LMFDB - Embedded newform 380.2.k.c.267.2

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			267.2
Character	$\chi$	$=$	380.267
Dual form			380.2.k.c.343.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38561 - 0.282971i) q^{2} +(0.321015 + 0.321015i) q^{3} +(1.83985 + 0.784178i) q^{4} +(1.77712 + 1.35715i) q^{5} +(-0.353965 - 0.535642i) q^{6} +(1.91243 - 1.91243i) q^{7} +(-2.32743 - 1.60719i) q^{8} -2.79390i q^{9} +O(q^{10})$	\(q+(-1.38561 - 0.282971i) q^{2} +(0.321015 + 0.321015i) q^{3} +(1.83985 + 0.784178i) q^{4} +(1.77712 + 1.35715i) q^{5} +(-0.353965 - 0.535642i) q^{6} +(1.91243 - 1.91243i) q^{7} +(-2.32743 - 1.60719i) q^{8} -2.79390i q^{9} +(-2.07836 - 2.38336i) q^{10} -5.65006i q^{11} +(0.338888 + 0.842355i) q^{12} +(-2.00460 + 2.00460i) q^{13} +(-3.19106 + 2.10873i) q^{14} +(0.134816 + 1.00615i) q^{15} +(2.77013 + 2.88555i) q^{16} +(3.89197 + 3.89197i) q^{17} +(-0.790593 + 3.87127i) q^{18} +1.00000 q^{19} +(2.20539 + 3.89054i) q^{20} +1.22784 q^{21} +(-1.59880 + 7.82880i) q^{22} +(-3.04830 - 3.04830i) q^{23} +(-0.231207 - 1.26307i) q^{24} +(1.31629 + 4.82363i) q^{25} +(3.34485 - 2.21036i) q^{26} +(1.85993 - 1.85993i) q^{27} +(5.01829 - 2.01891i) q^{28} -8.56783i q^{29} +(0.0979086 - 1.43228i) q^{30} +3.58721i q^{31} +(-3.02180 - 4.78212i) q^{32} +(1.81376 - 1.81376i) q^{33} +(-4.29145 - 6.49409i) q^{34} +(5.99408 - 0.803157i) q^{35} +(2.19091 - 5.14037i) q^{36} +(3.87230 + 3.87230i) q^{37} +(-1.38561 - 0.282971i) q^{38} -1.28702 q^{39} +(-1.95491 - 6.01484i) q^{40} -0.0555658 q^{41} +(-1.70132 - 0.347444i) q^{42} +(1.97854 + 1.97854i) q^{43} +(4.43065 - 10.3953i) q^{44} +(3.79174 - 4.96508i) q^{45} +(3.36118 + 5.08634i) q^{46} +(-4.74358 + 4.74358i) q^{47} +(-0.0370507 + 1.81556i) q^{48} -0.314813i q^{49} +(-0.458916 - 7.05616i) q^{50} +2.49877i q^{51} +(-5.26015 + 2.11621i) q^{52} +(-7.95199 + 7.95199i) q^{53} +(-3.10345 + 2.05084i) q^{54} +(7.66798 - 10.0408i) q^{55} +(-7.52471 + 1.37740i) q^{56} +(0.321015 + 0.321015i) q^{57} +(-2.42445 + 11.8717i) q^{58} +8.34740 q^{59} +(-0.540958 + 1.95689i) q^{60} +12.0737 q^{61} +(1.01508 - 4.97049i) q^{62} +(-5.34315 - 5.34315i) q^{63} +(2.83385 + 7.48126i) q^{64} +(-6.28297 + 0.841866i) q^{65} +(-3.02641 + 1.99992i) q^{66} +(6.55823 - 6.55823i) q^{67} +(4.10866 + 10.2127i) q^{68} -1.95710i q^{69} +(-8.53275 - 0.583286i) q^{70} +7.24112i q^{71} +(-4.49034 + 6.50260i) q^{72} +(-3.34075 + 3.34075i) q^{73} +(-4.26977 - 6.46127i) q^{74} +(-1.12591 + 1.97101i) q^{75} +(1.83985 + 0.784178i) q^{76} +(-10.8054 - 10.8054i) q^{77} +(1.78331 + 0.364189i) q^{78} -13.0319 q^{79} +(1.00672 + 8.88744i) q^{80} -7.18756 q^{81} +(0.0769927 + 0.0157235i) q^{82} +(-4.60217 - 4.60217i) q^{83} +(2.25905 + 0.962847i) q^{84} +(1.63450 + 12.1985i) q^{85} +(-2.18162 - 3.30136i) q^{86} +(2.75040 - 2.75040i) q^{87} +(-9.08074 + 13.1501i) q^{88} +4.22554i q^{89} +(-6.65887 + 5.80674i) q^{90} +7.66735i q^{91} +(-3.21801 - 7.99883i) q^{92} +(-1.15155 + 1.15155i) q^{93} +(7.91506 - 5.23047i) q^{94} +(1.77712 + 1.35715i) q^{95} +(0.565089 - 2.50518i) q^{96} +(-3.74804 - 3.74804i) q^{97} +(-0.0890829 + 0.436209i) q^{98} -15.7857 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 $

$2$	−1.38561	−	0.282971i	−0.979777	−	0.200091i
$2$	−1.38561	−	0.282971i	−0.979777	−	0.200091i
$3$	0.321015	+	0.321015i	0.185338	+	0.185338i	0.793677	−	0.608339i	$-0.208164\pi$
$3$	0.321015	+	0.321015i	0.185338	+	0.185338i	−0.608339	+	0.793677i	$0.708164\pi$
$4$	1.83985	+	0.784178i	0.919927	+	0.392089i
$5$	1.77712	+	1.35715i	0.794751	+	0.606936i
$5$	1.77712	+	1.35715i	0.794751	+	0.606936i
$6$	−0.353965	−	0.535642i	−0.144506	−	0.218675i
$7$	1.91243	−	1.91243i	0.722832	−	0.722832i	−0.246349	−	0.969181i	$-0.579231\pi$
$7$	1.91243	−	1.91243i	0.722832	−	0.722832i	0.969181	+	0.246349i	$0.0792309\pi$
$8$	−2.32743	−	1.60719i	−0.822870	−	0.568229i
$9$		−	2.79390i		−	0.931299i
$10$	−2.07836	−	2.38336i	−0.657236	−	0.753685i
$11$		−	5.65006i		−	1.70356i	−0.523903	−	0.851778i	$-0.675525\pi$
$11$		−	5.65006i		−	1.70356i	0.523903	−	0.851778i	$-0.324475\pi$
$12$	0.338888	+	0.842355i	0.0978287	+	0.243167i
$13$	−2.00460	+	2.00460i	−0.555977	+	0.555977i	−0.928160	−	0.372182i	$-0.878610\pi$
$13$	−2.00460	+	2.00460i	−0.555977	+	0.555977i	0.372182	+	0.928160i	$0.378610\pi$
$14$	−3.19106	+	2.10873i	−0.852847	+	0.563583i
$15$	0.134816	+	1.00615i	0.0348092	+	0.259786i
$16$	2.77013	+	2.88555i	0.692532	+	0.721387i
$17$	3.89197	+	3.89197i	0.943942	+	0.943942i	0.998510	−	0.0545685i	$-0.0173783\pi$
$17$	3.89197	+	3.89197i	0.943942	+	0.943942i	−0.0545685	+	0.998510i	$0.517378\pi$
$18$	−0.790593	+	3.87127i	−0.186345	+	0.912466i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	2.20539	+	3.89054i	0.493140	+	0.869950i
$21$	1.22784			0.267937
$22$	−1.59880	+	7.82880i	−0.340866	+	1.66911i
$23$	−3.04830	−	3.04830i	−0.635614	−	0.635614i	0.313857	−	0.949470i	$-0.398379\pi$
$23$	−3.04830	−	3.04830i	−0.635614	−	0.635614i	−0.949470	+	0.313857i	$0.898379\pi$
$24$	−0.231207	−	1.26307i	−0.0471948	−	0.257824i
$25$	1.31629	+	4.82363i	0.263257	+	0.964726i
$26$	3.34485	−	2.21036i	0.655980	−	0.433488i
$27$	1.85993	−	1.85993i	0.357944	−	0.357944i
$28$	5.01829	−	2.01891i	0.948368	−	0.381539i
$29$		−	8.56783i		−	1.59101i	−0.605950	−	0.795503i	$-0.707207\pi$
$29$		−	8.56783i		−	1.59101i	0.605950	−	0.795503i	$-0.292793\pi$
$30$	0.0979086	−	1.43228i	0.0178756	−	0.261498i
$31$			3.58721i			0.644282i	0.946692	+	0.322141i	$0.104403\pi$
$31$			3.58721i			0.644282i	−0.946692	+	0.322141i	$0.895597\pi$
$32$	−3.02180	−	4.78212i	−0.534185	−	0.845368i
$33$	1.81376	−	1.81376i	0.315734	−	0.315734i
$34$	−4.29145	−	6.49409i	−0.735978	−	1.11373i
$35$	5.99408	−	0.803157i	1.01318	−	0.135758i
$36$	2.19091	−	5.14037i	0.365152	−	0.856728i
$37$	3.87230	+	3.87230i	0.636603	+	0.636603i	0.949716	−	0.313113i	$-0.101372\pi$
$37$	3.87230	+	3.87230i	0.636603	+	0.636603i	−0.313113	+	0.949716i	$0.601372\pi$
$38$	−1.38561	−	0.282971i	−0.224776	−	0.0459040i
$39$	−1.28702			−0.206088
$40$	−1.95491	−	6.01484i	−0.309098	−	0.951030i
$41$	−0.0555658			−0.00867792			−0.00433896	−	0.999991i	$-0.501381\pi$
$41$	−0.0555658			−0.00867792			−0.00433896	+	0.999991i	$0.501381\pi$
$42$	−1.70132	−	0.347444i	−0.262519	−	0.0536118i
$43$	1.97854	+	1.97854i	0.301724	+	0.301724i	0.841688	−	0.539964i	$-0.181562\pi$
$43$	1.97854	+	1.97854i	0.301724	+	0.301724i	−0.539964	+	0.841688i	$0.681562\pi$
$44$	4.43065	−	10.3953i	0.667946	−	1.56715i
$45$	3.79174	−	4.96508i	0.565239	−	0.740151i
$46$	3.36118	+	5.08634i	0.495579	+	0.749940i
$47$	−4.74358	+	4.74358i	−0.691922	+	0.691922i	−0.962655	−	0.270733i	$-0.912734\pi$
$47$	−4.74358	+	4.74358i	−0.691922	+	0.691922i	0.270733	+	0.962655i	$0.412734\pi$
$48$	−0.0370507	+	1.81556i	−0.00534781	+	0.262053i
$49$		−	0.314813i		−	0.0449732i
$50$	−0.458916	−	7.05616i	−0.0649005	−	0.997892i
$51$			2.49877i			0.349897i
$52$	−5.26015	+	2.11621i	−0.729451	+	0.293466i
$53$	−7.95199	+	7.95199i	−1.09229	+	1.09229i	−0.0970058	+	0.995284i	$0.530927\pi$
$53$	−7.95199	+	7.95199i	−1.09229	+	1.09229i	−0.995284	+	0.0970058i	$0.969073\pi$
$54$	−3.10345	+	2.05084i	−0.422327	+	0.279084i
$55$	7.66798	−	10.0408i	1.03395	−	1.35390i
$56$	−7.52471	+	1.37740i	−1.00553	+	0.184063i
$57$	0.321015	+	0.321015i	0.0425195	+	0.0425195i
$58$	−2.42445	+	11.8717i	−0.318346	+	1.55883i
$59$	8.34740			1.08674			0.543369	−	0.839494i	$-0.317148\pi$
$59$	8.34740			1.08674			0.543369	+	0.839494i	$0.317148\pi$
$60$	−0.540958	+	1.95689i	−0.0698374	+	0.252633i
$61$	12.0737			1.54588			0.772939	−	0.634481i	$-0.218786\pi$
$61$	12.0737			1.54588			0.772939	+	0.634481i	$0.218786\pi$
$62$	1.01508	−	4.97049i	0.128915	−	0.631253i
$63$	−5.34315	−	5.34315i	−0.673173	−	0.673173i
$64$	2.83385	+	7.48126i	0.354232	+	0.935158i
$65$	−6.28297	+	0.841866i	−0.779306	+	0.104421i
$66$	−3.02641	+	1.99992i	−0.372525	+	0.246174i
$67$	6.55823	−	6.55823i	0.801215	−	0.801215i	−0.182071	−	0.983285i	$-0.558280\pi$
$67$	6.55823	−	6.55823i	0.801215	−	0.801215i	0.983285	+	0.182071i	$0.0582800\pi$
$68$	4.10866	+	10.2127i	0.498248	+	1.23847i
$69$		−	1.95710i		−	0.235607i
$70$	−8.53275	−	0.583286i	−1.01986	−	0.0697160i
$71$			7.24112i			0.859363i	0.902980	+	0.429682i	$0.141374\pi$
$71$			7.24112i			0.859363i	−0.902980	+	0.429682i	$0.858626\pi$
$72$	−4.49034	+	6.50260i	−0.529191	+	0.766339i
$73$	−3.34075	+	3.34075i	−0.391005	+	0.391005i	−0.875046	−	0.484040i	$-0.839169\pi$
$73$	−3.34075	+	3.34075i	−0.391005	+	0.391005i	0.484040	+	0.875046i	$0.339169\pi$
$74$	−4.26977	−	6.46127i	−0.496351	−	0.751107i
$75$	−1.12591	+	1.97101i	−0.130009	+	0.227592i
$76$	1.83985	+	0.784178i	0.211046	+	0.0899514i
$77$	−10.8054	−	10.8054i	−1.23139	−	1.23139i
$78$	1.78331	+	0.364189i	0.201920	+	0.0412363i
$79$	−13.0319			−1.46620			−0.733100	−	0.680121i	$-0.761927\pi$
$79$	−13.0319			−1.46620			−0.733100	+	0.680121i	$0.761927\pi$
$80$	1.00672	+	8.88744i	0.112555	+	0.993646i
$81$	−7.18756			−0.798618
$82$	0.0769927	+	0.0157235i	0.00850242	+	0.00173637i
$83$	−4.60217	−	4.60217i	−0.505154	−	0.505154i	0.407881	−	0.913035i	$-0.366268\pi$
$83$	−4.60217	−	4.60217i	−0.505154	−	0.505154i	−0.913035	+	0.407881i	$0.866268\pi$
$84$	2.25905	+	0.962847i	0.246483	+	0.105055i
$85$	1.63450	+	12.1985i	0.177286	+	1.32311i
$86$	−2.18162	−	3.30136i	−0.235250	−	0.355994i
$87$	2.75040	−	2.75040i	0.294874	−	0.294874i
$88$	−9.08074	+	13.1501i	−0.968010	+	1.40181i
$89$			4.22554i			0.447906i	0.974600	+	0.223953i	$0.0718962\pi$
$89$			4.22554i			0.447906i	−0.974600	+	0.223953i	$0.928104\pi$
$90$	−6.65887	+	5.80674i	−0.701906	+	0.612084i
$91$			7.66735i			0.803757i
$92$	−3.21801	−	7.99883i	−0.335501	−	0.833935i
$93$	−1.15155	+	1.15155i	−0.119410	+	0.119410i
$94$	7.91506	−	5.23047i	0.816376	−	0.539482i
$95$	1.77712	+	1.35715i	0.182328	+	0.139241i
$96$	0.565089	−	2.50518i	0.0576742	−	0.255684i
$97$	−3.74804	−	3.74804i	−0.380556	−	0.380556i	0.490747	−	0.871302i	$-0.336724\pi$
$97$	−3.74804	−	3.74804i	−0.380556	−	0.380556i	−0.871302	+	0.490747i	$0.836724\pi$
$98$	−0.0890829	+	0.436209i	−0.00899873	+	0.0440637i
$99$	−15.7857			−1.58652
$100$	−1.36081	+	9.90698i	−0.136081	+	0.990698i
$101$	−2.63822			−0.262513			−0.131256	−	0.991348i	$-0.541901\pi$
$101$	−2.63822			−0.262513			−0.131256	+	0.991348i	$0.541901\pi$
$102$	0.707079	−	3.46232i	0.0700112	−	0.342821i
$103$	6.61857	+	6.61857i	0.652147	+	0.652147i	0.953510	−	0.301363i	$-0.0974415\pi$
$103$	6.61857	+	6.61857i	0.652147	+	0.652147i	−0.301363	+	0.953510i	$0.597441\pi$
$104$	7.88736	−	1.44379i	0.773420	−	0.141575i
$105$	2.18202	+	1.66637i	0.212943	+	0.162621i
$106$	13.2686	−	8.76821i	1.28876	−	0.851643i
$107$	−6.65655	+	6.65655i	−0.643513	+	0.643513i	−0.951417	−	0.307904i	$-0.900372\pi$
$107$	−6.65655	+	6.65655i	−0.643513	+	0.643513i	0.307904	+	0.951417i	$0.400372\pi$
$108$	4.88052	−	1.96349i	0.469628	−	0.188936i
$109$			0.604648i			0.0579148i	0.999581	+	0.0289574i	$0.00921871\pi$
$109$			0.604648i			0.0579148i	−0.999581	+	0.0289574i	$0.990781\pi$
$110$	−13.4661	+	11.7429i	−1.28394	+	1.11964i
$111$			2.48614i			0.235974i
$112$	10.8161	+	0.220728i	1.02203	+	0.0208568i
$113$	3.55461	−	3.55461i	0.334389	−	0.334389i	−0.519861	−	0.854251i	$-0.674016\pi$
$113$	3.55461	−	3.55461i	0.334389	−	0.334389i	0.854251	+	0.519861i	$0.174016\pi$
$114$	−0.353965	−	0.535642i	−0.0331519	−	0.0501674i
$115$	−1.28018	−	9.55417i	−0.119377	−	0.890931i
$116$	6.71870	−	15.7636i	0.623816	−	1.46361i
$117$	5.60066	+	5.60066i	0.517781	+	0.517781i
$118$	−11.5663	−	2.36207i	−1.06476	−	0.217447i
$119$	14.8863			1.36462
$120$	1.30330	−	2.55841i	0.118975	−	0.233550i
$121$	−20.9231			−1.90210
$122$	−16.7295	−	3.41651i	−1.51462	−	0.309316i
$123$	−0.0178375	−	0.0178375i	−0.00160835	−	0.00160835i
$124$	−2.81301	+	6.59995i	−0.252616	+	0.592693i
$125$	−4.20720	+	10.3585i	−0.376303	+	0.926497i
$126$	5.89159	+	8.91550i	0.524864	+	0.794256i
$127$	−8.47034	+	8.47034i	−0.751621	+	0.751621i	−0.974782	−	0.223161i	$-0.928363\pi$
$127$	−8.47034	+	8.47034i	−0.751621	+	0.751621i	0.223161	+	0.974782i	$0.428363\pi$
$128$	−1.80965	−	11.1680i	−0.159952	−	0.987125i
$129$			1.27028i			0.111842i
$130$	8.94399	+	0.611397i	0.784440	+	0.0536231i
$131$			0.0987163i			0.00862489i	0.999991	+	0.00431244i	$0.00137270\pi$
$131$			0.0987163i			0.00862489i	−0.999991	+	0.00431244i	$0.998627\pi$
$132$	4.75935	−	1.91474i	0.414248	−	0.166657i
$133$	1.91243	−	1.91243i	0.165829	−	0.165829i
$134$	−10.9430	+	7.23138i	−0.945328	+	0.624696i
$135$	5.82952	−	0.781108i	0.501725	−	0.0672270i
$136$	−2.80313	−	15.3134i	−0.240367	−	1.31312i
$137$	−10.4246	−	10.4246i	−0.890634	−	0.890634i	0.103949	−	0.994583i	$-0.466852\pi$
$137$	−10.4246	−	10.4246i	−0.890634	−	0.890634i	−0.994583	+	0.103949i	$0.966852\pi$
$138$	−0.553803	+	2.71179i	−0.0471428	+	0.230843i
$139$	−8.14601			−0.690935			−0.345468	−	0.938431i	$-0.612280\pi$
$139$	−8.14601			−0.690935			−0.345468	+	0.938431i	$0.612280\pi$
$140$	11.6581	+	3.22273i	0.985285	+	0.272371i
$141$	−3.04552			−0.256479
$142$	2.04903	−	10.0334i	0.171951	−	0.841985i
$143$	11.3261	+	11.3261i	0.947139	+	0.947139i
$144$	8.06192	−	7.73946i	0.671827	−	0.644955i
$145$	11.6278	−	15.2260i	0.965639	−	1.26445i
$146$	5.57433	−	3.68366i	0.461335	−	0.304862i
$147$	0.101060	−	0.101060i	0.00833526	−	0.00833526i
$148$	4.08790	+	10.1611i	0.336023	+	0.835233i
$149$		−	20.1596i		−	1.65154i	−0.564009	−	0.825769i	$-0.690742\pi$
$149$		−	20.1596i		−	1.65154i	0.564009	−	0.825769i	$-0.309258\pi$
$150$	2.11782	−	2.41246i	0.172919	−	0.196976i
$151$			4.29284i			0.349346i	0.984626	+	0.174673i	$0.0558869\pi$
$151$			4.29284i			0.349346i	−0.984626	+	0.174673i	$0.944113\pi$
$152$	−2.32743	−	1.60719i	−0.188779	−	0.130361i
$153$	10.8738	−	10.8738i	0.879092	−	0.879092i
$154$	11.9145	+	18.0297i	0.960095	+	1.45287i
$155$	−4.86839	+	6.37489i	−0.391038	+	0.512044i
$156$	−2.36793	−	1.00925i	−0.189586	−	0.0808048i
$157$	−0.932967	−	0.932967i	−0.0744589	−	0.0744589i	0.668897	−	0.743355i	$-0.266767\pi$
$157$	−0.932967	−	0.932967i	−0.0744589	−	0.0744589i	−0.743355	+	0.668897i	$0.766767\pi$
$158$	18.0571	+	3.68764i	1.43655	+	0.293373i
$159$	−5.10542			−0.404886
$160$	1.11996	−	12.5994i	0.0885407	−	0.996073i
$161$	−11.6593			−0.918884
$162$	9.95919	+	2.03387i	0.782468	+	0.159796i
$163$	1.46169	+	1.46169i	0.114488	+	0.114488i	0.762030	−	0.647542i	$-0.224203\pi$
$163$	1.46169	+	1.46169i	0.114488	+	0.114488i	−0.647542	+	0.762030i	$0.724203\pi$
$164$	−0.102233	−	0.0435735i	−0.00798305	−	0.00340252i
$165$	5.68479	−	0.761715i	0.442560	−	0.0592995i
$166$	5.07455	+	7.67912i	0.393862	+	0.596015i
$167$	−8.67695	+	8.67695i	−0.671442	+	0.671442i	−0.958049	−	0.286606i	$-0.907473\pi$
$167$	−8.67695	+	8.67695i	−0.671442	+	0.671442i	0.286606	+	0.958049i	$0.407473\pi$
$168$	−2.85772	−	1.97338i	−0.220478	−	0.152250i
$169$			4.96312i			0.381778i
$170$	1.18704	−	17.3649i	0.0910416	−	1.33183i
$171$		−	2.79390i		−	0.213655i
$172$	2.08869	+	5.19174i	0.159261	+	0.395867i
$173$	6.45817	−	6.45817i	0.491005	−	0.491005i	−0.417617	−	0.908623i	$-0.637135\pi$
$173$	6.45817	−	6.45817i	0.491005	−	0.491005i	0.908623	+	0.417617i	$0.137135\pi$
$174$	−4.58928	+	3.03271i	−0.347913	+	0.229909i
$175$	11.7422	+	6.70756i	0.887626	+	0.507044i
$176$	16.3035	−	15.6514i	1.22892	−	1.17977i
$177$	2.67964	+	2.67964i	0.201414	+	0.201414i
$178$	1.19571	−	5.85497i	0.0896219	−	0.438848i
$179$	−23.2404			−1.73707			−0.868535	−	0.495627i	$-0.834938\pi$
$179$	−23.2404			−1.73707			−0.868535	+	0.495627i	$0.834938\pi$
$180$	10.8698	−	6.16163i	0.810184	−	0.459261i
$181$	7.16494			0.532566			0.266283	−	0.963895i	$-0.414204\pi$
$181$	7.16494			0.532566			0.266283	+	0.963895i	$0.414204\pi$
$182$	2.16964	−	10.6240i	0.160824	−	0.787503i
$183$	3.87584	+	3.87584i	0.286510	+	0.286510i
$184$	2.19549	+	11.9939i	0.161854	+	0.884202i
$185$	1.62624	+	12.1368i	0.119563	+	0.892318i
$186$	1.92146	−	1.26975i	0.140888	−	0.0931025i
$187$	21.9899	−	21.9899i	1.60806	−	1.60806i
$188$	−12.4473	+	5.00768i	−0.907813	+	0.365223i
$189$		−	7.11399i		−	0.517467i
$190$	−2.07836	−	2.38336i	−0.150780	−	0.172907i
$191$			19.7928i			1.43215i	0.698022	+	0.716077i	$0.254064\pi$
$191$			19.7928i			1.43215i	−0.698022	+	0.716077i	$0.745936\pi$
$192$	−1.49189	+	3.31131i	−0.107668	+	0.238973i
$193$	4.77524	−	4.77524i	0.343730	−	0.343730i	−0.514038	−	0.857767i	$-0.671851\pi$
$193$	4.77524	−	4.77524i	0.343730	−	0.343730i	0.857767	+	0.514038i	$0.171851\pi$
$194$	4.13275	+	6.25392i	0.296714	+	0.449005i
$195$	−2.28718	−	1.74668i	−0.163788	−	0.125082i
$196$	0.246869	−	0.579209i	0.0176335	−	0.0413721i
$197$	12.5130	+	12.5130i	0.891516	+	0.891516i	0.994666	−	0.103150i	$-0.0328923\pi$
$197$	12.5130	+	12.5130i	0.891516	+	0.891516i	−0.103150	+	0.994666i	$0.532892\pi$
$198$	21.8729	+	4.46689i	1.55444	+	0.317448i
$199$	−15.8810			−1.12577			−0.562886	−	0.826534i	$-0.690309\pi$
$199$	−15.8810			−1.12577			−0.562886	+	0.826534i	$0.690309\pi$
$200$	4.68895	−	13.3422i	0.331559	−	0.943435i
$201$	4.21058			0.296992
$202$	3.65556	+	0.746541i	0.257204	+	0.0525264i
$203$	−16.3854	−	16.3854i	−1.15003	−	1.15003i
$204$	−1.95948	+	4.59736i	−0.137191	+	0.321880i
$205$	−0.0987468	−	0.0754111i	−0.00689678	−	0.00526694i
$206$	−7.29792	−	11.0436i	−0.508470	−	0.769447i
$207$	−8.51663	+	8.51663i	−0.591946	+	0.591946i
$208$	−11.3374	−	0.231366i	−0.786107	−	0.0160424i
$209$		−	5.65006i		−	0.390823i
$210$	−2.55190	−	2.92639i	−0.176098	−	0.201940i
$211$		−	10.7864i		−	0.742568i	−0.928519	−	0.371284i	$-0.878918\pi$
$211$		−	10.7864i		−	0.742568i	0.928519	−	0.371284i	$-0.121082\pi$
$212$	−20.8663	+	8.39473i	−1.43310	+	0.576552i
$213$	−2.32451	+	2.32451i	−0.159273	+	0.159273i
$214$	11.1070	−	7.33980i	0.759260	−	0.501738i
$215$	0.830917	+	6.20126i	0.0566681	+	0.422922i
$216$	−7.31813	+	1.33959i	−0.497935	+	0.0911473i
$217$	6.86031	+	6.86031i	0.465708	+	0.465708i
$218$	0.171098	−	0.837809i	0.0115882	−	0.0567436i
$219$	−2.14486			−0.144937
$220$	21.9817	−	12.4606i	1.48201	−	0.840091i
$221$	−15.6037			−1.04962
$222$	0.703506	−	3.44483i	0.0472162	−	0.231202i
$223$	−14.8860	−	14.8860i	−0.996843	−	0.996843i	0.00315185	−	0.999995i	$-0.498997\pi$
$223$	−14.8860	−	14.8860i	−0.996843	−	0.996843i	−0.999995	+	0.00315185i	$0.998997\pi$
$224$	−14.9245	−	3.36649i	−0.997185	−	0.224933i
$225$	13.4767	−	3.67757i	0.898448	−	0.245171i
$226$	−5.93117	+	3.91946i	−0.394535	+	0.260719i
$227$	16.9491	−	16.9491i	1.12495	−	1.12495i	0.133963	−	0.990986i	$-0.457230\pi$
$227$	16.9491	−	16.9491i	1.12495	−	1.12495i	0.990986	−	0.133963i	$-0.0427705\pi$
$228$	0.338888	+	0.842355i	0.0224434	+	0.0557863i
$229$			12.2209i			0.807580i	0.914852	+	0.403790i	$0.132307\pi$
$229$			12.2209i			0.807580i	−0.914852	+	0.403790i	$0.867693\pi$
$230$	−0.929719	+	13.6007i	−0.0613039	+	0.896800i
$231$		−	6.93738i		−	0.456446i
$232$	−13.7702	+	19.9410i	−0.904055	+	1.30919i
$233$	13.3876	−	13.3876i	0.877051	−	0.877051i	−0.116178	−	0.993228i	$-0.537064\pi$
$233$	13.3876	−	13.3876i	0.877051	−	0.877051i	0.993228	+	0.116178i	$0.0370642\pi$
$234$	−6.17553	−	9.34518i	−0.403707	−	0.610914i
$235$	−14.8676	+	1.99214i	−0.969857	+	0.129953i
$236$	15.3580	+	6.54585i	0.999721	+	0.426098i
$237$	−4.18343	−	4.18343i	−0.271743	−	0.271743i
$238$	−20.6266	−	4.21239i	−1.33703	−	0.273049i
$239$	25.0913			1.62302			0.811511	−	0.584338i	$-0.198646\pi$
$239$	25.0913			1.62302			0.811511	+	0.584338i	$0.198646\pi$
$240$	−2.52983	+	3.17618i	−0.163300	+	0.205021i
$241$	20.2239			1.30274			0.651369	−	0.758761i	$-0.274195\pi$
$241$	20.2239			1.30274			0.651369	+	0.758761i	$0.274195\pi$
$242$	28.9914	+	5.92064i	1.86364	+	0.380593i
$243$	−7.88711	−	7.88711i	−0.505958	−	0.505958i
$244$	22.2138	+	9.46792i	1.42209	+	0.606121i
$245$	0.427248	−	0.559459i	0.0272959	−	0.0357425i
$246$	0.0196684	+	0.0297633i	0.00125401	+	0.00189764i
$247$	−2.00460	+	2.00460i	−0.127550	+	0.127550i
$248$	5.76535	−	8.34898i	0.366100	−	0.530161i
$249$		−	2.95474i		−	0.187249i
$250$	8.76072	−	13.1624i	0.554077	−	0.832466i
$251$			14.1483i			0.893034i	0.894775	+	0.446517i	$0.147336\pi$
$251$			14.1483i			0.893034i	−0.894775	+	0.446517i	$0.852664\pi$
$252$	−5.64064	−	14.0206i	−0.355327	−	0.883214i
$253$	−17.2230	+	17.2230i	−1.08280	+	1.08280i
$254$	14.1335	−	9.33976i	0.886814	−	0.586029i
$255$	−3.39120	+	4.44060i	−0.212365	+	0.278081i
$256$	−0.652763	+	15.9867i	−0.0407977	+	0.999167i
$257$	1.76563	+	1.76563i	0.110137	+	0.110137i	0.760028	−	0.649891i	$-0.225185\pi$
$257$	1.76563	+	1.76563i	0.110137	+	0.110137i	−0.649891	+	0.760028i	$0.725185\pi$
$258$	0.359453	−	1.76012i	0.0223786	−	0.109580i
$259$	14.8111			0.920314
$260$	−12.2199	−	3.37805i	−0.757847	−	0.209498i
$261$	−23.9376			−1.48170
$262$	0.0279339	−	0.136783i	0.00172576	−	0.00845047i
$263$	1.92483	+	1.92483i	0.118690	+	0.118690i	0.763957	−	0.645267i	$-0.223254\pi$
$263$	1.92483	+	1.92483i	0.118690	+	0.118690i	−0.645267	+	0.763957i	$0.723254\pi$
$264$	−7.13644	+	1.30633i	−0.439218	+	0.0803990i
$265$	−24.9237	+	3.33956i	−1.53105	+	0.205148i
$266$	−3.19106	+	2.10873i	−0.195657	+	0.129295i
$267$	−1.35646	+	1.35646i	−0.0830142	+	0.0830142i
$268$	17.2090	−	6.92336i	1.05121	−	0.422912i
$269$		−	2.85728i		−	0.174211i	−0.996199	−	0.0871056i	$-0.972238\pi$
$269$		−	2.85728i		−	0.174211i	0.996199	−	0.0871056i	$-0.0277618\pi$
$270$	−8.29850	−	0.567272i	−0.505030	−	0.0345231i
$271$			23.3292i			1.41715i	0.705637	+	0.708573i	$0.250661\pi$
$271$			23.3292i			1.41715i	−0.705637	+	0.708573i	$0.749339\pi$
$272$	−0.449201	+	22.0117i	−0.0272368	+	1.33466i
$273$	−2.46134	+	2.46134i	−0.148967	+	0.148967i
$274$	11.4946	+	17.3943i	0.694415	+	1.05083i
$275$	27.2538	−	7.43709i	1.64346	−	0.448473i
$276$	1.53471	−	3.60078i	0.0923790	−	0.216741i
$277$	−10.1512	−	10.1512i	−0.609928	−	0.609928i	0.332999	−	0.942927i	$-0.391939\pi$
$277$	−10.1512	−	10.1512i	−0.609928	−	0.609928i	−0.942927	+	0.332999i	$0.891939\pi$
$278$	11.2872	+	2.30509i	0.676963	+	0.138250i
$279$	10.0223			0.600020
$280$	−15.2416	−	7.76436i	−0.910861	−	0.464009i
$281$	−2.12728			−0.126903			−0.0634515	−	0.997985i	$-0.520211\pi$
$281$	−2.12728			−0.126903			−0.0634515	+	0.997985i	$0.520211\pi$
$282$	4.21992	+	0.861795i	0.251293	+	0.0513192i
$283$	−15.7907	−	15.7907i	−0.938660	−	0.938660i	0.0595643	−	0.998224i	$-0.481029\pi$
$283$	−15.7907	−	15.7907i	−0.938660	−	0.938660i	−0.998224	+	0.0595643i	$0.981029\pi$
$284$	−5.67833	+	13.3226i	−0.336947	+	0.790552i
$285$	0.134816	+	1.00615i	0.00798578	+	0.0595991i
$286$	−12.4887	−	18.8986i	−0.738471	−	1.11750i
$287$	−0.106266	+	0.106266i	−0.00627268	+	0.00627268i
$288$	−13.3608	+	8.44262i	−0.787291	+	0.497486i
$289$			13.2949i			0.782051i
$290$	−20.4202	+	17.8071i	−1.19912	+	1.04567i
$291$		−	2.40636i		−	0.141063i
$292$	−8.76624	+	3.52675i	−0.513005	+	0.206388i
$293$	−5.98202	+	5.98202i	−0.349473	+	0.349473i	−0.859913	−	0.510440i	$-0.829482\pi$
$293$	−5.98202	+	5.98202i	−0.349473	+	0.349473i	0.510440	+	0.859913i	$0.329482\pi$
$294$	−0.168627	+	0.111433i	−0.00983451	+	0.00649889i
$295$	14.8343	+	11.3287i	0.863686	+	0.659581i
$296$	−2.78897	−	15.2361i	−0.162106	−	0.885578i
$297$	−10.5087	−	10.5087i	−0.609777	−	0.609777i
$298$	−5.70458	+	27.9334i	−0.330458	+	1.61814i
$299$	12.2213			0.706773
$300$	−3.61713	+	2.74345i	−0.208835	+	0.158393i
$301$	7.56764			0.436191
$302$	1.21475	−	5.94822i	0.0699010	−	0.342282i
$303$	−0.846910	−	0.846910i	−0.0486537	−	0.0486537i
$304$	2.77013	+	2.88555i	0.158878	+	0.165497i
$305$	21.4563	+	16.3858i	1.22859	+	0.938249i
$306$	−18.1438	+	11.9899i	−1.03721	+	0.685416i
$307$	−12.9642	+	12.9642i	−0.739909	+	0.739909i	−0.972560	−	0.232651i	$-0.925260\pi$
$307$	−12.9642	+	12.9642i	−0.739909	+	0.739909i	0.232651	+	0.972560i	$0.425260\pi$
$308$	−11.4070	−	28.3536i	−0.649972	−	1.61560i
$309$			4.24932i			0.241736i
$310$	8.54962	−	7.45553i	0.485586	−	0.423446i
$311$			0.353348i			0.0200365i	0.999950	+	0.0100183i	$0.00318896\pi$
$311$			0.353348i			0.0200365i	−0.999950	+	0.0100183i	$0.996811\pi$
$312$	2.99544	+	2.06849i	0.169584	+	0.117105i
$313$	8.56622	−	8.56622i	0.484191	−	0.484191i	−0.422276	−	0.906467i	$-0.638769\pi$
$313$	8.56622	−	8.56622i	0.484191	−	0.484191i	0.906467	+	0.422276i	$0.138769\pi$
$314$	1.02873	+	1.55674i	0.0580546	+	0.0878517i
$315$	−2.24394	−	16.7469i	−0.126432	−	0.943578i
$316$	−23.9767	−	10.2193i	−1.34880	−	0.574881i
$317$	−3.15859	−	3.15859i	−0.177404	−	0.177404i	0.612819	−	0.790223i	$-0.290035\pi$
$317$	−3.15859	−	3.15859i	−0.177404	−	0.177404i	−0.790223	+	0.612819i	$0.790035\pi$
$318$	7.07415	+	1.44469i	0.396698	+	0.0810140i
$319$	−48.4087			−2.71037
$320$	−5.11711	+	17.1410i	−0.286055	+	0.958213i
$321$	−4.27371			−0.238535
$322$	16.1553	+	3.29926i	0.900302	+	0.183860i
$323$	3.89197	+	3.89197i	0.216555	+	0.216555i
$324$	−13.2241	−	5.63633i	−0.734670	−	0.313129i
$325$	−12.3081	−	7.03084i	−0.682731	−	0.390001i
$326$	−1.61172	−	2.43895i	−0.0892650	−	0.135081i
$327$	−0.194101	+	0.194101i	−0.0107338	+	0.0107338i
$328$	0.129325	+	0.0893050i	0.00714080	+	0.00493104i
$329$			18.1436i			1.00029i
$330$	−8.09247	−	0.553189i	−0.445476	−	0.0304520i
$331$		−	21.2084i		−	1.16572i	−0.812573	−	0.582859i	$-0.801934\pi$
$331$		−	21.2084i		−	1.16572i	0.812573	−	0.582859i	$-0.198066\pi$
$332$	−4.85840	−	12.0762i	−0.266640	−	0.662770i
$333$	10.8188	−	10.8188i	0.592868	−	0.592868i
$334$	14.4782	−	9.56758i	0.792214	−	0.523515i
$335$	20.5552	−	2.75423i	1.12305	−	0.150480i
$336$	3.40128	+	3.54300i	0.185555	+	0.193286i
$337$	1.23960	+	1.23960i	0.0675252	+	0.0675252i	0.740063	−	0.672538i	$-0.234796\pi$
$337$	1.23960	+	1.23960i	0.0675252	+	0.0675252i	−0.672538	+	0.740063i	$0.734796\pi$
$338$	1.40442	−	6.87697i	0.0763904	−	0.374058i
$339$	2.28217			0.123950
$340$	−6.55854	+	23.7252i	−0.355687	+	1.28668i
$341$	20.2679			1.09757
$342$	−0.790593	+	3.87127i	−0.0427504	+	0.209334i
$343$	12.7850	+	12.7850i	0.690324	+	0.690324i
$344$	−1.42501	−	7.78479i	−0.0768314	−	0.419728i
$345$	2.65608	−	3.47799i	0.142998	−	0.187249i
$346$	−10.7760	+	7.12106i	−0.579322	+	0.382830i
$347$	12.6644	−	12.6644i	0.679859	−	0.679859i	−0.280109	−	0.959968i	$-0.590371\pi$
$347$	12.6644	−	12.6644i	0.679859	−	0.679859i	0.959968	+	0.280109i	$0.0903706\pi$
$348$	7.21715	−	2.90354i	0.386880	−	0.155646i
$349$			16.0318i			0.858164i	0.903266	+	0.429082i	$0.141163\pi$
$349$			16.0318i			0.858164i	−0.903266	+	0.429082i	$0.858837\pi$
$350$	−14.3721	−	12.6168i	−0.768221	−	0.674396i
$351$			7.45685i			0.398017i
$352$	−27.0193	+	17.0734i	−1.44013	+	0.910013i
$353$	−25.1710	+	25.1710i	−1.33972	+	1.33972i	−0.443387	+	0.896330i	$0.646223\pi$
$353$	−25.1710	+	25.1710i	−1.33972	+	1.33972i	−0.896330	+	0.443387i	$0.853777\pi$
$354$	−2.95469	−	4.47121i	−0.157040	−	0.237642i
$355$	−9.82730	+	12.8683i	−0.521579	+	0.682980i
$356$	−3.31357	+	7.77438i	−0.175619	+	0.412041i
$357$	4.77872	+	4.77872i	0.252917	+	0.252917i
$358$	32.2023	+	6.57637i	1.70194	+	0.347572i
$359$	−0.347833			−0.0183579			−0.00917897	−	0.999958i	$-0.502922\pi$
$359$	−0.347833			−0.0183579			−0.00917897	+	0.999958i	$0.502922\pi$
$360$	−16.8049	+	5.46181i	−0.885694	+	0.287863i
$361$	1.00000			0.0526316
$362$	−9.92784	−	2.02747i	−0.521796	−	0.106562i
$363$	−6.71665	−	6.71665i	−0.352533	−	0.352533i
$364$	−6.01257	+	14.1068i	−0.315144	+	0.739398i
$365$	−10.4708	+	1.40300i	−0.548067	+	0.0734365i
$366$	−4.27367	−	6.46717i	−0.223388	−	0.338044i
$367$	−4.99380	+	4.99380i	−0.260674	+	0.260674i	−0.825328	−	0.564654i	$-0.809010\pi$
$367$	−4.99380	+	4.99380i	−0.260674	+	0.260674i	0.564654	+	0.825328i	$0.309010\pi$
$368$	0.351826	−	17.2402i	0.0183402	−	0.898706i
$369$			0.155245i			0.00808174i
$370$	1.18104	−	17.2771i	0.0613993	−	0.898196i
$371$			30.4153i			1.57908i
$372$	−3.02171	+	1.21566i	−0.156668	+	0.0630293i
$373$	14.4139	−	14.4139i	0.746325	−	0.746325i	−0.227462	−	0.973787i	$-0.573043\pi$
$373$	14.4139	−	14.4139i	0.746325	−	0.746325i	0.973787	+	0.227462i	$0.0730428\pi$
$374$	−36.6920	+	24.2470i	−1.89730	+	1.25378i
$375$	−4.67583	+	1.97468i	−0.241459	+	0.101972i
$376$	18.6642	−	3.41649i	0.962532	−	0.176192i
$377$	17.1751	+	17.1751i	0.884563	+	0.884563i
$378$	−2.01305	+	9.85725i	−0.103540	+	0.507002i
$379$	20.2693			1.04117			0.520583	−	0.853811i	$-0.325715\pi$
$379$	20.2693			1.04117			0.520583	+	0.853811i	$0.325715\pi$
$380$	2.20539	+	3.89054i	0.113134	+	0.199580i
$381$	−5.43822			−0.278608
$382$	5.60078	−	27.4251i	0.286561	−	1.40319i
$383$	21.4388	+	21.4388i	1.09547	+	1.09547i	0.994933	+	0.100539i	$0.0320567\pi$
$383$	21.4388	+	21.4388i	1.09547	+	1.09547i	0.100539	+	0.994933i	$0.467943\pi$
$384$	3.00419	−	4.16604i	0.153307	−	0.212597i
$385$	−4.53788	−	33.8669i	−0.231272	−	1.72602i
$386$	−7.96790	+	5.26539i	−0.405556	+	0.268001i
$387$	5.52783	−	5.52783i	0.280995	−	0.280995i
$388$	−3.95672	−	9.83497i	−0.200872	−	0.499295i
$389$			0.701293i			0.0355570i	0.999842	+	0.0177785i	$0.00565937\pi$
$389$			0.701293i			0.0355570i	−0.999842	+	0.0177785i	$0.994341\pi$
$390$	2.67489	+	3.06743i	0.135448	+	0.155325i
$391$		−	23.7278i		−	1.19996i
$392$	−0.505965	+	0.732704i	−0.0255551	+	0.0370071i
$393$	−0.0316895	+	0.0316895i	−0.00159852	+	0.00159852i
$394$	−13.7974	−	20.8790i	−0.695103	−	1.05187i
$395$	−23.1592	−	17.6862i	−1.16526	−	0.889890i
$396$	−29.0434	−	12.3788i	−1.45948	−	0.622057i
$397$	5.76351	+	5.76351i	0.289262	+	0.289262i	0.836789	−	0.547526i	$-0.184430\pi$
$397$	5.76351	+	5.76351i	0.289262	+	0.289262i	−0.547526	+	0.836789i	$0.684430\pi$
$398$	22.0049	+	4.49386i	1.10301	+	0.225257i
$399$	1.22784			0.0614690
$400$	−10.2725	+	17.1603i	−0.513626	+	0.858014i
$401$	−9.38653			−0.468741			−0.234370	−	0.972147i	$-0.575303\pi$
$401$	−9.38653			−0.468741			−0.234370	+	0.972147i	$0.575303\pi$
$402$	−5.83424	−	1.19147i	−0.290986	−	0.0594253i
$403$	−7.19094	−	7.19094i	−0.358206	−	0.358206i
$404$	−4.85394	−	2.06884i	−0.241493	−	0.102928i
$405$	−12.7731	−	9.75460i	−0.634702	−	0.484710i
$406$	18.0673	+	27.3405i	0.896663	+	1.35688i
$407$	21.8787	−	21.8787i	1.08449	−	1.08449i
$408$	4.01600	−	5.81570i	0.198822	−	0.287920i
$409$		−	35.3014i		−	1.74554i	−0.488128	−	0.872772i	$-0.662320\pi$
$409$		−	35.3014i		−	1.74554i	0.488128	−	0.872772i	$-0.337680\pi$
$410$	0.115486	+	0.132433i	0.00570344	+	0.00654041i
$411$		−	6.69292i		−	0.330137i
$412$	6.98707	+	17.3673i	0.344228	+	0.855627i
$413$	15.9639	−	15.9639i	0.785530	−	0.785530i
$414$	14.2107	−	9.39080i	0.698419	−	0.461533i
$415$	−1.93275	−	14.4244i	−0.0948752	−	0.708067i
$416$	15.6438	+	3.52874i	0.767000	+	0.173011i
$417$	−2.61499	−	2.61499i	−0.128057	−	0.128057i
$418$	−1.59880	+	7.82880i	−0.0782000	+	0.382919i
$419$	20.7626			1.01432			0.507160	−	0.861852i	$-0.330695\pi$
$419$	20.7626			1.01432			0.507160	+	0.861852i	$0.330695\pi$
$420$	2.70787	+	4.77696i	0.132130	+	0.233092i
$421$	−7.87092			−0.383605			−0.191803	−	0.981434i	$-0.561433\pi$
$421$	−7.87092			−0.383605			−0.191803	+	0.981434i	$0.561433\pi$
$422$	−3.05225	+	14.9458i	−0.148581	+	0.727552i
$423$	13.2531	+	13.2531i	0.644386	+	0.644386i
$424$	31.2881	−	5.72730i	1.51948	−	0.278142i
$425$	−13.6505	+	23.8964i	−0.662145	+	1.15914i
$426$	3.87865	−	2.56311i	0.187921	−	0.124183i
$427$	23.0901	−	23.0901i	1.11741	−	1.11741i
$428$	−17.4670	+	7.02716i	−0.844299	+	0.339671i
$429$			7.27172i			0.351082i
$430$	0.603446	−	8.82768i	0.0291008	−	0.425708i
$431$		−	22.8584i		−	1.10105i	−0.834819	−	0.550525i	$-0.814428\pi$
$431$		−	22.8584i		−	1.10105i	0.834819	−	0.550525i	$-0.185572\pi$
$432$	10.5192	+	0.214668i	0.506104	+	0.0103282i
$433$	−0.545440	+	0.545440i	−0.0262122	+	0.0262122i	−0.720091	−	0.693879i	$-0.755900\pi$
$433$	−0.545440	+	0.545440i	−0.0262122	+	0.0262122i	0.693879	+	0.720091i	$0.255900\pi$
$434$	−7.56447	−	11.4470i	−0.363106	−	0.549474i
$435$	8.62050	−	1.15508i	0.413321	−	0.0553817i
$436$	−0.474152	+	1.11246i	−0.0227077	+	0.0532774i
$437$	−3.04830	−	3.04830i	−0.145820	−	0.145820i
$438$	2.97196	+	0.606935i	0.142006	+	0.0290005i
$439$	3.55487			0.169665			0.0848324	−	0.996395i	$-0.472965\pi$
$439$	3.55487			0.169665			0.0848324	+	0.996395i	$0.472965\pi$
$440$	−33.9842	+	11.0453i	−1.62013	+	0.526566i
$441$	−0.879554			−0.0418835
$442$	21.6207	+	4.41541i	1.02839	+	0.210019i
$443$	−12.5438	−	12.5438i	−0.595974	−	0.595974i	0.343264	−	0.939239i	$-0.388467\pi$
$443$	−12.5438	−	12.5438i	−0.595974	−	0.595974i	−0.939239	+	0.343264i	$0.888467\pi$
$444$	−1.94958	+	4.57413i	−0.0925227	+	0.217079i
$445$	−5.73469	+	7.50927i	−0.271850	+	0.355974i
$446$	16.4140	+	24.8386i	0.777225	+	1.17614i
$447$	6.47154	−	6.47154i	0.306093	−	0.306093i
$448$	19.7270	+	8.88786i	0.932012	+	0.419912i
$449$			32.9577i			1.55537i	0.628655	+	0.777685i	$0.283606\pi$
$449$			32.9577i			1.55537i	−0.628655	+	0.777685i	$0.716394\pi$
$450$	−19.7142	+	1.28216i	−0.929336	+	0.0604418i
$451$			0.313950i			0.0147833i
$452$	9.32741	−	3.75252i	0.438724	−	0.176504i
$453$	−1.37807	+	1.37807i	−0.0647473	+	0.0647473i
$454$	−28.2810	+	18.6888i	−1.32729	+	0.877108i
$455$	−10.4057	+	13.6258i	−0.487829	+	0.638786i
$456$	−0.231207	−	1.26307i	−0.0108272	−	0.0591489i
$457$	0.759073	+	0.759073i	0.0355079	+	0.0355079i	0.724638	−	0.689130i	$-0.242007\pi$
$457$	0.759073	+	0.759073i	0.0355079	+	0.0355079i	−0.689130	+	0.724638i	$0.742007\pi$
$458$	3.45816	−	16.9335i	0.161589	−	0.791249i
$459$	14.4776			0.675756
$460$	5.13683	−	18.5822i	0.239506	−	0.866398i
$461$	34.3719			1.60086			0.800429	−	0.599427i	$-0.204605\pi$
$461$	34.3719			1.60086			0.800429	+	0.599427i	$0.204605\pi$
$462$	−1.96308	+	9.61253i	−0.0913306	+	0.447215i
$463$	−7.60575	−	7.60575i	−0.353469	−	0.353469i	0.507930	−	0.861399i	$-0.330411\pi$
$463$	−7.60575	−	7.60575i	−0.353469	−	0.353469i	−0.861399	+	0.507930i	$0.830411\pi$
$464$	24.7229	−	23.7340i	1.14773	−	1.10182i
$465$	−3.60927	+	0.483612i	−0.167376	+	0.0224270i
$466$	−22.3384	+	14.7617i	−1.03480	+	0.683825i
$467$	−18.0342	+	18.0342i	−0.834521	+	0.834521i	−0.988131	−	0.153611i	$-0.950910\pi$
$467$	−18.0342	+	18.0342i	−0.834521	+	0.834521i	0.153611	+	0.988131i	$0.450910\pi$
$468$	5.91249	+	14.6963i	0.273305	+	0.679338i
$469$		−	25.0844i		−	1.15829i
$470$	21.1645	+	1.44677i	0.976247	+	0.0667347i
$471$		−	0.598994i		−	0.0276002i
$472$	−19.4280	−	13.4159i	−0.894245	−	0.617516i
$473$	11.1788	−	11.1788i	0.514003	−	0.514003i
$474$	4.61283	+	6.98041i	0.211874	+	0.320621i
$475$	1.31629	+	4.82363i	0.0603953	+	0.221323i
$476$	27.3886	+	11.6735i	1.25535	+	0.535054i
$477$	22.2170	+	22.2170i	1.01725	+	1.01725i
$478$	−34.7669	−	7.10012i	−1.59020	−	0.324752i
$479$	−12.8104			−0.585323			−0.292662	−	0.956216i	$-0.594541\pi$
$479$	−12.8104			−0.585323			−0.292662	+	0.956216i	$0.594541\pi$
$480$	4.40414	−	3.68509i	0.201020	−	0.168200i
$481$	−15.5249			−0.707873
$482$	−28.0226	−	5.72279i	−1.27639	−	0.260666i
$483$	−3.74283	−	3.74283i	−0.170304	−	0.170304i
$484$	−38.4955	−	16.4075i	−1.74980	−	0.745794i
$485$	−1.57405	−	11.7473i	−0.0714738	−	0.533420i
$486$	8.69667	+	13.1603i	0.394489	+	0.596964i
$487$	11.2221	−	11.2221i	0.508520	−	0.508520i	−0.405552	−	0.914072i	$-0.632921\pi$
$487$	11.2221	−	11.2221i	0.508520	−	0.508520i	0.914072	+	0.405552i	$0.132921\pi$
$488$	−28.1006	−	19.4048i	−1.27206	−	0.878412i
$489$			0.938449i			0.0424382i
$490$	−0.750312	+	0.654295i	−0.0338956	+	0.0295580i
$491$			30.6682i			1.38403i	0.721881	+	0.692017i	$0.243278\pi$
$491$			30.6682i			1.38403i	−0.721881	+	0.692017i	$0.756722\pi$
$492$	−0.0188306	−	0.0468061i	−0.000848949	−	0.00211018i
$493$	33.3457	−	33.3457i	1.50182	−	1.50182i
$494$	3.34485	−	2.21036i	0.150492	−	0.0994490i
$495$	−28.0530	−	21.4235i	−1.26089	−	0.962917i
$496$	−10.3511	+	9.93704i	−0.464777	+	0.446186i
$497$	13.8482	+	13.8482i	0.621176	+	0.621176i
$498$	−0.836105	+	4.09412i	−0.0374668	+	0.183462i
$499$	23.9769			1.07335			0.536676	−	0.843788i	$-0.319680\pi$
$499$	23.9769			1.07335			0.536676	+	0.843788i	$0.319680\pi$
$500$	−15.8636	+	15.7590i	−0.709441	+	0.704765i
$501$	−5.57087			−0.248888
$502$	4.00357	−	19.6041i	0.178688	−	0.874974i
$503$	−0.229488	−	0.229488i	−0.0102324	−	0.0102324i	0.701972	−	0.712204i	$-0.252303\pi$
$503$	−0.229488	−	0.229488i	−0.0102324	−	0.0102324i	−0.712204	+	0.701972i	$0.752303\pi$
$504$	3.84832	+	21.0233i	0.171418	+	0.936451i
$505$	−4.68843	−	3.58046i	−0.208632	−	0.159329i
$506$	28.7381	−	18.9909i	1.27757	−	0.844247i
$507$	−1.59324	+	1.59324i	−0.0707582	+	0.0707582i
$508$	−22.2264	+	8.94194i	−0.986139	+	0.396734i
$509$			40.6326i			1.80101i	0.434846	+	0.900505i	$0.356803\pi$
$509$			40.6326i			1.80101i	−0.434846	+	0.900505i	$0.643197\pi$
$510$	5.95546	−	5.19334i	0.263712	−	0.229965i
$511$			12.7779i			0.565263i
$512$	5.42825	−	21.9667i	0.239897	−	0.970798i
$513$	1.85993	−	1.85993i	0.0821179	−	0.0821179i
$514$	−1.94685	−	2.94610i	−0.0858721	−	0.129947i
$515$	2.77957	+	20.7444i	0.122483	+	0.914106i
$516$	−0.996126	+	2.33713i	−0.0438520	+	0.102886i
$517$	26.8015	+	26.8015i	1.17873	+	1.17873i
$518$	−20.5224	−	4.19110i	−0.901703	−	0.184146i
$519$	4.14634			0.182004
$520$	15.9762	+	8.13856i	0.700603	+	0.356900i
$521$	0.640624			0.0280662			0.0140331	−	0.999902i	$-0.495533\pi$
$521$	0.640624			0.0280662			0.0140331	+	0.999902i	$0.495533\pi$
$522$	33.1683	+	6.77366i	1.45174	+	0.296475i
$523$	−12.4974	−	12.4974i	−0.546474	−	0.546474i	0.378945	−	0.925419i	$-0.376287\pi$
$523$	−12.4974	−	12.4974i	−0.546474	−	0.546474i	−0.925419	+	0.378945i	$0.876287\pi$
$524$	−0.0774112	+	0.181624i	−0.00338172	+	0.00793427i
$525$	1.61619	+	5.92265i	0.0705363	+	0.258486i
$526$	−2.12240	−	3.21175i	−0.0925412	−	0.140039i
$527$	−13.9613	+	13.9613i	−0.608165	+	0.608165i
$528$	10.2580	+	0.209339i	0.446423	+	0.00911030i
$529$		−	4.41579i		−	0.191991i
$530$	35.4796	+	2.42533i	1.54113	+	0.105350i
$531$		−	23.3218i		−	1.01208i
$532$	5.01829	−	2.01891i	0.217571	−	0.0875310i
$533$	0.111387	−	0.111387i	0.00482472	−	0.00482472i
$534$	2.26337	−	1.49569i	0.0979458	−	0.0647250i
$535$	−20.8634	+	2.79552i	−0.902003	+	0.120861i
$536$	−25.8041	+	4.72346i	−1.11457	+	0.204023i
$537$	−7.46053	−	7.46053i	−0.321946	−	0.321946i
$538$	−0.808527	+	3.95908i	−0.0348581	+	0.170688i
$539$	−1.77871			−0.0766144
$540$	11.3380	+	3.13426i	0.487910	+	0.134877i
$541$	17.4549			0.750445			0.375223	−	0.926935i	$-0.377566\pi$
$541$	17.4549			0.750445			0.375223	+	0.926935i	$0.377566\pi$
$542$	6.60149	−	32.3253i	0.283558	−	1.38849i
$543$	2.30006	+	2.30006i	0.0987048	+	0.0987048i
$544$	6.85110	−	30.3727i	0.293739	−	1.30222i
$545$	−0.820598	+	1.07453i	−0.0351506	+	0.0460278i
$546$	4.10695	−	2.71398i	0.175761	−	0.116148i
$547$	14.4169	−	14.4169i	0.616423	−	0.616423i	−0.328189	−	0.944612i	$-0.606438\pi$
$547$	14.4169	−	14.4169i	0.616423	−	0.616423i	0.944612	+	0.328189i	$0.106438\pi$
$548$	−11.0050	−	27.3545i	−0.470111	−	1.16853i
$549$		−	33.7327i		−	1.43967i
$550$	−39.8677	+	2.59290i	−1.69996	+	0.110562i
$551$		−	8.56783i		−	0.365002i
$552$	−3.14544	+	4.55501i	−0.133879	+	0.193874i
$553$	−24.9226	+	24.9226i	−1.05982	+	1.05982i
$554$	11.1932	+	16.9382i	0.475552	+	0.719634i
$555$	−3.37406	+	4.41816i	−0.143221	+	0.187540i
$556$	−14.9875	−	6.38792i	−0.635610	−	0.270908i
$557$	−12.4086	−	12.4086i	−0.525768	−	0.525768i	0.393539	−	0.919308i	$-0.371250\pi$
$557$	−12.4086	−	12.4086i	−0.525768	−	0.525768i	−0.919308	+	0.393539i	$0.871250\pi$
$558$	−13.8870	−	2.83602i	−0.587886	−	0.120058i
$559$	−7.93236			−0.335503
$560$	18.9219	+	15.0714i	0.799597	+	0.636881i
$561$	14.1182			0.596069
$562$	2.94759	+	0.601959i	0.124337	+	0.0253921i
$563$	−11.6114	−	11.6114i	−0.489364	−	0.489364i	0.418742	−	0.908105i	$-0.362471\pi$
$563$	−11.6114	−	11.6114i	−0.489364	−	0.489364i	−0.908105	+	0.418742i	$0.862471\pi$
$564$	−5.60332	−	2.38823i	−0.235942	−	0.100563i
$565$	11.1411	−	1.49281i	0.468709	−	0.0628032i
$566$	17.4115	+	26.3481i	0.731861	+	1.10750i
$567$	−13.7457	+	13.7457i	−0.577267	+	0.577267i
$568$	11.6379	−	16.8532i	0.488315	−	0.707145i
$569$			14.6399i			0.613737i	0.951752	+	0.306869i	$0.0992813\pi$
$569$			14.6399i			0.613737i	−0.951752	+	0.306869i	$0.900719\pi$
$570$	0.0979086	−	1.43228i	0.00410094	−	0.0599917i
$571$		−	23.5114i		−	0.983922i	−0.870617	−	0.491961i	$-0.836280\pi$
$571$		−	23.5114i		−	0.983922i	0.870617	−	0.491961i	$-0.163720\pi$
$572$	11.9567	+	29.7201i	0.499936	+	1.24266i
$573$	−6.35378	+	6.35378i	−0.265433	+	0.265433i
$574$	0.177314	−	0.117173i	0.00740093	−	0.00489072i
$575$	10.6914	−	18.7163i	0.445863	−	0.780522i
$576$	20.9019	−	7.91750i	0.870912	−	0.329896i
$577$	7.05916	+	7.05916i	0.293877	+	0.293877i	0.838610	−	0.544733i	$-0.183369\pi$
$577$	7.05916	+	7.05916i	0.293877	+	0.293877i	−0.544733	+	0.838610i	$0.683369\pi$
$578$	3.76207	−	18.4216i	0.156481	−	0.766236i
$579$	3.06585			0.127413
$580$	33.3334	−	18.8954i	1.38410	−	0.784588i
$581$	−17.6027			−0.730283
$582$	−0.680929	+	3.33428i	−0.0282254	+	0.138210i
$583$	44.9292	+	44.9292i	1.86078	+	1.86078i
$584$	13.1446	−	2.40613i	0.543927	−	0.0995662i
$585$	2.35209	+	17.5540i	0.0972468	+	0.725767i
$586$	9.98151	−	6.59603i	0.412332	−	0.272479i
$587$	−33.5755	+	33.5755i	−1.38581	+	1.38581i	−0.551899	+	0.833911i	$0.686097\pi$
$587$	−33.5755	+	33.5755i	−1.38581	+	1.38581i	−0.833911	+	0.551899i	$0.813903\pi$
$588$	0.265184	−	0.106686i	0.0109360	−	0.00439967i
$589$			3.58721i			0.147808i
$590$	−17.3489	−	19.8949i	−0.714244	−	0.819058i
$591$			8.03374i			0.330464i
$592$	−0.446931	+	21.9005i	−0.0183688	+	0.900105i
$593$	7.65769	−	7.65769i	0.314464	−	0.314464i	−0.532172	−	0.846636i	$-0.678624\pi$
$593$	7.65769	−	7.65769i	0.314464	−	0.314464i	0.846636	+	0.532172i	$0.178624\pi$
$594$	11.5874	+	17.5347i	0.475435	+	0.719457i
$595$	26.4546	+	20.2029i	1.08453	+	0.828239i
$596$	15.8087	−	37.0907i	0.647550	−	1.51929i
$597$	−5.09804	−	5.09804i	−0.208649	−	0.208649i
$598$	−16.9339	−	3.45826i	−0.692481	−	0.141419i
$599$	11.2535			0.459804			0.229902	−	0.973214i	$-0.426159\pi$
$599$	11.2535			0.459804			0.229902	+	0.973214i	$0.426159\pi$
$600$	5.78827	−	2.77782i	0.236305	−	0.113404i
$601$	28.4675			1.16121			0.580606	−	0.814185i	$-0.302816\pi$
$601$	28.4675			1.16121			0.580606	+	0.814185i	$0.302816\pi$
$602$	−10.4858	−	2.14142i	−0.427371	−	0.0872779i
$603$	−18.3230	−	18.3230i	−0.746171	−	0.746171i
$604$	−3.36635	+	7.89820i	−0.136975	+	0.321373i
$605$	−37.1828	−	28.3958i	−1.51170	−	1.15446i
$606$	0.933839	+	1.41314i	0.0379346	+	0.0574049i
$607$	−21.9473	+	21.9473i	−0.890812	+	0.890812i	−0.994599	−	0.103788i	$-0.966904\pi$
$607$	−21.9473	+	21.9473i	−0.890812	+	0.890812i	0.103788	+	0.994599i	$0.466904\pi$
$608$	−3.02180	−	4.78212i	−0.122550	−	0.193941i
$609$		−	10.5199i		−	0.426289i
$610$	−25.0935	−	28.7759i	−1.01601	−	1.16510i
$611$		−	19.0180i		−	0.769386i
$612$	28.5331	−	11.4792i	1.15338	−	0.464018i
$613$	9.00839	−	9.00839i	0.363845	−	0.363845i	−0.501381	−	0.865226i	$-0.667175\pi$
$613$	9.00839	−	9.00839i	0.363845	−	0.363845i	0.865226	+	0.501381i	$0.167175\pi$
$614$	21.6320	−	14.2949i	0.872995	−	0.576897i
$615$	−0.00749113	−	0.0559074i	−0.000302071	−	0.00225440i
$616$	7.78240	+	42.5150i	0.313562	+	1.71298i
$617$	−3.55609	−	3.55609i	−0.143163	−	0.143163i	0.631893	−	0.775056i	$-0.282278\pi$
$617$	−3.55609	−	3.55609i	−0.143163	−	0.143163i	−0.775056	+	0.631893i	$0.782278\pi$
$618$	1.20244	−	5.88793i	0.0483691	−	0.236847i
$619$	−39.9486			−1.60567			−0.802834	−	0.596202i	$-0.796676\pi$
$619$	−39.9486			−1.60567			−0.802834	+	0.596202i	$0.796676\pi$
$620$	−13.9562	+	7.91119i	−0.560493	+	0.317721i
$621$	−11.3392			−0.455028
$622$	0.0999872	−	0.489604i	0.00400912	−	0.0196313i
$623$	8.08107	+	8.08107i	0.323761	+	0.323761i
$624$	−3.56521	−	3.71375i	−0.142722	−	0.148669i
$625$	−21.5348	+	12.6985i	−0.861391	+	0.507942i
$626$	−14.2935	+	9.44548i	−0.571282	+	0.377517i
$627$	1.81376	−	1.81376i	0.0724344	−	0.0724344i
$628$	−0.984912	−	2.44814i	−0.0393023	−	0.0976913i
$629$			30.1418i			1.20183i
$630$	−1.62964	+	23.8396i	−0.0649265	+	0.949794i
$631$		−	10.1547i		−	0.404254i	−0.979359	−	0.202127i	$-0.935215\pi$
$631$		−	10.1547i		−	0.404254i	0.979359	−	0.202127i	$-0.0647854\pi$
$632$	30.3308	+	20.9447i	1.20649	+	0.833137i
$633$	3.46261	−	3.46261i	0.137626	−	0.137626i
$634$	3.48280	+	5.27038i	0.138320	+	0.209314i
$635$	−26.5483	+	3.55725i	−1.05354	+	0.141165i
$636$	−9.39323	−	4.00356i	−0.372466	−	0.158751i
$637$	0.631075	+	0.631075i	0.0250041	+	0.0250041i
$638$	67.0758	+	13.6983i	2.65556	+	0.542320i
$639$	20.2310			0.800325
$640$	11.9408	−	22.3029i	0.472000	−	0.881599i
$641$	−20.4445			−0.807510			−0.403755	−	0.914867i	$-0.632295\pi$
$641$	−20.4445			−0.807510			−0.403755	+	0.914867i	$0.632295\pi$
$642$	5.92171	+	1.20934i	0.233711	+	0.0477287i
$643$	17.7673	+	17.7673i	0.700672	+	0.700672i	0.964555	−	0.263883i	$-0.0850032\pi$
$643$	17.7673	+	17.7673i	0.700672	+	0.700672i	−0.263883	+	0.964555i	$0.585003\pi$
$644$	−21.4515	−	9.14299i	−0.845307	−	0.360284i
$645$	−1.72396	+	2.25744i	−0.0678809	+	0.0888865i
$646$	−4.29145	−	6.49409i	−0.168845	−	0.255506i
$647$	3.58437	−	3.58437i	0.140916	−	0.140916i	−0.633130	−	0.774046i	$-0.718230\pi$
$647$	3.58437	−	3.58437i	0.140916	−	0.140916i	0.774046	+	0.633130i	$0.218230\pi$
$648$	16.7285	+	11.5518i	0.657159	+	0.453798i
$649$		−	47.1633i		−	1.85132i
$650$	15.0648	+	13.2249i	0.590888	+	0.518722i
$651$			4.40453i			0.172627i
$652$	1.54307	+	3.83552i	0.0604313	+	0.150211i
$653$	−17.1613	+	17.1613i	−0.671572	+	0.671572i	−0.958078	−	0.286506i	$-0.907506\pi$
$653$	−17.1613	+	17.1613i	−0.671572	+	0.671572i	0.286506	+	0.958078i	$0.407506\pi$
$654$	0.323875	−	0.214025i	0.0126645	−	0.00836902i
$655$	−0.133973	+	0.175430i	−0.00523475	+	0.00685463i
$656$	−0.153924	−	0.160338i	−0.00600974	−	0.00626013i
$657$	9.33372	+	9.33372i	0.364143	+	0.364143i
$658$	5.13410	−	25.1400i	0.200148	−	0.980058i
$659$	−3.92382			−0.152851			−0.0764253	−	0.997075i	$-0.524351\pi$
$659$	−3.92382			−0.152851			−0.0764253	+	0.997075i	$0.524351\pi$
$660$	11.0565	+	3.05644i	0.430374	+	0.118972i
$661$	−7.98789			−0.310693			−0.155347	−	0.987860i	$-0.549649\pi$
$661$	−7.98789			−0.310693			−0.155347	+	0.987860i	$0.549649\pi$
$662$	−6.00136	+	29.3866i	−0.233249	+	1.14214i
$663$	−5.00904	−	5.00904i	−0.194535	−	0.194535i
$664$	3.31464	+	18.1078i	0.128633	+	0.702719i
$665$	5.99408	−	0.803157i	0.232440	−	0.0311451i
$666$	−18.0521	+	11.9293i	−0.699506	+	0.462251i
$667$	−26.1173	+	26.1173i	−1.01126	+	1.01126i
$668$	−22.7686	+	9.16005i	−0.880943	+	0.354413i
$669$		−	9.55730i		−	0.369507i
$670$	−29.2610	−	2.00024i	−1.13045	−	0.0772758i
$671$		−	68.2170i		−	2.63349i
$672$	−3.71030	−	5.87169i	−0.143128	−	0.226505i
$673$	−17.1641	+	17.1641i	−0.661626	+	0.661626i	−0.955763	−	0.294137i	$-0.904968\pi$
$673$	−17.1641	+	17.1641i	−0.661626	+	0.661626i	0.294137	+	0.955763i	$0.404968\pi$
$674$	−1.36683	−	2.06838i	−0.0526485	−	0.0796709i
$675$	11.4198	+	6.52342i	0.439549	+	0.251086i
$676$	−3.89197	+	9.13142i	−0.149691	+	0.351208i
$677$	−17.0473	−	17.0473i	−0.655180	−	0.655180i	0.299055	−	0.954236i	$-0.403328\pi$
$677$	−17.0473	−	17.0473i	−0.655180	−	0.655180i	−0.954236	+	0.299055i	$0.903328\pi$
$678$	−3.16221	−	0.645788i	−0.121444	−	0.0248013i
$679$	−14.3358			−0.550156
$680$	15.8011	−	31.0180i	0.605946	−	1.18949i
$681$	10.8818			0.416993
$682$	−28.0836	−	5.73525i	−1.07537	−	0.219614i
$683$	19.4927	+	19.4927i	0.745869	+	0.745869i	0.973701	−	0.227832i	$-0.0731636\pi$
$683$	19.4927	+	19.4927i	0.745869	+	0.745869i	−0.227832	+	0.973701i	$0.573164\pi$
$684$	2.19091	−	5.14037i	0.0837717	−	0.196547i
$685$	−4.37798	−	32.6735i	−0.167274	−	1.24839i
$686$	−14.0973	−	21.3328i	−0.538236	−	0.814492i
$687$	−3.92310	+	3.92310i	−0.149676	+	0.149676i
$688$	−0.228357	+	11.1900i	−0.00870604	+	0.426613i
$689$		−	31.8812i		−	1.21458i
$690$	−4.66447	+	4.06756i	−0.177573	+	0.154850i
$691$		−	10.0408i		−	0.381969i	−0.981593	−	0.190985i	$-0.938832\pi$
$691$		−	10.0408i		−	0.381969i	0.981593	−	0.190985i	$-0.0611681\pi$
$692$	16.9464	−	6.81774i	0.644207	−	0.259171i
$693$	−30.1891	+	30.1891i	−1.14679	+	1.14679i
$694$	−21.1316	+	13.9643i	−0.802144	+	0.530077i
$695$	−14.4764	−	11.0554i	−0.549121	−	0.419354i
$696$	−10.8218	+	1.98094i	−0.410199	+	0.0750872i
$697$	−0.216260	−	0.216260i	−0.00819144	−	0.00819144i
$698$	4.53655	−	22.2139i	0.171711	−	0.840810i
$699$	8.59525			0.325102
$700$	16.3440	+	21.5489i	0.617745	+	0.814472i
$701$	5.87705			0.221973			0.110987	−	0.993822i	$-0.464599\pi$
$701$	5.87705			0.221973			0.110987	+	0.993822i	$0.464599\pi$
$702$	2.11007	−	10.3323i	0.0796396	−	0.389968i
$703$	3.87230	+	3.87230i	0.146047	+	0.146047i
$704$	42.2695	−	16.0114i	1.59309	−	0.603453i
$705$	−5.41225	−	4.13323i	−0.203837	−	0.155667i
$706$	42.0000	−	27.7546i	1.58069	−	1.04456i
$707$	−5.04543	+	5.04543i	−0.189753	+	0.189753i
$708$	2.82884	+	7.03147i	0.106314	+	0.264259i
$709$			3.43572i			0.129031i	0.997917	+	0.0645156i	$0.0205502\pi$
$709$			3.43572i			0.129031i	−0.997917	+	0.0645156i	$0.979450\pi$
$710$	17.2582	−	15.0497i	0.647689	−	0.564805i
$711$			36.4097i			1.36547i
$712$	6.79126	−	9.83464i	0.254513	−	0.368569i
$713$	10.9349	−	10.9349i	0.409514	−	0.409514i
$714$	−5.26923	−	7.97371i	−0.197196	−	0.298409i
$715$	4.75659	+	35.4991i	0.177886	+	1.32759i
$716$	−42.7590	−	18.2246i	−1.59798	−	0.681086i
$717$	8.05469	+	8.05469i	0.300808	+	0.300808i
$718$	0.481963	+	0.0984269i	0.0179867	+	0.00367326i
$719$	−0.800777			−0.0298640			−0.0149320	−	0.999889i	$-0.504753\pi$
$719$	−0.800777			−0.0298640			−0.0149320	+	0.999889i	$0.504753\pi$
$720$	24.8306	−	2.81268i	0.925381	−	0.104822i
$721$	25.3152			0.942786
$722$	−1.38561	−	0.282971i	−0.0515672	−	0.0105311i
$723$	6.49220	+	6.49220i	0.241447	+	0.241447i
$724$	13.1824	+	5.61859i	0.489922	+	0.208813i
$725$	41.3280	−	11.2777i	1.53488	−	0.418843i
$726$	7.40607	+	11.2073i	0.274865	+	0.415942i
$727$	15.8191	−	15.8191i	0.586696	−	0.586696i	−0.350039	−	0.936735i	$-0.613832\pi$
$727$	15.8191	−	15.8191i	0.586696	−	0.586696i	0.936735	+	0.350039i	$0.113832\pi$
$728$	12.3229	−	17.8452i	0.456718	−	0.661388i
$729$			16.4989i			0.611071i
$730$	14.9055	+	1.01892i	0.551678	+	0.0377118i
$731$			15.4008i			0.569619i
$732$	4.09163	+	10.1703i	0.151231	+	0.375906i
$733$	−29.5915	+	29.5915i	−1.09299	+	1.09299i	−0.0977792	+	0.995208i	$0.531174\pi$
$733$	−29.5915	+	29.5915i	−1.09299	+	1.09299i	−0.995208	+	0.0977792i	$0.968826\pi$
$734$	8.33258	−	5.50638i	0.307561	−	0.203244i
$735$	0.316748	−	0.0424416i	0.0116834	−	0.00156548i
$736$	−5.36597	+	23.7887i	−0.197792	+	0.876862i
$737$	−37.0543	−	37.0543i	−1.36491	−	1.36491i
$738$	0.0439299	−	0.215110i	0.00161708	−	0.00791830i
$739$	15.3771			0.565656			0.282828	−	0.959171i	$-0.408727\pi$
$739$	15.3771			0.565656			0.282828	+	0.959171i	$0.408727\pi$
$740$	−6.52540	+	23.6053i	−0.239879	+	0.867747i
$741$	−1.28702			−0.0472798
$742$	8.60666	−	42.1439i	0.315960	−	1.54715i
$743$	−0.642631	−	0.642631i	−0.0235758	−	0.0235758i	0.695221	−	0.718796i	$-0.255307\pi$
$743$	−0.642631	−	0.642631i	−0.0235758	−	0.0235758i	−0.718796	+	0.695221i	$0.755307\pi$
$744$	4.53092	−	0.829387i	0.166111	−	0.0304068i
$745$	27.3596	−	35.8259i	1.00238	−	1.31256i
$746$	−24.0509	+	15.8934i	−0.880565	+	0.581899i
$747$	−12.8580	+	12.8580i	−0.470449	+	0.470449i
$748$	57.7021	−	23.2142i	2.10980	−	0.848794i
$749$			25.4604i			0.930304i
$750$	7.03767	−	1.41302i	0.256979	−	0.0515961i
$751$		−	8.45843i		−	0.308652i	−0.988020	−	0.154326i	$-0.950679\pi$
$751$		−	8.45843i		−	0.308652i	0.988020	−	0.154326i	$-0.0493207\pi$
$752$	−26.8281	−	0.547491i	−0.978321	−	0.0199649i
$753$	−4.54183	+	4.54183i	−0.165513	+	0.165513i
$754$	−18.9380	−	28.6581i	−0.689682	−	1.04367i
$755$	−5.82603	+	7.62888i	−0.212031	+	0.277643i
$756$	5.57864	−	13.0887i	0.202893	−	0.476032i
$757$	−20.6260	−	20.6260i	−0.749665	−	0.749665i	0.224752	−	0.974416i	$-0.427843\pi$
$757$	−20.6260	−	20.6260i	−0.749665	−	0.749665i	−0.974416	+	0.224752i	$0.927843\pi$
$758$	−28.0855	−	5.73564i	−1.02011	−	0.208328i
$759$	−11.0577			−0.401370
$760$	−1.95491	−	6.01484i	−0.0709120	−	0.218181i
$761$	19.3261			0.700571			0.350286	−	0.936643i	$-0.386085\pi$
$761$	19.3261			0.700571			0.350286	+	0.936643i	$0.386085\pi$
$762$	7.53527	+	1.53886i	0.272974	+	0.0557470i
$763$	1.15635	+	1.15635i	0.0418627	+	0.0418627i
$764$	−15.5210	+	36.4158i	−0.561532	+	1.31748i
$765$	34.0813	−	4.56661i	1.23221	−	0.165106i
$766$	−23.6394	−	35.7725i	−0.854125	−	1.29251i
$767$	−16.7332	+	16.7332i	−0.604202	+	0.604202i
$768$	−5.34152	+	4.92242i	−0.192745	+	0.177623i
$769$		−	16.9936i		−	0.612803i	−0.951902	−	0.306402i	$-0.900875\pi$
$769$		−	16.9936i		−	0.612803i	0.951902	−	0.306402i	$-0.0991251\pi$
$770$	−3.29560	+	48.2105i	−0.118765	+	1.73739i
$771$			1.13359i

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)

\(f(q)\)	\(=\)	\(q+(-1.38561 - 0.282971i) q^{2} +(0.321015 + 0.321015i) q^{3} +(1.83985 + 0.784178i) q^{4} +(1.77712 + 1.35715i) q^{5} +(-0.353965 - 0.535642i) q^{6} +(1.91243 - 1.91243i) q^{7} +(-2.32743 - 1.60719i) q^{8} -2.79390i q^{9} +O(q^{10})\)	\(q+(-1.38561 - 0.282971i) q^{2} +(0.321015 + 0.321015i) q^{3} +(1.83985 + 0.784178i) q^{4} +(1.77712 + 1.35715i) q^{5} +(-0.353965 - 0.535642i) q^{6} +(1.91243 - 1.91243i) q^{7} +(-2.32743 - 1.60719i) q^{8} -2.79390i q^{9} +(-2.07836 - 2.38336i) q^{10} -5.65006i q^{11} +(0.338888 + 0.842355i) q^{12} +(-2.00460 + 2.00460i) q^{13} +(-3.19106 + 2.10873i) q^{14} +(0.134816 + 1.00615i) q^{15} +(2.77013 + 2.88555i) q^{16} +(3.89197 + 3.89197i) q^{17} +(-0.790593 + 3.87127i) q^{18} +1.00000 q^{19} +(2.20539 + 3.89054i) q^{20} +1.22784 q^{21} +(-1.59880 + 7.82880i) q^{22} +(-3.04830 - 3.04830i) q^{23} +(-0.231207 - 1.26307i) q^{24} +(1.31629 + 4.82363i) q^{25} +(3.34485 - 2.21036i) q^{26} +(1.85993 - 1.85993i) q^{27} +(5.01829 - 2.01891i) q^{28} -8.56783i q^{29} +(0.0979086 - 1.43228i) q^{30} +3.58721i q^{31} +(-3.02180 - 4.78212i) q^{32} +(1.81376 - 1.81376i) q^{33} +(-4.29145 - 6.49409i) q^{34} +(5.99408 - 0.803157i) q^{35} +(2.19091 - 5.14037i) q^{36} +(3.87230 + 3.87230i) q^{37} +(-1.38561 - 0.282971i) q^{38} -1.28702 q^{39} +(-1.95491 - 6.01484i) q^{40} -0.0555658 q^{41} +(-1.70132 - 0.347444i) q^{42} +(1.97854 + 1.97854i) q^{43} +(4.43065 - 10.3953i) q^{44} +(3.79174 - 4.96508i) q^{45} +(3.36118 + 5.08634i) q^{46} +(-4.74358 + 4.74358i) q^{47} +(-0.0370507 + 1.81556i) q^{48} -0.314813i q^{49} +(-0.458916 - 7.05616i) q^{50} +2.49877i q^{51} +(-5.26015 + 2.11621i) q^{52} +(-7.95199 + 7.95199i) q^{53} +(-3.10345 + 2.05084i) q^{54} +(7.66798 - 10.0408i) q^{55} +(-7.52471 + 1.37740i) q^{56} +(0.321015 + 0.321015i) q^{57} +(-2.42445 + 11.8717i) q^{58} +8.34740 q^{59} +(-0.540958 + 1.95689i) q^{60} +12.0737 q^{61} +(1.01508 - 4.97049i) q^{62} +(-5.34315 - 5.34315i) q^{63} +(2.83385 + 7.48126i) q^{64} +(-6.28297 + 0.841866i) q^{65} +(-3.02641 + 1.99992i) q^{66} +(6.55823 - 6.55823i) q^{67} +(4.10866 + 10.2127i) q^{68} -1.95710i q^{69} +(-8.53275 - 0.583286i) q^{70} +7.24112i q^{71} +(-4.49034 + 6.50260i) q^{72} +(-3.34075 + 3.34075i) q^{73} +(-4.26977 - 6.46127i) q^{74} +(-1.12591 + 1.97101i) q^{75} +(1.83985 + 0.784178i) q^{76} +(-10.8054 - 10.8054i) q^{77} +(1.78331 + 0.364189i) q^{78} -13.0319 q^{79} +(1.00672 + 8.88744i) q^{80} -7.18756 q^{81} +(0.0769927 + 0.0157235i) q^{82} +(-4.60217 - 4.60217i) q^{83} +(2.25905 + 0.962847i) q^{84} +(1.63450 + 12.1985i) q^{85} +(-2.18162 - 3.30136i) q^{86} +(2.75040 - 2.75040i) q^{87} +(-9.08074 + 13.1501i) q^{88} +4.22554i q^{89} +(-6.65887 + 5.80674i) q^{90} +7.66735i q^{91} +(-3.21801 - 7.99883i) q^{92} +(-1.15155 + 1.15155i) q^{93} +(7.91506 - 5.23047i) q^{94} +(1.77712 + 1.35715i) q^{95} +(0.565089 - 2.50518i) q^{96} +(-3.74804 - 3.74804i) q^{97} +(-0.0890829 + 0.436209i) q^{98} -15.7857 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

L-functions

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Varieties

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