LMFDB - Embedded newform 65.2.k.a.57.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(8,65)]

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, 1]))

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

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

chi := DirichletCharacter("65.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.519027613138$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			57.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	65.57
Dual form			65.2.k.a.8.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.00000			0.707107			0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000			0.707107			0.353553	+	0.935414i	$0.384973\pi$
$3$	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
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$6$	1.00000	−	1.00000i	0.408248	−	0.408248i
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$	−3.00000			−1.06066
$9$			1.00000i			0.333333i
$10$	−1.00000	+	2.00000i	−0.316228	+	0.632456i
$11$	−1.00000	−	1.00000i	−0.301511	−	0.301511i	0.540094	−	0.841605i	$-0.318389\pi$
$11$	−1.00000	−	1.00000i	−0.301511	−	0.301511i	−0.841605	+	0.540094i	$0.818389\pi$
$12$	−1.00000	+	1.00000i	−0.288675	+	0.288675i
$13$	3.00000	+	2.00000i	0.832050	+	0.554700i
$13$	3.00000	+	2.00000i	0.832050	+	0.554700i
$14$		−	2.00000i		−	0.534522i
$15$	1.00000	+	3.00000i	0.258199	+	0.774597i
$16$	−1.00000			−0.250000
$17$	1.00000	−	1.00000i	0.242536	−	0.242536i	−0.575363	−	0.817898i	$-0.695139\pi$
$17$	1.00000	−	1.00000i	0.242536	−	0.242536i	0.817898	+	0.575363i	$0.195139\pi$
$18$			1.00000i			0.235702i
$19$	−5.00000	−	5.00000i	−1.14708	−	1.14708i	−0.987124	−	0.159954i	$-0.948865\pi$
$19$	−5.00000	−	5.00000i	−1.14708	−	1.14708i	−0.159954	−	0.987124i	$-0.551135\pi$
$20$	1.00000	−	2.00000i	0.223607	−	0.447214i
$21$	−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	0.946943	−	0.321400i	$-0.104153\pi$
$23$	3.00000	+	3.00000i	0.625543	+	0.625543i	−0.321400	+	0.946943i	$0.604153\pi$
$24$	−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
$28$			2.00000i			0.377964i
$29$		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	−0.0972349	−	0.995261i	$-0.531000\pi$
$31$	5.00000	−	5.00000i	0.898027	−	0.898027i	0.995261	+	0.0972349i	$0.0309998\pi$
$32$	5.00000			0.883883
$33$	−2.00000			−0.348155
$34$	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		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	−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	−0.0980332	+	0.995183i	$0.531255\pi$
$41$	−7.00000	+	7.00000i	−1.09322	+	1.09322i	−0.995183	+	0.0980332i	$0.968745\pi$
$42$	−2.00000	−	2.00000i	−0.308607	−	0.308607i
$43$	−1.00000	−	1.00000i	−0.152499	−	0.152499i	0.626734	−	0.779233i	$-0.284391\pi$
$43$	−1.00000	−	1.00000i	−0.152499	−	0.152499i	−0.779233	+	0.626734i	$0.784391\pi$
$44$	1.00000	+	1.00000i	0.150756	+	0.150756i
$45$	−2.00000	−	1.00000i	−0.298142	−	0.149071i
$46$	3.00000	+	3.00000i	0.442326	+	0.442326i
$47$			6.00000i			0.875190i	0.899172	+	0.437595i	$0.144170\pi$
$47$			6.00000i			0.875190i	−0.899172	+	0.437595i	$0.855830\pi$
$48$	−1.00000	+	1.00000i	−0.144338	+	0.144338i
$49$	3.00000			0.428571
$50$	−3.00000	−	4.00000i	−0.424264	−	0.565685i
$51$		−	2.00000i		−	0.280056i
$52$	−3.00000	−	2.00000i	−0.416025	−	0.277350i
$53$	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
$57$	−10.0000			−1.32453
$58$		0			0
$59$	−7.00000	+	7.00000i	−0.911322	+	0.911322i	−0.996376	−	0.0850540i	$-0.972894\pi$
$59$	−7.00000	+	7.00000i	−0.911322	+	0.911322i	0.0850540	+	0.996376i	$0.472894\pi$
$60$	−1.00000	−	3.00000i	−0.129099	−	0.387298i
$61$	−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
$63$	2.00000			0.251976
$64$	7.00000			0.875000
$65$	−7.00000	+	4.00000i	−0.868243	+	0.496139i
$66$	−2.00000			−0.246183
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$	−1.00000	+	1.00000i	−0.121268	+	0.121268i
$69$	6.00000			0.722315
$70$	4.00000	+	2.00000i	0.478091	+	0.239046i
$71$	1.00000	−	1.00000i	0.118678	−	0.118678i	−0.645273	−	0.763952i	$-0.723257\pi$
$71$	1.00000	−	1.00000i	0.118678	−	0.118678i	0.763952	+	0.645273i	$0.223257\pi$
$72$		−	3.00000i		−	0.353553i
$73$	−10.0000			−1.17041			−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000			−1.17041			−0.585206	+	0.810885i	$0.698986\pi$
$74$		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
$78$	5.00000	−	1.00000i	0.566139	−	0.113228i
$79$		−	2.00000i		−	0.225018i	−0.993651	−	0.112509i	$-0.964111\pi$
$79$		−	2.00000i		−	0.225018i	0.993651	−	0.112509i	$-0.0358886\pi$
$80$	1.00000	−	2.00000i	0.111803	−	0.223607i
$81$	5.00000			0.555556
$82$	−7.00000	+	7.00000i	−0.773021	+	0.773021i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$	2.00000	+	2.00000i	0.218218	+	0.218218i
$85$	1.00000	+	3.00000i	0.108465	+	0.325396i
$86$	−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	$-0.627723\pi$
$89$	5.00000	−	5.00000i	0.529999	−	0.529999i	0.920572	+	0.390573i	$0.127723\pi$
$90$	−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
$93$		−	10.0000i		−	1.03695i
$94$			6.00000i			0.618853i
$95$	15.0000	−	5.00000i	1.53897	−	0.512989i
$96$	5.00000	−	5.00000i	0.510310	−	0.510310i
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$	3.00000			0.303046
$99$	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	$0.203650\pi$
$101$			12.0000i			1.19404i	−0.802225	+	0.597022i	$0.796350\pi$
$102$		−	2.00000i		−	0.198030i
$103$	7.00000	+	7.00000i	0.689730	+	0.689730i	0.962172	−	0.272442i	$-0.0878312\pi$
$103$	7.00000	+	7.00000i	0.689730	+	0.689730i	−0.272442	+	0.962172i	$0.587831\pi$
$104$	−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	$-0.0413474\pi$
$109$	9.00000	+	9.00000i	0.862044	+	0.862044i	−0.129532	+	0.991575i	$0.541347\pi$
$110$	3.00000	−	1.00000i	0.286039	−	0.0953463i
$111$		0			0
$112$			2.00000i			0.188982i
$113$	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
$115$	−9.00000	+	3.00000i	−0.839254	+	0.279751i
$116$		0			0
$117$	−2.00000	+	3.00000i	−0.184900	+	0.277350i
$118$	−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
$122$	−14.0000			−1.26750
$123$			14.0000i			1.26234i
$124$	−5.00000	+	5.00000i	−0.449013	+	0.449013i
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$	2.00000			0.178174
$127$	9.00000	−	9.00000i	0.798621	−	0.798621i	−0.184257	−	0.982878i	$-0.558988\pi$
$127$	9.00000	−	9.00000i	0.798621	−	0.798621i	0.982878	+	0.184257i	$0.0589879\pi$
$128$	−3.00000			−0.265165
$129$	−2.00000			−0.176090
$130$	−7.00000	+	4.00000i	−0.613941	+	0.350823i
$131$	−20.0000			−1.74741			−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000			−1.74741			−0.873704	+	0.486458i	$0.838289\pi$
$132$	2.00000			0.174078
$133$	−10.0000	+	10.0000i	−0.867110	+	0.867110i
$134$	−4.00000			−0.345547
$135$	−12.0000	+	4.00000i	−1.03280	+	0.344265i
$136$	−3.00000	+	3.00000i	−0.257248	+	0.257248i
$137$		−	16.0000i		−	1.36697i	−0.729964	−	0.683486i	$-0.760463\pi$
$137$		−	16.0000i		−	1.36697i	0.729964	−	0.683486i	$-0.239537\pi$
$138$	6.00000			0.510754
$139$		−	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
$143$	−1.00000	−	5.00000i	−0.0836242	−	0.418121i
$144$		−	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	$-0.305600\pi$
$149$	−3.00000	−	3.00000i	−0.245770	−	0.245770i	−0.819232	+	0.573462i	$0.805600\pi$
$150$	−7.00000	−	1.00000i	−0.571548	−	0.0816497i
$151$	7.00000	+	7.00000i	0.569652	+	0.569652i	0.932031	−	0.362379i	$-0.118035\pi$
$151$	7.00000	+	7.00000i	0.569652	+	0.569652i	−0.362379	+	0.932031i	$0.618035\pi$
$152$	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	$0.487823\pi$
$158$		−	2.00000i		−	0.159111i
$159$		−	10.0000i		−	0.793052i
$160$	−5.00000	+	10.0000i	−0.395285	+	0.790569i
$161$	6.00000	−	6.00000i	0.472866	−	0.472866i
$162$	5.00000			0.392837
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$	7.00000	−	7.00000i	0.546608	−	0.546608i
$165$	2.00000	−	4.00000i	0.155700	−	0.311400i
$166$		−	6.00000i		−	0.465690i
$167$		−	18.0000i		−	1.39288i	−0.717614	−	0.696441i	$-0.754766\pi$
$167$		−	18.0000i		−	1.39288i	0.717614	−	0.696441i	$-0.245234\pi$
$168$	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	0.152057	−	0.988372i	$-0.451410\pi$
$173$	−11.0000	−	11.0000i	−0.836315	−	0.836315i	−0.988372	+	0.152057i	$0.951410\pi$
$174$		0			0
$175$	−8.00000	+	6.00000i	−0.604743	+	0.453557i
$176$	1.00000	+	1.00000i	0.0753778	+	0.0753778i
$177$			14.0000i			1.05230i
$178$	5.00000	−	5.00000i	0.374766	−	0.374766i
$179$	−20.0000			−1.49487			−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000			−1.49487			−0.747435	+	0.664335i	$0.768715\pi$
$180$	2.00000	+	1.00000i	0.149071	+	0.0745356i
$181$		−	8.00000i		−	0.594635i	−0.954779	−	0.297318i	$-0.903908\pi$
$181$		−	8.00000i		−	0.594635i	0.954779	−	0.297318i	$-0.0960920\pi$
$182$	4.00000	−	6.00000i	0.296500	−	0.444750i
$183$	−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
$187$	−2.00000			−0.146254
$188$		−	6.00000i		−	0.437595i
$189$	8.00000	−	8.00000i	0.581914	−	0.581914i
$190$	15.0000	−	5.00000i	1.08821	−	0.362738i
$191$	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
$193$	18.0000			1.29567			0.647834	−	0.761781i	$-0.275675\pi$
$193$	18.0000			1.29567			0.647834	+	0.761781i	$0.275675\pi$
$194$	2.00000			0.143592
$195$	−3.00000	+	11.0000i	−0.214834	+	0.787726i
$196$	−3.00000			−0.214286
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$	1.00000	−	1.00000i	0.0710669	−	0.0710669i
$199$	−8.00000			−0.567105			−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000			−0.567105			−0.283552	+	0.958957i	$0.591513\pi$
$200$	9.00000	+	12.0000i	0.636396	+	0.848528i
$201$	−4.00000	+	4.00000i	−0.282138	+	0.282138i
$202$			12.0000i			0.844317i
$203$		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
$208$	−3.00000	−	2.00000i	−0.208013	−	0.138675i
$209$			10.0000i			0.691714i
$210$	6.00000	−	2.00000i	0.414039	−	0.138013i
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	−5.00000	+	5.00000i	−0.343401	+	0.343401i
$213$		−	2.00000i		−	0.137038i
$214$	7.00000	+	7.00000i	0.478510	+	0.478510i
$215$	3.00000	−	1.00000i	0.204598	−	0.0681994i
$216$	−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
$223$		−	2.00000i		−	0.133930i	−0.997755	−	0.0669650i	$-0.978668\pi$
$223$		−	2.00000i		−	0.133930i	0.997755	−	0.0669650i	$-0.0213316\pi$
$224$		−	10.0000i		−	0.668153i
$225$	4.00000	−	3.00000i	0.266667	−	0.200000i
$226$	5.00000	−	5.00000i	0.332595	−	0.332595i
$227$	−12.0000			−0.796468			−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000			−0.796468			−0.398234	+	0.917284i	$0.630377\pi$
$228$	10.0000			0.662266
$229$	−3.00000	+	3.00000i	−0.198246	+	0.198246i	−0.799248	−	0.601002i	$-0.794768\pi$
$229$	−3.00000	+	3.00000i	−0.198246	+	0.198246i	0.601002	+	0.799248i	$0.294768\pi$
$230$	−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	0.739104	−	0.673592i	$-0.235249\pi$
$233$	1.00000	+	1.00000i	0.0655122	+	0.0655122i	−0.673592	+	0.739104i	$0.735249\pi$
$234$	−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	$-0.206184\pi$
$239$	3.00000	+	3.00000i	0.194054	+	0.194054i	−0.603391	+	0.797445i	$0.706184\pi$
$240$	−1.00000	−	3.00000i	−0.0645497	−	0.193649i
$241$	17.0000	+	17.0000i	1.09507	+	1.09507i	0.994979	+	0.100088i	$0.0319123\pi$
$241$	17.0000	+	17.0000i	1.09507	+	1.09507i	0.100088	+	0.994979i	$0.468088\pi$
$242$		−	9.00000i		−	0.578542i
$243$	−7.00000	+	7.00000i	−0.449050	+	0.449050i
$244$	14.0000			0.896258
$245$	−3.00000	+	6.00000i	−0.191663	+	0.383326i
$246$			14.0000i			0.892607i
$247$	−5.00000	−	25.0000i	−0.318142	−	1.59071i
$248$	−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	$0.0201049\pi$
$251$			2.00000i			0.126239i	−0.998006	+	0.0631194i	$0.979895\pi$
$252$	−2.00000			−0.125988
$253$		−	6.00000i		−	0.377217i
$254$	9.00000	−	9.00000i	0.564710	−	0.564710i
$255$	4.00000	+	2.00000i	0.250490	+	0.125245i
$256$	−17.0000			−1.06250
$257$	−11.0000	+	11.0000i	−0.686161	+	0.686161i	−0.961381	−	0.275220i	$-0.911249\pi$
$257$	−11.0000	+	11.0000i	−0.686161	+	0.686161i	0.275220	+	0.961381i	$0.411249\pi$
$258$	−2.00000			−0.124515
$259$		0			0
$260$	7.00000	−	4.00000i	0.434122	−	0.248069i
$261$		0			0
$262$	−20.0000			−1.23560
$263$	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
$265$	5.00000	+	15.0000i	0.307148	+	0.921443i
$266$	−10.0000	+	10.0000i	−0.613139	+	0.613139i
$267$		−	10.0000i		−	0.611990i
$268$	4.00000			0.244339
$269$			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	0.378777	−	0.925488i	$-0.376345\pi$
$271$	−9.00000	−	9.00000i	−0.546711	−	0.546711i	−0.925488	+	0.378777i	$0.876345\pi$
$272$	−1.00000	+	1.00000i	−0.0606339	+	0.0606339i
$273$	−2.00000	−	10.0000i	−0.121046	−	0.605228i
$274$		−	16.0000i		−	0.966595i
$275$	−1.00000	+	7.00000i	−0.0603023	+	0.422116i
$276$	−6.00000			−0.361158
$277$	−15.0000	+	15.0000i	−0.901263	+	0.901263i	−0.995545	−	0.0942828i	$-0.969944\pi$
$277$	−15.0000	+	15.0000i	−0.901263	+	0.901263i	0.0942828	+	0.995545i	$0.469944\pi$
$278$		−	14.0000i		−	0.839664i
$279$	5.00000	+	5.00000i	0.299342	+	0.299342i
$280$	−12.0000	−	6.00000i	−0.717137	−	0.358569i
$281$	1.00000	+	1.00000i	0.0596550	+	0.0596550i	0.736305	−	0.676650i	$-0.236569\pi$
$281$	1.00000	+	1.00000i	0.0596550	+	0.0596550i	−0.676650	+	0.736305i	$0.736569\pi$
$282$	6.00000	+	6.00000i	0.357295	+	0.357295i
$283$	−9.00000	−	9.00000i	−0.534994	−	0.534994i	0.387060	−	0.922055i	$-0.373491\pi$
$283$	−9.00000	−	9.00000i	−0.534994	−	0.534994i	−0.922055	+	0.387060i	$0.873491\pi$
$284$	−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
$288$			5.00000i			0.294628i
$289$			15.0000i			0.882353i
$290$		0			0
$291$	2.00000	−	2.00000i	0.117242	−	0.117242i
$292$	10.0000			0.585206
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$	3.00000	−	3.00000i	0.174964	−	0.174964i
$295$	−7.00000	−	21.0000i	−0.407556	−	1.22267i
$296$		0			0
$297$		−	8.00000i		−	0.464207i
$298$	−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
$305$	14.0000	−	28.0000i	0.801638	−	1.60328i
$306$	1.00000	+	1.00000i	0.0571662	+	0.0571662i
$307$			18.0000i			1.02731i	0.857996	+	0.513657i	$0.171710\pi$
$307$			18.0000i			1.02731i	−0.857996	+	0.513657i	$0.828290\pi$
$308$	2.00000	−	2.00000i	0.113961	−	0.113961i
$309$	14.0000			0.796432
$310$	5.00000	+	15.0000i	0.283981	+	0.851943i
$311$			6.00000i			0.340229i	0.985424	+	0.170114i	$0.0544137\pi$
$311$			6.00000i			0.340229i	−0.985424	+	0.170114i	$0.945586\pi$
$312$	−15.0000	+	3.00000i	−0.849208	+	0.169842i
$313$	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
$317$	−14.0000			−0.786318			−0.393159	−	0.919470i	$-0.628618\pi$
$317$	−14.0000			−0.786318			−0.393159	+	0.919470i	$0.628618\pi$
$318$		−	10.0000i		−	0.560772i
$319$		0			0
$320$	−7.00000	+	14.0000i	−0.391312	+	0.782624i
$321$	14.0000			0.781404
$322$	6.00000	−	6.00000i	0.334367	−	0.334367i
$323$	−10.0000			−0.556415
$324$	−5.00000			−0.277778
$325$	−1.00000	−	18.0000i	−0.0554700	−	0.998460i
$326$	4.00000			0.221540
$327$	18.0000			0.995402
$328$	21.0000	−	21.0000i	1.15953	−	1.15953i
$329$	12.0000			0.661581
$330$	2.00000	−	4.00000i	0.110096	−	0.220193i
$331$	−3.00000	+	3.00000i	−0.164895	+	0.164895i	−0.784731	−	0.619836i	$-0.787199\pi$
$331$	−3.00000	+	3.00000i	−0.164895	+	0.164895i	0.619836	+	0.784731i	$0.287199\pi$
$332$			6.00000i			0.329293i
$333$		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	−0.257992	−	0.966147i	$-0.583061\pi$
$337$	13.0000	−	13.0000i	0.708155	−	0.708155i	0.966147	+	0.257992i	$0.0830608\pi$
$338$	5.00000	+	12.0000i	0.271964	+	0.652714i
$339$		−	10.0000i		−	0.543125i
$340$	−1.00000	−	3.00000i	−0.0542326	−	0.162698i
$341$	−10.0000			−0.541530
$342$	5.00000	−	5.00000i	0.270369	−	0.270369i
$343$		−	20.0000i		−	1.07990i
$344$	3.00000	+	3.00000i	0.161749	+	0.161749i
$345$	−6.00000	+	12.0000i	−0.323029	+	0.646058i
$346$	−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	$-0.639351\pi$
$349$	9.00000	−	9.00000i	0.481759	−	0.481759i	0.905693	+	0.423934i	$0.139351\pi$
$350$	−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
$353$			12.0000i			0.638696i	0.947638	+	0.319348i	$0.103464\pi$
$353$			12.0000i			0.638696i	−0.947638	+	0.319348i	$0.896536\pi$
$354$			14.0000i			0.744092i
$355$	1.00000	+	3.00000i	0.0530745	+	0.159223i
$356$	−5.00000	+	5.00000i	−0.264999	+	0.264999i
$357$	−4.00000			−0.211702
$358$	−20.0000			−1.05703
$359$	1.00000	−	1.00000i	0.0527780	−	0.0527780i	−0.680225	−	0.733003i	$-0.738118\pi$
$359$	1.00000	−	1.00000i	0.0527780	−	0.0527780i	0.733003	+	0.680225i	$0.238118\pi$
$360$	6.00000	+	3.00000i	0.316228	+	0.158114i
$361$			31.0000i			1.63158i
$362$		−	8.00000i		−	0.420471i
$363$	−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
$372$			10.0000i			0.518476i
$373$	−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
$375$	9.00000	−	13.0000i	0.464758	−	0.671317i
$376$		−	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	$-0.261564\pi$
$379$	−1.00000	−	1.00000i	−0.0513665	−	0.0513665i	−0.732323	+	0.680957i	$0.761564\pi$
$380$	−15.0000	+	5.00000i	−0.769484	+	0.256495i
$381$		−	18.0000i		−	0.922168i
$382$	8.00000			0.409316
$383$			30.0000i			1.53293i	0.642287	+	0.766464i	$0.277986\pi$
$383$			30.0000i			1.53293i	−0.642287	+	0.766464i	$0.722014\pi$
$384$	−3.00000	+	3.00000i	−0.153093	+	0.153093i
$385$	−2.00000	−	6.00000i	−0.101929	−	0.305788i
$386$	18.0000			0.916176
$387$	1.00000	−	1.00000i	0.0508329	−	0.0508329i
$388$	−2.00000			−0.101535
$389$	−18.0000			−0.912636			−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000			−0.912636			−0.456318	+	0.889817i	$0.650832\pi$
$390$	−3.00000	+	11.0000i	−0.151911	+	0.557007i
$391$	6.00000			0.303433
$392$	−9.00000			−0.454569
$393$	−20.0000	+	20.0000i	−1.00887	+	1.00887i
$394$	6.00000			0.302276
$395$	4.00000	+	2.00000i	0.201262	+	0.100631i
$396$	−1.00000	+	1.00000i	−0.0502519	+	0.0502519i
$397$			16.0000i			0.803017i	0.915855	+	0.401508i	$0.131514\pi$
$397$			16.0000i			0.803017i	−0.915855	+	0.401508i	$0.868486\pi$
$398$	−8.00000			−0.401004
$399$			20.0000i			1.00125i
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	−11.0000	−	11.0000i	−0.549314	−	0.549314i	0.376929	−	0.926242i	$-0.376980\pi$
$401$	−11.0000	−	11.0000i	−0.549314	−	0.549314i	−0.926242	+	0.376929i	$0.876980\pi$
$402$	−4.00000	+	4.00000i	−0.199502	+	0.199502i
$403$	25.0000	−	5.00000i	1.24534	−	0.249068i
$404$		−	12.0000i		−	0.597022i
$405$	−5.00000	+	10.0000i	−0.248452	+	0.496904i
$406$		0			0
$407$		0			0
$408$			6.00000i			0.297044i
$409$	−7.00000	−	7.00000i	−0.346128	−	0.346128i	0.512537	−	0.858665i	$-0.328706\pi$
$409$	−7.00000	−	7.00000i	−0.346128	−	0.346128i	−0.858665	+	0.512537i	$0.828706\pi$
$410$	−7.00000	−	21.0000i	−0.345705	−	1.03712i
$411$	−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
$418$			10.0000i			0.489116i
$419$		−	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	−0.922383	−	0.386276i	$-0.873761\pi$
$421$	−11.0000	+	11.0000i	−0.536107	+	0.536107i	0.386276	+	0.922383i	$0.373761\pi$
$422$	4.00000			0.194717
$423$	−6.00000			−0.291730
$424$	−15.0000	+	15.0000i	−0.728464	+	0.728464i
$425$	−7.00000	−	1.00000i	−0.339550	−	0.0485071i
$426$		−	2.00000i		−	0.0969003i
$427$			28.0000i			1.35501i
$428$	−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	−0.320919	−	0.947107i	$-0.603992\pi$
$431$	13.0000	−	13.0000i	0.626188	−	0.626188i	0.947107	+	0.320919i	$0.103992\pi$
$432$	−4.00000	−	4.00000i	−0.192450	−	0.192450i
$433$	17.0000	+	17.0000i	0.816968	+	0.816968i	0.985668	−	0.168700i	$-0.0539568\pi$
$433$	17.0000	+	17.0000i	0.816968	+	0.816968i	−0.168700	+	0.985668i	$0.553957\pi$
$434$	−10.0000	−	10.0000i	−0.480015	−	0.480015i
$435$		0			0
$436$	−9.00000	−	9.00000i	−0.431022	−	0.431022i
$437$		−	30.0000i		−	1.43509i
$438$	−10.0000	+	10.0000i	−0.477818	+	0.477818i
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$	−9.00000	+	3.00000i	−0.429058	+	0.143019i
$441$			3.00000i			0.142857i
$442$	5.00000	−	1.00000i	0.237826	−	0.0475651i
$443$	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
$447$	−6.00000			−0.283790
$448$		−	14.0000i		−	0.661438i
$449$	−3.00000	+	3.00000i	−0.141579	+	0.141579i	−0.774344	−	0.632765i	$-0.781920\pi$
$449$	−3.00000	+	3.00000i	−0.141579	+	0.141579i	0.632765	+	0.774344i	$0.281920\pi$
$450$	4.00000	−	3.00000i	0.188562	−	0.141421i
$451$	14.0000			0.659234
$452$	−5.00000	+	5.00000i	−0.235180	+	0.235180i
$453$	14.0000			0.657777
$454$	−12.0000			−0.563188
$455$	8.00000	+	14.0000i	0.375046	+	0.656330i
$456$	30.0000			1.40488
$457$	2.00000			0.0935561			0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000			0.0935561			0.0467780	+	0.998905i	$0.485105\pi$
$458$	−3.00000	+	3.00000i	−0.140181	+	0.140181i
$459$	8.00000			0.373408
$460$	9.00000	−	3.00000i	0.419627	−	0.139876i
$461$	17.0000	−	17.0000i	0.791769	−	0.791769i	−0.190013	−	0.981782i	$-0.560853\pi$
$461$	17.0000	−	17.0000i	0.791769	−	0.791769i	0.981782	+	0.190013i	$0.0608529\pi$
$462$			4.00000i			0.186097i
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$		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	−0.467515	−	0.883985i	$-0.654851\pi$
$467$	9.00000	−	9.00000i	0.416470	−	0.416470i	0.883985	+	0.467515i	$0.154851\pi$
$468$	2.00000	−	3.00000i	0.0924500	−	0.138675i
$469$			8.00000i			0.369406i
$470$	−12.0000	−	6.00000i	−0.553519	−	0.276759i
$471$	26.0000			1.19802
$472$	21.0000	−	21.0000i	0.966603	−	0.966603i
$473$			2.00000i			0.0919601i
$474$	−2.00000	−	2.00000i	−0.0918630	−	0.0918630i
$475$	−5.00000	+	35.0000i	−0.229416	+	1.60591i
$476$	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	$-0.822617\pi$
$479$	−7.00000	+	7.00000i	−0.319838	+	0.319838i	0.528867	+	0.848705i	$0.322617\pi$
$480$	5.00000	+	15.0000i	0.228218	+	0.684653i
$481$		0			0
$482$	17.0000	+	17.0000i	0.774329	+	0.774329i
$483$		−	12.0000i		−	0.546019i
$484$			9.00000i			0.409091i
$485$	−2.00000	+	4.00000i	−0.0908153	+	0.181631i
$486$	−7.00000	+	7.00000i	−0.317526	+	0.317526i
$487$	16.0000			0.725029			0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000			0.725029			0.362515	+	0.931978i	$0.381918\pi$
$488$	42.0000			1.90125
$489$	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	$-0.834646\pi$
$491$		−	22.0000i		−	0.992846i	0.868081	−	0.496423i	$-0.165354\pi$
$492$		−	14.0000i		−	0.631169i
$493$		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	$-0.219727\pi$
$499$	3.00000	+	3.00000i	0.134298	+	0.134298i	−0.636762	+	0.771060i	$0.719727\pi$
$500$	−11.0000	+	2.00000i	−0.491935	+	0.0894427i
$501$	−18.0000	−	18.0000i	−0.804181	−	0.804181i
$502$			2.00000i			0.0892644i
$503$	−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
$505$	−24.0000	−	12.0000i	−1.06799	−	0.533993i
$506$		−	6.00000i		−	0.266733i
$507$	17.0000	+	7.00000i	0.754997	+	0.310881i
$508$	−9.00000	+	9.00000i	−0.399310	+	0.399310i
$509$	13.0000	+	13.0000i	0.576215	+	0.576215i	0.933858	−	0.357643i	$-0.116420\pi$
$509$	13.0000	+	13.0000i	0.576215	+	0.576215i	−0.357643	+	0.933858i	$0.616420\pi$
$510$	4.00000	+	2.00000i	0.177123	+	0.0885615i
$511$			20.0000i			0.884748i
$512$	−11.0000			−0.486136
$513$		−	40.0000i		−	1.76604i
$514$	−11.0000	+	11.0000i	−0.485189	+	0.485189i
$515$	−21.0000	+	7.00000i	−0.925371	+	0.308457i
$516$	2.00000			0.0880451
$517$	6.00000	−	6.00000i	0.263880	−	0.263880i
$518$		0			0
$519$	−22.0000			−0.965693
$520$	21.0000	−	12.0000i	0.920911	−	0.526235i
$521$	−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
$525$	−2.00000	+	14.0000i	−0.0872872	+	0.611010i
$526$	1.00000	−	1.00000i	0.0436021	−	0.0436021i
$527$		−	10.0000i		−	0.435607i
$528$	2.00000			0.0870388
$529$		−	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
$533$	−35.0000	+	7.00000i	−1.51602	+	0.303204i
$534$		−	10.0000i		−	0.432742i
$535$	−21.0000	+	7.00000i	−0.907909	+	0.302636i
$536$	12.0000			0.518321
$537$	−20.0000	+	20.0000i	−0.863064	+	0.863064i
$538$			12.0000i			0.517357i
$539$	−3.00000	−	3.00000i	−0.129219	−	0.129219i
$540$	12.0000	−	4.00000i	0.516398	−	0.172133i
$541$	9.00000	+	9.00000i	0.386940	+	0.386940i	0.873595	−	0.486654i	$-0.161783\pi$
$541$	9.00000	+	9.00000i	0.386940	+	0.386940i	−0.486654	+	0.873595i	$0.661783\pi$
$542$	−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	$0.837719\pi$
$548$			16.0000i			0.683486i
$549$		−	14.0000i		−	0.597505i
$550$	−1.00000	+	7.00000i	−0.0426401	+	0.298481i
$551$		0			0
$552$	−18.0000			−0.766131
$553$	−4.00000			−0.170097
$554$	−15.0000	+	15.0000i	−0.637289	+	0.637289i
$555$		0			0
$556$			14.0000i			0.593732i
$557$			24.0000i			1.01691i	0.861088	+	0.508456i	$0.169784\pi$
$557$			24.0000i			1.01691i	−0.861088	+	0.508456i	$0.830216\pi$
$558$	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	0.948613	−	0.316438i	$-0.102487\pi$
$563$	15.0000	+	15.0000i	0.632175	+	0.632175i	−0.316438	+	0.948613i	$0.602487\pi$
$564$	−6.00000	−	6.00000i	−0.252646	−	0.252646i
$565$	5.00000	+	15.0000i	0.210352	+	0.631055i
$566$	−9.00000	−	9.00000i	−0.378298	−	0.378298i
$567$		−	10.0000i		−	0.419961i
$568$	−3.00000	+	3.00000i	−0.125877	+	0.125877i
$569$	6.00000			0.251533			0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000			0.251533			0.125767	+	0.992060i	$0.459861\pi$
$570$	10.0000	−	20.0000i	0.418854	−	0.837708i
$571$		−	6.00000i		−	0.251092i	−0.992088	−	0.125546i	$-0.959932\pi$
$571$		−	6.00000i		−	0.251092i	0.992088	−	0.125546i	$-0.0400683\pi$
$572$	1.00000	+	5.00000i	0.0418121	+	0.209061i
$573$	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
$577$	46.0000			1.91501			0.957503	−	0.288425i	$-0.0931316\pi$
$577$	46.0000			1.91501			0.957503	+	0.288425i	$0.0931316\pi$
$578$			15.0000i			0.623918i
$579$	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
$583$	−10.0000			−0.414158
$584$	30.0000			1.24141
$585$	−4.00000	−	7.00000i	−0.165380	−	0.289414i
$586$	−6.00000			−0.247858
$587$	−4.00000			−0.165098			−0.0825488	−	0.996587i	$-0.526306\pi$
$587$	−4.00000			−0.165098			−0.0825488	+	0.996587i	$0.526306\pi$
$588$	−3.00000	+	3.00000i	−0.123718	+	0.123718i
$589$	−50.0000			−2.06021
$590$	−7.00000	−	21.0000i	−0.288185	−	0.864556i
$591$	6.00000	−	6.00000i	0.246807	−	0.246807i
$592$		0			0
$593$	10.0000			0.410651			0.205325	−	0.978694i	$-0.434175\pi$
$593$	10.0000			0.410651			0.205325	+	0.978694i	$0.434175\pi$
$594$		−	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
$598$	3.00000	+	15.0000i	0.122679	+	0.613396i
$599$			30.0000i			1.22577i	0.790173	+	0.612883i	$0.209990\pi$
$599$			30.0000i			1.22577i	−0.790173	+	0.612883i	$0.790010\pi$
$600$	21.0000	+	3.00000i	0.857321	+	0.122474i
$601$	−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
$603$		−	4.00000i		−	0.162893i
$604$	−7.00000	−	7.00000i	−0.284826	−	0.284826i
$605$	18.0000	+	9.00000i	0.731804	+	0.365902i
$606$	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
$613$			20.0000i			0.807792i	0.914805	+	0.403896i	$0.132344\pi$
$613$			20.0000i			0.807792i	−0.914805	+	0.403896i	$0.867656\pi$
$614$			18.0000i			0.726421i
$615$	−28.0000	−	14.0000i	−1.12907	−	0.564534i
$616$	6.00000	−	6.00000i	0.241747	−	0.241747i
$617$	−22.0000			−0.885687			−0.442843	−	0.896599i	$-0.646030\pi$
$617$	−22.0000			−0.885687			−0.442843	+	0.896599i	$0.646030\pi$
$618$	14.0000			0.563163
$619$	25.0000	−	25.0000i	1.00483	−	1.00483i	0.00484658	−	0.999988i	$-0.498457\pi$
$619$	25.0000	−	25.0000i	1.00483	−	1.00483i	0.999988	−	0.00484658i	$-0.00154272\pi$
$620$	−5.00000	−	15.0000i	−0.200805	−	0.602414i
$621$			24.0000i			0.963087i
$622$			6.00000i			0.240578i
$623$	−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
$630$	−2.00000	+	4.00000i	−0.0796819	+	0.159364i
$631$	11.0000	+	11.0000i	0.437903	+	0.437903i	0.891306	−	0.453403i	$-0.149790\pi$
$631$	11.0000	+	11.0000i	0.437903	+	0.437903i	−0.453403	+	0.891306i	$0.649790\pi$
$632$			6.00000i			0.238667i
$633$	4.00000	−	4.00000i	0.158986	−	0.158986i
$634$	−14.0000			−0.556011
$635$	9.00000	+	27.0000i	0.357154	+	1.07146i
$636$			10.0000i			0.396526i
$637$	9.00000	+	6.00000i	0.356593	+	0.237729i
$638$		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	$-0.842820\pi$
$641$		−	24.0000i		−	0.947943i	0.880540	−	0.473972i	$-0.157180\pi$
$642$	14.0000			0.552536
$643$			34.0000i			1.34083i	0.741987	+	0.670415i	$0.233884\pi$
$643$			34.0000i			1.34083i	−0.741987	+	0.670415i	$0.766116\pi$
$644$	−6.00000	+	6.00000i	−0.236433	+	0.236433i
$645$	2.00000	−	4.00000i	0.0787499	−	0.157500i
$646$	−10.0000			−0.393445
$647$	1.00000	−	1.00000i	0.0393141	−	0.0393141i	−0.687176	−	0.726491i	$-0.741150\pi$
$647$	1.00000	−	1.00000i	0.0393141	−	0.0393141i	0.726491	+	0.687176i	$0.241150\pi$
$648$	−15.0000			−0.589256
$649$	14.0000			0.549548
$650$	−1.00000	−	18.0000i	−0.0392232	−	0.706018i
$651$	−20.0000			−0.783862
$652$	−4.00000			−0.156652
$653$	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
$655$	20.0000	−	40.0000i	0.781465	−	1.56293i
$656$	7.00000	−	7.00000i	0.273304	−	0.273304i
$657$		−	10.0000i		−	0.390137i
$658$	12.0000			0.467809
$659$			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	0.955668	−	0.294445i	$-0.0951348\pi$
$661$	17.0000	+	17.0000i	0.661223	+	0.661223i	−0.294445	+	0.955668i	$0.595135\pi$
$662$	−3.00000	+	3.00000i	−0.116598	+	0.116598i
$663$	4.00000	−	6.00000i	0.155347	−	0.233021i
$664$			18.0000i			0.698535i
$665$	−10.0000	−	30.0000i	−0.387783	−	1.16335i
$666$		0			0
$667$		0			0
$668$			18.0000i			0.696441i
$669$	−2.00000	−	2.00000i	−0.0773245	−	0.0773245i
$670$	4.00000	−	8.00000i	0.154533	−	0.309067i
$671$	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	0.356202	−	0.934409i	$-0.384072\pi$
$673$	−15.0000	−	15.0000i	−0.578208	−	0.578208i	−0.934409	+	0.356202i	$0.884072\pi$
$674$	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	$0.964924\pi$
$678$		−	10.0000i		−	0.384048i
$679$		−	4.00000i		−	0.153506i
$680$	−3.00000	−	9.00000i	−0.115045	−	0.345134i
$681$	−12.0000	+	12.0000i	−0.459841	+	0.459841i
$682$	−10.0000			−0.382920
$683$	−12.0000			−0.459167			−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000			−0.459167			−0.229584	+	0.973289i	$0.573736\pi$
$684$	−5.00000	+	5.00000i	−0.191180	+	0.191180i
$685$	32.0000	+	16.0000i	1.22266	+	0.611329i
$686$		−	20.0000i		−	0.763604i
$687$			6.00000i			0.228914i
$688$	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	−0.761863	−	0.647738i	$-0.775715\pi$
$691$	−3.00000	+	3.00000i	−0.114125	+	0.114125i	0.647738	+	0.761863i	$0.275715\pi$
$692$	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
$695$	28.0000	+	14.0000i	1.06210	+	0.531050i
$696$		0			0
$697$			14.0000i			0.530288i
$698$	9.00000	−	9.00000i	0.340655	−	0.340655i
$699$	2.00000			0.0756469
$700$	8.00000	−	6.00000i	0.302372	−	0.226779i
$701$			12.0000i			0.453234i	0.973984	+	0.226617i	$0.0727665\pi$
$701$			12.0000i			0.453234i	−0.973984	+	0.226617i	$0.927233\pi$
$702$	4.00000	+	20.0000i	0.150970	+	0.754851i
$703$		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
$707$	24.0000			0.902613
$708$		−	14.0000i		−	0.526152i
$709$	29.0000	−	29.0000i	1.08912	−	1.08912i	0.0934984	−	0.995619i	$-0.470195\pi$
$709$	29.0000	−	29.0000i	1.08912	−	1.08912i	0.995619	−	0.0934984i	$-0.0298050\pi$
$710$	1.00000	+	3.00000i	0.0375293	+	0.112588i
$711$	2.00000			0.0750059
$712$	−15.0000	+	15.0000i	−0.562149	+	0.562149i
$713$	30.0000			1.12351
$714$	−4.00000			−0.149696
$715$	11.0000	+	3.00000i	0.411377	+	0.112194i
$716$	20.0000			0.747435
$717$	6.00000			0.224074
$718$	1.00000	−	1.00000i	0.0373197	−	0.0373197i
$719$	−8.00000			−0.298350			−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000			−0.298350			−0.149175	+	0.988811i	$0.547662\pi$
$720$	2.00000	+	1.00000i	0.0745356	+	0.0372678i
$721$	14.0000	−	14.0000i	0.521387	−	0.521387i
$722$			31.0000i			1.15370i
$723$	34.0000			1.26447
$724$			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	$0.620100\pi$
$727$	−35.0000	+	35.0000i	−1.29808	+	1.29808i	−0.929660	+	0.368418i	$0.879900\pi$
$728$	−12.0000	+	18.0000i	−0.444750	+	0.667124i
$729$			29.0000i			1.07407i
$730$	10.0000	−	20.0000i	0.370117	−	0.740233i
$731$	−2.00000			−0.0739727
$732$	14.0000	−	14.0000i	0.517455	−	0.517455i
$733$			4.00000i			0.147743i	0.997268	+	0.0738717i	$0.0235355\pi$
$733$			4.00000i			0.147743i	−0.997268	+	0.0738717i	$0.976464\pi$
$734$	−1.00000	−	1.00000i	−0.0369107	−	0.0369107i
$735$	3.00000	+	9.00000i	0.110657	+	0.331970i
$736$	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	$-0.774864\pi$
$739$	−3.00000	+	3.00000i	−0.110357	+	0.110357i	0.649772	+	0.760129i	$0.274864\pi$
$740$		0			0
$741$	−30.0000	−	20.0000i	−1.10208	−	0.734718i
$742$	−10.0000	−	10.0000i	−0.367112	−	0.367112i
$743$		−	34.0000i		−	1.24734i	−0.781688	−	0.623670i	$-0.785641\pi$
$743$		−	34.0000i		−	1.24734i	0.781688	−	0.623670i	$-0.214359\pi$
$744$			30.0000i			1.09985i
$745$	9.00000	−	3.00000i	0.329734	−	0.109911i
$746$	−15.0000	+	15.0000i	−0.549189	+	0.549189i
$747$	6.00000			0.219529
$748$	2.00000			0.0731272
$749$	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	$-0.634333\pi$
$751$		−	50.0000i		−	1.82453i	0.409605	−	0.912263i	$-0.365667\pi$
$752$		−	6.00000i		−	0.218797i
$753$	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
$760$	−45.0000	+	15.0000i	−1.63232	+	0.544107i
$761$	−7.00000	−	7.00000i	−0.253750	−	0.253750i	0.568756	−	0.822506i	$-0.307425\pi$
$761$	−7.00000	−	7.00000i	−0.253750	−	0.253750i	−0.822506	+	0.568756i	$0.807425\pi$
$762$		−	18.0000i		−	0.652071i
$763$	18.0000	−	18.0000i	0.651644	−	0.651644i
$764$	−8.00000			−0.289430
$765$	−3.00000	+	1.00000i	−0.108465	+	0.0361551i
$766$			30.0000i			1.08394i
$767$	−35.0000	+	7.00000i	−1.26378	+	0.252755i
$768$	−17.0000	+	17.0000i	−0.613435	+	0.613435i
$769$	−15.0000	−	15.0000i	−0.540914	−	0.540914i	0.382883	−	0.923797i	$-0.374931\pi$
$769$	−15.0000	−	15.0000i	−0.540914	−	0.540914i	−0.923797	+	0.382883i	$0.874931\pi$
$770$	−2.00000	−	6.00000i	−0.0720750	−	0.216225i
$771$			22.0000i			0.792311i
$772$	−18.0000			−0.647834
$773$			32.0000i			1.15096i	0.817816	+	0.575480i	$0.195185\pi$
$773$			32.0000i			1.15096i	−0.817816	+	0.575480i	$0.804815\pi$
$774$	1.00000	−	1.00000i	0.0359443	−	0.0359443i
$775$	−35.0000	−	5.00000i	−1.25724	−	0.179605i
$776$	−6.00000			−0.215387
$777$		0			0
$778$	−18.0000			−0.645331
$779$	70.0000			2.50801
$780$	3.00000	−	11.0000i	0.107417	−	0.393863i
$781$	−2.00000			−0.0715656
$782$	6.00000			0.214560
$783$		0			0
$784$	−3.00000			−0.107143
$785$	−39.0000	+	13.0000i	−1.39197	+	0.463990i
$786$	−20.0000	+	20.0000i	−0.713376	+	0.713376i
$787$		−	22.0000i		−	0.784215i	−0.919919	−	0.392108i	$-0.871746\pi$
$787$		−	22.0000i		−	0.784215i	0.919919	−	0.392108i	$-0.128254\pi$
$788$	−6.00000			−0.213741
$789$		−	2.00000i		−	0.0712019i
$790$	4.00000	+	2.00000i	0.142314	+	0.0711568i
$791$	−10.0000	−	10.0000i	−0.355559	−	0.355559i
$792$	−3.00000	+	3.00000i	−0.106600	+	0.106600i
$793$	−42.0000	−	28.0000i	−1.49146	−	0.994309i
$794$			16.0000i			0.567819i
$795$	20.0000	+	10.0000i	0.709327	+	0.354663i
$796$	8.00000			0.283552
$797$	17.0000	−	17.0000i	0.602171	−	0.602171i	−0.338717	−	0.940888i	$-0.609993\pi$
$797$	17.0000	−	17.0000i	0.602171	−	0.602171i	0.940888	+	0.338717i	$0.109993\pi$
$798$			20.0000i			0.707992i
$799$	6.00000	+	6.00000i	0.212265	+	0.212265i
$800$	−15.0000	−	20.0000i	−0.530330	−	0.707107i
$801$	5.00000	+	5.00000i	0.176666	+	0.176666i
$802$	−11.0000	−	11.0000i	−0.388424	−	0.388424i
$803$	10.0000	+	10.0000i	0.352892	+	0.352892i
$804$	4.00000	−	4.00000i	0.141069	−	0.141069i
$805$	6.00000	+	18.0000i	0.211472	+	0.634417i
$806$	25.0000	−	5.00000i	0.880587	−	0.176117i
$807$	12.0000	+	12.0000i	0.422420	+	0.422420i
$808$		−	36.0000i		−	1.26648i
$809$			28.0000i			0.984428i	0.870474	+	0.492214i	$0.163812\pi$
$809$			28.0000i			0.984428i	−0.870474	+	0.492214i	$0.836188\pi$
$810$	−5.00000	+	10.0000i	−0.175682	+	0.351364i
$811$	−27.0000	+	27.0000i	−0.948098	+	0.948098i	−0.998718	−	0.0506198i	$-0.983880\pi$
$811$	−27.0000	+	27.0000i	−0.948098	+	0.948098i	0.0506198	+	0.998718i	$0.483880\pi$
$812$		0			0
$813$	−18.0000			−0.631288
$814$		0			0
$815$	−4.00000	+	8.00000i	−0.140114	+	0.280228i
$816$			2.00000i			0.0700140i
$817$			10.0000i			0.349856i
$818$	−7.00000	−	7.00000i	−0.244749	−	0.244749i
$819$	6.00000	+	4.00000i	0.209657	+	0.139771i
$820$	7.00000	+	21.0000i	0.244451	+	0.733352i
$821$	9.00000	−	9.00000i	0.314102	−	0.314102i	−0.532394	−	0.846496i	$-0.678708\pi$
$821$	9.00000	−	9.00000i	0.314102	−	0.314102i	0.846496	+	0.532394i	$0.178708\pi$
$822$	−16.0000	−	16.0000i	−0.558064	−	0.558064i
$823$	−9.00000	−	9.00000i	−0.313720	−	0.313720i	0.532629	−	0.846349i	$-0.321204\pi$
$823$	−9.00000	−	9.00000i	−0.313720	−	0.313720i	−0.846349	+	0.532629i	$0.821204\pi$
$824$	−21.0000	−	21.0000i	−0.731570	−	0.731570i
$825$	6.00000	+	8.00000i	0.208893	+	0.278524i
$826$	14.0000	+	14.0000i	0.487122	+	0.487122i
$827$		−	46.0000i		−	1.59958i	−0.600282	−	0.799788i	$-0.704945\pi$
$827$		−	46.0000i		−	1.59958i	0.600282	−	0.799788i	$-0.295055\pi$
$828$	3.00000	−	3.00000i	0.104257	−	0.104257i
$829$	34.0000			1.18087			0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000			1.18087			0.590434	+	0.807086i	$0.298956\pi$
$830$	12.0000	+	6.00000i	0.416526	+	0.208263i
$831$			30.0000i			1.04069i
$832$	21.0000	+	14.0000i	0.728044	+	0.485363i
$833$	3.00000	−	3.00000i	0.103944	−	0.103944i
$834$	−14.0000	−	14.0000i	−0.484780	−	0.484780i
$835$	36.0000	+	18.0000i	1.24583	+	0.622916i
$836$		−	10.0000i		−	0.345857i
$837$	40.0000			1.38260
$838$		−	38.0000i		−	1.31269i
$839$	−35.0000	+	35.0000i	−1.20833	+	1.20833i	−0.236768	+	0.971566i	$0.576088\pi$
$839$	−35.0000	+	35.0000i	−1.20833	+	1.20833i	−0.971566	+	0.236768i	$0.923912\pi$
$840$	−18.0000	+	6.00000i	−0.621059	+	0.207020i
$841$	29.0000			1.00000
$842$	−11.0000	+	11.0000i	−0.379085	+	0.379085i
$843$	2.00000			0.0688837
$844$	−4.00000			−0.137686
$845$	−29.0000	−	2.00000i	−0.997630	−	0.0688021i
$846$	−6.00000			−0.206284
$847$	−18.0000			−0.618487
$848$	−5.00000	+	5.00000i	−0.171701	+	0.171701i
$849$	−18.0000			−0.617758
$850$	−7.00000	−	1.00000i	−0.240098	−	0.0342997i
$851$		0			0
$852$			2.00000i			0.0685189i
$853$	26.0000			0.890223			0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000			0.890223			0.445112	+	0.895475i	$0.353164\pi$
$854$			28.0000i			0.958140i
$855$	5.00000	+	15.0000i	0.170996	+	0.512989i
$856$	−21.0000	−	21.0000i	−0.717765	−	0.717765i
$857$	−3.00000	+	3.00000i	−0.102478	+	0.102478i	−0.756487	−	0.654009i	$-0.773086\pi$
$857$	−3.00000	+	3.00000i	−0.102478	+	0.102478i	0.654009	+	0.756487i	$0.273086\pi$
$858$	−6.00000	−	4.00000i	−0.204837	−	0.136558i
$859$		−	30.0000i		−	1.02359i	−0.859109	−	0.511793i	$-0.828981\pi$
$859$		−	30.0000i		−	1.02359i	0.859109	−	0.511793i	$-0.171019\pi$
$860$	−3.00000	+	1.00000i	−0.102299	+	0.0340997i
$861$	28.0000			0.954237
$862$	13.0000	−	13.0000i	0.442782	−	0.442782i
$863$			30.0000i			1.02121i	0.859815	+	0.510606i	$0.170579\pi$
$863$			30.0000i			1.02121i	−0.859815	+	0.510606i	$0.829421\pi$
$864$	20.0000	+	20.0000i	0.680414	+	0.680414i
$865$	33.0000	−	11.0000i	1.12203	−	0.374011i
$866$	17.0000	+	17.0000i	0.577684	+	0.577684i
$867$	15.0000	+	15.0000i	0.509427	+	0.509427i
$868$	10.0000	+	10.0000i	0.339422	+	0.339422i
$869$	−2.00000	+	2.00000i	−0.0678454	+	0.0678454i
$870$		0			0
$871$	−12.0000	−	8.00000i	−0.406604	−	0.271070i
$872$	−27.0000	−	27.0000i	−0.914335	−	0.914335i
$873$			2.00000i			0.0676897i
$874$		−	30.0000i		−	1.01477i
$875$	−4.00000	−	22.0000i	−0.135225	−	0.743736i
$876$	10.0000	−	10.0000i	0.337869	−	0.337869i
$877$	38.0000			1.28317			0.641584	−	0.767052i	$-0.278277\pi$
$877$	38.0000			1.28317			0.641584	+	0.767052i	$0.278277\pi$
$878$		0			0
$879$	−6.00000	+	6.00000i	−0.202375	+	0.202375i
$880$	−3.00000	+	1.00000i	−0.101130	+	0.0337100i
$881$		−	52.0000i		−	1.75192i	−0.482380	−	0.875962i	$-0.660227\pi$
$881$		−	52.0000i		−	1.75192i	0.482380	−	0.875962i	$-0.339773\pi$
$882$			3.00000i			0.101015i
$883$	39.0000	+	39.0000i	1.31245	+	1.31245i	0.919601	+	0.392853i	$0.128512\pi$
$883$	39.0000	+	39.0000i	1.31245	+	1.31245i	0.392853	+	0.919601i	$0.371488\pi$
$884$	−5.00000	+	1.00000i	−0.168168	+	0.0336336i
$885$	−28.0000	−	14.0000i	−0.941210	−	0.470605i
$886$	25.0000	−	25.0000i	0.839891	−	0.839891i
$887$	−1.00000	−	1.00000i	−0.0335767	−	0.0335767i	0.690119	−	0.723696i	$-0.257558\pi$
$887$	−1.00000	−	1.00000i	−0.0335767	−	0.0335767i	−0.723696	+	0.690119i	$0.757558\pi$
$888$		0			0
$889$	−18.0000	−	18.0000i	−0.603701	−	0.603701i
$890$	5.00000	+	15.0000i	0.167600	+	0.502801i
$891$	−5.00000	−	5.00000i	−0.167506	−	0.167506i
$892$			2.00000i			0.0669650i
$893$	30.0000	−	30.0000i	1.00391	−	1.00391i
$894$	−6.00000			−0.200670
$895$	20.0000	−	40.0000i	0.668526	−	1.33705i
$896$			6.00000i			0.200446i
$897$	18.0000	+	12.0000i	0.601003	+	0.400668i
$898$	−3.00000	+	3.00000i	−0.100111	+	0.100111i
$899$		0			0
$900$	−4.00000	+	3.00000i	−0.133333	+	0.100000i
$901$		−	10.0000i		−	0.333148i
$902$	14.0000			0.466149
$903$			4.00000i			0.133112i
$904$	−15.0000	+	15.0000i	−0.498893	+	0.498893i
$905$	16.0000	+	8.00000i	0.531858	+	0.265929i
$906$	14.0000			0.465119
$907$	−39.0000	+	39.0000i	−1.29497	+	1.29497i	−0.363303	+	0.931671i	$0.618351\pi$
$907$	−39.0000	+	39.0000i	−1.29497	+	1.29497i	−0.931671	+	0.363303i	$0.881649\pi$
$908$	12.0000			0.398234
$909$	−12.0000			−0.398015
$910$	8.00000	+	14.0000i	0.265197	+	0.464095i
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$	10.0000			0.331133
$913$	−6.00000	+	6.00000i	−0.198571	+	0.198571i
$914$	2.00000			0.0661541
$915$	−14.0000	−	42.0000i	−0.462826	−	1.38848i
$916$	3.00000	−	3.00000i	0.0991228	−	0.0991228i
$917$			40.0000i			1.32092i
$918$	8.00000			0.264039
$919$		−	10.0000i		−	0.329870i	−0.986304	−	0.164935i	$-0.947259\pi$
$919$		−	10.0000i		−	0.329870i	0.986304	−	0.164935i	$-0.0527414\pi$
$920$	27.0000	−	9.00000i	0.890164	−	0.296721i
$921$	18.0000	+	18.0000i	0.593120	+	0.593120i
$922$	17.0000	−	17.0000i	0.559865	−	0.559865i
$923$	5.00000	−	1.00000i	0.164577	−	0.0329154i
$924$		−	4.00000i		−	0.131590i
$925$		0			0
$926$	−24.0000			−0.788689
$927$	−7.00000	+	7.00000i	−0.229910	+	0.229910i
$928$		0			0
$929$	−19.0000	−	19.0000i	−0.623370	−	0.623370i	0.323022	−	0.946392i	$-0.395301\pi$
$929$	−19.0000	−	19.0000i	−0.623370	−	0.623370i	−0.946392	+	0.323022i	$0.895301\pi$
$930$	20.0000	+	10.0000i	0.655826	+	0.327913i
$931$	−15.0000	−	15.0000i	−0.491605	−	0.491605i
$932$	−1.00000	−	1.00000i	−0.0327561	−	0.0327561i
$933$	6.00000	+	6.00000i	0.196431	+	0.196431i
$934$	9.00000	−	9.00000i	0.294489	−	0.294489i
$935$	2.00000	−	4.00000i	0.0654070	−	0.130814i
$936$	6.00000	−	9.00000i	0.196116	−	0.294174i
$937$	−7.00000	−	7.00000i	−0.228680	−	0.228680i	0.583461	−	0.812141i	$-0.301698\pi$
$937$	−7.00000	−	7.00000i	−0.228680	−	0.228680i	−0.812141	+	0.583461i	$0.801698\pi$
$938$			8.00000i			0.261209i
$939$		−	18.0000i		−	0.587408i
$940$	12.0000	+	6.00000i	0.391397	+	0.195698i
$941$	21.0000	−	21.0000i	0.684580	−	0.684580i	−0.276448	−	0.961029i	$-0.589157\pi$
$941$	21.0000	−	21.0000i	0.684580	−	0.684580i	0.961029	+	0.276448i	$0.0891575\pi$
$942$	26.0000			0.847126
$943$	−42.0000			−1.36771
$944$	7.00000	−	7.00000i	0.227831	−	0.227831i
$945$	8.00000	+	24.0000i	0.260240	+	0.780720i
$946$			2.00000i			0.0650256i
$947$			18.0000i			0.584921i	0.956278	+	0.292461i	$0.0944741\pi$
$947$			18.0000i			0.584921i	−0.956278	+	0.292461i	$0.905526\pi$
$948$	2.00000	+	2.00000i	0.0649570	+	0.0649570i
$949$	−30.0000	−	20.0000i	−0.973841	−	0.649227i
$950$	−5.00000	+	35.0000i	−0.162221	+	1.13555i
$951$	−14.0000	+	14.0000i	−0.453981	+	0.453981i
$952$	6.00000	+	6.00000i	0.194461	+	0.194461i
$953$	13.0000	+	13.0000i	0.421111	+	0.421111i	0.885586	−	0.464475i	$-0.153757\pi$
$953$	13.0000	+	13.0000i	0.421111	+	0.421111i	−0.464475	+	0.885586i	$0.653757\pi$
$954$	5.00000	+	5.00000i	0.161881	+	0.161881i
$955$	−8.00000	+	16.0000i	−0.258874	+	0.517748i
$956$	−3.00000	−	3.00000i	−0.0970269	−	0.0970269i
$957$		0			0
$958$	−7.00000	+	7.00000i	−0.226160	+	0.226160i
$959$	−32.0000			−1.03333
$960$	7.00000	+	21.0000i	0.225924	+	0.677772i
$961$		−	19.0000i		−	0.612903i
$962$		0			0
$963$	−7.00000	+	7.00000i	−0.225572	+	0.225572i
$964$	−17.0000	−	17.0000i	−0.547533	−	0.547533i
$965$	−18.0000	+	36.0000i	−0.579441	+	1.15888i
$966$		−	12.0000i		−	0.386094i
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$			27.0000i			0.867813i
$969$	−10.0000	+	10.0000i	−0.321246	+	0.321246i
$970$	−2.00000	+	4.00000i	−0.0642161	+	0.128432i
$971$	−60.0000			−1.92549			−0.962746	−	0.270408i	$-0.912841\pi$
$971$	−60.0000			−1.92549			−0.962746	+	0.270408i	$0.912841\pi$
$972$	7.00000	−	7.00000i	0.224525	−	0.224525i
$973$	−28.0000			−0.897639
$974$	16.0000			0.512673
$975$	−19.0000	−	17.0000i	−0.608487	−	0.544436i
$976$	14.0000			0.448129
$977$	62.0000			1.98356			0.991778	−	0.127971i	$-0.0408466\pi$
$977$	62.0000			1.98356			0.991778	+	0.127971i	$0.0408466\pi$
$978$	4.00000	−	4.00000i	0.127906	−	0.127906i
$979$	−10.0000			−0.319601
$980$	3.00000	−	6.00000i	0.0958315	−	0.191663i
$981$	−9.00000	+	9.00000i	−0.287348	+	0.287348i
$982$		−	22.0000i		−	0.702048i
$983$	−24.0000			−0.765481			−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000			−0.765481			−0.382741	+	0.923856i	$0.625020\pi$
$984$		−	42.0000i		−	1.33891i
$985$	−6.00000	+	12.0000i	−0.191176	+	0.382352i
$986$		0			0
$987$	12.0000	−	12.0000i	0.381964	−	0.381964i
$988$	5.00000	+	25.0000i	0.159071	+	0.795356i
$989$		−	6.00000i		−	0.190789i
$990$	1.00000	+	3.00000i	0.0317821	+	0.0953463i
$991$		0			0			−	1.00000i	$-0.5\pi$
$991$		0			0				1.00000i	$0.5\pi$
$992$	25.0000	−	25.0000i	0.793751	−	0.793751i
$993$			6.00000i			0.190404i
$994$	−2.00000	−	2.00000i	−0.0634361	−	0.0634361i
$995$	8.00000	−	16.0000i	0.253617	−	0.507234i
$996$	6.00000	+	6.00000i	0.190117	+	0.190117i
$997$	9.00000	+	9.00000i	0.285033	+	0.285033i	0.835112	−	0.550079i	$-0.185403\pi$
$997$	9.00000	+	9.00000i	0.285033	+	0.285033i	−0.550079	+	0.835112i	$0.685403\pi$
$998$	3.00000	+	3.00000i	0.0949633	+	0.0949633i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.k.a.57.1	yes	2
3.2	odd	2		585.2.w.b.577.1		2
4.3	odd	2		1040.2.bg.a.577.1		2
5.2	odd	4		325.2.f.a.18.1		2
5.3	odd	4		65.2.f.a.18.1	✓	2
5.4	even	2		325.2.k.a.57.1		2
13.2	odd	12		845.2.t.b.657.1		4
13.3	even	3		845.2.o.a.357.1		4
13.4	even	6		845.2.o.b.587.1		4
13.5	odd	4		845.2.f.a.437.1		2
13.6	odd	12		845.2.t.b.427.1		4
13.7	odd	12		845.2.t.a.427.1		4
13.8	odd	4		65.2.f.a.47.1	yes	2
13.9	even	3		845.2.o.a.587.1		4
13.10	even	6		845.2.o.b.357.1		4
13.11	odd	12		845.2.t.a.657.1		4
13.12	even	2		845.2.k.a.577.1		2
15.8	even	4		585.2.n.c.343.1		2
20.3	even	4		1040.2.cd.b.993.1		2
39.8	even	4		585.2.n.c.307.1		2
52.47	even	4		1040.2.cd.b.177.1		2
65.3	odd	12		845.2.t.a.188.1		4
65.8	even	4	inner	65.2.k.a.8.1	yes	2
65.18	even	4		845.2.k.a.268.1		2
65.23	odd	12		845.2.t.b.188.1		4
65.28	even	12		845.2.o.b.488.1		4
65.33	even	12		845.2.o.a.258.1		4
65.34	odd	4		325.2.f.a.307.1		2
65.38	odd	4		845.2.f.a.408.1		2
65.43	odd	12		845.2.t.b.418.1		4
65.47	even	4		325.2.k.a.268.1		2
65.48	odd	12		845.2.t.a.418.1		4
65.58	even	12		845.2.o.b.258.1		4
65.63	even	12		845.2.o.a.488.1		4
195.8	odd	4		585.2.w.b.73.1		2
260.203	odd	4		1040.2.bg.a.593.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.a.18.1	✓	2	5.3	odd	4
65.2.f.a.47.1	yes	2	13.8	odd	4
65.2.k.a.8.1	yes	2	65.8	even	4	inner
65.2.k.a.57.1	yes	2	1.1	even	1	trivial
325.2.f.a.18.1		2	5.2	odd	4
325.2.f.a.307.1		2	65.34	odd	4
325.2.k.a.57.1		2	5.4	even	2
325.2.k.a.268.1		2	65.47	even	4
585.2.n.c.307.1		2	39.8	even	4
585.2.n.c.343.1		2	15.8	even	4
585.2.w.b.73.1		2	195.8	odd	4
585.2.w.b.577.1		2	3.2	odd	2
845.2.f.a.408.1		2	65.38	odd	4
845.2.f.a.437.1		2	13.5	odd	4
845.2.k.a.268.1		2	65.18	even	4
845.2.k.a.577.1		2	13.12	even	2
845.2.o.a.258.1		4	65.33	even	12
845.2.o.a.357.1		4	13.3	even	3
845.2.o.a.488.1		4	65.63	even	12
845.2.o.a.587.1		4	13.9	even	3
845.2.o.b.258.1		4	65.58	even	12
845.2.o.b.357.1		4	13.10	even	6
845.2.o.b.488.1		4	65.28	even	12
845.2.o.b.587.1		4	13.4	even	6
845.2.t.a.188.1		4	65.3	odd	12
845.2.t.a.418.1		4	65.48	odd	12
845.2.t.a.427.1		4	13.7	odd	12
845.2.t.a.657.1		4	13.11	odd	12
845.2.t.b.188.1		4	65.23	odd	12
845.2.t.b.418.1		4	65.43	odd	12
845.2.t.b.427.1		4	13.6	odd	12
845.2.t.b.657.1		4	13.2	odd	12
1040.2.bg.a.577.1		2	4.3	odd	2
1040.2.bg.a.593.1		2	260.203	odd	4
1040.2.cd.b.177.1		2	52.47	even	4
1040.2.cd.b.993.1		2	20.3	even	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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.k (of order \(4\), degree \(2\), minimal)

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

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