LMFDB - Embedded newform 418.2.u.b.251.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(5,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([36, 80]))

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

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

chi := DirichletCharacter("418.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.u (of order $45$, degree $24$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$11$ over $\Q(\zeta_{45})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{45}]$

Embedding invariants

Embedding label			251.7
Character	$\chi$	$=$	418.251
Dual form			418.2.u.b.5.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.615661 + 0.788011i) q^{2} +(0.555466 + 0.536408i) q^{3} +(-0.241922 - 0.970296i) q^{4} +(-0.977067 - 0.610539i) q^{5} +(-0.764674 + 0.107468i) q^{6} +(2.99213 - 1.33218i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-0.0838888 - 2.40226i) q^{9} +O(q^{10})$	\(q+(-0.615661 + 0.788011i) q^{2} +(0.555466 + 0.536408i) q^{3} +(-0.241922 - 0.970296i) q^{4} +(-0.977067 - 0.610539i) q^{5} +(-0.764674 + 0.107468i) q^{6} +(2.99213 - 1.33218i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-0.0838888 - 2.40226i) q^{9} +(1.08265 - 0.394054i) q^{10} +(-1.05491 - 3.14439i) q^{11} +(0.386095 - 0.668735i) q^{12} +(-5.35486 - 2.84723i) q^{13} +(-0.792365 + 3.17800i) q^{14} +(-0.215230 - 0.863241i) q^{15} +(-0.882948 + 0.469472i) q^{16} +(-0.0924834 + 2.64838i) q^{17} +(1.94465 + 1.41287i) q^{18} +(3.04547 - 3.11851i) q^{19} +(-0.356030 + 1.09575i) q^{20} +(2.37662 + 0.865019i) q^{21} +(3.12728 + 1.10459i) q^{22} +(1.68098 + 1.41051i) q^{23} +(0.289267 + 0.715961i) q^{24} +(-1.60995 - 3.30089i) q^{25} +(5.54043 - 2.46676i) q^{26} +(2.79208 - 3.10092i) q^{27} +(-2.01647 - 2.58097i) q^{28} +(5.90592 + 1.69349i) q^{29} +(0.812752 + 0.361860i) q^{30} +(1.33412 + 1.48169i) q^{31} +(0.173648 - 0.984808i) q^{32} +(1.10070 - 2.31246i) q^{33} +(-2.03001 - 1.70338i) q^{34} +(-3.73686 - 0.525182i) q^{35} +(-2.31061 + 0.662556i) q^{36} +(0.617677 + 0.448769i) q^{37} +(0.582442 + 4.31981i) q^{38} +(-1.44717 - 4.45393i) q^{39} +(-0.644267 - 0.955165i) q^{40} +(5.47478 + 5.28693i) q^{41} +(-2.14484 + 1.34024i) q^{42} +(0.491108 - 0.412089i) q^{43} +(-2.79578 + 1.78427i) q^{44} +(-1.38471 + 2.39839i) q^{45} +(-2.14641 + 0.456233i) q^{46} +(-3.59165 + 5.32484i) q^{47} +(-0.742276 - 0.212844i) q^{48} +(2.49421 - 2.77010i) q^{49} +(3.59233 + 0.763573i) q^{50} +(-1.47198 + 1.42148i) q^{51} +(-1.46720 + 5.88461i) q^{52} +(-2.32788 + 1.45462i) q^{53} +(0.724581 + 4.10930i) q^{54} +(-0.889051 + 3.71634i) q^{55} +3.27529 q^{56} +(3.36445 - 0.0986147i) q^{57} +(-4.97054 + 3.61131i) q^{58} +(-1.50875 - 2.23681i) q^{59} +(-0.785530 + 0.417674i) q^{60} +(3.85045 - 9.53020i) q^{61} +(-1.98896 + 0.139081i) q^{62} +(-3.45125 - 7.07611i) q^{63} +(0.669131 + 0.743145i) q^{64} +(3.49371 + 6.05129i) q^{65} +(1.14459 + 2.29106i) q^{66} +(-0.920997 + 0.335215i) q^{67} +(2.59208 - 0.550964i) q^{68} +(0.177119 + 1.68518i) q^{69} +(2.71449 - 2.62135i) q^{70} +(1.36358 + 0.852057i) q^{71} +(0.900451 - 2.22869i) q^{72} +(0.445178 - 0.912750i) q^{73} +(-0.733915 + 0.210447i) q^{74} +(0.876350 - 2.69713i) q^{75} +(-3.76264 - 2.20057i) q^{76} +(-7.34533 - 8.00307i) q^{77} +(4.40071 + 1.60173i) q^{78} +(5.47815 + 0.769904i) q^{79} +(1.14933 + 0.0803690i) q^{80} +(-3.97934 + 0.278263i) q^{81} +(-7.53677 + 1.05922i) q^{82} +(-8.72343 - 1.85422i) q^{83} +(0.264368 - 2.51529i) q^{84} +(1.70730 - 2.53118i) q^{85} +(0.0223739 + 0.640706i) q^{86} +(2.37214 + 4.10866i) q^{87} +(0.315226 - 3.30161i) q^{88} +(-2.25465 + 12.7868i) q^{89} +(-1.03744 - 2.56776i) q^{90} +(-19.8155 - 1.38563i) q^{91} +(0.961945 - 1.97228i) q^{92} +(-0.0537313 + 1.53866i) q^{93} +(-1.98479 - 6.10856i) q^{94} +(-4.87960 + 1.18762i) q^{95} +(0.624714 - 0.453881i) q^{96} +(2.24259 - 2.87038i) q^{97} +(0.647281 + 3.67091i) q^{98} +(-7.46513 + 2.79795i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.615661	+	0.788011i	−0.435338	+	0.557208i
$2$	−0.615661	+	0.788011i	−0.435338	+	0.557208i
$3$	0.555466	+	0.536408i	0.320699	+	0.309695i	0.837529	−	0.546393i	$-0.183999\pi$
$3$	0.555466	+	0.536408i	0.320699	+	0.309695i	−0.516830	+	0.856088i	$0.672888\pi$
$4$	−0.241922	−	0.970296i	−0.120961	−	0.485148i
$5$	−0.977067	−	0.610539i	−0.436958	−	0.273042i	0.293553	−	0.955943i	$-0.405162\pi$
$5$	−0.977067	−	0.610539i	−0.436958	−	0.273042i	−0.730511	+	0.682901i	$0.760718\pi$
$6$	−0.764674	+	0.107468i	−0.312177	+	0.0438736i
$7$	2.99213	−	1.33218i	1.13092	−	0.503517i	0.246003	−	0.969269i	$-0.420883\pi$
$7$	2.99213	−	1.33218i	1.13092	−	0.503517i	0.884915	+	0.465752i	$0.154216\pi$
$8$	0.913545	+	0.406737i	0.322987	+	0.143803i
$9$	−0.0838888	−	2.40226i	−0.0279629	−	0.800753i
$10$	1.08265	−	0.394054i	0.342365	−	0.124611i
$11$	−1.05491	−	3.14439i	−0.318068	−	0.948068i
$11$	−1.05491	−	3.14439i	−0.318068	−	0.948068i
$12$	0.386095	−	0.668735i	0.111456	−	0.193047i
$13$	−5.35486	−	2.84723i	−1.48517	−	0.789680i	−0.488608	−	0.872504i	$-0.662495\pi$
$13$	−5.35486	−	2.84723i	−1.48517	−	0.789680i	−0.996564	+	0.0828238i	$0.973606\pi$
$14$	−0.792365	+	3.17800i	−0.211768	+	0.849357i
$15$	−0.215230	−	0.863241i	−0.0555722	−	0.222888i
$16$	−0.882948	+	0.469472i	−0.220737	+	0.117368i
$17$	−0.0924834	+	2.64838i	−0.0224305	+	0.642326i	0.935165	+	0.354211i	$0.115251\pi$
$17$	−0.0924834	+	2.64838i	−0.0224305	+	0.642326i	−0.957596	+	0.288115i	$0.906972\pi$
$18$	1.94465	+	1.41287i	0.458359	+	0.333017i
$19$	3.04547	−	3.11851i	0.698679	−	0.715436i
$19$	3.04547	−	3.11851i	0.698679	−	0.715436i
$20$	−0.356030	+	1.09575i	−0.0796107	+	0.245017i
$21$	2.37662	+	0.865019i	0.518621	+	0.188763i
$22$	3.12728	+	1.10459i	0.666738	+	0.235500i
$23$	1.68098	+	1.41051i	0.350508	+	0.294111i	0.800994	−	0.598672i	$-0.204305\pi$
$23$	1.68098	+	1.41051i	0.350508	+	0.294111i	−0.450486	+	0.892784i	$0.648749\pi$
$24$	0.289267	+	0.715961i	0.0590464	+	0.146145i
$25$	−1.60995	−	3.30089i	−0.321991	−	0.660179i
$26$	5.54043	−	2.46676i	1.08657	−	0.483771i
$27$	2.79208	−	3.10092i	0.537336	−	0.596772i
$28$	−2.01647	−	2.58097i	−0.381077	−	0.487757i
$29$	5.90592	+	1.69349i	1.09670	+	0.314474i	0.774741	−	0.632279i	$-0.217880\pi$
$29$	5.90592	+	1.69349i	1.09670	+	0.314474i	0.321961	+	0.946753i	$0.395658\pi$
$30$	0.812752	+	0.361860i	0.148387	+	0.0660664i
$31$	1.33412	+	1.48169i	0.239615	+	0.266120i	0.850943	−	0.525258i	$-0.176031\pi$
$31$	1.33412	+	1.48169i	0.239615	+	0.266120i	−0.611328	+	0.791377i	$0.709364\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	1.10070	−	2.31246i	0.191608	−	0.402548i
$34$	−2.03001	−	1.70338i	−0.348144	−	0.292128i
$35$	−3.73686	−	0.525182i	−0.631645	−	0.0887719i
$36$	−2.31061	+	0.662556i	−0.385101	+	0.110426i
$37$	0.617677	+	0.448769i	0.101545	+	0.0737771i	0.637399	−	0.770534i	$-0.280010\pi$
$37$	0.617677	+	0.448769i	0.101545	+	0.0737771i	−0.535854	+	0.844311i	$0.680010\pi$
$38$	0.582442	+	4.31981i	0.0944845	+	0.700766i
$39$	−1.44717	−	4.45393i	−0.231733	−	0.713200i
$40$	−0.644267	−	0.955165i	−0.101868	−	0.151025i
$41$	5.47478	+	5.28693i	0.855017	+	0.825680i	0.986179	−	0.165680i	$-0.0529820\pi$
$41$	5.47478	+	5.28693i	0.855017	+	0.825680i	−0.131162	+	0.991361i	$0.541871\pi$
$42$	−2.14484	+	1.34024i	−0.330956	+	0.206804i
$43$	0.491108	−	0.412089i	0.0748933	−	0.0628429i	−0.604573	−	0.796550i	$-0.706656\pi$
$43$	0.491108	−	0.412089i	0.0748933	−	0.0628429i	0.679466	+	0.733707i	$0.262212\pi$
$44$	−2.79578	+	1.78427i	−0.421479	+	0.268989i
$45$	−1.38471	+	2.39839i	−0.206420	+	0.357530i
$46$	−2.14641	+	0.456233i	−0.316471	+	0.0672679i
$47$	−3.59165	+	5.32484i	−0.523896	+	0.776708i	−0.994399	−	0.105691i	$-0.966295\pi$
$47$	−3.59165	+	5.32484i	−0.523896	+	0.776708i	0.470503	+	0.882398i	$0.344072\pi$
$48$	−0.742276	−	0.212844i	−0.107138	−	0.0307214i
$49$	2.49421	−	2.77010i	0.356316	−	0.395729i
$50$	3.59233	+	0.763573i	0.508032	+	0.107985i
$51$	−1.47198	+	1.42148i	−0.206119	+	0.199047i
$52$	−1.46720	+	5.88461i	−0.203464	+	0.816048i
$53$	−2.32788	+	1.45462i	−0.319758	+	0.199807i	−0.680296	−	0.732937i	$-0.738149\pi$
$53$	−2.32788	+	1.45462i	−0.319758	+	0.199807i	0.360538	+	0.932745i	$0.382593\pi$
$54$	0.724581	+	4.10930i	0.0986030	+	0.559205i
$55$	−0.889051	+	3.71634i	−0.119880	+	0.501111i
$56$	3.27529			0.437679
$57$	3.36445	−	0.0986147i	0.445632	−	0.0130618i
$58$	−4.97054	+	3.61131i	−0.652664	+	0.474188i
$59$	−1.50875	−	2.23681i	−0.196422	−	0.291208i	0.717940	−	0.696105i	$-0.245085\pi$
$59$	−1.50875	−	2.23681i	−0.196422	−	0.291208i	−0.914362	+	0.404897i	$0.867307\pi$
$60$	−0.785530	+	0.417674i	−0.101411	+	0.0539214i
$61$	3.85045	−	9.53020i	0.493000	−	1.22022i	−0.451667	−	0.892186i	$-0.649171\pi$
$61$	3.85045	−	9.53020i	0.493000	−	1.22022i	0.944667	−	0.328031i	$-0.106385\pi$
$62$	−1.98896	+	0.139081i	−0.252598	+	0.0176634i
$63$	−3.45125	−	7.07611i	−0.434817	−	0.891507i
$64$	0.669131	+	0.743145i	0.0836413	+	0.0928931i
$65$	3.49371	+	6.05129i	0.433342	+	0.750570i
$66$	1.14459	+	2.29106i	0.140889	+	0.282010i
$67$	−0.920997	+	0.335215i	−0.112518	+	0.0409531i	−0.397665	−	0.917530i	$-0.630180\pi$
$67$	−0.920997	+	0.335215i	−0.112518	+	0.0409531i	0.285148	+	0.958484i	$0.407957\pi$
$68$	2.59208	−	0.550964i	0.314336	−	0.0668143i
$69$	0.177119	+	1.68518i	0.0213227	+	0.202872i
$70$	2.71449	−	2.62135i	0.324444	−	0.313312i
$71$	1.36358	+	0.852057i	0.161827	+	0.101121i	0.608415	−	0.793619i	$-0.291806\pi$
$71$	1.36358	+	0.852057i	0.161827	+	0.101121i	−0.446588	+	0.894740i	$0.647361\pi$
$72$	0.900451	−	2.22869i	0.106119	−	0.262654i
$73$	0.445178	−	0.912750i	0.0521041	−	0.106829i	−0.871153	−	0.491011i	$-0.836627\pi$
$73$	0.445178	−	0.912750i	0.0521041	−	0.106829i	0.923258	+	0.384182i	$0.125516\pi$
$74$	−0.733915	+	0.210447i	−0.0853158	+	0.0244639i
$75$	0.876350	−	2.69713i	0.101192	−	0.311437i
$76$	−3.76264	−	2.20057i	−0.431605	−	0.252423i
$77$	−7.34533	−	8.00307i	−0.837078	−	0.912035i
$78$	4.40071	+	1.60173i	0.498283	+	0.181360i
$79$	5.47815	+	0.769904i	0.616340	+	0.0866210i	0.440433	−	0.897786i	$-0.354825\pi$
$79$	5.47815	+	0.769904i	0.616340	+	0.0866210i	0.175908	+	0.984407i	$0.443714\pi$
$80$	1.14933	+	0.0803690i	0.128499	+	0.00898553i
$81$	−3.97934	+	0.278263i	−0.442149	+	0.0309181i
$82$	−7.53677	+	1.05922i	−0.832297	+	0.116972i
$83$	−8.72343	−	1.85422i	−0.957521	−	0.203527i	−0.297456	−	0.954736i	$-0.596138\pi$
$83$	−8.72343	−	1.85422i	−0.957521	−	0.203527i	−0.660065	+	0.751208i	$0.729471\pi$
$84$	0.264368	−	2.51529i	0.0288449	−	0.274441i
$85$	1.70730	−	2.53118i	0.185183	−	0.274545i
$86$	0.0223739	+	0.640706i	0.00241264	+	0.0690891i
$87$	2.37214	+	4.10866i	0.254320	+	0.440494i
$88$	0.315226	−	3.30161i	0.0336032	−	0.351953i
$89$	−2.25465	+	12.7868i	−0.238993	+	1.35540i	0.595046	+	0.803691i	$0.297134\pi$
$89$	−2.25465	+	12.7868i	−0.238993	+	1.35540i	−0.834039	+	0.551705i	$0.813977\pi$
$90$	−1.03744	−	2.56776i	−0.109356	−	0.270666i
$91$	−19.8155	−	1.38563i	−2.07723	−	0.145254i
$92$	0.961945	−	1.97228i	0.100290	−	0.205624i
$93$	−0.0537313	+	1.53866i	−0.00557168	+	0.159552i
$94$	−1.98479	−	6.10856i	−0.204716	−	0.630050i
$95$	−4.87960	+	1.18762i	−0.500637	+	0.121847i
$96$	0.624714	−	0.453881i	0.0637596	−	0.0463241i
$97$	2.24259	−	2.87038i	0.227700	−	0.291443i	−0.660570	−	0.750765i	$-0.729685\pi$
$97$	2.24259	−	2.87038i	0.227700	−	0.291443i	0.888270	+	0.459322i	$0.151907\pi$
$98$	0.647281	+	3.67091i	0.0653852	+	0.370818i
$99$	−7.46513	+	2.79795i	−0.750274	+	0.281205i
$100$	−2.81336	+	2.36069i	−0.281336	+	0.236069i
$101$	5.93026	+	3.15317i	0.590083	+	0.313752i	0.737527	−	0.675318i	$-0.235994\pi$
$101$	5.93026	+	3.15317i	0.590083	+	0.313752i	−0.147444	+	0.989070i	$0.547105\pi$
$102$	−0.213896	−	2.03509i	−0.0211789	−	0.201504i
$103$	−1.70889	+	16.2590i	−0.168382	+	1.60204i	0.505248	+	0.862974i	$0.331401\pi$
$103$	−1.70889	+	16.2590i	−0.168382	+	1.60204i	−0.673629	+	0.739069i	$0.735266\pi$
$104$	−3.73384	−	4.77909i	−0.366133	−	0.468629i
$105$	−1.79399	−	2.29620i	−0.175075	−	0.224086i
$106$	0.286929	−	2.72994i	0.0278690	−	0.265156i
$107$	−0.0686457	−	0.653120i	−0.00663623	−	0.0631395i	0.990703	−	0.136046i	$-0.0434394\pi$
$107$	−0.0686457	−	0.653120i	−0.00663623	−	0.0631395i	−0.997339	+	0.0729060i	$0.976773\pi$
$108$	−3.68427	−	1.95896i	−0.354519	−	0.188501i
$109$	15.7596	−	13.2239i	1.50949	−	1.26662i	0.644760	−	0.764385i	$-0.276957\pi$
$109$	15.7596	−	13.2239i	1.50949	−	1.26662i	0.864733	−	0.502231i	$-0.167487\pi$
$110$	−2.38116	−	2.98859i	−0.227035	−	0.284951i
$111$	0.102376	+	0.580603i	0.00971709	+	0.0551084i
$112$	−2.01647	+	2.58097i	−0.190539	+	0.243878i
$113$	−9.26108	+	6.72857i	−0.871209	+	0.632971i	−0.930911	−	0.365246i	$-0.880985\pi$
$113$	−9.26108	+	6.72857i	−0.871209	+	0.632971i	0.0597019	+	0.998216i	$0.480985\pi$
$114$	−1.99365	+	2.71194i	−0.186723	+	0.253996i
$115$	−0.781258	−	2.40446i	−0.0728527	−	0.224217i
$116$	0.214420	−	6.14018i	0.0199084	−	0.570101i
$117$	−6.39058	+	13.1026i	−0.590809	+	1.21134i
$118$	2.69150	+	0.188208i	0.247773	+	0.0173260i
$119$	3.25140	+	8.04749i	0.298055	+	0.737713i
$120$	0.154489	−	0.876151i	0.0141029	−	0.0799813i
$121$	−8.77432	+	6.63410i	−0.797665	+	0.603100i
$122$	5.13933	+	8.90157i	0.465293	+	0.805911i
$123$	0.205105	+	5.87343i	0.0184937	+	0.529589i
$124$	1.11493	−	1.65295i	0.100123	−	0.148439i
$125$	−1.04445	+	9.93726i	−0.0934183	+	0.888816i
$126$	7.70086	+	1.63687i	0.686047	+	0.145824i
$127$	−7.82467	+	1.09969i	−0.694327	+	0.0975813i	−0.477504	−	0.878630i	$-0.658458\pi$
$127$	−7.82467	+	1.09969i	−0.694327	+	0.0975813i	−0.216823	+	0.976211i	$0.569569\pi$
$128$	−0.997564	+	0.0697565i	−0.0881730	+	0.00616566i
$129$	0.493842	+	0.0345328i	0.0434803	+	0.00304044i
$130$	−6.91943	−	0.972462i	−0.606874	−	0.0852906i
$131$	−18.4681	−	6.72186i	−1.61357	−	0.587291i	−0.631428	−	0.775435i	$-0.717531\pi$
$131$	−18.4681	−	6.72186i	−1.61357	−	0.587291i	−0.982142	+	0.188143i	$0.939753\pi$
$132$	−2.51006	−	0.508573i	−0.218472	−	0.0442656i
$133$	4.95802	−	13.3881i	0.429914	−	1.16090i
$134$	0.302869	−	0.932135i	0.0261639	−	0.0805242i
$135$	−4.62128	+	1.32513i	−0.397737	+	0.114049i
$136$	−1.16168	+	2.38180i	−0.0996133	+	0.204237i
$137$	7.02179	−	17.3795i	0.599912	−	1.48483i	−0.255460	−	0.966820i	$-0.582227\pi$
$137$	7.02179	−	17.3795i	0.599912	−	1.48483i	0.855372	−	0.518014i	$-0.173329\pi$
$138$	−1.43699	−	0.897928i	−0.122324	−	0.0764367i
$139$	8.53988	−	8.24687i	0.724344	−	0.699490i	−0.238019	−	0.971261i	$-0.576498\pi$
$139$	8.53988	−	8.24687i	0.724344	−	0.699490i	0.962362	+	0.271770i	$0.0876090\pi$
$140$	0.394447	+	3.75291i	0.0333369	+	0.317179i
$141$	−4.85133	+	1.03118i	−0.408555	+	0.0868411i
$142$	−1.51093	+	0.549934i	−0.126795	+	0.0461495i
$143$	−3.30388	+	19.8413i	−0.276284	+	1.65922i
$144$	1.20186	+	2.08169i	0.100155	+	0.173474i
$145$	−4.73653	−	5.26045i	−0.393348	−	0.436857i
$146$	0.445178	+	0.912750i	0.0368432	+	0.0755397i
$147$	2.87136	−	0.200785i	0.236825	−	0.0165604i
$148$	0.286009	−	0.707896i	0.0235098	−	0.0581887i
$149$	10.7133	−	5.69636i	0.877667	−	0.466664i	0.0314520	−	0.999505i	$-0.489987\pi$
$149$	10.7133	−	5.69636i	0.877667	−	0.466664i	0.846215	+	0.532841i	$0.178876\pi$
$150$	1.58583	+	2.35109i	0.129483	+	0.191966i
$151$	2.46303	−	1.78950i	0.200438	−	0.145627i	−0.483039	−	0.875599i	$-0.660467\pi$
$151$	2.46303	−	1.78950i	0.200438	−	0.145627i	0.683477	+	0.729972i	$0.260467\pi$
$152$	4.05059	−	1.61020i	0.328546	−	0.130604i
$153$	6.36985			0.514972
$154$	10.8287	−	0.861014i	0.872605	−	0.0693825i
$155$	−0.398895	−	2.26225i	−0.0320400	−	0.181708i
$156$	−3.97153	+	2.48169i	−0.317977	+	0.198694i
$157$	−3.16739	+	12.7037i	−0.252786	+	1.01387i	0.700948	+	0.713213i	$0.252761\pi$
$157$	−3.16739	+	12.7037i	−0.252786	+	1.01387i	−0.953733	+	0.300655i	$0.902795\pi$
$158$	−3.97938	+	3.84284i	−0.316582	+	0.305720i
$159$	−2.07333	−	0.440699i	−0.164425	−	0.0349497i
$160$	−0.770930	+	0.856204i	−0.0609474	+	0.0676889i
$161$	6.90876	+	1.98105i	0.544486	+	0.156129i
$162$	2.23065	−	3.30708i	0.175257	−	0.259829i
$163$	4.13824	−	0.879611i	0.324132	−	0.0688964i	−0.0429719	−	0.999076i	$-0.513683\pi$
$163$	4.13824	−	0.879611i	0.324132	−	0.0688964i	0.367104	+	0.930180i	$0.380349\pi$
$164$	3.80542	−	6.59118i	0.297153	−	0.514685i
$165$	−2.48731	+	1.58741i	−0.193637	+	0.123580i
$166$	6.83183	−	5.73258i	0.530253	−	0.444935i
$167$	−3.06986	+	1.91826i	−0.237553	+	0.148439i	−0.643472	−	0.765469i	$-0.722507\pi$
$167$	−3.06986	+	1.91826i	−0.237553	+	0.148439i	0.405920	+	0.913909i	$0.366951\pi$
$168$	1.81931	+	1.75689i	0.140363	+	0.135547i
$169$	13.2983	+	19.7156i	1.02295	+	1.51658i
$170$	0.943476	+	2.90372i	0.0723613	+	0.222705i
$171$	−7.74695	−	7.05440i	−0.592424	−	0.539464i
$172$	−0.518658	−	0.376827i	−0.0395473	−	0.0287328i
$173$	23.9318	−	6.86234i	1.81950	−	0.521734i	0.820733	−	0.571312i	$-0.193565\pi$
$173$	23.9318	−	6.86234i	1.81950	−	0.521734i	0.998770	+	0.0495775i	$0.0157875\pi$
$174$	−4.69810	−	0.660275i	−0.356162	−	0.0500553i
$175$	−9.21458	−	7.73195i	−0.696557	−	0.584480i
$176$	2.40763	+	2.28108i	0.181482	+	0.171943i
$177$	0.361783	−	2.05177i	0.0271933	−	0.154221i
$178$	−8.68802	−	9.64902i	−0.651194	−	0.723225i
$179$	6.46544	+	2.87860i	0.483250	+	0.215157i	0.633877	−	0.773434i	$-0.281463\pi$
$179$	6.46544	+	2.87860i	0.483250	+	0.215157i	−0.150627	+	0.988591i	$0.548129\pi$
$180$	2.66214	+	0.763355i	0.198424	+	0.0568971i
$181$	8.50730	+	10.8888i	0.632343	+	0.809362i	0.992333	−	0.123594i	$-0.0394422\pi$
$181$	8.50730	+	10.8888i	0.632343	+	0.809362i	−0.359990	+	0.932956i	$0.617220\pi$
$182$	13.2915	−	14.7617i	0.985233	−	1.09421i
$183$	7.25087	−	3.22829i	0.536000	−	0.238642i
$184$	0.961945	+	1.97228i	0.0709155	+	0.145398i
$185$	−0.329521	−	0.815593i	−0.0242269	−	0.0599636i
$186$	−1.17940	−	0.989637i	−0.0864780	−	0.0725637i
$187$	8.42508	−	2.50300i	0.616103	−	0.183038i
$188$	6.03557	+	2.19677i	0.440189	+	0.160216i
$189$	4.22327	−	12.9979i	0.307198	−	0.945458i
$190$	2.06833	−	4.57635i	0.150052	−	0.332003i
$191$	−6.90086	−	5.01377i	−0.499329	−	0.362784i	0.309432	−	0.950922i	$-0.399861\pi$
$191$	−6.90086	−	5.01377i	−0.499329	−	0.362784i	−0.808761	+	0.588138i	$0.799861\pi$
$192$	−0.0269490	+	0.771719i	−0.00194488	+	0.0556940i
$193$	3.41148	−	1.81392i	0.245564	−	0.130568i	−0.342128	−	0.939653i	$-0.611148\pi$
$193$	3.41148	−	1.81392i	0.245564	−	0.130568i	0.587692	+	0.809085i	$0.300037\pi$
$194$	0.881216	+	3.53437i	0.0632676	+	0.253753i
$195$	−1.30532	+	5.23534i	−0.0934758	+	0.374911i
$196$	−3.29122	−	1.74997i	−0.235087	−	0.124998i
$197$	2.49182	−	4.31596i	0.177535	−	0.307500i	−0.763501	−	0.645807i	$-0.776521\pi$
$197$	2.49182	−	4.31596i	0.177535	−	0.307500i	0.941036	+	0.338307i	$0.109854\pi$
$198$	2.39118	−	7.60520i	0.169934	−	0.540478i
$199$	7.91205	−	2.87975i	0.560870	−	0.204140i	−0.0459993	−	0.998941i	$-0.514647\pi$
$199$	7.91205	−	2.87975i	0.560870	−	0.204140i	0.606870	+	0.794801i	$0.292425\pi$
$200$	−0.128171	−	3.67034i	−0.00906307	−	0.259532i
$201$	−0.691395	−	0.307829i	−0.0487672	−	0.0217126i
$202$	−6.13576	+	2.73182i	−0.431711	+	0.192210i
$203$	19.9273	−	2.80060i	1.39862	−	0.196564i
$204$	1.73536	+	1.08437i	0.121499	+	0.0759212i
$205$	−2.12135	−	8.50826i	−0.148161	−	0.594243i
$206$	−11.7601	−	11.3566i	−0.819368	−	0.791255i
$207$	3.24739	−	4.15647i	0.225709	−	0.288895i
$208$	6.06476			0.420515
$209$	−13.0185	−	6.28638i	−0.900509	−	0.434838i
$210$	2.91392			0.201080
$211$	−10.9543	+	14.0208i	−0.754122	+	0.965232i	−0.999992	−	0.00407054i	$-0.998704\pi$
$211$	−10.9543	+	14.0208i	−0.754122	+	0.965232i	0.245870	+	0.969303i	$0.420927\pi$
$212$	1.97457	+	1.90682i	0.135614	+	0.130961i
$213$	0.300371	+	1.20472i	0.0205811	+	0.0825462i
$214$	0.556928	+	0.348008i	0.0380708	+	0.0237893i
$215$	−0.731442	+	0.102797i	−0.0498839	+	0.00701073i
$216$	3.81195	−	1.69719i	0.259370	−	0.115479i
$217$	5.96575	+	2.65612i	0.404981	+	0.180309i
$218$	0.717976	+	20.5601i	0.0486275	+	1.39251i
$219$	0.736887	−	0.268205i	0.0497942	−	0.0181236i
$220$	3.82103	−	0.0364224i	0.257614	−	0.00245560i
$221$	8.03578	−	13.9184i	0.540545	−	0.936252i
$222$	−0.520550	−	0.276781i	−0.0349370	−	0.0185763i
$223$	−0.319614	+	1.28190i	−0.0214030	+	0.0858426i	−0.980047	−	0.198764i	$-0.936307\pi$
$223$	−0.319614	+	1.28190i	−0.0214030	+	0.0858426i	0.958644	+	0.284606i	$0.0918629\pi$
$224$	−0.792365	−	3.17800i	−0.0529421	−	0.212339i
$225$	−7.79455	+	4.14443i	−0.519636	+	0.276296i
$226$	0.399506	−	11.4404i	0.0265747	−	0.761001i
$227$	10.1279	+	7.35834i	0.672211	+	0.488390i	0.870765	−	0.491700i	$-0.163624\pi$
$227$	10.1279	+	7.35834i	0.672211	+	0.488390i	−0.198553	+	0.980090i	$0.563624\pi$
$228$	−0.909619	−	3.24065i	−0.0602410	−	0.214618i
$229$	−7.71052	+	23.7306i	−0.509526	+	1.56816i	0.283501	+	0.958972i	$0.408504\pi$
$229$	−7.71052	+	23.7306i	−0.509526	+	1.56816i	−0.793027	+	0.609187i	$0.791496\pi$
$230$	2.37573	+	0.864697i	0.156651	+	0.0570164i
$231$	0.212827	−	8.38553i	0.0140030	−	0.551727i
$232$	4.70652	+	3.94924i	0.308998	+	0.259280i
$233$	8.15628	+	20.1875i	0.534336	+	1.32253i	0.917091	+	0.398677i	$0.130531\pi$
$233$	8.15628	+	20.1875i	0.534336	+	1.32253i	−0.382756	+	0.923850i	$0.625025\pi$
$234$	−6.39058	−	13.1026i	−0.417765	−	0.856545i
$235$	6.76031	−	3.00988i	0.440994	−	0.196343i
$236$	−1.80537	+	2.00506i	−0.117519	+	0.130518i
$237$	2.62995	+	3.36618i	0.170833	+	0.218657i
$238$	−8.34327	−	2.39239i	−0.540814	−	0.155076i
$239$	20.5395	+	9.14475i	1.32859	+	0.591525i	0.943505	−	0.331358i	$-0.107507\pi$
$239$	20.5395	+	9.14475i	1.32859	+	0.591525i	0.385081	+	0.922883i	$0.374173\pi$
$240$	0.595304	+	0.661152i	0.0384267	+	0.0426772i
$241$	4.10594	−	23.2860i	0.264487	−	1.49998i	−0.506005	−	0.862531i	$-0.668878\pi$
$241$	4.10594	−	23.2860i	0.264487	−	1.49998i	0.770492	−	0.637450i	$-0.220011\pi$
$242$	0.174266	−	10.9986i	0.0112022	−	0.707018i
$243$	−11.9491	−	10.0265i	−0.766533	−	0.643198i
$244$	−10.1786	−	1.43051i	−0.651620	−	0.0915791i
$245$	−4.12827	+	1.18376i	−0.263746	+	0.0756278i
$246$	−4.75460	−	3.45442i	−0.303142	−	0.220246i
$247$	−25.1872	+	8.02804i	−1.60262	+	0.510812i
$248$	0.616122	+	1.89623i	0.0391238	+	0.120411i
$249$	−3.85095	−	5.70927i	−0.244044	−	0.361810i
$250$	−7.18764	−	6.94103i	−0.454586	−	0.438989i
$251$	−13.2938	+	8.30690i	−0.839099	+	0.524327i	−0.880076	−	0.474833i	$-0.842508\pi$
$251$	−13.2938	+	8.30690i	−0.839099	+	0.524327i	0.0409773	+	0.999160i	$0.486953\pi$
$252$	−6.03099	+	5.06060i	−0.379917	+	0.318788i
$253$	2.66190	−	6.77361i	0.167352	−	0.425853i
$254$	3.95078	−	6.84296i	0.247894	−	0.429365i
$255$	2.30609	−	0.490175i	0.144413	−	0.0306960i
$256$	0.559193	−	0.829038i	0.0349496	−	0.0518148i
$257$	16.0562	+	4.60404i	1.00156	+	0.287192i	0.736058	−	0.676919i	$-0.236685\pi$
$257$	16.0562	+	4.60404i	1.00156	+	0.287192i	0.265500	+	0.964111i	$0.414463\pi$
$258$	−0.331251	+	0.367892i	−0.0206228	+	0.0229040i
$259$	2.44601	+	0.519916i	0.151988	+	0.0323060i
$260$	5.02634	−	4.85388i	0.311720	−	0.301025i
$261$	3.57277	−	14.3296i	0.221149	−	0.886981i
$262$	16.6670	−	10.4147i	1.02969	−	0.643423i
$263$	4.17836	+	23.6967i	0.257649	+	1.46120i	0.789181	+	0.614161i	$0.210505\pi$
$263$	4.17836	+	23.6967i	0.257649	+	1.46120i	−0.531532	+	0.847038i	$0.678384\pi$
$264$	1.94611	−	1.66484i	0.119775	−	0.102464i
$265$	3.16259			0.194277
$266$	7.49751	+	12.1495i	0.459702	+	0.744934i
$267$	−8.11131	+	5.89321i	−0.496404	+	0.360659i
$268$	0.548067	+	0.812543i	0.0334785	+	0.0496340i
$269$	−7.00900	+	3.72675i	−0.427347	+	0.227224i	−0.669190	−	0.743091i	$-0.733359\pi$
$269$	−7.00900	+	3.72675i	−0.427347	+	0.227224i	0.241844	+	0.970315i	$0.422248\pi$
$270$	1.80093	−	4.45745i	0.109601	−	0.271272i
$271$	−25.9952	+	1.81776i	−1.57910	+	0.110421i	−0.832184	−	0.554500i	$-0.812909\pi$
$271$	−25.9952	+	1.81776i	−1.57910	+	0.110421i	−0.746913	+	0.664921i	$0.768465\pi$
$272$	−1.16168	−	2.38180i	−0.0704372	−	0.144418i
$273$	−10.2636	−	11.3988i	−0.621179	−	0.689889i
$274$	9.37221	+	16.2332i	0.566196	+	0.980681i
$275$	−8.68092	+	8.54447i	−0.523479	+	0.515251i
$276$	1.59227	−	0.579540i	0.0958436	−	0.0348842i
$277$	16.3145	−	3.46775i	0.980242	−	0.208357i	0.310193	−	0.950674i	$-0.399606\pi$
$277$	16.3145	−	3.46775i	0.980242	−	0.208357i	0.670049	+	0.742317i	$0.266273\pi$
$278$	1.24094	+	11.8068i	0.0744269	+	0.708125i
$279$	3.44749	−	3.32920i	0.206396	−	0.199314i
$280$	−3.20018	−	1.99970i	−0.191247	−	0.119505i
$281$	5.22230	−	12.9256i	0.311536	−	0.771079i	−0.687457	−	0.726225i	$-0.741273\pi$
$281$	5.22230	−	12.9256i	0.311536	−	0.771079i	0.998994	−	0.0448542i	$-0.0142823\pi$
$282$	2.17419	−	4.45776i	0.129471	−	0.265455i
$283$	27.1815	−	7.79418i	1.61578	−	0.463316i	0.658521	−	0.752563i	$-0.271183\pi$
$283$	27.1815	−	7.79418i	1.61578	−	0.463316i	0.957255	+	0.289247i	$0.0934048\pi$
$284$	0.496868	−	1.52920i	0.0294837	−	0.0907416i
$285$	−3.34750	−	1.95778i	−0.198289	−	0.115969i
$286$	−13.6011	−	14.8190i	−0.804251	−	0.876268i
$287$	23.4244	+	8.52579i	1.38270	+	0.503261i
$288$	−2.38033	−	0.334534i	−0.140262	−	0.0197126i
$289$	9.95323	+	0.695998i	0.585484	+	0.0409411i
$290$	7.06140	−	0.493781i	0.414659	−	0.0289958i
$291$	2.78538	−	0.391459i	0.163282	−	0.0229477i
$292$	−0.993335	−	0.211140i	−0.0581306	−	0.0123560i
$293$	−2.50425	+	23.8263i	−0.146300	+	1.39195i	0.637268	+	0.770642i	$0.280065\pi$
$293$	−2.50425	+	23.8263i	−0.146300	+	1.39195i	−0.783568	+	0.621307i	$0.786602\pi$
$294$	−1.60956	+	2.38627i	−0.0938716	+	0.139170i
$295$	0.108487	+	3.10666i	0.00631636	+	0.180877i
$296$	0.381745	+	0.661202i	0.0221885	+	0.0384316i
$297$	−12.6959	−	5.50818i	−0.736690	−	0.319617i
$298$	−2.10697	+	11.9492i	−0.122053	+	0.692200i
$299$	−4.98536	−	12.3392i	−0.288311	−	0.713595i
$300$	−2.82902	−	0.197824i	−0.163333	−	0.0114214i
$301$	0.920482	−	1.88727i	0.0530557	−	0.108780i
$302$	−0.106251	+	3.04262i	−0.00611403	+	0.175083i
$303$	1.60267	+	4.93252i	0.0920711	+	0.283366i
$304$	−1.22494	+	4.18324i	−0.0702550	+	0.239925i
$305$	−9.58071	+	6.96080i	−0.548590	+	0.398574i
$306$	−3.92167	+	5.01951i	−0.224187	+	0.286946i
$307$	1.98935	+	11.2821i	0.113538	+	0.643906i	0.987464	+	0.157846i	$0.0504551\pi$
$307$	1.98935	+	11.2821i	0.113538	+	0.643906i	−0.873926	+	0.486060i	$0.838434\pi$
$308$	−5.98835	+	9.06326i	−0.341218	+	0.516427i
$309$	−9.67066	+	8.11465i	−0.550145	+	0.461626i
$310$	2.02826	+	1.07844i	0.115197	+	0.0612515i
$311$	−2.89440	−	27.5384i	−0.164126	−	1.56156i	−0.698064	−	0.716035i	$-0.745955\pi$
$311$	−2.89440	−	27.5384i	−0.164126	−	1.56156i	0.533938	−	0.845524i	$-0.320712\pi$
$312$	0.489521	−	4.65749i	0.0277137	−	0.263678i
$313$	−16.3367	−	20.9100i	−0.923403	−	1.18190i	−0.982986	−	0.183678i	$-0.941200\pi$
$313$	−16.3367	−	20.9100i	−0.923403	−	1.18190i	0.0595839	−	0.998223i	$-0.481023\pi$
$314$	−8.06063	−	10.3171i	−0.454888	−	0.582229i
$315$	−0.948142	+	9.02097i	−0.0534217	+	0.508274i
$316$	−0.578250	−	5.50168i	−0.0325291	−	0.309494i
$317$	1.69592	+	0.901739i	0.0952526	+	0.0506467i	0.516414	−	0.856339i	$-0.327266\pi$
$317$	1.69592	+	0.901739i	0.0952526	+	0.0506467i	−0.421162	+	0.906986i	$0.638378\pi$
$318$	1.62374	−	1.36248i	0.0910550	−	0.0764042i
$319$	−0.905227	−	20.3570i	−0.0506830	−	1.13977i
$320$	−0.200066	−	1.13463i	−0.0111841	−	0.0634279i
$321$	0.312208	−	0.399609i	0.0174258	−	0.0223040i
$322$	−5.81455	+	4.22452i	−0.324032	+	0.235423i
$323$	7.97734	+	8.35397i	0.443871	+	0.464827i
$324$	1.23269	+	3.79382i	0.0684826	+	0.210768i
$325$	−0.777327	+	22.2597i	−0.0431184	+	1.23475i
$326$	−1.85461	+	3.80252i	−0.102718	+	0.210602i
$327$	15.8473	+	1.10815i	0.876357	+	0.0612809i
$328$	2.85107	+	7.05665i	0.157424	+	0.389638i
$329$	−3.65303	+	20.7173i	−0.201398	+	1.14218i
$330$	0.280446	−	2.93734i	0.0154381	−	0.161695i
$331$	−15.9073	−	27.5522i	−0.874343	−	1.51441i	−0.857461	−	0.514550i	$-0.827959\pi$
$331$	−15.9073	−	27.5522i	−0.874343	−	1.51441i	−0.0168829	−	0.999857i	$-0.505374\pi$
$332$	0.311245	+	8.91288i	0.0170818	+	0.489158i
$333$	1.02624	−	1.52147i	0.0562378	−	0.0833759i
$334$	0.378384	−	3.60008i	0.0207042	−	0.196988i
$335$	1.10454	+	0.234777i	0.0603474	+	0.0128272i
$336$	−2.50453	+	0.351989i	−0.136633	+	0.0192026i
$337$	−20.3538	+	1.42328i	−1.10874	+	0.0775309i	−0.612365	−	0.790575i	$-0.709782\pi$
$337$	−20.3538	+	1.42328i	−1.10874	+	0.0775309i	−0.496379	+	0.868106i	$0.665337\pi$
$338$	−23.7234	−	1.65890i	−1.29038	−	0.0902322i
$339$	−8.75348	−	1.23022i	−0.475424	−	0.0668164i
$340$	−2.86903	−	1.04424i	−0.155595	−	0.0566319i
$341$	3.25163	−	5.75805i	0.176086	−	0.311816i
$342$	10.3284	−	1.76156i	0.558498	−	0.0952542i
$343$	−3.31212	+	10.1937i	−0.178838	+	0.550406i
$344$	0.616261	−	0.176710i	0.0332266	−	0.00952757i
$345$	0.855811	−	1.75467i	0.0460753	−	0.0944684i
$346$	−9.32631	+	23.0834i	−0.501385	+	1.24097i
$347$	−4.00659	−	2.50360i	−0.215085	−	0.134400i	0.418098	−	0.908402i	$-0.362697\pi$
$347$	−4.00659	−	2.50360i	−0.215085	−	0.134400i	−0.633184	+	0.774002i	$0.718252\pi$
$348$	3.41274	−	3.29565i	0.182942	−	0.176665i
$349$	1.52274	+	14.4879i	0.0815105	+	0.775521i	0.956569	+	0.291504i	$0.0941558\pi$
$349$	1.52274	+	14.4879i	0.0815105	+	0.775521i	−0.875059	+	0.484016i	$0.839178\pi$
$350$	11.7659	−	2.50092i	0.628915	−	0.133680i
$351$	−23.7802	+	8.65530i	−1.26929	+	0.461986i
$352$	−3.27980	+	0.492869i	−0.174814	+	0.0262700i
$353$	2.42726	+	4.20414i	0.129190	+	0.223764i	0.923363	−	0.383928i	$-0.125429\pi$
$353$	2.42726	+	4.20414i	0.129190	+	0.223764i	−0.794173	+	0.607692i	$0.792096\pi$
$354$	1.39408	+	1.54829i	0.0740947	+	0.0822905i
$355$	−0.812092	−	1.66503i	−0.0431014	−	0.0883709i
$356$	12.9524	−	0.905721i	0.686476	−	0.0480031i
$357$	−2.51069	+	6.21419i	−0.132880	+	0.328890i
$358$	−6.24889	+	3.32259i	−0.330264	+	0.175605i
$359$	−5.73712	−	8.50563i	−0.302794	−	0.448910i	0.646678	−	0.762763i	$-0.276158\pi$
$359$	−5.73712	−	8.50563i	−0.302794	−	0.448910i	−0.949472	+	0.313853i	$0.898380\pi$
$360$	−2.24051	+	1.62782i	−0.118085	+	0.0857938i
$361$	−0.450224	−	18.9947i	−0.0236960	−	0.999719i
$362$	−13.8181			−0.726266
$363$	−8.43242	−	1.02159i	−0.442587	−	0.0536196i
$364$	3.44932	+	19.5621i	0.180794	+	1.02533i
$365$	−0.992238	+	0.620019i	−0.0519361	+	0.0324533i
$366$	−1.92015	+	7.70130i	−0.100368	+	0.402553i
$367$	2.24608	−	2.16902i	0.117245	−	0.113222i	−0.633726	−	0.773558i	$-0.718475\pi$
$367$	2.24608	−	2.16902i	0.117245	−	0.113222i	0.750970	+	0.660336i	$0.229586\pi$
$368$	−2.14641	−	0.456233i	−0.111889	−	0.0237828i
$369$	12.2413	−	13.5954i	0.637257	−	0.707746i
$370$	0.845570	+	0.242463i	0.0439591	+	0.0126051i
$371$	−5.02749	+	7.45356i	−0.261014	+	0.386970i
$372$	1.50596	−	0.320101i	0.0780803	−	0.0165965i
$373$	−2.67352	+	4.63068i	−0.138430	+	0.239767i	−0.926902	−	0.375302i	$-0.877539\pi$
$373$	−2.67352	+	4.63068i	−0.138430	+	0.239767i	0.788473	+	0.615070i	$0.210872\pi$
$374$	−3.21461	+	8.18006i	−0.166223	+	0.422981i
$375$	−5.91058	+	4.95956i	−0.305221	+	0.256111i
$376$	−5.44694	+	3.40363i	−0.280905	+	0.175529i
$377$	−26.8036	−	25.8839i	−1.38046	−	1.33309i
$378$	7.64238	+	11.3303i	0.393082	+	0.582767i
$379$	−1.35876	−	4.18183i	−0.0697947	−	0.214806i	0.910075	−	0.414443i	$-0.136024\pi$
$379$	−1.35876	−	4.18183i	−0.0697947	−	0.214806i	−0.979870	+	0.199637i	$0.936024\pi$
$380$	2.33282	+	4.44735i	0.119671	+	0.228144i
$381$	−4.93622	−	3.58637i	−0.252890	−	0.183735i
$382$	8.19950	−	2.35117i	0.419523	−	0.120296i
$383$	33.5435	+	4.71423i	1.71399	+	0.240886i	0.926729	−	0.375730i	$-0.122608\pi$
$383$	33.5435	+	4.71423i	1.71399	+	0.240886i	0.787264	+	0.616616i	$0.211497\pi$
$384$	−0.591531	−	0.496354i	−0.0301865	−	0.0253294i
$385$	2.29069	+	12.3042i	0.116744	+	0.627078i
$386$	−0.670931	+	3.80504i	−0.0341495	+	0.193671i
$387$	−1.03114	−	1.14520i	−0.0524159	−	0.0582138i
$388$	−3.32765	−	1.48156i	−0.168936	−	0.0752151i
$389$	−29.7485	−	8.53024i	−1.50831	−	0.432500i	−0.583239	−	0.812301i	$-0.698215\pi$
$389$	−29.7485	−	8.53024i	−1.50831	−	0.432500i	−0.925068	+	0.379801i	$0.875993\pi$
$390$	−3.32187	−	4.25180i	−0.168210	−	0.215298i
$391$	−3.89102	+	4.32142i	−0.196777	+	0.218543i
$392$	3.40528	−	1.51613i	0.171993	−	0.0765760i
$393$	−6.65278	−	13.6402i	−0.335588	−	0.688058i
$394$	1.86691	+	4.62075i	0.0940534	+	0.232790i
$395$	−4.88247	−	4.09688i	−0.245664	−	0.206136i
$396$	4.52082	+	6.56650i	0.227180	+	0.329979i
$397$	−1.04816	−	0.381498i	−0.0526055	−	0.0191468i	0.315583	−	0.948898i	$-0.397800\pi$
$397$	−1.04816	−	0.381498i	−0.0526055	−	0.0191468i	−0.368189	+	0.929751i	$0.620022\pi$
$398$	−2.60187	+	8.00773i	−0.130420	+	0.401391i
$399$	9.93549	−	4.77713i	0.497397	−	0.239155i
$400$	2.97118	+	2.15869i	0.148559	+	0.107934i
$401$	1.01050	−	28.9370i	0.0504621	−	1.44505i	−0.665234	−	0.746635i	$-0.731668\pi$
$401$	1.01050	−	28.9370i	0.0504621	−	1.44505i	0.715696	−	0.698412i	$-0.246110\pi$
$402$	0.668238	−	0.355308i	0.0333287	−	0.0177212i
$403$	−2.92532	−	11.7328i	−0.145721	−	0.584453i
$404$	1.62485	−	6.51692i	0.0808394	−	0.324229i
$405$	4.05798	+	2.15766i	0.201642	+	0.107215i
$406$	−10.0616	+	17.4272i	−0.499347	+	0.864895i
$407$	0.759506	−	2.41563i	0.0376473	−	0.119738i
$408$	−1.92289	+	0.699874i	−0.0951972	+	0.0346489i
$409$	0.717593	+	20.5492i	0.0354827	+	1.01609i	0.878364	+	0.477992i	$0.158635\pi$
$409$	0.717593	+	20.5492i	0.0354827	+	1.01609i	−0.842881	+	0.538099i	$0.819142\pi$
$410$	8.01063	+	3.56656i	0.395617	+	0.176140i
$411$	13.2229	−	5.88721i	0.652237	−	0.290394i
$412$	16.1894	−	2.27527i	0.797596	−	0.112095i
$413$	−7.49419	−	4.68289i	−0.368765	−	0.230430i
$414$	1.27605	+	5.11796i	0.0627145	+	0.251534i
$415$	7.39130	+	7.13770i	0.362825	+	0.350376i
$416$	−3.73384	+	4.77909i	−0.183066	+	0.234314i
$417$	9.16730			0.448925
$418$	12.9687	−	6.38844i	0.634321	−	0.312469i
$419$	−37.5185			−1.83290			−0.916448	−	0.400153i	$-0.868957\pi$
$419$	−37.5185			−1.83290			−0.916448	+	0.400153i	$0.868957\pi$
$420$	−1.79399	+	2.29620i	−0.0875377	+	0.112043i
$421$	14.2275	+	13.7394i	0.693407	+	0.669616i	0.955353	−	0.295467i	$-0.0954752\pi$
$421$	14.2275	+	13.7394i	0.693407	+	0.669616i	−0.261946	+	0.965083i	$0.584364\pi$
$422$	−4.30443	−	17.2641i	−0.209537	−	0.840405i
$423$	13.0929	+	8.18138i	0.636601	+	0.397792i
$424$	−2.71827	+	0.382028i	−0.132011	+	0.0185529i
$425$	8.89091	−	3.95849i	0.431272	−	0.192015i
$426$	−1.13426	−	0.505005i	−0.0549551	−	0.0244676i
$427$	−1.17491	−	33.6451i	−0.0568580	−	1.62820i
$428$	−0.617113	+	0.224611i	−0.0298293	+	0.0108570i
$429$	−12.4782	+	9.24897i	−0.602455	+	0.446544i
$430$	0.369315	−	0.639673i	0.0178100	−	0.0308478i
$431$	−35.0546	−	18.6389i	−1.68852	−	0.897802i	−0.981706	−	0.190402i	$-0.939021\pi$
$431$	−35.0546	−	18.6389i	−1.68852	−	0.897802i	−0.706814	−	0.707400i	$-0.749868\pi$
$432$	−1.00947	+	4.04875i	−0.0485680	+	0.194796i
$433$	4.88700	+	19.6007i	0.234854	+	0.941950i	0.965753	+	0.259463i	$0.0835457\pi$
$433$	4.88700	+	19.6007i	0.234854	+	0.941950i	−0.730899	+	0.682486i	$0.760899\pi$
$434$	−5.76593	+	3.06580i	−0.276774	+	0.147163i
$435$	0.190762	−	5.46272i	0.00914635	−	0.261917i
$436$	−16.6436	−	12.0923i	−0.797086	−	0.579117i
$437$	9.51805	−	0.946489i	0.455310	−	0.0452767i
$438$	−0.242325	+	0.745799i	−0.0115787	+	0.0356356i
$439$	35.3366	+	12.8615i	1.68652	+	0.613844i	0.994181	−	0.107724i	$-0.0343564\pi$
$439$	35.3366	+	12.8615i	1.68652	+	0.613844i	0.692343	+	0.721569i	$0.256579\pi$
$440$	−2.32376	+	3.03344i	−0.110781	+	0.144613i
$441$	−6.86374	−	5.75937i	−0.326845	−	0.274255i
$442$	6.02051	+	14.9013i	0.286367	+	0.708782i
$443$	−3.56054	−	7.30019i	−0.169166	−	0.346842i	0.797321	−	0.603555i	$-0.206250\pi$
$443$	−3.56054	−	7.30019i	−0.169166	−	0.346842i	−0.966488	+	0.256712i	$0.917361\pi$
$444$	0.538589	−	0.239795i	0.0255603	−	0.0113802i
$445$	10.0098	−	11.1170i	0.474509	−	0.526996i
$446$	−0.813379	−	1.04108i	−0.0385146	−	0.0492965i
$447$	9.00644	+	2.58256i	0.425990	+	0.122151i
$448$	2.99213	+	1.33218i	0.141365	+	0.0629397i
$449$	0.0316659	+	0.0351686i	0.00149441	+	0.00165971i	0.743892	−	0.668300i	$-0.232978\pi$
$449$	0.0316659	+	0.0351686i	0.00149441	+	0.00165971i	−0.742397	+	0.669960i	$0.766311\pi$
$450$	1.53294	−	8.69376i	0.0722637	−	0.409828i
$451$	10.8487	−	22.7921i	0.510847	−	1.07324i
$452$	8.76916	+	7.35820i	0.412467	+	0.346101i
$453$	2.32803	+	0.327183i	0.109380	+	0.0153724i
$454$	−12.0338	+	3.45064i	−0.564774	+	0.161946i
$455$	18.5151	+	13.4520i	0.868000	+	0.630639i
$456$	3.11369	+	1.27836i	0.145812	+	0.0598645i
$457$	12.0867	+	37.1989i	0.565391	+	1.74009i	0.666788	+	0.745247i	$0.267668\pi$
$457$	12.0867	+	37.1989i	0.565391	+	1.74009i	−0.101398	+	0.994846i	$0.532332\pi$
$458$	−13.9529	−	20.6860i	−0.651974	−	0.966591i
$459$	7.95418	+	7.68127i	0.371269	+	0.358531i
$460$	−2.14404	+	1.33974i	−0.0999663	+	0.0624659i
$461$	−6.67280	+	5.59915i	−0.310783	+	0.260778i	−0.784816	−	0.619729i	$-0.787242\pi$
$461$	−6.67280	+	5.59915i	−0.310783	+	0.260778i	0.474032	+	0.880507i	$0.342798\pi$
$462$	6.47686	+	5.33035i	0.301331	+	0.247991i
$463$	−3.71324	+	6.43153i	−0.172569	+	0.298898i	−0.939317	−	0.343050i	$-0.888540\pi$
$463$	−3.71324	+	6.43153i	−0.172569	+	0.298898i	0.766748	+	0.641948i	$0.221873\pi$
$464$	−6.00966	+	1.27739i	−0.278992	+	0.0593015i
$465$	0.991914	−	1.47057i	0.0459989	−	0.0681962i
$466$	−20.9295	−	6.00143i	−0.969539	−	0.278011i
$467$	−5.87075	+	6.52012i	−0.271666	+	0.301715i	−0.863505	−	0.504341i	$-0.831736\pi$
$467$	−5.87075	+	6.52012i	−0.271666	+	0.301715i	0.591839	+	0.806056i	$0.298402\pi$
$468$	14.2594	+	3.03094i	0.659143	+	0.140105i
$469$	−2.30917	+	2.22994i	−0.106628	+	0.102969i
$470$	−1.79024	+	7.18027i	−0.0825777	+	0.331201i
$471$	−8.57375	+	5.35748i	−0.395058	+	0.246859i
$472$	−0.468516	−	2.65709i	−0.0215652	−	0.122302i
$473$	−1.81384	−	1.10952i	−0.0834005	−	0.0510156i
$474$	−4.27174			−0.196208
$475$	−15.1969	−	5.03212i	−0.697283	−	0.230889i
$476$	7.02186	−	5.10168i	0.321847	−	0.233835i
$477$	3.68966	+	5.47014i	0.168938	+	0.250460i
$478$	−19.8515	+	10.5552i	−0.907987	+	0.482785i
$479$	−4.00972	+	9.92440i	−0.183209	+	0.453457i	−0.990639	−	0.136505i	$-0.956413\pi$
$479$	−4.00972	+	9.92440i	−0.183209	+	0.453457i	0.807431	+	0.589962i	$0.200857\pi$
$480$	−0.887500	+	0.0620601i	−0.0405087	+	0.00283264i
$481$	−2.02983	−	4.16176i	−0.0925522	−	0.189760i
$482$	15.8217	+	17.5718i	0.720659	+	0.800373i
$483$	2.77493	+	4.80632i	0.126264	+	0.218695i
$484$	8.55974	+	6.90875i	0.389079	+	0.314034i
$485$	−3.94364	+	1.43537i	−0.179071	+	0.0651767i
$486$	15.2575	−	3.24309i	0.692096	−	0.147110i
$487$	3.49722	+	33.2738i	0.158474	+	1.50778i	0.727869	+	0.685716i	$0.240511\pi$
$487$	3.49722	+	33.2738i	0.158474	+	1.50778i	−0.569395	+	0.822064i	$0.692823\pi$
$488$	7.39384	−	7.14015i	0.334704	−	0.323220i
$489$	2.77048	+	1.73119i	0.125286	+	0.0782872i
$490$	1.60880	−	3.98192i	0.0726782	−	0.179885i
$491$	10.1137	−	20.7362i	0.456425	−	0.935811i	−0.539183	−	0.842189i	$-0.681267\pi$
$491$	10.1137	−	20.7362i	0.456425	−	0.935811i	0.995608	−	0.0936217i	$-0.0298444\pi$
$492$	5.64934	−	1.61992i	0.254692	−	0.0730318i
$493$	−5.03121	+	15.4845i	−0.226594	+	0.697386i
$494$	9.18060	−	24.7903i	0.413055	−	1.11537i
$495$	9.00220	+	1.82397i	0.404619	+	0.0819814i
$496$	−1.87357	−	0.681924i	−0.0841259	−	0.0306193i
$497$	5.21509	+	0.732933i	0.233929	+	0.0328766i
$498$	6.86985	+	0.480387i	0.307845	+	0.0215266i
$499$	−10.4006	+	0.727280i	−0.465595	+	0.0325575i	−0.300628	−	0.953742i	$-0.597196\pi$
$499$	−10.4006	+	0.727280i	−0.465595	+	0.0325575i	−0.164967	+	0.986299i	$0.552752\pi$
$500$	9.89476	−	1.39062i	0.442507	−	0.0621903i
$501$	−2.73417	−	0.581166i	−0.122154	−	0.0259646i
$502$	1.63857	−	15.5899i	0.0731328	−	0.695812i
$503$	9.51162	−	14.1016i	0.424102	−	0.628757i	−0.555067	−	0.831806i	$-0.687307\pi$
$503$	9.51162	−	14.1016i	0.424102	−	0.628757i	0.979169	+	0.203049i	$0.0650850\pi$
$504$	−0.274760	−	7.86810i	−0.0122388	−	0.350473i
$505$	−3.86912	−	6.70152i	−0.172174	−	0.298214i
$506$	3.69885	+	6.26785i	0.164434	+	0.278640i
$507$	−3.18881	+	18.0847i	−0.141620	+	0.803168i
$508$	2.95998	+	7.32620i	0.131328	+	0.325048i
$509$	13.0087	+	0.909656i	0.576600	+	0.0403198i	0.355080	−	0.934836i	$-0.384454\pi$
$509$	13.0087	+	0.909656i	0.576600	+	0.0403198i	0.221520	+	0.975156i	$0.428898\pi$
$510$	−1.03351	+	2.11901i	−0.0457646	+	0.0938312i
$511$	0.116081	−	3.32412i	0.00513512	−	0.147051i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−1.16705	−	18.1509i	−0.0515267	−	0.801381i
$514$	−13.5132	+	9.81792i	−0.596042	+	0.433050i
$515$	11.5964	−	14.8428i	0.511000	−	0.654050i
$516$	−0.0859641	−	0.487527i	−0.00378436	−	0.0214622i
$517$	20.5322	+	5.67629i	0.903006	+	0.249643i
$518$	−1.91561	+	1.60739i	−0.0841672	+	0.0706247i
$519$	16.9743	+	9.02542i	0.745091	+	0.396172i
$520$	0.730385	+	6.94915i	0.0320295	+	0.304740i
$521$	−1.62309	+	15.4426i	−0.0711087	+	0.676554i	0.899669	+	0.436573i	$0.143808\pi$
$521$	−1.62309	+	15.4426i	−0.0711087	+	0.676554i	−0.970778	+	0.239981i	$0.922859\pi$
$522$	9.09227	+	11.6376i	0.397958	+	0.509363i
$523$	−14.0229	−	17.9485i	−0.613180	−	0.784835i	0.376762	−	0.926310i	$-0.377038\pi$
$523$	−14.0229	−	17.9485i	−0.613180	−	0.784835i	−0.989942	+	0.141475i	$0.954815\pi$
$524$	−2.05434	+	19.5457i	−0.0897442	+	0.853859i
$525$	−0.970912	−	9.23761i	−0.0423741	−	0.403162i
$526$	−21.2457	−	11.2965i	−0.926356	−	0.492552i
$527$	−4.04747	+	3.39623i	−0.176310	+	0.147942i
$528$	0.113772	+	2.55853i	0.00495129	+	0.111346i
$529$	−3.15775	−	17.9085i	−0.137294	−	0.778631i
$530$	−1.94709	+	2.49216i	−0.0845761	+	0.108252i
$531$	−5.24683	+	3.81204i	−0.227693	+	0.165429i
$532$	−14.1899	−	1.57187i	−0.615209	−	0.0681490i
$533$	−14.2636	−	43.8988i	−0.617824	−	1.90147i
$534$	0.349907	−	10.0200i	0.0151420	−	0.433609i
$535$	−0.331684	+	0.680054i	−0.0143400	+	0.0294013i
$536$	−0.977717	−	0.0683686i	−0.0422309	−	0.00295307i
$537$	2.04723	+	5.06708i	0.0883446	+	0.218661i
$538$	1.37845	−	7.81759i	0.0594293	−	0.337040i
$539$	−11.3414	−	4.92055i	−0.488511	−	0.211943i
$540$	2.40376	+	4.16343i	0.103441	+	0.179166i
$541$	1.09306	+	31.3013i	0.0469945	+	1.34575i	0.762432	+	0.647069i	$0.224005\pi$
$541$	1.09306	+	31.3013i	0.0469945	+	1.34575i	−0.715437	+	0.698677i	$0.753772\pi$
$542$	14.5718	−	21.6036i	0.625914	−	0.927956i
$543$	−1.11534	+	10.6118i	−0.0478639	+	0.455395i
$544$	2.59208	+	0.550964i	0.111135	+	0.0236224i
$545$	−23.4719	+	3.29875i	−1.00542	+	0.141303i
$546$	15.3013	−	1.06997i	0.654835	−	0.0457905i
$547$	−43.1108	−	3.01460i	−1.84329	−	0.128895i	−0.894950	−	0.446165i	$-0.852789\pi$
$547$	−43.1108	−	3.01460i	−1.84329	−	0.128895i	−0.948335	+	0.317270i	$0.897234\pi$
$548$	−18.5620	−	2.60872i	−0.792930	−	0.111439i
$549$	−23.2170	−	8.45031i	−0.990879	−	0.360650i
$550$	−1.38862	−	12.1012i	−0.0592111	−	0.515995i
$551$	23.2675	−	13.2602i	0.991228	−	0.564903i
$552$	−0.523617	+	1.61153i	−0.0222866	+	0.0685912i
$553$	17.4170	−	4.99424i	0.740646	−	0.212377i
$554$	−7.31157	+	14.9909i	−0.310639	+	0.636904i
$555$	0.254453	−	0.629792i	0.0108009	−	0.0267332i
$556$	−10.0679	−	6.29111i	−0.426974	−	0.266803i
$557$	14.5982	−	14.0973i	0.618546	−	0.597323i	−0.317905	−	0.948123i	$-0.602979\pi$
$557$	14.5982	−	14.0973i	0.618546	−	0.597323i	0.936450	+	0.350800i	$0.114090\pi$
$558$	0.500961	+	4.76632i	0.0212074	+	0.201775i
$559$	−3.80313	+	0.808380i	−0.160855	+	0.0341908i
$560$	3.54601	−	1.29064i	0.149846	−	0.0545396i
$561$	6.02248	+	3.12895i	0.254269	+	0.132104i
$562$	6.97037	+	12.0730i	0.294028	+	0.509271i
$563$	−4.13642	−	4.59396i	−0.174329	−	0.193612i	0.649648	−	0.760235i	$-0.274916\pi$
$563$	−4.13642	−	4.59396i	−0.174329	−	0.193612i	−0.823977	+	0.566623i	$0.808250\pi$
$564$	2.17419	+	4.45776i	0.0915500	+	0.187705i
$565$	13.1568	−	0.920010i	0.553509	−	0.0387051i
$566$	−10.5927	+	26.2179i	−0.445246	+	1.10202i
$567$	−11.5360	+	6.13381i	−0.484467	+	0.257596i
$568$	0.899126	+	1.33301i	0.0377265	+	0.0559318i
$569$	−10.1507	+	7.37489i	−0.425538	+	0.309172i	−0.779862	−	0.625951i	$-0.784711\pi$
$569$	−10.1507	+	7.37489i	−0.425538	+	0.309172i	0.354324	+	0.935123i	$0.384711\pi$
$570$	3.60368	−	1.43254i	0.150941	−	0.0600025i
$571$	36.1939			1.51467			0.757333	−	0.653029i	$-0.226502\pi$
$571$	36.1939			1.51467			0.757333	+	0.653029i	$0.226502\pi$
$572$	20.0512	−	1.59431i	0.838385	−	0.0666615i
$573$	−1.14377	−	6.48666i	−0.0477818	−	0.270984i
$574$	−21.1399	+	13.2097i	−0.882363	+	0.551362i
$575$	1.94964	−	7.81958i	0.0813056	−	0.326099i
$576$	1.72909	−	1.66977i	0.0720456	−	0.0695736i
$577$	17.9353	+	3.81226i	0.746656	+	0.158707i	0.565501	−	0.824748i	$-0.308683\pi$
$577$	17.9353	+	3.81226i	0.746656	+	0.158707i	0.181155	+	0.983454i	$0.442016\pi$
$578$	−6.67628	+	7.41476i	−0.277696	+	0.308413i
$579$	2.86796	+	0.822374i	0.119188	+	0.0341767i
$580$	−3.95832	+	5.86846i	−0.164360	+	0.243674i
$581$	−28.5718	+	6.07312i	−1.18536	+	0.251955i
$582$	−1.40637	+	2.43591i	−0.0582961	+	0.100972i
$583$	7.02959	+	5.78525i	0.291136	+	0.239600i
$584$	0.777939	−	0.652768i	0.0321913	−	0.0270117i
$585$	14.2437	−	8.90045i	0.588904	−	0.367988i
$586$	−17.2336	−	16.6423i	−0.711915	−	0.687488i
$587$	7.01705	+	10.4032i	0.289625	+	0.429386i	0.945568	−	0.325423i	$-0.105507\pi$
$587$	7.01705	+	10.4032i	0.289625	+	0.429386i	−0.655944	+	0.754810i	$0.727729\pi$
$588$	−0.889464	−	2.73749i	−0.0366809	−	0.112892i
$589$	8.68370	+	0.351976i	0.357806	+	0.0145029i
$590$	−2.51487	−	1.82716i	−0.103536	−	0.0752231i
$591$	3.69924	−	1.06074i	0.152166	−	0.0436330i
$592$	−0.756061	−	0.106257i	−0.0310739	−	0.00436715i
$593$	−18.7180	−	15.7063i	−0.768657	−	0.644979i	0.171708	−	0.985148i	$-0.445071\pi$
$593$	−18.7180	−	15.7063i	−0.768657	−	0.644979i	−0.940365	+	0.340168i	$0.889516\pi$
$594$	12.1569	−	6.61332i	0.498802	−	0.271348i
$595$	1.73648	−	9.84805i	0.0711886	−	0.403731i
$596$	−8.11893	−	9.01699i	−0.332564	−	0.369350i
$597$	5.93960	+	2.64448i	0.243092	+	0.108231i
$598$	12.7927	+	3.66826i	0.523134	+	0.150006i
$599$	7.00280	+	8.96318i	0.286127	+	0.366225i	0.909504	−	0.415696i	$-0.136462\pi$
$599$	7.00280	+	8.96318i	0.286127	+	0.366225i	−0.623377	+	0.781921i	$0.714240\pi$
$600$	1.89761	−	2.10750i	0.0774694	−	0.0860385i
$601$	−10.7195	+	4.77264i	−0.437258	+	0.194680i	−0.613546	−	0.789659i	$-0.710258\pi$
$601$	−10.7195	+	4.77264i	−0.437258	+	0.194680i	0.176288	+	0.984339i	$0.443591\pi$
$602$	0.920482	+	1.88727i	0.0375160	+	0.0769193i
$603$	0.882536	+	2.18435i	0.0359396	+	0.0889537i
$604$	−2.33220	−	1.95695i	−0.0948959	−	0.0796271i
$605$	12.6235	−	1.12490i	0.513218	−	0.0457336i
$606$	−4.87358	−	1.77384i	−0.197976	−	0.0720572i
$607$	12.7594	−	39.2693i	0.517887	−	1.59389i	−0.260081	−	0.965587i	$-0.583749\pi$
$607$	12.7594	−	39.2693i	0.517887	−	1.59389i	0.777968	−	0.628304i	$-0.216251\pi$
$608$	−2.54229	−	3.54073i	−0.103104	−	0.143595i
$609$	12.5712	+	9.13352i	0.509411	+	0.370109i
$610$	0.413294	−	11.8352i	0.0167338	−	0.479193i
$611$	34.3938	−	18.2875i	1.39143	−	0.739834i
$612$	−1.54101	−	6.18064i	−0.0622915	−	0.249838i
$613$	6.37436	−	25.5661i	0.257458	−	1.03261i	−0.692797	−	0.721133i	$-0.743622\pi$
$613$	6.37436	−	25.5661i	0.257458	−	1.03261i	0.950255	−	0.311474i	$-0.100823\pi$
$614$	−10.1152	−	5.37836i	−0.408217	−	0.217053i
$615$	3.38556	−	5.86396i	0.136519	−	0.236458i
$616$	−3.45515	−	10.2988i	−0.139212	−	0.414950i
$617$	−13.0165	+	4.73761i	−0.524024	+	0.190729i	−0.590468	−	0.807061i	$-0.701057\pi$
$617$	−13.0165	+	4.73761i	−0.524024	+	0.190729i	0.0664441	+	0.997790i	$0.478835\pi$
$618$	−0.440577	−	12.6165i	−0.0177226	−	0.507509i
$619$	12.2217	+	5.44147i	0.491233	+	0.218711i	0.637377	−	0.770552i	$-0.280020\pi$
$619$	12.2217	+	5.44147i	0.491233	+	0.218711i	−0.146144	+	0.989263i	$0.546686\pi$
$620$	−2.09855	+	0.934334i	−0.0842797	+	0.0375237i
$621$	9.06729	−	1.27433i	0.363858	−	0.0511369i
$622$	23.4825	+	14.6735i	0.941563	+	0.588354i
$623$	10.2881	+	41.2633i	0.412184	+	1.65318i
$624$	3.36877	+	3.25318i	0.134859	+	0.130232i
$625$	−4.21775	+	5.39847i	−0.168710	+	0.215939i
$626$	26.5351			1.06056
$627$	−3.85928	−	10.4751i	−0.154125	−	0.418335i
$628$	13.0926			0.522453
$629$	−1.24563	+	1.59434i	−0.0496667	+	0.0635705i
$630$	−6.52488	−	6.30101i	−0.259958	−	0.251038i
$631$	1.98492	+	7.96109i	0.0790185	+	0.316926i	0.996778	−	0.0802108i	$-0.0255594\pi$
$631$	1.98492	+	7.96109i	0.0790185	+	0.316926i	−0.917759	+	0.397137i	$0.870004\pi$
$632$	4.69139	+	2.93151i	0.186614	+	0.116609i
$633$	−13.6056	+	1.91214i	−0.540774	+	0.0760008i
$634$	−1.75470	+	0.781241i	−0.0696879	+	0.0310270i
$635$	8.31663	+	3.70280i	0.330035	+	0.146941i
$636$	0.0739746	+	2.11835i	0.00293328	+	0.0839982i
$637$	−21.2433	+	7.73193i	−0.841690	+	0.306350i
$638$	16.5988	+	11.8197i	0.657154	+	0.467945i
$639$	1.93247	−	3.34714i	0.0764475	−	0.132411i
$640$	1.01728	+	0.540895i	0.0402114	+	0.0213808i
$641$	9.26320	−	37.1526i	0.365874	−	1.46744i	−0.451986	−	0.892025i	$-0.649284\pi$
$641$	9.26320	−	37.1526i	0.365874	−	1.46744i	0.817861	−	0.575417i	$-0.195160\pi$
$642$	0.122681	+	0.492047i	0.00484184	+	0.0194196i
$643$	27.9972	−	14.8864i	1.10410	−	0.587062i	0.185660	−	0.982614i	$-0.440558\pi$
$643$	27.9972	−	14.8864i	1.10410	−	0.587062i	0.918444	+	0.395552i	$0.129447\pi$
$644$	0.250829	−	7.18280i	0.00988404	−	0.283042i
$645$	−0.461433	−	0.335251i	−0.0181689	−	0.0132005i
$646$	−11.4944	+	1.14302i	−0.452239	+	0.0449713i
$647$	5.36744	−	16.5193i	0.211016	−	0.649440i	−0.788397	−	0.615167i	$-0.789088\pi$
$647$	5.36744	−	16.5193i	0.211016	−	0.649440i	0.999413	−	0.0342729i	$-0.0109115\pi$
$648$	−3.74849	−	1.36434i	−0.147255	−	0.0535963i
$649$	−5.44179	+	7.10371i	−0.213609	+	0.278845i
$650$	−17.0623	−	14.3170i	−0.669240	−	0.561559i
$651$	1.88901	+	4.67546i	0.0740361	+	0.183246i
$652$	−1.85461	−	3.80252i	−0.0726323	−	0.148918i
$653$	−3.20666	+	1.42770i	−0.125486	+	0.0558701i	−0.468519	−	0.883453i	$-0.655212\pi$
$653$	−3.20666	+	1.42770i	−0.125486	+	0.0558701i	0.343033	+	0.939323i	$0.388546\pi$
$654$	−10.6298	+	11.8056i	−0.415658	+	0.461635i
$655$	13.9407	+	17.8432i	0.544707	+	0.697193i
$656$	−7.31601	−	2.09783i	−0.285642	−	0.0819066i
$657$	−2.23001	−	0.992863i	−0.0870009	−	0.0387353i
$658$	−14.0765	−	15.6335i	−0.548757	−	0.609457i
$659$	7.40403	−	41.9903i	0.288420	−	1.63571i	−0.404387	−	0.914588i	$-0.632515\pi$
$659$	7.40403	−	41.9903i	0.288420	−	1.63571i	0.692807	−	0.721123i	$-0.256374\pi$
$660$	2.14199	+	2.02940i	0.0833769	+	0.0789943i
$661$	−11.3569	−	9.52959i	−0.441733	−	0.370658i	0.394624	−	0.918843i	$-0.370875\pi$
$661$	−11.3569	−	9.52959i	−0.441733	−	0.370658i	−0.836357	+	0.548184i	$0.815319\pi$
$662$	31.5050	+	4.42773i	1.22447	+	0.172089i
$663$	11.9295	−	3.42074i	0.463305	−	0.132850i
$664$	−7.21507	−	5.24205i	−0.279999	−	0.203431i
$665$	−13.0183	+	10.0540i	−0.504827	+	0.389878i
$666$	0.567115	+	1.74540i	0.0219752	+	0.0676328i
$667$	7.53903	+	11.1771i	0.291912	+	0.432778i
$668$	2.60394	+	2.51460i	0.100750	+	0.0972928i
$669$	−0.865158	+	0.540611i	−0.0334489	+	0.0209012i
$670$	−0.865028	+	0.725845i	−0.0334190	+	0.0280418i
$671$	−34.0285	−	2.05377i	−1.31366	−	0.0792851i
$672$	1.26457	−	2.19030i	0.0487820	−	0.0844928i
$673$	22.8664	−	4.86040i	0.881434	−	0.187355i	0.255105	−	0.966913i	$-0.417890\pi$
$673$	22.8664	−	4.86040i	0.881434	−	0.187355i	0.626329	+	0.779559i	$0.284557\pi$
$674$	11.4095	−	16.9153i	0.439478	−	0.651553i
$675$	−14.7309	−	4.22402i	−0.566993	−	0.162583i
$676$	15.9128	−	17.6729i	0.612030	−	0.679728i
$677$	−39.6170	−	8.42085i	−1.52260	−	0.323639i	−0.630758	−	0.775979i	$-0.717256\pi$
$677$	−39.6170	−	8.42085i	−1.52260	−	0.323639i	−0.891846	+	0.452340i	$0.850589\pi$
$678$	6.35861	−	6.14043i	0.244201	−	0.235822i
$679$	2.88624	−	11.5761i	0.110764	−	0.444249i
$680$	2.58922	−	1.61793i	0.0992921	−	0.0620446i
$681$	1.67863	+	9.51998i	0.0643252	+	0.364807i
$682$	2.53550	+	6.10733i	0.0970894	+	0.233862i
$683$	−34.7278			−1.32882			−0.664411	−	0.747367i	$-0.731318\pi$
$683$	−34.7278			−1.32882			−0.664411	+	0.747367i	$0.731318\pi$
$684$	−4.97070	+	9.22345i	−0.190059	+	0.352667i
$685$	−17.4716	+	12.6939i	−0.667557	+	0.485009i
$686$	−5.99357	−	8.88584i	−0.228836	−	0.339263i
$687$	−17.0122	+	9.04554i	−0.649055	+	0.345109i
$688$	−0.240159	+	0.594414i	−0.00915597	+	0.0226618i
$689$	16.6071	−	1.16128i	0.632680	−	0.0442413i
$690$	0.855811	+	1.75467i	0.0325802	+	0.0667992i
$691$	23.8662	+	26.5061i	0.907914	+	1.00834i	0.999921	+	0.0125825i	$0.00400524\pi$
$691$	23.8662	+	26.5061i	0.907914	+	1.00834i	−0.0920066	+	0.995758i	$0.529328\pi$
$692$	−12.4481	−	21.5608i	−0.473207	−	0.819619i
$693$	−18.6093	+	18.3167i	−0.706907	+	0.695796i
$694$	4.43957	−	1.61587i	0.168524	−	0.0613376i
$695$	−13.3791	+	2.84381i	−0.507498	+	0.107872i
$696$	0.495911	+	4.71828i	0.0187975	+	0.178846i
$697$	−14.5081	+	14.0103i	−0.549535	+	0.530679i
$698$	−12.3541	−	7.71972i	−0.467611	−	0.292196i
$699$	−6.29819	+	15.5886i	−0.238219	+	0.589614i
$700$	−5.27307	+	10.8114i	−0.199303	+	0.408632i
$701$	−49.0737	+	14.0717i	−1.85349	+	0.531479i	−0.853543	+	0.521023i	$0.825550\pi$
$701$	−49.0737	+	14.0717i	−1.85349	+	0.531479i	−0.999945	+	0.0104559i	$0.996672\pi$
$702$	7.82011	−	24.0678i	0.295151	−	0.908381i
$703$	3.28061	−	0.559521i	0.123730	−	0.0211027i
$704$	1.63086	−	2.88796i	0.0614653	−	0.108844i
$705$	5.36965	+	1.95439i	0.202233	+	0.0736067i
$706$	−4.80728	−	0.675619i	−0.180924	−	0.0254273i
$707$	21.9447	+	1.53452i	0.825315	+	0.0577116i
$708$	−2.07835	+	0.145332i	−0.0781092	+	0.00546193i
$709$	50.2016	−	7.05537i	1.88536	−	0.264970i	0.900055	−	0.435777i	$-0.143526\pi$
$709$	50.2016	−	7.05537i	1.88536	−	0.264970i	0.985304	+	0.170807i	$0.0546376\pi$
$710$	1.81204	+	0.385161i	0.0680046	+	0.0144548i
$711$	1.38995	−	13.2245i	0.0521273	−	0.495959i
$712$	−7.26058	+	10.7643i	−0.272102	+	0.403408i
$713$	0.152690	+	4.37248i	0.00571830	+	0.163751i
$714$	−3.35111	−	5.80429i	−0.125412	−	0.217220i
$715$	15.3420	−	17.3692i	0.573759	−	0.649570i
$716$	1.22896	−	6.96979i	0.0459284	−	0.260473i
$717$	6.50366	+	16.0971i	0.242884	+	0.601158i
$718$	10.2347	+	0.715677i	0.381954	+	0.0267088i
$719$	12.6138	−	25.8622i	0.470416	−	0.964496i	−0.523256	−	0.852176i	$-0.675283\pi$
$719$	12.6138	−	25.8622i	0.470416	−	0.964496i	0.993672	−	0.112321i	$-0.0358284\pi$
$720$	0.0966513	−	2.76773i	0.00360198	−	0.103147i
$721$	16.5467	+	50.9255i	0.616231	+	1.89656i
$722$	15.2452	+	11.3395i	0.567367	+	0.422013i
$723$	14.7715	−	10.7321i	0.549357	−	0.399131i
$724$	8.50730	−	10.8888i	0.316171	−	0.404681i
$725$	−3.91821	−	22.2213i	−0.145519	−	0.825277i
$726$	5.99654	−	6.01589i	0.222553	−	0.223270i
$727$	0.0174446	−	0.0146378i	0.000646986	−	0.000542885i	−0.642464	−	0.766316i	$-0.722088\pi$
$727$	0.0174446	−	0.0146378i	0.000646986	−	0.000542885i	0.643111	+	0.765773i	$0.277643\pi$
$728$	−17.5387	−	9.32552i	−0.650029	−	0.345627i
$729$	−0.00812539	−	0.0773079i	−0.000300940	−	0.00286326i
$730$	0.122301	−	1.16362i	0.00452656	−	0.0430674i
$731$	1.04595	+	1.33875i	0.0386858	+	0.0495155i
$732$	−4.88654	−	6.25449i	−0.180612	−	0.231173i
$733$	−3.63270	+	34.5628i	−0.134177	+	1.27661i	0.695567	+	0.718462i	$0.255153\pi$
$733$	−3.63270	+	34.5628i	−0.134177	+	1.27661i	−0.829743	+	0.558145i	$0.811513\pi$
$734$	0.326382	+	3.10532i	0.0120470	+	0.114619i
$735$	−2.92810	−	1.55690i	−0.108004	−	0.0574270i
$736$	1.68098	−	1.41051i	0.0619617	−	0.0519920i
$737$	2.02562	+	2.54235i	0.0746146	+	0.0936485i
$738$	3.17678	+	18.0164i	0.116939	+	0.663194i
$739$	21.3298	−	27.3009i	0.784630	−	1.00428i	−0.214987	−	0.976617i	$-0.568971\pi$
$739$	21.3298	−	27.3009i	0.784630	−	1.00428i	0.999617	−	0.0276640i	$-0.00880684\pi$
$740$	−0.711648	+	0.517043i	−0.0261607	+	0.0190069i
$741$	−18.2969	−	9.05130i	−0.672155	−	0.332508i
$742$	−2.77825	−	8.55059i	−0.101993	−	0.313902i
$743$	−1.58912	+	45.5065i	−0.0582992	+	1.66947i	0.520395	+	0.853926i	$0.325785\pi$
$743$	−1.58912	+	45.5065i	−0.0582992	+	1.66947i	−0.578694	+	0.815545i	$0.696437\pi$
$744$	−0.674917	+	1.38378i	−0.0247437	+	0.0507320i
$745$	−13.9455	−	0.975162i	−0.510922	−	0.0357272i
$746$	−2.00304	−	4.95769i	−0.0733364	−	0.181514i
$747$	−3.72253	+	21.1115i	−0.136200	+	0.772429i
$748$	−4.46687	−	7.56929i	−0.163325	−	0.276761i
$749$	−1.07547	−	1.86277i	−0.0392969	−	0.0680642i
$750$	−0.269275	−	7.71101i	−0.00983251	−	0.281566i
$751$	−4.53510	+	6.72356i	−0.165488	+	0.245346i	−0.902655	−	0.430364i	$-0.858385\pi$
$751$	−4.53510	+	6.72356i	−0.165488	+	0.245346i	0.737167	+	0.675710i	$0.236163\pi$
$752$	0.671378	−	6.38773i	0.0244826	−	0.232937i
$753$	−11.8402	−	2.51670i	−0.431479	−	0.0917138i
$754$	36.8988	−	5.18579i	1.34377	−	0.188855i
$755$	−3.49910	+	0.244681i	−0.127345	+	0.00890486i
$756$	−13.6335	−	0.953348i	−0.495846	−	0.0346729i
$757$	−13.4491	−	1.89014i	−0.488815	−	0.0686985i	−0.109540	−	0.993982i	$-0.534938\pi$
$757$	−13.4491	−	1.89014i	−0.488815	−	0.0686985i	−0.379275	+	0.925284i	$0.623827\pi$
$758$	4.13186	+	1.50387i	0.150076	+	0.0546231i
$759$	5.11201	−	2.33465i	0.185554	−	0.0847424i
$760$	−4.94079	−	0.899772i	−0.179221	−	0.0326382i
$761$	−7.69175	+	23.6728i	−0.278826	+	0.858138i	0.709356	+	0.704850i	$0.248986\pi$
$761$	−7.69175	+	23.6728i	−0.278826	+	0.858138i	−0.988182	+	0.153287i	$0.951014\pi$
$762$	5.86514	−	1.68180i	0.212472	−	0.0609253i
$763$	29.5381	−	60.5621i	1.06935	−	2.19250i
$764$	−3.19537	+	7.90882i	−0.115604	+	0.286131i
$765$	−6.22377	−	3.88905i	−0.225021	−	0.140609i
$766$	−24.3663	+	23.5303i	−0.880391	+	0.850183i
$767$	1.71042	+	16.2735i	0.0617596	+	0.587604i
$768$	0.755315	−	0.160547i	0.0272551	−	0.00579325i
$769$	11.7952	−	4.29310i	0.425346	−	0.154813i	−0.120473	−	0.992717i	$-0.538441\pi$
$769$	11.7952	−	4.29310i	0.425346	−	0.154813i	0.545818	+	0.837904i	$0.316219\pi$
$770$	−11.1061	−	5.77010i	−0.400236	−	0.207940i
$771$	6.44903	+	11.1701i	0.232256	+	0.402280i
$772$	−2.58535	−	2.87132i	−0.0930486	−	0.103341i
$773$	−16.7164	−	34.2737i	−0.601247	−	1.23274i	−0.954779	−	0.297317i	$-0.903908\pi$
$773$	−16.7164	−	34.2737i	−0.601247	−	1.23274i	0.353531	−	0.935423i	$-0.384981\pi$
$774$	1.53726	−	0.107496i	0.0552558	−	0.00386386i
$775$	2.74304	−	6.78925i	0.0985327	−	0.243877i
$776$	3.21619	−	1.71008i	0.115455	−	0.0613883i
$777$	1.07979	+	1.60085i	0.0387372	+	0.0574303i
$778$	25.0369	−	18.1904i	0.897616	−	0.652157i
$779$	33.1606	−	0.971965i	1.18810	−	0.0348242i
$780$	5.39562			0.193194
$781$	1.24074	−	5.18646i	0.0443973	−	0.185586i
$782$	−1.00977	−	5.72670i	−0.0361093	−	0.204786i
$783$	21.7412	−	13.5854i	0.776966	−	0.485502i
$784$	−0.901774	+	3.61682i	−0.0322062	+	0.129172i
$785$	10.8509	−	10.4786i	0.387285	−	0.373996i
$786$	14.8445	+	3.15530i	0.529486	+	0.112546i
$787$	−0.919650	+	1.02137i	−0.0327820	+	0.0364081i	−0.759313	−	0.650726i	$-0.774465\pi$
$787$	−0.919650	+	1.02137i	−0.0327820	+	0.0364081i	0.726531	+	0.687134i	$0.241131\pi$
$788$	−4.79059	−	1.37368i	−0.170658	−	0.0489353i
$789$	−10.3901	+	15.4040i	−0.369899	+	0.548397i
$790$	6.23433	−	1.32515i	0.221807	−	0.0471466i
$791$	−18.7467	+	32.4702i	−0.666555	+	1.15451i
$792$	−7.95777	−	0.480287i	−0.282767	−	0.0170663i
$793$	−47.7533	+	40.0698i	−1.69577	+	1.42292i
$794$	0.945934	−	0.591085i	0.0335699	−	0.0209768i
$795$	1.75672	+	1.69644i	0.0623043	+	0.0601665i
$796$	−4.70831	−	6.98035i	−0.166882	−	0.247412i
$797$	5.30210	+	16.3182i	0.187810	+	0.578019i	0.999985	−	0.00539372i	$-0.00171688\pi$
$797$	5.30210	+	16.3182i	0.187810	+	0.578019i	−0.812176	+	0.583413i	$0.801717\pi$
$798$	−2.35247	+	10.7704i	−0.0832767	+	0.381267i
$799$	−13.7700	−	10.0045i	−0.487148	−	0.353934i
$800$	−3.53031	+	1.01230i	−0.124815	+	0.0357902i
$801$	30.9063	+	4.34360i	1.09202	+	0.153474i
$802$	22.1806	+	18.6117i	0.783223	+	0.657202i
$803$	−3.33966	−	0.436939i	−0.117854	−	0.0154193i
$804$	−0.131421	+	0.745328i	−0.00463488	+	0.0262857i
$805$	−5.54081	−	6.15369i	−0.195288	−	0.216889i
$806$	11.0466	+	4.91826i	0.389100	+	0.173238i
$807$	−5.89233	−	1.68960i	−0.207420	−	0.0594766i
$808$	4.13505	+	5.29262i	0.145470	+	0.186194i
$809$	22.7779	−	25.2974i	0.800827	−	0.889408i	−0.194988	−	0.980806i	$-0.562467\pi$
$809$	22.7779	−	25.2974i	0.800827	−	0.889408i	0.995814	+	0.0913974i	$0.0291333\pi$
$810$	−4.19860	+	1.86934i	−0.147524	+	0.0656819i
$811$	8.00252	+	16.4076i	0.281007	+	0.576149i	0.991881	−	0.127170i	$-0.0405894\pi$
$811$	8.00252	+	16.4076i	0.281007	+	0.576149i	−0.710874	+	0.703319i	$0.751701\pi$
$812$	−7.53826	−	18.6579i	−0.264541	−	0.654762i
$813$	−15.4145	−	12.9343i	−0.540611	−	0.453627i
$814$	1.43594	+	2.08571i	0.0503297	+	0.0731040i
$815$	−4.58038	−	1.66712i	−0.160444	−	0.0583967i
$816$	0.632340	−	1.94614i	0.0221363	−	0.0681286i
$817$	0.210552	−	2.78653i	0.00736628	−	0.0974884i
$818$	−16.6348	−	12.0859i	−0.581621	−	0.422572i
$819$	−1.66635	+	47.7181i	−0.0582271	+	1.66741i
$820$	−7.74233	+	4.11667i	−0.270374	+	0.143760i
$821$	3.93217	+	15.7711i	0.137234	+	0.550414i	0.999066	+	0.0432203i	$0.0137617\pi$
$821$	3.93217	+	15.7711i	0.137234	+	0.550414i	−0.861832	+	0.507194i	$0.830683\pi$
$822$	−3.50164	+	14.0443i	−0.122134	+	0.489851i
$823$	−7.88049	−	4.19013i	−0.274697	−	0.146059i	0.326408	−	0.945229i	$-0.394162\pi$
$823$	−7.88049	−	4.19013i	−0.274697	−	0.146059i	−0.601105	+	0.799170i	$0.705273\pi$
$824$	−8.17426	+	14.1582i	−0.284764	+	0.493226i
$825$	−9.40528	+	0.0896520i	−0.327450	+	0.00312128i
$826$	8.30406	−	3.02243i	0.288935	−	0.105164i
$827$	0.223219	+	6.39215i	0.00776207	+	0.222277i	0.997073	+	0.0764553i	$0.0243603\pi$
$827$	0.223219	+	6.39215i	0.00776207	+	0.222277i	−0.989311	+	0.145821i	$0.953418\pi$
$828$	−4.81862	−	2.14539i	−0.167459	−	0.0745574i
$829$	−10.5099	+	4.67929i	−0.365022	+	0.162518i	−0.581048	−	0.813869i	$-0.697357\pi$
$829$	−10.5099	+	4.67929i	−0.365022	+	0.162518i	0.216026	+	0.976388i	$0.430691\pi$
$830$	−10.1751	+	1.43002i	−0.353184	+	0.0496367i
$831$	10.9223	+	6.82499i	0.378889	+	0.236756i
$832$	−1.46720	−	5.88461i	−0.0508659	−	0.204012i
$833$	7.10561	+	6.86181i	0.246195	+	0.237748i
$834$	−5.64396	+	7.22393i	−0.195434	+	0.250144i
$835$	4.17063			0.144331
$836$	−2.95018	+	14.1526i	−0.102034	+	0.489478i
$837$	8.31958			0.287567
$838$	23.0987	−	29.5649i	0.797930	−	1.02130i
$839$	29.3538	+	28.3466i	1.01340	+	0.978634i	0.999774	−	0.0212734i	$-0.00677204\pi$
$839$	29.3538	+	28.3466i	1.01340	+	0.978634i	0.0136312	+	0.999907i	$0.495661\pi$
$840$	−0.704941	−	2.82737i	−0.0243228	−	0.0975534i
$841$	7.41855	+	4.63562i	0.255812	+	0.159849i
$842$	−19.5861	+	2.75265i	−0.674982	+	0.0948625i
$843$	9.83422	−	4.37848i	0.338709	−	0.150803i
$844$	16.2544	+	7.23693i	0.559500	+	0.249105i
$845$	−0.956221	−	27.3826i	−0.0328950	−	0.941990i
$846$	−14.5078	+	5.28042i	−0.498790	+	0.181545i
$847$	−17.4161	+	31.5391i	−0.598423	+	1.08370i
$848$	1.37249	−	2.37722i	0.0471315	−	0.0816342i
$849$	19.2793	+	10.2510i	0.661664	+	0.351813i
$850$	−2.35446	+	9.44322i	−0.0807573	+	0.323900i
$851$	0.405310	+	1.62561i	0.0138938	+	0.0557251i
$852$	1.09627	−	0.582897i	0.0375576	−	0.0199697i
$853$	−0.514894	+	14.7446i	−0.0176296	+	0.504846i	0.958173	+	0.286191i	$0.0923892\pi$
$853$	−0.514894	+	14.7446i	−0.0176296	+	0.504846i	−0.975802	+	0.218655i	$0.929833\pi$
$854$	27.2360	+	19.7881i	0.931998	+	0.677136i
$855$	3.26231	+	11.6224i	0.111568	+	0.397479i
$856$	0.202937	−	0.624576i	0.00693625	−	0.0213476i
$857$	−13.8705	−	5.04846i	−0.473808	−	0.172452i	0.0940683	−	0.995566i	$-0.470013\pi$
$857$	−13.8705	−	5.04846i	−0.473808	−	0.172452i	−0.567877	+	0.823114i	$0.692235\pi$
$858$	0.394084	−	15.5272i	0.0134538	−	0.530090i
$859$	3.98011	+	3.33971i	0.135799	+	0.113949i	0.708157	−	0.706055i	$-0.249527\pi$
$859$	3.98011	+	3.33971i	0.135799	+	0.113949i	−0.572358	+	0.820004i	$0.693971\pi$
$860$	0.276696	+	0.684846i	0.00943525	+	0.0233531i
$861$	8.43817	+	17.3008i	0.287572	+	0.589610i
$862$	36.2694	−	16.1482i	1.23534	−	0.550009i
$863$	−24.5009	+	27.2110i	−0.834019	+	0.926272i	−0.998189	−	0.0601605i	$-0.980839\pi$
$863$	−24.5009	+	27.2110i	−0.834019	+	0.926272i	0.164170	+	0.986432i	$0.447505\pi$
$864$	−2.56897	−	3.28813i	−0.0873981	−	0.111864i
$865$	−27.5727	−	7.90636i	−0.937501	−	0.268824i
$866$	−18.4543	−	8.21639i	−0.627103	−	0.279204i
$867$	5.15535	+	5.72559i	0.175085	+	0.194451i
$868$	1.13398	−	6.43111i	0.0384897	−	0.218286i
$869$	−3.35810	−	18.0376i	−0.113916	−	0.611884i
$870$	4.18724	+	3.51351i	0.141961	+	0.119119i
$871$	5.88625	+	0.827258i	0.199448	+	0.0280306i
$872$	19.7757	−	5.67060i	0.669690	−	0.192031i
$873$	−7.08353	−	5.14648i	−0.239741	−	0.174182i
$874$	−5.11406	+	8.08305i	−0.172986	+	0.273413i
$875$	10.1131	+	31.1250i	0.341886	+	1.05222i
$876$	−0.438507	−	0.650114i	−0.0148158	−	0.0219653i
$877$	−6.48058	−	6.25822i	−0.218834	−	0.211325i	0.577159	−	0.816632i	$-0.304161\pi$
$877$	−6.48058	−	6.25822i	−0.218834	−	0.211325i	−0.795992	+	0.605307i	$0.793050\pi$
$878$	−31.8904	+	19.9273i	−1.07625	+	0.672514i
$879$	−14.1717	+	11.8914i	−0.477998	+	0.401088i
$880$	−0.959732	−	3.69872i	−0.0323526	−	0.124684i
$881$	3.59787	−	6.23169i	0.121215	−	0.209951i	−0.799032	−	0.601289i	$-0.794654\pi$
$881$	3.59787	−	6.23169i	0.121215	−	0.209951i	0.920247	+	0.391338i	$0.127988\pi$
$882$	8.76418	−	1.86288i	0.295105	−	0.0627266i
$883$	−20.4400	+	30.3035i	−0.687860	+	1.01979i	0.309758	+	0.950815i	$0.399752\pi$
$883$	−20.4400	+	30.3035i	−0.687860	+	1.01979i	−0.997618	+	0.0689790i	$0.978026\pi$
$884$	−15.4490	−	4.42992i	−0.519605	−	0.148994i
$885$	−1.60618	+	1.78384i	−0.0539910	+	0.0599631i
$886$	7.94471	+	1.68870i	0.266908	+	0.0567330i
$887$	2.61974	−	2.52985i	0.0879623	−	0.0849442i	−0.649378	−	0.760466i	$-0.724971\pi$
$887$	2.61974	−	2.52985i	0.0879623	−	0.0849442i	0.737340	+	0.675522i	$0.236082\pi$
$888$	−0.142627	+	0.572047i	−0.00478626	+	0.0191966i
$889$	−21.9474	+	13.7143i	−0.736093	+	0.459962i
$890$	2.59767	+	14.7321i	0.0870741	+	0.493822i
$891$	5.07282	+	12.2190i	0.169946	+	0.409353i
$892$	1.32115			0.0442353
$893$	5.66731	+	27.4172i	0.189649	+	0.917483i
$894$	−7.58000	+	5.50719i	−0.253513	+	0.184188i
$895$	−4.55967	−	6.75999i	−0.152413	−	0.225962i
$896$	−2.89191	+	1.53766i	−0.0966120	+	0.0513695i
$897$	3.84964	−	9.52820i	0.128536	−	0.318137i
$898$	−0.0472087	+	0.00330116i	−0.00157538	+	0.000110161i
$899$	5.36998	+	11.0101i	0.179099	+	0.367207i
$900$	5.90700	+	6.56039i	0.196900	+	0.218680i
$901$	−3.63709	−	6.29963i	−0.121169	−	0.209871i
$902$	11.2812	+	22.5811i	0.375624	+	0.751869i
$903$	1.52364	−	0.554560i	0.0507036	−	0.0184546i
$904$	−11.1972	+	2.38003i	−0.372412	+	0.0791587i
$905$	−1.66413	−	15.8332i	−0.0553177	−	0.526313i
$906$	−1.69110	+	1.63308i	−0.0561831	+	0.0542554i
$907$	−41.6768	−	26.0426i	−1.38386	−	0.864729i	−0.385537	−	0.922692i	$-0.625984\pi$
$907$	−41.6768	−	26.0426i	−1.38386	−	0.864729i	−0.998319	+	0.0579631i	$0.981539\pi$
$908$	4.68961	−	11.6072i	0.155630	−	0.385198i
$909$	7.07726	−	14.5105i	0.234738	−	0.481284i
$910$	−21.9993	+	6.30820i	−0.729270	+	0.209115i
$911$	−3.84309	+	11.8278i	−0.127327	+	0.391873i	−0.994318	−	0.106452i	$-0.966051\pi$
$911$	−3.84309	+	11.8278i	−0.127327	+	0.391873i	0.866991	+	0.498324i	$0.166051\pi$
$912$	−2.92434	+	1.66658i	−0.0968344	+	0.0551861i
$913$	3.37207	+	29.3859i	0.111599	+	0.972530i
$914$	−36.7545	−	13.3775i	−1.21573	−	0.442489i
$915$	−9.05559	−	1.27268i	−0.299369	−	0.0420735i
$916$	24.8910	+	1.74055i	0.822422	+	0.0575093i
$917$	−64.2138	+	4.49027i	−2.12053	+	0.148282i
$918$	−10.9500	+	1.53892i	−0.361404	+	0.0507920i
$919$	−41.4195	−	8.80399i	−1.36630	−	0.290417i	−0.534350	−	0.845263i	$-0.679444\pi$
$919$	−41.4195	−	8.80399i	−1.36630	−	0.290417i	−0.831953	+	0.554846i	$0.812777\pi$
$920$	0.264269	−	2.51435i	0.00871270	−	0.0828958i
$921$	−4.94681	+	7.33395i	−0.163003	+	0.241662i
$922$	−0.304000	−	8.70542i	−0.0100117	−	0.286698i
$923$	−4.87576	−	8.44507i	−0.160488	−	0.277973i
$924$	−8.18793	+	1.82214i	−0.269363	+	0.0599439i
$925$	0.486906	−	2.76138i	0.0160094	−	0.0907937i
$926$	−2.78201	−	6.88572i	−0.0914226	−	0.226279i
$927$	39.2016	+	2.74124i	1.28755	+	0.0900343i
$928$	2.69332	−	5.52212i	0.0884125	−	0.181273i
$929$	0.648521	−	18.5712i	0.0212773	−	0.609302i	−0.941186	−	0.337889i	$-0.890287\pi$
$929$	0.648521	−	18.5712i	0.0212773	−	0.609302i	0.962463	−	0.271413i	$-0.0874908\pi$
$930$	0.548144	+	1.68701i	0.0179744	+	0.0553194i
$931$	−1.04255	−	16.2145i	−0.0341682	−	0.531409i
$932$	17.6147	−	12.7978i	0.576987	−	0.419206i
$933$	13.1641	−	16.8492i	0.430972	−	0.551619i
$934$	−1.52354	−	8.64040i	−0.0498516	−	0.282723i
$935$	−9.76006	−	2.69824i	−0.319188	−	0.0882420i
$936$	−11.1674	+	9.37056i	−0.365018	+	0.306286i
$937$	−36.5155	−	19.4156i	−1.19291	−	0.634281i	−0.250297	−	0.968169i	$-0.580528\pi$
$937$	−36.5155	−	19.4156i	−1.19291	−	0.634281i	−0.942613	+	0.333888i	$0.891639\pi$
$938$	−0.335550	−	3.19254i	−0.0109561	−	0.104240i
$939$	2.14180	−	20.3779i	0.0698951	−	0.665007i
$940$	−4.55594	−	5.83134i	−0.148599	−	0.190197i
$941$	8.93956	+	11.4421i	0.291421	+	0.373002i	0.911333	−	0.411669i	$-0.135054\pi$
$941$	8.93956	+	11.4421i	0.291421	+	0.373002i	−0.619912	+	0.784671i	$0.712832\pi$
$942$	1.05678	−	10.0546i	0.0344318	−	0.327597i
$943$	1.74572	+	16.6094i	0.0568486	+	0.540878i
$944$	2.38226	+	1.26667i	0.0775360	+	0.0412266i
$945$	−12.0622	+	10.1214i	−0.392382	+	0.329248i
$946$	1.99102	−	0.746241i	0.0647337	−	0.0242624i
$947$	−2.17500	−	12.3350i	−0.0706780	−	0.400835i	−0.999538	−	0.0304031i	$-0.990321\pi$
$947$	−2.17500	−	12.3350i	−0.0706780	−	0.400835i	0.928860	−	0.370432i	$-0.120790\pi$
$948$	2.62995	−	3.36618i	0.0854167	−	0.109328i
$949$	−4.98268	+	3.62013i	−0.161745	+	0.117514i
$950$	13.3215	−	8.87727i	0.432208	−	0.288017i
$951$	0.458329	+	1.41059i	0.0148623	+	0.0457416i
$952$	−0.302910	+	8.67421i	−0.00981738	+	0.281133i
$953$	7.21998	−	14.8031i	0.233878	−	0.479521i	−0.749286	−	0.662247i	$-0.769603\pi$
$953$	7.21998	−	14.8031i	0.233878	−	0.479521i	0.983164	+	0.182726i	$0.0584920\pi$
$954$	−6.58211	−	0.460266i	−0.213104	−	0.0149017i
$955$	3.68150	+	9.11204i	0.119131	+	0.294859i
$956$	3.90417	−	22.1417i	0.126270	−	0.716112i
$957$	10.4168	−	11.7932i	0.336728	−	0.381219i
$958$	−5.35190	−	9.26977i	−0.172912	−	0.299493i
$959$	−2.14260	−	61.3561i	−0.0691882	−	1.98129i
$960$	0.497496	−	0.737568i	0.0160566	−	0.0238049i
$961$	2.82485	−	26.8767i	0.0911242	−	0.866989i
$962$	4.52920	+	0.962712i	0.146027	+	0.0310391i
$963$	−1.56321	+	0.219694i	−0.0503736	+	0.00707955i
$964$	−23.5876	+	1.64940i	−0.759705	+	0.0531237i
$965$	−4.44071	−	0.310525i	−0.142952	−	0.00999615i
$966$	−5.49585	−	0.772391i	−0.176826	−	0.0248513i
$967$	−0.118320	−	0.0430649i	−0.00380491	−	0.00138487i	0.340117	−	0.940383i	$-0.389533\pi$
$967$	−0.118320	−	0.0430649i	−0.00380491	−	0.00138487i	−0.343922	+	0.938998i	$0.611756\pi$
$968$	−10.7141	+	2.49172i	−0.344363	+	0.0800868i
$969$	−0.0499868	+	8.91946i	−0.00160581	+	0.286534i
$970$	1.29686	−	3.99133i	0.0416397	−	0.128154i
$971$	−19.5412	+	5.60334i	−0.627106	+	0.179820i	−0.574114	−	0.818775i	$-0.694654\pi$
$971$	−19.5412	+	5.60334i	−0.627106	+	0.179820i	−0.0529918	+	0.998595i	$0.516876\pi$
$972$	−6.83789	+	14.0197i	−0.219325	+	0.449684i
$973$	14.5661	−	36.0524i	0.466968	−	1.15579i
$974$	−28.3732	−	17.7296i	−0.909136	−	0.568092i
$975$	−12.3721	+	11.9476i	−0.396224	+	0.382629i
$976$	1.07441	+	10.2223i	0.0343911	+	0.327209i
$977$	19.0974	−	4.05928i	0.610980	−	0.129868i	0.107978	−	0.994153i	$-0.465562\pi$
$977$	19.0974	−	4.05928i	0.610980	−	0.129868i	0.503002	+	0.864286i	$0.332229\pi$
$978$	−3.06988	+	1.11734i	−0.0981639	+	0.0357287i
$979$	42.5850	−	6.39943i	1.36102	−	0.204527i
$980$	2.14732	+	3.71927i	0.0685936	+	0.118808i
$981$	−33.0892	−	36.7493i	−1.05646	−	1.17331i
$982$	10.1137	+	20.7362i	0.322741	+	0.661718i
$983$	−22.8230	+	1.59594i	−0.727940	+	0.0509025i	−0.428918	−	0.903344i	$-0.641105\pi$
$983$	−22.8230	+	1.59594i	−0.727940	+	0.0509025i	−0.299023	+	0.954246i	$0.596661\pi$
$984$	−2.20157	+	5.44907i	−0.0701834	+	0.173710i
$985$	−5.06974	+	2.69563i	−0.161535	+	0.0858899i
$986$	−9.10442	−	13.4979i	−0.289944	−	0.429859i
$987$	−13.1421	+	9.54827i	−0.418317	+	0.303925i
$988$	13.8829	+	22.4969i	0.441674	+	0.715721i
$989$	1.40680			0.0447335
$990$	−6.97962	+	5.97088i	−0.221827	+	0.189767i
$991$	−1.29334	−	7.33490i	−0.0410843	−	0.233001i	0.957350	−	0.288929i	$-0.0932992\pi$
$991$	−1.29334	−	7.33490i	−0.0410843	−	0.233001i	−0.998435	+	0.0559285i	$0.982188\pi$
$992$	1.69085	−	1.05656i	0.0536845	−	0.0335458i
$993$	5.94326	−	23.8371i	0.188604	−	0.756448i
$994$	−3.78829	+	3.65831i	−0.120157	+	0.116035i
$995$	−9.48881	−	2.01691i	−0.300815	−	0.0639403i
$996$	−4.60805	+	5.11776i	−0.146012	+	0.162162i
$997$	54.2407	+	15.5533i	1.71782	+	0.492577i	0.982676	−	0.185334i	$-0.0593366\pi$
$997$	54.2407	+	15.5533i	1.71782	+	0.492577i	0.735144	+	0.677911i	$0.237114\pi$
$998$	5.83014	−	8.64354i	0.184550	−	0.273606i
$999$	3.11620	−	0.662368i	0.0985921	−	0.0209564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.u.b.251.7	yes	264
11.5	even	5	inner	418.2.u.b.137.5	yes	264
19.5	even	9	inner	418.2.u.b.119.5	yes	264
209.5	even	45	inner	418.2.u.b.5.7	✓	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.u.b.5.7	✓	264	209.5	even	45	inner
418.2.u.b.119.5	yes	264	19.5	even	9	inner
418.2.u.b.137.5	yes	264	11.5	even	5	inner
418.2.u.b.251.7	yes	264	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.u (of order \(45\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.615661 + 0.788011i) q^{2} +(0.555466 + 0.536408i) q^{3} +(-0.241922 - 0.970296i) q^{4} +(-0.977067 - 0.610539i) q^{5} +(-0.764674 + 0.107468i) q^{6} +(2.99213 - 1.33218i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-0.0838888 - 2.40226i) q^{9} +O(q^{10})\)	\(q+(-0.615661 + 0.788011i) q^{2} +(0.555466 + 0.536408i) q^{3} +(-0.241922 - 0.970296i) q^{4} +(-0.977067 - 0.610539i) q^{5} +(-0.764674 + 0.107468i) q^{6} +(2.99213 - 1.33218i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-0.0838888 - 2.40226i) q^{9} +(1.08265 - 0.394054i) q^{10} +(-1.05491 - 3.14439i) q^{11} +(0.386095 - 0.668735i) q^{12} +(-5.35486 - 2.84723i) q^{13} +(-0.792365 + 3.17800i) q^{14} +(-0.215230 - 0.863241i) q^{15} +(-0.882948 + 0.469472i) q^{16} +(-0.0924834 + 2.64838i) q^{17} +(1.94465 + 1.41287i) q^{18} +(3.04547 - 3.11851i) q^{19} +(-0.356030 + 1.09575i) q^{20} +(2.37662 + 0.865019i) q^{21} +(3.12728 + 1.10459i) q^{22} +(1.68098 + 1.41051i) q^{23} +(0.289267 + 0.715961i) q^{24} +(-1.60995 - 3.30089i) q^{25} +(5.54043 - 2.46676i) q^{26} +(2.79208 - 3.10092i) q^{27} +(-2.01647 - 2.58097i) q^{28} +(5.90592 + 1.69349i) q^{29} +(0.812752 + 0.361860i) q^{30} +(1.33412 + 1.48169i) q^{31} +(0.173648 - 0.984808i) q^{32} +(1.10070 - 2.31246i) q^{33} +(-2.03001 - 1.70338i) q^{34} +(-3.73686 - 0.525182i) q^{35} +(-2.31061 + 0.662556i) q^{36} +(0.617677 + 0.448769i) q^{37} +(0.582442 + 4.31981i) q^{38} +(-1.44717 - 4.45393i) q^{39} +(-0.644267 - 0.955165i) q^{40} +(5.47478 + 5.28693i) q^{41} +(-2.14484 + 1.34024i) q^{42} +(0.491108 - 0.412089i) q^{43} +(-2.79578 + 1.78427i) q^{44} +(-1.38471 + 2.39839i) q^{45} +(-2.14641 + 0.456233i) q^{46} +(-3.59165 + 5.32484i) q^{47} +(-0.742276 - 0.212844i) q^{48} +(2.49421 - 2.77010i) q^{49} +(3.59233 + 0.763573i) q^{50} +(-1.47198 + 1.42148i) q^{51} +(-1.46720 + 5.88461i) q^{52} +(-2.32788 + 1.45462i) q^{53} +(0.724581 + 4.10930i) q^{54} +(-0.889051 + 3.71634i) q^{55} +3.27529 q^{56} +(3.36445 - 0.0986147i) q^{57} +(-4.97054 + 3.61131i) q^{58} +(-1.50875 - 2.23681i) q^{59} +(-0.785530 + 0.417674i) q^{60} +(3.85045 - 9.53020i) q^{61} +(-1.98896 + 0.139081i) q^{62} +(-3.45125 - 7.07611i) q^{63} +(0.669131 + 0.743145i) q^{64} +(3.49371 + 6.05129i) q^{65} +(1.14459 + 2.29106i) q^{66} +(-0.920997 + 0.335215i) q^{67} +(2.59208 - 0.550964i) q^{68} +(0.177119 + 1.68518i) q^{69} +(2.71449 - 2.62135i) q^{70} +(1.36358 + 0.852057i) q^{71} +(0.900451 - 2.22869i) q^{72} +(0.445178 - 0.912750i) q^{73} +(-0.733915 + 0.210447i) q^{74} +(0.876350 - 2.69713i) q^{75} +(-3.76264 - 2.20057i) q^{76} +(-7.34533 - 8.00307i) q^{77} +(4.40071 + 1.60173i) q^{78} +(5.47815 + 0.769904i) q^{79} +(1.14933 + 0.0803690i) q^{80} +(-3.97934 + 0.278263i) q^{81} +(-7.53677 + 1.05922i) q^{82} +(-8.72343 - 1.85422i) q^{83} +(0.264368 - 2.51529i) q^{84} +(1.70730 - 2.53118i) q^{85} +(0.0223739 + 0.640706i) q^{86} +(2.37214 + 4.10866i) q^{87} +(0.315226 - 3.30161i) q^{88} +(-2.25465 + 12.7868i) q^{89} +(-1.03744 - 2.56776i) q^{90} +(-19.8155 - 1.38563i) q^{91} +(0.961945 - 1.97228i) q^{92} +(-0.0537313 + 1.53866i) q^{93} +(-1.98479 - 6.10856i) q^{94} +(-4.87960 + 1.18762i) q^{95} +(0.624714 - 0.453881i) q^{96} +(2.24259 - 2.87038i) q^{97} +(0.647281 + 3.67091i) q^{98} +(-7.46513 + 2.79795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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