LMFDB - Embedded newform 490.2.e.g.471.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(361,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("490.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.e (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:	$3.91266969904$
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 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			471.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	490.471
Dual form			490.2.e.g.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(-1.00000 + 1.73205i) q^{12} +1.00000 q^{13} -2.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} -1.00000 q^{20} -3.00000 q^{22} +(-4.50000 + 7.79423i) q^{23} +(1.00000 + 1.73205i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.500000 - 0.866025i) q^{26} -4.00000 q^{27} +6.00000 q^{29} +(-1.00000 + 1.73205i) q^{30} +(4.00000 + 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{33} -6.00000 q^{34} +1.00000 q^{36} +(3.50000 - 6.06218i) q^{37} +(0.500000 + 0.866025i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(-0.500000 + 0.866025i) q^{40} -3.00000 q^{41} +2.00000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(0.500000 + 0.866025i) q^{45} +(4.50000 + 7.79423i) q^{46} +(4.50000 - 7.79423i) q^{47} +2.00000 q^{48} -1.00000 q^{50} +(-6.00000 + 10.3923i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(-4.50000 - 7.79423i) q^{53} +(-2.00000 + 3.46410i) q^{54} -3.00000 q^{55} +2.00000 q^{57} +(3.00000 - 5.19615i) q^{58} +(1.00000 + 1.73205i) q^{60} +(4.00000 - 6.92820i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(3.00000 + 5.19615i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(-3.00000 + 5.19615i) q^{68} +18.0000 q^{69} +(0.500000 - 0.866025i) q^{72} +(-2.00000 - 3.46410i) q^{73} +(-3.50000 - 6.06218i) q^{74} +(-1.00000 + 1.73205i) q^{75} +1.00000 q^{76} -2.00000 q^{78} +(5.00000 - 8.66025i) q^{79} +(0.500000 + 0.866025i) q^{80} +(5.50000 + 9.52628i) q^{81} +(-1.50000 + 2.59808i) q^{82} -6.00000 q^{85} +(1.00000 - 1.73205i) q^{86} +(-6.00000 - 10.3923i) q^{87} +(1.50000 + 2.59808i) q^{88} +(3.00000 - 5.19615i) q^{89} +1.00000 q^{90} +9.00000 q^{92} +(8.00000 - 13.8564i) q^{93} +(-4.50000 - 7.79423i) q^{94} +(0.500000 + 0.866025i) q^{95} +(1.00000 - 1.73205i) q^{96} +10.0000 q^{97} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 4 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - 2 * q^3 - q^4 + q^5 - 4 * q^6 - 2 * q^8 - q^9	$ 2 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 4 q^{6} - 2 q^{8} - q^{9} - q^{10} - 3 q^{11} - 2 q^{12} + 2 q^{13} - 4 q^{15} - q^{16} - 6 q^{17} + q^{18} - q^{19} - 2 q^{20} - 6 q^{22} - 9 q^{23} + 2 q^{24} - q^{25} + q^{26} - 8 q^{27} + 12 q^{29} - 2 q^{30} + 8 q^{31} + q^{32} - 6 q^{33} - 12 q^{34} + 2 q^{36} + 7 q^{37} + q^{38} - 2 q^{39} - q^{40} - 6 q^{41} + 4 q^{43} - 3 q^{44} + q^{45} + 9 q^{46} + 9 q^{47} + 4 q^{48} - 2 q^{50} - 12 q^{51} - q^{52} - 9 q^{53} - 4 q^{54} - 6 q^{55} + 4 q^{57} + 6 q^{58} + 2 q^{60} + 8 q^{61} + 16 q^{62} + 2 q^{64} + q^{65} + 6 q^{66} - 8 q^{67} - 6 q^{68} + 36 q^{69} + q^{72} - 4 q^{73} - 7 q^{74} - 2 q^{75} + 2 q^{76} - 4 q^{78} + 10 q^{79} + q^{80} + 11 q^{81} - 3 q^{82} - 12 q^{85} + 2 q^{86} - 12 q^{87} + 3 q^{88} + 6 q^{89} + 2 q^{90} + 18 q^{92} + 16 q^{93} - 9 q^{94} + q^{95} + 2 q^{96} + 20 q^{97} + 6 q^{99}+O(q^{100}) $ 2 * q + q^2 - 2 * q^3 - q^4 + q^5 - 4 * q^6 - 2 * q^8 - q^9 - q^10 - 3 * q^11 - 2 * q^12 + 2 * q^13 - 4 * q^15 - q^16 - 6 * q^17 + q^18 - q^19 - 2 * q^20 - 6 * q^22 - 9 * q^23 + 2 * q^24 - q^25 + q^26 - 8 * q^27 + 12 * q^29 - 2 * q^30 + 8 * q^31 + q^32 - 6 * q^33 - 12 * q^34 + 2 * q^36 + 7 * q^37 + q^38 - 2 * q^39 - q^40 - 6 * q^41 + 4 * q^43 - 3 * q^44 + q^45 + 9 * q^46 + 9 * q^47 + 4 * q^48 - 2 * q^50 - 12 * q^51 - q^52 - 9 * q^53 - 4 * q^54 - 6 * q^55 + 4 * q^57 + 6 * q^58 + 2 * q^60 + 8 * q^61 + 16 * q^62 + 2 * q^64 + q^65 + 6 * q^66 - 8 * q^67 - 6 * q^68 + 36 * q^69 + q^72 - 4 * q^73 - 7 * q^74 - 2 * q^75 + 2 * q^76 - 4 * q^78 + 10 * q^79 + q^80 + 11 * q^81 - 3 * q^82 - 12 * q^85 + 2 * q^86 - 12 * q^87 + 3 * q^88 + 6 * q^89 + 2 * q^90 + 18 * q^92 + 16 * q^93 - 9 * q^94 + q^95 + 2 * q^96 + 20 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	−0.995782	−	0.0917517i	$-0.970753\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	0.418432	−	0.908248i	$-0.362580\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−2.00000			−0.816497
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$	−1.00000	+	1.73205i	−0.288675	+	0.500000i
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$		0			0
$15$	−2.00000			−0.516398
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	−3.00000			−0.639602
$23$	−4.50000	+	7.79423i	−0.938315	+	1.62521i	−0.169701	+	0.985496i	$0.554280\pi$
$23$	−4.50000	+	7.79423i	−0.938315	+	1.62521i	−0.768613	+	0.639713i	$0.779053\pi$
$24$	1.00000	+	1.73205i	0.204124	+	0.353553i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	−4.00000			−0.769800
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	−1.00000	+	1.73205i	−0.182574	+	0.316228i
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−3.00000	+	5.19615i	−0.522233	+	0.904534i
$34$	−6.00000			−1.02899
$35$		0			0
$36$	1.00000			0.166667
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	−0.420602	−	0.907245i	$-0.638181\pi$
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$	0.500000	+	0.866025i	0.0811107	+	0.140488i
$39$	−1.00000	−	1.73205i	−0.160128	−	0.277350i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	−1.50000	+	2.59808i	−0.226134	+	0.391675i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	4.50000	+	7.79423i	0.663489	+	1.14920i
$47$	4.50000	−	7.79423i	0.656392	−	1.13691i	−0.325150	−	0.945662i	$-0.605415\pi$
$47$	4.50000	−	7.79423i	0.656392	−	1.13691i	0.981543	−	0.191243i	$-0.0612518\pi$
$48$	2.00000			0.288675
$49$		0			0
$50$	−1.00000			−0.141421
$51$	−6.00000	+	10.3923i	−0.840168	+	1.45521i
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	−4.50000	−	7.79423i	−0.618123	−	1.07062i	−0.989828	−	0.142269i	$-0.954560\pi$
$53$	−4.50000	−	7.79423i	−0.618123	−	1.07062i	0.371706	−	0.928351i	$-0.378773\pi$
$54$	−2.00000	+	3.46410i	−0.272166	+	0.471405i
$55$	−3.00000			−0.404520
$56$		0			0
$57$	2.00000			0.264906
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	1.00000	+	1.73205i	0.129099	+	0.223607i
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	−0.487753	−	0.872982i	$-0.662183\pi$
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	0.999901	−	0.0140840i	$-0.00448323\pi$
$62$	8.00000			1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$	3.00000	+	5.19615i	0.369274	+	0.639602i
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$	18.0000			2.16695
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−2.00000	−	3.46410i	−0.234082	−	0.405442i	0.724923	−	0.688830i	$-0.241875\pi$
$73$	−2.00000	−	3.46410i	−0.234082	−	0.405442i	−0.959006	+	0.283387i	$0.908542\pi$
$74$	−3.50000	−	6.06218i	−0.406867	−	0.704714i
$75$	−1.00000	+	1.73205i	−0.115470	+	0.200000i
$76$	1.00000			0.114708
$77$		0			0
$78$	−2.00000			−0.226455
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	−0.434730	−	0.900561i	$-0.643156\pi$
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	0.997274	−	0.0737937i	$-0.0235106\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$	−1.50000	+	2.59808i	−0.165647	+	0.286910i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	−6.00000			−0.650791
$86$	1.00000	−	1.73205i	0.107833	−	0.186772i
$87$	−6.00000	−	10.3923i	−0.643268	−	1.11417i
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$	9.00000			0.938315
$93$	8.00000	−	13.8564i	0.829561	−	1.43684i
$94$	−4.50000	−	7.79423i	−0.464140	−	0.803913i
$95$	0.500000	+	0.866025i	0.0512989	+	0.0888523i
$96$	1.00000	−	1.73205i	0.102062	−	0.176777i
$97$	10.0000			1.01535			0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000			1.01535			0.507673	+	0.861550i	$0.330506\pi$
$98$		0			0
$99$	3.00000			0.301511
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	0.993258	+	0.115924i	$0.0369830\pi$
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	−0.396236	+	0.918149i	$0.629684\pi$
$102$	6.00000	+	10.3923i	0.594089	+	1.02899i
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	−0.947576	−	0.319531i	$-0.896475\pi$
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	0.750510	+	0.660859i	$0.229808\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	−9.00000			−0.874157
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	−0.415432	−	0.909624i	$-0.636370\pi$
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	0.995474	−	0.0950377i	$-0.0302972\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	0.939577	+	0.342337i	$0.111218\pi$
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	−0.173316	+	0.984866i	$0.555448\pi$
$110$	−1.50000	+	2.59808i	−0.143019	+	0.247717i
$111$	−14.0000			−1.32882
$112$		0			0
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$	4.50000	+	7.79423i	0.419627	+	0.726816i
$116$	−3.00000	−	5.19615i	−0.278543	−	0.482451i
$117$	−0.500000	+	0.866025i	−0.0462250	+	0.0800641i
$118$		0			0
$119$		0			0
$120$	2.00000			0.182574
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−4.00000	−	6.92820i	−0.362143	−	0.627250i
$123$	3.00000	+	5.19615i	0.270501	+	0.468521i
$124$	4.00000	−	6.92820i	0.359211	−	0.622171i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−1.00000			−0.0887357			−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	−1.00000			−0.0887357			−0.0443678	+	0.999015i	$0.514127\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−2.00000	−	3.46410i	−0.176090	−	0.304997i
$130$	−0.500000	−	0.866025i	−0.0438529	−	0.0759555i
$131$	1.50000	−	2.59808i	0.131056	−	0.226995i	−0.793028	−	0.609185i	$-0.791497\pi$
$131$	1.50000	−	2.59808i	0.131056	−	0.226995i	0.924084	+	0.382190i	$0.124830\pi$
$132$	6.00000			0.522233
$133$		0			0
$134$	−8.00000			−0.691095
$135$	−2.00000	+	3.46410i	−0.172133	+	0.298142i
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$	9.00000	−	15.5885i	0.766131	−	1.32698i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−18.0000			−1.51587
$142$		0			0
$143$	−1.50000	−	2.59808i	−0.125436	−	0.217262i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	3.00000	−	5.19615i	0.249136	−	0.431517i
$146$	−4.00000			−0.331042
$147$		0			0
$148$	−7.00000			−0.575396
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	1.00000	+	1.73205i	0.0816497	+	0.141421i
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$	0.500000	−	0.866025i	0.0405554	−	0.0702439i
$153$	6.00000			0.485071
$154$		0			0
$155$	8.00000			0.642575
$156$	−1.00000	+	1.73205i	−0.0800641	+	0.138675i
$157$	11.5000	+	19.9186i	0.917800	+	1.58968i	0.802749	+	0.596316i	$0.203370\pi$
$157$	11.5000	+	19.9186i	0.917800	+	1.58968i	0.115050	+	0.993360i	$0.463297\pi$
$158$	−5.00000	−	8.66025i	−0.397779	−	0.688973i
$159$	−9.00000	+	15.5885i	−0.713746	+	1.23625i
$160$	1.00000			0.0790569
$161$		0			0
$162$	11.0000			0.864242
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$	1.50000	+	2.59808i	0.117130	+	0.202876i
$165$	3.00000	+	5.19615i	0.233550	+	0.404520i
$166$		0			0
$167$	−3.00000			−0.232147			−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000			−0.232147			−0.116073	+	0.993241i	$0.537031\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$	−3.00000	+	5.19615i	−0.230089	+	0.398527i
$171$	−0.500000	−	0.866025i	−0.0382360	−	0.0662266i
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	4.50000	−	7.79423i	0.342129	−	0.592584i	−0.642699	−	0.766119i	$-0.722185\pi$
$173$	4.50000	−	7.79423i	0.342129	−	0.592584i	0.984828	+	0.173534i	$0.0555188\pi$
$174$	−12.0000			−0.909718
$175$		0			0
$176$	3.00000			0.226134
$177$		0			0
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	1.50000	+	2.59808i	0.112115	+	0.194189i	0.916623	−	0.399753i	$-0.130904\pi$
$179$	1.50000	+	2.59808i	0.112115	+	0.194189i	−0.804508	+	0.593942i	$0.797571\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	−16.0000			−1.18275
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$	−3.50000	−	6.06218i	−0.257325	−	0.445700i
$186$	−8.00000	−	13.8564i	−0.586588	−	1.01600i
$187$	−9.00000	+	15.5885i	−0.658145	+	1.13994i
$188$	−9.00000			−0.656392
$189$		0			0
$190$	1.00000			0.0725476
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$	−1.00000	−	1.73205i	−0.0721688	−	0.125000i
$193$	8.00000	+	13.8564i	0.575853	+	0.997406i	0.995948	+	0.0899262i	$0.0286631\pi$
$193$	8.00000	+	13.8564i	0.575853	+	0.997406i	−0.420096	+	0.907480i	$0.638004\pi$
$194$	5.00000	−	8.66025i	0.358979	−	0.621770i
$195$	−2.00000			−0.143223
$196$		0			0
$197$	15.0000			1.06871			0.534353	−	0.845262i	$-0.320555\pi$
$197$	15.0000			1.06871			0.534353	+	0.845262i	$0.320555\pi$
$198$	1.50000	−	2.59808i	0.106600	−	0.184637i
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	−0.996850	−	0.0793045i	$-0.974730\pi$
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	0.429745	−	0.902950i	$-0.358603\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−8.00000	+	13.8564i	−0.564276	+	0.977356i
$202$	12.0000			0.844317
$203$		0			0
$204$	12.0000			0.840168
$205$	−1.50000	+	2.59808i	−0.104765	+	0.181458i
$206$	2.00000	+	3.46410i	0.139347	+	0.241355i
$207$	−4.50000	−	7.79423i	−0.312772	−	0.541736i
$208$	−0.500000	+	0.866025i	−0.0346688	+	0.0600481i
$209$	3.00000			0.207514
$210$		0			0
$211$	23.0000			1.58339			0.791693	−	0.610920i	$-0.209200\pi$
$211$	23.0000			1.58339			0.791693	+	0.610920i	$0.209200\pi$
$212$	−4.50000	+	7.79423i	−0.309061	+	0.535310i
$213$		0			0
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	1.00000	−	1.73205i	0.0681994	−	0.118125i
$216$	4.00000			0.272166
$217$		0			0
$218$	16.0000			1.08366
$219$	−4.00000	+	6.92820i	−0.270295	+	0.468165i
$220$	1.50000	+	2.59808i	0.101130	+	0.175162i
$221$	−3.00000	−	5.19615i	−0.201802	−	0.349531i
$222$	−7.00000	+	12.1244i	−0.469809	+	0.813733i
$223$	−8.00000			−0.535720			−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000			−0.535720			−0.267860	+	0.963458i	$0.586316\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$	−1.00000	−	1.73205i	−0.0662266	−	0.114708i
$229$	−2.00000	+	3.46410i	−0.132164	+	0.228914i	−0.924510	−	0.381157i	$-0.875526\pi$
$229$	−2.00000	+	3.46410i	−0.132164	+	0.228914i	0.792347	+	0.610071i	$0.208859\pi$
$230$	9.00000			0.593442
$231$		0			0
$232$	−6.00000			−0.393919
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$	0.500000	+	0.866025i	0.0326860	+	0.0566139i
$235$	−4.50000	−	7.79423i	−0.293548	−	0.508439i
$236$		0			0
$237$	−20.0000			−1.29914
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$	1.00000	−	1.73205i	0.0645497	−	0.111803i
$241$	−0.500000	−	0.866025i	−0.0322078	−	0.0557856i	0.849472	−	0.527633i	$-0.176921\pi$
$241$	−0.500000	−	0.866025i	−0.0322078	−	0.0557856i	−0.881680	+	0.471848i	$0.843587\pi$
$242$	−1.00000	−	1.73205i	−0.0642824	−	0.111340i
$243$	5.00000	−	8.66025i	0.320750	−	0.555556i
$244$	−8.00000			−0.512148
$245$		0			0
$246$	6.00000			0.382546
$247$	−0.500000	+	0.866025i	−0.0318142	+	0.0551039i
$248$	−4.00000	−	6.92820i	−0.254000	−	0.439941i
$249$		0			0
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	15.0000			0.946792			0.473396	−	0.880850i	$-0.343028\pi$
$251$	15.0000			0.946792			0.473396	+	0.880850i	$0.343028\pi$
$252$		0			0
$253$	27.0000			1.69748
$254$	−0.500000	+	0.866025i	−0.0313728	+	0.0543393i
$255$	6.00000	+	10.3923i	0.375735	+	0.650791i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$257$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$258$	−4.00000			−0.249029
$259$		0			0
$260$	−1.00000			−0.0620174
$261$	−3.00000	+	5.19615i	−0.185695	+	0.321634i
$262$	−1.50000	−	2.59808i	−0.0926703	−	0.160510i
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$	3.00000	−	5.19615i	0.184637	−	0.319801i
$265$	−9.00000			−0.552866
$266$		0			0
$267$	−12.0000			−0.734388
$268$	−4.00000	+	6.92820i	−0.244339	+	0.423207i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$	2.00000	+	3.46410i	0.121716	+	0.210819i
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	−0.999870	−	0.0161307i	$-0.994865\pi$
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	0.513905	+	0.857847i	$0.328199\pi$
$272$	6.00000			0.363803
$273$		0			0
$274$	−12.0000			−0.724947
$275$	−1.50000	+	2.59808i	−0.0904534	+	0.156670i
$276$	−9.00000	−	15.5885i	−0.541736	−	0.938315i
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$	2.00000	−	3.46410i	0.119952	−	0.207763i
$279$	−8.00000			−0.478947
$280$		0			0
$281$	−27.0000			−1.61068			−0.805342	−	0.592810i	$-0.798019\pi$
$281$	−27.0000			−1.61068			−0.805342	+	0.592810i	$0.798019\pi$
$282$	−9.00000	+	15.5885i	−0.535942	+	0.928279i
$283$	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
$285$	1.00000	−	1.73205i	0.0592349	−	0.102598i
$286$	−3.00000			−0.177394
$287$		0			0
$288$	−1.00000			−0.0589256
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	−3.00000	−	5.19615i	−0.176166	−	0.305129i
$291$	−10.0000	−	17.3205i	−0.586210	−	1.01535i
$292$	−2.00000	+	3.46410i	−0.117041	+	0.202721i
$293$	9.00000			0.525786			0.262893	−	0.964825i	$-0.415323\pi$
$293$	9.00000			0.525786			0.262893	+	0.964825i	$0.415323\pi$
$294$		0			0
$295$		0			0
$296$	−3.50000	+	6.06218i	−0.203433	+	0.352357i
$297$	6.00000	+	10.3923i	0.348155	+	0.603023i
$298$	−3.00000	−	5.19615i	−0.173785	−	0.301005i
$299$	−4.50000	+	7.79423i	−0.260242	+	0.450752i
$300$	2.00000			0.115470
$301$		0			0
$302$	10.0000			0.575435
$303$	12.0000	−	20.7846i	0.689382	−	1.19404i
$304$	−0.500000	−	0.866025i	−0.0286770	−	0.0496700i
$305$	−4.00000	−	6.92820i	−0.229039	−	0.396708i
$306$	3.00000	−	5.19615i	0.171499	−	0.297044i
$307$	−14.0000			−0.799022			−0.399511	−	0.916728i	$-0.630820\pi$
$307$	−14.0000			−0.799022			−0.399511	+	0.916728i	$0.630820\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$	4.00000	−	6.92820i	0.227185	−	0.393496i
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$	1.00000	+	1.73205i	0.0566139	+	0.0980581i
$313$	−14.0000	+	24.2487i	−0.791327	+	1.37062i	0.133819	+	0.991006i	$0.457276\pi$
$313$	−14.0000	+	24.2487i	−0.791327	+	1.37062i	−0.925146	+	0.379612i	$0.876057\pi$
$314$	23.0000			1.29797
$315$		0			0
$316$	−10.0000			−0.562544
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$	9.00000	+	15.5885i	0.504695	+	0.874157i
$319$	−9.00000	−	15.5885i	−0.503903	−	0.872786i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−24.0000			−1.33955
$322$		0			0
$323$	6.00000			0.333849
$324$	5.50000	−	9.52628i	0.305556	−	0.529238i
$325$	−0.500000	−	0.866025i	−0.0277350	−	0.0480384i
$326$	10.0000	+	17.3205i	0.553849	+	0.959294i
$327$	16.0000	−	27.7128i	0.884802	−	1.53252i
$328$	3.00000			0.165647
$329$		0			0
$330$	6.00000			0.330289
$331$	3.50000	−	6.06218i	0.192377	−	0.333207i	−0.753660	−	0.657264i	$-0.771714\pi$
$331$	3.50000	−	6.06218i	0.192377	−	0.333207i	0.946038	+	0.324057i	$0.105047\pi$
$332$		0			0
$333$	3.50000	+	6.06218i	0.191799	+	0.332205i
$334$	−1.50000	+	2.59808i	−0.0820763	+	0.142160i
$335$	−8.00000			−0.437087
$336$		0			0
$337$	−22.0000			−1.19842			−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000			−1.19842			−0.599208	+	0.800593i	$0.704518\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$		0			0
$340$	3.00000	+	5.19615i	0.162698	+	0.281801i
$341$	12.0000	−	20.7846i	0.649836	−	1.12555i
$342$	−1.00000			−0.0540738
$343$		0			0
$344$	−2.00000			−0.107833
$345$	9.00000	−	15.5885i	0.484544	−	0.839254i
$346$	−4.50000	−	7.79423i	−0.241921	−	0.419020i
$347$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$347$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$348$	−6.00000	+	10.3923i	−0.321634	+	0.557086i
$349$	−26.0000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	6.00000	+	10.3923i	0.319348	+	0.553127i	0.980352	−	0.197256i	$-0.0632029\pi$
$353$	6.00000	+	10.3923i	0.319348	+	0.553127i	−0.661004	+	0.750382i	$0.729870\pi$
$354$		0			0
$355$		0			0
$356$	−6.00000			−0.317999
$357$		0			0
$358$	3.00000			0.158555
$359$	−9.00000	+	15.5885i	−0.475002	+	0.822727i	−0.999590	−	0.0286287i	$-0.990886\pi$
$359$	−9.00000	+	15.5885i	−0.475002	+	0.822727i	0.524588	+	0.851356i	$0.324219\pi$
$360$	−0.500000	−	0.866025i	−0.0263523	−	0.0456435i
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	−1.00000	+	1.73205i	−0.0525588	+	0.0910346i
$363$	−4.00000			−0.209946
$364$		0			0
$365$	−4.00000			−0.209370
$366$	−8.00000	+	13.8564i	−0.418167	+	0.724286i
$367$	−9.50000	−	16.4545i	−0.495896	−	0.858917i	0.504093	−	0.863649i	$-0.331827\pi$
$367$	−9.50000	−	16.4545i	−0.495896	−	0.858917i	−0.999989	+	0.00473247i	$0.998494\pi$
$368$	−4.50000	−	7.79423i	−0.234579	−	0.406302i
$369$	1.50000	−	2.59808i	0.0780869	−	0.135250i
$370$	−7.00000			−0.363913
$371$		0			0
$372$	−16.0000			−0.829561
$373$	−1.00000	+	1.73205i	−0.0517780	+	0.0896822i	−0.890753	−	0.454488i	$-0.849822\pi$
$373$	−1.00000	+	1.73205i	−0.0517780	+	0.0896822i	0.838975	+	0.544170i	$0.183156\pi$
$374$	9.00000	+	15.5885i	0.465379	+	0.806060i
$375$	1.00000	+	1.73205i	0.0516398	+	0.0894427i
$376$	−4.50000	+	7.79423i	−0.232070	+	0.401957i
$377$	6.00000			0.309016
$378$		0			0
$379$	23.0000			1.18143			0.590715	−	0.806880i	$-0.298846\pi$
$379$	23.0000			1.18143			0.590715	+	0.806880i	$0.298846\pi$
$380$	0.500000	−	0.866025i	0.0256495	−	0.0444262i
$381$	1.00000	+	1.73205i	0.0512316	+	0.0887357i
$382$	6.00000	+	10.3923i	0.306987	+	0.531717i
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	−0.462563	−	0.886586i	$-0.653070\pi$
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	0.999088	−	0.0427020i	$-0.0135966\pi$
$384$	−2.00000			−0.102062
$385$		0			0
$386$	16.0000			0.814379
$387$	−1.00000	+	1.73205i	−0.0508329	+	0.0880451i
$388$	−5.00000	−	8.66025i	−0.253837	−	0.439658i
$389$	6.00000	+	10.3923i	0.304212	+	0.526911i	0.977086	−	0.212847i	$-0.0682735\pi$
$389$	6.00000	+	10.3923i	0.304212	+	0.526911i	−0.672874	+	0.739758i	$0.734940\pi$
$390$	−1.00000	+	1.73205i	−0.0506370	+	0.0877058i
$391$	54.0000			2.73090
$392$		0			0
$393$	−6.00000			−0.302660
$394$	7.50000	−	12.9904i	0.377845	−	0.654446i
$395$	−5.00000	−	8.66025i	−0.251577	−	0.435745i
$396$	−1.50000	−	2.59808i	−0.0753778	−	0.130558i
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	−0.635161	−	0.772380i	$-0.719066\pi$
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	0.986481	+	0.163876i	$0.0523996\pi$
$398$	−16.0000			−0.802008
$399$		0			0
$400$	1.00000			0.0500000
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	−0.302556	−	0.953131i	$-0.597840\pi$
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	0.976714	−	0.214544i	$-0.0688266\pi$
$402$	8.00000	+	13.8564i	0.399004	+	0.691095i
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$	6.00000	−	10.3923i	0.298511	−	0.517036i
$405$	11.0000			0.546594
$406$		0			0
$407$	−21.0000			−1.04093
$408$	6.00000	−	10.3923i	0.297044	−	0.514496i
$409$	13.0000	+	22.5167i	0.642809	+	1.11338i	0.984803	+	0.173675i	$0.0555643\pi$
$409$	13.0000	+	22.5167i	0.642809	+	1.11338i	−0.341994	+	0.939702i	$0.611102\pi$
$410$	1.50000	+	2.59808i	0.0740797	+	0.128310i
$411$	−12.0000	+	20.7846i	−0.591916	+	1.02523i
$412$	4.00000			0.197066
$413$		0			0
$414$	−9.00000			−0.442326
$415$		0			0
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	−4.00000	−	6.92820i	−0.195881	−	0.339276i
$418$	1.50000	−	2.59808i	0.0733674	−	0.127076i
$419$	9.00000			0.439679			0.219839	−	0.975536i	$-0.429447\pi$
$419$	9.00000			0.439679			0.219839	+	0.975536i	$0.429447\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$	11.5000	−	19.9186i	0.559811	−	0.969622i
$423$	4.50000	+	7.79423i	0.218797	+	0.378968i
$424$	4.50000	+	7.79423i	0.218539	+	0.378521i
$425$	−3.00000	+	5.19615i	−0.145521	+	0.252050i
$426$		0			0
$427$		0			0
$428$	−12.0000			−0.580042
$429$	−3.00000	+	5.19615i	−0.144841	+	0.250873i
$430$	−1.00000	−	1.73205i	−0.0482243	−	0.0835269i
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	40.0000			1.92228			0.961139	−	0.276066i	$-0.0890309\pi$
$433$	40.0000			1.92228			0.961139	+	0.276066i	$0.0890309\pi$
$434$		0			0
$435$	−12.0000			−0.575356
$436$	8.00000	−	13.8564i	0.383131	−	0.663602i
$437$	−4.50000	−	7.79423i	−0.215264	−	0.372849i
$438$	4.00000	+	6.92820i	0.191127	+	0.331042i
$439$	13.0000	−	22.5167i	0.620456	−	1.07466i	−0.368945	−	0.929451i	$-0.620281\pi$
$439$	13.0000	−	22.5167i	0.620456	−	1.07466i	0.989401	−	0.145210i	$-0.0463858\pi$
$440$	3.00000			0.143019
$441$		0			0
$442$	−6.00000			−0.285391
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	−0.972626	−	0.232377i	$-0.925350\pi$
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	0.687557	+	0.726130i	$0.258683\pi$
$444$	7.00000	+	12.1244i	0.332205	+	0.575396i
$445$	−3.00000	−	5.19615i	−0.142214	−	0.246321i
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$	−12.0000			−0.567581
$448$		0			0
$449$	21.0000			0.991051			0.495526	−	0.868593i	$-0.334975\pi$
$449$	21.0000			0.991051			0.495526	+	0.868593i	$0.334975\pi$
$450$	0.500000	−	0.866025i	0.0235702	−	0.0408248i
$451$	4.50000	+	7.79423i	0.211897	+	0.367016i
$452$		0			0
$453$	10.0000	−	17.3205i	0.469841	−	0.813788i
$454$	−12.0000			−0.563188
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	−7.00000	+	12.1244i	−0.327446	+	0.567153i	−0.982004	−	0.188858i	$-0.939521\pi$
$457$	−7.00000	+	12.1244i	−0.327446	+	0.567153i	0.654558	+	0.756012i	$0.272855\pi$
$458$	2.00000	+	3.46410i	0.0934539	+	0.161867i
$459$	12.0000	+	20.7846i	0.560112	+	0.970143i
$460$	4.50000	−	7.79423i	0.209814	−	0.363408i
$461$	30.0000			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$		0			0
$463$	−1.00000			−0.0464739			−0.0232370	−	0.999730i	$-0.507397\pi$
$463$	−1.00000			−0.0464739			−0.0232370	+	0.999730i	$0.507397\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	−8.00000	−	13.8564i	−0.370991	−	0.642575i
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$	−3.00000	+	5.19615i	−0.138823	+	0.240449i	−0.927052	−	0.374934i	$-0.877665\pi$
$467$	−3.00000	+	5.19615i	−0.138823	+	0.240449i	0.788228	+	0.615383i	$0.210999\pi$
$468$	1.00000			0.0462250
$469$		0			0
$470$	−9.00000			−0.415139
$471$	23.0000	−	39.8372i	1.05978	−	1.83560i
$472$		0			0
$473$	−3.00000	−	5.19615i	−0.137940	−	0.238919i
$474$	−10.0000	+	17.3205i	−0.459315	+	0.795557i
$475$	1.00000			0.0458831
$476$		0			0
$477$	9.00000			0.412082
$478$	−3.00000	+	5.19615i	−0.137217	+	0.237666i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$	−1.00000	−	1.73205i	−0.0456435	−	0.0790569i
$481$	3.50000	−	6.06218i	0.159586	−	0.276412i
$482$	−1.00000			−0.0455488
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	5.00000	−	8.66025i	0.227038	−	0.393242i
$486$	−5.00000	−	8.66025i	−0.226805	−	0.392837i
$487$	8.00000	+	13.8564i	0.362515	+	0.627894i	0.988374	−	0.152042i	$-0.0485850\pi$
$487$	8.00000	+	13.8564i	0.362515	+	0.627894i	−0.625859	+	0.779936i	$0.715252\pi$
$488$	−4.00000	+	6.92820i	−0.181071	+	0.313625i
$489$	40.0000			1.80886
$490$		0			0
$491$	36.0000			1.62466			0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000			1.62466			0.812329	+	0.583200i	$0.198200\pi$
$492$	3.00000	−	5.19615i	0.135250	−	0.234261i
$493$	−18.0000	−	31.1769i	−0.810679	−	1.40414i
$494$	0.500000	+	0.866025i	0.0224961	+	0.0389643i
$495$	1.50000	−	2.59808i	0.0674200	−	0.116775i
$496$	−8.00000			−0.359211
$497$		0			0
$498$		0			0
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	−0.817781	−	0.575529i	$-0.804796\pi$
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	0.907314	+	0.420455i	$0.138129\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	3.00000	+	5.19615i	0.134030	+	0.232147i
$502$	7.50000	−	12.9904i	0.334741	−	0.579789i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	12.0000			0.533993
$506$	13.5000	−	23.3827i	0.600148	−	1.03949i
$507$	12.0000	+	20.7846i	0.532939	+	0.923077i
$508$	0.500000	+	0.866025i	0.0221839	+	0.0384237i
$509$	−21.0000	+	36.3731i	−0.930809	+	1.61221i	−0.148866	+	0.988857i	$0.547562\pi$
$509$	−21.0000	+	36.3731i	−0.930809	+	1.61221i	−0.781943	+	0.623350i	$0.785771\pi$
$510$	12.0000			0.531369
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	2.00000	−	3.46410i	0.0883022	−	0.152944i
$514$		0			0
$515$	2.00000	+	3.46410i	0.0881305	+	0.152647i
$516$	−2.00000	+	3.46410i	−0.0880451	+	0.152499i
$517$	−27.0000			−1.18746
$518$		0			0
$519$	−18.0000			−0.790112
$520$	−0.500000	+	0.866025i	−0.0219265	+	0.0379777i
$521$	−7.50000	−	12.9904i	−0.328581	−	0.569119i	0.653650	−	0.756797i	$-0.273237\pi$
$521$	−7.50000	−	12.9904i	−0.328581	−	0.569119i	−0.982231	+	0.187678i	$0.939904\pi$
$522$	3.00000	+	5.19615i	0.131306	+	0.227429i
$523$	−14.0000	+	24.2487i	−0.612177	+	1.06032i	0.378695	+	0.925521i	$0.376373\pi$
$523$	−14.0000	+	24.2487i	−0.612177	+	1.06032i	−0.990873	+	0.134801i	$0.956961\pi$
$524$	−3.00000			−0.131056
$525$		0			0
$526$		0			0
$527$	24.0000	−	41.5692i	1.04546	−	1.81078i
$528$	−3.00000	−	5.19615i	−0.130558	−	0.226134i
$529$	−29.0000	−	50.2295i	−1.26087	−	2.18389i
$530$	−4.50000	+	7.79423i	−0.195468	+	0.338560i
$531$		0			0
$532$		0			0
$533$	−3.00000			−0.129944
$534$	−6.00000	+	10.3923i	−0.259645	+	0.449719i
$535$	−6.00000	−	10.3923i	−0.259403	−	0.449299i
$536$	4.00000	+	6.92820i	0.172774	+	0.299253i
$537$	3.00000	−	5.19615i	0.129460	−	0.224231i
$538$		0			0
$539$		0			0
$540$	4.00000			0.172133
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	−0.939110	−	0.343617i	$-0.888348\pi$
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	0.767136	+	0.641484i	$0.221681\pi$
$542$	8.00000	+	13.8564i	0.343629	+	0.595184i
$543$	2.00000	+	3.46410i	0.0858282	+	0.148659i
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$	16.0000			0.685365
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	−6.00000	+	10.3923i	−0.256307	+	0.443937i
$549$	4.00000	+	6.92820i	0.170716	+	0.295689i
$550$	1.50000	+	2.59808i	0.0639602	+	0.110782i
$551$	−3.00000	+	5.19615i	−0.127804	+	0.221364i
$552$	−18.0000			−0.766131
$553$		0			0
$554$	10.0000			0.424859
$555$	−7.00000	+	12.1244i	−0.297133	+	0.514650i
$556$	−2.00000	−	3.46410i	−0.0848189	−	0.146911i
$557$	4.50000	+	7.79423i	0.190671	+	0.330252i	0.945473	−	0.325701i	$-0.105600\pi$
$557$	4.50000	+	7.79423i	0.190671	+	0.330252i	−0.754802	+	0.655953i	$0.772267\pi$
$558$	−4.00000	+	6.92820i	−0.169334	+	0.293294i
$559$	2.00000			0.0845910
$560$		0			0
$561$	36.0000			1.51992
$562$	−13.5000	+	23.3827i	−0.569463	+	0.986339i
$563$	21.0000	+	36.3731i	0.885044	+	1.53294i	0.845663	+	0.533718i	$0.179206\pi$
$563$	21.0000	+	36.3731i	0.885044	+	1.53294i	0.0393818	+	0.999224i	$0.487461\pi$
$564$	9.00000	+	15.5885i	0.378968	+	0.656392i
$565$		0			0
$566$	14.0000			0.588464
$567$		0			0
$568$		0			0
$569$	−10.5000	+	18.1865i	−0.440183	+	0.762419i	−0.997703	−	0.0677445i	$-0.978420\pi$
$569$	−10.5000	+	18.1865i	−0.440183	+	0.762419i	0.557520	+	0.830164i	$0.311753\pi$
$570$	−1.00000	−	1.73205i	−0.0418854	−	0.0725476i
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	−1.50000	+	2.59808i	−0.0627182	+	0.108631i
$573$	24.0000			1.00261
$574$		0			0
$575$	9.00000			0.375326
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	22.0000	+	38.1051i	0.915872	+	1.58634i	0.805620	+	0.592433i	$0.201833\pi$
$577$	22.0000	+	38.1051i	0.915872	+	1.58634i	0.110252	+	0.993904i	$0.464834\pi$
$578$	9.50000	+	16.4545i	0.395148	+	0.684416i
$579$	16.0000	−	27.7128i	0.664937	−	1.15171i
$580$	−6.00000			−0.249136
$581$		0			0
$582$	−20.0000			−0.829027
$583$	−13.5000	+	23.3827i	−0.559113	+	0.968412i
$584$	2.00000	+	3.46410i	0.0827606	+	0.143346i
$585$	0.500000	+	0.866025i	0.0206725	+	0.0358057i
$586$	4.50000	−	7.79423i	0.185893	−	0.321977i
$587$	24.0000			0.990586			0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000			0.990586			0.495293	+	0.868726i	$0.335061\pi$
$588$		0			0
$589$	−8.00000			−0.329634
$590$		0			0
$591$	−15.0000	−	25.9808i	−0.617018	−	1.06871i
$592$	3.50000	+	6.06218i	0.143849	+	0.249154i
$593$	12.0000	−	20.7846i	0.492781	−	0.853522i	−0.507184	−	0.861838i	$-0.669314\pi$
$593$	12.0000	−	20.7846i	0.492781	−	0.853522i	0.999965	+	0.00831589i	$0.00264706\pi$
$594$	12.0000			0.492366
$595$		0			0
$596$	−6.00000			−0.245770
$597$	−16.0000	+	27.7128i	−0.654836	+	1.13421i
$598$	4.50000	+	7.79423i	0.184019	+	0.318730i
$599$	21.0000	+	36.3731i	0.858037	+	1.48616i	0.873799	+	0.486287i	$0.161649\pi$
$599$	21.0000	+	36.3731i	0.858037	+	1.48616i	−0.0157622	+	0.999876i	$0.505017\pi$
$600$	1.00000	−	1.73205i	0.0408248	−	0.0707107i
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$		0			0
$603$	8.00000			0.325785
$604$	5.00000	−	8.66025i	0.203447	−	0.352381i
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$	−12.0000	−	20.7846i	−0.487467	−	0.844317i
$607$	−0.500000	+	0.866025i	−0.0202944	+	0.0351509i	−0.875994	−	0.482322i	$-0.839794\pi$
$607$	−0.500000	+	0.866025i	−0.0202944	+	0.0351509i	0.855700	+	0.517472i	$0.173127\pi$
$608$	−1.00000			−0.0405554
$609$		0			0
$610$	−8.00000			−0.323911
$611$	4.50000	−	7.79423i	0.182051	−	0.315321i
$612$	−3.00000	−	5.19615i	−0.121268	−	0.210042i
$613$	−14.5000	−	25.1147i	−0.585649	−	1.01437i	−0.994794	−	0.101905i	$-0.967506\pi$
$613$	−14.5000	−	25.1147i	−0.585649	−	1.01437i	0.409145	−	0.912470i	$-0.365827\pi$
$614$	−7.00000	+	12.1244i	−0.282497	+	0.489299i
$615$	6.00000			0.241943
$616$		0			0
$617$	−18.0000			−0.724653			−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000			−0.724653			−0.362326	+	0.932051i	$0.618017\pi$
$618$	4.00000	−	6.92820i	0.160904	−	0.278693i
$619$	11.5000	+	19.9186i	0.462224	+	0.800595i	0.999071	−	0.0430838i	$-0.0137183\pi$
$619$	11.5000	+	19.9186i	0.462224	+	0.800595i	−0.536847	+	0.843679i	$0.680385\pi$
$620$	−4.00000	−	6.92820i	−0.160644	−	0.278243i
$621$	18.0000	−	31.1769i	0.722315	−	1.25109i
$622$	−24.0000			−0.962312
$623$		0			0
$624$	2.00000			0.0800641
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	14.0000	+	24.2487i	0.559553	+	0.969173i
$627$	−3.00000	−	5.19615i	−0.119808	−	0.207514i
$628$	11.5000	−	19.9186i	0.458900	−	0.794838i
$629$	−42.0000			−1.67465
$630$		0			0
$631$	20.0000			0.796187			0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000			0.796187			0.398094	+	0.917345i	$0.369672\pi$
$632$	−5.00000	+	8.66025i	−0.198889	+	0.344486i
$633$	−23.0000	−	39.8372i	−0.914168	−	1.58339i
$634$	3.00000	+	5.19615i	0.119145	+	0.206366i
$635$	−0.500000	+	0.866025i	−0.0198419	+	0.0343672i
$636$	18.0000			0.713746
$637$		0			0
$638$	−18.0000			−0.712627
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−13.5000	−	23.3827i	−0.533218	−	0.923561i	−0.999247	−	0.0387913i	$-0.987649\pi$
$641$	−13.5000	−	23.3827i	−0.533218	−	0.923561i	0.466029	−	0.884769i	$-0.345684\pi$
$642$	−12.0000	+	20.7846i	−0.473602	+	0.820303i
$643$	−2.00000			−0.0788723			−0.0394362	−	0.999222i	$-0.512556\pi$
$643$	−2.00000			−0.0788723			−0.0394362	+	0.999222i	$0.512556\pi$
$644$		0			0
$645$	−4.00000			−0.157500
$646$	3.00000	−	5.19615i	0.118033	−	0.204440i
$647$	16.5000	+	28.5788i	0.648682	+	1.12355i	0.983438	+	0.181245i	$0.0580128\pi$
$647$	16.5000	+	28.5788i	0.648682	+	1.12355i	−0.334756	+	0.942305i	$0.608654\pi$
$648$	−5.50000	−	9.52628i	−0.216060	−	0.374228i
$649$		0			0
$650$	−1.00000			−0.0392232
$651$		0			0
$652$	20.0000			0.783260
$653$	4.50000	−	7.79423i	0.176099	−	0.305012i	−0.764442	−	0.644692i	$-0.776986\pi$
$653$	4.50000	−	7.79423i	0.176099	−	0.305012i	0.940541	+	0.339680i	$0.110319\pi$
$654$	−16.0000	−	27.7128i	−0.625650	−	1.08366i
$655$	−1.50000	−	2.59808i	−0.0586098	−	0.101515i
$656$	1.50000	−	2.59808i	0.0585652	−	0.101438i
$657$	4.00000			0.156055
$658$		0			0
$659$	−24.0000			−0.934907			−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000			−0.934907			−0.467454	+	0.884018i	$0.654829\pi$
$660$	3.00000	−	5.19615i	0.116775	−	0.202260i
$661$	−14.0000	−	24.2487i	−0.544537	−	0.943166i	−0.998636	−	0.0522143i	$-0.983372\pi$
$661$	−14.0000	−	24.2487i	−0.544537	−	0.943166i	0.454099	−	0.890951i	$-0.349961\pi$
$662$	−3.50000	−	6.06218i	−0.136031	−	0.235613i
$663$	−6.00000	+	10.3923i	−0.233021	+	0.403604i
$664$		0			0
$665$		0			0
$666$	7.00000			0.271244
$667$	−27.0000	+	46.7654i	−1.04544	+	1.81076i
$668$	1.50000	+	2.59808i	0.0580367	+	0.100523i
$669$	8.00000	+	13.8564i	0.309298	+	0.535720i
$670$	−4.00000	+	6.92820i	−0.154533	+	0.267660i
$671$	−24.0000			−0.926510
$672$		0			0
$673$	−34.0000			−1.31060			−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000			−1.31060			−0.655302	+	0.755367i	$0.727459\pi$
$674$	−11.0000	+	19.0526i	−0.423704	+	0.733877i
$675$	2.00000	+	3.46410i	0.0769800	+	0.133333i
$676$	6.00000	+	10.3923i	0.230769	+	0.399704i
$677$	−4.50000	+	7.79423i	−0.172949	+	0.299557i	−0.939450	−	0.342687i	$-0.888663\pi$
$677$	−4.50000	+	7.79423i	−0.172949	+	0.299557i	0.766501	+	0.642244i	$0.221996\pi$
$678$		0			0
$679$		0			0
$680$	6.00000			0.230089
$681$	−12.0000	+	20.7846i	−0.459841	+	0.796468i
$682$	−12.0000	−	20.7846i	−0.459504	−	0.795884i
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	0.728101	−	0.685470i	$-0.240403\pi$
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	−0.957685	+	0.287819i	$0.907070\pi$
$684$	−0.500000	+	0.866025i	−0.0191180	+	0.0331133i
$685$	−12.0000			−0.458496
$686$		0			0
$687$	8.00000			0.305219
$688$	−1.00000	+	1.73205i	−0.0381246	+	0.0660338i
$689$	−4.50000	−	7.79423i	−0.171436	−	0.296936i
$690$	−9.00000	−	15.5885i	−0.342624	−	0.593442i
$691$	16.0000	−	27.7128i	0.608669	−	1.05425i	−0.382791	−	0.923835i	$-0.625037\pi$
$691$	16.0000	−	27.7128i	0.608669	−	1.05425i	0.991460	−	0.130410i	$-0.0416295\pi$
$692$	−9.00000			−0.342129
$693$		0			0
$694$		0			0
$695$	2.00000	−	3.46410i	0.0758643	−	0.131401i
$696$	6.00000	+	10.3923i	0.227429	+	0.393919i
$697$	9.00000	+	15.5885i	0.340899	+	0.590455i
$698$	−13.0000	+	22.5167i	−0.492057	+	0.852268i
$699$	−12.0000			−0.453882
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$	−2.00000	+	3.46410i	−0.0754851	+	0.130744i
$703$	3.50000	+	6.06218i	0.132005	+	0.228639i
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$	−9.00000	+	15.5885i	−0.338960	+	0.587095i
$706$	12.0000			0.451626
$707$		0			0
$708$		0			0
$709$	23.0000	−	39.8372i	0.863783	−	1.49612i	−0.00446726	−	0.999990i	$-0.501422\pi$
$709$	23.0000	−	39.8372i	0.863783	−	1.49612i	0.868250	−	0.496126i	$-0.165245\pi$
$710$		0			0
$711$	5.00000	+	8.66025i	0.187515	+	0.324785i
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$	−72.0000			−2.69642
$714$		0			0
$715$	−3.00000			−0.112194
$716$	1.50000	−	2.59808i	0.0560576	−	0.0970947i
$717$	6.00000	+	10.3923i	0.224074	+	0.388108i
$718$	9.00000	+	15.5885i	0.335877	+	0.581756i
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$	−1.00000			−0.0372678
$721$		0			0
$722$	18.0000			0.669891
$723$	−1.00000	+	1.73205i	−0.0371904	+	0.0644157i
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	−2.00000	+	3.46410i	−0.0742270	+	0.128565i
$727$	1.00000			0.0370879			0.0185440	−	0.999828i	$-0.494097\pi$
$727$	1.00000			0.0370879			0.0185440	+	0.999828i	$0.494097\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−2.00000	+	3.46410i	−0.0740233	+	0.128212i
$731$	−6.00000	−	10.3923i	−0.221918	−	0.384373i
$732$	8.00000	+	13.8564i	0.295689	+	0.512148i
$733$	−21.5000	+	37.2391i	−0.794121	+	1.37546i	0.129275	+	0.991609i	$0.458735\pi$
$733$	−21.5000	+	37.2391i	−0.794121	+	1.37546i	−0.923396	+	0.383849i	$0.874598\pi$
$734$	−19.0000			−0.701303
$735$		0			0
$736$	−9.00000			−0.331744
$737$	−12.0000	+	20.7846i	−0.442026	+	0.765611i
$738$	−1.50000	−	2.59808i	−0.0552158	−	0.0956365i
$739$	−17.5000	−	30.3109i	−0.643748	−	1.11500i	−0.984589	−	0.174883i	$-0.944045\pi$
$739$	−17.5000	−	30.3109i	−0.643748	−	1.11500i	0.340841	−	0.940121i	$-0.389288\pi$
$740$	−3.50000	+	6.06218i	−0.128663	+	0.222850i
$741$	2.00000			0.0734718
$742$		0			0
$743$	−45.0000			−1.65089			−0.825445	−	0.564483i	$-0.809076\pi$
$743$	−45.0000			−1.65089			−0.825445	+	0.564483i	$0.809076\pi$
$744$	−8.00000	+	13.8564i	−0.293294	+	0.508001i
$745$	−3.00000	−	5.19615i	−0.109911	−	0.190372i
$746$	1.00000	+	1.73205i	0.0366126	+	0.0634149i
$747$		0			0
$748$	18.0000			0.658145
$749$		0			0
$750$	2.00000			0.0730297
$751$	5.00000	−	8.66025i	0.182453	−	0.316017i	−0.760263	−	0.649616i	$-0.774930\pi$
$751$	5.00000	−	8.66025i	0.182453	−	0.316017i	0.942715	+	0.333599i	$0.108263\pi$
$752$	4.50000	+	7.79423i	0.164098	+	0.284226i
$753$	−15.0000	−	25.9808i	−0.546630	−	0.946792i
$754$	3.00000	−	5.19615i	0.109254	−	0.189233i
$755$	10.0000			0.363937
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$	11.5000	−	19.9186i	0.417699	−	0.723476i
$759$	−27.0000	−	46.7654i	−0.980038	−	1.69748i
$760$	−0.500000	−	0.866025i	−0.0181369	−	0.0314140i
$761$	−13.5000	+	23.3827i	−0.489375	+	0.847622i	−0.999925	−	0.0122260i	$-0.996108\pi$
$761$	−13.5000	+	23.3827i	−0.489375	+	0.847622i	0.510551	+	0.859848i	$0.329442\pi$
$762$	2.00000			0.0724524
$763$		0			0
$764$	12.0000			0.434145
$765$	3.00000	−	5.19615i	0.108465	−	0.187867i
$766$	−10.5000	−	18.1865i	−0.379380	−	0.657106i
$767$		0			0
$768$	−1.00000	+	1.73205i	−0.0360844	+	0.0625000i
$769$	−23.0000			−0.829401			−0.414701	−	0.909958i	$-0.636114\pi$
$769$	−23.0000			−0.829401			−0.414701	+	0.909958i	$0.636114\pi$
$770$		0			0
$771$		0			0
$772$	8.00000	−	13.8564i	0.287926	−	0.498703i
$773$	−25.5000	−	44.1673i	−0.917171	−	1.58859i	−0.803691	−	0.595047i	$-0.797133\pi$
$773$	−25.5000	−	44.1673i	−0.917171	−	1.58859i	−0.113480	−	0.993540i	$-0.536200\pi$
$774$	1.00000	+	1.73205i	0.0359443	+	0.0622573i
$775$	4.00000	−	6.92820i	0.143684	−	0.248868i
$776$	−10.0000			−0.358979
$777$		0			0
$778$	12.0000			0.430221
$779$	1.50000	−	2.59808i	0.0537431	−	0.0930857i
$780$	1.00000	+	1.73205i	0.0358057	+	0.0620174i
$781$		0			0
$782$	27.0000	−	46.7654i	0.965518	−	1.67233i
$783$	−24.0000			−0.857690
$784$		0			0
$785$	23.0000			0.820905
$786$	−3.00000	+	5.19615i	−0.107006	+	0.185341i
$787$	−11.0000	−	19.0526i	−0.392108	−	0.679150i	0.600620	−	0.799535i	$-0.294921\pi$
$787$	−11.0000	−	19.0526i	−0.392108	−	0.679150i	−0.992727	+	0.120384i	$0.961587\pi$
$788$	−7.50000	−	12.9904i	−0.267176	−	0.462763i
$789$		0			0
$790$	−10.0000			−0.355784
$791$		0			0
$792$	−3.00000			−0.106600
$793$	4.00000	−	6.92820i	0.142044	−	0.246028i
$794$	−7.00000	−	12.1244i	−0.248421	−	0.430277i
$795$	9.00000	+	15.5885i	0.319197	+	0.552866i
$796$	−8.00000	+	13.8564i	−0.283552	+	0.491127i
$797$	−6.00000			−0.212531			−0.106265	−	0.994338i	$-0.533889\pi$
$797$	−6.00000			−0.212531			−0.106265	+	0.994338i	$0.533889\pi$
$798$		0			0
$799$	−54.0000			−1.91038
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	3.00000	+	5.19615i	0.106000	+	0.183597i
$802$	−13.5000	−	23.3827i	−0.476702	−	0.825671i
$803$	−6.00000	+	10.3923i	−0.211735	+	0.366736i
$804$	16.0000			0.564276
$805$		0			0
$806$	8.00000			0.281788
$807$		0			0
$808$	−6.00000	−	10.3923i	−0.211079	−	0.365600i
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	0.934224	−	0.356687i	$-0.116094\pi$
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	−0.776012	+	0.630718i	$0.782761\pi$
$810$	5.50000	−	9.52628i	0.193250	−	0.334719i
$811$	25.0000			0.877869			0.438934	−	0.898519i	$-0.355356\pi$
$811$	25.0000			0.877869			0.438934	+	0.898519i	$0.355356\pi$
$812$		0			0
$813$	32.0000			1.12229
$814$	−10.5000	+	18.1865i	−0.368025	+	0.637438i
$815$	10.0000	+	17.3205i	0.350285	+	0.606711i
$816$	−6.00000	−	10.3923i	−0.210042	−	0.363803i
$817$	−1.00000	+	1.73205i	−0.0349856	+	0.0605968i
$818$	26.0000			0.909069
$819$		0			0
$820$	3.00000			0.104765
$821$	−15.0000	+	25.9808i	−0.523504	+	0.906735i	0.476122	+	0.879379i	$0.342042\pi$
$821$	−15.0000	+	25.9808i	−0.523504	+	0.906735i	−0.999626	+	0.0273557i	$0.991291\pi$
$822$	12.0000	+	20.7846i	0.418548	+	0.724947i
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	0.898776	−	0.438408i	$-0.144457\pi$
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	−0.829060	+	0.559159i	$0.811124\pi$
$824$	2.00000	−	3.46410i	0.0696733	−	0.120678i
$825$	6.00000			0.208893
$826$		0			0
$827$	6.00000			0.208640			0.104320	−	0.994544i	$-0.466733\pi$
$827$	6.00000			0.208640			0.104320	+	0.994544i	$0.466733\pi$
$828$	−4.50000	+	7.79423i	−0.156386	+	0.270868i
$829$	7.00000	+	12.1244i	0.243120	+	0.421096i	0.961601	−	0.274450i	$-0.0884958\pi$
$829$	7.00000	+	12.1244i	0.243120	+	0.421096i	−0.718481	+	0.695546i	$0.755162\pi$
$830$		0			0
$831$	10.0000	−	17.3205i	0.346896	−	0.600842i
$832$	1.00000			0.0346688
$833$		0			0
$834$	−8.00000			−0.277017
$835$	−1.50000	+	2.59808i	−0.0519096	+	0.0899101i
$836$	−1.50000	−	2.59808i	−0.0518786	−	0.0898563i
$837$	−16.0000	−	27.7128i	−0.553041	−	0.957895i
$838$	4.50000	−	7.79423i	0.155450	−	0.269247i
$839$	30.0000			1.03572			0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000			1.03572			0.517858	+	0.855467i	$0.326730\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	1.00000	−	1.73205i	0.0344623	−	0.0596904i
$843$	27.0000	+	46.7654i	0.929929	+	1.61068i
$844$	−11.5000	−	19.9186i	−0.395846	−	0.685626i
$845$	−6.00000	+	10.3923i	−0.206406	+	0.357506i
$846$	9.00000			0.309426
$847$		0			0
$848$	9.00000			0.309061
$849$	14.0000	−	24.2487i	0.480479	−	0.832214i
$850$	3.00000	+	5.19615i	0.102899	+	0.178227i
$851$	31.5000	+	54.5596i	1.07981	+	1.87028i
$852$		0			0
$853$	19.0000			0.650548			0.325274	−	0.945620i	$-0.394544\pi$
$853$	19.0000			0.650548			0.325274	+	0.945620i	$0.394544\pi$
$854$		0			0
$855$	−1.00000			−0.0341993
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	0.670366	−	0.742030i	$-0.266137\pi$
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	−0.977800	+	0.209539i	$0.932804\pi$
$858$	3.00000	+	5.19615i	0.102418	+	0.177394i
$859$	16.0000	−	27.7128i	0.545913	−	0.945549i	−0.452636	−	0.891695i	$-0.649516\pi$
$859$	16.0000	−	27.7128i	0.545913	−	0.945549i	0.998549	−	0.0538535i	$-0.0171504\pi$
$860$	−2.00000			−0.0681994
$861$		0			0
$862$	−12.0000			−0.408722
$863$	1.50000	−	2.59808i	0.0510606	−	0.0884395i	−0.839365	−	0.543568i	$-0.817073\pi$
$863$	1.50000	−	2.59808i	0.0510606	−	0.0884395i	0.890426	+	0.455128i	$0.150407\pi$
$864$	−2.00000	−	3.46410i	−0.0680414	−	0.117851i
$865$	−4.50000	−	7.79423i	−0.153005	−	0.265012i
$866$	20.0000	−	34.6410i	0.679628	−	1.17715i
$867$	38.0000			1.29055
$868$		0			0
$869$	−30.0000			−1.01768
$870$	−6.00000	+	10.3923i	−0.203419	+	0.352332i
$871$	−4.00000	−	6.92820i	−0.135535	−	0.234753i
$872$	−8.00000	−	13.8564i	−0.270914	−	0.469237i
$873$	−5.00000	+	8.66025i	−0.169224	+	0.293105i
$874$	−9.00000			−0.304430
$875$		0			0
$876$	8.00000			0.270295
$877$	6.50000	−	11.2583i	0.219489	−	0.380167i	−0.735163	−	0.677891i	$-0.762894\pi$
$877$	6.50000	−	11.2583i	0.219489	−	0.380167i	0.954652	+	0.297724i	$0.0962275\pi$
$878$	−13.0000	−	22.5167i	−0.438729	−	0.759900i
$879$	−9.00000	−	15.5885i	−0.303562	−	0.525786i
$880$	1.50000	−	2.59808i	0.0505650	−	0.0875811i
$881$	−33.0000			−1.11180			−0.555899	−	0.831250i	$-0.687626\pi$
$881$	−33.0000			−1.11180			−0.555899	+	0.831250i	$0.687626\pi$
$882$		0			0
$883$	8.00000			0.269221			0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000			0.269221			0.134611	+	0.990899i	$0.457022\pi$
$884$	−3.00000	+	5.19615i	−0.100901	+	0.174766i
$885$		0			0
$886$	6.00000	+	10.3923i	0.201574	+	0.349136i
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	0.109881	+	0.993945i	$0.464953\pi$
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	−0.915722	+	0.401813i	$0.868380\pi$
$888$	14.0000			0.469809
$889$		0			0
$890$	−6.00000			−0.201120
$891$	16.5000	−	28.5788i	0.552771	−	0.957427i
$892$	4.00000	+	6.92820i	0.133930	+	0.231973i
$893$	4.50000	+	7.79423i	0.150587	+	0.260824i
$894$	−6.00000	+	10.3923i	−0.200670	+	0.347571i
$895$	3.00000			0.100279
$896$		0			0
$897$	18.0000			0.601003
$898$	10.5000	−	18.1865i	0.350390	−	0.606892i
$899$	24.0000	+	41.5692i	0.800445	+	1.38641i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−27.0000	+	46.7654i	−0.899500	+	1.55798i
$902$	9.00000			0.299667
$903$		0			0
$904$		0			0
$905$	−1.00000	+	1.73205i	−0.0332411	+	0.0575753i
$906$	−10.0000	−	17.3205i	−0.332228	−	0.575435i
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	0.937018	−	0.349281i	$-0.113574\pi$
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	−0.770996	+	0.636841i	$0.780241\pi$
$908$	−6.00000	+	10.3923i	−0.199117	+	0.344881i
$909$	−12.0000			−0.398015
$910$		0			0
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$	−1.00000	+	1.73205i	−0.0331133	+	0.0573539i
$913$		0			0
$914$	7.00000	+	12.1244i	0.231539	+	0.401038i
$915$	−8.00000	+	13.8564i	−0.264472	+	0.458079i
$916$	4.00000			0.132164
$917$		0			0
$918$	24.0000			0.792118
$919$	11.0000	−	19.0526i	0.362857	−	0.628486i	−0.625573	−	0.780165i	$-0.715135\pi$
$919$	11.0000	−	19.0526i	0.362857	−	0.628486i	0.988430	+	0.151680i	$0.0484682\pi$
$920$	−4.50000	−	7.79423i	−0.148361	−	0.256968i
$921$	14.0000	+	24.2487i	0.461316	+	0.799022i
$922$	15.0000	−	25.9808i	0.493999	−	0.855631i
$923$		0			0
$924$		0			0
$925$	−7.00000			−0.230159
$926$	−0.500000	+	0.866025i	−0.0164310	+	0.0284594i
$927$	−2.00000	−	3.46410i	−0.0656886	−	0.113776i
$928$	3.00000	+	5.19615i	0.0984798	+	0.170572i
$929$	28.5000	−	49.3634i	0.935055	−	1.61956i	0.160518	−	0.987033i	$-0.448683\pi$
$929$	28.5000	−	49.3634i	0.935055	−	1.61956i	0.774536	−	0.632529i	$-0.217983\pi$
$930$	−16.0000			−0.524661
$931$		0			0
$932$	−6.00000			−0.196537
$933$	−24.0000	+	41.5692i	−0.785725	+	1.36092i
$934$	3.00000	+	5.19615i	0.0981630	+	0.170023i
$935$	9.00000	+	15.5885i	0.294331	+	0.509797i
$936$	0.500000	−	0.866025i	0.0163430	−	0.0283069i
$937$	10.0000			0.326686			0.163343	−	0.986569i	$-0.447772\pi$
$937$	10.0000			0.326686			0.163343	+	0.986569i	$0.447772\pi$
$938$		0			0
$939$	56.0000			1.82749
$940$	−4.50000	+	7.79423i	−0.146774	+	0.254220i
$941$	24.0000	+	41.5692i	0.782378	+	1.35512i	0.930553	+	0.366157i	$0.119327\pi$
$941$	24.0000	+	41.5692i	0.782378	+	1.35512i	−0.148176	+	0.988961i	$0.547340\pi$
$942$	−23.0000	−	39.8372i	−0.749380	−	1.29797i
$943$	13.5000	−	23.3827i	0.439620	−	0.761445i
$944$		0			0
$945$		0			0
$946$	−6.00000			−0.195077
$947$	−3.00000	+	5.19615i	−0.0974869	+	0.168852i	−0.910644	−	0.413192i	$-0.864414\pi$
$947$	−3.00000	+	5.19615i	−0.0974869	+	0.168852i	0.813157	+	0.582045i	$0.197747\pi$
$948$	10.0000	+	17.3205i	0.324785	+	0.562544i
$949$	−2.00000	−	3.46410i	−0.0649227	−	0.112449i
$950$	0.500000	−	0.866025i	0.0162221	−	0.0280976i
$951$	12.0000			0.389127
$952$		0			0
$953$	36.0000			1.16615			0.583077	−	0.812417i	$-0.301849\pi$
$953$	36.0000			1.16615			0.583077	+	0.812417i	$0.301849\pi$
$954$	4.50000	−	7.79423i	0.145693	−	0.252347i
$955$	6.00000	+	10.3923i	0.194155	+	0.336287i
$956$	3.00000	+	5.19615i	0.0970269	+	0.168056i
$957$	−18.0000	+	31.1769i	−0.581857	+	1.00781i
$958$		0			0
$959$		0			0
$960$	−2.00000			−0.0645497
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	−3.50000	−	6.06218i	−0.112845	−	0.195452i
$963$	6.00000	+	10.3923i	0.193347	+	0.334887i
$964$	−0.500000	+	0.866025i	−0.0161039	+	0.0278928i
$965$	16.0000			0.515058
$966$		0			0
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$	−6.00000	−	10.3923i	−0.192748	−	0.333849i
$970$	−5.00000	−	8.66025i	−0.160540	−	0.278064i
$971$	−22.5000	+	38.9711i	−0.722059	+	1.25064i	0.238114	+	0.971237i	$0.423471\pi$
$971$	−22.5000	+	38.9711i	−0.722059	+	1.25064i	−0.960173	+	0.279406i	$0.909862\pi$
$972$	−10.0000			−0.320750
$973$		0			0
$974$	16.0000			0.512673
$975$	−1.00000	+	1.73205i	−0.0320256	+	0.0554700i
$976$	4.00000	+	6.92820i	0.128037	+	0.221766i
$977$	21.0000	+	36.3731i	0.671850	+	1.16368i	0.977379	+	0.211495i	$0.0678332\pi$
$977$	21.0000	+	36.3731i	0.671850	+	1.16368i	−0.305530	+	0.952183i	$0.598833\pi$
$978$	20.0000	−	34.6410i	0.639529	−	1.10770i
$979$	−18.0000			−0.575282
$980$		0			0
$981$	−16.0000			−0.510841
$982$	18.0000	−	31.1769i	0.574403	−	0.994895i
$983$	1.50000	+	2.59808i	0.0478426	+	0.0828658i	0.888955	−	0.457995i	$-0.151432\pi$
$983$	1.50000	+	2.59808i	0.0478426	+	0.0828658i	−0.841112	+	0.540860i	$0.818099\pi$
$984$	−3.00000	−	5.19615i	−0.0956365	−	0.165647i
$985$	7.50000	−	12.9904i	0.238970	−	0.413908i
$986$	−36.0000			−1.14647
$987$		0			0
$988$	1.00000			0.0318142
$989$	−9.00000	+	15.5885i	−0.286183	+	0.495684i
$990$	−1.50000	−	2.59808i	−0.0476731	−	0.0825723i
$991$	−22.0000	−	38.1051i	−0.698853	−	1.21045i	−0.968864	−	0.247592i	$-0.920361\pi$
$991$	−22.0000	−	38.1051i	−0.698853	−	1.21045i	0.270011	−	0.962857i	$-0.412973\pi$
$992$	−4.00000	+	6.92820i	−0.127000	+	0.219971i
$993$	−14.0000			−0.444277
$994$		0			0
$995$	−16.0000			−0.507234
$996$		0			0
$997$	−11.0000	−	19.0526i	−0.348373	−	0.603401i	0.637587	−	0.770378i	$-0.279933\pi$
$997$	−11.0000	−	19.0526i	−0.348373	−	0.603401i	−0.985961	+	0.166978i	$0.946599\pi$
$998$	−2.00000	−	3.46410i	−0.0633089	−	0.109654i
$999$	−14.0000	+	24.2487i	−0.442940	+	0.767195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.e.g.471.1		2
7.2	even	3		490.2.a.d.1.1		1
7.3	odd	6		70.2.e.d.11.1	✓	2
7.4	even	3	inner	490.2.e.g.361.1		2
7.5	odd	6		490.2.a.a.1.1		1
7.6	odd	2		70.2.e.d.51.1	yes	2
21.2	odd	6		4410.2.a.bg.1.1		1
21.5	even	6		4410.2.a.x.1.1		1
21.17	even	6		630.2.k.d.361.1		2
21.20	even	2		630.2.k.d.541.1		2
28.3	even	6		560.2.q.b.81.1		2
28.19	even	6		3920.2.a.bh.1.1		1
28.23	odd	6		3920.2.a.e.1.1		1
28.27	even	2		560.2.q.b.401.1		2
35.2	odd	12		2450.2.c.e.99.1		2
35.3	even	12		350.2.j.d.249.2		4
35.9	even	6		2450.2.a.v.1.1		1
35.12	even	12		2450.2.c.q.99.1		2
35.13	even	4		350.2.j.d.149.1		4
35.17	even	12		350.2.j.d.249.1		4
35.19	odd	6		2450.2.a.bf.1.1		1
35.23	odd	12		2450.2.c.e.99.2		2
35.24	odd	6		350.2.e.b.151.1		2
35.27	even	4		350.2.j.d.149.2		4
35.33	even	12		2450.2.c.q.99.2		2
35.34	odd	2		350.2.e.b.51.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.e.d.11.1	✓	2	7.3	odd	6
70.2.e.d.51.1	yes	2	7.6	odd	2
350.2.e.b.51.1		2	35.34	odd	2
350.2.e.b.151.1		2	35.24	odd	6
350.2.j.d.149.1		4	35.13	even	4
350.2.j.d.149.2		4	35.27	even	4
350.2.j.d.249.1		4	35.17	even	12
350.2.j.d.249.2		4	35.3	even	12
490.2.a.a.1.1		1	7.5	odd	6
490.2.a.d.1.1		1	7.2	even	3
490.2.e.g.361.1		2	7.4	even	3	inner
490.2.e.g.471.1		2	1.1	even	1	trivial
560.2.q.b.81.1		2	28.3	even	6
560.2.q.b.401.1		2	28.27	even	2
630.2.k.d.361.1		2	21.17	even	6
630.2.k.d.541.1		2	21.20	even	2
2450.2.a.v.1.1		1	35.9	even	6
2450.2.a.bf.1.1		1	35.19	odd	6
2450.2.c.e.99.1		2	35.2	odd	12
2450.2.c.e.99.2		2	35.23	odd	12
2450.2.c.q.99.1		2	35.12	even	12
2450.2.c.q.99.2		2	35.33	even	12
3920.2.a.e.1.1		1	28.23	odd	6
3920.2.a.bh.1.1		1	28.19	even	6
4410.2.a.x.1.1		1	21.5	even	6
4410.2.a.bg.1.1		1	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(-1.00000 + 1.73205i) q^{12} +1.00000 q^{13} -2.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} -1.00000 q^{20} -3.00000 q^{22} +(-4.50000 + 7.79423i) q^{23} +(1.00000 + 1.73205i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.500000 - 0.866025i) q^{26} -4.00000 q^{27} +6.00000 q^{29} +(-1.00000 + 1.73205i) q^{30} +(4.00000 + 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{33} -6.00000 q^{34} +1.00000 q^{36} +(3.50000 - 6.06218i) q^{37} +(0.500000 + 0.866025i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(-0.500000 + 0.866025i) q^{40} -3.00000 q^{41} +2.00000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(0.500000 + 0.866025i) q^{45} +(4.50000 + 7.79423i) q^{46} +(4.50000 - 7.79423i) q^{47} +2.00000 q^{48} -1.00000 q^{50} +(-6.00000 + 10.3923i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(-4.50000 - 7.79423i) q^{53} +(-2.00000 + 3.46410i) q^{54} -3.00000 q^{55} +2.00000 q^{57} +(3.00000 - 5.19615i) q^{58} +(1.00000 + 1.73205i) q^{60} +(4.00000 - 6.92820i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(3.00000 + 5.19615i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(-3.00000 + 5.19615i) q^{68} +18.0000 q^{69} +(0.500000 - 0.866025i) q^{72} +(-2.00000 - 3.46410i) q^{73} +(-3.50000 - 6.06218i) q^{74} +(-1.00000 + 1.73205i) q^{75} +1.00000 q^{76} -2.00000 q^{78} +(5.00000 - 8.66025i) q^{79} +(0.500000 + 0.866025i) q^{80} +(5.50000 + 9.52628i) q^{81} +(-1.50000 + 2.59808i) q^{82} -6.00000 q^{85} +(1.00000 - 1.73205i) q^{86} +(-6.00000 - 10.3923i) q^{87} +(1.50000 + 2.59808i) q^{88} +(3.00000 - 5.19615i) q^{89} +1.00000 q^{90} +9.00000 q^{92} +(8.00000 - 13.8564i) q^{93} +(-4.50000 - 7.79423i) q^{94} +(0.500000 + 0.866025i) q^{95} +(1.00000 - 1.73205i) q^{96} +10.0000 q^{97} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 4 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - 2 * q^3 - q^4 + q^5 - 4 * q^6 - 2 * q^8 - q^9	\( 2 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 4 q^{6} - 2 q^{8} - q^{9} - q^{10} - 3 q^{11} - 2 q^{12} + 2 q^{13} - 4 q^{15} - q^{16} - 6 q^{17} + q^{18} - q^{19} - 2 q^{20} - 6 q^{22} - 9 q^{23} + 2 q^{24} - q^{25} + q^{26} - 8 q^{27} + 12 q^{29} - 2 q^{30} + 8 q^{31} + q^{32} - 6 q^{33} - 12 q^{34} + 2 q^{36} + 7 q^{37} + q^{38} - 2 q^{39} - q^{40} - 6 q^{41} + 4 q^{43} - 3 q^{44} + q^{45} + 9 q^{46} + 9 q^{47} + 4 q^{48} - 2 q^{50} - 12 q^{51} - q^{52} - 9 q^{53} - 4 q^{54} - 6 q^{55} + 4 q^{57} + 6 q^{58} + 2 q^{60} + 8 q^{61} + 16 q^{62} + 2 q^{64} + q^{65} + 6 q^{66} - 8 q^{67} - 6 q^{68} + 36 q^{69} + q^{72} - 4 q^{73} - 7 q^{74} - 2 q^{75} + 2 q^{76} - 4 q^{78} + 10 q^{79} + q^{80} + 11 q^{81} - 3 q^{82} - 12 q^{85} + 2 q^{86} - 12 q^{87} + 3 q^{88} + 6 q^{89} + 2 q^{90} + 18 q^{92} + 16 q^{93} - 9 q^{94} + q^{95} + 2 q^{96} + 20 q^{97} + 6 q^{99}+O(q^{100}) \) 2 * q + q^2 - 2 * q^3 - q^4 + q^5 - 4 * q^6 - 2 * q^8 - q^9 - q^10 - 3 * q^11 - 2 * q^12 + 2 * q^13 - 4 * q^15 - q^16 - 6 * q^17 + q^18 - q^19 - 2 * q^20 - 6 * q^22 - 9 * q^23 + 2 * q^24 - q^25 + q^26 - 8 * q^27 + 12 * q^29 - 2 * q^30 + 8 * q^31 + q^32 - 6 * q^33 - 12 * q^34 + 2 * q^36 + 7 * q^37 + q^38 - 2 * q^39 - q^40 - 6 * q^41 + 4 * q^43 - 3 * q^44 + q^45 + 9 * q^46 + 9 * q^47 + 4 * q^48 - 2 * q^50 - 12 * q^51 - q^52 - 9 * q^53 - 4 * q^54 - 6 * q^55 + 4 * q^57 + 6 * q^58 + 2 * q^60 + 8 * q^61 + 16 * q^62 + 2 * q^64 + q^65 + 6 * q^66 - 8 * q^67 - 6 * q^68 + 36 * q^69 + q^72 - 4 * q^73 - 7 * q^74 - 2 * q^75 + 2 * q^76 - 4 * q^78 + 10 * q^79 + q^80 + 11 * q^81 - 3 * q^82 - 12 * q^85 + 2 * q^86 - 12 * q^87 + 3 * q^88 + 6 * q^89 + 2 * q^90 + 18 * q^92 + 16 * q^93 - 9 * q^94 + q^95 + 2 * q^96 + 20 * q^97 + 6 * q^99

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