LMFDB - Embedded newform 637.2.g.a.263.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(263,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("637.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			263.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	637.263
Dual form			637.2.g.a.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +3.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-1.50000 + 2.59808i) q^{6} -3.00000 q^{8} +6.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +3.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-1.50000 + 2.59808i) q^{6} -3.00000 q^{8} +6.00000 q^{9} -3.00000 q^{10} -3.00000 q^{11} +(1.50000 + 2.59808i) q^{12} +(1.00000 - 3.46410i) q^{13} +(4.50000 + 7.79423i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(-3.00000 + 5.19615i) q^{18} +1.00000 q^{19} +(-1.50000 + 2.59808i) q^{20} +(1.50000 - 2.59808i) q^{22} -9.00000 q^{24} +(-2.00000 + 3.46410i) q^{25} +(2.50000 + 2.59808i) q^{26} +9.00000 q^{27} +(-3.50000 - 6.06218i) q^{29} -9.00000 q^{30} +(1.50000 - 2.59808i) q^{31} +(-2.50000 - 4.33013i) q^{32} -9.00000 q^{33} +2.00000 q^{34} +(3.00000 + 5.19615i) q^{36} +(-1.00000 + 1.73205i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(3.00000 - 10.3923i) q^{39} +(-4.50000 - 7.79423i) q^{40} +(1.50000 + 2.59808i) q^{41} +(3.50000 - 6.06218i) q^{43} +(-1.50000 - 2.59808i) q^{44} +(9.00000 + 15.5885i) q^{45} +(0.500000 + 0.866025i) q^{47} +(1.50000 - 2.59808i) q^{48} +(-2.00000 - 3.46410i) q^{50} +(-3.00000 - 5.19615i) q^{51} +(3.50000 - 0.866025i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(-4.50000 + 7.79423i) q^{54} +(-4.50000 - 7.79423i) q^{55} +3.00000 q^{57} +7.00000 q^{58} +(-2.00000 - 3.46410i) q^{59} +(-4.50000 + 7.79423i) q^{60} +13.0000 q^{61} +(1.50000 + 2.59808i) q^{62} +7.00000 q^{64} +(10.5000 - 2.59808i) q^{65} +(4.50000 - 7.79423i) q^{66} -3.00000 q^{67} +(1.00000 - 1.73205i) q^{68} +(-6.50000 + 11.2583i) q^{71} -18.0000 q^{72} +(-6.50000 + 11.2583i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-6.00000 + 10.3923i) q^{75} +(0.500000 + 0.866025i) q^{76} +(7.50000 + 7.79423i) q^{78} +(1.50000 + 2.59808i) q^{79} +3.00000 q^{80} +9.00000 q^{81} -3.00000 q^{82} +(3.00000 - 5.19615i) q^{85} +(3.50000 + 6.06218i) q^{86} +(-10.5000 - 18.1865i) q^{87} +9.00000 q^{88} +(3.00000 - 5.19615i) q^{89} -18.0000 q^{90} +(4.50000 - 7.79423i) q^{93} -1.00000 q^{94} +(1.50000 + 2.59808i) q^{95} +(-7.50000 - 12.9904i) q^{96} +(-2.50000 + 4.33013i) q^{97} -18.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 6 q^{3} + q^{4} + 3 q^{5} - 3 q^{6} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 2 * q - q^2 + 6 * q^3 + q^4 + 3 * q^5 - 3 * q^6 - 6 * q^8 + 12 * q^9	$ 2 q - q^{2} + 6 q^{3} + q^{4} + 3 q^{5} - 3 q^{6} - 6 q^{8} + 12 q^{9} - 6 q^{10} - 6 q^{11} + 3 q^{12} + 2 q^{13} + 9 q^{15} + q^{16} - 2 q^{17} - 6 q^{18} + 2 q^{19} - 3 q^{20} + 3 q^{22} - 18 q^{24} - 4 q^{25} + 5 q^{26} + 18 q^{27} - 7 q^{29} - 18 q^{30} + 3 q^{31} - 5 q^{32} - 18 q^{33} + 4 q^{34} + 6 q^{36} - 2 q^{37} - q^{38} + 6 q^{39} - 9 q^{40} + 3 q^{41} + 7 q^{43} - 3 q^{44} + 18 q^{45} + q^{47} + 3 q^{48} - 4 q^{50} - 6 q^{51} + 7 q^{52} - 3 q^{53} - 9 q^{54} - 9 q^{55} + 6 q^{57} + 14 q^{58} - 4 q^{59} - 9 q^{60} + 26 q^{61} + 3 q^{62} + 14 q^{64} + 21 q^{65} + 9 q^{66} - 6 q^{67} + 2 q^{68} - 13 q^{71} - 36 q^{72} - 13 q^{73} - 2 q^{74} - 12 q^{75} + q^{76} + 15 q^{78} + 3 q^{79} + 6 q^{80} + 18 q^{81} - 6 q^{82} + 6 q^{85} + 7 q^{86} - 21 q^{87} + 18 q^{88} + 6 q^{89} - 36 q^{90} + 9 q^{93} - 2 q^{94} + 3 q^{95} - 15 q^{96} - 5 q^{97} - 36 q^{99}+O(q^{100}) $ 2 * q - q^2 + 6 * q^3 + q^4 + 3 * q^5 - 3 * q^6 - 6 * q^8 + 12 * q^9 - 6 * q^10 - 6 * q^11 + 3 * q^12 + 2 * q^13 + 9 * q^15 + q^16 - 2 * q^17 - 6 * q^18 + 2 * q^19 - 3 * q^20 + 3 * q^22 - 18 * q^24 - 4 * q^25 + 5 * q^26 + 18 * q^27 - 7 * q^29 - 18 * q^30 + 3 * q^31 - 5 * q^32 - 18 * q^33 + 4 * q^34 + 6 * q^36 - 2 * q^37 - q^38 + 6 * q^39 - 9 * q^40 + 3 * q^41 + 7 * q^43 - 3 * q^44 + 18 * q^45 + q^47 + 3 * q^48 - 4 * q^50 - 6 * q^51 + 7 * q^52 - 3 * q^53 - 9 * q^54 - 9 * q^55 + 6 * q^57 + 14 * q^58 - 4 * q^59 - 9 * q^60 + 26 * q^61 + 3 * q^62 + 14 * q^64 + 21 * q^65 + 9 * q^66 - 6 * q^67 + 2 * q^68 - 13 * q^71 - 36 * q^72 - 13 * q^73 - 2 * q^74 - 12 * q^75 + q^76 + 15 * q^78 + 3 * q^79 + 6 * q^80 + 18 * q^81 - 6 * q^82 + 6 * q^85 + 7 * q^86 - 21 * q^87 + 18 * q^88 + 6 * q^89 - 36 * q^90 + 9 * q^93 - 2 * q^94 + 3 * q^95 - 15 * q^96 - 5 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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	−0.986869	−	0.161521i	$-0.948360\pi$
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	0.633316	+	0.773893i	$0.281693\pi$
$3$	3.00000			1.73205			0.866025	−	0.500000i	$-0.166667\pi$
$3$	3.00000			1.73205			0.866025	+	0.500000i	$0.166667\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$	−1.50000	+	2.59808i	−0.612372	+	1.06066i
$7$		0			0
$7$		0			0
$8$	−3.00000			−1.06066
$9$	6.00000			2.00000
$10$	−3.00000			−0.948683
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$	1.50000	+	2.59808i	0.433013	+	0.750000i
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$14$		0			0
$15$	4.50000	+	7.79423i	1.16190	+	2.01246i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$	−3.00000	+	5.19615i	−0.707107	+	1.22474i
$19$	1.00000			0.229416			0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000			0.229416			0.114708	+	0.993399i	$0.463407\pi$
$20$	−1.50000	+	2.59808i	−0.335410	+	0.580948i
$21$		0			0
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	−9.00000			−1.83712
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	2.50000	+	2.59808i	0.490290	+	0.509525i
$27$	9.00000			1.73205
$28$		0			0
$29$	−3.50000	−	6.06218i	−0.649934	−	1.12572i	−0.983138	−	0.182864i	$-0.941463\pi$
$29$	−3.50000	−	6.06218i	−0.649934	−	1.12572i	0.333205	−	0.942855i	$-0.391870\pi$
$30$	−9.00000			−1.64317
$31$	1.50000	−	2.59808i	0.269408	−	0.466628i	−0.699301	−	0.714827i	$-0.746505\pi$
$31$	1.50000	−	2.59808i	0.269408	−	0.466628i	0.968709	+	0.248199i	$0.0798387\pi$
$32$	−2.50000	−	4.33013i	−0.441942	−	0.765466i
$33$	−9.00000			−1.56670
$34$	2.00000			0.342997
$35$		0			0
$36$	3.00000	+	5.19615i	0.500000	+	0.866025i
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$	−0.500000	+	0.866025i	−0.0811107	+	0.140488i
$39$	3.00000	−	10.3923i	0.480384	−	1.66410i
$40$	−4.50000	−	7.79423i	−0.711512	−	1.23238i
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	3.50000	−	6.06218i	0.533745	−	0.924473i	−0.465478	−	0.885059i	$-0.654118\pi$
$43$	3.50000	−	6.06218i	0.533745	−	0.924473i	0.999223	−	0.0394140i	$-0.0125491\pi$
$44$	−1.50000	−	2.59808i	−0.226134	−	0.391675i
$45$	9.00000	+	15.5885i	1.34164	+	2.32379i
$46$		0			0
$47$	0.500000	+	0.866025i	0.0729325	+	0.126323i	0.900185	−	0.435507i	$-0.143431\pi$
$47$	0.500000	+	0.866025i	0.0729325	+	0.126323i	−0.827253	+	0.561830i	$0.810098\pi$
$48$	1.50000	−	2.59808i	0.216506	−	0.375000i
$49$		0			0
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$	−3.00000	−	5.19615i	−0.420084	−	0.727607i
$52$	3.50000	−	0.866025i	0.485363	−	0.120096i
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$	−4.50000	+	7.79423i	−0.612372	+	1.06066i
$55$	−4.50000	−	7.79423i	−0.606780	−	1.05097i
$56$		0			0
$57$	3.00000			0.397360
$58$	7.00000			0.919145
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	0.705965	−	0.708247i	$-0.250514\pi$
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	−0.966342	+	0.257260i	$0.917180\pi$
$60$	−4.50000	+	7.79423i	−0.580948	+	1.00623i
$61$	13.0000			1.66448			0.832240	−	0.554416i	$-0.187058\pi$
$61$	13.0000			1.66448			0.832240	+	0.554416i	$0.187058\pi$
$62$	1.50000	+	2.59808i	0.190500	+	0.329956i
$63$		0			0
$64$	7.00000			0.875000
$65$	10.5000	−	2.59808i	1.30236	−	0.322252i
$66$	4.50000	−	7.79423i	0.553912	−	0.959403i
$67$	−3.00000			−0.366508			−0.183254	−	0.983066i	$-0.558663\pi$
$67$	−3.00000			−0.366508			−0.183254	+	0.983066i	$0.558663\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$		0			0
$70$		0			0
$71$	−6.50000	+	11.2583i	−0.771408	+	1.33612i	0.165383	+	0.986229i	$0.447114\pi$
$71$	−6.50000	+	11.2583i	−0.771408	+	1.33612i	−0.936791	+	0.349889i	$0.886219\pi$
$72$	−18.0000			−2.12132
$73$	−6.50000	+	11.2583i	−0.760767	+	1.31769i	0.181688	+	0.983356i	$0.441844\pi$
$73$	−6.50000	+	11.2583i	−0.760767	+	1.31769i	−0.942455	+	0.334332i	$0.891489\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$	−6.00000	+	10.3923i	−0.692820	+	1.20000i
$76$	0.500000	+	0.866025i	0.0573539	+	0.0993399i
$77$		0			0
$78$	7.50000	+	7.79423i	0.849208	+	0.882523i
$79$	1.50000	+	2.59808i	0.168763	+	0.292306i	0.937985	−	0.346675i	$-0.112689\pi$
$79$	1.50000	+	2.59808i	0.168763	+	0.292306i	−0.769222	+	0.638982i	$0.779356\pi$
$80$	3.00000			0.335410
$81$	9.00000			1.00000
$82$	−3.00000			−0.331295
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	3.00000	−	5.19615i	0.325396	−	0.563602i
$86$	3.50000	+	6.06218i	0.377415	+	0.653701i
$87$	−10.5000	−	18.1865i	−1.12572	−	1.94980i
$88$	9.00000			0.959403
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$	−18.0000			−1.89737
$91$		0			0
$92$		0			0
$93$	4.50000	−	7.79423i	0.466628	−	0.808224i
$94$	−1.00000			−0.103142
$95$	1.50000	+	2.59808i	0.153897	+	0.266557i
$96$	−7.50000	−	12.9904i	−0.765466	−	1.32583i
$97$	−2.50000	+	4.33013i	−0.253837	+	0.439658i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$	−2.50000	+	4.33013i	−0.253837	+	0.439658i	0.710742	+	0.703452i	$0.248359\pi$
$98$		0			0
$99$	−18.0000			−1.80907
$100$	−4.00000			−0.400000
$101$	5.00000			0.497519			0.248759	−	0.968565i	$-0.419977\pi$
$101$	5.00000			0.497519			0.248759	+	0.968565i	$0.419977\pi$
$102$	6.00000			0.594089
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	0.962505	−	0.271263i	$-0.0874412\pi$
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	−0.716173	+	0.697923i	$0.754108\pi$
$104$	−3.00000	+	10.3923i	−0.294174	+	1.01905i
$105$		0			0
$106$	−1.50000	−	2.59808i	−0.145693	−	0.252347i
$107$	−4.00000	+	6.92820i	−0.386695	+	0.669775i	−0.992003	−	0.126217i	$-0.959717\pi$
$107$	−4.00000	+	6.92820i	−0.386695	+	0.669775i	0.605308	+	0.795991i	$0.293050\pi$
$108$	4.50000	+	7.79423i	0.433013	+	0.750000i
$109$	−3.50000	+	6.06218i	−0.335239	+	0.580651i	−0.983531	−	0.180741i	$-0.942150\pi$
$109$	−3.50000	+	6.06218i	−0.335239	+	0.580651i	0.648292	+	0.761392i	$0.275484\pi$
$110$	9.00000			0.858116
$111$	−3.00000	+	5.19615i	−0.284747	+	0.493197i
$112$		0			0
$113$	−7.50000	+	12.9904i	−0.705541	+	1.22203i	0.260955	+	0.965351i	$0.415962\pi$
$113$	−7.50000	+	12.9904i	−0.705541	+	1.22203i	−0.966496	+	0.256681i	$0.917371\pi$
$114$	−1.50000	+	2.59808i	−0.140488	+	0.243332i
$115$		0			0
$116$	3.50000	−	6.06218i	0.324967	−	0.562859i
$117$	6.00000	−	20.7846i	0.554700	−	1.92154i
$118$	4.00000			0.368230
$119$		0			0
$120$	−13.5000	−	23.3827i	−1.23238	−	2.13454i
$121$	−2.00000			−0.181818
$122$	−6.50000	+	11.2583i	−0.588482	+	1.01928i
$123$	4.50000	+	7.79423i	0.405751	+	0.702782i
$124$	3.00000			0.269408
$125$	3.00000			0.268328
$126$		0			0
$127$	−5.50000	−	9.52628i	−0.488046	−	0.845321i	0.511859	−	0.859069i	$-0.328957\pi$
$127$	−5.50000	−	9.52628i	−0.488046	−	0.845321i	−0.999905	+	0.0137486i	$0.995624\pi$
$128$	1.50000	−	2.59808i	0.132583	−	0.229640i
$129$	10.5000	−	18.1865i	0.924473	−	1.60123i
$130$	−3.00000	+	10.3923i	−0.263117	+	0.911465i
$131$	2.50000	+	4.33013i	0.218426	+	0.378325i	0.954327	−	0.298764i	$-0.0965744\pi$
$131$	2.50000	+	4.33013i	0.218426	+	0.378325i	−0.735901	+	0.677089i	$0.763241\pi$
$132$	−4.50000	−	7.79423i	−0.391675	−	0.678401i
$133$		0			0
$134$	1.50000	−	2.59808i	0.129580	−	0.224440i
$135$	13.5000	+	23.3827i	1.16190	+	2.01246i
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	−5.00000	−	8.66025i	−0.427179	−	0.739895i	0.569442	−	0.822031i	$-0.307159\pi$
$137$	−5.00000	−	8.66025i	−0.427179	−	0.739895i	−0.996621	+	0.0821359i	$0.973826\pi$
$138$		0			0
$139$	−7.50000	+	12.9904i	−0.636142	+	1.10183i	0.350130	+	0.936701i	$0.386137\pi$
$139$	−7.50000	+	12.9904i	−0.636142	+	1.10183i	−0.986272	+	0.165129i	$0.947196\pi$
$140$		0			0
$141$	1.50000	+	2.59808i	0.126323	+	0.218797i
$142$	−6.50000	−	11.2583i	−0.545468	−	0.944778i
$143$	−3.00000	+	10.3923i	−0.250873	+	0.869048i
$144$	3.00000	−	5.19615i	0.250000	−	0.433013i
$145$	10.5000	−	18.1865i	0.871978	−	1.51031i
$146$	−6.50000	−	11.2583i	−0.537944	−	0.931746i
$147$		0			0
$148$	−2.00000			−0.164399
$149$	15.0000			1.22885			0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000			1.22885			0.614424	+	0.788976i	$0.289388\pi$
$150$	−6.00000	−	10.3923i	−0.489898	−	0.848528i
$151$	10.5000	−	18.1865i	0.854478	−	1.48000i	−0.0226507	−	0.999743i	$-0.507211\pi$
$151$	10.5000	−	18.1865i	0.854478	−	1.48000i	0.877129	−	0.480256i	$-0.159456\pi$
$152$	−3.00000			−0.243332
$153$	−6.00000	−	10.3923i	−0.485071	−	0.840168i
$154$		0			0
$155$	9.00000			0.722897
$156$	10.5000	−	2.59808i	0.840673	−	0.208013i
$157$	9.50000	−	16.4545i	0.758183	−	1.31321i	−0.185594	−	0.982627i	$-0.559421\pi$
$157$	9.50000	−	16.4545i	0.758183	−	1.31321i	0.943777	−	0.330584i	$-0.107246\pi$
$158$	−3.00000			−0.238667
$159$	−4.50000	+	7.79423i	−0.356873	+	0.618123i
$160$	7.50000	−	12.9904i	0.592927	−	1.02698i
$161$		0			0
$162$	−4.50000	+	7.79423i	−0.353553	+	0.612372i
$163$	−1.00000			−0.0783260			−0.0391630	−	0.999233i	$-0.512469\pi$
$163$	−1.00000			−0.0783260			−0.0391630	+	0.999233i	$0.512469\pi$
$164$	−1.50000	+	2.59808i	−0.117130	+	0.202876i
$165$	−13.5000	−	23.3827i	−1.05097	−	1.82034i
$166$		0			0
$167$	−6.50000	−	11.2583i	−0.502985	−	0.871196i	−0.999994	−	0.00345033i	$-0.998902\pi$
$167$	−6.50000	−	11.2583i	−0.502985	−	0.871196i	0.497009	−	0.867745i	$-0.334432\pi$
$168$		0			0
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$	3.00000	+	5.19615i	0.230089	+	0.398527i
$171$	6.00000			0.458831
$172$	7.00000			0.533745
$173$	−19.0000			−1.44454			−0.722272	−	0.691609i	$-0.756902\pi$
$173$	−19.0000			−1.44454			−0.722272	+	0.691609i	$0.756902\pi$
$174$	21.0000			1.59201
$175$		0			0
$176$	−1.50000	+	2.59808i	−0.113067	+	0.195837i
$177$	−6.00000	−	10.3923i	−0.450988	−	0.781133i
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	17.0000			1.27064			0.635320	−	0.772249i	$-0.280868\pi$
$179$	17.0000			1.27064			0.635320	+	0.772249i	$0.280868\pi$
$180$	−9.00000	+	15.5885i	−0.670820	+	1.16190i
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$		0			0
$183$	39.0000			2.88296
$184$		0			0
$185$	−6.00000			−0.441129
$186$	4.50000	+	7.79423i	0.329956	+	0.571501i
$187$	3.00000	+	5.19615i	0.219382	+	0.379980i
$188$	−0.500000	+	0.866025i	−0.0364662	+	0.0631614i
$189$		0			0
$190$	−3.00000			−0.217643
$191$	−17.0000			−1.23008			−0.615038	−	0.788497i	$-0.710860\pi$
$191$	−17.0000			−1.23008			−0.615038	+	0.788497i	$0.710860\pi$
$192$	21.0000			1.51554
$193$	7.00000			0.503871			0.251936	−	0.967744i	$-0.418933\pi$
$193$	7.00000			0.503871			0.251936	+	0.967744i	$0.418933\pi$
$194$	−2.50000	−	4.33013i	−0.179490	−	0.310885i
$195$	31.5000	−	7.79423i	2.25576	−	0.558156i
$196$		0			0
$197$	0.500000	+	0.866025i	0.0356235	+	0.0617018i	0.883287	−	0.468832i	$-0.155325\pi$
$197$	0.500000	+	0.866025i	0.0356235	+	0.0617018i	−0.847664	+	0.530534i	$0.821992\pi$
$198$	9.00000	−	15.5885i	0.639602	−	1.10782i
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	−0.965272	−	0.261245i	$-0.915867\pi$
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	0.256391	−	0.966573i	$-0.417466\pi$
$200$	6.00000	−	10.3923i	0.424264	−	0.734847i
$201$	−9.00000			−0.634811
$202$	−2.50000	+	4.33013i	−0.175899	+	0.304667i
$203$		0			0
$204$	3.00000	−	5.19615i	0.210042	−	0.363803i
$205$	−4.50000	+	7.79423i	−0.314294	+	0.544373i
$206$	−5.00000			−0.348367
$207$		0			0
$208$	−2.50000	−	2.59808i	−0.173344	−	0.180144i
$209$	−3.00000			−0.207514
$210$		0			0
$211$	−3.50000	−	6.06218i	−0.240950	−	0.417338i	0.720035	−	0.693938i	$-0.244126\pi$
$211$	−3.50000	−	6.06218i	−0.240950	−	0.417338i	−0.960985	+	0.276600i	$0.910792\pi$
$212$	−3.00000			−0.206041
$213$	−19.5000	+	33.7750i	−1.33612	+	2.31422i
$214$	−4.00000	−	6.92820i	−0.273434	−	0.473602i
$215$	21.0000			1.43219
$216$	−27.0000			−1.83712
$217$		0			0
$218$	−3.50000	−	6.06218i	−0.237050	−	0.410582i
$219$	−19.5000	+	33.7750i	−1.31769	+	2.28230i
$220$	4.50000	−	7.79423i	0.303390	−	0.525487i
$221$	−7.00000	+	1.73205i	−0.470871	+	0.116510i
$222$	−3.00000	−	5.19615i	−0.201347	−	0.348743i
$223$	−4.50000	−	7.79423i	−0.301342	−	0.521940i	0.675098	−	0.737728i	$-0.264101\pi$
$223$	−4.50000	−	7.79423i	−0.301342	−	0.521940i	−0.976440	+	0.215788i	$0.930768\pi$
$224$		0			0
$225$	−12.0000	+	20.7846i	−0.800000	+	1.38564i
$226$	−7.50000	−	12.9904i	−0.498893	−	0.864107i
$227$	−2.00000	−	3.46410i	−0.132745	−	0.229920i	0.791989	−	0.610535i	$-0.209046\pi$
$227$	−2.00000	−	3.46410i	−0.132745	−	0.229920i	−0.924734	+	0.380615i	$0.875712\pi$
$228$	1.50000	+	2.59808i	0.0993399	+	0.172062i
$229$	−6.50000	−	11.2583i	−0.429532	−	0.743971i	0.567300	−	0.823511i	$-0.307988\pi$
$229$	−6.50000	−	11.2583i	−0.429532	−	0.743971i	−0.996832	+	0.0795401i	$0.974655\pi$
$230$		0			0
$231$		0			0
$232$	10.5000	+	18.1865i	0.689359	+	1.19400i
$233$	10.5000	+	18.1865i	0.687878	+	1.19144i	0.972523	+	0.232806i	$0.0747909\pi$
$233$	10.5000	+	18.1865i	0.687878	+	1.19144i	−0.284645	+	0.958633i	$0.591876\pi$
$234$	15.0000	+	15.5885i	0.980581	+	1.01905i
$235$	−1.50000	+	2.59808i	−0.0978492	+	0.169480i
$236$	2.00000	−	3.46410i	0.130189	−	0.225494i
$237$	4.50000	+	7.79423i	0.292306	+	0.506290i
$238$		0			0
$239$	−4.00000			−0.258738			−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000			−0.258738			−0.129369	+	0.991596i	$0.541295\pi$
$240$	9.00000			0.580948
$241$	−13.0000	−	22.5167i	−0.837404	−	1.45043i	−0.892058	−	0.451920i	$-0.850739\pi$
$241$	−13.0000	−	22.5167i	−0.837404	−	1.45043i	0.0546547	−	0.998505i	$-0.482594\pi$
$242$	1.00000	−	1.73205i	0.0642824	−	0.111340i
$243$		0			0
$244$	6.50000	+	11.2583i	0.416120	+	0.720741i
$245$		0			0
$246$	−9.00000			−0.573819
$247$	1.00000	−	3.46410i	0.0636285	−	0.220416i
$248$	−4.50000	+	7.79423i	−0.285750	+	0.494934i
$249$		0			0
$250$	−1.50000	+	2.59808i	−0.0948683	+	0.164317i
$251$	−11.5000	+	19.9186i	−0.725874	+	1.25725i	0.232740	+	0.972539i	$0.425231\pi$
$251$	−11.5000	+	19.9186i	−0.725874	+	1.25725i	−0.958613	+	0.284711i	$0.908102\pi$
$252$		0			0
$253$		0			0
$254$	11.0000			0.690201
$255$	9.00000	−	15.5885i	0.563602	−	0.976187i
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	−0.895528	−	0.445005i	$-0.853202\pi$
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	0.833150	+	0.553047i	$0.186535\pi$
$258$	10.5000	+	18.1865i	0.653701	+	1.13224i
$259$		0			0
$260$	7.50000	+	7.79423i	0.465130	+	0.483378i
$261$	−21.0000	−	36.3731i	−1.29987	−	2.25144i
$262$	−5.00000			−0.308901
$263$	−27.0000			−1.66489			−0.832446	−	0.554107i	$-0.813060\pi$
$263$	−27.0000			−1.66489			−0.832446	+	0.554107i	$0.813060\pi$
$264$	27.0000			1.66174
$265$	−9.00000			−0.552866
$266$		0			0
$267$	9.00000	−	15.5885i	0.550791	−	0.953998i
$268$	−1.50000	−	2.59808i	−0.0916271	−	0.158703i
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	0.998361	+	0.0572259i	$0.0182255\pi$
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	−0.449622	+	0.893219i	$0.648441\pi$
$270$	−27.0000			−1.64317
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	−0.999870	−	0.0161307i	$-0.994865\pi$
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	0.513905	+	0.857847i	$0.328199\pi$
$272$	−2.00000			−0.121268
$273$		0			0
$274$	10.0000			0.604122
$275$	6.00000	−	10.3923i	0.361814	−	0.626680i
$276$		0			0
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	−0.980373	−	0.197153i	$-0.936830\pi$
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	0.319447	−	0.947604i	$-0.396503\pi$
$278$	−7.50000	−	12.9904i	−0.449820	−	0.779111i
$279$	9.00000	−	15.5885i	0.538816	−	0.933257i
$280$		0			0
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$	−3.00000			−0.178647
$283$	−1.00000			−0.0594438			−0.0297219	−	0.999558i	$-0.509462\pi$
$283$	−1.00000			−0.0594438			−0.0297219	+	0.999558i	$0.509462\pi$
$284$	−13.0000			−0.771408
$285$	4.50000	+	7.79423i	0.266557	+	0.461690i
$286$	−7.50000	−	7.79423i	−0.443484	−	0.460882i
$287$		0			0
$288$	−15.0000	−	25.9808i	−0.883883	−	1.53093i
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	10.5000	+	18.1865i	0.616581	+	1.06795i
$291$	−7.50000	+	12.9904i	−0.439658	+	0.761510i
$292$	−13.0000			−0.760767
$293$	5.50000	−	9.52628i	0.321313	−	0.556531i	−0.659446	−	0.751752i	$-0.729209\pi$
$293$	5.50000	−	9.52628i	0.321313	−	0.556531i	0.980759	+	0.195221i	$0.0625424\pi$
$294$		0			0
$295$	6.00000	−	10.3923i	0.349334	−	0.605063i
$296$	3.00000	−	5.19615i	0.174371	−	0.302020i
$297$	−27.0000			−1.56670
$298$	−7.50000	+	12.9904i	−0.434463	+	0.752513i
$299$		0			0
$300$	−12.0000			−0.692820
$301$		0			0
$302$	10.5000	+	18.1865i	0.604207	+	1.04652i
$303$	15.0000			0.861727
$304$	0.500000	−	0.866025i	0.0286770	−	0.0496700i
$305$	19.5000	+	33.7750i	1.11657	+	1.93395i
$306$	12.0000			0.685994
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		0			0
$309$	7.50000	+	12.9904i	0.426660	+	0.738997i
$310$	−4.50000	+	7.79423i	−0.255583	+	0.442682i
$311$	−4.50000	+	7.79423i	−0.255172	+	0.441970i	−0.964942	−	0.262463i	$-0.915465\pi$
$311$	−4.50000	+	7.79423i	−0.255172	+	0.441970i	0.709771	+	0.704433i	$0.248799\pi$
$312$	−9.00000	+	31.1769i	−0.509525	+	1.76505i
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	0.999065	+	0.0432311i	$0.0137652\pi$
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	−0.462093	+	0.886831i	$0.652902\pi$
$314$	9.50000	+	16.4545i	0.536116	+	0.928580i
$315$		0			0
$316$	−1.50000	+	2.59808i	−0.0843816	+	0.146153i
$317$	4.50000	+	7.79423i	0.252745	+	0.437767i	0.964281	−	0.264883i	$-0.0853332\pi$
$317$	4.50000	+	7.79423i	0.252745	+	0.437767i	−0.711535	+	0.702650i	$0.752000\pi$
$318$	−4.50000	−	7.79423i	−0.252347	−	0.437079i
$319$	10.5000	+	18.1865i	0.587887	+	1.01825i
$320$	10.5000	+	18.1865i	0.586968	+	1.01666i
$321$	−12.0000	+	20.7846i	−0.669775	+	1.16008i
$322$		0			0
$323$	−1.00000	−	1.73205i	−0.0556415	−	0.0963739i
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$	10.0000	+	10.3923i	0.554700	+	0.576461i
$326$	0.500000	−	0.866025i	0.0276924	−	0.0479647i
$327$	−10.5000	+	18.1865i	−0.580651	+	1.00572i
$328$	−4.50000	−	7.79423i	−0.248471	−	0.430364i
$329$		0			0
$330$	27.0000			1.48630
$331$	−29.0000			−1.59398			−0.796992	−	0.603990i	$-0.793577\pi$
$331$	−29.0000			−1.59398			−0.796992	+	0.603990i	$0.793577\pi$
$332$		0			0
$333$	−6.00000	+	10.3923i	−0.328798	+	0.569495i
$334$	13.0000			0.711328
$335$	−4.50000	−	7.79423i	−0.245861	−	0.425844i
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	11.5000	−	6.06218i	0.625518	−	0.329739i
$339$	−22.5000	+	38.9711i	−1.22203	+	2.11662i
$340$	6.00000			0.325396
$341$	−4.50000	+	7.79423i	−0.243689	+	0.422081i
$342$	−3.00000	+	5.19615i	−0.162221	+	0.280976i
$343$		0			0
$344$	−10.5000	+	18.1865i	−0.566122	+	0.980552i
$345$		0			0
$346$	9.50000	−	16.4545i	0.510723	−	0.884598i
$347$	4.00000	+	6.92820i	0.214731	+	0.371925i	0.953189	−	0.302374i	$-0.0977791\pi$
$347$	4.00000	+	6.92820i	0.214731	+	0.371925i	−0.738458	+	0.674299i	$0.764446\pi$
$348$	10.5000	−	18.1865i	0.562859	−	0.974901i
$349$	11.5000	+	19.9186i	0.615581	+	1.06622i	0.990282	+	0.139072i	$0.0444119\pi$
$349$	11.5000	+	19.9186i	0.615581	+	1.06622i	−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$	9.00000	−	31.1769i	0.480384	−	1.66410i
$352$	7.50000	+	12.9904i	0.399751	+	0.692390i
$353$	25.0000			1.33062			0.665308	−	0.746569i	$-0.268300\pi$
$353$	25.0000			1.33062			0.665308	+	0.746569i	$0.268300\pi$
$354$	12.0000			0.637793
$355$	−39.0000			−2.06991
$356$	6.00000			0.317999
$357$		0			0
$358$	−8.50000	+	14.7224i	−0.449239	+	0.778105i
$359$	−8.50000	−	14.7224i	−0.448613	−	0.777020i	0.549683	−	0.835373i	$-0.314748\pi$
$359$	−8.50000	−	14.7224i	−0.448613	−	0.777020i	−0.998296	+	0.0583530i	$0.981415\pi$
$360$	−27.0000	−	46.7654i	−1.42302	−	2.46475i
$361$	−18.0000			−0.947368
$362$	−11.0000	+	19.0526i	−0.578147	+	1.00138i
$363$	−6.00000			−0.314918
$364$		0			0
$365$	−39.0000			−2.04135
$366$	−19.5000	+	33.7750i	−1.01928	+	1.76545i
$367$	31.0000			1.61819			0.809093	−	0.587680i	$-0.199959\pi$
$367$	31.0000			1.61819			0.809093	+	0.587680i	$0.199959\pi$
$368$		0			0
$369$	9.00000	+	15.5885i	0.468521	+	0.811503i
$370$	3.00000	−	5.19615i	0.155963	−	0.270135i
$371$		0			0
$372$	9.00000			0.466628
$373$	−9.00000			−0.466002			−0.233001	−	0.972476i	$-0.574855\pi$
$373$	−9.00000			−0.466002			−0.233001	+	0.972476i	$0.574855\pi$
$374$	−6.00000			−0.310253
$375$	9.00000			0.464758
$376$	−1.50000	−	2.59808i	−0.0773566	−	0.133986i
$377$	−24.5000	+	6.06218i	−1.26181	+	0.312218i
$378$		0			0
$379$	16.5000	+	28.5788i	0.847548	+	1.46800i	0.883390	+	0.468639i	$0.155255\pi$
$379$	16.5000	+	28.5788i	0.847548	+	1.46800i	−0.0358418	+	0.999357i	$0.511411\pi$
$380$	−1.50000	+	2.59808i	−0.0769484	+	0.133278i
$381$	−16.5000	−	28.5788i	−0.845321	−	1.46414i
$382$	8.50000	−	14.7224i	0.434898	−	0.753265i
$383$	21.0000			1.07305			0.536525	−	0.843884i	$-0.319737\pi$
$383$	21.0000			1.07305			0.536525	+	0.843884i	$0.319737\pi$
$384$	4.50000	−	7.79423i	0.229640	−	0.397748i
$385$		0			0
$386$	−3.50000	+	6.06218i	−0.178145	+	0.308557i
$387$	21.0000	−	36.3731i	1.06749	−	1.84895i
$388$	−5.00000			−0.253837
$389$	16.5000	−	28.5788i	0.836583	−	1.44900i	−0.0561516	−	0.998422i	$-0.517883\pi$
$389$	16.5000	−	28.5788i	0.836583	−	1.44900i	0.892735	−	0.450582i	$-0.148784\pi$
$390$	−9.00000	+	31.1769i	−0.455733	+	1.57870i
$391$		0			0
$392$		0			0
$393$	7.50000	+	12.9904i	0.378325	+	0.655278i
$394$	−1.00000			−0.0503793
$395$	−4.50000	+	7.79423i	−0.226420	+	0.392170i
$396$	−9.00000	−	15.5885i	−0.452267	−	0.783349i
$397$	1.00000			0.0501886			0.0250943	−	0.999685i	$-0.492011\pi$
$397$	1.00000			0.0501886			0.0250943	+	0.999685i	$0.492011\pi$
$398$	20.0000			1.00251
$399$		0			0
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	1.00000	−	1.73205i	0.0499376	−	0.0864945i	−0.839976	−	0.542623i	$-0.817431\pi$
$401$	1.00000	−	1.73205i	0.0499376	−	0.0864945i	0.889914	+	0.456129i	$0.150764\pi$
$402$	4.50000	−	7.79423i	0.224440	−	0.388741i
$403$	−7.50000	−	7.79423i	−0.373602	−	0.388258i
$404$	2.50000	+	4.33013i	0.124380	+	0.215432i
$405$	13.5000	+	23.3827i	0.670820	+	1.16190i
$406$		0			0
$407$	3.00000	−	5.19615i	0.148704	−	0.257564i
$408$	9.00000	+	15.5885i	0.445566	+	0.771744i
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	0.985558	−	0.169338i	$-0.0541630\pi$
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	−0.639430	+	0.768849i	$0.720830\pi$
$410$	−4.50000	−	7.79423i	−0.222239	−	0.384930i
$411$	−15.0000	−	25.9808i	−0.739895	−	1.28154i
$412$	−2.50000	+	4.33013i	−0.123166	+	0.213330i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−17.5000	+	4.33013i	−0.858008	+	0.212302i
$417$	−22.5000	+	38.9711i	−1.10183	+	1.90843i
$418$	1.50000	−	2.59808i	0.0733674	−	0.127076i
$419$	−12.5000	−	21.6506i	−0.610665	−	1.05770i	−0.991129	−	0.132907i	$-0.957569\pi$
$419$	−12.5000	−	21.6506i	−0.610665	−	1.05770i	0.380464	−	0.924796i	$-0.375764\pi$
$420$		0			0
$421$	18.0000			0.877266			0.438633	−	0.898666i	$-0.355463\pi$
$421$	18.0000			0.877266			0.438633	+	0.898666i	$0.355463\pi$
$422$	7.00000			0.340755
$423$	3.00000	+	5.19615i	0.145865	+	0.252646i
$424$	4.50000	−	7.79423i	0.218539	−	0.378521i
$425$	8.00000			0.388057
$426$	−19.5000	−	33.7750i	−0.944778	−	1.63640i
$427$		0			0
$428$	−8.00000			−0.386695
$429$	−9.00000	+	31.1769i	−0.434524	+	1.50524i
$430$	−10.5000	+	18.1865i	−0.506355	+	0.877033i
$431$	9.00000			0.433515			0.216757	−	0.976226i	$-0.430452\pi$
$431$	9.00000			0.433515			0.216757	+	0.976226i	$0.430452\pi$
$432$	4.50000	−	7.79423i	0.216506	−	0.375000i
$433$	13.5000	−	23.3827i	0.648769	−	1.12370i	−0.334649	−	0.942343i	$-0.608618\pi$
$433$	13.5000	−	23.3827i	0.648769	−	1.12370i	0.983417	−	0.181357i	$-0.0580490\pi$
$434$		0			0
$435$	31.5000	−	54.5596i	1.51031	−	2.61593i
$436$	−7.00000			−0.335239
$437$		0			0
$438$	−19.5000	−	33.7750i	−0.931746	−	1.61383i
$439$	−8.00000	+	13.8564i	−0.381819	+	0.661330i	−0.991322	−	0.131453i	$-0.958036\pi$
$439$	−8.00000	+	13.8564i	−0.381819	+	0.661330i	0.609503	+	0.792784i	$0.291369\pi$
$440$	13.5000	+	23.3827i	0.643587	+	1.11473i
$441$		0			0
$442$	2.00000	−	6.92820i	0.0951303	−	0.329541i
$443$	5.50000	+	9.52628i	0.261313	+	0.452607i	0.966591	−	0.256323i	$-0.0825112\pi$
$443$	5.50000	+	9.52628i	0.261313	+	0.452607i	−0.705278	+	0.708931i	$0.749178\pi$
$444$	−6.00000			−0.284747
$445$	18.0000			0.853282
$446$	9.00000			0.426162
$447$	45.0000			2.12843
$448$		0			0
$449$	−7.50000	+	12.9904i	−0.353947	+	0.613054i	−0.986937	−	0.161106i	$-0.948494\pi$
$449$	−7.50000	+	12.9904i	−0.353947	+	0.613054i	0.632990	+	0.774160i	$0.281827\pi$
$450$	−12.0000	−	20.7846i	−0.565685	−	0.979796i
$451$	−4.50000	−	7.79423i	−0.211897	−	0.367016i
$452$	−15.0000			−0.705541
$453$	31.5000	−	54.5596i	1.48000	−	2.56343i
$454$	4.00000			0.187729
$455$		0			0
$456$	−9.00000			−0.421464
$457$	9.00000	−	15.5885i	0.421002	−	0.729197i	−0.575036	−	0.818128i	$-0.695012\pi$
$457$	9.00000	−	15.5885i	0.421002	−	0.729197i	0.996038	+	0.0889312i	$0.0283451\pi$
$458$	13.0000			0.607450
$459$	−9.00000	−	15.5885i	−0.420084	−	0.727607i
$460$		0			0
$461$	17.5000	−	30.3109i	0.815056	−	1.41172i	−0.0942312	−	0.995550i	$-0.530039\pi$
$461$	17.5000	−	30.3109i	0.815056	−	1.41172i	0.909288	−	0.416169i	$-0.136627\pi$
$462$		0			0
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$	−7.00000			−0.324967
$465$	27.0000			1.25210
$466$	−21.0000			−0.972806
$467$	−3.50000	−	6.06218i	−0.161961	−	0.280524i	0.773611	−	0.633661i	$-0.218448\pi$
$467$	−3.50000	−	6.06218i	−0.161961	−	0.280524i	−0.935572	+	0.353137i	$0.885115\pi$
$468$	21.0000	−	5.19615i	0.970725	−	0.240192i
$469$		0			0
$470$	−1.50000	−	2.59808i	−0.0691898	−	0.119840i
$471$	28.5000	−	49.3634i	1.31321	−	2.27455i
$472$	6.00000	+	10.3923i	0.276172	+	0.478345i
$473$	−10.5000	+	18.1865i	−0.482791	+	0.836218i
$474$	−9.00000			−0.413384
$475$	−2.00000	+	3.46410i	−0.0917663	+	0.158944i
$476$		0			0
$477$	−9.00000	+	15.5885i	−0.412082	+	0.713746i
$478$	2.00000	−	3.46410i	0.0914779	−	0.158444i
$479$	35.0000			1.59919			0.799595	−	0.600539i	$-0.205047\pi$
$479$	35.0000			1.59919			0.799595	+	0.600539i	$0.205047\pi$
$480$	22.5000	−	38.9711i	1.02698	−	1.77878i
$481$	5.00000	+	5.19615i	0.227980	+	0.236924i
$482$	26.0000			1.18427
$483$		0			0
$484$	−1.00000	−	1.73205i	−0.0454545	−	0.0787296i
$485$	−15.0000			−0.681115
$486$		0			0
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	0.625859	−	0.779936i	$-0.284748\pi$
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	−0.988374	+	0.152042i	$0.951415\pi$
$488$	−39.0000			−1.76545
$489$	−3.00000			−0.135665
$490$		0			0
$491$	−7.50000	−	12.9904i	−0.338470	−	0.586248i	0.645675	−	0.763612i	$-0.276576\pi$
$491$	−7.50000	−	12.9904i	−0.338470	−	0.586248i	−0.984145	+	0.177365i	$0.943243\pi$
$492$	−4.50000	+	7.79423i	−0.202876	+	0.351391i
$493$	−7.00000	+	12.1244i	−0.315264	+	0.546054i
$494$	2.50000	+	2.59808i	0.112480	+	0.116893i
$495$	−27.0000	−	46.7654i	−1.21356	−	2.10195i
$496$	−1.50000	−	2.59808i	−0.0673520	−	0.116657i
$497$		0			0
$498$		0			0
$499$	15.5000	+	26.8468i	0.693875	+	1.20183i	0.970558	+	0.240866i	$0.0774314\pi$
$499$	15.5000	+	26.8468i	0.693875	+	1.20183i	−0.276683	+	0.960961i	$0.589235\pi$
$500$	1.50000	+	2.59808i	0.0670820	+	0.116190i
$501$	−19.5000	−	33.7750i	−0.871196	−	1.50896i
$502$	−11.5000	−	19.9186i	−0.513270	−	0.889010i
$503$	−15.5000	+	26.8468i	−0.691111	+	1.19704i	0.280363	+	0.959894i	$0.409545\pi$
$503$	−15.5000	+	26.8468i	−0.691111	+	1.19704i	−0.971474	+	0.237145i	$0.923788\pi$
$504$		0			0
$505$	7.50000	+	12.9904i	0.333746	+	0.578064i
$506$		0			0
$507$	−33.0000	−	20.7846i	−1.46558	−	0.923077i
$508$	5.50000	−	9.52628i	0.244023	−	0.422660i
$509$	−17.0000	+	29.4449i	−0.753512	+	1.30512i	0.192599	+	0.981278i	$0.438308\pi$
$509$	−17.0000	+	29.4449i	−0.753512	+	1.30512i	−0.946111	+	0.323843i	$0.895025\pi$
$510$	9.00000	+	15.5885i	0.398527	+	0.690268i
$511$		0			0
$512$	−11.0000			−0.486136
$513$	9.00000			0.397360
$514$	−1.00000	−	1.73205i	−0.0441081	−	0.0763975i
$515$	−7.50000	+	12.9904i	−0.330489	+	0.572425i
$516$	21.0000			0.924473
$517$	−1.50000	−	2.59808i	−0.0659699	−	0.114263i
$518$		0			0
$519$	−57.0000			−2.50202
$520$	−31.5000	+	7.79423i	−1.38137	+	0.341800i
$521$	−8.50000	+	14.7224i	−0.372392	+	0.645001i	−0.989933	−	0.141537i	$-0.954796\pi$
$521$	−8.50000	+	14.7224i	−0.372392	+	0.645001i	0.617541	+	0.786539i	$0.288129\pi$
$522$	42.0000			1.83829
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	−0.818980	−	0.573822i	$-0.805460\pi$
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	0.906434	+	0.422347i	$0.138794\pi$
$524$	−2.50000	+	4.33013i	−0.109213	+	0.189162i
$525$		0			0
$526$	13.5000	−	23.3827i	0.588628	−	1.01953i
$527$	−6.00000			−0.261364
$528$	−4.50000	+	7.79423i	−0.195837	+	0.339200i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	4.50000	−	7.79423i	0.195468	−	0.338560i
$531$	−12.0000	−	20.7846i	−0.520756	−	0.901975i
$532$		0			0
$533$	10.5000	−	2.59808i	0.454805	−	0.112535i
$534$	9.00000	+	15.5885i	0.389468	+	0.674579i
$535$	−24.0000			−1.03761
$536$	9.00000			0.388741
$537$	51.0000			2.20081
$538$	−18.0000			−0.776035
$539$		0			0
$540$	−13.5000	+	23.3827i	−0.580948	+	1.00623i
$541$	18.5000	+	32.0429i	0.795377	+	1.37763i	0.922599	+	0.385759i	$0.126061\pi$
$541$	18.5000	+	32.0429i	0.795377	+	1.37763i	−0.127222	+	0.991874i	$0.540606\pi$
$542$	−8.00000	−	13.8564i	−0.343629	−	0.595184i
$543$	66.0000			2.83233
$544$	−5.00000	+	8.66025i	−0.214373	+	0.371305i
$545$	−21.0000			−0.899541
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	5.00000	−	8.66025i	0.213589	−	0.369948i
$549$	78.0000			3.32896
$550$	6.00000	+	10.3923i	0.255841	+	0.443129i
$551$	−3.50000	−	6.06218i	−0.149105	−	0.258257i
$552$		0			0
$553$		0			0
$554$	22.0000			0.934690
$555$	−18.0000			−0.764057
$556$	−15.0000			−0.636142
$557$	3.00000			0.127114			0.0635570	−	0.997978i	$-0.479756\pi$
$557$	3.00000			0.127114			0.0635570	+	0.997978i	$0.479756\pi$
$558$	9.00000	+	15.5885i	0.381000	+	0.659912i
$559$	−17.5000	−	18.1865i	−0.740171	−	0.769208i
$560$		0			0
$561$	9.00000	+	15.5885i	0.379980	+	0.658145i
$562$	9.00000	−	15.5885i	0.379642	−	0.657559i
$563$	2.00000	+	3.46410i	0.0842900	+	0.145994i	0.905088	−	0.425223i	$-0.139804\pi$
$563$	2.00000	+	3.46410i	0.0842900	+	0.145994i	−0.820798	+	0.571218i	$0.806471\pi$
$564$	−1.50000	+	2.59808i	−0.0631614	+	0.109399i
$565$	−45.0000			−1.89316
$566$	0.500000	−	0.866025i	0.0210166	−	0.0364018i
$567$		0			0
$568$	19.5000	−	33.7750i	0.818202	−	1.41717i
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	−0.951592	−	0.307364i	$-0.900553\pi$
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	0.741981	+	0.670421i	$0.233886\pi$
$570$	−9.00000			−0.376969
$571$	−21.5000	+	37.2391i	−0.899747	+	1.55841i	−0.0719297	+	0.997410i	$0.522916\pi$
$571$	−21.5000	+	37.2391i	−0.899747	+	1.55841i	−0.827817	+	0.560998i	$0.810418\pi$
$572$	−10.5000	+	2.59808i	−0.439027	+	0.108631i
$573$	−51.0000			−2.13056
$574$		0			0
$575$		0			0
$576$	42.0000			1.75000
$577$	−0.500000	+	0.866025i	−0.0208153	+	0.0360531i	−0.876245	−	0.481865i	$-0.839960\pi$
$577$	−0.500000	+	0.866025i	−0.0208153	+	0.0360531i	0.855430	+	0.517918i	$0.173293\pi$
$578$	6.50000	+	11.2583i	0.270364	+	0.468285i
$579$	21.0000			0.872730
$580$	21.0000			0.871978
$581$		0			0
$582$	−7.50000	−	12.9904i	−0.310885	−	0.538469i
$583$	4.50000	−	7.79423i	0.186371	−	0.322804i
$584$	19.5000	−	33.7750i	0.806916	−	1.39762i
$585$	63.0000	−	15.5885i	2.60473	−	0.644503i
$586$	5.50000	+	9.52628i	0.227203	+	0.393527i
$587$	−16.5000	−	28.5788i	−0.681028	−	1.17957i	−0.974668	−	0.223659i	$-0.928200\pi$
$587$	−16.5000	−	28.5788i	−0.681028	−	1.17957i	0.293640	−	0.955916i	$-0.405133\pi$
$588$		0			0
$589$	1.50000	−	2.59808i	0.0618064	−	0.107052i
$590$	6.00000	+	10.3923i	0.247016	+	0.427844i
$591$	1.50000	+	2.59808i	0.0617018	+	0.106871i
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	13.5000	+	23.3827i	0.554379	+	0.960212i	0.997952	+	0.0639736i	$0.0203773\pi$
$593$	13.5000	+	23.3827i	0.554379	+	0.960212i	−0.443573	+	0.896238i	$0.646289\pi$
$594$	13.5000	−	23.3827i	0.553912	−	0.959403i
$595$		0			0
$596$	7.50000	+	12.9904i	0.307212	+	0.532107i
$597$	−30.0000	−	51.9615i	−1.22782	−	2.12664i
$598$		0			0
$599$	12.5000	−	21.6506i	0.510736	−	0.884621i	−0.489186	−	0.872179i	$-0.662706\pi$
$599$	12.5000	−	21.6506i	0.510736	−	0.884621i	0.999923	−	0.0124417i	$-0.00396043\pi$
$600$	18.0000	−	31.1769i	0.734847	−	1.27279i
$601$	17.5000	+	30.3109i	0.713840	+	1.23641i	0.963405	+	0.268049i	$0.0863789\pi$
$601$	17.5000	+	30.3109i	0.713840	+	1.23641i	−0.249565	+	0.968358i	$0.580288\pi$
$602$		0			0
$603$	−18.0000			−0.733017
$604$	21.0000			0.854478
$605$	−3.00000	−	5.19615i	−0.121967	−	0.211254i
$606$	−7.50000	+	12.9904i	−0.304667	+	0.527698i
$607$	−11.0000			−0.446476			−0.223238	−	0.974764i	$-0.571663\pi$
$607$	−11.0000			−0.446476			−0.223238	+	0.974764i	$0.571663\pi$
$608$	−2.50000	−	4.33013i	−0.101388	−	0.175610i
$609$		0			0
$610$	−39.0000			−1.57906
$611$	3.50000	−	0.866025i	0.141595	−	0.0350356i
$612$	6.00000	−	10.3923i	0.242536	−	0.420084i
$613$	−25.0000			−1.00974			−0.504870	−	0.863195i	$-0.668460\pi$
$613$	−25.0000			−1.00974			−0.504870	+	0.863195i	$0.668460\pi$
$614$	6.00000	−	10.3923i	0.242140	−	0.419399i
$615$	−13.5000	+	23.3827i	−0.544373	+	0.942881i
$616$		0			0
$617$	16.5000	−	28.5788i	0.664265	−	1.15054i	−0.315219	−	0.949019i	$-0.602078\pi$
$617$	16.5000	−	28.5788i	0.664265	−	1.15054i	0.979484	−	0.201522i	$-0.0645887\pi$
$618$	−15.0000			−0.603388
$619$	5.50000	−	9.52628i	0.221064	−	0.382893i	−0.734068	−	0.679076i	$-0.762380\pi$
$619$	5.50000	−	9.52628i	0.221064	−	0.382893i	0.955131	+	0.296183i	$0.0957138\pi$
$620$	4.50000	+	7.79423i	0.180724	+	0.313024i
$621$		0			0
$622$	−4.50000	−	7.79423i	−0.180434	−	0.312520i
$623$		0			0
$624$	−7.50000	−	7.79423i	−0.300240	−	0.312019i
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−19.0000			−0.759393
$627$	−9.00000			−0.359425
$628$	19.0000			0.758183
$629$	4.00000			0.159490
$630$		0			0
$631$	−12.5000	+	21.6506i	−0.497617	+	0.861898i	−0.999996	−	0.00274930i	$-0.999125\pi$
$631$	−12.5000	+	21.6506i	−0.497617	+	0.861898i	0.502379	+	0.864647i	$0.332458\pi$
$632$	−4.50000	−	7.79423i	−0.179000	−	0.310038i
$633$	−10.5000	−	18.1865i	−0.417338	−	0.722850i
$634$	−9.00000			−0.357436
$635$	16.5000	−	28.5788i	0.654783	−	1.13412i
$636$	−9.00000			−0.356873
$637$		0			0
$638$	−21.0000			−0.831398
$639$	−39.0000	+	67.5500i	−1.54282	+	2.67224i
$640$	9.00000			0.355756
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	0.987200	−	0.159489i	$-0.0509845\pi$
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	−0.631721	+	0.775196i	$0.717651\pi$
$642$	−12.0000	−	20.7846i	−0.473602	−	0.820303i
$643$	−9.50000	+	16.4545i	−0.374643	+	0.648901i	−0.990274	−	0.139134i	$-0.955568\pi$
$643$	−9.50000	+	16.4545i	−0.374643	+	0.648901i	0.615630	+	0.788035i	$0.288902\pi$
$644$		0			0
$645$	63.0000			2.48062
$646$	2.00000			0.0786889
$647$	−9.00000			−0.353827			−0.176913	−	0.984226i	$-0.556611\pi$
$647$	−9.00000			−0.353827			−0.176913	+	0.984226i	$0.556611\pi$
$648$	−27.0000			−1.06066
$649$	6.00000	+	10.3923i	0.235521	+	0.407934i
$650$	−14.0000	+	3.46410i	−0.549125	+	0.135873i
$651$		0			0
$652$	−0.500000	−	0.866025i	−0.0195815	−	0.0339162i
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	−0.986634	−	0.162951i	$-0.947899\pi$
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	0.634437	+	0.772975i	$0.281232\pi$
$654$	−10.5000	−	18.1865i	−0.410582	−	0.711150i
$655$	−7.50000	+	12.9904i	−0.293049	+	0.507576i
$656$	3.00000			0.117130
$657$	−39.0000	+	67.5500i	−1.52153	+	2.63538i
$658$		0			0
$659$	−14.5000	+	25.1147i	−0.564840	+	0.978331i	0.432225	+	0.901766i	$0.357729\pi$
$659$	−14.5000	+	25.1147i	−0.564840	+	0.978331i	−0.997065	+	0.0765653i	$0.975605\pi$
$660$	13.5000	−	23.3827i	0.525487	−	0.910170i
$661$	9.00000			0.350059			0.175030	−	0.984563i	$-0.443998\pi$
$661$	9.00000			0.350059			0.175030	+	0.984563i	$0.443998\pi$
$662$	14.5000	−	25.1147i	0.563559	−	0.976112i
$663$	−21.0000	+	5.19615i	−0.815572	+	0.201802i
$664$		0			0
$665$		0			0
$666$	−6.00000	−	10.3923i	−0.232495	−	0.402694i
$667$		0			0
$668$	6.50000	−	11.2583i	0.251493	−	0.435598i
$669$	−13.5000	−	23.3827i	−0.521940	−	0.904027i
$670$	9.00000			0.347700
$671$	−39.0000			−1.50558
$672$		0			0
$673$	20.5000	+	35.5070i	0.790217	+	1.36870i	0.925832	+	0.377934i	$0.123365\pi$
$673$	20.5000	+	35.5070i	0.790217	+	1.36870i	−0.135615	+	0.990762i	$0.543301\pi$
$674$	−7.00000	+	12.1244i	−0.269630	+	0.467013i
$675$	−18.0000	+	31.1769i	−0.692820	+	1.20000i
$676$	0.500000	−	12.9904i	0.0192308	−	0.499630i
$677$	3.50000	+	6.06218i	0.134516	+	0.232988i	0.925412	−	0.378962i	$-0.123719\pi$
$677$	3.50000	+	6.06218i	0.134516	+	0.232988i	−0.790897	+	0.611950i	$0.790385\pi$
$678$	−22.5000	−	38.9711i	−0.864107	−	1.49668i
$679$		0			0
$680$	−9.00000	+	15.5885i	−0.345134	+	0.597790i
$681$	−6.00000	−	10.3923i	−0.229920	−	0.398234i
$682$	−4.50000	−	7.79423i	−0.172314	−	0.298456i
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	0.728101	−	0.685470i	$-0.240403\pi$
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	−0.957685	+	0.287819i	$0.907070\pi$
$684$	3.00000	+	5.19615i	0.114708	+	0.198680i
$685$	15.0000	−	25.9808i	0.573121	−	0.992674i
$686$		0			0
$687$	−19.5000	−	33.7750i	−0.743971	−	1.28860i
$688$	−3.50000	−	6.06218i	−0.133436	−	0.231118i
$689$	7.50000	+	7.79423i	0.285727	+	0.296936i
$690$		0			0
$691$	−2.00000	+	3.46410i	−0.0760836	+	0.131781i	−0.901557	−	0.432660i	$-0.857575\pi$
$691$	−2.00000	+	3.46410i	−0.0760836	+	0.131781i	0.825473	+	0.564441i	$0.190908\pi$
$692$	−9.50000	−	16.4545i	−0.361136	−	0.625506i
$693$		0			0
$694$	−8.00000			−0.303676
$695$	−45.0000			−1.70695
$696$	31.5000	+	54.5596i	1.19400	+	2.06808i
$697$	3.00000	−	5.19615i	0.113633	−	0.196818i
$698$	−23.0000			−0.870563
$699$	31.5000	+	54.5596i	1.19144	+	2.06363i
$700$		0			0
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$	22.5000	+	23.3827i	0.849208	+	0.882523i
$703$	−1.00000	+	1.73205i	−0.0377157	+	0.0653255i
$704$	−21.0000			−0.791467
$705$	−4.50000	+	7.79423i	−0.169480	+	0.293548i
$706$	−12.5000	+	21.6506i	−0.470444	+	0.814832i
$707$		0			0
$708$	6.00000	−	10.3923i	0.225494	−	0.390567i
$709$	11.0000			0.413114			0.206557	−	0.978435i	$-0.433774\pi$
$709$	11.0000			0.413114			0.206557	+	0.978435i	$0.433774\pi$
$710$	19.5000	−	33.7750i	0.731822	−	1.26755i
$711$	9.00000	+	15.5885i	0.337526	+	0.584613i
$712$	−9.00000	+	15.5885i	−0.337289	+	0.584202i
$713$		0			0
$714$		0			0
$715$	−31.5000	+	7.79423i	−1.17803	+	0.291488i
$716$	8.50000	+	14.7224i	0.317660	+	0.550203i
$717$	−12.0000			−0.448148
$718$	17.0000			0.634434
$719$	9.00000			0.335643			0.167822	−	0.985817i	$-0.446327\pi$
$719$	9.00000			0.335643			0.167822	+	0.985817i	$0.446327\pi$
$720$	18.0000			0.670820
$721$		0			0
$722$	9.00000	−	15.5885i	0.334945	−	0.580142i
$723$	−39.0000	−	67.5500i	−1.45043	−	2.51221i
$724$	11.0000	+	19.0526i	0.408812	+	0.708083i
$725$	28.0000			1.03989
$726$	3.00000	−	5.19615i	0.111340	−	0.192847i
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	19.5000	−	33.7750i	0.721727	−	1.25007i
$731$	−14.0000			−0.517809
$732$	19.5000	+	33.7750i	0.720741	+	1.24836i
$733$	−4.50000	−	7.79423i	−0.166211	−	0.287886i	0.770873	−	0.636988i	$-0.219820\pi$
$733$	−4.50000	−	7.79423i	−0.166211	−	0.287886i	−0.937085	+	0.349102i	$0.886487\pi$
$734$	−15.5000	+	26.8468i	−0.572115	+	0.990933i
$735$		0			0
$736$		0			0
$737$	9.00000			0.331519
$738$	−18.0000			−0.662589
$739$	1.00000			0.0367856			0.0183928	−	0.999831i	$-0.494145\pi$
$739$	1.00000			0.0367856			0.0183928	+	0.999831i	$0.494145\pi$
$740$	−3.00000	−	5.19615i	−0.110282	−	0.191014i
$741$	3.00000	−	10.3923i	0.110208	−	0.381771i
$742$		0			0
$743$	−25.5000	−	44.1673i	−0.935504	−	1.62034i	−0.773732	−	0.633513i	$-0.781612\pi$
$743$	−25.5000	−	44.1673i	−0.935504	−	1.62034i	−0.161772	−	0.986828i	$-0.551721\pi$
$744$	−13.5000	+	23.3827i	−0.494934	+	0.857251i
$745$	22.5000	+	38.9711i	0.824336	+	1.42779i
$746$	4.50000	−	7.79423i	0.164757	−	0.285367i
$747$		0			0
$748$	−3.00000	+	5.19615i	−0.109691	+	0.189990i
$749$		0			0
$750$	−4.50000	+	7.79423i	−0.164317	+	0.284605i
$751$	−14.0000	+	24.2487i	−0.510867	+	0.884848i	0.489053	+	0.872254i	$0.337342\pi$
$751$	−14.0000	+	24.2487i	−0.510867	+	0.884848i	−0.999921	+	0.0125942i	$0.995991\pi$
$752$	1.00000			0.0364662
$753$	−34.5000	+	59.7558i	−1.25725	+	2.17762i
$754$	7.00000	−	24.2487i	0.254925	−	0.883086i
$755$	63.0000			2.29280
$756$		0			0
$757$	−1.50000	−	2.59808i	−0.0545184	−	0.0944287i	0.837478	−	0.546471i	$-0.184029\pi$
$757$	−1.50000	−	2.59808i	−0.0545184	−	0.0944287i	−0.891997	+	0.452042i	$0.850696\pi$
$758$	−33.0000			−1.19861
$759$		0			0
$760$	−4.50000	−	7.79423i	−0.163232	−	0.282726i
$761$	9.00000			0.326250			0.163125	−	0.986605i	$-0.447843\pi$
$761$	9.00000			0.326250			0.163125	+	0.986605i	$0.447843\pi$
$762$	33.0000			1.19546
$763$		0			0
$764$	−8.50000	−	14.7224i	−0.307519	−	0.532639i
$765$	18.0000	−	31.1769i	0.650791	−	1.12720i
$766$	−10.5000	+	18.1865i	−0.379380	+	0.657106i
$767$	−14.0000	+	3.46410i	−0.505511	+	0.125081i
$768$	25.5000	+	44.1673i	0.920152	+	1.59375i
$769$	9.50000	+	16.4545i	0.342579	+	0.593364i	0.984911	−	0.173063i	$-0.0553663\pi$
$769$	9.50000	+	16.4545i	0.342579	+	0.593364i	−0.642332	+	0.766426i	$0.722033\pi$
$770$		0			0
$771$	−3.00000	+	5.19615i	−0.108042	+	0.187135i
$772$	3.50000	+	6.06218i	0.125968	+	0.218183i
$773$	−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	$0.867747\pi$
$774$	21.0000	+	36.3731i	0.754829	+	1.30740i
$775$	6.00000	+	10.3923i	0.215526	+	0.373303i
$776$	7.50000	−	12.9904i	0.269234	−	0.466328i
$777$		0			0
$778$	16.5000	+	28.5788i	0.591554	+	1.02460i
$779$	1.50000	+	2.59808i	0.0537431	+	0.0930857i
$780$	22.5000	+	23.3827i	0.805629	+	0.837234i
$781$	19.5000	−	33.7750i	0.697765	−	1.20856i
$782$		0			0
$783$	−31.5000	−	54.5596i	−1.12572	−	1.94980i
$784$		0			0
$785$	57.0000			2.03442
$786$	−15.0000			−0.535032
$787$	−10.0000	−	17.3205i	−0.356462	−	0.617409i	0.630905	−	0.775860i	$-0.282684\pi$
$787$	−10.0000	−	17.3205i	−0.356462	−	0.617409i	−0.987367	+	0.158450i	$0.949350\pi$
$788$	−0.500000	+	0.866025i	−0.0178118	+	0.0308509i
$789$	−81.0000			−2.88368
$790$	−4.50000	−	7.79423i	−0.160103	−	0.277306i
$791$		0			0
$792$	54.0000			1.91881
$793$	13.0000	−	45.0333i	0.461644	−	1.59918i
$794$	−0.500000	+	0.866025i	−0.0177443	+	0.0307341i
$795$	−27.0000			−0.957591
$796$	10.0000	−	17.3205i	0.354441	−	0.613909i
$797$	1.50000	−	2.59808i	0.0531327	−	0.0920286i	−0.838236	−	0.545308i	$-0.816413\pi$
$797$	1.50000	−	2.59808i	0.0531327	−	0.0920286i	0.891368	+	0.453279i	$0.149746\pi$
$798$		0			0
$799$	1.00000	−	1.73205i	0.0353775	−	0.0612756i
$800$	20.0000			0.707107
$801$	18.0000	−	31.1769i	0.635999	−	1.10158i
$802$	1.00000	+	1.73205i	0.0353112	+	0.0611608i
$803$	19.5000	−	33.7750i	0.688140	−	1.19189i
$804$	−4.50000	−	7.79423i	−0.158703	−	0.274881i
$805$		0			0
$806$	10.5000	−	2.59808i	0.369847	−	0.0915133i
$807$	27.0000	+	46.7654i	0.950445	+	1.64622i
$808$	−15.0000			−0.527698
$809$	11.0000			0.386739			0.193370	−	0.981126i	$-0.438058\pi$
$809$	11.0000			0.386739			0.193370	+	0.981126i	$0.438058\pi$
$810$	−27.0000			−0.948683
$811$	4.00000			0.140459			0.0702295	−	0.997531i	$-0.477627\pi$
$811$	4.00000			0.140459			0.0702295	+	0.997531i	$0.477627\pi$
$812$		0			0
$813$	−24.0000	+	41.5692i	−0.841717	+	1.45790i
$814$	3.00000	+	5.19615i	0.105150	+	0.182125i
$815$	−1.50000	−	2.59808i	−0.0525427	−	0.0910066i
$816$	−6.00000			−0.210042
$817$	3.50000	−	6.06218i	0.122449	−	0.212089i
$818$	−14.0000			−0.489499
$819$		0			0
$820$	−9.00000			−0.314294
$821$	27.0000	−	46.7654i	0.942306	−	1.63212i	0.181250	−	0.983437i	$-0.441986\pi$
$821$	27.0000	−	46.7654i	0.942306	−	1.63212i	0.761056	−	0.648686i	$-0.224681\pi$
$822$	30.0000			1.04637
$823$	−20.0000	−	34.6410i	−0.697156	−	1.20751i	−0.969448	−	0.245295i	$-0.921115\pi$
$823$	−20.0000	−	34.6410i	−0.697156	−	1.20751i	0.272292	−	0.962215i	$-0.412218\pi$
$824$	−7.50000	−	12.9904i	−0.261275	−	0.452541i
$825$	18.0000	−	31.1769i	0.626680	−	1.08544i
$826$		0			0
$827$	4.00000			0.139094			0.0695468	−	0.997579i	$-0.477845\pi$
$827$	4.00000			0.139094			0.0695468	+	0.997579i	$0.477845\pi$
$828$		0			0
$829$	−11.0000			−0.382046			−0.191023	−	0.981586i	$-0.561180\pi$
$829$	−11.0000			−0.382046			−0.191023	+	0.981586i	$0.561180\pi$
$830$		0			0
$831$	−33.0000	−	57.1577i	−1.14476	−	1.98278i
$832$	7.00000	−	24.2487i	0.242681	−	0.840673i
$833$		0			0
$834$	−22.5000	−	38.9711i	−0.779111	−	1.34946i
$835$	19.5000	−	33.7750i	0.674825	−	1.16883i
$836$	−1.50000	−	2.59808i	−0.0518786	−	0.0898563i
$837$	13.5000	−	23.3827i	0.466628	−	0.808224i
$838$	25.0000			0.863611
$839$	18.5000	−	32.0429i	0.638691	−	1.10625i	−0.347029	−	0.937854i	$-0.612810\pi$
$839$	18.5000	−	32.0429i	0.638691	−	1.10625i	0.985720	−	0.168391i	$-0.0538571\pi$
$840$		0			0
$841$	−10.0000	+	17.3205i	−0.344828	+	0.597259i
$842$	−9.00000	+	15.5885i	−0.310160	+	0.537214i
$843$	−54.0000			−1.85986
$844$	3.50000	−	6.06218i	0.120475	−	0.208669i
$845$	1.50000	−	38.9711i	0.0516016	−	1.34065i
$846$	−6.00000			−0.206284
$847$		0			0
$848$	1.50000	+	2.59808i	0.0515102	+	0.0892183i
$849$	−3.00000			−0.102960
$850$	−4.00000	+	6.92820i	−0.137199	+	0.237635i
$851$		0			0
$852$	−39.0000			−1.33612
$853$	6.00000			0.205436			0.102718	−	0.994711i	$-0.467246\pi$
$853$	6.00000			0.205436			0.102718	+	0.994711i	$0.467246\pi$
$854$		0			0
$855$	9.00000	+	15.5885i	0.307794	+	0.533114i
$856$	12.0000	−	20.7846i	0.410152	−	0.710403i
$857$	−16.5000	+	28.5788i	−0.563629	+	0.976235i	0.433546	+	0.901131i	$0.357262\pi$
$857$	−16.5000	+	28.5788i	−0.563629	+	0.976235i	−0.997176	+	0.0751033i	$0.976071\pi$
$858$	−22.5000	−	23.3827i	−0.768137	−	0.798272i
$859$	12.5000	+	21.6506i	0.426494	+	0.738710i	0.996559	−	0.0828900i	$-0.0264150\pi$
$859$	12.5000	+	21.6506i	0.426494	+	0.738710i	−0.570064	+	0.821600i	$0.693082\pi$
$860$	10.5000	+	18.1865i	0.358047	+	0.620156i
$861$		0			0
$862$	−4.50000	+	7.79423i	−0.153271	+	0.265472i
$863$	−18.5000	−	32.0429i	−0.629747	−	1.09075i	−0.987602	−	0.156977i	$-0.949825\pi$
$863$	−18.5000	−	32.0429i	−0.629747	−	1.09075i	0.357855	−	0.933777i	$-0.383508\pi$
$864$	−22.5000	−	38.9711i	−0.765466	−	1.32583i
$865$	−28.5000	−	49.3634i	−0.969029	−	1.67841i
$866$	13.5000	+	23.3827i	0.458749	+	0.794576i
$867$	19.5000	−	33.7750i	0.662255	−	1.14706i
$868$		0			0
$869$	−4.50000	−	7.79423i	−0.152652	−	0.264401i
$870$	31.5000	+	54.5596i	1.06795	+	1.84974i
$871$	−3.00000	+	10.3923i	−0.101651	+	0.352130i
$872$	10.5000	−	18.1865i	0.355575	−	0.615874i
$873$	−15.0000	+	25.9808i	−0.507673	+	0.879316i
$874$		0			0
$875$		0			0
$876$	−39.0000			−1.31769
$877$	−45.0000			−1.51954			−0.759771	−	0.650191i	$-0.774689\pi$
$877$	−45.0000			−1.51954			−0.759771	+	0.650191i	$0.774689\pi$
$878$	−8.00000	−	13.8564i	−0.269987	−	0.467631i
$879$	16.5000	−	28.5788i	0.556531	−	0.963940i
$880$	−9.00000			−0.303390
$881$	7.50000	+	12.9904i	0.252681	+	0.437657i	0.964263	−	0.264946i	$-0.0853542\pi$
$881$	7.50000	+	12.9904i	0.252681	+	0.437657i	−0.711582	+	0.702603i	$0.752021\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	−5.00000	−	5.19615i	−0.168168	−	0.174766i
$885$	18.0000	−	31.1769i	0.605063	−	1.04800i
$886$	−11.0000			−0.369552
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	−0.591156	−	0.806557i	$-0.701328\pi$
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	0.994077	+	0.108678i	$0.0346618\pi$
$888$	9.00000	−	15.5885i	0.302020	−	0.523114i
$889$		0			0
$890$	−9.00000	+	15.5885i	−0.301681	+	0.522526i
$891$	−27.0000			−0.904534
$892$	4.50000	−	7.79423i	0.150671	−	0.260970i
$893$	0.500000	+	0.866025i	0.0167319	+	0.0289804i
$894$	−22.5000	+	38.9711i	−0.752513	+	1.30339i
$895$	25.5000	+	44.1673i	0.852371	+	1.47635i
$896$		0			0
$897$		0			0
$898$	−7.50000	−	12.9904i	−0.250278	−	0.433495i
$899$	−21.0000			−0.700389
$900$	−24.0000			−0.800000
$901$	6.00000			0.199889
$902$	9.00000			0.299667
$903$		0			0
$904$	22.5000	−	38.9711i	0.748339	−	1.29616i
$905$	33.0000	+	57.1577i	1.09696	+	1.89999i
$906$	31.5000	+	54.5596i	1.04652	+	1.81262i
$907$	−47.0000			−1.56061			−0.780305	−	0.625400i	$-0.784936\pi$
$907$	−47.0000			−1.56061			−0.780305	+	0.625400i	$0.784936\pi$
$908$	2.00000	−	3.46410i	0.0663723	−	0.114960i
$909$	30.0000			0.995037
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$	1.50000	−	2.59808i	0.0496700	−	0.0860309i
$913$		0			0
$914$	9.00000	+	15.5885i	0.297694	+	0.515620i
$915$	58.5000	+	101.325i	1.93395	+	3.34970i
$916$	6.50000	−	11.2583i	0.214766	−	0.371986i
$917$		0			0
$918$	18.0000			0.594089
$919$	−25.0000			−0.824674			−0.412337	−	0.911031i	$-0.635287\pi$
$919$	−25.0000			−0.824674			−0.412337	+	0.911031i	$0.635287\pi$
$920$		0			0
$921$	−36.0000			−1.18624
$922$	17.5000	+	30.3109i	0.576332	+	0.998236i
$923$	32.5000	+	33.7750i	1.06975	+	1.11172i
$924$		0			0
$925$	−4.00000	−	6.92820i	−0.131519	−	0.227798i
$926$	4.00000	−	6.92820i	0.131448	−	0.227675i
$927$	15.0000	+	25.9808i	0.492665	+	0.853320i
$928$	−17.5000	+	30.3109i	−0.574466	+	0.995004i
$929$	13.0000			0.426516			0.213258	−	0.976996i	$-0.431592\pi$
$929$	13.0000			0.426516			0.213258	+	0.976996i	$0.431592\pi$
$930$	−13.5000	+	23.3827i	−0.442682	+	0.766748i
$931$		0			0
$932$	−10.5000	+	18.1865i	−0.343939	+	0.595720i
$933$	−13.5000	+	23.3827i	−0.441970	+	0.765515i
$934$	7.00000			0.229047
$935$	−9.00000	+	15.5885i	−0.294331	+	0.509797i
$936$	−18.0000	+	62.3538i	−0.588348	+	2.03810i
$937$	−22.0000			−0.718709			−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000			−0.718709			−0.359354	+	0.933201i	$0.617003\pi$
$938$		0			0
$939$	28.5000	+	49.3634i	0.930062	+	1.61092i
$940$	−3.00000			−0.0978492
$941$	−8.50000	+	14.7224i	−0.277092	+	0.479938i	−0.970661	−	0.240453i	$-0.922704\pi$
$941$	−8.50000	+	14.7224i	−0.277092	+	0.479938i	0.693569	+	0.720390i	$0.256037\pi$
$942$	28.5000	+	49.3634i	0.928580	+	1.60835i
$943$		0			0
$944$	−4.00000			−0.130189
$945$		0			0
$946$	−10.5000	−	18.1865i	−0.341384	−	0.591295i
$947$	6.00000	−	10.3923i	0.194974	−	0.337705i	−0.751918	−	0.659256i	$-0.770871\pi$
$947$	6.00000	−	10.3923i	0.194974	−	0.337705i	0.946892	+	0.321552i	$0.104204\pi$
$948$	−4.50000	+	7.79423i	−0.146153	+	0.253145i
$949$	32.5000	+	33.7750i	1.05499	+	1.09638i
$950$	−2.00000	−	3.46410i	−0.0648886	−	0.112390i
$951$	13.5000	+	23.3827i	0.437767	+	0.758236i
$952$		0			0
$953$	16.5000	−	28.5788i	0.534487	−	0.925759i	−0.464701	−	0.885468i	$-0.653838\pi$
$953$	16.5000	−	28.5788i	0.534487	−	0.925759i	0.999188	−	0.0402915i	$-0.0128286\pi$
$954$	−9.00000	−	15.5885i	−0.291386	−	0.504695i
$955$	−25.5000	−	44.1673i	−0.825161	−	1.42922i
$956$	−2.00000	−	3.46410i	−0.0646846	−	0.112037i
$957$	31.5000	+	54.5596i	1.01825	+	1.76366i
$958$	−17.5000	+	30.3109i	−0.565399	+	0.979300i
$959$		0			0
$960$	31.5000	+	54.5596i	1.01666	+	1.76090i
$961$	11.0000	+	19.0526i	0.354839	+	0.614599i
$962$	−7.00000	+	1.73205i	−0.225689	+	0.0558436i
$963$	−24.0000	+	41.5692i	−0.773389	+	1.33955i
$964$	13.0000	−	22.5167i	0.418702	−	0.725213i
$965$	10.5000	+	18.1865i	0.338007	+	0.585445i
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$	6.00000			0.192847
$969$	−3.00000	−	5.19615i	−0.0963739	−	0.166924i
$970$	7.50000	−	12.9904i	0.240810	−	0.417096i
$971$	1.00000			0.0320915			0.0160458	−	0.999871i	$-0.494892\pi$
$971$	1.00000			0.0320915			0.0160458	+	0.999871i	$0.494892\pi$
$972$		0			0
$973$		0			0
$974$	16.0000			0.512673
$975$	30.0000	+	31.1769i	0.960769	+	0.998460i
$976$	6.50000	−	11.2583i	0.208060	−	0.360370i
$977$	−5.00000			−0.159964			−0.0799821	−	0.996796i	$-0.525486\pi$
$977$	−5.00000			−0.159964			−0.0799821	+	0.996796i	$0.525486\pi$
$978$	1.50000	−	2.59808i	0.0479647	−	0.0830773i
$979$	−9.00000	+	15.5885i	−0.287641	+	0.498209i
$980$		0			0
$981$	−21.0000	+	36.3731i	−0.670478	+	1.16130i
$982$	15.0000			0.478669
$983$	23.5000	−	40.7032i	0.749534	−	1.29823i	−0.198513	−	0.980098i	$-0.563611\pi$
$983$	23.5000	−	40.7032i	0.749534	−	1.29823i	0.948046	−	0.318132i	$-0.103056\pi$
$984$	−13.5000	−	23.3827i	−0.430364	−	0.745413i
$985$	−1.50000	+	2.59808i	−0.0477940	+	0.0827816i
$986$	−7.00000	−	12.1244i	−0.222925	−	0.386118i
$987$		0			0
$988$	3.50000	−	0.866025i	0.111350	−	0.0275519i
$989$		0			0
$990$	54.0000			1.71623
$991$	13.0000			0.412959			0.206479	−	0.978451i	$-0.433799\pi$
$991$	13.0000			0.412959			0.206479	+	0.978451i	$0.433799\pi$
$992$	−15.0000			−0.476250
$993$	−87.0000			−2.76086
$994$		0			0
$995$	30.0000	−	51.9615i	0.951064	−	1.64729i
$996$		0			0
$997$	1.00000	+	1.73205i	0.0316703	+	0.0548546i	0.881426	−	0.472322i	$-0.156584\pi$
$997$	1.00000	+	1.73205i	0.0316703	+	0.0548546i	−0.849756	+	0.527176i	$0.823251\pi$
$998$	−31.0000			−0.981288
$999$	−9.00000	+	15.5885i	−0.284747	+	0.493197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.g.a.263.1		2
7.2	even	3		637.2.h.a.471.1		2
7.3	odd	6		637.2.f.b.393.1		2
7.4	even	3		637.2.f.a.393.1		2
7.5	odd	6		91.2.h.a.16.1	yes	2
7.6	odd	2		91.2.g.a.81.1	yes	2
13.9	even	3		637.2.h.a.165.1		2
21.5	even	6		819.2.s.a.289.1		2
21.20	even	2		819.2.n.c.172.1		2
91.3	odd	6		8281.2.a.i.1.1		1
91.9	even	3	inner	637.2.g.a.373.1		2
91.10	odd	6		8281.2.a.c.1.1		1
91.48	odd	6		91.2.h.a.74.1	yes	2
91.55	odd	6		1183.2.e.a.508.1		2
91.61	odd	6		91.2.g.a.9.1	✓	2
91.62	odd	6		1183.2.e.c.508.1		2
91.68	odd	6		1183.2.e.a.170.1		2
91.74	even	3		637.2.f.a.295.1		2
91.75	odd	6		1183.2.e.c.170.1		2
91.81	even	3		8281.2.a.j.1.1		1
91.87	odd	6		637.2.f.b.295.1		2
91.88	even	6		8281.2.a.g.1.1		1
273.152	even	6		819.2.n.c.100.1		2
273.230	even	6		819.2.s.a.802.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.a.9.1	✓	2	91.61	odd	6
91.2.g.a.81.1	yes	2	7.6	odd	2
91.2.h.a.16.1	yes	2	7.5	odd	6
91.2.h.a.74.1	yes	2	91.48	odd	6
637.2.f.a.295.1		2	91.74	even	3
637.2.f.a.393.1		2	7.4	even	3
637.2.f.b.295.1		2	91.87	odd	6
637.2.f.b.393.1		2	7.3	odd	6
637.2.g.a.263.1		2	1.1	even	1	trivial
637.2.g.a.373.1		2	91.9	even	3	inner
637.2.h.a.165.1		2	13.9	even	3
637.2.h.a.471.1		2	7.2	even	3
819.2.n.c.100.1		2	273.152	even	6
819.2.n.c.172.1		2	21.20	even	2
819.2.s.a.289.1		2	21.5	even	6
819.2.s.a.802.1		2	273.230	even	6
1183.2.e.a.170.1		2	91.68	odd	6
1183.2.e.a.508.1		2	91.55	odd	6
1183.2.e.c.170.1		2	91.75	odd	6
1183.2.e.c.508.1		2	91.62	odd	6
8281.2.a.c.1.1		1	91.10	odd	6
8281.2.a.g.1.1		1	91.88	even	6
8281.2.a.i.1.1		1	91.3	odd	6
8281.2.a.j.1.1		1	91.81	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +3.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-1.50000 + 2.59808i) q^{6} -3.00000 q^{8} +6.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +3.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-1.50000 + 2.59808i) q^{6} -3.00000 q^{8} +6.00000 q^{9} -3.00000 q^{10} -3.00000 q^{11} +(1.50000 + 2.59808i) q^{12} +(1.00000 - 3.46410i) q^{13} +(4.50000 + 7.79423i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(-3.00000 + 5.19615i) q^{18} +1.00000 q^{19} +(-1.50000 + 2.59808i) q^{20} +(1.50000 - 2.59808i) q^{22} -9.00000 q^{24} +(-2.00000 + 3.46410i) q^{25} +(2.50000 + 2.59808i) q^{26} +9.00000 q^{27} +(-3.50000 - 6.06218i) q^{29} -9.00000 q^{30} +(1.50000 - 2.59808i) q^{31} +(-2.50000 - 4.33013i) q^{32} -9.00000 q^{33} +2.00000 q^{34} +(3.00000 + 5.19615i) q^{36} +(-1.00000 + 1.73205i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(3.00000 - 10.3923i) q^{39} +(-4.50000 - 7.79423i) q^{40} +(1.50000 + 2.59808i) q^{41} +(3.50000 - 6.06218i) q^{43} +(-1.50000 - 2.59808i) q^{44} +(9.00000 + 15.5885i) q^{45} +(0.500000 + 0.866025i) q^{47} +(1.50000 - 2.59808i) q^{48} +(-2.00000 - 3.46410i) q^{50} +(-3.00000 - 5.19615i) q^{51} +(3.50000 - 0.866025i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(-4.50000 + 7.79423i) q^{54} +(-4.50000 - 7.79423i) q^{55} +3.00000 q^{57} +7.00000 q^{58} +(-2.00000 - 3.46410i) q^{59} +(-4.50000 + 7.79423i) q^{60} +13.0000 q^{61} +(1.50000 + 2.59808i) q^{62} +7.00000 q^{64} +(10.5000 - 2.59808i) q^{65} +(4.50000 - 7.79423i) q^{66} -3.00000 q^{67} +(1.00000 - 1.73205i) q^{68} +(-6.50000 + 11.2583i) q^{71} -18.0000 q^{72} +(-6.50000 + 11.2583i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-6.00000 + 10.3923i) q^{75} +(0.500000 + 0.866025i) q^{76} +(7.50000 + 7.79423i) q^{78} +(1.50000 + 2.59808i) q^{79} +3.00000 q^{80} +9.00000 q^{81} -3.00000 q^{82} +(3.00000 - 5.19615i) q^{85} +(3.50000 + 6.06218i) q^{86} +(-10.5000 - 18.1865i) q^{87} +9.00000 q^{88} +(3.00000 - 5.19615i) q^{89} -18.0000 q^{90} +(4.50000 - 7.79423i) q^{93} -1.00000 q^{94} +(1.50000 + 2.59808i) q^{95} +(-7.50000 - 12.9904i) q^{96} +(-2.50000 + 4.33013i) q^{97} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 6 q^{3} + q^{4} + 3 q^{5} - 3 q^{6} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 2 * q - q^2 + 6 * q^3 + q^4 + 3 * q^5 - 3 * q^6 - 6 * q^8 + 12 * q^9	\( 2 q - q^{2} + 6 q^{3} + q^{4} + 3 q^{5} - 3 q^{6} - 6 q^{8} + 12 q^{9} - 6 q^{10} - 6 q^{11} + 3 q^{12} + 2 q^{13} + 9 q^{15} + q^{16} - 2 q^{17} - 6 q^{18} + 2 q^{19} - 3 q^{20} + 3 q^{22} - 18 q^{24} - 4 q^{25} + 5 q^{26} + 18 q^{27} - 7 q^{29} - 18 q^{30} + 3 q^{31} - 5 q^{32} - 18 q^{33} + 4 q^{34} + 6 q^{36} - 2 q^{37} - q^{38} + 6 q^{39} - 9 q^{40} + 3 q^{41} + 7 q^{43} - 3 q^{44} + 18 q^{45} + q^{47} + 3 q^{48} - 4 q^{50} - 6 q^{51} + 7 q^{52} - 3 q^{53} - 9 q^{54} - 9 q^{55} + 6 q^{57} + 14 q^{58} - 4 q^{59} - 9 q^{60} + 26 q^{61} + 3 q^{62} + 14 q^{64} + 21 q^{65} + 9 q^{66} - 6 q^{67} + 2 q^{68} - 13 q^{71} - 36 q^{72} - 13 q^{73} - 2 q^{74} - 12 q^{75} + q^{76} + 15 q^{78} + 3 q^{79} + 6 q^{80} + 18 q^{81} - 6 q^{82} + 6 q^{85} + 7 q^{86} - 21 q^{87} + 18 q^{88} + 6 q^{89} - 36 q^{90} + 9 q^{93} - 2 q^{94} + 3 q^{95} - 15 q^{96} - 5 q^{97} - 36 q^{99}+O(q^{100}) \) 2 * q - q^2 + 6 * q^3 + q^4 + 3 * q^5 - 3 * q^6 - 6 * q^8 + 12 * q^9 - 6 * q^10 - 6 * q^11 + 3 * q^12 + 2 * q^13 + 9 * q^15 + q^16 - 2 * q^17 - 6 * q^18 + 2 * q^19 - 3 * q^20 + 3 * q^22 - 18 * q^24 - 4 * q^25 + 5 * q^26 + 18 * q^27 - 7 * q^29 - 18 * q^30 + 3 * q^31 - 5 * q^32 - 18 * q^33 + 4 * q^34 + 6 * q^36 - 2 * q^37 - q^38 + 6 * q^39 - 9 * q^40 + 3 * q^41 + 7 * q^43 - 3 * q^44 + 18 * q^45 + q^47 + 3 * q^48 - 4 * q^50 - 6 * q^51 + 7 * q^52 - 3 * q^53 - 9 * q^54 - 9 * q^55 + 6 * q^57 + 14 * q^58 - 4 * q^59 - 9 * q^60 + 26 * q^61 + 3 * q^62 + 14 * q^64 + 21 * q^65 + 9 * q^66 - 6 * q^67 + 2 * q^68 - 13 * q^71 - 36 * q^72 - 13 * q^73 - 2 * q^74 - 12 * q^75 + q^76 + 15 * q^78 + 3 * q^79 + 6 * q^80 + 18 * q^81 - 6 * q^82 + 6 * q^85 + 7 * q^86 - 21 * q^87 + 18 * q^88 + 6 * q^89 - 36 * q^90 + 9 * q^93 - 2 * q^94 + 3 * q^95 - 15 * q^96 - 5 * q^97 - 36 * q^99

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