LMFDB - Embedded newform 507.2.j.e.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(316,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("507.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	507.361
Dual form			507.2.j.e.316.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(3.46410 + 2.00000i) q^{7} -3.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(3.46410 + 2.00000i) q^{7} -3.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(3.46410 - 2.00000i) q^{11} -1.00000 q^{12} -4.00000 q^{14} +(1.73205 - 1.00000i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} -1.00000i q^{18} +(1.73205 + 1.00000i) q^{20} +4.00000i q^{21} +(-2.00000 + 3.46410i) q^{22} +(2.59808 - 1.50000i) q^{24} +1.00000 q^{25} -1.00000 q^{27} +(-3.46410 + 2.00000i) q^{28} +(5.00000 + 8.66025i) q^{29} +(-1.00000 + 1.73205i) q^{30} -4.00000i q^{31} +(4.33013 + 2.50000i) q^{32} +(3.46410 + 2.00000i) q^{33} +2.00000i q^{34} +(4.00000 - 6.92820i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.73205 + 1.00000i) q^{37} -6.00000 q^{40} +(-5.19615 + 3.00000i) q^{41} +(-2.00000 - 3.46410i) q^{42} +(-6.00000 + 10.3923i) q^{43} +4.00000i q^{44} +(1.73205 + 1.00000i) q^{45} +(-0.500000 + 0.866025i) q^{48} +(4.50000 + 7.79423i) q^{49} +(-0.866025 + 0.500000i) q^{50} +2.00000 q^{51} +6.00000 q^{53} +(0.866025 - 0.500000i) q^{54} +(-4.00000 - 6.92820i) q^{55} +(6.00000 - 10.3923i) q^{56} +(-8.66025 - 5.00000i) q^{58} +(-10.3923 - 6.00000i) q^{59} +2.00000i q^{60} +(1.00000 - 1.73205i) q^{61} +(2.00000 + 3.46410i) q^{62} +(-3.46410 + 2.00000i) q^{63} -7.00000 q^{64} -4.00000 q^{66} +(6.92820 - 4.00000i) q^{67} +(1.00000 + 1.73205i) q^{68} +8.00000i q^{70} +(2.59808 + 1.50000i) q^{72} +2.00000i q^{73} +(1.00000 - 1.73205i) q^{74} +(0.500000 + 0.866025i) q^{75} +16.0000 q^{77} +8.00000 q^{79} +(1.73205 - 1.00000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} -4.00000i q^{83} +(-3.46410 - 2.00000i) q^{84} +(-3.46410 - 2.00000i) q^{85} -12.0000i q^{86} +(-5.00000 + 8.66025i) q^{87} +(-6.00000 - 10.3923i) q^{88} +(-1.73205 + 1.00000i) q^{89} -2.00000 q^{90} +(3.46410 - 2.00000i) q^{93} +5.00000i q^{96} +(8.66025 + 5.00000i) q^{97} +(-7.79423 - 4.50000i) q^{98} +4.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 2 q^{4} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 2 * q^4 - 2 * q^9	$ 4 q + 2 q^{3} - 2 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} - 16 q^{14} + 2 q^{16} + 4 q^{17} - 8 q^{22} + 4 q^{25} - 4 q^{27} + 20 q^{29} - 4 q^{30} + 16 q^{35} - 2 q^{36} - 24 q^{40} - 8 q^{42} - 24 q^{43} - 2 q^{48} + 18 q^{49} + 8 q^{51} + 24 q^{53} - 16 q^{55} + 24 q^{56} + 4 q^{61} + 8 q^{62} - 28 q^{64} - 16 q^{66} + 4 q^{68} + 4 q^{74} + 2 q^{75} + 64 q^{77} + 32 q^{79} - 2 q^{81} + 12 q^{82} - 20 q^{87} - 24 q^{88} - 8 q^{90}+O(q^{100}) $ 4 * q + 2 * q^3 - 2 * q^4 - 2 * q^9 + 4 * q^10 - 4 * q^12 - 16 * q^14 + 2 * q^16 + 4 * q^17 - 8 * q^22 + 4 * q^25 - 4 * q^27 + 20 * q^29 - 4 * q^30 + 16 * q^35 - 2 * q^36 - 24 * q^40 - 8 * q^42 - 24 * q^43 - 2 * q^48 + 18 * q^49 + 8 * q^51 + 24 * q^53 - 16 * q^55 + 24 * q^56 + 4 * q^61 + 8 * q^62 - 28 * q^64 - 16 * q^66 + 4 * q^68 + 4 * q^74 + 2 * q^75 + 64 * q^77 + 32 * q^79 - 2 * q^81 + 12 * q^82 - 20 * q^87 - 24 * q^88 - 8 * q^90

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i	−0.773893	−	0.633316i	$-0.781693\pi$
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i	0.161521	+	0.986869i	$0.448360\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		−	2.00000i		−	0.894427i	−0.894427	−	0.447214i	$-0.852416\pi$
$5$		−	2.00000i		−	0.894427i	0.894427	−	0.447214i	$-0.147584\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	3.46410	+	2.00000i	1.30931	+	0.755929i	0.981981	−	0.188982i	$-0.0605189\pi$
$7$	3.46410	+	2.00000i	1.30931	+	0.755929i	0.327327	+	0.944911i	$0.393852\pi$
$8$		−	3.00000i		−	1.06066i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	3.46410	−	2.00000i	1.04447	−	0.603023i	0.123371	−	0.992361i	$-0.460630\pi$
$11$	3.46410	−	2.00000i	1.04447	−	0.603023i	0.921095	+	0.389338i	$0.127296\pi$
$12$	−1.00000			−0.288675
$13$		0			0
$13$		0			0
$14$	−4.00000			−1.06904
$15$	1.73205	−	1.00000i	0.447214	−	0.258199i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$		−	1.00000i		−	0.235702i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	1.73205	+	1.00000i	0.387298	+	0.223607i
$21$			4.00000i			0.872872i
$22$	−2.00000	+	3.46410i	−0.426401	+	0.738549i
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	2.59808	−	1.50000i	0.530330	−	0.306186i
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$	−3.46410	+	2.00000i	−0.654654	+	0.377964i
$29$	5.00000	+	8.66025i	0.928477	+	1.60817i	0.785872	+	0.618389i	$0.212214\pi$
$29$	5.00000	+	8.66025i	0.928477	+	1.60817i	0.142605	+	0.989780i	$0.454452\pi$
$30$	−1.00000	+	1.73205i	−0.182574	+	0.316228i
$31$		−	4.00000i		−	0.718421i	−0.933257	−	0.359211i	$-0.883046\pi$
$31$		−	4.00000i		−	0.718421i	0.933257	−	0.359211i	$-0.116954\pi$
$32$	4.33013	+	2.50000i	0.765466	+	0.441942i
$33$	3.46410	+	2.00000i	0.603023	+	0.348155i
$34$			2.00000i			0.342997i
$35$	4.00000	−	6.92820i	0.676123	−	1.17108i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−1.73205	+	1.00000i	−0.284747	+	0.164399i	−0.635571	−	0.772043i	$-0.719235\pi$
$37$	−1.73205	+	1.00000i	−0.284747	+	0.164399i	0.350823	+	0.936442i	$0.385902\pi$
$38$		0			0
$39$		0			0
$40$	−6.00000			−0.948683
$41$	−5.19615	+	3.00000i	−0.811503	+	0.468521i	−0.847477	−	0.530831i	$-0.821880\pi$
$41$	−5.19615	+	3.00000i	−0.811503	+	0.468521i	0.0359748	+	0.999353i	$0.488546\pi$
$42$	−2.00000	−	3.46410i	−0.308607	−	0.534522i
$43$	−6.00000	+	10.3923i	−0.914991	+	1.58481i	−0.108078	+	0.994142i	$0.534469\pi$
$43$	−6.00000	+	10.3923i	−0.914991	+	1.58481i	−0.806914	+	0.590669i	$0.798864\pi$
$44$			4.00000i			0.603023i
$45$	1.73205	+	1.00000i	0.258199	+	0.149071i
$46$		0			0
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	4.50000	+	7.79423i	0.642857	+	1.11346i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	2.00000			0.280056
$52$		0			0
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−4.00000	−	6.92820i	−0.539360	−	0.934199i
$56$	6.00000	−	10.3923i	0.801784	−	1.38873i
$57$		0			0
$58$	−8.66025	−	5.00000i	−1.13715	−	0.656532i
$59$	−10.3923	−	6.00000i	−1.35296	−	0.781133i	−0.364299	−	0.931282i	$-0.618692\pi$
$59$	−10.3923	−	6.00000i	−1.35296	−	0.781133i	−0.988663	+	0.150148i	$0.952025\pi$
$60$			2.00000i			0.258199i
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$	2.00000	+	3.46410i	0.254000	+	0.439941i
$63$	−3.46410	+	2.00000i	−0.436436	+	0.251976i
$64$	−7.00000			−0.875000
$65$		0			0
$66$	−4.00000			−0.492366
$67$	6.92820	−	4.00000i	0.846415	−	0.488678i	−0.0130248	−	0.999915i	$-0.504146\pi$
$67$	6.92820	−	4.00000i	0.846415	−	0.488678i	0.859440	+	0.511237i	$0.170813\pi$
$68$	1.00000	+	1.73205i	0.121268	+	0.210042i
$69$		0			0
$70$			8.00000i			0.956183i
$71$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$71$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$72$	2.59808	+	1.50000i	0.306186	+	0.176777i
$73$			2.00000i			0.234082i	0.993127	+	0.117041i	$0.0373409\pi$
$73$			2.00000i			0.234082i	−0.993127	+	0.117041i	$0.962659\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$		0			0
$77$	16.0000			1.82337
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	1.73205	−	1.00000i	0.193649	−	0.111803i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.00000	−	5.19615i	0.331295	−	0.573819i
$83$		−	4.00000i		−	0.439057i	−0.975606	−	0.219529i	$-0.929548\pi$
$83$		−	4.00000i		−	0.439057i	0.975606	−	0.219529i	$-0.0704519\pi$
$84$	−3.46410	−	2.00000i	−0.377964	−	0.218218i
$85$	−3.46410	−	2.00000i	−0.375735	−	0.216930i
$86$		−	12.0000i		−	1.29399i
$87$	−5.00000	+	8.66025i	−0.536056	+	0.928477i
$88$	−6.00000	−	10.3923i	−0.639602	−	1.10782i
$89$	−1.73205	+	1.00000i	−0.183597	+	0.106000i	−0.588982	−	0.808146i	$-0.700471\pi$
$89$	−1.73205	+	1.00000i	−0.183597	+	0.106000i	0.405385	+	0.914146i	$0.367138\pi$
$90$	−2.00000			−0.210819
$91$		0			0
$92$		0			0
$93$	3.46410	−	2.00000i	0.359211	−	0.207390i
$94$		0			0
$95$		0			0
$96$			5.00000i			0.510310i
$97$	8.66025	+	5.00000i	0.879316	+	0.507673i	0.870433	−	0.492287i	$-0.163839\pi$
$97$	8.66025	+	5.00000i	0.879316	+	0.507673i	0.00888289	+	0.999961i	$0.497172\pi$
$98$	−7.79423	−	4.50000i	−0.787336	−	0.454569i
$99$			4.00000i			0.402015i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.833143	−	0.553058i	$-0.813461\pi$
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.0623905	−	0.998052i	$-0.519872\pi$
$102$	−1.73205	+	1.00000i	−0.171499	+	0.0990148i
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$		0			0
$105$	8.00000			0.780720
$106$	−5.19615	+	3.00000i	−0.504695	+	0.291386i
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$			2.00000i			0.191565i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$			2.00000i			0.191565i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$	6.92820	+	4.00000i	0.660578	+	0.381385i
$111$	−1.73205	−	1.00000i	−0.164399	−	0.0949158i
$112$			4.00000i			0.377964i
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	−0.689714	−	0.724082i	$-0.742264\pi$
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	0.971930	+	0.235269i	$0.0755971\pi$
$114$		0			0
$115$		0			0
$116$	−10.0000			−0.928477
$117$		0			0
$118$	12.0000			1.10469
$119$	6.92820	−	4.00000i	0.635107	−	0.366679i
$120$	−3.00000	−	5.19615i	−0.273861	−	0.474342i
$121$	2.50000	−	4.33013i	0.227273	−	0.393648i
$122$			2.00000i			0.181071i
$123$	−5.19615	−	3.00000i	−0.468521	−	0.270501i
$124$	3.46410	+	2.00000i	0.311086	+	0.179605i
$125$		−	12.0000i		−	1.07331i
$126$	2.00000	−	3.46410i	0.178174	−	0.308607i
$127$	−8.00000	−	13.8564i	−0.709885	−	1.22956i	−0.964899	−	0.262620i	$-0.915413\pi$
$127$	−8.00000	−	13.8564i	−0.709885	−	1.22956i	0.255014	−	0.966937i	$-0.417920\pi$
$128$	−2.59808	+	1.50000i	−0.229640	+	0.132583i
$129$	−12.0000			−1.05654
$130$		0			0
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$	−3.46410	+	2.00000i	−0.301511	+	0.174078i
$133$		0			0
$134$	−4.00000	+	6.92820i	−0.345547	+	0.598506i
$135$			2.00000i			0.172133i
$136$	−5.19615	−	3.00000i	−0.445566	−	0.257248i
$137$	−5.19615	−	3.00000i	−0.443937	−	0.256307i	0.261329	−	0.965250i	$-0.415839\pi$
$137$	−5.19615	−	3.00000i	−0.443937	−	0.256307i	−0.705266	+	0.708942i	$0.749173\pi$
$138$		0			0
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	0.491033	+	0.871141i	$0.336619\pi$
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	−0.999947	+	0.0103230i	$0.996714\pi$
$140$	4.00000	+	6.92820i	0.338062	+	0.585540i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	17.3205	−	10.0000i	1.43839	−	0.830455i
$146$	−1.00000	−	1.73205i	−0.0827606	−	0.143346i
$147$	−4.50000	+	7.79423i	−0.371154	+	0.642857i
$148$		−	2.00000i		−	0.164399i
$149$	−5.19615	−	3.00000i	−0.425685	−	0.245770i	0.271821	−	0.962348i	$-0.412374\pi$
$149$	−5.19615	−	3.00000i	−0.425685	−	0.245770i	−0.697507	+	0.716578i	$0.745707\pi$
$150$	−0.866025	−	0.500000i	−0.0707107	−	0.0408248i
$151$			4.00000i			0.325515i	0.986666	+	0.162758i	$0.0520389\pi$
$151$			4.00000i			0.325515i	−0.986666	+	0.162758i	$0.947961\pi$
$152$		0			0
$153$	1.00000	+	1.73205i	0.0808452	+	0.140028i
$154$	−13.8564	+	8.00000i	−1.11658	+	0.644658i
$155$	−8.00000			−0.642575
$156$		0			0
$157$	−18.0000			−1.43656			−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000			−1.43656			−0.718278	+	0.695756i	$0.755069\pi$
$158$	−6.92820	+	4.00000i	−0.551178	+	0.318223i
$159$	3.00000	+	5.19615i	0.237915	+	0.412082i
$160$	5.00000	−	8.66025i	0.395285	−	0.684653i
$161$		0			0
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	−6.92820	−	4.00000i	−0.542659	−	0.313304i	0.203497	−	0.979076i	$-0.434769\pi$
$163$	−6.92820	−	4.00000i	−0.542659	−	0.313304i	−0.746156	+	0.665771i	$0.768103\pi$
$164$		−	6.00000i		−	0.468521i
$165$	4.00000	−	6.92820i	0.311400	−	0.539360i
$166$	2.00000	+	3.46410i	0.155230	+	0.268866i
$167$	−6.92820	+	4.00000i	−0.536120	+	0.309529i	−0.743505	−	0.668730i	$-0.766838\pi$
$167$	−6.92820	+	4.00000i	−0.536120	+	0.309529i	0.207385	+	0.978259i	$0.433505\pi$
$168$	12.0000			0.925820
$169$		0			0
$170$	4.00000			0.306786
$171$		0			0
$172$	−6.00000	−	10.3923i	−0.457496	−	0.792406i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		−	10.0000i		−	0.758098i
$175$	3.46410	+	2.00000i	0.261861	+	0.151186i
$176$	3.46410	+	2.00000i	0.261116	+	0.150756i
$177$		−	12.0000i		−	0.901975i
$178$	1.00000	−	1.73205i	0.0749532	−	0.129823i
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	0.931038	−	0.364922i	$-0.118904\pi$
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	−0.781551	+	0.623841i	$0.785571\pi$
$180$	−1.73205	+	1.00000i	−0.129099	+	0.0745356i
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$		0			0
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$	−2.00000	+	3.46410i	−0.146647	+	0.254000i
$187$		−	8.00000i		−	0.585018i
$188$		0			0
$189$	−3.46410	−	2.00000i	−0.251976	−	0.145479i
$190$		0			0
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	−0.973674	−	0.227946i	$-0.926799\pi$
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	0.684244	+	0.729253i	$0.260132\pi$
$192$	−3.50000	−	6.06218i	−0.252591	−	0.437500i
$193$	15.5885	−	9.00000i	1.12208	−	0.647834i	0.180150	−	0.983639i	$-0.442342\pi$
$193$	15.5885	−	9.00000i	1.12208	−	0.647834i	0.941932	+	0.335805i	$0.109008\pi$
$194$	−10.0000			−0.717958
$195$		0			0
$196$	−9.00000			−0.642857
$197$	−15.5885	+	9.00000i	−1.11063	+	0.641223i	−0.938993	−	0.343937i	$-0.888239\pi$
$197$	−15.5885	+	9.00000i	−1.11063	+	0.641223i	−0.171639	+	0.985160i	$0.554906\pi$
$198$	−2.00000	−	3.46410i	−0.142134	−	0.246183i
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	−0.688705	−	0.725042i	$-0.741820\pi$
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	0.972257	+	0.233915i	$0.0751537\pi$
$200$		−	3.00000i		−	0.212132i
$201$	6.92820	+	4.00000i	0.488678	+	0.282138i
$202$	15.5885	+	9.00000i	1.09680	+	0.633238i
$203$			40.0000i			2.80745i
$204$	−1.00000	+	1.73205i	−0.0700140	+	0.121268i
$205$	6.00000	+	10.3923i	0.419058	+	0.725830i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$	−6.92820	+	4.00000i	−0.478091	+	0.276026i
$211$	10.0000	+	17.3205i	0.688428	+	1.19239i	0.972346	+	0.233544i	$0.0750324\pi$
$211$	10.0000	+	17.3205i	0.688428	+	1.19239i	−0.283918	+	0.958849i	$0.591634\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$		0			0
$214$	10.3923	+	6.00000i	0.710403	+	0.410152i
$215$	20.7846	+	12.0000i	1.41750	+	0.818393i
$216$			3.00000i			0.204124i
$217$	8.00000	−	13.8564i	0.543075	−	0.940634i
$218$	−1.00000	−	1.73205i	−0.0677285	−	0.117309i
$219$	−1.73205	+	1.00000i	−0.117041	+	0.0675737i
$220$	8.00000			0.539360
$221$		0			0
$222$	2.00000			0.134231
$223$	−3.46410	+	2.00000i	−0.231973	+	0.133930i	−0.611482	−	0.791258i	$-0.709426\pi$
$223$	−3.46410	+	2.00000i	−0.231973	+	0.133930i	0.379509	+	0.925188i	$0.376093\pi$
$224$	10.0000	+	17.3205i	0.668153	+	1.15728i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$			6.00000i			0.399114i
$227$	−17.3205	−	10.0000i	−1.14960	−	0.663723i	−0.200812	−	0.979630i	$-0.564358\pi$
$227$	−17.3205	−	10.0000i	−1.14960	−	0.663723i	−0.948790	+	0.315906i	$0.897691\pi$
$228$		0			0
$229$		−	10.0000i		−	0.660819i	−0.943838	−	0.330409i	$-0.892813\pi$
$229$		−	10.0000i		−	0.660819i	0.943838	−	0.330409i	$-0.107187\pi$
$230$		0			0
$231$	8.00000	+	13.8564i	0.526361	+	0.911685i
$232$	25.9808	−	15.0000i	1.70572	−	0.984798i
$233$	14.0000			0.917170			0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000			0.917170			0.458585	+	0.888650i	$0.348356\pi$
$234$		0			0
$235$		0			0
$236$	10.3923	−	6.00000i	0.676481	−	0.390567i
$237$	4.00000	+	6.92820i	0.259828	+	0.450035i
$238$	−4.00000	+	6.92820i	−0.259281	+	0.449089i
$239$			24.0000i			1.55243i	0.630468	+	0.776215i	$0.282863\pi$
$239$			24.0000i			1.55243i	−0.630468	+	0.776215i	$0.717137\pi$
$240$	1.73205	+	1.00000i	0.111803	+	0.0645497i
$241$	−8.66025	−	5.00000i	−0.557856	−	0.322078i	0.194429	−	0.980917i	$-0.437715\pi$
$241$	−8.66025	−	5.00000i	−0.557856	−	0.322078i	−0.752285	+	0.658838i	$0.771048\pi$
$242$			5.00000i			0.321412i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	1.00000	+	1.73205i	0.0640184	+	0.110883i
$245$	15.5885	−	9.00000i	0.995910	−	0.574989i
$246$	6.00000			0.382546
$247$		0			0
$248$	−12.0000			−0.762001
$249$	3.46410	−	2.00000i	0.219529	−	0.126745i
$250$	6.00000	+	10.3923i	0.379473	+	0.657267i
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	−0.990876	−	0.134778i	$-0.956968\pi$
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	0.612159	+	0.790735i	$0.290301\pi$
$252$		−	4.00000i		−	0.251976i
$253$		0			0
$254$	13.8564	+	8.00000i	0.869428	+	0.501965i
$255$		−	4.00000i		−	0.250490i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	13.0000	+	22.5167i	0.810918	+	1.40455i	0.912222	+	0.409695i	$0.134365\pi$
$257$	13.0000	+	22.5167i	0.810918	+	1.40455i	−0.101305	+	0.994855i	$0.532302\pi$
$258$	10.3923	−	6.00000i	0.646997	−	0.373544i
$259$	−8.00000			−0.497096
$260$		0			0
$261$	−10.0000			−0.618984
$262$	−3.46410	+	2.00000i	−0.214013	+	0.123560i
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$	6.00000	−	10.3923i	0.369274	−	0.639602i
$265$		−	12.0000i		−	0.737154i
$266$		0			0
$267$	−1.73205	−	1.00000i	−0.106000	−	0.0611990i
$268$			8.00000i			0.488678i
$269$	−11.0000	+	19.0526i	−0.670682	+	1.16166i	0.307029	+	0.951700i	$0.400665\pi$
$269$	−11.0000	+	19.0526i	−0.670682	+	1.16166i	−0.977711	+	0.209955i	$0.932668\pi$
$270$	−1.00000	−	1.73205i	−0.0608581	−	0.105409i
$271$	−10.3923	+	6.00000i	−0.631288	+	0.364474i	−0.781251	−	0.624218i	$-0.785418\pi$
$271$	−10.3923	+	6.00000i	−0.631288	+	0.364474i	0.149963	+	0.988692i	$0.452085\pi$
$272$	2.00000			0.121268
$273$		0			0
$274$	6.00000			0.362473
$275$	3.46410	−	2.00000i	0.208893	−	0.120605i
$276$		0			0
$277$	−5.00000	+	8.66025i	−0.300421	+	0.520344i	−0.976231	−	0.216731i	$-0.930460\pi$
$277$	−5.00000	+	8.66025i	−0.300421	+	0.520344i	0.675810	+	0.737075i	$0.263794\pi$
$278$		−	12.0000i		−	0.719712i
$279$	3.46410	+	2.00000i	0.207390	+	0.119737i
$280$	−20.7846	−	12.0000i	−1.24212	−	0.717137i
$281$		−	10.0000i		−	0.596550i	−0.954480	−	0.298275i	$-0.903589\pi$
$281$		−	10.0000i		−	0.596550i	0.954480	−	0.298275i	$-0.0964112\pi$
$282$		0			0
$283$	6.00000	+	10.3923i	0.356663	+	0.617758i	0.987401	−	0.158237i	$-0.0505811\pi$
$283$	6.00000	+	10.3923i	0.356663	+	0.617758i	−0.630738	+	0.775996i	$0.717248\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−24.0000			−1.41668
$288$	−4.33013	+	2.50000i	−0.255155	+	0.147314i
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	−10.0000	+	17.3205i	−0.587220	+	1.01710i
$291$			10.0000i			0.586210i
$292$	−1.73205	−	1.00000i	−0.101361	−	0.0585206i
$293$	5.19615	+	3.00000i	0.303562	+	0.175262i	0.644042	−	0.764990i	$-0.277256\pi$
$293$	5.19615	+	3.00000i	0.303562	+	0.175262i	−0.340480	+	0.940252i	$0.610589\pi$
$294$		−	9.00000i		−	0.524891i
$295$	−12.0000	+	20.7846i	−0.698667	+	1.21013i
$296$	3.00000	+	5.19615i	0.174371	+	0.302020i
$297$	−3.46410	+	2.00000i	−0.201008	+	0.116052i
$298$	6.00000			0.347571
$299$		0			0
$300$	−1.00000			−0.0577350
$301$	−41.5692	+	24.0000i	−2.39601	+	1.38334i
$302$	−2.00000	−	3.46410i	−0.115087	−	0.199337i
$303$	9.00000	−	15.5885i	0.517036	−	0.895533i
$304$		0			0
$305$	−3.46410	−	2.00000i	−0.198354	−	0.114520i
$306$	−1.73205	−	1.00000i	−0.0990148	−	0.0571662i
$307$		−	16.0000i		−	0.913168i	−0.889680	−	0.456584i	$-0.849073\pi$
$307$		−	16.0000i		−	0.913168i	0.889680	−	0.456584i	$-0.150927\pi$
$308$	−8.00000	+	13.8564i	−0.455842	+	0.789542i
$309$		0			0
$310$	6.92820	−	4.00000i	0.393496	−	0.227185i
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	15.5885	−	9.00000i	0.879708	−	0.507899i
$315$	4.00000	+	6.92820i	0.225374	+	0.390360i
$316$	−4.00000	+	6.92820i	−0.225018	+	0.389742i
$317$		−	26.0000i		−	1.46031i	−0.683284	−	0.730153i	$-0.739449\pi$
$317$		−	26.0000i		−	1.46031i	0.683284	−	0.730153i	$-0.260551\pi$
$318$	−5.19615	−	3.00000i	−0.291386	−	0.168232i
$319$	34.6410	+	20.0000i	1.93952	+	1.11979i
$320$			14.0000i			0.782624i
$321$	6.00000	−	10.3923i	0.334887	−	0.580042i
$322$		0			0
$323$		0			0
$324$	1.00000			0.0555556
$325$		0			0
$326$	8.00000			0.443079
$327$	−1.73205	+	1.00000i	−0.0957826	+	0.0553001i
$328$	9.00000	+	15.5885i	0.496942	+	0.860729i
$329$		0			0
$330$			8.00000i			0.440386i
$331$	−13.8564	−	8.00000i	−0.761617	−	0.439720i	0.0682590	−	0.997668i	$-0.478256\pi$
$331$	−13.8564	−	8.00000i	−0.761617	−	0.439720i	−0.829876	+	0.557948i	$0.811589\pi$
$332$	3.46410	+	2.00000i	0.190117	+	0.109764i
$333$		−	2.00000i		−	0.109599i
$334$	4.00000	−	6.92820i	0.218870	−	0.379094i
$335$	−8.00000	−	13.8564i	−0.437087	−	0.757056i
$336$	−3.46410	+	2.00000i	−0.188982	+	0.109109i
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$		0			0
$339$	6.00000			0.325875
$340$	3.46410	−	2.00000i	0.187867	−	0.108465i
$341$	−8.00000	−	13.8564i	−0.433224	−	0.750366i
$342$		0			0
$343$			8.00000i			0.431959i
$344$	31.1769	+	18.0000i	1.68095	+	0.970495i
$345$		0			0
$346$			6.00000i			0.322562i
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$	−5.00000	−	8.66025i	−0.268028	−	0.464238i
$349$	−22.5167	+	13.0000i	−1.20529	+	0.695874i	−0.961727	−	0.274011i	$-0.911649\pi$
$349$	−22.5167	+	13.0000i	−1.20529	+	0.695874i	−0.243563	+	0.969885i	$0.578316\pi$
$350$	−4.00000			−0.213809
$351$		0			0
$352$	20.0000			1.06600
$353$	1.73205	−	1.00000i	0.0921878	−	0.0532246i	−0.453197	−	0.891410i	$-0.649717\pi$
$353$	1.73205	−	1.00000i	0.0921878	−	0.0532246i	0.545385	+	0.838186i	$0.316383\pi$
$354$	6.00000	+	10.3923i	0.318896	+	0.552345i
$355$		0			0
$356$		−	2.00000i		−	0.106000i
$357$	6.92820	+	4.00000i	0.366679	+	0.211702i
$358$	−3.46410	−	2.00000i	−0.183083	−	0.105703i
$359$			24.0000i			1.26667i	0.773877	+	0.633336i	$0.218315\pi$
$359$			24.0000i			1.26667i	−0.773877	+	0.633336i	$0.781685\pi$
$360$	3.00000	−	5.19615i	0.158114	−	0.273861i
$361$	−9.50000	−	16.4545i	−0.500000	−	0.866025i
$362$	−8.66025	+	5.00000i	−0.455173	+	0.262794i
$363$	5.00000			0.262432
$364$		0			0
$365$	4.00000			0.209370
$366$	−1.73205	+	1.00000i	−0.0905357	+	0.0522708i
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	0.578101	−	0.815966i	$-0.303794\pi$
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	−0.995697	+	0.0926670i	$0.970461\pi$
$368$		0			0
$369$		−	6.00000i		−	0.312348i
$370$	−3.46410	−	2.00000i	−0.180090	−	0.103975i
$371$	20.7846	+	12.0000i	1.07908	+	0.623009i
$372$			4.00000i			0.207390i
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	−0.303902	−	0.952703i	$-0.598289\pi$
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	0.977016	−	0.213165i	$-0.0683772\pi$
$374$	4.00000	+	6.92820i	0.206835	+	0.358249i
$375$	10.3923	−	6.00000i	0.536656	−	0.309839i
$376$		0			0
$377$		0			0
$378$	4.00000			0.205738
$379$	20.7846	−	12.0000i	1.06763	−	0.616399i	0.140100	−	0.990137i	$-0.455258\pi$
$379$	20.7846	−	12.0000i	1.06763	−	0.616399i	0.927534	+	0.373739i	$0.121924\pi$
$380$		0			0
$381$	8.00000	−	13.8564i	0.409852	−	0.709885i
$382$		−	8.00000i		−	0.409316i
$383$	−13.8564	−	8.00000i	−0.708029	−	0.408781i	0.102302	−	0.994753i	$-0.467379\pi$
$383$	−13.8564	−	8.00000i	−0.708029	−	0.408781i	−0.810331	+	0.585973i	$0.800713\pi$
$384$	−2.59808	−	1.50000i	−0.132583	−	0.0765466i
$385$		−	32.0000i		−	1.63087i
$386$	−9.00000	+	15.5885i	−0.458088	+	0.793432i
$387$	−6.00000	−	10.3923i	−0.304997	−	0.528271i
$388$	−8.66025	+	5.00000i	−0.439658	+	0.253837i
$389$	−22.0000			−1.11544			−0.557722	−	0.830028i	$-0.688325\pi$
$389$	−22.0000			−1.11544			−0.557722	+	0.830028i	$0.688325\pi$
$390$		0			0
$391$		0			0
$392$	23.3827	−	13.5000i	1.18100	−	0.681853i
$393$	2.00000	+	3.46410i	0.100887	+	0.174741i
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$		−	16.0000i		−	0.805047i
$396$	−3.46410	−	2.00000i	−0.174078	−	0.100504i
$397$	−32.9090	−	19.0000i	−1.65165	−	0.953583i	−0.976392	−	0.216004i	$-0.930698\pi$
$397$	−32.9090	−	19.0000i	−1.65165	−	0.953583i	−0.675261	−	0.737579i	$-0.735969\pi$
$398$			8.00000i			0.401004i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	19.0526	−	11.0000i	0.951439	−	0.549314i	0.0579116	−	0.998322i	$-0.481556\pi$
$401$	19.0526	−	11.0000i	0.951439	−	0.549314i	0.893528	+	0.449008i	$0.148223\pi$
$402$	−8.00000			−0.399004
$403$		0			0
$404$	18.0000			0.895533
$405$	−1.73205	+	1.00000i	−0.0860663	+	0.0496904i
$406$	−20.0000	−	34.6410i	−0.992583	−	1.71920i
$407$	−4.00000	+	6.92820i	−0.198273	+	0.343418i
$408$		−	6.00000i		−	0.297044i
$409$	29.4449	+	17.0000i	1.45595	+	0.840596i	0.998809	−	0.0487958i	$-0.0155383\pi$
$409$	29.4449	+	17.0000i	1.45595	+	0.840596i	0.457146	+	0.889392i	$0.348872\pi$
$410$	−10.3923	−	6.00000i	−0.513239	−	0.296319i
$411$		−	6.00000i		−	0.295958i
$412$		0			0
$413$	−24.0000	−	41.5692i	−1.18096	−	2.04549i
$414$		0			0
$415$	−8.00000			−0.392705
$416$		0			0
$417$	−12.0000			−0.587643
$418$		0			0
$419$	−2.00000	−	3.46410i	−0.0977064	−	0.169232i	0.813029	−	0.582224i	$-0.197817\pi$
$419$	−2.00000	−	3.46410i	−0.0977064	−	0.169232i	−0.910735	+	0.412991i	$0.864484\pi$
$420$	−4.00000	+	6.92820i	−0.195180	+	0.338062i
$421$			10.0000i			0.487370i	0.969854	+	0.243685i	$0.0783563\pi$
$421$			10.0000i			0.487370i	−0.969854	+	0.243685i	$0.921644\pi$
$422$	−17.3205	−	10.0000i	−0.843149	−	0.486792i
$423$		0			0
$424$		−	18.0000i		−	0.874157i
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$		0			0
$427$	6.92820	−	4.00000i	0.335279	−	0.193574i
$428$	12.0000			0.580042
$429$		0			0
$430$	−24.0000			−1.15738
$431$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$431$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	17.0000	−	29.4449i	0.816968	−	1.41503i	−0.0909384	−	0.995857i	$-0.528987\pi$
$433$	17.0000	−	29.4449i	0.816968	−	1.41503i	0.907906	−	0.419173i	$-0.137680\pi$
$434$			16.0000i			0.768025i
$435$	17.3205	+	10.0000i	0.830455	+	0.479463i
$436$	−1.73205	−	1.00000i	−0.0829502	−	0.0478913i
$437$		0			0
$438$	1.00000	−	1.73205i	0.0477818	−	0.0827606i
$439$	16.0000	+	27.7128i	0.763638	+	1.32266i	0.940963	+	0.338508i	$0.109922\pi$
$439$	16.0000	+	27.7128i	0.763638	+	1.32266i	−0.177325	+	0.984152i	$0.556744\pi$
$440$	−20.7846	+	12.0000i	−0.990867	+	0.572078i
$441$	−9.00000			−0.428571
$442$		0			0
$443$	−4.00000			−0.190046			−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000			−0.190046			−0.0950229	+	0.995475i	$0.530292\pi$
$444$	1.73205	−	1.00000i	0.0821995	−	0.0474579i
$445$	2.00000	+	3.46410i	0.0948091	+	0.164214i
$446$	2.00000	−	3.46410i	0.0947027	−	0.164030i
$447$		−	6.00000i		−	0.283790i
$448$	−24.2487	−	14.0000i	−1.14564	−	0.661438i
$449$	−19.0526	−	11.0000i	−0.899146	−	0.519122i	−0.0222229	−	0.999753i	$-0.507074\pi$
$449$	−19.0526	−	11.0000i	−0.899146	−	0.519122i	−0.876923	+	0.480631i	$0.840408\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	−12.0000	+	20.7846i	−0.565058	+	0.978709i
$452$	3.00000	+	5.19615i	0.141108	+	0.244406i
$453$	−3.46410	+	2.00000i	−0.162758	+	0.0939682i
$454$	20.0000			0.938647
$455$		0			0
$456$		0			0
$457$	−1.73205	+	1.00000i	−0.0810219	+	0.0467780i	−0.539964	−	0.841688i	$-0.681562\pi$
$457$	−1.73205	+	1.00000i	−0.0810219	+	0.0467780i	0.458942	+	0.888466i	$0.348229\pi$
$458$	5.00000	+	8.66025i	0.233635	+	0.404667i
$459$	−1.00000	+	1.73205i	−0.0466760	+	0.0808452i
$460$		0			0
$461$	−32.9090	−	19.0000i	−1.53272	−	0.884918i	−0.999235	−	0.0391109i	$-0.987547\pi$
$461$	−32.9090	−	19.0000i	−1.53272	−	0.884918i	−0.533488	−	0.845807i	$-0.679119\pi$
$462$	−13.8564	−	8.00000i	−0.644658	−	0.372194i
$463$			4.00000i			0.185896i	0.995671	+	0.0929479i	$0.0296290\pi$
$463$			4.00000i			0.185896i	−0.995671	+	0.0929479i	$0.970371\pi$
$464$	−5.00000	+	8.66025i	−0.232119	+	0.402042i
$465$	−4.00000	−	6.92820i	−0.185496	−	0.321288i
$466$	−12.1244	+	7.00000i	−0.561650	+	0.324269i
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$		0			0
$469$	32.0000			1.47762
$470$		0			0
$471$	−9.00000	−	15.5885i	−0.414698	−	0.718278i
$472$	−18.0000	+	31.1769i	−0.828517	+	1.43503i
$473$			48.0000i			2.20704i
$474$	−6.92820	−	4.00000i	−0.318223	−	0.183726i
$475$		0			0
$476$			8.00000i			0.366679i
$477$	−3.00000	+	5.19615i	−0.137361	+	0.237915i
$478$	−12.0000	−	20.7846i	−0.548867	−	0.950666i
$479$	−20.7846	+	12.0000i	−0.949673	+	0.548294i	−0.892979	−	0.450098i	$-0.851389\pi$
$479$	−20.7846	+	12.0000i	−0.949673	+	0.548294i	−0.0566937	+	0.998392i	$0.518056\pi$
$480$	10.0000			0.456435
$481$		0			0
$482$	10.0000			0.455488
$483$		0			0
$484$	2.50000	+	4.33013i	0.113636	+	0.196824i
$485$	10.0000	−	17.3205i	0.454077	−	0.786484i
$486$			1.00000i			0.0453609i
$487$	10.3923	+	6.00000i	0.470920	+	0.271886i	0.716625	−	0.697459i	$-0.245686\pi$
$487$	10.3923	+	6.00000i	0.470920	+	0.271886i	−0.245705	+	0.969345i	$0.579019\pi$
$488$	−5.19615	−	3.00000i	−0.235219	−	0.135804i
$489$		−	8.00000i		−	0.361773i
$490$	−9.00000	+	15.5885i	−0.406579	+	0.704215i
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	0.698285	−	0.715820i	$-0.253947\pi$
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	−0.969061	+	0.246822i	$0.920614\pi$
$492$	5.19615	−	3.00000i	0.234261	−	0.135250i
$493$	20.0000			0.900755
$494$		0			0
$495$	8.00000			0.359573
$496$	3.46410	−	2.00000i	0.155543	−	0.0898027i
$497$		0			0
$498$	−2.00000	+	3.46410i	−0.0896221	+	0.155230i
$499$			24.0000i			1.07439i	0.843459	+	0.537194i	$0.180516\pi$
$499$			24.0000i			1.07439i	−0.843459	+	0.537194i	$0.819484\pi$
$500$	10.3923	+	6.00000i	0.464758	+	0.268328i
$501$	−6.92820	−	4.00000i	−0.309529	−	0.178707i
$502$		−	12.0000i		−	0.535586i
$503$	4.00000	−	6.92820i	0.178351	−	0.308913i	−0.762965	−	0.646440i	$-0.776257\pi$
$503$	4.00000	−	6.92820i	0.178351	−	0.308913i	0.941316	+	0.337527i	$0.109590\pi$
$504$	6.00000	+	10.3923i	0.267261	+	0.462910i
$505$	−31.1769	+	18.0000i	−1.38735	+	0.800989i
$506$		0			0
$507$		0			0
$508$	16.0000			0.709885
$509$	−8.66025	+	5.00000i	−0.383859	+	0.221621i	−0.679496	−	0.733679i	$-0.737801\pi$
$509$	−8.66025	+	5.00000i	−0.383859	+	0.221621i	0.295637	+	0.955300i	$0.404468\pi$
$510$	2.00000	+	3.46410i	0.0885615	+	0.153393i
$511$	−4.00000	+	6.92820i	−0.176950	+	0.306486i
$512$			11.0000i			0.486136i
$513$		0			0
$514$	−22.5167	−	13.0000i	−0.993167	−	0.573405i
$515$		0			0
$516$	6.00000	−	10.3923i	0.264135	−	0.457496i
$517$		0			0
$518$	6.92820	−	4.00000i	0.304408	−	0.175750i
$519$	6.00000			0.263371
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$	8.66025	−	5.00000i	0.379049	−	0.218844i
$523$	−22.0000	−	38.1051i	−0.961993	−	1.66622i	−0.717486	−	0.696573i	$-0.754707\pi$
$523$	−22.0000	−	38.1051i	−0.961993	−	1.66622i	−0.244507	−	0.969648i	$-0.578626\pi$
$524$	−2.00000	+	3.46410i	−0.0873704	+	0.151330i
$525$			4.00000i			0.174574i
$526$	20.7846	+	12.0000i	0.906252	+	0.523225i
$527$	−6.92820	−	4.00000i	−0.301797	−	0.174243i
$528$			4.00000i			0.174078i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	6.00000	+	10.3923i	0.260623	+	0.451413i
$531$	10.3923	−	6.00000i	0.450988	−	0.260378i
$532$		0			0
$533$		0			0
$534$	2.00000			0.0865485
$535$	−20.7846	+	12.0000i	−0.898597	+	0.518805i
$536$	−12.0000	−	20.7846i	−0.518321	−	0.897758i
$537$	−2.00000	+	3.46410i	−0.0863064	+	0.149487i
$538$		−	22.0000i		−	0.948487i
$539$	31.1769	+	18.0000i	1.34288	+	0.775315i
$540$	−1.73205	−	1.00000i	−0.0745356	−	0.0430331i
$541$			30.0000i			1.28980i	0.764267	+	0.644900i	$0.223101\pi$
$541$			30.0000i			1.28980i	−0.764267	+	0.644900i	$0.776899\pi$
$542$	6.00000	−	10.3923i	0.257722	−	0.446388i
$543$	5.00000	+	8.66025i	0.214571	+	0.371647i
$544$	8.66025	−	5.00000i	0.371305	−	0.214373i
$545$	4.00000			0.171341
$546$		0			0
$547$	4.00000			0.171028			0.0855138	−	0.996337i	$-0.472747\pi$
$547$	4.00000			0.171028			0.0855138	+	0.996337i	$0.472747\pi$
$548$	5.19615	−	3.00000i	0.221969	−	0.128154i
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$	−2.00000	+	3.46410i	−0.0852803	+	0.147710i
$551$		0			0
$552$		0			0
$553$	27.7128	+	16.0000i	1.17847	+	0.680389i
$554$		−	10.0000i		−	0.424859i
$555$	−2.00000	+	3.46410i	−0.0848953	+	0.147043i
$556$	−6.00000	−	10.3923i	−0.254457	−	0.440732i
$557$	15.5885	−	9.00000i	0.660504	−	0.381342i	−0.131965	−	0.991254i	$-0.542129\pi$
$557$	15.5885	−	9.00000i	0.660504	−	0.381342i	0.792469	+	0.609912i	$0.208795\pi$
$558$	−4.00000			−0.169334
$559$		0			0
$560$	8.00000			0.338062
$561$	6.92820	−	4.00000i	0.292509	−	0.168880i
$562$	5.00000	+	8.66025i	0.210912	+	0.365311i
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	−0.964315	−	0.264758i	$-0.914708\pi$
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	0.711445	+	0.702742i	$0.248041\pi$
$564$		0			0
$565$	−10.3923	−	6.00000i	−0.437208	−	0.252422i
$566$	−10.3923	−	6.00000i	−0.436821	−	0.252199i
$567$		−	4.00000i		−	0.167984i
$568$		0			0
$569$	17.0000	+	29.4449i	0.712677	+	1.23439i	0.963849	+	0.266450i	$0.0858508\pi$
$569$	17.0000	+	29.4449i	0.712677	+	1.23439i	−0.251172	+	0.967943i	$0.580816\pi$
$570$		0			0
$571$	4.00000			0.167395			0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000			0.167395			0.0836974	+	0.996491i	$0.473327\pi$
$572$		0			0
$573$	−8.00000			−0.334205
$574$	20.7846	−	12.0000i	0.867533	−	0.500870i
$575$		0			0
$576$	3.50000	−	6.06218i	0.145833	−	0.252591i
$577$			46.0000i			1.91501i	0.288425	+	0.957503i	$0.406868\pi$
$577$			46.0000i			1.91501i	−0.288425	+	0.957503i	$0.593132\pi$
$578$	−11.2583	−	6.50000i	−0.468285	−	0.270364i
$579$	15.5885	+	9.00000i	0.647834	+	0.374027i
$580$			20.0000i			0.830455i
$581$	8.00000	−	13.8564i	0.331896	−	0.574861i
$582$	−5.00000	−	8.66025i	−0.207257	−	0.358979i
$583$	20.7846	−	12.0000i	0.860811	−	0.496989i
$584$	6.00000			0.248282
$585$		0			0
$586$	−6.00000			−0.247858
$587$	−24.2487	+	14.0000i	−1.00085	+	0.577842i	−0.908500	−	0.417885i	$-0.862772\pi$
$587$	−24.2487	+	14.0000i	−1.00085	+	0.577842i	−0.0923513	+	0.995726i	$0.529438\pi$
$588$	−4.50000	−	7.79423i	−0.185577	−	0.321429i
$589$		0			0
$590$		−	24.0000i		−	0.988064i
$591$	−15.5885	−	9.00000i	−0.641223	−	0.370211i
$592$	−1.73205	−	1.00000i	−0.0711868	−	0.0410997i
$593$		−	26.0000i		−	1.06769i	−0.845582	−	0.533846i	$-0.820746\pi$
$593$		−	26.0000i		−	1.06769i	0.845582	−	0.533846i	$-0.179254\pi$
$594$	2.00000	−	3.46410i	0.0820610	−	0.142134i
$595$	−8.00000	−	13.8564i	−0.327968	−	0.568057i
$596$	5.19615	−	3.00000i	0.212843	−	0.122885i
$597$	8.00000			0.327418
$598$		0			0
$599$	−40.0000			−1.63436			−0.817178	−	0.576386i	$-0.804463\pi$
$599$	−40.0000			−1.63436			−0.817178	+	0.576386i	$0.804463\pi$
$600$	2.59808	−	1.50000i	0.106066	−	0.0612372i
$601$	19.0000	+	32.9090i	0.775026	+	1.34238i	0.934780	+	0.355228i	$0.115597\pi$
$601$	19.0000	+	32.9090i	0.775026	+	1.34238i	−0.159754	+	0.987157i	$0.551070\pi$
$602$	24.0000	−	41.5692i	0.978167	−	1.69423i
$603$			8.00000i			0.325785i
$604$	−3.46410	−	2.00000i	−0.140952	−	0.0813788i
$605$	−8.66025	−	5.00000i	−0.352089	−	0.203279i
$606$			18.0000i			0.731200i
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	−0.656744	−	0.754114i	$-0.728067\pi$
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	0.981454	+	0.191700i	$0.0614000\pi$
$608$		0			0
$609$	−34.6410	+	20.0000i	−1.40372	+	0.810441i
$610$	4.00000			0.161955
$611$		0			0
$612$	−2.00000			−0.0808452
$613$	1.73205	−	1.00000i	0.0699569	−	0.0403896i	−0.464614	−	0.885514i	$-0.653807\pi$
$613$	1.73205	−	1.00000i	0.0699569	−	0.0403896i	0.534570	+	0.845124i	$0.320473\pi$
$614$	8.00000	+	13.8564i	0.322854	+	0.559199i
$615$	−6.00000	+	10.3923i	−0.241943	+	0.419058i
$616$		−	48.0000i		−	1.93398i
$617$	19.0526	+	11.0000i	0.767027	+	0.442843i	0.831813	−	0.555056i	$-0.187303\pi$
$617$	19.0526	+	11.0000i	0.767027	+	0.442843i	−0.0647859	+	0.997899i	$0.520636\pi$
$618$		0			0
$619$			24.0000i			0.964641i	0.875995	+	0.482321i	$0.160206\pi$
$619$			24.0000i			0.964641i	−0.875995	+	0.482321i	$0.839794\pi$
$620$	4.00000	−	6.92820i	0.160644	−	0.278243i
$621$		0			0
$622$		0			0
$623$	−8.00000			−0.320513
$624$		0			0
$625$	−19.0000			−0.760000
$626$	5.19615	−	3.00000i	0.207680	−	0.119904i
$627$		0			0
$628$	9.00000	−	15.5885i	0.359139	−	0.622047i
$629$			4.00000i			0.159490i
$630$	−6.92820	−	4.00000i	−0.276026	−	0.159364i
$631$	−17.3205	−	10.0000i	−0.689519	−	0.398094i	0.113913	−	0.993491i	$-0.463661\pi$
$631$	−17.3205	−	10.0000i	−0.689519	−	0.398094i	−0.803432	+	0.595397i	$0.796995\pi$
$632$		−	24.0000i		−	0.954669i
$633$	−10.0000	+	17.3205i	−0.397464	+	0.688428i
$634$	13.0000	+	22.5167i	0.516296	+	0.894251i
$635$	−27.7128	+	16.0000i	−1.09975	+	0.634941i
$636$	−6.00000			−0.237915
$637$		0			0
$638$	−40.0000			−1.58362
$639$		0			0
$640$	3.00000	+	5.19615i	0.118585	+	0.205396i
$641$	1.00000	−	1.73205i	0.0394976	−	0.0684119i	−0.845601	−	0.533816i	$-0.820758\pi$
$641$	1.00000	−	1.73205i	0.0394976	−	0.0684119i	0.885098	+	0.465404i	$0.154091\pi$
$642$			12.0000i			0.473602i
$643$	−34.6410	−	20.0000i	−1.36611	−	0.788723i	−0.375680	−	0.926750i	$-0.622591\pi$
$643$	−34.6410	−	20.0000i	−1.36611	−	0.788723i	−0.990429	+	0.138027i	$0.955924\pi$
$644$		0			0
$645$			24.0000i			0.944999i
$646$		0			0
$647$	−4.00000	−	6.92820i	−0.157256	−	0.272376i	0.776622	−	0.629967i	$-0.216932\pi$
$647$	−4.00000	−	6.92820i	−0.157256	−	0.272376i	−0.933878	+	0.357591i	$0.883598\pi$
$648$	−2.59808	+	1.50000i	−0.102062	+	0.0589256i
$649$	−48.0000			−1.88416
$650$		0			0
$651$	16.0000			0.627089
$652$	6.92820	−	4.00000i	0.271329	−	0.156652i
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	0.801337	−	0.598213i	$-0.204122\pi$
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	−0.918736	+	0.394872i	$0.870789\pi$
$654$	1.00000	−	1.73205i	0.0391031	−	0.0677285i
$655$		−	8.00000i		−	0.312586i
$656$	−5.19615	−	3.00000i	−0.202876	−	0.117130i
$657$	−1.73205	−	1.00000i	−0.0675737	−	0.0390137i
$658$		0			0
$659$	−14.0000	+	24.2487i	−0.545363	+	0.944596i	0.453221	+	0.891398i	$0.350275\pi$
$659$	−14.0000	+	24.2487i	−0.545363	+	0.944596i	−0.998584	+	0.0531977i	$0.983059\pi$
$660$	4.00000	+	6.92820i	0.155700	+	0.269680i
$661$	25.9808	−	15.0000i	1.01053	−	0.583432i	0.0991864	−	0.995069i	$-0.468376\pi$
$661$	25.9808	−	15.0000i	1.01053	−	0.583432i	0.911348	+	0.411636i	$0.135043\pi$
$662$	16.0000			0.621858
$663$		0			0
$664$	−12.0000			−0.465690
$665$		0			0
$666$	1.00000	+	1.73205i	0.0387492	+	0.0671156i
$667$		0			0
$668$		−	8.00000i		−	0.309529i
$669$	−3.46410	−	2.00000i	−0.133930	−	0.0773245i
$670$	13.8564	+	8.00000i	0.535320	+	0.309067i
$671$		−	8.00000i		−	0.308837i
$672$	−10.0000	+	17.3205i	−0.385758	+	0.668153i
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	0.698988	−	0.715134i	$-0.253634\pi$
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	−0.968818	+	0.247774i	$0.920301\pi$
$674$	15.5885	−	9.00000i	0.600445	−	0.346667i
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	22.0000			0.845529			0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000			0.845529			0.422764	+	0.906240i	$0.361060\pi$
$678$	−5.19615	+	3.00000i	−0.199557	+	0.115214i
$679$	20.0000	+	34.6410i	0.767530	+	1.32940i
$680$	−6.00000	+	10.3923i	−0.230089	+	0.398527i
$681$		−	20.0000i		−	0.766402i
$682$	13.8564	+	8.00000i	0.530589	+	0.306336i
$683$	10.3923	+	6.00000i	0.397650	+	0.229584i	0.685470	−	0.728101i	$-0.259597\pi$
$683$	10.3923	+	6.00000i	0.397650	+	0.229584i	−0.287819	+	0.957685i	$0.592930\pi$
$684$		0			0
$685$	−6.00000	+	10.3923i	−0.229248	+	0.397070i
$686$	−4.00000	−	6.92820i	−0.152721	−	0.264520i
$687$	8.66025	−	5.00000i	0.330409	−	0.190762i
$688$	−12.0000			−0.457496
$689$		0			0
$690$		0			0
$691$	20.7846	−	12.0000i	0.790684	−	0.456502i	−0.0495194	−	0.998773i	$-0.515769\pi$
$691$	20.7846	−	12.0000i	0.790684	−	0.456502i	0.840203	+	0.542272i	$0.182436\pi$
$692$	3.00000	+	5.19615i	0.114043	+	0.197528i
$693$	−8.00000	+	13.8564i	−0.303895	+	0.526361i
$694$			12.0000i			0.455514i
$695$	20.7846	+	12.0000i	0.788405	+	0.455186i
$696$	25.9808	+	15.0000i	0.984798	+	0.568574i
$697$			12.0000i			0.454532i
$698$	13.0000	−	22.5167i	0.492057	−	0.852268i
$699$	7.00000	+	12.1244i	0.264764	+	0.458585i
$700$	−3.46410	+	2.00000i	−0.130931	+	0.0755929i
$701$	34.0000			1.28416			0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000			1.28416			0.642081	+	0.766637i	$0.278071\pi$
$702$		0			0
$703$		0			0
$704$	−24.2487	+	14.0000i	−0.913908	+	0.527645i
$705$		0			0
$706$	−1.00000	+	1.73205i	−0.0376355	+	0.0651866i
$707$		−	72.0000i		−	2.70784i
$708$	10.3923	+	6.00000i	0.390567	+	0.225494i
$709$	22.5167	+	13.0000i	0.845631	+	0.488225i	0.859174	−	0.511683i	$-0.170978\pi$
$709$	22.5167	+	13.0000i	0.845631	+	0.488225i	−0.0135434	+	0.999908i	$0.504311\pi$
$710$		0			0
$711$	−4.00000	+	6.92820i	−0.150012	+	0.259828i
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$		0			0
$714$	−8.00000			−0.299392
$715$		0			0
$716$	−4.00000			−0.149487
$717$	−20.7846	+	12.0000i	−0.776215	+	0.448148i
$718$	−12.0000	−	20.7846i	−0.447836	−	0.775675i
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	−0.998224	−	0.0595683i	$-0.981028\pi$
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	0.550700	+	0.834703i	$0.314361\pi$
$720$			2.00000i			0.0745356i
$721$		0			0
$722$	16.4545	+	9.50000i	0.612372	+	0.353553i
$723$		−	10.0000i		−	0.371904i
$724$	−5.00000	+	8.66025i	−0.185824	+	0.321856i
$725$	5.00000	+	8.66025i	0.185695	+	0.321634i
$726$	−4.33013	+	2.50000i	−0.160706	+	0.0927837i
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−3.46410	+	2.00000i	−0.128212	+	0.0740233i
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$	−1.00000	+	1.73205i	−0.0369611	+	0.0640184i
$733$		−	30.0000i		−	1.10808i	−0.832492	−	0.554038i	$-0.813086\pi$
$733$		−	30.0000i		−	1.10808i	0.832492	−	0.554038i	$-0.186914\pi$
$734$	13.8564	+	8.00000i	0.511449	+	0.295285i
$735$	15.5885	+	9.00000i	0.574989	+	0.331970i
$736$		0			0
$737$	16.0000	−	27.7128i	0.589368	−	1.02081i
$738$	3.00000	+	5.19615i	0.110432	+	0.191273i
$739$	27.7128	−	16.0000i	1.01943	−	0.588570i	0.105493	−	0.994420i	$-0.466358\pi$
$739$	27.7128	−	16.0000i	1.01943	−	0.588570i	0.913939	+	0.405851i	$0.133025\pi$
$740$	−4.00000			−0.147043
$741$		0			0
$742$	−24.0000			−0.881068
$743$	−41.5692	+	24.0000i	−1.52503	+	0.880475i	−0.525467	+	0.850814i	$0.676109\pi$
$743$	−41.5692	+	24.0000i	−1.52503	+	0.880475i	−0.999560	+	0.0296605i	$0.990557\pi$
$744$	−6.00000	−	10.3923i	−0.219971	−	0.381000i
$745$	−6.00000	+	10.3923i	−0.219823	+	0.380745i
$746$			26.0000i			0.951928i
$747$	3.46410	+	2.00000i	0.126745	+	0.0731762i
$748$	6.92820	+	4.00000i	0.253320	+	0.146254i
$749$		−	48.0000i		−	1.75388i
$750$	−6.00000	+	10.3923i	−0.219089	+	0.379473i
$751$	4.00000	+	6.92820i	0.145962	+	0.252814i	0.929731	−	0.368238i	$-0.120039\pi$
$751$	4.00000	+	6.92820i	0.145962	+	0.252814i	−0.783769	+	0.621052i	$0.786706\pi$
$752$		0			0
$753$	−12.0000			−0.437304
$754$		0			0
$755$	8.00000			0.291150
$756$	3.46410	−	2.00000i	0.125988	−	0.0727393i
$757$	−11.0000	−	19.0526i	−0.399802	−	0.692477i	0.593899	−	0.804539i	$-0.297588\pi$
$757$	−11.0000	−	19.0526i	−0.399802	−	0.692477i	−0.993701	+	0.112062i	$0.964254\pi$
$758$	−12.0000	+	20.7846i	−0.435860	+	0.754931i
$759$		0			0
$760$		0			0
$761$	8.66025	+	5.00000i	0.313934	+	0.181250i	0.648686	−	0.761057i	$-0.275319\pi$
$761$	8.66025	+	5.00000i	0.313934	+	0.181250i	−0.334752	+	0.942306i	$0.608652\pi$
$762$			16.0000i			0.579619i
$763$	−4.00000	+	6.92820i	−0.144810	+	0.250818i
$764$	−4.00000	−	6.92820i	−0.144715	−	0.250654i
$765$	3.46410	−	2.00000i	0.125245	−	0.0723102i
$766$	16.0000			0.578103
$767$		0			0
$768$	17.0000			0.613435
$769$	25.9808	−	15.0000i	0.936890	−	0.540914i	0.0479061	−	0.998852i	$-0.484745\pi$
$769$	25.9808	−	15.0000i	0.936890	−	0.540914i	0.888984	+	0.457938i	$0.151412\pi$
$770$	16.0000	+	27.7128i	0.576600	+	0.998700i
$771$	−13.0000	+	22.5167i	−0.468184	+	0.810918i
$772$			18.0000i			0.647834i
$773$	8.66025	+	5.00000i	0.311488	+	0.179838i	0.647592	−	0.761987i	$-0.275776\pi$
$773$	8.66025	+	5.00000i	0.311488	+	0.179838i	−0.336104	+	0.941825i	$0.609109\pi$
$774$	10.3923	+	6.00000i	0.373544	+	0.215666i
$775$		−	4.00000i		−	0.143684i
$776$	15.0000	−	25.9808i	0.538469	−	0.932655i
$777$	−4.00000	−	6.92820i	−0.143499	−	0.248548i
$778$	19.0526	−	11.0000i	0.683067	−	0.394369i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−5.00000	−	8.66025i	−0.178685	−	0.309492i
$784$	−4.50000	+	7.79423i	−0.160714	+	0.278365i
$785$			36.0000i			1.28490i
$786$	−3.46410	−	2.00000i	−0.123560	−	0.0713376i
$787$	27.7128	+	16.0000i	0.987855	+	0.570338i	0.904632	−	0.426193i	$-0.140145\pi$
$787$	27.7128	+	16.0000i	0.987855	+	0.570338i	0.0832226	+	0.996531i	$0.473479\pi$
$788$		−	18.0000i		−	0.641223i
$789$	12.0000	−	20.7846i	0.427211	−	0.739952i
$790$	8.00000	+	13.8564i	0.284627	+	0.492989i
$791$	20.7846	−	12.0000i	0.739016	−	0.426671i
$792$	12.0000			0.426401
$793$		0			0
$794$	38.0000			1.34857
$795$	10.3923	−	6.00000i	0.368577	−	0.212798i
$796$	4.00000	+	6.92820i	0.141776	+	0.245564i
$797$	23.0000	−	39.8372i	0.814702	−	1.41110i	−0.0948400	−	0.995493i	$-0.530234\pi$
$797$	23.0000	−	39.8372i	0.814702	−	1.41110i	0.909542	−	0.415612i	$-0.136433\pi$
$798$		0			0
$799$		0			0
$800$	4.33013	+	2.50000i	0.153093	+	0.0883883i
$801$		−	2.00000i		−	0.0706665i
$802$	−11.0000	+	19.0526i	−0.388424	+	0.672769i
$803$	4.00000	+	6.92820i	0.141157	+	0.244491i
$804$	−6.92820	+	4.00000i	−0.244339	+	0.141069i
$805$		0			0
$806$		0			0
$807$	−22.0000			−0.774437
$808$	−46.7654	+	27.0000i	−1.64520	+	0.949857i
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	0.999491	+	0.0319002i	$0.0101559\pi$
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	−0.472119	+	0.881535i	$0.656511\pi$
$810$	1.00000	−	1.73205i	0.0351364	−	0.0608581i
$811$		−	8.00000i		−	0.280918i	−0.990086	−	0.140459i	$-0.955142\pi$
$811$		−	8.00000i		−	0.280918i	0.990086	−	0.140459i	$-0.0448578\pi$
$812$	−34.6410	−	20.0000i	−1.21566	−	0.701862i
$813$	−10.3923	−	6.00000i	−0.364474	−	0.210429i
$814$		−	8.00000i		−	0.280400i
$815$	−8.00000	+	13.8564i	−0.280228	+	0.485369i
$816$	1.00000	+	1.73205i	0.0350070	+	0.0606339i
$817$		0			0
$818$	−34.0000			−1.18878
$819$		0			0
$820$	−12.0000			−0.419058
$821$	19.0526	−	11.0000i	0.664939	−	0.383903i	−0.129217	−	0.991616i	$-0.541246\pi$
$821$	19.0526	−	11.0000i	0.664939	−	0.383903i	0.794156	+	0.607714i	$0.207913\pi$
$822$	3.00000	+	5.19615i	0.104637	+	0.181237i
$823$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$823$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$824$		0			0
$825$	3.46410	+	2.00000i	0.120605	+	0.0696311i
$826$	41.5692	+	24.0000i	1.44638	+	0.835067i
$827$			4.00000i			0.139094i	0.997579	+	0.0695468i	$0.0221553\pi$
$827$			4.00000i			0.139094i	−0.997579	+	0.0695468i	$0.977845\pi$
$828$		0			0
$829$	−17.0000	−	29.4449i	−0.590434	−	1.02266i	−0.994174	−	0.107788i	$-0.965623\pi$
$829$	−17.0000	−	29.4449i	−0.590434	−	1.02266i	0.403739	−	0.914874i	$-0.367710\pi$
$830$	6.92820	−	4.00000i	0.240481	−	0.138842i
$831$	−10.0000			−0.346896
$832$		0			0
$833$	18.0000			0.623663
$834$	10.3923	−	6.00000i	0.359856	−	0.207763i
$835$	8.00000	+	13.8564i	0.276851	+	0.479521i
$836$		0			0
$837$			4.00000i			0.138260i
$838$	3.46410	+	2.00000i	0.119665	+	0.0690889i
$839$	−41.5692	−	24.0000i	−1.43513	−	0.828572i	−0.437623	−	0.899158i	$-0.644180\pi$
$839$	−41.5692	−	24.0000i	−1.43513	−	0.828572i	−0.997506	+	0.0705865i	$0.977513\pi$
$840$		−	24.0000i		−	0.828079i
$841$	−35.5000	+	61.4878i	−1.22414	+	2.12027i
$842$	−5.00000	−	8.66025i	−0.172311	−	0.298452i
$843$	8.66025	−	5.00000i	0.298275	−	0.172209i
$844$	−20.0000			−0.688428
$845$		0			0
$846$		0			0
$847$	17.3205	−	10.0000i	0.595140	−	0.343604i
$848$	3.00000	+	5.19615i	0.103020	+	0.178437i
$849$	−6.00000	+	10.3923i	−0.205919	+	0.356663i
$850$			2.00000i			0.0685994i
$851$		0			0
$852$		0			0
$853$			30.0000i			1.02718i	0.858036	+	0.513590i	$0.171685\pi$
$853$			30.0000i			1.02718i	−0.858036	+	0.513590i	$0.828315\pi$
$854$	−4.00000	+	6.92820i	−0.136877	+	0.237078i
$855$		0			0
$856$	−31.1769	+	18.0000i	−1.06561	+	0.615227i
$857$	46.0000			1.57133			0.785665	−	0.618652i	$-0.212321\pi$
$857$	46.0000			1.57133			0.785665	+	0.618652i	$0.212321\pi$
$858$		0			0
$859$	−44.0000			−1.50126			−0.750630	−	0.660722i	$-0.770250\pi$
$859$	−44.0000			−1.50126			−0.750630	+	0.660722i	$0.770250\pi$
$860$	−20.7846	+	12.0000i	−0.708749	+	0.409197i
$861$	−12.0000	−	20.7846i	−0.408959	−	0.708338i
$862$		0			0
$863$		−	16.0000i		−	0.544646i	−0.962206	−	0.272323i	$-0.912208\pi$
$863$		−	16.0000i		−	0.544646i	0.962206	−	0.272323i	$-0.0877920\pi$
$864$	−4.33013	−	2.50000i	−0.147314	−	0.0850517i
$865$	−10.3923	−	6.00000i	−0.353349	−	0.204006i
$866$			34.0000i			1.15537i
$867$	−6.50000	+	11.2583i	−0.220752	+	0.382353i
$868$	8.00000	+	13.8564i	0.271538	+	0.470317i
$869$	27.7128	−	16.0000i	0.940093	−	0.542763i
$870$	−20.0000			−0.678064
$871$		0			0
$872$	6.00000			0.203186
$873$	−8.66025	+	5.00000i	−0.293105	+	0.169224i
$874$		0			0
$875$	24.0000	−	41.5692i	0.811348	−	1.40530i
$876$		−	2.00000i		−	0.0675737i
$877$	−8.66025	−	5.00000i	−0.292436	−	0.168838i	0.346604	−	0.938012i	$-0.387335\pi$
$877$	−8.66025	−	5.00000i	−0.292436	−	0.168838i	−0.639040	+	0.769174i	$0.720668\pi$
$878$	−27.7128	−	16.0000i	−0.935262	−	0.539974i
$879$			6.00000i			0.202375i
$880$	4.00000	−	6.92820i	0.134840	−	0.233550i
$881$	29.0000	+	50.2295i	0.977035	+	1.69227i	0.673050	+	0.739597i	$0.264984\pi$
$881$	29.0000	+	50.2295i	0.977035	+	1.69227i	0.303985	+	0.952677i	$0.401683\pi$
$882$	7.79423	−	4.50000i	0.262445	−	0.151523i
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$		0			0
$885$	−24.0000			−0.806751
$886$	3.46410	−	2.00000i	0.116379	−	0.0671913i
$887$	24.0000	+	41.5692i	0.805841	+	1.39576i	0.915722	+	0.401813i	$0.131620\pi$
$887$	24.0000	+	41.5692i	0.805841	+	1.39576i	−0.109881	+	0.993945i	$0.535047\pi$
$888$	−3.00000	+	5.19615i	−0.100673	+	0.174371i
$889$		−	64.0000i		−	2.14649i
$890$	−3.46410	−	2.00000i	−0.116117	−	0.0670402i
$891$	−3.46410	−	2.00000i	−0.116052	−	0.0670025i
$892$		−	4.00000i		−	0.133930i
$893$		0			0
$894$	3.00000	+	5.19615i	0.100335	+	0.173785i
$895$	6.92820	−	4.00000i	0.231584	−	0.133705i
$896$	−12.0000			−0.400892
$897$		0			0
$898$	22.0000			0.734150
$899$	34.6410	−	20.0000i	1.15534	−	0.667037i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	6.00000	−	10.3923i	0.199889	−	0.346218i
$902$		−	24.0000i		−	0.799113i
$903$	−41.5692	−	24.0000i	−1.38334	−	0.798670i
$904$	−15.5885	−	9.00000i	−0.518464	−	0.299336i
$905$		−	20.0000i		−	0.664822i
$906$	2.00000	−	3.46410i	0.0664455	−	0.115087i
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	0.948278	−	0.317441i	$-0.102824\pi$
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	−0.749051	+	0.662512i	$0.769490\pi$
$908$	17.3205	−	10.0000i	0.574801	−	0.331862i
$909$	18.0000			0.597022
$910$		0			0
$911$	−40.0000			−1.32526			−0.662630	−	0.748947i	$-0.730560\pi$
$911$	−40.0000			−1.32526			−0.662630	+	0.748947i	$0.730560\pi$
$912$		0			0
$913$	−8.00000	−	13.8564i	−0.264761	−	0.458580i
$914$	1.00000	−	1.73205i	0.0330771	−	0.0572911i
$915$		−	4.00000i		−	0.132236i
$916$	8.66025	+	5.00000i	0.286143	+	0.165205i
$917$	13.8564	+	8.00000i	0.457579	+	0.264183i
$918$		−	2.00000i		−	0.0660098i
$919$	24.0000	−	41.5692i	0.791687	−	1.37124i	−0.133235	−	0.991084i	$-0.542536\pi$
$919$	24.0000	−	41.5692i	0.791687	−	1.37124i	0.924922	−	0.380158i	$-0.124130\pi$
$920$		0			0
$921$	13.8564	−	8.00000i	0.456584	−	0.263609i
$922$	38.0000			1.25146
$923$		0			0
$924$	−16.0000			−0.526361
$925$	−1.73205	+	1.00000i	−0.0569495	+	0.0328798i
$926$	−2.00000	−	3.46410i	−0.0657241	−	0.113837i
$927$		0			0
$928$			50.0000i			1.64133i
$929$	25.9808	+	15.0000i	0.852401	+	0.492134i	0.861460	−	0.507825i	$-0.169550\pi$
$929$	25.9808	+	15.0000i	0.852401	+	0.492134i	−0.00905914	+	0.999959i	$0.502884\pi$
$930$	6.92820	+	4.00000i	0.227185	+	0.131165i
$931$		0			0
$932$	−7.00000	+	12.1244i	−0.229293	+	0.397146i
$933$		0			0
$934$	10.3923	−	6.00000i	0.340047	−	0.196326i
$935$	−16.0000			−0.523256
$936$		0			0
$937$	26.0000			0.849383			0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000			0.849383			0.424691	+	0.905338i	$0.360383\pi$
$938$	−27.7128	+	16.0000i	−0.904855	+	0.522419i
$939$	−3.00000	−	5.19615i	−0.0979013	−	0.169570i
$940$		0			0
$941$			14.0000i			0.456387i	0.973616	+	0.228193i	$0.0732819\pi$
$941$			14.0000i			0.456387i	−0.973616	+	0.228193i	$0.926718\pi$
$942$	15.5885	+	9.00000i	0.507899	+	0.293236i
$943$		0			0
$944$		−	12.0000i		−	0.390567i
$945$	−4.00000	+	6.92820i	−0.130120	+	0.225374i
$946$	−24.0000	−	41.5692i	−0.780307	−	1.35153i
$947$	−51.9615	+	30.0000i	−1.68852	+	0.974869i	−0.732872	+	0.680367i	$0.761821\pi$
$947$	−51.9615	+	30.0000i	−1.68852	+	0.974869i	−0.955651	+	0.294502i	$0.904846\pi$
$948$	−8.00000			−0.259828
$949$		0			0
$950$		0			0
$951$	22.5167	−	13.0000i	0.730153	−	0.421554i
$952$	−12.0000	−	20.7846i	−0.388922	−	0.673633i
$953$	−15.0000	+	25.9808i	−0.485898	+	0.841599i	−0.999869	−	0.0162081i	$-0.994841\pi$
$953$	−15.0000	+	25.9808i	−0.485898	+	0.841599i	0.513971	+	0.857808i	$0.328174\pi$
$954$		−	6.00000i		−	0.194257i
$955$	13.8564	+	8.00000i	0.448383	+	0.258874i
$956$	−20.7846	−	12.0000i	−0.672222	−	0.388108i
$957$			40.0000i			1.29302i
$958$	12.0000	−	20.7846i	0.387702	−	0.671520i
$959$	−12.0000	−	20.7846i	−0.387500	−	0.671170i
$960$	−12.1244	+	7.00000i	−0.391312	+	0.225924i
$961$	15.0000			0.483871
$962$		0			0
$963$	12.0000			0.386695
$964$	8.66025	−	5.00000i	0.278928	−	0.161039i
$965$	−18.0000	−	31.1769i	−0.579441	−	1.00362i
$966$		0			0
$967$			52.0000i			1.67221i	0.548572	+	0.836104i	$0.315172\pi$
$967$			52.0000i			1.67221i	−0.548572	+	0.836104i	$0.684828\pi$
$968$	−12.9904	−	7.50000i	−0.417527	−	0.241059i
$969$		0			0
$970$			20.0000i			0.642161i
$971$	30.0000	−	51.9615i	0.962746	−	1.66752i	0.247193	−	0.968966i	$-0.420492\pi$
$971$	30.0000	−	51.9615i	0.962746	−	1.66752i	0.715553	−	0.698558i	$-0.246175\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−41.5692	+	24.0000i	−1.33265	+	0.769405i
$974$	−12.0000			−0.384505
$975$		0			0
$976$	2.00000			0.0640184
$977$	36.3731	−	21.0000i	1.16368	−	0.671850i	0.211495	−	0.977379i	$-0.432167\pi$
$977$	36.3731	−	21.0000i	1.16368	−	0.671850i	0.952183	+	0.305530i	$0.0988335\pi$
$978$	4.00000	+	6.92820i	0.127906	+	0.221540i
$979$	−4.00000	+	6.92820i	−0.127841	+	0.221426i
$980$			18.0000i			0.574989i
$981$	−1.73205	−	1.00000i	−0.0553001	−	0.0319275i
$982$	10.3923	+	6.00000i	0.331632	+	0.191468i
$983$			16.0000i			0.510321i	0.966899	+	0.255160i	$0.0821283\pi$
$983$			16.0000i			0.510321i	−0.966899	+	0.255160i	$0.917872\pi$
$984$	−9.00000	+	15.5885i	−0.286910	+	0.496942i
$985$	18.0000	+	31.1769i	0.573528	+	0.993379i
$986$	−17.3205	+	10.0000i	−0.551597	+	0.318465i
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−6.92820	+	4.00000i	−0.220193	+	0.127128i
$991$	−8.00000	−	13.8564i	−0.254128	−	0.440163i	0.710530	−	0.703667i	$-0.248455\pi$
$991$	−8.00000	−	13.8564i	−0.254128	−	0.440163i	−0.964658	+	0.263504i	$0.915122\pi$
$992$	10.0000	−	17.3205i	0.317500	−	0.549927i
$993$		−	16.0000i		−	0.507745i
$994$		0			0
$995$	−13.8564	−	8.00000i	−0.439278	−	0.253617i
$996$			4.00000i			0.126745i
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	−0.583363	−	0.812211i	$-0.698264\pi$
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	0.995077	+	0.0991016i	$0.0315969\pi$
$998$	−12.0000	−	20.7846i	−0.379853	−	0.657925i
$999$	1.73205	−	1.00000i	0.0547997	−	0.0316386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.j.e.361.1		4
13.2	odd	12		507.2.a.a.1.1		1
13.3	even	3		507.2.b.a.337.1		2
13.4	even	6	inner	507.2.j.e.316.1		4
13.5	odd	4		507.2.e.b.484.1		2
13.6	odd	12		507.2.e.b.22.1		2
13.7	odd	12		507.2.e.a.22.1		2
13.8	odd	4		507.2.e.a.484.1		2
13.9	even	3	inner	507.2.j.e.316.2		4
13.10	even	6		507.2.b.a.337.2		2
13.11	odd	12		39.2.a.a.1.1	✓	1
13.12	even	2	inner	507.2.j.e.361.2		4
39.2	even	12		1521.2.a.e.1.1		1
39.11	even	12		117.2.a.a.1.1		1
39.23	odd	6		1521.2.b.b.1351.1		2
39.29	odd	6		1521.2.b.b.1351.2		2
52.11	even	12		624.2.a.i.1.1		1
52.15	even	12		8112.2.a.s.1.1		1
65.24	odd	12		975.2.a.f.1.1		1
65.37	even	12		975.2.c.f.274.2		2
65.63	even	12		975.2.c.f.274.1		2
91.76	even	12		1911.2.a.f.1.1		1
104.11	even	12		2496.2.a.e.1.1		1
104.37	odd	12		2496.2.a.q.1.1		1
117.11	even	12		1053.2.e.d.352.1		2
117.50	even	12		1053.2.e.d.703.1		2
117.76	odd	12		1053.2.e.b.703.1		2
117.115	odd	12		1053.2.e.b.352.1		2
143.76	even	12		4719.2.a.c.1.1		1
156.11	odd	12		1872.2.a.h.1.1		1
195.89	even	12		2925.2.a.p.1.1		1
195.128	odd	12		2925.2.c.e.2224.2		2
195.167	odd	12		2925.2.c.e.2224.1		2
273.167	odd	12		5733.2.a.e.1.1		1
312.11	odd	12		7488.2.a.by.1.1		1
312.245	even	12		7488.2.a.bl.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.a.a.1.1	✓	1	13.11	odd	12
117.2.a.a.1.1		1	39.11	even	12
507.2.a.a.1.1		1	13.2	odd	12
507.2.b.a.337.1		2	13.3	even	3
507.2.b.a.337.2		2	13.10	even	6
507.2.e.a.22.1		2	13.7	odd	12
507.2.e.a.484.1		2	13.8	odd	4
507.2.e.b.22.1		2	13.6	odd	12
507.2.e.b.484.1		2	13.5	odd	4
507.2.j.e.316.1		4	13.4	even	6	inner
507.2.j.e.316.2		4	13.9	even	3	inner
507.2.j.e.361.1		4	1.1	even	1	trivial
507.2.j.e.361.2		4	13.12	even	2	inner
624.2.a.i.1.1		1	52.11	even	12
975.2.a.f.1.1		1	65.24	odd	12
975.2.c.f.274.1		2	65.63	even	12
975.2.c.f.274.2		2	65.37	even	12
1053.2.e.b.352.1		2	117.115	odd	12
1053.2.e.b.703.1		2	117.76	odd	12
1053.2.e.d.352.1		2	117.11	even	12
1053.2.e.d.703.1		2	117.50	even	12
1521.2.a.e.1.1		1	39.2	even	12
1521.2.b.b.1351.1		2	39.23	odd	6
1521.2.b.b.1351.2		2	39.29	odd	6
1872.2.a.h.1.1		1	156.11	odd	12
1911.2.a.f.1.1		1	91.76	even	12
2496.2.a.e.1.1		1	104.11	even	12
2496.2.a.q.1.1		1	104.37	odd	12
2925.2.a.p.1.1		1	195.89	even	12
2925.2.c.e.2224.1		2	195.167	odd	12
2925.2.c.e.2224.2		2	195.128	odd	12
4719.2.a.c.1.1		1	143.76	even	12
5733.2.a.e.1.1		1	273.167	odd	12
7488.2.a.bl.1.1		1	312.245	even	12
7488.2.a.by.1.1		1	312.11	odd	12
8112.2.a.s.1.1		1	52.15	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(3.46410 + 2.00000i) q^{7} -3.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(3.46410 + 2.00000i) q^{7} -3.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(3.46410 - 2.00000i) q^{11} -1.00000 q^{12} -4.00000 q^{14} +(1.73205 - 1.00000i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} -1.00000i q^{18} +(1.73205 + 1.00000i) q^{20} +4.00000i q^{21} +(-2.00000 + 3.46410i) q^{22} +(2.59808 - 1.50000i) q^{24} +1.00000 q^{25} -1.00000 q^{27} +(-3.46410 + 2.00000i) q^{28} +(5.00000 + 8.66025i) q^{29} +(-1.00000 + 1.73205i) q^{30} -4.00000i q^{31} +(4.33013 + 2.50000i) q^{32} +(3.46410 + 2.00000i) q^{33} +2.00000i q^{34} +(4.00000 - 6.92820i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.73205 + 1.00000i) q^{37} -6.00000 q^{40} +(-5.19615 + 3.00000i) q^{41} +(-2.00000 - 3.46410i) q^{42} +(-6.00000 + 10.3923i) q^{43} +4.00000i q^{44} +(1.73205 + 1.00000i) q^{45} +(-0.500000 + 0.866025i) q^{48} +(4.50000 + 7.79423i) q^{49} +(-0.866025 + 0.500000i) q^{50} +2.00000 q^{51} +6.00000 q^{53} +(0.866025 - 0.500000i) q^{54} +(-4.00000 - 6.92820i) q^{55} +(6.00000 - 10.3923i) q^{56} +(-8.66025 - 5.00000i) q^{58} +(-10.3923 - 6.00000i) q^{59} +2.00000i q^{60} +(1.00000 - 1.73205i) q^{61} +(2.00000 + 3.46410i) q^{62} +(-3.46410 + 2.00000i) q^{63} -7.00000 q^{64} -4.00000 q^{66} +(6.92820 - 4.00000i) q^{67} +(1.00000 + 1.73205i) q^{68} +8.00000i q^{70} +(2.59808 + 1.50000i) q^{72} +2.00000i q^{73} +(1.00000 - 1.73205i) q^{74} +(0.500000 + 0.866025i) q^{75} +16.0000 q^{77} +8.00000 q^{79} +(1.73205 - 1.00000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} -4.00000i q^{83} +(-3.46410 - 2.00000i) q^{84} +(-3.46410 - 2.00000i) q^{85} -12.0000i q^{86} +(-5.00000 + 8.66025i) q^{87} +(-6.00000 - 10.3923i) q^{88} +(-1.73205 + 1.00000i) q^{89} -2.00000 q^{90} +(3.46410 - 2.00000i) q^{93} +5.00000i q^{96} +(8.66025 + 5.00000i) q^{97} +(-7.79423 - 4.50000i) q^{98} +4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 2 q^{4} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 2 * q^4 - 2 * q^9	\( 4 q + 2 q^{3} - 2 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} - 16 q^{14} + 2 q^{16} + 4 q^{17} - 8 q^{22} + 4 q^{25} - 4 q^{27} + 20 q^{29} - 4 q^{30} + 16 q^{35} - 2 q^{36} - 24 q^{40} - 8 q^{42} - 24 q^{43} - 2 q^{48} + 18 q^{49} + 8 q^{51} + 24 q^{53} - 16 q^{55} + 24 q^{56} + 4 q^{61} + 8 q^{62} - 28 q^{64} - 16 q^{66} + 4 q^{68} + 4 q^{74} + 2 q^{75} + 64 q^{77} + 32 q^{79} - 2 q^{81} + 12 q^{82} - 20 q^{87} - 24 q^{88} - 8 q^{90}+O(q^{100}) \) 4 * q + 2 * q^3 - 2 * q^4 - 2 * q^9 + 4 * q^10 - 4 * q^12 - 16 * q^14 + 2 * q^16 + 4 * q^17 - 8 * q^22 + 4 * q^25 - 4 * q^27 + 20 * q^29 - 4 * q^30 + 16 * q^35 - 2 * q^36 - 24 * q^40 - 8 * q^42 - 24 * q^43 - 2 * q^48 + 18 * q^49 + 8 * q^51 + 24 * q^53 - 16 * q^55 + 24 * q^56 + 4 * q^61 + 8 * q^62 - 28 * q^64 - 16 * q^66 + 4 * q^68 + 4 * q^74 + 2 * q^75 + 64 * q^77 + 32 * q^79 - 2 * q^81 + 12 * q^82 - 20 * q^87 - 24 * q^88 - 8 * q^90

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