LMFDB - Embedded newform 722.2.c.a.653.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [722,2,Mod(429,722)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [2,-1,-3,-1,-2,-3,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.76519902594$
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:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			653.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	722.653
Dual form			722.2.c.a.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} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(-1.50000 + 2.59808i) q^{6} -3.00000 q^{7} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(-1.00000 + 1.73205i) q^{10} -2.00000 q^{11} +3.00000 q^{12} +(1.50000 - 2.59808i) q^{13} +(1.50000 + 2.59808i) q^{14} +(-3.00000 + 5.19615i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{17} +6.00000 q^{18} +2.00000 q^{20} +(4.50000 + 7.79423i) q^{21} +(1.00000 + 1.73205i) q^{22} +(-2.50000 + 4.33013i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(0.500000 - 0.866025i) q^{25} -3.00000 q^{26} +9.00000 q^{27} +(1.50000 - 2.59808i) q^{28} +(1.50000 - 2.59808i) q^{29} +6.00000 q^{30} -6.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{33} +(0.500000 - 0.866025i) q^{34} +(3.00000 + 5.19615i) q^{35} +(-3.00000 - 5.19615i) q^{36} +6.00000 q^{37} -9.00000 q^{39} +(-1.00000 - 1.73205i) q^{40} +(-6.00000 - 10.3923i) q^{41} +(4.50000 - 7.79423i) q^{42} +(5.00000 + 8.66025i) q^{43} +(1.00000 - 1.73205i) q^{44} +12.0000 q^{45} +5.00000 q^{46} +(4.00000 - 6.92820i) q^{47} +(-1.50000 + 2.59808i) q^{48} +2.00000 q^{49} -1.00000 q^{50} +(1.50000 - 2.59808i) q^{51} +(1.50000 + 2.59808i) q^{52} +(1.50000 - 2.59808i) q^{53} +(-4.50000 - 7.79423i) q^{54} +(2.00000 + 3.46410i) q^{55} -3.00000 q^{56} -3.00000 q^{58} +(-1.50000 - 2.59808i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(3.00000 + 5.19615i) q^{62} +(9.00000 - 15.5885i) q^{63} +1.00000 q^{64} -6.00000 q^{65} +(3.00000 - 5.19615i) q^{66} +(-7.50000 + 12.9904i) q^{67} -1.00000 q^{68} +15.0000 q^{69} +(3.00000 - 5.19615i) q^{70} +(-3.00000 + 5.19615i) q^{72} +(5.50000 + 9.52628i) q^{73} +(-3.00000 - 5.19615i) q^{74} -3.00000 q^{75} +6.00000 q^{77} +(4.50000 + 7.79423i) q^{78} +(6.00000 + 10.3923i) q^{79} +(-1.00000 + 1.73205i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 + 10.3923i) q^{82} +2.00000 q^{83} -9.00000 q^{84} +(1.00000 - 1.73205i) q^{85} +(5.00000 - 8.66025i) q^{86} -9.00000 q^{87} -2.00000 q^{88} +(-3.00000 + 5.19615i) q^{89} +(-6.00000 - 10.3923i) q^{90} +(-4.50000 + 7.79423i) q^{91} +(-2.50000 - 4.33013i) q^{92} +(9.00000 + 15.5885i) q^{93} -8.00000 q^{94} +3.00000 q^{96} +(-6.00000 - 10.3923i) q^{97} +(-1.00000 - 1.73205i) q^{98} +(6.00000 - 10.3923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 3 q^{3} - q^{4} - 2 q^{5} - 3 q^{6} - 6 q^{7} + 2 q^{8} - 6 q^{9} - 2 q^{10} - 4 q^{11} + 6 q^{12} + 3 q^{13} + 3 q^{14} - 6 q^{15} - q^{16} + q^{17} + 12 q^{18} + 4 q^{20} + 9 q^{21}+ \cdots + 12 q^{99}+O(q^{100}) $ 2 * q - q^2 - 3 * q^3 - q^4 - 2 * q^5 - 3 * q^6 - 6 * q^7 + 2 * q^8 - 6 * q^9 - 2 * q^10 - 4 * q^11 + 6 * q^12 + 3 * q^13 + 3 * q^14 - 6 * q^15 - q^16 + q^17 + 12 * q^18 + 4 * q^20 + 9 * q^21 + 2 * q^22 - 5 * q^23 - 3 * q^24 + q^25 - 6 * q^26 + 18 * q^27 + 3 * q^28 + 3 * q^29 + 12 * q^30 - 12 * q^31 - q^32 + 6 * q^33 + q^34 + 6 * q^35 - 6 * q^36 + 12 * q^37 - 18 * q^39 - 2 * q^40 - 12 * q^41 + 9 * q^42 + 10 * q^43 + 2 * q^44 + 24 * q^45 + 10 * q^46 + 8 * q^47 - 3 * q^48 + 4 * q^49 - 2 * q^50 + 3 * q^51 + 3 * q^52 + 3 * q^53 - 9 * q^54 + 4 * q^55 - 6 * q^56 - 6 * q^58 - 3 * q^59 - 6 * q^60 + 6 * q^62 + 18 * q^63 + 2 * q^64 - 12 * q^65 + 6 * q^66 - 15 * q^67 - 2 * q^68 + 30 * q^69 + 6 * q^70 - 6 * q^72 + 11 * q^73 - 6 * q^74 - 6 * q^75 + 12 * q^77 + 9 * q^78 + 12 * q^79 - 2 * q^80 - 9 * q^81 - 12 * q^82 + 4 * q^83 - 18 * q^84 + 2 * q^85 + 10 * q^86 - 18 * q^87 - 4 * q^88 - 6 * q^89 - 12 * q^90 - 9 * q^91 - 5 * q^92 + 18 * q^93 - 16 * q^94 + 6 * q^96 - 12 * q^97 - 2 * q^98 + 12 * 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
$3$	−1.50000	−	2.59808i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−1.50000	−	2.59808i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	0.550990	−	0.834512i	$-0.314250\pi$
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$	−1.50000	+	2.59808i	−0.612372	+	1.06066i
$7$	−3.00000			−1.13389			−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000			−1.13389			−0.566947	+	0.823754i	$0.691875\pi$
$8$	1.00000			0.353553
$9$	−3.00000	+	5.19615i	−1.00000	+	1.73205i
$10$	−1.00000	+	1.73205i	−0.316228	+	0.547723i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$	3.00000			0.866025
$13$	1.50000	−	2.59808i	0.416025	−	0.720577i	−0.579510	−	0.814965i	$-0.696756\pi$
$13$	1.50000	−	2.59808i	0.416025	−	0.720577i	0.995535	+	0.0943882i	$0.0300895\pi$
$14$	1.50000	+	2.59808i	0.400892	+	0.694365i
$15$	−3.00000	+	5.19615i	−0.774597	+	1.34164i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i	0.920268	−	0.391289i	$-0.127971\pi$
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i	−0.799000	+	0.601331i	$0.794637\pi$
$18$	6.00000			1.41421
$19$		0			0
$19$		0			0
$20$	2.00000			0.447214
$21$	4.50000	+	7.79423i	0.981981	+	1.70084i
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	−2.50000	+	4.33013i	−0.521286	+	0.902894i	0.478407	+	0.878138i	$0.341214\pi$
$23$	−2.50000	+	4.33013i	−0.521286	+	0.902894i	−0.999694	+	0.0247559i	$0.992119\pi$
$24$	−1.50000	−	2.59808i	−0.306186	−	0.530330i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−3.00000			−0.588348
$27$	9.00000			1.73205
$28$	1.50000	−	2.59808i	0.283473	−	0.490990i
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$	6.00000			1.09545
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	3.00000	+	5.19615i	0.522233	+	0.904534i
$34$	0.500000	−	0.866025i	0.0857493	−	0.148522i
$35$	3.00000	+	5.19615i	0.507093	+	0.878310i
$36$	−3.00000	−	5.19615i	−0.500000	−	0.866025i
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$		0			0
$39$	−9.00000			−1.44115
$40$	−1.00000	−	1.73205i	−0.158114	−	0.273861i
$41$	−6.00000	−	10.3923i	−0.937043	−	1.62301i	−0.770950	−	0.636895i	$-0.780218\pi$
$41$	−6.00000	−	10.3923i	−0.937043	−	1.62301i	−0.166092	−	0.986110i	$-0.553115\pi$
$42$	4.50000	−	7.79423i	0.694365	−	1.20268i
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	0.941562	+	0.336840i	$0.109358\pi$
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	−0.179069	+	0.983836i	$0.557309\pi$
$44$	1.00000	−	1.73205i	0.150756	−	0.261116i
$45$	12.0000			1.78885
$46$	5.00000			0.737210
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	−0.411606	−	0.911362i	$-0.635032\pi$
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	0.995066	−	0.0992202i	$-0.0316348\pi$
$48$	−1.50000	+	2.59808i	−0.216506	+	0.375000i
$49$	2.00000			0.285714
$50$	−1.00000			−0.141421
$51$	1.50000	−	2.59808i	0.210042	−	0.363803i
$52$	1.50000	+	2.59808i	0.208013	+	0.360288i
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	−0.744423	−	0.667708i	$-0.767275\pi$
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	0.950464	+	0.310835i	$0.100609\pi$
$54$	−4.50000	−	7.79423i	−0.612372	−	1.06066i
$55$	2.00000	+	3.46410i	0.269680	+	0.467099i
$56$	−3.00000			−0.400892
$57$		0			0
$58$	−3.00000			−0.393919
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	0.751710	−	0.659494i	$-0.229229\pi$
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	−0.946993	+	0.321253i	$0.895896\pi$
$60$	−3.00000	−	5.19615i	−0.387298	−	0.670820i
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$	3.00000	+	5.19615i	0.381000	+	0.659912i
$63$	9.00000	−	15.5885i	1.13389	−	1.96396i
$64$	1.00000			0.125000
$65$	−6.00000			−0.744208
$66$	3.00000	−	5.19615i	0.369274	−	0.639602i
$67$	−7.50000	+	12.9904i	−0.916271	+	1.58703i	−0.111241	+	0.993793i	$0.535483\pi$
$67$	−7.50000	+	12.9904i	−0.916271	+	1.58703i	−0.805030	+	0.593234i	$0.797851\pi$
$68$	−1.00000			−0.121268
$69$	15.0000			1.80579
$70$	3.00000	−	5.19615i	0.358569	−	0.621059i
$71$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$71$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$72$	−3.00000	+	5.19615i	−0.353553	+	0.612372i
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	0.984594	+	0.174855i	$0.0559458\pi$
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	−0.340868	+	0.940111i	$0.610721\pi$
$74$	−3.00000	−	5.19615i	−0.348743	−	0.604040i
$75$	−3.00000			−0.346410
$76$		0			0
$77$	6.00000			0.683763
$78$	4.50000	+	7.79423i	0.509525	+	0.882523i
$79$	6.00000	+	10.3923i	0.675053	+	1.16923i	0.976453	+	0.215728i	$0.0692125\pi$
$79$	6.00000	+	10.3923i	0.675053	+	1.16923i	−0.301401	+	0.953498i	$0.597454\pi$
$80$	−1.00000	+	1.73205i	−0.111803	+	0.193649i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−6.00000	+	10.3923i	−0.662589	+	1.14764i
$83$	2.00000			0.219529			0.109764	−	0.993958i	$-0.464990\pi$
$83$	2.00000			0.219529			0.109764	+	0.993958i	$0.464990\pi$
$84$	−9.00000			−0.981981
$85$	1.00000	−	1.73205i	0.108465	−	0.187867i
$86$	5.00000	−	8.66025i	0.539164	−	0.933859i
$87$	−9.00000			−0.964901
$88$	−2.00000			−0.213201
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$	−6.00000	−	10.3923i	−0.632456	−	1.09545i
$91$	−4.50000	+	7.79423i	−0.471728	+	0.817057i
$92$	−2.50000	−	4.33013i	−0.260643	−	0.451447i
$93$	9.00000	+	15.5885i	0.933257	+	1.61645i
$94$	−8.00000			−0.825137
$95$		0			0
$96$	3.00000			0.306186
$97$	−6.00000	−	10.3923i	−0.609208	−	1.05518i	−0.991371	−	0.131084i	$-0.958154\pi$
$97$	−6.00000	−	10.3923i	−0.609208	−	1.05518i	0.382164	−	0.924095i	$-0.375179\pi$
$98$	−1.00000	−	1.73205i	−0.101015	−	0.174964i
$99$	6.00000	−	10.3923i	0.603023	−	1.04447i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$	−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	$0.404481\pi$
$104$	1.50000	−	2.59808i	0.147087	−	0.254762i
$105$	9.00000	−	15.5885i	0.878310	−	1.52128i
$106$	−3.00000			−0.291386
$107$	−3.00000			−0.290021			−0.145010	−	0.989430i	$-0.546322\pi$
$107$	−3.00000			−0.290021			−0.145010	+	0.989430i	$0.546322\pi$
$108$	−4.50000	+	7.79423i	−0.433013	+	0.750000i
$109$	−1.50000	−	2.59808i	−0.143674	−	0.248851i	0.785203	−	0.619238i	$-0.212558\pi$
$109$	−1.50000	−	2.59808i	−0.143674	−	0.248851i	−0.928877	+	0.370387i	$0.879225\pi$
$110$	2.00000	−	3.46410i	0.190693	−	0.330289i
$111$	−9.00000	−	15.5885i	−0.854242	−	1.47959i
$112$	1.50000	+	2.59808i	0.141737	+	0.245495i
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$		0			0
$115$	10.0000			0.932505
$116$	1.50000	+	2.59808i	0.139272	+	0.241225i
$117$	9.00000	+	15.5885i	0.832050	+	1.44115i
$118$	−1.50000	+	2.59808i	−0.138086	+	0.239172i
$119$	−1.50000	−	2.59808i	−0.137505	−	0.238165i
$120$	−3.00000	+	5.19615i	−0.273861	+	0.474342i
$121$	−7.00000			−0.636364
$122$		0			0
$123$	−18.0000	+	31.1769i	−1.62301	+	2.81113i
$124$	3.00000	−	5.19615i	0.269408	−	0.466628i
$125$	−12.0000			−1.07331
$126$	−18.0000			−1.60357
$127$	−6.00000	+	10.3923i	−0.532414	+	0.922168i	0.466870	+	0.884326i	$0.345382\pi$
$127$	−6.00000	+	10.3923i	−0.532414	+	0.922168i	−0.999284	+	0.0378419i	$0.987952\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	15.0000	−	25.9808i	1.32068	−	2.28748i
$130$	3.00000	+	5.19615i	0.263117	+	0.455733i
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	−0.990972	−	0.134069i	$-0.957196\pi$
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	0.379379	−	0.925241i	$-0.376138\pi$
$132$	−6.00000			−0.522233
$133$		0			0
$134$	15.0000			1.29580
$135$	−9.00000	−	15.5885i	−0.774597	−	1.34164i
$136$	0.500000	+	0.866025i	0.0428746	+	0.0742611i
$137$	−9.50000	+	16.4545i	−0.811640	+	1.40580i	0.100076	+	0.994980i	$0.468091\pi$
$137$	−9.50000	+	16.4545i	−0.811640	+	1.40580i	−0.911716	+	0.410822i	$0.865242\pi$
$138$	−7.50000	−	12.9904i	−0.638442	−	1.10581i
$139$	−3.00000	+	5.19615i	−0.254457	+	0.440732i	−0.964748	−	0.263176i	$-0.915230\pi$
$139$	−3.00000	+	5.19615i	−0.254457	+	0.440732i	0.710291	+	0.703908i	$0.248563\pi$
$140$	−6.00000			−0.507093
$141$	−24.0000			−2.02116
$142$		0			0
$143$	−3.00000	+	5.19615i	−0.250873	+	0.434524i
$144$	6.00000			0.500000
$145$	−6.00000			−0.498273
$146$	5.50000	−	9.52628i	0.455183	−	0.788400i
$147$	−3.00000	−	5.19615i	−0.247436	−	0.428571i
$148$	−3.00000	+	5.19615i	−0.246598	+	0.427121i
$149$	4.00000	+	6.92820i	0.327693	+	0.567581i	0.982054	−	0.188602i	$-0.0603956\pi$
$149$	4.00000	+	6.92820i	0.327693	+	0.567581i	−0.654361	+	0.756182i	$0.727062\pi$
$150$	1.50000	+	2.59808i	0.122474	+	0.212132i
$151$	−18.0000			−1.46482			−0.732410	−	0.680864i	$-0.761604\pi$
$151$	−18.0000			−1.46482			−0.732410	+	0.680864i	$0.761604\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$	−3.00000	−	5.19615i	−0.241747	−	0.418718i
$155$	6.00000	+	10.3923i	0.481932	+	0.834730i
$156$	4.50000	−	7.79423i	0.360288	−	0.624038i
$157$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$157$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$158$	6.00000	−	10.3923i	0.477334	−	0.826767i
$159$	−9.00000			−0.713746
$160$	2.00000			0.158114
$161$	7.50000	−	12.9904i	0.591083	−	1.02379i
$162$	−4.50000	+	7.79423i	−0.353553	+	0.612372i
$163$	−6.00000			−0.469956			−0.234978	−	0.972001i	$-0.575502\pi$
$163$	−6.00000			−0.469956			−0.234978	+	0.972001i	$0.575502\pi$
$164$	12.0000			0.937043
$165$	6.00000	−	10.3923i	0.467099	−	0.809040i
$166$	−1.00000	−	1.73205i	−0.0776151	−	0.134433i
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	−0.534875	−	0.844931i	$-0.679641\pi$
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	0.999169	+	0.0407502i	$0.0129748\pi$
$168$	4.50000	+	7.79423i	0.347183	+	0.601338i
$169$	2.00000	+	3.46410i	0.153846	+	0.266469i
$170$	−2.00000			−0.153393
$171$		0			0
$172$	−10.0000			−0.762493
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	0.973670	+	0.227964i	$0.0732068\pi$
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	−0.289412	+	0.957205i	$0.593460\pi$
$174$	4.50000	+	7.79423i	0.341144	+	0.590879i
$175$	−1.50000	+	2.59808i	−0.113389	+	0.196396i
$176$	1.00000	+	1.73205i	0.0753778	+	0.130558i
$177$	−4.50000	+	7.79423i	−0.338241	+	0.585850i
$178$	6.00000			0.449719
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	−6.00000	+	10.3923i	−0.447214	+	0.774597i
$181$	−9.00000	+	15.5885i	−0.668965	+	1.15868i	0.309229	+	0.950988i	$0.399929\pi$
$181$	−9.00000	+	15.5885i	−0.668965	+	1.15868i	−0.978194	+	0.207693i	$0.933404\pi$
$182$	9.00000			0.667124
$183$		0			0
$184$	−2.50000	+	4.33013i	−0.184302	+	0.319221i
$185$	−6.00000	−	10.3923i	−0.441129	−	0.764057i
$186$	9.00000	−	15.5885i	0.659912	−	1.14300i
$187$	−1.00000	−	1.73205i	−0.0731272	−	0.126660i
$188$	4.00000	+	6.92820i	0.291730	+	0.505291i
$189$	−27.0000			−1.96396
$190$		0			0
$191$	−11.0000			−0.795932			−0.397966	−	0.917400i	$-0.630284\pi$
$191$	−11.0000			−0.795932			−0.397966	+	0.917400i	$0.630284\pi$
$192$	−1.50000	−	2.59808i	−0.108253	−	0.187500i
$193$	−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	$0.902616\pi$
$194$	−6.00000	+	10.3923i	−0.430775	+	0.746124i
$195$	9.00000	+	15.5885i	0.644503	+	1.11631i
$196$	−1.00000	+	1.73205i	−0.0714286	+	0.123718i
$197$	4.00000			0.284988			0.142494	−	0.989796i	$-0.454488\pi$
$197$	4.00000			0.284988			0.142494	+	0.989796i	$0.454488\pi$
$198$	−12.0000			−0.852803
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	−0.714893	−	0.699234i	$-0.753524\pi$
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	0.963001	+	0.269498i	$0.0868577\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	45.0000			3.17406
$202$	10.0000			0.703598
$203$	−4.50000	+	7.79423i	−0.315838	+	0.547048i
$204$	1.50000	+	2.59808i	0.105021	+	0.181902i
$205$	−12.0000	+	20.7846i	−0.838116	+	1.45166i
$206$	−3.00000	−	5.19615i	−0.209020	−	0.362033i
$207$	−15.0000	−	25.9808i	−1.04257	−	1.80579i
$208$	−3.00000			−0.208013
$209$		0			0
$210$	−18.0000			−1.24212
$211$	−1.50000	−	2.59808i	−0.103264	−	0.178859i	0.809763	−	0.586756i	$-0.199595\pi$
$211$	−1.50000	−	2.59808i	−0.103264	−	0.178859i	−0.913028	+	0.407898i	$0.866262\pi$
$212$	1.50000	+	2.59808i	0.103020	+	0.178437i
$213$		0			0
$214$	1.50000	+	2.59808i	0.102538	+	0.177601i
$215$	10.0000	−	17.3205i	0.681994	−	1.18125i
$216$	9.00000			0.612372
$217$	18.0000			1.22192
$218$	−1.50000	+	2.59808i	−0.101593	+	0.175964i
$219$	16.5000	−	28.5788i	1.11497	−	1.93118i
$220$	−4.00000			−0.269680
$221$	3.00000			0.201802
$222$	−9.00000	+	15.5885i	−0.604040	+	1.04623i
$223$	−9.00000	−	15.5885i	−0.602685	−	1.04388i	−0.992413	−	0.122950i	$-0.960764\pi$
$223$	−9.00000	−	15.5885i	−0.602685	−	1.04388i	0.389728	−	0.920930i	$-0.372569\pi$
$224$	1.50000	−	2.59808i	0.100223	−	0.173591i
$225$	3.00000	+	5.19615i	0.200000	+	0.346410i
$226$	−6.00000	−	10.3923i	−0.399114	−	0.691286i
$227$	3.00000			0.199117			0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000			0.199117			0.0995585	+	0.995032i	$0.468257\pi$
$228$		0			0
$229$	−12.0000			−0.792982			−0.396491	−	0.918039i	$-0.629772\pi$
$229$	−12.0000			−0.792982			−0.396491	+	0.918039i	$0.629772\pi$
$230$	−5.00000	−	8.66025i	−0.329690	−	0.571040i
$231$	−9.00000	−	15.5885i	−0.592157	−	1.02565i
$232$	1.50000	−	2.59808i	0.0984798	−	0.170572i
$233$	−7.00000	−	12.1244i	−0.458585	−	0.794293i	0.540301	−	0.841472i	$-0.318310\pi$
$233$	−7.00000	−	12.1244i	−0.458585	−	0.794293i	−0.998886	+	0.0471787i	$0.984977\pi$
$234$	9.00000	−	15.5885i	0.588348	−	1.01905i
$235$	−16.0000			−1.04372
$236$	3.00000			0.195283
$237$	18.0000	−	31.1769i	1.16923	−	2.02516i
$238$	−1.50000	+	2.59808i	−0.0972306	+	0.168408i
$239$	1.00000			0.0646846			0.0323423	−	0.999477i	$-0.489703\pi$
$239$	1.00000			0.0646846			0.0323423	+	0.999477i	$0.489703\pi$
$240$	6.00000			0.387298
$241$	−12.0000	+	20.7846i	−0.772988	+	1.33885i	0.162930	+	0.986638i	$0.447905\pi$
$241$	−12.0000	+	20.7846i	−0.772988	+	1.33885i	−0.935918	+	0.352217i	$0.885428\pi$
$242$	3.50000	+	6.06218i	0.224989	+	0.389692i
$243$		0			0
$244$		0			0
$245$	−2.00000	−	3.46410i	−0.127775	−	0.221313i
$246$	36.0000			2.29528
$247$		0			0
$248$	−6.00000			−0.381000
$249$	−3.00000	−	5.19615i	−0.190117	−	0.329293i
$250$	6.00000	+	10.3923i	0.379473	+	0.657267i
$251$	10.0000	−	17.3205i	0.631194	−	1.09326i	−0.356113	−	0.934443i	$-0.615898\pi$
$251$	10.0000	−	17.3205i	0.631194	−	1.09326i	0.987308	−	0.158818i	$-0.0507683\pi$
$252$	9.00000	+	15.5885i	0.566947	+	0.981981i
$253$	5.00000	−	8.66025i	0.314347	−	0.544466i
$254$	12.0000			0.752947
$255$	−6.00000			−0.375735
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$	−30.0000			−1.86772
$259$	−18.0000			−1.11847
$260$	3.00000	−	5.19615i	0.186052	−	0.322252i
$261$	9.00000	+	15.5885i	0.557086	+	0.964901i
$262$	−7.00000	+	12.1244i	−0.432461	+	0.749045i
$263$	4.00000	+	6.92820i	0.246651	+	0.427211i	0.962594	−	0.270947i	$-0.0873367\pi$
$263$	4.00000	+	6.92820i	0.246651	+	0.427211i	−0.715944	+	0.698158i	$0.754003\pi$
$264$	3.00000	+	5.19615i	0.184637	+	0.319801i
$265$	−6.00000			−0.368577
$266$		0			0
$267$	18.0000			1.10158
$268$	−7.50000	−	12.9904i	−0.458135	−	0.793514i
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	0.942871	−	0.333157i	$-0.108114\pi$
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	−0.759958	+	0.649972i	$0.774781\pi$
$270$	−9.00000	+	15.5885i	−0.547723	+	0.948683i
$271$	5.50000	+	9.52628i	0.334101	+	0.578680i	0.983312	−	0.181928i	$-0.0582339\pi$
$271$	5.50000	+	9.52628i	0.334101	+	0.578680i	−0.649211	+	0.760609i	$0.724901\pi$
$272$	0.500000	−	0.866025i	0.0303170	−	0.0525105i
$273$	27.0000			1.63411
$274$	19.0000			1.14783
$275$	−1.00000	+	1.73205i	−0.0603023	+	0.104447i
$276$	−7.50000	+	12.9904i	−0.451447	+	0.781929i
$277$	30.0000			1.80253			0.901263	−	0.433273i	$-0.142641\pi$
$277$	30.0000			1.80253			0.901263	+	0.433273i	$0.142641\pi$
$278$	6.00000			0.359856
$279$	18.0000	−	31.1769i	1.07763	−	1.86651i
$280$	3.00000	+	5.19615i	0.179284	+	0.310530i
$281$	−6.00000	+	10.3923i	−0.357930	+	0.619953i	−0.987615	−	0.156898i	$-0.949851\pi$
$281$	−6.00000	+	10.3923i	−0.357930	+	0.619953i	0.629685	+	0.776851i	$0.283184\pi$
$282$	12.0000	+	20.7846i	0.714590	+	1.23771i
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	0.995544	−	0.0942988i	$-0.0300609\pi$
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	−0.579437	+	0.815017i	$0.696728\pi$
$284$		0			0
$285$		0			0
$286$	6.00000			0.354787
$287$	18.0000	+	31.1769i	1.06251	+	1.84032i
$288$	−3.00000	−	5.19615i	−0.176777	−	0.306186i
$289$	8.00000	−	13.8564i	0.470588	−	0.815083i
$290$	3.00000	+	5.19615i	0.176166	+	0.305129i
$291$	−18.0000	+	31.1769i	−1.05518	+	1.82762i
$292$	−11.0000			−0.643726
$293$	−9.00000			−0.525786			−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000			−0.525786			−0.262893	+	0.964825i	$0.584677\pi$
$294$	−3.00000	+	5.19615i	−0.174964	+	0.303046i
$295$	−3.00000	+	5.19615i	−0.174667	+	0.302532i
$296$	6.00000			0.348743
$297$	−18.0000			−1.04447
$298$	4.00000	−	6.92820i	0.231714	−	0.401340i
$299$	7.50000	+	12.9904i	0.433736	+	0.751253i
$300$	1.50000	−	2.59808i	0.0866025	−	0.150000i
$301$	−15.0000	−	25.9808i	−0.864586	−	1.49751i
$302$	9.00000	+	15.5885i	0.517892	+	0.897015i
$303$	30.0000			1.72345
$304$		0			0
$305$		0			0
$306$	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
$309$	−9.00000	−	15.5885i	−0.511992	−	0.886796i
$310$	6.00000	−	10.3923i	0.340777	−	0.590243i
$311$	−11.0000			−0.623753			−0.311876	−	0.950123i	$-0.600957\pi$
$311$	−11.0000			−0.623753			−0.311876	+	0.950123i	$0.600957\pi$
$312$	−9.00000			−0.509525
$313$	−10.5000	+	18.1865i	−0.593495	+	1.02796i	0.400262	+	0.916401i	$0.368919\pi$
$313$	−10.5000	+	18.1865i	−0.593495	+	1.02796i	−0.993757	+	0.111563i	$0.964414\pi$
$314$		0			0
$315$	−36.0000			−2.02837
$316$	−12.0000			−0.675053
$317$	16.5000	−	28.5788i	0.926732	−	1.60515i	0.137981	−	0.990435i	$-0.455939\pi$
$317$	16.5000	−	28.5788i	0.926732	−	1.60515i	0.788751	−	0.614713i	$-0.210728\pi$
$318$	4.50000	+	7.79423i	0.252347	+	0.437079i
$319$	−3.00000	+	5.19615i	−0.167968	+	0.290929i
$320$	−1.00000	−	1.73205i	−0.0559017	−	0.0968246i
$321$	4.50000	+	7.79423i	0.251166	+	0.435031i
$322$	−15.0000			−0.835917
$323$		0			0
$324$	9.00000			0.500000
$325$	−1.50000	−	2.59808i	−0.0832050	−	0.144115i
$326$	3.00000	+	5.19615i	0.166155	+	0.287788i
$327$	−4.50000	+	7.79423i	−0.248851	+	0.431022i
$328$	−6.00000	−	10.3923i	−0.331295	−	0.573819i
$329$	−12.0000	+	20.7846i	−0.661581	+	1.14589i
$330$	−12.0000			−0.660578
$331$	9.00000			0.494685			0.247342	−	0.968928i	$-0.420443\pi$
$331$	9.00000			0.494685			0.247342	+	0.968928i	$0.420443\pi$
$332$	−1.00000	+	1.73205i	−0.0548821	+	0.0950586i
$333$	−18.0000	+	31.1769i	−0.986394	+	1.70848i
$334$	−12.0000			−0.656611
$335$	30.0000			1.63908
$336$	4.50000	−	7.79423i	0.245495	−	0.425210i
$337$	−9.00000	−	15.5885i	−0.490261	−	0.849157i	0.509676	−	0.860366i	$-0.329765\pi$
$337$	−9.00000	−	15.5885i	−0.490261	−	0.849157i	−0.999937	+	0.0112091i	$0.996432\pi$
$338$	2.00000	−	3.46410i	0.108786	−	0.188422i
$339$	−18.0000	−	31.1769i	−0.977626	−	1.69330i
$340$	1.00000	+	1.73205i	0.0542326	+	0.0939336i
$341$	12.0000			0.649836
$342$		0			0
$343$	15.0000			0.809924
$344$	5.00000	+	8.66025i	0.269582	+	0.466930i
$345$	−15.0000	−	25.9808i	−0.807573	−	1.39876i
$346$	9.00000	−	15.5885i	0.483843	−	0.838041i
$347$	−8.00000	−	13.8564i	−0.429463	−	0.743851i	0.567363	−	0.823468i	$-0.307964\pi$
$347$	−8.00000	−	13.8564i	−0.429463	−	0.743851i	−0.996826	+	0.0796169i	$0.974630\pi$
$348$	4.50000	−	7.79423i	0.241225	−	0.417815i
$349$	28.0000			1.49881			0.749403	−	0.662114i	$-0.230341\pi$
$349$	28.0000			1.49881			0.749403	+	0.662114i	$0.230341\pi$
$350$	3.00000			0.160357
$351$	13.5000	−	23.3827i	0.720577	−	1.24808i
$352$	1.00000	−	1.73205i	0.0533002	−	0.0923186i
$353$	−31.0000			−1.64996			−0.824982	−	0.565159i	$-0.808815\pi$
$353$	−31.0000			−1.64996			−0.824982	+	0.565159i	$0.808815\pi$
$354$	9.00000			0.478345
$355$		0			0
$356$	−3.00000	−	5.19615i	−0.159000	−	0.275396i
$357$	−4.50000	+	7.79423i	−0.238165	+	0.412514i
$358$	6.00000	+	10.3923i	0.317110	+	0.549250i
$359$	−9.50000	−	16.4545i	−0.501391	−	0.868434i	−0.999999	−	0.00160673i	$-0.999489\pi$
$359$	−9.50000	−	16.4545i	−0.501391	−	0.868434i	0.498608	−	0.866828i	$-0.333845\pi$
$360$	12.0000			0.632456
$361$		0			0
$362$	18.0000			0.946059
$363$	10.5000	+	18.1865i	0.551107	+	0.954545i
$364$	−4.50000	−	7.79423i	−0.235864	−	0.408529i
$365$	11.0000	−	19.0526i	0.575766	−	0.997257i
$366$		0			0
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$	5.00000			0.260643
$369$	72.0000			3.74817
$370$	−6.00000	+	10.3923i	−0.311925	+	0.540270i
$371$	−4.50000	+	7.79423i	−0.233628	+	0.404656i
$372$	−18.0000			−0.933257
$373$	−21.0000			−1.08734			−0.543669	−	0.839299i	$-0.682965\pi$
$373$	−21.0000			−1.08734			−0.543669	+	0.839299i	$0.682965\pi$
$374$	−1.00000	+	1.73205i	−0.0517088	+	0.0895622i
$375$	18.0000	+	31.1769i	0.929516	+	1.60997i
$376$	4.00000	−	6.92820i	0.206284	−	0.357295i
$377$	−4.50000	−	7.79423i	−0.231762	−	0.401423i
$378$	13.5000	+	23.3827i	0.694365	+	1.20268i
$379$	3.00000			0.154100			0.0770498	−	0.997027i	$-0.475450\pi$
$379$	3.00000			0.154100			0.0770498	+	0.997027i	$0.475450\pi$
$380$		0			0
$381$	36.0000			1.84434
$382$	5.50000	+	9.52628i	0.281404	+	0.487407i
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	0.539076	−	0.842257i	$-0.318774\pi$
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	−0.998954	+	0.0457244i	$0.985440\pi$
$384$	−1.50000	+	2.59808i	−0.0765466	+	0.132583i
$385$	−6.00000	−	10.3923i	−0.305788	−	0.529641i
$386$	−3.00000	+	5.19615i	−0.152696	+	0.264477i
$387$	−60.0000			−3.04997
$388$	12.0000			0.609208
$389$	−13.0000	+	22.5167i	−0.659126	+	1.14164i	0.321716	+	0.946836i	$0.395740\pi$
$389$	−13.0000	+	22.5167i	−0.659126	+	1.14164i	−0.980842	+	0.194804i	$0.937593\pi$
$390$	9.00000	−	15.5885i	0.455733	−	0.789352i
$391$	−5.00000			−0.252861
$392$	2.00000			0.101015
$393$	−21.0000	+	36.3731i	−1.05931	+	1.83478i
$394$	−2.00000	−	3.46410i	−0.100759	−	0.174519i
$395$	12.0000	−	20.7846i	0.603786	−	1.04579i
$396$	6.00000	+	10.3923i	0.301511	+	0.522233i
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	0.839840	−	0.542834i	$-0.182649\pi$
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	−0.890028	+	0.455905i	$0.849316\pi$
$398$	−7.00000			−0.350878
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−18.0000	−	31.1769i	−0.898877	−	1.55690i	−0.828932	−	0.559350i	$-0.811051\pi$
$401$	−18.0000	−	31.1769i	−0.898877	−	1.55690i	−0.0699455	−	0.997551i	$-0.522283\pi$
$402$	−22.5000	−	38.9711i	−1.12220	−	1.94370i
$403$	−9.00000	+	15.5885i	−0.448322	+	0.776516i
$404$	−5.00000	−	8.66025i	−0.248759	−	0.430864i
$405$	−9.00000	+	15.5885i	−0.447214	+	0.774597i
$406$	9.00000			0.446663
$407$	−12.0000			−0.594818
$408$	1.50000	−	2.59808i	0.0742611	−	0.128624i
$409$	−3.00000	+	5.19615i	−0.148340	+	0.256933i	−0.930614	−	0.366002i	$-0.880726\pi$
$409$	−3.00000	+	5.19615i	−0.148340	+	0.256933i	0.782274	+	0.622935i	$0.214060\pi$
$410$	24.0000			1.18528
$411$	57.0000			2.81160
$412$	−3.00000	+	5.19615i	−0.147799	+	0.255996i
$413$	4.50000	+	7.79423i	0.221431	+	0.383529i
$414$	−15.0000	+	25.9808i	−0.737210	+	1.27688i
$415$	−2.00000	−	3.46410i	−0.0981761	−	0.170046i
$416$	1.50000	+	2.59808i	0.0735436	+	0.127381i
$417$	18.0000			0.881464
$418$		0			0
$419$	−14.0000			−0.683945			−0.341972	−	0.939710i	$-0.611095\pi$
$419$	−14.0000			−0.683945			−0.341972	+	0.939710i	$0.611095\pi$
$420$	9.00000	+	15.5885i	0.439155	+	0.760639i
$421$	13.5000	+	23.3827i	0.657950	+	1.13960i	0.981146	+	0.193270i	$0.0619094\pi$
$421$	13.5000	+	23.3827i	0.657950	+	1.13960i	−0.323196	+	0.946332i	$0.604757\pi$
$422$	−1.50000	+	2.59808i	−0.0730189	+	0.126472i
$423$	24.0000	+	41.5692i	1.16692	+	2.02116i
$424$	1.50000	−	2.59808i	0.0728464	−	0.126174i
$425$	1.00000			0.0485071
$426$		0			0
$427$		0			0
$428$	1.50000	−	2.59808i	0.0725052	−	0.125583i
$429$	18.0000			0.869048
$430$	−20.0000			−0.964486
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	0.417687	+	0.908591i	$0.362841\pi$
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	−0.995706	+	0.0925683i	$0.970492\pi$
$432$	−4.50000	−	7.79423i	−0.216506	−	0.375000i
$433$	−15.0000	+	25.9808i	−0.720854	+	1.24856i	0.239804	+	0.970821i	$0.422917\pi$
$433$	−15.0000	+	25.9808i	−0.720854	+	1.24856i	−0.960658	+	0.277734i	$0.910416\pi$
$434$	−9.00000	−	15.5885i	−0.432014	−	0.748270i
$435$	9.00000	+	15.5885i	0.431517	+	0.747409i
$436$	3.00000			0.143674
$437$		0			0
$438$	−33.0000			−1.57680
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$	2.00000	+	3.46410i	0.0953463	+	0.165145i
$441$	−6.00000	+	10.3923i	−0.285714	+	0.494872i
$442$	−1.50000	−	2.59808i	−0.0713477	−	0.123578i
$443$	11.0000	−	19.0526i	0.522626	−	0.905214i	−0.477028	−	0.878888i	$-0.658286\pi$
$443$	11.0000	−	19.0526i	0.522626	−	0.905214i	0.999653	−	0.0263261i	$-0.00838082\pi$
$444$	18.0000			0.854242
$445$	12.0000			0.568855
$446$	−9.00000	+	15.5885i	−0.426162	+	0.738135i
$447$	12.0000	−	20.7846i	0.567581	−	0.983078i
$448$	−3.00000			−0.141737
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	3.00000	−	5.19615i	0.141421	−	0.244949i
$451$	12.0000	+	20.7846i	0.565058	+	0.978709i
$452$	−6.00000	+	10.3923i	−0.282216	+	0.488813i
$453$	27.0000	+	46.7654i	1.26857	+	2.19723i
$454$	−1.50000	−	2.59808i	−0.0703985	−	0.121934i
$455$	18.0000			0.843853
$456$		0			0
$457$	1.00000			0.0467780			0.0233890	−	0.999726i	$-0.492554\pi$
$457$	1.00000			0.0467780			0.0233890	+	0.999726i	$0.492554\pi$
$458$	6.00000	+	10.3923i	0.280362	+	0.485601i
$459$	4.50000	+	7.79423i	0.210042	+	0.363803i
$460$	−5.00000	+	8.66025i	−0.233126	+	0.403786i
$461$	−2.00000	−	3.46410i	−0.0931493	−	0.161339i	0.815685	−	0.578496i	$-0.196360\pi$
$461$	−2.00000	−	3.46410i	−0.0931493	−	0.161339i	−0.908835	+	0.417156i	$0.863027\pi$
$462$	−9.00000	+	15.5885i	−0.418718	+	0.725241i
$463$	32.0000			1.48717			0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000			1.48717			0.743583	+	0.668644i	$0.233125\pi$
$464$	−3.00000			−0.139272
$465$	18.0000	−	31.1769i	0.834730	−	1.44579i
$466$	−7.00000	+	12.1244i	−0.324269	+	0.561650i
$467$	8.00000			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$	−18.0000			−0.832050
$469$	22.5000	−	38.9711i	1.03895	−	1.79952i
$470$	8.00000	+	13.8564i	0.369012	+	0.639148i
$471$		0			0
$472$	−1.50000	−	2.59808i	−0.0690431	−	0.119586i
$473$	−10.0000	−	17.3205i	−0.459800	−	0.796398i
$474$	−36.0000			−1.65353
$475$		0			0
$476$	3.00000			0.137505
$477$	9.00000	+	15.5885i	0.412082	+	0.713746i
$478$	−0.500000	−	0.866025i	−0.0228695	−	0.0396111i
$479$	20.0000	−	34.6410i	0.913823	−	1.58279i	0.105208	−	0.994450i	$-0.466449\pi$
$479$	20.0000	−	34.6410i	0.913823	−	1.58279i	0.808615	−	0.588338i	$-0.200218\pi$
$480$	−3.00000	−	5.19615i	−0.136931	−	0.237171i
$481$	9.00000	−	15.5885i	0.410365	−	0.710772i
$482$	24.0000			1.09317
$483$	−45.0000			−2.04757
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	−12.0000	+	20.7846i	−0.544892	+	0.943781i
$486$		0			0
$487$	−18.0000			−0.815658			−0.407829	−	0.913058i	$-0.633714\pi$
$487$	−18.0000			−0.815658			−0.407829	+	0.913058i	$0.633714\pi$
$488$		0			0
$489$	9.00000	+	15.5885i	0.406994	+	0.704934i
$490$	−2.00000	+	3.46410i	−0.0903508	+	0.156492i
$491$	−4.00000	−	6.92820i	−0.180517	−	0.312665i	0.761539	−	0.648119i	$-0.224444\pi$
$491$	−4.00000	−	6.92820i	−0.180517	−	0.312665i	−0.942057	+	0.335453i	$0.891111\pi$
$492$	−18.0000	−	31.1769i	−0.811503	−	1.40556i
$493$	3.00000			0.135113
$494$		0			0
$495$	−24.0000			−1.07872
$496$	3.00000	+	5.19615i	0.134704	+	0.233314i
$497$		0			0
$498$	−3.00000	+	5.19615i	−0.134433	+	0.232845i
$499$	−9.00000	−	15.5885i	−0.402895	−	0.697835i	0.591179	−	0.806541i	$-0.298663\pi$
$499$	−9.00000	−	15.5885i	−0.402895	−	0.697835i	−0.994074	+	0.108705i	$0.965329\pi$
$500$	6.00000	−	10.3923i	0.268328	−	0.464758i
$501$	−36.0000			−1.60836
$502$	−20.0000			−0.892644
$503$	−0.500000	+	0.866025i	−0.0222939	+	0.0386142i	−0.876957	−	0.480569i	$-0.840430\pi$
$503$	−0.500000	+	0.866025i	−0.0222939	+	0.0386142i	0.854663	+	0.519183i	$0.173764\pi$
$504$	9.00000	−	15.5885i	0.400892	−	0.694365i
$505$	20.0000			0.889988
$506$	−10.0000			−0.444554
$507$	6.00000	−	10.3923i	0.266469	−	0.461538i
$508$	−6.00000	−	10.3923i	−0.266207	−	0.461084i
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	−0.993593	−	0.113020i	$-0.963948\pi$
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	0.594675	+	0.803966i	$0.297281\pi$
$510$	3.00000	+	5.19615i	0.132842	+	0.230089i
$511$	−16.5000	−	28.5788i	−0.729917	−	1.26425i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−18.0000			−0.793946
$515$	−6.00000	−	10.3923i	−0.264392	−	0.457940i
$516$	15.0000	+	25.9808i	0.660338	+	1.14374i
$517$	−8.00000	+	13.8564i	−0.351840	+	0.609404i
$518$	9.00000	+	15.5885i	0.395437	+	0.684917i
$519$	27.0000	−	46.7654i	1.18517	−	2.05277i
$520$	−6.00000			−0.263117
$521$	−12.0000			−0.525730			−0.262865	−	0.964833i	$-0.584667\pi$
$521$	−12.0000			−0.525730			−0.262865	+	0.964833i	$0.584667\pi$
$522$	9.00000	−	15.5885i	0.393919	−	0.682288i
$523$	−4.50000	+	7.79423i	−0.196771	+	0.340818i	−0.947480	−	0.319816i	$-0.896379\pi$
$523$	−4.50000	+	7.79423i	−0.196771	+	0.340818i	0.750708	+	0.660634i	$0.229712\pi$
$524$	14.0000			0.611593
$525$	9.00000			0.392792
$526$	4.00000	−	6.92820i	0.174408	−	0.302084i
$527$	−3.00000	−	5.19615i	−0.130682	−	0.226348i
$528$	3.00000	−	5.19615i	0.130558	−	0.226134i
$529$	−1.00000	−	1.73205i	−0.0434783	−	0.0753066i
$530$	3.00000	+	5.19615i	0.130312	+	0.225706i
$531$	18.0000			0.781133
$532$		0			0
$533$	−36.0000			−1.55933
$534$	−9.00000	−	15.5885i	−0.389468	−	0.674579i
$535$	3.00000	+	5.19615i	0.129701	+	0.224649i
$536$	−7.50000	+	12.9904i	−0.323951	+	0.561099i
$537$	18.0000	+	31.1769i	0.776757	+	1.34538i
$538$	3.00000	−	5.19615i	0.129339	−	0.224022i
$539$	−4.00000			−0.172292
$540$	18.0000			0.774597
$541$	−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	$0.180356\pi$
$542$	5.50000	−	9.52628i	0.236245	−	0.409189i
$543$	54.0000			2.31736
$544$	−1.00000			−0.0428746
$545$	−3.00000	+	5.19615i	−0.128506	+	0.222579i
$546$	−13.5000	−	23.3827i	−0.577747	−	1.00069i
$547$	18.0000	−	31.1769i	0.769624	−	1.33303i	−0.168142	−	0.985763i	$-0.553777\pi$
$547$	18.0000	−	31.1769i	0.769624	−	1.33303i	0.937767	−	0.347266i	$-0.112890\pi$
$548$	−9.50000	−	16.4545i	−0.405820	−	0.702901i
$549$		0			0
$550$	2.00000			0.0852803
$551$		0			0
$552$	15.0000			0.638442
$553$	−18.0000	−	31.1769i	−0.765438	−	1.32578i
$554$	−15.0000	−	25.9808i	−0.637289	−	1.10382i
$555$	−18.0000	+	31.1769i	−0.764057	+	1.32339i
$556$	−3.00000	−	5.19615i	−0.127228	−	0.220366i
$557$	−11.0000	+	19.0526i	−0.466085	+	0.807283i	−0.999250	−	0.0387286i	$-0.987669\pi$
$557$	−11.0000	+	19.0526i	−0.466085	+	0.807283i	0.533165	+	0.846011i	$0.321003\pi$
$558$	−36.0000			−1.52400
$559$	30.0000			1.26886
$560$	3.00000	−	5.19615i	0.126773	−	0.219578i
$561$	−3.00000	+	5.19615i	−0.126660	+	0.219382i
$562$	12.0000			0.506189
$563$	−24.0000			−1.01148			−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000			−1.01148			−0.505740	+	0.862686i	$0.668780\pi$
$564$	12.0000	−	20.7846i	0.505291	−	0.875190i
$565$	−12.0000	−	20.7846i	−0.504844	−	0.874415i
$566$	7.00000	−	12.1244i	0.294232	−	0.509625i
$567$	13.5000	+	23.3827i	0.566947	+	0.981981i
$568$		0			0
$569$	−24.0000			−1.00613			−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000			−1.00613			−0.503066	+	0.864248i	$0.667795\pi$
$570$		0			0
$571$	−32.0000			−1.33916			−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000			−1.33916			−0.669579	+	0.742741i	$0.733526\pi$
$572$	−3.00000	−	5.19615i	−0.125436	−	0.217262i
$573$	16.5000	+	28.5788i	0.689297	+	1.19390i
$574$	18.0000	−	31.1769i	0.751305	−	1.30130i
$575$	2.50000	+	4.33013i	0.104257	+	0.180579i
$576$	−3.00000	+	5.19615i	−0.125000	+	0.216506i
$577$	15.0000			0.624458			0.312229	−	0.950007i	$-0.398924\pi$
$577$	15.0000			0.624458			0.312229	+	0.950007i	$0.398924\pi$
$578$	−16.0000			−0.665512
$579$	−9.00000	+	15.5885i	−0.374027	+	0.647834i
$580$	3.00000	−	5.19615i	0.124568	−	0.215758i
$581$	−6.00000			−0.248922
$582$	36.0000			1.49225
$583$	−3.00000	+	5.19615i	−0.124247	+	0.215203i
$584$	5.50000	+	9.52628i	0.227592	+	0.394200i
$585$	18.0000	−	31.1769i	0.744208	−	1.28901i
$586$	4.50000	+	7.79423i	0.185893	+	0.321977i
$587$	14.0000	+	24.2487i	0.577842	+	1.00085i	0.995726	+	0.0923513i	$0.0294383\pi$
$587$	14.0000	+	24.2487i	0.577842	+	1.00085i	−0.417885	+	0.908500i	$0.637228\pi$
$588$	6.00000			0.247436
$589$		0			0
$590$	6.00000			0.247016
$591$	−6.00000	−	10.3923i	−0.246807	−	0.427482i
$592$	−3.00000	−	5.19615i	−0.123299	−	0.213561i
$593$	1.00000	−	1.73205i	0.0410651	−	0.0711268i	−0.844762	−	0.535142i	$-0.820258\pi$
$593$	1.00000	−	1.73205i	0.0410651	−	0.0711268i	0.885827	+	0.464015i	$0.153592\pi$
$594$	9.00000	+	15.5885i	0.369274	+	0.639602i
$595$	−3.00000	+	5.19615i	−0.122988	+	0.213021i
$596$	−8.00000			−0.327693
$597$	−21.0000			−0.859473
$598$	7.50000	−	12.9904i	0.306698	−	0.531216i
$599$	18.0000	−	31.1769i	0.735460	−	1.27385i	−0.219061	−	0.975711i	$-0.570299\pi$
$599$	18.0000	−	31.1769i	0.735460	−	1.27385i	0.954521	−	0.298143i	$-0.0963673\pi$
$600$	−3.00000			−0.122474
$601$	−6.00000			−0.244745			−0.122373	−	0.992484i	$-0.539050\pi$
$601$	−6.00000			−0.244745			−0.122373	+	0.992484i	$0.539050\pi$
$602$	−15.0000	+	25.9808i	−0.611354	+	1.05890i
$603$	−45.0000	−	77.9423i	−1.83254	−	3.17406i
$604$	9.00000	−	15.5885i	0.366205	−	0.634285i
$605$	7.00000	+	12.1244i	0.284590	+	0.492925i
$606$	−15.0000	−	25.9808i	−0.609333	−	1.05540i
$607$	−12.0000			−0.487065			−0.243532	−	0.969893i	$-0.578306\pi$
$607$	−12.0000			−0.487065			−0.243532	+	0.969893i	$0.578306\pi$
$608$		0			0
$609$	27.0000			1.09410
$610$		0			0
$611$	−12.0000	−	20.7846i	−0.485468	−	0.840855i
$612$	3.00000	−	5.19615i	0.121268	−	0.210042i
$613$	−9.00000	−	15.5885i	−0.363507	−	0.629612i	0.625029	−	0.780602i	$-0.285087\pi$
$613$	−9.00000	−	15.5885i	−0.363507	−	0.629612i	−0.988535	+	0.150990i	$0.951754\pi$
$614$	−6.00000	+	10.3923i	−0.242140	+	0.419399i
$615$	72.0000			2.90332
$616$	6.00000			0.241747
$617$	−5.00000	+	8.66025i	−0.201292	+	0.348649i	−0.948945	−	0.315441i	$-0.897847\pi$
$617$	−5.00000	+	8.66025i	−0.201292	+	0.348649i	0.747653	+	0.664090i	$0.231181\pi$
$618$	−9.00000	+	15.5885i	−0.362033	+	0.627060i
$619$	−24.0000			−0.964641			−0.482321	−	0.875995i	$-0.660206\pi$
$619$	−24.0000			−0.964641			−0.482321	+	0.875995i	$0.660206\pi$
$620$	−12.0000			−0.481932
$621$	−22.5000	+	38.9711i	−0.902894	+	1.56386i
$622$	5.50000	+	9.52628i	0.220530	+	0.381969i
$623$	9.00000	−	15.5885i	0.360577	−	0.624538i
$624$	4.50000	+	7.79423i	0.180144	+	0.312019i
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	21.0000			0.839329
$627$		0			0
$628$		0			0
$629$	3.00000	+	5.19615i	0.119618	+	0.207184i
$630$	18.0000	+	31.1769i	0.717137	+	1.24212i
$631$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$631$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$632$	6.00000	+	10.3923i	0.238667	+	0.413384i
$633$	−4.50000	+	7.79423i	−0.178859	+	0.309793i
$634$	−33.0000			−1.31060
$635$	24.0000			0.952411
$636$	4.50000	−	7.79423i	0.178437	−	0.309061i
$637$	3.00000	−	5.19615i	0.118864	−	0.205879i
$638$	6.00000			0.237542
$639$		0			0
$640$	−1.00000	+	1.73205i	−0.0395285	+	0.0684653i
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	0.631721	−	0.775196i	$-0.282349\pi$
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	−0.987200	+	0.159489i	$0.949015\pi$
$642$	4.50000	−	7.79423i	0.177601	−	0.307614i
$643$	−16.0000	−	27.7128i	−0.630978	−	1.09289i	−0.987352	−	0.158543i	$-0.949320\pi$
$643$	−16.0000	−	27.7128i	−0.630978	−	1.09289i	0.356374	−	0.934344i	$-0.384013\pi$
$644$	7.50000	+	12.9904i	0.295541	+	0.511893i
$645$	−60.0000			−2.36250
$646$		0			0
$647$	−23.0000			−0.904223			−0.452112	−	0.891961i	$-0.649329\pi$
$647$	−23.0000			−0.904223			−0.452112	+	0.891961i	$0.649329\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	3.00000	+	5.19615i	0.117760	+	0.203967i
$650$	−1.50000	+	2.59808i	−0.0588348	+	0.101905i
$651$	−27.0000	−	46.7654i	−1.05821	−	1.83288i
$652$	3.00000	−	5.19615i	0.117489	−	0.203497i
$653$	−10.0000			−0.391330			−0.195665	−	0.980671i	$-0.562687\pi$
$653$	−10.0000			−0.391330			−0.195665	+	0.980671i	$0.562687\pi$
$654$	9.00000			0.351928
$655$	−14.0000	+	24.2487i	−0.547025	+	0.947476i
$656$	−6.00000	+	10.3923i	−0.234261	+	0.405751i
$657$	−66.0000			−2.57491
$658$	24.0000			0.935617
$659$	7.50000	−	12.9904i	0.292159	−	0.506033i	−0.682161	−	0.731202i	$-0.738960\pi$
$659$	7.50000	−	12.9904i	0.292159	−	0.506033i	0.974320	+	0.225168i	$0.0722932\pi$
$660$	6.00000	+	10.3923i	0.233550	+	0.404520i
$661$	−7.50000	+	12.9904i	−0.291716	+	0.505267i	−0.974216	−	0.225619i	$-0.927560\pi$
$661$	−7.50000	+	12.9904i	−0.291716	+	0.505267i	0.682499	+	0.730886i	$0.260893\pi$
$662$	−4.50000	−	7.79423i	−0.174897	−	0.302931i
$663$	−4.50000	−	7.79423i	−0.174766	−	0.302703i
$664$	2.00000			0.0776151
$665$		0			0
$666$	36.0000			1.39497
$667$	7.50000	+	12.9904i	0.290401	+	0.502990i
$668$	6.00000	+	10.3923i	0.232147	+	0.402090i
$669$	−27.0000	+	46.7654i	−1.04388	+	1.80805i
$670$	−15.0000	−	25.9808i	−0.579501	−	1.00372i
$671$		0			0
$672$	−9.00000			−0.347183
$673$	−48.0000			−1.85026			−0.925132	−	0.379646i	$-0.876046\pi$
$673$	−48.0000			−1.85026			−0.925132	+	0.379646i	$0.876046\pi$
$674$	−9.00000	+	15.5885i	−0.346667	+	0.600445i
$675$	4.50000	−	7.79423i	0.173205	−	0.300000i
$676$	−4.00000			−0.153846
$677$	3.00000			0.115299			0.0576497	−	0.998337i	$-0.481639\pi$
$677$	3.00000			0.115299			0.0576497	+	0.998337i	$0.481639\pi$
$678$	−18.0000	+	31.1769i	−0.691286	+	1.19734i
$679$	18.0000	+	31.1769i	0.690777	+	1.19646i
$680$	1.00000	−	1.73205i	0.0383482	−	0.0664211i
$681$	−4.50000	−	7.79423i	−0.172440	−	0.298675i
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$		0			0
$685$	38.0000			1.45191
$686$	−7.50000	−	12.9904i	−0.286351	−	0.495975i
$687$	18.0000	+	31.1769i	0.686743	+	1.18947i
$688$	5.00000	−	8.66025i	0.190623	−	0.330169i
$689$	−4.50000	−	7.79423i	−0.171436	−	0.296936i
$690$	−15.0000	+	25.9808i	−0.571040	+	0.989071i
$691$	−8.00000			−0.304334			−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000			−0.304334			−0.152167	+	0.988355i	$0.548625\pi$
$692$	−18.0000			−0.684257
$693$	−18.0000	+	31.1769i	−0.683763	+	1.18431i
$694$	−8.00000	+	13.8564i	−0.303676	+	0.525982i
$695$	12.0000			0.455186
$696$	−9.00000			−0.341144
$697$	6.00000	−	10.3923i	0.227266	−	0.393637i
$698$	−14.0000	−	24.2487i	−0.529908	−	0.917827i
$699$	−21.0000	+	36.3731i	−0.794293	+	1.37576i
$700$	−1.50000	−	2.59808i	−0.0566947	−	0.0981981i
$701$	20.0000	+	34.6410i	0.755390	+	1.30837i	0.945180	+	0.326549i	$0.105886\pi$
$701$	20.0000	+	34.6410i	0.755390	+	1.30837i	−0.189791	+	0.981825i	$0.560781\pi$
$702$	−27.0000			−1.01905
$703$		0			0
$704$	−2.00000			−0.0753778
$705$	24.0000	+	41.5692i	0.903892	+	1.56559i
$706$	15.5000	+	26.8468i	0.583350	+	1.01039i
$707$	15.0000	−	25.9808i	0.564133	−	0.977107i
$708$	−4.50000	−	7.79423i	−0.169120	−	0.292925i
$709$	4.00000	−	6.92820i	0.150223	−	0.260194i	−0.781086	−	0.624423i	$-0.785334\pi$
$709$	4.00000	−	6.92820i	0.150223	−	0.260194i	0.931309	+	0.364229i	$0.118667\pi$
$710$		0			0
$711$	−72.0000			−2.70021
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$	15.0000	−	25.9808i	0.561754	−	0.972987i
$714$	9.00000			0.336817
$715$	12.0000			0.448775
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$	−1.50000	−	2.59808i	−0.0560185	−	0.0970269i
$718$	−9.50000	+	16.4545i	−0.354537	+	0.614076i
$719$	21.5000	+	37.2391i	0.801815	+	1.38878i	0.918421	+	0.395606i	$0.129465\pi$
$719$	21.5000	+	37.2391i	0.801815	+	1.38878i	−0.116606	+	0.993178i	$0.537201\pi$
$720$	−6.00000	−	10.3923i	−0.223607	−	0.387298i
$721$	−18.0000			−0.670355
$722$		0			0
$723$	72.0000			2.67771
$724$	−9.00000	−	15.5885i	−0.334482	−	0.579340i
$725$	−1.50000	−	2.59808i	−0.0557086	−	0.0964901i
$726$	10.5000	−	18.1865i	0.389692	−	0.674966i
$727$	17.5000	+	30.3109i	0.649039	+	1.12417i	0.983353	+	0.181707i	$0.0581622\pi$
$727$	17.5000	+	30.3109i	0.649039	+	1.12417i	−0.334314	+	0.942462i	$0.608504\pi$
$728$	−4.50000	+	7.79423i	−0.166781	+	0.288873i
$729$	−27.0000			−1.00000
$730$	−22.0000			−0.814257
$731$	−5.00000	+	8.66025i	−0.184932	+	0.320311i
$732$		0			0
$733$	−22.0000			−0.812589			−0.406294	−	0.913742i	$-0.633179\pi$
$733$	−22.0000			−0.812589			−0.406294	+	0.913742i	$0.633179\pi$
$734$	8.00000			0.295285
$735$	−6.00000	+	10.3923i	−0.221313	+	0.383326i
$736$	−2.50000	−	4.33013i	−0.0921512	−	0.159611i
$737$	15.0000	−	25.9808i	0.552532	−	0.957014i
$738$	−36.0000	−	62.3538i	−1.32518	−	2.29528i
$739$	6.00000	+	10.3923i	0.220714	+	0.382287i	0.955025	−	0.296526i	$-0.0958281\pi$
$739$	6.00000	+	10.3923i	0.220714	+	0.382287i	−0.734311	+	0.678813i	$0.762495\pi$
$740$	12.0000			0.441129
$741$		0			0
$742$	9.00000			0.330400
$743$	−3.00000	−	5.19615i	−0.110059	−	0.190628i	0.805735	−	0.592277i	$-0.201771\pi$
$743$	−3.00000	−	5.19615i	−0.110059	−	0.190628i	−0.915794	+	0.401648i	$0.868437\pi$
$744$	9.00000	+	15.5885i	0.329956	+	0.571501i
$745$	8.00000	−	13.8564i	0.293097	−	0.507659i
$746$	10.5000	+	18.1865i	0.384432	+	0.665856i
$747$	−6.00000	+	10.3923i	−0.219529	+	0.380235i
$748$	2.00000			0.0731272
$749$	9.00000			0.328853
$750$	18.0000	−	31.1769i	0.657267	−	1.13842i
$751$	−6.00000	+	10.3923i	−0.218943	+	0.379221i	−0.954485	−	0.298259i	$-0.903594\pi$
$751$	−6.00000	+	10.3923i	−0.218943	+	0.379221i	0.735542	+	0.677479i	$0.236928\pi$
$752$	−8.00000			−0.291730
$753$	−60.0000			−2.18652
$754$	−4.50000	+	7.79423i	−0.163880	+	0.283849i
$755$	18.0000	+	31.1769i	0.655087	+	1.13464i
$756$	13.5000	−	23.3827i	0.490990	−	0.850420i
$757$	−6.00000	−	10.3923i	−0.218074	−	0.377715i	0.736145	−	0.676824i	$-0.236644\pi$
$757$	−6.00000	−	10.3923i	−0.218074	−	0.377715i	−0.954219	+	0.299109i	$0.903311\pi$
$758$	−1.50000	−	2.59808i	−0.0544825	−	0.0943664i
$759$	−30.0000			−1.08893
$760$		0			0
$761$	−13.0000			−0.471250			−0.235625	−	0.971844i	$-0.575714\pi$
$761$	−13.0000			−0.471250			−0.235625	+	0.971844i	$0.575714\pi$
$762$	−18.0000	−	31.1769i	−0.652071	−	1.12942i
$763$	4.50000	+	7.79423i	0.162911	+	0.282170i
$764$	5.50000	−	9.52628i	0.198983	−	0.344649i
$765$	6.00000	+	10.3923i	0.216930	+	0.375735i
$766$	−9.00000	+	15.5885i	−0.325183	+	0.563234i
$767$	−9.00000			−0.324971
$768$	3.00000			0.108253
$769$	7.50000	−	12.9904i	0.270457	−	0.468445i	−0.698522	−	0.715589i	$-0.746159\pi$
$769$	7.50000	−	12.9904i	0.270457	−	0.468445i	0.968979	+	0.247143i	$0.0794919\pi$
$770$	−6.00000	+	10.3923i	−0.216225	+	0.374513i
$771$	−54.0000			−1.94476
$772$	6.00000			0.215945
$773$	−7.50000	+	12.9904i	−0.269756	+	0.467232i	−0.968799	−	0.247849i	$-0.920276\pi$
$773$	−7.50000	+	12.9904i	−0.269756	+	0.467232i	0.699043	+	0.715080i	$0.253610\pi$
$774$	30.0000	+	51.9615i	1.07833	+	1.86772i
$775$	−3.00000	+	5.19615i	−0.107763	+	0.186651i
$776$	−6.00000	−	10.3923i	−0.215387	−	0.373062i
$777$	27.0000	+	46.7654i	0.968620	+	1.67770i
$778$	26.0000			0.932145
$779$		0			0
$780$	−18.0000			−0.644503
$781$		0			0
$782$	2.50000	+	4.33013i	0.0893998	+	0.154845i
$783$	13.5000	−	23.3827i	0.482451	−	0.835629i
$784$	−1.00000	−	1.73205i	−0.0357143	−	0.0618590i
$785$		0			0
$786$	42.0000			1.49809
$787$	−9.00000			−0.320815			−0.160408	−	0.987051i	$-0.551281\pi$
$787$	−9.00000			−0.320815			−0.160408	+	0.987051i	$0.551281\pi$
$788$	−2.00000	+	3.46410i	−0.0712470	+	0.123404i
$789$	12.0000	−	20.7846i	0.427211	−	0.739952i
$790$	−24.0000			−0.853882
$791$	−36.0000			−1.28001
$792$	6.00000	−	10.3923i	0.213201	−	0.369274i
$793$		0			0
$794$	−1.00000	+	1.73205i	−0.0354887	+	0.0614682i
$795$	9.00000	+	15.5885i	0.319197	+	0.552866i
$796$	3.50000	+	6.06218i	0.124054	+	0.214868i
$797$	33.0000			1.16892			0.584460	−	0.811423i	$-0.301306\pi$
$797$	33.0000			1.16892			0.584460	+	0.811423i	$0.301306\pi$
$798$		0			0
$799$	8.00000			0.283020
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−18.0000	−	31.1769i	−0.635999	−	1.10158i
$802$	−18.0000	+	31.1769i	−0.635602	+	1.10090i
$803$	−11.0000	−	19.0526i	−0.388182	−	0.672350i
$804$	−22.5000	+	38.9711i	−0.793514	+	1.37441i
$805$	−30.0000			−1.05736
$806$	18.0000			0.634023
$807$	9.00000	−	15.5885i	0.316815	−	0.548740i
$808$	−5.00000	+	8.66025i	−0.175899	+	0.304667i
$809$	−11.0000			−0.386739			−0.193370	−	0.981126i	$-0.561942\pi$
$809$	−11.0000			−0.386739			−0.193370	+	0.981126i	$0.561942\pi$
$810$	18.0000			0.632456
$811$	−16.5000	+	28.5788i	−0.579393	+	1.00354i	0.416156	+	0.909293i	$0.363377\pi$
$811$	−16.5000	+	28.5788i	−0.579393	+	1.00354i	−0.995549	+	0.0942453i	$0.969956\pi$
$812$	−4.50000	−	7.79423i	−0.157919	−	0.273524i
$813$	16.5000	−	28.5788i	0.578680	−	1.00230i
$814$	6.00000	+	10.3923i	0.210300	+	0.364250i
$815$	6.00000	+	10.3923i	0.210171	+	0.364027i
$816$	−3.00000			−0.105021
$817$		0			0
$818$	6.00000			0.209785
$819$	−27.0000	−	46.7654i	−0.943456	−	1.63411i
$820$	−12.0000	−	20.7846i	−0.419058	−	0.725830i
$821$	−1.00000	+	1.73205i	−0.0349002	+	0.0604490i	−0.882948	−	0.469471i	$-0.844445\pi$
$821$	−1.00000	+	1.73205i	−0.0349002	+	0.0604490i	0.848048	+	0.529920i	$0.177778\pi$
$822$	−28.5000	−	49.3634i	−0.994052	−	1.72175i
$823$	−1.50000	+	2.59808i	−0.0522867	+	0.0905632i	−0.890984	−	0.454034i	$-0.849984\pi$
$823$	−1.50000	+	2.59808i	−0.0522867	+	0.0905632i	0.838697	+	0.544598i	$0.183318\pi$
$824$	6.00000			0.209020
$825$	6.00000			0.208893
$826$	4.50000	−	7.79423i	0.156575	−	0.271196i
$827$	−7.50000	+	12.9904i	−0.260801	+	0.451720i	−0.966455	−	0.256836i	$-0.917320\pi$
$827$	−7.50000	+	12.9904i	−0.260801	+	0.451720i	0.705654	+	0.708556i	$0.250653\pi$
$828$	30.0000			1.04257
$829$	51.0000			1.77130			0.885652	−	0.464350i	$-0.153712\pi$
$829$	51.0000			1.77130			0.885652	+	0.464350i	$0.153712\pi$
$830$	−2.00000	+	3.46410i	−0.0694210	+	0.120241i
$831$	−45.0000	−	77.9423i	−1.56103	−	2.70379i
$832$	1.50000	−	2.59808i	0.0520031	−	0.0900721i
$833$	1.00000	+	1.73205i	0.0346479	+	0.0600120i
$834$	−9.00000	−	15.5885i	−0.311645	−	0.539784i
$835$	−24.0000			−0.830554
$836$		0			0
$837$	−54.0000			−1.86651
$838$	7.00000	+	12.1244i	0.241811	+	0.418829i
$839$	9.00000	+	15.5885i	0.310715	+	0.538173i	0.978517	−	0.206165i	$-0.0660984\pi$
$839$	9.00000	+	15.5885i	0.310715	+	0.538173i	−0.667803	+	0.744338i	$0.732765\pi$
$840$	9.00000	−	15.5885i	0.310530	−	0.537853i
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	13.5000	−	23.3827i	0.465241	−	0.805821i
$843$	36.0000			1.23991
$844$	3.00000			0.103264
$845$	4.00000	−	6.92820i	0.137604	−	0.238337i
$846$	24.0000	−	41.5692i	0.825137	−	1.42918i
$847$	21.0000			0.721569
$848$	−3.00000			−0.103020
$849$	21.0000	−	36.3731i	0.720718	−	1.24832i
$850$	−0.500000	−	0.866025i	−0.0171499	−	0.0297044i
$851$	−15.0000	+	25.9808i	−0.514193	+	0.890609i
$852$		0			0
$853$	−23.0000	−	39.8372i	−0.787505	−	1.36400i	−0.927491	−	0.373845i	$-0.878039\pi$
$853$	−23.0000	−	39.8372i	−0.787505	−	1.36400i	0.139986	−	0.990153i	$-0.455294\pi$
$854$		0			0
$855$		0			0
$856$	−3.00000			−0.102538
$857$	−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	$0.967774\pi$
$858$	−9.00000	−	15.5885i	−0.307255	−	0.532181i
$859$	−27.0000	+	46.7654i	−0.921228	+	1.59561i	−0.123710	+	0.992318i	$0.539479\pi$
$859$	−27.0000	+	46.7654i	−0.921228	+	1.59561i	−0.797518	+	0.603296i	$0.793854\pi$
$860$	10.0000	+	17.3205i	0.340997	+	0.590624i
$861$	54.0000	−	93.5307i	1.84032	−	3.18752i
$862$	24.0000			0.817443
$863$	48.0000			1.63394			0.816970	−	0.576681i	$-0.195652\pi$
$863$	48.0000			1.63394			0.816970	+	0.576681i	$0.195652\pi$
$864$	−4.50000	+	7.79423i	−0.153093	+	0.265165i
$865$	18.0000	−	31.1769i	0.612018	−	1.06005i
$866$	30.0000			1.01944
$867$	−48.0000			−1.63017
$868$	−9.00000	+	15.5885i	−0.305480	+	0.529107i
$869$	−12.0000	−	20.7846i	−0.407072	−	0.705070i
$870$	9.00000	−	15.5885i	0.305129	−	0.528498i
$871$	22.5000	+	38.9711i	0.762383	+	1.32049i
$872$	−1.50000	−	2.59808i	−0.0507964	−	0.0879820i
$873$	72.0000			2.43683
$874$		0			0
$875$	36.0000			1.21702
$876$	16.5000	+	28.5788i	0.557483	+	0.965589i
$877$	−13.5000	−	23.3827i	−0.455863	−	0.789577i	0.542875	−	0.839814i	$-0.317336\pi$
$877$	−13.5000	−	23.3827i	−0.455863	−	0.789577i	−0.998737	+	0.0502365i	$0.984002\pi$
$878$		0			0
$879$	13.5000	+	23.3827i	0.455344	+	0.788678i
$880$	2.00000	−	3.46410i	0.0674200	−	0.116775i
$881$	34.0000			1.14549			0.572745	−	0.819734i	$-0.305879\pi$
$881$	34.0000			1.14549			0.572745	+	0.819734i	$0.305879\pi$
$882$	12.0000			0.404061
$883$	12.0000	−	20.7846i	0.403832	−	0.699458i	−0.590353	−	0.807145i	$-0.701011\pi$
$883$	12.0000	−	20.7846i	0.403832	−	0.699458i	0.994185	+	0.107688i	$0.0343446\pi$
$884$	−1.50000	+	2.59808i	−0.0504505	+	0.0873828i
$885$	18.0000			0.605063
$886$	−22.0000			−0.739104
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	−0.591156	−	0.806557i	$-0.701328\pi$
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	0.994077	+	0.108678i	$0.0346618\pi$
$888$	−9.00000	−	15.5885i	−0.302020	−	0.523114i
$889$	18.0000	−	31.1769i	0.603701	−	1.04564i
$890$	−6.00000	−	10.3923i	−0.201120	−	0.348351i
$891$	9.00000	+	15.5885i	0.301511	+	0.522233i
$892$	18.0000			0.602685
$893$		0			0
$894$	−24.0000			−0.802680
$895$	12.0000	+	20.7846i	0.401116	+	0.694753i
$896$	1.50000	+	2.59808i	0.0501115	+	0.0867956i
$897$	22.5000	−	38.9711i	0.751253	−	1.30121i
$898$	−3.00000	−	5.19615i	−0.100111	−	0.173398i
$899$	−9.00000	+	15.5885i	−0.300167	+	0.519904i
$900$	−6.00000			−0.200000
$901$	3.00000			0.0999445
$902$	12.0000	−	20.7846i	0.399556	−	0.692052i
$903$	−45.0000	+	77.9423i	−1.49751	+	2.59376i
$904$	12.0000			0.399114
$905$	36.0000			1.19668
$906$	27.0000	−	46.7654i	0.897015	−	1.55368i
$907$	7.50000	+	12.9904i	0.249033	+	0.431339i	0.963258	−	0.268578i	$-0.0865538\pi$
$907$	7.50000	+	12.9904i	0.249033	+	0.431339i	−0.714224	+	0.699917i	$0.753220\pi$
$908$	−1.50000	+	2.59808i	−0.0497792	+	0.0862202i
$909$	−30.0000	−	51.9615i	−0.995037	−	1.72345i
$910$	−9.00000	−	15.5885i	−0.298347	−	0.516752i
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$		0			0
$913$	−4.00000			−0.132381
$914$	−0.500000	−	0.866025i	−0.0165385	−	0.0286456i
$915$		0			0
$916$	6.00000	−	10.3923i	0.198246	−	0.343371i
$917$	21.0000	+	36.3731i	0.693481	+	1.20114i
$918$	4.50000	−	7.79423i	0.148522	−	0.257248i
$919$	15.0000			0.494804			0.247402	−	0.968913i	$-0.420423\pi$
$919$	15.0000			0.494804			0.247402	+	0.968913i	$0.420423\pi$
$920$	10.0000			0.329690
$921$	−18.0000	+	31.1769i	−0.593120	+	1.02731i
$922$	−2.00000	+	3.46410i	−0.0658665	+	0.114084i
$923$		0			0
$924$	18.0000			0.592157
$925$	3.00000	−	5.19615i	0.0986394	−	0.170848i
$926$	−16.0000	−	27.7128i	−0.525793	−	0.910700i
$927$	−18.0000	+	31.1769i	−0.591198	+	1.02398i
$928$	1.50000	+	2.59808i	0.0492399	+	0.0852860i
$929$	−20.5000	−	35.5070i	−0.672583	−	1.16495i	−0.977169	−	0.212463i	$-0.931851\pi$
$929$	−20.5000	−	35.5070i	−0.672583	−	1.16495i	0.304586	−	0.952485i	$-0.401482\pi$
$930$	−36.0000			−1.18049
$931$		0			0
$932$	14.0000			0.458585
$933$	16.5000	+	28.5788i	0.540186	+	0.935629i
$934$	−4.00000	−	6.92820i	−0.130884	−	0.226698i
$935$	−2.00000	+	3.46410i	−0.0654070	+	0.113288i
$936$	9.00000	+	15.5885i	0.294174	+	0.509525i
$937$	23.5000	−	40.7032i	0.767712	−	1.32972i	−0.171089	−	0.985255i	$-0.554729\pi$
$937$	23.5000	−	40.7032i	0.767712	−	1.32972i	0.938801	−	0.344460i	$-0.111938\pi$
$938$	−45.0000			−1.46930
$939$	63.0000			2.05593
$940$	8.00000	−	13.8564i	0.260931	−	0.451946i
$941$	13.5000	−	23.3827i	0.440087	−	0.762254i	−0.557608	−	0.830104i	$-0.688281\pi$
$941$	13.5000	−	23.3827i	0.440087	−	0.762254i	0.997695	+	0.0678506i	$0.0216141\pi$
$942$		0			0
$943$	60.0000			1.95387
$944$	−1.50000	+	2.59808i	−0.0488208	+	0.0845602i
$945$	27.0000	+	46.7654i	0.878310	+	1.52128i
$946$	−10.0000	+	17.3205i	−0.325128	+	0.563138i
$947$	23.0000	+	39.8372i	0.747400	+	1.29453i	0.949065	+	0.315080i	$0.102031\pi$
$947$	23.0000	+	39.8372i	0.747400	+	1.29453i	−0.201666	+	0.979454i	$0.564635\pi$
$948$	18.0000	+	31.1769i	0.584613	+	1.01258i
$949$	33.0000			1.07123
$950$		0			0
$951$	−99.0000			−3.21029
$952$	−1.50000	−	2.59808i	−0.0486153	−	0.0842041i
$953$	15.0000	+	25.9808i	0.485898	+	0.841599i	0.999869	−	0.0162081i	$-0.00515944\pi$
$953$	15.0000	+	25.9808i	0.485898	+	0.841599i	−0.513971	+	0.857808i	$0.671826\pi$
$954$	9.00000	−	15.5885i	0.291386	−	0.504695i
$955$	11.0000	+	19.0526i	0.355952	+	0.616526i
$956$	−0.500000	+	0.866025i	−0.0161712	+	0.0280093i
$957$	18.0000			0.581857
$958$	−40.0000			−1.29234
$959$	28.5000	−	49.3634i	0.920313	−	1.59403i
$960$	−3.00000	+	5.19615i	−0.0968246	+	0.167705i
$961$	5.00000			0.161290
$962$	−18.0000			−0.580343
$963$	9.00000	−	15.5885i	0.290021	−	0.502331i
$964$	−12.0000	−	20.7846i	−0.386494	−	0.669427i
$965$	−6.00000	+	10.3923i	−0.193147	+	0.334540i
$966$	22.5000	+	38.9711i	0.723926	+	1.25388i
$967$	12.0000	+	20.7846i	0.385894	+	0.668388i	0.991893	−	0.127078i	$-0.0405597\pi$
$967$	12.0000	+	20.7846i	0.385894	+	0.668388i	−0.605999	+	0.795466i	$0.707226\pi$
$968$	−7.00000			−0.224989
$969$		0			0
$970$	24.0000			0.770594
$971$	24.0000	+	41.5692i	0.770197	+	1.33402i	0.937455	+	0.348107i	$0.113175\pi$
$971$	24.0000	+	41.5692i	0.770197	+	1.33402i	−0.167258	+	0.985913i	$0.553491\pi$
$972$		0			0
$973$	9.00000	−	15.5885i	0.288527	−	0.499743i
$974$	9.00000	+	15.5885i	0.288379	+	0.499486i
$975$	−4.50000	+	7.79423i	−0.144115	+	0.249615i
$976$		0			0
$977$	−30.0000			−0.959785			−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000			−0.959785			−0.479893	+	0.877327i	$0.659324\pi$
$978$	9.00000	−	15.5885i	0.287788	−	0.498464i
$979$	6.00000	−	10.3923i	0.191761	−	0.332140i
$980$	4.00000			0.127775
$981$	18.0000			0.574696
$982$	−4.00000	+	6.92820i	−0.127645	+	0.221088i
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	0.991453	−	0.130465i	$-0.0416470\pi$
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	−0.608712	+	0.793391i	$0.708314\pi$
$984$	−18.0000	+	31.1769i	−0.573819	+	0.993884i
$985$	−4.00000	−	6.92820i	−0.127451	−	0.220751i
$986$	−1.50000	−	2.59808i	−0.0477697	−	0.0827396i
$987$	72.0000			2.29179
$988$		0			0
$989$	−50.0000			−1.58991
$990$	12.0000	+	20.7846i	0.381385	+	0.660578i
$991$	−3.00000	−	5.19615i	−0.0952981	−	0.165061i	0.814435	−	0.580255i	$-0.197047\pi$
$991$	−3.00000	−	5.19615i	−0.0952981	−	0.165061i	−0.909733	+	0.415194i	$0.863714\pi$
$992$	3.00000	−	5.19615i	0.0952501	−	0.164978i
$993$	−13.5000	−	23.3827i	−0.428410	−	0.742027i
$994$		0			0
$995$	−14.0000			−0.443830
$996$	6.00000			0.190117
$997$	−3.00000	+	5.19615i	−0.0950110	+	0.164564i	−0.909613	−	0.415456i	$-0.863622\pi$
$997$	−3.00000	+	5.19615i	−0.0950110	+	0.164564i	0.814602	+	0.580020i	$0.196955\pi$
$998$	−9.00000	+	15.5885i	−0.284890	+	0.493444i
$999$	54.0000			1.70848

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.c.a.653.1		2
19.2	odd	18		722.2.e.h.389.1		6
19.3	odd	18		722.2.e.h.595.1		6
19.4	even	9		722.2.e.g.245.1		6
19.5	even	9		722.2.e.g.99.1		6
19.6	even	9		722.2.e.g.423.1		6
19.7	even	3		722.2.a.f.1.1	yes	1
19.8	odd	6		722.2.c.g.429.1		2
19.9	even	9		722.2.e.g.415.1		6
19.10	odd	18		722.2.e.h.415.1		6
19.11	even	3	inner	722.2.c.a.429.1		2
19.12	odd	6		722.2.a.a.1.1	✓	1
19.13	odd	18		722.2.e.h.423.1		6
19.14	odd	18		722.2.e.h.99.1		6
19.15	odd	18		722.2.e.h.245.1		6
19.16	even	9		722.2.e.g.595.1		6
19.17	even	9		722.2.e.g.389.1		6
19.18	odd	2		722.2.c.g.653.1		2
57.26	odd	6		6498.2.a.a.1.1		1
57.50	even	6		6498.2.a.m.1.1		1
76.7	odd	6		5776.2.a.a.1.1		1
76.31	even	6		5776.2.a.q.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.a.1.1	✓	1	19.12	odd	6
722.2.a.f.1.1	yes	1	19.7	even	3
722.2.c.a.429.1		2	19.11	even	3	inner
722.2.c.a.653.1		2	1.1	even	1	trivial
722.2.c.g.429.1		2	19.8	odd	6
722.2.c.g.653.1		2	19.18	odd	2
722.2.e.g.99.1		6	19.5	even	9
722.2.e.g.245.1		6	19.4	even	9
722.2.e.g.389.1		6	19.17	even	9
722.2.e.g.415.1		6	19.9	even	9
722.2.e.g.423.1		6	19.6	even	9
722.2.e.g.595.1		6	19.16	even	9
722.2.e.h.99.1		6	19.14	odd	18
722.2.e.h.245.1		6	19.15	odd	18
722.2.e.h.389.1		6	19.2	odd	18
722.2.e.h.415.1		6	19.10	odd	18
722.2.e.h.423.1		6	19.13	odd	18
722.2.e.h.595.1		6	19.3	odd	18
5776.2.a.a.1.1		1	76.7	odd	6
5776.2.a.q.1.1		1	76.31	even	6
6498.2.a.a.1.1		1	57.26	odd	6
6498.2.a.m.1.1		1	57.50	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 $\F_{q}$
Belyi maps

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} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(-1.50000 + 2.59808i) q^{6} -3.00000 q^{7} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(-1.00000 + 1.73205i) q^{10} -2.00000 q^{11} +3.00000 q^{12} +(1.50000 - 2.59808i) q^{13} +(1.50000 + 2.59808i) q^{14} +(-3.00000 + 5.19615i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{17} +6.00000 q^{18} +2.00000 q^{20} +(4.50000 + 7.79423i) q^{21} +(1.00000 + 1.73205i) q^{22} +(-2.50000 + 4.33013i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(0.500000 - 0.866025i) q^{25} -3.00000 q^{26} +9.00000 q^{27} +(1.50000 - 2.59808i) q^{28} +(1.50000 - 2.59808i) q^{29} +6.00000 q^{30} -6.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{33} +(0.500000 - 0.866025i) q^{34} +(3.00000 + 5.19615i) q^{35} +(-3.00000 - 5.19615i) q^{36} +6.00000 q^{37} -9.00000 q^{39} +(-1.00000 - 1.73205i) q^{40} +(-6.00000 - 10.3923i) q^{41} +(4.50000 - 7.79423i) q^{42} +(5.00000 + 8.66025i) q^{43} +(1.00000 - 1.73205i) q^{44} +12.0000 q^{45} +5.00000 q^{46} +(4.00000 - 6.92820i) q^{47} +(-1.50000 + 2.59808i) q^{48} +2.00000 q^{49} -1.00000 q^{50} +(1.50000 - 2.59808i) q^{51} +(1.50000 + 2.59808i) q^{52} +(1.50000 - 2.59808i) q^{53} +(-4.50000 - 7.79423i) q^{54} +(2.00000 + 3.46410i) q^{55} -3.00000 q^{56} -3.00000 q^{58} +(-1.50000 - 2.59808i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(3.00000 + 5.19615i) q^{62} +(9.00000 - 15.5885i) q^{63} +1.00000 q^{64} -6.00000 q^{65} +(3.00000 - 5.19615i) q^{66} +(-7.50000 + 12.9904i) q^{67} -1.00000 q^{68} +15.0000 q^{69} +(3.00000 - 5.19615i) q^{70} +(-3.00000 + 5.19615i) q^{72} +(5.50000 + 9.52628i) q^{73} +(-3.00000 - 5.19615i) q^{74} -3.00000 q^{75} +6.00000 q^{77} +(4.50000 + 7.79423i) q^{78} +(6.00000 + 10.3923i) q^{79} +(-1.00000 + 1.73205i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 + 10.3923i) q^{82} +2.00000 q^{83} -9.00000 q^{84} +(1.00000 - 1.73205i) q^{85} +(5.00000 - 8.66025i) q^{86} -9.00000 q^{87} -2.00000 q^{88} +(-3.00000 + 5.19615i) q^{89} +(-6.00000 - 10.3923i) q^{90} +(-4.50000 + 7.79423i) q^{91} +(-2.50000 - 4.33013i) q^{92} +(9.00000 + 15.5885i) q^{93} -8.00000 q^{94} +3.00000 q^{96} +(-6.00000 - 10.3923i) q^{97} +(-1.00000 - 1.73205i) q^{98} +(6.00000 - 10.3923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 3 q^{3} - q^{4} - 2 q^{5} - 3 q^{6} - 6 q^{7} + 2 q^{8} - 6 q^{9} - 2 q^{10} - 4 q^{11} + 6 q^{12} + 3 q^{13} + 3 q^{14} - 6 q^{15} - q^{16} + q^{17} + 12 q^{18} + 4 q^{20} + 9 q^{21}+ \cdots + 12 q^{99}+O(q^{100}) \) 2 * q - q^2 - 3 * q^3 - q^4 - 2 * q^5 - 3 * q^6 - 6 * q^7 + 2 * q^8 - 6 * q^9 - 2 * q^10 - 4 * q^11 + 6 * q^12 + 3 * q^13 + 3 * q^14 - 6 * q^15 - q^16 + q^17 + 12 * q^18 + 4 * q^20 + 9 * q^21 + 2 * q^22 - 5 * q^23 - 3 * q^24 + q^25 - 6 * q^26 + 18 * q^27 + 3 * q^28 + 3 * q^29 + 12 * q^30 - 12 * q^31 - q^32 + 6 * q^33 + q^34 + 6 * q^35 - 6 * q^36 + 12 * q^37 - 18 * q^39 - 2 * q^40 - 12 * q^41 + 9 * q^42 + 10 * q^43 + 2 * q^44 + 24 * q^45 + 10 * q^46 + 8 * q^47 - 3 * q^48 + 4 * q^49 - 2 * q^50 + 3 * q^51 + 3 * q^52 + 3 * q^53 - 9 * q^54 + 4 * q^55 - 6 * q^56 - 6 * q^58 - 3 * q^59 - 6 * q^60 + 6 * q^62 + 18 * q^63 + 2 * q^64 - 12 * q^65 + 6 * q^66 - 15 * q^67 - 2 * q^68 + 30 * q^69 + 6 * q^70 - 6 * q^72 + 11 * q^73 - 6 * q^74 - 6 * q^75 + 12 * q^77 + 9 * q^78 + 12 * q^79 - 2 * q^80 - 9 * q^81 - 12 * q^82 + 4 * q^83 - 18 * q^84 + 2 * q^85 + 10 * q^86 - 18 * q^87 - 4 * q^88 - 6 * q^89 - 12 * q^90 - 9 * q^91 - 5 * q^92 + 18 * q^93 - 16 * q^94 + 6 * q^96 - 12 * q^97 - 2 * q^98 + 12 * q^99

Introduction

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