LMFDB - Embedded newform 552.2.bf.a.5.1

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			5.1
Character	$\chi$	$=$	552.5
Dual form			552.2.bf.a.221.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41419 + 0.00734365i) q^{2} +(0.191591 - 1.72142i) q^{3} +(1.99989 - 0.0207707i) q^{4} +(3.15950 + 0.454268i) q^{5} +(-0.258305 + 2.43583i) q^{6} +(0.966873 - 0.441556i) q^{7} +(-2.82808 + 0.0440603i) q^{8} +(-2.92659 - 0.659617i) q^{9} +O(q^{10})$	\(q+(-1.41419 + 0.00734365i) q^{2} +(0.191591 - 1.72142i) q^{3} +(1.99989 - 0.0207707i) q^{4} +(3.15950 + 0.454268i) q^{5} +(-0.258305 + 2.43583i) q^{6} +(0.966873 - 0.441556i) q^{7} +(-2.82808 + 0.0440603i) q^{8} +(-2.92659 - 0.659617i) q^{9} +(-4.47149 - 0.619221i) q^{10} +(-1.45838 - 4.96677i) q^{11} +(0.347406 - 3.44664i) q^{12} +(5.38000 + 2.45696i) q^{13} +(-1.36410 + 0.631547i) q^{14} +(1.38732 - 5.35180i) q^{15} +(3.99914 - 0.0830783i) q^{16} +(1.57359 - 1.01129i) q^{17} +(4.14361 + 0.911335i) q^{18} +(-1.16859 - 0.751005i) q^{19} +(6.32810 + 0.842862i) q^{20} +(-0.574860 - 1.74899i) q^{21} +(2.09890 + 7.01327i) q^{22} +(-4.68944 + 1.00455i) q^{23} +(-0.465989 + 4.87677i) q^{24} +(4.97864 + 1.46186i) q^{25} +(-7.62641 - 3.43512i) q^{26} +(-1.69619 + 4.91151i) q^{27} +(1.92447 - 0.903147i) q^{28} +(-1.58834 + 1.02077i) q^{29} +(-1.92264 + 7.57868i) q^{30} +(5.21351 + 6.01671i) q^{31} +(-5.65495 + 0.146857i) q^{32} +(-8.82932 + 1.55889i) q^{33} +(-2.21794 + 1.44171i) q^{34} +(3.25542 - 0.955879i) q^{35} +(-5.86656 - 1.25838i) q^{36} +(-0.881073 - 6.12800i) q^{37} +(1.65812 + 1.05349i) q^{38} +(5.26023 - 8.79052i) q^{39} +(-8.95536 - 1.14550i) q^{40} +(8.01106 + 1.15182i) q^{41} +(0.825808 + 2.46920i) q^{42} +(2.14799 - 2.47891i) q^{43} +(-3.01976 - 9.90271i) q^{44} +(-8.94692 - 3.41352i) q^{45} +(6.62441 - 1.45506i) q^{46} -7.43194i q^{47} +(0.623185 - 6.90012i) q^{48} +(-3.84415 + 4.43639i) q^{49} +(-7.05150 - 2.03079i) q^{50} +(-1.43937 - 2.90257i) q^{51} +(10.8105 + 4.80192i) q^{52} +(1.31544 - 0.600740i) q^{53} +(2.36267 - 6.95829i) q^{54} +(-2.35150 - 16.3550i) q^{55} +(-2.71494 + 1.29136i) q^{56} +(-1.51669 + 1.86775i) q^{57} +(2.23873 - 1.45523i) q^{58} +(-0.468756 + 1.02643i) q^{59} +(2.66333 - 10.7318i) q^{60} +(-8.03054 - 9.26774i) q^{61} +(-7.41710 - 8.47051i) q^{62} +(-3.12090 + 0.654486i) q^{63} +(7.99612 - 0.249212i) q^{64} +(15.8820 + 10.2068i) q^{65} +(12.4749 - 2.26941i) q^{66} +(-3.53167 - 1.03699i) q^{67} +(3.12601 - 2.05515i) q^{68} +(0.830797 + 8.26497i) q^{69} +(-4.59678 + 1.37571i) q^{70} +(-1.09880 + 3.74217i) q^{71} +(8.30569 + 1.73651i) q^{72} +(-0.799168 - 0.513594i) q^{73} +(1.29101 + 8.65971i) q^{74} +(3.47034 - 8.29026i) q^{75} +(-2.35265 - 1.47766i) q^{76} +(-3.60317 - 4.15828i) q^{77} +(-7.37444 + 12.4701i) q^{78} +(4.02179 + 1.83669i) q^{79} +(12.6730 + 1.55419i) q^{80} +(8.12981 + 3.86085i) q^{81} +(-11.3377 - 1.57006i) q^{82} +(-14.2163 + 2.04399i) q^{83} +(-1.18599 - 3.48586i) q^{84} +(5.43117 - 2.48033i) q^{85} +(-3.01947 + 3.52144i) q^{86} +(1.45286 + 2.92978i) q^{87} +(4.34324 + 13.9822i) q^{88} +(-6.78673 + 7.83230i) q^{89} +(12.6777 + 4.76168i) q^{90} +6.28667 q^{91} +(-9.35752 + 2.10639i) q^{92} +(11.3562 - 7.82190i) q^{93} +(0.0545775 + 10.5102i) q^{94} +(-3.35100 - 2.90366i) q^{95} +(-0.830633 + 9.76269i) q^{96} +(-7.60162 - 1.09295i) q^{97} +(5.40380 - 6.30215i) q^{98} +(0.991893 + 15.4976i) 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 $

$2$	−1.41419	+	0.00734365i	−0.999987	+	0.00519274i
$2$	−1.41419	+	0.00734365i	−0.999987	+	0.00519274i
$3$	0.191591	−	1.72142i	0.110615	−	0.993863i
$3$	0.191591	−	1.72142i	0.110615	−	0.993863i
$4$	1.99989	−	0.0207707i	0.999946	−	0.0103853i
$5$	3.15950	+	0.454268i	1.41297	+	0.203155i	0.806164	−	0.591693i	$-0.201540\pi$
$5$	3.15950	+	0.454268i	1.41297	+	0.203155i	0.606809	+	0.794847i	$0.292449\pi$
$6$	−0.258305	+	2.43583i	−0.105453	+	0.994424i
$7$	0.966873	−	0.441556i	0.365444	−	0.166893i	−0.224226	−	0.974537i	$-0.571985\pi$
$7$	0.966873	−	0.441556i	0.365444	−	0.166893i	0.589669	+	0.807645i	$0.299258\pi$
$8$	−2.82808	+	0.0440603i	−0.999879	+	0.0155777i
$9$	−2.92659	−	0.659617i	−0.975529	−	0.219872i
$10$	−4.47149	−	0.619221i	−1.41401	−	0.195815i
$11$	−1.45838	−	4.96677i	−0.439717	−	1.49754i	−0.819835	−	0.572600i	$-0.805935\pi$
$11$	−1.45838	−	4.96677i	−0.439717	−	1.49754i	0.380119	−	0.924938i	$-0.375883\pi$
$12$	0.347406	−	3.44664i	0.100287	−	0.994959i
$13$	5.38000	+	2.45696i	1.49214	+	0.681439i	0.983727	−	0.179672i	$-0.0575035\pi$
$13$	5.38000	+	2.45696i	1.49214	+	0.681439i	0.508417	+	0.861111i	$0.330231\pi$
$14$	−1.36410	+	0.631547i	−0.364572	+	0.168788i
$15$	1.38732	−	5.35180i	0.358204	−	1.38183i
$16$	3.99914	−	0.0830783i	0.999784	−	0.0207696i
$17$	1.57359	−	1.01129i	0.381652	−	0.245273i	−0.335722	−	0.941961i	$-0.608980\pi$
$17$	1.57359	−	1.01129i	0.381652	−	0.245273i	0.717374	+	0.696688i	$0.245344\pi$
$18$	4.14361	+	0.911335i	0.976657	+	0.214804i
$19$	−1.16859	−	0.751005i	−0.268092	−	0.172292i	0.399687	−	0.916652i	$-0.369119\pi$
$19$	−1.16859	−	0.751005i	−0.268092	−	0.172292i	−0.667779	+	0.744359i	$0.732755\pi$
$20$	6.32810	+	0.842862i	1.41501	+	0.188470i
$21$	−0.574860	−	1.74899i	−0.125445	−	0.381662i
$22$	2.09890	+	7.01327i	0.447487	+	1.49523i
$23$	−4.68944	+	1.00455i	−0.977817	+	0.209463i
$23$	−4.68944	+	1.00455i	−0.977817	+	0.209463i
$24$	−0.465989	+	4.87677i	−0.0951195	+	0.995466i
$25$	4.97864	+	1.46186i	0.995728	+	0.292372i
$26$	−7.62641	−	3.43512i	−1.49566	−	0.673682i
$27$	−1.69619	+	4.91151i	−0.326431	+	0.945221i
$28$	1.92447	−	0.903147i	0.363691	−	0.170679i
$29$	−1.58834	+	1.02077i	−0.294948	+	0.189551i	−0.679743	−	0.733451i	$-0.737909\pi$
$29$	−1.58834	+	1.02077i	−0.294948	+	0.189551i	0.384795	+	0.923002i	$0.374272\pi$
$30$	−1.92264	+	7.57868i	−0.351024	+	1.38367i
$31$	5.21351	+	6.01671i	0.936373	+	1.08063i	0.996595	+	0.0824475i	$0.0262737\pi$
$31$	5.21351	+	6.01671i	0.936373	+	1.08063i	−0.0602220	+	0.998185i	$0.519181\pi$
$32$	−5.65495	+	0.146857i	−0.999663	+	0.0259609i
$33$	−8.82932	+	1.55889i	−1.53699	+	0.271368i
$34$	−2.21794	+	1.44171i	−0.380374	+	0.247252i
$35$	3.25542	−	0.955879i	0.550267	−	0.161573i
$36$	−5.86656	−	1.25838i	−0.977759	−	0.209729i
$37$	−0.881073	−	6.12800i	−0.144848	−	1.00744i	−0.924488	−	0.381210i	$-0.875507\pi$
$37$	−0.881073	−	6.12800i	−0.144848	−	1.00744i	0.779641	−	0.626227i	$-0.215402\pi$
$38$	1.65812	+	1.05349i	0.268983	+	0.170898i
$39$	5.26023	−	8.79052i	0.842311	−	1.40761i
$40$	−8.95536	−	1.14550i	−1.41597	−	0.181119i
$41$	8.01106	+	1.15182i	1.25112	+	0.179883i	0.735849	−	0.677146i	$-0.236783\pi$
$41$	8.01106	+	1.15182i	1.25112	+	0.179883i	0.515268	+	0.857029i	$0.327692\pi$
$42$	0.825808	+	2.46920i	0.127425	+	0.381005i
$43$	2.14799	−	2.47891i	0.327565	−	0.378031i	−0.567949	−	0.823064i	$-0.692263\pi$
$43$	2.14799	−	2.47891i	0.327565	−	0.378031i	0.895514	+	0.445034i	$0.146808\pi$
$44$	−3.01976	−	9.90271i	−0.455245	−	1.49289i
$45$	−8.94692	−	3.41352i	−1.33373	−	0.508857i
$46$	6.62441	−	1.45506i	0.976716	−	0.214538i
$47$		−	7.43194i		−	1.08406i	−0.840359	−	0.542030i	$-0.817656\pi$
$47$		−	7.43194i		−	1.08406i	0.840359	−	0.542030i	$-0.182344\pi$
$48$	0.623185	−	6.90012i	0.0899491	−	0.995946i
$49$	−3.84415	+	4.43639i	−0.549165	+	0.633770i
$50$	−7.05150	−	2.03079i	−0.997233	−	0.287198i
$51$	−1.43937	−	2.90257i	−0.201551	−	0.406441i
$52$	10.8105	+	4.80192i	1.49914	+	0.665906i
$53$	1.31544	−	0.600740i	0.180689	−	0.0825180i	−0.323016	−	0.946393i	$-0.604697\pi$
$53$	1.31544	−	0.600740i	0.180689	−	0.0825180i	0.503706	+	0.863875i	$0.331970\pi$
$54$	2.36267	−	6.95829i	0.321519	−	0.946903i
$55$	−2.35150	−	16.3550i	−0.317076	−	2.20531i
$56$	−2.71494	+	1.29136i	−0.362800	+	0.172565i
$57$	−1.51669	+	1.86775i	−0.200890	+	0.247389i
$58$	2.23873	−	1.45523i	0.293960	−	0.191081i
$59$	−0.468756	+	1.02643i	−0.0610268	+	0.133630i	−0.937688	−	0.347478i	$-0.887038\pi$
$59$	−0.468756	+	1.02643i	−0.0610268	+	0.133630i	0.876661	+	0.481108i	$0.159765\pi$
$60$	2.66333	−	10.7318i	0.343834	−	1.38548i
$61$	−8.03054	−	9.26774i	−1.02821	−	1.18661i	−0.982232	−	0.187670i	$-0.939907\pi$
$61$	−8.03054	−	9.26774i	−1.02821	−	1.18661i	−0.0459733	−	0.998943i	$-0.514639\pi$
$62$	−7.41710	−	8.47051i	−0.941972	−	1.07576i
$63$	−3.12090	+	0.654486i	−0.393196	+	0.0824574i
$64$	7.99612	−	0.249212i	0.999515	−	0.0311515i
$65$	15.8820	+	10.2068i	1.96992	+	1.26599i
$66$	12.4749	−	2.26941i	1.53556	−	0.279346i
$67$	−3.53167	−	1.03699i	−0.431462	−	0.126689i	0.0587881	−	0.998270i	$-0.481276\pi$
$67$	−3.53167	−	1.03699i	−0.431462	−	0.126689i	−0.490250	+	0.871582i	$0.663095\pi$
$68$	3.12601	−	2.05515i	0.379085	−	0.249224i
$69$	0.830797	+	8.26497i	0.100016	+	0.994986i
$70$	−4.59678	+	1.37571i	−0.549421	+	0.164428i
$71$	−1.09880	+	3.74217i	−0.130403	+	0.444114i	−0.998646	−	0.0520271i	$-0.983432\pi$
$71$	−1.09880	+	3.74217i	−0.130403	+	0.444114i	0.868242	+	0.496141i	$0.165250\pi$
$72$	8.30569	+	1.73651i	0.978835	+	0.204649i
$73$	−0.799168	−	0.513594i	−0.0935355	−	0.0601116i	0.493037	−	0.870008i	$-0.335887\pi$
$73$	−0.799168	−	0.513594i	−0.0935355	−	0.0601116i	−0.586572	+	0.809897i	$0.699523\pi$
$74$	1.29101	+	8.65971i	0.150077	+	1.00667i
$75$	3.47034	−	8.29026i	0.400720	−	0.957277i
$76$	−2.35265	−	1.47766i	−0.269867	−	0.169499i
$77$	−3.60317	−	4.15828i	−0.410619	−	0.473880i
$78$	−7.37444	+	12.4701i	−0.834990	+	1.41196i
$79$	4.02179	+	1.83669i	0.452486	+	0.206644i	0.628604	−	0.777726i	$-0.283627\pi$
$79$	4.02179	+	1.83669i	0.452486	+	0.206644i	−0.176118	+	0.984369i	$0.556354\pi$
$80$	12.6730	+	1.55419i	1.41689	+	0.173764i
$81$	8.12981	+	3.86085i	0.903312	+	0.428984i
$82$	−11.3377	−	1.57006i	−1.25203	−	0.173384i
$83$	−14.2163	+	2.04399i	−1.56044	+	0.224357i	−0.867795	−	0.496922i	$-0.834463\pi$
$83$	−14.2163	+	2.04399i	−1.56044	+	0.224357i	−0.692644	+	0.721280i	$0.743554\pi$
$84$	−1.18599	−	3.48586i	−0.129402	−	0.380339i
$85$	5.43117	−	2.48033i	0.589093	−	0.269030i
$86$	−3.01947	+	3.52144i	−0.325598	+	0.379726i
$87$	1.45286	+	2.92978i	0.155763	+	0.314105i
$88$	4.34324	+	13.9822i	0.462991	+	1.49051i
$89$	−6.78673	+	7.83230i	−0.719391	+	0.830222i	−0.991234	−	0.132120i	$-0.957822\pi$
$89$	−6.78673	+	7.83230i	−0.719391	+	0.830222i	0.271842	+	0.962342i	$0.412367\pi$
$90$	12.6777	+	4.76168i	1.33635	+	0.501925i
$91$	6.28667			0.659022
$92$	−9.35752	+	2.10639i	−0.975589	+	0.219607i
$93$	11.3562	−	7.82190i	1.17758	−	0.811093i
$94$	0.0545775	+	10.5102i	0.00562924	+	1.08405i
$95$	−3.35100	−	2.90366i	−0.343805	−	0.297909i
$96$	−0.830633	+	9.76269i	−0.0847762	+	0.996400i
$97$	−7.60162	−	1.09295i	−0.771828	−	0.110972i	−0.254861	−	0.966978i	$-0.582030\pi$
$97$	−7.60162	−	1.09295i	−0.771828	−	0.110972i	−0.516967	+	0.856005i	$0.672939\pi$
$98$	5.40380	−	6.30215i	0.545866	−	0.636613i
$99$	0.991893	+	15.4976i	0.0996890	+	1.55757i
$100$	9.98710	+	2.82015i	0.998710	+	0.282015i
$101$	1.10295	+	7.67120i	0.109748	+	0.763313i	0.968156	+	0.250346i	$0.0805445\pi$
$101$	1.10295	+	7.67120i	0.109748	+	0.763313i	−0.858408	+	0.512967i	$0.828546\pi$
$102$	2.05686	+	4.09423i	0.203659	+	0.405389i
$103$	1.66083	+	5.65628i	0.163647	+	0.557330i	0.999959	+	0.00907627i	$0.00288910\pi$
$103$	1.66083	+	5.65628i	0.163647	+	0.557330i	−0.836312	+	0.548254i	$0.815293\pi$
$104$	−15.3234	−	6.71146i	−1.50258	−	0.658112i
$105$	−1.02176	−	5.78709i	−0.0997137	−	0.564763i
$106$	−1.85587	+	0.859223i	−0.180258	+	0.0834551i
$107$	14.6499	−	12.6942i	1.41626	−	1.22720i	0.479352	−	0.877623i	$-0.340872\pi$
$107$	14.6499	−	12.6942i	1.41626	−	1.22720i	0.936909	−	0.349574i	$-0.113674\pi$
$108$	−3.29018	+	9.85773i	−0.316597	+	0.948560i
$109$	−0.644837	+	0.414412i	−0.0617642	+	0.0396934i	−0.571159	−	0.820840i	$-0.693506\pi$
$109$	−0.644837	+	0.414412i	−0.0617642	+	0.0396934i	0.509394	+	0.860533i	$0.329869\pi$
$110$	3.44558	+	23.1119i	0.328523	+	2.20363i
$111$	−10.7177	+	0.342630i	−1.01728	+	0.0325210i
$112$	3.82997	−	1.84617i	0.361899	−	0.174447i
$113$	0.511394	+	0.150159i	0.0481079	+	0.0141257i	0.305698	−	0.952129i	$-0.401110\pi$
$113$	0.511394	+	0.150159i	0.0481079	+	0.0141257i	−0.257590	+	0.966254i	$0.582928\pi$
$114$	2.13117	−	2.65249i	0.199603	−	0.248429i
$115$	−15.2726	+	1.04361i	−1.42418	+	0.0973172i
$116$	−3.15531	+	2.07441i	−0.292963	+	0.192604i
$117$	−14.1244	−	10.7393i	−1.30580	−	0.992845i
$118$	0.655374	−	1.45502i	0.0603321	−	0.133945i
$119$	1.07493	−	1.67262i	0.0985382	−	0.153328i
$120$	−3.68765	+	15.1965i	−0.336635	+	1.38724i
$121$	−13.2882	+	8.53978i	−1.20801	+	0.776343i
$122$	11.4248	+	13.0474i	1.03435	+	1.18126i
$123$	3.51761	−	13.5697i	0.317172	−	1.22354i
$124$	10.5514	+	11.9245i	0.947546	+	1.07085i
$125$	0.548254	+	0.250379i	0.0490374	+	0.0223946i
$126$	4.40875	−	0.948489i	0.392762	−	0.0844981i
$127$	9.66424	−	2.83768i	0.857563	−	0.251803i	0.176746	−	0.984257i	$-0.443443\pi$
$127$	9.66424	−	2.83768i	0.857563	−	0.251803i	0.680817	+	0.732453i	$0.261625\pi$
$128$	−11.3062	+	0.411155i	−0.999339	+	0.0363414i
$129$	−3.85572	−	4.17253i	−0.339477	−	0.367371i
$130$	−22.5352	−	14.3177i	−1.97647	−	1.25575i
$131$	7.76606	+	17.0053i	0.678524	+	1.48576i	0.864200	+	0.503149i	$0.167825\pi$
$131$	7.76606	+	17.0053i	0.678524	+	1.48576i	−0.185675	+	0.982611i	$0.559447\pi$
$132$	−17.6253	+	3.30100i	−1.53409	+	0.287316i
$133$	−1.46149	−	0.210130i	−0.126727	−	0.0182206i
$134$	5.00208	+	1.44057i	0.432114	+	0.124446i
$135$	−7.59025	+	14.7474i	−0.653265	+	1.26926i
$136$	−4.40570	+	2.92934i	−0.377785	+	0.251189i
$137$	20.8156			1.77839			0.889197	−	0.457525i	$-0.151264\pi$
$137$	20.8156			1.77839			0.889197	+	0.457525i	$0.151264\pi$
$138$	−1.23560	−	11.6822i	−0.105182	−	0.994453i
$139$		−	2.75564i		−	0.233730i	−0.993148	−	0.116865i	$-0.962715\pi$
$139$		−	2.75564i		−	0.233730i	0.993148	−	0.116865i	$-0.0372845\pi$
$140$	6.49064	−	1.97927i	0.548559	−	0.167279i
$141$	−12.7935	−	1.42389i	−1.07741	−	0.119913i
$142$	1.52643	−	5.30022i	0.128096	−	0.444785i
$143$	4.35712	−	30.3044i	0.364360	−	2.53418i
$144$	−11.7586	−	2.39476i	−0.979885	−	0.199564i
$145$	−5.48208	+	2.50358i	−0.455262	+	0.207911i
$146$	1.13395	+	0.720453i	0.0938464	+	0.0596251i
$147$	6.90039	+	7.46738i	0.569135	+	0.615899i
$148$	−1.88933	−	12.2370i	−0.155302	−	1.00588i
$149$	3.84792	+	13.1048i	0.315234	+	1.07359i	0.952902	+	0.303278i	$0.0980811\pi$
$149$	3.84792	+	13.1048i	0.315234	+	1.07359i	−0.637668	+	0.770311i	$0.720101\pi$
$150$	−4.84685	+	11.7495i	−0.395744	+	0.959345i
$151$	0.787976	−	1.72543i	0.0641245	−	0.140413i	−0.874856	−	0.484382i	$-0.839044\pi$
$151$	0.787976	−	1.72543i	0.0641245	−	0.140413i	0.938981	+	0.343969i	$0.111772\pi$
$152$	3.33795	+	2.07242i	0.270744	+	0.168095i
$153$	−5.27232	+	1.92165i	−0.426242	+	0.155356i
$154$	5.12612	+	5.85416i	0.413075	+	0.471741i
$155$	13.7389	+	21.3781i	1.10353	+	1.71713i
$156$	10.3373	−	17.6893i	0.827647	−	1.41628i
$157$	16.8034	+	10.7989i	1.34106	+	0.861846i	0.997023	−	0.0771109i	$-0.0245695\pi$
$157$	16.8034	+	10.7989i	1.34106	+	0.861846i	0.344036	+	0.938957i	$0.388206\pi$
$158$	−5.70108	−	2.56790i	−0.453553	−	0.204291i
$159$	−0.782101	−	2.37952i	−0.0620246	−	0.188708i
$160$	−17.9335	−	2.10487i	−1.41777	−	0.166404i
$161$	−4.09053	+	3.04192i	−0.322379	+	0.239737i
$162$	−11.5255	−	5.40030i	−0.905528	−	0.424287i
$163$	−6.86756	+	23.3888i	−0.537909	+	1.83195i	0.0167325	+	0.999860i	$0.494674\pi$
$163$	−6.86756	+	23.3888i	−0.537909	+	1.83195i	−0.554641	+	0.832090i	$0.687145\pi$
$164$	16.0452	+	2.13711i	1.25292	+	0.166881i
$165$	−28.6044	+	0.914446i	−2.22685	+	0.0711895i
$166$	20.0896	−	2.99500i	1.55925	−	0.232457i
$167$	5.71969	+	8.90002i	0.442603	+	0.688704i	0.988849	−	0.148921i	$-0.0475800\pi$
$167$	5.71969	+	8.90002i	0.442603	+	0.688704i	−0.546246	+	0.837625i	$0.683944\pi$
$168$	1.70281	+	4.92097i	0.131375	+	0.379661i
$169$	14.3946	+	16.6122i	1.10727	+	1.27786i
$170$	−7.66252	+	3.54756i	−0.587688	+	0.272085i
$171$	2.92459	+	2.96870i	0.223649	+	0.227022i
$172$	4.24426	−	5.00217i	0.323622	−	0.381412i
$173$	−23.7645	+	6.97790i	−1.80678	+	0.530520i	−0.998316	−	0.0580183i	$-0.981522\pi$
$173$	−23.7645	+	6.97790i	−1.80678	+	0.530520i	−0.808469	+	0.588538i	$0.799704\pi$
$174$	−2.07614	−	4.13261i	−0.157392	−	0.313292i
$175$	5.45921	−	0.784915i	0.412677	−	0.0593340i
$176$	−6.24487	−	19.7416i	−0.470725	−	1.48808i
$177$	1.67711	+	1.00358i	0.126060	+	0.0754338i
$178$	9.54023	−	11.1262i	0.715071	−	0.833946i
$179$	0.227632	−	1.58321i	0.0170140	−	0.118335i	−0.979544	−	0.201228i	$-0.935507\pi$
$179$	0.227632	−	1.58321i	0.0170140	−	0.118335i	0.996558	+	0.0828929i	$0.0264159\pi$
$180$	−17.9638	−	6.64083i	−1.33894	−	0.494979i
$181$	−9.29756	+	10.7300i	−0.691082	+	0.797551i	−0.987519	−	0.157501i	$-0.949656\pi$
$181$	−9.29756	+	10.7300i	−0.691082	+	0.797551i	0.296437	+	0.955053i	$0.404202\pi$
$182$	−8.89057	+	0.0461670i	−0.659013	+	0.00342213i
$183$	−17.4923	+	12.0483i	−1.29307	+	0.890639i
$184$	13.2179	−	3.04757i	0.974435	−	0.224670i
$185$		−	19.7617i		−	1.45291i
$186$	−16.0024	+	11.1451i	−1.17335	+	0.817197i
$187$	−7.31772	−	6.34084i	−0.535125	−	0.463688i
$188$	−0.154367	−	14.8631i	−0.0112583	−	1.08400i
$189$	0.528711	+	5.49777i	0.0384581	+	0.399904i
$190$	4.76028	+	4.08172i	0.345347	+	0.296119i
$191$	6.02692	+	13.1971i	0.436093	+	0.954910i	0.992299	+	0.123865i	$0.0395291\pi$
$191$	6.02692	+	13.1971i	0.436093	+	0.954910i	−0.556206	+	0.831044i	$0.687744\pi$
$192$	1.10298	−	13.8124i	0.0796010	−	0.996827i
$193$	−2.14425	−	14.9136i	−0.154346	−	1.07350i	−0.908825	−	0.417178i	$-0.863019\pi$
$193$	−2.14425	−	14.9136i	−0.154346	−	1.07350i	0.754478	−	0.656325i	$-0.227890\pi$
$194$	10.7582	+	1.48982i	0.772394	+	0.106963i
$195$	20.6130	−	25.3841i	1.47613	−	1.81779i
$196$	−7.59575	+	8.95215i	−0.542553	+	0.639439i
$197$	2.64733	−	5.79685i	0.188615	−	0.413009i	−0.791574	−	0.611073i	$-0.790738\pi$
$197$	2.64733	−	5.79685i	0.188615	−	0.413009i	0.980189	+	0.198064i	$0.0634655\pi$
$198$	−1.51654	−	21.9094i	−0.107776	−	1.55703i
$199$	−12.8515	+	11.1359i	−0.911019	+	0.789402i	−0.978055	−	0.208348i	$-0.933191\pi$
$199$	−12.8515	+	11.1359i	−0.911019	+	0.789402i	0.0670360	+	0.997751i	$0.478646\pi$
$200$	−14.1444	−	3.91490i	−1.00016	−	0.276825i
$201$	−2.46174	+	5.88081i	−0.173637	+	0.414801i
$202$	−1.61612	−	10.8405i	−0.113710	−	0.762733i
$203$	−1.08500	+	1.68829i	−0.0761521	+	0.118495i
$204$	−2.93886	−	5.77493i	−0.205762	−	0.404326i
$205$	24.7877	+	7.27834i	1.73125	+	0.508341i
$206$	−2.39028	−	7.98689i	−0.166539	−	0.556473i
$207$	14.3867	+	0.153340i	0.999943	+	0.0106579i
$208$	21.7195	+	9.37878i	1.50598	+	0.650301i
$209$	−2.02583	+	6.89935i	−0.140130	+	0.477238i
$210$	1.48747	+	8.17657i	0.102645	+	0.564237i
$211$	0.102277	−	0.159146i	0.00704103	−	0.0109561i	−0.837715	−	0.546107i	$-0.816109\pi$
$211$	0.102277	−	0.159146i	0.00704103	−	0.0109561i	0.844756	+	0.535151i	$0.179745\pi$
$212$	2.61825	−	1.22874i	0.179822	−	0.0843900i
$213$	6.23133	+	2.60846i	0.426964	+	0.178729i
$214$	−20.6246	+	18.0597i	−1.40987	+	1.23453i
$215$	7.91267	−	6.85637i	0.539640	−	0.467600i
$216$	4.58056	−	13.9649i	0.311667	−	0.950191i
$217$	7.69751	+	3.51534i	0.522541	+	0.238637i
$218$	0.908882	−	0.590794i	0.0615573	−	0.0400136i
$219$	−1.03723	+	1.27731i	−0.0700892	+	0.0863123i
$220$	−5.04244	−	32.6594i	−0.339962	−	2.20190i
$221$	10.9506	−	1.57446i	0.736619	−	0.105910i
$222$	15.1544	−	0.563252i	1.01709	−	0.0378030i
$223$	−5.87793	−	12.8709i	−0.393615	−	0.861897i	−0.997878	−	0.0651117i	$-0.979260\pi$
$223$	−5.87793	−	12.8709i	−0.393615	−	0.861897i	0.604263	−	0.796785i	$-0.293468\pi$
$224$	−5.40277	+	2.63897i	−0.360988	+	0.176324i
$225$	−13.6061	−	7.56226i	−0.907076	−	0.504150i
$226$	−0.724313	−	0.208598i	−0.0481806	−	0.0138757i
$227$	2.04813	+	1.77472i	0.135939	+	0.117792i	0.720177	−	0.693791i	$-0.244061\pi$
$227$	2.04813	+	1.77472i	0.135939	+	0.117792i	−0.584237	+	0.811583i	$0.698606\pi$
$228$	−2.99442	+	3.76679i	−0.198310	+	0.249462i
$229$	1.49217			0.0986052			0.0493026	−	0.998784i	$-0.484300\pi$
$229$	1.49217			0.0986052			0.0493026	+	0.998784i	$0.484300\pi$
$230$	21.5908	−	1.58803i	1.42366	−	0.104711i
$231$	−7.84849	+	5.40589i	−0.516393	+	0.355681i
$232$	4.44699	−	2.95679i	0.291959	−	0.194123i
$233$	−6.53167	−	5.65972i	−0.427904	−	0.370781i	0.414119	−	0.910223i	$-0.364090\pi$
$233$	−6.53167	−	5.65972i	−0.427904	−	0.370781i	−0.842023	+	0.539442i	$0.818635\pi$
$234$	20.0535	+	15.0837i	1.31094	+	0.986051i
$235$	3.37609	−	23.4812i	0.220232	−	1.53175i
$236$	−0.916142	+	2.06249i	−0.0596357	+	0.134257i
$237$	3.93225	−	6.57130i	0.255427	−	0.426852i
$238$	−1.50787	+	2.37330i	−0.0977407	+	0.153838i
$239$	−1.83648	+	0.264046i	−0.118792	+	0.0170797i	−0.201454	−	0.979498i	$-0.564567\pi$
$239$	−1.83648	+	0.264046i	−0.118792	+	0.0170797i	0.0826624	+	0.996578i	$0.473658\pi$
$240$	5.10346	−	21.5179i	0.329427	−	1.38897i
$241$	0.302917	+	1.03164i	0.0195126	+	0.0664538i	0.968674	−	0.248337i	$-0.0798839\pi$
$241$	0.302917	+	1.03164i	0.0195126	+	0.0664538i	−0.949161	+	0.314790i	$0.898066\pi$
$242$	18.7293	−	12.1745i	1.20397	−	0.782606i
$243$	8.20375	−	13.2551i	0.526271	−	0.850317i
$244$	−16.2527	−	18.3677i	−1.04047	−	1.17587i
$245$	−14.1609	+	12.2705i	−0.904708	+	0.783934i
$246$	−4.87493	+	19.2161i	−0.310814	+	1.22517i
$247$	−4.44181	−	6.91159i	−0.282625	−	0.439774i
$248$	−15.0093	−	16.7860i	−0.953094	−	1.06591i
$249$	0.794864	+	24.8638i	0.0503724	+	1.57568i
$250$	−0.777177	−	0.350059i	−0.0491530	−	0.0221397i
$251$	−3.97610	+	13.5413i	−0.250969	+	0.854722i	0.733578	+	0.679605i	$0.237849\pi$
$251$	−3.97610	+	13.5413i	−0.250969	+	0.854722i	−0.984548	+	0.175117i	$0.943969\pi$
$252$	−6.22786	+	1.37372i	−0.392318	+	0.0865365i
$253$	11.8283	+	21.8264i	0.743641	+	1.37221i
$254$	−13.6463	+	4.08400i	−0.856244	+	0.256253i
$255$	−3.22914	−	9.82454i	−0.202216	−	0.615237i
$256$	15.9862	−	0.664483i	0.999137	−	0.0415302i
$257$	−3.63840	+	5.66146i	−0.226957	+	0.353152i	−0.935992	−	0.352021i	$-0.885494\pi$
$257$	−3.63840	+	5.66146i	−0.226957	+	0.353152i	0.709035	+	0.705173i	$0.249131\pi$
$258$	5.48338	+	5.87246i	0.341380	+	0.365603i
$259$	−3.55774	−	5.53595i	−0.221067	−	0.343987i
$260$	31.9743	+	20.0825i	1.98296	+	1.24547i
$261$	5.32174	−	1.93966i	0.329407	−	0.120062i
$262$	−11.1076	−	23.9918i	−0.686230	−	1.48222i
$263$	2.37306	−	5.19628i	0.146329	−	0.320416i	−0.822248	−	0.569129i	$-0.807280\pi$
$263$	2.37306	−	5.19628i	0.146329	−	0.320416i	0.968577	+	0.248713i	$0.0800077\pi$
$264$	24.9014	−	4.79770i	1.53257	−	0.295278i
$265$	4.42902	−	1.30048i	0.272073	−	0.0798878i
$266$	2.06837	+	0.286432i	0.126820	+	0.0175623i
$267$	12.1824	+	13.1834i	0.745552	+	0.806812i
$268$	−7.08450	−	2.00052i	−0.432754	−	0.122201i
$269$	8.33133	+	18.2431i	0.507970	+	1.11230i	0.973796	+	0.227423i	$0.0730299\pi$
$269$	8.33133	+	18.2431i	0.507970	+	1.11230i	−0.465826	+	0.884876i	$0.654243\pi$
$270$	10.6258	−	20.9115i	0.646665	−	1.27263i
$271$	1.84365	−	12.8229i	0.111994	−	0.778934i	−0.853982	−	0.520302i	$-0.825819\pi$
$271$	1.84365	−	12.8229i	0.111994	−	0.778934i	0.965976	−	0.258632i	$-0.0832716\pi$
$272$	6.20900	−	4.17501i	0.376476	−	0.253147i
$273$	1.20447	−	10.8220i	0.0728977	−	0.654977i
$274$	−29.4373	+	0.152862i	−1.77837	+	0.00923474i
$275$		−	26.8597i		−	1.61970i
$276$	1.83317	+	16.5118i	0.110344	+	0.993893i
$277$		−	12.7415i		−	0.765562i	−0.923839	−	0.382781i	$-0.874966\pi$
$277$		−	12.7415i		−	0.765562i	0.923839	−	0.382781i	$-0.125034\pi$
$278$	0.0202364	+	3.89701i	0.00121370	+	0.233727i
$279$	−11.2891	−	21.0473i	−0.675858	−	1.26007i
$280$	−9.16450	+	2.84674i	−0.547683	+	0.170125i
$281$	−0.637448	+	4.43355i	−0.0380270	+	0.264483i	−0.999961	−	0.00879737i	$-0.997200\pi$
$281$	−0.637448	+	4.43355i	−0.0380270	+	0.264483i	0.961934	+	0.273281i	$0.0881088\pi$
$282$	18.1030	+	1.91971i	1.07802	+	0.114317i
$283$	−1.40692	−	3.08072i	−0.0836327	−	0.183130i	0.863195	−	0.504870i	$-0.168460\pi$
$283$	−1.40692	−	3.08072i	−0.0836327	−	0.183130i	−0.946828	+	0.321740i	$0.895732\pi$
$284$	−2.11975	+	7.50675i	−0.125784	+	0.445444i
$285$	−5.64044	+	5.21217i	−0.334111	+	0.308742i
$286$	−5.93926	+	42.8883i	−0.351196	+	2.53604i
$287$	8.25427	−	2.42367i	0.487234	−	0.143065i
$288$	16.6466	+	3.30031i	0.980908	+	0.194473i
$289$	−5.60856	+	12.2810i	−0.329915	+	0.722414i
$290$	7.73434	−	3.58081i	0.454176	−	0.210272i
$291$	−3.33783	+	12.8762i	−0.195667	+	0.754816i
$292$	−1.60892	−	1.01053i	−0.0941548	−	0.0591370i
$293$	−3.51413	−	5.46810i	−0.205298	−	0.319450i	0.723302	−	0.690531i	$-0.242623\pi$
$293$	−3.51413	−	5.46810i	−0.205298	−	0.319450i	−0.928600	+	0.371082i	$0.878987\pi$
$294$	−9.81334	−	10.5097i	−0.572325	−	0.612936i
$295$	−1.94731	+	3.03008i	−0.113377	+	0.176418i
$296$	2.76175	+	17.2917i	0.160524	+	1.00506i
$297$	26.8680	+	1.26174i	1.55904	+	0.0732137i
$298$	−5.53795	−	18.5045i	−0.320805	−	1.07194i
$299$	−27.6974	−	6.11732i	−1.60178	−	0.353774i
$300$	6.76811	−	16.6517i	0.390757	−	0.961387i
$301$	0.982254	−	3.34525i	0.0566162	−	0.192817i
$302$	−1.10168	+	2.44587i	−0.0633945	+	0.140744i
$303$	13.4167	−	0.428914i	0.770769	−	0.0246405i
$304$	−4.73573	−	2.90629i	−0.271613	−	0.166687i
$305$	−21.1625	−	32.9295i	−1.21176	−	1.88554i
$306$	7.44197	−	2.75630i	0.425429	−	0.157567i
$307$	−18.4424	+	15.9804i	−1.05256	+	0.912050i	−0.996264	−	0.0863636i	$-0.972475\pi$
$307$	−18.4424	+	15.9804i	−1.05256	+	0.912050i	−0.0562986	+	0.998414i	$0.517930\pi$
$308$	−7.29232	−	8.24127i	−0.415519	−	0.469590i
$309$	10.0551	−	1.77531i	0.572012	−	0.100994i
$310$	−19.5865	−	30.1320i	−1.11244	−	1.71138i
$311$	7.53709	+	25.6690i	0.427389	+	1.45555i	0.838968	+	0.544180i	$0.183159\pi$
$311$	7.53709	+	25.6690i	0.427389	+	1.45555i	−0.411579	+	0.911374i	$0.635023\pi$
$312$	−14.4891	+	25.0921i	−0.820282	+	1.42056i
$313$	−11.6370	+	1.67315i	−0.657765	+	0.0945723i	−0.463112	−	0.886300i	$-0.653267\pi$
$313$	−11.6370	+	1.67315i	−0.657765	+	0.0945723i	−0.194653	+	0.980872i	$0.562358\pi$
$314$	−23.8426	−	15.1483i	−1.34552	−	0.854870i
$315$	−10.1578	+	0.650127i	−0.572327	+	0.0366305i
$316$	8.08129	+	3.58964i	0.454608	+	0.201933i
$317$	2.66230	−	18.5167i	0.149530	−	1.04000i	−0.767461	−	0.641095i	$-0.778480\pi$
$317$	2.66230	−	18.5167i	0.149530	−	1.04000i	0.916991	−	0.398907i	$-0.130611\pi$
$318$	1.12352	+	3.35936i	0.0630037	+	0.188383i
$319$	7.38631	+	6.40027i	0.413554	+	0.358347i
$320$	25.3770	+	2.84499i	1.41862	+	0.159040i
$321$	−19.0453	−	27.6508i	−1.06301	−	1.54332i
$322$	5.76247	−	4.33191i	0.321130	−	0.241408i
$323$	−2.59836			−0.144577
$324$	16.3389	+	7.55243i	0.907719	+	0.419579i
$325$	23.1933	+	20.0971i	1.28654	+	1.11479i
$326$	9.54031	−	33.1267i	0.528389	−	1.83472i
$327$	0.589832	+	1.18943i	0.0326178	+	0.0657759i
$328$	−22.7067	−	2.90446i	−1.25377	−	0.160372i
$329$	−3.28162	−	7.18574i	−0.180922	−	0.396163i
$330$	40.4455	−	1.50326i	2.22645	−	0.0827520i
$331$	−1.87868	+	0.270114i	−0.103262	+	0.0148468i	−0.193752	−	0.981051i	$-0.562066\pi$
$331$	−1.87868	+	0.270114i	−0.103262	+	0.0148468i	0.0904902	+	0.995897i	$0.471157\pi$
$332$	−28.3886	+	4.38304i	−1.55802	+	0.240551i
$333$	−1.46360	+	18.5153i	−0.0802047	+	1.01463i
$334$	−8.15412	−	12.5443i	−0.446173	−	0.686396i
$335$	−10.6872	−	4.88070i	−0.583907	−	0.266661i
$336$	−2.44425	−	6.94671i	−0.133345	−	0.378974i
$337$	25.6895	−	22.2601i	1.39940	−	1.21259i	0.452208	−	0.891913i	$-0.350637\pi$
$337$	25.6895	−	22.2601i	1.39940	−	1.21259i	0.947190	−	0.320673i	$-0.103909\pi$
$338$	−20.4787	−	23.3872i	−1.11389	−	1.27209i
$339$	0.356465	−	0.851555i	0.0193605	−	0.0462501i
$340$	10.8102	−	5.07321i	0.586267	−	0.275133i
$341$	22.2804	−	34.6689i	1.20655	−	1.87743i
$342$	−4.15775	−	4.17684i	−0.224825	−	0.225858i
$343$	−3.85412	+	13.1259i	−0.208103	+	0.708734i
$344$	−5.96547	+	7.10521i	−0.321637	+	0.383087i
$345$	−1.12961	+	26.4906i	−0.0608159	+	1.42621i
$346$	33.5564	−	10.0426i	1.80401	−	0.539895i
$347$	7.15627	+	2.10127i	0.384168	+	0.112802i	0.468114	−	0.883668i	$-0.344934\pi$
$347$	7.15627	+	2.10127i	0.384168	+	0.112802i	−0.0839450	+	0.996470i	$0.526752\pi$
$348$	2.96641	+	5.82906i	0.159016	+	0.312471i
$349$	14.5562	−	22.6500i	0.779178	−	1.21242i	−0.193690	−	0.981063i	$-0.562045\pi$
$349$	14.5562	−	22.6500i	0.779178	−	1.21242i	0.972868	−	0.231362i	$-0.0743182\pi$
$350$	−7.71461	+	1.15011i	−0.412363	+	0.0614761i
$351$	−21.1929	+	22.2565i	−1.13119	+	1.18796i
$352$	8.97644	+	27.8726i	0.478446	+	1.48562i
$353$	−23.8810	+	20.6930i	−1.27105	+	1.10138i	−0.281147	+	0.959665i	$0.590715\pi$
$353$	−23.8810	+	20.6930i	−1.27105	+	1.10138i	−0.989908	+	0.141710i	$0.954740\pi$
$354$	−2.37913	−	1.40694i	−0.126450	−	0.0747782i
$355$	−5.17161	+	11.3242i	−0.274480	+	0.601028i
$356$	−13.4100	+	15.8047i	−0.710731	+	0.837648i
$357$	−2.67333	−	2.17086i	−0.141488	−	0.114894i
$358$	−0.310289	+	2.24064i	−0.0163993	+	0.118422i
$359$	1.07362	+	7.46716i	0.0566633	+	0.394102i	0.998341	+	0.0575846i	$0.0183399\pi$
$359$	1.07362	+	7.46716i	0.0566633	+	0.394102i	−0.941677	+	0.336517i	$0.890751\pi$
$360$	25.4530	+	9.25951i	1.34149	+	0.488019i
$361$	−7.09130	−	15.5278i	−0.373226	−	0.817251i
$362$	13.0698	−	15.2425i	0.686931	−	0.801129i
$363$	12.1547	+	24.5107i	0.637955	+	1.28648i
$364$	12.5727	−	0.130578i	0.658986	−	0.00684417i
$365$	−2.29166	−	1.98574i	−0.119951	−	0.103938i
$366$	24.6490	−	17.1671i	1.28842	−	0.897341i
$367$		−	7.88612i		−	0.411652i	−0.978589	−	0.205826i	$-0.934012\pi$
$367$		−	7.88612i		−	0.411652i	0.978589	−	0.205826i	$-0.0659881\pi$
$368$	−18.6703	+	4.40692i	−0.973255	+	0.229727i
$369$	−22.6853	−	8.65512i	−1.18095	−	0.450568i
$370$	0.145123	+	27.9469i	0.00754457	+	1.45289i
$371$	1.00660	−	1.16168i	0.0522601	−	0.0603113i
$372$	22.5486	−	15.8788i	1.16909	−	0.823279i
$373$	3.63454	−	25.2788i	0.188189	−	1.30888i	−0.648503	−	0.761212i	$-0.724605\pi$
$373$	3.63454	−	25.2788i	0.188189	−	1.30888i	0.836693	−	0.547673i	$-0.184486\pi$
$374$	10.3952	+	8.91344i	0.537525	+	0.460903i
$375$	0.536049	−	0.895807i	0.0276815	−	0.0462593i
$376$	0.327454	+	21.0182i	0.0168871	+	1.08393i
$377$	−11.0533	+	1.58922i	−0.569273	+	0.0818490i
$378$	−0.788074	−	7.77103i	−0.0405341	−	0.399699i
$379$	19.7556	−	5.80078i	1.01478	−	0.297966i	0.268272	−	0.963343i	$-0.413547\pi$
$379$	19.7556	−	5.80078i	1.01478	−	0.297966i	0.746507	+	0.665377i	$0.231729\pi$
$380$	−6.76194	−	5.73739i	−0.346880	−	0.294322i
$381$	−3.03326	−	17.1799i	−0.155399	−	0.880153i
$382$	−8.62015	−	18.6190i	−0.441045	−	0.952632i
$383$	4.31480	+	4.97954i	0.220476	+	0.254443i	0.855202	−	0.518294i	$-0.173433\pi$
$383$	4.31480	+	4.97954i	0.220476	+	0.254443i	−0.634727	+	0.772737i	$0.718887\pi$
$384$	−1.45840	+	19.5416i	−0.0744236	+	0.997227i
$385$	−9.49526	−	14.7749i	−0.483923	−	0.752999i
$386$	3.14190	+	21.0750i	0.159919	+	1.07269i
$387$	−7.92141	+	5.83790i	−0.402668	+	0.296757i
$388$	−15.2251	−	2.02789i	−0.772939	−	0.102950i
$389$	−1.11359	+	3.79255i	−0.0564614	+	0.192290i	−0.982894	−	0.184170i	$-0.941040\pi$
$389$	−1.11359	+	3.79255i	−0.0564614	+	0.192290i	0.926433	+	0.376460i	$0.122859\pi$
$390$	−28.9643	+	36.0495i	−1.46667	+	1.82544i
$391$	−6.36339	+	6.32312i	−0.321810	+	0.319774i
$392$	10.6761	−	12.7159i	0.539225	−	0.642248i
$393$	30.7612	−	10.1106i	1.55170	−	0.510013i
$394$	−3.70127	+	8.21732i	−0.186467	+	0.413982i
$395$	11.8725	+	7.62999i	0.597370	+	0.383907i
$396$	2.30558	+	30.9730i	0.115860	+	1.55645i
$397$	4.20568	+	6.54417i	0.211077	+	0.328443i	0.930608	−	0.366018i	$-0.119279\pi$
$397$	4.20568	+	6.54417i	0.211077	+	0.328443i	−0.719530	+	0.694461i	$0.755643\pi$
$398$	18.0927	−	15.8427i	0.906907	−	0.794122i
$399$	−0.641730	+	2.47557i	−0.0321267	+	0.123934i
$400$	20.0317	+	5.43256i	1.00159	+	0.271628i
$401$	10.9377	−	23.9503i	0.546204	−	1.19602i	−0.412328	−	0.911035i	$-0.635284\pi$
$401$	10.9377	−	23.9503i	0.546204	−	1.19602i	0.958532	−	0.284985i	$-0.0919885\pi$
$402$	3.43819	−	8.33469i	0.171481	−	0.415697i
$403$	13.2658	+	45.1793i	0.660818	+	2.25054i
$404$	2.36512	+	15.3187i	0.117669	+	0.762132i
$405$	23.9323	+	15.8915i	1.18921	+	0.789655i
$406$	1.52200	−	2.39554i	0.0755358	−	0.118889i
$407$	−29.1514	+	13.3130i	−1.44498	+	0.659901i
$408$	4.19853	+	8.14530i	0.207858	+	0.403252i
$409$	−1.99225	+	13.8564i	−0.0985104	+	0.685155i	0.879393	+	0.476097i	$0.157949\pi$
$409$	−1.99225	+	13.8564i	−0.0985104	+	0.685155i	−0.977903	+	0.209058i	$0.932960\pi$
$410$	−35.1081	−	10.1110i	−1.73387	−	0.499344i
$411$	3.98807	−	35.8324i	0.196717	−	1.76748i
$412$	3.43898	+	11.2775i	0.169426	+	0.555601i
$413$			1.19941i			0.0590192i
$414$	−20.3467	−	0.111203i	−0.999985	−	0.00546531i
$415$	−45.8449			−2.25044
$416$	−30.7844	−	13.1039i	−1.50933	−	0.642472i
$417$	−4.74361	−	0.527955i	−0.232296	−	0.0258541i
$418$	2.81425	−	9.77190i	0.137650	−	0.477959i
$419$	−35.5415	−	5.11010i	−1.73632	−	0.249645i	−0.799801	−	0.600266i	$-0.795061\pi$
$419$	−35.5415	−	5.11010i	−1.73632	−	0.249645i	−0.936517	+	0.350621i	$0.885971\pi$
$420$	−2.16361	−	11.5523i	−0.105574	−	0.563697i
$421$	−10.7379	−	23.5126i	−0.523332	−	1.14594i	−0.968163	−	0.250322i	$-0.919464\pi$
$421$	−10.7379	−	23.5126i	−0.523332	−	1.14594i	0.444831	−	0.895614i	$-0.353264\pi$
$422$	−0.143471	+	0.225814i	−0.00698404	+	0.0109925i
$423$	−4.90224	+	21.7502i	−0.238355	+	1.05753i
$424$	−3.69370	+	1.75690i	−0.179382	+	0.0853227i
$425$	9.31271	−	2.73446i	0.451733	−	0.132641i
$426$	−8.83147	−	3.64311i	−0.427886	−	0.176509i
$427$	−11.8567	−	5.41479i	−0.573788	−	0.262040i
$428$	29.0346	−	25.6914i	1.40344	−	1.24184i
$429$	−51.3319	−	13.3065i	−2.47833	−	0.642443i
$430$	−11.1397	+	9.75435i	−0.537204	+	0.470396i
$431$	1.16575	−	0.749184i	0.0561524	−	0.0360869i	−0.512263	−	0.858828i	$-0.671193\pi$
$431$	1.16575	−	0.749184i	0.0561524	−	0.0360869i	0.568416	+	0.822741i	$0.307557\pi$
$432$	−6.37524	+	19.7827i	−0.306729	+	0.951797i
$433$	−13.2499	+	20.6173i	−0.636750	+	0.990803i	0.361540	+	0.932356i	$0.382251\pi$
$433$	−13.2499	+	20.6173i	−0.636750	+	0.990803i	−0.998291	+	0.0584463i	$0.981385\pi$
$434$	−10.9116	−	4.91484i	−0.523773	−	0.235920i
$435$	3.25940	+	9.91663i	0.156276	+	0.475466i
$436$	−1.28100	+	0.842173i	−0.0613486	+	0.0403327i
$437$	6.23444	+	2.34789i	0.298234	+	0.112315i
$438$	1.45746	−	1.81398i	0.0696401	−	0.0866751i
$439$	−12.1655	−	3.57210i	−0.580626	−	0.170487i	−0.0217858	−	0.999763i	$-0.506935\pi$
$439$	−12.1655	−	3.57210i	−0.580626	−	0.170487i	−0.558840	+	0.829276i	$0.688753\pi$
$440$	7.37084	+	46.1498i	0.351391	+	2.20010i
$441$	14.1766	−	10.4478i	0.675075	−	0.497515i
$442$	−15.4748	+	2.30701i	−0.736059	+	0.109733i
$443$	−8.57219	+	5.50901i	−0.407277	+	0.261741i	−0.728201	−	0.685364i	$-0.759643\pi$
$443$	−8.57219	+	5.50901i	−0.407277	+	0.261741i	0.320924	+	0.947105i	$0.396007\pi$
$444$	−21.4271	+	0.907837i	−1.01688	+	0.0430840i
$445$	−25.0006	+	21.6632i	−1.18514	+	1.02693i
$446$	8.40705	+	18.1587i	0.398085	+	0.859841i
$447$	23.2962	−	4.11314i	1.10187	−	0.194545i
$448$	7.62119	−	3.77169i	0.360067	−	0.178196i
$449$	6.46487	+	22.0173i	0.305096	+	1.03906i	0.959217	+	0.282671i	$0.0912205\pi$
$449$	6.46487	+	22.0173i	0.305096	+	1.03906i	−0.654121	+	0.756390i	$0.726961\pi$
$450$	19.2973	+	10.5946i	0.909682	+	0.499433i
$451$	−5.96232	−	41.4689i	−0.280755	−	1.95269i
$452$	1.02585	+	0.289679i	0.0482520	+	0.0136254i
$453$	−2.81922	−	1.68701i	−0.132458	−	0.0792628i
$454$	−2.90949	−	2.49475i	−0.136549	−	0.117085i
$455$	19.8627	+	2.85583i	0.931180	+	0.133883i
$456$	4.20703	−	5.34897i	0.197012	−	0.250488i
$457$	5.31811	+	4.60816i	0.248770	+	0.215561i	0.770316	−	0.637663i	$-0.220099\pi$
$457$	5.31811	+	4.60816i	0.248770	+	0.215561i	−0.521545	+	0.853224i	$0.674644\pi$
$458$	−2.11022	+	0.0109580i	−0.0986039	+	0.000512031i
$459$	2.29784	+	9.44405i	0.107254	+	0.440811i
$460$	−30.5220	+	2.40433i	−1.42309	+	0.112103i
$461$	24.6982			1.15031			0.575156	−	0.818044i	$-0.304941\pi$
$461$	24.6982			1.15031			0.575156	+	0.818044i	$0.304941\pi$
$462$	11.0596	−	7.70261i	0.514539	−	0.358358i
$463$	−12.8043	+	14.7770i	−0.595068	+	0.686745i	−0.970774	−	0.239994i	$-0.922855\pi$
$463$	−12.8043	+	14.7770i	−0.595068	+	0.686745i	0.375706	+	0.926739i	$0.377400\pi$
$464$	−6.26720	+	4.21414i	−0.290947	+	0.195637i
$465$	39.4330	−	19.5546i	1.82866	−	0.906822i
$466$	9.27861	+	7.95598i	0.429823	+	0.368554i
$467$	−26.7932	+	12.2360i	−1.23984	+	0.566217i	−0.923926	−	0.382571i	$-0.875039\pi$
$467$	−26.7932	+	12.2360i	−1.23984	+	0.566217i	−0.315915	+	0.948787i	$0.602312\pi$
$468$	−28.4703	−	21.1840i	−1.31604	−	0.979230i
$469$	−3.87257	+	0.556791i	−0.178818	+	0.0257102i
$470$	−4.60201	+	33.2318i	−0.212275	+	1.53287i
$471$	21.8088	−	26.8568i	1.00490	−	1.23750i
$472$	1.28046	−	2.92349i	0.0589378	−	0.134565i
$473$	−15.4448	−	7.05338i	−0.710151	−	0.324315i
$474$	−5.51271	+	9.32197i	−0.253207	+	0.428172i
$475$	−4.72011	−	5.44729i	−0.216573	−	0.249939i
$476$	2.11499	−	3.36738i	0.0969405	−	0.154344i
$477$	−4.24600	+	0.890432i	−0.194411	+	0.0407701i
$478$	2.59520	−	0.386899i	0.118702	−	0.0176963i
$479$	25.8823	+	16.6335i	1.18259	+	0.760006i	0.975861	−	0.218392i	$-0.0700812\pi$
$479$	25.8823	+	16.6335i	1.18259	+	0.760006i	0.206731	+	0.978398i	$0.433718\pi$
$480$	−7.05927	+	30.4679i	−0.322210	+	1.39066i
$481$	10.3161	−	35.1334i	0.470374	−	1.60195i
$482$	−0.435959	−	1.45671i	−0.0198574	−	0.0663515i
$483$	4.45272	+	7.62434i	0.202606	+	0.346919i
$484$	−26.3975	+	17.3546i	−1.19989	+	0.788847i
$485$	−23.5209	−	6.90635i	−1.06803	−	0.313601i
$486$	−11.5044	+	18.8056i	−0.521849	+	0.853038i
$487$	17.7860	+	11.4304i	0.805961	+	0.517960i	0.877556	−	0.479474i	$-0.159173\pi$
$487$	17.7860	+	11.4304i	0.805961	+	0.517960i	−0.0715951	+	0.997434i	$0.522809\pi$
$488$	23.1194	+	25.8561i	1.04657	+	1.17045i
$489$	38.9462	+	16.3030i	1.76121	+	0.737249i
$490$	19.9362	−	17.4569i	0.900625	−	0.788622i
$491$	−9.25413	−	10.6798i	−0.417633	−	0.481974i	0.507481	−	0.861663i	$-0.330577\pi$
$491$	−9.25413	−	10.6798i	−0.417633	−	0.481974i	−0.925114	+	0.379689i	$0.876031\pi$
$492$	6.75298	−	27.2111i	0.304448	−	1.22677i
$493$	−1.46712	+	3.21254i	−0.0660757	+	0.144686i
$494$	6.33233	+	9.74171i	0.284905	+	0.438300i
$495$	−3.90620	+	49.4155i	−0.175571	+	2.22106i
$496$	21.3494	+	23.6285i	0.958616	+	1.06095i
$497$	0.589977	+	4.10338i	0.0264641	+	0.184062i
$498$	−1.30668	−	35.1564i	−0.0585539	−	1.57540i
$499$	−33.3058	+	15.2102i	−1.49097	+	0.680904i	−0.983524	−	0.180779i	$-0.942138\pi$
$499$	−33.3058	+	15.2102i	−1.49097	+	0.680904i	−0.507447	+	0.861683i	$0.669411\pi$
$500$	1.10165	+	0.489344i	0.0492673	+	0.0218841i
$501$	16.4165	−	8.14084i	0.733436	−	0.363706i
$502$	5.52353	−	19.1793i	0.246527	−	0.856014i
$503$	9.31266	−	10.7474i	0.415231	−	0.479202i	−0.509147	−	0.860679i	$-0.670039\pi$
$503$	9.31266	−	10.7474i	0.415231	−	0.479202i	0.924378	+	0.381477i	$0.124585\pi$
$504$	8.79732	−	1.98845i	0.391864	−	0.0885725i
$505$			24.7382i			1.10084i
$506$	−16.8878	−	30.7799i	−0.750756	−	1.36833i
$507$	31.3545	−	21.5964i	1.39250	−	0.959128i
$508$	19.2685	−	5.87578i	0.854901	−	0.260696i
$509$	18.3187	−	21.1409i	0.811961	−	0.937052i	−0.187013	−	0.982358i	$-0.559881\pi$
$509$	18.3187	−	21.1409i	0.811961	−	0.937052i	0.998973	+	0.0453051i	$0.0144260\pi$
$510$	4.63877	+	13.8701i	0.205408	+	0.614178i
$511$	−0.999475	−	0.143703i	−0.0442142	−	0.00635704i
$512$	−22.6027	+	1.05710i	−0.998908	+	0.0467179i
$513$	5.67071	−	4.46568i	0.250368	−	0.197165i
$514$	5.10383	−	8.03312i	0.225120	−	0.354326i
$515$	2.67794	+	18.6255i	0.118004	+	0.820738i
$516$	−7.79769	−	8.26453i	−0.343274	−	0.363826i
$517$	−36.9127	+	10.8386i	−1.62342	+	0.476679i
$518$	5.07199	+	7.80279i	0.222851	+	0.342835i
$519$	7.45884	+	42.2457i	0.327407	+	1.85438i
$520$	−45.3654	−	28.1658i	−1.98940	−	1.23515i
$521$	0.242262	+	0.279586i	0.0106137	+	0.0122489i	0.761032	−	0.648715i	$-0.224693\pi$
$521$	0.242262	+	0.279586i	0.0106137	+	0.0122489i	−0.750418	+	0.660964i	$0.770148\pi$
$522$	−7.51173	+	2.78214i	−0.328779	+	0.121771i
$523$	−12.1829	+	7.82946i	−0.532720	+	0.342358i	−0.779186	−	0.626793i	$-0.784367\pi$
$523$	−12.1829	+	7.82946i	−0.532720	+	0.342358i	0.246466	+	0.969151i	$0.420731\pi$
$524$	15.8845	+	33.8475i	0.693918	+	1.47863i
$525$	−0.305236	−	9.54798i	−0.0133216	−	0.416708i
$526$	−3.31781	+	7.36597i	−0.144663	+	0.321172i
$527$	14.2886	+	4.19550i	0.622419	+	0.182759i
$528$	−35.1801	+	6.96774i	−1.53102	+	0.303232i
$529$	20.9818	−	9.42155i	0.912251	−	0.409633i
$530$	−6.25395	+	1.87166i	−0.271654	+	0.0812995i
$531$	2.04891	−	2.69474i	0.0889150	−	0.116942i
$532$	−2.92718	−	0.389881i	−0.126909	−	0.0169035i
$533$	40.2695	+	25.8797i	1.74427	+	1.12097i
$534$	−17.3251	−	18.5544i	−0.749731	−	0.802929i
$535$	52.0530	−	33.4525i	2.25045	−	1.44628i
$536$	10.0335	+	2.77709i	0.433383	+	0.119952i
$537$	−2.68177	−	0.695179i	−0.115727	−	0.0299992i
$538$	−11.9161	−	25.7381i	−0.513739	−	1.10965i
$539$	27.6407	+	12.6231i	1.19057	+	0.543716i
$540$	−14.8734	+	29.6509i	−0.640048	+	1.27597i
$541$	−0.733265	−	2.49727i	−0.0315255	−	0.107366i	0.942227	−	0.334974i	$-0.108728\pi$
$541$	−0.733265	−	2.49727i	−0.0315255	−	0.107366i	−0.973753	+	0.227608i	$0.926909\pi$
$542$	−2.51311	+	18.1476i	−0.107947	+	0.779505i
$543$	16.6895	+	18.0608i	0.716213	+	0.775062i
$544$	−8.75007	+	5.94987i	−0.375156	+	0.255099i
$545$	−2.22562	+	1.01641i	−0.0953351	+	0.0435381i
$546$	−1.62388	+	15.3133i	−0.0694956	+	0.655347i
$547$	−2.67534	−	0.384656i	−0.114389	−	0.0164467i	0.0848823	−	0.996391i	$-0.472949\pi$
$547$	−2.67534	−	0.384656i	−0.114389	−	0.0164467i	−0.199272	+	0.979944i	$0.563858\pi$
$548$	41.6289	−	0.432354i	1.77830	−	0.0184692i
$549$	17.3889	+	32.4199i	0.742140	+	1.38365i
$550$	0.197248	+	37.9848i	0.00841069	+	1.61968i
$551$	2.62272			0.111732
$552$	−2.71372	−	23.3374i	−0.115504	−	0.993307i
$553$	4.69956			0.199846
$554$	0.0935690	+	18.0190i	0.00397537	+	0.765552i
$555$	−34.0182	−	3.78616i	−1.44399	−	0.160713i
$556$	−0.0572365	−	5.51098i	−0.00242737	−	0.233718i
$557$	−16.8027	−	2.41587i	−0.711954	−	0.102364i	−0.223184	−	0.974776i	$-0.571645\pi$
$557$	−16.8027	−	2.41587i	−0.711954	−	0.102364i	−0.488770	+	0.872413i	$0.662554\pi$
$558$	16.1195	+	29.6821i	0.682392	+	1.25654i
$559$	17.6468	−	8.05902i	0.746379	−	0.340860i
$560$	12.9395	−	4.09314i	0.546793	−	0.172967i
$561$	−12.3173	+	11.3820i	−0.520035	+	0.480550i
$562$	0.868917	−	6.27458i	0.0366530	−	0.264677i
$563$	−10.1306	−	34.5016i	−0.426953	−	1.45407i	−0.839614	−	0.543184i	$-0.817219\pi$
$563$	−10.1306	−	34.5016i	−0.426953	−	1.45407i	0.412661	−	0.910885i	$-0.364600\pi$
$564$	−25.6152	−	2.58190i	−1.07859	−	0.108718i
$565$	1.54754	+	0.706737i	0.0651054	+	0.0297326i
$566$	2.01228	+	4.34641i	0.0845825	+	0.182693i
$567$	9.56528	+	0.143188i	0.401704	+	0.00601333i
$568$	2.94262	−	10.6316i	0.123469	−	0.446091i
$569$	−0.245797	+	0.157964i	−0.0103043	+	0.00662220i	−0.545783	−	0.837927i	$-0.683768\pi$
$569$	−0.245797	+	0.157964i	−0.0103043	+	0.00662220i	0.535479	+	0.844549i	$0.320131\pi$
$570$	7.93840	−	7.41244i	0.332503	−	0.310473i
$571$	−30.4873	−	19.5930i	−1.27585	−	0.819941i	−0.285483	−	0.958384i	$-0.592154\pi$
$571$	−30.4873	−	19.5930i	−1.27585	−	0.819941i	−0.990370	+	0.138443i	$0.955790\pi$
$572$	8.08432	−	60.6960i	0.338022	−	2.53783i
$573$	23.8725	−	7.84642i	0.997288	−	0.327789i
$574$	−11.6553	+	3.48816i	−0.486485	+	0.145593i
$575$	−24.8156	−	1.85403i	−1.03488	−	0.0773182i
$576$	−23.5657	−	4.54504i	−0.981905	−	0.189377i
$577$	11.4767	+	3.36987i	0.477782	+	0.140290i	0.511752	−	0.859133i	$-0.328997\pi$
$577$	11.4767	+	3.36987i	0.477782	+	0.140290i	−0.0339696	+	0.999423i	$0.510815\pi$
$578$	7.84141	−	17.4090i	0.326160	−	0.724117i
$579$	−26.0834	+	0.833851i	−1.08399	+	0.0346537i
$580$	−10.9116	+	5.12076i	−0.453078	+	0.212628i
$581$	−12.8428	+	8.25356i	−0.532809	+	0.342416i
$582$	4.62578	−	18.2340i	0.191745	−	0.755822i
$583$	−4.90214	−	5.65737i	−0.203026	−	0.234304i
$584$	2.28274	+	1.41728i	0.0944606	+	0.0586473i
$585$	−39.7475	−	40.3470i	−1.64336	−	1.66814i
$586$	5.00982	+	7.70714i	0.206954	+	0.318379i
$587$	32.5422	−	9.55524i	1.34316	−	0.394387i	0.470363	−	0.882473i	$-0.344123\pi$
$587$	32.5422	−	9.55524i	1.34316	−	0.394387i	0.872795	+	0.488086i	$0.162305\pi$
$588$	13.9551	+	14.7906i	0.575500	+	0.609955i
$589$	−1.57386	−	10.9464i	−0.0648496	−	0.451039i
$590$	2.73163	−	4.29942i	0.112459	−	0.177004i
$591$	−9.47162	−	5.66780i	−0.389610	−	0.233142i
$592$	−4.03264	−	24.4335i	−0.165740	−	1.00421i
$593$	31.4674	+	4.52433i	1.29221	+	0.185792i	0.753920	−	0.656966i	$-0.228160\pi$
$593$	31.4674	+	4.52433i	1.29221	+	0.185792i	0.538293	+	0.842758i	$0.319070\pi$
$594$	−38.0059	−	1.58704i	−1.55940	−	0.0651170i
$595$	4.15605	−	4.79633i	0.170381	−	0.196630i
$596$	7.96763	+	26.1283i	0.326367	+	1.07026i
$597$	16.7073	+	24.2564i	0.683786	+	0.992748i
$598$	39.2144	+	8.44768i	1.60359	+	0.345452i
$599$		−	9.46996i		−	0.386932i	−0.981107	−	0.193466i	$-0.938027\pi$
$599$		−	9.46996i		−	0.386932i	0.981107	−	0.193466i	$-0.0619730\pi$
$600$	−9.44914	+	23.5985i	−0.385760	+	0.963403i
$601$	23.6893	−	27.3389i	0.966307	−	1.11518i	−0.0269957	−	0.999636i	$-0.508594\pi$
$601$	23.6893	−	27.3389i	0.966307	−	1.11518i	0.993303	−	0.115542i	$-0.0368605\pi$
$602$	−1.36453	+	4.73805i	−0.0556142	+	0.193108i
$603$	9.65171	+	5.36439i	0.393048	+	0.218455i
$604$	1.54003	−	3.46703i	0.0626628	−	0.141072i
$605$	−45.8633	+	20.9451i	−1.86461	+	0.851538i
$606$	−18.9707	+	0.705095i	−0.770631	+	0.0286425i
$607$	−6.50166	−	45.2200i	−0.263894	−	1.83542i	−0.502826	−	0.864388i	$-0.667706\pi$
$607$	−6.50166	−	45.2200i	−0.263894	−	1.83542i	0.238931	−	0.971036i	$-0.423203\pi$
$608$	6.71859	+	4.07528i	0.272475	+	0.165274i
$609$	2.69839	+	2.19121i	0.109344	+	0.0887921i
$610$	30.1697	+	46.4133i	1.22154	+	1.87922i
$611$	18.2600	−	39.9839i	0.738721	−	1.61757i
$612$	−10.5042	+	3.95260i	−0.424605	+	0.159774i
$613$	5.65182	+	6.52254i	0.228275	+	0.263443i	0.858319	−	0.513116i	$-0.171509\pi$
$613$	5.65182	+	6.52254i	0.228275	+	0.263443i	−0.630045	+	0.776559i	$0.716963\pi$
$614$	25.9638	−	22.7348i	1.04781	−	0.917504i
$615$	17.2782	−	41.2757i	0.696724	−	1.66440i
$616$	10.3733	+	11.6012i	0.417952	+	0.467426i
$617$	−31.1290	−	20.0054i	−1.25321	−	0.805388i	−0.265868	−	0.964009i	$-0.585659\pi$
$617$	−31.1290	−	20.0054i	−1.25321	−	0.805388i	−0.987339	+	0.158622i	$0.949295\pi$
$618$	−14.2068	+	2.58447i	−0.571480	+	0.103963i
$619$	−11.8319	−	3.47417i	−0.475566	−	0.139639i	0.0351611	−	0.999382i	$-0.488806\pi$
$619$	−11.8319	−	3.47417i	−0.475566	−	0.139639i	−0.510727	+	0.859743i	$0.670624\pi$
$620$	27.9203	+	42.4686i	1.12131	+	1.70558i
$621$	3.02032	−	24.7362i	0.121201	−	0.992628i
$622$	−10.8474	−	36.2456i	−0.434942	−	1.45332i
$623$	−3.10350	+	10.5696i	−0.124339	+	0.423460i
$624$	20.3061	−	35.5915i	0.812894	−	1.42480i
$625$	−20.2071	−	12.9863i	−0.808284	−	0.519453i
$626$	16.4448	−	2.45162i	0.657265	−	0.0979866i
$627$	11.4886	+	4.80916i	0.458809	+	0.192059i
$628$	33.8293	+	21.2476i	1.34994	+	0.847872i
$629$	−7.58362	−	8.75196i	−0.302379	−	0.348964i
$630$	14.3603	−	0.994001i	0.572129	−	0.0396020i
$631$	−7.18424	−	3.28093i	−0.286000	−	0.130612i	0.267250	−	0.963627i	$-0.413885\pi$
$631$	−7.18424	−	3.28093i	−0.286000	−	0.130612i	−0.553250	+	0.833015i	$0.686612\pi$
$632$	−11.4549	−	5.01711i	−0.455651	−	0.199570i
$633$	−0.254362	−	0.206552i	−0.0101100	−	0.00820972i
$634$	−3.62903	+	26.2058i	−0.144127	+	1.04077i
$635$	31.8233	−	4.57550i	1.26287	−	0.181573i
$636$	−1.61354	−	4.74253i	−0.0639811	−	0.188054i
$637$	−31.5816	+	14.4228i	−1.25131	+	0.571454i
$638$	−10.4927	−	8.99699i	−0.415409	−	0.356194i
$639$	5.68413	−	10.2270i	0.224861	−	0.404573i
$640$	−35.9089	−	3.83701i	−1.41942	−	0.151671i
$641$	−3.47068	+	4.00538i	−0.137084	+	0.158203i	−0.820140	−	0.572162i	$-0.806105\pi$
$641$	−3.47068	+	4.00538i	−0.137084	+	0.158203i	0.683057	+	0.730365i	$0.260650\pi$
$642$	27.1368	+	38.9637i	1.07101	+	1.53778i
$643$	10.0786			0.397462			0.198731	−	0.980054i	$-0.436318\pi$
$643$	10.0786			0.397462			0.198731	+	0.980054i	$0.436318\pi$
$644$	−8.11744	+	6.16848i	−0.319872	+	0.243072i
$645$	−10.2867	−	14.9347i	−0.405039	−	0.588052i
$646$	3.67459	−	0.0190815i	0.144575	−	0.000750750i
$647$	−9.57802	−	8.29940i	−0.376551	−	0.326283i	0.445939	−	0.895064i	$-0.352870\pi$
$647$	−9.57802	−	8.29940i	−0.376551	−	0.326283i	−0.822489	+	0.568780i	$0.807415\pi$
$648$	−23.1619	−	10.5606i	−0.909885	−	0.414860i
$649$	5.78167	+	0.831279i	0.226951	+	0.0326306i
$650$	−32.9475	−	28.2510i	−1.29231	−	1.10809i
$651$	7.52615	−	12.5772i	0.294973	−	0.492938i
$652$	−13.2486	+	46.9177i	−0.518854	+	1.83744i
$653$	−4.06994	−	28.3070i	−0.159269	−	1.10774i	−0.899985	−	0.435922i	$-0.856423\pi$
$653$	−4.06994	−	28.3070i	−0.159269	−	1.10774i	0.740716	−	0.671819i	$-0.234487\pi$
$654$	−0.842873	−	1.67776i	−0.0329589	−	0.0656056i
$655$	16.8119	+	57.2562i	0.656897	+	2.23718i
$656$	32.1330	+	3.94073i	1.25458	+	0.153860i
$657$	2.00006	+	2.03022i	0.0780297	+	0.0792065i
$658$	4.69362	+	10.1379i	0.182976	+	0.395218i
$659$	−5.83484	+	5.05592i	−0.227293	+	0.196951i	−0.761061	−	0.648681i	$-0.775321\pi$
$659$	−5.83484	+	5.05592i	−0.227293	+	0.196951i	0.533768	+	0.845631i	$0.320776\pi$
$660$	−57.1867	+	2.42293i	−2.22599	+	0.0943123i
$661$	38.5401	−	24.7682i	1.49904	−	0.963372i	0.504017	−	0.863694i	$-0.331855\pi$
$661$	38.5401	−	24.7682i	1.49904	−	0.963372i	0.995020	−	0.0996781i	$-0.0317813\pi$
$662$	2.65484	−	0.395790i	0.103183	−	0.0153828i
$663$	−0.612274	−	19.1523i	−0.0237788	−	0.743814i
$664$	40.1148	−	6.40695i	1.55675	−	0.248638i
$665$	−4.52212	−	1.32781i	−0.175360	−	0.0514904i
$666$	1.93384	−	26.1950i	0.0749349	−	1.01503i
$667$	6.42304	−	6.38239i	0.248701	−	0.247127i
$668$	11.6236	+	17.6803i	0.449732	+	0.684070i
$669$	−23.2823	+	7.65245i	−0.900147	+	0.295861i
$670$	15.1497	+	6.82378i	0.585284	+	0.263626i
$671$	−34.3192	+	53.4017i	−1.32488	+	2.06155i
$672$	3.50766	+	9.80605i	0.135311	+	0.378277i
$673$	−4.79105	+	3.07902i	−0.184681	+	0.118687i	−0.629715	−	0.776827i	$-0.716828\pi$
$673$	−4.79105	+	3.07902i	−0.184681	+	0.118687i	0.445033	+	0.895514i	$0.353192\pi$
$674$	−36.1665	+	31.6688i	−1.39308	+	1.21984i
$675$	−15.6246	+	21.9731i	−0.601393	+	0.845743i
$676$	29.1326	+	32.9236i	1.12048	+	1.26629i
$677$	−19.7048	−	8.99887i	−0.757316	−	0.345855i	−0.000946951	−	1.00000i	$-0.500301\pi$
$677$	−19.7048	−	8.99887i	−0.757316	−	0.345855i	−0.756369	+	0.654145i	$0.773029\pi$
$678$	−0.497857	+	1.20688i	−0.0191201	+	0.0463500i
$679$	−7.83240	+	2.29980i	−0.300580	+	0.0882583i
$680$	−15.2505	+	7.25389i	−0.584831	+	0.278174i
$681$	3.44744	−	3.18568i	0.132106	−	0.122075i
$682$	−31.2542	+	49.1922i	−1.19678	+	1.88367i
$683$	4.20547	+	9.20870i	0.160918	+	0.352361i	0.972866	−	0.231368i	$-0.0743202\pi$
$683$	4.20547	+	9.20870i	0.160918	+	0.352361i	−0.811948	+	0.583729i	$0.801593\pi$
$684$	5.91053	+	5.87634i	0.225995	+	0.224687i
$685$	65.7668	+	9.45585i	2.51282	+	0.361289i
$686$	5.35409	−	18.5909i	0.204420	−	0.709805i
$687$	0.285886	−	2.56865i	0.0109072	−	0.0980001i
$688$	8.38416	−	10.0920i	0.319643	−	0.384752i
$689$	8.55305			0.325845
$690$	1.40294	−	37.4712i	0.0534092	−	1.42650i
$691$			34.1044i			1.29739i	0.761047	+	0.648696i	$0.224686\pi$
$691$			34.1044i			1.29739i	−0.761047	+	0.648696i	$0.775314\pi$
$692$	−47.3816	+	14.4487i	−1.80118	+	0.549255i
$693$	7.80212	+	14.5463i	0.296378	+	0.552568i
$694$	−10.1358	−	2.91905i	−0.384749	−	0.110806i
$695$	1.25180	−	8.70645i	0.0474834	−	0.330254i
$696$	−4.23789	−	8.22164i	−0.160637	−	0.311641i
$697$	13.7710	−	6.28899i	0.521613	−	0.238212i
$698$	−20.4190	+	32.1384i	−0.772872	+	1.21645i
$699$	−10.9942	+	10.1594i	−0.415838	+	0.384264i
$700$	10.9015	−	1.68314i	0.412039	−	0.0636166i
$701$	−4.53047	−	15.4294i	−0.171113	−	0.582759i	−0.999737	−	0.0229520i	$-0.992694\pi$
$701$	−4.53047	−	15.4294i	−0.171113	−	0.582759i	0.828623	−	0.559807i	$-0.189125\pi$
$702$	29.8074	−	31.6306i	1.12501	−	1.19382i
$703$	−3.57255	+	7.82279i	−0.134741	+	0.295042i
$704$	−12.8991	−	39.3514i	−0.486154	−	1.48311i
$705$	−39.7743	−	10.3105i	−1.49799	−	0.388315i
$706$	33.6203	−	29.4392i	1.26532	−	1.10796i
$707$	4.45368	+	6.93006i	0.167498	+	0.260632i
$708$	3.37489	+	1.97222i	0.126836	+	0.0741206i
$709$	−3.11500	−	2.00189i	−0.116986	−	0.0751825i	0.480839	−	0.876809i	$-0.340332\pi$
$709$	−3.11500	−	2.00189i	−0.116986	−	0.0751825i	−0.597825	+	0.801626i	$0.703968\pi$
$710$	7.23050	−	16.0527i	0.271356	−	0.602446i
$711$	−10.5586	−	8.02807i	−0.395978	−	0.301076i
$712$	18.8483	−	22.4494i	0.706371	−	0.841328i
$713$	−30.4925	−	22.9778i	−1.14195	−	0.860525i
$714$	3.79655	+	3.05038i	0.142082	+	0.114158i
$715$	27.5326	−	93.7676i	1.02966	−	3.50671i
$716$	0.422354	−	3.17098i	0.0157841	−	0.118505i
$717$	0.102682	+	3.21195i	0.00383472	+	0.119952i
$718$	−1.57314	−	10.5521i	−0.0587090	−	0.393802i
$719$	−13.7112	−	21.3351i	−0.511343	−	0.795665i	0.485569	−	0.874198i	$-0.338613\pi$
$719$	−13.7112	−	21.3351i	−0.511343	−	0.795665i	−0.996911	+	0.0785337i	$0.974976\pi$
$720$	−36.0635	−	12.9078i	−1.34401	−	0.481046i
$721$	4.10338	+	4.73556i	0.152818	+	0.176361i
$722$	10.1425	+	21.9072i	0.377465	+	0.815302i
$723$	1.83392	−	0.323795i	0.0682043	−	0.0120421i
$724$	−18.3712	+	21.6519i	−0.682762	+	0.804685i
$725$	−9.40000	+	2.76009i	−0.349107	+	0.102507i
$726$	−17.3691	−	34.5736i	−0.644626	−	1.28315i
$727$	−10.9683	+	1.57700i	−0.406792	+	0.0584879i	−0.342674	−	0.939454i	$-0.611333\pi$
$727$	−10.9683	+	1.57700i	−0.406792	+	0.0584879i	−0.0641182	+	0.997942i	$0.520423\pi$
$728$	−17.7792	+	0.276992i	−0.658942	+	0.0102660i
$729$	−21.2459	−	16.6617i	−0.786885	−	0.617099i
$730$	3.25544	+	2.79139i	0.120489	+	0.103314i
$731$	0.873170	−	6.07303i	0.0322954	−	0.224619i
$732$	−34.7324	+	24.4587i	−1.28375	+	0.904019i
$733$	−25.7265	+	29.6900i	−0.950230	+	1.09662i	0.0449922	+	0.998987i	$0.485674\pi$
$733$	−25.7265	+	29.6900i	−0.950230	+	1.09662i	−0.995222	+	0.0976365i	$0.968872\pi$
$734$	0.0579129	+	11.1525i	0.00213760	+	0.411647i
$735$	18.4096	+	26.7278i	0.679049	+	0.985871i
$736$	26.3710	−	6.36935i	0.972049	−	0.234777i
$737$			19.0533i			0.701838i
$738$	32.1450	+	12.0734i	1.18327	+	0.444429i
$739$	−32.1912	−	27.8938i	−1.18417	−	1.02609i	−0.999059	−	0.0433727i	$-0.986190\pi$
$739$	−32.1912	−	27.8938i	−1.18417	−	1.02609i	−0.185112	−	0.982717i	$-0.559265\pi$
$740$	−0.410464	−	39.5212i	−0.0150889	−	1.45283i
$741$	−12.7488	+	6.32203i	−0.468337	+	0.232245i
$742$	−1.41500	+	1.65023i	−0.0519462	+	0.0605819i
$743$	−6.04961	−	13.2468i	−0.221939	−	0.485978i	0.765607	−	0.643308i	$-0.222439\pi$
$743$	−6.04961	−	13.2468i	−0.221939	−	0.485978i	−0.987546	+	0.157330i	$0.949711\pi$
$744$	−31.7715	+	22.6213i	−1.16480	+	0.829339i
$745$	6.20443	+	43.1527i	0.227313	+	1.58099i
$746$	−4.95430	+	35.7758i	−0.181390	+	1.30984i
$747$	42.9534	+	3.39538i	1.57158	+	0.124231i
$748$	−14.7664	−	12.5290i	−0.539911	−	0.458106i
$749$	8.55939	−	18.7425i	0.312753	−	0.684835i
$750$	−0.751499	+	1.27078i	−0.0274409	+	0.0464024i
$751$	−15.0056	+	13.0024i	−0.547561	+	0.474465i	−0.884160	−	0.467183i	$-0.845269\pi$
$751$	−15.0056	+	13.0024i	−0.547561	+	0.474465i	0.336599	+	0.941648i	$0.390723\pi$
$752$	−0.617433	−	29.7214i	−0.0225155	−	1.08383i
$753$	22.5486	+	9.43894i	0.821716	+	0.343974i
$754$	15.6198	−	2.32864i	0.568840	−	0.0848040i
$755$	3.27342	−	5.09354i	0.119132	−	0.185373i
$756$	1.17156	+	10.9840i	0.0426091	+	0.399483i
$757$	−30.7079	−	9.01665i	−1.11610	−	0.327716i	−0.328868	−	0.944376i	$-0.606667\pi$
$757$	−30.7079	−	9.01665i	−1.11610	−	0.327716i	−0.787229	+	0.616660i	$0.788485\pi$
$758$	−27.8957	+	8.34851i	−1.01322	+	0.303232i
$759$	39.8386	−	16.1798i	1.44605	−	0.587290i
$760$	9.60484	+	8.06413i	0.348404	+	0.292517i
$761$	8.37394	−	28.5190i	0.303555	−	1.03381i	−0.656575	−	0.754261i	$-0.727996\pi$
$761$	8.37394	−	28.5190i	0.303555	−	1.03381i	0.960130	−	0.279553i	$-0.0901863\pi$
$762$	4.41578	+	24.2735i	0.159967	+	0.879334i
$763$	−0.440490	+	0.685415i	−0.0159468	+	0.0248137i
$764$	12.3273	+	26.2676i	0.445986	+	0.950329i
$765$	−17.5309	+	3.67641i	−0.633829	+	0.132921i
$766$	−6.13853	−	7.01035i	−0.221794	−	0.253294i
$767$	−5.04382	+	4.37049i	−0.182122	+	0.157809i
$768$	1.91895	−	27.6463i	0.0692443	−	0.997600i
$769$	11.5041	+	5.25375i	0.414849	+	0.189455i	0.611895	−	0.790939i	$-0.290408\pi$
$769$	11.5041	+	5.25375i	0.414849	+	0.189455i	−0.197046	+	0.980394i	$0.563135\pi$
$770$	13.5366	+	20.8249i	0.487827	+	0.750476i
$771$	9.04867	+	7.34790i	0.325880	+	0.264628i
$772$	−4.59803	−	29.7810i	−0.165487	−	1.07184i
$773$	2.15890	−	0.310402i	0.0776501	−	0.0111644i	−0.103380	−	0.994642i	$-0.532966\pi$
$773$	2.15890	−	0.310402i	0.0776501	−	0.0111644i	0.181030	+	0.983478i	$0.442057\pi$
$774$	11.1595	−	8.31409i	0.401121	−	0.298844i
$775$	17.1606	+	37.5764i	0.616426	+	1.34979i
$776$	21.5462	+	2.75602i	0.773463	+	0.0989354i
$777$	−10.2113	+	5.06374i	−0.366330	+	0.181661i
$778$	1.54699	−	5.37158i	0.0554622	−	0.192581i
$779$	−8.49660	−	7.36234i	−0.304422	−	0.263783i
$780$	40.6965	−	51.1937i	1.45717	−	1.83303i
$781$	20.1889			0.722417
$782$	8.95264	−	8.98886i	0.320146	−	0.321441i
$783$	−2.31938	−	9.53258i	−0.0828878	−	0.340666i
$784$	−15.0047	+	18.0611i	−0.535883	+	0.645039i
$785$	48.1848	+	41.7524i	1.71979	+	1.49021i
$786$	−43.4281	+	14.5243i	−1.54903	+	0.518063i
$787$	−1.48514	+	10.3294i	−0.0529396	+	0.368203i	0.946080	+	0.323933i	$0.105005\pi$
$787$	−1.48514	+	10.3294i	−0.0529396	+	0.368203i	−0.999020	+	0.0442700i	$0.985904\pi$
$788$	5.17398	−	11.6481i	0.184315	−	0.414945i
$789$	−8.49033	−	5.08060i	−0.302264	−	0.180874i
$790$	−16.8461	−	10.7031i	−0.599356	−	0.380799i
$791$	0.560756	−	0.0806246i	0.0199382	−	0.00286668i
$792$	−3.48799	−	43.7849i	−0.123940	−	1.55583i
$793$	−20.4338	−	69.5912i	−0.725626	−	2.47126i
$794$	−5.99571	−	9.22385i	−0.212780	−	0.327342i
$795$	−1.39011	−	7.87338i	−0.0493022	−	0.279240i
$796$	−25.4703	+	22.5375i	−0.902771	+	0.798821i
$797$	21.1861	−	18.3579i	0.750450	−	0.650269i	−0.193220	−	0.981155i	$-0.561893\pi$
$797$	21.1861	−	18.3579i	0.750450	−	0.650269i	0.943670	+	0.330887i	$0.107348\pi$
$798$	0.889351	−	3.50566i	0.0314827	−	0.124099i
$799$	−7.51583	−	11.6949i	−0.265891	−	0.413734i
$800$	−28.3686	−	7.53560i	−1.00298	−	0.266424i
$801$	25.0283	−	18.4453i	0.884330	−	0.651731i
$802$	−15.2922	+	33.9507i	−0.539986	+	1.19884i
$803$	−1.38542	+	4.71830i	−0.0488903	+	0.166505i
$804$	−4.80106	+	11.8121i	−0.169320	+	0.416581i
$805$	−14.3059	+	7.75277i	−0.504217	+	0.273249i
$806$	−19.0923	−	63.7949i	−0.672496	−	2.24708i
$807$	33.0002	−	10.8465i	1.16166	−	0.381816i
$808$	−3.45724	−	21.6462i	−0.121625	−	0.761511i
$809$	10.9123	−	16.9799i	0.383658	−	0.596983i	−0.594689	−	0.803956i	$-0.702725\pi$
$809$	10.9123	−	16.9799i	0.383658	−	0.596983i	0.978347	+	0.206973i	$0.0663612\pi$
$810$	−33.9616	−	22.2979i	−1.19329	−	0.783469i
$811$	23.3574	+	36.3448i	0.820189	+	1.27624i	0.958283	+	0.285820i	$0.0922660\pi$
$811$	23.3574	+	36.3448i	0.820189	+	1.27624i	−0.138094	+	0.990419i	$0.544098\pi$
$812$	−2.13482	+	3.39894i	−0.0749174	+	0.119279i
$813$	−21.7203	−	5.63045i	−0.761766	−	0.197468i
$814$	41.1280	−	19.0413i	1.44154	−	0.667396i
$815$	−32.3229	+	70.7772i	−1.13222	+	2.47922i
$816$	−5.99736	−	11.4882i	−0.209950	−	0.402167i
$817$	−4.37179	+	1.28367i	−0.152949	+	0.0449100i
$818$	2.71567	−	19.6103i	0.0949512	−	0.685657i
$819$	−18.3985	−	4.14679i	−0.642894	−	0.144901i
$820$	49.7240	+	14.0410i	1.73644	+	0.490334i
$821$	3.39054	+	7.42424i	0.118331	+	0.259108i	0.959524	−	0.281626i	$-0.0908738\pi$
$821$	3.39054	+	7.42424i	0.118331	+	0.259108i	−0.841194	+	0.540734i	$0.818147\pi$
$822$	−5.37677	+	50.7032i	−0.187536	+	1.76848i
$823$	4.80208	−	33.3992i	0.167390	−	1.16422i	−0.716863	−	0.697214i	$-0.754423\pi$
$823$	4.80208	−	33.3992i	0.167390	−	1.16422i	0.884253	−	0.467008i	$-0.154668\pi$
$824$	−4.94620	−	15.9233i	−0.172309	−	0.554713i
$825$	−46.2369	−	5.14607i	−1.60976	−	0.179163i
$826$	−0.00880806	−	1.69620i	−0.000306471	−	0.0590184i
$827$		−	34.0967i		−	1.18566i	−0.805328	−	0.592830i	$-0.798011\pi$
$827$		−	34.0967i		−	1.18566i	0.805328	−	0.592830i	$-0.201989\pi$
$828$	28.7750	+	0.00784320i	1.00000	+	0.000272570i
$829$			6.53521i			0.226977i	0.993539	+	0.113489i	$0.0362025\pi$
$829$			6.53521i			0.226977i	−0.993539	+	0.113489i	$0.963797\pi$
$830$	64.8336	−	0.336669i	2.25041	−	0.0116859i
$831$	−21.9335	−	2.44115i	−0.760864	−	0.0846827i
$832$	43.6314	+	18.3054i	1.51265	+	0.634626i
$833$	−1.56267	+	10.8686i	−0.0541433	+	0.376575i
$834$	6.71227	+	0.711796i	0.232427	+	0.0246475i
$835$	14.0284	+	30.7179i	0.485473	+	1.06304i
$836$	−3.90814	+	13.8400i	−0.135166	+	0.478667i
$837$	−38.3942	+	15.4007i	−1.32710	+	0.532327i
$838$	50.3002	+	6.96567i	1.73759	+	0.240625i
$839$	−1.39600	+	0.409903i	−0.0481954	+	0.0141514i	−0.305741	−	0.952115i	$-0.598904\pi$
$839$	−1.39600	+	0.409903i	−0.0481954	+	0.0141514i	0.257546	+	0.966266i	$0.417086\pi$
$840$	3.14461	+	16.3214i	0.108499	+	0.563141i
$841$	−10.5662	+	23.1367i	−0.364351	+	0.797816i
$842$	15.3581	+	33.1726i	0.529275	+	1.14320i
$843$	7.50988	+	1.94674i	0.258654	+	0.0670494i
$844$	0.201237	−	0.320399i	0.00692686	−	0.0110286i
$845$	37.9332	+	59.0253i	1.30494	+	2.03053i
$846$	6.77299	−	30.7950i	0.232860	−	1.05876i
$847$	−9.07717	+	14.1243i	−0.311895	+	0.485318i
$848$	5.21070	−	2.51173i	0.178936	−	0.0862530i
$849$	−5.57278	+	1.83166i	−0.191257	+	0.0628625i
$850$	−13.1499	+	3.93545i	−0.451038	+	0.134985i
$851$	10.2876	+	27.8518i	0.352655	+	0.954748i
$852$	12.5162	+	5.08721i	0.428797	+	0.174285i
$853$	8.04230	−	27.3896i	0.275363	−	0.937801i	−0.699432	−	0.714699i	$-0.746564\pi$
$853$	8.04230	−	27.3896i	0.275363	−	0.937801i	0.974795	−	0.223102i	$-0.0716182\pi$
$854$	16.8075	+	7.57050i	0.575141	+	0.259057i
$855$	7.89168	+	10.7082i	0.269890	+	0.366212i
$856$	−40.8719	+	36.5458i	−1.39697	+	1.24911i
$857$	17.7706	+	27.6516i	0.607032	+	0.944560i	0.999691	+	0.0248757i	$0.00791899\pi$
$857$	17.7706	+	27.6516i	0.607032	+	0.944560i	−0.392659	+	0.919684i	$0.628445\pi$
$858$	72.6910	+	18.4410i	2.48163	+	0.629565i
$859$	1.05412	−	0.913400i	0.0359661	−	0.0311648i	−0.636692	−	0.771118i	$-0.719698\pi$
$859$	1.05412	−	0.913400i	0.0359661	−	0.0311648i	0.672658	+	0.739953i	$0.265152\pi$
$860$	15.6821	−	13.8763i	0.534754	−	0.473180i
$861$	−2.59072	−	14.6734i	−0.0882915	−	0.500069i
$862$	−1.64310	+	1.06805i	−0.0559642	+	0.0363780i
$863$	−10.5466	−	35.9184i	−0.359010	−	1.22268i	−0.919027	−	0.394194i	$-0.871024\pi$
$863$	−10.5466	−	35.9184i	−0.359010	−	1.22268i	0.560017	−	0.828481i	$-0.310795\pi$
$864$	8.87056	−	28.0234i	0.301782	−	0.953377i
$865$	−78.2540	+	11.2512i	−2.66072	+	0.382553i
$866$	18.5866	−	29.2541i	0.631597	−	0.994096i
$867$	20.0663	+	12.0076i	0.681487	+	0.407801i
$868$	15.4672	+	6.87041i	0.524991	+	0.233197i
$869$	3.25713	−	22.6539i	0.110491	−	0.768480i
$870$	−4.68225	−	14.0001i	−0.158743	−	0.474648i
$871$	−16.4525	−	14.2562i	−0.557473	−	0.483053i
$872$	1.80539	−	1.20040i	0.0611384	−	0.0406508i
$873$	21.5259	+	8.21277i	0.728541	+	0.277960i
$874$	−8.83396	−	3.27460i	−0.298813	−	0.110765i
$875$	0.640649			0.0216579
$876$	−2.04781	+	2.57602i	−0.0691890	+	0.0870355i
$877$	18.1874	+	15.7595i	0.614146	+	0.532160i	0.905441	−	0.424473i	$-0.139541\pi$
$877$	18.1874	+	15.7595i	0.614146	+	0.532160i	−0.291295	+	0.956633i	$0.594086\pi$
$878$	17.2306	+	4.96231i	0.581503	+	0.167470i
$879$	−10.0862	+	5.00167i	−0.340198	+	0.168702i
$880$	−10.7627	−	65.2106i	−0.362811	−	2.19825i
$881$	−20.9261	−	45.8218i	−0.705019	−	1.54378i	−0.833777	−	0.552101i	$-0.813826\pi$
$881$	−20.9261	−	45.8218i	−0.705019	−	1.54378i	0.128758	−	0.991676i	$-0.458901\pi$
$882$	−19.9717	+	14.8793i	−0.672482	+	0.501013i
$883$	55.8516	−	8.03024i	1.87955	−	0.270239i	0.895099	−	0.445868i	$-0.147105\pi$
$883$	55.8516	−	8.03024i	1.87955	−	0.270239i	0.984456	+	0.175629i	$0.0561960\pi$
$884$	21.8674	−	3.37621i	0.735480	−	0.113554i
$885$	4.84295	+	3.93268i	0.162794	+	0.132196i
$886$	12.0823	−	7.85376i	0.405912	−	0.263852i
$887$	−30.7284	−	14.0332i	−1.03176	−	0.471189i	−0.173732	−	0.984793i	$-0.555583\pi$
$887$	−30.7284	−	14.0332i	−1.03176	−	0.471189i	−0.858027	+	0.513604i	$0.828310\pi$
$888$	30.2954	−	1.44121i	1.01665	−	0.0483639i
$889$	8.09110	−	7.01098i	0.271367	−	0.235141i
$890$	35.1967	−	30.8196i	1.17980	−	1.03307i
$891$	7.31966	−	46.0095i	0.245218	−	1.54138i
$892$	−12.0226	−	25.6182i	−0.402545	−	0.857762i
$893$	−5.58143	+	8.68487i	−0.186775	+	0.290628i
$894$	−32.9151	+	5.98785i	−1.10085	+	0.200264i
$895$	1.43841	−	4.89876i	0.0480806	−	0.163748i
$896$	−10.7501	+	5.38987i	−0.359137	+	0.180063i
$897$	−15.8371	+	46.5068i	−0.528784	+	1.55282i
$898$	−9.30426	−	31.0893i	−0.310487	−	1.03746i
$899$	−14.4225	−	4.23482i	−0.481017	−	0.141239i
$900$	−27.3679	−	14.8411i	−0.912263	−	0.494703i
$901$	1.46244	−	2.27560i	0.0487210	−	0.0758114i
$902$	8.73642	+	58.6013i	0.290891	+	1.95121i
$903$	−5.57040	−	2.33179i	−0.185371	−	0.0775972i
$904$	−1.45288	−	0.402129i	−0.0483221	−	0.0133746i
$905$	−34.2499	+	29.6777i	−1.13851	+	0.986522i
$906$	3.99931	+	2.36506i	0.132868	+	0.0785739i
$907$	2.36570	−	5.18017i	0.0785519	−	0.172005i	−0.866281	−	0.499557i	$-0.833496\pi$
$907$	2.36570	−	5.18017i	0.0785519	−	0.172005i	0.944833	+	0.327552i	$0.106224\pi$
$908$	4.13290	+	3.50670i	0.137155	+	0.116374i
$909$	1.83217	−	23.1780i	0.0607694	−	0.768765i
$910$	−28.1108	−	3.89284i	−0.931862	−	0.129046i
$911$	−1.01264	−	7.04306i	−0.0335502	−	0.233347i	0.966146	−	0.257996i	$-0.0830622\pi$
$911$	−1.01264	−	7.04306i	−0.0335502	−	0.233347i	−0.999696	+	0.0246492i	$0.992153\pi$
$912$	−5.91027	+	7.59537i	−0.195709	+	0.251508i
$913$	30.8847	+	67.6281i	1.02213	+	2.23816i
$914$	−7.55468	−	6.47779i	−0.249886	−	0.214266i
$915$	−60.7401	+	30.1206i	−2.00800	+	0.995756i
$916$	2.98417	−	0.0309934i	0.0985999	−	0.00102405i
$917$	15.0176	+	13.0128i	0.495925	+	0.429721i
$918$	−3.31895	−	13.3389i	−0.109542	−	0.440248i
$919$			25.2882i			0.834182i	0.908865	+	0.417091i	$0.136950\pi$
$919$			25.2882i			0.834182i	−0.908865	+	0.417091i	$0.863050\pi$
$920$	43.1464	−	3.62434i	1.42249	−	0.119491i
$921$	23.9756	+	34.8088i	0.790024	+	1.14699i
$922$	−34.9281	+	0.181375i	−1.15030	+	0.00597327i
$923$	−15.1059	+	17.4332i	−0.497217	+	0.573819i
$924$	−15.5838	+	10.9742i	−0.512671	+	0.361025i
$925$	4.57173	−	31.7971i	0.150318	−	1.04548i
$926$	17.9993	−	20.9916i	0.591494	−	0.689826i
$927$	−1.12959	−	17.6491i	−0.0371007	−	0.579673i
$928$	8.83209	−	6.00564i	0.289928	−	0.197145i
$929$	−39.6267	+	5.69746i	−1.30011	+	0.186928i	−0.757377	−	0.652978i	$-0.773519\pi$
$929$	−39.6267	+	5.69746i	−1.30011	+	0.186928i	−0.542733	+	0.839906i	$0.682610\pi$
$930$	−55.6224	+	27.9436i	−1.82393	+	0.916305i
$931$	7.82398	−	2.29733i	0.256421	−	0.0752919i
$932$	−13.1802	−	11.1832i	−0.431731	−	0.366317i
$933$	45.6312	−	8.05657i	1.49390	−	0.263760i
$934$	37.8009	−	17.5009i	1.23688	−	0.572647i
$935$	−20.2399	−	23.3581i	−0.661916	−	0.763892i
$936$	40.4181	+	29.7492i	1.32111	+	0.972383i
$937$	−0.293317	−	0.456409i	−0.00958223	−	0.0149102i	0.836429	−	0.548075i	$-0.184639\pi$
$937$	−0.293317	−	0.456409i	−0.00958223	−	0.0149102i	−0.846012	+	0.533164i	$0.821003\pi$
$938$	5.47247	−	0.815849i	0.178683	−	0.0266384i
$939$	0.650653	+	20.3528i	0.0212333	+	0.664190i
$940$	6.26410	−	47.0301i	0.204312	−	1.53395i
$941$	−12.6834	+	43.1956i	−0.413466	+	1.40813i	0.445123	+	0.895470i	$0.353160\pi$
$941$	−12.6834	+	43.1956i	−0.413466	+	1.40813i	−0.858588	+	0.512665i	$0.828658\pi$
$942$	−30.6447	+	38.1409i	−0.998459	+	1.24270i
$943$	−38.7245	+	2.64612i	−1.26104	+	0.0861695i
$944$	−1.78935	+	4.14379i	−0.0582382	+	0.134869i
$945$	−0.826997	+	17.6104i	−0.0269022	+	0.572866i
$946$	21.8937	+	9.86144i	0.711825	+	0.320623i
$947$	−15.5453	−	9.99034i	−0.505153	−	0.324642i	0.263121	−	0.964763i	$-0.415248\pi$
$947$	−15.5453	−	9.99034i	−0.505153	−	0.324642i	−0.768275	+	0.640120i	$0.778884\pi$
$948$	7.72759	−	13.2236i	0.250981	−	0.429481i
$949$	−3.03764	−	4.72666i	−0.0986061	−	0.153434i
$950$	6.71515	+	7.66887i	0.217868	+	0.248811i
$951$	−31.3650	−	8.13058i	−1.01708	−	0.263652i
$952$	−2.96628	+	4.77766i	−0.0961378	+	0.154845i
$953$	−0.943180	+	2.06528i	−0.0305526	+	0.0669009i	−0.924293	−	0.381684i	$-0.875344\pi$
$953$	−0.943180	+	2.06528i	−0.0305526	+	0.0669009i	0.893740	+	0.448584i	$0.148072\pi$
$954$	5.99813	−	1.29042i	0.194197	−	0.0417790i
$955$	13.0470	+	44.4342i	0.422193	+	1.43786i
$956$	−3.66728	+	0.566209i	−0.118608	+	0.0183125i
$957$	12.4327	−	11.4887i	0.401893	−	0.371378i
$958$	−36.7247	−	23.3330i	−1.18652	−	0.753854i
$959$	20.1260	−	9.19124i	0.649903	−	0.296801i
$960$	9.75943	−	43.1394i	0.314984	−	1.39232i
$961$	−4.60836	+	32.0518i	−0.148657	+	1.03393i
$962$	−14.3310	+	49.7612i	−0.462049	+	1.60437i
$963$	−51.2476	+	27.4874i	−1.65143	+	0.885769i
$964$	0.627229	+	2.05688i	0.0202017	+	0.0662475i
$965$		−	48.0936i		−	1.54819i
$966$	−6.35301	−	10.7496i	−0.204405	−	0.345863i
$967$	34.7425			1.11724			0.558622	−	0.829422i	$-0.311330\pi$
$967$	34.7425			1.11724			0.558622	+	0.829422i	$0.311330\pi$
$968$	37.2037	−	24.7367i	1.19577	−	0.795067i
$969$	−0.497822	+	4.47288i	−0.0159924	+	0.143690i
$970$	33.3138	+	9.59419i	1.06964	+	0.308051i
$971$	9.80923	+	1.41035i	0.314793	+	0.0452604i	0.297901	−	0.954597i	$-0.403714\pi$
$971$	9.80923	+	1.41035i	0.314793	+	0.0452604i	0.0168925	+	0.999857i	$0.494623\pi$
$972$	16.1313	−	26.6792i	0.517412	−	0.855736i
$973$	−1.21677	−	2.66435i	−0.0390078	−	0.0854152i
$974$	−25.2368	−	16.0342i	−0.808640	−	0.513768i
$975$	39.0393	−	36.0751i	1.25026	−	1.15533i
$976$	−32.8852	−	36.3958i	−1.05263	−	1.16500i
$977$	27.5401	−	8.08649i	0.881084	−	0.258710i	0.190261	−	0.981734i	$-0.439067\pi$
$977$	27.5401	−	8.08649i	0.881084	−	0.258710i	0.690823	+	0.723024i	$0.257248\pi$
$978$	−55.1972	−	22.7697i	−1.76501	−	0.728094i
$979$	48.7988	+	22.2857i	1.55962	+	0.712253i
$980$	−28.0655	+	24.8338i	−0.896518	+	0.793288i
$981$	2.16052	−	0.787466i	0.0689802	−	0.0251418i
$982$	13.1656	+	15.0354i	0.420130	+	0.479799i
$983$	22.4414	−	14.4222i	0.715771	−	0.459998i	−0.131393	−	0.991330i	$-0.541945\pi$
$983$	22.4414	−	14.4222i	0.715771	−	0.459998i	0.847163	+	0.531332i	$0.178308\pi$
$984$	−9.35020	+	38.5313i	−0.298074	+	1.22833i
$985$	10.9976	−	17.1126i	0.350412	−	0.545252i
$986$	2.05120	−	4.55393i	0.0653235	−	0.145027i
$987$	−12.9984	+	4.27233i	−0.413744	+	0.135990i
$988$	−9.02669	−	13.7302i	−0.287177	−	0.436815i
$989$	−7.58269	+	13.7825i	−0.241115	+	0.438257i
$990$	5.16123	−	69.9118i	0.164035	−	2.22194i
$991$	29.2747	+	8.59581i	0.929940	+	0.273055i	0.711412	−	0.702776i	$-0.248056\pi$
$991$	29.2747	+	8.59581i	0.929940	+	0.273055i	0.218528	+	0.975831i	$0.429874\pi$
$992$	−30.3657	−	33.2585i	−0.964112	−	1.05596i
$993$	0.105041	+	3.28576i	0.00333339	+	0.104270i
$994$	−0.864476	−	5.79865i	−0.0274195	−	0.183922i
$995$	−45.6630	+	29.3459i	−1.44762	+	0.930326i
$996$	2.10608	+	49.7084i	0.0667337	+	1.57507i
$997$	3.49002	−	3.02412i	0.110530	−	0.0957748i	−0.597842	−	0.801614i	$-0.703975\pi$
$997$	3.49002	−	3.02412i	0.110530	−	0.0957748i	0.708372	+	0.705839i	$0.249430\pi$
$998$	46.9891	−	21.7548i	1.48742	−	0.688637i
$999$	31.5922	+	6.06683i	0.999533	+	0.191946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bf.a.5.1	✓	920
3.2	odd	2	inner	552.2.bf.a.5.92	yes	920
8.5	even	2	inner	552.2.bf.a.5.76	yes	920
23.14	odd	22	inner	552.2.bf.a.221.17	yes	920
24.5	odd	2	inner	552.2.bf.a.5.17	yes	920
69.14	even	22	inner	552.2.bf.a.221.76	yes	920
184.37	odd	22	inner	552.2.bf.a.221.92	yes	920
552.221	even	22	inner	552.2.bf.a.221.1	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bf.a.5.1	✓	920	1.1	even	1	trivial
552.2.bf.a.5.17	yes	920	24.5	odd	2	inner
552.2.bf.a.5.76	yes	920	8.5	even	2	inner
552.2.bf.a.5.92	yes	920	3.2	odd	2	inner
552.2.bf.a.221.1	yes	920	552.221	even	22	inner
552.2.bf.a.221.17	yes	920	23.14	odd	22	inner
552.2.bf.a.221.76	yes	920	69.14	even	22	inner
552.2.bf.a.221.92	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)

\(f(q)\)	\(=\)	\(q+(-1.41419 + 0.00734365i) q^{2} +(0.191591 - 1.72142i) q^{3} +(1.99989 - 0.0207707i) q^{4} +(3.15950 + 0.454268i) q^{5} +(-0.258305 + 2.43583i) q^{6} +(0.966873 - 0.441556i) q^{7} +(-2.82808 + 0.0440603i) q^{8} +(-2.92659 - 0.659617i) q^{9} +O(q^{10})\)	\(q+(-1.41419 + 0.00734365i) q^{2} +(0.191591 - 1.72142i) q^{3} +(1.99989 - 0.0207707i) q^{4} +(3.15950 + 0.454268i) q^{5} +(-0.258305 + 2.43583i) q^{6} +(0.966873 - 0.441556i) q^{7} +(-2.82808 + 0.0440603i) q^{8} +(-2.92659 - 0.659617i) q^{9} +(-4.47149 - 0.619221i) q^{10} +(-1.45838 - 4.96677i) q^{11} +(0.347406 - 3.44664i) q^{12} +(5.38000 + 2.45696i) q^{13} +(-1.36410 + 0.631547i) q^{14} +(1.38732 - 5.35180i) q^{15} +(3.99914 - 0.0830783i) q^{16} +(1.57359 - 1.01129i) q^{17} +(4.14361 + 0.911335i) q^{18} +(-1.16859 - 0.751005i) q^{19} +(6.32810 + 0.842862i) q^{20} +(-0.574860 - 1.74899i) q^{21} +(2.09890 + 7.01327i) q^{22} +(-4.68944 + 1.00455i) q^{23} +(-0.465989 + 4.87677i) q^{24} +(4.97864 + 1.46186i) q^{25} +(-7.62641 - 3.43512i) q^{26} +(-1.69619 + 4.91151i) q^{27} +(1.92447 - 0.903147i) q^{28} +(-1.58834 + 1.02077i) q^{29} +(-1.92264 + 7.57868i) q^{30} +(5.21351 + 6.01671i) q^{31} +(-5.65495 + 0.146857i) q^{32} +(-8.82932 + 1.55889i) q^{33} +(-2.21794 + 1.44171i) q^{34} +(3.25542 - 0.955879i) q^{35} +(-5.86656 - 1.25838i) q^{36} +(-0.881073 - 6.12800i) q^{37} +(1.65812 + 1.05349i) q^{38} +(5.26023 - 8.79052i) q^{39} +(-8.95536 - 1.14550i) q^{40} +(8.01106 + 1.15182i) q^{41} +(0.825808 + 2.46920i) q^{42} +(2.14799 - 2.47891i) q^{43} +(-3.01976 - 9.90271i) q^{44} +(-8.94692 - 3.41352i) q^{45} +(6.62441 - 1.45506i) q^{46} -7.43194i q^{47} +(0.623185 - 6.90012i) q^{48} +(-3.84415 + 4.43639i) q^{49} +(-7.05150 - 2.03079i) q^{50} +(-1.43937 - 2.90257i) q^{51} +(10.8105 + 4.80192i) q^{52} +(1.31544 - 0.600740i) q^{53} +(2.36267 - 6.95829i) q^{54} +(-2.35150 - 16.3550i) q^{55} +(-2.71494 + 1.29136i) q^{56} +(-1.51669 + 1.86775i) q^{57} +(2.23873 - 1.45523i) q^{58} +(-0.468756 + 1.02643i) q^{59} +(2.66333 - 10.7318i) q^{60} +(-8.03054 - 9.26774i) q^{61} +(-7.41710 - 8.47051i) q^{62} +(-3.12090 + 0.654486i) q^{63} +(7.99612 - 0.249212i) q^{64} +(15.8820 + 10.2068i) q^{65} +(12.4749 - 2.26941i) q^{66} +(-3.53167 - 1.03699i) q^{67} +(3.12601 - 2.05515i) q^{68} +(0.830797 + 8.26497i) q^{69} +(-4.59678 + 1.37571i) q^{70} +(-1.09880 + 3.74217i) q^{71} +(8.30569 + 1.73651i) q^{72} +(-0.799168 - 0.513594i) q^{73} +(1.29101 + 8.65971i) q^{74} +(3.47034 - 8.29026i) q^{75} +(-2.35265 - 1.47766i) q^{76} +(-3.60317 - 4.15828i) q^{77} +(-7.37444 + 12.4701i) q^{78} +(4.02179 + 1.83669i) q^{79} +(12.6730 + 1.55419i) q^{80} +(8.12981 + 3.86085i) q^{81} +(-11.3377 - 1.57006i) q^{82} +(-14.2163 + 2.04399i) q^{83} +(-1.18599 - 3.48586i) q^{84} +(5.43117 - 2.48033i) q^{85} +(-3.01947 + 3.52144i) q^{86} +(1.45286 + 2.92978i) q^{87} +(4.34324 + 13.9822i) q^{88} +(-6.78673 + 7.83230i) q^{89} +(12.6777 + 4.76168i) q^{90} +6.28667 q^{91} +(-9.35752 + 2.10639i) q^{92} +(11.3562 - 7.82190i) q^{93} +(0.0545775 + 10.5102i) q^{94} +(-3.35100 - 2.90366i) q^{95} +(-0.830633 + 9.76269i) q^{96} +(-7.60162 - 1.09295i) q^{97} +(5.40380 - 6.30215i) q^{98} +(0.991893 + 15.4976i) 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

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