LMFDB - Embedded newform 552.2.bb.a.13.19

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			13.19
Character	$\chi$	$=$	552.13
Dual form			552.2.bb.a.85.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.464427 + 1.33578i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(-1.56862 - 1.24074i) q^{4} +(0.798595 + 0.364706i) q^{5} +(-0.872641 - 1.11288i) q^{6} +(2.23854 + 0.657294i) q^{7} +(2.38587 - 1.51909i) q^{8} +(-0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.464427 + 1.33578i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(-1.56862 - 1.24074i) q^{4} +(0.798595 + 0.364706i) q^{5} +(-0.872641 - 1.11288i) q^{6} +(2.23854 + 0.657294i) q^{7} +(2.38587 - 1.51909i) q^{8} +(-0.415415 - 0.909632i) q^{9} +(-0.858056 + 0.897368i) q^{10} +(-0.502993 - 0.435846i) q^{11} +(1.89184 - 0.648807i) q^{12} +(0.537093 + 1.82917i) q^{13} +(-1.91764 + 2.68493i) q^{14} +(-0.738563 + 0.474646i) q^{15} +(0.921110 + 3.89250i) q^{16} +(0.515855 + 3.58785i) q^{17} +(1.40800 - 0.132446i) q^{18} +(7.17209 + 1.03119i) q^{19} +(-0.800182 - 1.56294i) q^{20} +(-1.76320 + 1.52782i) q^{21} +(0.815797 - 0.469469i) q^{22} +(2.85319 + 3.85478i) q^{23} +(-0.0119570 + 2.82840i) q^{24} +(-2.76956 - 3.19624i) q^{25} +(-2.69281 - 0.132078i) q^{26} +(0.989821 + 0.142315i) q^{27} +(-2.69587 - 3.80849i) q^{28} +(-7.91207 + 1.13758i) q^{29} +(-0.291014 - 1.20700i) q^{30} +(0.262872 - 0.168938i) q^{31} +(-5.62731 - 0.577381i) q^{32} +(0.638595 - 0.187509i) q^{33} +(-5.03215 - 0.977225i) q^{34} +(1.54797 + 1.34132i) q^{35} +(-0.476994 + 1.94229i) q^{36} +(5.02490 - 2.29479i) q^{37} +(-4.70835 + 9.10142i) q^{38} +(-1.82917 - 0.537093i) q^{39} +(2.45936 - 0.342998i) q^{40} +(-4.68380 + 10.2561i) q^{41} +(-1.22195 - 3.06480i) q^{42} +(-4.26279 + 6.63302i) q^{43} +(0.248230 + 1.30776i) q^{44} -0.877932i q^{45} +(-6.47423 + 2.02097i) q^{46} -1.07988 q^{47} +(-3.77257 - 1.32956i) q^{48} +(-1.30976 - 0.841729i) q^{49} +(5.55574 - 2.21510i) q^{50} +(-3.29718 - 1.50577i) q^{51} +(1.42704 - 3.53566i) q^{52} +(1.94531 - 6.62511i) q^{53} +(-0.649801 + 1.25609i) q^{54} +(-0.242732 - 0.531509i) q^{55} +(6.33935 - 1.83233i) q^{56} +(-4.74502 + 5.47604i) q^{57} +(2.15501 - 11.0971i) q^{58} +(1.87348 + 6.38048i) q^{59} +(1.74744 + 0.171831i) q^{60} +(-3.59725 - 5.59743i) q^{61} +(0.103579 + 0.429599i) q^{62} +(-0.332027 - 2.30930i) q^{63} +(3.38473 - 7.24870i) q^{64} +(-0.238190 + 1.65665i) q^{65} +(-0.0461107 + 0.940107i) q^{66} +(11.3947 - 9.87360i) q^{67} +(3.64242 - 6.26800i) q^{68} +(-4.78540 + 0.316205i) q^{69} +(-2.51063 + 1.44480i) q^{70} +(0.962374 + 1.11064i) q^{71} +(-2.37294 - 1.53921i) q^{72} +(-1.90058 + 13.2188i) q^{73} +(0.731643 + 7.77792i) q^{74} +(4.18619 - 0.601883i) q^{75} +(-9.97080 - 10.5163i) q^{76} +(-0.839490 - 1.30627i) q^{77} +(1.56695 - 2.19393i) q^{78} +(7.03350 - 2.06522i) q^{79} +(-0.684025 + 3.44446i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-11.5246 - 11.0197i) q^{82} +(2.45570 - 1.12148i) q^{83} +(4.66141 - 0.208885i) q^{84} +(-0.896551 + 3.05337i) q^{85} +(-6.88051 - 8.77470i) q^{86} +(3.32059 - 7.27108i) q^{87} +(-1.86216 - 0.275779i) q^{88} +(6.06892 + 3.90026i) q^{89} +(1.17272 + 0.407735i) q^{90} +4.44770i q^{91} +(0.307234 - 9.58674i) q^{92} +0.312477i q^{93} +(0.501525 - 1.44248i) q^{94} +(5.35151 + 3.43921i) q^{95} +(3.52808 - 4.42184i) q^{96} +(-2.94001 + 6.43773i) q^{97} +(1.73265 - 1.35862i) q^{98} +(-0.187509 + 0.638595i) 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 $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	−0.464427	+	1.33578i	−0.328399	+	0.944539i
$2$	−0.464427	+	1.33578i	−0.328399	+	0.944539i
$3$	−0.540641	+	0.841254i	−0.312139	+	0.485698i
$3$	−0.540641	+	0.841254i	−0.312139	+	0.485698i
$4$	−1.56862	−	1.24074i	−0.784308	−	0.620372i
$5$	0.798595	+	0.364706i	0.357142	+	0.163102i	0.585903	−	0.810381i	$-0.300740\pi$
$5$	0.798595	+	0.364706i	0.357142	+	0.163102i	−0.228760	+	0.973483i	$0.573467\pi$
$6$	−0.872641	−	1.11288i	−0.356254	−	0.454330i
$7$	2.23854	+	0.657294i	0.846088	+	0.248434i	0.675914	−	0.736980i	$-0.263749\pi$
$7$	2.23854	+	0.657294i	0.846088	+	0.248434i	0.170174	+	0.985414i	$0.445567\pi$
$8$	2.38587	−	1.51909i	0.843532	−	0.537080i
$9$	−0.415415	−	0.909632i	−0.138472	−	0.303211i
$10$	−0.858056	+	0.897368i	−0.271341	+	0.283773i
$11$	−0.502993	−	0.435846i	−0.151658	−	0.131412i	0.575727	−	0.817642i	$-0.304719\pi$
$11$	−0.502993	−	0.435846i	−0.151658	−	0.131412i	−0.727385	+	0.686230i	$0.759265\pi$
$12$	1.89184	−	0.648807i	0.546126	−	0.187294i
$13$	0.537093	+	1.82917i	0.148963	+	0.507321i	0.999837	−	0.0180485i	$-0.00574533\pi$
$13$	0.537093	+	1.82917i	0.148963	+	0.507321i	−0.850874	+	0.525369i	$0.823927\pi$
$14$	−1.91764	+	2.68493i	−0.512510	+	0.717578i
$15$	−0.738563	+	0.474646i	−0.190696	+	0.122553i
$16$	0.921110	+	3.89250i	0.230277	+	0.973125i
$17$	0.515855	+	3.58785i	0.125113	+	0.870181i	0.951625	+	0.307262i	$0.0994127\pi$
$17$	0.515855	+	3.58785i	0.125113	+	0.870181i	−0.826512	+	0.562919i	$0.809678\pi$
$18$	1.40800	−	0.132446i	0.331868	−	0.0312177i
$19$	7.17209	+	1.03119i	1.64539	+	0.236571i	0.901828	−	0.432096i	$-0.142226\pi$
$19$	7.17209	+	1.03119i	1.64539	+	0.236571i	0.743562	+	0.668667i	$0.233135\pi$
$20$	−0.800182	−	1.56294i	−0.178926	−	0.349483i
$21$	−1.76320	+	1.52782i	−0.384761	+	0.333397i
$22$	0.815797	−	0.469469i	0.173929	−	0.100091i
$23$	2.85319	+	3.85478i	0.594931	+	0.803777i
$23$	2.85319	+	3.85478i	0.594931	+	0.803777i
$24$	−0.0119570	+	2.82840i	−0.00244072	+	0.577345i
$25$	−2.76956	−	3.19624i	−0.553912	−	0.639249i
$26$	−2.69281	−	0.132078i	−0.528104	−	0.0259026i
$27$	0.989821	+	0.142315i	0.190491	+	0.0273885i
$28$	−2.69587	−	3.80849i	−0.509472	−	0.719738i
$29$	−7.91207	+	1.13758i	−1.46923	+	0.211244i	−0.829998	−	0.557766i	$-0.811658\pi$
$29$	−7.91207	+	1.13758i	−1.46923	+	0.211244i	−0.639236	+	0.769010i	$0.720749\pi$
$30$	−0.291014	−	1.20700i	−0.0531316	−	0.220366i
$31$	0.262872	−	0.168938i	0.0472133	−	0.0303421i	−0.516821	−	0.856093i	$-0.672885\pi$
$31$	0.262872	−	0.168938i	0.0472133	−	0.0303421i	0.564035	+	0.825751i	$0.309248\pi$
$32$	−5.62731	−	0.577381i	−0.994777	−	0.102067i
$33$	0.638595	−	0.187509i	0.111165	−	0.0326410i
$34$	−5.03215	−	0.977225i	−0.863007	−	0.167593i
$35$	1.54797	+	1.34132i	0.261654	+	0.226725i
$36$	−0.476994	+	1.94229i	−0.0794990	+	0.323714i
$37$	5.02490	−	2.29479i	0.826088	−	0.377262i	0.0429253	−	0.999078i	$-0.486332\pi$
$37$	5.02490	−	2.29479i	0.826088	−	0.377262i	0.783163	+	0.621816i	$0.213605\pi$
$38$	−4.70835	+	9.10142i	−0.763796	+	1.47644i
$39$	−1.82917	−	0.537093i	−0.292902	−	0.0860037i
$40$	2.45936	−	0.342998i	0.388859	−	0.0542327i
$41$	−4.68380	+	10.2561i	−0.731487	+	1.60173i	0.0655839	+	0.997847i	$0.479109\pi$
$41$	−4.68380	+	10.2561i	−0.731487	+	1.60173i	−0.797071	+	0.603886i	$0.793618\pi$
$42$	−1.22195	−	3.06480i	−0.188552	−	0.472909i
$43$	−4.26279	+	6.63302i	−0.650069	+	1.01153i	0.347209	+	0.937788i	$0.387130\pi$
$43$	−4.26279	+	6.63302i	−0.650069	+	1.01153i	−0.997278	+	0.0737389i	$0.976507\pi$
$44$	0.248230	+	1.30776i	0.0374220	+	0.197152i
$45$		−	0.877932i		−	0.130874i
$46$	−6.47423	+	2.02097i	−0.954573	+	0.297976i
$47$	−1.07988			−0.157517			−0.0787583	−	0.996894i	$-0.525096\pi$
$47$	−1.07988			−0.157517			−0.0787583	+	0.996894i	$0.525096\pi$
$48$	−3.77257	−	1.32956i	−0.544523	−	0.191905i
$49$	−1.30976	−	0.841729i	−0.187108	−	0.120247i
$50$	5.55574	−	2.21510i	0.785700	−	0.313263i
$51$	−3.29718	−	1.50577i	−0.461698	−	0.210850i
$52$	1.42704	−	3.53566i	0.197895	−	0.490308i
$53$	1.94531	−	6.62511i	0.267209	−	0.910029i	−0.711137	−	0.703053i	$-0.751820\pi$
$53$	1.94531	−	6.62511i	0.267209	−	0.910029i	0.978346	−	0.206976i	$-0.0663622\pi$
$54$	−0.649801	+	1.25609i	−0.0884267	+	0.170932i
$55$	−0.242732	−	0.531509i	−0.0327300	−	0.0716686i
$56$	6.33935	−	1.83233i	0.847131	−	0.244855i
$57$	−4.74502	+	5.47604i	−0.628493	+	0.725319i
$58$	2.15501	−	11.0971i	0.282967	−	1.45712i
$59$	1.87348	+	6.38048i	0.243906	+	0.830668i	0.986895	+	0.161364i	$0.0515893\pi$
$59$	1.87348	+	6.38048i	0.243906	+	0.830668i	−0.742989	+	0.669304i	$0.766593\pi$
$60$	1.74744	+	0.171831i	0.225593	+	0.0221833i
$61$	−3.59725	−	5.59743i	−0.460581	−	0.716678i	0.530827	−	0.847480i	$-0.321881\pi$
$61$	−3.59725	−	5.59743i	−0.460581	−	0.716678i	−0.991409	+	0.130802i	$0.958245\pi$
$62$	0.103579	+	0.429599i	0.0131545	+	0.0545591i
$63$	−0.332027	−	2.30930i	−0.0418314	−	0.290944i
$64$	3.38473	−	7.24870i	0.423091	−	0.906087i
$65$	−0.238190	+	1.65665i	−0.0295438	+	0.205482i
$66$	−0.0461107	+	0.940107i	−0.00567583	+	0.115719i
$67$	11.3947	−	9.87360i	1.39209	−	1.20625i	0.440933	−	0.897540i	$-0.354648\pi$
$67$	11.3947	−	9.87360i	1.39209	−	1.20625i	0.951156	−	0.308712i	$-0.0998979\pi$
$68$	3.64242	−	6.26800i	0.441709	−	0.760107i
$69$	−4.78540	+	0.316205i	−0.576094	+	0.0380666i
$70$	−2.51063	+	1.44480i	−0.300077	+	0.172686i
$71$	0.962374	+	1.11064i	0.114213	+	0.131809i	0.809977	−	0.586462i	$-0.199480\pi$
$71$	0.962374	+	1.11064i	0.114213	+	0.131809i	−0.695764	+	0.718270i	$0.744934\pi$
$72$	−2.37294	−	1.53921i	−0.279653	−	0.181397i
$73$	−1.90058	+	13.2188i	−0.222446	+	1.54715i	0.506298	+	0.862359i	$0.331014\pi$
$73$	−1.90058	+	13.2188i	−0.222446	+	1.54715i	−0.728744	+	0.684787i	$0.759895\pi$
$74$	0.731643	+	7.77792i	0.0850518	+	0.904165i
$75$	4.18619	−	0.601883i	0.483379	−	0.0694995i
$76$	−9.97080	−	10.5163i	−1.14373	−	1.20630i
$77$	−0.839490	−	1.30627i	−0.0956688	−	0.148864i
$78$	1.56695	−	2.19393i	0.177423	−	0.248414i
$79$	7.03350	−	2.06522i	0.791330	−	0.232356i	0.139002	−	0.990292i	$-0.455611\pi$
$79$	7.03350	−	2.06522i	0.791330	−	0.232356i	0.652328	+	0.757936i	$0.273792\pi$
$80$	−0.684025	+	3.44446i	−0.0764763	+	0.385103i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	−11.5246	−	11.0197i	−1.27268	−	1.21693i
$83$	2.45570	−	1.12148i	0.269548	−	0.123098i	−0.276056	−	0.961142i	$-0.589028\pi$
$83$	2.45570	−	1.12148i	0.269548	−	0.123098i	0.545604	+	0.838043i	$0.316300\pi$
$84$	4.66141	−	0.208885i	0.508601	−	0.0227912i
$85$	−0.896551	+	3.05337i	−0.0972446	+	0.331185i
$86$	−6.88051	−	8.77470i	−0.741944	−	0.946200i
$87$	3.32059	−	7.27108i	0.356005	−	0.779542i
$88$	−1.86216	−	0.275779i	−0.198507	−	0.0293981i
$89$	6.06892	+	3.90026i	0.643304	+	0.413426i	0.821214	−	0.570621i	$-0.193297\pi$
$89$	6.06892	+	3.90026i	0.643304	+	0.413426i	−0.177910	+	0.984047i	$0.556934\pi$
$90$	1.17272	+	0.407735i	0.123616	+	0.0429790i
$91$			4.44770i			0.466246i
$92$	0.307234	−	9.58674i	0.0320314	−	0.999487i
$93$			0.312477i			0.0324024i
$94$	0.501525	−	1.44248i	0.0517283	−	0.148780i
$95$	5.35151	+	3.43921i	0.549053	+	0.352855i
$96$	3.52808	−	4.42184i	0.360083	−	0.451302i
$97$	−2.94001	+	6.43773i	−0.298513	+	0.653653i	−0.998147	−	0.0608488i	$-0.980619\pi$
$97$	−2.94001	+	6.43773i	−0.298513	+	0.653653i	0.699634	+	0.714502i	$0.253347\pi$
$98$	1.73265	−	1.35862i	0.175024	−	0.137242i
$99$	−0.187509	+	0.638595i	−0.0188453	+	0.0641812i
$100$	0.378657	+	8.44999i	0.0378657	+	0.844999i
$101$	7.46545	−	3.40936i	0.742840	−	0.339244i	−0.00778702	−	0.999970i	$-0.502479\pi$
$101$	7.46545	−	3.40936i	0.742840	−	0.339244i	0.750627	+	0.660726i	$0.229751\pi$
$102$	3.54268	−	3.70499i	0.350778	−	0.366849i
$103$	7.77399	−	8.97167i	0.765994	−	0.884005i	−0.230021	−	0.973186i	$-0.573879\pi$
$103$	7.77399	−	8.97167i	0.765994	−	0.884005i	0.996015	+	0.0891810i	$0.0284249\pi$
$104$	4.06011	+	3.54827i	0.398127	+	0.347936i
$105$	−1.96528	+	0.577059i	−0.191792	+	0.0563152i
$106$	7.94624	+	5.67538i	0.771807	+	0.551242i
$107$	1.28815	+	2.00440i	0.124530	+	0.193772i	0.897921	−	0.440157i	$-0.145077\pi$
$107$	1.28815	+	2.00440i	0.124530	+	0.193772i	−0.773391	+	0.633930i	$0.781441\pi$
$108$	−1.37607	−	1.45135i	−0.132413	−	0.139656i
$109$	−0.950732	+	0.136695i	−0.0910636	+	0.0130930i	−0.187696	−	0.982227i	$-0.560102\pi$
$109$	−0.950732	+	0.136695i	−0.0910636	+	0.0130930i	0.0966324	+	0.995320i	$0.469193\pi$
$110$	0.822710	−	0.0773895i	0.0784423	−	0.00737880i
$111$	−0.786162	+	5.46787i	−0.0746192	+	0.518988i
$112$	−0.496578	+	9.31895i	−0.0469222	+	0.880558i
$113$	−0.474768	−	0.547912i	−0.0446625	−	0.0515432i	0.732979	−	0.680251i	$-0.238129\pi$
$113$	−0.474768	−	0.547912i	−0.0446625	−	0.0515432i	−0.777641	+	0.628708i	$0.783584\pi$
$114$	−5.11107	−	8.88151i	−0.478696	−	0.831830i
$115$	0.872681	+	4.11898i	0.0813780	+	0.384097i
$116$	13.8224	+	8.03242i	1.28338	+	0.745791i
$117$	1.44076	−	1.24842i	0.133198	−	0.115417i
$118$	−9.39301	−	0.460711i	−0.864697	−	0.0424119i
$119$	−1.20351	+	8.37061i	−0.110326	+	0.767332i
$120$	−1.04108	+	2.25439i	−0.0950375	+	0.205796i
$121$	−1.50242	−	10.4496i	−0.136584	−	0.949962i
$122$	9.14760	−	2.20554i	0.828185	−	0.199680i
$123$	−6.09572	−	9.48513i	−0.549633	−	0.855245i
$124$	−0.621954	−	0.0611587i	−0.0558531	−	0.00549222i
$125$	−2.28278	−	7.77443i	−0.204178	−	0.695366i
$126$	3.23891	+	0.628984i	0.288545	+	0.0560344i
$127$	8.84513	−	10.2078i	0.784878	−	0.905798i	−0.212573	−	0.977145i	$-0.568184\pi$
$127$	8.84513	−	10.2078i	0.784878	−	0.905798i	0.997452	+	0.0713474i	$0.0227299\pi$
$128$	8.11071	+	7.88774i	0.716892	+	0.697184i
$129$	−3.27542	−	7.17217i	−0.288385	−	0.631474i
$130$	−2.10230	−	1.08756i	−0.184383	−	0.0953854i
$131$	−2.44317	+	8.32066i	−0.213461	+	0.726980i	0.781246	+	0.624223i	$0.214584\pi$
$131$	−2.44317	+	8.32066i	−0.213461	+	0.726980i	−0.994707	+	0.102757i	$0.967234\pi$
$132$	−1.23436	−	0.498204i	−0.107437	−	0.0433631i
$133$	15.3772	+	7.02253i	1.33337	+	0.608931i
$134$	7.89693	+	19.8064i	0.682191	+	1.71101i
$135$	0.738563	+	0.474646i	0.0635654	+	0.0408510i
$136$	6.68103	+	7.77650i	0.572893	+	0.666830i
$137$	0.315194			0.0269289			0.0134644	−	0.999909i	$-0.495714\pi$
$137$	0.315194			0.0269289			0.0134644	+	0.999909i	$0.495714\pi$
$138$	1.80009	−	6.53909i	0.153233	−	0.556644i
$139$		−	4.50500i		−	0.382109i	−0.981579	−	0.191055i	$-0.938809\pi$
$139$		−	4.50500i		−	0.382109i	0.981579	−	0.191055i	$-0.0611908\pi$
$140$	−0.763929	−	4.02465i	−0.0645638	−	0.340145i
$141$	0.583827	−	0.908452i	0.0491671	−	0.0765054i
$142$	−1.93052	+	0.769710i	−0.162006	+	0.0645926i
$143$	0.527083	−	1.15415i	0.0440769	−	0.0965149i
$144$	3.15810	−	2.45487i	0.263175	−	0.204573i
$145$	−6.73342	−	1.97711i	−0.559180	−	0.164190i
$146$	−16.7747	−	8.67793i	−1.38829	−	0.718190i
$147$	1.41621	−	0.646764i	0.116807	−	0.0533442i
$148$	−10.7294	−	2.63496i	−0.881950	−	0.216593i
$149$	−8.03928	−	6.96608i	−0.658604	−	0.570683i	0.260124	−	0.965575i	$-0.416237\pi$
$149$	−8.03928	−	6.96608i	−0.658604	−	0.570683i	−0.918728	+	0.394892i	$0.870782\pi$
$150$	−1.14019	+	5.87136i	−0.0930965	+	0.479394i
$151$	−13.7869	+	4.04820i	−1.12196	+	0.329438i	−0.789544	−	0.613694i	$-0.789683\pi$
$151$	−13.7869	+	4.04820i	−1.12196	+	0.329438i	−0.332419	+	0.943132i	$0.607865\pi$
$152$	18.6781	−	8.43477i	1.51500	−	0.684150i
$153$	3.04933	−	1.95968i	0.246524	−	0.158431i
$154$	2.13477	−	0.514706i	0.172025	−	0.0414762i
$155$	0.271541	−	0.0390417i	0.0218107	−	0.00313591i
$156$	2.20287	+	3.11203i	0.176371	+	0.249161i
$157$	13.7536	+	1.97747i	1.09766	+	0.157819i	0.667263	−	0.744822i	$-0.267466\pi$
$157$	13.7536	+	1.97747i	1.09766	+	0.157819i	0.430393	+	0.902641i	$0.358375\pi$
$158$	−0.507863	+	10.3544i	−0.0404034	+	0.823748i
$159$	4.52169	+	5.21830i	0.358593	+	0.413838i
$160$	−4.28337	−	2.51341i	−0.338630	−	0.198702i
$161$	3.85325	+	10.5045i	0.303679	+	0.827867i
$162$	−0.705380	−	1.22574i	−0.0554199	−	0.0963032i
$163$	−5.72439	+	4.96021i	−0.448369	+	0.388514i	−0.849570	−	0.527476i	$-0.823138\pi$
$163$	−5.72439	+	4.96021i	−0.448369	+	0.388514i	0.401201	+	0.915990i	$0.368593\pi$
$164$	20.0723	−	10.2765i	1.56738	−	0.802458i
$165$	0.578364	+	0.0831563i	0.0450256	+	0.00647371i
$166$	0.357558	+	3.80112i	0.0277519	+	0.295024i
$167$	−2.65157	−	18.4421i	−0.205185	−	1.42709i	−0.788594	−	0.614914i	$-0.789191\pi$
$167$	−2.65157	−	18.4421i	−0.205185	−	1.42709i	0.583409	−	0.812178i	$-0.301718\pi$
$168$	−1.88586	+	6.32363i	−0.145497	+	0.487878i
$169$	7.87890	−	5.06346i	0.606069	−	0.389497i
$170$	−3.66225	−	2.61566i	−0.280882	−	0.200612i
$171$	−2.04139	−	6.95233i	−0.156109	−	0.531658i
$172$	14.9166	−	5.11564i	1.13738	−	0.390064i
$173$	−4.89436	−	4.24098i	−0.372111	−	0.322436i	0.448650	−	0.893707i	$-0.351905\pi$
$173$	−4.89436	−	4.24098i	−0.372111	−	0.322436i	−0.820761	+	0.571271i	$0.806450\pi$
$174$	8.17039	+	7.81246i	0.619396	+	0.592261i
$175$	−4.09890	−	8.97533i	−0.309847	−	0.678471i
$176$	1.23322	−	2.35936i	0.0929573	−	0.177844i
$177$	−6.38048	−	1.87348i	−0.479586	−	0.140819i
$178$	−8.02845	+	6.29535i	−0.601758	+	0.471857i
$179$	12.1040	+	5.52770i	0.904693	+	0.413160i	0.812755	−	0.582605i	$-0.197967\pi$
$179$	12.1040	+	5.52770i	0.904693	+	0.413160i	0.0919381	+	0.995765i	$0.470694\pi$
$180$	−1.08929	+	1.37714i	−0.0811908	+	0.102646i
$181$	−5.24150	+	8.15593i	−0.389597	+	0.606225i	−0.979547	−	0.201215i	$-0.935511\pi$
$181$	−5.24150	+	8.15593i	−0.389597	+	0.606225i	0.589950	+	0.807440i	$0.299147\pi$
$182$	−5.94115	−	2.06563i	−0.440387	−	0.153115i
$183$	6.65368			0.491854
$184$	12.6631	+	4.86274i	0.933535	+	0.358486i
$185$	4.84978			0.356563
$186$	−0.417400	−	0.145123i	−0.0306053	−	0.0106409i
$187$	1.30428	−	2.02950i	0.0953782	−	0.148411i
$188$	1.69391	+	1.33985i	0.123541	+	0.0977188i
$189$	2.12221	+	0.969181i	0.154368	+	0.0704976i
$190$	−7.07941	+	5.55118i	−0.513594	+	0.402725i
$191$	−20.4317	−	5.99928i	−1.47838	−	0.434092i	−0.559569	−	0.828784i	$-0.689033\pi$
$191$	−20.4317	−	5.99928i	−1.47838	−	0.434092i	−0.918814	+	0.394691i	$0.870852\pi$
$192$	4.26807	+	6.76636i	0.308021	+	0.488320i
$193$	−8.45357	−	18.5107i	−0.608501	−	1.33243i	−0.923594	−	0.383371i	$-0.874763\pi$
$193$	−8.45357	−	18.5107i	−0.608501	−	1.33243i	0.315093	−	0.949061i	$-0.397964\pi$
$194$	−7.23397	−	6.91707i	−0.519369	−	0.496617i
$195$	−1.26489	−	1.09603i	−0.0905803	−	0.0784883i
$196$	1.01013	+	2.94542i	0.0721524	+	0.210387i
$197$	−7.06945	−	24.0763i	−0.503677	−	1.71537i	−0.681962	−	0.731388i	$-0.738873\pi$
$197$	−7.06945	−	24.0763i	−0.503677	−	1.71537i	0.178284	−	0.983979i	$-0.442945\pi$
$198$	−0.765939	−	0.547051i	−0.0544329	−	0.0388772i
$199$	19.5169	−	12.5428i	1.38352	−	0.889133i	0.384101	−	0.923291i	$-0.374511\pi$
$199$	19.5169	−	12.5428i	1.38352	−	0.889133i	0.999416	+	0.0341581i	$0.0108750\pi$
$200$	−11.4632	−	3.41860i	−0.810570	−	0.241731i
$201$	2.14574	+	14.9239i	0.151349	+	1.05265i
$202$	1.08700	+	11.5556i	0.0764808	+	0.813049i
$203$	−18.4592	−	2.65403i	−1.29558	−	0.186277i
$204$	3.30373	+	6.45294i	0.231308	+	0.451796i
$205$	−7.48092	+	6.48225i	−0.522490	+	0.452740i
$206$	8.37372	+	14.5510i	0.583425	+	1.01382i
$207$	2.32117	−	4.19668i	0.161333	−	0.291690i
$208$	−6.62533	+	3.77550i	−0.459384	+	0.261784i
$209$	−3.15807	−	3.64461i	−0.218448	−	0.252103i
$210$	0.141906	−	2.89319i	0.00979245	−	0.199649i
$211$	3.44198	+	0.494881i	0.236955	+	0.0340690i	0.259769	−	0.965671i	$-0.416353\pi$
$211$	3.44198	+	0.494881i	0.236955	+	0.0340690i	−0.0228140	+	0.999740i	$0.507263\pi$
$212$	−11.2715	+	7.97862i	−0.774130	+	0.547974i
$213$	−1.45463	+	0.209144i	−0.0996695	+	0.0143303i
$214$	−3.27568	+	0.789786i	−0.223921	+	0.0539887i
$215$	−5.82334	+	3.74244i	−0.397149	+	0.255232i
$216$	2.57777	−	1.16408i	0.175395	−	0.0792059i
$217$	0.699492	−	0.205389i	0.0474846	−	0.0139427i
$218$	0.258951	−	1.33345i	0.0175384	−	0.0903129i
$219$	−10.0928	−	8.74550i	−0.682011	−	0.590966i
$220$	−0.278713	+	1.13490i	−0.0187908	+	0.0765150i
$221$	−6.28573	+	2.87060i	−0.422824	+	0.193097i
$222$	−6.93876	−	3.58957i	−0.465699	−	0.240916i
$223$	−4.84012	−	1.42119i	−0.324119	−	0.0951698i	0.115626	−	0.993293i	$-0.463113\pi$
$223$	−4.84012	−	1.42119i	−0.324119	−	0.0951698i	−0.439744	+	0.898123i	$0.644931\pi$
$224$	−12.2174	−	4.99129i	−0.816312	−	0.333494i
$225$	−1.75689	+	3.84705i	−0.117126	+	0.256470i
$226$	0.952385	−	0.379721i	0.0633517	−	0.0252587i
$227$	−5.55146	+	8.63825i	−0.368464	+	0.573341i	−0.975135	−	0.221612i	$-0.928868\pi$
$227$	−5.55146	+	8.63825i	−0.368464	+	0.573341i	0.606671	+	0.794953i	$0.292504\pi$
$228$	14.2375	−	2.70245i	0.942899	−	0.178974i
$229$			20.2737i			1.33973i	0.742484	+	0.669863i	$0.233647\pi$
$229$			20.2737i			1.33973i	−0.742484	+	0.669863i	$0.766353\pi$
$230$	−5.90735	−	0.747255i	−0.389519	−	0.0492725i
$231$	1.55277			0.102165
$232$	−17.1491	+	14.7333i	−1.12589	+	0.967287i
$233$	−6.16918	−	3.96469i	−0.404157	−	0.259736i	0.322733	−	0.946490i	$-0.395398\pi$
$233$	−6.16918	−	3.96469i	−0.404157	−	0.259736i	−0.726890	+	0.686754i	$0.759035\pi$
$234$	0.998492	+	2.50433i	0.0652735	+	0.163713i
$235$	−0.862386	−	0.393838i	−0.0562558	−	0.0256912i
$236$	4.97777	−	12.3330i	0.324025	−	0.802812i
$237$	−2.06522	+	7.03350i	−0.134151	+	0.456875i
$238$	−10.6223	−	5.49516i	−0.688544	−	0.356198i
$239$	−3.70057	−	8.10313i	−0.239370	−	0.524148i	0.751376	−	0.659874i	$-0.229390\pi$
$239$	−3.70057	−	8.10313i	−0.239370	−	0.524148i	−0.990746	+	0.135727i	$0.956663\pi$
$240$	−2.52786	−	2.43766i	−0.163172	−	0.157350i
$241$	−9.39161	+	10.8385i	−0.604967	+	0.698169i	−0.972780	−	0.231731i	$-0.925561\pi$
$241$	−9.39161	+	10.8385i	−0.604967	+	0.698169i	0.367813	+	0.929900i	$0.380107\pi$
$242$	14.6561	+	2.84616i	0.942130	+	0.182958i
$243$	−0.281733	−	0.959493i	−0.0180732	−	0.0615515i
$244$	−1.30228	+	13.2435i	−0.0833696	+	0.847828i
$245$	−0.738981	−	1.14988i	−0.0472117	−	0.0734629i
$246$	15.5011	−	3.73740i	0.988311	−	0.238288i
$247$	1.96585	+	13.6728i	0.125084	+	0.869981i
$248$	0.370547	−	0.802390i	0.0235297	−	0.0509518i
$249$	−0.384202	+	2.67218i	−0.0243478	+	0.169343i
$250$	11.4451	+	0.561363i	0.723852	+	0.0355037i
$251$	5.02321	−	4.35264i	0.317062	−	0.274736i	−0.481760	−	0.876303i	$-0.660002\pi$
$251$	5.02321	−	4.35264i	0.317062	−	0.274736i	0.798822	+	0.601567i	$0.205457\pi$
$252$	−2.34442	+	4.03436i	−0.147685	+	0.254141i
$253$	0.244955	−	3.18248i	0.0154002	−	0.200081i
$254$	9.52749	+	16.5559i	0.597808	+	1.03881i
$255$	−2.08395	−	2.40500i	−0.130502	−	0.150607i
$256$	−14.3031	+	7.17084i	−0.893945	+	0.448178i
$257$	4.12070	−	28.6601i	0.257042	−	1.78777i	−0.296589	−	0.955005i	$-0.595849\pi$
$257$	4.12070	−	28.6601i	0.257042	−	1.78777i	0.553631	−	0.832762i	$-0.313242\pi$
$258$	11.1016	−	1.04429i	0.691157	−	0.0650148i
$259$	12.7568	−	1.83415i	0.792668	−	0.113968i
$260$	2.42910	−	2.30311i	0.150647	−	0.142833i
$261$	4.32157	+	6.72450i	0.267499	+	0.416236i
$262$	−9.97990	−	7.12787i	−0.616560	−	0.440361i
$263$	16.5426	−	4.85735i	1.02006	−	0.299517i	0.271398	−	0.962467i	$-0.412514\pi$
$263$	16.5426	−	4.85735i	1.02006	−	0.299517i	0.748663	+	0.662950i	$0.230696\pi$
$264$	1.23876	−	1.41745i	0.0762405	−	0.0872383i
$265$	3.96973	−	4.58131i	0.243859	−	0.281428i
$266$	−16.5221	+	17.2791i	−1.01304	+	1.05945i
$267$	−6.56221	+	2.99686i	−0.401601	+	0.183405i
$268$	−30.1246	+	1.34993i	−1.84015	+	0.0824600i
$269$	4.22166	−	14.3777i	0.257399	−	0.876621i	−0.724829	−	0.688929i	$-0.758081\pi$
$269$	4.22166	−	14.3777i	0.257399	−	0.876621i	0.982228	−	0.187692i	$-0.0601007\pi$
$270$	−0.977031	+	0.766120i	−0.0594602	+	0.0466246i
$271$	4.45409	−	9.75309i	0.270567	−	0.592458i	−0.724762	−	0.688999i	$-0.758050\pi$
$271$	4.45409	−	9.75309i	0.270567	−	0.592458i	0.995329	+	0.0965406i	$0.0307778\pi$
$272$	−13.4905	+	5.31277i	−0.817984	+	0.322134i
$273$	−3.74164	−	2.40461i	−0.226455	−	0.145533i
$274$	−0.146385	+	0.421030i	−0.00884342	+	0.0254354i
$275$			2.81479i			0.169738i
$276$	7.89878	+	5.44145i	0.475450	+	0.327537i
$277$			6.61011i			0.397163i	0.980084	+	0.198582i	$0.0636335\pi$
$277$			6.61011i			0.397163i	−0.980084	+	0.198582i	$0.936367\pi$
$278$	6.01769	+	2.09224i	0.360917	+	0.125484i
$279$	−0.262872	−	0.168938i	−0.0157378	−	0.0101140i
$280$	5.73083	+	0.848712i	0.342483	+	0.0507202i
$281$	1.77236	−	3.88094i	0.105730	−	0.231517i	−0.849371	−	0.527796i	$-0.823018\pi$
$281$	1.77236	−	3.88094i	0.105730	−	0.231517i	0.955101	+	0.296279i	$0.0957458\pi$
$282$	0.942347	+	1.20177i	0.0561159	+	0.0715645i
$283$	3.70161	−	12.6065i	0.220038	−	0.749380i	−0.773290	−	0.634053i	$-0.781390\pi$
$283$	3.70161	−	12.6065i	0.220038	−	0.749380i	0.993328	−	0.115327i	$-0.0367917\pi$
$284$	−0.131577	−	2.93623i	−0.00780765	−	0.174233i
$285$	−5.78649	+	2.64260i	−0.342762	+	0.156534i
$286$	1.29690	+	1.24008i	0.0766873	+	0.0733277i
$287$	−17.2261	+	19.8800i	−1.01683	+	1.17348i
$288$	1.81247	+	5.35864i	0.106801	+	0.315761i
$289$	3.70483	−	1.08784i	0.217931	−	0.0639903i
$290$	5.76816	−	8.07614i	0.338718	−	0.474248i
$291$	−3.82627	−	5.95380i	−0.224300	−	0.349018i
$292$	19.3824	−	18.3771i	1.13427	−	1.07544i
$293$	−23.8605	+	3.43062i	−1.39395	+	0.200419i	−0.798025	−	0.602624i	$-0.794122\pi$
$293$	−23.8605	+	3.43062i	−1.39395	+	0.200419i	−0.595921	+	0.803043i	$0.703213\pi$
$294$	0.206206	+	2.19213i	0.0120262	+	0.127847i
$295$	−0.830850	+	5.77869i	−0.0483739	+	0.336448i
$296$	8.50274	−	13.1084i	0.494212	−	0.761908i
$297$	−0.435846	−	0.502993i	−0.0252903	−	0.0291866i
$298$	13.0388	−	7.50348i	0.755318	−	0.434665i
$299$	−5.51862	+	7.28935i	−0.319150	+	0.421554i
$300$	−7.31330	−	4.24986i	−0.422234	−	0.245366i
$301$	−13.9023	+	12.0464i	−0.801313	+	0.694342i
$302$	0.995503	−	20.2964i	0.0572848	−	1.16792i
$303$	−1.16799	+	8.12358i	−0.0670995	+	0.466687i
$304$	2.59237	+	28.8672i	0.148683	+	1.65565i
$305$	−0.831329	−	5.78202i	−0.0476018	−	0.331078i
$306$	1.20152	+	4.98336i	0.0686862	+	0.284880i
$307$	−1.39345	−	2.16826i	−0.0795286	−	0.123749i	0.799211	−	0.601051i	$-0.205251\pi$
$307$	−1.39345	−	2.16826i	−0.0795286	−	0.123749i	−0.878739	+	0.477302i	$0.841615\pi$
$308$	−0.303912	+	3.09063i	−0.0173170	+	0.176105i
$309$	3.34451	+	11.3904i	0.190262	+	0.647974i
$310$	−0.0739598	+	0.380851i	−0.00420064	+	0.0216309i
$311$	−3.09626	+	3.57327i	−0.175573	+	0.202622i	−0.836715	−	0.547639i	$-0.815527\pi$
$311$	−3.09626	+	3.57327i	−0.175573	+	0.202622i	0.661142	+	0.750261i	$0.270072\pi$
$312$	−5.18005	+	1.49724i	−0.293263	+	0.0847647i
$313$	3.75403	+	8.22018i	0.212190	+	0.464632i	0.985561	−	0.169322i	$-0.0541579\pi$
$313$	3.75403	+	8.22018i	0.212190	+	0.464632i	−0.773370	+	0.633954i	$0.781431\pi$
$314$	−9.02900	+	17.4534i	−0.509536	+	0.984952i
$315$	0.577059	−	1.96528i	0.0325136	−	0.110731i
$316$	−13.5953	−	5.48723i	−0.764794	−	0.308681i
$317$	4.95748	+	2.26400i	0.278440	+	0.127159i	0.549741	−	0.835335i	$-0.314727\pi$
$317$	4.95748	+	2.26400i	0.278440	+	0.127159i	−0.271301	+	0.962495i	$0.587454\pi$
$318$	−9.07050	+	3.61646i	−0.508648	+	0.202801i
$319$	4.47553	+	2.87625i	0.250581	+	0.161039i
$320$	5.34667	−	4.55434i	0.298888	−	0.254595i
$321$	−2.38263			−0.132985
$322$	−15.8212	+	0.268546i	−0.881680	+	0.0149655i
$323$			26.2643i			1.46139i
$324$	1.96492	−	0.372966i	0.109162	−	0.0207203i
$325$	4.35896	−	6.78268i	0.241792	−	0.376235i
$326$	−3.96719	−	9.95018i	−0.219722	−	0.551090i
$327$	0.399010	−	0.873709i	0.0220653	−	0.0483162i
$328$	4.40501	+	31.5848i	0.243226	+	1.74398i
$329$	−2.41735	−	0.709798i	−0.133273	−	0.0391324i
$330$	−0.379686	+	0.733948i	−0.0209010	+	0.0404025i
$331$	−25.0898	+	11.4581i	−1.37906	+	0.629796i	−0.960471	−	0.278380i	$-0.910203\pi$
$331$	−25.0898	+	11.4581i	−1.37906	+	0.629796i	−0.418589	+	0.908176i	$0.637475\pi$
$332$	−5.24351	−	1.28772i	−0.287775	−	0.0706729i
$333$	−4.17484	−	3.61752i	−0.228780	−	0.198239i
$334$	25.8660	+	5.02309i	1.41533	+	0.274851i
$335$	12.7007	−	3.72927i	0.693916	−	0.203752i
$336$	−7.57113	−	5.45595i	−0.413039	−	0.297647i
$337$	−7.88030	+	5.06436i	−0.429267	+	0.275873i	−0.737382	−	0.675476i	$-0.763938\pi$
$337$	−7.88030	+	5.06436i	−0.429267	+	0.275873i	0.308115	+	0.951349i	$0.400302\pi$
$338$	3.10450	+	12.8761i	0.168862	+	0.700366i
$339$	0.717612	−	0.103177i	0.0389753	−	0.00560381i
$340$	5.19480	−	3.67718i	0.281727	−	0.199423i
$341$	−0.205854	−	0.0295973i	−0.0111476	−	0.00160278i
$342$	10.2349	+	0.502003i	0.553438	+	0.0271452i
$343$	−13.0734	−	15.0875i	−0.705897	−	0.814649i
$344$	−0.0942776	+	22.3011i	−0.00508311	+	1.20239i
$345$	−3.93691	−	1.49274i	−0.211956	−	0.0803666i
$346$	7.93809	−	4.56816i	0.426754	−	0.245586i
$347$	−22.7208	+	19.6877i	−1.21972	+	1.05689i	−0.223094	+	0.974797i	$0.571616\pi$
$347$	−22.7208	+	19.6877i	−1.21972	+	1.05689i	−0.996625	+	0.0820947i	$0.973839\pi$
$348$	−14.2303	+	7.28553i	−0.762823	+	0.390545i
$349$	18.0808	+	2.59962i	0.967841	+	0.139155i	0.608068	−	0.793885i	$-0.291945\pi$
$349$	18.0808	+	2.59962i	0.967841	+	0.139155i	0.359774	+	0.933040i	$0.382854\pi$
$350$	13.8927	−	1.30684i	0.742596	−	0.0698535i
$351$	0.271308	+	1.88699i	0.0144814	+	0.100720i
$352$	2.57885	+	2.74306i	0.137453	+	0.146206i
$353$	12.5909	−	8.09165i	0.670144	−	0.430675i	−0.160834	−	0.986982i	$-0.551418\pi$
$353$	12.5909	−	8.09165i	0.670144	−	0.430675i	0.830977	+	0.556306i	$0.187782\pi$
$354$	5.46582	−	7.65282i	0.290505	−	0.406743i
$355$	0.363490	+	1.23793i	0.0192921	+	0.0657027i
$356$	−4.68058	−	13.6480i	−0.248070	−	0.723341i
$357$	−6.39113	−	5.53795i	−0.338255	−	0.293099i
$358$	−13.0052	+	13.6010i	−0.687346	+	0.718837i
$359$	−7.29491	−	15.9736i	−0.385011	−	0.843056i	−0.998573	−	0.0534092i	$-0.982991\pi$
$359$	−7.29491	−	15.9736i	−0.385011	−	0.843056i	0.613562	−	0.789646i	$-0.289736\pi$
$360$	−1.33366	−	2.09463i	−0.0702899	−	0.110397i
$361$	32.1451	+	9.43865i	1.69185	+	0.496771i
$362$	−8.46023	−	10.7893i	−0.444660	−	0.567074i
$363$	9.60302	+	4.38555i	0.504028	+	0.230182i
$364$	5.51845	−	6.97673i	0.289246	−	0.365680i
$365$	−6.33877	+	9.86333i	−0.331787	+	0.516270i
$366$	−3.09015	+	8.88786i	−0.161525	+	0.464576i
$367$	−15.4518			−0.806575			−0.403288	−	0.915073i	$-0.632133\pi$
$367$	−15.4518			−0.806575			−0.403288	+	0.915073i	$0.632133\pi$
$368$	−12.3766	+	14.6567i	−0.645176	+	0.764034i
$369$	11.2750			0.586953
$370$	−2.25237	+	6.47824i	−0.117095	+	0.336788i
$371$	8.70930	−	13.5519i	0.452164	−	0.703581i
$372$	0.387704	−	0.490156i	0.0201015	−	0.0254134i
$373$	−30.6188	−	13.9831i	−1.58538	−	0.724020i	−0.588931	−	0.808184i	$-0.700451\pi$
$373$	−30.6188	−	13.9831i	−1.58538	−	0.724020i	−0.996452	+	0.0841635i	$0.973178\pi$
$374$	2.10522	+	2.68478i	0.108858	+	0.138827i
$375$	7.77443	+	2.28278i	0.401470	+	0.117882i
$376$	−2.57645	+	1.64043i	−0.132870	+	0.0845989i
$377$	−6.33035	−	13.8615i	−0.326030	−	0.713906i
$378$	−2.28022	+	2.38469i	−0.117282	+	0.122655i
$379$	−7.44903	−	6.45462i	−0.382631	−	0.331552i	0.442215	−	0.896909i	$-0.354193\pi$
$379$	−7.44903	−	6.45462i	−0.382631	−	0.331552i	−0.824846	+	0.565357i	$0.808738\pi$
$380$	−4.12729	−	12.0346i	−0.211725	−	0.617364i
$381$	3.80533	+	12.9598i	0.194953	+	0.663949i
$382$	17.5027	−	24.5060i	0.895517	−	1.25383i
$383$	−14.4963	+	9.31621i	−0.740727	+	0.476036i	−0.855791	−	0.517322i	$-0.826929\pi$
$383$	−14.4963	+	9.31621i	−0.740727	+	0.476036i	0.115064	+	0.993358i	$0.463293\pi$
$384$	−11.0206	+	2.55873i	−0.562391	+	0.130574i
$385$	−0.194007	−	1.34935i	−0.00988752	−	0.0687692i
$386$	28.6523	−	2.69523i	1.45837	−	0.137183i
$387$	7.80444	+	1.12211i	0.396722	+	0.0570400i
$388$	12.5993	−	6.45053i	0.639634	−	0.327476i
$389$	22.5564	−	19.5452i	1.14365	−	0.990981i	0.143654	−	0.989628i	$-0.454115\pi$
$389$	22.5564	−	19.5452i	1.14365	−	0.990981i	0.999999	−	0.00135346i	$-0.000430819\pi$
$390$	2.05150	−	1.18058i	0.103882	−	0.0597812i
$391$	−12.3585	+	12.2253i	−0.624998	+	0.618261i
$392$	−4.40357	−	0.0186160i	−0.222414	−	0.000940252i
$393$	−5.67891	−	6.55381i	−0.286463	−	0.330596i
$394$	35.4439	+	1.73846i	1.78564	+	0.0875826i
$395$	6.37011	+	0.915884i	0.320515	+	0.0460831i
$396$	1.08646	−	0.769061i	0.0545968	−	0.0386467i
$397$	4.25668	−	0.612018i	0.213637	−	0.0307163i	−0.0346654	−	0.999399i	$-0.511037\pi$
$397$	4.25668	−	0.612018i	0.213637	−	0.0307163i	0.248302	+	0.968683i	$0.420127\pi$
$398$	7.69019	+	31.8955i	0.385474	+	1.59878i
$399$	−14.2213	+	9.13945i	−0.711954	+	0.457545i
$400$	9.89031	−	13.7246i	0.494515	−	0.686230i
$401$	33.5212	−	9.84271i	1.67397	−	0.491521i	0.699235	−	0.714892i	$-0.253524\pi$
$401$	33.5212	−	9.84271i	1.67397	−	0.491521i	0.974734	+	0.223371i	$0.0717060\pi$
$402$	−20.9316	−	4.06484i	−1.04397	−	0.202736i
$403$	0.450203	+	0.390103i	0.0224262	+	0.0194324i
$404$	−15.9406	−	3.91474i	−0.793073	−	0.194766i
$405$	−0.798595	+	0.364706i	−0.0396825	+	0.0181224i
$406$	12.1181	−	23.4248i	0.601413	−	1.16255i
$407$	−3.52767	−	1.03582i	−0.174860	−	0.0513435i
$408$	−10.1540	+	1.41614i	−0.502700	+	0.0701096i
$409$	−2.94211	+	6.44232i	−0.145478	+	0.318552i	−0.968318	−	0.249721i	$-0.919661\pi$
$409$	−2.94211	+	6.44232i	−0.145478	+	0.318552i	0.822840	+	0.568273i	$0.192388\pi$
$410$	−5.18452	−	13.0034i	−0.256045	−	0.642192i
$411$	−0.170407	+	0.265158i	−0.00840556	+	0.0130793i
$412$	−23.3260	+	4.42756i	−1.14919	+	0.218130i
$413$			15.5144i			0.763412i
$414$	4.52783	+	5.04963i	0.222531	+	0.248176i
$415$	2.37012			0.116345
$416$	−1.96626	−	10.6034i	−0.0964039	−	0.519876i
$417$	3.78985	+	2.43559i	0.185590	+	0.119271i
$418$	6.33508	−	2.52583i	0.309859	−	0.123542i
$419$	27.6188	+	12.6131i	1.34927	+	0.616190i	0.953286	−	0.302068i	$-0.0976770\pi$
$419$	27.6188	+	12.6131i	1.34927	+	0.616190i	0.395982	+	0.918258i	$0.370404\pi$
$420$	3.79876	+	1.53323i	0.185360	+	0.0748139i
$421$	−1.65958	+	5.65201i	−0.0808829	+	0.275462i	−0.989998	−	0.141084i	$-0.954941\pi$
$421$	−1.65958	+	5.65201i	−0.0808829	+	0.275462i	0.909115	+	0.416546i	$0.136759\pi$
$422$	−2.25960	+	4.36788i	−0.109995	+	0.212625i
$423$	0.448598	+	0.982292i	0.0218116	+	0.0477607i
$424$	−5.42290	−	18.7617i	−0.263359	−	0.911151i
$425$	10.0389	−	11.5856i	0.486960	−	0.561982i
$426$	0.396198	−	2.04019i	0.0191958	−	0.0988478i
$427$	−4.37343	−	14.8945i	−0.211645	−	0.720797i
$428$	0.466334	−	4.74239i	0.0225411	−	0.229232i
$429$	0.685970	+	1.06739i	0.0331190	+	0.0515341i
$430$	−2.29455	−	9.51679i	−0.110653	−	0.458940i
$431$	1.65536	+	11.5133i	0.0797360	+	0.554576i	0.990056	+	0.140672i	$0.0449262\pi$
$431$	1.65536	+	11.5133i	0.0797360	+	0.554576i	−0.910320	+	0.413905i	$0.864165\pi$
$432$	0.357774	+	3.98397i	0.0172134	+	0.191679i
$433$	4.46528	−	31.0567i	0.214588	−	1.49249i	−0.542986	−	0.839742i	$-0.682706\pi$
$433$	4.46528	−	31.0567i	0.214588	−	1.49249i	0.757574	−	0.652750i	$-0.226385\pi$
$434$	−0.0505078	+	1.02976i	−0.00242445	+	0.0494298i
$435$	5.30361	−	4.59561i	0.254289	−	0.220342i
$436$	1.66094	+	0.965193i	0.0795444	+	0.0462244i
$437$	16.4883	+	30.5890i	0.788743	+	1.46327i
$438$	16.3695	−	9.42018i	0.782163	−	0.450113i
$439$	12.9001	+	14.8875i	0.615688	+	0.710542i	0.974882	−	0.222721i	$-0.0714939\pi$
$439$	12.9001	+	14.8875i	0.615688	+	0.710542i	−0.359194	+	0.933263i	$0.616948\pi$
$440$	−1.38654	−	0.899378i	−0.0661005	−	0.0428762i
$441$	−0.221571	+	1.54106i	−0.0105510	+	0.0733839i
$442$	−0.915224	−	9.72953i	−0.0435328	−	0.462787i
$443$	−6.51246	+	0.936351i	−0.309416	+	0.0444874i	−0.295274	−	0.955413i	$-0.595411\pi$
$443$	−6.51246	+	0.936351i	−0.309416	+	0.0444874i	−0.0141424	+	0.999900i	$0.504502\pi$
$444$	8.01742	−	7.60157i	0.380490	−	0.360754i
$445$	3.42416	+	5.32809i	0.162321	+	0.252576i
$446$	4.14628	−	5.80530i	0.196332	−	0.274889i
$447$	10.2066	−	2.99693i	0.482756	−	0.141750i
$448$	12.3414	−	14.0017i	0.583075	−	0.661519i
$449$	−4.20060	+	4.84775i	−0.198239	+	0.228779i	−0.846162	−	0.532926i	$-0.821092\pi$
$449$	−4.20060	+	4.84775i	−0.198239	+	0.228779i	0.647923	+	0.761706i	$0.275638\pi$
$450$	−4.32286	−	4.13349i	−0.203782	−	0.194854i
$451$	6.82600	−	3.11733i	0.321424	−	0.146789i
$452$	0.0649108	+	1.44853i	0.00305315	+	0.0681331i
$453$	4.04820	−	13.7869i	0.190201	−	0.647766i
$454$	−8.96055	−	11.4274i	−0.420539	−	0.536313i
$455$	−1.62210	+	3.55191i	−0.0760453	+	0.166516i
$456$	−3.00238	+	20.2732i	−0.140599	+	0.949380i
$457$	−8.42472	−	5.41424i	−0.394092	−	0.253267i	0.328555	−	0.944485i	$-0.393438\pi$
$457$	−8.42472	−	5.41424i	−0.394092	−	0.253267i	−0.722647	+	0.691217i	$0.757075\pi$
$458$	−27.0813	−	9.41567i	−1.26542	−	0.439965i
$459$			3.62474i			0.169189i
$460$	3.74170	−	7.54387i	0.174458	−	0.351735i
$461$		−	7.19455i		−	0.335084i	−0.985865	−	0.167542i	$-0.946417\pi$
$461$		−	7.19455i		−	0.335084i	0.985865	−	0.167542i	$-0.0535830\pi$
$462$	−0.721147	+	2.07416i	−0.0335508	+	0.0964985i
$463$	31.8319	+	20.4571i	1.47935	+	0.950723i	0.997211	+	0.0746309i	$0.0237779\pi$
$463$	31.8319	+	20.4571i	1.47935	+	0.950723i	0.482143	+	0.876092i	$0.339859\pi$
$464$	−11.7159	−	29.7499i	−0.543898	−	1.38110i
$465$	−0.113962	+	0.249542i	−0.00528487	+	0.0115723i
$466$	8.16109	−	6.39936i	0.378055	−	0.296445i
$467$	7.70595	−	26.2440i	0.356589	−	1.21443i	−0.564617	−	0.825353i	$-0.690976\pi$
$467$	7.70595	−	26.2440i	0.356589	−	1.21443i	0.921205	−	0.389076i	$-0.127206\pi$
$468$	−3.80897	+	0.170686i	−0.176069	+	0.00788994i
$469$	31.9974	−	14.6127i	1.47750	−	0.674753i
$470$	0.926596	−	0.969048i	0.0427407	−	0.0446989i
$471$	−9.09931	+	10.5012i	−0.419274	+	0.483868i
$472$	14.1624	+	12.3770i	0.651877	+	0.569697i
$473$	5.03513	−	1.47845i	0.231515	−	0.0679791i
$474$	−8.43606	−	6.02523i	−0.387481	−	0.276748i
$475$	−16.5676	−	25.7797i	−0.760173	−	1.18285i
$476$	12.2736	−	11.6370i	0.562561	−	0.533382i
$477$	−6.83452	+	0.982656i	−0.312931	+	0.0449927i
$478$	12.5426	−	1.17984i	0.573687	−	0.0539648i
$479$	−1.56196	+	10.8637i	−0.0713679	+	0.496374i	0.922517	+	0.385956i	$0.126128\pi$
$479$	−1.56196	+	10.8637i	−0.0713679	+	0.496374i	−0.993885	+	0.110419i	$0.964781\pi$
$480$	4.43018	−	2.24455i	0.202209	−	0.102449i
$481$	6.89641	+	7.95888i	0.314449	+	0.362894i
$482$	−10.1161	−	17.5788i	−0.460777	−	0.800693i
$483$	−10.9201	−	2.43758i	−0.496883	−	0.110914i
$484$	−10.6085	+	18.2555i	−0.482206	+	0.829795i
$485$	−4.69576	+	4.06890i	−0.213224	+	0.184759i
$486$	1.41252	+	0.0692815i	0.0640730	+	0.00314267i
$487$	−6.02842	+	41.9286i	−0.273174	+	1.89997i	0.141403	+	0.989952i	$0.454839\pi$
$487$	−6.02842	+	41.9286i	−0.273174	+	1.89997i	−0.414577	+	0.910014i	$0.636071\pi$
$488$	−17.0856	−	7.89018i	−0.773428	−	0.357172i
$489$	−1.07796	−	7.49736i	−0.0487469	−	0.339042i
$490$	1.87918	−	0.453082i	0.0848929	−	0.0204682i
$491$	−6.62591	−	10.3101i	−0.299023	−	0.465289i	0.658934	−	0.752201i	$-0.271008\pi$
$491$	−6.62591	−	10.3101i	−0.299023	−	0.465289i	−0.957957	+	0.286912i	$0.907371\pi$
$492$	−2.20677	+	22.4417i	−0.0994888	+	1.01175i
$493$	−8.16296	−	27.8005i	−0.367641	−	1.25207i
$494$	−19.1769	−	3.72407i	−0.862808	−	0.167554i
$495$	−0.382643	+	0.441593i	−0.0171985	+	0.0198481i
$496$	0.899725	+	0.867620i	0.0403988	+	0.0389573i
$497$	1.42430	+	3.11877i	0.0638884	+	0.139896i
$498$	−3.39101	−	1.75424i	−0.151955	−	0.0786095i
$499$	7.98942	−	27.2095i	0.357656	−	1.21806i	−0.562595	−	0.826733i	$-0.690197\pi$
$499$	7.98942	−	27.2095i	0.357656	−	1.21806i	0.920250	−	0.391330i	$-0.127985\pi$
$500$	−6.06527	+	15.0274i	−0.271247	+	0.672047i
$501$	16.9480	+	7.73991i	0.757182	+	0.345794i
$502$	3.48125	+	8.73139i	0.155376	+	0.389701i
$503$	−16.7847	−	10.7869i	−0.748394	−	0.480964i	0.110015	−	0.993930i	$-0.464910\pi$
$503$	−16.7847	−	10.7869i	−0.748394	−	0.480964i	−0.858409	+	0.512966i	$0.828547\pi$
$504$	−4.30020	−	5.00530i	−0.191546	−	0.222954i
$505$	7.20528			0.320631
$506$	4.13732	+	1.80523i	0.183926	+	0.0802524i
$507$			9.36566i			0.415944i
$508$	−26.5399	+	5.03761i	−1.17752	+	0.223508i
$509$	22.7821	−	35.4496i	1.00980	−	1.57128i	0.204103	−	0.978950i	$-0.434572\pi$
$509$	22.7821	−	35.4496i	1.00980	−	1.57128i	0.805697	−	0.592329i	$-0.201791\pi$
$510$	4.18040	−	1.66675i	0.185111	−	0.0738048i
$511$	−12.9432	+	28.3416i	−0.572572	+	1.25376i
$512$	−2.93592	−	22.4361i	−0.129750	−	0.991547i
$513$	6.95233	+	2.04139i	0.306953	+	0.0901295i
$514$	36.3698	+	18.8149i	1.60420	+	0.829888i
$515$	9.48029	−	4.32950i	0.417752	−	0.190781i
$516$	−3.76095	+	15.3143i	−0.165567	+	0.674176i
$517$	0.543171	+	0.470661i	0.0238886	+	0.0206996i
$518$	−3.47457	+	17.8921i	−0.152664	+	0.786133i
$519$	6.21383	−	1.82455i	0.272757	−	0.0800887i
$520$	1.94831	+	4.31437i	0.0854390	+	0.189198i
$521$	−1.82807	+	1.17483i	−0.0800894	+	0.0514703i	−0.580073	−	0.814565i	$-0.696976\pi$
$521$	−1.82807	+	1.17483i	−0.0800894	+	0.0514703i	0.499983	+	0.866035i	$0.333339\pi$
$522$	−10.9895	+	2.64963i	−0.480998	+	0.115971i
$523$	3.22775	−	0.464081i	0.141140	−	0.0202928i	−0.0713828	−	0.997449i	$-0.522741\pi$
$523$	3.22775	−	0.464081i	0.141140	−	0.0202928i	0.212523	+	0.977156i	$0.431832\pi$
$524$	14.1562	−	10.0206i	0.618417	−	0.437751i
$525$	9.76656	+	1.40422i	0.426248	+	0.0612851i
$526$	−1.19448	+	24.3532i	−0.0520819	+	1.06185i
$527$	0.741727	+	0.855999i	0.0323101	+	0.0372879i
$528$	1.31809	+	2.31302i	0.0573627	+	0.100661i
$529$	−6.71862	+	21.9968i	−0.292114	+	0.956383i
$530$	4.27598	+	7.43037i	0.185737	+	0.322755i
$531$	5.02562	−	4.35472i	0.218093	−	0.188979i
$532$	−15.4078	−	30.0948i	−0.668011	−	1.30478i
$533$	−21.2758	−	3.05900i	−0.921557	−	0.132500i
$534$	−0.955480	−	10.1575i	−0.0413477	−	0.439557i
$535$	0.297692	+	2.07050i	0.0128704	+	0.0895153i
$536$	12.1874	−	40.8667i	0.526418	−	1.76517i
$537$	−11.1941	+	7.19401i	−0.483061	+	0.310444i
$538$	17.2447	+	12.3166i	0.743473	+	0.531006i
$539$	0.291934	+	0.994235i	0.0125745	+	0.0428247i
$540$	−0.569608	−	1.66090i	−0.0245120	−	0.0714739i
$541$	16.4337	+	14.2399i	0.706539	+	0.612219i	0.932182	−	0.361991i	$-0.117903\pi$
$541$	16.4337	+	14.2399i	0.706539	+	0.612219i	−0.225643	+	0.974210i	$0.572448\pi$
$542$	10.9594	+	10.4793i	0.470746	+	0.450124i
$543$	−4.02744	−	8.81885i	−0.172834	−	0.378453i
$544$	−0.831320	−	20.4878i	−0.0356425	−	0.878407i
$545$	−0.809103	−	0.237574i	−0.0346582	−	0.0101766i
$546$	4.94975	−	3.88125i	0.211830	−	0.166102i
$547$	9.26717	+	4.23218i	0.396236	+	0.180955i	0.603560	−	0.797317i	$-0.293748\pi$
$547$	9.26717	+	4.23218i	0.396236	+	0.180955i	−0.207324	+	0.978272i	$0.566476\pi$
$548$	−0.494419	−	0.391075i	−0.0211205	−	0.0167059i
$549$	−3.59725	+	5.59743i	−0.153527	+	0.238893i
$550$	−3.75994	−	1.30726i	−0.160324	−	0.0557419i
$551$	−57.9191			−2.46744
$552$	−10.9370	+	8.02387i	−0.465509	+	0.341519i
$553$	17.1022			0.727260
$554$	−8.82965	−	3.06991i	−0.375136	−	0.130428i
$555$	−2.62199	+	4.07990i	−0.111297	+	0.173182i
$556$	−5.58955	+	7.06662i	−0.237050	+	0.299691i
$557$	39.8617	+	18.2042i	1.68900	+	0.771339i	0.998864	+	0.0476549i	$0.0151748\pi$
$557$	39.8617	+	18.2042i	1.68900	+	0.771339i	0.690132	+	0.723684i	$0.257553\pi$
$558$	0.347749	−	0.272680i	0.0147214	−	0.0115435i
$559$	−14.4225	−	4.23481i	−0.610005	−	0.179114i
$560$	−3.79524	+	7.26096i	−0.160378	+	0.306832i
$561$	1.00217	+	2.19446i	0.0423118	+	0.0926500i
$562$	4.36095	+	4.16990i	0.183955	+	0.175897i
$563$	−1.23562	−	1.07067i	−0.0520752	−	0.0451234i	0.628434	−	0.777863i	$-0.283696\pi$
$563$	−1.23562	−	1.07067i	−0.0520752	−	0.0451234i	−0.680510	+	0.732739i	$0.738242\pi$
$564$	−2.04296	+	0.700633i	−0.0860239	+	0.0295020i
$565$	−0.179321	−	0.610711i	−0.00754408	−	0.0256928i
$566$	15.1204	+	10.7993i	0.635558	+	0.453930i
$567$	−1.96268	+	1.26134i	−0.0824248	+	0.0529712i
$568$	3.98326	+	1.18790i	0.167134	+	0.0498433i
$569$	5.16449	+	35.9198i	0.216507	+	1.50584i	0.750795	+	0.660536i	$0.229671\pi$
$569$	5.16449	+	35.9198i	0.216507	+	1.50584i	−0.534288	+	0.845303i	$0.679420\pi$
$570$	−0.842533	−	8.95677i	−0.0352898	−	0.375158i
$571$	−0.275956	−	0.0396764i	−0.0115484	−	0.00166041i	0.136538	−	0.990635i	$-0.456402\pi$
$571$	−0.275956	−	0.0396764i	−0.0115484	−	0.00166041i	−0.148087	+	0.988974i	$0.547311\pi$
$572$	−2.25879	+	1.15644i	−0.0944449	+	0.0483533i
$573$	16.0931	−	13.9448i	0.672299	−	0.582550i
$574$	−18.5551	−	32.2431i	−0.774473	−	1.34580i
$575$	4.41873	−	19.7955i	0.184274	−	0.825531i
$576$	−7.99971	−	0.0676386i	−0.333321	−	0.00281828i
$577$	9.43503	+	10.8886i	0.392785	+	0.453298i	0.917356	−	0.398069i	$-0.130319\pi$
$577$	9.43503	+	10.8886i	0.392785	+	0.453298i	−0.524570	+	0.851367i	$0.675774\pi$
$578$	−0.267512	+	5.45405i	−0.0111270	+	0.226859i
$579$	20.1426	+	2.89606i	0.837097	+	0.120356i
$580$	8.10906	+	11.4558i	0.336710	+	0.475675i
$581$	6.23432	−	0.896359i	0.258643	−	0.0371873i
$582$	9.72999	−	2.34596i	0.403321	−	0.0972430i
$583$	−3.86600	+	2.48453i	−0.160114	+	0.102899i
$584$	15.5461	+	34.4255i	0.643300	+	1.42454i
$585$	1.60589	−	0.471531i	0.0663953	−	0.0194954i
$586$	6.49890	−	33.4657i	0.268467	−	1.38245i
$587$	−8.10819	−	7.02578i	−0.334661	−	0.289985i	0.471277	−	0.881985i	$-0.343793\pi$
$587$	−8.10819	−	7.02578i	−0.334661	−	0.289985i	−0.805938	+	0.592000i	$0.798339\pi$
$588$	−3.02396	−	0.742636i	−0.124706	−	0.0306258i
$589$	2.05955	−	0.940565i	0.0848623	−	0.0387553i
$590$	−7.33318	−	3.79361i	−0.301902	−	0.156180i
$591$	24.0763	+	7.06945i	0.990368	+	0.290798i
$592$	13.5610	+	17.4457i	0.557353	+	0.717012i
$593$	−1.56557	+	3.42812i	−0.0642903	+	0.140776i	−0.939050	−	0.343781i	$-0.888292\pi$
$593$	−1.56557	+	3.42812i	−0.0642903	+	0.140776i	0.874759	+	0.484557i	$0.161019\pi$
$594$	0.874306	−	0.348591i	0.0358732	−	0.0143029i
$595$	−4.01393	+	6.24580i	−0.164555	+	0.256053i
$596$	3.96743	+	20.9018i	0.162512	+	0.856171i
$597$			23.1998i			0.949505i
$598$	−7.17397	−	10.7570i	−0.293365	−	0.439888i
$599$	4.73711			0.193553			0.0967765	−	0.995306i	$-0.469147\pi$
$599$	4.73711			0.193553			0.0967765	+	0.995306i	$0.469147\pi$
$600$	9.07338	−	7.79521i	0.370419	−	0.318238i
$601$	−25.3023	−	16.2608i	−1.03210	−	0.663293i	−0.0890819	−	0.996024i	$-0.528393\pi$
$601$	−25.3023	−	16.2608i	−1.03210	−	0.663293i	−0.943022	+	0.332732i	$0.892030\pi$
$602$	−9.63473	−	24.1650i	−0.392682	−	0.984893i
$603$	−13.7149	−	6.26338i	−0.558513	−	0.255064i
$604$	26.6491	+	10.7560i	1.08434	+	0.437653i
$605$	2.61120	−	8.89292i	0.106160	−	0.361549i
$606$	−10.3089	−	5.33299i	−0.418769	−	0.216638i
$607$	−9.24100	−	20.2350i	−0.375081	−	0.821312i	−0.999200	−	0.0399833i	$-0.987270\pi$
$607$	−9.24100	−	20.2350i	−0.375081	−	0.821312i	0.624120	−	0.781329i	$-0.285458\pi$
$608$	−39.7642	−	9.94386i	−1.61265	−	0.403277i
$609$	12.2125	−	14.0940i	0.494876	−	0.571117i
$610$	8.10960	+	1.57485i	0.328348	+	0.0637639i
$611$	−0.579996	−	1.97528i	−0.0234641	−	0.0799114i
$612$	−7.21469	−	0.709444i	−0.291637	−	0.0286776i
$613$	−3.74485	−	5.82711i	−0.151253	−	0.235355i	0.757356	−	0.653003i	$-0.226491\pi$
$613$	−3.74485	−	5.82711i	−0.151253	−	0.235355i	−0.908609	+	0.417648i	$0.862855\pi$
$614$	3.54347	−	0.854352i	0.143003	−	0.0344788i
$615$	−1.40873	−	9.79792i	−0.0568054	−	0.395090i
$616$	−3.98726	−	1.84133i	−0.160651	−	0.0741893i
$617$	0.335075	−	2.33050i	0.0134896	−	0.0938223i	−0.981964	−	0.189066i	$-0.939454\pi$
$617$	0.335075	−	2.33050i	0.0134896	−	0.0938223i	0.995454	+	0.0952438i	$0.0303631\pi$
$618$	−16.7683	−	0.822456i	−0.674519	−	0.0330840i
$619$	9.04859	−	7.84065i	0.363694	−	0.315142i	−0.453774	−	0.891117i	$-0.649923\pi$
$619$	9.04859	−	7.84065i	0.363694	−	0.315142i	0.817468	+	0.575974i	$0.195377\pi$
$620$	−0.474384	−	0.275672i	−0.0190517	−	0.0110712i
$621$	2.27556	+	4.22159i	0.0913149	+	0.169407i
$622$	−3.33512	−	5.79544i	−0.133726	−	0.232376i
$623$	11.0219	+	12.7199i	0.441583	+	0.509613i
$624$	0.405767	−	7.61477i	0.0162437	−	0.304835i
$625$	−1.99705	+	13.8898i	−0.0798820	+	0.555591i
$626$	−12.7238	+	1.19689i	−0.508546	+	0.0478372i
$627$	4.77342	−	0.686314i	0.190632	−	0.0274087i
$628$	−19.1206	−	20.1666i	−0.762994	−	0.804734i
$629$	10.8255	+	16.8448i	0.431641	+	0.671646i
$630$	2.35719	+	1.68355i	0.0939125	+	0.0670744i
$631$	−20.3419	+	5.97293i	−0.809800	+	0.237779i	−0.660318	−	0.750986i	$-0.729579\pi$
$631$	−20.3419	+	5.97293i	−0.809800	+	0.237779i	−0.149481	+	0.988765i	$0.547760\pi$
$632$	13.6437	−	15.6119i	0.542719	−	0.621007i
$633$	−2.27719	+	2.62802i	−0.0905103	+	0.104454i
$634$	−5.32660	+	5.57063i	−0.211546	+	0.221238i
$635$	10.7865	−	4.92604i	0.428050	−	0.195484i
$636$	−0.618209	−	13.7958i	−0.0245136	−	0.547038i
$637$	0.836206	−	2.84785i	0.0331317	−	0.112836i
$638$	−5.92058	+	4.64251i	−0.234398	+	0.183799i
$639$	0.610488	−	1.33678i	0.0241505	−	0.0528823i
$640$	3.60046	+	9.25713i	0.142321	+	0.365920i
$641$	−33.4828	−	21.5181i	−1.32249	−	0.849914i	−0.327024	−	0.945016i	$-0.606046\pi$
$641$	−33.4828	−	21.5181i	−1.32249	−	0.849914i	−0.995468	+	0.0951019i	$0.969682\pi$
$642$	1.10656	−	3.18267i	0.0436723	−	0.125610i
$643$			29.7780i			1.17433i	0.809468	+	0.587165i	$0.199756\pi$
$643$			29.7780i			1.17433i	−0.809468	+	0.587165i	$0.800244\pi$
$644$	6.98907	−	21.2583i	0.275408	−	0.837696i
$645$		−	6.92222i		−	0.272562i
$646$	−35.0833	−	12.1978i	−1.38034	−	0.479918i
$647$	33.2305	+	21.3559i	1.30643	+	0.839589i	0.993896	−	0.110319i	$-0.0351873\pi$
$647$	33.2305	+	21.3559i	1.30643	+	0.839589i	0.312530	+	0.949908i	$0.398824\pi$
$648$	−0.414359	+	2.79791i	−0.0162776	+	0.109912i
$649$	1.83856	−	4.02588i	0.0721698	−	0.158030i
$650$	7.03575	+	8.97268i	0.275965	+	0.351937i
$651$	−0.205389	+	0.699492i	−0.00804984	+	0.0274152i
$652$	15.1337	−	0.678165i	0.592682	−	0.0265590i
$653$	−23.1685	+	10.5807i	−0.906655	+	0.414055i	−0.813479	−	0.581594i	$-0.802429\pi$
$653$	−23.1685	+	10.5807i	−0.906655	+	0.414055i	−0.0931757	+	0.995650i	$0.529702\pi$
$654$	0.981773	+	0.938763i	0.0383903	+	0.0367085i
$655$	−4.98570	+	5.75380i	−0.194807	+	0.224820i
$656$	−44.2361	−	8.78471i	−1.72713	−	0.342985i
$657$	12.8138	−	3.76247i	0.499913	−	0.146788i
$658$	2.07082	−	2.89940i	0.0807288	−	0.113030i
$659$	11.9780	+	18.6382i	0.466598	+	0.726041i	0.992195	−	0.124693i	$-0.0397945\pi$
$659$	11.9780	+	18.6382i	0.466598	+	0.726041i	−0.525597	+	0.850733i	$0.676158\pi$
$660$	−0.804056	−	0.848042i	−0.0312978	−	0.0330100i
$661$	−30.9087	+	4.44400i	−1.20221	+	0.172852i	−0.714171	−	0.699971i	$-0.753196\pi$
$661$	−30.9087	+	4.44400i	−1.20221	+	0.172852i	−0.488038	+	0.872822i	$0.662287\pi$
$662$	−3.65316	−	38.8359i	−0.141984	−	1.50940i
$663$	0.983422	−	6.83985i	0.0381930	−	0.265638i
$664$	4.15534	−	6.40613i	0.161258	−	0.248606i
$665$	9.71899	+	11.2163i	0.376886	+	0.434950i
$666$	6.77111	−	3.89659i	0.262375	−	0.150990i
$667$	−26.9598	−	27.2535i	−1.04389	−	1.05526i
$668$	−18.7226	+	32.2185i	−0.724400	+	1.24657i
$669$	3.81235	−	3.30342i	0.147394	−	0.127718i
$670$	−0.917074	+	18.6974i	−0.0354297	+	0.722342i
$671$	−0.630226	+	4.38332i	−0.0243296	+	0.169216i
$672$	10.8042	−	7.57947i	0.416781	−	0.292385i
$673$	2.82944	+	19.6792i	0.109067	+	0.758576i	0.968802	+	0.247836i	$0.0797195\pi$
$673$	2.82944	+	19.6792i	0.109067	+	0.758576i	−0.859735	+	0.510740i	$0.829371\pi$
$674$	−3.10505	−	12.8784i	−0.119602	−	0.496056i
$675$	−2.28650	−	3.55786i	−0.0880073	−	0.136942i
$676$	−18.6414	−	1.83307i	−0.716978	−	0.0705027i
$677$	−11.1832	−	38.0865i	−0.429806	−	1.46378i	−0.835355	−	0.549711i	$-0.814738\pi$
$677$	−11.1832	−	38.0865i	−0.429806	−	1.46378i	0.405549	−	0.914073i	$-0.367080\pi$
$678$	−0.195456	+	1.00649i	−0.00750646	+	0.0386540i
$679$	−10.8128	+	12.4787i	−0.414958	+	0.478887i
$680$	2.49930	+	8.64689i	0.0958437	+	0.331593i
$681$	−4.26561	−	9.34038i	−0.163458	−	0.357924i
$682$	0.135139	−	0.261230i	0.00517476	−	0.0100030i
$683$	8.25029	−	28.0979i	0.315688	−	1.07514i	−0.636918	−	0.770931i	$-0.719791\pi$
$683$	8.25029	−	28.0979i	0.315688	−	1.07514i	0.952607	−	0.304205i	$-0.0983907\pi$
$684$	−5.42391	+	13.4384i	−0.207388	+	0.513829i
$685$	0.251713	+	0.114953i	0.00961744	+	0.00439214i
$686$	26.2252	−	10.4561i	1.00128	−	0.399217i
$687$	−17.0554	−	10.9608i	−0.650703	−	0.418181i
$688$	−29.7455	−	10.4831i	−1.13404	−	0.399666i
$689$	13.1633			0.501481
$690$	3.82238	−	4.56558i	0.145516	−	0.173809i
$691$		−	9.33930i		−	0.355284i	−0.984095	−	0.177642i	$-0.943153\pi$
$691$		−	9.33930i		−	0.355284i	0.984095	−	0.177642i	$-0.0568468\pi$
$692$	2.41539	+	12.7251i	0.0918193	+	0.483736i
$693$	−0.839490	+	1.30627i	−0.0318896	+	0.0496212i
$694$	−15.7463	−	39.4935i	−0.597721	−	1.49915i
$695$	1.64300	−	3.59767i	0.0623226	−	0.136467i
$696$	−3.12294	−	22.3921i	−0.118375	−	0.848771i
$697$	−39.2135	−	11.5141i	−1.48532	−	0.436128i
$698$	−11.8697	+	22.9446i	−0.449275	+	0.868466i
$699$	6.67063	−	3.04637i	0.252306	−	0.115224i
$700$	−4.70649	+	19.1645i	−0.177889	+	0.724351i
$701$	2.49087	+	2.15835i	0.0940790	+	0.0815199i	0.700630	−	0.713524i	$-0.252902\pi$
$701$	2.49087	+	2.15835i	0.0940790	+	0.0815199i	−0.606552	+	0.795044i	$0.707448\pi$
$702$	−2.64661	−	0.513960i	−0.0998897	−	0.0193982i
$703$	38.4054	−	11.2768i	1.44849	−	0.425314i
$704$	−4.86181	+	2.17082i	−0.183236	+	0.0818160i
$705$	0.797559	−	0.512560i	0.0300378	−	0.0193041i
$706$	4.96114	+	20.5766i	0.186715	+	0.774410i
$707$	18.9527	−	2.72498i	0.712788	−	0.102483i
$708$	7.68401	+	10.8553i	0.288783	+	0.407967i
$709$	0.557821	+	0.0802025i	0.0209494	+	0.00301207i	0.152782	−	0.988260i	$-0.451177\pi$
$709$	0.557821	+	0.0802025i	0.0209494	+	0.00301207i	−0.131832	+	0.991272i	$0.542086\pi$
$710$	−1.82242	−	0.0893868i	−0.0683943	−	0.00335463i
$711$	−4.80041	−	5.53997i	−0.180030	−	0.207765i
$712$	20.4045	+	0.0862597i	0.764690	+	0.00323272i
$713$	1.40124	+	0.531303i	0.0524769	+	0.0198975i
$714$	10.3657	−	5.96518i	0.387926	−	0.223241i
$715$	0.841851	−	0.729468i	0.0314834	−	0.0272806i
$716$	−12.1280	−	23.6888i	−0.453246	−	0.885291i
$717$	8.81746	+	1.26776i	0.329294	+	0.0473454i
$718$	24.7252	−	2.32582i	0.922736	−	0.0867987i
$719$	2.42245	+	16.8485i	0.0903422	+	0.628344i	0.983810	+	0.179216i	$0.0573561\pi$
$719$	2.42245	+	16.8485i	0.0903422	+	0.628344i	−0.893468	+	0.449128i	$0.851735\pi$
$720$	3.41735	−	0.808672i	0.127357	−	0.0301374i
$721$	23.2994	−	14.9736i	0.867715	−	0.557647i
$722$	−27.5370	+	38.5552i	−1.02482	+	1.43488i
$723$	−4.04043	−	13.7605i	−0.150265	−	0.511757i
$724$	18.3413	−	6.29016i	0.681649	−	0.233772i
$725$	25.5489	+	22.1383i	0.948864	+	0.822195i
$726$	−10.3180	+	10.7908i	−0.382938	+	0.400482i
$727$	−11.7079	−	25.6367i	−0.434222	−	0.950813i	−0.992623	−	0.121242i	$-0.961312\pi$
$727$	−11.7079	−	25.6367i	−0.434222	−	0.950813i	0.558401	−	0.829571i	$-0.311415\pi$
$728$	6.75646	+	10.6116i	0.250411	+	0.393293i
$729$	0.959493	+	0.281733i	0.0355368	+	0.0104345i
$730$	−10.2313	−	13.0480i	−0.378679	−	0.482928i
$731$	−25.9973	−	11.8726i	−0.961544	−	0.439122i
$732$	−10.4371	−	8.25552i	−0.385765	−	0.305133i
$733$	−13.2937	+	20.6854i	−0.491015	+	0.764034i	−0.995021	−	0.0996660i	$-0.968223\pi$
$733$	−13.2937	+	20.6854i	−0.491015	+	0.764034i	0.504006	+	0.863700i	$0.331859\pi$
$734$	7.17621	−	20.6401i	0.264879	−	0.761842i
$735$	1.36686			0.0504174
$736$	−13.8301	−	23.3394i	−0.509785	−	0.860302i
$737$	−10.0348			−0.369638
$738$	−5.23641	+	15.0609i	−0.192755	+	0.554400i
$739$	−22.5657	+	35.1130i	−0.830094	+	1.29165i	0.124042	+	0.992277i	$0.460414\pi$
$739$	−22.5657	+	35.1130i	−0.830094	+	1.29165i	−0.954136	+	0.299374i	$0.903222\pi$
$740$	−7.60745	−	6.01734i	−0.279655	−	0.221202i
$741$	−12.5651	−	5.73830i	−0.461592	−	0.210802i
$742$	14.0576	+	17.9276i	0.516069	+	0.658142i
$743$	51.1839	+	15.0290i	1.87776	+	0.551359i	0.996965	+	0.0778525i	$0.0248063\pi$
$743$	51.1839	+	15.0290i	1.87776	+	0.551359i	0.880790	+	0.473506i	$0.157012\pi$
$744$	0.474681	+	0.745529i	0.0174026	+	0.0273324i
$745$	−3.87956	−	8.49505i	−0.142136	−	0.311235i
$746$	32.8986	−	34.4059i	1.20450	−	1.25969i
$747$	−2.04027	−	1.76790i	−0.0746495	−	0.0646841i
$748$	−4.56399	+	1.56522i	−0.166876	+	0.0572303i
$749$	1.56609	+	5.33361i	0.0572237	+	0.194886i
$750$	−6.65994	+	9.32474i	−0.243187	+	0.340491i
$751$	6.57342	−	4.22448i	0.239867	−	0.154153i	−0.415185	−	0.909737i	$-0.636283\pi$
$751$	6.57342	−	4.22448i	0.239867	−	0.154153i	0.655052	+	0.755584i	$0.272647\pi$
$752$	−0.994687	−	4.20343i	−0.0362725	−	0.153283i
$753$	0.945919	+	6.57901i	0.0344712	+	0.239752i
$754$	21.4560	−	2.01829i	0.781380	−	0.0735017i
$755$	−12.4866	−	1.79530i	−0.454432	−	0.0653375i
$756$	−2.12643	−	4.15339i	−0.0773374	−	0.151057i
$757$	−14.1903	+	12.2960i	−0.515756	+	0.446905i	−0.873436	−	0.486939i	$-0.838113\pi$
$757$	−14.1903	+	12.2960i	−0.515756	+	0.446905i	0.357680	+	0.933844i	$0.383568\pi$
$758$	12.0815	−	6.95257i	0.438819	−	0.252529i
$759$	2.54484	+	1.92665i	0.0923717	+	0.0699328i
$760$	17.9925	+	0.0760629i	0.652655	+	0.00275909i
$761$	25.5824	+	29.5237i	0.927362	+	1.07023i	0.997355	+	0.0726854i	$0.0231569\pi$
$761$	25.5824	+	29.5237i	0.927362	+	1.07023i	−0.0699929	+	0.997547i	$0.522298\pi$
$762$	−19.0787	−	0.935777i	−0.691148	−	0.0338996i
$763$	−2.21810	−	0.318914i	−0.0803006	−	0.0115455i
$764$	24.6059	+	34.7610i	0.890209	+	1.25761i
$765$	3.14989	−	0.452885i	0.113884	−	0.0163741i
$766$	−5.71193	−	23.6906i	−0.206381	−	0.855975i
$767$	−10.6648	+	6.85382i	−0.385082	+	0.247477i
$768$	1.70035	−	15.9094i	0.0613561	−	0.574081i
$769$	−25.7863	+	7.57153i	−0.929876	+	0.273036i	−0.711385	−	0.702803i	$-0.751932\pi$
$769$	−25.7863	+	7.57153i	−0.929876	+	0.273036i	−0.218491	+	0.975839i	$0.570113\pi$
$770$	1.89254	+	0.367523i	0.0682022	+	0.0132446i
$771$	21.8826	+	18.9614i	0.788082	+	0.682877i
$772$	−9.70668	+	39.5249i	−0.349351	+	1.42253i
$773$	−2.56210	+	1.17007i	−0.0921522	+	0.0420845i	−0.460958	−	0.887422i	$-0.652494\pi$
$773$	−2.56210	+	1.17007i	−0.0921522	+	0.0420845i	0.368806	+	0.929507i	$0.379767\pi$
$774$	−5.12348	+	9.90387i	−0.184160	+	0.355987i
$775$	−1.26801	−	0.372320i	−0.0455482	−	0.0133741i
$776$	2.76502	+	19.8257i	0.0992583	+	0.711702i
$777$	−5.35385	+	11.7233i	−0.192068	+	0.420571i
$778$	15.6323	+	39.2077i	0.560446	+	1.40566i
$779$	−44.1686	+	68.7277i	−1.58250	+	2.46243i
$780$	0.624228	+	3.28865i	0.0223509	+	0.117753i
$781$		−	0.978090i		−	0.0349988i
$782$	−10.5907	−	22.1860i	−0.378723	−	0.793371i
$783$	−7.99343			−0.285662
$784$	2.07000	−	5.87355i	0.0739286	−	0.209770i
$785$	10.2624	+	6.59522i	0.366279	+	0.235393i
$786$	11.3919	−	4.54201i	0.406335	−	0.162008i
$787$	20.7822	+	9.49092i	0.740806	+	0.338315i	0.749818	−	0.661645i	$-0.230141\pi$
$787$	20.7822	+	9.49092i	0.740806	+	0.338315i	−0.00901147	+	0.999959i	$0.502868\pi$
$788$	−18.7833	+	46.5379i	−0.669127	+	1.65784i
$789$	−4.85735	+	16.5426i	−0.172926	+	0.588932i
$790$	−4.18187	+	8.08371i	−0.148784	+	0.287605i
$791$	−0.702648	−	1.53858i	−0.0249833	−	0.0547058i
$792$	0.522714	+	1.80845i	0.0185738	+	0.0642603i
$793$	8.30661	−	9.58634i	0.294976	−	0.340421i
$794$	−1.15939	+	5.97022i	−0.0411454	+	0.211875i
$795$	1.70785	+	5.81640i	0.0605711	+	0.206286i
$796$	−46.1769	−	4.54072i	−1.63670	−	0.160942i
$797$	7.93713	+	12.3504i	0.281147	+	0.437474i	0.952892	−	0.303309i	$-0.0980913\pi$
$797$	7.93713	+	12.3504i	0.281147	+	0.437474i	−0.671745	+	0.740782i	$0.734455\pi$
$798$	−5.60356	−	23.2411i	−0.198364	−	0.822726i
$799$	−0.557061	−	3.87444i	−0.0197074	−	0.137068i
$800$	13.7397	+	19.5853i	0.485773	+	0.692447i
$801$	1.02668	−	7.14070i	0.0362759	−	0.252304i
$802$	−2.42044	+	49.3482i	−0.0854688	+	1.74254i
$803$	6.71734	−	5.82061i	0.237050	−	0.205405i
$804$	15.1509	−	26.0722i	0.534332	−	0.919496i
$805$	−0.753852	+	9.79411i	−0.0265698	+	0.345197i
$806$	−0.730178	+	0.420198i	−0.0257194	+	0.0148008i
$807$	9.81285	+	11.3246i	0.345429	+	0.398646i
$808$	12.6325	−	19.4750i	0.444408	−	0.685127i
$809$	−6.24539	+	43.4377i	−0.219576	+	1.52719i	0.520030	+	0.854148i	$0.325921\pi$
$809$	−6.24539	+	43.4377i	−0.219576	+	1.52719i	−0.739607	+	0.673039i	$0.764988\pi$
$810$	−0.116278	−	1.23613i	−0.00408560	−	0.0434330i
$811$	−50.5792	+	7.27220i	−1.77608	+	0.255361i	−0.950897	−	0.309508i	$-0.899836\pi$
$811$	−50.5792	+	7.27220i	−1.77608	+	0.255361i	−0.825180	+	0.564869i	$0.808927\pi$
$812$	25.6624	+	27.0663i	0.900574	+	0.949840i
$813$	5.79676	+	9.01994i	0.203301	+	0.316343i
$814$	3.02196	−	4.23112i	0.105920	−	0.148301i
$815$	−6.38049	+	1.87348i	−0.223499	+	0.0656252i
$816$	2.82415	−	14.2213i	0.0988651	−	0.497844i
$817$	−37.4130	+	43.1769i	−1.30891	+	1.51057i
$818$	−7.23913	−	6.92200i	−0.253110	−	0.242022i
$819$	4.04577	−	1.84764i	0.141371	−	0.0645618i
$820$	19.7775	−	0.886260i	0.690660	−	0.0309496i
$821$	−0.635469	+	2.16421i	−0.0221780	+	0.0755314i	−0.969838	−	0.243749i	$-0.921623\pi$
$821$	−0.635469	+	2.16421i	−0.0221780	+	0.0755314i	0.947660	+	0.319280i	$0.103441\pi$
$822$	−0.275052	−	0.350773i	−0.00959353	−	0.0122346i
$823$	3.49513	−	7.65328i	0.121833	−	0.266776i	−0.838882	−	0.544313i	$-0.816791\pi$
$823$	3.49513	−	7.65328i	0.121833	−	0.266776i	0.960715	+	0.277536i	$0.0895178\pi$
$824$	4.91894	−	33.2146i	0.171360	−	1.15709i
$825$	−2.36795	−	1.52179i	−0.0824415	−	0.0529819i
$826$	−20.7238	−	7.20529i	−0.721073	−	0.250704i
$827$			26.9708i			0.937867i	0.883233	+	0.468934i	$0.155362\pi$
$827$			26.9708i			0.937867i	−0.883233	+	0.468934i	$0.844638\pi$
$828$	−8.84804	+	3.70301i	−0.307491	+	0.128688i
$829$		−	13.3153i		−	0.462458i	−0.972899	−	0.231229i	$-0.925725\pi$
$829$		−	13.3153i		−	0.462458i	0.972899	−	0.231229i	$-0.0742747\pi$
$830$	−1.10075	+	3.16596i	−0.0382075	+	0.109892i
$831$	−5.56078	−	3.57370i	−0.192901	−	0.123970i
$832$	15.0770	+	2.29802i	0.522702	+	0.0796695i
$833$	2.34435	−	5.13342i	0.0812270	−	0.177862i
$834$	−5.01352	+	3.93125i	−0.173604	+	0.136128i
$835$	4.60841	−	15.6948i	0.159481	−	0.543141i
$836$	0.431774	+	9.63534i	0.0149332	+	0.333245i
$837$	0.284239	−	0.129808i	0.00982474	−	0.00448681i
$838$	−29.6752	+	31.0348i	−1.02511	+	1.07208i
$839$	−24.1693	+	27.8928i	−0.834415	+	0.962967i	−0.999729	−	0.0232743i	$-0.992591\pi$
$839$	−24.1693	+	27.8928i	−0.834415	+	0.962967i	0.165314	+	0.986241i	$0.447136\pi$
$840$	−3.81230	+	4.36223i	−0.131537	+	0.150511i
$841$	33.4814	−	9.83103i	1.15453	−	0.339001i
$842$	−6.77909	−	4.84178i	−0.233623	−	0.166859i
$843$	2.30664	+	3.58920i	0.0794449	+	0.123619i
$844$	−4.78512	−	5.04689i	−0.164710	−	0.173721i
$845$	8.13872	−	1.17017i	0.279981	−	0.0402551i
$846$	−1.52047	+	0.143025i	−0.0522747	+	0.00491731i
$847$	3.50522	−	24.3793i	0.120441	−	0.837683i
$848$	27.5801	+	1.46966i	0.947104	+	0.0504682i
$849$	8.60404	+	9.92959i	0.295290	+	0.340783i
$850$	10.8134	+	18.7905i	0.370897	+	0.644508i
$851$	23.1829	+	12.8224i	0.794700	+	0.439546i
$852$	2.54125	+	1.47675i	0.0870617	+	0.0505928i
$853$	−3.09445	+	2.68136i	−0.105952	+	0.0918079i	−0.706226	−	0.707987i	$-0.749604\pi$
$853$	−3.09445	+	2.68136i	−0.105952	+	0.0918079i	0.600274	+	0.799794i	$0.295058\pi$
$854$	21.9269	+	1.07548i	0.750325	+	0.0368022i
$855$	0.905315	−	6.29660i	0.0309611	−	0.215339i
$856$	6.11821	+	2.82541i	0.209116	+	0.0965706i
$857$	−6.63729	−	46.1633i	−0.226725	−	1.57691i	−0.711765	−	0.702418i	$-0.752104\pi$
$857$	−6.63729	−	46.1633i	−0.226725	−	1.57691i	0.485040	−	0.874492i	$-0.338805\pi$
$858$	−1.74438	+	0.420581i	−0.0595522	+	0.0143584i
$859$	3.58753	+	5.58231i	0.122405	+	0.190466i	0.897048	−	0.441933i	$-0.145707\pi$
$859$	3.58753	+	5.58231i	0.122405	+	0.190466i	−0.774643	+	0.632398i	$0.782071\pi$
$860$	13.7780	+	1.35483i	0.469826	+	0.0461995i
$861$	−7.41099	−	25.2395i	−0.252566	−	0.860160i
$862$	−16.1480	−	3.13588i	−0.550004	−	0.106809i
$863$	32.2392	−	37.2060i	1.09743	−	1.26651i	0.136227	−	0.990678i	$-0.456502\pi$
$863$	32.2392	−	37.2060i	1.09743	−	1.26651i	0.961207	−	0.275829i	$-0.0889524\pi$
$864$	−5.48786	−	1.37235i	−0.186701	−	0.0466884i
$865$	−2.36190	−	5.17183i	−0.0803069	−	0.175847i
$866$	39.4112	+	20.3882i	1.33925	+	0.692820i
$867$	−1.08784	+	3.70483i	−0.0369448	+	0.125823i
$868$	−1.35207	−	0.545713i	−0.0458922	−	0.0185227i
$869$	−4.43792	−	2.02673i	−0.150546	−	0.0687521i
$870$	3.67558	+	9.21878i	0.124614	+	0.312546i
$871$	24.1805	+	15.5399i	0.819326	+	0.526549i
$872$	−2.06067	+	1.77038i	−0.0697831	+	0.0599527i
$873$	7.07730			0.239530
$874$	−48.5178	+	7.81841i	−1.64114	+	0.264462i
$875$		−	18.9038i		−	0.639065i
$876$	4.98087	+	26.2410i	0.168288	+	0.886600i
$877$	7.56357	−	11.7691i	0.255404	−	0.397416i	−0.689747	−	0.724050i	$-0.742278\pi$
$877$	7.56357	−	11.7691i	0.255404	−	0.397416i	0.945151	+	0.326635i	$0.105915\pi$
$878$	−25.8776	+	10.3175i	−0.873326	+	0.348200i
$879$	10.0139	−	21.9275i	0.337762	−	0.739595i
$880$	1.84532	−	1.43441i	0.0622056	−	0.0483540i
$881$	10.9149	+	3.20489i	0.367731	+	0.107975i	0.460377	−	0.887724i	$-0.347714\pi$
$881$	10.9149	+	3.20489i	0.367731	+	0.107975i	−0.0926460	+	0.995699i	$0.529532\pi$
$882$	−1.95562	−	1.01168i	−0.0658490	−	0.0340651i
$883$	−37.0043	+	16.8993i	−1.24530	+	0.568707i	−0.925489	−	0.378775i	$-0.876345\pi$
$883$	−37.0043	+	16.8993i	−1.24530	+	0.568707i	−0.319807	+	0.947483i	$0.603618\pi$
$884$	13.4216	+	3.29612i	0.451416	+	0.110860i
$885$	−4.41215	−	3.82315i	−0.148313	−	0.128514i
$886$	1.77380	−	9.13408i	0.0595921	−	0.306865i
$887$	15.0205	−	4.41041i	0.504338	−	0.148087i	−0.0196595	−	0.999807i	$-0.506258\pi$
$887$	15.0205	−	4.41041i	0.504338	−	0.148087i	0.523998	+	0.851720i	$0.324440\pi$
$888$	6.43052	+	14.2399i	0.215794	+	0.477859i
$889$	26.5097	−	17.0367i	0.889107	−	0.571394i
$890$	−8.70743	+	2.09941i	−0.291874	+	0.0703725i
$891$	0.658781	−	0.0947184i	0.0220700	−	0.00317318i
$892$	5.82896	+	8.23465i	0.195168	+	0.275717i
$893$	−7.74498	−	1.11356i	−0.259176	−	0.0372639i
$894$	−0.736982	+	15.0256i	−0.0246484	+	0.502532i
$895$	7.65019	+	8.82878i	0.255717	+	0.295114i
$896$	12.9716	+	22.9881i	0.433350	+	0.767980i
$897$	−3.14860	−	8.58348i	−0.105129	−	0.286594i
$898$	−4.52466	−	7.86250i	−0.150990	−	0.262375i
$899$	−1.88768	+	1.63569i	−0.0629578	+	0.0545532i
$900$	7.52908	−	3.85469i	0.250969	−	0.128490i
$901$	24.7734	+	3.56188i	0.825322	+	0.118663i
$902$	0.993889	+	10.5658i	0.0330929	+	0.351803i
$903$	−2.61793	−	18.2081i	−0.0871192	−	0.605927i
$904$	−1.96506	−	0.586029i	−0.0653570	−	0.0194910i
$905$	−7.16035	+	4.60168i	−0.238018	+	0.152965i
$906$	16.5362	+	11.8105i	0.549378	+	0.392378i
$907$	−0.641700	−	2.18543i	−0.0213073	−	0.0725660i	0.948153	−	0.317814i	$-0.102949\pi$
$907$	−0.641700	−	2.18543i	−0.0213073	−	0.0725660i	−0.969460	+	0.245248i	$0.921131\pi$
$908$	19.4260	−	6.66214i	0.644673	−	0.221091i
$909$	−6.20252	−	5.37452i	−0.205725	−	0.178261i
$910$	−3.99122	−	3.81637i	−0.132308	−	0.126512i
$911$	1.20657	+	2.64201i	0.0399754	+	0.0875338i	0.928566	−	0.371167i	$-0.121042\pi$
$911$	1.20657	+	2.64201i	0.0399754	+	0.0875338i	−0.888591	+	0.458701i	$0.848315\pi$
$912$	−25.6862	−	13.4259i	−0.850554	−	0.444577i
$913$	−1.72399	−	0.506209i	−0.0570558	−	0.0167531i
$914$	11.1449	−	8.73905i	0.368640	−	0.289062i
$915$	5.31360	+	2.42664i	0.175662	+	0.0802222i
$916$	25.1545	−	31.8017i	0.831129	−	1.05076i
$917$	−10.9382	+	17.0202i	−0.361213	+	0.562058i
$918$	−4.84186	−	1.68343i	−0.159805	−	0.0555614i
$919$	−31.8478			−1.05056			−0.525281	−	0.850929i	$-0.676040\pi$
$919$	−31.8478			−1.05056			−0.525281	+	0.850929i	$0.676040\pi$
$920$	8.33921	+	8.50166i	0.274936	+	0.280291i
$921$	2.57741			0.0849286
$922$	9.61034	+	3.34134i	0.316500	+	0.110041i
$923$	−1.51466	+	2.35686i	−0.0498558	+	0.0775771i
$924$	−2.43570	−	1.92659i	−0.0801285	−	0.0633801i
$925$	−21.2515	−	9.70523i	−0.698745	−	0.319106i
$926$	−42.1098	+	33.0196i	−1.38381	+	1.08509i
$927$	−11.3904	−	3.34451i	−0.374108	−	0.109848i
$928$	45.1805	−	1.83326i	1.48312	−	0.0601797i
$929$	−17.0996	−	37.4429i	−0.561020	−	1.22846i	−0.951442	−	0.307827i	$-0.900398\pi$
$929$	−17.0996	−	37.4429i	−0.561020	−	1.22846i	0.390422	−	0.920636i	$-0.372329\pi$
$930$	−0.280407	−	0.268123i	−0.00919490	−	0.00879209i
$931$	−8.52570	−	7.38756i	−0.279419	−	0.242118i
$932$	4.75791	+	13.8735i	0.155851	+	0.454440i
$933$	−1.33206	−	4.53659i	−0.0436098	−	0.148521i
$934$	31.4774	+	22.4819i	1.02997	+	0.735630i
$935$	1.78176	−	1.14507i	0.0582697	−	0.0374477i
$936$	1.54099	−	5.16721i	0.0503687	−	0.168896i
$937$	0.349529	+	2.43103i	0.0114186	+	0.0794182i	0.994734	−	0.102491i	$-0.0326813\pi$
$937$	0.349529	+	2.43103i	0.0114186	+	0.0794182i	−0.983315	+	0.181909i	$0.941772\pi$
$938$	4.65894	+	49.5280i	0.152120	+	1.61715i
$939$	−8.94484	−	1.28607i	−0.291904	−	0.0419694i
$940$	0.864099	+	1.68778i	0.0281838	+	0.0550493i
$941$	−42.2526	+	36.6121i	−1.37740	+	1.19352i	−0.419031	+	0.907972i	$0.637630\pi$
$941$	−42.2526	+	36.6121i	−1.37740	+	1.19352i	−0.958364	+	0.285548i	$0.907824\pi$
$942$	−9.80128	−	17.0317i	−0.319343	−	0.554923i
$943$	−52.8987	+	11.2076i	−1.72262	+	0.364968i
$944$	−23.1103	+	13.1696i	−0.752177	+	0.428635i
$945$	1.34132	+	1.54797i	0.0436332	+	0.0503553i
$946$	−0.363568	+	7.41245i	−0.0118206	+	0.241000i
$947$	33.9894	+	4.88693i	1.10451	+	0.158804i	0.670358	−	0.742038i	$-0.266140\pi$
$947$	33.9894	+	4.88693i	1.10451	+	0.158804i	0.434148	+	0.900842i	$0.357049\pi$
$948$	11.9663	−	8.47045i	0.388648	−	0.275107i
$949$	−25.2003	+	3.62325i	−0.818035	+	0.117616i
$950$	42.1304	−	10.1579i	1.36689	−	0.329565i
$951$	−4.58482	+	2.94648i	−0.148673	+	0.0955462i
$952$	9.84429	+	21.7994i	0.319055	+	0.706523i
$953$	7.72226	−	2.26746i	0.250149	−	0.0734502i	−0.154254	−	0.988031i	$-0.549298\pi$
$953$	7.72226	−	2.26746i	0.250149	−	0.0734502i	0.404403	+	0.914581i	$0.367479\pi$
$954$	1.86152	−	9.58579i	0.0602690	−	0.310351i
$955$	−14.1286	−	12.2425i	−0.457192	−	0.396159i
$956$	−4.24912	+	17.3022i	−0.137427	+	0.559592i
$957$	−4.83930	+	2.21004i	−0.156432	+	0.0714403i
$958$	−13.7861	−	7.13182i	−0.445408	−	0.230419i
$959$	0.705575	+	0.207175i	0.0227842	+	0.00669004i
$960$	0.940728	+	6.96017i	0.0303619	+	0.224638i
$961$	−12.8373	+	28.1098i	−0.414107	+	0.906767i
$962$	−13.8342	+	5.51577i	−0.446032	+	0.177836i
$963$	1.28815	−	2.00440i	0.0415100	−	0.0645908i
$964$	28.1796	−	5.34885i	0.907604	−	0.172275i
$965$		−	17.8656i		−	0.575116i
$966$	8.32767	−	13.4548i	0.267938	−	0.432902i
$967$	53.5201			1.72109			0.860546	−	0.509373i	$-0.170123\pi$
$967$	53.5201			1.72109			0.860546	+	0.509373i	$0.170123\pi$
$968$	−19.4584	−	22.6490i	−0.625418	−	0.727966i
$969$	−22.0949	−	14.1996i	−0.709792	−	0.456155i
$970$	−3.25432	−	8.16221i	−0.104490	−	0.262073i
$971$	8.68502	+	3.96632i	0.278716	+	0.127285i	0.549869	−	0.835251i	$-0.314678\pi$
$971$	8.68502	+	3.96632i	0.278716	+	0.127285i	−0.271153	+	0.962536i	$0.587405\pi$
$972$	−0.748555	+	1.85463i	−0.0240099	+	0.0594874i
$973$	2.96111	−	10.0846i	0.0949289	−	0.323298i
$974$	−53.2076	−	27.5254i	−1.70488	−	0.881971i
$975$	3.34932	+	7.33399i	0.107264	+	0.234876i
$976$	18.4746	−	19.1582i	0.591356	−	0.613238i
$977$	−12.7655	+	14.7322i	−0.408404	+	0.471323i	−0.922270	−	0.386547i	$-0.873668\pi$
$977$	−12.7655	+	14.7322i	−0.408404	+	0.471323i	0.513866	+	0.857871i	$0.328213\pi$
$978$	10.5155	+	2.04206i	0.336247	+	0.0652979i
$979$	−1.35271	−	4.60691i	−0.0432328	−	0.147238i
$980$	−0.267525	+	2.72060i	−0.00854578	+	0.0869064i
$981$	0.519290	+	0.808031i	0.0165797	+	0.0257985i
$982$	16.8493	−	4.06246i	0.537682	−	0.129638i
$983$	−6.53494	−	45.4515i	−0.208432	−	1.44968i	−0.778275	−	0.627924i	$-0.783905\pi$
$983$	−6.53494	−	45.4515i	−0.208432	−	1.44968i	0.569842	−	0.821754i	$-0.307004\pi$
$984$	−28.9524	−	13.3703i	−0.922967	−	0.426230i
$985$	3.13516	−	21.8055i	0.0998944	−	0.694781i
$986$	40.9264	+	2.00737i	1.30336	+	0.0639277i
$987$	1.90404	−	1.64986i	0.0606062	−	0.0525156i
$988$	13.8808	−	23.8865i	0.441607	−	0.759932i
$989$	−37.7314	+	2.49318i	−1.19979	+	0.0792785i
$990$	−0.412162	−	0.716214i	−0.0130994	−	0.0227628i
$991$	−22.3623	−	25.8075i	−0.710363	−	0.819803i	0.279750	−	0.960073i	$-0.409748\pi$
$991$	−22.3623	−	25.8075i	−0.710363	−	0.819803i	−0.990113	+	0.140270i	$0.955203\pi$
$992$	−1.57681	+	0.798888i	−0.0500636	+	0.0253647i
$993$	3.92538	−	27.3016i	0.124568	−	0.866391i
$994$	−4.82747	+	0.454104i	−0.153118	+	0.0144033i
$995$	20.1605	−	2.89865i	0.639132	−	0.0918933i
$996$	3.91816	−	3.71493i	0.124152	−	0.117712i
$997$	−15.4573	−	24.0520i	−0.489537	−	0.761734i	0.505330	−	0.862926i	$-0.331371\pi$
$997$	−15.4573	−	24.0520i	−0.489537	−	0.761734i	−0.994867	+	0.101192i	$0.967734\pi$
$998$	32.6354	+	23.3089i	1.03305	+	0.737831i
$999$	5.30034	−	1.55632i	0.167695	−	0.0492398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.13.19	✓	480
8.5	even	2	inner	552.2.bb.a.13.46	yes	480
23.16	even	11	inner	552.2.bb.a.85.46	yes	480
184.85	even	22	inner	552.2.bb.a.85.19	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.13.19	✓	480	1.1	even	1	trivial
552.2.bb.a.13.46	yes	480	8.5	even	2	inner
552.2.bb.a.85.19	yes	480	184.85	even	22	inner
552.2.bb.a.85.46	yes	480	23.16	even	11	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)

\(f(q)\)	\(=\)	\(q+(-0.464427 + 1.33578i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(-1.56862 - 1.24074i) q^{4} +(0.798595 + 0.364706i) q^{5} +(-0.872641 - 1.11288i) q^{6} +(2.23854 + 0.657294i) q^{7} +(2.38587 - 1.51909i) q^{8} +(-0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.464427 + 1.33578i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(-1.56862 - 1.24074i) q^{4} +(0.798595 + 0.364706i) q^{5} +(-0.872641 - 1.11288i) q^{6} +(2.23854 + 0.657294i) q^{7} +(2.38587 - 1.51909i) q^{8} +(-0.415415 - 0.909632i) q^{9} +(-0.858056 + 0.897368i) q^{10} +(-0.502993 - 0.435846i) q^{11} +(1.89184 - 0.648807i) q^{12} +(0.537093 + 1.82917i) q^{13} +(-1.91764 + 2.68493i) q^{14} +(-0.738563 + 0.474646i) q^{15} +(0.921110 + 3.89250i) q^{16} +(0.515855 + 3.58785i) q^{17} +(1.40800 - 0.132446i) q^{18} +(7.17209 + 1.03119i) q^{19} +(-0.800182 - 1.56294i) q^{20} +(-1.76320 + 1.52782i) q^{21} +(0.815797 - 0.469469i) q^{22} +(2.85319 + 3.85478i) q^{23} +(-0.0119570 + 2.82840i) q^{24} +(-2.76956 - 3.19624i) q^{25} +(-2.69281 - 0.132078i) q^{26} +(0.989821 + 0.142315i) q^{27} +(-2.69587 - 3.80849i) q^{28} +(-7.91207 + 1.13758i) q^{29} +(-0.291014 - 1.20700i) q^{30} +(0.262872 - 0.168938i) q^{31} +(-5.62731 - 0.577381i) q^{32} +(0.638595 - 0.187509i) q^{33} +(-5.03215 - 0.977225i) q^{34} +(1.54797 + 1.34132i) q^{35} +(-0.476994 + 1.94229i) q^{36} +(5.02490 - 2.29479i) q^{37} +(-4.70835 + 9.10142i) q^{38} +(-1.82917 - 0.537093i) q^{39} +(2.45936 - 0.342998i) q^{40} +(-4.68380 + 10.2561i) q^{41} +(-1.22195 - 3.06480i) q^{42} +(-4.26279 + 6.63302i) q^{43} +(0.248230 + 1.30776i) q^{44} -0.877932i q^{45} +(-6.47423 + 2.02097i) q^{46} -1.07988 q^{47} +(-3.77257 - 1.32956i) q^{48} +(-1.30976 - 0.841729i) q^{49} +(5.55574 - 2.21510i) q^{50} +(-3.29718 - 1.50577i) q^{51} +(1.42704 - 3.53566i) q^{52} +(1.94531 - 6.62511i) q^{53} +(-0.649801 + 1.25609i) q^{54} +(-0.242732 - 0.531509i) q^{55} +(6.33935 - 1.83233i) q^{56} +(-4.74502 + 5.47604i) q^{57} +(2.15501 - 11.0971i) q^{58} +(1.87348 + 6.38048i) q^{59} +(1.74744 + 0.171831i) q^{60} +(-3.59725 - 5.59743i) q^{61} +(0.103579 + 0.429599i) q^{62} +(-0.332027 - 2.30930i) q^{63} +(3.38473 - 7.24870i) q^{64} +(-0.238190 + 1.65665i) q^{65} +(-0.0461107 + 0.940107i) q^{66} +(11.3947 - 9.87360i) q^{67} +(3.64242 - 6.26800i) q^{68} +(-4.78540 + 0.316205i) q^{69} +(-2.51063 + 1.44480i) q^{70} +(0.962374 + 1.11064i) q^{71} +(-2.37294 - 1.53921i) q^{72} +(-1.90058 + 13.2188i) q^{73} +(0.731643 + 7.77792i) q^{74} +(4.18619 - 0.601883i) q^{75} +(-9.97080 - 10.5163i) q^{76} +(-0.839490 - 1.30627i) q^{77} +(1.56695 - 2.19393i) q^{78} +(7.03350 - 2.06522i) q^{79} +(-0.684025 + 3.44446i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-11.5246 - 11.0197i) q^{82} +(2.45570 - 1.12148i) q^{83} +(4.66141 - 0.208885i) q^{84} +(-0.896551 + 3.05337i) q^{85} +(-6.88051 - 8.77470i) q^{86} +(3.32059 - 7.27108i) q^{87} +(-1.86216 - 0.275779i) q^{88} +(6.06892 + 3.90026i) q^{89} +(1.17272 + 0.407735i) q^{90} +4.44770i q^{91} +(0.307234 - 9.58674i) q^{92} +0.312477i q^{93} +(0.501525 - 1.44248i) q^{94} +(5.35151 + 3.43921i) q^{95} +(3.52808 - 4.42184i) q^{96} +(-2.94001 + 6.43773i) q^{97} +(1.73265 - 1.35862i) q^{98} +(-0.187509 + 0.638595i) 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

Groups

Database

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