LMFDB - Embedded newform 114.2.h.c.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(65,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("114.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	114.65
Dual form			114.2.h.c.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.00000 - 1.73205i) q^{5} +(-1.50000 + 0.866025i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.00000 - 1.73205i) q^{5} +(-1.50000 + 0.866025i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-3.00000 + 1.73205i) q^{10} -3.46410i q^{11} +1.73205i q^{12} +(4.50000 - 2.59808i) q^{13} +(0.500000 - 0.866025i) q^{14} +(3.00000 + 5.19615i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 1.73205i) q^{17} +3.00000 q^{18} +(-4.00000 - 1.73205i) q^{19} +3.46410i q^{20} +(-1.50000 - 0.866025i) q^{21} +(-3.00000 - 1.73205i) q^{22} +(1.50000 + 0.866025i) q^{24} +(3.50000 + 6.06218i) q^{25} -5.19615i q^{26} -5.19615i q^{27} +(-0.500000 - 0.866025i) q^{28} +(3.00000 + 5.19615i) q^{29} +6.00000 q^{30} -1.73205i q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{33} +(3.00000 - 1.73205i) q^{34} +(-3.00000 - 1.73205i) q^{35} +(1.50000 - 2.59808i) q^{36} +5.19615i q^{37} +(-3.50000 + 2.59808i) q^{38} -9.00000 q^{39} +(3.00000 + 1.73205i) q^{40} +(6.00000 - 10.3923i) q^{41} +(-1.50000 + 0.866025i) q^{42} +(0.500000 - 0.866025i) q^{43} +(-3.00000 + 1.73205i) q^{44} -10.3923i q^{45} +(-6.00000 + 3.46410i) q^{47} +(1.50000 - 0.866025i) q^{48} -6.00000 q^{49} +7.00000 q^{50} +(-3.00000 - 5.19615i) q^{51} +(-4.50000 - 2.59808i) q^{52} +(6.00000 + 10.3923i) q^{53} +(-4.50000 - 2.59808i) q^{54} +(-6.00000 + 10.3923i) q^{55} -1.00000 q^{56} +(4.50000 + 6.06218i) q^{57} +6.00000 q^{58} +(3.00000 - 5.19615i) q^{60} +(-3.50000 - 6.06218i) q^{61} +(-1.50000 - 0.866025i) q^{62} +(1.50000 + 2.59808i) q^{63} +1.00000 q^{64} -18.0000 q^{65} +(3.00000 + 5.19615i) q^{66} +(7.50000 - 4.33013i) q^{67} -3.46410i q^{68} +(-3.00000 + 1.73205i) q^{70} +(3.00000 - 5.19615i) q^{71} +(-1.50000 - 2.59808i) q^{72} +(3.50000 - 6.06218i) q^{73} +(4.50000 + 2.59808i) q^{74} -12.1244i q^{75} +(0.500000 + 4.33013i) q^{76} -3.46410i q^{77} +(-4.50000 + 7.79423i) q^{78} +(4.50000 + 2.59808i) q^{79} +(3.00000 - 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-6.00000 - 10.3923i) q^{82} +10.3923i q^{83} +1.73205i q^{84} +(-6.00000 - 10.3923i) q^{85} +(-0.500000 - 0.866025i) q^{86} -10.3923i q^{87} +3.46410i q^{88} +(-9.00000 - 5.19615i) q^{90} +(4.50000 - 2.59808i) q^{91} +(-1.50000 + 2.59808i) q^{93} +6.92820i q^{94} +(9.00000 + 12.1244i) q^{95} -1.73205i q^{96} +(6.00000 + 3.46410i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(9.00000 - 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 3 q^{3} - q^{4} - 6 q^{5} - 3 q^{6} + 2 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + q^2 - 3 * q^3 - q^4 - 6 * q^5 - 3 * q^6 + 2 * q^7 - 2 * q^8 + 3 * q^9	$ 2 q + q^{2} - 3 q^{3} - q^{4} - 6 q^{5} - 3 q^{6} + 2 q^{7} - 2 q^{8} + 3 q^{9} - 6 q^{10} + 9 q^{13} + q^{14} + 6 q^{15} - q^{16} + 6 q^{17} + 6 q^{18} - 8 q^{19} - 3 q^{21} - 6 q^{22} + 3 q^{24} + 7 q^{25} - q^{28} + 6 q^{29} + 12 q^{30} + q^{32} - 6 q^{33} + 6 q^{34} - 6 q^{35} + 3 q^{36} - 7 q^{38} - 18 q^{39} + 6 q^{40} + 12 q^{41} - 3 q^{42} + q^{43} - 6 q^{44} - 12 q^{47} + 3 q^{48} - 12 q^{49} + 14 q^{50} - 6 q^{51} - 9 q^{52} + 12 q^{53} - 9 q^{54} - 12 q^{55} - 2 q^{56} + 9 q^{57} + 12 q^{58} + 6 q^{60} - 7 q^{61} - 3 q^{62} + 3 q^{63} + 2 q^{64} - 36 q^{65} + 6 q^{66} + 15 q^{67} - 6 q^{70} + 6 q^{71} - 3 q^{72} + 7 q^{73} + 9 q^{74} + q^{76} - 9 q^{78} + 9 q^{79} + 6 q^{80} - 9 q^{81} - 12 q^{82} - 12 q^{85} - q^{86} - 18 q^{90} + 9 q^{91} - 3 q^{93} + 18 q^{95} + 12 q^{97} - 6 q^{98} + 18 q^{99}+O(q^{100}) $ 2 * q + q^2 - 3 * q^3 - q^4 - 6 * q^5 - 3 * q^6 + 2 * q^7 - 2 * q^8 + 3 * q^9 - 6 * q^10 + 9 * q^13 + q^14 + 6 * q^15 - q^16 + 6 * q^17 + 6 * q^18 - 8 * q^19 - 3 * q^21 - 6 * q^22 + 3 * q^24 + 7 * q^25 - q^28 + 6 * q^29 + 12 * q^30 + q^32 - 6 * q^33 + 6 * q^34 - 6 * q^35 + 3 * q^36 - 7 * q^38 - 18 * q^39 + 6 * q^40 + 12 * q^41 - 3 * q^42 + q^43 - 6 * q^44 - 12 * q^47 + 3 * q^48 - 12 * q^49 + 14 * q^50 - 6 * q^51 - 9 * q^52 + 12 * q^53 - 9 * q^54 - 12 * q^55 - 2 * q^56 + 9 * q^57 + 12 * q^58 + 6 * q^60 - 7 * q^61 - 3 * q^62 + 3 * q^63 + 2 * q^64 - 36 * q^65 + 6 * q^66 + 15 * q^67 - 6 * q^70 + 6 * q^71 - 3 * q^72 + 7 * q^73 + 9 * q^74 + q^76 - 9 * q^78 + 9 * q^79 + 6 * q^80 - 9 * q^81 - 12 * q^82 - 12 * q^85 - q^86 - 18 * q^90 + 9 * q^91 - 3 * q^93 + 18 * q^95 + 12 * q^97 - 6 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−3.00000	−	1.73205i	−1.34164	−	0.774597i	−0.354593	−	0.935021i	$-0.615380\pi$
$5$	−3.00000	−	1.73205i	−1.34164	−	0.774597i	−0.987048	+	0.160424i	$0.948714\pi$
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$	1.00000			0.377964			0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000			0.377964			0.188982	+	0.981981i	$0.439481\pi$
$8$	−1.00000			−0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−3.00000	+	1.73205i	−0.948683	+	0.547723i
$11$		−	3.46410i		−	1.04447i	−0.852803	−	0.522233i	$-0.825099\pi$
$11$		−	3.46410i		−	1.04447i	0.852803	−	0.522233i	$-0.174901\pi$
$12$			1.73205i			0.500000i
$13$	4.50000	−	2.59808i	1.24808	−	0.720577i	0.277350	−	0.960769i	$-0.410544\pi$
$13$	4.50000	−	2.59808i	1.24808	−	0.720577i	0.970725	+	0.240192i	$0.0772105\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$	3.00000	+	5.19615i	0.774597	+	1.34164i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.00000	+	1.73205i	0.727607	+	0.420084i	0.817546	−	0.575863i	$-0.195334\pi$
$17$	3.00000	+	1.73205i	0.727607	+	0.420084i	−0.0899392	+	0.995947i	$0.528667\pi$
$18$	3.00000			0.707107
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$20$			3.46410i			0.774597i
$21$	−1.50000	−	0.866025i	−0.327327	−	0.188982i
$22$	−3.00000	−	1.73205i	−0.639602	−	0.369274i
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	3.50000	+	6.06218i	0.700000	+	1.21244i
$26$		−	5.19615i		−	1.01905i
$27$		−	5.19615i		−	1.00000i
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$	6.00000			1.09545
$31$		−	1.73205i		−	0.311086i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$		−	1.73205i		−	0.311086i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−3.00000	+	5.19615i	−0.522233	+	0.904534i
$34$	3.00000	−	1.73205i	0.514496	−	0.297044i
$35$	−3.00000	−	1.73205i	−0.507093	−	0.292770i
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$			5.19615i			0.854242i	0.904194	+	0.427121i	$0.140472\pi$
$37$			5.19615i			0.854242i	−0.904194	+	0.427121i	$0.859528\pi$
$38$	−3.50000	+	2.59808i	−0.567775	+	0.421464i
$39$	−9.00000			−1.44115
$40$	3.00000	+	1.73205i	0.474342	+	0.273861i
$41$	6.00000	−	10.3923i	0.937043	−	1.62301i	0.166092	−	0.986110i	$-0.446885\pi$
$41$	6.00000	−	10.3923i	0.937043	−	1.62301i	0.770950	−	0.636895i	$-0.219782\pi$
$42$	−1.50000	+	0.866025i	−0.231455	+	0.133631i
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	−3.00000	+	1.73205i	−0.452267	+	0.261116i
$45$		−	10.3923i		−	1.54919i
$46$		0			0
$47$	−6.00000	+	3.46410i	−0.875190	+	0.505291i	−0.869069	−	0.494690i	$-0.835282\pi$
$47$	−6.00000	+	3.46410i	−0.875190	+	0.505291i	−0.00612051	+	0.999981i	$0.501948\pi$
$48$	1.50000	−	0.866025i	0.216506	−	0.125000i
$49$	−6.00000			−0.857143
$50$	7.00000			0.989949
$51$	−3.00000	−	5.19615i	−0.420084	−	0.727607i
$52$	−4.50000	−	2.59808i	−0.624038	−	0.360288i
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	0.902557	+	0.430570i	$0.141688\pi$
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	−0.0783936	+	0.996922i	$0.524979\pi$
$54$	−4.50000	−	2.59808i	−0.612372	−	0.353553i
$55$	−6.00000	+	10.3923i	−0.809040	+	1.40130i
$56$	−1.00000			−0.133631
$57$	4.50000	+	6.06218i	0.596040	+	0.802955i
$58$	6.00000			0.787839
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$	3.00000	−	5.19615i	0.387298	−	0.670820i
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	0.550135	−	0.835076i	$-0.314576\pi$
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	−0.998264	+	0.0588933i	$0.981243\pi$
$62$	−1.50000	−	0.866025i	−0.190500	−	0.109985i
$63$	1.50000	+	2.59808i	0.188982	+	0.327327i
$64$	1.00000			0.125000
$65$	−18.0000			−2.23263
$66$	3.00000	+	5.19615i	0.369274	+	0.639602i
$67$	7.50000	−	4.33013i	0.916271	−	0.529009i	0.0338274	−	0.999428i	$-0.489230\pi$
$67$	7.50000	−	4.33013i	0.916271	−	0.529009i	0.882443	+	0.470418i	$0.155897\pi$
$68$		−	3.46410i		−	0.420084i
$69$		0			0
$70$	−3.00000	+	1.73205i	−0.358569	+	0.207020i
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	0.994850	+	0.101361i	$0.0323196\pi$
$74$	4.50000	+	2.59808i	0.523114	+	0.302020i
$75$		−	12.1244i		−	1.40000i
$76$	0.500000	+	4.33013i	0.0573539	+	0.496700i
$77$		−	3.46410i		−	0.394771i
$78$	−4.50000	+	7.79423i	−0.509525	+	0.882523i
$79$	4.50000	+	2.59808i	0.506290	+	0.292306i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	4.50000	+	2.59808i	0.506290	+	0.292306i	−0.225018	+	0.974355i	$0.572244\pi$
$80$	3.00000	−	1.73205i	0.335410	−	0.193649i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−6.00000	−	10.3923i	−0.662589	−	1.14764i
$83$			10.3923i			1.14070i	0.821401	+	0.570352i	$0.193193\pi$
$83$			10.3923i			1.14070i	−0.821401	+	0.570352i	$0.806807\pi$
$84$			1.73205i			0.188982i
$85$	−6.00000	−	10.3923i	−0.650791	−	1.12720i
$86$	−0.500000	−	0.866025i	−0.0539164	−	0.0933859i
$87$		−	10.3923i		−	1.11417i
$88$			3.46410i			0.369274i
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$	−9.00000	−	5.19615i	−0.948683	−	0.547723i
$91$	4.50000	−	2.59808i	0.471728	−	0.272352i
$92$		0			0
$93$	−1.50000	+	2.59808i	−0.155543	+	0.269408i
$94$			6.92820i			0.714590i
$95$	9.00000	+	12.1244i	0.923381	+	1.24393i
$96$		−	1.73205i		−	0.176777i
$97$	6.00000	+	3.46410i	0.609208	+	0.351726i	0.772655	−	0.634826i	$-0.218928\pi$
$97$	6.00000	+	3.46410i	0.609208	+	0.351726i	−0.163448	+	0.986552i	$0.552261\pi$
$98$	−3.00000	+	5.19615i	−0.303046	+	0.524891i
$99$	9.00000	−	5.19615i	0.904534	−	0.522233i
$100$	3.50000	−	6.06218i	0.350000	−	0.606218i
$101$	−9.00000	+	5.19615i	−0.895533	+	0.517036i	−0.875748	−	0.482768i	$-0.839632\pi$
$101$	−9.00000	+	5.19615i	−0.895533	+	0.517036i	−0.0197851	+	0.999804i	$0.506298\pi$
$102$	−6.00000			−0.594089
$103$			8.66025i			0.853320i	0.904412	+	0.426660i	$0.140310\pi$
$103$			8.66025i			0.853320i	−0.904412	+	0.426660i	$0.859690\pi$
$104$	−4.50000	+	2.59808i	−0.441261	+	0.254762i
$105$	3.00000	+	5.19615i	0.292770	+	0.507093i
$106$	12.0000			1.16554
$107$	18.0000			1.74013			0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000			1.74013			0.870063	+	0.492941i	$0.164078\pi$
$108$	−4.50000	+	2.59808i	−0.433013	+	0.250000i
$109$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$109$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$110$	6.00000	+	10.3923i	0.572078	+	0.990867i
$111$	4.50000	−	7.79423i	0.427121	−	0.739795i
$112$	−0.500000	+	0.866025i	−0.0472456	+	0.0818317i
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$	7.50000	−	0.866025i	0.702439	−	0.0811107i
$115$		0			0
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$	13.5000	+	7.79423i	1.24808	+	0.720577i
$118$		0			0
$119$	3.00000	+	1.73205i	0.275010	+	0.158777i
$120$	−3.00000	−	5.19615i	−0.273861	−	0.474342i
$121$	−1.00000			−0.0909091
$122$	−7.00000			−0.633750
$123$	−18.0000	+	10.3923i	−1.62301	+	0.937043i
$124$	−1.50000	+	0.866025i	−0.134704	+	0.0777714i
$125$		−	6.92820i		−	0.619677i
$126$	3.00000			0.267261
$127$	−9.00000	+	5.19615i	−0.798621	+	0.461084i	−0.842989	−	0.537931i	$-0.819206\pi$
$127$	−9.00000	+	5.19615i	−0.798621	+	0.461084i	0.0443678	+	0.999015i	$0.485873\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−1.50000	+	0.866025i	−0.132068	+	0.0762493i
$130$	−9.00000	+	15.5885i	−0.789352	+	1.36720i
$131$	−3.00000	−	1.73205i	−0.262111	−	0.151330i	0.363186	−	0.931717i	$-0.381689\pi$
$131$	−3.00000	−	1.73205i	−0.262111	−	0.151330i	−0.625297	+	0.780387i	$0.715022\pi$
$132$	6.00000			0.522233
$133$	−4.00000	−	1.73205i	−0.346844	−	0.150188i
$134$		−	8.66025i		−	0.748132i
$135$	−9.00000	+	15.5885i	−0.774597	+	1.34164i
$136$	−3.00000	−	1.73205i	−0.257248	−	0.148522i
$137$	3.00000	−	1.73205i	0.256307	−	0.147979i	−0.366342	−	0.930480i	$-0.619390\pi$
$137$	3.00000	−	1.73205i	0.256307	−	0.147979i	0.622649	+	0.782501i	$0.286057\pi$
$138$		0			0
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	0.952355	−	0.304991i	$-0.0986536\pi$
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	−0.740308	+	0.672268i	$0.765320\pi$
$140$			3.46410i			0.292770i
$141$	12.0000			1.01058
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	−9.00000	−	15.5885i	−0.752618	−	1.30357i
$144$	−3.00000			−0.250000
$145$		−	20.7846i		−	1.72607i
$146$	−3.50000	−	6.06218i	−0.289662	−	0.501709i
$147$	9.00000	+	5.19615i	0.742307	+	0.428571i
$148$	4.50000	−	2.59808i	0.369898	−	0.213561i
$149$	−15.0000	−	8.66025i	−1.22885	−	0.709476i	−0.262059	−	0.965052i	$-0.584401\pi$
$149$	−15.0000	−	8.66025i	−1.22885	−	0.709476i	−0.966789	+	0.255576i	$0.917735\pi$
$150$	−10.5000	−	6.06218i	−0.857321	−	0.494975i
$151$			3.46410i			0.281905i	0.990016	+	0.140952i	$0.0450164\pi$
$151$			3.46410i			0.281905i	−0.990016	+	0.140952i	$0.954984\pi$
$152$	4.00000	+	1.73205i	0.324443	+	0.140488i
$153$			10.3923i			0.840168i
$154$	−3.00000	−	1.73205i	−0.241747	−	0.139573i
$155$	−3.00000	+	5.19615i	−0.240966	+	0.417365i
$156$	4.50000	+	7.79423i	0.360288	+	0.624038i
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	−0.971219	−	0.238190i	$-0.923446\pi$
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	0.691888	+	0.722005i	$0.256779\pi$
$158$	4.50000	−	2.59808i	0.358001	−	0.206692i
$159$		−	20.7846i		−	1.64833i
$160$		−	3.46410i		−	0.273861i
$161$		0			0
$162$	4.50000	+	7.79423i	0.353553	+	0.612372i
$163$	−11.0000			−0.861586			−0.430793	−	0.902451i	$-0.641766\pi$
$163$	−11.0000			−0.861586			−0.430793	+	0.902451i	$0.641766\pi$
$164$	−12.0000			−0.937043
$165$	18.0000	−	10.3923i	1.40130	−	0.809040i
$166$	9.00000	+	5.19615i	0.698535	+	0.403300i
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	0.534875	−	0.844931i	$-0.320359\pi$
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	−0.999169	+	0.0407502i	$0.987025\pi$
$168$	1.50000	+	0.866025i	0.115728	+	0.0668153i
$169$	7.00000	−	12.1244i	0.538462	−	0.932643i
$170$	−12.0000			−0.920358
$171$	−1.50000	−	12.9904i	−0.114708	−	0.993399i
$172$	−1.00000			−0.0762493
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$	−9.00000	−	5.19615i	−0.682288	−	0.393919i
$175$	3.50000	+	6.06218i	0.264575	+	0.458258i
$176$	3.00000	+	1.73205i	0.226134	+	0.130558i
$177$		0			0
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	−9.00000	+	5.19615i	−0.670820	+	0.387298i
$181$	−6.00000	+	3.46410i	−0.445976	+	0.257485i	−0.706129	−	0.708083i	$-0.749560\pi$
$181$	−6.00000	+	3.46410i	−0.445976	+	0.257485i	0.260153	+	0.965567i	$0.416227\pi$
$182$		−	5.19615i		−	0.385164i
$183$			12.1244i			0.896258i
$184$		0			0
$185$	9.00000	−	15.5885i	0.661693	−	1.14609i
$186$	1.50000	+	2.59808i	0.109985	+	0.190500i
$187$	6.00000	−	10.3923i	0.438763	−	0.759961i
$188$	6.00000	+	3.46410i	0.437595	+	0.252646i
$189$		−	5.19615i		−	0.377964i
$190$	15.0000	−	1.73205i	1.08821	−	0.125656i
$191$		−	17.3205i		−	1.25327i	−0.779314	−	0.626634i	$-0.784432\pi$
$191$		−	17.3205i		−	1.25327i	0.779314	−	0.626634i	$-0.215568\pi$
$192$	−1.50000	−	0.866025i	−0.108253	−	0.0625000i
$193$	−10.5000	−	6.06218i	−0.755807	−	0.436365i	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	−10.5000	−	6.06218i	−0.755807	−	0.436365i	−0.827788	+	0.561041i	$0.810401\pi$
$194$	6.00000	−	3.46410i	0.430775	−	0.248708i
$195$	27.0000	+	15.5885i	1.93351	+	1.11631i
$196$	3.00000	+	5.19615i	0.214286	+	0.371154i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		−	10.3923i		−	0.738549i
$199$	12.5000	+	21.6506i	0.886102	+	1.53477i	0.844446	+	0.535641i	$0.179930\pi$
$199$	12.5000	+	21.6506i	0.886102	+	1.53477i	0.0416556	+	0.999132i	$0.486737\pi$
$200$	−3.50000	−	6.06218i	−0.247487	−	0.428661i
$201$	−15.0000			−1.05802
$202$			10.3923i			0.731200i
$203$	3.00000	+	5.19615i	0.210559	+	0.364698i
$204$	−3.00000	+	5.19615i	−0.210042	+	0.363803i
$205$	−36.0000	+	20.7846i	−2.51435	+	1.45166i
$206$	7.50000	+	4.33013i	0.522550	+	0.301694i
$207$		0			0
$208$			5.19615i			0.360288i
$209$	−6.00000	+	13.8564i	−0.415029	+	0.958468i
$210$	6.00000			0.414039
$211$	−19.5000	−	11.2583i	−1.34244	−	0.775055i	−0.355271	−	0.934763i	$-0.615611\pi$
$211$	−19.5000	−	11.2583i	−1.34244	−	0.775055i	−0.987164	+	0.159708i	$0.948945\pi$
$212$	6.00000	−	10.3923i	0.412082	−	0.713746i
$213$	−9.00000	+	5.19615i	−0.616670	+	0.356034i
$214$	9.00000	−	15.5885i	0.615227	−	1.06561i
$215$	−3.00000	+	1.73205i	−0.204598	+	0.118125i
$216$			5.19615i			0.353553i
$217$		−	1.73205i		−	0.117579i
$218$		0			0
$219$	−10.5000	+	6.06218i	−0.709524	+	0.409644i
$220$	12.0000			0.809040
$221$	18.0000			1.21081
$222$	−4.50000	−	7.79423i	−0.302020	−	0.523114i
$223$	16.5000	+	9.52628i	1.10492	+	0.637927i	0.937509	−	0.347960i	$-0.113126\pi$
$223$	16.5000	+	9.52628i	1.10492	+	0.637927i	0.167412	+	0.985887i	$0.446459\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$	−10.5000	+	18.1865i	−0.700000	+	1.21244i
$226$	6.00000	−	10.3923i	0.399114	−	0.691286i
$227$	−18.0000			−1.19470			−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000			−1.19470			−0.597351	+	0.801980i	$0.703780\pi$
$228$	3.00000	−	6.92820i	0.198680	−	0.458831i
$229$	13.0000			0.859064			0.429532	−	0.903052i	$-0.358679\pi$
$229$	13.0000			0.859064			0.429532	+	0.903052i	$0.358679\pi$
$230$		0			0
$231$	−3.00000	+	5.19615i	−0.197386	+	0.341882i
$232$	−3.00000	−	5.19615i	−0.196960	−	0.341144i
$233$	−15.0000	−	8.66025i	−0.982683	−	0.567352i	−0.0796037	−	0.996827i	$-0.525365\pi$
$233$	−15.0000	−	8.66025i	−0.982683	−	0.567352i	−0.903079	+	0.429474i	$0.858699\pi$
$234$	13.5000	−	7.79423i	0.882523	−	0.509525i
$235$	24.0000			1.56559
$236$		0			0
$237$	−4.50000	−	7.79423i	−0.292306	−	0.506290i
$238$	3.00000	−	1.73205i	0.194461	−	0.112272i
$239$			24.2487i			1.56852i	0.620433	+	0.784259i	$0.286957\pi$
$239$			24.2487i			1.56852i	−0.620433	+	0.784259i	$0.713043\pi$
$240$	−6.00000			−0.387298
$241$	−1.50000	+	0.866025i	−0.0966235	+	0.0557856i	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−1.50000	+	0.866025i	−0.0966235	+	0.0557856i	0.450910	+	0.892570i	$0.351100\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	−3.50000	+	6.06218i	−0.224065	+	0.388091i
$245$	18.0000	+	10.3923i	1.14998	+	0.663940i
$246$			20.7846i			1.32518i
$247$	−22.5000	+	2.59808i	−1.43164	+	0.165312i
$248$			1.73205i			0.109985i
$249$	9.00000	−	15.5885i	0.570352	−	0.987878i
$250$	−6.00000	−	3.46410i	−0.379473	−	0.219089i
$251$	6.00000	−	3.46410i	0.378717	−	0.218652i	−0.298543	−	0.954396i	$-0.596501\pi$
$251$	6.00000	−	3.46410i	0.378717	−	0.218652i	0.677260	+	0.735744i	$0.263167\pi$
$252$	1.50000	−	2.59808i	0.0944911	−	0.163663i
$253$		0			0
$254$			10.3923i			0.652071i
$255$			20.7846i			1.30158i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$			1.73205i			0.107833i
$259$			5.19615i			0.322873i
$260$	9.00000	+	15.5885i	0.558156	+	0.966755i
$261$	−9.00000	+	15.5885i	−0.557086	+	0.964901i
$262$	−3.00000	+	1.73205i	−0.185341	+	0.107006i
$263$	21.0000	+	12.1244i	1.29492	+	0.747620i	0.979521	−	0.201341i	$-0.0645299\pi$
$263$	21.0000	+	12.1244i	1.29492	+	0.747620i	0.315394	+	0.948961i	$0.397863\pi$
$264$	3.00000	−	5.19615i	0.184637	−	0.319801i
$265$		−	41.5692i		−	2.55358i
$266$	−3.50000	+	2.59808i	−0.214599	+	0.159298i
$267$		0			0
$268$	−7.50000	−	4.33013i	−0.458135	−	0.264505i
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$	9.00000	+	15.5885i	0.547723	+	0.948683i
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	−0.961563	−	0.274586i	$-0.911459\pi$
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	0.718580	+	0.695444i	$0.244792\pi$
$272$	−3.00000	+	1.73205i	−0.181902	+	0.105021i
$273$	−9.00000			−0.544705
$274$		−	3.46410i		−	0.209274i
$275$	21.0000	−	12.1244i	1.26635	−	0.731126i
$276$		0			0
$277$	−2.00000			−0.120168			−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000			−0.120168			−0.0600842	+	0.998193i	$0.519137\pi$
$278$	5.00000			0.299880
$279$	4.50000	−	2.59808i	0.269408	−	0.155543i
$280$	3.00000	+	1.73205i	0.179284	+	0.103510i
$281$	3.00000	+	5.19615i	0.178965	+	0.309976i	0.941526	−	0.336939i	$-0.109392\pi$
$281$	3.00000	+	5.19615i	0.178965	+	0.309976i	−0.762561	+	0.646916i	$0.776058\pi$
$282$	6.00000	−	10.3923i	0.357295	−	0.618853i
$283$	14.0000	−	24.2487i	0.832214	−	1.44144i	−0.0640654	−	0.997946i	$-0.520407\pi$
$283$	14.0000	−	24.2487i	0.832214	−	1.44144i	0.896279	−	0.443491i	$-0.146260\pi$
$284$	−6.00000			−0.356034
$285$	−3.00000	−	25.9808i	−0.177705	−	1.53897i
$286$	−18.0000			−1.06436
$287$	6.00000	−	10.3923i	0.354169	−	0.613438i
$288$	−1.50000	+	2.59808i	−0.0883883	+	0.153093i
$289$	−2.50000	−	4.33013i	−0.147059	−	0.254713i
$290$	−18.0000	−	10.3923i	−1.05700	−	0.610257i
$291$	−6.00000	−	10.3923i	−0.351726	−	0.609208i
$292$	−7.00000			−0.409644
$293$		0			0			−	1.00000i	$-0.5\pi$
$293$		0			0				1.00000i	$0.5\pi$
$294$	9.00000	−	5.19615i	0.524891	−	0.303046i
$295$		0			0
$296$		−	5.19615i		−	0.302020i
$297$	−18.0000			−1.04447
$298$	−15.0000	+	8.66025i	−0.868927	+	0.501675i
$299$		0			0
$300$	−10.5000	+	6.06218i	−0.606218	+	0.350000i
$301$	0.500000	−	0.866025i	0.0288195	−	0.0499169i
$302$	3.00000	+	1.73205i	0.172631	+	0.0996683i
$303$	18.0000			1.03407
$304$	3.50000	−	2.59808i	0.200739	−	0.149010i
$305$			24.2487i			1.38848i
$306$	9.00000	+	5.19615i	0.514496	+	0.297044i
$307$	27.0000	+	15.5885i	1.54097	+	0.889680i	0.998778	+	0.0494267i	$0.0157394\pi$
$307$	27.0000	+	15.5885i	1.54097	+	0.889680i	0.542194	+	0.840254i	$0.317594\pi$
$308$	−3.00000	+	1.73205i	−0.170941	+	0.0986928i
$309$	7.50000	−	12.9904i	0.426660	−	0.738997i
$310$	3.00000	+	5.19615i	0.170389	+	0.295122i
$311$			13.8564i			0.785725i	0.919597	+	0.392862i	$0.128515\pi$
$311$			13.8564i			0.785725i	−0.919597	+	0.392862i	$0.871485\pi$
$312$	9.00000			0.509525
$313$	7.00000	+	12.1244i	0.395663	+	0.685309i	0.993186	−	0.116543i	$-0.0371814\pi$
$313$	7.00000	+	12.1244i	0.395663	+	0.685309i	−0.597522	+	0.801852i	$0.703848\pi$
$314$	3.50000	+	6.06218i	0.197516	+	0.342108i
$315$		−	10.3923i		−	0.585540i
$316$		−	5.19615i		−	0.292306i
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	0.769395	−	0.638774i	$-0.220558\pi$
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	−0.937892	+	0.346929i	$0.887225\pi$
$318$	−18.0000	−	10.3923i	−1.00939	−	0.582772i
$319$	18.0000	−	10.3923i	1.00781	−	0.581857i
$320$	−3.00000	−	1.73205i	−0.167705	−	0.0968246i
$321$	−27.0000	−	15.5885i	−1.50699	−	0.870063i
$322$		0			0
$323$	−9.00000	−	12.1244i	−0.500773	−	0.674617i
$324$	9.00000			0.500000
$325$	31.5000	+	18.1865i	1.74731	+	1.00881i
$326$	−5.50000	+	9.52628i	−0.304617	+	0.527612i
$327$		0			0
$328$	−6.00000	+	10.3923i	−0.331295	+	0.573819i
$329$	−6.00000	+	3.46410i	−0.330791	+	0.190982i
$330$		−	20.7846i		−	1.14416i
$331$			5.19615i			0.285606i	0.989751	+	0.142803i	$0.0456116\pi$
$331$			5.19615i			0.285606i	−0.989751	+	0.142803i	$0.954388\pi$
$332$	9.00000	−	5.19615i	0.493939	−	0.285176i
$333$	−13.5000	+	7.79423i	−0.739795	+	0.427121i
$334$	−12.0000			−0.656611
$335$	−30.0000			−1.63908
$336$	1.50000	−	0.866025i	0.0818317	−	0.0472456i
$337$	1.50000	+	0.866025i	0.0817102	+	0.0471754i	0.540298	−	0.841473i	$-0.318311\pi$
$337$	1.50000	+	0.866025i	0.0817102	+	0.0471754i	−0.458588	+	0.888649i	$0.651645\pi$
$338$	−7.00000	−	12.1244i	−0.380750	−	0.659478i
$339$	−18.0000	−	10.3923i	−0.977626	−	0.564433i
$340$	−6.00000	+	10.3923i	−0.325396	+	0.563602i
$341$	−6.00000			−0.324918
$342$	−12.0000	−	5.19615i	−0.648886	−	0.280976i
$343$	−13.0000			−0.701934
$344$	−0.500000	+	0.866025i	−0.0269582	+	0.0466930i
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	−21.0000	−	12.1244i	−1.12734	−	0.650870i	−0.184075	−	0.982912i	$-0.558929\pi$
$347$	−21.0000	−	12.1244i	−1.12734	−	0.650870i	−0.943264	+	0.332043i	$0.892262\pi$
$348$	−9.00000	+	5.19615i	−0.482451	+	0.278543i
$349$	−7.00000			−0.374701			−0.187351	−	0.982293i	$-0.559990\pi$
$349$	−7.00000			−0.374701			−0.187351	+	0.982293i	$0.559990\pi$
$350$	7.00000			0.374166
$351$	−13.5000	−	23.3827i	−0.720577	−	1.24808i
$352$	3.00000	−	1.73205i	0.159901	−	0.0923186i
$353$		−	10.3923i		−	0.553127i	−0.960996	−	0.276563i	$-0.910804\pi$
$353$		−	10.3923i		−	0.553127i	0.960996	−	0.276563i	$-0.0891955\pi$
$354$		0			0
$355$	−18.0000	+	10.3923i	−0.955341	+	0.551566i
$356$		0			0
$357$	−3.00000	−	5.19615i	−0.158777	−	0.275010i
$358$	−6.00000	+	10.3923i	−0.317110	+	0.549250i
$359$	6.00000	+	3.46410i	0.316668	+	0.182828i	0.649906	−	0.760014i	$-0.274808\pi$
$359$	6.00000	+	3.46410i	0.316668	+	0.182828i	−0.333238	+	0.942843i	$0.608141\pi$
$360$			10.3923i			0.547723i
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$			6.92820i			0.364138i
$363$	1.50000	+	0.866025i	0.0787296	+	0.0454545i
$364$	−4.50000	−	2.59808i	−0.235864	−	0.136176i
$365$	−21.0000	+	12.1244i	−1.09919	+	0.634618i
$366$	10.5000	+	6.06218i	0.548844	+	0.316875i
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	0.554264	−	0.832341i	$-0.313000\pi$
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	−0.997960	+	0.0638362i	$0.979666\pi$
$368$		0			0
$369$	36.0000			1.87409
$370$	−9.00000	−	15.5885i	−0.467888	−	0.810405i
$371$	6.00000	+	10.3923i	0.311504	+	0.539542i
$372$	3.00000			0.155543
$373$		−	6.92820i		−	0.358729i	−0.983783	−	0.179364i	$-0.942596\pi$
$373$		−	6.92820i		−	0.358729i	0.983783	−	0.179364i	$-0.0574041\pi$
$374$	−6.00000	−	10.3923i	−0.310253	−	0.537373i
$375$	−6.00000	+	10.3923i	−0.309839	+	0.536656i
$376$	6.00000	−	3.46410i	0.309426	−	0.178647i
$377$	27.0000	+	15.5885i	1.39057	+	0.802846i
$378$	−4.50000	−	2.59808i	−0.231455	−	0.133631i
$379$			12.1244i			0.622786i	0.950281	+	0.311393i	$0.100796\pi$
$379$			12.1244i			0.622786i	−0.950281	+	0.311393i	$0.899204\pi$
$380$	6.00000	−	13.8564i	0.307794	−	0.710819i
$381$	18.0000			0.922168
$382$	−15.0000	−	8.66025i	−0.767467	−	0.443097i
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	−0.932436	−	0.361335i	$-0.882321\pi$
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	0.779143	+	0.626846i	$0.215654\pi$
$384$	−1.50000	+	0.866025i	−0.0765466	+	0.0441942i
$385$	−6.00000	+	10.3923i	−0.305788	+	0.529641i
$386$	−10.5000	+	6.06218i	−0.534436	+	0.308557i
$387$	3.00000			0.152499
$388$		−	6.92820i		−	0.351726i
$389$	24.0000	−	13.8564i	1.21685	−	0.702548i	0.252606	−	0.967569i	$-0.418712\pi$
$389$	24.0000	−	13.8564i	1.21685	−	0.702548i	0.964242	+	0.265022i	$0.0853791\pi$
$390$	27.0000	−	15.5885i	1.36720	−	0.789352i
$391$		0			0
$392$	6.00000			0.303046
$393$	3.00000	+	5.19615i	0.151330	+	0.262111i
$394$		0			0
$395$	−9.00000	−	15.5885i	−0.452839	−	0.784340i
$396$	−9.00000	−	5.19615i	−0.452267	−	0.261116i
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	0.230105	+	0.973166i	$0.426093\pi$
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	−0.957839	+	0.287307i	$0.907240\pi$
$398$	25.0000			1.25314
$399$	4.50000	+	6.06218i	0.225282	+	0.303488i
$400$	−7.00000			−0.350000
$401$	12.0000	−	20.7846i	0.599251	−	1.03793i	−0.393680	−	0.919247i	$-0.628798\pi$
$401$	12.0000	−	20.7846i	0.599251	−	1.03793i	0.992932	−	0.118686i	$-0.0378683\pi$
$402$	−7.50000	+	12.9904i	−0.374066	+	0.647901i
$403$	−4.50000	−	7.79423i	−0.224161	−	0.388258i
$404$	9.00000	+	5.19615i	0.447767	+	0.258518i
$405$	27.0000	−	15.5885i	1.34164	−	0.774597i
$406$	6.00000			0.297775
$407$	18.0000			0.892227
$408$	3.00000	+	5.19615i	0.148522	+	0.257248i
$409$	30.0000	−	17.3205i	1.48340	−	0.856444i	0.483582	−	0.875299i	$-0.339335\pi$
$409$	30.0000	−	17.3205i	1.48340	−	0.856444i	0.999822	+	0.0188549i	$0.00600205\pi$
$410$			41.5692i			2.05296i
$411$	−6.00000			−0.295958
$412$	7.50000	−	4.33013i	0.369498	−	0.213330i
$413$		0			0
$414$		0			0
$415$	18.0000	−	31.1769i	0.883585	−	1.53041i
$416$	4.50000	+	2.59808i	0.220631	+	0.127381i
$417$		−	8.66025i		−	0.424094i
$418$	9.00000	+	12.1244i	0.440204	+	0.593022i
$419$			10.3923i			0.507697i	0.967244	+	0.253849i	$0.0816965\pi$
$419$			10.3923i			0.507697i	−0.967244	+	0.253849i	$0.918303\pi$
$420$	3.00000	−	5.19615i	0.146385	−	0.253546i
$421$	12.0000	+	6.92820i	0.584844	+	0.337660i	0.763056	−	0.646332i	$-0.223698\pi$
$421$	12.0000	+	6.92820i	0.584844	+	0.337660i	−0.178212	+	0.983992i	$0.557031\pi$
$422$	−19.5000	+	11.2583i	−0.949245	+	0.548047i
$423$	−18.0000	−	10.3923i	−0.875190	−	0.505291i
$424$	−6.00000	−	10.3923i	−0.291386	−	0.504695i
$425$			24.2487i			1.17624i
$426$			10.3923i			0.503509i
$427$	−3.50000	−	6.06218i	−0.169377	−	0.293369i
$428$	−9.00000	−	15.5885i	−0.435031	−	0.753497i
$429$			31.1769i			1.50524i
$430$			3.46410i			0.167054i
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	0.973574	−	0.228373i	$-0.0733406\pi$
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	−0.684564	+	0.728953i	$0.740007\pi$
$432$	4.50000	+	2.59808i	0.216506	+	0.125000i
$433$	−16.5000	+	9.52628i	−0.792939	+	0.457804i	−0.840996	−	0.541041i	$-0.818030\pi$
$433$	−16.5000	+	9.52628i	−0.792939	+	0.457804i	0.0480569	+	0.998845i	$0.484697\pi$
$434$	−1.50000	−	0.866025i	−0.0720023	−	0.0415705i
$435$	−18.0000	+	31.1769i	−0.863034	+	1.49482i
$436$		0			0
$437$		0			0
$438$			12.1244i			0.579324i
$439$	−7.50000	−	4.33013i	−0.357955	−	0.206666i	0.310228	−	0.950662i	$-0.399595\pi$
$439$	−7.50000	−	4.33013i	−0.357955	−	0.206666i	−0.668184	+	0.743996i	$0.732928\pi$
$440$	6.00000	−	10.3923i	0.286039	−	0.495434i
$441$	−9.00000	−	15.5885i	−0.428571	−	0.742307i
$442$	9.00000	−	15.5885i	0.428086	−	0.741467i
$443$	21.0000	−	12.1244i	0.997740	−	0.576046i	0.0901612	−	0.995927i	$-0.471262\pi$
$443$	21.0000	−	12.1244i	0.997740	−	0.576046i	0.907579	+	0.419882i	$0.137928\pi$
$444$	−9.00000			−0.427121
$445$		0			0
$446$	16.5000	−	9.52628i	0.781298	−	0.451082i
$447$	15.0000	+	25.9808i	0.709476	+	1.22885i
$448$	1.00000			0.0472456
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$	10.5000	+	18.1865i	0.494975	+	0.857321i
$451$	−36.0000	−	20.7846i	−1.69517	−	0.978709i
$452$	−6.00000	−	10.3923i	−0.282216	−	0.488813i
$453$	3.00000	−	5.19615i	0.140952	−	0.244137i
$454$	−9.00000	+	15.5885i	−0.422391	+	0.731603i
$455$	−18.0000			−0.843853
$456$	−4.50000	−	6.06218i	−0.210732	−	0.283887i
$457$	17.0000			0.795226			0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000			0.795226			0.397613	+	0.917553i	$0.369839\pi$
$458$	6.50000	−	11.2583i	0.303725	−	0.526067i
$459$	9.00000	−	15.5885i	0.420084	−	0.727607i
$460$		0			0
$461$	−6.00000	−	3.46410i	−0.279448	−	0.161339i	0.353726	−	0.935349i	$-0.384915\pi$
$461$	−6.00000	−	3.46410i	−0.279448	−	0.161339i	−0.633173	+	0.774010i	$0.718248\pi$
$462$	3.00000	+	5.19615i	0.139573	+	0.241747i
$463$	−19.0000			−0.883005			−0.441502	−	0.897260i	$-0.645554\pi$
$463$	−19.0000			−0.883005			−0.441502	+	0.897260i	$0.645554\pi$
$464$	−6.00000			−0.278543
$465$	9.00000	−	5.19615i	0.417365	−	0.240966i
$466$	−15.0000	+	8.66025i	−0.694862	+	0.401179i
$467$			27.7128i			1.28240i	0.767375	+	0.641198i	$0.221562\pi$
$467$			27.7128i			1.28240i	−0.767375	+	0.641198i	$0.778438\pi$
$468$		−	15.5885i		−	0.720577i
$469$	7.50000	−	4.33013i	0.346318	−	0.199947i
$470$	12.0000	−	20.7846i	0.553519	−	0.958723i
$471$	10.5000	−	6.06218i	0.483814	−	0.279330i
$472$		0			0
$473$	−3.00000	−	1.73205i	−0.137940	−	0.0796398i
$474$	−9.00000			−0.413384
$475$	−3.50000	−	30.3109i	−0.160591	−	1.39076i
$476$		−	3.46410i		−	0.158777i
$477$	−18.0000	+	31.1769i	−0.824163	+	1.42749i
$478$	21.0000	+	12.1244i	0.960518	+	0.554555i
$479$	−9.00000	+	5.19615i	−0.411220	+	0.237418i	−0.691314	−	0.722554i	$-0.742968\pi$
$479$	−9.00000	+	5.19615i	−0.411220	+	0.237418i	0.280094	+	0.959973i	$0.409635\pi$
$480$	−3.00000	+	5.19615i	−0.136931	+	0.237171i
$481$	13.5000	+	23.3827i	0.615547	+	1.06616i
$482$			1.73205i			0.0788928i
$483$		0			0
$484$	0.500000	+	0.866025i	0.0227273	+	0.0393648i
$485$	−12.0000	−	20.7846i	−0.544892	−	0.943781i
$486$		−	15.5885i		−	0.707107i
$487$			3.46410i			0.156973i	0.996915	+	0.0784867i	$0.0250088\pi$
$487$			3.46410i			0.156973i	−0.996915	+	0.0784867i	$0.974991\pi$
$488$	3.50000	+	6.06218i	0.158438	+	0.274422i
$489$	16.5000	+	9.52628i	0.746156	+	0.430793i
$490$	18.0000	−	10.3923i	0.813157	−	0.469476i
$491$	9.00000	+	5.19615i	0.406164	+	0.234499i	0.689140	−	0.724628i	$-0.257988\pi$
$491$	9.00000	+	5.19615i	0.406164	+	0.234499i	−0.282976	+	0.959127i	$0.591322\pi$
$492$	18.0000	+	10.3923i	0.811503	+	0.468521i
$493$			20.7846i			0.936092i
$494$	−9.00000	+	20.7846i	−0.404929	+	0.935144i
$495$	−36.0000			−1.61808
$496$	1.50000	+	0.866025i	0.0673520	+	0.0388857i
$497$	3.00000	−	5.19615i	0.134568	−	0.233079i
$498$	−9.00000	−	15.5885i	−0.403300	−	0.698535i
$499$	−15.5000	+	26.8468i	−0.693875	+	1.20183i	0.276683	+	0.960961i	$0.410765\pi$
$499$	−15.5000	+	26.8468i	−0.693875	+	1.20183i	−0.970558	+	0.240866i	$0.922569\pi$
$500$	−6.00000	+	3.46410i	−0.268328	+	0.154919i
$501$			20.7846i			0.928588i
$502$		−	6.92820i		−	0.309221i
$503$	27.0000	−	15.5885i	1.20387	−	0.695055i	0.242457	−	0.970162i	$-0.422047\pi$
$503$	27.0000	−	15.5885i	1.20387	−	0.695055i	0.961414	+	0.275107i	$0.0887134\pi$
$504$	−1.50000	−	2.59808i	−0.0668153	−	0.115728i
$505$	36.0000			1.60198
$506$		0			0
$507$	−21.0000	+	12.1244i	−0.932643	+	0.538462i
$508$	9.00000	+	5.19615i	0.399310	+	0.230542i
$509$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$509$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$510$	18.0000	+	10.3923i	0.797053	+	0.460179i
$511$	3.50000	−	6.06218i	0.154831	−	0.268175i
$512$	−1.00000			−0.0441942
$513$	−9.00000	+	20.7846i	−0.397360	+	0.917663i
$514$		0			0
$515$	15.0000	−	25.9808i	0.660979	−	1.14485i
$516$	1.50000	+	0.866025i	0.0660338	+	0.0381246i
$517$	12.0000	+	20.7846i	0.527759	+	0.914106i
$518$	4.50000	+	2.59808i	0.197719	+	0.114153i
$519$	9.00000	−	5.19615i	0.395056	−	0.228086i
$520$	18.0000			0.789352
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$	9.00000	+	15.5885i	0.393919	+	0.682288i
$523$	−4.50000	+	2.59808i	−0.196771	+	0.113606i	−0.595149	−	0.803616i	$-0.702907\pi$
$523$	−4.50000	+	2.59808i	−0.196771	+	0.113606i	0.398377	+	0.917222i	$0.369573\pi$
$524$			3.46410i			0.151330i
$525$		−	12.1244i		−	0.529150i
$526$	21.0000	−	12.1244i	0.915644	−	0.528647i
$527$	3.00000	−	5.19615i	0.130682	−	0.226348i
$528$	−3.00000	−	5.19615i	−0.130558	−	0.226134i
$529$	−11.5000	+	19.9186i	−0.500000	+	0.866025i
$530$	−36.0000	−	20.7846i	−1.56374	−	0.902826i
$531$		0			0
$532$	0.500000	+	4.33013i	0.0216777	+	0.187735i
$533$		−	62.3538i		−	2.70084i
$534$		0			0
$535$	−54.0000	−	31.1769i	−2.33462	−	1.34790i
$536$	−7.50000	+	4.33013i	−0.323951	+	0.187033i
$537$	18.0000	+	10.3923i	0.776757	+	0.448461i
$538$		0			0
$539$			20.7846i			0.895257i
$540$	18.0000			0.774597
$541$	6.50000	+	11.2583i	0.279457	+	0.484033i	0.971250	−	0.238062i	$-0.0765123\pi$
$541$	6.50000	+	11.2583i	0.279457	+	0.484033i	−0.691793	+	0.722096i	$0.743179\pi$
$542$	4.00000	+	6.92820i	0.171815	+	0.297592i
$543$	12.0000			0.514969
$544$			3.46410i			0.148522i
$545$		0			0
$546$	−4.50000	+	7.79423i	−0.192582	+	0.333562i
$547$	22.5000	−	12.9904i	0.962031	−	0.555429i	0.0652331	−	0.997870i	$-0.479221\pi$
$547$	22.5000	−	12.9904i	0.962031	−	0.555429i	0.896797	+	0.442441i	$0.145888\pi$
$548$	−3.00000	−	1.73205i	−0.128154	−	0.0739895i
$549$	10.5000	−	18.1865i	0.448129	−	0.776182i
$550$		−	24.2487i		−	1.03397i
$551$	−3.00000	−	25.9808i	−0.127804	−	1.10682i
$552$		0			0
$553$	4.50000	+	2.59808i	0.191359	+	0.110481i
$554$	−1.00000	+	1.73205i	−0.0424859	+	0.0735878i
$555$	−27.0000	+	15.5885i	−1.14609	+	0.661693i
$556$	2.50000	−	4.33013i	0.106024	−	0.183638i
$557$	3.00000	−	1.73205i	0.127114	−	0.0733893i	−0.435095	−	0.900385i	$-0.643285\pi$
$557$	3.00000	−	1.73205i	0.127114	−	0.0733893i	0.562209	+	0.826995i	$0.309952\pi$
$558$		−	5.19615i		−	0.219971i
$559$		−	5.19615i		−	0.219774i
$560$	3.00000	−	1.73205i	0.126773	−	0.0731925i
$561$	−18.0000	+	10.3923i	−0.759961	+	0.438763i
$562$	6.00000			0.253095
$563$	−18.0000			−0.758610			−0.379305	−	0.925272i	$-0.623837\pi$
$563$	−18.0000			−0.758610			−0.379305	+	0.925272i	$0.623837\pi$
$564$	−6.00000	−	10.3923i	−0.252646	−	0.437595i
$565$	−36.0000	−	20.7846i	−1.51453	−	0.874415i
$566$	−14.0000	−	24.2487i	−0.588464	−	1.01925i
$567$	−4.50000	+	7.79423i	−0.188982	+	0.327327i
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	−24.0000			−1.00613			−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000			−1.00613			−0.503066	+	0.864248i	$0.667795\pi$
$570$	−24.0000	−	10.3923i	−1.00525	−	0.435286i
$571$	5.00000			0.209243			0.104622	−	0.994512i	$-0.466637\pi$
$571$	5.00000			0.209243			0.104622	+	0.994512i	$0.466637\pi$
$572$	−9.00000	+	15.5885i	−0.376309	+	0.651786i
$573$	−15.0000	+	25.9808i	−0.626634	+	1.08536i
$574$	−6.00000	−	10.3923i	−0.250435	−	0.433766i
$575$		0			0
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	−38.0000			−1.58196			−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000			−1.58196			−0.790980	+	0.611842i	$0.790429\pi$
$578$	−5.00000			−0.207973
$579$	10.5000	+	18.1865i	0.436365	+	0.755807i
$580$	−18.0000	+	10.3923i	−0.747409	+	0.431517i
$581$			10.3923i			0.431145i
$582$	−12.0000			−0.497416
$583$	36.0000	−	20.7846i	1.49097	−	0.860811i
$584$	−3.50000	+	6.06218i	−0.144831	+	0.250855i
$585$	−27.0000	−	46.7654i	−1.11631	−	1.93351i
$586$		0			0
$587$	−6.00000	−	3.46410i	−0.247647	−	0.142979i	0.371040	−	0.928617i	$-0.379001\pi$
$587$	−6.00000	−	3.46410i	−0.247647	−	0.142979i	−0.618686	+	0.785638i	$0.712335\pi$
$588$		−	10.3923i		−	0.428571i
$589$	−3.00000	+	6.92820i	−0.123613	+	0.285472i
$590$		0			0
$591$		0			0
$592$	−4.50000	−	2.59808i	−0.184949	−	0.106780i
$593$	36.0000	−	20.7846i	1.47834	−	0.853522i	0.478643	−	0.878010i	$-0.341129\pi$
$593$	36.0000	−	20.7846i	1.47834	−	0.853522i	0.999700	+	0.0244882i	$0.00779560\pi$
$594$	−9.00000	+	15.5885i	−0.369274	+	0.639602i
$595$	−6.00000	−	10.3923i	−0.245976	−	0.426043i
$596$			17.3205i			0.709476i
$597$		−	43.3013i		−	1.77220i
$598$		0			0
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	−0.990752	−	0.135686i	$-0.956676\pi$
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	0.377869	−	0.925859i	$-0.376657\pi$
$600$			12.1244i			0.494975i
$601$			1.73205i			0.0706518i	0.999376	+	0.0353259i	$0.0112469\pi$
$601$			1.73205i			0.0706518i	−0.999376	+	0.0353259i	$0.988753\pi$
$602$	−0.500000	−	0.866025i	−0.0203785	−	0.0352966i
$603$	22.5000	+	12.9904i	0.916271	+	0.529009i
$604$	3.00000	−	1.73205i	0.122068	−	0.0704761i
$605$	3.00000	+	1.73205i	0.121967	+	0.0704179i
$606$	9.00000	−	15.5885i	0.365600	−	0.633238i
$607$			32.9090i			1.33573i	0.744281	+	0.667867i	$0.232792\pi$
$607$			32.9090i			1.33573i	−0.744281	+	0.667867i	$0.767208\pi$
$608$	−0.500000	−	4.33013i	−0.0202777	−	0.175610i
$609$		−	10.3923i		−	0.421117i
$610$	21.0000	+	12.1244i	0.850265	+	0.490901i
$611$	−18.0000	+	31.1769i	−0.728202	+	1.26128i
$612$	9.00000	−	5.19615i	0.363803	−	0.210042i
$613$	19.0000	−	32.9090i	0.767403	−	1.32918i	−0.171564	−	0.985173i	$-0.554882\pi$
$613$	19.0000	−	32.9090i	0.767403	−	1.32918i	0.938967	−	0.344008i	$-0.111785\pi$
$614$	27.0000	−	15.5885i	1.08963	−	0.629099i
$615$	72.0000			2.90332
$616$			3.46410i			0.139573i
$617$	−33.0000	+	19.0526i	−1.32853	+	0.767027i	−0.985072	−	0.172141i	$-0.944932\pi$
$617$	−33.0000	+	19.0526i	−1.32853	+	0.767027i	−0.343458	+	0.939168i	$0.611598\pi$
$618$	−7.50000	−	12.9904i	−0.301694	−	0.522550i
$619$	−17.0000			−0.683288			−0.341644	−	0.939829i	$-0.610984\pi$
$619$	−17.0000			−0.683288			−0.341644	+	0.939829i	$0.610984\pi$
$620$	6.00000			0.240966
$621$		0			0
$622$	12.0000	+	6.92820i	0.481156	+	0.277796i
$623$		0			0
$624$	4.50000	−	7.79423i	0.180144	−	0.312019i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	14.0000			0.559553
$627$	21.0000	−	15.5885i	0.838659	−	0.622543i
$628$	7.00000			0.279330
$629$	−9.00000	+	15.5885i	−0.358854	+	0.621552i
$630$	−9.00000	−	5.19615i	−0.358569	−	0.207020i
$631$	−6.50000	−	11.2583i	−0.258761	−	0.448187i	0.707149	−	0.707064i	$-0.249981\pi$
$631$	−6.50000	−	11.2583i	−0.258761	−	0.448187i	−0.965910	+	0.258877i	$0.916648\pi$
$632$	−4.50000	−	2.59808i	−0.179000	−	0.103346i
$633$	19.5000	+	33.7750i	0.775055	+	1.34244i
$634$	−6.00000			−0.238290
$635$	36.0000			1.42862
$636$	−18.0000	+	10.3923i	−0.713746	+	0.412082i
$637$	−27.0000	+	15.5885i	−1.06978	+	0.617637i
$638$		−	20.7846i		−	0.822871i
$639$	18.0000			0.712069
$640$	−3.00000	+	1.73205i	−0.118585	+	0.0684653i
$641$	−12.0000	+	20.7846i	−0.473972	+	0.820943i	−0.999556	−	0.0297987i	$-0.990513\pi$
$641$	−12.0000	+	20.7846i	−0.473972	+	0.820943i	0.525584	+	0.850741i	$0.323847\pi$
$642$	−27.0000	+	15.5885i	−1.06561	+	0.615227i
$643$	−2.50000	+	4.33013i	−0.0985904	+	0.170764i	−0.911101	−	0.412182i	$-0.864767\pi$
$643$	−2.50000	+	4.33013i	−0.0985904	+	0.170764i	0.812511	+	0.582946i	$0.198100\pi$
$644$		0			0
$645$	6.00000			0.236250
$646$	−15.0000	+	1.73205i	−0.590167	+	0.0681466i
$647$			38.1051i			1.49807i	0.662532	+	0.749033i	$0.269482\pi$
$647$			38.1051i			1.49807i	−0.662532	+	0.749033i	$0.730518\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$		0			0
$650$	31.5000	−	18.1865i	1.23553	−	0.713335i
$651$	−1.50000	+	2.59808i	−0.0587896	+	0.101827i
$652$	5.50000	+	9.52628i	0.215397	+	0.373078i
$653$		−	17.3205i		−	0.677804i	−0.940822	−	0.338902i	$-0.889945\pi$
$653$		−	17.3205i		−	0.677804i	0.940822	−	0.338902i	$-0.110055\pi$
$654$		0			0
$655$	6.00000	+	10.3923i	0.234439	+	0.406061i
$656$	6.00000	+	10.3923i	0.234261	+	0.405751i
$657$	21.0000			0.819288
$658$			6.92820i			0.270089i
$659$	3.00000	+	5.19615i	0.116863	+	0.202413i	0.918523	−	0.395367i	$-0.129383\pi$
$659$	3.00000	+	5.19615i	0.116863	+	0.202413i	−0.801660	+	0.597781i	$0.796049\pi$
$660$	−18.0000	−	10.3923i	−0.700649	−	0.404520i
$661$	−12.0000	+	6.92820i	−0.466746	+	0.269476i	−0.714877	−	0.699251i	$-0.753517\pi$
$661$	−12.0000	+	6.92820i	−0.466746	+	0.269476i	0.248131	+	0.968727i	$0.420184\pi$
$662$	4.50000	+	2.59808i	0.174897	+	0.100977i
$663$	−27.0000	−	15.5885i	−1.04859	−	0.605406i
$664$		−	10.3923i		−	0.403300i
$665$	9.00000	+	12.1244i	0.349005	+	0.470162i
$666$			15.5885i			0.604040i
$667$		0			0
$668$	−6.00000	+	10.3923i	−0.232147	+	0.402090i
$669$	−16.5000	−	28.5788i	−0.637927	−	1.10492i
$670$	−15.0000	+	25.9808i	−0.579501	+	1.00372i
$671$	−21.0000	+	12.1244i	−0.810696	+	0.468056i
$672$		−	1.73205i		−	0.0668153i
$673$		−	12.1244i		−	0.467360i	−0.972314	−	0.233680i	$-0.924923\pi$
$673$		−	12.1244i		−	0.467360i	0.972314	−	0.233680i	$-0.0750767\pi$
$674$	1.50000	−	0.866025i	0.0577778	−	0.0333581i
$675$	31.5000	−	18.1865i	1.21244	−	0.700000i
$676$	−14.0000			−0.538462
$677$	36.0000			1.38359			0.691796	−	0.722093i	$-0.256820\pi$
$677$	36.0000			1.38359			0.691796	+	0.722093i	$0.256820\pi$
$678$	−18.0000	+	10.3923i	−0.691286	+	0.399114i
$679$	6.00000	+	3.46410i	0.230259	+	0.132940i
$680$	6.00000	+	10.3923i	0.230089	+	0.398527i
$681$	27.0000	+	15.5885i	1.03464	+	0.597351i
$682$	−3.00000	+	5.19615i	−0.114876	+	0.198971i
$683$	30.0000			1.14792			0.573959	−	0.818884i	$-0.305407\pi$
$683$	30.0000			1.14792			0.573959	+	0.818884i	$0.305407\pi$
$684$	−10.5000	+	7.79423i	−0.401478	+	0.298020i
$685$	−12.0000			−0.458496
$686$	−6.50000	+	11.2583i	−0.248171	+	0.429845i
$687$	−19.5000	−	11.2583i	−0.743971	−	0.429532i
$688$	0.500000	+	0.866025i	0.0190623	+	0.0330169i
$689$	54.0000	+	31.1769i	2.05724	+	1.18775i
$690$		0			0
$691$	20.0000			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$692$	6.00000			0.228086
$693$	9.00000	−	5.19615i	0.341882	−	0.197386i
$694$	−21.0000	+	12.1244i	−0.797149	+	0.460234i
$695$		−	17.3205i		−	0.657004i
$696$			10.3923i			0.393919i
$697$	36.0000	−	20.7846i	1.36360	−	0.787273i
$698$	−3.50000	+	6.06218i	−0.132477	+	0.229457i
$699$	15.0000	+	25.9808i	0.567352	+	0.982683i
$700$	3.50000	−	6.06218i	0.132288	−	0.229129i
$701$	9.00000	+	5.19615i	0.339925	+	0.196256i	0.660239	−	0.751056i	$-0.270455\pi$
$701$	9.00000	+	5.19615i	0.339925	+	0.196256i	−0.320314	+	0.947312i	$0.603788\pi$
$702$	−27.0000			−1.01905
$703$	9.00000	−	20.7846i	0.339441	−	0.783906i
$704$		−	3.46410i		−	0.130558i
$705$	−36.0000	−	20.7846i	−1.35584	−	0.782794i
$706$	−9.00000	−	5.19615i	−0.338719	−	0.195560i
$707$	−9.00000	+	5.19615i	−0.338480	+	0.195421i
$708$		0			0
$709$	6.50000	+	11.2583i	0.244113	+	0.422815i	0.961882	−	0.273466i	$-0.0881700\pi$
$709$	6.50000	+	11.2583i	0.244113	+	0.422815i	−0.717769	+	0.696281i	$0.754837\pi$
$710$			20.7846i			0.780033i
$711$			15.5885i			0.584613i
$712$		0			0
$713$		0			0
$714$	−6.00000			−0.224544
$715$			62.3538i			2.33190i
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$	21.0000	−	36.3731i	0.784259	−	1.35838i
$718$	6.00000	−	3.46410i	0.223918	−	0.129279i
$719$	−24.0000	−	13.8564i	−0.895049	−	0.516757i	−0.0194584	−	0.999811i	$-0.506194\pi$
$719$	−24.0000	−	13.8564i	−0.895049	−	0.516757i	−0.875591	+	0.483054i	$0.839528\pi$
$720$	9.00000	+	5.19615i	0.335410	+	0.193649i
$721$			8.66025i			0.322525i
$722$	18.5000	−	4.33013i	0.688499	−	0.161151i
$723$	3.00000			0.111571
$724$	6.00000	+	3.46410i	0.222988	+	0.128742i
$725$	−21.0000	+	36.3731i	−0.779920	+	1.35086i
$726$	1.50000	−	0.866025i	0.0556702	−	0.0321412i
$727$	18.5000	−	32.0429i	0.686127	−	1.18841i	−0.286954	−	0.957944i	$-0.592643\pi$
$727$	18.5000	−	32.0429i	0.686127	−	1.18841i	0.973081	−	0.230463i	$-0.0740239\pi$
$728$	−4.50000	+	2.59808i	−0.166781	+	0.0962911i
$729$	−27.0000			−1.00000
$730$			24.2487i			0.897485i
$731$	3.00000	−	1.73205i	0.110959	−	0.0640622i
$732$	10.5000	−	6.06218i	0.388091	−	0.224065i
$733$	−22.0000			−0.812589			−0.406294	−	0.913742i	$-0.633179\pi$
$733$	−22.0000			−0.812589			−0.406294	+	0.913742i	$0.633179\pi$
$734$	−17.0000			−0.627481
$735$	−18.0000	−	31.1769i	−0.663940	−	1.14998i
$736$		0			0
$737$	−15.0000	−	25.9808i	−0.552532	−	0.957014i
$738$	18.0000	−	31.1769i	0.662589	−	1.14764i
$739$	−12.5000	+	21.6506i	−0.459820	+	0.796431i	−0.998951	−	0.0457903i	$-0.985419\pi$
$739$	−12.5000	+	21.6506i	−0.459820	+	0.796431i	0.539131	+	0.842222i	$0.318753\pi$
$740$	−18.0000			−0.661693
$741$	36.0000	+	15.5885i	1.32249	+	0.572656i
$742$	12.0000			0.440534
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	−0.805735	−	0.592277i	$-0.798229\pi$
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	0.915794	+	0.401648i	$0.131563\pi$
$744$	1.50000	−	2.59808i	0.0549927	−	0.0952501i
$745$	30.0000	+	51.9615i	1.09911	+	1.90372i
$746$	−6.00000	−	3.46410i	−0.219676	−	0.126830i
$747$	−27.0000	+	15.5885i	−0.987878	+	0.570352i
$748$	−12.0000			−0.438763
$749$	18.0000			0.657706
$750$	6.00000	+	10.3923i	0.219089	+	0.379473i
$751$	31.5000	−	18.1865i	1.14945	−	0.663636i	0.200698	−	0.979653i	$-0.435679\pi$
$751$	31.5000	−	18.1865i	1.14945	−	0.663636i	0.948753	+	0.316017i	$0.102346\pi$
$752$		−	6.92820i		−	0.252646i
$753$	−12.0000			−0.437304
$754$	27.0000	−	15.5885i	0.983282	−	0.567698i
$755$	6.00000	−	10.3923i	0.218362	−	0.378215i
$756$	−4.50000	+	2.59808i	−0.163663	+	0.0944911i
$757$	−6.50000	+	11.2583i	−0.236247	+	0.409191i	−0.959634	−	0.281251i	$-0.909251\pi$
$757$	−6.50000	+	11.2583i	−0.236247	+	0.409191i	0.723388	+	0.690442i	$0.242584\pi$
$758$	10.5000	+	6.06218i	0.381377	+	0.220188i
$759$		0			0
$760$	−9.00000	−	12.1244i	−0.326464	−	0.439797i
$761$			27.7128i			1.00459i	0.864697	+	0.502294i	$0.167511\pi$
$761$			27.7128i			1.00459i	−0.864697	+	0.502294i	$0.832489\pi$
$762$	9.00000	−	15.5885i	0.326036	−	0.564710i
$763$		0			0
$764$	−15.0000	+	8.66025i	−0.542681	+	0.313317i
$765$	18.0000	−	31.1769i	0.650791	−	1.12720i
$766$	3.00000	+	5.19615i	0.108394	+	0.187745i
$767$		0			0
$768$			1.73205i			0.0625000i
$769$	−18.5000	−	32.0429i	−0.667127	−	1.15550i	−0.978704	−	0.205277i	$-0.934190\pi$
$769$	−18.5000	−	32.0429i	−0.667127	−	1.15550i	0.311577	−	0.950221i	$-0.399143\pi$
$770$	6.00000	+	10.3923i	0.216225	+	0.374513i
$771$		0			0
$772$			12.1244i			0.436365i
$773$	12.0000	+	20.7846i	0.431610	+	0.747570i	0.997012	−	0.0772449i	$-0.0246123\pi$
$773$	12.0000	+	20.7846i	0.431610	+	0.747570i	−0.565402	+	0.824815i	$0.691279\pi$
$774$	1.50000	−	2.59808i	0.0539164	−	0.0933859i
$775$	10.5000	−	6.06218i	0.377171	−	0.217760i
$776$	−6.00000	−	3.46410i	−0.215387	−	0.124354i
$777$	4.50000	−	7.79423i	0.161437	−	0.279616i
$778$		−	27.7128i		−	0.993552i
$779$	−42.0000	+	31.1769i	−1.50481	+	1.11703i
$780$		−	31.1769i		−	1.11631i
$781$	−18.0000	−	10.3923i	−0.644091	−	0.371866i
$782$		0			0
$783$	27.0000	−	15.5885i	0.964901	−	0.557086i
$784$	3.00000	−	5.19615i	0.107143	−	0.185577i
$785$	21.0000	−	12.1244i	0.749522	−	0.432737i
$786$	6.00000			0.214013
$787$		−	25.9808i		−	0.926114i	−0.886328	−	0.463057i	$-0.846752\pi$
$787$		−	25.9808i		−	0.926114i	0.886328	−	0.463057i	$-0.153248\pi$
$788$		0			0
$789$	−21.0000	−	36.3731i	−0.747620	−	1.29492i
$790$	−18.0000			−0.640411
$791$	12.0000			0.426671
$792$	−9.00000	+	5.19615i	−0.319801	+	0.184637i
$793$	−31.5000	−	18.1865i	−1.11860	−	0.645823i
$794$	14.5000	+	25.1147i	0.514586	+	0.891289i
$795$	−36.0000	+	62.3538i	−1.27679	+	2.21146i
$796$	12.5000	−	21.6506i	0.443051	−	0.767386i
$797$	−42.0000			−1.48772			−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000			−1.48772			−0.743858	+	0.668338i	$0.767006\pi$
$798$	7.50000	−	0.866025i	0.265497	−	0.0306570i
$799$	−24.0000			−0.849059
$800$	−3.50000	+	6.06218i	−0.123744	+	0.214330i
$801$		0			0
$802$	−12.0000	−	20.7846i	−0.423735	−	0.733930i
$803$	−21.0000	−	12.1244i	−0.741074	−	0.427859i
$804$	7.50000	+	12.9904i	0.264505	+	0.458135i
$805$		0			0
$806$	−9.00000			−0.317011
$807$		0			0
$808$	9.00000	−	5.19615i	0.316619	−	0.182800i
$809$		−	3.46410i		−	0.121791i	−0.998144	−	0.0608957i	$-0.980604\pi$
$809$		−	3.46410i		−	0.121791i	0.998144	−	0.0608957i	$-0.0193957\pi$
$810$		−	31.1769i		−	1.09545i
$811$	−27.0000	+	15.5885i	−0.948098	+	0.547385i	−0.892490	−	0.451068i	$-0.851043\pi$
$811$	−27.0000	+	15.5885i	−0.948098	+	0.547385i	−0.0556086	+	0.998453i	$0.517710\pi$
$812$	3.00000	−	5.19615i	0.105279	−	0.182349i
$813$	12.0000	−	6.92820i	0.420858	−	0.242983i
$814$	9.00000	−	15.5885i	0.315450	−	0.546375i
$815$	33.0000	+	19.0526i	1.15594	+	0.667382i
$816$	6.00000			0.210042
$817$	−3.50000	+	2.59808i	−0.122449	+	0.0908952i
$818$		−	34.6410i		−	1.21119i
$819$	13.5000	+	7.79423i	0.471728	+	0.272352i
$820$	36.0000	+	20.7846i	1.25717	+	0.725830i
$821$	21.0000	−	12.1244i	0.732905	−	0.423143i	−0.0865789	−	0.996245i	$-0.527593\pi$
$821$	21.0000	−	12.1244i	0.732905	−	0.423143i	0.819484	+	0.573102i	$0.194260\pi$
$822$	−3.00000	+	5.19615i	−0.104637	+	0.181237i
$823$	−20.0000	−	34.6410i	−0.697156	−	1.20751i	−0.969448	−	0.245295i	$-0.921115\pi$
$823$	−20.0000	−	34.6410i	−0.697156	−	1.20751i	0.272292	−	0.962215i	$-0.412218\pi$
$824$		−	8.66025i		−	0.301694i
$825$	−42.0000			−1.46225
$826$		0			0
$827$	3.00000	+	5.19615i	0.104320	+	0.180688i	0.913460	−	0.406928i	$-0.133400\pi$
$827$	3.00000	+	5.19615i	0.104320	+	0.180688i	−0.809140	+	0.587616i	$0.800067\pi$
$828$		0			0
$829$		−	50.2295i		−	1.74454i	−0.489023	−	0.872271i	$-0.662647\pi$
$829$		−	50.2295i		−	1.74454i	0.489023	−	0.872271i	$-0.337353\pi$
$830$	−18.0000	−	31.1769i	−0.624789	−	1.08217i
$831$	3.00000	+	1.73205i	0.104069	+	0.0600842i
$832$	4.50000	−	2.59808i	0.156009	−	0.0900721i
$833$	−18.0000	−	10.3923i	−0.623663	−	0.360072i
$834$	−7.50000	−	4.33013i	−0.259704	−	0.149940i
$835$			41.5692i			1.43856i
$836$	15.0000	−	1.73205i	0.518786	−	0.0599042i
$837$	−9.00000			−0.311086
$838$	9.00000	+	5.19615i	0.310900	+	0.179498i
$839$	27.0000	−	46.7654i	0.932144	−	1.61452i	0.152493	−	0.988304i	$-0.451270\pi$
$839$	27.0000	−	46.7654i	0.932144	−	1.61452i	0.779650	−	0.626215i	$-0.215397\pi$
$840$	−3.00000	−	5.19615i	−0.103510	−	0.179284i
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	12.0000	−	6.92820i	0.413547	−	0.238762i
$843$		−	10.3923i		−	0.357930i
$844$			22.5167i			0.775055i
$845$	−42.0000	+	24.2487i	−1.44484	+	0.834181i
$846$	−18.0000	+	10.3923i	−0.618853	+	0.357295i
$847$	−1.00000			−0.0343604
$848$	−12.0000			−0.412082
$849$	−42.0000	+	24.2487i	−1.44144	+	0.832214i
$850$	21.0000	+	12.1244i	0.720294	+	0.415862i
$851$		0			0
$852$	9.00000	+	5.19615i	0.308335	+	0.178017i
$853$	−2.50000	+	4.33013i	−0.0855984	+	0.148261i	−0.905646	−	0.424034i	$-0.860614\pi$
$853$	−2.50000	+	4.33013i	−0.0855984	+	0.148261i	0.820048	+	0.572295i	$0.193947\pi$
$854$	−7.00000			−0.239535
$855$	−18.0000	+	41.5692i	−0.615587	+	1.42164i
$856$	−18.0000			−0.615227
$857$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$857$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$858$	27.0000	+	15.5885i	0.921765	+	0.532181i
$859$	17.5000	+	30.3109i	0.597092	+	1.03419i	0.993248	+	0.116011i	$0.0370107\pi$
$859$	17.5000	+	30.3109i	0.597092	+	1.03419i	−0.396156	+	0.918183i	$0.629656\pi$
$860$	3.00000	+	1.73205i	0.102299	+	0.0590624i
$861$	−18.0000	+	10.3923i	−0.613438	+	0.354169i
$862$	12.0000			0.408722
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$	4.50000	−	2.59808i	0.153093	−	0.0883883i
$865$	18.0000	−	10.3923i	0.612018	−	0.353349i
$866$			19.0526i			0.647432i
$867$			8.66025i			0.294118i
$868$	−1.50000	+	0.866025i	−0.0509133	+	0.0293948i
$869$	9.00000	−	15.5885i	0.305304	−	0.528802i
$870$	18.0000	+	31.1769i	0.610257	+	1.05700i
$871$	22.5000	−	38.9711i	0.762383	−	1.32049i
$872$		0			0
$873$			20.7846i			0.703452i
$874$		0			0
$875$		−	6.92820i		−	0.234216i
$876$	10.5000	+	6.06218i	0.354762	+	0.204822i
$877$	4.50000	+	2.59808i	0.151954	+	0.0877308i	0.574049	−	0.818821i	$-0.305372\pi$
$877$	4.50000	+	2.59808i	0.151954	+	0.0877308i	−0.422095	+	0.906552i	$0.638705\pi$
$878$	−7.50000	+	4.33013i	−0.253113	+	0.146135i
$879$		0			0
$880$	−6.00000	−	10.3923i	−0.202260	−	0.350325i
$881$		−	38.1051i		−	1.28379i	−0.766791	−	0.641897i	$-0.778148\pi$
$881$		−	38.1051i		−	1.28379i	0.766791	−	0.641897i	$-0.221852\pi$
$882$	−18.0000			−0.606092
$883$	−6.50000	−	11.2583i	−0.218742	−	0.378873i	0.735681	−	0.677328i	$-0.236862\pi$
$883$	−6.50000	−	11.2583i	−0.218742	−	0.378873i	−0.954424	+	0.298455i	$0.903529\pi$
$884$	−9.00000	−	15.5885i	−0.302703	−	0.524297i
$885$		0			0
$886$		−	24.2487i		−	0.814651i
$887$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$887$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$888$	−4.50000	+	7.79423i	−0.151010	+	0.261557i
$889$	−9.00000	+	5.19615i	−0.301850	+	0.174273i
$890$		0			0
$891$	27.0000	+	15.5885i	0.904534	+	0.522233i
$892$		−	19.0526i		−	0.637927i
$893$	30.0000	−	3.46410i	1.00391	−	0.115922i
$894$	30.0000			1.00335
$895$	36.0000	+	20.7846i	1.20335	+	0.694753i
$896$	0.500000	−	0.866025i	0.0167038	−	0.0289319i
$897$		0			0
$898$	−15.0000	+	25.9808i	−0.500556	+	0.866989i
$899$	9.00000	−	5.19615i	0.300167	−	0.173301i
$900$	21.0000			0.700000
$901$			41.5692i			1.38487i
$902$	−36.0000	+	20.7846i	−1.19867	+	0.692052i
$903$	−1.50000	+	0.866025i	−0.0499169	+	0.0288195i
$904$	−12.0000			−0.399114
$905$	24.0000			0.797787
$906$	−3.00000	−	5.19615i	−0.0996683	−	0.172631i
$907$	21.0000	+	12.1244i	0.697294	+	0.402583i	0.806339	−	0.591454i	$-0.201446\pi$
$907$	21.0000	+	12.1244i	0.697294	+	0.402583i	−0.109045	+	0.994037i	$0.534779\pi$
$908$	9.00000	+	15.5885i	0.298675	+	0.517321i
$909$	−27.0000	−	15.5885i	−0.895533	−	0.517036i
$910$	−9.00000	+	15.5885i	−0.298347	+	0.516752i
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	−7.50000	+	0.866025i	−0.248350	+	0.0286770i
$913$	36.0000			1.19143
$914$	8.50000	−	14.7224i	0.281155	−	0.486975i
$915$	21.0000	−	36.3731i	0.694239	−	1.20246i
$916$	−6.50000	−	11.2583i	−0.214766	−	0.371986i
$917$	−3.00000	−	1.73205i	−0.0990687	−	0.0571974i
$918$	−9.00000	−	15.5885i	−0.297044	−	0.514496i
$919$	−53.0000			−1.74831			−0.874154	−	0.485648i	$-0.838584\pi$
$919$	−53.0000			−1.74831			−0.874154	+	0.485648i	$0.838584\pi$
$920$		0			0
$921$	−27.0000	−	46.7654i	−0.889680	−	1.54097i
$922$	−6.00000	+	3.46410i	−0.197599	+	0.114084i
$923$		−	31.1769i		−	1.02620i
$924$	6.00000			0.197386
$925$	−31.5000	+	18.1865i	−1.03571	+	0.597970i
$926$	−9.50000	+	16.4545i	−0.312189	+	0.540728i
$927$	−22.5000	+	12.9904i	−0.738997	+	0.426660i
$928$	−3.00000	+	5.19615i	−0.0984798	+	0.170572i
$929$	−45.0000	−	25.9808i	−1.47640	−	0.852401i	−0.476757	−	0.879035i	$-0.658188\pi$
$929$	−45.0000	−	25.9808i	−1.47640	−	0.852401i	−0.999645	+	0.0266341i	$0.991521\pi$
$930$		−	10.3923i		−	0.340777i
$931$	24.0000	+	10.3923i	0.786568	+	0.340594i
$932$			17.3205i			0.567352i
$933$	12.0000	−	20.7846i	0.392862	−	0.680458i
$934$	24.0000	+	13.8564i	0.785304	+	0.453395i
$935$	−36.0000	+	20.7846i	−1.17733	+	0.679729i
$936$	−13.5000	−	7.79423i	−0.441261	−	0.254762i
$937$	−11.5000	−	19.9186i	−0.375689	−	0.650712i	0.614741	−	0.788729i	$-0.289260\pi$
$937$	−11.5000	−	19.9186i	−0.375689	−	0.650712i	−0.990430	+	0.138017i	$0.955927\pi$
$938$		−	8.66025i		−	0.282767i
$939$		−	24.2487i		−	0.791327i
$940$	−12.0000	−	20.7846i	−0.391397	−	0.677919i
$941$	12.0000	+	20.7846i	0.391189	+	0.677559i	0.992607	−	0.121376i	$-0.0387306\pi$
$941$	12.0000	+	20.7846i	0.391189	+	0.677559i	−0.601418	+	0.798935i	$0.705397\pi$
$942$		−	12.1244i		−	0.395033i
$943$		0			0
$944$		0			0
$945$	−9.00000	+	15.5885i	−0.292770	+	0.507093i
$946$	−3.00000	+	1.73205i	−0.0975384	+	0.0563138i
$947$	27.0000	+	15.5885i	0.877382	+	0.506557i	0.869794	−	0.493414i	$-0.164251\pi$
$947$	27.0000	+	15.5885i	0.877382	+	0.506557i	0.00758776	+	0.999971i	$0.497585\pi$
$948$	−4.50000	+	7.79423i	−0.146153	+	0.253145i
$949$		−	36.3731i		−	1.18072i
$950$	−28.0000	−	12.1244i	−0.908440	−	0.393366i
$951$			10.3923i			0.336994i
$952$	−3.00000	−	1.73205i	−0.0972306	−	0.0561361i
$953$	3.00000	−	5.19615i	0.0971795	−	0.168320i	−0.813337	−	0.581793i	$-0.802351\pi$
$953$	3.00000	−	5.19615i	0.0971795	−	0.168320i	0.910516	+	0.413473i	$0.135685\pi$
$954$	18.0000	+	31.1769i	0.582772	+	1.00939i
$955$	−30.0000	+	51.9615i	−0.970777	+	1.68144i
$956$	21.0000	−	12.1244i	0.679189	−	0.392130i
$957$	−36.0000			−1.16371
$958$			10.3923i			0.335760i
$959$	3.00000	−	1.73205i	0.0968751	−	0.0559308i
$960$	3.00000	+	5.19615i	0.0968246	+	0.167705i
$961$	28.0000			0.903226
$962$	27.0000			0.870515
$963$	27.0000	+	46.7654i	0.870063	+	1.50699i
$964$	1.50000	+	0.866025i	0.0483117	+	0.0278928i
$965$	21.0000	+	36.3731i	0.676014	+	1.17089i
$966$		0			0
$967$	14.5000	−	25.1147i	0.466289	−	0.807635i	−0.532970	−	0.846134i	$-0.678924\pi$
$967$	14.5000	−	25.1147i	0.466289	−	0.807635i	0.999259	+	0.0384986i	$0.0122575\pi$
$968$	1.00000			0.0321412
$969$	3.00000	+	25.9808i	0.0963739	+	0.834622i
$970$	−24.0000			−0.770594
$971$	−24.0000	+	41.5692i	−0.770197	+	1.33402i	0.167258	+	0.985913i	$0.446509\pi$
$971$	−24.0000	+	41.5692i	−0.770197	+	1.33402i	−0.937455	+	0.348107i	$0.886825\pi$
$972$	−13.5000	−	7.79423i	−0.433013	−	0.250000i
$973$	2.50000	+	4.33013i	0.0801463	+	0.138817i
$974$	3.00000	+	1.73205i	0.0961262	+	0.0554985i
$975$	−31.5000	−	54.5596i	−1.00881	−	1.74731i
$976$	7.00000			0.224065
$977$	−12.0000			−0.383914			−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000			−0.383914			−0.191957	+	0.981403i	$0.561483\pi$
$978$	16.5000	−	9.52628i	0.527612	−	0.304617i
$979$		0			0
$980$		−	20.7846i		−	0.663940i
$981$		0			0
$982$	9.00000	−	5.19615i	0.287202	−	0.165816i
$983$	−21.0000	+	36.3731i	−0.669796	+	1.16012i	0.308165	+	0.951333i	$0.400285\pi$
$983$	−21.0000	+	36.3731i	−0.669796	+	1.16012i	−0.977961	+	0.208788i	$0.933048\pi$
$984$	18.0000	−	10.3923i	0.573819	−	0.331295i
$985$		0			0
$986$	18.0000	+	10.3923i	0.573237	+	0.330958i
$987$	12.0000			0.381964
$988$	13.5000	+	18.1865i	0.429492	+	0.578591i
$989$		0			0
$990$	−18.0000	+	31.1769i	−0.572078	+	0.990867i
$991$	31.5000	+	18.1865i	1.00063	+	0.577714i	0.908435	−	0.418027i	$-0.137278\pi$
$991$	31.5000	+	18.1865i	1.00063	+	0.577714i	0.0921957	+	0.995741i	$0.470611\pi$
$992$	1.50000	−	0.866025i	0.0476250	−	0.0274963i
$993$	4.50000	−	7.79423i	0.142803	−	0.247342i
$994$	−3.00000	−	5.19615i	−0.0951542	−	0.164812i
$995$		−	86.6025i		−	2.74549i
$996$	−18.0000			−0.570352
$997$	26.5000	+	45.8993i	0.839263	+	1.45365i	0.890511	+	0.454961i	$0.150347\pi$
$997$	26.5000	+	45.8993i	0.839263	+	1.45365i	−0.0512480	+	0.998686i	$0.516320\pi$
$998$	15.5000	+	26.8468i	0.490644	+	0.849820i
$999$	27.0000			0.854242

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.h.c.65.1	yes	2
3.2	odd	2		114.2.h.b.65.1	✓	2
4.3	odd	2		912.2.bn.c.65.1		2
12.11	even	2		912.2.bn.f.65.1		2
19.12	odd	6		114.2.h.b.107.1	yes	2
57.50	even	6	inner	114.2.h.c.107.1	yes	2
76.31	even	6		912.2.bn.f.449.1		2
228.107	odd	6		912.2.bn.c.449.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.h.b.65.1	✓	2	3.2	odd	2
114.2.h.b.107.1	yes	2	19.12	odd	6
114.2.h.c.65.1	yes	2	1.1	even	1	trivial
114.2.h.c.107.1	yes	2	57.50	even	6	inner
912.2.bn.c.65.1		2	4.3	odd	2
912.2.bn.c.449.1		2	228.107	odd	6
912.2.bn.f.65.1		2	12.11	even	2
912.2.bn.f.449.1		2	76.31	even	6

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.00000 - 1.73205i) q^{5} +(-1.50000 + 0.866025i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.00000 - 1.73205i) q^{5} +(-1.50000 + 0.866025i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-3.00000 + 1.73205i) q^{10} -3.46410i q^{11} +1.73205i q^{12} +(4.50000 - 2.59808i) q^{13} +(0.500000 - 0.866025i) q^{14} +(3.00000 + 5.19615i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 1.73205i) q^{17} +3.00000 q^{18} +(-4.00000 - 1.73205i) q^{19} +3.46410i q^{20} +(-1.50000 - 0.866025i) q^{21} +(-3.00000 - 1.73205i) q^{22} +(1.50000 + 0.866025i) q^{24} +(3.50000 + 6.06218i) q^{25} -5.19615i q^{26} -5.19615i q^{27} +(-0.500000 - 0.866025i) q^{28} +(3.00000 + 5.19615i) q^{29} +6.00000 q^{30} -1.73205i q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{33} +(3.00000 - 1.73205i) q^{34} +(-3.00000 - 1.73205i) q^{35} +(1.50000 - 2.59808i) q^{36} +5.19615i q^{37} +(-3.50000 + 2.59808i) q^{38} -9.00000 q^{39} +(3.00000 + 1.73205i) q^{40} +(6.00000 - 10.3923i) q^{41} +(-1.50000 + 0.866025i) q^{42} +(0.500000 - 0.866025i) q^{43} +(-3.00000 + 1.73205i) q^{44} -10.3923i q^{45} +(-6.00000 + 3.46410i) q^{47} +(1.50000 - 0.866025i) q^{48} -6.00000 q^{49} +7.00000 q^{50} +(-3.00000 - 5.19615i) q^{51} +(-4.50000 - 2.59808i) q^{52} +(6.00000 + 10.3923i) q^{53} +(-4.50000 - 2.59808i) q^{54} +(-6.00000 + 10.3923i) q^{55} -1.00000 q^{56} +(4.50000 + 6.06218i) q^{57} +6.00000 q^{58} +(3.00000 - 5.19615i) q^{60} +(-3.50000 - 6.06218i) q^{61} +(-1.50000 - 0.866025i) q^{62} +(1.50000 + 2.59808i) q^{63} +1.00000 q^{64} -18.0000 q^{65} +(3.00000 + 5.19615i) q^{66} +(7.50000 - 4.33013i) q^{67} -3.46410i q^{68} +(-3.00000 + 1.73205i) q^{70} +(3.00000 - 5.19615i) q^{71} +(-1.50000 - 2.59808i) q^{72} +(3.50000 - 6.06218i) q^{73} +(4.50000 + 2.59808i) q^{74} -12.1244i q^{75} +(0.500000 + 4.33013i) q^{76} -3.46410i q^{77} +(-4.50000 + 7.79423i) q^{78} +(4.50000 + 2.59808i) q^{79} +(3.00000 - 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-6.00000 - 10.3923i) q^{82} +10.3923i q^{83} +1.73205i q^{84} +(-6.00000 - 10.3923i) q^{85} +(-0.500000 - 0.866025i) q^{86} -10.3923i q^{87} +3.46410i q^{88} +(-9.00000 - 5.19615i) q^{90} +(4.50000 - 2.59808i) q^{91} +(-1.50000 + 2.59808i) q^{93} +6.92820i q^{94} +(9.00000 + 12.1244i) q^{95} -1.73205i q^{96} +(6.00000 + 3.46410i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(9.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 3 q^{3} - q^{4} - 6 q^{5} - 3 q^{6} + 2 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + q^2 - 3 * q^3 - q^4 - 6 * q^5 - 3 * q^6 + 2 * q^7 - 2 * q^8 + 3 * q^9	\( 2 q + q^{2} - 3 q^{3} - q^{4} - 6 q^{5} - 3 q^{6} + 2 q^{7} - 2 q^{8} + 3 q^{9} - 6 q^{10} + 9 q^{13} + q^{14} + 6 q^{15} - q^{16} + 6 q^{17} + 6 q^{18} - 8 q^{19} - 3 q^{21} - 6 q^{22} + 3 q^{24} + 7 q^{25} - q^{28} + 6 q^{29} + 12 q^{30} + q^{32} - 6 q^{33} + 6 q^{34} - 6 q^{35} + 3 q^{36} - 7 q^{38} - 18 q^{39} + 6 q^{40} + 12 q^{41} - 3 q^{42} + q^{43} - 6 q^{44} - 12 q^{47} + 3 q^{48} - 12 q^{49} + 14 q^{50} - 6 q^{51} - 9 q^{52} + 12 q^{53} - 9 q^{54} - 12 q^{55} - 2 q^{56} + 9 q^{57} + 12 q^{58} + 6 q^{60} - 7 q^{61} - 3 q^{62} + 3 q^{63} + 2 q^{64} - 36 q^{65} + 6 q^{66} + 15 q^{67} - 6 q^{70} + 6 q^{71} - 3 q^{72} + 7 q^{73} + 9 q^{74} + q^{76} - 9 q^{78} + 9 q^{79} + 6 q^{80} - 9 q^{81} - 12 q^{82} - 12 q^{85} - q^{86} - 18 q^{90} + 9 q^{91} - 3 q^{93} + 18 q^{95} + 12 q^{97} - 6 q^{98} + 18 q^{99}+O(q^{100}) \) 2 * q + q^2 - 3 * q^3 - q^4 - 6 * q^5 - 3 * q^6 + 2 * q^7 - 2 * q^8 + 3 * q^9 - 6 * q^10 + 9 * q^13 + q^14 + 6 * q^15 - q^16 + 6 * q^17 + 6 * q^18 - 8 * q^19 - 3 * q^21 - 6 * q^22 + 3 * q^24 + 7 * q^25 - q^28 + 6 * q^29 + 12 * q^30 + q^32 - 6 * q^33 + 6 * q^34 - 6 * q^35 + 3 * q^36 - 7 * q^38 - 18 * q^39 + 6 * q^40 + 12 * q^41 - 3 * q^42 + q^43 - 6 * q^44 - 12 * q^47 + 3 * q^48 - 12 * q^49 + 14 * q^50 - 6 * q^51 - 9 * q^52 + 12 * q^53 - 9 * q^54 - 12 * q^55 - 2 * q^56 + 9 * q^57 + 12 * q^58 + 6 * q^60 - 7 * q^61 - 3 * q^62 + 3 * q^63 + 2 * q^64 - 36 * q^65 + 6 * q^66 + 15 * q^67 - 6 * q^70 + 6 * q^71 - 3 * q^72 + 7 * q^73 + 9 * q^74 + q^76 - 9 * q^78 + 9 * q^79 + 6 * q^80 - 9 * q^81 - 12 * q^82 - 12 * q^85 - q^86 - 18 * q^90 + 9 * q^91 - 3 * q^93 + 18 * q^95 + 12 * q^97 - 6 * q^98 + 18 * q^99

Introduction

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