LMFDB - Embedded newform 756.2.cf.a.659.81

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(155,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 7, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.155"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.cf (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$108$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			659.81
Character	$\chi$	$=$	756.659
Dual form			756.2.cf.a.491.81

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.961880 + 1.03672i) q^{2} +(-1.03042 + 1.39220i) q^{3} +(-0.149574 + 1.99440i) q^{4} +(-0.337395 + 0.926986i) q^{5} +(-2.43447 + 0.270870i) q^{6} +(0.984808 + 0.173648i) q^{7} +(-2.21150 + 1.76331i) q^{8} +(-0.876451 - 2.86912i) q^{9} +(-1.28556 + 0.541865i) q^{10} +(-4.05547 + 1.47607i) q^{11} +(-2.62248 - 2.26331i) q^{12} +(1.89865 - 1.59316i) q^{13} +(0.767242 + 1.18800i) q^{14} +(-0.942891 - 1.42491i) q^{15} +(-3.95526 - 0.596620i) q^{16} +(-4.64721 + 2.68307i) q^{17} +(2.13143 - 3.66838i) q^{18} +(-3.40172 - 1.96398i) q^{19} +(-1.79831 - 0.811554i) q^{20} +(-1.25652 + 1.19212i) q^{21} +(-5.43115 - 2.78458i) q^{22} +(1.28913 + 7.31104i) q^{23} +(-0.176090 - 4.89581i) q^{24} +(3.08475 + 2.58842i) q^{25} +(3.47793 + 0.435942i) q^{26} +(4.89751 + 1.73621i) q^{27} +(-0.493625 + 1.93813i) q^{28} +(5.80611 - 6.91945i) q^{29} +(0.570285 - 2.34811i) q^{30} +(-0.573485 + 0.101121i) q^{31} +(-3.18595 - 4.67437i) q^{32} +(2.12387 - 7.16702i) q^{33} +(-7.25164 - 2.23706i) q^{34} +(-0.493239 + 0.854315i) q^{35} +(5.85326 - 1.31885i) q^{36} +(-0.657893 - 1.13950i) q^{37} +(-1.23595 - 5.41574i) q^{38} +(0.261580 + 4.28493i) q^{39} +(-0.888409 - 2.64496i) q^{40} +(-6.21257 - 7.40386i) q^{41} +(-2.44452 - 0.155986i) q^{42} +(0.107479 + 0.295296i) q^{43} +(-2.33728 - 8.30901i) q^{44} +(2.95534 + 0.155569i) q^{45} +(-6.33951 + 8.36882i) q^{46} +(-1.36505 + 7.74157i) q^{47} +(4.90621 - 4.89174i) q^{48} +(0.939693 + 0.342020i) q^{49} +(0.283702 + 5.68777i) q^{50} +(1.05323 - 9.23455i) q^{51} +(2.89340 + 4.02496i) q^{52} +4.31297i q^{53} +(2.91085 + 6.74737i) q^{54} -4.25739i q^{55} +(-2.48410 + 1.35249i) q^{56} +(6.23947 - 2.71214i) q^{57} +(12.7583 - 0.636376i) q^{58} +(-5.36732 - 1.95354i) q^{59} +(2.98287 - 1.66737i) q^{60} +(-0.255302 + 1.44789i) q^{61} +(-0.656458 - 0.497277i) q^{62} +(-0.364919 - 2.97772i) q^{63} +(1.78150 - 7.79912i) q^{64} +(0.836238 + 2.29755i) q^{65} +(9.47309 - 4.69195i) q^{66} +(2.87683 + 3.42848i) q^{67} +(-4.65600 - 9.66970i) q^{68} +(-11.5068 - 5.73874i) q^{69} +(-1.36012 + 0.310398i) q^{70} +(8.25153 + 14.2921i) q^{71} +(6.99741 + 4.79961i) q^{72} +(-3.58347 + 6.20674i) q^{73} +(0.548532 - 1.77812i) q^{74} +(-6.78220 + 1.62743i) q^{75} +(4.42577 - 6.49062i) q^{76} +(-4.25018 + 0.749421i) q^{77} +(-4.19066 + 4.39277i) q^{78} +(-5.03644 + 6.00220i) q^{79} +(1.88754 - 3.46517i) q^{80} +(-7.46367 + 5.02928i) q^{81} +(1.69997 - 13.5623i) q^{82} +(-5.55219 - 4.65884i) q^{83} +(-2.18962 - 2.68432i) q^{84} +(-0.919219 - 5.21315i) q^{85} +(-0.202757 + 0.395464i) q^{86} +(3.65051 + 15.2132i) q^{87} +(6.36593 - 10.4154i) q^{88} +(12.4036 + 7.16122i) q^{89} +(2.68140 + 3.21350i) q^{90} +(2.14645 - 1.23926i) q^{91} +(-14.7740 + 1.47751i) q^{92} +(0.450153 - 0.902605i) q^{93} +(-9.33884 + 6.03129i) q^{94} +(2.96831 - 2.49071i) q^{95} +(9.79054 + 0.381093i) q^{96} +(-4.61957 + 1.68139i) q^{97} +(0.549293 + 1.30318i) q^{98} +(7.78944 + 10.3419i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) $ 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$-1$

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 $

$2$	0.961880	+	1.03672i	0.680152	+	0.733071i
$2$	0.961880	+	1.03672i	0.680152	+	0.733071i
$3$	−1.03042	+	1.39220i	−0.594916	+	0.803788i
$3$	−1.03042	+	1.39220i	−0.594916	+	0.803788i
$4$	−0.149574	+	1.99440i	−0.0747870	+	0.997200i
$5$	−0.337395	+	0.926986i	−0.150888	+	0.414561i	−0.991990	−	0.126315i	$-0.959685\pi$
$5$	−0.337395	+	0.926986i	−0.150888	+	0.414561i	0.841102	+	0.540876i	$0.181907\pi$
$6$	−2.43447	+	0.270870i	−0.993867	+	0.110582i
$7$	0.984808	+	0.173648i	0.372222	+	0.0656328i
$7$	0.984808	+	0.173648i	0.372222	+	0.0656328i
$8$	−2.21150	+	1.76331i	−0.781885	+	0.623423i
$9$	−0.876451	−	2.86912i	−0.292150	−	0.956372i
$10$	−1.28556	+	0.541865i	−0.406529	+	0.171353i
$11$	−4.05547	+	1.47607i	−1.22277	+	0.445052i	−0.871116	−	0.491077i	$-0.836603\pi$
$11$	−4.05547	+	1.47607i	−1.22277	+	0.445052i	−0.351655	+	0.936130i	$0.614381\pi$
$12$	−2.62248	−	2.26331i	−0.757045	−	0.653363i
$13$	1.89865	−	1.59316i	0.526591	−	0.441862i	−0.340331	−	0.940306i	$-0.610539\pi$
$13$	1.89865	−	1.59316i	0.526591	−	0.441862i	0.866922	+	0.498443i	$0.166095\pi$
$14$	0.767242	+	1.18800i	0.205054	+	0.317506i
$15$	−0.942891	−	1.42491i	−0.243453	−	0.367911i
$16$	−3.95526	−	0.596620i	−0.988814	−	0.149155i
$17$	−4.64721	+	2.68307i	−1.12711	+	0.650739i	−0.943207	−	0.332205i	$-0.892207\pi$
$17$	−4.64721	+	2.68307i	−1.12711	+	0.650739i	−0.183906	+	0.982944i	$0.558874\pi$
$18$	2.13143	−	3.66838i	0.502383	−	0.864645i
$19$	−3.40172	−	1.96398i	−0.780408	−	0.450569i	0.0561670	−	0.998421i	$-0.482112\pi$
$19$	−3.40172	−	1.96398i	−0.780408	−	0.450569i	−0.836575	+	0.547853i	$0.815445\pi$
$20$	−1.79831	−	0.811554i	−0.402115	−	0.181469i
$21$	−1.25652	+	1.19212i	−0.274196	+	0.260142i
$22$	−5.43115	−	2.78458i	−1.15792	−	0.593675i
$23$	1.28913	+	7.31104i	0.268803	+	1.52446i	0.757982	+	0.652275i	$0.226185\pi$
$23$	1.28913	+	7.31104i	0.268803	+	1.52446i	−0.489179	+	0.872183i	$0.662704\pi$
$24$	−0.176090	−	4.89581i	−0.0359441	−	0.999354i
$25$	3.08475	+	2.58842i	0.616951	+	0.517683i
$26$	3.47793	+	0.435942i	0.682078	+	0.0854952i
$27$	4.89751	+	1.73621i	0.942526	+	0.334134i
$28$	−0.493625	+	1.93813i	−0.0932864	+	0.366271i
$29$	5.80611	−	6.91945i	1.07817	−	1.28491i	0.121859	−	0.992547i	$-0.461114\pi$
$29$	5.80611	−	6.91945i	1.07817	−	1.28491i	0.956308	−	0.292362i	$-0.0944413\pi$
$30$	0.570285	−	2.34811i	0.104119	−	0.428704i
$31$	−0.573485	+	0.101121i	−0.103001	+	0.0181619i	−0.224911	−	0.974379i	$-0.572209\pi$
$31$	−0.573485	+	0.101121i	−0.103001	+	0.0181619i	0.121910	+	0.992541i	$0.461098\pi$
$32$	−3.18595	−	4.67437i	−0.563202	−	0.826319i
$33$	2.12387	−	7.16702i	0.369718	−	1.24762i
$34$	−7.25164	−	2.23706i	−1.24365	−	0.383653i
$35$	−0.493239	+	0.854315i	−0.0833726	+	0.144406i
$36$	5.85326	−	1.31885i	0.975543	−	0.219808i
$37$	−0.657893	−	1.13950i	−0.108157	−	0.187333i	0.806867	−	0.590734i	$-0.201162\pi$
$37$	−0.657893	−	1.13950i	−0.108157	−	0.187333i	−0.915024	+	0.403400i	$0.867828\pi$
$38$	−1.23595	−	5.41574i	−0.200497	−	0.878550i
$39$	0.261580	+	4.28493i	0.0418863	+	0.686138i
$40$	−0.888409	−	2.64496i	−0.140470	−	0.418206i
$41$	−6.21257	−	7.40386i	−0.970241	−	1.15629i	−0.987687	−	0.156441i	$-0.949998\pi$
$41$	−6.21257	−	7.40386i	−0.970241	−	1.15629i	0.0174462	−	0.999848i	$-0.494446\pi$
$42$	−2.44452	−	0.155986i	−0.377197	−	0.0240692i
$43$	0.107479	+	0.295296i	0.0163904	+	0.0450322i	0.947618	−	0.319406i	$-0.103483\pi$
$43$	0.107479	+	0.295296i	0.0163904	+	0.0450322i	−0.931228	+	0.364438i	$0.881261\pi$
$44$	−2.33728	−	8.30901i	−0.352358	−	1.25263i
$45$	2.95534	+	0.155569i	0.440556	+	0.0231909i
$46$	−6.33951	+	8.36882i	−0.934710	+	1.23391i
$47$	−1.36505	+	7.74157i	−0.199113	+	1.12922i	0.707326	+	0.706887i	$0.249901\pi$
$47$	−1.36505	+	7.74157i	−0.199113	+	1.12922i	−0.906439	+	0.422337i	$0.861210\pi$
$48$	4.90621	−	4.89174i	0.708150	−	0.706062i
$49$	0.939693	+	0.342020i	0.134242	+	0.0488600i
$50$	0.283702	+	5.68777i	0.0401215	+	0.804372i
$51$	1.05323	−	9.23455i	0.147481	−	1.29310i
$52$	2.89340	+	4.02496i	0.401243	+	0.558162i
$53$			4.31297i			0.592432i	0.955121	+	0.296216i	$0.0957248\pi$
$53$			4.31297i			0.592432i	−0.955121	+	0.296216i	$0.904275\pi$
$54$	2.91085	+	6.74737i	0.396116	+	0.918200i
$55$		−	4.25739i		−	0.574066i
$56$	−2.48410	+	1.35249i	−0.331952	+	0.180735i
$57$	6.23947	−	2.71214i	0.826439	−	0.359232i
$58$	12.7583	−	0.636376i	1.67525	−	0.0835602i
$59$	−5.36732	−	1.95354i	−0.698766	−	0.254330i	−0.0318818	−	0.999492i	$-0.510150\pi$
$59$	−5.36732	−	1.95354i	−0.698766	−	0.254330i	−0.666884	+	0.745162i	$0.732372\pi$
$60$	2.98287	−	1.66737i	0.385087	−	0.215257i
$61$	−0.255302	+	1.44789i	−0.0326881	+	0.185383i	−0.996780	−	0.0801857i	$-0.974449\pi$
$61$	−0.255302	+	1.44789i	−0.0326881	+	0.185383i	0.964092	+	0.265569i	$0.0855598\pi$
$62$	−0.656458	−	0.497277i	−0.0833702	−	0.0631542i
$63$	−0.364919	−	2.97772i	−0.0459754	−	0.375158i
$64$	1.78150	−	7.79912i	0.222688	−	0.974890i
$65$	0.836238	+	2.29755i	0.103723	+	0.284975i
$66$	9.47309	−	4.69195i	1.16606	−	0.577539i
$67$	2.87683	+	3.42848i	0.351461	+	0.418855i	0.912592	−	0.408872i	$-0.134078\pi$
$67$	2.87683	+	3.42848i	0.351461	+	0.418855i	−0.561131	+	0.827727i	$0.689633\pi$
$68$	−4.65600	−	9.66970i	−0.564623	−	1.17262i
$69$	−11.5068	−	5.73874i	−1.38526	−	0.690864i
$70$	−1.36012	+	0.310398i	−0.162566	+	0.0370997i
$71$	8.25153	+	14.2921i	0.979276	+	1.69616i	0.665034	+	0.746813i	$0.268417\pi$
$71$	8.25153	+	14.2921i	0.979276	+	1.69616i	0.314242	+	0.949343i	$0.398250\pi$
$72$	6.99741	+	4.79961i	0.824652	+	0.565640i
$73$	−3.58347	+	6.20674i	−0.419413	+	0.726444i	−0.995880	−	0.0906756i	$-0.971097\pi$
$73$	−3.58347	+	6.20674i	−0.419413	+	0.726444i	0.576468	+	0.817120i	$0.304431\pi$
$74$	0.548532	−	1.77812i	0.0637656	−	0.206702i
$75$	−6.78220	+	1.62743i	−0.783142	+	0.187920i
$76$	4.42577	−	6.49062i	0.507671	−	0.744526i
$77$	−4.25018	+	0.749421i	−0.484353	+	0.0854044i
$78$	−4.19066	+	4.39277i	−0.474499	+	0.497384i
$79$	−5.03644	+	6.00220i	−0.566644	+	0.675300i	−0.970939	−	0.239329i	$-0.923073\pi$
$79$	−5.03644	+	6.00220i	−0.566644	+	0.675300i	0.404294	+	0.914629i	$0.367517\pi$
$80$	1.88754	−	3.46517i	0.211034	−	0.387418i
$81$	−7.46367	+	5.02928i	−0.829296	+	0.558809i
$82$	1.69997	−	13.5623i	0.187731	−	1.49771i
$83$	−5.55219	−	4.65884i	−0.609432	−	0.511374i	0.285030	−	0.958519i	$-0.407997\pi$
$83$	−5.55219	−	4.65884i	−0.609432	−	0.511374i	−0.894462	+	0.447144i	$0.852441\pi$
$84$	−2.18962	−	2.68432i	−0.238907	−	0.292883i
$85$	−0.919219	−	5.21315i	−0.0997033	−	0.565445i
$86$	−0.202757	+	0.395464i	−0.0218638	+	0.0426440i
$87$	3.65051	+	15.2132i	0.391376	+	1.63103i
$88$	6.36593	−	10.4154i	0.678610	−	1.11028i
$89$	12.4036	+	7.16122i	1.31478	+	0.759087i	0.982883	−	0.184229i	$-0.0589788\pi$
$89$	12.4036	+	7.16122i	1.31478	+	0.759087i	0.331895	+	0.943316i	$0.392312\pi$
$90$	2.68140	+	3.21350i	0.282645	+	0.338733i
$91$	2.14645	−	1.23926i	0.225010	−	0.129909i
$92$	−14.7740	+	1.47751i	−1.54029	+	0.154041i
$93$	0.450153	−	0.902605i	0.0466786	−	0.0935957i
$94$	−9.33884	+	6.03129i	−0.963228	+	0.622080i
$95$	2.96831	−	2.49071i	0.304542	−	0.255541i
$96$	9.79054	+	0.381093i	0.999243	+	0.0388952i
$97$	−4.61957	+	1.68139i	−0.469046	+	0.170719i	−0.565720	−	0.824597i	$-0.691402\pi$
$97$	−4.61957	+	1.68139i	−0.469046	+	0.170719i	0.0966739	+	0.995316i	$0.469180\pi$
$98$	0.549293	+	1.30318i	0.0554869	+	0.131641i
$99$	7.78944	+	10.3419i	0.782869	+	1.03940i
$100$	−5.62373	+	5.76507i	−0.562373	+	0.576507i
$101$	−1.44452	−	0.254708i	−0.143735	−	0.0253444i	0.101318	−	0.994854i	$-0.467694\pi$
$101$	−1.44452	−	0.254708i	−0.143735	−	0.0253444i	−0.245053	+	0.969510i	$0.578805\pi$
$102$	10.5867	−	7.79062i	1.04824	−	0.771387i
$103$	0.204101	−	0.560763i	0.0201107	−	0.0552536i	−0.929231	−	0.369499i	$-0.879529\pi$
$103$	0.204101	−	0.560763i	0.0201107	−	0.0552536i	0.949342	+	0.314246i	$0.101752\pi$
$104$	−1.38965	+	6.87117i	−0.136266	+	0.673774i
$105$	−0.681133	−	1.56699i	−0.0664718	−	0.152923i
$106$	−4.47134	+	4.14856i	−0.434295	+	0.402944i
$107$	5.31350			0.513676			0.256838	−	0.966455i	$-0.417319\pi$
$107$	5.31350			0.513676			0.256838	+	0.966455i	$0.417319\pi$
$108$	−4.19524	+	9.50789i	−0.403687	+	0.914897i
$109$	18.7744			1.79826			0.899132	−	0.437677i	$-0.144199\pi$
$109$	18.7744			1.79826			0.899132	+	0.437677i	$0.144199\pi$
$110$	4.41371	−	4.09509i	0.420831	−	0.390452i
$111$	2.26433	+	0.258253i	0.214921	+	0.0245123i
$112$	−3.79156	−	1.27438i	−0.358269	−	0.120418i
$113$	−6.46151	+	17.7529i	−0.607848	+	1.67005i	0.127072	+	0.991894i	$0.459442\pi$
$113$	−6.46151	+	17.7529i	−0.607848	+	1.67005i	−0.734919	+	0.678155i	$0.762780\pi$
$114$	8.81336	+	3.85983i	0.825446	+	0.361506i
$115$	−7.21218	−	1.27170i	−0.672540	−	0.118587i
$116$	12.9317	+	12.6147i	1.20068	+	1.17124i
$117$	−6.23503	−	4.05113i	−0.576428	−	0.374527i
$118$	−3.13744	−	7.44348i	−0.288825	−	0.685228i
$119$	−5.04251	+	1.83533i	−0.462247	+	0.168244i
$120$	4.59776	+	1.48859i	0.419716	+	0.135889i
$121$	5.84158	−	4.90167i	0.531053	−	0.445606i
$122$	−1.74662	+	1.12802i	−0.158132	+	0.102126i
$123$	16.7093	−	1.02004i	1.50662	−	0.0919739i
$124$	−0.115897	−	1.15888i	−0.0104079	−	0.104071i
$125$	−7.71178	+	4.45240i	−0.689763	+	0.398235i
$126$	2.73606	−	3.24253i	0.243747	−	0.288868i
$127$	8.99218	+	5.19163i	0.797927	+	0.460683i	0.842746	−	0.538312i	$-0.180938\pi$
$127$	8.99218	+	5.19163i	0.797927	+	0.460683i	−0.0448191	+	0.998995i	$0.514271\pi$
$128$	9.79909	−	5.65490i	0.866125	−	0.499827i
$129$	−0.521860	−	0.154648i	−0.0459472	−	0.0136160i
$130$	−1.57755	+	3.07691i	−0.138360	+	0.269863i
$131$	−1.79681	−	10.1902i	−0.156988	−	0.890323i	−0.956946	−	0.290267i	$-0.906256\pi$
$131$	−1.79681	−	10.1902i	−0.156988	−	0.890323i	0.799958	−	0.600056i	$-0.204855\pi$
$132$	13.9762	+	5.30784i	1.21647	+	0.461988i
$133$	−3.00900	−	2.52485i	−0.260913	−	0.218932i
$134$	−0.787199	+	6.28025i	−0.0680037	+	0.542531i
$135$	−3.26184	+	3.95413i	−0.280734	+	0.340317i
$136$	5.54625	−	14.1281i	0.475587	−	1.21147i
$137$	−10.1474	+	12.0932i	−0.866949	+	1.03319i	0.132170	+	0.991227i	$0.457805\pi$
$137$	−10.1474	+	12.0932i	−0.866949	+	1.03319i	−0.999119	+	0.0419626i	$0.986639\pi$
$138$	−5.11870	−	17.4493i	−0.435732	−	1.48538i
$139$	−9.66940	+	1.70498i	−0.820148	+	0.144614i	−0.567952	−	0.823062i	$-0.692264\pi$
$139$	−9.66940	+	1.70498i	−0.820148	+	0.144614i	−0.252196	+	0.967676i	$0.581153\pi$
$140$	−1.63007	−	1.11150i	−0.137766	−	0.0939388i
$141$	−9.37124	−	9.87752i	−0.789201	−	0.831837i
$142$	−6.87988	+	22.3018i	−0.577347	+	1.87152i
$143$	−5.34831	+	9.26354i	−0.447248	+	0.774657i
$144$	1.75481	+	11.8710i	0.146234	+	0.989250i
$145$	4.45528	+	7.71677i	0.369991	+	0.640843i
$146$	−9.88152	+	2.25509i	−0.817800	+	0.186633i
$147$	−1.44444	+	0.955816i	−0.119136	+	0.0788343i
$148$	2.37103	−	1.14166i	0.194898	−	0.0938440i
$149$	−0.647120	−	0.771208i	−0.0530142	−	0.0631798i	0.738886	−	0.673831i	$-0.235352\pi$
$149$	−0.647120	−	0.771208i	−0.0530142	−	0.0631798i	−0.791900	+	0.610651i	$0.790908\pi$
$150$	−8.21086	−	5.46585i	−0.670414	−	0.446285i
$151$	−5.19403	−	14.2705i	−0.422684	−	1.16131i	−0.950165	−	0.311747i	$-0.899086\pi$
$151$	−5.19403	−	14.2705i	−0.422684	−	1.16131i	0.527481	−	0.849567i	$-0.323136\pi$
$152$	10.9860	−	1.65491i	0.891084	−	0.134231i
$153$	11.7711	+	10.9818i	0.951635	+	0.887826i
$154$	−4.86510	−	3.68539i	−0.392041	−	0.296977i
$155$	0.0997535	−	0.565730i	0.00801240	−	0.0454406i
$156$	−8.58499	−	0.119220i	−0.687349	−	0.00954524i
$157$	8.20612	+	2.98678i	0.654920	+	0.238371i	0.648041	−	0.761605i	$-0.275588\pi$
$157$	8.20612	+	2.98678i	0.654920	+	0.238371i	0.00687831	+	0.999976i	$0.497811\pi$
$158$	−11.0671	+	0.552017i	−0.880447	+	0.0439161i
$159$	−6.00453	−	4.44419i	−0.476190	−	0.352447i
$160$	5.40800	−	1.37622i	0.427540	−	0.108800i
$161$			7.42383i			0.585080i
$162$	−12.3931	−	2.90016i	−0.973694	−	0.227858i
$163$		−	5.30704i		−	0.415680i	−0.978163	−	0.207840i	$-0.933357\pi$
$163$		−	5.30704i		−	0.415680i	0.978163	−	0.207840i	$-0.0666433\pi$
$164$	15.6955	−	11.2829i	1.22561	−	0.881049i
$165$	5.92714	+	4.38691i	0.461427	+	0.341521i
$166$	−0.510630	−	10.2373i	−0.0396326	−	0.794569i
$167$	6.43319	+	2.34149i	0.497815	+	0.181190i	0.578711	−	0.815533i	$-0.303556\pi$
$167$	6.43319	+	2.34149i	0.497815	+	0.181190i	−0.0808961	+	0.996723i	$0.525778\pi$
$168$	0.676735	−	4.85201i	0.0522112	−	0.374341i
$169$	−1.19070	+	6.75281i	−0.0915925	+	0.519447i
$170$	4.52039	−	5.96740i	0.346698	−	0.457678i
$171$	−2.65346	+	11.4813i	−0.202915	+	0.877994i
$172$	−0.605013	+	0.170187i	−0.0461318	+	0.0129766i
$173$	1.78209	+	4.89624i	0.135489	+	0.372254i	0.988820	−	0.149117i	$-0.0476430\pi$
$173$	1.78209	+	4.89624i	0.135489	+	0.372254i	−0.853330	+	0.521371i	$0.825421\pi$
$174$	−12.2605	+	18.4179i	−0.929467	+	1.39626i
$175$	2.58842	+	3.08475i	0.195666	+	0.233186i
$176$	16.9211	−	3.41866i	1.27547	−	0.257691i
$177$	8.25035	−	5.45941i	0.620134	−	0.410355i
$178$	4.50659	+	19.7473i	0.337783	+	1.48012i
$179$	10.3500	+	17.9267i	0.773594	+	1.33990i	0.935581	+	0.353111i	$0.114876\pi$
$179$	10.3500	+	17.9267i	0.773594	+	1.33990i	−0.161988	+	0.986793i	$0.551790\pi$
$180$	−0.752309	+	5.87086i	−0.0560738	+	0.437588i
$181$	10.1787	−	17.6300i	0.756575	−	1.31043i	−0.188012	−	0.982167i	$-0.560204\pi$
$181$	10.1787	−	17.6300i	0.756575	−	1.31043i	0.944587	−	0.328260i	$-0.106462\pi$
$182$	3.34939	+	1.03326i	0.248273	+	0.0765900i
$183$	−1.75268	−	1.84737i	−0.129562	−	0.136562i
$184$	−15.7425	−	13.8953i	−1.16056	−	1.02437i
$185$	1.27828	−	0.225394i	0.0939807	−	0.0165713i
$186$	1.36874	−	0.401515i	0.100361	−	0.0294405i
$187$	14.8862	−	17.7407i	1.08859	−	1.29733i
$188$	−15.2356	−	3.88039i	−1.11117	−	0.283006i
$189$	4.52161	+	2.56028i	0.328899	+	0.186233i
$190$	5.43732	+	0.681542i	0.394465	+	0.0494443i
$191$	−20.3220	−	17.0521i	−1.47045	−	1.23385i	−0.915720	−	0.401816i	$-0.868379\pi$
$191$	−20.3220	−	17.0521i	−1.47045	−	1.23385i	−0.554725	−	0.832034i	$-0.687177\pi$
$192$	9.02224	+	10.5166i	0.651124	+	0.758971i
$193$	−2.07296	−	11.7564i	−0.149215	−	0.846241i	−0.963886	−	0.266317i	$-0.914193\pi$
$193$	−2.07296	−	11.7564i	−0.149215	−	0.846241i	0.814670	−	0.579924i	$-0.196918\pi$
$194$	−6.18660	−	3.17191i	−0.444172	−	0.227730i
$195$	−4.06033	−	1.20323i	−0.290766	−	0.0861654i
$196$	−0.822678	+	1.82296i	−0.0587627	+	0.130212i
$197$	11.6600	+	6.73188i	0.830737	+	0.479627i	0.854105	−	0.520100i	$-0.174105\pi$
$197$	11.6600	+	6.73188i	0.830737	+	0.479627i	−0.0233676	+	0.999727i	$0.507439\pi$
$198$	−3.22916	+	18.0232i	−0.229486	+	1.28085i
$199$	−8.95958	+	5.17282i	−0.635128	+	0.366691i	−0.782735	−	0.622355i	$-0.786176\pi$
$199$	−8.95958	+	5.17282i	−0.635128	+	0.366691i	0.147607	+	0.989046i	$0.452843\pi$
$200$	−11.3861	−	0.284927i	−0.805120	−	0.0201474i
$201$	−7.73749	+	0.472346i	−0.545760	+	0.0333167i
$202$	−1.12540	−	1.74256i	−0.0791826	−	0.122606i
$203$	6.91945	−	5.80611i	0.485650	−	0.407509i
$204$	18.2598	+	3.48180i	1.27844	+	0.243775i
$205$	8.95937	−	3.26094i	0.625749	−	0.227754i
$206$	0.777674	−	0.327791i	0.0541831	−	0.0228383i
$207$	19.8464	−	10.1064i	1.37942	−	0.702447i
$208$	−8.46016	+	5.16857i	−0.586606	+	0.358376i
$209$	16.6946	+	2.94370i	1.15479	+	0.203620i
$210$	0.969366	−	2.21340i	0.0668926	−	0.152739i
$211$	4.18320	−	11.4933i	0.287983	−	0.791228i	−0.708365	−	0.705846i	$-0.750567\pi$
$211$	4.18320	−	11.4933i	0.287983	−	0.791228i	0.996348	−	0.0853816i	$-0.0272109\pi$
$212$	−8.60179	−	0.645108i	−0.590773	−	0.0443062i
$213$	−28.4000	−	3.23910i	−1.94594	−	0.221940i
$214$	5.11095	+	5.50861i	0.349377	+	0.376561i
$215$	−0.309998			−0.0211417
$216$	−13.8923	+	4.79616i	−0.945253	+	0.326337i
$217$	−0.582332			−0.0395313
$218$	18.0588	+	19.4638i	1.22309	+	1.31826i
$219$	−4.94855	−	11.3845i	−0.334392	−	0.769292i
$220$	8.49093	+	0.636794i	0.572458	+	0.0429326i
$221$	−4.54887	+	12.4979i	−0.305990	+	0.840702i
$222$	1.91028	+	2.59588i	0.128209	+	0.174224i
$223$	−4.71959	−	0.832191i	−0.316047	−	0.0557277i	0.0133744	−	0.999911i	$-0.495743\pi$
$223$	−4.71959	−	0.832191i	−0.316047	−	0.0557277i	−0.329422	+	0.944183i	$0.606854\pi$
$224$	−2.32586	−	5.15659i	−0.155403	−	0.344539i
$225$	4.72284	−	11.1191i	0.314856	−	0.741276i
$226$	−24.6199	+	10.3773i	−1.63769	+	0.690291i
$227$	−12.4287	+	4.52367i	−0.824921	+	0.300247i	−0.719772	−	0.694210i	$-0.755754\pi$
$227$	−12.4287	+	4.52367i	−0.824921	+	0.300247i	−0.105148	+	0.994457i	$0.533532\pi$
$228$	4.47583	+	12.8497i	0.296419	+	0.850990i
$229$	−20.9867	+	17.6099i	−1.38684	+	1.16370i	−0.420236	+	0.907415i	$0.638053\pi$
$229$	−20.9867	+	17.6099i	−1.38684	+	1.16370i	−0.966602	+	0.256281i	$0.917503\pi$
$230$	−5.61886	−	8.70023i	−0.370496	−	0.573677i
$231$	3.33614	−	6.68933i	0.219502	−	0.440125i
$232$	−0.639124	+	25.5403i	−0.0419605	+	1.67681i
$233$	21.8105	−	12.5923i	1.42885	−	0.824948i	0.431821	−	0.901959i	$-0.357871\pi$
$233$	21.8105	−	12.5923i	1.42885	−	0.824948i	0.997030	+	0.0770113i	$0.0245378\pi$
$234$	−1.79747	−	10.3607i	−0.117504	−	0.677298i
$235$	−6.71576	−	3.87735i	−0.438088	−	0.252930i
$236$	4.69896	−	10.4124i	0.305876	−	0.677788i
$237$	−3.16660	−	13.1966i	−0.205693	−	0.857209i
$238$	−6.75301	−	3.46231i	−0.437733	−	0.224428i
$239$	0.210346	+	1.19293i	0.0136062	+	0.0771643i	0.990855	−	0.134933i	$-0.0430818\pi$
$239$	0.210346	+	1.19293i	0.0136062	+	0.0771643i	−0.977249	+	0.212097i	$0.931971\pi$
$240$	2.87924	+	6.19844i	0.185854	+	0.400107i
$241$	22.2173	+	18.6426i	1.43114	+	1.20087i	0.945033	+	0.326975i	$0.106029\pi$
$241$	22.2173	+	18.6426i	1.43114	+	1.20087i	0.486111	+	0.873897i	$0.338415\pi$
$242$	10.7006	+	1.34126i	0.687858	+	0.0862197i
$243$	0.688974	−	15.5732i	0.0441977	−	0.999023i
$244$	−2.84948	−	0.725740i	−0.182419	−	0.0464608i
$245$	−0.634096	+	0.755686i	−0.0405109	+	0.0482790i
$246$	17.1298	+	16.3416i	1.09216	+	1.04191i
$247$	−9.58761	+	1.69055i	−0.610045	+	0.107567i
$248$	1.08996	−	1.23486i	0.0692124	−	0.0784137i
$249$	12.2072	−	2.92919i	0.773597	−	0.185630i
$250$	−12.0337	−	3.71228i	−0.761078	−	0.234785i
$251$	2.97174	−	5.14720i	0.187574	−	0.324888i	−0.756867	−	0.653569i	$-0.773271\pi$
$251$	2.97174	−	5.14720i	0.187574	−	0.324888i	0.944441	+	0.328681i	$0.106604\pi$
$252$	5.99335	−	0.282403i	0.377546	−	0.0177897i
$253$	−16.0197	−	27.7469i	−1.00715	−	1.74443i
$254$	3.26712	+	14.3161i	0.204998	+	0.898271i
$255$	8.20494	+	4.09202i	0.513813	+	0.256252i
$256$	15.2881	+	4.71957i	0.955506	+	0.294973i
$257$	6.26712	+	7.46887i	0.390933	+	0.465895i	0.925233	−	0.379399i	$-0.123869\pi$
$257$	6.26712	+	7.46887i	0.390933	+	0.465895i	−0.534300	+	0.845295i	$0.679425\pi$
$258$	−0.341640	−	0.689775i	−0.0212696	−	0.0429435i
$259$	−0.450026	−	1.23644i	−0.0279632	−	0.0768284i
$260$	−4.70730	+	1.32414i	−0.291934	+	0.0821196i
$261$	−24.9415	−	10.5938i	−1.54384	−	0.655743i
$262$	8.83608	−	11.6645i	0.545895	−	0.720638i
$263$	3.72353	−	21.1172i	0.229603	−	1.30214i	−0.624084	−	0.781357i	$-0.714528\pi$
$263$	3.72353	−	21.1172i	0.229603	−	1.30214i	0.853687	−	0.520786i	$-0.174361\pi$
$264$	7.94070	+	19.5949i	0.488716	+	1.20598i
$265$	−3.99806	−	1.45518i	−0.245599	−	0.0893908i
$266$	−0.276735	−	5.54809i	−0.0169677	−	0.340175i
$267$	−22.7508	+	9.88921i	−1.39233	+	0.605210i
$268$	−7.26805	+	5.22474i	−0.443967	+	0.319152i
$269$			13.4779i			0.821761i	0.911689	+	0.410881i	$0.134779\pi$
$269$			13.4779i			0.821761i	−0.911689	+	0.410881i	$0.865221\pi$
$270$	−7.23682	+	0.421785i	−0.440419	+	0.0256690i
$271$		−	19.9770i		−	1.21352i	−0.794886	−	0.606758i	$-0.792470\pi$
$271$		−	19.9770i		−	1.21352i	0.794886	−	0.606758i	$-0.207530\pi$
$272$	19.9817	−	7.83959i	1.21157	−	0.475345i
$273$	−0.486465	+	4.26526i	−0.0294422	+	0.258145i
$274$	−22.2978	+	1.11220i	−1.34706	+	0.0671904i
$275$	−16.3308	−	5.94393i	−0.984786	−	0.358433i
$276$	13.1665	−	22.0908i	0.792528	−	1.32971i
$277$	1.54162	−	8.74298i	0.0926272	−	0.525315i	−0.902821	−	0.430016i	$-0.858508\pi$
$277$	1.54162	−	8.74298i	0.0926272	−	0.525315i	0.995449	−	0.0952994i	$-0.0303808\pi$
$278$	−11.0684	−	8.38447i	−0.663837	−	0.502867i
$279$	0.792759	+	1.55677i	0.0474613	+	0.0932013i
$280$	−0.415619	−	2.75905i	−0.0248380	−	0.164885i
$281$	−1.07856	−	2.96332i	−0.0643415	−	0.176777i	0.903356	−	0.428892i	$-0.141096\pi$
$281$	−1.07856	−	2.96332i	−0.0643415	−	0.176777i	−0.967697	+	0.252115i	$0.918874\pi$
$282$	1.22621	−	19.2163i	0.0730195	−	1.14432i
$283$	10.5641	+	12.5898i	0.627971	+	0.748387i	0.982419	−	0.186689i	$-0.0597756\pi$
$283$	10.5641	+	12.5898i	0.627971	+	0.748387i	−0.354448	+	0.935076i	$0.615331\pi$
$284$	−29.7383	+	14.3191i	−1.76464	+	0.849683i
$285$	0.408948	+	6.69897i	0.0242240	+	0.396813i
$286$	−14.7481	+	3.36572i	−0.872075	+	0.199019i
$287$	−4.83253	−	8.37018i	−0.285255	−	0.494076i
$288$	−10.6190	+	13.2377i	−0.625729	+	0.780040i
$289$	5.89769	−	10.2151i	0.346923	−	0.600888i
$290$	−3.71468	+	12.0415i	−0.218134	+	0.707100i
$291$	2.41929	−	8.16392i	0.141821	−	0.478577i
$292$	−11.8427	−	8.07523i	−0.693043	−	0.472567i
$293$	−7.28794	+	1.28506i	−0.425766	+	0.0750740i	−0.382425	−	0.923986i	$-0.624911\pi$
$293$	−7.28794	+	1.28506i	−0.425766	+	0.0750740i	−0.0433404	+	0.999060i	$0.513800\pi$
$294$	−2.38029	−	0.578102i	−0.138822	−	0.0337156i
$295$	3.62182	−	4.31631i	0.210870	−	0.251306i
$296$	3.46423	+	1.35995i	0.201354	+	0.0790456i
$297$	−22.4245	+	0.187907i	−1.30120	+	0.0109034i
$298$	0.177074	−	1.41269i	0.0102576	−	0.0818350i
$299$	14.0953	+	11.8273i	0.815150	+	0.683992i
$300$	−2.23131	−	13.7698i	−0.128825	−	0.795002i
$301$	0.0545684	+	0.309473i	0.00314527	+	0.0178377i
$302$	9.79844	−	19.1112i	0.563837	−	1.09973i
$303$	1.84308	−	1.74861i	0.105882	−	0.100455i
$304$	12.2829	+	9.79759i	0.704473	+	0.561930i
$305$	−1.25603	−	0.725172i	−0.0719203	−	0.0415232i
$306$	−0.0626853	+	22.7665i	−0.00358348	+	1.30147i
$307$	12.0328	−	6.94713i	0.686747	−	0.396494i	−0.115645	−	0.993291i	$-0.536893\pi$
$307$	12.0328	−	6.94713i	0.686747	−	0.396494i	0.802392	+	0.596797i	$0.203560\pi$
$308$	−0.858928	−	8.58864i	−0.0489420	−	0.489383i
$309$	0.570384	+	0.861973i	0.0324480	+	0.0490359i
$310$	0.682455	−	0.440748i	0.0387608	−	0.0250328i
$311$	20.1845	−	16.9368i	1.14456	−	0.960399i	0.144980	−	0.989435i	$-0.453688\pi$
$311$	20.1845	−	16.9368i	1.14456	−	0.960399i	0.999578	+	0.0290357i	$0.00924363\pi$
$312$	−8.13413	−	9.01490i	−0.460504	−	0.510368i
$313$	7.68653	−	2.79767i	0.434468	−	0.158133i	−0.115521	−	0.993305i	$-0.536854\pi$
$313$	7.68653	−	2.79767i	0.434468	−	0.158133i	0.549990	+	0.835172i	$0.314632\pi$
$314$	4.79685	+	11.3804i	0.270702	+	0.642232i
$315$	2.88343	+	0.666395i	0.162463	+	0.0375471i
$316$	−11.2175	−	10.9425i	−0.631031	−	0.615561i
$317$	−3.06488	−	0.540420i	−0.172141	−	0.0303530i	0.0869134	−	0.996216i	$-0.472300\pi$
$317$	−3.06488	−	0.540420i	−0.172141	−	0.0303530i	−0.259054	+	0.965863i	$0.583411\pi$
$318$	−1.16825	−	10.4998i	−0.0655124	−	0.588799i
$319$	−13.3329	+	36.6319i	−0.746500	+	2.05099i
$320$	6.62860	+	4.28281i	0.370550	+	0.239417i
$321$	−5.47516	+	7.39747i	−0.305594	+	0.412886i
$322$	−7.69643	+	7.14083i	−0.428905	+	0.397943i
$323$	21.0780			1.17281
$324$	−8.91402	−	15.6378i	−0.495223	−	0.868766i
$325$	9.98062			0.553625
$326$	5.50192	−	5.10474i	0.304723	−	0.282725i
$327$	−19.3456	+	26.1378i	−1.06982	+	1.44542i
$328$	26.7944	+	5.41899i	1.47947	+	0.299214i
$329$	−2.68862	+	7.38692i	−0.148228	+	0.407254i
$330$	1.15320	+	10.3645i	0.0634814	+	0.570545i
$331$	20.6594	+	3.64282i	1.13555	+	0.200227i	0.709656	−	0.704548i	$-0.248850\pi$
$331$	20.6594	+	3.64282i	1.13555	+	0.200227i	0.425889	+	0.904775i	$0.359961\pi$
$332$	10.1221	−	10.3764i	0.555520	−	0.569481i
$333$	−2.69276	+	2.88629i	−0.147562	+	0.158168i
$334$	3.76049	+	8.92164i	0.205765	+	0.488170i
$335$	−4.14878	+	1.51003i	−0.226672	+	0.0825018i
$336$	5.68111	−	3.96547i	0.309930	−	0.216334i
$337$	13.2688	−	11.1338i	0.722797	−	0.606499i	−0.205360	−	0.978686i	$-0.565837\pi$
$337$	13.2688	−	11.1338i	0.722797	−	0.606499i	0.928158	+	0.372187i	$0.121392\pi$
$338$	−8.14608	+	5.26097i	−0.443088	+	0.286159i
$339$	−18.0575	−	27.2887i	−0.980746	−	1.48212i
$340$	10.5346	−	1.05354i	0.571318	−	0.0571361i
$341$	2.17649	−	1.25660i	0.117864	−	0.0680486i
$342$	−14.4552	+	8.29271i	−0.781645	+	0.448418i
$343$	0.866025	+	0.500000i	0.0467610	+	0.0269975i
$344$	−0.758387	−	0.463530i	−0.0408895	−	0.0249918i
$345$	9.20208	−	8.73042i	0.495423	−	0.470030i
$346$	−3.36187	+	6.55712i	−0.180736	+	0.352513i
$347$	−1.25430	−	7.11348i	−0.0673343	−	0.381872i	−0.999788	−	0.0205827i	$-0.993448\pi$
$347$	−1.25430	−	7.11348i	−0.0673343	−	0.381872i	0.932454	−	0.361289i	$-0.117663\pi$
$348$	−30.8873	+	5.00508i	−1.65573	+	0.268300i
$349$	6.36498	+	5.34085i	0.340710	+	0.285889i	0.797047	−	0.603918i	$-0.206394\pi$
$349$	6.36498	+	5.34085i	0.340710	+	0.285889i	−0.456337	+	0.889807i	$0.650839\pi$
$350$	−0.708279	+	5.65063i	−0.0378591	+	0.302039i
$351$	12.0647	−	4.50603i	0.643966	−	0.240514i
$352$	19.8202	+	14.2541i	1.05642	+	0.759745i
$353$	7.25096	−	8.64136i	0.385930	−	0.459933i	−0.537747	−	0.843106i	$-0.680724\pi$
$353$	7.25096	−	8.64136i	0.385930	−	0.459933i	0.923676	+	0.383173i	$0.125169\pi$
$354$	13.5957	+	3.30200i	0.722604	+	0.175499i
$355$	−16.0326	+	2.82697i	−0.850920	+	0.150040i
$356$	−16.1376	+	23.6666i	−0.855290	+	1.25433i
$357$	2.64079	−	8.91136i	0.139765	−	0.471639i
$358$	−8.62951	+	27.9734i	−0.456084	+	1.47844i
$359$	−3.53969	+	6.13093i	−0.186818	+	0.323578i	−0.944188	−	0.329408i	$-0.893151\pi$
$359$	−3.53969	+	6.13093i	−0.186818	+	0.323578i	0.757370	+	0.652986i	$0.226484\pi$
$360$	−6.81007	+	4.86713i	−0.358922	+	0.256520i
$361$	−1.78554	−	3.09265i	−0.0939758	−	0.162771i
$362$	28.0680	−	6.40550i	1.47522	−	0.336666i
$363$	0.804803	+	13.1835i	0.0422412	+	0.691952i
$364$	2.15052	+	4.46625i	0.112718	+	0.234095i
$365$	−4.54452	−	5.41595i	−0.237871	−	0.283484i
$366$	0.229335	−	3.59399i	0.0119875	−	0.187861i
$367$	−1.70023	−	4.67135i	−0.0887515	−	0.243843i	0.887374	−	0.461050i	$-0.152527\pi$
$367$	−1.70023	−	4.67135i	−0.0887515	−	0.243843i	−0.976125	+	0.217208i	$0.930305\pi$
$368$	−0.736937	−	29.6862i	−0.0384155	−	1.54750i
$369$	−15.7975	+	24.3137i	−0.822386	+	1.26572i
$370$	1.46322	+	1.10841i	0.0760691	+	0.0576235i
$371$	−0.748940	+	4.24745i	−0.0388830	+	0.220516i
$372$	1.73282	+	1.03279i	0.0898427	+	0.0535477i
$373$	−3.25963	−	1.18641i	−0.168777	−	0.0614298i	0.256250	−	0.966611i	$-0.417513\pi$
$373$	−3.25963	−	1.18641i	−0.168777	−	0.0614298i	−0.425027	+	0.905181i	$0.639735\pi$
$374$	32.7109	−	1.63160i	1.69144	−	0.0843679i
$375$	1.74777	−	15.3242i	0.0902545	−	0.791339i
$376$	−10.6319	−	19.5275i	−0.548301	−	1.00705i
$377$		−	22.3877i		−	1.15302i
$378$	1.69496	+	7.15032i	0.0871792	+	0.367773i
$379$			29.9699i			1.53945i	0.638374	+	0.769726i	$0.279607\pi$
$379$			29.9699i			1.53945i	−0.638374	+	0.769726i	$0.720393\pi$
$380$	4.52348	+	6.29254i	0.232050	+	0.322800i
$381$	−16.4936	+	7.16933i	−0.844991	+	0.367296i
$382$	−1.86899	−	37.4703i	−0.0956260	−	1.91715i
$383$	32.3927	+	11.7900i	1.65519	+	0.602440i	0.989596	−	0.143875i	$-0.0459562\pi$
$383$	32.3927	+	11.7900i	1.65519	+	0.602440i	0.665594	+	0.746314i	$0.268178\pi$
$384$	−2.22446	+	19.4693i	−0.113517	+	0.993536i
$385$	0.739287	−	4.19271i	0.0376776	−	0.213680i
$386$	10.1941	−	13.4573i	0.518866	−	0.684958i
$387$	0.753038	−	0.567181i	0.0382791	−	0.0288315i
$388$	−2.66239	−	9.46476i	−0.135162	−	0.480500i
$389$	−5.82288	−	15.9982i	−0.295232	−	0.811143i	−0.995280	−	0.0970472i	$-0.969060\pi$
$389$	−5.82288	−	15.9982i	−0.295232	−	0.811143i	0.700048	−	0.714096i	$-0.253162\pi$
$390$	−2.65813	−	5.36679i	−0.134600	−	0.271758i
$391$	−25.6069	−	30.5171i	−1.29500	−	1.54332i
$392$	−2.68122	+	0.900587i	−0.135422	+	0.0454865i
$393$	16.0383	+	7.99872i	0.809026	+	0.403482i
$394$	4.23641	+	18.5634i	0.213427	+	0.935209i
$395$	−3.86468	−	6.69383i	−0.194453	−	0.336803i
$396$	−21.7910	+	13.9884i	−1.09504	+	0.702942i
$397$	−2.22346	+	3.85114i	−0.111592	+	0.193283i	−0.916412	−	0.400235i	$-0.868928\pi$
$397$	−2.22346	+	3.85114i	−0.111592	+	0.193283i	0.804820	+	0.593519i	$0.202262\pi$
$398$	−13.9808	−	4.31294i	−0.700794	−	0.216188i
$399$	6.61564	−	1.58746i	0.331196	−	0.0794727i
$400$	−10.6567	−	12.0783i	−0.532835	−	0.603914i
$401$	−13.8428	+	2.44086i	−0.691277	+	0.121891i	−0.508240	−	0.861215i	$-0.669704\pi$
$401$	−13.8428	+	2.44086i	−0.691277	+	0.121891i	−0.183036	+	0.983106i	$0.558593\pi$
$402$	−7.93222	−	7.56726i	−0.395623	−	0.377421i
$403$	−0.927746	+	1.10564i	−0.0462143	+	0.0550761i
$404$	0.724053	−	2.84286i	0.0360230	−	0.141437i
$405$	−2.14387	−	8.61557i	−0.106530	−	0.428111i
$406$	12.6750	+	1.58875i	0.629049	+	0.0788483i
$407$	4.35006	+	3.65013i	0.215624	+	0.180930i
$408$	13.9541	+	22.2794i	0.690832	+	1.10299i
$409$	−2.73310	−	15.5002i	−0.135143	−	0.766434i	−0.974760	−	0.223255i	$-0.928332\pi$
$409$	−2.73310	−	15.5002i	−0.135143	−	0.766434i	0.839617	−	0.543179i	$-0.182779\pi$
$410$	11.9985	+	6.15171i	0.592564	+	0.303811i
$411$	−6.38003	−	26.5883i	−0.314704	−	1.31150i
$412$	1.08786	+	0.490934i	0.0535948	+	0.0241866i
$413$	−4.94655	−	2.85589i	−0.243404	−	0.140529i
$414$	29.5674	+	10.8539i	1.45316	+	0.533442i
$415$	6.19196	−	3.57493i	0.303952	−	0.175487i
$416$	−13.4960	−	3.79927i	−0.661696	−	0.186274i
$417$	7.58991	−	15.2186i	0.371680	−	0.745258i
$418$	13.0064	+	20.1391i	0.636162	+	0.985033i
$419$	24.8202	−	20.8266i	1.21254	−	1.01745i	0.213363	−	0.976973i	$-0.431558\pi$
$419$	24.8202	−	20.8266i	1.21254	−	1.01745i	0.999181	−	0.0404721i	$-0.0128862\pi$
$420$	3.22709	−	1.12407i	0.157466	−	0.0548490i
$421$	1.67815	−	0.610796i	0.0817879	−	0.0297684i	−0.300802	−	0.953687i	$-0.597254\pi$
$421$	1.67815	−	0.610796i	0.0817879	−	0.0297684i	0.382590	+	0.923918i	$0.375032\pi$
$422$	15.9390	−	6.71832i	0.775899	−	0.327043i
$423$	23.4079	−	2.86862i	1.13813	−	0.139477i
$424$	−7.60509	−	9.53815i	−0.369336	−	0.463214i
$425$	−21.2804	−	3.75231i	−1.03225	−	0.182014i
$426$	−23.9594	−	32.5585i	−1.16083	−	1.57746i
$427$	−0.502846	+	1.38156i	−0.0243344	+	0.0668583i
$428$	−0.794762	+	10.5972i	−0.0384163	+	0.512237i
$429$	−7.38569	−	16.9913i	−0.356585	−	0.820348i
$430$	−0.298181	−	0.321381i	−0.0143795	−	0.0154984i
$431$	−3.51924			−0.169516			−0.0847578	−	0.996402i	$-0.527012\pi$
$431$	−3.51924			−0.169516			−0.0847578	+	0.996402i	$0.527012\pi$
$432$	−18.3350	−	9.78912i	−0.882144	−	0.470979i
$433$	21.7238			1.04398			0.521991	−	0.852951i	$-0.325190\pi$
$433$	21.7238			1.04398			0.521991	+	0.852951i	$0.325190\pi$
$434$	−0.560134	−	0.603715i	−0.0268873	−	0.0289792i
$435$	−15.3341	−	1.74890i	−0.735215	−	0.0838534i
$436$	−2.80817	+	37.4437i	−0.134487	+	1.79323i
$437$	9.97350	−	27.4020i	0.477097	−	1.31081i
$438$	7.04261	−	16.0808i	0.336509	−	0.768369i
$439$	−3.97535	−	0.700961i	−0.189733	−	0.0334551i	0.0779741	−	0.996955i	$-0.475155\pi$
$439$	−3.97535	−	0.700961i	−0.189733	−	0.0334551i	−0.267707	+	0.963500i	$0.586266\pi$
$440$	7.50707	+	9.41523i	0.357886	+	0.448853i
$441$	0.157702	−	2.99585i	0.00750960	−	0.142660i
$442$	−17.3323	+	7.30560i	−0.824414	+	0.347492i
$443$	−13.5376	+	4.92727i	−0.643189	+	0.234102i	−0.642962	−	0.765898i	$-0.722295\pi$
$443$	−13.5376	+	4.92727i	−0.643189	+	0.234102i	−0.000227546		1.00000i	$0.500072\pi$
$444$	−0.853745	+	4.47735i	−0.0405170	+	0.212486i
$445$	−10.8233	+	9.08179i	−0.513072	+	0.430518i
$446$	−3.67693	−	5.69336i	−0.174108	−	0.269588i
$447$	1.74049	−	0.106250i	0.0823222	−	0.00502547i
$448$	3.10874	−	7.37128i	0.146874	−	0.348260i
$449$	−17.6211	+	10.1735i	−0.831591	+	0.480120i	−0.854397	−	0.519620i	$-0.826073\pi$
$449$	−17.6211	+	10.1735i	−0.831591	+	0.480120i	0.0228059	+	0.999740i	$0.492740\pi$
$450$	16.0702	−	5.79903i	0.757558	−	0.273369i
$451$	36.1235	+	20.8559i	1.70099	+	0.982068i
$452$	−34.4398	−	15.5422i	−1.61991	−	0.731043i
$453$	25.2194	+	7.47351i	1.18491	+	0.351136i
$454$	−16.6447	−	8.53383i	−0.781173	−	0.400512i
$455$	0.424569	+	2.40785i	0.0199041	+	0.112882i
$456$	−9.01629	+	17.0000i	−0.422226	+	0.796099i
$457$	−5.43328	−	4.55907i	−0.254158	−	0.213264i	0.506802	−	0.862062i	$-0.330827\pi$
$457$	−5.43328	−	4.55907i	−0.254158	−	0.213264i	−0.760960	+	0.648798i	$0.775272\pi$
$458$	−38.4432	−	4.81867i	−1.79633	−	0.225162i
$459$	−27.4181	+	5.07179i	−1.27977	+	0.236731i
$460$	3.61504	−	14.1938i	0.168552	−	0.661787i
$461$	−15.7901	+	18.8179i	−0.735417	+	0.876435i	−0.996031	−	0.0890076i	$-0.971630\pi$
$461$	−15.7901	+	18.8179i	−0.735417	+	0.876435i	0.260614	+	0.965443i	$0.416075\pi$
$462$	10.1439	−	2.97569i	0.471938	−	0.138441i
$463$	14.8683	−	2.62168i	0.690988	−	0.121840i	0.182883	−	0.983135i	$-0.441457\pi$
$463$	14.8683	−	2.62168i	0.690988	−	0.121840i	0.508106	+	0.861295i	$0.330346\pi$
$464$	−27.0929	+	23.9041i	−1.25776	+	1.10972i
$465$	0.684822	+	0.721820i	0.0317579	+	0.0334736i
$466$	34.0337	+	10.4991i	1.57658	+	0.486360i
$467$	6.16291	−	10.6745i	0.285186	−	0.493956i	−0.687469	−	0.726214i	$-0.741278\pi$
$467$	6.16291	−	10.6745i	0.285186	−	0.493956i	0.972654	+	0.232258i	$0.0746114\pi$
$468$	9.01216	−	11.8292i	0.416587	−	0.546804i
$469$	2.23778	+	3.87595i	0.103331	+	0.178975i
$470$	−2.44004	−	10.6919i	−0.112550	−	0.493181i
$471$	−12.6140	+	8.34692i	−0.581222	+	0.384606i
$472$	15.3146	−	5.14396i	0.704909	−	0.236770i
$473$	−0.871755	−	1.03892i	−0.0400833	−	0.0477694i
$474$	10.6352	−	15.9764i	0.488493	−	0.733819i
$475$	−5.40986	−	14.8635i	−0.248221	−	0.681983i
$476$	−2.90614	−	10.3313i	−0.133203	−	0.473535i
$477$	12.3744	−	3.78011i	0.566586	−	0.173079i
$478$	−1.03441	+	1.36553i	−0.0473127	+	0.0624577i
$479$	0.612093	−	3.47135i	0.0279672	−	0.158610i	−0.967626	−	0.252389i	$-0.918784\pi$
$479$	0.612093	−	3.47135i	0.0279672	−	0.158610i	0.995593	+	0.0937792i	$0.0298948\pi$
$480$	−3.65655	+	8.94712i	−0.166898	+	0.408378i
$481$	−3.06452	−	1.11539i	−0.139730	−	0.0508576i
$482$	2.04331	+	40.9650i	0.0930701	+	1.86591i
$483$	−10.3355	−	7.64970i	−0.470280	−	0.348073i
$484$	8.90213	+	12.3836i	0.404642	+	0.562891i
$485$		−	4.84957i		−	0.220208i
$486$	16.8078	−	14.2653i	0.762416	−	0.647087i
$487$			11.0382i			0.500189i	0.968221	+	0.250095i	$0.0804618\pi$
$487$			11.0382i			0.500189i	−0.968221	+	0.250095i	$0.919538\pi$
$488$	−1.98847	−	3.65219i	−0.0900138	−	0.165327i
$489$	7.38848	+	5.46851i	0.334118	+	0.247294i
$490$	−1.39336	+	0.0694998i	−0.0629455	+	0.00313968i
$491$	0.825550	+	0.300476i	0.0372566	+	0.0135603i	0.360581	−	0.932728i	$-0.382578\pi$
$491$	0.825550	+	0.300476i	0.0372566	+	0.0135603i	−0.323325	+	0.946288i	$0.604801\pi$
$492$	−0.464903	+	33.4775i	−0.0209594	+	1.50928i
$493$	−8.41684	+	47.7343i	−0.379076	+	2.14984i
$494$	−10.9748	−	8.31355i	−0.493778	−	0.374044i
$495$	−12.2149	+	3.73139i	−0.549021	+	0.167713i
$496$	2.32861	−	0.0578060i	0.104558	−	0.00259557i
$497$	5.64438	+	15.5078i	0.253185	+	0.695620i
$498$	14.7786	+	9.83788i	0.662243	+	0.440846i
$499$	4.23068	+	5.04193i	0.189391	+	0.225708i	0.852382	−	0.522920i	$-0.175157\pi$
$499$	4.23068	+	5.04193i	0.189391	+	0.225708i	−0.662990	+	0.748628i	$0.730713\pi$
$500$	−7.72638	−	16.0463i	−0.345534	−	0.717614i
$501$	−9.88873	+	6.54356i	−0.441796	+	0.292345i
$502$	8.19465	−	1.87013i	0.365745	−	0.0834680i
$503$	−15.7466	−	27.2739i	−0.702105	−	1.21608i	−0.967726	−	0.252004i	$-0.918910\pi$
$503$	−15.7466	−	27.2739i	−0.702105	−	1.21608i	0.265621	−	0.964077i	$-0.414423\pi$
$504$	6.05766	+	5.94178i	0.269829	+	0.264668i
$505$	0.723486	−	1.25311i	0.0321947	−	0.0557628i
$506$	13.3567	−	43.2971i	0.593779	−	1.92479i
$507$	−8.17434	−	8.61596i	−0.363035	−	0.382648i
$508$	−11.6992	+	17.1575i	−0.519067	+	0.761239i
$509$	−37.0009	+	6.52426i	−1.64004	+	0.289183i	−0.916180	−	0.400767i	$-0.868744\pi$
$509$	−37.0009	+	6.52426i	−1.64004	+	0.289183i	−0.723857	+	0.689950i	$0.757632\pi$
$510$	3.64989	+	12.4423i	0.161620	+	0.550952i
$511$	−4.60681	+	5.49019i	−0.203793	+	0.242872i
$512$	9.81243	+	20.3891i	0.433652	+	0.901080i
$513$	−13.2500	−	15.5247i	−0.585004	−	0.685433i
$514$	−1.71490	+	13.6814i	−0.0756409	+	0.603461i
$515$	0.450956	+	0.378397i	0.0198715	+	0.0166742i
$516$	0.386486	−	1.01767i	0.0170141	−	0.0448002i
$517$	−5.89119	−	33.4106i	−0.259094	−	1.46940i
$518$	0.848966	−	1.65585i	0.0373014	−	0.0727540i
$519$	−8.65286	−	2.56418i	−0.379818	−	0.112555i
$520$	−5.90062	−	3.60649i	−0.258759	−	0.158155i
$521$	24.8278	+	14.3343i	1.08772	+	0.627997i	0.932969	−	0.359956i	$-0.117208\pi$
$521$	24.8278	+	14.3343i	1.08772	+	0.627997i	0.154754	+	0.987953i	$0.450541\pi$
$522$	−13.0079	−	36.0473i	−0.569339	−	1.57775i
$523$	14.5518	−	8.40146i	0.636304	−	0.367370i	−0.146885	−	0.989154i	$-0.546925\pi$
$523$	14.5518	−	8.40146i	0.636304	−	0.367370i	0.783189	+	0.621783i	$0.213592\pi$
$524$	20.5921	−	2.05936i	0.899570	−	0.0899637i
$525$	−6.96177	+	0.424991i	−0.303836	+	0.0185481i
$526$	25.4742	−	16.4520i	1.11073	−	0.717339i
$527$	2.39379	−	2.00863i	0.104275	−	0.0874972i
$528$	−12.6764	+	27.0802i	−0.551671	+	1.17852i
$529$	−30.1766	+	10.9834i	−1.31202	+	0.477538i
$530$	−2.33705	−	5.54457i	−0.101515	−	0.240841i
$531$	−0.900757	+	17.1117i	−0.0390895	+	0.742583i
$532$	5.48562	−	5.62349i	0.237832	−	0.243809i
$533$	−23.5910	−	4.15973i	−1.02184	−	0.180178i
$534$	−32.1359	−	14.0740i	−1.39066	−	0.609041i
$535$	−1.79275	+	4.92554i	−0.0775074	+	0.212950i
$536$	−12.4076	−	2.50935i	−0.535926	−	0.108387i
$537$	−35.6224	−	4.06284i	−1.53722	−	0.175325i
$538$	−13.9728	+	12.9641i	−0.602410	+	0.558922i
$539$	−4.31574			−0.185892
$540$	−7.39823	−	7.09685i	−0.318369	−	0.305400i
$541$	17.7897			0.764839			0.382420	−	0.923989i	$-0.375091\pi$
$541$	17.7897			0.764839			0.382420	+	0.923989i	$0.375091\pi$
$542$	20.7105	−	19.2155i	0.889594	−	0.825376i
$543$	14.0561	+	32.3371i	0.603207	+	1.38772i
$544$	27.3474	+	13.1746i	1.17251	+	0.564857i
$545$	−6.33441	+	17.4036i	−0.271336	+	0.745490i
$546$	−4.88979	+	3.59834i	−0.209264	+	0.153995i
$547$	5.15169	+	0.908381i	0.220270	+	0.0388396i	0.282694	−	0.959210i	$-0.408772\pi$
$547$	5.15169	+	0.908381i	0.220270	+	0.0388396i	−0.0624238	+	0.998050i	$0.519883\pi$
$548$	−22.6008	−	22.0467i	−0.965460	−	0.941790i
$549$	4.37792	−	0.536512i	0.186845	−	0.0228978i
$550$	−9.54610	−	22.6478i	−0.407047	−	0.965707i
$551$	−33.3404	+	12.1349i	−1.42035	+	0.516965i
$552$	35.5665	−	7.59876i	1.51381	−	0.323425i
$553$	−6.00220	+	5.03644i	−0.255240	+	0.214171i
$554$	10.5469	−	6.81147i	0.448094	−	0.289392i
$555$	−1.00337	+	2.01187i	−0.0425908	+	0.0853991i
$556$	−1.95411	−	19.5397i	−0.0828728	−	0.828666i
$557$	−29.7970	+	17.2033i	−1.26254	+	0.728927i	−0.973565	−	0.228410i	$-0.926647\pi$
$557$	−29.7970	+	17.2033i	−1.26254	+	0.728927i	−0.288974	+	0.957337i	$0.593314\pi$
$558$	−0.851393	+	2.31929i	−0.0360423	+	0.0981835i
$559$	0.674517	+	0.389432i	0.0285290	+	0.0164712i
$560$	2.46059	−	3.08476i	0.103979	−	0.130355i
$561$	9.35952	+	39.0051i	0.395159	+	1.64680i
$562$	2.03468	−	3.96852i	0.0858280	−	0.167402i
$563$	−4.57179	−	25.9279i	−0.192678	−	1.09273i	−0.915687	−	0.401892i	$-0.868353\pi$
$563$	−4.57179	−	25.9279i	−0.192678	−	1.09273i	0.723009	−	0.690838i	$-0.242758\pi$
$564$	21.1014	−	17.2126i	0.888530	−	0.724780i
$565$	−14.2766	−	11.9795i	−0.600620	−	0.503980i
$566$	−2.89070	+	23.0619i	−0.121505	+	0.969364i
$567$	−8.22360	+	3.65682i	−0.345359	+	0.153572i
$568$	−43.4496	−	17.0570i	−1.82310	−	0.715696i
$569$	26.7944	−	31.9324i	1.12328	−	1.33867i	0.189066	−	0.981964i	$-0.439454\pi$
$569$	26.7944	−	31.9324i	1.12328	−	1.33867i	0.934215	−	0.356710i	$-0.116102\pi$
$570$	−6.55159	+	6.86757i	−0.274416	+	0.287651i
$571$	−14.7739	+	2.60504i	−0.618268	+	0.109017i	−0.474005	−	0.880522i	$-0.657192\pi$
$571$	−14.7739	+	2.60504i	−0.618268	+	0.109017i	−0.144263	+	0.989539i	$0.546081\pi$
$572$	−17.6752	−	12.0523i	−0.739039	−	0.503930i
$573$	44.6803	−	10.7213i	1.86655	−	0.447889i
$574$	4.02922	−	13.0611i	0.168176	−	0.545159i
$575$	−14.9474	+	25.8896i	−0.623348	+	1.07967i
$576$	−23.9380	+	1.72420i	−0.997416	+	0.0718418i
$577$	7.04222	+	12.1975i	0.293171	+	0.507788i	0.974558	−	0.224136i	$-0.0719560\pi$
$577$	7.04222	+	12.1975i	0.293171	+	0.507788i	−0.681387	+	0.731924i	$0.738623\pi$
$578$	16.2631	−	3.71145i	0.676454	−	0.154376i
$579$	18.5033	+	9.22806i	0.768969	+	0.383505i
$580$	−16.0567	+	7.73138i	−0.666719	+	0.321028i
$581$	−4.65884	−	5.55219i	−0.193281	−	0.230344i
$582$	10.7908	−	5.34458i	0.447291	−	0.221540i
$583$	−6.36625	−	17.4911i	−0.263663	−	0.724409i
$584$	−3.01954	−	20.0450i	−0.124950	−	0.829468i
$585$	5.85901	−	4.41295i	0.242240	−	0.182453i
$586$	−8.34237	−	6.31947i	−0.344620	−	0.261055i
$587$	7.93519	−	45.0027i	0.327520	−	1.85746i	−0.163817	−	0.986491i	$-0.552381\pi$
$587$	7.93519	−	45.0027i	0.327520	−	1.85746i	0.491338	−	0.870969i	$-0.336508\pi$
$588$	−1.69023	−	3.02376i	−0.0697038	−	0.124698i
$589$	2.14944	+	0.782330i	0.0885659	+	0.0322354i
$590$	7.95856	−	0.396968i	0.327649	−	0.0163429i
$591$	−21.3868	+	9.29632i	−0.879737	+	0.382399i
$592$	1.92228	+	4.89955i	0.0790054	+	0.201370i
$593$		−	3.88748i		−	0.159640i	−0.996809	−	0.0798199i	$-0.974565\pi$
$593$		−	3.88748i		−	0.159640i	0.996809	−	0.0798199i	$-0.0254345\pi$
$594$	−21.7645	−	23.0671i	−0.893007	−	0.946456i
$595$		−	5.29357i		−	0.217015i
$596$	1.63489	−	1.17526i	0.0669677	−	0.0481407i
$597$	2.03057	−	17.8037i	0.0831056	−	0.728659i
$598$	1.29633	+	25.9893i	0.0530108	+	1.06278i
$599$	−10.4647	−	3.80883i	−0.427575	−	0.155625i	0.119263	−	0.992863i	$-0.461947\pi$
$599$	−10.4647	−	3.80883i	−0.427575	−	0.155625i	−0.546839	+	0.837238i	$0.684169\pi$
$600$	12.1292	−	15.5582i	0.495173	−	0.635160i
$601$	−0.800982	+	4.54259i	−0.0326727	+	0.185296i	−0.996776	−	0.0802299i	$-0.974435\pi$
$601$	−0.800982	+	4.54259i	−0.0326727	+	0.185296i	0.964104	+	0.265526i	$0.0855457\pi$
$602$	−0.268348	+	0.354248i	−0.0109371	+	0.0144381i
$603$	7.31530	−	11.2589i	0.297902	−	0.458496i
$604$	29.2379	−	8.22447i	1.18967	−	0.334649i
$605$	2.57286	+	7.06886i	0.104601	+	0.287390i
$606$	3.58563	+	0.228801i	0.145656	+	0.00929442i
$607$	11.4868	+	13.6894i	0.466234	+	0.555637i	0.947009	−	0.321208i	$-0.104089\pi$
$607$	11.4868	+	13.6894i	0.466234	+	0.555637i	−0.480774	+	0.876844i	$0.659644\pi$
$608$	1.65734	+	22.1580i	0.0672139	+	0.898627i
$609$	0.953302	+	15.6160i	0.0386298	+	0.632793i
$610$	−0.456355	−	1.99968i	−0.0184773	−	0.0809648i
$611$	9.74178	+	16.8733i	0.394110	+	0.682619i
$612$	−23.6628	+	21.8336i	−0.956510	+	0.882572i
$613$	−10.7220	+	18.5710i	−0.433057	+	0.750077i	−0.997135	−	0.0756446i	$-0.975899\pi$
$613$	−10.7220	+	18.5710i	−0.433057	+	0.750077i	0.564078	+	0.825722i	$0.309232\pi$
$614$	18.7763	+	5.79232i	0.757751	+	0.233759i
$615$	−4.69206	+	15.8334i	−0.189202	+	0.638464i
$616$	8.07783	−	9.15171i	0.325465	−	0.368733i
$617$	11.3980	−	2.00978i	0.458867	−	0.0809106i	0.0605633	−	0.998164i	$-0.480710\pi$
$617$	11.3980	−	2.00978i	0.458867	−	0.0809106i	0.398303	+	0.917254i	$0.369599\pi$
$618$	−0.344983	+	1.42044i	−0.0138773	+	0.0571386i
$619$	25.5009	−	30.3908i	1.02497	−	1.22151i	0.0500950	−	0.998744i	$-0.484048\pi$
$619$	25.5009	−	30.3908i	1.02497	−	1.22151i	0.974872	−	0.222764i	$-0.0715080\pi$
$620$	1.11337	+	0.283567i	0.0447141	+	0.0113883i
$621$	−6.37998	+	38.0441i	−0.256020	+	1.52666i
$622$	36.9738	+	4.63449i	1.48251	+	0.185826i
$623$	10.9716	+	9.20628i	0.439569	+	0.368842i
$624$	1.52186	−	17.1041i	0.0609233	−	0.684710i
$625$	1.97089	+	11.1775i	0.0788357	+	0.447100i
$626$	10.2939	+	5.27775i	0.411427	+	0.210941i
$627$	−21.3007	+	20.2089i	−0.850668	+	0.807067i
$628$	−7.18426	+	15.9195i	−0.286683	+	0.635259i
$629$	6.11473	+	3.53034i	0.243810	+	0.140764i
$630$	2.08265	+	3.63030i	0.0829747	+	0.144635i
$631$	2.40181	−	1.38669i	0.0956146	−	0.0552031i	−0.451430	−	0.892306i	$-0.649086\pi$
$631$	2.40181	−	1.38669i	0.0956146	−	0.0552031i	0.547045	+	0.837103i	$0.315753\pi$
$632$	0.554401	−	22.1547i	0.0220529	−	0.881266i
$633$	11.6905	+	17.6668i	0.464654	+	0.702192i
$634$	−2.38778	−	3.69724i	−0.0948308	−	0.146836i
$635$	−7.84649	+	6.58399i	−0.311378	+	0.261278i
$636$	9.76161	−	11.3107i	0.387073	−	0.448498i
$637$	2.32904	−	0.847701i	0.0922799	−	0.0335871i
$638$	−50.8016	+	21.4130i	−2.01126	+	0.847748i
$639$	33.7736	−	36.2009i	1.33606	−	1.43209i
$640$	1.93584	+	10.9916i	0.0765210	+	0.434479i
$641$	1.16673	+	0.205726i	0.0460830	+	0.00812568i	0.196642	−	0.980475i	$-0.436996\pi$
$641$	1.16673	+	0.205726i	0.0460830	+	0.00812568i	−0.150559	+	0.988601i	$0.548107\pi$
$642$	−12.9355	+	1.43927i	−0.510525	+	0.0568034i
$643$	−14.9226	+	40.9995i	−0.588490	+	1.61686i	0.184774	+	0.982781i	$0.440845\pi$
$643$	−14.9226	+	40.9995i	−0.588490	+	1.61686i	−0.773265	+	0.634083i	$0.781378\pi$
$644$	−14.8061	−	1.11041i	−0.583441	−	0.0437564i
$645$	0.319429	−	0.431579i	0.0125775	−	0.0169934i
$646$	20.2745	+	21.8520i	0.797689	+	0.859754i
$647$	7.93604			0.311998			0.155999	−	0.987757i	$-0.450140\pi$
$647$	7.93604			0.311998			0.155999	+	0.987757i	$0.450140\pi$
$648$	7.63777	−	24.2830i	0.300040	−	0.953927i
$649$	24.6506			0.967620
$650$	9.60016	+	10.3471i	0.376549	+	0.405847i
$651$	0.600049	−	0.810724i	0.0235178	−	0.0317748i
$652$	10.5844	+	0.793796i	0.414516	+	0.0310874i
$653$	14.3361	−	39.3882i	0.561016	−	1.54138i	−0.257135	−	0.966375i	$-0.582779\pi$
$653$	14.3361	−	39.3882i	0.561016	−	1.54138i	0.818151	−	0.575003i	$-0.194999\pi$
$654$	−45.7057	+	5.08543i	−1.78724	+	0.198856i
$655$	10.0524	+	1.77251i	0.392781	+	0.0692578i
$656$	20.1550	+	32.9907i	0.786922	+	1.28807i
$657$	20.9486	+	4.84148i	0.817283	+	0.188884i
$658$	−10.2443	+	4.31799i	−0.399364	+	0.168333i
$659$	−29.2861	+	10.6593i	−1.14083	+	0.415226i	−0.842211	−	0.539148i	$-0.818746\pi$
$659$	−29.2861	+	10.6593i	−1.14083	+	0.415226i	−0.298614	+	0.954374i	$0.596524\pi$
$660$	−9.63580	+	11.1649i	−0.375073	+	0.434594i
$661$	−22.4763	+	18.8598i	−0.874226	+	0.733563i	−0.964984	−	0.262310i	$-0.915516\pi$
$661$	−22.4763	+	18.8598i	−0.874226	+	0.733563i	0.0907575	+	0.995873i	$0.471071\pi$
$662$	16.0953	+	24.9220i	0.625563	+	0.968621i
$663$	−12.7124	−	19.2111i	−0.493707	−	0.746098i
$664$	20.4937	+	0.512835i	0.795308	+	0.0199019i
$665$	3.35572	−	1.93743i	0.130129	−	0.0751302i
$666$	−5.58239	−	0.0153706i	−0.216313	−	0.000595598i
$667$	58.0733	+	33.5286i	2.24861	+	1.29823i
$668$	−5.63210	+	12.4801i	−0.217912	+	0.482870i
$669$	6.02176	−	5.71311i	0.232815	−	0.220882i
$670$	−5.55611	−	2.84865i	−0.214651	−	0.110053i
$671$	−1.10182	−	6.24872i	−0.0425352	−	0.241229i
$672$	9.57563	+	2.07541i	0.369388	+	0.0800608i
$673$	16.5972	+	13.9267i	0.639777	+	0.536836i	0.903950	−	0.427639i	$-0.140655\pi$
$673$	16.5972	+	13.9267i	0.639777	+	0.536836i	−0.264173	+	0.964475i	$0.585099\pi$
$674$	24.3057	+	3.04660i	0.936219	+	0.117351i
$675$	10.6136	+	18.0326i	0.408516	+	0.694074i
$676$	−13.2897	−	3.38478i	−0.511142	−	0.130184i
$677$	27.1075	−	32.3055i	1.04183	−	1.24160i	0.0721032	−	0.997397i	$-0.477029\pi$
$677$	27.1075	−	32.3055i	1.04183	−	1.24160i	0.969724	−	0.244204i	$-0.0785267\pi$
$678$	10.9216	−	44.9690i	0.419442	−	1.72702i
$679$	−4.84136	+	0.853662i	−0.185794	+	0.0327606i
$680$	11.2252	+	9.90804i	0.430468	+	0.379956i
$681$	6.50896	−	21.9645i	0.249424	−	0.841683i
$682$	3.39626	+	1.04771i	0.130050	+	0.0401191i
$683$	7.26027	−	12.5752i	0.277807	−	0.481175i	−0.693033	−	0.720906i	$-0.743726\pi$
$683$	7.26027	−	12.5752i	0.277807	−	0.481175i	0.970839	+	0.239731i	$0.0770592\pi$
$684$	−22.5013	−	7.00935i	−0.860360	−	0.268009i
$685$	−7.78653	−	13.4867i	−0.297508	−	0.515299i
$686$	0.314653	+	1.37877i	0.0120135	+	0.0526415i
$687$	−2.89136	−	47.3634i	−0.110312	−	1.80702i
$688$	−0.248927	−	1.23209i	−0.00949024	−	0.0469731i
$689$	6.87124	+	8.18882i	0.261773	+	0.311969i
$690$	17.9023	+	1.14235i	0.681528	+	0.0434887i
$691$	6.04236	+	16.6012i	0.229862	+	0.631541i	0.999980	−	0.00636093i	$-0.00202476\pi$
$691$	6.04236	+	16.6012i	0.229862	+	0.631541i	−0.770118	+	0.637902i	$0.779803\pi$
$692$	−10.0316	+	2.82184i	−0.381345	+	0.107270i
$693$	5.87525	+	11.5374i	0.223182	+	0.438271i
$694$	6.16820	−	8.14267i	0.234142	−	0.309092i
$695$	1.68192	−	9.53865i	0.0637989	−	0.361822i
$696$	−34.8987	−	27.2072i	−1.32283	−	1.03129i
$697$	48.7362	+	17.7385i	1.84601	+	0.671894i
$698$	0.585381	+	11.7360i	0.0221570	+	0.444212i
$699$	−4.94305	+	43.3400i	−0.186963	+	1.63927i
$700$	−6.53939	+	4.70094i	−0.247166	+	0.177679i
$701$			0.645862i			0.0243939i	0.999926	+	0.0121969i	$0.00388250\pi$
$701$			0.645862i			0.0243939i	−0.999926	+	0.0121969i	$0.996117\pi$
$702$	16.2763	+	8.17345i	0.614309	+	0.308487i
$703$			5.16837i			0.194929i
$704$	4.28722	+	34.2587i	0.161581	+	1.29117i
$705$	12.3181	−	5.35438i	0.463928	−	0.201658i
$706$	15.9332	−	0.794738i	0.599655	−	0.0299104i
$707$	−1.37835	−	0.501677i	−0.0518381	−	0.0188675i
$708$	9.65421	+	17.2711i	0.362827	+	0.649087i
$709$	2.71750	−	15.4117i	0.102058	−	0.578798i	−0.890297	−	0.455380i	$-0.849503\pi$
$709$	2.71750	−	15.4117i	0.102058	−	0.578798i	0.992355	−	0.123418i	$-0.0393855\pi$
$710$	−18.3522	−	13.9021i	−0.688745	−	0.521735i
$711$	21.6352	+	9.18951i	0.811384	+	0.344634i
$712$	−40.0580	+	6.03427i	−1.50124	+	0.226144i
$713$	−1.47860	−	4.06242i	−0.0553740	−	0.152139i
$714$	11.7787	−	5.83390i	0.440807	−	0.218328i
$715$	−6.78268	−	8.08328i	−0.253658	−	0.302298i
$716$	−37.3011	+	17.9606i	−1.39401	+	0.671220i
$717$	−1.87755	−	0.936382i	−0.0701183	−	0.0349698i
$718$	−9.76081	+	2.22755i	−0.364270	+	0.0831313i
$719$	25.2430	+	43.7222i	0.941406	+	1.63056i	0.762791	+	0.646645i	$0.223828\pi$
$719$	25.2430	+	43.7222i	0.941406	+	1.63056i	0.178615	+	0.983919i	$0.442838\pi$
$720$	−11.5963	−	2.37853i	−0.432169	−	0.0886427i
$721$	0.298376	−	0.516802i	0.0111121	−	0.0192467i
$722$	1.48873	−	4.82586i	0.0554048	−	0.179600i
$723$	−48.8475	+	11.7213i	−1.81666	+	0.435918i
$724$	33.6388	+	22.9373i	1.25017	+	0.852459i
$725$	35.8208	−	6.31618i	1.33035	−	0.234577i
$726$	−12.8934	+	13.5153i	−0.478520	+	0.501598i
$727$	−28.2438	+	33.6596i	−1.04750	+	1.24837i	−0.0796576	+	0.996822i	$0.525383\pi$
$727$	−28.2438	+	33.6596i	−1.04750	+	1.24837i	−0.967846	+	0.251544i	$0.919062\pi$
$728$	−2.56170	+	6.52548i	−0.0949431	+	0.241850i
$729$	20.9711	+	17.0062i	0.776709	+	0.629860i
$730$	1.24354	−	9.92088i	0.0460253	−	0.367188i
$731$	−1.29177	−	1.08393i	−0.0477780	−	0.0400905i
$732$	3.94655	−	3.21923i	0.145869	−	0.118986i
$733$	3.07790	+	17.4557i	0.113685	+	0.644740i	0.987393	+	0.158289i	$0.0505977\pi$
$733$	3.07790	+	17.4557i	0.113685	+	0.644740i	−0.873708	+	0.486451i	$0.838291\pi$
$734$	3.20746	−	6.25595i	0.118390	−	0.230911i
$735$	−0.398679	−	1.66147i	−0.0147055	−	0.0612841i
$736$	30.0674	−	29.3185i	1.10830	−	1.08070i
$737$	−16.7276	−	9.65768i	−0.616169	−	0.355745i
$738$	−40.4018	+	7.00929i	−1.48721	+	0.258015i
$739$	−39.6044	+	22.8656i	−1.45687	+	0.841124i	−0.998856	−	0.0478205i	$-0.984772\pi$
$739$	−39.6044	+	22.8656i	−1.45687	+	0.841124i	−0.458014	+	0.888945i	$0.651439\pi$
$740$	0.258330	+	2.58310i	0.00949639	+	0.0949568i
$741$	7.52571	−	15.0899i	0.276464	−	0.554340i
$742$	−5.12380	+	3.30909i	−0.188101	+	0.121481i
$743$	−17.7377	+	14.8837i	−0.650732	+	0.546029i	−0.907293	−	0.420499i	$-0.861855\pi$
$743$	−17.7377	+	14.8837i	−0.650732	+	0.546029i	0.256561	+	0.966528i	$0.417411\pi$
$744$	0.596054	+	2.78987i	0.0218524	+	0.102282i
$745$	0.933234	−	0.339670i	0.0341911	−	0.0124445i
$746$	−1.90540	−	4.52050i	−0.0697616	−	0.165507i
$747$	−8.50054	+	20.0131i	−0.311019	+	0.732242i
$748$	33.1555	+	32.3426i	1.21228	+	1.18256i
$749$	5.23278	+	0.922680i	0.191202	+	0.0337140i
$750$	17.5681	−	12.9281i	0.641495	−	0.472068i
$751$	11.5045	−	31.6083i	0.419805	−	1.15340i	−0.532012	−	0.846737i	$-0.678564\pi$
$751$	11.5045	−	31.6083i	0.419805	−	1.15340i	0.951817	−	0.306668i	$-0.0992140\pi$
$752$	10.0179	−	29.8055i	0.365315	−	1.08689i
$753$	4.10379	+	9.44106i	0.149550	+	0.344051i
$754$	23.2097	−	21.5342i	0.845248	−	0.784231i
$755$	14.9810			0.545213
$756$	−5.78253	+	8.63495i	−0.210309	+	0.314050i
$757$	3.74915			0.136265			0.0681325	−	0.997676i	$-0.478296\pi$
$757$	3.74915			0.136265			0.0681325	+	0.997676i	$0.478296\pi$
$758$	−31.0704	+	28.8275i	−1.12853	+	1.04706i
$759$	55.1363	+	6.28846i	2.00132	+	0.228256i
$760$	−2.17255	+	10.7422i	−0.0788066	+	0.389662i
$761$	2.92689	−	8.04156i	0.106100	−	0.291506i	−0.875270	−	0.483634i	$-0.839317\pi$
$761$	2.92689	−	8.04156i	0.106100	−	0.291506i	0.981370	+	0.192128i	$0.0615388\pi$
$762$	−23.2974	−	10.2032i	−0.843976	−	0.369621i
$763$	18.4892	+	3.26015i	0.669354	+	0.118025i
$764$	37.0484	−	37.9795i	1.34036	−	1.37405i
$765$	−14.1515	+	7.20642i	−0.511648	+	0.260549i
$766$	18.9350	+	44.9227i	0.684149	+	1.62312i
$767$	−13.3030	+	4.84188i	−0.480342	+	0.174830i
$768$	−22.3238	+	16.4209i	−0.805541	+	0.592540i
$769$	−41.9323	+	35.1854i	−1.51212	+	1.26882i	−0.652609	+	0.757695i	$0.726325\pi$
$769$	−41.9323	+	35.1854i	−1.51212	+	1.26882i	−0.859508	+	0.511122i	$0.829230\pi$
$770$	5.05776	−	3.26645i	0.182269	−	0.117715i
$771$	−16.8560	+	1.02900i	−0.607053	+	0.0370584i
$772$	23.7569	−	2.37587i	0.855031	−	0.0855094i
$773$	16.3551	−	9.44261i	0.588251	−	0.339627i	−0.176155	−	0.984363i	$-0.556366\pi$
$773$	16.3551	−	9.44261i	0.588251	−	0.339627i	0.764406	+	0.644736i	$0.223033\pi$
$774$	1.31234	+	0.235129i	0.0471711	+	0.00845152i
$775$	−2.03080	−	1.17249i	−0.0729486	−	0.0421169i
$776$	7.25140	−	11.8641i	0.260310	−	0.425897i
$777$	2.18508	+	0.647527i	0.0783895	+	0.0232299i
$778$	10.9848	−	21.4251i	0.393823	−	0.768127i
$779$	6.59238	+	37.3872i	0.236196	+	1.33954i
$780$	3.00705	−	7.91794i	0.107670	−	0.283508i
$781$	−54.5599	−	45.7812i	−1.95231	−	1.63818i
$782$	7.00692	−	55.9009i	0.250567	−	1.99901i
$783$	40.4491	−	23.8074i	1.44553	−	0.850807i
$784$	−3.51267	−	1.91342i	−0.125452	−	0.0683363i
$785$	−5.53741	+	6.59923i	−0.197639	+	0.235537i
$786$	7.13449	+	24.3210i	0.254479	+	0.867503i
$787$	−52.2194	+	9.20770i	−1.86142	+	0.328219i	−0.987472	−	0.157796i	$-0.949561\pi$
$787$	−52.2194	+	9.20770i	−1.86142	+	0.328219i	−0.873950	+	0.486015i	$0.838450\pi$
$788$	−15.1701	+	22.2477i	−0.540412	+	0.792541i
$789$	25.5626	+	26.9436i	0.910052	+	0.959217i
$790$	3.22226	−	10.4452i	0.114643	−	0.371625i
$791$	−9.44610	+	16.3611i	−0.335865	+	0.581734i
$792$	−35.4624	−	9.13603i	−1.26010	−	0.324635i
$793$	1.82198	+	3.15577i	0.0647006	+	0.112065i
$794$	−6.13125	+	1.39923i	−0.217590	+	0.0496570i
$795$	6.14560	−	4.06666i	0.217962	−	0.144230i
$796$	−8.97654	−	18.6427i	−0.318165	−	0.660773i
$797$	−27.3758	−	32.6252i	−0.969700	−	1.15564i	−0.987787	−	0.155807i	$-0.950202\pi$
$797$	−27.3758	−	32.6252i	−0.969700	−	1.15564i	0.0180873	−	0.999836i	$-0.494242\pi$
$798$	8.00921	+	5.33161i	0.283523	+	0.188737i
$799$	−14.4275	−	39.6392i	−0.510408	−	1.40233i
$800$	2.27133	−	22.6658i	0.0803035	−	0.801359i
$801$	9.67523	−	41.8638i	0.341858	−	1.47919i
$802$	−15.8456	−	12.0033i	−0.559528	−	0.423851i
$803$	5.37105	−	30.4607i	0.189540	−	1.07494i
$804$	0.215281	−	15.5023i	0.00759236	−	0.546724i
$805$	−6.88179	−	2.50476i	−0.242551	−	0.0882814i
$806$	−2.03862	+	0.101685i	−0.0718075	+	0.00358171i
$807$	−18.7639	−	13.8879i	−0.660522	−	0.488879i
$808$	3.64370	−	1.98385i	0.128185	−	0.0697915i
$809$			51.4500i			1.80889i	0.426595	+	0.904443i	$0.359713\pi$
$809$			51.4500i			1.80889i	−0.426595	+	0.904443i	$0.640287\pi$
$810$	6.86979	−	10.5097i	0.241380	−	0.369274i
$811$			40.8705i			1.43516i	0.696478	+	0.717578i	$0.254750\pi$
$811$			40.8705i			1.43516i	−0.696478	+	0.717578i	$0.745250\pi$
$812$	10.5447	+	14.6686i	0.370047	+	0.514766i
$813$	27.8120	+	20.5848i	0.975410	+	0.721940i
$814$	0.400071	+	8.02078i	0.0140225	+	0.281128i
$815$	4.91956	+	1.79057i	0.172325	+	0.0627210i
$816$	−9.67530	+	35.8966i	−0.338703	+	1.25663i
$817$	0.214343	−	1.21560i	0.00749891	−	0.0425284i
$818$	13.4404	−	17.7428i	0.469933	−	0.620361i
$819$	−5.43683	−	5.07228i	−0.189978	−	0.177240i
$820$	5.16353	+	18.3563i	0.180318	+	0.641030i
$821$	3.35894	+	9.22861i	0.117228	+	0.322081i	0.984405	−	0.175920i	$-0.0562899\pi$
$821$	3.35894	+	9.22861i	0.117228	+	0.322081i	−0.867177	+	0.498001i	$0.834068\pi$
$822$	21.4278	−	32.1891i	0.747380	−	1.12272i
$823$	−10.0188	−	11.9399i	−0.349233	−	0.416199i	0.562621	−	0.826715i	$-0.309793\pi$
$823$	−10.0188	−	11.9399i	−0.349233	−	0.416199i	−0.911853	+	0.410516i	$0.865349\pi$
$824$	0.537426	+	1.60002i	0.0187221	+	0.0557394i
$825$	25.1028	−	16.6110i	0.873969	−	0.578322i
$826$	−1.79723	−	7.87521i	−0.0625336	−	0.274014i
$827$	3.86022	+	6.68610i	0.134233	+	0.232499i	0.925304	−	0.379226i	$-0.123810\pi$
$827$	3.86022	+	6.68610i	0.134233	+	0.232499i	−0.791071	+	0.611724i	$0.790476\pi$
$828$	17.1878	+	41.0933i	0.597317	+	1.42809i
$829$	−24.6587	+	42.7101i	−0.856432	+	1.48338i	0.0188778	+	0.999822i	$0.493991\pi$
$829$	−24.6587	+	42.7101i	−0.856432	+	1.48338i	−0.875310	+	0.483562i	$0.839343\pi$
$830$	9.66213	+	2.98067i	0.335377	+	0.103461i
$831$	10.5835	+	11.1552i	0.367137	+	0.386971i
$832$	−9.04277	−	17.6460i	−0.313502	−	0.611765i
$833$	−5.28461	+	0.931819i	−0.183101	+	0.0322856i
$834$	23.0780	−	6.76986i	0.799126	−	0.234421i
$835$	−4.34105	+	5.17347i	−0.150228	+	0.179035i
$836$	−8.36798	+	32.8553i	−0.289413	+	1.13632i
$837$	−2.98421	−	0.500452i	−0.103150	−	0.0172981i
$838$	45.4653	+	5.69886i	1.57057	+	0.196864i
$839$	24.5520	+	20.6015i	0.847628	+	0.711244i	0.959266	−	0.282504i	$-0.0911652\pi$
$839$	24.5520	+	20.6015i	0.847628	+	0.711244i	−0.111638	+	0.993749i	$0.535610\pi$
$840$	4.26942	+	2.26437i	0.147309	+	0.0781282i
$841$	−9.13210	−	51.7907i	−0.314900	−	1.78589i
$842$	2.24740	+	1.15226i	0.0774505	+	0.0397093i
$843$	5.23691	+	1.55190i	0.180369	+	0.0534504i
$844$	22.2964	+	10.0621i	0.767475	+	0.346351i
$845$	−5.85802	−	3.38213i	−0.201522	−	0.116349i
$846$	25.4895	+	21.5081i	0.876347	+	0.739464i
$847$	6.60400	−	3.81282i	0.226916	−	0.131010i
$848$	2.57321	−	17.0589i	0.0883643	−	0.585805i
$849$	−28.4131	+	1.73452i	−0.975134	+	0.0595285i
$850$	−16.5791	−	25.6711i	−0.568658	−	0.880510i
$851$	7.48286	−	6.27886i	0.256509	−	0.215237i
$852$	10.7080	−	56.1565i	0.366849	−	1.92389i
$853$	24.2535	−	8.82754i	0.830423	−	0.302249i	0.108390	−	0.994108i	$-0.465430\pi$
$853$	24.2535	−	8.82754i	0.830423	−	0.302249i	0.722032	+	0.691859i	$0.243208\pi$
$854$	−1.91597	+	0.807583i	−0.0655630	+	0.0276349i
$855$	−9.74771	−	6.33344i	−0.333365	−	0.216599i
$856$	−11.7508	+	9.36933i	−0.401635	+	0.320237i
$857$	10.4503	+	1.84267i	0.356976	+	0.0629445i	0.349260	−	0.937026i	$-0.386433\pi$
$857$	10.4503	+	1.84267i	0.356976	+	0.0629445i	0.00771559	+	0.999970i	$0.497544\pi$
$858$	10.5111	−	24.0005i	0.358842	−	0.819363i
$859$	−7.22808	+	19.8590i	−0.246619	+	0.677580i	0.753186	+	0.657808i	$0.228516\pi$
$859$	−7.22808	+	19.8590i	−0.246619	+	0.677580i	−0.999805	+	0.0197718i	$0.993706\pi$
$860$	0.0463676	−	0.618259i	0.00158112	−	0.0210825i
$861$	16.6325	+	1.89699i	0.566835	+	0.0646492i
$862$	−3.38508	−	3.64846i	−0.115296	−	0.124267i
$863$	1.73102			0.0589245			0.0294623	−	0.999566i	$-0.490621\pi$
$863$	1.73102			0.0589245			0.0294623	+	0.999566i	$0.490621\pi$
$864$	−7.48753	−	28.4242i	−0.254731	−	0.967012i
$865$	−5.14001			−0.174766
$866$	20.8957	+	22.5215i	0.710066	+	0.765313i
$867$	8.14435	+	18.7367i	0.276597	+	0.636330i
$868$	0.0871017	−	1.16140i	0.00295643	−	0.0394206i
$869$	11.5655	−	31.7759i	0.392332	−	1.07792i
$870$	−12.9365	−	17.5794i	−0.438587	−	0.595998i
$871$	10.9242	+	1.92623i	0.370152	+	0.0652678i
$872$	−41.5197	+	33.1051i	−1.40604	+	1.12108i
$873$	8.87292	+	11.7804i	0.300303	+	0.398707i
$874$	38.0014	−	16.0177i	1.28542	−	0.541806i
$875$	−8.36777	+	3.04562i	−0.282882	+	0.102961i
$876$	23.4454	−	8.16656i	0.792146	−	0.275922i
$877$	−1.10470	+	0.926949i	−0.0373029	+	0.0313009i	−0.661249	−	0.750167i	$-0.729973\pi$
$877$	−1.10470	+	0.926949i	−0.0373029	+	0.0313009i	0.623946	+	0.781468i	$0.285529\pi$
$878$	−3.09711	−	4.79556i	−0.104522	−	0.161842i
$879$	5.72061	−	11.4704i	0.192951	−	0.386888i
$880$	−2.54004	+	16.8390i	−0.0856248	+	0.567644i
$881$	43.1983	−	24.9406i	1.45539	−	0.840269i	0.456610	−	0.889667i	$-0.349063\pi$
$881$	43.1983	−	24.9406i	1.45539	−	0.840269i	0.998779	+	0.0493974i	$0.0157301\pi$
$882$	3.25755	−	2.71816i	0.109687	−	0.0915251i
$883$	16.9815	+	9.80425i	0.571471	+	0.329939i	0.757737	−	0.652560i	$-0.226305\pi$
$883$	16.9815	+	9.80425i	0.571471	+	0.329939i	−0.186265	+	0.982499i	$0.559638\pi$
$884$	−24.2455	−	10.9416i	−0.815463	−	0.368007i
$885$	2.27717	+	9.48994i	0.0765462	+	0.319001i
$886$	−18.1297	−	9.29522i	−0.609080	−	0.312279i
$887$	−0.0584203	−	0.331318i	−0.00196156	−	0.0111246i	0.983811	−	0.179208i	$-0.0573534\pi$
$887$	−0.0584203	−	0.331318i	−0.00196156	−	0.0111246i	−0.985773	+	0.168083i	$0.946242\pi$
$888$	−5.46296	+	3.42158i	−0.183325	+	0.114821i
$889$	7.95405	+	6.67424i	0.266770	+	0.223847i
$890$	−19.8259	−	2.48509i	−0.664567	−	0.0833003i
$891$	22.8451	−	31.4130i	0.765340	−	1.05238i
$892$	2.36565	−	9.28828i	0.0792078	−	0.310994i
$893$	19.8478	−	23.6537i	0.664182	−	0.791541i
$894$	1.78429	+	1.70220i	0.0596756	+	0.0569299i
$895$	−20.1098	+	3.54591i	−0.672197	+	0.118527i
$896$	10.6322	−	3.86739i	0.355196	−	0.129201i
$897$	−30.9901	+	7.43627i	−1.03473	+	0.248290i
$898$	−27.4965	−	8.48241i	−0.917570	−	0.283062i
$899$	−2.63002	+	4.55532i	−0.0877159	+	0.151928i
$900$	21.4696	+	11.0824i	0.715653	+	0.369412i
$901$	−11.5720	−	20.0433i	−0.385519	−	0.667738i
$902$	13.1248	+	57.5109i	0.437007	+	1.91490i
$903$	−0.487077	−	0.242918i	−0.0162089	−	0.00808381i
$904$	−17.0141	−	50.6541i	−0.565879	−	1.68473i
$905$	12.9085	+	15.3838i	0.429094	+	0.511374i
$906$	16.5101	+	33.3341i	0.548512	+	1.10745i
$907$	−2.28017	−	6.26471i	−0.0757117	−	0.208016i	0.896063	−	0.443927i	$-0.146415\pi$
$907$	−2.28017	−	6.26471i	−0.0757117	−	0.208016i	−0.971775	+	0.235911i	$0.924193\pi$
$908$	−7.16300	−	25.4644i	−0.237712	−	0.845065i
$909$	0.535265	+	4.36774i	0.0177536	+	0.144869i
$910$	−2.08788	+	2.75622i	−0.0692126	+	0.0913679i
$911$	−3.18695	+	18.0741i	−0.105588	+	0.598821i	0.885395	+	0.464839i	$0.153888\pi$
$911$	−3.18695	+	18.0741i	−0.105588	+	0.598821i	−0.990984	+	0.133983i	$0.957223\pi$
$912$	−26.2968	+	7.00462i	−0.870775	+	0.231946i
$913$	29.3935	+	10.6984i	0.972784	+	0.354065i
$914$	−0.499694	−	10.0181i	−0.0165284	−	0.331368i
$915$	2.30383	−	1.00142i	0.0761624	−	0.0331059i
$916$	−31.9821	−	44.4898i	−1.05672	−	1.46998i
$917$		−	10.3474i		−	0.341702i
$918$	−31.6309	−	23.5464i	−1.04398	−	0.777147i
$919$			21.0251i			0.693554i	0.937948	+	0.346777i	$0.112724\pi$
$919$			21.0251i			0.693554i	−0.937948	+	0.346777i	$0.887276\pi$
$920$	18.1922	−	9.90491i	0.599778	−	0.326555i
$921$	−2.72707	+	23.9106i	−0.0898600	+	0.787880i
$922$	−34.6970	+	1.73066i	−1.14268	+	0.0569963i
$923$	38.4363	+	13.9897i	1.26514	+	0.460475i
$924$	12.8422	+	7.65415i	0.422477	+	0.251803i
$925$	0.920073	−	5.21800i	0.0302518	−	0.171567i
$926$	17.0195	+	12.8925i	0.559294	+	0.423674i
$927$	−1.78778	−	0.0941086i	−0.0587183	−	0.00309093i
$928$	−50.8420	−	5.09484i	−1.66897	−	0.167246i
$929$	−2.07657	−	5.70533i	−0.0681300	−	0.187186i	0.900955	−	0.433912i	$-0.142867\pi$
$929$	−2.07657	−	5.70533i	−0.0681300	−	0.187186i	−0.969085	+	0.246727i	$0.920645\pi$
$930$	−0.0896074	+	1.40427i	−0.00293834	+	0.0460479i
$931$	−2.52485	−	3.00900i	−0.0827486	−	0.0986159i
$932$	21.8518	+	45.3823i	0.715778	+	1.48655i
$933$	2.78085	+	45.5530i	0.0910409	+	1.49134i
$934$	16.9944	−	3.87836i	0.556074	−	0.126904i
$935$	11.4228	+	19.7849i	0.373567	+	0.647037i
$936$	20.9322	−	2.03518i	0.684189	−	0.0665219i
$937$	−9.62642	+	16.6735i	−0.314482	+	0.544698i	−0.979327	−	0.202283i	$-0.935164\pi$
$937$	−9.62642	+	16.6735i	−0.314482	+	0.544698i	0.664846	+	0.746981i	$0.268497\pi$
$938$	−1.86579	+	6.04814i	−0.0609203	+	0.197479i
$939$	−4.02547	+	13.5840i	−0.131366	+	0.443296i
$940$	8.73748	−	12.8140i	0.284985	−	0.417945i
$941$	−19.2850	+	3.40046i	−0.628672	+	0.110852i	−0.478901	−	0.877869i	$-0.658965\pi$
$941$	−19.2850	+	3.40046i	−0.628672	+	0.110852i	−0.149771	+	0.988721i	$0.547854\pi$
$942$	−20.7866	−	5.04844i	−0.677263	−	0.164487i
$943$	46.1211	−	54.9650i	1.50191	−	1.78991i
$944$	20.0636	+	10.9290i	0.653014	+	0.355709i
$945$	−3.89891	+	3.32764i	−0.126832	+	0.108248i
$946$	0.238542	−	1.90308i	0.00775566	−	0.0618744i
$947$	28.3474	+	23.7863i	0.921166	+	0.772950i	0.974210	−	0.225642i	$-0.0724480\pi$
$947$	28.3474	+	23.7863i	0.921166	+	0.772950i	−0.0530444	+	0.998592i	$0.516892\pi$
$948$	26.7928	−	4.34160i	0.870191	−	0.141009i
$949$	3.08457	+	17.4935i	0.100129	+	0.567862i
$950$	10.2056	−	19.9054i	0.331114	−	0.645816i
$951$	3.91050	−	3.71006i	0.126807	−	0.120307i
$952$	7.91530	−	12.9503i	0.256536	−	0.419723i
$953$	−2.89030	−	1.66872i	−0.0936260	−	0.0540550i	0.452456	−	0.891787i	$-0.350548\pi$
$953$	−2.89030	−	1.66872i	−0.0936260	−	0.0540550i	−0.546082	+	0.837732i	$0.683881\pi$
$954$	15.8216	+	9.19279i	0.512244	+	0.297628i
$955$	22.6636	−	13.0849i	0.733378	−	0.423416i
$956$	−2.41064	+	0.241082i	−0.0779658	+	0.00779716i
$957$	−37.2604	−	56.3085i	−1.20446	−	1.82019i
$958$	4.18758	−	2.70445i	0.135294	−	0.0873769i
$959$	−12.0932	+	10.1474i	−0.390509	+	0.327676i
$960$	−12.7928	+	4.81524i	−0.412886	+	0.155411i
$961$	−28.8118	+	10.4866i	−0.929413	+	0.338279i
$962$	−1.79135	−	4.24992i	−0.0577554	−	0.137023i
$963$	−4.65702	−	15.2451i	−0.150070	−	0.491265i
$964$	−40.5038	+	41.5218i	−1.30454	+	1.33733i
$965$	11.5974	+	2.04493i	0.373333	+	0.0658287i
$966$	−2.01089	−	18.0731i	−0.0646994	−	0.581491i
$967$	3.09624	−	8.50685i	0.0995684	−	0.273562i	−0.879900	−	0.475158i	$-0.842391\pi$
$967$	3.09624	−	8.50685i	0.0995684	−	0.273562i	0.979469	+	0.201597i	$0.0646130\pi$
$968$	−4.27554	+	21.1406i	−0.137421	+	0.679483i
$969$	−21.7193	+	29.3448i	−0.697724	+	0.942691i
$970$	5.02764	−	4.66470i	0.161428	−	0.149775i
$971$	−54.9997			−1.76502			−0.882512	−	0.470291i	$-0.844149\pi$
$971$	−54.9997			−1.76502			−0.882512	+	0.470291i	$0.844149\pi$
$972$	30.9562	+	3.70344i	0.992920	+	0.118788i
$973$	−9.81856			−0.314769
$974$	−11.4435	+	10.6174i	−0.366674	+	0.340205i
$975$	−10.2843	+	13.8950i	−0.329360	+	0.444997i
$976$	1.87362	−	5.57445i	0.0599732	−	0.178434i
$977$	−16.1586	+	44.3955i	−0.516960	+	1.42034i	0.356892	+	0.934146i	$0.383836\pi$
$977$	−16.1586	+	44.3955i	−0.516960	+	1.42034i	−0.873853	+	0.486191i	$0.838386\pi$
$978$	1.43752	+	12.9198i	0.0459668	+	0.413130i
$979$	−60.8729	−	10.7335i	−1.94551	−	0.343045i
$980$	−1.41229	−	1.37767i	−0.0451141	−	0.0440081i
$981$	−16.4549	−	53.8661i	−0.525364	−	1.71981i
$982$	0.482571	+	1.14489i	0.0153995	+	0.0365348i
$983$	8.76948	−	3.19183i	0.279703	−	0.101804i	−0.198360	−	0.980129i	$-0.563561\pi$
$983$	8.76948	−	3.19183i	0.279703	−	0.101804i	0.478063	+	0.878326i	$0.341339\pi$
$984$	−35.1539	+	31.7194i	−1.12067	+	1.01118i
$985$	−10.1744	+	8.53731i	−0.324182	+	0.272021i
$986$	−57.5830	+	37.1887i	−1.83382	+	1.18433i
$987$	−7.51366	−	11.3548i	−0.239162	−	0.361426i
$988$	−1.93758	−	19.3744i	−0.0616427	−	0.616381i
$989$	−2.02036	+	1.16646i	−0.0642439	+	0.0370912i
$990$	−15.6177	−	9.07431i	−0.496363	−	0.288401i
$991$	9.93598	+	5.73654i	0.315627	+	0.182227i	0.649442	−	0.760411i	$-0.275003\pi$
$991$	9.93598	+	5.73654i	0.315627	+	0.182227i	−0.333815	+	0.942639i	$0.608336\pi$
$992$	2.29977	+	2.35851i	0.0730179	+	0.0748829i
$993$	−26.3595	+	25.0085i	−0.836495	+	0.793620i
$994$	−10.6480	+	20.7683i	−0.337735	+	0.658730i
$995$	−1.77221	−	10.0507i	−0.0561828	−	0.318628i
$996$	4.01609	+	24.7841i	0.127255	+	0.785314i
$997$	−21.0339	−	17.6496i	−0.666151	−	0.558967i	0.245772	−	0.969328i	$-0.420958\pi$
$997$	−21.0339	−	17.6496i	−0.666151	−	0.558967i	−0.911923	+	0.410360i	$0.865403\pi$
$998$	−1.15766	+	9.23575i	−0.0366450	+	0.292353i
$999$	−1.24361	−	6.72298i	−0.0393462	−	0.212706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.cf.a.659.81	yes	648
4.3	odd	2	inner	756.2.cf.a.659.20	yes	648
27.5	odd	18	inner	756.2.cf.a.491.20	✓	648
108.59	even	18	inner	756.2.cf.a.491.81	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.20	✓	648	27.5	odd	18	inner
756.2.cf.a.491.81	yes	648	108.59	even	18	inner
756.2.cf.a.659.20	yes	648	4.3	odd	2	inner
756.2.cf.a.659.81	yes	648	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.961880 + 1.03672i) q^{2} +(-1.03042 + 1.39220i) q^{3} +(-0.149574 + 1.99440i) q^{4} +(-0.337395 + 0.926986i) q^{5} +(-2.43447 + 0.270870i) q^{6} +(0.984808 + 0.173648i) q^{7} +(-2.21150 + 1.76331i) q^{8} +(-0.876451 - 2.86912i) q^{9} +(-1.28556 + 0.541865i) q^{10} +(-4.05547 + 1.47607i) q^{11} +(-2.62248 - 2.26331i) q^{12} +(1.89865 - 1.59316i) q^{13} +(0.767242 + 1.18800i) q^{14} +(-0.942891 - 1.42491i) q^{15} +(-3.95526 - 0.596620i) q^{16} +(-4.64721 + 2.68307i) q^{17} +(2.13143 - 3.66838i) q^{18} +(-3.40172 - 1.96398i) q^{19} +(-1.79831 - 0.811554i) q^{20} +(-1.25652 + 1.19212i) q^{21} +(-5.43115 - 2.78458i) q^{22} +(1.28913 + 7.31104i) q^{23} +(-0.176090 - 4.89581i) q^{24} +(3.08475 + 2.58842i) q^{25} +(3.47793 + 0.435942i) q^{26} +(4.89751 + 1.73621i) q^{27} +(-0.493625 + 1.93813i) q^{28} +(5.80611 - 6.91945i) q^{29} +(0.570285 - 2.34811i) q^{30} +(-0.573485 + 0.101121i) q^{31} +(-3.18595 - 4.67437i) q^{32} +(2.12387 - 7.16702i) q^{33} +(-7.25164 - 2.23706i) q^{34} +(-0.493239 + 0.854315i) q^{35} +(5.85326 - 1.31885i) q^{36} +(-0.657893 - 1.13950i) q^{37} +(-1.23595 - 5.41574i) q^{38} +(0.261580 + 4.28493i) q^{39} +(-0.888409 - 2.64496i) q^{40} +(-6.21257 - 7.40386i) q^{41} +(-2.44452 - 0.155986i) q^{42} +(0.107479 + 0.295296i) q^{43} +(-2.33728 - 8.30901i) q^{44} +(2.95534 + 0.155569i) q^{45} +(-6.33951 + 8.36882i) q^{46} +(-1.36505 + 7.74157i) q^{47} +(4.90621 - 4.89174i) q^{48} +(0.939693 + 0.342020i) q^{49} +(0.283702 + 5.68777i) q^{50} +(1.05323 - 9.23455i) q^{51} +(2.89340 + 4.02496i) q^{52} +4.31297i q^{53} +(2.91085 + 6.74737i) q^{54} -4.25739i q^{55} +(-2.48410 + 1.35249i) q^{56} +(6.23947 - 2.71214i) q^{57} +(12.7583 - 0.636376i) q^{58} +(-5.36732 - 1.95354i) q^{59} +(2.98287 - 1.66737i) q^{60} +(-0.255302 + 1.44789i) q^{61} +(-0.656458 - 0.497277i) q^{62} +(-0.364919 - 2.97772i) q^{63} +(1.78150 - 7.79912i) q^{64} +(0.836238 + 2.29755i) q^{65} +(9.47309 - 4.69195i) q^{66} +(2.87683 + 3.42848i) q^{67} +(-4.65600 - 9.66970i) q^{68} +(-11.5068 - 5.73874i) q^{69} +(-1.36012 + 0.310398i) q^{70} +(8.25153 + 14.2921i) q^{71} +(6.99741 + 4.79961i) q^{72} +(-3.58347 + 6.20674i) q^{73} +(0.548532 - 1.77812i) q^{74} +(-6.78220 + 1.62743i) q^{75} +(4.42577 - 6.49062i) q^{76} +(-4.25018 + 0.749421i) q^{77} +(-4.19066 + 4.39277i) q^{78} +(-5.03644 + 6.00220i) q^{79} +(1.88754 - 3.46517i) q^{80} +(-7.46367 + 5.02928i) q^{81} +(1.69997 - 13.5623i) q^{82} +(-5.55219 - 4.65884i) q^{83} +(-2.18962 - 2.68432i) q^{84} +(-0.919219 - 5.21315i) q^{85} +(-0.202757 + 0.395464i) q^{86} +(3.65051 + 15.2132i) q^{87} +(6.36593 - 10.4154i) q^{88} +(12.4036 + 7.16122i) q^{89} +(2.68140 + 3.21350i) q^{90} +(2.14645 - 1.23926i) q^{91} +(-14.7740 + 1.47751i) q^{92} +(0.450153 - 0.902605i) q^{93} +(-9.33884 + 6.03129i) q^{94} +(2.96831 - 2.49071i) q^{95} +(9.79054 + 0.381093i) q^{96} +(-4.61957 + 1.68139i) q^{97} +(0.549293 + 1.30318i) q^{98} +(7.78944 + 10.3419i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) \) 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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