LMFDB - Embedded newform 950.2.e.b.201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(201,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("950.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.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:	$7.58578819202$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	950.201
Dual form			950.2.e.b.501.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +1.00000 q^{12} +(-3.00000 - 5.19615i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.50000 + 6.06218i) q^{17} -2.00000 q^{18} +(3.50000 - 2.59808i) q^{19} +(1.00000 - 1.73205i) q^{21} +(-1.00000 - 1.73205i) q^{23} +(-0.500000 + 0.866025i) q^{24} +6.00000 q^{26} -5.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(-5.00000 - 8.66025i) q^{29} -2.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.50000 - 6.06218i) q^{34} +(1.00000 - 1.73205i) q^{36} +4.00000 q^{37} +(0.500000 + 4.33013i) q^{38} +6.00000 q^{39} +(-1.00000 + 1.73205i) q^{41} +(1.00000 + 1.73205i) q^{42} +(6.00000 - 10.3923i) q^{43} +2.00000 q^{46} +(-0.500000 - 0.866025i) q^{48} -3.00000 q^{49} +(-3.50000 - 6.06218i) q^{51} +(-3.00000 + 5.19615i) q^{52} +(2.50000 - 4.33013i) q^{54} -2.00000 q^{56} +(0.500000 + 4.33013i) q^{57} +10.0000 q^{58} +(0.500000 - 0.866025i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(1.00000 - 1.73205i) q^{62} +(-2.00000 - 3.46410i) q^{63} +1.00000 q^{64} +(-4.00000 - 6.92820i) q^{67} +7.00000 q^{68} +2.00000 q^{69} +(6.00000 - 10.3923i) q^{71} +(1.00000 + 1.73205i) q^{72} +(1.50000 - 2.59808i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(-4.00000 - 1.73205i) q^{76} +(-3.00000 + 5.19615i) q^{78} +(2.00000 - 3.46410i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.00000 - 1.73205i) q^{82} -13.0000 q^{83} -2.00000 q^{84} +(6.00000 + 10.3923i) q^{86} +10.0000 q^{87} +(6.50000 + 11.2583i) q^{89} +(6.00000 + 10.3923i) q^{91} +(-1.00000 + 1.73205i) q^{92} +(1.00000 - 1.73205i) q^{93} +1.00000 q^{96} +(-7.50000 + 12.9904i) q^{97} +(1.50000 - 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 - q^3 - q^4 - q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{12} - 6 q^{13} + 2 q^{14} - q^{16} - 7 q^{17} - 4 q^{18} + 7 q^{19} + 2 q^{21} - 2 q^{23} - q^{24} + 12 q^{26} - 10 q^{27} + 2 q^{28} - 10 q^{29} - 4 q^{31} - q^{32} - 7 q^{34} + 2 q^{36} + 8 q^{37} + q^{38} + 12 q^{39} - 2 q^{41} + 2 q^{42} + 12 q^{43} + 4 q^{46} - q^{48} - 6 q^{49} - 7 q^{51} - 6 q^{52} + 5 q^{54} - 4 q^{56} + q^{57} + 20 q^{58} + q^{59} - 8 q^{61} + 2 q^{62} - 4 q^{63} + 2 q^{64} - 8 q^{67} + 14 q^{68} + 4 q^{69} + 12 q^{71} + 2 q^{72} + 3 q^{73} - 4 q^{74} - 8 q^{76} - 6 q^{78} + 4 q^{79} - q^{81} - 2 q^{82} - 26 q^{83} - 4 q^{84} + 12 q^{86} + 20 q^{87} + 13 q^{89} + 12 q^{91} - 2 q^{92} + 2 q^{93} + 2 q^{96} - 15 q^{97} + 3 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^3 - q^4 - q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^12 - 6 * q^13 + 2 * q^14 - q^16 - 7 * q^17 - 4 * q^18 + 7 * q^19 + 2 * q^21 - 2 * q^23 - q^24 + 12 * q^26 - 10 * q^27 + 2 * q^28 - 10 * q^29 - 4 * q^31 - q^32 - 7 * q^34 + 2 * q^36 + 8 * q^37 + q^38 + 12 * q^39 - 2 * q^41 + 2 * q^42 + 12 * q^43 + 4 * q^46 - q^48 - 6 * q^49 - 7 * q^51 - 6 * q^52 + 5 * q^54 - 4 * q^56 + q^57 + 20 * q^58 + q^59 - 8 * q^61 + 2 * q^62 - 4 * q^63 + 2 * q^64 - 8 * q^67 + 14 * q^68 + 4 * q^69 + 12 * q^71 + 2 * q^72 + 3 * q^73 - 4 * q^74 - 8 * q^76 - 6 * q^78 + 4 * q^79 - q^81 - 2 * q^82 - 26 * q^83 - 4 * q^84 + 12 * q^86 + 20 * q^87 + 13 * q^89 + 12 * q^91 - 2 * q^92 + 2 * q^93 + 2 * q^96 - 15 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	0.684819	+	0.728714i	$0.259881\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$	1.00000			0.353553
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$		0			0
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	1.00000			0.288675
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	0.0643593	−	0.997927i	$-0.479500\pi$
$14$	1.00000	−	1.73205i	0.267261	−	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.50000	+	6.06218i	−0.848875	+	1.47029i	0.0333386	+	0.999444i	$0.489386\pi$
$17$	−3.50000	+	6.06218i	−0.848875	+	1.47029i	−0.882213	+	0.470850i	$0.843947\pi$
$18$	−2.00000			−0.471405
$19$	3.50000	−	2.59808i	0.802955	−	0.596040i
$19$	3.50000	−	2.59808i	0.802955	−	0.596040i
$20$		0			0
$21$	1.00000	−	1.73205i	0.218218	−	0.377964i
$22$		0			0
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	0.742732	−	0.669588i	$-0.233529\pi$
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	−0.951247	+	0.308431i	$0.900196\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$		0			0
$26$	6.00000			1.17670
$27$	−5.00000			−0.962250
$28$	1.00000	+	1.73205i	0.188982	+	0.327327i
$29$	−5.00000	−	8.66025i	−0.928477	−	1.60817i	−0.785872	−	0.618389i	$-0.787786\pi$
$29$	−5.00000	−	8.66025i	−0.928477	−	1.60817i	−0.142605	−	0.989780i	$-0.545548\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−3.50000	−	6.06218i	−0.600245	−	1.03965i
$35$		0			0
$36$	1.00000	−	1.73205i	0.166667	−	0.288675i
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$	0.500000	+	4.33013i	0.0811107	+	0.702439i
$39$	6.00000			0.960769
$40$		0			0
$41$	−1.00000	+	1.73205i	−0.156174	+	0.270501i	−0.933486	−	0.358614i	$-0.883249\pi$
$41$	−1.00000	+	1.73205i	−0.156174	+	0.270501i	0.777312	+	0.629115i	$0.216583\pi$
$42$	1.00000	+	1.73205i	0.154303	+	0.267261i
$43$	6.00000	−	10.3923i	0.914991	−	1.58481i	0.108078	−	0.994142i	$-0.465531\pi$
$43$	6.00000	−	10.3923i	0.914991	−	1.58481i	0.806914	−	0.590669i	$-0.201136\pi$
$44$		0			0
$45$		0			0
$46$	2.00000			0.294884
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−3.00000			−0.428571
$50$		0			0
$51$	−3.50000	−	6.06218i	−0.490098	−	0.848875i
$52$	−3.00000	+	5.19615i	−0.416025	+	0.720577i
$53$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$53$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$54$	2.50000	−	4.33013i	0.340207	−	0.589256i
$55$		0			0
$56$	−2.00000			−0.267261
$57$	0.500000	+	4.33013i	0.0662266	+	0.573539i
$58$	10.0000			1.31306
$59$	0.500000	−	0.866025i	0.0650945	−	0.112747i	−0.831641	−	0.555313i	$-0.812598\pi$
$59$	0.500000	−	0.866025i	0.0650945	−	0.112747i	0.896736	+	0.442566i	$0.145932\pi$
$60$		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	$-0.337817\pi$
$62$	1.00000	−	1.73205i	0.127000	−	0.219971i
$63$	−2.00000	−	3.46410i	−0.251976	−	0.436436i
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	7.00000			0.848875
$69$	2.00000			0.240772
$70$		0			0
$71$	6.00000	−	10.3923i	0.712069	−	1.23334i	−0.252010	−	0.967725i	$-0.581092\pi$
$71$	6.00000	−	10.3923i	0.712069	−	1.23334i	0.964079	−	0.265615i	$-0.0855750\pi$
$72$	1.00000	+	1.73205i	0.117851	+	0.204124i
$73$	1.50000	−	2.59808i	0.175562	−	0.304082i	−0.764794	−	0.644275i	$-0.777159\pi$
$73$	1.50000	−	2.59808i	0.175562	−	0.304082i	0.940356	+	0.340193i	$0.110493\pi$
$74$	−2.00000	+	3.46410i	−0.232495	+	0.402694i
$75$		0			0
$76$	−4.00000	−	1.73205i	−0.458831	−	0.198680i
$77$		0			0
$78$	−3.00000	+	5.19615i	−0.339683	+	0.588348i
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.00000	−	1.73205i	−0.110432	−	0.191273i
$83$	−13.0000			−1.42694			−0.713468	−	0.700688i	$-0.752876\pi$
$83$	−13.0000			−1.42694			−0.713468	+	0.700688i	$0.752876\pi$
$84$	−2.00000			−0.218218
$85$		0			0
$86$	6.00000	+	10.3923i	0.646997	+	1.12063i
$87$	10.0000			1.07211
$88$		0			0
$89$	6.50000	+	11.2583i	0.688999	+	1.19338i	0.972162	+	0.234309i	$0.0752827\pi$
$89$	6.50000	+	11.2583i	0.688999	+	1.19338i	−0.283164	+	0.959072i	$0.591384\pi$
$90$		0			0
$91$	6.00000	+	10.3923i	0.628971	+	1.08941i
$92$	−1.00000	+	1.73205i	−0.104257	+	0.180579i
$93$	1.00000	−	1.73205i	0.103695	−	0.179605i
$94$		0			0
$95$		0			0
$96$	1.00000			0.102062
$97$	−7.50000	+	12.9904i	−0.761510	+	1.31897i	0.180563	+	0.983563i	$0.442208\pi$
$97$	−7.50000	+	12.9904i	−0.761510	+	1.31897i	−0.942072	+	0.335410i	$0.891125\pi$
$98$	1.50000	−	2.59808i	0.151523	−	0.262445i
$99$		0			0
$100$		0			0
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	0.811976	−	0.583691i	$-0.198392\pi$
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	−0.911479	+	0.411346i	$0.865059\pi$
$102$	7.00000			0.693103
$103$	12.0000			1.18240			0.591198	−	0.806527i	$-0.298655\pi$
$103$	12.0000			1.18240			0.591198	+	0.806527i	$0.298655\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$		0			0
$106$		0			0
$107$	15.0000			1.45010			0.725052	−	0.688694i	$-0.241816\pi$
$107$	15.0000			1.45010			0.725052	+	0.688694i	$0.241816\pi$
$108$	2.50000	+	4.33013i	0.240563	+	0.416667i
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$		0			0
$111$	−2.00000	+	3.46410i	−0.189832	+	0.328798i
$112$	1.00000	−	1.73205i	0.0944911	−	0.163663i
$113$	1.00000			0.0940721			0.0470360	−	0.998893i	$-0.485022\pi$
$113$	1.00000			0.0940721			0.0470360	+	0.998893i	$0.485022\pi$
$114$	−4.00000	−	1.73205i	−0.374634	−	0.162221i
$115$		0			0
$116$	−5.00000	+	8.66025i	−0.464238	+	0.804084i
$117$	6.00000	−	10.3923i	0.554700	−	0.960769i
$118$	0.500000	+	0.866025i	0.0460287	+	0.0797241i
$119$	7.00000	−	12.1244i	0.641689	−	1.11144i
$120$		0			0
$121$	−11.0000			−1.00000
$122$	8.00000			0.724286
$123$	−1.00000	−	1.73205i	−0.0901670	−	0.156174i
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$		0			0
$126$	4.00000			0.356348
$127$	−6.00000	−	10.3923i	−0.532414	−	0.922168i	−0.999284	−	0.0378419i	$-0.987952\pi$
$127$	−6.00000	−	10.3923i	−0.532414	−	0.922168i	0.466870	−	0.884326i	$-0.345382\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	6.00000	+	10.3923i	0.528271	+	0.914991i
$130$		0			0
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	−0.887041	−	0.461690i	$-0.847243\pi$
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	0.843356	+	0.537355i	$0.180577\pi$
$132$		0			0
$133$	−7.00000	+	5.19615i	−0.606977	+	0.450564i
$134$	8.00000			0.691095
$135$		0			0
$136$	−3.50000	+	6.06218i	−0.300123	+	0.519827i
$137$	−7.50000	−	12.9904i	−0.640768	−	1.10984i	−0.985262	−	0.171054i	$-0.945283\pi$
$137$	−7.50000	−	12.9904i	−0.640768	−	1.10984i	0.344493	−	0.938789i	$-0.388051\pi$
$138$	−1.00000	+	1.73205i	−0.0851257	+	0.147442i
$139$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$139$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$140$		0			0
$141$		0			0
$142$	6.00000	+	10.3923i	0.503509	+	0.872103i
$143$		0			0
$144$	−2.00000			−0.166667
$145$		0			0
$146$	1.50000	+	2.59808i	0.124141	+	0.215018i
$147$	1.50000	−	2.59808i	0.123718	−	0.214286i
$148$	−2.00000	−	3.46410i	−0.164399	−	0.284747i
$149$	−8.00000	+	13.8564i	−0.655386	+	1.13516i	0.326411	+	0.945228i	$0.394160\pi$
$149$	−8.00000	+	13.8564i	−0.655386	+	1.13516i	−0.981797	+	0.189933i	$0.939173\pi$
$150$		0			0
$151$	−12.0000			−0.976546			−0.488273	−	0.872691i	$-0.662373\pi$
$151$	−12.0000			−0.976546			−0.488273	+	0.872691i	$0.662373\pi$
$152$	3.50000	−	2.59808i	0.283887	−	0.210732i
$153$	−14.0000			−1.13183
$154$		0			0
$155$		0			0
$156$	−3.00000	−	5.19615i	−0.240192	−	0.416025i
$157$	−3.00000	+	5.19615i	−0.239426	+	0.414698i	−0.960550	−	0.278108i	$-0.910293\pi$
$157$	−3.00000	+	5.19615i	−0.239426	+	0.414698i	0.721124	+	0.692806i	$0.243626\pi$
$158$	2.00000	+	3.46410i	0.159111	+	0.275589i
$159$		0			0
$160$		0			0
$161$	2.00000	+	3.46410i	0.157622	+	0.273009i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−12.0000			−0.939913			−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000			−0.939913			−0.469956	+	0.882690i	$0.655730\pi$
$164$	2.00000			0.156174
$165$		0			0
$166$	6.50000	−	11.2583i	0.504498	−	0.873816i
$167$	−5.00000	−	8.66025i	−0.386912	−	0.670151i	0.605121	−	0.796134i	$-0.293125\pi$
$167$	−5.00000	−	8.66025i	−0.386912	−	0.670151i	−0.992032	+	0.125983i	$0.959791\pi$
$168$	1.00000	−	1.73205i	0.0771517	−	0.133631i
$169$	−11.5000	+	19.9186i	−0.884615	+	1.53220i
$170$		0			0
$171$	8.00000	+	3.46410i	0.611775	+	0.264906i
$172$	−12.0000			−0.914991
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$	−5.00000	+	8.66025i	−0.379049	+	0.656532i
$175$		0			0
$176$		0			0
$177$	0.500000	+	0.866025i	0.0375823	+	0.0650945i
$178$	−13.0000			−0.974391
$179$	−9.00000			−0.672692			−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000			−0.672692			−0.336346	+	0.941739i	$0.609191\pi$
$180$		0			0
$181$	−10.0000	−	17.3205i	−0.743294	−	1.28742i	−0.950988	−	0.309229i	$-0.899929\pi$
$181$	−10.0000	−	17.3205i	−0.743294	−	1.28742i	0.207693	−	0.978194i	$-0.433404\pi$
$182$	−12.0000			−0.889499
$183$	8.00000			0.591377
$184$	−1.00000	−	1.73205i	−0.0737210	−	0.127688i
$185$		0			0
$186$	1.00000	+	1.73205i	0.0733236	+	0.127000i
$187$		0			0
$188$		0			0
$189$	10.0000			0.727393
$190$		0			0
$191$	−10.0000			−0.723575			−0.361787	−	0.932261i	$-0.617833\pi$
$191$	−10.0000			−0.723575			−0.361787	+	0.932261i	$0.617833\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	−0.993215	−	0.116289i	$-0.962900\pi$
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	0.597317	+	0.802005i	$0.296234\pi$
$194$	−7.50000	−	12.9904i	−0.538469	−	0.932655i
$195$		0			0
$196$	1.50000	+	2.59808i	0.107143	+	0.185577i
$197$	4.00000			0.284988			0.142494	−	0.989796i	$-0.454488\pi$
$197$	4.00000			0.284988			0.142494	+	0.989796i	$0.454488\pi$
$198$		0			0
$199$	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			0.564276
$202$	2.00000			0.140720
$203$	10.0000	+	17.3205i	0.701862	+	1.21566i
$204$	−3.50000	+	6.06218i	−0.245049	+	0.424437i
$205$		0			0
$206$	−6.00000	+	10.3923i	−0.418040	+	0.724066i
$207$	2.00000	−	3.46410i	0.139010	−	0.240772i
$208$	6.00000			0.416025
$209$		0			0
$210$		0			0
$211$	−11.5000	+	19.9186i	−0.791693	+	1.37125i	0.133226	+	0.991086i	$0.457467\pi$
$211$	−11.5000	+	19.9186i	−0.791693	+	1.37125i	−0.924918	+	0.380166i	$0.875867\pi$
$212$		0			0
$213$	6.00000	+	10.3923i	0.411113	+	0.712069i
$214$	−7.50000	+	12.9904i	−0.512689	+	0.888004i
$215$		0			0
$216$	−5.00000			−0.340207
$217$	4.00000			0.271538
$218$	1.00000	+	1.73205i	0.0677285	+	0.117309i
$219$	1.50000	+	2.59808i	0.101361	+	0.175562i
$220$		0			0
$221$	42.0000			2.82523
$222$	−2.00000	−	3.46410i	−0.134231	−	0.232495i
$223$	1.00000	−	1.73205i	0.0669650	−	0.115987i	−0.830599	−	0.556871i	$-0.812002\pi$
$223$	1.00000	−	1.73205i	0.0669650	−	0.115987i	0.897564	+	0.440884i	$0.145335\pi$
$224$	1.00000	+	1.73205i	0.0668153	+	0.115728i
$225$		0			0
$226$	−0.500000	+	0.866025i	−0.0332595	+	0.0576072i
$227$	13.0000			0.862840			0.431420	−	0.902151i	$-0.358013\pi$
$227$	13.0000			0.862840			0.431420	+	0.902151i	$0.358013\pi$
$228$	3.50000	−	2.59808i	0.231793	−	0.172062i
$229$	−18.0000			−1.18947			−0.594737	−	0.803921i	$-0.702744\pi$
$229$	−18.0000			−1.18947			−0.594737	+	0.803921i	$0.702744\pi$
$230$		0			0
$231$		0			0
$232$	−5.00000	−	8.66025i	−0.328266	−	0.568574i
$233$	−6.50000	+	11.2583i	−0.425829	+	0.737558i	−0.996497	−	0.0836229i	$-0.973351\pi$
$233$	−6.50000	+	11.2583i	−0.425829	+	0.737558i	0.570668	+	0.821181i	$0.306684\pi$
$234$	6.00000	+	10.3923i	0.392232	+	0.679366i
$235$		0			0
$236$	−1.00000			−0.0650945
$237$	2.00000	+	3.46410i	0.129914	+	0.225018i
$238$	7.00000	+	12.1244i	0.453743	+	0.785905i
$239$	−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
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	5.50000	−	9.52628i	0.353553	−	0.612372i
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	−4.00000	+	6.92820i	−0.256074	+	0.443533i
$245$		0			0
$246$	2.00000			0.127515
$247$	−24.0000	−	10.3923i	−1.52708	−	0.661247i
$248$	−2.00000			−0.127000
$249$	6.50000	−	11.2583i	0.411921	−	0.713468i
$250$		0			0
$251$	10.0000	+	17.3205i	0.631194	+	1.09326i	0.987308	+	0.158818i	$0.0507683\pi$
$251$	10.0000	+	17.3205i	0.631194	+	1.09326i	−0.356113	+	0.934443i	$0.615898\pi$
$252$	−2.00000	+	3.46410i	−0.125988	+	0.218218i
$253$		0			0
$254$	12.0000			0.752947
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	0.999325	−	0.0367485i	$-0.0117000\pi$
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	−0.531487	+	0.847066i	$0.678367\pi$
$258$	−12.0000			−0.747087
$259$	−8.00000			−0.497096
$260$		0			0
$261$	10.0000	−	17.3205i	0.618984	−	1.07211i
$262$	−0.500000	−	0.866025i	−0.0308901	−	0.0535032i
$263$	−7.00000	+	12.1244i	−0.431638	+	0.747620i	−0.997015	−	0.0772134i	$-0.975398\pi$
$263$	−7.00000	+	12.1244i	−0.431638	+	0.747620i	0.565376	+	0.824833i	$0.308731\pi$
$264$		0			0
$265$		0			0
$266$	−1.00000	−	8.66025i	−0.0613139	−	0.530994i
$267$	−13.0000			−0.795587
$268$	−4.00000	+	6.92820i	−0.244339	+	0.423207i
$269$	−13.0000	+	22.5167i	−0.792624	+	1.37287i	0.131713	+	0.991288i	$0.457952\pi$
$269$	−13.0000	+	22.5167i	−0.792624	+	1.37287i	−0.924337	+	0.381577i	$0.875381\pi$
$270$		0			0
$271$	−13.0000	+	22.5167i	−0.789694	+	1.36779i	0.136461	+	0.990645i	$0.456427\pi$
$271$	−13.0000	+	22.5167i	−0.789694	+	1.36779i	−0.926155	+	0.377144i	$0.876906\pi$
$272$	−3.50000	−	6.06218i	−0.212219	−	0.367574i
$273$	−12.0000			−0.726273
$274$	15.0000			0.906183
$275$		0			0
$276$	−1.00000	−	1.73205i	−0.0601929	−	0.104257i
$277$	−22.0000			−1.32185			−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000			−1.32185			−0.660926	+	0.750451i	$0.729836\pi$
$278$		0			0
$279$	−2.00000	−	3.46410i	−0.119737	−	0.207390i
$280$		0			0
$281$	−3.50000	−	6.06218i	−0.208792	−	0.361639i	0.742542	−	0.669800i	$-0.233620\pi$
$281$	−3.50000	−	6.06218i	−0.208792	−	0.361639i	−0.951334	+	0.308160i	$0.900287\pi$
$282$		0			0
$283$	14.0000	−	24.2487i	0.832214	−	1.44144i	−0.0640654	−	0.997946i	$-0.520407\pi$
$283$	14.0000	−	24.2487i	0.832214	−	1.44144i	0.896279	−	0.443491i	$-0.146260\pi$
$284$	−12.0000			−0.712069
$285$		0			0
$286$		0			0
$287$	2.00000	−	3.46410i	0.118056	−	0.204479i
$288$	1.00000	−	1.73205i	0.0589256	−	0.102062i
$289$	−16.0000	−	27.7128i	−0.941176	−	1.63017i
$290$		0			0
$291$	−7.50000	−	12.9904i	−0.439658	−	0.761510i
$292$	−3.00000			−0.175562
$293$	32.0000			1.86946			0.934730	−	0.355359i	$-0.115641\pi$
$293$	32.0000			1.86946			0.934730	+	0.355359i	$0.115641\pi$
$294$	1.50000	+	2.59808i	0.0874818	+	0.151523i
$295$		0			0
$296$	4.00000			0.232495
$297$		0			0
$298$	−8.00000	−	13.8564i	−0.463428	−	0.802680i
$299$	−6.00000	+	10.3923i	−0.346989	+	0.601003i
$300$		0			0
$301$	−12.0000	+	20.7846i	−0.691669	+	1.19800i
$302$	6.00000	−	10.3923i	0.345261	−	0.598010i
$303$	2.00000			0.114897
$304$	0.500000	+	4.33013i	0.0286770	+	0.248350i
$305$		0			0
$306$	7.00000	−	12.1244i	0.400163	−	0.693103i
$307$	9.50000	−	16.4545i	0.542194	−	0.939107i	−0.456584	−	0.889680i	$-0.650927\pi$
$307$	9.50000	−	16.4545i	0.542194	−	0.939107i	0.998778	−	0.0494267i	$-0.0157394\pi$
$308$		0			0
$309$	−6.00000	+	10.3923i	−0.341328	+	0.591198i
$310$		0			0
$311$	30.0000			1.70114			0.850572	−	0.525859i	$-0.176256\pi$
$311$	30.0000			1.70114			0.850572	+	0.525859i	$0.176256\pi$
$312$	6.00000			0.339683
$313$	−5.50000	−	9.52628i	−0.310878	−	0.538457i	0.667674	−	0.744453i	$-0.267290\pi$
$313$	−5.50000	−	9.52628i	−0.310878	−	0.538457i	−0.978553	+	0.205996i	$0.933957\pi$
$314$	−3.00000	−	5.19615i	−0.169300	−	0.293236i
$315$		0			0
$316$	−4.00000			−0.225018
$317$	12.0000	+	20.7846i	0.673987	+	1.16738i	0.976764	+	0.214318i	$0.0687530\pi$
$317$	12.0000	+	20.7846i	0.673987	+	1.16738i	−0.302777	+	0.953062i	$0.597914\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−7.50000	+	12.9904i	−0.418609	+	0.725052i
$322$	−4.00000			−0.222911
$323$	3.50000	+	30.3109i	0.194745	+	1.68654i
$324$	1.00000			0.0555556
$325$		0			0
$326$	6.00000	−	10.3923i	0.332309	−	0.575577i
$327$	1.00000	+	1.73205i	0.0553001	+	0.0957826i
$328$	−1.00000	+	1.73205i	−0.0552158	+	0.0956365i
$329$		0			0
$330$		0			0
$331$	−17.0000			−0.934405			−0.467202	−	0.884150i	$-0.654738\pi$
$331$	−17.0000			−0.934405			−0.467202	+	0.884150i	$0.654738\pi$
$332$	6.50000	+	11.2583i	0.356734	+	0.617881i
$333$	4.00000	+	6.92820i	0.219199	+	0.379663i
$334$	10.0000			0.547176
$335$		0			0
$336$	1.00000	+	1.73205i	0.0545545	+	0.0944911i
$337$	11.0000	−	19.0526i	0.599208	−	1.03786i	−0.393730	−	0.919226i	$-0.628816\pi$
$337$	11.0000	−	19.0526i	0.599208	−	1.03786i	0.992938	−	0.118633i	$-0.0378512\pi$
$338$	−11.5000	−	19.9186i	−0.625518	−	1.08343i
$339$	−0.500000	+	0.866025i	−0.0271563	+	0.0470360i
$340$		0			0
$341$		0			0
$342$	−7.00000	+	5.19615i	−0.378517	+	0.280976i
$343$	20.0000			1.07990
$344$	6.00000	−	10.3923i	0.323498	−	0.560316i
$345$		0			0
$346$	−3.00000	−	5.19615i	−0.161281	−	0.279347i
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$	−5.00000	−	8.66025i	−0.268028	−	0.464238i
$349$	16.0000			0.856460			0.428230	−	0.903670i	$-0.359137\pi$
$349$	16.0000			0.856460			0.428230	+	0.903670i	$0.359137\pi$
$350$		0			0
$351$	15.0000	+	25.9808i	0.800641	+	1.38675i
$352$		0			0
$353$	−3.00000			−0.159674			−0.0798369	−	0.996808i	$-0.525440\pi$
$353$	−3.00000			−0.159674			−0.0798369	+	0.996808i	$0.525440\pi$
$354$	−1.00000			−0.0531494
$355$		0			0
$356$	6.50000	−	11.2583i	0.344499	−	0.596690i
$357$	7.00000	+	12.1244i	0.370479	+	0.641689i
$358$	4.50000	−	7.79423i	0.237832	−	0.411938i
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	−0.353529	−	0.935423i	$-0.615019\pi$
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	0.986865	−	0.161546i	$-0.0516481\pi$
$360$		0			0
$361$	5.50000	−	18.1865i	0.289474	−	0.957186i
$362$	20.0000			1.05118
$363$	5.50000	−	9.52628i	0.288675	−	0.500000i
$364$	6.00000	−	10.3923i	0.314485	−	0.544705i
$365$		0			0
$366$	−4.00000	+	6.92820i	−0.209083	+	0.362143i
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	0.951336	−	0.308155i	$-0.0997115\pi$
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	−0.742538	+	0.669804i	$0.766378\pi$
$368$	2.00000			0.104257
$369$	−4.00000			−0.208232
$370$		0			0
$371$		0			0
$372$	−2.00000			−0.103695
$373$	−6.00000			−0.310668			−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000			−0.310668			−0.155334	+	0.987862i	$0.549645\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−30.0000	+	51.9615i	−1.54508	+	2.67615i
$378$	−5.00000	+	8.66025i	−0.257172	+	0.445435i
$379$	−1.00000			−0.0513665			−0.0256833	−	0.999670i	$-0.508176\pi$
$379$	−1.00000			−0.0513665			−0.0256833	+	0.999670i	$0.508176\pi$
$380$		0			0
$381$	12.0000			0.614779
$382$	5.00000	−	8.66025i	0.255822	−	0.443097i
$383$	6.00000	−	10.3923i	0.306586	−	0.531022i	−0.671027	−	0.741433i	$-0.734147\pi$
$383$	6.00000	−	10.3923i	0.306586	−	0.531022i	0.977613	+	0.210411i	$0.0674801\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$		0			0
$386$	−5.50000	−	9.52628i	−0.279943	−	0.484875i
$387$	24.0000			1.21999
$388$	15.0000			0.761510
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	0.542445	−	0.840091i	$-0.317499\pi$
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	−0.998763	+	0.0497253i	$0.984165\pi$
$390$		0			0
$391$	14.0000			0.708010
$392$	−3.00000			−0.151523
$393$	−0.500000	−	0.866025i	−0.0252217	−	0.0436852i
$394$	−2.00000	+	3.46410i	−0.100759	+	0.174519i
$395$		0			0
$396$		0			0
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	−0.986481	−	0.163876i	$-0.947600\pi$
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	0.635161	+	0.772380i	$0.280934\pi$
$398$	−16.0000			−0.802008
$399$	−1.00000	−	8.66025i	−0.0500626	−	0.433555i
$400$		0			0
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	0.931158	+	0.364615i	$0.118800\pi$
$402$	−4.00000	+	6.92820i	−0.199502	+	0.345547i
$403$	6.00000	+	10.3923i	0.298881	+	0.517678i
$404$	−1.00000	+	1.73205i	−0.0497519	+	0.0861727i
$405$		0			0
$406$	−20.0000			−0.992583
$407$		0			0
$408$	−3.50000	−	6.06218i	−0.173276	−	0.300123i
$409$	−1.00000	−	1.73205i	−0.0494468	−	0.0856444i	0.840243	−	0.542211i	$-0.182412\pi$
$409$	−1.00000	−	1.73205i	−0.0494468	−	0.0856444i	−0.889689	+	0.456566i	$0.849079\pi$
$410$		0			0
$411$	15.0000			0.739895
$412$	−6.00000	−	10.3923i	−0.295599	−	0.511992i
$413$	−1.00000	+	1.73205i	−0.0492068	+	0.0852286i
$414$	2.00000	+	3.46410i	0.0982946	+	0.170251i
$415$		0			0
$416$	−3.00000	+	5.19615i	−0.147087	+	0.254762i
$417$		0			0
$418$		0			0
$419$	13.0000			0.635092			0.317546	−	0.948243i	$-0.397141\pi$
$419$	13.0000			0.635092			0.317546	+	0.948243i	$0.397141\pi$
$420$		0			0
$421$	−17.0000	+	29.4449i	−0.828529	+	1.43505i	0.0706626	+	0.997500i	$0.477489\pi$
$421$	−17.0000	+	29.4449i	−0.828529	+	1.43505i	−0.899192	+	0.437555i	$0.855845\pi$
$422$	−11.5000	−	19.9186i	−0.559811	−	0.969622i
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−12.0000			−0.581402
$427$	8.00000	+	13.8564i	0.387147	+	0.670559i
$428$	−7.50000	−	12.9904i	−0.362526	−	0.627914i
$429$		0			0
$430$		0			0
$431$	−15.0000	−	25.9808i	−0.722525	−	1.25145i	−0.959985	−	0.280052i	$-0.909648\pi$
$431$	−15.0000	−	25.9808i	−0.722525	−	1.25145i	0.237460	−	0.971397i	$-0.423685\pi$
$432$	2.50000	−	4.33013i	0.120281	−	0.208333i
$433$	10.5000	+	18.1865i	0.504598	+	0.873989i	0.999986	+	0.00531724i	$0.00169254\pi$
$433$	10.5000	+	18.1865i	0.504598	+	0.873989i	−0.495388	+	0.868672i	$0.664974\pi$
$434$	−2.00000	+	3.46410i	−0.0960031	+	0.166282i
$435$		0			0
$436$	−2.00000			−0.0957826
$437$	−8.00000	−	3.46410i	−0.382692	−	0.165710i
$438$	−3.00000			−0.143346
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$		0			0
$441$	−3.00000	−	5.19615i	−0.142857	−	0.247436i
$442$	−21.0000	+	36.3731i	−0.998868	+	1.73009i
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	−0.876454	−	0.481486i	$-0.840097\pi$
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	0.0212481	−	0.999774i	$-0.493236\pi$
$444$	4.00000			0.189832
$445$		0			0
$446$	1.00000	+	1.73205i	0.0473514	+	0.0820150i
$447$	−8.00000	−	13.8564i	−0.378387	−	0.655386i
$448$	−2.00000			−0.0944911
$449$	41.0000			1.93491			0.967455	−	0.253044i	$-0.0814317\pi$
$449$	41.0000			1.93491			0.967455	+	0.253044i	$0.0814317\pi$
$450$		0			0
$451$		0			0
$452$	−0.500000	−	0.866025i	−0.0235180	−	0.0407344i
$453$	6.00000	−	10.3923i	0.281905	−	0.488273i
$454$	−6.50000	+	11.2583i	−0.305060	+	0.528380i
$455$		0			0
$456$	0.500000	+	4.33013i	0.0234146	+	0.202777i
$457$	11.0000			0.514558			0.257279	−	0.966337i	$-0.417174\pi$
$457$	11.0000			0.514558			0.257279	+	0.966337i	$0.417174\pi$
$458$	9.00000	−	15.5885i	0.420542	−	0.728401i
$459$	17.5000	−	30.3109i	0.816830	−	1.41479i
$460$		0			0
$461$	−1.00000	+	1.73205i	−0.0465746	+	0.0806696i	−0.888373	−	0.459123i	$-0.848164\pi$
$461$	−1.00000	+	1.73205i	−0.0465746	+	0.0806696i	0.841798	+	0.539792i	$0.181497\pi$
$462$		0			0
$463$	−22.0000			−1.02243			−0.511213	−	0.859454i	$-0.670804\pi$
$463$	−22.0000			−1.02243			−0.511213	+	0.859454i	$0.670804\pi$
$464$	10.0000			0.464238
$465$		0			0
$466$	−6.50000	−	11.2583i	−0.301107	−	0.521532i
$467$	23.0000			1.06431			0.532157	−	0.846646i	$-0.321382\pi$
$467$	23.0000			1.06431			0.532157	+	0.846646i	$0.321382\pi$
$468$	−12.0000			−0.554700
$469$	8.00000	+	13.8564i	0.369406	+	0.639829i
$470$		0			0
$471$	−3.00000	−	5.19615i	−0.138233	−	0.239426i
$472$	0.500000	−	0.866025i	0.0230144	−	0.0398621i
$473$		0			0
$474$	−4.00000			−0.183726
$475$		0			0
$476$	−14.0000			−0.641689
$477$		0			0
$478$	3.00000	−	5.19615i	0.137217	−	0.237666i
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	−0.998392	−	0.0566937i	$-0.981944\pi$
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	0.450098	−	0.892979i	$-0.351389\pi$
$480$		0			0
$481$	−12.0000	−	20.7846i	−0.547153	−	0.947697i
$482$	14.0000			0.637683
$483$	−4.00000			−0.182006
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$		0			0
$486$	16.0000			0.725775
$487$	20.0000			0.906287			0.453143	−	0.891438i	$-0.350303\pi$
$487$	20.0000			0.906287			0.453143	+	0.891438i	$0.350303\pi$
$488$	−4.00000	−	6.92820i	−0.181071	−	0.313625i
$489$	6.00000	−	10.3923i	0.271329	−	0.469956i
$490$		0			0
$491$	−4.00000	+	6.92820i	−0.180517	+	0.312665i	−0.942057	−	0.335453i	$-0.891111\pi$
$491$	−4.00000	+	6.92820i	−0.180517	+	0.312665i	0.761539	+	0.648119i	$0.224444\pi$
$492$	−1.00000	+	1.73205i	−0.0450835	+	0.0780869i
$493$	70.0000			3.15264
$494$	21.0000	−	15.5885i	0.944835	−	0.701358i
$495$		0			0
$496$	1.00000	−	1.73205i	0.0449013	−	0.0777714i
$497$	−12.0000	+	20.7846i	−0.538274	+	0.932317i
$498$	6.50000	+	11.2583i	0.291272	+	0.504498i
$499$	16.5000	−	28.5788i	0.738641	−	1.27936i	−0.214466	−	0.976732i	$-0.568801\pi$
$499$	16.5000	−	28.5788i	0.738641	−	1.27936i	0.953107	−	0.302633i	$-0.0978656\pi$
$500$		0			0
$501$	10.0000			0.446767
$502$	−20.0000			−0.892644
$503$	−4.00000	−	6.92820i	−0.178351	−	0.308913i	0.762965	−	0.646440i	$-0.223743\pi$
$503$	−4.00000	−	6.92820i	−0.178351	−	0.308913i	−0.941316	+	0.337527i	$0.890410\pi$
$504$	−2.00000	−	3.46410i	−0.0890871	−	0.154303i
$505$		0			0
$506$		0			0
$507$	−11.5000	−	19.9186i	−0.510733	−	0.884615i
$508$	−6.00000	+	10.3923i	−0.266207	+	0.461084i
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	0.791849	−	0.610718i	$-0.209119\pi$
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	−0.924821	+	0.380402i	$0.875786\pi$
$510$		0			0
$511$	−3.00000	+	5.19615i	−0.132712	+	0.229864i
$512$	1.00000			0.0441942
$513$	−17.5000	+	12.9904i	−0.772644	+	0.573539i
$514$	−15.0000			−0.661622
$515$		0			0
$516$	6.00000	−	10.3923i	0.264135	−	0.457496i
$517$		0			0
$518$	4.00000	−	6.92820i	0.175750	−	0.304408i
$519$	−3.00000	−	5.19615i	−0.131685	−	0.228086i
$520$		0			0
$521$	−6.00000			−0.262865			−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000			−0.262865			−0.131432	+	0.991325i	$0.541958\pi$
$522$	10.0000	+	17.3205i	0.437688	+	0.758098i
$523$	14.5000	+	25.1147i	0.634041	+	1.09819i	0.986718	+	0.162446i	$0.0519382\pi$
$523$	14.5000	+	25.1147i	0.634041	+	1.09819i	−0.352677	+	0.935745i	$0.614728\pi$
$524$	1.00000			0.0436852
$525$		0			0
$526$	−7.00000	−	12.1244i	−0.305215	−	0.528647i
$527$	7.00000	−	12.1244i	0.304925	−	0.528145i
$528$		0			0
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$		0			0
$531$	2.00000			0.0867926
$532$	8.00000	+	3.46410i	0.346844	+	0.150188i
$533$	12.0000			0.519778
$534$	6.50000	−	11.2583i	0.281283	−	0.487196i
$535$		0			0
$536$	−4.00000	−	6.92820i	−0.172774	−	0.299253i
$537$	4.50000	−	7.79423i	0.194189	−	0.336346i
$538$	−13.0000	−	22.5167i	−0.560470	−	0.970762i
$539$		0			0
$540$		0			0
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	0.953262	−	0.302144i	$-0.0977023\pi$
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	−0.738296	+	0.674477i	$0.764369\pi$
$542$	−13.0000	−	22.5167i	−0.558398	−	0.967173i
$543$	20.0000			0.858282
$544$	7.00000			0.300123
$545$		0			0
$546$	6.00000	−	10.3923i	0.256776	−	0.444750i
$547$	0.500000	+	0.866025i	0.0213785	+	0.0370286i	0.876517	−	0.481371i	$-0.159861\pi$
$547$	0.500000	+	0.866025i	0.0213785	+	0.0370286i	−0.855138	+	0.518400i	$0.826528\pi$
$548$	−7.50000	+	12.9904i	−0.320384	+	0.554922i
$549$	8.00000	−	13.8564i	0.341432	−	0.591377i
$550$		0			0
$551$	−40.0000	−	17.3205i	−1.70406	−	0.737878i
$552$	2.00000			0.0851257
$553$	−4.00000	+	6.92820i	−0.170097	+	0.294617i
$554$	11.0000	−	19.0526i	0.467345	−	0.809466i
$555$		0			0
$556$		0			0
$557$	1.00000	+	1.73205i	0.0423714	+	0.0733893i	0.886433	−	0.462856i	$-0.153175\pi$
$557$	1.00000	+	1.73205i	0.0423714	+	0.0733893i	−0.844062	+	0.536246i	$0.819842\pi$
$558$	4.00000			0.169334
$559$	−72.0000			−3.04528
$560$		0			0
$561$		0			0
$562$	7.00000			0.295277
$563$	−43.0000			−1.81223			−0.906117	−	0.423027i	$-0.860967\pi$
$563$	−43.0000			−1.81223			−0.906117	+	0.423027i	$0.860967\pi$
$564$		0			0
$565$		0			0
$566$	14.0000	+	24.2487i	0.588464	+	1.01925i
$567$	1.00000	−	1.73205i	0.0419961	−	0.0727393i
$568$	6.00000	−	10.3923i	0.251754	−	0.436051i
$569$	1.00000			0.0419222			0.0209611	−	0.999780i	$-0.493327\pi$
$569$	1.00000			0.0419222			0.0209611	+	0.999780i	$0.493327\pi$
$570$		0			0
$571$	1.00000			0.0418487			0.0209243	−	0.999781i	$-0.493339\pi$
$571$	1.00000			0.0418487			0.0209243	+	0.999781i	$0.493339\pi$
$572$		0			0
$573$	5.00000	−	8.66025i	0.208878	−	0.361787i
$574$	2.00000	+	3.46410i	0.0834784	+	0.144589i
$575$		0			0
$576$	1.00000	+	1.73205i	0.0416667	+	0.0721688i
$577$	−34.0000			−1.41544			−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000			−1.41544			−0.707719	+	0.706494i	$0.750276\pi$
$578$	32.0000			1.33102
$579$	−5.50000	−	9.52628i	−0.228572	−	0.395899i
$580$		0			0
$581$	26.0000			1.07866
$582$	15.0000			0.621770
$583$		0			0
$584$	1.50000	−	2.59808i	0.0620704	−	0.107509i
$585$		0			0
$586$	−16.0000	+	27.7128i	−0.660954	+	1.14481i
$587$	−22.5000	+	38.9711i	−0.928674	+	1.60851i	−0.143132	+	0.989704i	$0.545717\pi$
$587$	−22.5000	+	38.9711i	−0.928674	+	1.60851i	−0.785543	+	0.618808i	$0.787616\pi$
$588$	−3.00000			−0.123718
$589$	−7.00000	+	5.19615i	−0.288430	+	0.214104i
$590$		0			0
$591$	−2.00000	+	3.46410i	−0.0822690	+	0.142494i
$592$	−2.00000	+	3.46410i	−0.0821995	+	0.142374i
$593$	7.00000	+	12.1244i	0.287456	+	0.497888i	0.973202	−	0.229953i	$-0.0738573\pi$
$593$	7.00000	+	12.1244i	0.287456	+	0.497888i	−0.685746	+	0.727841i	$0.740524\pi$
$594$		0			0
$595$		0			0
$596$	16.0000			0.655386
$597$	−16.0000			−0.654836
$598$	−6.00000	−	10.3923i	−0.245358	−	0.424973i
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	0.962175	−	0.272433i	$-0.0878284\pi$
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	−0.717021	+	0.697051i	$0.754495\pi$
$600$		0			0
$601$	35.0000			1.42768			0.713840	−	0.700309i	$-0.246954\pi$
$601$	35.0000			1.42768			0.713840	+	0.700309i	$0.246954\pi$
$602$	−12.0000	−	20.7846i	−0.489083	−	0.847117i
$603$	8.00000	−	13.8564i	0.325785	−	0.564276i
$604$	6.00000	+	10.3923i	0.244137	+	0.422857i
$605$		0			0
$606$	−1.00000	+	1.73205i	−0.0406222	+	0.0703598i
$607$	14.0000			0.568242			0.284121	−	0.958788i	$-0.408298\pi$
$607$	14.0000			0.568242			0.284121	+	0.958788i	$0.408298\pi$
$608$	−4.00000	−	1.73205i	−0.162221	−	0.0702439i
$609$	−20.0000			−0.810441
$610$		0			0
$611$		0			0
$612$	7.00000	+	12.1244i	0.282958	+	0.490098i
$613$	7.00000	−	12.1244i	0.282727	−	0.489698i	−0.689328	−	0.724449i	$-0.742094\pi$
$613$	7.00000	−	12.1244i	0.282727	−	0.489698i	0.972056	+	0.234751i	$0.0754275\pi$
$614$	9.50000	+	16.4545i	0.383389	+	0.664049i
$615$		0			0
$616$		0			0
$617$	3.50000	+	6.06218i	0.140905	+	0.244054i	0.927838	−	0.372985i	$-0.121666\pi$
$617$	3.50000	+	6.06218i	0.140905	+	0.244054i	−0.786933	+	0.617039i	$0.788332\pi$
$618$	−6.00000	−	10.3923i	−0.241355	−	0.418040i
$619$	4.00000			0.160774			0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000			0.160774			0.0803868	+	0.996764i	$0.474384\pi$
$620$		0			0
$621$	5.00000	+	8.66025i	0.200643	+	0.347524i
$622$	−15.0000	+	25.9808i	−0.601445	+	1.04173i
$623$	−13.0000	−	22.5167i	−0.520834	−	0.902111i
$624$	−3.00000	+	5.19615i	−0.120096	+	0.208013i
$625$		0			0
$626$	11.0000			0.439648
$627$		0			0
$628$	6.00000			0.239426
$629$	−14.0000	+	24.2487i	−0.558217	+	0.966859i
$630$		0			0
$631$	−24.0000	−	41.5692i	−0.955425	−	1.65484i	−0.733393	−	0.679805i	$-0.762064\pi$
$631$	−24.0000	−	41.5692i	−0.955425	−	1.65484i	−0.222032	−	0.975039i	$-0.571269\pi$
$632$	2.00000	−	3.46410i	0.0795557	−	0.137795i
$633$	−11.5000	−	19.9186i	−0.457084	−	0.791693i
$634$	−24.0000			−0.953162
$635$		0			0
$636$		0			0
$637$	9.00000	+	15.5885i	0.356593	+	0.617637i
$638$		0			0
$639$	24.0000			0.949425
$640$		0			0
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	−0.167247	−	0.985915i	$-0.553488\pi$
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	0.937451	−	0.348117i	$-0.113179\pi$
$642$	−7.50000	−	12.9904i	−0.296001	−	0.512689i
$643$	12.5000	−	21.6506i	0.492952	−	0.853818i	−0.507015	−	0.861937i	$-0.669251\pi$
$643$	12.5000	−	21.6506i	0.492952	−	0.853818i	0.999967	+	0.00811944i	$0.00258453\pi$
$644$	2.00000	−	3.46410i	0.0788110	−	0.136505i
$645$		0			0
$646$	−28.0000	−	12.1244i	−1.10165	−	0.477026i
$647$	−12.0000			−0.471769			−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000			−0.471769			−0.235884	+	0.971781i	$0.575799\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$		0			0
$650$		0			0
$651$	−2.00000	+	3.46410i	−0.0783862	+	0.135769i
$652$	6.00000	+	10.3923i	0.234978	+	0.406994i
$653$	−12.0000			−0.469596			−0.234798	−	0.972044i	$-0.575443\pi$
$653$	−12.0000			−0.469596			−0.234798	+	0.972044i	$0.575443\pi$
$654$	−2.00000			−0.0782062
$655$		0			0
$656$	−1.00000	−	1.73205i	−0.0390434	−	0.0676252i
$657$	6.00000			0.234082
$658$		0			0
$659$	−1.50000	−	2.59808i	−0.0584317	−	0.101207i	0.835330	−	0.549749i	$-0.185277\pi$
$659$	−1.50000	−	2.59808i	−0.0584317	−	0.101207i	−0.893762	+	0.448542i	$0.851943\pi$
$660$		0			0
$661$	2.00000	+	3.46410i	0.0777910	+	0.134738i	0.902297	−	0.431116i	$-0.141880\pi$
$661$	2.00000	+	3.46410i	0.0777910	+	0.134738i	−0.824506	+	0.565854i	$0.808547\pi$
$662$	8.50000	−	14.7224i	0.330362	−	0.572204i
$663$	−21.0000	+	36.3731i	−0.815572	+	1.41261i
$664$	−13.0000			−0.504498
$665$		0			0
$666$	−8.00000			−0.309994
$667$	−10.0000	+	17.3205i	−0.387202	+	0.670653i
$668$	−5.00000	+	8.66025i	−0.193456	+	0.335075i
$669$	1.00000	+	1.73205i	0.0386622	+	0.0669650i
$670$		0			0
$671$		0			0
$672$	−2.00000			−0.0771517
$673$	−26.0000			−1.00223			−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000			−1.00223			−0.501113	+	0.865382i	$0.667076\pi$
$674$	11.0000	+	19.0526i	0.423704	+	0.733877i
$675$		0			0
$676$	23.0000			0.884615
$677$	26.0000			0.999261			0.499631	−	0.866239i	$-0.333469\pi$
$677$	26.0000			0.999261			0.499631	+	0.866239i	$0.333469\pi$
$678$	−0.500000	−	0.866025i	−0.0192024	−	0.0332595i
$679$	15.0000	−	25.9808i	0.575647	−	0.997050i
$680$		0			0
$681$	−6.50000	+	11.2583i	−0.249081	+	0.431420i
$682$		0			0
$683$	15.0000			0.573959			0.286980	−	0.957937i	$-0.407349\pi$
$683$	15.0000			0.573959			0.286980	+	0.957937i	$0.407349\pi$
$684$	−1.00000	−	8.66025i	−0.0382360	−	0.331133i
$685$		0			0
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$	9.00000	−	15.5885i	0.343371	−	0.594737i
$688$	6.00000	+	10.3923i	0.228748	+	0.396203i
$689$		0			0
$690$		0			0
$691$	37.0000			1.40755			0.703773	−	0.710425i	$-0.251497\pi$
$691$	37.0000			1.40755			0.703773	+	0.710425i	$0.251497\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	6.00000	+	10.3923i	0.227757	+	0.394486i
$695$		0			0
$696$	10.0000			0.379049
$697$	−7.00000	−	12.1244i	−0.265144	−	0.459243i
$698$	−8.00000	+	13.8564i	−0.302804	+	0.524473i
$699$	−6.50000	−	11.2583i	−0.245853	−	0.425829i
$700$		0			0
$701$	12.0000	−	20.7846i	0.453234	−	0.785024i	−0.545351	−	0.838208i	$-0.683604\pi$
$701$	12.0000	−	20.7846i	0.453234	−	0.785024i	0.998585	+	0.0531839i	$0.0169370\pi$
$702$	−30.0000			−1.13228
$703$	14.0000	−	10.3923i	0.528020	−	0.391953i
$704$		0			0
$705$		0			0
$706$	1.50000	−	2.59808i	0.0564532	−	0.0977799i
$707$	2.00000	+	3.46410i	0.0752177	+	0.130281i
$708$	0.500000	−	0.866025i	0.0187912	−	0.0325472i
$709$	14.0000	+	24.2487i	0.525781	+	0.910679i	0.999549	+	0.0300298i	$0.00956021\pi$
$709$	14.0000	+	24.2487i	0.525781	+	0.910679i	−0.473768	+	0.880650i	$0.657106\pi$
$710$		0			0
$711$	8.00000			0.300023
$712$	6.50000	+	11.2583i	0.243598	+	0.421924i
$713$	2.00000	+	3.46410i	0.0749006	+	0.129732i
$714$	−14.0000			−0.523937
$715$		0			0
$716$	4.50000	+	7.79423i	0.168173	+	0.291284i
$717$	3.00000	−	5.19615i	0.112037	−	0.194054i
$718$	12.0000	+	20.7846i	0.447836	+	0.775675i
$719$	−16.0000	+	27.7128i	−0.596699	+	1.03351i	0.396605	+	0.917989i	$0.370188\pi$
$719$	−16.0000	+	27.7128i	−0.596699	+	1.03351i	−0.993305	+	0.115524i	$0.963145\pi$
$720$		0			0
$721$	−24.0000			−0.893807
$722$	13.0000	+	13.8564i	0.483810	+	0.515682i
$723$	14.0000			0.520666
$724$	−10.0000	+	17.3205i	−0.371647	+	0.643712i
$725$		0			0
$726$	5.50000	+	9.52628i	0.204124	+	0.353553i
$727$	7.00000	−	12.1244i	0.259616	−	0.449667i	−0.706523	−	0.707690i	$-0.749737\pi$
$727$	7.00000	−	12.1244i	0.259616	−	0.449667i	0.966139	+	0.258022i	$0.0830708\pi$
$728$	6.00000	+	10.3923i	0.222375	+	0.385164i
$729$	13.0000			0.481481
$730$		0			0
$731$	42.0000	+	72.7461i	1.55343	+	2.69061i
$732$	−4.00000	−	6.92820i	−0.147844	−	0.256074i
$733$	−6.00000			−0.221615			−0.110808	−	0.993842i	$-0.535344\pi$
$733$	−6.00000			−0.221615			−0.110808	+	0.993842i	$0.535344\pi$
$734$	−8.00000			−0.295285
$735$		0			0
$736$	−1.00000	+	1.73205i	−0.0368605	+	0.0638442i
$737$		0			0
$738$	2.00000	−	3.46410i	0.0736210	−	0.127515i
$739$	−23.5000	+	40.7032i	−0.864461	+	1.49729i	0.00311943	+	0.999995i	$0.499007\pi$
$739$	−23.5000	+	40.7032i	−0.864461	+	1.49729i	−0.867581	+	0.497296i	$0.834326\pi$
$740$		0			0
$741$	21.0000	−	15.5885i	0.771454	−	0.572656i
$742$		0			0
$743$	−13.0000	+	22.5167i	−0.476924	+	0.826056i	−0.999650	−	0.0264443i	$-0.991582\pi$
$743$	−13.0000	+	22.5167i	−0.476924	+	0.826056i	0.522727	+	0.852500i	$0.324915\pi$
$744$	1.00000	−	1.73205i	0.0366618	−	0.0635001i
$745$		0			0
$746$	3.00000	−	5.19615i	0.109838	−	0.190245i
$747$	−13.0000	−	22.5167i	−0.475645	−	0.823842i
$748$		0			0
$749$	−30.0000			−1.09618
$750$		0			0
$751$	13.0000	+	22.5167i	0.474377	+	0.821645i	0.999570	−	0.0293387i	$-0.00934013\pi$
$751$	13.0000	+	22.5167i	0.474377	+	0.821645i	−0.525193	+	0.850983i	$0.676007\pi$
$752$		0			0
$753$	−20.0000			−0.728841
$754$	−30.0000	−	51.9615i	−1.09254	−	1.89233i
$755$		0			0
$756$	−5.00000	−	8.66025i	−0.181848	−	0.314970i
$757$	−16.0000	+	27.7128i	−0.581530	+	1.00724i	0.413768	+	0.910382i	$0.364212\pi$
$757$	−16.0000	+	27.7128i	−0.581530	+	1.00724i	−0.995298	+	0.0968571i	$0.969121\pi$
$758$	0.500000	−	0.866025i	0.0181608	−	0.0314555i
$759$		0			0
$760$		0			0
$761$	−6.00000			−0.217500			−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000			−0.217500			−0.108750	+	0.994069i	$0.534685\pi$
$762$	−6.00000	+	10.3923i	−0.217357	+	0.376473i
$763$	−2.00000	+	3.46410i	−0.0724049	+	0.125409i
$764$	5.00000	+	8.66025i	0.180894	+	0.313317i
$765$		0			0
$766$	6.00000	+	10.3923i	0.216789	+	0.375489i
$767$	−6.00000			−0.216647
$768$	1.00000			0.0360844
$769$	11.5000	+	19.9186i	0.414701	+	0.718283i	0.995397	−	0.0958377i	$-0.0305530\pi$
$769$	11.5000	+	19.9186i	0.414701	+	0.718283i	−0.580696	+	0.814120i	$0.697220\pi$
$770$		0			0
$771$	−15.0000			−0.540212
$772$	11.0000			0.395899
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	0.807018	−	0.590527i	$-0.201080\pi$
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	−0.914920	+	0.403634i	$0.867747\pi$
$774$	−12.0000	+	20.7846i	−0.431331	+	0.747087i
$775$		0			0
$776$	−7.50000	+	12.9904i	−0.269234	+	0.466328i
$777$	4.00000	−	6.92820i	0.143499	−	0.248548i
$778$	18.0000			0.645331
$779$	1.00000	+	8.66025i	0.0358287	+	0.310286i
$780$		0			0
$781$		0			0
$782$

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +1.00000 q^{12} +(-3.00000 - 5.19615i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.50000 + 6.06218i) q^{17} -2.00000 q^{18} +(3.50000 - 2.59808i) q^{19} +(1.00000 - 1.73205i) q^{21} +(-1.00000 - 1.73205i) q^{23} +(-0.500000 + 0.866025i) q^{24} +6.00000 q^{26} -5.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(-5.00000 - 8.66025i) q^{29} -2.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.50000 - 6.06218i) q^{34} +(1.00000 - 1.73205i) q^{36} +4.00000 q^{37} +(0.500000 + 4.33013i) q^{38} +6.00000 q^{39} +(-1.00000 + 1.73205i) q^{41} +(1.00000 + 1.73205i) q^{42} +(6.00000 - 10.3923i) q^{43} +2.00000 q^{46} +(-0.500000 - 0.866025i) q^{48} -3.00000 q^{49} +(-3.50000 - 6.06218i) q^{51} +(-3.00000 + 5.19615i) q^{52} +(2.50000 - 4.33013i) q^{54} -2.00000 q^{56} +(0.500000 + 4.33013i) q^{57} +10.0000 q^{58} +(0.500000 - 0.866025i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(1.00000 - 1.73205i) q^{62} +(-2.00000 - 3.46410i) q^{63} +1.00000 q^{64} +(-4.00000 - 6.92820i) q^{67} +7.00000 q^{68} +2.00000 q^{69} +(6.00000 - 10.3923i) q^{71} +(1.00000 + 1.73205i) q^{72} +(1.50000 - 2.59808i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(-4.00000 - 1.73205i) q^{76} +(-3.00000 + 5.19615i) q^{78} +(2.00000 - 3.46410i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.00000 - 1.73205i) q^{82} -13.0000 q^{83} -2.00000 q^{84} +(6.00000 + 10.3923i) q^{86} +10.0000 q^{87} +(6.50000 + 11.2583i) q^{89} +(6.00000 + 10.3923i) q^{91} +(-1.00000 + 1.73205i) q^{92} +(1.00000 - 1.73205i) q^{93} +1.00000 q^{96} +(-7.50000 + 12.9904i) q^{97} +(1.50000 - 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 - q^3 - q^4 - q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{12} - 6 q^{13} + 2 q^{14} - q^{16} - 7 q^{17} - 4 q^{18} + 7 q^{19} + 2 q^{21} - 2 q^{23} - q^{24} + 12 q^{26} - 10 q^{27} + 2 q^{28} - 10 q^{29} - 4 q^{31} - q^{32} - 7 q^{34} + 2 q^{36} + 8 q^{37} + q^{38} + 12 q^{39} - 2 q^{41} + 2 q^{42} + 12 q^{43} + 4 q^{46} - q^{48} - 6 q^{49} - 7 q^{51} - 6 q^{52} + 5 q^{54} - 4 q^{56} + q^{57} + 20 q^{58} + q^{59} - 8 q^{61} + 2 q^{62} - 4 q^{63} + 2 q^{64} - 8 q^{67} + 14 q^{68} + 4 q^{69} + 12 q^{71} + 2 q^{72} + 3 q^{73} - 4 q^{74} - 8 q^{76} - 6 q^{78} + 4 q^{79} - q^{81} - 2 q^{82} - 26 q^{83} - 4 q^{84} + 12 q^{86} + 20 q^{87} + 13 q^{89} + 12 q^{91} - 2 q^{92} + 2 q^{93} + 2 q^{96} - 15 q^{97} + 3 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 - q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^12 - 6 * q^13 + 2 * q^14 - q^16 - 7 * q^17 - 4 * q^18 + 7 * q^19 + 2 * q^21 - 2 * q^23 - q^24 + 12 * q^26 - 10 * q^27 + 2 * q^28 - 10 * q^29 - 4 * q^31 - q^32 - 7 * q^34 + 2 * q^36 + 8 * q^37 + q^38 + 12 * q^39 - 2 * q^41 + 2 * q^42 + 12 * q^43 + 4 * q^46 - q^48 - 6 * q^49 - 7 * q^51 - 6 * q^52 + 5 * q^54 - 4 * q^56 + q^57 + 20 * q^58 + q^59 - 8 * q^61 + 2 * q^62 - 4 * q^63 + 2 * q^64 - 8 * q^67 + 14 * q^68 + 4 * q^69 + 12 * q^71 + 2 * q^72 + 3 * q^73 - 4 * q^74 - 8 * q^76 - 6 * q^78 + 4 * q^79 - q^81 - 2 * q^82 - 26 * q^83 - 4 * q^84 + 12 * q^86 + 20 * q^87 + 13 * q^89 + 12 * q^91 - 2 * q^92 + 2 * q^93 + 2 * q^96 - 15 * q^97 + 3 * q^98

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