LMFDB - Embedded newform 240.2.y.a.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(163,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))

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

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

chi := DirichletCharacter("240.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.y (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:	$1.91640964851$
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			163.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	240.163
Dual form			240.2.y.a.187.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} -1.00000 q^{3} -2.00000i q^{4} +(-1.00000 + 2.00000i) q^{5} +(1.00000 - 1.00000i) q^{6} +(-1.00000 + 1.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} -1.00000 q^{3} -2.00000i q^{4} +(-1.00000 + 2.00000i) q^{5} +(1.00000 - 1.00000i) q^{6} +(-1.00000 + 1.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +1.00000 q^{9} +(-1.00000 - 3.00000i) q^{10} +(-3.00000 - 3.00000i) q^{11} +2.00000i q^{12} -4.00000i q^{13} -2.00000i q^{14} +(1.00000 - 2.00000i) q^{15} -4.00000 q^{16} +(-5.00000 + 5.00000i) q^{17} +(-1.00000 + 1.00000i) q^{18} +(-5.00000 - 5.00000i) q^{19} +(4.00000 + 2.00000i) q^{20} +(1.00000 - 1.00000i) q^{21} +6.00000 q^{22} +(-1.00000 - 1.00000i) q^{23} +(-2.00000 - 2.00000i) q^{24} +(-3.00000 - 4.00000i) q^{25} +(4.00000 + 4.00000i) q^{26} -1.00000 q^{27} +(2.00000 + 2.00000i) q^{28} +(5.00000 - 5.00000i) q^{29} +(1.00000 + 3.00000i) q^{30} +2.00000i q^{31} +(4.00000 - 4.00000i) q^{32} +(3.00000 + 3.00000i) q^{33} -10.0000i q^{34} +(-1.00000 - 3.00000i) q^{35} -2.00000i q^{36} +8.00000i q^{37} +10.0000 q^{38} +4.00000i q^{39} +(-6.00000 + 2.00000i) q^{40} +8.00000i q^{41} +2.00000i q^{42} +2.00000i q^{43} +(-6.00000 + 6.00000i) q^{44} +(-1.00000 + 2.00000i) q^{45} +2.00000 q^{46} +(-5.00000 - 5.00000i) q^{47} +4.00000 q^{48} +5.00000i q^{49} +(7.00000 + 1.00000i) q^{50} +(5.00000 - 5.00000i) q^{51} -8.00000 q^{52} -6.00000 q^{53} +(1.00000 - 1.00000i) q^{54} +(9.00000 - 3.00000i) q^{55} -4.00000 q^{56} +(5.00000 + 5.00000i) q^{57} +10.0000i q^{58} +(-5.00000 + 5.00000i) q^{59} +(-4.00000 - 2.00000i) q^{60} +(-1.00000 - 1.00000i) q^{61} +(-2.00000 - 2.00000i) q^{62} +(-1.00000 + 1.00000i) q^{63} +8.00000i q^{64} +(8.00000 + 4.00000i) q^{65} -6.00000 q^{66} +2.00000i q^{67} +(10.0000 + 10.0000i) q^{68} +(1.00000 + 1.00000i) q^{69} +(4.00000 + 2.00000i) q^{70} +(2.00000 + 2.00000i) q^{72} +(5.00000 - 5.00000i) q^{73} +(-8.00000 - 8.00000i) q^{74} +(3.00000 + 4.00000i) q^{75} +(-10.0000 + 10.0000i) q^{76} +6.00000 q^{77} +(-4.00000 - 4.00000i) q^{78} +8.00000 q^{79} +(4.00000 - 8.00000i) q^{80} +1.00000 q^{81} +(-8.00000 - 8.00000i) q^{82} -12.0000 q^{83} +(-2.00000 - 2.00000i) q^{84} +(-5.00000 - 15.0000i) q^{85} +(-2.00000 - 2.00000i) q^{86} +(-5.00000 + 5.00000i) q^{87} -12.0000i q^{88} -2.00000 q^{89} +(-1.00000 - 3.00000i) q^{90} +(4.00000 + 4.00000i) q^{91} +(-2.00000 + 2.00000i) q^{92} -2.00000i q^{93} +10.0000 q^{94} +(15.0000 - 5.00000i) q^{95} +(-4.00000 + 4.00000i) q^{96} +(1.00000 - 1.00000i) q^{97} +(-5.00000 - 5.00000i) q^{98} +(-3.00000 - 3.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} + 2 q^{9} - 2 q^{10} - 6 q^{11} + 2 q^{15} - 8 q^{16} - 10 q^{17} - 2 q^{18} - 10 q^{19} + 8 q^{20} + 2 q^{21} + 12 q^{22} - 2 q^{23} - 4 q^{24} - 6 q^{25} + 8 q^{26} - 2 q^{27} + 4 q^{28} + 10 q^{29} + 2 q^{30} + 8 q^{32} + 6 q^{33} - 2 q^{35} + 20 q^{38} - 12 q^{40} - 12 q^{44} - 2 q^{45} + 4 q^{46} - 10 q^{47} + 8 q^{48} + 14 q^{50} + 10 q^{51} - 16 q^{52} - 12 q^{53} + 2 q^{54} + 18 q^{55} - 8 q^{56} + 10 q^{57} - 10 q^{59} - 8 q^{60} - 2 q^{61} - 4 q^{62} - 2 q^{63} + 16 q^{65} - 12 q^{66} + 20 q^{68} + 2 q^{69} + 8 q^{70} + 4 q^{72} + 10 q^{73} - 16 q^{74} + 6 q^{75} - 20 q^{76} + 12 q^{77} - 8 q^{78} + 16 q^{79} + 8 q^{80} + 2 q^{81} - 16 q^{82} - 24 q^{83} - 4 q^{84} - 10 q^{85} - 4 q^{86} - 10 q^{87} - 4 q^{89} - 2 q^{90} + 8 q^{91} - 4 q^{92} + 20 q^{94} + 30 q^{95} - 8 q^{96} + 2 q^{97} - 10 q^{98} - 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 + 2 * q^9 - 2 * q^10 - 6 * q^11 + 2 * q^15 - 8 * q^16 - 10 * q^17 - 2 * q^18 - 10 * q^19 + 8 * q^20 + 2 * q^21 + 12 * q^22 - 2 * q^23 - 4 * q^24 - 6 * q^25 + 8 * q^26 - 2 * q^27 + 4 * q^28 + 10 * q^29 + 2 * q^30 + 8 * q^32 + 6 * q^33 - 2 * q^35 + 20 * q^38 - 12 * q^40 - 12 * q^44 - 2 * q^45 + 4 * q^46 - 10 * q^47 + 8 * q^48 + 14 * q^50 + 10 * q^51 - 16 * q^52 - 12 * q^53 + 2 * q^54 + 18 * q^55 - 8 * q^56 + 10 * q^57 - 10 * q^59 - 8 * q^60 - 2 * q^61 - 4 * q^62 - 2 * q^63 + 16 * q^65 - 12 * q^66 + 20 * q^68 + 2 * q^69 + 8 * q^70 + 4 * q^72 + 10 * q^73 - 16 * q^74 + 6 * q^75 - 20 * q^76 + 12 * q^77 - 8 * q^78 + 16 * q^79 + 8 * q^80 + 2 * q^81 - 16 * q^82 - 24 * q^83 - 4 * q^84 - 10 * q^85 - 4 * q^86 - 10 * q^87 - 4 * q^89 - 2 * q^90 + 8 * q^91 - 4 * q^92 + 20 * q^94 + 30 * q^95 - 8 * q^96 + 2 * q^97 - 10 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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	+	1.00000i	−0.707107	+	0.707107i
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		−	2.00000i		−	1.00000i
$5$	−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
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	−0.870367	−	0.492403i	$-0.836119\pi$
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	0.492403	+	0.870367i	$0.336119\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	1.00000			0.333333
$10$	−1.00000	−	3.00000i	−0.316228	−	0.948683i
$11$	−3.00000	−	3.00000i	−0.904534	−	0.904534i	0.0912903	−	0.995824i	$-0.470901\pi$
$11$	−3.00000	−	3.00000i	−0.904534	−	0.904534i	−0.995824	+	0.0912903i	$0.970901\pi$
$12$			2.00000i			0.577350i
$13$		−	4.00000i		−	1.10940i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$		−	4.00000i		−	1.10940i	0.832050	−	0.554700i	$-0.187167\pi$
$14$		−	2.00000i		−	0.534522i
$15$	1.00000	−	2.00000i	0.258199	−	0.516398i
$16$	−4.00000			−1.00000
$17$	−5.00000	+	5.00000i	−1.21268	+	1.21268i	−0.242536	+	0.970143i	$0.577979\pi$
$17$	−5.00000	+	5.00000i	−1.21268	+	1.21268i	−0.970143	+	0.242536i	$0.922021\pi$
$18$	−1.00000	+	1.00000i	−0.235702	+	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	$-0.551135\pi$
$20$	4.00000	+	2.00000i	0.894427	+	0.447214i
$21$	1.00000	−	1.00000i	0.218218	−	0.218218i
$22$	6.00000			1.27920
$23$	−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	$0.797104\pi$
$24$	−2.00000	−	2.00000i	−0.408248	−	0.408248i
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$	4.00000	+	4.00000i	0.784465	+	0.784465i
$27$	−1.00000			−0.192450
$28$	2.00000	+	2.00000i	0.377964	+	0.377964i
$29$	5.00000	−	5.00000i	0.928477	−	0.928477i	−0.0691309	−	0.997608i	$-0.522023\pi$
$29$	5.00000	−	5.00000i	0.928477	−	0.928477i	0.997608	+	0.0691309i	$0.0220226\pi$
$30$	1.00000	+	3.00000i	0.182574	+	0.547723i
$31$			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
$33$	3.00000	+	3.00000i	0.522233	+	0.522233i
$34$		−	10.0000i		−	1.71499i
$35$	−1.00000	−	3.00000i	−0.169031	−	0.507093i
$36$		−	2.00000i		−	0.333333i
$37$			8.00000i			1.31519i	0.753371	+	0.657596i	$0.228427\pi$
$37$			8.00000i			1.31519i	−0.753371	+	0.657596i	$0.771573\pi$
$38$	10.0000			1.62221
$39$			4.00000i			0.640513i
$40$	−6.00000	+	2.00000i	−0.948683	+	0.316228i
$41$			8.00000i			1.24939i	0.780869	+	0.624695i	$0.214777\pi$
$41$			8.00000i			1.24939i	−0.780869	+	0.624695i	$0.785223\pi$
$42$			2.00000i			0.308607i
$43$			2.00000i			0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$	−6.00000	+	6.00000i	−0.904534	+	0.904534i
$45$	−1.00000	+	2.00000i	−0.149071	+	0.298142i
$46$	2.00000			0.294884
$47$	−5.00000	−	5.00000i	−0.729325	−	0.729325i	0.241160	−	0.970485i	$-0.422472\pi$
$47$	−5.00000	−	5.00000i	−0.729325	−	0.729325i	−0.970485	+	0.241160i	$0.922472\pi$
$48$	4.00000			0.577350
$49$			5.00000i			0.714286i
$50$	7.00000	+	1.00000i	0.989949	+	0.141421i
$51$	5.00000	−	5.00000i	0.700140	−	0.700140i
$52$	−8.00000			−1.10940
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$	1.00000	−	1.00000i	0.136083	−	0.136083i
$55$	9.00000	−	3.00000i	1.21356	−	0.404520i
$56$	−4.00000			−0.534522
$57$	5.00000	+	5.00000i	0.662266	+	0.662266i
$58$			10.0000i			1.31306i
$59$	−5.00000	+	5.00000i	−0.650945	+	0.650945i	−0.953220	−	0.302276i	$-0.902254\pi$
$59$	−5.00000	+	5.00000i	−0.650945	+	0.650945i	0.302276	+	0.953220i	$0.402254\pi$
$60$	−4.00000	−	2.00000i	−0.516398	−	0.258199i
$61$	−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
$63$	−1.00000	+	1.00000i	−0.125988	+	0.125988i
$64$			8.00000i			1.00000i
$65$	8.00000	+	4.00000i	0.992278	+	0.496139i
$66$	−6.00000			−0.738549
$67$			2.00000i			0.244339i	0.992509	+	0.122169i	$0.0389851\pi$
$67$			2.00000i			0.244339i	−0.992509	+	0.122169i	$0.961015\pi$
$68$	10.0000	+	10.0000i	1.21268	+	1.21268i
$69$	1.00000	+	1.00000i	0.120386	+	0.120386i
$70$	4.00000	+	2.00000i	0.478091	+	0.239046i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	2.00000	+	2.00000i	0.235702	+	0.235702i
$73$	5.00000	−	5.00000i	0.585206	−	0.585206i	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	5.00000	−	5.00000i	0.585206	−	0.585206i	0.936329	+	0.351123i	$0.114200\pi$
$74$	−8.00000	−	8.00000i	−0.929981	−	0.929981i
$75$	3.00000	+	4.00000i	0.346410	+	0.461880i
$76$	−10.0000	+	10.0000i	−1.14708	+	1.14708i
$77$	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	$0.351411\pi$
$80$	4.00000	−	8.00000i	0.447214	−	0.894427i
$81$	1.00000			0.111111
$82$	−8.00000	−	8.00000i	−0.883452	−	0.883452i
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$	−2.00000	−	2.00000i	−0.218218	−	0.218218i
$85$	−5.00000	−	15.0000i	−0.542326	−	1.62698i
$86$	−2.00000	−	2.00000i	−0.215666	−	0.215666i
$87$	−5.00000	+	5.00000i	−0.536056	+	0.536056i
$88$		−	12.0000i		−	1.27920i
$89$	−2.00000			−0.212000			−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000			−0.212000			−0.106000	+	0.994366i	$0.533804\pi$
$90$	−1.00000	−	3.00000i	−0.105409	−	0.316228i
$91$	4.00000	+	4.00000i	0.419314	+	0.419314i
$92$	−2.00000	+	2.00000i	−0.208514	+	0.208514i
$93$		−	2.00000i		−	0.207390i
$94$	10.0000			1.03142
$95$	15.0000	−	5.00000i	1.53897	−	0.512989i
$96$	−4.00000	+	4.00000i	−0.408248	+	0.408248i
$97$	1.00000	−	1.00000i	0.101535	−	0.101535i	−0.654515	−	0.756049i	$-0.727127\pi$
$97$	1.00000	−	1.00000i	0.101535	−	0.101535i	0.756049	+	0.654515i	$0.227127\pi$
$98$	−5.00000	−	5.00000i	−0.505076	−	0.505076i
$99$	−3.00000	−	3.00000i	−0.301511	−	0.301511i
$100$	−8.00000	+	6.00000i	−0.800000	+	0.600000i
$101$	1.00000	−	1.00000i	0.0995037	−	0.0995037i	−0.655602	−	0.755106i	$-0.727585\pi$
$101$	1.00000	−	1.00000i	0.0995037	−	0.0995037i	0.755106	+	0.655602i	$0.227585\pi$
$102$			10.0000i			0.990148i
$103$	5.00000	+	5.00000i	0.492665	+	0.492665i	0.909145	−	0.416480i	$-0.136736\pi$
$103$	5.00000	+	5.00000i	0.492665	+	0.492665i	−0.416480	+	0.909145i	$0.636736\pi$
$104$	8.00000	−	8.00000i	0.784465	−	0.784465i
$105$	1.00000	+	3.00000i	0.0975900	+	0.292770i
$106$	6.00000	−	6.00000i	0.582772	−	0.582772i
$107$	4.00000			0.386695			0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000			0.386695			0.193347	+	0.981130i	$0.438066\pi$
$108$			2.00000i			0.192450i
$109$	3.00000	−	3.00000i	0.287348	−	0.287348i	−0.548683	−	0.836031i	$-0.684871\pi$
$109$	3.00000	−	3.00000i	0.287348	−	0.287348i	0.836031	+	0.548683i	$0.184871\pi$
$110$	−6.00000	+	12.0000i	−0.572078	+	1.14416i
$111$		−	8.00000i		−	0.759326i
$112$	4.00000	−	4.00000i	0.377964	−	0.377964i
$113$	−9.00000	−	9.00000i	−0.846649	−	0.846649i	0.143065	−	0.989713i	$-0.454304\pi$
$113$	−9.00000	−	9.00000i	−0.846649	−	0.846649i	−0.989713	+	0.143065i	$0.954304\pi$
$114$	−10.0000			−0.936586
$115$	3.00000	−	1.00000i	0.279751	−	0.0932505i
$116$	−10.0000	−	10.0000i	−0.928477	−	0.928477i
$117$		−	4.00000i		−	0.369800i
$118$		−	10.0000i		−	0.920575i
$119$		−	10.0000i		−	0.916698i
$120$	6.00000	−	2.00000i	0.547723	−	0.182574i
$121$			7.00000i			0.636364i
$122$	2.00000			0.181071
$123$		−	8.00000i		−	0.721336i
$124$	4.00000			0.359211
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		−	2.00000i		−	0.178174i
$127$	9.00000	+	9.00000i	0.798621	+	0.798621i	0.982878	−	0.184257i	$-0.0589879\pi$
$127$	9.00000	+	9.00000i	0.798621	+	0.798621i	−0.184257	+	0.982878i	$0.558988\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$		−	2.00000i		−	0.176090i
$130$	−12.0000	+	4.00000i	−1.05247	+	0.350823i
$131$	−5.00000	+	5.00000i	−0.436852	+	0.436852i	−0.890951	−	0.454099i	$-0.849961\pi$
$131$	−5.00000	+	5.00000i	−0.436852	+	0.436852i	0.454099	+	0.890951i	$0.349961\pi$
$132$	6.00000	−	6.00000i	0.522233	−	0.522233i
$133$	10.0000			0.867110
$134$	−2.00000	−	2.00000i	−0.172774	−	0.172774i
$135$	1.00000	−	2.00000i	0.0860663	−	0.172133i
$136$	−20.0000			−1.71499
$137$	−13.0000	−	13.0000i	−1.11066	−	1.11066i	−0.993061	−	0.117604i	$-0.962479\pi$
$137$	−13.0000	−	13.0000i	−1.11066	−	1.11066i	−0.117604	−	0.993061i	$-0.537521\pi$
$138$	−2.00000			−0.170251
$139$	−11.0000	+	11.0000i	−0.933008	+	0.933008i	−0.997893	−	0.0648849i	$-0.979332\pi$
$139$	−11.0000	+	11.0000i	−0.933008	+	0.933008i	0.0648849	+	0.997893i	$0.479332\pi$
$140$	−6.00000	+	2.00000i	−0.507093	+	0.169031i
$141$	5.00000	+	5.00000i	0.421076	+	0.421076i
$142$		0			0
$143$	−12.0000	+	12.0000i	−1.00349	+	1.00349i
$144$	−4.00000			−0.333333
$145$	5.00000	+	15.0000i	0.415227	+	1.24568i
$146$			10.0000i			0.827606i
$147$		−	5.00000i		−	0.412393i
$148$	16.0000			1.31519
$149$	5.00000	+	5.00000i	0.409616	+	0.409616i	0.881605	−	0.471989i	$-0.156464\pi$
$149$	5.00000	+	5.00000i	0.409616	+	0.409616i	−0.471989	+	0.881605i	$0.656464\pi$
$150$	−7.00000	−	1.00000i	−0.571548	−	0.0816497i
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$		−	20.0000i		−	1.62221i
$153$	−5.00000	+	5.00000i	−0.404226	+	0.404226i
$154$	−6.00000	+	6.00000i	−0.483494	+	0.483494i
$155$	−4.00000	−	2.00000i	−0.321288	−	0.160644i
$156$	8.00000			0.640513
$157$	−18.0000			−1.43656			−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000			−1.43656			−0.718278	+	0.695756i	$0.755069\pi$
$158$	−8.00000	+	8.00000i	−0.636446	+	0.636446i
$159$	6.00000			0.475831
$160$	4.00000	+	12.0000i	0.316228	+	0.948683i
$161$	2.00000			0.157622
$162$	−1.00000	+	1.00000i	−0.0785674	+	0.0785674i
$163$	−12.0000			−0.939913			−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000			−0.939913			−0.469956	+	0.882690i	$0.655730\pi$
$164$	16.0000			1.24939
$165$	−9.00000	+	3.00000i	−0.700649	+	0.233550i
$166$	12.0000	−	12.0000i	0.931381	−	0.931381i
$167$	5.00000	−	5.00000i	0.386912	−	0.386912i	−0.486673	−	0.873584i	$-0.661790\pi$
$167$	5.00000	−	5.00000i	0.386912	−	0.386912i	0.873584	+	0.486673i	$0.161790\pi$
$168$	4.00000			0.308607
$169$	−3.00000			−0.230769
$170$	20.0000	+	10.0000i	1.53393	+	0.766965i
$171$	−5.00000	−	5.00000i	−0.382360	−	0.382360i
$172$	4.00000			0.304997
$173$		−	12.0000i		−	0.912343i	−0.889892	−	0.456172i	$-0.849220\pi$
$173$		−	12.0000i		−	0.912343i	0.889892	−	0.456172i	$-0.150780\pi$
$174$		−	10.0000i		−	0.758098i
$175$	7.00000	+	1.00000i	0.529150	+	0.0755929i
$176$	12.0000	+	12.0000i	0.904534	+	0.904534i
$177$	5.00000	−	5.00000i	0.375823	−	0.375823i
$178$	2.00000	−	2.00000i	0.149906	−	0.149906i
$179$	17.0000	+	17.0000i	1.27064	+	1.27064i	0.945753	+	0.324887i	$0.105326\pi$
$179$	17.0000	+	17.0000i	1.27064	+	1.27064i	0.324887	+	0.945753i	$0.394674\pi$
$180$	4.00000	+	2.00000i	0.298142	+	0.149071i
$181$	7.00000	−	7.00000i	0.520306	−	0.520306i	−0.397358	−	0.917664i	$-0.630073\pi$
$181$	7.00000	−	7.00000i	0.520306	−	0.520306i	0.917664	+	0.397358i	$0.130073\pi$
$182$	−8.00000			−0.592999
$183$	1.00000	+	1.00000i	0.0739221	+	0.0739221i
$184$		−	4.00000i		−	0.294884i
$185$	−16.0000	−	8.00000i	−1.17634	−	0.588172i
$186$	2.00000	+	2.00000i	0.146647	+	0.146647i
$187$	30.0000			2.19382
$188$	−10.0000	+	10.0000i	−0.729325	+	0.729325i
$189$	1.00000	−	1.00000i	0.0727393	−	0.0727393i
$190$	−10.0000	+	20.0000i	−0.725476	+	1.45095i
$191$		−	18.0000i		−	1.30243i	−0.758891	−	0.651217i	$-0.774259\pi$
$191$		−	18.0000i		−	1.30243i	0.758891	−	0.651217i	$-0.225741\pi$
$192$		−	8.00000i		−	0.577350i
$193$	−7.00000	−	7.00000i	−0.503871	−	0.503871i	0.408768	−	0.912639i	$-0.365959\pi$
$193$	−7.00000	−	7.00000i	−0.503871	−	0.503871i	−0.912639	+	0.408768i	$0.865959\pi$
$194$			2.00000i			0.143592i
$195$	−8.00000	−	4.00000i	−0.572892	−	0.286446i
$196$	10.0000			0.714286
$197$			8.00000i			0.569976i	0.958531	+	0.284988i	$0.0919897\pi$
$197$			8.00000i			0.569976i	−0.958531	+	0.284988i	$0.908010\pi$
$198$	6.00000			0.426401
$199$			18.0000i			1.27599i	0.770042	+	0.637993i	$0.220235\pi$
$199$			18.0000i			1.27599i	−0.770042	+	0.637993i	$0.779765\pi$
$200$	2.00000	−	14.0000i	0.141421	−	0.989949i
$201$		−	2.00000i		−	0.141069i
$202$			2.00000i			0.140720i
$203$			10.0000i			0.701862i
$204$	−10.0000	−	10.0000i	−0.700140	−	0.700140i
$205$	−16.0000	−	8.00000i	−1.11749	−	0.558744i
$206$	−10.0000			−0.696733
$207$	−1.00000	−	1.00000i	−0.0695048	−	0.0695048i
$208$			16.0000i			1.10940i
$209$			30.0000i			2.07514i
$210$	−4.00000	−	2.00000i	−0.276026	−	0.138013i
$211$	9.00000	−	9.00000i	0.619586	−	0.619586i	−0.325840	−	0.945425i	$-0.605647\pi$
$211$	9.00000	−	9.00000i	0.619586	−	0.619586i	0.945425	+	0.325840i	$0.105647\pi$
$212$			12.0000i			0.824163i
$213$		0			0
$214$	−4.00000	+	4.00000i	−0.273434	+	0.273434i
$215$	−4.00000	−	2.00000i	−0.272798	−	0.136399i
$216$	−2.00000	−	2.00000i	−0.136083	−	0.136083i
$217$	−2.00000	−	2.00000i	−0.135769	−	0.135769i
$218$			6.00000i			0.406371i
$219$	−5.00000	+	5.00000i	−0.337869	+	0.337869i
$220$	−6.00000	−	18.0000i	−0.404520	−	1.21356i
$221$	20.0000	+	20.0000i	1.34535	+	1.34535i
$222$	8.00000	+	8.00000i	0.536925	+	0.536925i
$223$	3.00000	−	3.00000i	0.200895	−	0.200895i	−0.599489	−	0.800383i	$-0.704629\pi$
$223$	3.00000	−	3.00000i	0.200895	−	0.200895i	0.800383	+	0.599489i	$0.204629\pi$
$224$			8.00000i			0.534522i
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$	18.0000			1.19734
$227$			6.00000i			0.398234i	0.979976	+	0.199117i	$0.0638074\pi$
$227$			6.00000i			0.398234i	−0.979976	+	0.199117i	$0.936193\pi$
$228$	10.0000	−	10.0000i	0.662266	−	0.662266i
$229$	−9.00000	−	9.00000i	−0.594737	−	0.594737i	0.344170	−	0.938907i	$-0.388160\pi$
$229$	−9.00000	−	9.00000i	−0.594737	−	0.594737i	−0.938907	+	0.344170i	$0.888160\pi$
$230$	−2.00000	+	4.00000i	−0.131876	+	0.263752i
$231$	−6.00000			−0.394771
$232$	20.0000			1.31306
$233$	−5.00000	+	5.00000i	−0.327561	+	0.327561i	−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−5.00000	+	5.00000i	−0.327561	+	0.327561i	0.524097	+	0.851658i	$0.324403\pi$
$234$	4.00000	+	4.00000i	0.261488	+	0.261488i
$235$	15.0000	−	5.00000i	0.978492	−	0.326164i
$236$	10.0000	+	10.0000i	0.650945	+	0.650945i
$237$	−8.00000			−0.519656
$238$	10.0000	+	10.0000i	0.648204	+	0.648204i
$239$	8.00000			0.517477			0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000			0.517477			0.258738	+	0.965947i	$0.416693\pi$
$240$	−4.00000	+	8.00000i	−0.258199	+	0.516398i
$241$	−14.0000			−0.901819			−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000			−0.901819			−0.450910	+	0.892570i	$0.648900\pi$
$242$	−7.00000	−	7.00000i	−0.449977	−	0.449977i
$243$	−1.00000			−0.0641500
$244$	−2.00000	+	2.00000i	−0.128037	+	0.128037i
$245$	−10.0000	−	5.00000i	−0.638877	−	0.319438i
$246$	8.00000	+	8.00000i	0.510061	+	0.510061i
$247$	−20.0000	+	20.0000i	−1.27257	+	1.27257i
$248$	−4.00000	+	4.00000i	−0.254000	+	0.254000i
$249$	12.0000			0.760469
$250$	−9.00000	+	13.0000i	−0.569210	+	0.822192i
$251$	−19.0000	−	19.0000i	−1.19927	−	1.19927i	−0.974386	−	0.224884i	$-0.927800\pi$
$251$	−19.0000	−	19.0000i	−1.19927	−	1.19927i	−0.224884	−	0.974386i	$-0.572200\pi$
$252$	2.00000	+	2.00000i	0.125988	+	0.125988i
$253$			6.00000i			0.377217i
$254$	−18.0000			−1.12942
$255$	5.00000	+	15.0000i	0.313112	+	0.939336i
$256$	16.0000			1.00000
$257$	15.0000	−	15.0000i	0.935674	−	0.935674i	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	15.0000	−	15.0000i	0.935674	−	0.935674i	0.998053	+	0.0623783i	$0.0198685\pi$
$258$	2.00000	+	2.00000i	0.124515	+	0.124515i
$259$	−8.00000	−	8.00000i	−0.497096	−	0.497096i
$260$	8.00000	−	16.0000i	0.496139	−	0.992278i
$261$	5.00000	−	5.00000i	0.309492	−	0.309492i
$262$		−	10.0000i		−	0.617802i
$263$	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	$0.651272\pi$
$264$			12.0000i			0.738549i
$265$	6.00000	−	12.0000i	0.368577	−	0.737154i
$266$	−10.0000	+	10.0000i	−0.613139	+	0.613139i
$267$	2.00000			0.122398
$268$	4.00000			0.244339
$269$	9.00000	−	9.00000i	0.548740	−	0.548740i	−0.377337	−	0.926076i	$-0.623160\pi$
$269$	9.00000	−	9.00000i	0.548740	−	0.548740i	0.926076	+	0.377337i	$0.123160\pi$
$270$	1.00000	+	3.00000i	0.0608581	+	0.182574i
$271$			26.0000i			1.57939i	0.613501	+	0.789694i	$0.289761\pi$
$271$			26.0000i			1.57939i	−0.613501	+	0.789694i	$0.710239\pi$
$272$	20.0000	−	20.0000i	1.21268	−	1.21268i
$273$	−4.00000	−	4.00000i	−0.242091	−	0.242091i
$274$	26.0000			1.57072
$275$	−3.00000	+	21.0000i	−0.180907	+	1.26635i
$276$	2.00000	−	2.00000i	0.120386	−	0.120386i
$277$		−	8.00000i		−	0.480673i	−0.970690	−	0.240337i	$-0.922742\pi$
$277$		−	8.00000i		−	0.480673i	0.970690	−	0.240337i	$-0.0772579\pi$
$278$		−	22.0000i		−	1.31947i
$279$			2.00000i			0.119737i
$280$	4.00000	−	8.00000i	0.239046	−	0.478091i
$281$		−	4.00000i		−	0.238620i	−0.992857	−	0.119310i	$-0.961932\pi$
$281$		−	4.00000i		−	0.238620i	0.992857	−	0.119310i	$-0.0380682\pi$
$282$	−10.0000			−0.595491
$283$		−	6.00000i		−	0.356663i	−0.983970	−	0.178331i	$-0.942930\pi$
$283$		−	6.00000i		−	0.356663i	0.983970	−	0.178331i	$-0.0570699\pi$
$284$		0			0
$285$	−15.0000	+	5.00000i	−0.888523	+	0.296174i
$286$		−	24.0000i		−	1.41915i
$287$	−8.00000	−	8.00000i	−0.472225	−	0.472225i
$288$	4.00000	−	4.00000i	0.235702	−	0.235702i
$289$		−	33.0000i		−	1.94118i
$290$	−20.0000	−	10.0000i	−1.17444	−	0.587220i
$291$	−1.00000	+	1.00000i	−0.0586210	+	0.0586210i
$292$	−10.0000	−	10.0000i	−0.585206	−	0.585206i
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$	5.00000	+	5.00000i	0.291606	+	0.291606i
$295$	−5.00000	−	15.0000i	−0.291111	−	0.873334i
$296$	−16.0000	+	16.0000i	−0.929981	+	0.929981i
$297$	3.00000	+	3.00000i	0.174078	+	0.174078i
$298$	−10.0000			−0.579284
$299$	−4.00000	+	4.00000i	−0.231326	+	0.231326i
$300$	8.00000	−	6.00000i	0.461880	−	0.346410i
$301$	−2.00000	−	2.00000i	−0.115278	−	0.115278i
$302$	8.00000	−	8.00000i	0.460348	−	0.460348i
$303$	−1.00000	+	1.00000i	−0.0574485	+	0.0574485i
$304$	20.0000	+	20.0000i	1.14708	+	1.14708i
$305$	3.00000	−	1.00000i	0.171780	−	0.0572598i
$306$		−	10.0000i		−	0.571662i
$307$			26.0000i			1.48390i	0.670456	+	0.741949i	$0.266098\pi$
$307$			26.0000i			1.48390i	−0.670456	+	0.741949i	$0.733902\pi$
$308$		−	12.0000i		−	0.683763i
$309$	−5.00000	−	5.00000i	−0.284440	−	0.284440i
$310$	6.00000	−	2.00000i	0.340777	−	0.113592i
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$	−8.00000	+	8.00000i	−0.452911	+	0.452911i
$313$	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	$0.132875\pi$
$314$	18.0000	−	18.0000i	1.01580	−	1.01580i
$315$	−1.00000	−	3.00000i	−0.0563436	−	0.169031i
$316$		−	16.0000i		−	0.900070i
$317$	−30.0000			−1.68497			−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000			−1.68497			−0.842484	+	0.538721i	$0.818908\pi$
$318$	−6.00000	+	6.00000i	−0.336463	+	0.336463i
$319$	−30.0000			−1.67968
$320$	−16.0000	−	8.00000i	−0.894427	−	0.447214i
$321$	−4.00000			−0.223258
$322$	−2.00000	+	2.00000i	−0.111456	+	0.111456i
$323$	50.0000			2.78207
$324$		−	2.00000i		−	0.111111i
$325$	−16.0000	+	12.0000i	−0.887520	+	0.665640i
$326$	12.0000	−	12.0000i	0.664619	−	0.664619i
$327$	−3.00000	+	3.00000i	−0.165900	+	0.165900i
$328$	−16.0000	+	16.0000i	−0.883452	+	0.883452i
$329$	10.0000			0.551318
$330$	6.00000	−	12.0000i	0.330289	−	0.660578i
$331$	−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	$-0.553917\pi$
$332$			24.0000i			1.31717i
$333$			8.00000i			0.438397i
$334$			10.0000i			0.547176i
$335$	−4.00000	−	2.00000i	−0.218543	−	0.109272i
$336$	−4.00000	+	4.00000i	−0.218218	+	0.218218i
$337$	9.00000	−	9.00000i	0.490261	−	0.490261i	−0.418127	−	0.908388i	$-0.637313\pi$
$337$	9.00000	−	9.00000i	0.490261	−	0.490261i	0.908388	+	0.418127i	$0.137313\pi$
$338$	3.00000	−	3.00000i	0.163178	−	0.163178i
$339$	9.00000	+	9.00000i	0.488813	+	0.488813i
$340$	−30.0000	+	10.0000i	−1.62698	+	0.542326i
$341$	6.00000	−	6.00000i	0.324918	−	0.324918i
$342$	10.0000			0.540738
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$	−4.00000	+	4.00000i	−0.215666	+	0.215666i
$345$	−3.00000	+	1.00000i	−0.161515	+	0.0538382i
$346$	12.0000	+	12.0000i	0.645124	+	0.645124i
$347$	12.0000			0.644194			0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000			0.644194			0.322097	+	0.946707i	$0.395612\pi$
$348$	10.0000	+	10.0000i	0.536056	+	0.536056i
$349$	−17.0000	+	17.0000i	−0.909989	+	0.909989i	−0.996271	−	0.0862816i	$-0.972502\pi$
$349$	−17.0000	+	17.0000i	−0.909989	+	0.909989i	0.0862816	+	0.996271i	$0.472502\pi$
$350$	−8.00000	+	6.00000i	−0.427618	+	0.320713i
$351$			4.00000i			0.213504i
$352$	−24.0000			−1.27920
$353$	−5.00000	−	5.00000i	−0.266123	−	0.266123i	0.561413	−	0.827536i	$-0.310258\pi$
$353$	−5.00000	−	5.00000i	−0.266123	−	0.266123i	−0.827536	+	0.561413i	$0.810258\pi$
$354$			10.0000i			0.531494i
$355$		0			0
$356$			4.00000i			0.212000i
$357$			10.0000i			0.529256i
$358$	−34.0000			−1.79696
$359$		−	26.0000i		−	1.37223i	−0.727494	−	0.686114i	$-0.759315\pi$
$359$		−	26.0000i		−	1.37223i	0.727494	−	0.686114i	$-0.240685\pi$
$360$	−6.00000	+	2.00000i	−0.316228	+	0.105409i
$361$			31.0000i			1.63158i
$362$			14.0000i			0.735824i
$363$		−	7.00000i		−	0.367405i
$364$	8.00000	−	8.00000i	0.419314	−	0.419314i
$365$	5.00000	+	15.0000i	0.261712	+	0.785136i
$366$	−2.00000			−0.104542
$367$	−19.0000	−	19.0000i	−0.991792	−	0.991792i	0.00817466	−	0.999967i	$-0.497398\pi$
$367$	−19.0000	−	19.0000i	−0.991792	−	0.991792i	−0.999967	+	0.00817466i	$0.997398\pi$
$368$	4.00000	+	4.00000i	0.208514	+	0.208514i
$369$			8.00000i			0.416463i
$370$	24.0000	−	8.00000i	1.24770	−	0.415900i
$371$	6.00000	−	6.00000i	0.311504	−	0.311504i
$372$	−4.00000			−0.207390
$373$	6.00000			0.310668			0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000			0.310668			0.155334	+	0.987862i	$0.450355\pi$
$374$	−30.0000	+	30.0000i	−1.55126	+	1.55126i
$375$	−11.0000	+	2.00000i	−0.568038	+	0.103280i
$376$		−	20.0000i		−	1.03142i
$377$	−20.0000	−	20.0000i	−1.03005	−	1.03005i
$378$			2.00000i			0.102869i
$379$	5.00000	−	5.00000i	0.256833	−	0.256833i	−0.566932	−	0.823765i	$-0.691870\pi$
$379$	5.00000	−	5.00000i	0.256833	−	0.256833i	0.823765	+	0.566932i	$0.191870\pi$
$380$	−10.0000	−	30.0000i	−0.512989	−	1.53897i
$381$	−9.00000	−	9.00000i	−0.461084	−	0.461084i
$382$	18.0000	+	18.0000i	0.920960	+	0.920960i
$383$	−23.0000	+	23.0000i	−1.17525	+	1.17525i	−0.194304	+	0.980941i	$0.562245\pi$
$383$	−23.0000	+	23.0000i	−1.17525	+	1.17525i	−0.980941	+	0.194304i	$0.937755\pi$
$384$	8.00000	+	8.00000i	0.408248	+	0.408248i
$385$	−6.00000	+	12.0000i	−0.305788	+	0.611577i
$386$	14.0000			0.712581
$387$			2.00000i			0.101666i
$388$	−2.00000	−	2.00000i	−0.101535	−	0.101535i
$389$	21.0000	+	21.0000i	1.06474	+	1.06474i	0.997754	+	0.0669885i	$0.0213391\pi$
$389$	21.0000	+	21.0000i	1.06474	+	1.06474i	0.0669885	+	0.997754i	$0.478661\pi$
$390$	12.0000	−	4.00000i	0.607644	−	0.202548i
$391$	10.0000			0.505722
$392$	−10.0000	+	10.0000i	−0.505076	+	0.505076i
$393$	5.00000	−	5.00000i	0.252217	−	0.252217i
$394$	−8.00000	−	8.00000i	−0.403034	−	0.403034i
$395$	−8.00000	+	16.0000i	−0.402524	+	0.805047i
$396$	−6.00000	+	6.00000i	−0.301511	+	0.301511i
$397$	26.0000			1.30490			0.652451	−	0.757831i	$-0.273741\pi$
$397$	26.0000			1.30490			0.652451	+	0.757831i	$0.273741\pi$
$398$	−18.0000	−	18.0000i	−0.902258	−	0.902258i
$399$	−10.0000			−0.500626
$400$	12.0000	+	16.0000i	0.600000	+	0.800000i
$401$	−18.0000			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$402$	2.00000	+	2.00000i	0.0997509	+	0.0997509i
$403$	8.00000			0.398508
$404$	−2.00000	−	2.00000i	−0.0995037	−	0.0995037i
$405$	−1.00000	+	2.00000i	−0.0496904	+	0.0993808i
$406$	−10.0000	−	10.0000i	−0.496292	−	0.496292i
$407$	24.0000	−	24.0000i	1.18964	−	1.18964i
$408$	20.0000			0.990148
$409$	6.00000			0.296681			0.148340	−	0.988936i	$-0.452607\pi$
$409$	6.00000			0.296681			0.148340	+	0.988936i	$0.452607\pi$
$410$	24.0000	−	8.00000i	1.18528	−	0.395092i
$411$	13.0000	+	13.0000i	0.641243	+	0.641243i
$412$	10.0000	−	10.0000i	0.492665	−	0.492665i
$413$		−	10.0000i		−	0.492068i
$414$	2.00000			0.0982946
$415$	12.0000	−	24.0000i	0.589057	−	1.17811i
$416$	−16.0000	−	16.0000i	−0.784465	−	0.784465i
$417$	11.0000	−	11.0000i	0.538672	−	0.538672i
$418$	−30.0000	−	30.0000i	−1.46735	−	1.46735i
$419$	−7.00000	−	7.00000i	−0.341972	−	0.341972i	0.515136	−	0.857108i	$-0.327741\pi$
$419$	−7.00000	−	7.00000i	−0.341972	−	0.341972i	−0.857108	+	0.515136i	$0.827741\pi$
$420$	6.00000	−	2.00000i	0.292770	−	0.0975900i
$421$	−9.00000	+	9.00000i	−0.438633	+	0.438633i	−0.891552	−	0.452919i	$-0.850383\pi$
$421$	−9.00000	+	9.00000i	−0.438633	+	0.438633i	0.452919	+	0.891552i	$0.350383\pi$
$422$			18.0000i			0.876226i
$423$	−5.00000	−	5.00000i	−0.243108	−	0.243108i
$424$	−12.0000	−	12.0000i	−0.582772	−	0.582772i
$425$	35.0000	+	5.00000i	1.69775	+	0.242536i
$426$		0			0
$427$	2.00000			0.0967868
$428$		−	8.00000i		−	0.386695i
$429$	12.0000	−	12.0000i	0.579365	−	0.579365i
$430$	6.00000	−	2.00000i	0.289346	−	0.0964486i
$431$			6.00000i			0.289010i	0.989504	+	0.144505i	$0.0461589\pi$
$431$			6.00000i			0.289010i	−0.989504	+	0.144505i	$0.953841\pi$
$432$	4.00000			0.192450
$433$	−3.00000	−	3.00000i	−0.144171	−	0.144171i	0.631337	−	0.775508i	$-0.282506\pi$
$433$	−3.00000	−	3.00000i	−0.144171	−	0.144171i	−0.775508	+	0.631337i	$0.782506\pi$
$434$	4.00000			0.192006
$435$	−5.00000	−	15.0000i	−0.239732	−	0.719195i
$436$	−6.00000	−	6.00000i	−0.287348	−	0.287348i
$437$			10.0000i			0.478365i
$438$		−	10.0000i		−	0.477818i
$439$		−	22.0000i		−	1.05000i	−0.851101	−	0.525001i	$-0.824065\pi$
$439$		−	22.0000i		−	1.05000i	0.851101	−	0.525001i	$-0.175935\pi$
$440$	24.0000	+	12.0000i	1.14416	+	0.572078i
$441$			5.00000i			0.238095i
$442$	−40.0000			−1.90261
$443$		−	10.0000i		−	0.475114i	−0.971374	−	0.237557i	$-0.923653\pi$
$443$		−	10.0000i		−	0.475114i	0.971374	−	0.237557i	$-0.0763467\pi$
$444$	−16.0000			−0.759326
$445$	2.00000	−	4.00000i	0.0948091	−	0.189618i
$446$			6.00000i			0.284108i
$447$	−5.00000	−	5.00000i	−0.236492	−	0.236492i
$448$	−8.00000	−	8.00000i	−0.377964	−	0.377964i
$449$		−	12.0000i		−	0.566315i	−0.959073	−	0.283158i	$-0.908618\pi$
$449$		−	12.0000i		−	0.566315i	0.959073	−	0.283158i	$-0.0913819\pi$
$450$	7.00000	+	1.00000i	0.329983	+	0.0471405i
$451$	24.0000	−	24.0000i	1.13012	−	1.13012i
$452$	−18.0000	+	18.0000i	−0.846649	+	0.846649i
$453$	8.00000			0.375873
$454$	−6.00000	−	6.00000i	−0.281594	−	0.281594i
$455$	−12.0000	+	4.00000i	−0.562569	+	0.187523i
$456$			20.0000i			0.936586i
$457$	25.0000	+	25.0000i	1.16945	+	1.16945i	0.982339	+	0.187112i	$0.0599128\pi$
$457$	25.0000	+	25.0000i	1.16945	+	1.16945i	0.187112	+	0.982339i	$0.440087\pi$
$458$	18.0000			0.841085
$459$	5.00000	−	5.00000i	0.233380	−	0.233380i
$460$	−2.00000	−	6.00000i	−0.0932505	−	0.279751i
$461$	29.0000	+	29.0000i	1.35066	+	1.35066i	0.884918	+	0.465746i	$0.154214\pi$
$461$	29.0000	+	29.0000i	1.35066	+	1.35066i	0.465746	+	0.884918i	$0.345786\pi$
$462$	6.00000	−	6.00000i	0.279145	−	0.279145i
$463$	−13.0000	+	13.0000i	−0.604161	+	0.604161i	−0.941414	−	0.337253i	$-0.890502\pi$
$463$	−13.0000	+	13.0000i	−0.604161	+	0.604161i	0.337253	+	0.941414i	$0.390502\pi$
$464$	−20.0000	+	20.0000i	−0.928477	+	0.928477i
$465$	4.00000	+	2.00000i	0.185496	+	0.0927478i
$466$		−	10.0000i		−	0.463241i
$467$			6.00000i			0.277647i	0.990317	+	0.138823i	$0.0443321\pi$
$467$			6.00000i			0.277647i	−0.990317	+	0.138823i	$0.955668\pi$
$468$	−8.00000			−0.369800
$469$	−2.00000	−	2.00000i	−0.0923514	−	0.0923514i
$470$	−10.0000	+	20.0000i	−0.461266	+	0.922531i
$471$	18.0000			0.829396
$472$	−20.0000			−0.920575
$473$	6.00000	−	6.00000i	0.275880	−	0.275880i
$474$	8.00000	−	8.00000i	0.367452	−	0.367452i
$475$	−5.00000	+	35.0000i	−0.229416	+	1.60591i
$476$	−20.0000			−0.916698
$477$	−6.00000			−0.274721
$478$	−8.00000	+	8.00000i	−0.365911	+	0.365911i
$479$	−8.00000			−0.365529			−0.182765	−	0.983157i	$-0.558505\pi$
$479$	−8.00000			−0.365529			−0.182765	+	0.983157i	$0.558505\pi$
$480$	−4.00000	−	12.0000i	−0.182574	−	0.547723i
$481$	32.0000			1.45907
$482$	14.0000	−	14.0000i	0.637683	−	0.637683i
$483$	−2.00000			−0.0910032
$484$	14.0000			0.636364
$485$	1.00000	+	3.00000i	0.0454077	+	0.136223i
$486$	1.00000	−	1.00000i	0.0453609	−	0.0453609i
$487$	15.0000	−	15.0000i	0.679715	−	0.679715i	−0.280221	−	0.959936i	$-0.590408\pi$
$487$	15.0000	−	15.0000i	0.679715	−	0.679715i	0.959936	+	0.280221i	$0.0904077\pi$
$488$		−	4.00000i		−	0.181071i
$489$	12.0000			0.542659
$490$	15.0000	−	5.00000i	0.677631	−	0.225877i
$491$	9.00000	+	9.00000i	0.406164	+	0.406164i	0.880399	−	0.474234i	$-0.157275\pi$
$491$	9.00000	+	9.00000i	0.406164	+	0.406164i	−0.474234	+	0.880399i	$0.657275\pi$
$492$	−16.0000			−0.721336
$493$			50.0000i			2.25189i
$494$		−	40.0000i		−	1.79969i
$495$	9.00000	−	3.00000i	0.404520	−	0.134840i
$496$		−	8.00000i		−	0.359211i
$497$		0			0
$498$	−12.0000	+	12.0000i	−0.537733	+	0.537733i
$499$	−21.0000	−	21.0000i	−0.940089	−	0.940089i	0.0582150	−	0.998304i	$-0.481459\pi$
$499$	−21.0000	−	21.0000i	−0.940089	−	0.940089i	−0.998304	+	0.0582150i	$0.981459\pi$
$500$	−4.00000	−	22.0000i	−0.178885	−	0.983870i
$501$	−5.00000	+	5.00000i	−0.223384	+	0.223384i
$502$	38.0000			1.69602
$503$	23.0000	+	23.0000i	1.02552	+	1.02552i	0.999666	+	0.0258536i	$0.00823036\pi$
$503$	23.0000	+	23.0000i	1.02552	+	1.02552i	0.0258536	+	0.999666i	$0.491770\pi$
$504$	−4.00000			−0.178174
$505$	1.00000	+	3.00000i	0.0444994	+	0.133498i
$506$	−6.00000	−	6.00000i	−0.266733	−	0.266733i
$507$	3.00000			0.133235
$508$	18.0000	−	18.0000i	0.798621	−	0.798621i
$509$	−11.0000	+	11.0000i	−0.487566	+	0.487566i	−0.907537	−	0.419971i	$-0.862040\pi$
$509$	−11.0000	+	11.0000i	−0.487566	+	0.487566i	0.419971	+	0.907537i	$0.362040\pi$
$510$	−20.0000	−	10.0000i	−0.885615	−	0.442807i
$511$			10.0000i			0.442374i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	5.00000	+	5.00000i	0.220755	+	0.220755i
$514$			30.0000i			1.32324i
$515$	−15.0000	+	5.00000i	−0.660979	+	0.220326i
$516$	−4.00000			−0.176090
$517$			30.0000i			1.31940i
$518$	16.0000			0.703000
$519$			12.0000i			0.526742i
$520$	8.00000	+	24.0000i	0.350823	+	1.05247i
$521$		−	4.00000i		−	0.175243i	−0.996154	−	0.0876216i	$-0.972073\pi$
$521$		−	4.00000i		−	0.175243i	0.996154	−	0.0876216i	$-0.0279266\pi$
$522$			10.0000i			0.437688i
$523$		−	22.0000i		−	0.961993i	−0.876723	−	0.480996i	$-0.840275\pi$
$523$		−	22.0000i		−	0.961993i	0.876723	−	0.480996i	$-0.159725\pi$
$524$	10.0000	+	10.0000i	0.436852	+	0.436852i
$525$	−7.00000	−	1.00000i	−0.305505	−	0.0436436i
$526$	−14.0000			−0.610429
$527$	−10.0000	−	10.0000i	−0.435607	−	0.435607i
$528$	−12.0000	−	12.0000i	−0.522233	−	0.522233i
$529$		−	21.0000i		−	0.913043i
$530$	6.00000	+	18.0000i	0.260623	+	0.781870i
$531$	−5.00000	+	5.00000i	−0.216982	+	0.216982i
$532$		−	20.0000i		−	0.867110i
$533$	32.0000			1.38607
$534$	−2.00000	+	2.00000i	−0.0865485	+	0.0865485i
$535$	−4.00000	+	8.00000i	−0.172935	+	0.345870i
$536$	−4.00000	+	4.00000i	−0.172774	+	0.172774i
$537$	−17.0000	−	17.0000i	−0.733604	−	0.733604i
$538$			18.0000i			0.776035i
$539$	15.0000	−	15.0000i	0.646096	−	0.646096i
$540$	−4.00000	−	2.00000i	−0.172133	−	0.0860663i
$541$	−13.0000	−	13.0000i	−0.558914	−	0.558914i	0.370084	−	0.928998i	$-0.379329\pi$
$541$	−13.0000	−	13.0000i	−0.558914	−	0.558914i	−0.928998	+	0.370084i	$0.879329\pi$
$542$	−26.0000	−	26.0000i	−1.11680	−	1.11680i
$543$	−7.00000	+	7.00000i	−0.300399	+	0.300399i
$544$			40.0000i			1.71499i
$545$	3.00000	+	9.00000i	0.128506	+	0.385518i
$546$	8.00000			0.342368
$547$		−	6.00000i		−	0.256541i	−0.991739	−	0.128271i	$-0.959057\pi$
$547$		−	6.00000i		−	0.256541i	0.991739	−	0.128271i	$-0.0409426\pi$
$548$	−26.0000	+	26.0000i	−1.11066	+	1.11066i
$549$	−1.00000	−	1.00000i	−0.0426790	−	0.0426790i
$550$	−18.0000	−	24.0000i	−0.767523	−	1.02336i
$551$	−50.0000			−2.13007
$552$			4.00000i			0.170251i
$553$	−8.00000	+	8.00000i	−0.340195	+	0.340195i
$554$	8.00000	+	8.00000i	0.339887	+	0.339887i
$555$	16.0000	+	8.00000i	0.679162	+	0.339581i
$556$	22.0000	+	22.0000i	0.933008	+	0.933008i
$557$	6.00000			0.254228			0.127114	−	0.991888i	$-0.459429\pi$
$557$	6.00000			0.254228			0.127114	+	0.991888i	$0.459429\pi$
$558$	−2.00000	−	2.00000i	−0.0846668	−	0.0846668i
$559$	8.00000			0.338364
$560$	4.00000	+	12.0000i	0.169031	+	0.507093i
$561$	−30.0000			−1.26660
$562$	4.00000	+	4.00000i	0.168730	+	0.168730i
$563$	4.00000			0.168580			0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000			0.168580			0.0842900	+	0.996441i	$0.473138\pi$
$564$	10.0000	−	10.0000i	0.421076	−	0.421076i
$565$	27.0000	−	9.00000i	1.13590	−	0.378633i
$566$	6.00000	+	6.00000i	0.252199	+	0.252199i
$567$	−1.00000	+	1.00000i	−0.0419961	+	0.0419961i
$568$		0			0
$569$	−26.0000			−1.08998			−0.544988	−	0.838444i	$-0.683466\pi$
$569$	−26.0000			−1.08998			−0.544988	+	0.838444i	$0.683466\pi$
$570$	10.0000	−	20.0000i	0.418854	−	0.837708i
$571$	−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	$-0.515074\pi$
$572$	24.0000	+	24.0000i	1.00349	+	1.00349i
$573$			18.0000i			0.751961i
$574$	16.0000			0.667827
$575$	−1.00000	+	7.00000i	−0.0417029	+	0.291920i
$576$			8.00000i			0.333333i
$577$	1.00000	−	1.00000i	0.0416305	−	0.0416305i	−0.685985	−	0.727616i	$-0.740628\pi$
$577$	1.00000	−	1.00000i	0.0416305	−	0.0416305i	0.727616	+	0.685985i	$0.240628\pi$
$578$	33.0000	+	33.0000i	1.37262	+	1.37262i
$579$	7.00000	+	7.00000i	0.290910	+	0.290910i
$580$	30.0000	−	10.0000i	1.24568	−	0.415227i
$581$	12.0000	−	12.0000i	0.497844	−	0.497844i
$582$		−	2.00000i		−	0.0829027i
$583$	18.0000	+	18.0000i	0.745484	+	0.745484i
$584$	20.0000			0.827606
$585$	8.00000	+	4.00000i	0.330759	+	0.165380i
$586$	−6.00000	+	6.00000i	−0.247858	+	0.247858i
$587$	28.0000			1.15568			0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000			1.15568			0.577842	+	0.816149i	$0.303895\pi$
$588$	−10.0000			−0.412393
$589$	10.0000	−	10.0000i	0.412043	−	0.412043i
$590$	20.0000	+	10.0000i	0.823387	+	0.411693i
$591$		−	8.00000i		−	0.329076i
$592$		−	32.0000i		−	1.31519i
$593$	−5.00000	−	5.00000i	−0.205325	−	0.205325i	0.596952	−	0.802277i	$-0.296378\pi$
$593$	−5.00000	−	5.00000i	−0.205325	−	0.205325i	−0.802277	+	0.596952i	$0.796378\pi$
$594$	−6.00000			−0.246183
$595$	20.0000	+	10.0000i	0.819920	+	0.409960i
$596$	10.0000	−	10.0000i	0.409616	−	0.409616i
$597$		−	18.0000i		−	0.736691i
$598$		−	8.00000i		−	0.327144i
$599$			6.00000i			0.245153i	0.992459	+	0.122577i	$0.0391157\pi$
$599$			6.00000i			0.245153i	−0.992459	+	0.122577i	$0.960884\pi$
$600$	−2.00000	+	14.0000i	−0.0816497	+	0.571548i
$601$			8.00000i			0.326327i	0.986599	+	0.163163i	$0.0521698\pi$
$601$			8.00000i			0.326327i	−0.986599	+	0.163163i	$0.947830\pi$
$602$	4.00000			0.163028
$603$			2.00000i			0.0814463i
$604$			16.0000i			0.651031i
$605$	−14.0000	−	7.00000i	−0.569181	−	0.284590i
$606$		−	2.00000i		−	0.0812444i
$607$	−27.0000	−	27.0000i	−1.09590	−	1.09590i	−0.994885	−	0.101011i	$-0.967792\pi$
$607$	−27.0000	−	27.0000i	−1.09590	−	1.09590i	−0.101011	−	0.994885i	$-0.532208\pi$
$608$	−40.0000			−1.62221
$609$		−	10.0000i		−	0.405220i
$610$	−2.00000	+	4.00000i	−0.0809776	+	0.161955i
$611$	−20.0000	+	20.0000i	−0.809113	+	0.809113i
$612$	10.0000	+	10.0000i	0.404226	+	0.404226i
$613$	34.0000			1.37325			0.686624	−	0.727013i	$-0.259092\pi$
$613$	34.0000			1.37325			0.686624	+	0.727013i	$0.259092\pi$
$614$	−26.0000	−	26.0000i	−1.04927	−	1.04927i
$615$	16.0000	+	8.00000i	0.645182	+	0.322591i
$616$	12.0000	+	12.0000i	0.483494	+	0.483494i
$617$	11.0000	+	11.0000i	0.442843	+	0.442843i	0.892966	−	0.450123i	$-0.148620\pi$
$617$	11.0000	+	11.0000i	0.442843	+	0.442843i	−0.450123	+	0.892966i	$0.648620\pi$
$618$	10.0000			0.402259
$619$	−27.0000	+	27.0000i	−1.08522	+	1.08522i	−0.0892087	+	0.996013i	$0.528434\pi$
$619$	−27.0000	+	27.0000i	−1.08522	+	1.08522i	−0.996013	+	0.0892087i	$0.971566\pi$
$620$	−4.00000	+	8.00000i	−0.160644	+	0.321288i
$621$	1.00000	+	1.00000i	0.0401286	+	0.0401286i
$622$	−24.0000	+	24.0000i	−0.962312	+	0.962312i
$623$	2.00000	−	2.00000i	0.0801283	−	0.0801283i
$624$		−	16.0000i		−	0.640513i
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$			18.0000i			0.719425i
$627$		−	30.0000i		−	1.19808i
$628$			36.0000i			1.43656i
$629$	−40.0000	−	40.0000i	−1.59490	−	1.59490i
$630$	4.00000	+	2.00000i	0.159364	+	0.0796819i
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	16.0000	+	16.0000i	0.636446	+	0.636446i
$633$	−9.00000	+	9.00000i	−0.357718	+	0.357718i
$634$	30.0000	−	30.0000i	1.19145	−	1.19145i
$635$	−27.0000	+	9.00000i	−1.07146	+	0.357154i
$636$		−	12.0000i		−	0.475831i
$637$	20.0000			0.792429
$638$	30.0000	−	30.0000i	1.18771	−	1.18771i
$639$		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	$0.701845\pi$
$642$	4.00000	−	4.00000i	0.157867	−	0.157867i
$643$	20.0000			0.788723			0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000			0.788723			0.394362	+	0.918955i	$0.370966\pi$
$644$		−	4.00000i		−	0.157622i
$645$	4.00000	+	2.00000i	0.157500	+	0.0787499i
$646$	−50.0000	+	50.0000i	−1.96722	+	1.96722i
$647$	−11.0000	+	11.0000i	−0.432455	+	0.432455i	−0.889463	−	0.457008i	$-0.848921\pi$
$647$	−11.0000	+	11.0000i	−0.432455	+	0.432455i	0.457008	+	0.889463i	$0.348921\pi$
$648$	2.00000	+	2.00000i	0.0785674	+	0.0785674i
$649$	30.0000			1.17760
$650$	4.00000	−	28.0000i	0.156893	−	1.09825i
$651$	2.00000	+	2.00000i	0.0783862	+	0.0783862i
$652$			24.0000i			0.939913i
$653$		−	48.0000i		−	1.87839i	−0.343391	−	0.939193i	$-0.611576\pi$
$653$		−	48.0000i		−	1.87839i	0.343391	−	0.939193i	$-0.388424\pi$
$654$		−	6.00000i		−	0.234619i
$655$	−5.00000	−	15.0000i	−0.195366	−	0.586098i
$656$		−	32.0000i		−	1.24939i
$657$	5.00000	−	5.00000i	0.195069	−	0.195069i
$658$	−10.0000	+	10.0000i	−0.389841	+	0.389841i
$659$	−19.0000	−	19.0000i	−0.740135	−	0.740135i	0.232469	−	0.972604i	$-0.425320\pi$
$659$	−19.0000	−	19.0000i	−0.740135	−	0.740135i	−0.972604	+	0.232469i	$0.925320\pi$
$660$	6.00000	+	18.0000i	0.233550	+	0.700649i
$661$	−33.0000	+	33.0000i	−1.28355	+	1.28355i	−0.344919	+	0.938633i	$0.612094\pi$
$661$	−33.0000	+	33.0000i	−1.28355	+	1.28355i	−0.938633	+	0.344919i	$0.887906\pi$
$662$	42.0000			1.63238
$663$	−20.0000	−	20.0000i	−0.776736	−	0.776736i
$664$	−24.0000	−	24.0000i	−0.931381	−	0.931381i
$665$	−10.0000	+	20.0000i	−0.387783	+	0.775567i
$666$	−8.00000	−	8.00000i	−0.309994	−	0.309994i
$667$	−10.0000			−0.387202
$668$	−10.0000	−	10.0000i	−0.386912	−	0.386912i
$669$	−3.00000	+	3.00000i	−0.115987	+	0.115987i
$670$	6.00000	−	2.00000i	0.231800	−	0.0772667i
$671$			6.00000i			0.231627i
$672$		−	8.00000i		−	0.308607i
$673$	−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	$0.884072\pi$
$674$			18.0000i			0.693334i
$675$	3.00000	+	4.00000i	0.115470	+	0.153960i
$676$			6.00000i			0.230769i
$677$			40.0000i			1.53732i	0.639655	+	0.768662i	$0.279077\pi$
$677$			40.0000i			1.53732i	−0.639655	+	0.768662i	$0.720923\pi$
$678$	−18.0000			−0.691286
$679$			2.00000i			0.0767530i
$680$	20.0000	−	40.0000i	0.766965	−	1.53393i
$681$		−	6.00000i		−	0.229920i
$682$			12.0000i			0.459504i
$683$			30.0000i			1.14792i	0.818884	+	0.573959i	$0.194593\pi$
$683$			30.0000i			1.14792i	−0.818884	+	0.573959i	$0.805407\pi$
$684$	−10.0000	+	10.0000i	−0.382360	+	0.382360i
$685$	39.0000	−	13.0000i	1.49011	−	0.496704i
$686$	24.0000			0.916324
$687$	9.00000	+	9.00000i	0.343371	+	0.343371i
$688$		−	8.00000i		−	0.304997i
$689$			24.0000i			0.914327i
$690$	2.00000	−	4.00000i	0.0761387	−	0.152277i
$691$	−19.0000	+	19.0000i	−0.722794	+	0.722794i	−0.969173	−	0.246379i	$-0.920759\pi$
$691$	−19.0000	+	19.0000i	−0.722794	+	0.722794i	0.246379	+	0.969173i	$0.420759\pi$
$692$	−24.0000			−0.912343
$693$	6.00000			0.227921
$694$	−12.0000	+	12.0000i	−0.455514	+	0.455514i
$695$	−11.0000	−	33.0000i	−0.417254	−	1.25176i
$696$	−20.0000			−0.758098
$697$	−40.0000	−	40.0000i	−1.51511	−	1.51511i
$698$		−	34.0000i		−	1.28692i
$699$	5.00000	−	5.00000i	0.189117	−	0.189117i
$700$	2.00000	−	14.0000i	0.0755929	−	0.529150i
$701$	−35.0000	−	35.0000i	−1.32193	−	1.32193i	−0.912211	−	0.409721i	$-0.865626\pi$
$701$	−35.0000	−	35.0000i	−1.32193	−	1.32193i	−0.409721	−	0.912211i	$-0.634374\pi$
$702$	−4.00000	−	4.00000i	−0.150970	−	0.150970i
$703$	40.0000	−	40.0000i	1.50863	−	1.50863i
$704$	24.0000	−	24.0000i	0.904534	−	0.904534i
$705$	−15.0000	+	5.00000i	−0.564933	+	0.188311i
$706$	10.0000			0.376355
$707$			2.00000i			0.0752177i
$708$	−10.0000	−	10.0000i	−0.375823	−	0.375823i
$709$	−9.00000	−	9.00000i	−0.338002	−	0.338002i	0.517613	−	0.855615i	$-0.326821\pi$
$709$	−9.00000	−	9.00000i	−0.338002	−	0.338002i	−0.855615	+	0.517613i	$0.826821\pi$
$710$		0			0
$711$	8.00000			0.300023
$712$	−4.00000	−	4.00000i	−0.149906	−	0.149906i
$713$	2.00000	−	2.00000i	0.0749006	−	0.0749006i
$714$	−10.0000	−	10.0000i	−0.374241	−	0.374241i
$715$	−12.0000	−	36.0000i	−0.448775	−	1.34632i
$716$	34.0000	−	34.0000i	1.27064	−	1.27064i
$717$	−8.00000			−0.298765
$718$	26.0000	+	26.0000i	0.970311	+	0.970311i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	4.00000	−	8.00000i	0.149071	−	0.298142i
$721$	−10.0000			−0.372419
$722$	−31.0000	−	31.0000i	−1.15370	−	1.15370i
$723$	14.0000			0.520666
$724$	−14.0000	−	14.0000i	−0.520306	−	0.520306i
$725$	−35.0000	−	5.00000i	−1.29987	−	0.185695i
$726$	7.00000	+	7.00000i	0.259794	+	0.259794i
$727$	−17.0000	+	17.0000i	−0.630495	+	0.630495i	−0.948192	−	0.317697i	$-0.897090\pi$
$727$	−17.0000	+	17.0000i	−0.630495	+	0.630495i	0.317697	+	0.948192i	$0.397090\pi$
$728$			16.0000i			0.592999i
$729$	1.00000			0.0370370
$730$	−20.0000	−	10.0000i	−0.740233	−	0.370117i
$731$	−10.0000	−	10.0000i	−0.369863	−	0.369863i
$732$	2.00000	−	2.00000i	0.0739221	−	0.0739221i
$733$			24.0000i			0.886460i	0.896408	+	0.443230i	$0.146168\pi$
$733$			24.0000i			0.886460i	−0.896408	+	0.443230i	$0.853832\pi$
$734$	38.0000			1.40261
$735$	10.0000	+	5.00000i	0.368856	+	0.184428i
$736$	−8.00000			−0.294884
$737$	6.00000	−	6.00000i	0.221013	−	0.221013i
$738$	−8.00000	−	8.00000i	−0.294484	−	0.294484i
$739$	3.00000	+	3.00000i	0.110357	+	0.110357i	0.760129	−	0.649772i	$-0.225136\pi$
$739$	3.00000	+	3.00000i	0.110357	+	0.110357i	−0.649772	+	0.760129i	$0.725136\pi$
$740$	−16.0000	+	32.0000i	−0.588172	+	1.17634i
$741$	20.0000	−	20.0000i	0.734718	−	0.734718i
$742$			12.0000i			0.440534i
$743$	−5.00000	−	5.00000i	−0.183432	−	0.183432i	0.609417	−	0.792850i	$-0.291403\pi$
$743$	−5.00000	−	5.00000i	−0.183432	−	0.183432i	−0.792850	+	0.609417i	$0.791403\pi$
$744$	4.00000	−	4.00000i	0.146647	−	0.146647i
$745$	−15.0000	+	5.00000i	−0.549557	+	0.183186i
$746$	−6.00000	+	6.00000i	−0.219676	+	0.219676i
$747$	−12.0000			−0.439057
$748$		−	60.0000i		−	2.19382i
$749$	−4.00000	+	4.00000i	−0.146157	+	0.146157i
$750$	9.00000	−	13.0000i	0.328634	−	0.474693i
$751$			26.0000i			0.948753i	0.880322	+	0.474377i	$0.157327\pi$
$751$			26.0000i			0.948753i	−0.880322	+	0.474377i	$0.842673\pi$
$752$	20.0000	+	20.0000i	0.729325	+	0.729325i
$753$	19.0000	+	19.0000i	0.692398	+	0.692398i
$754$	40.0000			1.45671
$755$	8.00000	−	16.0000i	0.291150	−	0.582300i
$756$	−2.00000	−	2.00000i	−0.0727393	−	0.0727393i
$757$			16.0000i			0.581530i	0.956795	+	0.290765i	$0.0939098\pi$
$757$			16.0000i			0.581530i	−0.956795	+	0.290765i	$0.906090\pi$
$758$			10.0000i			0.363216i
$759$		−	6.00000i		−	0.217786i
$760$	40.0000	+	20.0000i	1.45095	+	0.725476i
$761$		−	28.0000i		−	1.01500i	−0.861652	−	0.507500i	$-0.830570\pi$
$761$		−	28.0000i		−	1.01500i	0.861652	−	0.507500i	$-0.169430\pi$
$762$	18.0000			0.652071
$763$			6.00000i			0.217215i
$764$	−36.0000			−1.30243
$765$	−5.00000	−	15.0000i	−0.180775	−	0.542326i
$766$		−	46.0000i		−	1.66205i
$767$	20.0000	+	20.0000i	0.722158	+	0.722158i
$768$	−16.0000			−0.577350
$769$			28.0000i			1.00971i	0.863205	+	0.504853i	$0.168453\pi$
$769$			28.0000i			1.00971i	−0.863205	+	0.504853i	$0.831547\pi$
$770$	−6.00000	−	18.0000i	−0.216225	−	0.648675i
$771$	−15.0000	+	15.0000i	−0.540212	+	0.540212i
$772$	−14.0000	+	14.0000i	−0.503871	+	0.503871i
$773$	−38.0000			−1.36677			−0.683383	−	0.730061i	$-0.739492\pi$
$773$	−38.0000			−1.36677			−0.683383	+	0.730061i	$0.739492\pi$
$774$	−2.00000	−	2.00000i	−0.0718885	−	0.0718885i
$775$	8.00000	−	6.00000i	0.287368	−	0.215526i
$776$	4.00000			0.143592
$777$	8.00000	+	8.00000i	0.286998	+	0.286998i
$778$	−42.0000			−1.50577
$779$	40.0000	−	40.0000i	1.43315	−	1.43315i
$780$	−8.00000	+	16.0000i	−0.286446	+	0.572892i
$781$		0			0
$782$	−10.0000	+	10.0000i	−0.357599	+	0.357599i
$783$	−5.00000	+	5.00000i	−0.178685	+	0.178685i
$784$		−	20.0000i		−	0.714286i
$785$	18.0000	−	36.0000i	0.642448	−	1.28490i
$786$			10.0000i			0.356688i
$787$			18.0000i			0.641631i	0.947142	+	0.320815i	$0.103957\pi$
$787$			18.0000i			0.641631i	−0.947142	+	0.320815i	$0.896043\pi$
$788$	16.0000			0.569976
$789$	−7.00000	−	7.00000i	−0.249207	−	0.249207i
$790$	−8.00000	−	24.0000i	−0.284627	−	0.853882i
$791$	18.0000			0.640006
$792$		−	12.0000i		−	0.426401i
$793$	−4.00000	+	4.00000i	−0.142044	+	0.142044i
$794$	−26.0000	+	26.0000i	−0.922705	+	0.922705i
$795$	−6.00000	+	12.0000i	−0.212798	+	0.425596i
$796$	36.0000			1.27599
$797$	−30.0000			−1.06265			−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000			−1.06265			−0.531327	+	0.847167i	$0.678307\pi$
$798$	10.0000	−	10.0000i	0.353996	−	0.353996i
$799$	50.0000			1.76887
$800$	−28.0000	−	4.00000i	−0.989949	−	0.141421i
$801$	−2.00000			−0.0706665
$802$	18.0000	−	18.0000i	0.635602	−	0.635602i
$803$	−30.0000			−1.05868
$804$	−4.00000			−0.141069
$805$	−2.00000	+	4.00000i	−0.0704907	+	0.140981i
$806$	−8.00000	+	8.00000i	−0.281788	+	0.281788i
$807$	−9.00000	+	9.00000i	−0.316815	+	0.316815i
$808$	4.00000			0.140720
$809$	−6.00000			−0.210949			−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000			−0.210949			−0.105474	+	0.994422i	$0.533636\pi$
$810$	−1.00000	−	3.00000i	−0.0351364	−	0.105409i
$811$	19.0000	+	19.0000i	0.667180	+	0.667180i	0.957062	−	0.289882i	$-0.0936161\pi$
$811$	19.0000	+	19.0000i	0.667180	+	0.667180i	−0.289882	+	0.957062i	$0.593616\pi$
$812$	20.0000			0.701862
$813$		−	26.0000i		−	0.911860i
$814$			48.0000i			1.68240i
$815$	12.0000	−	24.0000i	0.420342	−	0.840683i
$816$	−20.0000	+	20.0000i	−0.700140	+	0.700140i
$817$	10.0000	−	10.0000i	0.349856	−	0.349856i
$818$	−6.00000	+	6.00000i	−0.209785	+	0.209785i
$819$	4.00000	+	4.00000i	0.139771	+	0.139771i
$820$	−16.0000	+	32.0000i	−0.558744	+	1.11749i
$821$	17.0000	−	17.0000i	0.593304	−	0.593304i	−0.345218	−	0.938522i	$-0.612195\pi$
$821$	17.0000	−	17.0000i	0.593304	−	0.593304i	0.938522	+	0.345218i	$0.112195\pi$
$822$	−26.0000			−0.906854
$823$	9.00000	+	9.00000i	0.313720	+	0.313720i	0.846349	−	0.532629i	$-0.178796\pi$
$823$	9.00000	+	9.00000i	0.313720	+	0.313720i	−0.532629	+	0.846349i	$0.678796\pi$
$824$			20.0000i			0.696733i
$825$	3.00000	−	21.0000i	0.104447	−	0.731126i
$826$	10.0000	+	10.0000i	0.347945	+	0.347945i
$827$	−4.00000			−0.139094			−0.0695468	−	0.997579i	$-0.522155\pi$
$827$	−4.00000			−0.139094			−0.0695468	+	0.997579i	$0.522155\pi$
$828$	−2.00000	+	2.00000i	−0.0695048	+	0.0695048i
$829$	−21.0000	+	21.0000i	−0.729360	+	0.729360i	−0.970492	−	0.241132i	$-0.922481\pi$
$829$	−21.0000	+	21.0000i	−0.729360	+	0.729360i	0.241132	+	0.970492i	$0.422481\pi$
$830$	12.0000	+	36.0000i	0.416526	+	1.24958i
$831$			8.00000i			0.277517i
$832$	32.0000			1.10940
$833$	−25.0000	−	25.0000i	−0.866199	−	0.866199i
$834$			22.0000i			0.761798i
$835$	5.00000	+	15.0000i	0.173032	+	0.519096i
$836$	60.0000			2.07514
$837$		−	2.00000i		−	0.0691301i
$838$	14.0000			0.483622
$839$		−	18.0000i		−	0.621429i	−0.950503	−	0.310715i	$-0.899432\pi$
$839$		−	18.0000i		−	0.621429i	0.950503	−	0.310715i	$-0.100568\pi$
$840$	−4.00000	+	8.00000i	−0.138013	+	0.276026i
$841$		−	21.0000i		−	0.724138i
$842$		−	18.0000i		−	0.620321i
$843$			4.00000i			0.137767i
$844$	−18.0000	−	18.0000i	−0.619586	−	0.619586i
$845$	3.00000	−	6.00000i	0.103203	−	0.206406i
$846$	10.0000			0.343807
$847$	−7.00000	−	7.00000i	−0.240523	−	0.240523i
$848$	24.0000			0.824163
$849$			6.00000i			0.205919i
$850$	−40.0000	+	30.0000i	−1.37199	+	1.02899i
$851$	8.00000	−	8.00000i	0.274236	−	0.274236i
$852$		0			0
$853$	10.0000			0.342393			0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000			0.342393			0.171197	+	0.985237i	$0.445237\pi$
$854$	−2.00000	+	2.00000i	−0.0684386	+	0.0684386i
$855$	15.0000	−	5.00000i	0.512989	−	0.170996i
$856$	8.00000	+	8.00000i	0.273434	+	0.273434i
$857$	19.0000	+	19.0000i	0.649028	+	0.649028i	0.952758	−	0.303730i	$-0.0982322\pi$
$857$	19.0000	+	19.0000i	0.649028	+	0.649028i	−0.303730	+	0.952758i	$0.598232\pi$
$858$			24.0000i			0.819346i
$859$	−7.00000	+	7.00000i	−0.238837	+	0.238837i	−0.816368	−	0.577531i	$-0.804016\pi$
$859$	−7.00000	+	7.00000i	−0.238837	+	0.238837i	0.577531	+	0.816368i	$0.304016\pi$
$860$	−4.00000	+	8.00000i	−0.136399	+	0.272798i
$861$	8.00000	+	8.00000i	0.272639	+	0.272639i
$862$	−6.00000	−	6.00000i	−0.204361	−	0.204361i
$863$	13.0000	−	13.0000i	0.442525	−	0.442525i	−0.450335	−	0.892860i	$-0.648695\pi$
$863$	13.0000	−	13.0000i	0.442525	−	0.442525i	0.892860	+	0.450335i	$0.148695\pi$
$864$	−4.00000	+	4.00000i	−0.136083	+	0.136083i
$865$	24.0000	+	12.0000i	0.816024	+	0.408012i
$866$	6.00000			0.203888
$867$			33.0000i			1.12074i
$868$	−4.00000	+	4.00000i	−0.135769	+	0.135769i
$869$	−24.0000	−	24.0000i	−0.814144	−	0.814144i
$870$	20.0000	+	10.0000i	0.678064	+	0.339032i
$871$	8.00000			0.271070
$872$	12.0000			0.406371
$873$	1.00000	−	1.00000i	0.0338449	−	0.0338449i
$874$	−10.0000	−	10.0000i	−0.338255	−	0.338255i
$875$	−9.00000	+	13.0000i	−0.304256	+	0.439480i
$876$	10.0000	+	10.0000i	0.337869	+	0.337869i
$877$	−2.00000			−0.0675352			−0.0337676	−	0.999430i	$-0.510751\pi$
$877$	−2.00000			−0.0675352			−0.0337676	+	0.999430i	$0.510751\pi$
$878$	22.0000	+	22.0000i	0.742464	+	0.742464i
$879$	−6.00000			−0.202375
$880$	−36.0000	+	12.0000i	−1.21356	+	0.404520i
$881$	6.00000			0.202145			0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000			0.202145			0.101073	+	0.994879i	$0.467773\pi$
$882$	−5.00000	−	5.00000i	−0.168359	−	0.168359i
$883$	−36.0000			−1.21150			−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000			−1.21150			−0.605748	+	0.795656i	$0.707126\pi$
$884$	40.0000	−	40.0000i	1.34535	−	1.34535i
$885$	5.00000	+	15.0000i	0.168073	+	0.504219i
$886$	10.0000	+	10.0000i	0.335957	+	0.335957i
$887$	−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	$0.433878\pi$
$888$	16.0000	−	16.0000i	0.536925	−	0.536925i
$889$	−18.0000			−0.603701
$890$	2.00000	+	6.00000i	0.0670402	+	0.201120i
$891$	−3.00000	−	3.00000i	−0.100504	−	0.100504i
$892$	−6.00000	−	6.00000i	−0.200895	−	0.200895i
$893$			50.0000i			1.67319i
$894$	10.0000			0.334450
$895$	−51.0000	+	17.0000i	−1.70474	+	0.568247i
$896$	16.0000			0.534522
$897$	4.00000	−	4.00000i	0.133556	−	0.133556i
$898$	12.0000	+	12.0000i	0.400445	+	0.400445i
$899$	10.0000	+	10.0000i	0.333519	+	0.333519i
$900$	−8.00000	+	6.00000i	−0.266667	+	0.200000i
$901$	30.0000	−	30.0000i	0.999445	−	0.999445i
$902$			48.0000i			1.59823i
$903$	2.00000	+	2.00000i	0.0665558	+	0.0665558i
$904$		−	36.0000i		−	1.19734i
$905$	7.00000	+	21.0000i	0.232688	+	0.698064i
$906$	−8.00000	+	8.00000i	−0.265782	+	0.265782i
$907$	−20.0000			−0.664089			−0.332045	−	0.943264i	$-0.607738\pi$
$907$	−20.0000			−0.664089			−0.332045	+	0.943264i	$0.607738\pi$
$908$	12.0000			0.398234
$909$	1.00000	−	1.00000i	0.0331679	−	0.0331679i
$910$	8.00000	−	16.0000i	0.265197	−	0.530395i
$911$			30.0000i			0.993944i	0.867766	+	0.496972i	$0.165555\pi$
$911$			30.0000i			0.993944i	−0.867766	+	0.496972i	$0.834445\pi$
$912$	−20.0000	−	20.0000i	−0.662266	−	0.662266i
$913$	36.0000	+	36.0000i	1.19143	+	1.19143i
$914$	−50.0000			−1.65385
$915$	−3.00000	+	1.00000i	−0.0991769	+	0.0330590i
$916$	−18.0000	+	18.0000i	−0.594737	+	0.594737i
$917$		−	10.0000i		−	0.330229i
$918$			10.0000i			0.330049i
$919$			34.0000i			1.12156i	0.827966	+	0.560778i	$0.189498\pi$
$919$			34.0000i			1.12156i	−0.827966	+	0.560778i	$0.810502\pi$
$920$	8.00000	+	4.00000i	0.263752	+	0.131876i
$921$		−	26.0000i		−	0.856729i
$922$	−58.0000			−1.91013
$923$		0			0
$924$			12.0000i			0.394771i
$925$	32.0000	−	24.0000i	1.05215	−	0.789115i
$926$		−	26.0000i		−	0.854413i
$927$	5.00000	+	5.00000i	0.164222	+	0.164222i
$928$		−	40.0000i		−	1.31306i
$929$			36.0000i			1.18112i	0.806993	+	0.590561i	$0.201093\pi$
$929$			36.0000i			1.18112i	−0.806993	+	0.590561i	$0.798907\pi$
$930$	−6.00000	+	2.00000i	−0.196748	+	0.0655826i
$931$	25.0000	−	25.0000i	0.819342	−	0.819342i
$932$	10.0000	+	10.0000i	0.327561	+	0.327561i
$933$	−24.0000			−0.785725
$934$	−6.00000	−	6.00000i	−0.196326	−	0.196326i
$935$	−30.0000	+	60.0000i	−0.981105	+	1.96221i
$936$	8.00000	−	8.00000i	0.261488	−	0.261488i
$937$	17.0000	+	17.0000i	0.555366	+	0.555366i	0.927985	−	0.372619i	$-0.121540\pi$
$937$	17.0000	+	17.0000i	0.555366	+	0.555366i	−0.372619	+	0.927985i	$0.621540\pi$
$938$	4.00000			0.130605
$939$	−9.00000	+	9.00000i	−0.293704	+	0.293704i
$940$	−10.0000	−	30.0000i	−0.326164	−	0.978492i
$941$	9.00000	+	9.00000i	0.293392	+	0.293392i	0.838419	−	0.545027i	$-0.183481\pi$
$941$	9.00000	+	9.00000i	0.293392	+	0.293392i	−0.545027	+	0.838419i	$0.683481\pi$
$942$	−18.0000	+	18.0000i	−0.586472	+	0.586472i
$943$	8.00000	−	8.00000i	0.260516	−	0.260516i
$944$	20.0000	−	20.0000i	0.650945	−	0.650945i
$945$	1.00000	+	3.00000i	0.0325300	+	0.0975900i
$946$			12.0000i			0.390154i
$947$		−	18.0000i		−	0.584921i	−0.956278	−	0.292461i	$-0.905526\pi$
$947$		−	18.0000i		−	0.584921i	0.956278	−	0.292461i	$-0.0944741\pi$
$948$			16.0000i			0.519656i
$949$	−20.0000	−	20.0000i	−0.649227	−	0.649227i
$950$	−30.0000	−	40.0000i	−0.973329	−	1.29777i
$951$	30.0000			0.972817
$952$	20.0000	−	20.0000i	0.648204	−	0.648204i
$953$	−5.00000	+	5.00000i	−0.161966	+	0.161966i	−0.783437	−	0.621471i	$-0.786535\pi$
$953$	−5.00000	+	5.00000i	−0.161966	+	0.161966i	0.621471	+	0.783437i	$0.286535\pi$
$954$	6.00000	−	6.00000i	0.194257	−	0.194257i
$955$	36.0000	+	18.0000i	1.16493	+	0.582466i
$956$		−	16.0000i		−	0.517477i
$957$	30.0000			0.969762
$958$	8.00000	−	8.00000i	0.258468	−	0.258468i
$959$	26.0000			0.839584
$960$	16.0000	+	8.00000i	0.516398	+	0.258199i
$961$	27.0000			0.870968
$962$	−32.0000	+	32.0000i	−1.03172	+	1.03172i
$963$	4.00000			0.128898
$964$			28.0000i			0.901819i
$965$	21.0000	−	7.00000i	0.676014	−	0.225338i
$966$	2.00000	−	2.00000i	0.0643489	−	0.0643489i
$967$	27.0000	−	27.0000i	0.868261	−	0.868261i	−0.124018	−	0.992280i	$-0.539578\pi$
$967$	27.0000	−	27.0000i	0.868261	−	0.868261i	0.992280	+	0.124018i	$0.0395782\pi$
$968$	−14.0000	+	14.0000i	−0.449977	+	0.449977i
$969$	−50.0000			−1.60623
$970$	−4.00000	−	2.00000i	−0.128432	−	0.0642161i
$971$	9.00000	+	9.00000i	0.288824	+	0.288824i	0.836615	−	0.547791i	$-0.184531\pi$
$971$	9.00000	+	9.00000i	0.288824	+	0.288824i	−0.547791	+	0.836615i	$0.684531\pi$
$972$			2.00000i			0.0641500i
$973$		−	22.0000i		−	0.705288i
$974$			30.0000i			0.961262i
$975$	16.0000	−	12.0000i	0.512410	−	0.384308i
$976$	4.00000	+	4.00000i	0.128037	+	0.128037i
$977$	−13.0000	+	13.0000i	−0.415907	+	0.415907i	−0.883790	−	0.467883i	$-0.845017\pi$
$977$	−13.0000	+	13.0000i	−0.415907	+	0.415907i	0.467883	+	0.883790i	$0.345017\pi$
$978$	−12.0000	+	12.0000i	−0.383718	+	0.383718i
$979$	6.00000	+	6.00000i	0.191761	+	0.191761i
$980$	−10.0000	+	20.0000i	−0.319438	+	0.638877i
$981$	3.00000	−	3.00000i	0.0957826	−	0.0957826i
$982$	−18.0000			−0.574403
$983$	7.00000	+	7.00000i	0.223265	+	0.223265i	0.809872	−	0.586607i	$-0.199537\pi$
$983$	7.00000	+	7.00000i	0.223265	+	0.223265i	−0.586607	+	0.809872i	$0.699537\pi$
$984$	16.0000	−	16.0000i	0.510061	−	0.510061i
$985$	−16.0000	−	8.00000i	−0.509802	−	0.254901i
$986$	−50.0000	−	50.0000i	−1.59232	−	1.59232i
$987$	−10.0000			−0.318304
$988$	40.0000	+	40.0000i	1.27257	+	1.27257i
$989$	2.00000	−	2.00000i	0.0635963	−	0.0635963i
$990$	−6.00000	+	12.0000i	−0.190693	+	0.381385i
$991$			42.0000i			1.33417i	0.744980	+	0.667087i	$0.232459\pi$
$991$			42.0000i			1.33417i	−0.744980	+	0.667087i	$0.767541\pi$
$992$	8.00000	+	8.00000i	0.254000	+	0.254000i
$993$	21.0000	+	21.0000i	0.666415	+	0.666415i
$994$		0			0
$995$	−36.0000	−	18.0000i	−1.14128	−	0.570638i
$996$		−	24.0000i		−	0.760469i
$997$		−	36.0000i		−	1.14013i	−0.821599	−	0.570066i	$-0.806918\pi$
$997$		−	36.0000i		−	1.14013i	0.821599	−	0.570066i	$-0.193082\pi$
$998$	42.0000			1.32949
$999$		−	8.00000i		−	0.253109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.y.a.163.1	✓	2
3.2	odd	2		720.2.z.b.163.1		2
4.3	odd	2		960.2.y.b.943.1		2
5.2	odd	4		240.2.bc.b.67.1	yes	2
8.3	odd	2		1920.2.y.b.223.1		2
8.5	even	2		1920.2.y.f.223.1		2
15.2	even	4		720.2.bd.c.307.1		2
16.3	odd	4		1920.2.bc.c.1183.1		2
16.5	even	4		960.2.bc.c.463.1		2
16.11	odd	4		240.2.bc.b.43.1	yes	2
16.13	even	4		1920.2.bc.d.1183.1		2
20.7	even	4		960.2.bc.c.367.1		2
40.27	even	4		1920.2.bc.d.607.1		2
40.37	odd	4		1920.2.bc.c.607.1		2
48.11	even	4		720.2.bd.c.523.1		2
80.27	even	4	inner	240.2.y.a.187.1	yes	2
80.37	odd	4		960.2.y.b.847.1		2
80.67	even	4		1920.2.y.f.1567.1		2
80.77	odd	4		1920.2.y.b.1567.1		2
240.107	odd	4		720.2.z.b.667.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.a.163.1	✓	2	1.1	even	1	trivial
240.2.y.a.187.1	yes	2	80.27	even	4	inner
240.2.bc.b.43.1	yes	2	16.11	odd	4
240.2.bc.b.67.1	yes	2	5.2	odd	4
720.2.z.b.163.1		2	3.2	odd	2
720.2.z.b.667.1		2	240.107	odd	4
720.2.bd.c.307.1		2	15.2	even	4
720.2.bd.c.523.1		2	48.11	even	4
960.2.y.b.847.1		2	80.37	odd	4
960.2.y.b.943.1		2	4.3	odd	2
960.2.bc.c.367.1		2	20.7	even	4
960.2.bc.c.463.1		2	16.5	even	4
1920.2.y.b.223.1		2	8.3	odd	2
1920.2.y.b.1567.1		2	80.77	odd	4
1920.2.y.f.223.1		2	8.5	even	2
1920.2.y.f.1567.1		2	80.67	even	4
1920.2.bc.c.607.1		2	40.37	odd	4
1920.2.bc.c.1183.1		2	16.3	odd	4
1920.2.bc.d.607.1		2	40.27	even	4
1920.2.bc.d.1183.1		2	16.13	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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} -1.00000 q^{3} -2.00000i q^{4} +(-1.00000 + 2.00000i) q^{5} +(1.00000 - 1.00000i) q^{6} +(-1.00000 + 1.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} -1.00000 q^{3} -2.00000i q^{4} +(-1.00000 + 2.00000i) q^{5} +(1.00000 - 1.00000i) q^{6} +(-1.00000 + 1.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +1.00000 q^{9} +(-1.00000 - 3.00000i) q^{10} +(-3.00000 - 3.00000i) q^{11} +2.00000i q^{12} -4.00000i q^{13} -2.00000i q^{14} +(1.00000 - 2.00000i) q^{15} -4.00000 q^{16} +(-5.00000 + 5.00000i) q^{17} +(-1.00000 + 1.00000i) q^{18} +(-5.00000 - 5.00000i) q^{19} +(4.00000 + 2.00000i) q^{20} +(1.00000 - 1.00000i) q^{21} +6.00000 q^{22} +(-1.00000 - 1.00000i) q^{23} +(-2.00000 - 2.00000i) q^{24} +(-3.00000 - 4.00000i) q^{25} +(4.00000 + 4.00000i) q^{26} -1.00000 q^{27} +(2.00000 + 2.00000i) q^{28} +(5.00000 - 5.00000i) q^{29} +(1.00000 + 3.00000i) q^{30} +2.00000i q^{31} +(4.00000 - 4.00000i) q^{32} +(3.00000 + 3.00000i) q^{33} -10.0000i q^{34} +(-1.00000 - 3.00000i) q^{35} -2.00000i q^{36} +8.00000i q^{37} +10.0000 q^{38} +4.00000i q^{39} +(-6.00000 + 2.00000i) q^{40} +8.00000i q^{41} +2.00000i q^{42} +2.00000i q^{43} +(-6.00000 + 6.00000i) q^{44} +(-1.00000 + 2.00000i) q^{45} +2.00000 q^{46} +(-5.00000 - 5.00000i) q^{47} +4.00000 q^{48} +5.00000i q^{49} +(7.00000 + 1.00000i) q^{50} +(5.00000 - 5.00000i) q^{51} -8.00000 q^{52} -6.00000 q^{53} +(1.00000 - 1.00000i) q^{54} +(9.00000 - 3.00000i) q^{55} -4.00000 q^{56} +(5.00000 + 5.00000i) q^{57} +10.0000i q^{58} +(-5.00000 + 5.00000i) q^{59} +(-4.00000 - 2.00000i) q^{60} +(-1.00000 - 1.00000i) q^{61} +(-2.00000 - 2.00000i) q^{62} +(-1.00000 + 1.00000i) q^{63} +8.00000i q^{64} +(8.00000 + 4.00000i) q^{65} -6.00000 q^{66} +2.00000i q^{67} +(10.0000 + 10.0000i) q^{68} +(1.00000 + 1.00000i) q^{69} +(4.00000 + 2.00000i) q^{70} +(2.00000 + 2.00000i) q^{72} +(5.00000 - 5.00000i) q^{73} +(-8.00000 - 8.00000i) q^{74} +(3.00000 + 4.00000i) q^{75} +(-10.0000 + 10.0000i) q^{76} +6.00000 q^{77} +(-4.00000 - 4.00000i) q^{78} +8.00000 q^{79} +(4.00000 - 8.00000i) q^{80} +1.00000 q^{81} +(-8.00000 - 8.00000i) q^{82} -12.0000 q^{83} +(-2.00000 - 2.00000i) q^{84} +(-5.00000 - 15.0000i) q^{85} +(-2.00000 - 2.00000i) q^{86} +(-5.00000 + 5.00000i) q^{87} -12.0000i q^{88} -2.00000 q^{89} +(-1.00000 - 3.00000i) q^{90} +(4.00000 + 4.00000i) q^{91} +(-2.00000 + 2.00000i) q^{92} -2.00000i q^{93} +10.0000 q^{94} +(15.0000 - 5.00000i) q^{95} +(-4.00000 + 4.00000i) q^{96} +(1.00000 - 1.00000i) q^{97} +(-5.00000 - 5.00000i) q^{98} +(-3.00000 - 3.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} + 2 q^{9} - 2 q^{10} - 6 q^{11} + 2 q^{15} - 8 q^{16} - 10 q^{17} - 2 q^{18} - 10 q^{19} + 8 q^{20} + 2 q^{21} + 12 q^{22} - 2 q^{23} - 4 q^{24} - 6 q^{25} + 8 q^{26} - 2 q^{27} + 4 q^{28} + 10 q^{29} + 2 q^{30} + 8 q^{32} + 6 q^{33} - 2 q^{35} + 20 q^{38} - 12 q^{40} - 12 q^{44} - 2 q^{45} + 4 q^{46} - 10 q^{47} + 8 q^{48} + 14 q^{50} + 10 q^{51} - 16 q^{52} - 12 q^{53} + 2 q^{54} + 18 q^{55} - 8 q^{56} + 10 q^{57} - 10 q^{59} - 8 q^{60} - 2 q^{61} - 4 q^{62} - 2 q^{63} + 16 q^{65} - 12 q^{66} + 20 q^{68} + 2 q^{69} + 8 q^{70} + 4 q^{72} + 10 q^{73} - 16 q^{74} + 6 q^{75} - 20 q^{76} + 12 q^{77} - 8 q^{78} + 16 q^{79} + 8 q^{80} + 2 q^{81} - 16 q^{82} - 24 q^{83} - 4 q^{84} - 10 q^{85} - 4 q^{86} - 10 q^{87} - 4 q^{89} - 2 q^{90} + 8 q^{91} - 4 q^{92} + 20 q^{94} + 30 q^{95} - 8 q^{96} + 2 q^{97} - 10 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 + 2 * q^9 - 2 * q^10 - 6 * q^11 + 2 * q^15 - 8 * q^16 - 10 * q^17 - 2 * q^18 - 10 * q^19 + 8 * q^20 + 2 * q^21 + 12 * q^22 - 2 * q^23 - 4 * q^24 - 6 * q^25 + 8 * q^26 - 2 * q^27 + 4 * q^28 + 10 * q^29 + 2 * q^30 + 8 * q^32 + 6 * q^33 - 2 * q^35 + 20 * q^38 - 12 * q^40 - 12 * q^44 - 2 * q^45 + 4 * q^46 - 10 * q^47 + 8 * q^48 + 14 * q^50 + 10 * q^51 - 16 * q^52 - 12 * q^53 + 2 * q^54 + 18 * q^55 - 8 * q^56 + 10 * q^57 - 10 * q^59 - 8 * q^60 - 2 * q^61 - 4 * q^62 - 2 * q^63 + 16 * q^65 - 12 * q^66 + 20 * q^68 + 2 * q^69 + 8 * q^70 + 4 * q^72 + 10 * q^73 - 16 * q^74 + 6 * q^75 - 20 * q^76 + 12 * q^77 - 8 * q^78 + 16 * q^79 + 8 * q^80 + 2 * q^81 - 16 * q^82 - 24 * q^83 - 4 * q^84 - 10 * q^85 - 4 * q^86 - 10 * q^87 - 4 * q^89 - 2 * q^90 + 8 * q^91 - 4 * q^92 + 20 * q^94 + 30 * q^95 - 8 * q^96 + 2 * q^97 - 10 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more