LMFDB - Embedded newform 380.2.k.d.343.9

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			343.9
Character	$\chi$	$=$	380.343
Dual form			380.2.k.d.267.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.615749 - 1.27313i) q^{2} +(1.93808 - 1.93808i) q^{3} +(-1.24171 + 1.56785i) q^{4} +(-0.168423 + 2.22972i) q^{5} +(-3.66079 - 1.27405i) q^{6} +(2.91797 + 2.91797i) q^{7} +(2.76066 + 0.615446i) q^{8} -4.51229i q^{9} +O(q^{10})$	\(q+(-0.615749 - 1.27313i) q^{2} +(1.93808 - 1.93808i) q^{3} +(-1.24171 + 1.56785i) q^{4} +(-0.168423 + 2.22972i) q^{5} +(-3.66079 - 1.27405i) q^{6} +(2.91797 + 2.91797i) q^{7} +(2.76066 + 0.615446i) q^{8} -4.51229i q^{9} +(2.94242 - 1.15852i) q^{10} -3.32134i q^{11} +(0.632099 + 5.44515i) q^{12} +(-0.313990 - 0.313990i) q^{13} +(1.91821 - 5.51168i) q^{14} +(3.99495 + 4.64778i) q^{15} +(-0.916331 - 3.89363i) q^{16} +(3.64947 - 3.64947i) q^{17} +(-5.74472 + 2.77844i) q^{18} -1.00000 q^{19} +(-3.28674 - 3.03272i) q^{20} +11.3105 q^{21} +(-4.22849 + 2.04511i) q^{22} +(2.24564 - 2.24564i) q^{23} +(6.54315 - 4.15759i) q^{24} +(-4.94327 - 0.751073i) q^{25} +(-0.206410 + 0.593088i) q^{26} +(-2.93094 - 2.93094i) q^{27} +(-8.19821 + 0.951689i) q^{28} +8.34169i q^{29} +(3.45733 - 7.94794i) q^{30} -0.286602i q^{31} +(-4.39285 + 3.56410i) q^{32} +(-6.43702 - 6.43702i) q^{33} +(-6.89340 - 2.39908i) q^{34} +(-6.99770 + 6.01479i) q^{35} +(7.07462 + 5.60294i) q^{36} +(-6.20546 + 6.20546i) q^{37} +(0.615749 + 1.27313i) q^{38} -1.21707 q^{39} +(-1.83723 + 6.05183i) q^{40} +4.08205 q^{41} +(-6.96443 - 14.3997i) q^{42} +(-1.71974 + 1.71974i) q^{43} +(5.20738 + 4.12413i) q^{44} +(10.0611 + 0.759976i) q^{45} +(-4.24174 - 1.47624i) q^{46} +(-8.21884 - 8.21884i) q^{47} +(-9.32208 - 5.77023i) q^{48} +10.0291i q^{49} +(2.08760 + 6.75588i) q^{50} -14.1459i q^{51} +(0.882173 - 0.102407i) q^{52} +(0.195783 + 0.195783i) q^{53} +(-1.92674 + 5.53619i) q^{54} +(7.40565 + 0.559392i) q^{55} +(6.25966 + 9.85136i) q^{56} +(-1.93808 + 1.93808i) q^{57} +(10.6200 - 5.13639i) q^{58} -1.88043 q^{59} +(-12.2476 + 0.492312i) q^{60} +6.98686 q^{61} +(-0.364881 + 0.176475i) q^{62} +(13.1667 - 13.1667i) q^{63} +(7.24245 + 3.39807i) q^{64} +(0.752991 - 0.647225i) q^{65} +(-4.23156 + 12.1587i) q^{66} +(0.844003 + 0.844003i) q^{67} +(1.19027 + 10.2534i) q^{68} -8.70446i q^{69} +(11.9664 + 5.20536i) q^{70} -6.69878i q^{71} +(2.77707 - 12.4569i) q^{72} +(-6.74894 - 6.74894i) q^{73} +(11.7213 + 4.07933i) q^{74} +(-11.0361 + 8.12480i) q^{75} +(1.24171 - 1.56785i) q^{76} +(9.69158 - 9.69158i) q^{77} +(0.749411 + 1.54949i) q^{78} -16.9538 q^{79} +(8.83602 - 1.38738i) q^{80} +2.17609 q^{81} +(-2.51352 - 5.19697i) q^{82} +(-4.69046 + 4.69046i) q^{83} +(-14.0443 + 17.7332i) q^{84} +(7.52263 + 8.75194i) q^{85} +(3.24838 + 1.13052i) q^{86} +(16.1668 + 16.1668i) q^{87} +(2.04411 - 9.16909i) q^{88} -9.12769i q^{89} +(-5.22759 - 13.2771i) q^{90} -1.83242i q^{91} +(0.732411 + 6.30927i) q^{92} +(-0.555457 - 0.555457i) q^{93} +(-5.40289 + 15.5244i) q^{94} +(0.168423 - 2.22972i) q^{95} +(-1.60618 + 15.4212i) q^{96} +(-5.27833 + 5.27833i) q^{97} +(12.7683 - 6.17540i) q^{98} -14.9869 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.615749	−	1.27313i	−0.435400	−	0.900237i
$2$	−0.615749	−	1.27313i	−0.435400	−	0.900237i
$3$	1.93808	−	1.93808i	1.11895	−	1.11895i	0.127054	−	0.991896i	$-0.459448\pi$
$3$	1.93808	−	1.93808i	1.11895	−	1.11895i	0.991896	−	0.127054i	$-0.0405522\pi$
$4$	−1.24171	+	1.56785i	−0.620853	+	0.783927i
$5$	−0.168423	+	2.22972i	−0.0753213	+	0.997159i
$5$	−0.168423	+	2.22972i	−0.0753213	+	0.997159i
$6$	−3.66079	−	1.27405i	−1.49451	−	0.520129i
$7$	2.91797	+	2.91797i	1.10289	+	1.10289i	0.994061	+	0.108828i	$0.0347098\pi$
$7$	2.91797	+	2.91797i	1.10289	+	1.10289i	0.108828	+	0.994061i	$0.465290\pi$
$8$	2.76066	+	0.615446i	0.976040	+	0.217593i
$9$		−	4.51229i		−	1.50410i
$10$	2.94242	−	1.15852i	0.930475	−	0.366357i
$11$		−	3.32134i		−	1.00142i	−0.865614	−	0.500711i	$-0.833072\pi$
$11$		−	3.32134i		−	1.00142i	0.865614	−	0.500711i	$-0.166928\pi$
$12$	0.632099	+	5.44515i	0.182471	+	1.57188i
$13$	−0.313990	−	0.313990i	−0.0870851	−	0.0870851i	0.662222	−	0.749307i	$-0.269613\pi$
$13$	−0.313990	−	0.313990i	−0.0870851	−	0.0870851i	−0.749307	+	0.662222i	$0.769613\pi$
$14$	1.91821	−	5.51168i	0.512663	−	1.47306i
$15$	3.99495	+	4.64778i	1.03149	+	1.20005i
$16$	−0.916331	−	3.89363i	−0.229083	−	0.973407i
$17$	3.64947	−	3.64947i	0.885127	−	0.885127i	−0.108923	−	0.994050i	$-0.534740\pi$
$17$	3.64947	−	3.64947i	0.885127	−	0.885127i	0.994050	+	0.108923i	$0.0347403\pi$
$18$	−5.74472	+	2.77844i	−1.35404	+	0.654885i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−3.28674	−	3.03272i	−0.734937	−	0.678136i
$21$	11.3105			2.46815
$22$	−4.22849	+	2.04511i	−0.901518	+	0.436020i
$23$	2.24564	−	2.24564i	0.468249	−	0.468249i	−0.433098	−	0.901347i	$-0.642580\pi$
$23$	2.24564	−	2.24564i	0.468249	−	0.468249i	0.901347	+	0.433098i	$0.142580\pi$
$24$	6.54315	−	4.15759i	1.33561	−	0.848664i
$25$	−4.94327	−	0.751073i	−0.988653	−	0.150215i
$26$	−0.206410	+	0.593088i	−0.0404803	+	0.116314i
$27$	−2.93094	−	2.93094i	−0.564060	−	0.564060i
$28$	−8.19821	+	0.951689i	−1.54932	+	0.179852i
$29$			8.34169i			1.54901i	0.632566	+	0.774506i	$0.282002\pi$
$29$			8.34169i			1.54901i	−0.632566	+	0.774506i	$0.717998\pi$
$30$	3.45733	−	7.94794i	0.631220	−	1.45109i
$31$		−	0.286602i		−	0.0514753i	−0.999669	−	0.0257376i	$-0.991807\pi$
$31$		−	0.286602i		−	0.0514753i	0.999669	−	0.0257376i	$-0.00819345\pi$
$32$	−4.39285	+	3.56410i	−0.776554	+	0.630050i
$33$	−6.43702	−	6.43702i	−1.12054	−	1.12054i
$34$	−6.89340	−	2.39908i	−1.18221	−	0.411439i
$35$	−6.99770	+	6.01479i	−1.18283	+	1.01668i
$36$	7.07462	+	5.60294i	1.17910	+	0.933824i
$37$	−6.20546	+	6.20546i	−1.02017	+	1.02017i	−0.0203790	+	0.999792i	$0.506487\pi$
$37$	−6.20546	+	6.20546i	−1.02017	+	1.02017i	−0.999792	+	0.0203790i	$0.993513\pi$
$38$	0.615749	+	1.27313i	0.0998877	+	0.206529i
$39$	−1.21707			−0.194888
$40$	−1.83723	+	6.05183i	−0.290491	+	0.956878i
$41$	4.08205			0.637509			0.318754	−	0.947837i	$-0.396735\pi$
$41$	4.08205			0.637509			0.318754	+	0.947837i	$0.396735\pi$
$42$	−6.96443	−	14.3997i	−1.07464	−	2.22192i
$43$	−1.71974	+	1.71974i	−0.262258	+	0.262258i	−0.825971	−	0.563713i	$-0.809372\pi$
$43$	−1.71974	+	1.71974i	−0.262258	+	0.262258i	0.563713	+	0.825971i	$0.309372\pi$
$44$	5.20738	+	4.12413i	0.785042	+	0.621736i
$45$	10.0611	+	0.759976i	1.49983	+	0.113291i
$46$	−4.24174	−	1.47624i	−0.625411	−	0.217659i
$47$	−8.21884	−	8.21884i	−1.19884	−	1.19884i	−0.974514	−	0.224328i	$-0.927981\pi$
$47$	−8.21884	−	8.21884i	−1.19884	−	1.19884i	−0.224328	−	0.974514i	$-0.572019\pi$
$48$	−9.32208	−	5.77023i	−1.34553	−	0.832861i
$49$			10.0291i			1.43273i
$50$	2.08760	+	6.75588i	0.295231	+	0.955426i
$51$		−	14.1459i		−	1.98082i
$52$	0.882173	−	0.102407i	0.122335	−	0.0142013i
$53$	0.195783	+	0.195783i	0.0268928	+	0.0268928i	0.720425	−	0.693533i	$-0.243947\pi$
$53$	0.195783	+	0.195783i	0.0268928	+	0.0268928i	−0.693533	+	0.720425i	$0.743947\pi$
$54$	−1.92674	+	5.53619i	−0.262196	+	0.753380i
$55$	7.40565	+	0.559392i	0.998578	+	0.0754284i
$56$	6.25966	+	9.85136i	0.836482	+	1.31644i
$57$	−1.93808	+	1.93808i	−0.256705	+	0.256705i
$58$	10.6200	−	5.13639i	1.39448	−	0.674441i
$59$	−1.88043			−0.244811			−0.122405	−	0.992480i	$-0.539061\pi$
$59$	−1.88043			−0.244811			−0.122405	+	0.992480i	$0.539061\pi$
$60$	−12.2476	+	0.492312i	−1.58116	+	0.0635572i
$61$	6.98686			0.894576			0.447288	−	0.894390i	$-0.352390\pi$
$61$	6.98686			0.894576			0.447288	+	0.894390i	$0.352390\pi$
$62$	−0.364881	+	0.176475i	−0.0463399	+	0.0224123i
$63$	13.1667	−	13.1667i	1.65885	−	1.65885i
$64$	7.24245	+	3.39807i	0.905307	+	0.424759i
$65$	0.752991	−	0.647225i	0.0933970	−	0.0802783i
$66$	−4.23156	+	12.1587i	−0.520869	+	1.49664i
$67$	0.844003	+	0.844003i	0.103111	+	0.103111i	0.756780	−	0.653669i	$-0.226771\pi$
$67$	0.844003	+	0.844003i	0.103111	+	0.103111i	−0.653669	+	0.756780i	$0.726771\pi$
$68$	1.19027	+	10.2534i	0.144341	+	1.24341i
$69$		−	8.70446i		−	1.04789i
$70$	11.9664	+	5.20536i	1.43026	+	0.622159i
$71$		−	6.69878i		−	0.794999i	−0.917602	−	0.397499i	$-0.869878\pi$
$71$		−	6.69878i		−	0.794999i	0.917602	−	0.397499i	$-0.130122\pi$
$72$	2.77707	−	12.4569i	0.327281	−	1.46806i
$73$	−6.74894	−	6.74894i	−0.789903	−	0.789903i	0.191575	−	0.981478i	$-0.438641\pi$
$73$	−6.74894	−	6.74894i	−0.789903	−	0.789903i	−0.981478	+	0.191575i	$0.938641\pi$
$74$	11.7213	+	4.07933i	1.36258	+	0.474213i
$75$	−11.0361	+	8.12480i	−1.27434	+	0.938171i
$76$	1.24171	−	1.56785i	0.142433	−	0.179845i
$77$	9.69158	−	9.69158i	1.10446	−	1.10446i
$78$	0.749411	+	1.54949i	0.0848541	+	0.175445i
$79$	−16.9538			−1.90745			−0.953726	−	0.300678i	$-0.902787\pi$
$79$	−16.9538			−1.90745			−0.953726	+	0.300678i	$0.902787\pi$
$80$	8.83602	−	1.38738i	0.987897	−	0.155114i
$81$	2.17609			0.241788
$82$	−2.51352	−	5.19697i	−0.277572	−	0.573909i
$83$	−4.69046	+	4.69046i	−0.514845	+	0.514845i	−0.916007	−	0.401162i	$-0.868606\pi$
$83$	−4.69046	+	4.69046i	−0.514845	+	0.514845i	0.401162	+	0.916007i	$0.368606\pi$
$84$	−14.0443	+	17.7332i	−1.53236	+	1.93485i
$85$	7.52263	+	8.75194i	0.815944	+	0.949281i
$86$	3.24838	+	1.13052i	0.350282	+	0.121907i
$87$	16.1668	+	16.1668i	1.73327	+	1.73327i
$88$	2.04411	−	9.16909i	0.217903	−	0.977428i
$89$		−	9.12769i		−	0.967533i	−0.875197	−	0.483767i	$-0.839268\pi$
$89$		−	9.12769i		−	0.967533i	0.875197	−	0.483767i	$-0.160732\pi$
$90$	−5.22759	−	13.2771i	−0.551036	−	1.39952i
$91$		−	1.83242i		−	0.192090i
$92$	0.732411	+	6.30927i	0.0763591	+	0.657787i
$93$	−0.555457	−	0.555457i	−0.0575982	−	0.0575982i
$94$	−5.40289	+	15.5244i	−0.557265	+	1.60122i
$95$	0.168423	−	2.22972i	0.0172799	−	0.228764i
$96$	−1.60618	+	15.4212i	−0.163930	+	1.57392i
$97$	−5.27833	+	5.27833i	−0.535933	+	0.535933i	−0.922332	−	0.386399i	$-0.873719\pi$
$97$	−5.27833	+	5.27833i	−0.535933	+	0.535933i	0.386399	+	0.922332i	$0.373719\pi$
$98$	12.7683	−	6.17540i	1.28979	−	0.623810i
$99$	−14.9869			−1.50624
$100$	7.31566	−	6.81771i	0.731566	−	0.681771i
$101$	−8.19646			−0.815578			−0.407789	−	0.913076i	$-0.633700\pi$
$101$	−8.19646			−0.815578			−0.407789	+	0.913076i	$0.633700\pi$
$102$	−18.0096	+	8.71034i	−1.78321	+	0.862452i
$103$	−13.2230	+	13.2230i	−1.30290	+	1.30290i	−0.376479	+	0.926425i	$0.622865\pi$
$103$	−13.2230	+	13.2230i	−1.30290	+	1.30290i	−0.926425	+	0.376479i	$0.877135\pi$
$104$	−0.673574	−	1.06006i	−0.0660494	−	0.103948i
$105$	−1.90495	+	25.2192i	−0.185904	+	2.46114i
$106$	0.128703	−	0.369809i	0.0125008	−	0.0359191i
$107$	8.88416	+	8.88416i	0.858864	+	0.858864i	0.991204	−	0.132340i	$-0.0422492\pi$
$107$	8.88416	+	8.88416i	0.858864	+	0.858864i	−0.132340	+	0.991204i	$0.542249\pi$
$108$	8.23466	−	0.955920i	0.792380	−	0.0919834i
$109$			5.88513i			0.563694i	0.959459	+	0.281847i	$0.0909470\pi$
$109$			5.88513i			0.563694i	−0.959459	+	0.281847i	$0.909053\pi$
$110$	−3.84785	−	9.77278i	−0.366878	−	0.931798i
$111$			24.0533i			2.28304i
$112$	8.68766	−	14.0353i	0.820907	−	1.32621i
$113$	2.15814	+	2.15814i	0.203021	+	0.203021i	0.801293	−	0.598272i	$-0.204146\pi$
$113$	2.15814	+	2.15814i	0.203021	+	0.203021i	−0.598272	+	0.801293i	$0.704146\pi$
$114$	3.66079	+	1.27405i	0.342864	+	0.119326i
$115$	4.62893	+	5.38536i	0.431650	+	0.502188i
$116$	−13.0786	−	10.3579i	−1.21431	−	0.961710i
$117$	−1.41681	+	1.41681i	−0.130984	+	0.130984i
$118$	1.15787	+	2.39402i	0.106591	+	0.220388i
$119$	21.2981			1.95239
$120$	8.16822	+	15.2896i	0.745653	+	1.39574i
$121$	−0.0313237			−0.00284761
$122$	−4.30215	−	8.89516i	−0.389499	−	0.805330i
$123$	7.91133	−	7.91133i	0.713341	−	0.713341i
$124$	0.449350	+	0.355876i	0.0403528	+	0.0319586i
$125$	2.50724	−	10.8956i	0.224254	−	0.974531i
$126$	−24.8703	−	8.65552i	−2.21563	−	0.771095i
$127$	−8.73311	−	8.73311i	−0.774938	−	0.774938i	0.204027	−	0.978965i	$-0.434597\pi$
$127$	−8.73311	−	8.73311i	−0.774938	−	0.774938i	−0.978965	+	0.204027i	$0.934597\pi$
$128$	−0.133359	−	11.3129i	−0.0117874	−	0.999931i
$129$			6.66599i			0.586907i
$130$	−1.28765	−	0.560125i	−0.112935	−	0.0491263i
$131$			6.75742i			0.590399i	0.955436	+	0.295199i	$0.0953861\pi$
$131$			6.75742i			0.590399i	−0.955436	+	0.295199i	$0.904614\pi$
$132$	18.0852	−	2.09942i	1.57411	−	0.182731i
$133$	−2.91797	−	2.91797i	−0.253020	−	0.253020i
$134$	0.554829	−	1.59422i	0.0479299	−	0.137719i
$135$	7.02881	−	6.04153i	0.604943	−	0.519972i
$136$	12.3210	−	7.82889i	1.05652	−	0.671321i
$137$	−4.40517	+	4.40517i	−0.376359	+	0.376359i	−0.869787	−	0.493428i	$-0.835744\pi$
$137$	−4.40517	+	4.40517i	−0.376359	+	0.376359i	0.493428	+	0.869787i	$0.335744\pi$
$138$	−11.0819	+	5.35976i	−0.943353	+	0.456253i
$139$	3.98115			0.337677			0.168838	−	0.985644i	$-0.445998\pi$
$139$	3.98115			0.337677			0.168838	+	0.985644i	$0.445998\pi$
$140$	−0.741224	−	18.4400i	−0.0626449	−	1.55846i
$141$	−31.8575			−2.68289
$142$	−8.52840	+	4.12477i	−0.715687	+	0.346143i
$143$	−1.04287	+	1.04287i	−0.0872090	+	0.0872090i
$144$	−17.5692	+	4.13475i	−1.46410	+	0.344563i
$145$	−18.5996	−	1.40494i	−1.54461	−	0.116674i
$146$	−4.43661	+	12.7479i	−0.367176	+	1.05502i
$147$	19.4372	+	19.4372i	1.60315	+	1.60315i
$148$	−2.02390	−	17.4346i	−0.166363	−	1.43312i
$149$		−	13.7794i		−	1.12885i	−0.825485	−	0.564425i	$-0.809098\pi$
$149$		−	13.7794i		−	1.12885i	0.825485	−	0.564425i	$-0.190902\pi$
$150$	17.1394	+	9.04749i	1.39942	+	0.738725i
$151$		−	13.9949i		−	1.13889i	−0.822030	−	0.569444i	$-0.807158\pi$
$151$		−	13.9949i		−	1.13889i	0.822030	−	0.569444i	$-0.192842\pi$
$152$	−2.76066	−	0.615446i	−0.223919	−	0.0499192i
$153$	−16.4675	−	16.4675i	−1.33132	−	1.33132i
$154$	−18.3062	−	6.37103i	−1.47516	−	0.513393i
$155$	0.639041	+	0.0482705i	0.0513290	+	0.00387718i
$156$	1.51125	−	1.90819i	0.120997	−	0.152778i
$157$	−10.6551	+	10.6551i	−0.850367	+	0.850367i	−0.990178	−	0.139811i	$-0.955351\pi$
$157$	−10.6551	+	10.6551i	−0.850367	+	0.850367i	0.139811	+	0.990178i	$0.455351\pi$
$158$	10.4393	+	21.5843i	0.830505	+	1.71716i
$159$	0.758884			0.0601834
$160$	−7.20708	−	10.3951i	−0.569770	−	0.821804i
$161$	13.1054			1.03285
$162$	−1.33993	−	2.77044i	−0.105274	−	0.217666i
$163$	1.50236	−	1.50236i	0.117674	−	0.117674i	−0.645818	−	0.763492i	$-0.723483\pi$
$163$	1.50236	−	1.50236i	0.117674	−	0.117674i	0.763492	+	0.645818i	$0.223483\pi$
$164$	−5.06871	+	6.40006i	−0.395799	+	0.499760i
$165$	15.4369	−	13.2686i	1.20176	−	1.03296i
$166$	8.85970	+	3.08341i	0.687646	+	0.239319i
$167$	−11.8667	−	11.8667i	−0.918275	−	0.918275i	0.0786286	−	0.996904i	$-0.474946\pi$
$167$	−11.8667	−	11.8667i	−0.918275	−	0.918275i	−0.996904	+	0.0786286i	$0.974946\pi$
$168$	31.2244	+	6.96100i	2.40902	+	0.537053i
$169$		−	12.8028i		−	0.984832i
$170$	6.51028	−	14.9663i	0.499316	−	1.14786i
$171$			4.51229i			0.345064i
$172$	−0.560889	−	4.83172i	−0.0427674	−	0.368415i
$173$	17.5745	+	17.5745i	1.33617	+	1.33617i	0.899739	+	0.436428i	$0.143757\pi$
$173$	17.5745	+	17.5745i	1.33617	+	1.33617i	0.436428	+	0.899739i	$0.356243\pi$
$174$	10.6277	−	30.5372i	0.805686	−	2.31502i
$175$	−12.2327	−	16.6159i	−0.924705	−	1.25604i
$176$	−12.9321	+	3.04345i	−0.974792	+	0.229409i
$177$	−3.64441	+	3.64441i	−0.273931	+	0.273931i
$178$	−11.6207	+	5.62037i	−0.871009	+	0.421264i
$179$	6.95028			0.519488			0.259744	−	0.965678i	$-0.416362\pi$
$179$	6.95028			0.519488			0.259744	+	0.965678i	$0.416362\pi$
$180$	−13.6845	+	14.8307i	−1.01998	+	1.10542i
$181$	9.68986			0.720241			0.360121	−	0.932906i	$-0.382736\pi$
$181$	9.68986			0.720241			0.360121	+	0.932906i	$0.382736\pi$
$182$	−2.33291	+	1.12831i	−0.172927	+	0.0836362i
$183$	13.5411	−	13.5411i	1.00099	−	1.00099i
$184$	7.58152	−	4.81738i	0.558917	−	0.355142i
$185$	−12.7913	−	14.8816i	−0.940433	−	1.09411i
$186$	−0.365146	+	1.04919i	−0.0267738	+	0.0769304i
$187$	−12.1211	−	12.1211i	−0.886386	−	0.886386i
$188$	23.0913	−	2.68056i	1.68411	−	0.195500i
$189$		−	17.1048i		−	1.24419i
$190$	−2.94242	+	1.15852i	−0.213466	+	0.0840479i
$191$			14.8881i			1.07727i	0.842540	+	0.538634i	$0.181059\pi$
$191$			14.8881i			1.07727i	−0.842540	+	0.538634i	$0.818941\pi$
$192$	20.6222	−	7.45072i	1.48828	−	0.537709i
$193$	5.83463	+	5.83463i	0.419986	+	0.419986i	0.885199	−	0.465213i	$-0.154022\pi$
$193$	5.83463	+	5.83463i	0.419986	+	0.419986i	−0.465213	+	0.885199i	$0.654022\pi$
$194$	9.97011	+	3.46986i	0.715812	+	0.249121i
$195$	0.204984	−	2.71373i	0.0146792	−	0.194334i
$196$	−15.7241	−	12.4532i	−1.12315	−	0.889513i
$197$	15.5394	−	15.5394i	1.10713	−	1.10713i	0.113608	−	0.993526i	$-0.463759\pi$
$197$	15.5394	−	15.5394i	1.10713	−	1.10713i	0.993526	−	0.113608i	$-0.0362407\pi$
$198$	9.22815	+	19.0802i	0.655816	+	1.35597i
$199$	21.5116			1.52492			0.762459	−	0.647036i	$-0.223992\pi$
$199$	21.5116			1.52492			0.762459	+	0.647036i	$0.223992\pi$
$200$	−13.1844	−	5.11577i	−0.932279	−	0.361739i
$201$	3.27149			0.230753
$202$	5.04696	+	10.4351i	0.355103	+	0.734213i
$203$	−24.3408	+	24.3408i	−1.70839	+	1.70839i
$204$	22.1787	+	17.5651i	1.55282	+	1.22980i
$205$	−0.687513	+	9.10181i	−0.0480180	+	0.635698i
$206$	24.9767	+	8.69253i	1.74021	+	0.605638i
$207$	−10.1330	−	10.1330i	−0.704292	−	0.704292i
$208$	−0.934840	+	1.51028i	−0.0648195	+	0.104719i
$209$			3.32134i			0.229742i
$210$	33.2802	−	13.1035i	2.29656	−	0.904224i
$211$			28.1084i			1.93506i	0.252754	+	0.967530i	$0.418664\pi$
$211$			28.1084i			1.93506i	−0.252754	+	0.967530i	$0.581336\pi$
$212$	−0.550063	+	0.0638540i	−0.0377785	+	0.00438551i
$213$	−12.9828	−	12.9828i	−0.889564	−	0.889564i
$214$	5.84025	−	16.7811i	0.399231	−	1.14713i
$215$	−3.54489	−	4.12418i	−0.241760	−	0.281267i
$216$	−6.28749	−	9.89516i	−0.427809	−	0.673280i
$217$	0.836296	−	0.836296i	0.0567715	−	0.0567715i
$218$	7.49252	−	3.62377i	0.507458	−	0.245432i
$219$	−26.1599			−1.76772
$220$	−10.0727	+	10.9164i	−0.679101	+	0.735982i
$221$	−2.29179			−0.154163
$222$	30.6230	−	14.8108i	2.05528	−	0.994037i
$223$	−5.49622	+	5.49622i	−0.368054	+	0.368054i	−0.866767	−	0.498713i	$-0.833806\pi$
$223$	−5.49622	+	5.49622i	−0.368054	+	0.368054i	0.498713	+	0.866767i	$0.333806\pi$
$224$	−23.2182	−	2.41827i	−1.55133	−	0.161577i
$225$	−3.38906	+	22.3055i	−0.225937	+	1.48703i
$226$	1.41871	−	4.07646i	0.0943715	−	0.271162i
$227$	−4.64878	−	4.64878i	−0.308550	−	0.308550i	0.535797	−	0.844347i	$-0.320011\pi$
$227$	−4.64878	−	4.64878i	−0.308550	−	0.308550i	−0.844347	+	0.535797i	$0.820011\pi$
$228$	−0.632099	−	5.44515i	−0.0418618	−	0.360614i
$229$		−	7.40542i		−	0.489364i	−0.969603	−	0.244682i	$-0.921317\pi$
$229$		−	7.40542i		−	0.489364i	0.969603	−	0.244682i	$-0.0786835\pi$
$230$	4.00600	−	9.20924i	0.264148	−	0.607240i
$231$		−	37.5661i		−	2.47167i
$232$	−5.13386	+	23.0285i	−0.337054	+	1.51190i
$233$	−19.5089	−	19.5089i	−1.27807	−	1.27807i	−0.941747	−	0.336322i	$-0.890817\pi$
$233$	−19.5089	−	19.5089i	−1.27807	−	1.27807i	−0.336322	−	0.941747i	$-0.609183\pi$
$234$	2.67619	+	0.931382i	0.174948	+	0.0608864i
$235$	19.7099	−	16.9414i	1.28573	−	1.10514i
$236$	2.33494	−	2.94823i	0.151991	−	0.191914i
$237$	−32.8578	+	32.8578i	−2.13434	+	2.13434i
$238$	−13.1143	−	27.1152i	−0.850072	−	1.75762i
$239$	5.96128			0.385603			0.192802	−	0.981238i	$-0.438243\pi$
$239$	5.96128			0.385603			0.192802	+	0.981238i	$0.438243\pi$
$240$	14.4360	−	19.8137i	0.931842	−	1.27897i
$241$	2.04156			0.131509			0.0657543	−	0.997836i	$-0.479055\pi$
$241$	2.04156			0.131509			0.0657543	+	0.997836i	$0.479055\pi$
$242$	0.0192876	+	0.0398791i	0.00123985	+	0.00256353i
$243$	13.0103	−	13.0103i	0.834609	−	0.834609i
$244$	−8.67563	+	10.9544i	−0.555400	+	0.701282i
$245$	−22.3620	−	1.68913i	−1.42866	−	0.107915i
$246$	−14.9435	−	5.20074i	−0.952764	−	0.331587i
$247$	0.313990	+	0.313990i	0.0199787	+	0.0199787i
$248$	0.176388	−	0.791210i	0.0112007	−	0.0502419i
$249$			18.1810i			1.15217i
$250$	−15.4153	+	3.51691i	−0.974949	+	0.222429i
$251$			6.12850i			0.386828i	0.981117	+	0.193414i	$0.0619560\pi$
$251$			6.12850i			0.386828i	−0.981117	+	0.193414i	$0.938044\pi$
$252$	4.29430	+	36.9927i	0.270515	+	2.33032i
$253$	−7.45855	−	7.45855i	−0.468915	−	0.468915i
$254$	−5.74096	+	16.4958i	−0.360220	+	1.03504i
$255$	31.5414	+	2.38250i	1.97520	+	0.149198i
$256$	−14.3207	+	7.13570i	−0.895042	+	0.445982i
$257$	3.57823	−	3.57823i	0.223204	−	0.223204i	−0.586642	−	0.809846i	$-0.699551\pi$
$257$	3.57823	−	3.57823i	0.223204	−	0.223204i	0.809846	+	0.586642i	$0.199551\pi$
$258$	8.48665	−	4.10457i	0.528356	−	0.255540i
$259$	−36.2147			−2.25027
$260$	0.0797598	+	1.98424i	0.00494650	+	0.123057i
$261$	37.6402			2.32987
$262$	8.60306	−	4.16088i	0.531499	−	0.257060i
$263$	4.71761	−	4.71761i	0.290900	−	0.290900i	−0.546536	−	0.837436i	$-0.684054\pi$
$263$	4.71761	−	4.71761i	0.290900	−	0.290900i	0.837436	+	0.546536i	$0.184054\pi$
$264$	−13.8088	−	21.7321i	−0.849871	−	1.33752i
$265$	−0.469514	+	0.403565i	−0.0288420	+	0.0247908i
$266$	−1.91821	+	5.51168i	−0.117613	+	0.337943i
$267$	−17.6902	−	17.6902i	−1.08262	−	1.08262i
$268$	−2.37128	+	0.275269i	−0.144849	+	0.0168148i
$269$		−	5.33876i		−	0.325510i	−0.986667	−	0.162755i	$-0.947962\pi$
$269$		−	5.33876i		−	0.325510i	0.986667	−	0.162755i	$-0.0520380\pi$
$270$	−12.0196	−	5.22850i	−0.731491	−	0.318196i
$271$		−	6.85376i		−	0.416336i	−0.978093	−	0.208168i	$-0.933250\pi$
$271$		−	6.85376i		−	0.416336i	0.978093	−	0.208168i	$-0.0667501\pi$
$272$	−17.5538	−	10.8656i	−1.06436	−	0.658821i
$273$	−3.55138	−	3.55138i	−0.214939	−	0.214939i
$274$	8.32082	+	2.89586i	0.502679	+	0.174945i
$275$	−2.49457	+	16.4183i	−0.150428	+	0.990060i
$276$	13.6473	+	10.8084i	0.821472	+	0.650588i
$277$	0.270432	−	0.270432i	0.0162487	−	0.0162487i	−0.698936	−	0.715184i	$-0.746343\pi$
$277$	0.270432	−	0.270432i	0.0162487	−	0.0162487i	0.715184	+	0.698936i	$0.246343\pi$
$278$	−2.45139	−	5.06851i	−0.147025	−	0.303989i
$279$	−1.29323			−0.0774238
$280$	−23.0200	+	12.2981i	−1.37571	+	0.734950i
$281$	23.7256			1.41535			0.707674	−	0.706539i	$-0.249745\pi$
$281$	23.7256			1.41535			0.707674	+	0.706539i	$0.249745\pi$
$282$	19.6162	+	40.5587i	1.16813	+	2.41523i
$283$	−0.320449	+	0.320449i	−0.0190487	+	0.0190487i	−0.716567	−	0.697518i	$-0.754288\pi$
$283$	−0.320449	+	0.320449i	−0.0190487	+	0.0190487i	0.697518	+	0.716567i	$0.254288\pi$
$284$	10.5027	+	8.31792i	0.623221	+	0.493578i
$285$	−3.99495	−	4.64778i	−0.236640	−	0.275311i
$286$	1.96985	+	0.685558i	0.116480	+	0.0405379i
$287$	11.9113	+	11.9113i	0.703101	+	0.703101i
$288$	16.0823	+	19.8218i	0.947657	+	1.16801i
$289$		−	9.63728i		−	0.566899i
$290$	9.66402	+	24.5447i	0.567491	+	1.44132i
$291$			20.4596i			1.19936i
$292$	18.9615	−	2.20115i	1.10964	−	0.128813i
$293$	−12.2113	−	12.2113i	−0.713390	−	0.713390i	0.253853	−	0.967243i	$-0.418302\pi$
$293$	−12.2113	−	12.2113i	−0.713390	−	0.713390i	−0.967243	+	0.253853i	$0.918302\pi$
$294$	12.7776	−	36.7144i	0.745203	−	2.14123i
$295$	0.316708	−	4.19282i	0.0184394	−	0.244115i
$296$	−20.9503	+	13.3120i	−1.21771	+	0.773746i
$297$	−9.73467	+	9.73467i	−0.564863	+	0.564863i
$298$	−17.5429	+	8.48463i	−1.01623	+	0.491501i
$299$	−1.41022			−0.0815549
$300$	0.965066	−	27.3916i	0.0557181	−	1.58145i
$301$	−10.0363			−0.578483
$302$	−17.8173	+	8.61735i	−1.02527	+	0.495873i
$303$	−15.8854	+	15.8854i	−0.912591	+	0.912591i
$304$	0.916331	+	3.89363i	0.0525552	+	0.223315i
$305$	−1.17675	+	15.5787i	−0.0673806	+	0.892035i
$306$	−10.8254	+	31.1050i	−0.618845	+	1.77816i
$307$	−3.93802	−	3.93802i	−0.224755	−	0.224755i	0.585742	−	0.810497i	$-0.300803\pi$
$307$	−3.93802	−	3.93802i	−0.224755	−	0.224755i	−0.810497	+	0.585742i	$0.800803\pi$
$308$	3.16088	+	27.2291i	0.180108	+	1.55152i
$309$			51.2545i			2.91577i
$310$	−0.332035	−	0.843304i	−0.0188583	−	0.0478964i
$311$		−	5.86740i		−	0.332710i	−0.986066	−	0.166355i	$-0.946800\pi$
$311$		−	5.86740i		−	0.332710i	0.986066	−	0.166355i	$-0.0531997\pi$
$312$	−3.35992	−	0.749042i	−0.190218	−	0.0424062i
$313$	11.5218	+	11.5218i	0.651248	+	0.651248i	0.953294	−	0.302045i	$-0.0976694\pi$
$313$	11.5218	+	11.5218i	0.651248	+	0.651248i	−0.302045	+	0.953294i	$0.597669\pi$
$314$	20.1261	+	7.00441i	1.13578	+	0.395282i
$315$	27.1405	+	31.5757i	1.52919	+	1.77909i
$316$	21.0516	−	26.5811i	1.18425	−	1.49530i
$317$	−14.2004	+	14.2004i	−0.797572	+	0.797572i	−0.982712	−	0.185140i	$-0.940726\pi$
$317$	−14.2004	+	14.2004i	−0.797572	+	0.797572i	0.185140	+	0.982712i	$0.440726\pi$
$318$	−0.467282	−	0.966156i	−0.0262039	−	0.0541794i
$319$	27.7056			1.55122
$320$	−8.79653	+	15.5763i	−0.491741	+	0.870742i
$321$	34.4364			1.92205
$322$	−8.06966	−	16.6849i	−0.449704	−	0.929812i
$323$	−3.64947	+	3.64947i	−0.203062	+	0.203062i
$324$	−2.70207	+	3.41179i	−0.150115	+	0.189544i
$325$	1.31631	+	1.78796i	0.0730155	+	0.0991784i
$326$	−2.83777	−	0.987617i	−0.157169	−	0.0546990i
$327$	11.4058	+	11.4058i	0.630745	+	0.630745i
$328$	11.2691	+	2.51228i	0.622234	+	0.138717i
$329$		−	47.9647i		−	2.64438i
$330$	−26.3978	−	11.4830i	−1.45315	−	0.632118i
$331$		−	20.0980i		−	1.10469i	−0.833617	−	0.552343i	$-0.813734\pi$
$331$		−	20.0980i		−	1.10469i	0.833617	−	0.552343i	$-0.186266\pi$
$332$	−1.52978	−	13.1781i	−0.0839577	−	0.723244i
$333$	28.0009	+	28.0009i	1.53444	+	1.53444i
$334$	−7.80093	+	22.4148i	−0.426848	+	1.22648i
$335$	−2.02404	+	1.73974i	−0.110585	+	0.0950519i
$336$	−10.3642	−	44.0389i	−0.565412	−	2.40252i
$337$	−6.14538	+	6.14538i	−0.334760	+	0.334760i	−0.854391	−	0.519631i	$-0.826069\pi$
$337$	−6.14538	+	6.14538i	−0.334760	+	0.334760i	0.519631	+	0.854391i	$0.326069\pi$
$338$	−16.2996	+	7.88332i	−0.886583	+	0.428796i
$339$	8.36529			0.454340
$340$	−23.0627	+	0.927041i	−1.25075	+	0.0502759i
$341$	−0.951904			−0.0515485
$342$	5.74472	−	2.77844i	0.310639	−	0.150241i
$343$	−8.83880	+	8.83880i	−0.477250	+	0.477250i
$344$	−5.80602	+	3.68921i	−0.313040	+	0.198909i
$345$	19.4085	+	1.46604i	1.04492	+	0.0789287i
$346$	11.5531	−	33.1961i	0.621100	−	1.78463i
$347$	−20.8203	−	20.8203i	−1.11769	−	1.11769i	−0.992079	−	0.125613i	$-0.959910\pi$
$347$	−20.8203	−	20.8203i	−1.11769	−	1.11769i	−0.125613	−	0.992079i	$-0.540090\pi$
$348$	−45.4217	+	5.27278i	−2.43486	+	0.282651i
$349$			0.392903i			0.0210316i	0.999945	+	0.0105158i	$0.00334735\pi$
$349$			0.392903i			0.0210316i	−0.999945	+	0.0105158i	$0.996653\pi$
$350$	−13.6219	+	25.8050i	−0.728121	+	1.37934i
$351$			1.84057i			0.0982424i
$352$	11.8376	+	14.5902i	0.630947	+	0.777659i
$353$	12.9637	+	12.9637i	0.689988	+	0.689988i	0.962229	−	0.272241i	$-0.0877649\pi$
$353$	12.9637	+	12.9637i	0.689988	+	0.689988i	−0.272241	+	0.962229i	$0.587765\pi$
$354$	6.88384	+	2.39576i	0.365872	+	0.127333i
$355$	14.9364	+	1.12823i	0.792741	+	0.0598803i
$356$	14.3109	+	11.3339i	0.758476	+	0.600696i
$357$	41.2774	−	41.2774i	2.18463	−	2.18463i
$358$	−4.27963	−	8.84859i	−0.226185	−	0.467662i
$359$	−11.9013			−0.628126			−0.314063	−	0.949402i	$-0.601690\pi$
$359$	−11.9013			−0.628126			−0.314063	+	0.949402i	$0.601690\pi$
$360$	27.3076	+	8.29011i	1.43924	+	0.436927i
$361$	1.00000			0.0526316
$362$	−5.96652	−	12.3364i	−0.313593	−	0.648388i
$363$	−0.0607078	+	0.0607078i	−0.00318634	+	0.00318634i
$364$	2.87297	+	2.27533i	0.150585	+	0.119260i
$365$	16.1849	−	13.9115i	0.847156	−	0.728163i
$366$	−25.5774	−	8.90161i	−1.33695	−	0.465295i
$367$	7.08566	+	7.08566i	0.369868	+	0.369868i	0.867429	−	0.497561i	$-0.165771\pi$
$367$	7.08566	+	7.08566i	0.369868	+	0.369868i	−0.497561	+	0.867429i	$0.665771\pi$
$368$	−10.8014	−	6.68594i	−0.563064	−	0.348529i
$369$		−	18.4194i		−	0.958876i
$370$	−11.0699	+	25.4482i	−0.575497	+	1.32299i
$371$			1.14258i			0.0593196i
$372$	1.56059	−	0.181161i	0.0809129	−	0.00939276i
$373$	26.3446	+	26.3446i	1.36407	+	1.36407i	0.868654	+	0.495419i	$0.164985\pi$
$373$	26.3446	+	26.3446i	1.36407	+	1.36407i	0.495419	+	0.868654i	$0.335015\pi$
$374$	−7.96818	+	22.8953i	−0.412025	+	1.18389i
$375$	−16.2573	−	25.9757i	−0.839521	−	1.34138i
$376$	−17.6312	−	27.7477i	−0.909257	−	1.43098i
$377$	2.61920	−	2.61920i	0.134896	−	0.134896i
$378$	−21.7766	+	10.5323i	−1.12007	+	0.541721i
$379$	13.5623			0.696650			0.348325	−	0.937374i	$-0.386751\pi$
$379$	13.5623			0.696650			0.348325	+	0.937374i	$0.386751\pi$
$380$	3.28674	+	3.03272i	0.168606	+	0.155575i
$381$	−33.8509			−1.73423
$382$	18.9545	−	9.16735i	0.969796	−	0.469043i
$383$	−5.92151	+	5.92151i	−0.302575	+	0.302575i	−0.842020	−	0.539446i	$-0.818634\pi$
$383$	−5.92151	+	5.92151i	−0.302575	+	0.302575i	0.539446	+	0.842020i	$0.318634\pi$
$384$	−22.1838	−	21.6669i	−1.13206	−	1.10568i
$385$	19.9772	+	23.2418i	1.01813	+	1.18451i
$386$	3.83556	−	11.0209i	0.195225	−	0.560949i
$387$	7.75998	+	7.75998i	0.394462	+	0.394462i
$388$	−1.72151	−	14.8298i	−0.0873966	−	0.752868i
$389$		−	21.4154i		−	1.08580i	−0.839796	−	0.542902i	$-0.817326\pi$
$389$		−	21.4154i		−	1.08580i	0.839796	−	0.542902i	$-0.182674\pi$
$390$	−3.58114	+	1.41000i	−0.181338	+	0.0713984i
$391$		−	16.3908i		−	0.828919i
$392$	−6.17236	+	27.6869i	−0.311751	+	1.39840i
$393$	13.0964	+	13.0964i	0.660627	+	0.660627i
$394$	−29.3519	−	10.2152i	−1.47873	−	0.514636i
$395$	2.85542	−	37.8022i	0.143672	−	1.90203i
$396$	18.6093	−	23.4972i	0.935152	−	1.18078i
$397$	7.98906	−	7.98906i	0.400960	−	0.400960i	−0.477612	−	0.878571i	$-0.658497\pi$
$397$	7.98906	−	7.98906i	0.400960	−	0.400960i	0.878571	+	0.477612i	$0.158497\pi$
$398$	−13.2458	−	27.3870i	−0.663950	−	1.37279i
$399$	−11.3105			−0.566233
$400$	1.60527	+	19.9355i	0.0802636	+	0.996774i
$401$	11.0072			0.549675			0.274838	−	0.961491i	$-0.411376\pi$
$401$	11.0072			0.549675			0.274838	+	0.961491i	$0.411376\pi$
$402$	−2.01441	−	4.16502i	−0.100470	−	0.207732i
$403$	−0.0899901	+	0.0899901i	−0.00448273	+	0.00448273i
$404$	10.1776	−	12.8508i	0.506354	−	0.639354i
$405$	−0.366505	+	4.85206i	−0.0182118	+	0.241101i
$406$	45.9768	+	16.0011i	2.28179	+	0.794122i
$407$	20.6105	+	20.6105i	1.02162	+	1.02162i
$408$	8.70605	−	39.0520i	0.431013	−	1.93336i
$409$		−	11.3378i		−	0.560617i	−0.959910	−	0.280308i	$-0.909563\pi$
$409$		−	11.3378i		−	0.560617i	0.959910	−	0.280308i	$-0.0904367\pi$
$410$	12.0111	−	4.72914i	0.593186	−	0.233556i
$411$			17.0751i			0.842254i
$412$	−4.31266	−	37.1509i	−0.212469	−	1.83029i
$413$	−5.48702	−	5.48702i	−0.269999	−	0.269999i
$414$	−6.66121	+	19.1400i	−0.327381	+	0.940679i
$415$	−9.66842	−	11.2484i	−0.474604	−	0.552161i
$416$	2.49840	+	0.260219i	0.122494	+	0.0127583i
$417$	7.71578	−	7.71578i	0.377843	−	0.377843i
$418$	4.22849	−	2.04511i	0.206822	−	0.100030i
$419$	−15.6393			−0.764030			−0.382015	−	0.924156i	$-0.624770\pi$
$419$	−15.6393			−0.764030			−0.382015	+	0.924156i	$0.624770\pi$
$420$	−37.1746	−	34.3015i	−1.81394	−	1.67374i
$421$	−21.7737			−1.06119			−0.530593	−	0.847627i	$-0.678031\pi$
$421$	−21.7737			−1.06119			−0.530593	+	0.847627i	$0.678031\pi$
$422$	35.7856	−	17.3077i	1.74201	−	0.842526i
$423$	−37.0858	+	37.0858i	−1.80317	+	1.80317i
$424$	0.419995	+	0.660982i	0.0203968	+	0.0321001i
$425$	−20.7813	+	15.2993i	−1.00804	+	0.742125i
$426$	−8.53458	+	24.5228i	−0.413502	+	1.18813i
$427$	20.3874	+	20.3874i	0.986618	+	0.986618i
$428$	−24.9606	+	2.89755i	−1.20652	+	0.140058i
$429$			4.04232i			0.195165i
$430$	−3.06784	+	7.05256i	−0.147945	+	0.340104i
$431$		−	11.7068i		−	0.563896i	−0.959430	−	0.281948i	$-0.909019\pi$
$431$		−	11.7068i		−	0.563896i	0.959430	−	0.281948i	$-0.0909805\pi$
$432$	−8.72628	+	14.0977i	−0.419844	+	0.678276i
$433$	1.08422	+	1.08422i	0.0521044	+	0.0521044i	0.732679	−	0.680574i	$-0.238270\pi$
$433$	1.08422	+	1.08422i	0.0521044	+	0.0521044i	−0.680574	+	0.732679i	$0.738270\pi$
$434$	−1.57966	−	0.549763i	−0.0758261	−	0.0263895i
$435$	−38.7704	+	33.3246i	−1.85890	+	1.59779i
$436$	−9.22703	−	7.30761i	−0.441895	−	0.349971i
$437$	−2.24564	+	2.24564i	−0.107424	+	0.107424i
$438$	16.1080	+	33.3049i	0.769668	+	1.59137i
$439$	20.1168			0.960122			0.480061	−	0.877235i	$-0.340615\pi$
$439$	20.1168			0.960122			0.480061	+	0.877235i	$0.340615\pi$
$440$	20.1002	+	6.10207i	0.958239	+	0.290905i
$441$	45.2542			2.15496
$442$	1.41117	+	2.91774i	0.0671225	+	0.138783i
$443$	−13.9904	+	13.9904i	−0.664706	+	0.664706i	−0.956485	−	0.291780i	$-0.905753\pi$
$443$	−13.9904	+	13.9904i	−0.664706	+	0.664706i	0.291780	+	0.956485i	$0.405753\pi$
$444$	−37.7121	−	29.8672i	−1.78974	−	1.41743i
$445$	20.3522	+	1.53732i	0.964785	+	0.0728758i
$446$	10.3817	+	3.61309i	0.491587	+	0.171085i
$447$	−26.7055	−	26.7055i	−1.26313	−	1.26313i
$448$	11.2178	+	31.0487i	0.529991	+	1.46691i
$449$			26.5330i			1.25217i	0.779756	+	0.626084i	$0.215343\pi$
$449$			26.5330i			1.25217i	−0.779756	+	0.626084i	$0.784657\pi$
$450$	30.4845	−	9.41987i	1.43705	−	0.444057i
$451$		−	13.5579i		−	0.638416i
$452$	−6.06342	+	0.703872i	−0.285199	+	0.0331074i
$453$	−27.1232	−	27.1232i	−1.27436	−	1.27436i
$454$	−3.05601	+	8.78097i	−0.143426	+	0.412111i
$455$	4.08579	+	0.308623i	0.191545	+	0.0144685i
$456$	−6.54315	+	4.15759i	−0.306411	+	0.194697i
$457$	12.1440	−	12.1440i	0.568072	−	0.568072i	−0.363516	−	0.931588i	$-0.618424\pi$
$457$	12.1440	−	12.1440i	0.568072	−	0.568072i	0.931588	+	0.363516i	$0.118424\pi$
$458$	−9.42804	+	4.55988i	−0.440543	+	0.213069i
$459$	−21.3928			−0.998529
$460$	−14.1912	+	0.570439i	−0.661669	+	0.0265969i
$461$	−30.9596			−1.44193			−0.720967	−	0.692970i	$-0.756302\pi$
$461$	−30.9596			−1.44193			−0.720967	+	0.692970i	$0.756302\pi$
$462$	−47.8264	+	23.1313i	−2.22509	+	1.07616i
$463$	1.55496	−	1.55496i	0.0722653	−	0.0722653i	−0.670050	−	0.742316i	$-0.733728\pi$
$463$	1.55496	−	1.55496i	0.0722653	−	0.0722653i	0.742316	+	0.670050i	$0.233728\pi$
$464$	32.4794	−	7.64375i	1.50782	−	0.354852i
$465$	1.33206	−	1.14496i	0.0617730	−	0.0530962i
$466$	−12.8247	+	36.8499i	−0.594093	+	1.70704i
$467$	5.44589	+	5.44589i	0.252006	+	0.252006i	0.821793	−	0.569787i	$-0.192974\pi$
$467$	5.44589	+	5.44589i	0.252006	+	0.252006i	−0.569787	+	0.821793i	$0.692974\pi$
$468$	−0.462090	−	3.98062i	−0.0213601	−	0.184004i
$469$			4.92555i			0.227441i
$470$	−33.7050	−	14.6616i	−1.55469	−	0.676288i
$471$			41.3007i			1.90304i
$472$	−5.19121	−	1.15730i	−0.238945	−	0.0532690i
$473$	5.71185	+	5.71185i	0.262631	+	0.262631i
$474$	62.0643	+	21.6000i	2.85071	+	0.992121i
$475$	4.94327	+	0.751073i	0.226813	+	0.0344616i
$476$	−26.4460	+	33.3923i	−1.21215	+	1.53053i
$477$	0.883429	−	0.883429i	0.0404494	−	0.0404494i
$478$	−3.67065	−	7.58947i	−0.167892	−	0.347134i
$479$	31.7741			1.45180			0.725899	−	0.687801i	$-0.241424\pi$
$479$	31.7741			1.45180			0.725899	+	0.687801i	$0.241424\pi$
$480$	−34.1144	−	6.17862i	−1.55710	−	0.282014i
$481$	3.89690			0.177683
$482$	−1.25709	−	2.59917i	−0.0572589	−	0.118389i
$483$	25.3993	−	25.3993i	1.15571	−	1.15571i
$484$	0.0388949	−	0.0491110i	0.00176795	−	0.00223232i
$485$	−10.8802	−	12.6582i	−0.494043	−	0.574778i
$486$	−24.5748	−	8.55266i	−1.11473	−	0.387957i
$487$	18.8991	+	18.8991i	0.856399	+	0.856399i	0.990912	−	0.134513i	$-0.0429470\pi$
$487$	18.8991	+	18.8991i	0.856399	+	0.856399i	−0.134513	+	0.990912i	$0.542947\pi$
$488$	19.2883	+	4.30003i	0.873141	+	0.194653i
$489$		−	5.82337i		−	0.263342i
$490$	11.6189	+	29.5098i	0.524889	+	1.33312i
$491$		−	5.90797i		−	0.266623i	−0.991074	−	0.133311i	$-0.957439\pi$
$491$		−	5.90797i		−	0.266623i	0.991074	−	0.133311i	$-0.0425611\pi$
$492$	2.58026	+	22.2274i	0.116327	+	1.00209i
$493$	30.4428	+	30.4428i	1.37107	+	1.37107i
$494$	0.206410	−	0.593088i	0.00928682	−	0.0266843i
$495$	2.52414	−	33.4165i	0.113452	−	1.50196i
$496$	−1.11592	+	0.262622i	−0.0501064	+	0.0117921i
$497$	19.5468	−	19.5468i	0.876795	−	0.876795i
$498$	23.1467	−	11.1949i	1.03723	−	0.501656i
$499$	−2.61746			−0.117173			−0.0585867	−	0.998282i	$-0.518659\pi$
$499$	−2.61746			−0.117173			−0.0585867	+	0.998282i	$0.518659\pi$
$500$	13.9694	+	17.4601i	0.624732	+	0.780840i
$501$	−45.9973			−2.05501
$502$	7.80236	−	3.77362i	0.348237	−	0.168425i
$503$	−3.79043	+	3.79043i	−0.169007	+	0.169007i	−0.786543	−	0.617536i	$-0.788131\pi$
$503$	−3.79043	+	3.79043i	−0.169007	+	0.169007i	0.617536	+	0.786543i	$0.288131\pi$
$504$	44.4522	−	28.2454i	1.98006	−	1.25815i
$505$	1.38048	−	18.2758i	0.0614304	−	0.813261i
$506$	−4.90309	+	14.0883i	−0.217969	+	0.626300i
$507$	−24.8129	−	24.8129i	−1.10198	−	1.10198i
$508$	24.5362	−	2.84828i	1.08862	−	0.126372i
$509$			9.70891i			0.430340i	0.976577	+	0.215170i	$0.0690305\pi$
$509$			9.70891i			0.430340i	−0.976577	+	0.215170i	$0.930969\pi$
$510$	−16.3883	−	41.6232i	−0.725688	−	1.84311i
$511$		−	39.3864i		−	1.74235i
$512$	17.9026	+	13.8382i	0.791191	+	0.611570i
$513$	2.93094	+	2.93094i	0.129404	+	0.129404i
$514$	−6.75883	−	2.35225i	−0.298119	−	0.103753i
$515$	−27.2565	−	31.7107i	−1.20107	−	1.39734i
$516$	−10.4513	−	8.27720i	−0.460093	−	0.364383i
$517$	−27.2976	+	27.2976i	−1.20055	+	1.20055i
$518$	22.2992	+	46.1059i	0.979769	+	2.02578i
$519$	68.1217			2.99021
$520$	2.47708	−	1.32334i	0.108627	−	0.0580323i
$521$	21.3337			0.934645			0.467323	−	0.884087i	$-0.345219\pi$
$521$	21.3337			0.934645			0.467323	+	0.884087i	$0.345219\pi$
$522$	−23.1769	−	47.9207i	−1.01442	−	2.09743i
$523$	5.64962	−	5.64962i	0.247041	−	0.247041i	−0.572714	−	0.819755i	$-0.694110\pi$
$523$	5.64962	−	5.64962i	0.247041	−	0.247041i	0.819755	+	0.572714i	$0.194110\pi$
$524$	−10.5947	−	8.39074i	−0.462830	−	0.366551i
$525$	−55.9108	−	8.49501i	−2.44015	−	0.370753i
$526$	−8.91097	−	3.10125i	−0.388537	−	0.135221i
$527$	−1.04595	−	1.04595i	−0.0455621	−	0.0455621i
$528$	−19.1649	+	30.9618i	−0.834046	+	1.34744i
$529$			12.9142i			0.561486i
$530$	0.802893	+	0.349256i	0.0348754	+	0.0151707i
$531$			8.48503i			0.368219i
$532$	8.19821	−	0.951689i	0.355438	−	0.0412609i
$533$	−1.28172	−	1.28172i	−0.0555175	−	0.0555175i
$534$	−11.6291	+	33.4146i	−0.503242	+	1.44599i
$535$	−21.3055	+	18.3129i	−0.921115	+	0.791734i
$536$	1.81056	+	2.84944i	0.0782044	+	0.123077i
$537$	13.4702	−	13.4702i	0.581281	−	0.581281i
$538$	−6.79692	+	3.28734i	−0.293036	+	0.141727i
$539$	33.3101			1.43477
$540$	0.744520	+	18.5219i	0.0320390	+	0.797058i
$541$	13.0694			0.561896			0.280948	−	0.959723i	$-0.409351\pi$
$541$	13.0694			0.561896			0.280948	+	0.959723i	$0.409351\pi$
$542$	−8.72571	+	4.22020i	−0.374801	+	0.181273i
$543$	18.7797	−	18.7797i	0.805914	−	0.805914i
$544$	−3.02450	+	29.0387i	−0.129674	+	1.24502i
$545$	−13.1222	−	0.991194i	−0.562092	−	0.0424581i
$546$	−2.33460	+	6.70812i	−0.0999117	+	0.287081i
$547$	−5.01001	−	5.01001i	−0.214212	−	0.214212i	0.591842	−	0.806054i	$-0.298401\pi$
$547$	−5.01001	−	5.01001i	−0.214212	−	0.214212i	−0.806054	+	0.591842i	$0.798401\pi$
$548$	−1.43673	−	12.3766i	−0.0613743	−	0.528702i
$549$		−	31.5268i		−	1.34553i
$550$	22.4386	−	6.93364i	0.956785	−	0.295651i
$551$		−	8.34169i		−	0.355368i
$552$	5.35712	−	24.0300i	0.228014	−	1.02279i
$553$	−49.4707	−	49.4707i	−2.10371	−	2.10371i
$554$	−0.510813	−	0.177776i	−0.0217024	−	0.00755299i
$555$	−53.6321	−	4.05114i	−2.27656	−	0.171962i
$556$	−4.94342	+	6.24186i	−0.209648	+	0.264714i
$557$	−3.98866	+	3.98866i	−0.169005	+	0.169005i	−0.786542	−	0.617537i	$-0.788131\pi$
$557$	−3.98866	+	3.98866i	−0.169005	+	0.169005i	0.617537	+	0.786542i	$0.288131\pi$
$558$	0.796307	+	1.64645i	0.0337104	+	0.0696998i
$559$	1.07996			0.0456775
$560$	29.8316	+	21.7349i	1.26061	+	0.918467i
$561$	−46.9835			−1.98364
$562$	−14.6090	−	30.2057i	−0.616243	−	1.27415i
$563$	10.0011	−	10.0011i	0.421496	−	0.421496i	−0.464223	−	0.885719i	$-0.653666\pi$
$563$	10.0011	−	10.0011i	0.421496	−	0.421496i	0.885719	+	0.464223i	$0.153666\pi$
$564$	39.5577	−	49.9479i	1.66568	−	2.10319i
$565$	−5.17552	+	4.44856i	−0.217736	+	0.187152i
$566$	0.605289	+	0.210656i	0.0254422	+	0.00885454i
$567$	6.34977	+	6.34977i	0.266665	+	0.266665i
$568$	4.12274	−	18.4930i	0.172986	−	0.775950i
$569$		−	11.0692i		−	0.464044i	−0.972711	−	0.232022i	$-0.925466\pi$
$569$		−	11.0692i		−	0.464044i	0.972711	−	0.232022i	$-0.0745341\pi$
$570$	−3.45733	+	7.94794i	−0.144812	+	0.332903i
$571$		−	11.3312i		−	0.474197i	−0.971486	−	0.237099i	$-0.923804\pi$
$571$		−	11.3312i		−	0.474197i	0.971486	−	0.237099i	$-0.0761964\pi$
$572$	−0.340129	−	2.93000i	−0.0142215	−	0.122509i
$573$	28.8544	+	28.8544i	1.20541	+	1.20541i
$574$	7.83023	−	22.4990i	0.326827	−	0.939088i
$575$	−12.7875	+	9.41417i	−0.533274	+	0.392598i
$576$	15.3331	−	32.6801i	0.638878	−	1.36167i
$577$	9.74084	−	9.74084i	0.405517	−	0.405517i	−0.474655	−	0.880172i	$-0.657427\pi$
$577$	9.74084	−	9.74084i	0.405517	−	0.405517i	0.880172	+	0.474655i	$0.157427\pi$
$578$	−12.2695	+	5.93414i	−0.510343	+	0.246828i
$579$	22.6160			0.939887
$580$	25.2980	−	27.4169i	1.05044	−	1.13843i
$581$	−27.3733			−1.13563
$582$	26.0477	−	12.5980i	1.07971	−	0.522203i
$583$	0.650262	−	0.650262i	0.0269311	−	0.0269311i
$584$	−14.4779	−	22.7851i	−0.599100	−	0.942854i
$585$	−2.92047	−	3.39772i	−0.120746	−	0.140478i
$586$	−8.02742	+	23.0656i	−0.331610	+	0.952830i
$587$	−6.85139	−	6.85139i	−0.282787	−	0.282787i	0.551432	−	0.834220i	$-0.314081\pi$
$587$	−6.85139	−	6.85139i	−0.282787	−	0.282787i	−0.834220	+	0.551432i	$0.814081\pi$
$588$	−54.6099	+	6.33938i	−2.25207	+	0.261432i
$589$			0.286602i			0.0118092i
$590$	−5.53300	+	2.17851i	−0.227790	+	0.0896879i
$591$		−	60.2330i		−	2.47765i
$592$	29.8480	+	18.4755i	1.22675	+	0.759338i
$593$	−33.6118	−	33.6118i	−1.38027	−	1.38027i	−0.844122	−	0.536151i	$-0.819878\pi$
$593$	−33.6118	−	33.6118i	−1.38027	−	1.38027i	−0.536151	−	0.844122i	$-0.680122\pi$
$594$	18.3876	+	6.39936i	0.754452	+	0.262569i
$595$	−3.58710	+	47.4887i	−0.147057	+	1.94685i
$596$	21.6040	+	17.1099i	0.884935	+	0.700850i
$597$	41.6912	−	41.6912i	1.70631	−	1.70631i
$598$	0.868340	+	1.79539i	0.0355090	+	0.0734188i
$599$	−7.79214			−0.318378			−0.159189	−	0.987248i	$-0.550888\pi$
$599$	−7.79214			−0.318378			−0.159189	+	0.987248i	$0.550888\pi$
$600$	−35.4672	+	15.6377i	−1.44794	+	0.638406i
$601$	9.32575			0.380405			0.190203	−	0.981745i	$-0.439085\pi$
$601$	9.32575			0.380405			0.190203	+	0.981745i	$0.439085\pi$
$602$	6.17985	+	12.7775i	0.251872	+	0.520772i
$603$	3.80839	−	3.80839i	0.155090	−	0.155090i
$604$	21.9420	+	17.3776i	0.892806	+	0.707083i
$605$	0.00527565	−	0.0698430i	0.000214486	−	0.00283952i
$606$	30.0055	+	10.4427i	1.21889	+	0.424206i
$607$	15.5800	+	15.5800i	0.632372	+	0.632372i	0.948662	−	0.316291i	$-0.102437\pi$
$607$	15.5800	+	15.5800i	0.632372	+	0.632372i	−0.316291	+	0.948662i	$0.602437\pi$
$608$	4.39285	−	3.56410i	0.178154	−	0.144543i
$609$			94.3487i			3.82320i
$610$	20.5583	−	8.09442i	0.832380	−	0.327734i
$611$			5.16126i			0.208802i
$612$	46.2664	−	5.37083i	1.87021	−	0.217103i
$613$	21.5286	+	21.5286i	0.869534	+	0.869534i	0.992421	−	0.122887i	$-0.0392153\pi$
$613$	21.5286	+	21.5286i	0.869534	+	0.869534i	−0.122887	+	0.992421i	$0.539215\pi$
$614$	−2.58877	+	7.43844i	−0.104474	+	0.300191i
$615$	16.3076	+	18.9725i	0.657584	+	0.765044i
$616$	32.7198	−	20.7905i	1.31832	−	0.837673i
$617$	−0.647959	+	0.647959i	−0.0260858	+	0.0260858i	−0.720029	−	0.693944i	$-0.755872\pi$
$617$	−0.647959	+	0.647959i	−0.0260858	+	0.0260858i	0.693944	+	0.720029i	$0.255872\pi$
$618$	65.2535	−	31.5599i	2.62488	−	1.26953i
$619$	30.9040			1.24214			0.621068	−	0.783757i	$-0.286699\pi$
$619$	30.9040			1.24214			0.621068	+	0.783757i	$0.286699\pi$
$620$	−0.869183	+	0.941986i	−0.0349072	+	0.0378311i
$621$	−13.1637			−0.528241
$622$	−7.46995	+	3.61285i	−0.299518	+	0.144862i
$623$	26.6343	−	26.6343i	1.06708	−	1.06708i
$624$	1.11524	+	4.73883i	0.0446454	+	0.189705i
$625$	23.8718	+	7.42551i	0.954871	+	0.297020i
$626$	7.57415	−	21.7632i	0.302724	−	0.869832i
$627$	6.43702	+	6.43702i	0.257070	+	0.257070i
$628$	−3.47513	−	29.9361i	−0.138673	−	1.19458i
$629$			45.2933i			1.80596i
$630$	23.4881	−	53.9960i	0.935789	−	2.15125i
$631$			2.36911i			0.0943127i	0.998888	+	0.0471564i	$0.0150159\pi$
$631$			2.36911i			0.0943127i	−0.998888	+	0.0471564i	$0.984984\pi$
$632$	−46.8036	−	10.4341i	−1.86175	−	0.415048i
$633$	54.4762	+	54.4762i	2.16524	+	2.16524i
$634$	26.8227	+	9.33501i	1.06527	+	0.370741i
$635$	20.9432	−	18.0015i	0.831106	−	0.714368i
$636$	−0.942311	+	1.18982i	−0.0373651	+	0.0471794i
$637$	3.14903	−	3.14903i	0.124769	−	0.124769i
$638$	−17.0597	−	35.2728i	−0.675400	−	1.39646i
$639$	−30.2269			−1.19576
$640$	25.2471	+	1.60801i	0.997978	+	0.0635621i
$641$	−4.82531			−0.190588			−0.0952941	−	0.995449i	$-0.530379\pi$
$641$	−4.82531			−0.190588			−0.0952941	+	0.995449i	$0.530379\pi$
$642$	−21.2042	−	43.8419i	−0.836862	−	1.73030i
$643$	−8.61139	+	8.61139i	−0.339600	+	0.339600i	−0.856217	−	0.516617i	$-0.827191\pi$
$643$	−8.61139	+	8.61139i	−0.339600	+	0.339600i	0.516617	+	0.856217i	$0.327191\pi$
$644$	−16.2731	+	20.5474i	−0.641250	+	0.809681i
$645$	−14.8633	−	1.12271i	−0.585240	−	0.0442066i
$646$	6.89340	+	2.39908i	0.271217	+	0.0943907i
$647$	7.54307	+	7.54307i	0.296549	+	0.296549i	0.839660	−	0.543112i	$-0.182754\pi$
$647$	7.54307	+	7.54307i	0.296549	+	0.296549i	−0.543112	+	0.839660i	$0.682754\pi$
$648$	6.00744	+	1.33927i	0.235994	+	0.0526113i
$649$			6.24554i			0.245159i
$650$	1.46579	−	2.77676i	0.0574931	−	0.108914i
$651$		−	3.24161i		−	0.127049i
$652$	0.489990	+	4.22096i	0.0191895	+	0.165306i
$653$	18.3174	+	18.3174i	0.716815	+	0.716815i	0.967952	−	0.251137i	$-0.0808044\pi$
$653$	18.3174	+	18.3174i	0.716815	+	0.716815i	−0.251137	+	0.967952i	$0.580804\pi$
$654$	7.49796	−	21.5442i	0.293193	−	0.842446i
$655$	−15.0671	−	1.13811i	−0.588722	−	0.0444696i
$656$	−3.74051	−	15.8940i	−0.146042	−	0.620556i
$657$	−30.4532	+	30.4532i	−1.18809	+	1.18809i
$658$	−61.0651	+	29.5342i	−2.38057	+	1.15136i
$659$	−27.5365			−1.07267			−0.536336	−	0.844005i	$-0.680192\pi$
$659$	−27.5365			−1.07267			−0.536336	+	0.844005i	$0.680192\pi$
$660$	1.63514	+	40.6785i	0.0636476	+	1.58341i
$661$	−4.37109			−0.170016			−0.0850078	−	0.996380i	$-0.527092\pi$
$661$	−4.37109			−0.170016			−0.0850078	+	0.996380i	$0.527092\pi$
$662$	−25.5873	+	12.3753i	−0.994480	+	0.480981i
$663$	−4.44167	+	4.44167i	−0.172500	+	0.172500i
$664$	−15.8355	+	10.0620i	−0.614536	+	0.390483i
$665$	6.99770	−	6.01479i	0.271359	−	0.233244i
$666$	18.4072	−	52.8901i	0.713263	−	2.04945i
$667$	18.7325	+	18.7325i	0.725323	+	0.725323i
$668$	33.3403	−	3.87031i	1.28997	−	0.149747i
$669$			21.3042i			0.823668i
$670$	3.46120	+	1.50561i	0.133718	+	0.0581670i
$671$		−	23.2058i		−	0.895849i
$672$	−49.6854	+	40.3118i	−1.91666	+	1.55506i
$673$	−33.4629	−	33.4629i	−1.28990	−	1.28990i	−0.934845	−	0.355057i	$-0.884461\pi$
$673$	−33.4629	−	33.4629i	−1.28990	−	1.28990i	−0.355057	−	0.934845i	$-0.615539\pi$
$674$	11.6079	+	4.03984i	0.447118	+	0.155609i
$675$	12.2871	+	16.6898i	0.472930	+	0.642390i
$676$	20.0730	+	15.8973i	0.772037	+	0.611436i
$677$	7.25738	−	7.25738i	0.278924	−	0.278924i	−0.553756	−	0.832679i	$-0.686806\pi$
$677$	7.25738	−	7.25738i	0.278924	−	0.278924i	0.832679	+	0.553756i	$0.186806\pi$
$678$	−5.15092	−	10.6501i	−0.197820	−	0.409014i
$679$	−30.8040			−1.18215
$680$	15.3810	+	28.7909i	0.589836	+	1.10408i
$681$	−18.0194			−0.690505
$682$	0.586134	+	1.21190i	0.0224442	+	0.0464059i
$683$	7.64579	−	7.64579i	0.292558	−	0.292558i	−0.545532	−	0.838090i	$-0.683672\pi$
$683$	7.64579	−	7.64579i	0.292558	−	0.292558i	0.838090	+	0.545532i	$0.183672\pi$
$684$	−7.07462	−	5.60294i	−0.270505	−	0.214234i
$685$	−9.08034	−	10.5642i	−0.346942	−	0.403638i
$686$	16.6954	+	5.81043i	0.637433	+	0.221843i
$687$	−14.3523	−	14.3523i	−0.547573	−	0.547573i
$688$	8.27189	+	5.12018i	0.315363	+	0.195205i
$689$		−	0.122947i		−	0.00468393i
$690$	−10.0843	−	25.6122i	−0.383903	−	0.975039i
$691$			38.9576i			1.48202i	0.671496	+	0.741008i	$0.265652\pi$
$691$			38.9576i			1.48202i	−0.671496	+	0.741008i	$0.734348\pi$
$692$	−49.3767	+	5.73189i	−1.87702	+	0.217894i
$693$	−43.7312	−	43.7312i	−1.66121	−	1.66121i
$694$	−13.6868	+	39.3270i	−0.519544	+	1.49283i
$695$	−0.670519	+	8.87683i	−0.0254342	+	0.336717i
$696$	34.6813	+	54.5809i	1.31459	+	2.06888i
$697$	14.8973	−	14.8973i	0.564276	−	0.564276i
$698$	0.500216	−	0.241930i	0.0189334	−	0.00915717i
$699$	−75.6195			−2.86019
$700$	41.2407	+	1.45300i	1.55875	+	0.0549183i
$701$	−14.0147			−0.529328			−0.264664	−	0.964341i	$-0.585261\pi$
$701$	−14.0147			−0.529328			−0.264664	+	0.964341i	$0.585261\pi$
$702$	2.34328	−	1.13333i	0.0884414	−	0.0427748i
$703$	6.20546	−	6.20546i	0.234043	−	0.234043i
$704$	11.2862	−	24.0547i	0.425363	−	0.906595i
$705$	5.36555	−	71.0332i	0.202078	−	2.67527i
$706$	8.52205	−	24.4868i	0.320732	−	0.921573i
$707$	−23.9170	−	23.9170i	−0.899492	−	0.899492i
$708$	−1.18862	−	10.2392i	−0.0446709	−	0.384812i
$709$		−	15.5953i		−	0.585694i	−0.956159	−	0.292847i	$-0.905397\pi$
$709$		−	15.5953i		−	0.585694i	0.956159	−	0.292847i	$-0.0946026\pi$
$710$	−7.76068	−	19.7106i	−0.291253	−	0.739726i
$711$			76.5005i			2.86899i
$712$	5.61760	−	25.1984i	0.210528	−	0.944351i
$713$	−0.643606	−	0.643606i	−0.0241032	−	0.0241032i
$714$	−77.9678	−	27.1348i	−2.91787	−	1.01550i
$715$	−2.14966	−	2.50094i	−0.0803925	−	0.0935299i
$716$	−8.63020	+	10.8970i	−0.322526	+	0.407241i
$717$	11.5534	−	11.5534i	0.431471	−	0.431471i
$718$	7.32821	+	15.1519i	0.273486	+	0.565462i
$719$	23.0710			0.860402			0.430201	−	0.902733i	$-0.358443\pi$
$719$	23.0710			0.860402			0.430201	+	0.902733i	$0.358443\pi$
$720$	−6.26026	−	39.8707i	−0.233306	−	1.48589i
$721$	−77.1688			−2.87392
$722$	−0.615749	−	1.27313i	−0.0229158	−	0.0473809i
$723$	3.95671	−	3.95671i	0.147152	−	0.147152i
$724$	−12.0320	+	15.1923i	−0.447164	+	0.564617i
$725$	6.26522	−	41.2352i	0.232684	−	1.53144i
$726$	0.114670	+	0.0399080i	0.00425579	+	0.00148113i
$727$	20.6037	+	20.6037i	0.764147	+	0.764147i	0.977069	−	0.212922i	$-0.0682980\pi$
$727$	20.6037	+	20.6037i	0.764147	+	0.764147i	−0.212922	+	0.977069i	$0.568298\pi$
$728$	1.12776	−	5.05870i	0.0417975	−	0.187488i
$729$		−	43.9015i		−	1.62598i
$730$	−27.6770	−	12.0394i	−1.02437	−	0.445599i
$731$			12.5523i			0.464263i
$732$	4.41639	+	38.0445i	0.163234	+	1.40616i
$733$	−25.5311	−	25.5311i	−0.943014	−	0.943014i	0.0554473	−	0.998462i	$-0.482342\pi$
$733$	−25.5311	−	25.5311i	−0.943014	−	0.943014i	−0.998462	+	0.0554473i	$0.982342\pi$
$734$	4.65796	−	13.3839i	0.171928	−	0.494010i
$735$	−46.6130	+	40.0657i	−1.71935	+	1.47784i
$736$	−1.86108	+	17.8685i	−0.0686002	+	0.658641i
$737$	2.80322	−	2.80322i	0.103258	−	0.103258i
$738$	−23.4502	+	11.3417i	−0.863215	+	0.417495i
$739$	42.1569			1.55077			0.775383	−	0.631491i	$-0.217557\pi$
$739$	42.1569			1.55077			0.775383	+	0.631491i	$0.217557\pi$
$740$	39.2151	−	1.57631i	1.44158	−	0.0579465i
$741$	1.21707			0.0447103
$742$	1.45464	−	0.703540i	0.0534017	−	0.0258278i
$743$	−4.93815	+	4.93815i	−0.181163	+	0.181163i	−0.791863	−	0.610699i	$-0.790888\pi$
$743$	−4.93815	+	4.93815i	−0.181163	+	0.181163i	0.610699	+	0.791863i	$0.290888\pi$
$744$	−1.19157	−	1.87528i	−0.0436852	−	0.0687511i
$745$	30.7241	+	2.32077i	1.12564	+	0.0850264i
$746$	17.3184	−	49.7617i	0.634071	−	1.82191i
$747$	21.1647	+	21.1647i	0.774377	+	0.774377i
$748$	34.0551	−	3.95328i	1.24518	−	0.144546i
$749$			51.8474i			1.89446i
$750$	−23.0600	+	36.6921i	−0.842032	+	1.33981i
$751$			28.2717i			1.03165i	0.856694	+	0.515825i	$0.172515\pi$
$751$			28.2717i			1.03165i	−0.856694	+	0.515825i	$0.827485\pi$
$752$	−24.4699	+	39.5323i	−0.892327	+	1.44159i
$753$	11.8775	+	11.8775i	0.432841	+	0.432841i
$754$	−4.94735	−	1.72181i	−0.180172	−	0.0627046i
$755$	31.2047	+	2.35707i	1.13565	+	0.0857825i
$756$	26.8178	+	21.2391i	0.975355	+	0.772460i
$757$	10.6188	−	10.6188i	0.385946	−	0.385946i	−0.487293	−	0.873239i	$-0.662016\pi$
$757$	10.6188	−	10.6188i	0.385946	−	0.385946i	0.873239	+	0.487293i	$0.162016\pi$
$758$	−8.35099	−	17.2666i	−0.303321	−	0.627150i
$759$	−28.9105			−1.04938
$760$	1.83723	−	6.05183i	0.0666433	−	0.219523i
$761$	44.9037			1.62776			0.813879	−	0.581034i	$-0.197352\pi$
$761$	44.9037			1.62776			0.813879	+	0.581034i	$0.197352\pi$
$762$	20.8437	+	43.0965i	0.755086	+	1.56122i
$763$	−17.1726	+	17.1726i	−0.621691	+	0.621691i
$764$	−23.3424	−	18.4867i	−0.844499	−	0.668825i
$765$	39.4913	−	33.9443i	1.42781	−	1.22726i
$766$	11.1850	+	3.89267i	0.404130	+	0.140648i
$767$	0.590434	+	0.590434i	0.0213193	+	0.0213193i
$768$	−13.9250	+	41.5841i	−0.502476	+	1.50054i
$769$			17.3394i			0.625274i	0.949873	+	0.312637i	$0.101212\pi$
$769$			17.3394i			0.625274i	−0.949873	+	0.312637i	$0.898788\pi$
$770$	17.2888	−	39.7446i	0.623045	−

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)

\(f(q)\)	\(=\)	\(q+(-0.615749 - 1.27313i) q^{2} +(1.93808 - 1.93808i) q^{3} +(-1.24171 + 1.56785i) q^{4} +(-0.168423 + 2.22972i) q^{5} +(-3.66079 - 1.27405i) q^{6} +(2.91797 + 2.91797i) q^{7} +(2.76066 + 0.615446i) q^{8} -4.51229i q^{9} +O(q^{10})\)	\(q+(-0.615749 - 1.27313i) q^{2} +(1.93808 - 1.93808i) q^{3} +(-1.24171 + 1.56785i) q^{4} +(-0.168423 + 2.22972i) q^{5} +(-3.66079 - 1.27405i) q^{6} +(2.91797 + 2.91797i) q^{7} +(2.76066 + 0.615446i) q^{8} -4.51229i q^{9} +(2.94242 - 1.15852i) q^{10} -3.32134i q^{11} +(0.632099 + 5.44515i) q^{12} +(-0.313990 - 0.313990i) q^{13} +(1.91821 - 5.51168i) q^{14} +(3.99495 + 4.64778i) q^{15} +(-0.916331 - 3.89363i) q^{16} +(3.64947 - 3.64947i) q^{17} +(-5.74472 + 2.77844i) q^{18} -1.00000 q^{19} +(-3.28674 - 3.03272i) q^{20} +11.3105 q^{21} +(-4.22849 + 2.04511i) q^{22} +(2.24564 - 2.24564i) q^{23} +(6.54315 - 4.15759i) q^{24} +(-4.94327 - 0.751073i) q^{25} +(-0.206410 + 0.593088i) q^{26} +(-2.93094 - 2.93094i) q^{27} +(-8.19821 + 0.951689i) q^{28} +8.34169i q^{29} +(3.45733 - 7.94794i) q^{30} -0.286602i q^{31} +(-4.39285 + 3.56410i) q^{32} +(-6.43702 - 6.43702i) q^{33} +(-6.89340 - 2.39908i) q^{34} +(-6.99770 + 6.01479i) q^{35} +(7.07462 + 5.60294i) q^{36} +(-6.20546 + 6.20546i) q^{37} +(0.615749 + 1.27313i) q^{38} -1.21707 q^{39} +(-1.83723 + 6.05183i) q^{40} +4.08205 q^{41} +(-6.96443 - 14.3997i) q^{42} +(-1.71974 + 1.71974i) q^{43} +(5.20738 + 4.12413i) q^{44} +(10.0611 + 0.759976i) q^{45} +(-4.24174 - 1.47624i) q^{46} +(-8.21884 - 8.21884i) q^{47} +(-9.32208 - 5.77023i) q^{48} +10.0291i q^{49} +(2.08760 + 6.75588i) q^{50} -14.1459i q^{51} +(0.882173 - 0.102407i) q^{52} +(0.195783 + 0.195783i) q^{53} +(-1.92674 + 5.53619i) q^{54} +(7.40565 + 0.559392i) q^{55} +(6.25966 + 9.85136i) q^{56} +(-1.93808 + 1.93808i) q^{57} +(10.6200 - 5.13639i) q^{58} -1.88043 q^{59} +(-12.2476 + 0.492312i) q^{60} +6.98686 q^{61} +(-0.364881 + 0.176475i) q^{62} +(13.1667 - 13.1667i) q^{63} +(7.24245 + 3.39807i) q^{64} +(0.752991 - 0.647225i) q^{65} +(-4.23156 + 12.1587i) q^{66} +(0.844003 + 0.844003i) q^{67} +(1.19027 + 10.2534i) q^{68} -8.70446i q^{69} +(11.9664 + 5.20536i) q^{70} -6.69878i q^{71} +(2.77707 - 12.4569i) q^{72} +(-6.74894 - 6.74894i) q^{73} +(11.7213 + 4.07933i) q^{74} +(-11.0361 + 8.12480i) q^{75} +(1.24171 - 1.56785i) q^{76} +(9.69158 - 9.69158i) q^{77} +(0.749411 + 1.54949i) q^{78} -16.9538 q^{79} +(8.83602 - 1.38738i) q^{80} +2.17609 q^{81} +(-2.51352 - 5.19697i) q^{82} +(-4.69046 + 4.69046i) q^{83} +(-14.0443 + 17.7332i) q^{84} +(7.52263 + 8.75194i) q^{85} +(3.24838 + 1.13052i) q^{86} +(16.1668 + 16.1668i) q^{87} +(2.04411 - 9.16909i) q^{88} -9.12769i q^{89} +(-5.22759 - 13.2771i) q^{90} -1.83242i q^{91} +(0.732411 + 6.30927i) q^{92} +(-0.555457 - 0.555457i) q^{93} +(-5.40289 + 15.5244i) q^{94} +(0.168423 - 2.22972i) q^{95} +(-1.60618 + 15.4212i) q^{96} +(-5.27833 + 5.27833i) q^{97} +(12.7683 - 6.17540i) q^{98} -14.9869 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

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