LMFDB - Embedded newform 722.2.c.f.653.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(429,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("722.429");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.c (of order $3$, degree $2$, not 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			653.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	722.653
Dual form			722.2.c.f.429.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.00000 q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(-2.00000 + 3.46410i) q^{10} +2.00000 q^{11} +1.00000 q^{12} +(-0.500000 + 0.866025i) q^{13} +(1.50000 + 2.59808i) q^{14} +(2.00000 - 3.46410i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +2.00000 q^{18} -4.00000 q^{20} +(-1.50000 - 2.59808i) q^{21} +(1.00000 + 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-5.50000 + 9.52628i) q^{25} -1.00000 q^{26} -5.00000 q^{27} +(-1.50000 + 2.59808i) q^{28} +(-2.50000 + 4.33013i) q^{29} +4.00000 q^{30} +8.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +(1.50000 - 2.59808i) q^{34} +(6.00000 + 10.3923i) q^{35} +(1.00000 + 1.73205i) q^{36} +2.00000 q^{37} +1.00000 q^{39} +(-2.00000 - 3.46410i) q^{40} +(-4.00000 - 6.92820i) q^{41} +(1.50000 - 2.59808i) q^{42} +(-2.00000 - 3.46410i) q^{43} +(-1.00000 + 1.73205i) q^{44} +8.00000 q^{45} +1.00000 q^{46} +(-4.00000 + 6.92820i) q^{47} +(-0.500000 + 0.866025i) q^{48} +2.00000 q^{49} -11.0000 q^{50} +(-1.50000 + 2.59808i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(-0.500000 + 0.866025i) q^{53} +(-2.50000 - 4.33013i) q^{54} +(4.00000 + 6.92820i) q^{55} -3.00000 q^{56} -5.00000 q^{58} +(7.50000 + 12.9904i) q^{59} +(2.00000 + 3.46410i) q^{60} +(-1.00000 + 1.73205i) q^{61} +(4.00000 + 6.92820i) q^{62} +(3.00000 - 5.19615i) q^{63} +1.00000 q^{64} -4.00000 q^{65} +(1.00000 - 1.73205i) q^{66} +(1.50000 - 2.59808i) q^{67} +3.00000 q^{68} -1.00000 q^{69} +(-6.00000 + 10.3923i) q^{70} +(1.00000 + 1.73205i) q^{71} +(-1.00000 + 1.73205i) q^{72} +(-4.50000 - 7.79423i) q^{73} +(1.00000 + 1.73205i) q^{74} +11.0000 q^{75} +6.00000 q^{77} +(0.500000 + 0.866025i) q^{78} +(-5.00000 - 8.66025i) q^{79} +(2.00000 - 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.00000 - 6.92820i) q^{82} -6.00000 q^{83} +3.00000 q^{84} +(6.00000 - 10.3923i) q^{85} +(2.00000 - 3.46410i) q^{86} +5.00000 q^{87} -2.00000 q^{88} +(4.00000 + 6.92820i) q^{90} +(-1.50000 + 2.59808i) q^{91} +(0.500000 + 0.866025i) q^{92} +(-4.00000 - 6.92820i) q^{93} -8.00000 q^{94} -1.00000 q^{96} +(-1.00000 - 1.73205i) q^{97} +(1.00000 + 1.73205i) q^{98} +(2.00000 - 3.46410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} + 4 q^{5} + q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{11} + 2 q^{12} - q^{13} + 3 q^{14} + 4 q^{15} - q^{16} - 3 q^{17} + 4 q^{18} - 8 q^{20} - 3 q^{21} + 2 q^{22}+ \cdots + 4 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 + 4 * q^5 + q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^11 + 2 * q^12 - q^13 + 3 * q^14 + 4 * q^15 - q^16 - 3 * q^17 + 4 * q^18 - 8 * q^20 - 3 * q^21 + 2 * q^22 + q^23 + q^24 - 11 * q^25 - 2 * q^26 - 10 * q^27 - 3 * q^28 - 5 * q^29 + 8 * q^30 + 16 * q^31 + q^32 - 2 * q^33 + 3 * q^34 + 12 * q^35 + 2 * q^36 + 4 * q^37 + 2 * q^39 - 4 * q^40 - 8 * q^41 + 3 * q^42 - 4 * q^43 - 2 * q^44 + 16 * q^45 + 2 * q^46 - 8 * q^47 - q^48 + 4 * q^49 - 22 * q^50 - 3 * q^51 - q^52 - q^53 - 5 * q^54 + 8 * q^55 - 6 * q^56 - 10 * q^58 + 15 * q^59 + 4 * q^60 - 2 * q^61 + 8 * q^62 + 6 * q^63 + 2 * q^64 - 8 * q^65 + 2 * q^66 + 3 * q^67 + 6 * q^68 - 2 * q^69 - 12 * q^70 + 2 * q^71 - 2 * q^72 - 9 * q^73 + 2 * q^74 + 22 * q^75 + 12 * q^77 + q^78 - 10 * q^79 + 4 * q^80 - q^81 + 8 * q^82 - 12 * q^83 + 6 * q^84 + 12 * q^85 + 4 * q^86 + 10 * q^87 - 4 * q^88 + 8 * q^90 - 3 * q^91 + q^92 - 8 * q^93 - 16 * q^94 - 2 * q^96 - 2 * q^97 + 2 * q^98 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.00000	+	3.46410i	0.894427	+	1.54919i	0.834512	+	0.550990i	$0.185750\pi$
$5$	2.00000	+	3.46410i	0.894427	+	1.54919i	0.0599153	+	0.998203i	$0.480917\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	3.00000			1.13389			0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000			1.13389			0.566947	+	0.823754i	$0.308125\pi$
$8$	−1.00000			−0.353553
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$	−2.00000	+	3.46410i	−0.632456	+	1.09545i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$	1.00000			0.288675
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	−0.926995	−	0.375073i	$-0.877618\pi$
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	0.788320	+	0.615265i	$0.210951\pi$
$14$	1.50000	+	2.59808i	0.400892	+	0.694365i
$15$	2.00000	−	3.46410i	0.516398	−	0.894427i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	2.00000			0.471405
$19$		0			0
$19$		0			0
$20$	−4.00000			−0.894427
$21$	−1.50000	−	2.59808i	−0.327327	−	0.566947i
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−5.50000	+	9.52628i	−1.10000	+	1.90526i
$26$	−1.00000			−0.196116
$27$	−5.00000			−0.962250
$28$	−1.50000	+	2.59808i	−0.283473	+	0.490990i
$29$	−2.50000	+	4.33013i	−0.464238	+	0.804084i	−0.999167	−	0.0408130i	$-0.987005\pi$
$29$	−2.50000	+	4.33013i	−0.464238	+	0.804084i	0.534928	+	0.844897i	$0.320339\pi$
$30$	4.00000			0.730297
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$	1.50000	−	2.59808i	0.257248	−	0.445566i
$35$	6.00000	+	10.3923i	1.01419	+	1.75662i
$36$	1.00000	+	1.73205i	0.166667	+	0.288675i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$	1.00000			0.160128
$40$	−2.00000	−	3.46410i	−0.316228	−	0.547723i
$41$	−4.00000	−	6.92820i	−0.624695	−	1.08200i	−0.988600	−	0.150567i	$-0.951890\pi$
$41$	−4.00000	−	6.92820i	−0.624695	−	1.08200i	0.363905	−	0.931436i	$-0.381443\pi$
$42$	1.50000	−	2.59808i	0.231455	−	0.400892i
$43$	−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	$0.931989\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$	8.00000			1.19257
$46$	1.00000			0.147442
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	0.411606	+	0.911362i	$0.364968\pi$
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	−0.995066	+	0.0992202i	$0.968365\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	2.00000			0.285714
$50$	−11.0000			−1.55563
$51$	−1.50000	+	2.59808i	−0.210042	+	0.363803i
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	−0.500000	+	0.866025i	−0.0686803	+	0.118958i	−0.898321	−	0.439340i	$-0.855212\pi$
$53$	−0.500000	+	0.866025i	−0.0686803	+	0.118958i	0.829640	+	0.558298i	$0.188546\pi$
$54$	−2.50000	−	4.33013i	−0.340207	−	0.589256i
$55$	4.00000	+	6.92820i	0.539360	+	0.934199i
$56$	−3.00000			−0.400892
$57$		0			0
$58$	−5.00000			−0.656532
$59$	7.50000	+	12.9904i	0.976417	+	1.69120i	0.675178	+	0.737655i	$0.264067\pi$
$59$	7.50000	+	12.9904i	0.976417	+	1.69120i	0.301239	+	0.953549i	$0.402600\pi$
$60$	2.00000	+	3.46410i	0.258199	+	0.447214i
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$	4.00000	+	6.92820i	0.508001	+	0.879883i
$63$	3.00000	−	5.19615i	0.377964	−	0.654654i
$64$	1.00000			0.125000
$65$	−4.00000			−0.496139
$66$	1.00000	−	1.73205i	0.123091	−	0.213201i
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	−0.759733	−	0.650236i	$-0.774670\pi$
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	0.942987	+	0.332830i	$0.108004\pi$
$68$	3.00000			0.363803
$69$	−1.00000			−0.120386
$70$	−6.00000	+	10.3923i	−0.717137	+	1.24212i
$71$	1.00000	+	1.73205i	0.118678	+	0.205557i	0.919244	−	0.393688i	$-0.128801\pi$
$71$	1.00000	+	1.73205i	0.118678	+	0.205557i	−0.800566	+	0.599245i	$0.795468\pi$
$72$	−1.00000	+	1.73205i	−0.117851	+	0.204124i
$73$	−4.50000	−	7.79423i	−0.526685	−	0.912245i	−0.999517	−	0.0310925i	$-0.990101\pi$
$73$	−4.50000	−	7.79423i	−0.526685	−	0.912245i	0.472831	−	0.881153i	$-0.343232\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$	11.0000			1.27017
$76$		0			0
$77$	6.00000			0.683763
$78$	0.500000	+	0.866025i	0.0566139	+	0.0980581i
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	−0.997274	−	0.0737937i	$-0.976489\pi$
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	0.434730	−	0.900561i	$-0.356844\pi$
$80$	2.00000	−	3.46410i	0.223607	−	0.387298i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.00000	−	6.92820i	0.441726	−	0.765092i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	3.00000			0.327327
$85$	6.00000	−	10.3923i	0.650791	−	1.12720i
$86$	2.00000	−	3.46410i	0.215666	−	0.373544i
$87$	5.00000			0.536056
$88$	−2.00000			−0.213201
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$	4.00000	+	6.92820i	0.421637	+	0.730297i
$91$	−1.50000	+	2.59808i	−0.157243	+	0.272352i
$92$	0.500000	+	0.866025i	0.0521286	+	0.0902894i
$93$	−4.00000	−	6.92820i	−0.414781	−	0.718421i
$94$	−8.00000			−0.825137
$95$		0			0
$96$	−1.00000			−0.102062
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	1.00000	+	1.73205i	0.101015	+	0.174964i
$99$	2.00000	−	3.46410i	0.201008	−	0.348155i
$100$	−5.50000	−	9.52628i	−0.550000	−	0.952628i
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	−0.911479	−	0.411346i	$-0.865059\pi$
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	0.811976	+	0.583691i	$0.198392\pi$
$102$	−3.00000			−0.297044
$103$	6.00000			0.591198			0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000			0.591198			0.295599	+	0.955312i	$0.404481\pi$
$104$	0.500000	−	0.866025i	0.0490290	−	0.0849208i
$105$	6.00000	−	10.3923i	0.585540	−	1.01419i
$106$	−1.00000			−0.0971286
$107$	7.00000			0.676716			0.338358	−	0.941018i	$-0.390129\pi$
$107$	7.00000			0.676716			0.338358	+	0.941018i	$0.390129\pi$
$108$	2.50000	−	4.33013i	0.240563	−	0.416667i
$109$	−7.50000	−	12.9904i	−0.718370	−	1.24425i	−0.961645	−	0.274296i	$-0.911555\pi$
$109$	−7.50000	−	12.9904i	−0.718370	−	1.24425i	0.243276	−	0.969957i	$-0.421778\pi$
$110$	−4.00000	+	6.92820i	−0.381385	+	0.660578i
$111$	−1.00000	−	1.73205i	−0.0949158	−	0.164399i
$112$	−1.50000	−	2.59808i	−0.141737	−	0.245495i
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$		0			0
$115$	4.00000			0.373002
$116$	−2.50000	−	4.33013i	−0.232119	−	0.402042i
$117$	1.00000	+	1.73205i	0.0924500	+	0.160128i
$118$	−7.50000	+	12.9904i	−0.690431	+	1.19586i
$119$	−4.50000	−	7.79423i	−0.412514	−	0.714496i
$120$	−2.00000	+	3.46410i	−0.182574	+	0.316228i
$121$	−7.00000			−0.636364
$122$	−2.00000			−0.181071
$123$	−4.00000	+	6.92820i	−0.360668	+	0.624695i
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$	−24.0000			−2.14663
$126$	6.00000			0.534522
$127$	9.00000	−	15.5885i	0.798621	−	1.38325i	−0.121894	−	0.992543i	$-0.538897\pi$
$127$	9.00000	−	15.5885i	0.798621	−	1.38325i	0.920514	−	0.390709i	$-0.127770\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−2.00000	+	3.46410i	−0.176090	+	0.304997i
$130$	−2.00000	−	3.46410i	−0.175412	−	0.303822i
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$	2.00000			0.174078
$133$		0			0
$134$	3.00000			0.259161
$135$	−10.0000	−	17.3205i	−0.860663	−	1.49071i
$136$	1.50000	+	2.59808i	0.128624	+	0.222783i
$137$	8.50000	−	14.7224i	0.726204	−	1.25782i	−0.232273	−	0.972651i	$-0.574616\pi$
$137$	8.50000	−	14.7224i	0.726204	−	1.25782i	0.958477	−	0.285171i	$-0.0920506\pi$
$138$	−0.500000	−	0.866025i	−0.0425628	−	0.0737210i
$139$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$139$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$140$	−12.0000			−1.01419
$141$	8.00000			0.673722
$142$	−1.00000	+	1.73205i	−0.0839181	+	0.145350i
$143$	−1.00000	+	1.73205i	−0.0836242	+	0.144841i
$144$	−2.00000			−0.166667
$145$	−20.0000			−1.66091
$146$	4.50000	−	7.79423i	0.372423	−	0.645055i
$147$	−1.00000	−	1.73205i	−0.0824786	−	0.142857i
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$	5.50000	+	9.52628i	0.449073	+	0.777817i
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$	3.00000	+	5.19615i	0.241747	+	0.418718i
$155$	16.0000	+	27.7128i	1.28515	+	2.22595i
$156$	−0.500000	+	0.866025i	−0.0400320	+	0.0693375i
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	0.903167	−	0.429289i	$-0.141236\pi$
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	−0.823359	+	0.567521i	$0.807902\pi$
$158$	5.00000	−	8.66025i	0.397779	−	0.688973i
$159$	1.00000			0.0793052
$160$	4.00000			0.316228
$161$	1.50000	−	2.59808i	0.118217	−	0.204757i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−16.0000			−1.25322			−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000			−1.25322			−0.626608	+	0.779334i	$0.715557\pi$
$164$	8.00000			0.624695
$165$	4.00000	−	6.92820i	0.311400	−	0.539360i
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$	1.50000	+	2.59808i	0.115728	+	0.200446i
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	12.0000			0.920358
$171$		0			0
$172$	4.00000			0.304997
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$	2.50000	+	4.33013i	0.189525	+	0.328266i
$175$	−16.5000	+	28.5788i	−1.24728	+	2.16036i
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$	7.50000	−	12.9904i	0.563735	−	0.976417i
$178$		0			0
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	−4.00000	+	6.92820i	−0.298142	+	0.516398i
$181$	11.0000	−	19.0526i	0.817624	−	1.41617i	−0.0898051	−	0.995959i	$-0.528624\pi$
$181$	11.0000	−	19.0526i	0.817624	−	1.41617i	0.907429	−	0.420206i	$-0.138042\pi$
$182$	−3.00000			−0.222375
$183$	2.00000			0.147844
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	4.00000	+	6.92820i	0.294086	+	0.509372i
$186$	4.00000	−	6.92820i	0.293294	−	0.508001i
$187$	−3.00000	−	5.19615i	−0.219382	−	0.379980i
$188$	−4.00000	−	6.92820i	−0.291730	−	0.505291i
$189$	−15.0000			−1.09109
$190$		0			0
$191$	7.00000			0.506502			0.253251	−	0.967401i	$-0.418500\pi$
$191$	7.00000			0.506502			0.253251	+	0.967401i	$0.418500\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−3.00000	−	5.19615i	−0.215945	−	0.374027i	0.737620	−	0.675216i	$-0.235950\pi$
$193$	−3.00000	−	5.19615i	−0.215945	−	0.374027i	−0.953564	+	0.301189i	$0.902616\pi$
$194$	1.00000	−	1.73205i	0.0717958	−	0.124354i
$195$	2.00000	+	3.46410i	0.143223	+	0.248069i
$196$	−1.00000	+	1.73205i	−0.0714286	+	0.123718i
$197$	8.00000			0.569976			0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000			0.569976			0.284988	+	0.958531i	$0.408010\pi$
$198$	4.00000			0.284268
$199$	12.5000	−	21.6506i	0.886102	−	1.53477i	0.0416556	−	0.999132i	$-0.486737\pi$
$199$	12.5000	−	21.6506i	0.886102	−	1.53477i	0.844446	−	0.535641i	$-0.179930\pi$
$200$	5.50000	−	9.52628i	0.388909	−	0.673610i
$201$	−3.00000			−0.211604
$202$	−2.00000			−0.140720
$203$	−7.50000	+	12.9904i	−0.526397	+	0.911746i
$204$	−1.50000	−	2.59808i	−0.105021	−	0.181902i
$205$	16.0000	−	27.7128i	1.11749	−	1.93555i
$206$	3.00000	+	5.19615i	0.209020	+	0.362033i
$207$	−1.00000	−	1.73205i	−0.0695048	−	0.120386i
$208$	1.00000			0.0693375
$209$		0			0
$210$	12.0000			0.828079
$211$	13.5000	+	23.3827i	0.929378	+	1.60973i	0.784364	+	0.620301i	$0.212990\pi$
$211$	13.5000	+	23.3827i	0.929378	+	1.60973i	0.145014	+	0.989430i	$0.453677\pi$
$212$	−0.500000	−	0.866025i	−0.0343401	−	0.0594789i
$213$	1.00000	−	1.73205i	0.0685189	−	0.118678i
$214$	3.50000	+	6.06218i	0.239255	+	0.414402i
$215$	8.00000	−	13.8564i	0.545595	−	0.944999i
$216$	5.00000			0.340207
$217$	24.0000			1.62923
$218$	7.50000	−	12.9904i	0.507964	−	0.879820i
$219$	−4.50000	+	7.79423i	−0.304082	+	0.526685i
$220$	−8.00000			−0.539360
$221$	3.00000			0.201802
$222$	1.00000	−	1.73205i	0.0671156	−	0.116248i
$223$	7.00000	+	12.1244i	0.468755	+	0.811907i	0.999362	−	0.0357107i	$-0.0113695\pi$
$223$	7.00000	+	12.1244i	0.468755	+	0.811907i	−0.530607	+	0.847618i	$0.678036\pi$
$224$	1.50000	−	2.59808i	0.100223	−	0.173591i
$225$	11.0000	+	19.0526i	0.733333	+	1.27017i
$226$	−7.00000	−	12.1244i	−0.465633	−	0.806500i
$227$	17.0000			1.12833			0.564165	−	0.825662i	$-0.309198\pi$
$227$	17.0000			1.12833			0.564165	+	0.825662i	$0.309198\pi$
$228$		0			0
$229$	−10.0000			−0.660819			−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000			−0.660819			−0.330409	+	0.943838i	$0.607187\pi$
$230$	2.00000	+	3.46410i	0.131876	+	0.228416i
$231$	−3.00000	−	5.19615i	−0.197386	−	0.341882i
$232$	2.50000	−	4.33013i	0.164133	−	0.284287i
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$	−1.00000	+	1.73205i	−0.0653720	+	0.113228i
$235$	−32.0000			−2.08745
$236$	−15.0000			−0.976417
$237$	−5.00000	+	8.66025i	−0.324785	+	0.562544i
$238$	4.50000	−	7.79423i	0.291692	−	0.505225i
$239$	15.0000			0.970269			0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000			0.970269			0.485135	+	0.874439i	$0.338771\pi$
$240$	−4.00000			−0.258199
$241$	−4.00000	+	6.92820i	−0.257663	+	0.446285i	−0.965615	−	0.259975i	$-0.916286\pi$
$241$	−4.00000	+	6.92820i	−0.257663	+	0.446285i	0.707953	+	0.706260i	$0.249619\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$	−1.00000	−	1.73205i	−0.0640184	−	0.110883i
$245$	4.00000	+	6.92820i	0.255551	+	0.442627i
$246$	−8.00000			−0.510061
$247$		0			0
$248$	−8.00000			−0.508001
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$	−12.0000	−	20.7846i	−0.758947	−	1.31453i
$251$	−1.00000	+	1.73205i	−0.0631194	+	0.109326i	−0.895858	−	0.444340i	$-0.853438\pi$
$251$	−1.00000	+	1.73205i	−0.0631194	+	0.109326i	0.832739	+	0.553666i	$0.186772\pi$
$252$	3.00000	+	5.19615i	0.188982	+	0.327327i
$253$	1.00000	−	1.73205i	0.0628695	−	0.108893i
$254$	18.0000			1.12942
$255$	−12.0000			−0.751469
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.00000	−	6.92820i	0.249513	−	0.432169i	−0.713878	−	0.700270i	$-0.753063\pi$
$257$	4.00000	−	6.92820i	0.249513	−	0.432169i	0.963391	+	0.268101i	$0.0863961\pi$
$258$	−4.00000			−0.249029
$259$	6.00000			0.372822
$260$	2.00000	−	3.46410i	0.124035	−	0.214834i
$261$	5.00000	+	8.66025i	0.309492	+	0.536056i
$262$	6.00000	−	10.3923i	0.370681	−	0.642039i
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$	1.00000	+	1.73205i	0.0615457	+	0.106600i
$265$	−4.00000			−0.245718
$266$		0			0
$267$		0			0
$268$	1.50000	+	2.59808i	0.0916271	+	0.158703i
$269$	15.0000	+	25.9808i	0.914566	+	1.58408i	0.807535	+	0.589819i	$0.200801\pi$
$269$	15.0000	+	25.9808i	0.914566	+	1.58408i	0.107031	+	0.994256i	$0.465866\pi$
$270$	10.0000	−	17.3205i	0.608581	−	1.05409i
$271$	−3.50000	−	6.06218i	−0.212610	−	0.368251i	0.739921	−	0.672694i	$-0.234863\pi$
$271$	−3.50000	−	6.06218i	−0.212610	−	0.368251i	−0.952531	+	0.304443i	$0.901530\pi$
$272$	−1.50000	+	2.59808i	−0.0909509	+	0.157532i
$273$	3.00000			0.181568
$274$	17.0000			1.02701
$275$	−11.0000	+	19.0526i	−0.663325	+	1.14891i
$276$	0.500000	−	0.866025i	0.0300965	−	0.0521286i
$277$	28.0000			1.68236			0.841178	−	0.540758i	$-0.181862\pi$
$277$	28.0000			1.68236			0.841178	+	0.540758i	$0.181862\pi$
$278$		0			0
$279$	8.00000	−	13.8564i	0.478947	−	0.829561i
$280$	−6.00000	−	10.3923i	−0.358569	−	0.621059i
$281$	−4.00000	+	6.92820i	−0.238620	+	0.413302i	−0.960319	−	0.278906i	$-0.910028\pi$
$281$	−4.00000	+	6.92820i	−0.238620	+	0.413302i	0.721699	+	0.692207i	$0.243362\pi$
$282$	4.00000	+	6.92820i	0.238197	+	0.412568i
$283$	3.00000	+	5.19615i	0.178331	+	0.308879i	0.941309	−	0.337546i	$-0.109597\pi$
$283$	3.00000	+	5.19615i	0.178331	+	0.308879i	−0.762978	+	0.646425i	$0.776263\pi$
$284$	−2.00000			−0.118678
$285$		0			0
$286$	−2.00000			−0.118262
$287$	−12.0000	−	20.7846i	−0.708338	−	1.22688i
$288$	−1.00000	−	1.73205i	−0.0589256	−	0.102062i
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	−10.0000	−	17.3205i	−0.587220	−	1.01710i
$291$	−1.00000	+	1.73205i	−0.0586210	+	0.101535i
$292$	9.00000			0.526685
$293$	−9.00000			−0.525786			−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000			−0.525786			−0.262893	+	0.964825i	$0.584677\pi$
$294$	1.00000	−	1.73205i	0.0583212	−	0.101015i
$295$	−30.0000	+	51.9615i	−1.74667	+	3.02532i
$296$	−2.00000			−0.116248
$297$	−10.0000			−0.580259
$298$		0			0
$299$	0.500000	+	0.866025i	0.0289157	+	0.0500835i
$300$	−5.50000	+	9.52628i	−0.317543	+	0.550000i
$301$	−6.00000	−	10.3923i	−0.345834	−	0.599002i
$302$	−1.00000	−	1.73205i	−0.0575435	−	0.0996683i
$303$	2.00000			0.114897
$304$		0			0
$305$	−8.00000			−0.458079
$306$	−3.00000	−	5.19615i	−0.171499	−	0.297044i
$307$	−6.00000	−	10.3923i	−0.342438	−	0.593120i	0.642447	−	0.766330i	$-0.277919\pi$
$307$	−6.00000	−	10.3923i	−0.342438	−	0.593120i	−0.984885	+	0.173210i	$0.944586\pi$
$308$	−3.00000	+	5.19615i	−0.170941	+	0.296078i
$309$	−3.00000	−	5.19615i	−0.170664	−	0.295599i
$310$	−16.0000	+	27.7128i	−0.908739	+	1.57398i
$311$	7.00000			0.396934			0.198467	−	0.980108i	$-0.436404\pi$
$311$	7.00000			0.396934			0.198467	+	0.980108i	$0.436404\pi$
$312$	−1.00000			−0.0566139
$313$	−14.5000	+	25.1147i	−0.819588	+	1.41957i	0.0863973	+	0.996261i	$0.472465\pi$
$313$	−14.5000	+	25.1147i	−0.819588	+	1.41957i	−0.905986	+	0.423308i	$0.860869\pi$
$314$	−1.00000	+	1.73205i	−0.0564333	+	0.0977453i
$315$	24.0000			1.35225
$316$	10.0000			0.562544
$317$	−13.5000	+	23.3827i	−0.758236	+	1.31330i	0.185514	+	0.982642i	$0.440605\pi$
$317$	−13.5000	+	23.3827i	−0.758236	+	1.31330i	−0.943750	+	0.330661i	$0.892728\pi$
$318$	0.500000	+	0.866025i	0.0280386	+	0.0485643i
$319$	−5.00000	+	8.66025i	−0.279946	+	0.484881i
$320$	2.00000	+	3.46410i	0.111803	+	0.193649i
$321$	−3.50000	−	6.06218i	−0.195351	−	0.338358i
$322$	3.00000			0.167183
$323$		0			0
$324$	1.00000			0.0555556
$325$	−5.50000	−	9.52628i	−0.305085	−	0.528423i
$326$	−8.00000	−	13.8564i	−0.443079	−	0.767435i
$327$	−7.50000	+	12.9904i	−0.414751	+	0.718370i
$328$	4.00000	+	6.92820i	0.220863	+	0.382546i
$329$	−12.0000	+	20.7846i	−0.661581	+	1.14589i
$330$	8.00000			0.440386
$331$	−17.0000			−0.934405			−0.467202	−	0.884150i	$-0.654738\pi$
$331$	−17.0000			−0.934405			−0.467202	+	0.884150i	$0.654738\pi$
$332$	3.00000	−	5.19615i	0.164646	−	0.285176i
$333$	2.00000	−	3.46410i	0.109599	−	0.189832i
$334$	−12.0000			−0.656611
$335$	12.0000			0.655630
$336$	−1.50000	+	2.59808i	−0.0818317	+	0.141737i
$337$	−16.0000	−	27.7128i	−0.871576	−	1.50961i	−0.860366	−	0.509676i	$-0.829765\pi$
$337$	−16.0000	−	27.7128i	−0.871576	−	1.50961i	−0.0112091	−	0.999937i	$-0.503568\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$	7.00000	+	12.1244i	0.380188	+	0.658505i
$340$	6.00000	+	10.3923i	0.325396	+	0.563602i
$341$	16.0000			0.866449
$342$		0			0
$343$	−15.0000			−0.809924
$344$	2.00000	+	3.46410i	0.107833	+	0.186772i
$345$	−2.00000	−	3.46410i	−0.107676	−	0.186501i
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	1.00000	+	1.73205i	0.0536828	+	0.0929814i	0.891618	−	0.452788i	$-0.149571\pi$
$347$	1.00000	+	1.73205i	0.0536828	+	0.0929814i	−0.837935	+	0.545770i	$0.816237\pi$
$348$	−2.50000	+	4.33013i	−0.134014	+	0.232119i
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$	−33.0000			−1.76392
$351$	2.50000	−	4.33013i	0.133440	−	0.231125i
$352$	1.00000	−	1.73205i	0.0533002	−	0.0923186i
$353$	9.00000			0.479022			0.239511	−	0.970894i	$-0.423013\pi$
$353$	9.00000			0.479022			0.239511	+	0.970894i	$0.423013\pi$
$354$	15.0000			0.797241
$355$	−4.00000	+	6.92820i	−0.212298	+	0.367711i
$356$		0			0
$357$	−4.50000	+	7.79423i	−0.238165	+	0.412514i
$358$		0			0
$359$	7.50000	+	12.9904i	0.395835	+	0.685606i	0.993207	−	0.116358i	$-0.0371219\pi$
$359$	7.50000	+	12.9904i	0.395835	+	0.685606i	−0.597372	+	0.801964i	$0.703789\pi$
$360$	−8.00000			−0.421637
$361$		0			0
$362$	22.0000			1.15629
$363$	3.50000	+	6.06218i	0.183702	+	0.318182i
$364$	−1.50000	−	2.59808i	−0.0786214	−	0.136176i
$365$	18.0000	−	31.1769i	0.942163	−	1.63187i
$366$	1.00000	+	1.73205i	0.0522708	+	0.0905357i
$367$	−14.0000	+	24.2487i	−0.730794	+	1.26577i	0.225750	+	0.974185i	$0.427517\pi$
$367$	−14.0000	+	24.2487i	−0.730794	+	1.26577i	−0.956544	+	0.291587i	$0.905817\pi$
$368$	−1.00000			−0.0521286
$369$	−16.0000			−0.832927
$370$	−4.00000	+	6.92820i	−0.207950	+	0.360180i
$371$	−1.50000	+	2.59808i	−0.0778761	+	0.134885i
$372$	8.00000			0.414781
$373$	−29.0000			−1.50156			−0.750782	−	0.660551i	$-0.770323\pi$
$373$	−29.0000			−1.50156			−0.750782	+	0.660551i	$0.770323\pi$
$374$	3.00000	−	5.19615i	0.155126	−	0.268687i
$375$	12.0000	+	20.7846i	0.619677	+	1.07331i
$376$	4.00000	−	6.92820i	0.206284	−	0.357295i
$377$	−2.50000	−	4.33013i	−0.128757	−	0.223013i
$378$	−7.50000	−	12.9904i	−0.385758	−	0.668153i
$379$	−15.0000			−0.770498			−0.385249	−	0.922813i	$-0.625884\pi$
$379$	−15.0000			−0.770498			−0.385249	+	0.922813i	$0.625884\pi$
$380$		0			0
$381$	−18.0000			−0.922168
$382$	3.50000	+	6.06218i	0.179076	+	0.310168i
$383$	−13.0000	−	22.5167i	−0.664269	−	1.15055i	−0.979483	−	0.201527i	$-0.935410\pi$
$383$	−13.0000	−	22.5167i	−0.664269	−	1.15055i	0.315214	−	0.949021i	$-0.397924\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	12.0000	+	20.7846i	0.611577	+	1.05928i
$386$	3.00000	−	5.19615i	0.152696	−	0.264477i
$387$	−8.00000			−0.406663
$388$	2.00000			0.101535
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	−0.182047	−	0.983290i	$-0.558272\pi$
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	0.942578	−	0.333987i	$-0.108394\pi$
$390$	−2.00000	+	3.46410i	−0.101274	+	0.175412i
$391$	−3.00000			−0.151717
$392$	−2.00000			−0.101015
$393$	−6.00000	+	10.3923i	−0.302660	+	0.524222i
$394$	4.00000	+	6.92820i	0.201517	+	0.349038i
$395$	20.0000	−	34.6410i	1.00631	−	1.74298i
$396$	2.00000	+	3.46410i	0.100504	+	0.174078i
$397$	−4.00000	−	6.92820i	−0.200754	−	0.347717i	0.748017	−	0.663679i	$-0.231006\pi$
$397$	−4.00000	−	6.92820i	−0.200754	−	0.347717i	−0.948772	+	0.315963i	$0.897673\pi$
$398$	25.0000			1.25314
$399$		0			0
$400$	11.0000			0.550000
$401$	−4.00000	−	6.92820i	−0.199750	−	0.345978i	0.748697	−	0.662912i	$-0.230680\pi$
$401$	−4.00000	−	6.92820i	−0.199750	−	0.345978i	−0.948447	+	0.316934i	$0.897346\pi$
$402$	−1.50000	−	2.59808i	−0.0748132	−	0.129580i
$403$	−4.00000	+	6.92820i	−0.199254	+	0.345118i
$404$	−1.00000	−	1.73205i	−0.0497519	−	0.0861727i
$405$	2.00000	−	3.46410i	0.0993808	−	0.172133i
$406$	−15.0000			−0.744438
$407$	4.00000			0.198273
$408$	1.50000	−	2.59808i	0.0742611	−	0.128624i
$409$	−10.0000	+	17.3205i	−0.494468	+	0.856444i	−0.999980	−	0.00637586i	$-0.997970\pi$
$409$	−10.0000	+	17.3205i	−0.494468	+	0.856444i	0.505511	+	0.862820i	$0.331304\pi$
$410$	32.0000			1.58037
$411$	−17.0000			−0.838548
$412$	−3.00000	+	5.19615i	−0.147799	+	0.255996i
$413$	22.5000	+	38.9711i	1.10715	+	1.91764i
$414$	1.00000	−	1.73205i	0.0491473	−	0.0851257i
$415$	−12.0000	−	20.7846i	−0.589057	−	1.02028i
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$		0			0
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$	6.00000	+	10.3923i	0.292770	+	0.507093i
$421$	−6.50000	−	11.2583i	−0.316791	−	0.548697i	0.663026	−	0.748596i	$-0.269272\pi$
$421$	−6.50000	−	11.2583i	−0.316791	−	0.548697i	−0.979817	+	0.199899i	$0.935939\pi$
$422$	−13.5000	+	23.3827i	−0.657170	+	1.13825i
$423$	8.00000	+	13.8564i	0.388973	+	0.673722i
$424$	0.500000	−	0.866025i	0.0242821	−	0.0420579i
$425$	33.0000			1.60074
$426$	2.00000			0.0969003
$427$	−3.00000	+	5.19615i	−0.145180	+	0.251459i
$428$	−3.50000	+	6.06218i	−0.169179	+	0.293026i
$429$	2.00000			0.0965609
$430$	16.0000			0.771589
$431$	−9.00000	+	15.5885i	−0.433515	+	0.750870i	−0.997173	−	0.0751385i	$-0.976060\pi$
$431$	−9.00000	+	15.5885i	−0.433515	+	0.750870i	0.563658	+	0.826008i	$0.309393\pi$
$432$	2.50000	+	4.33013i	0.120281	+	0.208333i
$433$	7.00000	−	12.1244i	0.336399	−	0.582659i	−0.647354	−	0.762190i	$-0.724124\pi$
$433$	7.00000	−	12.1244i	0.336399	−	0.582659i	0.983752	+	0.179530i	$0.0574578\pi$
$434$	12.0000	+	20.7846i	0.576018	+	0.997693i
$435$	10.0000	+	17.3205i	0.479463	+	0.830455i
$436$	15.0000			0.718370
$437$		0			0
$438$	−9.00000			−0.430037
$439$	10.0000	+	17.3205i	0.477274	+	0.826663i	0.999661	−	0.0260459i	$-0.00829161\pi$
$439$	10.0000	+	17.3205i	0.477274	+	0.826663i	−0.522387	+	0.852709i	$0.674958\pi$
$440$	−4.00000	−	6.92820i	−0.190693	−	0.330289i
$441$	2.00000	−	3.46410i	0.0952381	−	0.164957i
$442$	1.50000	+	2.59808i	0.0713477	+	0.123578i
$443$	13.0000	−	22.5167i	0.617649	−	1.06980i	−0.372265	−	0.928126i	$-0.621419\pi$
$443$	13.0000	−	22.5167i	0.617649	−	1.06980i	0.989914	−	0.141672i	$-0.0452479\pi$
$444$	2.00000			0.0949158
$445$		0			0
$446$	−7.00000	+	12.1244i	−0.331460	+	0.574105i
$447$		0			0
$448$	3.00000			0.141737
$449$	−10.0000			−0.471929			−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000			−0.471929			−0.235965	+	0.971762i	$0.575825\pi$
$450$	−11.0000	+	19.0526i	−0.518545	+	0.898146i
$451$	−8.00000	−	13.8564i	−0.376705	−	0.652473i
$452$	7.00000	−	12.1244i	0.329252	−	0.570282i
$453$	1.00000	+	1.73205i	0.0469841	+	0.0813788i
$454$	8.50000	+	14.7224i	0.398925	+	0.690958i
$455$	−12.0000			−0.562569
$456$		0			0
$457$	−7.00000			−0.327446			−0.163723	−	0.986506i	$-0.552350\pi$
$457$	−7.00000			−0.327446			−0.163723	+	0.986506i	$0.552350\pi$
$458$	−5.00000	−	8.66025i	−0.233635	−	0.404667i
$459$	7.50000	+	12.9904i	0.350070	+	0.606339i
$460$	−2.00000	+	3.46410i	−0.0932505	+	0.161515i
$461$	14.0000	+	24.2487i	0.652045	+	1.12938i	0.982626	+	0.185597i	$0.0594220\pi$
$461$	14.0000	+	24.2487i	0.652045	+	1.12938i	−0.330581	+	0.943778i	$0.607245\pi$
$462$	3.00000	−	5.19615i	0.139573	−	0.241747i
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$	5.00000			0.232119
$465$	16.0000	−	27.7128i	0.741982	−	1.28515i
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	−2.00000			−0.0925490			−0.0462745	−	0.998929i	$-0.514735\pi$
$467$	−2.00000			−0.0925490			−0.0462745	+	0.998929i	$0.514735\pi$
$468$	−2.00000			−0.0924500
$469$	4.50000	−	7.79423i	0.207791	−	0.359904i
$470$	−16.0000	−	27.7128i	−0.738025	−	1.27830i
$471$	1.00000	−	1.73205i	0.0460776	−	0.0798087i
$472$	−7.50000	−	12.9904i	−0.345215	−	0.597931i
$473$	−4.00000	−	6.92820i	−0.183920	−	0.318559i
$474$	−10.0000			−0.459315
$475$		0			0
$476$	9.00000			0.412514
$477$	1.00000	+	1.73205i	0.0457869	+	0.0793052i
$478$	7.50000	+	12.9904i	0.343042	+	0.594166i
$479$	10.0000	−	17.3205i	0.456912	−	0.791394i	−0.541884	−	0.840453i	$-0.682289\pi$
$479$	10.0000	−	17.3205i	0.456912	−	0.791394i	0.998796	+	0.0490589i	$0.0156222\pi$
$480$	−2.00000	−	3.46410i	−0.0912871	−	0.158114i
$481$	−1.00000	+	1.73205i	−0.0455961	+	0.0789747i
$482$	−8.00000			−0.364390
$483$	−3.00000			−0.136505
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	4.00000	−	6.92820i	0.181631	−	0.314594i
$486$	−16.0000			−0.725775
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$	1.00000	−	1.73205i	0.0452679	−	0.0784063i
$489$	8.00000	+	13.8564i	0.361773	+	0.626608i
$490$	−4.00000	+	6.92820i	−0.180702	+	0.312984i
$491$	14.0000	+	24.2487i	0.631811	+	1.09433i	0.987181	+	0.159603i	$0.0510215\pi$
$491$	14.0000	+	24.2487i	0.631811	+	1.09433i	−0.355370	+	0.934726i	$0.615645\pi$
$492$	−4.00000	−	6.92820i	−0.180334	−	0.312348i
$493$	15.0000			0.675566
$494$		0			0
$495$	16.0000			0.719147
$496$	−4.00000	−	6.92820i	−0.179605	−	0.311086i
$497$	3.00000	+	5.19615i	0.134568	+	0.233079i
$498$	−3.00000	+	5.19615i	−0.134433	+	0.232845i
$499$	−20.0000	−	34.6410i	−0.895323	−	1.55074i	−0.833404	−	0.552664i	$-0.813611\pi$
$499$	−20.0000	−	34.6410i	−0.895323	−	1.55074i	−0.0619186	−	0.998081i	$-0.519722\pi$
$500$	12.0000	−	20.7846i	0.536656	−	0.929516i
$501$	12.0000			0.536120
$502$	−2.00000			−0.0892644
$503$	−19.5000	+	33.7750i	−0.869462	+	1.50595i	−0.00691465	+	0.999976i	$0.502201\pi$
$503$	−19.5000	+	33.7750i	−0.869462	+	1.50595i	−0.862547	+	0.505976i	$0.831132\pi$
$504$	−3.00000	+	5.19615i	−0.133631	+	0.231455i
$505$	−8.00000			−0.355995
$506$	2.00000			0.0889108
$507$	6.00000	−	10.3923i	0.266469	−	0.461538i
$508$	9.00000	+	15.5885i	0.399310	+	0.691626i
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	0.314459	+	0.949271i	$0.398177\pi$
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	−0.979322	+	0.202306i	$0.935156\pi$
$510$	−6.00000	−	10.3923i	−0.265684	−	0.460179i
$511$	−13.5000	−	23.3827i	−0.597205	−	1.03439i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	8.00000			0.352865
$515$	12.0000	+	20.7846i	0.528783	+	0.915879i
$516$	−2.00000	−	3.46410i	−0.0880451	−	0.152499i
$517$	−8.00000	+	13.8564i	−0.351840	+	0.609404i
$518$	3.00000	+	5.19615i	0.131812	+	0.228306i
$519$	−3.00000	+	5.19615i	−0.131685	+	0.228086i
$520$	4.00000			0.175412
$521$	28.0000			1.22670			0.613351	−	0.789810i	$-0.289821\pi$
$521$	28.0000			1.22670			0.613351	+	0.789810i	$0.289821\pi$
$522$	−5.00000	+	8.66025i	−0.218844	+	0.379049i
$523$	14.5000	−	25.1147i	0.634041	−	1.09819i	−0.352677	−	0.935745i	$-0.614728\pi$
$523$	14.5000	−	25.1147i	0.634041	−	1.09819i	0.986718	−	0.162446i	$-0.0519382\pi$
$524$	12.0000			0.524222
$525$	33.0000			1.44024
$526$	12.0000	−	20.7846i	0.523225	−	0.906252i
$527$	−12.0000	−	20.7846i	−0.522728	−	0.905392i
$528$	−1.00000	+	1.73205i	−0.0435194	+	0.0753778i
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	−2.00000	−	3.46410i	−0.0868744	−	0.150471i
$531$	30.0000			1.30189
$532$		0			0
$533$	8.00000			0.346518
$534$		0			0
$535$	14.0000	+	24.2487i	0.605273	+	1.04836i
$536$	−1.50000	+	2.59808i	−0.0647901	+	0.112220i
$537$		0			0
$538$	−15.0000	+	25.9808i	−0.646696	+	1.12011i
$539$	4.00000			0.172292
$540$	20.0000			0.860663
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	−0.886721	−	0.462304i	$-0.847023\pi$
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	0.843728	+	0.536771i	$0.180356\pi$
$542$	3.50000	−	6.06218i	0.150338	−	0.260393i
$543$	−22.0000			−0.944110
$544$	−3.00000			−0.128624
$545$	30.0000	−	51.9615i	1.28506	−	2.22579i
$546$	1.50000	+	2.59808i	0.0641941	+	0.111187i
$547$	14.0000	−	24.2487i	0.598597	−	1.03680i	−0.394432	−	0.918925i	$-0.629059\pi$
$547$	14.0000	−	24.2487i	0.598597	−	1.03680i	0.993028	−	0.117875i	$-0.0376081\pi$
$548$	8.50000	+	14.7224i	0.363102	+	0.628911i
$549$	2.00000	+	3.46410i	0.0853579	+	0.147844i
$550$	−22.0000			−0.938083
$551$		0			0
$552$	1.00000			0.0425628
$553$	−15.0000	−	25.9808i	−0.637865	−	1.10481i
$554$	14.0000	+	24.2487i	0.594803	+	1.03023i
$555$	4.00000	−	6.92820i	0.169791	−	0.294086i
$556$		0			0
$557$	−14.0000	+	24.2487i	−0.593199	+	1.02745i	0.400599	+	0.916253i	$0.368802\pi$
$557$	−14.0000	+	24.2487i	−0.593199	+	1.02745i	−0.993798	+	0.111198i	$0.964531\pi$
$558$	16.0000			0.677334
$559$	4.00000			0.169182
$560$	6.00000	−	10.3923i	0.253546	−	0.439155i
$561$	−3.00000	+	5.19615i	−0.126660	+	0.219382i
$562$	−8.00000			−0.337460
$563$	36.0000			1.51722			0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000			1.51722			0.758610	+	0.651546i	$0.225879\pi$
$564$	−4.00000	+	6.92820i	−0.168430	+	0.291730i
$565$	−28.0000	−	48.4974i	−1.17797	−	2.04030i
$566$	−3.00000	+	5.19615i	−0.126099	+	0.218411i
$567$	−1.50000	−	2.59808i	−0.0629941	−	0.109109i
$568$	−1.00000	−	1.73205i	−0.0419591	−	0.0726752i
$569$	−40.0000			−1.67689			−0.838444	−	0.544988i	$-0.816534\pi$
$569$	−40.0000			−1.67689			−0.838444	+	0.544988i	$0.816534\pi$
$570$		0			0
$571$	−28.0000			−1.17176			−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000			−1.17176			−0.585882	+	0.810397i	$0.699252\pi$
$572$	−1.00000	−	1.73205i	−0.0418121	−	0.0724207i
$573$	−3.50000	−	6.06218i	−0.146215	−	0.253251i
$574$	12.0000	−	20.7846i	0.500870	−	0.867533i
$575$	5.50000	+	9.52628i	0.229366	+	0.397273i
$576$	1.00000	−	1.73205i	0.0416667	−	0.0721688i
$577$	−37.0000			−1.54033			−0.770165	−	0.637845i	$-0.779826\pi$
$577$	−37.0000			−1.54033			−0.770165	+	0.637845i	$0.779826\pi$
$578$	8.00000			0.332756
$579$	−3.00000	+	5.19615i	−0.124676	+	0.215945i
$580$	10.0000	−	17.3205i	0.415227	−	0.719195i
$581$	−18.0000			−0.746766
$582$	−2.00000			−0.0829027
$583$	−1.00000	+	1.73205i	−0.0414158	+	0.0717342i
$584$	4.50000	+	7.79423i	0.186211	+	0.322527i
$585$	−4.00000	+	6.92820i	−0.165380	+	0.286446i
$586$	−4.50000	−	7.79423i	−0.185893	−	0.321977i
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	0.962872	−	0.269957i	$-0.0870095\pi$
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	−0.715226	+	0.698893i	$0.753676\pi$
$588$	2.00000			0.0824786
$589$		0			0
$590$	−60.0000			−2.47016
$591$	−4.00000	−	6.92820i	−0.164538	−	0.284988i
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$	−17.0000	+	29.4449i	−0.698106	+	1.20916i	0.271016	+	0.962575i	$0.412640\pi$
$593$	−17.0000	+	29.4449i	−0.698106	+	1.20916i	−0.969122	+	0.246581i	$0.920693\pi$
$594$	−5.00000	−	8.66025i	−0.205152	−	0.355335i
$595$	18.0000	−	31.1769i	0.737928	−	1.27813i
$596$		0			0
$597$	−25.0000			−1.02318
$598$	−0.500000	+	0.866025i	−0.0204465	+	0.0354144i
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$	−11.0000			−0.449073
$601$	8.00000			0.326327			0.163163	−	0.986599i	$-0.447830\pi$
$601$	8.00000			0.326327			0.163163	+	0.986599i	$0.447830\pi$
$602$	6.00000	−	10.3923i	0.244542	−	0.423559i
$603$	−3.00000	−	5.19615i	−0.122169	−	0.211604i
$604$	1.00000	−	1.73205i	0.0406894	−	0.0704761i
$605$	−14.0000	−	24.2487i	−0.569181	−	0.985850i
$606$	1.00000	+	1.73205i	0.0406222	+	0.0703598i
$607$	22.0000			0.892952			0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000			0.892952			0.446476	+	0.894795i	$0.352679\pi$
$608$		0			0
$609$	15.0000			0.607831
$610$	−4.00000	−	6.92820i	−0.161955	−	0.280515i
$611$	−4.00000	−	6.92820i	−0.161823	−	0.280285i
$612$	3.00000	−	5.19615i	0.121268	−	0.210042i
$613$	−17.0000	−	29.4449i	−0.686624	−	1.18927i	−0.972924	−	0.231127i	$-0.925759\pi$
$613$	−17.0000	−	29.4449i	−0.686624	−	1.18927i	0.286300	−	0.958140i	$-0.407575\pi$
$614$	6.00000	−	10.3923i	0.242140	−	0.419399i
$615$	−32.0000			−1.29036
$616$	−6.00000			−0.241747
$617$	−9.00000	+	15.5885i	−0.362326	+	0.627568i	−0.988343	−	0.152242i	$-0.951351\pi$
$617$	−9.00000	+	15.5885i	−0.362326	+	0.627568i	0.626017	+	0.779809i	$0.284684\pi$
$618$	3.00000	−	5.19615i	0.120678	−	0.209020i
$619$	10.0000			0.401934			0.200967	−	0.979598i	$-0.435592\pi$
$619$	10.0000			0.401934			0.200967	+	0.979598i	$0.435592\pi$
$620$	−32.0000			−1.28515
$621$	−2.50000	+	4.33013i	−0.100322	+	0.173762i
$622$	3.50000	+	6.06218i	0.140337	+	0.243071i
$623$		0			0
$624$	−0.500000	−	0.866025i	−0.0200160	−	0.0346688i
$625$	−20.5000	−	35.5070i	−0.820000	−	1.42028i
$626$	−29.0000			−1.15907
$627$		0			0
$628$	−2.00000			−0.0798087
$629$	−3.00000	−	5.19615i	−0.119618	−	0.207184i
$630$	12.0000	+	20.7846i	0.478091	+	0.828079i
$631$	−16.0000	+	27.7128i	−0.636950	+	1.10323i	0.349148	+	0.937067i	$0.386471\pi$
$631$	−16.0000	+	27.7128i	−0.636950	+	1.10323i	−0.986098	+	0.166162i	$0.946862\pi$
$632$	5.00000	+	8.66025i	0.198889	+	0.344486i
$633$	13.5000	−	23.3827i	0.536577	−	0.929378i
$634$	−27.0000			−1.07231
$635$	72.0000			2.85723
$636$	−0.500000	+	0.866025i	−0.0198263	+	0.0343401i
$637$	−1.00000	+	1.73205i	−0.0396214	+	0.0686264i
$638$	−10.0000			−0.395904
$639$	4.00000			0.158238
$640$	−2.00000	+	3.46410i	−0.0790569	+	0.136931i
$641$	21.0000	+	36.3731i	0.829450	+	1.43665i	0.898470	+	0.439034i	$0.144679\pi$
$641$	21.0000	+	36.3731i	0.829450	+	1.43665i	−0.0690201	+	0.997615i	$0.521987\pi$
$642$	3.50000	−	6.06218i	0.138134	−	0.239255i
$643$	13.0000	+	22.5167i	0.512670	+	0.887970i	0.999892	+	0.0146923i	$0.00467688\pi$
$643$	13.0000	+	22.5167i	0.512670	+	0.887970i	−0.487222	+	0.873278i	$0.661990\pi$
$644$	1.50000	+	2.59808i	0.0591083	+	0.102379i
$645$	−16.0000			−0.629999
$646$		0			0
$647$	23.0000			0.904223			0.452112	−	0.891961i	$-0.350671\pi$
$647$	23.0000			0.904223			0.452112	+	0.891961i	$0.350671\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	15.0000	+	25.9808i	0.588802	+	1.01983i
$650$	5.50000	−	9.52628i	0.215728	−	0.373651i
$651$	−12.0000	−	20.7846i	−0.470317	−	0.814613i
$652$	8.00000	−	13.8564i	0.313304	−	0.542659i
$653$	−36.0000			−1.40879			−0.704394	−	0.709809i	$-0.748781\pi$
$653$	−36.0000			−1.40879			−0.704394	+	0.709809i	$0.748781\pi$
$654$	−15.0000			−0.586546
$655$	24.0000	−	41.5692i	0.937758	−	1.62424i
$656$	−4.00000	+	6.92820i	−0.156174	+	0.270501i
$657$	−18.0000			−0.702247
$658$	−24.0000			−0.935617
$659$	2.50000	−	4.33013i	0.0973862	−	0.168678i	−0.813216	−	0.581962i	$-0.802285\pi$
$659$	2.50000	−	4.33013i	0.0973862	−	0.168678i	0.910602	+	0.413284i	$0.135618\pi$
$660$	4.00000	+	6.92820i	0.155700	+	0.269680i
$661$	−11.5000	+	19.9186i	−0.447298	+	0.774743i	−0.998209	−	0.0598209i	$-0.980947\pi$
$661$	−11.5000	+	19.9186i	−0.447298	+	0.774743i	0.550911	+	0.834564i	$0.314280\pi$
$662$	−8.50000	−	14.7224i	−0.330362	−	0.572204i
$663$	−1.50000	−	2.59808i	−0.0582552	−	0.100901i
$664$	6.00000			0.232845
$665$		0			0
$666$	4.00000			0.154997
$667$	2.50000	+	4.33013i	0.0968004	+	0.167663i
$668$	−6.00000	−	10.3923i	−0.232147	−	0.402090i
$669$	7.00000	−	12.1244i	0.270636	−	0.468755i
$670$	6.00000	+	10.3923i	0.231800	+	0.401490i
$671$	−2.00000	+	3.46410i	−0.0772091	+	0.133730i
$672$	−3.00000			−0.115728
$673$	−44.0000			−1.69608			−0.848038	−	0.529936i	$-0.822216\pi$
$673$	−44.0000			−1.69608			−0.848038	+	0.529936i	$0.822216\pi$
$674$	16.0000	−	27.7128i	0.616297	−	1.06746i
$675$	27.5000	−	47.6314i	1.05848	−	1.83333i
$676$	−12.0000			−0.461538
$677$	−13.0000			−0.499631			−0.249815	−	0.968294i	$-0.580370\pi$
$677$	−13.0000			−0.499631			−0.249815	+	0.968294i	$0.580370\pi$
$678$	−7.00000	+	12.1244i	−0.268833	+	0.465633i
$679$	−3.00000	−	5.19615i	−0.115129	−	0.199410i
$680$	−6.00000	+	10.3923i	−0.230089	+	0.398527i
$681$	−8.50000	−	14.7224i	−0.325721	−	0.564165i
$682$	8.00000	+	13.8564i	0.306336	+	0.530589i
$683$	−4.00000			−0.153056			−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000			−0.153056			−0.0765279	+	0.997067i	$0.524383\pi$
$684$		0			0
$685$	68.0000			2.59815
$686$	−7.50000	−	12.9904i	−0.286351	−	0.495975i
$687$	5.00000	+	8.66025i	0.190762	+	0.330409i
$688$	−2.00000	+	3.46410i	−0.0762493	+	0.132068i
$689$	−0.500000	−	0.866025i	−0.0190485	−	0.0329929i
$690$	2.00000	−	3.46410i	0.0761387	−	0.131876i
$691$	42.0000			1.59776			0.798878	−	0.601494i	$-0.205427\pi$
$691$	42.0000			1.59776			0.798878	+	0.601494i	$0.205427\pi$
$692$	6.00000			0.228086
$693$	6.00000	−	10.3923i	0.227921	−	0.394771i
$694$	−1.00000	+	1.73205i	−0.0379595	+	0.0657477i
$695$		0			0
$696$	−5.00000			−0.189525
$697$	−12.0000	+	20.7846i	−0.454532	+	0.787273i
$698$	5.00000	+	8.66025i	0.189253	+	0.327795i
$699$	3.00000	−	5.19615i	0.113470	−	0.196537i
$700$	−16.5000	−	28.5788i	−0.623641	−	1.08018i
$701$	14.0000	+	24.2487i	0.528773	+	0.915861i	0.999437	+	0.0335489i	$0.0106809\pi$
$701$	14.0000	+	24.2487i	0.528773	+	0.915861i	−0.470664	+	0.882312i	$0.655986\pi$
$702$	5.00000			0.188713
$703$		0			0
$704$	2.00000			0.0753778
$705$	16.0000	+	27.7128i	0.602595	+	1.04372i
$706$	4.50000	+	7.79423i	0.169360	+	0.293340i
$707$	−3.00000	+	5.19615i	−0.112827	+	0.195421i
$708$	7.50000	+	12.9904i	0.281867	+	0.488208i
$709$	15.0000	−	25.9808i	0.563337	−	0.975728i	−0.433865	−	0.900978i	$-0.642851\pi$
$709$	15.0000	−	25.9808i	0.563337	−	0.975728i	0.997202	−	0.0747503i	$-0.0238160\pi$
$710$	−8.00000			−0.300235
$711$	−20.0000			−0.750059
$712$		0			0
$713$	4.00000	−	6.92820i	0.149801	−	0.259463i
$714$	−9.00000			−0.336817
$715$	−8.00000			−0.299183
$716$		0			0
$717$	−7.50000	−	12.9904i	−0.280093	−	0.485135i
$718$	−7.50000	+	12.9904i	−0.279898	+	0.484797i
$719$	2.50000	+	4.33013i	0.0932343	+	0.161486i	0.908870	−	0.417079i	$-0.136946\pi$
$719$	2.50000	+	4.33013i	0.0932343	+	0.161486i	−0.815636	+	0.578565i	$0.803613\pi$
$720$	−4.00000	−	6.92820i	−0.149071	−	0.258199i
$721$	18.0000			0.670355
$722$		0			0
$723$	8.00000			0.297523
$724$	11.0000	+	19.0526i	0.408812	+	0.708083i
$725$	−27.5000	−	47.6314i	−1.02132	−	1.76899i
$726$	−3.50000	+	6.06218i	−0.129897	+	0.224989i
$727$	8.50000	+	14.7224i	0.315248	+	0.546025i	0.979490	−	0.201492i	$-0.0645791\pi$
$727$	8.50000	+	14.7224i	0.315248	+	0.546025i	−0.664243	+	0.747517i	$0.731246\pi$
$728$	1.50000	−	2.59808i	0.0555937	−	0.0962911i
$729$	13.0000			0.481481
$730$	36.0000			1.33242
$731$	−6.00000	+	10.3923i	−0.221918	+	0.384373i
$732$	−1.00000	+	1.73205i	−0.0369611	+	0.0640184i
$733$	−36.0000			−1.32969			−0.664845	−	0.746981i	$-0.731502\pi$
$733$	−36.0000			−1.32969			−0.664845	+	0.746981i	$0.731502\pi$
$734$	−28.0000			−1.03350
$735$	4.00000	−	6.92820i	0.147542	−	0.255551i
$736$	−0.500000	−	0.866025i	−0.0184302	−	0.0319221i
$737$	3.00000	−	5.19615i	0.110506	−	0.191403i
$738$	−8.00000	−	13.8564i	−0.294484	−	0.510061i
$739$	20.0000	+	34.6410i	0.735712	+	1.27429i	0.954410	+	0.298498i	$0.0964856\pi$
$739$	20.0000	+	34.6410i	0.735712	+	1.27429i	−0.218698	+	0.975793i	$0.570181\pi$
$740$	−8.00000			−0.294086
$741$		0			0
$742$	−3.00000			−0.110133
$743$	−8.00000	−	13.8564i	−0.293492	−	0.508342i	0.681141	−	0.732152i	$-0.261484\pi$
$743$	−8.00000	−	13.8564i	−0.293492	−	0.508342i	−0.974633	+	0.223810i	$0.928151\pi$
$744$	4.00000	+	6.92820i	0.146647	+	0.254000i
$745$		0			0
$746$	−14.5000	−	25.1147i	−0.530883	−	0.919516i
$747$	−6.00000	+	10.3923i	−0.219529	+	0.380235i
$748$	6.00000			0.219382
$749$	21.0000			0.767323
$750$	−12.0000	+	20.7846i	−0.438178	+	0.758947i
$751$	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	$-0.0317870\pi$
$752$	8.00000			0.291730
$753$	2.00000			0.0728841
$754$	2.50000	−	4.33013i	0.0910446	−	0.157694i
$755$	−4.00000	−	6.92820i	−0.145575	−	0.252143i
$756$	7.50000	−	12.9904i	0.272772	−	0.472456i
$757$	1.00000	+	1.73205i	0.0363456	+	0.0629525i	0.883626	−	0.468193i	$-0.155095\pi$
$757$	1.00000	+	1.73205i	0.0363456	+	0.0629525i	−0.847280	+	0.531146i	$0.821762\pi$
$758$	−7.50000	−	12.9904i	−0.272412	−	0.471832i
$759$	−2.00000			−0.0725954
$760$		0			0
$761$	27.0000			0.978749			0.489375	−	0.872074i	$-0.337225\pi$
$761$	27.0000			0.978749			0.489375	+	0.872074i	$0.337225\pi$
$762$	−9.00000	−	15.5885i	−0.326036	−	0.564710i
$763$	−22.5000	−	38.9711i	−0.814555	−	1.41085i
$764$	−3.50000	+	6.06218i	−0.126626	+	0.219322i
$765$	−12.0000	−	20.7846i	−0.433861	−	0.751469i
$766$	13.0000	−	22.5167i	0.469709	−	0.813560i
$767$	−15.0000			−0.541619
$768$	1.00000			0.0360844
$769$	17.5000	−	30.3109i	0.631066	−	1.09304i	−0.356268	−	0.934384i	$-0.615951\pi$
$769$	17.5000	−	30.3109i	0.631066	−	1.09304i	0.987334	−	0.158655i	$-0.0507157\pi$
$770$	−12.0000	+	20.7846i	−0.432450	+	0.749025i
$771$	−8.00000			−0.288113
$772$	6.00000			0.215945
$773$	4.50000	−	7.79423i	0.161854	−	0.280339i	−0.773680	−	0.633577i	$-0.781586\pi$
$773$	4.50000	−	7.79423i	0.161854	−	0.280339i	0.935534	+	0.353238i	$0.114919\pi$
$774$	−4.00000	−	6.92820i	−0.143777	−	0.249029i
$775$	−44.0000	+	76.2102i	−1.58053	+	2.73755i
$776$	1.00000	+	1.73205i	0.0358979	+	0.0621770i
$777$	−3.00000	−	5.19615i	−0.107624	−	0.186411i
$778$	30.0000			1.07555
$779$		0			0
$780$	−4.00000			−0.143223
$781$	2.00000	+	3.46410i	0.0715656	+	0.123955i
$782$	−1.50000	−	2.59808i	−0.0536399	−	0.0929070i
$783$	12.5000	−	21.6506i	0.446714	−	0.773731i
$784$	−1.00000	−	1.73205i	−0.0357143	−	0.0618590i
$785$	−4.00000	+	6.92820i	−0.142766	+	0.247278i
$786$	−12.0000			−0.428026
$787$	17.0000			0.605985			0.302992	−	0.952993i	$-0.402014\pi$
$787$	17.0000			0.605985			0.302992	+	0.952993i	$0.402014\pi$
$788$	−4.00000	+	6.92820i	−0.142494	+	0.246807i
$789$	−12.0000	+	20.7846i	−0.427211	+	0.739952i
$790$	40.0000			1.42314
$791$	−42.0000			−1.49335
$792$	−2.00000	+	3.46410i	−0.0710669	+	0.123091i
$793$	−1.00000	−	1.73205i	−0.0355110	−	0.0615069i
$794$	4.00000	−	6.92820i	0.141955	−	0.245873i
$795$	2.00000	+	3.46410i	0.0709327	+	0.122859i
$796$	12.5000	+	21.6506i	0.443051	+	0.767386i
$797$	−3.00000			−0.106265			−0.0531327	−	0.998587i	$-0.516921\pi$
$797$	−3.00000			−0.106265			−0.0531327	+	0.998587i	$0.516921\pi$
$798$		0			0
$799$	24.0000			0.849059
$800$	5.50000	+	9.52628i	0.194454	+	0.336805i
$801$		0			0
$802$	4.00000	−	6.92820i	0.141245	−	0.244643i
$803$	−9.00000	−	15.5885i	−0.317603	−	0.550105i
$804$	1.50000	−	2.59808i	0.0529009	−	0.0916271i
$805$	12.0000			0.422944
$806$	−8.00000			−0.281788
$807$	15.0000	−	25.9808i	0.528025	−	0.914566i
$808$	1.00000	−	1.73205i	0.0351799	−	0.0609333i
$809$	−15.0000			−0.527372			−0.263686	−	0.964609i	$-0.584938\pi$
$809$	−15.0000			−0.527372			−0.263686	+	0.964609i	$0.584938\pi$
$810$	4.00000			0.140546
$811$	−1.50000	+	2.59808i	−0.0526721	+	0.0912308i	−0.891159	−	0.453691i	$-0.850107\pi$
$811$	−1.50000	+	2.59808i	−0.0526721	+	0.0912308i	0.838487	+	0.544921i	$0.183440\pi$
$812$	−7.50000	−	12.9904i	−0.263198	−	0.455873i
$813$	−3.50000	+	6.06218i	−0.122750	+	0.212610i
$814$	2.00000	+	3.46410i	0.0701000	+	0.121417i
$815$	−32.0000	−	55.4256i	−1.12091	−	1.94147i
$816$	3.00000			0.105021
$817$		0			0
$818$	−20.0000			−0.699284
$819$	3.00000	+	5.19615i	0.104828	+	0.181568i
$820$	16.0000	+	27.7128i	0.558744	+	0.967773i
$821$	−6.00000	+	10.3923i	−0.209401	+	0.362694i	−0.951526	−	0.307568i	$-0.900485\pi$
$821$	−6.00000	+	10.3923i	−0.209401	+	0.362694i	0.742125	+	0.670262i	$0.233818\pi$
$822$	−8.50000	−	14.7224i	−0.296472	−	0.513504i
$823$	−14.5000	+	25.1147i	−0.505438	+	0.875445i	0.494542	+	0.869154i	$0.335336\pi$
$823$	−14.5000	+	25.1147i	−0.505438	+	0.875445i	−0.999980	+	0.00629095i	$0.997998\pi$
$824$	−6.00000			−0.209020
$825$	22.0000			0.765942
$826$	−22.5000	+	38.9711i	−0.782875	+	1.35598i
$827$	11.5000	−	19.9186i	0.399894	−	0.692637i	−0.593818	−	0.804599i	$-0.702380\pi$
$827$	11.5000	−	19.9186i	0.399894	−	0.692637i	0.993712	+	0.111962i	$0.0357135\pi$
$828$	2.00000			0.0695048
$829$	15.0000			0.520972			0.260486	−	0.965478i	$-0.416117\pi$
$829$	15.0000			0.520972			0.260486	+	0.965478i	$0.416117\pi$
$830$	12.0000	−	20.7846i	0.416526	−	0.721444i
$831$	−14.0000	−	24.2487i	−0.485655	−	0.841178i
$832$	−0.500000	+	0.866025i	−0.0173344	+	0.0300240i
$833$	−3.00000	−	5.19615i	−0.103944	−	0.180036i
$834$		0			0
$835$	−48.0000			−1.66111
$836$		0			0
$837$	−40.0000			−1.38260
$838$		0			0
$839$	10.0000	+	17.3205i	0.345238	+	0.597970i	0.985397	−	0.170272i	$-0.0544647\pi$
$839$	10.0000	+	17.3205i	0.345238	+	0.597970i	−0.640159	+	0.768243i	$0.721131\pi$
$840$	−6.00000	+	10.3923i	−0.207020	+	0.358569i
$841$	2.00000	+	3.46410i	0.0689655	+	0.119452i
$842$	6.50000	−	11.2583i	0.224005	−	0.387988i
$843$	8.00000			0.275535
$844$	−27.0000			−0.929378
$845$	−24.0000	+	41.5692i	−0.825625	+	1.43002i
$846$	−8.00000	+	13.8564i	−0.275046	+	0.476393i
$847$	−21.0000			−0.721569
$848$	1.00000			0.0343401
$849$	3.00000	−	5.19615i	0.102960	−	0.178331i
$850$	16.5000	+	28.5788i	0.565945	+	0.980246i
$851$	1.00000	−	1.73205i	0.0342796	−	0.0593739i
$852$	1.00000	+	1.73205i	0.0342594	+	0.0593391i
$853$	3.00000	+	5.19615i	0.102718	+	0.177913i	0.912804	−	0.408399i	$-0.133913\pi$
$853$	3.00000	+	5.19615i	0.102718	+	0.177913i	−0.810086	+	0.586312i	$0.800579\pi$
$854$	−6.00000			−0.205316
$855$		0			0
$856$	−7.00000			−0.239255
$857$	−6.00000	−	10.3923i	−0.204956	−	0.354994i	0.745163	−	0.666883i	$-0.232372\pi$
$857$	−6.00000	−	10.3923i	−0.204956	−	0.354994i	−0.950119	+	0.311888i	$0.899038\pi$
$858$	1.00000	+	1.73205i	0.0341394	+	0.0591312i
$859$	25.0000	−	43.3013i	0.852989	−	1.47742i	−0.0255092	−	0.999675i	$-0.508121\pi$
$859$	25.0000	−	43.3013i	0.852989	−	1.47742i	0.878498	−	0.477746i	$-0.158546\pi$
$860$	8.00000	+	13.8564i	0.272798	+	0.472500i
$861$	−12.0000	+	20.7846i	−0.408959	+	0.708338i
$862$	−18.0000			−0.613082
$863$	−54.0000			−1.83818			−0.919091	−	0.394046i	$-0.871075\pi$
$863$	−54.0000			−1.83818			−0.919091	+	0.394046i	$0.871075\pi$
$864$	−2.50000	+	4.33013i	−0.0850517	+	0.147314i
$865$	12.0000	−	20.7846i	0.408012	−	0.706698i
$866$	14.0000			0.475739
$867$	−8.00000			−0.271694
$868$	−12.0000	+	20.7846i	−0.407307	+	0.705476i
$869$	−10.0000	−	17.3205i	−0.339227	−	0.587558i
$870$	−10.0000	+	17.3205i	−0.339032	+	0.587220i
$871$	1.50000	+	2.59808i	0.0508256	+	0.0880325i
$872$	7.50000	+	12.9904i	0.253982	+	0.439910i
$873$	−4.00000			−0.135379
$874$		0			0
$875$	−72.0000			−2.43404
$876$	−4.50000	−	7.79423i	−0.152041	−	0.263343i
$877$	6.50000	+	11.2583i	0.219489	+	0.380167i	0.954652	−	0.297724i	$-0.0962275\pi$
$877$	6.50000	+	11.2583i	0.219489	+	0.380167i	−0.735163	+	0.677891i	$0.762894\pi$
$878$	−10.0000	+	17.3205i	−0.337484	+	0.584539i
$879$	4.50000	+	7.79423i	0.151781	+	0.262893i
$880$	4.00000	−	6.92820i	0.134840	−	0.233550i
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$	4.00000			0.134687
$883$	−17.0000	+	29.4449i	−0.572096	+	0.990899i	0.424255	+	0.905543i	$0.360536\pi$
$883$	−17.0000	+	29.4449i	−0.572096	+	0.990899i	−0.996351	+	0.0853558i	$0.972797\pi$
$884$	−1.50000	+	2.59808i	−0.0504505	+	0.0873828i
$885$	60.0000			2.01688
$886$	26.0000			0.873487
$887$	−1.00000	+	1.73205i	−0.0335767	+	0.0581566i	−0.882325	−	0.470640i	$-0.844023\pi$
$887$	−1.00000	+	1.73205i	−0.0335767	+	0.0581566i	0.848749	+	0.528796i	$0.177356\pi$
$888$	1.00000	+	1.73205i	0.0335578	+	0.0581238i
$889$	27.0000	−	46.7654i	0.905551	−	1.56846i
$890$		0			0
$891$	−1.00000	−	1.73205i	−0.0335013	−	0.0580259i
$892$	−14.0000			−0.468755
$893$		0			0
$894$		0			0
$895$		0			0
$896$	1.50000	+	2.59808i	0.0501115	+	0.0867956i
$897$	0.500000	−	0.866025i	0.0166945	−	0.0289157i
$898$	−5.00000	−	8.66025i	−0.166852	−	0.288996i
$899$	−20.0000	+	34.6410i	−0.667037	+	1.15534i
$900$	−22.0000			−0.733333
$901$	3.00000			0.0999445
$902$	8.00000	−	13.8564i	0.266371	−	0.461368i
$903$	−6.00000	+	10.3923i	−0.199667	+	0.345834i
$904$	14.0000			0.465633
$905$	88.0000			2.92522
$906$	−1.00000	+	1.73205i	−0.0332228	+	0.0575435i
$907$	26.5000	+	45.8993i	0.879918	+	1.52406i	0.851430	+	0.524469i	$0.175736\pi$
$907$	26.5000	+	45.8993i	0.879918	+	1.52406i	0.0284883	+	0.999594i	$0.490931\pi$
$908$	−8.50000	+	14.7224i	−0.282082	+	0.488581i
$909$	2.00000	+	3.46410i	0.0663358	+	0.114897i
$910$	−6.00000	−	10.3923i	−0.198898	−	0.344502i
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$	−12.0000			−0.397142
$914$	−3.50000	−	6.06218i	−0.115770	−	0.200519i
$915$	4.00000	+	6.92820i	0.132236	+	0.229039i
$916$	5.00000	−	8.66025i	0.165205	−	0.286143i
$917$	−18.0000	−	31.1769i	−0.594412	−	1.02955i
$918$	−7.50000	+	12.9904i	−0.247537	+	0.428746i
$919$	5.00000			0.164935			0.0824674	−	0.996594i	$-0.473720\pi$
$919$	5.00000			0.164935			0.0824674	+	0.996594i	$0.473720\pi$
$920$	−4.00000			−0.131876
$921$	−6.00000	+	10.3923i	−0.197707	+	0.342438i
$922$	−14.0000	+	24.2487i	−0.461065	+	0.798589i
$923$	−2.00000			−0.0658308
$924$	6.00000			0.197386
$925$	−11.0000	+	19.0526i	−0.361678	+	0.626444i
$926$	2.00000	+	3.46410i	0.0657241	+	0.113837i
$927$	6.00000	−	10.3923i	0.197066	−	0.341328i
$928$	2.50000	+	4.33013i	0.0820665	+	0.142143i
$929$	27.5000	+	47.6314i	0.902246	+	1.56274i	0.824572	+	0.565757i	$0.191416\pi$
$929$	27.5000	+	47.6314i	0.902246	+	1.56274i	0.0776734	+	0.996979i	$0.475251\pi$
$930$	32.0000			1.04932
$931$		0			0
$932$	−6.00000			−0.196537
$933$	−3.50000	−	6.06218i	−0.114585	−	0.198467i
$934$	−1.00000	−	1.73205i	−0.0327210	−	0.0566744i
$935$	12.0000	−	20.7846i	0.392442	−	0.679729i
$936$	−1.00000	−	1.73205i	−0.0326860	−	0.0566139i
$937$	3.50000	−	6.06218i	0.114340	−	0.198043i	−0.803176	−	0.595742i	$-0.796858\pi$
$937$	3.50000	−	6.06218i	0.114340	−	0.198043i	0.917516	+	0.397699i	$0.130191\pi$
$938$	9.00000			0.293860
$939$	29.0000			0.946379
$940$	16.0000	−	27.7128i	0.521862	−	0.903892i
$941$	3.50000	−	6.06218i	0.114097	−	0.197621i	−0.803322	−	0.595545i	$-0.796936\pi$
$941$	3.50000	−	6.06218i	0.114097	−	0.197621i	0.917418	+	0.397924i	$0.130269\pi$
$942$	2.00000			0.0651635
$943$	−8.00000			−0.260516
$944$	7.50000	−	12.9904i	0.244104	−	0.422801i
$945$	−30.0000	−	51.9615i	−0.975900	−	1.69031i
$946$	4.00000	−	6.92820i	0.130051	−	0.225255i
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	0.946892	−	0.321552i	$-0.104204\pi$
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	−0.751918	+	0.659256i	$0.770871\pi$
$948$	−5.00000	−	8.66025i	−0.162392	−	0.281272i
$949$	9.00000			0.292152
$950$		0			0
$951$	27.0000			0.875535
$952$	4.50000	+	7.79423i	0.145846	+	0.252612i
$953$	−23.0000	−	39.8372i	−0.745043	−	1.29045i	−0.950175	−	0.311718i	$-0.899096\pi$
$953$	−23.0000	−	39.8372i	−0.745043	−	1.29045i	0.205132	−	0.978734i	$-0.434238\pi$
$954$	−1.00000	+	1.73205i	−0.0323762	+	0.0560772i
$955$	14.0000	+	24.2487i	0.453029	+	0.784670i
$956$	−7.50000	+	12.9904i	−0.242567	+	0.420139i
$957$	10.0000			0.323254
$958$	20.0000			0.646171
$959$	25.5000	−	44.1673i	0.823438	−	1.42624i
$960$	2.00000	−	3.46410i	0.0645497	−	0.111803i
$961$	33.0000			1.06452
$962$	−2.00000			−0.0644826
$963$	7.00000	−	12.1244i	0.225572	−	0.390702i
$964$	−4.00000	−	6.92820i	−0.128831	−	0.223142i
$965$	12.0000	−	20.7846i	0.386294	−	0.669080i
$966$	−1.50000	−	2.59808i	−0.0482617	−	0.0835917i
$967$	−24.0000	−	41.5692i	−0.771788	−	1.33678i	−0.936582	−	0.350448i	$-0.886029\pi$
$967$	−24.0000	−	41.5692i	−0.771788	−	1.33678i	0.164794	−	0.986328i	$-0.447304\pi$
$968$	7.00000			0.224989
$969$		0			0
$970$	8.00000			0.256865
$971$	−14.0000	−	24.2487i	−0.449281	−	0.778178i	0.549058	−	0.835784i	$-0.314987\pi$
$971$	−14.0000	−	24.2487i	−0.449281	−	0.778178i	−0.998339	+	0.0576061i	$0.981653\pi$
$972$	−8.00000	−	13.8564i	−0.256600	−	0.444444i
$973$		0			0
$974$	1.00000	+	1.73205i	0.0320421	+	0.0554985i
$975$	−5.50000	+	9.52628i	−0.176141	+	0.305085i
$976$	2.00000			0.0640184
$977$	−8.00000			−0.255943			−0.127971	−	0.991778i	$-0.540847\pi$
$977$	−8.00000			−0.255943			−0.127971	+	0.991778i	$0.540847\pi$
$978$	−8.00000	+	13.8564i	−0.255812	+	0.443079i
$979$		0			0
$980$	−8.00000			−0.255551
$981$	−30.0000			−0.957826
$982$	−14.0000	+	24.2487i	−0.446758	+	0.773807i
$983$	−3.00000	−	5.19615i	−0.0956851	−	0.165732i	0.814209	−	0.580572i	$-0.197171\pi$
$983$	−3.00000	−	5.19615i	−0.0956851	−	0.165732i	−0.909894	+	0.414840i	$0.863838\pi$
$984$	4.00000	−	6.92820i	0.127515	−	0.220863i
$985$	16.0000	+	27.7128i	0.509802	+	0.883004i
$986$	7.50000	+	12.9904i	0.238849	+	0.413698i
$987$	24.0000			0.763928
$988$		0			0
$989$	−4.00000			−0.127193
$990$	8.00000	+	13.8564i	0.254257	+	0.440386i
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	0.795474	−	0.605988i	$-0.207222\pi$
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	−0.922538	+	0.385906i	$0.873889\pi$
$992$	4.00000	−	6.92820i	0.127000	−	0.219971i
$993$	8.50000	+	14.7224i	0.269739	+	0.467202i
$994$	−3.00000	+	5.19615i	−0.0951542	+	0.164812i
$995$	100.000			3.17021
$996$	−6.00000			−0.190117
$997$	−14.0000	+	24.2487i	−0.443384	+	0.767964i	−0.997938	−	0.0641836i	$-0.979556\pi$
$997$	−14.0000	+	24.2487i	−0.443384	+	0.767964i	0.554554	+	0.832148i	$0.312889\pi$
$998$	20.0000	−	34.6410i	0.633089	−	1.09654i
$999$	−10.0000			−0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.c.f.653.1		2
19.2	odd	18		722.2.e.c.389.1		6
19.3	odd	18		722.2.e.c.595.1		6
19.4	even	9		722.2.e.d.245.1		6
19.5	even	9		722.2.e.d.99.1		6
19.6	even	9		722.2.e.d.423.1		6
19.7	even	3		722.2.a.b.1.1		1
19.8	odd	6		722.2.c.d.429.1		2
19.9	even	9		722.2.e.d.415.1		6
19.10	odd	18		722.2.e.c.415.1		6
19.11	even	3	inner	722.2.c.f.429.1		2
19.12	odd	6		38.2.a.b.1.1	✓	1
19.13	odd	18		722.2.e.c.423.1		6
19.14	odd	18		722.2.e.c.99.1		6
19.15	odd	18		722.2.e.c.245.1		6
19.16	even	9		722.2.e.d.595.1		6
19.17	even	9		722.2.e.d.389.1		6
19.18	odd	2		722.2.c.d.653.1		2
57.26	odd	6		6498.2.a.y.1.1		1
57.50	even	6		342.2.a.d.1.1		1
76.7	odd	6		5776.2.a.d.1.1		1
76.31	even	6		304.2.a.d.1.1		1
95.12	even	12		950.2.b.c.799.2		2
95.69	odd	6		950.2.a.b.1.1		1
95.88	even	12		950.2.b.c.799.1		2
133.69	even	6		1862.2.a.f.1.1		1
152.69	odd	6		1216.2.a.n.1.1		1
152.107	even	6		1216.2.a.g.1.1		1
209.164	even	6		4598.2.a.a.1.1		1
228.107	odd	6		2736.2.a.w.1.1		1
247.12	odd	6		6422.2.a.b.1.1		1
285.164	even	6		8550.2.a.u.1.1		1
380.259	even	6		7600.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.a.b.1.1	✓	1	19.12	odd	6
304.2.a.d.1.1		1	76.31	even	6
342.2.a.d.1.1		1	57.50	even	6
722.2.a.b.1.1		1	19.7	even	3
722.2.c.d.429.1		2	19.8	odd	6
722.2.c.d.653.1		2	19.18	odd	2
722.2.c.f.429.1		2	19.11	even	3	inner
722.2.c.f.653.1		2	1.1	even	1	trivial
722.2.e.c.99.1		6	19.14	odd	18
722.2.e.c.245.1		6	19.15	odd	18
722.2.e.c.389.1		6	19.2	odd	18
722.2.e.c.415.1		6	19.10	odd	18
722.2.e.c.423.1		6	19.13	odd	18
722.2.e.c.595.1		6	19.3	odd	18
722.2.e.d.99.1		6	19.5	even	9
722.2.e.d.245.1		6	19.4	even	9
722.2.e.d.389.1		6	19.17	even	9
722.2.e.d.415.1		6	19.9	even	9
722.2.e.d.423.1		6	19.6	even	9
722.2.e.d.595.1		6	19.16	even	9
950.2.a.b.1.1		1	95.69	odd	6
950.2.b.c.799.1		2	95.88	even	12
950.2.b.c.799.2		2	95.12	even	12
1216.2.a.g.1.1		1	152.107	even	6
1216.2.a.n.1.1		1	152.69	odd	6
1862.2.a.f.1.1		1	133.69	even	6
2736.2.a.w.1.1		1	228.107	odd	6
4598.2.a.a.1.1		1	209.164	even	6
5776.2.a.d.1.1		1	76.7	odd	6
6422.2.a.b.1.1		1	247.12	odd	6
6498.2.a.y.1.1		1	57.26	odd	6
7600.2.a.h.1.1		1	380.259	even	6
8550.2.a.u.1.1		1	285.164	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.00000 q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(-2.00000 + 3.46410i) q^{10} +2.00000 q^{11} +1.00000 q^{12} +(-0.500000 + 0.866025i) q^{13} +(1.50000 + 2.59808i) q^{14} +(2.00000 - 3.46410i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +2.00000 q^{18} -4.00000 q^{20} +(-1.50000 - 2.59808i) q^{21} +(1.00000 + 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-5.50000 + 9.52628i) q^{25} -1.00000 q^{26} -5.00000 q^{27} +(-1.50000 + 2.59808i) q^{28} +(-2.50000 + 4.33013i) q^{29} +4.00000 q^{30} +8.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +(1.50000 - 2.59808i) q^{34} +(6.00000 + 10.3923i) q^{35} +(1.00000 + 1.73205i) q^{36} +2.00000 q^{37} +1.00000 q^{39} +(-2.00000 - 3.46410i) q^{40} +(-4.00000 - 6.92820i) q^{41} +(1.50000 - 2.59808i) q^{42} +(-2.00000 - 3.46410i) q^{43} +(-1.00000 + 1.73205i) q^{44} +8.00000 q^{45} +1.00000 q^{46} +(-4.00000 + 6.92820i) q^{47} +(-0.500000 + 0.866025i) q^{48} +2.00000 q^{49} -11.0000 q^{50} +(-1.50000 + 2.59808i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(-0.500000 + 0.866025i) q^{53} +(-2.50000 - 4.33013i) q^{54} +(4.00000 + 6.92820i) q^{55} -3.00000 q^{56} -5.00000 q^{58} +(7.50000 + 12.9904i) q^{59} +(2.00000 + 3.46410i) q^{60} +(-1.00000 + 1.73205i) q^{61} +(4.00000 + 6.92820i) q^{62} +(3.00000 - 5.19615i) q^{63} +1.00000 q^{64} -4.00000 q^{65} +(1.00000 - 1.73205i) q^{66} +(1.50000 - 2.59808i) q^{67} +3.00000 q^{68} -1.00000 q^{69} +(-6.00000 + 10.3923i) q^{70} +(1.00000 + 1.73205i) q^{71} +(-1.00000 + 1.73205i) q^{72} +(-4.50000 - 7.79423i) q^{73} +(1.00000 + 1.73205i) q^{74} +11.0000 q^{75} +6.00000 q^{77} +(0.500000 + 0.866025i) q^{78} +(-5.00000 - 8.66025i) q^{79} +(2.00000 - 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.00000 - 6.92820i) q^{82} -6.00000 q^{83} +3.00000 q^{84} +(6.00000 - 10.3923i) q^{85} +(2.00000 - 3.46410i) q^{86} +5.00000 q^{87} -2.00000 q^{88} +(4.00000 + 6.92820i) q^{90} +(-1.50000 + 2.59808i) q^{91} +(0.500000 + 0.866025i) q^{92} +(-4.00000 - 6.92820i) q^{93} -8.00000 q^{94} -1.00000 q^{96} +(-1.00000 - 1.73205i) q^{97} +(1.00000 + 1.73205i) q^{98} +(2.00000 - 3.46410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} + 4 q^{5} + q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{11} + 2 q^{12} - q^{13} + 3 q^{14} + 4 q^{15} - q^{16} - 3 q^{17} + 4 q^{18} - 8 q^{20} - 3 q^{21} + 2 q^{22}+ \cdots + 4 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 + 4 * q^5 + q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^11 + 2 * q^12 - q^13 + 3 * q^14 + 4 * q^15 - q^16 - 3 * q^17 + 4 * q^18 - 8 * q^20 - 3 * q^21 + 2 * q^22 + q^23 + q^24 - 11 * q^25 - 2 * q^26 - 10 * q^27 - 3 * q^28 - 5 * q^29 + 8 * q^30 + 16 * q^31 + q^32 - 2 * q^33 + 3 * q^34 + 12 * q^35 + 2 * q^36 + 4 * q^37 + 2 * q^39 - 4 * q^40 - 8 * q^41 + 3 * q^42 - 4 * q^43 - 2 * q^44 + 16 * q^45 + 2 * q^46 - 8 * q^47 - q^48 + 4 * q^49 - 22 * q^50 - 3 * q^51 - q^52 - q^53 - 5 * q^54 + 8 * q^55 - 6 * q^56 - 10 * q^58 + 15 * q^59 + 4 * q^60 - 2 * q^61 + 8 * q^62 + 6 * q^63 + 2 * q^64 - 8 * q^65 + 2 * q^66 + 3 * q^67 + 6 * q^68 - 2 * q^69 - 12 * q^70 + 2 * q^71 - 2 * q^72 - 9 * q^73 + 2 * q^74 + 22 * q^75 + 12 * q^77 + q^78 - 10 * q^79 + 4 * q^80 - q^81 + 8 * q^82 - 12 * q^83 + 6 * q^84 + 12 * q^85 + 4 * q^86 + 10 * q^87 - 4 * q^88 + 8 * q^90 - 3 * q^91 + q^92 - 8 * q^93 - 16 * q^94 - 2 * q^96 - 2 * q^97 + 2 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more