LMFDB - Embedded newform 350.2.e.b.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(51,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("350.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.79476407074$
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			51.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	350.51
Dual form			350.2.e.b.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{6} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{6} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-1.00000 + 1.73205i) q^{12} +1.00000 q^{13} +(-2.50000 + 0.866025i) q^{14} +(-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 - 5.19615i) q^{21} +3.00000 q^{22} +(4.50000 - 7.79423i) q^{23} +(-1.00000 - 1.73205i) q^{24} +(-0.500000 + 0.866025i) q^{26} -4.00000 q^{27} +(0.500000 - 2.59808i) q^{28} +6.00000 q^{29} +(-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} +3.00000 q^{41} +(4.00000 + 3.46410i) q^{42} -2.00000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(4.50000 + 7.79423i) q^{46} +(4.50000 - 7.79423i) q^{47} +2.00000 q^{48} +(1.00000 + 6.92820i) q^{49} +(-6.00000 + 10.3923i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(4.50000 + 7.79423i) q^{53} +(2.00000 - 3.46410i) q^{54} +(2.00000 + 1.73205i) q^{56} -2.00000 q^{57} +(-3.00000 + 5.19615i) q^{58} +(-4.00000 + 6.92820i) q^{61} +8.00000 q^{62} +(-2.50000 + 0.866025i) q^{63} +1.00000 q^{64} +(-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 q^{76} +(1.50000 - 7.79423i) q^{77} +2.00000 q^{78} +(5.00000 - 8.66025i) q^{79} +(5.50000 + 9.52628i) q^{81} +(-1.50000 + 2.59808i) q^{82} +(-5.00000 + 1.73205i) q^{84} +(1.00000 - 1.73205i) q^{86} +(-6.00000 - 10.3923i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(-3.00000 + 5.19615i) q^{89} +(2.00000 + 1.73205i) q^{91} -9.00000 q^{92} +(-8.00000 + 13.8564i) q^{93} +(4.50000 + 7.79423i) q^{94} +(-1.00000 + 1.73205i) q^{96} +10.0000 q^{97} +(-6.50000 - 2.59808i) q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 2 q^{3} - q^{4} + 4 q^{6} + 4 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 - 2 * q^3 - q^4 + 4 * q^6 + 4 * q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} - 2 q^{3} - q^{4} + 4 q^{6} + 4 q^{7} + 2 q^{8} - q^{9} - 3 q^{11} - 2 q^{12} + 2 q^{13} - 5 q^{14} - q^{16} - 6 q^{17} - q^{18} + q^{19} + 2 q^{21} + 6 q^{22} + 9 q^{23} - 2 q^{24} - q^{26} - 8 q^{27} + q^{28} + 12 q^{29} - 8 q^{31} - q^{32} - 6 q^{33} + 12 q^{34} + 2 q^{36} - 7 q^{37} + q^{38} - 2 q^{39} + 6 q^{41} + 8 q^{42} - 4 q^{43} - 3 q^{44} + 9 q^{46} + 9 q^{47} + 4 q^{48} + 2 q^{49} - 12 q^{51} - q^{52} + 9 q^{53} + 4 q^{54} + 4 q^{56} - 4 q^{57} - 6 q^{58} - 8 q^{61} + 16 q^{62} - 5 q^{63} + 2 q^{64} - 6 q^{66} + 8 q^{67} - 6 q^{68} - 36 q^{69} - q^{72} - 4 q^{73} - 7 q^{74} - 2 q^{76} + 3 q^{77} + 4 q^{78} + 10 q^{79} + 11 q^{81} - 3 q^{82} - 10 q^{84} + 2 q^{86} - 12 q^{87} - 3 q^{88} - 6 q^{89} + 4 q^{91} - 18 q^{92} - 16 q^{93} + 9 q^{94} - 2 q^{96} + 20 q^{97} - 13 q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q - q^2 - 2 * q^3 - q^4 + 4 * q^6 + 4 * q^7 + 2 * q^8 - q^9 - 3 * q^11 - 2 * q^12 + 2 * q^13 - 5 * q^14 - q^16 - 6 * q^17 - q^18 + q^19 + 2 * q^21 + 6 * q^22 + 9 * q^23 - 2 * q^24 - q^26 - 8 * q^27 + q^28 + 12 * q^29 - 8 * q^31 - q^32 - 6 * q^33 + 12 * q^34 + 2 * q^36 - 7 * q^37 + q^38 - 2 * q^39 + 6 * q^41 + 8 * q^42 - 4 * q^43 - 3 * q^44 + 9 * q^46 + 9 * q^47 + 4 * q^48 + 2 * q^49 - 12 * q^51 - q^52 + 9 * q^53 + 4 * q^54 + 4 * q^56 - 4 * q^57 - 6 * q^58 - 8 * q^61 + 16 * q^62 - 5 * q^63 + 2 * q^64 - 6 * q^66 + 8 * q^67 - 6 * q^68 - 36 * q^69 - q^72 - 4 * q^73 - 7 * q^74 - 2 * q^76 + 3 * q^77 + 4 * q^78 + 10 * q^79 + 11 * q^81 - 3 * q^82 - 10 * q^84 + 2 * q^86 - 12 * q^87 - 3 * q^88 - 6 * q^89 + 4 * q^91 - 18 * q^92 - 16 * q^93 + 9 * q^94 - 2 * q^96 + 20 * q^97 - 13 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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			0
$5$		0			0
$6$	2.00000			0.816497
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−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	$0.455716\pi$
$14$	−2.50000	+	0.866025i	−0.668153	+	0.231455i
$15$		0			0
$16$	−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	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$		0			0
$21$	1.00000	−	5.19615i	0.218218	−	1.13389i
$22$	3.00000			0.639602
$23$	4.50000	−	7.79423i	0.938315	−	1.62521i	0.169701	−	0.985496i	$-0.445720\pi$
$23$	4.50000	−	7.79423i	0.938315	−	1.62521i	0.768613	−	0.639713i	$-0.220947\pi$
$24$	−1.00000	−	1.73205i	−0.204124	−	0.353553i
$25$		0			0
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$	−4.00000			−0.769800
$28$	0.500000	−	2.59808i	0.0944911	−	0.490990i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$	−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	$0.361819\pi$
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	−0.995998	+	0.0893706i	$0.971514\pi$
$38$	0.500000	+	0.866025i	0.0811107	+	0.140488i
$39$	−1.00000	−	1.73205i	−0.160128	−	0.277350i
$40$		0			0
$41$	3.00000			0.468521			0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000			0.468521			0.234261	+	0.972174i	$0.424733\pi$
$42$	4.00000	+	3.46410i	0.617213	+	0.534522i
$43$	−2.00000			−0.304997			−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000			−0.304997			−0.152499	+	0.988304i	$0.548732\pi$
$44$	−1.50000	+	2.59808i	−0.226134	+	0.391675i
$45$		0			0
$46$	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
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$	−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	$0.0454398\pi$
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	−0.371706	+	0.928351i	$0.621227\pi$
$54$	2.00000	−	3.46410i	0.272166	−	0.471405i
$55$		0			0
$56$	2.00000	+	1.73205i	0.267261	+	0.231455i
$57$	−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	$0.833333\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	8.00000			1.01600
$63$	−2.50000	+	0.866025i	−0.314970	+	0.109109i
$64$	1.00000			0.125000
$65$		0			0
$66$	−3.00000	−	5.19615i	−0.369274	−	0.639602i
$67$	4.00000	+	6.92820i	0.488678	+	0.846415i	0.999915	−	0.0130248i	$-0.00414604\pi$
$67$	4.00000	+	6.92820i	0.488678	+	0.846415i	−0.511237	+	0.859440i	$0.670813\pi$
$68$	−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
$75$		0			0
$76$	−1.00000			−0.114708
$77$	1.50000	−	7.79423i	0.170941	−	0.888235i
$78$	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			0
$81$	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	$0.5\pi$
$84$	−5.00000	+	1.73205i	−0.545545	+	0.188982i
$85$		0			0
$86$	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	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$		0			0
$91$	2.00000	+	1.73205i	0.209657	+	0.181568i
$92$	−9.00000			−0.938315
$93$	−8.00000	+	13.8564i	−0.829561	+	1.43684i
$94$	4.50000	+	7.79423i	0.464140	+	0.803913i
$95$		0			0
$96$	−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	$0.330506\pi$
$98$	−6.50000	−	2.59808i	−0.656599	−	0.262445i
$99$	3.00000			0.301511
$100$		0			0
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	−0.993258	−	0.115924i	$-0.963017\pi$
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	0.396236	−	0.918149i	$-0.370316\pi$
$102$	−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	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	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	$0.555448\pi$
$110$		0			0
$111$	14.0000			1.32882
$112$	−2.50000	+	0.866025i	−0.236228	+	0.0818317i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$		0			0
$116$	−3.00000	−	5.19615i	−0.278543	−	0.482451i
$117$	−0.500000	+	0.866025i	−0.0462250	+	0.0800641i
$118$		0			0
$119$	3.00000	−	15.5885i	0.275010	−	1.42899i
$120$		0			0
$121$	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
$125$		0			0
$126$	0.500000	−	2.59808i	0.0445435	−	0.231455i
$127$	1.00000			0.0887357			0.0443678	−	0.999015i	$-0.485873\pi$
$127$	1.00000			0.0887357			0.0443678	+	0.999015i	$0.485873\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$		0			0
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	−0.924084	−	0.382190i	$-0.875170\pi$
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	0.793028	+	0.609185i	$0.208503\pi$
$132$	6.00000			0.522233
$133$	2.50000	−	0.866025i	0.216777	−	0.0750939i
$134$	−8.00000			−0.691095
$135$		0			0
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$	9.00000	−	15.5885i	0.766131	−	1.32698i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$		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
$145$		0			0
$146$	4.00000			0.331042
$147$	11.0000	−	8.66025i	0.907265	−	0.714286i
$148$	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	$0.0876260\pi$
$150$		0			0
$151$	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
$154$	6.00000	+	5.19615i	0.483494	+	0.418718i
$155$		0			0
$156$	−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
$160$		0			0
$161$	22.5000	−	7.79423i	1.77325	−	0.614271i
$162$	−11.0000			−0.864242
$163$	10.0000	−	17.3205i	0.783260	−	1.35665i	−0.146772	−	0.989170i	$-0.546888\pi$
$163$	10.0000	−	17.3205i	0.783260	−	1.35665i	0.930033	−	0.367477i	$-0.119778\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$		0			0
$166$		0			0
$167$	−3.00000			−0.232147			−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000			−0.232147			−0.116073	+	0.993241i	$0.537031\pi$
$168$	1.00000	−	5.19615i	0.0771517	−	0.400892i
$169$	−12.0000			−0.923077
$170$		0			0
$171$	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			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−2.50000	+	0.866025i	−0.185312	+	0.0641941i
$183$	16.0000			1.18275
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$		0			0
$186$	−8.00000	−	13.8564i	−0.586588	−	1.01600i
$187$	−9.00000	+	15.5885i	−0.658145	+	1.13994i
$188$	−9.00000			−0.656392
$189$	−8.00000	−	6.92820i	−0.581914	−	0.503953i
$190$		0			0
$191$	−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	$-0.971337\pi$
$193$	−8.00000	−	13.8564i	−0.575853	−	0.997406i	0.420096	−	0.907480i	$-0.361996\pi$
$194$	−5.00000	+	8.66025i	−0.358979	+	0.621770i
$195$		0			0
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$	−15.0000			−1.06871			−0.534353	−	0.845262i	$-0.679445\pi$
$197$	−15.0000			−1.06871			−0.534353	+	0.845262i	$0.679445\pi$
$198$	−1.50000	+	2.59808i	−0.106600	+	0.184637i
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	0.996850	+	0.0793045i	$0.0252700\pi$
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	−0.429745	+	0.902950i	$0.641397\pi$
$200$		0			0
$201$	8.00000	−	13.8564i	0.564276	−	0.977356i
$202$	12.0000			0.844317
$203$	12.0000	+	10.3923i	0.842235	+	0.729397i
$204$	12.0000			0.840168
$205$		0			0
$206$	−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
$215$		0			0
$216$	−4.00000			−0.272166
$217$	4.00000	−	20.7846i	0.271538	−	1.41095i
$218$	−16.0000			−1.08366
$219$	−4.00000	+	6.92820i	−0.270295	+	0.468165i
$220$		0			0
$221$	−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	$0.586316\pi$
$224$	0.500000	−	2.59808i	0.0334077	−	0.173591i
$225$		0			0
$226$		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	−0.792347	−	0.610071i	$-0.791141\pi$
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	0.924510	+	0.381157i	$0.124474\pi$
$230$		0			0
$231$	−15.0000	+	5.19615i	−0.986928	+	0.341882i
$232$	6.00000			0.393919
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$	−0.500000	−	0.866025i	−0.0326860	−	0.0566139i
$235$		0			0
$236$		0			0
$237$	−20.0000			−1.29914
$238$	12.0000	+	10.3923i	0.777844	+	0.673633i
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	0.881680	−	0.471848i	$-0.156413\pi$
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	−0.849472	+	0.527633i	$0.823079\pi$
$242$	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			0
$251$	−15.0000			−0.946792			−0.473396	−	0.880850i	$-0.656972\pi$
$251$	−15.0000			−0.946792			−0.473396	+	0.880850i	$0.656972\pi$
$252$	2.00000	+	1.73205i	0.125988	+	0.109109i
$253$	−27.0000			−1.69748
$254$	−0.500000	+	0.866025i	−0.0313728	+	0.0543393i
$255$		0			0
$256$	−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
$259$	−17.5000	+	6.06218i	−1.08740	+	0.376685i
$260$		0			0
$261$	−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
$265$		0			0
$266$	−0.500000	+	2.59808i	−0.0306570	+	0.159298i
$267$	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	$0.833333\pi$
$270$		0			0
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$	6.00000			0.363803
$273$	1.00000	−	5.19615i	0.0605228	−	0.314485i
$274$	−12.0000			−0.724947
$275$		0			0
$276$	9.00000	+	15.5885i	0.541736	+	0.938315i
$277$	−5.00000	−	8.66025i	−0.300421	−	0.520344i	0.675810	−	0.737075i	$-0.263794\pi$
$277$	−5.00000	−	8.66025i	−0.300421	−	0.520344i	−0.976231	+	0.216731i	$0.930460\pi$
$278$	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
$285$		0			0
$286$	3.00000			0.177394
$287$	6.00000	+	5.19615i	0.354169	+	0.306719i
$288$	1.00000			0.0589256
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	−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	$0.415323\pi$
$294$	2.00000	+	13.8564i	0.116642	+	0.808122i
$295$		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
$300$		0			0
$301$	−4.00000	−	3.46410i	−0.230556	−	0.199667i
$302$	−10.0000			−0.575435
$303$	−12.0000	+	20.7846i	−0.689382	+	1.19404i
$304$	0.500000	+	0.866025i	0.0286770	+	0.0496700i
$305$		0			0
$306$	−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	$0.630820\pi$
$308$	−7.50000	+	2.59808i	−0.427352	+	0.148039i
$309$	8.00000			0.455104
$310$		0			0
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	0.974841	+	0.222900i	$0.0715523\pi$
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	−0.294384	+	0.955687i	$0.595114\pi$
$312$	−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	−0.769395	−	0.638774i	$-0.779442\pi$
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	0.937892	+	0.346929i	$0.112775\pi$
$318$	9.00000	+	15.5885i	0.504695	+	0.874157i
$319$	−9.00000	−	15.5885i	−0.503903	−	0.872786i
$320$		0			0
$321$	24.0000			1.33955
$322$	−4.50000	+	23.3827i	−0.250775	+	1.30307i
$323$	−6.00000			−0.333849
$324$	5.50000	−	9.52628i	0.305556	−	0.529238i
$325$		0			0
$326$	10.0000	+	17.3205i	0.553849	+	0.959294i
$327$	16.0000	−	27.7128i	0.884802	−	1.53252i
$328$	3.00000			0.165647
$329$	22.5000	−	7.79423i	1.24047	−	0.429710i
$330$		0			0
$331$	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
$335$		0			0
$336$	4.00000	+	3.46410i	0.218218	+	0.188982i
$337$	22.0000			1.19842			0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000			1.19842			0.599208	+	0.800593i	$0.295482\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$		0			0
$340$		0			0
$341$	−12.0000	+	20.7846i	−0.649836	+	1.12555i
$342$	−1.00000			−0.0540738
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−2.00000			−0.107833
$345$		0			0
$346$	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	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$		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
$357$	−30.0000	+	10.3923i	−1.58777	+	0.550019i
$358$	−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			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	−1.00000	+	1.73205i	−0.0525588	+	0.0910346i
$363$	−4.00000			−0.209946
$364$	0.500000	−	2.59808i	0.0262071	−	0.136176i
$365$		0			0
$366$	−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
$370$		0			0
$371$	−4.50000	+	23.3827i	−0.233628	+	1.21397i
$372$	16.0000			0.829561
$373$	1.00000	−	1.73205i	0.0517780	−	0.0896822i	−0.838975	−	0.544170i	$-0.816844\pi$
$373$	1.00000	−	1.73205i	0.0517780	−	0.0896822i	0.890753	+	0.454488i	$0.150178\pi$
$374$	−9.00000	−	15.5885i	−0.465379	−	0.806060i
$375$		0			0
$376$	4.50000	−	7.79423i	0.232070	−	0.401957i
$377$	6.00000			0.309016
$378$	10.0000	−	3.46410i	0.514344	−	0.178174i
$379$	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			0
$381$	−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	$0.734940\pi$
$390$		0			0
$391$	−54.0000			−2.73090
$392$	1.00000	+	6.92820i	0.0505076	+	0.349927i
$393$	6.00000			0.302660
$394$	7.50000	−	12.9904i	0.377845	−	0.654446i
$395$		0			0
$396$	−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
$399$	−4.00000	−	3.46410i	−0.200250	−	0.173422i
$400$		0			0
$401$	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
$405$		0			0
$406$	−15.0000	+	5.19615i	−0.744438	+	0.257881i
$407$	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	$-0.944436\pi$
$409$	−13.0000	−	22.5167i	−0.642809	−	1.11338i	0.341994	−	0.939702i	$-0.388898\pi$
$410$		0			0
$411$	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	$-0.570553\pi$
$419$	−9.00000			−0.439679			−0.219839	+	0.975536i	$0.570553\pi$
$420$		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
$425$		0			0
$426$		0			0
$427$	−20.0000	+	6.92820i	−0.967868	+	0.335279i
$428$	12.0000			0.580042
$429$	−3.00000	+	5.19615i	−0.144841	+	0.250873i
$430$		0			0
$431$	−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	$0.0890309\pi$
$434$	16.0000	+	13.8564i	0.768025	+	0.665129i
$435$		0			0
$436$	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	$0.379719\pi$
$439$	−13.0000	+	22.5167i	−0.620456	+	1.07466i	−0.989401	+	0.145210i	$0.953614\pi$
$440$		0			0
$441$	−6.50000	−	2.59808i	−0.309524	−	0.123718i
$442$	6.00000			0.285391
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	−0.687557	−	0.726130i	$-0.741317\pi$
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	0.972626	+	0.232377i	$0.0746503\pi$
$444$	−7.00000	−	12.1244i	−0.332205	−	0.575396i
$445$		0			0
$446$	4.00000	−	6.92820i	0.189405	−	0.328060i
$447$	−12.0000			−0.567581
$448$	2.00000	+	1.73205i	0.0944911	+	0.0818317i
$449$	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			0
$451$	−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	−0.654558	−	0.756012i	$-0.727145\pi$
$457$	7.00000	−	12.1244i	0.327446	−	0.567153i	0.982004	+	0.188858i	$0.0604787\pi$
$458$	2.00000	+	3.46410i	0.0934539	+	0.161867i
$459$	12.0000	+	20.7846i	0.560112	+	0.970143i
$460$		0			0
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$	3.00000	−	15.5885i	0.139573	−	0.725241i
$463$	1.00000			0.0464739			0.0232370	−	0.999730i	$-0.492603\pi$
$463$	1.00000			0.0464739			0.0232370	+	0.999730i	$0.492603\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$		0			0
$466$	−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
$469$	−4.00000	+	20.7846i	−0.184703	+	0.959744i
$470$		0			0
$471$	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
$475$		0			0
$476$	−15.0000	+	5.19615i	−0.687524	+	0.238165i
$477$	−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	$0.833333\pi$
$480$		0			0
$481$	−3.50000	+	6.06218i	−0.159586	+	0.276412i
$482$	−1.00000			−0.0455488
$483$	−36.0000	−	31.1769i	−1.63806	−	1.41860i
$484$	−2.00000			−0.0909091
$485$		0			0
$486$	5.00000	+	8.66025i	0.226805	+	0.392837i
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	0.625859	−	0.779936i	$-0.284748\pi$
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	−0.988374	+	0.152042i	$0.951415\pi$
$488$	−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
$495$		0			0
$496$	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			0
$501$	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	$0.679709\pi$
$504$	−2.50000	+	0.866025i	−0.111359	+	0.0385758i
$505$		0			0
$506$	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	$-0.452438\pi$
$509$	21.0000	−	36.3731i	0.930809	−	1.61221i	0.781943	−	0.623350i	$-0.214229\pi$
$510$		0			0
$511$	2.00000	−	10.3923i	0.0884748	−	0.459728i
$512$	1.00000			0.0441942
$513$	−2.00000	+	3.46410i	−0.0883022	+	0.152944i
$514$		0			0
$515$		0			0
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$	−27.0000			−1.18746
$518$	3.50000	−	18.1865i	0.153781	−	0.799070i
$519$	−18.0000			−0.790112
$520$		0			0
$521$	7.50000	+	12.9904i	0.328581	+	0.569119i	0.982231	−	0.187678i	$-0.0600963\pi$
$521$	7.50000	+	12.9904i	0.328581	+	0.569119i	−0.653650	+	0.756797i	$0.726763\pi$
$522$	−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
$530$		0			0
$531$		0			0
$532$	−2.00000	−	1.73205i	−0.0867110	−	0.0750939i
$533$	3.00000			0.129944
$534$	−6.00000	+	10.3923i	−0.259645	+	0.449719i
$535$		0			0
$536$	4.00000	+	6.92820i	0.172774	+	0.299253i
$537$	3.00000	−	5.19615i	0.129460	−	0.224231i
$538$		0			0
$539$	16.5000	−	12.9904i	0.710705	−	0.559535i
$540$		0			0
$541$	−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
$545$		0			0
$546$	4.00000	+	3.46410i	0.171184	+	0.148250i
$547$	−8.00000			−0.342055			−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000			−0.342055			−0.171028	+	0.985266i	$0.554709\pi$
$548$	6.00000	−	10.3923i	0.256307	−	0.443937i
$549$	−4.00000	−	6.92820i	−0.170716	−	0.295689i
$550$		0			0
$551$	3.00000	−	5.19615i	0.127804	−	0.221364i
$552$	−18.0000			−0.766131
$553$	25.0000	−	8.66025i	1.06311	−	0.368271i
$554$	10.0000			0.424859
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	0.754802	−	0.655953i	$-0.227733\pi$
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	−0.945473	+	0.325701i	$0.894400\pi$
$558$	−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
$567$	−5.50000	+	28.5788i	−0.230978	+	1.20020i
$568$		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	$0.311753\pi$
$570$		0			0
$571$	−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
$574$	−7.50000	+	2.59808i	−0.313044	+	0.108442i
$575$		0			0
$576$	−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
$580$		0			0
$581$		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			0
$586$	−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	$0.335061\pi$
$588$	−13.0000	−	5.19615i	−0.536111	−	0.214286i
$589$	−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	$0.505017\pi$
$600$		0			0
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$	5.00000	−	1.73205i	0.203785	−	0.0705931i
$603$	−8.00000			−0.325785
$604$	5.00000	−	8.66025i	0.203447	−	0.352381i
$605$		0			0
$606$	−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
$609$	6.00000	−	31.1769i	0.243132	−	1.26335i
$610$		0			0
$611$	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	$0.0324938\pi$
$613$	14.5000	+	25.1147i	0.585649	+	1.01437i	−0.409145	+	0.912470i	$0.634173\pi$
$614$	7.00000	−	12.1244i	0.282497	−	0.489299i
$615$		0			0
$616$	1.50000	−	7.79423i	0.0604367	−	0.314038i
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$	−4.00000	+	6.92820i	−0.160904	+	0.278693i
$619$	−11.5000	−	19.9186i	−0.462224	−	0.800595i	0.536847	−	0.843679i	$-0.319615\pi$
$619$	−11.5000	−	19.9186i	−0.462224	−	0.800595i	−0.999071	+	0.0430838i	$0.986282\pi$
$620$		0			0
$621$	−18.0000	+	31.1769i	−0.722315	+	1.25109i
$622$	−24.0000			−0.962312
$623$	−15.0000	+	5.19615i	−0.600962	+	0.208179i
$624$	2.00000			0.0800641
$625$		0			0
$626$	−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			0
$636$	−18.0000			−0.713746
$637$	1.00000	+	6.92820i	0.0396214	+	0.274505i
$638$	18.0000			0.712627
$639$		0			0
$640$		0			0
$641$	−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	$0.512556\pi$
$644$	−18.0000	−	15.5885i	−0.709299	−	0.614271i
$645$		0			0
$646$	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
$650$		0			0
$651$	−40.0000	+	13.8564i	−1.56772	+	0.543075i
$652$	−20.0000			−0.783260
$653$	−4.50000	+	7.79423i	−0.176099	+	0.305012i	−0.940541	−	0.339680i	$-0.889681\pi$
$653$	−4.50000	+	7.79423i	−0.176099	+	0.305012i	0.764442	+	0.644692i	$0.223014\pi$
$654$	16.0000	+	27.7128i	0.625650	+	1.08366i
$655$		0			0
$656$	−1.50000	+	2.59808i	−0.0585652	+	0.101438i
$657$	4.00000			0.156055
$658$	−4.50000	+	23.3827i	−0.175428	+	0.911552i
$659$	−24.0000			−0.934907			−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000			−0.934907			−0.467454	+	0.884018i	$0.654829\pi$
$660$		0			0
$661$	14.0000	+	24.2487i	0.544537	+	0.943166i	0.998636	+	0.0522143i	$0.0166279\pi$
$661$	14.0000	+	24.2487i	0.544537	+	0.943166i	−0.454099	+	0.890951i	$0.650039\pi$
$662$	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
$670$		0			0
$671$	24.0000			0.926510
$672$	−5.00000	+	1.73205i	−0.192879	+	0.0668153i
$673$	34.0000			1.31060			0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000			1.31060			0.655302	+	0.755367i	$0.272541\pi$
$674$	−11.0000	+	19.0526i	−0.423704	+	0.733877i
$675$		0			0
$676$	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
$679$	20.0000	+	17.3205i	0.767530	+	0.664700i
$680$		0			0
$681$	−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	0.957685	−	0.287819i	$-0.0929302\pi$
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	−0.728101	+	0.685470i	$0.759597\pi$
$684$	0.500000	−	0.866025i	0.0191180	−	0.0331133i
$685$		0			0
$686$	−8.50000	−	16.4545i	−0.324532	−	0.628235i
$687$	−8.00000			−0.305219
$688$	1.00000	−	1.73205i	0.0381246	−	0.0660338i
$689$	4.50000	+	7.79423i	0.171436	+	0.296936i
$690$		0			0
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	0.382791	+	0.923835i	$0.374963\pi$
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	−0.991460	+	0.130410i	$0.958371\pi$
$692$	−9.00000			−0.342129
$693$	6.00000	+	5.19615i	0.227921	+	0.197386i
$694$		0			0
$695$		0			0
$696$	−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
$705$		0			0
$706$	−12.0000			−0.451626
$707$	6.00000	−	31.1769i	0.225653	−	1.17253i
$708$		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
$714$	6.00000	−	31.1769i	0.224544	−	1.16677i
$715$		0			0
$716$	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	$0.166667\pi$
$720$		0			0
$721$	−10.0000	+	3.46410i	−0.372419	+	0.129010i
$722$	−18.0000			−0.669891
$723$	1.00000	−	1.73205i	0.0371904	−	0.0644157i
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$		0			0
$726$	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	$0.494097\pi$
$728$	2.00000	+	1.73205i	0.0741249	+	0.0641941i
$729$	13.0000			0.481481
$730$		0			0
$731$	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	$-0.389288\pi$
$740$		0			0
$741$	−2.00000			−0.0734718
$742$	−18.0000	−	15.5885i	−0.660801	−	0.572270i
$743$	45.0000			1.65089			0.825445	−	0.564483i	$-0.190924\pi$
$743$	45.0000			1.65089			0.825445	+	0.564483i	$0.190924\pi$
$744$	−8.00000	+	13.8564i	−0.293294	+	0.508001i
$745$		0			0
$746$	1.00000	+	1.73205i	0.0366126	+	0.0634149i
$747$		0			0
$748$	18.0000			0.658145
$749$	−30.0000	+	10.3923i	−1.09618	+	0.379727i
$750$		0			0
$751$	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
$755$		0			0
$756$	−2.00000	+	10.3923i	−0.0727393	+	0.377964i
$757$	−38.0000			−1.38113			−0.690567	−	0.723269i	$-0.742639\pi$
$757$	−38.0000			−1.38113			−0.690567	+	0.723269i	$0.742639\pi$
$758$	−11.5000	+	19.9186i	−0.417699	+	0.723476i
$759$	27.0000	+	46.7654i	0.980038	+	1.69748i
$760$		0			0
$761$	13.5000	−	23.3827i	0.489375	−	0.847622i	−0.510551	−	0.859848i	$-0.670558\pi$
$761$	13.5000	−	23.3827i	0.489375	−	0.847622i	0.999925	+	0.0122260i	$0.00389175\pi$
$762$	2.00000			0.0724524
$763$	−8.00000	+	41.5692i	−0.289619	+	1.50491i
$764$	12.0000			0.434145
$765$		0			0
$766$	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	$-0.363886\pi$
$769$	23.0000			0.829401			0.414701	+	0.909958i	$0.363886\pi$
$770$		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
$775$		0			0
$776$	10.0000			0.358979
$777$	28.0000	+	24.2487i	1.00449	+	0.869918i
$778$	−12.0000			−0.430221
$779$	1.50000	−	2.59808i	0.0537431	−	0.0930857i
$780$		0			0
$781$		0			0
$782$	27.0000	−	46.7654i	0.965518	−	1.67233i
$783$	−24.0000			−0.857690
$784$	−6.50000	−	2.59808i	−0.232143	−	0.0927884i
$785$		0			0
$786$	−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
$790$		0			0
$791$		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
$795$		0			0
$796$	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	$0.533889\pi$
$798$	5.00000	−	1.73205i	0.176998	−	0.0613139i
$799$	−54.0000			−1.91038
$800$		0			0
$801$	−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	$0.782761\pi$
$810$		0			0
$811$	−25.0000			−0.877869			−0.438934	−	0.898519i	$-0.644644\pi$
$811$	−25.0000			−0.877869			−0.438934	+	0.898519i	$0.644644\pi$
$812$	3.00000	−	15.5885i	0.105279	−	0.547048i
$813$	−32.0000			−1.12229
$814$	−10.5000	+	18.1865i	−0.368025	+	0.637438i
$815$		0			0
$816$	−6.00000	−	10.3923i	−0.210042	−	0.363803i
$817$	−1.00000	+	1.73205i	−0.0349856	+	0.0605968i
$818$	26.0000			0.909069
$819$	−2.50000	+	0.866025i	−0.0873571	+	0.0302614i
$820$		0			0
$821$	−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	0.829060	−	0.559159i	$-0.188876\pi$
$823$	−2.00000	−	3.46410i	−0.0697156	−	0.120751i	−0.898776	+	0.438408i	$0.855543\pi$
$824$	−2.00000	+	3.46410i	−0.0696733	+	0.120678i
$825$		0			0
$826$		0			0
$827$	−6.00000			−0.208640			−0.104320	−	0.994544i	$-0.533267\pi$
$827$	−6.00000			−0.208640			−0.104320	+	0.994544i	$0.533267\pi$
$828$	4.50000	−	7.79423i	0.156386	−	0.270868i
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	0.718481	−	0.695546i	$-0.244838\pi$
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	−0.961601	+	0.274450i	$0.911504\pi$
$830$		0			0
$831$	−10.0000	+	17.3205i	−0.346896	+	0.600842i
$832$	1.00000			0.0346688
$833$	33.0000	−	25.9808i	1.14338	−	0.900180i
$834$	−8.00000			−0.277017
$835$		0			0
$836$	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	$-0.673270\pi$
$839$	−30.0000			−1.03572			−0.517858	+	0.855467i	$0.673270\pi$
$840$		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
$845$		0			0
$846$	−9.00000			−0.309426
$847$	5.00000	−	1.73205i	0.171802	−	0.0595140i
$848$	−9.00000			−0.309061
$849$	14.0000	−	24.2487i	0.480479	−	0.832214i
$850$		0			0
$851$	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	$0.394544\pi$
$854$	4.00000	−	20.7846i	0.136877	−	0.711235i
$855$		0			0
$856$	−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	$0.350484\pi$
$859$	−16.0000	+	27.7128i	−0.545913	+	0.945549i	−0.998549	+	0.0538535i	$0.982850\pi$
$860$		0			0
$861$	3.00000	−	15.5885i	0.102240	−	0.531253i
$862$	12.0000			0.408722
$863$	−1.50000	+	2.59808i	−0.0510606	+	0.0884395i	−0.890426	−	0.455128i	$-0.849593\pi$
$863$	−1.50000	+	2.59808i	−0.0510606	+	0.0884395i	0.839365	+	0.543568i	$0.182927\pi$
$864$	2.00000	+	3.46410i	0.0680414	+	0.117851i
$865$		0			0
$866$	−20.0000	+	34.6410i	−0.679628	+	1.17715i
$867$	38.0000			1.29055
$868$	−20.0000	+	6.92820i	−0.678844	+	0.235159i
$869$	−30.0000			−1.01768
$870$		0			0
$871$	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	−0.954652	−	0.297724i	$-0.903772\pi$
$877$	−6.50000	+	11.2583i	−0.219489	+	0.380167i	0.735163	+	0.677891i	$0.237106\pi$
$878$	−13.0000	−	22.5167i	−0.438729	−	0.759900i
$879$	−9.00000	−	15.5885i	−0.303562	−	0.525786i
$880$		0			0
$881$	33.0000			1.11180			0.555899	−	0.831250i	$-0.312374\pi$
$881$	33.0000			1.11180			0.555899	+	0.831250i	$0.312374\pi$
$882$	5.50000	−	4.33013i	0.185195	−	0.145803i
$883$	−8.00000			−0.269221			−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000			−0.269221			−0.134611	+	0.990899i	$0.542978\pi$
$884$	−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
$889$	2.00000	+	1.73205i	0.0670778	+	0.0580911i
$890$		0			0
$891$	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
$895$		0			0
$896$	−2.50000	+	0.866025i	−0.0835191	+	0.0289319i
$897$	−18.0000			−0.601003
$898$	−10.5000	+	18.1865i	−0.350390	+	0.606892i
$899$	−24.0000	−	41.5692i	−0.800445	−	1.38641i
$900$		0			0
$901$	27.0000	−	46.7654i	0.899500	−	1.55798i
$902$	9.00000			0.299667
$903$	−2.00000	+	10.3923i	−0.0665558	+	0.345834i
$904$		0			0
$905$		0			0
$906$	10.0000	+	17.3205i	0.332228	+	0.575435i
$907$	−5.00000	−	8.66025i	−0.166022	−	0.287559i	0.770996	−	0.636841i	$-0.219759\pi$
$907$	−5.00000	−	8.66025i	−0.166022	−	0.287559i	−0.937018	+	0.349281i	$0.886426\pi$
$908$	−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
$915$		0			0
$916$	−4.00000			−0.132164
$917$	−7.50000	+	2.59808i	−0.247672	+	0.0857960i
$918$	−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	$0.0484682\pi$
$920$		0			0
$921$	14.0000	+	24.2487i	0.461316	+	0.799022i
$922$	15.0000	−	25.9808i	0.493999	−	0.855631i
$923$		0			0
$924$	12.0000	+	10.3923i	0.394771	+	0.341882i
$925$		0			0
$926$	−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	$0.551317\pi$
$929$	−28.5000	+	49.3634i	−0.935055	+	1.61956i	−0.774536	+	0.632529i	$0.782017\pi$
$930$		0			0
$931$	6.50000	+	2.59808i	0.213029	+	0.0851485i
$932$	6.00000			0.196537
$933$	24.0000	−	41.5692i	0.785725	−	1.36092i
$934$	−3.00000	−	5.19615i	−0.0981630	−	0.170023i
$935$		0			0
$936$	−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	$0.447772\pi$
$938$	−16.0000	−	13.8564i	−0.522419	−	0.452428i
$939$	56.0000			1.82749
$940$		0			0
$941$	−24.0000	−	41.5692i	−0.782378	−	1.35512i	−0.930553	−	0.366157i	$-0.880673\pi$
$941$	−24.0000	−	41.5692i	−0.782378	−	1.35512i	0.148176	−	0.988961i	$-0.452660\pi$
$942$	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	−0.813157	−	0.582045i	$-0.802253\pi$
$947$	3.00000	−	5.19615i	0.0974869	−	0.168852i	0.910644	+	0.413192i	$0.135586\pi$
$948$	10.0000	+	17.3205i	0.324785	+	0.562544i
$949$	−2.00000	−	3.46410i	−0.0649227	−	0.112449i
$950$		0			0
$951$	−12.0000			−0.389127
$952$	3.00000	−	15.5885i	0.0972306	−	0.505225i
$953$	−36.0000			−1.16615			−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000			−1.16615			−0.583077	+	0.812417i	$0.698151\pi$
$954$	4.50000	−	7.79423i	0.145693	−	0.252347i
$955$		0			0
$956$	3.00000	+	5.19615i	0.0970269	+	0.168056i
$957$	−18.0000	+	31.1769i	−0.581857	+	1.00781i
$958$		0			0
$959$	−6.00000	+	31.1769i	−0.193750	+	1.00676i
$960$		0			0
$961$	−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
$965$		0			0
$966$	45.0000	−	15.5885i	1.44785	−	0.501550i
$967$	−32.0000			−1.02905			−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000			−1.02905			−0.514525	+	0.857475i	$0.672032\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$	6.00000	+	10.3923i	0.192748	+	0.333849i
$970$		0			0
$971$	22.5000	−	38.9711i	0.722059	−	1.25064i	−0.238114	−	0.971237i	$-0.576529\pi$
$971$	22.5000	−	38.9711i	0.722059	−	1.25064i	0.960173	−	0.279406i	$-0.0901376\pi$
$972$	−10.0000			−0.320750
$973$	−8.00000	−	6.92820i	−0.256468	−	0.222108i
$974$	16.0000			0.512673
$975$		0			0
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	−21.0000	−	36.3731i	−0.671850	−	1.16368i	−0.977379	−	0.211495i	$-0.932167\pi$
$977$	−21.0000	−	36.3731i	−0.671850	−	1.16368i	0.305530	−	0.952183i	$-0.401167\pi$
$978$	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
$985$		0			0
$986$	36.0000			1.14647
$987$	−36.0000	−	31.1769i	−1.14589	−	0.992372i
$988$	−1.00000			−0.0318142
$989$	−9.00000	+	15.5885i	−0.286183	+	0.495684i
$990$		0			0
$991$	−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
$995$		0			0
$996$		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	350.2.e.b.51.1		2
5.2	odd	4		350.2.j.d.149.1		4
5.3	odd	4		350.2.j.d.149.2		4
5.4	even	2		70.2.e.d.51.1	yes	2
7.2	even	3		2450.2.a.bf.1.1		1
7.4	even	3	inner	350.2.e.b.151.1		2
7.5	odd	6		2450.2.a.v.1.1		1
15.14	odd	2		630.2.k.d.541.1		2
20.19	odd	2		560.2.q.b.401.1		2
35.2	odd	12		2450.2.c.q.99.2		2
35.4	even	6		70.2.e.d.11.1	✓	2
35.9	even	6		490.2.a.a.1.1		1
35.12	even	12		2450.2.c.e.99.2		2
35.18	odd	12		350.2.j.d.249.1		4
35.19	odd	6		490.2.a.d.1.1		1
35.23	odd	12		2450.2.c.q.99.1		2
35.24	odd	6		490.2.e.g.361.1		2
35.32	odd	12		350.2.j.d.249.2		4
35.33	even	12		2450.2.c.e.99.1		2
35.34	odd	2		490.2.e.g.471.1		2
105.44	odd	6		4410.2.a.x.1.1		1
105.74	odd	6		630.2.k.d.361.1		2
105.89	even	6		4410.2.a.bg.1.1		1
140.19	even	6		3920.2.a.e.1.1		1
140.39	odd	6		560.2.q.b.81.1		2
140.79	odd	6		3920.2.a.bh.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.e.d.11.1	✓	2	35.4	even	6
70.2.e.d.51.1	yes	2	5.4	even	2
350.2.e.b.51.1		2	1.1	even	1	trivial
350.2.e.b.151.1		2	7.4	even	3	inner
350.2.j.d.149.1		4	5.2	odd	4
350.2.j.d.149.2		4	5.3	odd	4
350.2.j.d.249.1		4	35.18	odd	12
350.2.j.d.249.2		4	35.32	odd	12
490.2.a.a.1.1		1	35.9	even	6
490.2.a.d.1.1		1	35.19	odd	6
490.2.e.g.361.1		2	35.24	odd	6
490.2.e.g.471.1		2	35.34	odd	2
560.2.q.b.81.1		2	140.39	odd	6
560.2.q.b.401.1		2	20.19	odd	2
630.2.k.d.361.1		2	105.74	odd	6
630.2.k.d.541.1		2	15.14	odd	2
2450.2.a.v.1.1		1	7.5	odd	6
2450.2.a.bf.1.1		1	7.2	even	3
2450.2.c.e.99.1		2	35.33	even	12
2450.2.c.e.99.2		2	35.12	even	12
2450.2.c.q.99.1		2	35.23	odd	12
2450.2.c.q.99.2		2	35.2	odd	12
3920.2.a.e.1.1		1	140.19	even	6
3920.2.a.bh.1.1		1	140.79	odd	6
4410.2.a.x.1.1		1	105.44	odd	6
4410.2.a.bg.1.1		1	105.89	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{6} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{6} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-1.00000 + 1.73205i) q^{12} +1.00000 q^{13} +(-2.50000 + 0.866025i) q^{14} +(-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 - 5.19615i) q^{21} +3.00000 q^{22} +(4.50000 - 7.79423i) q^{23} +(-1.00000 - 1.73205i) q^{24} +(-0.500000 + 0.866025i) q^{26} -4.00000 q^{27} +(0.500000 - 2.59808i) q^{28} +6.00000 q^{29} +(-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} +3.00000 q^{41} +(4.00000 + 3.46410i) q^{42} -2.00000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(4.50000 + 7.79423i) q^{46} +(4.50000 - 7.79423i) q^{47} +2.00000 q^{48} +(1.00000 + 6.92820i) q^{49} +(-6.00000 + 10.3923i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(4.50000 + 7.79423i) q^{53} +(2.00000 - 3.46410i) q^{54} +(2.00000 + 1.73205i) q^{56} -2.00000 q^{57} +(-3.00000 + 5.19615i) q^{58} +(-4.00000 + 6.92820i) q^{61} +8.00000 q^{62} +(-2.50000 + 0.866025i) q^{63} +1.00000 q^{64} +(-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 q^{76} +(1.50000 - 7.79423i) q^{77} +2.00000 q^{78} +(5.00000 - 8.66025i) q^{79} +(5.50000 + 9.52628i) q^{81} +(-1.50000 + 2.59808i) q^{82} +(-5.00000 + 1.73205i) q^{84} +(1.00000 - 1.73205i) q^{86} +(-6.00000 - 10.3923i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(-3.00000 + 5.19615i) q^{89} +(2.00000 + 1.73205i) q^{91} -9.00000 q^{92} +(-8.00000 + 13.8564i) q^{93} +(4.50000 + 7.79423i) q^{94} +(-1.00000 + 1.73205i) q^{96} +10.0000 q^{97} +(-6.50000 - 2.59808i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 2 q^{3} - q^{4} + 4 q^{6} + 4 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - 2 * q^3 - q^4 + 4 * q^6 + 4 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} - 2 q^{3} - q^{4} + 4 q^{6} + 4 q^{7} + 2 q^{8} - q^{9} - 3 q^{11} - 2 q^{12} + 2 q^{13} - 5 q^{14} - q^{16} - 6 q^{17} - q^{18} + q^{19} + 2 q^{21} + 6 q^{22} + 9 q^{23} - 2 q^{24} - q^{26} - 8 q^{27} + q^{28} + 12 q^{29} - 8 q^{31} - q^{32} - 6 q^{33} + 12 q^{34} + 2 q^{36} - 7 q^{37} + q^{38} - 2 q^{39} + 6 q^{41} + 8 q^{42} - 4 q^{43} - 3 q^{44} + 9 q^{46} + 9 q^{47} + 4 q^{48} + 2 q^{49} - 12 q^{51} - q^{52} + 9 q^{53} + 4 q^{54} + 4 q^{56} - 4 q^{57} - 6 q^{58} - 8 q^{61} + 16 q^{62} - 5 q^{63} + 2 q^{64} - 6 q^{66} + 8 q^{67} - 6 q^{68} - 36 q^{69} - q^{72} - 4 q^{73} - 7 q^{74} - 2 q^{76} + 3 q^{77} + 4 q^{78} + 10 q^{79} + 11 q^{81} - 3 q^{82} - 10 q^{84} + 2 q^{86} - 12 q^{87} - 3 q^{88} - 6 q^{89} + 4 q^{91} - 18 q^{92} - 16 q^{93} + 9 q^{94} - 2 q^{96} + 20 q^{97} - 13 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 - q^4 + 4 * q^6 + 4 * q^7 + 2 * q^8 - q^9 - 3 * q^11 - 2 * q^12 + 2 * q^13 - 5 * q^14 - q^16 - 6 * q^17 - q^18 + q^19 + 2 * q^21 + 6 * q^22 + 9 * q^23 - 2 * q^24 - q^26 - 8 * q^27 + q^28 + 12 * q^29 - 8 * q^31 - q^32 - 6 * q^33 + 12 * q^34 + 2 * q^36 - 7 * q^37 + q^38 - 2 * q^39 + 6 * q^41 + 8 * q^42 - 4 * q^43 - 3 * q^44 + 9 * q^46 + 9 * q^47 + 4 * q^48 + 2 * q^49 - 12 * q^51 - q^52 + 9 * q^53 + 4 * q^54 + 4 * q^56 - 4 * q^57 - 6 * q^58 - 8 * q^61 + 16 * q^62 - 5 * q^63 + 2 * q^64 - 6 * q^66 + 8 * q^67 - 6 * q^68 - 36 * q^69 - q^72 - 4 * q^73 - 7 * q^74 - 2 * q^76 + 3 * q^77 + 4 * q^78 + 10 * q^79 + 11 * q^81 - 3 * q^82 - 10 * q^84 + 2 * q^86 - 12 * q^87 - 3 * q^88 - 6 * q^89 + 4 * q^91 - 18 * q^92 - 16 * q^93 + 9 * q^94 - 2 * q^96 + 20 * q^97 - 13 * q^98 + 6 * q^99

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