LMFDB - Embedded newform 1050.2.i.c.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(151,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1050.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.i (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:	$8.38429221223$
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			151.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1050.151
Dual form			1050.2.i.c.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.00000 + 5.19615i) q^{11} +(-0.500000 - 0.866025i) q^{12} -4.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} +(-2.00000 + 1.73205i) q^{21} +6.00000 q^{22} +(-1.50000 - 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(-2.00000 + 1.73205i) q^{28} -6.00000 q^{29} +(-2.50000 + 4.33013i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} -3.00000 q^{34} +1.00000 q^{36} +(-4.00000 - 6.92820i) q^{37} +(2.00000 - 3.46410i) q^{38} +(2.00000 - 3.46410i) q^{39} -3.00000 q^{41} +(2.50000 + 0.866025i) q^{42} +8.00000 q^{43} +(-3.00000 - 5.19615i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(-4.50000 - 7.79423i) q^{47} +1.00000 q^{48} +(5.50000 + 4.33013i) q^{49} +(1.50000 + 2.59808i) q^{51} +(2.00000 - 3.46410i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(2.50000 + 0.866025i) q^{56} -4.00000 q^{57} +(3.00000 + 5.19615i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(-1.00000 - 1.73205i) q^{61} +5.00000 q^{62} +(-0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{66} +(-4.00000 + 6.92820i) q^{67} +(1.50000 + 2.59808i) q^{68} +3.00000 q^{69} -9.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-7.00000 + 12.1244i) q^{73} +(-4.00000 + 6.92820i) q^{74} -4.00000 q^{76} +(-12.0000 + 10.3923i) q^{77} -4.00000 q^{78} +(3.50000 + 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.50000 + 2.59808i) q^{82} -6.00000 q^{83} +(-0.500000 - 2.59808i) q^{84} +(-4.00000 - 6.92820i) q^{86} +(3.00000 - 5.19615i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(-1.50000 - 2.59808i) q^{89} +(-10.0000 - 3.46410i) q^{91} +3.00000 q^{92} +(-2.50000 - 4.33013i) q^{93} +(-4.50000 + 7.79423i) q^{94} +(-0.500000 - 0.866025i) q^{96} +17.0000 q^{97} +(1.00000 - 6.92820i) q^{98} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} - q^{4} + 2 q^{6} + 5 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 - q^3 - q^4 + 2 * q^6 + 5 * q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} - q^{3} - q^{4} + 2 q^{6} + 5 q^{7} + 2 q^{8} - q^{9} - 6 q^{11} - q^{12} - 8 q^{13} - q^{14} - q^{16} + 3 q^{17} - q^{18} + 4 q^{19} - 4 q^{21} + 12 q^{22} - 3 q^{23} - q^{24} + 4 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 5 q^{31} - q^{32} - 6 q^{33} - 6 q^{34} + 2 q^{36} - 8 q^{37} + 4 q^{38} + 4 q^{39} - 6 q^{41} + 5 q^{42} + 16 q^{43} - 6 q^{44} - 3 q^{46} - 9 q^{47} + 2 q^{48} + 11 q^{49} + 3 q^{51} + 4 q^{52} - 12 q^{53} - q^{54} + 5 q^{56} - 8 q^{57} + 6 q^{58} - 6 q^{59} - 2 q^{61} + 10 q^{62} - q^{63} + 2 q^{64} - 6 q^{66} - 8 q^{67} + 3 q^{68} + 6 q^{69} - 18 q^{71} - q^{72} - 14 q^{73} - 8 q^{74} - 8 q^{76} - 24 q^{77} - 8 q^{78} + 7 q^{79} - q^{81} + 3 q^{82} - 12 q^{83} - q^{84} - 8 q^{86} + 6 q^{87} - 6 q^{88} - 3 q^{89} - 20 q^{91} + 6 q^{92} - 5 q^{93} - 9 q^{94} - q^{96} + 34 q^{97} + 2 q^{98} + 12 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^3 - q^4 + 2 * q^6 + 5 * q^7 + 2 * q^8 - q^9 - 6 * q^11 - q^12 - 8 * q^13 - q^14 - q^16 + 3 * q^17 - q^18 + 4 * q^19 - 4 * q^21 + 12 * q^22 - 3 * q^23 - q^24 + 4 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 5 * q^31 - q^32 - 6 * q^33 - 6 * q^34 + 2 * q^36 - 8 * q^37 + 4 * q^38 + 4 * q^39 - 6 * q^41 + 5 * q^42 + 16 * q^43 - 6 * q^44 - 3 * q^46 - 9 * q^47 + 2 * q^48 + 11 * q^49 + 3 * q^51 + 4 * q^52 - 12 * q^53 - q^54 + 5 * q^56 - 8 * q^57 + 6 * q^58 - 6 * q^59 - 2 * q^61 + 10 * q^62 - q^63 + 2 * q^64 - 6 * q^66 - 8 * q^67 + 3 * q^68 + 6 * q^69 - 18 * q^71 - q^72 - 14 * q^73 - 8 * q^74 - 8 * q^76 - 24 * q^77 - 8 * q^78 + 7 * q^79 - q^81 + 3 * q^82 - 12 * q^83 - q^84 - 8 * q^86 + 6 * q^87 - 6 * q^88 - 3 * q^89 - 20 * q^91 + 6 * q^92 - 5 * q^93 - 9 * q^94 - q^96 + 34 * q^97 + 2 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.00000			0.408248
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.0829925	+	0.996550i	$0.526448\pi$
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.821541	+	0.570149i	$0.806886\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$	−0.500000	−	2.59808i	−0.133631	−	0.694365i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$		0			0
$21$	−2.00000	+	1.73205i	−0.436436	+	0.377964i
$22$	6.00000			1.27920
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$		0			0
$26$	2.00000	+	3.46410i	0.392232	+	0.679366i
$27$	1.00000			0.192450
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$	−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
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	−0.998322	−	0.0579057i	$-0.981558\pi$
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	0.549309	+	0.835619i	$0.314891\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−3.00000	−	5.19615i	−0.522233	−	0.904534i
$34$	−3.00000			−0.514496
$35$		0			0
$36$	1.00000			0.166667
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	−0.981236	−	0.192809i	$-0.938240\pi$
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	0.323640	−	0.946180i	$-0.395093\pi$
$38$	2.00000	−	3.46410i	0.324443	−	0.561951i
$39$	2.00000	−	3.46410i	0.320256	−	0.554700i
$40$		0			0
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$	2.50000	+	0.866025i	0.385758	+	0.133631i
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$	−3.00000	−	5.19615i	−0.452267	−	0.783349i
$45$		0			0
$46$	−1.50000	+	2.59808i	−0.221163	+	0.383065i
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	−0.981543	−	0.191243i	$-0.938748\pi$
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	0.325150	−	0.945662i	$-0.394585\pi$
$48$	1.00000			0.144338
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		0			0
$51$	1.50000	+	2.59808i	0.210042	+	0.363803i
$52$	2.00000	−	3.46410i	0.277350	−	0.480384i
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	0.0783936	+	0.996922i	$0.475021\pi$
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	−0.902557	+	0.430570i	$0.858312\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	2.50000	+	0.866025i	0.334077	+	0.115728i
$57$	−4.00000			−0.529813
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$		0			0
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$	5.00000			0.635001
$63$	−0.500000	−	2.59808i	−0.0629941	−	0.327327i
$64$	1.00000			0.125000
$65$		0			0
$66$	−3.00000	+	5.19615i	−0.369274	+	0.639602i
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	3.00000			0.361158
$70$		0			0
$71$	−9.00000			−1.06810			−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000			−1.06810			−0.534052	+	0.845452i	$0.679331\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−7.00000	+	12.1244i	−0.819288	+	1.41905i	0.0869195	+	0.996215i	$0.472298\pi$
$73$	−7.00000	+	12.1244i	−0.819288	+	1.41905i	−0.906208	+	0.422833i	$0.861036\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$		0			0
$76$	−4.00000			−0.458831
$77$	−12.0000	+	10.3923i	−1.36753	+	1.18431i
$78$	−4.00000			−0.452911
$79$	3.50000	+	6.06218i	0.393781	+	0.682048i	0.992945	−	0.118578i	$-0.0378336\pi$
$79$	3.50000	+	6.06218i	0.393781	+	0.682048i	−0.599164	+	0.800626i	$0.704500\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.50000	+	2.59808i	0.165647	+	0.286910i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	−0.500000	−	2.59808i	−0.0545545	−	0.283473i
$85$		0			0
$86$	−4.00000	−	6.92820i	−0.431331	−	0.747087i
$87$	3.00000	−	5.19615i	0.321634	−	0.557086i
$88$	−3.00000	+	5.19615i	−0.319801	+	0.553912i
$89$	−1.50000	−	2.59808i	−0.159000	−	0.275396i	0.775509	−	0.631337i	$-0.217494\pi$
$89$	−1.50000	−	2.59808i	−0.159000	−	0.275396i	−0.934508	+	0.355942i	$0.884160\pi$
$90$		0			0
$91$	−10.0000	−	3.46410i	−1.04828	−	0.363137i
$92$	3.00000			0.312772
$93$	−2.50000	−	4.33013i	−0.259238	−	0.449013i
$94$	−4.50000	+	7.79423i	−0.464140	+	0.803913i
$95$		0			0
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	17.0000			1.72609			0.863044	−	0.505128i	$-0.168555\pi$
$97$	17.0000			1.72609			0.863044	+	0.505128i	$0.168555\pi$
$98$	1.00000	−	6.92820i	0.101015	−	0.699854i
$99$	6.00000			0.603023
$100$		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	$0.963017\pi$
$102$	1.50000	−	2.59808i	0.148522	−	0.257248i
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	0.985329	+	0.170664i	$0.0545913\pi$
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	−0.344865	+	0.938652i	$0.612075\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$	12.0000			1.16554
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	0.683793	−	0.729676i	$-0.260329\pi$
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	−0.973814	+	0.227345i	$0.926996\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	2.00000	−	3.46410i	0.191565	−	0.331801i	−0.754204	−	0.656640i	$-0.771977\pi$
$109$	2.00000	−	3.46410i	0.191565	−	0.331801i	0.945769	+	0.324840i	$0.105310\pi$
$110$		0			0
$111$	8.00000			0.759326
$112$	−0.500000	−	2.59808i	−0.0472456	−	0.245495i
$113$	3.00000			0.282216			0.141108	−	0.989994i	$-0.454933\pi$
$113$	3.00000			0.282216			0.141108	+	0.989994i	$0.454933\pi$
$114$	2.00000	+	3.46410i	0.187317	+	0.324443i
$115$		0			0
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$	2.00000	+	3.46410i	0.184900	+	0.320256i
$118$	6.00000			0.552345
$119$	6.00000	−	5.19615i	0.550019	−	0.476331i
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$	−1.00000	+	1.73205i	−0.0905357	+	0.156813i
$123$	1.50000	−	2.59808i	0.135250	−	0.234261i
$124$	−2.50000	−	4.33013i	−0.224507	−	0.388857i
$125$		0			0
$126$	−2.00000	+	1.73205i	−0.178174	+	0.154303i
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−4.00000	+	6.92820i	−0.352180	+	0.609994i
$130$		0			0
$131$	9.00000	+	15.5885i	0.786334	+	1.36197i	0.928199	+	0.372084i	$0.121357\pi$
$131$	9.00000	+	15.5885i	0.786334	+	1.36197i	−0.141865	+	0.989886i	$0.545310\pi$
$132$	6.00000			0.522233
$133$	2.00000	+	10.3923i	0.173422	+	0.901127i
$134$	8.00000			0.691095
$135$		0			0
$136$	1.50000	−	2.59808i	0.128624	−	0.222783i
$137$	7.50000	−	12.9904i	0.640768	−	1.10984i	−0.344493	−	0.938789i	$-0.611949\pi$
$137$	7.50000	−	12.9904i	0.640768	−	1.10984i	0.985262	−	0.171054i	$-0.0547174\pi$
$138$	−1.50000	−	2.59808i	−0.127688	−	0.221163i
$139$	2.00000			0.169638			0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000			0.169638			0.0848189	+	0.996396i	$0.472969\pi$
$140$		0			0
$141$	9.00000			0.757937
$142$	4.50000	+	7.79423i	0.377632	+	0.654077i
$143$	12.0000	−	20.7846i	1.00349	−	1.73810i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$		0			0
$146$	14.0000			1.15865
$147$	−6.50000	+	2.59808i	−0.536111	+	0.214286i
$148$	8.00000			0.657596
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$	2.00000	+	3.46410i	0.162221	+	0.280976i
$153$	−3.00000			−0.242536
$154$	15.0000	+	5.19615i	1.20873	+	0.418718i
$155$		0			0
$156$	2.00000	+	3.46410i	0.160128	+	0.277350i
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	3.50000	−	6.06218i	0.278445	−	0.482281i
$159$	−6.00000	−	10.3923i	−0.475831	−	0.824163i
$160$		0			0
$161$	−1.50000	−	7.79423i	−0.118217	−	0.614271i
$162$	1.00000			0.0785674
$163$	−4.00000	−	6.92820i	−0.313304	−	0.542659i	0.665771	−	0.746156i	$-0.268103\pi$
$163$	−4.00000	−	6.92820i	−0.313304	−	0.542659i	−0.979076	+	0.203497i	$0.934769\pi$
$164$	1.50000	−	2.59808i	0.117130	−	0.202876i
$165$		0			0
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$	−2.00000	+	1.73205i	−0.154303	+	0.133631i
$169$	3.00000			0.230769
$170$		0			0
$171$	2.00000	−	3.46410i	0.152944	−	0.264906i
$172$	−4.00000	+	6.92820i	−0.304997	+	0.528271i
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$	−6.00000			−0.454859
$175$		0			0
$176$	6.00000			0.452267
$177$	−3.00000	−	5.19615i	−0.225494	−	0.390567i
$178$	−1.50000	+	2.59808i	−0.112430	+	0.194734i
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	−0.304446	−	0.952529i	$-0.598471\pi$
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	0.977138	−	0.212607i	$-0.0681952\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	2.00000	+	10.3923i	0.148250	+	0.770329i
$183$	2.00000			0.147844
$184$	−1.50000	−	2.59808i	−0.110581	−	0.191533i
$185$		0			0
$186$	−2.50000	+	4.33013i	−0.183309	+	0.317500i
$187$	9.00000	+	15.5885i	0.658145	+	1.13994i
$188$	9.00000			0.656392
$189$	2.50000	+	0.866025i	0.181848	+	0.0629941i
$190$		0			0
$191$	−7.50000	−	12.9904i	−0.542681	−	0.939951i	−0.998749	−	0.0500060i	$-0.984076\pi$
$191$	−7.50000	−	12.9904i	−0.542681	−	0.939951i	0.456068	−	0.889945i	$-0.349257\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	−0.941865	−	0.335993i	$-0.890928\pi$
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	0.761911	+	0.647682i	$0.224262\pi$
$194$	−8.50000	−	14.7224i	−0.610264	−	1.05701i
$195$		0			0
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$	−3.00000	−	5.19615i	−0.213201	−	0.369274i
$199$	−2.50000	+	4.33013i	−0.177220	+	0.306955i	−0.940927	−	0.338608i	$-0.890044\pi$
$199$	−2.50000	+	4.33013i	−0.177220	+	0.306955i	0.763707	+	0.645563i	$0.223377\pi$
$200$		0			0
$201$	−4.00000	−	6.92820i	−0.282138	−	0.488678i
$202$	12.0000			0.844317
$203$	−15.0000	−	5.19615i	−1.05279	−	0.364698i
$204$	−3.00000			−0.210042
$205$		0			0
$206$	6.50000	−	11.2583i	0.452876	−	0.784405i
$207$	−1.50000	+	2.59808i	−0.104257	+	0.180579i
$208$	2.00000	+	3.46410i	0.138675	+	0.240192i
$209$	−24.0000			−1.66011
$210$		0			0
$211$	8.00000			0.550743			0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000			0.550743			0.275371	+	0.961338i	$0.411199\pi$
$212$	−6.00000	−	10.3923i	−0.412082	−	0.713746i
$213$	4.50000	−	7.79423i	0.308335	−	0.534052i
$214$	−3.00000	+	5.19615i	−0.205076	+	0.355202i
$215$		0			0
$216$	1.00000			0.0680414
$217$	−10.0000	+	8.66025i	−0.678844	+	0.587896i
$218$	−4.00000			−0.270914
$219$	−7.00000	−	12.1244i	−0.473016	−	0.819288i
$220$		0			0
$221$	−6.00000	+	10.3923i	−0.403604	+	0.699062i
$222$	−4.00000	−	6.92820i	−0.268462	−	0.464991i
$223$	11.0000			0.736614			0.368307	−	0.929704i	$-0.379937\pi$
$223$	11.0000			0.736614			0.368307	+	0.929704i	$0.379937\pi$
$224$	−2.00000	+	1.73205i	−0.133631	+	0.115728i
$225$		0			0
$226$	−1.50000	−	2.59808i	−0.0997785	−	0.172821i
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	−0.395860	−	0.918311i	$-0.629553\pi$
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	0.993210	−	0.116331i	$-0.0371134\pi$
$228$	2.00000	−	3.46410i	0.132453	−	0.229416i
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	0.958187	+	0.286143i	$0.0923732\pi$
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	−0.231287	+	0.972886i	$0.574293\pi$
$230$		0			0
$231$	−3.00000	−	15.5885i	−0.197386	−	1.02565i
$232$	−6.00000			−0.393919
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	0.750867	−	0.660454i	$-0.229636\pi$
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	−0.947403	+	0.320043i	$0.896303\pi$
$234$	2.00000	−	3.46410i	0.130744	−	0.226455i
$235$		0			0
$236$	−3.00000	−	5.19615i	−0.195283	−	0.338241i
$237$	−7.00000			−0.454699
$238$	−7.50000	−	2.59808i	−0.486153	−	0.168408i
$239$	3.00000			0.194054			0.0970269	−	0.995282i	$-0.469067\pi$
$239$	3.00000			0.194054			0.0970269	+	0.995282i	$0.469067\pi$
$240$		0			0
$241$	11.0000	−	19.0526i	0.708572	−	1.22728i	−0.256814	−	0.966461i	$-0.582673\pi$
$241$	11.0000	−	19.0526i	0.708572	−	1.22728i	0.965387	−	0.260822i	$-0.0839937\pi$
$242$	−12.5000	+	21.6506i	−0.803530	+	1.39176i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	2.00000			0.128037
$245$		0			0
$246$	−3.00000			−0.191273
$247$	−8.00000	−	13.8564i	−0.509028	−	0.881662i
$248$	−2.50000	+	4.33013i	−0.158750	+	0.274963i
$249$	3.00000	−	5.19615i	0.190117	−	0.329293i
$250$		0			0
$251$	24.0000			1.51487			0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000			1.51487			0.757433	+	0.652913i	$0.226453\pi$
$252$	2.50000	+	0.866025i	0.157485	+	0.0545545i
$253$	18.0000			1.13165
$254$	8.00000	+	13.8564i	0.501965	+	0.869428i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	0.997374	+	0.0724199i	$0.0230722\pi$
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	−0.435970	+	0.899961i	$0.643595\pi$
$258$	8.00000			0.498058
$259$	−4.00000	−	20.7846i	−0.248548	−	1.29149i
$260$		0			0
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$	9.00000	−	15.5885i	0.556022	−	0.963058i
$263$	1.50000	−	2.59808i	0.0924940	−	0.160204i	−0.816066	−	0.577959i	$-0.803849\pi$
$263$	1.50000	−	2.59808i	0.0924940	−	0.160204i	0.908560	+	0.417755i	$0.137183\pi$
$264$	−3.00000	−	5.19615i	−0.184637	−	0.319801i
$265$		0			0
$266$	8.00000	−	6.92820i	0.490511	−	0.424795i
$267$	3.00000			0.183597
$268$	−4.00000	−	6.92820i	−0.244339	−	0.423207i
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	12.5000	+	21.6506i	0.759321	+	1.31518i	0.943197	+	0.332233i	$0.107802\pi$
$271$	12.5000	+	21.6506i	0.759321	+	1.31518i	−0.183876	+	0.982949i	$0.558865\pi$
$272$	−3.00000			−0.181902
$273$	8.00000	−	6.92820i	0.484182	−	0.419314i
$274$	−15.0000			−0.906183
$275$		0			0
$276$	−1.50000	+	2.59808i	−0.0902894	+	0.156386i
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	0.150210	+	0.988654i	$0.452005\pi$
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	−0.931305	+	0.364241i	$0.881328\pi$
$278$	−1.00000	−	1.73205i	−0.0599760	−	0.103882i
$279$	5.00000			0.299342
$280$		0			0
$281$	27.0000			1.61068			0.805342	−	0.592810i	$-0.201981\pi$
$281$	27.0000			1.61068			0.805342	+	0.592810i	$0.201981\pi$
$282$	−4.50000	−	7.79423i	−0.267971	−	0.464140i
$283$	11.0000	−	19.0526i	0.653882	−	1.13256i	−0.328291	−	0.944577i	$-0.606473\pi$
$283$	11.0000	−	19.0526i	0.653882	−	1.13256i	0.982173	−	0.187980i	$-0.0601941\pi$
$284$	4.50000	−	7.79423i	0.267026	−	0.462502i
$285$		0			0
$286$	−24.0000			−1.41915
$287$	−7.50000	−	2.59808i	−0.442711	−	0.153360i
$288$	1.00000			0.0589256
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	−8.50000	+	14.7224i	−0.498279	+	0.863044i
$292$	−7.00000	−	12.1244i	−0.409644	−	0.709524i
$293$	−18.0000			−1.05157			−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000			−1.05157			−0.525786	+	0.850617i	$0.676229\pi$
$294$	5.50000	+	4.33013i	0.320767	+	0.252538i
$295$		0			0
$296$	−4.00000	−	6.92820i	−0.232495	−	0.402694i
$297$	−3.00000	+	5.19615i	−0.174078	+	0.301511i
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$		0			0
$301$	20.0000	+	6.92820i	1.15278	+	0.399335i
$302$	−16.0000			−0.920697
$303$	−6.00000	−	10.3923i	−0.344691	−	0.597022i
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$		0			0
$306$	1.50000	+	2.59808i	0.0857493	+	0.148522i
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$	−3.00000	−	15.5885i	−0.170941	−	0.888235i
$309$	−13.0000			−0.739544
$310$		0			0
$311$	−10.5000	+	18.1865i	−0.595400	+	1.03126i	0.398090	+	0.917346i	$0.369673\pi$
$311$	−10.5000	+	18.1865i	−0.595400	+	1.03126i	−0.993490	+	0.113917i	$0.963660\pi$
$312$	2.00000	−	3.46410i	0.113228	−	0.196116i
$313$	−8.50000	−	14.7224i	−0.480448	−	0.832161i	0.519300	−	0.854592i	$-0.326193\pi$
$313$	−8.50000	−	14.7224i	−0.480448	−	0.832161i	−0.999748	+	0.0224310i	$0.992859\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	−7.00000			−0.393781
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	0.646872	−	0.762598i	$-0.276077\pi$
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	−0.983866	+	0.178908i	$0.942743\pi$
$318$	−6.00000	+	10.3923i	−0.336463	+	0.582772i
$319$	18.0000	−	31.1769i	1.00781	−	1.74557i
$320$		0			0
$321$	6.00000			0.334887
$322$	−6.00000	+	5.19615i	−0.334367	+	0.289570i
$323$	12.0000			0.667698
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	−4.00000	+	6.92820i	−0.221540	+	0.383718i
$327$	2.00000	+	3.46410i	0.110600	+	0.191565i
$328$	−3.00000			−0.165647
$329$	−4.50000	−	23.3827i	−0.248093	−	1.28913i
$330$		0			0
$331$	−13.0000	−	22.5167i	−0.714545	−	1.23763i	−0.963135	−	0.269019i	$-0.913301\pi$
$331$	−13.0000	−	22.5167i	−0.714545	−	1.23763i	0.248590	−	0.968609i	$-0.420033\pi$
$332$	3.00000	−	5.19615i	0.164646	−	0.285176i
$333$	−4.00000	+	6.92820i	−0.219199	+	0.379663i
$334$		0			0
$335$		0			0
$336$	2.50000	+	0.866025i	0.136386	+	0.0472456i
$337$	−13.0000			−0.708155			−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000			−0.708155			−0.354078	+	0.935216i	$0.615205\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$	−1.50000	+	2.59808i	−0.0814688	+	0.141108i
$340$		0			0
$341$	−15.0000	−	25.9808i	−0.812296	−	1.40694i
$342$	−4.00000			−0.216295
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	8.00000			0.431331
$345$		0			0
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	−0.999813	−	0.0193540i	$-0.993839\pi$
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	0.516667	+	0.856186i	$0.327172\pi$
$348$	3.00000	+	5.19615i	0.160817	+	0.278543i
$349$	−28.0000			−1.49881			−0.749403	−	0.662114i	$-0.769659\pi$
$349$	−28.0000			−1.49881			−0.749403	+	0.662114i	$0.769659\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$	−3.00000	−	5.19615i	−0.159901	−	0.276956i
$353$	−7.50000	+	12.9904i	−0.399185	+	0.691408i	−0.993626	−	0.112731i	$-0.964040\pi$
$353$	−7.50000	+	12.9904i	−0.399185	+	0.691408i	0.594441	+	0.804139i	$0.297373\pi$
$354$	−3.00000	+	5.19615i	−0.159448	+	0.276172i
$355$		0			0
$356$	3.00000			0.159000
$357$	1.50000	+	7.79423i	0.0793884	+	0.412514i
$358$	−18.0000			−0.951330
$359$	18.0000	+	31.1769i	0.950004	+	1.64545i	0.745409	+	0.666608i	$0.232254\pi$
$359$	18.0000	+	31.1769i	0.950004	+	1.64545i	0.204595	+	0.978847i	$0.434412\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	−1.00000	−	1.73205i	−0.0525588	−	0.0910346i
$363$	25.0000			1.31216
$364$	8.00000	−	6.92820i	0.419314	−	0.363137i
$365$		0			0
$366$	−1.00000	−	1.73205i	−0.0522708	−	0.0905357i
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	−0.225750	−	0.974185i	$-0.572483\pi$
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	0.956544	−	0.291587i	$-0.0941834\pi$
$368$	−1.50000	+	2.59808i	−0.0781929	+	0.135434i
$369$	1.50000	+	2.59808i	0.0780869	+	0.135250i
$370$		0			0
$371$	−24.0000	+	20.7846i	−1.24602	+	1.07908i
$372$	5.00000			0.259238
$373$	−4.00000	−	6.92820i	−0.207112	−	0.358729i	0.743691	−	0.668523i	$-0.233073\pi$
$373$	−4.00000	−	6.92820i	−0.207112	−	0.358729i	−0.950804	+	0.309794i	$0.899740\pi$
$374$	9.00000	−	15.5885i	0.465379	−	0.806060i
$375$		0			0
$376$	−4.50000	−	7.79423i	−0.232070	−	0.401957i
$377$	24.0000			1.23606
$378$	−0.500000	−	2.59808i	−0.0257172	−	0.133631i
$379$	−10.0000			−0.513665			−0.256833	−	0.966456i	$-0.582679\pi$
$379$	−10.0000			−0.513665			−0.256833	+	0.966456i	$0.582679\pi$
$380$		0			0
$381$	8.00000	−	13.8564i	0.409852	−	0.709885i
$382$	−7.50000	+	12.9904i	−0.383733	+	0.664646i
$383$	−10.5000	−	18.1865i	−0.536525	−	0.929288i	−0.999088	−	0.0427020i	$-0.986403\pi$
$383$	−10.5000	−	18.1865i	−0.536525	−	0.929288i	0.462563	−	0.886586i	$-0.346930\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	5.00000			0.254493
$387$	−4.00000	−	6.92820i	−0.203331	−	0.352180i
$388$	−8.50000	+	14.7224i	−0.431522	+	0.747418i
$389$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$389$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$390$		0			0
$391$	−9.00000			−0.455150
$392$	5.50000	+	4.33013i	0.277792	+	0.218704i
$393$	−18.0000			−0.907980
$394$		0			0
$395$		0			0
$396$	−3.00000	+	5.19615i	−0.150756	+	0.261116i
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	0.839840	−	0.542834i	$-0.182649\pi$
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	−0.890028	+	0.455905i	$0.849316\pi$
$398$	5.00000			0.250627
$399$	−10.0000	−	3.46410i	−0.500626	−	0.173422i
$400$		0			0
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	0.931158	−	0.364615i	$-0.118800\pi$
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	−0.781345	+	0.624099i	$0.785466\pi$
$402$	−4.00000	+	6.92820i	−0.199502	+	0.345547i
$403$	10.0000	−	17.3205i	0.498135	−	0.862796i
$404$	−6.00000	−	10.3923i	−0.298511	−	0.517036i
$405$		0			0
$406$	3.00000	+	15.5885i	0.148888	+	0.773642i
$407$	48.0000			2.37927
$408$	1.50000	+	2.59808i	0.0742611	+	0.128624i
$409$	−14.5000	+	25.1147i	−0.716979	+	1.24184i	0.245212	+	0.969469i	$0.421142\pi$
$409$	−14.5000	+	25.1147i	−0.716979	+	1.24184i	−0.962191	+	0.272374i	$0.912191\pi$
$410$		0			0
$411$	7.50000	+	12.9904i	0.369948	+	0.640768i
$412$	−13.0000			−0.640464
$413$	−12.0000	+	10.3923i	−0.590481	+	0.511372i
$414$	3.00000			0.147442
$415$		0			0
$416$	2.00000	−	3.46410i	0.0980581	−	0.169842i
$417$	−1.00000	+	1.73205i	−0.0489702	+	0.0848189i
$418$	12.0000	+	20.7846i	0.586939	+	1.01661i
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$		0			0
$421$	−4.00000			−0.194948			−0.0974740	−	0.995238i	$-0.531076\pi$
$421$	−4.00000			−0.194948			−0.0974740	+	0.995238i	$0.531076\pi$
$422$	−4.00000	−	6.92820i	−0.194717	−	0.337260i
$423$	−4.50000	+	7.79423i	−0.218797	+	0.378968i
$424$	−6.00000	+	10.3923i	−0.291386	+	0.504695i
$425$		0			0
$426$	−9.00000			−0.436051
$427$	−1.00000	−	5.19615i	−0.0483934	−	0.251459i
$428$	6.00000			0.290021
$429$	12.0000	+	20.7846i	0.579365	+	1.00349i
$430$		0			0
$431$	−10.5000	+	18.1865i	−0.505767	+	0.876014i	0.494211	+	0.869342i	$0.335457\pi$
$431$	−10.5000	+	18.1865i	−0.505767	+	0.876014i	−0.999978	+	0.00667224i	$0.997876\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−7.00000			−0.336399			−0.168199	−	0.985753i	$-0.553795\pi$
$433$	−7.00000			−0.336399			−0.168199	+	0.985753i	$0.553795\pi$
$434$	12.5000	+	4.33013i	0.600019	+	0.207853i
$435$		0			0
$436$	2.00000	+	3.46410i	0.0957826	+	0.165900i
$437$	6.00000	−	10.3923i	0.287019	−	0.497131i
$438$	−7.00000	+	12.1244i	−0.334473	+	0.579324i
$439$	6.50000	+	11.2583i	0.310228	+	0.537331i	0.978412	−	0.206666i	$-0.0662612\pi$
$439$	6.50000	+	11.2583i	0.310228	+	0.537331i	−0.668184	+	0.743996i	$0.732928\pi$
$440$		0			0
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$	12.0000			0.570782
$443$	12.0000	+	20.7846i	0.570137	+	0.987507i	0.996551	+	0.0829786i	$0.0264433\pi$
$443$	12.0000	+	20.7846i	0.570137	+	0.987507i	−0.426414	+	0.904528i	$0.640223\pi$
$444$	−4.00000	+	6.92820i	−0.189832	+	0.328798i
$445$		0			0
$446$	−5.50000	−	9.52628i	−0.260433	−	0.451082i
$447$	−6.00000			−0.283790
$448$	2.50000	+	0.866025i	0.118114	+	0.0409159i
$449$	−3.00000			−0.141579			−0.0707894	−	0.997491i	$-0.522552\pi$
$449$	−3.00000			−0.141579			−0.0707894	+	0.997491i	$0.522552\pi$
$450$		0			0
$451$	9.00000	−	15.5885i	0.423793	−	0.734032i
$452$	−1.50000	+	2.59808i	−0.0705541	+	0.122203i
$453$	8.00000	+	13.8564i	0.375873	+	0.651031i
$454$	−18.0000			−0.844782
$455$		0			0
$456$	−4.00000			−0.187317
$457$	−1.00000	−	1.73205i	−0.0467780	−	0.0810219i	0.841688	−	0.539964i	$-0.181562\pi$
$457$	−1.00000	−	1.73205i	−0.0467780	−	0.0810219i	−0.888466	+	0.458942i	$0.848229\pi$
$458$	11.0000	−	19.0526i	0.513996	−	0.890268i
$459$	1.50000	−	2.59808i	0.0700140	−	0.121268i
$460$		0			0
$461$	36.0000			1.67669			0.838344	−	0.545142i	$-0.183524\pi$
$461$	36.0000			1.67669			0.838344	+	0.545142i	$0.183524\pi$
$462$	−12.0000	+	10.3923i	−0.558291	+	0.483494i
$463$	−13.0000			−0.604161			−0.302081	−	0.953282i	$-0.597681\pi$
$463$	−13.0000			−0.604161			−0.302081	+	0.953282i	$0.597681\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	15.0000	+	25.9808i	0.694117	+	1.20225i	0.970477	+	0.241192i	$0.0775384\pi$
$467$	15.0000	+	25.9808i	0.694117	+	1.20225i	−0.276360	+	0.961054i	$0.589128\pi$
$468$	−4.00000			−0.184900
$469$	−16.0000	+	13.8564i	−0.738811	+	0.639829i
$470$		0			0
$471$	−7.00000	−	12.1244i	−0.322543	−	0.558661i
$472$	−3.00000	+	5.19615i	−0.138086	+	0.239172i
$473$	−24.0000	+	41.5692i	−1.10352	+	1.91135i
$474$	3.50000	+	6.06218i	0.160760	+	0.278445i
$475$		0			0
$476$	1.50000	+	7.79423i	0.0687524	+	0.357248i
$477$	12.0000			0.549442
$478$	−1.50000	−	2.59808i	−0.0686084	−	0.118833i
$479$	−10.5000	+	18.1865i	−0.479757	+	0.830964i	−0.999730	−	0.0232187i	$-0.992609\pi$
$479$	−10.5000	+	18.1865i	−0.479757	+	0.830964i	0.519973	+	0.854183i	$0.325942\pi$
$480$		0			0
$481$	16.0000	+	27.7128i	0.729537	+	1.26360i
$482$	−22.0000			−1.00207
$483$	7.50000	+	2.59808i	0.341262	+	0.118217i
$484$	25.0000			1.13636
$485$		0			0
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	12.5000	−	21.6506i	0.566429	−	0.981084i	−0.430486	−	0.902597i	$-0.641658\pi$
$487$	12.5000	−	21.6506i	0.566429	−	0.981084i	0.996915	−	0.0784867i	$-0.0250088\pi$
$488$	−1.00000	−	1.73205i	−0.0452679	−	0.0784063i
$489$	8.00000			0.361773
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$	1.50000	+	2.59808i	0.0676252	+	0.117130i
$493$	−9.00000	+	15.5885i	−0.405340	+	0.702069i
$494$	−8.00000	+	13.8564i	−0.359937	+	0.623429i
$495$		0			0
$496$	5.00000			0.224507
$497$	−22.5000	−	7.79423i	−1.00926	−	0.349619i
$498$	−6.00000			−0.268866
$499$	−19.0000	−	32.9090i	−0.850557	−	1.47321i	−0.880707	−	0.473662i	$-0.842932\pi$
$499$	−19.0000	−	32.9090i	−0.850557	−	1.47321i	0.0301498	−	0.999545i	$-0.490402\pi$
$500$		0			0
$501$		0			0
$502$	−12.0000	−	20.7846i	−0.535586	−	0.927663i
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$	−0.500000	−	2.59808i	−0.0222718	−	0.115728i
$505$		0			0
$506$	−9.00000	−	15.5885i	−0.400099	−	0.692991i
$507$	−1.50000	+	2.59808i	−0.0666173	+	0.115385i
$508$	8.00000	−	13.8564i	0.354943	−	0.614779i
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$		0			0
$511$	−28.0000	+	24.2487i	−1.23865	+	1.07270i
$512$	1.00000			0.0441942
$513$	2.00000	+	3.46410i	0.0883022	+	0.152944i
$514$	9.00000	−	15.5885i	0.396973	−	0.687577i
$515$		0			0
$516$	−4.00000	−	6.92820i	−0.176090	−	0.304997i
$517$	54.0000			2.37492
$518$	−16.0000	+	13.8564i	−0.703000	+	0.608816i
$519$	−6.00000			−0.263371
$520$		0			0
$521$	−10.5000	+	18.1865i	−0.460013	+	0.796766i	−0.998961	−	0.0455727i	$-0.985489\pi$
$521$	−10.5000	+	18.1865i	−0.460013	+	0.796766i	0.538948	+	0.842339i	$0.318822\pi$
$522$	3.00000	−	5.19615i	0.131306	−	0.227429i
$523$	17.0000	+	29.4449i	0.743358	+	1.28753i	0.950958	+	0.309320i	$0.100101\pi$
$523$	17.0000	+	29.4449i	0.743358	+	1.28753i	−0.207600	+	0.978214i	$0.566565\pi$
$524$	−18.0000			−0.786334
$525$		0			0
$526$	−3.00000			−0.130806
$527$	7.50000	+	12.9904i	0.326705	+	0.565870i
$528$	−3.00000	+	5.19615i	−0.130558	+	0.226134i
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$		0			0
$531$	6.00000			0.260378
$532$	−10.0000	−	3.46410i	−0.433555	−	0.150188i
$533$	12.0000			0.519778
$534$	−1.50000	−	2.59808i	−0.0649113	−	0.112430i
$535$		0			0
$536$	−4.00000	+	6.92820i	−0.172774	+	0.299253i
$537$	9.00000	+	15.5885i	0.388379	+	0.672692i
$538$		0			0
$539$	−39.0000	+	15.5885i	−1.67985	+	0.671442i
$540$		0			0
$541$	14.0000	+	24.2487i	0.601907	+	1.04253i	0.992532	+	0.121984i	$0.0389256\pi$
$541$	14.0000	+	24.2487i	0.601907	+	1.04253i	−0.390625	+	0.920550i	$0.627741\pi$
$542$	12.5000	−	21.6506i	0.536921	−	0.929974i
$543$	−1.00000	+	1.73205i	−0.0429141	+	0.0743294i
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$		0			0
$546$	−10.0000	−	3.46410i	−0.427960	−	0.148250i
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	7.50000	+	12.9904i	0.320384	+	0.554922i
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$		0			0
$551$	−12.0000	−	20.7846i	−0.511217	−	0.885454i
$552$	3.00000			0.127688
$553$	3.50000	+	18.1865i	0.148835	+	0.773370i
$554$	26.0000			1.10463
$555$		0			0
$556$	−1.00000	+	1.73205i	−0.0424094	+	0.0734553i
$557$	15.0000	−	25.9808i	0.635570	−	1.10084i	−0.350824	−	0.936442i	$-0.614098\pi$
$557$	15.0000	−	25.9808i	0.635570	−	1.10084i	0.986394	−	0.164399i	$-0.0525683\pi$
$558$	−2.50000	−	4.33013i	−0.105833	−	0.183309i
$559$	−32.0000			−1.35346
$560$		0			0
$561$	−18.0000			−0.759961
$562$	−13.5000	−	23.3827i	−0.569463	−	0.986339i
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	−0.964315	−	0.264758i	$-0.914708\pi$
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	0.711445	+	0.702742i	$0.248041\pi$
$564$	−4.50000	+	7.79423i	−0.189484	+	0.328196i
$565$		0			0
$566$	−22.0000			−0.924729
$567$	−2.00000	+	1.73205i	−0.0839921	+	0.0727393i
$568$	−9.00000			−0.377632
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	0.979313	−	0.202350i	$-0.0648579\pi$
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	−0.664897	+	0.746935i	$0.731525\pi$
$570$		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	$0.304106\pi$
$572$	12.0000	+	20.7846i	0.501745	+	0.869048i
$573$	15.0000			0.626634
$574$	1.50000	+	7.79423i	0.0626088	+	0.325325i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	−0.886090	−	0.463513i	$-0.846589\pi$
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	0.844459	+	0.535620i	$0.179922\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	−2.50000	−	4.33013i	−0.103896	−	0.179954i
$580$		0			0
$581$	−15.0000	−	5.19615i	−0.622305	−	0.215573i
$582$	17.0000			0.704673
$583$	−36.0000	−	62.3538i	−1.49097	−	2.58243i
$584$	−7.00000	+	12.1244i	−0.289662	+	0.501709i
$585$		0			0
$586$	9.00000	+	15.5885i	0.371787	+	0.643953i
$587$	18.0000			0.742940			0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000			0.742940			0.371470	+	0.928445i	$0.378854\pi$
$588$	1.00000	−	6.92820i	0.0412393	−	0.285714i
$589$	−20.0000			−0.824086
$590$		0			0
$591$		0			0
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$	16.5000	+	28.5788i	0.677574	+	1.17359i	0.975709	+	0.219069i	$0.0703019\pi$
$593$	16.5000	+	28.5788i	0.677574	+	1.17359i	−0.298136	+	0.954524i	$0.596365\pi$
$594$	6.00000			0.246183
$595$		0			0
$596$	−6.00000			−0.245770
$597$	−2.50000	−	4.33013i	−0.102318	−	0.177220i
$598$	6.00000	−	10.3923i	0.245358	−	0.424973i
$599$	−4.50000	+	7.79423i	−0.183865	+	0.318464i	−0.943193	−	0.332244i	$-0.892194\pi$
$599$	−4.50000	+	7.79423i	−0.183865	+	0.318464i	0.759328	+	0.650708i	$0.225528\pi$
$600$		0			0
$601$	−34.0000			−1.38689			−0.693444	−	0.720510i	$-0.743908\pi$
$601$	−34.0000			−1.38689			−0.693444	+	0.720510i	$0.743908\pi$
$602$	−4.00000	−	20.7846i	−0.163028	−	0.847117i
$603$	8.00000			0.325785
$604$	8.00000	+	13.8564i	0.325515	+	0.563809i
$605$		0			0
$606$	−6.00000	+	10.3923i	−0.243733	+	0.422159i
$607$	−5.50000	−	9.52628i	−0.223238	−	0.386660i	0.732551	−	0.680712i	$-0.238329\pi$
$607$	−5.50000	−	9.52628i	−0.223238	−	0.386660i	−0.955789	+	0.294052i	$0.904996\pi$
$608$	−4.00000			−0.162221
$609$	12.0000	−	10.3923i	0.486265	−	0.421117i
$610$		0			0
$611$	18.0000	+	31.1769i	0.728202	+	1.26128i
$612$	1.50000	−	2.59808i	0.0606339	−	0.105021i
$613$	17.0000	−	29.4449i	0.686624	−	1.18927i	−0.286300	−	0.958140i	$-0.592425\pi$
$613$	17.0000	−	29.4449i	0.686624	−	1.18927i	0.972924	−	0.231127i	$-0.0742412\pi$
$614$	−10.0000	−	17.3205i	−0.403567	−	0.698999i
$615$		0			0
$616$	−12.0000	+	10.3923i	−0.483494	+	0.418718i
$617$	−21.0000			−0.845428			−0.422714	−	0.906263i	$-0.638923\pi$
$617$	−21.0000			−0.845428			−0.422714	+	0.906263i	$0.638923\pi$
$618$	6.50000	+	11.2583i	0.261468	+	0.452876i
$619$	23.0000	−	39.8372i	0.924448	−	1.60119i	0.132002	−	0.991250i	$-0.457860\pi$
$619$	23.0000	−	39.8372i	0.924448	−	1.60119i	0.792446	−	0.609941i	$-0.208807\pi$
$620$		0			0
$621$	−1.50000	−	2.59808i	−0.0601929	−	0.104257i
$622$	21.0000			0.842023
$623$	−1.50000	−	7.79423i	−0.0600962	−	0.312269i
$624$	−4.00000			−0.160128
$625$		0			0
$626$	−8.50000	+	14.7224i	−0.339728	+	0.588427i
$627$	12.0000	−	20.7846i	0.479234	−	0.830057i
$628$	−7.00000	−	12.1244i	−0.279330	−	0.483814i
$629$	−24.0000			−0.956943
$630$		0			0
$631$	17.0000			0.676759			0.338380	−	0.941010i	$-0.390121\pi$
$631$	17.0000			0.676759			0.338380	+	0.941010i	$0.390121\pi$
$632$	3.50000	+	6.06218i	0.139223	+	0.241140i
$633$	−4.00000	+	6.92820i	−0.158986	+	0.275371i
$634$	−6.00000	+	10.3923i	−0.238290	+	0.412731i
$635$		0			0
$636$	12.0000			0.475831
$637$	−22.0000	−	17.3205i	−0.871672	−	0.686264i
$638$	−36.0000			−1.42525
$639$	4.50000	+	7.79423i	0.178017	+	0.308335i
$640$		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	$-0.113179\pi$
$642$	−3.00000	−	5.19615i	−0.118401	−	0.205076i
$643$	−34.0000			−1.34083			−0.670415	−	0.741987i	$-0.733884\pi$
$643$	−34.0000			−1.34083			−0.670415	+	0.741987i	$0.733884\pi$
$644$	7.50000	+	2.59808i	0.295541	+	0.102379i
$645$		0			0
$646$	−6.00000	−	10.3923i	−0.236067	−	0.408880i
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	−0.959529	−	0.281609i	$-0.909132\pi$
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	0.723645	+	0.690172i	$0.242465\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−18.0000	−	31.1769i	−0.706562	−	1.22380i
$650$		0			0
$651$	−2.50000	−	12.9904i	−0.0979827	−	0.509133i
$652$	8.00000			0.313304
$653$	18.0000	+	31.1769i	0.704394	+	1.22005i	0.966910	+	0.255119i	$0.0821147\pi$
$653$	18.0000	+	31.1769i	0.704394	+	1.22005i	−0.262515	+	0.964928i	$0.584552\pi$
$654$	2.00000	−	3.46410i	0.0782062	−	0.135457i
$655$		0			0
$656$	1.50000	+	2.59808i	0.0585652	+	0.101438i
$657$	14.0000			0.546192
$658$	−18.0000	+	15.5885i	−0.701713	+	0.607701i
$659$	−30.0000			−1.16863			−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000			−1.16863			−0.584317	+	0.811525i	$0.698638\pi$
$660$		0			0
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	−0.752252	−	0.658876i	$-0.771032\pi$
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	0.946729	+	0.322031i	$0.104366\pi$
$662$	−13.0000	+	22.5167i	−0.505259	+	0.875135i
$663$	−6.00000	−	10.3923i	−0.233021	−	0.403604i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	8.00000			0.309994
$667$	9.00000	+	15.5885i	0.348481	+	0.603587i
$668$		0			0
$669$	−5.50000	+	9.52628i	−0.212642	+	0.368307i
$670$		0			0
$671$	12.0000			0.463255
$672$	−0.500000	−	2.59808i	−0.0192879	−	0.100223i
$673$	−19.0000			−0.732396			−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000			−0.732396			−0.366198	+	0.930537i	$0.619341\pi$
$674$	6.50000	+	11.2583i	0.250371	+	0.433655i
$675$		0			0
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	0.639618	−	0.768693i	$-0.279092\pi$
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	−0.985517	+	0.169580i	$0.945759\pi$
$678$	3.00000			0.115214
$679$	42.5000	+	14.7224i	1.63100	+	0.564995i
$680$		0			0
$681$	9.00000	+	15.5885i	0.344881	+	0.597351i
$682$	−15.0000	+	25.9808i	−0.574380	+	0.994855i
$683$	−9.00000	+	15.5885i	−0.344375	+	0.596476i	−0.985240	−	0.171178i	$-0.945243\pi$
$683$	−9.00000	+	15.5885i	−0.344375	+	0.596476i	0.640865	+	0.767654i	$0.278576\pi$
$684$	2.00000	+	3.46410i	0.0764719	+	0.132453i
$685$		0			0
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$	−22.0000			−0.839352
$688$	−4.00000	−	6.92820i	−0.152499	−	0.264135i
$689$	24.0000	−	41.5692i	0.914327	−	1.58366i
$690$		0			0
$691$	17.0000	+	29.4449i	0.646710	+	1.12014i	0.983904	+	0.178700i	$0.0571891\pi$
$691$	17.0000	+	29.4449i	0.646710	+	1.12014i	−0.337193	+	0.941435i	$0.609478\pi$
$692$	−6.00000			−0.228086
$693$	15.0000	+	5.19615i	0.569803	+	0.197386i
$694$	18.0000			0.683271
$695$		0			0
$696$	3.00000	−	5.19615i	0.113715	−	0.196960i
$697$	−4.50000	+	7.79423i	−0.170450	+	0.295227i
$698$	14.0000	+	24.2487i	0.529908	+	0.917827i
$699$	6.00000			0.226941
$700$		0			0
$701$	−48.0000			−1.81293			−0.906467	−	0.422276i	$-0.861231\pi$
$701$	−48.0000			−1.81293			−0.906467	+	0.422276i	$0.861231\pi$
$702$	2.00000	+	3.46410i	0.0754851	+	0.130744i
$703$	16.0000	−	27.7128i	0.603451	−	1.04521i
$704$	−3.00000	+	5.19615i	−0.113067	+	0.195837i
$705$		0			0
$706$	15.0000			0.564532
$707$	−24.0000	+	20.7846i	−0.902613	+	0.781686i
$708$	6.00000			0.225494
$709$	23.0000	+	39.8372i	0.863783	+	1.49612i	0.868250	+	0.496126i	$0.165245\pi$
$709$	23.0000	+	39.8372i	0.863783	+	1.49612i	−0.00446726	+	0.999990i	$0.501422\pi$
$710$		0			0
$711$	3.50000	−	6.06218i	0.131260	−	0.227349i
$712$	−1.50000	−	2.59808i	−0.0562149	−	0.0973670i
$713$	15.0000			0.561754
$714$	6.00000	−	5.19615i	0.224544	−	0.194461i
$715$		0			0
$716$	9.00000	+	15.5885i	0.336346	+	0.582568i
$717$	−1.50000	+	2.59808i	−0.0560185	+	0.0970269i
$718$	18.0000	−	31.1769i	0.671754	−	1.16351i
$719$	13.5000	+	23.3827i	0.503465	+	0.872027i	0.999992	+	0.00400572i	$0.00127506\pi$
$719$	13.5000	+	23.3827i	0.503465	+	0.872027i	−0.496527	+	0.868021i	$0.665392\pi$
$720$		0			0
$721$	6.50000	+	33.7750i	0.242073	+	1.25785i
$722$	−3.00000			−0.111648
$723$	11.0000	+	19.0526i	0.409094	+	0.708572i
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$		0			0
$726$	−12.5000	−	21.6506i	−0.463919	−	0.803530i
$727$	−31.0000			−1.14973			−0.574863	−	0.818250i	$-0.694945\pi$
$727$	−31.0000			−1.14973			−0.574863	+	0.818250i	$0.694945\pi$
$728$	−10.0000	−	3.46410i	−0.370625	−	0.128388i
$729$	1.00000			0.0370370
$730$		0			0
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$	−1.00000	+	1.73205i	−0.0369611	+	0.0640184i
$733$	−25.0000	−	43.3013i	−0.923396	−	1.59937i	−0.794121	−	0.607760i	$-0.792068\pi$
$733$	−25.0000	−	43.3013i	−0.923396	−	1.59937i	−0.129275	−	0.991609i	$-0.541265\pi$
$734$	−28.0000			−1.03350
$735$		0			0
$736$	3.00000			0.110581
$737$	−24.0000	−	41.5692i	−0.884051	−	1.53122i
$738$	1.50000	−	2.59808i	0.0552158	−	0.0956365i
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	−0.680534	−	0.732717i	$-0.738252\pi$
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	0.974818	+	0.223001i	$0.0715853\pi$
$740$		0			0
$741$	16.0000			0.587775
$742$	30.0000	+	10.3923i	1.10133	+	0.381514i
$743$	9.00000			0.330178			0.165089	−	0.986279i	$-0.447209\pi$
$743$	9.00000			0.330178			0.165089	+	0.986279i	$0.447209\pi$
$744$	−2.50000	−	4.33013i	−0.0916544	−	0.158750i
$745$		0			0
$746$	−4.00000	+	6.92820i	−0.146450	+	0.253660i
$747$	3.00000	+	5.19615i	0.109764	+	0.190117i
$748$	−18.0000			−0.658145
$749$	−3.00000	−	15.5885i	−0.109618	−	0.569590i
$750$		0			0
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	0.974265	−	0.225407i	$-0.0723712\pi$
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	−0.682341	+	0.731034i	$0.739038\pi$
$752$	−4.50000	+	7.79423i	−0.164098	+	0.284226i
$753$	−12.0000	+	20.7846i	−0.437304	+	0.757433i
$754$	−12.0000	−	20.7846i	−0.437014	−	0.756931i
$755$		0			0
$756$	−2.00000	+	1.73205i	−0.0727393	+	0.0629941i
$757$	−4.00000			−0.145382			−0.0726912	−	0.997354i	$-0.523159\pi$
$757$	−4.00000			−0.145382			−0.0726912	+	0.997354i	$0.523159\pi$
$758$	5.00000	+	8.66025i	0.181608	+	0.314555i
$759$	−9.00000	+	15.5885i	−0.326679	+	0.565825i
$760$		0			0
$761$	−4.50000	−	7.79423i	−0.163125	−	0.282541i	0.772863	−	0.634573i	$-0.218824\pi$
$761$	−4.50000	−	7.79423i	−0.163125	−	0.282541i	−0.935988	+	0.352032i	$0.885491\pi$
$762$	−16.0000			−0.579619
$763$	8.00000	−	6.92820i	0.289619	−	0.250818i
$764$	15.0000			0.542681
$765$		0			0
$766$	−10.5000	+	18.1865i	−0.379380	+	0.657106i
$767$	12.0000	−	20.7846i	0.433295	−	0.750489i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	50.0000			1.80305			0.901523	−	0.432731i	$-0.142450\pi$
$769$	50.0000			1.80305			0.901523	+	0.432731i	$0.142450\pi$
$770$		0			0
$771$	−18.0000			−0.648254
$772$	−2.50000	−	4.33013i	−0.0899770	−	0.155845i
$773$	6.00000	−	10.3923i	0.215805	−	0.373785i	−0.737716	−	0.675111i	$-0.764096\pi$
$773$	6.00000	−	10.3923i	0.215805	−	0.373785i	0.953521	+	0.301326i	$0.0974291\pi$
$774$	−4.00000	+	6.92820i	−0.143777	+	0.249029i
$775$		0			0
$776$	17.0000			0.610264
$777$	20.0000	+	6.92820i	0.717496	+	0.248548i
$778$		0			0
$779$	−6.00000	−	10.3923i	−0.214972	−	0.372343i
$780$		0			0
$781$	27.0000	−	46.7654i	0.966136	−	1.67340i
$782$	4.50000	+	7.79423i	0.160920	+	0.278721i
$783$	−6.00000			−0.214423
$784$	1.00000	−	6.92820i	0.0357143	−	0.247436i
$785$		0			0
$786$	9.00000	+	15.5885i	0.321019	+	0.556022i
$787$	−4.00000	+	6.92820i	−0.142585	+	0.246964i	−0.928469	−	0.371409i	$-0.878875\pi$
$787$	−4.00000	+	6.92820i	−0.142585	+	0.246964i	0.785885	+	0.618373i	$0.212208\pi$
$788$		0			0
$789$	1.50000	+	2.59808i	0.0534014	+	0.0924940i
$790$		0			0
$791$	7.50000	+	2.59808i	0.266669	+	0.0923770i
$792$	6.00000			0.213201
$793$	4.00000	+	6.92820i	0.142044	+	0.246028i
$794$	−1.00000	+	1.73205i	−0.0354887	+	0.0614682i
$795$		0			0
$796$	−2.50000	−	4.33013i	−0.0886102	−	0.153477i
$797$	−18.0000			−0.637593			−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000			−0.637593			−0.318796	+	0.947823i	$0.603279\pi$
$798$	2.00000	+	10.3923i	0.0707992	+	0.367884i
$799$	−27.0000			−0.955191
$800$		0			0
$801$	−1.50000	+	2.59808i	−0.0529999	+	0.0917985i
$802$	3.00000	−	5.19615i	0.105934	−	0.183483i
$803$	−42.0000	−	72.7461i	−1.48215	−	2.56716i
$804$	8.00000			0.282138
$805$		0			0
$806$	−20.0000			−0.704470
$807$		0			0
$808$	−6.00000	+	10.3923i	−0.211079	+	0.365600i
$809$	3.00000	−	5.19615i	0.105474	−	0.182687i	−0.808458	−	0.588555i	$-0.799697\pi$
$809$	3.00000	−	5.19615i	0.105474	−	0.182687i	0.913932	+	0.405868i	$0.133031\pi$
$810$		0			0
$811$	−40.0000			−1.40459			−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000			−1.40459			−0.702295	+	0.711886i	$0.747841\pi$
$812$	12.0000	−	10.3923i	0.421117	−	0.364698i
$813$	−25.0000			−0.876788
$814$	−24.0000	−	41.5692i	−0.841200	−	1.45700i
$815$		0			0
$816$	1.50000	−	2.59808i	0.0525105	−	0.0909509i
$817$	16.0000	+	27.7128i	0.559769	+	0.969549i
$818$	29.0000			1.01396
$819$	2.00000	+	10.3923i	0.0698857	+	0.363137i
$820$		0			0
$821$	−18.0000	−	31.1769i	−0.628204	−	1.08808i	−0.987912	−	0.155017i	$-0.950457\pi$
$821$	−18.0000	−	31.1769i	−0.628204	−	1.08808i	0.359708	−	0.933065i	$-0.382876\pi$
$822$	7.50000	−	12.9904i	0.261593	−	0.453092i
$823$	−22.0000	+	38.1051i	−0.766872	+	1.32826i	0.172379	+	0.985031i	$0.444854\pi$
$823$	−22.0000	+	38.1051i	−0.766872	+	1.32826i	−0.939251	+	0.343230i	$0.888479\pi$
$824$	6.50000	+	11.2583i	0.226438	+	0.392203i
$825$		0			0
$826$	15.0000	+	5.19615i	0.521917	+	0.180797i
$827$	30.0000			1.04320			0.521601	−	0.853189i	$-0.325335\pi$
$827$	30.0000			1.04320			0.521601	+	0.853189i	$0.325335\pi$
$828$	−1.50000	−	2.59808i	−0.0521286	−	0.0902894i
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	−0.882869	−	0.469620i	$-0.844391\pi$
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	0.848137	+	0.529777i	$0.177724\pi$
$830$		0			0
$831$	−13.0000	−	22.5167i	−0.450965	−	0.781094i
$832$	−4.00000			−0.138675
$833$	19.5000	−	7.79423i	0.675635	−	0.270054i
$834$	2.00000			0.0692543
$835$		0			0
$836$	12.0000	−	20.7846i	0.415029	−	0.718851i
$837$	−2.50000	+	4.33013i	−0.0864126	+	0.149671i
$838$	−12.0000	−	20.7846i	−0.414533	−	0.717992i
$839$	15.0000			0.517858			0.258929	−	0.965896i	$-0.416631\pi$
$839$	15.0000			0.517858			0.258929	+	0.965896i	$0.416631\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	2.00000	+	3.46410i	0.0689246	+	0.119381i
$843$	−13.5000	+	23.3827i	−0.464965	+	0.805342i
$844$	−4.00000	+	6.92820i	−0.137686	+	0.238479i
$845$		0			0
$846$	9.00000			0.309426
$847$	−12.5000	−	64.9519i	−0.429505	−	2.23177i
$848$	12.0000			0.412082
$849$	11.0000	+	19.0526i	0.377519	+	0.653882i
$850$		0			0
$851$	−12.0000	+	20.7846i	−0.411355	+	0.712487i
$852$	4.50000	+	7.79423i	0.154167	+	0.267026i
$853$	−28.0000			−0.958702			−0.479351	−	0.877623i	$-0.659128\pi$
$853$	−28.0000			−0.958702			−0.479351	+	0.877623i	$0.659128\pi$
$854$	−4.00000	+	3.46410i	−0.136877	+	0.118539i
$855$		0			0
$856$	−3.00000	−	5.19615i	−0.102538	−	0.177601i
$857$	−3.00000	+	5.19615i	−0.102478	+	0.177497i	−0.912705	−	0.408619i	$-0.866010\pi$
$857$	−3.00000	+	5.19615i	−0.102478	+	0.177497i	0.810227	+	0.586116i	$0.199344\pi$
$858$	12.0000	−	20.7846i	0.409673	−	0.709575i
$859$	−7.00000	−	12.1244i	−0.238837	−	0.413678i	0.721544	−	0.692369i	$-0.243433\pi$
$859$	−7.00000	−	12.1244i	−0.238837	−	0.413678i	−0.960381	+	0.278691i	$0.910099\pi$
$860$		0			0
$861$	6.00000	−	5.19615i	0.204479	−	0.177084i
$862$	21.0000			0.715263
$863$	−10.5000	−	18.1865i	−0.357424	−	0.619077i	0.630106	−	0.776509i	$-0.283012\pi$
$863$	−10.5000	−	18.1865i	−0.357424	−	0.619077i	−0.987530	+	0.157433i	$0.949678\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$		0			0
$866$	3.50000	+	6.06218i	0.118935	+	0.206001i
$867$	−8.00000			−0.271694
$868$	−2.50000	−	12.9904i	−0.0848555	−	0.440922i
$869$	−42.0000			−1.42475
$870$		0			0
$871$	16.0000	−	27.7128i	0.542139	−	0.939013i
$872$	2.00000	−	3.46410i	0.0677285	−	0.117309i
$873$	−8.50000	−	14.7224i	−0.287681	−	0.498279i
$874$	−12.0000			−0.405906
$875$		0			0
$876$	14.0000			0.473016
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	0.848648	−	0.528958i	$-0.177417\pi$
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	−0.882415	+	0.470471i	$0.844084\pi$
$878$	6.50000	−	11.2583i	0.219364	−	0.379950i
$879$	9.00000	−	15.5885i	0.303562	−	0.525786i
$880$		0			0
$881$	15.0000			0.505363			0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000			0.505363			0.252681	+	0.967550i	$0.418688\pi$
$882$	−6.50000	+	2.59808i	−0.218866	+	0.0874818i
$883$	14.0000			0.471138			0.235569	−	0.971858i	$-0.424305\pi$
$883$	14.0000			0.471138			0.235569	+	0.971858i	$0.424305\pi$
$884$	−6.00000	−	10.3923i	−0.201802	−	0.349531i
$885$		0			0
$886$	12.0000	−	20.7846i	0.403148	−	0.698273i
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	0.591156	−	0.806557i	$-0.298672\pi$
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	−0.994077	+	0.108678i	$0.965338\pi$
$888$	8.00000			0.268462
$889$	−40.0000	−	13.8564i	−1.34156	−	0.464729i
$890$		0			0
$891$	−3.00000	−	5.19615i	−0.100504	−	0.174078i
$892$	−5.50000	+	9.52628i	−0.184154	+	0.318963i
$893$	18.0000	−	31.1769i	0.602347	−	1.04330i
$894$	3.00000	+	5.19615i	0.100335	+	0.173785i
$895$		0			0
$896$	−0.500000	−	2.59808i	−0.0167038	−	0.0867956i
$897$	−12.0000			−0.400668
$898$	1.50000	+	2.59808i	0.0500556	+	0.0866989i
$899$	15.0000	−	25.9808i	0.500278	−	0.866507i
$900$		0			0
$901$	18.0000	+	31.1769i	0.599667	+	1.03865i
$902$	−18.0000			−0.599334
$903$	−16.0000	+	13.8564i	−0.532447	+	0.461112i
$904$	3.00000			0.0997785
$905$		0			0
$906$	8.00000	−	13.8564i	0.265782	−	0.460348i
$907$	−19.0000	+	32.9090i	−0.630885	+	1.09272i	0.356487	+	0.934300i	$0.383975\pi$
$907$	−19.0000	+	32.9090i	−0.630885	+	1.09272i	−0.987371	+	0.158424i	$0.949359\pi$
$908$	9.00000	+	15.5885i	0.298675	+	0.517321i
$909$	12.0000			0.398015
$910$		0			0
$911$	−21.0000			−0.695761			−0.347881	−	0.937539i	$-0.613099\pi$
$911$	−21.0000			−0.695761			−0.347881	+	0.937539i	$0.613099\pi$
$912$	2.00000	+	3.46410i	0.0662266	+	0.114708i
$913$	18.0000	−	31.1769i	0.595713	−	1.03181i
$914$	−1.00000	+	1.73205i	−0.0330771	+	0.0572911i
$915$		0			0
$916$	−22.0000			−0.726900
$917$	9.00000	+	46.7654i	0.297206	+	1.54433i
$918$	−3.00000			−0.0990148
$919$	−5.50000	−	9.52628i	−0.181428	−	0.314243i	0.760939	−	0.648824i	$-0.224739\pi$
$919$	−5.50000	−	9.52628i	−0.181428	−	0.314243i	−0.942367	+	0.334581i	$0.891405\pi$
$920$		0			0
$921$	−10.0000	+	17.3205i	−0.329511	+	0.570730i
$922$	−18.0000	−	31.1769i	−0.592798	−	1.02676i
$923$	36.0000			1.18495
$924$	15.0000	+	5.19615i	0.493464	+	0.170941i
$925$		0			0
$926$	6.50000	+	11.2583i	0.213603	+	0.369972i
$927$	6.50000	−	11.2583i	0.213488	−	0.369772i
$928$	3.00000	−	5.19615i	0.0984798	−	0.170572i
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	0.999959	−	0.00905914i	$-0.00288365\pi$
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	−0.507825	+	0.861460i	$0.669550\pi$
$930$		0			0
$931$	−4.00000	+	27.7128i	−0.131095	+	0.908251i
$932$	6.00000			0.196537
$933$	−10.5000	−	18.1865i	−0.343755	−	0.595400i
$934$	15.0000	−	25.9808i	0.490815	−	0.850117i
$935$		0			0
$936$	2.00000	+	3.46410i	0.0653720	+	0.113228i
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$	20.0000	+	6.92820i	0.653023	+	0.226214i
$939$	17.0000			0.554774
$940$		0			0
$941$	−6.00000	+	10.3923i	−0.195594	+	0.338779i	−0.947095	−	0.320953i	$-0.895997\pi$
$941$	−6.00000	+	10.3923i	−0.195594	+	0.338779i	0.751501	+	0.659732i	$0.229330\pi$
$942$	−7.00000	+	12.1244i	−0.228072	+	0.395033i
$943$	4.50000	+	7.79423i	0.146540	+	0.253815i
$944$	6.00000			0.195283
$945$		0			0
$946$	48.0000			1.56061
$947$	24.0000	+	41.5692i	0.779895	+	1.35082i	0.932002	+	0.362454i	$0.118061\pi$
$947$	24.0000	+	41.5692i	0.779895	+	1.35082i	−0.152106	+	0.988364i	$0.548606\pi$
$948$	3.50000	−	6.06218i	0.113675	−	0.196890i
$949$	28.0000	−	48.4974i	0.908918	−	1.57429i
$950$		0			0
$951$	12.0000			0.389127
$952$	6.00000	−	5.19615i	0.194461	−	0.168408i
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$	−6.00000	−	10.3923i	−0.194257	−	0.336463i
$955$		0			0
$956$	−1.50000	+	2.59808i	−0.0485135	+	0.0840278i
$957$	18.0000	+	31.1769i	0.581857	+	1.00781i
$958$	21.0000			0.678479
$959$	30.0000	−	25.9808i	0.968751	−	0.838963i
$960$		0			0
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$	16.0000	−	27.7128i	0.515861	−	0.893497i
$963$	−3.00000	+	5.19615i	−0.0966736	+	0.167444i
$964$	11.0000	+	19.0526i	0.354286	+	0.613642i
$965$		0			0
$966$	−1.50000	−	7.79423i	−0.0482617	−	0.250775i
$967$	−31.0000			−0.996893			−0.498446	−	0.866921i	$-0.666096\pi$
$967$	−31.0000			−0.996893			−0.498446	+	0.866921i	$0.666096\pi$
$968$	−12.5000	−	21.6506i	−0.401765	−	0.695878i
$969$	−6.00000	+	10.3923i	−0.192748	+	0.333849i
$970$		0			0
$971$	−3.00000	−	5.19615i	−0.0962746	−	0.166752i	0.813865	−	0.581054i	$-0.197359\pi$
$971$	−3.00000	−	5.19615i	−0.0962746	−	0.166752i	−0.910140	+	0.414301i	$0.864026\pi$
$972$	1.00000			0.0320750
$973$	5.00000	+	1.73205i	0.160293	+	0.0555270i
$974$	−25.0000			−0.801052
$975$		0			0
$976$	−1.00000	+	1.73205i	−0.0320092	+	0.0554416i
$977$	−28.5000	+	49.3634i	−0.911796	+	1.57928i	−0.100270	+	0.994960i	$0.531971\pi$
$977$	−28.5000	+	49.3634i	−0.911796	+	1.57928i	−0.811526	+	0.584316i	$0.801363\pi$
$978$	−4.00000	−	6.92820i	−0.127906	−	0.221540i
$979$	18.0000			0.575282
$980$		0			0
$981$	−4.00000			−0.127710
$982$	6.00000	+	10.3923i	0.191468	+	0.331632i
$983$	24.0000	−	41.5692i	0.765481	−	1.32585i	−0.174511	−	0.984655i	$-0.555834\pi$
$983$	24.0000	−	41.5692i	0.765481	−	1.32585i	0.939992	−	0.341197i	$-0.110832\pi$
$984$	1.50000	−	2.59808i	0.0478183	−	0.0828236i
$985$		0			0
$986$	18.0000			0.573237
$987$	22.5000	+	7.79423i	0.716183	+	0.248093i
$988$	16.0000			0.509028
$989$	−12.0000	−	20.7846i	−0.381578	−	0.660912i
$990$		0			0
$991$	21.5000	−	37.2391i	0.682970	−	1.18294i	−0.291100	−	0.956693i	$-0.594021\pi$
$991$	21.5000	−	37.2391i	0.682970	−	1.18294i	0.974070	−	0.226246i	$-0.0726454\pi$
$992$	−2.50000	−	4.33013i	−0.0793751	−	0.137482i
$993$	26.0000			0.825085
$994$	4.50000	+	23.3827i	0.142731	+	0.741654i
$995$		0			0
$996$	3.00000	+	5.19615i	0.0950586	+	0.164646i
$997$	2.00000	−	3.46410i	0.0633406	−	0.109709i	−0.832616	−	0.553851i	$-0.813158\pi$
$997$	2.00000	−	3.46410i	0.0633406	−	0.109709i	0.895957	+	0.444141i	$0.146491\pi$
$998$	−19.0000	+	32.9090i	−0.601434	+	1.04172i
$999$	−4.00000	−	6.92820i	−0.126554	−	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.i.c.151.1	✓	2
5.2	odd	4		1050.2.o.h.949.2		4
5.3	odd	4		1050.2.o.h.949.1		4
5.4	even	2		1050.2.i.q.151.1	yes	2
7.2	even	3	inner	1050.2.i.c.751.1	yes	2
7.3	odd	6		7350.2.a.cg.1.1		1
7.4	even	3		7350.2.a.cy.1.1		1
35.2	odd	12		1050.2.o.h.499.1		4
35.4	even	6		7350.2.a.s.1.1		1
35.9	even	6		1050.2.i.q.751.1	yes	2
35.23	odd	12		1050.2.o.h.499.2		4
35.24	odd	6		7350.2.a.bm.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.i.c.151.1	✓	2	1.1	even	1	trivial
1050.2.i.c.751.1	yes	2	7.2	even	3	inner
1050.2.i.q.151.1	yes	2	5.4	even	2
1050.2.i.q.751.1	yes	2	35.9	even	6
1050.2.o.h.499.1		4	35.2	odd	12
1050.2.o.h.499.2		4	35.23	odd	12
1050.2.o.h.949.1		4	5.3	odd	4
1050.2.o.h.949.2		4	5.2	odd	4
7350.2.a.s.1.1		1	35.4	even	6
7350.2.a.bm.1.1		1	35.24	odd	6
7350.2.a.cg.1.1		1	7.3	odd	6
7350.2.a.cy.1.1		1	7.4	even	3

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.00000 + 5.19615i) q^{11} +(-0.500000 - 0.866025i) q^{12} -4.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} +(-2.00000 + 1.73205i) q^{21} +6.00000 q^{22} +(-1.50000 - 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(-2.00000 + 1.73205i) q^{28} -6.00000 q^{29} +(-2.50000 + 4.33013i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} -3.00000 q^{34} +1.00000 q^{36} +(-4.00000 - 6.92820i) q^{37} +(2.00000 - 3.46410i) q^{38} +(2.00000 - 3.46410i) q^{39} -3.00000 q^{41} +(2.50000 + 0.866025i) q^{42} +8.00000 q^{43} +(-3.00000 - 5.19615i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(-4.50000 - 7.79423i) q^{47} +1.00000 q^{48} +(5.50000 + 4.33013i) q^{49} +(1.50000 + 2.59808i) q^{51} +(2.00000 - 3.46410i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(2.50000 + 0.866025i) q^{56} -4.00000 q^{57} +(3.00000 + 5.19615i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(-1.00000 - 1.73205i) q^{61} +5.00000 q^{62} +(-0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{66} +(-4.00000 + 6.92820i) q^{67} +(1.50000 + 2.59808i) q^{68} +3.00000 q^{69} -9.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-7.00000 + 12.1244i) q^{73} +(-4.00000 + 6.92820i) q^{74} -4.00000 q^{76} +(-12.0000 + 10.3923i) q^{77} -4.00000 q^{78} +(3.50000 + 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.50000 + 2.59808i) q^{82} -6.00000 q^{83} +(-0.500000 - 2.59808i) q^{84} +(-4.00000 - 6.92820i) q^{86} +(3.00000 - 5.19615i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(-1.50000 - 2.59808i) q^{89} +(-10.0000 - 3.46410i) q^{91} +3.00000 q^{92} +(-2.50000 - 4.33013i) q^{93} +(-4.50000 + 7.79423i) q^{94} +(-0.500000 - 0.866025i) q^{96} +17.0000 q^{97} +(1.00000 - 6.92820i) q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} + 2 q^{6} + 5 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - q^3 - q^4 + 2 * q^6 + 5 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} - q^{3} - q^{4} + 2 q^{6} + 5 q^{7} + 2 q^{8} - q^{9} - 6 q^{11} - q^{12} - 8 q^{13} - q^{14} - q^{16} + 3 q^{17} - q^{18} + 4 q^{19} - 4 q^{21} + 12 q^{22} - 3 q^{23} - q^{24} + 4 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 5 q^{31} - q^{32} - 6 q^{33} - 6 q^{34} + 2 q^{36} - 8 q^{37} + 4 q^{38} + 4 q^{39} - 6 q^{41} + 5 q^{42} + 16 q^{43} - 6 q^{44} - 3 q^{46} - 9 q^{47} + 2 q^{48} + 11 q^{49} + 3 q^{51} + 4 q^{52} - 12 q^{53} - q^{54} + 5 q^{56} - 8 q^{57} + 6 q^{58} - 6 q^{59} - 2 q^{61} + 10 q^{62} - q^{63} + 2 q^{64} - 6 q^{66} - 8 q^{67} + 3 q^{68} + 6 q^{69} - 18 q^{71} - q^{72} - 14 q^{73} - 8 q^{74} - 8 q^{76} - 24 q^{77} - 8 q^{78} + 7 q^{79} - q^{81} + 3 q^{82} - 12 q^{83} - q^{84} - 8 q^{86} + 6 q^{87} - 6 q^{88} - 3 q^{89} - 20 q^{91} + 6 q^{92} - 5 q^{93} - 9 q^{94} - q^{96} + 34 q^{97} + 2 q^{98} + 12 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 + 2 * q^6 + 5 * q^7 + 2 * q^8 - q^9 - 6 * q^11 - q^12 - 8 * q^13 - q^14 - q^16 + 3 * q^17 - q^18 + 4 * q^19 - 4 * q^21 + 12 * q^22 - 3 * q^23 - q^24 + 4 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 5 * q^31 - q^32 - 6 * q^33 - 6 * q^34 + 2 * q^36 - 8 * q^37 + 4 * q^38 + 4 * q^39 - 6 * q^41 + 5 * q^42 + 16 * q^43 - 6 * q^44 - 3 * q^46 - 9 * q^47 + 2 * q^48 + 11 * q^49 + 3 * q^51 + 4 * q^52 - 12 * q^53 - q^54 + 5 * q^56 - 8 * q^57 + 6 * q^58 - 6 * q^59 - 2 * q^61 + 10 * q^62 - q^63 + 2 * q^64 - 6 * q^66 - 8 * q^67 + 3 * q^68 + 6 * q^69 - 18 * q^71 - q^72 - 14 * q^73 - 8 * q^74 - 8 * q^76 - 24 * q^77 - 8 * q^78 + 7 * q^79 - q^81 + 3 * q^82 - 12 * q^83 - q^84 - 8 * q^86 + 6 * q^87 - 6 * q^88 - 3 * q^89 - 20 * q^91 + 6 * q^92 - 5 * q^93 - 9 * q^94 - q^96 + 34 * q^97 + 2 * q^98 + 12 * q^99

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