LMFDB - Embedded newform 370.2.g.a.327.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(43,370)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("370.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.g (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			327.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	370.327
Dual form			370.2.g.a.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.00000 - 1.00000i) q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +(1.00000 - 1.00000i) q^{6} +(1.00000 + 1.00000i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.00000 - 1.00000i) q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +(1.00000 - 1.00000i) q^{6} +(1.00000 + 1.00000i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(-1.00000 + 2.00000i) q^{10} +2.00000i q^{11} +(1.00000 + 1.00000i) q^{12} -2.00000i q^{13} +(-1.00000 + 1.00000i) q^{14} +(-1.00000 - 3.00000i) q^{15} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{18} +(5.00000 + 5.00000i) q^{19} +(-2.00000 - 1.00000i) q^{20} -2.00000i q^{21} -2.00000 q^{22} +(-1.00000 + 1.00000i) q^{24} +(3.00000 + 4.00000i) q^{25} +2.00000 q^{26} +(-4.00000 + 4.00000i) q^{27} +(-1.00000 - 1.00000i) q^{28} +(3.00000 - 3.00000i) q^{29} +(3.00000 - 1.00000i) q^{30} +(7.00000 + 7.00000i) q^{31} +1.00000i q^{32} +(2.00000 - 2.00000i) q^{33} +4.00000i q^{34} +(1.00000 + 3.00000i) q^{35} +1.00000i q^{36} +(-6.00000 - 1.00000i) q^{37} +(-5.00000 + 5.00000i) q^{38} +(-2.00000 + 2.00000i) q^{39} +(1.00000 - 2.00000i) q^{40} +2.00000 q^{42} -4.00000i q^{43} -2.00000i q^{44} +(1.00000 - 2.00000i) q^{45} +(-7.00000 - 7.00000i) q^{47} +(-1.00000 - 1.00000i) q^{48} -5.00000i q^{49} +(-4.00000 + 3.00000i) q^{50} +(-4.00000 - 4.00000i) q^{51} +2.00000i q^{52} +(1.00000 - 1.00000i) q^{53} +(-4.00000 - 4.00000i) q^{54} +(-2.00000 + 4.00000i) q^{55} +(1.00000 - 1.00000i) q^{56} -10.0000i q^{57} +(3.00000 + 3.00000i) q^{58} +(1.00000 + 1.00000i) q^{59} +(1.00000 + 3.00000i) q^{60} +(-3.00000 - 3.00000i) q^{61} +(-7.00000 + 7.00000i) q^{62} +(1.00000 - 1.00000i) q^{63} -1.00000 q^{64} +(2.00000 - 4.00000i) q^{65} +(2.00000 + 2.00000i) q^{66} +(-3.00000 + 3.00000i) q^{67} -4.00000 q^{68} +(-3.00000 + 1.00000i) q^{70} -8.00000 q^{71} -1.00000 q^{72} +(-9.00000 - 9.00000i) q^{73} +(1.00000 - 6.00000i) q^{74} +(1.00000 - 7.00000i) q^{75} +(-5.00000 - 5.00000i) q^{76} +(-2.00000 + 2.00000i) q^{77} +(-2.00000 - 2.00000i) q^{78} +(1.00000 + 1.00000i) q^{79} +(2.00000 + 1.00000i) q^{80} +5.00000 q^{81} +(-5.00000 + 5.00000i) q^{83} +2.00000i q^{84} +(8.00000 + 4.00000i) q^{85} +4.00000 q^{86} -6.00000 q^{87} +2.00000 q^{88} +(-5.00000 + 5.00000i) q^{89} +(2.00000 + 1.00000i) q^{90} +(2.00000 - 2.00000i) q^{91} -14.0000i q^{93} +(7.00000 - 7.00000i) q^{94} +(5.00000 + 15.0000i) q^{95} +(1.00000 - 1.00000i) q^{96} +8.00000 q^{97} +5.00000 q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{7}+O(q^{10}) $ 2 * q - 2 * q^3 - 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^7	$ 2 q - 2 q^{3} - 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{10} + 2 q^{12} - 2 q^{14} - 2 q^{15} + 2 q^{16} + 8 q^{17} + 2 q^{18} + 10 q^{19} - 4 q^{20} - 4 q^{22} - 2 q^{24} + 6 q^{25} + 4 q^{26} - 8 q^{27} - 2 q^{28} + 6 q^{29} + 6 q^{30} + 14 q^{31} + 4 q^{33} + 2 q^{35} - 12 q^{37} - 10 q^{38} - 4 q^{39} + 2 q^{40} + 4 q^{42} + 2 q^{45} - 14 q^{47} - 2 q^{48} - 8 q^{50} - 8 q^{51} + 2 q^{53} - 8 q^{54} - 4 q^{55} + 2 q^{56} + 6 q^{58} + 2 q^{59} + 2 q^{60} - 6 q^{61} - 14 q^{62} + 2 q^{63} - 2 q^{64} + 4 q^{65} + 4 q^{66} - 6 q^{67} - 8 q^{68} - 6 q^{70} - 16 q^{71} - 2 q^{72} - 18 q^{73} + 2 q^{74} + 2 q^{75} - 10 q^{76} - 4 q^{77} - 4 q^{78} + 2 q^{79} + 4 q^{80} + 10 q^{81} - 10 q^{83} + 16 q^{85} + 8 q^{86} - 12 q^{87} + 4 q^{88} - 10 q^{89} + 4 q^{90} + 4 q^{91} + 14 q^{94} + 10 q^{95} + 2 q^{96} + 16 q^{97} + 10 q^{98} + 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 - 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^10 + 2 * q^12 - 2 * q^14 - 2 * q^15 + 2 * q^16 + 8 * q^17 + 2 * q^18 + 10 * q^19 - 4 * q^20 - 4 * q^22 - 2 * q^24 + 6 * q^25 + 4 * q^26 - 8 * q^27 - 2 * q^28 + 6 * q^29 + 6 * q^30 + 14 * q^31 + 4 * q^33 + 2 * q^35 - 12 * q^37 - 10 * q^38 - 4 * q^39 + 2 * q^40 + 4 * q^42 + 2 * q^45 - 14 * q^47 - 2 * q^48 - 8 * q^50 - 8 * q^51 + 2 * q^53 - 8 * q^54 - 4 * q^55 + 2 * q^56 + 6 * q^58 + 2 * q^59 + 2 * q^60 - 6 * q^61 - 14 * q^62 + 2 * q^63 - 2 * q^64 + 4 * q^65 + 4 * q^66 - 6 * q^67 - 8 * q^68 - 6 * q^70 - 16 * q^71 - 2 * q^72 - 18 * q^73 + 2 * q^74 + 2 * q^75 - 10 * q^76 - 4 * q^77 - 4 * q^78 + 2 * q^79 + 4 * q^80 + 10 * q^81 - 10 * q^83 + 16 * q^85 + 8 * q^86 - 12 * q^87 + 4 * q^88 - 10 * q^89 + 4 * q^90 + 4 * q^91 + 14 * q^94 + 10 * q^95 + 2 * q^96 + 16 * q^97 + 10 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.00000	−	1.00000i	−0.577350	−	0.577350i	0.356822	−	0.934172i	$-0.383860\pi$
$3$	−1.00000	−	1.00000i	−0.577350	−	0.577350i	−0.934172	+	0.356822i	$0.883860\pi$
$4$	−1.00000			−0.500000
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$6$	1.00000	−	1.00000i	0.408248	−	0.408248i
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	0.870367	−	0.492403i	$-0.163881\pi$
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	−0.492403	+	0.870367i	$0.663881\pi$
$8$		−	1.00000i		−	0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	−1.00000	+	2.00000i	−0.316228	+	0.632456i
$11$			2.00000i			0.603023i	0.953463	+	0.301511i	$0.0974911\pi$
$11$			2.00000i			0.603023i	−0.953463	+	0.301511i	$0.902509\pi$
$12$	1.00000	+	1.00000i	0.288675	+	0.288675i
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	−1.00000	+	1.00000i	−0.267261	+	0.267261i
$15$	−1.00000	−	3.00000i	−0.258199	−	0.774597i
$16$	1.00000			0.250000
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$	1.00000			0.235702
$19$	5.00000	+	5.00000i	1.14708	+	1.14708i	0.987124	+	0.159954i	$0.0511347\pi$
$19$	5.00000	+	5.00000i	1.14708	+	1.14708i	0.159954	+	0.987124i	$0.448865\pi$
$20$	−2.00000	−	1.00000i	−0.447214	−	0.223607i
$21$		−	2.00000i		−	0.436436i
$22$	−2.00000			−0.426401
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	−1.00000	+	1.00000i	−0.204124	+	0.204124i
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	2.00000			0.392232
$27$	−4.00000	+	4.00000i	−0.769800	+	0.769800i
$28$	−1.00000	−	1.00000i	−0.188982	−	0.188982i
$29$	3.00000	−	3.00000i	0.557086	−	0.557086i	−0.371391	−	0.928477i	$-0.621119\pi$
$29$	3.00000	−	3.00000i	0.557086	−	0.557086i	0.928477	+	0.371391i	$0.121119\pi$
$30$	3.00000	−	1.00000i	0.547723	−	0.182574i
$31$	7.00000	+	7.00000i	1.25724	+	1.25724i	0.952407	+	0.304830i	$0.0985998\pi$
$31$	7.00000	+	7.00000i	1.25724	+	1.25724i	0.304830	+	0.952407i	$0.401400\pi$
$32$			1.00000i			0.176777i
$33$	2.00000	−	2.00000i	0.348155	−	0.348155i
$34$			4.00000i			0.685994i
$35$	1.00000	+	3.00000i	0.169031	+	0.507093i
$36$			1.00000i			0.166667i
$37$	−6.00000	−	1.00000i	−0.986394	−	0.164399i
$37$	−6.00000	−	1.00000i	−0.986394	−	0.164399i
$38$	−5.00000	+	5.00000i	−0.811107	+	0.811107i
$39$	−2.00000	+	2.00000i	−0.320256	+	0.320256i
$40$	1.00000	−	2.00000i	0.158114	−	0.316228i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$	2.00000			0.308607
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$		−	2.00000i		−	0.301511i
$45$	1.00000	−	2.00000i	0.149071	−	0.298142i
$46$		0			0
$47$	−7.00000	−	7.00000i	−1.02105	−	1.02105i	−0.999774	−	0.0212814i	$-0.993225\pi$
$47$	−7.00000	−	7.00000i	−1.02105	−	1.02105i	−0.0212814	−	0.999774i	$-0.506775\pi$
$48$	−1.00000	−	1.00000i	−0.144338	−	0.144338i
$49$		−	5.00000i		−	0.714286i
$50$	−4.00000	+	3.00000i	−0.565685	+	0.424264i
$51$	−4.00000	−	4.00000i	−0.560112	−	0.560112i
$52$			2.00000i			0.277350i
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	−0.635083	−	0.772444i	$-0.719034\pi$
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	0.772444	+	0.635083i	$0.219034\pi$
$54$	−4.00000	−	4.00000i	−0.544331	−	0.544331i
$55$	−2.00000	+	4.00000i	−0.269680	+	0.539360i
$56$	1.00000	−	1.00000i	0.133631	−	0.133631i
$57$		−	10.0000i		−	1.32453i
$58$	3.00000	+	3.00000i	0.393919	+	0.393919i
$59$	1.00000	+	1.00000i	0.130189	+	0.130189i	0.769199	−	0.639010i	$-0.220656\pi$
$59$	1.00000	+	1.00000i	0.130189	+	0.130189i	−0.639010	+	0.769199i	$0.720656\pi$
$60$	1.00000	+	3.00000i	0.129099	+	0.387298i
$61$	−3.00000	−	3.00000i	−0.384111	−	0.384111i	0.488470	−	0.872581i	$-0.337555\pi$
$61$	−3.00000	−	3.00000i	−0.384111	−	0.384111i	−0.872581	+	0.488470i	$0.837555\pi$
$62$	−7.00000	+	7.00000i	−0.889001	+	0.889001i
$63$	1.00000	−	1.00000i	0.125988	−	0.125988i
$64$	−1.00000			−0.125000
$65$	2.00000	−	4.00000i	0.248069	−	0.496139i
$66$	2.00000	+	2.00000i	0.246183	+	0.246183i
$67$	−3.00000	+	3.00000i	−0.366508	+	0.366508i	−0.866202	−	0.499694i	$-0.833446\pi$
$67$	−3.00000	+	3.00000i	−0.366508	+	0.366508i	0.499694	+	0.866202i	$0.333446\pi$
$68$	−4.00000			−0.485071
$69$		0			0
$70$	−3.00000	+	1.00000i	−0.358569	+	0.119523i
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	−1.00000			−0.117851
$73$	−9.00000	−	9.00000i	−1.05337	−	1.05337i	−0.998493	−	0.0548772i	$-0.982523\pi$
$73$	−9.00000	−	9.00000i	−1.05337	−	1.05337i	−0.0548772	−	0.998493i	$-0.517477\pi$
$74$	1.00000	−	6.00000i	0.116248	−	0.697486i
$75$	1.00000	−	7.00000i	0.115470	−	0.808290i
$76$	−5.00000	−	5.00000i	−0.573539	−	0.573539i
$77$	−2.00000	+	2.00000i	−0.227921	+	0.227921i
$78$	−2.00000	−	2.00000i	−0.226455	−	0.226455i
$79$	1.00000	+	1.00000i	0.112509	+	0.112509i	0.761120	−	0.648611i	$-0.224650\pi$
$79$	1.00000	+	1.00000i	0.112509	+	0.112509i	−0.648611	+	0.761120i	$0.724650\pi$
$80$	2.00000	+	1.00000i	0.223607	+	0.111803i
$81$	5.00000			0.555556
$82$		0			0
$83$	−5.00000	+	5.00000i	−0.548821	+	0.548821i	−0.926100	−	0.377279i	$-0.876860\pi$
$83$	−5.00000	+	5.00000i	−0.548821	+	0.548821i	0.377279	+	0.926100i	$0.376860\pi$
$84$			2.00000i			0.218218i
$85$	8.00000	+	4.00000i	0.867722	+	0.433861i
$86$	4.00000			0.431331
$87$	−6.00000			−0.643268
$88$	2.00000			0.213201
$89$	−5.00000	+	5.00000i	−0.529999	+	0.529999i	−0.920572	−	0.390573i	$-0.872277\pi$
$89$	−5.00000	+	5.00000i	−0.529999	+	0.529999i	0.390573	+	0.920572i	$0.372277\pi$
$90$	2.00000	+	1.00000i	0.210819	+	0.105409i
$91$	2.00000	−	2.00000i	0.209657	−	0.209657i
$92$		0			0
$93$		−	14.0000i		−	1.45173i
$94$	7.00000	−	7.00000i	0.721995	−	0.721995i
$95$	5.00000	+	15.0000i	0.512989	+	1.53897i
$96$	1.00000	−	1.00000i	0.102062	−	0.102062i
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$	5.00000			0.505076
$99$	2.00000			0.201008
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$		−	8.00000i		−	0.796030i	−0.917379	−	0.398015i	$-0.869699\pi$
$101$		−	8.00000i		−	0.796030i	0.917379	−	0.398015i	$-0.130301\pi$
$102$	4.00000	−	4.00000i	0.396059	−	0.396059i
$103$	14.0000			1.37946			0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000			1.37946			0.689730	+	0.724066i	$0.257729\pi$
$104$	−2.00000			−0.196116
$105$	2.00000	−	4.00000i	0.195180	−	0.390360i
$106$	1.00000	+	1.00000i	0.0971286	+	0.0971286i
$107$	−11.0000	−	11.0000i	−1.06341	−	1.06341i	−0.997849	−	0.0655616i	$-0.979116\pi$
$107$	−11.0000	−	11.0000i	−1.06341	−	1.06341i	−0.0655616	−	0.997849i	$-0.520884\pi$
$108$	4.00000	−	4.00000i	0.384900	−	0.384900i
$109$	7.00000	+	7.00000i	0.670478	+	0.670478i	0.957826	−	0.287348i	$-0.0927736\pi$
$109$	7.00000	+	7.00000i	0.670478	+	0.670478i	−0.287348	+	0.957826i	$0.592774\pi$
$110$	−4.00000	−	2.00000i	−0.381385	−	0.190693i
$111$	5.00000	+	7.00000i	0.474579	+	0.664411i
$112$	1.00000	+	1.00000i	0.0944911	+	0.0944911i
$113$	−12.0000			−1.12887			−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000			−1.12887			−0.564433	+	0.825479i	$0.690905\pi$
$114$	10.0000			0.936586
$115$		0			0
$116$	−3.00000	+	3.00000i	−0.278543	+	0.278543i
$117$	−2.00000			−0.184900
$118$	−1.00000	+	1.00000i	−0.0920575	+	0.0920575i
$119$	4.00000	+	4.00000i	0.366679	+	0.366679i
$120$	−3.00000	+	1.00000i	−0.273861	+	0.0912871i
$121$	7.00000			0.636364
$122$	3.00000	−	3.00000i	0.271607	−	0.271607i
$123$		0			0
$124$	−7.00000	−	7.00000i	−0.628619	−	0.628619i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	1.00000	+	1.00000i	0.0890871	+	0.0890871i
$127$	−3.00000	−	3.00000i	−0.266207	−	0.266207i	0.561363	−	0.827570i	$-0.310277\pi$
$127$	−3.00000	−	3.00000i	−0.266207	−	0.266207i	−0.827570	+	0.561363i	$0.810277\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−4.00000	+	4.00000i	−0.352180	+	0.352180i
$130$	4.00000	+	2.00000i	0.350823	+	0.175412i
$131$	−13.0000	−	13.0000i	−1.13582	−	1.13582i	−0.989192	−	0.146623i	$-0.953160\pi$
$131$	−13.0000	−	13.0000i	−1.13582	−	1.13582i	−0.146623	−	0.989192i	$-0.546840\pi$
$132$	−2.00000	+	2.00000i	−0.174078	+	0.174078i
$133$			10.0000i			0.867110i
$134$	−3.00000	−	3.00000i	−0.259161	−	0.259161i
$135$	−12.0000	+	4.00000i	−1.03280	+	0.344265i
$136$		−	4.00000i		−	0.342997i
$137$	−7.00000	−	7.00000i	−0.598050	−	0.598050i	0.341743	−	0.939793i	$-0.388983\pi$
$137$	−7.00000	−	7.00000i	−0.598050	−	0.598050i	−0.939793	+	0.341743i	$0.888983\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	−1.00000	−	3.00000i	−0.0845154	−	0.253546i
$141$			14.0000i			1.17901i
$142$		−	8.00000i		−	0.671345i
$143$	4.00000			0.334497
$144$		−	1.00000i		−	0.0833333i
$145$	9.00000	−	3.00000i	0.747409	−	0.249136i
$146$	9.00000	−	9.00000i	0.744845	−	0.744845i
$147$	−5.00000	+	5.00000i	−0.412393	+	0.412393i
$148$	6.00000	+	1.00000i	0.493197	+	0.0821995i
$149$			24.0000i			1.96616i	0.183186	+	0.983078i	$0.441359\pi$
$149$			24.0000i			1.96616i	−0.183186	+	0.983078i	$0.558641\pi$
$150$	7.00000	+	1.00000i	0.571548	+	0.0816497i
$151$		−	10.0000i		−	0.813788i	−0.913475	−	0.406894i	$-0.866612\pi$
$151$		−	10.0000i		−	0.813788i	0.913475	−	0.406894i	$-0.133388\pi$
$152$	5.00000	−	5.00000i	0.405554	−	0.405554i
$153$		−	4.00000i		−	0.323381i
$154$	−2.00000	−	2.00000i	−0.161165	−	0.161165i
$155$	7.00000	+	21.0000i	0.562254	+	1.68676i
$156$	2.00000	−	2.00000i	0.160128	−	0.160128i
$157$	9.00000	+	9.00000i	0.718278	+	0.718278i	0.968252	−	0.249974i	$-0.0804222\pi$
$157$	9.00000	+	9.00000i	0.718278	+	0.718278i	−0.249974	+	0.968252i	$0.580422\pi$
$158$	−1.00000	+	1.00000i	−0.0795557	+	0.0795557i
$159$	−2.00000			−0.158610
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$		0			0
$162$			5.00000i			0.392837i
$163$	2.00000			0.156652			0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000			0.156652			0.0783260	+	0.996928i	$0.475042\pi$
$164$		0			0
$165$	6.00000	−	2.00000i	0.467099	−	0.155700i
$166$	−5.00000	−	5.00000i	−0.388075	−	0.388075i
$167$	−22.0000			−1.70241			−0.851206	−	0.524832i	$-0.824128\pi$
$167$	−22.0000			−1.70241			−0.851206	+	0.524832i	$0.824128\pi$
$168$	−2.00000			−0.154303
$169$	9.00000			0.692308
$170$	−4.00000	+	8.00000i	−0.306786	+	0.613572i
$171$	5.00000	−	5.00000i	0.382360	−	0.382360i
$172$			4.00000i			0.304997i
$173$	3.00000	+	3.00000i	0.228086	+	0.228086i	0.811893	−	0.583807i	$-0.198437\pi$
$173$	3.00000	+	3.00000i	0.228086	+	0.228086i	−0.583807	+	0.811893i	$0.698437\pi$
$174$		−	6.00000i		−	0.454859i
$175$	−1.00000	+	7.00000i	−0.0755929	+	0.529150i
$176$			2.00000i			0.150756i
$177$		−	2.00000i		−	0.150329i
$178$	−5.00000	−	5.00000i	−0.374766	−	0.374766i
$179$	−9.00000	+	9.00000i	−0.672692	+	0.672692i	−0.958336	−	0.285644i	$-0.907792\pi$
$179$	−9.00000	+	9.00000i	−0.672692	+	0.672692i	0.285644	+	0.958336i	$0.407792\pi$
$180$	−1.00000	+	2.00000i	−0.0745356	+	0.149071i
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$	2.00000	+	2.00000i	0.148250	+	0.148250i
$183$			6.00000i			0.443533i
$184$		0			0
$185$	−11.0000	−	8.00000i	−0.808736	−	0.588172i
$186$	14.0000			1.02653
$187$			8.00000i			0.585018i
$188$	7.00000	+	7.00000i	0.510527	+	0.510527i
$189$	−8.00000			−0.581914
$190$	−15.0000	+	5.00000i	−1.08821	+	0.362738i
$191$	1.00000	−	1.00000i	0.0723575	−	0.0723575i	−0.670002	−	0.742359i	$-0.733707\pi$
$191$	1.00000	−	1.00000i	0.0723575	−	0.0723575i	0.742359	+	0.670002i	$0.233707\pi$
$192$	1.00000	+	1.00000i	0.0721688	+	0.0721688i
$193$		−	18.0000i		−	1.29567i	−0.761781	−	0.647834i	$-0.775675\pi$
$193$		−	18.0000i		−	1.29567i	0.761781	−	0.647834i	$-0.224325\pi$
$194$			8.00000i			0.574367i
$195$	−6.00000	+	2.00000i	−0.429669	+	0.143223i
$196$			5.00000i			0.357143i
$197$	13.0000	+	13.0000i	0.926212	+	0.926212i	0.997459	−	0.0712470i	$-0.0226979\pi$
$197$	13.0000	+	13.0000i	0.926212	+	0.926212i	−0.0712470	+	0.997459i	$0.522698\pi$
$198$			2.00000i			0.142134i
$199$	11.0000	−	11.0000i	0.779769	−	0.779769i	−0.200022	−	0.979791i	$-0.564101\pi$
$199$	11.0000	−	11.0000i	0.779769	−	0.779769i	0.979791	+	0.200022i	$0.0641014\pi$
$200$	4.00000	−	3.00000i	0.282843	−	0.212132i
$201$	6.00000			0.423207
$202$	8.00000			0.562878
$203$	6.00000			0.421117
$204$	4.00000	+	4.00000i	0.280056	+	0.280056i
$205$		0			0
$206$			14.0000i			0.975426i
$207$		0			0
$208$		−	2.00000i		−	0.138675i
$209$	−10.0000	+	10.0000i	−0.691714	+	0.691714i
$210$	4.00000	+	2.00000i	0.276026	+	0.138013i
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	−1.00000	+	1.00000i	−0.0686803	+	0.0686803i
$213$	8.00000	+	8.00000i	0.548151	+	0.548151i
$214$	11.0000	−	11.0000i	0.751945	−	0.751945i
$215$	4.00000	−	8.00000i	0.272798	−	0.545595i
$216$	4.00000	+	4.00000i	0.272166	+	0.272166i
$217$			14.0000i			0.950382i
$218$	−7.00000	+	7.00000i	−0.474100	+	0.474100i
$219$			18.0000i			1.21633i
$220$	2.00000	−	4.00000i	0.134840	−	0.269680i
$221$		−	8.00000i		−	0.538138i
$222$	−7.00000	+	5.00000i	−0.469809	+	0.335578i
$223$	3.00000	−	3.00000i	0.200895	−	0.200895i	−0.599489	−	0.800383i	$-0.704629\pi$
$223$	3.00000	−	3.00000i	0.200895	−	0.200895i	0.800383	+	0.599489i	$0.204629\pi$
$224$	−1.00000	+	1.00000i	−0.0668153	+	0.0668153i
$225$	4.00000	−	3.00000i	0.266667	−	0.200000i
$226$		−	12.0000i		−	0.798228i
$227$	6.00000			0.398234			0.199117	−	0.979976i	$-0.436193\pi$
$227$	6.00000			0.398234			0.199117	+	0.979976i	$0.436193\pi$
$228$			10.0000i			0.662266i
$229$			12.0000i			0.792982i	0.918039	+	0.396491i	$0.129772\pi$
$229$			12.0000i			0.792982i	−0.918039	+	0.396491i	$0.870228\pi$
$230$		0			0
$231$	4.00000			0.263181
$232$	−3.00000	−	3.00000i	−0.196960	−	0.196960i
$233$	7.00000	+	7.00000i	0.458585	+	0.458585i	0.898191	−	0.439606i	$-0.144882\pi$
$233$	7.00000	+	7.00000i	0.458585	+	0.458585i	−0.439606	+	0.898191i	$0.644882\pi$
$234$		−	2.00000i		−	0.130744i
$235$	−7.00000	−	21.0000i	−0.456630	−	1.36989i
$236$	−1.00000	−	1.00000i	−0.0650945	−	0.0650945i
$237$		−	2.00000i		−	0.129914i
$238$	−4.00000	+	4.00000i	−0.259281	+	0.259281i
$239$	−3.00000	−	3.00000i	−0.194054	−	0.194054i	0.603391	−	0.797445i	$-0.293816\pi$
$239$	−3.00000	−	3.00000i	−0.194054	−	0.194054i	−0.797445	+	0.603391i	$0.793816\pi$
$240$	−1.00000	−	3.00000i	−0.0645497	−	0.193649i
$241$	1.00000	−	1.00000i	0.0644157	−	0.0644157i	−0.674165	−	0.738581i	$-0.735496\pi$
$241$	1.00000	−	1.00000i	0.0644157	−	0.0644157i	0.738581	+	0.674165i	$0.235496\pi$
$242$			7.00000i			0.449977i
$243$	7.00000	+	7.00000i	0.449050	+	0.449050i
$244$	3.00000	+	3.00000i	0.192055	+	0.192055i
$245$	5.00000	−	10.0000i	0.319438	−	0.638877i
$246$		0			0
$247$	10.0000	−	10.0000i	0.636285	−	0.636285i
$248$	7.00000	−	7.00000i	0.444500	−	0.444500i
$249$	10.0000			0.633724
$250$	−11.0000	+	2.00000i	−0.695701	+	0.126491i
$251$	−5.00000	−	5.00000i	−0.315597	−	0.315597i	0.531476	−	0.847073i	$-0.321638\pi$
$251$	−5.00000	−	5.00000i	−0.315597	−	0.315597i	−0.847073	+	0.531476i	$0.821638\pi$
$252$	−1.00000	+	1.00000i	−0.0629941	+	0.0629941i
$253$		0			0
$254$	3.00000	−	3.00000i	0.188237	−	0.188237i
$255$	−4.00000	−	12.0000i	−0.250490	−	0.751469i
$256$	1.00000			0.0625000
$257$	12.0000			0.748539			0.374270	−	0.927320i	$-0.377893\pi$
$257$	12.0000			0.748539			0.374270	+	0.927320i	$0.377893\pi$
$258$	−4.00000	−	4.00000i	−0.249029	−	0.249029i
$259$	−5.00000	−	7.00000i	−0.310685	−	0.434959i
$260$	−2.00000	+	4.00000i	−0.124035	+	0.248069i
$261$	−3.00000	−	3.00000i	−0.185695	−	0.185695i
$262$	13.0000	−	13.0000i	0.803143	−	0.803143i
$263$	11.0000	+	11.0000i	0.678289	+	0.678289i	0.959613	−	0.281324i	$-0.0907735\pi$
$263$	11.0000	+	11.0000i	0.678289	+	0.678289i	−0.281324	+	0.959613i	$0.590774\pi$
$264$	−2.00000	−	2.00000i	−0.123091	−	0.123091i
$265$	3.00000	−	1.00000i	0.184289	−	0.0614295i
$266$	−10.0000			−0.613139
$267$	10.0000			0.611990
$268$	3.00000	−	3.00000i	0.183254	−	0.183254i
$269$		−	24.0000i		−	1.46331i	−0.681677	−	0.731653i	$-0.738749\pi$
$269$		−	24.0000i		−	1.46331i	0.681677	−	0.731653i	$-0.261251\pi$
$270$	−4.00000	−	12.0000i	−0.243432	−	0.730297i
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$	4.00000			0.242536
$273$	−4.00000			−0.242091
$274$	7.00000	−	7.00000i	0.422885	−	0.422885i
$275$	−8.00000	+	6.00000i	−0.482418	+	0.361814i
$276$		0			0
$277$			10.0000i			0.600842i	0.953807	+	0.300421i	$0.0971271\pi$
$277$			10.0000i			0.600842i	−0.953807	+	0.300421i	$0.902873\pi$
$278$		−	4.00000i		−	0.239904i
$279$	7.00000	−	7.00000i	0.419079	−	0.419079i
$280$	3.00000	−	1.00000i	0.179284	−	0.0597614i
$281$	1.00000	−	1.00000i	0.0596550	−	0.0596550i	−0.676650	−	0.736305i	$-0.736569\pi$
$281$	1.00000	−	1.00000i	0.0596550	−	0.0596550i	0.736305	+	0.676650i	$0.236569\pi$
$282$	−14.0000			−0.833688
$283$	−14.0000			−0.832214			−0.416107	−	0.909316i	$-0.636606\pi$
$283$	−14.0000			−0.832214			−0.416107	+	0.909316i	$0.636606\pi$
$284$	8.00000			0.474713
$285$	10.0000	−	20.0000i	0.592349	−	1.18470i
$286$			4.00000i			0.236525i
$287$		0			0
$288$	1.00000			0.0589256
$289$	−1.00000			−0.0588235
$290$	3.00000	+	9.00000i	0.176166	+	0.528498i
$291$	−8.00000	−	8.00000i	−0.468968	−	0.468968i
$292$	9.00000	+	9.00000i	0.526685	+	0.526685i
$293$	−19.0000	+	19.0000i	−1.10999	+	1.10999i	−0.116841	+	0.993151i	$0.537277\pi$
$293$	−19.0000	+	19.0000i	−1.10999	+	1.10999i	−0.993151	+	0.116841i	$0.962723\pi$
$294$	−5.00000	−	5.00000i	−0.291606	−	0.291606i
$295$	1.00000	+	3.00000i	0.0582223	+	0.174667i
$296$	−1.00000	+	6.00000i	−0.0581238	+	0.348743i
$297$	−8.00000	−	8.00000i	−0.464207	−	0.464207i
$298$	−24.0000			−1.39028
$299$		0			0
$300$	−1.00000	+	7.00000i	−0.0577350	+	0.404145i
$301$	4.00000	−	4.00000i	0.230556	−	0.230556i
$302$	10.0000			0.575435
$303$	−8.00000	+	8.00000i	−0.459588	+	0.459588i
$304$	5.00000	+	5.00000i	0.286770	+	0.286770i
$305$	−3.00000	−	9.00000i	−0.171780	−	0.515339i
$306$	4.00000			0.228665
$307$	−15.0000	+	15.0000i	−0.856095	+	0.856095i	−0.990876	−	0.134780i	$-0.956967\pi$
$307$	−15.0000	+	15.0000i	−0.856095	+	0.856095i	0.134780	+	0.990876i	$0.456967\pi$
$308$	2.00000	−	2.00000i	0.113961	−	0.113961i
$309$	−14.0000	−	14.0000i	−0.796432	−	0.796432i
$310$	−21.0000	+	7.00000i	−1.19272	+	0.397573i
$311$	−17.0000	−	17.0000i	−0.963982	−	0.963982i	0.0353919	−	0.999374i	$-0.488732\pi$
$311$	−17.0000	−	17.0000i	−0.963982	−	0.963982i	−0.999374	+	0.0353919i	$0.988732\pi$
$312$	2.00000	+	2.00000i	0.113228	+	0.113228i
$313$		−	34.0000i		−	1.92179i	−0.276907	−	0.960897i	$-0.589309\pi$
$313$		−	34.0000i		−	1.92179i	0.276907	−	0.960897i	$-0.410691\pi$
$314$	−9.00000	+	9.00000i	−0.507899	+	0.507899i
$315$	3.00000	−	1.00000i	0.169031	−	0.0563436i
$316$	−1.00000	−	1.00000i	−0.0562544	−	0.0562544i
$317$	19.0000	−	19.0000i	1.06715	−	1.06715i	0.0695692	−	0.997577i	$-0.477838\pi$
$317$	19.0000	−	19.0000i	1.06715	−	1.06715i	0.997577	−	0.0695692i	$-0.0221625\pi$
$318$		−	2.00000i		−	0.112154i
$319$	6.00000	+	6.00000i	0.335936	+	0.335936i
$320$	−2.00000	−	1.00000i	−0.111803	−	0.0559017i
$321$			22.0000i			1.22792i
$322$		0			0
$323$	20.0000	+	20.0000i	1.11283	+	1.11283i
$324$	−5.00000			−0.277778
$325$	8.00000	−	6.00000i	0.443760	−	0.332820i
$326$			2.00000i			0.110770i
$327$		−	14.0000i		−	0.774202i
$328$		0			0
$329$		−	14.0000i		−	0.771845i
$330$	2.00000	+	6.00000i	0.110096	+	0.330289i
$331$	−23.0000	+	23.0000i	−1.26419	+	1.26419i	−0.315154	+	0.949041i	$0.602056\pi$
$331$	−23.0000	+	23.0000i	−1.26419	+	1.26419i	−0.949041	+	0.315154i	$0.897944\pi$
$332$	5.00000	−	5.00000i	0.274411	−	0.274411i
$333$	−1.00000	+	6.00000i	−0.0547997	+	0.328798i
$334$		−	22.0000i		−	1.20379i
$335$	−9.00000	+	3.00000i	−0.491723	+	0.163908i
$336$		−	2.00000i		−	0.109109i
$337$	−9.00000	+	9.00000i	−0.490261	+	0.490261i	−0.908388	−	0.418127i	$-0.862687\pi$
$337$	−9.00000	+	9.00000i	−0.490261	+	0.490261i	0.418127	+	0.908388i	$0.362687\pi$
$338$			9.00000i			0.489535i
$339$	12.0000	+	12.0000i	0.651751	+	0.651751i
$340$	−8.00000	−	4.00000i	−0.433861	−	0.216930i
$341$	−14.0000	+	14.0000i	−0.758143	+	0.758143i
$342$	5.00000	+	5.00000i	0.270369	+	0.270369i
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$	−4.00000			−0.215666
$345$		0			0
$346$	−3.00000	+	3.00000i	−0.161281	+	0.161281i
$347$			12.0000i			0.644194i	0.946707	+	0.322097i	$0.104388\pi$
$347$			12.0000i			0.644194i	−0.946707	+	0.322097i	$0.895612\pi$
$348$	6.00000			0.321634
$349$		−	24.0000i		−	1.28469i	−0.766415	−	0.642345i	$-0.777962\pi$
$349$		−	24.0000i		−	1.28469i	0.766415	−	0.642345i	$-0.222038\pi$
$350$	−7.00000	−	1.00000i	−0.374166	−	0.0534522i
$351$	8.00000	+	8.00000i	0.427008	+	0.427008i
$352$	−2.00000			−0.106600
$353$		0			0			−	1.00000i	$-0.5\pi$
$353$		0			0				1.00000i	$0.5\pi$
$354$	2.00000			0.106299
$355$	−16.0000	−	8.00000i	−0.849192	−	0.424596i
$356$	5.00000	−	5.00000i	0.264999	−	0.264999i
$357$		−	8.00000i		−	0.423405i
$358$	−9.00000	−	9.00000i	−0.475665	−	0.475665i
$359$		−	22.0000i		−	1.16112i	−0.814219	−	0.580558i	$-0.802835\pi$
$359$		−	22.0000i		−	1.16112i	0.814219	−	0.580558i	$-0.197165\pi$
$360$	−2.00000	−	1.00000i	−0.105409	−	0.0527046i
$361$			31.0000i			1.63158i
$362$		−	22.0000i		−	1.15629i
$363$	−7.00000	−	7.00000i	−0.367405	−	0.367405i
$364$	−2.00000	+	2.00000i	−0.104828	+	0.104828i
$365$	−9.00000	−	27.0000i	−0.471082	−	1.41324i
$366$	−6.00000			−0.313625
$367$	5.00000	+	5.00000i	0.260998	+	0.260998i	0.825459	−	0.564462i	$-0.190916\pi$
$367$	5.00000	+	5.00000i	0.260998	+	0.260998i	−0.564462	+	0.825459i	$0.690916\pi$
$368$		0			0
$369$		0			0
$370$	8.00000	−	11.0000i	0.415900	−	0.571863i
$371$	2.00000			0.103835
$372$			14.0000i			0.725866i
$373$	15.0000	+	15.0000i	0.776671	+	0.776671i	0.979263	−	0.202593i	$-0.0649367\pi$
$373$	15.0000	+	15.0000i	0.776671	+	0.776671i	−0.202593	+	0.979263i	$0.564937\pi$
$374$	−8.00000			−0.413670
$375$	9.00000	−	13.0000i	0.464758	−	0.671317i
$376$	−7.00000	+	7.00000i	−0.360997	+	0.360997i
$377$	−6.00000	−	6.00000i	−0.309016	−	0.309016i
$378$		−	8.00000i		−	0.411476i
$379$			30.0000i			1.54100i	0.637442	+	0.770498i	$0.279993\pi$
$379$			30.0000i			1.54100i	−0.637442	+	0.770498i	$0.720007\pi$
$380$	−5.00000	−	15.0000i	−0.256495	−	0.769484i
$381$			6.00000i			0.307389i
$382$	1.00000	+	1.00000i	0.0511645	+	0.0511645i
$383$		0			0		1.00000			$0$
$383$		0			0		−1.00000			$\pi$
$384$	−1.00000	+	1.00000i	−0.0510310	+	0.0510310i
$385$	−6.00000	+	2.00000i	−0.305788	+	0.101929i
$386$	18.0000			0.916176
$387$	−4.00000			−0.203331
$388$	−8.00000			−0.406138
$389$	−25.0000	−	25.0000i	−1.26755	−	1.26755i	−0.947350	−	0.320201i	$-0.896250\pi$
$389$	−25.0000	−	25.0000i	−1.26755	−	1.26755i	−0.320201	−	0.947350i	$-0.603750\pi$
$390$	−2.00000	−	6.00000i	−0.101274	−	0.303822i
$391$		0			0
$392$	−5.00000			−0.252538
$393$			26.0000i			1.31153i
$394$	−13.0000	+	13.0000i	−0.654931	+	0.654931i
$395$	1.00000	+	3.00000i	0.0503155	+	0.150946i
$396$	−2.00000			−0.100504
$397$	15.0000	−	15.0000i	0.752828	−	0.752828i	−0.222178	−	0.975006i	$-0.571317\pi$
$397$	15.0000	−	15.0000i	0.752828	−	0.752828i	0.975006	+	0.222178i	$0.0713165\pi$
$398$	11.0000	+	11.0000i	0.551380	+	0.551380i
$399$	10.0000	−	10.0000i	0.500626	−	0.500626i
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	−7.00000	−	7.00000i	−0.349563	−	0.349563i	0.510384	−	0.859947i	$-0.329503\pi$
$401$	−7.00000	−	7.00000i	−0.349563	−	0.349563i	−0.859947	+	0.510384i	$0.829503\pi$
$402$			6.00000i			0.299253i
$403$	14.0000	−	14.0000i	0.697390	−	0.697390i
$404$			8.00000i			0.398015i
$405$	10.0000	+	5.00000i	0.496904	+	0.248452i
$406$			6.00000i			0.297775i
$407$	2.00000	−	12.0000i	0.0991363	−	0.594818i
$408$	−4.00000	+	4.00000i	−0.198030	+	0.198030i
$409$	−13.0000	+	13.0000i	−0.642809	+	0.642809i	−0.951245	−	0.308436i	$-0.900194\pi$
$409$	−13.0000	+	13.0000i	−0.642809	+	0.642809i	0.308436	+	0.951245i	$0.400194\pi$
$410$		0			0
$411$			14.0000i			0.690569i
$412$	−14.0000			−0.689730
$413$			2.00000i			0.0984136i
$414$		0			0
$415$	−15.0000	+	5.00000i	−0.736321	+	0.245440i
$416$	2.00000			0.0980581
$417$	4.00000	+	4.00000i	0.195881	+	0.195881i
$418$	−10.0000	−	10.0000i	−0.489116	−	0.489116i
$419$		−	26.0000i		−	1.27018i	−0.772437	−	0.635092i	$-0.780962\pi$
$419$		−	26.0000i		−	1.27018i	0.772437	−	0.635092i	$-0.219038\pi$
$420$	−2.00000	+	4.00000i	−0.0975900	+	0.195180i
$421$	9.00000	+	9.00000i	0.438633	+	0.438633i	0.891552	−	0.452919i	$-0.149617\pi$
$421$	9.00000	+	9.00000i	0.438633	+	0.438633i	−0.452919	+	0.891552i	$0.649617\pi$
$422$			4.00000i			0.194717i
$423$	−7.00000	+	7.00000i	−0.340352	+	0.340352i
$424$	−1.00000	−	1.00000i	−0.0485643	−	0.0485643i
$425$	12.0000	+	16.0000i	0.582086	+	0.776114i
$426$	−8.00000	+	8.00000i	−0.387601	+	0.387601i
$427$		−	6.00000i		−	0.290360i
$428$	11.0000	+	11.0000i	0.531705	+	0.531705i
$429$	−4.00000	−	4.00000i	−0.193122	−	0.193122i
$430$	8.00000	+	4.00000i	0.385794	+	0.192897i
$431$	−1.00000	−	1.00000i	−0.0481683	−	0.0481683i	0.682612	−	0.730781i	$-0.260844\pi$
$431$	−1.00000	−	1.00000i	−0.0481683	−	0.0481683i	−0.730781	+	0.682612i	$0.760844\pi$
$432$	−4.00000	+	4.00000i	−0.192450	+	0.192450i
$433$	−11.0000	+	11.0000i	−0.528626	+	0.528626i	−0.920163	−	0.391536i	$-0.871944\pi$
$433$	−11.0000	+	11.0000i	−0.528626	+	0.528626i	0.391536	+	0.920163i	$0.371944\pi$
$434$	−14.0000			−0.672022
$435$	−12.0000	−	6.00000i	−0.575356	−	0.287678i
$436$	−7.00000	−	7.00000i	−0.335239	−	0.335239i
$437$		0			0
$438$	−18.0000			−0.860073
$439$	27.0000	−	27.0000i	1.28864	−	1.28864i	0.353026	−	0.935613i	$-0.385153\pi$
$439$	27.0000	−	27.0000i	1.28864	−	1.28864i	0.935613	−	0.353026i	$-0.114847\pi$
$440$	4.00000	+	2.00000i	0.190693	+	0.0953463i
$441$	−5.00000			−0.238095
$442$	8.00000			0.380521
$443$	−21.0000	−	21.0000i	−0.997740	−	0.997740i	0.00225734	−	0.999997i	$-0.499281\pi$
$443$	−21.0000	−	21.0000i	−0.997740	−	0.997740i	−0.999997	+	0.00225734i	$0.999281\pi$
$444$	−5.00000	−	7.00000i	−0.237289	−	0.332205i
$445$	−15.0000	+	5.00000i	−0.711068	+	0.237023i
$446$	3.00000	+	3.00000i	0.142054	+	0.142054i
$447$	24.0000	−	24.0000i	1.13516	−	1.13516i
$448$	−1.00000	−	1.00000i	−0.0472456	−	0.0472456i
$449$	11.0000	+	11.0000i	0.519122	+	0.519122i	0.917306	−	0.398184i	$-0.130359\pi$
$449$	11.0000	+	11.0000i	0.519122	+	0.519122i	−0.398184	+	0.917306i	$0.630359\pi$
$450$	3.00000	+	4.00000i	0.141421	+	0.188562i
$451$		0			0
$452$	12.0000			0.564433
$453$	−10.0000	+	10.0000i	−0.469841	+	0.469841i
$454$			6.00000i			0.281594i
$455$	6.00000	−	2.00000i	0.281284	−	0.0937614i
$456$	−10.0000			−0.468293
$457$		0			0			−	1.00000i	$-0.5\pi$
$457$		0			0				1.00000i	$0.5\pi$
$458$	−12.0000			−0.560723
$459$	−16.0000	+	16.0000i	−0.746816	+	0.746816i
$460$		0			0
$461$	1.00000	−	1.00000i	0.0465746	−	0.0465746i	−0.683436	−	0.730011i	$-0.739515\pi$
$461$	1.00000	−	1.00000i	0.0465746	−	0.0465746i	0.730011	+	0.683436i	$0.239515\pi$
$462$			4.00000i			0.186097i
$463$			16.0000i			0.743583i	0.928316	+	0.371792i	$0.121256\pi$
$463$			16.0000i			0.743583i	−0.928316	+	0.371792i	$0.878744\pi$
$464$	3.00000	−	3.00000i	0.139272	−	0.139272i
$465$	14.0000	−	28.0000i	0.649234	−	1.29847i
$466$	−7.00000	+	7.00000i	−0.324269	+	0.324269i
$467$	14.0000			0.647843			0.323921	−	0.946084i	$-0.394999\pi$
$467$	14.0000			0.647843			0.323921	+	0.946084i	$0.394999\pi$
$468$	2.00000			0.0924500
$469$	−6.00000			−0.277054
$470$	21.0000	−	7.00000i	0.968658	−	0.322886i
$471$		−	18.0000i		−	0.829396i
$472$	1.00000	−	1.00000i	0.0460287	−	0.0460287i
$473$	8.00000			0.367840
$474$	2.00000			0.0918630
$475$	−5.00000	+	35.0000i	−0.229416	+	1.60591i
$476$	−4.00000	−	4.00000i	−0.183340	−	0.183340i
$477$	−1.00000	−	1.00000i	−0.0457869	−	0.0457869i
$478$	3.00000	−	3.00000i	0.137217	−	0.137217i
$479$	13.0000	+	13.0000i	0.593985	+	0.593985i	0.938705	−	0.344720i	$-0.112026\pi$
$479$	13.0000	+	13.0000i	0.593985	+	0.593985i	−0.344720	+	0.938705i	$0.612026\pi$
$480$	3.00000	−	1.00000i	0.136931	−	0.0456435i
$481$	−2.00000	+	12.0000i	−0.0911922	+	0.547153i
$482$	1.00000	+	1.00000i	0.0455488	+	0.0455488i
$483$		0			0
$484$	−7.00000			−0.318182
$485$	16.0000	+	8.00000i	0.726523	+	0.363261i
$486$	−7.00000	+	7.00000i	−0.317526	+	0.317526i
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$	−3.00000	+	3.00000i	−0.135804	+	0.135804i
$489$	−2.00000	−	2.00000i	−0.0904431	−	0.0904431i
$490$	10.0000	+	5.00000i	0.451754	+	0.225877i
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$		0			0
$493$	12.0000	−	12.0000i	0.540453	−	0.540453i
$494$	10.0000	+	10.0000i	0.449921	+	0.449921i
$495$	4.00000	+	2.00000i	0.179787	+	0.0898933i
$496$	7.00000	+	7.00000i	0.314309	+	0.314309i
$497$	−8.00000	−	8.00000i	−0.358849	−	0.358849i
$498$			10.0000i			0.448111i
$499$	−13.0000	+	13.0000i	−0.581960	+	0.581960i	−0.935441	−	0.353482i	$-0.884998\pi$
$499$	−13.0000	+	13.0000i	−0.581960	+	0.581960i	0.353482	+	0.935441i	$0.384998\pi$
$500$	−2.00000	−	11.0000i	−0.0894427	−	0.491935i
$501$	22.0000	+	22.0000i	0.982888	+	0.982888i
$502$	5.00000	−	5.00000i	0.223161	−	0.223161i
$503$		−	24.0000i		−	1.07011i	−0.844818	−	0.535054i	$-0.820291\pi$
$503$		−	24.0000i		−	1.07011i	0.844818	−	0.535054i	$-0.179709\pi$
$504$	−1.00000	−	1.00000i	−0.0445435	−	0.0445435i
$505$	8.00000	−	16.0000i	0.355995	−	0.711991i
$506$		0			0
$507$	−9.00000	−	9.00000i	−0.399704	−	0.399704i
$508$	3.00000	+	3.00000i	0.133103	+	0.133103i
$509$	−30.0000			−1.32973			−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000			−1.32973			−0.664863	+	0.746965i	$0.731510\pi$
$510$	12.0000	−	4.00000i	0.531369	−	0.177123i
$511$		−	18.0000i		−	0.796273i
$512$			1.00000i			0.0441942i
$513$	−40.0000			−1.76604
$514$			12.0000i			0.529297i
$515$	28.0000	+	14.0000i	1.23383	+	0.616914i
$516$	4.00000	−	4.00000i	0.176090	−	0.176090i
$517$	14.0000	−	14.0000i	0.615719	−	0.615719i
$518$	7.00000	−	5.00000i	0.307562	−	0.219687i
$519$		−	6.00000i		−	0.263371i
$520$	−4.00000	−	2.00000i	−0.175412	−	0.0877058i
$521$			12.0000i			0.525730i	0.964833	+	0.262865i	$0.0846673\pi$
$521$			12.0000i			0.525730i	−0.964833	+	0.262865i	$0.915333\pi$
$522$	3.00000	−	3.00000i	0.131306	−	0.131306i
$523$		−	20.0000i		−	0.874539i	−0.899331	−	0.437269i	$-0.855946\pi$
$523$		−	20.0000i		−	0.874539i	0.899331	−	0.437269i	$-0.144054\pi$
$524$	13.0000	+	13.0000i	0.567908	+	0.567908i
$525$	8.00000	−	6.00000i	0.349149	−	0.261861i
$526$	−11.0000	+	11.0000i	−0.479623	+	0.479623i
$527$	28.0000	+	28.0000i	1.21970	+	1.21970i
$528$	2.00000	−	2.00000i	0.0870388	−	0.0870388i
$529$	23.0000			1.00000
$530$	1.00000	+	3.00000i	0.0434372	+	0.130312i
$531$	1.00000	−	1.00000i	0.0433963	−	0.0433963i
$532$		−	10.0000i		−	0.433555i
$533$		0			0
$534$			10.0000i			0.432742i
$535$	−11.0000	−	33.0000i	−0.475571	−	1.42671i
$536$	3.00000	+	3.00000i	0.129580	+	0.129580i
$537$	18.0000			0.776757
$538$	24.0000			1.03471
$539$	10.0000			0.430730
$540$	12.0000	−	4.00000i	0.516398	−	0.172133i
$541$	−3.00000	+	3.00000i	−0.128980	+	0.128980i	−0.768650	−	0.639670i	$-0.779071\pi$
$541$	−3.00000	+	3.00000i	−0.128980	+	0.128980i	0.639670	+	0.768650i	$0.279071\pi$
$542$			8.00000i			0.343629i
$543$	22.0000	+	22.0000i	0.944110	+	0.944110i
$544$			4.00000i			0.171499i
$545$	7.00000	+	21.0000i	0.299847	+	0.899541i
$546$		−	4.00000i		−	0.171184i
$547$		−	20.0000i		−	0.855138i	−0.903983	−	0.427569i	$-0.859370\pi$
$547$		−	20.0000i		−	0.855138i	0.903983	−	0.427569i	$-0.140630\pi$
$548$	7.00000	+	7.00000i	0.299025	+	0.299025i
$549$	−3.00000	+	3.00000i	−0.128037	+	0.128037i
$550$	−6.00000	−	8.00000i	−0.255841	−	0.341121i
$551$	30.0000			1.27804
$552$		0			0
$553$			2.00000i			0.0850487i
$554$	−10.0000			−0.424859
$555$	3.00000	+	19.0000i	0.127343	+	0.806505i
$556$	4.00000			0.169638
$557$			18.0000i			0.762684i	0.924434	+	0.381342i	$0.124538\pi$
$557$			18.0000i			0.762684i	−0.924434	+	0.381342i	$0.875462\pi$
$558$	7.00000	+	7.00000i	0.296334	+	0.296334i
$559$	−8.00000			−0.338364
$560$	1.00000	+	3.00000i	0.0422577	+	0.126773i
$561$	8.00000	−	8.00000i	0.337760	−	0.337760i
$562$	1.00000	+	1.00000i	0.0421825	+	0.0421825i
$563$			4.00000i			0.168580i	0.996441	+	0.0842900i	$0.0268622\pi$
$563$			4.00000i			0.168580i	−0.996441	+	0.0842900i	$0.973138\pi$
$564$		−	14.0000i		−	0.589506i
$565$	−24.0000	−	12.0000i	−1.00969	−	0.504844i
$566$		−	14.0000i		−	0.588464i
$567$	5.00000	+	5.00000i	0.209980	+	0.209980i
$568$			8.00000i			0.335673i
$569$	7.00000	−	7.00000i	0.293455	−	0.293455i	−0.544988	−	0.838444i	$-0.683466\pi$
$569$	7.00000	−	7.00000i	0.293455	−	0.293455i	0.838444	+	0.544988i	$0.183466\pi$
$570$	20.0000	+	10.0000i	0.837708	+	0.418854i
$571$	20.0000			0.836974			0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000			0.836974			0.418487	+	0.908223i	$0.362561\pi$
$572$	−4.00000			−0.167248
$573$	−2.00000			−0.0835512
$574$		0			0
$575$		0			0
$576$			1.00000i			0.0416667i
$577$	12.0000			0.499567			0.249783	−	0.968302i	$-0.419641\pi$
$577$	12.0000			0.499567			0.249783	+	0.968302i	$0.419641\pi$
$578$		−	1.00000i		−	0.0415945i
$579$	−18.0000	+	18.0000i	−0.748054	+	0.748054i
$580$	−9.00000	+	3.00000i	−0.373705	+	0.124568i
$581$	−10.0000			−0.414870
$582$	8.00000	−	8.00000i	0.331611	−	0.331611i
$583$	2.00000	+	2.00000i	0.0828315	+	0.0828315i
$584$	−9.00000	+	9.00000i	−0.372423	+	0.372423i
$585$	−4.00000	−	2.00000i	−0.165380	−	0.0826898i
$586$	−19.0000	−	19.0000i	−0.784883	−	0.784883i
$587$			36.0000i			1.48588i	0.669359	+	0.742940i	$0.266569\pi$
$587$			36.0000i			1.48588i	−0.669359	+	0.742940i	$0.733431\pi$
$588$	5.00000	−	5.00000i	0.206197	−	0.206197i
$589$			70.0000i			2.88430i
$590$	−3.00000	+	1.00000i	−0.123508	+	0.0411693i
$591$		−	26.0000i		−	1.06950i
$592$	−6.00000	−	1.00000i	−0.246598	−	0.0410997i
$593$	29.0000	−	29.0000i	1.19089	−	1.19089i	0.214069	−	0.976819i	$-0.431328\pi$
$593$	29.0000	−	29.0000i	1.19089	−	1.19089i	0.976819	−	0.214069i	$-0.0686716\pi$
$594$	8.00000	−	8.00000i	0.328244	−	0.328244i
$595$	4.00000	+	12.0000i	0.163984	+	0.491952i
$596$		−	24.0000i		−	0.983078i
$597$	−22.0000			−0.900400
$598$		0			0
$599$		−	14.0000i		−	0.572024i	−0.958226	−	0.286012i	$-0.907670\pi$
$599$		−	14.0000i		−	0.572024i	0.958226	−	0.286012i	$-0.0923298\pi$
$600$	−7.00000	−	1.00000i	−0.285774	−	0.0408248i
$601$	−42.0000			−1.71322			−0.856608	−	0.515968i	$-0.827432\pi$
$601$	−42.0000			−1.71322			−0.856608	+	0.515968i	$0.827432\pi$
$602$	4.00000	+	4.00000i	0.163028	+	0.163028i
$603$	3.00000	+	3.00000i	0.122169	+	0.122169i
$604$			10.0000i			0.406894i
$605$	14.0000	+	7.00000i	0.569181	+	0.284590i
$606$	−8.00000	−	8.00000i	−0.324978	−	0.324978i
$607$			40.0000i			1.62355i	0.583970	+	0.811775i	$0.301498\pi$
$607$			40.0000i			1.62355i	−0.583970	+	0.811775i	$0.698502\pi$
$608$	−5.00000	+	5.00000i	−0.202777	+	0.202777i
$609$	−6.00000	−	6.00000i	−0.243132	−	0.243132i
$610$	9.00000	−	3.00000i	0.364399	−	0.121466i
$611$	−14.0000	+	14.0000i	−0.566379	+	0.566379i
$612$			4.00000i			0.161690i
$613$	−17.0000	−	17.0000i	−0.686624	−	0.686624i	0.274861	−	0.961484i	$-0.411368\pi$
$613$	−17.0000	−	17.0000i	−0.686624	−	0.686624i	−0.961484	+	0.274861i	$0.911368\pi$
$614$	−15.0000	−	15.0000i	−0.605351	−	0.605351i
$615$		0			0
$616$	2.00000	+	2.00000i	0.0805823	+	0.0805823i
$617$	15.0000	−	15.0000i	0.603877	−	0.603877i	−0.337462	−	0.941339i	$-0.609568\pi$
$617$	15.0000	−	15.0000i	0.603877	−	0.603877i	0.941339	+	0.337462i	$0.109568\pi$
$618$	14.0000	−	14.0000i	0.563163	−	0.563163i
$619$	4.00000			0.160774			0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000			0.160774			0.0803868	+	0.996764i	$0.474384\pi$
$620$	−7.00000	−	21.0000i	−0.281127	−	0.843380i
$621$		0			0
$622$	17.0000	−	17.0000i	0.681638	−	0.681638i
$623$	−10.0000			−0.400642
$624$	−2.00000	+	2.00000i	−0.0800641	+	0.0800641i
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	34.0000			1.35891
$627$	20.0000			0.798723
$628$	−9.00000	−	9.00000i	−0.359139	−	0.359139i
$629$	−24.0000	−	4.00000i	−0.956943	−	0.159490i
$630$	1.00000	+	3.00000i	0.0398410	+	0.119523i
$631$	19.0000	+	19.0000i	0.756378	+	0.756378i	0.975661	−	0.219283i	$-0.0703719\pi$
$631$	19.0000	+	19.0000i	0.756378	+	0.756378i	−0.219283	+	0.975661i	$0.570372\pi$
$632$	1.00000	−	1.00000i	0.0397779	−	0.0397779i
$633$	−4.00000	−	4.00000i	−0.158986	−	0.158986i
$634$	19.0000	+	19.0000i	0.754586	+	0.754586i
$635$	−3.00000	−	9.00000i	−0.119051	−	0.357154i
$636$	2.00000			0.0793052
$637$	−10.0000			−0.396214
$638$	−6.00000	+	6.00000i	−0.237542	+	0.237542i
$639$			8.00000i			0.316475i
$640$	1.00000	−	2.00000i	0.0395285	−	0.0790569i
$641$	−18.0000			−0.710957			−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000			−0.710957			−0.355479	+	0.934684i	$0.615682\pi$
$642$	−22.0000			−0.868271
$643$	−14.0000			−0.552106			−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000			−0.552106			−0.276053	+	0.961142i	$0.589027\pi$
$644$		0			0
$645$	−12.0000	+	4.00000i	−0.472500	+	0.157500i
$646$	−20.0000	+	20.0000i	−0.786889	+	0.786889i
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$		−	5.00000i		−	0.196419i
$649$	−2.00000	+	2.00000i	−0.0785069	+	0.0785069i
$650$	6.00000	+	8.00000i	0.235339	+	0.313786i
$651$	14.0000	−	14.0000i	0.548703	−	0.548703i
$652$	−2.00000			−0.0783260
$653$	−12.0000			−0.469596			−0.234798	−	0.972044i	$-0.575443\pi$
$653$	−12.0000			−0.469596			−0.234798	+	0.972044i	$0.575443\pi$
$654$	14.0000			0.547443
$655$	−13.0000	−	39.0000i	−0.507952	−	1.52386i
$656$		0			0
$657$	−9.00000	+	9.00000i	−0.351123	+	0.351123i
$658$	14.0000			0.545777
$659$	−20.0000			−0.779089			−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000			−0.779089			−0.389545	+	0.921008i	$0.627368\pi$
$660$	−6.00000	+	2.00000i	−0.233550	+	0.0778499i
$661$	21.0000	+	21.0000i	0.816805	+	0.816805i	0.985644	−	0.168838i	$-0.0540016\pi$
$661$	21.0000	+	21.0000i	0.816805	+	0.816805i	−0.168838	+	0.985644i	$0.554002\pi$
$662$	−23.0000	−	23.0000i	−0.893920	−	0.893920i
$663$	−8.00000	+	8.00000i	−0.310694	+	0.310694i
$664$	5.00000	+	5.00000i	0.194038	+	0.194038i
$665$	−10.0000	+	20.0000i	−0.387783	+	0.775567i
$666$	−6.00000	−	1.00000i	−0.232495	−	0.0387492i
$667$		0			0
$668$	22.0000			0.851206
$669$	−6.00000			−0.231973
$670$	−3.00000	−	9.00000i	−0.115900	−	0.347700i
$671$	6.00000	−	6.00000i	0.231627	−	0.231627i
$672$	2.00000			0.0771517
$673$	−23.0000	+	23.0000i	−0.886585	+	0.886585i	−0.994193	−	0.107609i	$-0.965681\pi$
$673$	−23.0000	+	23.0000i	−0.886585	+	0.886585i	0.107609	+	0.994193i	$0.465681\pi$
$674$	−9.00000	−	9.00000i	−0.346667	−	0.346667i
$675$	−28.0000	−	4.00000i	−1.07772	−	0.153960i
$676$	−9.00000			−0.346154
$677$	−13.0000	+	13.0000i	−0.499631	+	0.499631i	−0.911323	−	0.411692i	$-0.864938\pi$
$677$	−13.0000	+	13.0000i	−0.499631	+	0.499631i	0.411692	+	0.911323i	$0.364938\pi$
$678$	−12.0000	+	12.0000i	−0.460857	+	0.460857i
$679$	8.00000	+	8.00000i	0.307012	+	0.307012i
$680$	4.00000	−	8.00000i	0.153393	−	0.306786i
$681$	−6.00000	−	6.00000i	−0.229920	−	0.229920i
$682$	−14.0000	−	14.0000i	−0.536088	−	0.536088i
$683$			36.0000i			1.37750i	0.724998	+	0.688751i	$0.241841\pi$
$683$			36.0000i			1.37750i	−0.724998	+	0.688751i	$0.758159\pi$
$684$	−5.00000	+	5.00000i	−0.191180	+	0.191180i
$685$	−7.00000	−	21.0000i	−0.267456	−	0.802369i
$686$	12.0000	+	12.0000i	0.458162	+	0.458162i
$687$	12.0000	−	12.0000i	0.457829	−	0.457829i
$688$		−	4.00000i		−	0.152499i
$689$	−2.00000	−	2.00000i	−0.0761939	−	0.0761939i
$690$		0			0
$691$		−	46.0000i		−	1.74992i	−0.484193	−	0.874961i	$-0.660887\pi$
$691$		−	46.0000i		−	1.74992i	0.484193	−	0.874961i	$-0.339113\pi$
$692$	−3.00000	−	3.00000i	−0.114043	−	0.114043i
$693$	2.00000	+	2.00000i	0.0759737	+	0.0759737i
$694$	−12.0000			−0.455514
$695$	−8.00000	−	4.00000i	−0.303457	−	0.151729i
$696$			6.00000i			0.227429i
$697$		0			0
$698$	24.0000			0.908413
$699$		−	14.0000i		−	0.529529i
$700$	1.00000	−	7.00000i	0.0377964	−	0.264575i
$701$	−19.0000	+	19.0000i	−0.717620	+	0.717620i	−0.968117	−	0.250497i	$-0.919406\pi$
$701$	−19.0000	+	19.0000i	−0.717620	+	0.717620i	0.250497	+	0.968117i	$0.419406\pi$
$702$	−8.00000	+	8.00000i	−0.301941	+	0.301941i
$703$	−25.0000	−	35.0000i	−0.942893	−	1.32005i
$704$		−	2.00000i		−	0.0753778i
$705$	−14.0000	+	28.0000i	−0.527271	+	1.05454i
$706$		0			0
$707$	8.00000	−	8.00000i	0.300871	−	0.300871i
$708$			2.00000i			0.0751646i
$709$	27.0000	+	27.0000i	1.01401	+	1.01401i	0.999901	+	0.0141058i	$0.00449016\pi$
$709$	27.0000	+	27.0000i	1.01401	+	1.01401i	0.0141058	+	0.999901i	$0.495510\pi$
$710$	8.00000	−	16.0000i	0.300235	−	0.600469i
$711$	1.00000	−	1.00000i	0.0375029	−	0.0375029i
$712$	5.00000	+	5.00000i	0.187383	+	0.187383i
$713$		0			0
$714$	8.00000			0.299392
$715$	8.00000	+	4.00000i	0.299183	+	0.149592i
$716$	9.00000	−	9.00000i	0.336346	−	0.336346i
$717$			6.00000i			0.224074i
$718$	22.0000			0.821033
$719$		−	46.0000i		−	1.71551i	−0.514058	−	0.857755i	$-0.671858\pi$
$719$		−	46.0000i		−	1.71551i	0.514058	−	0.857755i	$-0.328142\pi$
$720$	1.00000	−	2.00000i	0.0372678	−	0.0745356i
$721$	14.0000	+	14.0000i	0.521387	+	0.521387i
$722$	−31.0000			−1.15370
$723$	−2.00000			−0.0743808
$724$	22.0000			0.817624
$725$	21.0000	+	3.00000i	0.779920	+	0.111417i
$726$	7.00000	−	7.00000i	0.259794	−	0.259794i
$727$		−	24.0000i		−	0.890111i	−0.895503	−	0.445055i	$-0.853184\pi$
$727$		−	24.0000i		−	0.890111i	0.895503	−	0.445055i	$-0.146816\pi$
$728$	−2.00000	−	2.00000i	−0.0741249	−	0.0741249i
$729$		−	29.0000i		−	1.07407i
$730$	27.0000	−	9.00000i	0.999315	−	0.333105i
$731$		−	16.0000i		−	0.591781i
$732$		−	6.00000i		−	0.221766i
$733$	23.0000	+	23.0000i	0.849524	+	0.849524i	0.990074	−	0.140549i	$-0.0448868\pi$
$733$	23.0000	+	23.0000i	0.849524	+	0.849524i	−0.140549	+	0.990074i	$0.544887\pi$
$734$	−5.00000	+	5.00000i	−0.184553	+	0.184553i
$735$	−15.0000	+	5.00000i	−0.553283	+	0.184428i
$736$		0			0
$737$	−6.00000	−	6.00000i	−0.221013	−	0.221013i
$738$		0			0
$739$	4.00000			0.147142			0.0735712	−	0.997290i	$-0.476560\pi$
$739$	4.00000			0.147142			0.0735712	+	0.997290i	$0.476560\pi$
$740$	11.0000	+	8.00000i	0.404368	+	0.294086i
$741$	−20.0000			−0.734718
$742$			2.00000i			0.0734223i
$743$	23.0000	+	23.0000i	0.843788	+	0.843788i	0.989349	−	0.145561i	$-0.0464987\pi$
$743$	23.0000	+	23.0000i	0.843788	+	0.843788i	−0.145561	+	0.989349i	$0.546499\pi$
$744$	−14.0000			−0.513265
$745$	−24.0000	+	48.0000i	−0.879292	+	1.75858i
$746$	−15.0000	+	15.0000i	−0.549189	+	0.549189i
$747$	5.00000	+	5.00000i	0.182940	+	0.182940i
$748$		−	8.00000i		−	0.292509i
$749$		−	22.0000i		−	0.803863i
$750$	13.0000	+	9.00000i	0.474693	+	0.328634i
$751$		−	2.00000i		−	0.0729810i	−0.999334	−	0.0364905i	$-0.988382\pi$
$751$		−	2.00000i		−	0.0729810i	0.999334	−	0.0364905i	$-0.0116179\pi$
$752$	−7.00000	−	7.00000i	−0.255264	−	0.255264i
$753$			10.0000i			0.364420i
$754$	6.00000	−	6.00000i	0.218507	−	0.218507i
$755$	10.0000	−	20.0000i	0.363937	−	0.727875i
$756$	8.00000			0.290957
$757$	−28.0000			−1.01768			−0.508839	−	0.860862i	$-0.669925\pi$
$757$	−28.0000			−1.01768			−0.508839	+	0.860862i	$0.669925\pi$
$758$	−30.0000			−1.08965
$759$		0			0
$760$	15.0000	−	5.00000i	0.544107	−	0.181369i
$761$			8.00000i			0.290000i	0.989432	+	0.145000i	$0.0463182\pi$
$761$			8.00000i			0.290000i	−0.989432	+	0.145000i	$0.953682\pi$
$762$	−6.00000			−0.217357
$763$			14.0000i			0.506834i
$764$	−1.00000	+	1.00000i	−0.0361787	+	0.0361787i
$765$	4.00000	−	8.00000i	0.144620	−	0.289241i
$766$		0			0
$767$	2.00000	−	2.00000i	0.0722158	−	0.0722158i
$768$	−1.00000	−	1.00000i	−0.0360844	−	0.0360844i
$769$	39.0000	−	39.0000i	1.40638	−	1.40638i	0.628846	−	0.777529i	$-0.283527\pi$
$769$	39.0000	−	39.0000i	1.40638	−	1.40638i	0.777529	−	0.628846i	$-0.216473\pi$
$770$	−2.00000	−	6.00000i	−0.0720750	−	0.216225i
$771$	−12.0000	−	12.0000i	−0.432169	−	0.432169i
$772$			18.0000i			0.647834i
$773$	25.0000	−	25.0000i	0.899188	−	0.899188i	−0.0961768	−	0.995364i	$-0.530661\pi$
$773$	25.0000	−	25.0000i	0.899188	−	0.899188i	0.995364	+	0.0961768i	$0.0306614\pi$
$774$		−	4.00000i		−	0.143777i
$775$	−7.00000	+	49.0000i	−0.251447	+	1.76013i
$776$		−	8.00000i		−	0.287183i
$777$	−2.00000	+	12.0000i	−0.0717496	+	0.430498i
$778$	25.0000	−	25.0000i	0.896293	−	0.896293i
$779$		0			0
$780$	6.00000	−	2.00000i	0.214834	−	0.0716115i
$781$		−	16.0000i		−	0.572525i
$782$		0			0
$783$			24.0000i			0.857690i
$784$		−	5.00000i		−	0.178571i
$785$	9.00000	+	27.0000i	0.321224	+	0.963671i
$786$	−26.0000			−0.927389
$787$	13.0000	+	13.0000i	0.463400	+	0.463400i	0.899768	−	0.436368i	$-0.143735\pi$
$787$	13.0000	+	13.0000i	0.463400	+	0.463400i	−0.436368	+	0.899768i	$0.643735\pi$
$788$	−13.0000	−	13.0000i	−0.463106	−	0.463106i
$789$		−	22.0000i		−	0.783221i
$790$	−3.00000	+	1.00000i	−0.106735	+	0.0355784i
$791$	−12.0000	−	12.0000i	−0.426671	−	0.426671i
$792$		−	2.00000i		−	0.0710669i
$793$	−6.00000	+	6.00000i	−0.213066	+	0.213066i
$794$	15.0000	+	15.0000i	0.532330	+	0.532330i
$795$	−4.00000	−	2.00000i	−0.141865	−	0.0709327i
$796$	−11.0000	+	11.0000i	−0.389885	+	0.389885i
$797$			2.00000i			0.0708436i	0.999372	+	0.0354218i	$0.0112775\pi$
$797$			2.00000i			0.0708436i	−0.999372	+	0.0354218i	$0.988723\pi$
$798$	10.0000	+	10.0000i	0.353996	+	0.353996i
$799$	−28.0000	−	28.0000i	−0.990569	−	0.990569i
$800$	−4.00000	+	3.00000i	−0.141421	+	0.106066i
$801$	5.00000	+	5.00000i	0.176666	+	0.176666i
$802$	7.00000	−	7.00000i	0.247179	−	0.247179i
$803$	18.0000	−	18.0000i	0.635206	−	0.635206i
$804$	−6.00000			−0.211604
$805$		0			0
$806$	14.0000	+	14.0000i	0.493129	+	0.493129i
$807$	−24.0000	+	24.0000i	−0.844840	+	0.844840i
$808$	−8.00000			−0.281439
$809$	−33.0000	+	33.0000i	−1.16022	+	1.16022i	−0.175791	+	0.984428i	$0.556248\pi$
$809$	−33.0000	+	33.0000i	−1.16022	+	1.16022i	−0.984428	+	0.175791i	$0.943752\pi$
$810$	−5.00000	+	10.0000i	−0.175682	+	0.351364i
$811$	−44.0000			−1.54505			−0.772524	−	0.634985i	$-0.781006\pi$
$811$	−44.0000			−1.54505			−0.772524	+	0.634985i	$0.781006\pi$
$812$	−6.00000			−0.210559
$813$	−8.00000	−	8.00000i	−0.280572	−	0.280572i
$814$	12.0000	+	2.00000i	0.420600	+	0.0701000i
$815$	4.00000	+	2.00000i	0.140114	+	0.0700569i
$816$	−4.00000	−	4.00000i	−0.140028	−	0.140028i
$817$	20.0000	−	20.0000i	0.699711	−	0.699711i
$818$	−13.0000	−	13.0000i	−0.454534	−	0.454534i
$819$	−2.00000	−	2.00000i	−0.0698857	−	0.0698857i
$820$		0			0
$821$	30.0000			1.04701			0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000			1.04701			0.523504	+	0.852023i	$0.324625\pi$
$822$	−14.0000			−0.488306
$823$	31.0000	−	31.0000i	1.08059	−	1.08059i	0.0841380	−	0.996454i	$-0.473186\pi$
$823$	31.0000	−	31.0000i	1.08059	−	1.08059i	0.996454	−	0.0841380i	$-0.0268136\pi$
$824$		−	14.0000i		−	0.487713i
$825$	14.0000	+	2.00000i	0.487417	+	0.0696311i
$826$	−2.00000			−0.0695889
$827$	−18.0000			−0.625921			−0.312961	−	0.949766i	$-0.601321\pi$
$827$	−18.0000			−0.625921			−0.312961	+	0.949766i	$0.601321\pi$
$828$		0			0
$829$	15.0000	−	15.0000i	0.520972	−	0.520972i	−0.396893	−	0.917865i	$-0.629912\pi$
$829$	15.0000	−	15.0000i	0.520972	−	0.520972i	0.917865	+	0.396893i	$0.129912\pi$
$830$	−5.00000	−	15.0000i	−0.173553	−	0.520658i
$831$	10.0000	−	10.0000i	0.346896	−	0.346896i
$832$			2.00000i			0.0693375i
$833$		−	20.0000i		−	0.692959i
$834$	−4.00000	+	4.00000i	−0.138509	+	0.138509i
$835$	−44.0000	−	22.0000i	−1.52268	−	0.761341i
$836$	10.0000	−	10.0000i	0.345857	−	0.345857i
$837$	−56.0000			−1.93564
$838$	26.0000			0.898155
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$	−4.00000	−	2.00000i	−0.138013	−	0.0690066i
$841$			11.0000i			0.379310i
$842$	−9.00000	+	9.00000i	−0.310160	+	0.310160i
$843$	−2.00000			−0.0688837
$844$	−4.00000			−0.137686
$845$	18.0000	+	9.00000i	0.619219	+	0.309609i
$846$	−7.00000	−	7.00000i	−0.240665	−	0.240665i
$847$	7.00000	+	7.00000i	0.240523	+	0.240523i
$848$	1.00000	−	1.00000i	0.0343401	−	0.0343401i
$849$	14.0000	+	14.0000i	0.480479	+	0.480479i
$850$	−16.0000	+	12.0000i	−0.548795	+	0.411597i
$851$		0			0
$852$	−8.00000	−	8.00000i	−0.274075	−	0.274075i
$853$	−44.0000			−1.50653			−0.753266	−	0.657716i	$-0.771523\pi$
$853$	−44.0000			−1.50653			−0.753266	+	0.657716i	$0.771523\pi$
$854$	6.00000			0.205316
$855$	15.0000	−	5.00000i	0.512989	−	0.170996i
$856$	−11.0000	+	11.0000i	−0.375972	+	0.375972i
$857$	−48.0000			−1.63965			−0.819824	−	0.572615i	$-0.805929\pi$
$857$	−48.0000			−1.63965			−0.819824	+	0.572615i	$0.805929\pi$
$858$	4.00000	−	4.00000i	0.136558	−	0.136558i
$859$	33.0000	+	33.0000i	1.12595	+	1.12595i	0.990830	+	0.135116i	$0.0431406\pi$
$859$	33.0000	+	33.0000i	1.12595	+	1.12595i	0.135116	+	0.990830i	$0.456859\pi$
$860$	−4.00000	+	8.00000i	−0.136399	+	0.272798i
$861$		0			0
$862$	1.00000	−	1.00000i	0.0340601	−	0.0340601i
$863$	−5.00000	+	5.00000i	−0.170202	+	0.170202i	−0.787068	−	0.616866i	$-0.788402\pi$
$863$	−5.00000	+	5.00000i	−0.170202	+	0.170202i	0.616866	+	0.787068i	$0.288402\pi$
$864$	−4.00000	−	4.00000i	−0.136083	−	0.136083i
$865$	3.00000	+	9.00000i	0.102003	+	0.306009i
$866$	−11.0000	−	11.0000i	−0.373795	−	0.373795i
$867$	1.00000	+	1.00000i	0.0339618	+	0.0339618i
$868$		−	14.0000i		−	0.475191i
$869$	−2.00000	+	2.00000i	−0.0678454	+	0.0678454i
$870$	6.00000	−	12.0000i	0.203419	−	0.406838i
$871$	6.00000	+	6.00000i	0.203302	+	0.203302i
$872$	7.00000	−	7.00000i	0.237050	−	0.237050i
$873$		−	8.00000i		−	0.270759i
$874$		0			0
$875$	−9.00000	+	13.0000i	−0.304256	+	0.439480i
$876$		−	18.0000i		−	0.608164i
$877$	33.0000	+	33.0000i	1.11433	+	1.11433i	0.992558	+	0.121773i	$0.0388579\pi$
$877$	33.0000	+	33.0000i	1.11433	+	1.11433i	0.121773	+	0.992558i	$0.461142\pi$
$878$	27.0000	+	27.0000i	0.911206	+	0.911206i
$879$	38.0000			1.28171
$880$	−2.00000	+	4.00000i	−0.0674200	+	0.134840i
$881$		−	44.0000i		−	1.48240i	−0.671286	−	0.741199i	$-0.734258\pi$
$881$		−	44.0000i		−	1.48240i	0.671286	−	0.741199i	$-0.265742\pi$
$882$		−	5.00000i		−	0.168359i
$883$	−38.0000			−1.27880			−0.639401	−	0.768874i	$-0.720818\pi$
$883$	−38.0000			−1.27880			−0.639401	+	0.768874i	$0.720818\pi$
$884$			8.00000i			0.269069i
$885$	2.00000	−	4.00000i	0.0672293	−	0.134459i
$886$	21.0000	−	21.0000i	0.705509	−	0.705509i
$887$	−23.0000	+	23.0000i	−0.772264	+	0.772264i	−0.978502	−	0.206238i	$-0.933878\pi$
$887$	−23.0000	+	23.0000i	−0.772264	+	0.772264i	0.206238	+	0.978502i	$0.433878\pi$
$888$	7.00000	−	5.00000i	0.234905	−	0.167789i
$889$		−	6.00000i		−	0.201234i
$890$	−5.00000	−	15.0000i	−0.167600	−	0.502801i
$891$			10.0000i			0.335013i
$892$	−3.00000	+	3.00000i	−0.100447	+	0.100447i
$893$		−	70.0000i		−	2.34246i
$894$	24.0000	+	24.0000i	0.802680	+	0.802680i
$895$	−27.0000	+	9.00000i	−0.902510	+	0.300837i
$896$	1.00000	−	1.00000i	0.0334077	−	0.0334077i
$897$		0			0
$898$	−11.0000	+	11.0000i	−0.367075	+	0.367075i
$899$	42.0000			1.40078
$900$	−4.00000	+	3.00000i	−0.133333	+	0.100000i
$901$	4.00000	−	4.00000i	0.133259	−	0.133259i
$902$		0			0
$903$	−8.00000			−0.266223
$904$			12.0000i			0.399114i
$905$	−44.0000	−	22.0000i	−1.46261	−	0.731305i
$906$	−10.0000	−	10.0000i	−0.332228	−	0.332228i
$907$	−42.0000			−1.39459			−0.697294	−	0.716786i	$-0.745613\pi$
$907$	−42.0000			−1.39459			−0.697294	+	0.716786i	$0.745613\pi$
$908$	−6.00000			−0.199117
$909$	−8.00000			−0.265343
$910$	2.00000	+	6.00000i	0.0662994	+	0.198898i
$911$	41.0000	−	41.0000i	1.35839	−	1.35839i	0.482488	−	0.875903i	$-0.339733\pi$
$911$	41.0000	−	41.0000i	1.35839	−	1.35839i	0.875903	−	0.482488i	$-0.160267\pi$
$912$		−	10.0000i		−	0.331133i
$913$	−10.0000	−	10.0000i	−0.330952	−	0.330952i
$914$		0			0
$915$	−6.00000	+	12.0000i	−0.198354	+	0.396708i
$916$		−	12.0000i		−	0.396491i
$917$		−	26.0000i		−	0.858596i
$918$	−16.0000	−	16.0000i	−0.528079	−	0.528079i
$919$	7.00000	−	7.00000i	0.230909	−	0.230909i	−0.582163	−	0.813072i	$-0.697794\pi$
$919$	7.00000	−	7.00000i	0.230909	−	0.230909i	0.813072	+	0.582163i	$0.197794\pi$
$920$		0			0
$921$	30.0000			0.988534
$922$	1.00000	+	1.00000i	0.0329332	+	0.0329332i
$923$			16.0000i			0.526646i
$924$	−4.00000			−0.131590
$925$	−14.0000	−	27.0000i	−0.460317	−	0.887755i
$926$	−16.0000			−0.525793
$927$		−	14.0000i		−	0.459820i
$928$	3.00000	+	3.00000i	0.0984798	+	0.0984798i
$929$	−34.0000			−1.11550			−0.557752	−	0.830008i	$-0.688336\pi$
$929$	−34.0000			−1.11550			−0.557752	+	0.830008i	$0.688336\pi$
$930$	28.0000	+	14.0000i	0.918156	+	0.459078i
$931$	25.0000	−	25.0000i	0.819342	−	0.819342i
$932$	−7.00000	−	7.00000i	−0.229293	−	0.229293i
$933$			34.0000i			1.11311i
$934$			14.0000i			0.458094i
$935$	−8.00000	+	16.0000i	−0.261628	+	0.523256i
$936$			2.00000i			0.0653720i
$937$	−11.0000	−	11.0000i	−0.359354	−	0.359354i	0.504221	−	0.863575i	$-0.331780\pi$
$937$	−11.0000	−	11.0000i	−0.359354	−	0.359354i	−0.863575	+	0.504221i	$0.831780\pi$
$938$		−	6.00000i		−	0.195907i
$939$	−34.0000	+	34.0000i	−1.10955	+	1.10955i
$940$	7.00000	+	21.0000i	0.228315	+	0.684944i
$941$	50.0000			1.62995			0.814977	−	0.579494i	$-0.196750\pi$
$941$	50.0000			1.62995			0.814977	+	0.579494i	$0.196750\pi$
$942$	18.0000			0.586472
$943$		0			0
$944$	1.00000	+	1.00000i	0.0325472	+	0.0325472i
$945$	−16.0000	−	8.00000i	−0.520480	−	0.260240i
$946$			8.00000i			0.260102i
$947$	−10.0000			−0.324956			−0.162478	−	0.986712i	$-0.551949\pi$
$947$	−10.0000			−0.324956			−0.162478	+	0.986712i	$0.551949\pi$
$948$			2.00000i			0.0649570i
$949$	−18.0000	+	18.0000i	−0.584305	+	0.584305i
$950$	−35.0000	−	5.00000i	−1.13555	−	0.162221i
$951$	−38.0000			−1.23223
$952$	4.00000	−	4.00000i	0.129641	−	0.129641i
$953$	−1.00000	−	1.00000i	−0.0323932	−	0.0323932i	0.690725	−	0.723118i	$-0.257292\pi$
$953$	−1.00000	−	1.00000i	−0.0323932	−	0.0323932i	−0.723118	+	0.690725i	$0.757292\pi$
$954$	1.00000	−	1.00000i	0.0323762	−	0.0323762i
$955$	3.00000	−	1.00000i	0.0970777	−	0.0323592i
$956$	3.00000	+	3.00000i	0.0970269	+	0.0970269i
$957$		−	12.0000i		−	0.387905i
$958$	−13.0000	+	13.0000i	−0.420011	+	0.420011i
$959$		−	14.0000i		−	0.452084i
$960$	1.00000	+	3.00000i	0.0322749	+	0.0968246i
$961$			67.0000i			2.16129i
$962$	−12.0000	−	2.00000i	−0.386896	−	0.0644826i
$963$	−11.0000	+	11.0000i	−0.354470	+	0.354470i
$964$	−1.00000	+	1.00000i	−0.0322078	+	0.0322078i
$965$	18.0000	−	36.0000i	0.579441	−	1.15888i
$966$		0			0
$967$	34.0000			1.09337			0.546683	−	0.837340i	$-0.315890\pi$
$967$	34.0000			1.09337			0.546683	+	0.837340i	$0.315890\pi$
$968$		−	7.00000i		−	0.224989i
$969$		−	40.0000i		−	1.28499i
$970$	−8.00000	+	16.0000i	−0.256865	+	0.513729i
$971$	52.0000			1.66876			0.834380	−	0.551190i	$-0.185826\pi$
$971$	52.0000			1.66876			0.834380	+	0.551190i	$0.185826\pi$
$972$	−7.00000	−	7.00000i	−0.224525	−	0.224525i
$973$	−4.00000	−	4.00000i	−0.128234	−	0.128234i
$974$			2.00000i			0.0640841i
$975$	−14.0000	−	2.00000i	−0.448359	−	0.0640513i
$976$	−3.00000	−	3.00000i	−0.0960277	−	0.0960277i
$977$			2.00000i			0.0639857i	0.999488	+	0.0319928i	$0.0101854\pi$
$977$			2.00000i			0.0639857i	−0.999488	+	0.0319928i	$0.989815\pi$
$978$	2.00000	−	2.00000i	0.0639529	−	0.0639529i
$979$	−10.0000	−	10.0000i	−0.319601	−	0.319601i
$980$	−5.00000	+	10.0000i	−0.159719	+	0.319438i
$981$	7.00000	−	7.00000i	0.223493	−	0.223493i
$982$			12.0000i			0.382935i
$983$	−21.0000	−	21.0000i	−0.669796	−	0.669796i	0.287873	−	0.957669i	$-0.407052\pi$
$983$	−21.0000	−	21.0000i	−0.669796	−	0.669796i	−0.957669	+	0.287873i	$0.907052\pi$
$984$		0			0
$985$	13.0000	+	39.0000i	0.414214	+	1.24264i
$986$	12.0000	+	12.0000i	0.382158	+	0.382158i
$987$	−14.0000	+	14.0000i	−0.445625	+	0.445625i
$988$	−10.0000	+	10.0000i	−0.318142	+	0.318142i
$989$		0			0
$990$	−2.00000	+	4.00000i	−0.0635642	+	0.127128i
$991$	3.00000	+	3.00000i	0.0952981	+	0.0952981i	0.753149	−	0.657850i	$-0.228534\pi$
$991$	3.00000	+	3.00000i	0.0952981	+	0.0952981i	−0.657850	+	0.753149i	$0.728534\pi$
$992$	−7.00000	+	7.00000i	−0.222250	+	0.222250i
$993$	46.0000			1.45977
$994$	8.00000	−	8.00000i	0.253745	−	0.253745i
$995$	33.0000	−	11.0000i	1.04617	−	0.348723i
$996$	−10.0000			−0.316862
$997$	20.0000			0.633406			0.316703	−	0.948525i	$-0.397424\pi$
$997$	20.0000			0.633406			0.316703	+	0.948525i	$0.397424\pi$
$998$	−13.0000	−	13.0000i	−0.411508	−	0.411508i
$999$	28.0000	−	20.0000i	0.885881	−	0.632772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.g.a.327.1	yes	2
5.3	odd	4		370.2.h.b.253.1	yes	2
37.6	odd	4		370.2.h.b.117.1	yes	2
185.43	even	4	inner	370.2.g.a.43.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.a.43.1	✓	2	185.43	even	4	inner
370.2.g.a.327.1	yes	2	1.1	even	1	trivial
370.2.h.b.117.1	yes	2	37.6	odd	4
370.2.h.b.253.1	yes	2	5.3	odd	4

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.00000 - 1.00000i) q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +(1.00000 - 1.00000i) q^{6} +(1.00000 + 1.00000i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.00000 - 1.00000i) q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +(1.00000 - 1.00000i) q^{6} +(1.00000 + 1.00000i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(-1.00000 + 2.00000i) q^{10} +2.00000i q^{11} +(1.00000 + 1.00000i) q^{12} -2.00000i q^{13} +(-1.00000 + 1.00000i) q^{14} +(-1.00000 - 3.00000i) q^{15} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{18} +(5.00000 + 5.00000i) q^{19} +(-2.00000 - 1.00000i) q^{20} -2.00000i q^{21} -2.00000 q^{22} +(-1.00000 + 1.00000i) q^{24} +(3.00000 + 4.00000i) q^{25} +2.00000 q^{26} +(-4.00000 + 4.00000i) q^{27} +(-1.00000 - 1.00000i) q^{28} +(3.00000 - 3.00000i) q^{29} +(3.00000 - 1.00000i) q^{30} +(7.00000 + 7.00000i) q^{31} +1.00000i q^{32} +(2.00000 - 2.00000i) q^{33} +4.00000i q^{34} +(1.00000 + 3.00000i) q^{35} +1.00000i q^{36} +(-6.00000 - 1.00000i) q^{37} +(-5.00000 + 5.00000i) q^{38} +(-2.00000 + 2.00000i) q^{39} +(1.00000 - 2.00000i) q^{40} +2.00000 q^{42} -4.00000i q^{43} -2.00000i q^{44} +(1.00000 - 2.00000i) q^{45} +(-7.00000 - 7.00000i) q^{47} +(-1.00000 - 1.00000i) q^{48} -5.00000i q^{49} +(-4.00000 + 3.00000i) q^{50} +(-4.00000 - 4.00000i) q^{51} +2.00000i q^{52} +(1.00000 - 1.00000i) q^{53} +(-4.00000 - 4.00000i) q^{54} +(-2.00000 + 4.00000i) q^{55} +(1.00000 - 1.00000i) q^{56} -10.0000i q^{57} +(3.00000 + 3.00000i) q^{58} +(1.00000 + 1.00000i) q^{59} +(1.00000 + 3.00000i) q^{60} +(-3.00000 - 3.00000i) q^{61} +(-7.00000 + 7.00000i) q^{62} +(1.00000 - 1.00000i) q^{63} -1.00000 q^{64} +(2.00000 - 4.00000i) q^{65} +(2.00000 + 2.00000i) q^{66} +(-3.00000 + 3.00000i) q^{67} -4.00000 q^{68} +(-3.00000 + 1.00000i) q^{70} -8.00000 q^{71} -1.00000 q^{72} +(-9.00000 - 9.00000i) q^{73} +(1.00000 - 6.00000i) q^{74} +(1.00000 - 7.00000i) q^{75} +(-5.00000 - 5.00000i) q^{76} +(-2.00000 + 2.00000i) q^{77} +(-2.00000 - 2.00000i) q^{78} +(1.00000 + 1.00000i) q^{79} +(2.00000 + 1.00000i) q^{80} +5.00000 q^{81} +(-5.00000 + 5.00000i) q^{83} +2.00000i q^{84} +(8.00000 + 4.00000i) q^{85} +4.00000 q^{86} -6.00000 q^{87} +2.00000 q^{88} +(-5.00000 + 5.00000i) q^{89} +(2.00000 + 1.00000i) q^{90} +(2.00000 - 2.00000i) q^{91} -14.0000i q^{93} +(7.00000 - 7.00000i) q^{94} +(5.00000 + 15.0000i) q^{95} +(1.00000 - 1.00000i) q^{96} +8.00000 q^{97} +5.00000 q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{7}+O(q^{10}) \) 2 * q - 2 * q^3 - 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^7	\( 2 q - 2 q^{3} - 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{10} + 2 q^{12} - 2 q^{14} - 2 q^{15} + 2 q^{16} + 8 q^{17} + 2 q^{18} + 10 q^{19} - 4 q^{20} - 4 q^{22} - 2 q^{24} + 6 q^{25} + 4 q^{26} - 8 q^{27} - 2 q^{28} + 6 q^{29} + 6 q^{30} + 14 q^{31} + 4 q^{33} + 2 q^{35} - 12 q^{37} - 10 q^{38} - 4 q^{39} + 2 q^{40} + 4 q^{42} + 2 q^{45} - 14 q^{47} - 2 q^{48} - 8 q^{50} - 8 q^{51} + 2 q^{53} - 8 q^{54} - 4 q^{55} + 2 q^{56} + 6 q^{58} + 2 q^{59} + 2 q^{60} - 6 q^{61} - 14 q^{62} + 2 q^{63} - 2 q^{64} + 4 q^{65} + 4 q^{66} - 6 q^{67} - 8 q^{68} - 6 q^{70} - 16 q^{71} - 2 q^{72} - 18 q^{73} + 2 q^{74} + 2 q^{75} - 10 q^{76} - 4 q^{77} - 4 q^{78} + 2 q^{79} + 4 q^{80} + 10 q^{81} - 10 q^{83} + 16 q^{85} + 8 q^{86} - 12 q^{87} + 4 q^{88} - 10 q^{89} + 4 q^{90} + 4 q^{91} + 14 q^{94} + 10 q^{95} + 2 q^{96} + 16 q^{97} + 10 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 - 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^10 + 2 * q^12 - 2 * q^14 - 2 * q^15 + 2 * q^16 + 8 * q^17 + 2 * q^18 + 10 * q^19 - 4 * q^20 - 4 * q^22 - 2 * q^24 + 6 * q^25 + 4 * q^26 - 8 * q^27 - 2 * q^28 + 6 * q^29 + 6 * q^30 + 14 * q^31 + 4 * q^33 + 2 * q^35 - 12 * q^37 - 10 * q^38 - 4 * q^39 + 2 * q^40 + 4 * q^42 + 2 * q^45 - 14 * q^47 - 2 * q^48 - 8 * q^50 - 8 * q^51 + 2 * q^53 - 8 * q^54 - 4 * q^55 + 2 * q^56 + 6 * q^58 + 2 * q^59 + 2 * q^60 - 6 * q^61 - 14 * q^62 + 2 * q^63 - 2 * q^64 + 4 * q^65 + 4 * q^66 - 6 * q^67 - 8 * q^68 - 6 * q^70 - 16 * q^71 - 2 * q^72 - 18 * q^73 + 2 * q^74 + 2 * q^75 - 10 * q^76 - 4 * q^77 - 4 * q^78 + 2 * q^79 + 4 * q^80 + 10 * q^81 - 10 * q^83 + 16 * q^85 + 8 * q^86 - 12 * q^87 + 4 * q^88 - 10 * q^89 + 4 * q^90 + 4 * q^91 + 14 * q^94 + 10 * q^95 + 2 * q^96 + 16 * q^97 + 10 * q^98 + 4 * q^99

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