LMFDB - Embedded newform 380.2.k.d.267.12

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			267.12
Character	$\chi$	$=$	380.267
Dual form			380.2.k.d.343.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.282971 - 1.38561i) q^{2} +(-0.321015 - 0.321015i) q^{3} +(-1.83985 + 0.784178i) q^{4} +(1.77712 + 1.35715i) q^{5} +(-0.353965 + 0.535642i) q^{6} +(-1.91243 + 1.91243i) q^{7} +(1.60719 + 2.32743i) q^{8} -2.79390i q^{9} +O(q^{10})$	\(q+(-0.282971 - 1.38561i) 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} +(1.60719 + 2.32743i) q^{8} -2.79390i q^{9} +(1.37761 - 2.84643i) q^{10} +5.65006i q^{11} +(0.842355 + 0.338888i) 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} +(-3.87127 + 0.790593i) q^{18} -1.00000 q^{19} +(-4.33388 - 1.10338i) q^{20} +1.22784 q^{21} +(7.82880 - 1.59880i) 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} +(2.01891 - 5.01829i) q^{28} -8.56783i q^{29} +(-1.35598 + 0.471513i) q^{30} -3.58721i q^{31} +(-4.78212 - 3.02180i) 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} +(0.282971 + 1.38561i) q^{38} +1.28702 q^{39} +(-0.302500 + 6.31732i) q^{40} -0.0555658 q^{41} +(-0.347444 - 1.70132i) 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} +(-1.81556 + 0.0370507i) q^{48} -0.314813i q^{49} +(6.31122 - 3.18881i) q^{50} -2.49877i q^{51} +(2.11621 - 5.26015i) 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} +(-11.8717 + 2.42445i) q^{58} -8.34740 q^{59} +(1.03704 + 1.74545i) q^{60} +12.0737 q^{61} +(-4.97049 + 1.01508i) 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} +(-10.2127 - 4.10866i) q^{68} -1.95710i q^{69} +(2.80902 + 8.07821i) q^{70} -7.24112i q^{71} +(6.50260 - 4.49034i) 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} +(-0.364189 - 1.78331i) q^{78} +13.0319 q^{79} +(8.83896 - 1.36847i) q^{80} -7.18756 q^{81} +(0.0157235 + 0.0769927i) 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} +(-13.1501 + 9.08074i) q^{88} +4.22554i q^{89} +(-7.95264 - 3.84891i) q^{90} -7.66735i q^{91} +(-7.99883 - 3.21801i) 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} +(-0.436209 + 0.0890829i) 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} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 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 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * 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 $

$2$	−0.282971	−	1.38561i	−0.200091	−	0.979777i
$2$	−0.282971	−	1.38561i	−0.200091	−	0.979777i
$3$	−0.321015	−	0.321015i	−0.185338	−	0.185338i	0.608339	−	0.793677i	$-0.291836\pi$
$3$	−0.321015	−	0.321015i	−0.185338	−	0.185338i	−0.793677	+	0.608339i	$0.791836\pi$
$4$	−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	−0.969181	−	0.246349i	$-0.920769\pi$
$7$	−1.91243	+	1.91243i	−0.722832	+	0.722832i	0.246349	+	0.969181i	$0.420769\pi$
$8$	1.60719	+	2.32743i	0.568229	+	0.822870i
$9$		−	2.79390i		−	0.931299i
$10$	1.37761	−	2.84643i	0.435640	−	0.900121i
$11$			5.65006i			1.70356i	0.523903	+	0.851778i	$0.324475\pi$
$11$			5.65006i			1.70356i	−0.523903	+	0.851778i	$0.675525\pi$
$12$	0.842355	+	0.338888i	0.243167	+	0.0978287i
$13$	−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	$0.517378\pi$
$18$	−3.87127	+	0.790593i	−0.912466	+	0.186345i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−4.33388	−	1.10338i	−0.969086	−	0.246724i
$21$	1.22784			0.267937
$22$	7.82880	−	1.59880i	1.66911	−	0.340866i
$23$	3.04830	+	3.04830i	0.635614	+	0.635614i	0.949470	−	0.313857i	$-0.101621\pi$
$23$	3.04830	+	3.04830i	0.635614	+	0.635614i	−0.313857	+	0.949470i	$0.601621\pi$
$24$	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
$28$	2.01891	−	5.01829i	0.381539	−	0.948368i
$29$		−	8.56783i		−	1.59101i	−0.605950	−	0.795503i	$-0.707207\pi$
$29$		−	8.56783i		−	1.59101i	0.605950	−	0.795503i	$-0.292793\pi$
$30$	−1.35598	+	0.471513i	−0.247568	+	0.0860862i
$31$		−	3.58721i		−	0.644282i	−0.946692	−	0.322141i	$-0.895597\pi$
$31$		−	3.58721i		−	0.644282i	0.946692	−	0.322141i	$-0.104403\pi$
$32$	−4.78212	−	3.02180i	−0.845368	−	0.534185i
$33$	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	$0.601372\pi$
$38$	0.282971	+	1.38561i	0.0459040	+	0.224776i
$39$	1.28702			0.206088
$40$	−0.302500	+	6.31732i	−0.0478295	+	0.998856i
$41$	−0.0555658			−0.00867792			−0.00433896	−	0.999991i	$-0.501381\pi$
$41$	−0.0555658			−0.00867792			−0.00433896	+	0.999991i	$0.501381\pi$
$42$	−0.347444	−	1.70132i	−0.0536118	−	0.262519i
$43$	−1.97854	−	1.97854i	−0.301724	−	0.301724i	0.539964	−	0.841688i	$-0.318438\pi$
$43$	−1.97854	−	1.97854i	−0.301724	−	0.301724i	−0.841688	+	0.539964i	$0.818438\pi$
$44$	−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	−0.270733	−	0.962655i	$-0.587266\pi$
$47$	4.74358	−	4.74358i	0.691922	−	0.691922i	0.962655	+	0.270733i	$0.0872660\pi$
$48$	−1.81556	+	0.0370507i	−0.262053	+	0.00534781i
$49$		−	0.314813i		−	0.0449732i
$50$	6.31122	−	3.18881i	0.892541	−	0.450966i
$51$		−	2.49877i		−	0.349897i
$52$	2.11621	−	5.26015i	0.293466	−	0.729451i
$53$	−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
$58$	−11.8717	+	2.42445i	−1.55883	+	0.318346i
$59$	−8.34740			−1.08674			−0.543369	−	0.839494i	$-0.682852\pi$
$59$	−8.34740			−1.08674			−0.543369	+	0.839494i	$0.682852\pi$
$60$	1.03704	+	1.74545i	0.133881	+	0.225336i
$61$	12.0737			1.54588			0.772939	−	0.634481i	$-0.218786\pi$
$61$	12.0737			1.54588			0.772939	+	0.634481i	$0.218786\pi$
$62$	−4.97049	+	1.01508i	−0.631253	+	0.128915i
$63$	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	−0.983285	−	0.182071i	$-0.941720\pi$
$67$	−6.55823	+	6.55823i	−0.801215	+	0.801215i	0.182071	+	0.983285i	$0.441720\pi$
$68$	−10.2127	−	4.10866i	−1.23847	−	0.498248i
$69$		−	1.95710i		−	0.235607i
$70$	2.80902	+	8.07821i	0.335742	+	0.965531i
$71$		−	7.24112i		−	0.859363i	−0.902980	−	0.429682i	$-0.858626\pi$
$71$		−	7.24112i		−	0.859363i	0.902980	−	0.429682i	$-0.141374\pi$
$72$	6.50260	−	4.49034i	0.766339	−	0.529191i
$73$	−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
$78$	−0.364189	−	1.78331i	−0.0412363	−	0.201920i
$79$	13.0319			1.46620			0.733100	−	0.680121i	$-0.238073\pi$
$79$	13.0319			1.46620			0.733100	+	0.680121i	$0.238073\pi$
$80$	8.83896	−	1.36847i	0.988226	−	0.153000i
$81$	−7.18756			−0.798618
$82$	0.0157235	+	0.0769927i	0.00173637	+	0.00850242i
$83$	4.60217	+	4.60217i	0.505154	+	0.505154i	0.913035	−	0.407881i	$-0.133732\pi$
$83$	4.60217	+	4.60217i	0.505154	+	0.505154i	−0.407881	+	0.913035i	$0.633732\pi$
$84$	−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
$88$	−13.1501	+	9.08074i	−1.40181	+	0.968010i
$89$			4.22554i			0.447906i	0.974600	+	0.223953i	$0.0718962\pi$
$89$			4.22554i			0.447906i	−0.974600	+	0.223953i	$0.928104\pi$
$90$	−7.95264	−	3.84891i	−0.838282	−	0.405711i
$91$		−	7.66735i		−	0.803757i
$92$	−7.99883	−	3.21801i	−0.833935	−	0.335501i
$93$	−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	$0.836724\pi$
$98$	−0.436209	+	0.0890829i	−0.0440637	+	0.00899873i
$99$	15.7857			1.58652
$100$	−6.20436	−	7.84257i	−0.620436	−	0.784257i
$101$	−2.63822			−0.262513			−0.131256	−	0.991348i	$-0.541901\pi$
$101$	−2.63822			−0.262513			−0.131256	+	0.991348i	$0.541901\pi$
$102$	−3.46232	+	0.707079i	−0.342821	+	0.0700112i
$103$	−6.61857	−	6.61857i	−0.652147	−	0.652147i	0.301363	−	0.953510i	$-0.402559\pi$
$103$	−6.61857	−	6.61857i	−0.652147	−	0.652147i	−0.953510	+	0.301363i	$0.902559\pi$
$104$	−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	−0.307904	−	0.951417i	$-0.599628\pi$
$107$	6.65655	−	6.65655i	0.643513	−	0.643513i	0.951417	+	0.307904i	$0.0996277\pi$
$108$	1.96349	−	4.88052i	0.188936	−	0.469628i
$109$			0.604648i			0.0579148i	0.999581	+	0.0289574i	$0.00921871\pi$
$109$			0.604648i			0.0579148i	−0.999581	+	0.0289574i	$0.990781\pi$
$110$	16.0825	+	7.78360i	1.53341	+	0.742137i
$111$		−	2.48614i		−	0.235974i
$112$	0.220728	+	10.8161i	0.0208568	+	1.02203i
$113$	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
$118$	2.36207	+	11.5663i	0.217447	+	1.06476i
$119$	−14.8863			−1.36462
$120$	2.12506	−	1.93085i	0.193991	−	0.176262i
$121$	−20.9231			−1.90210
$122$	−3.41651	−	16.7295i	−0.309316	−	1.51462i
$123$	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	−0.223161	−	0.974782i	$-0.571637\pi$
$127$	8.47034	−	8.47034i	0.751621	−	0.751621i	0.974782	+	0.223161i	$0.0716374\pi$
$128$	11.1680	+	1.80965i	0.987125	+	0.159952i
$129$			1.27028i			0.111842i
$130$	2.94440	+	8.46754i	0.258241	+	0.742653i
$131$		−	0.0987163i		−	0.00862489i	−0.999991	−	0.00431244i	$-0.998627\pi$
$131$		−	0.0987163i		−	0.00862489i	0.999991	−	0.00431244i	$-0.00137270\pi$
$132$	−1.91474	+	4.75935i	−0.166657	+	0.414248i
$133$	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	$0.966852\pi$
$138$	−2.71179	+	0.553803i	−0.230843	+	0.0471428i
$139$	8.14601			0.690935			0.345468	−	0.938431i	$-0.387720\pi$
$139$	8.14601			0.690935			0.345468	+	0.938431i	$0.387720\pi$
$140$	10.3984	−	6.17812i	0.878827	−	0.522146i
$141$	−3.04552			−0.256479
$142$	−10.0334	+	2.04903i	−0.841985	+	0.171951i
$143$	−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
$148$	−10.1611	−	4.08790i	−0.835233	−	0.336023i
$149$		−	20.1596i		−	1.65154i	−0.564009	−	0.825769i	$-0.690742\pi$
$149$		−	20.1596i		−	1.65154i	0.564009	−	0.825769i	$-0.309258\pi$
$150$	−3.04966	−	1.00234i	−0.249003	−	0.0818408i
$151$		−	4.29284i		−	0.349346i	−0.984626	−	0.174673i	$-0.944113\pi$
$151$		−	4.29284i		−	0.349346i	0.984626	−	0.174673i	$-0.0558869\pi$
$152$	−1.60719	−	2.32743i	−0.130361	−	0.188779i
$153$	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	$0.766767\pi$
$158$	−3.68764	−	18.0571i	−0.293373	−	1.43655i
$159$	5.10542			0.404886
$160$	−4.39734	−	11.8602i	−0.347641	−	0.937628i
$161$	−11.6593			−0.918884
$162$	2.03387	+	9.95919i	0.159796	+	0.782468i
$163$	−1.46169	−	1.46169i	−0.114488	−	0.114488i	0.647542	−	0.762030i	$-0.275797\pi$
$163$	−1.46169	−	1.46169i	−0.114488	−	0.114488i	−0.762030	+	0.647542i	$0.775797\pi$
$164$	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	−0.286606	−	0.958049i	$-0.592527\pi$
$167$	8.67695	−	8.67695i	0.671442	−	0.671442i	0.958049	+	0.286606i	$0.0925271\pi$
$168$	1.97338	+	2.85772i	0.152250	+	0.220478i
$169$			4.96312i			0.381778i
$170$	16.4399	−	5.71660i	1.26088	−	0.438443i
$171$			2.79390i			0.213655i
$172$	5.19174	+	2.08869i	0.395867	+	0.159261i
$173$	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
$178$	5.85497	−	1.19571i	0.438848	−	0.0896219i
$179$	23.2404			1.73707			0.868535	−	0.495627i	$-0.165062\pi$
$179$	23.2404			1.73707			0.868535	+	0.495627i	$0.165062\pi$
$180$	−3.08274	+	12.1084i	−0.229774	+	0.902509i
$181$	7.16494			0.532566			0.266283	−	0.963895i	$-0.414204\pi$
$181$	7.16494			0.532566			0.266283	+	0.963895i	$0.414204\pi$
$182$	−10.6240	+	2.16964i	−0.787503	+	0.160824i
$183$	−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
$188$	−5.00768	+	12.4473i	−0.365223	+	0.907813i
$189$		−	7.11399i		−	0.517467i
$190$	−1.37761	+	2.84643i	−0.0999427	+	0.206502i
$191$		−	19.7928i		−	1.43215i	−0.698022	−	0.716077i	$-0.745936\pi$
$191$		−	19.7928i		−	1.43215i	0.698022	−	0.716077i	$-0.254064\pi$
$192$	3.31131	−	1.49189i	0.238973	−	0.107668i
$193$	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	$0.532892\pi$
$198$	−4.46689	−	21.8729i	−0.317448	−	1.55444i
$199$	15.8810			1.12577			0.562886	−	0.826534i	$-0.309691\pi$
$199$	15.8810			1.12577			0.562886	+	0.826534i	$0.309691\pi$
$200$	−9.11113	+	10.8161i	−0.644254	+	0.764812i
$201$	4.21058			0.296992
$202$	0.746541	+	3.65556i	0.0525264	+	0.257204i
$203$	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
$208$	0.231366	+	11.3374i	0.0160424	+	0.786107i
$209$		−	5.65006i		−	0.390823i
$210$	1.69149	−	3.49497i	0.116724	−	0.241176i
$211$			10.7864i			0.742568i	0.928519	+	0.371284i	$0.121082\pi$
$211$			10.7864i			0.742568i	−0.928519	+	0.371284i	$0.878918\pi$
$212$	8.39473	−	20.8663i	0.576552	−	1.43310i
$213$	−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
$218$	0.837809	−	0.171098i	0.0567436	−	0.0115882i
$219$	2.14486			0.144937
$220$	6.23418	−	24.4867i	0.420308	−	1.65089i
$221$	−15.6037			−1.04962
$222$	−3.44483	+	0.703506i	−0.231202	+	0.0472162i
$223$	14.8860	+	14.8860i	0.996843	+	0.996843i	0.999995	−	0.00315185i	$-0.00100327\pi$
$223$	14.8860	+	14.8860i	0.996843	+	0.996843i	−0.00315185	+	0.999995i	$0.501003\pi$
$224$	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	$0.542770\pi$
$227$	−16.9491	+	16.9491i	−1.12495	+	1.12495i	−0.990986	+	0.133963i	$0.957230\pi$
$228$	−0.842355	−	0.338888i	−0.0557863	−	0.0224434i
$229$			12.2209i			0.807580i	0.914852	+	0.403790i	$0.132307\pi$
$229$			12.2209i			0.807580i	−0.914852	+	0.403790i	$0.867693\pi$
$230$	12.8761	−	4.47739i	0.849028	−	0.295230i
$231$			6.93738i			0.456446i
$232$	19.9410	−	13.7702i	1.30919	−	0.904055i
$233$	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
$238$	4.21239	+	20.6266i	0.273049	+	1.33703i
$239$	−25.0913			−1.62302			−0.811511	−	0.584338i	$-0.801354\pi$
$239$	−25.0913			−1.62302			−0.811511	+	0.584338i	$0.801354\pi$
$240$	−3.27674	−	2.39814i	−0.211513	−	0.154800i
$241$	20.2239			1.30274			0.651369	−	0.758761i	$-0.274195\pi$
$241$	20.2239			1.30274			0.651369	+	0.758761i	$0.274195\pi$
$242$	5.92064	+	28.9914i	0.380593	+	1.86364i
$243$	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
$248$	8.34898	−	5.76535i	0.530161	−	0.366100i
$249$		−	2.95474i		−	0.187249i
$250$	15.5435	+	2.89838i	0.983055	+	0.183310i
$251$		−	14.1483i		−	0.893034i	−0.894775	−	0.446517i	$-0.852664\pi$
$251$		−	14.1483i		−	0.893034i	0.894775	−	0.446517i	$-0.147336\pi$
$252$	−14.0206	−	5.64064i	−0.883214	−	0.355327i
$253$	−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	$0.725185\pi$
$258$	1.76012	−	0.359453i	0.109580	−	0.0223786i
$259$	−14.8111			−0.920314
$260$	10.8996	−	6.47587i	0.675963	−	0.401617i
$261$	−23.9376			−1.48170
$262$	−0.136783	+	0.0279339i	−0.00845047	+	0.00172576i
$263$	−1.92483	−	1.92483i	−0.118690	−	0.118690i	0.645267	−	0.763957i	$-0.276746\pi$
$263$	−1.92483	−	1.92483i	−0.118690	−	0.118690i	−0.763957	+	0.645267i	$0.776746\pi$
$264$	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
$268$	6.92336	−	17.2090i	0.422912	−	1.05121i
$269$		−	2.85728i		−	0.174211i	−0.996199	−	0.0871056i	$-0.972238\pi$
$269$		−	2.85728i		−	0.174211i	0.996199	−	0.0871056i	$-0.0277618\pi$
$270$	2.73190	+	7.85643i	0.166258	+	0.478127i
$271$		−	23.3292i		−	1.41715i	−0.705637	−	0.708573i	$-0.749339\pi$
$271$		−	23.3292i		−	1.41715i	0.705637	−	0.708573i	$-0.250661\pi$
$272$	22.0117	−	0.449201i	1.33466	−	0.0272368i
$273$	−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	$0.891939\pi$
$278$	−2.30509	−	11.2872i	−0.138250	−	0.676963i
$279$	−10.0223			−0.600020
$280$	−11.5029	−	12.6600i	−0.687432	−	0.756578i
$281$	−2.12728			−0.126903			−0.0634515	−	0.997985i	$-0.520211\pi$
$281$	−2.12728			−0.126903			−0.0634515	+	0.997985i	$0.520211\pi$
$282$	0.861795	+	4.21992i	0.0513192	+	0.251293i
$283$	15.7907	+	15.7907i	0.938660	+	0.938660i	0.998224	−	0.0595643i	$-0.0189711\pi$
$283$	15.7907	+	15.7907i	0.938660	+	0.938660i	−0.0595643	+	0.998224i	$0.518971\pi$
$284$	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
$288$	−8.44262	+	13.3608i	−0.497486	+	0.787291i
$289$			13.2949i			0.782051i
$290$	−24.3877	−	11.8032i	−1.43210	−	0.693105i
$291$			2.40636i			0.141063i
$292$	3.52675	−	8.76624i	0.206388	−	0.513005i
$293$	−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
$298$	−27.9334	+	5.70458i	−1.61814	+	0.330458i
$299$	−12.2213			−0.706773
$300$	−0.525893	+	4.50928i	−0.0303624	+	0.260343i
$301$	7.56764			0.436191
$302$	−5.94822	+	1.21475i	−0.342282	+	0.0699010i
$303$	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	−0.232651	−	0.972560i	$-0.574740\pi$
$307$	12.9642	−	12.9642i	0.739909	−	0.739909i	0.972560	+	0.232651i	$0.0747401\pi$
$308$	28.3536	+	11.4070i	1.61560	+	0.649972i
$309$			4.24932i			0.241736i
$310$	−10.2108	−	4.94179i	−0.579932	−	0.280675i
$311$		−	0.353348i		−	0.0200365i	−0.999950	−	0.0100183i	$-0.996811\pi$
$311$		−	0.353348i		−	0.0200365i	0.999950	−	0.0100183i	$-0.00318896\pi$
$312$	2.06849	+	2.99544i	0.117105	+	0.169584i
$313$	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	$0.790035\pi$
$318$	−1.44469	−	7.07415i	−0.0810140	−	0.396698i
$319$	48.4087			2.71037
$320$	−15.1893	+	9.44911i	−0.849107	+	0.528221i
$321$	−4.27371			−0.238535
$322$	3.29926	+	16.1553i	0.183860	+	0.900302i
$323$	−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
$328$	−0.0893050	−	0.129325i	−0.00493104	−	0.00714080i
$329$			18.1436i			1.00029i
$330$	−2.66408	−	7.66139i	−0.146653	−	0.421745i
$331$			21.2084i			1.16572i	0.812573	+	0.582859i	$0.198066\pi$
$331$			21.2084i			1.16572i	−0.812573	+	0.582859i	$0.801934\pi$
$332$	−12.0762	−	4.85840i	−0.662770	−	0.266640i
$333$	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	$0.734796\pi$
$338$	6.87697	−	1.40442i	0.374058	−	0.0763904i
$339$	−2.28217			−0.123950
$340$	−12.5730	−	21.1617i	−0.681867	−	1.14765i
$341$	20.2679			1.09757
$342$	3.87127	−	0.790593i	0.209334	−	0.0427504i
$343$	−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	−0.959968	−	0.280109i	$-0.909629\pi$
$347$	−12.6644	+	12.6644i	−0.679859	+	0.679859i	0.280109	+	0.959968i	$0.409629\pi$
$348$	2.90354	−	7.21715i	0.155646	−	0.386880i
$349$			16.0318i			0.858164i	0.903266	+	0.429082i	$0.141163\pi$
$349$			16.0318i			0.858164i	−0.903266	+	0.429082i	$0.858837\pi$
$350$	−5.97140	+	18.1682i	−0.319185	+	0.971130i
$351$		−	7.45685i		−	0.398017i
$352$	17.0734	−	27.0193i	0.910013	−	1.44013i
$353$	−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
$358$	−6.57637	−	32.2023i	−0.347572	−	1.70194i
$359$	0.347833			0.0183579			0.00917897	−	0.999958i	$-0.497078\pi$
$359$	0.347833			0.0183579			0.00917897	+	0.999958i	$0.497078\pi$
$360$	17.6499	+	0.845155i	0.930234	+	0.0445436i
$361$	1.00000			0.0526316
$362$	−2.02747	−	9.92784i	−0.106562	−	0.521796i
$363$	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	−0.564654	−	0.825328i	$-0.690990\pi$
$367$	4.99380	−	4.99380i	0.260674	−	0.260674i	0.825328	+	0.564654i	$0.190990\pi$
$368$	17.2402	−	0.351826i	0.898706	−	0.0183402i
$369$			0.155245i			0.00808174i
$370$	16.3568	−	5.68771i	0.850349	−	0.295690i
$371$		−	30.4153i		−	1.57908i
$372$	1.21566	−	3.02171i	0.0630293	−	0.156668i
$373$	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
$378$	−9.85725	+	2.01305i	−0.507002	+	0.103540i
$379$	−20.2693			−1.04117			−0.520583	−	0.853811i	$-0.674285\pi$
$379$	−20.2693			−1.04117			−0.520583	+	0.853811i	$0.674285\pi$
$380$	4.33388	+	1.10338i	0.222324	+	0.0566024i
$381$	−5.43822			−0.278608
$382$	−27.4251	+	5.60078i	−1.40319	+	0.286561i
$383$	−21.4388	−	21.4388i	−1.09547	−	1.09547i	−0.994933	−	0.100539i	$-0.967943\pi$
$383$	−21.4388	−	21.4388i	−1.09547	−	1.09547i	−0.100539	−	0.994933i	$-0.532057\pi$
$384$	−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
$388$	9.83497	+	3.95672i	0.499295	+	0.200872i
$389$			0.701293i			0.0355570i	0.999842	+	0.0177785i	$0.00565937\pi$
$389$			0.701293i			0.0355570i	−0.999842	+	0.0177785i	$0.994341\pi$
$390$	1.77301	−	3.66341i	0.0897801	−	0.185504i
$391$			23.7278i			1.19996i
$392$	0.732704	−	0.505965i	0.0370071	−	0.0255551i
$393$	−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	$0.684430\pi$
$398$	−4.49386	−	22.0049i	−0.225257	−	1.10301i
$399$	−1.22784			−0.0614690
$400$	17.5651	+	9.56387i	0.878254	+	0.478194i
$401$	−9.38653			−0.468741			−0.234370	−	0.972147i	$-0.575303\pi$
$401$	−9.38653			−0.468741			−0.234370	+	0.972147i	$0.575303\pi$
$402$	−1.19147	−	5.83424i	−0.0594253	−	0.290986i
$403$	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
$408$	5.81570	−	4.01600i	0.287920	−	0.198822i
$409$		−	35.3014i		−	1.74554i	−0.488128	−	0.872772i	$-0.662320\pi$
$409$		−	35.3014i		−	1.74554i	0.488128	−	0.872772i	$-0.337680\pi$
$410$	−0.0765482	+	0.158164i	−0.00378045	+	0.00781117i
$411$			6.69292i			0.330137i
$412$	17.3673	+	6.98707i	0.855627	+	0.344228i
$413$	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
$418$	−7.82880	+	1.59880i	−0.382919	+	0.0782000i
$419$	−20.7626			−1.01432			−0.507160	−	0.861852i	$-0.669305\pi$
$419$	−20.7626			−1.01432			−0.507160	+	0.861852i	$0.669305\pi$
$420$	−5.32132	−	1.35478i	−0.259654	−	0.0661065i
$421$	−7.87092			−0.383605			−0.191803	−	0.981434i	$-0.561433\pi$
$421$	−7.87092			−0.383605			−0.191803	+	0.981434i	$0.561433\pi$
$422$	14.9458	−	3.05225i	0.727552	−	0.148581i
$423$	−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
$428$	−7.02716	+	17.4670i	−0.339671	+	0.844299i
$429$			7.27172i			0.351082i
$430$	−8.35743	+	2.90611i	−0.403031	+	0.140145i
$431$			22.8584i			1.10105i	0.834819	+	0.550525i	$0.185572\pi$
$431$			22.8584i			1.10105i	−0.834819	+	0.550525i	$0.814428\pi$
$432$	0.214668	+	10.5192i	0.0103282	+	0.506104i
$433$	−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
$438$	−0.606935	−	2.97196i	−0.0290005	−	0.142006i
$439$	−3.55487			−0.169665			−0.0848324	−	0.996395i	$-0.527035\pi$
$439$	−3.55487			−0.169665			−0.0848324	+	0.996395i	$0.527035\pi$
$440$	−35.6932	−	1.70914i	−1.70161	−	0.0814802i
$441$	−0.879554			−0.0418835
$442$	4.41541	+	21.6207i	0.210019	+	1.02839i
$443$	12.5438	+	12.5438i	0.595974	+	0.595974i	0.939239	−	0.343264i	$-0.111533\pi$
$443$	12.5438	+	12.5438i	0.595974	+	0.595974i	−0.343264	+	0.939239i	$0.611533\pi$
$444$	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
$448$	−8.88786	−	19.7270i	−0.419912	−	0.932012i
$449$			32.9577i			1.55537i	0.628655	+	0.777685i	$0.283606\pi$
$449$			32.9577i			1.55537i	−0.628655	+	0.777685i	$0.716394\pi$
$450$	−8.90922	−	17.6329i	−0.419984	−	0.831223i
$451$		−	0.313950i		−	0.0147833i
$452$	−3.75252	+	9.32741i	−0.176504	+	0.438724i
$453$	−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	$0.742007\pi$
$458$	16.9335	−	3.45816i	0.791249	−	0.161589i
$459$	−14.4776			−0.675756
$460$	−9.84752	−	16.5744i	−0.459143	−	0.772785i
$461$	34.3719			1.60086			0.800429	−	0.599427i	$-0.204605\pi$
$461$	34.3719			1.60086			0.800429	+	0.599427i	$0.204605\pi$
$462$	9.61253	−	1.96308i	0.447215	−	0.0913306i
$463$	7.60575	+	7.60575i	0.353469	+	0.353469i	0.861399	−	0.507930i	$-0.169589\pi$
$463$	7.60575	+	7.60575i	0.353469	+	0.353469i	−0.507930	+	0.861399i	$0.669589\pi$
$464$	−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	−0.153611	−	0.988131i	$-0.549090\pi$
$467$	18.0342	−	18.0342i	0.834521	−	0.834521i	0.988131	+	0.153611i	$0.0490901\pi$
$468$	−14.6963	−	5.91249i	−0.679338	−	0.273305i
$469$		−	25.0844i		−	1.15829i
$470$	−6.96745	−	20.0371i	−0.321385	−	0.924242i
$471$			0.598994i			0.0276002i
$472$	−13.4159	−	19.4280i	−0.617516	−	0.894245i
$473$	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
$478$	7.10012	+	34.7669i	0.324752	+	1.59020i
$479$	12.8104			0.585323			0.292662	−	0.956216i	$-0.405459\pi$
$479$	12.8104			0.585323			0.292662	+	0.956216i	$0.405459\pi$
$480$	−2.39568	+	5.21891i	−0.109347	+	0.238210i
$481$	−15.5249			−0.707873
$482$	−5.72279	−	28.0226i	−0.260666	−	1.27639i
$483$	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	−0.914072	−	0.405552i	$-0.867079\pi$
$487$	−11.2221	+	11.2221i	−0.508520	+	0.508520i	0.405552	+	0.914072i	$0.367079\pi$
$488$	19.4048	+	28.1006i	0.878412	+	1.27206i
$489$			0.938449i			0.0424382i
$490$	−0.896093	−	0.433690i	−0.0404813	−	0.0195921i
$491$		−	30.6682i		−	1.38403i	−0.721881	−	0.692017i	$-0.756722\pi$
$491$		−	30.6682i		−	1.38403i	0.721881	−	0.692017i	$-0.243278\pi$
$492$	−0.0468061	−	0.0188306i	−0.00211018	−	0.000848949i
$493$	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
$498$	−4.09412	+	0.836105i	−0.183462	+	0.0374668i
$499$	−23.9769			−1.07335			−0.536676	−	0.843788i	$-0.680320\pi$
$499$	−23.9769			−1.07335			−0.536676	+	0.843788i	$0.680320\pi$
$500$	−0.382313	−	22.3574i	−0.0170976	−	0.999854i
$501$	−5.57087			−0.248888
$502$	−19.6041	+	4.00357i	−0.874974	+	0.178688i
$503$	0.229488	+	0.229488i	0.0102324	+	0.0102324i	0.712204	−	0.701972i	$-0.247697\pi$
$503$	0.229488	+	0.229488i	0.0102324	+	0.0102324i	−0.701972	+	0.712204i	$0.747697\pi$
$504$	−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
$508$	−8.94194	+	22.2264i	−0.396734	+	0.986139i
$509$			40.6326i			1.80101i	0.434846	+	0.900505i	$0.356803\pi$
$509$			40.6326i			1.80101i	−0.434846	+	0.900505i	$0.643197\pi$
$510$	−7.11257	−	3.44233i	−0.314950	−	0.152429i
$511$		−	12.7779i		−	0.565263i
$512$	−21.9667	+	5.42825i	−0.970798	+	0.239897i
$513$	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
$518$	4.19110	+	20.5224i	0.184146	+	0.901703i
$519$	−4.14634			−0.182004
$520$	−12.0573	−	13.2701i	−0.528749	−	0.581933i
$521$	0.640624			0.0280662			0.0140331	−	0.999902i	$-0.495533\pi$
$521$	0.640624			0.0280662			0.0140331	+	0.999902i	$0.495533\pi$
$522$	6.77366	+	33.1683i	0.296475	+	1.45174i
$523$	12.4974	+	12.4974i	0.546474	+	0.546474i	0.925419	−	0.378945i	$-0.123713\pi$
$523$	12.4974	+	12.4974i	0.546474	+	0.546474i	−0.378945	+	0.925419i	$0.623713\pi$
$524$	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
$528$	−0.209339	−	10.2580i	−0.00911030	−	0.446423i
$529$		−	4.41579i		−	0.191991i
$530$	11.6800	+	33.5896i	0.507348	+	1.45904i
$531$			23.3218i			1.01208i
$532$	−2.01891	+	5.01829i	−0.0875310	+	0.217571i
$533$	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
$538$	−3.95908	+	0.808527i	−0.170688	+	0.0348581i
$539$	1.77871			0.0766144
$540$	10.1129	−	6.00850i	0.435192	−	0.258565i
$541$	17.4549			0.750445			0.375223	−	0.926935i	$-0.377566\pi$
$541$	17.4549			0.750445			0.375223	+	0.926935i	$0.377566\pi$
$542$	−32.3253	+	6.60149i	−1.38849	+	0.283558i
$543$	−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	−0.944612	−	0.328189i	$-0.893562\pi$
$547$	−14.4169	+	14.4169i	−0.616423	+	0.616423i	0.328189	+	0.944612i	$0.393562\pi$
$548$	27.3545	+	11.0050i	1.16853	+	0.470111i
$549$		−	33.7327i		−	1.43967i
$550$	18.0170	+	35.6587i	0.768246	+	1.52049i
$551$			8.56783i			0.365002i
$552$	4.55501	−	3.14544i	0.193874	−	0.133879i
$553$	−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	$0.871250\pi$
$558$	2.83602	+	13.8870i	0.120058	+	0.587886i
$559$	7.93236			0.335503
$560$	−14.2868	+	19.5211i	−0.603729	+	0.824915i
$561$	14.1182			0.596069
$562$	0.601959	+	2.94759i	0.0253921	+	0.124337i
$563$	11.6114	+	11.6114i	0.489364	+	0.489364i	0.908105	−	0.418742i	$-0.137529\pi$
$563$	11.6114	+	11.6114i	0.489364	+	0.489364i	−0.418742	+	0.908105i	$0.637529\pi$
$564$	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
$568$	16.8532	−	11.6379i	0.707145	−	0.488315i
$569$			14.6399i			0.613737i	0.951752	+	0.306869i	$0.0992813\pi$
$569$			14.6399i			0.613737i	−0.951752	+	0.306869i	$0.900719\pi$
$570$	1.35598	−	0.471513i	0.0567959	−	0.0197495i
$571$			23.5114i			0.983922i	0.870617	+	0.491961i	$0.163720\pi$
$571$			23.5114i			0.983922i	−0.870617	+	0.491961i	$0.836280\pi$
$572$	29.7201	+	11.9567i	1.24266	+	0.499936i
$573$	−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	$0.683369\pi$
$578$	18.4216	−	3.76207i	0.766236	−	0.156481i
$579$	−3.06585			−0.127413
$580$	−9.45360	+	37.1320i	−0.392539	+	1.54182i
$581$	−17.6027			−0.730283
$582$	3.33428	−	0.680929i	0.138210	−	0.0282254i
$583$	−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	$-0.313903\pi$
$587$	33.5755	−	33.5755i	1.38581	−	1.38581i	0.833911	−	0.551899i	$-0.186097\pi$
$588$	0.106686	−	0.265184i	0.00439967	−	0.0109360i
$589$			3.58721i			0.147808i
$590$	−11.4995	+	23.7603i	−0.473427	+	0.978196i
$591$		−	8.03374i		−	0.330464i
$592$	21.9005	−	0.446931i	0.900105	−	0.0183688i
$593$	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
$598$	3.45826	+	16.9339i	0.141419	+	0.692481i
$599$	−11.2535			−0.459804			−0.229902	−	0.973214i	$-0.573841\pi$
$599$	−11.2535			−0.459804			−0.229902	+	0.973214i	$0.573841\pi$
$600$	6.39694	−	0.547312i	0.261154	−	0.0223439i
$601$	28.4675			1.16121			0.580606	−	0.814185i	$-0.302816\pi$
$601$	28.4675			1.16121			0.580606	+	0.814185i	$0.302816\pi$
$602$	−2.14142	−	10.4858i	−0.0872779	−	0.427371i
$603$	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	−0.103788	−	0.994599i	$-0.533096\pi$
$607$	21.9473	−	21.9473i	0.890812	−	0.890812i	0.994599	+	0.103788i	$0.0330963\pi$
$608$	4.78212	+	3.02180i	0.193941	+	0.122550i
$609$		−	10.5199i		−	0.426289i
$610$	16.6329	−	34.3669i	0.673446	−	1.39148i
$611$			19.0180i			0.769386i
$612$	−11.4792	+	28.5331i	−0.464018	+	1.15338i
$613$	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	$0.782278\pi$
$618$	5.88793	−	1.20244i	0.236847	−	0.0483691i
$619$	39.9486			1.60567			0.802834	−	0.596202i	$-0.203324\pi$
$619$	39.9486			1.60567			0.802834	+	0.596202i	$0.203324\pi$
$620$	−3.95807	+	15.5466i	−0.158960	+	0.624365i
$621$	−11.3392			−0.455028
$622$	−0.489604	+	0.0999872i	−0.0196313	+	0.00400912i
$623$	−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
$628$	2.44814	+	0.984912i	0.0976913	+	0.0393023i
$629$			30.1418i			1.20183i
$630$	22.5697	−	7.84811i	0.899199	−	0.312676i
$631$			10.1547i			0.404254i	0.979359	+	0.202127i	$0.0647854\pi$
$631$			10.1547i			0.404254i	−0.979359	+	0.202127i	$0.935215\pi$
$632$	20.9447	+	30.3308i	0.833137	+	1.20649i
$633$	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
$638$	−13.6983	−	67.0758i	−0.542320	−	2.65556i
$639$	−20.2310			−0.800325
$640$	17.3910	+	18.3727i	0.687438	+	0.726243i
$641$	−20.4445			−0.807510			−0.403755	−	0.914867i	$-0.632295\pi$
$641$	−20.4445			−0.807510			−0.403755	+	0.914867i	$0.632295\pi$
$642$	1.20934	+	5.92171i	0.0477287	+	0.233711i
$643$	−17.7673	−	17.7673i	−0.700672	−	0.700672i	0.263883	−	0.964555i	$-0.414997\pi$
$643$	−17.7673	−	17.7673i	−0.700672	−	0.700672i	−0.964555	+	0.263883i	$0.914997\pi$
$644$	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	−0.774046	−	0.633130i	$-0.781770\pi$
$647$	−3.58437	+	3.58437i	−0.140916	+	0.140916i	0.633130	+	0.774046i	$0.281770\pi$
$648$	−11.5518	−	16.7285i	−0.453798	−	0.657159i
$649$		−	47.1633i		−	1.85132i
$650$	−6.25919	+	19.0438i	−0.245506	+	0.746960i
$651$		−	4.40453i		−	0.172627i
$652$	3.83552	+	1.54307i	0.150211	+	0.0604313i
$653$	−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
$658$	25.1400	−	5.13410i	0.980058	−	0.200148i
$659$	3.92382			0.152851			0.0764253	−	0.997075i	$-0.475649\pi$
$659$	3.92382			0.152851			0.0764253	+	0.997075i	$0.475649\pi$
$660$	−9.86187	+	5.85933i	−0.383873	+	0.228074i
$661$	−7.98789			−0.310693			−0.155347	−	0.987860i	$-0.549649\pi$
$661$	−7.98789			−0.310693			−0.155347	+	0.987860i	$0.549649\pi$
$662$	29.3866	−	6.00136i	1.14214	−	0.233249i
$663$	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
$668$	−9.16005	+	22.7686i	−0.354413	+	0.880943i
$669$		−	9.55730i		−	0.369507i
$670$	9.63284	+	27.7023i	0.372149	+	1.07023i
$671$			68.2170i			2.63349i
$672$	−5.87169	−	3.71030i	−0.226505	−	0.143128i
$673$	−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	$0.903328\pi$
$678$	0.645788	+	3.16221i	0.0248013	+	0.121444i
$679$	14.3358			0.550156
$680$	−25.7641	+	23.4095i	−0.988009	+	0.897713i
$681$	10.8818			0.416993
$682$	−5.73525	−	28.0836i	−0.219614	−	1.07537i
$683$	−19.4927	−	19.4927i	−0.745869	−	0.745869i	0.227832	−	0.973701i	$-0.426836\pi$
$683$	−19.4927	−	19.4927i	−0.745869	−	0.745869i	−0.973701	+	0.227832i	$0.926836\pi$
$684$	−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
$688$	−11.1900	+	0.228357i	−0.426613	+	0.00870604i
$689$		−	31.8812i		−	1.21458i
$690$	−5.57075	−	2.69613i	−0.212075	−	0.102640i
$691$			10.0408i			0.381969i	0.981593	+	0.190985i	$0.0611681\pi$
$691$			10.0408i			0.381969i	−0.981593	+	0.190985i	$0.938832\pi$
$692$	−6.81774	+	16.9464i	−0.259171	+	0.644207i
$693$	−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
$698$	22.2139	−	4.53655i	0.840810	−	0.171711i
$699$	−8.59525			−0.325102
$700$	26.8638	+	3.13298i	1.01536	+	0.118416i
$701$	5.87705			0.221973			0.110987	−	0.993822i	$-0.464599\pi$
$701$	5.87705			0.221973			0.110987	+	0.993822i	$0.464599\pi$
$702$	−10.3323	+	2.11007i	−0.389968	+	0.0796396i
$703$	−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
$708$	−7.03147	−	2.82884i	−0.264259	−	0.106314i
$709$			3.43572i			0.129031i	0.997917	+	0.0645156i	$0.0205502\pi$
$709$			3.43572i			0.129031i	−0.997917	+	0.0645156i	$0.979450\pi$
$710$	−20.6114	−	9.97548i	−0.773531	−	0.374373i
$711$		−	36.4097i		−	1.36547i
$712$	−9.83464	+	6.79126i	−0.368569	+	0.254513i
$713$	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
$718$	−0.0984269	−	0.481963i	−0.00367326	−	0.0179867i
$719$	0.800777			0.0298640			0.0149320	−	0.999889i	$-0.495247\pi$
$719$	0.800777			0.0298640			0.0149320	+	0.999889i	$0.495247\pi$
$720$	−3.82337	−	24.6952i	−0.142488	−	0.920335i
$721$	25.3152			0.942786
$722$	−0.282971	−	1.38561i	−0.0105311	−	0.0515672i
$723$	−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	−0.936735	−	0.350039i	$-0.886168\pi$
$727$	−15.8191	+	15.8191i	−0.586696	+	0.586696i	0.350039	+	0.936735i	$0.386168\pi$
$728$	17.8452	−	12.3229i	0.661388	−	0.456718i
$729$			16.4989i			0.611071i
$730$	4.90696	+	14.1115i	0.181615	+	0.522290i
$731$		−	15.4008i		−	0.569619i
$732$	10.1703	+	4.09163i	0.375906	+	0.151231i
$733$	−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
$738$	0.215110	−	0.0439299i	0.00791830	−	0.00161708i
$739$	−15.3771			−0.565656			−0.282828	−	0.959171i	$-0.591273\pi$
$739$	−15.3771			−0.565656			−0.282828	+	0.959171i	$0.591273\pi$
$740$	−12.5095	−	21.0548i	−0.459857	−	0.773988i
$741$	−1.28702			−0.0472798
$742$	−42.1439	+	8.60666i	−1.54715	+	0.315960i
$743$	0.642631	+	0.642631i	0.0235758	+	0.0235758i	0.718796	−	0.695221i	$-0.244693\pi$
$743$	0.642631	+	0.642631i	0.0235758	+	0.0235758i	−0.695221	+	0.718796i	$0.744693\pi$
$744$	−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
$748$	23.2142	−	57.7021i	0.848794	−	2.10980i
$749$			25.4604i			0.930304i
$750$	−4.05927	−	5.92012i	−0.148223	−	0.216172i
$751$			8.45843i			0.308652i	0.988020	+	0.154326i	$0.0493207\pi$
$751$			8.45843i			0.308652i	−0.988020	+	0.154326i	$0.950679\pi$
$752$	−0.547491	−	26.8281i	−0.0199649	−	0.978321i
$753$	−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	$0.927843\pi$
$758$	5.73564	+	28.0855i	0.208328	+	1.02011i
$759$	11.0577			0.401370
$760$	0.302500	−	6.31732i	0.0109728	−	0.229153i
$761$	19.3261			0.700571			0.350286	−	0.936643i	$-0.386085\pi$
$761$	19.3261			0.700571			0.350286	+	0.936643i	$0.386085\pi$
$762$	1.53886	+	7.53527i	0.0557470	+	0.272974i
$763$	−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
$768$	−4.92242	+	5.34152i	−0.177623	+	0.192745i
$769$		−	16.9936i		−	0.612803i	−0.951902	−	0.306402i	$-0.900875\pi$
$769$		−	16.9936i		−	0.612803i	0.951902	−	0.306402i	$-0.0991251\pi$

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)

\(f(q)\)	\(=\)	\(q+(-0.282971 - 1.38561i) q^{2} +(-0.321015 - 0.321015i) q^{3} +(-1.83985 + 0.784178i) q^{4} +(1.77712 + 1.35715i) q^{5} +(-0.353965 + 0.535642i) q^{6} +(-1.91243 + 1.91243i) q^{7} +(1.60719 + 2.32743i) q^{8} -2.79390i q^{9} +O(q^{10})\)	\(q+(-0.282971 - 1.38561i) 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} +(1.60719 + 2.32743i) q^{8} -2.79390i q^{9} +(1.37761 - 2.84643i) q^{10} +5.65006i q^{11} +(0.842355 + 0.338888i) 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} +(-3.87127 + 0.790593i) q^{18} -1.00000 q^{19} +(-4.33388 - 1.10338i) q^{20} +1.22784 q^{21} +(7.82880 - 1.59880i) 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} +(2.01891 - 5.01829i) q^{28} -8.56783i q^{29} +(-1.35598 + 0.471513i) q^{30} -3.58721i q^{31} +(-4.78212 - 3.02180i) 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} +(0.282971 + 1.38561i) q^{38} +1.28702 q^{39} +(-0.302500 + 6.31732i) q^{40} -0.0555658 q^{41} +(-0.347444 - 1.70132i) 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} +(-1.81556 + 0.0370507i) q^{48} -0.314813i q^{49} +(6.31122 - 3.18881i) q^{50} -2.49877i q^{51} +(2.11621 - 5.26015i) 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} +(-11.8717 + 2.42445i) q^{58} -8.34740 q^{59} +(1.03704 + 1.74545i) q^{60} +12.0737 q^{61} +(-4.97049 + 1.01508i) 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} +(-10.2127 - 4.10866i) q^{68} -1.95710i q^{69} +(2.80902 + 8.07821i) q^{70} -7.24112i q^{71} +(6.50260 - 4.49034i) 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} +(-0.364189 - 1.78331i) q^{78} +13.0319 q^{79} +(8.83896 - 1.36847i) q^{80} -7.18756 q^{81} +(0.0157235 + 0.0769927i) 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} +(-13.1501 + 9.08074i) q^{88} +4.22554i q^{89} +(-7.95264 - 3.84891i) q^{90} -7.66735i q^{91} +(-7.99883 - 3.21801i) 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} +(-0.436209 + 0.0890829i) 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	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more