LMFDB - Embedded newform 114.2.h.d.107.1

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			107.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	114.107
Dual form			114.2.h.d.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +(3.00000 - 1.73205i) q^{5} +(-1.50000 + 0.866025i) q^{6} -2.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +(3.00000 - 1.73205i) q^{5} +(-1.50000 + 0.866025i) q^{6} -2.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +(3.00000 + 1.73205i) q^{10} +1.73205i q^{11} +(-1.50000 - 0.866025i) q^{12} +(-3.00000 - 1.73205i) q^{13} +(-1.00000 - 1.73205i) q^{14} +(3.00000 + 5.19615i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(6.00000 - 3.46410i) q^{17} +(-1.50000 - 2.59808i) q^{18} +(0.500000 - 4.33013i) q^{19} +3.46410i q^{20} -3.46410i q^{21} +(-1.50000 + 0.866025i) q^{22} -1.73205i q^{24} +(3.50000 - 6.06218i) q^{25} -3.46410i q^{26} -5.19615i q^{27} +(1.00000 - 1.73205i) q^{28} +(-3.00000 + 5.19615i) q^{29} +(-3.00000 + 5.19615i) q^{30} +6.92820i q^{31} +(0.500000 - 0.866025i) q^{32} -3.00000 q^{33} +(6.00000 + 3.46410i) q^{34} +(-6.00000 + 3.46410i) q^{35} +(1.50000 - 2.59808i) q^{36} +6.92820i q^{37} +(4.00000 - 1.73205i) q^{38} +(3.00000 - 5.19615i) q^{39} +(-3.00000 + 1.73205i) q^{40} +(-1.50000 - 2.59808i) q^{41} +(3.00000 - 1.73205i) q^{42} +(-4.00000 - 6.92820i) q^{43} +(-1.50000 - 0.866025i) q^{44} +(-9.00000 + 5.19615i) q^{45} +(-3.00000 - 1.73205i) q^{47} +(1.50000 - 0.866025i) q^{48} -3.00000 q^{49} +7.00000 q^{50} +(6.00000 + 10.3923i) q^{51} +(3.00000 - 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +(4.50000 - 2.59808i) q^{54} +(3.00000 + 5.19615i) q^{55} +2.00000 q^{56} +(7.50000 + 0.866025i) q^{57} -6.00000 q^{58} +(1.50000 + 2.59808i) q^{59} -6.00000 q^{60} +(-5.00000 + 8.66025i) q^{61} +(-6.00000 + 3.46410i) q^{62} +6.00000 q^{63} +1.00000 q^{64} -12.0000 q^{65} +(-1.50000 - 2.59808i) q^{66} +(4.50000 + 2.59808i) q^{67} +6.92820i q^{68} +(-6.00000 - 3.46410i) q^{70} +(3.00000 + 5.19615i) q^{71} +3.00000 q^{72} +(-2.50000 - 4.33013i) q^{73} +(-6.00000 + 3.46410i) q^{74} +(10.5000 + 6.06218i) q^{75} +(3.50000 + 2.59808i) q^{76} -3.46410i q^{77} +6.00000 q^{78} +(-12.0000 + 6.92820i) q^{79} +(-3.00000 - 1.73205i) q^{80} +9.00000 q^{81} +(1.50000 - 2.59808i) q^{82} +5.19615i q^{83} +(3.00000 + 1.73205i) q^{84} +(12.0000 - 20.7846i) q^{85} +(4.00000 - 6.92820i) q^{86} +(-9.00000 - 5.19615i) q^{87} -1.73205i q^{88} +(-3.00000 + 5.19615i) q^{89} +(-9.00000 - 5.19615i) q^{90} +(6.00000 + 3.46410i) q^{91} -12.0000 q^{93} -3.46410i q^{94} +(-6.00000 - 13.8564i) q^{95} +(1.50000 + 0.866025i) q^{96} +(7.50000 - 4.33013i) q^{97} +(-1.50000 - 2.59808i) q^{98} -5.19615i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} + 6 q^{5} - 3 q^{6} - 4 q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q + q^2 - q^4 + 6 * q^5 - 3 * q^6 - 4 * q^7 - 2 * q^8 - 6 * q^9	$ 2 q + q^{2} - q^{4} + 6 q^{5} - 3 q^{6} - 4 q^{7} - 2 q^{8} - 6 q^{9} + 6 q^{10} - 3 q^{12} - 6 q^{13} - 2 q^{14} + 6 q^{15} - q^{16} + 12 q^{17} - 3 q^{18} + q^{19} - 3 q^{22} + 7 q^{25} + 2 q^{28} - 6 q^{29} - 6 q^{30} + q^{32} - 6 q^{33} + 12 q^{34} - 12 q^{35} + 3 q^{36} + 8 q^{38} + 6 q^{39} - 6 q^{40} - 3 q^{41} + 6 q^{42} - 8 q^{43} - 3 q^{44} - 18 q^{45} - 6 q^{47} + 3 q^{48} - 6 q^{49} + 14 q^{50} + 12 q^{51} + 6 q^{52} + 6 q^{53} + 9 q^{54} + 6 q^{55} + 4 q^{56} + 15 q^{57} - 12 q^{58} + 3 q^{59} - 12 q^{60} - 10 q^{61} - 12 q^{62} + 12 q^{63} + 2 q^{64} - 24 q^{65} - 3 q^{66} + 9 q^{67} - 12 q^{70} + 6 q^{71} + 6 q^{72} - 5 q^{73} - 12 q^{74} + 21 q^{75} + 7 q^{76} + 12 q^{78} - 24 q^{79} - 6 q^{80} + 18 q^{81} + 3 q^{82} + 6 q^{84} + 24 q^{85} + 8 q^{86} - 18 q^{87} - 6 q^{89} - 18 q^{90} + 12 q^{91} - 24 q^{93} - 12 q^{95} + 3 q^{96} + 15 q^{97} - 3 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 + 6 * q^5 - 3 * q^6 - 4 * q^7 - 2 * q^8 - 6 * q^9 + 6 * q^10 - 3 * q^12 - 6 * q^13 - 2 * q^14 + 6 * q^15 - q^16 + 12 * q^17 - 3 * q^18 + q^19 - 3 * q^22 + 7 * q^25 + 2 * q^28 - 6 * q^29 - 6 * q^30 + q^32 - 6 * q^33 + 12 * q^34 - 12 * q^35 + 3 * q^36 + 8 * q^38 + 6 * q^39 - 6 * q^40 - 3 * q^41 + 6 * q^42 - 8 * q^43 - 3 * q^44 - 18 * q^45 - 6 * q^47 + 3 * q^48 - 6 * q^49 + 14 * q^50 + 12 * q^51 + 6 * q^52 + 6 * q^53 + 9 * q^54 + 6 * q^55 + 4 * q^56 + 15 * q^57 - 12 * q^58 + 3 * q^59 - 12 * q^60 - 10 * q^61 - 12 * q^62 + 12 * q^63 + 2 * q^64 - 24 * q^65 - 3 * q^66 + 9 * q^67 - 12 * q^70 + 6 * q^71 + 6 * q^72 - 5 * q^73 - 12 * q^74 + 21 * q^75 + 7 * q^76 + 12 * q^78 - 24 * q^79 - 6 * q^80 + 18 * q^81 + 3 * q^82 + 6 * q^84 + 24 * q^85 + 8 * q^86 - 18 * q^87 - 6 * q^89 - 18 * q^90 + 12 * q^91 - 24 * q^93 - 12 * q^95 + 3 * q^96 + 15 * q^97 - 3 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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
$3$			1.73205i			1.00000i
$3$			1.73205i			1.00000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	3.00000	−	1.73205i	1.34164	−	0.774597i	0.354593	−	0.935021i	$-0.384620\pi$
$5$	3.00000	−	1.73205i	1.34164	−	0.774597i	0.987048	+	0.160424i	$0.0512862\pi$
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$	−1.00000			−0.353553
$9$	−3.00000			−1.00000
$10$	3.00000	+	1.73205i	0.948683	+	0.547723i
$11$			1.73205i			0.522233i	0.965307	+	0.261116i	$0.0840907\pi$
$11$			1.73205i			0.522233i	−0.965307	+	0.261116i	$0.915909\pi$
$12$	−1.50000	−	0.866025i	−0.433013	−	0.250000i
$13$	−3.00000	−	1.73205i	−0.832050	−	0.480384i	0.0225039	−	0.999747i	$-0.492836\pi$
$13$	−3.00000	−	1.73205i	−0.832050	−	0.480384i	−0.854554	+	0.519362i	$0.826170\pi$
$14$	−1.00000	−	1.73205i	−0.267261	−	0.462910i
$15$	3.00000	+	5.19615i	0.774597	+	1.34164i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	6.00000	−	3.46410i	1.45521	−	0.840168i	0.456444	−	0.889752i	$-0.349123\pi$
$17$	6.00000	−	3.46410i	1.45521	−	0.840168i	0.998770	+	0.0495842i	$0.0157896\pi$
$18$	−1.50000	−	2.59808i	−0.353553	−	0.612372i
$19$	0.500000	−	4.33013i	0.114708	−	0.993399i
$19$	0.500000	−	4.33013i	0.114708	−	0.993399i
$20$			3.46410i			0.774597i
$21$		−	3.46410i		−	0.755929i
$22$	−1.50000	+	0.866025i	−0.319801	+	0.184637i
$23$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$23$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$24$		−	1.73205i		−	0.353553i
$25$	3.50000	−	6.06218i	0.700000	−	1.21244i
$26$		−	3.46410i		−	0.679366i
$27$		−	5.19615i		−	1.00000i
$28$	1.00000	−	1.73205i	0.188982	−	0.327327i
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$	−3.00000	+	5.19615i	−0.547723	+	0.948683i
$31$			6.92820i			1.24434i	0.782881	+	0.622171i	$0.213749\pi$
$31$			6.92820i			1.24434i	−0.782881	+	0.622171i	$0.786251\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−3.00000			−0.522233
$34$	6.00000	+	3.46410i	1.02899	+	0.594089i
$35$	−6.00000	+	3.46410i	−1.01419	+	0.585540i
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$			6.92820i			1.13899i	0.821995	+	0.569495i	$0.192861\pi$
$37$			6.92820i			1.13899i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	4.00000	−	1.73205i	0.648886	−	0.280976i
$39$	3.00000	−	5.19615i	0.480384	−	0.832050i
$40$	−3.00000	+	1.73205i	−0.474342	+	0.273861i
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$	3.00000	−	1.73205i	0.462910	−	0.267261i
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	0.381246	−	0.924473i	$-0.375495\pi$
$44$	−1.50000	−	0.866025i	−0.226134	−	0.130558i
$45$	−9.00000	+	5.19615i	−1.34164	+	0.774597i
$46$		0			0
$47$	−3.00000	−	1.73205i	−0.437595	−	0.252646i	0.264982	−	0.964253i	$-0.414634\pi$
$47$	−3.00000	−	1.73205i	−0.437595	−	0.252646i	−0.702577	+	0.711608i	$0.747967\pi$
$48$	1.50000	−	0.866025i	0.216506	−	0.125000i
$49$	−3.00000			−0.428571
$50$	7.00000			0.989949
$51$	6.00000	+	10.3923i	0.840168	+	1.45521i
$52$	3.00000	−	1.73205i	0.416025	−	0.240192i
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	−0.583036	−	0.812447i	$-0.698135\pi$
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	0.995117	+	0.0987002i	$0.0314685\pi$
$54$	4.50000	−	2.59808i	0.612372	−	0.353553i
$55$	3.00000	+	5.19615i	0.404520	+	0.700649i
$56$	2.00000			0.267261
$57$	7.50000	+	0.866025i	0.993399	+	0.114708i
$58$	−6.00000			−0.787839
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	0.946993	−	0.321253i	$-0.104104\pi$
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	−0.751710	+	0.659494i	$0.770771\pi$
$60$	−6.00000			−0.774597
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	0.345207	+	0.938527i	$0.387809\pi$
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	−0.985391	+	0.170305i	$0.945525\pi$
$62$	−6.00000	+	3.46410i	−0.762001	+	0.439941i
$63$	6.00000			0.755929
$64$	1.00000			0.125000
$65$	−12.0000			−1.48842
$66$	−1.50000	−	2.59808i	−0.184637	−	0.319801i
$67$	4.50000	+	2.59808i	0.549762	+	0.317406i	0.749026	−	0.662540i	$-0.230522\pi$
$67$	4.50000	+	2.59808i	0.549762	+	0.317406i	−0.199264	+	0.979946i	$0.563855\pi$
$68$			6.92820i			0.840168i
$69$		0			0
$70$	−6.00000	−	3.46410i	−0.717137	−	0.414039i
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$	3.00000			0.353553
$73$	−2.50000	−	4.33013i	−0.292603	−	0.506803i	0.681822	−	0.731519i	$-0.261188\pi$
$73$	−2.50000	−	4.33013i	−0.292603	−	0.506803i	−0.974424	+	0.224716i	$0.927855\pi$
$74$	−6.00000	+	3.46410i	−0.697486	+	0.402694i
$75$	10.5000	+	6.06218i	1.21244	+	0.700000i
$76$	3.50000	+	2.59808i	0.401478	+	0.298020i
$77$		−	3.46410i		−	0.394771i
$78$	6.00000			0.679366
$79$	−12.0000	+	6.92820i	−1.35011	+	0.779484i	−0.988264	−	0.152756i	$-0.951185\pi$
$79$	−12.0000	+	6.92820i	−1.35011	+	0.779484i	−0.361842	+	0.932240i	$0.617852\pi$
$80$	−3.00000	−	1.73205i	−0.335410	−	0.193649i
$81$	9.00000			1.00000
$82$	1.50000	−	2.59808i	0.165647	−	0.286910i
$83$			5.19615i			0.570352i	0.958475	+	0.285176i	$0.0920520\pi$
$83$			5.19615i			0.570352i	−0.958475	+	0.285176i	$0.907948\pi$
$84$	3.00000	+	1.73205i	0.327327	+	0.188982i
$85$	12.0000	−	20.7846i	1.30158	−	2.25441i
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$	−9.00000	−	5.19615i	−0.964901	−	0.557086i
$88$		−	1.73205i		−	0.184637i
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$	−9.00000	−	5.19615i	−0.948683	−	0.547723i
$91$	6.00000	+	3.46410i	0.628971	+	0.363137i
$92$		0			0
$93$	−12.0000			−1.24434
$94$		−	3.46410i		−	0.357295i
$95$	−6.00000	−	13.8564i	−0.615587	−	1.42164i
$96$	1.50000	+	0.866025i	0.153093	+	0.0883883i
$97$	7.50000	−	4.33013i	0.761510	−	0.439658i	−0.0683279	−	0.997663i	$-0.521766\pi$
$97$	7.50000	−	4.33013i	0.761510	−	0.439658i	0.829837	+	0.558005i	$0.188433\pi$
$98$	−1.50000	−	2.59808i	−0.151523	−	0.262445i
$99$		−	5.19615i		−	0.522233i
$100$	3.50000	+	6.06218i	0.350000	+	0.606218i
$101$	9.00000	+	5.19615i	0.895533	+	0.517036i	0.875748	−	0.482768i	$-0.160368\pi$
$101$	9.00000	+	5.19615i	0.895533	+	0.517036i	0.0197851	+	0.999804i	$0.493702\pi$
$102$	−6.00000	+	10.3923i	−0.594089	+	1.02899i
$103$		−	10.3923i		−	1.02398i	−0.858990	−	0.511992i	$-0.828908\pi$
$103$		−	10.3923i		−	1.02398i	0.858990	−	0.511992i	$-0.171092\pi$
$104$	3.00000	+	1.73205i	0.294174	+	0.169842i
$105$	−6.00000	−	10.3923i	−0.585540	−	1.01419i
$106$	6.00000			0.582772
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$	4.50000	+	2.59808i	0.433013	+	0.250000i
$109$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$109$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$110$	−3.00000	+	5.19615i	−0.286039	+	0.495434i
$111$	−12.0000			−1.13899
$112$	1.00000	+	1.73205i	0.0944911	+	0.163663i
$113$	−15.0000			−1.41108			−0.705541	−	0.708669i	$-0.749296\pi$
$113$	−15.0000			−1.41108			−0.705541	+	0.708669i	$0.749296\pi$
$114$	3.00000	+	6.92820i	0.280976	+	0.648886i
$115$		0			0
$116$	−3.00000	−	5.19615i	−0.278543	−	0.482451i
$117$	9.00000	+	5.19615i	0.832050	+	0.480384i
$118$	−1.50000	+	2.59808i	−0.138086	+	0.239172i
$119$	−12.0000	+	6.92820i	−1.10004	+	0.635107i
$120$	−3.00000	−	5.19615i	−0.273861	−	0.474342i
$121$	8.00000			0.727273
$122$	−10.0000			−0.905357
$123$	4.50000	−	2.59808i	0.405751	−	0.234261i
$124$	−6.00000	−	3.46410i	−0.538816	−	0.311086i
$125$		−	6.92820i		−	0.619677i
$126$	3.00000	+	5.19615i	0.267261	+	0.462910i
$127$	−9.00000	−	5.19615i	−0.798621	−	0.461084i	0.0443678	−	0.999015i	$-0.485873\pi$
$127$	−9.00000	−	5.19615i	−0.798621	−	0.461084i	−0.842989	+	0.537931i	$0.819206\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	12.0000	−	6.92820i	1.05654	−	0.609994i
$130$	−6.00000	−	10.3923i	−0.526235	−	0.911465i
$131$	16.5000	−	9.52628i	1.44161	−	0.832315i	0.443654	−	0.896198i	$-0.353682\pi$
$131$	16.5000	−	9.52628i	1.44161	−	0.832315i	0.997957	+	0.0638831i	$0.0203485\pi$
$132$	1.50000	−	2.59808i	0.130558	−	0.226134i
$133$	−1.00000	+	8.66025i	−0.0867110	+	0.750939i
$134$			5.19615i			0.448879i
$135$	−9.00000	−	15.5885i	−0.774597	−	1.34164i
$136$	−6.00000	+	3.46410i	−0.514496	+	0.297044i
$137$	1.50000	+	0.866025i	0.128154	+	0.0739895i	0.562706	−	0.826657i	$-0.309760\pi$
$137$	1.50000	+	0.866025i	0.128154	+	0.0739895i	−0.434553	+	0.900646i	$0.643094\pi$
$138$		0			0
$139$	−0.500000	+	0.866025i	−0.0424094	+	0.0734553i	−0.886451	−	0.462822i	$-0.846837\pi$
$139$	−0.500000	+	0.866025i	−0.0424094	+	0.0734553i	0.844042	+	0.536278i	$0.180170\pi$
$140$		−	6.92820i		−	0.585540i
$141$	3.00000	−	5.19615i	0.252646	−	0.437595i
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$			20.7846i			1.72607i
$146$	2.50000	−	4.33013i	0.206901	−	0.358364i
$147$		−	5.19615i		−	0.428571i
$148$	−6.00000	−	3.46410i	−0.493197	−	0.284747i
$149$	6.00000	−	3.46410i	0.491539	−	0.283790i	−0.233674	−	0.972315i	$-0.575075\pi$
$149$	6.00000	−	3.46410i	0.491539	−	0.283790i	0.725213	+	0.688525i	$0.241741\pi$
$150$			12.1244i			0.989949i
$151$		−	6.92820i		−	0.563809i	−0.959442	−	0.281905i	$-0.909034\pi$
$151$		−	6.92820i		−	0.563809i	0.959442	−	0.281905i	$-0.0909662\pi$
$152$	−0.500000	+	4.33013i	−0.0405554	+	0.351220i
$153$	−18.0000	+	10.3923i	−1.45521	+	0.840168i
$154$	3.00000	−	1.73205i	0.241747	−	0.139573i
$155$	12.0000	+	20.7846i	0.963863	+	1.66946i
$156$	3.00000	+	5.19615i	0.240192	+	0.416025i
$157$	10.0000	+	17.3205i	0.798087	+	1.38233i	0.920860	+	0.389892i	$0.127488\pi$
$157$	10.0000	+	17.3205i	0.798087	+	1.38233i	−0.122774	+	0.992435i	$0.539179\pi$
$158$	−12.0000	−	6.92820i	−0.954669	−	0.551178i
$159$	9.00000	+	5.19615i	0.713746	+	0.412082i
$160$		−	3.46410i		−	0.273861i
$161$		0			0
$162$	4.50000	+	7.79423i	0.353553	+	0.612372i
$163$	−17.0000			−1.33154			−0.665771	−	0.746156i	$-0.731897\pi$
$163$	−17.0000			−1.33154			−0.665771	+	0.746156i	$0.731897\pi$
$164$	3.00000			0.234261
$165$	−9.00000	+	5.19615i	−0.700649	+	0.404520i
$166$	−4.50000	+	2.59808i	−0.349268	+	0.201650i
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	−0.534875	−	0.844931i	$-0.679641\pi$
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	0.999169	+	0.0407502i	$0.0129748\pi$
$168$			3.46410i			0.267261i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	24.0000			1.84072
$171$	−1.50000	+	12.9904i	−0.114708	+	0.993399i
$172$	8.00000			0.609994
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	0.973670	+	0.227964i	$0.0732068\pi$
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	−0.289412	+	0.957205i	$0.593460\pi$
$174$		−	10.3923i		−	0.787839i
$175$	−7.00000	+	12.1244i	−0.529150	+	0.916515i
$176$	1.50000	−	0.866025i	0.113067	−	0.0652791i
$177$	−4.50000	+	2.59808i	−0.338241	+	0.195283i
$178$	−6.00000			−0.449719
$179$	−3.00000			−0.224231			−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000			−0.224231			−0.112115	+	0.993695i	$0.535763\pi$
$180$		−	10.3923i		−	0.774597i
$181$	6.00000	+	3.46410i	0.445976	+	0.257485i	0.706129	−	0.708083i	$-0.250440\pi$
$181$	6.00000	+	3.46410i	0.445976	+	0.257485i	−0.260153	+	0.965567i	$0.583773\pi$
$182$			6.92820i			0.513553i
$183$	−15.0000	−	8.66025i	−1.10883	−	0.640184i
$184$		0			0
$185$	12.0000	+	20.7846i	0.882258	+	1.52811i
$186$	−6.00000	−	10.3923i	−0.439941	−	0.762001i
$187$	6.00000	+	10.3923i	0.438763	+	0.759961i
$188$	3.00000	−	1.73205i	0.218797	−	0.126323i
$189$			10.3923i			0.755929i
$190$	9.00000	−	12.1244i	0.652929	−	0.879593i
$191$		−	6.92820i		−	0.501307i	−0.968077	−	0.250654i	$-0.919354\pi$
$191$		−	6.92820i		−	0.501307i	0.968077	−	0.250654i	$-0.0806455\pi$
$192$			1.73205i			0.125000i
$193$	18.0000	−	10.3923i	1.29567	−	0.748054i	0.316016	−	0.948754i	$-0.397655\pi$
$193$	18.0000	−	10.3923i	1.29567	−	0.748054i	0.979653	+	0.200700i	$0.0643215\pi$
$194$	7.50000	+	4.33013i	0.538469	+	0.310885i
$195$		−	20.7846i		−	1.48842i
$196$	1.50000	−	2.59808i	0.107143	−	0.185577i
$197$		−	20.7846i		−	1.48084i	−0.672143	−	0.740421i	$-0.734626\pi$
$197$		−	20.7846i		−	1.48084i	0.672143	−	0.740421i	$-0.265374\pi$
$198$	4.50000	−	2.59808i	0.319801	−	0.184637i
$199$	−7.00000	+	12.1244i	−0.496217	+	0.859473i	−0.999990	−	0.00436292i	$-0.998611\pi$
$199$	−7.00000	+	12.1244i	−0.496217	+	0.859473i	0.503774	+	0.863836i	$0.331945\pi$
$200$	−3.50000	+	6.06218i	−0.247487	+	0.428661i
$201$	−4.50000	+	7.79423i	−0.317406	+	0.549762i
$202$			10.3923i			0.731200i
$203$	6.00000	−	10.3923i	0.421117	−	0.729397i
$204$	−12.0000			−0.840168
$205$	−9.00000	−	5.19615i	−0.628587	−	0.362915i
$206$	9.00000	−	5.19615i	0.627060	−	0.362033i
$207$		0			0
$208$			3.46410i			0.240192i
$209$	7.50000	+	0.866025i	0.518786	+	0.0599042i
$210$	6.00000	−	10.3923i	0.414039	−	0.717137i
$211$	9.00000	−	5.19615i	0.619586	−	0.357718i	−0.157122	−	0.987579i	$-0.550222\pi$
$211$	9.00000	−	5.19615i	0.619586	−	0.357718i	0.776708	+	0.629861i	$0.216888\pi$
$212$	3.00000	+	5.19615i	0.206041	+	0.356873i
$213$	−9.00000	+	5.19615i	−0.616670	+	0.356034i
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	−24.0000	−	13.8564i	−1.63679	−	0.944999i
$216$			5.19615i			0.353553i
$217$		−	13.8564i		−	0.940634i
$218$		0			0
$219$	7.50000	−	4.33013i	0.506803	−	0.292603i
$220$	−6.00000			−0.404520
$221$	−24.0000			−1.61441
$222$	−6.00000	−	10.3923i	−0.402694	−	0.697486i
$223$	12.0000	−	6.92820i	0.803579	−	0.463947i	−0.0411418	−	0.999153i	$-0.513100\pi$
$223$	12.0000	−	6.92820i	0.803579	−	0.463947i	0.844721	+	0.535207i	$0.179766\pi$
$224$	−1.00000	+	1.73205i	−0.0668153	+	0.115728i
$225$	−10.5000	+	18.1865i	−0.700000	+	1.21244i
$226$	−7.50000	−	12.9904i	−0.498893	−	0.864107i
$227$	−21.0000			−1.39382			−0.696909	−	0.717159i	$-0.745442\pi$
$227$	−21.0000			−1.39382			−0.696909	+	0.717159i	$0.745442\pi$
$228$	−4.50000	+	6.06218i	−0.298020	+	0.401478i
$229$	4.00000			0.264327			0.132164	−	0.991228i	$-0.457808\pi$
$229$	4.00000			0.264327			0.132164	+	0.991228i	$0.457808\pi$
$230$		0			0
$231$	6.00000			0.394771
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$	1.50000	−	0.866025i	0.0982683	−	0.0567352i	−0.450060	−	0.892998i	$-0.648598\pi$
$233$	1.50000	−	0.866025i	0.0982683	−	0.0567352i	0.548329	+	0.836263i	$0.315264\pi$
$234$			10.3923i			0.679366i
$235$	−12.0000			−0.782794
$236$	−3.00000			−0.195283
$237$	−12.0000	−	20.7846i	−0.779484	−	1.35011i
$238$	−12.0000	−	6.92820i	−0.777844	−	0.449089i
$239$		−	6.92820i		−	0.448148i	−0.974572	−	0.224074i	$-0.928064\pi$
$239$		−	6.92820i		−	0.448148i	0.974572	−	0.224074i	$-0.0719358\pi$
$240$	3.00000	−	5.19615i	0.193649	−	0.335410i
$241$	4.50000	+	2.59808i	0.289870	+	0.167357i	0.637883	−	0.770133i	$-0.279810\pi$
$241$	4.50000	+	2.59808i	0.289870	+	0.167357i	−0.348013	+	0.937490i	$0.613143\pi$
$242$	4.00000	+	6.92820i	0.257130	+	0.445362i
$243$			15.5885i			1.00000i
$244$	−5.00000	−	8.66025i	−0.320092	−	0.554416i
$245$	−9.00000	+	5.19615i	−0.574989	+	0.331970i
$246$	4.50000	+	2.59808i	0.286910	+	0.165647i
$247$	−9.00000	+	12.1244i	−0.572656	+	0.771454i
$248$		−	6.92820i		−	0.439941i
$249$	−9.00000			−0.570352
$250$	6.00000	−	3.46410i	0.379473	−	0.219089i
$251$	7.50000	+	4.33013i	0.473396	+	0.273315i	0.717660	−	0.696393i	$-0.245213\pi$
$251$	7.50000	+	4.33013i	0.473396	+	0.273315i	−0.244264	+	0.969709i	$0.578546\pi$
$252$	−3.00000	+	5.19615i	−0.188982	+	0.327327i
$253$		0			0
$254$		−	10.3923i		−	0.652071i
$255$	36.0000	+	20.7846i	2.25441	+	1.30158i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	−0.999325	−	0.0367485i	$-0.988300\pi$
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	0.531487	+	0.847066i	$0.321633\pi$
$258$	12.0000	+	6.92820i	0.747087	+	0.431331i
$259$		−	13.8564i		−	0.860995i
$260$	6.00000	−	10.3923i	0.372104	−	0.644503i
$261$	9.00000	−	15.5885i	0.557086	−	0.964901i
$262$	16.5000	+	9.52628i	1.01937	+	0.588536i
$263$	−3.00000	+	1.73205i	−0.184988	+	0.106803i	−0.589634	−	0.807671i	$-0.700728\pi$
$263$	−3.00000	+	1.73205i	−0.184988	+	0.106803i	0.404646	+	0.914473i	$0.367395\pi$
$264$	3.00000			0.184637
$265$		−	20.7846i		−	1.27679i
$266$	−8.00000	+	3.46410i	−0.490511	+	0.212398i
$267$	−9.00000	−	5.19615i	−0.550791	−	0.317999i
$268$	−4.50000	+	2.59808i	−0.274881	+	0.158703i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$	9.00000	−	15.5885i	0.547723	−	0.948683i
$271$	−13.0000	−	22.5167i	−0.789694	−	1.36779i	−0.926155	−	0.377144i	$-0.876906\pi$
$271$	−13.0000	−	22.5167i	−0.789694	−	1.36779i	0.136461	−	0.990645i	$-0.456427\pi$
$272$	−6.00000	−	3.46410i	−0.363803	−	0.210042i
$273$	−6.00000	+	10.3923i	−0.363137	+	0.628971i
$274$			1.73205i			0.104637i
$275$	10.5000	+	6.06218i	0.633174	+	0.365563i
$276$		0			0
$277$	−2.00000			−0.120168			−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000			−0.120168			−0.0600842	+	0.998193i	$0.519137\pi$
$278$	−1.00000			−0.0599760
$279$		−	20.7846i		−	1.24434i
$280$	6.00000	−	3.46410i	0.358569	−	0.207020i
$281$	7.50000	−	12.9904i	0.447412	−	0.774941i	−0.550804	−	0.834634i	$-0.685679\pi$
$281$	7.50000	−	12.9904i	0.447412	−	0.774941i	0.998217	+	0.0596933i	$0.0190123\pi$
$282$	6.00000			0.357295
$283$	0.500000	+	0.866025i	0.0297219	+	0.0514799i	0.880504	−	0.474039i	$-0.157204\pi$
$283$	0.500000	+	0.866025i	0.0297219	+	0.0514799i	−0.850782	+	0.525519i	$0.823871\pi$
$284$	−6.00000			−0.356034
$285$	24.0000	−	10.3923i	1.42164	−	0.615587i
$286$	6.00000			0.354787
$287$	3.00000	+	5.19615i	0.177084	+	0.306719i
$288$	−1.50000	+	2.59808i	−0.0883883	+	0.153093i
$289$	15.5000	−	26.8468i	0.911765	−	1.57922i
$290$	−18.0000	+	10.3923i	−1.05700	+	0.610257i
$291$	7.50000	+	12.9904i	0.439658	+	0.761510i
$292$	5.00000			0.292603
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$	4.50000	−	2.59808i	0.262445	−	0.151523i
$295$	9.00000	+	5.19615i	0.524000	+	0.302532i
$296$		−	6.92820i		−	0.402694i
$297$	9.00000			0.522233
$298$	6.00000	+	3.46410i	0.347571	+	0.200670i
$299$		0			0
$300$	−10.5000	+	6.06218i	−0.606218	+	0.350000i
$301$	8.00000	+	13.8564i	0.461112	+	0.798670i
$302$	6.00000	−	3.46410i	0.345261	−	0.199337i
$303$	−9.00000	+	15.5885i	−0.517036	+	0.895533i
$304$	−4.00000	+	1.73205i	−0.229416	+	0.0993399i
$305$			34.6410i			1.98354i
$306$	−18.0000	−	10.3923i	−1.02899	−	0.594089i
$307$	−4.50000	+	2.59808i	−0.256829	+	0.148280i	−0.622887	−	0.782312i	$-0.714040\pi$
$307$	−4.50000	+	2.59808i	−0.256829	+	0.148280i	0.366058	+	0.930592i	$0.380707\pi$
$308$	3.00000	+	1.73205i	0.170941	+	0.0986928i
$309$	18.0000			1.02398
$310$	−12.0000	+	20.7846i	−0.681554	+	1.18049i
$311$			13.8564i			0.785725i	0.919597	+	0.392862i	$0.128515\pi$
$311$			13.8564i			0.785725i	−0.919597	+	0.392862i	$0.871485\pi$
$312$	−3.00000	+	5.19615i	−0.169842	+	0.294174i
$313$	−15.5000	+	26.8468i	−0.876112	+	1.51747i	−0.0205381	+	0.999789i	$0.506538\pi$
$313$	−15.5000	+	26.8468i	−0.876112	+	1.51747i	−0.855574	+	0.517681i	$0.826795\pi$
$314$	−10.0000	+	17.3205i	−0.564333	+	0.977453i
$315$	18.0000	−	10.3923i	1.01419	−	0.585540i
$316$		−	13.8564i		−	0.779484i
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$			10.3923i			0.582772i
$319$	−9.00000	−	5.19615i	−0.503903	−	0.290929i
$320$	3.00000	−	1.73205i	0.167705	−	0.0968246i
$321$			20.7846i			1.16008i
$322$		0			0
$323$	−12.0000	−	27.7128i	−0.667698	−	1.54198i
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−21.0000	+	12.1244i	−1.16487	+	0.672538i
$326$	−8.50000	−	14.7224i	−0.470771	−	0.815400i
$327$		0			0
$328$	1.50000	+	2.59808i	0.0828236	+	0.143455i
$329$	6.00000	+	3.46410i	0.330791	+	0.190982i
$330$	−9.00000	−	5.19615i	−0.495434	−	0.286039i
$331$			8.66025i			0.476011i	0.971264	+	0.238005i	$0.0764936\pi$
$331$			8.66025i			0.476011i	−0.971264	+	0.238005i	$0.923506\pi$
$332$	−4.50000	−	2.59808i	−0.246970	−	0.142588i
$333$		−	20.7846i		−	1.13899i
$334$	12.0000			0.656611
$335$	18.0000			0.983445
$336$	−3.00000	+	1.73205i	−0.163663	+	0.0944911i
$337$	−22.5000	+	12.9904i	−1.22565	+	0.707631i	−0.966118	−	0.258102i	$-0.916903\pi$
$337$	−22.5000	+	12.9904i	−1.22565	+	0.707631i	−0.259536	+	0.965734i	$0.583569\pi$
$338$	0.500000	−	0.866025i	0.0271964	−	0.0471056i
$339$		−	25.9808i		−	1.41108i
$340$	12.0000	+	20.7846i	0.650791	+	1.12720i
$341$	−12.0000			−0.649836
$342$	−12.0000	+	5.19615i	−0.648886	+	0.280976i
$343$	20.0000			1.07990
$344$	4.00000	+	6.92820i	0.215666	+	0.373544i
$345$		0			0
$346$	−9.00000	+	15.5885i	−0.483843	+	0.838041i
$347$	7.50000	−	4.33013i	0.402621	−	0.232453i	−0.284993	−	0.958530i	$-0.591991\pi$
$347$	7.50000	−	4.33013i	0.402621	−	0.232453i	0.687614	+	0.726076i	$0.258658\pi$
$348$	9.00000	−	5.19615i	0.482451	−	0.278543i
$349$	8.00000			0.428230			0.214115	−	0.976808i	$-0.431313\pi$
$349$	8.00000			0.428230			0.214115	+	0.976808i	$0.431313\pi$
$350$	−14.0000			−0.748331
$351$	−9.00000	+	15.5885i	−0.480384	+	0.832050i
$352$	1.50000	+	0.866025i	0.0799503	+	0.0461593i
$353$		−	25.9808i		−	1.38282i	−0.722464	−	0.691408i	$-0.756991\pi$
$353$		−	25.9808i		−	1.38282i	0.722464	−	0.691408i	$-0.243009\pi$
$354$	−4.50000	−	2.59808i	−0.239172	−	0.138086i
$355$	18.0000	+	10.3923i	0.955341	+	0.551566i
$356$	−3.00000	−	5.19615i	−0.159000	−	0.275396i
$357$	−12.0000	−	20.7846i	−0.635107	−	1.10004i
$358$	−1.50000	−	2.59808i	−0.0792775	−	0.137313i
$359$	−6.00000	+	3.46410i	−0.316668	+	0.182828i	−0.649906	−	0.760014i	$-0.725192\pi$
$359$	−6.00000	+	3.46410i	−0.316668	+	0.182828i	0.333238	+	0.942843i	$0.391859\pi$
$360$	9.00000	−	5.19615i	0.474342	−	0.273861i
$361$	−18.5000	−	4.33013i	−0.973684	−	0.227901i
$362$			6.92820i			0.364138i
$363$			13.8564i			0.727273i
$364$	−6.00000	+	3.46410i	−0.314485	+	0.181568i
$365$	−15.0000	−	8.66025i	−0.785136	−	0.453298i
$366$		−	17.3205i		−	0.905357i
$367$	2.00000	−	3.46410i	0.104399	−	0.180825i	−0.809093	−	0.587680i	$-0.800041\pi$
$367$	2.00000	−	3.46410i	0.104399	−	0.180825i	0.913493	+	0.406855i	$0.133375\pi$
$368$		0			0
$369$	4.50000	+	7.79423i	0.234261	+	0.405751i
$370$	−12.0000	+	20.7846i	−0.623850	+	1.08054i
$371$	−6.00000	+	10.3923i	−0.311504	+	0.539542i
$372$	6.00000	−	10.3923i	0.311086	−	0.538816i
$373$		−	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
$375$	12.0000			0.619677
$376$	3.00000	+	1.73205i	0.154713	+	0.0893237i
$377$	18.0000	−	10.3923i	0.927047	−	0.535231i
$378$	−9.00000	+	5.19615i	−0.462910	+	0.267261i
$379$		−	10.3923i		−	0.533817i	−0.963722	−	0.266908i	$-0.913998\pi$
$379$		−	10.3923i		−	0.533817i	0.963722	−	0.266908i	$-0.0860021\pi$
$380$	15.0000	+	1.73205i	0.769484	+	0.0888523i
$381$	9.00000	−	15.5885i	0.461084	−	0.798621i
$382$	6.00000	−	3.46410i	0.306987	−	0.177239i
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	0.539076	−	0.842257i	$-0.318774\pi$
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	−0.998954	+	0.0457244i	$0.985440\pi$
$384$	−1.50000	+	0.866025i	−0.0765466	+	0.0441942i
$385$	−6.00000	−	10.3923i	−0.305788	−	0.529641i
$386$	18.0000	+	10.3923i	0.916176	+	0.528954i
$387$	12.0000	+	20.7846i	0.609994	+	1.05654i
$388$			8.66025i			0.439658i
$389$	30.0000	+	17.3205i	1.52106	+	0.878185i	0.999691	+	0.0248535i	$0.00791191\pi$
$389$	30.0000	+	17.3205i	1.52106	+	0.878185i	0.521369	+	0.853331i	$0.325421\pi$
$390$	18.0000	−	10.3923i	0.911465	−	0.526235i
$391$		0			0
$392$	3.00000			0.151523
$393$	16.5000	+	28.5788i	0.832315	+	1.44161i
$394$	18.0000	−	10.3923i	0.906827	−	0.523557i
$395$	−24.0000	+	41.5692i	−1.20757	+	2.09157i
$396$	4.50000	+	2.59808i	0.226134	+	0.130558i
$397$	−10.0000	−	17.3205i	−0.501886	−	0.869291i	−0.999998	−	0.00217869i	$-0.999307\pi$
$397$	−10.0000	−	17.3205i	−0.501886	−	0.869291i	0.498112	−	0.867113i	$-0.334027\pi$
$398$	−14.0000			−0.701757
$399$	−15.0000	−	1.73205i	−0.750939	−	0.0867110i
$400$	−7.00000			−0.350000
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$	−9.00000			−0.448879
$403$	12.0000	−	20.7846i	0.597763	−	1.03536i
$404$	−9.00000	+	5.19615i	−0.447767	+	0.258518i
$405$	27.0000	−	15.5885i	1.34164	−	0.774597i
$406$	12.0000			0.595550
$407$	−12.0000			−0.594818
$408$	−6.00000	−	10.3923i	−0.297044	−	0.514496i
$409$	−16.5000	−	9.52628i	−0.815872	−	0.471044i	0.0331186	−	0.999451i	$-0.489456\pi$
$409$	−16.5000	−	9.52628i	−0.815872	−	0.471044i	−0.848991	+	0.528407i	$0.822789\pi$
$410$		−	10.3923i		−	0.513239i
$411$	−1.50000	+	2.59808i	−0.0739895	+	0.128154i
$412$	9.00000	+	5.19615i	0.443398	+	0.255996i
$413$	−3.00000	−	5.19615i	−0.147620	−	0.255686i
$414$		0			0
$415$	9.00000	+	15.5885i	0.441793	+	0.765207i
$416$	−3.00000	+	1.73205i	−0.147087	+	0.0849208i
$417$	−1.50000	−	0.866025i	−0.0734553	−	0.0424094i
$418$	3.00000	+	6.92820i	0.146735	+	0.338869i
$419$		−	10.3923i		−	0.507697i	−0.967244	−	0.253849i	$-0.918303\pi$
$419$		−	10.3923i		−	0.507697i	0.967244	−	0.253849i	$-0.0816965\pi$
$420$	12.0000			0.585540
$421$	−12.0000	+	6.92820i	−0.584844	+	0.337660i	−0.763056	−	0.646332i	$-0.776302\pi$
$421$	−12.0000	+	6.92820i	−0.584844	+	0.337660i	0.178212	+	0.983992i	$0.442969\pi$
$422$	9.00000	+	5.19615i	0.438113	+	0.252945i
$423$	9.00000	+	5.19615i	0.437595	+	0.252646i
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$		−	48.4974i		−	2.35247i
$426$	−9.00000	−	5.19615i	−0.436051	−	0.251754i
$427$	10.0000	−	17.3205i	0.483934	−	0.838198i
$428$	−6.00000	+	10.3923i	−0.290021	+	0.502331i
$429$	9.00000	+	5.19615i	0.434524	+	0.250873i
$430$		−	27.7128i		−	1.33643i
$431$	−3.00000	+	5.19615i	−0.144505	+	0.250290i	−0.929188	−	0.369607i	$-0.879492\pi$
$431$	−3.00000	+	5.19615i	−0.144505	+	0.250290i	0.784683	+	0.619897i	$0.212826\pi$
$432$	−4.50000	+	2.59808i	−0.216506	+	0.125000i
$433$	−12.0000	−	6.92820i	−0.576683	−	0.332948i	0.183131	−	0.983089i	$-0.441377\pi$
$433$	−12.0000	−	6.92820i	−0.576683	−	0.332948i	−0.759814	+	0.650140i	$0.774710\pi$
$434$	12.0000	−	6.92820i	0.576018	−	0.332564i
$435$	−36.0000			−1.72607
$436$		0			0
$437$		0			0
$438$	7.50000	+	4.33013i	0.358364	+	0.206901i
$439$	−12.0000	+	6.92820i	−0.572729	+	0.330665i	−0.758238	−	0.651977i	$-0.773940\pi$
$439$	−12.0000	+	6.92820i	−0.572729	+	0.330665i	0.185510	+	0.982642i	$0.440606\pi$
$440$	−3.00000	−	5.19615i	−0.143019	−	0.247717i
$441$	9.00000			0.428571
$442$	−12.0000	−	20.7846i	−0.570782	−	0.988623i
$443$	10.5000	+	6.06218i	0.498870	+	0.288023i	0.728247	−	0.685315i	$-0.240335\pi$
$443$	10.5000	+	6.06218i	0.498870	+	0.288023i	−0.229377	+	0.973338i	$0.573669\pi$
$444$	6.00000	−	10.3923i	0.284747	−	0.493197i
$445$			20.7846i			0.985285i
$446$	12.0000	+	6.92820i	0.568216	+	0.328060i
$447$	6.00000	+	10.3923i	0.283790	+	0.491539i
$448$	−2.00000			−0.0944911
$449$	−3.00000			−0.141579			−0.0707894	−	0.997491i	$-0.522552\pi$
$449$	−3.00000			−0.141579			−0.0707894	+	0.997491i	$0.522552\pi$
$450$	−21.0000			−0.989949
$451$	4.50000	−	2.59808i	0.211897	−	0.122339i
$452$	7.50000	−	12.9904i	0.352770	−	0.611016i
$453$	12.0000			0.563809
$454$	−10.5000	−	18.1865i	−0.492789	−	0.853536i
$455$	24.0000			1.12514
$456$	−7.50000	−	0.866025i	−0.351220	−	0.0405554i
$457$	17.0000			0.795226			0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000			0.795226			0.397613	+	0.917553i	$0.369839\pi$
$458$	2.00000	+	3.46410i	0.0934539	+	0.161867i
$459$	−18.0000	−	31.1769i	−0.840168	−	1.45521i
$460$		0			0
$461$	−21.0000	+	12.1244i	−0.978068	+	0.564688i	−0.901686	−	0.432391i	$-0.857670\pi$
$461$	−21.0000	+	12.1244i	−0.978068	+	0.564688i	−0.0763814	+	0.997079i	$0.524337\pi$
$462$	3.00000	+	5.19615i	0.139573	+	0.241747i
$463$	14.0000			0.650635			0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000			0.650635			0.325318	+	0.945605i	$0.394529\pi$
$464$	6.00000			0.278543
$465$	−36.0000	+	20.7846i	−1.66946	+	0.963863i
$466$	1.50000	+	0.866025i	0.0694862	+	0.0401179i
$467$			12.1244i			0.561048i	0.959847	+	0.280524i	$0.0905083\pi$
$467$			12.1244i			0.561048i	−0.959847	+	0.280524i	$0.909492\pi$
$468$	−9.00000	+	5.19615i	−0.416025	+	0.240192i
$469$	−9.00000	−	5.19615i	−0.415581	−	0.239936i
$470$	−6.00000	−	10.3923i	−0.276759	−	0.479361i
$471$	−30.0000	+	17.3205i	−1.38233	+	0.798087i
$472$	−1.50000	−	2.59808i	−0.0690431	−	0.119586i
$473$	12.0000	−	6.92820i	0.551761	−	0.318559i
$474$	12.0000	−	20.7846i	0.551178	−	0.954669i
$475$	−24.5000	−	18.1865i	−1.12414	−	0.834455i
$476$		−	13.8564i		−	0.635107i
$477$	−9.00000	+	15.5885i	−0.412082	+	0.713746i
$478$	6.00000	−	3.46410i	0.274434	−	0.158444i
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$	6.00000			0.273861
$481$	12.0000	−	20.7846i	0.547153	−	0.947697i
$482$			5.19615i			0.236678i
$483$		0			0
$484$	−4.00000	+	6.92820i	−0.181818	+	0.314918i
$485$	15.0000	−	25.9808i	0.681115	−	1.17973i
$486$	−13.5000	+	7.79423i	−0.612372	+	0.353553i
$487$		−	6.92820i		−	0.313947i	−0.987603	−	0.156973i	$-0.949826\pi$
$487$		−	6.92820i		−	0.313947i	0.987603	−	0.156973i	$-0.0501737\pi$
$488$	5.00000	−	8.66025i	0.226339	−	0.392031i
$489$		−	29.4449i		−	1.33154i
$490$	−9.00000	−	5.19615i	−0.406579	−	0.234738i
$491$	−27.0000	+	15.5885i	−1.21849	+	0.703497i	−0.964595	−	0.263734i	$-0.915046\pi$
$491$	−27.0000	+	15.5885i	−1.21849	+	0.703497i	−0.253897	+	0.967231i	$0.581713\pi$
$492$			5.19615i			0.234261i
$493$			41.5692i			1.87218i
$494$	−15.0000	−	1.73205i	−0.674882	−	0.0779287i
$495$	−9.00000	−	15.5885i	−0.404520	−	0.700649i
$496$	6.00000	−	3.46410i	0.269408	−	0.155543i
$497$	−6.00000	−	10.3923i	−0.269137	−	0.466159i
$498$	−4.50000	−	7.79423i	−0.201650	−	0.349268i
$499$	20.5000	+	35.5070i	0.917706	+	1.58951i	0.802890	+	0.596127i	$0.203294\pi$
$499$	20.5000	+	35.5070i	0.917706	+	1.58951i	0.114816	+	0.993387i	$0.463372\pi$
$500$	6.00000	+	3.46410i	0.268328	+	0.154919i
$501$	18.0000	+	10.3923i	0.804181	+	0.464294i
$502$			8.66025i			0.386526i
$503$	18.0000	+	10.3923i	0.802580	+	0.463370i	0.844373	−	0.535756i	$-0.179973\pi$
$503$	18.0000	+	10.3923i	0.802580	+	0.463370i	−0.0417923	+	0.999126i	$0.513307\pi$
$504$	−6.00000			−0.267261
$505$	36.0000			1.60198
$506$		0			0
$507$	1.50000	−	0.866025i	0.0666173	−	0.0384615i
$508$	9.00000	−	5.19615i	0.399310	−	0.230542i
$509$	−12.0000	+	20.7846i	−0.531891	+	0.921262i	0.467416	+	0.884037i	$0.345185\pi$
$509$	−12.0000	+	20.7846i	−0.531891	+	0.921262i	−0.999307	+	0.0372243i	$0.988148\pi$
$510$			41.5692i			1.84072i
$511$	5.00000	+	8.66025i	0.221187	+	0.383107i
$512$	−1.00000			−0.0441942
$513$	−22.5000	−	2.59808i	−0.993399	−	0.114708i
$514$	−15.0000			−0.661622
$515$	−18.0000	−	31.1769i	−0.793175	−	1.37382i
$516$			13.8564i			0.609994i
$517$	3.00000	−	5.19615i	0.131940	−	0.228527i
$518$	12.0000	−	6.92820i	0.527250	−	0.304408i
$519$	−27.0000	+	15.5885i	−1.18517	+	0.684257i
$520$	12.0000			0.526235
$521$	21.0000			0.920027			0.460013	−	0.887912i	$-0.347845\pi$
$521$	21.0000			0.920027			0.460013	+	0.887912i	$0.347845\pi$
$522$	18.0000			0.787839
$523$	15.0000	+	8.66025i	0.655904	+	0.378686i	0.790715	−	0.612185i	$-0.209709\pi$
$523$	15.0000	+	8.66025i	0.655904	+	0.378686i	−0.134810	+	0.990871i	$0.543043\pi$
$524$			19.0526i			0.832315i
$525$	−21.0000	−	12.1244i	−0.916515	−	0.529150i
$526$	−3.00000	−	1.73205i	−0.130806	−	0.0755210i
$527$	24.0000	+	41.5692i	1.04546	+	1.81078i
$528$	1.50000	+	2.59808i	0.0652791	+	0.113067i
$529$	−11.5000	−	19.9186i	−0.500000	−	0.866025i
$530$	18.0000	−	10.3923i	0.781870	−	0.451413i
$531$	−4.50000	−	7.79423i	−0.195283	−	0.338241i
$532$	−7.00000	−	5.19615i	−0.303488	−	0.225282i
$533$			10.3923i			0.450141i
$534$		−	10.3923i		−	0.449719i
$535$	36.0000	−	20.7846i	1.55642	−	0.898597i
$536$	−4.50000	−	2.59808i	−0.194370	−	0.112220i
$537$		−	5.19615i		−	0.224231i
$538$		0			0
$539$		−	5.19615i		−	0.223814i
$540$	18.0000			0.774597
$541$	−10.0000	+	17.3205i	−0.429934	+	0.744667i	−0.996867	−	0.0790969i	$-0.974796\pi$
$541$	−10.0000	+	17.3205i	−0.429934	+	0.744667i	0.566933	+	0.823764i	$0.308130\pi$
$542$	13.0000	−	22.5167i	0.558398	−	0.967173i
$543$	−6.00000	+	10.3923i	−0.257485	+	0.445976i
$544$		−	6.92820i		−	0.297044i
$545$		0			0
$546$	−12.0000			−0.513553
$547$	−21.0000	−	12.1244i	−0.897895	−	0.518400i	−0.0213785	−	0.999771i	$-0.506805\pi$
$547$	−21.0000	−	12.1244i	−0.897895	−	0.518400i	−0.876517	+	0.481371i	$0.840139\pi$
$548$	−1.50000	+	0.866025i	−0.0640768	+	0.0369948i
$549$	15.0000	−	25.9808i	0.640184	−	1.10883i
$550$			12.1244i			0.516984i
$551$	21.0000	+	15.5885i	0.894630	+	0.664091i
$552$		0			0
$553$	24.0000	−	13.8564i	1.02058	−	0.589234i
$554$	−1.00000	−	1.73205i	−0.0424859	−	0.0735878i
$555$	−36.0000	+	20.7846i	−1.52811	+	0.882258i
$556$	−0.500000	−	0.866025i	−0.0212047	−	0.0367277i
$557$	−12.0000	−	6.92820i	−0.508456	−	0.293557i	0.223743	−	0.974648i	$-0.428173\pi$
$557$	−12.0000	−	6.92820i	−0.508456	−	0.293557i	−0.732199	+	0.681091i	$0.761506\pi$
$558$	18.0000	−	10.3923i	0.762001	−	0.439941i
$559$			27.7128i			1.17213i
$560$	6.00000	+	3.46410i	0.253546	+	0.146385i
$561$	−18.0000	+	10.3923i	−0.759961	+	0.438763i
$562$	15.0000			0.632737
$563$	21.0000			0.885044			0.442522	−	0.896758i	$-0.354084\pi$
$563$	21.0000			0.885044			0.442522	+	0.896758i	$0.354084\pi$
$564$	3.00000	+	5.19615i	0.126323	+	0.218797i
$565$	−45.0000	+	25.9808i	−1.89316	+	1.09302i
$566$	−0.500000	+	0.866025i	−0.0210166	+	0.0364018i
$567$	−18.0000			−0.755929
$568$	−3.00000	−	5.19615i	−0.125877	−	0.218026i
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$	21.0000	+	15.5885i	0.879593	+	0.652929i
$571$	−43.0000			−1.79949			−0.899747	−	0.436412i	$-0.856249\pi$
$571$	−43.0000			−1.79949			−0.899747	+	0.436412i	$0.856249\pi$
$572$	3.00000	+	5.19615i	0.125436	+	0.217262i
$573$	12.0000			0.501307
$574$	−3.00000	+	5.19615i	−0.125218	+	0.216883i
$575$		0			0
$576$	−3.00000			−0.125000
$577$	−29.0000			−1.20729			−0.603643	−	0.797255i	$-0.706285\pi$
$577$	−29.0000			−1.20729			−0.603643	+	0.797255i	$0.706285\pi$
$578$	31.0000			1.28943
$579$	18.0000	+	31.1769i	0.748054	+	1.29567i
$580$	−18.0000	−	10.3923i	−0.747409	−	0.431517i
$581$		−	10.3923i		−	0.431145i
$582$	−7.50000	+	12.9904i	−0.310885	+	0.538469i
$583$	9.00000	+	5.19615i	0.372742	+	0.215203i
$584$	2.50000	+	4.33013i	0.103451	+	0.179182i
$585$	36.0000			1.48842
$586$	3.00000	+	5.19615i	0.123929	+	0.214651i
$587$	33.0000	−	19.0526i	1.36206	−	0.786383i	0.372158	−	0.928169i	$-0.378618\pi$
$587$	33.0000	−	19.0526i	1.36206	−	0.786383i	0.989897	+	0.141786i	$0.0452845\pi$
$588$	4.50000	+	2.59808i	0.185577	+	0.107143i
$589$	30.0000	+	3.46410i	1.23613	+	0.142736i
$590$			10.3923i			0.427844i
$591$	36.0000			1.48084
$592$	6.00000	−	3.46410i	0.246598	−	0.142374i
$593$	−22.5000	−	12.9904i	−0.923964	−	0.533451i	−0.0390666	−	0.999237i	$-0.512438\pi$
$593$	−22.5000	−	12.9904i	−0.923964	−	0.533451i	−0.884898	+	0.465786i	$0.845772\pi$
$594$	4.50000	+	7.79423i	0.184637	+	0.319801i
$595$	−24.0000	+	41.5692i	−0.983904	+	1.70417i
$596$			6.92820i			0.283790i
$597$	−21.0000	−	12.1244i	−0.859473	−	0.496217i
$598$		0			0
$599$	−18.0000	+	31.1769i	−0.735460	+	1.27385i	0.219061	+	0.975711i	$0.429701\pi$
$599$	−18.0000	+	31.1769i	−0.735460	+	1.27385i	−0.954521	+	0.298143i	$0.903633\pi$
$600$	−10.5000	−	6.06218i	−0.428661	−	0.247487i
$601$			8.66025i			0.353259i	0.984277	+	0.176630i	$0.0565195\pi$
$601$			8.66025i			0.353259i	−0.984277	+	0.176630i	$0.943481\pi$
$602$	−8.00000	+	13.8564i	−0.326056	+	0.564745i
$603$	−13.5000	−	7.79423i	−0.549762	−	0.317406i
$604$	6.00000	+	3.46410i	0.244137	+	0.140952i
$605$	24.0000	−	13.8564i	0.975739	−	0.563343i
$606$	−18.0000			−0.731200
$607$		−	31.1769i		−	1.26543i	−0.774384	−	0.632716i	$-0.781940\pi$
$607$		−	31.1769i		−	1.26543i	0.774384	−	0.632716i	$-0.218060\pi$
$608$	−3.50000	−	2.59808i	−0.141944	−	0.105366i
$609$	18.0000	+	10.3923i	0.729397	+	0.421117i
$610$	−30.0000	+	17.3205i	−1.21466	+	0.701287i
$611$	6.00000	+	10.3923i	0.242734	+	0.420428i
$612$		−	20.7846i		−	0.840168i
$613$	−17.0000	−	29.4449i	−0.686624	−	1.18927i	−0.972924	−	0.231127i	$-0.925759\pi$
$613$	−17.0000	−	29.4449i	−0.686624	−	1.18927i	0.286300	−	0.958140i	$-0.407575\pi$
$614$	−4.50000	−	2.59808i	−0.181605	−	0.104850i
$615$	9.00000	−	15.5885i	0.362915	−	0.628587i
$616$			3.46410i			0.139573i
$617$	1.50000	+	0.866025i	0.0603877	+	0.0348649i	0.529890	−	0.848066i	$-0.322233\pi$
$617$	1.50000	+	0.866025i	0.0603877	+	0.0348649i	−0.469502	+	0.882931i	$0.655567\pi$
$618$	9.00000	+	15.5885i	0.362033	+	0.627060i
$619$	40.0000			1.60774			0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$	−24.0000			−0.963863
$621$		0			0
$622$	−12.0000	+	6.92820i	−0.481156	+	0.277796i
$623$	6.00000	−	10.3923i	0.240385	−	0.416359i
$624$	−6.00000			−0.240192
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	−31.0000			−1.23901
$627$	−1.50000	+	12.9904i	−0.0599042	+	0.518786i
$628$	−20.0000			−0.798087
$629$	24.0000	+	41.5692i	0.956943	+	1.65747i
$630$	18.0000	+	10.3923i	0.717137	+	0.414039i
$631$	1.00000	−	1.73205i	0.0398094	−	0.0689519i	−0.845434	−	0.534080i	$-0.820658\pi$
$631$	1.00000	−	1.73205i	0.0398094	−	0.0689519i	0.885244	+	0.465128i	$0.153992\pi$
$632$	12.0000	−	6.92820i	0.477334	−	0.275589i
$633$	9.00000	+	15.5885i	0.357718	+	0.619586i
$634$	−6.00000			−0.238290
$635$	−36.0000			−1.42862
$636$	−9.00000	+	5.19615i	−0.356873	+	0.206041i
$637$	9.00000	+	5.19615i	0.356593	+	0.205879i
$638$		−	10.3923i		−	0.411435i
$639$	−9.00000	−	15.5885i	−0.356034	−	0.616670i
$640$	3.00000	+	1.73205i	0.118585	+	0.0684653i
$641$	−22.5000	−	38.9711i	−0.888697	−	1.53927i	−0.841417	−	0.540386i	$-0.818278\pi$
$641$	−22.5000	−	38.9711i	−0.888697	−	1.53927i	−0.0472793	−	0.998882i	$-0.515055\pi$
$642$	−18.0000	+	10.3923i	−0.710403	+	0.410152i
$643$	24.5000	+	42.4352i	0.966186	+	1.67348i	0.706395	+	0.707818i	$0.250320\pi$
$643$	24.5000	+	42.4352i	0.966186	+	1.67348i	0.259791	+	0.965665i	$0.416346\pi$
$644$		0			0
$645$	24.0000	−	41.5692i	0.944999	−	1.63679i
$646$	18.0000	−	24.2487i	0.708201	−	0.954053i
$647$		−	24.2487i		−	0.953315i	−0.879089	−	0.476658i	$-0.841848\pi$
$647$		−	24.2487i		−	0.953315i	0.879089	−	0.476658i	$-0.158152\pi$
$648$	−9.00000			−0.353553
$649$	−4.50000	+	2.59808i	−0.176640	+	0.101983i
$650$	−21.0000	−	12.1244i	−0.823688	−	0.475556i
$651$	24.0000			0.940634
$652$	8.50000	−	14.7224i	0.332886	−	0.576575i
$653$		−	6.92820i		−	0.271122i	−0.990769	−	0.135561i	$-0.956716\pi$
$653$		−	6.92820i		−	0.271122i	0.990769	−	0.135561i	$-0.0432836\pi$
$654$		0			0
$655$	33.0000	−	57.1577i	1.28942	−	2.23334i
$656$	−1.50000	+	2.59808i	−0.0585652	+	0.101438i
$657$	7.50000	+	12.9904i	0.292603	+	0.506803i
$658$			6.92820i			0.270089i
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$		−	10.3923i		−	0.404520i
$661$	−33.0000	−	19.0526i	−1.28355	−	0.741059i	−0.306055	−	0.952014i	$-0.599009\pi$
$661$	−33.0000	−	19.0526i	−1.28355	−	0.741059i	−0.977496	+	0.210955i	$0.932343\pi$
$662$	−7.50000	+	4.33013i	−0.291496	+	0.168295i
$663$		−	41.5692i		−	1.61441i
$664$		−	5.19615i		−	0.201650i
$665$	12.0000	+	27.7128i	0.465340	+	1.07466i
$666$	18.0000	−	10.3923i	0.697486	−	0.402694i
$667$		0			0
$668$	6.00000	+	10.3923i	0.232147	+	0.402090i
$669$	12.0000	+	20.7846i	0.463947	+	0.803579i
$670$	9.00000	+	15.5885i	0.347700	+	0.602235i
$671$	−15.0000	−	8.66025i	−0.579069	−	0.334325i
$672$	−3.00000	−	1.73205i	−0.115728	−	0.0668153i
$673$			20.7846i			0.801188i	0.916256	+	0.400594i	$0.131196\pi$
$673$			20.7846i			0.801188i	−0.916256	+	0.400594i	$0.868804\pi$
$674$	−22.5000	−	12.9904i	−0.866668	−	0.500371i
$675$	−31.5000	−	18.1865i	−1.21244	−	0.700000i
$676$	1.00000			0.0384615
$677$	−42.0000			−1.61419			−0.807096	−	0.590421i	$-0.798962\pi$
$677$	−42.0000			−1.61419			−0.807096	+	0.590421i	$0.798962\pi$
$678$	22.5000	−	12.9904i	0.864107	−	0.498893i
$679$	−15.0000	+	8.66025i	−0.575647	+	0.332350i
$680$	−12.0000	+	20.7846i	−0.460179	+	0.797053i
$681$		−	36.3731i		−	1.39382i
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$	−10.5000	−	7.79423i	−0.401478	−	0.298020i
$685$	6.00000			0.229248
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$			6.92820i			0.264327i
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$	−18.0000	+	10.3923i	−0.685745	+	0.395915i
$690$		0			0
$691$	20.0000			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$692$	−18.0000			−0.684257
$693$			10.3923i			0.394771i
$694$	7.50000	+	4.33013i	0.284696	+	0.164369i
$695$			3.46410i			0.131401i
$696$	9.00000	+	5.19615i	0.341144	+	0.196960i
$697$	−18.0000	−	10.3923i	−0.681799	−	0.393637i
$698$	4.00000	+	6.92820i	0.151402	+	0.262236i
$699$	1.50000	+	2.59808i	0.0567352	+	0.0982683i
$700$	−7.00000	−	12.1244i	−0.264575	−	0.458258i
$701$	−9.00000	+	5.19615i	−0.339925	+	0.196256i	−0.660239	−	0.751056i	$-0.729545\pi$
$701$	−9.00000	+	5.19615i	−0.339925	+	0.196256i	0.320314	+	0.947312i	$0.396212\pi$
$702$	−18.0000			−0.679366
$703$	30.0000	+	3.46410i	1.13147	+	0.130651i
$704$			1.73205i			0.0652791i
$705$		−	20.7846i		−	0.782794i
$706$	22.5000	−	12.9904i	0.846799	−	0.488899i
$707$	−18.0000	−	10.3923i	−0.676960	−	0.390843i
$708$		−	5.19615i		−	0.195283i
$709$	−4.00000	+	6.92820i	−0.150223	+	0.260194i	−0.931309	−	0.364229i	$-0.881333\pi$
$709$	−4.00000	+	6.92820i	−0.150223	+	0.260194i	0.781086	+	0.624423i	$0.214666\pi$
$710$			20.7846i			0.780033i
$711$	36.0000	−	20.7846i	1.35011	−	0.779484i
$712$	3.00000	−	5.19615i	0.112430	−	0.194734i
$713$		0			0
$714$	12.0000	−	20.7846i	0.449089	−	0.777844i
$715$		−	20.7846i		−	0.777300i
$716$	1.50000	−	2.59808i	0.0560576	−	0.0970947i
$717$	12.0000			0.448148
$718$	−6.00000	−	3.46410i	−0.223918	−	0.129279i
$719$	−3.00000	+	1.73205i	−0.111881	+	0.0645946i	−0.554896	−	0.831919i	$-0.687242\pi$
$719$	−3.00000	+	1.73205i	−0.111881	+	0.0645946i	0.443015	+	0.896514i	$0.353909\pi$
$720$	9.00000	+	5.19615i	0.335410	+	0.193649i
$721$			20.7846i			0.774059i
$722$	−5.50000	−	18.1865i	−0.204689	−	0.676833i
$723$	−4.50000	+	7.79423i	−0.167357	+	0.289870i
$724$	−6.00000	+	3.46410i	−0.222988	+	0.128742i
$725$	21.0000	+	36.3731i	0.779920	+	1.35086i
$726$	−12.0000	+	6.92820i	−0.445362	+	0.257130i
$727$	−4.00000	−	6.92820i	−0.148352	−	0.256953i	0.782267	−	0.622944i	$-0.214063\pi$
$727$	−4.00000	−	6.92820i	−0.148352	−	0.256953i	−0.930618	+	0.365991i	$0.880730\pi$
$728$	−6.00000	−	3.46410i	−0.222375	−	0.128388i
$729$	−27.0000			−1.00000
$730$		−	17.3205i		−	0.641061i
$731$	−48.0000	−	27.7128i	−1.77534	−	1.02500i
$732$	15.0000	−	8.66025i	0.554416	−	0.320092i
$733$	−4.00000			−0.147743			−0.0738717	−	0.997268i	$-0.523536\pi$
$733$	−4.00000			−0.147743			−0.0738717	+	0.997268i	$0.523536\pi$
$734$	4.00000			0.147643
$735$	−9.00000	−	15.5885i	−0.331970	−	0.574989i
$736$		0			0
$737$	−4.50000	+	7.79423i	−0.165760	+	0.287104i
$738$	−4.50000	+	7.79423i	−0.165647	+	0.286910i
$739$	5.50000	+	9.52628i	0.202321	+	0.350430i	0.949276	−	0.314445i	$-0.101818\pi$
$739$	5.50000	+	9.52628i	0.202321	+	0.350430i	−0.746955	+	0.664875i	$0.768485\pi$
$740$	−24.0000			−0.882258
$741$	−21.0000	−	15.5885i	−0.771454	−	0.572656i
$742$	−12.0000			−0.440534
$743$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$743$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$744$	12.0000			0.439941
$745$	12.0000	−	20.7846i	0.439646	−	0.761489i
$746$	6.00000	−	3.46410i	0.219676	−	0.126830i
$747$		−	15.5885i		−	0.570352i
$748$	−12.0000			−0.438763
$749$	−24.0000			−0.876941
$750$	6.00000	+	10.3923i	0.219089	+	0.379473i
$751$	−33.0000	−	19.0526i	−1.20419	−	0.695238i	−0.242704	−	0.970100i	$-0.578034\pi$
$751$	−33.0000	−	19.0526i	−1.20419	−	0.695238i	−0.961483	+	0.274863i	$0.911368\pi$
$752$			3.46410i			0.126323i
$753$	−7.50000	+	12.9904i	−0.273315	+	0.473396i
$754$	18.0000	+	10.3923i	0.655521	+	0.378465i
$755$	−12.0000	−	20.7846i	−0.436725	−	0.756429i
$756$	−9.00000	−	5.19615i	−0.327327	−	0.188982i
$757$	19.0000	+	32.9090i	0.690567	+	1.19610i	0.971652	+	0.236414i	$0.0759722\pi$
$757$	19.0000	+	32.9090i	0.690567	+	1.19610i	−0.281086	+	0.959683i	$0.590695\pi$
$758$	9.00000	−	5.19615i	0.326895	−	0.188733i
$759$		0			0
$760$	6.00000	+	13.8564i	0.217643	+	0.502625i
$761$		−	8.66025i		−	0.313934i	−0.987604	−	0.156967i	$-0.949828\pi$
$761$		−	8.66025i		−	0.313934i	0.987604	−	0.156967i	$-0.0501716\pi$
$762$	18.0000			0.652071
$763$		0			0
$764$	6.00000	+	3.46410i	0.217072	+	0.125327i
$765$	−36.0000	+	62.3538i	−1.30158	+	2.25441i
$766$	9.00000	−	15.5885i	0.325183	−	0.563234i
$767$		−	10.3923i		−	0.375244i
$768$	−1.50000	−	0.866025i	−0.0541266	−	0.0312500i
$769$	7.00000	−	12.1244i	0.252426	−	0.437215i	−0.711767	−	0.702416i	$-0.752105\pi$
$769$	7.00000	−	12.1244i	0.252426	−	0.437215i	0.964193	+	0.265200i	$0.0854381\pi$
$770$	6.00000	−	10.3923i	0.216225	−	0.374513i
$771$	−22.5000	−	12.9904i	−0.810318	−	0.467837i
$772$			20.7846i			0.748054i
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	−0.807018	−	0.590527i	$-0.798920\pi$
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	0.914920	+	0.403634i	$0.132253\pi$
$774$	−12.0000	+	20.7846i	−0.431331	+	0.747087i
$775$	42.0000	+	24.2487i	1.50868	+	0.871039i
$776$	−7.50000	+	4.33013i	−0.269234	+	0.155443i
$777$	24.0000			0.860995
$778$			34.6410i			1.24194i
$779$	−12.0000	+	5.19615i	−0.429945	+	0.186171i
$780$	18.0000	+	10.3923i	0.644503	+	0.372104i
$781$	−9.00000	+	5.19615i	−0.322045	+	0.185933i
$782$		0			0
$783$	27.0000	+	15.5885i	0.964901	+	0.557086i
$784$	1.50000	+	2.59808i	0.0535714	+	0.0927884i
$785$	60.0000	+	34.6410i	2.14149	+	1.23639i
$786$	−16.5000	+	28.5788i	−0.588536	+	1.01937i
$787$		−	1.73205i		−	0.0617409i	−0.999523	−	0.0308705i	$-0.990172\pi$
$787$		−	1.73205i		−	0.0617409i	0.999523	−	0.0308705i	$-0.00982794\pi$
$788$	18.0000	+	10.3923i	0.641223	+	0.370211i
$789$	−3.00000	−	5.19615i	−0.106803	−	0.184988i
$790$	−48.0000			−1.70776
$791$	30.0000			1.06668
$792$			5.19615i			0.184637i
$793$	30.0000	−	17.3205i	1.06533	−	0.615069i
$794$	10.0000	−	17.3205i	0.354887	−	0.614682i
$795$	36.0000			1.27679
$796$	−7.00000	−	12.1244i	−0.248108	−	0.429736i
$797$	12.0000			0.425062			0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000			0.425062			0.212531	+	0.977154i	$0.431829\pi$
$798$	−6.00000	−	13.8564i	−0.212398	−	0.490511i
$799$	−24.0000			−0.849059
$800$	−3.50000	−	6.06218i	−0.123744	−	0.214330i
$801$	9.00000	−	15.5885i	0.317999	−	0.550791i
$802$	1.50000	−	2.59808i	0.0529668	−	0.0917413i
$803$	7.50000	−	4.33013i	0.264669	−	0.152807i
$804$	−4.50000	−	7.79423i	−0.158703	−	0.274881i
$805$		0			0
$806$	24.0000			0.845364
$807$		0			0
$808$	−9.00000	−	5.19615i	−0.316619	−	0.182800i
$809$			32.9090i			1.15702i	0.815676	+	0.578509i	$0.196365\pi$
$809$			32.9090i			1.15702i	−0.815676	+	0.578509i	$0.803635\pi$
$810$	27.0000	+	15.5885i	0.948683	+	0.547723i
$811$	−27.0000	−	15.5885i	−0.948098	−	0.547385i	−0.0556086	−	0.998453i	$-0.517710\pi$
$811$	−27.0000	−	15.5885i	−0.948098	−	0.547385i	−0.892490	+	0.451068i	$0.851043\pi$
$812$	6.00000	+	10.3923i	0.210559	+	0.364698i
$813$	39.0000	−	22.5167i	1.36779	−	0.789694i
$814$	−6.00000	−	10.3923i	−0.210300	−	0.364250i
$815$	−51.0000	+	29.4449i	−1.78645	+	1.03141i
$816$	6.00000	−	10.3923i	0.210042	−	0.363803i
$817$	−32.0000	+	13.8564i	−1.11954	+	0.484774i
$818$		−	19.0526i		−	0.666157i
$819$	−18.0000	−	10.3923i	−0.628971	−	0.363137i
$820$	9.00000	−	5.19615i	0.314294	−	0.181458i
$821$	33.0000	+	19.0526i	1.15171	+	0.664939i	0.949303	−	0.314363i	$-0.101791\pi$
$821$	33.0000	+	19.0526i	1.15171	+	0.664939i	0.202405	+	0.979302i	$0.435124\pi$
$822$	−3.00000			−0.104637
$823$	−11.0000	+	19.0526i	−0.383436	+	0.664130i	−0.991551	−	0.129719i	$-0.958593\pi$
$823$	−11.0000	+	19.0526i	−0.383436	+	0.664130i	0.608115	+	0.793849i	$0.291926\pi$
$824$			10.3923i			0.362033i
$825$	−10.5000	+	18.1865i	−0.365563	+	0.633174i
$826$	3.00000	−	5.19615i	0.104383	−	0.180797i
$827$	−4.50000	+	7.79423i	−0.156480	+	0.271032i	−0.933597	−	0.358325i	$-0.883348\pi$
$827$	−4.50000	+	7.79423i	−0.156480	+	0.271032i	0.777117	+	0.629356i	$0.216681\pi$
$828$		0			0
$829$		−	20.7846i		−	0.721879i	−0.932589	−	0.360940i	$-0.882456\pi$
$829$		−	20.7846i		−	0.721879i	0.932589	−	0.360940i	$-0.117544\pi$
$830$	−9.00000	+	15.5885i	−0.312395	+	0.541083i
$831$		−	3.46410i		−	0.120168i
$832$	−3.00000	−	1.73205i	−0.104006	−	0.0600481i
$833$	−18.0000	+	10.3923i	−0.623663	+	0.360072i
$834$		−	1.73205i		−	0.0599760i
$835$		−	41.5692i		−	1.43856i
$836$	−4.50000	+	6.06218i	−0.155636	+	0.209665i
$837$	36.0000			1.24434
$838$	9.00000	−	5.19615i	0.310900	−	0.179498i
$839$	−21.0000	−	36.3731i	−0.725001	−	1.25574i	−0.958974	−	0.283495i	$-0.908506\pi$
$839$	−21.0000	−	36.3731i	−0.725001	−	1.25574i	0.233973	−	0.972243i	$-0.424827\pi$
$840$	6.00000	+	10.3923i	0.207020	+	0.358569i
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−12.0000	−	6.92820i	−0.413547	−	0.238762i
$843$	22.5000	+	12.9904i	0.774941	+	0.447412i
$844$			10.3923i			0.357718i
$845$	−3.00000	−	1.73205i	−0.103203	−	0.0595844i
$846$			10.3923i			0.357295i
$847$	−16.0000			−0.549767
$848$	−6.00000			−0.206041
$849$	−1.50000	+	0.866025i	−0.0514799	+	0.0297219i
$850$	42.0000	−	24.2487i	1.44059	−	0.831724i
$851$		0			0
$852$		−	10.3923i		−	0.356034i
$853$	5.00000	+	8.66025i	0.171197	+	0.296521i	0.938839	−	0.344358i	$-0.111903\pi$
$853$	5.00000	+	8.66025i	0.171197	+	0.296521i	−0.767642	+	0.640879i	$0.778570\pi$
$854$	20.0000			0.684386
$855$	18.0000	+	41.5692i	0.615587	+	1.42164i
$856$	−12.0000			−0.410152
$857$	−10.5000	−	18.1865i	−0.358673	−	0.621240i	0.629066	−	0.777352i	$-0.283437\pi$
$857$	−10.5000	−	18.1865i	−0.358673	−	0.621240i	−0.987739	+	0.156112i	$0.950104\pi$
$858$			10.3923i			0.354787i
$859$	−24.5000	+	42.4352i	−0.835929	+	1.44787i	0.0573424	+	0.998355i	$0.481737\pi$
$859$	−24.5000	+	42.4352i	−0.835929	+	1.44787i	−0.893272	+	0.449517i	$0.851596\pi$
$860$	24.0000	−	13.8564i	0.818393	−	0.472500i
$861$	−9.00000	+	5.19615i	−0.306719	+	0.177084i
$862$	−6.00000			−0.204361
$863$	12.0000			0.408485			0.204242	−	0.978920i	$-0.434527\pi$
$863$	12.0000			0.408485			0.204242	+	0.978920i	$0.434527\pi$
$864$	−4.50000	−	2.59808i	−0.153093	−	0.0883883i
$865$	54.0000	+	31.1769i	1.83606	+	1.06005i
$866$		−	13.8564i		−	0.470860i
$867$	46.5000	+	26.8468i	1.57922	+	0.911765i
$868$	12.0000	+	6.92820i	0.407307	+	0.235159i
$869$	−12.0000	−	20.7846i	−0.407072	−	0.705070i
$870$	−18.0000	−	31.1769i	−0.610257	−	1.05700i
$871$	−9.00000	−	15.5885i	−0.304953	−	0.528195i
$872$		0			0
$873$	−22.5000	+	12.9904i	−0.761510	+	0.439658i
$874$		0			0
$875$			13.8564i			0.468432i
$876$			8.66025i			0.292603i
$877$	−33.0000	+	19.0526i	−1.11433	+	0.643359i	−0.939948	−	0.341319i	$-0.889126\pi$
$877$	−33.0000	+	19.0526i	−1.11433	+	0.643359i	−0.174383	+	0.984678i	$0.555793\pi$
$878$	−12.0000	−	6.92820i	−0.404980	−	0.233816i
$879$			10.3923i			0.350524i
$880$	3.00000	−	5.19615i	0.101130	−	0.175162i
$881$			19.0526i			0.641897i	0.947097	+	0.320949i	$0.104002\pi$
$881$			19.0526i			0.641897i	−0.947097	+	0.320949i	$0.895998\pi$
$882$	4.50000	+	7.79423i	0.151523	+	0.262445i
$883$	5.50000	−	9.52628i	0.185090	−	0.320585i	−0.758517	−	0.651653i	$-0.774076\pi$
$883$	5.50000	−	9.52628i	0.185090	−	0.320585i	0.943607	+	0.331068i	$0.107409\pi$
$884$	12.0000	−	20.7846i	0.403604	−	0.699062i
$885$	−9.00000	+	15.5885i	−0.302532	+	0.524000i
$886$			12.1244i			0.407326i
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	0.387768	+	0.921757i	$0.373246\pi$
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	−0.992149	+	0.125061i	$0.960087\pi$
$888$	12.0000			0.402694
$889$	18.0000	+	10.3923i	0.603701	+	0.348547i
$890$	−18.0000	+	10.3923i	−0.603361	+	0.348351i
$891$			15.5885i			0.522233i
$892$			13.8564i			0.463947i
$893$	−9.00000	+	12.1244i	−0.301174	+	0.405726i
$894$	−6.00000	+	10.3923i	−0.200670	+	0.347571i
$895$	−9.00000	+	5.19615i	−0.300837	+	0.173688i
$896$	−1.00000	−	1.73205i	−0.0334077	−	0.0578638i
$897$		0			0
$898$	−1.50000	−	2.59808i	−0.0500556	−	0.0866989i
$899$	−36.0000	−	20.7846i	−1.20067	−	0.693206i
$900$	−10.5000	−	18.1865i	−0.350000	−	0.606218i
$901$		−	41.5692i		−	1.38487i
$902$	4.50000	+	2.59808i	0.149834	+	0.0865065i
$903$	−24.0000	+	13.8564i	−0.798670	+	0.461112i
$904$	15.0000			0.498893
$905$	24.0000			0.797787
$906$	6.00000	+	10.3923i	0.199337	+	0.345261i
$907$	1.50000	−	0.866025i	0.0498067	−	0.0287559i	−0.474890	−	0.880045i	$-0.657512\pi$
$907$	1.50000	−	0.866025i	0.0498067	−	0.0287559i	0.524697	+	0.851289i	$0.324179\pi$
$908$	10.5000	−	18.1865i	0.348455	−	0.603541i
$909$	−27.0000	−	15.5885i	−0.895533	−	0.517036i
$910$	12.0000	+	20.7846i	0.397796	+	0.689003i
$911$	36.0000			1.19273			0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000			1.19273			0.596367	+	0.802712i	$0.296610\pi$
$912$	−3.00000	−	6.92820i	−0.0993399	−	0.229416i
$913$	−9.00000			−0.297857
$914$	8.50000	+	14.7224i	0.281155	+	0.486975i
$915$	−60.0000			−1.98354
$916$	−2.00000	+	3.46410i	−0.0660819	+	0.114457i
$917$	−33.0000	+	19.0526i	−1.08976	+	0.629171i
$918$	18.0000	−	31.1769i	0.594089	−	1.02899i
$919$	−26.0000			−0.857661			−0.428830	−	0.903385i	$-0.641074\pi$
$919$	−26.0000			−0.857661			−0.428830	+	0.903385i	$0.641074\pi$
$920$		0			0
$921$	−4.50000	−	7.79423i	−0.148280	−	0.256829i
$922$	−21.0000	−	12.1244i	−0.691598	−	0.399294i
$923$		−	20.7846i		−	0.684134i
$924$	−3.00000	+	5.19615i	−0.0986928	+	0.170941i
$925$	42.0000	+	24.2487i	1.38095	+	0.797293i
$926$	7.00000	+	12.1244i	0.230034	+	0.398431i
$927$			31.1769i			1.02398i
$928$	3.00000	+	5.19615i	0.0984798	+	0.170572i
$929$	−31.5000	+	18.1865i	−1.03348	+	0.596681i	−0.917980	−	0.396627i	$-0.870181\pi$
$929$	−31.5000	+	18.1865i	−1.03348	+	0.596681i	−0.115501	+	0.993307i	$0.536847\pi$
$930$	−36.0000	−	20.7846i	−1.18049	−	0.681554i
$931$	−1.50000	+	12.9904i	−0.0491605	+	0.425743i
$932$			1.73205i			0.0567352i
$933$	−24.0000			−0.785725
$934$	−10.5000	+	6.06218i	−0.343570	+	0.198361i
$935$	36.0000	+	20.7846i	1.17733	+	0.679729i
$936$	−9.00000	−	5.19615i	−0.294174	−	0.169842i
$937$	3.50000	−	6.06218i	0.114340	−	0.198043i	−0.803176	−	0.595742i	$-0.796858\pi$
$937$	3.50000	−	6.06218i	0.114340	−	0.198043i	0.917516	+	0.397699i	$0.130191\pi$
$938$		−	10.3923i		−	0.339321i
$939$	−46.5000	−	26.8468i	−1.51747	−	0.876112i
$940$	6.00000	−	10.3923i	0.195698	−	0.338960i
$941$	27.0000	−	46.7654i	0.880175	−	1.52451i	0.0290288	−	0.999579i	$-0.490759\pi$
$941$	27.0000	−	46.7654i	0.880175	−	1.52451i	0.851146	−	0.524929i	$-0.175908\pi$
$942$	−30.0000	−	17.3205i	−0.977453	−	0.564333i
$943$		0			0
$944$	1.50000	−	2.59808i	0.0488208	−	0.0845602i
$945$	18.0000	+	31.1769i	0.585540	+	1.01419i
$946$	12.0000	+	6.92820i	0.390154	+	0.225255i
$947$	45.0000	−	25.9808i	1.46230	−	0.844261i	0.463186	−	0.886261i	$-0.346706\pi$
$947$	45.0000	−	25.9808i	1.46230	−	0.844261i	0.999118	+	0.0419998i	$0.0133729\pi$
$948$	24.0000			0.779484
$949$			17.3205i			0.562247i
$950$	3.50000	−	30.3109i	0.113555	−	0.983415i
$951$	−9.00000	−	5.19615i	−0.291845	−	0.168497i
$952$	12.0000	−	6.92820i	0.388922	−	0.224544i
$953$	−25.5000	−	44.1673i	−0.826026	−	1.43072i	−0.901133	−	0.433544i	$-0.857263\pi$
$953$	−25.5000	−	44.1673i	−0.826026	−	1.43072i	0.0751066	−	0.997176i	$-0.476070\pi$
$954$	−18.0000			−0.582772
$955$	−12.0000	−	20.7846i	−0.388311	−	0.672574i
$956$	6.00000	+	3.46410i	0.194054	+	0.112037i
$957$	9.00000	−	15.5885i	0.290929	−	0.503903i
$958$		0			0
$959$	−3.00000	−	1.73205i	−0.0968751	−	0.0559308i
$960$	3.00000	+	5.19615i	0.0968246	+	0.167705i
$961$	−17.0000			−0.548387
$962$	24.0000			0.773791
$963$	−36.0000			−1.16008
$964$	−4.50000	+	2.59808i	−0.144935	+	0.0836784i
$965$	36.0000	−	62.3538i	1.15888	−	2.00724i
$966$		0			0
$967$	25.0000	+	43.3013i	0.803946	+	1.39247i	0.917000	+	0.398886i	$0.130603\pi$
$967$	25.0000	+	43.3013i	0.803946	+	1.39247i	−0.113055	+	0.993589i	$0.536064\pi$
$968$	−8.00000			−0.257130
$969$	48.0000	−	20.7846i	1.54198	−	0.667698i
$970$	30.0000			0.963242
$971$	−4.50000	−	7.79423i	−0.144412	−	0.250129i	0.784741	−	0.619823i	$-0.212796\pi$
$971$	−4.50000	−	7.79423i	−0.144412	−	0.250129i	−0.929153	+	0.369694i	$0.879462\pi$
$972$	−13.5000	−	7.79423i	−0.433013	−	0.250000i
$973$	1.00000	−	1.73205i	0.0320585	−	0.0555270i
$974$	6.00000	−	3.46410i	0.192252	−	0.110997i
$975$	−21.0000	−	36.3731i	−0.672538	−	1.16487i
$976$	10.0000			0.320092
$977$	27.0000			0.863807			0.431903	−	0.901920i	$-0.357842\pi$
$977$	27.0000			0.863807			0.431903	+	0.901920i	$0.357842\pi$
$978$	25.5000	−	14.7224i	0.815400	−	0.470771i
$979$	−9.00000	−	5.19615i	−0.287641	−	0.166070i
$980$		−	10.3923i		−	0.331970i
$981$		0			0
$982$	−27.0000	−	15.5885i	−0.861605	−	0.497448i
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	0.996138	+	0.0878058i	$0.0279855\pi$
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	−0.422027	+	0.906583i	$0.638681\pi$
$984$	−4.50000	+	2.59808i	−0.143455	+	0.0828236i
$985$	−36.0000	−	62.3538i	−1.14706	−	1.98676i
$986$	−36.0000	+	20.7846i	−1.14647	+	0.661917i
$987$	−6.00000	+	10.3923i	−0.190982	+	0.330791i
$988$	−6.00000	−	13.8564i	−0.190885	−	0.440831i
$989$		0			0
$990$	9.00000	−	15.5885i	0.286039	−	0.495434i
$991$	6.00000	−	3.46410i	0.190596	−	0.110041i	−0.401665	−	0.915786i	$-0.631569\pi$
$991$	6.00000	−	3.46410i	0.190596	−	0.110041i	0.592262	+	0.805746i	$0.298235\pi$
$992$	6.00000	+	3.46410i	0.190500	+	0.109985i
$993$	−15.0000			−0.476011
$994$	6.00000	−	10.3923i	0.190308	−	0.329624i
$995$			48.4974i			1.53747i
$996$	4.50000	−	7.79423i	0.142588	−	0.246970i
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	−0.583363	−	0.812211i	$-0.698264\pi$
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	0.995077	+	0.0991016i	$0.0315969\pi$
$998$	−20.5000	+	35.5070i	−0.648916	+	1.12396i
$999$	36.0000			1.13899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.h.d.107.1	yes	2
3.2	odd	2		114.2.h.a.107.1	yes	2
4.3	odd	2		912.2.bn.b.449.1		2
12.11	even	2		912.2.bn.d.449.1		2
19.8	odd	6		114.2.h.a.65.1	✓	2
57.8	even	6	inner	114.2.h.d.65.1	yes	2
76.27	even	6		912.2.bn.d.65.1		2
228.179	odd	6		912.2.bn.b.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.h.a.65.1	✓	2	19.8	odd	6
114.2.h.a.107.1	yes	2	3.2	odd	2
114.2.h.d.65.1	yes	2	57.8	even	6	inner
114.2.h.d.107.1	yes	2	1.1	even	1	trivial
912.2.bn.b.65.1		2	228.179	odd	6
912.2.bn.b.449.1		2	4.3	odd	2
912.2.bn.d.65.1		2	76.27	even	6
912.2.bn.d.449.1		2	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +(3.00000 - 1.73205i) q^{5} +(-1.50000 + 0.866025i) q^{6} -2.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +(3.00000 - 1.73205i) q^{5} +(-1.50000 + 0.866025i) q^{6} -2.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +(3.00000 + 1.73205i) q^{10} +1.73205i q^{11} +(-1.50000 - 0.866025i) q^{12} +(-3.00000 - 1.73205i) q^{13} +(-1.00000 - 1.73205i) q^{14} +(3.00000 + 5.19615i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(6.00000 - 3.46410i) q^{17} +(-1.50000 - 2.59808i) q^{18} +(0.500000 - 4.33013i) q^{19} +3.46410i q^{20} -3.46410i q^{21} +(-1.50000 + 0.866025i) q^{22} -1.73205i q^{24} +(3.50000 - 6.06218i) q^{25} -3.46410i q^{26} -5.19615i q^{27} +(1.00000 - 1.73205i) q^{28} +(-3.00000 + 5.19615i) q^{29} +(-3.00000 + 5.19615i) q^{30} +6.92820i q^{31} +(0.500000 - 0.866025i) q^{32} -3.00000 q^{33} +(6.00000 + 3.46410i) q^{34} +(-6.00000 + 3.46410i) q^{35} +(1.50000 - 2.59808i) q^{36} +6.92820i q^{37} +(4.00000 - 1.73205i) q^{38} +(3.00000 - 5.19615i) q^{39} +(-3.00000 + 1.73205i) q^{40} +(-1.50000 - 2.59808i) q^{41} +(3.00000 - 1.73205i) q^{42} +(-4.00000 - 6.92820i) q^{43} +(-1.50000 - 0.866025i) q^{44} +(-9.00000 + 5.19615i) q^{45} +(-3.00000 - 1.73205i) q^{47} +(1.50000 - 0.866025i) q^{48} -3.00000 q^{49} +7.00000 q^{50} +(6.00000 + 10.3923i) q^{51} +(3.00000 - 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +(4.50000 - 2.59808i) q^{54} +(3.00000 + 5.19615i) q^{55} +2.00000 q^{56} +(7.50000 + 0.866025i) q^{57} -6.00000 q^{58} +(1.50000 + 2.59808i) q^{59} -6.00000 q^{60} +(-5.00000 + 8.66025i) q^{61} +(-6.00000 + 3.46410i) q^{62} +6.00000 q^{63} +1.00000 q^{64} -12.0000 q^{65} +(-1.50000 - 2.59808i) q^{66} +(4.50000 + 2.59808i) q^{67} +6.92820i q^{68} +(-6.00000 - 3.46410i) q^{70} +(3.00000 + 5.19615i) q^{71} +3.00000 q^{72} +(-2.50000 - 4.33013i) q^{73} +(-6.00000 + 3.46410i) q^{74} +(10.5000 + 6.06218i) q^{75} +(3.50000 + 2.59808i) q^{76} -3.46410i q^{77} +6.00000 q^{78} +(-12.0000 + 6.92820i) q^{79} +(-3.00000 - 1.73205i) q^{80} +9.00000 q^{81} +(1.50000 - 2.59808i) q^{82} +5.19615i q^{83} +(3.00000 + 1.73205i) q^{84} +(12.0000 - 20.7846i) q^{85} +(4.00000 - 6.92820i) q^{86} +(-9.00000 - 5.19615i) q^{87} -1.73205i q^{88} +(-3.00000 + 5.19615i) q^{89} +(-9.00000 - 5.19615i) q^{90} +(6.00000 + 3.46410i) q^{91} -12.0000 q^{93} -3.46410i q^{94} +(-6.00000 - 13.8564i) q^{95} +(1.50000 + 0.866025i) q^{96} +(7.50000 - 4.33013i) q^{97} +(-1.50000 - 2.59808i) q^{98} -5.19615i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} + 6 q^{5} - 3 q^{6} - 4 q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q + q^2 - q^4 + 6 * q^5 - 3 * q^6 - 4 * q^7 - 2 * q^8 - 6 * q^9	\( 2 q + q^{2} - q^{4} + 6 q^{5} - 3 q^{6} - 4 q^{7} - 2 q^{8} - 6 q^{9} + 6 q^{10} - 3 q^{12} - 6 q^{13} - 2 q^{14} + 6 q^{15} - q^{16} + 12 q^{17} - 3 q^{18} + q^{19} - 3 q^{22} + 7 q^{25} + 2 q^{28} - 6 q^{29} - 6 q^{30} + q^{32} - 6 q^{33} + 12 q^{34} - 12 q^{35} + 3 q^{36} + 8 q^{38} + 6 q^{39} - 6 q^{40} - 3 q^{41} + 6 q^{42} - 8 q^{43} - 3 q^{44} - 18 q^{45} - 6 q^{47} + 3 q^{48} - 6 q^{49} + 14 q^{50} + 12 q^{51} + 6 q^{52} + 6 q^{53} + 9 q^{54} + 6 q^{55} + 4 q^{56} + 15 q^{57} - 12 q^{58} + 3 q^{59} - 12 q^{60} - 10 q^{61} - 12 q^{62} + 12 q^{63} + 2 q^{64} - 24 q^{65} - 3 q^{66} + 9 q^{67} - 12 q^{70} + 6 q^{71} + 6 q^{72} - 5 q^{73} - 12 q^{74} + 21 q^{75} + 7 q^{76} + 12 q^{78} - 24 q^{79} - 6 q^{80} + 18 q^{81} + 3 q^{82} + 6 q^{84} + 24 q^{85} + 8 q^{86} - 18 q^{87} - 6 q^{89} - 18 q^{90} + 12 q^{91} - 24 q^{93} - 12 q^{95} + 3 q^{96} + 15 q^{97} - 3 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 + 6 * q^5 - 3 * q^6 - 4 * q^7 - 2 * q^8 - 6 * q^9 + 6 * q^10 - 3 * q^12 - 6 * q^13 - 2 * q^14 + 6 * q^15 - q^16 + 12 * q^17 - 3 * q^18 + q^19 - 3 * q^22 + 7 * q^25 + 2 * q^28 - 6 * q^29 - 6 * q^30 + q^32 - 6 * q^33 + 12 * q^34 - 12 * q^35 + 3 * q^36 + 8 * q^38 + 6 * q^39 - 6 * q^40 - 3 * q^41 + 6 * q^42 - 8 * q^43 - 3 * q^44 - 18 * q^45 - 6 * q^47 + 3 * q^48 - 6 * q^49 + 14 * q^50 + 12 * q^51 + 6 * q^52 + 6 * q^53 + 9 * q^54 + 6 * q^55 + 4 * q^56 + 15 * q^57 - 12 * q^58 + 3 * q^59 - 12 * q^60 - 10 * q^61 - 12 * q^62 + 12 * q^63 + 2 * q^64 - 24 * q^65 - 3 * q^66 + 9 * q^67 - 12 * q^70 + 6 * q^71 + 6 * q^72 - 5 * q^73 - 12 * q^74 + 21 * q^75 + 7 * q^76 + 12 * q^78 - 24 * q^79 - 6 * q^80 + 18 * q^81 + 3 * q^82 + 6 * q^84 + 24 * q^85 + 8 * q^86 - 18 * q^87 - 6 * q^89 - 18 * q^90 + 12 * q^91 - 24 * q^93 - 12 * q^95 + 3 * q^96 + 15 * q^97 - 3 * q^98

Introduction

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