LMFDB - Embedded newform 65.2.f.a.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(18,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, 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("65.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.f (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:	$0.519027613138$
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			47.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	65.47
Dual form			65.2.f.a.18.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.00000 - 1.00000i) q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +(1.00000 + 1.00000i) q^{6} -2.00000 q^{7} +3.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(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} -2.00000 q^{7} +3.00000i q^{8} +1.00000i q^{9} +(1.00000 - 2.00000i) q^{10} +(-1.00000 + 1.00000i) q^{11} +(1.00000 - 1.00000i) q^{12} +(-2.00000 - 3.00000i) q^{13} -2.00000i q^{14} +(-3.00000 + 1.00000i) q^{15} -1.00000 q^{16} +(-1.00000 + 1.00000i) q^{17} -1.00000 q^{18} +(5.00000 - 5.00000i) q^{19} +(-2.00000 - 1.00000i) q^{20} +(-2.00000 + 2.00000i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(-3.00000 - 3.00000i) q^{23} +(3.00000 + 3.00000i) q^{24} +(3.00000 + 4.00000i) q^{25} +(3.00000 - 2.00000i) q^{26} +(4.00000 + 4.00000i) q^{27} -2.00000 q^{28} +(-1.00000 - 3.00000i) q^{30} +(5.00000 + 5.00000i) q^{31} +5.00000i q^{32} +2.00000i q^{33} +(-1.00000 - 1.00000i) q^{34} +(4.00000 + 2.00000i) q^{35} +1.00000i q^{36} +(5.00000 + 5.00000i) q^{38} +(-5.00000 - 1.00000i) q^{39} +(3.00000 - 6.00000i) q^{40} +(-7.00000 - 7.00000i) q^{41} +(-2.00000 - 2.00000i) q^{42} +(1.00000 + 1.00000i) q^{43} +(-1.00000 + 1.00000i) q^{44} +(1.00000 - 2.00000i) q^{45} +(3.00000 - 3.00000i) q^{46} +6.00000 q^{47} +(-1.00000 + 1.00000i) q^{48} -3.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +2.00000i q^{51} +(-2.00000 - 3.00000i) q^{52} +(5.00000 - 5.00000i) q^{53} +(-4.00000 + 4.00000i) q^{54} +(3.00000 - 1.00000i) q^{55} -6.00000i q^{56} -10.0000i q^{57} +(7.00000 + 7.00000i) q^{59} +(-3.00000 + 1.00000i) q^{60} -14.0000 q^{61} +(-5.00000 + 5.00000i) q^{62} -2.00000i q^{63} -7.00000 q^{64} +(1.00000 + 8.00000i) q^{65} -2.00000 q^{66} -4.00000i q^{67} +(-1.00000 + 1.00000i) q^{68} -6.00000 q^{69} +(-2.00000 + 4.00000i) q^{70} +(1.00000 + 1.00000i) q^{71} -3.00000 q^{72} +10.0000i q^{73} +(7.00000 + 1.00000i) q^{75} +(5.00000 - 5.00000i) q^{76} +(2.00000 - 2.00000i) q^{77} +(1.00000 - 5.00000i) q^{78} -2.00000i q^{79} +(2.00000 + 1.00000i) q^{80} +5.00000 q^{81} +(7.00000 - 7.00000i) q^{82} +6.00000 q^{83} +(-2.00000 + 2.00000i) q^{84} +(3.00000 - 1.00000i) q^{85} +(-1.00000 + 1.00000i) q^{86} +(-3.00000 - 3.00000i) q^{88} +(-5.00000 - 5.00000i) q^{89} +(2.00000 + 1.00000i) q^{90} +(4.00000 + 6.00000i) q^{91} +(-3.00000 - 3.00000i) q^{92} +10.0000 q^{93} +6.00000i q^{94} +(-15.0000 + 5.00000i) q^{95} +(5.00000 + 5.00000i) q^{96} +2.00000i q^{97} -3.00000i q^{98} +(-1.00000 - 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7}+O(q^{10}) $ 2 * q + 2 * q^3 + 2 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7	$ 2 q + 2 q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} + 2 q^{10} - 2 q^{11} + 2 q^{12} - 4 q^{13} - 6 q^{15} - 2 q^{16} - 2 q^{17} - 2 q^{18} + 10 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{22} - 6 q^{23} + 6 q^{24} + 6 q^{25} + 6 q^{26} + 8 q^{27} - 4 q^{28} - 2 q^{30} + 10 q^{31} - 2 q^{34} + 8 q^{35} + 10 q^{38} - 10 q^{39} + 6 q^{40} - 14 q^{41} - 4 q^{42} + 2 q^{43} - 2 q^{44} + 2 q^{45} + 6 q^{46} + 12 q^{47} - 2 q^{48} - 6 q^{49} - 8 q^{50} - 4 q^{52} + 10 q^{53} - 8 q^{54} + 6 q^{55} + 14 q^{59} - 6 q^{60} - 28 q^{61} - 10 q^{62} - 14 q^{64} + 2 q^{65} - 4 q^{66} - 2 q^{68} - 12 q^{69} - 4 q^{70} + 2 q^{71} - 6 q^{72} + 14 q^{75} + 10 q^{76} + 4 q^{77} + 2 q^{78} + 4 q^{80} + 10 q^{81} + 14 q^{82} + 12 q^{83} - 4 q^{84} + 6 q^{85} - 2 q^{86} - 6 q^{88} - 10 q^{89} + 4 q^{90} + 8 q^{91} - 6 q^{92} + 20 q^{93} - 30 q^{95} + 10 q^{96} - 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 + 2 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 + 2 * q^10 - 2 * q^11 + 2 * q^12 - 4 * q^13 - 6 * q^15 - 2 * q^16 - 2 * q^17 - 2 * q^18 + 10 * q^19 - 4 * q^20 - 4 * q^21 - 2 * q^22 - 6 * q^23 + 6 * q^24 + 6 * q^25 + 6 * q^26 + 8 * q^27 - 4 * q^28 - 2 * q^30 + 10 * q^31 - 2 * q^34 + 8 * q^35 + 10 * q^38 - 10 * q^39 + 6 * q^40 - 14 * q^41 - 4 * q^42 + 2 * q^43 - 2 * q^44 + 2 * q^45 + 6 * q^46 + 12 * q^47 - 2 * q^48 - 6 * q^49 - 8 * q^50 - 4 * q^52 + 10 * q^53 - 8 * q^54 + 6 * q^55 + 14 * q^59 - 6 * q^60 - 28 * q^61 - 10 * q^62 - 14 * q^64 + 2 * q^65 - 4 * q^66 - 2 * q^68 - 12 * q^69 - 4 * q^70 + 2 * q^71 - 6 * q^72 + 14 * q^75 + 10 * q^76 + 4 * q^77 + 2 * q^78 + 4 * q^80 + 10 * q^81 + 14 * q^82 + 12 * q^83 - 4 * q^84 + 6 * q^85 - 2 * q^86 - 6 * q^88 - 10 * q^89 + 4 * q^90 + 8 * q^91 - 6 * q^92 + 20 * q^93 - 30 * q^95 + 10 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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	0.935414	+	0.353553i	$0.115027\pi$
$2$			1.00000i			0.707107i	−0.935414	+	0.353553i	$0.884973\pi$
$3$	1.00000	−	1.00000i	0.577350	−	0.577350i	−0.356822	−	0.934172i	$-0.616140\pi$
$3$	1.00000	−	1.00000i	0.577350	−	0.577350i	0.934172	+	0.356822i	$0.116140\pi$
$4$	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
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$			3.00000i			1.06066i
$9$			1.00000i			0.333333i
$10$	1.00000	−	2.00000i	0.316228	−	0.632456i
$11$	−1.00000	+	1.00000i	−0.301511	+	0.301511i	−0.841605	−	0.540094i	$-0.818389\pi$
$11$	−1.00000	+	1.00000i	−0.301511	+	0.301511i	0.540094	+	0.841605i	$0.318389\pi$
$12$	1.00000	−	1.00000i	0.288675	−	0.288675i
$13$	−2.00000	−	3.00000i	−0.554700	−	0.832050i
$13$	−2.00000	−	3.00000i	−0.554700	−	0.832050i
$14$		−	2.00000i		−	0.534522i
$15$	−3.00000	+	1.00000i	−0.774597	+	0.258199i
$16$	−1.00000			−0.250000
$17$	−1.00000	+	1.00000i	−0.242536	+	0.242536i	−0.817898	−	0.575363i	$-0.804861\pi$
$17$	−1.00000	+	1.00000i	−0.242536	+	0.242536i	0.575363	+	0.817898i	$0.304861\pi$
$18$	−1.00000			−0.235702
$19$	5.00000	−	5.00000i	1.14708	−	1.14708i	0.159954	−	0.987124i	$-0.448865\pi$
$19$	5.00000	−	5.00000i	1.14708	−	1.14708i	0.987124	−	0.159954i	$-0.0511347\pi$
$20$	−2.00000	−	1.00000i	−0.447214	−	0.223607i
$21$	−2.00000	+	2.00000i	−0.436436	+	0.436436i
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$	−3.00000	−	3.00000i	−0.625543	−	0.625543i	0.321400	−	0.946943i	$-0.395847\pi$
$23$	−3.00000	−	3.00000i	−0.625543	−	0.625543i	−0.946943	+	0.321400i	$0.895847\pi$
$24$	3.00000	+	3.00000i	0.612372	+	0.612372i
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	3.00000	−	2.00000i	0.588348	−	0.392232i
$27$	4.00000	+	4.00000i	0.769800	+	0.769800i
$28$	−2.00000			−0.377964
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$	−1.00000	−	3.00000i	−0.182574	−	0.547723i
$31$	5.00000	+	5.00000i	0.898027	+	0.898027i	0.995261	−	0.0972349i	$-0.0309998\pi$
$31$	5.00000	+	5.00000i	0.898027	+	0.898027i	−0.0972349	+	0.995261i	$0.531000\pi$
$32$			5.00000i			0.883883i
$33$			2.00000i			0.348155i
$34$	−1.00000	−	1.00000i	−0.171499	−	0.171499i
$35$	4.00000	+	2.00000i	0.676123	+	0.338062i
$36$			1.00000i			0.166667i
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	5.00000	+	5.00000i	0.811107	+	0.811107i
$39$	−5.00000	−	1.00000i	−0.800641	−	0.160128i
$40$	3.00000	−	6.00000i	0.474342	−	0.948683i
$41$	−7.00000	−	7.00000i	−1.09322	−	1.09322i	−0.995183	−	0.0980332i	$-0.968745\pi$
$41$	−7.00000	−	7.00000i	−1.09322	−	1.09322i	−0.0980332	−	0.995183i	$-0.531255\pi$
$42$	−2.00000	−	2.00000i	−0.308607	−	0.308607i
$43$	1.00000	+	1.00000i	0.152499	+	0.152499i	0.779233	−	0.626734i	$-0.215609\pi$
$43$	1.00000	+	1.00000i	0.152499	+	0.152499i	−0.626734	+	0.779233i	$0.715609\pi$
$44$	−1.00000	+	1.00000i	−0.150756	+	0.150756i
$45$	1.00000	−	2.00000i	0.149071	−	0.298142i
$46$	3.00000	−	3.00000i	0.442326	−	0.442326i
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$	−1.00000	+	1.00000i	−0.144338	+	0.144338i
$49$	−3.00000			−0.428571
$50$	−4.00000	+	3.00000i	−0.565685	+	0.424264i
$51$			2.00000i			0.280056i
$52$	−2.00000	−	3.00000i	−0.277350	−	0.416025i
$53$	5.00000	−	5.00000i	0.686803	−	0.686803i	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	5.00000	−	5.00000i	0.686803	−	0.686803i	0.961524	+	0.274721i	$0.0885855\pi$
$54$	−4.00000	+	4.00000i	−0.544331	+	0.544331i
$55$	3.00000	−	1.00000i	0.404520	−	0.134840i
$56$		−	6.00000i		−	0.801784i
$57$		−	10.0000i		−	1.32453i
$58$		0			0
$59$	7.00000	+	7.00000i	0.911322	+	0.911322i	0.996376	−	0.0850540i	$-0.0271063\pi$
$59$	7.00000	+	7.00000i	0.911322	+	0.911322i	−0.0850540	+	0.996376i	$0.527106\pi$
$60$	−3.00000	+	1.00000i	−0.387298	+	0.129099i
$61$	−14.0000			−1.79252			−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000			−1.79252			−0.896258	+	0.443533i	$0.853725\pi$
$62$	−5.00000	+	5.00000i	−0.635001	+	0.635001i
$63$		−	2.00000i		−	0.251976i
$64$	−7.00000			−0.875000
$65$	1.00000	+	8.00000i	0.124035	+	0.992278i
$66$	−2.00000			−0.246183
$67$		−	4.00000i		−	0.488678i	−0.969690	−	0.244339i	$-0.921429\pi$
$67$		−	4.00000i		−	0.488678i	0.969690	−	0.244339i	$-0.0785709\pi$
$68$	−1.00000	+	1.00000i	−0.121268	+	0.121268i
$69$	−6.00000			−0.722315
$70$	−2.00000	+	4.00000i	−0.239046	+	0.478091i
$71$	1.00000	+	1.00000i	0.118678	+	0.118678i	0.763952	−	0.645273i	$-0.223257\pi$
$71$	1.00000	+	1.00000i	0.118678	+	0.118678i	−0.645273	+	0.763952i	$0.723257\pi$
$72$	−3.00000			−0.353553
$73$			10.0000i			1.17041i	0.810885	+	0.585206i	$0.198986\pi$
$73$			10.0000i			1.17041i	−0.810885	+	0.585206i	$0.801014\pi$
$74$		0			0
$75$	7.00000	+	1.00000i	0.808290	+	0.115470i
$76$	5.00000	−	5.00000i	0.573539	−	0.573539i
$77$	2.00000	−	2.00000i	0.227921	−	0.227921i
$78$	1.00000	−	5.00000i	0.113228	−	0.566139i
$79$		−	2.00000i		−	0.225018i	−0.993651	−	0.112509i	$-0.964111\pi$
$79$		−	2.00000i		−	0.225018i	0.993651	−	0.112509i	$-0.0358886\pi$
$80$	2.00000	+	1.00000i	0.223607	+	0.111803i
$81$	5.00000			0.555556
$82$	7.00000	−	7.00000i	0.773021	−	0.773021i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	−2.00000	+	2.00000i	−0.218218	+	0.218218i
$85$	3.00000	−	1.00000i	0.325396	−	0.108465i
$86$	−1.00000	+	1.00000i	−0.107833	+	0.107833i
$87$		0			0
$88$	−3.00000	−	3.00000i	−0.319801	−	0.319801i
$89$	−5.00000	−	5.00000i	−0.529999	−	0.529999i	0.390573	−	0.920572i	$-0.372277\pi$
$89$	−5.00000	−	5.00000i	−0.529999	−	0.529999i	−0.920572	+	0.390573i	$0.872277\pi$
$90$	2.00000	+	1.00000i	0.210819	+	0.105409i
$91$	4.00000	+	6.00000i	0.419314	+	0.628971i
$92$	−3.00000	−	3.00000i	−0.312772	−	0.312772i
$93$	10.0000			1.03695
$94$			6.00000i			0.618853i
$95$	−15.0000	+	5.00000i	−1.53897	+	0.512989i
$96$	5.00000	+	5.00000i	0.510310	+	0.510310i
$97$			2.00000i			0.203069i	0.994832	+	0.101535i	$0.0323753\pi$
$97$			2.00000i			0.203069i	−0.994832	+	0.101535i	$0.967625\pi$
$98$		−	3.00000i		−	0.303046i
$99$	−1.00000	−	1.00000i	−0.100504	−	0.100504i
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$		−	12.0000i		−	1.19404i	−0.802225	−	0.597022i	$-0.796350\pi$
$101$		−	12.0000i		−	1.19404i	0.802225	−	0.597022i	$-0.203650\pi$
$102$	−2.00000			−0.198030
$103$	−7.00000	−	7.00000i	−0.689730	−	0.689730i	0.272442	−	0.962172i	$-0.412169\pi$
$103$	−7.00000	−	7.00000i	−0.689730	−	0.689730i	−0.962172	+	0.272442i	$0.912169\pi$
$104$	9.00000	−	6.00000i	0.882523	−	0.588348i
$105$	6.00000	−	2.00000i	0.585540	−	0.195180i
$106$	5.00000	+	5.00000i	0.485643	+	0.485643i
$107$	7.00000	+	7.00000i	0.676716	+	0.676716i	0.959256	−	0.282540i	$-0.0911770\pi$
$107$	7.00000	+	7.00000i	0.676716	+	0.676716i	−0.282540	+	0.959256i	$0.591177\pi$
$108$	4.00000	+	4.00000i	0.384900	+	0.384900i
$109$	−9.00000	+	9.00000i	−0.862044	+	0.862044i	−0.991575	−	0.129532i	$-0.958653\pi$
$109$	−9.00000	+	9.00000i	−0.862044	+	0.862044i	0.129532	+	0.991575i	$0.458653\pi$
$110$	1.00000	+	3.00000i	0.0953463	+	0.286039i
$111$		0			0
$112$	2.00000			0.188982
$113$	5.00000	−	5.00000i	0.470360	−	0.470360i	−0.431671	−	0.902031i	$-0.642076\pi$
$113$	5.00000	−	5.00000i	0.470360	−	0.470360i	0.902031	+	0.431671i	$0.142076\pi$
$114$	10.0000			0.936586
$115$	3.00000	+	9.00000i	0.279751	+	0.839254i
$116$		0			0
$117$	3.00000	−	2.00000i	0.277350	−	0.184900i
$118$	−7.00000	+	7.00000i	−0.644402	+	0.644402i
$119$	2.00000	−	2.00000i	0.183340	−	0.183340i
$120$	−3.00000	−	9.00000i	−0.273861	−	0.821584i
$121$			9.00000i			0.818182i
$122$		−	14.0000i		−	1.26750i
$123$	−14.0000			−1.26234
$124$	5.00000	+	5.00000i	0.449013	+	0.449013i
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$	2.00000			0.178174
$127$	−9.00000	+	9.00000i	−0.798621	+	0.798621i	−0.982878	−	0.184257i	$-0.941012\pi$
$127$	−9.00000	+	9.00000i	−0.798621	+	0.798621i	0.184257	+	0.982878i	$0.441012\pi$
$128$			3.00000i			0.265165i
$129$	2.00000			0.176090
$130$	−8.00000	+	1.00000i	−0.701646	+	0.0877058i
$131$	−20.0000			−1.74741			−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000			−1.74741			−0.873704	+	0.486458i	$0.838289\pi$
$132$			2.00000i			0.174078i
$133$	−10.0000	+	10.0000i	−0.867110	+	0.867110i
$134$	4.00000			0.345547
$135$	−4.00000	−	12.0000i	−0.344265	−	1.03280i
$136$	−3.00000	−	3.00000i	−0.257248	−	0.257248i
$137$	−16.0000			−1.36697			−0.683486	−	0.729964i	$-0.739537\pi$
$137$	−16.0000			−1.36697			−0.683486	+	0.729964i	$0.739537\pi$
$138$		−	6.00000i		−	0.510754i
$139$		−	14.0000i		−	1.18746i	−0.804663	−	0.593732i	$-0.797654\pi$
$139$		−	14.0000i		−	1.18746i	0.804663	−	0.593732i	$-0.202346\pi$
$140$	4.00000	+	2.00000i	0.338062	+	0.169031i
$141$	6.00000	−	6.00000i	0.505291	−	0.505291i
$142$	−1.00000	+	1.00000i	−0.0839181	+	0.0839181i
$143$	5.00000	+	1.00000i	0.418121	+	0.0836242i
$144$		−	1.00000i		−	0.0833333i
$145$		0			0
$146$	−10.0000			−0.827606
$147$	−3.00000	+	3.00000i	−0.247436	+	0.247436i
$148$		0			0
$149$	3.00000	−	3.00000i	0.245770	−	0.245770i	−0.573462	−	0.819232i	$-0.694400\pi$
$149$	3.00000	−	3.00000i	0.245770	−	0.245770i	0.819232	+	0.573462i	$0.194400\pi$
$150$	−1.00000	+	7.00000i	−0.0816497	+	0.571548i
$151$	7.00000	−	7.00000i	0.569652	−	0.569652i	−0.362379	−	0.932031i	$-0.618035\pi$
$151$	7.00000	−	7.00000i	0.569652	−	0.569652i	0.932031	+	0.362379i	$0.118035\pi$
$152$	15.0000	+	15.0000i	1.21666	+	1.21666i
$153$	−1.00000	−	1.00000i	−0.0808452	−	0.0808452i
$154$	2.00000	+	2.00000i	0.161165	+	0.161165i
$155$	−5.00000	−	15.0000i	−0.401610	−	1.20483i
$156$	−5.00000	−	1.00000i	−0.400320	−	0.0800641i
$157$	13.0000	+	13.0000i	1.03751	+	1.03751i	0.999268	+	0.0382445i	$0.0121766\pi$
$157$	13.0000	+	13.0000i	1.03751	+	1.03751i	0.0382445	+	0.999268i	$0.487823\pi$
$158$	2.00000			0.159111
$159$		−	10.0000i		−	0.793052i
$160$	5.00000	−	10.0000i	0.395285	−	0.790569i
$161$	6.00000	+	6.00000i	0.472866	+	0.472866i
$162$			5.00000i			0.392837i
$163$		−	4.00000i		−	0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$		−	4.00000i		−	0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$	−7.00000	−	7.00000i	−0.546608	−	0.546608i
$165$	2.00000	−	4.00000i	0.155700	−	0.311400i
$166$			6.00000i			0.465690i
$167$	−18.0000			−1.39288			−0.696441	−	0.717614i	$-0.745234\pi$
$167$	−18.0000			−1.39288			−0.696441	+	0.717614i	$0.745234\pi$
$168$	−6.00000	−	6.00000i	−0.462910	−	0.462910i
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$	1.00000	+	3.00000i	0.0766965	+	0.230089i
$171$	5.00000	+	5.00000i	0.382360	+	0.382360i
$172$	1.00000	+	1.00000i	0.0762493	+	0.0762493i
$173$	11.0000	+	11.0000i	0.836315	+	0.836315i	0.988372	−	0.152057i	$-0.0485898\pi$
$173$	11.0000	+	11.0000i	0.836315	+	0.836315i	−0.152057	+	0.988372i	$0.548590\pi$
$174$		0			0
$175$	−6.00000	−	8.00000i	−0.453557	−	0.604743i
$176$	1.00000	−	1.00000i	0.0753778	−	0.0753778i
$177$	14.0000			1.05230
$178$	5.00000	−	5.00000i	0.374766	−	0.374766i
$179$	20.0000			1.49487			0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000			1.49487			0.747435	+	0.664335i	$0.231285\pi$
$180$	1.00000	−	2.00000i	0.0745356	−	0.149071i
$181$			8.00000i			0.594635i	0.954779	+	0.297318i	$0.0960920\pi$
$181$			8.00000i			0.594635i	−0.954779	+	0.297318i	$0.903908\pi$
$182$	−6.00000	+	4.00000i	−0.444750	+	0.296500i
$183$	−14.0000	+	14.0000i	−1.03491	+	1.03491i
$184$	9.00000	−	9.00000i	0.663489	−	0.663489i
$185$		0			0
$186$			10.0000i			0.733236i
$187$		−	2.00000i		−	0.146254i
$188$	6.00000			0.437595
$189$	−8.00000	−	8.00000i	−0.581914	−	0.581914i
$190$	−5.00000	−	15.0000i	−0.362738	−	1.08821i
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$	−7.00000	+	7.00000i	−0.505181	+	0.505181i
$193$		−	18.0000i		−	1.29567i	−0.761781	−	0.647834i	$-0.775675\pi$
$193$		−	18.0000i		−	1.29567i	0.761781	−	0.647834i	$-0.224325\pi$
$194$	−2.00000			−0.143592
$195$	9.00000	+	7.00000i	0.644503	+	0.501280i
$196$	−3.00000			−0.214286
$197$			6.00000i			0.427482i	0.976890	+	0.213741i	$0.0685649\pi$
$197$			6.00000i			0.427482i	−0.976890	+	0.213741i	$0.931435\pi$
$198$	1.00000	−	1.00000i	0.0710669	−	0.0710669i
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	−12.0000	+	9.00000i	−0.848528	+	0.636396i
$201$	−4.00000	−	4.00000i	−0.282138	−	0.282138i
$202$	12.0000			0.844317
$203$		0			0
$204$			2.00000i			0.140028i
$205$	7.00000	+	21.0000i	0.488901	+	1.46670i
$206$	7.00000	−	7.00000i	0.487713	−	0.487713i
$207$	3.00000	−	3.00000i	0.208514	−	0.208514i
$208$	2.00000	+	3.00000i	0.138675	+	0.208013i
$209$			10.0000i			0.691714i
$210$	2.00000	+	6.00000i	0.138013	+	0.414039i
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	5.00000	−	5.00000i	0.343401	−	0.343401i
$213$	2.00000			0.137038
$214$	−7.00000	+	7.00000i	−0.478510	+	0.478510i
$215$	−1.00000	−	3.00000i	−0.0681994	−	0.204598i
$216$	−12.0000	+	12.0000i	−0.816497	+	0.816497i
$217$	−10.0000	−	10.0000i	−0.678844	−	0.678844i
$218$	−9.00000	−	9.00000i	−0.609557	−	0.609557i
$219$	10.0000	+	10.0000i	0.675737	+	0.675737i
$220$	3.00000	−	1.00000i	0.202260	−	0.0674200i
$221$	5.00000	+	1.00000i	0.336336	+	0.0672673i
$222$		0			0
$223$	2.00000			0.133930			0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000			0.133930			0.0669650	+	0.997755i	$0.478668\pi$
$224$		−	10.0000i		−	0.668153i
$225$	−4.00000	+	3.00000i	−0.266667	+	0.200000i
$226$	5.00000	+	5.00000i	0.332595	+	0.332595i
$227$		−	12.0000i		−	0.796468i	−0.917284	−	0.398234i	$-0.869623\pi$
$227$		−	12.0000i		−	0.796468i	0.917284	−	0.398234i	$-0.130377\pi$
$228$		−	10.0000i		−	0.662266i
$229$	3.00000	+	3.00000i	0.198246	+	0.198246i	0.799248	−	0.601002i	$-0.205232\pi$
$229$	3.00000	+	3.00000i	0.198246	+	0.198246i	−0.601002	+	0.799248i	$0.705232\pi$
$230$	−9.00000	+	3.00000i	−0.593442	+	0.197814i
$231$		−	4.00000i		−	0.263181i
$232$		0			0
$233$	−1.00000	−	1.00000i	−0.0655122	−	0.0655122i	0.673592	−	0.739104i	$-0.264751\pi$
$233$	−1.00000	−	1.00000i	−0.0655122	−	0.0655122i	−0.739104	+	0.673592i	$0.764751\pi$
$234$	2.00000	+	3.00000i	0.130744	+	0.196116i
$235$	−12.0000	−	6.00000i	−0.782794	−	0.391397i
$236$	7.00000	+	7.00000i	0.455661	+	0.455661i
$237$	−2.00000	−	2.00000i	−0.129914	−	0.129914i
$238$	2.00000	+	2.00000i	0.129641	+	0.129641i
$239$	−3.00000	+	3.00000i	−0.194054	+	0.194054i	−0.797445	−	0.603391i	$-0.793816\pi$
$239$	−3.00000	+	3.00000i	−0.194054	+	0.194054i	0.603391	+	0.797445i	$0.293816\pi$
$240$	3.00000	−	1.00000i	0.193649	−	0.0645497i
$241$	17.0000	−	17.0000i	1.09507	−	1.09507i	0.100088	−	0.994979i	$-0.468088\pi$
$241$	17.0000	−	17.0000i	1.09507	−	1.09507i	0.994979	−	0.100088i	$-0.0319123\pi$
$242$	−9.00000			−0.578542
$243$	−7.00000	+	7.00000i	−0.449050	+	0.449050i
$244$	−14.0000			−0.896258
$245$	6.00000	+	3.00000i	0.383326	+	0.191663i
$246$		−	14.0000i		−	0.892607i
$247$	−25.0000	−	5.00000i	−1.59071	−	0.318142i
$248$	−15.0000	+	15.0000i	−0.952501	+	0.952501i
$249$	6.00000	−	6.00000i	0.380235	−	0.380235i
$250$	11.0000	−	2.00000i	0.695701	−	0.126491i
$251$		−	2.00000i		−	0.126239i	−0.998006	−	0.0631194i	$-0.979895\pi$
$251$		−	2.00000i		−	0.126239i	0.998006	−	0.0631194i	$-0.0201049\pi$
$252$		−	2.00000i		−	0.125988i
$253$	6.00000			0.377217
$254$	−9.00000	−	9.00000i	−0.564710	−	0.564710i
$255$	2.00000	−	4.00000i	0.125245	−	0.250490i
$256$	−17.0000			−1.06250
$257$	11.0000	−	11.0000i	0.686161	−	0.686161i	−0.275220	−	0.961381i	$-0.588751\pi$
$257$	11.0000	−	11.0000i	0.686161	−	0.686161i	0.961381	+	0.275220i	$0.0887507\pi$
$258$			2.00000i			0.124515i
$259$		0			0
$260$	1.00000	+	8.00000i	0.0620174	+	0.496139i
$261$		0			0
$262$		−	20.0000i		−	1.23560i
$263$	1.00000	−	1.00000i	0.0616626	−	0.0616626i	−0.675603	−	0.737266i	$-0.736117\pi$
$263$	1.00000	−	1.00000i	0.0616626	−	0.0616626i	0.737266	+	0.675603i	$0.236117\pi$
$264$	−6.00000			−0.369274
$265$	−15.0000	+	5.00000i	−0.921443	+	0.307148i
$266$	−10.0000	−	10.0000i	−0.613139	−	0.613139i
$267$	−10.0000			−0.611990
$268$		−	4.00000i		−	0.244339i
$269$			12.0000i			0.731653i	0.930683	+	0.365826i	$0.119214\pi$
$269$			12.0000i			0.731653i	−0.930683	+	0.365826i	$0.880786\pi$
$270$	12.0000	−	4.00000i	0.730297	−	0.243432i
$271$	−9.00000	+	9.00000i	−0.546711	+	0.546711i	−0.925488	−	0.378777i	$-0.876345\pi$
$271$	−9.00000	+	9.00000i	−0.546711	+	0.546711i	0.378777	+	0.925488i	$0.376345\pi$
$272$	1.00000	−	1.00000i	0.0606339	−	0.0606339i
$273$	10.0000	+	2.00000i	0.605228	+	0.121046i
$274$		−	16.0000i		−	0.966595i
$275$	−7.00000	−	1.00000i	−0.422116	−	0.0603023i
$276$	−6.00000			−0.361158
$277$	15.0000	−	15.0000i	0.901263	−	0.901263i	−0.0942828	−	0.995545i	$-0.530056\pi$
$277$	15.0000	−	15.0000i	0.901263	−	0.901263i	0.995545	+	0.0942828i	$0.0300558\pi$
$278$	14.0000			0.839664
$279$	−5.00000	+	5.00000i	−0.299342	+	0.299342i
$280$	−6.00000	+	12.0000i	−0.358569	+	0.717137i
$281$	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	$0.236569\pi$
$282$	6.00000	+	6.00000i	0.357295	+	0.357295i
$283$	9.00000	+	9.00000i	0.534994	+	0.534994i	0.922055	−	0.387060i	$-0.126509\pi$
$283$	9.00000	+	9.00000i	0.534994	+	0.534994i	−0.387060	+	0.922055i	$0.626509\pi$
$284$	1.00000	+	1.00000i	0.0593391	+	0.0593391i
$285$	−10.0000	+	20.0000i	−0.592349	+	1.18470i
$286$	−1.00000	+	5.00000i	−0.0591312	+	0.295656i
$287$	14.0000	+	14.0000i	0.826394	+	0.826394i
$288$	−5.00000			−0.294628
$289$			15.0000i			0.882353i
$290$		0			0
$291$	2.00000	+	2.00000i	0.117242	+	0.117242i
$292$			10.0000i			0.585206i
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$	−3.00000	−	3.00000i	−0.174964	−	0.174964i
$295$	−7.00000	−	21.0000i	−0.407556	−	1.22267i
$296$		0			0
$297$	−8.00000			−0.464207
$298$	3.00000	+	3.00000i	0.173785	+	0.173785i
$299$	−3.00000	+	15.0000i	−0.173494	+	0.867472i
$300$	7.00000	+	1.00000i	0.404145	+	0.0577350i
$301$	−2.00000	−	2.00000i	−0.115278	−	0.115278i
$302$	7.00000	+	7.00000i	0.402805	+	0.402805i
$303$	−12.0000	−	12.0000i	−0.689382	−	0.689382i
$304$	−5.00000	+	5.00000i	−0.286770	+	0.286770i
$305$	28.0000	+	14.0000i	1.60328	+	0.801638i
$306$	1.00000	−	1.00000i	0.0571662	−	0.0571662i
$307$	18.0000			1.02731			0.513657	−	0.857996i	$-0.328290\pi$
$307$	18.0000			1.02731			0.513657	+	0.857996i	$0.328290\pi$
$308$	2.00000	−	2.00000i	0.113961	−	0.113961i
$309$	−14.0000			−0.796432
$310$	15.0000	−	5.00000i	0.851943	−	0.283981i
$311$		−	6.00000i		−	0.340229i	−0.985424	−	0.170114i	$-0.945586\pi$
$311$		−	6.00000i		−	0.340229i	0.985424	−	0.170114i	$-0.0544137\pi$
$312$	3.00000	−	15.0000i	0.169842	−	0.849208i
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	−0.405420	−	0.914130i	$-0.632875\pi$
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	0.914130	+	0.405420i	$0.132875\pi$
$314$	−13.0000	+	13.0000i	−0.733632	+	0.733632i
$315$	−2.00000	+	4.00000i	−0.112687	+	0.225374i
$316$		−	2.00000i		−	0.112509i
$317$		−	14.0000i		−	0.786318i	−0.919470	−	0.393159i	$-0.871382\pi$
$317$		−	14.0000i		−	0.786318i	0.919470	−	0.393159i	$-0.128618\pi$
$318$	10.0000			0.560772
$319$		0			0
$320$	14.0000	+	7.00000i	0.782624	+	0.391312i
$321$	14.0000			0.781404
$322$	−6.00000	+	6.00000i	−0.334367	+	0.334367i
$323$			10.0000i			0.556415i
$324$	5.00000			0.277778
$325$	6.00000	−	17.0000i	0.332820	−	0.942990i
$326$	4.00000			0.221540
$327$			18.0000i			0.995402i
$328$	21.0000	−	21.0000i	1.15953	−	1.15953i
$329$	−12.0000			−0.661581
$330$	4.00000	+	2.00000i	0.220193	+	0.110096i
$331$	−3.00000	−	3.00000i	−0.164895	−	0.164895i	0.619836	−	0.784731i	$-0.287199\pi$
$331$	−3.00000	−	3.00000i	−0.164895	−	0.164895i	−0.784731	+	0.619836i	$0.787199\pi$
$332$	6.00000			0.329293
$333$		0			0
$334$		−	18.0000i		−	0.984916i
$335$	−4.00000	+	8.00000i	−0.218543	+	0.437087i
$336$	2.00000	−	2.00000i	0.109109	−	0.109109i
$337$	−13.0000	+	13.0000i	−0.708155	+	0.708155i	−0.966147	−	0.257992i	$-0.916939\pi$
$337$	−13.0000	+	13.0000i	−0.708155	+	0.708155i	0.257992	+	0.966147i	$0.416939\pi$
$338$	−12.0000	−	5.00000i	−0.652714	−	0.271964i
$339$		−	10.0000i		−	0.543125i
$340$	3.00000	−	1.00000i	0.162698	−	0.0542326i
$341$	−10.0000			−0.541530
$342$	−5.00000	+	5.00000i	−0.270369	+	0.270369i
$343$	20.0000			1.07990
$344$	−3.00000	+	3.00000i	−0.161749	+	0.161749i
$345$	12.0000	+	6.00000i	0.646058	+	0.323029i
$346$	−11.0000	+	11.0000i	−0.591364	+	0.591364i
$347$	3.00000	+	3.00000i	0.161048	+	0.161048i	0.783031	−	0.621983i	$-0.213673\pi$
$347$	3.00000	+	3.00000i	0.161048	+	0.161048i	−0.621983	+	0.783031i	$0.713673\pi$
$348$		0			0
$349$	−9.00000	−	9.00000i	−0.481759	−	0.481759i	0.423934	−	0.905693i	$-0.360649\pi$
$349$	−9.00000	−	9.00000i	−0.481759	−	0.481759i	−0.905693	+	0.423934i	$0.860649\pi$
$350$	8.00000	−	6.00000i	0.427618	−	0.320713i
$351$	4.00000	−	20.0000i	0.213504	−	1.06752i
$352$	−5.00000	−	5.00000i	−0.266501	−	0.266501i
$353$	−12.0000			−0.638696			−0.319348	−	0.947638i	$-0.603464\pi$
$353$	−12.0000			−0.638696			−0.319348	+	0.947638i	$0.603464\pi$
$354$			14.0000i			0.744092i
$355$	−1.00000	−	3.00000i	−0.0530745	−	0.159223i
$356$	−5.00000	−	5.00000i	−0.264999	−	0.264999i
$357$		−	4.00000i		−	0.211702i
$358$			20.0000i			1.05703i
$359$	−1.00000	−	1.00000i	−0.0527780	−	0.0527780i	0.680225	−	0.733003i	$-0.261882\pi$
$359$	−1.00000	−	1.00000i	−0.0527780	−	0.0527780i	−0.733003	+	0.680225i	$0.761882\pi$
$360$	6.00000	+	3.00000i	0.316228	+	0.158114i
$361$		−	31.0000i		−	1.63158i
$362$	−8.00000			−0.420471
$363$	9.00000	+	9.00000i	0.472377	+	0.472377i
$364$	4.00000	+	6.00000i	0.209657	+	0.314485i
$365$	10.0000	−	20.0000i	0.523424	−	1.04685i
$366$	−14.0000	−	14.0000i	−0.731792	−	0.731792i
$367$	−1.00000	−	1.00000i	−0.0521996	−	0.0521996i	0.680525	−	0.732725i	$-0.261752\pi$
$367$	−1.00000	−	1.00000i	−0.0521996	−	0.0521996i	−0.732725	+	0.680525i	$0.761752\pi$
$368$	3.00000	+	3.00000i	0.156386	+	0.156386i
$369$	7.00000	−	7.00000i	0.364405	−	0.364405i
$370$		0			0
$371$	−10.0000	+	10.0000i	−0.519174	+	0.519174i
$372$	10.0000			0.518476
$373$	−15.0000	+	15.0000i	−0.776671	+	0.776671i	−0.979263	−	0.202593i	$-0.935063\pi$
$373$	−15.0000	+	15.0000i	−0.776671	+	0.776671i	0.202593	+	0.979263i	$0.435063\pi$
$374$	2.00000			0.103418
$375$	−13.0000	−	9.00000i	−0.671317	−	0.464758i
$376$			18.0000i			0.928279i
$377$		0			0
$378$	8.00000	−	8.00000i	0.411476	−	0.411476i
$379$	1.00000	−	1.00000i	0.0513665	−	0.0513665i	−0.680957	−	0.732323i	$-0.738436\pi$
$379$	1.00000	−	1.00000i	0.0513665	−	0.0513665i	0.732323	+	0.680957i	$0.238436\pi$
$380$	−15.0000	+	5.00000i	−0.769484	+	0.256495i
$381$			18.0000i			0.922168i
$382$			8.00000i			0.409316i
$383$	−30.0000			−1.53293			−0.766464	−	0.642287i	$-0.777986\pi$
$383$	−30.0000			−1.53293			−0.766464	+	0.642287i	$0.777986\pi$
$384$	3.00000	+	3.00000i	0.153093	+	0.153093i
$385$	−6.00000	+	2.00000i	−0.305788	+	0.101929i
$386$	18.0000			0.916176
$387$	−1.00000	+	1.00000i	−0.0508329	+	0.0508329i
$388$			2.00000i			0.101535i
$389$	18.0000			0.912636			0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000			0.912636			0.456318	+	0.889817i	$0.349168\pi$
$390$	−7.00000	+	9.00000i	−0.354459	+	0.455733i
$391$	6.00000			0.303433
$392$		−	9.00000i		−	0.454569i
$393$	−20.0000	+	20.0000i	−1.00887	+	1.00887i
$394$	−6.00000			−0.302276
$395$	−2.00000	+	4.00000i	−0.100631	+	0.201262i
$396$	−1.00000	−	1.00000i	−0.0502519	−	0.0502519i
$397$	16.0000			0.803017			0.401508	−	0.915855i	$-0.368486\pi$
$397$	16.0000			0.803017			0.401508	+	0.915855i	$0.368486\pi$
$398$			8.00000i			0.401004i
$399$			20.0000i			1.00125i
$400$	−3.00000	−	4.00000i	−0.150000	−	0.200000i
$401$	−11.0000	+	11.0000i	−0.549314	+	0.549314i	−0.926242	−	0.376929i	$-0.876980\pi$
$401$	−11.0000	+	11.0000i	−0.549314	+	0.549314i	0.376929	+	0.926242i	$0.376980\pi$
$402$	4.00000	−	4.00000i	0.199502	−	0.199502i
$403$	5.00000	−	25.0000i	0.249068	−	1.24534i
$404$		−	12.0000i		−	0.597022i
$405$	−10.0000	−	5.00000i	−0.496904	−	0.248452i
$406$		0			0
$407$		0			0
$408$	−6.00000			−0.297044
$409$	7.00000	−	7.00000i	0.346128	−	0.346128i	−0.512537	−	0.858665i	$-0.671294\pi$
$409$	7.00000	−	7.00000i	0.346128	−	0.346128i	0.858665	+	0.512537i	$0.171294\pi$
$410$	−21.0000	+	7.00000i	−1.03712	+	0.345705i
$411$	−16.0000	+	16.0000i	−0.789222	+	0.789222i
$412$	−7.00000	−	7.00000i	−0.344865	−	0.344865i
$413$	−14.0000	−	14.0000i	−0.688895	−	0.688895i
$414$	3.00000	+	3.00000i	0.147442	+	0.147442i
$415$	−12.0000	−	6.00000i	−0.589057	−	0.294528i
$416$	15.0000	−	10.0000i	0.735436	−	0.490290i
$417$	−14.0000	−	14.0000i	−0.685583	−	0.685583i
$418$	−10.0000			−0.489116
$419$		−	38.0000i		−	1.85642i	−0.372055	−	0.928211i	$-0.621347\pi$
$419$		−	38.0000i		−	1.85642i	0.372055	−	0.928211i	$-0.378653\pi$
$420$	6.00000	−	2.00000i	0.292770	−	0.0975900i
$421$	−11.0000	−	11.0000i	−0.536107	−	0.536107i	0.386276	−	0.922383i	$-0.373761\pi$
$421$	−11.0000	−	11.0000i	−0.536107	−	0.536107i	−0.922383	+	0.386276i	$0.873761\pi$
$422$			4.00000i			0.194717i
$423$			6.00000i			0.291730i
$424$	15.0000	+	15.0000i	0.728464	+	0.728464i
$425$	−7.00000	−	1.00000i	−0.339550	−	0.0485071i
$426$			2.00000i			0.0969003i
$427$	28.0000			1.35501
$428$	7.00000	+	7.00000i	0.338358	+	0.338358i
$429$	6.00000	−	4.00000i	0.289683	−	0.193122i
$430$	3.00000	−	1.00000i	0.144673	−	0.0482243i
$431$	13.0000	+	13.0000i	0.626188	+	0.626188i	0.947107	−	0.320919i	$-0.103992\pi$
$431$	13.0000	+	13.0000i	0.626188	+	0.626188i	−0.320919	+	0.947107i	$0.603992\pi$
$432$	−4.00000	−	4.00000i	−0.192450	−	0.192450i
$433$	−17.0000	−	17.0000i	−0.816968	−	0.816968i	0.168700	−	0.985668i	$-0.446043\pi$
$433$	−17.0000	−	17.0000i	−0.816968	−	0.816968i	−0.985668	+	0.168700i	$0.946043\pi$
$434$	10.0000	−	10.0000i	0.480015	−	0.480015i
$435$		0			0
$436$	−9.00000	+	9.00000i	−0.431022	+	0.431022i
$437$	−30.0000			−1.43509
$438$	−10.0000	+	10.0000i	−0.477818	+	0.477818i
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$	3.00000	+	9.00000i	0.143019	+	0.429058i
$441$		−	3.00000i		−	0.142857i
$442$	−1.00000	+	5.00000i	−0.0475651	+	0.237826i
$443$	25.0000	−	25.0000i	1.18779	−	1.18779i	0.210108	−	0.977678i	$-0.432619\pi$
$443$	25.0000	−	25.0000i	1.18779	−	1.18779i	0.977678	−	0.210108i	$-0.0673814\pi$
$444$		0			0
$445$	5.00000	+	15.0000i	0.237023	+	0.711068i
$446$			2.00000i			0.0947027i
$447$		−	6.00000i		−	0.283790i
$448$	14.0000			0.661438
$449$	3.00000	+	3.00000i	0.141579	+	0.141579i	0.774344	−	0.632765i	$-0.218080\pi$
$449$	3.00000	+	3.00000i	0.141579	+	0.141579i	−0.632765	+	0.774344i	$0.718080\pi$
$450$	−3.00000	−	4.00000i	−0.141421	−	0.188562i
$451$	14.0000			0.659234
$452$	5.00000	−	5.00000i	0.235180	−	0.235180i
$453$		−	14.0000i		−	0.657777i
$454$	12.0000			0.563188
$455$	−2.00000	−	16.0000i	−0.0937614	−	0.750092i
$456$	30.0000			1.40488
$457$			2.00000i			0.0935561i	0.998905	+	0.0467780i	$0.0148953\pi$
$457$			2.00000i			0.0935561i	−0.998905	+	0.0467780i	$0.985105\pi$
$458$	−3.00000	+	3.00000i	−0.140181	+	0.140181i
$459$	−8.00000			−0.373408
$460$	3.00000	+	9.00000i	0.139876	+	0.419627i
$461$	17.0000	+	17.0000i	0.791769	+	0.791769i	0.981782	−	0.190013i	$-0.0608529\pi$
$461$	17.0000	+	17.0000i	0.791769	+	0.791769i	−0.190013	+	0.981782i	$0.560853\pi$
$462$	4.00000			0.186097
$463$			24.0000i			1.11537i	0.830051	+	0.557687i	$0.188311\pi$
$463$			24.0000i			1.11537i	−0.830051	+	0.557687i	$0.811689\pi$
$464$		0			0
$465$	−20.0000	−	10.0000i	−0.927478	−	0.463739i
$466$	1.00000	−	1.00000i	0.0463241	−	0.0463241i
$467$	−9.00000	+	9.00000i	−0.416470	+	0.416470i	−0.883985	−	0.467515i	$-0.845149\pi$
$467$	−9.00000	+	9.00000i	−0.416470	+	0.416470i	0.467515	+	0.883985i	$0.345149\pi$
$468$	3.00000	−	2.00000i	0.138675	−	0.0924500i
$469$			8.00000i			0.369406i
$470$	6.00000	−	12.0000i	0.276759	−	0.553519i
$471$	26.0000			1.19802
$472$	−21.0000	+	21.0000i	−0.966603	+	0.966603i
$473$	−2.00000			−0.0919601
$474$	2.00000	−	2.00000i	0.0918630	−	0.0918630i
$475$	35.0000	+	5.00000i	1.60591	+	0.229416i
$476$	2.00000	−	2.00000i	0.0916698	−	0.0916698i
$477$	5.00000	+	5.00000i	0.228934	+	0.228934i
$478$	−3.00000	−	3.00000i	−0.137217	−	0.137217i
$479$	7.00000	+	7.00000i	0.319838	+	0.319838i	0.848705	−	0.528867i	$-0.177383\pi$
$479$	7.00000	+	7.00000i	0.319838	+	0.319838i	−0.528867	+	0.848705i	$0.677383\pi$
$480$	−5.00000	−	15.0000i	−0.228218	−	0.684653i
$481$		0			0
$482$	17.0000	+	17.0000i	0.774329	+	0.774329i
$483$	12.0000			0.546019
$484$			9.00000i			0.409091i
$485$	2.00000	−	4.00000i	0.0908153	−	0.181631i
$486$	−7.00000	−	7.00000i	−0.317526	−	0.317526i
$487$			16.0000i			0.725029i	0.931978	+	0.362515i	$0.118082\pi$
$487$			16.0000i			0.725029i	−0.931978	+	0.362515i	$0.881918\pi$
$488$		−	42.0000i		−	1.90125i
$489$	−4.00000	−	4.00000i	−0.180886	−	0.180886i
$490$	−3.00000	+	6.00000i	−0.135526	+	0.271052i
$491$			22.0000i			0.992846i	0.868081	+	0.496423i	$0.165354\pi$
$491$			22.0000i			0.992846i	−0.868081	+	0.496423i	$0.834646\pi$
$492$	−14.0000			−0.631169
$493$		0			0
$494$	5.00000	−	25.0000i	0.224961	−	1.12480i
$495$	1.00000	+	3.00000i	0.0449467	+	0.134840i
$496$	−5.00000	−	5.00000i	−0.224507	−	0.224507i
$497$	−2.00000	−	2.00000i	−0.0897123	−	0.0897123i
$498$	6.00000	+	6.00000i	0.268866	+	0.268866i
$499$	−3.00000	+	3.00000i	−0.134298	+	0.134298i	−0.771060	−	0.636762i	$-0.780273\pi$
$499$	−3.00000	+	3.00000i	−0.134298	+	0.134298i	0.636762	+	0.771060i	$0.280273\pi$
$500$	−2.00000	−	11.0000i	−0.0894427	−	0.491935i
$501$	−18.0000	+	18.0000i	−0.804181	+	0.804181i
$502$	2.00000			0.0892644
$503$	−3.00000	+	3.00000i	−0.133763	+	0.133763i	−0.770818	−	0.637055i	$-0.780152\pi$
$503$	−3.00000	+	3.00000i	−0.133763	+	0.133763i	0.637055	+	0.770818i	$0.280152\pi$
$504$	6.00000			0.267261
$505$	−12.0000	+	24.0000i	−0.533993	+	1.06799i
$506$			6.00000i			0.266733i
$507$	7.00000	+	17.0000i	0.310881	+	0.754997i
$508$	−9.00000	+	9.00000i	−0.399310	+	0.399310i
$509$	−13.0000	+	13.0000i	−0.576215	+	0.576215i	−0.933858	−	0.357643i	$-0.883580\pi$
$509$	−13.0000	+	13.0000i	−0.576215	+	0.576215i	0.357643	+	0.933858i	$0.383580\pi$
$510$	4.00000	+	2.00000i	0.177123	+	0.0885615i
$511$		−	20.0000i		−	0.884748i
$512$		−	11.0000i		−	0.486136i
$513$	40.0000			1.76604
$514$	11.0000	+	11.0000i	0.485189	+	0.485189i
$515$	7.00000	+	21.0000i	0.308457	+	0.925371i
$516$	2.00000			0.0880451
$517$	−6.00000	+	6.00000i	−0.263880	+	0.263880i
$518$		0			0
$519$	22.0000			0.965693
$520$	−24.0000	+	3.00000i	−1.05247	+	0.131559i
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$		0			0
$523$	9.00000	−	9.00000i	0.393543	−	0.393543i	−0.482405	−	0.875948i	$-0.660237\pi$
$523$	9.00000	−	9.00000i	0.393543	−	0.393543i	0.875948	+	0.482405i	$0.160237\pi$
$524$	−20.0000			−0.873704
$525$	−14.0000	−	2.00000i	−0.611010	−	0.0872872i
$526$	1.00000	+	1.00000i	0.0436021	+	0.0436021i
$527$	−10.0000			−0.435607
$528$		−	2.00000i		−	0.0870388i
$529$		−	5.00000i		−	0.217391i
$530$	−5.00000	−	15.0000i	−0.217186	−	0.651558i
$531$	−7.00000	+	7.00000i	−0.303774	+	0.303774i
$532$	−10.0000	+	10.0000i	−0.433555	+	0.433555i
$533$	−7.00000	+	35.0000i	−0.303204	+	1.51602i
$534$		−	10.0000i		−	0.432742i
$535$	−7.00000	−	21.0000i	−0.302636	−	0.907909i
$536$	12.0000			0.518321
$537$	20.0000	−	20.0000i	0.863064	−	0.863064i
$538$	−12.0000			−0.517357
$539$	3.00000	−	3.00000i	0.129219	−	0.129219i
$540$	−4.00000	−	12.0000i	−0.172133	−	0.516398i
$541$	9.00000	−	9.00000i	0.386940	−	0.386940i	−0.486654	−	0.873595i	$-0.661783\pi$
$541$	9.00000	−	9.00000i	0.386940	−	0.386940i	0.873595	+	0.486654i	$0.161783\pi$
$542$	−9.00000	−	9.00000i	−0.386583	−	0.386583i
$543$	8.00000	+	8.00000i	0.343313	+	0.343313i
$544$	−5.00000	−	5.00000i	−0.214373	−	0.214373i
$545$	27.0000	−	9.00000i	1.15655	−	0.385518i
$546$	−2.00000	+	10.0000i	−0.0855921	+	0.427960i
$547$	−9.00000	−	9.00000i	−0.384812	−	0.384812i	0.488020	−	0.872832i	$-0.337719\pi$
$547$	−9.00000	−	9.00000i	−0.384812	−	0.384812i	−0.872832	+	0.488020i	$0.837719\pi$
$548$	−16.0000			−0.683486
$549$		−	14.0000i		−	0.597505i
$550$	1.00000	−	7.00000i	0.0426401	−	0.298481i
$551$		0			0
$552$		−	18.0000i		−	0.766131i
$553$			4.00000i			0.170097i
$554$	15.0000	+	15.0000i	0.637289	+	0.637289i
$555$		0			0
$556$		−	14.0000i		−	0.593732i
$557$	24.0000			1.01691			0.508456	−	0.861088i	$-0.330216\pi$
$557$	24.0000			1.01691			0.508456	+	0.861088i	$0.330216\pi$
$558$	−5.00000	−	5.00000i	−0.211667	−	0.211667i
$559$	1.00000	−	5.00000i	0.0422955	−	0.211477i
$560$	−4.00000	−	2.00000i	−0.169031	−	0.0845154i
$561$	−2.00000	−	2.00000i	−0.0844401	−	0.0844401i
$562$	1.00000	+	1.00000i	0.0421825	+	0.0421825i
$563$	−15.0000	−	15.0000i	−0.632175	−	0.632175i	0.316438	−	0.948613i	$-0.397513\pi$
$563$	−15.0000	−	15.0000i	−0.632175	−	0.632175i	−0.948613	+	0.316438i	$0.897513\pi$
$564$	6.00000	−	6.00000i	0.252646	−	0.252646i
$565$	−15.0000	+	5.00000i	−0.631055	+	0.210352i
$566$	−9.00000	+	9.00000i	−0.378298	+	0.378298i
$567$	−10.0000			−0.419961
$568$	−3.00000	+	3.00000i	−0.125877	+	0.125877i
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$	−20.0000	−	10.0000i	−0.837708	−	0.418854i
$571$			6.00000i			0.251092i	0.992088	+	0.125546i	$0.0400683\pi$
$571$			6.00000i			0.251092i	−0.992088	+	0.125546i	$0.959932\pi$
$572$	5.00000	+	1.00000i	0.209061	+	0.0418121i
$573$	8.00000	−	8.00000i	0.334205	−	0.334205i
$574$	−14.0000	+	14.0000i	−0.584349	+	0.584349i
$575$	3.00000	−	21.0000i	0.125109	−	0.875761i
$576$		−	7.00000i		−	0.291667i
$577$			46.0000i			1.91501i	0.288425	+	0.957503i	$0.406868\pi$
$577$			46.0000i			1.91501i	−0.288425	+	0.957503i	$0.593132\pi$
$578$	−15.0000			−0.623918
$579$	−18.0000	−	18.0000i	−0.748054	−	0.748054i
$580$		0			0
$581$	−12.0000			−0.497844
$582$	−2.00000	+	2.00000i	−0.0829027	+	0.0829027i
$583$			10.0000i			0.414158i
$584$	−30.0000			−1.24141
$585$	−8.00000	+	1.00000i	−0.330759	+	0.0413449i
$586$	−6.00000			−0.247858
$587$		−	4.00000i		−	0.165098i	−0.996587	−	0.0825488i	$-0.973694\pi$
$587$		−	4.00000i		−	0.165098i	0.996587	−	0.0825488i	$-0.0263060\pi$
$588$	−3.00000	+	3.00000i	−0.123718	+	0.123718i
$589$	50.0000			2.06021
$590$	21.0000	−	7.00000i	0.864556	−	0.288185i
$591$	6.00000	+	6.00000i	0.246807	+	0.246807i
$592$		0			0
$593$		−	10.0000i		−	0.410651i	−0.978694	−	0.205325i	$-0.934175\pi$
$593$		−	10.0000i		−	0.410651i	0.978694	−	0.205325i	$-0.0658253\pi$
$594$		−	8.00000i		−	0.328244i
$595$	−6.00000	+	2.00000i	−0.245976	+	0.0819920i
$596$	3.00000	−	3.00000i	0.122885	−	0.122885i
$597$	8.00000	−	8.00000i	0.327418	−	0.327418i
$598$	−15.0000	−	3.00000i	−0.613396	−	0.122679i
$599$			30.0000i			1.22577i	0.790173	+	0.612883i	$0.209990\pi$
$599$			30.0000i			1.22577i	−0.790173	+	0.612883i	$0.790010\pi$
$600$	−3.00000	+	21.0000i	−0.122474	+	0.857321i
$601$	−38.0000			−1.55005			−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000			−1.55005			−0.775026	+	0.631929i	$0.782263\pi$
$602$	2.00000	−	2.00000i	0.0815139	−	0.0815139i
$603$	4.00000			0.162893
$604$	7.00000	−	7.00000i	0.284826	−	0.284826i
$605$	9.00000	−	18.0000i	0.365902	−	0.731804i
$606$	12.0000	−	12.0000i	0.487467	−	0.487467i
$607$	−13.0000	−	13.0000i	−0.527654	−	0.527654i	0.392218	−	0.919872i	$-0.371708\pi$
$607$	−13.0000	−	13.0000i	−0.527654	−	0.527654i	−0.919872	+	0.392218i	$0.871708\pi$
$608$	25.0000	+	25.0000i	1.01388	+	1.01388i
$609$		0			0
$610$	−14.0000	+	28.0000i	−0.566843	+	1.13369i
$611$	−12.0000	−	18.0000i	−0.485468	−	0.728202i
$612$	−1.00000	−	1.00000i	−0.0404226	−	0.0404226i
$613$	−20.0000			−0.807792			−0.403896	−	0.914805i	$-0.632344\pi$
$613$	−20.0000			−0.807792			−0.403896	+	0.914805i	$0.632344\pi$
$614$			18.0000i			0.726421i
$615$	28.0000	+	14.0000i	1.12907	+	0.564534i
$616$	6.00000	+	6.00000i	0.241747	+	0.241747i
$617$		−	22.0000i		−	0.885687i	−0.896599	−	0.442843i	$-0.853970\pi$
$617$		−	22.0000i		−	0.885687i	0.896599	−	0.442843i	$-0.146030\pi$
$618$		−	14.0000i		−	0.563163i
$619$	−25.0000	−	25.0000i	−1.00483	−	1.00483i	−0.999988	−	0.00484658i	$-0.998457\pi$
$619$	−25.0000	−	25.0000i	−1.00483	−	1.00483i	−0.00484658	−	0.999988i	$-0.501543\pi$
$620$	−5.00000	−	15.0000i	−0.200805	−	0.602414i
$621$		−	24.0000i		−	0.963087i
$622$	6.00000			0.240578
$623$	10.0000	+	10.0000i	0.400642	+	0.400642i
$624$	5.00000	+	1.00000i	0.200160	+	0.0400320i
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	9.00000	+	9.00000i	0.359712	+	0.359712i
$627$	10.0000	+	10.0000i	0.399362	+	0.399362i
$628$	13.0000	+	13.0000i	0.518756	+	0.518756i
$629$		0			0
$630$	−4.00000	−	2.00000i	−0.159364	−	0.0796819i
$631$	11.0000	−	11.0000i	0.437903	−	0.437903i	−0.453403	−	0.891306i	$-0.649790\pi$
$631$	11.0000	−	11.0000i	0.437903	−	0.437903i	0.891306	+	0.453403i	$0.149790\pi$
$632$	6.00000			0.238667
$633$	4.00000	−	4.00000i	0.158986	−	0.158986i
$634$	14.0000			0.556011
$635$	27.0000	−	9.00000i	1.07146	−	0.357154i
$636$		−	10.0000i		−	0.396526i
$637$	6.00000	+	9.00000i	0.237729	+	0.356593i
$638$		0			0
$639$	−1.00000	+	1.00000i	−0.0395594	+	0.0395594i
$640$	3.00000	−	6.00000i	0.118585	−	0.237171i
$641$			24.0000i			0.947943i	0.880540	+	0.473972i	$0.157180\pi$
$641$			24.0000i			0.947943i	−0.880540	+	0.473972i	$0.842820\pi$
$642$			14.0000i			0.552536i
$643$	−34.0000			−1.34083			−0.670415	−	0.741987i	$-0.733884\pi$
$643$	−34.0000			−1.34083			−0.670415	+	0.741987i	$0.733884\pi$
$644$	6.00000	+	6.00000i	0.236433	+	0.236433i
$645$	−4.00000	−	2.00000i	−0.157500	−	0.0787499i
$646$	−10.0000			−0.393445
$647$	−1.00000	+	1.00000i	−0.0393141	+	0.0393141i	−0.726491	−	0.687176i	$-0.758850\pi$
$647$	−1.00000	+	1.00000i	−0.0393141	+	0.0393141i	0.687176	+	0.726491i	$0.258850\pi$
$648$			15.0000i			0.589256i
$649$	−14.0000			−0.549548
$650$	17.0000	+	6.00000i	0.666795	+	0.235339i
$651$	−20.0000			−0.783862
$652$		−	4.00000i		−	0.156652i
$653$	13.0000	−	13.0000i	0.508729	−	0.508729i	−0.405407	−	0.914136i	$-0.632870\pi$
$653$	13.0000	−	13.0000i	0.508729	−	0.508729i	0.914136	+	0.405407i	$0.132870\pi$
$654$	−18.0000			−0.703856
$655$	40.0000	+	20.0000i	1.56293	+	0.781465i
$656$	7.00000	+	7.00000i	0.273304	+	0.273304i
$657$	−10.0000			−0.390137
$658$		−	12.0000i		−	0.467809i
$659$			26.0000i			1.01282i	0.862294	+	0.506408i	$0.169027\pi$
$659$			26.0000i			1.01282i	−0.862294	+	0.506408i	$0.830973\pi$
$660$	2.00000	−	4.00000i	0.0778499	−	0.155700i
$661$	17.0000	−	17.0000i	0.661223	−	0.661223i	−0.294445	−	0.955668i	$-0.595135\pi$
$661$	17.0000	−	17.0000i	0.661223	−	0.661223i	0.955668	+	0.294445i	$0.0951348\pi$
$662$	3.00000	−	3.00000i	0.116598	−	0.116598i
$663$	6.00000	−	4.00000i	0.233021	−	0.155347i
$664$			18.0000i			0.698535i
$665$	30.0000	−	10.0000i	1.16335	−	0.387783i
$666$		0			0
$667$		0			0
$668$	−18.0000			−0.696441
$669$	2.00000	−	2.00000i	0.0773245	−	0.0773245i
$670$	−8.00000	−	4.00000i	−0.309067	−	0.154533i
$671$	14.0000	−	14.0000i	0.540464	−	0.540464i
$672$	−10.0000	−	10.0000i	−0.385758	−	0.385758i
$673$	15.0000	+	15.0000i	0.578208	+	0.578208i	0.934409	−	0.356202i	$-0.115928\pi$
$673$	15.0000	+	15.0000i	0.578208	+	0.578208i	−0.356202	+	0.934409i	$0.615928\pi$
$674$	−13.0000	−	13.0000i	−0.500741	−	0.500741i
$675$	−4.00000	+	28.0000i	−0.153960	+	1.07772i
$676$	−5.00000	+	12.0000i	−0.192308	+	0.461538i
$677$	−23.0000	−	23.0000i	−0.883962	−	0.883962i	0.109973	−	0.993935i	$-0.464924\pi$
$677$	−23.0000	−	23.0000i	−0.883962	−	0.883962i	−0.993935	+	0.109973i	$0.964924\pi$
$678$	10.0000			0.384048
$679$		−	4.00000i		−	0.153506i
$680$	3.00000	+	9.00000i	0.115045	+	0.345134i
$681$	−12.0000	−	12.0000i	−0.459841	−	0.459841i
$682$		−	10.0000i		−	0.382920i
$683$			12.0000i			0.459167i	0.973289	+	0.229584i	$0.0737364\pi$
$683$			12.0000i			0.459167i	−0.973289	+	0.229584i	$0.926264\pi$
$684$	5.00000	+	5.00000i	0.191180	+	0.191180i
$685$	32.0000	+	16.0000i	1.22266	+	0.611329i
$686$			20.0000i			0.763604i
$687$	6.00000			0.228914
$688$	−1.00000	−	1.00000i	−0.0381246	−	0.0381246i
$689$	−25.0000	−	5.00000i	−0.952424	−	0.190485i
$690$	−6.00000	+	12.0000i	−0.228416	+	0.456832i
$691$	−3.00000	−	3.00000i	−0.114125	−	0.114125i	0.647738	−	0.761863i	$-0.275715\pi$
$691$	−3.00000	−	3.00000i	−0.114125	−	0.114125i	−0.761863	+	0.647738i	$0.775715\pi$
$692$	11.0000	+	11.0000i	0.418157	+	0.418157i
$693$	2.00000	+	2.00000i	0.0759737	+	0.0759737i
$694$	−3.00000	+	3.00000i	−0.113878	+	0.113878i
$695$	−14.0000	+	28.0000i	−0.531050	+	1.06210i
$696$		0			0
$697$	14.0000			0.530288
$698$	9.00000	−	9.00000i	0.340655	−	0.340655i
$699$	−2.00000			−0.0756469
$700$	−6.00000	−	8.00000i	−0.226779	−	0.302372i
$701$		−	12.0000i		−	0.453234i	−0.973984	−	0.226617i	$-0.927233\pi$
$701$		−	12.0000i		−	0.453234i	0.973984	−	0.226617i	$-0.0727665\pi$
$702$	20.0000	+	4.00000i	0.754851	+	0.150970i
$703$		0			0
$704$	7.00000	−	7.00000i	0.263822	−	0.263822i
$705$	−18.0000	+	6.00000i	−0.677919	+	0.225973i
$706$		−	12.0000i		−	0.451626i
$707$			24.0000i			0.902613i
$708$	14.0000			0.526152
$709$	−29.0000	−	29.0000i	−1.08912	−	1.08912i	−0.995619	−	0.0934984i	$-0.970195\pi$
$709$	−29.0000	−	29.0000i	−1.08912	−	1.08912i	−0.0934984	−	0.995619i	$-0.529805\pi$
$710$	3.00000	−	1.00000i	0.112588	−	0.0375293i
$711$	2.00000			0.0750059
$712$	15.0000	−	15.0000i	0.562149	−	0.562149i
$713$		−	30.0000i		−	1.12351i
$714$	4.00000			0.149696
$715$	−9.00000	−	7.00000i	−0.336581	−	0.261785i
$716$	20.0000			0.747435
$717$			6.00000i			0.224074i
$718$	1.00000	−	1.00000i	0.0373197	−	0.0373197i
$719$	8.00000			0.298350			0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000			0.298350			0.149175	+	0.988811i	$0.452338\pi$
$720$	−1.00000	+	2.00000i	−0.0372678	+	0.0745356i
$721$	14.0000	+	14.0000i	0.521387	+	0.521387i
$722$	31.0000			1.15370
$723$		−	34.0000i		−	1.26447i
$724$			8.00000i			0.297318i
$725$		0			0
$726$	−9.00000	+	9.00000i	−0.334021	+	0.334021i
$727$	35.0000	−	35.0000i	1.29808	−	1.29808i	0.368418	−	0.929660i	$-0.379900\pi$
$727$	35.0000	−	35.0000i	1.29808	−	1.29808i	0.929660	−	0.368418i	$-0.120100\pi$
$728$	−18.0000	+	12.0000i	−0.667124	+	0.444750i
$729$			29.0000i			1.07407i
$730$	20.0000	+	10.0000i	0.740233	+	0.370117i
$731$	−2.00000			−0.0739727
$732$	−14.0000	+	14.0000i	−0.517455	+	0.517455i
$733$	−4.00000			−0.147743			−0.0738717	−	0.997268i	$-0.523536\pi$
$733$	−4.00000			−0.147743			−0.0738717	+	0.997268i	$0.523536\pi$
$734$	1.00000	−	1.00000i	0.0369107	−	0.0369107i
$735$	9.00000	−	3.00000i	0.331970	−	0.110657i
$736$	15.0000	−	15.0000i	0.552907	−	0.552907i
$737$	4.00000	+	4.00000i	0.147342	+	0.147342i
$738$	7.00000	+	7.00000i	0.257674	+	0.257674i
$739$	3.00000	+	3.00000i	0.110357	+	0.110357i	0.760129	−	0.649772i	$-0.225136\pi$
$739$	3.00000	+	3.00000i	0.110357	+	0.110357i	−0.649772	+	0.760129i	$0.725136\pi$
$740$		0			0
$741$	−30.0000	+	20.0000i	−1.10208	+	0.734718i
$742$	−10.0000	−	10.0000i	−0.367112	−	0.367112i
$743$	34.0000			1.24734			0.623670	−	0.781688i	$-0.285641\pi$
$743$	34.0000			1.24734			0.623670	+	0.781688i	$0.285641\pi$
$744$			30.0000i			1.09985i
$745$	−9.00000	+	3.00000i	−0.329734	+	0.109911i
$746$	−15.0000	−	15.0000i	−0.549189	−	0.549189i
$747$			6.00000i			0.219529i
$748$		−	2.00000i		−	0.0731272i
$749$	−14.0000	−	14.0000i	−0.511549	−	0.511549i
$750$	9.00000	−	13.0000i	0.328634	−	0.474693i
$751$			50.0000i			1.82453i	0.409605	+	0.912263i	$0.365667\pi$
$751$			50.0000i			1.82453i	−0.409605	+	0.912263i	$0.634333\pi$
$752$	−6.00000			−0.218797
$753$	−2.00000	−	2.00000i	−0.0728841	−	0.0728841i
$754$		0			0
$755$	−21.0000	+	7.00000i	−0.764268	+	0.254756i
$756$	−8.00000	−	8.00000i	−0.290957	−	0.290957i
$757$	−35.0000	−	35.0000i	−1.27210	−	1.27210i	−0.944986	−	0.327111i	$-0.893925\pi$
$757$	−35.0000	−	35.0000i	−1.27210	−	1.27210i	−0.327111	−	0.944986i	$-0.606075\pi$
$758$	1.00000	+	1.00000i	0.0363216	+	0.0363216i
$759$	6.00000	−	6.00000i	0.217786	−	0.217786i
$760$	−15.0000	−	45.0000i	−0.544107	−	1.63232i
$761$	−7.00000	+	7.00000i	−0.253750	+	0.253750i	−0.822506	−	0.568756i	$-0.807425\pi$
$761$	−7.00000	+	7.00000i	−0.253750	+	0.253750i	0.568756	+	0.822506i	$0.307425\pi$
$762$	−18.0000			−0.652071
$763$	18.0000	−	18.0000i	0.651644	−	0.651644i
$764$	8.00000			0.289430
$765$	1.00000	+	3.00000i	0.0361551	+	0.108465i
$766$		−	30.0000i		−	1.08394i
$767$	7.00000	−	35.0000i	0.252755	−	1.26378i
$768$	−17.0000	+	17.0000i	−0.613435	+	0.613435i
$769$	15.0000	−	15.0000i	0.540914	−	0.540914i	−0.382883	−	0.923797i	$-0.625069\pi$
$769$	15.0000	−	15.0000i	0.540914	−	0.540914i	0.923797	+	0.382883i	$0.125069\pi$
$770$	−2.00000	−	6.00000i	−0.0720750	−	0.216225i
$771$		−	22.0000i		−	0.792311i
$772$		−	18.0000i

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.00000 - 1.00000i) q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +(1.00000 + 1.00000i) q^{6} -2.00000 q^{7} +3.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(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} -2.00000 q^{7} +3.00000i q^{8} +1.00000i q^{9} +(1.00000 - 2.00000i) q^{10} +(-1.00000 + 1.00000i) q^{11} +(1.00000 - 1.00000i) q^{12} +(-2.00000 - 3.00000i) q^{13} -2.00000i q^{14} +(-3.00000 + 1.00000i) q^{15} -1.00000 q^{16} +(-1.00000 + 1.00000i) q^{17} -1.00000 q^{18} +(5.00000 - 5.00000i) q^{19} +(-2.00000 - 1.00000i) q^{20} +(-2.00000 + 2.00000i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(-3.00000 - 3.00000i) q^{23} +(3.00000 + 3.00000i) q^{24} +(3.00000 + 4.00000i) q^{25} +(3.00000 - 2.00000i) q^{26} +(4.00000 + 4.00000i) q^{27} -2.00000 q^{28} +(-1.00000 - 3.00000i) q^{30} +(5.00000 + 5.00000i) q^{31} +5.00000i q^{32} +2.00000i q^{33} +(-1.00000 - 1.00000i) q^{34} +(4.00000 + 2.00000i) q^{35} +1.00000i q^{36} +(5.00000 + 5.00000i) q^{38} +(-5.00000 - 1.00000i) q^{39} +(3.00000 - 6.00000i) q^{40} +(-7.00000 - 7.00000i) q^{41} +(-2.00000 - 2.00000i) q^{42} +(1.00000 + 1.00000i) q^{43} +(-1.00000 + 1.00000i) q^{44} +(1.00000 - 2.00000i) q^{45} +(3.00000 - 3.00000i) q^{46} +6.00000 q^{47} +(-1.00000 + 1.00000i) q^{48} -3.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +2.00000i q^{51} +(-2.00000 - 3.00000i) q^{52} +(5.00000 - 5.00000i) q^{53} +(-4.00000 + 4.00000i) q^{54} +(3.00000 - 1.00000i) q^{55} -6.00000i q^{56} -10.0000i q^{57} +(7.00000 + 7.00000i) q^{59} +(-3.00000 + 1.00000i) q^{60} -14.0000 q^{61} +(-5.00000 + 5.00000i) q^{62} -2.00000i q^{63} -7.00000 q^{64} +(1.00000 + 8.00000i) q^{65} -2.00000 q^{66} -4.00000i q^{67} +(-1.00000 + 1.00000i) q^{68} -6.00000 q^{69} +(-2.00000 + 4.00000i) q^{70} +(1.00000 + 1.00000i) q^{71} -3.00000 q^{72} +10.0000i q^{73} +(7.00000 + 1.00000i) q^{75} +(5.00000 - 5.00000i) q^{76} +(2.00000 - 2.00000i) q^{77} +(1.00000 - 5.00000i) q^{78} -2.00000i q^{79} +(2.00000 + 1.00000i) q^{80} +5.00000 q^{81} +(7.00000 - 7.00000i) q^{82} +6.00000 q^{83} +(-2.00000 + 2.00000i) q^{84} +(3.00000 - 1.00000i) q^{85} +(-1.00000 + 1.00000i) q^{86} +(-3.00000 - 3.00000i) q^{88} +(-5.00000 - 5.00000i) q^{89} +(2.00000 + 1.00000i) q^{90} +(4.00000 + 6.00000i) q^{91} +(-3.00000 - 3.00000i) q^{92} +10.0000 q^{93} +6.00000i q^{94} +(-15.0000 + 5.00000i) q^{95} +(5.00000 + 5.00000i) q^{96} +2.00000i q^{97} -3.00000i q^{98} +(-1.00000 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7}+O(q^{10}) \) 2 * q + 2 * q^3 + 2 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7	\( 2 q + 2 q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} + 2 q^{10} - 2 q^{11} + 2 q^{12} - 4 q^{13} - 6 q^{15} - 2 q^{16} - 2 q^{17} - 2 q^{18} + 10 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{22} - 6 q^{23} + 6 q^{24} + 6 q^{25} + 6 q^{26} + 8 q^{27} - 4 q^{28} - 2 q^{30} + 10 q^{31} - 2 q^{34} + 8 q^{35} + 10 q^{38} - 10 q^{39} + 6 q^{40} - 14 q^{41} - 4 q^{42} + 2 q^{43} - 2 q^{44} + 2 q^{45} + 6 q^{46} + 12 q^{47} - 2 q^{48} - 6 q^{49} - 8 q^{50} - 4 q^{52} + 10 q^{53} - 8 q^{54} + 6 q^{55} + 14 q^{59} - 6 q^{60} - 28 q^{61} - 10 q^{62} - 14 q^{64} + 2 q^{65} - 4 q^{66} - 2 q^{68} - 12 q^{69} - 4 q^{70} + 2 q^{71} - 6 q^{72} + 14 q^{75} + 10 q^{76} + 4 q^{77} + 2 q^{78} + 4 q^{80} + 10 q^{81} + 14 q^{82} + 12 q^{83} - 4 q^{84} + 6 q^{85} - 2 q^{86} - 6 q^{88} - 10 q^{89} + 4 q^{90} + 8 q^{91} - 6 q^{92} + 20 q^{93} - 30 q^{95} + 10 q^{96} - 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 + 2 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 + 2 * q^10 - 2 * q^11 + 2 * q^12 - 4 * q^13 - 6 * q^15 - 2 * q^16 - 2 * q^17 - 2 * q^18 + 10 * q^19 - 4 * q^20 - 4 * q^21 - 2 * q^22 - 6 * q^23 + 6 * q^24 + 6 * q^25 + 6 * q^26 + 8 * q^27 - 4 * q^28 - 2 * q^30 + 10 * q^31 - 2 * q^34 + 8 * q^35 + 10 * q^38 - 10 * q^39 + 6 * q^40 - 14 * q^41 - 4 * q^42 + 2 * q^43 - 2 * q^44 + 2 * q^45 + 6 * q^46 + 12 * q^47 - 2 * q^48 - 6 * q^49 - 8 * q^50 - 4 * q^52 + 10 * q^53 - 8 * q^54 + 6 * q^55 + 14 * q^59 - 6 * q^60 - 28 * q^61 - 10 * q^62 - 14 * q^64 + 2 * q^65 - 4 * q^66 - 2 * q^68 - 12 * q^69 - 4 * q^70 + 2 * q^71 - 6 * q^72 + 14 * q^75 + 10 * q^76 + 4 * q^77 + 2 * q^78 + 4 * q^80 + 10 * q^81 + 14 * q^82 + 12 * q^83 - 4 * q^84 + 6 * q^85 - 2 * q^86 - 6 * q^88 - 10 * q^89 + 4 * q^90 + 8 * q^91 - 6 * q^92 + 20 * q^93 - 30 * q^95 + 10 * q^96 - 2 * q^99

Introduction

L-functions

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Varieties

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