LMFDB - Embedded newform 1734.2.f.b.1483.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1734,2,Mod(829,1734)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1734, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1734.829"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1734 = 2 \cdot 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1734.f (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-4,0,0,0,0,0,0,0,0,-8,0,0,4,0,-4,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(21)] == traces)

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

Self dual:	no
Analytic conductor:	$13.8460597105$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 102)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1483.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1734.1483
Dual form			1734.2.f.b.829.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(0.707107 + 0.707107i) q^{6} +(1.41421 + 1.41421i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(0.707107 - 0.707107i) q^{12} -2.00000 q^{13} +(1.41421 - 1.41421i) q^{14} +1.00000 q^{16} -1.00000 q^{18} -4.00000i q^{19} -2.00000 q^{21} +(4.24264 + 4.24264i) q^{23} +(-0.707107 - 0.707107i) q^{24} +5.00000i q^{25} +2.00000i q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.41421 - 1.41421i) q^{28} +(7.07107 - 7.07107i) q^{31} -1.00000i q^{32} +1.00000i q^{36} +(-5.65685 + 5.65685i) q^{37} -4.00000 q^{38} +(1.41421 - 1.41421i) q^{39} +(4.24264 + 4.24264i) q^{41} +2.00000i q^{42} +4.00000i q^{43} +(4.24264 - 4.24264i) q^{46} -12.0000 q^{47} +(-0.707107 + 0.707107i) q^{48} -3.00000i q^{49} +5.00000 q^{50} +2.00000 q^{52} +6.00000i q^{53} +(0.707107 - 0.707107i) q^{54} +(-1.41421 + 1.41421i) q^{56} +(2.82843 + 2.82843i) q^{57} +12.0000i q^{59} +(5.65685 + 5.65685i) q^{61} +(-7.07107 - 7.07107i) q^{62} +(1.41421 - 1.41421i) q^{63} -1.00000 q^{64} -4.00000 q^{67} -6.00000 q^{69} +(-4.24264 + 4.24264i) q^{71} +1.00000 q^{72} +(1.41421 - 1.41421i) q^{73} +(5.65685 + 5.65685i) q^{74} +(-3.53553 - 3.53553i) q^{75} +4.00000i q^{76} +(-1.41421 - 1.41421i) q^{78} +(7.07107 + 7.07107i) q^{79} -1.00000 q^{81} +(4.24264 - 4.24264i) q^{82} +12.0000i q^{83} +2.00000 q^{84} +4.00000 q^{86} +18.0000 q^{89} +(-2.82843 - 2.82843i) q^{91} +(-4.24264 - 4.24264i) q^{92} +10.0000i q^{93} +12.0000i q^{94} +(0.707107 + 0.707107i) q^{96} +(9.89949 - 9.89949i) q^{97} -3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 8 q^{13} + 4 q^{16} - 4 q^{18} - 8 q^{21} - 16 q^{38} - 48 q^{47} + 20 q^{50} + 8 q^{52} - 4 q^{64} - 16 q^{67} - 24 q^{69} + 4 q^{72} - 4 q^{81} + 8 q^{84} + 16 q^{86} + 72 q^{89} - 12 q^{98}+O(q^{100}) $ 4 * q - 4 * q^4 - 8 * q^13 + 4 * q^16 - 4 * q^18 - 8 * q^21 - 16 * q^38 - 48 * q^47 + 20 * q^50 + 8 * q^52 - 4 * q^64 - 16 * q^67 - 24 * q^69 + 4 * q^72 - 4 * q^81 + 8 * q^84 + 16 * q^86 + 72 * q^89 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1734\mathbb{Z}\right)^\times$.

$n$	$1157$	$1159$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$5$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	1.41421	+	1.41421i	0.534522	+	0.534522i	0.921915	−	0.387392i	$-0.126624\pi$
$7$	1.41421	+	1.41421i	0.534522	+	0.534522i	−0.387392	+	0.921915i	$0.626624\pi$
$8$			1.00000i			0.353553i
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$11$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$	1.41421	−	1.41421i	0.377964	−	0.377964i
$15$		0			0
$16$	1.00000			0.250000
$17$		0			0
$17$		0			0
$18$	−1.00000			−0.235702
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$		0			0
$21$	−2.00000			−0.436436
$22$		0			0
$23$	4.24264	+	4.24264i	0.884652	+	0.884652i	0.994003	−	0.109351i	$-0.0348774\pi$
$23$	4.24264	+	4.24264i	0.884652	+	0.884652i	−0.109351	+	0.994003i	$0.534877\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$			5.00000i			1.00000i
$26$			2.00000i			0.392232i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−1.41421	−	1.41421i	−0.267261	−	0.267261i
$29$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$29$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$30$		0			0
$31$	7.07107	−	7.07107i	1.27000	−	1.27000i	0.323915	−	0.946086i	$-0.395001\pi$
$31$	7.07107	−	7.07107i	1.27000	−	1.27000i	0.946086	−	0.323915i	$-0.104999\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$		0			0
$35$		0			0
$36$			1.00000i			0.166667i
$37$	−5.65685	+	5.65685i	−0.929981	+	0.929981i	−0.997704	−	0.0677230i	$-0.978427\pi$
$37$	−5.65685	+	5.65685i	−0.929981	+	0.929981i	0.0677230	+	0.997704i	$0.478427\pi$
$38$	−4.00000			−0.648886
$39$	1.41421	−	1.41421i	0.226455	−	0.226455i
$40$		0			0
$41$	4.24264	+	4.24264i	0.662589	+	0.662589i	0.955990	−	0.293400i	$-0.0947869\pi$
$41$	4.24264	+	4.24264i	0.662589	+	0.662589i	−0.293400	+	0.955990i	$0.594787\pi$
$42$			2.00000i			0.308607i
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$		0			0
$45$		0			0
$46$	4.24264	−	4.24264i	0.625543	−	0.625543i
$47$	−12.0000			−1.75038			−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000			−1.75038			−0.875190	+	0.483779i	$0.839264\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$		−	3.00000i		−	0.428571i
$50$	5.00000			0.707107
$51$		0			0
$52$	2.00000			0.277350
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$		0			0
$56$	−1.41421	+	1.41421i	−0.188982	+	0.188982i
$57$	2.82843	+	2.82843i	0.374634	+	0.374634i
$58$		0			0
$59$			12.0000i			1.56227i	0.624364	+	0.781133i	$0.285358\pi$
$59$			12.0000i			1.56227i	−0.624364	+	0.781133i	$0.714642\pi$
$60$		0			0
$61$	5.65685	+	5.65685i	0.724286	+	0.724286i	0.969475	−	0.245189i	$-0.0788501\pi$
$61$	5.65685	+	5.65685i	0.724286	+	0.724286i	−0.245189	+	0.969475i	$0.578850\pi$
$62$	−7.07107	−	7.07107i	−0.898027	−	0.898027i
$63$	1.41421	−	1.41421i	0.178174	−	0.178174i
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		0			0
$69$	−6.00000			−0.722315
$70$		0			0
$71$	−4.24264	+	4.24264i	−0.503509	+	0.503509i	−0.912526	−	0.409018i	$-0.865871\pi$
$71$	−4.24264	+	4.24264i	−0.503509	+	0.503509i	0.409018	+	0.912526i	$0.365871\pi$
$72$	1.00000			0.117851
$73$	1.41421	−	1.41421i	0.165521	−	0.165521i	−0.619486	−	0.785007i	$-0.712659\pi$
$73$	1.41421	−	1.41421i	0.165521	−	0.165521i	0.785007	+	0.619486i	$0.212659\pi$
$74$	5.65685	+	5.65685i	0.657596	+	0.657596i
$75$	−3.53553	−	3.53553i	−0.408248	−	0.408248i
$76$			4.00000i			0.458831i
$77$		0			0
$78$	−1.41421	−	1.41421i	−0.160128	−	0.160128i
$79$	7.07107	+	7.07107i	0.795557	+	0.795557i	0.982391	−	0.186834i	$-0.0598227\pi$
$79$	7.07107	+	7.07107i	0.795557	+	0.795557i	−0.186834	+	0.982391i	$0.559823\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	4.24264	−	4.24264i	0.468521	−	0.468521i
$83$			12.0000i			1.31717i	0.752506	+	0.658586i	$0.228845\pi$
$83$			12.0000i			1.31717i	−0.752506	+	0.658586i	$0.771155\pi$
$84$	2.00000			0.218218
$85$		0			0
$86$	4.00000			0.431331
$87$		0			0
$88$		0			0
$89$	18.0000			1.90800			0.953998	−	0.299813i	$-0.0969242\pi$
$89$	18.0000			1.90800			0.953998	+	0.299813i	$0.0969242\pi$
$90$		0			0
$91$	−2.82843	−	2.82843i	−0.296500	−	0.296500i
$92$	−4.24264	−	4.24264i	−0.442326	−	0.442326i
$93$			10.0000i			1.03695i
$94$			12.0000i			1.23771i
$95$		0			0
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	9.89949	−	9.89949i	1.00514	−	1.00514i	0.00515471	−	0.999987i	$-0.498359\pi$
$97$	9.89949	−	9.89949i	1.00514	−	1.00514i	0.999987	−	0.00515471i	$-0.00164080\pi$
$98$	−3.00000			−0.303046
$99$		0			0
$100$		−	5.00000i		−	0.500000i
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$		0			0
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$		−	2.00000i		−	0.196116i
$105$		0			0
$106$	6.00000			0.582772
$107$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$107$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	14.1421	+	14.1421i	1.35457	+	1.35457i	0.880471	+	0.474100i	$0.157226\pi$
$109$	14.1421	+	14.1421i	1.35457	+	1.35457i	0.474100	+	0.880471i	$0.342774\pi$
$110$		0			0
$111$		−	8.00000i		−	0.759326i
$112$	1.41421	+	1.41421i	0.133631	+	0.133631i
$113$	4.24264	+	4.24264i	0.399114	+	0.399114i	0.877920	−	0.478806i	$-0.158930\pi$
$113$	4.24264	+	4.24264i	0.399114	+	0.399114i	−0.478806	+	0.877920i	$0.658930\pi$
$114$	2.82843	−	2.82843i	0.264906	−	0.264906i
$115$		0			0
$116$		0			0
$117$			2.00000i			0.184900i
$118$	12.0000			1.10469
$119$		0			0
$120$		0			0
$121$		−	11.0000i		−	1.00000i
$122$	5.65685	−	5.65685i	0.512148	−	0.512148i
$123$	−6.00000			−0.541002
$124$	−7.07107	+	7.07107i	−0.635001	+	0.635001i
$125$		0			0
$126$	−1.41421	−	1.41421i	−0.125988	−	0.125988i
$127$		−	8.00000i		−	0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$		−	8.00000i		−	0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$			1.00000i			0.0883883i
$129$	−2.82843	−	2.82843i	−0.249029	−	0.249029i
$130$		0			0
$131$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$131$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$132$		0			0
$133$	5.65685	−	5.65685i	0.490511	−	0.490511i
$134$			4.00000i			0.345547i
$135$		0			0
$136$		0			0
$137$	−6.00000			−0.512615			−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000			−0.512615			−0.256307	+	0.966595i	$0.582506\pi$
$138$			6.00000i			0.510754i
$139$	−5.65685	+	5.65685i	−0.479808	+	0.479808i	−0.905070	−	0.425262i	$-0.860182\pi$
$139$	−5.65685	+	5.65685i	−0.479808	+	0.479808i	0.425262	+	0.905070i	$0.360182\pi$
$140$		0			0
$141$	8.48528	−	8.48528i	0.714590	−	0.714590i
$142$	4.24264	+	4.24264i	0.356034	+	0.356034i
$143$		0			0
$144$		−	1.00000i		−	0.0833333i
$145$		0			0
$146$	−1.41421	−	1.41421i	−0.117041	−	0.117041i
$147$	2.12132	+	2.12132i	0.174964	+	0.174964i
$148$	5.65685	−	5.65685i	0.464991	−	0.464991i
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$	−3.53553	+	3.53553i	−0.288675	+	0.288675i
$151$			8.00000i			0.651031i	0.945537	+	0.325515i	$0.105538\pi$
$151$			8.00000i			0.651031i	−0.945537	+	0.325515i	$0.894462\pi$
$152$	4.00000			0.324443
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−1.41421	+	1.41421i	−0.113228	+	0.113228i
$157$	10.0000			0.798087			0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000			0.798087			0.399043	+	0.916932i	$0.369342\pi$
$158$	7.07107	−	7.07107i	0.562544	−	0.562544i
$159$	−4.24264	−	4.24264i	−0.336463	−	0.336463i
$160$		0			0
$161$			12.0000i			0.945732i
$162$			1.00000i			0.0785674i
$163$	14.1421	+	14.1421i	1.10770	+	1.10770i	0.993453	+	0.114245i	$0.0364449\pi$
$163$	14.1421	+	14.1421i	1.10770	+	1.10770i	0.114245	+	0.993453i	$0.463555\pi$
$164$	−4.24264	−	4.24264i	−0.331295	−	0.331295i
$165$		0			0
$166$	12.0000			0.931381
$167$	−12.7279	+	12.7279i	−0.984916	+	0.984916i	−0.999888	−	0.0149717i	$-0.995234\pi$
$167$	−12.7279	+	12.7279i	−0.984916	+	0.984916i	0.0149717	+	0.999888i	$0.495234\pi$
$168$		−	2.00000i		−	0.154303i
$169$	−9.00000			−0.692308
$170$		0			0
$171$	−4.00000			−0.305888
$172$		−	4.00000i		−	0.304997i
$173$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$173$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$174$		0			0
$175$	−7.07107	+	7.07107i	−0.534522	+	0.534522i
$176$		0			0
$177$	−8.48528	−	8.48528i	−0.637793	−	0.637793i
$178$		−	18.0000i		−	1.34916i
$179$			12.0000i			0.896922i	0.893802	+	0.448461i	$0.148028\pi$
$179$			12.0000i			0.896922i	−0.893802	+	0.448461i	$0.851972\pi$
$180$		0			0
$181$	−5.65685	−	5.65685i	−0.420471	−	0.420471i	0.464895	−	0.885366i	$-0.346092\pi$
$181$	−5.65685	−	5.65685i	−0.420471	−	0.420471i	−0.885366	+	0.464895i	$0.846092\pi$
$182$	−2.82843	+	2.82843i	−0.209657	+	0.209657i
$183$	−8.00000			−0.591377
$184$	−4.24264	+	4.24264i	−0.312772	+	0.312772i
$185$		0			0
$186$	10.0000			0.733236
$187$		0			0
$188$	12.0000			0.875190
$189$			2.00000i			0.145479i
$190$		0			0
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	−9.89949	−	9.89949i	−0.712581	−	0.712581i	0.254493	−	0.967075i	$-0.418091\pi$
$193$	−9.89949	−	9.89949i	−0.712581	−	0.712581i	−0.967075	+	0.254493i	$0.918091\pi$
$194$	−9.89949	−	9.89949i	−0.710742	−	0.710742i
$195$		0			0
$196$			3.00000i			0.214286i
$197$	−8.48528	−	8.48528i	−0.604551	−	0.604551i	0.336966	−	0.941517i	$-0.390599\pi$
$197$	−8.48528	−	8.48528i	−0.604551	−	0.604551i	−0.941517	+	0.336966i	$0.890599\pi$
$198$		0			0
$199$	1.41421	−	1.41421i	0.100251	−	0.100251i	−0.655202	−	0.755453i	$-0.727417\pi$
$199$	1.41421	−	1.41421i	0.100251	−	0.100251i	0.755453	+	0.655202i	$0.227417\pi$
$200$	−5.00000			−0.353553
$201$	2.82843	−	2.82843i	0.199502	−	0.199502i
$202$		−	6.00000i		−	0.422159i
$203$		0			0
$204$		0			0
$205$		0			0
$206$			4.00000i			0.278693i
$207$	4.24264	−	4.24264i	0.294884	−	0.294884i
$208$	−2.00000			−0.138675
$209$		0			0
$210$		0			0
$211$	5.65685	+	5.65685i	0.389434	+	0.389434i	0.874486	−	0.485052i	$-0.161199\pi$
$211$	5.65685	+	5.65685i	0.389434	+	0.389434i	−0.485052	+	0.874486i	$0.661199\pi$
$212$		−	6.00000i		−	0.412082i
$213$		−	6.00000i		−	0.411113i
$214$		0			0
$215$		0			0
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	20.0000			1.35769
$218$	14.1421	−	14.1421i	0.957826	−	0.957826i
$219$			2.00000i			0.135147i
$220$		0			0
$221$		0			0
$222$	−8.00000			−0.536925
$223$		−	28.0000i		−	1.87502i	−0.347960	−	0.937509i	$-0.613126\pi$
$223$		−	28.0000i		−	1.87502i	0.347960	−	0.937509i	$-0.386874\pi$
$224$	1.41421	−	1.41421i	0.0944911	−	0.0944911i
$225$	5.00000			0.333333
$226$	4.24264	−	4.24264i	0.282216	−	0.282216i
$227$	−8.48528	−	8.48528i	−0.563188	−	0.563188i	0.367024	−	0.930212i	$-0.380377\pi$
$227$	−8.48528	−	8.48528i	−0.563188	−	0.563188i	−0.930212	+	0.367024i	$0.880377\pi$
$228$	−2.82843	−	2.82843i	−0.187317	−	0.187317i
$229$		−	14.0000i		−	0.925146i	−0.886581	−	0.462573i	$-0.846926\pi$
$229$		−	14.0000i		−	0.925146i	0.886581	−	0.462573i	$-0.153074\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−21.2132	+	21.2132i	−1.38972	+	1.38972i	−0.563837	+	0.825886i	$0.690675\pi$
$233$	−21.2132	+	21.2132i	−1.38972	+	1.38972i	−0.825886	+	0.563837i	$0.809325\pi$
$234$	2.00000			0.130744
$235$		0			0
$236$		−	12.0000i		−	0.781133i
$237$	−10.0000			−0.649570
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	7.07107	−	7.07107i	0.455488	−	0.455488i	−0.441683	−	0.897171i	$-0.645619\pi$
$241$	7.07107	−	7.07107i	0.455488	−	0.455488i	0.897171	+	0.441683i	$0.145619\pi$
$242$	−11.0000			−0.707107
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−5.65685	−	5.65685i	−0.362143	−	0.362143i
$245$		0			0
$246$			6.00000i			0.382546i
$247$			8.00000i			0.509028i
$248$	7.07107	+	7.07107i	0.449013	+	0.449013i
$249$	−8.48528	−	8.48528i	−0.537733	−	0.537733i
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$	−1.41421	+	1.41421i	−0.0890871	+	0.0890871i
$253$		0			0
$254$	−8.00000			−0.501965
$255$		0			0
$256$	1.00000			0.0625000
$257$			18.0000i			1.12281i	0.827541	+	0.561405i	$0.189739\pi$
$257$			18.0000i			1.12281i	−0.827541	+	0.561405i	$0.810261\pi$
$258$	−2.82843	+	2.82843i	−0.176090	+	0.176090i
$259$	−16.0000			−0.994192
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	12.0000i		−	0.739952i	−0.929041	−	0.369976i	$-0.879366\pi$
$263$		−	12.0000i		−	0.739952i	0.929041	−	0.369976i	$-0.120634\pi$
$264$		0			0
$265$		0			0
$266$	−5.65685	−	5.65685i	−0.346844	−	0.346844i
$267$	−12.7279	+	12.7279i	−0.778936	+	0.778936i
$268$	4.00000			0.244339
$269$	−16.9706	+	16.9706i	−1.03471	+	1.03471i	−0.0353381	+	0.999375i	$0.511251\pi$
$269$	−16.9706	+	16.9706i	−1.03471	+	1.03471i	−0.999375	+	0.0353381i	$0.988749\pi$
$270$		0			0
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$		0			0
$273$	4.00000			0.242091
$274$			6.00000i			0.362473i
$275$		0			0
$276$	6.00000			0.361158
$277$	−2.82843	+	2.82843i	−0.169944	+	0.169944i	−0.786955	−	0.617011i	$-0.788343\pi$
$277$	−2.82843	+	2.82843i	−0.169944	+	0.169944i	0.617011	+	0.786955i	$0.288343\pi$
$278$	5.65685	+	5.65685i	0.339276	+	0.339276i
$279$	−7.07107	−	7.07107i	−0.423334	−	0.423334i
$280$		0			0
$281$		−	30.0000i		−	1.78965i	−0.446417	−	0.894825i	$-0.647300\pi$
$281$		−	30.0000i		−	1.78965i	0.446417	−	0.894825i	$-0.352700\pi$
$282$	−8.48528	−	8.48528i	−0.505291	−	0.505291i
$283$	11.3137	+	11.3137i	0.672530	+	0.672530i	0.958299	−	0.285769i	$-0.0922488\pi$
$283$	11.3137	+	11.3137i	0.672530	+	0.672530i	−0.285769	+	0.958299i	$0.592249\pi$
$284$	4.24264	−	4.24264i	0.251754	−	0.251754i
$285$		0			0
$286$		0			0
$287$			12.0000i			0.708338i
$288$	−1.00000			−0.0589256
$289$		0			0
$290$		0			0
$291$			14.0000i			0.820695i
$292$	−1.41421	+	1.41421i	−0.0827606	+	0.0827606i
$293$	−18.0000			−1.05157			−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000			−1.05157			−0.525786	+	0.850617i	$0.676229\pi$
$294$	2.12132	−	2.12132i	0.123718	−	0.123718i
$295$		0			0
$296$	−5.65685	−	5.65685i	−0.328798	−	0.328798i
$297$		0			0
$298$		−	6.00000i		−	0.347571i
$299$	−8.48528	−	8.48528i	−0.490716	−	0.490716i
$300$	3.53553	+	3.53553i	0.204124	+	0.204124i
$301$	−5.65685	+	5.65685i	−0.326056	+	0.326056i
$302$	8.00000			0.460348
$303$	−4.24264	+	4.24264i	−0.243733	+	0.243733i
$304$		−	4.00000i		−	0.229416i
$305$		0			0
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$	2.82843	−	2.82843i	0.160904	−	0.160904i
$310$		0			0
$311$	12.7279	−	12.7279i	0.721734	−	0.721734i	−0.247224	−	0.968958i	$-0.579518\pi$
$311$	12.7279	−	12.7279i	0.721734	−	0.721734i	0.968958	+	0.247224i	$0.0795184\pi$
$312$	1.41421	+	1.41421i	0.0800641	+	0.0800641i
$313$	9.89949	+	9.89949i	0.559553	+	0.559553i	0.929180	−	0.369627i	$-0.120515\pi$
$313$	9.89949	+	9.89949i	0.559553	+	0.559553i	−0.369627	+	0.929180i	$0.620515\pi$
$314$		−	10.0000i		−	0.564333i
$315$		0			0
$316$	−7.07107	−	7.07107i	−0.397779	−	0.397779i
$317$	−8.48528	−	8.48528i	−0.476581	−	0.476581i	0.427456	−	0.904036i	$-0.359410\pi$
$317$	−8.48528	−	8.48528i	−0.476581	−	0.476581i	−0.904036	+	0.427456i	$0.859410\pi$
$318$	−4.24264	+	4.24264i	−0.237915	+	0.237915i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	12.0000			0.668734
$323$		0			0
$324$	1.00000			0.0555556
$325$		−	10.0000i		−	0.554700i
$326$	14.1421	−	14.1421i	0.783260	−	0.783260i
$327$	−20.0000			−1.10600
$328$	−4.24264	+	4.24264i	−0.234261	+	0.234261i
$329$	−16.9706	−	16.9706i	−0.935617	−	0.935617i
$330$		0			0
$331$		−	20.0000i		−	1.09930i	−0.835395	−	0.549650i	$-0.814761\pi$
$331$		−	20.0000i		−	1.09930i	0.835395	−	0.549650i	$-0.185239\pi$
$332$		−	12.0000i		−	0.658586i
$333$	5.65685	+	5.65685i	0.309994	+	0.309994i
$334$	12.7279	+	12.7279i	0.696441	+	0.696441i
$335$		0			0
$336$	−2.00000			−0.109109
$337$	15.5563	−	15.5563i	0.847408	−	0.847408i	−0.142401	−	0.989809i	$-0.545482\pi$
$337$	15.5563	−	15.5563i	0.847408	−	0.847408i	0.989809	+	0.142401i	$0.0454822\pi$
$338$			9.00000i			0.489535i
$339$	−6.00000			−0.325875
$340$		0			0
$341$		0			0
$342$			4.00000i			0.216295i
$343$	14.1421	−	14.1421i	0.763604	−	0.763604i
$344$	−4.00000			−0.215666
$345$		0			0
$346$		0			0
$347$	−8.48528	−	8.48528i	−0.455514	−	0.455514i	0.441666	−	0.897180i	$-0.354388\pi$
$347$	−8.48528	−	8.48528i	−0.455514	−	0.455514i	−0.897180	+	0.441666i	$0.854388\pi$
$348$		0			0
$349$		−	26.0000i		−	1.39175i	−0.718164	−	0.695874i	$-0.755017\pi$
$349$		−	26.0000i		−	1.39175i	0.718164	−	0.695874i	$-0.244983\pi$
$350$	7.07107	+	7.07107i	0.377964	+	0.377964i
$351$	−1.41421	−	1.41421i	−0.0754851	−	0.0754851i
$352$		0			0
$353$	18.0000			0.958043			0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000			0.958043			0.479022	+	0.877803i	$0.340992\pi$
$354$	−8.48528	+	8.48528i	−0.450988	+	0.450988i
$355$		0			0
$356$	−18.0000			−0.953998
$357$		0			0
$358$	12.0000			0.634220
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−5.65685	+	5.65685i	−0.297318	+	0.297318i
$363$	7.77817	+	7.77817i	0.408248	+	0.408248i
$364$	2.82843	+	2.82843i	0.148250	+	0.148250i
$365$		0			0
$366$			8.00000i			0.418167i
$367$	−7.07107	−	7.07107i	−0.369107	−	0.369107i	0.498045	−	0.867151i	$-0.334052\pi$
$367$	−7.07107	−	7.07107i	−0.369107	−	0.369107i	−0.867151	+	0.498045i	$0.834052\pi$
$368$	4.24264	+	4.24264i	0.221163	+	0.221163i
$369$	4.24264	−	4.24264i	0.220863	−	0.220863i
$370$		0			0
$371$	−8.48528	+	8.48528i	−0.440534	+	0.440534i
$372$		−	10.0000i		−	0.518476i
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$		0			0
$375$		0			0
$376$		−	12.0000i		−	0.618853i
$377$		0			0
$378$	2.00000			0.102869
$379$	−19.7990	+	19.7990i	−1.01701	+	1.01701i	−0.0171529	+	0.999853i	$0.505460\pi$
$379$	−19.7990	+	19.7990i	−1.01701	+	1.01701i	−0.999853	+	0.0171529i	$0.994540\pi$
$380$		0			0
$381$	5.65685	+	5.65685i	0.289809	+	0.289809i
$382$		−	12.0000i		−	0.613973i
$383$			12.0000i			0.613171i	0.951843	+	0.306586i	$0.0991866\pi$
$383$			12.0000i			0.613171i	−0.951843	+	0.306586i	$0.900813\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$		0			0
$386$	−9.89949	+	9.89949i	−0.503871	+	0.503871i
$387$	4.00000			0.203331
$388$	−9.89949	+	9.89949i	−0.502571	+	0.502571i
$389$		−	30.0000i		−	1.52106i	−0.649303	−	0.760530i	$-0.724939\pi$
$389$		−	30.0000i		−	1.52106i	0.649303	−	0.760530i	$-0.275061\pi$
$390$		0			0
$391$		0			0
$392$	3.00000			0.151523
$393$		0			0
$394$	−8.48528	+	8.48528i	−0.427482	+	0.427482i
$395$		0			0
$396$		0			0
$397$	11.3137	+	11.3137i	0.567819	+	0.567819i	0.931517	−	0.363698i	$-0.118486\pi$
$397$	11.3137	+	11.3137i	0.567819	+	0.567819i	−0.363698	+	0.931517i	$0.618486\pi$
$398$	−1.41421	−	1.41421i	−0.0708881	−	0.0708881i
$399$			8.00000i			0.400501i
$400$			5.00000i			0.250000i
$401$	−12.7279	−	12.7279i	−0.635602	−	0.635602i	0.313865	−	0.949467i	$-0.398376\pi$
$401$	−12.7279	−	12.7279i	−0.635602	−	0.635602i	−0.949467	+	0.313865i	$0.898376\pi$
$402$	−2.82843	−	2.82843i	−0.141069	−	0.141069i
$403$	−14.1421	+	14.1421i	−0.704470	+	0.704470i
$404$	−6.00000			−0.298511
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	38.0000			1.87898			0.939490	−	0.342578i	$-0.111300\pi$
$409$	38.0000			1.87898			0.939490	+	0.342578i	$0.111300\pi$
$410$		0			0
$411$	4.24264	−	4.24264i	0.209274	−	0.209274i
$412$	4.00000			0.197066
$413$	−16.9706	+	16.9706i	−0.835067	+	0.835067i
$414$	−4.24264	−	4.24264i	−0.208514	−	0.208514i
$415$		0			0
$416$			2.00000i			0.0980581i
$417$		−	8.00000i		−	0.391762i
$418$		0			0
$419$	25.4558	+	25.4558i	1.24360	+	1.24360i	0.958497	+	0.285102i	$0.0920276\pi$
$419$	25.4558	+	25.4558i	1.24360	+	1.24360i	0.285102	+	0.958497i	$0.407972\pi$
$420$		0			0
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$	5.65685	−	5.65685i	0.275371	−	0.275371i
$423$			12.0000i			0.583460i
$424$	−6.00000			−0.291386
$425$		0			0
$426$	−6.00000			−0.290701
$427$			16.0000i			0.774294i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	21.2132	+	21.2132i	1.02180	+	1.02180i	0.999757	+	0.0220471i	$0.00701839\pi$
$431$	21.2132	+	21.2132i	1.02180	+	1.02180i	0.0220471	+	0.999757i	$0.492982\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$		−	14.0000i		−	0.672797i	−0.941720	−	0.336399i	$-0.890791\pi$
$433$		−	14.0000i		−	0.672797i	0.941720	−	0.336399i	$-0.109209\pi$
$434$		−	20.0000i		−	0.960031i
$435$		0			0
$436$	−14.1421	−	14.1421i	−0.677285	−	0.677285i
$437$	16.9706	−	16.9706i	0.811812	−	0.811812i
$438$	2.00000			0.0955637
$439$	−18.3848	+	18.3848i	−0.877457	+	0.877457i	−0.993271	−	0.115813i	$-0.963053\pi$
$439$	−18.3848	+	18.3848i	−0.877457	+	0.877457i	0.115813	+	0.993271i	$0.463053\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$		0			0
$443$	−36.0000			−1.71041			−0.855206	−	0.518289i	$-0.826569\pi$
$443$	−36.0000			−1.71041			−0.855206	+	0.518289i	$0.826569\pi$
$444$			8.00000i			0.379663i
$445$		0			0
$446$	−28.0000			−1.32584
$447$	−4.24264	+	4.24264i	−0.200670	+	0.200670i
$448$	−1.41421	−	1.41421i	−0.0668153	−	0.0668153i
$449$	4.24264	+	4.24264i	0.200223	+	0.200223i	0.800095	−	0.599873i	$-0.204782\pi$
$449$	4.24264	+	4.24264i	0.200223	+	0.200223i	−0.599873	+	0.800095i	$0.704782\pi$
$450$		−	5.00000i		−	0.235702i
$451$		0			0
$452$	−4.24264	−	4.24264i	−0.199557	−	0.199557i
$453$	−5.65685	−	5.65685i	−0.265782	−	0.265782i
$454$	−8.48528	+	8.48528i	−0.398234	+	0.398234i
$455$		0			0
$456$	−2.82843	+	2.82843i	−0.132453	+	0.132453i
$457$		−	10.0000i		−	0.467780i	−0.972263	−	0.233890i	$-0.924854\pi$
$457$		−	10.0000i		−	0.467780i	0.972263	−	0.233890i	$-0.0751456\pi$
$458$	−14.0000			−0.654177
$459$		0			0
$460$		0			0
$461$			30.0000i			1.39724i	0.715493	+	0.698620i	$0.246202\pi$
$461$			30.0000i			1.39724i	−0.715493	+	0.698620i	$0.753798\pi$
$462$		0			0
$463$	−20.0000			−0.929479			−0.464739	−	0.885448i	$-0.653852\pi$
$463$	−20.0000			−0.929479			−0.464739	+	0.885448i	$0.653852\pi$
$464$		0			0
$465$		0			0
$466$	21.2132	+	21.2132i	0.982683	+	0.982683i
$467$		−	12.0000i		−	0.555294i	−0.960683	−	0.277647i	$-0.910445\pi$
$467$		−	12.0000i		−	0.555294i	0.960683	−	0.277647i	$-0.0895545\pi$
$468$		−	2.00000i		−	0.0924500i
$469$	−5.65685	−	5.65685i	−0.261209	−	0.261209i
$470$		0			0
$471$	−7.07107	+	7.07107i	−0.325818	+	0.325818i
$472$	−12.0000			−0.552345
$473$		0			0
$474$			10.0000i			0.459315i
$475$	20.0000			0.917663
$476$		0			0
$477$	6.00000			0.274721
$478$			12.0000i			0.548867i
$479$	−4.24264	+	4.24264i	−0.193851	+	0.193851i	−0.797358	−	0.603507i	$-0.793770\pi$
$479$	−4.24264	+	4.24264i	−0.193851	+	0.193851i	0.603507	+	0.797358i	$0.293770\pi$
$480$		0			0
$481$	11.3137	−	11.3137i	0.515861	−	0.515861i
$482$	−7.07107	−	7.07107i	−0.322078	−	0.322078i
$483$	−8.48528	−	8.48528i	−0.386094	−	0.386094i
$484$			11.0000i			0.500000i
$485$		0			0
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	7.07107	+	7.07107i	0.320421	+	0.320421i	0.848928	−	0.528508i	$-0.177248\pi$
$487$	7.07107	+	7.07107i	0.320421	+	0.320421i	−0.528508	+	0.848928i	$0.677248\pi$
$488$	−5.65685	+	5.65685i	−0.256074	+	0.256074i
$489$	−20.0000			−0.904431
$490$		0			0
$491$		−	36.0000i		−	1.62466i	−0.583200	−	0.812329i	$-0.698200\pi$
$491$		−	36.0000i		−	1.62466i	0.583200	−	0.812329i	$-0.301800\pi$
$492$	6.00000			0.270501
$493$		0			0
$494$	8.00000			0.359937
$495$		0			0
$496$	7.07107	−	7.07107i	0.317500	−	0.317500i
$497$	−12.0000			−0.538274
$498$	−8.48528	+	8.48528i	−0.380235	+	0.380235i
$499$	−22.6274	−	22.6274i	−1.01294	−	1.01294i	−0.999915	−	0.0130272i	$-0.995853\pi$
$499$	−22.6274	−	22.6274i	−1.01294	−	1.01294i	−0.0130272	−	0.999915i	$-0.504147\pi$
$500$		0			0
$501$		−	18.0000i		−	0.804181i
$502$			12.0000i			0.535586i
$503$	−4.24264	−	4.24264i	−0.189170	−	0.189170i	0.606167	−	0.795337i	$-0.292706\pi$
$503$	−4.24264	−	4.24264i	−0.189170	−	0.189170i	−0.795337	+	0.606167i	$0.792706\pi$
$504$	1.41421	+	1.41421i	0.0629941	+	0.0629941i
$505$		0			0
$506$		0			0
$507$	6.36396	−	6.36396i	0.282633	−	0.282633i
$508$			8.00000i			0.354943i
$509$	−6.00000			−0.265945			−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000			−0.265945			−0.132973	+	0.991120i	$0.542452\pi$
$510$		0			0
$511$	4.00000			0.176950
$512$		−	1.00000i		−	0.0441942i
$513$	2.82843	−	2.82843i	0.124878	−	0.124878i
$514$	18.0000			0.793946
$515$		0			0
$516$	2.82843	+	2.82843i	0.124515	+	0.124515i
$517$		0			0
$518$			16.0000i			0.703000i
$519$		0			0
$520$		0			0
$521$	−4.24264	−	4.24264i	−0.185873	−	0.185873i	0.608036	−	0.793909i	$-0.291958\pi$
$521$	−4.24264	−	4.24264i	−0.185873	−	0.185873i	−0.793909	+	0.608036i	$0.791958\pi$
$522$		0			0
$523$	−20.0000			−0.874539			−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000			−0.874539			−0.437269	+	0.899331i	$0.644054\pi$
$524$		0			0
$525$		−	10.0000i		−	0.436436i
$526$	−12.0000			−0.523225
$527$		0			0
$528$		0			0
$529$			13.0000i			0.565217i
$530$		0			0
$531$	12.0000			0.520756
$532$	−5.65685	+	5.65685i	−0.245256	+	0.245256i
$533$	−8.48528	−	8.48528i	−0.367538	−	0.367538i
$534$	12.7279	+	12.7279i	0.550791	+	0.550791i
$535$		0			0
$536$		−	4.00000i		−	0.172774i
$537$	−8.48528	−	8.48528i	−0.366167	−	0.366167i
$538$	16.9706	+	16.9706i	0.731653	+	0.731653i
$539$		0			0
$540$		0			0
$541$	11.3137	−	11.3137i	0.486414	−	0.486414i	−0.420758	−	0.907173i	$-0.638236\pi$
$541$	11.3137	−	11.3137i	0.486414	−	0.486414i	0.907173	+	0.420758i	$0.138236\pi$
$542$			16.0000i			0.687259i
$543$	8.00000			0.343313
$544$		0			0
$545$		0			0
$546$		−	4.00000i		−	0.171184i
$547$	−5.65685	+	5.65685i	−0.241870	+	0.241870i	−0.817623	−	0.575754i	$-0.804709\pi$
$547$	−5.65685	+	5.65685i	−0.241870	+	0.241870i	0.575754	+	0.817623i	$0.304709\pi$
$548$	6.00000			0.256307
$549$	5.65685	−	5.65685i	0.241429	−	0.241429i
$550$		0			0
$551$		0			0
$552$		−	6.00000i		−	0.255377i
$553$			20.0000i			0.850487i
$554$	2.82843	+	2.82843i	0.120168	+	0.120168i
$555$		0			0
$556$	5.65685	−	5.65685i	0.239904	−	0.239904i
$557$	42.0000			1.77960			0.889799	−	0.456354i	$-0.150845\pi$
$557$	42.0000			1.77960			0.889799	+	0.456354i	$0.150845\pi$
$558$	−7.07107	+	7.07107i	−0.299342	+	0.299342i
$559$		−	8.00000i		−	0.338364i
$560$		0			0
$561$		0			0
$562$	−30.0000			−1.26547
$563$		−	12.0000i		−	0.505740i	−0.967500	−	0.252870i	$-0.918626\pi$
$563$		−	12.0000i		−	0.505740i	0.967500	−	0.252870i	$-0.0813744\pi$
$564$	−8.48528	+	8.48528i	−0.357295	+	0.357295i
$565$		0			0
$566$	11.3137	−	11.3137i	0.475551	−	0.475551i
$567$	−1.41421	−	1.41421i	−0.0593914	−	0.0593914i
$568$	−4.24264	−	4.24264i	−0.178017	−	0.178017i
$569$			6.00000i			0.251533i	0.992060	+	0.125767i	$0.0401390\pi$
$569$			6.00000i			0.251533i	−0.992060	+	0.125767i	$0.959861\pi$
$570$		0			0
$571$	14.1421	+	14.1421i	0.591830	+	0.591830i	0.938125	−	0.346296i	$-0.112561\pi$
$571$	14.1421	+	14.1421i	0.591830	+	0.591830i	−0.346296	+	0.938125i	$0.612561\pi$
$572$		0			0
$573$	−8.48528	+	8.48528i	−0.354478	+	0.354478i
$574$	12.0000			0.500870
$575$	−21.2132	+	21.2132i	−0.884652	+	0.884652i
$576$			1.00000i			0.0416667i
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$		0			0
$579$	14.0000			0.581820
$580$		0			0
$581$	−16.9706	+	16.9706i	−0.704058	+	0.704058i
$582$	14.0000			0.580319
$583$		0			0
$584$	1.41421	+	1.41421i	0.0585206	+	0.0585206i
$585$		0			0
$586$			18.0000i			0.743573i
$587$			12.0000i			0.495293i	0.968850	+	0.247647i	$0.0796572\pi$
$587$			12.0000i			0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$	−2.12132	−	2.12132i	−0.0874818	−	0.0874818i
$589$	−28.2843	−	28.2843i	−1.16543	−	1.16543i
$590$		0			0
$591$	12.0000			0.493614
$592$	−5.65685	+	5.65685i	−0.232495	+	0.232495i
$593$			18.0000i			0.739171i	0.929197	+	0.369586i	$0.120500\pi$
$593$			18.0000i			0.739171i	−0.929197	+	0.369586i	$0.879500\pi$
$594$		0			0
$595$		0			0
$596$	−6.00000			−0.245770
$597$			2.00000i			0.0818546i
$598$	−8.48528	+	8.48528i	−0.346989	+	0.346989i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	3.53553	−	3.53553i	0.144338	−	0.144338i
$601$	15.5563	+	15.5563i	0.634557	+	0.634557i	0.949208	−	0.314651i	$-0.101887\pi$
$601$	15.5563	+	15.5563i	0.634557	+	0.634557i	−0.314651	+	0.949208i	$0.601887\pi$
$602$	5.65685	+	5.65685i	0.230556	+	0.230556i
$603$			4.00000i			0.162893i
$604$		−	8.00000i		−	0.325515i
$605$		0			0
$606$	4.24264	+	4.24264i	0.172345	+	0.172345i
$607$	−7.07107	+	7.07107i	−0.287006	+	0.287006i	−0.835895	−	0.548889i	$-0.815051\pi$
$607$	−7.07107	+	7.07107i	−0.287006	+	0.287006i	0.548889	+	0.835895i	$0.315051\pi$
$608$	−4.00000			−0.162221
$609$		0			0
$610$		0			0
$611$	24.0000			0.970936
$612$		0			0
$613$	−34.0000			−1.37325			−0.686624	−	0.727013i	$-0.740908\pi$
$613$	−34.0000			−1.37325			−0.686624	+	0.727013i	$0.740908\pi$
$614$		−	20.0000i		−	0.807134i
$615$		0			0
$616$		0			0
$617$	12.7279	−	12.7279i	0.512407	−	0.512407i	−0.402856	−	0.915263i	$-0.631983\pi$
$617$	12.7279	−	12.7279i	0.512407	−	0.512407i	0.915263	+	0.402856i	$0.131983\pi$
$618$	−2.82843	−	2.82843i	−0.113776	−	0.113776i
$619$	−19.7990	−	19.7990i	−0.795789	−	0.795789i	0.186640	−	0.982428i	$-0.440240\pi$
$619$	−19.7990	−	19.7990i	−0.795789	−	0.795789i	−0.982428	+	0.186640i	$0.940240\pi$
$620$		0			0
$621$			6.00000i			0.240772i
$622$	−12.7279	−	12.7279i	−0.510343	−	0.510343i
$623$	25.4558	+	25.4558i	1.01987	+	1.01987i
$624$	1.41421	−	1.41421i	0.0566139	−	0.0566139i
$625$	−25.0000			−1.00000
$626$	9.89949	−	9.89949i	0.395663	−	0.395663i
$627$		0			0
$628$	−10.0000			−0.399043
$629$		0			0
$630$		0			0
$631$		−	4.00000i		−	0.159237i	−0.996825	−	0.0796187i	$-0.974630\pi$
$631$		−	4.00000i		−	0.159237i	0.996825	−	0.0796187i	$-0.0253703\pi$
$632$	−7.07107	+	7.07107i	−0.281272	+	0.281272i
$633$	−8.00000			−0.317971
$634$	−8.48528	+	8.48528i	−0.336994	+	0.336994i
$635$		0			0
$636$	4.24264	+	4.24264i	0.168232	+	0.168232i
$637$			6.00000i			0.237729i
$638$		0			0
$639$	4.24264	+	4.24264i	0.167836	+	0.167836i
$640$		0			0
$641$	21.2132	−	21.2132i	0.837871	−	0.837871i	−0.150707	−	0.988578i	$-0.548155\pi$
$641$	21.2132	−	21.2132i	0.837871	−	0.837871i	0.988578	+	0.150707i	$0.0481551\pi$
$642$		0			0
$643$	2.82843	−	2.82843i	0.111542	−	0.111542i	−0.649133	−	0.760675i	$-0.724868\pi$
$643$	2.82843	−	2.82843i	0.111542	−	0.111542i	0.760675	+	0.649133i	$0.224868\pi$
$644$		−	12.0000i		−	0.472866i
$645$		0			0
$646$		0			0
$647$	36.0000			1.41531			0.707653	−	0.706560i	$-0.249754\pi$
$647$	36.0000			1.41531			0.707653	+	0.706560i	$0.249754\pi$
$648$		−	1.00000i		−	0.0392837i
$649$		0			0
$650$	−10.0000			−0.392232
$651$	−14.1421	+	14.1421i	−0.554274	+	0.554274i
$652$	−14.1421	−	14.1421i	−0.553849	−	0.553849i
$653$	−16.9706	−	16.9706i	−0.664109	−	0.664109i	0.292237	−	0.956346i	$-0.405601\pi$
$653$	−16.9706	−	16.9706i	−0.664109	−	0.664109i	−0.956346	+	0.292237i	$0.905601\pi$
$654$			20.0000i			0.782062i
$655$		0			0
$656$	4.24264	+	4.24264i	0.165647	+	0.165647i
$657$	−1.41421	−	1.41421i	−0.0551737	−	0.0551737i
$658$	−16.9706	+	16.9706i	−0.661581	+	0.661581i
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$		−	22.0000i		−	0.855701i	−0.903850	−	0.427850i	$-0.859271\pi$
$661$		−	22.0000i		−	0.855701i	0.903850	−	0.427850i	$-0.140729\pi$
$662$	−20.0000			−0.777322
$663$		0			0
$664$	−12.0000			−0.465690
$665$		0			0
$666$	5.65685	−	5.65685i	0.219199	−	0.219199i
$667$		0			0
$668$	12.7279	−	12.7279i	0.492458	−	0.492458i
$669$	19.7990	+	19.7990i	0.765473	+	0.765473i
$670$		0			0
$671$		0			0
$672$			2.00000i			0.0771517i
$673$	−24.0416	−	24.0416i	−0.926737	−	0.926737i	0.0707568	−	0.997494i	$-0.477459\pi$
$673$	−24.0416	−	24.0416i	−0.926737	−	0.926737i	−0.997494	+	0.0707568i	$0.977459\pi$
$674$	−15.5563	−	15.5563i	−0.599208	−	0.599208i
$675$	−3.53553	+	3.53553i	−0.136083	+	0.136083i
$676$	9.00000			0.346154
$677$	8.48528	−	8.48528i	0.326116	−	0.326116i	−0.524992	−	0.851107i	$-0.675932\pi$
$677$	8.48528	−	8.48528i	0.326116	−	0.326116i	0.851107	+	0.524992i	$0.175932\pi$
$678$			6.00000i			0.230429i
$679$	28.0000			1.07454
$680$		0			0
$681$	12.0000			0.459841
$682$		0			0
$683$	8.48528	−	8.48528i	0.324680	−	0.324680i	−0.525879	−	0.850559i	$-0.676264\pi$
$683$	8.48528	−	8.48528i	0.324680	−	0.324680i	0.850559	+	0.525879i	$0.176264\pi$
$684$	4.00000			0.152944
$685$		0			0
$686$	−14.1421	−	14.1421i	−0.539949	−	0.539949i
$687$	9.89949	+	9.89949i	0.377689	+	0.377689i
$688$			4.00000i			0.152499i
$689$		−	12.0000i		−	0.457164i
$690$		0			0
$691$	−22.6274	−	22.6274i	−0.860788	−	0.860788i	0.130642	−	0.991430i	$-0.458296\pi$
$691$	−22.6274	−	22.6274i	−0.860788	−	0.860788i	−0.991430	+	0.130642i	$0.958296\pi$
$692$		0			0
$693$		0			0
$694$	−8.48528	+	8.48528i	−0.322097	+	0.322097i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−26.0000			−0.984115
$699$		−	30.0000i		−	1.13470i
$700$	7.07107	−	7.07107i	0.267261	−	0.267261i
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$	−1.41421	+	1.41421i	−0.0533761	+	0.0533761i
$703$	22.6274	+	22.6274i	0.853409	+	0.853409i
$704$		0			0
$705$		0			0
$706$		−	18.0000i		−	0.677439i
$707$	8.48528	+	8.48528i	0.319122	+	0.319122i
$708$	8.48528	+	8.48528i	0.318896	+	0.318896i
$709$	14.1421	−	14.1421i	0.531119	−	0.531119i	−0.389786	−	0.920905i	$-0.627451\pi$
$709$	14.1421	−	14.1421i	0.531119	−	0.531119i	0.920905	+	0.389786i	$0.127451\pi$
$710$		0			0
$711$	7.07107	−	7.07107i	0.265186	−	0.265186i
$712$			18.0000i			0.674579i
$713$	60.0000			2.24702
$714$		0			0
$715$		0			0
$716$		−	12.0000i		−	0.448461i
$717$	8.48528	−	8.48528i	0.316889	−	0.316889i
$718$		0			0
$719$	4.24264	−	4.24264i	0.158224	−	0.158224i	−0.623555	−	0.781779i	$-0.714312\pi$
$719$	4.24264	−	4.24264i	0.158224	−	0.158224i	0.781779	+	0.623555i	$0.214312\pi$
$720$		0			0
$721$	−5.65685	−	5.65685i	−0.210672	−	0.210672i
$722$		−	3.00000i		−	0.111648i
$723$			10.0000i			0.371904i
$724$	5.65685	+	5.65685i	0.210235	+	0.210235i
$725$		0			0
$726$	7.77817	−	7.77817i	0.288675	−	0.288675i
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$	2.82843	−	2.82843i	0.104828	−	0.104828i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		0			0
$732$	8.00000			0.295689
$733$			26.0000i			0.960332i	0.877178	+	0.480166i	$0.159424\pi$
$733$			26.0000i			0.960332i	−0.877178	+	0.480166i	$0.840576\pi$
$734$	−7.07107	+	7.07107i	−0.260998	+	0.260998i
$735$		0			0
$736$	4.24264	−	4.24264i	0.156386	−	0.156386i
$737$		0			0
$738$	−4.24264	−	4.24264i	−0.156174	−	0.156174i
$739$			4.00000i			0.147142i	0.997290	+	0.0735712i	$0.0234396\pi$
$739$			4.00000i			0.147142i	−0.997290	+	0.0735712i	$0.976560\pi$
$740$		0			0
$741$	−5.65685	−	5.65685i	−0.207810	−	0.207810i
$742$	8.48528	+	8.48528i	0.311504	+	0.311504i
$743$	29.6985	−	29.6985i	1.08953	−	1.08953i	0.0939553	−	0.995576i	$-0.470049\pi$
$743$	29.6985	−	29.6985i	1.08953	−	1.08953i	0.995576	−	0.0939553i	$-0.0299511\pi$
$744$	−10.0000			−0.366618
$745$		0			0
$746$			22.0000i			0.805477i
$747$	12.0000			0.439057
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−1.41421	+	1.41421i	−0.0516054	+	0.0516054i	−0.732439	−	0.680833i	$-0.761618\pi$
$751$	−1.41421	+	1.41421i	−0.0516054	+	0.0516054i	0.680833	+	0.732439i	$0.261618\pi$
$752$	−12.0000			−0.437595
$753$	8.48528	−	8.48528i	0.309221	−	0.309221i
$754$		0			0
$755$		0			0
$756$		−	2.00000i		−	0.0727393i
$757$			34.0000i			1.23575i	0.786276	+	0.617876i	$0.212006\pi$
$757$			34.0000i			1.23575i	−0.786276	+	0.617876i	$0.787994\pi$
$758$	19.7990	+	19.7990i	0.719132	+	0.719132i
$759$		0			0
$760$		0			0
$761$	54.0000			1.95750			0.978749	−	0.205061i	$-0.0657392\pi$
$761$	54.0000			1.95750			0.978749	+	0.205061i	$0.0657392\pi$
$762$	5.65685	−	5.65685i	0.204926	−	0.204926i
$763$			40.0000i			1.44810i
$764$	−12.0000			−0.434145
$765$		0			0
$766$	12.0000			0.433578
$767$		−	24.0000i		−	0.866590i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	22.0000			0.793340			0.396670	−	0.917961i	$-0.370166\pi$
$769$	22.0000			0.793340			0.396670	+	0.917961i	$0.370166\pi$
$770$		0			0
$771$	−12.7279	−	12.7279i	−0.458385	−	0.458385i
$772$	9.89949	+	9.89949i	0.356291	+	0.356291i
$773$			6.00000i			0.215805i	0.994161	+	0.107903i	$0.0344134\pi$
$773$			6.00000i			0.215805i	−0.994161	+	0.107903i	$0.965587\pi$
$774$		−	4.00000i		−	0.143777i
$775$	35.3553	+	35.3553i	1.27000	+	1.27000i
$776$	9.89949	+	9.89949i	0.355371	+	0.355371i
$777$	11.3137	−	11.3137i	0.405877	−	0.405877i
$778$	−30.0000			−1.07555
$779$	16.9706	−	16.9706i	0.608034	−	0.608034i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		−	3.00000i		−	0.107143i
$785$		0			0
$786$		0			0
$787$	22.6274	−	22.6274i	0.806580	−	0.806580i	−0.177534	−	0.984115i	$-0.556812\pi$
$787$	22.6274	−	22.6274i	0.806580	−	0.806580i	0.984115	+	0.177534i	$0.0568121\pi$
$788$	8.48528	+	8.48528i	0.302276	+	0.302276i
$789$	8.48528	+	8.48528i	0.302084	+	0.302084i
$790$		0			0
$791$			12.0000i			0.426671i
$792$		0			0
$793$	−11.3137	−	11.3137i	−0.401762	−	0.401762i
$794$	11.3137	−	11.3137i	0.401508	−	0.401508i
$795$		0			0
$796$	−1.41421	+	1.41421i	−0.0501255	+	0.0501255i
$797$			6.00000i			0.212531i	0.994338	+	0.106265i	$0.0338893\pi$
$797$			6.00000i			0.212531i	−0.994338	+	0.106265i	$0.966111\pi$
$798$	8.00000			0.283197
$799$		0			0
$800$	5.00000			0.176777
$801$		−	18.0000i		−	0.635999i
$802$	−12.7279	+	12.7279i	−0.449439	+	0.449439i
$803$		0			0
$804$	−2.82843	+	2.82843i	−0.0997509	+	0.0997509i
$805$		0			0
$806$	14.1421	+	14.1421i	0.498135	+	0.498135i
$807$		−	24.0000i		−	0.844840i
$808$			6.00000i			0.211079i
$809$	4.24264	+	4.24264i	0.149163	+	0.149163i	0.777744	−	0.628581i	$-0.216364\pi$
$809$	4.24264	+	4.24264i	0.149163	+	0.149163i	−0.628581	+	0.777744i	$0.716364\pi$
$810$		0			0
$811$	−2.82843	+	2.82843i	−0.0993195	+	0.0993195i	−0.755021	−	0.655701i	$-0.772373\pi$
$811$	−2.82843	+	2.82843i	−0.0993195	+	0.0993195i	0.655701	+	0.755021i	$0.272373\pi$
$812$		0			0
$813$	11.3137	−	11.3137i	0.396789	−	0.396789i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	16.0000			0.559769
$818$		−	38.0000i		−	1.32864i
$819$	−2.82843	+	2.82843i	−0.0988332	+	0.0988332i
$820$		0			0
$821$	−25.4558	+	25.4558i	−0.888415	+	0.888415i	−0.994371	−	0.105956i	$-0.966210\pi$
$821$	−25.4558	+	25.4558i	−0.888415	+	0.888415i	0.105956	+	0.994371i	$0.466210\pi$
$822$	−4.24264	−	4.24264i	−0.147979	−	0.147979i
$823$	−24.0416	−	24.0416i	−0.838039	−	0.838039i	0.150562	−	0.988601i	$-0.451892\pi$
$823$	−24.0416	−	24.0416i	−0.838039	−	0.838039i	−0.988601	+	0.150562i	$0.951892\pi$
$824$		−	4.00000i		−	0.139347i
$825$		0			0
$826$	16.9706	+	16.9706i	0.590481	+	0.590481i
$827$	−33.9411	−	33.9411i	−1.18025	−	1.18025i	−0.979680	−	0.200569i	$-0.935721\pi$
$827$	−33.9411	−	33.9411i	−1.18025	−	1.18025i	−0.200569	−	0.979680i	$-0.564279\pi$
$828$	−4.24264	+	4.24264i	−0.147442	+	0.147442i
$829$	10.0000			0.347314			0.173657	−	0.984806i	$-0.444442\pi$
$829$	10.0000			0.347314			0.173657	+	0.984806i	$0.444442\pi$
$830$		0			0
$831$		−	4.00000i		−	0.138758i
$832$	2.00000			0.0693375
$833$		0			0
$834$	−8.00000			−0.277017
$835$		0			0
$836$		0			0
$837$	10.0000			0.345651
$838$	25.4558	−	25.4558i	0.879358	−	0.879358i
$839$	12.7279	+	12.7279i	0.439417	+	0.439417i	0.891816	−	0.452399i	$-0.149432\pi$
$839$	12.7279	+	12.7279i	0.439417	+	0.439417i	−0.452399	+	0.891816i	$0.649432\pi$
$840$		0			0
$841$			29.0000i			1.00000i
$842$		−	22.0000i		−	0.758170i
$843$	21.2132	+	21.2132i	0.730622	+	0.730622i
$844$	−5.65685	−	5.65685i	−0.194717	−	0.194717i
$845$		0			0
$846$	12.0000			0.412568
$847$	15.5563	−	15.5563i	0.534522	−	0.534522i
$848$			6.00000i			0.206041i
$849$	−16.0000			−0.549119
$850$		0			0
$851$	−48.0000			−1.64542
$852$			6.00000i			0.205557i
$853$	19.7990	−	19.7990i	0.677905	−	0.677905i	−0.281621	−	0.959526i	$-0.590872\pi$
$853$	19.7990	−	19.7990i	0.677905	−	0.677905i	0.959526	+	0.281621i	$0.0908721\pi$
$854$	16.0000			0.547509
$855$		0			0
$856$		0			0
$857$	4.24264	+	4.24264i	0.144926	+	0.144926i	0.775847	−	0.630921i	$-0.217323\pi$
$857$	4.24264	+	4.24264i	0.144926	+	0.144926i	−0.630921	+	0.775847i	$0.717323\pi$
$858$		0			0
$859$			28.0000i			0.955348i	0.878537	+	0.477674i	$0.158520\pi$
$859$			28.0000i			0.955348i	−0.878537	+	0.477674i	$0.841480\pi$
$860$		0			0
$861$	−8.48528	−	8.48528i	−0.289178	−	0.289178i
$862$	21.2132	−	21.2132i	0.722525	−	0.722525i
$863$	−48.0000			−1.63394			−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000			−1.63394			−0.816970	+	0.576681i	$0.804348\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$		0			0
$866$	−14.0000			−0.475739
$867$		0			0
$868$	−20.0000			−0.678844
$869$		0			0
$870$		0			0
$871$	8.00000			0.271070
$872$	−14.1421	+	14.1421i	−0.478913	+	0.478913i
$873$	−9.89949	−	9.89949i	−0.335047	−	0.335047i
$874$	−16.9706	−	16.9706i	−0.574038	−	0.574038i
$875$		0			0
$876$		−	2.00000i		−	0.0675737i
$877$	−2.82843	−	2.82843i	−0.0955092	−	0.0955092i	0.657738	−	0.753247i	$-0.271513\pi$
$877$	−2.82843	−	2.82843i	−0.0955092	−	0.0955092i	−0.753247	+	0.657738i	$0.771513\pi$
$878$	18.3848	+	18.3848i	0.620456	+	0.620456i
$879$	12.7279	−	12.7279i	0.429302	−	0.429302i
$880$		0			0
$881$	38.1838	−	38.1838i	1.28644	−	1.28644i	0.349512	−	0.936932i	$-0.386347\pi$
$881$	38.1838	−	38.1838i	1.28644	−	1.28644i	0.936932	−	0.349512i	$-0.113653\pi$
$882$			3.00000i			0.101015i
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$		0			0
$885$		0			0
$886$			36.0000i			1.20944i
$887$	12.7279	−	12.7279i	0.427362	−	0.427362i	−0.460367	−	0.887729i	$-0.652282\pi$
$887$	12.7279	−	12.7279i	0.427362	−	0.427362i	0.887729	+	0.460367i	$0.152282\pi$
$888$	8.00000			0.268462
$889$	11.3137	−	11.3137i	0.379450	−	0.379450i
$890$		0			0
$891$		0			0
$892$			28.0000i			0.937509i
$893$			48.0000i			1.60626i
$894$	4.24264	+	4.24264i	0.141895	+	0.141895i
$895$		0			0
$896$	−1.41421	+	1.41421i	−0.0472456	+	0.0472456i
$897$	12.0000			0.400668
$898$	4.24264	−	4.24264i	0.141579	−	0.141579i
$899$		0			0
$900$	−5.00000			−0.166667
$901$		0			0
$902$		0			0
$903$		−	8.00000i		−	0.266223i
$904$	−4.24264	+	4.24264i	−0.141108	+	0.141108i
$905$		0			0
$906$	−5.65685	+	5.65685i	−0.187936	+	0.187936i
$907$	28.2843	+	28.2843i	0.939164	+	0.939164i	0.998253	−	0.0590889i	$-0.0188195\pi$
$907$	28.2843	+	28.2843i	0.939164	+	0.939164i	−0.0590889	+	0.998253i	$0.518820\pi$
$908$	8.48528	+	8.48528i	0.281594	+	0.281594i
$909$		−	6.00000i		−	0.199007i
$910$		0			0
$911$	4.24264	+	4.24264i	0.140565	+	0.140565i	0.773888	−	0.633323i	$-0.218309\pi$
$911$	4.24264	+	4.24264i	0.140565	+	0.140565i	−0.633323	+	0.773888i	$0.718309\pi$
$912$	2.82843	+	2.82843i	0.0936586	+	0.0936586i
$913$		0			0
$914$	−10.0000			−0.330771
$915$		0			0
$916$			14.0000i			0.462573i
$917$		0			0
$918$		0			0
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$		0			0
$921$	−14.1421	+	14.1421i	−0.465999	+	0.465999i
$922$	30.0000			0.987997
$923$	8.48528	−	8.48528i	0.279296	−	0.279296i
$924$		0			0
$925$	−28.2843	−	28.2843i	−0.929981	−	0.929981i
$926$			20.0000i			0.657241i
$927$			4.00000i			0.131377i
$928$		0			0
$929$	12.7279	+	12.7279i	0.417590	+	0.417590i	0.884372	−	0.466783i	$-0.154587\pi$
$929$	12.7279	+	12.7279i	0.417590	+	0.417590i	−0.466783	+	0.884372i	$0.654587\pi$
$930$		0			0
$931$	−12.0000			−0.393284
$932$	21.2132	−	21.2132i	0.694862	−	0.694862i
$933$			18.0000i			0.589294i
$934$	−12.0000			−0.392652
$935$		0			0
$936$	−2.00000			−0.0653720
$937$		−	10.0000i		−	0.326686i	−0.986569	−	0.163343i	$-0.947772\pi$
$937$		−	10.0000i		−	0.326686i	0.986569	−	0.163343i	$-0.0522277\pi$
$938$	−5.65685	+	5.65685i	−0.184703	+	0.184703i
$939$	−14.0000			−0.456873
$940$		0			0
$941$	−8.48528	−	8.48528i	−0.276612	−	0.276612i	0.555143	−	0.831755i	$-0.312664\pi$
$941$	−8.48528	−	8.48528i	−0.276612	−	0.276612i	−0.831755	+	0.555143i	$0.812664\pi$
$942$	7.07107	+	7.07107i	0.230388	+	0.230388i
$943$			36.0000i			1.17232i
$944$			12.0000i			0.390567i
$945$		0			0
$946$		0			0
$947$	16.9706	−	16.9706i	0.551469	−	0.551469i	−0.375396	−	0.926865i	$-0.622493\pi$
$947$	16.9706	−	16.9706i	0.551469	−	0.551469i	0.926865	+	0.375396i	$0.122493\pi$
$948$	10.0000			0.324785
$949$	−2.82843	+	2.82843i	−0.0918146	+	0.0918146i
$950$		−	20.0000i		−	0.648886i
$951$	12.0000			0.389127
$952$		0			0
$953$	54.0000			1.74923			0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000			1.74923			0.874616	+	0.484817i	$0.161114\pi$
$954$		−	6.00000i		−	0.194257i
$955$		0			0
$956$	12.0000			0.388108
$957$		0			0
$958$	4.24264	+	4.24264i	0.137073	+	0.137073i
$959$	−8.48528	−	8.48528i	−0.274004	−	0.274004i
$960$		0			0
$961$		−	69.0000i		−	2.22581i
$962$	−11.3137	−	11.3137i	−0.364769	−	0.364769i
$963$		0			0
$964$	−7.07107	+	7.07107i	−0.227744	+	0.227744i
$965$		0			0
$966$	−8.48528	+	8.48528i	−0.273009	+	0.273009i
$967$		−	4.00000i		−	0.128631i	−0.997930	−	0.0643157i	$-0.979514\pi$
$967$		−	4.00000i		−	0.128631i	0.997930	−	0.0643157i	$-0.0204865\pi$
$968$	11.0000			0.353553
$969$		0			0
$970$		0			0
$971$			12.0000i			0.385098i	0.981287	+	0.192549i	$0.0616755\pi$
$971$			12.0000i			0.385098i	−0.981287	+	0.192549i	$0.938325\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−16.0000			−0.512936
$974$	7.07107	−	7.07107i	0.226572	−	0.226572i
$975$	7.07107	+	7.07107i	0.226455	+	0.226455i
$976$	5.65685	+	5.65685i	0.181071	+	0.181071i
$977$			30.0000i			0.959785i	0.877327	+	0.479893i	$0.159324\pi$
$977$			30.0000i			0.959785i	−0.877327	+	0.479893i	$0.840676\pi$
$978$			20.0000i			0.639529i
$979$		0			0
$980$		0			0
$981$	14.1421	−	14.1421i	0.451524	−	0.451524i
$982$	−36.0000			−1.14881
$983$	−4.24264	+	4.24264i	−0.135319	+	0.135319i	−0.771522	−	0.636203i	$-0.780504\pi$
$983$	−4.24264	+	4.24264i	−0.135319	+	0.135319i	0.636203	+	0.771522i	$0.280504\pi$
$984$		−	6.00000i		−	0.191273i
$985$		0			0
$986$		0			0
$987$	24.0000			0.763928
$988$		−	8.00000i		−	0.254514i
$989$	−16.9706	+	16.9706i	−0.539633	+	0.539633i
$990$		0			0
$991$	1.41421	−	1.41421i	0.0449240	−	0.0449240i	−0.684288	−	0.729212i	$-0.739887\pi$
$991$	1.41421	−	1.41421i	0.0449240	−	0.0449240i	0.729212	+	0.684288i	$0.239887\pi$
$992$	−7.07107	−	7.07107i	−0.224507	−	0.224507i
$993$	14.1421	+	14.1421i	0.448787	+	0.448787i
$994$			12.0000i			0.380617i
$995$		0			0
$996$	8.48528	+	8.48528i	0.268866	+	0.268866i
$997$	−5.65685	−	5.65685i	−0.179154	−	0.179154i	0.611833	−	0.790987i	$-0.290433\pi$
$997$	−5.65685	−	5.65685i	−0.179154	−	0.179154i	−0.790987	+	0.611833i	$0.790433\pi$
$998$	−22.6274	+	22.6274i	−0.716258	+	0.716258i
$999$	−8.00000			−0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1734.2.f.b.1483.1		4
17.2	even	8		1734.2.b.f.577.2		2
17.4	even	4	inner	1734.2.f.b.829.2		4
17.8	even	8		102.2.a.b.1.1	✓	1
17.9	even	8		1734.2.a.b.1.1		1
17.13	even	4	inner	1734.2.f.b.829.1		4
17.15	even	8		1734.2.b.f.577.1		2
17.16	even	2	inner	1734.2.f.b.1483.2		4
51.8	odd	8		306.2.a.c.1.1		1
51.26	odd	8		5202.2.a.j.1.1		1
68.59	odd	8		816.2.a.d.1.1		1
85.8	odd	8		2550.2.d.g.2449.2		2
85.42	odd	8		2550.2.d.g.2449.1		2
85.59	even	8		2550.2.a.u.1.1		1
119.76	odd	8		4998.2.a.d.1.1		1
136.59	odd	8		3264.2.a.w.1.1		1
136.93	even	8		3264.2.a.i.1.1		1
204.59	even	8		2448.2.a.i.1.1		1
255.59	odd	8		7650.2.a.j.1.1		1
408.59	even	8		9792.2.a.ba.1.1		1
408.365	odd	8		9792.2.a.bg.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.2.a.b.1.1	✓	1	17.8	even	8
306.2.a.c.1.1		1	51.8	odd	8
816.2.a.d.1.1		1	68.59	odd	8
1734.2.a.b.1.1		1	17.9	even	8
1734.2.b.f.577.1		2	17.15	even	8
1734.2.b.f.577.2		2	17.2	even	8
1734.2.f.b.829.1		4	17.13	even	4	inner
1734.2.f.b.829.2		4	17.4	even	4	inner
1734.2.f.b.1483.1		4	1.1	even	1	trivial
1734.2.f.b.1483.2		4	17.16	even	2	inner
2448.2.a.i.1.1		1	204.59	even	8
2550.2.a.u.1.1		1	85.59	even	8
2550.2.d.g.2449.1		2	85.42	odd	8
2550.2.d.g.2449.2		2	85.8	odd	8
3264.2.a.i.1.1		1	136.93	even	8
3264.2.a.w.1.1		1	136.59	odd	8
4998.2.a.d.1.1		1	119.76	odd	8
5202.2.a.j.1.1		1	51.26	odd	8
7650.2.a.j.1.1		1	255.59	odd	8
9792.2.a.ba.1.1		1	408.59	even	8
9792.2.a.bg.1.1		1	408.365	odd	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1734.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(0.707107 + 0.707107i) q^{6} +(1.41421 + 1.41421i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(0.707107 - 0.707107i) q^{12} -2.00000 q^{13} +(1.41421 - 1.41421i) q^{14} +1.00000 q^{16} -1.00000 q^{18} -4.00000i q^{19} -2.00000 q^{21} +(4.24264 + 4.24264i) q^{23} +(-0.707107 - 0.707107i) q^{24} +5.00000i q^{25} +2.00000i q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.41421 - 1.41421i) q^{28} +(7.07107 - 7.07107i) q^{31} -1.00000i q^{32} +1.00000i q^{36} +(-5.65685 + 5.65685i) q^{37} -4.00000 q^{38} +(1.41421 - 1.41421i) q^{39} +(4.24264 + 4.24264i) q^{41} +2.00000i q^{42} +4.00000i q^{43} +(4.24264 - 4.24264i) q^{46} -12.0000 q^{47} +(-0.707107 + 0.707107i) q^{48} -3.00000i q^{49} +5.00000 q^{50} +2.00000 q^{52} +6.00000i q^{53} +(0.707107 - 0.707107i) q^{54} +(-1.41421 + 1.41421i) q^{56} +(2.82843 + 2.82843i) q^{57} +12.0000i q^{59} +(5.65685 + 5.65685i) q^{61} +(-7.07107 - 7.07107i) q^{62} +(1.41421 - 1.41421i) q^{63} -1.00000 q^{64} -4.00000 q^{67} -6.00000 q^{69} +(-4.24264 + 4.24264i) q^{71} +1.00000 q^{72} +(1.41421 - 1.41421i) q^{73} +(5.65685 + 5.65685i) q^{74} +(-3.53553 - 3.53553i) q^{75} +4.00000i q^{76} +(-1.41421 - 1.41421i) q^{78} +(7.07107 + 7.07107i) q^{79} -1.00000 q^{81} +(4.24264 - 4.24264i) q^{82} +12.0000i q^{83} +2.00000 q^{84} +4.00000 q^{86} +18.0000 q^{89} +(-2.82843 - 2.82843i) q^{91} +(-4.24264 - 4.24264i) q^{92} +10.0000i q^{93} +12.0000i q^{94} +(0.707107 + 0.707107i) q^{96} +(9.89949 - 9.89949i) q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 8 q^{13} + 4 q^{16} - 4 q^{18} - 8 q^{21} - 16 q^{38} - 48 q^{47} + 20 q^{50} + 8 q^{52} - 4 q^{64} - 16 q^{67} - 24 q^{69} + 4 q^{72} - 4 q^{81} + 8 q^{84} + 16 q^{86} + 72 q^{89} - 12 q^{98}+O(q^{100}) \) 4 * q - 4 * q^4 - 8 * q^13 + 4 * q^16 - 4 * q^18 - 8 * q^21 - 16 * q^38 - 48 * q^47 + 20 * q^50 + 8 * q^52 - 4 * q^64 - 16 * q^67 - 24 * q^69 + 4 * q^72 - 4 * q^81 + 8 * q^84 + 16 * q^86 + 72 * q^89 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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