0.972195i	$0.424762\pi$
$230$	−1.97569	−	1.35351i	−0.130273	−	0.0892480i
$231$	−11.9427	+	9.84851i	−0.785774	+	0.647984i
$232$	3.36185	+	7.70711i	0.220716	+	0.505997i
$233$	16.2303	+	14.0637i	1.06328	+	0.921340i	0.997072	−	0.0764652i	$-0.0243634\pi$
$233$	16.2303	+	14.0637i	1.06328	+	0.921340i	0.0662113	+	0.997806i	$0.478909\pi$
$234$	−8.42026	−	0.0582071i	−0.550450	−	0.00380512i
$235$	−0.443250	+	3.08287i	−0.0289145	+	0.201104i
$236$	−6.63470	−	11.7999i	−0.431882	−	0.768108i
$237$	1.73568	−	3.56751i	0.112744	−	0.231735i
$238$	−1.75448	+	17.3305i	−0.113726	+	1.12337i
$239$	−7.93184	+	1.14043i	−0.513068	+	0.0737681i	−0.393986	−	0.919116i	$-0.628904\pi$
$239$	−7.93184	+	1.14043i	−0.513068	+	0.0737681i	−0.119082	+	0.992884i	$0.537995\pi$
$240$	−2.42132	+	0.349167i	−0.156295	+	0.0225386i
$241$	−0.360986	−	1.22941i	−0.0232531	−	0.0791929i	0.947049	−	0.321089i	$-0.104049\pi$
$241$	−0.360986	−	1.22941i	−0.0232531	−	0.0791929i	−0.970302	+	0.241896i	$0.922231\pi$
$242$	3.55181	−	6.07182i	0.228319	−	0.390312i
$243$	1.89783	−	15.4725i	0.121746	−	0.992561i
$244$	14.1196	−	1.18620i	0.903917	−	0.0759387i
$245$	−0.533652	+	0.462412i	−0.0340938	+	0.0295424i
$246$	−5.21963	−	16.6904i	−0.332792	−	1.06414i
$247$	5.48194	+	8.53006i	0.348807	+	0.542755i
$248$	−22.4994	+	13.9223i	−1.42871	+	0.884069i
$249$	1.70271	+	14.3150i	0.107905	+	0.907174i
$250$	4.92703	−	0.206598i	0.311613	−	0.0130664i
$251$	−5.59535	+	19.0560i	−0.353175	+	1.20280i	0.571037	+	0.820924i	$0.306541\pi$
$251$	−5.59535	+	19.0560i	−0.353175	+	1.20280i	−0.924212	+	0.381880i	$0.875277\pi$
$252$	3.32721	−	12.9976i	0.209595	−	0.818773i
$253$	−11.4861	+	15.3451i	−0.722126	+	0.964739i
$254$	11.2963	−	10.6489i	0.708791	−	0.668169i
$255$	1.32424	+	3.09761i	0.0829272	+	0.193980i
$256$	−13.0141	+	9.30769i	−0.813382	+	0.581731i
$257$	−10.2889	+	16.0098i	−0.641803	+	0.998666i	0.356132	+	0.934436i	$0.384095\pi$
$257$	−10.2889	+	16.0098i	−0.641803	+	0.998666i	−0.997935	+	0.0642298i	$0.979541\pi$
$258$	9.25948	+	2.54373i	0.576470	+	0.158366i
$259$	−0.146876	−	0.228543i	−0.00912642	−	0.0142010i
$260$	−1.30707	+	0.506080i	−0.0810608	+	0.0313858i
$261$	−7.72906	+	4.44982i	−0.478417	+	0.275437i
$262$	3.83683	+	3.05283i	0.237040	+	0.188604i
$263$	−2.71616	+	5.94756i	−0.167485	+	0.366742i	−0.974700	−	0.223516i	$-0.928247\pi$
$263$	−2.71616	+	5.94756i	−0.167485	+	0.366742i	0.807215	+	0.590258i	$0.200974\pi$
$264$	1.98028	+	19.4796i	0.121878	+	1.19889i
$265$	−3.77103	+	1.10727i	−0.231653	+	0.0680194i
$266$	−15.2973	+	5.19713i	−0.937939	+	0.318656i
$267$	11.6867	+	10.6369i	0.715213	+	0.650969i
$268$	−1.13355	+	0.870730i	−0.0692426	+	0.0531883i
$269$	2.21906	+	4.85905i	0.135298	+	0.296262i	0.965139	−	0.261739i	$-0.0842959\pi$
$269$	2.21906	+	4.85905i	0.135298	+	0.296262i	−0.829841	+	0.558001i	$0.811569\pi$
$270$	−0.652701	−	2.51133i	−0.0397221	−	0.152834i
$271$	1.67206	−	11.6295i	0.101571	−	0.706440i	−0.873867	−	0.486165i	$-0.838395\pi$
$271$	1.67206	−	11.6295i	0.101571	−	0.706440i	0.975438	−	0.220275i	$-0.0706954\pi$
$272$	17.0045	+	14.0107i	1.03105	+	0.849526i
$273$	0.187619	−	7.68469i	0.0113552	−	0.465098i
$274$	−17.9842	+	9.14228i	−1.08646	+	0.552305i
$275$		−	19.4855i		−	1.17502i
$276$	0.198527	−	16.6121i	0.0119499	−	0.999929i
$277$			2.72014i			0.163437i	0.996655	+	0.0817186i	$0.0260409\pi$
$277$			2.72014i			0.163437i	−0.996655	+	0.0817186i	$0.973959\pi$
$278$	1.67093	+	3.28697i	0.100216	+	0.197139i
$279$	−17.3208	−	22.0805i	−1.03697	−	1.32193i
$280$	−0.280029	−	2.21564i	−0.0167349	−	0.132410i
$281$	2.04170	−	14.2003i	0.121797	−	0.847119i	−0.833721	−	0.552186i	$-0.813794\pi$
$281$	2.04170	−	14.2003i	0.121797	−	0.847119i	0.955518	−	0.294933i	$-0.0952973\pi$
$282$	−19.4934	+	9.31794i	−1.16082	+	0.554875i
$283$	8.89100	+	19.4686i	0.528515	+	1.15729i	0.966114	+	0.258116i	$0.0831017\pi$
$283$	8.89100	+	19.4686i	0.528515	+	1.15729i	−0.437599	+	0.899170i	$0.644171\pi$
$284$	−8.44346	−	10.9920i	−0.501027	−	0.652257i
$285$	−2.10317	+	2.31073i	−0.124581	+	0.136876i
$286$	3.60870	+	10.6219i	0.213387	+	0.628086i
$287$	15.3176	−	4.49765i	0.904169	−	0.265488i
$288$	−11.3413	−	12.6243i	−0.668294	−	0.743897i
$289$	5.54202	−	12.1353i	0.326001	−	0.713843i
$290$	−0.924295	+	1.16167i	−0.0542765	+	0.0682154i
$291$	3.96206	−	23.4740i	0.232260	−	1.37607i
$292$	−27.6497	+	10.7056i	−1.61808	+	0.626500i
$293$	11.9059	+	18.5259i	0.695548	+	1.08229i	0.991876	+	0.127208i	$0.0406015\pi$
$293$	11.9059	+	18.5259i	0.695548	+	1.08229i	−0.296328	+	0.955086i	$0.595762\pi$
$294$	−4.72342	−	1.29760i	−0.275475	−	0.0756775i
$295$	1.29214	−	2.01061i	0.0752313	−	0.117062i
$296$	−0.343580	−	0.00586855i	−0.0199702	−	0.000341102i
$297$	−20.3012	+	4.37737i	−1.17799	+	0.254001i
$298$	−0.901022	−	0.955801i	−0.0521948	−	0.0553681i
$299$	−2.02370	−	9.30078i	−0.117034	−	0.537878i
$300$	9.95805	+	13.6405i	0.574928	+	0.787532i
$301$	−2.46969	+	8.41098i	−0.142350	+	0.484801i
$302$	−0.280349	−	6.68588i	−0.0161323	−	0.384729i
$303$	−26.2154	+	3.11822i	−1.50603	+	0.179137i
$304$	−5.26880	+	19.7446i	−0.302187	+	1.13243i
$305$	1.35248	+	2.10450i	0.0774426	+	0.120503i
$306$	−12.7701	+	19.5719i	−0.730020	+	1.11885i
$307$	−21.8265	+	18.9128i	−1.24570	+	1.07941i	−0.251958	+	0.967738i	$0.581074\pi$
$307$	−21.8265	+	18.9128i	−1.24570	+	1.07941i	−0.993745	+	0.111670i	$0.964380\pi$
$308$	−17.8117	+	1.49637i	−1.01492	+	0.0852637i
$309$	19.0766	−	5.09910i	1.08523	−	0.290078i
$310$	−4.03208	−	2.35863i	−0.229007	−	0.133961i
$311$	2.20490	+	7.50920i	0.125028	+	0.425807i	0.998088	−	0.0618056i	$-0.0196859\pi$
$311$	2.20490	+	7.50920i	0.125028	+	0.425807i	−0.873060	+	0.487613i	$0.837868\pi$
$312$	−7.95453	−	5.59145i	−0.450337	−	0.316554i
$313$	−1.12192	+	0.161308i	−0.0634147	+	0.00911766i	−0.173949	−	0.984755i	$-0.555653\pi$
$313$	−1.12192	+	0.161308i	−0.0634147	+	0.00911766i	0.110534	+	0.993872i	$0.464744\pi$
$314$	27.5906	+	2.79317i	1.55703	+	0.157628i
$315$	2.30264	−	0.555643i	0.129739	−	0.0313069i
$316$	3.99315	−	2.24522i	0.224632	−	0.126303i
$317$	0.380389	−	2.64566i	0.0213648	−	0.148595i	−0.976347	−	0.216211i	$-0.930630\pi$
$317$	0.380389	−	2.64566i	0.0213648	−	0.148595i	0.997711	+	0.0676157i	$0.0215392\pi$
$318$	−20.9142	−	17.4910i	−1.17281	−	0.980849i
$319$	8.97956	+	7.78083i	0.502759	+	0.435643i
$320$	−2.52797	−	1.26054i	−0.141318	−	0.0704663i
$321$	11.0708	+	13.4249i	0.617910	+	0.749304i
$322$	15.1595	+	0.446537i	0.844807	+	0.0248845i
$323$	28.1410			1.56581
$324$	11.9744	−	13.4392i	0.665246	−	0.746624i
$325$	7.31275	+	6.33653i	0.405638	+	0.351488i
$326$	2.53031	+	13.5429i	0.140141	+	0.750072i
$327$	−11.1188	−	18.2667i	−0.614873	−	1.01015i
$328$	6.01905	−	19.2750i	0.332347	−	1.06428i
$329$	−8.19362	−	17.9415i	−0.451729	−	0.989148i
$330$	−2.87496	+	1.91952i	−0.158262	+	0.105666i
$331$	34.8192	−	5.00625i	1.91384	−	0.275168i	0.920530	−	0.390671i	$-0.127757\pi$
$331$	34.8192	−	5.00625i	1.91384	−	0.275168i	0.993307	+	0.115503i	$0.0368480\pi$
$332$	−7.79561	+	14.7078i	−0.427840	+	0.807193i
$333$	−0.0342030	−	0.362866i	−0.00187431	−	0.0198850i
$334$	−3.01348	−	1.76278i	−0.164890	−	0.0964553i
$335$	−0.229552	−	0.104833i	−0.0125418	−	0.00572764i
$336$	11.7040	−	10.1502i	0.638508	−	0.553738i
$337$	15.2224	−	13.1903i	0.829216	−	0.718520i	−0.132909	−	0.991128i	$-0.542432\pi$
$337$	15.2224	−	13.1903i	0.829216	−	0.718520i	0.962125	+	0.272609i	$0.0878864\pi$
$338$	11.8688	+	4.83014i	0.645578	+	0.262725i
$339$	1.31013	−	4.08985i	0.0711567	−	0.222130i
$340$	−0.779621	+	3.81103i	−0.0422809	+	0.206682i
$341$	−20.2133	+	31.4525i	−1.09461	+	1.70325i
$342$	−21.4327	−	3.23293i	−1.15895	−	0.174817i
$343$	5.66974	−	19.3094i	0.306137	−	1.04261i
$344$	7.11695	+	8.50257i	0.383720	+	0.458428i
$345$	2.60779	−	1.34255i	0.140399	−	0.0722803i
$346$	16.7296	−	15.7708i	0.899390	−	0.847844i
$347$	−17.8101	−	5.22951i	−0.956094	−	0.280735i	−0.233772	−	0.972291i	$-0.575107\pi$
$347$	−17.8101	−	5.22951i	−0.956094	−	0.280735i	−0.722322	+	0.691557i	$0.756925\pi$
$348$	−10.2624	−	0.857827i	−0.550122	−	0.0459844i
$349$	−6.46313	+	10.0568i	−0.345963	+	0.538329i	−0.970012	−	0.243056i	$-0.921850\pi$
$349$	−6.46313	+	10.0568i	−0.345963	+	0.538329i	0.624049	+	0.781385i	$0.285487\pi$
$350$	−12.6094	+	8.87137i	−0.674001	+	0.474195i
$351$	4.95901	−	9.04238i	0.264692	−	0.482646i
$352$	−10.9278	+	19.7927i	−0.582455	+	1.05496i
$353$	−1.37908	+	1.19498i	−0.0734013	+	0.0636025i	−0.690789	−	0.723057i	$-0.742737\pi$
$353$	−1.37908	+	1.19498i	−0.0734013	+	0.0636025i	0.617387	+	0.786659i	$0.288191\pi$
$354$	16.5771	−	0.290082i	0.881065	−	0.0154177i
$355$	1.01657	−	2.22597i	0.0539537	−	0.118142i
$356$	4.09978	+	17.7808i	0.217288	+	0.942378i
$357$	−17.6604	−	11.9686i	−0.934685	−	0.633444i
$358$	−5.69190	−	16.7537i	−0.300827	−	0.885459i
$359$	4.36118	+	30.3327i	0.230174	+	1.60090i	0.697349	+	0.716732i	$0.254363\pi$
$359$	4.36118	+	30.3327i	0.230174	+	1.60090i	−0.467175	+	0.884165i	$0.654728\pi$
$360$	1.03159	−	2.81298i	0.0543698	−	0.148257i
$361$	2.94971	+	6.45896i	0.155248	+	0.339945i
$362$	6.02686	−	24.2399i	0.316765	−	1.27402i
$363$	4.47951	+	7.35919i	0.235113	+	0.386257i
$364$	5.23066	−	7.17121i	0.274161	−	0.375874i
$365$	−3.95614	−	3.42801i	−0.207074	−	0.179430i
$366$	−6.93177	+	15.9094i	−0.362329	+	0.831595i
$367$			23.0815i			1.20484i	0.798178	+	0.602421i	$0.205797\pi$
$367$			23.0815i			1.20484i	−0.798178	+	0.602421i	$0.794203\pi$
$368$	11.1106	−	15.6382i	0.579182	−	0.815198i
$369$	21.0258	+	4.07899i	1.09456	+	0.212344i
$370$	−0.0274924	−	0.0540815i	−0.00142926	−	0.00281156i
$371$	16.2990	−	18.8101i	0.846204	−	0.976572i
$372$	−1.92385	−	32.3478i	−0.0997470	−	1.67715i
$373$	−1.85482	+	12.9006i	−0.0960391	+	0.667967i	0.883754	+	0.467952i	$0.155008\pi$
$373$	−1.85482	+	12.9006i	−0.0960391	+	0.667967i	−0.979793	+	0.200015i	$0.935901\pi$
$374$	30.2142	+	7.51228i	1.56234	+	0.388451i
$375$	−2.64231	+	5.43099i	−0.136448	+	0.280455i
$376$	−24.6303	−	3.97175i	−1.27021	−	0.204827i
$377$	−5.84018	+	0.839691i	−0.300785	+	0.0432463i
$378$	12.0754	+	11.1443i	0.621093	+	0.573203i
$379$	36.5422	−	10.7298i	1.87705	−	0.551151i	0.879946	−	0.475074i	$-0.157579\pi$
$379$	36.5422	−	10.7298i	1.87705	−	0.551151i	0.997102	−	0.0760771i	$-0.0242395\pi$
$380$	−3.51567	+	0.810622i	−0.180350	+	0.0415840i
$381$	4.90981	+	18.3685i	0.251537	+	0.941044i
$382$	8.82452	+	7.02135i	0.451502	+	0.359244i
$383$	−3.91227	−	4.51500i	−0.199907	−	0.230706i	0.646941	−	0.762540i	$-0.276048\pi$
$383$	−3.91227	−	4.51500i	−0.199907	−	0.230706i	−0.846848	+	0.531835i	$0.821503\pi$
$384$	−2.46526	−	19.4402i	−0.125805	−	0.992055i
$385$	−1.70613	−	2.65479i	−0.0869524	−	0.135301i
$386$	7.75262	+	11.0193i	0.394598	+	0.560866i
$387$	−8.12615	+	8.50167i	−0.413075	+	0.432164i
$388$	19.1947	−	19.6773i	0.974464	−	0.998963i
$389$	0.367162	−	1.25044i	0.0186158	−	0.0633997i	−0.949661	−	0.313279i	$-0.898573\pi$
$389$	0.367162	−	1.25044i	0.0186158	−	0.0633997i	0.968277	+	0.249879i	$0.0803908\pi$
$390$	0.214535	−	1.70317i	0.0108634	−	0.0862433i
$391$	−24.7515	−	9.23056i	−1.25174	−	0.466809i
$392$	−3.63048	−	4.33730i	−0.183367	−	0.219067i
$393$	−5.52172	+	2.36055i	−0.278534	+	0.119074i
$394$	1.04368	+	24.8901i	0.0525798	+	1.25395i
$395$	0.680401	+	0.437267i	0.0342347	+	0.0220013i
$396$	−22.1486	−	9.19258i	−1.11301	−	0.461945i
$397$	11.1541	+	17.3562i	0.559810	+	0.871082i	0.999635	−	0.0270018i	$-0.00859599\pi$
$397$	11.1541	+	17.3562i	0.559810	+	0.871082i	−0.439825	+	0.898083i	$0.644960\pi$
$398$	−7.58047	+	18.6270i	−0.379974	+	0.933689i
$399$	3.29319	−	19.5111i	0.164866	−	0.976776i
$400$	0.484128	+	19.4953i	0.0242064	+	0.974763i
$401$	−2.34517	+	5.13520i	−0.117112	+	0.256440i	−0.959106	−	0.283047i	$-0.908655\pi$
$401$	−2.34517	+	5.13520i	−0.117112	+	0.256440i	0.841994	+	0.539487i	$0.181382\pi$
$402$	−0.279418	−	1.72817i	−0.0139361	−	0.0861935i
$403$	−5.23067	−	17.8140i	−0.260558	−	0.887379i
$404$	−26.9347	−	14.2763i	−1.34005	−	0.710273i
$405$	3.08650	+	0.756754i	0.153370	+	0.0376034i
$406$	0.946897	−	9.35331i	0.0469937	−	0.464197i
$407$	−0.441692	+	0.201714i	−0.0218939	+	0.00999859i
$408$	−24.9901	+	10.1822i	−1.23719	+	0.504092i
$409$	−5.40024	+	37.5595i	−0.267025	+	1.85720i	0.209199	+	0.977873i	$0.432914\pi$
$409$	−5.40024	+	37.5595i	−0.267025	+	1.85720i	−0.476224	+	0.879324i	$0.657995\pi$
$410$	3.50444	−	0.654755i	0.173072	−	0.0323361i
$411$	0.603073	−	24.7013i	0.0297474	−	1.21843i
$412$	21.4608	+	7.70237i	1.05730	+	0.379468i
$413$			15.1355i			0.744767i
$414$	17.7907	+	9.87368i	0.874367	+	0.485265i
$415$	−2.93887			−0.144264
$416$	−3.87442	−	10.5376i	−0.189959	−	0.516648i
$417$	−4.51466	−	0.110224i	−0.221084	−	0.00539768i
$418$	5.30345	+	28.3855i	0.259400	+	1.38838i
$419$	26.1615	+	3.76145i	1.27807	+	0.183759i	0.747718	−	0.664017i	$-0.231150\pi$
$419$	26.1615	+	3.76145i	1.27807	+	0.183759i	0.530355	+	0.847776i	$0.322059\pi$
$420$	2.55108	+	0.986520i	0.124480	+	0.0481373i
$421$	−12.3901	−	27.1306i	−0.603858	−	1.32227i	−0.926696	−	0.375811i	$-0.877364\pi$
$421$	−12.3901	−	27.1306i	−0.603858	−	1.32227i	0.322838	−	0.946454i	$-0.395363\pi$
$422$	−0.236627	+	2.33737i	−0.0115188	+	0.113782i
$423$	1.29134	−	26.4303i	0.0627871	−	1.28508i
$424$	−8.35235	−	30.3539i	−0.405626	−	1.47411i
$425$	25.7667	−	7.56579i	1.24987	−	0.366995i
$426$	16.7581	−	2.70952i	0.811932	−	0.131276i
$427$	−14.4106	−	6.58109i	−0.697377	−	0.318481i
$428$	1.68208	+	20.0222i	0.0813064	+	0.967811i
$429$	−13.5478	−	2.28667i	−0.654093	−	0.110401i
$430$	−0.737903	+	1.81321i	−0.0355848	+	0.0874406i
$431$	−19.9602	+	12.8277i	−0.961451	+	0.617887i	−0.924399	−	0.381426i	$-0.875433\pi$
$431$	−19.9602	+	12.8277i	−0.961451	+	0.617887i	−0.0370516	+	0.999313i	$0.511797\pi$
$432$	20.2026	−	4.88397i	0.972000	−	0.234980i
$433$	−9.68540	+	15.0708i	−0.465451	+	0.724256i	−0.992048	−	0.125859i	$-0.959831\pi$
$433$	−9.68540	+	15.0708i	−0.465451	+	0.724256i	0.526597	+	0.850115i	$0.323468\pi$
$434$	29.5562	−	1.23934i	1.41874	−	0.0594900i
$435$	−0.714697	−	1.67179i	−0.0342671	−	0.0801563i
$436$	1.45568	−	24.6498i	0.0697144	−	1.18051i
$437$	−1.74902	−	24.4388i	−0.0836669	−	1.16907i
$438$	4.53828	−	36.0288i	0.216847	−	1.72152i
$439$	24.8711	+	7.30282i	1.18703	+	0.348545i	0.814882	−	0.579627i	$-0.196802\pi$
$439$	24.8711	+	7.30282i	1.18703	+	0.348545i	0.372152	+	0.928172i	$0.378620\pi$
$440$	−3.99107	−	0.0681698i	−0.190267	−	0.00324987i
$441$	4.14529	−	4.33685i	0.197395	−	0.206517i
$442$	−12.6448	+	8.89624i	−0.601450	+	0.423151i
$443$	2.48087	−	1.59436i	0.117870	−	0.0757503i	−0.480378	−	0.877062i	$-0.659500\pi$
$443$	2.48087	−	1.59436i	0.117870	−	0.0757503i	0.598247	+	0.801311i	$0.295864\pi$
$444$	0.206113	−	0.366933i	0.00978168	−	0.0174139i
$445$	−2.43471	+	2.10968i	−0.115416	+	0.100009i
$446$	20.9475	+	16.6672i	0.991892	+	0.789213i
$447$	1.55419	−	0.415429i	0.0735108	−	0.0196491i
$448$	17.7835	−	1.93967i	0.840191	−	0.0916407i
$449$	−1.89638	−	6.45847i	−0.0894956	−	0.304794i	0.902565	−	0.430553i	$-0.141681\pi$
$449$	−1.89638	−	6.45847i	−0.0894956	−	0.304794i	−0.992061	+	0.125759i	$0.959863\pi$
$450$	−20.4935	+	2.80208i	−0.966075	+	0.132091i
$451$	−4.06080	−	28.2435i	−0.191215	−	1.32993i
$452$	3.93264	−	3.02084i	0.184976	−	0.142088i
$453$	7.36975	+	3.58556i	0.346261	+	0.168464i
$454$	23.7787	+	5.91219i	1.11599	+	0.277473i
$455$	1.55114	+	0.223021i	0.0727187	+	0.0104554i
$456$	−18.2190	−	17.1605i	−0.853184	−	0.803613i
$457$	−3.67193	−	3.18174i	−0.171765	−	0.148836i	0.564736	−	0.825272i	$-0.308978\pi$
$457$	−3.67193	−	3.18174i	−0.171765	−	0.148836i	−0.736501	+	0.676436i	$0.763523\pi$
$458$	−8.93481	+	4.54202i	−0.417496	+	0.212235i
$459$	−13.6710	−	25.1458i	−0.638106	−	1.17370i
$460$	3.35811	+	0.440192i	0.156573	+	0.0205240i
$461$	14.7457			0.686776			0.343388	−	0.939194i	$-0.388425\pi$
$461$	14.7457			0.686776			0.343388	+	0.939194i	$0.388425\pi$
$462$	8.74431	−	20.0694i	0.406822	−	0.933713i
$463$	5.12267	−	5.91188i	0.238071	−	0.274748i	−0.624124	−	0.781325i	$-0.714544\pi$
$463$	5.12267	−	5.91188i	0.238071	−	0.274748i	0.862195	+	0.506577i	$0.169089\pi$
$464$	−9.17740	−	7.56165i	−0.426050	−	0.351041i
$465$	4.88697	−	2.97468i	0.226628	−	0.137947i
$466$	−29.4740	−	7.32823i	−1.36536	−	0.339474i
$467$	−6.70441	+	3.06180i	−0.310243	+	0.141683i	−0.564452	−	0.825466i	$-0.690912\pi$
$467$	−6.70441	+	3.06180i	−0.310243	+	0.141683i	0.254209	+	0.967149i	$0.418185\pi$
$468$	10.6525	−	5.32286i	0.492412	−	0.246049i
$469$	1.58186	−	0.227437i	0.0730434	−	0.0105021i
$470$	−1.41691	−	4.17055i	−0.0653571	−	0.192373i
$471$	−19.0543	+	28.1158i	−0.877977	+	1.29551i
$472$	15.9263	+	10.6239i	0.733068	+	0.489003i
$473$	14.2522	+	6.50878i	0.655319	+	0.299274i
$474$	0.0981654	+	5.60979i	0.00450888	+	0.257666i
$475$	16.3109	+	18.8238i	0.748395	+	0.863693i
$476$	−8.89465	−	22.9724i	−0.407685	−	1.05294i
$477$	31.0150	−	12.3726i	1.42008	−	0.566504i
$478$	9.26859	−	6.52093i	0.423936	−	0.298261i
$479$	25.5054	+	16.3913i	1.16537	+	0.748938i	0.972641	−	0.232313i	$-0.0746295\pi$
$479$	25.5054	+	16.3913i	1.16537	+	0.748938i	0.192730	+	0.981252i	$0.438266\pi$
$480$	2.82872	−	1.99192i	0.129113	−	0.0909182i
$481$	0.0679334	−	0.231360i	0.00309749	−	0.0105491i
$482$	1.24297	+	1.31853i	0.0566155	+	0.0600576i
$483$	−9.29638	+	16.0808i	−0.423000	+	0.731703i
$484$	−0.586457	+	9.93080i	−0.0266571	+	0.451400i
$485$	4.65659	+	1.36730i	0.211445	+	0.0620858i
$486$	7.52322	+	20.7220i	0.341260	+	0.939969i
$487$	25.8751	+	16.6289i	1.17251	+	0.753528i	0.973995	−	0.226569i	$-0.0727509\pi$
$487$	25.8751	+	16.6289i	1.17251	+	0.753528i	0.198518	+	0.980097i	$0.436387\pi$
$488$	−17.0400	+	10.5442i	−0.771366	+	0.477312i
$489$	−16.0693	−	5.14759i	−0.726678	−	0.232782i
$490$	0.376417	−	0.924948i	0.0170048	−	0.0417849i
$491$	−20.7638	−	23.9627i	−0.937058	−	1.08142i	−0.996533	−	0.0831933i	$-0.973488\pi$
$491$	−20.7638	−	23.9627i	−0.937058	−	1.08142i	0.0594750	−	0.998230i	$-0.481057\pi$
$492$	17.2765	+	17.6961i	0.778886	+	0.797800i
$493$	−6.80246	+	14.8953i	−0.306368	+	0.670851i
$494$	−12.3775	−	7.24044i	−0.556891	−	0.325763i
$495$	−0.397306	−	4.21511i	−0.0178576	−	0.189455i
$496$	19.4420	−	31.9705i	0.872971	−	1.43552i
$497$	2.20545	+	15.3393i	0.0989281	+	0.688060i
$498$	−11.3205	−	16.9553i	−0.507283	−	0.759784i
$499$	1.20796	−	0.551657i	0.0540757	−	0.0246955i	−0.388194	−	0.921578i	$-0.626901\pi$
$499$	1.20796	−	0.551657i	0.0540757	−	0.0246955i	0.442269	+	0.896882i	$0.354174\pi$
$500$	−6.07897	+	3.41800i	−0.271860	+	0.152858i
$501$	3.65241	−	2.22320i	0.163178	−	0.0993255i
$502$	−5.15840	−	27.6092i	−0.230231	−	1.23226i
$503$	0.991985	−	1.14481i	0.0442304	−	0.0510446i	−0.733203	−	0.680010i	$-0.761976\pi$
$503$	0.991985	−	1.14481i	0.0442304	−	0.0510446i	0.777434	+	0.628965i	$0.216521\pi$
$504$	4.13517	+	18.5180i	0.184195	+	0.824858i
$505$		−	5.38204i		−	0.239498i
$506$	4.64610	−	26.7062i	0.206544	−	1.18723i
$507$	−12.1080	+	9.98477i	−0.537734	+	0.443439i
$508$	−7.41643	+	20.6641i	−0.329051	+	0.916821i
$509$	−14.9301	+	17.2302i	−0.661764	+	0.763716i	−0.983064	−	0.183261i	$-0.941335\pi$
$509$	−14.9301	+	17.2302i	−0.661764	+	0.763716i	0.321301	+	0.946977i	$0.395880\pi$
$510$	−3.65458	−	3.05642i	−0.161828	−	0.135340i
$511$	32.8129	+	4.71779i	1.45156	+	0.208703i
$512$	10.4416	−	20.0742i	0.461456	−	0.887163i
$513$	15.9476	−	21.2224i	0.704103	−	0.936993i
$514$	2.71080	−	26.7769i	0.119568	−	1.18108i
$515$	0.572898	+	3.98459i	0.0252449	+	0.175582i
$516$	−13.3033	+	2.72726i	−0.585647	+	0.120061i
$517$	−33.8258	+	9.93214i	−1.48766	+	0.436815i
$518$	0.331627	+	0.193991i	0.0145709	+	0.00852346i
$519$	7.27135	+	27.2034i	0.319177	+	1.19410i
$520$	1.32345	−	1.47565i	0.0580372	−	0.0647116i
$521$	0.129656	+	0.149631i	0.00568035	+	0.00655547i	0.758583	−	0.651577i	$-0.225892\pi$
$521$	0.129656	+	0.149631i	0.00568035	+	0.00655547i	−0.752902	+	0.658132i	$0.771347\pi$
$522$	6.89209	−	10.5630i	0.301659	−	0.462332i
$523$	16.4986	−	10.6030i	0.721432	−	0.463636i	−0.127702	−	0.991813i	$-0.540760\pi$
$523$	16.4986	−	10.6030i	0.721432	−	0.463636i	0.849135	+	0.528176i	$0.177124\pi$
$524$	−6.79344	−	1.38973i	−0.296773	−	0.0607107i
$525$	−2.23027	−	18.7503i	−0.0973372	−	0.818330i
$526$	−0.387388	−	9.23861i	−0.0168909	−	0.402822i
$527$	−49.4398	−	14.5168i	−2.15363	−	0.632363i
$528$	−14.9803	−	23.2883i	−0.651932	−	1.01349i
$529$	−6.47784	+	22.0689i	−0.281645	+	0.959519i
$530$	4.04442	−	3.81263i	0.175678	−	0.165610i
$531$	−9.32670	+	18.0372i	−0.404744	+	0.782749i
$532$	15.9543	−	16.3554i	0.691705	−	0.709095i
$533$	11.9201	+	7.66059i	0.516317	+	0.331817i
$534$	−21.5499	−	5.92010i	−0.932555	−	0.256188i
$535$	−2.98426	+	1.91787i	−0.129021	+	0.0829167i
$536$	0.871016	−	1.82416i	0.0376222	−	0.0787915i
$537$	21.3686	+	3.60670i	0.922122	+	0.155641i
$538$	−5.91149	−	4.70356i	−0.254863	−	0.202785i
$539$	−7.27031	−	3.32024i	−0.313154	−	0.143013i
$540$	2.43226	+	2.74767i	0.104668	+	0.118241i
$541$	5.64828	+	19.2363i	0.242839	+	0.827033i	0.987232	+	0.159291i	$0.0509208\pi$
$541$	5.64828	+	19.2363i	0.242839	+	0.827033i	−0.744393	+	0.667742i	$0.767261\pi$
$542$	5.34498	+	15.7325i	0.229586	+	0.675769i
$543$	22.6237	+	20.5915i	0.970877	+	0.883667i
$544$	−30.4161	−	6.76537i	−1.30408	−	0.290063i
$545$	3.96557	−	1.81102i	0.169867	−	0.0775754i
$546$	4.68831	+	9.80811i	0.200641	+	0.419748i
$547$	−2.71314	−	0.390091i	−0.116006	−	0.0166791i	0.0840675	−	0.996460i	$-0.473209\pi$
$547$	−2.71314	−	0.390091i	−0.116006	−	0.0166791i	−0.200073	+	0.979781i	$0.564118\pi$
$548$	16.8132	−	23.0508i	0.718225	−	0.984682i
$549$	−13.1180	−	16.7228i	−0.559863	−	0.713713i
$550$	12.4875	+	24.5648i	0.532470	+	1.04745i
$551$	−15.1878			−0.647022
$552$	10.3958	+	21.0696i	0.442474	+	0.896781i
$553$	−5.12192			−0.217806
$554$	−1.74324	−	3.42920i	−0.0740631	−	0.145693i
$555$	0.0742810	+	0.00181354i	0.00315305	+	7.69806e-5i
$556$	−4.21300	−	3.07295i	−0.178671	−	0.130322i
$557$	4.26927	+	0.613828i	0.180895	+	0.0260087i	0.232167	−	0.972676i	$-0.425418\pi$
$557$	4.26927	+	0.613828i	0.180895	+	0.0260087i	−0.0512720	+	0.998685i	$0.516328\pi$
$558$	35.9864	+	16.7360i	1.52343	+	0.708493i
$559$	−7.07742	+	3.23215i	−0.299343	+	0.136705i
$560$	1.77295	+	2.61373i	0.0749207	+	0.110450i
$561$	−25.6667	+	28.1997i	−1.08365	+	1.19059i
$562$	6.52655	+	19.2104i	0.275306	+	0.810341i
$563$	−2.40570	−	8.19308i	−0.101388	−	0.345297i	0.893138	−	0.449783i	$-0.148499\pi$
$563$	−2.40570	−	8.19308i	−0.101388	−	0.345297i	−0.994526	+	0.104486i	$0.966680\pi$
$564$	18.6033	−	24.2395i	0.783341	−	1.02067i
$565$	0.796389	+	0.363699i	0.0335043	+	0.0153009i
$566$	−23.6853	−	18.8456i	−0.995569	−	0.792138i
$567$	−19.0342	+	6.53586i	−0.799362	+	0.274480i
$568$	17.6888	+	8.44624i	0.742207	+	0.354396i
$569$	−5.73444	+	3.68530i	−0.240400	+	0.154496i	−0.655294	−	0.755374i	$-0.727455\pi$
$569$	−5.73444	+	3.68530i	−0.240400	+	0.154496i	0.414894	+	0.909870i	$0.363819\pi$
$570$	1.17054	−	4.26091i	0.0490286	−	0.178470i
$571$	16.3187	+	10.4874i	0.682915	+	0.438883i	0.835561	−	0.549398i	$-0.185143\pi$
$571$	16.3187	+	10.4874i	0.682915	+	0.438883i	−0.152646	+	0.988281i	$0.548779\pi$
$572$	−11.3566	−	11.0781i	−0.474842	−	0.463197i
$573$	−12.6997	+	5.42915i	−0.530536	+	0.226806i
$574$	−16.4281	+	15.4865i	−0.685695	+	0.646396i
$575$	−8.17189	−	21.9066i	−0.340792	−	0.913570i
$576$	22.3882	+	8.64691i	0.932841	+	0.360288i
$577$	22.7108	+	6.66849i	0.945462	+	0.277613i	0.717896	−	0.696150i	$-0.245105\pi$
$577$	22.7108	+	6.66849i	0.945462	+	0.277613i	0.227566	+	0.973763i	$0.426923\pi$
$578$	0.790422	+	18.8503i	0.0328772	+	0.784071i
$579$	−16.3857	+	1.94902i	−0.680968	+	0.0809985i
$580$	0.420764	−	2.05683i	0.0174713	−	0.0854051i
$581$	15.6568	−	10.0620i	0.649552	−	0.417442i
$582$	10.0487	+	32.1321i	0.416534	+	1.33192i
$583$	−29.1323	−	33.6204i	−1.20654	−	1.39242i
$584$	27.9963	−	31.2160i	1.15850	−	1.29173i
$585$	1.71110	+	1.22162i	0.0707453	+	0.0505076i
$586$	−26.8820	−	15.7250i	−1.11048	−	0.649595i
$587$	−7.99382	+	2.34720i	−0.329940	+	0.0968791i	−0.442507	−	0.896765i	$-0.645911\pi$
$587$	−7.99382	+	2.34720i	−0.329940	+	0.0968791i	0.112567	+	0.993644i	$0.464093\pi$
$588$	6.78626	−	1.39122i	0.279861	−	0.0573730i
$589$	−6.80136	−	47.3045i	−0.280245	−	1.94915i
$590$	−0.340438	+	3.36280i	−0.0140156	+	0.138444i
$591$	−27.4360	−	13.3483i	−1.12857	−	0.549074i
$592$	0.436903	−	0.212790i	0.0179566	−	0.00874560i
$593$	−17.0803	−	2.45578i	−0.701406	−	0.100847i	−0.217620	−	0.976034i	$-0.569829\pi$
$593$	−17.0803	−	2.45578i	−0.701406	−	0.100847i	−0.483786	+	0.875187i	$0.660739\pi$
$594$	22.7878	−	18.5287i	0.934996	−	0.760242i
$595$	2.84812	−	3.28691i	0.116762	−	0.134750i
$596$	1.74843	+	0.627519i	0.0716185	+	0.0257042i
$597$	−15.6702	−	19.0024i	−0.641339	−	0.777715i
$598$	8.51176	+	10.4283i	0.348072	+	0.426445i
$599$		−	2.69678i		−	0.110188i	−0.998481	−	0.0550938i	$-0.982454\pi$
$599$		−	2.69678i		−	0.110188i	0.998481	−	0.0550938i	$-0.0175458\pi$
$600$	−21.2955	−	10.8144i	−0.869386	−	0.441495i
$601$	−2.09498	+	2.41773i	−0.0854559	+	0.0986213i	−0.796867	−	0.604155i	$-0.793511\pi$
$601$	−2.09498	+	2.41773i	−0.0854559	+	0.0986213i	0.711411	+	0.702776i	$0.248056\pi$
$602$	−2.27683	−	12.1862i	−0.0927965	−	0.496673i
$603$	2.02528	+	0.703724i	0.0824758	+	0.0286578i
$604$	4.63816	+	8.24904i	0.188724	+	0.335648i
$605$	−1.59763	+	0.729614i	−0.0649529	+	0.0296630i
$606$	31.0506	−	20.7315i	1.26135	−	0.842161i
$607$	3.46252	+	24.0824i	0.140539	+	0.977473i	0.931015	+	0.364980i	$0.118924\pi$
$607$	3.46252	+	24.0824i	0.140539	+	0.977473i	−0.790476	+	0.612493i	$0.790167\pi$
$608$	−6.01137	−	28.2681i	−0.243793	−	1.14642i
$609$	9.53135	+	6.45949i	0.386230	+	0.261752i
$610$	−3.05373	−	1.78633i	−0.123642	−	0.0723262i
$611$	7.27244	−	15.9244i	0.294212	−	0.644234i
$612$	3.55602	−	32.8577i	0.143744	−	1.32819i
$613$	−25.7164	−	29.6783i	−1.03868	−	1.19870i	−0.979707	−	0.200437i	$-0.935764\pi$
$613$	−25.7164	−	29.6783i	−1.03868	−	1.19870i	−0.0589699	−	0.998260i	$-0.518782\pi$
$614$	15.3955	−	37.8306i	0.621313	−	1.52672i
$615$	−1.33202	+	4.15817i	−0.0537122	+	0.167674i
$616$	21.4957	−	13.3013i	0.866088	−	0.535925i
$617$	16.2625	+	10.4513i	0.654705	+	0.420754i	0.825383	−	0.564573i	$-0.190959\pi$
$617$	16.2625	+	10.4513i	0.654705	+	0.420754i	−0.170678	+	0.985327i	$0.554596\pi$
$618$	−20.7816	+	18.6538i	−0.835957	+	0.750367i
$619$	−10.2980	−	3.02375i	−0.413910	−	0.121535i	0.0681461	−	0.997675i	$-0.478292\pi$
$619$	−10.2980	−	3.02375i	−0.413910	−	0.121535i	−0.482056	+	0.876140i	$0.660110\pi$
$620$	6.59469	+	0.389445i	0.264849	+	0.0156405i
$621$	−20.9879	+	13.4353i	−0.842217	+	0.539139i
$622$	−7.59203	−	8.05359i	−0.304412	−	0.322920i
$623$	5.74778	−	19.5752i	0.230280	−	0.784262i
$624$	13.6114	+	1.95122i	0.544893	+	0.0781112i
$625$	19.4711	+	12.5133i	0.778844	+	0.500532i
$626$	1.31100	−	0.922355i	0.0523980	−	0.0368647i
$627$	−33.6807	−	10.7892i	−1.34508	−	0.430879i
$628$	−36.5727	+	14.1605i	−1.45941	+	0.565067i
$629$	−0.438238	−	0.505753i	−0.0174737	−	0.0201657i
$630$	−2.54679	+	2.17616i	−0.101466	+	0.0867005i
$631$	27.0722	+	12.3635i	1.07773	+	0.492182i	0.873541	−	0.486750i	$-0.161818\pi$
$631$	27.0722	+	12.3635i	1.07773	+	0.492182i	0.204187	+	0.978932i	$0.434545\pi$
$632$	−3.59517	+	5.38955i	−0.143008	+	0.214385i
$633$	−2.38186	−	1.61421i	−0.0946706	−	0.0641591i
$634$	1.21596	+	3.57909i	0.0482921	+	0.142144i
$635$	−3.83667	+	0.551630i	−0.152254	+	0.0218908i
$636$	37.5753	+	8.64734i	1.48996	+	0.342889i
$637$	3.61031	−	1.64878i	0.143046	−	0.0653269i
$638$	−16.3067	−	4.05441i	−0.645590	−	0.160515i
$639$	−6.82401	+	19.6391i	−0.269953	+	0.776912i
$640$	3.99477	−	0.0309565i	0.157907	−	0.00122366i
$641$	−4.06548	+	4.69182i	−0.160577	+	0.185316i	−0.830336	−	0.557262i	$-0.811852\pi$
$641$	−4.06548	+	4.69182i	−0.160577	+	0.185316i	0.669759	+	0.742578i	$0.266397\pi$
$642$	−22.5601	−	9.82953i	−0.890377	−	0.387941i
$643$	−11.1455			−0.439534			−0.219767	−	0.975552i	$-0.570530\pi$
$643$	−11.1455			−0.439534			−0.219767	+	0.975552i	$0.570530\pi$
$644$	−19.3974	+	9.15225i	−0.764363	+	0.360649i
$645$	−1.52538	−	1.84974i	−0.0600618	−	0.0728335i
$646$	−35.4766	+	18.0346i	−1.39581	+	0.709560i
$647$	−26.4882	−	22.9522i	−1.04136	−	0.902343i	−0.0460354	−	0.998940i	$-0.514659\pi$
$647$	−26.4882	−	22.9522i	−1.04136	−	0.902343i	−0.995324	+	0.0965971i	$0.969204\pi$
$648$	−6.48312	+	24.6164i	−0.254681	+	0.967025i
$649$	26.7772	+	3.84998i	1.05110	+	0.151125i
$650$	−13.2798	−	3.30182i	−0.520878	−	0.129508i
$651$	−15.8506	+	32.5794i	−0.621236	+	1.27689i
$652$	−11.8690	−	15.4516i	−0.464828	−	0.605131i
$653$	−1.74685	−	12.1496i	−0.0683596	−	0.475452i	−0.995030	−	0.0995764i	$-0.968251\pi$
$653$	−1.74685	−	12.1496i	−0.0683596	−	0.475452i	0.926670	−	0.375875i	$-0.122658\pi$
$654$	25.7237	+	15.9026i	1.00587	+	0.621842i
$655$	−0.344905	−	1.17464i	−0.0134765	−	0.0458969i
$656$	4.76457	+	28.1568i	0.186025	+	1.09934i
$657$	36.1966	+	25.8421i	1.41217	+	1.00820i
$658$	21.8275	+	17.3674i	0.850926	+	0.677051i
$659$	15.7440	−	13.6422i	0.613298	−	0.531426i	−0.291882	−	0.956454i	$-0.594281\pi$
$659$	15.7440	−	13.6422i	0.613298	−	0.531426i	0.905180	+	0.425028i	$0.139736\pi$
$660$	2.39423	−	4.26235i	0.0931954	−	0.165912i
$661$	−17.6539	+	11.3455i	−0.686659	+	0.441289i	−0.836897	−	0.547361i	$-0.815632\pi$
$661$	−17.6539	+	11.3455i	−0.686659	+	0.441289i	0.150238	+	0.988650i	$0.451996\pi$
$662$	−40.6873	+	28.6256i	−1.58136	+	1.11257i
$663$	−2.23653	−	18.8029i	−0.0868596	−	0.730243i
$664$	0.402035	−	23.5376i	0.0156020	−	0.913435i
$665$	3.87046	+	1.13647i	0.150090	+	0.0440704i
$666$	0.275667	+	0.435536i	0.0106819	+	0.0168767i
$667$	13.3585	+	4.98176i	0.517243	+	0.192895i
$668$	4.92872	+	0.291062i	0.190698	+	0.0112615i
$669$	−30.1462	+	12.8876i	−1.16552	+	0.498264i
$670$	0.356574	−	0.0149517i	0.0137756	−	0.000577633i
$671$	−15.3087	+	23.8207i	−0.590984	+	0.919589i
$672$	−8.25008	+	20.2968i	−0.318254	+	0.782965i
$673$	−19.2909	+	12.3975i	−0.743608	+	0.477888i	−0.856777	−	0.515688i	$-0.827536\pi$
$673$	−19.2909	+	12.3975i	−0.743608	+	0.477888i	0.113168	+	0.993576i	$0.463900\pi$
$674$	−10.7373	+	26.3841i	−0.413584	+	1.01628i
$675$	8.89635	−	23.7194i	0.342421	−	0.912961i
$676$	−18.0581	+	1.51708i	−0.694544	+	0.0583491i
$677$	32.7866	+	14.9732i	1.26009	+	0.575465i	0.929679	−	0.368371i	$-0.120084\pi$
$677$	32.7866	+	14.9732i	1.26009	+	0.575465i	0.330414	+	0.943836i	$0.392812\pi$
$678$	0.969389	+	5.99558i	0.0372292	+	0.230259i
$679$	−29.4892	+	8.65880i	−1.13169	+	0.332294i
$680$	−1.45950	−	5.30409i	−0.0559694	−	0.203403i
$681$	−20.1997	+	22.1933i	−0.774056	+	0.850448i
$682$	5.32556	−	52.6052i	0.203926	−	2.01436i
$683$	16.5755	+	36.2952i	0.634242	+	1.38880i	0.904694	+	0.426063i	$0.140100\pi$
$683$	16.5755	+	36.2952i	0.634242	+	1.38880i	−0.270451	+	0.962734i	$0.587173\pi$
$684$	29.0914	−	9.65976i	1.11234	−	0.369350i
$685$	4.98593	+	0.716868i	0.190503	+	0.0273901i
$686$	5.22699	+	27.9763i	0.199567	+	1.06814i
$687$	0.299616	−	12.2720i	0.0114310	−	0.468205i
$688$	−14.4211	−	6.15795i	−0.549800	−	0.234770i
$689$	22.0911			0.841605
$690$	−2.42718	+	3.36375i	−0.0924011	+	0.128056i
$691$			3.60703i			0.137218i	0.997644	+	0.0686089i	$0.0218561\pi$
$691$			3.60703i			0.137218i	−0.997644	+	0.0686089i	$0.978144\pi$
$692$	−10.9836	+	30.6032i	−0.417535	+	1.16336i
$693$	16.5482	+	21.0956i	0.628613	+	0.801355i
$694$	25.8040	−	4.82113i	0.979508	−	0.183008i
$695$	0.131022	−	0.911278i	0.00496995	−	0.0345667i
$696$	13.4873	−	5.49535i	0.511233	−	0.208301i
$697$	35.7712	−	16.3362i	1.35493	−	0.618776i
$698$	1.70283	−	16.8203i	0.0644531	−	0.636659i
$699$	25.0378	−	27.5088i	0.947018	−	1.04048i
$700$	10.2110	−	19.2648i	0.385939	−	0.728141i
$701$	12.8075	+	43.6185i	0.483734	+	1.64745i	0.733910	+	0.679247i	$0.237694\pi$
$701$	12.8075	+	43.6185i	0.483734	+	1.64745i	−0.250175	+	0.968201i	$0.580488\pi$
$702$	−0.456752	+	14.5775i	−0.0172390	+	0.550193i
$703$	0.257842	−	0.564596i	0.00972470	−	0.0212941i
$704$	1.09195	−	31.9554i	0.0411545	−	1.20436i
$705$	5.31936	+	0.897831i	0.200339	+	0.0338143i
$706$	0.972752	−	2.39029i	0.0366100	−	0.0899596i
$707$	18.4268	+	28.6727i	0.693012	+	1.07835i
$708$	−20.7124	+	10.9894i	−0.778421	+	0.413006i
$709$	17.5061	+	11.2505i	0.657457	+	0.422522i	0.826384	−	0.563107i	$-0.190394\pi$
$709$	17.5061	+	11.2505i	0.657457	+	0.422522i	−0.168927	+	0.985629i	$0.554030\pi$
$710$	0.144986	+	3.45769i	0.00544123	+	0.129765i
$711$	−6.10389	−	3.15620i	−0.228914	−	0.118367i
$712$	−16.5635	−	19.7883i	−0.620744	−	0.741598i
$713$	−9.53423	+	43.8378i	−0.357060	+	1.64174i
$714$	29.9341	+	3.77058i	1.12026	+	0.141110i
$715$	0.789123	−	2.68751i	0.0295115	−	0.100507i
$716$	17.9124	+	17.4731i	0.669419	+	0.653002i
$717$	1.63937	+	13.7825i	0.0612235	+	0.514716i
$718$	−24.9371	−	35.4446i	−0.930645	−	1.32278i
$719$	17.5457	+	27.3017i	0.654345	+	1.01818i	0.996900	+	0.0786829i	$0.0250715\pi$
$719$	17.5457	+	27.3017i	0.654345	+	1.01818i	−0.342555	+	0.939498i	$0.611292\pi$
$720$	0.502233	+	4.20736i	0.0187171	+	0.156799i
$721$	−16.6944	−	19.2664i	−0.621732	−	0.717516i
$722$	−7.85793	−	6.25227i	−0.292442	−	0.232685i
$723$	−2.14402	+	0.573087i	−0.0797369	+	0.0213133i
$724$	7.93658	+	34.4210i	0.294961	+	1.27924i
$725$	−13.9064	+	4.08329i	−0.516470	+	0.151649i
$726$	−10.3634	−	6.40677i	−0.384623	−	0.237777i
$727$	23.9528	−	3.44389i	0.888359	−	0.127727i	0.316998	−	0.948426i	$-0.397325\pi$
$727$	23.9528	−	3.44389i	0.888359	−	0.127727i	0.571360	+	0.820699i	$0.306416\pi$
$728$	−1.99838	+	12.3927i	−0.0740649	+	0.459304i
$729$	−26.7109	−	3.94026i	−0.989294	−	0.145936i
$730$	7.18428	+	1.78625i	0.265902	+	0.0661123i
$731$	−3.07308	+	21.3738i	−0.113662	+	0.790537i
$732$	−1.45704	−	24.4988i	−0.0538538	−	0.905501i
$733$	−20.2028	+	23.3153i	−0.746208	+	0.861169i	−0.994195	−	0.107594i	$-0.965685\pi$
$733$	−20.2028	+	23.3153i	−0.746208	+	0.861169i	0.247987	+	0.968763i	$0.420231\pi$
$734$	−14.7921	−	29.0981i	−0.545985	−	1.07403i
$735$	0.778122	+	0.943585i	0.0287015	+	0.0348046i
$736$	−3.98491	+	26.8351i	−0.146886	+	0.989153i
$737$		−	2.85643i		−	0.105218i
$738$	−29.1207	+	8.33239i	−1.07195	+	0.306720i
$739$	−22.6525	−	19.6285i	−0.833287	−	0.722047i	0.129712	−	0.991552i	$-0.458595\pi$
$739$	−22.6525	−	19.6285i	−0.833287	−	0.722047i	−0.962999	+	0.269504i	$0.913140\pi$
$740$	0.0693177	+	0.0505602i	0.00254817	+	0.00185863i
$741$	15.0018	−	9.13156i	0.551107	−	0.335456i
$742$	−8.49304	+	34.1588i	−0.311789	+	1.25401i
$743$	−10.9500	−	23.9771i	−0.401716	−	0.879634i	−0.997093	−	0.0761885i	$-0.975725\pi$
$743$	−10.9500	−	23.9771i	−0.401716	−	0.879634i	0.595378	−	0.803446i	$-0.297002\pi$
$744$	23.1558	+	39.5470i	0.848934	+	1.44986i
$745$	0.0466745	+	0.324628i	0.00171002	+	0.0118935i
$746$	−5.92919	−	17.4521i	−0.217083	−	0.638966i
$747$	24.8588	−	2.34314i	0.909537	−	0.0857309i
$748$	−42.9046	+	9.89269i	−1.56875	+	0.361712i
$749$	9.33226	−	20.4348i	0.340993	−	0.746671i
$750$	−0.149442	−	8.54005i	−0.00545684	−	0.311839i
$751$	−24.6218	+	21.3349i	−0.898463	+	0.778522i	−0.975842	−	0.218479i	$-0.929890\pi$
$751$	−24.6218	+	21.3349i	−0.898463	+	0.778522i	0.0773789	+	0.997002i	$0.475345\pi$
$752$	33.5960	−	10.7776i	1.22512	−	0.393017i
$753$	32.7596	+	10.4941i	1.19383	+	0.382427i
$754$	6.82442	−	4.80133i	0.248531	−	0.174854i
$755$	−0.903305	+	1.40557i	−0.0328746	+	0.0511539i
$756$	−22.3652	−	6.31066i	−0.813413	−	0.229516i
$757$	45.8614	+	13.4661i	1.66686	+	0.489434i	0.973025	−	0.230700i	$-0.0741016\pi$
$757$	45.8614	+	13.4661i	1.66686	+	0.489434i	0.693835	+	0.720134i	$0.255920\pi$
$758$	−39.1914	+	36.9453i	−1.42350	+	1.34191i
$759$	26.0850	+	20.5373i	0.946826	+	0.745457i
$760$	3.91261	−	3.27499i	0.141925	−	0.118796i
$761$	5.02691	−	17.1201i	0.182225	−	0.620602i	−0.816819	−	0.576894i	$-0.804265\pi$
$761$	5.02691	−	17.1201i	0.182225	−	0.620602i	0.999044	−	0.0437084i	$-0.0139173\pi$
$762$	−17.9613	−	20.0101i	−0.650670	−	0.724888i
$763$	−14.9260	+	23.2253i	−0.540358	+	0.840813i
$764$	−15.6246	−	3.19631i	−0.565276	−	0.115638i
$765$	5.41961	−	2.16202i	0.195946	−	0.0781679i
$766$	7.82558	+	3.18470i	0.282750	+	0.115068i
$767$	−10.1526	+	8.79729i	−0.366590	+	0.317652i
$768$	15.5664	+	22.9279i	0.561705	+	0.827338i
$769$	−43.0290	−	19.6507i	−1.55166	−	0.708621i	−0.558960	−	0.829195i	$-0.688799\pi$
$769$	−43.0290	−	19.6507i	−1.55166	−	0.708621i	−0.992704	+	0.120574i	$0.961527\pi$
$770$	3.85223	+	2.25342i	0.138825	+	0.0812077i
$771$	27.2866	+	18.4924i	0.982703	+	0.665987i
$772$	−16.8354	−	8.92330i	−0.605918	−	0.321157i
$773$	10.3305	−	1.48530i	0.371561	−	0.0534224i	0.0459950	−	0.998942i	$-0.485354\pi$
$773$	10.3305	−	1.48530i	0.371561	−	0.0534224i	0.325566	+	0.945519i	$0.394445\pi$
$774$	4.79599	−	15.9256i	0.172388	−	0.572433i
$775$	−18.9455	−	41.4848i	−0.680541	−	1.49018i
$776$	−11.5878	+	37.1078i	−0.415977	+	1.33209i
$777$	−0.401940	+	0.244659i	−0.0144195	+	0.00877709i
$778$	0.338490	+	1.81169i	0.0121354	+	0.0649524i
$779$	27.5649	+	23.8851i	0.987616	+	0.855774i
$780$	0.821040	+	2.28462i	0.0293979	+	0.0818027i
$781$	27.6988			0.991139
$782$	37.1191	−	4.22565i	1.32738	−	0.151109i
$783$	7.37827	+	13.5713i	0.263678	+	0.484997i
$784$	7.35646	+	3.14128i	0.262731	+	0.112188i
$785$	−5.23285	−	4.53429i	−0.186769	−	0.161836i
$786$	5.44828	−	6.51455i	0.194334	−	0.232366i
$787$	4.70886	−	32.7508i	0.167853	−	1.16744i	−0.715459	−	0.698655i	$-0.753782\pi$
$787$	4.70886	−	32.7508i	0.167853	−	1.16744i	0.883311	−	0.468787i	$-0.155309\pi$
$788$	−17.2669	−	30.7094i	−0.615108	−	1.09398i
$789$	10.1836	+	4.95455i	0.362545	+	0.176387i
$790$	−1.13799	−	0.115206i	−0.0404879	−	0.00409885i
$791$	−5.48796	+	0.789050i	−0.195130	+	0.0280554i
$792$	33.8134	−	2.60543i	1.20151	−	0.0925798i
$793$	−3.96148	−	13.4916i	−0.140676	−	0.479100i
$794$	−25.1847	−	14.7322i	−0.893770	−	0.522825i
$795$	1.75787	+	6.57648i	0.0623451	+	0.233244i
$796$	−2.38092	−	28.3406i	−0.0843893	−	1.00451i
$797$	17.4557	−	15.1255i	0.618314	−	0.535772i	−0.288404	−	0.957509i	$-0.593125\pi$
$797$	17.4557	−	15.1255i	0.618314	−	0.535772i	0.906718	+	0.421736i	$0.138579\pi$
$798$	8.35232	+	26.7076i	0.295669	+	0.945438i
$799$	−26.2677	−	40.8733i	−0.929283	−	1.44599i
$800$	−13.1041	−	24.2669i	−0.463301	−	0.857964i
$801$	18.9123	−	19.7862i	0.668232	−	0.699112i
$802$	−0.334476	−	7.97674i	−0.0118108	−	0.281668i
$803$	16.6931	−	56.8516i	0.589088	−	2.00625i
$804$	1.45978	+	1.99959i	0.0514824	+	0.0705201i
$805$	−3.03150	−	2.26914i	−0.106846	−	0.0799766i
$806$	18.0105	+	19.1055i	0.634393	+	0.672962i
$807$	8.50743	−	3.63696i	0.299476	−	0.128027i
$808$	43.1050	+	0.736259i	1.51643	+	0.0259015i
$809$	11.8912	−	18.5031i	0.418073	−	0.650535i	−0.566791	−	0.823862i	$-0.691815\pi$
$809$	11.8912	−	18.5031i	0.418073	−	0.650535i	0.984864	+	0.173327i	$0.0554517\pi$
$810$	−4.37604	+	1.02401i	−0.153758	+	0.0359800i
$811$	11.1312	+	17.3204i	0.390868	+	0.608202i	0.979800	−	0.199981i	$-0.0640879\pi$
$811$	11.1312	+	17.3204i	0.390868	+	0.608202i	−0.588932	+	0.808182i	$0.700452\pi$
$812$	4.80047	+	12.3983i	0.168464	+	0.435095i
$813$	−20.0661	−	3.38687i	−0.703750	−	0.118783i
$814$	0.427558	−	0.537360i	0.0149859	−	0.0188344i
$815$	1.42899	−	3.12906i	0.0500555	−	0.109606i
$816$	24.9790	−	28.8516i	0.874438	−	1.01001i
$817$	−19.2166	+	5.64251i	−0.672305	+	0.197406i
$818$	−17.2626	−	50.8110i	−0.603572	−	1.77657i
$819$	−13.2984	−	0.649737i	−0.464683	−	0.0227036i
$820$	−3.99833	+	3.07130i	−0.139628	+	0.107254i
$821$	−5.32352	−	11.6569i	−0.185792	−	0.406828i	0.793700	−	0.608309i	$-0.208152\pi$
$821$	−5.32352	−	11.6569i	−0.185792	−	0.406828i	−0.979492	+	0.201481i	$0.935425\pi$
$822$	15.0699	+	31.5267i	0.525623	+	1.09962i
$823$	−5.65708	+	39.3459i	−0.197194	+	1.37151i	0.615186	+	0.788382i	$0.289081\pi$
$823$	−5.65708	+	39.3459i	−0.197194	+	1.37151i	−0.812380	+	0.583129i	$0.801828\pi$
$824$	−31.9912	+	4.04328i	−1.11447	+	0.140854i
$825$	−33.7397	−	0.823743i	−1.17467	−	0.0286791i
$826$	−9.69976	−	19.0808i	−0.337498	−	0.663907i
$827$			46.5279i			1.61793i	0.587854	+	0.808967i	$0.299973\pi$
$827$			46.5279i			1.61793i	−0.587854	+	0.808967i	$0.700027\pi$
$828$	−28.7560	−	1.04603i	−0.999339	−	0.0363519i
$829$		−	55.0469i		−	1.91186i	−0.293596	−	0.955930i	$-0.594852\pi$
$829$		−	55.0469i		−	1.91186i	0.293596	−	0.955930i	$-0.405148\pi$
$830$	3.70495	−	1.88342i	0.128601	−	0.0653743i
$831$	4.71001	+	0.114993i	0.163389	+	0.00398907i
$832$	11.6375	+	10.8015i	0.403459	+	0.374474i
$833$	1.56763	−	10.9031i	0.0543152	−	0.377771i
$834$	5.76214	−	2.75432i	0.199527	−	0.0953744i
$835$	0.362112	+	0.792914i	0.0125314	+	0.0274399i
$836$	−24.8772	−	32.3861i	−0.860395	−	1.12010i
$837$	−38.9654	+	29.0581i	−1.34684	+	1.00439i
$838$	−35.3916	+	12.0240i	−1.22258	+	0.415362i
$839$	36.5096	−	10.7202i	1.26045	−	0.370102i	0.417789	−	0.908544i	$-0.362805\pi$
$839$	36.5096	−	10.7202i	1.26045	−	0.370102i	0.842663	+	0.538442i	$0.180987\pi$
$840$	−3.84830	+	0.391214i	−0.132779	+	0.0134982i
$841$	−8.37572	+	18.3403i	−0.288818	+	0.632423i
$842$	33.0069	+	26.2624i	1.13749	+	0.905063i
$843$	−24.5020	−	4.13558i	−0.843894	−	0.142437i
$844$	−1.19963	−	3.09831i	−0.0412929	−	0.106648i
$845$	−1.72973	−	2.69152i	−0.0595047	−	0.0925911i
$846$	15.3103	+	34.1475i	0.526377	+	1.17402i
$847$	6.01332	−	9.35691i	0.206620	−	0.321507i
$848$	29.9823	+	32.9136i	1.02960	+	1.13026i
$849$	34.0864	−	14.5720i	1.16984	−	0.500111i
$850$	−27.6347	+	26.0509i	−0.947864	+	0.893540i
$851$	−0.411979	+	0.412017i	−0.0141225	+	0.0141238i
$852$	−19.3900	+	14.1555i	−0.664291	+	0.484958i
$853$	−0.570618	+	1.94335i	−0.0195376	+	0.0665389i	−0.968685	−	0.248294i	$-0.920130\pi$
$853$	−0.570618	+	1.94335i	−0.0195376	+	0.0665389i	0.949147	+	0.314833i	$0.101948\pi$
$854$	22.3846	−	0.938619i	0.765985	−	0.0321189i
$855$	3.91219	+	3.73939i	0.133794	+	0.127884i
$856$	−14.9521	−	24.1635i	−0.511051	−	0.825891i
$857$	−17.8585	−	27.7884i	−0.610036	−	0.949234i	−0.999601	−	0.0282353i	$-0.991011\pi$
$857$	−17.8585	−	27.7884i	−0.610036	−	0.949234i	0.389566	−	0.920999i	$-0.372625\pi$
$858$	18.5448	−	5.79954i	0.633107	−	0.197993i
$859$	−7.87948	+	6.82761i	−0.268844	+	0.232955i	−0.778841	−	0.627221i	$-0.784192\pi$
$859$	−7.87948	+	6.82761i	−0.268844	+	0.232955i	0.509997	+	0.860176i	$0.329647\pi$
$860$	−0.231765	−	2.75875i	−0.00790311	−	0.0940727i
$861$	−7.14029	−	26.7131i	−0.243340	−	0.910379i
$862$	16.9425	−	28.9633i	0.577065	−	0.986493i
$863$	−3.20391	−	10.9115i	−0.109062	−	0.371432i	0.886817	−	0.462121i	$-0.152911\pi$
$863$	−3.20391	−	10.9115i	−0.109062	−	0.371432i	−0.995879	+	0.0906889i	$0.971093\pi$
$864$	−22.3390	+	19.1042i	−0.759987	+	0.649939i
$865$	−5.68205	+	0.816956i	−0.193196	+	0.0277773i
$866$	2.55180	−	25.2063i	0.0867137	−	0.856546i
$867$	−20.7784	−	10.1092i	−0.705673	−	0.343327i
$868$	−36.4664	+	20.5039i	−1.23775	+	0.695948i
$869$	−1.30285	+	9.06154i	−0.0441963	+	0.307392i
$870$	1.97239	+	1.64956i	0.0668703	+	0.0559253i
$871$	1.07200	+	0.928890i	0.0363232	+	0.0314742i
$872$	13.9620	+	32.0082i	0.472815	+	1.08394i
$873$	−40.4785	−	7.85281i	−1.36999	−	0.265777i
$874$	17.8669	+	29.6884i	0.604356	+	1.00423i
$875$	7.79734			0.263598
$876$	17.3683	+	48.3290i	0.586820	+	1.63288i
$877$	11.6614	+	10.1046i	0.393777	+	0.341209i	0.829136	−	0.559048i	$-0.188833\pi$
$877$	11.6614	+	10.1046i	0.393777	+	0.341209i	−0.435359	+	0.900257i	$0.643379\pi$
$878$	−36.0345	+	6.73254i	−1.21610	+	0.227212i
$879$	32.5815	−	19.8322i	1.09895	−	0.668925i
$880$	5.07512	−	2.47179i	0.171082	−	0.0833241i
$881$	−14.4212	−	31.5781i	−0.485863	−	1.06389i	−0.980809	−	0.194969i	$-0.937539\pi$
$881$	−14.4212	−	31.5781i	−0.485863	−	1.06389i	0.494946	−	0.868924i	$-0.335188\pi$
$882$	−2.44652	+	8.12391i	−0.0823786	+	0.273546i
$883$	−6.66937	+	0.958910i	−0.224442	+	0.0322699i	−0.253618	−	0.967304i	$-0.581621\pi$
$883$	−6.66937	+	0.958910i	−0.224442	+	0.0322699i	0.0291762	+	0.999574i	$0.490712\pi$
$884$	10.2396	−	19.3188i	0.344396	−	0.649762i
$885$	−3.42681	−	2.32238i	−0.115191	−	0.0780661i
$886$	−2.10580	+	3.59987i	−0.0707457	+	0.120940i
$887$	49.3812	+	22.5517i	1.65806	+	0.757211i	0.999991	+	0.00425286i	$0.00135373\pi$
$887$	49.3812	+	22.5517i	1.65806	+	0.757211i	0.658069	+	0.752958i	$0.271374\pi$
$888$	−0.0246864	+	0.594673i	−0.000828420	+	0.0199559i
$889$	18.5511	−	16.0746i	0.622185	−	0.539126i
$890$	1.71735	−	4.21994i	0.0575656	−	0.141453i
$891$	6.72134	+	35.3373i	0.225173	+	1.18384i
$892$	−37.0893	−	7.58734i	−1.24184	−	0.254043i
$893$	24.3631	−	37.9097i	0.815280	−	1.26860i
$894$	−1.69309	+	1.51974i	−0.0566255	+	0.0508279i
$895$	−1.24466	+	4.23894i	−0.0416045	+	0.141692i
$896$	−21.1761	+	13.8421i	−0.707443	+	0.462431i
$897$	−16.1902	+	3.11093i	−0.540574	+	0.103871i
$898$	6.52971	+	6.92669i	0.217899	+	0.231147i
$899$	26.6828	+	7.83478i	0.889922	+	0.261305i
$900$	24.0399	−	16.6661i	0.801330	−	0.555536i
$901$	33.1468	−	51.5774i	1.10428	−	1.71829i
$902$	23.2195	+	33.0033i	0.773126	+	1.09889i
$903$	14.4595	+	4.63192i	0.481182	+	0.154141i
$904$	−3.02183	+	6.32857i	−0.100505	+	0.210485i
$905$	−4.71324	+	4.08404i	−0.156673	+	0.135758i
$906$	−11.5887	+	0.202790i	−0.385008	+	0.00673723i
$907$	−13.4726	+	29.5008i	−0.447349	+	0.979559i	0.542841	+	0.839835i	$0.317349\pi$
$907$	−13.4726	+	29.5008i	−0.447349	+	0.979559i	−0.990191	+	0.139723i	$0.955379\pi$
$908$	−33.7660	+	7.78557i	−1.12057	+	0.258373i
$909$	4.29105	+	45.5247i	0.142325	+	1.50996i
$910$	−2.09841	+	0.712916i	−0.0695616	+	0.0236329i
$911$	−2.06836	−	14.3858i	−0.0685278	−	0.476621i	−0.994969	−	0.100182i	$-0.968057\pi$
$911$	−2.06836	−	14.3858i	−0.0685278	−	0.476621i	0.926441	−	0.376439i	$-0.122852\pi$
$912$	33.9657	+	9.95782i	1.12472	+	0.329736i
$913$	−13.8188	−	30.2589i	−0.457335	−	1.00142i
$914$	6.66816	+	1.65793i	0.220563	+	0.0548394i
$915$	3.70118	−	2.25289i	0.122357	−	0.0744784i
$916$	8.35305	−	11.4520i	0.275993	−	0.378384i
$917$	5.85915	+	5.07699i	0.193486	+	0.167657i
$918$	33.3496	+	22.9393i	1.10070	+	0.757111i
$919$			36.4774i			1.20328i	0.798768	+	0.601640i	$0.205486\pi$
$919$			36.4774i			1.20328i	−0.798768	+	0.601640i	$0.794514\pi$
$920$	−4.51558	+	1.59715i	−0.148874	+	0.0526566i
$921$	31.8254	+	38.5928i	1.04868	+	1.27168i
$922$	−18.5895	+	9.44998i	−0.612212	+	0.311219i
$923$	−9.00744	+	10.3951i	−0.296483	+	0.342160i
$924$	1.83804	+	30.9048i	0.0604669	+	1.01669i
$925$	0.0842946	−	0.586281i	0.00277159	−	0.0192768i
$926$	−2.66930	+	10.7359i	−0.0877187	+	0.352803i
$927$	−8.02281	−	33.2474i	−0.263504	−	1.09199i
$928$	16.4157	+	3.65130i	0.538871	+	0.119860i
$929$	−33.2148	+	4.77557i	−1.08974	+	0.156681i	−0.663683	−	0.748014i	$-0.731008\pi$
$929$	−33.2148	+	4.77557i	−1.08974	+	0.156681i	−0.426059	+	0.904695i	$0.640098\pi$
$930$	−4.25451	+	6.88198i	−0.139511	+	0.225669i
$931$	9.80273	−	2.87834i	0.321271	−	0.0943338i
$932$	41.8534	−	9.65031i	1.37095	−	0.316107i
$933$	13.0956	−	3.50041i	0.428732	−	0.114598i
$934$	6.48986	−	8.15654i	0.212355	−	0.266890i
$935$	−5.09063	−	5.87490i	−0.166481	−	0.192130i
$936$	−10.0181	+	13.5372i	−0.327451	+	0.442476i
$937$	12.7692	+	19.8693i	0.417153	+	0.649103i	0.984704	−	0.174235i	$-0.0557454\pi$
$937$	12.7692	+	19.8693i	0.417153	+	0.649103i	−0.567551	+	0.823338i	$0.692109\pi$
$938$	−1.84845	+	1.30048i	−0.0603539	+	0.0424621i
$939$	0.231881	+	1.94947i	0.00756716	+	0.0636184i
$940$	4.45901	+	4.34966i	0.145437	+	0.141870i
$941$	−2.85057	+	9.70815i	−0.0929259	+	0.316477i	−0.992818	−	0.119636i	$-0.961827\pi$
$941$	−2.85057	+	9.70815i	−0.0929259	+	0.316477i	0.899892	+	0.436113i	$0.143645\pi$
$942$	6.00287	−	47.6560i	0.195584	−	1.55272i
$943$	−16.4102	−	30.0499i	−0.534391	−	0.978558i
$944$	−26.8863	−	3.18662i	−0.875075	−	0.103716i
$945$	−0.864771	−	4.01060i	−0.0281310	−	0.130465i
$946$	−22.1386	+	0.928305i	−0.719789	+	0.0301818i
$947$	−23.6539	−	15.2015i	−0.768650	−	0.493981i	0.0965994	−	0.995323i	$-0.469203\pi$
$947$	−23.6539	−	15.2015i	−0.768650	−	0.493981i	−0.865249	+	0.501342i	$0.832840\pi$
$948$	−3.71887	−	7.00920i	−0.120783	−	0.227648i
$949$	15.9075	+	24.7525i	0.516379	+	0.803501i
$950$	−32.6261	−	13.2775i	−1.05853	−	0.430780i
$951$	−4.56498	−	0.770502i	−0.148030	−	0.0249852i
$952$	25.9354	+	23.2604i	0.840572	+	0.753875i
$953$	5.00426	−	10.9578i	0.162104	−	0.354958i	−0.811098	−	0.584910i	$-0.801130\pi$
$953$	5.00426	−	10.9578i	0.162104	−	0.354958i	0.973202	+	0.229952i	$0.0738570\pi$
$954$	−31.1705	+	35.4742i	−1.00918	+	1.14852i
$955$	−0.793263	−	2.70161i	−0.0256694	−	0.0874219i
$956$	−7.50563	+	14.1607i	−0.242749	+	0.457988i
$957$	13.8524	−	15.2195i	0.447784	−	0.491976i
$958$	−42.6585	−	4.31860i	−1.37823	−	0.139528i
$959$	−29.0168	+	13.2515i	−0.937001	+	0.427914i
$960$	−2.28954	+	4.32398i	−0.0738945	+	0.139556i
$961$	−8.04172	+	55.9314i	−0.259410	+	1.80424i
$962$	0.0626284	+	0.335205i	0.00201922	+	0.0108074i
$963$	23.7137	−	18.6019i	0.764162	−	0.599437i
$964$	−2.41197	−	0.865667i	−0.0776844	−	0.0278813i
$965$		−	3.36400i		−	0.108291i
$966$	1.41406	−	26.2304i	0.0454966	−	0.843948i
$967$	−39.3812			−1.26641			−0.633207	−	0.773982i	$-0.718262\pi$
$967$	−39.3812			−1.26641			−0.633207	+	0.773982i	$0.718262\pi$
$968$	−5.62496	−	12.8953i	−0.180793	−	0.414471i
$969$	1.18966	−	48.7272i	0.0382172	−	1.56534i
$970$	−6.74668	+	1.26052i	−0.216623	+	0.0404730i
$971$	−45.8429	−	6.59121i	−1.47117	−	0.211522i	−0.640357	−	0.768077i	$-0.721214\pi$
$971$	−45.8429	−	6.59121i	−1.47117	−	0.211522i	−0.830810	+	0.556556i	$0.812123\pi$
$972$	−22.7643	−	21.3023i	−0.730165	−	0.683271i
$973$	2.42198	+	5.30340i	0.0776452	+	0.170019i
$974$	−43.2769	−	4.38120i	−1.38668	−	0.140383i
$975$	11.2811	−	12.3944i	0.361284	−	0.396939i
$976$	14.7245	−	24.2131i	0.471321	−	0.775042i
$977$	−49.0674	+	14.4075i	−1.56981	+	0.460937i	−0.946945	−	0.321395i	$-0.895848\pi$
$977$	−49.0674	+	14.4075i	−1.56981	+	0.460937i	−0.622861	+	0.782332i	$0.714030\pi$
$978$	23.5570	−	3.80879i	0.753269	−	0.121792i
$979$	−33.1697	−	15.1481i	−1.06011	−	0.484135i
$980$	0.118227	+	1.40729i	0.00377663	+	0.0449541i
$981$	−32.0994	+	18.4804i	−1.02486	+	0.590035i
$982$	41.5332	+	16.9024i	1.32538	+	0.539376i
$983$	2.76531	−	1.77715i	0.0881996	−	0.0566824i	−0.495798	−	0.868438i	$-0.665124\pi$
$983$	2.76531	−	1.77715i	0.0881996	−	0.0566824i	0.583997	+	0.811756i	$0.301488\pi$
$984$	−33.1208	−	11.2370i	−1.05585	−	0.358224i
$985$	3.36281	−	5.23264i	0.107148	−	0.166726i
$986$	−0.970192	−	23.1376i	−0.0308972	−	0.736850i
$987$	−31.4128	+	13.4291i	−0.999879	+	0.427452i
$988$	20.2441	+	1.19550i	0.644052	+	0.0380341i
$989$	18.7528	+	1.34037i	0.596306	+	0.0426213i
$990$	3.20218	+	5.05925i	0.101772	+	0.160793i
$991$	−22.6082	−	6.63836i	−0.718173	−	0.210875i	−0.0978275	−	0.995203i	$-0.531189\pi$
$991$	−22.6082	−	6.63836i	−0.718173	−	0.210875i	−0.620345	+	0.784329i	$0.713008\pi$
$992$	−4.02124	+	52.7640i	−0.127674	+	1.67526i
$993$	−7.19652	−	60.5023i	−0.228375	−	1.91998i
$994$	−12.6107	−	17.9244i	−0.399988	−	0.568527i
$995$	4.22410	−	2.71466i	0.133913	−	0.0860606i
$996$	25.1374	+	14.1201i	0.796510	+	0.447414i
$997$	12.2738	−	10.6353i	0.388716	−	0.336824i	−0.438477	−	0.898743i	$-0.644482\pi$
$997$	12.2738	−	10.6353i	0.388716	−	0.336824i	0.827193	+	0.561918i	$0.189936\pi$
$998$	−1.16930	+	1.46960i	−0.0370137	+	0.0465192i
$999$	−0.629762	+	0.0438836i	−0.0199248	+	0.00138841i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bf.a.5.14	✓	920
3.2	odd	2	inner	552.2.bf.a.5.79	yes	920
8.5	even	2	inner	552.2.bf.a.5.62	yes	920
23.14	odd	22	inner	552.2.bf.a.221.31	yes	920
24.5	odd	2	inner	552.2.bf.a.5.31	yes	920
69.14	even	22	inner	552.2.bf.a.221.62	yes	920
184.37	odd	22	inner	552.2.bf.a.221.79	yes	920
552.221	even	22	inner	552.2.bf.a.221.14	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bf.a.5.14	✓	920	1.1	even	1	trivial
552.2.bf.a.5.31	yes	920	24.5	odd	2	inner
552.2.bf.a.5.62	yes	920	8.5	even	2	inner
552.2.bf.a.5.79	yes	920	3.2	odd	2	inner
552.2.bf.a.221.14	yes	920	552.221	even	22	inner
552.2.bf.a.221.31	yes	920	23.14	odd	22	inner
552.2.bf.a.221.62	yes	920	69.14	even	22	inner
552.2.bf.a.221.79	yes	920	184.37	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bf (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26067 + 0.640864i) q^{2} +(0.0422748 - 1.73153i) q^{3} +(1.17859 - 1.61584i) q^{4} +(0.349508 + 0.0502517i) q^{5} +(1.05638 + 2.20999i) q^{6} +(-2.03405 + 0.928918i) q^{7} +(-0.450281 + 2.79236i) q^{8} +(-2.99643 - 0.146400i) q^{9} +O(q^{10})\)	\(q+(-1.26067 + 0.640864i) q^{2} +(0.0422748 - 1.73153i) q^{3} +(1.17859 - 1.61584i) q^{4} +(0.349508 + 0.0502517i) q^{5} +(1.05638 + 2.20999i) q^{6} +(-2.03405 + 0.928918i) q^{7} +(-0.450281 + 2.79236i) q^{8} +(-2.99643 - 0.146400i) q^{9} +(-0.472820 + 0.160636i) q^{10} +(1.12602 + 3.83486i) q^{11} +(-2.74805 - 2.10907i) q^{12} +(-1.80537 - 0.824483i) q^{13} +(1.96896 - 2.47461i) q^{14} +(0.101788 - 0.603061i) q^{15} +(-1.22186 - 3.80881i) q^{16} +(-4.63384 + 2.97799i) q^{17} +(3.87133 - 1.73574i) q^{18} +(-4.29786 - 2.76207i) q^{19} +(0.493124 - 0.505522i) q^{20} +(1.52246 + 3.56129i) q^{21} +(-3.87716 - 4.11288i) q^{22} +(2.87421 + 3.83913i) q^{23} +(4.81602 + 0.897723i) q^{24} +(-4.67783 - 1.37354i) q^{25} +(2.80436 - 0.117591i) q^{26} +(-0.380171 + 5.18223i) q^{27} +(-0.896321 + 4.38150i) q^{28} +(2.50090 - 1.60723i) q^{29} +(0.258159 + 0.825494i) q^{30} +(6.12589 + 7.06965i) q^{31} +(3.98130 + 4.01862i) q^{32} +(6.68779 - 1.78762i) q^{33} +(3.93327 - 6.72393i) q^{34} +(-0.757595 + 0.222450i) q^{35} +(-3.76811 + 4.66919i) q^{36} +(0.0172901 + 0.120255i) q^{37} +(7.18830 + 0.727718i) q^{38} +(-1.50394 + 3.09120i) q^{39} +(-0.297697 + 0.953323i) q^{40} +(-7.06660 - 1.01602i) q^{41} +(-4.20163 - 3.51393i) q^{42} +(2.56719 - 2.96270i) q^{43} +(7.52362 + 2.70026i) q^{44} +(-1.03992 - 0.201744i) q^{45} +(-6.08379 - 2.99791i) q^{46} +8.82061i q^{47} +(-6.64675 + 1.95468i) q^{48} +(-1.30957 + 1.51132i) q^{49} +(6.77746 - 1.26628i) q^{50} +(4.96060 + 8.14955i) q^{51} +(-3.46001 + 1.94545i) q^{52} +(-10.1247 + 4.62381i) q^{53} +(-2.84183 - 6.77673i) q^{54} +(0.200844 + 1.39690i) q^{55} +(-1.67798 - 6.09805i) q^{56} +(-4.96431 + 7.32513i) q^{57} +(-2.12280 + 3.62893i) q^{58} +(2.81179 - 6.15696i) q^{59} +(-0.854483 - 0.875233i) q^{60} +(4.63948 + 5.35425i) q^{61} +(-12.2534 - 4.98665i) q^{62} +(6.23086 - 2.48565i) q^{63} +(-7.59449 - 2.51469i) q^{64} +(-0.589559 - 0.378886i) q^{65} +(-7.28549 + 6.53956i) q^{66} +(-0.685736 - 0.201350i) q^{67} +(-0.649442 + 10.9974i) q^{68} +(6.76909 - 4.81450i) q^{69} +(0.812519 - 0.765952i) q^{70} +(1.95249 - 6.64958i) q^{71} +(1.75804 - 8.30116i) q^{72} +(-12.4715 - 8.01497i) q^{73} +(-0.0988641 - 0.140522i) q^{74} +(-2.57608 + 8.04177i) q^{75} +(-9.52846 + 3.68931i) q^{76} +(-5.85264 - 6.75430i) q^{77} +(-0.0850590 - 4.86081i) q^{78} +(2.08355 + 0.951524i) q^{79} +(-0.235652 - 1.39261i) q^{80} +(8.95713 + 0.877356i) q^{81} +(9.55979 - 3.24785i) q^{82} +(-8.23829 + 1.18449i) q^{83} +(7.54883 + 1.73724i) q^{84} +(-1.76921 + 0.807973i) q^{85} +(-1.33770 + 5.38021i) q^{86} +(-2.67725 - 4.39834i) q^{87} +(-11.2153 + 1.41747i) q^{88} +(-5.97472 + 6.89519i) q^{89} +(1.44029 - 0.412113i) q^{90} +4.43808 q^{91} +(9.59092 - 0.119505i) q^{92} +(12.5003 - 10.3083i) q^{93} +(-5.65281 - 11.1199i) q^{94} +(-1.36334 - 1.18134i) q^{95} +(7.12668 - 6.72387i) q^{96} +(13.6045 + 1.95603i) q^{97} +(0.682385 - 2.74454i) q^{98} +(-2.81260 - 11.6557i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9}+O(q^{10}) \) 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9	\( 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9} - 22 q^{10} - 12 q^{12} - 22 q^{15} - 30 q^{16} - 10 q^{18} - 14 q^{24} + 40 q^{25} - 22 q^{28} - 11 q^{30} - 20 q^{31} - 22 q^{33} - 18 q^{36} - 42 q^{39} - 176 q^{40} - 11 q^{42} + 90 q^{46} - 64 q^{48} + 32 q^{49} - 90 q^{52} + 21 q^{54} - 76 q^{55} - 22 q^{57} + 76 q^{58} - 11 q^{60} - 22 q^{63} - 28 q^{64} - 44 q^{66} - 116 q^{70} - 79 q^{72} - 36 q^{73} - 22 q^{76} - 134 q^{78} - 44 q^{79} - 34 q^{81} - 40 q^{82} - 165 q^{84} - 18 q^{87} - 22 q^{88} - 198 q^{90} + 88 q^{94} - 231 q^{96} - 44 q^{97}+O(q^{100}) \) 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9 - 22 * q^10 - 12 * q^12 - 22 * q^15 - 30 * q^16 - 10 * q^18 - 14 * q^24 + 40 * q^25 - 22 * q^28 - 11 * q^30 - 20 * q^31 - 22 * q^33 - 18 * q^36 - 42 * q^39 - 176 * q^40 - 11 * q^42 + 90 * q^46 - 64 * q^48 + 32 * q^49 - 90 * q^52 + 21 * q^54 - 76 * q^55 - 22 * q^57 + 76 * q^58 - 11 * q^60 - 22 * q^63 - 28 * q^64 - 44 * q^66 - 116 * q^70 - 79 * q^72 - 36 * q^73 - 22 * q^76 - 134 * q^78 - 44 * q^79 - 34 * q^81 - 40 * q^82 - 165 * q^84 - 18 * q^87 - 22 * q^88 - 198 * q^90 + 88 * q^94 - 231 * q^96 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more