LMFDB - Embedded newform 380.2.k.c.267.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(267,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("380.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			267.23
Character	$\chi$	$=$	380.267
Dual form			380.2.k.c.343.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25747 + 0.647117i) q^{2} +(1.78847 + 1.78847i) q^{3} +(1.16248 + 1.62746i) q^{4} +(0.0829302 - 2.23453i) q^{5} +(1.09160 + 3.40630i) q^{6} +(0.904221 - 0.904221i) q^{7} +(0.408628 + 2.79875i) q^{8} +3.39723i q^{9} +O(q^{10})$	\(q+(1.25747 + 0.647117i) q^{2} +(1.78847 + 1.78847i) q^{3} +(1.16248 + 1.62746i) q^{4} +(0.0829302 - 2.23453i) q^{5} +(1.09160 + 3.40630i) q^{6} +(0.904221 - 0.904221i) q^{7} +(0.408628 + 2.79875i) q^{8} +3.39723i q^{9} +(1.55028 - 2.75620i) q^{10} -4.92807i q^{11} +(-0.831610 + 4.98972i) q^{12} +(-4.64598 + 4.64598i) q^{13} +(1.72217 - 0.551898i) q^{14} +(4.14470 - 3.84806i) q^{15} +(-1.29728 + 3.78379i) q^{16} +(-3.50664 - 3.50664i) q^{17} +(-2.19840 + 4.27193i) q^{18} +1.00000 q^{19} +(3.73302 - 2.46263i) q^{20} +3.23434 q^{21} +(3.18903 - 6.19691i) q^{22} +(-2.65546 - 2.65546i) q^{23} +(-4.27466 + 5.73630i) q^{24} +(-4.98625 - 0.370620i) q^{25} +(-8.84868 + 2.83570i) q^{26} +(-0.710431 + 0.710431i) q^{27} +(2.52273 + 0.420449i) q^{28} +4.23410i q^{29} +(7.70200 - 2.15673i) q^{30} +6.52947i q^{31} +(-4.07985 + 3.91852i) q^{32} +(8.81369 - 8.81369i) q^{33} +(-2.14030 - 6.67871i) q^{34} +(-1.94552 - 2.09550i) q^{35} +(-5.52887 + 3.94921i) q^{36} +(-4.68490 - 4.68490i) q^{37} +(1.25747 + 0.647117i) q^{38} -16.6184 q^{39} +(6.28779 - 0.680990i) q^{40} +3.99527 q^{41} +(4.06710 + 2.09300i) q^{42} +(1.41043 + 1.41043i) q^{43} +(8.02025 - 5.72878i) q^{44} +(7.59121 + 0.281733i) q^{45} +(-1.62078 - 5.05756i) q^{46} +(0.801371 - 0.801371i) q^{47} +(-9.08733 + 4.44704i) q^{48} +5.36477i q^{49} +(-6.03024 - 3.69273i) q^{50} -12.5430i q^{51} +(-12.9620 - 2.16031i) q^{52} +(-2.72848 + 2.72848i) q^{53} +(-1.35308 + 0.433616i) q^{54} +(-11.0119 - 0.408686i) q^{55} +(2.90018 + 2.16120i) q^{56} +(1.78847 + 1.78847i) q^{57} +(-2.73996 + 5.32427i) q^{58} +13.9835 q^{59} +(11.0807 + 2.27206i) q^{60} +6.61259 q^{61} +(-4.22533 + 8.21063i) q^{62} +(3.07185 + 3.07185i) q^{63} +(-7.66605 + 2.28730i) q^{64} +(9.99628 + 10.7669i) q^{65} +(16.7865 - 5.37949i) q^{66} +(1.41268 - 1.41268i) q^{67} +(1.63053 - 9.78333i) q^{68} -9.49840i q^{69} +(-1.09041 - 3.89401i) q^{70} -0.666584i q^{71} +(-9.50801 + 1.38820i) q^{72} +(9.09755 - 9.09755i) q^{73} +(-2.85946 - 8.92281i) q^{74} +(-8.25489 - 9.58058i) q^{75} +(1.16248 + 1.62746i) q^{76} +(-4.45606 - 4.45606i) q^{77} +(-20.8971 - 10.7540i) q^{78} +7.09809 q^{79} +(8.34741 + 3.21260i) q^{80} +7.65052 q^{81} +(5.02395 + 2.58541i) q^{82} +(6.54308 + 6.54308i) q^{83} +(3.75985 + 5.26377i) q^{84} +(-8.12650 + 7.54489i) q^{85} +(0.860863 + 2.68628i) q^{86} +(-7.57255 + 7.57255i) q^{87} +(13.7924 - 2.01375i) q^{88} -6.08572i q^{89} +(9.36343 + 5.26667i) q^{90} +8.40198i q^{91} +(1.23475 - 7.40858i) q^{92} +(-11.6777 + 11.6777i) q^{93} +(1.52628 - 0.489122i) q^{94} +(0.0829302 - 2.23453i) q^{95} +(-14.3048 - 0.288531i) q^{96} +(1.52334 + 1.52334i) q^{97} +(-3.47163 + 6.74605i) q^{98} +16.7418 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8	$ 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) $ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.25747	+	0.647117i	0.889168	+	0.457581i
$2$	1.25747	+	0.647117i	0.889168	+	0.457581i
$3$	1.78847	+	1.78847i	1.03257	+	1.03257i	0.999451	+	0.0331206i	$0.0105445\pi$
$3$	1.78847	+	1.78847i	1.03257	+	1.03257i	0.0331206	+	0.999451i	$0.489455\pi$
$4$	1.16248	+	1.62746i	0.581240	+	0.813732i
$5$	0.0829302	−	2.23453i	0.0370875	−	0.999312i
$5$	0.0829302	−	2.23453i	0.0370875	−	0.999312i
$6$	1.09160	+	3.40630i	0.445645	+	1.39061i
$7$	0.904221	−	0.904221i	0.341763	−	0.341763i	−0.515267	−	0.857030i	$-0.672307\pi$
$7$	0.904221	−	0.904221i	0.341763	−	0.341763i	0.857030	+	0.515267i	$0.172307\pi$
$8$	0.408628	+	2.79875i	0.144472	+	0.989509i
$9$			3.39723i			1.13241i
$10$	1.55028	−	2.75620i	0.490243	−	0.871586i
$11$		−	4.92807i		−	1.48587i	−0.669365	−	0.742934i	$-0.733434\pi$
$11$		−	4.92807i		−	1.48587i	0.669365	−	0.742934i	$-0.266566\pi$
$12$	−0.831610	+	4.98972i	−0.240065	+	1.44041i
$13$	−4.64598	+	4.64598i	−1.28856	+	1.28856i	−0.352902	+	0.935660i	$0.614805\pi$
$13$	−4.64598	+	4.64598i	−1.28856	+	1.28856i	−0.935660	+	0.352902i	$0.885195\pi$
$14$	1.72217	−	0.551898i	0.460270	−	0.147501i
$15$	4.14470	−	3.84806i	1.07016	−	0.993566i
$16$	−1.29728	+	3.78379i	−0.324320	+	0.945947i
$17$	−3.50664	−	3.50664i	−0.850485	−	0.850485i	0.139707	−	0.990193i	$-0.455384\pi$
$17$	−3.50664	−	3.50664i	−0.850485	−	0.850485i	−0.990193	+	0.139707i	$0.955384\pi$
$18$	−2.19840	+	4.27193i	−0.518169	+	1.00690i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	3.73302	−	2.46263i	0.834729	−	0.550661i
$21$	3.23434			0.705791
$22$	3.18903	−	6.19691i	0.679905	−	1.32119i
$23$	−2.65546	−	2.65546i	−0.553701	−	0.553701i	0.373806	−	0.927507i	$-0.378053\pi$
$23$	−2.65546	−	2.65546i	−0.553701	−	0.553701i	−0.927507	+	0.373806i	$0.878053\pi$
$24$	−4.27466	+	5.73630i	−0.872562	+	1.17092i
$25$	−4.98625	−	0.370620i	−0.997249	−	0.0741240i
$26$	−8.84868	+	2.83570i	−1.73537	+	0.556127i
$27$	−0.710431	+	0.710431i	−0.136722	+	0.136722i
$28$	2.52273	+	0.420449i	0.476751	+	0.0794574i
$29$			4.23410i			0.786253i	0.919484	+	0.393126i	$0.128606\pi$
$29$			4.23410i			0.786253i	−0.919484	+	0.393126i	$0.871394\pi$
$30$	7.70200	−	2.15673i	1.40619	−	0.393764i
$31$			6.52947i			1.17273i	0.810048	+	0.586364i	$0.199441\pi$
$31$			6.52947i			1.17273i	−0.810048	+	0.586364i	$0.800559\pi$
$32$	−4.07985	+	3.91852i	−0.721223	+	0.692703i
$33$	8.81369	−	8.81369i	1.53427	−	1.53427i
$34$	−2.14030	−	6.67871i	−0.367059	−	1.14539i
$35$	−1.94552	−	2.09550i	−0.328853	−	0.354204i
$36$	−5.52887	+	3.94921i	−0.921478	+	0.658202i
$37$	−4.68490	−	4.68490i	−0.770193	−	0.770193i	0.207947	−	0.978140i	$-0.433322\pi$
$37$	−4.68490	−	4.68490i	−0.770193	−	0.770193i	−0.978140	+	0.207947i	$0.933322\pi$
$38$	1.25747	+	0.647117i	0.203989	+	0.104976i
$39$	−16.6184			−2.66107
$40$	6.28779	−	0.680990i	0.994186	−	0.107674i
$41$	3.99527			0.623956			0.311978	−	0.950089i	$-0.399008\pi$
$41$	3.99527			0.623956			0.311978	+	0.950089i	$0.399008\pi$
$42$	4.06710	+	2.09300i	0.627567	+	0.322956i
$43$	1.41043	+	1.41043i	0.215088	+	0.215088i	0.806425	−	0.591337i	$-0.201400\pi$
$43$	1.41043	+	1.41043i	0.215088	+	0.215088i	−0.591337	+	0.806425i	$0.701400\pi$
$44$	8.02025	−	5.72878i	1.20910	−	0.863646i
$45$	7.59121	+	0.281733i	1.13163	+	0.0419983i
$46$	−1.62078	−	5.05756i	−0.238971	−	0.745697i
$47$	0.801371	−	0.801371i	0.116892	−	0.116892i	−0.646241	−	0.763133i	$-0.723660\pi$
$47$	0.801371	−	0.801371i	0.116892	−	0.116892i	0.763133	+	0.646241i	$0.223660\pi$
$48$	−9.08733	+	4.44704i	−1.31164	+	0.641874i
$49$			5.36477i			0.766395i
$50$	−6.03024	−	3.69273i	−0.852804	−	0.522231i
$51$		−	12.5430i		−	1.75637i
$52$	−12.9620	−	2.16031i	−1.79751	−	0.299581i
$53$	−2.72848	+	2.72848i	−0.374785	+	0.374785i	−0.869217	−	0.494431i	$-0.835376\pi$
$53$	−2.72848	+	2.72848i	−0.374785	+	0.374785i	0.494431	+	0.869217i	$0.335376\pi$
$54$	−1.35308	+	0.433616i	−0.184131	+	0.0590077i
$55$	−11.0119	−	0.408686i	−1.48485	−	0.0551072i
$56$	2.90018	+	2.16120i	0.387553	+	0.288803i
$57$	1.78847	+	1.78847i	0.236888	+	0.236888i
$58$	−2.73996	+	5.32427i	−0.359774	+	0.699111i
$59$	13.9835			1.82050			0.910248	−	0.414063i	$-0.135891\pi$
$59$	13.9835			1.82050			0.910248	+	0.414063i	$0.135891\pi$
$60$	11.0807	+	2.27206i	1.43051	+	0.293321i
$61$	6.61259			0.846655			0.423327	−	0.905977i	$-0.360862\pi$
$61$	6.61259			0.846655			0.423327	+	0.905977i	$0.360862\pi$
$62$	−4.22533	+	8.21063i	−0.536617	+	1.04275i
$63$	3.07185	+	3.07185i	0.387016	+	0.387016i
$64$	−7.66605	+	2.28730i	−0.958256	+	0.285912i
$65$	9.99628	+	10.7669i	1.23989	+	1.33547i
$66$	16.7865	−	5.37949i	2.06627	−	0.662170i
$67$	1.41268	−	1.41268i	0.172586	−	0.172586i	−0.615528	−	0.788115i	$-0.711057\pi$
$67$	1.41268	−	1.41268i	0.172586	−	0.172586i	0.788115	+	0.615528i	$0.211057\pi$
$68$	1.63053	−	9.78333i	0.197731	−	1.18640i
$69$		−	9.49840i		−	1.14347i
$70$	−1.09041	−	3.89401i	−0.130329	−	0.465423i
$71$		−	0.666584i		−	0.0791089i	−0.999217	−	0.0395545i	$-0.987406\pi$
$71$		−	0.666584i		−	0.0791089i	0.999217	−	0.0395545i	$-0.0125939\pi$
$72$	−9.50801	+	1.38820i	−1.12053	+	0.163601i
$73$	9.09755	−	9.09755i	1.06479	−	1.06479i	0.0670369	−	0.997750i	$-0.478645\pi$
$73$	9.09755	−	9.09755i	1.06479	−	1.06479i	0.997750	−	0.0670369i	$-0.0213545\pi$
$74$	−2.85946	−	8.92281i	−0.332406	−	1.03726i
$75$	−8.25489	−	9.58058i	−0.953193	−	1.10627i
$76$	1.16248	+	1.62746i	0.133346	+	0.186683i
$77$	−4.45606	−	4.45606i	−0.507815	−	0.507815i
$78$	−20.8971	−	10.7540i	−2.36614	−	1.21765i
$79$	7.09809			0.798598			0.399299	−	0.916821i	$-0.369254\pi$
$79$	7.09809			0.798598			0.399299	+	0.916821i	$0.369254\pi$
$80$	8.34741	+	3.21260i	0.933268	+	0.359180i
$81$	7.65052			0.850058
$82$	5.02395	+	2.58541i	0.554802	+	0.285510i
$83$	6.54308	+	6.54308i	0.718196	+	0.718196i	0.968236	−	0.250039i	$-0.0804435\pi$
$83$	6.54308	+	6.54308i	0.718196	+	0.718196i	−0.250039	+	0.968236i	$0.580444\pi$
$84$	3.75985	+	5.26377i	0.410234	+	0.574325i
$85$	−8.12650	+	7.54489i	−0.881443	+	0.818358i
$86$	0.860863	+	2.68628i	0.0928293	+	0.289669i
$87$	−7.57255	+	7.57255i	−0.811862	+	0.811862i
$88$	13.7924	−	2.01375i	1.47028	−	0.214666i
$89$		−	6.08572i		−	0.645085i	−0.946555	−	0.322542i	$-0.895462\pi$
$89$		−	6.08572i		−	0.645085i	0.946555	−	0.322542i	$-0.104538\pi$
$90$	9.36343	+	5.26667i	0.986992	+	0.555156i
$91$			8.40198i			0.880767i
$92$	1.23475	−	7.40858i	0.128731	−	0.772398i
$93$	−11.6777	+	11.6777i	−1.21092	+	1.21092i
$94$	1.52628	−	0.489122i	0.157424	−	0.0504491i
$95$	0.0829302	−	2.23453i	0.00850846	−	0.229258i
$96$	−14.3048	−	0.288531i	−1.45998	−	0.0294480i
$97$	1.52334	+	1.52334i	0.154672	+	0.154672i	0.780201	−	0.625529i	$-0.215117\pi$
$97$	1.52334	+	1.52334i	0.154672	+	0.154672i	−0.625529	+	0.780201i	$0.715117\pi$
$98$	−3.47163	+	6.74605i	−0.350688	+	0.681454i
$99$	16.7418			1.68261
$100$	−5.19324	−	8.54578i	−0.519324	−	0.854578i
$101$	−0.349073			−0.0347341			−0.0173670	−	0.999849i	$-0.505528\pi$
$101$	−0.349073			−0.0347341			−0.0173670	+	0.999849i	$0.505528\pi$
$102$	8.11680	−	15.7725i	0.803683	−	1.56171i
$103$	−6.13616	−	6.13616i	−0.604613	−	0.604613i	0.336920	−	0.941533i	$-0.390615\pi$
$103$	−6.13616	−	6.13616i	−0.604613	−	0.604613i	−0.941533	+	0.336920i	$0.890615\pi$
$104$	−14.9014	−	11.1045i	−1.46120	−	1.08888i
$105$	0.268225	−	7.22723i	0.0261760	−	0.705305i
$106$	−5.19663	+	1.66535i	−0.504742	+	0.161753i
$107$	−7.72854	+	7.72854i	−0.747146	+	0.747146i	−0.973942	−	0.226796i	$-0.927175\pi$
$107$	−7.72854	+	7.72854i	−0.747146	+	0.747146i	0.226796	+	0.973942i	$0.427175\pi$
$108$	−1.98206	−	0.330339i	−0.190724	−	0.0317869i
$109$		−	1.11697i		−	0.106986i	−0.998568	−	0.0534931i	$-0.982964\pi$
$109$		−	1.11697i		−	0.106986i	0.998568	−	0.0534931i	$-0.0170355\pi$
$110$	−13.5827	−	7.63990i	−1.29506	−	0.728436i
$111$		−	16.7576i		−	1.59056i
$112$	2.24835	+	4.59441i	0.212449	+	0.434131i
$113$	−7.06685	+	7.06685i	−0.664794	+	0.664794i	−0.956506	−	0.291712i	$-0.905775\pi$
$113$	−7.06685	+	7.06685i	−0.664794	+	0.664794i	0.291712	+	0.956506i	$0.405775\pi$
$114$	1.09160	+	3.40630i	0.102238	+	0.319029i
$115$	−6.15392	+	5.71348i	−0.573856	+	0.532785i
$116$	−6.89085	+	4.92206i	−0.639799	+	0.457001i
$117$	−15.7834	−	15.7834i	−1.45918	−	1.45918i
$118$	17.5839	+	9.04896i	1.61873	+	0.833024i
$119$	−6.34156			−0.581330
$120$	12.4634	+	10.0276i	1.13775	+	0.915388i
$121$	−13.2858			−1.20780
$122$	8.31515	+	4.27912i	0.752818	+	0.387413i
$123$	7.14541	+	7.14541i	0.644280	+	0.644280i
$124$	−10.6265	+	7.59037i	−0.954286	+	0.681636i
$125$	−1.24167	+	11.1112i	−0.111059	+	0.993814i
$126$	1.87492	+	5.85061i	0.167031	+	0.521214i
$127$	0.443269	−	0.443269i	0.0393338	−	0.0393338i	−0.687166	−	0.726500i	$-0.741146\pi$
$127$	0.443269	−	0.443269i	0.0393338	−	0.0393338i	0.726500	+	0.687166i	$0.241146\pi$
$128$	−11.1200	−	2.08461i	−0.982878	−	0.184255i
$129$			5.04500i			0.444188i
$130$	5.60264	+	20.0078i	0.491384	+	1.75480i
$131$		−	19.8615i		−	1.73531i	−0.497166	−	0.867655i	$-0.665626\pi$
$131$		−	19.8615i		−	1.73531i	0.497166	−	0.867655i	$-0.334374\pi$
$132$	24.5897	+	4.09823i	2.14026	+	0.356705i
$133$	0.904221	−	0.904221i	0.0784059	−	0.0784059i
$134$	2.69057	−	0.862238i	0.232430	−	0.0744860i
$135$	1.52856	+	1.64639i	0.131558	+	0.141699i
$136$	8.38131	−	11.2471i	0.718692	−	0.964434i
$137$	−10.4985	−	10.4985i	−0.896951	−	0.896951i	0.0982139	−	0.995165i	$-0.468687\pi$
$137$	−10.4985	−	10.4985i	−0.896951	−	0.896951i	−0.995165	+	0.0982139i	$0.968687\pi$
$138$	6.14658	−	11.9440i	0.523231	−	1.01674i
$139$	−18.2723			−1.54984			−0.774920	−	0.632060i	$-0.782210\pi$
$139$	−18.2723			−1.54984			−0.774920	+	0.632060i	$0.782210\pi$
$140$	1.14872	−	5.60224i	0.0970842	−	0.473476i
$141$	2.86645			0.241399
$142$	0.431358	−	0.838212i	0.0361987	−	0.0703411i
$143$	22.8957	+	22.8957i	1.91463	+	1.91463i
$144$	−12.8544	−	4.40716i	−1.07120	−	0.367264i
$145$	9.46122	+	0.351135i	0.785712	+	0.0291602i
$146$	17.3271	−	5.55275i	1.43400	−	0.459549i
$147$	−9.59471	+	9.59471i	−0.791358	+	0.791358i
$148$	2.17841	−	13.0706i	0.179064	−	1.07440i
$149$			20.0334i			1.64120i	0.571501	+	0.820601i	$0.306361\pi$
$149$			20.0334i			1.64120i	−0.571501	+	0.820601i	$0.693639\pi$
$150$	−4.18056	−	17.3892i	−0.341341	−	1.41982i
$151$			0.536358i			0.0436482i	0.999762	+	0.0218241i	$0.00694738\pi$
$151$			0.536358i			0.0436482i	−0.999762	+	0.0218241i	$0.993053\pi$
$152$	0.408628	+	2.79875i	0.0331441	+	0.227009i
$153$	11.9129	−	11.9129i	0.963098	−	0.963098i
$154$	−2.71979	−	8.48697i	−0.219167	−	0.683900i
$155$	14.5903	+	0.541490i	1.17192	+	0.0434936i
$156$	−19.3185	−	27.0458i	−1.54672	−	2.16540i
$157$	−3.05908	−	3.05908i	−0.244141	−	0.244141i	0.574420	−	0.818561i	$-0.305228\pi$
$157$	−3.05908	−	3.05908i	−0.244141	−	0.244141i	−0.818561	+	0.574420i	$0.805228\pi$
$158$	8.92567	+	4.59330i	0.710088	+	0.365423i
$159$	−9.75959			−0.773985
$160$	8.41771	+	9.44151i	0.665478	+	0.746417i
$161$	−4.80224			−0.378470
$162$	9.62033	+	4.95078i	0.755845	+	0.388970i
$163$	4.16638	+	4.16638i	0.326336	+	0.326336i	0.851191	−	0.524856i	$-0.175881\pi$
$163$	4.16638	+	4.16638i	0.326336	+	0.326336i	−0.524856	+	0.851191i	$0.675881\pi$
$164$	4.64442	+	6.50216i	0.362668	+	0.507734i
$165$	−18.9635	−	20.4254i	−1.47631	−	1.59011i
$166$	3.99361	+	12.4619i	0.309965	+	0.967230i
$167$	1.58055	−	1.58055i	0.122307	−	0.122307i	−0.643304	−	0.765611i	$-0.722437\pi$
$167$	1.58055	−	1.58055i	0.122307	−	0.122307i	0.765611	+	0.643304i	$0.222437\pi$
$168$	1.32164	+	9.05212i	0.101967	+	0.698386i
$169$		−	30.1702i		−	2.32079i
$170$	−15.1013	+	4.22870i	−1.15822	+	0.324327i
$171$			3.39723i			0.259793i
$172$	−0.655827	+	3.93501i	−0.0500063	+	0.300042i
$173$	−8.52546	+	8.52546i	−0.648179	+	0.648179i	−0.952553	−	0.304374i	$-0.901553\pi$
$173$	−8.52546	+	8.52546i	−0.648179	+	0.648179i	0.304374	+	0.952553i	$0.401553\pi$
$174$	−14.4226	+	4.62196i	−1.09337	+	0.350390i
$175$	−4.84379	+	4.17355i	−0.366156	+	0.315490i
$176$	18.6468	+	6.39309i	1.40555	+	0.481897i
$177$	25.0090	+	25.0090i	1.87979	+	1.87979i
$178$	3.93817	−	7.65263i	0.295178	−	0.573589i
$179$	15.0799			1.12713			0.563564	−	0.826073i	$-0.309430\pi$
$179$	15.0799			1.12713			0.563564	+	0.826073i	$0.309430\pi$
$180$	8.36612	+	12.6819i	0.623573	+	0.945255i
$181$	−7.85061			−0.583531			−0.291765	−	0.956490i	$-0.594243\pi$
$181$	−7.85061			−0.583531			−0.291765	+	0.956490i	$0.594243\pi$
$182$	−5.43706	+	10.5653i	−0.403022	+	0.783150i
$183$	11.8264	+	11.8264i	0.874232	+	0.874232i
$184$	6.34688	−	8.51707i	0.467898	−	0.627887i
$185$	−10.8571	+	10.0800i	−0.798227	+	0.741098i
$186$	−22.2413	+	7.12759i	−1.63081	+	0.522620i
$187$	−17.2810	+	17.2810i	−1.26371	+	1.26371i
$188$	2.23578	+	0.372625i	0.163061	+	0.0271765i
$189$			1.28477i			0.0934535i
$190$	1.55028	−	2.75620i	0.112469	−	0.199956i
$191$		−	9.49299i		−	0.686889i	−0.939173	−	0.343444i	$-0.888406\pi$
$191$		−	9.49299i		−	0.686889i	0.939173	−	0.343444i	$-0.111594\pi$
$192$	−17.8012	−	9.61971i	−1.28469	−	0.694243i
$193$	−6.06821	+	6.06821i	−0.436800	+	0.436800i	−0.890933	−	0.454134i	$-0.849949\pi$
$193$	−6.06821	+	6.06821i	−0.436800	+	0.436800i	0.454134	+	0.890933i	$0.349949\pi$
$194$	0.929783	+	2.90134i	0.0667545	+	0.208304i
$195$	−1.37816	+	37.1342i	−0.0986924	+	2.65924i
$196$	−8.73097	+	6.23643i	−0.623641	+	0.445460i
$197$	12.5816	+	12.5816i	0.896402	+	0.896402i	0.995116	−	0.0987143i	$-0.0314730\pi$
$197$	12.5816	+	12.5816i	0.896402	+	0.896402i	−0.0987143	+	0.995116i	$0.531473\pi$
$198$	21.0523	+	10.8339i	1.49612	+	0.769930i
$199$	9.07658			0.643422			0.321711	−	0.946838i	$-0.395742\pi$
$199$	9.07658			0.643422			0.321711	+	0.946838i	$0.395742\pi$
$200$	−1.00024	−	14.1067i	−0.0707280	−	0.997496i
$201$	5.05306			0.356415
$202$	−0.438950	−	0.225891i	−0.0308844	−	0.0158936i
$203$	3.82856	+	3.82856i	0.268712	+	0.268712i
$204$	20.4133	−	14.5810i	1.42922	−	1.02088i
$205$	0.331329	−	8.92755i	0.0231410	−	0.623527i
$206$	−3.74524	−	11.6869i	−0.260944	−	0.814262i
$207$	9.02120	−	9.02120i	0.627017	−	0.627017i
$208$	−11.5523	−	23.6065i	−0.801005	−	1.63682i
$209$		−	4.92807i		−	0.340882i
$210$	5.01415	−	8.91448i	0.346009	−	0.615157i
$211$			21.5273i			1.48200i	0.671506	+	0.740999i	$0.265648\pi$
$211$			21.5273i			1.48200i	−0.671506	+	0.740999i	$0.734352\pi$
$212$	−7.61230	−	1.26870i	−0.522815	−	0.0871347i
$213$	1.19216	−	1.19216i	0.0816857	−	0.0816857i
$214$	−14.7197	+	4.71717i	−1.00622	+	0.322459i
$215$	3.26861	−	3.03467i	0.222917	−	0.206963i
$216$	−2.27862	−	1.69802i	−0.155041	−	0.115536i
$217$	5.90408	+	5.90408i	0.400795	+	0.400795i
$218$	0.722809	−	1.40456i	0.0489548	−	0.0951287i
$219$	32.5413			2.19894
$220$	−12.1360	−	18.3966i	−0.818209	−	1.24030i
$221$	32.5836			2.19181
$222$	10.8441	−	21.0722i	0.727809	−	1.41427i
$223$	−11.2136	−	11.2136i	−0.750919	−	0.750919i	0.223732	−	0.974651i	$-0.428176\pi$
$223$	−11.2136	−	11.2136i	−0.750919	−	0.750919i	−0.974651	+	0.223732i	$0.928176\pi$
$224$	−0.145877	+	7.23230i	−0.00974679	+	0.483228i
$225$	1.25908	−	16.9394i	0.0839388	−	1.12929i
$226$	−13.4595	+	4.31330i	−0.895310	+	0.286917i
$227$	10.4346	−	10.4346i	0.692570	−	0.692570i	−0.270227	−	0.962797i	$-0.587099\pi$
$227$	10.4346	−	10.4346i	0.692570	−	0.692570i	0.962797	+	0.270227i	$0.0870986\pi$
$228$	−0.831610	+	4.98972i	−0.0550747	+	0.330453i
$229$		−	3.99464i		−	0.263973i	−0.991252	−	0.131987i	$-0.957864\pi$
$229$		−	3.99464i		−	0.263973i	0.991252	−	0.131987i	$-0.0421356\pi$
$230$	−11.4357	+	3.20225i	−0.754047	+	0.211150i
$231$		−	15.9390i		−	1.04871i
$232$	−11.8502	+	1.73017i	−0.778004	+	0.113591i
$233$	−12.5036	+	12.5036i	−0.819139	+	0.819139i	−0.985983	−	0.166844i	$-0.946642\pi$
$233$	−12.5036	+	12.5036i	−0.819139	+	0.819139i	0.166844	+	0.985983i	$0.446642\pi$
$234$	−9.63354	−	30.0610i	−0.629764	−	1.96515i
$235$	−1.72423	−	1.85715i	−0.112476	−	0.121147i
$236$	16.2555	+	22.7576i	1.05814	+	1.48140i
$237$	12.6947	+	12.6947i	0.824610	+	0.824610i
$238$	−7.97434	−	4.10373i	−0.516900	−	0.266005i
$239$	−10.1130			−0.654153			−0.327077	−	0.944998i	$-0.606064\pi$
$239$	−10.1130			−0.654153			−0.327077	+	0.944998i	$0.606064\pi$
$240$	9.18342	+	20.6747i	0.592787	+	1.33455i
$241$	−21.6620			−1.39537			−0.697687	−	0.716402i	$-0.745787\pi$
$241$	−21.6620			−1.39537			−0.697687	+	0.716402i	$0.745787\pi$
$242$	−16.7066	−	8.59749i	−1.07394	−	0.552668i
$243$	15.8140	+	15.8140i	1.01447	+	1.01447i
$244$	7.68700	+	10.7617i	0.492110	+	0.688950i
$245$	11.9877	+	0.444902i	0.765868	+	0.0284237i
$246$	4.36125	+	13.6091i	0.278063	+	0.867683i
$247$	−4.64598	+	4.64598i	−0.295616	+	0.295616i
$248$	−18.2744	+	2.66812i	−1.16042	+	0.169426i
$249$			23.4042i			1.48318i
$250$	−8.75160	+	13.1685i	−0.553500	+	0.832849i
$251$		−	2.50042i		−	0.157825i	−0.996882	−	0.0789125i	$-0.974855\pi$
$251$		−	2.50042i		−	0.157825i	0.996882	−	0.0789125i	$-0.0251448\pi$
$252$	−1.42836	+	8.57028i	−0.0899783	+	0.539877i
$253$	−13.0863	+	13.0863i	−0.822727	+	0.822727i
$254$	0.844246	−	0.270552i	0.0529727	−	0.0169760i
$255$	−28.0278	−	1.04020i	−1.75517	−	0.0651396i
$256$	−12.6341	−	9.81728i	−0.789633	−	0.613580i
$257$	3.26731	+	3.26731i	0.203809	+	0.203809i	0.801630	−	0.597821i	$-0.203966\pi$
$257$	3.26731	+	3.26731i	0.203809	+	0.203809i	−0.597821	+	0.801630i	$0.703966\pi$
$258$	−3.26470	+	6.34396i	−0.203252	+	0.394957i
$259$	−8.47237			−0.526447
$260$	−5.90222	+	28.7849i	−0.366040	+	1.78516i
$261$	−14.3842			−0.890360
$262$	12.8527	−	24.9754i	0.794044	−	1.54298i
$263$	−17.4522	−	17.4522i	−1.07615	−	1.07615i	−0.996851	−	0.0792985i	$-0.974732\pi$
$263$	−17.4522	−	17.4522i	−1.07615	−	1.07615i	−0.0792985	−	0.996851i	$-0.525268\pi$
$264$	28.2689	+	21.0658i	1.73983	+	1.29651i
$265$	5.87059	+	6.32314i	0.360628	+	0.388427i
$266$	1.72217	−	0.551898i	0.105593	−	0.0338390i
$267$	10.8841	−	10.8841i	0.666097	−	0.666097i
$268$	3.94129	+	0.656874i	0.240753	+	0.0401250i
$269$		−	13.8165i		−	0.842410i	−0.906965	−	0.421205i	$-0.861607\pi$
$269$		−	13.8165i		−	0.842410i	0.906965	−	0.421205i	$-0.138393\pi$
$270$	0.856717	+	3.05946i	0.0521381	+	0.186193i
$271$		−	1.41089i		−	0.0857053i	−0.999081	−	0.0428526i	$-0.986355\pi$
$271$		−	1.41089i		−	0.0857053i	0.999081	−	0.0428526i	$-0.0136446\pi$
$272$	17.8175	−	8.71929i	1.08034	−	0.528685i
$273$	−15.0267	+	15.0267i	−0.909455	+	0.909455i
$274$	−6.40786	−	19.9954i	−0.387113	−	1.20797i
$275$	−1.82644	+	24.5726i	−0.110139	+	1.48178i
$276$	15.4583	−	11.0417i	0.930481	−	0.664632i
$277$	10.5953	+	10.5953i	0.636609	+	0.636609i	0.949717	−	0.313108i	$-0.101370\pi$
$277$	10.5953	+	10.5953i	0.636609	+	0.636609i	−0.313108	+	0.949717i	$0.601370\pi$
$278$	−22.9770	−	11.8243i	−1.37807	−	0.709176i
$279$	−22.1821			−1.32801
$280$	5.06978	−	6.30131i	0.302978	−	0.376576i
$281$	3.69749			0.220574			0.110287	−	0.993900i	$-0.464823\pi$
$281$	3.69749			0.220574			0.110287	+	0.993900i	$0.464823\pi$
$282$	3.60449	+	1.85493i	0.214644	+	0.110459i
$283$	−10.5387	−	10.5387i	−0.626458	−	0.626458i	0.320717	−	0.947175i	$-0.396076\pi$
$283$	−10.5387	−	10.5387i	−0.626458	−	0.626458i	−0.947175	+	0.320717i	$0.896076\pi$
$284$	1.08484	−	0.774890i	0.0643735	−	0.0459813i
$285$	4.14470	−	3.84806i	0.245511	−	0.227940i
$286$	13.9745	+	43.6069i	0.826332	+	2.57853i
$287$	3.61261	−	3.61261i	0.213246	−	0.213246i
$288$	−13.3121	−	13.8602i	−0.784424	−	0.816719i
$289$			7.59306i			0.446651i
$290$	11.6700	+	6.56406i	0.685287	+	0.385455i
$291$			5.44890i			0.319420i
$292$	25.3817	+	4.23022i	1.48535	+	0.247555i
$293$	0.294186	−	0.294186i	0.0171865	−	0.0171865i	−0.698461	−	0.715648i	$-0.746132\pi$
$293$	0.294186	−	0.294186i	0.0171865	−	0.0171865i	0.715648	+	0.698461i	$0.246132\pi$
$294$	−18.2740	+	5.85620i	−1.06576	+	0.341540i
$295$	1.15965	−	31.2465i	0.0675177	−	1.81924i
$296$	11.1975	−	15.0263i	0.650841	−	0.873384i
$297$	3.50105	+	3.50105i	0.203152	+	0.203152i
$298$	−12.9640	+	25.1915i	−0.750983	+	1.45931i
$299$	24.6744			1.42696
$300$	5.99590	−	24.5718i	0.346174	−	1.41865i
$301$	2.55067			0.147018
$302$	−0.347086	+	0.674456i	−0.0199726	+	0.0388106i
$303$	−0.624306	−	0.624306i	−0.0358654	−	0.0358654i
$304$	−1.29728	+	3.78379i	−0.0744042	+	0.217015i
$305$	0.548383	−	14.7760i	0.0314003	−	0.846072i
$306$	22.6891	−	7.27110i	1.29705	−	0.415661i
$307$	0.725482	−	0.725482i	0.0414055	−	0.0414055i	−0.686101	−	0.727506i	$-0.740679\pi$
$307$	0.725482	−	0.725482i	0.0414055	−	0.0414055i	0.727506	+	0.686101i	$0.240679\pi$
$308$	2.07200	−	12.4322i	0.118063	−	0.708388i
$309$		−	21.9486i		−	1.24861i
$310$	17.9965	+	10.1225i	1.02213	+	0.574921i
$311$		−	13.6716i		−	0.775247i	−0.921818	−	0.387624i	$-0.873296\pi$
$311$		−	13.6716i		−	0.775247i	0.921818	−	0.387624i	$-0.126704\pi$
$312$	−6.79073	−	46.5107i	−0.384449	−	2.63315i
$313$	4.09570	−	4.09570i	0.231502	−	0.231502i	−0.581817	−	0.813320i	$-0.697658\pi$
$313$	4.09570	−	4.09570i	0.231502	−	0.231502i	0.813320	+	0.581817i	$0.197658\pi$
$314$	−1.86713	−	5.82629i	−0.105368	−	0.328797i
$315$	7.11888	−	6.60938i	0.401103	−	0.372397i
$316$	8.25139	+	11.5519i	0.464177	+	0.649845i
$317$	1.42470	+	1.42470i	0.0800191	+	0.0800191i	0.745983	−	0.665964i	$-0.231980\pi$
$317$	1.42470	+	1.42470i	0.0800191	+	0.0800191i	−0.665964	+	0.745983i	$0.731980\pi$
$318$	−12.2724	−	6.31559i	−0.688203	−	0.354161i
$319$	20.8659			1.16827
$320$	4.47529	+	17.3197i	0.250176	+	0.968200i
$321$	−27.6445			−1.54296
$322$	−6.03870	−	3.10761i	−0.336523	−	0.173181i
$323$	−3.50664	−	3.50664i	−0.195115	−	0.195115i
$324$	8.89358	+	12.4510i	0.494088	+	0.691720i
$325$	24.8879	−	21.4441i	1.38053	−	1.18950i
$326$	2.54298	+	7.93524i	0.140842	+	0.439492i
$327$	1.99766	−	1.99766i	0.110471	−	0.110471i
$328$	1.63258	+	11.1818i	0.0901441	+	0.617411i
$329$		−	1.44923i		−	0.0798988i
$330$	−10.6285	−	37.9560i	−0.585081	−	2.08941i
$331$			7.52474i			0.413597i	0.978384	+	0.206799i	$0.0663045\pi$
$331$			7.52474i			0.413597i	−0.978384	+	0.206799i	$0.933696\pi$
$332$	−3.04243	+	18.2548i	−0.166975	+	1.00186i
$333$	15.9157	−	15.9157i	0.872174	−	0.872174i
$334$	3.01030	−	0.964700i	0.164716	−	0.0527860i
$335$	−3.03952	−	3.27383i	−0.166067	−	0.178868i
$336$	−4.19585	+	12.2381i	−0.228902	+	0.667641i
$337$	13.7139	+	13.7139i	0.747045	+	0.747045i	0.973923	−	0.226878i	$-0.0728518\pi$
$337$	13.7139	+	13.7139i	0.747045	+	0.747045i	−0.226878	+	0.973923i	$0.572852\pi$
$338$	19.5237	−	37.9382i	1.06195	−	2.06357i
$339$	−25.2777			−1.37289
$340$	−21.7259	−	4.45481i	−1.17825	−	0.241596i
$341$	32.1777			1.74252
$342$	−2.19840	+	4.27193i	−0.118876	+	0.230999i
$343$	11.1805	+	11.1805i	0.603689	+	0.603689i
$344$	−3.37110	+	4.52377i	−0.181757	+	0.243906i
$345$	−21.2245	−	0.787705i	−1.14269	−	0.0424086i
$346$	−16.2375	+	5.20357i	−0.872934	+	0.279746i
$347$	22.6242	−	22.6242i	1.21453	−	1.21453i	0.245012	−	0.969520i	$-0.421208\pi$
$347$	22.6242	−	22.6242i	1.21453	−	1.21453i	0.969520	−	0.245012i	$-0.0787919\pi$
$348$	−21.1270	−	3.52112i	−1.13253	−	0.188752i
$349$			1.72511i			0.0923432i	0.998934	+	0.0461716i	$0.0147021\pi$
$349$			1.72511i			0.0923432i	−0.998934	+	0.0461716i	$0.985298\pi$
$350$	−8.79171	+	2.11363i	−0.469937	+	0.112978i
$351$		−	6.60129i		−	0.352351i
$352$	19.3107	+	20.1058i	1.02927	+	1.07164i
$353$	10.9581	−	10.9581i	0.583240	−	0.583240i	−0.352552	−	0.935792i	$-0.614686\pi$
$353$	10.9581	−	10.9581i	0.583240	−	0.583240i	0.935792	+	0.352552i	$0.114686\pi$
$354$	15.2644	+	47.6319i	0.811295	+	2.53161i
$355$	−1.48950	−	0.0552800i	−0.0790545	−	0.00293396i
$356$	9.90429	−	7.07453i	0.524926	−	0.374949i
$357$	−11.3417	−	11.3417i	−0.600265	−	0.600265i
$358$	18.9626	+	9.75848i	1.00221	+	0.515752i
$359$	−26.0612			−1.37546			−0.687728	−	0.725968i	$-0.741392\pi$
$359$	−26.0612			−1.37546			−0.687728	+	0.725968i	$0.741392\pi$
$360$	2.31348	+	21.3610i	0.121931	+	1.12583i
$361$	1.00000			0.0526316
$362$	−9.87193	−	5.08026i	−0.518857	−	0.267012i
$363$	−23.7613	−	23.7613i	−1.24714	−	1.24714i
$364$	−13.6739	+	9.76713i	−0.716709	+	0.511937i
$365$	−19.5743	−	21.0832i	−1.02456	−	1.10355i
$366$	7.21832	+	22.5244i	0.377308	+	1.17737i
$367$	−2.92099	+	2.92099i	−0.152474	+	0.152474i	−0.779222	−	0.626748i	$-0.784386\pi$
$367$	−2.92099	+	2.92099i	−0.152474	+	0.152474i	0.626748	+	0.779222i	$0.284386\pi$
$368$	13.4926	−	6.60282i	0.703349	−	0.344196i
$369$			13.5728i			0.706574i
$370$	−20.1754	+	5.64958i	−1.04887	+	0.293708i
$371$			4.93429i			0.256176i
$372$	−32.5802	−	5.42997i	−1.68921	−	0.281531i
$373$	−9.00352	+	9.00352i	−0.466185	+	0.466185i	−0.900676	−	0.434491i	$-0.856928\pi$
$373$	−9.00352	+	9.00352i	−0.466185	+	0.466185i	0.434491	+	0.900676i	$0.356928\pi$
$374$	−32.9132	+	10.5476i	−1.70190	+	0.545401i
$375$	−22.0927	+	17.6513i	−1.14086	+	0.911508i
$376$	2.57030	+	1.91538i	0.132553	+	0.0987781i
$377$	−19.6715	−	19.6715i	−1.01314	−	1.01314i
$378$	−0.831398	+	1.61557i	−0.0427625	+	0.0830959i
$379$	−11.5138			−0.591425			−0.295713	−	0.955277i	$-0.595557\pi$
$379$	−11.5138			−0.591425			−0.295713	+	0.955277i	$0.595557\pi$
$380$	3.73302	−	2.46263i	0.191500	−	0.126330i
$381$	1.58554			0.0812299
$382$	6.14307	−	11.9372i	0.314307	−	0.610760i
$383$	−19.1866	−	19.1866i	−0.980387	−	0.980387i	0.0194239	−	0.999811i	$-0.493817\pi$
$383$	−19.1866	−	19.1866i	−0.980387	−	0.980387i	−0.999811	+	0.0194239i	$0.993817\pi$
$384$	−16.1595	−	23.6160i	−0.824636	−	1.20515i
$385$	−10.3267	+	9.58766i	−0.526300	+	0.488632i
$386$	−11.5575	+	3.70378i	−0.588259	+	0.188517i
$387$	−4.79154	+	4.79154i	−0.243568	+	0.243568i
$388$	−0.708331	+	4.25004i	−0.0359601	+	0.215763i
$389$		−	19.3955i		−	0.983390i	−0.870767	−	0.491695i	$-0.836377\pi$
$389$		−	19.3955i		−	0.983390i	0.870767	−	0.491695i	$-0.163623\pi$
$390$	−25.7632	+	45.8035i	−1.30457	+	2.31935i
$391$			18.6235i			0.941830i
$392$	−15.0147	+	2.19219i	−0.758355	+	0.110723i
$393$	35.5217	−	35.5217i	1.79183	−	1.79183i
$394$	7.67926	+	23.9628i	0.386876	+	1.20723i
$395$	0.588647	−	15.8609i	0.0296180	−	0.798049i
$396$	19.4620	+	27.2466i	0.978001	+	1.36920i
$397$	7.98711	+	7.98711i	0.400862	+	0.400862i	0.878537	−	0.477675i	$-0.158520\pi$
$397$	7.98711	+	7.98711i	0.400862	+	0.400862i	−0.477675	+	0.878537i	$0.658520\pi$
$398$	11.4136	+	5.87361i	0.572110	+	0.294417i
$399$	3.23434			0.161920
$400$	7.87091	−	18.3861i	0.393546	−	0.919305i
$401$	−21.8145			−1.08936			−0.544682	−	0.838643i	$-0.683350\pi$
$401$	−21.8145			−1.08936			−0.544682	+	0.838643i	$0.683350\pi$
$402$	6.35409	+	3.26992i	0.316913	+	0.163089i
$403$	−30.3358	−	30.3358i	−1.51113	−	1.51113i
$404$	−0.405791	−	0.568104i	−0.0201888	−	0.0282642i
$405$	0.634460	−	17.0953i	0.0315266	−	0.849473i
$406$	2.33679	+	7.29184i	0.115973	+	0.361888i
$407$	−23.0875	+	23.0875i	−1.14440	+	1.14440i
$408$	35.1048	−	5.12543i	1.73795	−	0.253747i
$409$		−	26.8043i		−	1.32539i	−0.748890	−	0.662694i	$-0.769413\pi$
$409$		−	26.8043i		−	1.32539i	0.748890	−	0.662694i	$-0.230587\pi$
$410$	6.19381	−	11.0118i	0.305890	−	0.543832i
$411$		−	37.5526i		−	1.85233i
$412$	2.85322	−	17.1195i	0.140568	−	0.843419i
$413$	12.6442	−	12.6442i	0.622179	−	0.622179i
$414$	17.1817	−	5.50615i	0.844434	−	0.270613i
$415$	15.1633	−	14.0781i	0.744338	−	0.691066i
$416$	0.749528	−	37.1603i	0.0367487	−	1.82193i
$417$	−32.6795	−	32.6795i	−1.60032	−	1.60032i
$418$	3.18903	−	6.19691i	0.155981	−	0.303101i
$419$	22.9547			1.12141			0.560706	−	0.828015i	$-0.310530\pi$
$419$	22.9547			1.12141			0.560706	+	0.828015i	$0.310530\pi$
$420$	12.0739	−	7.96498i	0.589144	−	0.388651i
$421$	−22.1889			−1.08142			−0.540710	−	0.841209i	$-0.681844\pi$
$421$	−22.1889			−1.08142			−0.540710	+	0.841209i	$0.681844\pi$
$422$	−13.9307	+	27.0700i	−0.678134	+	1.31775i
$423$	2.72244	+	2.72244i	0.132370	+	0.132370i
$424$	−8.75127	−	6.52141i	−0.424999	−	0.316707i
$425$	16.1853	+	18.7846i	0.785104	+	0.911187i
$426$	2.27058	−	0.727645i	0.110010	−	0.0352545i
$427$	5.97924	−	5.97924i	0.289356	−	0.289356i
$428$	−21.5622	−	3.59365i	−1.04225	−	0.173706i
$429$			81.8964i			3.95399i
$430$	6.07397	−	1.70085i	0.292913	−	0.0820223i
$431$		−	3.20599i		−	0.154427i	−0.997015	−	0.0772135i	$-0.975398\pi$
$431$		−	3.20599i		−	0.154427i	0.997015	−	0.0772135i	$-0.0246023\pi$
$432$	−1.76649	−	3.60975i	−0.0849903	−	0.173674i
$433$	−16.1866	+	16.1866i	−0.777880	+	0.777880i	−0.979470	−	0.201590i	$-0.935389\pi$
$433$	−16.1866	+	16.1866i	−0.777880	+	0.777880i	0.201590	+	0.979470i	$0.435389\pi$
$434$	3.60360	+	11.2449i	0.172978	+	0.539771i
$435$	16.2931	+	17.5491i	0.781194	+	0.841414i
$436$	1.81783	−	1.29845i	0.0870581	−	0.0621847i
$437$	−2.65546	−	2.65546i	−0.127028	−	0.127028i
$438$	40.9199	+	21.0580i	1.95523	+	1.00619i
$439$	33.4711			1.59749			0.798745	−	0.601669i	$-0.205498\pi$
$439$	33.4711			1.59749			0.798745	+	0.601669i	$0.205498\pi$
$440$	−3.35596	−	30.9866i	−0.159989	−	1.47723i
$441$	−18.2253			−0.867874
$442$	40.9730	+	21.0854i	1.94888	+	1.00293i
$443$	−6.99853	−	6.99853i	−0.332510	−	0.332510i	0.521029	−	0.853539i	$-0.325548\pi$
$443$	−6.99853	−	6.99853i	−0.332510	−	0.332510i	−0.853539	+	0.521029i	$0.825548\pi$
$444$	27.2724	−	19.4803i	1.29429	−	0.924496i
$445$	−13.5987	−	0.504690i	−0.644641	−	0.0239246i
$446$	−6.84431	−	21.3573i	−0.324087	−	1.01130i
$447$	−35.8291	+	35.8291i	−1.69466	+	1.69466i
$448$	−4.86358	+	9.00003i	−0.229782	+	0.425211i
$449$			10.8774i			0.513334i	0.966500	+	0.256667i	$0.0826244\pi$
$449$			10.8774i			0.513334i	−0.966500	+	0.256667i	$0.917376\pi$
$450$	12.5450	−	20.4861i	0.591379	−	0.965724i
$451$		−	19.6890i		−	0.927117i
$452$	−19.7161	−	3.28598i	−0.927369	−	0.154559i
$453$	−0.959259	+	0.959259i	−0.0450699	+	0.0450699i
$454$	19.8737	−	6.36884i	0.932718	−	0.298905i
$455$	18.7745	+	0.696778i	0.880161	+	0.0326655i
$456$	−4.27466	+	5.73630i	−0.200179	+	0.268627i
$457$	−2.21461	−	2.21461i	−0.103595	−	0.103595i	0.653409	−	0.757005i	$-0.273338\pi$
$457$	−2.21461	−	2.21461i	−0.103595	−	0.103595i	−0.757005	+	0.653409i	$0.773338\pi$
$458$	2.58500	−	5.02315i	0.120789	−	0.234716i
$459$	4.98245			0.232561
$460$	−16.4523	−	3.37348i	−0.767092	−	0.157289i
$461$	32.4654			1.51207			0.756033	−	0.654534i	$-0.227135\pi$
$461$	32.4654			1.51207			0.756033	+	0.654534i	$0.227135\pi$
$462$	10.3144	−	20.0429i	0.479870	−	0.932481i
$463$	−17.6213	−	17.6213i	−0.818933	−	0.818933i	0.167020	−	0.985953i	$-0.446586\pi$
$463$	−17.6213	−	17.6213i	−0.818933	−	0.818933i	−0.985953	+	0.167020i	$0.946586\pi$
$464$	−16.0209	−	5.49282i	−0.743754	−	0.254998i
$465$	25.1258	+	27.0627i	1.16518	+	1.25500i
$466$	−23.8143	+	7.63167i	−1.10317	+	0.353530i
$467$	4.04114	−	4.04114i	0.187002	−	0.187002i	−0.607397	−	0.794399i	$-0.707786\pi$
$467$	4.04114	−	4.04114i	0.187002	−	0.187002i	0.794399	+	0.607397i	$0.207786\pi$
$468$	7.33906	−	44.0349i	0.339248	−	2.03552i
$469$		−	2.55475i		−	0.117967i
$470$	−0.966383	−	3.45109i	−0.0445759	−	0.159187i
$471$		−	10.9421i		−	0.504187i
$472$	5.71405	+	39.1364i	0.263010	+	1.80140i
$473$	6.95067	−	6.95067i	0.319592	−	0.319592i
$474$	7.74830	+	24.1782i	0.355891	+	1.11054i
$475$	−4.98625	−	0.370620i	−0.228785	−	0.0170052i
$476$	−7.37193	−	10.3207i	−0.337892	−	0.473047i
$477$	−9.26926	−	9.26926i	−0.424410	−	0.424410i
$478$	−12.7168	−	6.54427i	−0.581652	−	0.299328i
$479$	41.6363			1.90241			0.951205	−	0.308559i	$-0.0998468\pi$
$479$	41.6363			1.90241			0.951205	+	0.308559i	$0.0998468\pi$
$480$	−1.83103	+	31.9406i	−0.0835748	+	1.45788i
$481$	43.5319			1.98488
$482$	−27.2394	−	14.0179i	−1.24072	−	0.638496i
$483$	−8.58866	−	8.58866i	−0.390797	−	0.390797i
$484$	−15.4445	−	21.6222i	−0.702024	−	0.982829i
$485$	3.53029	−	3.27762i	0.160302	−	0.148829i
$486$	9.65218	+	30.1192i	0.437832	+	1.36623i
$487$	−20.9898	+	20.9898i	−0.951140	+	0.951140i	−0.998861	−	0.0477211i	$-0.984804\pi$
$487$	−20.9898	+	20.9898i	−0.951140	+	0.951140i	0.0477211	+	0.998861i	$0.484804\pi$
$488$	2.70209	+	18.5070i	0.122318	+	0.837772i
$489$			14.9029i			0.673930i
$490$	14.7864	+	8.31692i	0.667979	+	0.375720i
$491$			26.4536i			1.19384i	0.802302	+	0.596918i	$0.203608\pi$
$491$			26.4536i			1.19384i	−0.802302	+	0.596918i	$0.796392\pi$
$492$	−3.32251	+	19.9353i	−0.149790	+	0.898753i
$493$	14.8475	−	14.8475i	0.668696	−	0.668696i
$494$	−8.84868	+	2.83570i	−0.398121	+	0.127584i
$495$	1.38840	−	37.4100i	0.0624039	−	1.68145i
$496$	−24.7061	−	8.47056i	−1.10934	−	0.380339i
$497$	−0.602739	−	0.602739i	−0.0270365	−	0.0270365i
$498$	−15.1452	+	29.4301i	−0.678674	+	1.31880i
$499$	15.2356			0.682041			0.341021	−	0.940056i	$-0.389227\pi$
$499$	15.2356			0.682041			0.341021	+	0.940056i	$0.389227\pi$
$500$	−19.5265	+	10.8957i	−0.873250	+	0.487272i
$501$	5.65353			0.252581
$502$	1.61806	−	3.14421i	0.0722176	−	0.140333i
$503$	12.4917	+	12.4917i	0.556977	+	0.556977i	0.928445	−	0.371469i	$-0.121146\pi$
$503$	12.4917	+	12.4917i	0.556977	+	0.556977i	−0.371469	+	0.928445i	$0.621146\pi$
$504$	−7.34210	+	9.85258i	−0.327043	+	0.438869i
$505$	−0.0289487	+	0.780014i	−0.00128820	+	0.0347102i
$506$	−24.9240	+	7.98730i	−1.10801	+	0.355079i
$507$	53.9584	−	53.9584i	2.39638	−	2.39638i
$508$	1.23670	+	0.206113i	0.0548695	+	0.00914480i
$509$			17.6173i			0.780873i	0.920630	+	0.390437i	$0.127676\pi$
$509$			17.6173i			0.780873i	−0.920630	+	0.390437i	$0.872324\pi$
$510$	−34.5710	−	19.4453i	−1.53083	−	0.861050i
$511$		−	16.4524i		−	0.727811i
$512$	−9.53415	−	20.5207i	−0.421354	−	0.906896i
$513$	−0.710431	+	0.710431i	−0.0313663	+	0.0313663i
$514$	1.99423	+	6.22289i	0.0879616	+	0.274480i
$515$	−14.2203	+	13.2025i	−0.626621	+	0.581774i
$516$	−8.21056	+	5.86471i	−0.361450	+	0.258180i
$517$	−3.94921	−	3.94921i	−0.173686	−	0.173686i
$518$	−10.6538	−	5.48261i	−0.468100	−	0.240892i
$519$	−30.4950			−1.33858
$520$	−26.0490	+	32.3768i	−1.14233	+	1.41982i
$521$	11.6663			0.511111			0.255555	−	0.966794i	$-0.417742\pi$
$521$	11.6663			0.511111			0.255555	+	0.966794i	$0.417742\pi$
$522$	−18.0878	−	9.30826i	−0.791680	−	0.407412i
$523$	11.2249	+	11.2249i	0.490833	+	0.490833i	0.908569	−	0.417736i	$-0.137176\pi$
$523$	11.2249	+	11.2249i	0.490833	+	0.490833i	−0.417736	+	0.908569i	$0.637176\pi$
$524$	32.3239	−	23.0886i	1.41208	−	1.00863i
$525$	−16.1272	−	1.19871i	−0.703849	−	0.0523161i
$526$	−10.6521	−	33.2393i	−0.464453	−	1.44930i
$527$	22.8965	−	22.8965i	0.997387	−	0.997387i
$528$	21.9153	+	44.7830i	0.953741	+	1.94893i
$529$		−	8.89707i		−	0.386829i
$530$	3.29030	+	11.7501i	0.142922	+	0.510393i
$531$			47.5051i			2.06155i
$532$	2.52273	+	0.420449i	0.109374	+	0.0182288i
$533$	−18.5619	+	18.5619i	−0.804007	+	0.804007i
$534$	20.7298	−	6.64319i	0.897065	−	0.287479i
$535$	16.6287	+	17.9106i	0.718922	+	0.774342i
$536$	4.53100	+	3.37648i	0.195709	+	0.145842i
$537$	26.9700	+	26.9700i	1.16384	+	1.16384i
$538$	8.94092	−	17.3739i	0.385470	−	0.749044i
$539$	26.4379			1.13876
$540$	−0.902526	+	4.40158i	−0.0388385	+	0.189414i
$541$	11.7416			0.504811			0.252405	−	0.967622i	$-0.418778\pi$
$541$	11.7416			0.504811			0.252405	+	0.967622i	$0.418778\pi$
$542$	0.913008	−	1.77415i	0.0392171	−	0.0762064i
$543$	−14.0405	−	14.0405i	−0.602538	−	0.602538i
$544$	28.0474	+	0.565721i	1.20252	+	0.0242551i
$545$	−2.49590	−	0.0926305i	−0.106913	−	0.00396786i
$546$	−28.6196	+	9.17163i	−1.22481	+	0.392510i
$547$	−4.80032	+	4.80032i	−0.205247	+	0.205247i	−0.802244	−	0.596997i	$-0.796361\pi$
$547$	−4.80032	+	4.80032i	−0.205247	+	0.205247i	0.596997	+	0.802244i	$0.296361\pi$
$548$	4.88166	−	29.2904i	0.208534	−	1.25122i
$549$			22.4645i			0.958760i
$550$	−18.1980	+	29.7174i	−0.775966	+	1.26715i
$551$			4.23410i			0.180379i
$552$	26.5837	−	3.88131i	1.13148	−	0.165200i
$553$	6.41825	−	6.41825i	0.272932	−	0.272932i
$554$	6.46691	+	20.1797i	0.274753	+	0.857353i
$555$	−37.4453	−	1.38971i	−1.58946	−	0.0589899i
$556$	−21.2412	−	29.7376i	−0.900828	−	1.26115i
$557$	23.5262	+	23.5262i	0.996839	+	0.996839i	0.999995	−	0.00315589i	$-0.00100455\pi$
$557$	23.5262	+	23.5262i	0.996839	+	0.996839i	−0.00315589	+	0.999995i	$0.501005\pi$
$558$	−27.8934	−	14.3544i	−1.18082	−	0.607670i
$559$	−13.1056			−0.554308
$560$	10.4528	−	4.64300i	0.441712	−	0.196202i
$561$	−61.8129			−2.60974
$562$	4.64950	+	2.39271i	0.196127	+	0.100930i
$563$	16.6377	+	16.6377i	0.701194	+	0.701194i	0.964667	−	0.263473i	$-0.0848679\pi$
$563$	16.6377	+	16.6377i	0.701194	+	0.701194i	−0.263473	+	0.964667i	$0.584868\pi$
$564$	3.33219	+	4.66505i	0.140311	+	0.196434i
$565$	15.2050	+	16.3771i	0.639681	+	0.688992i
$566$	−6.43234	−	20.0718i	−0.270371	−	0.843682i
$567$	6.91776	−	6.91776i	0.290519	−	0.290519i
$568$	1.86560	−	0.272385i	0.0782790	−	0.0114290i
$569$		−	34.4084i		−	1.44247i	−0.692689	−	0.721237i	$-0.743574\pi$
$569$		−	34.4084i		−	1.44247i	0.692689	−	0.721237i	$-0.256426\pi$
$570$	7.70200	−	2.15673i	0.322601	−	0.0903357i
$571$			46.0355i			1.92652i	0.268563	+	0.963262i	$0.413451\pi$
$571$			46.0355i			1.92652i	−0.268563	+	0.963262i	$0.586549\pi$
$572$	−10.6461	+	63.8777i	−0.445138	+	2.67086i
$573$	16.9779	−	16.9779i	0.709262	−	0.709262i
$574$	6.88054	−	2.20498i	0.287188	−	0.0920341i
$575$	12.2566	+	14.2249i	0.511136	+	0.593221i
$576$	−7.77048	−	26.0433i	−0.323770	−	1.08514i
$577$	−20.6188	−	20.6188i	−0.858372	−	0.858372i	0.132775	−	0.991146i	$-0.457611\pi$
$577$	−20.6188	−	20.6188i	−0.858372	−	0.858372i	−0.991146	+	0.132775i	$0.957611\pi$
$578$	−4.91360	+	9.54808i	−0.204379	+	0.397148i
$579$	−21.7056			−0.902054
$580$	10.4270	+	15.8060i	0.432958	+	0.656308i
$581$	11.8328			0.490907
$582$	−3.52607	+	6.85185i	−0.146160	+	0.284018i
$583$	13.4461	+	13.4461i	0.556881	+	0.556881i
$584$	29.1793	+	21.7443i	1.20745	+	0.899785i
$585$	−36.5775	+	33.9597i	−1.51229	+	1.40406i
$586$	0.560303	−	0.179558i	0.0231459	−	0.00741749i
$587$	−10.5267	+	10.5267i	−0.434482	+	0.434482i	−0.890150	−	0.455668i	$-0.849401\pi$
$587$	−10.5267	+	10.5267i	−0.434482	+	0.434482i	0.455668	+	0.890150i	$0.349401\pi$
$588$	−26.7687	−	4.46139i	−1.10392	−	0.183985i
$589$			6.52947i			0.269042i
$590$	21.6784	−	38.5413i	0.892485	−	1.58672i
$591$			45.0035i			1.85120i
$592$	23.8043	−	11.6490i	0.978351	−	0.478773i
$593$	1.48897	−	1.48897i	0.0611445	−	0.0611445i	−0.675873	−	0.737018i	$-0.736233\pi$
$593$	1.48897	−	1.48897i	0.0611445	−	0.0611445i	0.737018	+	0.675873i	$0.236233\pi$
$594$	2.13689	+	6.66807i	0.0876777	+	0.273594i
$595$	−0.525907	+	14.1704i	−0.0215601	+	0.580930i
$596$	−32.6037	+	23.2885i	−1.33550	+	0.953933i
$597$	16.2332	+	16.2332i	0.664379	+	0.664379i
$598$	31.0274	+	15.9672i	1.26881	+	0.652948i
$599$	−40.1937			−1.64227			−0.821134	−	0.570735i	$-0.806658\pi$
$599$	−40.1937			−1.64227			−0.821134	+	0.570735i	$0.806658\pi$
$600$	23.4405	−	27.0183i	0.956954	−	1.10302i
$601$	−36.4888			−1.48841			−0.744204	−	0.667953i	$-0.767171\pi$
$601$	−36.4888			−1.48841			−0.744204	+	0.667953i	$0.767171\pi$
$602$	3.20741	+	1.65058i	0.130724	+	0.0672728i
$603$	4.79919	+	4.79919i	0.195438	+	0.195438i
$604$	−0.872904	+	0.623505i	−0.0355179	+	0.0253701i
$605$	−1.10180	+	29.6876i	−0.0447945	+	1.20697i
$606$	−0.381049	−	1.18905i	−0.0154791	−	0.0483017i
$607$	1.97147	−	1.97147i	0.0800195	−	0.0800195i	−0.665964	−	0.745984i	$-0.731980\pi$
$607$	1.97147	−	1.97147i	0.0800195	−	0.0800195i	0.745984	+	0.665964i	$0.231980\pi$
$608$	−4.07985	+	3.91852i	−0.165460	+	0.158917i
$609$			13.6945i			0.554930i
$610$	10.2514	−	18.2256i	0.415067	−	0.737932i
$611$			7.44631i			0.301245i
$612$	33.2362	+	5.53930i	1.34349	+	0.223913i
$613$	28.7912	−	28.7912i	1.16286	−	1.16286i	0.179019	−	0.983846i	$-0.442708\pi$
$613$	28.7912	−	28.7912i	1.16286	−	1.16286i	0.983846	−	0.179019i	$-0.0572924\pi$
$614$	1.38175	−	0.442803i	0.0557627	−	0.0178701i
$615$	16.5592	−	15.3741i	0.667731	−	0.619942i
$616$	10.6506	−	14.2923i	0.429123	−	0.575853i
$617$	−0.750563	−	0.750563i	−0.0302165	−	0.0302165i	0.691837	−	0.722054i	$-0.256802\pi$
$617$	−0.750563	−	0.750563i	−0.0302165	−	0.0302165i	−0.722054	+	0.691837i	$0.756802\pi$
$618$	14.2033	−	27.5998i	0.571341	−	1.11023i
$619$	−26.8459			−1.07903			−0.539514	−	0.841977i	$-0.681392\pi$
$619$	−26.8459			−1.07903			−0.539514	+	0.841977i	$0.681392\pi$
$620$	16.0797	+	24.3746i	0.645775	+	0.978909i
$621$	3.77304			0.151407
$622$	8.84715	−	17.1917i	0.354738	−	0.689325i
$623$	−5.50284	−	5.50284i	−0.220466	−	0.220466i
$624$	21.5587	−	62.8804i	0.863038	−	2.51723i
$625$	24.7253	+	3.69601i	0.989011	+	0.147840i
$626$	7.80063	−	2.49984i	0.311776	−	0.0999136i
$627$	8.81369	−	8.81369i	0.351985	−	0.351985i
$628$	1.42243	−	8.53466i	0.0567610	−	0.340570i
$629$			32.8565i			1.31008i
$630$	13.2288	−	3.70438i	0.527050	−	0.147586i
$631$		−	0.106404i		−	0.00423588i	−0.999998	−	0.00211794i	$-0.999326\pi$
$631$		−	0.106404i		−	0.00423588i	0.999998	−	0.00211794i	$-0.000674162\pi$
$632$	2.90048	+	19.8658i	0.115375	+	0.790220i
$633$	−38.5008	+	38.5008i	−1.53027	+	1.53027i
$634$	0.869575	+	2.71347i	0.0345352	+	0.107766i
$635$	−0.953738	−	1.02726i	−0.0378479	−	0.0407655i
$636$	−11.3453	−	15.8834i	−0.449871	−	0.629817i
$637$	−24.9246	−	24.9246i	−0.987548	−	0.987548i
$638$	26.2384	+	13.5027i	1.03879	+	0.534577i
$639$	2.26454			0.0895837
$640$	−5.58031	+	24.6751i	−0.220581	+	0.975369i
$641$	−13.7498			−0.543084			−0.271542	−	0.962427i	$-0.587534\pi$
$641$	−13.7498			−0.543084			−0.271542	+	0.962427i	$0.587534\pi$
$642$	−34.7622	−	17.8892i	−1.37195	−	0.706030i
$643$	23.5125	+	23.5125i	0.927244	+	0.927244i	0.997527	−	0.0702828i	$-0.0223902\pi$
$643$	23.5125	+	23.5125i	0.927244	+	0.927244i	−0.0702828	+	0.997527i	$0.522390\pi$
$644$	−5.58251	−	7.81548i	−0.219982	−	0.307973i
$645$	11.2732	+	0.418383i	0.443882	+	0.0164738i
$646$	−2.14030	−	6.67871i	−0.0842091	−	0.262771i
$647$	14.0408	−	14.0408i	0.552002	−	0.552002i	−0.375016	−	0.927018i	$-0.622363\pi$
$647$	14.0408	−	14.0408i	0.552002	−	0.552002i	0.927018	+	0.375016i	$0.122363\pi$
$648$	3.12622	+	21.4119i	0.122809	+	0.841140i
$649$		−	68.9116i		−	2.70502i
$650$	45.1727	−	10.8600i	1.77182	−	0.425965i
$651$			21.1185i			0.827700i
$652$	−1.93730	+	11.6240i	−0.0758706	+	0.455229i
$653$	−5.12437	+	5.12437i	−0.200532	+	0.200532i	−0.800228	−	0.599696i	$-0.795288\pi$
$653$	−5.12437	+	5.12437i	−0.200532	+	0.200532i	0.599696	+	0.800228i	$0.295288\pi$
$654$	3.80473	−	1.21929i	0.148777	−	0.0476779i
$655$	−44.3812	−	1.64712i	−1.73412	−	0.0643584i
$656$	−5.18299	+	15.1173i	−0.202362	+	0.590230i
$657$	30.9064	+	30.9064i	1.20578	+	1.20578i
$658$	0.937823	−	1.82237i	0.0365602	−	0.0710435i
$659$	3.86388			0.150515			0.0752576	−	0.997164i	$-0.476022\pi$
$659$	3.86388			0.150515			0.0752576	+	0.997164i	$0.476022\pi$
$660$	11.1968	−	54.6065i	0.435837	−	2.12556i
$661$	15.1842			0.590596			0.295298	−	0.955405i	$-0.404581\pi$
$661$	15.1842			0.590596			0.295298	+	0.955405i	$0.404581\pi$
$662$	−4.86939	+	9.46216i	−0.189254	+	0.367757i
$663$	58.2746	+	58.2746i	2.26320	+	2.26320i
$664$	−15.6388	+	20.9862i	−0.606903	+	0.814421i
$665$	−1.94552	−	2.09550i	−0.0754441	−	0.0812599i
$666$	30.3128	−	9.71424i	1.17460	−	0.376419i
$667$	11.2435	−	11.2435i	0.435349	−	0.435349i
$668$	4.40965	+	0.734932i	0.170614	+	0.0284354i
$669$		−	40.1104i		−	1.55076i
$670$	−1.70357	−	6.08367i	−0.0658145	−	0.235033i
$671$		−	32.5873i		−	1.25802i
$672$	−13.1956	+	12.6738i	−0.509032	+	0.488904i
$673$	16.4676	−	16.4676i	0.634778	−	0.634778i	−0.314485	−	0.949262i	$-0.601832\pi$
$673$	16.4676	−	16.4676i	0.634778	−	0.634778i	0.949262	+	0.314485i	$0.101832\pi$
$674$	8.37039	+	26.1194i	0.322415	+	1.00608i
$675$	3.80568	−	3.27908i	0.146481	−	0.126212i
$676$	49.1010	−	35.0723i	1.88850	−	1.34893i
$677$	−13.1053	−	13.1053i	−0.503676	−	0.503676i	0.408902	−	0.912578i	$-0.365912\pi$
$677$	−13.1053	−	13.1053i	−0.503676	−	0.503676i	−0.912578	+	0.408902i	$0.865912\pi$
$678$	−31.7860	−	16.3576i	−1.22073	−	0.628210i
$679$	2.75488			0.105723
$680$	−24.4370	−	19.6610i	−0.937116	−	0.753966i
$681$	37.3240			1.43026
$682$	40.4626	+	20.8227i	1.54939	+	0.797342i
$683$	10.6014	+	10.6014i	0.405652	+	0.405652i	0.880219	−	0.474567i	$-0.157395\pi$
$683$	10.6014	+	10.6014i	0.405652	+	0.405652i	−0.474567	+	0.880219i	$0.657395\pi$
$684$	−5.52887	+	3.94921i	−0.211402	+	0.151002i
$685$	−24.3300	+	22.5887i	−0.929600	+	0.863069i
$686$	6.82409	+	21.2942i	0.260545	+	0.813018i
$687$	7.14428	−	7.14428i	0.272571	−	0.272571i
$688$	−7.16647	+	3.50703i	−0.273219	+	0.133704i
$689$		−	25.3529i		−	0.965868i
$690$	−26.1795	−	14.7252i	−0.996635	−	0.560580i
$691$			16.8100i			0.639483i	0.947505	+	0.319742i	$0.103596\pi$
$691$			16.8100i			0.639483i	−0.947505	+	0.319742i	$0.896404\pi$
$692$	−23.7856	−	3.96421i	−0.904192	−	0.150697i
$693$	15.1383	−	15.1383i	0.575055	−	0.575055i
$694$	43.0899	−	13.8088i	1.63567	−	0.524177i
$695$	−1.51533	+	40.8301i	−0.0574797	+	1.54877i
$696$	−24.2881	−	18.0993i	−0.920636	−	0.686054i
$697$	−14.0100	−	14.0100i	−0.530666	−	0.530666i
$698$	−1.11635	+	2.16928i	−0.0422545	+	0.0821086i
$699$	−44.7246			−1.69164
$700$	−12.4231	−	3.03144i	−0.469549	−	0.114577i
$701$	−19.1823			−0.724505			−0.362253	−	0.932080i	$-0.617992\pi$
$701$	−19.1823			−0.724505			−0.362253	+	0.932080i	$0.617992\pi$
$702$	4.27181	−	8.30095i	0.161229	−	0.313299i
$703$	−4.68490	−	4.68490i	−0.176694	−	0.176694i
$704$	11.2720	+	37.7788i	0.424828	+	1.42384i
$705$	0.237716	−	6.40517i	0.00895289	−	0.241233i
$706$	20.8707	−	6.68835i	0.785478	−	0.251719i
$707$	−0.315639	+	0.315639i	−0.0118708	+	0.0118708i
$708$	−11.6288	+	69.7738i	−0.437038	+	2.62226i
$709$			22.4644i			0.843668i	0.906673	+	0.421834i	$0.138613\pi$
$709$			22.4644i			0.843668i	−0.906673	+	0.421834i	$0.861387\pi$
$710$	−1.83724	−	1.03339i	−0.0689502	−	0.0387826i
$711$			24.1139i			0.904340i
$712$	17.0324	−	2.48680i	0.638317	−	0.0931966i
$713$	17.3387	−	17.3387i	0.649341	−	0.649341i
$714$	−6.92246	−	21.6012i	−0.259067	−	0.808406i
$715$	53.0598	−	49.2624i	1.98433	−	1.84231i
$716$	17.5301	+	24.5421i	0.655131	+	0.917180i
$717$	−18.0867	−	18.0867i	−0.675460	−	0.675460i
$718$	−32.7712	−	16.8646i	−1.22301	−	0.629382i
$719$	45.9737			1.71453			0.857265	−	0.514876i	$-0.172162\pi$
$719$	45.9737			1.71453			0.857265	+	0.514876i	$0.172162\pi$
$720$	−10.9140	+	28.3580i	−0.406739	+	1.05684i
$721$	−11.0969			−0.413270
$722$	1.25747	+	0.647117i	0.0467983	+	0.0240832i
$723$	−38.7418	−	38.7418i	−1.44082	−	1.44082i
$724$	−9.12617	−	12.7766i	−0.339171	−	0.474838i
$725$	1.56924	−	21.1123i	0.0582802	−	0.784090i
$726$	−14.5029	−	45.2555i	−0.538252	−	1.67959i
$727$	19.6989	−	19.6989i	0.730592	−	0.730592i	−0.240145	−	0.970737i	$-0.577195\pi$
$727$	19.6989	−	19.6989i	0.730592	−	0.730592i	0.970737	+	0.240145i	$0.0771950\pi$
$728$	−23.5151	+	3.43329i	−0.871527	+	0.127246i
$729$			33.6141i			1.24497i
$730$	−10.9708	−	39.1784i	−0.406049	−	1.45006i
$731$		−	9.89172i		−	0.365858i
$732$	−5.49909	+	32.9950i	−0.203252	+	1.21953i
$733$	−26.8457	+	26.8457i	−0.991567	+	0.991567i	−0.999965	−	0.00839797i	$-0.997327\pi$
$733$	−26.8457	+	26.8457i	−0.991567	+	0.991567i	0.00839797	+	0.999965i	$0.497327\pi$
$734$	−5.56328	+	1.78284i	−0.205345	+	0.0658060i
$735$	20.6440	+	22.2354i	0.761464	+	0.820164i
$736$	21.2394	+	0.428401i	0.782893	+	0.0157911i
$737$	−6.96178	−	6.96178i	−0.256440	−	0.256440i
$738$	−8.78322	+	17.0675i	−0.323315	+	0.628263i
$739$	40.4662			1.48857			0.744286	−	0.667861i	$-0.232790\pi$
$739$	40.4662			1.48857			0.744286	+	0.667861i	$0.232790\pi$
$740$	−29.0260	−	5.95166i	−1.06702	−	0.218788i
$741$	−16.6184			−0.610491
$742$	−3.19307	+	6.20475i	−0.117221	+	0.227783i
$743$	−22.3693	−	22.3693i	−0.820650	−	0.820650i	0.165551	−	0.986201i	$-0.447060\pi$
$743$	−22.3693	−	22.3693i	−0.820650	−	0.820650i	−0.986201	+	0.165551i	$0.947060\pi$
$744$	−37.4550	−	27.9113i	−1.37317	−	1.02328i
$745$	44.7653	+	1.66138i	1.64007	+	0.0608682i
$746$	−17.1480	+	5.49536i	−0.627834	+	0.201199i
$747$	−22.2283	+	22.2283i	−0.813292	+	0.813292i
$748$	−48.2129	−	8.03538i	−1.76284	−	0.293803i
$749$			13.9766i			0.510694i
$750$	−39.2034	+	7.89949i	−1.43151	+	0.288449i
$751$		−	51.1851i		−	1.86777i	−0.357573	−	0.933885i	$-0.616396\pi$
$751$		−	51.1851i		−	1.86777i	0.357573	−	0.933885i	$-0.383604\pi$
$752$	1.99262	+	4.07182i	0.0726632	+	0.148484i
$753$	4.47191	−	4.47191i	0.162966	−	0.162966i
$754$	−12.0067	−	37.4662i	−0.437257	−	1.36444i
$755$	1.19851	+	0.0444803i	0.0436182	+	0.00161880i
$756$	−2.09092	+	1.49352i	−0.0760461	+	0.0543189i
$757$	−4.56094	−	4.56094i	−0.165770	−	0.165770i	0.619347	−	0.785117i	$-0.287397\pi$
$757$	−4.56094	−	4.56094i	−0.165770	−	0.165770i	−0.785117	+	0.619347i	$0.787397\pi$
$758$	−14.4783	−	7.45078i	−0.525876	−	0.270625i
$759$	−46.8088			−1.69905
$760$	6.28779	−	0.680990i	0.228082	−	0.0247021i
$761$	−16.9886			−0.615835			−0.307918	−	0.951413i	$-0.599632\pi$
$761$	−16.9886			−0.615835			−0.307918	+	0.951413i	$0.599632\pi$
$762$	1.99378	+	1.02603i	0.0722270	+	0.0371692i
$763$	−1.00999	−	1.00999i	−0.0365640	−	0.0365640i
$764$	15.4495	−	11.0354i	0.558944	−	0.399247i
$765$	−25.6317	−	27.6076i	−0.926716	−	0.998154i
$766$	−11.7106	−	36.5425i	−0.423123	−	1.32034i
$767$	−64.9670	+	64.9670i	−2.34582	+	2.34582i
$768$	−5.03783	−	40.1536i	−0.181787	−	1.44892i
$769$			34.8444i			1.25652i	0.778004	+	0.628260i	$0.216233\pi$
$769$			34.8444i			1.25652i	−0.778004	+	0.628260i	$0.783767\pi$
$770$	−19.1899	+	5.37362i	−0.691558	+	0.193652i
$771$			11.6870i			0.420896i

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25747 + 0.647117i) q^{2} +(1.78847 + 1.78847i) q^{3} +(1.16248 + 1.62746i) q^{4} +(0.0829302 - 2.23453i) q^{5} +(1.09160 + 3.40630i) q^{6} +(0.904221 - 0.904221i) q^{7} +(0.408628 + 2.79875i) q^{8} +3.39723i q^{9} +O(q^{10})\)	\(q+(1.25747 + 0.647117i) q^{2} +(1.78847 + 1.78847i) q^{3} +(1.16248 + 1.62746i) q^{4} +(0.0829302 - 2.23453i) q^{5} +(1.09160 + 3.40630i) q^{6} +(0.904221 - 0.904221i) q^{7} +(0.408628 + 2.79875i) q^{8} +3.39723i q^{9} +(1.55028 - 2.75620i) q^{10} -4.92807i q^{11} +(-0.831610 + 4.98972i) q^{12} +(-4.64598 + 4.64598i) q^{13} +(1.72217 - 0.551898i) q^{14} +(4.14470 - 3.84806i) q^{15} +(-1.29728 + 3.78379i) q^{16} +(-3.50664 - 3.50664i) q^{17} +(-2.19840 + 4.27193i) q^{18} +1.00000 q^{19} +(3.73302 - 2.46263i) q^{20} +3.23434 q^{21} +(3.18903 - 6.19691i) q^{22} +(-2.65546 - 2.65546i) q^{23} +(-4.27466 + 5.73630i) q^{24} +(-4.98625 - 0.370620i) q^{25} +(-8.84868 + 2.83570i) q^{26} +(-0.710431 + 0.710431i) q^{27} +(2.52273 + 0.420449i) q^{28} +4.23410i q^{29} +(7.70200 - 2.15673i) q^{30} +6.52947i q^{31} +(-4.07985 + 3.91852i) q^{32} +(8.81369 - 8.81369i) q^{33} +(-2.14030 - 6.67871i) q^{34} +(-1.94552 - 2.09550i) q^{35} +(-5.52887 + 3.94921i) q^{36} +(-4.68490 - 4.68490i) q^{37} +(1.25747 + 0.647117i) q^{38} -16.6184 q^{39} +(6.28779 - 0.680990i) q^{40} +3.99527 q^{41} +(4.06710 + 2.09300i) q^{42} +(1.41043 + 1.41043i) q^{43} +(8.02025 - 5.72878i) q^{44} +(7.59121 + 0.281733i) q^{45} +(-1.62078 - 5.05756i) q^{46} +(0.801371 - 0.801371i) q^{47} +(-9.08733 + 4.44704i) q^{48} +5.36477i q^{49} +(-6.03024 - 3.69273i) q^{50} -12.5430i q^{51} +(-12.9620 - 2.16031i) q^{52} +(-2.72848 + 2.72848i) q^{53} +(-1.35308 + 0.433616i) q^{54} +(-11.0119 - 0.408686i) q^{55} +(2.90018 + 2.16120i) q^{56} +(1.78847 + 1.78847i) q^{57} +(-2.73996 + 5.32427i) q^{58} +13.9835 q^{59} +(11.0807 + 2.27206i) q^{60} +6.61259 q^{61} +(-4.22533 + 8.21063i) q^{62} +(3.07185 + 3.07185i) q^{63} +(-7.66605 + 2.28730i) q^{64} +(9.99628 + 10.7669i) q^{65} +(16.7865 - 5.37949i) q^{66} +(1.41268 - 1.41268i) q^{67} +(1.63053 - 9.78333i) q^{68} -9.49840i q^{69} +(-1.09041 - 3.89401i) q^{70} -0.666584i q^{71} +(-9.50801 + 1.38820i) q^{72} +(9.09755 - 9.09755i) q^{73} +(-2.85946 - 8.92281i) q^{74} +(-8.25489 - 9.58058i) q^{75} +(1.16248 + 1.62746i) q^{76} +(-4.45606 - 4.45606i) q^{77} +(-20.8971 - 10.7540i) q^{78} +7.09809 q^{79} +(8.34741 + 3.21260i) q^{80} +7.65052 q^{81} +(5.02395 + 2.58541i) q^{82} +(6.54308 + 6.54308i) q^{83} +(3.75985 + 5.26377i) q^{84} +(-8.12650 + 7.54489i) q^{85} +(0.860863 + 2.68628i) q^{86} +(-7.57255 + 7.57255i) q^{87} +(13.7924 - 2.01375i) q^{88} -6.08572i q^{89} +(9.36343 + 5.26667i) q^{90} +8.40198i q^{91} +(1.23475 - 7.40858i) q^{92} +(-11.6777 + 11.6777i) q^{93} +(1.52628 - 0.489122i) q^{94} +(0.0829302 - 2.23453i) q^{95} +(-14.3048 - 0.288531i) q^{96} +(1.52334 + 1.52334i) q^{97} +(-3.47163 + 6.74605i) q^{98} +16.7418 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Introduction

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