LMFDB - Embedded newform 637.2.q.c.491.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(491,637)]

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([0, 5]))

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

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

chi := DirichletCharacter("637.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (of order $6$, 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:	$5.08647060876$
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:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	637.491
Dual form			637.2.q.c.589.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.73205i q^{5} +(1.50000 + 0.866025i) q^{6} +1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.73205i q^{5} +(1.50000 + 0.866025i) q^{6} +1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(4.50000 - 2.59808i) q^{11} +1.00000 q^{12} +(-1.00000 - 3.46410i) q^{13} +(1.50000 - 0.866025i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-3.00000 + 5.19615i) q^{17} -3.46410i q^{18} +(1.50000 + 0.866025i) q^{19} +(-1.50000 - 0.866025i) q^{20} +(4.50000 - 7.79423i) q^{22} +(-1.50000 + 0.866025i) q^{24} +2.00000 q^{25} +(-4.50000 - 4.33013i) q^{26} +5.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +(1.50000 - 2.59808i) q^{30} -1.73205i q^{31} +(4.50000 + 2.59808i) q^{32} +(4.50000 + 2.59808i) q^{33} +10.3923i q^{34} +(-1.00000 - 1.73205i) q^{36} +3.00000 q^{38} +(2.50000 - 2.59808i) q^{39} +3.00000 q^{40} +(-4.50000 + 2.59808i) q^{41} +(-5.50000 + 9.52628i) q^{43} -5.19615i q^{44} +(-3.00000 - 1.73205i) q^{45} -8.66025i q^{47} +(-2.50000 + 4.33013i) q^{48} +(3.00000 - 1.73205i) q^{50} -6.00000 q^{51} +(-3.50000 - 0.866025i) q^{52} -9.00000 q^{53} +(7.50000 - 4.33013i) q^{54} +(-4.50000 - 7.79423i) q^{55} +1.73205i q^{57} +(-4.50000 - 2.59808i) q^{58} +(3.00000 + 1.73205i) q^{59} -1.73205i q^{60} +(-3.50000 + 6.06218i) q^{61} +(-1.50000 - 2.59808i) q^{62} -1.00000 q^{64} +(-6.00000 + 1.73205i) q^{65} +9.00000 q^{66} +(-7.50000 + 4.33013i) q^{67} +(3.00000 + 5.19615i) q^{68} +(1.50000 + 0.866025i) q^{71} +(3.00000 + 1.73205i) q^{72} +8.66025i q^{73} +(1.00000 + 1.73205i) q^{75} +(1.50000 - 0.866025i) q^{76} +(1.50000 - 6.06218i) q^{78} -5.00000 q^{79} +(7.50000 - 4.33013i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.50000 + 7.79423i) q^{82} +3.46410i q^{83} +(9.00000 + 5.19615i) q^{85} +19.0526i q^{86} +(1.50000 - 2.59808i) q^{87} +(4.50000 + 7.79423i) q^{88} +(6.00000 - 3.46410i) q^{89} -6.00000 q^{90} +(1.50000 - 0.866025i) q^{93} +(-7.50000 - 12.9904i) q^{94} +(1.50000 - 2.59808i) q^{95} +5.19615i q^{96} +(-4.50000 - 2.59808i) q^{97} -10.3923i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + q^{3} + q^{4} + 3 q^{6} + 2 q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 + q^3 + q^4 + 3 * q^6 + 2 * q^9	$ 2 q + 3 q^{2} + q^{3} + q^{4} + 3 q^{6} + 2 q^{9} - 3 q^{10} + 9 q^{11} + 2 q^{12} - 2 q^{13} + 3 q^{15} + 5 q^{16} - 6 q^{17} + 3 q^{19} - 3 q^{20} + 9 q^{22} - 3 q^{24} + 4 q^{25} - 9 q^{26} + 10 q^{27} - 3 q^{29} + 3 q^{30} + 9 q^{32} + 9 q^{33} - 2 q^{36} + 6 q^{38} + 5 q^{39} + 6 q^{40} - 9 q^{41} - 11 q^{43} - 6 q^{45} - 5 q^{48} + 6 q^{50} - 12 q^{51} - 7 q^{52} - 18 q^{53} + 15 q^{54} - 9 q^{55} - 9 q^{58} + 6 q^{59} - 7 q^{61} - 3 q^{62} - 2 q^{64} - 12 q^{65} + 18 q^{66} - 15 q^{67} + 6 q^{68} + 3 q^{71} + 6 q^{72} + 2 q^{75} + 3 q^{76} + 3 q^{78} - 10 q^{79} + 15 q^{80} - q^{81} - 9 q^{82} + 18 q^{85} + 3 q^{87} + 9 q^{88} + 12 q^{89} - 12 q^{90} + 3 q^{93} - 15 q^{94} + 3 q^{95} - 9 q^{97}+O(q^{100}) $ 2 * q + 3 * q^2 + q^3 + q^4 + 3 * q^6 + 2 * q^9 - 3 * q^10 + 9 * q^11 + 2 * q^12 - 2 * q^13 + 3 * q^15 + 5 * q^16 - 6 * q^17 + 3 * q^19 - 3 * q^20 + 9 * q^22 - 3 * q^24 + 4 * q^25 - 9 * q^26 + 10 * q^27 - 3 * q^29 + 3 * q^30 + 9 * q^32 + 9 * q^33 - 2 * q^36 + 6 * q^38 + 5 * q^39 + 6 * q^40 - 9 * q^41 - 11 * q^43 - 6 * q^45 - 5 * q^48 + 6 * q^50 - 12 * q^51 - 7 * q^52 - 18 * q^53 + 15 * q^54 - 9 * q^55 - 9 * q^58 + 6 * q^59 - 7 * q^61 - 3 * q^62 - 2 * q^64 - 12 * q^65 + 18 * q^66 - 15 * q^67 + 6 * q^68 + 3 * q^71 + 6 * q^72 + 2 * q^75 + 3 * q^76 + 3 * q^78 - 10 * q^79 + 15 * q^80 - q^81 - 9 * q^82 + 18 * q^85 + 3 * q^87 + 9 * q^88 + 12 * q^89 - 12 * q^90 + 3 * q^93 - 15 * q^94 + 3 * q^95 - 9 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	1.50000	−	0.866025i	1.06066	−	0.612372i	0.135045	−	0.990839i	$-0.456882\pi$
$2$	1.50000	−	0.866025i	1.06066	−	0.612372i	0.925615	+	0.378467i	$0.123549\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	1.73205i		−	0.774597i	−0.921954	−	0.387298i	$-0.873408\pi$
$5$		−	1.73205i		−	0.774597i	0.921954	−	0.387298i	$-0.126592\pi$
$6$	1.50000	+	0.866025i	0.612372	+	0.353553i
$7$		0			0
$7$		0			0
$8$			1.73205i			0.612372i
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$	4.50000	−	2.59808i	1.35680	−	0.783349i	0.367610	−	0.929980i	$-0.380176\pi$
$11$	4.50000	−	2.59808i	1.35680	−	0.783349i	0.989191	+	0.146631i	$0.0468429\pi$
$12$	1.00000			0.288675
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$14$		0			0
$15$	1.50000	−	0.866025i	0.387298	−	0.223607i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$		−	3.46410i		−	0.816497i
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	0.662094	−	0.749421i	$-0.269668\pi$
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	−0.317970	+	0.948101i	$0.603001\pi$
$20$	−1.50000	−	0.866025i	−0.335410	−	0.193649i
$21$		0			0
$22$	4.50000	−	7.79423i	0.959403	−	1.66174i
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	−1.50000	+	0.866025i	−0.306186	+	0.176777i
$25$	2.00000			0.400000
$26$	−4.50000	−	4.33013i	−0.882523	−	0.849208i
$27$	5.00000			0.962250
$28$		0			0
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$	1.50000	−	2.59808i	0.273861	−	0.474342i
$31$		−	1.73205i		−	0.311086i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$		−	1.73205i		−	0.311086i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$	4.50000	+	2.59808i	0.795495	+	0.459279i
$33$	4.50000	+	2.59808i	0.783349	+	0.452267i
$34$			10.3923i			1.78227i
$35$		0			0
$36$	−1.00000	−	1.73205i	−0.166667	−	0.288675i
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$	3.00000			0.486664
$39$	2.50000	−	2.59808i	0.400320	−	0.416025i
$40$	3.00000			0.474342
$41$	−4.50000	+	2.59808i	−0.702782	+	0.405751i	−0.808383	−	0.588657i	$-0.799657\pi$
$41$	−4.50000	+	2.59808i	−0.702782	+	0.405751i	0.105601	+	0.994409i	$0.466323\pi$
$42$		0			0
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	0.0522047	+	0.998636i	$0.483375\pi$
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	−0.890947	+	0.454108i	$0.849958\pi$
$44$		−	5.19615i		−	0.783349i
$45$	−3.00000	−	1.73205i	−0.447214	−	0.258199i
$46$		0			0
$47$		−	8.66025i		−	1.26323i	−0.775283	−	0.631614i	$-0.782393\pi$
$47$		−	8.66025i		−	1.26323i	0.775283	−	0.631614i	$-0.217607\pi$
$48$	−2.50000	+	4.33013i	−0.360844	+	0.625000i
$49$		0			0
$50$	3.00000	−	1.73205i	0.424264	−	0.244949i
$51$	−6.00000			−0.840168
$52$	−3.50000	−	0.866025i	−0.485363	−	0.120096i
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$	7.50000	−	4.33013i	1.02062	−	0.589256i
$55$	−4.50000	−	7.79423i	−0.606780	−	1.05097i
$56$		0			0
$57$			1.73205i			0.229416i
$58$	−4.50000	−	2.59808i	−0.590879	−	0.341144i
$59$	3.00000	+	1.73205i	0.390567	+	0.225494i	0.682406	−	0.730974i	$-0.260934\pi$
$59$	3.00000	+	1.73205i	0.390567	+	0.225494i	−0.291839	+	0.956467i	$0.594267\pi$
$60$		−	1.73205i		−	0.223607i
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$	−1.50000	−	2.59808i	−0.190500	−	0.329956i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−6.00000	+	1.73205i	−0.744208	+	0.214834i
$66$	9.00000			1.10782
$67$	−7.50000	+	4.33013i	−0.916271	+	0.529009i	−0.882443	−	0.470418i	$-0.844103\pi$
$67$	−7.50000	+	4.33013i	−0.916271	+	0.529009i	−0.0338274	+	0.999428i	$0.510770\pi$
$68$	3.00000	+	5.19615i	0.363803	+	0.630126i
$69$		0			0
$70$		0			0
$71$	1.50000	+	0.866025i	0.178017	+	0.102778i	0.586361	−	0.810050i	$-0.300560\pi$
$71$	1.50000	+	0.866025i	0.178017	+	0.102778i	−0.408344	+	0.912828i	$0.633893\pi$
$72$	3.00000	+	1.73205i	0.353553	+	0.204124i
$73$			8.66025i			1.01361i	0.862062	+	0.506803i	$0.169173\pi$
$73$			8.66025i			1.01361i	−0.862062	+	0.506803i	$0.830827\pi$
$74$		0			0
$75$	1.00000	+	1.73205i	0.115470	+	0.200000i
$76$	1.50000	−	0.866025i	0.172062	−	0.0993399i
$77$		0			0
$78$	1.50000	−	6.06218i	0.169842	−	0.686406i
$79$	−5.00000			−0.562544			−0.281272	−	0.959628i	$-0.590756\pi$
$79$	−5.00000			−0.562544			−0.281272	+	0.959628i	$0.590756\pi$
$80$	7.50000	−	4.33013i	0.838525	−	0.484123i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.50000	+	7.79423i	−0.496942	+	0.860729i
$83$			3.46410i			0.380235i	0.981761	+	0.190117i	$0.0608868\pi$
$83$			3.46410i			0.380235i	−0.981761	+	0.190117i	$0.939113\pi$
$84$		0			0
$85$	9.00000	+	5.19615i	0.976187	+	0.563602i
$86$			19.0526i			2.05449i
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$	4.50000	+	7.79423i	0.479702	+	0.830868i
$89$	6.00000	−	3.46410i	0.635999	−	0.367194i	−0.147073	−	0.989126i	$-0.546985\pi$
$89$	6.00000	−	3.46410i	0.635999	−	0.367194i	0.783072	+	0.621932i	$0.213652\pi$
$90$	−6.00000			−0.632456
$91$		0			0
$92$		0			0
$93$	1.50000	−	0.866025i	0.155543	−	0.0898027i
$94$	−7.50000	−	12.9904i	−0.773566	−	1.33986i
$95$	1.50000	−	2.59808i	0.153897	−	0.266557i
$96$			5.19615i			0.530330i
$97$	−4.50000	−	2.59808i	−0.456906	−	0.263795i	0.253837	−	0.967247i	$-0.418307\pi$
$97$	−4.50000	−	2.59808i	−0.456906	−	0.263795i	−0.710742	+	0.703452i	$0.751641\pi$
$98$		0			0
$99$		−	10.3923i		−	1.04447i
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$	−9.00000	+	5.19615i	−0.891133	+	0.514496i
$103$	−13.0000			−1.28093			−0.640464	−	0.767988i	$-0.721258\pi$
$103$	−13.0000			−1.28093			−0.640464	+	0.767988i	$0.721258\pi$
$104$	6.00000	−	1.73205i	0.588348	−	0.169842i
$105$		0			0
$106$	−13.5000	+	7.79423i	−1.31124	+	0.757042i
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$	2.50000	−	4.33013i	0.240563	−	0.416667i
$109$		−	5.19615i		−	0.497701i	−0.968542	−	0.248851i	$-0.919947\pi$
$109$		−	5.19615i		−	0.497701i	0.968542	−	0.248851i	$-0.0800528\pi$
$110$	−13.5000	−	7.79423i	−1.28717	−	0.743151i
$111$		0			0
$112$		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
$116$	−3.00000			−0.278543
$117$	−7.00000	−	1.73205i	−0.647150	−	0.160128i
$118$	6.00000			0.552345
$119$		0			0
$120$	1.50000	+	2.59808i	0.136931	+	0.237171i
$121$	8.00000	−	13.8564i	0.727273	−	1.25967i
$122$			12.1244i			1.09769i
$123$	−4.50000	−	2.59808i	−0.405751	−	0.234261i
$124$	−1.50000	−	0.866025i	−0.134704	−	0.0777714i
$125$		−	12.1244i		−	1.08444i
$126$		0			0
$127$	−6.50000	−	11.2583i	−0.576782	−	0.999015i	−0.995846	−	0.0910585i	$-0.970975\pi$
$127$	−6.50000	−	11.2583i	−0.576782	−	0.999015i	0.419064	−	0.907957i	$-0.362358\pi$
$128$	−10.5000	+	6.06218i	−0.928078	+	0.535826i
$129$	−11.0000			−0.968496
$130$	−7.50000	+	7.79423i	−0.657794	+	0.683599i
$131$	15.0000			1.31056			0.655278	−	0.755388i	$-0.272551\pi$
$131$	15.0000			1.31056			0.655278	+	0.755388i	$0.272551\pi$
$132$	4.50000	−	2.59808i	0.391675	−	0.226134i
$133$		0			0
$134$	−7.50000	+	12.9904i	−0.647901	+	1.12220i
$135$		−	8.66025i		−	0.745356i
$136$	−9.00000	−	5.19615i	−0.771744	−	0.445566i
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	−0.446857	−	0.894606i	$-0.647457\pi$
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	0.998179	−	0.0603135i	$-0.0192101\pi$
$140$		0			0
$141$	7.50000	−	4.33013i	0.631614	−	0.364662i
$142$	3.00000			0.251754
$143$	−13.5000	−	12.9904i	−1.12893	−	1.08631i
$144$	10.0000			0.833333
$145$	−4.50000	+	2.59808i	−0.373705	+	0.215758i
$146$	7.50000	+	12.9904i	0.620704	+	1.07509i
$147$		0			0
$148$		0			0
$149$	16.5000	+	9.52628i	1.35173	+	0.780423i	0.988492	−	0.151272i	$-0.0483370\pi$
$149$	16.5000	+	9.52628i	1.35173	+	0.780423i	0.363241	+	0.931695i	$0.381670\pi$
$150$	3.00000	+	1.73205i	0.244949	+	0.141421i
$151$			12.1244i			0.986666i	0.869841	+	0.493333i	$0.164222\pi$
$151$			12.1244i			0.986666i	−0.869841	+	0.493333i	$0.835778\pi$
$152$	−1.50000	+	2.59808i	−0.121666	+	0.210732i
$153$	6.00000	+	10.3923i	0.485071	+	0.840168i
$154$		0			0
$155$	−3.00000			−0.240966
$156$	−1.00000	−	3.46410i	−0.0800641	−	0.277350i
$157$	23.0000			1.83560			0.917800	−	0.397043i	$-0.129964\pi$
$157$	23.0000			1.83560			0.917800	+	0.397043i	$0.129964\pi$
$158$	−7.50000	+	4.33013i	−0.596668	+	0.344486i
$159$	−4.50000	−	7.79423i	−0.356873	−	0.618123i
$160$	4.50000	−	7.79423i	0.355756	−	0.616188i
$161$		0			0
$162$	−1.50000	−	0.866025i	−0.117851	−	0.0680414i
$163$	−10.5000	−	6.06218i	−0.822423	−	0.474826i	0.0288280	−	0.999584i	$-0.490822\pi$
$163$	−10.5000	−	6.06218i	−0.822423	−	0.474826i	−0.851251	+	0.524758i	$0.824156\pi$
$164$			5.19615i			0.405751i
$165$	4.50000	−	7.79423i	0.350325	−	0.606780i
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$	−1.50000	+	0.866025i	−0.116073	+	0.0670151i	−0.556913	−	0.830571i	$-0.688014\pi$
$167$	−1.50000	+	0.866025i	−0.116073	+	0.0670151i	0.440839	+	0.897586i	$0.354681\pi$
$168$		0			0
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$	18.0000			1.38054
$171$	3.00000	−	1.73205i	0.229416	−	0.132453i
$172$	5.50000	+	9.52628i	0.419371	+	0.726372i
$173$	−7.50000	+	12.9904i	−0.570214	+	0.987640i	0.426329	+	0.904568i	$0.359807\pi$
$173$	−7.50000	+	12.9904i	−0.570214	+	0.987640i	−0.996544	+	0.0830722i	$0.973527\pi$
$174$		−	5.19615i		−	0.393919i
$175$		0			0
$176$	22.5000	+	12.9904i	1.69600	+	0.979187i
$177$			3.46410i			0.260378i
$178$	6.00000	−	10.3923i	0.449719	−	0.778936i
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	0.804508	−	0.593942i	$-0.202429\pi$
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	−0.916623	+	0.399753i	$0.869096\pi$
$180$	−3.00000	+	1.73205i	−0.223607	+	0.129099i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$	−7.00000			−0.517455
$184$		0			0
$185$		0			0
$186$	1.50000	−	2.59808i	0.109985	−	0.190500i
$187$			31.1769i			2.27988i
$188$	−7.50000	−	4.33013i	−0.546994	−	0.315807i
$189$		0			0
$190$		−	5.19615i		−	0.376969i
$191$	7.50000	−	12.9904i	0.542681	−	0.939951i	−0.456068	−	0.889945i	$-0.650743\pi$
$191$	7.50000	−	12.9904i	0.542681	−	0.939951i	0.998749	−	0.0500060i	$-0.0159241\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−1.50000	+	0.866025i	−0.107972	+	0.0623379i	−0.553014	−	0.833172i	$-0.686522\pi$
$193$	−1.50000	+	0.866025i	−0.107972	+	0.0623379i	0.445041	+	0.895510i	$0.353189\pi$
$194$	−9.00000			−0.646162
$195$	−4.50000	−	4.33013i	−0.322252	−	0.310087i
$196$		0			0
$197$	19.5000	−	11.2583i	1.38932	−	0.802123i	0.396079	−	0.918216i	$-0.370371\pi$
$197$	19.5000	−	11.2583i	1.38932	−	0.802123i	0.993238	+	0.116094i	$0.0370372\pi$
$198$	−9.00000	−	15.5885i	−0.639602	−	1.10782i
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	−0.928166	−	0.372168i	$-0.878615\pi$
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	0.786389	+	0.617731i	$0.211948\pi$
$200$			3.46410i			0.244949i
$201$	−7.50000	−	4.33013i	−0.529009	−	0.305424i
$202$	13.5000	+	7.79423i	0.949857	+	0.548400i
$203$		0			0
$204$	−3.00000	+	5.19615i	−0.210042	+	0.363803i
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$	−19.5000	+	11.2583i	−1.35863	+	0.784405i
$207$		0			0
$208$	12.5000	−	12.9904i	0.866719	−	0.900721i
$209$	9.00000			0.622543
$210$		0			0
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	0.550743	−	0.834675i	$-0.314345\pi$
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$	−4.50000	+	7.79423i	−0.309061	+	0.535310i
$213$			1.73205i			0.118678i
$214$		0			0
$215$	16.5000	+	9.52628i	1.12529	+	0.649687i
$216$			8.66025i			0.589256i
$217$		0			0
$218$	−4.50000	−	7.79423i	−0.304778	−	0.527892i
$219$	−7.50000	+	4.33013i	−0.506803	+	0.292603i
$220$	−9.00000			−0.606780
$221$	21.0000	+	5.19615i	1.41261	+	0.349531i
$222$		0			0
$223$	4.50000	−	2.59808i	0.301342	−	0.173980i	−0.341703	−	0.939808i	$-0.611004\pi$
$223$	4.50000	−	2.59808i	0.301342	−	0.173980i	0.643046	+	0.765828i	$0.277671\pi$
$224$		0			0
$225$	2.00000	−	3.46410i	0.133333	−	0.230940i
$226$			25.9808i			1.72821i
$227$	15.0000	+	8.66025i	0.995585	+	0.574801i	0.906939	−	0.421262i	$-0.138413\pi$
$227$	15.0000	+	8.66025i	0.995585	+	0.574801i	0.0886460	+	0.996063i	$0.471746\pi$
$228$	1.50000	+	0.866025i	0.0993399	+	0.0573539i
$229$			12.1244i			0.801200i	0.916253	+	0.400600i	$0.131198\pi$
$229$			12.1244i			0.801200i	−0.916253	+	0.400600i	$0.868802\pi$
$230$		0			0
$231$		0			0
$232$	4.50000	−	2.59808i	0.295439	−	0.170572i
$233$	3.00000			0.196537			0.0982683	−	0.995160i	$-0.468670\pi$
$233$	3.00000			0.196537			0.0982683	+	0.995160i	$0.468670\pi$
$234$	−12.0000	+	3.46410i	−0.784465	+	0.226455i
$235$	−15.0000			−0.978492
$236$	3.00000	−	1.73205i	0.195283	−	0.112747i
$237$	−2.50000	−	4.33013i	−0.162392	−	0.281272i
$238$		0			0
$239$			10.3923i			0.672222i	0.941822	+	0.336111i	$0.109112\pi$
$239$			10.3923i			0.672222i	−0.941822	+	0.336111i	$0.890888\pi$
$240$	7.50000	+	4.33013i	0.484123	+	0.279508i
$241$	6.00000	+	3.46410i	0.386494	+	0.223142i	0.680640	−	0.732618i	$-0.261702\pi$
$241$	6.00000	+	3.46410i	0.386494	+	0.223142i	−0.294146	+	0.955761i	$0.595035\pi$
$242$		−	27.7128i		−	1.78145i
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$	3.50000	+	6.06218i	0.224065	+	0.388091i
$245$		0			0
$246$	−9.00000			−0.573819
$247$	1.50000	−	6.06218i	0.0954427	−	0.385727i
$248$	3.00000			0.190500
$249$	−3.00000	+	1.73205i	−0.190117	+	0.109764i
$250$	−10.5000	−	18.1865i	−0.664078	−	1.15022i
$251$	−1.50000	+	2.59808i	−0.0946792	+	0.163989i	−0.909475	−	0.415759i	$-0.863516\pi$
$251$	−1.50000	+	2.59808i	−0.0946792	+	0.163989i	0.814795	+	0.579748i	$0.196849\pi$
$252$		0			0
$253$		0			0
$254$	−19.5000	−	11.2583i	−1.22354	−	0.706410i
$255$			10.3923i			0.650791i
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	−15.0000	−	25.9808i	−0.935674	−	1.62064i	−0.773427	−	0.633885i	$-0.781459\pi$
$257$	−15.0000	−	25.9808i	−0.935674	−	1.62064i	−0.162247	−	0.986750i	$-0.551874\pi$
$258$	−16.5000	+	9.52628i	−1.02725	+	0.593080i
$259$		0			0
$260$	−1.50000	+	6.06218i	−0.0930261	+	0.375960i
$261$	−6.00000			−0.371391
$262$	22.5000	−	12.9904i	1.39005	−	0.802548i
$263$	−1.50000	−	2.59808i	−0.0924940	−	0.160204i	0.816066	−	0.577959i	$-0.196151\pi$
$263$	−1.50000	−	2.59808i	−0.0924940	−	0.160204i	−0.908560	+	0.417755i	$0.862817\pi$
$264$	−4.50000	+	7.79423i	−0.276956	+	0.479702i
$265$			15.5885i			0.957591i
$266$		0			0
$267$	6.00000	+	3.46410i	0.367194	+	0.212000i
$268$			8.66025i			0.529009i
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	−0.759958	−	0.649972i	$-0.774781\pi$
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	0.942871	+	0.333157i	$0.108114\pi$
$270$	−7.50000	−	12.9904i	−0.456435	−	0.790569i
$271$	15.0000	−	8.66025i	0.911185	−	0.526073i	0.0303728	−	0.999539i	$-0.490331\pi$
$271$	15.0000	−	8.66025i	0.911185	−	0.526073i	0.880812	+	0.473466i	$0.156997\pi$
$272$	−30.0000			−1.81902
$273$		0			0
$274$		0			0
$275$	9.00000	−	5.19615i	0.542720	−	0.313340i
$276$		0			0
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	0.976231	+	0.216731i	$0.0695395\pi$
$278$		−	22.5167i		−	1.35046i
$279$	−3.00000	−	1.73205i	−0.179605	−	0.103695i
$280$		0			0
$281$		−	6.92820i		−	0.413302i	−0.978415	−	0.206651i	$-0.933744\pi$
$281$		−	6.92820i		−	0.413302i	0.978415	−	0.206651i	$-0.0662565\pi$
$282$	7.50000	−	12.9904i	0.446619	−	0.773566i
$283$	−9.50000	−	16.4545i	−0.564716	−	0.978117i	−0.997076	−	0.0764162i	$-0.975652\pi$
$283$	−9.50000	−	16.4545i	−0.564716	−	0.978117i	0.432360	−	0.901701i	$-0.357681\pi$
$284$	1.50000	−	0.866025i	0.0890086	−	0.0513892i
$285$	3.00000			0.177705
$286$	−31.5000	−	7.79423i	−1.86263	−	0.460882i
$287$		0			0
$288$	9.00000	−	5.19615i	0.530330	−	0.306186i
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	−4.50000	+	7.79423i	−0.264249	+	0.457693i
$291$		−	5.19615i		−	0.304604i
$292$	7.50000	+	4.33013i	0.438904	+	0.253402i
$293$	−22.5000	−	12.9904i	−1.31446	−	0.758906i	−0.331632	−	0.943409i	$-0.607599\pi$
$293$	−22.5000	−	12.9904i	−1.31446	−	0.758906i	−0.982832	+	0.184503i	$0.940933\pi$
$294$		0			0
$295$	3.00000	−	5.19615i	0.174667	−	0.302532i
$296$		0			0
$297$	22.5000	−	12.9904i	1.30558	−	0.753778i
$298$	33.0000			1.91164
$299$		0			0
$300$	2.00000			0.115470
$301$		0			0
$302$	10.5000	+	18.1865i	0.604207	+	1.04652i
$303$	−4.50000	+	7.79423i	−0.258518	+	0.447767i
$304$			8.66025i			0.496700i
$305$	10.5000	+	6.06218i	0.601228	+	0.347119i
$306$	18.0000	+	10.3923i	1.02899	+	0.594089i
$307$			24.2487i			1.38395i	0.721923	+	0.691974i	$0.243259\pi$
$307$			24.2487i			1.38395i	−0.721923	+	0.691974i	$0.756741\pi$
$308$		0			0
$309$	−6.50000	−	11.2583i	−0.369772	−	0.640464i
$310$	−4.50000	+	2.59808i	−0.255583	+	0.147561i
$311$	−15.0000			−0.850572			−0.425286	−	0.905059i	$-0.639826\pi$
$311$	−15.0000			−0.850572			−0.425286	+	0.905059i	$0.639826\pi$
$312$	4.50000	+	4.33013i	0.254762	+	0.245145i
$313$	19.0000			1.07394			0.536972	−	0.843600i	$-0.319568\pi$
$313$	19.0000			1.07394			0.536972	+	0.843600i	$0.319568\pi$
$314$	34.5000	−	19.9186i	1.94695	−	1.12407i
$315$		0			0
$316$	−2.50000	+	4.33013i	−0.140636	+	0.243589i
$317$			5.19615i			0.291845i	0.989296	+	0.145922i	$0.0466150\pi$
$317$			5.19615i			0.291845i	−0.989296	+	0.145922i	$0.953385\pi$
$318$	−13.5000	−	7.79423i	−0.757042	−	0.437079i
$319$	−13.5000	−	7.79423i	−0.755855	−	0.436393i
$320$			1.73205i			0.0968246i
$321$		0			0
$322$		0			0
$323$	−9.00000	+	5.19615i	−0.500773	+	0.289122i
$324$	−1.00000			−0.0555556
$325$	−2.00000	−	6.92820i	−0.110940	−	0.384308i
$326$	−21.0000			−1.16308
$327$	4.50000	−	2.59808i	0.248851	−	0.143674i
$328$	−4.50000	−	7.79423i	−0.248471	−	0.430364i
$329$		0			0
$330$		−	15.5885i		−	0.858116i
$331$	−28.5000	−	16.4545i	−1.56650	−	0.904420i	−0.996572	−	0.0827265i	$-0.973637\pi$
$331$	−28.5000	−	16.4545i	−1.56650	−	0.904420i	−0.569929	−	0.821694i	$-0.693029\pi$
$332$	3.00000	+	1.73205i	0.164646	+	0.0950586i
$333$		0			0
$334$	−1.50000	+	2.59808i	−0.0820763	+	0.142160i
$335$	7.50000	+	12.9904i	0.409769	+	0.709740i
$336$		0			0
$337$	22.0000			1.19842			0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000			1.19842			0.599208	+	0.800593i	$0.295482\pi$
$338$	−10.5000	+	19.9186i	−0.571125	+	1.08343i
$339$	−15.0000			−0.814688
$340$	9.00000	−	5.19615i	0.488094	−	0.281801i
$341$	−4.50000	−	7.79423i	−0.243689	−	0.422081i
$342$	3.00000	−	5.19615i	0.162221	−	0.280976i
$343$		0			0
$344$	−16.5000	−	9.52628i	−0.889620	−	0.513623i
$345$		0			0
$346$			25.9808i			1.39673i
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$	−1.50000	−	2.59808i	−0.0804084	−	0.139272i
$349$	−4.50000	+	2.59808i	−0.240879	+	0.139072i	−0.615581	−	0.788074i	$-0.711079\pi$
$349$	−4.50000	+	2.59808i	−0.240879	+	0.139072i	0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$	−5.00000	−	17.3205i	−0.266880	−	0.924500i
$352$	27.0000			1.43910
$353$	−1.50000	+	0.866025i	−0.0798369	+	0.0460939i	−0.539387	−	0.842058i	$-0.681344\pi$
$353$	−1.50000	+	0.866025i	−0.0798369	+	0.0460939i	0.459550	+	0.888152i	$0.348011\pi$
$354$	3.00000	+	5.19615i	0.159448	+	0.276172i
$355$	1.50000	−	2.59808i	0.0796117	−	0.137892i
$356$		−	6.92820i		−	0.367194i
$357$		0			0
$358$	−4.50000	−	2.59808i	−0.237832	−	0.137313i
$359$			19.0526i			1.00556i	0.864416	+	0.502778i	$0.167689\pi$
$359$			19.0526i			1.00556i	−0.864416	+	0.502778i	$0.832311\pi$
$360$	3.00000	−	5.19615i	0.158114	−	0.273861i
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$	3.00000	−	1.73205i	0.157676	−	0.0910346i
$363$	16.0000			0.839782
$364$		0			0
$365$	15.0000			0.785136
$366$	−10.5000	+	6.06218i	−0.548844	+	0.316875i
$367$	−11.5000	−	19.9186i	−0.600295	−	1.03974i	−0.992776	−	0.119982i	$-0.961716\pi$
$367$	−11.5000	−	19.9186i	−0.600295	−	1.03974i	0.392481	−	0.919760i	$-0.371617\pi$
$368$		0			0
$369$			10.3923i			0.541002i
$370$		0			0
$371$		0			0
$372$		−	1.73205i		−	0.0898027i
$373$	−9.50000	+	16.4545i	−0.491891	+	0.851981i	−0.999956	−	0.00933789i	$-0.997028\pi$
$373$	−9.50000	+	16.4545i	−0.491891	+	0.851981i	0.508065	+	0.861319i	$0.330361\pi$
$374$	27.0000	+	46.7654i	1.39614	+	2.41818i
$375$	10.5000	−	6.06218i	0.542218	−	0.313050i
$376$	15.0000			0.773566
$377$	−7.50000	+	7.79423i	−0.386270	+	0.401423i
$378$		0			0
$379$	−1.50000	+	0.866025i	−0.0770498	+	0.0444847i	−0.538030	−	0.842926i	$-0.680831\pi$
$379$	−1.50000	+	0.866025i	−0.0770498	+	0.0444847i	0.460980	+	0.887410i	$0.347498\pi$
$380$	−1.50000	−	2.59808i	−0.0769484	−	0.133278i
$381$	6.50000	−	11.2583i	0.333005	−	0.576782i
$382$		−	25.9808i		−	1.32929i
$383$	13.5000	+	7.79423i	0.689818	+	0.398266i	0.803544	−	0.595246i	$-0.202945\pi$
$383$	13.5000	+	7.79423i	0.689818	+	0.398266i	−0.113726	+	0.993512i	$0.536279\pi$
$384$	−10.5000	−	6.06218i	−0.535826	−	0.309359i
$385$		0			0
$386$	−1.50000	+	2.59808i	−0.0763480	+	0.132239i
$387$	11.0000	+	19.0526i	0.559161	+	0.968496i
$388$	−4.50000	+	2.59808i	−0.228453	+	0.131897i
$389$	3.00000			0.152106			0.0760530	−	0.997104i	$-0.475768\pi$
$389$	3.00000			0.152106			0.0760530	+	0.997104i	$0.475768\pi$
$390$	−10.5000	−	2.59808i	−0.531688	−	0.131559i
$391$		0			0
$392$		0			0
$393$	7.50000	+	12.9904i	0.378325	+	0.655278i
$394$	19.5000	−	33.7750i	0.982396	−	1.70156i
$395$			8.66025i			0.435745i
$396$	−9.00000	−	5.19615i	−0.452267	−	0.261116i
$397$	−31.5000	−	18.1865i	−1.58094	−	0.912756i	−0.994722	−	0.102602i	$-0.967283\pi$
$397$	−31.5000	−	18.1865i	−1.58094	−	0.912756i	−0.586217	−	0.810154i	$-0.699383\pi$
$398$			6.92820i			0.347279i
$399$		0			0
$400$	5.00000	+	8.66025i	0.250000	+	0.433013i
$401$	6.00000	−	3.46410i	0.299626	−	0.172989i	−0.342649	−	0.939463i	$-0.611324\pi$
$401$	6.00000	−	3.46410i	0.299626	−	0.172989i	0.642275	+	0.766475i	$0.277991\pi$
$402$	−15.0000			−0.748132
$403$	−6.00000	+	1.73205i	−0.298881	+	0.0862796i
$404$	9.00000			0.447767
$405$	−1.50000	+	0.866025i	−0.0745356	+	0.0430331i
$406$		0			0
$407$		0			0
$408$		−	10.3923i		−	0.514496i
$409$	−6.00000	−	3.46410i	−0.296681	−	0.171289i	0.344270	−	0.938871i	$-0.388126\pi$
$409$	−6.00000	−	3.46410i	−0.296681	−	0.171289i	−0.640951	+	0.767582i	$0.721460\pi$
$410$	13.5000	+	7.79423i	0.666717	+	0.384930i
$411$		0			0
$412$	−6.50000	+	11.2583i	−0.320232	+	0.554658i
$413$		0			0
$414$		0			0
$415$	6.00000			0.294528
$416$	4.50000	−	18.1865i	0.220631	−	0.891668i
$417$	13.0000			0.636613
$418$	13.5000	−	7.79423i	0.660307	−	0.381228i
$419$	−10.5000	−	18.1865i	−0.512959	−	0.888470i	−0.999887	−	0.0150285i	$-0.995216\pi$
$419$	−10.5000	−	18.1865i	−0.512959	−	0.888470i	0.486928	−	0.873442i	$-0.338117\pi$
$420$		0			0
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$	−19.5000	−	11.2583i	−0.949245	−	0.548047i
$423$	−15.0000	−	8.66025i	−0.729325	−	0.421076i
$424$		−	15.5885i		−	0.757042i
$425$	−6.00000	+	10.3923i	−0.291043	+	0.504101i
$426$	1.50000	+	2.59808i	0.0726752	+	0.125877i
$427$		0			0
$428$		0			0
$429$	4.50000	−	18.1865i	0.217262	−	0.878054i
$430$	33.0000			1.59140
$431$	28.5000	−	16.4545i	1.37280	−	0.792585i	0.381517	−	0.924362i	$-0.375402\pi$
$431$	28.5000	−	16.4545i	1.37280	−	0.792585i	0.991279	+	0.131777i	$0.0420683\pi$
$432$	12.5000	+	21.6506i	0.601407	+	1.04167i
$433$	−9.50000	+	16.4545i	−0.456541	+	0.790752i	−0.998775	−	0.0494752i	$-0.984245\pi$
$433$	−9.50000	+	16.4545i	−0.456541	+	0.790752i	0.542234	+	0.840227i	$0.317578\pi$
$434$		0			0
$435$	−4.50000	−	2.59808i	−0.215758	−	0.124568i
$436$	−4.50000	−	2.59808i	−0.215511	−	0.124425i
$437$		0			0
$438$	−7.50000	+	12.9904i	−0.358364	+	0.620704i
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$	13.5000	−	7.79423i	0.643587	−	0.371575i
$441$		0			0
$442$	36.0000	−	10.3923i	1.71235	−	0.494312i
$443$	15.0000			0.712672			0.356336	−	0.934358i	$-0.384026\pi$
$443$	15.0000			0.712672			0.356336	+	0.934358i	$0.384026\pi$
$444$		0			0
$445$	−6.00000	−	10.3923i	−0.284427	−	0.492642i
$446$	4.50000	−	7.79423i	0.213081	−	0.369067i
$447$			19.0526i			0.901155i
$448$		0			0
$449$	1.50000	+	0.866025i	0.0707894	+	0.0408703i	0.534977	−	0.844867i	$-0.320320\pi$
$449$	1.50000	+	0.866025i	0.0707894	+	0.0408703i	−0.464188	+	0.885737i	$0.653654\pi$
$450$		−	6.92820i		−	0.326599i
$451$	−13.5000	+	23.3827i	−0.635690	+	1.10105i
$452$	7.50000	+	12.9904i	0.352770	+	0.611016i
$453$	−10.5000	+	6.06218i	−0.493333	+	0.284826i
$454$	30.0000			1.40797
$455$		0			0
$456$	−3.00000			−0.140488
$457$	30.0000	−	17.3205i	1.40334	−	0.810219i	0.408607	−	0.912710i	$-0.366015\pi$
$457$	30.0000	−	17.3205i	1.40334	−	0.810219i	0.994734	+	0.102491i	$0.0326814\pi$
$458$	10.5000	+	18.1865i	0.490633	+	0.849801i
$459$	−15.0000	+	25.9808i	−0.700140	+	1.21268i
$460$		0			0
$461$	25.5000	+	14.7224i	1.18765	+	0.685692i	0.957773	−	0.287527i	$-0.0928330\pi$
$461$	25.5000	+	14.7224i	1.18765	+	0.685692i	0.229881	+	0.973219i	$0.426166\pi$
$462$		0			0
$463$		−	24.2487i		−	1.12693i	−0.826139	−	0.563467i	$-0.809467\pi$
$463$		−	24.2487i		−	1.12693i	0.826139	−	0.563467i	$-0.190533\pi$
$464$	7.50000	−	12.9904i	0.348179	−	0.603063i
$465$	−1.50000	−	2.59808i	−0.0695608	−	0.120483i
$466$	4.50000	−	2.59808i	0.208458	−	0.120354i
$467$	−21.0000			−0.971764			−0.485882	−	0.874024i	$-0.661502\pi$
$467$	−21.0000			−0.971764			−0.485882	+	0.874024i	$0.661502\pi$
$468$	−5.00000	+	5.19615i	−0.231125	+	0.240192i
$469$		0			0
$470$	−22.5000	+	12.9904i	−1.03785	+	0.599202i
$471$	11.5000	+	19.9186i	0.529892	+	0.917800i
$472$	−3.00000	+	5.19615i	−0.138086	+	0.239172i
$473$			57.1577i			2.62811i
$474$	−7.50000	−	4.33013i	−0.344486	−	0.198889i
$475$	3.00000	+	1.73205i	0.137649	+	0.0794719i
$476$		0			0
$477$	−9.00000	+	15.5885i	−0.412082	+	0.713746i
$478$	9.00000	+	15.5885i	0.411650	+	0.712999i
$479$	−25.5000	+	14.7224i	−1.16512	+	0.672685i	−0.952527	−	0.304455i	$-0.901526\pi$
$479$	−25.5000	+	14.7224i	−1.16512	+	0.672685i	−0.212598	+	0.977140i	$0.568192\pi$
$480$	9.00000			0.410792
$481$		0			0
$482$	12.0000			0.546585
$483$		0			0
$484$	−8.00000	−	13.8564i	−0.363636	−	0.629837i
$485$	−4.50000	+	7.79423i	−0.204334	+	0.353918i
$486$		−	27.7128i		−	1.25708i
$487$	21.0000	+	12.1244i	0.951601	+	0.549407i	0.893578	−	0.448908i	$-0.148187\pi$
$487$	21.0000	+	12.1244i	0.951601	+	0.549407i	0.0580230	+	0.998315i	$0.481520\pi$
$488$	−10.5000	−	6.06218i	−0.475313	−	0.274422i
$489$		−	12.1244i		−	0.548282i
$490$		0			0
$491$	13.5000	+	23.3827i	0.609246	+	1.05525i	0.991365	+	0.131132i	$0.0418613\pi$
$491$	13.5000	+	23.3827i	0.609246	+	1.05525i	−0.382118	+	0.924113i	$0.624805\pi$
$492$	−4.50000	+	2.59808i	−0.202876	+	0.117130i
$493$	18.0000			0.810679
$494$	−3.00000	−	10.3923i	−0.134976	−	0.467572i
$495$	−18.0000			−0.809040
$496$	7.50000	−	4.33013i	0.336760	−	0.194428i
$497$		0			0
$498$	−3.00000	+	5.19615i	−0.134433	+	0.232845i
$499$		−	1.73205i		−	0.0775372i	−0.999248	−	0.0387686i	$-0.987656\pi$
$499$		−	1.73205i		−	0.0775372i	0.999248	−	0.0387686i	$-0.0123435\pi$
$500$	−10.5000	−	6.06218i	−0.469574	−	0.271109i
$501$	−1.50000	−	0.866025i	−0.0670151	−	0.0386912i
$502$			5.19615i			0.231916i
$503$	4.50000	−	7.79423i	0.200645	−	0.347527i	−0.748091	−	0.663596i	$-0.769030\pi$
$503$	4.50000	−	7.79423i	0.200645	−	0.347527i	0.948736	+	0.316068i	$0.102363\pi$
$504$		0			0
$505$	13.5000	−	7.79423i	0.600742	−	0.346839i
$506$		0			0
$507$	−11.5000	−	6.06218i	−0.510733	−	0.269231i
$508$	−13.0000			−0.576782
$509$	6.00000	−	3.46410i	0.265945	−	0.153544i	−0.361098	−	0.932528i	$-0.617598\pi$
$509$	6.00000	−	3.46410i	0.265945	−	0.153544i	0.627044	+	0.778984i	$0.284265\pi$
$510$	9.00000	+	15.5885i	0.398527	+	0.690268i
$511$		0			0
$512$			8.66025i			0.382733i
$513$	7.50000	+	4.33013i	0.331133	+	0.191180i
$514$	−45.0000	−	25.9808i	−1.98486	−	1.14596i
$515$			22.5167i			0.992203i
$516$	−5.50000	+	9.52628i	−0.242124	+	0.419371i
$517$	−22.5000	−	38.9711i	−0.989549	−	1.71395i
$518$		0			0
$519$	−15.0000			−0.658427
$520$	−3.00000	−	10.3923i	−0.131559	−	0.455733i
$521$	39.0000			1.70862			0.854311	−	0.519763i	$-0.173980\pi$
$521$	39.0000			1.70862			0.854311	+	0.519763i	$0.173980\pi$
$522$	−9.00000	+	5.19615i	−0.393919	+	0.227429i
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	0.906434	−	0.422347i	$-0.138794\pi$
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	−0.818980	+	0.573822i	$0.805460\pi$
$524$	7.50000	−	12.9904i	0.327639	−	0.567487i
$525$		0			0
$526$	−4.50000	−	2.59808i	−0.196209	−	0.113282i
$527$	9.00000	+	5.19615i	0.392046	+	0.226348i
$528$			25.9808i			1.13067i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	13.5000	+	23.3827i	0.586403	+	1.01568i
$531$	6.00000	−	3.46410i	0.260378	−	0.150329i
$532$		0			0
$533$	13.5000	+	12.9904i	0.584750	+	0.562676i
$534$	12.0000			0.519291
$535$		0			0
$536$	−7.50000	−	12.9904i	−0.323951	−	0.561099i
$537$	1.50000	−	2.59808i	0.0647298	−	0.112115i
$538$		−	10.3923i		−	0.448044i
$539$		0			0
$540$	−7.50000	−	4.33013i	−0.322749	−	0.186339i
$541$			12.1244i			0.521267i	0.965438	+	0.260633i	$0.0839314\pi$
$541$			12.1244i			0.521267i	−0.965438	+	0.260633i	$0.916069\pi$
$542$	15.0000	−	25.9808i	0.644305	−	1.11597i
$543$	1.00000	+	1.73205i	0.0429141	+	0.0743294i
$544$	−27.0000	+	15.5885i	−1.15762	+	0.668350i
$545$	−9.00000			−0.385518
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$		0			0
$549$	7.00000	+	12.1244i	0.298753	+	0.517455i
$550$	9.00000	−	15.5885i	0.383761	−	0.664694i
$551$		−	5.19615i		−	0.221364i
$552$		0			0
$553$		0			0
$554$		−	17.3205i		−	0.735878i
$555$		0			0
$556$	−6.50000	−	11.2583i	−0.275661	−	0.477460i
$557$	−13.5000	+	7.79423i	−0.572013	+	0.330252i	−0.757953	−	0.652309i	$-0.773800\pi$
$557$	−13.5000	+	7.79423i	−0.572013	+	0.330252i	0.185940	+	0.982561i	$0.440467\pi$
$558$	−6.00000			−0.254000
$559$	38.5000	+	9.52628i	1.62838	+	0.402919i
$560$		0			0
$561$	−27.0000	+	15.5885i	−1.13994	+	0.658145i
$562$	−6.00000	−	10.3923i	−0.253095	−	0.438373i
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	−0.184950	−	0.982748i	$-0.559212\pi$
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	0.943560	−	0.331202i	$-0.107454\pi$
$564$		−	8.66025i		−	0.364662i
$565$	22.5000	+	12.9904i	0.946582	+	0.546509i
$566$	−28.5000	−	16.4545i	−1.19794	−	0.691633i
$567$		0			0
$568$	−1.50000	+	2.59808i	−0.0629386	+	0.109013i
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$	4.50000	−	2.59808i	0.188484	−	0.108821i
$571$	−23.0000			−0.962520			−0.481260	−	0.876578i	$-0.659821\pi$
$571$	−23.0000			−0.962520			−0.481260	+	0.876578i	$0.659821\pi$
$572$	−18.0000	+	5.19615i	−0.752618	+	0.217262i
$573$	15.0000			0.626634
$574$		0			0
$575$		0			0
$576$	−1.00000	+	1.73205i	−0.0416667	+	0.0721688i
$577$			15.5885i			0.648956i	0.945893	+	0.324478i	$0.105189\pi$
$577$			15.5885i			0.648956i	−0.945893	+	0.324478i	$0.894811\pi$
$578$	−28.5000	−	16.4545i	−1.18544	−	0.684416i
$579$	−1.50000	−	0.866025i	−0.0623379	−	0.0359908i
$580$			5.19615i			0.215758i
$581$		0			0
$582$	−4.50000	−	7.79423i	−0.186531	−	0.323081i
$583$	−40.5000	+	23.3827i	−1.67734	+	0.968412i
$584$	−15.0000			−0.620704
$585$	−3.00000	+	12.1244i	−0.124035	+	0.501280i
$586$	−45.0000			−1.85893
$587$	−13.5000	+	7.79423i	−0.557205	+	0.321702i	−0.752023	−	0.659137i	$-0.770922\pi$
$587$	−13.5000	+	7.79423i	−0.557205	+	0.321702i	0.194818	+	0.980839i	$0.437588\pi$
$588$		0			0
$589$	1.50000	−	2.59808i	0.0618064	−	0.107052i
$590$		−	10.3923i		−	0.427844i
$591$	19.5000	+	11.2583i	0.802123	+	0.463106i
$592$		0			0
$593$			5.19615i			0.213380i	0.994292	+	0.106690i	$0.0340253\pi$
$593$			5.19615i			0.213380i	−0.994292	+	0.106690i	$0.965975\pi$
$594$	22.5000	−	38.9711i	0.923186	−	1.59901i
$595$		0			0
$596$	16.5000	−	9.52628i	0.675866	−	0.390212i
$597$	−4.00000			−0.163709
$598$		0			0
$599$	9.00000			0.367730			0.183865	−	0.982952i	$-0.441139\pi$
$599$	9.00000			0.367730			0.183865	+	0.982952i	$0.441139\pi$
$600$	−3.00000	+	1.73205i	−0.122474	+	0.0707107i
$601$	−9.50000	−	16.4545i	−0.387513	−	0.671192i	0.604601	−	0.796528i	$-0.293332\pi$
$601$	−9.50000	−	16.4545i	−0.387513	−	0.671192i	−0.992114	+	0.125336i	$0.959999\pi$
$602$		0			0
$603$			17.3205i			0.705346i
$604$	10.5000	+	6.06218i	0.427239	+	0.246667i
$605$	−24.0000	−	13.8564i	−0.975739	−	0.563343i
$606$			15.5885i			0.633238i
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.0134214	−	0.999910i	$-0.495728\pi$
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.859237	−	0.511578i	$-0.170939\pi$
$608$	4.50000	+	7.79423i	0.182499	+	0.316098i
$609$		0			0
$610$	21.0000			0.850265
$611$	−30.0000	+	8.66025i	−1.21367	+	0.350356i
$612$	12.0000			0.485071
$613$	−31.5000	+	18.1865i	−1.27227	+	0.734547i	−0.975415	−	0.220375i	$-0.929272\pi$
$613$	−31.5000	+	18.1865i	−1.27227	+	0.734547i	−0.296858	+	0.954922i	$0.595939\pi$
$614$	21.0000	+	36.3731i	0.847491	+	1.46790i
$615$	−4.50000	+	7.79423i	−0.181458	+	0.314294i
$616$		0			0
$617$	37.5000	+	21.6506i	1.50969	+	0.871622i	0.999936	+	0.0113033i	$0.00359804\pi$
$617$	37.5000	+	21.6506i	1.50969	+	0.871622i	0.509757	+	0.860318i	$0.329735\pi$
$618$	−19.5000	−	11.2583i	−0.784405	−	0.452876i
$619$			19.0526i			0.765787i	0.923792	+	0.382893i	$0.125072\pi$
$619$			19.0526i			0.765787i	−0.923792	+	0.382893i	$0.874928\pi$
$620$	−1.50000	+	2.59808i	−0.0602414	+	0.104341i
$621$		0			0
$622$	−22.5000	+	12.9904i	−0.902168	+	0.520867i
$623$		0			0
$624$	17.5000	+	4.33013i	0.700561	+	0.173344i
$625$	−11.0000			−0.440000
$626$	28.5000	−	16.4545i	1.13909	−	0.657653i
$627$	4.50000	+	7.79423i	0.179713	+	0.311272i
$628$	11.5000	−	19.9186i	0.458900	−	0.794838i
$629$		0			0
$630$		0			0
$631$	−40.5000	−	23.3827i	−1.61228	−	0.930850i	−0.988841	−	0.148978i	$-0.952402\pi$
$631$	−40.5000	−	23.3827i	−1.61228	−	0.930850i	−0.623439	−	0.781872i	$-0.714265\pi$
$632$		−	8.66025i		−	0.344486i
$633$	6.50000	−	11.2583i	0.258352	−	0.447478i
$634$	4.50000	+	7.79423i	0.178718	+	0.309548i
$635$	−19.5000	+	11.2583i	−0.773834	+	0.446773i
$636$	−9.00000			−0.356873
$637$		0			0
$638$	−27.0000			−1.06894
$639$	3.00000	−	1.73205i	0.118678	−	0.0685189i
$640$	10.5000	+	18.1865i	0.415049	+	0.718886i
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	0.401435	+	0.915888i	$0.368512\pi$
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	−0.993899	+	0.110291i	$0.964822\pi$
$642$		0			0
$643$	−4.50000	−	2.59808i	−0.177463	−	0.102458i	0.408637	−	0.912697i	$-0.366004\pi$
$643$	−4.50000	−	2.59808i	−0.177463	−	0.102458i	−0.586100	+	0.810239i	$0.699337\pi$
$644$		0			0
$645$			19.0526i			0.750194i
$646$	−9.00000	+	15.5885i	−0.354100	+	0.613320i
$647$	4.50000	+	7.79423i	0.176913	+	0.306423i	0.940822	−	0.338902i	$-0.110055\pi$
$647$	4.50000	+	7.79423i	0.176913	+	0.306423i	−0.763908	+	0.645325i	$0.776722\pi$
$648$	1.50000	−	0.866025i	0.0589256	−	0.0340207i
$649$	18.0000			0.706562
$650$	−9.00000	−	8.66025i	−0.353009	−	0.339683i
$651$		0			0
$652$	−10.5000	+	6.06218i	−0.411212	+	0.237413i
$653$	15.0000	+	25.9808i	0.586995	+	1.01671i	0.994623	+	0.103558i	$0.0330227\pi$
$653$	15.0000	+	25.9808i	0.586995	+	1.01671i	−0.407628	+	0.913148i	$0.633644\pi$
$654$	4.50000	−	7.79423i	0.175964	−	0.304778i
$655$		−	25.9808i		−	1.01515i
$656$	−22.5000	−	12.9904i	−0.878477	−	0.507189i
$657$	15.0000	+	8.66025i	0.585206	+	0.337869i
$658$		0			0
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	−0.974320	−	0.225168i	$-0.927707\pi$
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	0.682161	+	0.731202i	$0.261040\pi$
$660$	−4.50000	−	7.79423i	−0.175162	−	0.303390i
$661$	−31.5000	+	18.1865i	−1.22521	+	0.707374i	−0.966024	−	0.258454i	$-0.916787\pi$
$661$	−31.5000	+	18.1865i	−1.22521	+	0.707374i	−0.259184	+	0.965828i	$0.583454\pi$
$662$	−57.0000			−2.21537
$663$	6.00000	+	20.7846i	0.233021	+	0.807207i
$664$	−6.00000			−0.232845
$665$		0			0
$666$		0			0
$667$		0			0
$668$			1.73205i			0.0670151i
$669$	4.50000	+	2.59808i	0.173980	+	0.100447i
$670$	22.5000	+	12.9904i	0.869251	+	0.501862i
$671$			36.3731i			1.40417i
$672$		0			0
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	0.875501	−	0.483216i	$-0.160531\pi$
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	−0.856228	+	0.516599i	$0.827198\pi$
$674$	33.0000	−	19.0526i	1.27111	−	0.733877i
$675$	10.0000			0.384900
$676$	0.500000	+	12.9904i	0.0192308	+	0.499630i
$677$	27.0000			1.03769			0.518847	−	0.854867i	$-0.326361\pi$
$677$	27.0000			1.03769			0.518847	+	0.854867i	$0.326361\pi$
$678$	−22.5000	+	12.9904i	−0.864107	+	0.498893i
$679$		0			0
$680$	−9.00000	+	15.5885i	−0.345134	+	0.597790i
$681$			17.3205i			0.663723i
$682$	−13.5000	−	7.79423i	−0.516942	−	0.298456i
$683$	−21.0000	−	12.1244i	−0.803543	−	0.463926i	0.0411658	−	0.999152i	$-0.486893\pi$
$683$	−21.0000	−	12.1244i	−0.803543	−	0.463926i	−0.844708	+	0.535227i	$0.820226\pi$
$684$		−	3.46410i		−	0.132453i
$685$		0			0
$686$		0			0
$687$	−10.5000	+	6.06218i	−0.400600	+	0.231287i
$688$	−55.0000			−2.09686
$689$	9.00000	+	31.1769i	0.342873	+	1.18775i
$690$		0			0
$691$	−27.0000	+	15.5885i	−1.02713	+	0.593013i	−0.916161	−	0.400811i	$-0.868728\pi$
$691$	−27.0000	+	15.5885i	−1.02713	+	0.593013i	−0.110968	+	0.993824i	$0.535395\pi$
$692$	7.50000	+	12.9904i	0.285107	+	0.493820i
$693$		0			0
$694$		0			0
$695$	−19.5000	−	11.2583i	−0.739677	−	0.427053i
$696$	4.50000	+	2.59808i	0.170572	+	0.0984798i
$697$		−	31.1769i		−	1.18091i
$698$	−4.50000	+	7.79423i	−0.170328	+	0.295016i
$699$	1.50000	+	2.59808i	0.0567352	+	0.0982683i
$700$		0			0
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$	−22.5000	−	21.6506i	−0.849208	−	0.817151i
$703$		0			0
$704$	−4.50000	+	2.59808i	−0.169600	+	0.0979187i
$705$	−7.50000	−	12.9904i	−0.282466	−	0.489246i
$706$	−1.50000	+	2.59808i	−0.0564532	+	0.0977799i
$707$		0			0
$708$	3.00000	+	1.73205i	0.112747	+	0.0650945i
$709$	10.5000	+	6.06218i	0.394336	+	0.227670i	0.684037	−	0.729447i	$-0.260223\pi$
$709$	10.5000	+	6.06218i	0.394336	+	0.227670i	−0.289701	+	0.957117i	$0.593556\pi$
$710$		−	5.19615i		−	0.195008i
$711$	−5.00000	+	8.66025i	−0.187515	+	0.324785i
$712$	6.00000	+	10.3923i	0.224860	+	0.389468i
$713$		0			0
$714$		0			0
$715$	−22.5000	+	23.3827i	−0.841452	+	0.874463i
$716$	−3.00000			−0.112115
$717$	−9.00000	+	5.19615i	−0.336111	+	0.194054i
$718$	16.5000	+	28.5788i	0.615775	+	1.06655i
$719$	7.50000	−	12.9904i	0.279703	−	0.484459i	−0.691608	−	0.722273i	$-0.743097\pi$
$719$	7.50000	−	12.9904i	0.279703	−	0.484459i	0.971311	+	0.237814i	$0.0764307\pi$
$720$		−	17.3205i		−	0.645497i
$721$		0			0
$722$	−24.0000	−	13.8564i	−0.893188	−	0.515682i
$723$			6.92820i			0.257663i
$724$	1.00000	−	1.73205i	0.0371647	−	0.0643712i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	24.0000	−	13.8564i	0.890724	−	0.514259i
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	22.5000	−	12.9904i	0.832762	−	0.480796i
$731$	−33.0000	−	57.1577i	−1.22055	−	2.11405i
$732$	−3.50000	+	6.06218i	−0.129364	+	0.224065i
$733$		−	50.2295i		−	1.85527i	−0.373491	−	0.927634i	$-0.621839\pi$
$733$		−	50.2295i		−	1.85527i	0.373491	−	0.927634i	$-0.378161\pi$
$734$	−34.5000	−	19.9186i	−1.27342	−	0.735208i
$735$		0			0
$736$		0			0
$737$	−22.5000	+	38.9711i	−0.828798	+	1.43552i
$738$	9.00000	+	15.5885i	0.331295	+	0.573819i
$739$	34.5000	−	19.9186i	1.26910	−	0.732717i	0.294285	−	0.955718i	$-0.404919\pi$
$739$	34.5000	−	19.9186i	1.26910	−	0.732717i	0.974818	+	0.223001i	$0.0715853\pi$
$740$		0			0
$741$	6.00000	−	1.73205i	0.220416	−	0.0636285i
$742$		0			0
$743$	−1.50000	+	0.866025i	−0.0550297	+	0.0317714i	−0.527262	−	0.849703i	$-0.676782\pi$
$743$	−1.50000	+	0.866025i	−0.0550297	+	0.0317714i	0.472233	+	0.881474i	$0.343448\pi$
$744$	1.50000	+	2.59808i	0.0549927	+	0.0952501i
$745$	16.5000	−	28.5788i	0.604513	−	1.04705i
$746$			32.9090i			1.20488i
$747$	6.00000	+	3.46410i	0.219529	+	0.126745i
$748$	27.0000	+	15.5885i	0.987218	+	0.569970i
$749$		0			0
$750$	10.5000	−	18.1865i	0.383406	−	0.664078i
$751$	−10.0000	−	17.3205i	−0.364905	−	0.632034i	0.623856	−	0.781540i	$-0.285565\pi$
$751$	−10.0000	−	17.3205i	−0.364905	−	0.632034i	−0.988761	+	0.149505i	$0.952232\pi$
$752$	37.5000	−	21.6506i	1.36748	−	0.789517i
$753$	−3.00000			−0.109326
$754$	−4.50000	+	18.1865i	−0.163880	+	0.662314i
$755$	21.0000			0.764268
$756$		0			0
$757$	8.50000	+	14.7224i	0.308938	+	0.535096i	0.978130	−	0.207993i	$-0.0666932\pi$
$757$	8.50000	+	14.7224i	0.308938	+	0.535096i	−0.669193	+	0.743089i	$0.733360\pi$
$758$	−1.50000	+	2.59808i	−0.0544825	+	0.0943664i
$759$		0			0
$760$	4.50000	+	2.59808i	0.163232	+	0.0942421i
$761$	−25.5000	−	14.7224i	−0.924374	−	0.533688i	−0.0393463	−	0.999226i	$-0.512528\pi$
$761$	−25.5000	−	14.7224i	−0.924374	−	0.533688i	−0.885028	+	0.465538i	$0.845861\pi$
$762$		−	22.5167i		−	0.815693i
$763$		0			0
$764$	−7.50000	−	12.9904i	−0.271340	−	0.469975i
$765$	18.0000	−	10.3923i	0.650791	−	0.375735i
$766$	27.0000			0.975550
$767$	3.00000	−	12.1244i	0.108324	−	0.437785i
$768$	−19.0000			−0.685603
$769$	−16.5000	+	9.52628i	−0.595005	+	0.343526i	−0.767074	−	0.641558i	$-0.778288\pi$
$769$	−16.5000	+	9.52628i	−0.595005	+	0.343526i	0.172069	+	0.985085i	$0.444955\pi$
$770$		0			0
$771$	15.0000	−	25.9808i	0.540212	−	0.935674i
$772$			1.73205i			0.0623379i
$773$	12.0000	+	6.92820i	0.431610	+	0.249190i	0.700032	−	0.714111i	$-0.253169\pi$
$773$	12.0000	+	6.92820i	0.431610	+	0.249190i	−0.268422	+	0.963301i	$0.586502\pi$
$774$	33.0000	+	19.0526i	1.18616	+	0.684830i
$775$		−	3.46410i		−	0.124434i
$776$	4.50000	−	7.79423i	0.161541	−	0.279797i
$777$		0			0
$778$	4.50000	−	2.59808i	0.161333	−	0.0931455i
$779$	−9.00000			−0.322458
$780$	−6.00000	+	1.73205i	−0.214834	+	0.0620174i
$781$	9.00000			0.322045
$782$		0			0
$783$	−7.50000	−	12.9904i	−0.268028	−	0.464238i
$784$		0			0
$785$		−	39.8372i		−	1.42185i
$786$	22.5000	+	12.9904i	0.802548	+	0.463352i
$787$	27.0000	+	15.5885i	0.962446	+	0.555668i	0.896925	−	0.442183i	$-0.145796\pi$
$787$	27.0000	+	15.5885i	0.962446	+	0.555668i	0.0655211	+	0.997851i	$0.479129\pi$
$788$		−	22.5167i		−	0.802123i
$789$	1.50000	−	2.59808i	0.0534014	−	0.0924940i
$790$	7.50000	+	12.9904i	0.266838	+	0.462177i
$791$		0			0
$792$	18.0000			0.639602
$793$	24.5000	+	6.06218i	0.870021	+	0.215274i
$794$	−63.0000			−2.23579
$795$	−13.5000	+	7.79423i	−0.478796	+	0.276433i
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$	16.5000	−	28.5788i	0.584460	−	1.01231i	−0.410483	−	0.911868i	$-0.634640\pi$
$797$	16.5000	−	28.5788i	0.584460	−	1.01231i	0.994943	−	0.100446i	$-0.0320269\pi$
$798$		0			0
$799$	45.0000	+	25.9808i	1.59199	+	0.919133i
$800$	9.00000	+	5.19615i	0.318198	+	0.183712i
$801$		−	13.8564i		−	0.489592i
$802$	6.00000	−	10.3923i	0.211867	−	0.366965i
$803$	22.5000	+	38.9711i	0.794008	+	1.37526i
$804$	−7.50000	+	4.33013i	−0.264505	+	0.152712i
$805$		0			0
$806$	−7.50000	+	7.79423i	−0.264176	+	0.274540i
$807$	6.00000			0.211210
$808$	−13.5000	+	7.79423i	−0.474928	+	0.274200i
$809$	10.5000	+	18.1865i	0.369160	+	0.639404i	0.989434	−	0.144981i	$-0.0463120\pi$
$809$	10.5000	+	18.1865i	0.369160	+	0.639404i	−0.620274	+	0.784385i	$0.712979\pi$
$810$	−1.50000	+	2.59808i	−0.0527046	+	0.0912871i
$811$		−	3.46410i		−	0.121641i	−0.998149	−	0.0608205i	$-0.980628\pi$
$811$		−	3.46410i		−	0.121641i	0.998149	−	0.0608205i	$-0.0193717\pi$
$812$		0			0
$813$	15.0000	+	8.66025i	0.526073	+	0.303728i
$814$		0			0
$815$	−10.5000	+	18.1865i	−0.367799	+	0.637046i
$816$	−15.0000	−	25.9808i	−0.525105	−	0.909509i
$817$	−16.5000	+	9.52628i	−0.577262	+	0.333282i
$818$	−12.0000			−0.419570
$819$		0			0
$820$	9.00000			0.314294
$821$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$821$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$822$		0			0
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	0.439961	+	0.898017i	$0.354992\pi$
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	−0.997686	+	0.0679910i	$0.978341\pi$
$824$		−	22.5167i		−	0.784405i
$825$	9.00000	+	5.19615i	0.313340	+	0.180907i
$826$		0			0
$827$			10.3923i			0.361376i	0.983540	+	0.180688i	$0.0578324\pi$
$827$			10.3923i			0.361376i	−0.983540	+	0.180688i	$0.942168\pi$
$828$		0			0
$829$	−3.50000	−	6.06218i	−0.121560	−	0.210548i	0.798823	−	0.601566i	$-0.205456\pi$
$829$	−3.50000	−	6.06218i	−0.121560	−	0.210548i	−0.920383	+	0.391018i	$0.872123\pi$
$830$	9.00000	−	5.19615i	0.312395	−	0.180361i
$831$	10.0000			0.346896
$832$	1.00000	+	3.46410i	0.0346688	+	0.120096i
$833$		0			0
$834$	19.5000	−	11.2583i	0.675230	−	0.389844i
$835$	1.50000	+	2.59808i	0.0519096	+	0.0899101i
$836$	4.50000	−	7.79423i	0.155636	−	0.269569i
$837$		−	8.66025i		−	0.299342i
$838$	−31.5000	−	18.1865i	−1.08815	−	0.628243i
$839$	1.50000	+	0.866025i	0.0517858	+	0.0298985i	0.525669	−	0.850689i	$-0.323815\pi$
$839$	1.50000	+	0.866025i	0.0517858	+	0.0298985i	−0.473884	+	0.880587i	$0.657148\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$		0			0
$843$	6.00000	−	3.46410i	0.206651	−	0.119310i
$844$	−13.0000			−0.447478
$845$	12.0000	+	19.0526i	0.412813	+	0.655428i
$846$	−30.0000			−1.03142
$847$		0			0
$848$	−22.5000	−	38.9711i	−0.772653	−	1.33827i
$849$	9.50000	−	16.4545i	0.326039	−	0.564716i
$850$			20.7846i			0.712906i
$851$		0			0
$852$	1.50000	+	0.866025i	0.0513892	+	0.0296695i
$853$			41.5692i			1.42330i	0.702533	+	0.711651i	$0.252052\pi$
$853$			41.5692i			1.42330i	−0.702533	+	0.711651i	$0.747948\pi$
$854$		0			0
$855$	−3.00000	−	5.19615i	−0.102598	−	0.177705i
$856$		0			0
$857$	−33.0000			−1.12726			−0.563629	−	0.826028i	$-0.690595\pi$
$857$	−33.0000			−1.12726			−0.563629	+	0.826028i	$0.690595\pi$
$858$	−9.00000	−	31.1769i	−0.307255	−	1.06436i
$859$	−29.0000			−0.989467			−0.494734	−	0.869045i	$-0.664734\pi$
$859$	−29.0000			−0.989467			−0.494734	+	0.869045i	$0.664734\pi$
$860$	16.5000	−	9.52628i	0.562645	−	0.324843i
$861$		0			0
$862$	28.5000	−	49.3634i	0.970714	−	1.68133i
$863$		−	1.73205i		−	0.0589597i	−0.999565	−	0.0294798i	$-0.990615\pi$
$863$		−	1.73205i		−	0.0589597i	0.999565	−	0.0294798i	$-0.00938509\pi$
$864$	22.5000	+	12.9904i	0.765466	+	0.441942i
$865$	22.5000	+	12.9904i	0.765023	+	0.441686i
$866$			32.9090i			1.11829i
$867$	9.50000	−	16.4545i	0.322637	−	0.558824i
$868$		0			0
$869$	−22.5000	+	12.9904i	−0.763260	+	0.440668i
$870$	−9.00000			−0.305129
$871$	22.5000	+	21.6506i	0.762383	+	0.733604i
$872$	9.00000			0.304778
$873$	−9.00000	+	5.19615i	−0.304604	+	0.175863i
$874$		0			0
$875$		0			0
$876$			8.66025i			0.292603i
$877$	−1.50000	−	0.866025i	−0.0506514	−	0.0292436i	0.474460	−	0.880277i	$-0.342643\pi$
$877$	−1.50000	−	0.866025i	−0.0506514	−	0.0292436i	−0.525112	+	0.851033i	$0.675977\pi$
$878$	−12.0000	−	6.92820i	−0.404980	−	0.233816i
$879$		−	25.9808i		−	0.876309i
$880$	22.5000	−	38.9711i	0.758475	−	1.31372i
$881$	16.5000	+	28.5788i	0.555899	+	0.962846i	0.997833	+	0.0657979i	$0.0209593\pi$
$881$	16.5000	+	28.5788i	0.555899	+	0.962846i	−0.441934	+	0.897048i	$0.645707\pi$
$882$		0			0
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$	15.0000	−	15.5885i	0.504505	−	0.524297i
$885$	6.00000			0.201688
$886$	22.5000	−	12.9904i	0.755902	−	0.436420i
$887$	−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	$0.965338\pi$
$888$		0			0
$889$		0			0
$890$	−18.0000	−	10.3923i	−0.603361	−	0.348351i
$891$	−4.50000	−	2.59808i	−0.150756	−	0.0870388i
$892$		−	5.19615i		−	0.173980i
$893$	7.50000	−	12.9904i	0.250978	−	0.434707i
$894$	16.5000	+	28.5788i	0.551843	+	0.955819i
$895$	−4.50000	+	2.59808i	−0.150418	+	0.0868441i
$896$		0			0
$897$		0			0
$898$	3.00000			0.100111
$899$	−4.50000	+	2.59808i	−0.150083	+	0.0866507i
$900$	−2.00000	−	3.46410i	−0.0666667	−	0.115470i
$901$	27.0000	−	46.7654i	0.899500	−	1.55798i
$902$			46.7654i			1.55712i
$903$		0			0
$904$	−22.5000	−	12.9904i	−0.748339	−	0.432054i
$905$		−	3.46410i		−	0.115151i
$906$	−10.5000	+	18.1865i	−0.348839	+	0.604207i
$907$	14.5000	+	25.1147i	0.481465	+	0.833921i	0.999774	−	0.0212722i	$-0.00677166\pi$
$907$	14.5000	+	25.1147i	0.481465	+	0.833921i	−0.518309	+	0.855193i	$0.673438\pi$
$908$	15.0000	−	8.66025i	0.497792	−	0.287401i
$909$	18.0000			0.597022
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	−7.50000	+	4.33013i	−0.248350	+	0.143385i
$913$	9.00000	+	15.5885i	0.297857	+	0.515903i
$914$	30.0000	−	51.9615i	0.992312	−	1.71873i
$915$			12.1244i			0.400819i
$916$	10.5000	+	6.06218i	0.346930	+	0.200300i
$917$		0			0
$918$			51.9615i			1.71499i
$919$	23.5000	−	40.7032i	0.775193	−	1.34267i	−0.159492	−	0.987199i	$-0.550986\pi$
$919$	23.5000	−	40.7032i	0.775193	−	1.34267i	0.934686	−	0.355475i	$-0.115681\pi$
$920$		0			0
$921$	−21.0000	+	12.1244i	−0.691974	+	0.399511i
$922$	51.0000			1.67960
$923$	1.50000	−	6.06218i	0.0493731	−	0.199539i
$924$		0			0
$925$		0			0
$926$	−21.0000	−	36.3731i	−0.690103	−	1.19529i
$927$	−13.0000	+	22.5167i	−0.426976	+	0.739544i
$928$		−	15.5885i		−	0.511716i
$929$	40.5000	+	23.3827i	1.32876	+	0.767161i	0.985108	−	0.171935i	$-0.0550020\pi$
$929$	40.5000	+	23.3827i	1.32876	+	0.767161i	0.343654	+	0.939096i	$0.388335\pi$
$930$	−4.50000	−	2.59808i	−0.147561	−	0.0851943i
$931$		0			0
$932$	1.50000	−	2.59808i	0.0491341	−	0.0851028i
$933$	−7.50000	−	12.9904i	−0.245539	−	0.425286i
$934$	−31.5000	+	18.1865i	−1.03071	+	0.595082i
$935$	54.0000			1.76599
$936$	3.00000	−	12.1244i	0.0980581	−	0.396297i
$937$	22.0000			0.718709			0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000			0.718709			0.359354	+	0.933201i	$0.382997\pi$
$938$		0			0
$939$	9.50000	+	16.4545i	0.310021	+	0.536972i
$940$	−7.50000	+	12.9904i	−0.244623	+	0.423700i
$941$		−	5.19615i		−	0.169390i	−0.996407	−	0.0846949i	$-0.973008\pi$
$941$		−	5.19615i		−	0.169390i	0.996407	−	0.0846949i	$-0.0269915\pi$
$942$	34.5000	+	19.9186i	1.12407	+	0.648983i
$943$		0			0
$944$			17.3205i			0.563735i
$945$		0			0
$946$	49.5000	+	85.7365i	1.60938	+	2.78753i
$947$	33.0000	−	19.0526i	1.07236	−	0.619125i	0.143532	−	0.989646i	$-0.454154\pi$
$947$	33.0000	−	19.0526i	1.07236	−	0.619125i	0.928824	+	0.370521i	$0.120821\pi$
$948$	−5.00000			−0.162392
$949$	30.0000	−	8.66025i	0.973841	−	0.281124i
$950$	6.00000			0.194666
$951$	−4.50000	+	2.59808i	−0.145922	+	0.0842484i
$952$		0			0
$953$	28.5000	−	49.3634i	0.923206	−	1.59904i	0.128784	−	0.991673i	$-0.458893\pi$
$953$	28.5000	−	49.3634i	0.923206	−	1.59904i	0.794422	−	0.607366i	$-0.207774\pi$
$954$			31.1769i			1.00939i
$955$	−22.5000	−	12.9904i	−0.728083	−	0.420359i
$956$	9.00000	+	5.19615i	0.291081	+	0.168056i
$957$		−	15.5885i		−	0.503903i
$958$	−25.5000	+	44.1673i	−0.823868	+	1.42698i
$959$		0			0
$960$	−1.50000	+	0.866025i	−0.0484123	+	0.0279508i
$961$	28.0000			0.903226
$962$		0			0
$963$		0			0
$964$	6.00000	−	3.46410i	0.193247	−	0.111571i
$965$	1.50000	+	2.59808i	0.0482867	+	0.0836350i
$966$		0			0
$967$		−	10.3923i		−	0.334194i	−0.985940	−	0.167097i	$-0.946561\pi$
$967$		−	10.3923i		−	0.334194i	0.985940	−	0.167097i	$-0.0534393\pi$
$968$	24.0000	+	13.8564i	0.771389	+	0.445362i
$969$	−9.00000	−	5.19615i	−0.289122	−	0.166924i
$970$			15.5885i			0.500515i
$971$	−10.5000	+	18.1865i	−0.336961	+	0.583634i	−0.983860	−	0.178942i	$-0.942732\pi$
$971$	−10.5000	+	18.1865i	−0.336961	+	0.583634i	0.646899	+	0.762576i	$0.276066\pi$
$972$	−8.00000	−	13.8564i	−0.256600	−	0.444444i
$973$		0			0
$974$	42.0000			1.34577
$975$	5.00000	−	5.19615i	0.160128	−	0.166410i
$976$	−35.0000			−1.12032
$977$	16.5000	−	9.52628i	0.527882	−	0.304773i	−0.212272	−	0.977211i	$-0.568086\pi$
$977$	16.5000	−	9.52628i	0.527882	−	0.304773i	0.740153	+	0.672438i	$0.234753\pi$
$978$	−10.5000	−	18.1865i	−0.335753	−	0.581541i
$979$	18.0000	−	31.1769i	0.575282	−	0.996419i
$980$		0			0
$981$	−9.00000	−	5.19615i	−0.287348	−	0.165900i
$982$	40.5000	+	23.3827i	1.29241	+	0.746171i
$983$		−	36.3731i		−	1.16012i	−0.814574	−	0.580060i	$-0.803029\pi$
$983$		−	36.3731i		−	1.16012i	0.814574	−	0.580060i	$-0.196971\pi$
$984$	4.50000	−	7.79423i	0.143455	−	0.248471i
$985$	−19.5000	−	33.7750i	−0.621322	−	1.07616i
$986$	27.0000	−	15.5885i	0.859855	−	0.496438i
$987$		0			0
$988$	−4.50000	−	4.33013i	−0.143164	−	0.137760i
$989$		0			0
$990$	−27.0000	+	15.5885i	−0.858116	+	0.495434i
$991$	−29.5000	−	51.0955i	−0.937098	−	1.62310i	−0.770849	−	0.637018i	$-0.780168\pi$
$991$	−29.5000	−	51.0955i	−0.937098	−	1.62310i	−0.166250	−	0.986084i	$-0.553166\pi$
$992$	4.50000	−	7.79423i	0.142875	−	0.247467i
$993$		−	32.9090i		−	1.04433i
$994$		0			0
$995$	6.00000	+	3.46410i	0.190213	+	0.109819i
$996$			3.46410i			0.109764i
$997$	−1.00000	+	1.73205i	−0.0316703	+	0.0548546i	−0.881426	−	0.472322i	$-0.843416\pi$
$997$	−1.00000	+	1.73205i	−0.0316703	+	0.0548546i	0.849756	+	0.527176i	$0.176749\pi$
$998$	−1.50000	−	2.59808i	−0.0474817	−	0.0822407i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.q.c.491.1		2
7.2	even	3		91.2.u.a.88.1	yes	2
7.3	odd	6		637.2.k.b.569.1		2
7.4	even	3		91.2.k.a.23.1	yes	2
7.5	odd	6		637.2.u.a.361.1		2
7.6	odd	2		637.2.q.b.491.1		2
13.2	odd	12		8281.2.a.s.1.2		2
13.4	even	6	inner	637.2.q.c.589.1		2
13.11	odd	12		8281.2.a.s.1.1		2
21.2	odd	6		819.2.do.c.361.1		2
21.11	odd	6		819.2.bm.a.478.1		2
91.2	odd	12		1183.2.e.e.508.1		4
91.4	even	6		91.2.u.a.30.1	yes	2
91.11	odd	12		1183.2.e.e.170.2		4
91.17	odd	6		637.2.u.a.30.1		2
91.30	even	6		91.2.k.a.4.1	✓	2
91.37	odd	12		1183.2.e.e.508.2		4
91.41	even	12		8281.2.a.w.1.2		2
91.67	odd	12		1183.2.e.e.170.1		4
91.69	odd	6		637.2.q.b.589.1		2
91.76	even	12		8281.2.a.w.1.1		2
91.82	odd	6		637.2.k.b.459.1		2
273.95	odd	6		819.2.do.c.667.1		2
273.212	odd	6		819.2.bm.a.550.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.a.4.1	✓	2	91.30	even	6
91.2.k.a.23.1	yes	2	7.4	even	3
91.2.u.a.30.1	yes	2	91.4	even	6
91.2.u.a.88.1	yes	2	7.2	even	3
637.2.k.b.459.1		2	91.82	odd	6
637.2.k.b.569.1		2	7.3	odd	6
637.2.q.b.491.1		2	7.6	odd	2
637.2.q.b.589.1		2	91.69	odd	6
637.2.q.c.491.1		2	1.1	even	1	trivial
637.2.q.c.589.1		2	13.4	even	6	inner
637.2.u.a.30.1		2	91.17	odd	6
637.2.u.a.361.1		2	7.5	odd	6
819.2.bm.a.478.1		2	21.11	odd	6
819.2.bm.a.550.1		2	273.212	odd	6
819.2.do.c.361.1		2	21.2	odd	6
819.2.do.c.667.1		2	273.95	odd	6
1183.2.e.e.170.1		4	91.67	odd	12
1183.2.e.e.170.2		4	91.11	odd	12
1183.2.e.e.508.1		4	91.2	odd	12
1183.2.e.e.508.2		4	91.37	odd	12
8281.2.a.s.1.1		2	13.11	odd	12
8281.2.a.s.1.2		2	13.2	odd	12
8281.2.a.w.1.1		2	91.76	even	12
8281.2.a.w.1.2		2	91.41	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.73205i q^{5} +(1.50000 + 0.866025i) q^{6} +1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.73205i q^{5} +(1.50000 + 0.866025i) q^{6} +1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(4.50000 - 2.59808i) q^{11} +1.00000 q^{12} +(-1.00000 - 3.46410i) q^{13} +(1.50000 - 0.866025i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-3.00000 + 5.19615i) q^{17} -3.46410i q^{18} +(1.50000 + 0.866025i) q^{19} +(-1.50000 - 0.866025i) q^{20} +(4.50000 - 7.79423i) q^{22} +(-1.50000 + 0.866025i) q^{24} +2.00000 q^{25} +(-4.50000 - 4.33013i) q^{26} +5.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +(1.50000 - 2.59808i) q^{30} -1.73205i q^{31} +(4.50000 + 2.59808i) q^{32} +(4.50000 + 2.59808i) q^{33} +10.3923i q^{34} +(-1.00000 - 1.73205i) q^{36} +3.00000 q^{38} +(2.50000 - 2.59808i) q^{39} +3.00000 q^{40} +(-4.50000 + 2.59808i) q^{41} +(-5.50000 + 9.52628i) q^{43} -5.19615i q^{44} +(-3.00000 - 1.73205i) q^{45} -8.66025i q^{47} +(-2.50000 + 4.33013i) q^{48} +(3.00000 - 1.73205i) q^{50} -6.00000 q^{51} +(-3.50000 - 0.866025i) q^{52} -9.00000 q^{53} +(7.50000 - 4.33013i) q^{54} +(-4.50000 - 7.79423i) q^{55} +1.73205i q^{57} +(-4.50000 - 2.59808i) q^{58} +(3.00000 + 1.73205i) q^{59} -1.73205i q^{60} +(-3.50000 + 6.06218i) q^{61} +(-1.50000 - 2.59808i) q^{62} -1.00000 q^{64} +(-6.00000 + 1.73205i) q^{65} +9.00000 q^{66} +(-7.50000 + 4.33013i) q^{67} +(3.00000 + 5.19615i) q^{68} +(1.50000 + 0.866025i) q^{71} +(3.00000 + 1.73205i) q^{72} +8.66025i q^{73} +(1.00000 + 1.73205i) q^{75} +(1.50000 - 0.866025i) q^{76} +(1.50000 - 6.06218i) q^{78} -5.00000 q^{79} +(7.50000 - 4.33013i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.50000 + 7.79423i) q^{82} +3.46410i q^{83} +(9.00000 + 5.19615i) q^{85} +19.0526i q^{86} +(1.50000 - 2.59808i) q^{87} +(4.50000 + 7.79423i) q^{88} +(6.00000 - 3.46410i) q^{89} -6.00000 q^{90} +(1.50000 - 0.866025i) q^{93} +(-7.50000 - 12.9904i) q^{94} +(1.50000 - 2.59808i) q^{95} +5.19615i q^{96} +(-4.50000 - 2.59808i) q^{97} -10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + q^{3} + q^{4} + 3 q^{6} + 2 q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 + q^3 + q^4 + 3 * q^6 + 2 * q^9	\( 2 q + 3 q^{2} + q^{3} + q^{4} + 3 q^{6} + 2 q^{9} - 3 q^{10} + 9 q^{11} + 2 q^{12} - 2 q^{13} + 3 q^{15} + 5 q^{16} - 6 q^{17} + 3 q^{19} - 3 q^{20} + 9 q^{22} - 3 q^{24} + 4 q^{25} - 9 q^{26} + 10 q^{27} - 3 q^{29} + 3 q^{30} + 9 q^{32} + 9 q^{33} - 2 q^{36} + 6 q^{38} + 5 q^{39} + 6 q^{40} - 9 q^{41} - 11 q^{43} - 6 q^{45} - 5 q^{48} + 6 q^{50} - 12 q^{51} - 7 q^{52} - 18 q^{53} + 15 q^{54} - 9 q^{55} - 9 q^{58} + 6 q^{59} - 7 q^{61} - 3 q^{62} - 2 q^{64} - 12 q^{65} + 18 q^{66} - 15 q^{67} + 6 q^{68} + 3 q^{71} + 6 q^{72} + 2 q^{75} + 3 q^{76} + 3 q^{78} - 10 q^{79} + 15 q^{80} - q^{81} - 9 q^{82} + 18 q^{85} + 3 q^{87} + 9 q^{88} + 12 q^{89} - 12 q^{90} + 3 q^{93} - 15 q^{94} + 3 q^{95} - 9 q^{97}+O(q^{100}) \) 2 * q + 3 * q^2 + q^3 + q^4 + 3 * q^6 + 2 * q^9 - 3 * q^10 + 9 * q^11 + 2 * q^12 - 2 * q^13 + 3 * q^15 + 5 * q^16 - 6 * q^17 + 3 * q^19 - 3 * q^20 + 9 * q^22 - 3 * q^24 + 4 * q^25 - 9 * q^26 + 10 * q^27 - 3 * q^29 + 3 * q^30 + 9 * q^32 + 9 * q^33 - 2 * q^36 + 6 * q^38 + 5 * q^39 + 6 * q^40 - 9 * q^41 - 11 * q^43 - 6 * q^45 - 5 * q^48 + 6 * q^50 - 12 * q^51 - 7 * q^52 - 18 * q^53 + 15 * q^54 - 9 * q^55 - 9 * q^58 + 6 * q^59 - 7 * q^61 - 3 * q^62 - 2 * q^64 - 12 * q^65 + 18 * q^66 - 15 * q^67 + 6 * q^68 + 3 * q^71 + 6 * q^72 + 2 * q^75 + 3 * q^76 + 3 * q^78 - 10 * q^79 + 15 * q^80 - q^81 - 9 * q^82 + 18 * q^85 + 3 * q^87 + 9 * q^88 + 12 * q^89 - 12 * q^90 + 3 * q^93 - 15 * q^94 + 3 * q^95 - 9 * q^97

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