LMFDB - Embedded newform 170.2.g.d.89.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(89,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("170.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			89.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	170.89
Dual form			170.2.g.d.149.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.00000 - 1.00000i) q^{3} +1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +(-1.00000 - 1.00000i) q^{6} +(-1.00000 + 1.00000i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.00000 - 1.00000i) q^{3} +1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +(-1.00000 - 1.00000i) q^{6} +(-1.00000 + 1.00000i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +(2.00000 - 1.00000i) q^{10} +(1.00000 + 1.00000i) q^{11} +(-1.00000 - 1.00000i) q^{12} -4.00000i q^{13} +(-1.00000 + 1.00000i) q^{14} +(-3.00000 - 1.00000i) q^{15} +1.00000 q^{16} +(-1.00000 + 4.00000i) q^{17} -1.00000i q^{18} +6.00000i q^{19} +(2.00000 - 1.00000i) q^{20} +2.00000 q^{21} +(1.00000 + 1.00000i) q^{22} +(-1.00000 + 1.00000i) q^{23} +(-1.00000 - 1.00000i) q^{24} +(3.00000 - 4.00000i) q^{25} -4.00000i q^{26} +(-4.00000 + 4.00000i) q^{27} +(-1.00000 + 1.00000i) q^{28} +(-5.00000 + 5.00000i) q^{29} +(-3.00000 - 1.00000i) q^{30} +(-3.00000 + 3.00000i) q^{31} +1.00000 q^{32} -2.00000i q^{33} +(-1.00000 + 4.00000i) q^{34} +(-1.00000 + 3.00000i) q^{35} -1.00000i q^{36} +(1.00000 + 1.00000i) q^{37} +6.00000i q^{38} +(-4.00000 + 4.00000i) q^{39} +(2.00000 - 1.00000i) q^{40} +(-7.00000 - 7.00000i) q^{41} +2.00000 q^{42} +4.00000 q^{43} +(1.00000 + 1.00000i) q^{44} +(-1.00000 - 2.00000i) q^{45} +(-1.00000 + 1.00000i) q^{46} -6.00000i q^{47} +(-1.00000 - 1.00000i) q^{48} +5.00000i q^{49} +(3.00000 - 4.00000i) q^{50} +(5.00000 - 3.00000i) q^{51} -4.00000i q^{52} +10.0000 q^{53} +(-4.00000 + 4.00000i) q^{54} +(3.00000 + 1.00000i) q^{55} +(-1.00000 + 1.00000i) q^{56} +(6.00000 - 6.00000i) q^{57} +(-5.00000 + 5.00000i) q^{58} -10.0000i q^{59} +(-3.00000 - 1.00000i) q^{60} +(3.00000 + 3.00000i) q^{61} +(-3.00000 + 3.00000i) q^{62} +(1.00000 + 1.00000i) q^{63} +1.00000 q^{64} +(-4.00000 - 8.00000i) q^{65} -2.00000i q^{66} +2.00000i q^{67} +(-1.00000 + 4.00000i) q^{68} +2.00000 q^{69} +(-1.00000 + 3.00000i) q^{70} +(5.00000 - 5.00000i) q^{71} -1.00000i q^{72} +(-1.00000 - 1.00000i) q^{73} +(1.00000 + 1.00000i) q^{74} +(-7.00000 + 1.00000i) q^{75} +6.00000i q^{76} -2.00000 q^{77} +(-4.00000 + 4.00000i) q^{78} +(-1.00000 - 1.00000i) q^{79} +(2.00000 - 1.00000i) q^{80} +5.00000 q^{81} +(-7.00000 - 7.00000i) q^{82} -12.0000 q^{83} +2.00000 q^{84} +(2.00000 + 9.00000i) q^{85} +4.00000 q^{86} +10.0000 q^{87} +(1.00000 + 1.00000i) q^{88} +6.00000 q^{89} +(-1.00000 - 2.00000i) q^{90} +(4.00000 + 4.00000i) q^{91} +(-1.00000 + 1.00000i) q^{92} +6.00000 q^{93} -6.00000i q^{94} +(6.00000 + 12.0000i) q^{95} +(-1.00000 - 1.00000i) q^{96} +(3.00000 + 3.00000i) q^{97} +5.00000i q^{98} +(1.00000 - 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 4 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{14} - 6 q^{15} + 2 q^{16} - 2 q^{17} + 4 q^{20} + 4 q^{21} + 2 q^{22} - 2 q^{23} - 2 q^{24} + 6 q^{25} - 8 q^{27} - 2 q^{28} - 10 q^{29} - 6 q^{30} - 6 q^{31} + 2 q^{32} - 2 q^{34} - 2 q^{35} + 2 q^{37} - 8 q^{39} + 4 q^{40} - 14 q^{41} + 4 q^{42} + 8 q^{43} + 2 q^{44} - 2 q^{45} - 2 q^{46} - 2 q^{48} + 6 q^{50} + 10 q^{51} + 20 q^{53} - 8 q^{54} + 6 q^{55} - 2 q^{56} + 12 q^{57} - 10 q^{58} - 6 q^{60} + 6 q^{61} - 6 q^{62} + 2 q^{63} + 2 q^{64} - 8 q^{65} - 2 q^{68} + 4 q^{69} - 2 q^{70} + 10 q^{71} - 2 q^{73} + 2 q^{74} - 14 q^{75} - 4 q^{77} - 8 q^{78} - 2 q^{79} + 4 q^{80} + 10 q^{81} - 14 q^{82} - 24 q^{83} + 4 q^{84} + 4 q^{85} + 8 q^{86} + 20 q^{87} + 2 q^{88} + 12 q^{89} - 2 q^{90} + 8 q^{91} - 2 q^{92} + 12 q^{93} + 12 q^{95} - 2 q^{96} + 6 q^{97} + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 4 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^14 - 6 * q^15 + 2 * q^16 - 2 * q^17 + 4 * q^20 + 4 * q^21 + 2 * q^22 - 2 * q^23 - 2 * q^24 + 6 * q^25 - 8 * q^27 - 2 * q^28 - 10 * q^29 - 6 * q^30 - 6 * q^31 + 2 * q^32 - 2 * q^34 - 2 * q^35 + 2 * q^37 - 8 * q^39 + 4 * q^40 - 14 * q^41 + 4 * q^42 + 8 * q^43 + 2 * q^44 - 2 * q^45 - 2 * q^46 - 2 * q^48 + 6 * q^50 + 10 * q^51 + 20 * q^53 - 8 * q^54 + 6 * q^55 - 2 * q^56 + 12 * q^57 - 10 * q^58 - 6 * q^60 + 6 * q^61 - 6 * q^62 + 2 * q^63 + 2 * q^64 - 8 * q^65 - 2 * q^68 + 4 * q^69 - 2 * q^70 + 10 * q^71 - 2 * q^73 + 2 * q^74 - 14 * q^75 - 4 * q^77 - 8 * q^78 - 2 * q^79 + 4 * q^80 + 10 * q^81 - 14 * q^82 - 24 * q^83 + 4 * q^84 + 4 * q^85 + 8 * q^86 + 20 * q^87 + 2 * q^88 + 12 * q^89 - 2 * q^90 + 8 * q^91 - 2 * q^92 + 12 * q^93 + 12 * q^95 - 2 * q^96 + 6 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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			0.707107
$2$	1.00000			0.707107
$3$	−1.00000	−	1.00000i	−0.577350	−	0.577350i	0.356822	−	0.934172i	$-0.383860\pi$
$3$	−1.00000	−	1.00000i	−0.577350	−	0.577350i	−0.934172	+	0.356822i	$0.883860\pi$
$4$	1.00000			0.500000
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$6$	−1.00000	−	1.00000i	−0.408248	−	0.408248i
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	−0.870367	−	0.492403i	$-0.836119\pi$
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	0.492403	+	0.870367i	$0.336119\pi$
$8$	1.00000			0.353553
$9$		−	1.00000i		−	0.333333i
$10$	2.00000	−	1.00000i	0.632456	−	0.316228i
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	0.841605	−	0.540094i	$-0.181611\pi$
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	−0.540094	+	0.841605i	$0.681611\pi$
$12$	−1.00000	−	1.00000i	−0.288675	−	0.288675i
$13$		−	4.00000i		−	1.10940i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$		−	4.00000i		−	1.10940i	0.832050	−	0.554700i	$-0.187167\pi$
$14$	−1.00000	+	1.00000i	−0.267261	+	0.267261i
$15$	−3.00000	−	1.00000i	−0.774597	−	0.258199i
$16$	1.00000			0.250000
$17$	−1.00000	+	4.00000i	−0.242536	+	0.970143i
$17$	−1.00000	+	4.00000i	−0.242536	+	0.970143i
$18$		−	1.00000i		−	0.235702i
$19$			6.00000i			1.37649i	0.725476	+	0.688247i	$0.241620\pi$
$19$			6.00000i			1.37649i	−0.725476	+	0.688247i	$0.758380\pi$
$20$	2.00000	−	1.00000i	0.447214	−	0.223607i
$21$	2.00000			0.436436
$22$	1.00000	+	1.00000i	0.213201	+	0.213201i
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	0.595121	+	0.803636i	$0.297104\pi$
$24$	−1.00000	−	1.00000i	−0.204124	−	0.204124i
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$		−	4.00000i		−	0.784465i
$27$	−4.00000	+	4.00000i	−0.769800	+	0.769800i
$28$	−1.00000	+	1.00000i	−0.188982	+	0.188982i
$29$	−5.00000	+	5.00000i	−0.928477	+	0.928477i	−0.997608	−	0.0691309i	$-0.977977\pi$
$29$	−5.00000	+	5.00000i	−0.928477	+	0.928477i	0.0691309	+	0.997608i	$0.477977\pi$
$30$	−3.00000	−	1.00000i	−0.547723	−	0.182574i
$31$	−3.00000	+	3.00000i	−0.538816	+	0.538816i	−0.923181	−	0.384365i	$-0.874420\pi$
$31$	−3.00000	+	3.00000i	−0.538816	+	0.538816i	0.384365	+	0.923181i	$0.374420\pi$
$32$	1.00000			0.176777
$33$		−	2.00000i		−	0.348155i
$34$	−1.00000	+	4.00000i	−0.171499	+	0.685994i
$35$	−1.00000	+	3.00000i	−0.169031	+	0.507093i
$36$		−	1.00000i		−	0.166667i
$37$	1.00000	+	1.00000i	0.164399	+	0.164399i	0.784512	−	0.620113i	$-0.212913\pi$
$37$	1.00000	+	1.00000i	0.164399	+	0.164399i	−0.620113	+	0.784512i	$0.712913\pi$
$38$			6.00000i			0.973329i
$39$	−4.00000	+	4.00000i	−0.640513	+	0.640513i
$40$	2.00000	−	1.00000i	0.316228	−	0.158114i
$41$	−7.00000	−	7.00000i	−1.09322	−	1.09322i	−0.995183	−	0.0980332i	$-0.968745\pi$
$41$	−7.00000	−	7.00000i	−1.09322	−	1.09322i	−0.0980332	−	0.995183i	$-0.531255\pi$
$42$	2.00000			0.308607
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	1.00000	+	1.00000i	0.150756	+	0.150756i
$45$	−1.00000	−	2.00000i	−0.149071	−	0.298142i
$46$	−1.00000	+	1.00000i	−0.147442	+	0.147442i
$47$		−	6.00000i		−	0.875190i	−0.899172	−	0.437595i	$-0.855830\pi$
$47$		−	6.00000i		−	0.875190i	0.899172	−	0.437595i	$-0.144170\pi$
$48$	−1.00000	−	1.00000i	−0.144338	−	0.144338i
$49$			5.00000i			0.714286i
$50$	3.00000	−	4.00000i	0.424264	−	0.565685i
$51$	5.00000	−	3.00000i	0.700140	−	0.420084i
$52$		−	4.00000i		−	0.554700i
$53$	10.0000			1.37361			0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000			1.37361			0.686803	+	0.726844i	$0.259014\pi$
$54$	−4.00000	+	4.00000i	−0.544331	+	0.544331i
$55$	3.00000	+	1.00000i	0.404520	+	0.134840i
$56$	−1.00000	+	1.00000i	−0.133631	+	0.133631i
$57$	6.00000	−	6.00000i	0.794719	−	0.794719i
$58$	−5.00000	+	5.00000i	−0.656532	+	0.656532i
$59$		−	10.0000i		−	1.30189i	−0.759125	−	0.650945i	$-0.774373\pi$
$59$		−	10.0000i		−	1.30189i	0.759125	−	0.650945i	$-0.225627\pi$
$60$	−3.00000	−	1.00000i	−0.387298	−	0.129099i
$61$	3.00000	+	3.00000i	0.384111	+	0.384111i	0.872581	−	0.488470i	$-0.162445\pi$
$61$	3.00000	+	3.00000i	0.384111	+	0.384111i	−0.488470	+	0.872581i	$0.662445\pi$
$62$	−3.00000	+	3.00000i	−0.381000	+	0.381000i
$63$	1.00000	+	1.00000i	0.125988	+	0.125988i
$64$	1.00000			0.125000
$65$	−4.00000	−	8.00000i	−0.496139	−	0.992278i
$66$		−	2.00000i		−	0.246183i
$67$			2.00000i			0.244339i	0.992509	+	0.122169i	$0.0389851\pi$
$67$			2.00000i			0.244339i	−0.992509	+	0.122169i	$0.961015\pi$
$68$	−1.00000	+	4.00000i	−0.121268	+	0.485071i
$69$	2.00000			0.240772
$70$	−1.00000	+	3.00000i	−0.119523	+	0.358569i
$71$	5.00000	−	5.00000i	0.593391	−	0.593391i	−0.345155	−	0.938546i	$-0.612174\pi$
$71$	5.00000	−	5.00000i	0.593391	−	0.593391i	0.938546	+	0.345155i	$0.112174\pi$
$72$		−	1.00000i		−	0.117851i
$73$	−1.00000	−	1.00000i	−0.117041	−	0.117041i	0.646160	−	0.763202i	$-0.276374\pi$
$73$	−1.00000	−	1.00000i	−0.117041	−	0.117041i	−0.763202	+	0.646160i	$0.776374\pi$
$74$	1.00000	+	1.00000i	0.116248	+	0.116248i
$75$	−7.00000	+	1.00000i	−0.808290	+	0.115470i
$76$			6.00000i			0.688247i
$77$	−2.00000			−0.227921
$78$	−4.00000	+	4.00000i	−0.452911	+	0.452911i
$79$	−1.00000	−	1.00000i	−0.112509	−	0.112509i	0.648611	−	0.761120i	$-0.275350\pi$
$79$	−1.00000	−	1.00000i	−0.112509	−	0.112509i	−0.761120	+	0.648611i	$0.775350\pi$
$80$	2.00000	−	1.00000i	0.223607	−	0.111803i
$81$	5.00000			0.555556
$82$	−7.00000	−	7.00000i	−0.773021	−	0.773021i
$83$	−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			0.218218
$85$	2.00000	+	9.00000i	0.216930	+	0.976187i
$86$	4.00000			0.431331
$87$	10.0000			1.07211
$88$	1.00000	+	1.00000i	0.106600	+	0.106600i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$	−1.00000	−	2.00000i	−0.105409	−	0.210819i
$91$	4.00000	+	4.00000i	0.419314	+	0.419314i
$92$	−1.00000	+	1.00000i	−0.104257	+	0.104257i
$93$	6.00000			0.622171
$94$		−	6.00000i		−	0.618853i
$95$	6.00000	+	12.0000i	0.615587	+	1.23117i
$96$	−1.00000	−	1.00000i	−0.102062	−	0.102062i
$97$	3.00000	+	3.00000i	0.304604	+	0.304604i	0.842812	−	0.538208i	$-0.180899\pi$
$97$	3.00000	+	3.00000i	0.304604	+	0.304604i	−0.538208	+	0.842812i	$0.680899\pi$
$98$			5.00000i			0.505076i
$99$	1.00000	−	1.00000i	0.100504	−	0.100504i
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$	−14.0000			−1.39305			−0.696526	−	0.717532i	$-0.745272\pi$
$101$	−14.0000			−1.39305			−0.696526	+	0.717532i	$0.745272\pi$
$102$	5.00000	−	3.00000i	0.495074	−	0.297044i
$103$		−	14.0000i		−	1.37946i	−0.724066	−	0.689730i	$-0.757729\pi$
$103$		−	14.0000i		−	1.37946i	0.724066	−	0.689730i	$-0.242271\pi$
$104$		−	4.00000i		−	0.392232i
$105$	4.00000	−	2.00000i	0.390360	−	0.195180i
$106$	10.0000			0.971286
$107$	−13.0000	−	13.0000i	−1.25676	−	1.25676i	−0.952632	−	0.304125i	$-0.901636\pi$
$107$	−13.0000	−	13.0000i	−1.25676	−	1.25676i	−0.304125	−	0.952632i	$-0.598364\pi$
$108$	−4.00000	+	4.00000i	−0.384900	+	0.384900i
$109$	7.00000	+	7.00000i	0.670478	+	0.670478i	0.957826	−	0.287348i	$-0.0927736\pi$
$109$	7.00000	+	7.00000i	0.670478	+	0.670478i	−0.287348	+	0.957826i	$0.592774\pi$
$110$	3.00000	+	1.00000i	0.286039	+	0.0953463i
$111$		−	2.00000i		−	0.189832i
$112$	−1.00000	+	1.00000i	−0.0944911	+	0.0944911i
$113$	11.0000	−	11.0000i	1.03479	−	1.03479i	0.0354205	−	0.999372i	$-0.488723\pi$
$113$	11.0000	−	11.0000i	1.03479	−	1.03479i	0.999372	−	0.0354205i	$-0.0112770\pi$
$114$	6.00000	−	6.00000i	0.561951	−	0.561951i
$115$	−1.00000	+	3.00000i	−0.0932505	+	0.279751i
$116$	−5.00000	+	5.00000i	−0.464238	+	0.464238i
$117$	−4.00000			−0.369800
$118$		−	10.0000i		−	0.920575i
$119$	−3.00000	−	5.00000i	−0.275010	−	0.458349i
$120$	−3.00000	−	1.00000i	−0.273861	−	0.0912871i
$121$		−	9.00000i		−	0.818182i
$122$	3.00000	+	3.00000i	0.271607	+	0.271607i
$123$			14.0000i			1.26234i
$124$	−3.00000	+	3.00000i	−0.269408	+	0.269408i
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$	1.00000	+	1.00000i	0.0890871	+	0.0890871i
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	1.00000			0.0883883
$129$	−4.00000	−	4.00000i	−0.352180	−	0.352180i
$130$	−4.00000	−	8.00000i	−0.350823	−	0.701646i
$131$	−9.00000	+	9.00000i	−0.786334	+	0.786334i	−0.980891	−	0.194557i	$-0.937673\pi$
$131$	−9.00000	+	9.00000i	−0.786334	+	0.786334i	0.194557	+	0.980891i	$0.437673\pi$
$132$		−	2.00000i		−	0.174078i
$133$	−6.00000	−	6.00000i	−0.520266	−	0.520266i
$134$			2.00000i			0.172774i
$135$	−4.00000	+	12.0000i	−0.344265	+	1.03280i
$136$	−1.00000	+	4.00000i	−0.0857493	+	0.342997i
$137$			12.0000i			1.02523i	0.858619	+	0.512615i	$0.171323\pi$
$137$			12.0000i			1.02523i	−0.858619	+	0.512615i	$0.828677\pi$
$138$	2.00000			0.170251
$139$	3.00000	−	3.00000i	0.254457	−	0.254457i	−0.568338	−	0.822795i	$-0.692414\pi$
$139$	3.00000	−	3.00000i	0.254457	−	0.254457i	0.822795	+	0.568338i	$0.192414\pi$
$140$	−1.00000	+	3.00000i	−0.0845154	+	0.253546i
$141$	−6.00000	+	6.00000i	−0.505291	+	0.505291i
$142$	5.00000	−	5.00000i	0.419591	−	0.419591i
$143$	4.00000	−	4.00000i	0.334497	−	0.334497i
$144$		−	1.00000i		−	0.0833333i
$145$	−5.00000	+	15.0000i	−0.415227	+	1.24568i
$146$	−1.00000	−	1.00000i	−0.0827606	−	0.0827606i
$147$	5.00000	−	5.00000i	0.412393	−	0.412393i
$148$	1.00000	+	1.00000i	0.0821995	+	0.0821995i
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$	−7.00000	+	1.00000i	−0.571548	+	0.0816497i
$151$		−	2.00000i		−	0.162758i	−0.996683	−	0.0813788i	$-0.974068\pi$
$151$		−	2.00000i		−	0.162758i	0.996683	−	0.0813788i	$-0.0259324\pi$
$152$			6.00000i			0.486664i
$153$	4.00000	+	1.00000i	0.323381	+	0.0808452i
$154$	−2.00000			−0.161165
$155$	−3.00000	+	9.00000i	−0.240966	+	0.722897i
$156$	−4.00000	+	4.00000i	−0.320256	+	0.320256i
$157$			16.0000i			1.27694i	0.769647	+	0.638470i	$0.220432\pi$
$157$			16.0000i			1.27694i	−0.769647	+	0.638470i	$0.779568\pi$
$158$	−1.00000	−	1.00000i	−0.0795557	−	0.0795557i
$159$	−10.0000	−	10.0000i	−0.793052	−	0.793052i
$160$	2.00000	−	1.00000i	0.158114	−	0.0790569i
$161$		−	2.00000i		−	0.157622i
$162$	5.00000			0.392837
$163$	−15.0000	+	15.0000i	−1.17489	+	1.17489i	−0.193862	+	0.981029i	$0.562101\pi$
$163$	−15.0000	+	15.0000i	−1.17489	+	1.17489i	−0.981029	+	0.193862i	$0.937899\pi$
$164$	−7.00000	−	7.00000i	−0.546608	−	0.546608i
$165$	−2.00000	−	4.00000i	−0.155700	−	0.311400i
$166$	−12.0000			−0.931381
$167$	−7.00000	−	7.00000i	−0.541676	−	0.541676i	0.382344	−	0.924020i	$-0.375117\pi$
$167$	−7.00000	−	7.00000i	−0.541676	−	0.541676i	−0.924020	+	0.382344i	$0.875117\pi$
$168$	2.00000			0.154303
$169$	−3.00000			−0.230769
$170$	2.00000	+	9.00000i	0.153393	+	0.690268i
$171$	6.00000			0.458831
$172$	4.00000			0.304997
$173$	−7.00000	−	7.00000i	−0.532200	−	0.532200i	0.389026	−	0.921227i	$-0.372811\pi$
$173$	−7.00000	−	7.00000i	−0.532200	−	0.532200i	−0.921227	+	0.389026i	$0.872811\pi$
$174$	10.0000			0.758098
$175$	1.00000	+	7.00000i	0.0755929	+	0.529150i
$176$	1.00000	+	1.00000i	0.0753778	+	0.0753778i
$177$	−10.0000	+	10.0000i	−0.751646	+	0.751646i
$178$	6.00000			0.449719
$179$			6.00000i			0.448461i	0.974536	+	0.224231i	$0.0719869\pi$
$179$			6.00000i			0.448461i	−0.974536	+	0.224231i	$0.928013\pi$
$180$	−1.00000	−	2.00000i	−0.0745356	−	0.149071i
$181$	7.00000	+	7.00000i	0.520306	+	0.520306i	0.917664	−	0.397358i	$-0.130073\pi$
$181$	7.00000	+	7.00000i	0.520306	+	0.520306i	−0.397358	+	0.917664i	$0.630073\pi$
$182$	4.00000	+	4.00000i	0.296500	+	0.296500i
$183$		−	6.00000i		−	0.443533i
$184$	−1.00000	+	1.00000i	−0.0737210	+	0.0737210i
$185$	3.00000	+	1.00000i	0.220564	+	0.0735215i
$186$	6.00000			0.439941
$187$	−5.00000	+	3.00000i	−0.365636	+	0.219382i
$188$		−	6.00000i		−	0.437595i
$189$		−	8.00000i		−	0.581914i
$190$	6.00000	+	12.0000i	0.435286	+	0.870572i
$191$	−24.0000			−1.73658			−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000			−1.73658			−0.868290	+	0.496058i	$0.834780\pi$
$192$	−1.00000	−	1.00000i	−0.0721688	−	0.0721688i
$193$	−13.0000	+	13.0000i	−0.935760	+	0.935760i	−0.998058	−	0.0622972i	$-0.980157\pi$
$193$	−13.0000	+	13.0000i	−0.935760	+	0.935760i	0.0622972	+	0.998058i	$0.480157\pi$
$194$	3.00000	+	3.00000i	0.215387	+	0.215387i
$195$	−4.00000	+	12.0000i	−0.286446	+	0.859338i
$196$			5.00000i			0.357143i
$197$	−7.00000	+	7.00000i	−0.498729	+	0.498729i	−0.911042	−	0.412313i	$-0.864721\pi$
$197$	−7.00000	+	7.00000i	−0.498729	+	0.498729i	0.412313	+	0.911042i	$0.364721\pi$
$198$	1.00000	−	1.00000i	0.0710669	−	0.0710669i
$199$	17.0000	−	17.0000i	1.20510	−	1.20510i	0.232502	−	0.972596i	$-0.425309\pi$
$199$	17.0000	−	17.0000i	1.20510	−	1.20510i	0.972596	−	0.232502i	$-0.0746913\pi$
$200$	3.00000	−	4.00000i	0.212132	−	0.282843i
$201$	2.00000	−	2.00000i	0.141069	−	0.141069i
$202$	−14.0000			−0.985037
$203$		−	10.0000i		−	0.701862i
$204$	5.00000	−	3.00000i	0.350070	−	0.210042i
$205$	−21.0000	−	7.00000i	−1.46670	−	0.488901i
$206$		−	14.0000i		−	0.975426i
$207$	1.00000	+	1.00000i	0.0695048	+	0.0695048i
$208$		−	4.00000i		−	0.277350i
$209$	−6.00000	+	6.00000i	−0.415029	+	0.415029i
$210$	4.00000	−	2.00000i	0.276026	−	0.138013i
$211$	13.0000	+	13.0000i	0.894957	+	0.894957i	0.994985	−	0.100028i	$-0.0318932\pi$
$211$	13.0000	+	13.0000i	0.894957	+	0.894957i	−0.100028	+	0.994985i	$0.531893\pi$
$212$	10.0000			0.686803
$213$	−10.0000			−0.685189
$214$	−13.0000	−	13.0000i	−0.888662	−	0.888662i
$215$	8.00000	−	4.00000i	0.545595	−	0.272798i
$216$	−4.00000	+	4.00000i	−0.272166	+	0.272166i
$217$		−	6.00000i		−	0.407307i
$218$	7.00000	+	7.00000i	0.474100	+	0.474100i
$219$			2.00000i			0.135147i
$220$	3.00000	+	1.00000i	0.202260	+	0.0674200i
$221$	16.0000	+	4.00000i	1.07628	+	0.269069i
$222$		−	2.00000i		−	0.134231i
$223$	24.0000			1.60716			0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000			1.60716			0.803579	+	0.595198i	$0.202926\pi$
$224$	−1.00000	+	1.00000i	−0.0668153	+	0.0668153i
$225$	−4.00000	−	3.00000i	−0.266667	−	0.200000i
$226$	11.0000	−	11.0000i	0.731709	−	0.731709i
$227$	9.00000	−	9.00000i	0.597351	−	0.597351i	−0.342256	−	0.939607i	$-0.611191\pi$
$227$	9.00000	−	9.00000i	0.597351	−	0.597351i	0.939607	+	0.342256i	$0.111191\pi$
$228$	6.00000	−	6.00000i	0.397360	−	0.397360i
$229$		−	28.0000i		−	1.85029i	−0.379611	−	0.925146i	$-0.623942\pi$
$229$		−	28.0000i		−	1.85029i	0.379611	−	0.925146i	$-0.376058\pi$
$230$	−1.00000	+	3.00000i	−0.0659380	+	0.197814i
$231$	2.00000	+	2.00000i	0.131590	+	0.131590i
$232$	−5.00000	+	5.00000i	−0.328266	+	0.328266i
$233$	−1.00000	−	1.00000i	−0.0655122	−	0.0655122i	0.673592	−	0.739104i	$-0.264751\pi$
$233$	−1.00000	−	1.00000i	−0.0655122	−	0.0655122i	−0.739104	+	0.673592i	$0.764751\pi$
$234$	−4.00000			−0.261488
$235$	−6.00000	−	12.0000i	−0.391397	−	0.782794i
$236$		−	10.0000i		−	0.650945i
$237$			2.00000i			0.129914i
$238$	−3.00000	−	5.00000i	−0.194461	−	0.324102i
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$	−3.00000	−	1.00000i	−0.193649	−	0.0645497i
$241$	9.00000	−	9.00000i	0.579741	−	0.579741i	−0.355091	−	0.934832i	$-0.615550\pi$
$241$	9.00000	−	9.00000i	0.579741	−	0.579741i	0.934832	+	0.355091i	$0.115550\pi$
$242$		−	9.00000i		−	0.578542i
$243$	7.00000	+	7.00000i	0.449050	+	0.449050i
$244$	3.00000	+	3.00000i	0.192055	+	0.192055i
$245$	5.00000	+	10.0000i	0.319438	+	0.638877i
$246$			14.0000i			0.892607i
$247$	24.0000			1.52708
$248$	−3.00000	+	3.00000i	−0.190500	+	0.190500i
$249$	12.0000	+	12.0000i	0.760469	+	0.760469i
$250$	2.00000	−	11.0000i	0.126491	−	0.695701i
$251$	−20.0000			−1.26239			−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000			−1.26239			−0.631194	+	0.775625i	$0.717435\pi$
$252$	1.00000	+	1.00000i	0.0629941	+	0.0629941i
$253$	−2.00000			−0.125739
$254$	8.00000			0.501965
$255$	7.00000	−	11.0000i	0.438357	−	0.688847i
$256$	1.00000			0.0625000
$257$	−30.0000			−1.87135			−0.935674	−	0.352865i	$-0.885208\pi$
$257$	−30.0000			−1.87135			−0.935674	+	0.352865i	$0.885208\pi$
$258$	−4.00000	−	4.00000i	−0.249029	−	0.249029i
$259$	−2.00000			−0.124274
$260$	−4.00000	−	8.00000i	−0.248069	−	0.496139i
$261$	5.00000	+	5.00000i	0.309492	+	0.309492i
$262$	−9.00000	+	9.00000i	−0.556022	+	0.556022i
$263$	24.0000			1.47990			0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000			1.47990			0.739952	+	0.672660i	$0.234848\pi$
$264$		−	2.00000i		−	0.123091i
$265$	20.0000	−	10.0000i	1.22859	−	0.614295i
$266$	−6.00000	−	6.00000i	−0.367884	−	0.367884i
$267$	−6.00000	−	6.00000i	−0.367194	−	0.367194i
$268$			2.00000i			0.122169i
$269$	11.0000	−	11.0000i	0.670682	−	0.670682i	−0.287191	−	0.957873i	$-0.592722\pi$
$269$	11.0000	−	11.0000i	0.670682	−	0.670682i	0.957873	+	0.287191i	$0.0927216\pi$
$270$	−4.00000	+	12.0000i	−0.243432	+	0.730297i
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$	−1.00000	+	4.00000i	−0.0606339	+	0.242536i
$273$		−	8.00000i		−	0.484182i
$274$			12.0000i			0.724947i
$275$	7.00000	−	1.00000i	0.422116	−	0.0603023i
$276$	2.00000			0.120386
$277$	5.00000	+	5.00000i	0.300421	+	0.300421i	0.841178	−	0.540758i	$-0.181862\pi$
$277$	5.00000	+	5.00000i	0.300421	+	0.300421i	−0.540758	+	0.841178i	$0.681862\pi$
$278$	3.00000	−	3.00000i	0.179928	−	0.179928i
$279$	3.00000	+	3.00000i	0.179605	+	0.179605i
$280$	−1.00000	+	3.00000i	−0.0597614	+	0.179284i
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	−6.00000	+	6.00000i	−0.357295	+	0.357295i
$283$	−19.0000	+	19.0000i	−1.12943	+	1.12943i	−0.139163	+	0.990269i	$0.544441\pi$
$283$	−19.0000	+	19.0000i	−1.12943	+	1.12943i	−0.990269	+	0.139163i	$0.955559\pi$
$284$	5.00000	−	5.00000i	0.296695	−	0.296695i
$285$	6.00000	−	18.0000i	0.355409	−	1.06623i
$286$	4.00000	−	4.00000i	0.236525	−	0.236525i
$287$	14.0000			0.826394
$288$		−	1.00000i		−	0.0589256i
$289$	−15.0000	−	8.00000i	−0.882353	−	0.470588i
$290$	−5.00000	+	15.0000i	−0.293610	+	0.880830i
$291$		−	6.00000i		−	0.351726i
$292$	−1.00000	−	1.00000i	−0.0585206	−	0.0585206i
$293$			24.0000i			1.40209i	0.713115	+	0.701047i	$0.247284\pi$
$293$			24.0000i			1.40209i	−0.713115	+	0.701047i	$0.752716\pi$
$294$	5.00000	−	5.00000i	0.291606	−	0.291606i
$295$	−10.0000	−	20.0000i	−0.582223	−	1.16445i
$296$	1.00000	+	1.00000i	0.0581238	+	0.0581238i
$297$	−8.00000			−0.464207
$298$	6.00000			0.347571
$299$	4.00000	+	4.00000i	0.231326	+	0.231326i
$300$	−7.00000	+	1.00000i	−0.404145	+	0.0577350i
$301$	−4.00000	+	4.00000i	−0.230556	+	0.230556i
$302$		−	2.00000i		−	0.115087i
$303$	14.0000	+	14.0000i	0.804279	+	0.804279i
$304$			6.00000i			0.344124i
$305$	9.00000	+	3.00000i	0.515339	+	0.171780i
$306$	4.00000	+	1.00000i	0.228665	+	0.0571662i
$307$			2.00000i			0.114146i	0.998370	+	0.0570730i	$0.0181768\pi$
$307$			2.00000i			0.114146i	−0.998370	+	0.0570730i	$0.981823\pi$
$308$	−2.00000			−0.113961
$309$	−14.0000	+	14.0000i	−0.796432	+	0.796432i
$310$	−3.00000	+	9.00000i	−0.170389	+	0.511166i
$311$	17.0000	−	17.0000i	0.963982	−	0.963982i	−0.0353919	−	0.999374i	$-0.511268\pi$
$311$	17.0000	−	17.0000i	0.963982	−	0.963982i	0.999374	+	0.0353919i	$0.0112680\pi$
$312$	−4.00000	+	4.00000i	−0.226455	+	0.226455i
$313$	3.00000	−	3.00000i	0.169570	−	0.169570i	−0.617220	−	0.786790i	$-0.711741\pi$
$313$	3.00000	−	3.00000i	0.169570	−	0.169570i	0.786790	+	0.617220i	$0.211741\pi$
$314$			16.0000i			0.902932i
$315$	3.00000	+	1.00000i	0.169031	+	0.0563436i
$316$	−1.00000	−	1.00000i	−0.0562544	−	0.0562544i
$317$	5.00000	−	5.00000i	0.280828	−	0.280828i	−0.552611	−	0.833439i	$-0.686369\pi$
$317$	5.00000	−	5.00000i	0.280828	−	0.280828i	0.833439	+	0.552611i	$0.186369\pi$
$318$	−10.0000	−	10.0000i	−0.560772	−	0.560772i
$319$	−10.0000			−0.559893
$320$	2.00000	−	1.00000i	0.111803	−	0.0559017i
$321$			26.0000i			1.45118i
$322$		−	2.00000i		−	0.111456i
$323$	−24.0000	−	6.00000i	−1.33540	−	0.333849i
$324$	5.00000			0.277778
$325$	−16.0000	−	12.0000i	−0.887520	−	0.665640i
$326$	−15.0000	+	15.0000i	−0.830773	+	0.830773i
$327$		−	14.0000i		−	0.774202i
$328$	−7.00000	−	7.00000i	−0.386510	−	0.386510i
$329$	6.00000	+	6.00000i	0.330791	+	0.330791i
$330$	−2.00000	−	4.00000i	−0.110096	−	0.220193i
$331$		−	10.0000i		−	0.549650i	−0.961494	−	0.274825i	$-0.911380\pi$
$331$		−	10.0000i		−	0.549650i	0.961494	−	0.274825i	$-0.0886199\pi$
$332$	−12.0000			−0.658586
$333$	1.00000	−	1.00000i	0.0547997	−	0.0547997i
$334$	−7.00000	−	7.00000i	−0.383023	−	0.383023i
$335$	2.00000	+	4.00000i	0.109272	+	0.218543i
$336$	2.00000			0.109109
$337$	−5.00000	−	5.00000i	−0.272367	−	0.272367i	0.557685	−	0.830053i	$-0.311690\pi$
$337$	−5.00000	−	5.00000i	−0.272367	−	0.272367i	−0.830053	+	0.557685i	$0.811690\pi$
$338$	−3.00000			−0.163178
$339$	−22.0000			−1.19488
$340$	2.00000	+	9.00000i	0.108465	+	0.488094i
$341$	−6.00000			−0.324918
$342$	6.00000			0.324443
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$	4.00000			0.215666
$345$	4.00000	−	2.00000i	0.215353	−	0.107676i
$346$	−7.00000	−	7.00000i	−0.376322	−	0.376322i
$347$	25.0000	−	25.0000i	1.34207	−	1.34207i	0.448074	−	0.893997i	$-0.352110\pi$
$347$	25.0000	−	25.0000i	1.34207	−	1.34207i	0.893997	−	0.448074i	$-0.147890\pi$
$348$	10.0000			0.536056
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$	1.00000	+	7.00000i	0.0534522	+	0.374166i
$351$	16.0000	+	16.0000i	0.854017	+	0.854017i
$352$	1.00000	+	1.00000i	0.0533002	+	0.0533002i
$353$			24.0000i			1.27739i	0.769460	+	0.638696i	$0.220526\pi$
$353$			24.0000i			1.27739i	−0.769460	+	0.638696i	$0.779474\pi$
$354$	−10.0000	+	10.0000i	−0.531494	+	0.531494i
$355$	5.00000	−	15.0000i	0.265372	−	0.796117i
$356$	6.00000			0.317999
$357$	−2.00000	+	8.00000i	−0.105851	+	0.423405i
$358$			6.00000i			0.317110i
$359$			6.00000i			0.316668i	0.987386	+	0.158334i	$0.0506123\pi$
$359$			6.00000i			0.316668i	−0.987386	+	0.158334i	$0.949388\pi$
$360$	−1.00000	−	2.00000i	−0.0527046	−	0.105409i
$361$	−17.0000			−0.894737
$362$	7.00000	+	7.00000i	0.367912	+	0.367912i
$363$	−9.00000	+	9.00000i	−0.472377	+	0.472377i
$364$	4.00000	+	4.00000i	0.209657	+	0.209657i
$365$	−3.00000	−	1.00000i	−0.157027	−	0.0523424i
$366$		−	6.00000i		−	0.313625i
$367$	19.0000	−	19.0000i	0.991792	−	0.991792i	−0.00817466	−	0.999967i	$-0.502602\pi$
$367$	19.0000	−	19.0000i	0.991792	−	0.991792i	0.999967	+	0.00817466i	$0.00260210\pi$
$368$	−1.00000	+	1.00000i	−0.0521286	+	0.0521286i
$369$	−7.00000	+	7.00000i	−0.364405	+	0.364405i
$370$	3.00000	+	1.00000i	0.155963	+	0.0519875i
$371$	−10.0000	+	10.0000i	−0.519174	+	0.519174i
$372$	6.00000			0.311086
$373$		−	20.0000i		−	1.03556i	−0.855514	−	0.517780i	$-0.826758\pi$
$373$		−	20.0000i		−	1.03556i	0.855514	−	0.517780i	$-0.173242\pi$
$374$	−5.00000	+	3.00000i	−0.258544	+	0.155126i
$375$	−13.0000	+	9.00000i	−0.671317	+	0.464758i
$376$		−	6.00000i		−	0.309426i
$377$	20.0000	+	20.0000i	1.03005	+	1.03005i
$378$		−	8.00000i		−	0.411476i
$379$	−5.00000	+	5.00000i	−0.256833	+	0.256833i	−0.823765	−	0.566932i	$-0.808130\pi$
$379$	−5.00000	+	5.00000i	−0.256833	+	0.256833i	0.566932	+	0.823765i	$0.308130\pi$
$380$	6.00000	+	12.0000i	0.307794	+	0.615587i
$381$	−8.00000	−	8.00000i	−0.409852	−	0.409852i
$382$	−24.0000			−1.22795
$383$		0			0			−	1.00000i	$-0.5\pi$
$383$		0			0				1.00000i	$0.5\pi$
$384$	−1.00000	−	1.00000i	−0.0510310	−	0.0510310i
$385$	−4.00000	+	2.00000i	−0.203859	+	0.101929i
$386$	−13.0000	+	13.0000i	−0.661683	+	0.661683i
$387$		−	4.00000i		−	0.203331i
$388$	3.00000	+	3.00000i	0.152302	+	0.152302i
$389$			12.0000i			0.608424i	0.952604	+	0.304212i	$0.0983931\pi$
$389$			12.0000i			0.608424i	−0.952604	+	0.304212i	$0.901607\pi$
$390$	−4.00000	+	12.0000i	−0.202548	+	0.607644i
$391$	−3.00000	−	5.00000i	−0.151717	−	0.252861i
$392$			5.00000i			0.252538i
$393$	18.0000			0.907980
$394$	−7.00000	+	7.00000i	−0.352655	+	0.352655i
$395$	−3.00000	−	1.00000i	−0.150946	−	0.0503155i
$396$	1.00000	−	1.00000i	0.0502519	−	0.0502519i
$397$	−7.00000	+	7.00000i	−0.351320	+	0.351320i	−0.860601	−	0.509281i	$-0.829912\pi$
$397$	−7.00000	+	7.00000i	−0.351320	+	0.351320i	0.509281	+	0.860601i	$0.329912\pi$
$398$	17.0000	−	17.0000i	0.852133	−	0.852133i
$399$			12.0000i			0.600751i
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$	−19.0000	−	19.0000i	−0.948815	−	0.948815i	0.0499376	−	0.998752i	$-0.484098\pi$
$401$	−19.0000	−	19.0000i	−0.948815	−	0.948815i	−0.998752	+	0.0499376i	$0.984098\pi$
$402$	2.00000	−	2.00000i	0.0997509	−	0.0997509i
$403$	12.0000	+	12.0000i	0.597763	+	0.597763i
$404$	−14.0000			−0.696526
$405$	10.0000	−	5.00000i	0.496904	−	0.248452i
$406$		−	10.0000i		−	0.496292i
$407$			2.00000i			0.0991363i
$408$	5.00000	−	3.00000i	0.247537	−	0.148522i
$409$	−22.0000			−1.08783			−0.543915	−	0.839140i	$-0.683059\pi$
$409$	−22.0000			−1.08783			−0.543915	+	0.839140i	$0.683059\pi$
$410$	−21.0000	−	7.00000i	−1.03712	−	0.345705i
$411$	12.0000	−	12.0000i	0.591916	−	0.591916i
$412$		−	14.0000i		−	0.689730i
$413$	10.0000	+	10.0000i	0.492068	+	0.492068i
$414$	1.00000	+	1.00000i	0.0491473	+	0.0491473i
$415$	−24.0000	+	12.0000i	−1.17811	+	0.589057i
$416$		−	4.00000i		−	0.196116i
$417$	−6.00000			−0.293821
$418$	−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	$0.550208\pi$
$420$	4.00000	−	2.00000i	0.195180	−	0.0975900i
$421$	26.0000			1.26716			0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000			1.26716			0.633581	+	0.773676i	$0.281584\pi$
$422$	13.0000	+	13.0000i	0.632830	+	0.632830i
$423$	−6.00000			−0.291730
$424$	10.0000			0.485643
$425$	13.0000	+	16.0000i	0.630593	+	0.776114i
$426$	−10.0000			−0.484502
$427$	−6.00000			−0.290360
$428$	−13.0000	−	13.0000i	−0.628379	−	0.628379i
$429$	−8.00000			−0.386244
$430$	8.00000	−	4.00000i	0.385794	−	0.192897i
$431$	7.00000	+	7.00000i	0.337178	+	0.337178i	0.855304	−	0.518126i	$-0.173370\pi$
$431$	7.00000	+	7.00000i	0.337178	+	0.337178i	−0.518126	+	0.855304i	$0.673370\pi$
$432$	−4.00000	+	4.00000i	−0.192450	+	0.192450i
$433$	−30.0000			−1.44171			−0.720854	−	0.693087i	$-0.756250\pi$
$433$	−30.0000			−1.44171			−0.720854	+	0.693087i	$0.756250\pi$
$434$		−	6.00000i		−	0.288009i
$435$	20.0000	−	10.0000i	0.958927	−	0.479463i
$436$	7.00000	+	7.00000i	0.335239	+	0.335239i
$437$	−6.00000	−	6.00000i	−0.287019	−	0.287019i
$438$			2.00000i			0.0955637i
$439$	−11.0000	+	11.0000i	−0.525001	+	0.525001i	−0.919078	−	0.394076i	$-0.871065\pi$
$439$	−11.0000	+	11.0000i	−0.525001	+	0.525001i	0.394076	+	0.919078i	$0.371065\pi$
$440$	3.00000	+	1.00000i	0.143019	+	0.0476731i
$441$	5.00000			0.238095
$442$	16.0000	+	4.00000i	0.761042	+	0.190261i
$443$			10.0000i			0.475114i	0.971374	+	0.237557i	$0.0763467\pi$
$443$			10.0000i			0.475114i	−0.971374	+	0.237557i	$0.923653\pi$
$444$		−	2.00000i		−	0.0949158i
$445$	12.0000	−	6.00000i	0.568855	−	0.284427i
$446$	24.0000			1.13643
$447$	−6.00000	−	6.00000i	−0.283790	−	0.283790i
$448$	−1.00000	+	1.00000i	−0.0472456	+	0.0472456i
$449$	5.00000	+	5.00000i	0.235965	+	0.235965i	0.815177	−	0.579212i	$-0.196640\pi$
$449$	5.00000	+	5.00000i	0.235965	+	0.235965i	−0.579212	+	0.815177i	$0.696640\pi$
$450$	−4.00000	−	3.00000i	−0.188562	−	0.141421i
$451$		−	14.0000i		−	0.659234i
$452$	11.0000	−	11.0000i	0.517396	−	0.517396i
$453$	−2.00000	+	2.00000i	−0.0939682	+	0.0939682i
$454$	9.00000	−	9.00000i	0.422391	−	0.422391i
$455$	12.0000	+	4.00000i	0.562569	+	0.187523i
$456$	6.00000	−	6.00000i	0.280976	−	0.280976i
$457$	10.0000			0.467780			0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000			0.467780			0.233890	+	0.972263i	$0.424854\pi$
$458$		−	28.0000i		−	1.30835i
$459$	−12.0000	−	20.0000i	−0.560112	−	0.933520i
$460$	−1.00000	+	3.00000i	−0.0466252	+	0.139876i
$461$			8.00000i			0.372597i	0.982493	+	0.186299i	$0.0596492\pi$
$461$			8.00000i			0.372597i	−0.982493	+	0.186299i	$0.940351\pi$
$462$	2.00000	+	2.00000i	0.0930484	+	0.0930484i
$463$		−	30.0000i		−	1.39422i	−0.716965	−	0.697109i	$-0.754469\pi$
$463$		−	30.0000i		−	1.39422i	0.716965	−	0.697109i	$-0.245531\pi$
$464$	−5.00000	+	5.00000i	−0.232119	+	0.232119i
$465$	12.0000	−	6.00000i	0.556487	−	0.278243i
$466$	−1.00000	−	1.00000i	−0.0463241	−	0.0463241i
$467$	−28.0000			−1.29569			−0.647843	−	0.761774i	$-0.724329\pi$
$467$	−28.0000			−1.29569			−0.647843	+	0.761774i	$0.724329\pi$
$468$	−4.00000			−0.184900
$469$	−2.00000	−	2.00000i	−0.0923514	−	0.0923514i
$470$	−6.00000	−	12.0000i	−0.276759	−	0.553519i
$471$	16.0000	−	16.0000i	0.737241	−	0.737241i
$472$		−	10.0000i		−	0.460287i
$473$	4.00000	+	4.00000i	0.183920	+	0.183920i
$474$			2.00000i			0.0918630i
$475$	24.0000	+	18.0000i	1.10120	+	0.825897i
$476$	−3.00000	−	5.00000i	−0.137505	−	0.229175i
$477$		−	10.0000i		−	0.457869i
$478$	16.0000			0.731823
$479$	−15.0000	+	15.0000i	−0.685367	+	0.685367i	−0.961204	−	0.275837i	$-0.911045\pi$
$479$	−15.0000	+	15.0000i	−0.685367	+	0.685367i	0.275837	+	0.961204i	$0.411045\pi$
$480$	−3.00000	−	1.00000i	−0.136931	−	0.0456435i
$481$	4.00000	−	4.00000i	0.182384	−	0.182384i
$482$	9.00000	−	9.00000i	0.409939	−	0.409939i
$483$	−2.00000	+	2.00000i	−0.0910032	+	0.0910032i
$484$		−	9.00000i		−	0.409091i
$485$	9.00000	+	3.00000i	0.408669	+	0.136223i
$486$	7.00000	+	7.00000i	0.317526	+	0.317526i
$487$	−5.00000	+	5.00000i	−0.226572	+	0.226572i	−0.811259	−	0.584687i	$-0.801217\pi$
$487$	−5.00000	+	5.00000i	−0.226572	+	0.226572i	0.584687	+	0.811259i	$0.301217\pi$
$488$	3.00000	+	3.00000i	0.135804	+	0.135804i
$489$	30.0000			1.35665
$490$	5.00000	+	10.0000i	0.225877	+	0.451754i
$491$		−	18.0000i		−	0.812329i	−0.913800	−	0.406164i	$-0.866866\pi$
$491$		−	18.0000i		−	0.812329i	0.913800	−	0.406164i	$-0.133134\pi$
$492$			14.0000i			0.631169i
$493$	−15.0000	−	25.0000i	−0.675566	−	1.12594i
$494$	24.0000			1.07981
$495$	1.00000	−	3.00000i	0.0449467	−	0.134840i
$496$	−3.00000	+	3.00000i	−0.134704	+	0.134704i
$497$			10.0000i			0.448561i
$498$	12.0000	+	12.0000i	0.537733	+	0.537733i
$499$	21.0000	+	21.0000i	0.940089	+	0.940089i	0.998304	−	0.0582150i	$-0.0185409\pi$
$499$	21.0000	+	21.0000i	0.940089	+	0.940089i	−0.0582150	+	0.998304i	$0.518541\pi$
$500$	2.00000	−	11.0000i	0.0894427	−	0.491935i
$501$			14.0000i			0.625474i
$502$	−20.0000			−0.892644
$503$	−5.00000	+	5.00000i	−0.222939	+	0.222939i	−0.809735	−	0.586796i	$-0.800389\pi$
$503$	−5.00000	+	5.00000i	−0.222939	+	0.222939i	0.586796	+	0.809735i	$0.300389\pi$
$504$	1.00000	+	1.00000i	0.0445435	+	0.0445435i
$505$	−28.0000	+	14.0000i	−1.24598	+	0.622992i
$506$	−2.00000			−0.0889108
$507$	3.00000	+	3.00000i	0.133235	+	0.133235i
$508$	8.00000			0.354943
$509$	14.0000			0.620539			0.310270	−	0.950649i	$-0.399581\pi$
$509$	14.0000			0.620539			0.310270	+	0.950649i	$0.399581\pi$
$510$	7.00000	−	11.0000i	0.309965	−	0.487088i
$511$	2.00000			0.0884748
$512$	1.00000			0.0441942
$513$	−24.0000	−	24.0000i	−1.05963	−	1.05963i
$514$	−30.0000			−1.32324
$515$	−14.0000	−	28.0000i	−0.616914	−	1.23383i
$516$	−4.00000	−	4.00000i	−0.176090	−	0.176090i
$517$	6.00000	−	6.00000i	0.263880	−	0.263880i
$518$	−2.00000			−0.0878750
$519$			14.0000i			0.614532i
$520$	−4.00000	−	8.00000i	−0.175412	−	0.350823i
$521$	−11.0000	−	11.0000i	−0.481919	−	0.481919i	0.423825	−	0.905744i	$-0.360687\pi$
$521$	−11.0000	−	11.0000i	−0.481919	−	0.481919i	−0.905744	+	0.423825i	$0.860687\pi$
$522$	5.00000	+	5.00000i	0.218844	+	0.218844i
$523$			42.0000i			1.83653i	0.395964	+	0.918266i	$0.370410\pi$
$523$			42.0000i			1.83653i	−0.395964	+	0.918266i	$0.629590\pi$
$524$	−9.00000	+	9.00000i	−0.393167	+	0.393167i
$525$	6.00000	−	8.00000i	0.261861	−	0.349149i
$526$	24.0000			1.04645
$527$	−9.00000	−	15.0000i	−0.392046	−	0.653410i
$528$		−	2.00000i		−	0.0870388i
$529$			21.0000i			0.913043i
$530$	20.0000	−	10.0000i	0.868744	−	0.434372i
$531$	−10.0000			−0.433963
$532$	−6.00000	−	6.00000i	−0.260133	−	0.260133i
$533$	−28.0000	+	28.0000i	−1.21281	+	1.21281i
$534$	−6.00000	−	6.00000i	−0.259645	−	0.259645i
$535$	−39.0000	−	13.0000i	−1.68612	−	0.562039i
$536$			2.00000i			0.0863868i
$537$	6.00000	−	6.00000i	0.258919	−	0.258919i
$538$	11.0000	−	11.0000i	0.474244	−	0.474244i
$539$	−5.00000	+	5.00000i	−0.215365	+	0.215365i
$540$	−4.00000	+	12.0000i	−0.172133	+	0.516398i
$541$	3.00000	−	3.00000i	0.128980	−	0.128980i	−0.639670	−	0.768650i	$-0.720929\pi$
$541$	3.00000	−	3.00000i	0.128980	−	0.128980i	0.768650	+	0.639670i	$0.220929\pi$
$542$	−8.00000			−0.343629
$543$		−	14.0000i		−	0.600798i
$544$	−1.00000	+	4.00000i	−0.0428746	+	0.171499i
$545$	21.0000	+	7.00000i	0.899541	+	0.299847i
$546$		−	8.00000i		−	0.342368i
$547$	3.00000	+	3.00000i	0.128271	+	0.128271i	0.768328	−	0.640057i	$-0.221089\pi$
$547$	3.00000	+	3.00000i	0.128271	+	0.128271i	−0.640057	+	0.768328i	$0.721089\pi$
$548$			12.0000i			0.512615i
$549$	3.00000	−	3.00000i	0.128037	−	0.128037i
$550$	7.00000	−	1.00000i	0.298481	−	0.0426401i
$551$	−30.0000	−	30.0000i	−1.27804	−	1.27804i
$552$	2.00000			0.0851257
$553$	2.00000			0.0850487
$554$	5.00000	+	5.00000i	0.212430	+	0.212430i
$555$	−2.00000	−	4.00000i	−0.0848953	−	0.169791i
$556$	3.00000	−	3.00000i	0.127228	−	0.127228i
$557$			20.0000i			0.847427i	0.905796	+	0.423714i	$0.139274\pi$
$557$			20.0000i			0.847427i	−0.905796	+	0.423714i	$0.860726\pi$
$558$	3.00000	+	3.00000i	0.127000	+	0.127000i
$559$		−	16.0000i		−	0.676728i
$560$	−1.00000	+	3.00000i	−0.0422577	+	0.126773i
$561$	8.00000	+	2.00000i	0.337760	+	0.0844401i
$562$		0			0
$563$	−4.00000			−0.168580			−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000			−0.168580			−0.0842900	+	0.996441i	$0.526862\pi$
$564$	−6.00000	+	6.00000i	−0.252646	+	0.252646i
$565$	11.0000	−	33.0000i	0.462773	−	1.38832i
$566$	−19.0000	+	19.0000i	−0.798630	+	0.798630i
$567$	−5.00000	+	5.00000i	−0.209980	+	0.209980i
$568$	5.00000	−	5.00000i	0.209795	−	0.209795i
$569$		−	8.00000i		−	0.335377i	−0.985840	−	0.167689i	$-0.946370\pi$
$569$		−	8.00000i		−	0.335377i	0.985840	−	0.167689i	$-0.0536304\pi$
$570$	6.00000	−	18.0000i	0.251312	−	0.753937i
$571$	25.0000	+	25.0000i	1.04622	+	1.04622i	0.998879	+	0.0473385i	$0.0150740\pi$
$571$	25.0000	+	25.0000i	1.04622	+	1.04622i	0.0473385	+	0.998879i	$0.484926\pi$
$572$	4.00000	−	4.00000i	0.167248	−	0.167248i
$573$	24.0000	+	24.0000i	1.00261	+	1.00261i
$574$	14.0000			0.584349
$575$	1.00000	+	7.00000i	0.0417029	+	0.291920i
$576$		−	1.00000i		−	0.0416667i
$577$			20.0000i			0.832611i	0.909225	+	0.416305i	$0.136675\pi$
$577$			20.0000i			0.832611i	−0.909225	+	0.416305i	$0.863325\pi$
$578$	−15.0000	−	8.00000i	−0.623918	−	0.332756i
$579$	26.0000			1.08052
$580$	−5.00000	+	15.0000i	−0.207614	+	0.622841i
$581$	12.0000	−	12.0000i	0.497844	−	0.497844i
$582$		−	6.00000i		−	0.248708i
$583$	10.0000	+	10.0000i	0.414158	+	0.414158i
$584$	−1.00000	−	1.00000i	−0.0413803	−	0.0413803i
$585$	−8.00000	+	4.00000i	−0.330759	+	0.165380i
$586$			24.0000i			0.991431i
$587$	4.00000			0.165098			0.0825488	−	0.996587i	$-0.473694\pi$
$587$	4.00000			0.165098			0.0825488	+	0.996587i	$0.473694\pi$
$588$	5.00000	−	5.00000i	0.206197	−	0.206197i
$589$	−18.0000	−	18.0000i	−0.741677	−	0.741677i
$590$	−10.0000	−	20.0000i	−0.411693	−	0.823387i
$591$	14.0000			0.575883
$592$	1.00000	+	1.00000i	0.0410997	+	0.0410997i
$593$	38.0000			1.56047			0.780236	−	0.625485i	$-0.215099\pi$
$593$	38.0000			1.56047			0.780236	+	0.625485i	$0.215099\pi$
$594$	−8.00000			−0.328244
$595$	−11.0000	−	7.00000i	−0.450956	−	0.286972i
$596$	6.00000			0.245770
$597$	−34.0000			−1.39153
$598$	4.00000	+	4.00000i	0.163572	+	0.163572i
$599$	16.0000			0.653742			0.326871	−	0.945069i	$-0.394006\pi$
$599$	16.0000			0.653742			0.326871	+	0.945069i	$0.394006\pi$
$600$	−7.00000	+	1.00000i	−0.285774	+	0.0408248i
$601$	−11.0000	−	11.0000i	−0.448699	−	0.448699i	0.446223	−	0.894922i	$-0.352769\pi$
$601$	−11.0000	−	11.0000i	−0.448699	−	0.448699i	−0.894922	+	0.446223i	$0.852769\pi$
$602$	−4.00000	+	4.00000i	−0.163028	+	0.163028i
$603$	2.00000			0.0814463
$604$		−	2.00000i		−	0.0813788i
$605$	−9.00000	−	18.0000i	−0.365902	−	0.731804i
$606$	14.0000	+	14.0000i	0.568711	+	0.568711i
$607$	−3.00000	−	3.00000i	−0.121766	−	0.121766i	0.643598	−	0.765364i	$-0.277441\pi$
$607$	−3.00000	−	3.00000i	−0.121766	−	0.121766i	−0.765364	+	0.643598i	$0.777441\pi$
$608$			6.00000i			0.243332i
$609$	−10.0000	+	10.0000i	−0.405220	+	0.405220i
$610$	9.00000	+	3.00000i	0.364399	+	0.121466i
$611$	−24.0000			−0.970936
$612$	4.00000	+	1.00000i	0.161690	+	0.0404226i
$613$		−	8.00000i		−	0.323117i	−0.986863	−	0.161558i	$-0.948348\pi$
$613$		−	8.00000i		−	0.323117i	0.986863	−	0.161558i	$-0.0516520\pi$
$614$			2.00000i			0.0807134i
$615$	14.0000	+	28.0000i	0.564534	+	1.12907i
$616$	−2.00000			−0.0805823
$617$	−5.00000	−	5.00000i	−0.201292	−	0.201292i	0.599261	−	0.800554i	$-0.295461\pi$
$617$	−5.00000	−	5.00000i	−0.201292	−	0.201292i	−0.800554	+	0.599261i	$0.795461\pi$
$618$	−14.0000	+	14.0000i	−0.563163	+	0.563163i
$619$	5.00000	+	5.00000i	0.200967	+	0.200967i	0.800414	−	0.599447i	$-0.204613\pi$
$619$	5.00000	+	5.00000i	0.200967	+	0.200967i	−0.599447	+	0.800414i	$0.704613\pi$
$620$	−3.00000	+	9.00000i	−0.120483	+	0.361449i
$621$		−	8.00000i		−	0.321029i
$622$	17.0000	−	17.0000i	0.681638	−	0.681638i
$623$	−6.00000	+	6.00000i	−0.240385	+	0.240385i
$624$	−4.00000	+	4.00000i	−0.160128	+	0.160128i
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	3.00000	−	3.00000i	0.119904	−	0.119904i
$627$	12.0000			0.479234
$628$			16.0000i			0.638470i
$629$	−5.00000	+	3.00000i	−0.199363	+	0.119618i
$630$	3.00000	+	1.00000i	0.119523	+	0.0398410i
$631$			46.0000i			1.83123i	0.402055	+	0.915616i	$0.368296\pi$
$631$			46.0000i			1.83123i	−0.402055	+	0.915616i	$0.631704\pi$
$632$	−1.00000	−	1.00000i	−0.0397779	−	0.0397779i
$633$		−	26.0000i		−	1.03341i
$634$	5.00000	−	5.00000i	0.198575	−	0.198575i
$635$	16.0000	−	8.00000i	0.634941	−	0.317470i
$636$	−10.0000	−	10.0000i	−0.396526	−	0.396526i
$637$	20.0000			0.792429
$638$	−10.0000			−0.395904
$639$	−5.00000	−	5.00000i	−0.197797	−	0.197797i
$640$	2.00000	−	1.00000i	0.0790569	−	0.0395285i
$641$	−3.00000	+	3.00000i	−0.118493	+	0.118493i	−0.763867	−	0.645374i	$-0.776702\pi$
$641$	−3.00000	+	3.00000i	−0.118493	+	0.118493i	0.645374	+	0.763867i	$0.276702\pi$
$642$			26.0000i			1.02614i
$643$	31.0000	+	31.0000i	1.22252	+	1.22252i	0.966733	+	0.255788i	$0.0823348\pi$
$643$	31.0000	+	31.0000i	1.22252	+	1.22252i	0.255788	+	0.966733i	$0.417665\pi$
$644$		−	2.00000i		−	0.0788110i
$645$	−12.0000	−	4.00000i	−0.472500	−	0.157500i
$646$	−24.0000	−	6.00000i	−0.944267	−	0.236067i
$647$			26.0000i			1.02217i	0.859532	+	0.511083i	$0.170755\pi$
$647$			26.0000i			1.02217i	−0.859532	+	0.511083i	$0.829245\pi$
$648$	5.00000			0.196419
$649$	10.0000	−	10.0000i	0.392534	−	0.392534i
$650$	−16.0000	−	12.0000i	−0.627572	−	0.470679i
$651$	−6.00000	+	6.00000i	−0.235159	+	0.235159i
$652$	−15.0000	+	15.0000i	−0.587445	+	0.587445i
$653$	29.0000	−	29.0000i	1.13486	−	1.13486i	0.145499	−	0.989358i	$-0.453521\pi$
$653$	29.0000	−	29.0000i	1.13486	−	1.13486i	0.989358	−	0.145499i	$-0.0464789\pi$
$654$		−	14.0000i		−	0.547443i
$655$	−9.00000	+	27.0000i	−0.351659	+	1.05498i
$656$	−7.00000	−	7.00000i	−0.273304	−	0.273304i
$657$	−1.00000	+	1.00000i	−0.0390137	+	0.0390137i
$658$	6.00000	+	6.00000i	0.233904	+	0.233904i
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$	−2.00000	−	4.00000i	−0.0778499	−	0.155700i
$661$			40.0000i			1.55582i	0.628376	+	0.777910i	$0.283720\pi$
$661$			40.0000i			1.55582i	−0.628376	+	0.777910i	$0.716280\pi$
$662$		−	10.0000i		−	0.388661i
$663$	−12.0000	−	20.0000i	−0.466041	−	0.776736i
$664$	−12.0000			−0.465690
$665$	−18.0000	−	6.00000i	−0.698010	−	0.232670i
$666$	1.00000	−	1.00000i	0.0387492	−	0.0387492i
$667$		−	10.0000i		−	0.387202i
$668$	−7.00000	−	7.00000i	−0.270838	−	0.270838i
$669$	−24.0000	−	24.0000i	−0.927894	−	0.927894i
$670$	2.00000	+	4.00000i	0.0772667	+	0.154533i
$671$			6.00000i			0.231627i
$672$	2.00000			0.0771517
$673$	−1.00000	+	1.00000i	−0.0385472	+	0.0385472i	−0.726118	−	0.687570i	$-0.758677\pi$
$673$	−1.00000	+	1.00000i	−0.0385472	+	0.0385472i	0.687570	+	0.726118i	$0.258677\pi$
$674$	−5.00000	−	5.00000i	−0.192593	−	0.192593i
$675$	4.00000	+	28.0000i	0.153960	+	1.07772i
$676$	−3.00000			−0.115385
$677$	17.0000	+	17.0000i	0.653363	+	0.653363i	0.953801	−	0.300438i	$-0.0971329\pi$
$677$	17.0000	+	17.0000i	0.653363	+	0.653363i	−0.300438	+	0.953801i	$0.597133\pi$
$678$	−22.0000			−0.844905
$679$	−6.00000			−0.230259
$680$	2.00000	+	9.00000i	0.0766965	+	0.345134i
$681$	−18.0000			−0.689761
$682$	−6.00000			−0.229752
$683$	−17.0000	−	17.0000i	−0.650487	−	0.650487i	0.302623	−	0.953110i	$-0.402138\pi$
$683$	−17.0000	−	17.0000i	−0.650487	−	0.650487i	−0.953110	+	0.302623i	$0.902138\pi$
$684$	6.00000			0.229416
$685$	12.0000	+	24.0000i	0.458496	+	0.916993i
$686$	−12.0000	−	12.0000i	−0.458162	−	0.458162i
$687$	−28.0000	+	28.0000i	−1.06827	+	1.06827i
$688$	4.00000			0.152499
$689$		−	40.0000i		−	1.52388i
$690$	4.00000	−	2.00000i	0.152277	−	0.0761387i
$691$	−31.0000	−	31.0000i	−1.17930	−	1.17930i	−0.979924	−	0.199372i	$-0.936110\pi$
$691$	−31.0000	−	31.0000i	−1.17930	−	1.17930i	−0.199372	−	0.979924i	$-0.563890\pi$
$692$	−7.00000	−	7.00000i	−0.266100	−	0.266100i
$693$			2.00000i			0.0759737i
$694$	25.0000	−	25.0000i	0.948987	−	0.948987i
$695$	3.00000	−	9.00000i	0.113796	−	0.341389i
$696$	10.0000			0.379049
$697$	35.0000	−	21.0000i	1.32572	−	0.795432i
$698$		0			0
$699$			2.00000i			0.0756469i
$700$	1.00000	+	7.00000i	0.0377964	+	0.264575i
$701$	2.00000			0.0755390			0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000			0.0755390			0.0377695	+	0.999286i	$0.487975\pi$
$702$	16.0000	+	16.0000i	0.603881	+	0.603881i
$703$	−6.00000	+	6.00000i	−0.226294	+	0.226294i
$704$	1.00000	+	1.00000i	0.0376889	+	0.0376889i
$705$	−6.00000	+	18.0000i	−0.225973	+	0.677919i
$706$			24.0000i			0.903252i
$707$	14.0000	−	14.0000i	0.526524	−	0.526524i
$708$	−10.0000	+	10.0000i	−0.375823	+	0.375823i
$709$	−13.0000	+	13.0000i	−0.488225	+	0.488225i	−0.907746	−	0.419521i	$-0.862198\pi$
$709$	−13.0000	+	13.0000i	−0.488225	+	0.488225i	0.419521	+	0.907746i	$0.362198\pi$
$710$	5.00000	−	15.0000i	0.187647	−	0.562940i
$711$	−1.00000	+	1.00000i	−0.0375029	+	0.0375029i
$712$	6.00000			0.224860
$713$		−	6.00000i		−	0.224702i
$714$	−2.00000	+	8.00000i	−0.0748481	+	0.299392i
$715$	4.00000	−	12.0000i	0.149592	−	0.448775i
$716$			6.00000i			0.224231i
$717$	−16.0000	−	16.0000i	−0.597531	−	0.597531i
$718$			6.00000i			0.223918i
$719$	−3.00000	+	3.00000i	−0.111881	+	0.111881i	−0.760831	−	0.648950i	$-0.775208\pi$
$719$	−3.00000	+	3.00000i	−0.111881	+	0.111881i	0.648950	+	0.760831i	$0.275208\pi$
$720$	−1.00000	−	2.00000i	−0.0372678	−	0.0745356i
$721$	14.0000	+	14.0000i	0.521387	+	0.521387i
$722$	−17.0000			−0.632674
$723$	−18.0000			−0.669427
$724$	7.00000	+	7.00000i	0.260153	+	0.260153i
$725$	5.00000	+	35.0000i	0.185695	+	1.29987i
$726$	−9.00000	+	9.00000i	−0.334021	+	0.334021i
$727$			2.00000i			0.0741759i	0.999312	+	0.0370879i	$0.0118082\pi$
$727$			2.00000i			0.0741759i	−0.999312	+	0.0370879i	$0.988192\pi$
$728$	4.00000	+	4.00000i	0.148250	+	0.148250i
$729$		−	29.0000i		−	1.07407i
$730$	−3.00000	−	1.00000i	−0.111035	−	0.0370117i
$731$	−4.00000	+	16.0000i	−0.147945	+	0.591781i
$732$		−	6.00000i		−	0.221766i
$733$	50.0000			1.84679			0.923396	−	0.383849i	$-0.125402\pi$
$733$	50.0000			1.84679			0.923396	+	0.383849i	$0.125402\pi$
$734$	19.0000	−	19.0000i	0.701303	−	0.701303i
$735$	5.00000	−	15.0000i	0.184428	−	0.553283i
$736$	−1.00000	+	1.00000i	−0.0368605	+	0.0368605i
$737$	−2.00000	+	2.00000i	−0.0736709	+	0.0736709i
$738$	−7.00000	+	7.00000i	−0.257674	+	0.257674i
$739$			14.0000i			0.514998i	0.966279	+	0.257499i	$0.0828985\pi$
$739$			14.0000i			0.514998i	−0.966279	+	0.257499i	$0.917102\pi$
$740$	3.00000	+	1.00000i	0.110282	+	0.0367607i
$741$	−24.0000	−	24.0000i	−0.881662	−	0.881662i
$742$	−10.0000	+	10.0000i	−0.367112	+	0.367112i
$743$	−19.0000	−	19.0000i	−0.697042	−	0.697042i	0.266729	−	0.963772i	$-0.414057\pi$
$743$	−19.0000	−	19.0000i	−0.697042	−	0.697042i	−0.963772	+	0.266729i	$0.914057\pi$
$744$	6.00000			0.219971
$745$	12.0000	−	6.00000i	0.439646	−	0.219823i
$746$		−	20.0000i		−	0.732252i
$747$			12.0000i			0.439057i
$748$	−5.00000	+	3.00000i	−0.182818	+	0.109691i
$749$	26.0000			0.950019
$750$	−13.0000	+	9.00000i	−0.474693	+	0.328634i
$751$	−11.0000	+	11.0000i	−0.401396	+	0.401396i	−0.878725	−	0.477329i	$-0.841605\pi$
$751$	−11.0000	+	11.0000i	−0.401396	+	0.401396i	0.477329	+	0.878725i	$0.341605\pi$
$752$		−	6.00000i		−	0.218797i
$753$	20.0000	+	20.0000i	0.728841	+	0.728841i
$754$	20.0000	+	20.0000i	0.728357	+	0.728357i
$755$	−2.00000	−	4.00000i	−0.0727875	−	0.145575i
$756$		−	8.00000i		−	0.290957i
$757$	−18.0000			−0.654221			−0.327111	−	0.944986i	$-0.606075\pi$
$757$	−18.0000			−0.654221			−0.327111	+	0.944986i	$0.606075\pi$
$758$	−5.00000	+	5.00000i	−0.181608	+	0.181608i
$759$	2.00000	+	2.00000i	0.0725954	+	0.0725954i
$760$	6.00000	+	12.0000i	0.217643	+	0.435286i
$761$	22.0000			0.797499			0.398750	−	0.917060i	$-0.369444\pi$
$761$	22.0000			0.797499			0.398750	+	0.917060i	$0.369444\pi$
$762$	−8.00000	−	8.00000i	−0.289809	−	0.289809i
$763$	−14.0000			−0.506834
$764$	−24.0000			−0.868290
$765$	9.00000	−	2.00000i	0.325396	−	0.0723102i
$766$		0			0
$767$	−40.0000			−1.44432
$768$	−1.00000	−	1.00000i	−0.0360844	−	0.0360844i
$769$	30.0000			1.08183			0.540914	−	0.841078i	$-0.318079\pi$
$769$	30.0000			1.08183			0.540914	+	0.841078i	$0.318079\pi$
$770$	−4.00000	+	2.00000i	−0.144150	+	0.0720750i
$771$	30.0000	+	30.0000i	1.08042	+	1.08042i
$772$	−13.0000	+	13.0000i	−0.467880	+	0.467880i
$773$	6.00000			0.215805			0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000			0.215805			0.107903	+	0.994161i	$0.465587\pi$
$774$		−	4.00000i		−	0.143777i
$775$	3.00000	+	21.0000i	0.107763	+	0.754342i
$776$	3.00000	+	3.00000i	0.107694	+	0.107694i
$777$	2.00000	+	2.00000i	0.0717496	+	0.0717496i
$778$			12.0000i			0.430221i
$779$	42.0000	−	42.0000i	1.50481	−	1.50481i
$780$	−4.00000	+	12.0000i	−0.143223	+	0.429669i
$781$	10.0000			0.357828
$782$	−3.00000	−	5.00000i	−0.107280	−	0.178800i
$783$		−	40.0000i		−	1.42948i
$784$			5.00000i			0.178571i
$785$	16.0000	+	32.0000i	0.571064	+	1.14213i
$786$	18.0000			0.642039
$787$	15.0000	+	15.0000i	0.534692	+	0.534692i	0.921965	−	0.387273i	$-0.126583\pi$
$787$	15.0000	+	15.0000i	0.534692	+	0.534692i	−0.387273	+	0.921965i	$0.626583\pi$
$788$	−7.00000	+	7.00000i	−0.249365	+	0.249365i
$789$	−24.0000	−	24.0000i	−0.854423	−	0.854423i
$790$	−3.00000	−	1.00000i	−0.106735	−	0.0355784i
$791$			22.0000i			0.782230i
$792$	1.00000	−	1.00000i	0.0355335	−	0.0355335i
$793$	12.0000	−	12.0000i	0.426132	−	0.426132i
$794$	−7.00000	+	7.00000i	−0.248421	+	0.248421i
$795$	−30.0000	−	10.0000i	−1.06399	−	0.354663i
$796$	17.0000	−	17.0000i	0.602549	−	0.602549i
$797$	18.0000			0.637593			0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000			0.637593			0.318796	+	0.947823i	$0.396721\pi$
$798$			12.0000i			0.424795i
$799$	24.0000	+	6.00000i	0.849059	+	0.212265i
$800$	3.00000	−	4.00000i	0.106066	−	0.141421i
$801$		−	6.00000i		−	0.212000i
$802$	−19.0000	−	19.0000i	−0.670913	−	0.670913i
$803$		−	2.00000i		−	0.0705785i
$804$	2.00000	−	2.00000i	0.0705346	−	0.0705346i
$805$	−2.00000	−	4.00000i	−0.0704907	−	0.140981i
$806$	12.0000	+	12.0000i	0.422682	+	0.422682i
$807$	−22.0000			−0.774437
$808$	−14.0000			−0.492518
$809$	−23.0000	−	23.0000i	−0.808637	−	0.808637i	0.175791	−	0.984428i	$-0.443752\pi$
$809$	−23.0000	−	23.0000i	−0.808637	−	0.808637i	−0.984428	+	0.175791i	$0.943752\pi$
$810$	10.0000	−	5.00000i	0.351364	−	0.175682i
$811$	39.0000	−	39.0000i	1.36948	−	1.36948i	0.508288	−	0.861187i	$-0.330278\pi$
$811$	39.0000	−	39.0000i	1.36948	−	1.36948i	0.861187	−	0.508288i	$-0.169722\pi$
$812$		−	10.0000i		−	0.350931i
$813$	8.00000	+	8.00000i	0.280572	+	0.280572i
$814$			2.00000i			0.0701000i
$815$	−15.0000	+	45.0000i	−0.525427	+	1.57628i
$816$	5.00000	−	3.00000i	0.175035	−	0.105021i
$817$			24.0000i			0.839654i
$818$	−22.0000			−0.769212
$819$	4.00000	−	4.00000i	0.139771	−	0.139771i
$820$	−21.0000	−	7.00000i	−0.733352	−	0.244451i
$821$	−5.00000	+	5.00000i	−0.174501	+	0.174501i	−0.788954	−	0.614453i	$-0.789377\pi$
$821$	−5.00000	+	5.00000i	−0.174501	+	0.174501i	0.614453	+	0.788954i	$0.289377\pi$
$822$	12.0000	−	12.0000i	0.418548	−	0.418548i
$823$	15.0000	−	15.0000i	0.522867	−	0.522867i	−0.395569	−	0.918436i	$-0.629453\pi$
$823$	15.0000	−	15.0000i	0.522867	−	0.522867i	0.918436	+	0.395569i	$0.129453\pi$
$824$		−	14.0000i		−	0.487713i
$825$	−8.00000	−	6.00000i	−0.278524	−	0.208893i
$826$	10.0000	+	10.0000i	0.347945	+	0.347945i
$827$	9.00000	−	9.00000i	0.312961	−	0.312961i	−0.533095	−	0.846055i	$-0.678971\pi$
$827$	9.00000	−	9.00000i	0.312961	−	0.312961i	0.846055	+	0.533095i	$0.178971\pi$
$828$	1.00000	+	1.00000i	0.0347524	+	0.0347524i
$829$	14.0000			0.486240			0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000			0.486240			0.243120	+	0.969996i	$0.421829\pi$
$830$	−24.0000	+	12.0000i	−0.833052	+	0.416526i
$831$		−	10.0000i		−	0.346896i
$832$		−	4.00000i		−	0.138675i
$833$	−20.0000	−	5.00000i	−0.692959	−	0.173240i
$834$	−6.00000			−0.207763
$835$	−21.0000	−	7.00000i	−0.726735	−	0.242245i
$836$	−6.00000	+	6.00000i	−0.207514	+	0.207514i
$837$		−	24.0000i		−	0.829561i
$838$	17.0000	+	17.0000i	0.587255	+	0.587255i
$839$	−9.00000	−	9.00000i	−0.310715	−	0.310715i	0.534472	−	0.845186i	$-0.320511\pi$
$839$	−9.00000	−	9.00000i	−0.310715	−	0.310715i	−0.845186	+	0.534472i	$0.820511\pi$
$840$	4.00000	−	2.00000i	0.138013	−	0.0690066i
$841$		−	21.0000i		−	0.724138i
$842$	26.0000			0.896019
$843$		0			0
$844$	13.0000	+	13.0000i	0.447478	+	0.447478i
$845$	−6.00000	+	3.00000i	−0.206406	+	0.103203i
$846$	−6.00000			−0.206284
$847$	9.00000	+	9.00000i	0.309244	+	0.309244i
$848$	10.0000			0.343401
$849$	38.0000			1.30416
$850$	13.0000	+	16.0000i	0.445896	+	0.548795i
$851$	−2.00000			−0.0685591
$852$	−10.0000			−0.342594
$853$	−35.0000	−	35.0000i	−1.19838	−	1.19838i	−0.974652	−	0.223725i	$-0.928178\pi$
$853$	−35.0000	−	35.0000i	−1.19838	−	1.19838i	−0.223725	−	0.974652i	$-0.571822\pi$
$854$	−6.00000			−0.205316
$855$	12.0000	−	6.00000i	0.410391	−	0.205196i
$856$	−13.0000	−	13.0000i	−0.444331	−	0.444331i
$857$	27.0000	−	27.0000i	0.922302	−	0.922302i	−0.0748894	−	0.997192i	$-0.523860\pi$
$857$	27.0000	−	27.0000i	0.922302	−	0.922302i	0.997192	+	0.0748894i	$0.0238604\pi$
$858$	−8.00000			−0.273115
$859$			6.00000i			0.204717i	0.994748	+	0.102359i	$0.0326389\pi$
$859$			6.00000i			0.204717i	−0.994748	+	0.102359i	$0.967361\pi$
$860$	8.00000	−	4.00000i	0.272798	−	0.136399i
$861$	−14.0000	−	14.0000i	−0.477119	−	0.477119i
$862$	7.00000	+	7.00000i	0.238421	+	0.238421i
$863$		−	14.0000i		−	0.476566i	−0.971196	−	0.238283i	$-0.923415\pi$
$863$		−	14.0000i		−	0.476566i	0.971196	−	0.238283i	$-0.0765845\pi$
$864$	−4.00000	+	4.00000i	−0.136083	+	0.136083i
$865$	−21.0000	−	7.00000i	−0.714021	−	0.238007i
$866$	−30.0000			−1.01944
$867$	7.00000	+	23.0000i	0.237732	+	0.781121i
$868$		−	6.00000i		−	0.203653i
$869$		−	2.00000i		−	0.0678454i
$870$	20.0000	−	10.0000i	0.678064	−	0.339032i
$871$	8.00000			0.271070
$872$	7.00000	+	7.00000i	0.237050	+	0.237050i
$873$	3.00000	−	3.00000i	0.101535	−	0.101535i
$874$	−6.00000	−	6.00000i	−0.202953	−	0.202953i
$875$	9.00000	+	13.0000i	0.304256	+	0.439480i
$876$			2.00000i			0.0675737i
$877$	21.0000	−	21.0000i	0.709120	−	0.709120i	−0.257230	−	0.966350i	$-0.582810\pi$
$877$	21.0000	−	21.0000i	0.709120	−	0.709120i	0.966350	+	0.257230i	$0.0828100\pi$
$878$	−11.0000	+	11.0000i	−0.371232	+	0.371232i
$879$	24.0000	−	24.0000i	0.809500	−	0.809500i
$880$	3.00000	+	1.00000i	0.101130	+	0.0337100i
$881$	13.0000	−	13.0000i	0.437981	−	0.437981i	−0.453351	−	0.891332i	$-0.649772\pi$
$881$	13.0000	−	13.0000i	0.437981	−	0.437981i	0.891332	+	0.453351i	$0.149772\pi$
$882$	5.00000			0.168359
$883$		−	14.0000i		−	0.471138i	−0.971858	−	0.235569i	$-0.924305\pi$
$883$		−	14.0000i		−	0.471138i	0.971858	−	0.235569i	$-0.0756953\pi$
$884$	16.0000	+	4.00000i	0.538138	+	0.134535i
$885$	−10.0000	+	30.0000i	−0.336146	+	1.00844i
$886$			10.0000i			0.335957i
$887$	17.0000	+	17.0000i	0.570804	+	0.570804i	0.932353	−	0.361549i	$-0.117752\pi$
$887$	17.0000	+	17.0000i	0.570804	+	0.570804i	−0.361549	+	0.932353i	$0.617752\pi$
$888$		−	2.00000i		−	0.0671156i
$889$	−8.00000	+	8.00000i	−0.268311	+	0.268311i
$890$	12.0000	−	6.00000i	0.402241	−	0.201120i
$891$	5.00000	+	5.00000i	0.167506	+	0.167506i
$892$	24.0000			0.803579
$893$	36.0000			1.20469
$894$	−6.00000	−	6.00000i	−0.200670	−	0.200670i
$895$	6.00000	+	12.0000i	0.200558	+	0.401116i
$896$	−1.00000	+	1.00000i	−0.0334077	+	0.0334077i
$897$		−	8.00000i		−	0.267112i
$898$	5.00000	+	5.00000i	0.166852	+	0.166852i
$899$		−	30.0000i		−	1.00056i
$900$	−4.00000	−	3.00000i	−0.133333	−	0.100000i
$901$	−10.0000	+	40.0000i	−0.333148	+	1.33259i
$902$		−	14.0000i		−	0.466149i
$903$	8.00000			0.266223
$904$	11.0000	−	11.0000i	0.365855	−	0.365855i
$905$	21.0000	+	7.00000i	0.698064	+	0.232688i
$906$	−2.00000	+	2.00000i	−0.0664455	+	0.0664455i
$907$	21.0000	−	21.0000i	0.697294	−	0.697294i	−0.266532	−	0.963826i	$-0.585878\pi$
$907$	21.0000	−	21.0000i	0.697294	−	0.697294i	0.963826	+	0.266532i	$0.0858779\pi$
$908$	9.00000	−	9.00000i	0.298675	−	0.298675i
$909$			14.0000i			0.464351i
$910$	12.0000	+	4.00000i	0.397796	+	0.132599i
$911$	7.00000	+	7.00000i	0.231920	+	0.231920i	0.813494	−	0.581574i	$-0.197563\pi$
$911$	7.00000	+	7.00000i	0.231920	+	0.231920i	−0.581574	+	0.813494i	$0.697563\pi$
$912$	6.00000	−	6.00000i	0.198680	−	0.198680i
$913$	−12.0000	−	12.0000i	−0.397142	−	0.397142i
$914$	10.0000			0.330771
$915$	−6.00000	−	12.0000i	−0.198354	−	0.396708i
$916$		−	28.0000i		−	0.925146i
$917$		−	18.0000i		−	0.594412i
$918$	−12.0000	−	20.0000i	−0.396059	−	0.660098i
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	−1.00000	+	3.00000i	−0.0329690	+	0.0989071i
$921$	2.00000	−	2.00000i	0.0659022	−	0.0659022i
$922$			8.00000i			0.263466i
$923$	−20.0000	−	20.0000i	−0.658308	−	0.658308i
$924$	2.00000	+	2.00000i	0.0657952	+	0.0657952i
$925$	7.00000	−	1.00000i	0.230159	−	0.0328798i
$926$		−	30.0000i		−	0.985861i
$927$	−14.0000			−0.459820
$928$	−5.00000	+	5.00000i	−0.164133	+	0.164133i
$929$	9.00000	+	9.00000i	0.295280	+	0.295280i	0.839162	−	0.543882i	$-0.183046\pi$
$929$	9.00000	+	9.00000i	0.295280	+	0.295280i	−0.543882	+	0.839162i	$0.683046\pi$
$930$	12.0000	−	6.00000i	0.393496	−	0.196748i
$931$	−30.0000			−0.983210
$932$	−1.00000	−	1.00000i	−0.0327561	−	0.0327561i
$933$	−34.0000			−1.11311
$934$	−28.0000			−0.916188
$935$	−7.00000	+	11.0000i	−0.228924	+	0.359738i
$936$	−4.00000			−0.130744
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$	−2.00000	−	2.00000i	−0.0653023	−	0.0653023i
$939$	−6.00000			−0.195803
$940$	−6.00000	−	12.0000i	−0.195698	−	0.391397i
$941$	19.0000	+	19.0000i	0.619382	+	0.619382i	0.945373	−	0.325991i	$-0.105698\pi$
$941$	19.0000	+	19.0000i	0.619382	+	0.619382i	−0.325991	+	0.945373i	$0.605698\pi$
$942$	16.0000	−	16.0000i	0.521308	−	0.521308i
$943$	14.0000			0.455903
$944$		−	10.0000i		−	0.325472i
$945$	−8.00000	−	16.0000i	−0.260240	−	0.520480i
$946$	4.00000	+	4.00000i	0.130051	+	0.130051i
$947$	−25.0000	−	25.0000i	−0.812391	−	0.812391i	0.172601	−	0.984992i	$-0.444783\pi$
$947$	−25.0000	−	25.0000i	−0.812391	−	0.812391i	−0.984992	+	0.172601i	$0.944783\pi$
$948$			2.00000i			0.0649570i
$949$	−4.00000	+	4.00000i	−0.129845	+	0.129845i
$950$	24.0000	+	18.0000i	0.778663	+	0.583997i
$951$	−10.0000			−0.324272
$952$	−3.00000	−	5.00000i	−0.0972306	−	0.162051i
$953$			12.0000i			0.388718i	0.980930	+	0.194359i	$0.0622627\pi$
$953$			12.0000i			0.388718i	−0.980930	+	0.194359i	$0.937737\pi$
$954$		−	10.0000i		−	0.323762i
$955$	−48.0000	+	24.0000i	−1.55324	+	0.776622i
$956$	16.0000			0.517477
$957$	10.0000	+	10.0000i	0.323254	+	0.323254i
$958$	−15.0000	+	15.0000i	−0.484628	+	0.484628i
$959$	−12.0000	−	12.0000i	−0.387500	−	0.387500i
$960$	−3.00000	−	1.00000i	−0.0968246	−	0.0322749i
$961$			13.0000i			0.419355i
$962$	4.00000	−	4.00000i	0.128965	−	0.128965i
$963$	−13.0000	+	13.0000i	−0.418919	+	0.418919i
$964$	9.00000	−	9.00000i	0.289870	−	0.289870i
$965$	−13.0000	+	39.0000i	−0.418485	+	1.25545i
$966$	−2.00000	+	2.00000i	−0.0643489	+	0.0643489i
$967$	−48.0000			−1.54358			−0.771788	−	0.635880i	$-0.780637\pi$
$967$	−48.0000			−1.54358			−0.771788	+	0.635880i	$0.780637\pi$
$968$		−	9.00000i		−	0.289271i
$969$	18.0000	+	30.0000i	0.578243	+	0.963739i
$970$	9.00000	+	3.00000i	0.288973	+	0.0963242i
$971$			38.0000i			1.21948i	0.792602	+	0.609739i	$0.208726\pi$
$971$			38.0000i			1.21948i	−0.792602	+	0.609739i	$0.791274\pi$
$972$	7.00000	+	7.00000i	0.224525	+	0.224525i
$973$			6.00000i			0.192351i
$974$	−5.00000	+	5.00000i	−0.160210	+	0.160210i
$975$	4.00000	+	28.0000i	0.128103	+	0.896718i
$976$	3.00000	+	3.00000i	0.0960277	+	0.0960277i
$977$	−10.0000			−0.319928			−0.159964	−	0.987123i	$-0.551138\pi$
$977$	−10.0000			−0.319928			−0.159964	+	0.987123i	$0.551138\pi$
$978$	30.0000			0.959294
$979$	6.00000	+	6.00000i	0.191761	+	0.191761i
$980$	5.00000	+	10.0000i	0.159719	+	0.319438i
$981$	7.00000	−	7.00000i	0.223493	−	0.223493i
$982$		−	18.0000i		−	0.574403i
$983$	21.0000	+	21.0000i	0.669796	+	0.669796i	0.957669	−	0.287873i	$-0.0929480\pi$
$983$	21.0000	+	21.0000i	0.669796	+	0.669796i	−0.287873	+	0.957669i	$0.592948\pi$
$984$			14.0000i			0.446304i
$985$	−7.00000	+	21.0000i	−0.223039	+	0.669116i
$986$	−15.0000	−	25.0000i	−0.477697	−	0.796162i
$987$		−	12.0000i		−	0.381964i
$988$	24.0000			0.763542
$989$	−4.00000	+	4.00000i	−0.127193	+	0.127193i
$990$	1.00000	−	3.00000i	0.0317821	−	0.0953463i
$991$	−3.00000	+	3.00000i	−0.0952981	+	0.0952981i	−0.753149	−	0.657850i	$-0.771466\pi$
$991$	−3.00000	+	3.00000i	−0.0952981	+	0.0952981i	0.657850	+	0.753149i	$0.271466\pi$
$992$	−3.00000	+	3.00000i	−0.0952501	+	0.0952501i
$993$	−10.0000	+	10.0000i	−0.317340	+	0.317340i
$994$			10.0000i			0.317181i
$995$	17.0000	−	51.0000i	0.538936	−	1.61681i
$996$	12.0000	+	12.0000i	0.380235	+	0.380235i
$997$	−15.0000	+	15.0000i	−0.475055	+	0.475055i	−0.903546	−	0.428491i	$-0.859045\pi$
$997$	−15.0000	+	15.0000i	−0.475055	+	0.475055i	0.428491	+	0.903546i	$0.359045\pi$
$998$	21.0000	+	21.0000i	0.664743	+	0.664743i
$999$	−8.00000			−0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.g.d.89.1	yes	2
3.2	odd	2		1530.2.n.a.1279.1		2
5.2	odd	4		850.2.h.a.701.1		2
5.3	odd	4		850.2.h.e.701.1		2
5.4	even	2		170.2.g.b.89.1	✓	2
15.14	odd	2		1530.2.n.g.1279.1		2
17.13	even	4		170.2.g.b.149.1	yes	2
51.47	odd	4		1530.2.n.g.829.1		2
85.13	odd	4		850.2.h.e.251.1		2
85.47	odd	4		850.2.h.a.251.1		2
85.64	even	4	inner	170.2.g.d.149.1	yes	2
255.149	odd	4		1530.2.n.a.829.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.g.b.89.1	✓	2	5.4	even	2
170.2.g.b.149.1	yes	2	17.13	even	4
170.2.g.d.89.1	yes	2	1.1	even	1	trivial
170.2.g.d.149.1	yes	2	85.64	even	4	inner
850.2.h.a.251.1		2	85.47	odd	4
850.2.h.a.701.1		2	5.2	odd	4
850.2.h.e.251.1		2	85.13	odd	4
850.2.h.e.701.1		2	5.3	odd	4
1530.2.n.a.829.1		2	255.149	odd	4
1530.2.n.a.1279.1		2	3.2	odd	2
1530.2.n.g.829.1		2	51.47	odd	4
1530.2.n.g.1279.1		2	15.14	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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.00000 - 1.00000i) q^{3} +1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +(-1.00000 - 1.00000i) q^{6} +(-1.00000 + 1.00000i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.00000 - 1.00000i) q^{3} +1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +(-1.00000 - 1.00000i) q^{6} +(-1.00000 + 1.00000i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +(2.00000 - 1.00000i) q^{10} +(1.00000 + 1.00000i) q^{11} +(-1.00000 - 1.00000i) q^{12} -4.00000i q^{13} +(-1.00000 + 1.00000i) q^{14} +(-3.00000 - 1.00000i) q^{15} +1.00000 q^{16} +(-1.00000 + 4.00000i) q^{17} -1.00000i q^{18} +6.00000i q^{19} +(2.00000 - 1.00000i) q^{20} +2.00000 q^{21} +(1.00000 + 1.00000i) q^{22} +(-1.00000 + 1.00000i) q^{23} +(-1.00000 - 1.00000i) q^{24} +(3.00000 - 4.00000i) q^{25} -4.00000i q^{26} +(-4.00000 + 4.00000i) q^{27} +(-1.00000 + 1.00000i) q^{28} +(-5.00000 + 5.00000i) q^{29} +(-3.00000 - 1.00000i) q^{30} +(-3.00000 + 3.00000i) q^{31} +1.00000 q^{32} -2.00000i q^{33} +(-1.00000 + 4.00000i) q^{34} +(-1.00000 + 3.00000i) q^{35} -1.00000i q^{36} +(1.00000 + 1.00000i) q^{37} +6.00000i q^{38} +(-4.00000 + 4.00000i) q^{39} +(2.00000 - 1.00000i) q^{40} +(-7.00000 - 7.00000i) q^{41} +2.00000 q^{42} +4.00000 q^{43} +(1.00000 + 1.00000i) q^{44} +(-1.00000 - 2.00000i) q^{45} +(-1.00000 + 1.00000i) q^{46} -6.00000i q^{47} +(-1.00000 - 1.00000i) q^{48} +5.00000i q^{49} +(3.00000 - 4.00000i) q^{50} +(5.00000 - 3.00000i) q^{51} -4.00000i q^{52} +10.0000 q^{53} +(-4.00000 + 4.00000i) q^{54} +(3.00000 + 1.00000i) q^{55} +(-1.00000 + 1.00000i) q^{56} +(6.00000 - 6.00000i) q^{57} +(-5.00000 + 5.00000i) q^{58} -10.0000i q^{59} +(-3.00000 - 1.00000i) q^{60} +(3.00000 + 3.00000i) q^{61} +(-3.00000 + 3.00000i) q^{62} +(1.00000 + 1.00000i) q^{63} +1.00000 q^{64} +(-4.00000 - 8.00000i) q^{65} -2.00000i q^{66} +2.00000i q^{67} +(-1.00000 + 4.00000i) q^{68} +2.00000 q^{69} +(-1.00000 + 3.00000i) q^{70} +(5.00000 - 5.00000i) q^{71} -1.00000i q^{72} +(-1.00000 - 1.00000i) q^{73} +(1.00000 + 1.00000i) q^{74} +(-7.00000 + 1.00000i) q^{75} +6.00000i q^{76} -2.00000 q^{77} +(-4.00000 + 4.00000i) q^{78} +(-1.00000 - 1.00000i) q^{79} +(2.00000 - 1.00000i) q^{80} +5.00000 q^{81} +(-7.00000 - 7.00000i) q^{82} -12.0000 q^{83} +2.00000 q^{84} +(2.00000 + 9.00000i) q^{85} +4.00000 q^{86} +10.0000 q^{87} +(1.00000 + 1.00000i) q^{88} +6.00000 q^{89} +(-1.00000 - 2.00000i) q^{90} +(4.00000 + 4.00000i) q^{91} +(-1.00000 + 1.00000i) q^{92} +6.00000 q^{93} -6.00000i q^{94} +(6.00000 + 12.0000i) q^{95} +(-1.00000 - 1.00000i) q^{96} +(3.00000 + 3.00000i) q^{97} +5.00000i q^{98} +(1.00000 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 4 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{14} - 6 q^{15} + 2 q^{16} - 2 q^{17} + 4 q^{20} + 4 q^{21} + 2 q^{22} - 2 q^{23} - 2 q^{24} + 6 q^{25} - 8 q^{27} - 2 q^{28} - 10 q^{29} - 6 q^{30} - 6 q^{31} + 2 q^{32} - 2 q^{34} - 2 q^{35} + 2 q^{37} - 8 q^{39} + 4 q^{40} - 14 q^{41} + 4 q^{42} + 8 q^{43} + 2 q^{44} - 2 q^{45} - 2 q^{46} - 2 q^{48} + 6 q^{50} + 10 q^{51} + 20 q^{53} - 8 q^{54} + 6 q^{55} - 2 q^{56} + 12 q^{57} - 10 q^{58} - 6 q^{60} + 6 q^{61} - 6 q^{62} + 2 q^{63} + 2 q^{64} - 8 q^{65} - 2 q^{68} + 4 q^{69} - 2 q^{70} + 10 q^{71} - 2 q^{73} + 2 q^{74} - 14 q^{75} - 4 q^{77} - 8 q^{78} - 2 q^{79} + 4 q^{80} + 10 q^{81} - 14 q^{82} - 24 q^{83} + 4 q^{84} + 4 q^{85} + 8 q^{86} + 20 q^{87} + 2 q^{88} + 12 q^{89} - 2 q^{90} + 8 q^{91} - 2 q^{92} + 12 q^{93} + 12 q^{95} - 2 q^{96} + 6 q^{97} + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 4 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^14 - 6 * q^15 + 2 * q^16 - 2 * q^17 + 4 * q^20 + 4 * q^21 + 2 * q^22 - 2 * q^23 - 2 * q^24 + 6 * q^25 - 8 * q^27 - 2 * q^28 - 10 * q^29 - 6 * q^30 - 6 * q^31 + 2 * q^32 - 2 * q^34 - 2 * q^35 + 2 * q^37 - 8 * q^39 + 4 * q^40 - 14 * q^41 + 4 * q^42 + 8 * q^43 + 2 * q^44 - 2 * q^45 - 2 * q^46 - 2 * q^48 + 6 * q^50 + 10 * q^51 + 20 * q^53 - 8 * q^54 + 6 * q^55 - 2 * q^56 + 12 * q^57 - 10 * q^58 - 6 * q^60 + 6 * q^61 - 6 * q^62 + 2 * q^63 + 2 * q^64 - 8 * q^65 - 2 * q^68 + 4 * q^69 - 2 * q^70 + 10 * q^71 - 2 * q^73 + 2 * q^74 - 14 * q^75 - 4 * q^77 - 8 * q^78 - 2 * q^79 + 4 * q^80 + 10 * q^81 - 14 * q^82 - 24 * q^83 + 4 * q^84 + 4 * q^85 + 8 * q^86 + 20 * q^87 + 2 * q^88 + 12 * q^89 - 2 * q^90 + 8 * q^91 - 2 * q^92 + 12 * q^93 + 12 * q^95 - 2 * q^96 + 6 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more