LMFDB - Embedded newform 350.2.j.d.249.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(149,350)]

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([3, 2]))

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

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

chi := DirichletCharacter("350.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.j (of order $6$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	350.249
Dual form			350.2.j.d.149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.00000 q^{6} +(1.73205 + 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.00000 q^{6} +(1.73205 + 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(1.73205 - 1.00000i) q^{12} -1.00000i q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.19615 - 3.00000i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(1.00000 + 5.19615i) q^{21} +3.00000i q^{22} +(7.79423 - 4.50000i) q^{23} +(1.00000 - 1.73205i) q^{24} +(-0.500000 - 0.866025i) q^{26} -4.00000i q^{27} +(2.59808 - 0.500000i) q^{28} -6.00000 q^{29} +(-4.00000 + 6.92820i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-5.19615 + 3.00000i) q^{33} -6.00000 q^{34} +1.00000 q^{36} +(6.06218 - 3.50000i) q^{37} +(-0.866025 - 0.500000i) q^{38} +(1.00000 - 1.73205i) q^{39} +3.00000 q^{41} +(3.46410 + 4.00000i) q^{42} +2.00000i q^{43} +(1.50000 + 2.59808i) q^{44} +(4.50000 - 7.79423i) q^{46} +(-7.79423 + 4.50000i) q^{47} -2.00000i q^{48} +(-1.00000 + 6.92820i) q^{49} +(-6.00000 - 10.3923i) q^{51} +(-0.866025 - 0.500000i) q^{52} +(-7.79423 - 4.50000i) q^{53} +(-2.00000 - 3.46410i) q^{54} +(2.00000 - 1.73205i) q^{56} -2.00000i q^{57} +(-5.19615 + 3.00000i) q^{58} +(-4.00000 - 6.92820i) q^{61} +8.00000i q^{62} +(-0.866025 + 2.50000i) q^{63} -1.00000 q^{64} +(-3.00000 + 5.19615i) q^{66} +(6.92820 + 4.00000i) q^{67} +(-5.19615 + 3.00000i) q^{68} +18.0000 q^{69} +(0.866025 - 0.500000i) q^{72} +(3.46410 + 2.00000i) q^{73} +(3.50000 - 6.06218i) q^{74} -1.00000 q^{76} +(-7.79423 + 1.50000i) q^{77} -2.00000i q^{78} +(-5.00000 - 8.66025i) q^{79} +(5.50000 - 9.52628i) q^{81} +(2.59808 - 1.50000i) q^{82} +(5.00000 + 1.73205i) q^{84} +(1.00000 + 1.73205i) q^{86} +(-10.3923 - 6.00000i) q^{87} +(2.59808 + 1.50000i) q^{88} +(3.00000 + 5.19615i) q^{89} +(2.00000 - 1.73205i) q^{91} -9.00000i q^{92} +(-13.8564 + 8.00000i) q^{93} +(-4.50000 + 7.79423i) q^{94} +(-1.00000 - 1.73205i) q^{96} +10.0000i q^{97} +(2.59808 + 6.50000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 8 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 8 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} + 8 q^{6} + 2 q^{9} - 6 q^{11} + 10 q^{14} - 2 q^{16} - 2 q^{19} + 4 q^{21} + 4 q^{24} - 2 q^{26} - 24 q^{29} - 16 q^{31} - 24 q^{34} + 4 q^{36} + 4 q^{39} + 12 q^{41} + 6 q^{44} + 18 q^{46} - 4 q^{49} - 24 q^{51} - 8 q^{54} + 8 q^{56} - 16 q^{61} - 4 q^{64} - 12 q^{66} + 72 q^{69} + 14 q^{74} - 4 q^{76} - 20 q^{79} + 22 q^{81} + 20 q^{84} + 4 q^{86} + 12 q^{89} + 8 q^{91} - 18 q^{94} - 4 q^{96} - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 8 * q^6 + 2 * q^9 - 6 * q^11 + 10 * q^14 - 2 * q^16 - 2 * q^19 + 4 * q^21 + 4 * q^24 - 2 * q^26 - 24 * q^29 - 16 * q^31 - 24 * q^34 + 4 * q^36 + 4 * q^39 + 12 * q^41 + 6 * q^44 + 18 * q^46 - 4 * q^49 - 24 * q^51 - 8 * q^54 + 8 * q^56 - 16 * q^61 - 4 * q^64 - 12 * q^66 + 72 * q^69 + 14 * q^74 - 4 * q^76 - 20 * q^79 + 22 * q^81 + 20 * q^84 + 4 * q^86 + 12 * q^89 + 8 * q^91 - 18 * q^94 - 4 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	1.73205	+	1.00000i	1.00000	+	0.577350i	0.908248	−	0.418432i	$-0.137420\pi$
$3$	1.73205	+	1.00000i	1.00000	+	0.577350i	0.0917517	+	0.995782i	$0.470753\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	2.00000			0.816497
$7$	1.73205	+	2.00000i	0.654654	+	0.755929i
$7$	1.73205	+	2.00000i	0.654654	+	0.755929i
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$	1.73205	−	1.00000i	0.500000	−	0.288675i
$13$		−	1.00000i		−	0.277350i	−0.990338	−	0.138675i	$-0.955716\pi$
$13$		−	1.00000i		−	0.277350i	0.990338	−	0.138675i	$-0.0442844\pi$
$14$	2.50000	+	0.866025i	0.668153	+	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.19615	−	3.00000i	−1.26025	−	0.727607i	−0.287129	−	0.957892i	$-0.592701\pi$
$17$	−5.19615	−	3.00000i	−1.26025	−	0.727607i	−0.973123	+	0.230285i	$0.926034\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	1.00000	+	5.19615i	0.218218	+	1.13389i
$22$			3.00000i			0.639602i
$23$	7.79423	−	4.50000i	1.62521	−	0.938315i	0.639713	−	0.768613i	$-0.279053\pi$
$23$	7.79423	−	4.50000i	1.62521	−	0.938315i	0.985496	−	0.169701i	$-0.0542803\pi$
$24$	1.00000	−	1.73205i	0.204124	−	0.353553i
$25$		0			0
$26$	−0.500000	−	0.866025i	−0.0980581	−	0.169842i
$27$		−	4.00000i		−	0.769800i
$28$	2.59808	−	0.500000i	0.490990	−	0.0944911i
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	0.243204	+	0.969975i	$0.421802\pi$
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	−0.961625	+	0.274367i	$0.911532\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−5.19615	+	3.00000i	−0.904534	+	0.522233i
$34$	−6.00000			−1.02899
$35$		0			0
$36$	1.00000			0.166667
$37$	6.06218	−	3.50000i	0.996616	−	0.575396i	0.0893706	−	0.995998i	$-0.471514\pi$
$37$	6.06218	−	3.50000i	0.996616	−	0.575396i	0.907245	+	0.420602i	$0.138181\pi$
$38$	−0.866025	−	0.500000i	−0.140488	−	0.0811107i
$39$	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	$0.424733\pi$
$42$	3.46410	+	4.00000i	0.534522	+	0.617213i
$43$			2.00000i			0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$		0			0
$46$	4.50000	−	7.79423i	0.663489	−	1.14920i
$47$	−7.79423	+	4.50000i	−1.13691	+	0.656392i	−0.945662	−	0.325150i	$-0.894585\pi$
$47$	−7.79423	+	4.50000i	−1.13691	+	0.656392i	−0.191243	+	0.981543i	$0.561252\pi$
$48$		−	2.00000i		−	0.288675i
$49$	−1.00000	+	6.92820i	−0.142857	+	0.989743i
$50$		0			0
$51$	−6.00000	−	10.3923i	−0.840168	−	1.45521i
$52$	−0.866025	−	0.500000i	−0.120096	−	0.0693375i
$53$	−7.79423	−	4.50000i	−1.07062	−	0.618123i	−0.142269	−	0.989828i	$-0.545440\pi$
$53$	−7.79423	−	4.50000i	−1.07062	−	0.618123i	−0.928351	+	0.371706i	$0.878773\pi$
$54$	−2.00000	−	3.46410i	−0.272166	−	0.471405i
$55$		0			0
$56$	2.00000	−	1.73205i	0.267261	−	0.231455i
$57$		−	2.00000i		−	0.264906i
$58$	−5.19615	+	3.00000i	−0.682288	+	0.393919i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$			8.00000i			1.01600i
$63$	−0.866025	+	2.50000i	−0.109109	+	0.314970i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−3.00000	+	5.19615i	−0.369274	+	0.639602i
$67$	6.92820	+	4.00000i	0.846415	+	0.488678i	0.859440	−	0.511237i	$-0.170813\pi$
$67$	6.92820	+	4.00000i	0.846415	+	0.488678i	−0.0130248	+	0.999915i	$0.504146\pi$
$68$	−5.19615	+	3.00000i	−0.630126	+	0.363803i
$69$	18.0000			2.16695
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	3.46410	+	2.00000i	0.405442	+	0.234082i	0.688830	−	0.724923i	$-0.258125\pi$
$73$	3.46410	+	2.00000i	0.405442	+	0.234082i	−0.283387	+	0.959006i	$0.591458\pi$
$74$	3.50000	−	6.06218i	0.406867	−	0.704714i
$75$		0			0
$76$	−1.00000			−0.114708
$77$	−7.79423	+	1.50000i	−0.888235	+	0.170941i
$78$		−	2.00000i		−	0.226455i
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	−0.997274	−	0.0737937i	$-0.976489\pi$
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	0.434730	−	0.900561i	$-0.356844\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	2.59808	−	1.50000i	0.286910	−	0.165647i
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$	5.00000	+	1.73205i	0.545545	+	0.188982i
$85$		0			0
$86$	1.00000	+	1.73205i	0.107833	+	0.186772i
$87$	−10.3923	−	6.00000i	−1.11417	−	0.643268i
$88$	2.59808	+	1.50000i	0.276956	+	0.159901i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$	2.00000	−	1.73205i	0.209657	−	0.181568i
$92$		−	9.00000i		−	0.938315i
$93$	−13.8564	+	8.00000i	−1.43684	+	0.829561i
$94$	−4.50000	+	7.79423i	−0.464140	+	0.803913i
$95$		0			0
$96$	−1.00000	−	1.73205i	−0.102062	−	0.176777i
$97$			10.0000i			1.01535i	0.861550	+	0.507673i	$0.169494\pi$
$97$			10.0000i			1.01535i	−0.861550	+	0.507673i	$0.830506\pi$
$98$	2.59808	+	6.50000i	0.262445	+	0.656599i
$99$	−3.00000			−0.301511
$100$		0			0
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	0.396236	+	0.918149i	$0.370316\pi$
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	−0.993258	+	0.115924i	$0.963017\pi$
$102$	−10.3923	−	6.00000i	−1.02899	−	0.594089i
$103$	−3.46410	+	2.00000i	−0.341328	+	0.197066i	−0.660859	−	0.750510i	$-0.729808\pi$
$103$	−3.46410	+	2.00000i	−0.341328	+	0.197066i	0.319531	+	0.947576i	$0.396475\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	−9.00000			−0.874157
$107$	10.3923	−	6.00000i	1.00466	−	0.580042i	0.0950377	−	0.995474i	$-0.469703\pi$
$107$	10.3923	−	6.00000i	1.00466	−	0.580042i	0.909624	+	0.415432i	$0.136370\pi$
$108$	−3.46410	−	2.00000i	−0.333333	−	0.192450i
$109$	−8.00000	+	13.8564i	−0.766261	+	1.32720i	0.173316	+	0.984866i	$0.444552\pi$
$109$	−8.00000	+	13.8564i	−0.766261	+	1.32720i	−0.939577	+	0.342337i	$0.888782\pi$
$110$		0			0
$111$	14.0000			1.32882
$112$	0.866025	−	2.50000i	0.0818317	−	0.236228i
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$	−1.00000	−	1.73205i	−0.0936586	−	0.162221i
$115$		0			0
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$	0.866025	−	0.500000i	0.0800641	−	0.0462250i
$118$		0			0
$119$	−3.00000	−	15.5885i	−0.275010	−	1.42899i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−6.92820	−	4.00000i	−0.627250	−	0.362143i
$123$	5.19615	+	3.00000i	0.468521	+	0.270501i
$124$	4.00000	+	6.92820i	0.359211	+	0.622171i
$125$		0			0
$126$	0.500000	+	2.59808i	0.0445435	+	0.231455i
$127$			1.00000i			0.0887357i	0.999015	+	0.0443678i	$0.0141274\pi$
$127$			1.00000i			0.0887357i	−0.999015	+	0.0443678i	$0.985873\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−2.00000	+	3.46410i	−0.176090	+	0.304997i
$130$		0			0
$131$	−1.50000	−	2.59808i	−0.131056	−	0.226995i	0.793028	−	0.609185i	$-0.208503\pi$
$131$	−1.50000	−	2.59808i	−0.131056	−	0.226995i	−0.924084	+	0.382190i	$0.875170\pi$
$132$			6.00000i			0.522233i
$133$	0.866025	−	2.50000i	0.0750939	−	0.216777i
$134$	8.00000			0.691095
$135$		0			0
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$	10.3923	+	6.00000i	0.887875	+	0.512615i	0.873247	−	0.487278i	$-0.162010\pi$
$137$	10.3923	+	6.00000i	0.887875	+	0.512615i	0.0146279	+	0.999893i	$0.495344\pi$
$138$	15.5885	−	9.00000i	1.32698	−	0.766131i
$139$	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
$143$	2.59808	+	1.50000i	0.217262	+	0.125436i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$		0			0
$146$	4.00000			0.331042
$147$	−8.66025	+	11.0000i	−0.714286	+	0.907265i
$148$		−	7.00000i		−	0.575396i
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$		0			0
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	−0.587646	−	0.809118i	$-0.699945\pi$
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	0.994540	+	0.104357i	$0.0332784\pi$
$152$	−0.866025	+	0.500000i	−0.0702439	+	0.0405554i
$153$		−	6.00000i		−	0.485071i
$154$	−6.00000	+	5.19615i	−0.483494	+	0.418718i
$155$		0			0
$156$	−1.00000	−	1.73205i	−0.0800641	−	0.138675i
$157$	19.9186	+	11.5000i	1.58968	+	0.917800i	0.993360	+	0.115050i	$0.0367030\pi$
$157$	19.9186	+	11.5000i	1.58968	+	0.917800i	0.596316	+	0.802749i	$0.296630\pi$
$158$	−8.66025	−	5.00000i	−0.688973	−	0.397779i
$159$	−9.00000	−	15.5885i	−0.713746	−	1.23625i
$160$		0			0
$161$	22.5000	+	7.79423i	1.77325	+	0.614271i
$162$		−	11.0000i		−	0.864242i
$163$	17.3205	−	10.0000i	1.35665	−	0.783260i	0.367477	−	0.930033i	$-0.380222\pi$
$163$	17.3205	−	10.0000i	1.35665	−	0.783260i	0.989170	+	0.146772i	$0.0468885\pi$
$164$	1.50000	−	2.59808i	0.117130	−	0.202876i
$165$		0			0
$166$		0			0
$167$		−	3.00000i		−	0.232147i	−0.993241	−	0.116073i	$-0.962969\pi$
$167$		−	3.00000i		−	0.232147i	0.993241	−	0.116073i	$-0.0370308\pi$
$168$	5.19615	−	1.00000i	0.400892	−	0.0771517i
$169$	12.0000			0.923077
$170$		0			0
$171$	0.500000	−	0.866025i	0.0382360	−	0.0662266i
$172$	1.73205	+	1.00000i	0.132068	+	0.0762493i
$173$	7.79423	−	4.50000i	0.592584	−	0.342129i	−0.173534	−	0.984828i	$-0.555519\pi$
$173$	7.79423	−	4.50000i	0.592584	−	0.342129i	0.766119	+	0.642699i	$0.222185\pi$
$174$	−12.0000			−0.909718
$175$		0			0
$176$	3.00000			0.226134
$177$		0			0
$178$	5.19615	+	3.00000i	0.389468	+	0.224860i
$179$	−1.50000	+	2.59808i	−0.112115	+	0.194189i	−0.916623	−	0.399753i	$-0.869096\pi$
$179$	−1.50000	+	2.59808i	−0.112115	+	0.194189i	0.804508	+	0.593942i	$0.202429\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	0.866025	−	2.50000i	0.0641941	−	0.185312i
$183$		−	16.0000i		−	1.18275i
$184$	−4.50000	−	7.79423i	−0.331744	−	0.574598i
$185$		0			0
$186$	−8.00000	+	13.8564i	−0.586588	+	1.01600i
$187$	15.5885	−	9.00000i	1.13994	−	0.658145i
$188$			9.00000i			0.656392i
$189$	8.00000	−	6.92820i	0.581914	−	0.503953i
$190$		0			0
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$	−1.73205	−	1.00000i	−0.125000	−	0.0721688i
$193$	13.8564	+	8.00000i	0.997406	+	0.575853i	0.907480	−	0.420096i	$-0.138004\pi$
$193$	13.8564	+	8.00000i	0.997406	+	0.575853i	0.0899262	+	0.995948i	$0.471337\pi$
$194$	5.00000	+	8.66025i	0.358979	+	0.621770i
$195$		0			0
$196$	5.50000	+	4.33013i	0.392857	+	0.309295i
$197$		−	15.0000i		−	1.06871i	−0.845262	−	0.534353i	$-0.820555\pi$
$197$		−	15.0000i		−	1.06871i	0.845262	−	0.534353i	$-0.179445\pi$
$198$	−2.59808	+	1.50000i	−0.184637	+	0.106600i
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	0.429745	+	0.902950i	$0.358603\pi$
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	−0.996850	+	0.0793045i	$0.974730\pi$
$200$		0			0
$201$	8.00000	+	13.8564i	0.564276	+	0.977356i
$202$			12.0000i			0.844317i
$203$	−10.3923	−	12.0000i	−0.729397	−	0.842235i
$204$	−12.0000			−0.840168
$205$		0			0
$206$	−2.00000	+	3.46410i	−0.139347	+	0.241355i
$207$	7.79423	+	4.50000i	0.541736	+	0.312772i
$208$	−0.866025	+	0.500000i	−0.0600481	+	0.0346688i
$209$	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	$0.209200\pi$
$212$	−7.79423	+	4.50000i	−0.535310	+	0.309061i
$213$		0			0
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$		0			0
$216$	−4.00000			−0.272166
$217$	−20.7846	+	4.00000i	−1.41095	+	0.271538i
$218$			16.0000i			1.08366i
$219$	4.00000	+	6.92820i	0.270295	+	0.468165i
$220$		0			0
$221$	−3.00000	+	5.19615i	−0.201802	+	0.349531i
$222$	12.1244	−	7.00000i	0.813733	−	0.469809i
$223$			8.00000i			0.535720i	0.963458	+	0.267860i	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$	−0.500000	−	2.59808i	−0.0334077	−	0.173591i
$225$		0			0
$226$		0			0
$227$	−10.3923	−	6.00000i	−0.689761	−	0.398234i	0.113761	−	0.993508i	$-0.463710\pi$
$227$	−10.3923	−	6.00000i	−0.689761	−	0.398234i	−0.803523	+	0.595274i	$0.797043\pi$
$228$	−1.73205	−	1.00000i	−0.114708	−	0.0662266i
$229$	−2.00000	−	3.46410i	−0.132164	−	0.228914i	0.792347	−	0.610071i	$-0.208859\pi$
$229$	−2.00000	−	3.46410i	−0.132164	−	0.228914i	−0.924510	+	0.381157i	$0.875526\pi$
$230$		0			0
$231$	−15.0000	−	5.19615i	−0.986928	−	0.341882i
$232$			6.00000i			0.393919i
$233$	−5.19615	+	3.00000i	−0.340411	+	0.196537i	−0.660454	−	0.750867i	$-0.729636\pi$
$233$	−5.19615	+	3.00000i	−0.340411	+	0.196537i	0.320043	+	0.947403i	$0.396303\pi$
$234$	0.500000	−	0.866025i	0.0326860	−	0.0566139i
$235$		0			0
$236$		0			0
$237$		−	20.0000i		−	1.29914i
$238$	−10.3923	−	12.0000i	−0.673633	−	0.777844i
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$	1.73205	+	1.00000i	0.111340	+	0.0642824i
$243$	8.66025	−	5.00000i	0.555556	−	0.320750i
$244$	−8.00000			−0.512148
$245$		0			0
$246$	6.00000			0.382546
$247$	−0.866025	+	0.500000i	−0.0551039	+	0.0318142i
$248$	6.92820	+	4.00000i	0.439941	+	0.254000i
$249$		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	$0.656972\pi$
$252$	1.73205	+	2.00000i	0.109109	+	0.125988i
$253$			27.0000i			1.69748i
$254$	0.500000	+	0.866025i	0.0313728	+	0.0543393i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$257$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$258$			4.00000i			0.249029i
$259$	17.5000	+	6.06218i	1.08740	+	0.376685i
$260$		0			0
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$	−2.59808	−	1.50000i	−0.160510	−	0.0926703i
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$	3.00000	+	5.19615i	0.184637	+	0.319801i
$265$		0			0
$266$	−0.500000	−	2.59808i	−0.0306570	−	0.159298i
$267$			12.0000i			0.734388i
$268$	6.92820	−	4.00000i	0.423207	−	0.244339i
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$			6.00000i			0.363803i
$273$	5.19615	−	1.00000i	0.314485	−	0.0605228i
$274$	12.0000			0.724947
$275$		0			0
$276$	9.00000	−	15.5885i	0.541736	−	0.938315i
$277$	−8.66025	−	5.00000i	−0.520344	−	0.300421i	0.216731	−	0.976231i	$-0.430460\pi$
$277$	−8.66025	−	5.00000i	−0.520344	−	0.300421i	−0.737075	+	0.675810i	$0.763794\pi$
$278$	3.46410	−	2.00000i	0.207763	−	0.119952i
$279$	−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	$0.798019\pi$
$282$	−15.5885	+	9.00000i	−0.928279	+	0.535942i
$283$	−12.1244	−	7.00000i	−0.720718	−	0.416107i	0.0942988	−	0.995544i	$-0.469939\pi$
$283$	−12.1244	−	7.00000i	−0.720718	−	0.416107i	−0.815017	+	0.579437i	$0.803272\pi$
$284$		0			0
$285$		0			0
$286$	3.00000			0.177394
$287$	5.19615	+	6.00000i	0.306719	+	0.354169i
$288$		−	1.00000i		−	0.0589256i
$289$	9.50000	+	16.4545i	0.558824	+	0.967911i
$290$		0			0
$291$	−10.0000	+	17.3205i	−0.586210	+	1.01535i
$292$	3.46410	−	2.00000i	0.202721	−	0.117041i
$293$		−	9.00000i		−	0.525786i	−0.964825	−	0.262893i	$-0.915323\pi$
$293$		−	9.00000i		−	0.525786i	0.964825	−	0.262893i	$-0.0846766\pi$
$294$	−2.00000	+	13.8564i	−0.116642	+	0.808122i
$295$		0			0
$296$	−3.50000	−	6.06218i	−0.203433	−	0.352357i
$297$	10.3923	+	6.00000i	0.603023	+	0.348155i
$298$	−5.19615	−	3.00000i	−0.301005	−	0.173785i
$299$	−4.50000	−	7.79423i	−0.260242	−	0.450752i
$300$		0			0
$301$	−4.00000	+	3.46410i	−0.230556	+	0.199667i
$302$		−	10.0000i		−	0.575435i
$303$	−20.7846	+	12.0000i	−1.19404	+	0.689382i
$304$	−0.500000	+	0.866025i	−0.0286770	+	0.0496700i
$305$		0			0
$306$	−3.00000	−	5.19615i	−0.171499	−	0.297044i
$307$		−	14.0000i		−	0.799022i	−0.916728	−	0.399511i	$-0.869180\pi$
$307$		−	14.0000i		−	0.799022i	0.916728	−	0.399511i	$-0.130820\pi$
$308$	−2.59808	+	7.50000i	−0.148039	+	0.427352i
$309$	−8.00000			−0.455104
$310$		0			0
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	−0.294384	−	0.955687i	$-0.595114\pi$
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	0.974841	−	0.222900i	$-0.0715523\pi$
$312$	−1.73205	−	1.00000i	−0.0980581	−	0.0566139i
$313$	−24.2487	+	14.0000i	−1.37062	+	0.791327i	−0.991006	−	0.133819i	$-0.957276\pi$
$313$	−24.2487	+	14.0000i	−1.37062	+	0.791327i	−0.379612	+	0.925146i	$0.623943\pi$
$314$	23.0000			1.29797
$315$		0			0
$316$	−10.0000			−0.562544
$317$	−5.19615	+	3.00000i	−0.291845	+	0.168497i	−0.638774	−	0.769395i	$-0.720558\pi$
$317$	−5.19615	+	3.00000i	−0.291845	+	0.168497i	0.346929	+	0.937892i	$0.387225\pi$
$318$	−15.5885	−	9.00000i	−0.874157	−	0.504695i
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$		0			0
$321$	24.0000			1.33955
$322$	23.3827	−	4.50000i	1.30307	−	0.250775i
$323$			6.00000i			0.333849i
$324$	−5.50000	−	9.52628i	−0.305556	−	0.529238i
$325$		0			0
$326$	10.0000	−	17.3205i	0.553849	−	0.959294i
$327$	−27.7128	+	16.0000i	−1.53252	+	0.884802i
$328$		−	3.00000i		−	0.165647i
$329$	−22.5000	−	7.79423i	−1.24047	−	0.429710i
$330$		0			0
$331$	3.50000	+	6.06218i	0.192377	+	0.333207i	0.946038	−	0.324057i	$-0.105047\pi$
$331$	3.50000	+	6.06218i	0.192377	+	0.333207i	−0.753660	+	0.657264i	$0.771714\pi$
$332$		0			0
$333$	6.06218	+	3.50000i	0.332205	+	0.191799i
$334$	−1.50000	−	2.59808i	−0.0820763	−	0.142160i
$335$		0			0
$336$	4.00000	−	3.46410i	0.218218	−	0.188982i
$337$			22.0000i			1.19842i	0.800593	+	0.599208i	$0.204518\pi$
$337$			22.0000i			1.19842i	−0.800593	+	0.599208i	$0.795482\pi$
$338$	10.3923	−	6.00000i	0.565267	−	0.326357i
$339$		0			0
$340$		0			0
$341$	−12.0000	−	20.7846i	−0.649836	−	1.12555i
$342$		−	1.00000i		−	0.0540738i
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$	2.00000			0.107833
$345$		0			0
$346$	4.50000	−	7.79423i	0.241921	−	0.419020i
$347$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$347$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$348$	−10.3923	+	6.00000i	−0.557086	+	0.321634i
$349$	−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
$352$	2.59808	−	1.50000i	0.138478	−	0.0799503i
$353$	−10.3923	−	6.00000i	−0.553127	−	0.319348i	0.197256	−	0.980352i	$-0.436797\pi$
$353$	−10.3923	−	6.00000i	−0.553127	−	0.319348i	−0.750382	+	0.661004i	$0.770130\pi$
$354$		0			0
$355$		0			0
$356$	6.00000			0.317999
$357$	10.3923	−	30.0000i	0.550019	−	1.58777i
$358$			3.00000i			0.158555i
$359$	9.00000	+	15.5885i	0.475002	+	0.822727i	0.999590	−	0.0286287i	$-0.00911406\pi$
$359$	9.00000	+	15.5885i	0.475002	+	0.822727i	−0.524588	+	0.851356i	$0.675781\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	1.73205	−	1.00000i	0.0910346	−	0.0525588i
$363$			4.00000i			0.209946i
$364$	−0.500000	−	2.59808i	−0.0262071	−	0.136176i
$365$		0			0
$366$	−8.00000	−	13.8564i	−0.418167	−	0.724286i
$367$	−16.4545	−	9.50000i	−0.858917	−	0.495896i	0.00473247	−	0.999989i	$-0.498494\pi$
$367$	−16.4545	−	9.50000i	−0.858917	−	0.495896i	−0.863649	+	0.504093i	$0.831827\pi$
$368$	−7.79423	−	4.50000i	−0.406302	−	0.234579i
$369$	1.50000	+	2.59808i	0.0780869	+	0.135250i
$370$		0			0
$371$	−4.50000	−	23.3827i	−0.233628	−	1.21397i
$372$			16.0000i			0.829561i
$373$	1.73205	−	1.00000i	0.0896822	−	0.0517780i	−0.454488	−	0.890753i	$-0.650178\pi$
$373$	1.73205	−	1.00000i	0.0896822	−	0.0517780i	0.544170	+	0.838975i	$0.316844\pi$
$374$	9.00000	−	15.5885i	0.465379	−	0.806060i
$375$		0			0
$376$	4.50000	+	7.79423i	0.232070	+	0.401957i
$377$			6.00000i			0.309016i
$378$	3.46410	−	10.0000i	0.178174	−	0.514344i
$379$	−23.0000			−1.18143			−0.590715	−	0.806880i	$-0.701154\pi$
$379$	−23.0000			−1.18143			−0.590715	+	0.806880i	$0.701154\pi$
$380$		0			0
$381$	−1.00000	+	1.73205i	−0.0512316	+	0.0887357i
$382$	−10.3923	−	6.00000i	−0.531717	−	0.306987i
$383$	18.1865	−	10.5000i	0.929288	−	0.536525i	0.0427020	−	0.999088i	$-0.486403\pi$
$383$	18.1865	−	10.5000i	0.929288	−	0.536525i	0.886586	+	0.462563i	$0.153070\pi$
$384$	−2.00000			−0.102062
$385$		0			0
$386$	16.0000			0.814379
$387$	−1.73205	+	1.00000i	−0.0880451	+	0.0508329i
$388$	8.66025	+	5.00000i	0.439658	+	0.253837i
$389$	−6.00000	+	10.3923i	−0.304212	+	0.526911i	−0.977086	−	0.212847i	$-0.931726\pi$
$389$	−6.00000	+	10.3923i	−0.304212	+	0.526911i	0.672874	+	0.739758i	$0.265060\pi$
$390$		0			0
$391$	−54.0000			−2.73090
$392$	6.92820	+	1.00000i	0.349927	+	0.0505076i
$393$		−	6.00000i		−	0.302660i
$394$	−7.50000	−	12.9904i	−0.377845	−	0.654446i
$395$		0			0
$396$	−1.50000	+	2.59808i	−0.0753778	+	0.130558i
$397$	−12.1244	+	7.00000i	−0.608504	+	0.351320i	−0.772380	−	0.635161i	$-0.780934\pi$
$397$	−12.1244	+	7.00000i	−0.608504	+	0.351320i	0.163876	+	0.986481i	$0.447600\pi$
$398$			16.0000i			0.802008i
$399$	4.00000	−	3.46410i	0.200250	−	0.173422i
$400$		0			0
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	0.976714	+	0.214544i	$0.0688266\pi$
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	−0.302556	+	0.953131i	$0.597840\pi$
$402$	13.8564	+	8.00000i	0.691095	+	0.399004i
$403$	6.92820	+	4.00000i	0.345118	+	0.199254i
$404$	6.00000	+	10.3923i	0.298511	+	0.517036i
$405$		0			0
$406$	−15.0000	−	5.19615i	−0.744438	−	0.257881i
$407$			21.0000i			1.04093i
$408$	−10.3923	+	6.00000i	−0.514496	+	0.297044i
$409$	13.0000	−	22.5167i	0.642809	−	1.11338i	−0.341994	−	0.939702i	$-0.611102\pi$
$409$	13.0000	−	22.5167i	0.642809	−	1.11338i	0.984803	−	0.173675i	$-0.0555643\pi$
$410$		0			0
$411$	12.0000	+	20.7846i	0.591916	+	1.02523i
$412$			4.00000i			0.197066i
$413$		0			0
$414$	9.00000			0.442326
$415$		0			0
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$	6.92820	+	4.00000i	0.339276	+	0.195881i
$418$	2.59808	−	1.50000i	0.127076	−	0.0733674i
$419$	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	$0.484480\pi$
$422$	19.9186	−	11.5000i	0.969622	−	0.559811i
$423$	−7.79423	−	4.50000i	−0.378968	−	0.218797i
$424$	−4.50000	+	7.79423i	−0.218539	+	0.378521i
$425$		0			0
$426$		0			0
$427$	6.92820	−	20.0000i	0.335279	−	0.967868i
$428$		−	12.0000i		−	0.580042i
$429$	3.00000	+	5.19615i	0.144841	+	0.250873i
$430$		0			0
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$	−3.46410	+	2.00000i	−0.166667	+	0.0962250i
$433$		−	40.0000i		−	1.92228i	−0.276066	−	0.961139i	$-0.589031\pi$
$433$		−	40.0000i		−	1.92228i	0.276066	−	0.961139i	$-0.410969\pi$
$434$	−16.0000	+	13.8564i	−0.768025	+	0.665129i
$435$		0			0
$436$	8.00000	+	13.8564i	0.383131	+	0.663602i
$437$	−7.79423	−	4.50000i	−0.372849	−	0.215264i
$438$	6.92820	+	4.00000i	0.331042	+	0.191127i
$439$	13.0000	+	22.5167i	0.620456	+	1.07466i	0.989401	+	0.145210i	$0.0463858\pi$
$439$	13.0000	+	22.5167i	0.620456	+	1.07466i	−0.368945	+	0.929451i	$0.620281\pi$
$440$		0			0
$441$	−6.50000	+	2.59808i	−0.309524	+	0.123718i
$442$			6.00000i			0.285391i
$443$	10.3923	−	6.00000i	0.493753	−	0.285069i	−0.232377	−	0.972626i	$-0.574650\pi$
$443$	10.3923	−	6.00000i	0.493753	−	0.285069i	0.726130	+	0.687557i	$0.241317\pi$
$444$	7.00000	−	12.1244i	0.332205	−	0.575396i
$445$		0			0
$446$	4.00000	+	6.92820i	0.189405	+	0.328060i
$447$		−	12.0000i		−	0.567581i
$448$	−1.73205	−	2.00000i	−0.0818317	−	0.0944911i
$449$	−21.0000			−0.991051			−0.495526	−	0.868593i	$-0.665025\pi$
$449$	−21.0000			−0.991051			−0.495526	+	0.868593i	$0.665025\pi$
$450$		0			0
$451$	−4.50000	+	7.79423i	−0.211897	+	0.367016i
$452$		0			0
$453$	17.3205	−	10.0000i	0.813788	−	0.469841i
$454$	−12.0000			−0.563188
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	−12.1244	+	7.00000i	−0.567153	+	0.327446i	−0.756012	−	0.654558i	$-0.772855\pi$
$457$	−12.1244	+	7.00000i	−0.567153	+	0.327446i	0.188858	+	0.982004i	$0.439521\pi$
$458$	−3.46410	−	2.00000i	−0.161867	−	0.0934539i
$459$	−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	$0.746202\pi$
$462$	−15.5885	+	3.00000i	−0.725241	+	0.139573i
$463$		−	1.00000i		−	0.0464739i	−0.999730	−	0.0232370i	$-0.992603\pi$
$463$		−	1.00000i		−	0.0464739i	0.999730	−	0.0232370i	$-0.00739722\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	5.19615	−	3.00000i	0.240449	−	0.138823i	−0.374934	−	0.927052i	$-0.622335\pi$
$467$	5.19615	−	3.00000i	0.240449	−	0.138823i	0.615383	+	0.788228i	$0.289001\pi$
$468$		−	1.00000i		−	0.0462250i
$469$	4.00000	+	20.7846i	0.184703	+	0.959744i
$470$		0			0
$471$	23.0000	+	39.8372i	1.05978	+	1.83560i
$472$		0			0
$473$	−5.19615	−	3.00000i	−0.238919	−	0.137940i
$474$	−10.0000	−	17.3205i	−0.459315	−	0.795557i
$475$		0			0
$476$	−15.0000	−	5.19615i	−0.687524	−	0.238165i
$477$		−	9.00000i		−	0.412082i
$478$	5.19615	−	3.00000i	0.237666	−	0.137217i
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$		0			0
$481$	−3.50000	−	6.06218i	−0.159586	−	0.276412i
$482$		−	1.00000i		−	0.0455488i
$483$	31.1769	+	36.0000i	1.41860	+	1.63806i
$484$	2.00000			0.0909091
$485$		0			0
$486$	5.00000	−	8.66025i	0.226805	−	0.392837i
$487$	−13.8564	−	8.00000i	−0.627894	−	0.362515i	0.152042	−	0.988374i	$-0.451415\pi$
$487$	−13.8564	−	8.00000i	−0.627894	−	0.362515i	−0.779936	+	0.625859i	$0.784748\pi$
$488$	−6.92820	+	4.00000i	−0.313625	+	0.181071i
$489$	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	$0.198200\pi$
$492$	5.19615	−	3.00000i	0.234261	−	0.135250i
$493$	31.1769	+	18.0000i	1.40414	+	0.810679i
$494$	−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	$-0.195204\pi$
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	−0.907314	+	0.420455i	$0.861871\pi$
$500$		0			0
$501$	3.00000	−	5.19615i	0.134030	−	0.232147i
$502$	−12.9904	+	7.50000i	−0.579789	+	0.334741i
$503$			24.0000i			1.07011i	0.844818	+	0.535054i	$0.179709\pi$
$503$			24.0000i			1.07011i	−0.844818	+	0.535054i	$0.820291\pi$
$504$	2.50000	+	0.866025i	0.111359	+	0.0385758i
$505$		0			0
$506$	13.5000	+	23.3827i	0.600148	+	1.03949i
$507$	20.7846	+	12.0000i	0.923077	+	0.532939i
$508$	0.866025	+	0.500000i	0.0384237	+	0.0221839i
$509$	−21.0000	−	36.3731i	−0.930809	−	1.61221i	−0.781943	−	0.623350i	$-0.785771\pi$
$509$	−21.0000	−	36.3731i	−0.930809	−	1.61221i	−0.148866	−	0.988857i	$-0.547562\pi$
$510$		0			0
$511$	2.00000	+	10.3923i	0.0884748	+	0.459728i
$512$			1.00000i			0.0441942i
$513$	−3.46410	+	2.00000i	−0.152944	+	0.0883022i
$514$		0			0
$515$		0			0
$516$	2.00000	+	3.46410i	0.0880451	+	0.152499i
$517$		−	27.0000i		−	1.18746i
$518$	18.1865	−	3.50000i	0.799070	−	0.153781i
$519$	18.0000			0.790112
$520$		0			0
$521$	7.50000	−	12.9904i	0.328581	−	0.569119i	−0.653650	−	0.756797i	$-0.726763\pi$
$521$	7.50000	−	12.9904i	0.328581	−	0.569119i	0.982231	+	0.187678i	$0.0600963\pi$
$522$	−5.19615	−	3.00000i	−0.227429	−	0.131306i
$523$	−24.2487	+	14.0000i	−1.06032	+	0.612177i	−0.925521	−	0.378695i	$-0.876373\pi$
$523$	−24.2487	+	14.0000i	−1.06032	+	0.612177i	−0.134801	+	0.990873i	$0.543039\pi$
$524$	−3.00000			−0.131056
$525$		0			0
$526$		0			0
$527$	41.5692	−	24.0000i	1.81078	−	1.04546i
$528$	5.19615	+	3.00000i	0.226134	+	0.130558i
$529$	29.0000	−	50.2295i	1.26087	−	2.18389i
$530$		0			0
$531$		0			0
$532$	−1.73205	−	2.00000i	−0.0750939	−	0.0867110i
$533$		−	3.00000i		−	0.129944i
$534$	6.00000	+	10.3923i	0.259645	+	0.449719i
$535$		0			0
$536$	4.00000	−	6.92820i	0.172774	−	0.299253i
$537$	−5.19615	+	3.00000i	−0.224231	+	0.129460i
$538$		0			0
$539$	−16.5000	−	12.9904i	−0.710705	−	0.559535i
$540$		0			0
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	0.767136	−	0.641484i	$-0.221681\pi$
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	−0.939110	+	0.343617i	$0.888348\pi$
$542$	13.8564	+	8.00000i	0.595184	+	0.343629i
$543$	3.46410	+	2.00000i	0.148659	+	0.0858282i
$544$	3.00000	+	5.19615i	0.128624	+	0.222783i
$545$		0			0
$546$	4.00000	−	3.46410i	0.171184	−	0.148250i
$547$		−	8.00000i		−	0.342055i	−0.985266	−	0.171028i	$-0.945291\pi$
$547$		−	8.00000i		−	0.342055i	0.985266	−	0.171028i	$-0.0547087\pi$
$548$	10.3923	−	6.00000i	0.443937	−	0.256307i
$549$	4.00000	−	6.92820i	0.170716	−	0.295689i
$550$		0			0
$551$	3.00000	+	5.19615i	0.127804	+	0.221364i
$552$		−	18.0000i		−	0.766131i
$553$	8.66025	−	25.0000i	0.368271	−	1.06311i
$554$	−10.0000			−0.424859
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	−7.79423	−	4.50000i	−0.330252	−	0.190671i	0.325701	−	0.945473i	$-0.394400\pi$
$557$	−7.79423	−	4.50000i	−0.330252	−	0.190671i	−0.655953	+	0.754802i	$0.727733\pi$
$558$	−6.92820	+	4.00000i	−0.293294	+	0.169334i
$559$	2.00000			0.0845910
$560$		0			0
$561$	36.0000			1.51992
$562$	−23.3827	+	13.5000i	−0.986339	+	0.569463i
$563$	−36.3731	−	21.0000i	−1.53294	−	0.885044i	−0.999224	−	0.0393818i	$-0.987461\pi$
$563$	−36.3731	−	21.0000i	−1.53294	−	0.885044i	−0.533718	−	0.845663i	$-0.679206\pi$
$564$	−9.00000	+	15.5885i	−0.378968	+	0.656392i
$565$		0			0
$566$	−14.0000			−0.588464
$567$	28.5788	−	5.50000i	1.20020	−	0.230978i
$568$		0			0
$569$	10.5000	+	18.1865i	0.440183	+	0.762419i	0.997703	−	0.0677445i	$-0.0215803\pi$
$569$	10.5000	+	18.1865i	0.440183	+	0.762419i	−0.557520	+	0.830164i	$0.688247\pi$
$570$		0			0
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$	2.59808	−	1.50000i	0.108631	−	0.0627182i
$573$		−	24.0000i		−	1.00261i
$574$	7.50000	+	2.59808i	0.313044	+	0.108442i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	38.1051	+	22.0000i	1.58634	+	0.915872i	0.993904	+	0.110252i	$0.0351659\pi$
$577$	38.1051	+	22.0000i	1.58634	+	0.915872i	0.592433	+	0.805620i	$0.298167\pi$
$578$	16.4545	+	9.50000i	0.684416	+	0.395148i
$579$	16.0000	+	27.7128i	0.664937	+	1.15171i
$580$		0			0
$581$		0			0
$582$			20.0000i			0.829027i
$583$	23.3827	−	13.5000i	0.968412	−	0.559113i
$584$	2.00000	−	3.46410i	0.0827606	−	0.143346i
$585$		0			0
$586$	−4.50000	−	7.79423i	−0.185893	−	0.321977i
$587$			24.0000i			0.990586i	0.868726	+	0.495293i	$0.164939\pi$
$587$			24.0000i			0.990586i	−0.868726	+	0.495293i	$0.835061\pi$
$588$	5.19615	+	13.0000i	0.214286	+	0.536111i
$589$	8.00000			0.329634
$590$		0			0
$591$	15.0000	−	25.9808i	0.617018	−	1.06871i
$592$	−6.06218	−	3.50000i	−0.249154	−	0.143849i
$593$	20.7846	−	12.0000i	0.853522	−	0.492781i	−0.00831589	−	0.999965i	$-0.502647\pi$
$593$	20.7846	−	12.0000i	0.853522	−	0.492781i	0.861838	+	0.507184i	$0.169314\pi$
$594$	12.0000			0.492366
$595$		0			0
$596$	−6.00000			−0.245770
$597$	−27.7128	+	16.0000i	−1.13421	+	0.654836i
$598$	−7.79423	−	4.50000i	−0.318730	−	0.184019i
$599$	−21.0000	+	36.3731i	−0.858037	+	1.48616i	0.0157622	+	0.999876i	$0.494983\pi$
$599$	−21.0000	+	36.3731i	−0.858037	+	1.48616i	−0.873799	+	0.486287i	$0.838351\pi$
$600$		0			0
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$	−1.73205	+	5.00000i	−0.0705931	+	0.203785i
$603$			8.00000i			0.325785i
$604$	−5.00000	−	8.66025i	−0.203447	−	0.352381i
$605$		0			0
$606$	−12.0000	+	20.7846i	−0.487467	+	0.844317i
$607$	0.866025	−	0.500000i	0.0351509	−	0.0202944i	−0.482322	−	0.875994i	$-0.660206\pi$
$607$	0.866025	−	0.500000i	0.0351509	−	0.0202944i	0.517472	+	0.855700i	$0.326873\pi$
$608$			1.00000i			0.0405554i
$609$	−6.00000	−	31.1769i	−0.243132	−	1.26335i
$610$		0			0
$611$	4.50000	+	7.79423i	0.182051	+	0.315321i
$612$	−5.19615	−	3.00000i	−0.210042	−	0.121268i
$613$	−25.1147	−	14.5000i	−1.01437	−	0.585649i	−0.101905	−	0.994794i	$-0.532494\pi$
$613$	−25.1147	−	14.5000i	−1.01437	−	0.585649i	−0.912470	+	0.409145i	$0.865827\pi$
$614$	−7.00000	−	12.1244i	−0.282497	−	0.489299i
$615$		0			0
$616$	1.50000	+	7.79423i	0.0604367	+	0.314038i
$617$			18.0000i			0.724653i	0.932051	+	0.362326i	$0.118017\pi$
$617$			18.0000i			0.724653i	−0.932051	+	0.362326i	$0.881983\pi$
$618$	−6.92820	+	4.00000i	−0.278693	+	0.160904i
$619$	11.5000	−	19.9186i	0.462224	−	0.800595i	−0.536847	−	0.843679i	$-0.680385\pi$
$619$	11.5000	−	19.9186i	0.462224	−	0.800595i	0.999071	+	0.0430838i	$0.0137183\pi$
$620$		0			0
$621$	−18.0000	−	31.1769i	−0.722315	−	1.25109i
$622$		−	24.0000i		−	0.962312i
$623$	−5.19615	+	15.0000i	−0.208179	+	0.600962i
$624$	−2.00000			−0.0800641
$625$		0			0
$626$	−14.0000	+	24.2487i	−0.559553	+	0.969173i
$627$	5.19615	+	3.00000i	0.207514	+	0.119808i
$628$	19.9186	−	11.5000i	0.794838	−	0.458900i
$629$	−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	$0.369672\pi$
$632$	−8.66025	+	5.00000i	−0.344486	+	0.198889i
$633$	39.8372	+	23.0000i	1.58339	+	0.914168i
$634$	−3.00000	+	5.19615i	−0.119145	+	0.206366i
$635$		0			0
$636$	−18.0000			−0.713746
$637$	6.92820	+	1.00000i	0.274505	+	0.0396214i
$638$		−	18.0000i		−	0.712627i
$639$		0			0
$640$		0			0
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	0.466029	+	0.884769i	$0.345684\pi$
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	−0.999247	+	0.0387913i	$0.987649\pi$
$642$	20.7846	−	12.0000i	0.820303	−	0.473602i
$643$			2.00000i			0.0788723i	0.999222	+	0.0394362i	$0.0125562\pi$
$643$			2.00000i			0.0788723i	−0.999222	+	0.0394362i	$0.987444\pi$
$644$	18.0000	−	15.5885i	0.709299	−	0.614271i
$645$		0			0
$646$	3.00000	+	5.19615i	0.118033	+	0.204440i
$647$	28.5788	+	16.5000i	1.12355	+	0.648682i	0.942305	−	0.334756i	$-0.108654\pi$
$647$	28.5788	+	16.5000i	1.12355	+	0.648682i	0.181245	+	0.983438i	$0.441987\pi$
$648$	−9.52628	−	5.50000i	−0.374228	−	0.216060i
$649$		0			0
$650$		0			0
$651$	−40.0000	−	13.8564i	−1.56772	−	0.543075i
$652$		−	20.0000i		−	0.783260i
$653$	−7.79423	+	4.50000i	−0.305012	+	0.176099i	−0.644692	−	0.764442i	$-0.723014\pi$
$653$	−7.79423	+	4.50000i	−0.305012	+	0.176099i	0.339680	+	0.940541i	$0.389681\pi$
$654$	−16.0000	+	27.7128i	−0.625650	+	1.08366i
$655$		0			0
$656$	−1.50000	−	2.59808i	−0.0585652	−	0.101438i
$657$			4.00000i			0.156055i
$658$	−23.3827	+	4.50000i	−0.911552	+	0.175428i
$659$	24.0000			0.934907			0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000			0.934907			0.467454	+	0.884018i	$0.345171\pi$
$660$		0			0
$661$	14.0000	−	24.2487i	0.544537	−	0.943166i	−0.454099	−	0.890951i	$-0.650039\pi$
$661$	14.0000	−	24.2487i	0.544537	−	0.943166i	0.998636	−	0.0522143i	$-0.0166279\pi$
$662$	6.06218	+	3.50000i	0.235613	+	0.136031i
$663$	−10.3923	+	6.00000i	−0.403604	+	0.233021i
$664$		0			0
$665$		0			0
$666$	7.00000			0.271244
$667$	−46.7654	+	27.0000i	−1.81076	+	1.04544i
$668$	−2.59808	−	1.50000i	−0.100523	−	0.0580367i
$669$	−8.00000	+	13.8564i	−0.309298	+	0.535720i
$670$		0			0
$671$	24.0000			0.926510
$672$	1.73205	−	5.00000i	0.0668153	−	0.192879i
$673$		−	34.0000i		−	1.31060i	−0.755367	−	0.655302i	$-0.772541\pi$
$673$		−	34.0000i		−	1.31060i	0.755367	−	0.655302i	$-0.227459\pi$
$674$	11.0000	+	19.0526i	0.423704	+	0.733877i
$675$		0			0
$676$	6.00000	−	10.3923i	0.230769	−	0.399704i
$677$	7.79423	−	4.50000i	0.299557	−	0.172949i	−0.342687	−	0.939450i	$-0.611337\pi$
$677$	7.79423	−	4.50000i	0.299557	−	0.172949i	0.642244	+	0.766501i	$0.278004\pi$
$678$		0			0
$679$	−20.0000	+	17.3205i	−0.767530	+	0.664700i
$680$		0			0
$681$	−12.0000	−	20.7846i	−0.459841	−	0.796468i
$682$	−20.7846	−	12.0000i	−0.795884	−	0.459504i
$683$	−10.3923	−	6.00000i	−0.397650	−	0.229584i	0.287819	−	0.957685i	$-0.407070\pi$
$683$	−10.3923	−	6.00000i	−0.397650	−	0.229584i	−0.685470	+	0.728101i	$0.740403\pi$
$684$	−0.500000	−	0.866025i	−0.0191180	−	0.0331133i
$685$		0			0
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$		−	8.00000i		−	0.305219i
$688$	1.73205	−	1.00000i	0.0660338	−	0.0381246i
$689$	−4.50000	+	7.79423i	−0.171436	+	0.296936i
$690$		0			0
$691$	−16.0000	−	27.7128i	−0.608669	−	1.05425i	−0.991460	−	0.130410i	$-0.958371\pi$
$691$	−16.0000	−	27.7128i	−0.608669	−	1.05425i	0.382791	−	0.923835i	$-0.374963\pi$
$692$		−	9.00000i		−	0.342129i
$693$	−5.19615	−	6.00000i	−0.197386	−	0.227921i
$694$		0			0
$695$		0			0
$696$	−6.00000	+	10.3923i	−0.227429	+	0.393919i
$697$	−15.5885	−	9.00000i	−0.590455	−	0.340899i
$698$	−22.5167	+	13.0000i	−0.852268	+	0.492057i
$699$	−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	$0.691719\pi$
$702$	−3.46410	+	2.00000i	−0.130744	+	0.0754851i
$703$	−6.06218	−	3.50000i	−0.228639	−	0.132005i
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$		0			0
$706$	−12.0000			−0.451626
$707$	−31.1769	+	6.00000i	−1.17253	+	0.225653i
$708$		0			0
$709$	−23.0000	−	39.8372i	−0.863783	−	1.49612i	−0.868250	−	0.496126i	$-0.834755\pi$
$709$	−23.0000	−	39.8372i	−0.863783	−	1.49612i	0.00446726	−	0.999990i	$-0.498578\pi$
$710$		0			0
$711$	5.00000	−	8.66025i	0.187515	−	0.324785i
$712$	5.19615	−	3.00000i	0.194734	−	0.112430i
$713$			72.0000i			2.69642i
$714$	−6.00000	−	31.1769i	−0.224544	−	1.16677i
$715$		0			0
$716$	1.50000	+	2.59808i	0.0560576	+	0.0970947i
$717$	10.3923	+	6.00000i	0.388108	+	0.224074i
$718$	15.5885	+	9.00000i	0.581756	+	0.335877i
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$		0			0
$721$	−10.0000	−	3.46410i	−0.372419	−	0.129010i
$722$		−	18.0000i		−	0.669891i
$723$	1.73205	−	1.00000i	0.0644157	−	0.0371904i
$724$	1.00000	−	1.73205i	0.0371647	−	0.0643712i
$725$		0			0
$726$	2.00000	+	3.46410i	0.0742270	+	0.128565i
$727$			1.00000i			0.0370879i	0.999828	+	0.0185440i	$0.00590307\pi$
$727$			1.00000i			0.0370879i	−0.999828	+	0.0185440i	$0.994097\pi$
$728$	−1.73205	−	2.00000i	−0.0641941	−	0.0741249i
$729$	−13.0000			−0.481481
$730$		0			0
$731$	6.00000	−	10.3923i	0.221918	−	0.384373i
$732$	−13.8564	−	8.00000i	−0.512148	−	0.295689i
$733$	−37.2391	+	21.5000i	−1.37546	+	0.794121i	−0.991609	−	0.129275i	$-0.958735\pi$
$733$	−37.2391	+	21.5000i	−1.37546	+	0.794121i	−0.383849	+	0.923396i	$0.625402\pi$
$734$	−19.0000			−0.701303
$735$		0			0
$736$	−9.00000			−0.331744
$737$	−20.7846	+	12.0000i	−0.765611	+	0.442026i
$738$	2.59808	+	1.50000i	0.0956365	+	0.0552158i
$739$	17.5000	−	30.3109i	0.643748	−	1.11500i	−0.340841	−	0.940121i	$-0.610712\pi$
$739$	17.5000	−	30.3109i	0.643748	−	1.11500i	0.984589	−	0.174883i	$-0.0559548\pi$
$740$		0			0
$741$	−2.00000			−0.0734718
$742$	−15.5885	−	18.0000i	−0.572270	−	0.660801i
$743$		−	45.0000i		−	1.65089i	−0.564483	−	0.825445i	$-0.690924\pi$
$743$		−	45.0000i		−	1.65089i	0.564483	−	0.825445i	$-0.309076\pi$
$744$	8.00000	+	13.8564i	0.293294	+	0.508001i
$745$		0			0
$746$	1.00000	−	1.73205i	0.0366126	−	0.0634149i
$747$		0			0
$748$		−	18.0000i		−	0.658145i
$749$	30.0000	+	10.3923i	1.09618	+	0.379727i
$750$		0			0
$751$	5.00000	+	8.66025i	0.182453	+	0.316017i	0.942715	−	0.333599i	$-0.108263\pi$
$751$	5.00000	+	8.66025i	0.182453	+	0.316017i	−0.760263	+	0.649616i	$0.774930\pi$
$752$	7.79423	+	4.50000i	0.284226	+	0.164098i
$753$	−25.9808	−	15.0000i	−0.946792	−	0.546630i
$754$	3.00000	+	5.19615i	0.109254	+	0.189233i
$755$		0			0
$756$	−2.00000	−	10.3923i	−0.0727393	−	0.377964i
$757$		−	38.0000i		−	1.38113i	−0.723269	−	0.690567i	$-0.757361\pi$
$757$		−	38.0000i		−	1.38113i	0.723269	−	0.690567i	$-0.242639\pi$
$758$	−19.9186	+	11.5000i	−0.723476	+	0.417699i
$759$	−27.0000	+	46.7654i	−0.980038	+	1.69748i
$760$		0			0
$761$	13.5000	+	23.3827i	0.489375	+	0.847622i	0.999925	−	0.0122260i	$-0.00389175\pi$
$761$	13.5000	+	23.3827i	0.489375	+	0.847622i	−0.510551	+	0.859848i	$0.670558\pi$
$762$			2.00000i			0.0724524i
$763$	−41.5692	+	8.00000i	−1.50491	+	0.289619i
$764$	−12.0000			−0.434145
$765$		0			0
$766$	10.5000	−	18.1865i	0.379380	−	0.657106i
$767$		0			0
$768$	−1.73205	+	1.00000i	−0.0625000	+	0.0360844i
$769$	−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
$772$	13.8564	−	8.00000i	0.498703	−	0.287926i
$773$	44.1673	+	25.5000i	1.58859	+	0.917171i	0.993540	+	0.113480i	$0.0361999\pi$
$773$	44.1673	+	25.5000i	1.58859	+	0.917171i	0.595047	+	0.803691i	$0.297133\pi$
$774$	−1.00000	+	1.73205i	−0.0359443	+	0.0622573i
$775$		0			0
$776$	10.0000			0.358979
$777$	24.2487	+	28.0000i	0.869918	+	1.00449i
$778$			12.0000i			0.430221i
$779$	−1.50000	−	2.59808i	−0.0537431	−	0.0930857i
$780$		0			0
$781$		0			0
$782$	−46.7654	+	27.0000i	−1.67233	+	0.965518i
$783$			24.0000i			0.857690i
$784$	6.50000	−	2.59808i	0.232143	−	0.0927884i
$785$		0			0
$786$	−3.00000	−	5.19615i	−0.107006	−	0.185341i
$787$	−19.0526	−	11.0000i	−0.679150	−	0.392108i	0.120384	−	0.992727i	$-0.461587\pi$
$787$	−19.0526	−	11.0000i	−0.679150	−	0.392108i	−0.799535	+	0.600620i	$0.794921\pi$
$788$	−12.9904	−	7.50000i	−0.462763	−	0.267176i
$789$		0			0
$790$		0			0
$791$		0			0
$792$			3.00000i			0.106600i
$793$	−6.92820	+	4.00000i	−0.246028	+	0.142044i
$794$	−7.00000	+	12.1244i	−0.248421	+	0.430277i
$795$		0			0
$796$	8.00000	+	13.8564i	0.283552	+	0.491127i
$797$		−	6.00000i		−	0.212531i	−0.994338	−	0.106265i	$-0.966111\pi$
$797$		−	6.00000i		−	0.212531i	0.994338	−	0.106265i	$-0.0338893\pi$
$798$	1.73205	−	5.00000i	0.0613139	−	0.176998i
$799$	54.0000			1.91038
$800$		0			0
$801$	−3.00000	+	5.19615i	−0.106000	+	0.183597i
$802$	23.3827	+	13.5000i	0.825671	+	0.476702i
$803$	−10.3923	+	6.00000i	−0.366736	+	0.211735i
$804$	16.0000			0.564276
$805$		0			0
$806$	8.00000			0.281788
$807$		0			0
$808$	10.3923	+	6.00000i	0.365600	+	0.211079i
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	−0.934224	−	0.356687i	$-0.883906\pi$
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	0.776012	+	0.630718i	$0.217239\pi$
$810$		0			0
$811$	−25.0000			−0.877869			−0.438934	−	0.898519i	$-0.644644\pi$
$811$	−25.0000			−0.877869			−0.438934	+	0.898519i	$0.644644\pi$
$812$	−15.5885	+	3.00000i	−0.547048	+	0.105279i
$813$			32.0000i			1.12229i
$814$	10.5000	+	18.1865i	0.368025	+	0.637438i
$815$		0			0
$816$	−6.00000	+	10.3923i	−0.210042	+	0.363803i
$817$	1.73205	−	1.00000i	0.0605968	−	0.0349856i
$818$		−	26.0000i		−	0.909069i
$819$	2.50000	+	0.866025i	0.0873571	+	0.0302614i
$820$		0			0
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	−0.999626	−	0.0273557i	$-0.991291\pi$
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	0.476122	−	0.879379i	$-0.342042\pi$
$822$	20.7846	+	12.0000i	0.724947	+	0.418548i
$823$	3.46410	+	2.00000i	0.120751	+	0.0697156i	0.559159	−	0.829060i	$-0.311124\pi$
$823$	3.46410	+	2.00000i	0.120751	+	0.0697156i	−0.438408	+	0.898776i	$0.644457\pi$
$824$	2.00000	+	3.46410i	0.0696733	+	0.120678i
$825$		0			0
$826$		0			0
$827$		−	6.00000i		−	0.208640i	−0.994544	−	0.104320i	$-0.966733\pi$
$827$		−	6.00000i		−	0.208640i	0.994544	−	0.104320i	$-0.0332667\pi$
$828$	7.79423	−	4.50000i	0.270868	−	0.156386i
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	−0.718481	−	0.695546i	$-0.755162\pi$
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	0.961601	+	0.274450i	$0.0884958\pi$
$830$		0			0
$831$	−10.0000	−	17.3205i	−0.346896	−	0.600842i
$832$			1.00000i			0.0346688i
$833$	25.9808	−	33.0000i	0.900180	−	1.14338i
$834$	8.00000			0.277017
$835$		0			0
$836$	1.50000	−	2.59808i	0.0518786	−	0.0898563i
$837$	27.7128	+	16.0000i	0.957895	+	0.553041i
$838$	7.79423	−	4.50000i	0.269247	−	0.155450i
$839$	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
$842$	1.73205	−	1.00000i	0.0596904	−	0.0344623i
$843$	−46.7654	−	27.0000i	−1.61068	−	0.929929i
$844$	11.5000	−	19.9186i	0.395846	−	0.685626i
$845$		0			0
$846$	−9.00000			−0.309426
$847$	−1.73205	+	5.00000i	−0.0595140	+	0.171802i
$848$			9.00000i			0.309061i
$849$	−14.0000	−	24.2487i	−0.480479	−	0.832214i
$850$		0			0
$851$	31.5000	−	54.5596i	1.07981	−	1.87028i
$852$		0			0
$853$		−	19.0000i		−	0.650548i	−0.945620	−	0.325274i	$-0.894544\pi$
$853$		−	19.0000i		−	0.650548i	0.945620	−	0.325274i	$-0.105456\pi$
$854$	−4.00000	−	20.7846i	−0.136877	−	0.711235i
$855$		0			0
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$	−15.5885	−	9.00000i	−0.532492	−	0.307434i	0.209539	−	0.977800i	$-0.432804\pi$
$857$	−15.5885	−	9.00000i	−0.532492	−	0.307434i	−0.742030	+	0.670366i	$0.766137\pi$
$858$	5.19615	+	3.00000i	0.177394	+	0.102418i
$859$	16.0000	+	27.7128i	0.545913	+	0.945549i	0.998549	+	0.0538535i	$0.0171504\pi$
$859$	16.0000	+	27.7128i	0.545913	+	0.945549i	−0.452636	+	0.891695i	$0.649516\pi$
$860$		0			0
$861$	3.00000	+	15.5885i	0.102240	+	0.531253i
$862$			12.0000i			0.408722i
$863$	−2.59808	+	1.50000i	−0.0884395	+	0.0510606i	−0.543568	−	0.839365i	$-0.682927\pi$
$863$	−2.59808	+	1.50000i	−0.0884395	+	0.0510606i	0.455128	+	0.890426i	$0.349593\pi$
$864$	−2.00000	+	3.46410i	−0.0680414	+	0.117851i
$865$		0			0
$866$	−20.0000	−	34.6410i	−0.679628	−	1.17715i
$867$			38.0000i			1.29055i
$868$	−6.92820	+	20.0000i	−0.235159	+	0.678844i
$869$	30.0000			1.01768
$870$		0			0
$871$	4.00000	−	6.92820i	0.135535	−	0.234753i
$872$	13.8564	+	8.00000i	0.469237	+	0.270914i
$873$	−8.66025	+	5.00000i	−0.293105	+	0.169224i
$874$	−9.00000			−0.304430
$875$		0			0
$876$	8.00000			0.270295
$877$	11.2583	−	6.50000i	0.380167	−	0.219489i	−0.297724	−	0.954652i	$-0.596228\pi$
$877$	11.2583	−	6.50000i	0.380167	−	0.219489i	0.677891	+	0.735163i	$0.262894\pi$
$878$	22.5167	+	13.0000i	0.759900	+	0.438729i
$879$	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	$0.312374\pi$
$882$	−4.33013	+	5.50000i	−0.145803	+	0.185195i
$883$			8.00000i			0.269221i	0.990899	+	0.134611i	$0.0429784\pi$
$883$			8.00000i			0.269221i	−0.990899	+	0.134611i	$0.957022\pi$
$884$	3.00000	+	5.19615i	0.100901	+	0.174766i
$885$		0			0
$886$	6.00000	−	10.3923i	0.201574	−	0.349136i
$887$	41.5692	−	24.0000i	1.39576	−	0.805841i	0.401813	−	0.915722i	$-0.368380\pi$
$887$	41.5692	−	24.0000i	1.39576	−	0.805841i	0.993945	+	0.109881i	$0.0350469\pi$
$888$		−	14.0000i		−	0.469809i
$889$	−2.00000	+	1.73205i	−0.0670778	+	0.0580911i
$890$		0			0
$891$	16.5000	+	28.5788i	0.552771	+	0.957427i
$892$	6.92820	+	4.00000i	0.231973	+	0.133930i
$893$	7.79423	+	4.50000i	0.260824	+	0.150587i
$894$	−6.00000	−	10.3923i	−0.200670	−	0.347571i
$895$		0			0
$896$	−2.50000	−	0.866025i	−0.0835191	−	0.0289319i
$897$		−	18.0000i		−	0.601003i
$898$	−18.1865	+	10.5000i	−0.606892	+	0.350390i
$899$	24.0000	−	41.5692i	0.800445	−	1.38641i
$900$		0			0
$901$	27.0000	+	46.7654i	0.899500	+	1.55798i
$902$			9.00000i			0.299667i
$903$	−10.3923	+	2.00000i	−0.345834	+	0.0665558i
$904$		0			0
$905$		0			0
$906$	10.0000	−	17.3205i	0.332228	−	0.575435i
$907$	−8.66025	−	5.00000i	−0.287559	−	0.166022i	0.349281	−	0.937018i	$-0.386426\pi$
$907$	−8.66025	−	5.00000i	−0.287559	−	0.166022i	−0.636841	+	0.770996i	$0.719759\pi$
$908$	−10.3923	+	6.00000i	−0.344881	+	0.199117i
$909$	−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	$0.665555\pi$
$912$	−1.73205	+	1.00000i	−0.0573539	+	0.0331133i
$913$		0			0
$914$	−7.00000	+	12.1244i	−0.231539	+	0.401038i
$915$		0			0
$916$	−4.00000			−0.132164
$917$	2.59808	−	7.50000i	0.0857960	−	0.247672i
$918$			24.0000i			0.792118i
$919$	−11.0000	−	19.0526i	−0.362857	−	0.628486i	0.625573	−	0.780165i	$-0.284865\pi$
$919$	−11.0000	−	19.0526i	−0.362857	−	0.628486i	−0.988430	+	0.151680i	$0.951532\pi$
$920$		0			0
$921$	14.0000	−	24.2487i	0.461316	−	0.799022i
$922$	−25.9808	+	15.0000i	−0.855631	+	0.493999i
$923$		0			0
$924$	−12.0000	+	10.3923i	−0.394771	+	0.341882i
$925$		0			0
$926$	−0.500000	−	0.866025i	−0.0164310	−	0.0284594i
$927$	−3.46410	−	2.00000i	−0.113776	−	0.0656886i
$928$	5.19615	+	3.00000i	0.170572	+	0.0984798i
$929$	28.5000	+	49.3634i	0.935055	+	1.61956i	0.774536	+	0.632529i	$0.217983\pi$
$929$	28.5000	+	49.3634i	0.935055	+	1.61956i	0.160518	+	0.987033i	$0.448683\pi$
$930$		0			0
$931$	6.50000	−	2.59808i	0.213029	−	0.0851485i
$932$			6.00000i			0.196537i
$933$	41.5692	−	24.0000i	1.36092	−	0.785725i
$934$	3.00000	−	5.19615i	0.0981630	−	0.170023i
$935$		0			0
$936$	−0.500000	−	0.866025i	−0.0163430	−	0.0283069i
$937$			10.0000i			0.326686i	0.986569	+	0.163343i	$0.0522277\pi$
$937$			10.0000i			0.326686i	−0.986569	+	0.163343i	$0.947772\pi$
$938$	13.8564	+	16.0000i	0.452428	+	0.522419i
$939$	−56.0000			−1.82749
$940$		0			0
$941$	−24.0000	+	41.5692i	−0.782378	+	1.35512i	0.148176	+	0.988961i	$0.452660\pi$
$941$	−24.0000	+	41.5692i	−0.782378	+	1.35512i	−0.930553	+	0.366157i	$0.880673\pi$
$942$	39.8372	+	23.0000i	1.29797	+	0.749380i
$943$	23.3827	−	13.5000i	0.761445	−	0.439620i
$944$		0			0
$945$		0			0
$946$	−6.00000			−0.195077
$947$	−5.19615	+	3.00000i	−0.168852	+	0.0974869i	−0.582045	−	0.813157i	$-0.697747\pi$
$947$	−5.19615	+	3.00000i	−0.168852	+	0.0974869i	0.413192	+	0.910644i	$0.364414\pi$
$948$	−17.3205	−	10.0000i	−0.562544	−	0.324785i
$949$	2.00000	−	3.46410i	0.0649227	−	0.112449i
$950$		0			0
$951$	−12.0000			−0.389127
$952$	−15.5885	+	3.00000i	−0.505225	+	0.0972306i
$953$			36.0000i			1.16615i	0.812417	+	0.583077i	$0.198151\pi$
$953$			36.0000i			1.16615i	−0.812417	+	0.583077i	$0.801849\pi$
$954$	−4.50000	−	7.79423i	−0.145693	−	0.252347i
$955$		0			0
$956$	3.00000	−	5.19615i	0.0970269	−	0.168056i
$957$	31.1769	−	18.0000i	1.00781	−	0.581857i
$958$		0			0
$959$	6.00000	+	31.1769i	0.193750	+	1.00676i
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	−6.06218	−	3.50000i	−0.195452	−	0.112845i
$963$	10.3923	+	6.00000i	0.334887	+	0.193347i
$964$	−0.500000	−	0.866025i	−0.0161039	−	0.0278928i
$965$		0			0
$966$	45.0000	+	15.5885i	1.44785	+	0.501550i
$967$		−	32.0000i		−	1.02905i	−0.857475	−	0.514525i	$-0.827968\pi$
$967$		−	32.0000i		−	1.02905i	0.857475	−	0.514525i	$-0.172032\pi$
$968$	1.73205	−	1.00000i	0.0556702	−	0.0321412i
$969$	−6.00000	+	10.3923i	−0.192748	+	0.333849i
$970$		0			0
$971$	22.5000	+	38.9711i	0.722059	+	1.25064i	0.960173	+	0.279406i	$0.0901376\pi$
$971$	22.5000	+	38.9711i	0.722059	+	1.25064i	−0.238114	+	0.971237i	$0.576529\pi$
$972$		−	10.0000i		−	0.320750i
$973$	6.92820	+	8.00000i	0.222108	+	0.256468i
$974$	−16.0000			−0.512673
$975$		0			0
$976$	−4.00000	+	6.92820i	−0.128037	+	0.221766i
$977$	−36.3731	−	21.0000i	−1.16368	−	0.671850i	−0.211495	−	0.977379i	$-0.567833\pi$
$977$	−36.3731	−	21.0000i	−1.16368	−	0.671850i	−0.952183	+	0.305530i	$0.901167\pi$
$978$	34.6410	−	20.0000i	1.10770	−	0.639529i
$979$	−18.0000			−0.575282
$980$		0			0
$981$	−16.0000			−0.510841
$982$	31.1769	−	18.0000i	0.994895	−	0.574403i
$983$	−2.59808	−	1.50000i	−0.0828658	−	0.0478426i	0.457995	−	0.888955i	$-0.348568\pi$
$983$	−2.59808	−	1.50000i	−0.0828658	−	0.0478426i	−0.540860	+	0.841112i	$0.681901\pi$
$984$	3.00000	−	5.19615i	0.0956365	−	0.165647i
$985$		0			0
$986$	36.0000			1.14647
$987$	−31.1769	−	36.0000i	−0.992372	−	1.14589i
$988$			1.00000i			0.0318142i
$989$	9.00000	+	15.5885i	0.286183	+	0.495684i
$990$		0			0
$991$	−22.0000	+	38.1051i	−0.698853	+	1.21045i	0.270011	+	0.962857i	$0.412973\pi$
$991$	−22.0000	+	38.1051i	−0.698853	+	1.21045i	−0.968864	+	0.247592i	$0.920361\pi$
$992$	6.92820	−	4.00000i	0.219971	−	0.127000i
$993$			14.0000i			0.444277i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−19.0526	−	11.0000i	−0.603401	−	0.348373i	0.166978	−	0.985961i	$-0.446599\pi$
$997$	−19.0526	−	11.0000i	−0.603401	−	0.348373i	−0.770378	+	0.637587i	$0.779933\pi$
$998$	−3.46410	−	2.00000i	−0.109654	−	0.0633089i
$999$	−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.j.d.249.2		4
5.2	odd	4		70.2.e.d.11.1	✓	2
5.3	odd	4		350.2.e.b.151.1		2
5.4	even	2	inner	350.2.j.d.249.1		4
7.2	even	3	inner	350.2.j.d.149.1		4
7.3	odd	6		2450.2.c.e.99.2		2
7.4	even	3		2450.2.c.q.99.2		2
15.2	even	4		630.2.k.d.361.1		2
20.7	even	4		560.2.q.b.81.1		2
35.2	odd	12		70.2.e.d.51.1	yes	2
35.3	even	12		2450.2.a.v.1.1		1
35.4	even	6		2450.2.c.q.99.1		2
35.9	even	6	inner	350.2.j.d.149.2		4
35.12	even	12		490.2.e.g.471.1		2
35.17	even	12		490.2.a.d.1.1		1
35.18	odd	12		2450.2.a.bf.1.1		1
35.23	odd	12		350.2.e.b.51.1		2
35.24	odd	6		2450.2.c.e.99.1		2
35.27	even	4		490.2.e.g.361.1		2
35.32	odd	12		490.2.a.a.1.1		1
105.2	even	12		630.2.k.d.541.1		2
105.17	odd	12		4410.2.a.bg.1.1		1
105.32	even	12		4410.2.a.x.1.1		1
140.67	even	12		3920.2.a.bh.1.1		1
140.87	odd	12		3920.2.a.e.1.1		1
140.107	even	12		560.2.q.b.401.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.e.d.11.1	✓	2	5.2	odd	4
70.2.e.d.51.1	yes	2	35.2	odd	12
350.2.e.b.51.1		2	35.23	odd	12
350.2.e.b.151.1		2	5.3	odd	4
350.2.j.d.149.1		4	7.2	even	3	inner
350.2.j.d.149.2		4	35.9	even	6	inner
350.2.j.d.249.1		4	5.4	even	2	inner
350.2.j.d.249.2		4	1.1	even	1	trivial
490.2.a.a.1.1		1	35.32	odd	12
490.2.a.d.1.1		1	35.17	even	12
490.2.e.g.361.1		2	35.27	even	4
490.2.e.g.471.1		2	35.12	even	12
560.2.q.b.81.1		2	20.7	even	4
560.2.q.b.401.1		2	140.107	even	12
630.2.k.d.361.1		2	15.2	even	4
630.2.k.d.541.1		2	105.2	even	12
2450.2.a.v.1.1		1	35.3	even	12
2450.2.a.bf.1.1		1	35.18	odd	12
2450.2.c.e.99.1		2	35.24	odd	6
2450.2.c.e.99.2		2	7.3	odd	6
2450.2.c.q.99.1		2	35.4	even	6
2450.2.c.q.99.2		2	7.4	even	3
3920.2.a.e.1.1		1	140.87	odd	12
3920.2.a.bh.1.1		1	140.67	even	12
4410.2.a.x.1.1		1	105.32	even	12
4410.2.a.bg.1.1		1	105.17	odd	12

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.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.00000 q^{6} +(1.73205 + 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.00000 q^{6} +(1.73205 + 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(1.73205 - 1.00000i) q^{12} -1.00000i q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.19615 - 3.00000i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(1.00000 + 5.19615i) q^{21} +3.00000i q^{22} +(7.79423 - 4.50000i) q^{23} +(1.00000 - 1.73205i) q^{24} +(-0.500000 - 0.866025i) q^{26} -4.00000i q^{27} +(2.59808 - 0.500000i) q^{28} -6.00000 q^{29} +(-4.00000 + 6.92820i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-5.19615 + 3.00000i) q^{33} -6.00000 q^{34} +1.00000 q^{36} +(6.06218 - 3.50000i) q^{37} +(-0.866025 - 0.500000i) q^{38} +(1.00000 - 1.73205i) q^{39} +3.00000 q^{41} +(3.46410 + 4.00000i) q^{42} +2.00000i q^{43} +(1.50000 + 2.59808i) q^{44} +(4.50000 - 7.79423i) q^{46} +(-7.79423 + 4.50000i) q^{47} -2.00000i q^{48} +(-1.00000 + 6.92820i) q^{49} +(-6.00000 - 10.3923i) q^{51} +(-0.866025 - 0.500000i) q^{52} +(-7.79423 - 4.50000i) q^{53} +(-2.00000 - 3.46410i) q^{54} +(2.00000 - 1.73205i) q^{56} -2.00000i q^{57} +(-5.19615 + 3.00000i) q^{58} +(-4.00000 - 6.92820i) q^{61} +8.00000i q^{62} +(-0.866025 + 2.50000i) q^{63} -1.00000 q^{64} +(-3.00000 + 5.19615i) q^{66} +(6.92820 + 4.00000i) q^{67} +(-5.19615 + 3.00000i) q^{68} +18.0000 q^{69} +(0.866025 - 0.500000i) q^{72} +(3.46410 + 2.00000i) q^{73} +(3.50000 - 6.06218i) q^{74} -1.00000 q^{76} +(-7.79423 + 1.50000i) q^{77} -2.00000i q^{78} +(-5.00000 - 8.66025i) q^{79} +(5.50000 - 9.52628i) q^{81} +(2.59808 - 1.50000i) q^{82} +(5.00000 + 1.73205i) q^{84} +(1.00000 + 1.73205i) q^{86} +(-10.3923 - 6.00000i) q^{87} +(2.59808 + 1.50000i) q^{88} +(3.00000 + 5.19615i) q^{89} +(2.00000 - 1.73205i) q^{91} -9.00000i q^{92} +(-13.8564 + 8.00000i) q^{93} +(-4.50000 + 7.79423i) q^{94} +(-1.00000 - 1.73205i) q^{96} +10.0000i q^{97} +(2.59808 + 6.50000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 8 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 8 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} + 8 q^{6} + 2 q^{9} - 6 q^{11} + 10 q^{14} - 2 q^{16} - 2 q^{19} + 4 q^{21} + 4 q^{24} - 2 q^{26} - 24 q^{29} - 16 q^{31} - 24 q^{34} + 4 q^{36} + 4 q^{39} + 12 q^{41} + 6 q^{44} + 18 q^{46} - 4 q^{49} - 24 q^{51} - 8 q^{54} + 8 q^{56} - 16 q^{61} - 4 q^{64} - 12 q^{66} + 72 q^{69} + 14 q^{74} - 4 q^{76} - 20 q^{79} + 22 q^{81} + 20 q^{84} + 4 q^{86} + 12 q^{89} + 8 q^{91} - 18 q^{94} - 4 q^{96} - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 8 * q^6 + 2 * q^9 - 6 * q^11 + 10 * q^14 - 2 * q^16 - 2 * q^19 + 4 * q^21 + 4 * q^24 - 2 * q^26 - 24 * q^29 - 16 * q^31 - 24 * q^34 + 4 * q^36 + 4 * q^39 + 12 * q^41 + 6 * q^44 + 18 * q^46 - 4 * q^49 - 24 * q^51 - 8 * q^54 + 8 * q^56 - 16 * q^61 - 4 * q^64 - 12 * q^66 + 72 * q^69 + 14 * q^74 - 4 * q^76 - 20 * q^79 + 22 * q^81 + 20 * q^84 + 4 * q^86 + 12 * q^89 + 8 * q^91 - 18 * q^94 - 4 * q^96 - 12 * q^99

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