LMFDB - Embedded newform 930.2.v.b.401.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(401,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("930.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.v (of order $10$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			401.2
Character	$\chi$	$=$	930.401
Dual form			930.2.v.b.821.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-1.32297 - 1.11792i) q^{3} +(-0.309017 - 0.951057i) q^{4} +1.00000i q^{5} +(1.68204 - 0.413212i) q^{6} +(-1.31298 - 4.04094i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.500516 + 2.95795i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.32297 - 1.11792i) q^{3} +(-0.309017 - 0.951057i) q^{4} +1.00000i q^{5} +(1.68204 - 0.413212i) q^{6} +(-1.31298 - 4.04094i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.500516 + 2.95795i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(-0.752609 - 2.31629i) q^{11} +(-0.654383 + 1.60368i) q^{12} +(-1.50481 - 2.07119i) q^{13} +(4.04094 + 1.31298i) q^{14} +(1.11792 - 1.32297i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.642410 + 1.97714i) q^{17} +(-2.68723 - 1.33372i) q^{18} +(0.682533 + 0.495890i) q^{19} +(0.951057 - 0.309017i) q^{20} +(-2.78040 + 6.81386i) q^{21} +(2.31629 + 0.752609i) q^{22} +(-0.0307027 + 0.0944931i) q^{23} +(-0.912766 - 1.47202i) q^{24} -1.00000 q^{25} +2.56013 q^{26} +(2.64458 - 4.47283i) q^{27} +(-3.43743 + 2.49744i) q^{28} +(1.08772 + 0.790278i) q^{29} +(0.413212 + 1.68204i) q^{30} +(-1.37229 + 5.39600i) q^{31} -1.00000i q^{32} +(-1.59375 + 3.90575i) q^{33} +(-1.22194 - 1.68185i) q^{34} +(4.04094 - 1.31298i) q^{35} +(2.65851 - 1.39008i) q^{36} -3.16471i q^{37} +(-0.802366 + 0.260705i) q^{38} +(-0.324602 + 4.42239i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(-3.20849 + 4.41610i) q^{41} +(-3.87825 - 6.25448i) q^{42} +(-1.60651 + 2.21118i) q^{43} +(-1.97036 + 1.43155i) q^{44} +(-2.95795 + 0.500516i) q^{45} +(-0.0583999 - 0.0803806i) q^{46} +(-4.41559 - 6.07753i) q^{47} +(1.72740 + 0.126791i) q^{48} +(-8.94214 + 6.49684i) q^{49} +(0.587785 - 0.809017i) q^{50} +(3.06017 - 1.89753i) q^{51} +(-1.50481 + 2.07119i) q^{52} +(-3.52423 + 10.8465i) q^{53} +(2.06415 + 4.76857i) q^{54} +(2.31629 - 0.752609i) q^{55} -4.24889i q^{56} +(-0.348609 - 1.41907i) q^{57} +(-1.27870 + 0.415474i) q^{58} +(1.43216 + 1.97119i) q^{59} +(-1.60368 - 0.654383i) q^{60} +4.92809i q^{61} +(-3.55884 - 4.28190i) q^{62} +(11.2957 - 5.90629i) q^{63} +(0.809017 + 0.587785i) q^{64} +(2.07119 - 1.50481i) q^{65} +(-2.22304 - 3.58511i) q^{66} -7.99455 q^{67} +2.07888 q^{68} +(0.146254 - 0.0906887i) q^{69} +(-1.31298 + 4.04094i) q^{70} +(-6.04836 - 1.96523i) q^{71} +(-0.438039 + 2.96785i) q^{72} +(-10.1126 + 3.28577i) q^{73} +(2.56030 + 1.86017i) q^{74} +(1.32297 + 1.11792i) q^{75} +(0.260705 - 0.802366i) q^{76} +(-8.37184 + 6.08249i) q^{77} +(-3.38699 - 2.86202i) q^{78} +(-10.6818 - 3.47073i) q^{79} +(-0.587785 - 0.809017i) q^{80} +(-8.49897 + 2.96101i) q^{81} +(-1.68680 - 5.19144i) q^{82} +(7.57204 + 5.50141i) q^{83} +(7.33955 + 0.538722i) q^{84} +(-1.97714 - 0.642410i) q^{85} +(-0.844594 - 2.59939i) q^{86} +(-0.555564 - 2.26150i) q^{87} -2.43550i q^{88} +(4.72160 + 14.5316i) q^{89} +(1.33372 - 2.68723i) q^{90} +(-6.39378 + 8.80028i) q^{91} +0.0993559 q^{92} +(7.84780 - 5.60465i) q^{93} +7.51225 q^{94} +(-0.495890 + 0.682533i) q^{95} +(-1.11792 + 1.32297i) q^{96} +(-4.25765 - 13.1037i) q^{97} -11.0531i q^{98} +(6.47479 - 3.38552i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9}+O(q^{10}) $ 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9	$ 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9} - 20 q^{10} + 10 q^{13} - 20 q^{16} - 4 q^{18} - 12 q^{19} - 30 q^{21} - 10 q^{22} - 80 q^{25} + 60 q^{27} + 18 q^{28} + 8 q^{31} - 20 q^{33} + 10 q^{34} - 8 q^{36} - 46 q^{39} + 20 q^{40} + 50 q^{43} - 16 q^{45} - 10 q^{46} - 8 q^{49} - 20 q^{51} + 10 q^{52} - 10 q^{55} + 10 q^{58} + 44 q^{63} + 20 q^{64} - 10 q^{66} - 132 q^{67} - 16 q^{69} + 12 q^{70} + 4 q^{72} - 20 q^{73} - 18 q^{76} + 48 q^{78} - 120 q^{79} + 48 q^{81} - 20 q^{82} + 20 q^{84} - 136 q^{87} - 12 q^{90} - 110 q^{91} - 20 q^{93} - 28 q^{94} + 22 q^{97}+O(q^{100}) $ 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9 - 20 * q^10 + 10 * q^13 - 20 * q^16 - 4 * q^18 - 12 * q^19 - 30 * q^21 - 10 * q^22 - 80 * q^25 + 60 * q^27 + 18 * q^28 + 8 * q^31 - 20 * q^33 + 10 * q^34 - 8 * q^36 - 46 * q^39 + 20 * q^40 + 50 * q^43 - 16 * q^45 - 10 * q^46 - 8 * q^49 - 20 * q^51 + 10 * q^52 - 10 * q^55 + 10 * q^58 + 44 * q^63 + 20 * q^64 - 10 * q^66 - 132 * q^67 - 16 * q^69 + 12 * q^70 + 4 * q^72 - 20 * q^73 - 18 * q^76 + 48 * q^78 - 120 * q^79 + 48 * q^81 - 20 * q^82 + 20 * q^84 - 136 * q^87 - 12 * q^90 - 110 * q^91 - 20 * q^93 - 28 * q^94 + 22 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	−1.32297	−	1.11792i	−0.763819	−	0.645431i
$3$	−1.32297	−	1.11792i	−0.763819	−	0.645431i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	1.68204	−	0.413212i	0.686690	−	0.168693i
$7$	−1.31298	−	4.04094i	−0.496260	−	1.52733i	−0.814984	−	0.579483i	$-0.803254\pi$
$7$	−1.31298	−	4.04094i	−0.496260	−	1.52733i	0.318724	−	0.947847i	$-0.396746\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	0.500516	+	2.95795i	0.166839	+	0.985984i
$10$	−0.809017	−	0.587785i	−0.255834	−	0.185874i
$11$	−0.752609	−	2.31629i	−0.226920	−	0.698389i	−0.998091	−	0.0617604i	$-0.980329\pi$
$11$	−0.752609	−	2.31629i	−0.226920	−	0.698389i	0.771171	−	0.636628i	$-0.219671\pi$
$12$	−0.654383	+	1.60368i	−0.188904	+	0.462942i
$13$	−1.50481	−	2.07119i	−0.417359	−	0.574446i	0.547635	−	0.836717i	$-0.315528\pi$
$13$	−1.50481	−	2.07119i	−0.417359	−	0.574446i	−0.964994	+	0.262272i	$0.915528\pi$
$14$	4.04094	+	1.31298i	1.07999	+	0.350909i
$15$	1.11792	−	1.32297i	0.288645	−	0.341590i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.642410	+	1.97714i	−0.155807	+	0.479526i	−0.998242	−	0.0592731i	$-0.981122\pi$
$17$	−0.642410	+	1.97714i	−0.155807	+	0.479526i	0.842434	+	0.538799i	$0.181122\pi$
$18$	−2.68723	−	1.33372i	−0.633386	−	0.314360i
$19$	0.682533	+	0.495890i	0.156584	+	0.113765i	0.663318	−	0.748337i	$-0.269148\pi$
$19$	0.682533	+	0.495890i	0.156584	+	0.113765i	−0.506734	+	0.862102i	$0.669148\pi$
$20$	0.951057	−	0.309017i	0.212663	−	0.0690983i
$21$	−2.78040	+	6.81386i	−0.606733	+	1.48691i
$22$	2.31629	+	0.752609i	0.493835	+	0.160457i
$23$	−0.0307027	+	0.0944931i	−0.00640195	+	0.0197032i	−0.954206	−	0.299149i	$-0.903297\pi$
$23$	−0.0307027	+	0.0944931i	−0.00640195	+	0.0197032i	0.947805	+	0.318852i	$0.103297\pi$
$24$	−0.912766	−	1.47202i	−0.186318	−	0.300476i
$25$	−1.00000			−0.200000
$26$	2.56013			0.502084
$27$	2.64458	−	4.47283i	0.508950	−	0.860796i
$28$	−3.43743	+	2.49744i	−0.649613	+	0.471971i
$29$	1.08772	+	0.790278i	0.201985	+	0.146751i	0.684180	−	0.729313i	$-0.260160\pi$
$29$	1.08772	+	0.790278i	0.201985	+	0.146751i	−0.482195	+	0.876064i	$0.660160\pi$
$30$	0.413212	+	1.68204i	0.0754418	+	0.307097i
$31$	−1.37229	+	5.39600i	−0.246471	+	0.969150i
$31$	−1.37229	+	5.39600i	−0.246471	+	0.969150i
$32$		−	1.00000i		−	0.176777i
$33$	−1.59375	+	3.90575i	−0.277435	+	0.679904i
$34$	−1.22194	−	1.68185i	−0.209560	−	0.288435i
$35$	4.04094	−	1.31298i	0.683043	−	0.221934i
$36$	2.65851	−	1.39008i	0.443085	−	0.231679i
$37$		−	3.16471i		−	0.520275i	−0.965572	−	0.260137i	$-0.916232\pi$
$37$		−	3.16471i		−	0.520275i	0.965572	−	0.260137i	$-0.0837679\pi$
$38$	−0.802366	+	0.260705i	−0.130161	+	0.0422919i
$39$	−0.324602	+	4.42239i	−0.0519779	+	0.708149i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	−3.20849	+	4.41610i	−0.501081	+	0.689679i	−0.982384	−	0.186876i	$-0.940164\pi$
$41$	−3.20849	+	4.41610i	−0.501081	+	0.689679i	0.481302	+	0.876555i	$0.340164\pi$
$42$	−3.87825	−	6.25448i	−0.598426	−	0.965087i
$43$	−1.60651	+	2.21118i	−0.244991	+	0.337201i	−0.913749	−	0.406279i	$-0.866826\pi$
$43$	−1.60651	+	2.21118i	−0.244991	+	0.337201i	0.668758	+	0.743480i	$0.266826\pi$
$44$	−1.97036	+	1.43155i	−0.297042	+	0.215814i
$45$	−2.95795	+	0.500516i	−0.440946	+	0.0746125i
$46$	−0.0583999	−	0.0803806i	−0.00861060	−	0.0118515i
$47$	−4.41559	−	6.07753i	−0.644080	−	0.886500i	0.354745	−	0.934963i	$-0.384568\pi$
$47$	−4.41559	−	6.07753i	−0.644080	−	0.886500i	−0.998825	+	0.0484634i	$0.984568\pi$
$48$	1.72740	+	0.126791i	0.249329	+	0.0183007i
$49$	−8.94214	+	6.49684i	−1.27745	+	0.928121i
$50$	0.587785	−	0.809017i	0.0831254	−	0.114412i
$51$	3.06017	−	1.89753i	0.428509	−	0.265708i
$52$	−1.50481	+	2.07119i	−0.208680	+	0.287223i
$53$	−3.52423	+	10.8465i	−0.484090	+	1.48988i	0.349204	+	0.937047i	$0.386452\pi$
$53$	−3.52423	+	10.8465i	−0.484090	+	1.48988i	−0.833295	+	0.552829i	$0.813548\pi$
$54$	2.06415	+	4.76857i	0.280895	+	0.648921i
$55$	2.31629	−	0.752609i	0.312329	−	0.101482i
$56$		−	4.24889i		−	0.567782i
$57$	−0.348609	−	1.41907i	−0.0461744	−	0.187960i
$58$	−1.27870	+	0.415474i	−0.167901	+	0.0545544i
$59$	1.43216	+	1.97119i	0.186451	+	0.256628i	0.892002	−	0.452031i	$-0.149300\pi$
$59$	1.43216	+	1.97119i	0.186451	+	0.256628i	−0.705551	+	0.708659i	$0.749300\pi$
$60$	−1.60368	−	0.654383i	−0.207034	−	0.0844804i
$61$			4.92809i			0.630977i	0.948929	+	0.315489i	$0.102168\pi$
$61$			4.92809i			0.630977i	−0.948929	+	0.315489i	$0.897832\pi$
$62$	−3.55884	−	4.28190i	−0.451973	−	0.543802i
$63$	11.2957	−	5.90629i	1.42313	−	0.744122i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	2.07119	−	1.50481i	0.256900	−	0.186649i
$66$	−2.22304	−	3.58511i	−0.273637	−	0.441296i
$67$	−7.99455			−0.976690			−0.488345	−	0.872651i	$-0.662399\pi$
$67$	−7.99455			−0.976690			−0.488345	+	0.872651i	$0.662399\pi$
$68$	2.07888			0.252102
$69$	0.146254	−	0.0906887i	0.0176070	−	0.0109176i
$70$	−1.31298	+	4.04094i	−0.156931	+	0.482984i
$71$	−6.04836	−	1.96523i	−0.717808	−	0.233230i	−0.0727354	−	0.997351i	$-0.523173\pi$
$71$	−6.04836	−	1.96523i	−0.717808	−	0.233230i	−0.645073	+	0.764121i	$0.723173\pi$
$72$	−0.438039	+	2.96785i	−0.0516234	+	0.349764i
$73$	−10.1126	+	3.28577i	−1.18359	+	0.384570i	−0.833698	−	0.552221i	$-0.813780\pi$
$73$	−10.1126	+	3.28577i	−1.18359	+	0.384570i	−0.349888	+	0.936791i	$0.613780\pi$
$74$	2.56030	+	1.86017i	0.297629	+	0.216240i
$75$	1.32297	+	1.11792i	0.152764	+	0.129086i
$76$	0.260705	−	0.802366i	0.0299049	−	0.0920377i
$77$	−8.37184	+	6.08249i	−0.954059	+	0.693165i
$78$	−3.38699	−	2.86202i	−0.383501	−	0.324060i
$79$	−10.6818	−	3.47073i	−1.20180	−	0.390488i	−0.361376	−	0.932420i	$-0.617693\pi$
$79$	−10.6818	−	3.47073i	−1.20180	−	0.390488i	−0.840422	+	0.541932i	$0.817693\pi$
$80$	−0.587785	−	0.809017i	−0.0657164	−	0.0904508i
$81$	−8.49897	+	2.96101i	−0.944330	+	0.329001i
$82$	−1.68680	−	5.19144i	−0.186276	−	0.573298i
$83$	7.57204	+	5.50141i	0.831139	+	0.603858i	0.919881	−	0.392197i	$-0.128285\pi$
$83$	7.57204	+	5.50141i	0.831139	+	0.603858i	−0.0887421	+	0.996055i	$0.528285\pi$
$84$	7.33955	+	0.538722i	0.800811	+	0.0587793i
$85$	−1.97714	−	0.642410i	−0.214450	−	0.0696792i
$86$	−0.844594	−	2.59939i	−0.0910749	−	0.280300i
$87$	−0.555564	−	2.26150i	−0.0595627	−	0.242459i
$88$		−	2.43550i		−	0.259625i
$89$	4.72160	+	14.5316i	0.500488	+	1.54034i	0.808225	+	0.588873i	$0.200428\pi$
$89$	4.72160	+	14.5316i	0.500488	+	1.54034i	−0.307737	+	0.951471i	$0.599572\pi$
$90$	1.33372	−	2.68723i	0.140586	−	0.283259i
$91$	−6.39378	+	8.80028i	−0.670250	+	0.922520i
$92$	0.0993559			0.0103586
$93$	7.84780	−	5.60465i	0.813778	−	0.581175i
$94$	7.51225			0.774829
$95$	−0.495890	+	0.682533i	−0.0508772	+	0.0700265i
$96$	−1.11792	+	1.32297i	−0.114097	+	0.135025i
$97$	−4.25765	−	13.1037i	−0.432298	−	1.33048i	−0.895830	−	0.444397i	$-0.853418\pi$
$97$	−4.25765	−	13.1037i	−0.432298	−	1.33048i	0.463531	−	0.886080i	$-0.346582\pi$
$98$		−	11.0531i		−	1.11653i
$99$	6.47479	−	3.38552i	0.650741	−	0.340258i
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	−16.3021	−	5.29686i	−1.62212	−	0.527057i	−0.649676	−	0.760211i	$-0.725096\pi$
$101$	−16.3021	−	5.29686i	−1.62212	−	0.527057i	−0.972440	+	0.233154i	$0.925096\pi$
$102$	−0.263584	+	3.59107i	−0.0260987	+	0.355569i
$103$	6.67399	+	4.84893i	0.657607	+	0.477780i	0.865854	−	0.500297i	$-0.166776\pi$
$103$	6.67399	+	4.84893i	0.657607	+	0.477780i	−0.208247	+	0.978076i	$0.566776\pi$
$104$	−0.791125	−	2.43483i	−0.0775762	−	0.238755i
$105$	−6.81386	−	2.78040i	−0.664964	−	0.271339i
$106$	−6.70348	−	9.22655i	−0.651100	−	0.896162i
$107$	2.81144	+	0.913491i	0.271792	+	0.0883105i	0.441742	−	0.897142i	$-0.354361\pi$
$107$	2.81144	+	0.913491i	0.271792	+	0.0883105i	−0.169950	+	0.985453i	$0.554361\pi$
$108$	−5.07113	−	1.13297i	−0.487970	−	0.109020i
$109$	−1.85425	+	1.34719i	−0.177605	+	0.129037i	−0.673036	−	0.739610i	$-0.735010\pi$
$109$	−1.85425	+	1.34719i	−0.177605	+	0.129037i	0.495431	+	0.868647i	$0.335010\pi$
$110$	−0.752609	+	2.31629i	−0.0717585	+	0.220850i
$111$	−3.53789	+	4.18682i	−0.335801	+	0.397396i
$112$	3.43743	+	2.49744i	0.324806	+	0.235986i
$113$	−0.541199	+	0.175846i	−0.0509117	+	0.0165422i	−0.334362	−	0.942445i	$-0.608521\pi$
$113$	−0.541199	+	0.175846i	−0.0509117	+	0.0165422i	0.283450	+	0.958987i	$0.408521\pi$
$114$	1.35296	+	0.552075i	0.126716	+	0.0517066i
$115$	−0.0944931	−	0.0307027i	−0.00881152	−	0.00286304i
$116$	0.415474	−	1.27870i	0.0385758	−	0.118724i
$117$	5.37331	−	5.48782i	0.496763	−	0.507349i
$118$	−2.43653			−0.224301
$119$	8.83295			0.809715
$120$	1.47202	−	0.912766i	0.134377	−	0.0833238i
$121$	4.10039	−	2.97911i	0.372763	−	0.270828i
$122$	−3.98691	−	2.89666i	−0.360958	−	0.262251i
$123$	9.18158	−	2.25556i	0.827875	−	0.203377i
$124$	5.55596	−	0.362327i	0.498940	−	0.0325379i
$125$		−	1.00000i		−	0.0894427i
$126$	−1.86118	+	12.6101i	−0.165807	+	1.12339i
$127$	−2.87090	−	3.95145i	−0.254751	−	0.350634i	0.662417	−	0.749135i	$-0.269531\pi$
$127$	−2.87090	−	3.95145i	−0.254751	−	0.350634i	−0.917168	+	0.398501i	$0.869531\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	4.59729	−	1.12938i	0.404769	−	0.0994360i
$130$			2.56013i			0.224539i
$131$	−1.36259	+	0.442731i	−0.119050	+	0.0386816i	−0.367936	−	0.929851i	$-0.619935\pi$
$131$	−1.36259	+	0.442731i	−0.119050	+	0.0386816i	0.248886	+	0.968533i	$0.419935\pi$
$132$	4.20708	+	0.308799i	0.366180	+	0.0268775i
$133$	1.10771	−	3.40917i	0.0960503	−	0.295612i
$134$	4.69908	−	6.46773i	0.405939	−	0.558727i
$135$	4.47283	+	2.64458i	0.384960	+	0.227609i
$136$	−1.22194	+	1.68185i	−0.104780	+	0.144218i
$137$	9.51314	−	6.91170i	0.812763	−	0.590507i	−0.101868	−	0.994798i	$-0.532482\pi$
$137$	9.51314	−	6.91170i	0.812763	−	0.590507i	0.914630	+	0.404291i	$0.132482\pi$
$138$	−0.0125974	+	0.171628i	−0.00107237	+	0.0146099i
$139$	7.34643	+	10.1115i	0.623116	+	0.857646i	0.997575	−	0.0695978i	$-0.0221716\pi$
$139$	7.34643	+	10.1115i	0.623116	+	0.857646i	−0.374459	+	0.927243i	$0.622172\pi$
$140$	−2.49744	−	3.43743i	−0.211072	−	0.290516i
$141$	−0.952485	+	12.9767i	−0.0802137	+	1.09283i
$142$	5.14504	−	3.73809i	0.431762	−	0.313694i
$143$	−3.66496	+	5.04438i	−0.306479	+	0.421832i
$144$	−2.14357	−	2.09884i	−0.178631	−	0.174903i
$145$	−0.790278	+	1.08772i	−0.0656290	+	0.0903306i
$146$	3.28577	−	10.1126i	0.271932	−	0.836922i
$147$	19.0932	+	1.40143i	1.57478	+	0.115588i
$148$	−3.00982	+	0.977949i	−0.247405	+	0.0803869i
$149$			8.66230i			0.709644i	0.934934	+	0.354822i	$0.115458\pi$
$149$			8.66230i			0.709644i	−0.934934	+	0.354822i	$0.884542\pi$
$150$	−1.68204	+	0.413212i	−0.137338	+	0.0337386i
$151$	7.38808	−	2.40053i	0.601234	−	0.195353i	0.00744312	−	0.999972i	$-0.497631\pi$
$151$	7.38808	−	2.40053i	0.601234	−	0.195353i	0.593791	+	0.804620i	$0.297631\pi$
$152$	0.495890	+	0.682533i	0.0402220	+	0.0553608i
$153$	−6.16981	−	0.910631i	−0.498800	−	0.0736202i
$154$		−	10.3482i		−	0.833878i
$155$	−5.39600	−	1.37229i	−0.433417	−	0.110225i
$156$	4.30625	−	1.05788i	0.344776	−	0.0846980i
$157$	8.57876	+	6.23284i	0.684660	+	0.497434i	0.874900	−	0.484303i	$-0.160927\pi$
$157$	8.57876	+	6.23284i	0.684660	+	0.497434i	−0.190241	+	0.981738i	$0.560927\pi$
$158$	9.08650	−	6.60173i	0.722883	−	0.525205i
$159$	16.7879	−	10.4098i	1.33137	−	0.825549i
$160$	1.00000			0.0790569
$161$	0.422153			0.0332703
$162$	2.60006	−	8.61624i	0.204280	−	0.676956i
$163$	5.00851	−	15.4146i	0.392296	−	1.20736i	−0.538751	−	0.842465i	$-0.681103\pi$
$163$	5.00851	−	15.4146i	0.392296	−	1.20736i	0.931047	−	0.364899i	$-0.118897\pi$
$164$	5.19144	+	1.68680i	0.405383	+	0.131717i
$165$	−3.90575	−	1.59375i	−0.304062	−	0.124073i
$166$	−8.90147	+	2.89226i	−0.690888	+	0.224483i
$167$	−11.6468	−	8.46192i	−0.901260	−	0.654803i	0.0375297	−	0.999296i	$-0.488051\pi$
$167$	−11.6468	−	8.46192i	−0.901260	−	0.654803i	−0.938789	+	0.344492i	$0.888051\pi$
$168$	−4.74992	+	5.62117i	−0.366464	+	0.433683i
$169$	1.99183	−	6.13023i	0.153218	−	0.471556i
$170$	1.68185	−	1.22194i	0.128992	−	0.0937183i
$171$	−1.12520	+	2.26710i	−0.0860461	+	0.173370i
$172$	2.59939	+	0.844594i	0.198202	+	0.0643997i
$173$	9.15519	+	12.6010i	0.696057	+	0.958040i	0.999986	+	0.00534502i	$0.00170138\pi$
$173$	9.15519	+	12.6010i	0.696057	+	0.958040i	−0.303929	+	0.952695i	$0.598299\pi$
$174$	2.15615	+	0.879819i	0.163457	+	0.0666989i
$175$	1.31298	+	4.04094i	0.0992520	+	0.305466i
$176$	1.97036	+	1.43155i	0.148521	+	0.107907i
$177$	0.308930	−	4.20887i	0.0232206	−	0.316358i
$178$	−14.5316	−	4.72160i	−1.08919	−	0.353899i
$179$	6.68198	+	20.5650i	0.499435	+	1.53710i	0.809930	+	0.586527i	$0.199505\pi$
$179$	6.68198	+	20.5650i	0.499435	+	1.53710i	−0.310495	+	0.950575i	$0.600495\pi$
$180$	1.39008	+	2.65851i	0.103610	+	0.198154i
$181$		−	18.8037i		−	1.39767i	−0.715284	−	0.698833i	$-0.753703\pi$
$181$		−	18.8037i		−	1.39767i	0.715284	−	0.698833i	$-0.246297\pi$
$182$	−3.36141	−	10.3453i	−0.249164	−	0.766848i
$183$	5.50920	−	6.51973i	0.407252	−	0.481952i
$184$	−0.0583999	+	0.0803806i	−0.00430530	+	0.00592574i
$185$	3.16471			0.232674
$186$	−0.0785613	+	9.64333i	−0.00576039	+	0.707083i
$187$	5.06311			0.370251
$188$	−4.41559	+	6.07753i	−0.322040	+	0.443250i
$189$	−21.5467	−	4.81385i	−1.56729	−	0.350156i
$190$	−0.260705	−	0.802366i	−0.0189135	−	0.0582098i
$191$			8.59875i			0.622183i	0.950380	+	0.311092i	$0.100695\pi$
$191$			8.59875i			0.622183i	−0.950380	+	0.311092i	$0.899305\pi$
$192$	−0.413212	−	1.68204i	−0.0298210	−	0.121391i
$193$	−6.50212	−	20.0115i	−0.468033	−	1.44046i	−0.855128	−	0.518417i	$-0.826521\pi$
$193$	−6.50212	−	20.0115i	−0.468033	−	1.44046i	0.387095	−	0.922040i	$-0.373479\pi$
$194$	13.1037	+	4.25765i	0.940790	+	0.305681i
$195$	−4.42239	−	0.324602i	−0.316694	−	0.0232452i
$196$	8.94214	+	6.49684i	0.638724	+	0.464060i
$197$	−3.31358	−	10.1982i	−0.236083	−	0.726588i	−0.996976	−	0.0777109i	$-0.975239\pi$
$197$	−3.31358	−	10.1982i	−0.236083	−	0.726588i	0.760893	−	0.648877i	$-0.224761\pi$
$198$	−1.06684	+	7.22818i	−0.0758171	+	0.513684i
$199$	−12.3182	−	16.9545i	−0.873213	−	1.20187i	−0.978255	−	0.207407i	$-0.933498\pi$
$199$	−12.3182	−	16.9545i	−0.873213	−	1.20187i	0.105042	−	0.994468i	$-0.466502\pi$
$200$	−0.951057	−	0.309017i	−0.0672499	−	0.0218508i
$201$	10.5766	+	8.93726i	0.746015	+	0.630386i
$202$	13.8674	−	10.0752i	0.975704	−	0.708891i
$203$	1.76530	−	5.43305i	0.123900	−	0.381325i
$204$	−2.75031	−	2.32402i	−0.192560	−	0.162714i
$205$	−4.41610	−	3.20849i	−0.308434	−	0.224090i
$206$	−7.84574	+	2.54924i	−0.546639	+	0.177614i
$207$	−0.294873	−	0.0435217i	−0.0204951	−	0.00302497i
$208$	2.43483	+	0.791125i	0.168825	+	0.0548547i
$209$	0.634945	−	1.95416i	0.0439200	−	0.135172i
$210$	6.25448	−	3.87825i	0.431600	−	0.267624i
$211$	−20.2418			−1.39351			−0.696753	−	0.717311i	$-0.745372\pi$
$211$	−20.2418			−1.39351			−0.696753	+	0.717311i	$0.745372\pi$
$212$	11.4046			0.783274
$213$	5.80485	+	9.36152i	0.397742	+	0.641441i
$214$	−2.39155	+	1.73756i	−0.163483	+	0.118777i
$215$	−2.21118	−	1.60651i	−0.150801	−	0.109563i
$216$	3.89733	−	3.43669i	0.265179	−	0.233837i
$217$	23.6067	−	1.53949i	1.60253	−	0.104507i
$218$		−	2.29198i		−	0.155232i
$219$	17.0519	+	6.95803i	1.15226	+	0.470180i
$220$	−1.43155	−	1.97036i	−0.0965150	−	0.132841i
$221$	5.06173	−	1.64466i	0.340489	−	0.110632i
$222$	−1.30769	−	5.32316i	−0.0877667	−	0.357267i
$223$			0.856212i			0.0573362i	0.999589	+	0.0286681i	$0.00912659\pi$
$223$			0.856212i			0.0573362i	−0.999589	+	0.0286681i	$0.990873\pi$
$224$	−4.04094	+	1.31298i	−0.269996	+	0.0877272i
$225$	−0.500516	−	2.95795i	−0.0333677	−	0.197197i
$226$	0.175846	−	0.541199i	0.0116971	−	0.0360000i
$227$	−8.22904	+	11.3263i	−0.546180	+	0.751753i	−0.989488	−	0.144617i	$-0.953805\pi$
$227$	−8.22904	+	11.3263i	−0.546180	+	0.751753i	0.443307	+	0.896370i	$0.353805\pi$
$228$	−1.24189	+	0.770062i	−0.0822459	+	0.0509986i
$229$	−8.54997	+	11.7680i	−0.564998	+	0.777653i	−0.991951	−	0.126621i	$-0.959587\pi$
$229$	−8.54997	+	11.7680i	−0.564998	+	0.777653i	0.426953	+	0.904274i	$0.359587\pi$
$230$	0.0803806	−	0.0583999i	0.00530014	−	0.00385078i
$231$	17.8754	+	1.31205i	1.17612	+	0.0863268i
$232$	0.790278	+	1.08772i	0.0518843	+	0.0714126i
$233$	5.49122	+	7.55802i	0.359742	+	0.495142i	0.950077	−	0.312016i	$-0.101004\pi$
$233$	5.49122	+	7.55802i	0.359742	+	0.495142i	−0.590335	+	0.807158i	$0.701004\pi$
$234$	1.28139	+	7.57276i	0.0837670	+	0.495047i
$235$	6.07753	−	4.41559i	0.396455	−	0.288041i
$236$	1.43216	−	1.97119i	0.0932255	−	0.128314i
$237$	10.2518	+	16.5331i	0.665923	+	1.07394i
$238$	−5.19188	+	7.14601i	−0.336540	+	0.463207i
$239$	−2.66511	+	8.20236i	−0.172391	+	0.530566i	−0.999505	−	0.0314689i	$-0.989981\pi$
$239$	−2.66511	+	8.20236i	−0.172391	+	0.530566i	0.827113	+	0.562035i	$0.189981\pi$
$240$	−0.126791	+	1.72740i	−0.00818433	+	0.111503i
$241$	22.1604	−	7.20034i	1.42747	−	0.463814i	0.509505	−	0.860468i	$-0.329828\pi$
$241$	22.1604	−	7.20034i	1.42747	−	0.463814i	0.917969	+	0.396653i	$0.129828\pi$
$242$			5.06836i			0.325807i
$243$	14.5541	+	5.58382i	0.933644	+	0.358202i
$244$	4.68689	−	1.52286i	0.300048	−	0.0974913i
$245$	−6.49684	−	8.94214i	−0.415068	−	0.571292i
$246$	−3.57201	+	8.75384i	−0.227743	+	0.558124i
$247$		−	2.15988i		−	0.137430i
$248$	−2.97258	+	4.70784i	−0.188759	+	0.298948i
$249$	−3.86748	−	15.7431i	−0.245091	−	0.997681i
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	19.6944	−	14.3088i	1.24310	−	0.903166i	0.245300	−	0.969447i	$-0.421113\pi$
$251$	19.6944	−	14.3088i	1.24310	−	0.903166i	0.997801	+	0.0662812i	$0.0211135\pi$
$252$	−9.10779	−	8.91774i	−0.573737	−	0.561765i
$253$	0.241981			0.0152132
$254$	4.88426			0.306466
$255$	1.89753	+	3.06017i	0.118828	+	0.191635i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−25.0310	−	8.13306i	−1.56139	−	0.507326i	−0.604211	−	0.796824i	$-0.706512\pi$
$257$	−25.0310	−	8.13306i	−1.56139	−	0.507326i	−0.957179	+	0.289498i	$0.906512\pi$
$258$	−1.78854	+	4.38312i	−0.111349	+	0.272881i
$259$	−12.7884	+	4.15520i	−0.794632	+	0.258192i
$260$	−2.07119	−	1.50481i	−0.128450	−	0.0933243i
$261$	−1.79318	+	3.61299i	−0.110995	+	0.223638i
$262$	0.442731	−	1.36259i	0.0273520	−	0.0841809i
$263$	−8.36970	+	6.08095i	−0.516098	+	0.374967i	−0.815132	−	0.579275i	$-0.803336\pi$
$263$	−8.36970	+	6.08095i	−0.516098	+	0.374967i	0.299034	+	0.954242i	$0.403336\pi$
$264$	−2.72269	+	3.22209i	−0.167570	+	0.198306i
$265$	−10.8465	−	3.52423i	−0.666293	−	0.216492i
$266$	2.10698	+	2.90001i	0.129187	+	0.177811i
$267$	9.99858	−	24.5033i	0.611903	−	1.49957i
$268$	2.47045	+	7.60327i	0.150907	+	0.464444i
$269$	−0.387093	−	0.281240i	−0.0236015	−	0.0171475i	0.575922	−	0.817505i	$-0.304643\pi$
$269$	−0.387093	−	0.281240i	−0.0236015	−	0.0171475i	−0.599523	+	0.800357i	$0.704643\pi$
$270$	−4.76857	+	2.06415i	−0.290206	+	0.125620i
$271$	24.9024	+	8.09129i	1.51271	+	0.491511i	0.943696	−	0.330814i	$-0.107323\pi$
$271$	24.9024	+	8.09129i	1.51271	+	0.491511i	0.569018	+	0.822325i	$0.307323\pi$
$272$	−0.642410	−	1.97714i	−0.0389518	−	0.119881i
$273$	18.2968	−	4.49481i	1.10737	−	0.272038i
$274$			11.7589i			0.710381i
$275$	0.752609	+	2.31629i	0.0453841	+	0.139678i
$276$	−0.131445	−	0.111072i	−0.00791207	−	0.00668574i
$277$	−8.39217	+	11.5508i	−0.504237	+	0.694022i	−0.982934	−	0.183958i	$-0.941109\pi$
$277$	−8.39217	+	11.5508i	−0.504237	+	0.694022i	0.478698	+	0.877980i	$0.341109\pi$
$278$	−12.4985			−0.749610
$279$	−16.6480	−	1.35839i	−0.996688	−	0.0813250i
$280$	4.24889			0.253920
$281$	12.4196	−	17.0942i	0.740893	−	1.01975i	−0.257674	−	0.966232i	$-0.582956\pi$
$281$	12.4196	−	17.0942i	0.740893	−	1.01975i	0.998567	−	0.0535200i	$-0.0170441\pi$
$282$	−9.93850	−	8.39808i	−0.591829	−	0.500098i
$283$	8.47415	+	26.0808i	0.503736	+	1.55034i	0.802885	+	0.596134i	$0.203297\pi$
$283$	8.47415	+	26.0808i	0.503736	+	1.55034i	−0.299149	+	0.954206i	$0.596703\pi$
$284$			6.35962i			0.377374i
$285$	1.41907	−	0.348609i	0.0840582	−	0.0206498i
$286$	−1.92678	−	5.93002i	−0.113933	−	0.350650i
$287$	22.0579	+	7.16703i	1.30203	+	0.423057i
$288$	2.95795	−	0.500516i	0.174299	−	0.0294932i
$289$	10.2569	+	7.45209i	0.603348	+	0.438358i
$290$	−0.415474	−	1.27870i	−0.0243975	−	0.0750877i
$291$	−9.01610	+	22.0955i	−0.528533	+	1.29526i
$292$	6.24991	+	8.60226i	0.365748	+	0.503409i
$293$	−2.01156	−	0.653595i	−0.117517	−	0.0381834i	0.249668	−	0.968331i	$-0.419678\pi$
$293$	−2.01156	−	0.653595i	−0.117517	−	0.0381834i	−0.367185	+	0.930148i	$0.619678\pi$
$294$	−12.3565	+	14.6229i	−0.720643	+	0.852827i
$295$	−1.97119	+	1.43216i	−0.114767	+	0.0833834i
$296$	0.977949	−	3.00982i	0.0568421	−	0.174942i
$297$	−12.3507	−	2.75933i	−0.716661	−	0.160113i
$298$	−7.00795	−	5.09157i	−0.405960	−	0.294947i
$299$	0.241915	−	0.0786030i	0.0139903	−	0.00454573i
$300$	0.654383	−	1.60368i	0.0377808	−	0.0925884i
$301$	11.0445	+	3.58859i	0.636597	+	0.206843i
$302$	−2.40053	+	7.38808i	−0.138135	+	0.425136i
$303$	15.6457	+	25.2320i	0.898824	+	1.44954i
$304$	−0.843658			−0.0483871
$305$	−4.92809			−0.282182
$306$	4.36324	−	4.45623i	0.249430	−	0.254745i
$307$	−11.1433	+	8.09605i	−0.635979	+	0.462066i	−0.858467	−	0.512870i	$-0.828582\pi$
$307$	−11.1433	+	8.09605i	−0.635979	+	0.462066i	0.222487	+	0.974936i	$0.428582\pi$
$308$	8.37184	+	6.08249i	0.477030	+	0.346582i
$309$	−3.40879	−	13.8760i	−0.193919	−	0.789377i
$310$	4.28190	−	3.55884i	0.243195	−	0.202129i
$311$		−	13.4736i		−	0.764017i	−0.924159	−	0.382009i	$-0.875232\pi$
$311$		−	13.4736i		−	0.764017i	0.924159	−	0.382009i	$-0.124768\pi$
$312$	−1.67531	+	4.10563i	−0.0948456	+	0.232436i
$313$	1.24734	+	1.71682i	0.0705039	+	0.0970403i	0.842813	−	0.538207i	$-0.180898\pi$
$313$	1.24734	+	1.71682i	0.0705039	+	0.0970403i	−0.772309	+	0.635247i	$0.780898\pi$
$314$	−10.0849	+	3.27680i	−0.569126	+	0.184920i
$315$	5.90629	+	11.2957i	0.332782	+	0.636443i
$316$			11.2315i			0.631823i
$317$	−17.5554	+	5.70409i	−0.986008	+	0.320374i	−0.757261	−	0.653112i	$-0.773463\pi$
$317$	−17.5554	+	5.70409i	−0.986008	+	0.320374i	−0.228747	+	0.973486i	$0.573463\pi$
$318$	−1.44601	+	19.7004i	−0.0810880	+	1.10474i
$319$	1.01188	−	3.11426i	0.0566547	−	0.174365i
$320$	−0.587785	+	0.809017i	−0.0328582	+	0.0452254i
$321$	−2.69825	−	4.35148i	−0.150601	−	0.242876i
$322$	−0.248135	+	0.341529i	−0.0138280	+	0.0190326i
$323$	−1.41891	+	1.03090i	−0.0789501	+	0.0573606i
$324$	5.44241	+	7.16800i	0.302356	+	0.398222i
$325$	1.50481	+	2.07119i	0.0834718	+	0.114889i
$326$	9.52674	+	13.1124i	0.527638	+	0.726231i
$327$	3.95917	+	0.290602i	0.218943	+	0.0160703i
$328$	−4.41610	+	3.20849i	−0.243838	+	0.177159i
$329$	−18.7614	+	25.8228i	−1.03435	+	1.42366i
$330$	3.58511	−	2.22304i	0.197354	−	0.122374i
$331$	−3.35172	+	4.61325i	−0.184227	+	0.253567i	−0.891135	−	0.453739i	$-0.850090\pi$
$331$	−3.35172	+	4.61325i	−0.184227	+	0.253567i	0.706907	+	0.707306i	$0.250090\pi$
$332$	2.89226	−	8.90147i	0.158733	−	0.488531i
$333$	9.36106	−	1.58399i	0.512983	−	0.0868020i
$334$	13.6917	−	4.44870i	0.749175	−	0.243422i
$335$		−	7.99455i		−	0.436789i
$336$	−1.75569	−	7.14681i	−0.0957809	−	0.389890i
$337$	−12.6031	+	4.09499i	−0.686534	+	0.223069i	−0.631454	−	0.775413i	$-0.717542\pi$
$337$	−12.6031	+	4.09499i	−0.686534	+	0.223069i	−0.0550804	+	0.998482i	$0.517542\pi$
$338$	3.78869	+	5.21469i	0.206078	+	0.283642i
$339$	0.912573	+	0.372376i	0.0495642	+	0.0202247i
$340$			2.07888i			0.112743i
$341$	13.5315	−	0.882446i	0.732773	−	0.0477871i
$342$	−1.17275	−	2.24287i	−0.0634150	−	0.121281i
$343$	13.9322	+	10.1223i	0.752269	+	0.546555i
$344$	−2.21118	+	1.60651i	−0.119219	+	0.0866174i
$345$	0.0906887	+	0.146254i	0.00488252	+	0.00787407i
$346$	−15.5757			−0.837357
$347$	−33.5741			−1.80235			−0.901176	−	0.433454i	$-0.857295\pi$
$347$	−33.5741			−1.80235			−0.901176	+	0.433454i	$0.857295\pi$
$348$	−1.97914	+	1.22722i	−0.106093	+	0.0657857i
$349$	7.05946	−	21.7268i	0.377884	−	1.16301i	−0.563628	−	0.826029i	$-0.690595\pi$
$349$	7.05946	−	21.7268i	0.377884	−	1.16301i	0.941512	−	0.336979i	$-0.109405\pi$
$350$	−4.04094	−	1.31298i	−0.215997	−	0.0701817i
$351$	−13.2437	+	1.25332i	−0.706895	+	0.0668971i
$352$	−2.31629	+	0.752609i	−0.123459	+	0.0401142i
$353$	−16.8927	−	12.2733i	−0.899107	−	0.653240i	0.0391294	−	0.999234i	$-0.487542\pi$
$353$	−16.8927	−	12.2733i	−0.899107	−	0.653240i	−0.938237	+	0.345995i	$0.887542\pi$
$354$	3.22346	+	2.72384i	0.171325	+	0.144771i
$355$	1.96523	−	6.04836i	0.104304	−	0.321013i
$356$	12.3613	−	8.98101i	0.655148	−	0.475993i
$357$	−11.6858	−	9.87452i	−0.618476	−	0.522615i
$358$	−20.5650	−	6.68198i	−1.08690	−	0.353154i
$359$	−21.3693	−	29.4123i	−1.12783	−	1.55232i	−0.792127	−	0.610356i	$-0.791026\pi$
$359$	−21.3693	−	29.4123i	−1.12783	−	1.55232i	−0.335702	−	0.941968i	$-0.608974\pi$
$360$	−2.96785	−	0.438039i	−0.156419	−	0.0230867i
$361$	−5.65138	−	17.3932i	−0.297441	−	0.915429i
$362$	15.2125	+	11.0525i	0.799551	+	0.580908i
$363$	−8.75511	−	0.642623i	−0.459524	−	0.0337290i
$364$	10.3453	+	3.36141i	0.542243	+	0.176186i
$365$	−3.28577	−	10.1126i	−0.171985	−	0.529316i
$366$	2.03634	+	8.28924i	0.106441	+	0.433286i
$367$		−	4.62433i		−	0.241388i	−0.992690	−	0.120694i	$-0.961488\pi$
$367$		−	4.62433i		−	0.241388i	0.992690	−	0.120694i	$-0.0385120\pi$
$368$	−0.0307027	−	0.0944931i	−0.00160049	−	0.00492579i
$369$	−14.6685	−	7.28022i	−0.763612	−	0.378993i
$370$	−1.86017	+	2.56030i	−0.0967056	+	0.133104i
$371$	48.4571			2.51577
$372$	−7.75544	−	5.73177i	−0.402101	−	0.297178i
$373$	−6.80304			−0.352248			−0.176124	−	0.984368i	$-0.556356\pi$
$373$	−6.80304			−0.352248			−0.176124	+	0.984368i	$0.556356\pi$
$374$	−2.97602	+	4.09614i	−0.153886	+	0.211806i
$375$	−1.11792	+	1.32297i	−0.0577291	+	0.0683180i
$376$	−2.32141	−	7.14457i	−0.119718	−	0.368453i
$377$		−	3.44211i		−	0.177277i
$378$	16.5593	−	14.6021i	0.851720	−	0.751053i
$379$	−11.0586	−	34.0349i	−0.568042	−	1.74825i	−0.658734	−	0.752376i	$-0.728908\pi$
$379$	−11.0586	−	34.0349i	−0.568042	−	1.74825i	0.0906918	−	0.995879i	$-0.471092\pi$
$380$	0.802366	+	0.260705i	0.0411605	+	0.0133739i
$381$	−0.619280	+	8.43709i	−0.0317267	+	0.432245i
$382$	−6.95653	−	5.05422i	−0.355927	−	0.258596i
$383$	−7.66779	−	23.5990i	−0.391806	−	1.20585i	−0.931421	−	0.363943i	$-0.881430\pi$
$383$	−7.66779	−	23.5990i	−0.391806	−	1.20585i	0.539616	−	0.841912i	$-0.318570\pi$
$384$	1.60368	+	0.654383i	0.0818374	+	0.0333938i
$385$	−6.08249	−	8.37184i	−0.309993	−	0.426668i
$386$	20.0115	+	6.50212i	1.01856	+	0.330949i
$387$	−7.34464	−	3.64526i	−0.373349	−	0.185299i
$388$	−11.1467	+	8.09852i	−0.565886	+	0.411140i
$389$	9.84900	−	30.3121i	0.499364	−	1.53688i	−0.310680	−	0.950515i	$-0.600557\pi$
$389$	9.84900	−	30.3121i	0.499364	−	1.53688i	0.810044	−	0.586369i	$-0.199443\pi$
$390$	2.86202	−	3.38699i	0.144924	−	0.171507i
$391$	−0.167102	−	0.121407i	−0.00845071	−	0.00613980i
$392$	−10.5121	+	3.41559i	−0.530942	+	0.172514i
$393$	2.29760	+	0.937540i	0.115899	+	0.0472926i
$394$	10.1982	+	3.31358i	0.513775	+	0.166936i
$395$	3.47073	−	10.6818i	0.174631	−	0.537460i
$396$	−5.22065	−	5.11171i	−0.262347	−	0.256873i
$397$	−19.5369			−0.980528			−0.490264	−	0.871574i	$-0.663100\pi$
$397$	−19.5369			−0.980528			−0.490264	+	0.871574i	$0.663100\pi$
$398$	20.9569			1.05048
$399$	−5.27664	+	3.27191i	−0.264162	+	0.163801i
$400$	0.809017	−	0.587785i	0.0404508	−	0.0293893i
$401$	−8.13704	−	5.91191i	−0.406344	−	0.295226i	0.365776	−	0.930703i	$-0.380804\pi$
$401$	−8.13704	−	5.91191i	−0.406344	−	0.295226i	−0.772120	+	0.635477i	$0.780804\pi$
$402$	−13.4472	+	3.30344i	−0.670683	+	0.164761i
$403$	13.2412	−	5.27767i	0.659591	−	0.262899i
$404$			17.1410i			0.852797i
$405$	−2.96101	−	8.49897i	−0.147134	−	0.422317i
$406$	3.35781	+	4.62163i	0.166645	+	0.229367i
$407$	−7.33039	+	2.38179i	−0.363354	+	0.118061i
$408$	3.49676	−	0.859019i	0.173116	−	0.0425278i
$409$			34.6834i			1.71498i	0.514497	+	0.857492i	$0.327979\pi$
$409$			34.6834i			1.71498i	−0.514497	+	0.857492i	$0.672021\pi$
$410$	5.19144	−	1.68680i	0.256387	−	0.0833051i
$411$	−20.3124	−	1.49092i	−1.00193	−	0.0735418i
$412$	2.54924	−	7.84574i	0.125592	−	0.386532i
$413$	6.08508	−	8.37540i	0.299427	−	0.412126i
$414$	0.208532	−	0.212976i	0.0102488	−	0.0104672i
$415$	−5.50141	+	7.57204i	−0.270054	+	0.371697i
$416$	−2.07119	+	1.50481i	−0.101549	+	0.0737794i
$417$	1.58470	−	21.5899i	0.0776029	−	1.05726i
$418$	1.20774	+	1.66231i	0.0590723	+	0.0813061i
$419$	−4.72557	−	6.50419i	−0.230859	−	0.317751i	0.677834	−	0.735215i	$-0.262919\pi$
$419$	−4.72557	−	6.50419i	−0.230859	−	0.317751i	−0.908693	+	0.417464i	$0.862919\pi$
$420$	−0.538722	+	7.33955i	−0.0262869	+	0.358134i
$421$	12.6779	−	9.21101i	0.617881	−	0.448917i	−0.234299	−	0.972164i	$-0.575280\pi$
$421$	12.6779	−	9.21101i	0.617881	−	0.448917i	0.852181	+	0.523247i	$0.175280\pi$
$422$	11.8979	−	16.3760i	0.579178	−	0.797171i
$423$	15.7670	−	16.1030i	0.766617	−	0.782955i
$424$	−6.70348	+	9.22655i	−0.325550	+	0.448081i
$425$	0.642410	−	1.97714i	0.0311615	−	0.0959052i
$426$	−10.9856	−	0.806343i	−0.532256	−	0.0390674i
$427$	19.9141	−	6.47048i	0.963711	−	0.313129i
$428$		−	2.95612i		−	0.142889i
$429$	10.4878	−	2.57646i	0.506358	−	0.124392i
$430$	2.59939	−	0.844594i	0.125354	−	0.0407300i
$431$	−22.1557	−	30.4947i	−1.06720	−	1.46888i	−0.872876	−	0.487942i	$-0.837748\pi$
$431$	−22.1557	−	30.4947i	−1.06720	−	1.46888i	−0.194326	−	0.980937i	$-0.562252\pi$
$432$	0.489551	+	5.17304i	0.0235535	+	0.248888i
$433$			15.2552i			0.733117i	0.930395	+	0.366558i	$0.119464\pi$
$433$			15.2552i			0.733117i	−0.930395	+	0.366558i	$0.880536\pi$
$434$	−12.6302	+	20.0031i	−0.606269	+	0.960180i
$435$	2.26150	−	0.555564i	0.108431	−	0.0266372i
$436$	1.85425	+	1.34719i	0.0888024	+	0.0645187i
$437$	−0.0678137	+	0.0492696i	−0.00324397	+	0.00235688i
$438$	−15.6520	+	9.70542i	−0.747882	+	0.463743i
$439$	−18.3386			−0.875253			−0.437627	−	0.899157i	$-0.644181\pi$
$439$	−18.3386			−0.875253			−0.437627	+	0.899157i	$0.644181\pi$
$440$	2.43550			0.116108
$441$	−23.6930	−	23.1987i	−1.12824	−	1.10470i
$442$	−1.64466	+	5.06173i	−0.0782284	+	0.240762i
$443$	−2.46877	−	0.802152i	−0.117295	−	0.0381114i	0.249781	−	0.968302i	$-0.419641\pi$
$443$	−2.46877	−	0.802152i	−0.117295	−	0.0381114i	−0.367076	+	0.930191i	$0.619641\pi$
$444$	5.07517	+	2.07093i	0.240857	+	0.0982820i
$445$	−14.5316	+	4.72160i	−0.688863	+	0.223825i
$446$	−0.692690	−	0.503269i	−0.0327998	−	0.0238305i
$447$	9.68375	−	11.4600i	0.458026	−	0.542039i
$448$	1.31298	−	4.04094i	0.0620325	−	0.190916i
$449$	−23.7207	+	17.2341i	−1.11945	+	0.813329i	−0.984126	−	0.177473i	$-0.943208\pi$
$449$	−23.7207	+	17.2341i	−1.11945	+	0.813329i	−0.135325	+	0.990801i	$0.543208\pi$
$450$	2.68723	+	1.33372i	0.126677	+	0.0628719i
$451$	12.6437	+	4.10819i	0.595370	+	0.193447i
$452$	0.334479	+	0.460371i	0.0157326	+	0.0216540i
$453$	−12.4578	−	5.08343i	−0.585320	−	0.238841i
$454$	−4.32626	−	13.3149i	−0.203041	−	0.624897i
$455$	−8.80028	−	6.39378i	−0.412563	−	0.299745i
$456$	0.106968	−	1.45734i	0.00500925	−	0.0682461i
$457$	−6.78737	−	2.20535i	−0.317500	−	0.103162i	0.145932	−	0.989295i	$-0.453382\pi$
$457$	−6.78737	−	2.20535i	−0.317500	−	0.103162i	−0.463431	+	0.886133i	$0.653382\pi$
$458$	−4.49499	−	13.8341i	−0.210037	−	0.646427i
$459$	7.14448	+	8.10209i	0.333476	+	0.378173i
$460$			0.0993559i			0.00463249i
$461$	8.33109	+	25.6405i	0.388018	+	1.19420i	0.934267	+	0.356573i	$0.116055\pi$
$461$	8.33109	+	25.6405i	0.388018	+	1.19420i	−0.546250	+	0.837622i	$0.683945\pi$
$462$	−11.5684	+	13.6903i	−0.538211	+	0.636932i
$463$	−4.15978	+	5.72544i	−0.193321	+	0.266084i	−0.894663	−	0.446741i	$-0.852585\pi$
$463$	−4.15978	+	5.72544i	−0.193321	+	0.266084i	0.701342	+	0.712825i	$0.252585\pi$
$464$	−1.34450			−0.0624169
$465$	5.60465	+	7.84780i	0.259909	+	0.363933i
$466$	−9.34223			−0.432770
$467$	14.2073	−	19.5547i	0.657436	−	0.904883i	−0.341957	−	0.939716i	$-0.611090\pi$
$467$	14.2073	−	19.5547i	0.657436	−	0.904883i	0.999393	+	0.0348324i	$0.0110897\pi$
$468$	−6.87967	−	3.41449i	−0.318013	−	0.157835i
$469$	10.4967	+	32.3055i	0.484692	+	1.49173i
$470$			7.51225i			0.346514i
$471$	−4.38167	−	17.8362i	−0.201897	−	0.821850i
$472$	0.752929	+	2.31728i	0.0346564	+	0.106661i
$473$	6.33081	+	2.05701i	0.291091	+	0.0945812i
$474$	−19.4014	−	1.42406i	−0.891135	−	0.0654091i
$475$	−0.682533	−	0.495890i	−0.0313168	−	0.0227530i
$476$	−2.72953	−	8.40064i	−0.125108	−	0.385043i
$477$	−33.8472	−	4.99567i	−1.54976	−	0.228736i
$478$	−5.06933	−	6.97734i	−0.231866	−	0.319136i
$479$	−7.27079	−	2.36242i	−0.332211	−	0.107942i	0.138162	−	0.990410i	$-0.455881\pi$
$479$	−7.27079	−	2.36242i	−0.332211	−	0.107942i	−0.470373	+	0.882468i	$0.655881\pi$
$480$	−1.32297	−	1.11792i	−0.0603852	−	0.0510258i
$481$	−6.55472	+	4.76228i	−0.298870	+	0.217141i
$482$	−7.20034	+	22.1604i	−0.327966	+	1.00938i
$483$	−0.558497	−	0.471932i	−0.0254125	−	0.0214737i
$484$	−4.10039	−	2.97911i	−0.186381	−	0.135414i
$485$	13.1037	−	4.25765i	0.595008	−	0.193330i
$486$	−13.0721	+	8.49240i	−0.592961	+	0.385223i
$487$	12.7954	+	4.15749i	0.579817	+	0.188394i	0.584219	−	0.811596i	$-0.301401\pi$
$487$	12.7954	+	4.15749i	0.579817	+	0.188394i	−0.00440152	+	0.999990i	$0.501401\pi$
$488$	−1.52286	+	4.68689i	−0.0689368	+	0.212166i
$489$	−23.8584	+	14.7940i	−1.07891	+	0.669008i
$490$	11.0531			0.499328
$491$	−24.2627			−1.09496			−0.547479	−	0.836819i	$-0.684413\pi$
$491$	−24.2627			−1.09496			−0.547479	+	0.836819i	$0.684413\pi$
$492$	−4.98243	−	8.03520i	−0.224625	−	0.362255i
$493$	−2.26125	+	1.64290i	−0.101842	+	0.0739923i
$494$	1.74738	+	1.26954i	0.0786182	+	0.0571195i
$495$	3.38552	+	6.47479i	0.152168	+	0.291020i
$496$	−2.06148	−	5.17207i	−0.0925632	−	0.232233i
$497$			27.0213i			1.21207i
$498$	15.0097	+	6.12473i	0.672601	+	0.274456i
$499$	−14.0881	−	19.3907i	−0.630672	−	0.868045i	0.367403	−	0.930062i	$-0.380247\pi$
$499$	−14.0881	−	19.3907i	−0.630672	−	0.868045i	−0.998075	+	0.0620164i	$0.980247\pi$
$500$	−0.951057	+	0.309017i	−0.0425325	+	0.0138197i
$501$	5.94871	+	24.2151i	0.265769	+	1.08185i
$502$			24.3437i			1.08651i
$503$	−12.5891	+	4.09046i	−0.561322	+	0.182385i	−0.575916	−	0.817509i	$-0.695355\pi$
$503$	−12.5891	+	4.09046i	−0.561322	+	0.182385i	0.0145937	+	0.999894i	$0.495355\pi$
$504$	12.5680	−	2.12664i	0.559824	−	0.0947280i
$505$	5.29686	−	16.3021i	0.235707	−	0.725432i
$506$	−0.142233	+	0.195767i	−0.00632302	+	0.00870289i
$507$	−9.48824	+	5.88343i	−0.421388	+	0.261292i
$508$	−2.87090	+	3.95145i	−0.127375	+	0.175317i
$509$	−2.00721	+	1.45832i	−0.0889680	+	0.0646390i	−0.631380	−	0.775474i	$-0.717511\pi$
$509$	−2.00721	+	1.45832i	−0.0889680	+	0.0646390i	0.542412	+	0.840113i	$0.317511\pi$
$510$	−3.59107	−	0.263584i	−0.159015	−	0.0116717i
$511$	26.5552	+	36.5501i	1.17473	+	1.61688i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	4.02304	−	1.74143i	0.177622	−	0.0768862i
$514$	21.2926	−	15.4700i	0.939177	−	0.682352i
$515$	−4.84893	+	6.67399i	−0.213670	+	0.294091i
$516$	−2.49474	−	4.02329i	−0.109825	−	0.177115i
$517$	−10.7541	+	14.8018i	−0.472967	+	0.650983i
$518$	4.15520	−	12.7884i	0.182569	−	0.561890i
$519$	1.97487	−	26.9056i	0.0866870	−	1.18103i
$520$	2.43483	−	0.791125i	0.106774	−	0.0346931i
$521$			36.7482i			1.60997i	0.593296	+	0.804984i	$0.297826\pi$
$521$			36.7482i			1.60997i	−0.593296	+	0.804984i	$0.702174\pi$
$522$	−1.86896	−	3.57437i	−0.0818022	−	0.156446i
$523$	−12.6985	+	4.12599i	−0.555267	+	0.180417i	−0.573190	−	0.819422i	$-0.694294\pi$
$523$	−12.6985	+	4.12599i	−0.555267	+	0.180417i	0.0179236	+	0.999839i	$0.494294\pi$
$524$	0.842125	+	1.15909i	0.0367884	+	0.0506349i
$525$	2.78040	−	6.81386i	0.121347	−	0.297381i
$526$		−	10.3455i		−	0.451086i
$527$	−9.78705	−	6.17966i	−0.426330	−	0.269190i
$528$	−1.00638	−	4.09660i	−0.0437969	−	0.178282i
$529$	18.5994	+	13.5133i	0.808670	+	0.587533i
$530$	9.22655	−	6.70348i	0.400776	−	0.291181i
$531$	−5.11388	+	5.22287i	−0.221924	+	0.226653i
$532$	−3.58461			−0.155413
$533$	13.9748			0.605314
$534$	13.9465	+	22.4917i	0.603526	+	0.973310i
$535$	−0.913491	+	2.81144i	−0.0394937	+	0.121549i
$536$	−7.60327	−	2.47045i	−0.328411	−	0.106707i
$537$	14.1499	−	34.6769i	0.610615	−	1.49642i
$538$	0.455055	−	0.147856i	0.0196188	−	0.00637454i
$539$	21.7785	+	15.8230i	0.938068	+	0.681546i
$540$	1.13297	−	5.07113i	0.0487551	−	0.218227i
$541$	8.32168	−	25.6115i	0.357777	−	1.10112i	−0.596605	−	0.802535i	$-0.703484\pi$
$541$	8.32168	−	25.6115i	0.357777	−	1.10112i	0.954382	−	0.298589i	$-0.0965160\pi$
$542$	−21.1833	+	15.3905i	−0.909899	+	0.661080i
$543$	−21.0210	+	24.8768i	−0.902097	+	1.06756i
$544$	1.97714	+	0.642410i	0.0847690	+	0.0275431i
$545$	−1.34719	−	1.85425i	−0.0577073	−	0.0794273i
$546$	−7.11820	+	17.4444i	−0.304631	+	0.746551i
$547$	5.11961	+	15.7565i	0.218899	+	0.673701i	0.998854	+	0.0478653i	$0.0152418\pi$
$547$	5.11961	+	15.7565i	0.218899	+	0.673701i	−0.779955	+	0.625835i	$0.784758\pi$
$548$	−9.51314	−	6.91170i	−0.406381	−	0.295253i
$549$	−14.5771	+	2.46659i	−0.622134	+	0.105271i
$550$	−2.31629	−	0.752609i	−0.0987671	−	0.0320914i
$551$	0.350518	+	1.07878i	0.0149326	+	0.0459577i
$552$	0.167121	−	0.0410550i	0.00711312	−	0.00174742i
$553$			47.7216i			2.02933i
$554$	−4.41202	−	13.5788i	−0.187449	−	0.576909i
$555$	−4.18682	−	3.53789i	−0.177721	−	0.150175i
$556$	7.34643	−	10.1115i	0.311558	−	0.428823i
$557$	24.3729			1.03271			0.516357	−	0.856374i	$-0.327288\pi$
$557$	24.3729			1.03271			0.516357	+	0.856374i	$0.327288\pi$
$558$	10.8844	−	12.6700i	0.460773	−	0.536366i
$559$	6.99727			0.295953
$560$	−2.49744	+	3.43743i	−0.105536	+	0.145258i
$561$	−6.69836	−	5.66014i	−0.282805	−	0.238971i
$562$	6.52939	+	20.0954i	0.275426	+	0.847673i
$563$			10.1784i			0.428969i	0.976727	+	0.214484i	$0.0688071\pi$
$563$			10.1784i			0.428969i	−0.976727	+	0.214484i	$0.931193\pi$
$564$	12.6359	−	3.10415i	0.532067	−	0.130708i
$565$	−0.175846	−	0.541199i	−0.00739790	−	0.0227684i
$566$	−26.0808	−	8.47415i	−1.09626	−	0.356195i
$567$	23.1242	+	30.4561i	0.971126	+	1.27903i
$568$	−5.14504	−	3.73809i	−0.215881	−	0.156847i
$569$	−0.920899	−	2.83424i	−0.0386061	−	0.118817i	0.929896	−	0.367822i	$-0.119896\pi$
$569$	−0.920899	−	2.83424i	−0.0386061	−	0.118817i	−0.968502	+	0.249005i	$0.919896\pi$
$570$	−0.552075	+	1.35296i	−0.0231239	+	0.0566691i
$571$	−1.40704	−	1.93663i	−0.0588828	−	0.0810453i	0.778560	−	0.627570i	$-0.215950\pi$
$571$	−1.40704	−	1.93663i	−0.0588828	−	0.0810453i	−0.837443	+	0.546525i	$0.815950\pi$
$572$	5.93002	+	1.92678i	0.247947	+	0.0805628i
$573$	9.61270	−	11.3759i	0.401576	−	0.475235i
$574$	−18.7635	+	13.6325i	−0.783175	+	0.569010i
$575$	0.0307027	−	0.0944931i	0.00128039	−	0.00394063i
$576$	−1.33372	+	2.68723i	−0.0555715	+	0.111968i
$577$	−22.4207	−	16.2896i	−0.933386	−	0.678145i	0.0134332	−	0.999910i	$-0.495724\pi$
$577$	−22.4207	−	16.2896i	−0.933386	−	0.678145i	−0.946820	+	0.321765i	$0.895724\pi$
$578$	−12.0577	+	3.91779i	−0.501535	+	0.162959i
$579$	−13.7691	+	33.7435i	−0.572223	+	1.40233i
$580$	1.27870	+	0.415474i	0.0530950	+	0.0172516i
$581$	12.2889	−	37.8214i	0.509830	−	1.56910i
$582$	−12.5761	−	20.2816i	−0.521297	−	0.840700i
$583$	27.7760			1.15036
$584$	−10.6330			−0.439996
$585$	5.48782	+	5.37331i	0.226893	+	0.222159i
$586$	1.71113	−	1.24321i	0.0706863	−	0.0513566i
$587$	32.2721	+	23.4470i	1.33201	+	0.967762i	0.999698	+	0.0245928i	$0.00782891\pi$
$587$	32.2721	+	23.4470i	1.33201	+	0.967762i	0.332313	+	0.943169i	$0.392171\pi$
$588$	−4.56727	−	18.5917i	−0.188351	−	0.766710i
$589$	−3.61246	+	3.00244i	−0.148849	+	0.123714i
$590$		−	2.43653i		−	0.100310i
$591$	−7.01692	+	17.1962i	−0.288638	+	0.707357i
$592$	1.86017	+	2.56030i	0.0764525	+	0.105228i
$593$	−39.8128	+	12.9360i	−1.63492	+	0.531216i	−0.975394	−	0.220470i	$-0.929241\pi$
$593$	−39.8128	+	12.9360i	−1.63492	+	0.531216i	−0.659521	+	0.751686i	$0.729241\pi$
$594$	9.49192	−	8.37005i	0.389458	−	0.343427i
$595$			8.83295i			0.362116i
$596$	8.23834	−	2.67680i	0.337456	−	0.109646i
$597$	−2.65715	+	36.2011i	−0.108750	+	1.48161i
$598$	−0.0786030	+	0.241915i	−0.00321431	+	0.00989264i
$599$	25.3365	−	34.8727i	1.03522	−	1.42486i	0.134270	−	0.990945i	$-0.457131\pi$
$599$	25.3365	−	34.8727i	1.03522	−	1.42486i	0.900953	−	0.433917i	$-0.142869\pi$
$600$	0.912766	+	1.47202i	0.0372635	+	0.0600952i
$601$	9.71158	−	13.3668i	0.396144	−	0.545245i	−0.563627	−	0.826029i	$-0.690595\pi$
$601$	9.71158	−	13.3668i	0.396144	−	0.545245i	0.959771	+	0.280784i	$0.0905945\pi$
$602$	−9.39505	+	6.82590i	−0.382914	+	0.278203i
$603$	−4.00140	−	23.6475i	−0.162950	−	0.963001i
$604$	−4.56609	−	6.28468i	−0.185791	−	0.255720i
$605$	2.97911	+	4.10039i	0.121118	+	0.166705i
$606$	−29.6094	−	2.17333i	−1.20280	−	0.0882853i
$607$	35.5113	−	25.8004i	1.44136	−	1.04721i	0.453601	−	0.891205i	$-0.350139\pi$
$607$	35.5113	−	25.8004i	1.44136	−	1.04721i	0.987757	−	0.156002i	$-0.0498607\pi$
$608$	0.495890	−	0.682533i	0.0201110	−	0.0276804i
$609$	−8.40915	+	5.21431i	−0.340756	+	0.211294i
$610$	2.89666	−	3.98691i	0.117282	−	0.161425i
$611$	−5.94313	+	18.2911i	−0.240433	+	0.739977i
$612$	1.04051	+	6.14924i	0.0420603	+	0.248568i
$613$	17.1805	−	5.58229i	0.693914	−	0.225466i	0.0592373	−	0.998244i	$-0.481133\pi$
$613$	17.1805	−	5.58229i	0.693914	−	0.225466i	0.634677	+	0.772777i	$0.281133\pi$
$614$		−	13.7738i		−	0.555866i
$615$	2.25556	+	9.18158i	0.0909529	+	0.370237i
$616$	−9.84168	+	3.19776i	−0.396533	+	0.128841i
$617$	11.9693	+	16.4743i	0.481865	+	0.663231i	0.978862	−	0.204522i	$-0.0655639\pi$
$617$	11.9693	+	16.4743i	0.481865	+	0.663231i	−0.496997	+	0.867752i	$0.665564\pi$
$618$	13.2295	+	5.39833i	0.532170	+	0.217153i
$619$			21.3198i			0.856914i	0.903562	+	0.428457i	$0.140943\pi$
$619$			21.3198i			0.856914i	−0.903562	+	0.428457i	$0.859057\pi$
$620$	0.362327	+	5.55596i	0.0145514	+	0.223133i
$621$	0.341456	+	0.387222i	0.0137021	+	0.0155387i
$622$	10.9004	+	7.91958i	0.437065	+	0.317546i
$623$	52.5219	−	38.1594i	2.10424	−	1.52882i
$624$	−2.33681	−	3.76858i	−0.0935471	−	0.150864i
$625$	1.00000			0.0400000
$626$	−2.12210			−0.0848163
$627$	−3.02461	+	1.87548i	−0.120791	+	0.0748996i
$628$	3.27680	−	10.0849i	0.130758	−	0.402433i
$629$	6.25706	+	2.03304i	0.249485	+	0.0810627i
$630$	−12.6101	−	1.86118i	−0.502397	−	0.0741512i
$631$	−18.9885	+	6.16975i	−0.755921	+	0.245614i	−0.661527	−	0.749921i	$-0.730091\pi$
$631$	−18.9885	+	6.16975i	−0.755921	+	0.245614i	−0.0943942	+	0.995535i	$0.530091\pi$
$632$	−9.08650	−	6.60173i	−0.361441	−	0.262603i
$633$	26.7794	+	22.6287i	1.06439	+	0.899411i
$634$	5.70409	−	17.5554i	0.226538	−	0.697213i
$635$	3.95145	−	2.87090i	0.156809	−	0.113928i
$636$	−15.0880	−	12.7495i	−0.598280	−	0.505549i
$637$	26.9124	+	8.74438i	1.06631	+	0.346465i
$638$	1.92472	+	2.64915i	0.0762004	+	0.104881i
$639$	2.78576	−	18.8744i	0.110203	−	0.746659i
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	−23.6116	−	17.1548i	−0.932601	−	0.677574i	0.0140275	−	0.999902i	$-0.495535\pi$
$641$	−23.6116	−	17.1548i	−0.932601	−	0.677574i	−0.946628	+	0.322327i	$0.895535\pi$
$642$	5.10641	+	0.374809i	0.201534	+	0.0147925i
$643$	−37.0985	−	12.0540i	−1.46302	−	0.475365i	−0.534032	−	0.845465i	$-0.679324\pi$
$643$	−37.0985	−	12.0540i	−1.46302	−	0.475365i	−0.928992	+	0.370099i	$0.879324\pi$
$644$	−0.130452	−	0.401491i	−0.00514054	−	0.0158210i
$645$	1.12938	+	4.59729i	0.0444691	+	0.181018i
$646$		−	1.75387i		−	0.0690049i
$647$	−0.848999	−	2.61295i	−0.0333776	−	0.102726i	0.932980	−	0.359929i	$-0.117199\pi$
$647$	−0.848999	−	2.61295i	−0.0333776	−	0.102726i	−0.966357	+	0.257203i	$0.917199\pi$
$648$	−8.99800	+	0.189758i	−0.353475	+	0.00745439i
$649$	3.48801	−	4.80083i	0.136916	−	0.188449i
$650$	−2.56013			−0.100417
$651$	−32.9520	−	24.3537i	−1.29149	−	0.954495i
$652$	−16.2079			−0.634749
$653$	−15.6946	+	21.6017i	−0.614176	+	0.845341i	−0.996913	−	0.0785168i	$-0.974982\pi$
$653$	−15.6946	+	21.6017i	−0.614176	+	0.845341i	0.382737	+	0.923857i	$0.374982\pi$
$654$	−2.56224	+	3.03223i	−0.100192	+	0.118569i
$655$	−0.442731	−	1.36259i	−0.0172989	−	0.0532407i
$656$		−	5.45860i		−	0.213123i
$657$	−14.7807	−	28.2679i	−0.576648	−	1.10284i
$658$	−9.86343	−	30.3565i	−0.384517	−	1.18342i
$659$	21.1717	+	6.87910i	0.824732	+	0.267972i	0.690825	−	0.723022i	$-0.257248\pi$
$659$	21.1717	+	6.87910i	0.824732	+	0.267972i	0.133907	+	0.990994i	$0.457248\pi$
$660$	−0.308799	+	4.20708i	−0.0120200	+	0.163761i
$661$	1.08024	+	0.784837i	0.0420163	+	0.0305266i	0.608595	−	0.793481i	$-0.291733\pi$
$661$	1.08024	+	0.784837i	0.0420163	+	0.0305266i	−0.566579	+	0.824008i	$0.691733\pi$
$662$	−1.76210	−	5.42320i	−0.0684861	−	0.210779i
$663$	−8.53513	−	3.48277i	−0.331477	−	0.135260i
$664$	5.50141	+	7.57204i	0.213496	+	0.293852i
$665$	3.40917	+	1.10771i	0.132202	+	0.0429550i
$666$	−4.22082	+	8.50430i	−0.163553	+	0.329535i
$667$	−0.108072	+	0.0785188i	−0.00418456	+	0.00304026i
$668$	−4.44870	+	13.6917i	−0.172125	+	0.529747i
$669$	0.957176	−	1.13275i	0.0370066	−	0.0437945i
$670$	6.46773	+	4.69908i	0.249870	+	0.181541i
$671$	11.4149	−	3.70893i	0.440667	−	0.143182i
$672$	6.81386	+	2.78040i	0.262850	+	0.107256i
$673$	5.34246	+	1.73587i	0.205937	+	0.0669129i	0.410169	−	0.912010i	$-0.365470\pi$
$673$	5.34246	+	1.73587i	0.205937	+	0.0669129i	−0.204232	+	0.978922i	$0.565470\pi$
$674$	4.09499	−	12.6031i	0.157733	−	0.485453i
$675$	−2.64458	+	4.47283i	−0.101790	+	0.172159i
$676$	−6.44571			−0.247912
$677$	11.5872			0.445333			0.222666	−	0.974895i	$-0.428524\pi$
$677$	11.5872			0.445333			0.222666	+	0.974895i	$0.428524\pi$
$678$	−0.837656	+	0.519410i	−0.0321700	+	0.0199478i
$679$	−47.3610	+	34.4098i	−1.81755	+	1.32053i
$680$	−1.68185	−	1.22194i	−0.0644961	−	0.0468591i
$681$	23.5487	−	5.78499i	0.902387	−	0.221681i
$682$	−7.23971	+	11.4659i	−0.277223	+	0.439053i
$683$		−	14.5322i		−	0.556057i	−0.960573	−	0.278029i	$-0.910319\pi$
$683$		−	14.5322i		−	0.556057i	0.960573	−	0.278029i	$-0.0896810\pi$
$684$	2.50385	+	0.369555i	0.0957370	+	0.0141303i
$685$	6.91170	+	9.51314i	0.264083	+	0.363479i
$686$	−16.3783	+	5.32163i	−0.625326	+	0.203181i
$687$	24.4671	−	6.01061i	0.933477	−	0.229319i
$688$		−	2.73316i		−	0.104201i
$689$	27.7684	−	9.02250i	1.05789	−	0.343730i
$690$	−0.171628	−	0.0125974i	−0.00653376	−	0.000479576i
$691$	−5.71938	+	17.6024i	−0.217575	+	0.669628i	0.781385	+	0.624049i	$0.214513\pi$
$691$	−5.71938	+	17.6024i	−0.217575	+	0.669628i	−0.998961	+	0.0455792i	$0.985487\pi$
$692$	9.15519	−	12.6010i	0.348028	−	0.479020i
$693$	−22.1820	−	21.7191i	−0.842623	−	0.825041i
$694$	19.7343	−	27.1620i	0.749106	−	1.03106i
$695$	−10.1115	+	7.34643i	−0.383551	+	0.278666i
$696$	0.170471	−	2.32250i	0.00646168	−	0.0880340i
$697$	−6.67007	−	9.18056i	−0.252647	−	0.347738i
$698$	13.4279	+	18.4819i	0.508253	+	0.699551i
$699$	1.18451	−	16.1378i	0.0448023	−	0.610388i
$700$	3.43743	−	2.49744i	0.129923	−	0.0943942i
$701$	−20.2962	+	27.9353i	−0.766577	+	1.05510i	0.230061	+	0.973176i	$0.426107\pi$
$701$	−20.2962	+	27.9353i	−0.766577	+	1.05510i	−0.996638	+	0.0819265i	$0.973893\pi$
$702$	6.77048	−	11.4510i	0.255535	−	0.432192i
$703$	1.56935	−	2.16002i	0.0591890	−	0.0814667i
$704$	0.752609	−	2.31629i	0.0283650	−	0.0872986i
$705$	−12.9767	−	0.952485i	−0.488730	−	0.0358727i
$706$	19.8585	−	6.45243i	0.747386	−	0.242841i
$707$			72.8303i			2.73907i
$708$	−4.09834	+	1.00680i	−0.154025	+	0.0378380i
$709$	19.2478	−	6.25400i	0.722867	−	0.234874i	0.0756013	−	0.997138i	$-0.475912\pi$
$709$	19.2478	−	6.25400i	0.722867	−	0.234874i	0.647266	+	0.762264i	$0.275912\pi$
$710$	3.73809	+	5.14504i	0.140288	+	0.193090i
$711$	4.91984	−	33.3335i	0.184509	−	1.25010i
$712$			15.2794i			0.572620i
$713$	−0.467752	−	0.295344i	−0.0175174	−	0.0110607i
$714$	14.8574	−	3.64988i	0.556023	−	0.136593i
$715$	−5.04438	−	3.66496i	−0.188649	−	0.137062i
$716$	17.4937	−	12.7099i	0.653768	−	0.474991i
$717$	12.6954	−	7.87212i	0.474120	−	0.293990i
$718$	36.3557			1.35678
$719$	−28.9848			−1.08095			−0.540475	−	0.841360i	$-0.681756\pi$
$719$	−28.9848			−1.08095			−0.540475	+	0.841360i	$0.681756\pi$
$720$	2.09884	−	2.14357i	0.0782191	−	0.0798860i
$721$	10.8314	−	33.3357i	0.403384	−	1.24149i
$722$	17.3932	+	5.65138i	0.647306	+	0.210322i
$723$	−37.3669	−	15.2476i	−1.38969	−	0.567065i
$724$	−17.8834	+	5.81066i	−0.664630	+	0.215951i
$725$	−1.08772	−	0.790278i	−0.0403971	−	0.0293502i
$726$	5.66602	−	6.70531i	0.210286	−	0.248857i
$727$	16.0872	−	49.5112i	0.596640	−	1.83627i	0.0502543	−	0.998736i	$-0.483997\pi$
$727$	16.0872	−	49.5112i	0.596640	−	1.83627i	0.546386	−	0.837534i	$-0.316003\pi$
$728$	−8.80028	+	6.39378i	−0.326160	+	0.236969i
$729$	−13.0124	−	23.6575i	−0.481940	−	0.876204i
$730$	10.1126	+	3.28577i	0.374283	+	0.121612i
$731$	−3.33975	−	4.59678i	−0.123525	−	0.170018i
$732$	−7.90307	−	3.22486i	−0.292106	−	0.119194i
$733$	5.26468	+	16.2030i	0.194455	+	0.598472i	0.999983	+	0.00591334i	$0.00188229\pi$
$733$	5.26468	+	16.2030i	0.194455	+	0.598472i	−0.805527	+	0.592559i	$0.798118\pi$
$734$	3.74116	+	2.71811i	0.138089	+	0.100327i
$735$	−1.40143	+	19.0932i	−0.0516926	+	0.704262i
$736$	0.0944931	+	0.0307027i	0.00348306	+	0.00113172i
$737$	6.01678	+	18.5177i	0.221631	+	0.682110i
$738$	14.5118	−	7.58787i	0.534185	−	0.279313i
$739$			4.96564i			0.182664i	0.995820	+	0.0913320i	$0.0291125\pi$
$739$			4.96564i			0.182664i	−0.995820	+	0.0913320i	$0.970888\pi$
$740$	−0.977949	−	3.00982i	−0.0359501	−	0.110643i
$741$	−2.41457	+	2.85746i	−0.0887014	+	0.104971i
$742$	−28.4824	+	39.2026i	−1.04562	+	1.43917i
$743$	−21.1751			−0.776838			−0.388419	−	0.921483i	$-0.626979\pi$
$743$	−21.1751			−0.776838			−0.388419	+	0.921483i	$0.626979\pi$
$744$	9.19563	−	2.90524i	0.337128	−	0.106511i
$745$	−8.66230			−0.317362
$746$	3.99872	−	5.50377i	0.146404	−	0.201507i
$747$	−12.4830	+	25.1513i	−0.456728	+	0.920237i
$748$	−1.56459	−	4.81530i	−0.0572070	−	0.176065i
$749$		−	12.5602i		−	0.458941i
$750$	−0.413212	−	1.68204i	−0.0150884	−	0.0614194i
$751$	−1.22928	−	3.78332i	−0.0448569	−	0.138055i	0.926120	−	0.377230i	$-0.123123\pi$
$751$	−1.22928	−	3.78332i	−0.0448569	−	0.138055i	−0.970977	+	0.239174i	$0.923123\pi$
$752$	7.14457	+	2.32141i	0.260536	+	0.0846532i
$753$	−42.0513	−	3.08656i	−1.53244	−	0.112480i
$754$	2.78472	+	2.02322i	0.101414	+	0.0736813i
$755$	2.40053	+	7.38808i	0.0873644	+	0.268880i
$756$	2.08005	+	21.9797i	0.0756507	+	0.799394i
$757$	5.52810	+	7.60878i	0.200922	+	0.276546i	0.897574	−	0.440864i	$-0.145328\pi$
$757$	5.52810	+	7.60878i	0.200922	+	0.276546i	−0.696652	+	0.717409i	$0.745328\pi$
$758$	34.0349	+	11.0586i	1.23620	+	0.401667i
$759$	−0.320134	−	0.270515i	−0.0116201	−	0.00981907i
$760$	−0.682533	+	0.495890i	−0.0247581	+	0.0179878i
$761$	6.26538	−	19.2829i	0.227120	−	0.699003i	−0.770950	−	0.636896i	$-0.780218\pi$
$761$	6.26538	−	19.2829i	0.227120	−	0.699003i	0.998070	−	0.0621069i	$-0.0197820\pi$
$762$	−6.46175	−	5.46021i	−0.234084	−	0.197802i
$763$	7.87851	+	5.72407i	0.285221	+	0.207225i
$764$	8.17789	−	2.65716i	0.295866	−	0.0961326i
$765$	0.910631	−	6.16981i	0.0329239	−	0.223070i
$766$	23.5990	+	7.66779i	0.852668	+	0.277049i
$767$	1.92760	−	5.93255i	0.0696016	−	0.214212i
$768$	−1.47202	+	0.912766i	−0.0531171	+	0.0329366i
$769$	34.2450			1.23491			0.617454	−	0.786607i	$-0.288164\pi$
$769$	34.2450			1.23491			0.617454	+	0.786607i	$0.288164\pi$
$770$	10.3482			0.372922
$771$	24.0232	+	38.7424i	0.865175	+	1.39527i
$772$	−17.0228	+	12.3678i	−0.612663	+	0.445126i
$773$	22.3138	+	16.2119i	0.802571	+	0.583102i	0.911667	−	0.410929i	$-0.134796\pi$
$773$	22.3138	+	16.2119i	0.802571	+	0.583102i	−0.109096	+	0.994031i	$0.534796\pi$
$774$	7.26615	−	3.79931i	0.261176	−	0.136563i
$775$	1.37229	−	5.39600i	0.0492942	−	0.193830i
$776$		−	13.7780i		−	0.494602i
$777$	21.5639	+	8.79916i	0.773600	+	0.315668i
$778$	18.7339	+	25.7850i	0.671643	+	0.924437i
$779$	−4.37980	+	1.42308i	−0.156923	+	0.0509872i
$780$	1.05788	+	4.30625i	0.0378781	+	0.154188i
$781$			15.4888i			0.554234i
$782$	0.196440	−	0.0638272i	0.00702468	−	0.00228246i
$783$	6.41136	−	2.77525i	0.229123	−	0.0991794i
$784$	3.41559	−	10.5121i	0.121985	−	0.375433i
$785$	−6.23284	+	8.57876i	−0.222459	+	0.306189i
$786$	−2.10898	+	1.30773i	−0.0752249	+	0.0466451i
$787$	−15.9754	+	21.9883i	−0.569463	+	0.783798i	−0.992491	−	0.122318i	$-0.960967\pi$
$787$	−15.9754	+	21.9883i	−0.569463	+	0.783798i	0.423028	+	0.906117i	$0.360967\pi$
$788$	−8.67506	+	6.30280i	−0.309036	+	0.224528i
$789$	17.8709	+	1.31172i	0.636221	+	0.0466985i
$790$	6.60173	+	9.08650i	0.234879	+	0.323283i
$791$	1.42117	+	1.95607i	0.0505309	+	0.0695498i
$792$	7.20408	−	1.21900i	0.255986	−	0.0433154i
$793$	10.2070	−	7.41584i	0.362462	−	0.263344i
$794$	11.4835	−	15.8057i	0.407534	−	0.560922i
$795$	10.4098	+	16.7879i	0.369197	+	0.595406i
$796$	−12.3182	+	16.9545i	−0.436607	+	0.600937i
$797$	−10.5397	+	32.4379i	−0.373336	+	1.14901i	0.571259	+	0.820770i	$0.306455\pi$
$797$	−10.5397	+	32.4379i	−0.373336	+	1.14901i	−0.944595	+	0.328239i	$0.893545\pi$
$798$	0.454497	−	6.19207i	0.0160890	−	0.219197i
$799$	14.8527	−	4.82594i	0.525452	−	0.170730i
$800$			1.00000i			0.0353553i
$801$	−40.6205	+	21.2396i	−1.43525	+	0.750463i
$802$	9.56566	−	3.10807i	0.337775	−	0.109750i
$803$	15.2216	+	20.9508i	0.537159	+	0.739336i
$804$	5.23150	−	12.8207i	0.184501	−	0.452151i
$805$			0.422153i			0.0148789i
$806$	−3.51326	+	13.8145i	−0.123749	+	0.486595i
$807$	0.197711	+	0.804811i	0.00695975	+	0.0283307i
$808$	−13.8674	−	10.0752i	−0.487852	−	0.354445i
$809$	−43.7517	+	31.7875i	−1.53823	+	1.11759i	−0.586792	+	0.809737i	$0.699610\pi$
$809$	−43.7517	+	31.7875i	−1.53823	+	1.11759i	−0.951435	+	0.307850i	$0.900390\pi$
$810$	8.61624	+	2.60006i	0.302744	+	0.0913569i
$811$	43.8729			1.54059			0.770294	−	0.637689i	$-0.220110\pi$
$811$	43.8729			1.54059			0.770294	+	0.637689i	$0.220110\pi$
$812$	−5.71264			−0.200475
$813$	−23.8998	−	38.5434i	−0.838204	−	1.35178i
$814$	2.38179	−	7.33039i	0.0834817	−	0.256930i
$815$	15.4146	+	5.00851i	0.539950	+	0.175440i
$816$	−1.36038	+	3.33386i	−0.0476230	+	0.116708i
$817$	−2.19300	+	0.712548i	−0.0767233	+	0.0249289i
$818$	−28.0595	−	20.3864i	−0.981076	−	0.712793i
$819$	−29.2310	−	14.5078i	−1.02141	−	0.506944i
$820$	−1.68680	+	5.19144i	−0.0589056	+	0.181293i
$821$	40.6054	−	29.5015i	1.41714	−	1.02961i	0.424901	−	0.905240i	$-0.360309\pi$
$821$	40.6054	−	29.5015i	1.41714	−	1.02961i	0.992236	−	0.124371i	$-0.0396912\pi$
$822$	13.1455	−	15.5567i	0.458501	−	0.542602i
$823$	28.1388	+	9.14284i	0.980855	+	0.318699i	0.755190	−	0.655506i	$-0.227544\pi$
$823$	28.1388	+	9.14284i	0.980855	+	0.318699i	0.225665	+	0.974205i	$0.427544\pi$
$824$	4.84893	+	6.67399i	0.168921	+	0.232499i
$825$	1.59375	−	3.90575i	0.0554871	−	0.135981i
$826$	3.19912	+	9.84587i	0.111311	+	0.342582i
$827$	15.6277	+	11.3542i	0.543428	+	0.394824i	0.825357	−	0.564612i	$-0.190974\pi$
$827$	15.6277	+	11.3542i	0.543428	+	0.394824i	−0.281928	+	0.959435i	$0.590974\pi$
$828$	0.0497292	+	0.293890i	0.00172821	+	0.0102134i
$829$	12.2306	+	3.97398i	0.424788	+	0.138022i	0.513606	−	0.858026i	$-0.328309\pi$
$829$	12.2306	+	3.97398i	0.424788	+	0.138022i	−0.0888186	+	0.996048i	$0.528309\pi$
$830$	−2.89226	−	8.90147i	−0.100392	−	0.308974i
$831$	24.0155	−	5.89968i	0.833088	−	0.204657i
$832$		−	2.56013i		−	0.0887567i
$833$	−7.10062	−	21.8535i	−0.246022	−	0.757178i
$834$	16.5352	+	13.9723i	0.572566	+	0.483821i
$835$	8.46192	−	11.6468i	0.292837	−	0.403056i
$836$	−2.05472			−0.0710641
$837$	20.5062	+	20.4082i	0.708799	+	0.705410i
$838$	8.03962			0.277724
$839$	−1.47205	+	2.02610i	−0.0508208	+	0.0699488i	−0.833671	−	0.552261i	$-0.813765\pi$
$839$	−1.47205	+	2.02610i	−0.0508208	+	0.0699488i	0.782850	+	0.622210i	$0.213765\pi$
$840$	−5.62117	−	4.74992i	−0.193949	−	0.163888i
$841$	−8.40289	−	25.8614i	−0.289755	−	0.891773i
$842$			15.6707i			0.540048i
$843$	−35.5407	+	8.73097i	−1.22409	+	0.300711i
$844$	6.25507	+	19.2511i	0.215308	+	0.662651i
$845$	6.13023	+	1.99183i	0.210886	+	0.0685212i
$846$	3.76000	+	22.2209i	0.129271	+	0.763969i
$847$	−17.4221	−	12.6579i	−0.598631	−	0.434931i
$848$	−3.52423	−	10.8465i	−0.121023	−	0.372469i
$849$	17.9451	−	43.9775i	0.615874	−	1.50931i
$850$	1.22194	+	1.68185i	0.0419121	+	0.0576870i
$851$	0.299043	+	0.0971650i	0.0102511	+	0.00333077i
$852$	7.10954	−	8.41361i	0.243569	−	0.288245i
$853$	−18.0798	+	13.1358i	−0.619041	+	0.449760i	−0.852586	−	0.522586i	$-0.824967\pi$
$853$	−18.0798	+	13.1358i	−0.619041	+	0.449760i	0.233545	+	0.972346i	$0.424967\pi$
$854$	−6.47048	+	19.9141i	−0.221415	+	0.681447i
$855$	−2.26710	−	1.12520i	−0.0775333	−	0.0384810i
$856$	2.39155	+	1.73756i	0.0817415	+	0.0593887i
$857$	−48.7279	+	15.8327i	−1.66451	+	0.540834i	−0.981811	−	0.189861i	$-0.939196\pi$
$857$	−48.7279	+	15.8327i	−1.66451	+	0.540834i	−0.682704	+	0.730695i	$0.739196\pi$
$858$	−4.08020	+	9.99925i	−0.139296	+	0.341369i
$859$	−22.4932	−	7.30848i	−0.767457	−	0.249362i	−0.100981	−	0.994888i	$-0.532198\pi$
$859$	−22.4932	−	7.30848i	−0.767457	−	0.249362i	−0.666476	+	0.745526i	$0.732198\pi$
$860$	−0.844594	+	2.59939i	−0.0288004	+	0.0886386i
$861$	−21.1698	−	34.1407i	−0.721465	−	1.16351i
$862$	37.6935			1.28385
$863$	−26.4072			−0.898910			−0.449455	−	0.893303i	$-0.648382\pi$
$863$	−26.4072			−0.898910			−0.449455	+	0.893303i	$0.648382\pi$
$864$	−4.47283	−	2.64458i	−0.152169	−	0.0899705i
$865$	−12.6010	+	9.15519i	−0.428448	+	0.311286i
$866$	−12.3417	−	8.96677i	−0.419388	−	0.304703i
$867$	−5.23880	−	21.3253i	−0.177919	−	0.724245i
$868$	−8.75901	−	21.9756i	−0.297300	−	0.745899i
$869$			27.3543i			0.927932i
$870$	−0.879819	+	2.15615i	−0.0298286	+	0.0731003i
$871$	12.0303	+	16.5583i	0.407631	+	0.561055i
$872$	−2.17980	+	0.708260i	−0.0738174	+	0.0239847i
$873$	36.6291	−	19.1525i	1.23971	−	0.648214i
$874$		−	0.0838224i		−	0.00283533i
$875$	−4.04094	+	1.31298i	−0.136609	+	0.0443868i
$876$	1.34817	−	18.3674i	0.0455503	−	0.620578i
$877$	−1.04463	+	3.21505i	−0.0352748	+	0.108565i	−0.967144	−	0.254231i	$-0.918178\pi$
$877$	−1.04463	+	3.21505i	−0.0352748	+	0.108565i	0.931869	+	0.362796i	$0.118178\pi$
$878$	10.7792	−	14.8362i	0.363779	−	0.500699i
$879$	1.93057	+	3.11345i	0.0651166	+	0.105014i
$880$	−1.43155	+	1.97036i	−0.0482575	+	0.0664207i
$881$	37.3330	−	27.1240i	1.25778	−	0.913831i	0.259134	−	0.965841i	$-0.416563\pi$
$881$	37.3330	−	27.1240i	1.25778	−	0.913831i	0.998647	+	0.0520099i	$0.0165627\pi$
$882$	32.6945	−	5.53225i	1.10088	−	0.186281i
$883$	−11.0002	−	15.1405i	−0.370187	−	0.509518i	0.582765	−	0.812641i	$-0.301971\pi$
$883$	−11.0002	−	15.1405i	−0.370187	−	0.509518i	−0.952952	+	0.303122i	$0.901971\pi$
$884$	−3.12832	−	4.30577i	−0.105217	−	0.144819i
$885$	4.20887	+	0.308930i	0.141480	+	0.0103846i
$886$	2.10006	−	1.52578i	0.0705530	−	0.0512597i
$887$	20.9660	−	28.8572i	0.703969	−	0.968930i	−0.295937	−	0.955207i	$-0.595632\pi$
$887$	20.9660	−	28.8572i	0.703969	−	0.968930i	0.999906	−	0.0137226i	$-0.00436817\pi$
$888$	−4.65853	+	2.88864i	−0.156330	+	0.0969364i
$889$	−12.1981	+	16.7893i	−0.409112	+	0.563095i
$890$	4.72160	−	14.5316i	0.158268	−	0.487100i
$891$	13.2550	+	17.4576i	0.444058	+	0.584852i
$892$	0.814306	−	0.264584i	0.0272650	−	0.00885893i
$893$		−	6.33776i		−	0.212085i
$894$	3.57937	+	14.5703i	0.119712	+	0.487305i
$895$	−20.5650	+	6.68198i	−0.687413	+	0.223354i
$896$	2.49744	+	3.43743i	0.0834335	+	0.114836i
$897$	−0.407919	−	0.166452i	−0.0136200	−	0.00555766i
$898$		−	29.3204i		−	0.978436i
$899$	−5.75702	+	4.78487i	−0.192007	+	0.159584i
$900$	−2.65851	+	1.39008i	−0.0886171	+	0.0463359i
$901$	−19.1809	−	13.9358i	−0.639009	−	0.464267i
$902$	−10.7554	+	7.81425i	−0.358115	+	0.260186i
$903$	−10.5999	−	17.0945i	−0.352742	−	0.568870i
$904$	−0.569050			−0.0189263
$905$	18.8037			0.625056
$906$	11.4351	−	7.09063i	0.379906	−	0.235571i
$907$	12.7432	−	39.2194i	0.423130	−	1.30226i	−0.481644	−	0.876367i	$-0.659960\pi$
$907$	12.7432	−	39.2194i	0.423130	−	1.30226i	0.904774	−	0.425892i	$-0.140040\pi$
$908$	13.3149	+	4.32626i	0.441869	+	0.143572i
$909$	7.50842	−	50.8719i	0.249039	−	1.68731i
$910$	10.3453	−	3.36141i	0.342945	−	0.111430i
$911$	16.5789	+	12.0453i	0.549284	+	0.399078i	0.827521	−	0.561434i	$-0.189750\pi$
$911$	16.5789	+	12.0453i	0.549284	+	0.399078i	−0.278237	+	0.960512i	$0.589750\pi$
$912$	1.11614	+	0.943141i	0.0369590	+	0.0312305i
$913$	7.04409	−	21.6795i	0.233125	−	0.717486i
$914$	5.77368	−	4.19482i	0.190976	−	0.138752i
$915$	6.51973	+	5.50920i	0.215536	+	0.182129i
$916$	13.8341	+	4.49499i	0.457093	+	0.148519i
$917$	3.57810	+	4.92483i	0.118159	+	0.162632i
$918$	−10.7541	+	1.01772i	−0.354940	+	0.0335898i
$919$	−0.770087	−	2.37008i	−0.0254028	−	0.0781818i	0.937551	−	0.347847i	$-0.113087\pi$
$919$	−0.770087	−	2.37008i	−0.0254028	−	0.0781818i	−0.962954	+	0.269665i	$0.913087\pi$
$920$	−0.0803806	−	0.0583999i	−0.00265007	−	0.00192539i
$921$	23.7930	+	1.74640i	0.784005	+	0.0575458i
$922$	−25.6405	−	8.33109i	−0.844424	−	0.274370i
$923$	5.03126	+	15.4846i	0.165606	+	0.509682i
$924$	−4.27598	−	17.4060i	−0.140669	−	0.572616i
$925$			3.16471i			0.104055i
$926$	−2.18692	−	6.73066i	−0.0718668	−	0.221183i
$927$	−11.0025	+	22.1683i	−0.361369	+	0.728103i
$928$	0.790278	−	1.08772i	0.0259422	−	0.0357063i
$929$	22.8635			0.750126			0.375063	−	0.926999i	$-0.377621\pi$
$929$	22.8635			0.750126			0.375063	+	0.926999i	$0.377621\pi$
$930$	−9.64333	−	0.0785613i	−0.316217	−	0.00257613i
$931$	−9.32503			−0.305615
$932$	5.49122	−	7.55802i	0.179871	−	0.247571i
$933$	−15.0624	+	17.8252i	−0.493120	+	0.583571i
$934$	7.46923	+	22.9879i	0.244401	+	0.752188i
$935$			5.06311i			0.165581i
$936$	6.80615	−	3.55878i	0.222466	−	0.116322i
$937$	−7.06342	−	21.7390i	−0.230752	−	0.710181i	−0.997657	−	0.0684203i	$-0.978204\pi$
$937$	−7.06342	−	21.7390i	−0.230752	−	0.710181i	0.766905	−	0.641761i	$-0.221796\pi$
$938$	−32.3055	−	10.4967i	−1.05481	−	0.342729i
$939$	0.269064	−	3.66573i	0.00878056	−	0.119627i
$940$	−6.07753	−	4.41559i	−0.198227	−	0.144021i
$941$	−3.82194	−	11.7627i	−0.124592	−	0.383454i	0.869235	−	0.494400i	$-0.164612\pi$
$941$	−3.82194	−	11.7627i	−0.124592	−	0.383454i	−0.993826	+	0.110946i	$0.964612\pi$
$942$	17.0053	+	6.93903i	0.554063	+	0.226086i
$943$	−0.318782	−	0.438766i	−0.0103810	−	0.0142882i
$944$	−2.31728	−	0.752929i	−0.0754210	−	0.0245058i
$945$	4.81385	−	21.5467i	0.156595	−	0.700914i
$946$	−5.38531	+	3.91266i	−0.175092	+	0.127211i
$947$	−13.3150	+	40.9794i	−0.432680	+	1.33165i	0.462766	+	0.886481i	$0.346857\pi$
$947$	−13.3150	+	40.9794i	−0.432680	+	1.33165i	−0.895446	+	0.445171i	$0.853143\pi$
$948$	12.5559	−	14.8590i	0.407798	−	0.482598i
$949$	22.0229	+	16.0006i	0.714895	+	0.519402i
$950$	0.802366	−	0.260705i	0.0260322	−	0.00845837i
$951$	29.6020	+	12.0791i	0.959911	+	0.391693i
$952$	8.40064	+	2.72953i	0.272266	+	0.0884647i
$953$	−15.4433	+	47.5297i	−0.500259	+	1.53964i	0.308339	+	0.951277i	$0.400227\pi$
$953$	−15.4433	+	47.5297i	−0.500259	+	1.53964i	−0.808598	+	0.588362i	$0.799773\pi$
$954$	23.9365	−	24.4466i	0.774973	−	0.791488i
$955$	−8.59875			−0.278249
$956$	8.62447			0.278935
$957$	−4.82019	+	2.98888i	−0.155814	+	0.0966167i
$958$	6.18490	−	4.49359i	0.199825	−	0.145181i
$959$	−40.4203	−	29.3671i	−1.30524	−	0.948313i
$960$	1.68204	−	0.413212i	0.0542876	−	0.0133364i
$961$	−27.2336	−	14.8098i	−0.878504	−	0.477735i
$962$		−	8.10208i		−	0.261222i
$963$	−1.29489	+	8.77331i	−0.0417274	+	0.282716i
$964$	−13.6959	−	18.8507i	−0.441114	−	0.607141i
$965$	20.0115	−	6.50212i	0.644192	−	0.209311i
$966$	0.710077	−	0.174438i	0.0228464	−	0.00561246i
$967$		−	3.65973i		−	0.117689i	−0.998267	−	0.0588445i	$-0.981258\pi$
$967$		−	3.65973i		−	0.117689i	0.998267	−	0.0588445i	$-0.0187416\pi$
$968$	4.82030	−	1.56621i	0.154930	−	0.0503399i
$969$	3.02963	+	0.222374i	0.0973259	+	0.00714370i
$970$	−4.25765	+	13.1037i	−0.136705	+	0.420734i
$971$	−1.03725	+	1.42765i	−0.0332870	+	0.0458156i	−0.825336	−	0.564642i	$-0.809014\pi$
$971$	−1.03725	+	1.42765i	−0.0332870	+	0.0458156i	0.792049	+	0.610457i	$0.209014\pi$
$972$	0.813077	−	15.5672i	0.0260795	−	0.499319i
$973$	31.2142	−	42.9627i	1.00068	−	1.37732i
$974$	−10.8845	+	7.90802i	−0.348761	+	0.253389i
$975$	0.324602	−	4.42239i	0.0103956	−	0.141630i
$976$	−2.89666	−	3.98691i	−0.0927198	−	0.127618i
$977$	1.87779	+	2.58456i	0.0600759	+	0.0826873i	0.837998	−	0.545674i	$-0.183726\pi$
$977$	1.87779	+	2.58456i	0.0600759	+	0.0826873i	−0.777922	+	0.628361i	$0.783726\pi$
$978$	2.05501	−	27.9975i	0.0657120	−	0.895262i
$979$	30.1059	−	21.8732i	0.962189	−	0.699071i
$980$	−6.49684	+	8.94214i	−0.207534	+	0.285646i
$981$	−4.91301	−	4.81049i	−0.156860	−	0.153587i
$982$	14.2612	−	19.6289i	0.455094	−	0.626384i
$983$	−6.47882	+	19.9398i	−0.206642	+	0.635980i	0.793000	+	0.609222i	$0.208518\pi$
$983$	−6.47882	+	19.9398i	−0.206642	+	0.635980i	−0.999642	+	0.0267577i	$0.991482\pi$
$984$	9.42921	+	0.692102i	0.300592	+	0.0220634i
$985$	10.1982	−	3.31358i	0.324940	−	0.105579i
$986$		−	2.79506i		−	0.0890129i
$987$	53.6886	−	13.1892i	1.70893	−	0.419817i
$988$	−2.05417	+	0.667439i	−0.0653517	+	0.0212341i
$989$	−0.159617	−	0.219693i	−0.00507551	−	0.00698584i
$990$	−7.22818	−	1.06684i	−0.229727	−	0.0339064i
$991$		−	1.45273i		−	0.0461474i	−0.999734	−	0.0230737i	$-0.992655\pi$
$991$		−	1.45273i		−	0.0461474i	0.999734	−	0.0230737i	$-0.00734524\pi$
$992$	5.39600	+	1.37229i	0.171323	+	0.0435704i
$993$	9.59147	−	2.35625i	0.304376	−	0.0747734i
$994$	−21.8607	−	15.8827i	−0.693380	−	0.503770i
$995$	16.9545	−	12.3182i	0.537495	−	0.390513i
$996$	−13.7775	+	8.54309i	−0.436557	+	0.270698i
$997$	47.0685			1.49067			0.745337	−	0.666688i	$-0.232289\pi$
$997$	47.0685			1.49067			0.745337	+	0.666688i	$0.232289\pi$
$998$	23.9682			0.758699
$999$	−14.1552	−	8.36933i	−0.447851	−	0.264794i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.v.b.401.2	✓	80
3.2	odd	2	inner	930.2.v.b.401.15	yes	80
31.15	odd	10	inner	930.2.v.b.821.15	yes	80
93.77	even	10	inner	930.2.v.b.821.2	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.v.b.401.2	✓	80	1.1	even	1	trivial
930.2.v.b.401.15	yes	80	3.2	odd	2	inner
930.2.v.b.821.2	yes	80	93.77	even	10	inner
930.2.v.b.821.15	yes	80	31.15	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.v (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.32297 - 1.11792i) q^{3} +(-0.309017 - 0.951057i) q^{4} +1.00000i q^{5} +(1.68204 - 0.413212i) q^{6} +(-1.31298 - 4.04094i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.500516 + 2.95795i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.32297 - 1.11792i) q^{3} +(-0.309017 - 0.951057i) q^{4} +1.00000i q^{5} +(1.68204 - 0.413212i) q^{6} +(-1.31298 - 4.04094i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.500516 + 2.95795i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(-0.752609 - 2.31629i) q^{11} +(-0.654383 + 1.60368i) q^{12} +(-1.50481 - 2.07119i) q^{13} +(4.04094 + 1.31298i) q^{14} +(1.11792 - 1.32297i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.642410 + 1.97714i) q^{17} +(-2.68723 - 1.33372i) q^{18} +(0.682533 + 0.495890i) q^{19} +(0.951057 - 0.309017i) q^{20} +(-2.78040 + 6.81386i) q^{21} +(2.31629 + 0.752609i) q^{22} +(-0.0307027 + 0.0944931i) q^{23} +(-0.912766 - 1.47202i) q^{24} -1.00000 q^{25} +2.56013 q^{26} +(2.64458 - 4.47283i) q^{27} +(-3.43743 + 2.49744i) q^{28} +(1.08772 + 0.790278i) q^{29} +(0.413212 + 1.68204i) q^{30} +(-1.37229 + 5.39600i) q^{31} -1.00000i q^{32} +(-1.59375 + 3.90575i) q^{33} +(-1.22194 - 1.68185i) q^{34} +(4.04094 - 1.31298i) q^{35} +(2.65851 - 1.39008i) q^{36} -3.16471i q^{37} +(-0.802366 + 0.260705i) q^{38} +(-0.324602 + 4.42239i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(-3.20849 + 4.41610i) q^{41} +(-3.87825 - 6.25448i) q^{42} +(-1.60651 + 2.21118i) q^{43} +(-1.97036 + 1.43155i) q^{44} +(-2.95795 + 0.500516i) q^{45} +(-0.0583999 - 0.0803806i) q^{46} +(-4.41559 - 6.07753i) q^{47} +(1.72740 + 0.126791i) q^{48} +(-8.94214 + 6.49684i) q^{49} +(0.587785 - 0.809017i) q^{50} +(3.06017 - 1.89753i) q^{51} +(-1.50481 + 2.07119i) q^{52} +(-3.52423 + 10.8465i) q^{53} +(2.06415 + 4.76857i) q^{54} +(2.31629 - 0.752609i) q^{55} -4.24889i q^{56} +(-0.348609 - 1.41907i) q^{57} +(-1.27870 + 0.415474i) q^{58} +(1.43216 + 1.97119i) q^{59} +(-1.60368 - 0.654383i) q^{60} +4.92809i q^{61} +(-3.55884 - 4.28190i) q^{62} +(11.2957 - 5.90629i) q^{63} +(0.809017 + 0.587785i) q^{64} +(2.07119 - 1.50481i) q^{65} +(-2.22304 - 3.58511i) q^{66} -7.99455 q^{67} +2.07888 q^{68} +(0.146254 - 0.0906887i) q^{69} +(-1.31298 + 4.04094i) q^{70} +(-6.04836 - 1.96523i) q^{71} +(-0.438039 + 2.96785i) q^{72} +(-10.1126 + 3.28577i) q^{73} +(2.56030 + 1.86017i) q^{74} +(1.32297 + 1.11792i) q^{75} +(0.260705 - 0.802366i) q^{76} +(-8.37184 + 6.08249i) q^{77} +(-3.38699 - 2.86202i) q^{78} +(-10.6818 - 3.47073i) q^{79} +(-0.587785 - 0.809017i) q^{80} +(-8.49897 + 2.96101i) q^{81} +(-1.68680 - 5.19144i) q^{82} +(7.57204 + 5.50141i) q^{83} +(7.33955 + 0.538722i) q^{84} +(-1.97714 - 0.642410i) q^{85} +(-0.844594 - 2.59939i) q^{86} +(-0.555564 - 2.26150i) q^{87} -2.43550i q^{88} +(4.72160 + 14.5316i) q^{89} +(1.33372 - 2.68723i) q^{90} +(-6.39378 + 8.80028i) q^{91} +0.0993559 q^{92} +(7.84780 - 5.60465i) q^{93} +7.51225 q^{94} +(-0.495890 + 0.682533i) q^{95} +(-1.11792 + 1.32297i) q^{96} +(-4.25765 - 13.1037i) q^{97} -11.0531i q^{98} +(6.47479 - 3.38552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9}+O(q^{10}) \) 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9	\( 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9} - 20 q^{10} + 10 q^{13} - 20 q^{16} - 4 q^{18} - 12 q^{19} - 30 q^{21} - 10 q^{22} - 80 q^{25} + 60 q^{27} + 18 q^{28} + 8 q^{31} - 20 q^{33} + 10 q^{34} - 8 q^{36} - 46 q^{39} + 20 q^{40} + 50 q^{43} - 16 q^{45} - 10 q^{46} - 8 q^{49} - 20 q^{51} + 10 q^{52} - 10 q^{55} + 10 q^{58} + 44 q^{63} + 20 q^{64} - 10 q^{66} - 132 q^{67} - 16 q^{69} + 12 q^{70} + 4 q^{72} - 20 q^{73} - 18 q^{76} + 48 q^{78} - 120 q^{79} + 48 q^{81} - 20 q^{82} + 20 q^{84} - 136 q^{87} - 12 q^{90} - 110 q^{91} - 20 q^{93} - 28 q^{94} + 22 q^{97}+O(q^{100}) \) 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9 - 20 * q^10 + 10 * q^13 - 20 * q^16 - 4 * q^18 - 12 * q^19 - 30 * q^21 - 10 * q^22 - 80 * q^25 + 60 * q^27 + 18 * q^28 + 8 * q^31 - 20 * q^33 + 10 * q^34 - 8 * q^36 - 46 * q^39 + 20 * q^40 + 50 * q^43 - 16 * q^45 - 10 * q^46 - 8 * q^49 - 20 * q^51 + 10 * q^52 - 10 * q^55 + 10 * q^58 + 44 * q^63 + 20 * q^64 - 10 * q^66 - 132 * q^67 - 16 * q^69 + 12 * q^70 + 4 * q^72 - 20 * q^73 - 18 * q^76 + 48 * q^78 - 120 * q^79 + 48 * q^81 - 20 * q^82 + 20 * q^84 - 136 * q^87 - 12 * q^90 - 110 * q^91 - 20 * q^93 - 28 * q^94 + 22 * q^97

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