LMFDB - Embedded newform 552.2.bb.a.85.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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, 0, 14]))

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

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

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (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:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			85.5
Character	$\chi$	$=$	552.85
Dual form			552.2.bb.a.13.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36486 - 0.370358i) q^{2} +(0.540641 + 0.841254i) q^{3} +(1.72567 + 1.01097i) q^{4} +(0.808939 - 0.369430i) q^{5} +(-0.426333 - 1.34842i) q^{6} +(0.759802 - 0.223098i) q^{7} +(-1.98087 - 2.01895i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-1.36486 - 0.370358i) q^{2} +(0.540641 + 0.841254i) q^{3} +(1.72567 + 1.01097i) q^{4} +(0.808939 - 0.369430i) q^{5} +(-0.426333 - 1.34842i) q^{6} +(0.759802 - 0.223098i) q^{7} +(-1.98087 - 2.01895i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(-1.24091 + 0.204623i) q^{10} +(0.857262 - 0.742822i) q^{11} +(0.0824854 + 1.99830i) q^{12} +(1.80954 - 6.16272i) q^{13} +(-1.11965 + 0.0230985i) q^{14} +(0.748130 + 0.480794i) q^{15} +(1.95588 + 3.48920i) q^{16} +(0.262648 - 1.82676i) q^{17} +(0.903871 - 1.08767i) q^{18} +(6.71287 - 0.965165i) q^{19} +(1.76944 + 0.180299i) q^{20} +(0.598462 + 0.518570i) q^{21} +(-1.44515 + 0.696352i) q^{22} +(-4.76142 - 0.573480i) q^{23} +(0.627504 - 2.75794i) q^{24} +(-2.75640 + 3.18106i) q^{25} +(-4.75217 + 7.74106i) q^{26} +(-0.989821 + 0.142315i) q^{27} +(1.53671 + 0.383144i) q^{28} +(-0.980596 - 0.140988i) q^{29} +(-0.843025 - 0.933290i) q^{30} +(3.39749 + 2.18343i) q^{31} +(-1.37724 - 5.48664i) q^{32} +(1.08837 + 0.319575i) q^{33} +(-1.03503 + 2.39599i) q^{34} +(0.532214 - 0.461166i) q^{35} +(-1.63648 + 1.14975i) q^{36} +(6.20415 + 2.83334i) q^{37} +(-9.51957 - 1.16885i) q^{38} +(6.16272 - 1.80954i) q^{39} +(-2.34826 - 0.901410i) q^{40} +(0.147591 + 0.323180i) q^{41} +(-0.624759 - 0.929419i) q^{42} +(2.14419 + 3.33643i) q^{43} +(2.23032 - 0.415199i) q^{44} +0.889303i q^{45} +(6.28627 + 2.54615i) q^{46} +12.7492 q^{47} +(-1.87788 + 3.53179i) q^{48} +(-5.36125 + 3.44547i) q^{49} +(4.94022 - 3.32083i) q^{50} +(1.67876 - 0.766665i) q^{51} +(9.35299 - 8.80544i) q^{52} +(-2.70529 - 9.21338i) q^{53} +(1.40367 + 0.172348i) q^{54} +(0.419052 - 0.917596i) q^{55} +(-1.95549 - 1.09207i) q^{56} +(4.44120 + 5.12542i) q^{57} +(1.28616 + 0.555600i) q^{58} +(-2.36063 + 8.03958i) q^{59} +(0.804957 + 1.58603i) q^{60} +(4.32658 - 6.73229i) q^{61} +(-3.82843 - 4.23836i) q^{62} +(-0.112696 + 0.783819i) q^{63} +(-0.152282 + 7.99855i) q^{64} +(-0.812888 - 5.65376i) q^{65} +(-1.36712 - 0.839261i) q^{66} +(-9.22604 - 7.99441i) q^{67} +(2.30004 - 2.88685i) q^{68} +(-2.09178 - 4.31561i) q^{69} +(-0.897193 + 0.432317i) q^{70} +(1.86726 - 2.15493i) q^{71} +(2.65938 - 0.963165i) q^{72} +(0.472028 + 3.28303i) q^{73} +(-7.41843 - 6.16486i) q^{74} +(-4.16630 - 0.599023i) q^{75} +(12.5600 + 5.12096i) q^{76} +(0.485627 - 0.755651i) q^{77} +(-9.08141 + 0.187351i) q^{78} +(6.92887 + 2.03450i) q^{79} +(2.87120 + 2.09999i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-0.0817489 - 0.495756i) q^{82} +(11.7293 + 5.35658i) q^{83} +(0.508489 + 1.49991i) q^{84} +(-0.462392 - 1.57476i) q^{85} +(-1.69085 - 5.34787i) q^{86} +(-0.411543 - 0.901154i) q^{87} +(-3.19784 - 0.259330i) q^{88} +(1.13081 - 0.726727i) q^{89} +(0.329360 - 1.21377i) q^{90} -5.08615i q^{91} +(-7.63687 - 5.80329i) q^{92} +4.03860i q^{93} +(-17.4008 - 4.72176i) q^{94} +(5.07374 - 3.26070i) q^{95} +(3.87106 - 4.12491i) q^{96} +(-3.20667 - 7.02163i) q^{97} +(8.59339 - 2.71699i) q^{98} +(0.319575 + 1.08837i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	−1.36486	−	0.370358i	−0.965100	−	0.261882i
$2$	−1.36486	−	0.370358i	−0.965100	−	0.261882i
$3$	0.540641	+	0.841254i	0.312139	+	0.485698i
$3$	0.540641	+	0.841254i	0.312139	+	0.485698i
$4$	1.72567	+	1.01097i	0.862835	+	0.505485i
$5$	0.808939	−	0.369430i	0.361768	−	0.165214i	−0.226235	−	0.974073i	$-0.572642\pi$
$5$	0.808939	−	0.369430i	0.361768	−	0.165214i	0.588003	+	0.808859i	$0.299914\pi$
$6$	−0.426333	−	1.34842i	−0.174050	−	0.550491i
$7$	0.759802	−	0.223098i	0.287178	−	0.0843231i	−0.134971	−	0.990850i	$-0.543094\pi$
$7$	0.759802	−	0.223098i	0.287178	−	0.0843231i	0.422149	+	0.906526i	$0.361276\pi$
$8$	−1.98087	−	2.01895i	−0.700344	−	0.713805i
$9$	−0.415415	+	0.909632i	−0.138472	+	0.303211i
$10$	−1.24091	+	0.204623i	−0.392409	+	0.0647073i
$11$	0.857262	−	0.742822i	0.258474	−	0.223969i	−0.515978	−	0.856602i	$-0.672571\pi$
$11$	0.857262	−	0.742822i	0.258474	−	0.223969i	0.774452	+	0.632633i	$0.218026\pi$
$12$	0.0824854	+	1.99830i	0.0238115	+	0.576859i
$13$	1.80954	−	6.16272i	0.501876	−	1.70923i	−0.185249	−	0.982692i	$-0.559309\pi$
$13$	1.80954	−	6.16272i	0.501876	−	1.70923i	0.687125	−	0.726539i	$-0.258873\pi$
$14$	−1.11965	+	0.0230985i	−0.299238	+	0.00617333i
$15$	0.748130	+	0.480794i	0.193166	+	0.124140i
$16$	1.95588	+	3.48920i	0.488969	+	0.872301i
$17$	0.262648	−	1.82676i	0.0637014	−	0.443053i	−0.932863	−	0.360231i	$-0.882698\pi$
$17$	0.262648	−	1.82676i	0.0637014	−	0.443053i	0.996564	−	0.0828217i	$-0.0263932\pi$
$18$	0.903871	−	1.08767i	0.213045	−	0.256365i
$19$	6.71287	−	0.965165i	1.54004	−	0.221424i	0.680597	−	0.732658i	$-0.261720\pi$
$19$	6.71287	−	0.965165i	1.54004	−	0.221424i	0.859442	+	0.511234i	$0.170811\pi$
$20$	1.76944	+	0.180299i	0.395660	+	0.0403161i
$21$	0.598462	+	0.518570i	0.130595	+	0.113161i
$22$	−1.44515	+	0.696352i	−0.308107	+	0.148463i
$23$	−4.76142	−	0.573480i	−0.992825	−	0.119579i
$23$	−4.76142	−	0.573480i	−0.992825	−	0.119579i
$24$	0.627504	−	2.75794i	0.128089	−	0.562962i
$25$	−2.75640	+	3.18106i	−0.551280	+	0.636211i
$26$	−4.75217	+	7.74106i	−0.931977	+	1.51815i
$27$	−0.989821	+	0.142315i	−0.190491	+	0.0273885i
$28$	1.53671	+	0.383144i	0.290412	+	0.0724074i
$29$	−0.980596	−	0.140988i	−0.182092	−	0.0261809i	0.0506654	−	0.998716i	$-0.483866\pi$
$29$	−0.980596	−	0.140988i	−0.182092	−	0.0261809i	−0.232758	+	0.972535i	$0.574775\pi$
$30$	−0.843025	−	0.933290i	−0.153915	−	0.170395i
$31$	3.39749	+	2.18343i	0.610207	+	0.392156i	0.808935	−	0.587899i	$-0.200045\pi$
$31$	3.39749	+	2.18343i	0.610207	+	0.392156i	−0.198728	+	0.980055i	$0.563681\pi$
$32$	−1.37724	−	5.48664i	−0.243464	−	0.969910i
$33$	1.08837	+	0.319575i	0.189461	+	0.0556309i
$34$	−1.03503	+	2.39599i	−0.177506	+	0.410908i
$35$	0.532214	−	0.461166i	0.0899606	−	0.0779513i
$36$	−1.63648	+	1.14975i	−0.272747	+	0.191625i
$37$	6.20415	+	2.83334i	1.01996	+	0.465798i	0.853966	−	0.520329i	$-0.174191\pi$
$37$	6.20415	+	2.83334i	1.01996	+	0.465798i	0.165990	+	0.986127i	$0.446918\pi$
$38$	−9.51957	−	1.16885i	−1.54428	−	0.189613i
$39$	6.16272	−	1.80954i	0.986825	−	0.289758i
$40$	−2.34826	−	0.901410i	−0.371293	−	0.142525i
$41$	0.147591	+	0.323180i	0.0230499	+	0.0504722i	0.920807	−	0.390019i	$-0.127532\pi$
$41$	0.147591	+	0.323180i	0.0230499	+	0.0504722i	−0.897757	+	0.440491i	$0.854804\pi$
$42$	−0.624759	−	0.929419i	−0.0964024	−	0.143413i
$43$	2.14419	+	3.33643i	0.326986	+	0.508801i	0.965359	−	0.260927i	$-0.0840282\pi$
$43$	2.14419	+	3.33643i	0.326986	+	0.508801i	−0.638372	+	0.769728i	$0.720392\pi$
$44$	2.23032	−	0.415199i	0.336234	−	0.0625936i
$45$			0.889303i			0.132570i
$46$	6.28627	+	2.54615i	0.926859	+	0.375409i
$47$	12.7492			1.85966			0.929829	−	0.367991i	$-0.119954\pi$
$47$	12.7492			1.85966			0.929829	+	0.367991i	$0.119954\pi$
$48$	−1.87788	+	3.53179i	−0.271048	+	0.509771i
$49$	−5.36125	+	3.44547i	−0.765893	+	0.492209i
$50$	4.94022	−	3.32083i	0.698653	−	0.469637i
$51$	1.67876	−	0.766665i	0.235074	−	0.107355i
$52$	9.35299	−	8.80544i	1.29703	−	1.22109i
$53$	−2.70529	−	9.21338i	−0.371601	−	1.26556i	−0.907062	−	0.420996i	$-0.861681\pi$
$53$	−2.70529	−	9.21338i	−0.371601	−	1.26556i	0.535462	−	0.844559i	$-0.320138\pi$
$54$	1.40367	+	0.172348i	0.191016	+	0.0234537i
$55$	0.419052	−	0.917596i	0.0565049	−	0.123729i
$56$	−1.95549	−	1.09207i	−0.261314	−	0.145934i
$57$	4.44120	+	5.12542i	0.588252	+	0.678879i
$58$	1.28616	+	0.555600i	0.168881	+	0.0729539i
$59$	−2.36063	+	8.03958i	−0.307328	+	1.04666i	0.650544	+	0.759469i	$0.274541\pi$
$59$	−2.36063	+	8.03958i	−0.307328	+	1.04666i	−0.957872	+	0.287195i	$0.907277\pi$
$60$	0.804957	+	1.58603i	0.103920	+	0.204755i
$61$	4.32658	−	6.73229i	0.553962	−	0.861982i	−0.445483	−	0.895290i	$-0.646968\pi$
$61$	4.32658	−	6.73229i	0.553962	−	0.861982i	0.999445	+	0.0333085i	$0.0106044\pi$
$62$	−3.82843	−	4.23836i	−0.486212	−	0.538272i
$63$	−0.112696	+	0.783819i	−0.0141984	+	0.0987519i
$64$	−0.152282	+	7.99855i	−0.0190353	+	0.999819i
$65$	−0.812888	−	5.65376i	−0.100826	−	0.701263i
$66$	−1.36712	−	0.839261i	−0.168280	−	0.103306i
$67$	−9.22604	−	7.99441i	−1.12714	−	0.976673i	−0.127256	−	0.991870i	$-0.540617\pi$
$67$	−9.22604	−	7.99441i	−1.12714	−	0.976673i	−0.999885	+	0.0151969i	$0.995162\pi$
$68$	2.30004	−	2.88685i	0.278921	−	0.350082i
$69$	−2.09178	−	4.31561i	−0.251820	−	0.519538i
$70$	−0.897193	+	0.432317i	−0.107235	+	0.0516717i
$71$	1.86726	−	2.15493i	0.221603	−	0.255743i	−0.634052	−	0.773290i	$-0.718609\pi$
$71$	1.86726	−	2.15493i	0.221603	−	0.255743i	0.855655	+	0.517547i	$0.173155\pi$
$72$	2.65938	−	0.963165i	0.313411	−	0.113510i
$73$	0.472028	+	3.28303i	0.0552467	+	0.384249i	0.998620	+	0.0525163i	$0.0167241\pi$
$73$	0.472028	+	3.28303i	0.0552467	+	0.384249i	−0.943373	+	0.331733i	$0.892367\pi$
$74$	−7.41843	−	6.16486i	−0.862375	−	0.716650i
$75$	−4.16630	−	0.599023i	−0.481082	−	0.0691692i
$76$	12.5600	+	5.12096i	1.44073	+	0.587414i
$77$	0.485627	−	0.755651i	0.0553424	−	0.0861144i
$78$	−9.08141	+	0.187351i	−1.02827	+	0.0212133i
$79$	6.92887	+	2.03450i	0.779558	+	0.228899i	0.647218	−	0.762305i	$-0.275933\pi$
$79$	6.92887	+	2.03450i	0.779558	+	0.228899i	0.132341	+	0.991204i	$0.457751\pi$
$80$	2.87120	+	2.09999i	0.321010	+	0.234786i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−0.0817489	−	0.495756i	−0.00902765	−	0.0547470i
$83$	11.7293	+	5.35658i	1.28745	+	0.587961i	0.937232	−	0.348706i	$-0.113379\pi$
$83$	11.7293	+	5.35658i	1.28745	+	0.587961i	0.350223	+	0.936667i	$0.386106\pi$
$84$	0.508489	+	1.49991i	0.0554807	+	0.163653i
$85$	−0.462392	−	1.57476i	−0.0501535	−	0.170807i
$86$	−1.69085	−	5.34787i	−0.182329	−	0.576676i
$87$	−0.411543	−	0.901154i	−0.0441221	−	0.0966139i
$88$	−3.19784	−	0.259330i	−0.340891	−	0.0276446i
$89$	1.13081	−	0.726727i	0.119865	−	0.0770329i	−0.479334	−	0.877632i	$-0.659122\pi$
$89$	1.13081	−	0.726727i	0.119865	−	0.0770329i	0.599200	+	0.800600i	$0.295485\pi$
$90$	0.329360	−	1.21377i	0.0347176	−	0.127943i
$91$		−	5.08615i		−	0.533174i
$92$	−7.63687	−	5.80329i	−0.796199	−	0.605035i
$93$			4.03860i			0.418783i
$94$	−17.4008	−	4.72176i	−1.79476	−	0.487012i
$95$	5.07374	−	3.26070i	0.520555	−	0.334540i
$96$	3.87106	−	4.12491i	0.395089	−	0.420997i
$97$	−3.20667	−	7.02163i	−0.325588	−	0.712939i	0.674081	−	0.738657i	$-0.264540\pi$
$97$	−3.20667	−	7.02163i	−0.325588	−	0.712939i	−0.999669	+	0.0257186i	$0.991813\pi$
$98$	8.59339	−	2.71699i	0.868064	−	0.274457i
$99$	0.319575	+	1.08837i	0.0321185	+	0.109386i
$100$	−7.97259	+	2.70281i	−0.797259	+	0.270281i
$101$	−7.79464	−	3.55970i	−0.775596	−	0.354203i	−0.0120259	−	0.999928i	$-0.503828\pi$
$101$	−7.79464	−	3.55970i	−0.775596	−	0.354203i	−0.763570	+	0.645725i	$0.776555\pi$
$102$	−2.57521	+	0.424646i	−0.254984	+	0.0420462i
$103$	5.36254	+	6.18870i	0.528386	+	0.609790i	0.955711	−	0.294308i	$-0.0950892\pi$
$103$	5.36254	+	6.18870i	0.528386	+	0.609790i	−0.427324	+	0.904098i	$0.640544\pi$
$104$	−16.0267	+	8.55421i	−1.57154	+	0.838809i
$105$	0.675695	+	0.198402i	0.0659410	+	0.0193620i
$106$	0.280093	+	13.5769i	0.0272050	+	1.31870i
$107$	−5.94171	+	9.24548i	−0.574406	+	0.893794i	−0.999938	−	0.0111498i	$-0.996451\pi$
$107$	−5.94171	+	9.24548i	−0.574406	+	0.893794i	0.425531	+	0.904944i	$0.360087\pi$
$108$	−1.85198	−	0.755092i	−0.178207	−	0.0726587i
$109$	−18.4196	−	2.64835i	−1.76428	−	0.253666i	−0.817589	−	0.575802i	$-0.804690\pi$
$109$	−18.4196	−	2.64835i	−1.76428	−	0.253666i	−0.946693	+	0.322136i	$0.895599\pi$
$110$	−0.911785	+	1.09719i	−0.0869352	+	0.104613i
$111$	0.970659	+	6.75108i	0.0921308	+	0.640784i
$112$	2.26451	+	2.21475i	0.213976	+	0.209274i
$113$	−10.4783	+	12.0926i	−0.985712	+	1.13757i	0.00477784	+	0.999989i	$0.498479\pi$
$113$	−10.4783	+	12.0926i	−0.985712	+	1.13757i	−0.990490	+	0.137584i	$0.956066\pi$
$114$	−4.16337	−	8.64030i	−0.389935	−	0.809238i
$115$	−4.06356	+	1.29510i	−0.378929	+	0.120769i
$116$	−1.54965	−	1.23465i	−0.143881	−	0.114635i
$117$	4.85410	+	4.20610i	0.448762	+	0.388854i
$118$	6.19944	−	10.0986i	0.570705	−	0.929651i
$119$	−0.207985	−	1.44657i	−0.0190660	−	0.132607i
$120$	−0.511254	−	2.46282i	−0.0466709	−	0.224824i
$121$	−1.38235	+	9.61445i	−0.125668	+	0.874041i
$122$	−8.39852	+	7.58624i	−0.760367	+	0.686826i
$123$	−0.192082	+	0.298886i	−0.0173195	+	0.0269496i
$124$	3.65556	+	7.20264i	0.328279	+	0.646816i
$125$	−2.30731	+	7.85798i	−0.206372	+	0.702839i
$126$	0.444107	−	1.02806i	0.0395642	−	0.0915871i
$127$	−6.22427	−	7.18319i	−0.552315	−	0.637405i	0.409106	−	0.912487i	$-0.365841\pi$
$127$	−6.22427	−	7.18319i	−0.552315	−	0.637405i	−0.961421	+	0.275082i	$0.911295\pi$
$128$	3.17017	−	10.8605i	0.280206	−	0.959940i
$129$	−1.64755	+	3.60762i	−0.145058	+	0.317633i
$130$	−0.984437	+	8.01764i	−0.0863409	+	0.703193i
$131$	1.62113	+	5.52106i	0.141639	+	0.482377i	0.999504	−	0.0314977i	$-0.0100277\pi$
$131$	1.62113	+	5.52106i	0.141639	+	0.482377i	−0.857865	+	0.513875i	$0.828210\pi$
$132$	1.55509	+	1.65179i	0.135353	+	0.143770i
$133$	4.88513	−	2.23096i	0.423594	−	0.193449i
$134$	9.63144	+	14.3282i	0.832030	+	1.23777i
$135$	−0.748130	+	0.480794i	−0.0643888	+	0.0413801i
$136$	−4.20839	+	3.08830i	−0.360867	+	0.264819i
$137$	−6.82572			−0.583161			−0.291580	−	0.956546i	$-0.594181\pi$
$137$	−6.82572			−0.583161			−0.291580	+	0.956546i	$0.594181\pi$
$138$	1.25666	+	6.66489i	0.106974	+	0.567353i
$139$		−	2.95143i		−	0.250337i	−0.992135	−	0.125169i	$-0.960053\pi$
$139$		−	2.95143i		−	0.250337i	0.992135	−	0.125169i	$-0.0399471\pi$
$140$	1.38465	−	0.257768i	0.117024	−	0.0217854i
$141$	6.89273	+	10.7253i	0.580472	+	0.903233i
$142$	−3.34663	+	2.24962i	−0.280843	+	0.188784i
$143$	−3.02655	−	6.62723i	−0.253093	−	0.554197i
$144$	−3.98639	+	0.329661i	−0.332199	+	0.0274717i
$145$	−0.845328	+	0.248211i	−0.0702006	+	0.0206128i
$146$	0.571643	−	4.65568i	0.0473095	−	0.385307i
$147$	−5.79702	−	2.64741i	−0.478130	−	0.218355i
$148$	7.84189	+	11.1616i	0.644600	+	0.917479i
$149$	−13.1651	+	11.4076i	−1.07853	+	0.934550i	−0.998063	−	0.0622079i	$-0.980186\pi$
$149$	−13.1651	+	11.4076i	−1.07853	+	0.934550i	−0.0804645	+	0.996757i	$0.525640\pi$
$150$	5.46455	+	2.36060i	0.446178	+	0.192742i
$151$	2.09304	+	0.614571i	0.170329	+	0.0500131i	0.365785	−	0.930699i	$-0.380801\pi$
$151$	2.09304	+	0.614571i	0.170329	+	0.0500131i	−0.195456	+	0.980712i	$0.562619\pi$
$152$	−15.2460	−	11.6411i	−1.23661	−	0.944214i
$153$	1.55257	+	0.997774i	0.125518	+	0.0806653i
$154$	−0.942673	+	0.851500i	−0.0759628	+	0.0686158i
$155$	3.55498	+	0.511130i	0.285543	+	0.0410549i
$156$	12.4642	+	3.10766i	0.997936	+	0.248812i
$157$	4.42117	−	0.635668i	0.352848	−	0.0507318i	0.0363878	−	0.999338i	$-0.488415\pi$
$157$	4.42117	−	0.635668i	0.352848	−	0.0507318i	0.316460	+	0.948606i	$0.397506\pi$
$158$	−8.70342	−	5.34296i	−0.692407	−	0.425063i
$159$	6.28820	−	7.25697i	0.498687	−	0.575515i
$160$	−3.14103	−	3.92956i	−0.248320	−	0.310659i
$161$	−3.74568	+	0.626532i	−0.295201	+	0.0493776i
$162$	0.613894	+	1.27402i	0.0482321	+	0.100097i
$163$	−13.3038	−	11.5278i	−1.04204	−	0.902930i	−0.0466534	−	0.998911i	$-0.514856\pi$
$163$	−13.3038	−	11.5278i	−1.04204	−	0.902930i	−0.995383	+	0.0959813i	$0.969401\pi$
$164$	−0.0720313	+	0.706912i	−0.00562470	+	0.0552005i
$165$	0.998487	−	0.143561i	0.0777321	−	0.0111762i
$166$	−14.0249	−	11.6550i	−1.08855	−	0.904603i
$167$	−0.219565	+	1.52711i	−0.0169905	+	0.118171i	−0.996552	−	0.0829754i	$-0.973558\pi$
$167$	−0.219565	+	1.52711i	−0.0169905	+	0.118171i	0.979561	+	0.201147i	$0.0644668\pi$
$168$	−0.138512	−	2.23548i	−0.0106864	−	0.172471i
$169$	−23.7684	−	15.2750i	−1.82834	−	1.17500i
$170$	0.0478738	+	2.32058i	0.00367175	+	0.177980i
$171$	−1.91068	+	6.50719i	−0.146114	+	0.497617i
$172$	0.327139	+	7.92530i	0.0249441	+	0.604298i
$173$	−0.419528	+	0.363523i	−0.0318961	+	0.0276382i	−0.670663	−	0.741762i	$-0.733990\pi$
$173$	−0.419528	+	0.363523i	−0.0318961	+	0.0276382i	0.638767	+	0.769400i	$0.279445\pi$
$174$	0.227949	+	1.38236i	0.0172807	+	0.104797i
$175$	−1.38463	+	3.03192i	−0.104668	+	0.229192i
$176$	4.26856	+	1.53829i	0.321754	+	0.115953i
$177$	−8.03958	+	2.36063i	−0.604292	+	0.177436i
$178$	−1.81254	+	0.573075i	−0.135856	+	0.0429538i
$179$	14.1844	−	6.47779i	1.06019	−	0.484173i	0.192510	−	0.981295i	$-0.438337\pi$
$179$	14.1844	−	6.47779i	1.06019	−	0.484173i	0.867680	+	0.497123i	$0.165610\pi$
$180$	−0.899060	+	1.53464i	−0.0670119	+	0.114386i
$181$	−0.732616	−	1.13997i	−0.0544549	−	0.0847335i	0.812959	−	0.582322i	$-0.197856\pi$
$181$	−0.732616	−	1.13997i	−0.0544549	−	0.0847335i	−0.867413	+	0.497588i	$0.834219\pi$
$182$	−1.88370	+	6.94187i	−0.139629	+	0.514566i
$183$	8.00269			0.591576
$184$	8.27394	+	10.7490i	0.609963	+	0.792430i
$185$	6.06550			0.445944
$186$	1.49573	−	5.51211i	0.109672	−	0.404168i
$187$	−1.13180	−	1.76111i	−0.0827651	−	0.128785i
$188$	22.0009	+	12.8890i	1.60458	+	0.940030i
$189$	−0.720318	+	0.328958i	−0.0523954	+	0.0239282i
$190$	−8.13256	+	2.57129i	−0.589998	+	0.186541i
$191$	−11.5684	+	3.39679i	−0.837061	+	0.245783i	−0.672048	−	0.740508i	$-0.734585\pi$
$191$	−11.5684	+	3.39679i	−0.837061	+	0.245783i	−0.165014	+	0.986291i	$0.552767\pi$
$192$	−6.81114	+	4.19623i	−0.491552	+	0.302837i
$193$	−5.46934	+	11.9762i	−0.393692	+	0.862065i	0.604179	+	0.796848i	$0.293501\pi$
$193$	−5.46934	+	11.9762i	−0.393692	+	0.862065i	−0.997871	+	0.0652166i	$0.979226\pi$
$194$	1.77613	+	10.7711i	0.127519	+	0.773323i
$195$	4.31677	−	3.74050i	0.309130	−	0.267863i
$196$	−12.7350	+	0.525674i	−0.909644	+	0.0375481i
$197$	5.84775	−	19.9156i	0.416635	−	1.41893i	−0.437661	−	0.899140i	$-0.644193\pi$
$197$	5.84775	−	19.9156i	0.416635	−	1.41893i	0.854295	−	0.519788i	$-0.173989\pi$
$198$	−0.0330872	−	1.60383i	−0.00235141	−	0.113979i
$199$	−1.82084	−	1.17018i	−0.129076	−	0.0829519i	0.474510	−	0.880250i	$-0.342625\pi$
$199$	−1.82084	−	1.17018i	−0.129076	−	0.0829519i	−0.603585	+	0.797298i	$0.706262\pi$
$200$	11.8825	−	0.736246i	0.840217	−	0.0520604i
$201$	1.73735	−	12.0835i	0.122543	−	0.852308i
$202$	9.32022	+	7.74528i	0.655768	+	0.544956i
$203$	−0.776513	+	0.111646i	−0.0545005	+	0.00783600i
$204$	3.67207	+	0.374168i	0.257096	+	0.0261970i
$205$	0.238785	+	0.206908i	0.0166774	+	0.0144511i
$206$	−5.02707	−	10.4327i	−0.350252	−	0.726884i
$207$	2.49962	−	4.09291i	0.173736	−	0.284477i
$208$	25.0422	−	5.73968i	1.73637	−	0.397975i
$209$	5.03775	−	5.81387i	0.348468	−	0.402154i
$210$	−0.848747	−	0.521039i	−0.0585691	−	0.0359551i
$211$	−11.1942	+	1.60949i	−0.770643	+	0.110802i	−0.516410	−	0.856341i	$-0.672732\pi$
$211$	−11.1942	+	1.60949i	−0.770643	+	0.110802i	−0.254233	+	0.967143i	$0.581823\pi$
$212$	4.64601	−	18.6342i	0.319090	−	1.27980i
$213$	2.82236	+	0.405794i	0.193385	+	0.0278045i
$214$	11.5337	−	10.4182i	0.788428	−	0.712173i
$215$	2.96710	+	1.90684i	0.202354	+	0.130045i
$216$	2.24804	+	1.71649i	0.152960	+	0.116792i
$217$	3.06854	+	0.901004i	0.208306	+	0.0611641i
$218$	24.1594	+	10.4365i	1.63628	+	0.706847i
$219$	−2.50666	+	2.17203i	−0.169384	+	0.146772i
$220$	1.65081	−	1.15982i	0.111297	−	0.0781950i
$221$	−10.7825	−	4.92421i	−0.725310	−	0.331238i
$222$	1.17550	−	9.57375i	0.0788946	−	0.642548i
$223$	−16.8570	+	4.94966i	−1.12883	+	0.331453i	−0.792246	−	0.610201i	$-0.791089\pi$
$223$	−16.8570	+	4.94966i	−1.12883	+	0.331453i	−0.336580	+	0.941655i	$0.609270\pi$
$224$	−2.27049	−	3.86150i	−0.151703	−	0.258007i
$225$	−1.74854	−	3.82877i	−0.116569	−	0.255251i
$226$	18.7799	−	12.6239i	1.24922	−	0.839730i
$227$	4.30887	+	6.70473i	0.285989	+	0.445008i	0.954290	−	0.298883i	$-0.0966142\pi$
$227$	4.30887	+	6.70473i	0.285989	+	0.445008i	−0.668300	+	0.743892i	$0.732978\pi$
$228$	2.48240	+	13.3347i	0.164401	+	0.883113i
$229$			9.51660i			0.628875i	0.949278	+	0.314437i	$0.101816\pi$
$229$			9.51660i			0.628875i	−0.949278	+	0.314437i	$0.898184\pi$
$230$	6.02583	−	0.262658i	0.397331	−	0.0173192i
$231$	0.898244			0.0591001
$232$	1.65779	+	2.25905i	0.108839	+	0.148314i
$233$	20.4500	−	13.1424i	1.33973	−	0.860989i	0.342804	−	0.939407i	$-0.388623\pi$
$233$	20.4500	−	13.1424i	1.33973	−	0.860989i	0.996921	+	0.0784178i	$0.0249868\pi$
$234$	−5.06739	−	7.53848i	−0.331266	−	0.492806i
$235$	10.3133	−	4.70993i	0.672766	−	0.307242i
$236$	−12.2014	+	11.4871i	−0.794247	+	0.747748i
$237$	2.03450	+	6.92887i	0.132155	+	0.450078i
$238$	−0.251878	+	2.05139i	−0.0163268	+	0.132972i
$239$	−12.7572	+	27.9343i	−0.825193	+	1.80692i	−0.306814	+	0.951770i	$0.599263\pi$
$239$	−12.7572	+	27.9343i	−0.825193	+	1.80692i	−0.518379	+	0.855151i	$0.673464\pi$
$240$	−0.214338	+	3.55075i	−0.0138354	+	0.229200i
$241$	−12.4830	−	14.4061i	−0.804098	−	0.927978i	0.194501	−	0.980902i	$-0.437691\pi$
$241$	−12.4830	−	14.4061i	−0.804098	−	0.927978i	−0.998599	+	0.0529241i	$0.983146\pi$
$242$	5.44749	−	12.6104i	0.350178	−	0.810626i
$243$	0.281733	−	0.959493i	0.0180732	−	0.0615515i
$244$	14.2724	−	7.24367i	0.913697	−	0.463729i
$245$	−3.06406	+	4.76778i	−0.195756	+	0.304602i
$246$	0.372859	−	0.336797i	0.0237726	−	0.0214734i
$247$	6.19915	−	43.1161i	0.394443	−	2.74341i
$248$	−2.32176	−	11.1844i	−0.147432	−	0.710213i
$249$	1.83508	+	12.7633i	0.116294	+	0.808840i
$250$	6.05941	−	9.87049i	0.383231	−	0.624265i
$251$	21.6251	+	18.7383i	1.36497	+	1.18275i	0.963763	+	0.266760i	$0.0859530\pi$
$251$	21.6251	+	18.7383i	1.36497	+	1.18275i	0.401202	+	0.915989i	$0.368592\pi$
$252$	−0.986894	+	1.23868i	−0.0621685	+	0.0780295i
$253$	−4.50778	+	3.04526i	−0.283402	+	0.191454i
$254$	5.83489	+	12.1092i	0.366114	+	0.759801i
$255$	1.07479	−	1.24037i	0.0673058	−	0.0776750i
$256$	−8.34909	+	13.6489i	−0.521818	+	0.853057i
$257$	−2.66700	−	18.5494i	−0.166363	−	1.15708i	−0.886324	−	0.463066i	$-0.846749\pi$
$257$	−2.66700	−	18.5494i	−0.166363	−	1.15708i	0.719961	−	0.694015i	$-0.244160\pi$
$258$	3.58477	−	4.31371i	0.223178	−	0.268560i
$259$	5.34604	+	0.768644i	0.332187	+	0.0477612i
$260$	4.31301	−	10.5783i	0.267481	−	0.656041i
$261$	0.535602	−	0.833413i	0.0331529	−	0.0515870i
$262$	−0.167844	−	8.13586i	−0.0103694	−	0.502635i
$263$	8.63886	+	2.53660i	0.532695	+	0.156413i	0.537008	−	0.843577i	$-0.319555\pi$
$263$	8.63886	+	2.53660i	0.532695	+	0.156413i	−0.00431259	+	0.999991i	$0.501373\pi$
$264$	−1.51072	−	2.83040i	−0.0929786	−	0.174199i
$265$	−5.59212	−	6.45365i	−0.343521	−	0.396444i
$266$	−7.49376	+	1.23570i	−0.459472	+	0.0757658i
$267$	1.22272	+	0.558399i	0.0748294	+	0.0341735i
$268$	−7.83900	−	23.1230i	−0.478843	−	1.41246i
$269$	−0.511330	−	1.74143i	−0.0311764	−	0.106177i	0.942435	−	0.334389i	$-0.108530\pi$
$269$	−0.511330	−	1.74143i	−0.0311764	−	0.106177i	−0.973611	+	0.228213i	$0.926712\pi$
$270$	1.19916	−	0.379139i	0.0729783	−	0.0230737i
$271$	−7.75032	−	16.9708i	−0.470799	−	1.03090i	−0.984892	−	0.173171i	$-0.944599\pi$
$271$	−7.75032	−	16.9708i	−0.470799	−	1.03090i	0.514093	−	0.857734i	$-0.328129\pi$
$272$	6.88763	−	2.65648i	0.417624	−	0.161073i
$273$	4.27874	−	2.74978i	0.258961	−	0.166424i
$274$	9.31613	+	2.52796i	0.562808	+	0.152719i
$275$			4.77451i			0.287914i
$276$	0.753236	−	9.56204i	0.0453395	−	0.575567i
$277$		−	5.85173i		−	0.351596i	−0.984426	−	0.175798i	$-0.943749\pi$
$277$		−	5.85173i		−	0.351596i	0.984426	−	0.175798i	$-0.0562506\pi$
$278$	−1.09308	+	4.02828i	−0.0655589	+	0.241600i
$279$	−3.39749	+	2.18343i	−0.203402	+	0.130719i
$280$	−1.98532	−	0.161000i	−0.118645	−	0.00962157i
$281$	1.99010	+	4.35771i	0.118719	+	0.259959i	0.959657	−	0.281172i	$-0.0907233\pi$
$281$	1.99010	+	4.35771i	0.118719	+	0.259959i	−0.840938	+	0.541132i	$0.817996\pi$
$282$	−5.43539	−	17.1913i	−0.323673	−	1.02372i
$283$	6.29052	+	21.4235i	0.373932	+	1.27350i	0.904725	+	0.425995i	$0.140076\pi$
$283$	6.29052	+	21.4235i	0.373932	+	1.27350i	−0.530793	+	0.847502i	$0.678106\pi$
$284$	5.40084	−	1.83096i	0.320481	−	0.108647i
$285$	5.48615	+	2.50544i	0.324971	+	0.148409i
$286$	1.67637	+	10.1661i	0.0991258	+	0.601136i
$287$	0.184241	+	0.212625i	0.0108754	+	0.0125509i
$288$	5.56295	+	1.02645i	0.327800	+	0.0604842i
$289$	13.0433	+	3.82987i	0.767255	+	0.225286i
$290$	1.24568	−	0.0256985i	0.0731488	−	0.00150907i
$291$	4.17332	−	6.49381i	0.244644	−	0.380674i
$292$	−2.50448	+	6.14263i	−0.146563	+	0.359470i
$293$	−6.86929	−	0.987655i	−0.401308	−	0.0576994i	−0.0612941	−	0.998120i	$-0.519523\pi$
$293$	−6.86929	−	0.987655i	−0.401308	−	0.0576994i	−0.340014	+	0.940420i	$0.610432\pi$
$294$	6.93162	+	5.76031i	0.404260	+	0.335948i
$295$	1.06045	+	7.37561i	0.0617420	+	0.429425i
$296$	−6.56927	−	18.1383i	−0.381831	−	1.05427i
$297$	−0.742822	+	0.857262i	−0.0431029	+	0.0497434i
$298$	22.1934	−	10.6940i	1.28563	−	0.619486i
$299$	−12.1502	+	28.3056i	−0.702662	+	1.63695i
$300$	−6.58406	−	5.24572i	−0.380131	−	0.302862i
$301$	2.37351	+	2.05666i	0.136807	+	0.118544i
$302$	−2.62909	−	1.61397i	−0.151287	−	0.0928738i
$303$	−1.21950	−	8.48179i	−0.0700583	−	0.487266i
$304$	16.4972	+	21.5348i	0.946180	+	1.23511i
$305$	1.01283	−	7.04438i	0.0579944	−	0.403360i
$306$	−1.74950	−	1.93682i	−0.100012	−	0.110721i
$307$	13.2337	−	20.5921i	0.755288	−	1.17525i	−0.224355	−	0.974507i	$-0.572028\pi$
$307$	13.2337	−	20.5921i	0.755288	−	1.17525i	0.979644	−	0.200744i	$-0.0643360\pi$
$308$	1.60197	−	0.813050i	0.0912809	−	0.0463278i
$309$	−2.30706	+	7.85711i	−0.131244	+	0.446976i
$310$	−4.66275	−	2.01423i	−0.264826	−	0.114401i
$311$	5.03456	+	5.81019i	0.285484	+	0.329466i	0.880319	−	0.474382i	$-0.157328\pi$
$311$	5.03456	+	5.81019i	0.285484	+	0.329466i	−0.594836	+	0.803847i	$0.702783\pi$
$312$	−15.8609	−	8.85773i	−0.897948	−	0.501470i
$313$	−9.61647	+	21.0571i	−0.543555	+	1.19022i	0.416172	+	0.909286i	$0.363371\pi$
$313$	−9.61647	+	21.0571i	−0.543555	+	1.19022i	−0.959727	+	0.280934i	$0.909356\pi$
$314$	−6.26969	−	0.769817i	−0.353819	−	0.0434433i
$315$	0.198402	+	0.675695i	0.0111787	+	0.0380711i
$316$	9.90012	+	10.5158i	0.556925	+	0.591557i
$317$	19.0697	−	8.70884i	1.07106	−	0.489137i	0.199739	−	0.979849i	$-0.435990\pi$
$317$	19.0697	−	8.70884i	1.07106	−	0.489137i	0.871322	+	0.490712i	$0.163263\pi$
$318$	−11.2702	+	7.57584i	−0.632000	+	0.424832i
$319$	−0.945357	+	0.607544i	−0.0529298	+	0.0340159i
$320$	2.83172	+	6.52660i	0.158298	+	0.364848i
$321$	−10.9901			−0.613409
$322$	5.34436	+	0.532114i	0.297829	+	0.0296535i
$323$		−	12.5163i		−	0.696424i
$324$	−0.366033	−	1.96622i	−0.0203352	−	0.109234i
$325$	14.6161	+	22.7432i	0.810758	+	1.26156i
$326$	13.8884	+	20.6610i	0.769208	+	1.14431i
$327$	−7.73048	−	16.9274i	−0.427497	−	0.936087i
$328$	0.360123	−	0.938156i	0.0198844	−	0.0518010i
$329$	9.68685	−	2.84432i	0.534053	−	0.156812i
$330$	−1.41596	−	0.173857i	−0.0779461	−	0.00957053i
$331$	−20.5852	−	9.40095i	−1.13147	−	0.516723i	−0.240435	−	0.970665i	$-0.577290\pi$
$331$	−20.5852	−	9.40095i	−1.13147	−	0.516723i	−0.891031	+	0.453942i	$0.850017\pi$
$332$	14.8255	+	21.1016i	0.813656	+	1.15810i
$333$	−5.15459	+	4.46648i	−0.282470	+	0.244762i
$334$	0.865253	−	2.00297i	0.0473445	−	0.109598i
$335$	−10.4167	−	3.05861i	−0.569124	−	0.167110i
$336$	−0.638879	+	3.10242i	−0.0348537	+	0.169251i
$337$	8.25875	+	5.30757i	0.449883	+	0.289122i	0.745897	−	0.666062i	$-0.232021\pi$
$337$	8.25875	+	5.30757i	0.449883	+	0.289122i	−0.296014	+	0.955184i	$0.595658\pi$
$338$	26.7832	+	29.6510i	1.45682	+	1.61280i
$339$	−15.8379	−	2.27714i	−0.860196	−	0.123678i
$340$	0.794103	−	3.18499i	0.0430663	−	0.172730i
$341$	4.53444	−	0.651954i	0.245554	−	0.0353053i
$342$	5.01780	−	8.17375i	0.271331	−	0.441986i
$343$	−6.93480	+	8.00319i	−0.374444	+	0.432132i
$344$	2.48870	−	10.9381i	0.134181	−	0.589740i
$345$	−3.28643	−	2.71830i	−0.176936	−	0.146348i
$346$	0.707230	−	0.340782i	0.0380209	−	0.0183206i
$347$	−14.4921	−	12.5575i	−0.777976	−	0.674120i	0.172468	−	0.985015i	$-0.444826\pi$
$347$	−14.4921	−	12.5575i	−0.777976	−	0.674120i	−0.950444	+	0.310895i	$0.899371\pi$
$348$	0.200852	−	1.97115i	0.0107668	−	0.105665i
$349$	−0.0289926	+	0.00416851i	−0.00155194	+	0.000223135i	−0.143091	−	0.989710i	$-0.545704\pi$
$349$	−0.0289926	+	0.00416851i	−0.00155194	+	0.000223135i	0.141539	+	0.989933i	$0.454795\pi$
$350$	3.01272	−	3.62533i	0.161037	−	0.193782i
$351$	−0.914073	+	6.35752i	−0.0487896	+	0.339339i
$352$	−5.25625	−	3.68044i	−0.280159	−	0.196168i
$353$	−11.1652	−	7.17541i	−0.594262	−	0.381909i	0.208665	−	0.977987i	$-0.433088\pi$
$353$	−11.1652	−	7.17541i	−0.594262	−	0.381909i	−0.802926	+	0.596079i	$0.796725\pi$
$354$	11.8472	−	0.244408i	0.629669	−	0.0129902i
$355$	0.714401	−	2.43303i	0.0379165	−	0.129132i
$356$	2.68610	−	0.110876i	0.142363	−	0.00587644i
$357$	1.10449	−	0.957042i	0.0584556	−	0.0506520i
$358$	−21.7587	+	3.58796i	−1.14999	+	0.189630i
$359$	−4.40130	+	9.63751i	−0.232292	+	0.508648i	−0.989501	−	0.144524i	$-0.953835\pi$
$359$	−4.40130	+	9.63751i	−0.232292	+	0.508648i	0.757209	+	0.653172i	$0.226562\pi$
$360$	1.79546	−	1.76160i	0.0946288	−	0.0928443i
$361$	25.9008	−	7.60515i	1.36320	−	0.400271i
$362$	0.577719	+	1.82723i	0.0303642	+	0.0960371i
$363$	−8.83554	+	4.03506i	−0.463746	+	0.211786i
$364$	5.14195	−	8.77702i	0.269511	−	0.460041i
$365$	1.59469	+	2.48139i	0.0834699	+	0.129882i
$366$	−10.9225	−	2.96386i	−0.570930	−	0.154923i
$367$	−14.5413			−0.759051			−0.379525	−	0.925181i	$-0.623913\pi$
$367$	−14.5413			−0.759051			−0.379525	+	0.925181i	$0.623913\pi$
$368$	−7.31176	−	17.7352i	−0.381152	−	0.924512i
$369$	−0.355286			−0.0184955
$370$	−8.27854	−	2.24640i	−0.430381	−	0.116785i
$371$	−4.11098	−	6.39680i	−0.213431	−	0.332105i
$372$	−4.08291	+	6.96929i	−0.211689	+	0.361341i
$373$	17.5388	−	8.00970i	0.908124	−	0.414726i	0.0941036	−	0.995562i	$-0.470001\pi$
$373$	17.5388	−	8.00970i	0.908124	−	0.414726i	0.814021	+	0.580836i	$0.197274\pi$
$374$	0.892499	+	2.82283i	0.0461501	+	0.145965i
$375$	−7.85798	+	2.30731i	−0.405784	+	0.119149i
$376$	−25.2545	−	25.7399i	−1.30240	−	1.32743i
$377$	−2.64330	+	5.78802i	−0.136137	+	0.298098i
$378$	1.10496	−	0.182206i	0.0568332	−	0.00937165i
$379$	−19.5646	+	16.9528i	−1.00496	+	0.870806i	−0.991631	−	0.129105i	$-0.958790\pi$
$379$	−19.5646	+	16.9528i	−1.00496	+	0.870806i	−0.0133331	+	0.999911i	$0.504244\pi$
$380$	12.0521	−	0.497484i	0.618259	−	0.0255204i
$381$	2.67779	−	9.11972i	0.137187	−	0.467217i
$382$	17.0473	−	0.351687i	0.872214	−	0.0179939i
$383$	−7.35781	−	4.72858i	−0.375967	−	0.241619i	0.338987	−	0.940791i	$-0.389916\pi$
$383$	−7.35781	−	4.72858i	−0.375967	−	0.241619i	−0.714954	+	0.699172i	$0.753552\pi$
$384$	10.8503	−	3.20470i	0.553704	−	0.163539i
$385$	0.113683	−	0.790681i	0.00579381	−	0.0402968i
$386$	11.9003	−	14.3202i	0.605712	−	0.728878i
$387$	−3.92565	+	0.564424i	−0.199552	+	0.0286913i
$388$	1.56500	−	15.3589i	0.0794510	−	0.779729i
$389$	−4.84591	−	4.19901i	−0.245697	−	0.212898i	0.523302	−	0.852147i	$-0.324700\pi$
$389$	−4.84591	−	4.19901i	−0.245697	−	0.212898i	−0.769000	+	0.639249i	$0.779245\pi$
$390$	−7.27709	+	3.50650i	−0.368490	+	0.177559i
$391$	−2.29818	+	8.54733i	−0.116224	+	0.432257i
$392$	17.5762	+	3.99904i	0.887730	+	0.201982i
$393$	−3.76816	+	4.34869i	−0.190079	+	0.219362i
$394$	−15.3572	+	25.0162i	−0.773686	+	1.26030i
$395$	6.35663	−	0.913946i	0.319837	−	0.0459856i
$396$	−0.548831	+	2.20125i	−0.0275798	+	0.110617i
$397$	−6.69573	−	0.962700i	−0.336049	−	0.0483165i	−0.0277750	−	0.999614i	$-0.508842\pi$
$397$	−6.69573	−	0.962700i	−0.336049	−	0.0483165i	−0.308274	+	0.951298i	$0.599751\pi$
$398$	2.05180	+	2.27149i	0.102847	+	0.113859i
$399$	4.51791	+	2.90348i	0.226178	+	0.145356i
$400$	−16.4905	−	3.39589i	−0.824527	−	0.169794i
$401$	34.1537	+	10.0284i	1.70555	+	0.500796i	0.981905	−	0.189373i	$-0.0606455\pi$
$401$	34.1537	+	10.0284i	1.70555	+	0.500796i	0.723648	+	0.690169i	$0.242464\pi$
$402$	−6.84647	+	15.8489i	−0.341471	+	0.790470i
$403$	19.6038	−	16.9868i	0.976533	−	0.846171i
$404$	−9.85224	−	14.0230i	−0.490167	−	0.697671i
$405$	−0.808939	−	0.369430i	−0.0401965	−	0.0183571i
$406$	1.10118	+	0.135207i	0.0546506	+	0.00671021i
$407$	7.42325	−	2.17966i	0.367957	−	0.108042i
$408$	−4.87327	−	1.87066i	−0.241263	−	0.0926116i
$409$	11.9733	+	26.2178i	0.592040	+	1.29639i	0.934202	+	0.356746i	$0.116114\pi$
$409$	11.9733	+	26.2178i	0.592040	+	1.29639i	−0.342161	+	0.939641i	$0.611159\pi$
$410$	−0.249277	−	0.370835i	−0.0123109	−	0.0183143i
$411$	−3.69026	−	5.74216i	−0.182027	−	0.283240i
$412$	2.99738	+	16.1010i	0.147670	+	0.793240i
$413$			6.63514i			0.326494i
$414$	−4.92747	+	4.66048i	−0.242172	+	0.229050i
$415$	11.4671			0.562900
$416$	−36.3048	−	1.44074i	−1.77999	−	0.0706379i
$417$	2.48290	−	1.59566i	0.121588	−	0.0781400i
$418$	−9.02901	+	6.06933i	−0.441623	+	0.296861i
$419$	5.77576	−	2.63770i	0.282164	−	0.128860i	−0.269306	−	0.963055i	$-0.586794\pi$
$419$	5.77576	−	2.63770i	0.282164	−	0.128860i	0.551470	+	0.834195i	$0.314067\pi$
$420$	0.965448	+	1.02548i	0.0471090	+	0.0500385i
$421$	5.82648	+	19.8432i	0.283965	+	0.967097i	0.970721	+	0.240209i	$0.0772159\pi$
$421$	5.82648	+	19.8432i	0.283965	+	0.967097i	−0.686756	+	0.726888i	$0.740966\pi$
$422$	15.8746	+	1.94915i	0.772765	+	0.0948831i
$423$	−5.29620	+	11.5971i	−0.257510	+	0.563868i
$424$	−13.2425	+	23.7124i	−0.643111	+	1.15158i
$425$	5.08705	+	5.87077i	0.246758	+	0.284774i
$426$	−3.70183	−	1.59913i	−0.179354	−	0.0774782i
$427$	1.78539	−	6.08046i	0.0864008	−	0.294254i
$428$	−19.6003	+	9.94775i	−0.947418	+	0.480843i
$429$	3.93890	−	6.12905i	0.190172	−	0.295913i
$430$	−3.34345	−	3.70145i	−0.161236	−	0.178500i
$431$	−2.50765	+	17.4411i	−0.120789	+	0.840108i	0.835876	+	0.548918i	$0.184960\pi$
$431$	−2.50765	+	17.4411i	−0.120789	+	0.840108i	−0.956665	+	0.291189i	$0.905949\pi$
$432$	−2.43253	−	3.17534i	−0.117035	−	0.152774i
$433$	−3.23304	−	22.4863i	−0.155370	−	1.08062i	−0.907029	−	0.421069i	$-0.861655\pi$
$433$	−3.23304	−	22.4863i	−0.155370	−	1.08062i	0.751659	−	0.659552i	$-0.229254\pi$
$434$	−3.85442	−	2.36620i	−0.185018	−	0.113581i
$435$	−0.665827	−	0.576942i	−0.0319239	−	0.0276623i
$436$	−29.1088	−	23.1919i	−1.39406	−	1.11069i
$437$	−32.5163	+	0.745860i	−1.55547	+	0.0356793i
$438$	4.22566	−	2.03615i	0.201910	−	0.0972912i
$439$	−7.49398	+	8.64851i	−0.357668	+	0.412771i	−0.905857	−	0.423583i	$-0.860772\pi$
$439$	−7.49398	+	8.64851i	−0.357668	+	0.412771i	0.548189	+	0.836355i	$0.315317\pi$
$440$	−2.68266	+	0.971598i	−0.127891	+	0.0463191i
$441$	−0.906962	−	6.30806i	−0.0431887	−	0.300384i
$442$	12.8929	+	10.7142i	0.613251	+	0.509624i
$443$	16.8742	+	2.42615i	0.801718	+	0.115270i	0.530981	−	0.847384i	$-0.321823\pi$
$443$	16.8742	+	2.42615i	0.801718	+	0.115270i	0.270737	+	0.962653i	$0.412733\pi$
$444$	−5.15011	+	12.6314i	−0.244413	+	0.599462i
$445$	0.646281	−	1.00563i	0.0306366	−	0.0476715i
$446$	24.8405	−	0.512463i	1.17623	−	0.0242658i
$447$	−16.7143	−	4.90776i	−0.790560	−	0.232129i
$448$	1.66876	+	6.11129i	0.0788413	+	0.288731i
$449$	21.7897	+	25.1466i	1.02832	+	1.18674i	0.982206	+	0.187807i	$0.0601380\pi$
$449$	21.7897	+	25.1466i	1.02832	+	1.18674i	0.0461132	+	0.998936i	$0.485316\pi$
$450$	0.968494	+	5.87331i	0.0456552	+	0.276870i
$451$	0.366589	+	0.167416i	0.0172620	+	0.00788330i
$452$	−30.3073	+	10.2746i	−1.42553	+	0.483275i
$453$	0.614571	+	2.09304i	0.0288751	+	0.0983395i
$454$	−3.39784	−	10.7468i	−0.159469	−	0.504373i
$455$	−1.87898	−	4.11439i	−0.0880878	−	0.192885i
$456$	1.55049	−	19.1194i	0.0726082	−	0.895346i
$457$	−20.1637	+	12.9584i	−0.943219	+	0.606170i	−0.919306	−	0.393544i	$-0.871249\pi$
$457$	−20.1637	+	12.9584i	−0.943219	+	0.606170i	−0.0239134	+	0.999714i	$0.507613\pi$
$458$	3.52454	−	12.9888i	0.164691	−	0.606927i
$459$			1.84554i			0.0861424i
$460$	−8.32167	−	1.87322i	−0.388000	−	0.0873393i
$461$		−	0.746061i		−	0.0347475i	−0.999849	−	0.0173738i	$-0.994469\pi$
$461$		−	0.746061i		−	0.0347475i	0.999849	−	0.0173738i	$-0.00553052\pi$
$462$	−1.22597	−	0.332671i	−0.0570375	−	0.0154773i
$463$	−18.4416	+	11.8517i	−0.857054	+	0.550795i	−0.893767	−	0.448531i	$-0.851947\pi$
$463$	−18.4416	+	11.8517i	−0.857054	+	0.550795i	0.0367138	+	0.999326i	$0.488311\pi$
$464$	−1.42599	−	3.69726i	−0.0661998	−	0.171641i
$465$	1.49198	+	3.26698i	0.0691889	+	0.151503i
$466$	−32.7787	+	10.3637i	−1.51845	+	0.480090i
$467$	−3.37078	−	11.4798i	−0.155981	−	0.531222i	0.844006	−	0.536334i	$-0.180191\pi$
$467$	−3.37078	−	11.4798i	−0.155981	−	0.531222i	−0.999987	+	0.00511143i	$0.998373\pi$
$468$	4.12433	+	12.1657i	0.190647	+	0.562359i
$469$	−8.79350	−	4.01586i	−0.406046	−	0.185435i
$470$	−15.8205	+	2.60877i	−0.729748	+	0.120334i
$471$	2.92502	+	3.37566i	0.134778	+	0.155542i
$472$	20.9076	−	11.1594i	0.962349	−	0.513653i
$473$	4.31651	+	1.26744i	0.198473	+	0.0582770i
$474$	−0.210642	−	10.2104i	−0.00967511	−	0.468979i
$475$	−15.4331	+	24.0144i	−0.708120	+	1.10186i
$476$	1.10352	−	2.70657i	0.0505800	−	0.124055i
$477$	9.50461	+	1.36656i	0.435186	+	0.0625703i
$478$	27.7574	−	33.4016i	1.26959	−	1.52776i
$479$	−0.545301	−	3.79266i	−0.0249155	−	0.173291i	0.973564	−	0.228414i	$-0.0733540\pi$
$479$	−0.545301	−	3.79266i	−0.0249155	−	0.173291i	−0.998480	+	0.0551231i	$0.982445\pi$
$480$	1.60759	−	4.76689i	0.0733760	−	0.217578i
$481$	28.6877	−	33.1074i	1.30805	−	1.50957i
$482$	11.7020	+	24.2854i	0.533013	+	1.10617i
$483$	−2.55214	−	2.81234i	−0.116126	−	0.127966i
$484$	−12.1054	+	15.1939i	−0.550246	+	0.690630i
$485$	−5.18800	−	4.49543i	−0.235575	−	0.204127i
$486$	−0.739880	+	1.20523i	−0.0335616	+	0.0546703i
$487$	0.693513	+	4.82349i	0.0314261	+	0.218573i	0.999483	−	0.0321582i	$-0.0102380\pi$
$487$	0.693513	+	4.82349i	0.0314261	+	0.218573i	−0.968057	+	0.250731i	$0.919329\pi$
$488$	−22.1625	+	4.60069i	−1.00325	+	0.208263i
$489$	2.50524	−	17.4243i	0.113291	−	0.787955i
$490$	5.94779	−	5.37254i	0.268694	−	0.242706i
$491$	−0.0698481	+	0.108686i	−0.00315220	+	0.00490492i	−0.842826	−	0.538186i	$-0.819110\pi$
$491$	−0.0698481	+	0.108686i	−0.00315220	+	0.00490492i	0.839674	+	0.543091i	$0.182746\pi$
$492$	−0.633635	+	0.321589i	−0.0285665	+	0.0144983i
$493$	−0.515103	+	1.75428i	−0.0231991	+	0.0790087i
$494$	−24.4293	+	56.5514i	−1.09913	+	2.54437i
$495$	0.660594	+	0.762366i	0.0296915	+	0.0342658i
$496$	−0.973373	+	16.1250i	−0.0437057	+	0.724036i
$497$	0.937985	−	2.05390i	0.0420744	−	0.0921300i
$498$	2.22235	−	18.0997i	0.0995859	−	0.811066i
$499$	−3.00511	−	10.2345i	−0.134527	−	0.458158i	0.864482	−	0.502664i	$-0.167647\pi$
$499$	−3.00511	−	10.2345i	−0.134527	−	0.458158i	−0.999009	+	0.0445063i	$0.985829\pi$
$500$	−11.9258	+	11.2277i	−0.533340	+	0.502116i
$501$	−1.40339	+	0.640908i	−0.0626990	+	0.0286337i
$502$	−22.5753	−	33.5841i	−1.00759	−	1.49893i
$503$	−16.1529	+	10.3808i	−0.720221	+	0.462858i	−0.848714	−	0.528852i	$-0.822623\pi$
$503$	−16.1529	+	10.3808i	−0.720221	+	0.462858i	0.128493	+	0.991710i	$0.458986\pi$
$504$	1.80572	−	1.32512i	0.0804333	−	0.0590254i
$505$	−7.62045			−0.339106
$506$	7.28031	−	2.48686i	0.323649	−	0.110554i
$507$		−	28.2535i		−	1.25478i
$508$	−3.47905	−	18.6884i	−0.154358	−	0.829163i
$509$	−19.5110	−	30.3596i	−0.864808	−	1.34567i	−0.937381	−	0.348305i	$-0.886758\pi$
$509$	−19.5110	−	30.3596i	−0.864808	−	1.34567i	0.0725734	−	0.997363i	$-0.476879\pi$
$510$	−1.92631	+	1.29487i	−0.0852985	+	0.0573379i
$511$	1.09108	+	2.38914i	0.0482667	+	0.105689i
$512$	16.4503	−	15.5367i	0.727007	−	0.686630i
$513$	−6.50719	+	1.91068i	−0.287299	+	0.0843587i
$514$	−3.22984	+	26.3050i	−0.142462	+	1.16027i
$515$	6.62425	+	3.02520i	0.291900	+	0.133306i
$516$	−6.49032	+	4.55995i	−0.285720	+	0.200740i
$517$	10.9294	−	9.47037i	0.480674	−	0.416506i
$518$	−7.01190	−	3.02903i	−0.308085	−	0.133088i
$519$	−0.532629	−	0.156394i	−0.0233798	−	0.00686494i
$520$	−9.80441	+	12.8406i	−0.429952	+	0.563096i
$521$	14.4807	+	9.30618i	0.634411	+	0.407711i	0.817940	−	0.575303i	$-0.195116\pi$
$521$	14.4807	+	9.30618i	0.634411	+	0.407711i	−0.183529	+	0.983014i	$0.558752\pi$
$522$	−1.03968	+	0.939125i	−0.0455056	+	0.0411044i
$523$	17.7935	+	2.55832i	0.778054	+	0.111867i	0.519889	−	0.854234i	$-0.325973\pi$
$523$	17.7935	+	2.55832i	0.778054	+	0.111867i	0.258165	+	0.966101i	$0.416882\pi$
$524$	−2.78409	+	11.1664i	−0.121624	+	0.487808i
$525$	−3.29920	+	0.474354i	−0.143989	+	0.0207025i
$526$	−10.8514	−	6.66157i	−0.473142	−	0.290458i
$527$	4.88094	−	5.63290i	0.212617	−	0.245373i
$528$	1.01366	+	4.42260i	0.0441139	+	0.192469i
$529$	22.3422	+	5.46116i	0.971402	+	0.237442i
$530$	5.24228	+	10.8794i	0.227710	+	0.472571i
$531$	−6.33241	−	5.48707i	−0.274803	−	0.238118i
$532$	10.6856	+	1.08881i	0.463278	+	0.0472060i
$533$	2.25874	−	0.324757i	0.0978368	−	0.0140668i
$534$	−1.46203	−	1.21498i	−0.0632684	−	0.0525773i
$535$	−1.39092	+	9.67407i	−0.0601348	+	0.418246i
$536$	2.13534	+	34.4628i	0.0922326	+	1.48857i
$537$	13.1181	+	8.43050i	0.566088	+	0.363803i
$538$	0.0529406	+	2.56618i	0.00228243	+	0.110636i
$539$	−2.03663	+	6.93612i	−0.0877238	+	0.298760i
$540$	−1.77709	+	0.0733546i	−0.0764739	+	0.00315668i
$541$	9.84429	−	8.53013i	0.423239	−	0.366739i	−0.417044	−	0.908886i	$-0.636934\pi$
$541$	9.84429	−	8.53013i	0.423239	−	0.366739i	0.840283	+	0.542147i	$0.182389\pi$
$542$	4.29280	+	26.0332i	0.184392	+	1.11822i
$543$	0.562924	−	1.23263i	0.0241574	−	0.0528973i
$544$	−10.3845	+	1.07483i	−0.445231	+	0.0460828i
$545$	−15.8787	+	4.66242i	−0.680171	+	0.199716i
$546$	−6.85828	+	2.16839i	−0.293507	+	0.0927987i
$547$	5.73105	−	2.61728i	0.245042	−	0.111907i	−0.289108	−	0.957296i	$-0.593359\pi$
$547$	5.73105	−	2.61728i	0.245042	−	0.111907i	0.534151	+	0.845389i	$0.320632\pi$
$548$	−11.7789	−	6.90060i	−0.503172	−	0.294779i
$549$	4.32658	+	6.73229i	0.184654	+	0.287327i
$550$	1.76828	−	6.51653i	0.0753996	−	0.277866i
$551$	−6.71870			−0.286226
$552$	−4.56943	+	12.7719i	−0.194488	+	0.543606i
$553$	5.71846			0.243174
$554$	−2.16723	+	7.98678i	−0.0920769	+	0.339326i
$555$	3.27926	+	5.10262i	0.139197	+	0.216594i
$556$	2.98381	−	5.09320i	0.126542	−	0.216000i
$557$	7.29692	−	3.33239i	0.309180	−	0.141198i	−0.254782	−	0.966999i	$-0.582004\pi$
$557$	7.29692	−	3.33239i	0.309180	−	0.141198i	0.563962	+	0.825801i	$0.309276\pi$
$558$	5.44574	−	1.72179i	0.230536	−	0.0728891i
$559$	24.4415	−	7.17667i	1.03376	−	0.303541i
$560$	2.65005	+	0.955020i	0.111985	+	0.0403569i
$561$	0.869644	−	1.90425i	0.0367164	−	0.0803977i
$562$	−1.10229	−	6.68471i	−0.0464974	−	0.281977i
$563$	−13.1243	+	11.3723i	−0.553122	+	0.479283i	−0.885999	−	0.463687i	$-0.846526\pi$
$563$	−13.1243	+	11.3723i	−0.553122	+	0.479283i	0.332877	+	0.942970i	$0.391981\pi$
$564$	1.05162	+	25.4767i	0.0442812	+	1.07276i
$565$	−4.00892	+	13.6531i	−0.168657	+	0.574391i
$566$	−0.651289	−	31.5698i	−0.0273757	−	1.32698i
$567$	−0.666171	−	0.428122i	−0.0279765	−	0.0179794i
$568$	−8.04948	+	0.498752i	−0.337749	+	0.0209272i
$569$	1.19462	−	8.30879i	0.0500812	−	0.348322i	−0.949338	−	0.314256i	$-0.898245\pi$
$569$	1.19462	−	8.30879i	0.0500812	−	0.348322i	0.999420	−	0.0340667i	$-0.0108459\pi$
$570$	−6.55990	−	5.45140i	−0.274764	−	0.228334i
$571$	−41.6652	+	5.99056i	−1.74364	+	0.250697i	−0.939207	−	0.343352i	$-0.888438\pi$
$571$	−41.6652	+	5.99056i	−1.74364	+	0.250697i	−0.804429	+	0.594049i	$0.797529\pi$
$572$	1.47710	−	14.4962i	0.0617606	−	0.606115i
$573$	−9.11192	−	7.89553i	−0.380656	−	0.329840i
$574$	−0.172715	−	0.358438i	−0.00720899	−	0.0149609i
$575$	14.9487	−	13.5656i	0.623402	−	0.565725i
$576$	−7.21248	−	3.46124i	−0.300520	−	0.144218i
$577$	7.04697	−	8.13264i	0.293369	−	0.338566i	−0.589862	−	0.807504i	$-0.700818\pi$
$577$	7.04697	−	8.13264i	0.293369	−	0.338566i	0.883231	+	0.468938i	$0.155363\pi$
$578$	−16.3839	−	10.0579i	−0.681479	−	0.418354i
$579$	−13.0320	+	1.87371i	−0.541590	+	0.0778689i
$580$	−1.70969	−	0.426272i	−0.0709910	−	0.0177000i
$581$	10.1070	+	1.45316i	0.419308	+	0.0602873i
$582$	−8.10101	+	7.31750i	−0.335798	+	0.303320i
$583$	−9.16305	−	5.88873i	−0.379495	−	0.243886i
$584$	5.69322	−	7.45626i	0.235587	−	0.308542i
$585$	5.48053	+	1.60923i	0.226592	+	0.0665334i
$586$	9.00981	+	3.89210i	0.372192	+	0.160781i
$587$	7.16606	−	6.20943i	0.295775	−	0.256290i	−0.494313	−	0.869284i	$-0.664580\pi$
$587$	7.16606	−	6.20943i	0.295775	−	0.256290i	0.790088	+	0.612994i	$0.210035\pi$
$588$	−7.32729	−	10.4292i	−0.302172	−	0.430092i
$589$	24.9143	+	11.3780i	1.02657	+	0.468821i
$590$	1.28425	−	10.4594i	0.0528716	−	0.430607i
$591$	19.9156	−	5.84775i	0.819218	−	0.240544i
$592$	2.24845	+	27.1892i	0.0924108	+	1.11747i
$593$	−5.50888	−	12.0628i	−0.226223	−	0.495358i	0.762152	−	0.647398i	$-0.224143\pi$
$593$	−5.50888	−	12.0628i	−0.226223	−	0.495358i	−0.988374	+	0.152040i	$0.951416\pi$
$594$	1.33134	−	0.894931i	0.0546255	−	0.0367194i
$595$	−0.702653	−	1.09335i	−0.0288060	−	0.0448230i
$596$	−34.2514	+	6.37628i	−1.40299	+	0.261182i
$597$		−	2.16443i		−	0.0885843i
$598$	27.0664	−	34.1331i	1.10683	−	1.39581i
$599$	−22.7159			−0.928148			−0.464074	−	0.885797i	$-0.653613\pi$
$599$	−22.7159			−0.928148			−0.464074	+	0.885797i	$0.653613\pi$
$600$	7.04351	+	9.59811i	0.287550	+	0.391841i
$601$	36.7366	−	23.6092i	1.49852	−	0.963038i	0.503429	−	0.864036i	$-0.332071\pi$
$601$	36.7366	−	23.6092i	1.49852	−	0.963038i	0.995087	−	0.0990016i	$-0.0315649\pi$
$602$	−2.47781	−	3.68610i	−0.100988	−	0.150234i
$603$	11.1046	−	5.07131i	0.452215	−	0.206520i
$604$	2.99058	+	3.17655i	0.121685	+	0.129252i
$605$	2.43363	+	8.28818i	0.0989411	+	0.336963i
$606$	−1.47686	+	12.0281i	−0.0599932	+	0.488607i
$607$	−1.62460	+	3.55738i	−0.0659406	+	0.144390i	−0.939733	−	0.341910i	$-0.888926\pi$
$607$	−1.62460	+	3.55738i	−0.0659406	+	0.144390i	0.873792	+	0.486299i	$0.161654\pi$
$608$	−14.5408	−	35.5018i	−0.589705	−	1.43979i
$609$	−0.513737	−	0.592884i	−0.0208177	−	0.0240249i
$610$	−3.99131	+	9.23947i	−0.161603	+	0.374095i
$611$	23.0701	−	78.5696i	0.933317	−	3.17859i
$612$	1.67050	+	3.29143i	0.0675259	+	0.133048i
$613$	−15.2816	+	23.7786i	−0.617218	+	0.960409i	0.382123	+	0.924111i	$0.375193\pi$
$613$	−15.2816	+	23.7786i	−0.617218	+	0.960409i	−0.999341	+	0.0362980i	$0.988443\pi$
$614$	−25.6886	+	23.2040i	−1.03671	+	0.936438i
$615$	−0.0449654	+	0.312741i	−0.00181318	+	0.0126109i
$616$	−2.48758	+	0.516393i	−0.100228	+	0.0208061i
$617$	3.75600	+	26.1236i	0.151211	+	1.05169i	0.914194	+	0.405277i	$0.132825\pi$
$617$	3.75600	+	26.1236i	0.151211	+	1.05169i	−0.762983	+	0.646418i	$0.776266\pi$
$618$	6.05875	−	9.86940i	0.243718	−	0.397006i
$619$	10.8483	+	9.40011i	0.436030	+	0.377822i	0.845036	−	0.534710i	$-0.179579\pi$
$619$	10.8483	+	9.40011i	0.436030	+	0.377822i	−0.409006	+	0.912532i	$0.634124\pi$
$620$	5.61799	+	4.47603i	0.225624	+	0.179762i
$621$	4.79457	−	0.109978i	0.192399	−	0.00441326i
$622$	−4.71961	−	9.79467i	−0.189239	−	0.392730i
$623$	0.697060	−	0.804450i	0.0279271	−	0.0322296i
$624$	18.3674	+	17.9638i	0.735283	+	0.719126i
$625$	−1.95862	−	13.6225i	−0.0783446	−	0.544899i
$626$	20.9238	−	25.1784i	0.836282	−	1.00633i
$627$	7.61455	+	1.09481i	0.304096	+	0.0437224i
$628$	8.27212	+	3.37272i	0.330094	+	0.134586i
$629$	6.80532	−	10.5893i	0.271346	−	0.422223i
$630$	−0.0205415	−	0.995706i	−0.000818395	−	0.0396699i
$631$	42.4512	+	12.4648i	1.68995	+	0.496215i	0.978453	−	0.206469i	$-0.0661973\pi$
$631$	42.4512	+	12.4648i	1.68995	+	0.496215i	0.711501	+	0.702685i	$0.248016\pi$
$632$	−9.61766	−	18.0191i	−0.382570	−	0.716761i
$633$	−7.40605	−	8.54704i	−0.294364	−	0.339714i
$634$	−29.2528	+	4.82372i	−1.16178	+	0.191574i
$635$	−7.68874	−	3.51133i	−0.305118	−	0.139343i
$636$	18.1879	−	6.16595i	0.721199	−	0.244496i
$637$	11.5321	+	39.2746i	0.456917	+	1.55612i
$638$	1.51529	−	0.479091i	0.0599907	−	0.0189674i
$639$	1.18451	+	2.59371i	0.0468583	+	0.102605i
$640$	−1.44772	−	9.95662i	−0.0572260	−	0.393570i
$641$	35.1135	−	22.5661i	1.38690	−	0.891307i	0.387370	−	0.921925i	$-0.373384\pi$
$641$	35.1135	−	22.5661i	1.38690	−	0.891307i	0.999531	+	0.0306176i	$0.00974740\pi$
$642$	14.9999	+	4.07027i	0.592000	+	0.160641i
$643$		−	11.6049i		−	0.457653i	−0.973467	−	0.228827i	$-0.926511\pi$
$643$		−	11.6049i		−	0.457653i	0.973467	−	0.228827i	$-0.0734889\pi$
$644$	−7.09721	−	2.70558i	−0.279669	−	0.106615i
$645$			3.52700i			0.138875i
$646$	−4.63550	+	17.0829i	−0.182381	+	0.672119i
$647$	−5.04091	+	3.23960i	−0.198179	+	0.127362i	−0.635967	−	0.771717i	$-0.719398\pi$
$647$	−5.04091	+	3.23960i	−0.198179	+	0.127362i	0.437788	+	0.899078i	$0.355762\pi$
$648$	−0.228621	+	2.81917i	−0.00898109	+	0.110748i
$649$	3.94829	+	8.64555i	0.154984	+	0.339368i
$650$	−11.5258	−	36.4544i	−0.452081	−	1.42986i
$651$	0.901004	+	3.06854i	0.0353131	+	0.120265i
$652$	−11.3037	−	33.3430i	−0.442688	−	1.30581i
$653$	10.4282	+	4.76240i	0.408087	+	0.186367i	0.608872	−	0.793268i	$-0.291622\pi$
$653$	10.4282	+	4.76240i	0.408087	+	0.186367i	−0.200786	+	0.979635i	$0.564349\pi$
$654$	4.28182	+	25.9665i	0.167432	+	1.01537i
$655$	3.35104	+	3.86731i	0.130936	+	0.151108i
$656$	−0.838969	+	1.14708i	−0.0327563	+	0.0447858i
$657$	−3.18243	−	0.934447i	−0.124159	−	0.0364562i
$658$	−14.2746	+	0.294487i	−0.556481	+	0.0114803i
$659$	−0.721176	+	1.12217i	−0.0280930	+	0.0437136i	−0.855016	−	0.518602i	$-0.826453\pi$
$659$	−0.721176	+	1.12217i	−0.0280930	+	0.0437136i	0.826923	+	0.562315i	$0.190089\pi$
$660$	1.86820	+	0.761702i	0.0727194	+	0.0296492i
$661$	−25.0443	−	3.60083i	−0.974111	−	0.140056i	−0.363162	−	0.931726i	$-0.618303\pi$
$661$	−25.0443	−	3.60083i	−0.974111	−	0.140056i	−0.610949	+	0.791670i	$0.709212\pi$
$662$	24.6142	+	20.4549i	0.956657	+	0.795000i
$663$	−1.68696	−	11.7331i	−0.0655160	−	0.455674i
$664$	−12.4196	−	34.2915i	−0.481972	−	1.33077i
$665$	3.12759	−	3.60943i	0.121283	−	0.139968i
$666$	8.68948	−	4.18706i	0.336710	−	0.162245i
$667$	4.58818	+	1.23366i	0.177655	+	0.0477674i
$668$	−1.92276	+	2.41332i	−0.0743939	+	0.0933740i
$669$	−13.2775	−	11.5050i	−0.513337	−	0.444809i
$670$	13.0845	+	8.03247i	0.505498	+	0.310321i
$671$	−1.29188	−	8.98522i	−0.0498725	−	0.346871i
$672$	2.02098	−	3.99774i	0.0779611	−	0.154216i
$673$	−6.54254	+	45.5044i	−0.252196	+	1.75406i	0.332771	+	0.943008i	$0.392016\pi$
$673$	−6.54254	+	45.5044i	−0.252196	+	1.75406i	−0.584967	+	0.811057i	$0.698893\pi$
$674$	−9.30631	−	10.3028i	−0.358466	−	0.396848i
$675$	2.27563	−	3.54095i	0.0875891	−	0.136291i
$676$	−25.5738	−	50.3888i	−0.983609	−	1.93803i
$677$	−0.231590	+	0.788723i	−0.00890073	+	0.0303131i	−0.963824	−	0.266541i	$-0.914119\pi$
$677$	−0.231590	+	0.788723i	−0.00890073	+	0.0303131i	0.954923	+	0.296854i	$0.0959375\pi$
$678$	20.7731	+	8.97366i	0.797786	+	0.344631i
$679$	−4.00295	−	4.61965i	−0.153619	−	0.177286i
$680$	−2.26342	+	4.05295i	−0.0867982	+	0.155424i
$681$	−3.31083	+	7.24970i	−0.126871	+	0.277809i
$682$	−6.43032	−	0.789540i	−0.246229	−	0.0302330i
$683$	4.81528	+	16.3993i	0.184252	+	0.627503i	0.998871	+	0.0475073i	$0.0151277\pi$
$683$	4.81528	+	16.3993i	0.184252	+	0.627503i	−0.814619	+	0.579996i	$0.803054\pi$
$684$	−9.87579	+	9.29762i	−0.377610	+	0.355503i
$685$	−5.52159	+	2.52163i	−0.210969	+	0.0963464i
$686$	12.4291	−	8.35485i	0.474544	−	0.318990i
$687$	−8.00587	+	5.14506i	−0.305443	+	0.196296i
$688$	−7.44771	+	14.0072i	−0.283941	+	0.534019i
$689$	−61.6748			−2.34962
$690$	3.47877	+	4.92725i	0.132435	+	0.187577i
$691$		−	10.3711i		−	0.394536i	−0.980350	−	0.197268i	$-0.936793\pi$
$691$		−	10.3711i		−	0.394536i	0.980350	−	0.197268i	$-0.0632070\pi$
$692$	−1.09148	+	0.203191i	−0.0414918	+	0.00772415i
$693$	0.485627	+	0.755651i	0.0184475	+	0.0287048i
$694$	15.1289	+	22.5064i	0.574285	+	0.854332i
$695$	−1.09035	−	2.38753i	−0.0413592	−	0.0905640i
$696$	−1.00417	+	2.61596i	−0.0380628	+	0.0991575i
$697$	0.629135	−	0.184731i	0.0238302	−	0.00699717i
$698$	0.0411146	+	0.00504821i	0.00155621	+	0.000191078i
$699$	22.1122	+	10.0983i	0.836361	+	0.381953i
$700$	−5.45460	+	3.83227i	−0.206164	+	0.144846i
$701$	−11.0751	+	9.59667i	−0.418303	+	0.362461i	−0.838435	−	0.545002i	$-0.816529\pi$
$701$	−11.0751	+	9.59667i	−0.418303	+	0.362461i	0.420132	+	0.907463i	$0.361984\pi$
$702$	3.60213	−	8.33857i	0.135954	−	0.314719i
$703$	44.3823	+	13.0318i	1.67391	+	0.491504i
$704$	5.81095	+	6.96997i	0.219008	+	0.262691i
$705$	9.53804	+	6.12973i	0.359223	+	0.230859i
$706$	12.5814	+	13.9285i	0.473507	+	0.524207i
$707$	−6.71655	−	0.965694i	−0.252602	−	0.0363187i
$708$	−16.2602	−	4.05410i	−0.611095	−	0.152362i
$709$	35.2292	−	5.06520i	1.32306	−	0.190227i	0.555668	−	0.831405i	$-0.312463\pi$
$709$	35.2292	−	5.06520i	1.32306	−	0.190227i	0.767393	+	0.641177i	$0.221554\pi$
$710$	−1.87615	+	3.05615i	−0.0704105	+	0.114695i
$711$	−4.72900	+	5.45756i	−0.177351	+	0.204674i
$712$	−3.70721	−	0.843488i	−0.138934	−	0.0316110i
$713$	−14.9247	−	12.3446i	−0.558935	−	0.462310i
$714$	−1.86191	+	0.897171i	−0.0696803	+	0.0335758i
$715$	−4.89660	−	4.24292i	−0.183122	−	0.158676i
$716$	31.0264	+	3.16146i	1.15951	+	0.118149i
$717$	−30.3969	+	4.37041i	−1.13519	+	0.163216i
$718$	9.57647	−	11.5238i	0.357391	−	0.430063i
$719$	−4.52051	+	31.4409i	−0.168587	+	1.17255i	0.713222	+	0.700938i	$0.247235\pi$
$719$	−4.52051	+	31.4409i	−0.168587	+	1.17255i	−0.881808	+	0.471608i	$0.843674\pi$
$720$	−3.10296	+	1.73937i	−0.115641	+	0.0648224i
$721$	5.45515	+	3.50581i	0.203160	+	0.130563i
$722$	−38.1675	+	0.787400i	−1.42045	+	0.0293040i
$723$	5.37039	−	18.2899i	0.199727	−	0.680207i
$724$	−0.111775	−	2.70787i	−0.00415408	−	0.100637i
$725$	3.15141	−	2.73071i	0.117040	−	0.101416i
$726$	13.5537	−	2.23497i	0.503024	−	0.0829474i
$727$	7.98819	−	17.4917i	0.296266	−	0.648731i	−0.701701	−	0.712472i	$-0.747576\pi$
$727$	7.98819	−	17.4917i	0.296266	−	0.648731i	0.997967	+	0.0637405i	$0.0203030\pi$
$728$	−10.2687	+	10.0750i	−0.380582	+	0.373405i
$729$	0.959493	−	0.281733i	0.0355368	−	0.0104345i
$730$	−1.25752	−	3.97734i	−0.0465430	−	0.147208i
$731$	6.65801	−	3.04061i	0.246255	−	0.112461i
$732$	13.8100	+	8.09049i	0.510433	+	0.299033i
$733$	−6.20442	−	9.65426i	−0.229165	−	0.356588i	0.707560	−	0.706653i	$-0.249796\pi$
$733$	−6.20442	−	9.65426i	−0.229165	−	0.356588i	−0.936725	+	0.350065i	$0.886160\pi$
$734$	19.8468	+	5.38549i	0.732560	+	0.198782i
$735$	−5.66747			−0.209048
$736$	3.41114	+	26.9140i	0.125736	+	0.992064i
$737$	−13.8476			−0.510081
$738$	0.484915	+	0.131583i	0.0178500	+	0.00484363i
$739$	8.02780	+	12.4915i	0.295307	+	0.459507i	0.956925	−	0.290334i	$-0.0937663\pi$
$739$	8.02780	+	12.4915i	0.295307	+	0.459507i	−0.661618	+	0.749841i	$0.730130\pi$
$740$	10.4670	+	6.13204i	0.384776	+	0.225418i
$741$	39.6231	−	18.0952i	1.45559	−	0.664745i
$742$	3.24179	+	10.2533i	0.119010	+	0.376409i
$743$	−37.2247	+	10.9302i	−1.36564	+	0.400989i	−0.880749	−	0.473584i	$-0.842960\pi$
$743$	−37.2247	+	10.9302i	−1.36564	+	0.400989i	−0.484894	+	0.874573i	$0.661142\pi$
$744$	8.15371	−	7.99996i	0.298930	−	0.293293i
$745$	−6.43545	+	14.0917i	−0.235777	+	0.516279i
$746$	−26.9044	+	4.43647i	−0.985040	+	0.162431i
$747$	−9.74503	+	8.44412i	−0.356552	+	0.308954i
$748$	−0.172678	−	4.18330i	−0.00631372	−	0.152957i
$749$	−2.45187	+	8.35031i	−0.0895895	+	0.305114i
$750$	11.5795	−	0.238888i	0.422825	−	0.00872294i
$751$	10.1777	+	6.54080i	0.371389	+	0.238677i	0.713000	−	0.701164i	$-0.247336\pi$
$751$	10.1777	+	6.54080i	0.371389	+	0.238677i	−0.341611	+	0.939842i	$0.610972\pi$
$752$	24.9358	+	44.4845i	0.909316	+	1.62218i
$753$	−4.07222	+	28.3229i	−0.148400	+	1.03214i
$754$	5.75136	−	6.92085i	0.209452	−	0.252042i
$755$	1.92018	−	0.276080i	0.0698825	−	0.0100476i
$756$	−1.57560	−	0.160547i	−0.0573040	−	0.00583903i
$757$	−37.3684	−	32.3799i	−1.35818	−	1.17687i	−0.966470	−	0.256780i	$-0.917338\pi$
$757$	−37.3684	−	32.3799i	−1.35818	−	1.17687i	−0.391710	−	0.920089i	$-0.628116\pi$
$758$	32.9814	−	15.8923i	1.19794	−	0.577233i
$759$	−4.99893	−	2.14579i	−0.181450	−	0.0778872i
$760$	−16.6336	−	3.78458i	−0.603365	−	0.137281i
$761$	17.1963	−	19.8456i	0.623367	−	0.719403i	−0.352976	−	0.935632i	$-0.614830\pi$
$761$	17.1963	−	19.8456i	0.623367	−	0.719403i	0.976343	+	0.216229i	$0.0693757\pi$
$762$	−7.03236	+	11.4554i	−0.254755	+	0.414984i
$763$	−14.5861	+	2.09717i	−0.528053	+	0.0759226i
$764$	−23.3973	−	5.83358i	−0.846486	−	0.211052i
$765$	1.62454	+	0.233574i	0.0587354	+	0.00844487i
$766$	8.29110	+	9.17886i	0.299570	+	0.331646i
$767$	45.2740	+	29.0958i	1.63475	+	1.05059i
$768$	−15.9961	+	0.355458i	−0.577208	+	0.0128265i
$769$	34.3365	+	10.0821i	1.23820	+	0.363570i	0.834341	−	0.551249i	$-0.185849\pi$
$769$	34.3365	+	10.0821i	1.23820	+	0.363570i	0.403864	+	0.914819i	$0.367667\pi$
$770$	−0.447995	+	1.03706i	−0.0161446	+	0.0373732i
$771$	14.1629	−	12.2722i	0.510063	−	0.441972i
$772$	−21.5459	+	15.1376i	−0.775452	+	0.544815i
$773$	29.5560	+	13.4978i	1.06305	+	0.485480i	0.868642	−	0.495440i	$-0.164993\pi$
$773$	29.5560	+	13.4978i	1.06305	+	0.485480i	0.194412	+	0.980920i	$0.437720\pi$
$774$	5.56700	+	0.683538i	0.200102	+	0.0245693i
$775$	−16.3105	+	4.78918i	−0.585889	+	0.172032i
$776$	−7.82428	+	20.3831i	−0.280875	+	0.731709i
$777$	2.24366	+	4.91293i	0.0804909	+	0.176250i
$778$	5.05884	+	7.52576i	0.181368	+	0.269812i
$779$	1.30268	+	2.02701i	0.0466735	+	0.0726253i
$780$	11.2309	−	2.09075i	0.402129	−	0.0748607i
$781$		−	3.23438i		−	0.115735i
$782$	6.30226	−	10.8147i	0.225368	−	0.386734i
$783$	0.990680			0.0354040
$784$	−22.5079	−	11.9676i	−0.803853	−	0.427414i
$785$	3.34162	−	2.14753i	0.119268	−	0.0766486i
$786$	6.75358	−	4.53978i	0.240892	−	0.161928i
$787$	37.3841	−	17.0727i	1.33260	−	0.608578i	0.383496	−	0.923543i	$-0.374720\pi$
$787$	37.3841	−	17.0727i	1.33260	−	0.608578i	0.949103	+	0.314965i	$0.101993\pi$
$788$	30.2254	−	28.4559i	1.07673	−	1.01370i
$789$	2.53660	+	8.63886i	0.0903053	+	0.307552i
$790$	−9.01438	−	1.10682i	−0.320717	−	0.0393790i
$791$	−5.26358	+	11.5256i	−0.187151	+	0.409804i
$792$	1.56433	−	2.80113i	0.0555859	−	0.0995339i
$793$	−33.6601	−	38.8459i	−1.19531	−	1.37946i
$794$	8.78217	+	3.79376i	0.311667	+	0.134636i
$795$	2.40583	−	8.19349i	0.0853259	−	0.290593i
$796$	−1.95915	−	3.86016i	−0.0694401	−	0.136820i
$797$	−5.70804	+	8.88188i	−0.202189	+	0.314612i	−0.927510	−	0.373799i	$-0.878055\pi$
$797$	−5.70804	+	8.88188i	−0.202189	+	0.314612i	0.725321	+	0.688411i	$0.241691\pi$
$798$	−5.09097	−	5.63608i	−0.180218	−	0.199515i
$799$	3.34854	−	23.2896i	0.118463	−	0.823928i
$800$	21.2495	+	10.7423i	0.751284	+	0.379798i
$801$	0.191299	+	1.33051i	0.00675921	+	0.0470114i
$802$	−42.9008	−	26.3364i	−1.51488	−	0.929972i
$803$	2.84335	+	2.46378i	0.100340	+	0.0869449i
$804$	15.2142	−	19.0958i	0.536564	−	0.673457i
$805$	−2.79857	+	1.89059i	−0.0986365	+	0.0666346i
$806$	−33.0475	+	15.9241i	−1.16405	+	0.560902i
$807$	1.18854	−	1.37165i	0.0418386	−	0.0482843i
$808$	8.25337	+	22.7883i	0.290353	+	0.801688i
$809$	−3.81705	−	26.5482i	−0.134200	−	0.933384i	−0.939995	−	0.341189i	$-0.889170\pi$
$809$	−3.81705	−	26.5482i	−0.134200	−	0.933384i	0.805794	−	0.592195i	$-0.201739\pi$
$810$	0.967265	+	0.803816i	0.0339862	+	0.0282432i
$811$	20.2768	+	2.91536i	0.712015	+	0.102372i	0.488799	−	0.872397i	$-0.337435\pi$
$811$	20.2768	+	2.91536i	0.712015	+	0.102372i	0.223216	+	0.974769i	$0.428344\pi$
$812$	−1.45288	−	0.592368i	−0.0509860	−	0.0207880i
$813$	10.0866	−	15.6951i	0.353754	−	0.550452i
$814$	−10.9389	+	0.225671i	−0.383409	+	0.00790978i
$815$	−15.0207	−	4.41048i	−0.526153	−	0.154492i
$816$	5.95850	+	4.35804i	0.208589	+	0.152562i
$817$	17.6139	+	20.3275i	0.616233	+	0.711170i
$818$	−6.63184	−	40.2179i	−0.231877	−	1.40619i
$819$	4.62653	+	2.11286i	0.161664	+	0.0738294i
$820$	0.202886	+	0.598459i	0.00708507	+	0.0208991i
$821$	−0.247987	−	0.844565i	−0.00865480	−	0.0294755i	0.955052	−	0.296437i	$-0.0957985\pi$
$821$	−0.247987	−	0.844565i	−0.00865480	−	0.0294755i	−0.963707	+	0.266962i	$0.913980\pi$
$822$	2.91003	+	9.20395i	0.101499	+	0.321024i
$823$	−8.91991	−	19.5319i	−0.310928	−	0.680838i	0.688067	−	0.725647i	$-0.258459\pi$
$823$	−8.91991	−	19.5319i	−0.310928	−	0.680838i	−0.998996	+	0.0448087i	$0.985732\pi$
$824$	1.87214	−	23.0857i	0.0652190	−	0.804228i
$825$	−4.01657	+	2.58130i	−0.139839	+	0.0898692i
$826$	2.45737	−	9.05602i	0.0855030	−	0.315099i
$827$			30.0786i			1.04593i	0.852353	+	0.522967i	$0.175175\pi$
$827$			30.0786i			1.04593i	−0.852353	+	0.522967i	$0.824825\pi$
$828$	8.45133	−	4.53597i	0.293704	−	0.157636i
$829$			18.0525i			0.626989i	0.949590	+	0.313494i	$0.101500\pi$
$829$			18.0525i			0.626989i	−0.949590	+	0.313494i	$0.898500\pi$
$830$	−15.6510	−	4.24694i	−0.543255	−	0.147414i
$831$	4.92279	−	3.16369i	0.170770	−	0.109747i
$832$	49.0173	+	15.4122i	1.69937	+	0.534320i
$833$	4.88590	+	10.6986i	0.169286	+	0.370686i
$834$	−3.97977	+	1.25829i	−0.137808	+	0.0435711i
$835$	0.386546	+	1.31645i	0.0133770	+	0.0455578i
$836$	14.5711	−	4.93981i	0.503953	−	0.170847i
$837$	−3.67364	−	1.67770i	−0.126980	−	0.0579896i
$838$	−8.85998	+	1.46099i	−0.306063	+	0.0504690i
$839$	−26.8174	−	30.9489i	−0.925839	−	1.06847i	−0.997473	−	0.0710437i	$-0.977367\pi$
$839$	−26.8174	−	30.9489i	−0.925839	−	1.06847i	0.0716347	−	0.997431i	$-0.477178\pi$
$840$	−0.937903	−	1.75720i	−0.0323607	−	0.0606291i
$841$	−26.8836	−	7.89374i	−0.927021	−	0.272198i
$842$	−0.603245	−	29.2410i	−0.0207892	−	1.00771i
$843$	−2.59001	+	4.03014i	−0.0892048	+	0.138805i
$844$	−20.9447	−	8.53960i	−0.720947	−	0.293945i
$845$	−24.8702	−	3.57580i	−0.855562	−	0.123011i
$846$	11.5236	−	13.8668i	0.396190	−	0.476752i
$847$	1.09465	+	7.61348i	0.0376127	+	0.261602i
$848$	26.8562	−	27.4596i	0.922244	−	0.942965i
$849$	−14.6217	+	16.8744i	−0.501816	+	0.579127i
$850$	−4.76881	−	9.89678i	−0.163569	−	0.339457i
$851$	−27.9157	−	17.0487i	−0.956937	−	0.584421i
$852$	4.46021	+	3.55359i	0.152804	+	0.121744i
$853$	−32.5442	−	28.1997i	−1.11429	−	0.965539i	−0.114680	−	0.993403i	$-0.536584\pi$
$853$	−32.5442	−	28.1997i	−1.11429	−	0.965539i	−0.999612	+	0.0278636i	$0.991130\pi$
$854$	−4.68874	+	7.63773i	−0.160445	+	0.261358i
$855$	0.858325	+	5.96978i	0.0293541	+	0.204162i
$856$	30.4359	−	6.31813i	1.04028	−	0.215949i
$857$	0.705819	−	4.90908i	0.0241103	−	0.167691i	−0.974209	−	0.225649i	$-0.927550\pi$
$857$	0.705819	−	4.90908i	0.0241103	−	0.167691i	0.998319	+	0.0579579i	$0.0184589\pi$
$858$	−7.64598	+	6.90648i	−0.261029	+	0.235783i
$859$	−23.7105	+	36.8942i	−0.808991	+	1.25882i	0.153674	+	0.988122i	$0.450889\pi$
$859$	−23.7105	+	36.8942i	−0.808991	+	1.25882i	−0.962666	+	0.270694i	$0.912747\pi$
$860$	3.19248	+	6.29022i	0.108863	+	0.214495i
$861$	−0.0792636	+	0.269947i	−0.00270130	+	0.00919977i
$862$	9.88202	−	22.8759i	0.336583	−	0.779155i
$863$	−21.5612	−	24.8830i	−0.733953	−	0.847027i	0.258957	−	0.965889i	$-0.416621\pi$
$863$	−21.5612	−	24.8830i	−0.733953	−	0.847027i	−0.992911	+	0.118861i	$0.962076\pi$
$864$	2.14405	+	5.23479i	0.0729421	+	0.178091i
$865$	−0.205076	+	0.449055i	−0.00697280	+	0.0152683i
$866$	−3.91532	+	31.8879i	−0.133048	+	1.08360i
$867$	3.82987	+	13.0433i	0.130069	+	0.442975i
$868$	4.38440	+	4.65704i	0.148816	+	0.158070i
$869$	7.45112	−	3.40281i	0.252762	−	0.115433i
$870$	0.695084	+	1.03404i	0.0235655	+	0.0350572i
$871$	−65.9622	+	42.3913i	−2.23504	+	1.43638i
$872$	31.1401	+	42.4343i	1.05454	+	1.43701i
$873$	7.71920			0.261255
$874$	44.6564	+	11.0247i	1.51052	+	0.372915i
$875$			6.48526i			0.219242i
$876$	−6.52153	+	1.21405i	−0.220342	+	0.0410191i
$877$	14.5966	+	22.7127i	0.492891	+	0.766953i	0.995213	−	0.0977272i	$-0.0311573\pi$
$877$	14.5966	+	22.7127i	0.492891	+	0.766953i	−0.502322	+	0.864680i	$0.667521\pi$
$878$	13.4313	−	9.02853i	0.453283	−	0.304698i
$879$	−2.88295	−	6.31278i	−0.0972395	−	0.212925i
$880$	4.02129	−	0.332547i	0.135558	−	0.0112102i
$881$	−38.1914	+	11.2140i	−1.28670	+	0.377810i	−0.852368	−	0.522942i	$-0.824834\pi$
$881$	−38.1914	+	11.2140i	−1.28670	+	0.377810i	−0.434334	+	0.900752i	$0.643016\pi$
$882$	−1.09836	+	8.94550i	−0.0369839	+	0.301211i
$883$	14.3948	+	6.57389i	0.484424	+	0.221229i	0.642629	−	0.766177i	$-0.277844\pi$
$883$	14.3948	+	6.57389i	0.484424	+	0.221229i	−0.158205	+	0.987406i	$0.550571\pi$
$884$	−13.6288	−	19.3984i	−0.458387	−	0.652437i
$885$	−5.63144	+	4.87967i	−0.189299	+	0.164028i
$886$	−22.1324	−	9.56084i	−0.743551	−	0.321203i
$887$	49.3301	+	14.4846i	1.65634	+	0.486346i	0.970439	−	0.241348i	$-0.0775894\pi$
$887$	49.3301	+	14.4846i	1.65634	+	0.486346i	0.685903	+	0.727693i	$0.259408\pi$
$888$	11.7073	−	15.3327i	0.392872	−	0.514533i
$889$	−6.33177	−	4.06918i	−0.212361	−	0.136476i
$890$	−1.25452	+	1.13319i	−0.0420517	+	0.0379846i
$891$	−1.12277	−	0.161431i	−0.0376144	−	0.00540813i
$892$	−34.0935	−	8.50043i	−1.14154	−	0.284616i
$893$	85.5836	−	12.3051i	2.86395	−	0.411773i
$894$	20.9950	+	12.8887i	0.702178	+	0.431061i
$895$	9.08120	−	10.4803i	0.303551	−	0.350317i
$896$	−0.0142516	−	8.95907i	−0.000476113	−	0.299302i
$897$	−30.3810	+	5.08177i	−1.01439	+	0.169675i
$898$	−20.4266	−	42.3916i	−0.681643	−	1.41462i
$899$	−3.02372	−	2.62007i	−0.100847	−	0.0873843i
$900$	0.853368	−	8.37491i	0.0284456	−	0.279164i
$901$	−17.5411	+	2.52203i	−0.584380	+	0.0840212i
$902$	−0.438338	−	0.364268i	−0.0145951	−	0.0121288i
$903$	−0.446955	+	3.10864i	−0.0148737	+	0.103449i
$904$	45.1703	−	2.79879i	1.50234	−	0.0930863i
$905$	−1.01378	−	0.651518i	−0.0336992	−	0.0216572i
$906$	−0.0636297	−	3.08431i	−0.00211395	−	0.102469i
$907$	−9.45930	+	32.2154i	−0.314091	+	1.06970i	0.639550	+	0.768749i	$0.279121\pi$
$907$	−9.45930	+	32.2154i	−0.314091	+	1.06970i	−0.953641	+	0.300946i	$0.902698\pi$
$908$	0.657402	+	15.9263i	0.0218167	+	0.528532i
$909$	6.47603	−	5.61151i	0.214796	−	0.186122i
$910$	1.04074	+	6.31144i	0.0345002	+	0.209222i
$911$	16.7184	−	36.6083i	0.553906	−	1.21289i	−0.401027	−	0.916066i	$-0.631347\pi$
$911$	16.7184	−	36.6083i	0.553906	−	1.21289i	0.954934	−	0.296819i	$-0.0959259\pi$
$912$	−9.19719	+	25.5210i	−0.304549	+	0.845083i
$913$	14.0340	−	4.12077i	0.464459	−	0.136377i
$914$	32.3199	−	10.2186i	1.06905	−	0.338002i
$915$	6.47369	−	2.95644i	0.214014	−	0.0977367i
$916$	−9.62100	+	16.4225i	−0.317887	+	0.542615i
$917$	2.46348	+	3.83324i	0.0813511	+	0.126585i
$918$	0.683510	−	2.51890i	0.0225592	−	0.0831360i
$919$	50.4966			1.66573			0.832865	−	0.553476i	$-0.186699\pi$
$919$	50.4966			1.66573			0.832865	+	0.553476i	$0.186699\pi$
$920$	10.6641	+	5.63867i	0.351586	+	0.185902i
$921$	24.4778			0.806572
$922$	−0.276309	+	1.01827i	−0.00909977	+	0.0335348i
$923$	−9.90135	−	15.4068i	−0.325907	−	0.507121i
$924$	1.55007	+	0.908098i	0.0509937	+	0.0298742i
$925$	−26.1141	+	11.9259i	−0.858627	+	0.392122i
$926$	29.5595	−	9.34588i	0.971386	−	0.307125i
$927$	−7.85711	+	2.30706i	−0.258061	+	0.0757737i
$928$	0.576964	+	5.57435i	0.0189398	+	0.182987i
$929$	−10.7077	+	23.4465i	−0.351307	+	0.769255i	0.648659	+	0.761079i	$0.275330\pi$
$929$	−10.7077	+	23.4465i	−0.351307	+	0.769255i	−0.999967	+	0.00817647i	$0.997397\pi$
$930$	−0.826389	−	5.01153i	−0.0270984	−	0.164334i
$931$	−32.6639	+	28.3035i	−1.07052	+	0.927609i
$932$	48.5766	−	2.00514i	1.59118	−	0.0656804i
$933$	−2.16596	+	7.37657i	−0.0709102	+	0.241498i
$934$	0.348994	+	16.9167i	0.0114194	+	0.553531i
$935$	−1.56616	−	1.00651i	−0.0512189	−	0.0329164i
$936$	−1.12347	−	18.1319i	−0.0367216	−	0.592660i
$937$	−3.76997	+	26.2207i	−0.123159	+	0.856593i	0.830782	+	0.556599i	$0.187894\pi$
$937$	−3.76997	+	26.2207i	−0.123159	+	0.856593i	−0.953941	+	0.299994i	$0.903015\pi$
$938$	10.5146	+	8.73782i	0.343313	+	0.285300i
$939$	−22.9134	+	3.29446i	−0.747752	+	0.107511i
$940$	22.5590	+	2.29866i	0.735792	+	0.0749741i
$941$	−40.1152	−	34.7600i	−1.30772	−	1.13314i	−0.982247	−	0.187591i	$-0.939932\pi$
$941$	−40.1152	−	34.7600i	−1.30772	−	1.13314i	−0.325470	−	0.945552i	$-0.605523\pi$
$942$	−2.74204	−	5.69059i	−0.0893404	−	0.185410i
$943$	−0.517407	−	1.62343i	−0.0168491	−	0.0528663i
$944$	−32.6688	+	7.48770i	−1.06328	+	0.243704i
$945$	−0.461166	+	0.532214i	−0.0150017	+	0.0173129i
$946$	−5.42201	−	3.32853i	−0.176285	−	0.108220i
$947$	24.6349	−	3.54196i	0.800526	−	0.115098i	0.270103	−	0.962831i	$-0.412942\pi$
$947$	24.6349	−	3.54196i	0.800526	−	0.115098i	0.530423	+	0.847733i	$0.322033\pi$
$948$	−3.49400	+	14.0138i	−0.113480	+	0.455146i
$949$	21.0865	+	3.03178i	0.684497	+	0.0984159i
$950$	29.9579	−	27.0605i	0.971963	−	0.877957i
$951$	17.6362	+	11.3341i	0.571893	+	0.367533i
$952$	−2.50855	+	3.28538i	−0.0813026	+	0.106480i
$953$	−21.9830	−	6.45479i	−0.712100	−	0.209091i	−0.0944328	−	0.995531i	$-0.530104\pi$
$953$	−21.9830	−	6.45479i	−0.712100	−	0.209091i	−0.617667	+	0.786440i	$0.711922\pi$
$954$	−12.4663	−	5.38526i	−0.403612	−	0.174354i
$955$	−8.10326	+	7.02152i	−0.262215	+	0.227211i
$956$	−50.2554	+	35.3083i	−1.62538	+	1.14195i
$957$	−1.02220	−	0.466822i	−0.0330429	−	0.0150902i
$958$	−0.660380	+	5.37839i	−0.0213359	+	0.173768i
$959$	−5.18620	+	1.52280i	−0.167471	+	0.0491739i
$960$	−3.95958	+	5.91074i	−0.127795	+	0.190768i
$961$	−6.10232	−	13.3622i	−0.196849	−	0.431040i
$962$	−51.4162	+	34.5621i	−1.65773	+	1.11433i
$963$	−5.94171	−	9.24548i	−0.191469	−	0.297931i
$964$	−6.97733	−	37.4801i	−0.224725	−	1.20715i
$965$			11.7085i			0.376911i
$966$	2.44174	+	4.78364i	0.0785615	+	0.153911i
$967$	5.29527			0.170284			0.0851422	−	0.996369i	$-0.472866\pi$
$967$	5.29527			0.170284			0.0851422	+	0.996369i	$0.472866\pi$
$968$	22.1493	−	16.2541i	0.711906	−	0.522427i
$969$	10.5294	−	6.76681i	0.338252	−	0.217381i
$970$	5.41597	+	8.05704i	0.173896	+	0.258696i
$971$	−23.9576	+	10.9411i	−0.768836	+	0.351116i	−0.760914	−	0.648853i	$-0.775249\pi$
$971$	−23.9576	+	10.9411i	−0.768836	+	0.351116i	−0.00792235	+	0.999969i	$0.502522\pi$
$972$	1.45620	−	1.37095i	0.0467075	−	0.0439731i
$973$	−0.658458	−	2.24250i	−0.0211092	−	0.0718913i
$974$	0.839869	−	6.84022i	0.0269112	−	0.219175i
$975$	−11.2307	+	24.5918i	−0.359670	+	0.787567i
$976$	31.9526	+	1.92879i	1.02278	+	0.0617390i
$977$	−30.1546	−	34.8003i	−0.964731	−	1.11336i	−0.993507	−	0.113773i	$-0.963706\pi$
$977$	−30.1546	−	34.8003i	−0.964731	−	1.11336i	0.0287757	−	0.999586i	$-0.490839\pi$
$978$	−9.87252	+	22.8539i	−0.315688	+	0.730786i
$979$	0.429571	−	1.46298i	0.0137291	−	0.0467572i
$980$	−10.1076	+	5.12993i	−0.322877	+	0.163870i
$981$	10.0608	−	15.6549i	0.321217	−	0.499824i
$982$	0.135585	−	0.122472i	0.00432670	−	0.00390823i
$983$	7.28307	−	50.6548i	0.232294	−	1.61564i	−0.455845	−	0.890059i	$-0.650663\pi$
$983$	7.28307	−	50.6548i	0.232294	−	1.61564i	0.688139	−	0.725579i	$-0.258428\pi$
$984$	0.983924	−	0.204251i	0.0313664	−	0.00651129i
$985$	−2.62695	−	18.2708i	−0.0837016	−	0.582157i
$986$	1.35275	−	2.20357i	0.0430804	−	0.0701759i
$987$	7.62990	+	6.61135i	0.242862	+	0.210441i
$988$	54.2868	−	68.1370i	1.72709	−	2.16773i
$989$	−8.29603	−	17.1158i	−0.263798	−	0.544251i
$990$	−0.619268	−	1.28518i	−0.0196816	−	0.0408456i
$991$	18.7210	−	21.6052i	0.594693	−	0.686312i	−0.376005	−	0.926618i	$-0.622702\pi$
$991$	18.7210	−	21.6052i	0.594693	−	0.686312i	0.970697	+	0.240306i	$0.0772477\pi$
$992$	7.30055	−	21.6479i	0.231793	−	0.687321i
$993$	−3.22062	−	22.3999i	−0.102203	−	0.710840i
$994$	−2.04089	+	2.45589i	−0.0647332	+	0.0778962i
$995$	−1.90524	−	0.273933i	−0.0604003	−	0.00868426i
$996$	−9.73655	+	23.8804i	−0.308514	+	0.756680i
$997$	−3.87302	+	6.02653i	−0.122660	+	0.190862i	−0.897153	−	0.441720i	$-0.854369\pi$
$997$	−3.87302	+	6.02653i	−0.122660	+	0.190862i	0.774493	+	0.632582i	$0.218005\pi$
$998$	0.311134	+	15.0816i	0.00984879	+	0.477398i
$999$	−6.54422	−	1.92156i	−0.207050	−	0.0607954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.85.5	yes	480
8.5	even	2	inner	552.2.bb.a.85.30	yes	480
23.13	even	11	inner	552.2.bb.a.13.30	yes	480
184.13	even	22	inner	552.2.bb.a.13.5	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.13.5	✓	480	184.13	even	22	inner
552.2.bb.a.13.30	yes	480	23.13	even	11	inner
552.2.bb.a.85.5	yes	480	1.1	even	1	trivial
552.2.bb.a.85.30	yes	480	8.5	even	2	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.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36486 - 0.370358i) q^{2} +(0.540641 + 0.841254i) q^{3} +(1.72567 + 1.01097i) q^{4} +(0.808939 - 0.369430i) q^{5} +(-0.426333 - 1.34842i) q^{6} +(0.759802 - 0.223098i) q^{7} +(-1.98087 - 2.01895i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-1.36486 - 0.370358i) q^{2} +(0.540641 + 0.841254i) q^{3} +(1.72567 + 1.01097i) q^{4} +(0.808939 - 0.369430i) q^{5} +(-0.426333 - 1.34842i) q^{6} +(0.759802 - 0.223098i) q^{7} +(-1.98087 - 2.01895i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(-1.24091 + 0.204623i) q^{10} +(0.857262 - 0.742822i) q^{11} +(0.0824854 + 1.99830i) q^{12} +(1.80954 - 6.16272i) q^{13} +(-1.11965 + 0.0230985i) q^{14} +(0.748130 + 0.480794i) q^{15} +(1.95588 + 3.48920i) q^{16} +(0.262648 - 1.82676i) q^{17} +(0.903871 - 1.08767i) q^{18} +(6.71287 - 0.965165i) q^{19} +(1.76944 + 0.180299i) q^{20} +(0.598462 + 0.518570i) q^{21} +(-1.44515 + 0.696352i) q^{22} +(-4.76142 - 0.573480i) q^{23} +(0.627504 - 2.75794i) q^{24} +(-2.75640 + 3.18106i) q^{25} +(-4.75217 + 7.74106i) q^{26} +(-0.989821 + 0.142315i) q^{27} +(1.53671 + 0.383144i) q^{28} +(-0.980596 - 0.140988i) q^{29} +(-0.843025 - 0.933290i) q^{30} +(3.39749 + 2.18343i) q^{31} +(-1.37724 - 5.48664i) q^{32} +(1.08837 + 0.319575i) q^{33} +(-1.03503 + 2.39599i) q^{34} +(0.532214 - 0.461166i) q^{35} +(-1.63648 + 1.14975i) q^{36} +(6.20415 + 2.83334i) q^{37} +(-9.51957 - 1.16885i) q^{38} +(6.16272 - 1.80954i) q^{39} +(-2.34826 - 0.901410i) q^{40} +(0.147591 + 0.323180i) q^{41} +(-0.624759 - 0.929419i) q^{42} +(2.14419 + 3.33643i) q^{43} +(2.23032 - 0.415199i) q^{44} +0.889303i q^{45} +(6.28627 + 2.54615i) q^{46} +12.7492 q^{47} +(-1.87788 + 3.53179i) q^{48} +(-5.36125 + 3.44547i) q^{49} +(4.94022 - 3.32083i) q^{50} +(1.67876 - 0.766665i) q^{51} +(9.35299 - 8.80544i) q^{52} +(-2.70529 - 9.21338i) q^{53} +(1.40367 + 0.172348i) q^{54} +(0.419052 - 0.917596i) q^{55} +(-1.95549 - 1.09207i) q^{56} +(4.44120 + 5.12542i) q^{57} +(1.28616 + 0.555600i) q^{58} +(-2.36063 + 8.03958i) q^{59} +(0.804957 + 1.58603i) q^{60} +(4.32658 - 6.73229i) q^{61} +(-3.82843 - 4.23836i) q^{62} +(-0.112696 + 0.783819i) q^{63} +(-0.152282 + 7.99855i) q^{64} +(-0.812888 - 5.65376i) q^{65} +(-1.36712 - 0.839261i) q^{66} +(-9.22604 - 7.99441i) q^{67} +(2.30004 - 2.88685i) q^{68} +(-2.09178 - 4.31561i) q^{69} +(-0.897193 + 0.432317i) q^{70} +(1.86726 - 2.15493i) q^{71} +(2.65938 - 0.963165i) q^{72} +(0.472028 + 3.28303i) q^{73} +(-7.41843 - 6.16486i) q^{74} +(-4.16630 - 0.599023i) q^{75} +(12.5600 + 5.12096i) q^{76} +(0.485627 - 0.755651i) q^{77} +(-9.08141 + 0.187351i) q^{78} +(6.92887 + 2.03450i) q^{79} +(2.87120 + 2.09999i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-0.0817489 - 0.495756i) q^{82} +(11.7293 + 5.35658i) q^{83} +(0.508489 + 1.49991i) q^{84} +(-0.462392 - 1.57476i) q^{85} +(-1.69085 - 5.34787i) q^{86} +(-0.411543 - 0.901154i) q^{87} +(-3.19784 - 0.259330i) q^{88} +(1.13081 - 0.726727i) q^{89} +(0.329360 - 1.21377i) q^{90} -5.08615i q^{91} +(-7.63687 - 5.80329i) q^{92} +4.03860i q^{93} +(-17.4008 - 4.72176i) q^{94} +(5.07374 - 3.26070i) q^{95} +(3.87106 - 4.12491i) q^{96} +(-3.20667 - 7.02163i) q^{97} +(8.59339 - 2.71699i) q^{98} +(0.319575 + 1.08837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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