LMFDB - Embedded newform 380.2.k.d.267.1

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			267.1
Character	$\chi$	$=$	380.267
Dual form			380.2.k.d.343.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38393 - 0.291109i) q^{2} +(-1.18694 - 1.18694i) q^{3} +(1.83051 + 0.805748i) q^{4} +(1.27222 - 1.83887i) q^{5} +(1.29711 + 1.98816i) q^{6} +(1.53689 - 1.53689i) q^{7} +(-2.29873 - 1.64798i) q^{8} -0.182360i q^{9} +O(q^{10})$	\(q+(-1.38393 - 0.291109i) q^{2} +(-1.18694 - 1.18694i) q^{3} +(1.83051 + 0.805748i) q^{4} +(1.27222 - 1.83887i) q^{5} +(1.29711 + 1.98816i) q^{6} +(1.53689 - 1.53689i) q^{7} +(-2.29873 - 1.64798i) q^{8} -0.182360i q^{9} +(-2.29598 + 2.17451i) q^{10} +3.80154i q^{11} +(-1.21633 - 3.12907i) q^{12} +(4.33858 - 4.33858i) q^{13} +(-2.57434 + 1.67954i) q^{14} +(-3.69267 + 0.672572i) q^{15} +(2.70154 + 2.94986i) q^{16} +(3.54037 + 3.54037i) q^{17} +(-0.0530865 + 0.252372i) q^{18} -1.00000 q^{19} +(3.81049 - 2.34098i) q^{20} -3.64838 q^{21} +(1.10666 - 5.26106i) q^{22} +(-3.11551 - 3.11551i) q^{23} +(0.772410 + 4.68450i) q^{24} +(-1.76289 - 4.67891i) q^{25} +(-7.26728 + 4.74128i) q^{26} +(-3.77726 + 3.77726i) q^{27} +(4.05163 - 1.57495i) q^{28} +3.00176i q^{29} +(5.30619 + 0.144180i) q^{30} -8.41277i q^{31} +(-2.88001 - 4.86884i) q^{32} +(4.51219 - 4.51219i) q^{33} +(-3.86898 - 5.93024i) q^{34} +(-0.870870 - 4.78140i) q^{35} +(0.146936 - 0.333811i) q^{36} +(-8.05718 - 8.05718i) q^{37} +(1.38393 + 0.291109i) q^{38} -10.2992 q^{39} +(-5.95492 + 2.13048i) q^{40} -2.12365 q^{41} +(5.04909 + 1.06208i) q^{42} +(2.98171 + 2.98171i) q^{43} +(-3.06308 + 6.95876i) q^{44} +(-0.335336 - 0.232002i) q^{45} +(3.40469 + 5.21860i) q^{46} +(2.50153 - 2.50153i) q^{47} +(0.294740 - 6.70786i) q^{48} +2.27595i q^{49} +(1.07763 + 6.98847i) q^{50} -8.40439i q^{51} +(11.4376 - 4.44602i) q^{52} +(-6.45515 + 6.45515i) q^{53} +(6.32705 - 4.12786i) q^{54} +(6.99054 + 4.83641i) q^{55} +(-6.06565 + 1.00014i) q^{56} +(1.18694 + 1.18694i) q^{57} +(0.873840 - 4.15422i) q^{58} +9.56354 q^{59} +(-7.30141 - 1.74421i) q^{60} -0.367160 q^{61} +(-2.44903 + 11.6427i) q^{62} +(-0.280266 - 0.280266i) q^{63} +(2.56836 + 7.57651i) q^{64} +(-2.45844 - 13.4977i) q^{65} +(-7.55808 + 4.93100i) q^{66} +(-6.11984 + 6.11984i) q^{67} +(3.62804 + 9.33332i) q^{68} +7.39584i q^{69} +(-0.186689 + 6.87064i) q^{70} -4.48386i q^{71} +(-0.300524 + 0.419196i) q^{72} +(0.985330 - 0.985330i) q^{73} +(8.80503 + 13.4961i) q^{74} +(-3.46114 + 7.64601i) q^{75} +(-1.83051 - 0.805748i) q^{76} +(5.84254 + 5.84254i) q^{77} +(14.2534 + 2.99820i) q^{78} +14.1049 q^{79} +(8.86138 - 1.21490i) q^{80} +8.41967 q^{81} +(2.93898 + 0.618215i) q^{82} +(-4.61568 - 4.61568i) q^{83} +(-6.67840 - 2.93967i) q^{84} +(11.0144 - 2.00613i) q^{85} +(-3.25847 - 4.99447i) q^{86} +(3.56290 - 3.56290i) q^{87} +(6.26484 - 8.73873i) q^{88} +10.7179i q^{89} +(0.396542 + 0.418694i) q^{90} -13.3358i q^{91} +(-3.19266 - 8.21330i) q^{92} +(-9.98543 + 9.98543i) q^{93} +(-4.19016 + 2.73372i) q^{94} +(-1.27222 + 1.83887i) q^{95} +(-2.36062 + 9.19739i) q^{96} +(11.9851 + 11.9851i) q^{97} +(0.662550 - 3.14975i) q^{98} +0.693247 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.38393	−	0.291109i	−0.978585	−	0.205845i
$2$	−1.38393	−	0.291109i	−0.978585	−	0.205845i
$3$	−1.18694	−	1.18694i	−0.685279	−	0.685279i	0.275906	−	0.961185i	$-0.411022\pi$
$3$	−1.18694	−	1.18694i	−0.685279	−	0.685279i	−0.961185	+	0.275906i	$0.911022\pi$
$4$	1.83051	+	0.805748i	0.915255	+	0.402874i
$5$	1.27222	−	1.83887i	0.568956	−	0.822368i
$5$	1.27222	−	1.83887i	0.568956	−	0.822368i
$6$	1.29711	+	1.98816i	0.529542	+	0.811664i
$7$	1.53689	−	1.53689i	0.580889	−	0.580889i	−0.354259	−	0.935148i	$-0.615267\pi$
$7$	1.53689	−	1.53689i	0.580889	−	0.580889i	0.935148	+	0.354259i	$0.115267\pi$
$8$	−2.29873	−	1.64798i	−0.812725	−	0.582647i
$9$		−	0.182360i		−	0.0607865i
$10$	−2.29598	+	2.17451i	−0.726052	+	0.687639i
$11$			3.80154i			1.14621i	0.819483	+	0.573104i	$0.194261\pi$
$11$			3.80154i			1.14621i	−0.819483	+	0.573104i	$0.805739\pi$
$12$	−1.21633	−	3.12907i	−0.351124	−	0.903286i
$13$	4.33858	−	4.33858i	1.20331	−	1.20331i	0.230151	−	0.973155i	$-0.426078\pi$
$13$	4.33858	−	4.33858i	1.20331	−	1.20331i	0.973155	−	0.230151i	$-0.0739219\pi$
$14$	−2.57434	+	1.67954i	−0.688022	+	0.448876i
$15$	−3.69267	+	0.672572i	−0.953445	+	0.173657i
$16$	2.70154	+	2.94986i	0.675385	+	0.737465i
$17$	3.54037	+	3.54037i	0.858665	+	0.858665i	0.991181	−	0.132516i	$-0.0423056\pi$
$17$	3.54037	+	3.54037i	0.858665	+	0.858665i	−0.132516	+	0.991181i	$0.542306\pi$
$18$	−0.0530865	+	0.252372i	−0.0125126	+	0.0594847i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	3.81049	−	2.34098i	0.852051	−	0.523459i
$21$	−3.64838			−0.796142
$22$	1.10666	−	5.26106i	0.235941	−	1.12166i
$23$	−3.11551	−	3.11551i	−0.649630	−	0.649630i	0.303274	−	0.952903i	$-0.401920\pi$
$23$	−3.11551	−	3.11551i	−0.649630	−	0.649630i	−0.952903	+	0.303274i	$0.901920\pi$
$24$	0.772410	+	4.68450i	0.157668	+	0.956219i
$25$	−1.76289	−	4.67891i	−0.352577	−	0.935783i
$26$	−7.26728	+	4.74128i	−1.42523	+	0.929842i
$27$	−3.77726	+	3.77726i	−0.726934	+	0.726934i
$28$	4.05163	−	1.57495i	0.765687	−	0.297637i
$29$			3.00176i			0.557413i	0.960376	+	0.278706i	$0.0899056\pi$
$29$			3.00176i			0.557413i	−0.960376	+	0.278706i	$0.910094\pi$
$30$	5.30619	+	0.144180i	0.968773	+	0.0263235i
$31$		−	8.41277i		−	1.51098i	−0.655161	−	0.755489i	$-0.727399\pi$
$31$		−	8.41277i		−	1.51098i	0.655161	−	0.755489i	$-0.272601\pi$
$32$	−2.88001	−	4.86884i	−0.509118	−	0.860697i
$33$	4.51219	−	4.51219i	0.785471	−	0.785471i
$34$	−3.86898	−	5.93024i	−0.663524	−	1.01703i
$35$	−0.870870	−	4.78140i	−0.147204	−	0.808205i
$36$	0.146936	−	0.333811i	0.0244893	−	0.0556352i
$37$	−8.05718	−	8.05718i	−1.32459	−	1.32459i	−0.910014	−	0.414578i	$-0.863929\pi$
$37$	−8.05718	−	8.05718i	−1.32459	−	1.32459i	−0.414578	−	0.910014i	$-0.636071\pi$
$38$	1.38393	+	0.291109i	0.224503	+	0.0472241i
$39$	−10.2992			−1.64920
$40$	−5.95492	+	2.13048i	−0.941555	+	0.336858i
$41$	−2.12365			−0.331659			−0.165830	−	0.986154i	$-0.553030\pi$
$41$	−2.12365			−0.331659			−0.165830	+	0.986154i	$0.553030\pi$
$42$	5.04909	+	1.06208i	0.779092	+	0.163882i
$43$	2.98171	+	2.98171i	0.454706	+	0.454706i	0.896913	−	0.442207i	$-0.145804\pi$
$43$	2.98171	+	2.98171i	0.454706	+	0.454706i	−0.442207	+	0.896913i	$0.645804\pi$
$44$	−3.06308	+	6.95876i	−0.461777	+	1.04907i
$45$	−0.335336	−	0.232002i	−0.0499889	−	0.0345849i
$46$	3.40469	+	5.21860i	0.501994	+	0.769441i
$47$	2.50153	−	2.50153i	0.364886	−	0.364886i	−0.500722	−	0.865608i	$-0.666932\pi$
$47$	2.50153	−	2.50153i	0.364886	−	0.364886i	0.865608	+	0.500722i	$0.166932\pi$
$48$	0.294740	−	6.70786i	0.0425420	−	0.968196i
$49$			2.27595i			0.325136i
$50$	1.07763	+	6.98847i	0.152400	+	0.988319i
$51$		−	8.40439i		−	1.17685i
$52$	11.4376	−	4.44602i	1.58611	−	0.616552i
$53$	−6.45515	+	6.45515i	−0.886684	+	0.886684i	−0.994203	−	0.107519i	$-0.965709\pi$
$53$	−6.45515	+	6.45515i	−0.886684	+	0.886684i	0.107519	+	0.994203i	$0.465709\pi$
$54$	6.32705	−	4.12786i	0.861003	−	0.561731i
$55$	6.99054	+	4.83641i	0.942604	+	0.652142i
$56$	−6.06565	+	1.00014i	−0.810556	+	0.133650i
$57$	1.18694	+	1.18694i	0.157214	+	0.157214i
$58$	0.873840	−	4.15422i	0.114741	−	0.545476i
$59$	9.56354			1.24507			0.622533	−	0.782593i	$-0.286103\pi$
$59$	9.56354			1.24507			0.622533	+	0.782593i	$0.286103\pi$
$60$	−7.30141	−	1.74421i	−0.942607	−	0.225177i
$61$	−0.367160			−0.0470101			−0.0235050	−	0.999724i	$-0.507483\pi$
$61$	−0.367160			−0.0470101			−0.0235050	+	0.999724i	$0.507483\pi$
$62$	−2.44903	+	11.6427i	−0.311028	+	1.47862i
$63$	−0.280266	−	0.280266i	−0.0353102	−	0.0353102i
$64$	2.56836	+	7.57651i	0.321045	+	0.947064i
$65$	−2.45844	−	13.4977i	−0.304931	−	1.67419i
$66$	−7.55808	+	4.93100i	−0.930336	+	0.606965i
$67$	−6.11984	+	6.11984i	−0.747658	+	0.747658i	−0.974039	−	0.226381i	$-0.927311\pi$
$67$	−6.11984	+	6.11984i	−0.747658	+	0.747658i	0.226381	+	0.974039i	$0.427311\pi$
$68$	3.62804	+	9.33332i	0.439964	+	1.13183i
$69$			7.39584i			0.890355i
$70$	−0.186689	+	6.87064i	−0.0223136	+	0.821198i
$71$		−	4.48386i		−	0.532136i	−0.963954	−	0.266068i	$-0.914275\pi$
$71$		−	4.48386i		−	0.532136i	0.963954	−	0.266068i	$-0.0857245\pi$
$72$	−0.300524	+	0.419196i	−0.0354171	+	0.0494027i
$73$	0.985330	−	0.985330i	0.115324	−	0.115324i	−0.647090	−	0.762414i	$-0.724014\pi$
$73$	0.985330	−	0.985330i	0.115324	−	0.115324i	0.762414	+	0.647090i	$0.224014\pi$
$74$	8.80503	+	13.4961i	1.02356	+	1.56889i
$75$	−3.46114	+	7.64601i	−0.399658	+	0.882886i
$76$	−1.83051	−	0.805748i	−0.209974	−	0.0924256i
$77$	5.84254	+	5.84254i	0.665819	+	0.665819i
$78$	14.2534	+	2.99820i	1.61388	+	0.339480i
$79$	14.1049			1.58693			0.793463	−	0.608618i	$-0.208276\pi$
$79$	14.1049			1.58693			0.793463	+	0.608618i	$0.208276\pi$
$80$	8.86138	−	1.21490i	0.990732	−	0.135830i
$81$	8.41967			0.935518
$82$	2.93898	+	0.618215i	0.324556	+	0.0682704i
$83$	−4.61568	−	4.61568i	−0.506637	−	0.506637i	0.406856	−	0.913492i	$-0.366625\pi$
$83$	−4.61568	−	4.61568i	−0.506637	−	0.506637i	−0.913492	+	0.406856i	$0.866625\pi$
$84$	−6.67840	−	2.93967i	−0.728673	−	0.320745i
$85$	11.0144	−	2.00613i	1.19468	−	0.217596i
$86$	−3.25847	−	4.99447i	−0.351369	−	0.538567i
$87$	3.56290	−	3.56290i	0.381983	−	0.381983i
$88$	6.26484	−	8.73873i	0.667834	−	0.931552i
$89$			10.7179i			1.13610i	0.822995	+	0.568049i	$0.192301\pi$
$89$			10.7179i			1.13610i	−0.822995	+	0.568049i	$0.807699\pi$
$90$	0.396542	+	0.418694i	0.0417992	+	0.0441342i
$91$		−	13.3358i		−	1.39797i
$92$	−3.19266	−	8.21330i	−0.332858	−	0.856296i
$93$	−9.98543	+	9.98543i	−1.03544	+	1.03544i
$94$	−4.19016	+	2.73372i	−0.432182	+	0.281962i
$95$	−1.27222	+	1.83887i	−0.130528	+	0.188664i
$96$	−2.36062	+	9.19739i	−0.240930	+	0.938705i
$97$	11.9851	+	11.9851i	1.21691	+	1.21691i	0.968709	+	0.248198i	$0.0798384\pi$
$97$	11.9851	+	11.9851i	1.21691	+	1.21691i	0.248198	+	0.968709i	$0.420162\pi$
$98$	0.662550	−	3.14975i	0.0669277	−	0.318173i
$99$	0.693247			0.0696740
$100$	0.543040	−	9.98524i	0.0543040	−	0.998524i
$101$	−0.0884970			−0.00880578			−0.00440289	−	0.999990i	$-0.501401\pi$
$101$	−0.0884970			−0.00880578			−0.00440289	+	0.999990i	$0.501401\pi$
$102$	−2.44659	+	11.6311i	−0.242249	+	1.15165i
$103$	−4.11374	−	4.11374i	−0.405339	−	0.405339i	0.474771	−	0.880110i	$-0.342531\pi$
$103$	−4.11374	−	4.11374i	−0.405339	−	0.405339i	−0.880110	+	0.474771i	$0.842531\pi$
$104$	−17.1231	+	2.82337i	−1.67906	+	0.276854i
$105$	−4.64156	+	6.70890i	−0.452970	+	0.654721i
$106$	10.8126	−	7.05431i	1.05021	−	0.685175i
$107$	−6.63747	+	6.63747i	−0.641668	+	0.641668i	−0.950965	−	0.309297i	$-0.899906\pi$
$107$	−6.63747	+	6.63747i	−0.641668	+	0.641668i	0.309297	+	0.950965i	$0.399906\pi$
$108$	−9.95784	+	3.87080i	−0.958193	+	0.372468i
$109$			8.56202i			0.820093i	0.912065	+	0.410047i	$0.134488\pi$
$109$			8.56202i			0.820093i	−0.912065	+	0.410047i	$0.865512\pi$
$110$	−8.26647	−	8.72826i	−0.788177	−	0.832206i
$111$			19.1267i			1.81543i
$112$	8.68557	+	0.381640i	0.820709	+	0.0360615i
$113$	7.12934	−	7.12934i	0.670672	−	0.670672i	−0.287199	−	0.957871i	$-0.592724\pi$
$113$	7.12934	−	7.12934i	0.670672	−	0.670672i	0.957871	+	0.287199i	$0.0927241\pi$
$114$	−1.29711	−	1.98816i	−0.121485	−	0.186209i
$115$	−9.69266	+	1.76539i	−0.903845	+	0.164624i
$116$	−2.41866	+	5.49475i	−0.224567	+	0.510175i
$117$	−0.791182	−	0.791182i	−0.0731448	−	0.0731448i
$118$	−13.2352	−	2.78403i	−1.21840	−	0.256291i
$119$	10.8823			0.997578
$120$	9.59686	+	4.53937i	0.876069	+	0.414386i
$121$	−3.45170			−0.313791
$122$	0.508123	+	0.106884i	0.0460033	+	0.00967680i
$123$	2.52064	+	2.52064i	0.227279	+	0.227279i
$124$	6.77857	−	15.3997i	0.608734	−	1.38293i
$125$	−10.8467	−	2.71091i	−0.970159	−	0.242471i
$126$	0.306280	+	0.469456i	0.0272856	+	0.0418225i
$127$	−2.39718	+	2.39718i	−0.212715	+	0.212715i	−0.805420	−	0.592705i	$-0.798060\pi$
$127$	−2.39718	+	2.39718i	−0.212715	+	0.212715i	0.592705	+	0.805420i	$0.298060\pi$
$128$	−1.34883	−	11.2330i	−0.119221	−	0.992868i
$129$		−	7.07820i		−	0.623201i
$130$	−0.527017	+	19.3956i	−0.0462224	+	1.70110i
$131$		−	2.44655i		−	0.213756i	−0.994272	−	0.106878i	$-0.965915\pi$
$131$		−	2.44655i		−	0.213756i	0.994272	−	0.106878i	$-0.0340855\pi$
$132$	11.8953	−	4.62393i	1.03535	−	0.402461i
$133$	−1.53689	+	1.53689i	−0.133265	+	0.133265i
$134$	10.2510	−	6.68788i	0.885548	−	0.577745i
$135$	2.14037	+	11.7514i	0.184213	+	1.01140i
$136$	−2.30392	−	13.9728i	−0.197560	−	1.19816i
$137$	−4.35212	−	4.35212i	−0.371827	−	0.371827i	0.496316	−	0.868142i	$-0.334686\pi$
$137$	−4.35212	−	4.35212i	−0.371827	−	0.371827i	−0.868142	+	0.496316i	$0.834686\pi$
$138$	2.15300	−	10.2353i	0.183275	−	0.871287i
$139$	1.26585			0.107368			0.0536840	−	0.998558i	$-0.482904\pi$
$139$	1.26585			0.107368			0.0536840	+	0.998558i	$0.482904\pi$
$140$	2.25847	−	9.45411i	0.190875	−	0.799019i
$141$	−5.93832			−0.500097
$142$	−1.30529	+	6.20533i	−0.109538	+	0.520740i
$143$	16.4933	+	16.4933i	1.37924	+	1.37924i
$144$	0.537935	−	0.492652i	0.0448279	−	0.0410543i
$145$	5.51985	+	3.81891i	0.458398	+	0.317144i
$146$	−1.65046	+	1.07679i	−0.136593	+	0.0891155i
$147$	2.70141	−	2.70141i	0.222809	−	0.222809i
$148$	−8.25670	−	21.2408i	−0.678696	−	1.74598i
$149$		−	6.85430i		−	0.561526i	−0.959777	−	0.280763i	$-0.909413\pi$
$149$		−	6.85430i		−	0.561526i	0.959777	−	0.280763i	$-0.0905875\pi$
$150$	7.01579	−	9.57396i	0.572837	−	0.781711i
$151$			3.69443i			0.300648i	0.988637	+	0.150324i	$0.0480318\pi$
$151$			3.69443i			0.300648i	−0.988637	+	0.150324i	$0.951968\pi$
$152$	2.29873	+	1.64798i	0.186452	+	0.133668i
$153$	0.645620	−	0.645620i	0.0521952	−	0.0521952i
$154$	−6.38484	−	9.78647i	−0.514505	−	0.788616i
$155$	−15.4700	−	10.7029i	−1.24258	−	0.859680i
$156$	−18.8529	−	8.29859i	−1.50944	−	0.664419i
$157$	13.2728	+	13.2728i	1.05929	+	1.05929i	0.998128	+	0.0611582i	$0.0194794\pi$
$157$	13.2728	+	13.2728i	1.05929	+	1.05929i	0.0611582	+	0.998128i	$0.480521\pi$
$158$	−19.5202	−	4.10607i	−1.55294	−	0.326661i
$159$	15.3237			1.21525
$160$	−12.6172	−	0.898299i	−0.997475	−	0.0710168i
$161$	−9.57639			−0.754725
$162$	−11.6522	−	2.45104i	−0.915484	−	0.192572i
$163$	17.1216	+	17.1216i	1.34107	+	1.34107i	0.894998	+	0.446069i	$0.147177\pi$
$163$	17.1216	+	17.1216i	1.34107	+	1.34107i	0.446069	+	0.894998i	$0.352823\pi$
$164$	−3.88737	−	1.71113i	−0.303553	−	0.133617i
$165$	−2.55681	−	14.0379i	−0.199047	−	1.09285i
$166$	5.04410	+	7.73143i	0.391498	+	0.600076i
$167$	14.2420	−	14.2420i	1.10208	−	1.10208i	0.107921	−	0.994159i	$-0.465580\pi$
$167$	14.2420	−	14.2420i	1.10208	−	1.10208i	0.994159	−	0.107921i	$-0.0344195\pi$
$168$	8.38665	+	6.01244i	0.647044	+	0.463870i
$169$		−	24.6466i		−	1.89589i
$170$	−15.8272	−	0.430056i	−1.21389	−	0.0329838i
$171$			0.182360i			0.0139454i
$172$	3.05554	+	7.86055i	0.232983	+	0.599362i
$173$	−6.44735	+	6.44735i	−0.490183	+	0.490183i	−0.908364	−	0.418181i	$-0.862668\pi$
$173$	−6.44735	+	6.44735i	−0.490183	+	0.490183i	0.418181	+	0.908364i	$0.362668\pi$
$174$	−5.96799	+	3.89360i	−0.452432	+	0.295173i
$175$	−9.90032	−	4.48160i	−0.748394	−	0.338777i
$176$	−11.2140	+	10.2700i	−0.845288	+	0.774131i
$177$	−11.3513	−	11.3513i	−0.853218	−	0.853218i
$178$	3.12008	−	14.8328i	0.233860	−	1.11177i
$179$	−2.58550			−0.193249			−0.0966246	−	0.995321i	$-0.530805\pi$
$179$	−2.58550			−0.193249			−0.0966246	+	0.995321i	$0.530805\pi$
$180$	−0.426900	−	0.694879i	−0.0318192	−	0.0517932i
$181$	8.24031			0.612498			0.306249	−	0.951951i	$-0.400926\pi$
$181$	8.24031			0.612498			0.306249	+	0.951951i	$0.400926\pi$
$182$	−3.88218	+	18.4558i	−0.287766	+	1.36804i
$183$	0.435796	+	0.435796i	0.0322150	+	0.0322150i
$184$	2.02745	+	12.2960i	0.149466	+	0.906475i
$185$	−25.0666	+	4.56556i	−1.84294	+	0.335667i
$186$	16.7260	−	10.9123i	1.22641	−	0.800126i
$187$	−13.4588	+	13.4588i	−0.984208	+	0.984208i
$188$	6.59469	−	2.56348i	0.480967	−	0.186961i
$189$			11.6105i			0.844536i
$190$	2.29598	−	2.17451i	0.166568	−	0.157755i
$191$		−	10.8399i		−	0.784350i	−0.919891	−	0.392175i	$-0.871723\pi$
$191$		−	10.8399i		−	0.784350i	0.919891	−	0.392175i	$-0.128277\pi$
$192$	5.94437	−	12.0413i	0.428998	−	0.869008i
$193$	2.23316	−	2.23316i	0.160746	−	0.160746i	−0.622151	−	0.782897i	$-0.713741\pi$
$193$	2.23316	−	2.23316i	0.160746	−	0.160746i	0.782897	+	0.622151i	$0.213741\pi$
$194$	−13.0976	−	20.0756i	−0.940352	−	1.44134i
$195$	−13.1030	+	18.9390i	−0.938322	+	1.35625i
$196$	−1.83384	+	4.16615i	−0.130989	+	0.297582i
$197$	−4.56128	−	4.56128i	−0.324978	−	0.324978i	0.525695	−	0.850673i	$-0.323805\pi$
$197$	−4.56128	−	4.56128i	−0.324978	−	0.324978i	−0.850673	+	0.525695i	$0.823805\pi$
$198$	−0.959404	−	0.201811i	−0.0681819	−	0.0143421i
$199$	7.45582			0.528529			0.264264	−	0.964450i	$-0.414871\pi$
$199$	7.45582			0.528529			0.264264	+	0.964450i	$0.414871\pi$
$200$	−3.65832	+	13.6608i	−0.258683	+	0.965962i
$201$	14.5277			1.02471
$202$	0.122473	+	0.0257623i	0.00861720	+	0.00181263i
$203$	4.61337	+	4.61337i	0.323795	+	0.323795i
$204$	6.77182	−	15.3843i	0.474122	−	1.07712i
$205$	−2.70177	+	3.90512i	−0.188700	+	0.272746i
$206$	4.49557	+	6.89067i	0.313221	+	0.480095i
$207$	−0.568144	+	0.568144i	−0.0394887	+	0.0394887i
$208$	24.5191	+	1.07736i	1.70009	+	0.0747011i
$209$		−	3.80154i		−	0.262958i
$210$	8.37660	−	7.93343i	0.578040	−	0.547458i
$211$		−	6.58766i		−	0.453513i	−0.973951	−	0.226757i	$-0.927188\pi$
$211$		−	6.58766i		−	0.453513i	0.973951	−	0.226757i	$-0.0728122\pi$
$212$	−17.0175	+	6.61500i	−1.16876	+	0.454320i
$213$	−5.32206	+	5.32206i	−0.364661	+	0.364661i
$214$	11.1180	−	7.25355i	0.760011	−	0.495842i
$215$	9.27638	−	1.68957i	0.632644	−	0.115228i
$216$	14.9078	−	2.45809i	1.01434	−	0.167252i
$217$	−12.9295	−	12.9295i	−0.877710	−	0.877710i
$218$	2.49248	−	11.8492i	0.168812	−	0.802531i
$219$	−2.33905			−0.158058
$220$	8.89933	+	14.4857i	0.599992	+	0.976627i
$221$	30.7203			2.06647
$222$	5.56797	−	26.4700i	0.373697	−	1.77655i
$223$	−8.47362	−	8.47362i	−0.567435	−	0.567435i	0.363974	−	0.931409i	$-0.381420\pi$
$223$	−8.47362	−	8.47362i	−0.567435	−	0.567435i	−0.931409	+	0.363974i	$0.881420\pi$
$224$	−11.9091	−	3.05661i	−0.795710	−	0.204228i
$225$	−0.853245	+	0.321479i	−0.0568830	+	0.0214320i
$226$	−11.9419	+	7.79107i	−0.794364	+	0.518255i
$227$	−4.59972	+	4.59972i	−0.305294	+	0.305294i	−0.843081	−	0.537787i	$-0.819261\pi$
$227$	−4.59972	+	4.59972i	−0.305294	+	0.305294i	0.537787	+	0.843081i	$0.319261\pi$
$228$	1.21633	+	3.12907i	0.0805534	+	0.207228i
$229$		−	1.51885i		−	0.100369i	−0.998740	−	0.0501843i	$-0.984019\pi$
$229$		−	1.51885i		−	0.100369i	0.998740	−	0.0501843i	$-0.0159809\pi$
$230$	13.9279	+	0.378448i	0.918376	+	0.0249541i
$231$		−	13.8695i		−	0.912543i
$232$	4.94683	−	6.90025i	0.324775	−	0.453023i
$233$	0.157673	−	0.157673i	0.0103295	−	0.0103295i	−0.701923	−	0.712253i	$-0.747675\pi$
$233$	0.157673	−	0.157673i	0.0103295	−	0.0103295i	0.712253	+	0.701923i	$0.247675\pi$
$234$	0.864618	+	1.32526i	0.0565218	+	0.0866348i
$235$	−1.41748	−	7.78250i	−0.0924663	−	0.507675i
$236$	17.5062	+	7.70580i	1.13955	+	0.501605i
$237$	−16.7416	−	16.7416i	−1.08749	−	1.08749i
$238$	−15.0603	−	3.16793i	−0.976214	−	0.205347i
$239$	20.2669			1.31096			0.655480	−	0.755213i	$-0.272466\pi$
$239$	20.2669			1.31096			0.655480	+	0.755213i	$0.272466\pi$
$240$	−11.9599	−	9.07589i	−0.772009	−	0.585846i
$241$	−11.9811			−0.771771			−0.385885	−	0.922547i	$-0.626104\pi$
$241$	−11.9811			−0.771771			−0.385885	+	0.922547i	$0.626104\pi$
$242$	4.77691	+	1.00482i	0.307071	+	0.0645924i
$243$	1.33817	+	1.33817i	0.0858435	+	0.0858435i
$244$	−0.672091	−	0.295839i	−0.0430262	−	0.0189391i
$245$	4.18518	+	2.89552i	0.267381	+	0.184988i
$246$	−2.75461	−	4.22217i	−0.175627	−	0.269196i
$247$	−4.33858	+	4.33858i	−0.276057	+	0.276057i
$248$	−13.8640	+	19.3387i	−0.880367	+	1.22801i
$249$			10.9570i			0.694375i
$250$	14.2219	+	6.90928i	0.899471	+	0.436981i
$251$		−	2.88741i		−	0.182251i	−0.995839	−	0.0911257i	$-0.970953\pi$
$251$		−	2.88741i		−	0.182251i	0.995839	−	0.0911257i	$-0.0290465\pi$
$252$	−0.287206	−	0.738854i	−0.0180923	−	0.0465434i
$253$	11.8438	−	11.8438i	0.744610	−	0.744610i
$254$	4.01537	−	2.61968i	0.251946	−	0.164374i
$255$	−15.4546	−	10.6923i	−0.967803	−	0.669576i
$256$	−1.40335	+	15.9383i	−0.0877097	+	0.996146i
$257$	22.1754	+	22.1754i	1.38326	+	1.38326i	0.838756	+	0.544507i	$0.183283\pi$
$257$	22.1754	+	22.1754i	1.38326	+	1.38326i	0.544507	+	0.838756i	$0.316717\pi$
$258$	−2.06053	+	9.79572i	−0.128283	+	0.609855i
$259$	−24.7660			−1.53888
$260$	6.37558	−	26.6886i	0.395397	−	1.65516i
$261$	0.547400			0.0338832
$262$	−0.712214	+	3.38585i	−0.0440007	+	0.209179i
$263$	10.6310	+	10.6310i	0.655537	+	0.655537i	0.954321	−	0.298784i	$-0.0965811\pi$
$263$	10.6310	+	10.6310i	0.655537	+	0.655537i	−0.298784	+	0.954321i	$0.596581\pi$
$264$	−17.8083	+	2.93635i	−1.09603	+	0.180720i
$265$	3.65778	+	20.0826i	0.224696	+	1.23366i
$266$	2.57434	−	1.67954i	0.157843	−	0.102979i
$267$	12.7215	−	12.7215i	0.778543	−	0.778543i
$268$	−16.1335	+	6.27139i	−0.985510	+	0.383086i
$269$			13.7693i			0.839531i	0.907633	+	0.419765i	$0.137888\pi$
$269$			13.7693i			0.839531i	−0.907633	+	0.419765i	$0.862112\pi$
$270$	0.458832	−	16.8862i	0.0279236	−	1.02766i
$271$			22.8709i			1.38931i	0.719345	+	0.694653i	$0.244442\pi$
$271$			22.8709i			1.38931i	−0.719345	+	0.694653i	$0.755558\pi$
$272$	−0.879143	+	20.0080i	−0.0533059	+	1.21316i
$273$	−15.8288	+	15.8288i	−0.958002	+	0.958002i
$274$	4.75608	+	7.28996i	0.287325	+	0.440403i
$275$	17.7871	−	6.70169i	1.07260	−	0.404127i
$276$	−5.95918	+	13.5382i	−0.358701	+	0.814902i
$277$	−16.1699	−	16.1699i	−0.971556	−	0.971556i	0.0280505	−	0.999607i	$-0.491070\pi$
$277$	−16.1699	−	16.1699i	−0.971556	−	0.971556i	−0.999607	+	0.0280505i	$0.991070\pi$
$278$	−1.75184	−	0.368500i	−0.105069	−	0.0221012i
$279$	−1.53415			−0.0918471
$280$	−5.87774	+	12.4263i	−0.351262	+	0.742616i
$281$	−5.80090			−0.346052			−0.173026	−	0.984917i	$-0.555355\pi$
$281$	−5.80090			−0.346052			−0.173026	+	0.984917i	$0.555355\pi$
$282$	8.21821	+	1.72870i	0.489387	+	0.102943i
$283$	−7.95528	−	7.95528i	−0.472892	−	0.472892i	0.429957	−	0.902849i	$-0.358529\pi$
$283$	−7.95528	−	7.95528i	−0.472892	−	0.472892i	−0.902849	+	0.429957i	$0.858529\pi$
$284$	3.61286	−	8.20775i	0.214384	−	0.487040i
$285$	3.69267	−	0.672572i	0.218735	−	0.0398398i
$286$	−18.0242	−	27.6269i	−1.06579	−	1.63361i
$287$	−3.26382	+	3.26382i	−0.192657	+	0.192657i
$288$	−0.887879	+	0.525197i	−0.0523188	+	0.0309475i
$289$			8.06838i			0.474611i
$290$	−6.52735	−	6.89198i	−0.383299	−	0.404711i
$291$		−	28.4512i		−	1.66784i
$292$	2.59758	−	1.00973i	0.152012	−	0.0590900i
$293$	3.13243	−	3.13243i	0.182998	−	0.182998i	−0.609663	−	0.792661i	$-0.708695\pi$
$293$	3.13243	−	3.13243i	0.182998	−	0.182998i	0.792661	+	0.609663i	$0.208695\pi$
$294$	−4.52496	+	2.95215i	−0.263901	+	0.172173i
$295$	12.1670	−	17.5861i	0.708389	−	1.02390i
$296$	5.24328	+	31.7993i	0.304760	+	1.84830i
$297$	−14.3594	−	14.3594i	−0.833217	−	0.833217i
$298$	−1.99535	+	9.48585i	−0.115587	+	0.549501i
$299$	−27.0338			−1.56341
$300$	−12.4964	+	11.2073i	−0.721481	+	0.647054i
$301$	9.16510			0.528268
$302$	1.07548	−	5.11282i	0.0618870	−	0.294210i
$303$	0.105040	+	0.105040i	0.00603442	+	0.00603442i
$304$	−2.70154	−	2.94986i	−0.154944	−	0.169186i
$305$	−0.467111	+	0.675160i	−0.0267467	+	0.0386596i
$306$	−1.08144	+	0.705545i	−0.0618216	+	0.0403333i
$307$	−5.81276	+	5.81276i	−0.331752	+	0.331752i	−0.853251	−	0.521500i	$-0.825373\pi$
$307$	−5.81276	+	5.81276i	−0.331752	+	0.331752i	0.521500	+	0.853251i	$0.325373\pi$
$308$	5.98722	+	15.4024i	0.341153	+	0.877636i
$309$			9.76550i			0.555540i
$310$	18.2936	+	19.3155i	1.03901	+	1.09705i
$311$		−	8.39347i		−	0.475950i	−0.971271	−	0.237975i	$-0.923516\pi$
$311$		−	8.39347i		−	0.475950i	0.971271	−	0.237975i	$-0.0764836\pi$
$312$	23.6752	+	16.9729i	1.34035	+	0.960901i
$313$	10.6331	−	10.6331i	0.601018	−	0.601018i	−0.339565	−	0.940583i	$-0.610280\pi$
$313$	10.6331	−	10.6331i	0.601018	−	0.601018i	0.940583	+	0.339565i	$0.110280\pi$
$314$	−14.5048	−	22.2325i	−0.818552	−	1.25465i
$315$	−0.871935	+	0.158812i	−0.0491280	+	0.00894801i
$316$	25.8192	+	11.3650i	1.45244	+	0.639331i
$317$	8.44977	+	8.44977i	0.474586	+	0.474586i	0.903395	−	0.428809i	$-0.141067\pi$
$317$	8.44977	+	8.44977i	0.474586	+	0.474586i	−0.428809	+	0.903395i	$0.641067\pi$
$318$	−21.2069	−	4.46088i	−1.18923	−	0.250154i
$319$	−11.4113			−0.638911
$320$	17.1998	+	4.91615i	0.961495	+	0.274821i
$321$	15.7565			0.879443
$322$	13.2530	+	2.78777i	0.738563	+	0.155357i
$323$	−3.54037	−	3.54037i	−0.196991	−	0.196991i
$324$	15.4123	+	6.78413i	0.856238	+	0.376896i
$325$	−27.9483	−	12.6514i	−1.55029	−	0.701774i
$326$	−18.7108	−	28.6793i	−1.03630	−	1.58840i
$327$	10.1626	−	10.1626i	0.561992	−	0.561992i
$328$	4.88172	+	3.49973i	0.269548	+	0.193240i
$329$		−	7.68915i		−	0.423916i
$330$	−0.548105	+	20.1717i	−0.0301722	+	1.11041i
$331$			18.2260i			1.00179i	0.865507	+	0.500896i	$0.166996\pi$
$331$			18.2260i			1.00179i	−0.865507	+	0.500896i	$0.833004\pi$
$332$	−4.72998	−	12.1681i	−0.259591	−	0.667813i
$333$	−1.46930	+	1.46930i	−0.0805173	+	0.0805173i
$334$	−23.8559	+	15.5639i	−1.30534	+	0.851621i
$335$	3.46778	+	19.0394i	0.189465	+	1.04023i
$336$	−9.85625	−	10.7622i	−0.537702	−	0.587127i
$337$	13.3812	+	13.3812i	0.728918	+	0.728918i	0.970404	−	0.241486i	$-0.0776349\pi$
$337$	13.3812	+	13.3812i	0.728918	+	0.728918i	−0.241486	+	0.970404i	$0.577635\pi$
$338$	−7.17484	+	34.1090i	−0.390260	+	1.85529i
$339$	−16.9242			−0.919194
$340$	21.7784	+	5.20260i	1.18110	+	0.282150i
$341$	31.9815			1.73189
$342$	0.0530865	−	0.252372i	0.00287059	−	0.0136467i
$343$	14.2561	+	14.2561i	0.769757	+	0.769757i
$344$	−1.94037	−	11.7679i	−0.104618	−	0.634484i
$345$	13.6000	+	9.40917i	0.732199	+	0.506573i
$346$	10.7995	−	7.04578i	0.580587	−	0.378783i
$347$	8.82149	−	8.82149i	0.473562	−	0.473562i	−0.429503	−	0.903065i	$-0.641311\pi$
$347$	8.82149	−	8.82149i	0.473562	−	0.473562i	0.903065	+	0.429503i	$0.141311\pi$
$348$	9.39273	−	3.65113i	0.503503	−	0.195721i
$349$		−	25.6800i		−	1.37462i	−0.726365	−	0.687309i	$-0.758792\pi$
$349$		−	25.6800i		−	1.37462i	0.726365	−	0.687309i	$-0.241208\pi$
$350$	12.3967	+	9.08429i	0.662631	+	0.485576i
$351$			32.7759i			1.74945i
$352$	18.5091	−	10.9485i	0.986537	−	0.583555i
$353$	−11.0134	+	11.0134i	−0.586184	+	0.586184i	−0.936596	−	0.350412i	$-0.886042\pi$
$353$	−11.0134	+	11.0134i	−0.586184	+	0.586184i	0.350412	+	0.936596i	$0.386042\pi$
$354$	12.4049	+	19.0139i	0.659315	+	1.01058i
$355$	−8.24523	−	5.70447i	−0.437611	−	0.302762i
$356$	−8.63594	+	19.6193i	−0.457704	+	1.03982i
$357$	−12.9166	−	12.9166i	−0.683619	−	0.683619i
$358$	3.57814	+	0.752662i	0.189111	+	0.0397794i
$359$	−4.14442			−0.218734			−0.109367	−	0.994001i	$-0.534882\pi$
$359$	−4.14442			−0.218734			−0.109367	+	0.994001i	$0.534882\pi$
$360$	0.388513	+	1.08594i	0.0204764	+	0.0572339i
$361$	1.00000			0.0526316
$362$	−11.4040	−	2.39883i	−0.599381	−	0.126080i
$363$	4.09696	+	4.09696i	0.215034	+	0.215034i
$364$	10.7453	−	24.4114i	0.563207	−	1.27950i
$365$	−0.558333	−	3.06546i	−0.0292245	−	0.160453i
$366$	−0.476246	−	0.729975i	−0.0248938	−	0.0381564i
$367$	−21.3402	+	21.3402i	−1.11395	+	1.11395i	−0.121341	+	0.992611i	$0.538719\pi$
$367$	−21.3402	+	21.3402i	−1.11395	+	1.11395i	−0.992611	+	0.121341i	$0.961281\pi$
$368$	0.773644	−	17.6070i	0.0403290	−	0.917829i
$369$			0.387269i			0.0201604i
$370$	36.0195	+	0.978723i	1.87256	+	0.0508814i
$371$			19.8417i			1.03013i
$372$	−26.3242	+	10.2327i	−1.36484	+	0.530541i
$373$	−7.48124	+	7.48124i	−0.387364	+	0.387364i	−0.873746	−	0.486382i	$-0.838316\pi$
$373$	−7.48124	+	7.48124i	−0.387364	+	0.387364i	0.486382	+	0.873746i	$0.338316\pi$
$374$	22.5441	−	14.7081i	1.16573	−	0.760536i
$375$	9.65668	+	16.0920i	0.498669	+	0.830989i
$376$	−9.87282	+	1.62789i	−0.509152	+	0.0839522i
$377$	13.0234	+	13.0234i	0.670738	+	0.670738i
$378$	3.37991	−	16.0680i	0.173844	−	0.826450i
$379$	25.6659			1.31837			0.659184	−	0.751982i	$-0.270902\pi$
$379$	25.6659			1.31837			0.659184	+	0.751982i	$0.270902\pi$
$380$	−3.81049	+	2.34098i	−0.195474	+	0.120090i
$381$	5.69061			0.291539
$382$	−3.15560	+	15.0017i	−0.161455	+	0.767553i
$383$	−0.0728818	−	0.0728818i	−0.00372408	−	0.00372408i	0.705242	−	0.708966i	$-0.250838\pi$
$383$	−0.0728818	−	0.0728818i	−0.00372408	−	0.00372408i	−0.708966	+	0.705242i	$0.750838\pi$
$384$	−11.7319	+	14.9339i	−0.598692	+	0.762090i
$385$	18.1767	−	3.31065i	0.926370	−	0.168726i
$386$	−3.74062	+	2.44044i	−0.190393	+	0.124215i
$387$	0.543743	−	0.543743i	0.0276400	−	0.0276400i
$388$	12.2819	+	31.5960i	0.623521	+	1.60404i
$389$			28.4889i			1.44445i	0.691660	+	0.722223i	$0.256880\pi$
$389$			28.4889i			1.44445i	−0.691660	+	0.722223i	$0.743120\pi$
$390$	23.6469	−	22.3958i	1.19740	−	1.13405i
$391$		−	22.0601i		−	1.11563i
$392$	3.75071	−	5.23181i	0.189440	−	0.264246i
$393$	−2.90391	+	2.90391i	−0.146483	+	0.146483i
$394$	4.98465	+	7.64031i	0.251123	+	0.384913i
$395$	17.9446	−	25.9371i	0.902892	−	1.30504i
$396$	1.26900	+	0.558582i	0.0637695	+	0.0280698i
$397$	−14.0781	−	14.0781i	−0.706561	−	0.706561i	0.259249	−	0.965810i	$-0.416525\pi$
$397$	−14.0781	−	14.0781i	−0.706561	−	0.706561i	−0.965810	+	0.259249i	$0.916525\pi$
$398$	−10.3183	−	2.17046i	−0.517210	−	0.108795i
$399$	3.64838			0.182647
$400$	9.03963	−	17.8405i	0.451981	−	0.892027i
$401$	13.1548			0.656917			0.328459	−	0.944518i	$-0.393471\pi$
$401$	13.1548			0.656917			0.328459	+	0.944518i	$0.393471\pi$
$402$	−20.1053	−	4.22916i	−1.00276	−	0.210931i
$403$	−36.4995	−	36.4995i	−1.81817	−	1.81817i
$404$	−0.161995	−	0.0713063i	−0.00805954	−	0.00354762i
$405$	10.7117	−	15.4827i	0.532269	−	0.769340i
$406$	−5.04157	−	7.72756i	−0.250209	−	0.383512i
$407$	30.6297	−	30.6297i	1.51826	−	1.51826i
$408$	−13.8502	+	19.3194i	−0.685688	+	0.956455i
$409$			18.3619i			0.907938i	0.891018	+	0.453969i	$0.149992\pi$
$409$			18.3619i			0.907938i	−0.891018	+	0.453969i	$0.850008\pi$
$410$	4.87587	−	4.61790i	0.240802	−	0.228062i
$411$			10.3314i			0.509610i
$412$	−4.21561	−	10.8449i	−0.207688	−	0.534289i
$413$	14.6981	−	14.6981i	0.723246	−	0.723246i
$414$	0.951662	−	0.620878i	0.0467716	−	0.0305145i
$415$	−14.3598	+	2.61545i	−0.704896	+	0.128388i
$416$	−33.6190	−	8.62870i	−1.64831	−	0.423057i
$417$	−1.50248	−	1.50248i	−0.0735769	−	0.0735769i
$418$	−1.10666	+	5.26106i	−0.0541286	+	0.257327i
$419$	−19.6007			−0.957557			−0.478778	−	0.877936i	$-0.658920\pi$
$419$	−19.6007			−0.957557			−0.478778	+	0.877936i	$0.658920\pi$
$420$	−13.9021	+	8.54078i	−0.678353	+	0.416747i
$421$	8.18578			0.398950			0.199475	−	0.979903i	$-0.436076\pi$
$421$	8.18578			0.398950			0.199475	+	0.979903i	$0.436076\pi$
$422$	−1.91773	+	9.11685i	−0.0933536	+	0.443801i
$423$	−0.456178	−	0.456178i	−0.0221801	−	0.0221801i
$424$	25.4766	−	4.20075i	1.23725	−	0.204006i
$425$	10.3238	−	22.8063i	0.500778	−	1.10627i
$426$	8.91464	−	5.81604i	0.431916	−	0.281788i
$427$	−0.564284	+	0.564284i	−0.0273076	+	0.0273076i
$428$	−17.4981	+	6.80183i	−0.845802	+	0.328779i
$429$		−	39.1530i		−	1.89032i
$430$	−13.3297	−	0.362194i	−0.642814	−	0.0174666i
$431$		−	22.2804i		−	1.07321i	−0.843834	−	0.536605i	$-0.819707\pi$
$431$		−	22.2804i		−	1.07321i	0.843834	−	0.536605i	$-0.180293\pi$
$432$	−21.3468	−	0.937969i	−1.02705	−	0.0451280i
$433$	−14.6905	+	14.6905i	−0.705980	+	0.705980i	−0.965687	−	0.259707i	$-0.916374\pi$
$433$	−14.6905	+	14.6905i	−0.705980	+	0.705980i	0.259707	+	0.965687i	$0.416374\pi$
$434$	14.1296	+	21.6574i	0.678241	+	1.03959i
$435$	−2.01890	−	11.0845i	−0.0967989	−	0.531462i
$436$	−6.89883	+	15.6729i	−0.330394	+	0.750595i
$437$	3.11551	+	3.11551i	0.149035	+	0.149035i
$438$	3.23708	+	0.680919i	0.154673	+	0.0325356i
$439$	32.1489			1.53438			0.767191	−	0.641419i	$-0.221654\pi$
$439$	32.1489			1.53438			0.767191	+	0.641419i	$0.221654\pi$
$440$	−8.09910	−	22.6379i	−0.386109	−	1.07922i
$441$	0.415041			0.0197639
$442$	−42.5147	−	8.94297i	−2.02222	−	0.425374i
$443$	−3.60072	−	3.60072i	−0.171076	−	0.171076i	0.616376	−	0.787452i	$-0.288600\pi$
$443$	−3.60072	−	3.60072i	−0.171076	−	0.171076i	−0.787452	+	0.616376i	$0.788600\pi$
$444$	−15.4113	+	35.0117i	−0.731389	+	1.66158i
$445$	19.7089	+	13.6356i	0.934290	+	0.646390i
$446$	9.26013	+	14.1936i	0.438480	+	0.672087i
$447$	−8.13562	+	8.13562i	−0.384802	+	0.384802i
$448$	15.5915	+	7.69697i	0.736630	+	0.363648i
$449$		−	20.0423i		−	0.945855i	−0.881101	−	0.472927i	$-0.843197\pi$
$449$		−	20.0423i		−	0.945855i	0.881101	−	0.472927i	$-0.156803\pi$
$450$	1.27441	−	0.196517i	0.0600765	−	0.00926389i
$451$		−	8.07316i		−	0.380150i
$452$	18.7948	−	7.30589i	0.884032	−	0.343640i
$453$	4.38506	−	4.38506i	0.206028	−	0.206028i
$454$	7.70471	−	5.02666i	0.361600	−	0.235913i
$455$	−24.5228	−	16.9662i	−1.14965	−	0.795386i
$456$	−0.772410	−	4.68450i	−0.0361714	−	0.219372i
$457$	−10.0424	−	10.0424i	−0.469765	−	0.469765i	0.432073	−	0.901839i	$-0.357782\pi$
$457$	−10.0424	−	10.0424i	−0.469765	−	0.469765i	−0.901839	+	0.432073i	$0.857782\pi$
$458$	−0.442152	+	2.10198i	−0.0206604	+	0.0982192i
$459$	−26.7458			−1.24839
$460$	−19.1650	−	4.57827i	−0.893572	−	0.213463i
$461$	−13.0150			−0.606168			−0.303084	−	0.952964i	$-0.598016\pi$
$461$	−13.0150			−0.606168			−0.303084	+	0.952964i	$0.598016\pi$
$462$	−4.03753	+	19.1943i	−0.187843	+	0.893001i
$463$	10.0773	+	10.0773i	0.468334	+	0.468334i	0.901374	−	0.433041i	$-0.142559\pi$
$463$	10.0773	+	10.0773i	0.468334	+	0.468334i	−0.433041	+	0.901374i	$0.642559\pi$
$464$	−8.85477	+	8.10938i	−0.411073	+	0.376468i
$465$	5.65820	+	31.0656i	0.262393	+	1.44063i
$466$	−0.264108	+	0.172308i	−0.0122346	+	0.00798202i
$467$	−16.3296	+	16.3296i	−0.755643	+	0.755643i	−0.975526	−	0.219883i	$-0.929432\pi$
$467$	−16.3296	+	16.3296i	−0.755643	+	0.755643i	0.219883	+	0.975526i	$0.429432\pi$
$468$	−0.810774	−	2.08576i	−0.0374780	−	0.0964143i
$469$			18.8110i			0.868613i
$470$	−0.303866	+	11.1831i	−0.0140163	+	0.515836i
$471$		−	31.5080i		−	1.45181i
$472$	−21.9840	−	15.7605i	−1.01190	−	0.725435i
$473$	−11.3351	+	11.3351i	−0.521188	+	0.521188i
$474$	18.2956	+	28.0429i	0.840344	+	1.28805i
$475$	1.76289	+	4.67891i	0.0808868	+	0.214683i
$476$	19.9202	+	8.76838i	0.913039	+	0.401898i
$477$	1.17716	+	1.17716i	0.0538984	+	0.0538984i
$478$	−28.0480	−	5.89989i	−1.28289	−	0.269855i
$479$	6.20061			0.283313			0.141657	−	0.989916i	$-0.454757\pi$
$479$	6.20061			0.283313			0.141657	+	0.989916i	$0.454757\pi$
$480$	13.9096	+	16.0420i	0.634882	+	0.732215i
$481$	−69.9134			−3.18778
$482$	16.5810	+	3.48781i	0.755243	+	0.158865i
$483$	11.3666	+	11.3666i	0.517197	+	0.517197i
$484$	−6.31838	−	2.78120i	−0.287199	−	0.126418i
$485$	37.2869	−	6.79133i	1.69311	−	0.308378i
$486$	−1.46237	−	2.24148i	−0.0663347	−	0.101676i
$487$	−12.2791	+	12.2791i	−0.556418	+	0.556418i	−0.928286	−	0.371868i	$-0.878717\pi$
$487$	−12.2791	+	12.2791i	−0.556418	+	0.556418i	0.371868	+	0.928286i	$0.378717\pi$
$488$	0.844004	+	0.605071i	0.0382063	+	0.0273903i
$489$		−	40.6445i		−	1.83801i
$490$	−4.94907	−	5.22554i	−0.223576	−	0.236066i
$491$		−	10.5091i		−	0.474267i	−0.971477	−	0.237134i	$-0.923792\pi$
$491$		−	10.5091i		−	0.474267i	0.971477	−	0.237134i	$-0.0762079\pi$
$492$	2.58306	+	6.64507i	0.116453	+	0.299583i
$493$	−10.6273	+	10.6273i	−0.478631	+	0.478631i
$494$	7.26728	−	4.74128i	0.326970	−	0.213320i
$495$	0.881966	−	1.27479i	0.0396414	−	0.0572976i
$496$	24.8165	−	22.7274i	1.11429	−	1.02049i
$497$	−6.89118	−	6.89118i	−0.309112	−	0.309112i
$498$	3.18970	−	15.1638i	0.142934	−	0.679504i
$499$	−21.2547			−0.951490			−0.475745	−	0.879583i	$-0.657821\pi$
$499$	−21.2547			−0.951490			−0.475745	+	0.879583i	$0.657821\pi$
$500$	−17.6707	−	13.7021i	−0.790258	−	0.612775i
$501$	−33.8088			−1.51046
$502$	−0.840550	+	3.99596i	−0.0375156	+	0.178348i
$503$	−14.1016	−	14.1016i	−0.628761	−	0.628761i	0.318995	−	0.947756i	$-0.396655\pi$
$503$	−14.1016	−	14.1016i	−0.628761	−	0.628761i	−0.947756	+	0.318995i	$0.896655\pi$
$504$	0.182386	+	1.10613i	0.00812411	+	0.0492709i
$505$	−0.112588	+	0.162735i	−0.00501011	+	0.00724159i
$506$	−19.8387	+	12.9431i	−0.881939	+	0.575390i
$507$	−29.2539	+	29.2539i	−1.29921	+	1.29921i
$508$	−6.31959	+	2.45654i	−0.280386	+	0.108991i
$509$		−	10.3767i		−	0.459939i	−0.973198	−	0.229969i	$-0.926137\pi$
$509$		−	10.3767i		−	0.459939i	0.973198	−	0.229969i	$-0.0738626\pi$
$510$	18.2754	+	19.2963i	0.809248	+	0.854454i
$511$		−	3.02868i		−	0.133981i
$512$	6.58194	−	21.6490i	0.290883	−	0.956759i
$513$	3.77726	−	3.77726i	0.166770	−	0.166770i
$514$	−24.2337	−	37.1446i	−1.06890	−	1.63838i
$515$	−12.7982	+	2.33103i	−0.563958	+	0.102718i
$516$	5.70324	−	12.9567i	0.251071	−	0.570388i
$517$	9.50967	+	9.50967i	0.418235	+	0.418235i
$518$	34.2743	+	7.20960i	1.50593	+	0.316771i
$519$	15.3052			0.671823
$520$	−16.5926	+	35.0791i	−0.727635	+	1.53832i
$521$	−7.61874			−0.333783			−0.166891	−	0.985975i	$-0.553373\pi$
$521$	−7.61874			−0.333783			−0.166891	+	0.985975i	$0.553373\pi$
$522$	−0.757561	−	0.159353i	−0.0331576	−	0.00697469i
$523$	−14.6526	−	14.6526i	−0.640715	−	0.640715i	0.310016	−	0.950731i	$-0.399666\pi$
$523$	−14.6526	−	14.6526i	−0.640715	−	0.640715i	−0.950731	+	0.310016i	$0.899666\pi$
$524$	1.97131	−	4.47844i	0.0861169	−	0.195642i
$525$	6.43168	+	17.0704i	0.280702	+	0.745015i
$526$	−11.6178	−	17.8073i	−0.506559	−	0.776437i
$527$	29.7843	−	29.7843i	1.29742	−	1.29742i
$528$	25.5002	+	1.12047i	1.10975	+	0.0487620i
$529$		−	3.58714i		−	0.155963i
$530$	0.784122	−	28.8577i	0.0340601	−	1.25350i
$531$		−	1.74400i		−	0.0756833i
$532$	−4.05163	+	1.57495i	−0.175661	+	0.0682826i
$533$	−9.21364	+	9.21364i	−0.399087	+	0.399087i
$534$	−21.3090	+	13.9023i	−0.922130	+	0.601611i
$535$	3.76109	+	20.6498i	0.162606	+	0.892769i
$536$	24.1532	−	3.98254i	1.04326	−	0.172020i
$537$	3.06882	+	3.06882i	0.132430	+	0.132430i
$538$	4.00838	−	19.0558i	0.172813	−	0.821552i
$539$	−8.65212			−0.372673
$540$	−5.55072	+	23.2357i	−0.238865	+	0.999905i
$541$	−2.98167			−0.128192			−0.0640961	−	0.997944i	$-0.520416\pi$
$541$	−2.98167			−0.128192			−0.0640961	+	0.997944i	$0.520416\pi$
$542$	6.65792	−	31.6516i	0.285982	−	1.35955i
$543$	−9.78074	−	9.78074i	−0.419732	−	0.419732i
$544$	7.04119	−	27.4337i	0.301889	−	1.17621i
$545$	15.7445	+	10.8928i	0.674418	+	0.466597i
$546$	26.5138	−	17.2980i	1.13469	−	0.740286i
$547$	22.4853	−	22.4853i	0.961401	−	0.961401i	−0.0378814	−	0.999282i	$-0.512061\pi$
$547$	22.4853	−	22.4853i	0.961401	−	0.961401i	0.999282	+	0.0378814i	$0.0120609\pi$
$548$	−4.45989	−	11.4733i	−0.190517	−	0.490116i
$549$			0.0669552i			0.00285758i
$550$	−26.5669	+	4.09667i	−1.13282	+	0.174683i
$551$		−	3.00176i		−	0.127879i
$552$	12.1882	−	17.0011i	0.518763	−	0.723614i
$553$	21.6777	−	21.6777i	0.921828	−	0.921828i
$554$	17.6708	+	27.0852i	0.750760	+	1.15074i
$555$	35.1716	+	24.3335i	1.49295	+	1.03290i
$556$	2.31715	+	1.01996i	0.0982691	+	0.0432557i
$557$	−1.94430	−	1.94430i	−0.0823826	−	0.0823826i	0.664715	−	0.747097i	$-0.268553\pi$
$557$	−1.94430	−	1.94430i	−0.0823826	−	0.0823826i	−0.747097	+	0.664715i	$0.768553\pi$
$558$	2.12315	+	0.446605i	0.0898801	+	0.0189063i
$559$	25.8728			1.09430
$560$	11.7518	−	15.4861i	0.496604	−	0.654407i
$561$	31.9496			1.34891
$562$	8.02802	+	1.68869i	0.338642	+	0.0712332i
$563$	33.3549	+	33.3549i	1.40574	+	1.40574i	0.780163	+	0.625577i	$0.215136\pi$
$563$	33.3549	+	33.3549i	1.40574	+	1.40574i	0.625577	+	0.780163i	$0.284864\pi$
$564$	−10.8702	−	4.78479i	−0.457717	−	0.201476i
$565$	−4.03981	−	22.1801i	−0.169956	−	0.933122i
$566$	8.69368	+	13.3254i	0.365422	+	0.560108i
$567$	12.9401	−	12.9401i	0.543432	−	0.543432i
$568$	−7.38928	+	10.3072i	−0.310047	+	0.432480i
$569$		−	5.38489i		−	0.225746i	−0.993609	−	0.112873i	$-0.963995\pi$
$569$		−	5.38489i		−	0.225746i	0.993609	−	0.112873i	$-0.0360054\pi$
$570$	−5.30619	−	0.144180i	−0.222252	−	0.00603903i
$571$			27.7359i			1.16071i	0.814363	+	0.580356i	$0.197087\pi$
$571$			27.7359i			1.16071i	−0.814363	+	0.580356i	$0.802913\pi$
$572$	16.9017	+	43.4806i	0.706696	+	1.81801i
$573$	−12.8663	+	12.8663i	−0.537498	+	0.537498i
$574$	5.46702	−	3.56676i	0.228189	−	0.148874i
$575$	−9.08492	+	20.0695i	−0.378867	+	0.836957i
$576$	1.38165	−	0.468364i	0.0575687	−	0.0195152i
$577$	−6.92326	−	6.92326i	−0.288219	−	0.288219i	0.548157	−	0.836376i	$-0.315330\pi$
$577$	−6.92326	−	6.92326i	−0.288219	−	0.288219i	−0.836376	+	0.548157i	$0.815330\pi$
$578$	2.34878	−	11.1661i	0.0976964	−	0.464447i
$579$	−5.30124			−0.220312
$580$	7.02706	+	11.4382i	0.291783	+	0.474944i
$581$	−14.1876			−0.588599
$582$	−8.28242	+	39.3745i	−0.343317	+	1.63212i
$583$	−24.5395	−	24.5395i	−1.01632	−	1.01632i
$584$	−3.88881	+	0.641212i	−0.160920	+	0.0265336i
$585$	−2.46144	+	0.448319i	−0.101768	+	0.0185357i
$586$	−5.24693	+	3.42317i	−0.216749	+	0.141410i
$587$	−10.8409	+	10.8409i	−0.447453	+	0.447453i	−0.894507	−	0.447054i	$-0.852473\pi$
$587$	−10.8409	+	10.8409i	−0.447453	+	0.447453i	0.447054	+	0.894507i	$0.352473\pi$
$588$	7.12162	−	2.76831i	0.293691	−	0.114163i
$589$			8.41277i			0.346642i
$590$	−21.9577	+	20.7960i	−0.903984	+	0.856157i
$591$			10.8279i			0.445400i
$592$	2.00076	−	45.5343i	0.0822306	−	1.87145i
$593$	26.9019	−	26.9019i	1.10473	−	1.10473i	0.110895	−	0.993832i	$-0.464628\pi$
$593$	26.9019	−	26.9019i	1.10473	−	1.10473i	0.993832	−	0.110895i	$-0.0353718\pi$
$594$	15.6922	+	24.0525i	0.643860	+	0.986888i
$595$	13.8447	−	20.0111i	0.567578	−	0.820376i
$596$	5.52284	−	12.5469i	0.226224	−	0.513940i
$597$	−8.84959	−	8.84959i	−0.362190	−	0.362190i
$598$	37.4128	+	7.86979i	1.52992	+	0.321820i
$599$	−40.6502			−1.66092			−0.830462	−	0.557076i	$-0.811923\pi$
$599$	−40.6502			−1.66092			−0.830462	+	0.557076i	$0.811923\pi$
$600$	20.5567	−	11.8723i	0.839223	−	0.484684i
$601$	−25.6431			−1.04600			−0.523001	−	0.852332i	$-0.675188\pi$
$601$	−25.6431			−1.04600			−0.523001	+	0.852332i	$0.675188\pi$
$602$	−12.6838	−	2.66804i	−0.516955	−	0.108741i
$603$	1.11601	+	1.11601i	0.0454475	+	0.0454475i
$604$	−2.97678	+	6.76269i	−0.121123	+	0.275170i
$605$	−4.39134	+	6.34723i	−0.178534	+	0.258052i
$606$	−0.114790	−	0.175947i	−0.00466303	−	0.00714734i
$607$	−9.68289	+	9.68289i	−0.393016	+	0.393016i	−0.875761	−	0.482745i	$-0.839640\pi$
$607$	−9.68289	+	9.68289i	−0.393016	+	0.393016i	0.482745	+	0.875761i	$0.339640\pi$
$608$	2.88001	+	4.86884i	0.116800	+	0.197457i
$609$		−	10.9516i		−	0.443780i
$610$	0.842992	−	0.798393i	0.0341318	−	0.0323260i
$611$		−	21.7062i		−	0.878139i
$612$	1.70202	−	0.661607i	0.0688001	−	0.0267439i
$613$	14.9284	−	14.9284i	0.602952	−	0.602952i	−0.338143	−	0.941095i	$-0.609799\pi$
$613$	14.9284	−	14.9284i	0.602952	−	0.602952i	0.941095	+	0.338143i	$0.109799\pi$
$614$	9.73658	−	6.35229i	0.392937	−	0.256358i
$615$	7.84196	−	1.42831i	0.316219	−	0.0575951i
$616$	−3.80209	−	23.0588i	−0.153190	−	0.929066i
$617$	12.4652	+	12.4652i	0.501830	+	0.501830i	0.912006	−	0.410176i	$-0.134533\pi$
$617$	12.4652	+	12.4652i	0.501830	+	0.501830i	−0.410176	+	0.912006i	$0.634533\pi$
$618$	2.84283	−	13.5147i	0.114355	−	0.543643i
$619$	0.783581			0.0314948			0.0157474	−	0.999876i	$-0.494987\pi$
$619$	0.783581			0.0314948			0.0157474	+	0.999876i	$0.494987\pi$
$620$	−19.6941	−	32.0567i	−0.790935	−	1.28743i
$621$	23.5362			0.944476
$622$	−2.44341	+	11.6159i	−0.0979720	+	0.465757i
$623$	16.4722	+	16.4722i	0.659946	+	0.659946i
$624$	−27.8238	−	30.3813i	−1.11384	−	1.21623i
$625$	−18.7845	+	16.4968i	−0.751378	+	0.659872i
$626$	−17.8108	+	11.6200i	−0.711864	+	0.464430i
$627$	−4.51219	+	4.51219i	−0.180199	+	0.180199i
$628$	13.6015	+	34.9906i	0.542759	+	1.39628i
$629$		−	57.0507i		−	2.27476i
$630$	1.25293	+	0.0340445i	0.0499178	+	0.00135637i
$631$			36.7340i			1.46236i	0.682186	+	0.731179i	$0.261029\pi$
$631$			36.7340i			1.46236i	−0.682186	+	0.731179i	$0.738971\pi$
$632$	−32.4234	−	23.2445i	−1.28973	−	0.924618i
$633$	−7.81914	+	7.81914i	−0.310783	+	0.310783i
$634$	−9.23406	−	14.1537i	−0.366731	−	0.562114i
$635$	1.35835	+	7.45786i	0.0539045	+	0.295956i
$636$	28.0503	+	12.3471i	1.11226	+	0.489593i
$637$	9.87440	+	9.87440i	0.391238	+	0.391238i
$638$	15.7924	+	3.32194i	0.625228	+	0.131517i
$639$	−0.817674			−0.0323467
$640$	−22.3721	−	11.8106i	−0.884334	−	0.466855i
$641$	−30.6773			−1.21168			−0.605840	−	0.795586i	$-0.707163\pi$
$641$	−30.6773			−1.21168			−0.605840	+	0.795586i	$0.707163\pi$
$642$	−21.8059	−	4.58687i	−0.860609	−	0.181029i
$643$	13.0109	+	13.0109i	0.513098	+	0.513098i	0.915474	−	0.402376i	$-0.131816\pi$
$643$	13.0109	+	13.0109i	0.513098	+	0.513098i	−0.402376	+	0.915474i	$0.631816\pi$
$644$	−17.5297	−	7.71616i	−0.690767	−	0.304059i
$645$	−13.0159	−	9.00506i	−0.512500	−	0.354574i
$646$	3.86898	+	5.93024i	0.152223	+	0.233322i
$647$	−26.5081	+	26.5081i	−1.04214	+	1.04214i	−0.0430687	+	0.999072i	$0.513713\pi$
$647$	−26.5081	+	26.5081i	−1.04214	+	1.04214i	−0.999072	+	0.0430687i	$0.986287\pi$
$648$	−19.3546	−	13.8754i	−0.760319	−	0.545077i
$649$			36.3562i			1.42710i
$650$	34.9954	+	25.6446i	1.37263	+	1.00587i
$651$			30.6930i			1.20295i
$652$	17.5456	+	45.1370i	0.687138	+	1.76770i
$653$	−3.96735	+	3.96735i	−0.155255	+	0.155255i	−0.780460	−	0.625206i	$-0.785015\pi$
$653$	−3.96735	+	3.96735i	−0.155255	+	0.155255i	0.625206	+	0.780460i	$0.285015\pi$
$654$	−17.0227	+	11.1059i	−0.665640	+	0.434274i
$655$	−4.49890	−	3.11257i	−0.175786	−	0.121618i
$656$	−5.73714	−	6.26448i	−0.223998	−	0.244587i
$657$	−0.179684	−	0.179684i	−0.00701015	−	0.00701015i
$658$	−2.23838	+	10.6412i	−0.0872612	+	0.414838i
$659$	28.2509			1.10050			0.550250	−	0.835000i	$-0.314532\pi$
$659$	28.2509			1.10050			0.550250	+	0.835000i	$0.314532\pi$
$660$	6.63070	−	27.7566i	0.258100	−	1.08042i
$661$	1.71072			0.0665392			0.0332696	−	0.999446i	$-0.489408\pi$
$661$	1.71072			0.0665392			0.0332696	+	0.999446i	$0.489408\pi$
$662$	5.30576	−	25.2235i	0.206214	−	0.980339i
$663$	−36.4631	−	36.4631i	−1.41611	−	1.41611i
$664$	3.00370	+	18.2167i	0.116566	+	0.706947i
$665$	0.870870	+	4.78140i	0.0337709	+	0.185415i
$666$	2.46114	−	1.60568i	0.0953671	−	0.0622189i
$667$	9.35203	−	9.35203i	0.362112	−	0.362112i
$668$	37.5457	−	14.5947i	1.45269	−	0.564686i
$669$			20.1153i			0.777703i
$670$	0.743391	−	27.3587i	0.0287197	−	1.05696i
$671$		−	1.39577i		−	0.0538833i
$672$	10.5074	+	17.7634i	0.405330	+	0.685237i
$673$	7.10338	−	7.10338i	0.273815	−	0.273815i	−0.556819	−	0.830634i	$-0.687978\pi$
$673$	7.10338	−	7.10338i	0.273815	−	0.273815i	0.830634	+	0.556819i	$0.187978\pi$
$674$	−14.6232	−	22.4139i	−0.563264	−	0.863352i
$675$	24.3324	+	11.0146i	0.936553	+	0.423952i
$676$	19.8589	−	45.1158i	0.763804	−	1.73522i
$677$	13.1079	+	13.1079i	0.503779	+	0.503779i	0.912610	−	0.408831i	$-0.134063\pi$
$677$	13.1079	+	13.1079i	0.503779	+	0.503779i	−0.408831	+	0.912610i	$0.634063\pi$
$678$	23.4218	+	4.92678i	0.899509	+	0.189212i
$679$	36.8397			1.41378
$680$	−28.6253	−	13.5399i	−1.09773	−	0.519232i
$681$	10.9192			0.418423
$682$	−44.2600	−	9.31010i	−1.69480	−	0.356502i
$683$	23.7689	+	23.7689i	0.909491	+	0.909491i	0.996231	−	0.0867400i	$-0.0276449\pi$
$683$	23.7689	+	23.7689i	0.909491	+	0.909491i	−0.0867400	+	0.996231i	$0.527645\pi$
$684$	−0.146936	+	0.333811i	−0.00561823	+	0.0127636i
$685$	−13.5399	+	2.46611i	−0.517331	+	0.0942251i
$686$	−15.5793	−	23.8795i	−0.594821	−	0.911723i
$687$	−1.80278	+	1.80278i	−0.0687805	+	0.0687805i
$688$	−0.740417	+	16.8508i	−0.0282281	+	0.642432i
$689$			56.0124i			2.13390i
$690$	−16.0823	−	16.9807i	−0.612243	−	0.646444i
$691$		−	20.3717i		−	0.774975i	−0.921875	−	0.387488i	$-0.873343\pi$
$691$		−	20.3717i		−	0.774975i	0.921875	−	0.387488i	$-0.126657\pi$
$692$	−16.9969	+	6.60700i	−0.646124	+	0.251161i
$693$	1.06544	−	1.06544i	0.0404728	−	0.0404728i
$694$	−14.7763	+	9.64029i	−0.560901	+	0.365940i
$695$	1.61044	−	2.32773i	0.0610876	−	0.0882959i
$696$	−14.0617	+	2.31859i	−0.533009	+	0.0878859i
$697$	−7.51851	−	7.51851i	−0.284784	−	0.284784i
$698$	−7.47568	+	35.5393i	−0.282959	+	1.34518i
$699$	−0.374296			−0.0141572
$700$	−14.5116	−	16.1808i	−0.548487	−	0.611576i
$701$	−15.4547			−0.583718			−0.291859	−	0.956461i	$-0.594274\pi$
$701$	−15.4547			−0.583718			−0.291859	+	0.956461i	$0.594274\pi$
$702$	9.54136	−	45.3595i	0.360116	−	1.71198i
$703$	8.05718	+	8.05718i	0.303882	+	0.303882i
$704$	−28.8024	+	9.76371i	−1.08553	+	0.367984i
$705$	−7.55488	+	10.9198i	−0.284533	+	0.411264i
$706$	18.4479	−	12.0356i	0.694294	−	0.452968i
$707$	−0.136010	+	0.136010i	−0.00511518	+	0.00511518i
$708$	−11.6324	−	29.9250i	−0.437173	−	1.12465i
$709$			37.3153i			1.40141i	0.713454	+	0.700703i	$0.247130\pi$
$709$			37.3153i			1.40141i	−0.713454	+	0.700703i	$0.752870\pi$
$710$	9.75018	+	10.2948i	0.365918	+	0.386358i
$711$		−	2.57216i		−	0.0964637i
$712$	17.6629	−	24.6376i	0.661944	−	0.923335i
$713$	−26.2101	+	26.2101i	−0.981576	+	0.981576i
$714$	14.1155	+	21.6358i	0.528259	+	0.809699i
$715$	51.3122	−	9.34584i	1.91897	−	0.349515i
$716$	−4.73278	−	2.08326i	−0.176872	−	0.0778550i
$717$	−24.0556	−	24.0556i	−0.898373	−	0.898373i
$718$	5.73557	+	1.20648i	0.214050	+	0.0450253i
$719$	−20.7971			−0.775602			−0.387801	−	0.921743i	$-0.626765\pi$
$719$	−20.7971			−0.775602			−0.387801	+	0.921743i	$0.626765\pi$
$720$	−0.221548	−	1.61596i	−0.00825661	−	0.0602232i
$721$	−12.6447			−0.470914
$722$	−1.38393	−	0.291109i	−0.0515045	−	0.0108340i
$723$	14.2208	+	14.2208i	0.528878	+	0.528878i
$724$	15.0840	+	6.63961i	0.560592	+	0.246759i
$725$	14.0450	−	5.29176i	0.521617	−	0.196531i
$726$	−4.47723	−	6.86255i	−0.166166	−	0.254693i
$727$	−12.6284	+	12.6284i	−0.468361	+	0.468361i	−0.901383	−	0.433022i	$-0.857447\pi$
$727$	−12.6284	+	12.6284i	−0.468361	+	0.468361i	0.433022	+	0.901383i	$0.357447\pi$
$728$	−21.9771	+	30.6555i	−0.814526	+	1.13617i
$729$		−	28.4356i		−	1.05317i
$730$	−0.119690	+	4.40490i	−0.00442993	+	0.163033i
$731$			21.1127i			0.780880i
$732$	0.446588	+	1.14887i	0.0165064	+	0.0424635i
$733$	−0.538751	+	0.538751i	−0.0198992	+	0.0198992i	−0.716986	−	0.697087i	$-0.754479\pi$
$733$	−0.538751	+	0.538751i	−0.0198992	+	0.0198992i	0.697087	+	0.716986i	$0.254479\pi$
$734$	35.7457	−	23.3210i	1.31940	−	0.860794i
$735$	−1.53074	−	8.40435i	−0.0564623	−	0.309999i
$736$	−6.19623	+	24.1416i	−0.228396	+	0.889872i
$737$	−23.2648	−	23.2648i	−0.856971	−	0.856971i
$738$	0.112737	−	0.535952i	0.00414992	−	0.0197287i
$739$	−7.58704			−0.279094			−0.139547	−	0.990215i	$-0.544565\pi$
$739$	−7.58704			−0.279094			−0.139547	+	0.990215i	$0.544565\pi$
$740$	−49.5635	−	11.8401i	−1.82199	−	0.435250i
$741$	10.2992			0.378352
$742$	5.77610	−	27.4595i	0.212047	−	1.00807i
$743$	−35.1805	−	35.1805i	−1.29065	−	1.29065i	−0.934387	−	0.356259i	$-0.884052\pi$
$743$	−35.1805	−	35.1805i	−1.29065	−	1.29065i	−0.356259	−	0.934387i	$-0.615948\pi$
$744$	39.4096	−	6.49811i	1.44483	−	0.238232i
$745$	−12.6042	−	8.72021i	−0.461781	−	0.319484i
$746$	12.5314	−	8.17564i	0.458806	−	0.299331i
$747$	−0.841713	+	0.841713i	−0.0307967	+	0.0307967i
$748$	−35.4810	+	13.7921i	−1.29731	+	0.504290i
$749$			20.4021i			0.745476i
$750$	−8.67960	−	25.0814i	−0.316934	−	0.915842i
$751$			36.7777i			1.34204i	0.741441	+	0.671018i	$0.234143\pi$
$751$			36.7777i			1.34204i	−0.741441	+	0.671018i	$0.765857\pi$
$752$	14.1372	+	0.621180i	0.515529	+	0.0226521i
$753$	−3.42717	+	3.42717i	−0.124893	+	0.124893i
$754$	−14.2322	−	21.8146i	−0.518306	−	0.794442i
$755$	6.79358	+	4.70015i	0.247244	+	0.171056i
$756$	−9.35510	+	21.2531i	−0.340242	+	0.772966i
$757$	25.0633	+	25.0633i	0.910942	+	0.910942i	0.996346	−	0.0854047i	$-0.0272183\pi$
$757$	25.0633	+	25.0633i	0.910942	+	0.910942i	−0.0854047	+	0.996346i	$0.527218\pi$
$758$	−35.5197	−	7.47157i	−1.29013	−	0.271380i
$759$	−28.1156			−1.02053
$760$	5.95492	−	2.13048i	0.216008	−	0.0772806i
$761$	1.70937			0.0619646			0.0309823	−	0.999520i	$-0.490136\pi$
$761$	1.70937			0.0619646			0.0309823	+	0.999520i	$0.490136\pi$
$762$	−7.87539	−	1.65659i	−0.285295	−	0.0600118i
$763$	13.1589	+	13.1589i	0.476383	+	0.476383i
$764$	8.73426	−	19.8426i	0.315994	−	0.717881i
$765$	−0.365837	−	2.00858i	−0.0132269	−	0.0726205i
$766$	0.0796466	+	0.122080i	0.00287775	+	0.00441092i
$767$	41.4922	−	41.4922i	1.49820	−	1.49820i
$768$	20.5835	−	17.2521i	0.742743	−	0.622532i
$769$		−	21.7516i		−	0.784384i	−0.919883	−	0.392192i	$-0.871717\pi$
$769$		−	21.7516i		−	0.784384i	0.919883	−	0.392192i	$-0.128283\pi$
$770$	−26.1190	−	0.709706i	−0.941263	−	0.0255760i
$771$		−	52.6416i

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)

\(f(q)\)	\(=\)	\(q+(-1.38393 - 0.291109i) q^{2} +(-1.18694 - 1.18694i) q^{3} +(1.83051 + 0.805748i) q^{4} +(1.27222 - 1.83887i) q^{5} +(1.29711 + 1.98816i) q^{6} +(1.53689 - 1.53689i) q^{7} +(-2.29873 - 1.64798i) q^{8} -0.182360i q^{9} +O(q^{10})\)	\(q+(-1.38393 - 0.291109i) q^{2} +(-1.18694 - 1.18694i) q^{3} +(1.83051 + 0.805748i) q^{4} +(1.27222 - 1.83887i) q^{5} +(1.29711 + 1.98816i) q^{6} +(1.53689 - 1.53689i) q^{7} +(-2.29873 - 1.64798i) q^{8} -0.182360i q^{9} +(-2.29598 + 2.17451i) q^{10} +3.80154i q^{11} +(-1.21633 - 3.12907i) q^{12} +(4.33858 - 4.33858i) q^{13} +(-2.57434 + 1.67954i) q^{14} +(-3.69267 + 0.672572i) q^{15} +(2.70154 + 2.94986i) q^{16} +(3.54037 + 3.54037i) q^{17} +(-0.0530865 + 0.252372i) q^{18} -1.00000 q^{19} +(3.81049 - 2.34098i) q^{20} -3.64838 q^{21} +(1.10666 - 5.26106i) q^{22} +(-3.11551 - 3.11551i) q^{23} +(0.772410 + 4.68450i) q^{24} +(-1.76289 - 4.67891i) q^{25} +(-7.26728 + 4.74128i) q^{26} +(-3.77726 + 3.77726i) q^{27} +(4.05163 - 1.57495i) q^{28} +3.00176i q^{29} +(5.30619 + 0.144180i) q^{30} -8.41277i q^{31} +(-2.88001 - 4.86884i) q^{32} +(4.51219 - 4.51219i) q^{33} +(-3.86898 - 5.93024i) q^{34} +(-0.870870 - 4.78140i) q^{35} +(0.146936 - 0.333811i) q^{36} +(-8.05718 - 8.05718i) q^{37} +(1.38393 + 0.291109i) q^{38} -10.2992 q^{39} +(-5.95492 + 2.13048i) q^{40} -2.12365 q^{41} +(5.04909 + 1.06208i) q^{42} +(2.98171 + 2.98171i) q^{43} +(-3.06308 + 6.95876i) q^{44} +(-0.335336 - 0.232002i) q^{45} +(3.40469 + 5.21860i) q^{46} +(2.50153 - 2.50153i) q^{47} +(0.294740 - 6.70786i) q^{48} +2.27595i q^{49} +(1.07763 + 6.98847i) q^{50} -8.40439i q^{51} +(11.4376 - 4.44602i) q^{52} +(-6.45515 + 6.45515i) q^{53} +(6.32705 - 4.12786i) q^{54} +(6.99054 + 4.83641i) q^{55} +(-6.06565 + 1.00014i) q^{56} +(1.18694 + 1.18694i) q^{57} +(0.873840 - 4.15422i) q^{58} +9.56354 q^{59} +(-7.30141 - 1.74421i) q^{60} -0.367160 q^{61} +(-2.44903 + 11.6427i) q^{62} +(-0.280266 - 0.280266i) q^{63} +(2.56836 + 7.57651i) q^{64} +(-2.45844 - 13.4977i) q^{65} +(-7.55808 + 4.93100i) q^{66} +(-6.11984 + 6.11984i) q^{67} +(3.62804 + 9.33332i) q^{68} +7.39584i q^{69} +(-0.186689 + 6.87064i) q^{70} -4.48386i q^{71} +(-0.300524 + 0.419196i) q^{72} +(0.985330 - 0.985330i) q^{73} +(8.80503 + 13.4961i) q^{74} +(-3.46114 + 7.64601i) q^{75} +(-1.83051 - 0.805748i) q^{76} +(5.84254 + 5.84254i) q^{77} +(14.2534 + 2.99820i) q^{78} +14.1049 q^{79} +(8.86138 - 1.21490i) q^{80} +8.41967 q^{81} +(2.93898 + 0.618215i) q^{82} +(-4.61568 - 4.61568i) q^{83} +(-6.67840 - 2.93967i) q^{84} +(11.0144 - 2.00613i) q^{85} +(-3.25847 - 4.99447i) q^{86} +(3.56290 - 3.56290i) q^{87} +(6.26484 - 8.73873i) q^{88} +10.7179i q^{89} +(0.396542 + 0.418694i) q^{90} -13.3358i q^{91} +(-3.19266 - 8.21330i) q^{92} +(-9.98543 + 9.98543i) q^{93} +(-4.19016 + 2.73372i) q^{94} +(-1.27222 + 1.83887i) q^{95} +(-2.36062 + 9.19739i) q^{96} +(11.9851 + 11.9851i) q^{97} +(0.662550 - 3.14975i) q^{98} +0.693247 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Introduction

L-functions

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