LMFDB - Embedded newform 93.2.g.c.68.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(26,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, 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("93.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.g (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:	$0.742608738798$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	93.68
Dual form			93.2.g.c.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205i q^{2} +(1.50000 + 0.866025i) q^{3} -1.00000 q^{4} +(-1.50000 - 0.866025i) q^{5} +(1.50000 - 2.59808i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q-1.73205i q^{2} +(1.50000 + 0.866025i) q^{3} -1.00000 q^{4} +(-1.50000 - 0.866025i) q^{5} +(1.50000 - 2.59808i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(-1.50000 - 0.866025i) q^{12} +(-4.50000 - 2.59808i) q^{13} +(1.50000 - 0.866025i) q^{14} +(-1.50000 - 2.59808i) q^{15} -5.00000 q^{16} +(1.50000 + 2.59808i) q^{17} +(4.50000 - 2.59808i) q^{18} +(2.50000 + 4.33013i) q^{19} +(1.50000 + 0.866025i) q^{20} +1.73205i q^{21} +(4.50000 + 2.59808i) q^{22} +(1.50000 - 2.59808i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(-4.50000 + 7.79423i) q^{26} +5.19615i q^{27} +(-0.500000 - 0.866025i) q^{28} +6.00000 q^{29} +(-4.50000 + 2.59808i) q^{30} +(2.00000 - 5.19615i) q^{31} +5.19615i q^{32} +(-4.50000 + 2.59808i) q^{33} +(4.50000 - 2.59808i) q^{34} -1.73205i q^{35} +(-1.50000 - 2.59808i) q^{36} +(-4.50000 + 2.59808i) q^{37} +(7.50000 - 4.33013i) q^{38} +(-4.50000 - 7.79423i) q^{39} +(-1.50000 + 2.59808i) q^{40} +(-7.50000 - 4.33013i) q^{41} +3.00000 q^{42} +(1.50000 - 0.866025i) q^{43} +(1.50000 - 2.59808i) q^{44} -5.19615i q^{45} -10.3923i q^{47} +(-7.50000 - 4.33013i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-3.00000 + 1.73205i) q^{50} +5.19615i q^{51} +(4.50000 + 2.59808i) q^{52} +(1.50000 - 2.59808i) q^{53} +9.00000 q^{54} +(4.50000 - 2.59808i) q^{55} +(1.50000 - 0.866025i) q^{56} +8.66025i q^{57} -10.3923i q^{58} +(-7.50000 + 4.33013i) q^{59} +(1.50000 + 2.59808i) q^{60} +13.8564i q^{61} +(-9.00000 - 3.46410i) q^{62} +(-1.50000 + 2.59808i) q^{63} -1.00000 q^{64} +(4.50000 + 7.79423i) q^{65} +(4.50000 + 7.79423i) q^{66} +(5.50000 - 9.52628i) q^{67} +(-1.50000 - 2.59808i) q^{68} -3.00000 q^{70} +(1.50000 + 0.866025i) q^{71} +(4.50000 - 2.59808i) q^{72} +(7.50000 + 4.33013i) q^{73} +(4.50000 + 7.79423i) q^{74} -3.46410i q^{75} +(-2.50000 - 4.33013i) q^{76} -3.00000 q^{77} +(-13.5000 + 7.79423i) q^{78} +(7.50000 - 4.33013i) q^{79} +(7.50000 + 4.33013i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-7.50000 + 12.9904i) q^{82} +(4.50000 - 7.79423i) q^{83} -1.73205i q^{84} -5.19615i q^{85} +(-1.50000 - 2.59808i) q^{86} +(9.00000 + 5.19615i) q^{87} +(4.50000 + 2.59808i) q^{88} -6.00000 q^{89} -9.00000 q^{90} -5.19615i q^{91} +(7.50000 - 6.06218i) q^{93} -18.0000 q^{94} -8.66025i q^{95} +(-4.50000 + 7.79423i) q^{96} -10.0000 q^{97} +(-9.00000 - 5.19615i) q^{98} -9.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} - 2 q^{4} - 3 q^{5} + 3 q^{6} + q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 - 2 * q^4 - 3 * q^5 + 3 * q^6 + q^7 + 3 * q^9	$ 2 q + 3 q^{3} - 2 q^{4} - 3 q^{5} + 3 q^{6} + q^{7} + 3 q^{9} - 3 q^{10} - 3 q^{11} - 3 q^{12} - 9 q^{13} + 3 q^{14} - 3 q^{15} - 10 q^{16} + 3 q^{17} + 9 q^{18} + 5 q^{19} + 3 q^{20} + 9 q^{22} + 3 q^{24} - 2 q^{25} - 9 q^{26} - q^{28} + 12 q^{29} - 9 q^{30} + 4 q^{31} - 9 q^{33} + 9 q^{34} - 3 q^{36} - 9 q^{37} + 15 q^{38} - 9 q^{39} - 3 q^{40} - 15 q^{41} + 6 q^{42} + 3 q^{43} + 3 q^{44} - 15 q^{48} + 6 q^{49} - 6 q^{50} + 9 q^{52} + 3 q^{53} + 18 q^{54} + 9 q^{55} + 3 q^{56} - 15 q^{59} + 3 q^{60} - 18 q^{62} - 3 q^{63} - 2 q^{64} + 9 q^{65} + 9 q^{66} + 11 q^{67} - 3 q^{68} - 6 q^{70} + 3 q^{71} + 9 q^{72} + 15 q^{73} + 9 q^{74} - 5 q^{76} - 6 q^{77} - 27 q^{78} + 15 q^{79} + 15 q^{80} - 9 q^{81} - 15 q^{82} + 9 q^{83} - 3 q^{86} + 18 q^{87} + 9 q^{88} - 12 q^{89} - 18 q^{90} + 15 q^{93} - 36 q^{94} - 9 q^{96} - 20 q^{97} - 18 q^{98} - 18 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 - 2 * q^4 - 3 * q^5 + 3 * q^6 + q^7 + 3 * q^9 - 3 * q^10 - 3 * q^11 - 3 * q^12 - 9 * q^13 + 3 * q^14 - 3 * q^15 - 10 * q^16 + 3 * q^17 + 9 * q^18 + 5 * q^19 + 3 * q^20 + 9 * q^22 + 3 * q^24 - 2 * q^25 - 9 * q^26 - q^28 + 12 * q^29 - 9 * q^30 + 4 * q^31 - 9 * q^33 + 9 * q^34 - 3 * q^36 - 9 * q^37 + 15 * q^38 - 9 * q^39 - 3 * q^40 - 15 * q^41 + 6 * q^42 + 3 * q^43 + 3 * q^44 - 15 * q^48 + 6 * q^49 - 6 * q^50 + 9 * q^52 + 3 * q^53 + 18 * q^54 + 9 * q^55 + 3 * q^56 - 15 * q^59 + 3 * q^60 - 18 * q^62 - 3 * q^63 - 2 * q^64 + 9 * q^65 + 9 * q^66 + 11 * q^67 - 3 * q^68 - 6 * q^70 + 3 * q^71 + 9 * q^72 + 15 * q^73 + 9 * q^74 - 5 * q^76 - 6 * q^77 - 27 * q^78 + 15 * q^79 + 15 * q^80 - 9 * q^81 - 15 * q^82 + 9 * q^83 - 3 * q^86 + 18 * q^87 + 9 * q^88 - 12 * q^89 - 18 * q^90 + 15 * q^93 - 36 * q^94 - 9 * q^96 - 20 * q^97 - 18 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	1.73205i		−	1.22474i	−0.790569	−	0.612372i	$-0.790215\pi$
$2$		−	1.73205i		−	1.22474i	0.790569	−	0.612372i	$-0.209785\pi$
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$	−1.00000			−0.500000
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	0.125567	−	0.992085i	$-0.459925\pi$
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	−0.796387	+	0.604787i	$0.793258\pi$
$6$	1.50000	−	2.59808i	0.612372	−	1.06066i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	0.944911	−	0.327327i	$-0.106148\pi$
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$		−	1.73205i		−	0.612372i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$	−1.50000	−	0.866025i	−0.433013	−	0.250000i
$13$	−4.50000	−	2.59808i	−1.24808	−	0.720577i	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−4.50000	−	2.59808i	−1.24808	−	0.720577i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	1.50000	−	0.866025i	0.400892	−	0.231455i
$15$	−1.50000	−	2.59808i	−0.387298	−	0.670820i
$16$	−5.00000			−1.25000
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$	4.50000	−	2.59808i	1.06066	−	0.612372i
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$	1.50000	+	0.866025i	0.335410	+	0.193649i
$21$			1.73205i			0.377964i
$22$	4.50000	+	2.59808i	0.959403	+	0.553912i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	1.50000	−	2.59808i	0.306186	−	0.530330i
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$	−4.50000	+	7.79423i	−0.882523	+	1.52857i
$27$			5.19615i			1.00000i
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	−4.50000	+	2.59808i	−0.821584	+	0.474342i
$31$	2.00000	−	5.19615i	0.359211	−	0.933257i
$31$	2.00000	−	5.19615i	0.359211	−	0.933257i
$32$			5.19615i			0.918559i
$33$	−4.50000	+	2.59808i	−0.783349	+	0.452267i
$34$	4.50000	−	2.59808i	0.771744	−	0.445566i
$35$		−	1.73205i		−	0.292770i
$36$	−1.50000	−	2.59808i	−0.250000	−	0.433013i
$37$	−4.50000	+	2.59808i	−0.739795	+	0.427121i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−4.50000	+	2.59808i	−0.739795	+	0.427121i	0.0821995	+	0.996616i	$0.473806\pi$
$38$	7.50000	−	4.33013i	1.21666	−	0.702439i
$39$	−4.50000	−	7.79423i	−0.720577	−	1.24808i
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$	−7.50000	−	4.33013i	−1.17130	−	0.676252i	−0.217317	−	0.976101i	$-0.569730\pi$
$41$	−7.50000	−	4.33013i	−1.17130	−	0.676252i	−0.953987	+	0.299849i	$0.903064\pi$
$42$	3.00000			0.462910
$43$	1.50000	−	0.866025i	0.228748	−	0.132068i	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	1.50000	−	0.866025i	0.228748	−	0.132068i	0.609994	+	0.792406i	$0.291172\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$		−	5.19615i		−	0.774597i
$46$		0			0
$47$		−	10.3923i		−	1.51587i	−0.652328	−	0.757937i	$-0.726208\pi$
$47$		−	10.3923i		−	1.51587i	0.652328	−	0.757937i	$-0.273792\pi$
$48$	−7.50000	−	4.33013i	−1.08253	−	0.625000i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$	−3.00000	+	1.73205i	−0.424264	+	0.244949i
$51$			5.19615i			0.727607i
$52$	4.50000	+	2.59808i	0.624038	+	0.360288i
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	−0.744423	−	0.667708i	$-0.767275\pi$
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	0.950464	+	0.310835i	$0.100609\pi$
$54$	9.00000			1.22474
$55$	4.50000	−	2.59808i	0.606780	−	0.350325i
$56$	1.50000	−	0.866025i	0.200446	−	0.115728i
$57$			8.66025i			1.14708i
$58$		−	10.3923i		−	1.36458i
$59$	−7.50000	+	4.33013i	−0.976417	+	0.563735i	−0.901186	−	0.433432i	$-0.857303\pi$
$59$	−7.50000	+	4.33013i	−0.976417	+	0.563735i	−0.0752304	+	0.997166i	$0.523969\pi$
$60$	1.50000	+	2.59808i	0.193649	+	0.335410i
$61$			13.8564i			1.77413i	0.461644	+	0.887066i	$0.347260\pi$
$61$			13.8564i			1.77413i	−0.461644	+	0.887066i	$0.652740\pi$
$62$	−9.00000	−	3.46410i	−1.14300	−	0.439941i
$63$	−1.50000	+	2.59808i	−0.188982	+	0.327327i
$64$	−1.00000			−0.125000
$65$	4.50000	+	7.79423i	0.558156	+	0.966755i
$66$	4.50000	+	7.79423i	0.553912	+	0.959403i
$67$	5.50000	−	9.52628i	0.671932	−	1.16382i	−0.305424	−	0.952217i	$-0.598798\pi$
$67$	5.50000	−	9.52628i	0.671932	−	1.16382i	0.977356	−	0.211604i	$-0.0678686\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$		0			0
$70$	−3.00000			−0.358569
$71$	1.50000	+	0.866025i	0.178017	+	0.102778i	0.586361	−	0.810050i	$-0.300560\pi$
$71$	1.50000	+	0.866025i	0.178017	+	0.102778i	−0.408344	+	0.912828i	$0.633893\pi$
$72$	4.50000	−	2.59808i	0.530330	−	0.306186i
$73$	7.50000	+	4.33013i	0.877809	+	0.506803i	0.869935	−	0.493166i	$-0.164160\pi$
$73$	7.50000	+	4.33013i	0.877809	+	0.506803i	0.00787336	+	0.999969i	$0.497494\pi$
$74$	4.50000	+	7.79423i	0.523114	+	0.906061i
$75$		−	3.46410i		−	0.400000i
$76$	−2.50000	−	4.33013i	−0.286770	−	0.496700i
$77$	−3.00000			−0.341882
$78$	−13.5000	+	7.79423i	−1.52857	+	0.882523i
$79$	7.50000	−	4.33013i	0.843816	−	0.487177i	−0.0147436	−	0.999891i	$-0.504693\pi$
$79$	7.50000	−	4.33013i	0.843816	−	0.487177i	0.858559	+	0.512714i	$0.171360\pi$
$80$	7.50000	+	4.33013i	0.838525	+	0.484123i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−7.50000	+	12.9904i	−0.828236	+	1.43455i
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	−0.506036	−	0.862512i	$-0.668890\pi$
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	0.999976	+	0.00698436i	$0.00222321\pi$
$84$		−	1.73205i		−	0.188982i
$85$		−	5.19615i		−	0.563602i
$86$	−1.50000	−	2.59808i	−0.161749	−	0.280158i
$87$	9.00000	+	5.19615i	0.964901	+	0.557086i
$88$	4.50000	+	2.59808i	0.479702	+	0.276956i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$	−9.00000			−0.948683
$91$		−	5.19615i		−	0.544705i
$92$		0			0
$93$	7.50000	−	6.06218i	0.777714	−	0.628619i
$94$	−18.0000			−1.85656
$95$		−	8.66025i		−	0.888523i
$96$	−4.50000	+	7.79423i	−0.459279	+	0.795495i
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$	−9.00000	−	5.19615i	−0.909137	−	0.524891i
$99$	−9.00000			−0.904534
$100$	1.00000	+	1.73205i	0.100000	+	0.173205i
$101$			13.8564i			1.37876i	0.724398	+	0.689382i	$0.242118\pi$
$101$			13.8564i			1.37876i	−0.724398	+	0.689382i	$0.757882\pi$
$102$	9.00000			0.891133
$103$	−0.500000	+	0.866025i	−0.0492665	+	0.0853320i	−0.889607	−	0.456727i	$-0.849022\pi$
$103$	−0.500000	+	0.866025i	−0.0492665	+	0.0853320i	0.840341	+	0.542059i	$0.182355\pi$
$104$	−4.50000	+	7.79423i	−0.441261	+	0.764287i
$105$	1.50000	−	2.59808i	0.146385	−	0.253546i
$106$	−4.50000	−	2.59808i	−0.437079	−	0.252347i
$107$	10.5000	−	6.06218i	1.01507	−	0.586053i	0.102400	−	0.994743i	$-0.467348\pi$
$107$	10.5000	−	6.06218i	1.01507	−	0.586053i	0.912673	+	0.408690i	$0.134014\pi$
$108$		−	5.19615i		−	0.500000i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$	−4.50000	−	7.79423i	−0.429058	−	0.743151i
$111$	−9.00000			−0.854242
$112$	−2.50000	−	4.33013i	−0.236228	−	0.409159i
$113$	10.5000	+	6.06218i	0.987757	+	0.570282i	0.904603	−	0.426255i	$-0.140167\pi$
$113$	10.5000	+	6.06218i	0.987757	+	0.570282i	0.0831539	+	0.996537i	$0.473501\pi$
$114$	15.0000			1.40488
$115$		0			0
$116$	−6.00000			−0.557086
$117$		−	15.5885i		−	1.44115i
$118$	7.50000	+	12.9904i	0.690431	+	1.19586i
$119$	−1.50000	+	2.59808i	−0.137505	+	0.238165i
$120$	−4.50000	+	2.59808i	−0.410792	+	0.237171i
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	24.0000			2.17286
$123$	−7.50000	−	12.9904i	−0.676252	−	1.17130i
$124$	−2.00000	+	5.19615i	−0.179605	+	0.466628i
$125$			12.1244i			1.08444i
$126$	4.50000	+	2.59808i	0.400892	+	0.231455i
$127$	1.50000	−	0.866025i	0.133103	−	0.0768473i	−0.431970	−	0.901888i	$-0.642181\pi$
$127$	1.50000	−	0.866025i	0.133103	−	0.0768473i	0.565073	+	0.825041i	$0.308848\pi$
$128$			12.1244i			1.07165i
$129$	3.00000			0.264135
$130$	13.5000	−	7.79423i	1.18403	−	0.683599i
$131$	−13.5000	+	7.79423i	−1.17950	+	0.680985i	−0.955899	−	0.293696i	$-0.905115\pi$
$131$	−13.5000	+	7.79423i	−1.17950	+	0.680985i	−0.223602	+	0.974681i	$0.571781\pi$
$132$	4.50000	−	2.59808i	0.391675	−	0.226134i
$133$	−2.50000	+	4.33013i	−0.216777	+	0.375470i
$134$	−16.5000	−	9.52628i	−1.42538	−	0.822945i
$135$	4.50000	−	7.79423i	0.387298	−	0.670820i
$136$	4.50000	−	2.59808i	0.385872	−	0.222783i
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	−0.794808	−	0.606861i	$-0.792428\pi$
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$138$		0			0
$139$			17.3205i			1.46911i	0.678551	+	0.734553i	$0.262608\pi$
$139$			17.3205i			1.46911i	−0.678551	+	0.734553i	$0.737392\pi$
$140$			1.73205i			0.146385i
$141$	9.00000	−	15.5885i	0.757937	−	1.31278i
$142$	1.50000	−	2.59808i	0.125877	−	0.218026i
$143$	13.5000	−	7.79423i	1.12893	−	0.651786i
$144$	−7.50000	−	12.9904i	−0.625000	−	1.08253i
$145$	−9.00000	−	5.19615i	−0.747409	−	0.431517i
$146$	7.50000	−	12.9904i	0.620704	−	1.07509i
$147$	9.00000	−	5.19615i	0.742307	−	0.428571i
$148$	4.50000	−	2.59808i	0.369898	−	0.213561i
$149$	4.50000	−	2.59808i	0.368654	−	0.212843i	−0.304216	−	0.952603i	$-0.598394\pi$
$149$	4.50000	−	2.59808i	0.368654	−	0.212843i	0.672870	+	0.739760i	$0.265061\pi$
$150$	−6.00000			−0.489898
$151$			3.46410i			0.281905i	0.990016	+	0.140952i	$0.0450164\pi$
$151$			3.46410i			0.281905i	−0.990016	+	0.140952i	$0.954984\pi$
$152$	7.50000	−	4.33013i	0.608330	−	0.351220i
$153$	−4.50000	+	7.79423i	−0.363803	+	0.630126i
$154$			5.19615i			0.418718i
$155$	−7.50000	+	6.06218i	−0.602414	+	0.486926i
$156$	4.50000	+	7.79423i	0.360288	+	0.624038i
$157$	−14.0000			−1.11732			−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000			−1.11732			−0.558661	+	0.829396i	$0.688685\pi$
$158$	−7.50000	−	12.9904i	−0.596668	−	1.03346i
$159$	4.50000	−	2.59808i	0.356873	−	0.206041i
$160$	4.50000	−	7.79423i	0.355756	−	0.616188i
$161$		0			0
$162$	13.5000	+	7.79423i	1.06066	+	0.612372i
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	7.50000	+	4.33013i	0.585652	+	0.338126i
$165$	9.00000			0.700649
$166$	−13.5000	−	7.79423i	−1.04780	−	0.604949i
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	0.918208	−	0.396098i	$-0.129636\pi$
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	−0.802135	+	0.597143i	$0.796303\pi$
$168$	3.00000			0.231455
$169$	7.00000	+	12.1244i	0.538462	+	0.932643i
$170$	−9.00000			−0.690268
$171$	−7.50000	+	12.9904i	−0.573539	+	0.993399i
$172$	−1.50000	+	0.866025i	−0.114374	+	0.0660338i
$173$	−13.5000	−	7.79423i	−1.02639	−	0.592584i	−0.110439	−	0.993883i	$-0.535226\pi$
$173$	−13.5000	−	7.79423i	−1.02639	−	0.592584i	−0.915947	+	0.401299i	$0.868559\pi$
$174$	9.00000	−	15.5885i	0.682288	−	1.18176i
$175$	1.00000	−	1.73205i	0.0755929	−	0.130931i
$176$	7.50000	−	12.9904i	0.565334	−	0.979187i
$177$	−15.0000			−1.12747
$178$			10.3923i			0.778936i
$179$	7.50000	+	12.9904i	0.560576	+	0.970947i	0.997446	+	0.0714220i	$0.0227537\pi$
$179$	7.50000	+	12.9904i	0.560576	+	0.970947i	−0.436870	+	0.899525i	$0.643913\pi$
$180$			5.19615i			0.387298i
$181$	−22.5000	−	12.9904i	−1.67241	−	0.965567i	−0.966282	−	0.257485i	$-0.917106\pi$
$181$	−22.5000	−	12.9904i	−1.67241	−	0.965567i	−0.706129	−	0.708083i	$-0.749560\pi$
$182$	−9.00000			−0.667124
$183$	−12.0000	+	20.7846i	−0.887066	+	1.53644i
$184$		0			0
$185$	9.00000			0.661693
$186$	−10.5000	−	12.9904i	−0.769897	−	0.952501i
$187$	−9.00000			−0.658145
$188$			10.3923i			0.757937i
$189$	−4.50000	+	2.59808i	−0.327327	+	0.188982i
$190$	−15.0000			−1.08821
$191$	−10.5000	−	6.06218i	−0.759753	−	0.438644i	0.0694538	−	0.997585i	$-0.477874\pi$
$191$	−10.5000	−	6.06218i	−0.759753	−	0.438644i	−0.829207	+	0.558941i	$0.811208\pi$
$192$	−1.50000	−	0.866025i	−0.108253	−	0.0625000i
$193$	2.50000	+	4.33013i	0.179954	+	0.311689i	0.941865	−	0.335993i	$-0.109072\pi$
$193$	2.50000	+	4.33013i	0.179954	+	0.311689i	−0.761911	+	0.647682i	$0.775738\pi$
$194$			17.3205i			1.24354i
$195$			15.5885i			1.11631i
$196$	−3.00000	+	5.19615i	−0.214286	+	0.371154i
$197$	1.50000	−	2.59808i	0.106871	−	0.185105i	−0.807630	−	0.589689i	$-0.799250\pi$
$197$	1.50000	−	2.59808i	0.106871	−	0.185105i	0.914501	+	0.404584i	$0.132584\pi$
$198$			15.5885i			1.10782i
$199$	10.5000	+	6.06218i	0.744325	+	0.429736i	0.823640	−	0.567113i	$-0.191940\pi$
$199$	10.5000	+	6.06218i	0.744325	+	0.429736i	−0.0793146	+	0.996850i	$0.525273\pi$
$200$	−3.00000	+	1.73205i	−0.212132	+	0.122474i
$201$	16.5000	−	9.52628i	1.16382	−	0.671932i
$202$	24.0000			1.68863
$203$	3.00000	+	5.19615i	0.210559	+	0.364698i
$204$		−	5.19615i		−	0.363803i
$205$	7.50000	+	12.9904i	0.523823	+	0.907288i
$206$	1.50000	+	0.866025i	0.104510	+	0.0603388i
$207$		0			0
$208$	22.5000	+	12.9904i	1.56009	+	0.900721i
$209$	−15.0000			−1.03757
$210$	−4.50000	−	2.59808i	−0.310530	−	0.179284i
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	−0.924918	−	0.380166i	$-0.875867\pi$
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	0.133226	−	0.991086i	$-0.457467\pi$
$212$	−1.50000	+	2.59808i	−0.103020	+	0.178437i
$213$	1.50000	+	2.59808i	0.102778	+	0.178017i
$214$	−10.5000	−	18.1865i	−0.717765	−	1.24321i
$215$	−3.00000			−0.204598
$216$	9.00000			0.612372
$217$	5.50000	−	0.866025i	0.373364	−	0.0587896i
$218$		−	3.46410i		−	0.234619i
$219$	7.50000	+	12.9904i	0.506803	+	0.877809i
$220$	−4.50000	+	2.59808i	−0.303390	+	0.175162i
$221$		−	15.5885i		−	1.04859i
$222$			15.5885i			1.04623i
$223$	7.50000	−	4.33013i	0.502237	−	0.289967i	−0.227400	−	0.973801i	$-0.573022\pi$
$223$	7.50000	−	4.33013i	0.502237	−	0.289967i	0.729637	+	0.683835i	$0.239689\pi$
$224$	−4.50000	+	2.59808i	−0.300669	+	0.173591i
$225$	3.00000	−	5.19615i	0.200000	−	0.346410i
$226$	10.5000	−	18.1865i	0.698450	−	1.20975i
$227$	13.5000	+	7.79423i	0.896026	+	0.517321i	0.875909	−	0.482476i	$-0.160263\pi$
$227$	13.5000	+	7.79423i	0.896026	+	0.517321i	0.0201176	+	0.999798i	$0.493596\pi$
$228$		−	8.66025i		−	0.573539i
$229$	1.50000	−	0.866025i	0.0991228	−	0.0572286i	−0.449619	−	0.893220i	$-0.648440\pi$
$229$	1.50000	−	0.866025i	0.0991228	−	0.0572286i	0.548742	+	0.835992i	$0.315107\pi$
$230$		0			0
$231$	−4.50000	−	2.59808i	−0.296078	−	0.170941i
$232$		−	10.3923i		−	0.682288i
$233$			6.92820i			0.453882i	0.973909	+	0.226941i	$0.0728724\pi$
$233$			6.92820i			0.453882i	−0.973909	+	0.226941i	$0.927128\pi$
$234$	−27.0000			−1.76505
$235$	−9.00000	+	15.5885i	−0.587095	+	1.01688i
$236$	7.50000	−	4.33013i	0.488208	−	0.281867i
$237$	15.0000			0.974355
$238$	4.50000	+	2.59808i	0.291692	+	0.168408i
$239$	4.50000	−	7.79423i	0.291081	−	0.504167i	−0.682985	−	0.730433i	$-0.739318\pi$
$239$	4.50000	−	7.79423i	0.291081	−	0.504167i	0.974066	+	0.226266i	$0.0726518\pi$
$240$	7.50000	+	12.9904i	0.484123	+	0.838525i
$241$	−10.5000	+	6.06218i	−0.676364	+	0.390499i	−0.798484	−	0.602016i	$-0.794364\pi$
$241$	−10.5000	+	6.06218i	−0.676364	+	0.390499i	0.122119	+	0.992515i	$0.461031\pi$
$242$	3.00000	−	1.73205i	0.192847	−	0.111340i
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$		−	13.8564i		−	0.887066i
$245$	−9.00000	+	5.19615i	−0.574989	+	0.331970i
$246$	−22.5000	+	12.9904i	−1.43455	+	0.828236i
$247$		−	25.9808i		−	1.65312i
$248$	−9.00000	−	3.46410i	−0.571501	−	0.219971i
$249$	13.5000	−	7.79423i	0.855528	−	0.493939i
$250$	21.0000			1.32816
$251$	7.50000	+	12.9904i	0.473396	+	0.819946i	0.999536	−	0.0304521i	$-0.00969471\pi$
$251$	7.50000	+	12.9904i	0.473396	+	0.819946i	−0.526140	+	0.850398i	$0.676361\pi$
$252$	1.50000	−	2.59808i	0.0944911	−	0.163663i
$253$		0			0
$254$	−1.50000	−	2.59808i	−0.0941184	−	0.163018i
$255$	4.50000	−	7.79423i	0.281801	−	0.488094i
$256$	19.0000			1.18750
$257$	−1.50000	−	0.866025i	−0.0935674	−	0.0540212i	0.452486	−	0.891771i	$-0.350537\pi$
$257$	−1.50000	−	0.866025i	−0.0935674	−	0.0540212i	−0.546054	+	0.837750i	$0.683871\pi$
$258$		−	5.19615i		−	0.323498i
$259$	−4.50000	−	2.59808i	−0.279616	−	0.161437i
$260$	−4.50000	−	7.79423i	−0.279078	−	0.483378i
$261$	9.00000	+	15.5885i	0.557086	+	0.964901i
$262$	13.5000	+	23.3827i	0.834033	+	1.44459i
$263$	−24.0000			−1.47990			−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000			−1.47990			−0.739952	+	0.672660i	$0.765152\pi$
$264$	4.50000	+	7.79423i	0.276956	+	0.479702i
$265$	−4.50000	+	2.59808i	−0.276433	+	0.159599i
$266$	7.50000	+	4.33013i	0.459855	+	0.265497i
$267$	−9.00000	−	5.19615i	−0.550791	−	0.317999i
$268$	−5.50000	+	9.52628i	−0.335966	+	0.581910i
$269$	13.5000	−	23.3827i	0.823110	−	1.42567i	−0.0802460	−	0.996775i	$-0.525571\pi$
$269$	13.5000	−	23.3827i	0.823110	−	1.42567i	0.903356	−	0.428892i	$-0.141096\pi$
$270$	−13.5000	−	7.79423i	−0.821584	−	0.474342i
$271$			10.3923i			0.631288i	0.948878	+	0.315644i	$0.102220\pi$
$271$			10.3923i			0.631288i	−0.948878	+	0.315644i	$0.897780\pi$
$272$	−7.50000	−	12.9904i	−0.454754	−	0.787658i
$273$	4.50000	−	7.79423i	0.272352	−	0.471728i
$274$	−4.50000	−	2.59808i	−0.271855	−	0.156956i
$275$	6.00000			0.361814
$276$		0			0
$277$			13.8564i			0.832551i	0.909239	+	0.416275i	$0.136665\pi$
$277$			13.8564i			0.832551i	−0.909239	+	0.416275i	$0.863335\pi$
$278$	30.0000			1.79928
$279$	16.5000	−	2.59808i	0.987829	−	0.155543i
$280$	−3.00000			−0.179284
$281$		−	13.8564i		−	0.826604i	−0.910594	−	0.413302i	$-0.864375\pi$
$281$		−	13.8564i		−	0.826604i	0.910594	−	0.413302i	$-0.135625\pi$
$282$	−27.0000	−	15.5885i	−1.60783	−	0.928279i
$283$	20.0000			1.18888			0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000			1.18888			0.594438	+	0.804141i	$0.297374\pi$
$284$	−1.50000	−	0.866025i	−0.0890086	−	0.0513892i
$285$	7.50000	−	12.9904i	0.444262	−	0.769484i
$286$	−13.5000	−	23.3827i	−0.798272	−	1.38265i
$287$		−	8.66025i		−	0.511199i
$288$	−13.5000	+	7.79423i	−0.795495	+	0.459279i
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	−9.00000	+	15.5885i	−0.528498	+	0.915386i
$291$	−15.0000	−	8.66025i	−0.879316	−	0.507673i
$292$	−7.50000	−	4.33013i	−0.438904	−	0.253402i
$293$	−13.5000	+	7.79423i	−0.788678	+	0.455344i	−0.839497	−	0.543364i	$-0.817150\pi$
$293$	−13.5000	+	7.79423i	−0.788678	+	0.455344i	0.0508187	+	0.998708i	$0.483817\pi$
$294$	−9.00000	−	15.5885i	−0.524891	−	0.909137i
$295$	15.0000			0.873334
$296$	4.50000	+	7.79423i	0.261557	+	0.453030i
$297$	−13.5000	−	7.79423i	−0.783349	−	0.452267i
$298$	−4.50000	−	7.79423i	−0.260678	−	0.451508i
$299$		0			0
$300$			3.46410i			0.200000i
$301$	1.50000	+	0.866025i	0.0864586	+	0.0499169i
$302$	6.00000			0.345261
$303$	−12.0000	+	20.7846i	−0.689382	+	1.19404i
$304$	−12.5000	−	21.6506i	−0.716924	−	1.24175i
$305$	12.0000	−	20.7846i	0.687118	−	1.19012i
$306$	13.5000	+	7.79423i	0.771744	+	0.445566i
$307$	−3.50000	−	6.06218i	−0.199756	−	0.345987i	0.748694	−	0.662916i	$-0.230681\pi$
$307$	−3.50000	−	6.06218i	−0.199756	−	0.345987i	−0.948449	+	0.316929i	$0.897348\pi$
$308$	3.00000			0.170941
$309$	−1.50000	+	0.866025i	−0.0853320	+	0.0492665i
$310$	10.5000	+	12.9904i	0.596360	+	0.737804i
$311$			3.46410i			0.196431i	0.995165	+	0.0982156i	$0.0313135\pi$
$311$			3.46410i			0.196431i	−0.995165	+	0.0982156i	$0.968687\pi$
$312$	−13.5000	+	7.79423i	−0.764287	+	0.441261i
$313$	19.5000	−	11.2583i	1.10221	−	0.636358i	0.165406	−	0.986226i	$-0.447107\pi$
$313$	19.5000	−	11.2583i	1.10221	−	0.636358i	0.936799	+	0.349867i	$0.113773\pi$
$314$			24.2487i			1.36843i
$315$	4.50000	−	2.59808i	0.253546	−	0.146385i
$316$	−7.50000	+	4.33013i	−0.421908	+	0.243589i
$317$	−1.50000	+	0.866025i	−0.0842484	+	0.0486408i	−0.541532	−	0.840680i	$-0.682156\pi$
$317$	−1.50000	+	0.866025i	−0.0842484	+	0.0486408i	0.457284	+	0.889321i	$0.348822\pi$
$318$	−4.50000	−	7.79423i	−0.252347	−	0.437079i
$319$	−9.00000	+	15.5885i	−0.503903	+	0.872786i
$320$	1.50000	+	0.866025i	0.0838525	+	0.0484123i
$321$	21.0000			1.17211
$322$		0			0
$323$	−7.50000	+	12.9904i	−0.417311	+	0.722804i
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$			10.3923i			0.576461i
$326$			6.92820i			0.383718i
$327$	3.00000	+	1.73205i	0.165900	+	0.0957826i
$328$	−7.50000	+	12.9904i	−0.414118	+	0.717274i
$329$	9.00000	−	5.19615i	0.496186	−	0.286473i
$330$		−	15.5885i		−	0.858116i
$331$	−7.50000	−	4.33013i	−0.412237	−	0.238005i	0.279513	−	0.960142i	$-0.409827\pi$
$331$	−7.50000	−	4.33013i	−0.412237	−	0.238005i	−0.691751	+	0.722137i	$0.743160\pi$
$332$	−4.50000	+	7.79423i	−0.246970	+	0.427764i
$333$	−13.5000	−	7.79423i	−0.739795	−	0.427121i
$334$	4.50000	−	2.59808i	0.246229	−	0.142160i
$335$	−16.5000	+	9.52628i	−0.901491	+	0.520476i
$336$		−	8.66025i		−	0.472456i
$337$		−	13.8564i		−	0.754807i	−0.926049	−	0.377403i	$-0.876817\pi$
$337$		−	13.8564i		−	0.754807i	0.926049	−	0.377403i	$-0.123183\pi$
$338$	21.0000	−	12.1244i	1.14225	−	0.659478i
$339$	10.5000	+	18.1865i	0.570282	+	0.987757i
$340$			5.19615i			0.281801i
$341$	10.5000	+	12.9904i	0.568607	+	0.703469i
$342$	22.5000	+	12.9904i	1.21666	+	0.702439i
$343$	13.0000			0.701934
$344$	−1.50000	−	2.59808i	−0.0808746	−	0.140079i
$345$		0			0
$346$	−13.5000	+	23.3827i	−0.725764	+	1.25706i
$347$	13.5000	+	23.3827i	0.724718	+	1.25525i	0.959090	+	0.283101i	$0.0913633\pi$
$347$	13.5000	+	23.3827i	0.724718	+	1.25525i	−0.234372	+	0.972147i	$0.575303\pi$
$348$	−9.00000	−	5.19615i	−0.482451	−	0.278543i
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$	−3.00000	−	1.73205i	−0.160357	−	0.0925820i
$351$	13.5000	−	23.3827i	0.720577	−	1.24808i
$352$	−13.5000	−	7.79423i	−0.719552	−	0.415434i
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	0.721063	−	0.692869i	$-0.243654\pi$
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	−0.960574	+	0.278024i	$0.910320\pi$
$354$			25.9808i			1.38086i
$355$	−1.50000	−	2.59808i	−0.0796117	−	0.137892i
$356$	6.00000			0.317999
$357$	−4.50000	+	2.59808i	−0.238165	+	0.137505i
$358$	22.5000	−	12.9904i	1.18916	−	0.686563i
$359$	1.50000	+	0.866025i	0.0791670	+	0.0457071i	0.539061	−	0.842267i	$-0.318779\pi$
$359$	1.50000	+	0.866025i	0.0791670	+	0.0457071i	−0.459894	+	0.887974i	$0.652113\pi$
$360$	−9.00000			−0.474342
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	−22.5000	+	38.9711i	−1.18257	+	2.04828i
$363$			3.46410i			0.181818i
$364$			5.19615i			0.272352i
$365$	−7.50000	−	12.9904i	−0.392568	−	0.679948i
$366$	36.0000	+	20.7846i	1.88175	+	1.08643i
$367$	−1.50000	−	0.866025i	−0.0782994	−	0.0452062i	0.460339	−	0.887743i	$-0.347728\pi$
$367$	−1.50000	−	0.866025i	−0.0782994	−	0.0452062i	−0.538639	+	0.842537i	$0.681061\pi$
$368$		0			0
$369$		−	25.9808i		−	1.35250i
$370$		−	15.5885i		−	0.810405i
$371$	3.00000			0.155752
$372$	−7.50000	+	6.06218i	−0.388857	+	0.314309i
$373$	−10.0000			−0.517780			−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000			−0.517780			−0.258890	+	0.965907i	$0.583357\pi$
$374$			15.5885i			0.806060i
$375$	−10.5000	+	18.1865i	−0.542218	+	0.939149i
$376$	−18.0000			−0.928279
$377$	−27.0000	−	15.5885i	−1.39057	−	0.802846i
$378$	4.50000	+	7.79423i	0.231455	+	0.400892i
$379$	0.500000	+	0.866025i	0.0256833	+	0.0444847i	0.878581	−	0.477593i	$-0.158491\pi$
$379$	0.500000	+	0.866025i	0.0256833	+	0.0444847i	−0.852898	+	0.522077i	$0.825157\pi$
$380$			8.66025i			0.444262i
$381$	3.00000			0.153695
$382$	−10.5000	+	18.1865i	−0.537227	+	0.930504i
$383$	4.50000	−	7.79423i	0.229939	−	0.398266i	−0.727851	−	0.685736i	$-0.759481\pi$
$383$	4.50000	−	7.79423i	0.229939	−	0.398266i	0.957790	+	0.287469i	$0.0928139\pi$
$384$	−10.5000	+	18.1865i	−0.535826	+	0.928078i
$385$	4.50000	+	2.59808i	0.229341	+	0.132410i
$386$	7.50000	−	4.33013i	0.381740	−	0.220398i
$387$	4.50000	+	2.59808i	0.228748	+	0.132068i
$388$	10.0000			0.507673
$389$	7.50000	+	12.9904i	0.380265	+	0.658638i	0.991100	−	0.133120i	$-0.0424994\pi$
$389$	7.50000	+	12.9904i	0.380265	+	0.658638i	−0.610835	+	0.791758i	$0.709166\pi$
$390$	27.0000			1.36720
$391$		0			0
$392$	−9.00000	−	5.19615i	−0.454569	−	0.262445i
$393$	−27.0000			−1.36197
$394$	−4.50000	−	2.59808i	−0.226707	−	0.130889i
$395$	−15.0000			−0.754732
$396$	9.00000			0.452267
$397$	−11.5000	−	19.9186i	−0.577168	−	0.999685i	−0.995802	−	0.0915300i	$-0.970824\pi$
$397$	−11.5000	−	19.9186i	−0.577168	−	0.999685i	0.418634	−	0.908155i	$-0.362509\pi$
$398$	10.5000	−	18.1865i	0.526317	−	0.911609i
$399$	−7.50000	+	4.33013i	−0.375470	+	0.216777i
$400$	5.00000	+	8.66025i	0.250000	+	0.433013i
$401$	−6.00000			−0.299626			−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000			−0.299626			−0.149813	+	0.988714i	$0.547867\pi$
$402$	−16.5000	−	28.5788i	−0.822945	−	1.42538i
$403$	−22.5000	+	18.1865i	−1.12080	+	0.905936i
$404$		−	13.8564i		−	0.689382i
$405$	13.5000	−	7.79423i	0.670820	−	0.387298i
$406$	9.00000	−	5.19615i	0.446663	−	0.257881i
$407$		−	15.5885i		−	0.772691i
$408$	9.00000			0.445566
$409$	−22.5000	+	12.9904i	−1.11255	+	0.642333i	−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−22.5000	+	12.9904i	−1.11255	+	0.642333i	−0.173064	+	0.984911i	$0.555367\pi$
$410$	22.5000	−	12.9904i	1.11120	−	0.641549i
$411$	4.50000	−	2.59808i	0.221969	−	0.128154i
$412$	0.500000	−	0.866025i	0.0246332	−	0.0426660i
$413$	−7.50000	−	4.33013i	−0.369051	−	0.213072i
$414$		0			0
$415$	−13.5000	+	7.79423i	−0.662689	+	0.382604i
$416$	13.5000	−	23.3827i	0.661892	−	1.14643i
$417$	−15.0000	+	25.9808i	−0.734553	+	1.27228i
$418$			25.9808i			1.27076i
$419$		−	17.3205i		−	0.846162i	−0.906092	−	0.423081i	$-0.860949\pi$
$419$		−	17.3205i		−	0.846162i	0.906092	−	0.423081i	$-0.139051\pi$
$420$	−1.50000	+	2.59808i	−0.0731925	+	0.126773i
$421$	−9.50000	+	16.4545i	−0.463002	+	0.801942i	−0.999109	−	0.0422075i	$-0.986561\pi$
$421$	−9.50000	+	16.4545i	−0.463002	+	0.801942i	0.536107	+	0.844150i	$0.319894\pi$
$422$	−34.5000	+	19.9186i	−1.67943	+	0.969622i
$423$	27.0000	−	15.5885i	1.31278	−	0.757937i
$424$	−4.50000	−	2.59808i	−0.218539	−	0.126174i
$425$	3.00000	−	5.19615i	0.145521	−	0.252050i
$426$	4.50000	−	2.59808i	0.218026	−	0.125877i
$427$	−12.0000	+	6.92820i	−0.580721	+	0.335279i
$428$	−10.5000	+	6.06218i	−0.507537	+	0.293026i
$429$	27.0000			1.30357
$430$			5.19615i			0.250581i
$431$	22.5000	−	12.9904i	1.08379	−	0.625725i	0.151871	−	0.988400i	$-0.451470\pi$
$431$	22.5000	−	12.9904i	1.08379	−	0.625725i	0.931915	+	0.362676i	$0.118137\pi$
$432$		−	25.9808i		−	1.25000i
$433$		−	6.92820i		−	0.332948i	−0.986046	−	0.166474i	$-0.946762\pi$
$433$		−	6.92820i		−	0.332948i	0.986046	−	0.166474i	$-0.0532382\pi$
$434$	−1.50000	−	9.52628i	−0.0720023	−	0.457276i
$435$	−9.00000	−	15.5885i	−0.431517	−	0.747409i
$436$	−2.00000			−0.0957826
$437$		0			0
$438$	22.5000	−	12.9904i	1.07509	−	0.620704i
$439$	−0.500000	+	0.866025i	−0.0238637	+	0.0413331i	−0.877711	−	0.479191i	$-0.840930\pi$
$439$	−0.500000	+	0.866025i	−0.0238637	+	0.0413331i	0.853847	+	0.520524i	$0.174263\pi$
$440$	−4.50000	−	7.79423i	−0.214529	−	0.371575i
$441$	18.0000			0.857143
$442$	−27.0000			−1.28426
$443$	−10.5000	−	6.06218i	−0.498870	−	0.288023i	0.229377	−	0.973338i	$-0.426331\pi$
$443$	−10.5000	−	6.06218i	−0.498870	−	0.288023i	−0.728247	+	0.685315i	$0.759665\pi$
$444$	9.00000			0.427121
$445$	9.00000	+	5.19615i	0.426641	+	0.246321i
$446$	−7.50000	−	12.9904i	−0.355135	−	0.615112i
$447$	9.00000			0.425685
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$	−9.00000	−	5.19615i	−0.424264	−	0.244949i
$451$	22.5000	−	12.9904i	1.05948	−	0.611693i
$452$	−10.5000	−	6.06218i	−0.493878	−	0.285141i
$453$	−3.00000	+	5.19615i	−0.140952	+	0.244137i
$454$	13.5000	−	23.3827i	0.633586	−	1.09740i
$455$	−4.50000	+	7.79423i	−0.210963	+	0.365399i
$456$	15.0000			0.702439
$457$		−	6.92820i		−	0.324088i	−0.986784	−	0.162044i	$-0.948191\pi$
$457$		−	6.92820i		−	0.324088i	0.986784	−	0.162044i	$-0.0518086\pi$
$458$	−1.50000	−	2.59808i	−0.0700904	−	0.121400i
$459$	−13.5000	+	7.79423i	−0.630126	+	0.363803i
$460$		0			0
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$	−4.50000	+	7.79423i	−0.209359	+	0.362620i
$463$		−	17.3205i		−	0.804952i	−0.915430	−	0.402476i	$-0.868150\pi$
$463$		−	17.3205i		−	0.804952i	0.915430	−	0.402476i	$-0.131850\pi$
$464$	−30.0000			−1.39272
$465$	−16.5000	+	2.59808i	−0.765169	+	0.120483i
$466$	12.0000			0.555889
$467$		−	17.3205i		−	0.801498i	−0.916188	−	0.400749i	$-0.868750\pi$
$467$		−	17.3205i		−	0.801498i	0.916188	−	0.400749i	$-0.131250\pi$
$468$			15.5885i			0.720577i
$469$	11.0000			0.507933
$470$	27.0000	+	15.5885i	1.24542	+	0.719042i
$471$	−21.0000	−	12.1244i	−0.967629	−	0.558661i
$472$	7.50000	+	12.9904i	0.345215	+	0.597931i
$473$			5.19615i			0.238919i
$474$		−	25.9808i		−	1.19334i
$475$	5.00000	−	8.66025i	0.229416	−	0.397360i
$476$	1.50000	−	2.59808i	0.0687524	−	0.119083i
$477$	9.00000			0.412082
$478$	−13.5000	−	7.79423i	−0.617476	−	0.356500i
$479$	−7.50000	+	4.33013i	−0.342684	+	0.197849i	−0.661458	−	0.749982i	$-0.730062\pi$
$479$	−7.50000	+	4.33013i	−0.342684	+	0.197849i	0.318774	+	0.947831i	$0.396729\pi$
$480$	13.5000	−	7.79423i	0.616188	−	0.355756i
$481$	27.0000			1.23109
$482$	10.5000	+	18.1865i	0.478262	+	0.828374i
$483$		0			0
$484$	−1.00000	−	1.73205i	−0.0454545	−	0.0787296i
$485$	15.0000	+	8.66025i	0.681115	+	0.393242i
$486$	13.5000	+	23.3827i	0.612372	+	1.06066i
$487$	−1.50000	−	0.866025i	−0.0679715	−	0.0392434i	0.465629	−	0.884980i	$-0.345828\pi$
$487$	−1.50000	−	0.866025i	−0.0679715	−	0.0392434i	−0.533601	+	0.845737i	$0.679161\pi$
$488$	24.0000			1.08643
$489$	−6.00000	−	3.46410i	−0.271329	−	0.156652i
$490$	9.00000	+	15.5885i	0.406579	+	0.704215i
$491$	−13.5000	+	23.3827i	−0.609246	+	1.05525i	0.382118	+	0.924113i	$0.375195\pi$
$491$	−13.5000	+	23.3827i	−0.609246	+	1.05525i	−0.991365	+	0.131132i	$0.958139\pi$
$492$	7.50000	+	12.9904i	0.338126	+	0.585652i
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$	−45.0000			−2.02465
$495$	13.5000	+	7.79423i	0.606780	+	0.350325i
$496$	−10.0000	+	25.9808i	−0.449013	+	1.16657i
$497$			1.73205i			0.0776931i
$498$	−13.5000	−	23.3827i	−0.604949	−	1.04780i
$499$	13.5000	−	7.79423i	0.604343	−	0.348918i	−0.166405	−	0.986057i	$-0.553216\pi$
$499$	13.5000	−	7.79423i	0.604343	−	0.348918i	0.770748	+	0.637140i	$0.219883\pi$
$500$		−	12.1244i		−	0.542218i
$501$			5.19615i			0.232147i
$502$	22.5000	−	12.9904i	1.00422	−	0.579789i
$503$	−7.50000	+	4.33013i	−0.334408	+	0.193071i	−0.657797	−	0.753196i	$-0.728511\pi$
$503$	−7.50000	+	4.33013i	−0.334408	+	0.193071i	0.323388	+	0.946266i	$0.395178\pi$
$504$	4.50000	+	2.59808i	0.200446	+	0.115728i
$505$	12.0000	−	20.7846i	0.533993	−	0.924903i
$506$		0			0
$507$			24.2487i			1.07692i
$508$	−1.50000	+	0.866025i	−0.0665517	+	0.0384237i
$509$	−10.5000	+	18.1865i	−0.465404	+	0.806104i	−0.999220	−	0.0394971i	$-0.987424\pi$
$509$	−10.5000	+	18.1865i	−0.465404	+	0.806104i	0.533815	+	0.845601i	$0.320758\pi$
$510$	−13.5000	−	7.79423i	−0.597790	−	0.345134i
$511$			8.66025i			0.383107i
$512$		−	8.66025i		−	0.382733i
$513$	−22.5000	+	12.9904i	−0.993399	+	0.573539i
$514$	−1.50000	+	2.59808i	−0.0661622	+	0.114596i
$515$	1.50000	−	0.866025i	0.0660979	−	0.0381616i
$516$	−3.00000			−0.132068
$517$	27.0000	+	15.5885i	1.18746	+	0.685580i
$518$	−4.50000	+	7.79423i	−0.197719	+	0.342459i
$519$	−13.5000	−	23.3827i	−0.592584	−	1.02639i
$520$	13.5000	−	7.79423i	0.592014	−	0.341800i
$521$	4.50000	−	2.59808i	0.197149	−	0.113824i	−0.398176	−	0.917309i	$-0.630357\pi$
$521$	4.50000	−	2.59808i	0.197149	−	0.113824i	0.595325	+	0.803485i	$0.297023\pi$
$522$	27.0000	−	15.5885i	1.18176	−	0.682288i
$523$		−	24.2487i		−	1.06032i	−0.847897	−	0.530161i	$-0.822131\pi$
$523$		−	24.2487i		−	1.06032i	0.847897	−	0.530161i	$-0.177869\pi$
$524$	13.5000	−	7.79423i	0.589750	−	0.340492i
$525$	3.00000	−	1.73205i	0.130931	−	0.0755929i
$526$			41.5692i			1.81250i
$527$	16.5000	−	2.59808i	0.718751	−	0.113174i
$528$	22.5000	−	12.9904i	0.979187	−	0.565334i
$529$	−23.0000			−1.00000
$530$	4.50000	+	7.79423i	0.195468	+	0.338560i
$531$	−22.5000	−	12.9904i	−0.976417	−	0.563735i
$532$	2.50000	−	4.33013i	0.108389	−	0.187735i
$533$	22.5000	+	38.9711i	0.974583	+	1.68803i
$534$	−9.00000	+	15.5885i	−0.389468	+	0.674579i
$535$	−21.0000			−0.907909
$536$	−16.5000	−	9.52628i	−0.712691	−	0.411473i
$537$			25.9808i			1.12115i
$538$	−40.5000	−	23.3827i	−1.74608	−	1.00810i
$539$	9.00000	+	15.5885i	0.387657	+	0.671442i
$540$	−4.50000	+	7.79423i	−0.193649	+	0.335410i
$541$	−21.5000	−	37.2391i	−0.924357	−	1.60103i	−0.792592	−	0.609753i	$-0.791269\pi$
$541$	−21.5000	−	37.2391i	−0.924357	−	1.60103i	−0.131765	−	0.991281i	$-0.542065\pi$
$542$	18.0000			0.773166
$543$	−22.5000	−	38.9711i	−0.965567	−	1.67241i
$544$	−13.5000	+	7.79423i	−0.578808	+	0.334175i
$545$	−3.00000	−	1.73205i	−0.128506	−	0.0741929i
$546$	−13.5000	−	7.79423i	−0.577747	−	0.333562i
$547$	−12.5000	+	21.6506i	−0.534461	+	0.925714i	0.464728	+	0.885454i	$0.346152\pi$
$547$	−12.5000	+	21.6506i	−0.534461	+	0.925714i	−0.999189	+	0.0402607i	$0.987181\pi$
$548$	−1.50000	+	2.59808i	−0.0640768	+	0.110984i
$549$	−36.0000	+	20.7846i	−1.53644	+	0.887066i
$550$		−	10.3923i		−	0.443129i
$551$	15.0000	+	25.9808i	0.639021	+	1.10682i
$552$		0			0
$553$	7.50000	+	4.33013i	0.318932	+	0.184136i
$554$	24.0000			1.01966
$555$	13.5000	+	7.79423i	0.573043	+	0.330847i
$556$		−	17.3205i		−	0.734553i
$557$	−42.0000			−1.77960			−0.889799	−	0.456354i	$-0.849155\pi$
$557$	−42.0000			−1.77960			−0.889799	+	0.456354i	$0.849155\pi$
$558$	−4.50000	−	28.5788i	−0.190500	−	1.20984i
$559$	−9.00000			−0.380659
$560$			8.66025i			0.365963i
$561$	−13.5000	−	7.79423i	−0.569970	−	0.329073i
$562$	−24.0000			−1.01238
$563$	19.5000	+	11.2583i	0.821827	+	0.474482i	0.851046	−	0.525091i	$-0.175969\pi$
$563$	19.5000	+	11.2583i	0.821827	+	0.474482i	−0.0292191	+	0.999573i	$0.509302\pi$
$564$	−9.00000	+	15.5885i	−0.378968	+	0.656392i
$565$	−10.5000	−	18.1865i	−0.441738	−	0.765113i
$566$		−	34.6410i		−	1.45607i
$567$	−9.00000			−0.377964
$568$	1.50000	−	2.59808i	0.0629386	−	0.109013i
$569$	13.5000	−	23.3827i	0.565949	−	0.980253i	−0.431011	−	0.902347i	$-0.641843\pi$
$569$	13.5000	−	23.3827i	0.565949	−	0.980253i	0.996961	−	0.0779066i	$-0.0248236\pi$
$570$	−22.5000	−	12.9904i	−0.942421	−	0.544107i
$571$	4.50000	+	2.59808i	0.188319	+	0.108726i	0.591195	−	0.806528i	$-0.298656\pi$
$571$	4.50000	+	2.59808i	0.188319	+	0.108726i	−0.402876	+	0.915254i	$0.631990\pi$
$572$	−13.5000	+	7.79423i	−0.564463	+	0.325893i
$573$	−10.5000	−	18.1865i	−0.438644	−	0.759753i
$574$	−15.0000			−0.626088
$575$		0			0
$576$	−1.50000	−	2.59808i	−0.0625000	−	0.108253i
$577$	8.50000	+	14.7224i	0.353860	+	0.612903i	0.986922	−	0.161198i	$-0.0515357\pi$
$577$	8.50000	+	14.7224i	0.353860	+	0.612903i	−0.633062	+	0.774101i	$0.718202\pi$
$578$	−12.0000	−	6.92820i	−0.499134	−	0.288175i
$579$			8.66025i			0.359908i
$580$	9.00000	+	5.19615i	0.373705	+	0.215758i
$581$	9.00000			0.373383
$582$	−15.0000	+	25.9808i	−0.621770	+	1.07694i
$583$	4.50000	+	7.79423i	0.186371	+	0.322804i
$584$	7.50000	−	12.9904i	0.310352	−	0.537546i
$585$	−13.5000	+	23.3827i	−0.558156	+	0.966755i
$586$	13.5000	+	23.3827i	0.557680	+	0.965930i
$587$	24.0000			0.990586			0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000			0.990586			0.495293	+	0.868726i	$0.335061\pi$
$588$	−9.00000	+	5.19615i	−0.371154	+	0.214286i
$589$	27.5000	−	4.33013i	1.13312	−	0.178420i
$590$		−	25.9808i		−	1.06961i
$591$	4.50000	−	2.59808i	0.185105	−	0.106871i
$592$	22.5000	−	12.9904i	0.924744	−	0.533901i
$593$			27.7128i			1.13803i	0.822328	+	0.569014i	$0.192675\pi$
$593$			27.7128i			1.13803i	−0.822328	+	0.569014i	$0.807325\pi$
$594$	−13.5000	+	23.3827i	−0.553912	+	0.959403i
$595$	4.50000	−	2.59808i	0.184482	−	0.106511i
$596$	−4.50000	+	2.59808i	−0.184327	+	0.106421i
$597$	10.5000	+	18.1865i	0.429736	+	0.744325i
$598$		0			0
$599$	25.5000	+	14.7224i	1.04190	+	0.601542i	0.920371	−	0.391045i	$-0.127886\pi$
$599$	25.5000	+	14.7224i	1.04190	+	0.601542i	0.121530	+	0.992588i	$0.461220\pi$
$600$	−6.00000			−0.244949
$601$	31.5000	−	18.1865i	1.28491	−	0.741844i	0.307170	−	0.951655i	$-0.400618\pi$
$601$	31.5000	−	18.1865i	1.28491	−	0.741844i	0.977742	+	0.209811i	$0.0672847\pi$
$602$	1.50000	−	2.59808i	0.0611354	−	0.105890i
$603$	33.0000			1.34386
$604$		−	3.46410i		−	0.140952i
$605$		−	3.46410i		−	0.140836i
$606$	36.0000	+	20.7846i	1.46240	+	0.844317i
$607$	5.50000	−	9.52628i	0.223238	−	0.386660i	−0.732551	−	0.680712i	$-0.761671\pi$
$607$	5.50000	−	9.52628i	0.223238	−	0.386660i	0.955789	+	0.294052i	$0.0950039\pi$
$608$	−22.5000	+	12.9904i	−0.912495	+	0.526830i
$609$			10.3923i			0.421117i
$610$	−36.0000	−	20.7846i	−1.45760	−	0.841544i
$611$	−27.0000	+	46.7654i	−1.09230	+	1.89192i
$612$	4.50000	−	7.79423i	0.181902	−	0.315063i
$613$	−4.50000	+	2.59808i	−0.181753	+	0.104935i	−0.588116	−	0.808776i	$-0.700130\pi$
$613$	−4.50000	+	2.59808i	−0.181753	+	0.104935i	0.406363	+	0.913712i	$0.366797\pi$
$614$	−10.5000	+	6.06218i	−0.423746	+	0.244650i
$615$			25.9808i			1.04765i
$616$			5.19615i			0.209359i
$617$	−13.5000	+	7.79423i	−0.543490	+	0.313784i	−0.746492	−	0.665394i	$-0.768263\pi$
$617$	−13.5000	+	7.79423i	−0.543490	+	0.313784i	0.203002	+	0.979178i	$0.434930\pi$
$618$	1.50000	+	2.59808i	0.0603388	+	0.104510i
$619$			10.3923i			0.417702i	0.977947	+	0.208851i	$0.0669724\pi$
$619$			10.3923i			0.417702i	−0.977947	+	0.208851i	$0.933028\pi$
$620$	7.50000	−	6.06218i	0.301207	−	0.243463i
$621$		0			0
$622$	6.00000			0.240578
$623$	−3.00000	−	5.19615i	−0.120192	−	0.208179i
$624$	22.5000	+	38.9711i	0.900721	+	1.56009i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	−19.5000	−	33.7750i	−0.779377	−	1.34992i
$627$	−22.5000	−	12.9904i	−0.898563	−	0.518786i
$628$	14.0000			0.558661
$629$	−13.5000	−	7.79423i	−0.538280	−	0.310776i
$630$	−4.50000	−	7.79423i	−0.179284	−	0.310530i
$631$	34.5000	+	19.9186i	1.37342	+	0.792946i	0.991357	−	0.131189i	$-0.0418794\pi$
$631$	34.5000	+	19.9186i	1.37342	+	0.792946i	0.382066	+	0.924135i	$0.375213\pi$
$632$	−7.50000	−	12.9904i	−0.298334	−	0.516730i
$633$		−	39.8372i		−	1.58339i
$634$	1.50000	+	2.59808i	0.0595726	+	0.103183i
$635$	−3.00000			−0.119051
$636$	−4.50000	+	2.59808i	−0.178437	+	0.103020i
$637$	−27.0000	+	15.5885i	−1.06978	+	0.617637i
$638$	27.0000	+	15.5885i	1.06894	+	0.617153i
$639$			5.19615i			0.205557i
$640$	10.5000	−	18.1865i	0.415049	−	0.718886i
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	0.330997	+	0.943632i	$0.392615\pi$
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	−0.982708	+	0.185164i	$0.940718\pi$
$642$		−	36.3731i		−	1.43553i
$643$			3.46410i			0.136611i	0.997664	+	0.0683054i	$0.0217592\pi$
$643$			3.46410i			0.136611i	−0.997664	+	0.0683054i	$0.978241\pi$
$644$		0			0
$645$	−4.50000	−	2.59808i	−0.177187	−	0.102299i
$646$	22.5000	+	12.9904i	0.885251	+	0.511100i
$647$	−12.0000			−0.471769			−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000			−0.471769			−0.235884	+	0.971781i	$0.575799\pi$
$648$	13.5000	+	7.79423i	0.530330	+	0.306186i
$649$		−	25.9808i		−	1.01983i
$650$	18.0000			0.706018
$651$	9.00000	+	3.46410i	0.352738	+	0.135769i
$652$	4.00000			0.156652
$653$		0			0		1.00000			$0$
$653$		0			0		−1.00000			$\pi$
$654$	3.00000	−	5.19615i	0.117309	−	0.203186i
$655$	27.0000			1.05498
$656$	37.5000	+	21.6506i	1.46413	+	0.845315i
$657$			25.9808i			1.01361i
$658$	−9.00000	−	15.5885i	−0.350857	−	0.607701i
$659$		−	45.0333i		−	1.75425i	−0.480263	−	0.877125i	$-0.659459\pi$
$659$		−	45.0333i		−	1.75425i	0.480263	−	0.877125i	$-0.340541\pi$
$660$	−9.00000			−0.350325
$661$	−17.5000	+	30.3109i	−0.680671	+	1.17896i	0.294105	+	0.955773i	$0.404978\pi$
$661$	−17.5000	+	30.3109i	−0.680671	+	1.17896i	−0.974776	+	0.223184i	$0.928355\pi$
$662$	−7.50000	+	12.9904i	−0.291496	+	0.504885i
$663$	13.5000	−	23.3827i	0.524297	−	0.908108i
$664$	−13.5000	−	7.79423i	−0.523902	−	0.302475i
$665$	7.50000	−	4.33013i	0.290838	−	0.167915i
$666$	−13.5000	+	23.3827i	−0.523114	+	0.906061i
$667$		0			0
$668$	−1.50000	−	2.59808i	−0.0580367	−	0.100523i
$669$	15.0000			0.579934
$670$	16.5000	+	28.5788i	0.637451	+	1.10410i
$671$	−36.0000	−	20.7846i	−1.38976	−	0.802381i
$672$	−9.00000			−0.347183
$673$	1.50000	+	0.866025i	0.0578208	+	0.0333828i	0.528632	−	0.848851i	$-0.322705\pi$
$673$	1.50000	+	0.866025i	0.0578208	+	0.0333828i	−0.470811	+	0.882234i	$0.656039\pi$
$674$	−24.0000			−0.924445
$675$	9.00000	−	5.19615i	0.346410	−	0.200000i
$676$	−7.00000	−	12.1244i	−0.269231	−	0.466321i
$677$	7.50000	−	12.9904i	0.288248	−	0.499261i	−0.685143	−	0.728408i	$-0.740260\pi$
$677$	7.50000	−	12.9904i	0.288248	−	0.499261i	0.973392	+	0.229147i	$0.0735938\pi$
$678$	31.5000	−	18.1865i	1.20975	−	0.698450i
$679$	−5.00000	−	8.66025i	−0.191882	−	0.332350i
$680$	−9.00000			−0.345134
$681$	13.5000	+	23.3827i	0.517321	+	0.896026i
$682$	22.5000	−	18.1865i	0.861570	−	0.696398i
$683$		−	45.0333i		−	1.72315i	−0.507628	−	0.861576i	$-0.669478\pi$
$683$		−	45.0333i		−	1.72315i	0.507628	−	0.861576i	$-0.330522\pi$
$684$	7.50000	−	12.9904i	0.286770	−	0.496700i
$685$	−4.50000	+	2.59808i	−0.171936	+	0.0992674i
$686$		−	22.5167i		−	0.859690i
$687$	3.00000			0.114457
$688$	−7.50000	+	4.33013i	−0.285935	+	0.165085i
$689$	−13.5000	+	7.79423i	−0.514309	+	0.296936i
$690$		0			0
$691$	21.5000	−	37.2391i	0.817899	−	1.41664i	−0.0893292	−	0.996002i	$-0.528472\pi$
$691$	21.5000	−	37.2391i	0.817899	−	1.41664i	0.907228	−	0.420640i	$-0.138194\pi$
$692$	13.5000	+	7.79423i	0.513193	+	0.296292i
$693$	−4.50000	−	7.79423i	−0.170941	−	0.296078i
$694$	40.5000	−	23.3827i	1.53736	−	0.887595i
$695$	15.0000	−	25.9808i	0.568982	−	0.985506i
$696$	9.00000	−	15.5885i	0.341144	−	0.590879i
$697$		−	25.9808i		−	0.984092i
$698$		−	17.3205i		−	0.655591i
$699$	−6.00000	+	10.3923i	−0.226941	+	0.393073i
$700$	−1.00000	+	1.73205i	−0.0377964	+	0.0654654i
$701$	34.5000	−	19.9186i	1.30305	−	0.752315i	0.322121	−	0.946698i	$-0.395604\pi$
$701$	34.5000	−	19.9186i	1.30305	−	0.752315i	0.980926	+	0.194384i	$0.0622707\pi$
$702$	−40.5000	−	23.3827i	−1.52857	−	0.882523i
$703$	−22.5000	−	12.9904i	−0.848604	−	0.489942i
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$	−27.0000	+	15.5885i	−1.01688	+	0.587095i
$706$	−13.5000	+	7.79423i	−0.508079	+	0.293340i
$707$	−12.0000	+	6.92820i	−0.451306	+	0.260562i
$708$	15.0000			0.563735
$709$			34.6410i			1.30097i	0.759519	+	0.650485i	$0.225434\pi$
$709$			34.6410i			1.30097i	−0.759519	+	0.650485i	$0.774566\pi$
$710$	−4.50000	+	2.59808i	−0.168882	+	0.0975041i
$711$	22.5000	+	12.9904i	0.843816	+	0.487177i
$712$			10.3923i			0.389468i
$713$		0			0
$714$	4.50000	+	7.79423i	0.168408	+	0.291692i
$715$	−27.0000			−1.00974
$716$	−7.50000	−	12.9904i	−0.280288	−	0.485473i
$717$	13.5000	−	7.79423i	0.504167	−	0.291081i
$718$	1.50000	−	2.59808i	0.0559795	−	0.0969593i
$719$	−22.5000	−	38.9711i	−0.839108	−	1.45338i	−0.890641	−	0.454707i	$-0.849744\pi$
$719$	−22.5000	−	38.9711i	−0.839108	−	1.45338i	0.0515326	−	0.998671i	$-0.483589\pi$
$720$			25.9808i			0.968246i
$721$	−1.00000			−0.0372419
$722$	9.00000	+	5.19615i	0.334945	+	0.193381i
$723$	−21.0000			−0.780998
$724$	22.5000	+	12.9904i	0.836206	+	0.482784i
$725$	−6.00000	−	10.3923i	−0.222834	−	0.385961i
$726$	6.00000			0.222681
$727$	0.500000	+	0.866025i	0.0185440	+	0.0321191i	0.875148	−	0.483854i	$-0.160764\pi$
$727$	0.500000	+	0.866025i	0.0185440	+	0.0321191i	−0.856605	+	0.515974i	$0.827430\pi$
$728$	−9.00000			−0.333562
$729$	−27.0000			−1.00000
$730$	−22.5000	+	12.9904i	−0.832762	+	0.480796i
$731$	4.50000	+	2.59808i	0.166439	+	0.0960933i
$732$	12.0000	−	20.7846i	0.443533	−	0.768221i
$733$	−15.5000	+	26.8468i	−0.572506	+	0.991609i	0.423802	+	0.905755i	$0.360695\pi$
$733$	−15.5000	+	26.8468i	−0.572506	+	0.991609i	−0.996308	+	0.0858539i	$0.972638\pi$
$734$	−1.50000	+	2.59808i	−0.0553660	+	0.0958967i
$735$	−18.0000			−0.663940
$736$		0			0
$737$	16.5000	+	28.5788i	0.607785	+	1.05272i
$738$	−45.0000			−1.65647
$739$	10.5000	+	6.06218i	0.386249	+	0.223001i	0.680534	−	0.732717i	$-0.261748\pi$
$739$	10.5000	+	6.06218i	0.386249	+	0.223001i	−0.294285	+	0.955718i	$0.595081\pi$
$740$	−9.00000			−0.330847
$741$	22.5000	−	38.9711i	0.826558	−	1.43164i
$742$		−	5.19615i		−	0.190757i
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$	−10.5000	−	12.9904i	−0.384949	−	0.476250i
$745$	−9.00000			−0.329734
$746$			17.3205i			0.634149i
$747$	27.0000			0.987878
$748$	9.00000			0.329073
$749$	10.5000	+	6.06218i	0.383662	+	0.221507i
$750$	31.5000	+	18.1865i	1.15022	+	0.664078i
$751$	2.50000	+	4.33013i	0.0912263	+	0.158009i	0.908027	−	0.418911i	$-0.137588\pi$
$751$	2.50000	+	4.33013i	0.0912263	+	0.158009i	−0.816801	+	0.576919i	$0.804255\pi$
$752$			51.9615i			1.89484i
$753$			25.9808i			0.946792i
$754$	−27.0000	+	46.7654i	−0.983282	+	1.70309i
$755$	3.00000	−	5.19615i	0.109181	−	0.189107i
$756$	4.50000	−	2.59808i	0.163663	−	0.0944911i
$757$	−34.5000	−	19.9186i	−1.25392	−	0.723953i	−0.282037	−	0.959403i	$-0.591010\pi$
$757$	−34.5000	−	19.9186i	−1.25392	−	0.723953i	−0.971886	+	0.235450i	$0.924344\pi$
$758$	1.50000	−	0.866025i	0.0544825	−	0.0314555i
$759$		0			0
$760$	−15.0000			−0.544107
$761$	−22.5000	−	38.9711i	−0.815624	−	1.41270i	−0.908879	−	0.417061i	$-0.863060\pi$
$761$	−22.5000	−	38.9711i	−0.815624	−	1.41270i	0.0932544	−	0.995642i	$-0.470273\pi$
$762$		−	5.19615i		−	0.188237i
$763$	1.00000	+	1.73205i	0.0362024	+	0.0627044i
$764$	10.5000	+	6.06218i	0.379877	+	0.219322i
$765$	13.5000	−	7.79423i	0.488094	−	0.281801i
$766$	−13.5000	−	7.79423i	−0.487775	−	0.281617i
$767$	45.0000			1.62486
$768$	28.5000	+	16.4545i	1.02841	+	0.593750i
$769$	2.50000	+	4.33013i	0.0901523	+	0.156148i	0.907575	−	0.419890i	$-0.137931\pi$
$769$	2.50000	+	4.33013i	0.0901523	+	0.156148i	−0.817423	+	0.576038i	$0.804598\pi$
$770$	4.50000	−	7.79423i	0.162169	−	0.280885i
$771$	−1.50000	−	2.59808i	−0.0540212	−	0.0935674i
$772$	−2.50000	−	4.33013i	−0.0899770	−	0.155845i
$773$	−54.0000			−1.94225			−0.971123	−	0.238581i	$-0.923318\pi$
$773$	−54.0000			−1.94225			−0.971123	+	0.238581i	$0.923318\pi$
$774$	4.50000	−	7.79423i	0.161749	−	0.280158i
$775$	−11.0000	+	1.73205i	−0.395132	+	0.0622171i
$776$			17.3205i			0.621770i
$777$	−4.50000	−	7.79423i	−0.161437	−	0.279616i
$778$	22.5000	−	12.9904i	0.806664	−	0.465728i
$779$		−	43.3013i		−	1.55143i
$780$		−	15.5885i		−	0.558156i
$781$	−4.50000	+	2.59808i	−0.161023	+	0.0929665i
$782$		0			0
$783$			31.1769i			1.11417i
$784$	−15.0000	+	25.9808i	−0.535714	+	0.927884i
$785$	21.0000	+	12.1244i	0.749522	+	0.432737i
$786$			46.7654i			1.66807i
$787$	−4.50000	+	2.59808i	−0.160408	+	0.0926114i	−0.578055	−	0.815998i	$-0.696188\pi$
$787$	−4.50000	+	2.59808i	−0.160408	+	0.0926114i	0.417647	+	0.908609i	$0.362855\pi$
$788$	−1.50000	+	2.59808i	−0.0534353	+	0.0925526i
$789$	−36.0000	−	20.7846i	−1.28163	−	0.739952i
$790$			25.9808i			0.924354i
$791$			12.1244i			0.431092i
$792$			15.5885i			0.553912i
$793$	36.0000	−	62.3538i	1.27840	−	2.21425i
$794$	−34.5000	+	19.9186i	−1.22436	+	0.706884i
$795$	−9.00000			−0.319197
$796$	−10.5000	−	6.06218i	−0.372163	−	0.214868i
$797$	1.50000	−	2.59808i	0.0531327	−	0.0920286i	−0.838236	−	0.545308i	$-0.816413\pi$
$797$	1.50000	−	2.59808i	0.0531327	−	0.0920286i	0.891368	+	0.453279i	$0.149746\pi$
$798$	7.50000	+	12.9904i	0.265497	+	0.459855i
$799$	27.0000	−	15.5885i	0.955191	−	0.551480i
$800$	9.00000	−	5.19615i	0.318198	−	0.183712i
$801$	−9.00000	−	15.5885i	−0.317999	−	0.550791i
$802$			10.3923i			0.366965i
$803$	−22.5000	+	12.9904i	−0.794008	+	0.458421i
$804$	−16.5000	+	9.52628i	−0.581910	+	0.335966i
$805$		0			0
$806$	31.5000	+	38.9711i	1.10954	+	1.37270i
$807$	40.5000	−	23.3827i	1.42567	−	0.823110i
$808$	24.0000			0.844317
$809$	7.50000	+	12.9904i	0.263686	+	0.456717i	0.967219	−	0.253946i	$-0.0817284\pi$
$809$	7.50000	+	12.9904i	0.263686	+	0.456717i	−0.703533	+	0.710663i	$0.748395\pi$
$810$	−13.5000	−	23.3827i	−0.474342	−	0.821584i
$811$	−18.5000	+	32.0429i	−0.649623	+	1.12518i	0.333590	+	0.942718i	$0.391740\pi$
$811$	−18.5000	+	32.0429i	−0.649623	+	1.12518i	−0.983213	+	0.182462i	$0.941593\pi$
$812$	−3.00000	−	5.19615i	−0.105279	−	0.182349i
$813$	−9.00000	+	15.5885i	−0.315644	+	0.546711i
$814$	−27.0000			−0.946350
$815$	6.00000	+	3.46410i	0.210171	+	0.121342i
$816$		−	25.9808i		−	0.909509i
$817$	7.50000	+	4.33013i	0.262392	+	0.151492i
$818$	22.5000	+	38.9711i	0.786694	+	1.36259i
$819$	13.5000	−	7.79423i	0.471728	−	0.272352i
$820$	−7.50000	−	12.9904i	−0.261911	−	0.453644i
$821$	30.0000			1.04701			0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000			1.04701			0.523504	+	0.852023i	$0.324625\pi$
$822$	−4.50000	−	7.79423i	−0.156956	−	0.271855i
$823$	−10.5000	+	6.06218i	−0.366007	+	0.211314i	−0.671713	−	0.740812i	$-0.734441\pi$
$823$	−10.5000	+	6.06218i	−0.366007	+	0.211314i	0.305706	+	0.952126i	$0.401108\pi$
$824$	1.50000	+	0.866025i	0.0522550	+	0.0301694i
$825$	9.00000	+	5.19615i	0.313340	+	0.180907i
$826$	−7.50000	+	12.9904i	−0.260958	+	0.451993i
$827$	−1.50000	+	2.59808i	−0.0521601	+	0.0903440i	−0.890927	−	0.454147i	$-0.849944\pi$
$827$	−1.50000	+	2.59808i	−0.0521601	+	0.0903440i	0.838766	+	0.544491i	$0.183277\pi$
$828$		0			0
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$	13.5000	+	23.3827i	0.468592	+	0.811625i
$831$	−12.0000	+	20.7846i	−0.416275	+	0.721010i
$832$	4.50000	+	2.59808i	0.156009	+	0.0900721i
$833$	18.0000			0.623663
$834$	45.0000	+	25.9808i	1.55822	+	0.899640i
$835$		−	5.19615i		−	0.179820i
$836$	15.0000			0.518786
$837$	27.0000	+	10.3923i	0.933257	+	0.359211i
$838$	−30.0000			−1.03633
$839$		−	10.3923i		−	0.358782i	−0.983778	−	0.179391i	$-0.942587\pi$
$839$		−	10.3923i		−	0.358782i	0.983778	−	0.179391i	$-0.0574128\pi$
$840$	−4.50000	−	2.59808i	−0.155265	−	0.0896421i
$841$	7.00000			0.241379
$842$	28.5000	+	16.4545i	0.982175	+	0.567059i
$843$	12.0000	−	20.7846i	0.413302	−	0.715860i
$844$	11.5000	+	19.9186i	0.395846	+	0.685626i
$845$		−	24.2487i		−	0.834181i
$846$	−27.0000	−	46.7654i	−0.928279	−	1.60783i
$847$	−1.00000	+	1.73205i	−0.0343604	+	0.0595140i
$848$	−7.50000	+	12.9904i	−0.257551	+	0.446092i
$849$	30.0000	+	17.3205i	1.02960	+	0.594438i
$850$	−9.00000	−	5.19615i	−0.308697	−	0.178227i
$851$		0			0
$852$	−1.50000	−	2.59808i	−0.0513892	−	0.0890086i
$853$	−14.0000			−0.479351			−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000			−0.479351			−0.239675	+	0.970853i	$0.577041\pi$
$854$	12.0000	+	20.7846i	0.410632	+	0.711235i
$855$	22.5000	−	12.9904i	0.769484	−	0.444262i
$856$	−10.5000	−	18.1865i	−0.358883	−	0.621603i
$857$	−31.5000	−	18.1865i	−1.07602	−	0.621240i	−0.146200	−	0.989255i	$-0.546704\pi$
$857$	−31.5000	−	18.1865i	−1.07602	−	0.621240i	−0.929820	+	0.368015i	$0.880038\pi$
$858$		−	46.7654i		−	1.59654i
$859$	16.5000	+	9.52628i	0.562973	+	0.325032i	0.754338	−	0.656486i	$-0.227958\pi$
$859$	16.5000	+	9.52628i	0.562973	+	0.325032i	−0.191365	+	0.981519i	$0.561291\pi$
$860$	3.00000			0.102299
$861$	7.50000	−	12.9904i	0.255599	−	0.442711i
$862$	−22.5000	−	38.9711i	−0.766353	−	1.32736i
$863$	−19.5000	+	33.7750i	−0.663788	+	1.14971i	0.315825	+	0.948818i	$0.397719\pi$
$863$	−19.5000	+	33.7750i	−0.663788	+	1.14971i	−0.979612	+	0.200897i	$0.935615\pi$
$864$	−27.0000			−0.918559
$865$	13.5000	+	23.3827i	0.459014	+	0.795035i
$866$	−12.0000			−0.407777
$867$	12.0000	−	6.92820i	0.407541	−	0.235294i
$868$	−5.50000	+	0.866025i	−0.186682	+	0.0293948i
$869$			25.9808i			0.881337i
$870$	−27.0000	+	15.5885i	−0.915386	+	0.528498i
$871$	−49.5000	+	28.5788i	−1.67724	+	0.968357i
$872$		−	3.46410i		−	0.117309i
$873$	−15.0000	−	25.9808i	−0.507673	−	0.879316i
$874$		0			0
$875$	−10.5000	+	6.06218i	−0.354965	+	0.204939i
$876$	−7.50000	−	12.9904i	−0.253402	−	0.438904i
$877$	2.50000	−	4.33013i	0.0844190	−	0.146218i	−0.820724	−	0.571324i	$-0.806430\pi$
$877$	2.50000	−	4.33013i	0.0844190	−	0.146218i	0.905143	+	0.425106i	$0.139763\pi$
$878$	1.50000	+	0.866025i	0.0506225	+	0.0292269i
$879$	−27.0000			−0.910687
$880$	−22.5000	+	12.9904i	−0.758475	+	0.437906i
$881$	−28.5000	+	49.3634i	−0.960189	+	1.66310i	−0.238171	+	0.971223i	$0.576548\pi$
$881$	−28.5000	+	49.3634i	−0.960189	+	1.66310i	−0.722019	+	0.691873i	$0.756786\pi$
$882$		−	31.1769i		−	1.04978i
$883$			51.9615i			1.74864i	0.485346	+	0.874322i	$0.338694\pi$
$883$			51.9615i			1.74864i	−0.485346	+	0.874322i	$0.661306\pi$
$884$			15.5885i			0.524297i
$885$	22.5000	+	12.9904i	0.756329	+	0.436667i
$886$	−10.5000	+	18.1865i	−0.352754	+	0.610989i
$887$	16.5000	−	9.52628i	0.554016	−	0.319861i	−0.196724	−	0.980459i	$-0.563030\pi$
$887$	16.5000	−	9.52628i	0.554016	−	0.319861i	0.750740	+	0.660598i	$0.229697\pi$
$888$			15.5885i			0.523114i
$889$	1.50000	+	0.866025i	0.0503084	+	0.0290456i
$890$	9.00000	−	15.5885i	0.301681	−	0.522526i
$891$	−13.5000	−	23.3827i	−0.452267	−	0.783349i
$892$	−7.50000	+	4.33013i	−0.251119	+	0.144983i
$893$	45.0000	−	25.9808i	1.50587	−	0.869413i
$894$		−	15.5885i		−	0.521356i
$895$		−	25.9808i		−	0.868441i
$896$	−10.5000	+	6.06218i	−0.350780	+	0.202523i
$897$		0			0
$898$		−	51.9615i		−	1.73398i
$899$	12.0000	−	31.1769i	0.400222	−	1.03981i
$900$	−3.00000	+	5.19615i	−0.100000	+	0.173205i
$901$	9.00000			0.299833
$902$	−22.5000	−	38.9711i	−0.749168	−	1.29760i
$903$	1.50000	+	2.59808i	0.0499169	+	0.0864586i
$904$	10.5000	−	18.1865i	0.349225	−	0.604875i
$905$	22.5000	+	38.9711i	0.747925	+	1.29544i
$906$	9.00000	+	5.19615i	0.299005	+	0.172631i
$907$	28.0000			0.929725			0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000			0.929725			0.464862	+	0.885383i	$0.346104\pi$
$908$	−13.5000	−	7.79423i	−0.448013	−	0.258661i
$909$	−36.0000	+	20.7846i	−1.19404	+	0.689382i
$910$	13.5000	+	7.79423i	0.447521	+	0.258376i
$911$	7.50000	+	12.9904i	0.248486	+	0.430391i	0.963106	−	0.269122i	$-0.0867336\pi$
$911$	7.50000	+	12.9904i	0.248486	+	0.430391i	−0.714620	+	0.699513i	$0.753400\pi$
$912$		−	43.3013i		−	1.43385i
$913$	13.5000	+	23.3827i	0.446785	+	0.773854i
$914$	−12.0000			−0.396925
$915$	36.0000	−	20.7846i	1.19012	−	0.687118i
$916$	−1.50000	+	0.866025i	−0.0495614	+	0.0286143i
$917$	−13.5000	−	7.79423i	−0.445809	−	0.257388i
$918$	13.5000	+	23.3827i	0.445566	+	0.771744i
$919$	−0.500000	+	0.866025i	−0.0164935	+	0.0285675i	−0.874154	−	0.485648i	$-0.838584\pi$
$919$	−0.500000	+	0.866025i	−0.0164935	+	0.0285675i	0.857661	+	0.514216i	$0.171917\pi$
$920$		0			0
$921$		−	12.1244i		−	0.399511i
$922$		−	10.3923i		−	0.342252i
$923$	−4.50000	−	7.79423i	−0.148119	−	0.256550i
$924$	4.50000	+	2.59808i	0.148039	+	0.0854704i
$925$	9.00000	+	5.19615i	0.295918	+	0.170848i
$926$	−30.0000			−0.985861
$927$	−3.00000			−0.0985329
$928$			31.1769i			1.02343i
$929$	−6.00000			−0.196854			−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000			−0.196854			−0.0984268	+	0.995144i	$0.531381\pi$
$930$	4.50000	+	28.5788i	0.147561	+	0.937137i
$931$	30.0000			0.983210
$932$		−	6.92820i		−	0.226941i
$933$	−3.00000	+	5.19615i	−0.0982156	+	0.170114i
$934$	−30.0000			−0.981630
$935$	13.5000	+	7.79423i	0.441497	+	0.254899i
$936$	−27.0000			−0.882523
$937$	8.50000	+	14.7224i	0.277683	+	0.480961i	0.970808	−	0.239856i	$-0.0771002\pi$
$937$	8.50000	+	14.7224i	0.277683	+	0.480961i	−0.693126	+	0.720817i	$0.743767\pi$
$938$		−	19.0526i		−	0.622088i
$939$	39.0000			1.27272
$940$	9.00000	−	15.5885i	0.293548	−	0.508439i
$941$	7.50000	−	12.9904i	0.244493	−	0.423474i	−0.717496	−	0.696563i	$-0.754712\pi$
$941$	7.50000	−	12.9904i	0.244493	−	0.423474i	0.961989	+	0.273088i	$0.0880451\pi$
$942$	−21.0000	+	36.3731i	−0.684217	+	1.18510i
$943$		0			0
$944$	37.5000	−	21.6506i	1.22052	−	0.704668i
$945$	9.00000			0.292770
$946$	9.00000			0.292615
$947$	−28.5000	−	49.3634i	−0.926126	−	1.60410i	−0.789741	−	0.613441i	$-0.789785\pi$
$947$	−28.5000	−	49.3634i	−0.926126	−	1.60410i	−0.136385	−	0.990656i	$-0.543548\pi$
$948$	−15.0000			−0.487177
$949$	−22.5000	−	38.9711i	−0.730381	−	1.26506i
$950$	−15.0000	−	8.66025i	−0.486664	−	0.280976i
$951$	−3.00000			−0.0972817
$952$	4.50000	+	2.59808i	0.145846	+	0.0842041i
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		−	15.5885i		−	0.504695i
$955$	10.5000	+	18.1865i	0.339772	+	0.588502i
$956$	−4.50000	+	7.79423i	−0.145540	+	0.252083i
$957$	−27.0000	+	15.5885i	−0.872786	+	0.503903i
$958$	7.50000	+	12.9904i	0.242314	+	0.419700i
$959$	3.00000			0.0968751
$960$	1.50000	+	2.59808i	0.0484123	+	0.0838525i
$961$	−23.0000	−	20.7846i	−0.741935	−	0.670471i
$962$		−	46.7654i		−	1.50778i
$963$	31.5000	+	18.1865i	1.01507	+	0.586053i
$964$	10.5000	−	6.06218i	0.338182	−	0.195250i
$965$		−	8.66025i		−	0.278783i
$966$		0			0
$967$	−28.5000	+	16.4545i	−0.916498	+	0.529140i	−0.882516	−	0.470282i	$-0.844152\pi$
$967$	−28.5000	+	16.4545i	−0.916498	+	0.529140i	−0.0339820	+	0.999422i	$0.510819\pi$
$968$	3.00000	−	1.73205i	0.0964237	−	0.0556702i
$969$	−22.5000	+	12.9904i	−0.722804	+	0.417311i
$970$	15.0000	−	25.9808i	0.481621	−	0.834192i
$971$	−40.5000	−	23.3827i	−1.29971	−	0.750386i	−0.319354	−	0.947636i	$-0.603466\pi$
$971$	−40.5000	−	23.3827i	−1.29971	−	0.750386i	−0.980353	+	0.197250i	$0.936799\pi$
$972$	13.5000	−	7.79423i	0.433013	−	0.250000i
$973$	−15.0000	+	8.66025i	−0.480878	+	0.277635i
$974$	−1.50000	+	2.59808i	−0.0480631	+	0.0832477i
$975$	−9.00000	+	15.5885i	−0.288231	+	0.499230i
$976$		−	69.2820i		−	2.21766i
$977$			34.6410i			1.10826i	0.832429	+	0.554132i	$0.186950\pi$
$977$			34.6410i			1.10826i	−0.832429	+	0.554132i	$0.813050\pi$
$978$	−6.00000	+	10.3923i	−0.191859	+	0.332309i
$979$	9.00000	−	15.5885i	0.287641	−	0.498209i
$980$	9.00000	−	5.19615i	0.287494	−	0.165985i
$981$	3.00000	+	5.19615i	0.0957826	+	0.165900i
$982$	40.5000	+	23.3827i	1.29241	+	0.746171i
$983$	−13.5000	+	23.3827i	−0.430583	+	0.745792i	−0.996924	−	0.0783795i	$-0.975025\pi$
$983$	−13.5000	+	23.3827i	−0.430583	+	0.745792i	0.566340	+	0.824171i	$0.308359\pi$
$984$	−22.5000	+	12.9904i	−0.717274	+	0.414118i
$985$	−4.50000	+	2.59808i	−0.143382	+	0.0827816i
$986$	27.0000	−	15.5885i	0.859855	−	0.496438i
$987$	18.0000			0.572946
$988$			25.9808i			0.826558i
$989$		0			0
$990$	13.5000	−	23.3827i	0.429058	−	0.743151i
$991$			17.3205i			0.550204i	0.961415	+	0.275102i	$0.0887116\pi$
$991$			17.3205i			0.550204i	−0.961415	+	0.275102i	$0.911288\pi$
$992$	27.0000	+	10.3923i	0.857251	+	0.329956i
$993$	−7.50000	−	12.9904i	−0.238005	−	0.412237i
$994$	3.00000			0.0951542
$995$	−10.5000	−	18.1865i	−0.332872	−	0.576552i
$996$	−13.5000	+	7.79423i	−0.427764	+	0.246970i
$997$	12.5000	−	21.6506i	0.395879	−	0.685682i	−0.597334	−	0.801993i	$-0.703773\pi$
$997$	12.5000	−	21.6506i	0.395879	−	0.685682i	0.993213	+	0.116310i	$0.0371066\pi$
$998$	−13.5000	−	23.3827i	−0.427335	−	0.740166i
$999$	−13.5000	−	23.3827i	−0.427121	−	0.739795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.g.c.68.1	yes	2
3.2	odd	2		93.2.g.b.68.1	yes	2
31.26	odd	6		93.2.g.b.26.1	✓	2
93.26	even	6	inner	93.2.g.c.26.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.g.b.26.1	✓	2	31.26	odd	6
93.2.g.b.68.1	yes	2	3.2	odd	2
93.2.g.c.26.1	yes	2	93.26	even	6	inner
93.2.g.c.68.1	yes	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.73205i q^{2} +(1.50000 + 0.866025i) q^{3} -1.00000 q^{4} +(-1.50000 - 0.866025i) q^{5} +(1.50000 - 2.59808i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q-1.73205i q^{2} +(1.50000 + 0.866025i) q^{3} -1.00000 q^{4} +(-1.50000 - 0.866025i) q^{5} +(1.50000 - 2.59808i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(-1.50000 - 0.866025i) q^{12} +(-4.50000 - 2.59808i) q^{13} +(1.50000 - 0.866025i) q^{14} +(-1.50000 - 2.59808i) q^{15} -5.00000 q^{16} +(1.50000 + 2.59808i) q^{17} +(4.50000 - 2.59808i) q^{18} +(2.50000 + 4.33013i) q^{19} +(1.50000 + 0.866025i) q^{20} +1.73205i q^{21} +(4.50000 + 2.59808i) q^{22} +(1.50000 - 2.59808i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(-4.50000 + 7.79423i) q^{26} +5.19615i q^{27} +(-0.500000 - 0.866025i) q^{28} +6.00000 q^{29} +(-4.50000 + 2.59808i) q^{30} +(2.00000 - 5.19615i) q^{31} +5.19615i q^{32} +(-4.50000 + 2.59808i) q^{33} +(4.50000 - 2.59808i) q^{34} -1.73205i q^{35} +(-1.50000 - 2.59808i) q^{36} +(-4.50000 + 2.59808i) q^{37} +(7.50000 - 4.33013i) q^{38} +(-4.50000 - 7.79423i) q^{39} +(-1.50000 + 2.59808i) q^{40} +(-7.50000 - 4.33013i) q^{41} +3.00000 q^{42} +(1.50000 - 0.866025i) q^{43} +(1.50000 - 2.59808i) q^{44} -5.19615i q^{45} -10.3923i q^{47} +(-7.50000 - 4.33013i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-3.00000 + 1.73205i) q^{50} +5.19615i q^{51} +(4.50000 + 2.59808i) q^{52} +(1.50000 - 2.59808i) q^{53} +9.00000 q^{54} +(4.50000 - 2.59808i) q^{55} +(1.50000 - 0.866025i) q^{56} +8.66025i q^{57} -10.3923i q^{58} +(-7.50000 + 4.33013i) q^{59} +(1.50000 + 2.59808i) q^{60} +13.8564i q^{61} +(-9.00000 - 3.46410i) q^{62} +(-1.50000 + 2.59808i) q^{63} -1.00000 q^{64} +(4.50000 + 7.79423i) q^{65} +(4.50000 + 7.79423i) q^{66} +(5.50000 - 9.52628i) q^{67} +(-1.50000 - 2.59808i) q^{68} -3.00000 q^{70} +(1.50000 + 0.866025i) q^{71} +(4.50000 - 2.59808i) q^{72} +(7.50000 + 4.33013i) q^{73} +(4.50000 + 7.79423i) q^{74} -3.46410i q^{75} +(-2.50000 - 4.33013i) q^{76} -3.00000 q^{77} +(-13.5000 + 7.79423i) q^{78} +(7.50000 - 4.33013i) q^{79} +(7.50000 + 4.33013i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-7.50000 + 12.9904i) q^{82} +(4.50000 - 7.79423i) q^{83} -1.73205i q^{84} -5.19615i q^{85} +(-1.50000 - 2.59808i) q^{86} +(9.00000 + 5.19615i) q^{87} +(4.50000 + 2.59808i) q^{88} -6.00000 q^{89} -9.00000 q^{90} -5.19615i q^{91} +(7.50000 - 6.06218i) q^{93} -18.0000 q^{94} -8.66025i q^{95} +(-4.50000 + 7.79423i) q^{96} -10.0000 q^{97} +(-9.00000 - 5.19615i) q^{98} -9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} - 2 q^{4} - 3 q^{5} + 3 q^{6} + q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 - 2 * q^4 - 3 * q^5 + 3 * q^6 + q^7 + 3 * q^9	\( 2 q + 3 q^{3} - 2 q^{4} - 3 q^{5} + 3 q^{6} + q^{7} + 3 q^{9} - 3 q^{10} - 3 q^{11} - 3 q^{12} - 9 q^{13} + 3 q^{14} - 3 q^{15} - 10 q^{16} + 3 q^{17} + 9 q^{18} + 5 q^{19} + 3 q^{20} + 9 q^{22} + 3 q^{24} - 2 q^{25} - 9 q^{26} - q^{28} + 12 q^{29} - 9 q^{30} + 4 q^{31} - 9 q^{33} + 9 q^{34} - 3 q^{36} - 9 q^{37} + 15 q^{38} - 9 q^{39} - 3 q^{40} - 15 q^{41} + 6 q^{42} + 3 q^{43} + 3 q^{44} - 15 q^{48} + 6 q^{49} - 6 q^{50} + 9 q^{52} + 3 q^{53} + 18 q^{54} + 9 q^{55} + 3 q^{56} - 15 q^{59} + 3 q^{60} - 18 q^{62} - 3 q^{63} - 2 q^{64} + 9 q^{65} + 9 q^{66} + 11 q^{67} - 3 q^{68} - 6 q^{70} + 3 q^{71} + 9 q^{72} + 15 q^{73} + 9 q^{74} - 5 q^{76} - 6 q^{77} - 27 q^{78} + 15 q^{79} + 15 q^{80} - 9 q^{81} - 15 q^{82} + 9 q^{83} - 3 q^{86} + 18 q^{87} + 9 q^{88} - 12 q^{89} - 18 q^{90} + 15 q^{93} - 36 q^{94} - 9 q^{96} - 20 q^{97} - 18 q^{98} - 18 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 - 2 * q^4 - 3 * q^5 + 3 * q^6 + q^7 + 3 * q^9 - 3 * q^10 - 3 * q^11 - 3 * q^12 - 9 * q^13 + 3 * q^14 - 3 * q^15 - 10 * q^16 + 3 * q^17 + 9 * q^18 + 5 * q^19 + 3 * q^20 + 9 * q^22 + 3 * q^24 - 2 * q^25 - 9 * q^26 - q^28 + 12 * q^29 - 9 * q^30 + 4 * q^31 - 9 * q^33 + 9 * q^34 - 3 * q^36 - 9 * q^37 + 15 * q^38 - 9 * q^39 - 3 * q^40 - 15 * q^41 + 6 * q^42 + 3 * q^43 + 3 * q^44 - 15 * q^48 + 6 * q^49 - 6 * q^50 + 9 * q^52 + 3 * q^53 + 18 * q^54 + 9 * q^55 + 3 * q^56 - 15 * q^59 + 3 * q^60 - 18 * q^62 - 3 * q^63 - 2 * q^64 + 9 * q^65 + 9 * q^66 + 11 * q^67 - 3 * q^68 - 6 * q^70 + 3 * q^71 + 9 * q^72 + 15 * q^73 + 9 * q^74 - 5 * q^76 - 6 * q^77 - 27 * q^78 + 15 * q^79 + 15 * q^80 - 9 * q^81 - 15 * q^82 + 9 * q^83 - 3 * q^86 + 18 * q^87 + 9 * q^88 - 12 * q^89 - 18 * q^90 + 15 * q^93 - 36 * q^94 - 9 * q^96 - 20 * q^97 - 18 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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