LMFDB - Embedded newform 342.2.n.c.293.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(293,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("342.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.n (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:	$2.73088374913$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	342.293
Dual form			342.2.n.c.335.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.73205i q^{3} +1.00000 q^{4} +(1.50000 - 0.866025i) q^{5} -1.73205i q^{6} +(2.50000 + 4.33013i) q^{7} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.73205i q^{3} +1.00000 q^{4} +(1.50000 - 0.866025i) q^{5} -1.73205i q^{6} +(2.50000 + 4.33013i) q^{7} +1.00000 q^{8} -3.00000 q^{9} +(1.50000 - 0.866025i) q^{10} +(1.50000 - 0.866025i) q^{11} -1.73205i q^{12} +(2.50000 + 4.33013i) q^{14} +(-1.50000 - 2.59808i) q^{15} +1.00000 q^{16} +(-4.50000 - 2.59808i) q^{17} -3.00000 q^{18} +(-4.00000 - 1.73205i) q^{19} +(1.50000 - 0.866025i) q^{20} +(7.50000 - 4.33013i) q^{21} +(1.50000 - 0.866025i) q^{22} -3.46410i q^{23} -1.73205i q^{24} +(-1.00000 + 1.73205i) q^{25} +5.19615i q^{27} +(2.50000 + 4.33013i) q^{28} +(-1.50000 + 2.59808i) q^{29} +(-1.50000 - 2.59808i) q^{30} +(-7.50000 - 4.33013i) q^{31} +1.00000 q^{32} +(-1.50000 - 2.59808i) q^{33} +(-4.50000 - 2.59808i) q^{34} +(7.50000 + 4.33013i) q^{35} -3.00000 q^{36} +(-4.00000 - 1.73205i) q^{38} +(1.50000 - 0.866025i) q^{40} +(4.50000 + 7.79423i) q^{41} +(7.50000 - 4.33013i) q^{42} +8.00000 q^{43} +(1.50000 - 0.866025i) q^{44} +(-4.50000 + 2.59808i) q^{45} -3.46410i q^{46} +(4.50000 + 2.59808i) q^{47} -1.73205i q^{48} +(-9.00000 + 15.5885i) q^{49} +(-1.00000 + 1.73205i) q^{50} +(-4.50000 + 7.79423i) q^{51} +(-1.50000 - 2.59808i) q^{53} +5.19615i q^{54} +(1.50000 - 2.59808i) q^{55} +(2.50000 + 4.33013i) q^{56} +(-3.00000 + 6.92820i) q^{57} +(-1.50000 + 2.59808i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(-1.50000 - 2.59808i) q^{60} +(-3.50000 + 6.06218i) q^{61} +(-7.50000 - 4.33013i) q^{62} +(-7.50000 - 12.9904i) q^{63} +1.00000 q^{64} +(-1.50000 - 2.59808i) q^{66} +3.46410i q^{67} +(-4.50000 - 2.59808i) q^{68} -6.00000 q^{69} +(7.50000 + 4.33013i) q^{70} +(7.50000 - 12.9904i) q^{71} -3.00000 q^{72} +(-5.50000 + 9.52628i) q^{73} +(3.00000 + 1.73205i) q^{75} +(-4.00000 - 1.73205i) q^{76} +(7.50000 + 4.33013i) q^{77} -10.3923i q^{79} +(1.50000 - 0.866025i) q^{80} +9.00000 q^{81} +(4.50000 + 7.79423i) q^{82} +(-4.50000 + 2.59808i) q^{83} +(7.50000 - 4.33013i) q^{84} -9.00000 q^{85} +8.00000 q^{86} +(4.50000 + 2.59808i) q^{87} +(1.50000 - 0.866025i) q^{88} +(-7.50000 - 12.9904i) q^{89} +(-4.50000 + 2.59808i) q^{90} -3.46410i q^{92} +(-7.50000 + 12.9904i) q^{93} +(4.50000 + 2.59808i) q^{94} +(-7.50000 + 0.866025i) q^{95} -1.73205i q^{96} -6.92820i q^{97} +(-9.00000 + 15.5885i) q^{98} +(-4.50000 + 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} + 3 q^{5} + 5 q^{7} + 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 + 3 * q^5 + 5 * q^7 + 2 * q^8 - 6 * q^9	$ 2 q + 2 q^{2} + 2 q^{4} + 3 q^{5} + 5 q^{7} + 2 q^{8} - 6 q^{9} + 3 q^{10} + 3 q^{11} + 5 q^{14} - 3 q^{15} + 2 q^{16} - 9 q^{17} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 15 q^{21} + 3 q^{22} - 2 q^{25} + 5 q^{28} - 3 q^{29} - 3 q^{30} - 15 q^{31} + 2 q^{32} - 3 q^{33} - 9 q^{34} + 15 q^{35} - 6 q^{36} - 8 q^{38} + 3 q^{40} + 9 q^{41} + 15 q^{42} + 16 q^{43} + 3 q^{44} - 9 q^{45} + 9 q^{47} - 18 q^{49} - 2 q^{50} - 9 q^{51} - 3 q^{53} + 3 q^{55} + 5 q^{56} - 6 q^{57} - 3 q^{58} - 3 q^{59} - 3 q^{60} - 7 q^{61} - 15 q^{62} - 15 q^{63} + 2 q^{64} - 3 q^{66} - 9 q^{68} - 12 q^{69} + 15 q^{70} + 15 q^{71} - 6 q^{72} - 11 q^{73} + 6 q^{75} - 8 q^{76} + 15 q^{77} + 3 q^{80} + 18 q^{81} + 9 q^{82} - 9 q^{83} + 15 q^{84} - 18 q^{85} + 16 q^{86} + 9 q^{87} + 3 q^{88} - 15 q^{89} - 9 q^{90} - 15 q^{93} + 9 q^{94} - 15 q^{95} - 18 q^{98} - 9 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 + 3 * q^5 + 5 * q^7 + 2 * q^8 - 6 * q^9 + 3 * q^10 + 3 * q^11 + 5 * q^14 - 3 * q^15 + 2 * q^16 - 9 * q^17 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 15 * q^21 + 3 * q^22 - 2 * q^25 + 5 * q^28 - 3 * q^29 - 3 * q^30 - 15 * q^31 + 2 * q^32 - 3 * q^33 - 9 * q^34 + 15 * q^35 - 6 * q^36 - 8 * q^38 + 3 * q^40 + 9 * q^41 + 15 * q^42 + 16 * q^43 + 3 * q^44 - 9 * q^45 + 9 * q^47 - 18 * q^49 - 2 * q^50 - 9 * q^51 - 3 * q^53 + 3 * q^55 + 5 * q^56 - 6 * q^57 - 3 * q^58 - 3 * q^59 - 3 * q^60 - 7 * q^61 - 15 * q^62 - 15 * q^63 + 2 * q^64 - 3 * q^66 - 9 * q^68 - 12 * q^69 + 15 * q^70 + 15 * q^71 - 6 * q^72 - 11 * q^73 + 6 * q^75 - 8 * q^76 + 15 * q^77 + 3 * q^80 + 18 * q^81 + 9 * q^82 - 9 * q^83 + 15 * q^84 - 18 * q^85 + 16 * q^86 + 9 * q^87 + 3 * q^88 - 15 * q^89 - 9 * q^90 - 15 * q^93 + 9 * q^94 - 15 * q^95 - 18 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		−	1.73205i		−	1.00000i
$3$		−	1.73205i		−	1.00000i
$4$	1.00000			0.500000
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	−0.125567	−	0.992085i	$-0.540075\pi$
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	0.796387	+	0.604787i	$0.206742\pi$
$6$		−	1.73205i		−	0.707107i
$7$	2.50000	+	4.33013i	0.944911	+	1.63663i	0.755929	+	0.654654i	$0.227186\pi$
$7$	2.50000	+	4.33013i	0.944911	+	1.63663i	0.188982	+	0.981981i	$0.439481\pi$
$8$	1.00000			0.353553
$9$	−3.00000			−1.00000
$10$	1.50000	−	0.866025i	0.474342	−	0.273861i
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	−0.256520	−	0.966539i	$-0.582576\pi$
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	0.708787	+	0.705422i	$0.249243\pi$
$12$		−	1.73205i		−	0.500000i
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	2.50000	+	4.33013i	0.668153	+	1.15728i
$15$	−1.50000	−	2.59808i	−0.387298	−	0.670820i
$16$	1.00000			0.250000
$17$	−4.50000	−	2.59808i	−1.09141	−	0.630126i	−0.157459	−	0.987526i	$-0.550330\pi$
$17$	−4.50000	−	2.59808i	−1.09141	−	0.630126i	−0.933952	+	0.357400i	$0.883663\pi$
$18$	−3.00000			−0.707107
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$20$	1.50000	−	0.866025i	0.335410	−	0.193649i
$21$	7.50000	−	4.33013i	1.63663	−	0.944911i
$22$	1.50000	−	0.866025i	0.319801	−	0.184637i
$23$		−	3.46410i		−	0.722315i	−0.932505	−	0.361158i	$-0.882382\pi$
$23$		−	3.46410i		−	0.722315i	0.932505	−	0.361158i	$-0.117618\pi$
$24$		−	1.73205i		−	0.353553i
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$		0			0
$27$			5.19615i			1.00000i
$28$	2.50000	+	4.33013i	0.472456	+	0.818317i
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$	−1.50000	−	2.59808i	−0.273861	−	0.474342i
$31$	−7.50000	−	4.33013i	−1.34704	−	0.777714i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−7.50000	−	4.33013i	−1.34704	−	0.777714i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	1.00000			0.176777
$33$	−1.50000	−	2.59808i	−0.261116	−	0.452267i
$34$	−4.50000	−	2.59808i	−0.771744	−	0.445566i
$35$	7.50000	+	4.33013i	1.26773	+	0.731925i
$36$	−3.00000			−0.500000
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	−4.00000	−	1.73205i	−0.648886	−	0.280976i
$39$		0			0
$40$	1.50000	−	0.866025i	0.237171	−	0.136931i
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$	7.50000	−	4.33013i	1.15728	−	0.668153i
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$	1.50000	−	0.866025i	0.226134	−	0.130558i
$45$	−4.50000	+	2.59808i	−0.670820	+	0.387298i
$46$		−	3.46410i		−	0.510754i
$47$	4.50000	+	2.59808i	0.656392	+	0.378968i	0.790901	−	0.611944i	$-0.209612\pi$
$47$	4.50000	+	2.59808i	0.656392	+	0.378968i	−0.134509	+	0.990912i	$0.542946\pi$
$48$		−	1.73205i		−	0.250000i
$49$	−9.00000	+	15.5885i	−1.28571	+	2.22692i
$50$	−1.00000	+	1.73205i	−0.141421	+	0.244949i
$51$	−4.50000	+	7.79423i	−0.630126	+	1.09141i
$52$		0			0
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	0.744423	−	0.667708i	$-0.232725\pi$
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	−0.950464	+	0.310835i	$0.899391\pi$
$54$			5.19615i			0.707107i
$55$	1.50000	−	2.59808i	0.202260	−	0.350325i
$56$	2.50000	+	4.33013i	0.334077	+	0.578638i
$57$	−3.00000	+	6.92820i	−0.397360	+	0.917663i
$58$	−1.50000	+	2.59808i	−0.196960	+	0.341144i
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	0.751710	−	0.659494i	$-0.229229\pi$
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	−0.946993	+	0.321253i	$0.895896\pi$
$60$	−1.50000	−	2.59808i	−0.193649	−	0.335410i
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$	−7.50000	−	4.33013i	−0.952501	−	0.549927i
$63$	−7.50000	−	12.9904i	−0.944911	−	1.63663i
$64$	1.00000			0.125000
$65$		0			0
$66$	−1.50000	−	2.59808i	−0.184637	−	0.319801i
$67$			3.46410i			0.423207i	0.977356	+	0.211604i	$0.0678686\pi$
$67$			3.46410i			0.423207i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−4.50000	−	2.59808i	−0.545705	−	0.315063i
$69$	−6.00000			−0.722315
$70$	7.50000	+	4.33013i	0.896421	+	0.517549i
$71$	7.50000	−	12.9904i	0.890086	−	1.54167i	0.0503155	−	0.998733i	$-0.483977\pi$
$71$	7.50000	−	12.9904i	0.890086	−	1.54167i	0.839771	−	0.542941i	$-0.182689\pi$
$72$	−3.00000			−0.353553
$73$	−5.50000	+	9.52628i	−0.643726	+	1.11497i	0.340868	+	0.940111i	$0.389279\pi$
$73$	−5.50000	+	9.52628i	−0.643726	+	1.11497i	−0.984594	+	0.174855i	$0.944054\pi$
$74$		0			0
$75$	3.00000	+	1.73205i	0.346410	+	0.200000i
$76$	−4.00000	−	1.73205i	−0.458831	−	0.198680i
$77$	7.50000	+	4.33013i	0.854704	+	0.493464i
$78$		0			0
$79$		−	10.3923i		−	1.16923i	−0.811312	−	0.584613i	$-0.801246\pi$
$79$		−	10.3923i		−	1.16923i	0.811312	−	0.584613i	$-0.198754\pi$
$80$	1.50000	−	0.866025i	0.167705	−	0.0968246i
$81$	9.00000			1.00000
$82$	4.50000	+	7.79423i	0.496942	+	0.860729i
$83$	−4.50000	+	2.59808i	−0.493939	+	0.285176i	−0.726207	−	0.687476i	$-0.758719\pi$
$83$	−4.50000	+	2.59808i	−0.493939	+	0.285176i	0.232268	+	0.972652i	$0.425385\pi$
$84$	7.50000	−	4.33013i	0.818317	−	0.472456i
$85$	−9.00000			−0.976187
$86$	8.00000			0.862662
$87$	4.50000	+	2.59808i	0.482451	+	0.278543i
$88$	1.50000	−	0.866025i	0.159901	−	0.0923186i
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	−0.922840	−	0.385183i	$-0.874138\pi$
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	0.127842	−	0.991795i	$-0.459195\pi$
$90$	−4.50000	+	2.59808i	−0.474342	+	0.273861i
$91$		0			0
$92$		−	3.46410i		−	0.361158i
$93$	−7.50000	+	12.9904i	−0.777714	+	1.34704i
$94$	4.50000	+	2.59808i	0.464140	+	0.267971i
$95$	−7.50000	+	0.866025i	−0.769484	+	0.0888523i
$96$		−	1.73205i		−	0.176777i
$97$		−	6.92820i		−	0.703452i	−0.936103	−	0.351726i	$-0.885595\pi$
$97$		−	6.92820i		−	0.703452i	0.936103	−	0.351726i	$-0.114405\pi$
$98$	−9.00000	+	15.5885i	−0.909137	+	1.57467i
$99$	−4.50000	+	2.59808i	−0.452267	+	0.261116i
$100$	−1.00000	+	1.73205i	−0.100000	+	0.173205i
$101$	7.50000	+	4.33013i	0.746278	+	0.430864i	0.824347	−	0.566084i	$-0.191542\pi$
$101$	7.50000	+	4.33013i	0.746278	+	0.430864i	−0.0780696	+	0.996948i	$0.524876\pi$
$102$	−4.50000	+	7.79423i	−0.445566	+	0.771744i
$103$	−7.50000	−	4.33013i	−0.738997	−	0.426660i	0.0827075	−	0.996574i	$-0.473643\pi$
$103$	−7.50000	−	4.33013i	−0.738997	−	0.426660i	−0.821705	+	0.569914i	$0.806977\pi$
$104$		0			0
$105$	7.50000	−	12.9904i	0.731925	−	1.26773i
$106$	−1.50000	−	2.59808i	−0.145693	−	0.252347i
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$			5.19615i			0.500000i
$109$	13.5000	+	7.79423i	1.29307	+	0.746552i	0.979196	−	0.202915i	$-0.0650414\pi$
$109$	13.5000	+	7.79423i	1.29307	+	0.746552i	0.313869	+	0.949466i	$0.398375\pi$
$110$	1.50000	−	2.59808i	0.143019	−	0.247717i
$111$		0			0
$112$	2.50000	+	4.33013i	0.236228	+	0.409159i
$113$	4.50000	−	7.79423i	0.423324	−	0.733219i	−0.572938	−	0.819599i	$-0.694196\pi$
$113$	4.50000	−	7.79423i	0.423324	−	0.733219i	0.996262	+	0.0863794i	$0.0275297\pi$
$114$	−3.00000	+	6.92820i	−0.280976	+	0.648886i
$115$	−3.00000	−	5.19615i	−0.279751	−	0.484544i
$116$	−1.50000	+	2.59808i	−0.139272	+	0.241225i
$117$		0			0
$118$	−1.50000	−	2.59808i	−0.138086	−	0.239172i
$119$		−	25.9808i		−	2.38165i
$120$	−1.50000	−	2.59808i	−0.136931	−	0.237171i
$121$	−4.00000	+	6.92820i	−0.363636	+	0.629837i
$122$	−3.50000	+	6.06218i	−0.316875	+	0.548844i
$123$	13.5000	−	7.79423i	1.21725	−	0.702782i
$124$	−7.50000	−	4.33013i	−0.673520	−	0.388857i
$125$			12.1244i			1.08444i
$126$	−7.50000	−	12.9904i	−0.668153	−	1.15728i
$127$	−4.50000	+	2.59808i	−0.399310	+	0.230542i	−0.686186	−	0.727426i	$-0.740717\pi$
$127$	−4.50000	+	2.59808i	−0.399310	+	0.230542i	0.286876	+	0.957968i	$0.407383\pi$
$128$	1.00000			0.0883883
$129$		−	13.8564i		−	1.21999i
$130$		0			0
$131$	−4.50000	+	2.59808i	−0.393167	+	0.226995i	−0.683531	−	0.729921i	$-0.739557\pi$
$131$	−4.50000	+	2.59808i	−0.393167	+	0.226995i	0.290365	+	0.956916i	$0.406223\pi$
$132$	−1.50000	−	2.59808i	−0.130558	−	0.226134i
$133$	−2.50000	−	21.6506i	−0.216777	−	1.87735i
$134$			3.46410i			0.299253i
$135$	4.50000	+	7.79423i	0.387298	+	0.670820i
$136$	−4.50000	−	2.59808i	−0.385872	−	0.222783i
$137$	−4.50000	−	2.59808i	−0.384461	−	0.221969i	0.295296	−	0.955406i	$-0.404582\pi$
$137$	−4.50000	−	2.59808i	−0.384461	−	0.221969i	−0.679757	+	0.733437i	$0.737915\pi$
$138$	−6.00000			−0.510754
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$	7.50000	+	4.33013i	0.633866	+	0.365963i
$141$	4.50000	−	7.79423i	0.378968	−	0.656392i
$142$	7.50000	−	12.9904i	0.629386	−	1.09013i
$143$		0			0
$144$	−3.00000			−0.250000
$145$			5.19615i			0.431517i
$146$	−5.50000	+	9.52628i	−0.455183	+	0.788400i
$147$	27.0000	+	15.5885i	2.22692	+	1.28571i
$148$		0			0
$149$	−16.5000	+	9.52628i	−1.35173	+	0.780423i	−0.988492	−	0.151272i	$-0.951663\pi$
$149$	−16.5000	+	9.52628i	−1.35173	+	0.780423i	−0.363241	+	0.931695i	$0.618330\pi$
$150$	3.00000	+	1.73205i	0.244949	+	0.141421i
$151$	−10.5000	+	6.06218i	−0.854478	+	0.493333i	−0.862159	−	0.506637i	$-0.830888\pi$
$151$	−10.5000	+	6.06218i	−0.854478	+	0.493333i	0.00768132	+	0.999970i	$0.497555\pi$
$152$	−4.00000	−	1.73205i	−0.324443	−	0.140488i
$153$	13.5000	+	7.79423i	1.09141	+	0.630126i
$154$	7.50000	+	4.33013i	0.604367	+	0.348932i
$155$	−15.0000			−1.20483
$156$		0			0
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	0.691888	−	0.722005i	$-0.256779\pi$
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	−0.971219	+	0.238190i	$0.923446\pi$
$158$		−	10.3923i		−	0.826767i
$159$	−4.50000	+	2.59808i	−0.356873	+	0.206041i
$160$	1.50000	−	0.866025i	0.118585	−	0.0684653i
$161$	15.0000	−	8.66025i	1.18217	−	0.682524i
$162$	9.00000			0.707107
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$	4.50000	+	7.79423i	0.351391	+	0.608627i
$165$	−4.50000	−	2.59808i	−0.350325	−	0.202260i
$166$	−4.50000	+	2.59808i	−0.349268	+	0.201650i
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$	7.50000	−	4.33013i	0.578638	−	0.334077i
$169$	13.0000			1.00000
$170$	−9.00000			−0.690268
$171$	12.0000	+	5.19615i	0.917663	+	0.397360i
$172$	8.00000			0.609994
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$	4.50000	+	2.59808i	0.341144	+	0.196960i
$175$	−10.0000			−0.755929
$176$	1.50000	−	0.866025i	0.113067	−	0.0652791i
$177$	−4.50000	+	2.59808i	−0.338241	+	0.195283i
$178$	−7.50000	−	12.9904i	−0.562149	−	0.973670i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$	−4.50000	+	2.59808i	−0.335410	+	0.193649i
$181$	7.50000	−	4.33013i	0.557471	−	0.321856i	−0.194659	−	0.980871i	$-0.562360\pi$
$181$	7.50000	−	4.33013i	0.557471	−	0.321856i	0.752130	+	0.659015i	$0.229027\pi$
$182$		0			0
$183$	10.5000	+	6.06218i	0.776182	+	0.448129i
$184$		−	3.46410i		−	0.255377i
$185$		0			0
$186$	−7.50000	+	12.9904i	−0.549927	+	0.952501i
$187$	−9.00000			−0.658145
$188$	4.50000	+	2.59808i	0.328196	+	0.189484i
$189$	−22.5000	+	12.9904i	−1.63663	+	0.944911i
$190$	−7.50000	+	0.866025i	−0.544107	+	0.0628281i
$191$	7.50000	−	4.33013i	0.542681	−	0.313317i	−0.203484	−	0.979078i	$-0.565226\pi$
$191$	7.50000	−	4.33013i	0.542681	−	0.313317i	0.746165	+	0.665761i	$0.231893\pi$
$192$		−	1.73205i		−	0.125000i
$193$	1.50000	−	0.866025i	0.107972	−	0.0623379i	−0.445041	−	0.895510i	$-0.646811\pi$
$193$	1.50000	−	0.866025i	0.107972	−	0.0623379i	0.553014	+	0.833172i	$0.313478\pi$
$194$		−	6.92820i		−	0.497416i
$195$		0			0
$196$	−9.00000	+	15.5885i	−0.642857	+	1.11346i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	−4.50000	+	2.59808i	−0.319801	+	0.184637i
$199$	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	$0.486737\pi$
$200$	−1.00000	+	1.73205i	−0.0707107	+	0.122474i
$201$	6.00000			0.423207
$202$	7.50000	+	4.33013i	0.527698	+	0.304667i
$203$	−15.0000			−1.05279
$204$	−4.50000	+	7.79423i	−0.315063	+	0.545705i
$205$	13.5000	+	7.79423i	0.942881	+	0.544373i
$206$	−7.50000	−	4.33013i	−0.522550	−	0.301694i
$207$			10.3923i			0.722315i
$208$		0			0
$209$	−7.50000	+	0.866025i	−0.518786	+	0.0599042i
$210$	7.50000	−	12.9904i	0.517549	−	0.896421i
$211$	19.5000	−	11.2583i	1.34244	−	0.775055i	0.355271	−	0.934763i	$-0.384389\pi$
$211$	19.5000	−	11.2583i	1.34244	−	0.775055i	0.987164	+	0.159708i	$0.0510552\pi$
$212$	−1.50000	−	2.59808i	−0.103020	−	0.178437i
$213$	−22.5000	−	12.9904i	−1.54167	−	0.890086i
$214$	12.0000			0.820303
$215$	12.0000	−	6.92820i	0.818393	−	0.472500i
$216$			5.19615i			0.353553i
$217$		−	43.3013i		−	2.93948i
$218$	13.5000	+	7.79423i	0.914335	+	0.527892i
$219$	16.5000	+	9.52628i	1.11497	+	0.643726i
$220$	1.50000	−	2.59808i	0.101130	−	0.175162i
$221$		0			0
$222$		0			0
$223$		−	3.46410i		−	0.231973i	−0.993251	−	0.115987i	$-0.962997\pi$
$223$		−	3.46410i		−	0.231973i	0.993251	−	0.115987i	$-0.0370030\pi$
$224$	2.50000	+	4.33013i	0.167038	+	0.289319i
$225$	3.00000	−	5.19615i	0.200000	−	0.346410i
$226$	4.50000	−	7.79423i	0.299336	−	0.518464i
$227$	−13.5000	−	23.3827i	−0.896026	−	1.55196i	−0.832529	−	0.553981i	$-0.813108\pi$
$227$	−13.5000	−	23.3827i	−0.896026	−	1.55196i	−0.0634974	−	0.997982i	$-0.520225\pi$
$228$	−3.00000	+	6.92820i	−0.198680	+	0.458831i
$229$	14.5000	−	25.1147i	0.958187	−	1.65963i	0.231287	−	0.972886i	$-0.425707\pi$
$229$	14.5000	−	25.1147i	0.958187	−	1.65963i	0.726900	−	0.686743i	$-0.240960\pi$
$230$	−3.00000	−	5.19615i	−0.197814	−	0.342624i
$231$	7.50000	−	12.9904i	0.493464	−	0.854704i
$232$	−1.50000	+	2.59808i	−0.0984798	+	0.170572i
$233$	−10.5000	−	6.06218i	−0.687878	−	0.397146i	0.114939	−	0.993373i	$-0.463333\pi$
$233$	−10.5000	−	6.06218i	−0.687878	−	0.397146i	−0.802817	+	0.596226i	$0.796666\pi$
$234$		0			0
$235$	9.00000			0.587095
$236$	−1.50000	−	2.59808i	−0.0976417	−	0.169120i
$237$	−18.0000			−1.16923
$238$		−	25.9808i		−	1.68408i
$239$	10.5000	+	6.06218i	0.679189	+	0.392130i	0.799549	−	0.600601i	$-0.205072\pi$
$239$	10.5000	+	6.06218i	0.679189	+	0.392130i	−0.120361	+	0.992730i	$0.538405\pi$
$240$	−1.50000	−	2.59808i	−0.0968246	−	0.167705i
$241$	1.50000	+	0.866025i	0.0966235	+	0.0557856i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	1.50000	+	0.866025i	0.0966235	+	0.0557856i	−0.450910	+	0.892570i	$0.648900\pi$
$242$	−4.00000	+	6.92820i	−0.257130	+	0.445362i
$243$		−	15.5885i		−	1.00000i
$244$	−3.50000	+	6.06218i	−0.224065	+	0.388091i
$245$			31.1769i			1.99182i
$246$	13.5000	−	7.79423i	0.860729	−	0.496942i
$247$		0			0
$248$	−7.50000	−	4.33013i	−0.476250	−	0.274963i
$249$	4.50000	+	7.79423i	0.285176	+	0.493939i
$250$			12.1244i			0.766812i
$251$	−10.5000	+	6.06218i	−0.662754	+	0.382641i	−0.793326	−	0.608798i	$-0.791652\pi$
$251$	−10.5000	+	6.06218i	−0.662754	+	0.382641i	0.130571	+	0.991439i	$0.458319\pi$
$252$	−7.50000	−	12.9904i	−0.472456	−	0.818317i
$253$	−3.00000	−	5.19615i	−0.188608	−	0.326679i
$254$	−4.50000	+	2.59808i	−0.282355	+	0.163018i
$255$			15.5885i			0.976187i
$256$	1.00000			0.0625000
$257$	−18.0000			−1.12281			−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000			−1.12281			−0.561405	+	0.827541i	$0.689739\pi$
$258$		−	13.8564i		−	0.862662i
$259$		0			0
$260$		0			0
$261$	4.50000	−	7.79423i	0.278543	−	0.482451i
$262$	−4.50000	+	2.59808i	−0.278011	+	0.160510i
$263$		−	17.3205i		−	1.06803i	−0.845476	−	0.534014i	$-0.820683\pi$
$263$		−	17.3205i		−	1.06803i	0.845476	−	0.534014i	$-0.179317\pi$
$264$	−1.50000	−	2.59808i	−0.0923186	−	0.159901i
$265$	−4.50000	−	2.59808i	−0.276433	−	0.159599i
$266$	−2.50000	−	21.6506i	−0.153285	−	1.32749i
$267$	−22.5000	+	12.9904i	−1.37698	+	0.794998i
$268$			3.46410i			0.211604i
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	−0.908124	−	0.418701i	$-0.862486\pi$
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	0.816668	+	0.577108i	$0.195819\pi$
$270$	4.50000	+	7.79423i	0.273861	+	0.474342i
$271$	3.50000	−	6.06218i	0.212610	−	0.368251i	−0.739921	−	0.672694i	$-0.765137\pi$
$271$	3.50000	−	6.06218i	0.212610	−	0.368251i	0.952531	+	0.304443i	$0.0984703\pi$
$272$	−4.50000	−	2.59808i	−0.272853	−	0.157532i
$273$		0			0
$274$	−4.50000	−	2.59808i	−0.271855	−	0.156956i
$275$			3.46410i			0.208893i
$276$	−6.00000			−0.361158
$277$	−9.50000	−	16.4545i	−0.570800	−	0.988654i	−0.996484	−	0.0837823i	$-0.973300\pi$
$277$	−9.50000	−	16.4545i	−0.570800	−	0.988654i	0.425684	−	0.904872i	$-0.360033\pi$
$278$	4.00000			0.239904
$279$	22.5000	+	12.9904i	1.34704	+	0.777714i
$280$	7.50000	+	4.33013i	0.448211	+	0.258775i
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	0.110717	+	0.993852i	$0.464685\pi$
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	−0.916060	+	0.401042i	$0.868648\pi$
$282$	4.50000	−	7.79423i	0.267971	−	0.464140i
$283$	6.50000	+	11.2583i	0.386385	+	0.669238i	0.991960	−	0.126550i	$-0.0403903\pi$
$283$	6.50000	+	11.2583i	0.386385	+	0.669238i	−0.605575	+	0.795788i	$0.707057\pi$
$284$	7.50000	−	12.9904i	0.445043	−	0.770837i
$285$	1.50000	+	12.9904i	0.0888523	+	0.769484i
$286$		0			0
$287$	−22.5000	+	38.9711i	−1.32813	+	2.30039i
$288$	−3.00000			−0.176777
$289$	5.00000	+	8.66025i	0.294118	+	0.509427i
$290$			5.19615i			0.305129i
$291$	−12.0000			−0.703452
$292$	−5.50000	+	9.52628i	−0.321863	+	0.557483i
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	−0.704117	−	0.710084i	$-0.748657\pi$
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	0.967009	+	0.254741i	$0.0819901\pi$
$294$	27.0000	+	15.5885i	1.57467	+	0.909137i
$295$	−4.50000	−	2.59808i	−0.262000	−	0.151266i
$296$		0			0
$297$	4.50000	+	7.79423i	0.261116	+	0.452267i
$298$	−16.5000	+	9.52628i	−0.955819	+	0.551843i
$299$		0			0
$300$	3.00000	+	1.73205i	0.173205	+	0.100000i
$301$	20.0000	+	34.6410i	1.15278	+	1.99667i
$302$	−10.5000	+	6.06218i	−0.604207	+	0.348839i
$303$	7.50000	−	12.9904i	0.430864	−	0.746278i
$304$	−4.00000	−	1.73205i	−0.229416	−	0.0993399i
$305$			12.1244i			0.694239i
$306$	13.5000	+	7.79423i	0.771744	+	0.445566i
$307$	4.50000	+	2.59808i	0.256829	+	0.148280i	0.622887	−	0.782312i	$-0.285960\pi$
$307$	4.50000	+	2.59808i	0.256829	+	0.148280i	−0.366058	+	0.930592i	$0.619293\pi$
$308$	7.50000	+	4.33013i	0.427352	+	0.246732i
$309$	−7.50000	+	12.9904i	−0.426660	+	0.738997i
$310$	−15.0000			−0.851943
$311$	−19.5000	−	11.2583i	−1.10574	−	0.638401i	−0.168020	−	0.985784i	$-0.553737\pi$
$311$	−19.5000	−	11.2583i	−1.10574	−	0.638401i	−0.937724	+	0.347382i	$0.887071\pi$
$312$		0			0
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	−0.519300	−	0.854592i	$-0.673807\pi$
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	0.999748	+	0.0224310i	$0.00714060\pi$
$314$	−3.50000	−	6.06218i	−0.197516	−	0.342108i
$315$	−22.5000	−	12.9904i	−1.26773	−	0.731925i
$316$		−	10.3923i		−	0.584613i
$317$	−13.5000	+	23.3827i	−0.758236	+	1.31330i	0.185514	+	0.982642i	$0.440605\pi$
$317$	−13.5000	+	23.3827i	−0.758236	+	1.31330i	−0.943750	+	0.330661i	$0.892728\pi$
$318$	−4.50000	+	2.59808i	−0.252347	+	0.145693i
$319$			5.19615i			0.290929i
$320$	1.50000	−	0.866025i	0.0838525	−	0.0484123i
$321$		−	20.7846i		−	1.16008i
$322$	15.0000	−	8.66025i	0.835917	−	0.482617i
$323$	13.5000	+	18.1865i	0.751160	+	1.01193i
$324$	9.00000			0.500000
$325$		0			0
$326$	4.00000			0.221540
$327$	13.5000	−	23.3827i	0.746552	−	1.29307i
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$			25.9808i			1.43237i
$330$	−4.50000	−	2.59808i	−0.247717	−	0.143019i
$331$	−22.5000	+	12.9904i	−1.23671	+	0.714016i	−0.968421	−	0.249322i	$-0.919792\pi$
$331$	−22.5000	+	12.9904i	−1.23671	+	0.714016i	−0.268291	+	0.963338i	$0.586459\pi$
$332$	−4.50000	+	2.59808i	−0.246970	+	0.142588i
$333$		0			0
$334$	12.0000			0.656611
$335$	3.00000	+	5.19615i	0.163908	+	0.283896i
$336$	7.50000	−	4.33013i	0.409159	−	0.236228i
$337$	7.50000	−	4.33013i	0.408551	−	0.235877i	−0.281616	−	0.959527i	$-0.590870\pi$
$337$	7.50000	−	4.33013i	0.408551	−	0.235877i	0.690167	+	0.723650i	$0.257537\pi$
$338$	13.0000			0.707107
$339$	−13.5000	−	7.79423i	−0.733219	−	0.423324i
$340$	−9.00000			−0.488094
$341$	−15.0000			−0.812296
$342$	12.0000	+	5.19615i	0.648886	+	0.280976i
$343$	−55.0000			−2.96972
$344$	8.00000			0.431331
$345$	−9.00000	+	5.19615i	−0.484544	+	0.279751i
$346$	−6.00000			−0.322562
$347$	19.5000	−	11.2583i	1.04681	−	0.604379i	0.125059	−	0.992149i	$-0.460088\pi$
$347$	19.5000	−	11.2583i	1.04681	−	0.604379i	0.921756	+	0.387770i	$0.126755\pi$
$348$	4.50000	+	2.59808i	0.241225	+	0.139272i
$349$	−5.50000	−	9.52628i	−0.294408	−	0.509930i	0.680439	−	0.732805i	$-0.261789\pi$
$349$	−5.50000	−	9.52628i	−0.294408	−	0.509930i	−0.974847	+	0.222875i	$0.928456\pi$
$350$	−10.0000			−0.534522
$351$		0			0
$352$	1.50000	−	0.866025i	0.0799503	−	0.0461593i
$353$	7.50000	−	4.33013i	0.399185	−	0.230469i	−0.286947	−	0.957946i	$-0.592641\pi$
$353$	7.50000	−	4.33013i	0.399185	−	0.230469i	0.686132	+	0.727477i	$0.259307\pi$
$354$	−4.50000	+	2.59808i	−0.239172	+	0.138086i
$355$		−	25.9808i		−	1.37892i
$356$	−7.50000	−	12.9904i	−0.397499	−	0.688489i
$357$	−45.0000			−2.38165
$358$	12.0000			0.634220
$359$	16.5000	+	9.52628i	0.870837	+	0.502778i	0.867626	−	0.497217i	$-0.165645\pi$
$359$	16.5000	+	9.52628i	0.870837	+	0.502778i	0.00321050	+	0.999995i	$0.498978\pi$
$360$	−4.50000	+	2.59808i	−0.237171	+	0.136931i
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$	7.50000	−	4.33013i	0.394191	−	0.227586i
$363$	12.0000	+	6.92820i	0.629837	+	0.363636i
$364$		0			0
$365$			19.0526i			0.997257i
$366$	10.5000	+	6.06218i	0.548844	+	0.316875i
$367$	3.50000	−	6.06218i	0.182699	−	0.316443i	−0.760100	−	0.649806i	$-0.774850\pi$
$367$	3.50000	−	6.06218i	0.182699	−	0.316443i	0.942799	+	0.333363i	$0.108183\pi$
$368$		−	3.46410i		−	0.180579i
$369$	−13.5000	−	23.3827i	−0.702782	−	1.21725i
$370$		0			0
$371$	7.50000	−	12.9904i	0.389381	−	0.674427i
$372$	−7.50000	+	12.9904i	−0.388857	+	0.673520i
$373$	1.50000	+	0.866025i	0.0776671	+	0.0448411i	0.538331	−	0.842734i	$-0.319055\pi$
$373$	1.50000	+	0.866025i	0.0776671	+	0.0448411i	−0.460664	+	0.887575i	$0.652389\pi$
$374$	−9.00000			−0.465379
$375$	21.0000			1.08444
$376$	4.50000	+	2.59808i	0.232070	+	0.133986i
$377$		0			0
$378$	−22.5000	+	12.9904i	−1.15728	+	0.668153i
$379$			17.3205i			0.889695i	0.895606	+	0.444847i	$0.146742\pi$
$379$			17.3205i			0.889695i	−0.895606	+	0.444847i	$0.853258\pi$
$380$	−7.50000	+	0.866025i	−0.384742	+	0.0444262i
$381$	4.50000	+	7.79423i	0.230542	+	0.399310i
$382$	7.50000	−	4.33013i	0.383733	−	0.221549i
$383$	−13.5000	−	23.3827i	−0.689818	−	1.19480i	−0.971897	−	0.235408i	$-0.924357\pi$
$383$	−13.5000	−	23.3827i	−0.689818	−	1.19480i	0.282079	−	0.959391i	$-0.408976\pi$
$384$		−	1.73205i		−	0.0883883i
$385$	15.0000			0.764471
$386$	1.50000	−	0.866025i	0.0763480	−	0.0440795i
$387$	−24.0000			−1.21999
$388$		−	6.92820i		−	0.351726i
$389$	1.50000	+	0.866025i	0.0760530	+	0.0439092i	0.537544	−	0.843236i	$-0.319352\pi$
$389$	1.50000	+	0.866025i	0.0760530	+	0.0439092i	−0.461491	+	0.887145i	$0.652685\pi$
$390$		0			0
$391$	−9.00000	+	15.5885i	−0.455150	+	0.788342i
$392$	−9.00000	+	15.5885i	−0.454569	+	0.787336i
$393$	4.50000	+	7.79423i	0.226995	+	0.393167i
$394$		0			0
$395$	−9.00000	−	15.5885i	−0.452839	−	0.784340i
$396$	−4.50000	+	2.59808i	−0.226134	+	0.130558i
$397$	−5.50000	+	9.52628i	−0.276037	+	0.478110i	−0.970396	−	0.241518i	$-0.922355\pi$
$397$	−5.50000	+	9.52628i	−0.276037	+	0.478110i	0.694359	+	0.719629i	$0.255688\pi$
$398$	12.5000	+	21.6506i	0.626568	+	1.08525i
$399$	−37.5000	+	4.33013i	−1.87735	+	0.216777i
$400$	−1.00000	+	1.73205i	−0.0500000	+	0.0866025i
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	0.615725	−	0.787961i	$-0.288863\pi$
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	−0.990257	+	0.139253i	$0.955530\pi$
$402$	6.00000			0.299253
$403$		0			0
$404$	7.50000	+	4.33013i	0.373139	+	0.215432i
$405$	13.5000	−	7.79423i	0.670820	−	0.387298i
$406$	−15.0000			−0.744438
$407$		0			0
$408$	−4.50000	+	7.79423i	−0.222783	+	0.385872i
$409$			13.8564i			0.685155i	0.939490	+	0.342578i	$0.111300\pi$
$409$			13.8564i			0.685155i	−0.939490	+	0.342578i	$0.888700\pi$
$410$	13.5000	+	7.79423i	0.666717	+	0.384930i
$411$	−4.50000	+	7.79423i	−0.221969	+	0.384461i
$412$	−7.50000	−	4.33013i	−0.369498	−	0.213330i
$413$	7.50000	−	12.9904i	0.369051	−	0.639215i
$414$			10.3923i			0.510754i
$415$	−4.50000	+	7.79423i	−0.220896	+	0.382604i
$416$		0			0
$417$		−	6.92820i		−	0.339276i
$418$	−7.50000	+	0.866025i	−0.366837	+	0.0423587i
$419$	16.5000	+	9.52628i	0.806078	+	0.465389i	0.845592	−	0.533830i	$-0.179248\pi$
$419$	16.5000	+	9.52628i	0.806078	+	0.465389i	−0.0395142	+	0.999219i	$0.512581\pi$
$420$	7.50000	−	12.9904i	0.365963	−	0.633866i
$421$			27.7128i			1.35064i	0.737525	+	0.675320i	$0.235994\pi$
$421$			27.7128i			1.35064i	−0.737525	+	0.675320i	$0.764006\pi$
$422$	19.5000	−	11.2583i	0.949245	−	0.548047i
$423$	−13.5000	−	7.79423i	−0.656392	−	0.378968i
$424$	−1.50000	−	2.59808i	−0.0728464	−	0.126174i
$425$	9.00000	−	5.19615i	0.436564	−	0.252050i
$426$	−22.5000	−	12.9904i	−1.09013	−	0.629386i
$427$	−35.0000			−1.69377
$428$	12.0000			0.580042
$429$		0			0
$430$	12.0000	−	6.92820i	0.578691	−	0.334108i
$431$	−1.50000	−	2.59808i	−0.0722525	−	0.125145i	0.827636	−	0.561266i	$-0.189685\pi$
$431$	−1.50000	−	2.59808i	−0.0722525	−	0.125145i	−0.899888	+	0.436121i	$0.856352\pi$
$432$			5.19615i			0.250000i
$433$	19.5000	−	11.2583i	0.937110	−	0.541041i	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	19.5000	−	11.2583i	0.937110	−	0.541041i	0.889053	+	0.457804i	$0.151364\pi$
$434$		−	43.3013i		−	2.07853i
$435$	9.00000			0.431517
$436$	13.5000	+	7.79423i	0.646533	+	0.373276i
$437$	−6.00000	+	13.8564i	−0.287019	+	0.662842i
$438$	16.5000	+	9.52628i	0.788400	+	0.455183i
$439$			24.2487i			1.15733i	0.815566	+	0.578664i	$0.196426\pi$
$439$			24.2487i			1.15733i	−0.815566	+	0.578664i	$0.803574\pi$
$440$	1.50000	−	2.59808i	0.0715097	−	0.123858i
$441$	27.0000	−	46.7654i	1.28571	−	2.22692i
$442$		0			0
$443$	−19.5000	−	11.2583i	−0.926473	−	0.534899i	−0.0407786	−	0.999168i	$-0.512984\pi$
$443$	−19.5000	−	11.2583i	−0.926473	−	0.534899i	−0.885694	+	0.464269i	$0.846317\pi$
$444$		0			0
$445$	−22.5000	−	12.9904i	−1.06660	−	0.615803i
$446$		−	3.46410i		−	0.164030i
$447$	16.5000	+	28.5788i	0.780423	+	1.35173i
$448$	2.50000	+	4.33013i	0.118114	+	0.204579i
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	3.00000	−	5.19615i	0.141421	−	0.244949i
$451$	13.5000	+	7.79423i	0.635690	+	0.367016i
$452$	4.50000	−	7.79423i	0.211662	−	0.366610i
$453$	10.5000	+	18.1865i	0.493333	+	0.854478i
$454$	−13.5000	−	23.3827i	−0.633586	−	1.09740i
$455$		0			0
$456$	−3.00000	+	6.92820i	−0.140488	+	0.324443i
$457$	18.5000	+	32.0429i	0.865393	+	1.49891i	0.866656	+	0.498906i	$0.166265\pi$
$457$	18.5000	+	32.0429i	0.865393	+	1.49891i	−0.00126243	+	0.999999i	$0.500402\pi$
$458$	14.5000	−	25.1147i	0.677541	−	1.17353i
$459$	13.5000	−	23.3827i	0.630126	−	1.09141i
$460$	−3.00000	−	5.19615i	−0.139876	−	0.242272i
$461$		−	41.5692i		−	1.93607i	−0.250812	−	0.968036i	$-0.580698\pi$
$461$		−	41.5692i		−	1.93607i	0.250812	−	0.968036i	$-0.419302\pi$
$462$	7.50000	−	12.9904i	0.348932	−	0.604367i
$463$	−2.50000	+	4.33013i	−0.116185	+	0.201238i	−0.918253	−	0.395995i	$-0.870400\pi$
$463$	−2.50000	+	4.33013i	−0.116185	+	0.201238i	0.802068	+	0.597233i	$0.203733\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$			25.9808i			1.20483i
$466$	−10.5000	−	6.06218i	−0.486403	−	0.280825i
$467$		−	31.1769i		−	1.44270i	−0.692573	−	0.721348i	$-0.743523\pi$
$467$		−	31.1769i		−	1.44270i	0.692573	−	0.721348i	$-0.256477\pi$
$468$		0			0
$469$	−15.0000	+	8.66025i	−0.692636	+	0.399893i
$470$	9.00000			0.415139
$471$	−10.5000	+	6.06218i	−0.483814	+	0.279330i
$472$	−1.50000	−	2.59808i	−0.0690431	−	0.119586i
$473$	12.0000	−	6.92820i	0.551761	−	0.318559i
$474$	−18.0000			−0.826767
$475$	7.00000	−	5.19615i	0.321182	−	0.238416i
$476$		−	25.9808i		−	1.19083i
$477$	4.50000	+	7.79423i	0.206041	+	0.356873i
$478$	10.5000	+	6.06218i	0.480259	+	0.277278i
$479$	28.5000	+	16.4545i	1.30220	+	0.751825i	0.980781	−	0.195113i	$-0.0625074\pi$
$479$	28.5000	+	16.4545i	1.30220	+	0.751825i	0.321417	+	0.946938i	$0.395841\pi$
$480$	−1.50000	−	2.59808i	−0.0684653	−	0.118585i
$481$		0			0
$482$	1.50000	+	0.866025i	0.0683231	+	0.0394464i
$483$	−15.0000	−	25.9808i	−0.682524	−	1.18217i
$484$	−4.00000	+	6.92820i	−0.181818	+	0.314918i
$485$	−6.00000	−	10.3923i	−0.272446	−	0.471890i
$486$		−	15.5885i		−	0.707107i
$487$		−	17.3205i		−	0.784867i	−0.919780	−	0.392434i	$-0.871633\pi$
$487$		−	17.3205i		−	0.784867i	0.919780	−	0.392434i	$-0.128367\pi$
$488$	−3.50000	+	6.06218i	−0.158438	+	0.274422i
$489$		−	6.92820i		−	0.313304i
$490$			31.1769i			1.40843i
$491$	13.5000	−	7.79423i	0.609246	−	0.351749i	−0.163424	−	0.986556i	$-0.552254\pi$
$491$	13.5000	−	7.79423i	0.609246	−	0.351749i	0.772670	+	0.634807i	$0.218921\pi$
$492$	13.5000	−	7.79423i	0.608627	−	0.351391i
$493$	13.5000	−	7.79423i	0.608009	−	0.351034i
$494$		0			0
$495$	−4.50000	+	7.79423i	−0.202260	+	0.350325i
$496$	−7.50000	−	4.33013i	−0.336760	−	0.194428i
$497$	75.0000			3.36421
$498$	4.50000	+	7.79423i	0.201650	+	0.349268i
$499$	2.50000	+	4.33013i	0.111915	+	0.193843i	0.916542	−	0.399937i	$-0.130968\pi$
$499$	2.50000	+	4.33013i	0.111915	+	0.193843i	−0.804627	+	0.593780i	$0.797635\pi$
$500$			12.1244i			0.542218i
$501$		−	20.7846i		−	0.928588i
$502$	−10.5000	+	6.06218i	−0.468638	+	0.270568i
$503$	−28.5000	+	16.4545i	−1.27075	+	0.733669i	−0.975130	−	0.221636i	$-0.928860\pi$
$503$	−28.5000	+	16.4545i	−1.27075	+	0.733669i	−0.295623	+	0.955305i	$0.595527\pi$
$504$	−7.50000	−	12.9904i	−0.334077	−	0.578638i
$505$	15.0000			0.667491
$506$	−3.00000	−	5.19615i	−0.133366	−	0.230997i
$507$		−	22.5167i		−	1.00000i
$508$	−4.50000	+	2.59808i	−0.199655	+	0.115271i
$509$	18.0000			0.797836			0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000			0.797836			0.398918	+	0.916987i	$0.369386\pi$
$510$			15.5885i			0.690268i
$511$	−55.0000			−2.43306
$512$	1.00000			0.0441942
$513$	9.00000	−	20.7846i	0.397360	−	0.917663i
$514$	−18.0000			−0.793946
$515$	−15.0000			−0.660979
$516$		−	13.8564i		−	0.609994i
$517$	9.00000			0.395820
$518$		0			0
$519$			10.3923i			0.456172i
$520$		0			0
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$	4.50000	−	7.79423i	0.196960	−	0.341144i
$523$	13.5000	−	7.79423i	0.590314	−	0.340818i	−0.174908	−	0.984585i	$-0.555963\pi$
$523$	13.5000	−	7.79423i	0.590314	−	0.340818i	0.765222	+	0.643767i	$0.222629\pi$
$524$	−4.50000	+	2.59808i	−0.196583	+	0.113497i
$525$			17.3205i			0.755929i
$526$		−	17.3205i		−	0.755210i
$527$	22.5000	+	38.9711i	0.980115	+	1.69761i
$528$	−1.50000	−	2.59808i	−0.0652791	−	0.113067i
$529$	11.0000			0.478261
$530$	−4.50000	−	2.59808i	−0.195468	−	0.112853i
$531$	4.50000	+	7.79423i	0.195283	+	0.338241i
$532$	−2.50000	−	21.6506i	−0.108389	−	0.938674i
$533$		0			0
$534$	−22.5000	+	12.9904i	−0.973670	+	0.562149i
$535$	18.0000	−	10.3923i	0.778208	−	0.449299i
$536$			3.46410i			0.149626i
$537$		−	20.7846i		−	0.896922i
$538$	−1.50000	+	2.59808i	−0.0646696	+	0.112011i
$539$			31.1769i			1.34288i
$540$	4.50000	+	7.79423i	0.193649	+	0.335410i
$541$	−11.5000	−	19.9186i	−0.494424	−	0.856367i	0.505556	−	0.862794i	$-0.331288\pi$
$541$	−11.5000	−	19.9186i	−0.494424	−	0.856367i	−0.999979	+	0.00642713i	$0.997954\pi$
$542$	3.50000	−	6.06218i	0.150338	−	0.260393i
$543$	−7.50000	−	12.9904i	−0.321856	−	0.557471i
$544$	−4.50000	−	2.59808i	−0.192936	−	0.111392i
$545$	27.0000			1.15655
$546$		0			0
$547$	22.5000	+	12.9904i	0.962031	+	0.555429i	0.896797	−	0.442441i	$-0.145888\pi$
$547$	22.5000	+	12.9904i	0.962031	+	0.555429i	0.0652331	+	0.997870i	$0.479221\pi$
$548$	−4.50000	−	2.59808i	−0.192230	−	0.110984i
$549$	10.5000	−	18.1865i	0.448129	−	0.776182i
$550$			3.46410i			0.147710i
$551$	10.5000	−	7.79423i	0.447315	−	0.332045i
$552$	−6.00000			−0.255377
$553$	45.0000	−	25.9808i	1.91359	−	1.10481i
$554$	−9.50000	−	16.4545i	−0.403616	−	0.699084i
$555$		0			0
$556$	4.00000			0.169638
$557$	−10.5000	+	6.06218i	−0.444899	+	0.256863i	−0.705674	−	0.708537i	$-0.749355\pi$
$557$	−10.5000	+	6.06218i	−0.444899	+	0.256863i	0.260774	+	0.965400i	$0.416022\pi$
$558$	22.5000	+	12.9904i	0.952501	+	0.549927i
$559$		0			0
$560$	7.50000	+	4.33013i	0.316933	+	0.182981i
$561$			15.5885i			0.658145i
$562$	−13.5000	+	23.3827i	−0.569463	+	0.986339i
$563$	−10.5000	+	18.1865i	−0.442522	+	0.766471i	−0.997876	−	0.0651433i	$-0.979250\pi$
$563$	−10.5000	+	18.1865i	−0.442522	+	0.766471i	0.555354	+	0.831614i	$0.312583\pi$
$564$	4.50000	−	7.79423i	0.189484	−	0.328196i
$565$		−	15.5885i		−	0.655811i
$566$	6.50000	+	11.2583i	0.273215	+	0.473223i
$567$	22.5000	+	38.9711i	0.944911	+	1.63663i
$568$	7.50000	−	12.9904i	0.314693	−	0.545064i
$569$	−19.5000	−	33.7750i	−0.817483	−	1.41592i	−0.907532	−	0.419984i	$-0.862036\pi$
$569$	−19.5000	−	33.7750i	−0.817483	−	1.41592i	0.0900490	−	0.995937i	$-0.471298\pi$
$570$	1.50000	+	12.9904i	0.0628281	+	0.544107i
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	−0.595862	−	0.803087i	$-0.703189\pi$
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	0.993425	+	0.114488i	$0.0365228\pi$
$572$		0			0
$573$	−7.50000	−	12.9904i	−0.313317	−	0.542681i
$574$	−22.5000	+	38.9711i	−0.939132	+	1.62662i
$575$	6.00000	+	3.46410i	0.250217	+	0.144463i
$576$	−3.00000			−0.125000
$577$	−26.0000			−1.08239			−0.541197	−	0.840896i	$-0.682029\pi$
$577$	−26.0000			−1.08239			−0.541197	+	0.840896i	$0.682029\pi$
$578$	5.00000	+	8.66025i	0.207973	+	0.360219i
$579$	−1.50000	−	2.59808i	−0.0623379	−	0.107972i
$580$			5.19615i			0.215758i
$581$	−22.5000	−	12.9904i	−0.933457	−	0.538932i
$582$	−12.0000			−0.497416
$583$	−4.50000	−	2.59808i	−0.186371	−	0.107601i
$584$	−5.50000	+	9.52628i	−0.227592	+	0.394200i
$585$		0			0
$586$	4.50000	−	7.79423i	0.185893	−	0.321977i
$587$			45.0333i			1.85872i	0.369170	+	0.929362i	$0.379642\pi$
$587$			45.0333i			1.85872i	−0.369170	+	0.929362i	$0.620358\pi$
$588$	27.0000	+	15.5885i	1.11346	+	0.642857i
$589$	22.5000	+	30.3109i	0.927096	+	1.24894i
$590$	−4.50000	−	2.59808i	−0.185262	−	0.106961i
$591$		0			0
$592$		0			0
$593$	1.50000	−	0.866025i	0.0615976	−	0.0355634i	−0.468885	−	0.883259i	$-0.655344\pi$
$593$	1.50000	−	0.866025i	0.0615976	−	0.0355634i	0.530483	+	0.847696i	$0.322011\pi$
$594$	4.50000	+	7.79423i	0.184637	+	0.319801i
$595$	−22.5000	−	38.9711i	−0.922410	−	1.59766i
$596$	−16.5000	+	9.52628i	−0.675866	+	0.390212i
$597$	37.5000	−	21.6506i	1.53477	−	0.886102i
$598$		0			0
$599$	−12.0000			−0.490307			−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000			−0.490307			−0.245153	+	0.969484i	$0.578838\pi$
$600$	3.00000	+	1.73205i	0.122474	+	0.0707107i
$601$	19.5000	−	11.2583i	0.795422	−	0.459237i	−0.0464461	−	0.998921i	$-0.514790\pi$
$601$	19.5000	−	11.2583i	0.795422	−	0.459237i	0.841868	+	0.539684i	$0.181456\pi$
$602$	20.0000	+	34.6410i	0.815139	+	1.41186i
$603$		−	10.3923i		−	0.423207i
$604$	−10.5000	+	6.06218i	−0.427239	+	0.246667i
$605$			13.8564i			0.563343i
$606$	7.50000	−	12.9904i	0.304667	−	0.527698i
$607$	−1.50000	−	0.866025i	−0.0608831	−	0.0351509i	0.469249	−	0.883066i	$-0.344525\pi$
$607$	−1.50000	−	0.866025i	−0.0608831	−	0.0351509i	−0.530133	+	0.847915i	$0.677858\pi$
$608$	−4.00000	−	1.73205i	−0.162221	−	0.0702439i
$609$			25.9808i			1.05279i
$610$			12.1244i			0.490901i
$611$		0			0
$612$	13.5000	+	7.79423i	0.545705	+	0.315063i
$613$	−21.5000	+	37.2391i	−0.868377	+	1.50407i	−0.00472215	+	0.999989i	$0.501503\pi$
$613$	−21.5000	+	37.2391i	−0.868377	+	1.50407i	−0.863655	+	0.504084i	$0.831830\pi$
$614$	4.50000	+	2.59808i	0.181605	+	0.104850i
$615$	13.5000	−	23.3827i	0.544373	−	0.942881i
$616$	7.50000	+	4.33013i	0.302184	+	0.174466i
$617$			34.6410i			1.39459i	0.716782	+	0.697297i	$0.245614\pi$
$617$			34.6410i			1.39459i	−0.716782	+	0.697297i	$0.754386\pi$
$618$	−7.50000	+	12.9904i	−0.301694	+	0.522550i
$619$	14.5000	+	25.1147i	0.582804	+	1.00945i	0.995145	+	0.0984169i	$0.0313779\pi$
$619$	14.5000	+	25.1147i	0.582804	+	1.00945i	−0.412341	+	0.911030i	$0.635289\pi$
$620$	−15.0000			−0.602414
$621$	18.0000			0.722315
$622$	−19.5000	−	11.2583i	−0.781879	−	0.451418i
$623$	37.5000	−	64.9519i	1.50241	−	2.60224i
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	8.50000	−	14.7224i	0.339728	−	0.588427i
$627$	1.50000	+	12.9904i	0.0599042	+	0.518786i
$628$	−3.50000	−	6.06218i	−0.139665	−	0.241907i
$629$		0			0
$630$	−22.5000	−	12.9904i	−0.896421	−	0.517549i
$631$	2.50000	+	4.33013i	0.0995234	+	0.172380i	0.911487	−	0.411328i	$-0.134935\pi$
$631$	2.50000	+	4.33013i	0.0995234	+	0.172380i	−0.811964	+	0.583707i	$0.801602\pi$
$632$		−	10.3923i		−	0.413384i
$633$	−19.5000	−	33.7750i	−0.775055	−	1.34244i
$634$	−13.5000	+	23.3827i	−0.536153	+	0.928645i
$635$	−4.50000	+	7.79423i	−0.178577	+	0.309305i
$636$	−4.50000	+	2.59808i	−0.178437	+	0.103020i
$637$		0			0
$638$			5.19615i			0.205718i
$639$	−22.5000	+	38.9711i	−0.890086	+	1.54167i
$640$	1.50000	−	0.866025i	0.0592927	−	0.0342327i
$641$	−30.0000			−1.18493			−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000			−1.18493			−0.592464	+	0.805597i	$0.701845\pi$
$642$		−	20.7846i		−	0.820303i
$643$	−11.5000	−	19.9186i	−0.453516	−	0.785512i	0.545086	−	0.838380i	$-0.316497\pi$
$643$	−11.5000	−	19.9186i	−0.453516	−	0.785512i	−0.998602	+	0.0528680i	$0.983164\pi$
$644$	15.0000	−	8.66025i	0.591083	−	0.341262i
$645$	−12.0000	−	20.7846i	−0.472500	−	0.818393i
$646$	13.5000	+	18.1865i	0.531150	+	0.715540i
$647$		−	45.0333i		−	1.77044i	−0.465170	−	0.885221i	$-0.654007\pi$
$647$		−	45.0333i		−	1.77044i	0.465170	−	0.885221i	$-0.345993\pi$
$648$	9.00000			0.353553
$649$	−4.50000	−	2.59808i	−0.176640	−	0.101983i
$650$		0			0
$651$	−75.0000			−2.93948
$652$	4.00000			0.156652
$653$	−16.5000	−	9.52628i	−0.645695	−	0.372792i	0.141110	−	0.989994i	$-0.454933\pi$
$653$	−16.5000	−	9.52628i	−0.645695	−	0.372792i	−0.786805	+	0.617202i	$0.788266\pi$
$654$	13.5000	−	23.3827i	0.527892	−	0.914335i
$655$	−4.50000	+	7.79423i	−0.175830	+	0.304546i
$656$	4.50000	+	7.79423i	0.175695	+	0.304314i
$657$	16.5000	−	28.5788i	0.643726	−	1.11497i
$658$			25.9808i			1.01284i
$659$	−4.50000	+	7.79423i	−0.175295	+	0.303620i	−0.940263	−	0.340448i	$-0.889421\pi$
$659$	−4.50000	+	7.79423i	−0.175295	+	0.303620i	0.764968	+	0.644068i	$0.222755\pi$
$660$	−4.50000	−	2.59808i	−0.175162	−	0.101130i
$661$			27.7128i			1.07790i	0.842337	+	0.538952i	$0.181179\pi$
$661$			27.7128i			1.07790i	−0.842337	+	0.538952i	$0.818821\pi$
$662$	−22.5000	+	12.9904i	−0.874487	+	0.504885i
$663$		0			0
$664$	−4.50000	+	2.59808i	−0.174634	+	0.100825i
$665$	−22.5000	−	30.3109i	−0.872513	−	1.17541i
$666$		0			0
$667$	9.00000	+	5.19615i	0.348481	+	0.201196i
$668$	12.0000			0.464294
$669$	−6.00000			−0.231973
$670$	3.00000	+	5.19615i	0.115900	+	0.200745i
$671$			12.1244i			0.468056i
$672$	7.50000	−	4.33013i	0.289319	−	0.167038i
$673$	−10.5000	+	6.06218i	−0.404745	+	0.233680i	−0.688529	−	0.725208i	$-0.741743\pi$
$673$	−10.5000	+	6.06218i	−0.404745	+	0.233680i	0.283784	+	0.958888i	$0.408410\pi$
$674$	7.50000	−	4.33013i	0.288889	−	0.166790i
$675$	−9.00000	−	5.19615i	−0.346410	−	0.200000i
$676$	13.0000			0.500000
$677$	4.50000	+	7.79423i	0.172949	+	0.299557i	0.939450	−	0.342687i	$-0.111337\pi$
$677$	4.50000	+	7.79423i	0.172949	+	0.299557i	−0.766501	+	0.642244i	$0.778004\pi$
$678$	−13.5000	−	7.79423i	−0.518464	−	0.299336i
$679$	30.0000	−	17.3205i	1.15129	−	0.664700i
$680$	−9.00000			−0.345134
$681$	−40.5000	+	23.3827i	−1.55196	+	0.896026i
$682$	−15.0000			−0.574380
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$	12.0000	+	5.19615i	0.458831	+	0.198680i
$685$	−9.00000			−0.343872
$686$	−55.0000			−2.09991
$687$	−43.5000	−	25.1147i	−1.65963	−	0.958187i
$688$	8.00000			0.304997
$689$		0			0
$690$	−9.00000	+	5.19615i	−0.342624	+	0.197814i
$691$	−5.50000	−	9.52628i	−0.209230	−	0.362397i	0.742242	−	0.670132i	$-0.233762\pi$
$691$	−5.50000	−	9.52628i	−0.209230	−	0.362397i	−0.951472	+	0.307735i	$0.900429\pi$
$692$	−6.00000			−0.228086
$693$	−22.5000	−	12.9904i	−0.854704	−	0.493464i
$694$	19.5000	−	11.2583i	0.740210	−	0.427360i
$695$	6.00000	−	3.46410i	0.227593	−	0.131401i
$696$	4.50000	+	2.59808i	0.170572	+	0.0984798i
$697$		−	46.7654i		−	1.77136i
$698$	−5.50000	−	9.52628i	−0.208178	−	0.360575i
$699$	−10.5000	+	18.1865i	−0.397146	+	0.687878i
$700$	−10.0000			−0.377964
$701$	13.5000	+	7.79423i	0.509888	+	0.294384i	0.732788	−	0.680457i	$-0.238219\pi$
$701$	13.5000	+	7.79423i	0.509888	+	0.294384i	−0.222900	+	0.974841i	$0.571552\pi$
$702$		0			0
$703$		0			0
$704$	1.50000	−	0.866025i	0.0565334	−	0.0326396i
$705$		−	15.5885i		−	0.587095i
$706$	7.50000	−	4.33013i	0.282266	−	0.162966i
$707$			43.3013i			1.62851i
$708$	−4.50000	+	2.59808i	−0.169120	+	0.0976417i
$709$	−17.5000	+	30.3109i	−0.657226	+	1.13835i	0.324104	+	0.946021i	$0.394937\pi$
$709$	−17.5000	+	30.3109i	−0.657226	+	1.13835i	−0.981331	+	0.192328i	$0.938396\pi$
$710$		−	25.9808i		−	0.975041i
$711$			31.1769i			1.16923i
$712$	−7.50000	−	12.9904i	−0.281074	−	0.486835i
$713$	−15.0000	+	25.9808i	−0.561754	+	0.972987i
$714$	−45.0000			−1.68408
$715$		0			0
$716$	12.0000			0.448461
$717$	10.5000	−	18.1865i	0.392130	−	0.679189i
$718$	16.5000	+	9.52628i	0.615775	+	0.355518i
$719$	−7.50000	−	4.33013i	−0.279703	−	0.161486i	0.353586	−	0.935402i	$-0.384962\pi$
$719$	−7.50000	−	4.33013i	−0.279703	−	0.161486i	−0.633289	+	0.773916i	$0.718295\pi$
$720$	−4.50000	+	2.59808i	−0.167705	+	0.0968246i
$721$		−	43.3013i		−	1.61262i
$722$	13.0000	+	13.8564i	0.483810	+	0.515682i
$723$	1.50000	−	2.59808i	0.0557856	−	0.0966235i
$724$	7.50000	−	4.33013i	0.278735	−	0.160928i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	12.0000	+	6.92820i	0.445362	+	0.257130i
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$			19.0526i			0.705167i
$731$	−36.0000	−	20.7846i	−1.33151	−	0.768747i
$732$	10.5000	+	6.06218i	0.388091	+	0.224065i
$733$	0.500000	−	0.866025i	0.0184679	−	0.0319874i	−0.856644	−	0.515908i	$-0.827454\pi$
$733$	0.500000	−	0.866025i	0.0184679	−	0.0319874i	0.875112	+	0.483921i	$0.160788\pi$
$734$	3.50000	−	6.06218i	0.129187	−	0.223759i
$735$	54.0000			1.99182
$736$		−	3.46410i		−	0.127688i
$737$	3.00000	+	5.19615i	0.110506	+	0.191403i
$738$	−13.5000	−	23.3827i	−0.496942	−	0.860729i
$739$	5.50000	−	9.52628i	0.202321	−	0.350430i	−0.746955	−	0.664875i	$-0.768485\pi$
$739$	5.50000	−	9.52628i	0.202321	−	0.350430i	0.949276	+	0.314445i	$0.101818\pi$
$740$		0			0
$741$		0			0
$742$	7.50000	−	12.9904i	0.275334	−	0.476892i
$743$	−13.5000	−	23.3827i	−0.495267	−	0.857828i	0.504718	−	0.863284i	$-0.331596\pi$
$743$	−13.5000	−	23.3827i	−0.495267	−	0.857828i	−0.999985	+	0.00545664i	$0.998263\pi$
$744$	−7.50000	+	12.9904i	−0.274963	+	0.476250i
$745$	−16.5000	+	28.5788i	−0.604513	+	1.04705i
$746$	1.50000	+	0.866025i	0.0549189	+	0.0317074i
$747$	13.5000	−	7.79423i	0.493939	−	0.285176i
$748$	−9.00000			−0.329073
$749$	30.0000	+	51.9615i	1.09618	+	1.89863i
$750$	21.0000			0.766812
$751$			51.9615i			1.89610i	0.318117	+	0.948051i	$0.396950\pi$
$751$			51.9615i			1.89610i	−0.318117	+	0.948051i	$0.603050\pi$
$752$	4.50000	+	2.59808i	0.164098	+	0.0947421i
$753$	10.5000	+	18.1865i	0.382641	+	0.662754i
$754$		0			0
$755$	−10.5000	+	18.1865i	−0.382134	+	0.661876i
$756$	−22.5000	+	12.9904i	−0.818317	+	0.472456i
$757$	2.50000	−	4.33013i	0.0908640	−	0.157381i	−0.817011	−	0.576622i	$-0.804370\pi$
$757$	2.50000	−	4.33013i	0.0908640	−	0.157381i	0.907875	+	0.419241i	$0.137704\pi$
$758$			17.3205i			0.629109i
$759$	−9.00000	+	5.19615i	−0.326679	+	0.188608i
$760$	−7.50000	+	0.866025i	−0.272054	+	0.0314140i
$761$	1.50000	+	0.866025i	0.0543750	+	0.0313934i	0.526941	−	0.849902i	$-0.323339\pi$
$761$	1.50000	+	0.866025i	0.0543750	+	0.0313934i	−0.472566	+	0.881295i	$0.656672\pi$
$762$	4.50000	+	7.79423i	0.163018	+	0.282355i
$763$			77.9423i			2.82170i
$764$	7.50000	−	4.33013i	0.271340	−	0.156658i
$765$	27.0000			0.976187
$766$	−13.5000	−	23.3827i	−0.487775	−	0.844851i
$767$		0			0
$768$		−	1.73205i		−	0.0625000i
$769$	22.0000			0.793340			0.396670	−	0.917961i	$-0.370166\pi$
$769$	22.0000			0.793340			0.396670	+	0.917961i	$0.370166\pi$
$770$	15.0000			0.540562
$771$			31.1769i			1.12281i
$772$	1.50000	−	0.866025i	0.0539862	−	0.0311689i
$773$	10.5000	+	18.1865i	0.377659	+	0.654124i	0.990721	−	0.135910i	$-0.0433959\pi$
$773$	10.5000	+	18.1865i	0.377659	+	0.654124i	−0.613062	+	0.790034i	$0.710063\pi$
$774$	−24.0000			−0.862662
$775$	15.0000	−	8.66025i	0.538816	−	0.311086i
$776$		−	6.92820i		−	0.248708i
$777$		0			0
$778$	1.50000	+	0.866025i	0.0537776	+	0.0310485i
$779$	−4.50000	−	38.9711i	−0.161229	−	1.39629i
$780$		0			0
$781$		−	25.9808i		−	0.929665i
$782$	−9.00000	+	15.5885i	−0.321839	+	0.557442i
$783$	−13.5000	−	7.79423i	−0.482451	−	0.278543i
$784$	−9.00000	+	15.5885i	−0.321429	+	0.556731i
$785$	−10.5000	−	6.06218i	−0.374761	−	0.216368i
$786$	4.50000	+	7.79423i	0.160510	+	0.278011i
$787$	4.50000	+	2.59808i	0.160408	+	0.0926114i	0.578055	−	0.815998i	$-0.303812\pi$
$787$	4.50000	+	2.59808i	0.160408	+	0.0926114i	−0.417647	+	0.908609i	$0.637145\pi$
$788$		0			0
$789$	−30.0000			−1.06803
$790$	−9.00000	−	15.5885i	−0.320206	−	0.554612i
$791$	45.0000			1.60002
$792$	−4.50000	+	2.59808i	−0.159901	+	0.0923186i
$793$		0			0
$794$	−5.50000	+	9.52628i	−0.195188	+	0.338075i
$795$	−4.50000	+	7.79423i	−0.159599	+	0.276433i
$796$	12.5000	+	21.6506i	0.443051	+	0.767386i
$797$	−7.50000	+	12.9904i	−0.265664	+	0.460143i	−0.967737	−	0.251961i	$-0.918924\pi$
$797$	−7.50000	+	12.9904i	−0.265664	+	0.460143i	0.702074	+	0.712104i	$0.252258\pi$
$798$	−37.5000	+	4.33013i	−1.32749	+	0.153285i
$799$	−13.5000	−	23.3827i	−0.477596	−	0.827220i
$800$	−1.00000	+	1.73205i	−0.0353553	+	0.0612372i
$801$	22.5000	+	38.9711i	0.794998	+	1.37698i
$802$	−7.50000	−	12.9904i	−0.264834	−	0.458706i
$803$			19.0526i			0.672350i
$804$	6.00000			0.211604
$805$	15.0000	−	25.9808i	0.528681	−	0.915702i
$806$		0			0
$807$	4.50000	+	2.59808i	0.158408	+	0.0914566i
$808$	7.50000	+	4.33013i	0.263849	+	0.152333i
$809$		−	6.92820i		−	0.243583i	−0.992556	−	0.121791i	$-0.961136\pi$
$809$		−	6.92820i		−	0.243583i	0.992556	−	0.121791i	$-0.0388639\pi$
$810$	13.5000	−	7.79423i	0.474342	−	0.273861i
$811$	−4.50000	+	2.59808i	−0.158016	+	0.0912308i	−0.576923	−	0.816798i	$-0.695747\pi$
$811$	−4.50000	+	2.59808i	−0.158016	+	0.0912308i	0.418907	+	0.908029i	$0.362413\pi$
$812$	−15.0000			−0.526397
$813$	−10.5000	−	6.06218i	−0.368251	−	0.212610i
$814$		0			0
$815$	6.00000	−	3.46410i	0.210171	−	0.121342i
$816$	−4.50000	+	7.79423i	−0.157532	+	0.272853i
$817$	−32.0000	−	13.8564i	−1.11954	−	0.484774i
$818$			13.8564i			0.484478i
$819$		0			0
$820$	13.5000	+	7.79423i	0.471440	+	0.272186i
$821$	−16.5000	−	9.52628i	−0.575854	−	0.332469i	0.183630	−	0.982995i	$-0.441215\pi$
$821$	−16.5000	−	9.52628i	−0.575854	−	0.332469i	−0.759484	+	0.650526i	$0.774548\pi$
$822$	−4.50000	+	7.79423i	−0.156956	+	0.271855i
$823$	−32.0000			−1.11545			−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000			−1.11545			−0.557725	+	0.830026i	$0.688326\pi$
$824$	−7.50000	−	4.33013i	−0.261275	−	0.150847i
$825$	6.00000			0.208893
$826$	7.50000	−	12.9904i	0.260958	−	0.451993i
$827$	−7.50000	−	12.9904i	−0.260801	−	0.451720i	0.705654	−	0.708556i	$-0.250653\pi$
$827$	−7.50000	−	12.9904i	−0.260801	−	0.451720i	−0.966455	+	0.256836i	$0.917320\pi$
$828$			10.3923i			0.361158i
$829$		−	13.8564i		−	0.481253i	−0.970618	−	0.240626i	$-0.922647\pi$
$829$		−	13.8564i		−	0.481253i	0.970618	−	0.240626i	$-0.0773529\pi$
$830$	−4.50000	+	7.79423i	−0.156197	+	0.270542i
$831$	−28.5000	+	16.4545i	−0.988654	+	0.570800i
$832$		0			0
$833$	81.0000	−	46.7654i	2.80648	−	1.62032i
$834$		−	6.92820i		−	0.239904i
$835$	18.0000	−	10.3923i	0.622916	−	0.359641i
$836$	−7.50000	+	0.866025i	−0.259393	+	0.0299521i
$837$	22.5000	−	38.9711i	0.777714	−	1.34704i
$838$	16.5000	+	9.52628i	0.569983	+	0.329080i
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$	7.50000	−	12.9904i	0.258775	−	0.448211i
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$			27.7128i			0.955047i
$843$	40.5000	+	23.3827i	1.39489	+	0.805342i
$844$	19.5000	−	11.2583i	0.671218	−	0.387528i
$845$	19.5000	−	11.2583i	0.670820	−	0.387298i
$846$	−13.5000	−	7.79423i	−0.464140	−	0.267971i
$847$	−40.0000			−1.37442
$848$	−1.50000	−	2.59808i	−0.0515102	−	0.0892183i
$849$	19.5000	−	11.2583i	0.669238	−	0.386385i
$850$	9.00000	−	5.19615i	0.308697	−	0.178227i
$851$		0			0
$852$	−22.5000	−	12.9904i	−0.770837	−	0.445043i
$853$	26.0000			0.890223			0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000			0.890223			0.445112	+	0.895475i	$0.353164\pi$
$854$	−35.0000			−1.19768
$855$	22.5000	−	2.59808i	0.769484	−	0.0888523i
$856$	12.0000			0.410152
$857$	−42.0000			−1.43469			−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000			−1.43469			−0.717346	+	0.696717i	$0.754643\pi$
$858$		0			0
$859$	−44.0000			−1.50126			−0.750630	−	0.660722i	$-0.770250\pi$
$859$	−44.0000			−1.50126			−0.750630	+	0.660722i	$0.770250\pi$
$860$	12.0000	−	6.92820i	0.409197	−	0.236250i
$861$	67.5000	+	38.9711i	2.30039	+	1.32813i
$862$	−1.50000	−	2.59808i	−0.0510902	−	0.0884908i
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$			5.19615i			0.176777i
$865$	−9.00000	+	5.19615i	−0.306009	+	0.176674i
$866$	19.5000	−	11.2583i	0.662637	−	0.382574i
$867$	15.0000	−	8.66025i	0.509427	−	0.294118i
$868$		−	43.3013i		−	1.46974i
$869$	−9.00000	−	15.5885i	−0.305304	−	0.528802i
$870$	9.00000			0.305129
$871$		0			0
$872$	13.5000	+	7.79423i	0.457168	+	0.263946i
$873$			20.7846i			0.703452i
$874$	−6.00000	+	13.8564i	−0.202953	+	0.468700i
$875$	−52.5000	+	30.3109i	−1.77482	+	1.02470i
$876$	16.5000	+	9.52628i	0.557483	+	0.321863i
$877$	−40.5000	+	23.3827i	−1.36759	+	0.789577i	−0.990620	−	0.136649i	$-0.956367\pi$
$877$	−40.5000	+	23.3827i	−1.36759	+	0.789577i	−0.376968	+	0.926226i	$0.623033\pi$
$878$			24.2487i			0.818354i
$879$	−13.5000	−	7.79423i	−0.455344	−	0.262893i
$880$	1.50000	−	2.59808i	0.0505650	−	0.0875811i
$881$			20.7846i			0.700251i	0.936703	+	0.350126i	$0.113861\pi$
$881$			20.7846i			0.700251i	−0.936703	+	0.350126i	$0.886139\pi$
$882$	27.0000	−	46.7654i	0.909137	−	1.57467i
$883$	14.5000	+	25.1147i	0.487964	+	0.845178i	0.999904	−	0.0138428i	$-0.00440645\pi$
$883$	14.5000	+	25.1147i	0.487964	+	0.845178i	−0.511940	+	0.859021i	$0.671073\pi$
$884$		0			0
$885$	−4.50000	+	7.79423i	−0.151266	+	0.262000i
$886$	−19.5000	−	11.2583i	−0.655115	−	0.378231i
$887$	−24.0000			−0.805841			−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000			−0.805841			−0.402921	+	0.915235i	$0.632005\pi$
$888$		0			0
$889$	−22.5000	−	12.9904i	−0.754626	−	0.435683i
$890$	−22.5000	−	12.9904i	−0.754202	−	0.435439i
$891$	13.5000	−	7.79423i	0.452267	−	0.261116i
$892$		−	3.46410i		−	0.115987i
$893$	−13.5000	−	18.1865i	−0.451760	−	0.608589i
$894$	16.5000	+	28.5788i	0.551843	+	0.955819i
$895$	18.0000	−	10.3923i	0.601674	−	0.347376i
$896$	2.50000	+	4.33013i	0.0835191	+	0.144659i
$897$		0			0
$898$	6.00000			0.200223
$899$	22.5000	−	12.9904i	0.750417	−	0.433253i
$900$	3.00000	−	5.19615i	0.100000	−	0.173205i
$901$			15.5885i			0.519327i
$902$	13.5000	+	7.79423i	0.449501	+	0.259519i
$903$	60.0000	−	34.6410i	1.99667	−	1.15278i
$904$	4.50000	−	7.79423i	0.149668	−	0.259232i
$905$	7.50000	−	12.9904i	0.249308	−	0.431815i
$906$	10.5000	+	18.1865i	0.348839	+	0.604207i
$907$		−	45.0333i		−	1.49531i	−0.664089	−	0.747653i	$-0.731180\pi$
$907$		−	45.0333i		−	1.49531i	0.664089	−	0.747653i	$-0.268820\pi$
$908$	−13.5000	−	23.3827i	−0.448013	−	0.775982i
$909$	−22.5000	−	12.9904i	−0.746278	−	0.430864i
$910$		0			0
$911$	−7.50000	−	12.9904i	−0.248486	−	0.430391i	0.714620	−	0.699513i	$-0.246600\pi$
$911$	−7.50000	−	12.9904i	−0.248486	−	0.430391i	−0.963106	+	0.269122i	$0.913266\pi$
$912$	−3.00000	+	6.92820i	−0.0993399	+	0.229416i
$913$	−4.50000	+	7.79423i	−0.148928	+	0.257951i
$914$	18.5000	+	32.0429i	0.611926	+	1.05989i
$915$	21.0000			0.694239
$916$	14.5000	−	25.1147i	0.479093	−	0.829814i
$917$	−22.5000	−	12.9904i	−0.743015	−	0.428980i
$918$	13.5000	−	23.3827i	0.445566	−	0.771744i
$919$	52.0000			1.71532			0.857661	−	0.514216i	$-0.171917\pi$
$919$	52.0000			1.71532			0.857661	+	0.514216i	$0.171917\pi$
$920$	−3.00000	−	5.19615i	−0.0989071	−	0.171312i
$921$	4.50000	−	7.79423i	0.148280	−	0.256829i
$922$		−	41.5692i		−	1.36901i
$923$		0			0
$924$	7.50000	−	12.9904i	0.246732	−	0.427352i
$925$		0			0
$926$	−2.50000	+	4.33013i	−0.0821551	+	0.142297i
$927$	22.5000	+	12.9904i	0.738997	+	0.426660i
$928$	−1.50000	+	2.59808i	−0.0492399	+	0.0852860i
$929$			55.4256i			1.81846i	0.416299	+	0.909228i	$0.363327\pi$
$929$			55.4256i			1.81846i	−0.416299	+	0.909228i	$0.636673\pi$
$930$			25.9808i			0.851943i
$931$	63.0000	−	46.7654i	2.06474	−	1.53267i
$932$	−10.5000	−	6.06218i	−0.343939	−	0.198573i
$933$	−19.5000	+	33.7750i	−0.638401	+	1.10574i
$934$		−	31.1769i		−	1.02014i
$935$	−13.5000	+	7.79423i	−0.441497	+	0.254899i
$936$		0			0
$937$	−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	$0.955927\pi$
$938$	−15.0000	+	8.66025i	−0.489767	+	0.282767i
$939$	−25.5000	−	14.7224i	−0.832161	−	0.480448i
$940$	9.00000			0.293548
$941$	−30.0000			−0.977972			−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000			−0.977972			−0.488986	+	0.872292i	$0.662633\pi$
$942$	−10.5000	+	6.06218i	−0.342108	+	0.197516i
$943$	27.0000	−	15.5885i	0.879241	−	0.507630i
$944$	−1.50000	−	2.59808i	−0.0488208	−	0.0845602i
$945$	−22.5000	+	38.9711i	−0.731925	+	1.26773i
$946$	12.0000	−	6.92820i	0.390154	−	0.225255i
$947$			17.3205i			0.562841i	0.959585	+	0.281420i	$0.0908056\pi$
$947$			17.3205i			0.562841i	−0.959585	+	0.281420i	$0.909194\pi$
$948$	−18.0000			−0.584613
$949$		0			0
$950$	7.00000	−	5.19615i	0.227110	−	0.168585i
$951$	40.5000	+	23.3827i	1.31330	+	0.758236i
$952$		−	25.9808i		−	0.842041i
$953$	4.50000	−	7.79423i	0.145769	−	0.252480i	−0.783890	−	0.620899i	$-0.786768\pi$
$953$	4.50000	−	7.79423i	0.145769	−	0.252480i	0.929660	+	0.368419i	$0.120101\pi$
$954$	4.50000	+	7.79423i	0.145693	+	0.252347i
$955$	7.50000	−	12.9904i	0.242694	−	0.420359i
$956$	10.5000	+	6.06218i	0.339594	+	0.196065i
$957$	9.00000			0.290929
$958$	28.5000	+	16.4545i	0.920793	+	0.531620i
$959$		−	25.9808i		−	0.838963i
$960$	−1.50000	−	2.59808i	−0.0484123	−	0.0838525i
$961$	22.0000	+	38.1051i	0.709677	+	1.22920i
$962$		0			0
$963$	−36.0000			−1.16008
$964$	1.50000	+	0.866025i	0.0483117	+	0.0278928i
$965$	1.50000	−	2.59808i	0.0482867	−	0.0836350i
$966$	−15.0000	−	25.9808i	−0.482617	−	0.835917i
$967$	−15.5000	−	26.8468i	−0.498446	−	0.863334i	0.501552	−	0.865128i	$-0.332763\pi$
$967$	−15.5000	−	26.8468i	−0.498446	−	0.863334i	−0.999998	+	0.00179302i	$0.999429\pi$
$968$	−4.00000	+	6.92820i	−0.128565	+	0.222681i
$969$	31.5000	−	23.3827i	1.01193	−	0.751160i
$970$	−6.00000	−	10.3923i	−0.192648	−	0.333677i
$971$	−22.5000	+	38.9711i	−0.722059	+	1.25064i	0.238114	+	0.971237i	$0.423471\pi$
$971$	−22.5000	+	38.9711i	−0.722059	+	1.25064i	−0.960173	+	0.279406i	$0.909862\pi$
$972$		−	15.5885i		−	0.500000i
$973$	10.0000	+	17.3205i	0.320585	+	0.555270i
$974$		−	17.3205i		−	0.554985i
$975$		0			0
$976$	−3.50000	+	6.06218i	−0.112032	+	0.194046i
$977$	−1.50000	+	2.59808i	−0.0479893	+	0.0831198i	−0.889022	−	0.457864i	$-0.848615\pi$
$977$	−1.50000	+	2.59808i	−0.0479893	+	0.0831198i	0.841033	+	0.540984i	$0.181948\pi$
$978$		−	6.92820i		−	0.221540i
$979$	−22.5000	−	12.9904i	−0.719103	−	0.415174i
$980$			31.1769i			0.995910i
$981$	−40.5000	−	23.3827i	−1.29307	−	0.746552i
$982$	13.5000	−	7.79423i	0.430802	−	0.248724i
$983$		0			0			−	1.00000i	$-0.5\pi$
$983$		0			0				1.00000i	$0.5\pi$
$984$	13.5000	−	7.79423i	0.430364	−	0.248471i
$985$		0			0
$986$	13.5000	−	7.79423i	0.429928	−	0.248219i
$987$	45.0000			1.43237
$988$		0			0
$989$		−	27.7128i		−	0.881216i
$990$	−4.50000	+	7.79423i	−0.143019	+	0.247717i
$991$	−13.5000	−	7.79423i	−0.428842	−	0.247592i	0.270011	−	0.962857i	$-0.412973\pi$
$991$	−13.5000	−	7.79423i	−0.428842	−	0.247592i	−0.698853	+	0.715265i	$0.746306\pi$
$992$	−7.50000	−	4.33013i	−0.238125	−	0.137482i
$993$	22.5000	+	38.9711i	0.714016	+	1.23671i
$994$	75.0000			2.37886
$995$	37.5000	+	21.6506i	1.18883	+	0.686371i
$996$	4.50000	+	7.79423i	0.142588	+	0.246970i
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	−0.699457	−	0.714675i	$-0.746575\pi$
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	0.968655	+	0.248410i	$0.0799082\pi$
$998$	2.50000	+	4.33013i	0.0791361	+	0.137068i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.n.c.293.1	yes	2
3.2	odd	2		1026.2.n.a.179.1		2
9.2	odd	6		342.2.j.b.65.1	✓	2
9.7	even	3		1026.2.j.b.521.1		2
19.12	odd	6		342.2.j.b.221.1	yes	2
57.50	even	6		1026.2.j.b.449.1		2
171.88	odd	6		1026.2.n.a.791.1		2
171.164	even	6	inner	342.2.n.c.335.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.j.b.65.1	✓	2	9.2	odd	6
342.2.j.b.221.1	yes	2	19.12	odd	6
342.2.n.c.293.1	yes	2	1.1	even	1	trivial
342.2.n.c.335.1	yes	2	171.164	even	6	inner
1026.2.j.b.449.1		2	57.50	even	6
1026.2.j.b.521.1		2	9.7	even	3
1026.2.n.a.179.1		2	3.2	odd	2
1026.2.n.a.791.1		2	171.88	odd	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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.73205i q^{3} +1.00000 q^{4} +(1.50000 - 0.866025i) q^{5} -1.73205i q^{6} +(2.50000 + 4.33013i) q^{7} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.73205i q^{3} +1.00000 q^{4} +(1.50000 - 0.866025i) q^{5} -1.73205i q^{6} +(2.50000 + 4.33013i) q^{7} +1.00000 q^{8} -3.00000 q^{9} +(1.50000 - 0.866025i) q^{10} +(1.50000 - 0.866025i) q^{11} -1.73205i q^{12} +(2.50000 + 4.33013i) q^{14} +(-1.50000 - 2.59808i) q^{15} +1.00000 q^{16} +(-4.50000 - 2.59808i) q^{17} -3.00000 q^{18} +(-4.00000 - 1.73205i) q^{19} +(1.50000 - 0.866025i) q^{20} +(7.50000 - 4.33013i) q^{21} +(1.50000 - 0.866025i) q^{22} -3.46410i q^{23} -1.73205i q^{24} +(-1.00000 + 1.73205i) q^{25} +5.19615i q^{27} +(2.50000 + 4.33013i) q^{28} +(-1.50000 + 2.59808i) q^{29} +(-1.50000 - 2.59808i) q^{30} +(-7.50000 - 4.33013i) q^{31} +1.00000 q^{32} +(-1.50000 - 2.59808i) q^{33} +(-4.50000 - 2.59808i) q^{34} +(7.50000 + 4.33013i) q^{35} -3.00000 q^{36} +(-4.00000 - 1.73205i) q^{38} +(1.50000 - 0.866025i) q^{40} +(4.50000 + 7.79423i) q^{41} +(7.50000 - 4.33013i) q^{42} +8.00000 q^{43} +(1.50000 - 0.866025i) q^{44} +(-4.50000 + 2.59808i) q^{45} -3.46410i q^{46} +(4.50000 + 2.59808i) q^{47} -1.73205i q^{48} +(-9.00000 + 15.5885i) q^{49} +(-1.00000 + 1.73205i) q^{50} +(-4.50000 + 7.79423i) q^{51} +(-1.50000 - 2.59808i) q^{53} +5.19615i q^{54} +(1.50000 - 2.59808i) q^{55} +(2.50000 + 4.33013i) q^{56} +(-3.00000 + 6.92820i) q^{57} +(-1.50000 + 2.59808i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(-1.50000 - 2.59808i) q^{60} +(-3.50000 + 6.06218i) q^{61} +(-7.50000 - 4.33013i) q^{62} +(-7.50000 - 12.9904i) q^{63} +1.00000 q^{64} +(-1.50000 - 2.59808i) q^{66} +3.46410i q^{67} +(-4.50000 - 2.59808i) q^{68} -6.00000 q^{69} +(7.50000 + 4.33013i) q^{70} +(7.50000 - 12.9904i) q^{71} -3.00000 q^{72} +(-5.50000 + 9.52628i) q^{73} +(3.00000 + 1.73205i) q^{75} +(-4.00000 - 1.73205i) q^{76} +(7.50000 + 4.33013i) q^{77} -10.3923i q^{79} +(1.50000 - 0.866025i) q^{80} +9.00000 q^{81} +(4.50000 + 7.79423i) q^{82} +(-4.50000 + 2.59808i) q^{83} +(7.50000 - 4.33013i) q^{84} -9.00000 q^{85} +8.00000 q^{86} +(4.50000 + 2.59808i) q^{87} +(1.50000 - 0.866025i) q^{88} +(-7.50000 - 12.9904i) q^{89} +(-4.50000 + 2.59808i) q^{90} -3.46410i q^{92} +(-7.50000 + 12.9904i) q^{93} +(4.50000 + 2.59808i) q^{94} +(-7.50000 + 0.866025i) q^{95} -1.73205i q^{96} -6.92820i q^{97} +(-9.00000 + 15.5885i) q^{98} +(-4.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} + 3 q^{5} + 5 q^{7} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 + 3 * q^5 + 5 * q^7 + 2 * q^8 - 6 * q^9	\( 2 q + 2 q^{2} + 2 q^{4} + 3 q^{5} + 5 q^{7} + 2 q^{8} - 6 q^{9} + 3 q^{10} + 3 q^{11} + 5 q^{14} - 3 q^{15} + 2 q^{16} - 9 q^{17} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 15 q^{21} + 3 q^{22} - 2 q^{25} + 5 q^{28} - 3 q^{29} - 3 q^{30} - 15 q^{31} + 2 q^{32} - 3 q^{33} - 9 q^{34} + 15 q^{35} - 6 q^{36} - 8 q^{38} + 3 q^{40} + 9 q^{41} + 15 q^{42} + 16 q^{43} + 3 q^{44} - 9 q^{45} + 9 q^{47} - 18 q^{49} - 2 q^{50} - 9 q^{51} - 3 q^{53} + 3 q^{55} + 5 q^{56} - 6 q^{57} - 3 q^{58} - 3 q^{59} - 3 q^{60} - 7 q^{61} - 15 q^{62} - 15 q^{63} + 2 q^{64} - 3 q^{66} - 9 q^{68} - 12 q^{69} + 15 q^{70} + 15 q^{71} - 6 q^{72} - 11 q^{73} + 6 q^{75} - 8 q^{76} + 15 q^{77} + 3 q^{80} + 18 q^{81} + 9 q^{82} - 9 q^{83} + 15 q^{84} - 18 q^{85} + 16 q^{86} + 9 q^{87} + 3 q^{88} - 15 q^{89} - 9 q^{90} - 15 q^{93} + 9 q^{94} - 15 q^{95} - 18 q^{98} - 9 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 + 3 * q^5 + 5 * q^7 + 2 * q^8 - 6 * q^9 + 3 * q^10 + 3 * q^11 + 5 * q^14 - 3 * q^15 + 2 * q^16 - 9 * q^17 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 15 * q^21 + 3 * q^22 - 2 * q^25 + 5 * q^28 - 3 * q^29 - 3 * q^30 - 15 * q^31 + 2 * q^32 - 3 * q^33 - 9 * q^34 + 15 * q^35 - 6 * q^36 - 8 * q^38 + 3 * q^40 + 9 * q^41 + 15 * q^42 + 16 * q^43 + 3 * q^44 - 9 * q^45 + 9 * q^47 - 18 * q^49 - 2 * q^50 - 9 * q^51 - 3 * q^53 + 3 * q^55 + 5 * q^56 - 6 * q^57 - 3 * q^58 - 3 * q^59 - 3 * q^60 - 7 * q^61 - 15 * q^62 - 15 * q^63 + 2 * q^64 - 3 * q^66 - 9 * q^68 - 12 * q^69 + 15 * q^70 + 15 * q^71 - 6 * q^72 - 11 * q^73 + 6 * q^75 - 8 * q^76 + 15 * q^77 + 3 * q^80 + 18 * q^81 + 9 * q^82 - 9 * q^83 + 15 * q^84 - 18 * q^85 + 16 * q^86 + 9 * q^87 + 3 * q^88 - 15 * q^89 - 9 * q^90 - 15 * q^93 + 9 * q^94 - 15 * q^95 - 18 * q^98 - 9 * q^99

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