LMFDB - Embedded newform 380.2.k.c.267.24

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			267.24
Character	$\chi$	$=$	380.267
Dual form			380.2.k.c.343.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27313 - 0.615749i) q^{2} +(-1.93808 - 1.93808i) q^{3} +(1.24171 - 1.56785i) q^{4} +(-0.168423 - 2.22972i) q^{5} +(-3.66079 - 1.27405i) q^{6} +(-2.91797 + 2.91797i) q^{7} +(0.615446 - 2.76066i) q^{8} +4.51229i q^{9} +O(q^{10})$	\(q+(1.27313 - 0.615749i) 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} +(0.615446 - 2.76066i) q^{8} +4.51229i q^{9} +(-1.58737 - 2.73501i) q^{10} -3.32134i q^{11} +(-5.44515 + 0.632099i) 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} +(2.77844 + 5.74472i) q^{18} +1.00000 q^{19} +(-3.70500 - 2.50459i) q^{20} +11.3105 q^{21} +(-2.04511 - 4.22849i) 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} +(0.951689 + 8.19821i) q^{28} -8.34169i q^{29} +(-2.22421 + 8.37710i) q^{30} -0.286602i q^{31} +(-3.56410 - 4.39285i) 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} +(1.27313 - 0.615749i) q^{38} +1.21707 q^{39} +(-6.25914 - 0.907310i) q^{40} +4.08205 q^{41} +(14.3997 - 6.96443i) 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} +(-5.77023 + 9.32208i) q^{48} -10.0291i q^{49} +(-5.83094 + 4.00002i) q^{50} -14.1459i q^{51} +(0.102407 + 0.882173i) 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} +(-5.13639 - 10.6200i) q^{58} +1.88043 q^{59} +(2.32649 + 12.0347i) q^{60} +6.98686 q^{61} +(-0.176475 - 0.364881i) 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} +(10.2534 - 1.19027i) q^{68} +8.70446i q^{69} +(12.6126 + 3.34877i) q^{70} -6.69878i q^{71} +(12.4569 + 2.77707i) 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} +(1.54949 - 0.749411i) q^{78} +16.9538 q^{79} +(-8.52735 + 2.69894i) q^{80} +2.17609 q^{81} +(5.19697 - 2.51352i) 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} +(-9.16909 - 2.04411i) q^{88} +9.12769i q^{89} +(12.3411 - 7.16268i) q^{90} -1.83242i q^{91} +(-6.30927 + 0.732411i) 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} +(-6.17540 - 12.7683i) 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} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) $ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.27313	−	0.615749i	0.900237	−	0.435400i
$2$	1.27313	−	0.615749i	0.900237	−	0.435400i
$3$	−1.93808	−	1.93808i	−1.11895	−	1.11895i	−0.991896	−	0.127054i	$-0.959448\pi$
$3$	−1.93808	−	1.93808i	−1.11895	−	1.11895i	−0.127054	−	0.991896i	$-0.540552\pi$
$4$	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	−0.108828	+	0.994061i	$0.534710\pi$
$7$	−2.91797	+	2.91797i	−1.10289	+	1.10289i	−0.994061	+	0.108828i	$0.965290\pi$
$8$	0.615446	−	2.76066i	0.217593	−	0.976040i
$9$			4.51229i			1.50410i
$10$	−1.58737	−	2.73501i	−0.501970	−	0.864885i
$11$		−	3.32134i		−	1.00142i	−0.865614	−	0.500711i	$-0.833072\pi$
$11$		−	3.32134i		−	1.00142i	0.865614	−	0.500711i	$-0.166928\pi$
$12$	−5.44515	+	0.632099i	−1.57188	+	0.182471i
$13$	−0.313990	+	0.313990i	−0.0870851	+	0.0870851i	−0.749307	−	0.662222i	$-0.769613\pi$
$13$	−0.313990	+	0.313990i	−0.0870851	+	0.0870851i	0.662222	+	0.749307i	$0.269613\pi$
$14$	−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	0.994050	−	0.108923i	$-0.0347403\pi$
$17$	3.64947	+	3.64947i	0.885127	+	0.885127i	−0.108923	+	0.994050i	$0.534740\pi$
$18$	2.77844	+	5.74472i	0.654885	+	1.35404i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−3.70500	−	2.50459i	−0.828463	−	0.560043i
$21$	11.3105			2.46815
$22$	−2.04511	−	4.22849i	−0.436020	−	0.901518i
$23$	−2.24564	−	2.24564i	−0.468249	−	0.468249i	0.433098	−	0.901347i	$-0.357420\pi$
$23$	−2.24564	−	2.24564i	−0.468249	−	0.468249i	−0.901347	+	0.433098i	$0.857420\pi$
$24$	−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
$28$	0.951689	+	8.19821i	0.179852	+	1.54932i
$29$		−	8.34169i		−	1.54901i	−0.632566	−	0.774506i	$-0.717998\pi$
$29$		−	8.34169i		−	1.54901i	0.632566	−	0.774506i	$-0.282002\pi$
$30$	−2.22421	+	8.37710i	−0.406083	+	1.52944i
$31$		−	0.286602i		−	0.0514753i	−0.999669	−	0.0257376i	$-0.991807\pi$
$31$		−	0.286602i		−	0.0514753i	0.999669	−	0.0257376i	$-0.00819345\pi$
$32$	−3.56410	−	4.39285i	−0.630050	−	0.776554i
$33$	−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	−0.999792	−	0.0203790i	$-0.993513\pi$
$37$	−6.20546	−	6.20546i	−1.02017	−	1.02017i	−0.0203790	−	0.999792i	$-0.506487\pi$
$38$	1.27313	−	0.615749i	0.206529	−	0.0998877i
$39$	1.21707			0.194888
$40$	−6.25914	−	0.907310i	−0.989656	−	0.143458i
$41$	4.08205			0.637509			0.318754	−	0.947837i	$-0.396735\pi$
$41$	4.08205			0.637509			0.318754	+	0.947837i	$0.396735\pi$
$42$	14.3997	−	6.96443i	2.22192	−	1.07464i
$43$	1.71974	+	1.71974i	0.262258	+	0.262258i	0.825971	−	0.563713i	$-0.190628\pi$
$43$	1.71974	+	1.71974i	0.262258	+	0.262258i	−0.563713	+	0.825971i	$0.690628\pi$
$44$	−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	0.224328	−	0.974514i	$-0.427981\pi$
$47$	8.21884	−	8.21884i	1.19884	−	1.19884i	0.974514	−	0.224328i	$-0.0720186\pi$
$48$	−5.77023	+	9.32208i	−0.832861	+	1.34553i
$49$		−	10.0291i		−	1.43273i
$50$	−5.83094	+	4.00002i	−0.824619	+	0.565689i
$51$		−	14.1459i		−	1.98082i
$52$	0.102407	+	0.882173i	0.0142013	+	0.122335i
$53$	0.195783	−	0.195783i	0.0268928	−	0.0268928i	−0.693533	−	0.720425i	$-0.743947\pi$
$53$	0.195783	−	0.195783i	0.0268928	−	0.0268928i	0.720425	+	0.693533i	$0.243947\pi$
$54$	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
$58$	−5.13639	−	10.6200i	−0.674441	−	1.39448i
$59$	1.88043			0.244811			0.122405	−	0.992480i	$-0.460939\pi$
$59$	1.88043			0.244811			0.122405	+	0.992480i	$0.460939\pi$
$60$	2.32649	+	12.0347i	0.300349	+	1.55367i
$61$	6.98686			0.894576			0.447288	−	0.894390i	$-0.352390\pi$
$61$	6.98686			0.894576			0.447288	+	0.894390i	$0.352390\pi$
$62$	−0.176475	−	0.364881i	−0.0224123	−	0.0463399i
$63$	−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	$-0.773229\pi$
$67$	−0.844003	+	0.844003i	−0.103111	+	0.103111i	0.653669	+	0.756780i	$0.273229\pi$
$68$	10.2534	−	1.19027i	1.24341	−	0.144341i
$69$			8.70446i			1.04789i
$70$	12.6126	+	3.34877i	1.50749	+	0.400254i
$71$		−	6.69878i		−	0.794999i	−0.917602	−	0.397499i	$-0.869878\pi$
$71$		−	6.69878i		−	0.794999i	0.917602	−	0.397499i	$-0.130122\pi$
$72$	12.4569	+	2.77707i	1.46806	+	0.327281i
$73$	−6.74894	+	6.74894i	−0.789903	+	0.789903i	−0.981478	−	0.191575i	$-0.938641\pi$
$73$	−6.74894	+	6.74894i	−0.789903	+	0.789903i	0.191575	+	0.981478i	$0.438641\pi$
$74$	−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
$78$	1.54949	−	0.749411i	0.175445	−	0.0848541i
$79$	16.9538			1.90745			0.953726	−	0.300678i	$-0.0972130\pi$
$79$	16.9538			1.90745			0.953726	+	0.300678i	$0.0972130\pi$
$80$	−8.52735	+	2.69894i	−0.953387	+	0.301750i
$81$	2.17609			0.241788
$82$	5.19697	−	2.51352i	0.573909	−	0.277572i
$83$	4.69046	+	4.69046i	0.514845	+	0.514845i	0.916007	−	0.401162i	$-0.131394\pi$
$83$	4.69046	+	4.69046i	0.514845	+	0.514845i	−0.401162	+	0.916007i	$0.631394\pi$
$84$	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
$88$	−9.16909	−	2.04411i	−0.977428	−	0.217903i
$89$			9.12769i			0.967533i	0.875197	+	0.483767i	$0.160732\pi$
$89$			9.12769i			0.967533i	−0.875197	+	0.483767i	$0.839268\pi$
$90$	12.3411	−	7.16268i	1.30087	−	0.755013i
$91$		−	1.83242i		−	0.192090i
$92$	−6.30927	+	0.732411i	−0.657787	+	0.0763591i
$93$	−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	0.386399	−	0.922332i	$-0.373719\pi$
$97$	−5.27833	−	5.27833i	−0.535933	−	0.535933i	−0.922332	+	0.386399i	$0.873719\pi$
$98$	−6.17540	−	12.7683i	−0.623810	−	1.28979i
$99$	14.9869			1.50624
$100$	−4.96051	+	8.68293i	−0.496051	+	0.868293i
$101$	−8.19646			−0.815578			−0.407789	−	0.913076i	$-0.633700\pi$
$101$	−8.19646			−0.815578			−0.407789	+	0.913076i	$0.633700\pi$
$102$	−8.71034	−	18.0096i	−0.862452	−	1.78321i
$103$	13.2230	+	13.2230i	1.30290	+	1.30290i	0.926425	+	0.376479i	$0.122865\pi$
$103$	13.2230	+	13.2230i	1.30290	+	1.30290i	0.376479	+	0.926425i	$0.377135\pi$
$104$	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	$-0.957751\pi$
$107$	−8.88416	+	8.88416i	−0.858864	+	0.858864i	0.132340	+	0.991204i	$0.457751\pi$
$108$	−0.955920	−	8.23466i	−0.0919834	−	0.792380i
$109$		−	5.88513i		−	0.563694i	−0.959459	−	0.281847i	$-0.909053\pi$
$109$		−	5.88513i		−	0.563694i	0.959459	−	0.281847i	$-0.0909470\pi$
$110$	−9.08389	+	5.27220i	−0.866115	+	0.502685i
$111$			24.0533i			2.28304i
$112$	14.0353	+	8.68766i	1.32621	+	0.820907i
$113$	2.15814	−	2.15814i	0.203021	−	0.203021i	−0.598272	−	0.801293i	$-0.704146\pi$
$113$	2.15814	−	2.15814i	0.203021	−	0.203021i	0.801293	+	0.598272i	$0.204146\pi$
$114$	−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
$118$	2.39402	−	1.15787i	0.220388	−	0.106591i
$119$	−21.2981			−1.95239
$120$	10.3723	+	13.8891i	0.946853	+	1.26790i
$121$	−0.0313237			−0.00284761
$122$	8.89516	−	4.30215i	0.805330	−	0.389499i
$123$	−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	$-0.565403\pi$
$127$	8.73311	−	8.73311i	0.774938	−	0.774938i	0.978965	+	0.204027i	$0.0654030\pi$
$128$	−11.3129	+	0.133359i	−0.999931	+	0.0117874i
$129$		−	6.66599i		−	0.586907i
$130$	1.35718	+	0.360346i	0.119033	+	0.0316044i
$131$			6.75742i			0.590399i	0.955436	+	0.295199i	$0.0953861\pi$
$131$			6.75742i			0.590399i	−0.955436	+	0.295199i	$0.904614\pi$
$132$	2.09942	+	18.0852i	0.182731	+	1.57411i
$133$	−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	0.493428	−	0.869787i	$-0.335744\pi$
$137$	−4.40517	−	4.40517i	−0.376359	−	0.376359i	−0.869787	+	0.493428i	$0.835744\pi$
$138$	5.35976	+	11.0819i	0.456253	+	0.943353i
$139$	−3.98115			−0.337677			−0.168838	−	0.985644i	$-0.554002\pi$
$139$	−3.98115			−0.337677			−0.168838	+	0.985644i	$0.554002\pi$
$140$	18.1194	−	3.50277i	1.53137	−	0.296038i
$141$	−31.8575			−2.68289
$142$	−4.12477	−	8.52840i	−0.346143	−	0.715687i
$143$	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
$148$	−17.4346	+	2.02390i	−1.43312	+	0.166363i
$149$			13.7794i			1.12885i	0.825485	+	0.564425i	$0.190902\pi$
$149$			13.7794i			1.12885i	−0.825485	+	0.564425i	$0.809098\pi$
$150$	19.0532	+	3.54845i	1.55568	+	0.289730i
$151$		−	13.9949i		−	1.13889i	−0.822030	−	0.569444i	$-0.807158\pi$
$151$		−	13.9949i		−	1.13889i	0.822030	−	0.569444i	$-0.192842\pi$
$152$	0.615446	−	2.76066i	0.0499192	−	0.223919i
$153$	−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	0.139811	−	0.990178i	$-0.455351\pi$
$157$	−10.6551	−	10.6551i	−0.850367	−	0.850367i	−0.990178	+	0.139811i	$0.955351\pi$
$158$	21.5843	−	10.4393i	1.71716	−	0.830505i
$159$	−0.758884			−0.0601834
$160$	−9.19454	+	8.68680i	−0.726892	+	0.686752i
$161$	13.1054			1.03285
$162$	2.77044	−	1.33993i	0.217666	−	0.105274i
$163$	−1.50236	−	1.50236i	−0.117674	−	0.117674i	0.645818	−	0.763492i	$-0.276517\pi$
$163$	−1.50236	−	1.50236i	−0.117674	−	0.117674i	−0.763492	+	0.645818i	$0.776517\pi$
$164$	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	$-0.525054\pi$
$167$	11.8667	−	11.8667i	0.918275	−	0.918275i	0.996904	+	0.0786286i	$0.0250541\pi$
$168$	6.96100	−	31.2244i	0.537053	−	2.40902i
$169$			12.8028i			0.984832i
$170$	4.18826	−	15.7744i	0.321225	−	1.20984i
$171$			4.51229i			0.345064i
$172$	4.83172	−	0.560889i	0.368415	−	0.0427674i
$173$	17.5745	−	17.5745i	1.33617	−	1.33617i	0.436428	−	0.899739i	$-0.356243\pi$
$173$	17.5745	−	17.5745i	1.33617	−	1.33617i	0.899739	−	0.436428i	$-0.143757\pi$
$174$	−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
$178$	5.62037	+	11.6207i	0.421264	+	0.871009i
$179$	−6.95028			−0.519488			−0.259744	−	0.965678i	$-0.583638\pi$
$179$	−6.95028			−0.519488			−0.259744	+	0.965678i	$0.583638\pi$
$180$	11.3014	−	16.7181i	0.842360	−	1.24609i
$181$	9.68986			0.720241			0.360121	−	0.932906i	$-0.382736\pi$
$181$	9.68986			0.720241			0.360121	+	0.932906i	$0.382736\pi$
$182$	−1.12831	−	2.33291i	−0.0836362	−	0.172927i
$183$	−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
$188$	−2.68056	−	23.0913i	−0.195500	−	1.68411i
$189$			17.1048i			1.24419i
$190$	−1.58737	−	2.73501i	−0.115160	−	0.198418i
$191$			14.8881i			1.07727i	0.842540	+	0.538634i	$0.181059\pi$
$191$			14.8881i			1.07727i	−0.842540	+	0.538634i	$0.818941\pi$
$192$	7.45072	+	20.6222i	0.537709	+	1.48828i
$193$	5.83463	−	5.83463i	0.419986	−	0.419986i	−0.465213	−	0.885199i	$-0.654022\pi$
$193$	5.83463	−	5.83463i	0.419986	−	0.419986i	0.885199	+	0.465213i	$0.154022\pi$
$194$	−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	0.993526	+	0.113608i	$0.0362407\pi$
$197$	15.5394	+	15.5394i	1.10713	+	1.10713i	0.113608	+	0.993526i	$0.463759\pi$
$198$	19.0802	−	9.22815i	1.35597	−	0.655816i
$199$	−21.5116			−1.52492			−0.762459	−	0.647036i	$-0.776008\pi$
$199$	−21.5116			−1.52492			−0.762459	+	0.647036i	$0.776008\pi$
$200$	−0.968858	+	14.1089i	−0.0685086	+	0.997651i
$201$	3.27149			0.230753
$202$	−10.4351	+	5.04696i	−0.734213	+	0.355103i
$203$	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
$208$	1.51028	+	0.934840i	0.104719	+	0.0648195i
$209$		−	3.32134i		−	0.229742i
$210$	−17.9540	−	30.9343i	−1.23894	−	2.13467i
$211$			28.1084i			1.93506i	0.252754	+	0.967530i	$0.418664\pi$
$211$			28.1084i			1.93506i	−0.252754	+	0.967530i	$0.581336\pi$
$212$	−0.0638540	−	0.550063i	−0.00438551	−	0.0377785i
$213$	−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
$218$	−3.62377	−	7.49252i	−0.245432	−	0.507458i
$219$	26.1599			1.76772
$220$	−8.31860	+	12.3056i	−0.560840	+	0.829642i
$221$	−2.29179			−0.154163
$222$	14.8108	+	30.6230i	0.994037	+	2.05528i
$223$	5.49622	+	5.49622i	0.368054	+	0.368054i	0.866767	−	0.498713i	$-0.166194\pi$
$223$	5.49622	+	5.49622i	0.368054	+	0.368054i	−0.498713	+	0.866767i	$0.666194\pi$
$224$	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	$-0.679989\pi$
$227$	4.64878	−	4.64878i	0.308550	−	0.308550i	0.844347	+	0.535797i	$0.179989\pi$
$228$	−5.44515	+	0.632099i	−0.360614	+	0.0418618i
$229$			7.40542i			0.489364i	0.969603	+	0.244682i	$0.0786835\pi$
$229$			7.40542i			0.489364i	−0.969603	+	0.244682i	$0.921317\pi$
$230$	−2.57718	+	9.70651i	−0.169934	+	0.640028i
$231$		−	37.5661i		−	2.47167i
$232$	−23.0285	−	5.13386i	−1.51190	−	0.337054i
$233$	−19.5089	+	19.5089i	−1.27807	+	1.27807i	−0.336322	+	0.941747i	$0.609183\pi$
$233$	−19.5089	+	19.5089i	−1.27807	+	1.27807i	−0.941747	+	0.336322i	$0.890817\pi$
$234$	−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
$238$	−27.1152	+	13.1143i	−1.75762	+	0.850072i
$239$	−5.96128			−0.385603			−0.192802	−	0.981238i	$-0.561757\pi$
$239$	−5.96128			−0.385603			−0.192802	+	0.981238i	$0.561757\pi$
$240$	21.7574	+	11.2959i	1.40444	+	0.729149i
$241$	2.04156			0.131509			0.0657543	−	0.997836i	$-0.479055\pi$
$241$	2.04156			0.131509			0.0657543	+	0.997836i	$0.479055\pi$
$242$	−0.0398791	+	0.0192876i	−0.00256353	+	0.00123985i
$243$	−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
$248$	−0.791210	−	0.176388i	−0.0502419	−	0.0112007i
$249$		−	18.1810i		−	1.15217i
$250$	9.90098	+	12.3276i	0.626193	+	0.779668i
$251$			6.12850i			0.386828i	0.981117	+	0.193414i	$0.0619560\pi$
$251$			6.12850i			0.386828i	−0.981117	+	0.193414i	$0.938044\pi$
$252$	−36.9927	+	4.29430i	−2.33032	+	0.270515i
$253$	−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	0.809846	−	0.586642i	$-0.199551\pi$
$257$	3.57823	+	3.57823i	0.223204	+	0.223204i	−0.586642	+	0.809846i	$0.699551\pi$
$258$	−4.10457	−	8.48665i	−0.255540	−	0.528356i
$259$	36.2147			2.25027
$260$	1.94975	−	0.376917i	0.120918	−	0.0233754i
$261$	37.6402			2.32987
$262$	4.16088	+	8.60306i	0.257060	+	0.531499i
$263$	−4.71761	−	4.71761i	−0.290900	−	0.290900i	0.546536	−	0.837436i	$-0.315946\pi$
$263$	−4.71761	−	4.71761i	−0.290900	−	0.290900i	−0.837436	+	0.546536i	$0.815946\pi$
$264$	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
$268$	0.275269	+	2.37128i	0.0168148	+	0.144849i
$269$			5.33876i			0.325510i	0.986667	+	0.162755i	$0.0520380\pi$
$269$			5.33876i			0.325510i	−0.986667	+	0.162755i	$0.947962\pi$
$270$	−12.6686	−	3.36365i	−0.770988	−	0.204705i
$271$		−	6.85376i		−	0.416336i	−0.978093	−	0.208168i	$-0.933250\pi$
$271$		−	6.85376i		−	0.416336i	0.978093	−	0.208168i	$-0.0667501\pi$
$272$	10.8656	−	17.5538i	0.658821	−	1.06436i
$273$	−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	0.715184	−	0.698936i	$-0.246343\pi$
$277$	0.270432	+	0.270432i	0.0162487	+	0.0162487i	−0.698936	+	0.715184i	$0.746343\pi$
$278$	−5.06851	+	2.45139i	−0.303989	+	0.147025i
$279$	1.29323			0.0774238
$280$	20.9115	−	15.6165i	1.24970	−	0.933262i
$281$	23.7256			1.41535			0.707674	−	0.706539i	$-0.249745\pi$
$281$	23.7256			1.41535			0.707674	+	0.706539i	$0.249745\pi$
$282$	−40.5587	+	19.6162i	−2.41523	+	1.16813i
$283$	0.320449	+	0.320449i	0.0190487	+	0.0190487i	0.716567	−	0.697518i	$-0.245712\pi$
$283$	0.320449	+	0.320449i	0.0190487	+	0.0190487i	−0.697518	+	0.716567i	$0.745712\pi$
$284$	−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
$288$	19.8218	−	16.0823i	1.16801	−	0.947657i
$289$			9.63728i			0.566899i
$290$	−22.8146	+	13.2413i	−1.33972	+	0.777559i
$291$			20.4596i			1.19936i
$292$	2.20115	+	18.9615i	0.128813	+	1.10964i
$293$	−12.2113	+	12.2113i	−0.713390	+	0.713390i	−0.967243	−	0.253853i	$-0.918302\pi$
$293$	−12.2113	+	12.2113i	−0.713390	+	0.713390i	0.253853	+	0.967243i	$0.418302\pi$
$294$	−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
$298$	8.48463	+	17.5429i	0.491501	+	1.01623i
$299$	1.41022			0.0815549
$300$	26.4421	−	7.21434i	1.52663	−	0.416520i
$301$	−10.0363			−0.578483
$302$	−8.61735	−	17.8173i	−0.495873	−	1.02527i
$303$	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	$-0.699197\pi$
$307$	3.93802	−	3.93802i	0.224755	−	0.224755i	0.810497	+	0.585742i	$0.199197\pi$
$308$	27.2291	−	3.16088i	1.55152	−	0.180108i
$309$		−	51.2545i		−	2.91577i
$310$	−0.783858	+	0.454944i	−0.0445202	+	0.0258391i
$311$		−	5.86740i		−	0.332710i	−0.986066	−	0.166355i	$-0.946800\pi$
$311$		−	5.86740i		−	0.332710i	0.986066	−	0.166355i	$-0.0531997\pi$
$312$	0.749042	−	3.35992i	0.0424062	−	0.190218i
$313$	11.5218	−	11.5218i	0.651248	−	0.651248i	−0.302045	−	0.953294i	$-0.597669\pi$
$313$	11.5218	−	11.5218i	0.651248	−	0.651248i	0.953294	+	0.302045i	$0.0976694\pi$
$314$	−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	0.185140	−	0.982712i	$-0.440726\pi$
$317$	−14.2004	−	14.2004i	−0.797572	−	0.797572i	−0.982712	+	0.185140i	$0.940726\pi$
$318$	−0.966156	+	0.467282i	−0.0541794	+	0.0262039i
$319$	−27.7056			−1.55122
$320$	−6.35693	+	16.7209i	−0.355363	+	0.934728i
$321$	34.4364			1.92205
$322$	16.6849	−	8.06966i	0.929812	−	0.449704i
$323$	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
$328$	2.51228	−	11.2691i	0.138717	−	0.622234i
$329$			47.9647i			2.64438i
$330$	27.8232	+	7.38736i	1.53162	+	0.406661i
$331$		−	20.0980i		−	1.10469i	−0.833617	−	0.552343i	$-0.813734\pi$
$331$		−	20.0980i		−	1.10469i	0.833617	−	0.552343i	$-0.186266\pi$
$332$	13.1781	−	1.52978i	0.723244	−	0.0839577i
$333$	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	0.519631	−	0.854391i	$-0.326069\pi$
$337$	−6.14538	−	6.14538i	−0.334760	−	0.334760i	−0.854391	+	0.519631i	$0.826069\pi$
$338$	7.88332	+	16.2996i	0.428796	+	0.886583i
$339$	−8.36529			−0.454340
$340$	−4.38087	−	22.6617i	−0.237586	−	1.22900i
$341$	−0.951904			−0.0515485
$342$	2.77844	+	5.74472i	0.150241	+	0.310639i
$343$	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	0.125613	−	0.992079i	$-0.459910\pi$
$347$	20.8203	−	20.8203i	1.11769	−	1.11769i	0.992079	−	0.125613i	$-0.0400897\pi$
$348$	5.27278	+	45.4217i	0.282651	+	2.43486i
$349$		−	0.392903i		−	0.0210316i	−0.999945	−	0.0105158i	$-0.996653\pi$
$349$		−	0.392903i		−	0.0210316i	0.999945	−	0.0105158i	$-0.00334735\pi$
$350$	5.34255	−	28.6864i	0.285571	−	1.53335i
$351$			1.84057i			0.0982424i
$352$	−14.5902	+	11.8376i	−0.777659	+	0.630947i
$353$	12.9637	−	12.9637i	0.689988	−	0.689988i	−0.272241	−	0.962229i	$-0.587765\pi$
$353$	12.9637	−	12.9637i	0.689988	−	0.689988i	0.962229	+	0.272241i	$0.0877649\pi$
$354$	−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
$358$	−8.84859	+	4.27963i	−0.467662	+	0.226185i
$359$	11.9013			0.628126			0.314063	−	0.949402i	$-0.398310\pi$
$359$	11.9013			0.628126			0.314063	+	0.949402i	$0.398310\pi$
$360$	4.09405	−	28.2431i	0.215775	−	1.48854i
$361$	1.00000			0.0526316
$362$	12.3364	−	5.96652i	0.648388	−	0.313593i
$363$	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	$-0.834229\pi$
$367$	−7.08566	+	7.08566i	−0.369868	+	0.369868i	0.497561	+	0.867429i	$0.334229\pi$
$368$	−6.68594	+	10.8014i	−0.348529	+	0.563064i
$369$			18.4194i			0.958876i
$370$	−7.12161	+	26.8223i	−0.370235	+	1.39443i
$371$			1.14258i			0.0593196i
$372$	0.181161	+	1.56059i	0.00939276	+	0.0809129i
$373$	26.3446	−	26.3446i	1.36407	−	1.36407i	0.495419	−	0.868654i	$-0.335015\pi$
$373$	26.3446	−	26.3446i	1.36407	−	1.36407i	0.868654	−	0.495419i	$-0.164985\pi$
$374$	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
$378$	10.5323	+	21.7766i	0.541721	+	1.12007i
$379$	−13.5623			−0.696650			−0.348325	−	0.937374i	$-0.613249\pi$
$379$	−13.5623			−0.696650			−0.348325	+	0.937374i	$0.613249\pi$
$380$	−3.70500	−	2.50459i	−0.190063	−	0.128483i
$381$	−33.8509			−1.73423
$382$	9.16735	+	18.9545i	0.469043	+	0.969796i
$383$	5.92151	+	5.92151i	0.302575	+	0.302575i	0.842020	−	0.539446i	$-0.181366\pi$
$383$	5.92151	+	5.92151i	0.302575	+	0.302575i	−0.539446	+	0.842020i	$0.681366\pi$
$384$	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
$388$	−14.8298	+	1.72151i	−0.752868	+	0.0873966i
$389$			21.4154i			1.08580i	0.839796	+	0.542902i	$0.182674\pi$
$389$			21.4154i			1.08580i	−0.839796	+	0.542902i	$0.817326\pi$
$390$	−1.93194	−	3.32870i	−0.0978278	−	0.168555i
$391$		−	16.3908i		−	0.828919i
$392$	−27.6869	−	6.17236i	−1.39840	−	0.311751i
$393$	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	0.878571	−	0.477612i	$-0.158497\pi$
$397$	7.98906	+	7.98906i	0.400960	+	0.400960i	−0.477612	+	0.878571i	$0.658497\pi$
$398$	−27.3870	+	13.2458i	−1.37279	+	0.663950i
$399$	11.3105			0.566233
$400$	7.45407	+	18.5590i	0.372703	+	0.927951i
$401$	11.0072			0.549675			0.274838	−	0.961491i	$-0.411376\pi$
$401$	11.0072			0.549675			0.274838	+	0.961491i	$0.411376\pi$
$402$	4.16502	−	2.01441i	0.207732	−	0.100470i
$403$	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
$408$	−39.0520	−	8.70605i	−1.93336	−	0.431013i
$409$			11.3378i			0.560617i	0.959910	+	0.280308i	$0.0904367\pi$
$409$			11.3378i			0.560617i	−0.959910	+	0.280308i	$0.909563\pi$
$410$	−6.47972	−	11.1644i	−0.320011	−	0.551372i
$411$			17.0751i			0.842254i
$412$	37.1509	−	4.31266i	1.83029	−	0.212469i
$413$	−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
$418$	−2.04511	−	4.22849i	−0.100030	−	0.206822i
$419$	15.6393			0.764030			0.382015	−	0.924156i	$-0.375230\pi$
$419$	15.6393			0.764030			0.382015	+	0.924156i	$0.375230\pi$
$420$	−41.9054	−	28.3282i	−2.04478	−	1.38227i
$421$	−21.7737			−1.06119			−0.530593	−	0.847627i	$-0.678031\pi$
$421$	−21.7737			−1.06119			−0.530593	+	0.847627i	$0.678031\pi$
$422$	17.3077	+	35.7856i	0.842526	+	1.74201i
$423$	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
$428$	2.89755	+	24.9606i	0.140058	+	1.20652i
$429$		−	4.04232i		−	0.195165i
$430$	1.97364	−	7.43337i	0.0951772	−	0.358469i
$431$		−	11.7068i		−	0.563896i	−0.959430	−	0.281948i	$-0.909019\pi$
$431$		−	11.7068i		−	0.563896i	0.959430	−	0.281948i	$-0.0909805\pi$
$432$	−14.0977	−	8.72628i	−0.678276	−	0.419844i
$433$	1.08422	−	1.08422i	0.0521044	−	0.0521044i	−0.680574	−	0.732679i	$-0.738270\pi$
$433$	1.08422	−	1.08422i	0.0521044	−	0.0521044i	0.732679	+	0.680574i	$0.238270\pi$
$434$	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
$438$	33.3049	−	16.1080i	1.59137	−	0.769668i
$439$	−20.1168			−0.960122			−0.480061	−	0.877235i	$-0.659385\pi$
$439$	−20.1168			−0.960122			−0.480061	+	0.877235i	$0.659385\pi$
$440$	−3.01349	+	20.7887i	−0.143662	+	0.991064i
$441$	45.2542			2.15496
$442$	−2.91774	+	1.41117i	−0.138783	+	0.0671225i
$443$	13.9904	+	13.9904i	0.664706	+	0.664706i	0.956485	−	0.291780i	$-0.0942475\pi$
$443$	13.9904	+	13.9904i	0.664706	+	0.664706i	−0.291780	+	0.956485i	$0.594247\pi$
$444$	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
$448$	31.0487	−	11.2178i	1.46691	−	0.529991i
$449$		−	26.5330i		−	1.25217i	−0.779756	−	0.626084i	$-0.784657\pi$
$449$		−	26.5330i		−	1.25217i	0.779756	−	0.626084i	$-0.215343\pi$
$450$	−18.0493	−	26.3109i	−0.850851	−	1.24031i
$451$		−	13.5579i		−	0.638416i
$452$	−0.703872	−	6.06342i	−0.0331074	−	0.285199i
$453$	−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	0.931588	−	0.363516i	$-0.118424\pi$
$457$	12.1440	+	12.1440i	0.568072	+	0.568072i	−0.363516	+	0.931588i	$0.618424\pi$
$458$	4.55988	+	9.42804i	0.213069	+	0.440543i
$459$	21.3928			0.998529
$460$	2.69570	+	13.9445i	0.125687	+	0.650167i
$461$	−30.9596			−1.44193			−0.720967	−	0.692970i	$-0.756302\pi$
$461$	−30.9596			−1.44193			−0.720967	+	0.692970i	$0.756302\pi$
$462$	−23.1313	−	47.8264i	−1.07616	−	2.22509i
$463$	−1.55496	−	1.55496i	−0.0722653	−	0.0722653i	0.670050	−	0.742316i	$-0.266272\pi$
$463$	−1.55496	−	1.55496i	−0.0722653	−	0.0722653i	−0.742316	+	0.670050i	$0.766272\pi$
$464$	−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	$-0.807026\pi$
$467$	−5.44589	+	5.44589i	−0.252006	+	0.252006i	0.569787	+	0.821793i	$0.307026\pi$
$468$	−3.98062	+	0.462090i	−0.184004	+	0.0213601i
$469$		−	4.92555i		−	0.227441i
$470$	−35.5249	−	9.43224i	−1.63864	−	0.435077i
$471$			41.3007i			1.90304i
$472$	1.15730	−	5.19121i	0.0532690	−	0.238945i
$473$	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
$478$	−7.58947	+	3.67065i	−0.347134	+	0.167892i
$479$	−31.7741			−1.45180			−0.725899	−	0.687801i	$-0.758576\pi$
$479$	−31.7741			−1.45180			−0.725899	+	0.687801i	$0.758576\pi$
$480$	34.6554	+	0.984039i	1.58180	+	0.0449150i
$481$	3.89690			0.177683
$482$	2.59917	−	1.25709i	0.118389	−	0.0572589i
$483$	−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	$-0.957053\pi$
$487$	−18.8991	+	18.8991i	−0.856399	+	0.856399i	0.134513	+	0.990912i	$0.457053\pi$
$488$	4.30003	−	19.2883i	0.194653	−	0.873141i
$489$			5.82337i			0.263342i
$490$	−27.4296	+	15.9199i	−1.23914	+	0.719187i
$491$		−	5.90797i		−	0.266623i	−0.991074	−	0.133311i	$-0.957439\pi$
$491$		−	5.90797i		−	0.266623i	0.991074	−	0.133311i	$-0.0425611\pi$
$492$	−22.2274	+	2.58026i	−1.00209	+	0.116327i
$493$	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
$498$	−11.1949	−	23.1467i	−0.501656	−	1.03723i
$499$	2.61746			0.117173			0.0585867	−	0.998282i	$-0.481341\pi$
$499$	2.61746			0.117173			0.0585867	+	0.998282i	$0.481341\pi$
$500$	20.1959	+	9.59813i	0.903190	+	0.429241i
$501$	−45.9973			−2.05501
$502$	3.77362	+	7.80236i	0.168425	+	0.348237i
$503$	3.79043	+	3.79043i	0.169007	+	0.169007i	0.786543	−	0.617536i	$-0.211869\pi$
$503$	3.79043	+	3.79043i	0.169007	+	0.169007i	−0.617536	+	0.786543i	$0.711869\pi$
$504$	−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
$508$	−2.84828	−	24.5362i	−0.126372	−	1.08862i
$509$		−	9.70891i		−	0.430340i	−0.976577	−	0.215170i	$-0.930969\pi$
$509$		−	9.70891i		−	0.430340i	0.976577	−	0.215170i	$-0.0690305\pi$
$510$	−38.6892	+	22.4548i	−1.71319	+	0.994316i
$511$		−	39.3864i		−	1.74235i
$512$	−13.8382	+	17.9026i	−0.611570	+	0.791191i
$513$	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
$518$	46.1059	−	22.2992i	2.02578	−	0.979769i
$519$	−68.1217			−2.99021
$520$	2.25019	−	1.68042i	0.0986774	−	0.0736912i
$521$	21.3337			0.934645			0.467323	−	0.884087i	$-0.345219\pi$
$521$	21.3337			0.934645			0.467323	+	0.884087i	$0.345219\pi$
$522$	47.9207	−	23.1769i	2.09743	−	1.01442i
$523$	−5.64962	−	5.64962i	−0.247041	−	0.247041i	0.572714	−	0.819755i	$-0.305890\pi$
$523$	−5.64962	−	5.64962i	−0.247041	−	0.247041i	−0.819755	+	0.572714i	$0.805890\pi$
$524$	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
$528$	30.9618	+	19.1649i	1.34744	+	0.834046i
$529$		−	12.9142i		−	0.561486i
$530$	−0.846246	−	0.224687i	−0.0367586	−	0.00975979i
$531$			8.48503i			0.368219i
$532$	0.951689	+	8.19821i	0.0412609	+	0.355438i
$533$	−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
$538$	3.28734	+	6.79692i	0.141727	+	0.293036i
$539$	−33.3101			−1.43477
$540$	−18.1999	+	3.51834i	−0.783201	+	0.151405i
$541$	13.0694			0.561896			0.280948	−	0.959723i	$-0.409351\pi$
$541$	13.0694			0.561896			0.280948	+	0.959723i	$0.409351\pi$
$542$	−4.22020	−	8.72571i	−0.181273	−	0.374801i
$543$	−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	$-0.701599\pi$
$547$	5.01001	−	5.01001i	0.214212	−	0.214212i	0.806054	+	0.591842i	$0.201599\pi$
$548$	−12.3766	+	1.43673i	−0.528702	+	0.0613743i
$549$			31.5268i			1.34553i
$550$	13.2855	+	19.3665i	0.566494	+	0.825792i
$551$		−	8.34169i		−	0.355368i
$552$	24.0300	+	5.35712i	1.02279	+	0.228014i
$553$	−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	0.617537	−	0.786542i	$-0.288131\pi$
$557$	−3.98866	−	3.98866i	−0.169005	−	0.169005i	−0.786542	+	0.617537i	$0.788131\pi$
$558$	1.64645	−	0.796307i	0.0696998	−	0.0337104i
$559$	−1.07996			−0.0456775
$560$	17.0071	−	32.7580i	0.718683	−	1.38428i
$561$	−46.9835			−1.98364
$562$	30.2057	−	14.6090i	1.27415	−	0.616243i
$563$	−10.0011	−	10.0011i	−0.421496	−	0.421496i	0.464223	−	0.885719i	$-0.346334\pi$
$563$	−10.0011	−	10.0011i	−0.421496	−	0.421496i	−0.885719	+	0.464223i	$0.846334\pi$
$564$	−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
$568$	−18.4930	−	4.12274i	−0.775950	−	0.172986i
$569$			11.0692i			0.464044i	0.972711	+	0.232022i	$0.0745341\pi$
$569$			11.0692i			0.464044i	−0.972711	+	0.232022i	$0.925466\pi$
$570$	−2.22421	+	8.37710i	−0.0931618	+	0.350878i
$571$		−	11.3312i		−	0.474197i	−0.971486	−	0.237099i	$-0.923804\pi$
$571$		−	11.3312i		−	0.474197i	0.971486	−	0.237099i	$-0.0761964\pi$
$572$	2.93000	−	0.340129i	0.122509	−	0.0142215i
$573$	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	0.880172	−	0.474655i	$-0.157427\pi$
$577$	9.74084	+	9.74084i	0.405517	+	0.405517i	−0.474655	+	0.880172i	$0.657427\pi$
$578$	5.93414	+	12.2695i	0.246828	+	0.510343i
$579$	−22.6160			−0.939887
$580$	−20.8925	+	30.9060i	−0.867514	+	1.28330i
$581$	−27.3733			−1.13563
$582$	12.5980	+	26.0477i	0.522203	+	1.07971i
$583$	−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	$-0.685919\pi$
$587$	6.85139	−	6.85139i	0.282787	−	0.282787i	0.834220	+	0.551432i	$0.185919\pi$
$588$	6.33938	+	54.6099i	0.261432	+	2.25207i
$589$		−	0.286602i		−	0.0118092i
$590$	−2.98493	−	5.14298i	−0.122888	−	0.211733i
$591$		−	60.2330i		−	2.47765i
$592$	−18.4755	+	29.8480i	−0.759338	+	1.22675i
$593$	−33.6118	+	33.6118i	−1.38027	+	1.38027i	−0.536151	+	0.844122i	$0.680122\pi$
$593$	−33.6118	+	33.6118i	−1.38027	+	1.38027i	−0.844122	+	0.536151i	$0.819878\pi$
$594$	−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
$598$	1.79539	−	0.868340i	0.0734188	−	0.0355090i
$599$	7.79214			0.318378			0.159189	−	0.987248i	$-0.449112\pi$
$599$	7.79214			0.318378			0.159189	+	0.987248i	$0.449112\pi$
$600$	29.2219	−	25.4664i	1.19298	−	1.03966i
$601$	9.32575			0.380405			0.190203	−	0.981745i	$-0.439085\pi$
$601$	9.32575			0.380405			0.190203	+	0.981745i	$0.439085\pi$
$602$	−12.7775	+	6.17985i	−0.520772	+	0.251872i
$603$	−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	$-0.897563\pi$
$607$	−15.5800	+	15.5800i	−0.632372	+	0.632372i	0.316291	+	0.948662i	$0.397563\pi$
$608$	−3.56410	−	4.39285i	−0.144543	−	0.178154i
$609$		−	94.3487i		−	3.82320i
$610$	−11.0907	−	19.1091i	−0.449051	−	0.773705i
$611$			5.16126i			0.208802i
$612$	5.37083	+	46.2664i	0.217103	+	1.87021i
$613$	21.5286	−	21.5286i	0.869534	−	0.869534i	−0.122887	−	0.992421i	$-0.539215\pi$
$613$	21.5286	−	21.5286i	0.869534	−	0.869534i	0.992421	+	0.122887i	$0.0392153\pi$
$614$	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	0.693944	−	0.720029i	$-0.255872\pi$
$617$	−0.647959	−	0.647959i	−0.0260858	−	0.0260858i	−0.720029	+	0.693944i	$0.755872\pi$
$618$	−31.5599	−	65.2535i	−1.26953	−	2.62488i
$619$	−30.9040			−1.24214			−0.621068	−	0.783757i	$-0.713301\pi$
$619$	−30.9040			−1.24214			−0.621068	+	0.783757i	$0.713301\pi$
$620$	−0.717821	+	1.06186i	−0.0288284	+	0.0426454i
$621$	−13.1637			−0.528241
$622$	−3.61285	−	7.46995i	−0.144862	−	0.299518i
$623$	−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
$628$	−29.9361	+	3.47513i	−1.19458	+	0.138673i
$629$		−	45.2933i		−	1.80596i
$630$	−15.1106	+	56.9116i	−0.602021	+	2.26741i
$631$			2.36911i			0.0943127i	0.998888	+	0.0471564i	$0.0150159\pi$
$631$			2.36911i			0.0943127i	−0.998888	+	0.0471564i	$0.984984\pi$
$632$	10.4341	−	46.8036i	0.415048	−	1.86175i
$633$	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
$638$	−35.2728	+	17.0597i	−1.39646	+	0.675400i
$639$	30.2269			1.19576
$640$	2.20271	+	25.2021i	0.0870699	+	0.996202i
$641$	−4.82531			−0.190588			−0.0952941	−	0.995449i	$-0.530379\pi$
$641$	−4.82531			−0.190588			−0.0952941	+	0.995449i	$0.530379\pi$
$642$	43.8419	−	21.2042i	1.73030	−	0.836862i
$643$	8.61139	+	8.61139i	0.339600	+	0.339600i	0.856217	−	0.516617i	$-0.172809\pi$
$643$	8.61139	+	8.61139i	0.339600	+	0.339600i	−0.516617	+	0.856217i	$0.672809\pi$
$644$	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	$-0.817246\pi$
$647$	−7.54307	+	7.54307i	−0.296549	+	0.296549i	0.543112	+	0.839660i	$0.317246\pi$
$648$	1.33927	−	6.00744i	0.0526113	−	0.235994i
$649$		−	6.24554i		−	0.245159i
$650$	0.574888	−	3.08682i	0.0225489	−	0.121075i
$651$		−	3.24161i		−	0.127049i
$652$	−4.22096	+	0.489990i	−0.165306	+	0.0191895i
$653$	18.3174	−	18.3174i	0.716815	−	0.716815i	−0.251137	−	0.967952i	$-0.580804\pi$
$653$	18.3174	−	18.3174i	0.716815	−	0.716815i	0.967952	+	0.251137i	$0.0808044\pi$
$654$	−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
$658$	29.5342	+	61.0651i	1.15136	+	2.38057i
$659$	27.5365			1.07267			0.536336	−	0.844005i	$-0.319808\pi$
$659$	27.5365			1.07267			0.536336	+	0.844005i	$0.319808\pi$
$660$	39.9713	−	7.72708i	1.55588	−	0.300776i
$661$	−4.37109			−0.170016			−0.0850078	−	0.996380i	$-0.527092\pi$
$661$	−4.37109			−0.170016			−0.0850078	+	0.996380i	$0.527092\pi$
$662$	−12.3753	−	25.5873i	−0.480981	−	0.994480i
$663$	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
$668$	−3.87031	−	33.3403i	−0.149747	−	1.28997i
$669$		−	21.3042i		−	0.823668i
$670$	3.64810	+	0.968608i	0.140938	+	0.0374206i
$671$		−	23.2058i		−	0.895849i
$672$	−40.3118	−	49.6854i	−1.55506	−	1.91666i
$673$	−33.4629	+	33.4629i	−1.28990	+	1.28990i	−0.355057	+	0.934845i	$0.615539\pi$
$673$	−33.4629	+	33.4629i	−1.28990	+	1.28990i	−0.934845	+	0.355057i	$0.884461\pi$
$674$	−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	0.832679	−	0.553756i	$-0.186806\pi$
$677$	7.25738	+	7.25738i	0.278924	+	0.278924i	−0.553756	+	0.832679i	$0.686806\pi$
$678$	−10.6501	+	5.15092i	−0.409014	+	0.197820i
$679$	30.8040			1.18215
$680$	−19.5313	−	26.1537i	−0.748993	−	1.00295i
$681$	−18.0194			−0.690505
$682$	−1.21190	+	0.586134i	−0.0464059	+	0.0224442i
$683$	−7.64579	−	7.64579i	−0.292558	−	0.292558i	0.545532	−	0.838090i	$-0.316328\pi$
$683$	−7.64579	−	7.64579i	−0.292558	−	0.292558i	−0.838090	+	0.545532i	$0.816328\pi$
$684$	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
$688$	5.12018	−	8.27189i	0.195205	−	0.315363i
$689$			0.122947i			0.00468393i
$690$	23.8067	−	13.8172i	0.906307	−	0.526012i
$691$			38.9576i			1.48202i	0.671496	+	0.741008i	$0.265652\pi$
$691$			38.9576i			1.48202i	−0.671496	+	0.741008i	$0.734348\pi$
$692$	−5.73189	−	49.3767i	−0.217894	−	1.87702i
$693$	−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
$698$	−0.241930	−	0.500216i	−0.00915717	−	0.0189334i
$699$	75.6195			2.86019
$700$	−10.8619	−	39.8112i	−0.410541	−	1.50472i
$701$	−14.0147			−0.529328			−0.264664	−	0.964341i	$-0.585261\pi$
$701$	−14.0147			−0.529328			−0.264664	+	0.964341i	$0.585261\pi$
$702$	1.13333	+	2.34328i	0.0427748	+	0.0884414i
$703$	−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
$708$	−10.2392	+	1.18862i	−0.384812	+	0.0446709i
$709$			15.5953i			0.585694i	0.956159	+	0.292847i	$0.0946026\pi$
$709$			15.5953i			0.585694i	−0.956159	+	0.292847i	$0.905397\pi$
$710$	−18.3212	+	10.6334i	−0.687582	+	0.399066i
$711$			76.5005i			2.86899i
$712$	25.1984	+	5.61760i	0.944351	+	0.210528i
$713$	−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
$718$	15.1519	−	7.32821i	0.565462	−	0.273486i
$719$	−23.0710			−0.860402			−0.430201	−	0.902733i	$-0.641557\pi$
$719$	−23.0710			−0.860402			−0.430201	+	0.902733i	$0.641557\pi$
$720$	−12.1784	−	38.4779i	−0.453862	−	1.43399i
$721$	−77.1688			−2.87392
$722$	1.27313	−	0.615749i	0.0473809	−	0.0229158i
$723$	−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	$-0.931702\pi$
$727$	−20.6037	+	20.6037i	−0.764147	+	0.764147i	0.212922	+	0.977069i	$0.431702\pi$
$728$	−5.05870	−	1.12776i	−0.187488	−	0.0417975i
$729$			43.9015i			1.62598i
$730$	29.1714	+	7.74532i	1.07968	+	0.286667i
$731$			12.5523i			0.464263i
$732$	−38.0445	+	4.41639i	−1.40616	+	0.163234i
$733$	−25.5311	+	25.5311i	−0.943014	+	0.943014i	−0.998462	−	0.0554473i	$-0.982342\pi$
$733$	−25.5311	+	25.5311i	−0.943014	+	0.943014i	0.0554473	+	0.998462i	$0.482342\pi$
$734$	−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
$738$	11.3417	+	23.4502i	0.417495	+	0.863215i
$739$	−42.1569			−1.55077			−0.775383	−	0.631491i	$-0.782443\pi$
$739$	−42.1569			−1.55077			−0.775383	+	0.631491i	$0.782443\pi$
$740$	7.44911	+	38.5334i	0.273835	+	1.41651i
$741$	1.21707			0.0447103
$742$	0.703540	+	1.45464i	0.0258278	+	0.0534017i
$743$	4.93815	+	4.93815i	0.181163	+	0.181163i	0.791863	−	0.610699i	$-0.209112\pi$
$743$	4.93815	+	4.93815i	0.181163	+	0.181163i	−0.610699	+	0.791863i	$0.709112\pi$
$744$	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
$748$	−3.95328	−	34.0551i	−0.144546	−	1.24518i
$749$		−	51.8474i		−	1.89446i
$750$	4.70304	−	43.0808i	0.171731	−	1.57309i
$751$			28.2717i			1.03165i	0.856694	+	0.515825i	$0.172515\pi$
$751$			28.2717i			1.03165i	−0.856694	+	0.515825i	$0.827485\pi$
$752$	−39.5323	−	24.4699i	−1.44159	−	0.892327i
$753$	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	0.873239	−	0.487293i	$-0.162016\pi$
$757$	10.6188	+	10.6188i	0.385946	+	0.385946i	−0.487293	+	0.873239i	$0.662016\pi$
$758$	−17.2666	+	8.35099i	−0.627150	+	0.303321i
$759$	28.9105			1.04938
$760$	−6.25914	−	0.907310i	−0.227043	−	0.0329116i
$761$	44.9037			1.62776			0.813879	−	0.581034i	$-0.197352\pi$
$761$	44.9037			1.62776			0.813879	+	0.581034i	$0.197352\pi$
$762$	−43.0965	+	20.8437i	−1.56122	+	0.755086i
$763$	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
$768$	41.5841	+	13.9250i	1.50054	+	0.502476i
$769$		−	17.3394i		−	0.625274i	−0.949873	−	0.312637i	$-0.898788\pi$
$769$		−	17.3394i		−	0.625274i	0.949873	−	0.312637i	$-0.101212\pi$
$770$	11.1224	−	41.8906i	0.400824	−	1.50963i
$771$		−	13.8698i		−	0.499507i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.27313 - 0.615749i) q^{2} +(-1.93808 - 1.93808i) q^{3} +(1.24171 - 1.56785i) q^{4} +(-0.168423 - 2.22972i) q^{5} +(-3.66079 - 1.27405i) q^{6} +(-2.91797 + 2.91797i) q^{7} +(0.615446 - 2.76066i) q^{8} +4.51229i q^{9} +O(q^{10})\)	\(q+(1.27313 - 0.615749i) 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} +(0.615446 - 2.76066i) q^{8} +4.51229i q^{9} +(-1.58737 - 2.73501i) q^{10} -3.32134i q^{11} +(-5.44515 + 0.632099i) 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} +(2.77844 + 5.74472i) q^{18} +1.00000 q^{19} +(-3.70500 - 2.50459i) q^{20} +11.3105 q^{21} +(-2.04511 - 4.22849i) 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} +(0.951689 + 8.19821i) q^{28} -8.34169i q^{29} +(-2.22421 + 8.37710i) q^{30} -0.286602i q^{31} +(-3.56410 - 4.39285i) 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} +(1.27313 - 0.615749i) q^{38} +1.21707 q^{39} +(-6.25914 - 0.907310i) q^{40} +4.08205 q^{41} +(14.3997 - 6.96443i) 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} +(-5.77023 + 9.32208i) q^{48} -10.0291i q^{49} +(-5.83094 + 4.00002i) q^{50} -14.1459i q^{51} +(0.102407 + 0.882173i) 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} +(-5.13639 - 10.6200i) q^{58} +1.88043 q^{59} +(2.32649 + 12.0347i) q^{60} +6.98686 q^{61} +(-0.176475 - 0.364881i) 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} +(10.2534 - 1.19027i) q^{68} +8.70446i q^{69} +(12.6126 + 3.34877i) q^{70} -6.69878i q^{71} +(12.4569 + 2.77707i) 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} +(1.54949 - 0.749411i) q^{78} +16.9538 q^{79} +(-8.52735 + 2.69894i) q^{80} +2.17609 q^{81} +(5.19697 - 2.51352i) 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} +(-9.16909 - 2.04411i) q^{88} +9.12769i q^{89} +(12.3411 - 7.16268i) q^{90} -1.83242i q^{91} +(-6.30927 + 0.732411i) 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} +(-6.17540 - 12.7683i) 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	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Introduction

L-functions

Modular forms

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