LMFDB - Embedded newform 315.2.bl.a.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(41,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("315.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bl (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:	$2.51528766367$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	315.41
Dual form			315.2.bl.a.146.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +3.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +3.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} -1.73205i q^{10} +(-1.50000 + 0.866025i) q^{12} +(-3.00000 - 3.46410i) q^{14} +(1.50000 - 0.866025i) q^{15} +(2.50000 + 4.33013i) q^{16} -6.00000 q^{17} +(-4.50000 - 2.59808i) q^{18} -3.46410i q^{19} +(0.500000 + 0.866025i) q^{20} +(1.50000 - 4.33013i) q^{21} +(-7.50000 - 4.33013i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(-0.500000 - 0.866025i) q^{25} -5.19615i q^{27} +(2.50000 + 0.866025i) q^{28} +(-1.50000 + 0.866025i) q^{29} +(-1.50000 + 2.59808i) q^{30} +(-3.00000 - 1.73205i) q^{31} +(-4.50000 - 2.59808i) q^{32} +(9.00000 - 5.19615i) q^{34} +(-2.50000 - 0.866025i) q^{35} +3.00000 q^{36} -2.00000 q^{37} +(3.00000 + 5.19615i) q^{38} +(1.50000 + 0.866025i) q^{40} +(4.50000 - 7.79423i) q^{41} +(1.50000 + 7.79423i) q^{42} +(-2.00000 - 3.46410i) q^{43} -3.00000 q^{45} +15.0000 q^{46} +(1.50000 + 2.59808i) q^{47} -8.66025i q^{48} +(-6.50000 + 2.59808i) q^{49} +(1.50000 + 0.866025i) q^{50} +(9.00000 + 5.19615i) q^{51} +3.46410i q^{53} +(4.50000 + 7.79423i) q^{54} +(4.50000 - 0.866025i) q^{56} +(-3.00000 + 5.19615i) q^{57} +(1.50000 - 2.59808i) q^{58} +(-3.00000 + 5.19615i) q^{59} -1.73205i q^{60} +(-7.50000 + 4.33013i) q^{61} +6.00000 q^{62} +(-6.00000 + 5.19615i) q^{63} -1.00000 q^{64} +(6.50000 - 11.2583i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(7.50000 + 12.9904i) q^{69} +(4.50000 - 0.866025i) q^{70} +(4.50000 - 2.59808i) q^{72} +13.8564i q^{73} +(3.00000 - 1.73205i) q^{74} +1.73205i q^{75} +(-3.00000 - 1.73205i) q^{76} +(-7.00000 - 12.1244i) q^{79} -5.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +15.5885i q^{82} +(4.50000 + 7.79423i) q^{83} +(-3.00000 - 3.46410i) q^{84} +(3.00000 - 5.19615i) q^{85} +(6.00000 + 3.46410i) q^{86} +3.00000 q^{87} -15.0000 q^{89} +(4.50000 - 2.59808i) q^{90} +(-7.50000 + 4.33013i) q^{92} +(3.00000 + 5.19615i) q^{93} +(-4.50000 - 2.59808i) q^{94} +(3.00000 + 1.73205i) q^{95} +(4.50000 + 7.79423i) q^{96} +(3.00000 - 1.73205i) q^{97} +(7.50000 - 9.52628i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 3 q^{3} + q^{4} - q^{5} + 6 q^{6} + q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 - 3 * q^3 + q^4 - q^5 + 6 * q^6 + q^7 + 3 * q^9	$ 2 q - 3 q^{2} - 3 q^{3} + q^{4} - q^{5} + 6 q^{6} + q^{7} + 3 q^{9} - 3 q^{12} - 6 q^{14} + 3 q^{15} + 5 q^{16} - 12 q^{17} - 9 q^{18} + q^{20} + 3 q^{21} - 15 q^{23} - 3 q^{24} - q^{25} + 5 q^{28} - 3 q^{29} - 3 q^{30} - 6 q^{31} - 9 q^{32} + 18 q^{34} - 5 q^{35} + 6 q^{36} - 4 q^{37} + 6 q^{38} + 3 q^{40} + 9 q^{41} + 3 q^{42} - 4 q^{43} - 6 q^{45} + 30 q^{46} + 3 q^{47} - 13 q^{49} + 3 q^{50} + 18 q^{51} + 9 q^{54} + 9 q^{56} - 6 q^{57} + 3 q^{58} - 6 q^{59} - 15 q^{61} + 12 q^{62} - 12 q^{63} - 2 q^{64} + 13 q^{67} - 6 q^{68} + 15 q^{69} + 9 q^{70} + 9 q^{72} + 6 q^{74} - 6 q^{76} - 14 q^{79} - 10 q^{80} - 9 q^{81} + 9 q^{83} - 6 q^{84} + 6 q^{85} + 12 q^{86} + 6 q^{87} - 30 q^{89} + 9 q^{90} - 15 q^{92} + 6 q^{93} - 9 q^{94} + 6 q^{95} + 9 q^{96} + 6 q^{97} + 15 q^{98}+O(q^{100}) $ 2 * q - 3 * q^2 - 3 * q^3 + q^4 - q^5 + 6 * q^6 + q^7 + 3 * q^9 - 3 * q^12 - 6 * q^14 + 3 * q^15 + 5 * q^16 - 12 * q^17 - 9 * q^18 + q^20 + 3 * q^21 - 15 * q^23 - 3 * q^24 - q^25 + 5 * q^28 - 3 * q^29 - 3 * q^30 - 6 * q^31 - 9 * q^32 + 18 * q^34 - 5 * q^35 + 6 * q^36 - 4 * q^37 + 6 * q^38 + 3 * q^40 + 9 * q^41 + 3 * q^42 - 4 * q^43 - 6 * q^45 + 30 * q^46 + 3 * q^47 - 13 * q^49 + 3 * q^50 + 18 * q^51 + 9 * q^54 + 9 * q^56 - 6 * q^57 + 3 * q^58 - 6 * q^59 - 15 * q^61 + 12 * q^62 - 12 * q^63 - 2 * q^64 + 13 * q^67 - 6 * q^68 + 15 * q^69 + 9 * q^70 + 9 * q^72 + 6 * q^74 - 6 * q^76 - 14 * q^79 - 10 * q^80 - 9 * q^81 + 9 * q^83 - 6 * q^84 + 6 * q^85 + 12 * q^86 + 6 * q^87 - 30 * q^89 + 9 * q^90 - 15 * q^92 + 6 * q^93 - 9 * q^94 + 6 * q^95 + 9 * q^96 + 6 * q^97 + 15 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.50000	+	0.866025i	−1.06066	+	0.612372i	−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−1.50000	+	0.866025i	−1.06066	+	0.612372i	−0.135045	+	0.990839i	$0.543118\pi$
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	3.00000			1.22474
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$		−	1.73205i		−	0.612372i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		−	1.73205i		−	0.547723i
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$	−1.50000	+	0.866025i	−0.433013	+	0.250000i
$13$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$13$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$14$	−3.00000	−	3.46410i	−0.801784	−	0.925820i
$15$	1.50000	−	0.866025i	0.387298	−	0.223607i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$	−4.50000	−	2.59808i	−1.06066	−	0.612372i
$19$		−	3.46410i		−	0.794719i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$		−	3.46410i		−	0.794719i	0.917663	−	0.397360i	$-0.130073\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	1.50000	−	4.33013i	0.327327	−	0.944911i
$22$		0			0
$23$	−7.50000	−	4.33013i	−1.56386	−	0.902894i	−0.996861	−	0.0791743i	$-0.974772\pi$
$23$	−7.50000	−	4.33013i	−1.56386	−	0.902894i	−0.566997	−	0.823720i	$-0.691895\pi$
$24$	−1.50000	+	2.59808i	−0.306186	+	0.530330i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$	2.50000	+	0.866025i	0.472456	+	0.163663i
$29$	−1.50000	+	0.866025i	−0.278543	+	0.160817i	−0.632764	−	0.774345i	$-0.718080\pi$
$29$	−1.50000	+	0.866025i	−0.278543	+	0.160817i	0.354221	+	0.935162i	$0.384746\pi$
$30$	−1.50000	+	2.59808i	−0.273861	+	0.474342i
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	0.205783	−	0.978598i	$-0.434026\pi$
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	−0.744599	+	0.667512i	$0.767359\pi$
$32$	−4.50000	−	2.59808i	−0.795495	−	0.459279i
$33$		0			0
$34$	9.00000	−	5.19615i	1.54349	−	0.891133i
$35$	−2.50000	−	0.866025i	−0.422577	−	0.146385i
$36$	3.00000			0.500000
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	3.00000	+	5.19615i	0.486664	+	0.842927i
$39$		0			0
$40$	1.50000	+	0.866025i	0.237171	+	0.136931i
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	−0.264704	−	0.964330i	$-0.585274\pi$
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	0.967486	−	0.252924i	$-0.0813924\pi$
$42$	1.50000	+	7.79423i	0.231455	+	1.20268i
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	0.672264	−	0.740312i	$-0.265322\pi$
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	−0.977261	+	0.212041i	$0.931989\pi$
$44$		0			0
$45$	−3.00000			−0.447214
$46$	15.0000			2.21163
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	0.954441	−	0.298401i	$-0.0964533\pi$
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	−0.735643	+	0.677369i	$0.763120\pi$
$48$		−	8.66025i		−	1.25000i
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	1.50000	+	0.866025i	0.212132	+	0.122474i
$51$	9.00000	+	5.19615i	1.26025	+	0.727607i
$52$		0			0
$53$			3.46410i			0.475831i	0.971286	+	0.237915i	$0.0764641\pi$
$53$			3.46410i			0.475831i	−0.971286	+	0.237915i	$0.923536\pi$
$54$	4.50000	+	7.79423i	0.612372	+	1.06066i
$55$		0			0
$56$	4.50000	−	0.866025i	0.601338	−	0.115728i
$57$	−3.00000	+	5.19615i	−0.397360	+	0.688247i
$58$	1.50000	−	2.59808i	0.196960	−	0.341144i
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$		−	1.73205i		−	0.223607i
$61$	−7.50000	+	4.33013i	−0.960277	+	0.554416i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−7.50000	+	4.33013i	−0.960277	+	0.554416i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	6.00000			0.762001
$63$	−6.00000	+	5.19615i	−0.755929	+	0.654654i
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	−0.129307	−	0.991605i	$-0.541275\pi$
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	0.923408	−	0.383819i	$-0.125391\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$	7.50000	+	12.9904i	0.902894	+	1.56386i
$70$	4.50000	−	0.866025i	0.537853	−	0.103510i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	4.50000	−	2.59808i	0.530330	−	0.306186i
$73$			13.8564i			1.62177i	0.585206	+	0.810885i	$0.301014\pi$
$73$			13.8564i			1.62177i	−0.585206	+	0.810885i	$0.698986\pi$
$74$	3.00000	−	1.73205i	0.348743	−	0.201347i
$75$			1.73205i			0.200000i
$76$	−3.00000	−	1.73205i	−0.344124	−	0.198680i
$77$		0			0
$78$		0			0
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	−0.927457	−	0.373930i	$-0.878010\pi$
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	0.139895	−	0.990166i	$-0.455323\pi$
$80$	−5.00000			−0.559017
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$			15.5885i			1.72146i
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	0.999976	−	0.00698436i	$-0.00222321\pi$
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	−0.506036	+	0.862512i	$0.668890\pi$
$84$	−3.00000	−	3.46410i	−0.327327	−	0.377964i
$85$	3.00000	−	5.19615i	0.325396	−	0.563602i
$86$	6.00000	+	3.46410i	0.646997	+	0.373544i
$87$	3.00000			0.321634
$88$		0			0
$89$	−15.0000			−1.59000			−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000			−1.59000			−0.794998	+	0.606612i	$0.792528\pi$
$90$	4.50000	−	2.59808i	0.474342	−	0.273861i
$91$		0			0
$92$	−7.50000	+	4.33013i	−0.781929	+	0.451447i
$93$	3.00000	+	5.19615i	0.311086	+	0.538816i
$94$	−4.50000	−	2.59808i	−0.464140	−	0.267971i
$95$	3.00000	+	1.73205i	0.307794	+	0.177705i
$96$	4.50000	+	7.79423i	0.459279	+	0.795495i
$97$	3.00000	−	1.73205i	0.304604	−	0.175863i	−0.339905	−	0.940460i	$-0.610395\pi$
$97$	3.00000	−	1.73205i	0.304604	−	0.175863i	0.644509	+	0.764597i	$0.277062\pi$
$98$	7.50000	−	9.52628i	0.757614	−	0.962300i
$99$		0			0
$100$	−1.00000			−0.100000
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$	−18.0000			−1.78227
$103$	−3.00000	−	1.73205i	−0.295599	−	0.170664i	0.344865	−	0.938652i	$-0.387925\pi$
$103$	−3.00000	−	1.73205i	−0.295599	−	0.170664i	−0.640464	+	0.767988i	$0.721258\pi$
$104$		0			0
$105$	3.00000	+	3.46410i	0.292770	+	0.338062i
$106$	−3.00000	−	5.19615i	−0.291386	−	0.504695i
$107$		−	8.66025i		−	0.837218i	−0.908166	−	0.418609i	$-0.862518\pi$
$107$		−	8.66025i		−	0.837218i	0.908166	−	0.418609i	$-0.137482\pi$
$108$	−4.50000	−	2.59808i	−0.433013	−	0.250000i
$109$	7.00000			0.670478			0.335239	−	0.942133i	$-0.391183\pi$
$109$	7.00000			0.670478			0.335239	+	0.942133i	$0.391183\pi$
$110$		0			0
$111$	3.00000	+	1.73205i	0.284747	+	0.164399i
$112$	−10.0000	+	8.66025i	−0.944911	+	0.818317i
$113$	12.0000	+	6.92820i	1.12887	+	0.651751i	0.943649	−	0.330947i	$-0.107368\pi$
$113$	12.0000	+	6.92820i	1.12887	+	0.651751i	0.185216	+	0.982698i	$0.440702\pi$
$114$		−	10.3923i		−	0.973329i
$115$	7.50000	−	4.33013i	0.699379	−	0.403786i
$116$			1.73205i			0.160817i
$117$		0			0
$118$		−	10.3923i		−	0.956689i
$119$	−3.00000	−	15.5885i	−0.275010	−	1.42899i
$120$	−1.50000	−	2.59808i	−0.136931	−	0.237171i
$121$	−5.50000	+	9.52628i	−0.500000	+	0.866025i
$122$	7.50000	−	12.9904i	0.679018	−	1.17609i
$123$	−13.5000	+	7.79423i	−1.21725	+	0.702782i
$124$	−3.00000	+	1.73205i	−0.269408	+	0.155543i
$125$	1.00000			0.0894427
$126$	4.50000	−	12.9904i	0.400892	−	1.15728i
$127$	−13.0000			−1.15356			−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000			−1.15356			−0.576782	+	0.816898i	$0.695692\pi$
$128$	10.5000	−	6.06218i	0.928078	−	0.535826i
$129$			6.92820i			0.609994i
$130$		0			0
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	−0.141865	−	0.989886i	$-0.545310\pi$
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	0.928199	−	0.372084i	$-0.121357\pi$
$132$		0			0
$133$	9.00000	−	1.73205i	0.780399	−	0.150188i
$134$			22.5167i			1.94514i
$135$	4.50000	+	2.59808i	0.387298	+	0.223607i
$136$			10.3923i			0.891133i
$137$	6.00000	−	3.46410i	0.512615	−	0.295958i	−0.221293	−	0.975207i	$-0.571028\pi$
$137$	6.00000	−	3.46410i	0.512615	−	0.295958i	0.733908	+	0.679249i	$0.237694\pi$
$138$	−22.5000	−	12.9904i	−1.91533	−	1.10581i
$139$	6.00000	+	3.46410i	0.508913	+	0.293821i	0.732387	−	0.680889i	$-0.238406\pi$
$139$	6.00000	+	3.46410i	0.508913	+	0.293821i	−0.223474	+	0.974710i	$0.571740\pi$
$140$	−2.00000	+	1.73205i	−0.169031	+	0.146385i
$141$		−	5.19615i		−	0.437595i
$142$		0			0
$143$		0			0
$144$	−7.50000	+	12.9904i	−0.625000	+	1.08253i
$145$		−	1.73205i		−	0.143839i
$146$	−12.0000	−	20.7846i	−0.993127	−	1.72015i
$147$	12.0000	+	1.73205i	0.989743	+	0.142857i
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$	−16.5000	−	9.52628i	−1.35173	−	0.780423i	−0.363241	−	0.931695i	$-0.618330\pi$
$149$	−16.5000	−	9.52628i	−1.35173	−	0.780423i	−0.988492	+	0.151272i	$0.951663\pi$
$150$	−1.50000	−	2.59808i	−0.122474	−	0.212132i
$151$	−2.00000	−	3.46410i	−0.162758	−	0.281905i	0.773099	−	0.634285i	$-0.218706\pi$
$151$	−2.00000	−	3.46410i	−0.162758	−	0.281905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$	−6.00000			−0.486664
$153$	−9.00000	−	15.5885i	−0.727607	−	1.26025i
$154$		0			0
$155$	3.00000	−	1.73205i	0.240966	−	0.139122i
$156$		0			0
$157$	−15.0000	−	8.66025i	−1.19713	−	0.691164i	−0.237216	−	0.971457i	$-0.576235\pi$
$157$	−15.0000	−	8.66025i	−1.19713	−	0.691164i	−0.959914	+	0.280293i	$0.909568\pi$
$158$	21.0000	+	12.1244i	1.67067	+	0.964562i
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$	4.50000	−	2.59808i	0.355756	−	0.205396i
$161$	7.50000	−	21.6506i	0.591083	−	1.70631i
$162$		−	15.5885i		−	1.22474i
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	−4.50000	−	7.79423i	−0.351391	−	0.608627i
$165$		0			0
$166$	−13.5000	−	7.79423i	−1.04780	−	0.604949i
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	−0.918208	−	0.396098i	$-0.870364\pi$
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	0.802135	+	0.597143i	$0.203697\pi$
$168$	−7.50000	−	2.59808i	−0.578638	−	0.200446i
$169$	−6.50000	−	11.2583i	−0.500000	−	0.866025i
$170$			10.3923i			0.797053i
$171$	9.00000	−	5.19615i	0.688247	−	0.397360i
$172$	−4.00000			−0.304997
$173$	12.0000	+	20.7846i	0.912343	+	1.58022i	0.810745	+	0.585399i	$0.199062\pi$
$173$	12.0000	+	20.7846i	0.912343	+	1.58022i	0.101598	+	0.994826i	$0.467605\pi$
$174$	−4.50000	+	2.59808i	−0.341144	+	0.196960i
$175$	2.00000	−	1.73205i	0.151186	−	0.130931i
$176$		0			0
$177$	9.00000	−	5.19615i	0.676481	−	0.390567i
$178$	22.5000	−	12.9904i	1.68645	−	0.973670i
$179$			20.7846i			1.55351i	0.629800	+	0.776757i	$0.283137\pi$
$179$			20.7846i			1.55351i	−0.629800	+	0.776757i	$0.716863\pi$
$180$	−1.50000	+	2.59808i	−0.111803	+	0.193649i
$181$			15.5885i			1.15868i	0.815086	+	0.579340i	$0.196690\pi$
$181$			15.5885i			1.15868i	−0.815086	+	0.579340i	$0.803310\pi$
$182$		0			0
$183$	15.0000			1.10883
$184$	−7.50000	+	12.9904i	−0.552907	+	0.957664i
$185$	1.00000	−	1.73205i	0.0735215	−	0.127343i
$186$	−9.00000	−	5.19615i	−0.659912	−	0.381000i
$187$		0			0
$188$	3.00000			0.218797
$189$	13.5000	−	2.59808i	0.981981	−	0.188982i
$190$	−6.00000			−0.435286
$191$	−21.0000	+	12.1244i	−1.51951	+	0.877288i	−0.519771	+	0.854306i	$0.673983\pi$
$191$	−21.0000	+	12.1244i	−1.51951	+	0.877288i	−0.999736	+	0.0229818i	$0.992684\pi$
$192$	1.50000	+	0.866025i	0.108253	+	0.0625000i
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	−0.928986	−	0.370116i	$-0.879318\pi$
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	0.785022	+	0.619467i	$0.212651\pi$
$194$	−3.00000	+	5.19615i	−0.215387	+	0.373062i
$195$		0			0
$196$	−1.00000	+	6.92820i	−0.0714286	+	0.494872i
$197$			20.7846i			1.48084i	0.672143	+	0.740421i	$0.265374\pi$
$197$			20.7846i			1.48084i	−0.672143	+	0.740421i	$0.734626\pi$
$198$		0			0
$199$		−	10.3923i		−	0.736691i	−0.929689	−	0.368345i	$-0.879924\pi$
$199$		−	10.3923i		−	0.736691i	0.929689	−	0.368345i	$-0.120076\pi$
$200$	−1.50000	+	0.866025i	−0.106066	+	0.0612372i
$201$	−19.5000	+	11.2583i	−1.37542	+	0.794101i
$202$	−9.00000	−	5.19615i	−0.633238	−	0.365600i
$203$	−3.00000	−	3.46410i	−0.210559	−	0.243132i
$204$	9.00000	−	5.19615i	0.630126	−	0.363803i
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$	6.00000			0.418040
$207$		−	25.9808i		−	1.80579i
$208$		0			0
$209$		0			0
$210$	−7.50000	−	2.59808i	−0.517549	−	0.179284i
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	−0.694857	−	0.719148i	$-0.744533\pi$
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	0.970229	+	0.242190i	$0.0778659\pi$
$212$	3.00000	+	1.73205i	0.206041	+	0.118958i
$213$		0			0
$214$	7.50000	+	12.9904i	0.512689	+	0.888004i
$215$	4.00000			0.272798
$216$	−9.00000			−0.612372
$217$	3.00000	−	8.66025i	0.203653	−	0.587896i
$218$	−10.5000	+	6.06218i	−0.711150	+	0.410582i
$219$	12.0000	−	20.7846i	0.810885	−	1.40449i
$220$		0			0
$221$		0			0
$222$	−6.00000			−0.402694
$223$	−16.5000	+	9.52628i	−1.10492	+	0.637927i	−0.937509	−	0.347960i	$-0.886874\pi$
$223$	−16.5000	+	9.52628i	−1.10492	+	0.637927i	−0.167412	+	0.985887i	$0.553541\pi$
$224$	4.50000	−	12.9904i	0.300669	−	0.867956i
$225$	1.50000	−	2.59808i	0.100000	−	0.173205i
$226$	−24.0000			−1.59646
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	0.993508	−	0.113761i	$-0.0362899\pi$
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	−0.595274	+	0.803523i	$0.702957\pi$
$228$	3.00000	+	5.19615i	0.198680	+	0.344124i
$229$	16.5000	+	9.52628i	1.09035	+	0.629514i	0.933670	−	0.358135i	$-0.116587\pi$
$229$	16.5000	+	9.52628i	1.09035	+	0.629514i	0.156681	+	0.987649i	$0.449921\pi$
$230$	−7.50000	+	12.9904i	−0.494535	+	0.856560i
$231$		0			0
$232$	1.50000	+	2.59808i	0.0984798	+	0.170572i
$233$		−	3.46410i		−	0.226941i	−0.993541	−	0.113470i	$-0.963803\pi$
$233$		−	3.46410i		−	0.226941i	0.993541	−	0.113470i	$-0.0361967\pi$
$234$		0			0
$235$	−3.00000			−0.195698
$236$	3.00000	+	5.19615i	0.195283	+	0.338241i
$237$			24.2487i			1.57512i
$238$	18.0000	+	20.7846i	1.16677	+	1.34727i
$239$	6.00000	+	3.46410i	0.388108	+	0.224074i	0.681340	−	0.731967i	$-0.261398\pi$
$239$	6.00000	+	3.46410i	0.388108	+	0.224074i	−0.293232	+	0.956041i	$0.594731\pi$
$240$	7.50000	+	4.33013i	0.484123	+	0.279508i
$241$	−13.5000	+	7.79423i	−0.869611	+	0.502070i	−0.867219	−	0.497927i	$-0.834095\pi$
$241$	−13.5000	+	7.79423i	−0.869611	+	0.502070i	−0.00239235	+	0.999997i	$0.500762\pi$
$242$		−	19.0526i		−	1.22474i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$			8.66025i			0.554416i
$245$	1.00000	−	6.92820i	0.0638877	−	0.442627i
$246$	13.5000	−	23.3827i	0.860729	−	1.49083i
$247$		0			0
$248$	−3.00000	+	5.19615i	−0.190500	+	0.329956i
$249$		−	15.5885i		−	0.987878i
$250$	−1.50000	+	0.866025i	−0.0948683	+	0.0547723i
$251$	−6.00000			−0.378717			−0.189358	−	0.981908i	$-0.560641\pi$
$251$	−6.00000			−0.378717			−0.189358	+	0.981908i	$0.560641\pi$
$252$	1.50000	+	7.79423i	0.0944911	+	0.490990i
$253$		0			0
$254$	19.5000	−	11.2583i	1.22354	−	0.706410i
$255$	−9.00000	+	5.19615i	−0.563602	+	0.325396i
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$	−6.00000	−	10.3923i	−0.373544	−	0.646997i
$259$	−1.00000	−	5.19615i	−0.0621370	−	0.322873i
$260$		0			0
$261$	−4.50000	−	2.59808i	−0.278543	−	0.160817i
$262$			31.1769i			1.92612i
$263$	−9.00000	+	5.19615i	−0.554964	+	0.320408i	−0.751122	−	0.660164i	$-0.770487\pi$
$263$	−9.00000	+	5.19615i	−0.554964	+	0.320408i	0.196158	+	0.980572i	$0.437154\pi$
$264$		0			0
$265$	−3.00000	−	1.73205i	−0.184289	−	0.106399i
$266$	−12.0000	+	10.3923i	−0.735767	+	0.637193i
$267$	22.5000	+	12.9904i	1.37698	+	0.794998i
$268$	−6.50000	−	11.2583i	−0.397051	−	0.687712i
$269$	3.00000			0.182913			0.0914566	−	0.995809i	$-0.470848\pi$
$269$	3.00000			0.182913			0.0914566	+	0.995809i	$0.470848\pi$
$270$	−9.00000			−0.547723
$271$		−	3.46410i		−	0.210429i	−0.994450	−	0.105215i	$-0.966447\pi$
$271$		−	3.46410i		−	0.210429i	0.994450	−	0.105215i	$-0.0335529\pi$
$272$	−15.0000	−	25.9808i	−0.909509	−	1.57532i
$273$		0			0
$274$	−6.00000	+	10.3923i	−0.362473	+	0.627822i
$275$		0			0
$276$	15.0000			0.902894
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$	−12.0000			−0.719712
$279$		−	10.3923i		−	0.622171i
$280$	−1.50000	+	4.33013i	−0.0896421	+	0.258775i
$281$	−13.5000	+	7.79423i	−0.805342	+	0.464965i	−0.845336	−	0.534235i	$-0.820600\pi$
$281$	−13.5000	+	7.79423i	−0.805342	+	0.464965i	0.0399934	+	0.999200i	$0.487266\pi$
$282$	4.50000	+	7.79423i	0.267971	+	0.464140i
$283$	19.5000	+	11.2583i	1.15915	+	0.669238i	0.951101	−	0.308879i	$-0.0999539\pi$
$283$	19.5000	+	11.2583i	1.15915	+	0.669238i	0.208053	+	0.978117i	$0.433287\pi$
$284$		0			0
$285$	−3.00000	−	5.19615i	−0.177705	−	0.307794i
$286$		0			0
$287$	22.5000	+	7.79423i	1.32813	+	0.460079i
$288$		−	15.5885i		−	0.918559i
$289$	19.0000			1.11765
$290$	1.50000	+	2.59808i	0.0880830	+	0.152564i
$291$	−6.00000			−0.351726
$292$	12.0000	+	6.92820i	0.702247	+	0.405442i
$293$	−15.0000	+	25.9808i	−0.876309	+	1.51781i	−0.0209480	+	0.999781i	$0.506668\pi$
$293$	−15.0000	+	25.9808i	−0.876309	+	1.51781i	−0.855361	+	0.518032i	$0.826665\pi$
$294$	−19.5000	+	7.79423i	−1.13726	+	0.454569i
$295$	−3.00000	−	5.19615i	−0.174667	−	0.302532i
$296$			3.46410i			0.201347i
$297$		0			0
$298$	33.0000			1.91164
$299$		0			0
$300$	1.50000	+	0.866025i	0.0866025	+	0.0500000i
$301$	8.00000	−	6.92820i	0.461112	−	0.399335i
$302$	6.00000	+	3.46410i	0.345261	+	0.199337i
$303$		−	10.3923i		−	0.597022i
$304$	15.0000	−	8.66025i	0.860309	−	0.496700i
$305$		−	8.66025i		−	0.495885i
$306$	27.0000	+	15.5885i	1.54349	+	0.891133i
$307$		−	12.1244i		−	0.691974i	−0.938239	−	0.345987i	$-0.887544\pi$
$307$		−	12.1244i		−	0.691974i	0.938239	−	0.345987i	$-0.112456\pi$
$308$		0			0
$309$	3.00000	+	5.19615i	0.170664	+	0.295599i
$310$	−3.00000	+	5.19615i	−0.170389	+	0.295122i
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	−0.489585	−	0.871956i	$-0.662852\pi$
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	0.999928	−	0.0119847i	$-0.00381495\pi$
$312$		0			0
$313$	18.0000	−	10.3923i	1.01742	−	0.587408i	0.104065	−	0.994571i	$-0.466815\pi$
$313$	18.0000	−	10.3923i	1.01742	−	0.587408i	0.913356	+	0.407163i	$0.133482\pi$
$314$	30.0000			1.69300
$315$	−1.50000	−	7.79423i	−0.0845154	−	0.439155i
$316$	−14.0000			−0.787562
$317$	6.00000	−	3.46410i	0.336994	−	0.194563i	−0.321948	−	0.946757i	$-0.604338\pi$
$317$	6.00000	−	3.46410i	0.336994	−	0.194563i	0.658942	+	0.752194i	$0.271004\pi$
$318$			10.3923i			0.582772i
$319$		0			0
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−7.50000	+	12.9904i	−0.418609	+	0.725052i
$322$	7.50000	+	38.9711i	0.417959	+	2.17178i
$323$			20.7846i			1.15649i
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$		0			0
$326$	6.00000	−	3.46410i	0.332309	−	0.191859i
$327$	−10.5000	−	6.06218i	−0.580651	−	0.335239i
$328$	−13.5000	−	7.79423i	−0.745413	−	0.430364i
$329$	−6.00000	+	5.19615i	−0.330791	+	0.286473i
$330$		0			0
$331$	13.0000	+	22.5167i	0.714545	+	1.23763i	0.963135	+	0.269019i	$0.0866994\pi$
$331$	13.0000	+	22.5167i	0.714545	+	1.23763i	−0.248590	+	0.968609i	$0.579967\pi$
$332$	9.00000			0.493939
$333$	−3.00000	−	5.19615i	−0.164399	−	0.284747i
$334$		−	5.19615i		−	0.284321i
$335$	6.50000	+	11.2583i	0.355133	+	0.615108i
$336$	22.5000	−	4.33013i	1.22748	−	0.236228i
$337$	4.00000	−	6.92820i	0.217894	−	0.377403i	−0.736270	−	0.676688i	$-0.763415\pi$
$337$	4.00000	−	6.92820i	0.217894	−	0.377403i	0.954164	+	0.299285i	$0.0967480\pi$
$338$	19.5000	+	11.2583i	1.06066	+	0.612372i
$339$	−12.0000	−	20.7846i	−0.651751	−	1.12887i
$340$	−3.00000	−	5.19615i	−0.162698	−	0.281801i
$341$		0			0
$342$	−9.00000	+	15.5885i	−0.486664	+	0.842927i
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	−6.00000	+	3.46410i	−0.323498	+	0.186772i
$345$	−15.0000			−0.807573
$346$	−36.0000	−	20.7846i	−1.93537	−	1.11739i
$347$	−9.00000	−	5.19615i	−0.483145	−	0.278944i	0.238581	−	0.971123i	$-0.423318\pi$
$347$	−9.00000	−	5.19615i	−0.483145	−	0.278944i	−0.721726	+	0.692179i	$0.756651\pi$
$348$	1.50000	−	2.59808i	0.0804084	−	0.139272i
$349$	−19.5000	+	11.2583i	−1.04381	+	0.602645i	−0.920910	−	0.389774i	$-0.872553\pi$
$349$	−19.5000	+	11.2583i	−1.04381	+	0.602645i	−0.122901	+	0.992419i	$0.539220\pi$
$350$	−1.50000	+	4.33013i	−0.0801784	+	0.231455i
$351$		0			0
$352$		0			0
$353$	−18.0000	−	31.1769i	−0.958043	−	1.65938i	−0.727245	−	0.686378i	$-0.759200\pi$
$353$	−18.0000	−	31.1769i	−0.958043	−	1.65938i	−0.230799	−	0.973002i	$-0.574134\pi$
$354$	−9.00000	+	15.5885i	−0.478345	+	0.828517i
$355$		0			0
$356$	−7.50000	+	12.9904i	−0.397499	+	0.688489i
$357$	−9.00000	+	25.9808i	−0.476331	+	1.37505i
$358$	−18.0000	−	31.1769i	−0.951330	−	1.64775i
$359$		−	3.46410i		−	0.182828i	−0.995813	−	0.0914141i	$-0.970861\pi$
$359$		−	3.46410i		−	0.182828i	0.995813	−	0.0914141i	$-0.0291387\pi$
$360$			5.19615i			0.273861i
$361$	7.00000			0.368421
$362$	−13.5000	−	23.3827i	−0.709544	−	1.22897i
$363$	16.5000	−	9.52628i	0.866025	−	0.500000i
$364$		0			0
$365$	−12.0000	−	6.92820i	−0.628109	−	0.362639i
$366$	−22.5000	+	12.9904i	−1.17609	+	0.679018i
$367$	9.00000	−	5.19615i	0.469796	−	0.271237i	−0.246358	−	0.969179i	$-0.579234\pi$
$367$	9.00000	−	5.19615i	0.469796	−	0.271237i	0.716154	+	0.697942i	$0.245901\pi$
$368$		−	43.3013i		−	2.25723i
$369$	27.0000			1.40556
$370$			3.46410i			0.180090i
$371$	−9.00000	+	1.73205i	−0.467257	+	0.0899236i
$372$	6.00000			0.311086
$373$	−1.00000	+	1.73205i	−0.0517780	+	0.0896822i	−0.890753	−	0.454488i	$-0.849822\pi$
$373$	−1.00000	+	1.73205i	−0.0517780	+	0.0896822i	0.838975	+	0.544170i	$0.183156\pi$
$374$		0			0
$375$	−1.50000	−	0.866025i	−0.0774597	−	0.0447214i
$376$	4.50000	−	2.59808i	0.232070	−	0.133986i
$377$		0			0
$378$	−18.0000	+	15.5885i	−0.925820	+	0.801784i
$379$	−2.00000			−0.102733			−0.0513665	−	0.998680i	$-0.516358\pi$
$379$	−2.00000			−0.102733			−0.0513665	+	0.998680i	$0.516358\pi$
$380$	3.00000	−	1.73205i	0.153897	−	0.0888523i
$381$	19.5000	+	11.2583i	0.999015	+	0.576782i
$382$	21.0000	−	36.3731i	1.07445	−	1.86101i
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$	−21.0000			−1.07165
$385$		0			0
$386$		−	6.92820i		−	0.352636i
$387$	6.00000	−	10.3923i	0.304997	−	0.528271i
$388$		−	3.46410i		−	0.175863i
$389$	19.5000	−	11.2583i	0.988689	−	0.570820i	0.0838070	−	0.996482i	$-0.473292\pi$
$389$	19.5000	−	11.2583i	0.988689	−	0.570820i	0.904882	+	0.425662i	$0.139959\pi$
$390$		0			0
$391$	45.0000	+	25.9808i	2.27575	+	1.31390i
$392$	4.50000	+	11.2583i	0.227284	+	0.568632i
$393$	−27.0000	+	15.5885i	−1.36197	+	0.786334i
$394$	−18.0000	−	31.1769i	−0.906827	−	1.57067i
$395$	14.0000			0.704416
$396$		0			0
$397$		−	24.2487i		−	1.21701i	−0.793551	−	0.608504i	$-0.791770\pi$
$397$		−	24.2487i		−	1.21701i	0.793551	−	0.608504i	$-0.208230\pi$
$398$	9.00000	+	15.5885i	0.451129	+	0.781379i
$399$	−15.0000	−	5.19615i	−0.750939	−	0.260133i
$400$	2.50000	−	4.33013i	0.125000	−	0.216506i
$401$	−6.00000	−	3.46410i	−0.299626	−	0.172989i	0.342649	−	0.939463i	$-0.388676\pi$
$401$	−6.00000	−	3.46410i	−0.299626	−	0.172989i	−0.642275	+	0.766475i	$0.722009\pi$
$402$	19.5000	−	33.7750i	0.972572	−	1.68454i
$403$		0			0
$404$	6.00000			0.298511
$405$	−4.50000	−	7.79423i	−0.223607	−	0.387298i
$406$	7.50000	+	2.59808i	0.372219	+	0.128940i
$407$		0			0
$408$	9.00000	−	15.5885i	0.445566	−	0.771744i
$409$	−18.0000	−	10.3923i	−0.890043	−	0.513866i	−0.0160862	−	0.999871i	$-0.505121\pi$
$409$	−18.0000	−	10.3923i	−0.890043	−	0.513866i	−0.873956	+	0.486004i	$0.838454\pi$
$410$	−13.5000	−	7.79423i	−0.666717	−	0.384930i
$411$	−12.0000			−0.591916
$412$	−3.00000	+	1.73205i	−0.147799	+	0.0853320i
$413$	−15.0000	−	5.19615i	−0.738102	−	0.255686i
$414$	22.5000	+	38.9711i	1.10581	+	1.91533i
$415$	−9.00000			−0.441793
$416$		0			0
$417$	−6.00000	−	10.3923i	−0.293821	−	0.508913i
$418$		0			0
$419$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$419$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$420$	4.50000	−	0.866025i	0.219578	−	0.0422577i
$421$	−13.0000	−	22.5167i	−0.633581	−	1.09739i	−0.986814	−	0.161859i	$-0.948251\pi$
$421$	−13.0000	−	22.5167i	−0.633581	−	1.09739i	0.353233	−	0.935536i	$-0.385082\pi$
$422$			13.8564i			0.674519i
$423$	−4.50000	+	7.79423i	−0.218797	+	0.378968i
$424$	6.00000			0.291386
$425$	3.00000	+	5.19615i	0.145521	+	0.252050i
$426$		0			0
$427$	−15.0000	−	17.3205i	−0.725901	−	0.838198i
$428$	−7.50000	−	4.33013i	−0.362526	−	0.209305i
$429$		0			0
$430$	−6.00000	+	3.46410i	−0.289346	+	0.167054i
$431$			10.3923i			0.500580i	0.968171	+	0.250290i	$0.0805259\pi$
$431$			10.3923i			0.500580i	−0.968171	+	0.250290i	$0.919474\pi$
$432$	22.5000	−	12.9904i	1.08253	−	0.625000i
$433$		−	3.46410i		−	0.166474i	−0.996530	−	0.0832370i	$-0.973474\pi$
$433$		−	3.46410i		−	0.166474i	0.996530	−	0.0832370i	$-0.0265259\pi$
$434$	3.00000	+	15.5885i	0.144005	+	0.748270i
$435$	−1.50000	+	2.59808i	−0.0719195	+	0.124568i
$436$	3.50000	−	6.06218i	0.167620	−	0.290326i
$437$	−15.0000	+	25.9808i	−0.717547	+	1.24283i
$438$			41.5692i			1.98625i
$439$	−30.0000	+	17.3205i	−1.43182	+	0.826663i	−0.997260	−	0.0739791i	$-0.976430\pi$
$439$	−30.0000	+	17.3205i	−1.43182	+	0.826663i	−0.434562	+	0.900642i	$0.643097\pi$
$440$		0			0
$441$	−16.5000	−	12.9904i	−0.785714	−	0.618590i
$442$		0			0
$443$	−22.5000	+	12.9904i	−1.06901	+	0.617192i	−0.927910	−	0.372804i	$-0.878396\pi$
$443$	−22.5000	+	12.9904i	−1.06901	+	0.617192i	−0.141097	+	0.989996i	$0.545063\pi$
$444$	3.00000	−	1.73205i	0.142374	−	0.0821995i
$445$	7.50000	−	12.9904i	0.355534	−	0.615803i
$446$	16.5000	−	28.5788i	0.781298	−	1.35325i
$447$	16.5000	+	28.5788i	0.780423	+	1.35173i
$448$	−0.500000	−	2.59808i	−0.0236228	−	0.122748i
$449$		−	6.92820i		−	0.326962i	−0.986546	−	0.163481i	$-0.947728\pi$
$449$		−	6.92820i		−	0.326962i	0.986546	−	0.163481i	$-0.0522723\pi$
$450$			5.19615i			0.244949i
$451$		0			0
$452$	12.0000	−	6.92820i	0.564433	−	0.325875i
$453$			6.92820i			0.325515i
$454$	−18.0000	−	10.3923i	−0.844782	−	0.487735i
$455$		0			0
$456$	9.00000	+	5.19615i	0.421464	+	0.243332i
$457$	13.0000	+	22.5167i	0.608114	+	1.05328i	0.991551	+	0.129718i	$0.0414071\pi$
$457$	13.0000	+	22.5167i	0.608114	+	1.05328i	−0.383437	+	0.923567i	$0.625260\pi$
$458$	−33.0000			−1.54199
$459$			31.1769i			1.45521i
$460$		−	8.66025i		−	0.403786i
$461$	−10.5000	−	18.1865i	−0.489034	−	0.847031i	0.510887	−	0.859648i	$-0.329317\pi$
$461$	−10.5000	−	18.1865i	−0.489034	−	0.847031i	−0.999920	+	0.0126168i	$0.995984\pi$
$462$		0			0
$463$	2.00000	−	3.46410i	0.0929479	−	0.160990i	−0.815802	−	0.578331i	$-0.803704\pi$
$463$	2.00000	−	3.46410i	0.0929479	−	0.160990i	0.908750	+	0.417340i	$0.137038\pi$
$464$	−7.50000	−	4.33013i	−0.348179	−	0.201021i
$465$	−6.00000			−0.278243
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$		0			0
$469$	32.5000	+	11.2583i	1.50071	+	0.519861i
$470$	4.50000	−	2.59808i	0.207570	−	0.119840i
$471$	15.0000	+	25.9808i	0.691164	+	1.19713i
$472$	9.00000	+	5.19615i	0.414259	+	0.239172i
$473$		0			0
$474$	−21.0000	−	36.3731i	−0.964562	−	1.67067i
$475$	−3.00000	+	1.73205i	−0.137649	+	0.0794719i
$476$	−15.0000	−	5.19615i	−0.687524	−	0.238165i
$477$	−9.00000	+	5.19615i	−0.412082	+	0.237915i
$478$	−12.0000			−0.548867
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	0.995023	−	0.0996406i	$-0.0317693\pi$
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	−0.583803	+	0.811895i	$0.698436\pi$
$480$	−9.00000			−0.410792
$481$		0			0
$482$	13.5000	−	23.3827i	0.614908	−	1.06505i
$483$	−30.0000	+	25.9808i	−1.36505	+	1.18217i
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$			3.46410i			0.157297i
$486$	−13.5000	+	23.3827i	−0.612372	+	1.06066i
$487$	−32.0000			−1.45006			−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000			−1.45006			−0.725029	+	0.688718i	$0.758174\pi$
$488$	7.50000	+	12.9904i	0.339509	+	0.588047i
$489$	6.00000	+	3.46410i	0.271329	+	0.156652i
$490$	4.50000	+	11.2583i	0.203289	+	0.508600i
$491$	24.0000	+	13.8564i	1.08310	+	0.625331i	0.931732	−	0.363146i	$-0.118297\pi$
$491$	24.0000	+	13.8564i	1.08310	+	0.625331i	0.151373	+	0.988477i	$0.451631\pi$
$492$			15.5885i			0.702782i
$493$	9.00000	−	5.19615i	0.405340	−	0.234023i
$494$		0			0
$495$		0			0
$496$		−	17.3205i		−	0.777714i
$497$		0			0
$498$	13.5000	+	23.3827i	0.604949	+	1.04780i
$499$	10.0000	−	17.3205i	0.447661	−	0.775372i	−0.550572	−	0.834788i	$-0.685590\pi$
$499$	10.0000	−	17.3205i	0.447661	−	0.775372i	0.998233	+	0.0594153i	$0.0189236\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	4.50000	−	2.59808i	0.201045	−	0.116073i
$502$	9.00000	−	5.19615i	0.401690	−	0.231916i
$503$	9.00000			0.401290			0.200645	−	0.979664i	$-0.435696\pi$
$503$	9.00000			0.401290			0.200645	+	0.979664i	$0.435696\pi$
$504$	9.00000	+	10.3923i	0.400892	+	0.462910i
$505$	−6.00000			−0.266996
$506$		0			0
$507$			22.5167i			1.00000i
$508$	−6.50000	+	11.2583i	−0.288391	+	0.499508i
$509$	13.5000	−	23.3827i	0.598377	−	1.03642i	−0.394684	−	0.918817i	$-0.629146\pi$
$509$	13.5000	−	23.3827i	0.598377	−	1.03642i	0.993061	−	0.117602i	$-0.0375208\pi$
$510$	9.00000	−	15.5885i	0.398527	−	0.690268i
$511$	−36.0000	+	6.92820i	−1.59255	+	0.306486i
$512$		−	8.66025i		−	0.382733i
$513$	−18.0000			−0.794719
$514$			10.3923i			0.458385i
$515$	3.00000	−	1.73205i	0.132196	−	0.0763233i
$516$	6.00000	+	3.46410i	0.264135	+	0.152499i
$517$		0			0
$518$	6.00000	+	6.92820i	0.263625	+	0.304408i
$519$		−	41.5692i		−	1.82469i
$520$		0			0
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$	9.00000			0.393919
$523$		−	32.9090i		−	1.43901i	−0.694488	−	0.719504i	$-0.744369\pi$
$523$		−	32.9090i		−	1.43901i	0.694488	−	0.719504i	$-0.255631\pi$
$524$	−9.00000	−	15.5885i	−0.393167	−	0.680985i
$525$	−4.50000	+	0.866025i	−0.196396	+	0.0377964i
$526$	9.00000	−	15.5885i	0.392419	−	0.679689i
$527$	18.0000	+	10.3923i	0.784092	+	0.452696i
$528$		0			0
$529$	26.0000	+	45.0333i	1.13043	+	1.95797i
$530$	6.00000			0.260623
$531$	−18.0000			−0.781133
$532$	3.00000	−	8.66025i	0.130066	−	0.375470i
$533$		0			0
$534$	−45.0000			−1.94734
$535$	7.50000	+	4.33013i	0.324253	+	0.187208i
$536$	−19.5000	−	11.2583i	−0.842272	−	0.486286i
$537$	18.0000	−	31.1769i	0.776757	−	1.34538i
$538$	−4.50000	+	2.59808i	−0.194009	+	0.112011i
$539$		0			0
$540$	4.50000	−	2.59808i	0.193649	−	0.111803i
$541$	29.0000			1.24681			0.623404	−	0.781900i	$-0.285749\pi$
$541$	29.0000			1.24681			0.623404	+	0.781900i	$0.285749\pi$
$542$	3.00000	+	5.19615i	0.128861	+	0.223194i
$543$	13.5000	−	23.3827i	0.579340	−	1.00345i
$544$	27.0000	+	15.5885i	1.15762	+	0.668350i
$545$	−3.50000	+	6.06218i	−0.149924	+	0.259675i
$546$		0			0
$547$	−8.50000	−	14.7224i	−0.363434	−	0.629486i	0.625090	−	0.780553i	$-0.285062\pi$
$547$	−8.50000	−	14.7224i	−0.363434	−	0.629486i	−0.988524	+	0.151067i	$0.951729\pi$
$548$		−	6.92820i		−	0.295958i
$549$	−22.5000	−	12.9904i	−0.960277	−	0.554416i
$550$		0			0
$551$	3.00000	+	5.19615i	0.127804	+	0.221364i
$552$	22.5000	−	12.9904i	0.957664	−	0.552907i
$553$	28.0000	−	24.2487i	1.19068	−	1.03116i
$554$	−15.0000	−	8.66025i	−0.637289	−	0.367939i
$555$	−3.00000	+	1.73205i	−0.127343	+	0.0735215i
$556$	6.00000	−	3.46410i	0.254457	−	0.146911i
$557$		−	24.2487i		−	1.02745i	−0.857955	−	0.513725i	$-0.828265\pi$
$557$		−	24.2487i		−	1.02745i	0.857955	−	0.513725i	$-0.171735\pi$
$558$	9.00000	+	15.5885i	0.381000	+	0.659912i
$559$		0			0
$560$	−2.50000	−	12.9904i	−0.105644	−	0.548944i
$561$		0			0
$562$	13.5000	−	23.3827i	0.569463	−	0.986339i
$563$	16.5000	−	28.5788i	0.695392	−	1.20445i	−0.274656	−	0.961542i	$-0.588564\pi$
$563$	16.5000	−	28.5788i	0.695392	−	1.20445i	0.970048	−	0.242912i	$-0.0781026\pi$
$564$	−4.50000	−	2.59808i	−0.189484	−	0.109399i
$565$	−12.0000	+	6.92820i	−0.504844	+	0.291472i
$566$	−39.0000			−1.63929
$567$	−22.5000	−	7.79423i	−0.944911	−	0.327327i
$568$		0			0
$569$	6.00000	−	3.46410i	0.251533	−	0.145223i	−0.368933	−	0.929456i	$-0.620277\pi$
$569$	6.00000	−	3.46410i	0.251533	−	0.145223i	0.620466	+	0.784233i	$0.286943\pi$
$570$	9.00000	+	5.19615i	0.376969	+	0.217643i
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$		0			0
$573$	42.0000			1.75458
$574$	−40.5000	+	7.79423i	−1.69044	+	0.325325i
$575$			8.66025i			0.361158i
$576$	−1.50000	−	2.59808i	−0.0625000	−	0.108253i
$577$		−	24.2487i		−	1.00949i	−0.863269	−	0.504744i	$-0.831587\pi$
$577$		−	24.2487i		−	1.00949i	0.863269	−	0.504744i	$-0.168413\pi$
$578$	−28.5000	+	16.4545i	−1.18544	+	0.684416i
$579$	6.00000	−	3.46410i	0.249351	−	0.143963i
$580$	−1.50000	−	0.866025i	−0.0622841	−	0.0359597i
$581$	−18.0000	+	15.5885i	−0.746766	+	0.646718i
$582$	9.00000	−	5.19615i	0.373062	−	0.215387i
$583$		0			0
$584$	24.0000			0.993127
$585$		0			0
$586$		−	51.9615i		−	2.14651i
$587$	10.5000	+	18.1865i	0.433381	+	0.750639i	0.997162	−	0.0752860i	$-0.0239870\pi$
$587$	10.5000	+	18.1865i	0.433381	+	0.750639i	−0.563781	+	0.825925i	$0.690654\pi$
$588$	7.50000	−	9.52628i	0.309295	−	0.392857i
$589$	−6.00000	+	10.3923i	−0.247226	+	0.428207i
$590$	9.00000	+	5.19615i	0.370524	+	0.213922i
$591$	18.0000	−	31.1769i	0.740421	−	1.28245i
$592$	−5.00000	−	8.66025i	−0.205499	−	0.355934i
$593$	−18.0000			−0.739171			−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000			−0.739171			−0.369586	+	0.929197i	$0.620500\pi$
$594$		0			0
$595$	15.0000	+	5.19615i	0.614940	+	0.213021i
$596$	−16.5000	+	9.52628i	−0.675866	+	0.390212i
$597$	−9.00000	+	15.5885i	−0.368345	+	0.637993i
$598$		0			0
$599$	−3.00000	−	1.73205i	−0.122577	−	0.0707697i	0.437458	−	0.899239i	$-0.355879\pi$
$599$	−3.00000	−	1.73205i	−0.122577	−	0.0707697i	−0.560035	+	0.828469i	$0.689212\pi$
$600$	3.00000			0.122474
$601$	42.0000	−	24.2487i	1.71322	−	0.989126i	0.783071	−	0.621932i	$-0.213652\pi$
$601$	42.0000	−	24.2487i	1.71322	−	0.989126i	0.930145	−	0.367193i	$-0.119681\pi$
$602$	−6.00000	+	17.3205i	−0.244542	+	0.705931i
$603$	39.0000			1.58820
$604$	−4.00000			−0.162758
$605$	−5.50000	−	9.52628i	−0.223607	−	0.387298i
$606$	9.00000	+	15.5885i	0.365600	+	0.633238i
$607$	34.5000	+	19.9186i	1.40031	+	0.808470i	0.994424	−	0.105453i	$-0.0336291\pi$
$607$	34.5000	+	19.9186i	1.40031	+	0.808470i	0.405887	+	0.913923i	$0.366962\pi$
$608$	−9.00000	+	15.5885i	−0.364998	+	0.632195i
$609$	1.50000	+	7.79423i	0.0607831	+	0.315838i
$610$	7.50000	+	12.9904i	0.303666	+	0.525965i
$611$		0			0
$612$	−18.0000			−0.727607
$613$	−10.0000			−0.403896			−0.201948	−	0.979396i	$-0.564727\pi$
$613$	−10.0000			−0.403896			−0.201948	+	0.979396i	$0.564727\pi$
$614$	10.5000	+	18.1865i	0.423746	+	0.733949i
$615$		−	15.5885i		−	0.628587i
$616$		0			0
$617$	−12.0000	−	6.92820i	−0.483102	−	0.278919i	0.238606	−	0.971116i	$-0.423309\pi$
$617$	−12.0000	−	6.92820i	−0.483102	−	0.278919i	−0.721708	+	0.692197i	$0.756643\pi$
$618$	−9.00000	−	5.19615i	−0.362033	−	0.209020i
$619$	−15.0000	+	8.66025i	−0.602901	+	0.348085i	−0.770182	−	0.637824i	$-0.779835\pi$
$619$	−15.0000	+	8.66025i	−0.602901	+	0.348085i	0.167281	+	0.985909i	$0.446501\pi$
$620$		−	3.46410i		−	0.139122i
$621$	−22.5000	+	38.9711i	−0.902894	+	1.56386i
$622$			31.1769i			1.25008i
$623$	−7.50000	−	38.9711i	−0.300481	−	1.56135i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−18.0000	+	31.1769i	−0.719425	+	1.24608i
$627$		0			0
$628$	−15.0000	+	8.66025i	−0.598565	+	0.345582i
$629$	12.0000			0.478471
$630$	9.00000	+	10.3923i	0.358569	+	0.414039i
$631$	−4.00000			−0.159237			−0.0796187	−	0.996825i	$-0.525370\pi$
$631$	−4.00000			−0.159237			−0.0796187	+	0.996825i	$0.525370\pi$
$632$	−21.0000	+	12.1244i	−0.835335	+	0.482281i
$633$	−12.0000	+	6.92820i	−0.476957	+	0.275371i
$634$	−6.00000	+	10.3923i	−0.238290	+	0.412731i
$635$	6.50000	−	11.2583i	0.257945	−	0.446773i
$636$	−3.00000	−	5.19615i	−0.118958	−	0.206041i
$637$		0			0
$638$		0			0
$639$		0			0
$640$			12.1244i			0.479257i
$641$	7.50000	−	4.33013i	0.296232	−	0.171030i	−0.344517	−	0.938780i	$-0.611957\pi$
$641$	7.50000	−	4.33013i	0.296232	−	0.171030i	0.640749	+	0.767750i	$0.278624\pi$
$642$		−	25.9808i		−	1.02538i
$643$	−31.5000	−	18.1865i	−1.24224	−	0.717207i	−0.272689	−	0.962102i	$-0.587913\pi$
$643$	−31.5000	−	18.1865i	−1.24224	−	0.717207i	−0.969550	+	0.244895i	$0.921246\pi$
$644$	−15.0000	−	17.3205i	−0.591083	−	0.682524i
$645$	−6.00000	−	3.46410i	−0.236250	−	0.136399i
$646$	−18.0000	−	31.1769i	−0.708201	−	1.22664i
$647$	−21.0000			−0.825595			−0.412798	−	0.910823i	$-0.635448\pi$
$647$	−21.0000			−0.825595			−0.412798	+	0.910823i	$0.635448\pi$
$648$	13.5000	+	7.79423i	0.530330	+	0.306186i
$649$		0			0
$650$		0			0
$651$	−12.0000	+	10.3923i	−0.470317	+	0.407307i
$652$	−2.00000	+	3.46410i	−0.0783260	+	0.135665i
$653$	−15.0000	−	8.66025i	−0.586995	−	0.338902i	0.176913	−	0.984226i	$-0.443389\pi$
$653$	−15.0000	−	8.66025i	−0.586995	−	0.338902i	−0.763909	+	0.645325i	$0.776722\pi$
$654$	21.0000			0.821165
$655$	9.00000	+	15.5885i	0.351659	+	0.609091i
$656$	45.0000			1.75695
$657$	−36.0000	+	20.7846i	−1.40449	+	0.810885i
$658$	4.50000	−	12.9904i	0.175428	−	0.506418i
$659$	6.00000	−	3.46410i	0.233727	−	0.134942i	−0.378563	−	0.925575i	$-0.623582\pi$
$659$	6.00000	−	3.46410i	0.233727	−	0.134942i	0.612290	+	0.790633i	$0.290248\pi$
$660$		0			0
$661$	−6.00000	−	3.46410i	−0.233373	−	0.134738i	0.378754	−	0.925497i	$-0.376353\pi$
$661$	−6.00000	−	3.46410i	−0.233373	−	0.134738i	−0.612127	+	0.790759i	$0.709686\pi$
$662$	−39.0000	−	22.5167i	−1.51578	−	0.875135i
$663$		0			0
$664$	13.5000	−	7.79423i	0.523902	−	0.302475i
$665$	−3.00000	+	8.66025i	−0.116335	+	0.335830i
$666$	9.00000	+	5.19615i	0.348743	+	0.201347i
$667$	15.0000			0.580802
$668$	1.50000	+	2.59808i	0.0580367	+	0.100523i
$669$	33.0000			1.27585
$670$	−19.5000	−	11.2583i	−0.753351	−	0.434947i
$671$		0			0
$672$	−18.0000	+	15.5885i	−0.694365	+	0.601338i
$673$	22.0000	+	38.1051i	0.848038	+	1.46884i	0.882957	+	0.469454i	$0.155549\pi$
$673$	22.0000	+	38.1051i	0.848038	+	1.46884i	−0.0349191	+	0.999390i	$0.511117\pi$
$674$			13.8564i			0.533729i
$675$	−4.50000	+	2.59808i	−0.173205	+	0.100000i
$676$	−13.0000			−0.500000
$677$	24.0000	+	41.5692i	0.922395	+	1.59763i	0.795698	+	0.605693i	$0.207104\pi$
$677$	24.0000	+	41.5692i	0.922395	+	1.59763i	0.126697	+	0.991941i	$0.459562\pi$
$678$	36.0000	+	20.7846i	1.38257	+	0.798228i
$679$	6.00000	+	6.92820i	0.230259	+	0.265880i
$680$	−9.00000	−	5.19615i	−0.345134	−	0.199263i
$681$		−	20.7846i		−	0.796468i
$682$		0			0
$683$		−	10.3923i		−	0.397650i	−0.980035	−	0.198825i	$-0.936287\pi$
$683$		−	10.3923i		−	0.397650i	0.980035	−	0.198825i	$-0.0637126\pi$
$684$		−	10.3923i		−	0.397360i
$685$			6.92820i			0.264713i
$686$	28.5000	+	14.7224i	1.08814	+	0.562105i
$687$	−16.5000	−	28.5788i	−0.629514	−	1.09035i
$688$	10.0000	−	17.3205i	0.381246	−	0.660338i
$689$		0			0
$690$	22.5000	−	12.9904i	0.856560	−	0.494535i
$691$	−9.00000	+	5.19615i	−0.342376	+	0.197671i	−0.661322	−	0.750102i	$-0.730004\pi$
$691$	−9.00000	+	5.19615i	−0.342376	+	0.197671i	0.318946	+	0.947773i	$0.396671\pi$
$692$	24.0000			0.912343
$693$		0			0
$694$	18.0000			0.683271
$695$	−6.00000	+	3.46410i	−0.227593	+	0.131401i
$696$		−	5.19615i		−	0.196960i
$697$	−27.0000	+	46.7654i	−1.02270	+	1.77136i
$698$	19.5000	−	33.7750i	0.738086	−	1.27840i
$699$	−3.00000	+	5.19615i	−0.113470	+	0.196537i
$700$	−0.500000	−	2.59808i	−0.0188982	−	0.0981981i
$701$		−	29.4449i		−	1.11212i	−0.831143	−	0.556059i	$-0.812313\pi$
$701$		−	29.4449i		−	1.11212i	0.831143	−	0.556059i	$-0.187687\pi$
$702$		0			0
$703$			6.92820i			0.261302i
$704$		0			0
$705$	4.50000	+	2.59808i	0.169480	+	0.0978492i
$706$	54.0000	+	31.1769i	2.03232	+	1.17336i
$707$	−12.0000	+	10.3923i	−0.451306	+	0.390843i
$708$		−	10.3923i		−	0.390567i
$709$	8.50000	+	14.7224i	0.319224	+	0.552913i	0.980326	−	0.197383i	$-0.0632444\pi$
$709$	8.50000	+	14.7224i	0.319224	+	0.552913i	−0.661102	+	0.750296i	$0.729911\pi$
$710$		0			0
$711$	21.0000	−	36.3731i	0.787562	−	1.36410i
$712$			25.9808i			0.973670i
$713$	15.0000	+	25.9808i	0.561754	+	0.972987i
$714$	−9.00000	−	46.7654i	−0.336817	−	1.75015i
$715$		0			0
$716$	18.0000	+	10.3923i	0.672692	+	0.388379i
$717$	−6.00000	−	10.3923i	−0.224074	−	0.388108i
$718$	3.00000	+	5.19615i	0.111959	+	0.193919i
$719$	−30.0000			−1.11881			−0.559406	−	0.828894i	$-0.688971\pi$
$719$	−30.0000			−1.11881			−0.559406	+	0.828894i	$0.688971\pi$
$720$	−7.50000	−	12.9904i	−0.279508	−	0.484123i
$721$	3.00000	−	8.66025i	0.111726	−	0.322525i
$722$	−10.5000	+	6.06218i	−0.390770	+	0.225611i
$723$	27.0000			1.00414
$724$	13.5000	+	7.79423i	0.501724	+	0.289670i
$725$	1.50000	+	0.866025i	0.0557086	+	0.0321634i
$726$	−16.5000	+	28.5788i	−0.612372	+	1.06066i
$727$	7.50000	−	4.33013i	0.278160	−	0.160596i	−0.354430	−	0.935082i	$-0.615325\pi$
$727$	7.50000	−	4.33013i	0.278160	−	0.160596i	0.632590	+	0.774487i	$0.281992\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	24.0000			0.888280
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$	7.50000	−	12.9904i	0.277208	−	0.480138i
$733$	27.0000	+	15.5885i	0.997268	+	0.575773i	0.907439	−	0.420184i	$-0.138035\pi$
$733$	27.0000	+	15.5885i	0.997268	+	0.575773i	0.0898290	+	0.995957i	$0.471368\pi$
$734$	−9.00000	+	15.5885i	−0.332196	+	0.575380i
$735$	−7.50000	+	9.52628i	−0.276642	+	0.351382i
$736$	22.5000	+	38.9711i	0.829361	+	1.43650i
$737$		0			0
$738$	−40.5000	+	23.3827i	−1.49083	+	0.860729i
$739$	−34.0000			−1.25071			−0.625355	−	0.780340i	$-0.715046\pi$
$739$	−34.0000			−1.25071			−0.625355	+	0.780340i	$0.715046\pi$
$740$	−1.00000	−	1.73205i	−0.0367607	−	0.0636715i
$741$		0			0
$742$	12.0000	−	10.3923i	0.440534	−	0.381514i
$743$	25.5000	+	14.7224i	0.935504	+	0.540114i	0.888548	−	0.458783i	$-0.151715\pi$
$743$	25.5000	+	14.7224i	0.935504	+	0.540114i	0.0469561	+	0.998897i	$0.485048\pi$
$744$	9.00000	−	5.19615i	0.329956	−	0.190500i
$745$	16.5000	−	9.52628i	0.604513	−	0.349016i
$746$		−	3.46410i		−	0.126830i
$747$	−13.5000	+	23.3827i	−0.493939	+	0.855528i
$748$		0			0
$749$	22.5000	−	4.33013i	0.822132	−	0.158219i
$750$	3.00000			0.109545
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	−0.411170	−	0.911559i	$-0.634880\pi$
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	0.995018	−	0.0996961i	$-0.0317870\pi$
$752$	−7.50000	+	12.9904i	−0.273497	+	0.473710i
$753$	9.00000	+	5.19615i	0.327978	+	0.189358i
$754$		0			0
$755$	4.00000			0.145575
$756$	4.50000	−	12.9904i	0.163663	−	0.472456i
$757$	−20.0000			−0.726912			−0.363456	−	0.931611i	$-0.618403\pi$
$757$	−20.0000			−0.726912			−0.363456	+	0.931611i	$0.618403\pi$
$758$	3.00000	−	1.73205i	0.108965	−	0.0629109i
$759$		0			0
$760$	3.00000	−	5.19615i	0.108821	−	0.188484i
$761$	10.5000	−	18.1865i	0.380625	−	0.659261i	−0.610527	−	0.791995i	$-0.709042\pi$
$761$	10.5000	−	18.1865i	0.380625	−	0.659261i	0.991152	+	0.132734i	$0.0423756\pi$
$762$	−39.0000			−1.41282
$763$	3.50000	+	18.1865i	0.126709	+	0.658397i
$764$			24.2487i			0.877288i
$765$	18.0000			0.650791
$766$		0			0
$767$		0			0
$768$	28.5000	−	16.4545i	1.02841	−	0.593750i
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	0.236433	−	0.971648i	$-0.424022\pi$
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	−0.723255	+	0.690581i	$0.757355\pi$
$770$		0			0
$771$	−9.00000	+	5.19615i	−0.324127	+	0.187135i
$772$	2.00000	+	3.46410i	0.0719816	+	0.124676i
$773$	−24.0000			−0.863220			−0.431610	−	0.902060i	$-0.642054\pi$
$773$	−24.0000			−0.863220			−0.431610	+	0.902060i	$0.642054\pi$
$774$			20.7846i			0.747087i
$775$			3.46410i			0.124434i
$776$	−3.00000	−	5.19615i	−0.107694	−	0.186531i
$777$	−3.00000	+	8.66025i	−0.107624	+	0.310685i
$778$	−19.5000	+	33.7750i	−0.699109	+	1.21089i
$779$	−27.0000	−	15.5885i	−0.967375	−	0.558514i
$780$		0			0
$781$		0			0
$782$	−90.0000			−3.21839
$783$	4.50000	+	7.79423i	0.160817	+	0.278543i
$784$	−27.5000	−	21.6506i	−0.982143	−	0.773237i
$785$	15.0000	−	8.66025i	0.535373	−	0.309098i
$786$	27.0000	−	46.7654i	0.963058	−	1.66807i
$787$	−21.0000	−	12.1244i	−0.748569	−	0.432187i	0.0766075	−	0.997061i	$-0.475591\pi$
$787$	−21.0000	−	12.1244i	−0.748569	−	0.432187i	−0.825177	+	0.564875i	$0.808924\pi$
$788$	18.0000	+	10.3923i	0.641223	+	0.370211i
$789$	18.0000			0.640817
$790$	−21.0000	+	12.1244i	−0.747146	+	0.431365i
$791$	−12.0000	+	34.6410i	−0.426671	+	1.23169i
$792$		0			0
$793$		0			0
$794$	21.0000	+	36.3731i	0.745262	+	1.29083i
$795$	3.00000	+	5.19615i	0.106399	+	0.184289i
$796$	−9.00000	−	5.19615i	−0.318997	−	0.184173i
$797$	12.0000	−	20.7846i	0.425062	−	0.736229i	−0.571364	−	0.820696i	$-0.693586\pi$
$797$	12.0000	−	20.7846i	0.425062	−	0.736229i	0.996426	+	0.0844678i	$0.0269190\pi$
$798$	27.0000	−	5.19615i	0.955790	−	0.183942i
$799$	−9.00000	−	15.5885i	−0.318397	−	0.551480i
$800$			5.19615i			0.183712i
$801$	−22.5000	−	38.9711i	−0.794998	−	1.37698i
$802$	12.0000			0.423735
$803$		0			0
$804$			22.5167i			0.794101i
$805$	15.0000	+	17.3205i	0.528681	+	0.610468i
$806$		0			0
$807$	−4.50000	−	2.59808i	−0.158408	−	0.0914566i
$808$	9.00000	−	5.19615i	0.316619	−	0.182800i
$809$			20.7846i			0.730748i	0.930861	+	0.365374i	$0.119059\pi$
$809$			20.7846i			0.730748i	−0.930861	+	0.365374i	$0.880941\pi$
$810$	13.5000	+	7.79423i	0.474342	+	0.273861i
$811$			38.1051i			1.33805i	0.743239	+	0.669026i	$0.233288\pi$
$811$			38.1051i			1.33805i	−0.743239	+	0.669026i	$0.766712\pi$
$812$	−4.50000	+	0.866025i	−0.157919	+	0.0303915i
$813$	−3.00000	+	5.19615i	−0.105215	+	0.182237i
$814$		0			0
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$			51.9615i			1.81902i
$817$	−12.0000	+	6.92820i	−0.419827	+	0.242387i
$818$	36.0000			1.25871
$819$		0			0
$820$	9.00000			0.314294
$821$	25.5000	−	14.7224i	0.889956	−	0.513816i	0.0160280	−	0.999872i	$-0.494898\pi$
$821$	25.5000	−	14.7224i	0.889956	−	0.513816i	0.873928	+	0.486055i	$0.161565\pi$
$822$	18.0000	−	10.3923i	0.627822	−	0.362473i
$823$	−26.5000	+	45.8993i	−0.923732	+	1.59995i	−0.130144	+	0.991495i	$0.541544\pi$
$823$	−26.5000	+	45.8993i	−0.923732	+	1.59995i	−0.793588	+	0.608456i	$0.791789\pi$
$824$	−3.00000	+	5.19615i	−0.104510	+	0.181017i
$825$		0			0
$826$	27.0000	−	5.19615i	0.939450	−	0.180797i
$827$		−	15.5885i		−	0.542064i	−0.962570	−	0.271032i	$-0.912635\pi$
$827$		−	15.5885i		−	0.542064i	0.962570	−	0.271032i	$-0.0873649\pi$
$828$	−22.5000	−	12.9904i	−0.781929	−	0.451447i
$829$			32.9090i			1.14298i	0.820611	+	0.571488i	$0.193634\pi$
$829$			32.9090i			1.14298i	−0.820611	+	0.571488i	$0.806366\pi$
$830$	13.5000	−	7.79423i	0.468592	−	0.270542i
$831$		−	17.3205i		−	0.600842i
$832$		0			0
$833$	39.0000	−	15.5885i	1.35127	−	0.540108i
$834$	18.0000	+	10.3923i	0.623289	+	0.359856i
$835$	−1.50000	−	2.59808i	−0.0519096	−	0.0899101i
$836$		0			0
$837$	−9.00000	+	15.5885i	−0.311086	+	0.538816i
$838$		0			0
$839$	−21.0000	−	36.3731i	−0.725001	−	1.25574i	−0.958974	−	0.283495i	$-0.908506\pi$
$839$	−21.0000	−	36.3731i	−0.725001	−	1.25574i	0.233973	−	0.972243i	$-0.424827\pi$
$840$	6.00000	−	5.19615i	0.207020	−	0.179284i
$841$	−13.0000	+	22.5167i	−0.448276	+	0.776437i
$842$	39.0000	+	22.5167i	1.34403	+	0.775975i
$843$	27.0000			0.929929
$844$	−4.00000	−	6.92820i	−0.137686	−	0.238479i
$845$	13.0000			0.447214
$846$		−	15.5885i		−	0.535942i
$847$	−27.5000	−	9.52628i	−0.944911	−	0.327327i
$848$	−15.0000	+	8.66025i	−0.515102	+	0.297394i
$849$	−19.5000	−	33.7750i	−0.669238	−	1.15915i
$850$	−9.00000	−	5.19615i	−0.308697	−	0.178227i
$851$	15.0000	+	8.66025i	0.514193	+	0.296870i
$852$		0			0
$853$	−18.0000	+	10.3923i	−0.616308	+	0.355826i	−0.775430	−	0.631433i	$-0.782467\pi$
$853$	−18.0000	+	10.3923i	−0.616308	+	0.355826i	0.159122	+	0.987259i	$0.449134\pi$
$854$	37.5000	+	12.9904i	1.28322	+	0.444522i
$855$			10.3923i			0.355409i
$856$	−15.0000			−0.512689
$857$	−12.0000	−	20.7846i	−0.409912	−	0.709989i	0.584967	−	0.811057i	$-0.301107\pi$
$857$	−12.0000	−	20.7846i	−0.409912	−	0.709989i	−0.994880	+	0.101068i	$0.967774\pi$
$858$		0			0
$859$	12.0000	+	6.92820i	0.409435	+	0.236387i	0.690547	−	0.723288i	$-0.257370\pi$
$859$	12.0000	+	6.92820i	0.409435	+	0.236387i	−0.281112	+	0.959675i	$0.590703\pi$
$860$	2.00000	−	3.46410i	0.0681994	−	0.118125i
$861$	−27.0000	−	31.1769i	−0.920158	−	1.06251i
$862$	−9.00000	−	15.5885i	−0.306541	−	0.530945i
$863$			15.5885i			0.530637i	0.964161	+	0.265319i	$0.0854771\pi$
$863$			15.5885i			0.530637i	−0.964161	+	0.265319i	$0.914523\pi$
$864$	−13.5000	+	23.3827i	−0.459279	+	0.795495i
$865$	−24.0000			−0.816024
$866$	3.00000	+	5.19615i	0.101944	+	0.176572i
$867$	−28.5000	−	16.4545i	−0.967911	−	0.558824i
$868$	−6.00000	−	6.92820i	−0.203653	−	0.235159i
$869$		0			0
$870$		−	5.19615i		−	0.176166i
$871$		0			0
$872$		−	12.1244i		−	0.410582i
$873$	9.00000	+	5.19615i	0.304604	+	0.175863i
$874$		−	51.9615i		−	1.75762i
$875$	0.500000	+	2.59808i	0.0169031	+	0.0878310i
$876$	−12.0000	−	20.7846i	−0.405442	−	0.702247i
$877$	−16.0000	+	27.7128i	−0.540282	+	0.935795i	0.458606	+	0.888640i	$0.348349\pi$
$877$	−16.0000	+	27.7128i	−0.540282	+	0.935795i	−0.998888	+	0.0471555i	$0.984984\pi$
$878$	30.0000	−	51.9615i	1.01245	−	1.75362i
$879$	45.0000	−	25.9808i	1.51781	−	0.876309i
$880$		0			0
$881$	−15.0000			−0.505363			−0.252681	−	0.967550i	$-0.581312\pi$
$881$	−15.0000			−0.505363			−0.252681	+	0.967550i	$0.581312\pi$
$882$	36.0000	+	5.19615i	1.21218	+	0.174964i
$883$	−11.0000			−0.370179			−0.185090	−	0.982722i	$-0.559258\pi$
$883$	−11.0000			−0.370179			−0.185090	+	0.982722i	$0.559258\pi$
$884$		0			0
$885$			10.3923i			0.349334i
$886$	22.5000	−	38.9711i	0.755902	−	1.30926i
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	−0.994077	−	0.108678i	$-0.965338\pi$
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	0.591156	+	0.806557i	$0.298672\pi$
$888$	3.00000	−	5.19615i	0.100673	−	0.174371i
$889$	−6.50000	−	33.7750i	−0.218003	−	1.13278i
$890$			25.9808i			0.870877i
$891$		0			0
$892$			19.0526i			0.637927i
$893$	9.00000	−	5.19615i	0.301174	−	0.173883i
$894$	−49.5000	−	28.5788i	−1.65553	−	0.955819i
$895$	−18.0000	−	10.3923i	−0.601674	−	0.347376i
$896$	21.0000	+	24.2487i	0.701561	+	0.810093i
$897$		0			0
$898$	6.00000	+	10.3923i	0.200223	+	0.346796i
$899$	6.00000			0.200111
$900$	−1.50000	−	2.59808i	−0.0500000	−	0.0866025i
$901$		−	20.7846i		−	0.692436i
$902$		0			0
$903$	−18.0000	+	3.46410i	−0.599002	+	0.115278i
$904$	12.0000	−	20.7846i	0.399114	−	0.691286i
$905$	−13.5000	−	7.79423i	−0.448755	−	0.259089i
$906$	−6.00000	−	10.3923i	−0.199337	−	0.345261i
$907$	−27.5000	−	47.6314i	−0.913123	−	1.58157i	−0.809627	−	0.586945i	$-0.800331\pi$
$907$	−27.5000	−	47.6314i	−0.913123	−	1.58157i	−0.103495	−	0.994630i	$-0.533003\pi$
$908$	12.0000			0.398234
$909$	−9.00000	+	15.5885i	−0.298511	+	0.517036i
$910$		0			0
$911$	15.0000	−	8.66025i	0.496972	−	0.286927i	−0.230490	−	0.973075i	$-0.574033\pi$
$911$	15.0000	−	8.66025i	0.496972	−	0.286927i	0.727462	+	0.686148i	$0.240700\pi$
$912$	−30.0000			−0.993399
$913$		0			0
$914$	−39.0000	−	22.5167i	−1.29001	−	0.744785i
$915$	−7.50000	+	12.9904i	−0.247942	+	0.429449i
$916$	16.5000	−	9.52628i	0.545175	−	0.314757i
$917$	45.0000	+	15.5885i	1.48603	+	0.514776i
$918$	−27.0000	−	46.7654i	−0.891133	−	1.54349i
$919$	−2.00000			−0.0659739			−0.0329870	−	0.999456i	$-0.510502\pi$
$919$	−2.00000			−0.0659739			−0.0329870	+	0.999456i	$0.510502\pi$
$920$	−7.50000	−	12.9904i	−0.247268	−	0.428280i
$921$	−10.5000	+	18.1865i	−0.345987	+	0.599267i
$922$	31.5000	+	18.1865i	1.03740	+	0.598942i
$923$		0			0
$924$		0			0
$925$	1.00000	+	1.73205i	0.0328798	+	0.0569495i
$926$			6.92820i			0.227675i
$927$		−	10.3923i		−	0.341328i
$928$	9.00000			0.295439
$929$	−27.0000	−	46.7654i	−0.885841	−	1.53432i	−0.844746	−	0.535167i	$-0.820249\pi$
$929$	−27.0000	−	46.7654i	−0.885841	−	1.53432i	−0.0410949	−	0.999155i	$-0.513085\pi$
$930$	9.00000	−	5.19615i	0.295122	−	0.170389i
$931$	9.00000	+	22.5167i	0.294963	+	0.737954i
$932$	−3.00000	−	1.73205i	−0.0982683	−	0.0567352i
$933$	−27.0000	+	15.5885i	−0.883940	+	0.510343i
$934$	18.0000	−	10.3923i	0.588978	−	0.340047i
$935$		0			0
$936$		0			0
$937$		−	34.6410i		−	1.13167i	−0.824518	−	0.565836i	$-0.808553\pi$
$937$		−	34.6410i		−	1.13167i	0.824518	−	0.565836i	$-0.191447\pi$
$938$	−58.5000	+	11.2583i	−1.91009	+	0.367598i
$939$	−36.0000			−1.17482
$940$	−1.50000	+	2.59808i	−0.0489246	+	0.0847399i
$941$	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	$0.0880451\pi$
$942$	−45.0000	−	25.9808i	−1.46618	−	0.846499i
$943$	−67.5000	+	38.9711i	−2.19810	+	1.26908i
$944$	−30.0000			−0.976417
$945$	−4.50000	+	12.9904i	−0.146385	+	0.422577i
$946$		0			0
$947$	−40.5000	+	23.3827i	−1.31607	+	0.759835i	−0.983094	−	0.183099i	$-0.941387\pi$
$947$	−40.5000	+	23.3827i	−1.31607	+	0.759835i	−0.332979	+	0.942934i	$0.608054\pi$
$948$	21.0000	+	12.1244i	0.682048	+	0.393781i
$949$		0			0
$950$	3.00000	−	5.19615i	0.0973329	−	0.168585i
$951$	−12.0000			−0.389127
$952$	−27.0000	+	5.19615i	−0.875075	+	0.168408i
$953$		−	27.7128i		−	0.897706i	−0.893606	−	0.448853i	$-0.851833\pi$
$953$		−	27.7128i		−	0.897706i	0.893606	−	0.448853i	$-0.148167\pi$
$954$	9.00000	−	15.5885i	0.291386	−	0.504695i
$955$		−	24.2487i		−	0.784670i
$956$	6.00000	−	3.46410i	0.194054	−	0.112037i
$957$		0			0
$958$	−27.0000	−	15.5885i	−0.872330	−	0.503640i
$959$	12.0000	+	13.8564i	0.387500	+	0.447447i
$960$	−1.50000	+	0.866025i	−0.0484123	+	0.0279508i
$961$	−9.50000	−	16.4545i	−0.306452	−	0.530790i
$962$		0			0
$963$	22.5000	−	12.9904i	0.725052	−	0.418609i
$964$			15.5885i			0.502070i
$965$	−2.00000	−	3.46410i	−0.0643823	−	0.111513i
$966$	22.5000	−	64.9519i	0.723926	−	2.08979i
$967$	−5.50000	+	9.52628i	−0.176868	+	0.306344i	−0.940806	−	0.338945i	$-0.889930\pi$
$967$	−5.50000	+	9.52628i	−0.176868	+	0.306344i	0.763938	+	0.645290i	$0.223263\pi$
$968$	16.5000	+	9.52628i	0.530330	+	0.306186i
$969$	18.0000	−	31.1769i	0.578243	−	1.00155i
$970$	−3.00000	−	5.19615i	−0.0963242	−	0.166838i
$971$	−18.0000			−0.577647			−0.288824	−	0.957382i	$-0.593264\pi$
$971$	−18.0000			−0.577647			−0.288824	+	0.957382i	$0.593264\pi$
$972$		−	15.5885i		−	0.500000i
$973$	−6.00000	+	17.3205i	−0.192351	+	0.555270i
$974$	48.0000	−	27.7128i	1.53802	−	0.887976i
$975$		0			0
$976$	−37.5000	−	21.6506i	−1.20035	−	0.693020i
$977$	30.0000	+	17.3205i	0.959785	+	0.554132i	0.896107	−	0.443838i	$-0.146384\pi$
$977$	30.0000	+	17.3205i	0.959785	+	0.554132i	0.0636782	+	0.997970i	$0.479717\pi$
$978$	−12.0000			−0.383718
$979$		0			0
$980$	−5.50000	−	4.33013i	−0.175691	−	0.138321i
$981$	10.5000	+	18.1865i	0.335239	+	0.580651i
$982$	−48.0000			−1.53174
$983$	−22.5000	−	38.9711i	−0.717639	−	1.24299i	−0.961933	−	0.273285i	$-0.911890\pi$
$983$	−22.5000	−	38.9711i	−0.717639	−	1.24299i	0.244294	−	0.969701i	$-0.421444\pi$
$984$	13.5000	+	23.3827i	0.430364	+	0.745413i
$985$	−18.0000	−	10.3923i	−0.573528	−	0.331126i
$986$	−9.00000	+	15.5885i	−0.286618	+	0.496438i
$987$	13.5000	−	2.59808i	0.429710	−	0.0826977i
$988$		0			0
$989$			34.6410i			1.10152i
$990$		0			0
$991$	−2.00000			−0.0635321			−0.0317660	−	0.999495i	$-0.510113\pi$
$991$	−2.00000			−0.0635321			−0.0317660	+	0.999495i	$0.510113\pi$
$992$	9.00000	+	15.5885i	0.285750	+	0.494934i
$993$		−	45.0333i		−	1.42909i
$994$		0			0
$995$	9.00000	+	5.19615i	0.285319	+	0.164729i
$996$	−13.5000	−	7.79423i	−0.427764	−	0.246970i
$997$	27.0000	−	15.5885i	0.855099	−	0.493691i	−0.00726929	−	0.999974i	$-0.502314\pi$
$997$	27.0000	−	15.5885i	0.855099	−	0.493691i	0.862368	+	0.506282i	$0.168981\pi$
$998$			34.6410i			1.09654i
$999$			10.3923i			0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bl.a.41.1	✓	2
3.2	odd	2		945.2.bl.g.881.1		2
7.6	odd	2		315.2.bl.d.41.1	yes	2
9.2	odd	6		315.2.bl.d.146.1	yes	2
9.7	even	3		945.2.bl.f.251.1		2
21.20	even	2		945.2.bl.f.881.1		2
63.20	even	6	inner	315.2.bl.a.146.1	yes	2
63.34	odd	6		945.2.bl.g.251.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bl.a.41.1	✓	2	1.1	even	1	trivial
315.2.bl.a.146.1	yes	2	63.20	even	6	inner
315.2.bl.d.41.1	yes	2	7.6	odd	2
315.2.bl.d.146.1	yes	2	9.2	odd	6
945.2.bl.f.251.1		2	9.7	even	3
945.2.bl.f.881.1		2	21.20	even	2
945.2.bl.g.251.1		2	63.34	odd	6
945.2.bl.g.881.1		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +3.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +3.00000 q^{6} +(0.500000 + 2.59808i) q^{7} -1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} -1.73205i q^{10} +(-1.50000 + 0.866025i) q^{12} +(-3.00000 - 3.46410i) q^{14} +(1.50000 - 0.866025i) q^{15} +(2.50000 + 4.33013i) q^{16} -6.00000 q^{17} +(-4.50000 - 2.59808i) q^{18} -3.46410i q^{19} +(0.500000 + 0.866025i) q^{20} +(1.50000 - 4.33013i) q^{21} +(-7.50000 - 4.33013i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(-0.500000 - 0.866025i) q^{25} -5.19615i q^{27} +(2.50000 + 0.866025i) q^{28} +(-1.50000 + 0.866025i) q^{29} +(-1.50000 + 2.59808i) q^{30} +(-3.00000 - 1.73205i) q^{31} +(-4.50000 - 2.59808i) q^{32} +(9.00000 - 5.19615i) q^{34} +(-2.50000 - 0.866025i) q^{35} +3.00000 q^{36} -2.00000 q^{37} +(3.00000 + 5.19615i) q^{38} +(1.50000 + 0.866025i) q^{40} +(4.50000 - 7.79423i) q^{41} +(1.50000 + 7.79423i) q^{42} +(-2.00000 - 3.46410i) q^{43} -3.00000 q^{45} +15.0000 q^{46} +(1.50000 + 2.59808i) q^{47} -8.66025i q^{48} +(-6.50000 + 2.59808i) q^{49} +(1.50000 + 0.866025i) q^{50} +(9.00000 + 5.19615i) q^{51} +3.46410i q^{53} +(4.50000 + 7.79423i) q^{54} +(4.50000 - 0.866025i) q^{56} +(-3.00000 + 5.19615i) q^{57} +(1.50000 - 2.59808i) q^{58} +(-3.00000 + 5.19615i) q^{59} -1.73205i q^{60} +(-7.50000 + 4.33013i) q^{61} +6.00000 q^{62} +(-6.00000 + 5.19615i) q^{63} -1.00000 q^{64} +(6.50000 - 11.2583i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(7.50000 + 12.9904i) q^{69} +(4.50000 - 0.866025i) q^{70} +(4.50000 - 2.59808i) q^{72} +13.8564i q^{73} +(3.00000 - 1.73205i) q^{74} +1.73205i q^{75} +(-3.00000 - 1.73205i) q^{76} +(-7.00000 - 12.1244i) q^{79} -5.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +15.5885i q^{82} +(4.50000 + 7.79423i) q^{83} +(-3.00000 - 3.46410i) q^{84} +(3.00000 - 5.19615i) q^{85} +(6.00000 + 3.46410i) q^{86} +3.00000 q^{87} -15.0000 q^{89} +(4.50000 - 2.59808i) q^{90} +(-7.50000 + 4.33013i) q^{92} +(3.00000 + 5.19615i) q^{93} +(-4.50000 - 2.59808i) q^{94} +(3.00000 + 1.73205i) q^{95} +(4.50000 + 7.79423i) q^{96} +(3.00000 - 1.73205i) q^{97} +(7.50000 - 9.52628i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 3 q^{3} + q^{4} - q^{5} + 6 q^{6} + q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 - 3 * q^3 + q^4 - q^5 + 6 * q^6 + q^7 + 3 * q^9	\( 2 q - 3 q^{2} - 3 q^{3} + q^{4} - q^{5} + 6 q^{6} + q^{7} + 3 q^{9} - 3 q^{12} - 6 q^{14} + 3 q^{15} + 5 q^{16} - 12 q^{17} - 9 q^{18} + q^{20} + 3 q^{21} - 15 q^{23} - 3 q^{24} - q^{25} + 5 q^{28} - 3 q^{29} - 3 q^{30} - 6 q^{31} - 9 q^{32} + 18 q^{34} - 5 q^{35} + 6 q^{36} - 4 q^{37} + 6 q^{38} + 3 q^{40} + 9 q^{41} + 3 q^{42} - 4 q^{43} - 6 q^{45} + 30 q^{46} + 3 q^{47} - 13 q^{49} + 3 q^{50} + 18 q^{51} + 9 q^{54} + 9 q^{56} - 6 q^{57} + 3 q^{58} - 6 q^{59} - 15 q^{61} + 12 q^{62} - 12 q^{63} - 2 q^{64} + 13 q^{67} - 6 q^{68} + 15 q^{69} + 9 q^{70} + 9 q^{72} + 6 q^{74} - 6 q^{76} - 14 q^{79} - 10 q^{80} - 9 q^{81} + 9 q^{83} - 6 q^{84} + 6 q^{85} + 12 q^{86} + 6 q^{87} - 30 q^{89} + 9 q^{90} - 15 q^{92} + 6 q^{93} - 9 q^{94} + 6 q^{95} + 9 q^{96} + 6 q^{97} + 15 q^{98}+O(q^{100}) \) 2 * q - 3 * q^2 - 3 * q^3 + q^4 - q^5 + 6 * q^6 + q^7 + 3 * q^9 - 3 * q^12 - 6 * q^14 + 3 * q^15 + 5 * q^16 - 12 * q^17 - 9 * q^18 + q^20 + 3 * q^21 - 15 * q^23 - 3 * q^24 - q^25 + 5 * q^28 - 3 * q^29 - 3 * q^30 - 6 * q^31 - 9 * q^32 + 18 * q^34 - 5 * q^35 + 6 * q^36 - 4 * q^37 + 6 * q^38 + 3 * q^40 + 9 * q^41 + 3 * q^42 - 4 * q^43 - 6 * q^45 + 30 * q^46 + 3 * q^47 - 13 * q^49 + 3 * q^50 + 18 * q^51 + 9 * q^54 + 9 * q^56 - 6 * q^57 + 3 * q^58 - 6 * q^59 - 15 * q^61 + 12 * q^62 - 12 * q^63 - 2 * q^64 + 13 * q^67 - 6 * q^68 + 15 * q^69 + 9 * q^70 + 9 * q^72 + 6 * q^74 - 6 * q^76 - 14 * q^79 - 10 * q^80 - 9 * q^81 + 9 * q^83 - 6 * q^84 + 6 * q^85 + 12 * q^86 + 6 * q^87 - 30 * q^89 + 9 * q^90 - 15 * q^92 + 6 * q^93 - 9 * q^94 + 6 * q^95 + 9 * q^96 + 6 * q^97 + 15 * q^98

Introduction

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