LMFDB - Embedded newform 80.2.s.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(3,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("80.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.s (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:	$0.638803216170$
Analytic rank:	$1$
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			3.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	80.3
Dual form			80.2.s.a.27.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} -2.00000 q^{3} +2.00000i q^{4} +(-2.00000 - 1.00000i) q^{5} +(2.00000 + 2.00000i) q^{6} +(-3.00000 + 3.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} -2.00000 q^{3} +2.00000i q^{4} +(-2.00000 - 1.00000i) q^{5} +(2.00000 + 2.00000i) q^{6} +(-3.00000 + 3.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +1.00000 q^{9} +(1.00000 + 3.00000i) q^{10} +(-1.00000 - 1.00000i) q^{11} -4.00000i q^{12} -2.00000i q^{13} +6.00000 q^{14} +(4.00000 + 2.00000i) q^{15} -4.00000 q^{16} +(1.00000 - 1.00000i) q^{17} +(-1.00000 - 1.00000i) q^{18} +(-3.00000 - 3.00000i) q^{19} +(2.00000 - 4.00000i) q^{20} +(6.00000 - 6.00000i) q^{21} +2.00000i q^{22} +(-1.00000 - 1.00000i) q^{23} +(-4.00000 + 4.00000i) q^{24} +(3.00000 + 4.00000i) q^{25} +(-2.00000 + 2.00000i) q^{26} +4.00000 q^{27} +(-6.00000 - 6.00000i) q^{28} +(-7.00000 + 7.00000i) q^{29} +(-2.00000 - 6.00000i) q^{30} +2.00000i q^{31} +(4.00000 + 4.00000i) q^{32} +(2.00000 + 2.00000i) q^{33} -2.00000 q^{34} +(9.00000 - 3.00000i) q^{35} +2.00000i q^{36} +6.00000i q^{37} +6.00000i q^{38} +4.00000i q^{39} +(-6.00000 + 2.00000i) q^{40} -4.00000i q^{41} -12.0000 q^{42} +4.00000i q^{43} +(2.00000 - 2.00000i) q^{44} +(-2.00000 - 1.00000i) q^{45} +2.00000i q^{46} +(-7.00000 - 7.00000i) q^{47} +8.00000 q^{48} -11.0000i q^{49} +(1.00000 - 7.00000i) q^{50} +(-2.00000 + 2.00000i) q^{51} +4.00000 q^{52} -8.00000 q^{53} +(-4.00000 - 4.00000i) q^{54} +(1.00000 + 3.00000i) q^{55} +12.0000i q^{56} +(6.00000 + 6.00000i) q^{57} +14.0000 q^{58} +(3.00000 - 3.00000i) q^{59} +(-4.00000 + 8.00000i) q^{60} +(-1.00000 - 1.00000i) q^{61} +(2.00000 - 2.00000i) q^{62} +(-3.00000 + 3.00000i) q^{63} -8.00000i q^{64} +(-2.00000 + 4.00000i) q^{65} -4.00000i q^{66} -4.00000i q^{67} +(2.00000 + 2.00000i) q^{68} +(2.00000 + 2.00000i) q^{69} +(-12.0000 - 6.00000i) q^{70} +(2.00000 - 2.00000i) q^{72} +(3.00000 - 3.00000i) q^{73} +(6.00000 - 6.00000i) q^{74} +(-6.00000 - 8.00000i) q^{75} +(6.00000 - 6.00000i) q^{76} +6.00000 q^{77} +(4.00000 - 4.00000i) q^{78} +8.00000 q^{79} +(8.00000 + 4.00000i) q^{80} -11.0000 q^{81} +(-4.00000 + 4.00000i) q^{82} -2.00000 q^{83} +(12.0000 + 12.0000i) q^{84} +(-3.00000 + 1.00000i) q^{85} +(4.00000 - 4.00000i) q^{86} +(14.0000 - 14.0000i) q^{87} -4.00000 q^{88} -6.00000 q^{89} +(1.00000 + 3.00000i) q^{90} +(6.00000 + 6.00000i) q^{91} +(2.00000 - 2.00000i) q^{92} -4.00000i q^{93} +14.0000i q^{94} +(3.00000 + 9.00000i) q^{95} +(-8.00000 - 8.00000i) q^{96} +(-11.0000 + 11.0000i) q^{97} +(-11.0000 + 11.0000i) q^{98} +(-1.00000 - 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{3} - 4 q^{5} + 4 q^{6} - 6 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 4 * q^3 - 4 * q^5 + 4 * q^6 - 6 * q^7 + 4 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 4 q^{3} - 4 q^{5} + 4 q^{6} - 6 q^{7} + 4 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} + 12 q^{14} + 8 q^{15} - 8 q^{16} + 2 q^{17} - 2 q^{18} - 6 q^{19} + 4 q^{20} + 12 q^{21} - 2 q^{23} - 8 q^{24} + 6 q^{25} - 4 q^{26} + 8 q^{27} - 12 q^{28} - 14 q^{29} - 4 q^{30} + 8 q^{32} + 4 q^{33} - 4 q^{34} + 18 q^{35} - 12 q^{40} - 24 q^{42} + 4 q^{44} - 4 q^{45} - 14 q^{47} + 16 q^{48} + 2 q^{50} - 4 q^{51} + 8 q^{52} - 16 q^{53} - 8 q^{54} + 2 q^{55} + 12 q^{57} + 28 q^{58} + 6 q^{59} - 8 q^{60} - 2 q^{61} + 4 q^{62} - 6 q^{63} - 4 q^{65} + 4 q^{68} + 4 q^{69} - 24 q^{70} + 4 q^{72} + 6 q^{73} + 12 q^{74} - 12 q^{75} + 12 q^{76} + 12 q^{77} + 8 q^{78} + 16 q^{79} + 16 q^{80} - 22 q^{81} - 8 q^{82} - 4 q^{83} + 24 q^{84} - 6 q^{85} + 8 q^{86} + 28 q^{87} - 8 q^{88} - 12 q^{89} + 2 q^{90} + 12 q^{91} + 4 q^{92} + 6 q^{95} - 16 q^{96} - 22 q^{97} - 22 q^{98} - 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^3 - 4 * q^5 + 4 * q^6 - 6 * q^7 + 4 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 + 12 * q^14 + 8 * q^15 - 8 * q^16 + 2 * q^17 - 2 * q^18 - 6 * q^19 + 4 * q^20 + 12 * q^21 - 2 * q^23 - 8 * q^24 + 6 * q^25 - 4 * q^26 + 8 * q^27 - 12 * q^28 - 14 * q^29 - 4 * q^30 + 8 * q^32 + 4 * q^33 - 4 * q^34 + 18 * q^35 - 12 * q^40 - 24 * q^42 + 4 * q^44 - 4 * q^45 - 14 * q^47 + 16 * q^48 + 2 * q^50 - 4 * q^51 + 8 * q^52 - 16 * q^53 - 8 * q^54 + 2 * q^55 + 12 * q^57 + 28 * q^58 + 6 * q^59 - 8 * q^60 - 2 * q^61 + 4 * q^62 - 6 * q^63 - 4 * q^65 + 4 * q^68 + 4 * q^69 - 24 * q^70 + 4 * q^72 + 6 * q^73 + 12 * q^74 - 12 * q^75 + 12 * q^76 + 12 * q^77 + 8 * q^78 + 16 * q^79 + 16 * q^80 - 22 * q^81 - 8 * q^82 - 4 * q^83 + 24 * q^84 - 6 * q^85 + 8 * q^86 + 28 * q^87 - 8 * q^88 - 12 * q^89 + 2 * q^90 + 12 * q^91 + 4 * q^92 + 6 * q^95 - 16 * q^96 - 22 * q^97 - 22 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$3$	−2.00000			−1.15470			−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000			−1.15470			−0.577350	+	0.816497i	$0.695913\pi$
$4$			2.00000i			1.00000i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$	2.00000	+	2.00000i	0.816497	+	0.816497i
$7$	−3.00000	+	3.00000i	−1.13389	+	1.13389i	−0.144370	+	0.989524i	$0.546115\pi$
$7$	−3.00000	+	3.00000i	−1.13389	+	1.13389i	−0.989524	+	0.144370i	$0.953885\pi$
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$	1.00000			0.333333
$10$	1.00000	+	3.00000i	0.316228	+	0.948683i
$11$	−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	$0.818389\pi$
$12$		−	4.00000i		−	1.15470i
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	6.00000			1.60357
$15$	4.00000	+	2.00000i	1.03280	+	0.516398i
$16$	−4.00000			−1.00000
$17$	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	$0.195139\pi$
$18$	−1.00000	−	1.00000i	−0.235702	−	0.235702i
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	0.273597	−	0.961844i	$-0.411786\pi$
$19$	−3.00000	−	3.00000i	−0.688247	−	0.688247i	−0.961844	+	0.273597i	$0.911786\pi$
$20$	2.00000	−	4.00000i	0.447214	−	0.894427i
$21$	6.00000	−	6.00000i	1.30931	−	1.30931i
$22$			2.00000i			0.426401i
$23$	−1.00000	−	1.00000i	−0.208514	−	0.208514i	0.595121	−	0.803636i	$-0.297104\pi$
$23$	−1.00000	−	1.00000i	−0.208514	−	0.208514i	−0.803636	+	0.595121i	$0.797104\pi$
$24$	−4.00000	+	4.00000i	−0.816497	+	0.816497i
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	−2.00000	+	2.00000i	−0.392232	+	0.392232i
$27$	4.00000			0.769800
$28$	−6.00000	−	6.00000i	−1.13389	−	1.13389i
$29$	−7.00000	+	7.00000i	−1.29987	+	1.29987i	−0.371391	+	0.928477i	$0.621119\pi$
$29$	−7.00000	+	7.00000i	−1.29987	+	1.29987i	−0.928477	+	0.371391i	$0.878881\pi$
$30$	−2.00000	−	6.00000i	−0.365148	−	1.09545i
$31$			2.00000i			0.359211i	0.983739	+	0.179605i	$0.0574821\pi$
$31$			2.00000i			0.359211i	−0.983739	+	0.179605i	$0.942518\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$	2.00000	+	2.00000i	0.348155	+	0.348155i
$34$	−2.00000			−0.342997
$35$	9.00000	−	3.00000i	1.52128	−	0.507093i
$36$			2.00000i			0.333333i
$37$			6.00000i			0.986394i	0.869918	+	0.493197i	$0.164172\pi$
$37$			6.00000i			0.986394i	−0.869918	+	0.493197i	$0.835828\pi$
$38$			6.00000i			0.973329i
$39$			4.00000i			0.640513i
$40$	−6.00000	+	2.00000i	−0.948683	+	0.316228i
$41$		−	4.00000i		−	0.624695i	−0.949968	−	0.312348i	$-0.898885\pi$
$41$		−	4.00000i		−	0.624695i	0.949968	−	0.312348i	$-0.101115\pi$
$42$	−12.0000			−1.85164
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	2.00000	−	2.00000i	0.301511	−	0.301511i
$45$	−2.00000	−	1.00000i	−0.298142	−	0.149071i
$46$			2.00000i			0.294884i
$47$	−7.00000	−	7.00000i	−1.02105	−	1.02105i	−0.999774	−	0.0212814i	$-0.993225\pi$
$47$	−7.00000	−	7.00000i	−1.02105	−	1.02105i	−0.0212814	−	0.999774i	$-0.506775\pi$
$48$	8.00000			1.15470
$49$		−	11.0000i		−	1.57143i
$50$	1.00000	−	7.00000i	0.141421	−	0.989949i
$51$	−2.00000	+	2.00000i	−0.280056	+	0.280056i
$52$	4.00000			0.554700
$53$	−8.00000			−1.09888			−0.549442	−	0.835532i	$-0.685160\pi$
$53$	−8.00000			−1.09888			−0.549442	+	0.835532i	$0.685160\pi$
$54$	−4.00000	−	4.00000i	−0.544331	−	0.544331i
$55$	1.00000	+	3.00000i	0.134840	+	0.404520i
$56$			12.0000i			1.60357i
$57$	6.00000	+	6.00000i	0.794719	+	0.794719i
$58$	14.0000			1.83829
$59$	3.00000	−	3.00000i	0.390567	−	0.390567i	−0.484323	−	0.874889i	$-0.660934\pi$
$59$	3.00000	−	3.00000i	0.390567	−	0.390567i	0.874889	+	0.484323i	$0.160934\pi$
$60$	−4.00000	+	8.00000i	−0.516398	+	1.03280i
$61$	−1.00000	−	1.00000i	−0.128037	−	0.128037i	0.640184	−	0.768221i	$-0.278858\pi$
$61$	−1.00000	−	1.00000i	−0.128037	−	0.128037i	−0.768221	+	0.640184i	$0.778858\pi$
$62$	2.00000	−	2.00000i	0.254000	−	0.254000i
$63$	−3.00000	+	3.00000i	−0.377964	+	0.377964i
$64$		−	8.00000i		−	1.00000i
$65$	−2.00000	+	4.00000i	−0.248069	+	0.496139i
$66$		−	4.00000i		−	0.492366i
$67$		−	4.00000i		−	0.488678i	−0.969690	−	0.244339i	$-0.921429\pi$
$67$		−	4.00000i		−	0.488678i	0.969690	−	0.244339i	$-0.0785709\pi$
$68$	2.00000	+	2.00000i	0.242536	+	0.242536i
$69$	2.00000	+	2.00000i	0.240772	+	0.240772i
$70$	−12.0000	−	6.00000i	−1.43427	−	0.717137i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	2.00000	−	2.00000i	0.235702	−	0.235702i
$73$	3.00000	−	3.00000i	0.351123	−	0.351123i	−0.509404	−	0.860527i	$-0.670134\pi$
$73$	3.00000	−	3.00000i	0.351123	−	0.351123i	0.860527	+	0.509404i	$0.170134\pi$
$74$	6.00000	−	6.00000i	0.697486	−	0.697486i
$75$	−6.00000	−	8.00000i	−0.692820	−	0.923760i
$76$	6.00000	−	6.00000i	0.688247	−	0.688247i
$77$	6.00000			0.683763
$78$	4.00000	−	4.00000i	0.452911	−	0.452911i
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	8.00000	+	4.00000i	0.894427	+	0.447214i
$81$	−11.0000			−1.22222
$82$	−4.00000	+	4.00000i	−0.441726	+	0.441726i
$83$	−2.00000			−0.219529			−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000			−0.219529			−0.109764	+	0.993958i	$0.535010\pi$
$84$	12.0000	+	12.0000i	1.30931	+	1.30931i
$85$	−3.00000	+	1.00000i	−0.325396	+	0.108465i
$86$	4.00000	−	4.00000i	0.431331	−	0.431331i
$87$	14.0000	−	14.0000i	1.50096	−	1.50096i
$88$	−4.00000			−0.426401
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$	1.00000	+	3.00000i	0.105409	+	0.316228i
$91$	6.00000	+	6.00000i	0.628971	+	0.628971i
$92$	2.00000	−	2.00000i	0.208514	−	0.208514i
$93$		−	4.00000i		−	0.414781i
$94$			14.0000i			1.44399i
$95$	3.00000	+	9.00000i	0.307794	+	0.923381i
$96$	−8.00000	−	8.00000i	−0.816497	−	0.816497i
$97$	−11.0000	+	11.0000i	−1.11688	+	1.11688i	−0.124684	+	0.992196i	$0.539792\pi$
$97$	−11.0000	+	11.0000i	−1.11688	+	1.11688i	−0.992196	+	0.124684i	$0.960208\pi$
$98$	−11.0000	+	11.0000i	−1.11117	+	1.11117i
$99$	−1.00000	−	1.00000i	−0.100504	−	0.100504i
$100$	−8.00000	+	6.00000i	−0.800000	+	0.600000i
$101$	−5.00000	+	5.00000i	−0.497519	+	0.497519i	−0.910665	−	0.413146i	$-0.864430\pi$
$101$	−5.00000	+	5.00000i	−0.497519	+	0.497519i	0.413146	+	0.910665i	$0.364430\pi$
$102$	4.00000			0.396059
$103$	−5.00000	−	5.00000i	−0.492665	−	0.492665i	0.416480	−	0.909145i	$-0.363264\pi$
$103$	−5.00000	−	5.00000i	−0.492665	−	0.492665i	−0.909145	+	0.416480i	$0.863264\pi$
$104$	−4.00000	−	4.00000i	−0.392232	−	0.392232i
$105$	−18.0000	+	6.00000i	−1.75662	+	0.585540i
$106$	8.00000	+	8.00000i	0.777029	+	0.777029i
$107$	−6.00000			−0.580042			−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000			−0.580042			−0.290021	+	0.957020i	$0.593662\pi$
$108$			8.00000i			0.769800i
$109$	5.00000	−	5.00000i	0.478913	−	0.478913i	−0.425871	−	0.904784i	$-0.640032\pi$
$109$	5.00000	−	5.00000i	0.478913	−	0.478913i	0.904784	+	0.425871i	$0.140032\pi$
$110$	2.00000	−	4.00000i	0.190693	−	0.381385i
$111$		−	12.0000i		−	1.13899i
$112$	12.0000	−	12.0000i	1.13389	−	1.13389i
$113$	13.0000	+	13.0000i	1.22294	+	1.22294i	0.966583	+	0.256354i	$0.0825214\pi$
$113$	13.0000	+	13.0000i	1.22294	+	1.22294i	0.256354	+	0.966583i	$0.417479\pi$
$114$		−	12.0000i		−	1.12390i
$115$	1.00000	+	3.00000i	0.0932505	+	0.279751i
$116$	−14.0000	−	14.0000i	−1.29987	−	1.29987i
$117$		−	2.00000i		−	0.184900i
$118$	−6.00000			−0.552345
$119$			6.00000i			0.550019i
$120$	12.0000	−	4.00000i	1.09545	−	0.365148i
$121$		−	9.00000i		−	0.818182i
$122$			2.00000i			0.181071i
$123$			8.00000i			0.721336i
$124$	−4.00000			−0.359211
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$	6.00000			0.534522
$127$	−7.00000	−	7.00000i	−0.621150	−	0.621150i	0.324676	−	0.945825i	$-0.394745\pi$
$127$	−7.00000	−	7.00000i	−0.621150	−	0.621150i	−0.945825	+	0.324676i	$0.894745\pi$
$128$	−8.00000	+	8.00000i	−0.707107	+	0.707107i
$129$		−	8.00000i		−	0.704361i
$130$	6.00000	−	2.00000i	0.526235	−	0.175412i
$131$	−7.00000	+	7.00000i	−0.611593	+	0.611593i	−0.943361	−	0.331768i	$-0.892355\pi$
$131$	−7.00000	+	7.00000i	−0.611593	+	0.611593i	0.331768	+	0.943361i	$0.392355\pi$
$132$	−4.00000	+	4.00000i	−0.348155	+	0.348155i
$133$	18.0000			1.56080
$134$	−4.00000	+	4.00000i	−0.345547	+	0.345547i
$135$	−8.00000	−	4.00000i	−0.688530	−	0.344265i
$136$		−	4.00000i		−	0.342997i
$137$	−9.00000	−	9.00000i	−0.768922	−	0.768922i	0.208995	−	0.977917i	$-0.432981\pi$
$137$	−9.00000	−	9.00000i	−0.768922	−	0.768922i	−0.977917	+	0.208995i	$0.932981\pi$
$138$		−	4.00000i		−	0.340503i
$139$	−9.00000	+	9.00000i	−0.763370	+	0.763370i	−0.976930	−	0.213560i	$-0.931494\pi$
$139$	−9.00000	+	9.00000i	−0.763370	+	0.763370i	0.213560	+	0.976930i	$0.431494\pi$
$140$	6.00000	+	18.0000i	0.507093	+	1.52128i
$141$	14.0000	+	14.0000i	1.17901	+	1.17901i
$142$		0			0
$143$	−2.00000	+	2.00000i	−0.167248	+	0.167248i
$144$	−4.00000			−0.333333
$145$	21.0000	−	7.00000i	1.74396	−	0.581318i
$146$	−6.00000			−0.496564
$147$			22.0000i			1.81453i
$148$	−12.0000			−0.986394
$149$	1.00000	+	1.00000i	0.0819232	+	0.0819232i	0.746881	−	0.664958i	$-0.231550\pi$
$149$	1.00000	+	1.00000i	0.0819232	+	0.0819232i	−0.664958	+	0.746881i	$0.731550\pi$
$150$	−2.00000	+	14.0000i	−0.163299	+	1.14310i
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	−12.0000			−0.973329
$153$	1.00000	−	1.00000i	0.0808452	−	0.0808452i
$154$	−6.00000	−	6.00000i	−0.483494	−	0.483494i
$155$	2.00000	−	4.00000i	0.160644	−	0.321288i
$156$	−8.00000			−0.640513
$157$	20.0000			1.59617			0.798087	−	0.602542i	$-0.205846\pi$
$157$	20.0000			1.59617			0.798087	+	0.602542i	$0.205846\pi$
$158$	−8.00000	−	8.00000i	−0.636446	−	0.636446i
$159$	16.0000			1.26888
$160$	−4.00000	−	12.0000i	−0.316228	−	0.948683i
$161$	6.00000			0.472866
$162$	11.0000	+	11.0000i	0.864242	+	0.864242i
$163$	14.0000			1.09656			0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000			1.09656			0.548282	+	0.836293i	$0.315282\pi$
$164$	8.00000			0.624695
$165$	−2.00000	−	6.00000i	−0.155700	−	0.467099i
$166$	2.00000	+	2.00000i	0.155230	+	0.155230i
$167$	−3.00000	+	3.00000i	−0.232147	+	0.232147i	−0.813588	−	0.581441i	$-0.802489\pi$
$167$	−3.00000	+	3.00000i	−0.232147	+	0.232147i	0.581441	+	0.813588i	$0.302489\pi$
$168$		−	24.0000i		−	1.85164i
$169$	9.00000			0.692308
$170$	4.00000	+	2.00000i	0.306786	+	0.153393i
$171$	−3.00000	−	3.00000i	−0.229416	−	0.229416i
$172$	−8.00000			−0.609994
$173$		−	6.00000i		−	0.456172i	−0.973641	−	0.228086i	$-0.926753\pi$
$173$		−	6.00000i		−	0.456172i	0.973641	−	0.228086i	$-0.0732467\pi$
$174$	−28.0000			−2.12267
$175$	−21.0000	−	3.00000i	−1.58745	−	0.226779i
$176$	4.00000	+	4.00000i	0.301511	+	0.301511i
$177$	−6.00000	+	6.00000i	−0.450988	+	0.450988i
$178$	6.00000	+	6.00000i	0.449719	+	0.449719i
$179$	5.00000	+	5.00000i	0.373718	+	0.373718i	0.868829	−	0.495112i	$-0.164873\pi$
$179$	5.00000	+	5.00000i	0.373718	+	0.373718i	−0.495112	+	0.868829i	$0.664873\pi$
$180$	2.00000	−	4.00000i	0.149071	−	0.298142i
$181$	3.00000	−	3.00000i	0.222988	−	0.222988i	−0.586767	−	0.809756i	$-0.699600\pi$
$181$	3.00000	−	3.00000i	0.222988	−	0.222988i	0.809756	+	0.586767i	$0.199600\pi$
$182$		−	12.0000i		−	0.889499i
$183$	2.00000	+	2.00000i	0.147844	+	0.147844i
$184$	−4.00000			−0.294884
$185$	6.00000	−	12.0000i	0.441129	−	0.882258i
$186$	−4.00000	+	4.00000i	−0.293294	+	0.293294i
$187$	−2.00000			−0.146254
$188$	14.0000	−	14.0000i	1.02105	−	1.02105i
$189$	−12.0000	+	12.0000i	−0.872872	+	0.872872i
$190$	6.00000	−	12.0000i	0.435286	−	0.870572i
$191$			18.0000i			1.30243i	0.758891	+	0.651217i	$0.225741\pi$
$191$			18.0000i			1.30243i	−0.758891	+	0.651217i	$0.774259\pi$
$192$			16.0000i			1.15470i
$193$	−15.0000	−	15.0000i	−1.07972	−	1.07972i	−0.996534	−	0.0831899i	$-0.973489\pi$
$193$	−15.0000	−	15.0000i	−1.07972	−	1.07972i	−0.0831899	−	0.996534i	$-0.526511\pi$
$194$	22.0000			1.57951
$195$	4.00000	−	8.00000i	0.286446	−	0.572892i
$196$	22.0000			1.57143
$197$		−	6.00000i		−	0.427482i	−0.976890	−	0.213741i	$-0.931435\pi$
$197$		−	6.00000i		−	0.427482i	0.976890	−	0.213741i	$-0.0685649\pi$
$198$			2.00000i			0.142134i
$199$		−	10.0000i		−	0.708881i	−0.935079	−	0.354441i	$-0.884671\pi$
$199$		−	10.0000i		−	0.708881i	0.935079	−	0.354441i	$-0.115329\pi$
$200$	14.0000	+	2.00000i	0.989949	+	0.141421i
$201$			8.00000i			0.564276i
$202$	10.0000			0.703598
$203$		−	42.0000i		−	2.94782i
$204$	−4.00000	−	4.00000i	−0.280056	−	0.280056i
$205$	−4.00000	+	8.00000i	−0.279372	+	0.558744i
$206$			10.0000i			0.696733i
$207$	−1.00000	−	1.00000i	−0.0695048	−	0.0695048i
$208$			8.00000i			0.554700i
$209$			6.00000i			0.415029i
$210$	24.0000	+	12.0000i	1.65616	+	0.828079i
$211$	−19.0000	+	19.0000i	−1.30801	+	1.30801i	−0.385167	+	0.922847i	$0.625856\pi$
$211$	−19.0000	+	19.0000i	−1.30801	+	1.30801i	−0.922847	+	0.385167i	$0.874144\pi$
$212$		−	16.0000i		−	1.09888i
$213$		0			0
$214$	6.00000	+	6.00000i	0.410152	+	0.410152i
$215$	4.00000	−	8.00000i	0.272798	−	0.545595i
$216$	8.00000	−	8.00000i	0.544331	−	0.544331i
$217$	−6.00000	−	6.00000i	−0.407307	−	0.407307i
$218$	−10.0000			−0.677285
$219$	−6.00000	+	6.00000i	−0.405442	+	0.405442i
$220$	−6.00000	+	2.00000i	−0.404520	+	0.134840i
$221$	−2.00000	−	2.00000i	−0.134535	−	0.134535i
$222$	−12.0000	+	12.0000i	−0.805387	+	0.805387i
$223$	−9.00000	+	9.00000i	−0.602685	+	0.602685i	−0.941024	−	0.338340i	$-0.890135\pi$
$223$	−9.00000	+	9.00000i	−0.602685	+	0.602685i	0.338340	+	0.941024i	$0.390135\pi$
$224$	−24.0000			−1.60357
$225$	3.00000	+	4.00000i	0.200000	+	0.266667i
$226$		−	26.0000i		−	1.72949i
$227$		−	12.0000i		−	0.796468i	−0.917284	−	0.398234i	$-0.869623\pi$
$227$		−	12.0000i		−	0.796468i	0.917284	−	0.398234i	$-0.130377\pi$
$228$	−12.0000	+	12.0000i	−0.794719	+	0.794719i
$229$	1.00000	+	1.00000i	0.0660819	+	0.0660819i	0.739375	−	0.673293i	$-0.235121\pi$
$229$	1.00000	+	1.00000i	0.0660819	+	0.0660819i	−0.673293	+	0.739375i	$0.735121\pi$
$230$	2.00000	−	4.00000i	0.131876	−	0.263752i
$231$	−12.0000			−0.789542
$232$			28.0000i			1.83829i
$233$	−9.00000	+	9.00000i	−0.589610	+	0.589610i	−0.937526	−	0.347916i	$-0.886889\pi$
$233$	−9.00000	+	9.00000i	−0.589610	+	0.589610i	0.347916	+	0.937526i	$0.386889\pi$
$234$	−2.00000	+	2.00000i	−0.130744	+	0.130744i
$235$	7.00000	+	21.0000i	0.456630	+	1.36989i
$236$	6.00000	+	6.00000i	0.390567	+	0.390567i
$237$	−16.0000			−1.03931
$238$	6.00000	−	6.00000i	0.388922	−	0.388922i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	−16.0000	−	8.00000i	−1.03280	−	0.516398i
$241$	−14.0000			−0.901819			−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000			−0.901819			−0.450910	+	0.892570i	$0.648900\pi$
$242$	−9.00000	+	9.00000i	−0.578542	+	0.578542i
$243$	10.0000			0.641500
$244$	2.00000	−	2.00000i	0.128037	−	0.128037i
$245$	−11.0000	+	22.0000i	−0.702764	+	1.40553i
$246$	8.00000	−	8.00000i	0.510061	−	0.510061i
$247$	−6.00000	+	6.00000i	−0.381771	+	0.381771i
$248$	4.00000	+	4.00000i	0.254000	+	0.254000i
$249$	4.00000			0.253490
$250$	−9.00000	+	13.0000i	−0.569210	+	0.822192i
$251$	11.0000	+	11.0000i	0.694314	+	0.694314i	0.963178	−	0.268864i	$-0.0866483\pi$
$251$	11.0000	+	11.0000i	0.694314	+	0.694314i	−0.268864	+	0.963178i	$0.586648\pi$
$252$	−6.00000	−	6.00000i	−0.377964	−	0.377964i
$253$			2.00000i			0.125739i
$254$			14.0000i			0.878438i
$255$	6.00000	−	2.00000i	0.375735	−	0.125245i
$256$	16.0000			1.00000
$257$	13.0000	−	13.0000i	0.810918	−	0.810918i	−0.173854	−	0.984771i	$-0.555622\pi$
$257$	13.0000	−	13.0000i	0.810918	−	0.810918i	0.984771	+	0.173854i	$0.0556220\pi$
$258$	−8.00000	+	8.00000i	−0.498058	+	0.498058i
$259$	−18.0000	−	18.0000i	−1.11847	−	1.11847i
$260$	−8.00000	−	4.00000i	−0.496139	−	0.248069i
$261$	−7.00000	+	7.00000i	−0.433289	+	0.433289i
$262$	14.0000			0.864923
$263$	7.00000	+	7.00000i	0.431638	+	0.431638i	0.889185	−	0.457547i	$-0.151272\pi$
$263$	7.00000	+	7.00000i	0.431638	+	0.431638i	−0.457547	+	0.889185i	$0.651272\pi$
$264$	8.00000			0.492366
$265$	16.0000	+	8.00000i	0.982872	+	0.491436i
$266$	−18.0000	−	18.0000i	−1.10365	−	1.10365i
$267$	12.0000			0.734388
$268$	8.00000			0.488678
$269$	1.00000	−	1.00000i	0.0609711	−	0.0609711i	−0.675964	−	0.736935i	$-0.736272\pi$
$269$	1.00000	−	1.00000i	0.0609711	−	0.0609711i	0.736935	+	0.675964i	$0.236272\pi$
$270$	4.00000	+	12.0000i	0.243432	+	0.730297i
$271$		−	30.0000i		−	1.82237i	−0.411997	−	0.911185i	$-0.635169\pi$
$271$		−	30.0000i		−	1.82237i	0.411997	−	0.911185i	$-0.364831\pi$
$272$	−4.00000	+	4.00000i	−0.242536	+	0.242536i
$273$	−12.0000	−	12.0000i	−0.726273	−	0.726273i
$274$			18.0000i			1.08742i
$275$	1.00000	−	7.00000i	0.0603023	−	0.422116i
$276$	−4.00000	+	4.00000i	−0.240772	+	0.240772i
$277$		−	18.0000i		−	1.08152i	−0.841178	−	0.540758i	$-0.818138\pi$
$277$		−	18.0000i		−	1.08152i	0.841178	−	0.540758i	$-0.181862\pi$
$278$	18.0000			1.07957
$279$			2.00000i			0.119737i
$280$	12.0000	−	24.0000i	0.717137	−	1.43427i
$281$			16.0000i			0.954480i	0.878773	+	0.477240i	$0.158363\pi$
$281$			16.0000i			0.954480i	−0.878773	+	0.477240i	$0.841637\pi$
$282$		−	28.0000i		−	1.66738i
$283$			12.0000i			0.713326i	0.934233	+	0.356663i	$0.116086\pi$
$283$			12.0000i			0.713326i	−0.934233	+	0.356663i	$0.883914\pi$
$284$		0			0
$285$	−6.00000	−	18.0000i	−0.355409	−	1.06623i
$286$	4.00000			0.236525
$287$	12.0000	+	12.0000i	0.708338	+	0.708338i
$288$	4.00000	+	4.00000i	0.235702	+	0.235702i
$289$			15.0000i			0.882353i
$290$	−28.0000	−	14.0000i	−1.64422	−	0.822108i
$291$	22.0000	−	22.0000i	1.28966	−	1.28966i
$292$	6.00000	+	6.00000i	0.351123	+	0.351123i
$293$	−12.0000			−0.701047			−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000			−0.701047			−0.350524	+	0.936554i	$0.613996\pi$
$294$	22.0000	−	22.0000i	1.28307	−	1.28307i
$295$	−9.00000	+	3.00000i	−0.524000	+	0.174667i
$296$	12.0000	+	12.0000i	0.697486	+	0.697486i
$297$	−4.00000	−	4.00000i	−0.232104	−	0.232104i
$298$		−	2.00000i		−	0.115857i
$299$	−2.00000	+	2.00000i	−0.115663	+	0.115663i
$300$	16.0000	−	12.0000i	0.923760	−	0.692820i
$301$	−12.0000	−	12.0000i	−0.691669	−	0.691669i
$302$	−8.00000	−	8.00000i	−0.460348	−	0.460348i
$303$	10.0000	−	10.0000i	0.574485	−	0.574485i
$304$	12.0000	+	12.0000i	0.688247	+	0.688247i
$305$	1.00000	+	3.00000i	0.0572598	+	0.171780i
$306$	−2.00000			−0.114332
$307$			4.00000i			0.228292i	0.993464	+	0.114146i	$0.0364132\pi$
$307$			4.00000i			0.228292i	−0.993464	+	0.114146i	$0.963587\pi$
$308$			12.0000i			0.683763i
$309$	10.0000	+	10.0000i	0.568880	+	0.568880i
$310$	−6.00000	+	2.00000i	−0.340777	+	0.113592i
$311$	16.0000			0.907277			0.453638	−	0.891186i	$-0.350126\pi$
$311$	16.0000			0.907277			0.453638	+	0.891186i	$0.350126\pi$
$312$	8.00000	+	8.00000i	0.452911	+	0.452911i
$313$	−13.0000	+	13.0000i	−0.734803	+	0.734803i	−0.971567	−	0.236764i	$-0.923913\pi$
$313$	−13.0000	+	13.0000i	−0.734803	+	0.734803i	0.236764	+	0.971567i	$0.423913\pi$
$314$	−20.0000	−	20.0000i	−1.12867	−	1.12867i
$315$	9.00000	−	3.00000i	0.507093	−	0.169031i
$316$			16.0000i			0.900070i
$317$	8.00000			0.449325			0.224662	−	0.974437i	$-0.427872\pi$
$317$	8.00000			0.449325			0.224662	+	0.974437i	$0.427872\pi$
$318$	−16.0000	−	16.0000i	−0.897235	−	0.897235i
$319$	14.0000			0.783850
$320$	−8.00000	+	16.0000i	−0.447214	+	0.894427i
$321$	12.0000			0.669775
$322$	−6.00000	−	6.00000i	−0.334367	−	0.334367i
$323$	−6.00000			−0.333849
$324$		−	22.0000i		−	1.22222i
$325$	8.00000	−	6.00000i	0.443760	−	0.332820i
$326$	−14.0000	−	14.0000i	−0.775388	−	0.775388i
$327$	−10.0000	+	10.0000i	−0.553001	+	0.553001i
$328$	−8.00000	−	8.00000i	−0.441726	−	0.441726i
$329$	42.0000			2.31553
$330$	−4.00000	+	8.00000i	−0.220193	+	0.440386i
$331$	−21.0000	−	21.0000i	−1.15426	−	1.15426i	−0.985689	−	0.168576i	$-0.946083\pi$
$331$	−21.0000	−	21.0000i	−1.15426	−	1.15426i	−0.168576	−	0.985689i	$-0.553917\pi$
$332$		−	4.00000i		−	0.219529i
$333$			6.00000i			0.328798i
$334$	6.00000			0.328305
$335$	−4.00000	+	8.00000i	−0.218543	+	0.437087i
$336$	−24.0000	+	24.0000i	−1.30931	+	1.30931i
$337$	−11.0000	+	11.0000i	−0.599208	+	0.599208i	−0.940102	−	0.340894i	$-0.889270\pi$
$337$	−11.0000	+	11.0000i	−0.599208	+	0.599208i	0.340894	+	0.940102i	$0.389270\pi$
$338$	−9.00000	−	9.00000i	−0.489535	−	0.489535i
$339$	−26.0000	−	26.0000i	−1.41213	−	1.41213i
$340$	−2.00000	−	6.00000i	−0.108465	−	0.325396i
$341$	2.00000	−	2.00000i	0.108306	−	0.108306i
$342$			6.00000i			0.324443i
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	8.00000	+	8.00000i	0.431331	+	0.431331i
$345$	−2.00000	−	6.00000i	−0.107676	−	0.323029i
$346$	−6.00000	+	6.00000i	−0.322562	+	0.322562i
$347$	2.00000			0.107366			0.0536828	−	0.998558i	$-0.482904\pi$
$347$	2.00000			0.107366			0.0536828	+	0.998558i	$0.482904\pi$
$348$	28.0000	+	28.0000i	1.50096	+	1.50096i
$349$	−3.00000	+	3.00000i	−0.160586	+	0.160586i	−0.782826	−	0.622240i	$-0.786223\pi$
$349$	−3.00000	+	3.00000i	−0.160586	+	0.160586i	0.622240	+	0.782826i	$0.286223\pi$
$350$	18.0000	+	24.0000i	0.962140	+	1.28285i
$351$		−	8.00000i		−	0.427008i
$352$		−	8.00000i		−	0.426401i
$353$	13.0000	+	13.0000i	0.691920	+	0.691920i	0.962654	−	0.270734i	$-0.0872664\pi$
$353$	13.0000	+	13.0000i	0.691920	+	0.691920i	−0.270734	+	0.962654i	$0.587266\pi$
$354$	12.0000			0.637793
$355$		0			0
$356$		−	12.0000i		−	0.635999i
$357$		−	12.0000i		−	0.635107i
$358$		−	10.0000i		−	0.528516i
$359$			14.0000i			0.738892i	0.929252	+	0.369446i	$0.120452\pi$
$359$			14.0000i			0.738892i	−0.929252	+	0.369446i	$0.879548\pi$
$360$	−6.00000	+	2.00000i	−0.316228	+	0.105409i
$361$		−	1.00000i		−	0.0526316i
$362$	−6.00000			−0.315353
$363$			18.0000i			0.944755i
$364$	−12.0000	+	12.0000i	−0.628971	+	0.628971i
$365$	−9.00000	+	3.00000i	−0.471082	+	0.157027i
$366$		−	4.00000i		−	0.209083i
$367$	21.0000	+	21.0000i	1.09619	+	1.09619i	0.994852	+	0.101339i	$0.0323127\pi$
$367$	21.0000	+	21.0000i	1.09619	+	1.09619i	0.101339	+	0.994852i	$0.467687\pi$
$368$	4.00000	+	4.00000i	0.208514	+	0.208514i
$369$		−	4.00000i		−	0.208232i
$370$	−18.0000	+	6.00000i	−0.935775	+	0.311925i
$371$	24.0000	−	24.0000i	1.24602	−	1.24602i
$372$	8.00000			0.414781
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$	2.00000	+	2.00000i	0.103418	+	0.103418i
$375$	4.00000	+	22.0000i	0.206559	+	1.13608i
$376$	−28.0000			−1.44399
$377$	14.0000	+	14.0000i	0.721037	+	0.721037i
$378$	24.0000			1.23443
$379$	15.0000	−	15.0000i	0.770498	−	0.770498i	−0.207695	−	0.978194i	$-0.566596\pi$
$379$	15.0000	−	15.0000i	0.770498	−	0.770498i	0.978194	+	0.207695i	$0.0665963\pi$
$380$	−18.0000	+	6.00000i	−0.923381	+	0.307794i
$381$	14.0000	+	14.0000i	0.717242	+	0.717242i
$382$	18.0000	−	18.0000i	0.920960	−	0.920960i
$383$	−5.00000	+	5.00000i	−0.255488	+	0.255488i	−0.823216	−	0.567728i	$-0.807823\pi$
$383$	−5.00000	+	5.00000i	−0.255488	+	0.255488i	0.567728	+	0.823216i	$0.307823\pi$
$384$	16.0000	−	16.0000i	0.816497	−	0.816497i
$385$	−12.0000	−	6.00000i	−0.611577	−	0.305788i
$386$			30.0000i			1.52696i
$387$			4.00000i			0.203331i
$388$	−22.0000	−	22.0000i	−1.11688	−	1.11688i
$389$	−23.0000	−	23.0000i	−1.16615	−	1.16615i	−0.983105	−	0.183041i	$-0.941406\pi$
$389$	−23.0000	−	23.0000i	−1.16615	−	1.16615i	−0.183041	−	0.983105i	$-0.558594\pi$
$390$	−12.0000	+	4.00000i	−0.607644	+	0.202548i
$391$	−2.00000			−0.101144
$392$	−22.0000	−	22.0000i	−1.11117	−	1.11117i
$393$	14.0000	−	14.0000i	0.706207	−	0.706207i
$394$	−6.00000	+	6.00000i	−0.302276	+	0.302276i
$395$	−16.0000	−	8.00000i	−0.805047	−	0.402524i
$396$	2.00000	−	2.00000i	0.100504	−	0.100504i
$397$	−32.0000			−1.60603			−0.803017	−	0.595956i	$-0.796773\pi$
$397$	−32.0000			−1.60603			−0.803017	+	0.595956i	$0.796773\pi$
$398$	−10.0000	+	10.0000i	−0.501255	+	0.501255i
$399$	−36.0000			−1.80225
$400$	−12.0000	−	16.0000i	−0.600000	−	0.800000i
$401$	−2.00000			−0.0998752			−0.0499376	−	0.998752i	$-0.515902\pi$
$401$	−2.00000			−0.0998752			−0.0499376	+	0.998752i	$0.515902\pi$
$402$	8.00000	−	8.00000i	0.399004	−	0.399004i
$403$	4.00000			0.199254
$404$	−10.0000	−	10.0000i	−0.497519	−	0.497519i
$405$	22.0000	+	11.0000i	1.09319	+	0.546594i
$406$	−42.0000	+	42.0000i	−2.08443	+	2.08443i
$407$	6.00000	−	6.00000i	0.297409	−	0.297409i
$408$			8.00000i			0.396059i
$409$	−38.0000			−1.87898			−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−38.0000			−1.87898			−0.939490	+	0.342578i	$0.888700\pi$
$410$	12.0000	−	4.00000i	0.592638	−	0.197546i
$411$	18.0000	+	18.0000i	0.887875	+	0.887875i
$412$	10.0000	−	10.0000i	0.492665	−	0.492665i
$413$			18.0000i			0.885722i
$414$			2.00000i			0.0982946i
$415$	4.00000	+	2.00000i	0.196352	+	0.0981761i
$416$	8.00000	−	8.00000i	0.392232	−	0.392232i
$417$	18.0000	−	18.0000i	0.881464	−	0.881464i
$418$	6.00000	−	6.00000i	0.293470	−	0.293470i
$419$	17.0000	+	17.0000i	0.830504	+	0.830504i	0.987586	−	0.157081i	$-0.0502085\pi$
$419$	17.0000	+	17.0000i	0.830504	+	0.830504i	−0.157081	+	0.987586i	$0.550208\pi$
$420$	−12.0000	−	36.0000i	−0.585540	−	1.75662i
$421$	−5.00000	+	5.00000i	−0.243685	+	0.243685i	−0.818373	−	0.574688i	$-0.805124\pi$
$421$	−5.00000	+	5.00000i	−0.243685	+	0.243685i	0.574688	+	0.818373i	$0.305124\pi$
$422$	38.0000			1.84981
$423$	−7.00000	−	7.00000i	−0.340352	−	0.340352i
$424$	−16.0000	+	16.0000i	−0.777029	+	0.777029i
$425$	7.00000	+	1.00000i	0.339550	+	0.0485071i
$426$		0			0
$427$	6.00000			0.290360
$428$		−	12.0000i		−	0.580042i
$429$	4.00000	−	4.00000i	0.193122	−	0.193122i
$430$	−12.0000	+	4.00000i	−0.578691	+	0.192897i
$431$			2.00000i			0.0963366i	0.998839	+	0.0481683i	$0.0153384\pi$
$431$			2.00000i			0.0963366i	−0.998839	+	0.0481683i	$0.984662\pi$
$432$	−16.0000			−0.769800
$433$	5.00000	+	5.00000i	0.240285	+	0.240285i	0.816968	−	0.576683i	$-0.195653\pi$
$433$	5.00000	+	5.00000i	0.240285	+	0.240285i	−0.576683	+	0.816968i	$0.695653\pi$
$434$			12.0000i			0.576018i
$435$	−42.0000	+	14.0000i	−2.01375	+	0.671249i
$436$	10.0000	+	10.0000i	0.478913	+	0.478913i
$437$			6.00000i			0.287019i
$438$	12.0000			0.573382
$439$		−	26.0000i		−	1.24091i	−0.784241	−	0.620456i	$-0.786947\pi$
$439$		−	26.0000i		−	1.24091i	0.784241	−	0.620456i	$-0.213053\pi$
$440$	8.00000	+	4.00000i	0.381385	+	0.190693i
$441$		−	11.0000i		−	0.523810i
$442$			4.00000i			0.190261i
$443$		−	4.00000i		−	0.190046i	−0.995475	−	0.0950229i	$-0.969708\pi$
$443$		−	4.00000i		−	0.190046i	0.995475	−	0.0950229i	$-0.0302924\pi$
$444$	24.0000			1.13899
$445$	12.0000	+	6.00000i	0.568855	+	0.284427i
$446$	18.0000			0.852325
$447$	−2.00000	−	2.00000i	−0.0945968	−	0.0945968i
$448$	24.0000	+	24.0000i	1.13389	+	1.13389i
$449$		−	24.0000i		−	1.13263i	−0.824189	−	0.566315i	$-0.808369\pi$
$449$		−	24.0000i		−	1.13263i	0.824189	−	0.566315i	$-0.191631\pi$
$450$	1.00000	−	7.00000i	0.0471405	−	0.329983i
$451$	−4.00000	+	4.00000i	−0.188353	+	0.188353i
$452$	−26.0000	+	26.0000i	−1.22294	+	1.22294i
$453$	−16.0000			−0.751746
$454$	−12.0000	+	12.0000i	−0.563188	+	0.563188i
$455$	−6.00000	−	18.0000i	−0.281284	−	0.843853i
$456$	24.0000			1.12390
$457$	7.00000	+	7.00000i	0.327446	+	0.327446i	0.851615	−	0.524168i	$-0.175624\pi$
$457$	7.00000	+	7.00000i	0.327446	+	0.327446i	−0.524168	+	0.851615i	$0.675624\pi$
$458$		−	2.00000i		−	0.0934539i
$459$	4.00000	−	4.00000i	0.186704	−	0.186704i
$460$	−6.00000	+	2.00000i	−0.279751	+	0.0932505i
$461$	−21.0000	−	21.0000i	−0.978068	−	0.978068i	0.0216971	−	0.999765i	$-0.493093\pi$
$461$	−21.0000	−	21.0000i	−0.978068	−	0.978068i	−0.999765	+	0.0216971i	$0.993093\pi$
$462$	12.0000	+	12.0000i	0.558291	+	0.558291i
$463$	19.0000	−	19.0000i	0.883005	−	0.883005i	−0.110834	−	0.993839i	$-0.535352\pi$
$463$	19.0000	−	19.0000i	0.883005	−	0.883005i	0.993839	+	0.110834i	$0.0353522\pi$
$464$	28.0000	−	28.0000i	1.29987	−	1.29987i
$465$	−4.00000	+	8.00000i	−0.185496	+	0.370991i
$466$	18.0000			0.833834
$467$			28.0000i			1.29569i	0.761774	+	0.647843i	$0.224329\pi$
$467$			28.0000i			1.29569i	−0.761774	+	0.647843i	$0.775671\pi$
$468$	4.00000			0.184900
$469$	12.0000	+	12.0000i	0.554109	+	0.554109i
$470$	14.0000	−	28.0000i	0.645772	−	1.29154i
$471$	−40.0000			−1.84310
$472$		−	12.0000i		−	0.552345i
$473$	4.00000	−	4.00000i	0.183920	−	0.183920i
$474$	16.0000	+	16.0000i	0.734904	+	0.734904i
$475$	3.00000	−	21.0000i	0.137649	−	0.963546i
$476$	−12.0000			−0.550019
$477$	−8.00000			−0.366295
$478$		0			0
$479$	−32.0000			−1.46212			−0.731059	−	0.682315i	$-0.760973\pi$
$479$	−32.0000			−1.46212			−0.731059	+	0.682315i	$0.760973\pi$
$480$	8.00000	+	24.0000i	0.365148	+	1.09545i
$481$	12.0000			0.547153
$482$	14.0000	+	14.0000i	0.637683	+	0.637683i
$483$	−12.0000			−0.546019
$484$	18.0000			0.818182
$485$	33.0000	−	11.0000i	1.49845	−	0.499484i
$486$	−10.0000	−	10.0000i	−0.453609	−	0.453609i
$487$	−15.0000	+	15.0000i	−0.679715	+	0.679715i	−0.959936	−	0.280221i	$-0.909592\pi$
$487$	−15.0000	+	15.0000i	−0.679715	+	0.679715i	0.280221	+	0.959936i	$0.409592\pi$
$488$	−4.00000			−0.181071
$489$	−28.0000			−1.26620
$490$	33.0000	−	11.0000i	1.49079	−	0.496929i
$491$	−9.00000	−	9.00000i	−0.406164	−	0.406164i	0.474234	−	0.880399i	$-0.342725\pi$
$491$	−9.00000	−	9.00000i	−0.406164	−	0.406164i	−0.880399	+	0.474234i	$0.842725\pi$
$492$	−16.0000			−0.721336
$493$			14.0000i			0.630528i
$494$	12.0000			0.539906
$495$	1.00000	+	3.00000i	0.0449467	+	0.134840i
$496$		−	8.00000i		−	0.359211i
$497$		0			0
$498$	−4.00000	−	4.00000i	−0.179244	−	0.179244i
$499$	29.0000	+	29.0000i	1.29822	+	1.29822i	0.929568	+	0.368650i	$0.120180\pi$
$499$	29.0000	+	29.0000i	1.29822	+	1.29822i	0.368650	+	0.929568i	$0.379820\pi$
$500$	22.0000	−	4.00000i	0.983870	−	0.178885i
$501$	6.00000	−	6.00000i	0.268060	−	0.268060i
$502$		−	22.0000i		−	0.981908i
$503$	−29.0000	−	29.0000i	−1.29305	−	1.29305i	−0.932893	−	0.360153i	$-0.882725\pi$
$503$	−29.0000	−	29.0000i	−1.29305	−	1.29305i	−0.360153	−	0.932893i	$-0.617275\pi$
$504$			12.0000i			0.534522i
$505$	15.0000	−	5.00000i	0.667491	−	0.222497i
$506$	2.00000	−	2.00000i	0.0889108	−	0.0889108i
$507$	−18.0000			−0.799408
$508$	14.0000	−	14.0000i	0.621150	−	0.621150i
$509$	17.0000	−	17.0000i	0.753512	−	0.753512i	−0.221621	−	0.975133i	$-0.571135\pi$
$509$	17.0000	−	17.0000i	0.753512	−	0.753512i	0.975133	+	0.221621i	$0.0711348\pi$
$510$	−8.00000	−	4.00000i	−0.354246	−	0.177123i
$511$			18.0000i			0.796273i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$	−12.0000	−	12.0000i	−0.529813	−	0.529813i
$514$	−26.0000			−1.14681
$515$	5.00000	+	15.0000i	0.220326	+	0.660979i
$516$	16.0000			0.704361
$517$			14.0000i			0.615719i
$518$			36.0000i			1.58175i
$519$			12.0000i			0.526742i
$520$	4.00000	+	12.0000i	0.175412	+	0.526235i
$521$		−	16.0000i		−	0.700973i	−0.936568	−	0.350486i	$-0.886016\pi$
$521$		−	16.0000i		−	0.700973i	0.936568	−	0.350486i	$-0.113984\pi$
$522$	14.0000			0.612763
$523$			20.0000i			0.874539i	0.899331	+	0.437269i	$0.144054\pi$
$523$			20.0000i			0.874539i	−0.899331	+	0.437269i	$0.855946\pi$
$524$	−14.0000	−	14.0000i	−0.611593	−	0.611593i
$525$	42.0000	+	6.00000i	1.83303	+	0.261861i
$526$		−	14.0000i		−	0.610429i
$527$	2.00000	+	2.00000i	0.0871214	+	0.0871214i
$528$	−8.00000	−	8.00000i	−0.348155	−	0.348155i
$529$		−	21.0000i		−	0.913043i
$530$	−8.00000	−	24.0000i	−0.347498	−	1.04249i
$531$	3.00000	−	3.00000i	0.130189	−	0.130189i
$532$			36.0000i			1.56080i
$533$	−8.00000			−0.346518
$534$	−12.0000	−	12.0000i	−0.519291	−	0.519291i
$535$	12.0000	+	6.00000i	0.518805	+	0.259403i
$536$	−8.00000	−	8.00000i	−0.345547	−	0.345547i
$537$	−10.0000	−	10.0000i	−0.431532	−	0.431532i
$538$	−2.00000			−0.0862261
$539$	−11.0000	+	11.0000i	−0.473804	+	0.473804i
$540$	8.00000	−	16.0000i	0.344265	−	0.688530i
$541$	15.0000	+	15.0000i	0.644900	+	0.644900i	0.951756	−	0.306856i	$-0.0992769\pi$
$541$	15.0000	+	15.0000i	0.644900	+	0.644900i	−0.306856	+	0.951756i	$0.599277\pi$
$542$	−30.0000	+	30.0000i	−1.28861	+	1.28861i
$543$	−6.00000	+	6.00000i	−0.257485	+	0.257485i
$544$	8.00000			0.342997
$545$	−15.0000	+	5.00000i	−0.642529	+	0.214176i
$546$			24.0000i			1.02711i
$547$		−	28.0000i		−	1.19719i	−0.801050	−	0.598597i	$-0.795725\pi$
$547$		−	28.0000i		−	1.19719i	0.801050	−	0.598597i	$-0.204275\pi$
$548$	18.0000	−	18.0000i	0.768922	−	0.768922i
$549$	−1.00000	−	1.00000i	−0.0426790	−	0.0426790i
$550$	−8.00000	+	6.00000i	−0.341121	+	0.255841i
$551$	42.0000			1.78926
$552$	8.00000			0.340503
$553$	−24.0000	+	24.0000i	−1.02058	+	1.02058i
$554$	−18.0000	+	18.0000i	−0.764747	+	0.764747i
$555$	−12.0000	+	24.0000i	−0.509372	+	1.01874i
$556$	−18.0000	−	18.0000i	−0.763370	−	0.763370i
$557$	28.0000			1.18640			0.593199	−	0.805056i	$-0.297865\pi$
$557$	28.0000			1.18640			0.593199	+	0.805056i	$0.297865\pi$
$558$	2.00000	−	2.00000i	0.0846668	−	0.0846668i
$559$	8.00000			0.338364
$560$	−36.0000	+	12.0000i	−1.52128	+	0.507093i
$561$	4.00000			0.168880
$562$	16.0000	−	16.0000i	0.674919	−	0.674919i
$563$	−18.0000			−0.758610			−0.379305	−	0.925272i	$-0.623837\pi$
$563$	−18.0000			−0.758610			−0.379305	+	0.925272i	$0.623837\pi$
$564$	−28.0000	+	28.0000i	−1.17901	+	1.17901i
$565$	−13.0000	−	39.0000i	−0.546914	−	1.64074i
$566$	12.0000	−	12.0000i	0.504398	−	0.504398i
$567$	33.0000	−	33.0000i	1.38587	−	1.38587i
$568$		0			0
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$	−12.0000	+	24.0000i	−0.502625	+	1.00525i
$571$	−25.0000	−	25.0000i	−1.04622	−	1.04622i	−0.998879	−	0.0473385i	$-0.984926\pi$
$571$	−25.0000	−	25.0000i	−1.04622	−	1.04622i	−0.0473385	−	0.998879i	$-0.515074\pi$
$572$	−4.00000	−	4.00000i	−0.167248	−	0.167248i
$573$		−	36.0000i		−	1.50392i
$574$		−	24.0000i		−	1.00174i
$575$	1.00000	−	7.00000i	0.0417029	−	0.291920i
$576$		−	8.00000i		−	0.333333i
$577$	9.00000	−	9.00000i	0.374675	−	0.374675i	−0.494502	−	0.869177i	$-0.664649\pi$
$577$	9.00000	−	9.00000i	0.374675	−	0.374675i	0.869177	+	0.494502i	$0.164649\pi$
$578$	15.0000	−	15.0000i	0.623918	−	0.623918i
$579$	30.0000	+	30.0000i	1.24676	+	1.24676i
$580$	14.0000	+	42.0000i	0.581318	+	1.74396i
$581$	6.00000	−	6.00000i	0.248922	−	0.248922i
$582$	−44.0000			−1.82386
$583$	8.00000	+	8.00000i	0.331326	+	0.331326i
$584$		−	12.0000i		−	0.496564i
$585$	−2.00000	+	4.00000i	−0.0826898	+	0.165380i
$586$	12.0000	+	12.0000i	0.495715	+	0.495715i
$587$	2.00000			0.0825488			0.0412744	−	0.999148i	$-0.486858\pi$
$587$	2.00000			0.0825488			0.0412744	+	0.999148i	$0.486858\pi$
$588$	−44.0000			−1.81453
$589$	6.00000	−	6.00000i	0.247226	−	0.247226i
$590$	12.0000	+	6.00000i	0.494032	+	0.247016i
$591$			12.0000i			0.493614i
$592$		−	24.0000i		−	0.986394i
$593$	17.0000	+	17.0000i	0.698106	+	0.698106i	0.964002	−	0.265896i	$-0.0856676\pi$
$593$	17.0000	+	17.0000i	0.698106	+	0.698106i	−0.265896	+	0.964002i	$0.585668\pi$
$594$			8.00000i			0.328244i
$595$	6.00000	−	12.0000i	0.245976	−	0.491952i
$596$	−2.00000	+	2.00000i	−0.0819232	+	0.0819232i
$597$			20.0000i			0.818546i
$598$	4.00000			0.163572
$599$			30.0000i			1.22577i	0.790173	+	0.612883i	$0.209990\pi$
$599$			30.0000i			1.22577i	−0.790173	+	0.612883i	$0.790010\pi$
$600$	−28.0000	−	4.00000i	−1.14310	−	0.163299i
$601$			16.0000i			0.652654i	0.945257	+	0.326327i	$0.105811\pi$
$601$			16.0000i			0.652654i	−0.945257	+	0.326327i	$0.894189\pi$
$602$			24.0000i			0.978167i
$603$		−	4.00000i		−	0.162893i
$604$			16.0000i			0.651031i
$605$	−9.00000	+	18.0000i	−0.365902	+	0.731804i
$606$	−20.0000			−0.812444
$607$	−23.0000	−	23.0000i	−0.933541	−	0.933541i	0.0643840	−	0.997925i	$-0.479492\pi$
$607$	−23.0000	−	23.0000i	−0.933541	−	0.933541i	−0.997925	+	0.0643840i	$0.979492\pi$
$608$		−	24.0000i		−	0.973329i
$609$			84.0000i			3.40385i
$610$	2.00000	−	4.00000i	0.0809776	−	0.161955i
$611$	−14.0000	+	14.0000i	−0.566379	+	0.566379i
$612$	2.00000	+	2.00000i	0.0808452	+	0.0808452i
$613$	8.00000			0.323117			0.161558	−	0.986863i	$-0.448348\pi$
$613$	8.00000			0.323117			0.161558	+	0.986863i	$0.448348\pi$
$614$	4.00000	−	4.00000i	0.161427	−	0.161427i
$615$	8.00000	−	16.0000i	0.322591	−	0.645182i
$616$	12.0000	−	12.0000i	0.483494	−	0.483494i
$617$	−25.0000	−	25.0000i	−1.00646	−	1.00646i	−0.999979	−	0.00648312i	$-0.997936\pi$
$617$	−25.0000	−	25.0000i	−1.00646	−	1.00646i	−0.00648312	−	0.999979i	$-0.502064\pi$
$618$		−	20.0000i		−	0.804518i
$619$	7.00000	−	7.00000i	0.281354	−	0.281354i	−0.552295	−	0.833649i	$-0.686248\pi$
$619$	7.00000	−	7.00000i	0.281354	−	0.281354i	0.833649	+	0.552295i	$0.186248\pi$
$620$	8.00000	+	4.00000i	0.321288	+	0.160644i
$621$	−4.00000	−	4.00000i	−0.160514	−	0.160514i
$622$	−16.0000	−	16.0000i	−0.641542	−	0.641542i
$623$	18.0000	−	18.0000i	0.721155	−	0.721155i
$624$		−	16.0000i		−	0.640513i
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	26.0000			1.03917
$627$		−	12.0000i		−	0.479234i
$628$			40.0000i			1.59617i
$629$	6.00000	+	6.00000i	0.239236	+	0.239236i
$630$	−12.0000	−	6.00000i	−0.478091	−	0.239046i
$631$	24.0000			0.955425			0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000			0.955425			0.477712	+	0.878516i	$0.341466\pi$
$632$	16.0000	−	16.0000i	0.636446	−	0.636446i
$633$	38.0000	−	38.0000i	1.51036	−	1.51036i
$634$	−8.00000	−	8.00000i	−0.317721	−	0.317721i
$635$	7.00000	+	21.0000i	0.277787	+	0.833360i
$636$			32.0000i			1.26888i
$637$	−22.0000			−0.871672
$638$	−14.0000	−	14.0000i	−0.554265	−	0.554265i
$639$		0			0
$640$	24.0000	−	8.00000i	0.948683	−	0.316228i
$641$	−30.0000			−1.18493			−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000			−1.18493			−0.592464	+	0.805597i	$0.701845\pi$
$642$	−12.0000	−	12.0000i	−0.473602	−	0.473602i
$643$	−26.0000			−1.02534			−0.512670	−	0.858586i	$-0.671344\pi$
$643$	−26.0000			−1.02534			−0.512670	+	0.858586i	$0.671344\pi$
$644$			12.0000i			0.472866i
$645$	−8.00000	+	16.0000i	−0.315000	+	0.629999i
$646$	6.00000	+	6.00000i	0.236067	+	0.236067i
$647$	−15.0000	+	15.0000i	−0.589711	+	0.589711i	−0.937553	−	0.347842i	$-0.886914\pi$
$647$	−15.0000	+	15.0000i	−0.589711	+	0.589711i	0.347842	+	0.937553i	$0.386914\pi$
$648$	−22.0000	+	22.0000i	−0.864242	+	0.864242i
$649$	−6.00000			−0.235521
$650$	−14.0000	−	2.00000i	−0.549125	−	0.0784465i
$651$	12.0000	+	12.0000i	0.470317	+	0.470317i
$652$			28.0000i			1.09656i
$653$		−	2.00000i		−	0.0782660i	−0.999234	−	0.0391330i	$-0.987540\pi$
$653$		−	2.00000i		−	0.0782660i	0.999234	−	0.0391330i	$-0.0124596\pi$
$654$	20.0000			0.782062
$655$	21.0000	−	7.00000i	0.820538	−	0.273513i
$656$			16.0000i			0.624695i
$657$	3.00000	−	3.00000i	0.117041	−	0.117041i
$658$	−42.0000	−	42.0000i	−1.63733	−	1.63733i
$659$	−11.0000	−	11.0000i	−0.428499	−	0.428499i	0.459618	−	0.888117i	$-0.347986\pi$
$659$	−11.0000	−	11.0000i	−0.428499	−	0.428499i	−0.888117	+	0.459618i	$0.847986\pi$
$660$	12.0000	−	4.00000i	0.467099	−	0.155700i
$661$	−25.0000	+	25.0000i	−0.972387	+	0.972387i	−0.999629	−	0.0272416i	$-0.991328\pi$
$661$	−25.0000	+	25.0000i	−0.972387	+	0.972387i	0.0272416	+	0.999629i	$0.491328\pi$
$662$			42.0000i			1.63238i
$663$	4.00000	+	4.00000i	0.155347	+	0.155347i
$664$	−4.00000	+	4.00000i	−0.155230	+	0.155230i
$665$	−36.0000	−	18.0000i	−1.39602	−	0.698010i
$666$	6.00000	−	6.00000i	0.232495	−	0.232495i
$667$	14.0000			0.542082
$668$	−6.00000	−	6.00000i	−0.232147	−	0.232147i
$669$	18.0000	−	18.0000i	0.695920	−	0.695920i
$670$	12.0000	−	4.00000i	0.463600	−	0.154533i
$671$			2.00000i			0.0772091i
$672$	48.0000			1.85164
$673$	1.00000	+	1.00000i	0.0385472	+	0.0385472i	0.726118	−	0.687570i	$-0.241323\pi$
$673$	1.00000	+	1.00000i	0.0385472	+	0.0385472i	−0.687570	+	0.726118i	$0.741323\pi$
$674$	22.0000			0.847408
$675$	12.0000	+	16.0000i	0.461880	+	0.615840i
$676$			18.0000i			0.692308i
$677$			42.0000i			1.61419i	0.590421	+	0.807096i	$0.298962\pi$
$677$			42.0000i			1.61419i	−0.590421	+	0.807096i	$0.701038\pi$
$678$			52.0000i			1.99705i
$679$		−	66.0000i		−	2.53285i
$680$	−4.00000	+	8.00000i	−0.153393	+	0.306786i
$681$			24.0000i			0.919682i
$682$	−4.00000			−0.153168
$683$		−	4.00000i		−	0.153056i	−0.997067	−	0.0765279i	$-0.975617\pi$
$683$		−	4.00000i		−	0.153056i	0.997067	−	0.0765279i	$-0.0243834\pi$
$684$	6.00000	−	6.00000i	0.229416	−	0.229416i
$685$	9.00000	+	27.0000i	0.343872	+	1.03162i
$686$		−	24.0000i		−	0.916324i
$687$	−2.00000	−	2.00000i	−0.0763048	−	0.0763048i
$688$		−	16.0000i		−	0.609994i
$689$			16.0000i			0.609551i
$690$	−4.00000	+	8.00000i	−0.152277	+	0.304555i
$691$	21.0000	−	21.0000i	0.798878	−	0.798878i	−0.184041	−	0.982919i	$-0.558918\pi$
$691$	21.0000	−	21.0000i	0.798878	−	0.798878i	0.982919	+	0.184041i	$0.0589179\pi$
$692$	12.0000			0.456172
$693$	6.00000			0.227921
$694$	−2.00000	−	2.00000i	−0.0759190	−	0.0759190i
$695$	27.0000	−	9.00000i	1.02417	−	0.341389i
$696$		−	56.0000i		−	2.12267i
$697$	−4.00000	−	4.00000i	−0.151511	−	0.151511i
$698$	6.00000			0.227103
$699$	18.0000	−	18.0000i	0.680823	−	0.680823i
$700$	6.00000	−	42.0000i	0.226779	−	1.58745i
$701$	−13.0000	−	13.0000i	−0.491003	−	0.491003i	0.417619	−	0.908622i	$-0.362865\pi$
$701$	−13.0000	−	13.0000i	−0.491003	−	0.491003i	−0.908622	+	0.417619i	$0.862865\pi$
$702$	−8.00000	+	8.00000i	−0.301941	+	0.301941i
$703$	18.0000	−	18.0000i	0.678883	−	0.678883i
$704$	−8.00000	+	8.00000i	−0.301511	+	0.301511i
$705$	−14.0000	−	42.0000i	−0.527271	−	1.58181i
$706$		−	26.0000i		−	0.978523i
$707$		−	30.0000i		−	1.12827i
$708$	−12.0000	−	12.0000i	−0.450988	−	0.450988i
$709$	1.00000	+	1.00000i	0.0375558	+	0.0375558i	0.725635	−	0.688080i	$-0.241546\pi$
$709$	1.00000	+	1.00000i	0.0375558	+	0.0375558i	−0.688080	+	0.725635i	$0.741546\pi$
$710$		0			0
$711$	8.00000			0.300023
$712$	−12.0000	+	12.0000i	−0.449719	+	0.449719i
$713$	2.00000	−	2.00000i	0.0749006	−	0.0749006i
$714$	−12.0000	+	12.0000i	−0.449089	+	0.449089i
$715$	6.00000	−	2.00000i	0.224387	−	0.0747958i
$716$	−10.0000	+	10.0000i	−0.373718	+	0.373718i
$717$		0			0
$718$	14.0000	−	14.0000i	0.522475	−	0.522475i
$719$	−32.0000			−1.19340			−0.596699	−	0.802465i	$-0.703521\pi$
$719$	−32.0000			−1.19340			−0.596699	+	0.802465i	$0.703521\pi$
$720$	8.00000	+	4.00000i	0.298142	+	0.149071i
$721$	30.0000			1.11726
$722$	−1.00000	+	1.00000i	−0.0372161	+	0.0372161i
$723$	28.0000			1.04133
$724$	6.00000	+	6.00000i	0.222988	+	0.222988i
$725$	−49.0000	−	7.00000i	−1.81981	−	0.259973i
$726$	18.0000	−	18.0000i	0.668043	−	0.668043i
$727$	−7.00000	+	7.00000i	−0.259616	+	0.259616i	−0.824898	−	0.565282i	$-0.808767\pi$
$727$	−7.00000	+	7.00000i	−0.259616	+	0.259616i	0.565282	+	0.824898i	$0.308767\pi$
$728$	24.0000			0.889499
$729$	13.0000			0.481481
$730$	12.0000	+	6.00000i	0.444140	+	0.222070i
$731$	4.00000	+	4.00000i	0.147945	+	0.147945i
$732$	−4.00000	+	4.00000i	−0.147844	+	0.147844i
$733$		−	30.0000i		−	1.10808i	−0.832492	−	0.554038i	$-0.813086\pi$
$733$		−	30.0000i		−	1.10808i	0.832492	−	0.554038i	$-0.186914\pi$
$734$		−	42.0000i		−	1.55025i
$735$	22.0000	−	44.0000i	0.811482	−	1.62296i
$736$		−	8.00000i		−	0.294884i
$737$	−4.00000	+	4.00000i	−0.147342	+	0.147342i
$738$	−4.00000	+	4.00000i	−0.147242	+	0.147242i
$739$	21.0000	+	21.0000i	0.772497	+	0.772497i	0.978543	−	0.206045i	$-0.0660593\pi$
$739$	21.0000	+	21.0000i	0.772497	+	0.772497i	−0.206045	+	0.978543i	$0.566059\pi$
$740$	24.0000	+	12.0000i	0.882258	+	0.441129i
$741$	12.0000	−	12.0000i	0.440831	−	0.440831i
$742$	−48.0000			−1.76214
$743$	31.0000	+	31.0000i	1.13728	+	1.13728i	0.988936	+	0.148344i	$0.0473942\pi$
$743$	31.0000	+	31.0000i	1.13728	+	1.13728i	0.148344	+	0.988936i	$0.452606\pi$
$744$	−8.00000	−	8.00000i	−0.293294	−	0.293294i
$745$	−1.00000	−	3.00000i	−0.0366372	−	0.109911i
$746$	4.00000	+	4.00000i	0.146450	+	0.146450i
$747$	−2.00000			−0.0731762
$748$		−	4.00000i		−	0.146254i
$749$	18.0000	−	18.0000i	0.657706	−	0.657706i
$750$	18.0000	−	26.0000i	0.657267	−	0.949386i
$751$			50.0000i			1.82453i	0.409605	+	0.912263i	$0.365667\pi$
$751$			50.0000i			1.82453i	−0.409605	+	0.912263i	$0.634333\pi$
$752$	28.0000	+	28.0000i	1.02105	+	1.02105i
$753$	−22.0000	−	22.0000i	−0.801725	−	0.801725i
$754$		−	28.0000i		−	1.01970i
$755$	−16.0000	−	8.00000i	−0.582300	−	0.291150i
$756$	−24.0000	−	24.0000i	−0.872872	−	0.872872i
$757$		−	2.00000i		−	0.0726912i	−0.999339	−	0.0363456i	$-0.988428\pi$
$757$		−	2.00000i		−	0.0726912i	0.999339	−	0.0363456i	$-0.0115717\pi$
$758$	−30.0000			−1.08965
$759$		−	4.00000i		−	0.145191i
$760$	24.0000	+	12.0000i	0.870572	+	0.435286i
$761$			40.0000i			1.45000i	0.688749	+	0.724999i	$0.258160\pi$
$761$			40.0000i			1.45000i	−0.688749	+	0.724999i	$0.741840\pi$
$762$		−	28.0000i		−	1.01433i
$763$			30.0000i			1.08607i
$764$	−36.0000			−1.30243
$765$	−3.00000	+	1.00000i	−0.108465	+	0.0361551i
$766$	10.0000			0.361315
$767$	−6.00000	−	6.00000i	−0.216647	−	0.216647i
$768$	−32.0000			−1.15470
$769$		−	4.00000i		−	0.144244i	−0.997396	−	0.0721218i	$-0.977023\pi$
$769$		−	4.00000i		−	0.144244i	0.997396	−	0.0721218i	$-0.0229770\pi$
$770$	6.00000	+	18.0000i	0.216225	+	0.648675i
$771$	−26.0000	+	26.0000i	−0.936367	+	0.936367i
$772$	30.0000	−	30.0000i	1.07972	−	1.07972i
$773$	48.0000			1.72644			0.863220	−	0.504828i	$-0.168444\pi$
$773$	48.0000			1.72644			0.863220	+	0.504828i	$0.168444\pi$
$774$	4.00000	−	4.00000i	0.143777	−	0.143777i
$775$	−8.00000	+	6.00000i	−0.287368	+	0.215526i
$776$			44.0000i			1.57951i
$777$	36.0000	+	36.0000i	1.29149	+	1.29149i
$778$			46.0000i			1.64918i
$779$	−12.0000	+	12.0000i	−0.429945	+	0.429945i
$780$	16.0000	+	8.00000i	0.572892	+	0.286446i
$781$		0			0
$782$	2.00000	+	2.00000i	0.0715199	+	0.0715199i
$783$	−28.0000	+	28.0000i	−1.00064	+	1.00064i
$784$			44.0000i			1.57143i
$785$	−40.0000	−	20.0000i	−1.42766	−	0.713831i
$786$	−28.0000			−0.998727
$787$			4.00000i			0.142585i	0.997455	+	0.0712923i	$0.0227123\pi$
$787$			4.00000i			0.142585i	−0.997455	+	0.0712923i	$0.977288\pi$
$788$	12.0000			0.427482
$789$	−14.0000	−	14.0000i	−0.498413	−	0.498413i
$790$	8.00000	+	24.0000i	0.284627	+	0.853882i
$791$	−78.0000			−2.77336
$792$	−4.00000			−0.142134
$793$	−2.00000	+	2.00000i	−0.0710221	+	0.0710221i
$794$	32.0000	+	32.0000i	1.13564	+	1.13564i
$795$	−32.0000	−	16.0000i	−1.13492	−	0.567462i
$796$	20.0000			0.708881
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$	36.0000	+	36.0000i	1.27439	+	1.27439i
$799$	−14.0000			−0.495284
$800$	−4.00000	+	28.0000i	−0.141421	+	0.989949i
$801$	−6.00000			−0.212000
$802$	2.00000	+	2.00000i	0.0706225	+	0.0706225i
$803$	−6.00000			−0.211735
$804$	−16.0000			−0.564276
$805$	−12.0000	−	6.00000i	−0.422944	−	0.211472i
$806$	−4.00000	−	4.00000i	−0.140894	−	0.140894i
$807$	−2.00000	+	2.00000i	−0.0704033	+	0.0704033i
$808$			20.0000i			0.703598i
$809$	−26.0000			−0.914111			−0.457056	−	0.889438i	$-0.651096\pi$
$809$	−26.0000			−0.914111			−0.457056	+	0.889438i	$0.651096\pi$
$810$	−11.0000	−	33.0000i	−0.386501	−	1.15950i
$811$	−9.00000	−	9.00000i	−0.316033	−	0.316033i	0.531208	−	0.847241i	$-0.321738\pi$
$811$	−9.00000	−	9.00000i	−0.316033	−	0.316033i	−0.847241	+	0.531208i	$0.821738\pi$
$812$	84.0000			2.94782
$813$			60.0000i			2.10429i
$814$	−12.0000			−0.420600
$815$	−28.0000	−	14.0000i	−0.980797	−	0.490399i
$816$	8.00000	−	8.00000i	0.280056	−	0.280056i
$817$	12.0000	−	12.0000i	0.419827	−	0.419827i
$818$	38.0000	+	38.0000i	1.32864	+	1.32864i
$819$	6.00000	+	6.00000i	0.209657	+	0.209657i
$820$	−16.0000	−	8.00000i	−0.558744	−	0.279372i
$821$	15.0000	−	15.0000i	0.523504	−	0.523504i	−0.395124	−	0.918628i	$-0.629298\pi$
$821$	15.0000	−	15.0000i	0.523504	−	0.523504i	0.918628	+	0.395124i	$0.129298\pi$
$822$		−	36.0000i		−	1.25564i
$823$	−21.0000	−	21.0000i	−0.732014	−	0.732014i	0.239004	−	0.971018i	$-0.423179\pi$
$823$	−21.0000	−	21.0000i	−0.732014	−	0.732014i	−0.971018	+	0.239004i	$0.923179\pi$
$824$	−20.0000			−0.696733
$825$	−2.00000	+	14.0000i	−0.0696311	+	0.487417i
$826$	18.0000	−	18.0000i	0.626300	−	0.626300i
$827$	−54.0000			−1.87776			−0.938882	−	0.344239i	$-0.888137\pi$
$827$	−54.0000			−1.87776			−0.938882	+	0.344239i	$0.888137\pi$
$828$	2.00000	−	2.00000i	0.0695048	−	0.0695048i
$829$	−27.0000	+	27.0000i	−0.937749	+	0.937749i	−0.998173	−	0.0604240i	$-0.980755\pi$
$829$	−27.0000	+	27.0000i	−0.937749	+	0.937749i	0.0604240	+	0.998173i	$0.480755\pi$
$830$	−2.00000	−	6.00000i	−0.0694210	−	0.208263i
$831$			36.0000i			1.24883i
$832$	−16.0000			−0.554700
$833$	−11.0000	−	11.0000i	−0.381127	−	0.381127i
$834$	−36.0000			−1.24658
$835$	9.00000	−	3.00000i	0.311458	−	0.103819i
$836$	−12.0000			−0.415029
$837$			8.00000i			0.276520i
$838$		−	34.0000i		−	1.17451i
$839$		−	18.0000i		−	0.621429i	−0.950503	−	0.310715i	$-0.899432\pi$
$839$		−	18.0000i		−	0.621429i	0.950503	−	0.310715i	$-0.100568\pi$
$840$	−24.0000	+	48.0000i	−0.828079	+	1.65616i
$841$		−	69.0000i		−	2.37931i
$842$	10.0000			0.344623
$843$		−	32.0000i		−	1.10214i
$844$	−38.0000	−	38.0000i	−1.30801	−	1.30801i
$845$	−18.0000	−	9.00000i	−0.619219	−	0.309609i
$846$			14.0000i			0.481330i
$847$	27.0000	+	27.0000i	0.927731	+	0.927731i
$848$	32.0000			1.09888
$849$		−	24.0000i		−	0.823678i
$850$	−6.00000	−	8.00000i	−0.205798	−	0.274398i
$851$	6.00000	−	6.00000i	0.205677	−	0.205677i
$852$		0			0
$853$	16.0000			0.547830			0.273915	−	0.961754i	$-0.411681\pi$
$853$	16.0000			0.547830			0.273915	+	0.961754i	$0.411681\pi$
$854$	−6.00000	−	6.00000i	−0.205316	−	0.205316i
$855$	3.00000	+	9.00000i	0.102598	+	0.307794i
$856$	−12.0000	+	12.0000i	−0.410152	+	0.410152i
$857$	27.0000	+	27.0000i	0.922302	+	0.922302i	0.997192	−	0.0748894i	$-0.0238604\pi$
$857$	27.0000	+	27.0000i	0.922302	+	0.922302i	−0.0748894	+	0.997192i	$0.523860\pi$
$858$	−8.00000			−0.273115
$859$	19.0000	−	19.0000i	0.648272	−	0.648272i	−0.304303	−	0.952575i	$-0.598424\pi$
$859$	19.0000	−	19.0000i	0.648272	−	0.648272i	0.952575	+	0.304303i	$0.0984237\pi$
$860$	16.0000	+	8.00000i	0.545595	+	0.272798i
$861$	−24.0000	−	24.0000i	−0.817918	−	0.817918i
$862$	2.00000	−	2.00000i	0.0681203	−	0.0681203i
$863$	−5.00000	+	5.00000i	−0.170202	+	0.170202i	−0.787068	−	0.616866i	$-0.788402\pi$
$863$	−5.00000	+	5.00000i	−0.170202	+	0.170202i	0.616866	+	0.787068i	$0.288402\pi$
$864$	16.0000	+	16.0000i	0.544331	+	0.544331i
$865$	−6.00000	+	12.0000i	−0.204006	+	0.408012i
$866$		−	10.0000i		−	0.339814i
$867$		−	30.0000i		−	1.01885i
$868$	12.0000	−	12.0000i	0.407307	−	0.407307i
$869$	−8.00000	−	8.00000i	−0.271381	−	0.271381i
$870$	56.0000	+	28.0000i	1.89858	+	0.949289i
$871$	−8.00000			−0.271070
$872$		−	20.0000i		−	0.677285i
$873$	−11.0000	+	11.0000i	−0.372294	+	0.372294i
$874$	6.00000	−	6.00000i	0.202953	−	0.202953i
$875$	39.0000	+	27.0000i	1.31844	+	0.912767i
$876$	−12.0000	−	12.0000i	−0.405442	−	0.405442i
$877$	4.00000			0.135070			0.0675352	−	0.997717i	$-0.478487\pi$
$877$	4.00000			0.135070			0.0675352	+	0.997717i	$0.478487\pi$
$878$	−26.0000	+	26.0000i	−0.877457	+	0.877457i
$879$	24.0000			0.809500
$880$	−4.00000	−	12.0000i	−0.134840	−	0.404520i
$881$	46.0000			1.54978			0.774890	−	0.632096i	$-0.217805\pi$
$881$	46.0000			1.54978			0.774890	+	0.632096i	$0.217805\pi$
$882$	−11.0000	+	11.0000i	−0.370389	+	0.370389i
$883$	6.00000			0.201916			0.100958	−	0.994891i	$-0.467809\pi$
$883$	6.00000			0.201916			0.100958	+	0.994891i	$0.467809\pi$
$884$	4.00000	−	4.00000i	0.134535	−	0.134535i
$885$	18.0000	−	6.00000i	0.605063	−	0.201688i
$886$	−4.00000	+	4.00000i	−0.134383	+	0.134383i
$887$	−23.0000	+	23.0000i	−0.772264	+	0.772264i	−0.978502	−	0.206238i	$-0.933878\pi$
$887$	−23.0000	+	23.0000i	−0.772264	+	0.772264i	0.206238	+	0.978502i	$0.433878\pi$
$888$	−24.0000	−	24.0000i	−0.805387	−	0.805387i
$889$	42.0000			1.40863
$890$	−6.00000	−	18.0000i	−0.201120	−	0.603361i
$891$	11.0000	+	11.0000i	0.368514	+	0.368514i
$892$	−18.0000	−	18.0000i	−0.602685	−	0.602685i
$893$			42.0000i			1.40548i
$894$			4.00000i			0.133780i
$895$	−5.00000	−	15.0000i	−0.167132	−	0.501395i
$896$		−	48.0000i		−	1.60357i
$897$	4.00000	−	4.00000i	0.133556	−	0.133556i
$898$	−24.0000	+	24.0000i	−0.800890	+	0.800890i
$899$	−14.0000	−	14.0000i	−0.466926	−	0.466926i
$900$	−8.00000	+	6.00000i	−0.266667	+	0.200000i
$901$	−8.00000	+	8.00000i	−0.266519	+	0.266519i
$902$	8.00000			0.266371
$903$	24.0000	+	24.0000i	0.798670	+	0.798670i
$904$	52.0000			1.72949
$905$	−9.00000	+	3.00000i	−0.299170	+	0.0997234i
$906$	16.0000	+	16.0000i	0.531564	+	0.531564i
$907$	50.0000			1.66022			0.830111	−	0.557598i	$-0.188277\pi$
$907$	50.0000			1.66022			0.830111	+	0.557598i	$0.188277\pi$
$908$	24.0000			0.796468
$909$	−5.00000	+	5.00000i	−0.165840	+	0.165840i
$910$	−12.0000	+	24.0000i	−0.397796	+	0.795592i
$911$		−	38.0000i		−	1.25900i	−0.777002	−	0.629498i	$-0.783261\pi$
$911$		−	38.0000i		−	1.25900i	0.777002	−	0.629498i	$-0.216739\pi$
$912$	−24.0000	−	24.0000i	−0.794719	−	0.794719i
$913$	2.00000	+	2.00000i	0.0661903	+	0.0661903i
$914$		−	14.0000i		−	0.463079i
$915$	−2.00000	−	6.00000i	−0.0661180	−	0.198354i
$916$	−2.00000	+	2.00000i	−0.0660819	+	0.0660819i
$917$		−	42.0000i		−	1.38696i
$918$	−8.00000			−0.264039
$919$			46.0000i			1.51740i	0.651440	+	0.758700i	$0.274165\pi$
$919$			46.0000i			1.51740i	−0.651440	+	0.758700i	$0.725835\pi$
$920$	8.00000	+	4.00000i	0.263752	+	0.131876i
$921$		−	8.00000i		−	0.263609i
$922$			42.0000i			1.38320i
$923$		0			0
$924$		−	24.0000i		−	0.789542i
$925$	−24.0000	+	18.0000i	−0.789115	+	0.591836i
$926$	−38.0000			−1.24876
$927$	−5.00000	−	5.00000i	−0.164222	−	0.164222i
$928$	−56.0000			−1.83829
$929$			16.0000i			0.524943i	0.964940	+	0.262471i	$0.0845376\pi$
$929$			16.0000i			0.524943i	−0.964940	+	0.262471i	$0.915462\pi$
$930$	12.0000	−	4.00000i	0.393496	−	0.131165i
$931$	−33.0000	+	33.0000i	−1.08153	+	1.08153i
$932$	−18.0000	−	18.0000i	−0.589610	−	0.589610i
$933$	−32.0000			−1.04763
$934$	28.0000	−	28.0000i	0.916188	−	0.916188i
$935$	4.00000	+	2.00000i	0.130814	+	0.0654070i
$936$	−4.00000	−	4.00000i	−0.130744	−	0.130744i
$937$	3.00000	+	3.00000i	0.0980057	+	0.0980057i	0.754410	−	0.656404i	$-0.227923\pi$
$937$	3.00000	+	3.00000i	0.0980057	+	0.0980057i	−0.656404	+	0.754410i	$0.727923\pi$
$938$		−	24.0000i		−	0.783628i
$939$	26.0000	−	26.0000i	0.848478	−	0.848478i
$940$	−42.0000	+	14.0000i	−1.36989	+	0.456630i
$941$	−1.00000	−	1.00000i	−0.0325991	−	0.0325991i	0.690619	−	0.723218i	$-0.257338\pi$
$941$	−1.00000	−	1.00000i	−0.0325991	−	0.0325991i	−0.723218	+	0.690619i	$0.757338\pi$
$942$	40.0000	+	40.0000i	1.30327	+	1.30327i
$943$	−4.00000	+	4.00000i	−0.130258	+	0.130258i
$944$	−12.0000	+	12.0000i	−0.390567	+	0.390567i
$945$	36.0000	−	12.0000i	1.17108	−	0.390360i
$946$	−8.00000			−0.260102
$947$		−	28.0000i		−	0.909878i	−0.890523	−	0.454939i	$-0.849661\pi$
$947$		−	28.0000i		−	0.909878i	0.890523	−	0.454939i	$-0.150339\pi$
$948$		−	32.0000i		−	1.03931i
$949$	−6.00000	−	6.00000i	−0.194768	−	0.194768i
$950$	−24.0000	+	18.0000i	−0.778663	+	0.583997i
$951$	−16.0000			−0.518836
$952$	12.0000	+	12.0000i	0.388922	+	0.388922i
$953$	31.0000	−	31.0000i	1.00419	−	1.00419i	0.00419731	−	0.999991i	$-0.498664\pi$
$953$	31.0000	−	31.0000i	1.00419	−	1.00419i	0.999991	−	0.00419731i	$-0.00133605\pi$
$954$	8.00000	+	8.00000i	0.259010	+	0.259010i
$955$	18.0000	−	36.0000i	0.582466	−	1.16493i
$956$		0			0
$957$	−28.0000			−0.905111
$958$	32.0000	+	32.0000i	1.03387	+	1.03387i
$959$	54.0000			1.74375
$960$	16.0000	−	32.0000i	0.516398	−	1.03280i
$961$	27.0000			0.870968
$962$	−12.0000	−	12.0000i	−0.386896	−	0.386896i
$963$	−6.00000			−0.193347
$964$		−	28.0000i		−	0.901819i
$965$	15.0000	+	45.0000i	0.482867	+	1.44860i
$966$	12.0000	+	12.0000i	0.386094	+	0.386094i
$967$	33.0000	−	33.0000i	1.06121	−	1.06121i	0.0632081	−	0.998000i	$-0.479867\pi$
$967$	33.0000	−	33.0000i	1.06121	−	1.06121i	0.998000	−	0.0632081i	$-0.0201332\pi$
$968$	−18.0000	−	18.0000i	−0.578542	−	0.578542i
$969$	12.0000			0.385496
$970$	−44.0000	−	22.0000i	−1.41275	−	0.706377i
$971$	31.0000	+	31.0000i	0.994837	+	0.994837i	0.999987	−	0.00514940i	$-0.00163911\pi$
$971$	31.0000	+	31.0000i	0.994837	+	0.994837i	−0.00514940	+	0.999987i	$0.501639\pi$
$972$			20.0000i			0.641500i
$973$		−	54.0000i		−	1.73116i
$974$	30.0000			0.961262
$975$	−16.0000	+	12.0000i	−0.512410	+	0.384308i
$976$	4.00000	+	4.00000i	0.128037	+	0.128037i
$977$	17.0000	−	17.0000i	0.543878	−	0.543878i	−0.380785	−	0.924663i	$-0.624346\pi$
$977$	17.0000	−	17.0000i	0.543878	−	0.543878i	0.924663	+	0.380785i	$0.124346\pi$
$978$	28.0000	+	28.0000i	0.895341	+	0.895341i
$979$	6.00000	+	6.00000i	0.191761	+	0.191761i
$980$	−44.0000	−	22.0000i	−1.40553	−	0.702764i
$981$	5.00000	−	5.00000i	0.159638	−	0.159638i
$982$			18.0000i			0.574403i
$983$	−5.00000	−	5.00000i	−0.159475	−	0.159475i	0.622859	−	0.782334i	$-0.285971\pi$
$983$	−5.00000	−	5.00000i	−0.159475	−	0.159475i	−0.782334	+	0.622859i	$0.785971\pi$
$984$	16.0000	+	16.0000i	0.510061	+	0.510061i
$985$	−6.00000	+	12.0000i	−0.191176	+	0.382352i
$986$	14.0000	−	14.0000i	0.445851	−	0.445851i
$987$	−84.0000			−2.67375
$988$	−12.0000	−	12.0000i	−0.381771	−	0.381771i
$989$	4.00000	−	4.00000i	0.127193	−	0.127193i
$990$	2.00000	−	4.00000i	0.0635642	−	0.127128i
$991$			10.0000i			0.317660i	0.987306	+	0.158830i	$0.0507723\pi$
$991$			10.0000i			0.317660i	−0.987306	+	0.158830i	$0.949228\pi$
$992$	−8.00000	+	8.00000i	−0.254000	+	0.254000i
$993$	42.0000	+	42.0000i	1.33283	+	1.33283i
$994$		0			0
$995$	−10.0000	+	20.0000i	−0.317021	+	0.634043i
$996$			8.00000i			0.253490i
$997$		−	22.0000i		−	0.696747i	−0.937356	−	0.348373i	$-0.886734\pi$
$997$		−	22.0000i		−	0.696747i	0.937356	−	0.348373i	$-0.113266\pi$
$998$		−	58.0000i		−	1.83596i
$999$			24.0000i			0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.s.a.3.1	yes	2
3.2	odd	2		720.2.z.d.163.1		2
4.3	odd	2		320.2.s.a.303.1		2
5.2	odd	4		80.2.j.a.67.1	yes	2
5.3	odd	4		400.2.j.a.307.1		2
5.4	even	2		400.2.s.a.243.1		2
8.3	odd	2		640.2.s.a.223.1		2
8.5	even	2		640.2.s.b.223.1		2
15.2	even	4		720.2.bd.a.307.1		2
16.3	odd	4		640.2.j.a.543.1		2
16.5	even	4		320.2.j.a.143.1		2
16.11	odd	4		80.2.j.a.43.1	✓	2
16.13	even	4		640.2.j.b.543.1		2
20.3	even	4		1600.2.j.a.1007.1		2
20.7	even	4		320.2.j.a.47.1		2
20.19	odd	2		1600.2.s.a.943.1		2
40.27	even	4		640.2.j.b.607.1		2
40.37	odd	4		640.2.j.a.607.1		2
48.11	even	4		720.2.bd.a.523.1		2
80.27	even	4	inner	80.2.s.a.27.1	yes	2
80.37	odd	4		320.2.s.a.207.1		2
80.43	even	4		400.2.s.a.107.1		2
80.53	odd	4		1600.2.s.a.207.1		2
80.59	odd	4		400.2.j.a.43.1		2
80.67	even	4		640.2.s.b.287.1		2
80.69	even	4		1600.2.j.a.143.1		2
80.77	odd	4		640.2.s.a.287.1		2
240.107	odd	4		720.2.z.d.667.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.a.43.1	✓	2	16.11	odd	4
80.2.j.a.67.1	yes	2	5.2	odd	4
80.2.s.a.3.1	yes	2	1.1	even	1	trivial
80.2.s.a.27.1	yes	2	80.27	even	4	inner
320.2.j.a.47.1		2	20.7	even	4
320.2.j.a.143.1		2	16.5	even	4
320.2.s.a.207.1		2	80.37	odd	4
320.2.s.a.303.1		2	4.3	odd	2
400.2.j.a.43.1		2	80.59	odd	4
400.2.j.a.307.1		2	5.3	odd	4
400.2.s.a.107.1		2	80.43	even	4
400.2.s.a.243.1		2	5.4	even	2
640.2.j.a.543.1		2	16.3	odd	4
640.2.j.a.607.1		2	40.37	odd	4
640.2.j.b.543.1		2	16.13	even	4
640.2.j.b.607.1		2	40.27	even	4
640.2.s.a.223.1		2	8.3	odd	2
640.2.s.a.287.1		2	80.77	odd	4
640.2.s.b.223.1		2	8.5	even	2
640.2.s.b.287.1		2	80.67	even	4
720.2.z.d.163.1		2	3.2	odd	2
720.2.z.d.667.1		2	240.107	odd	4
720.2.bd.a.307.1		2	15.2	even	4
720.2.bd.a.523.1		2	48.11	even	4
1600.2.j.a.143.1		2	80.69	even	4
1600.2.j.a.1007.1		2	20.3	even	4
1600.2.s.a.207.1		2	80.53	odd	4
1600.2.s.a.943.1		2	20.19	odd	2

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} -2.00000 q^{3} +2.00000i q^{4} +(-2.00000 - 1.00000i) q^{5} +(2.00000 + 2.00000i) q^{6} +(-3.00000 + 3.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} -2.00000 q^{3} +2.00000i q^{4} +(-2.00000 - 1.00000i) q^{5} +(2.00000 + 2.00000i) q^{6} +(-3.00000 + 3.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +1.00000 q^{9} +(1.00000 + 3.00000i) q^{10} +(-1.00000 - 1.00000i) q^{11} -4.00000i q^{12} -2.00000i q^{13} +6.00000 q^{14} +(4.00000 + 2.00000i) q^{15} -4.00000 q^{16} +(1.00000 - 1.00000i) q^{17} +(-1.00000 - 1.00000i) q^{18} +(-3.00000 - 3.00000i) q^{19} +(2.00000 - 4.00000i) q^{20} +(6.00000 - 6.00000i) q^{21} +2.00000i q^{22} +(-1.00000 - 1.00000i) q^{23} +(-4.00000 + 4.00000i) q^{24} +(3.00000 + 4.00000i) q^{25} +(-2.00000 + 2.00000i) q^{26} +4.00000 q^{27} +(-6.00000 - 6.00000i) q^{28} +(-7.00000 + 7.00000i) q^{29} +(-2.00000 - 6.00000i) q^{30} +2.00000i q^{31} +(4.00000 + 4.00000i) q^{32} +(2.00000 + 2.00000i) q^{33} -2.00000 q^{34} +(9.00000 - 3.00000i) q^{35} +2.00000i q^{36} +6.00000i q^{37} +6.00000i q^{38} +4.00000i q^{39} +(-6.00000 + 2.00000i) q^{40} -4.00000i q^{41} -12.0000 q^{42} +4.00000i q^{43} +(2.00000 - 2.00000i) q^{44} +(-2.00000 - 1.00000i) q^{45} +2.00000i q^{46} +(-7.00000 - 7.00000i) q^{47} +8.00000 q^{48} -11.0000i q^{49} +(1.00000 - 7.00000i) q^{50} +(-2.00000 + 2.00000i) q^{51} +4.00000 q^{52} -8.00000 q^{53} +(-4.00000 - 4.00000i) q^{54} +(1.00000 + 3.00000i) q^{55} +12.0000i q^{56} +(6.00000 + 6.00000i) q^{57} +14.0000 q^{58} +(3.00000 - 3.00000i) q^{59} +(-4.00000 + 8.00000i) q^{60} +(-1.00000 - 1.00000i) q^{61} +(2.00000 - 2.00000i) q^{62} +(-3.00000 + 3.00000i) q^{63} -8.00000i q^{64} +(-2.00000 + 4.00000i) q^{65} -4.00000i q^{66} -4.00000i q^{67} +(2.00000 + 2.00000i) q^{68} +(2.00000 + 2.00000i) q^{69} +(-12.0000 - 6.00000i) q^{70} +(2.00000 - 2.00000i) q^{72} +(3.00000 - 3.00000i) q^{73} +(6.00000 - 6.00000i) q^{74} +(-6.00000 - 8.00000i) q^{75} +(6.00000 - 6.00000i) q^{76} +6.00000 q^{77} +(4.00000 - 4.00000i) q^{78} +8.00000 q^{79} +(8.00000 + 4.00000i) q^{80} -11.0000 q^{81} +(-4.00000 + 4.00000i) q^{82} -2.00000 q^{83} +(12.0000 + 12.0000i) q^{84} +(-3.00000 + 1.00000i) q^{85} +(4.00000 - 4.00000i) q^{86} +(14.0000 - 14.0000i) q^{87} -4.00000 q^{88} -6.00000 q^{89} +(1.00000 + 3.00000i) q^{90} +(6.00000 + 6.00000i) q^{91} +(2.00000 - 2.00000i) q^{92} -4.00000i q^{93} +14.0000i q^{94} +(3.00000 + 9.00000i) q^{95} +(-8.00000 - 8.00000i) q^{96} +(-11.0000 + 11.0000i) q^{97} +(-11.0000 + 11.0000i) q^{98} +(-1.00000 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{3} - 4 q^{5} + 4 q^{6} - 6 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 4 * q^3 - 4 * q^5 + 4 * q^6 - 6 * q^7 + 4 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 4 q^{3} - 4 q^{5} + 4 q^{6} - 6 q^{7} + 4 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} + 12 q^{14} + 8 q^{15} - 8 q^{16} + 2 q^{17} - 2 q^{18} - 6 q^{19} + 4 q^{20} + 12 q^{21} - 2 q^{23} - 8 q^{24} + 6 q^{25} - 4 q^{26} + 8 q^{27} - 12 q^{28} - 14 q^{29} - 4 q^{30} + 8 q^{32} + 4 q^{33} - 4 q^{34} + 18 q^{35} - 12 q^{40} - 24 q^{42} + 4 q^{44} - 4 q^{45} - 14 q^{47} + 16 q^{48} + 2 q^{50} - 4 q^{51} + 8 q^{52} - 16 q^{53} - 8 q^{54} + 2 q^{55} + 12 q^{57} + 28 q^{58} + 6 q^{59} - 8 q^{60} - 2 q^{61} + 4 q^{62} - 6 q^{63} - 4 q^{65} + 4 q^{68} + 4 q^{69} - 24 q^{70} + 4 q^{72} + 6 q^{73} + 12 q^{74} - 12 q^{75} + 12 q^{76} + 12 q^{77} + 8 q^{78} + 16 q^{79} + 16 q^{80} - 22 q^{81} - 8 q^{82} - 4 q^{83} + 24 q^{84} - 6 q^{85} + 8 q^{86} + 28 q^{87} - 8 q^{88} - 12 q^{89} + 2 q^{90} + 12 q^{91} + 4 q^{92} + 6 q^{95} - 16 q^{96} - 22 q^{97} - 22 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^3 - 4 * q^5 + 4 * q^6 - 6 * q^7 + 4 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 + 12 * q^14 + 8 * q^15 - 8 * q^16 + 2 * q^17 - 2 * q^18 - 6 * q^19 + 4 * q^20 + 12 * q^21 - 2 * q^23 - 8 * q^24 + 6 * q^25 - 4 * q^26 + 8 * q^27 - 12 * q^28 - 14 * q^29 - 4 * q^30 + 8 * q^32 + 4 * q^33 - 4 * q^34 + 18 * q^35 - 12 * q^40 - 24 * q^42 + 4 * q^44 - 4 * q^45 - 14 * q^47 + 16 * q^48 + 2 * q^50 - 4 * q^51 + 8 * q^52 - 16 * q^53 - 8 * q^54 + 2 * q^55 + 12 * q^57 + 28 * q^58 + 6 * q^59 - 8 * q^60 - 2 * q^61 + 4 * q^62 - 6 * q^63 - 4 * q^65 + 4 * q^68 + 4 * q^69 - 24 * q^70 + 4 * q^72 + 6 * q^73 + 12 * q^74 - 12 * q^75 + 12 * q^76 + 12 * q^77 + 8 * q^78 + 16 * q^79 + 16 * q^80 - 22 * q^81 - 8 * q^82 - 4 * q^83 + 24 * q^84 - 6 * q^85 + 8 * q^86 + 28 * q^87 - 8 * q^88 - 12 * q^89 + 2 * q^90 + 12 * q^91 + 4 * q^92 + 6 * q^95 - 16 * q^96 - 22 * q^97 - 22 * q^98 - 2 * q^99

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