LMFDB - Embedded newform 1134.2.g.k.163.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(163,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("1134.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.3
Root			$0.500000 - 2.05195i$ of defining polynomial
Character	$\chi$	$=$	1134.163
Dual form			1134.2.g.k.487.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.230252 - 0.398809i) q^{5} +(-2.32383 - 1.26483i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.230252 - 0.398809i) q^{5} +(-2.32383 - 1.26483i) q^{7} +1.00000 q^{8} +(0.230252 + 0.398809i) q^{10} +(1.82383 + 3.15897i) q^{11} -1.46050 q^{13} +(2.25729 - 1.38008i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.86693 - 3.23361i) q^{17} +(-2.02704 + 3.51094i) q^{19} -0.460505 q^{20} -3.64766 q^{22} +(-0.566537 + 0.981271i) q^{23} +(2.39397 + 4.14647i) q^{25} +(0.730252 - 1.26483i) q^{26} +(0.0665372 + 2.64491i) q^{28} +8.97509 q^{29} +(0.257295 + 0.445647i) q^{31} +(-0.500000 - 0.866025i) q^{32} +3.73385 q^{34} +(-1.03950 + 0.635534i) q^{35} +(-4.55408 + 7.88791i) q^{37} +(-2.02704 - 3.51094i) q^{38} +(0.230252 - 0.398809i) q^{40} +0.945916 q^{41} -9.32743 q^{43} +(1.82383 - 3.15897i) q^{44} +(-0.566537 - 0.981271i) q^{46} +(-1.16372 + 2.01561i) q^{47} +(3.80039 + 5.87852i) q^{49} -4.78794 q^{50} +(0.730252 + 1.26483i) q^{52} +(6.21780 + 10.7695i) q^{53} +1.67977 q^{55} +(-2.32383 - 1.26483i) q^{56} +(-4.48755 + 7.77266i) q^{58} +(6.44805 + 11.1684i) q^{59} +(-6.04163 + 10.4644i) q^{61} -0.514589 q^{62} +1.00000 q^{64} +(-0.336285 + 0.582462i) q^{65} +(1.16012 + 2.00938i) q^{67} +(-1.86693 + 3.23361i) q^{68} +(-0.0306407 - 1.21800i) q^{70} +1.67977 q^{71} +(-6.62062 - 11.4673i) q^{73} +(-4.55408 - 7.88791i) q^{74} +4.05408 q^{76} +(-0.242705 - 9.64776i) q^{77} +(2.50360 - 4.33636i) q^{79} +(0.230252 + 0.398809i) q^{80} +(-0.472958 + 0.819187i) q^{82} -6.64766 q^{83} -1.71946 q^{85} +(4.66372 - 8.07779i) q^{86} +(1.82383 + 3.15897i) q^{88} +(-1.36333 + 2.36135i) q^{89} +(3.39397 + 1.84730i) q^{91} +1.13307 q^{92} +(-1.16372 - 2.01561i) q^{94} +(0.933463 + 1.61680i) q^{95} +11.1872 q^{97} +(-6.99115 + 0.351971i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} - 5 q^{5} - 2 q^{7} + 6 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 - 5 * q^5 - 2 * q^7 + 6 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} - 5 q^{5} - 2 q^{7} + 6 q^{8} - 5 q^{10} - q^{11} + 4 q^{13} - 2 q^{14} - 3 q^{16} - 4 q^{17} - 3 q^{19} + 10 q^{20} + 2 q^{22} - 7 q^{23} - 2 q^{25} - 2 q^{26} + 4 q^{28} + 10 q^{29} - 14 q^{31} - 3 q^{32} + 8 q^{34} - 19 q^{35} - 9 q^{37} - 3 q^{38} - 5 q^{40} + 24 q^{41} - 36 q^{43} - q^{44} - 7 q^{46} + 3 q^{47} + 12 q^{49} + 4 q^{50} - 2 q^{52} + 9 q^{53} + 14 q^{55} - 2 q^{56} - 5 q^{58} + 4 q^{59} + 4 q^{61} + 28 q^{62} + 6 q^{64} - 12 q^{65} + 5 q^{67} - 4 q^{68} + 17 q^{70} + 14 q^{71} - 25 q^{73} - 9 q^{74} + 6 q^{76} - 17 q^{77} + 7 q^{79} - 5 q^{80} - 12 q^{82} - 16 q^{83} - 28 q^{85} + 18 q^{86} - q^{88} - 9 q^{89} + 4 q^{91} + 14 q^{92} + 3 q^{94} + 2 q^{95} + 56 q^{97} - 12 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 - 5 * q^5 - 2 * q^7 + 6 * q^8 - 5 * q^10 - q^11 + 4 * q^13 - 2 * q^14 - 3 * q^16 - 4 * q^17 - 3 * q^19 + 10 * q^20 + 2 * q^22 - 7 * q^23 - 2 * q^25 - 2 * q^26 + 4 * q^28 + 10 * q^29 - 14 * q^31 - 3 * q^32 + 8 * q^34 - 19 * q^35 - 9 * q^37 - 3 * q^38 - 5 * q^40 + 24 * q^41 - 36 * q^43 - q^44 - 7 * q^46 + 3 * q^47 + 12 * q^49 + 4 * q^50 - 2 * q^52 + 9 * q^53 + 14 * q^55 - 2 * q^56 - 5 * q^58 + 4 * q^59 + 4 * q^61 + 28 * q^62 + 6 * q^64 - 12 * q^65 + 5 * q^67 - 4 * q^68 + 17 * q^70 + 14 * q^71 - 25 * q^73 - 9 * q^74 + 6 * q^76 - 17 * q^77 + 7 * q^79 - 5 * q^80 - 12 * q^82 - 16 * q^83 - 28 * q^85 + 18 * q^86 - q^88 - 9 * q^89 + 4 * q^91 + 14 * q^92 + 3 * q^94 + 2 * q^95 + 56 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.230252	−	0.398809i	0.102972	−	0.178353i	−0.809936	−	0.586519i	$-0.800498\pi$
$5$	0.230252	−	0.398809i	0.102972	−	0.178353i	0.912908	+	0.408166i	$0.133831\pi$
$6$		0			0
$7$	−2.32383	−	1.26483i	−0.878326	−	0.478062i
$7$	−2.32383	−	1.26483i	−0.878326	−	0.478062i
$8$	1.00000			0.353553
$9$		0			0
$10$	0.230252	+	0.398809i	0.0728122	+	0.126114i
$11$	1.82383	+	3.15897i	0.549906	+	0.952465i	0.998280	+	0.0586193i	$0.0186698\pi$
$11$	1.82383	+	3.15897i	0.549906	+	0.952465i	−0.448374	+	0.893846i	$0.647997\pi$
$12$		0			0
$13$	−1.46050			−0.405071			−0.202536	−	0.979275i	$-0.564918\pi$
$13$	−1.46050			−0.405071			−0.202536	+	0.979275i	$0.564918\pi$
$14$	2.25729	−	1.38008i	0.603287	−	0.368842i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.86693	−	3.23361i	−0.452796	−	0.784266i	0.545763	−	0.837940i	$-0.316240\pi$
$17$	−1.86693	−	3.23361i	−0.452796	−	0.784266i	−0.998558	+	0.0536743i	$0.982907\pi$
$18$		0			0
$19$	−2.02704	+	3.51094i	−0.465035	+	0.805465i	−0.999203	−	0.0399136i	$-0.987292\pi$
$19$	−2.02704	+	3.51094i	−0.465035	+	0.805465i	0.534168	+	0.845378i	$0.320625\pi$
$20$	−0.460505			−0.102972
$21$		0			0
$22$	−3.64766			−0.777684
$23$	−0.566537	+	0.981271i	−0.118131	+	0.204609i	−0.919027	−	0.394194i	$-0.871024\pi$
$23$	−0.566537	+	0.981271i	−0.118131	+	0.204609i	0.800896	+	0.598804i	$0.204357\pi$
$24$		0			0
$25$	2.39397	+	4.14647i	0.478794	+	0.829295i
$26$	0.730252	−	1.26483i	0.143214	−	0.248054i
$27$		0			0
$28$	0.0665372	+	2.64491i	0.0125744	+	0.499842i
$29$	8.97509			1.66663			0.833317	−	0.552796i	$-0.186439\pi$
$29$	8.97509			1.66663			0.833317	+	0.552796i	$0.186439\pi$
$30$		0			0
$31$	0.257295	+	0.445647i	0.0462115	+	0.0800406i	0.888206	−	0.459446i	$-0.151952\pi$
$31$	0.257295	+	0.445647i	0.0462115	+	0.0800406i	−0.841994	+	0.539486i	$0.818619\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	3.73385			0.640350
$35$	−1.03950	+	0.635534i	−0.175707	+	0.107425i
$36$		0			0
$37$	−4.55408	+	7.88791i	−0.748687	+	1.29676i	0.199765	+	0.979844i	$0.435982\pi$
$37$	−4.55408	+	7.88791i	−0.748687	+	1.29676i	−0.948452	+	0.316920i	$0.897351\pi$
$38$	−2.02704	−	3.51094i	−0.328830	−	0.569550i
$39$		0			0
$40$	0.230252	−	0.398809i	0.0364061	−	0.0630572i
$41$	0.945916			0.147727			0.0738636	−	0.997268i	$-0.476467\pi$
$41$	0.945916			0.147727			0.0738636	+	0.997268i	$0.476467\pi$
$42$		0			0
$43$	−9.32743			−1.42242			−0.711210	−	0.702980i	$-0.751852\pi$
$43$	−9.32743			−1.42242			−0.711210	+	0.702980i	$0.751852\pi$
$44$	1.82383	−	3.15897i	0.274953	−	0.476233i
$45$		0			0
$46$	−0.566537	−	0.981271i	−0.0835314	−	0.144681i
$47$	−1.16372	+	2.01561i	−0.169745	+	0.294007i	−0.938330	−	0.345740i	$-0.887628\pi$
$47$	−1.16372	+	2.01561i	−0.169745	+	0.294007i	0.768585	+	0.639748i	$0.220961\pi$
$48$		0			0
$49$	3.80039	+	5.87852i	0.542913	+	0.839789i
$50$	−4.78794			−0.677116
$51$		0			0
$52$	0.730252	+	1.26483i	0.101268	+	0.175401i
$53$	6.21780	+	10.7695i	0.854080	+	1.47931i	0.877495	+	0.479585i	$0.159213\pi$
$53$	6.21780	+	10.7695i	0.854080	+	1.47931i	−0.0234151	+	0.999726i	$0.507454\pi$
$54$		0			0
$55$	1.67977			0.226500
$56$	−2.32383	−	1.26483i	−0.310535	−	0.169021i
$57$		0			0
$58$	−4.48755	+	7.77266i	−0.589244	+	1.02060i
$59$	6.44805	+	11.1684i	0.839465	+	1.45400i	0.890343	+	0.455291i	$0.150465\pi$
$59$	6.44805	+	11.1684i	0.839465	+	1.45400i	−0.0508779	+	0.998705i	$0.516202\pi$
$60$		0			0
$61$	−6.04163	+	10.4644i	−0.773552	+	1.33983i	0.162053	+	0.986782i	$0.448188\pi$
$61$	−6.04163	+	10.4644i	−0.773552	+	1.33983i	−0.935605	+	0.353049i	$0.885145\pi$
$62$	−0.514589			−0.0653529
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.336285	+	0.582462i	−0.0417110	+	0.0722456i
$66$		0			0
$67$	1.16012	+	2.00938i	0.141731	+	0.245485i	0.928148	−	0.372210i	$-0.121400\pi$
$67$	1.16012	+	2.00938i	0.141731	+	0.245485i	−0.786418	+	0.617695i	$0.788067\pi$
$68$	−1.86693	+	3.23361i	−0.226398	+	0.392133i
$69$		0			0
$70$	−0.0306407	−	1.21800i	−0.00366227	−	0.145578i
$71$	1.67977			0.199352			0.0996758	−	0.995020i	$-0.468219\pi$
$71$	1.67977			0.199352			0.0996758	+	0.995020i	$0.468219\pi$
$72$		0			0
$73$	−6.62062	−	11.4673i	−0.774885	−	1.34214i	−0.934859	−	0.355019i	$-0.884474\pi$
$73$	−6.62062	−	11.4673i	−0.774885	−	1.34214i	0.159974	−	0.987121i	$-0.448859\pi$
$74$	−4.55408	−	7.88791i	−0.529402	−	0.916950i
$75$		0			0
$76$	4.05408			0.465035
$77$	−0.242705	−	9.64776i	−0.0276589	−	1.09946i
$78$		0			0
$79$	2.50360	−	4.33636i	0.281677	−	0.487879i	−0.690121	−	0.723694i	$-0.742443\pi$
$79$	2.50360	−	4.33636i	0.281677	−	0.487879i	0.971798	+	0.235815i	$0.0757761\pi$
$80$	0.230252	+	0.398809i	0.0257430	+	0.0445882i
$81$		0			0
$82$	−0.472958	+	0.819187i	−0.0522295	+	0.0904641i
$83$	−6.64766			−0.729676			−0.364838	−	0.931071i	$-0.618876\pi$
$83$	−6.64766			−0.729676			−0.364838	+	0.931071i	$0.618876\pi$
$84$		0			0
$85$	−1.71946			−0.186501
$86$	4.66372	−	8.07779i	0.502901	−	0.871051i
$87$		0			0
$88$	1.82383	+	3.15897i	0.194421	+	0.336747i
$89$	−1.36333	+	2.36135i	−0.144512	+	0.250303i	−0.929191	−	0.369600i	$-0.879495\pi$
$89$	−1.36333	+	2.36135i	−0.144512	+	0.250303i	0.784679	+	0.619903i	$0.212828\pi$
$90$		0			0
$91$	3.39397	+	1.84730i	0.355784	+	0.193649i
$92$	1.13307			0.118131
$93$		0			0
$94$	−1.16372	−	2.01561i	−0.120028	−	0.207895i
$95$	0.933463	+	1.61680i	0.0957713	+	0.165881i
$96$		0			0
$97$	11.1872			1.13588			0.567942	−	0.823069i	$-0.307740\pi$
$97$	11.1872			1.13588			0.567942	+	0.823069i	$0.307740\pi$
$98$	−6.99115	+	0.351971i	−0.706212	+	0.0355544i
$99$		0			0
$100$	2.39397	−	4.14647i	0.239397	−	0.414647i
$101$	−6.87792	−	11.9129i	−0.684378	−	1.18538i	−0.973632	−	0.228125i	$-0.926740\pi$
$101$	−6.87792	−	11.9129i	−0.684378	−	1.18538i	0.289254	−	0.957253i	$-0.406593\pi$
$102$		0			0
$103$	−5.58113	+	9.66679i	−0.549925	+	0.952498i	0.448354	+	0.893856i	$0.352010\pi$
$103$	−5.58113	+	9.66679i	−0.549925	+	0.952498i	−0.998279	+	0.0586417i	$0.981323\pi$
$104$	−1.46050			−0.143214
$105$		0			0
$106$	−12.4356			−1.20785
$107$	−3.89037	+	6.73832i	−0.376096	+	0.651418i	−0.990490	−	0.137581i	$-0.956067\pi$
$107$	−3.89037	+	6.73832i	−0.376096	+	0.651418i	0.614394	+	0.788999i	$0.289400\pi$
$108$		0			0
$109$	−3.75729	−	6.50783i	−0.359884	−	0.623337i	0.628058	−	0.778167i	$-0.283850\pi$
$109$	−3.75729	−	6.50783i	−0.359884	−	0.623337i	−0.987941	+	0.154830i	$0.950517\pi$
$110$	−0.839883	+	1.45472i	−0.0800797	+	0.138702i
$111$		0			0
$112$	2.25729	−	1.38008i	0.213294	−	0.130405i
$113$	−6.06128			−0.570197			−0.285099	−	0.958498i	$-0.592026\pi$
$113$	−6.06128			−0.570197			−0.285099	+	0.958498i	$0.592026\pi$
$114$		0			0
$115$	0.260893	+	0.451880i	0.0243284	+	0.0421380i
$116$	−4.48755	−	7.77266i	−0.416658	−	0.721673i
$117$		0			0
$118$	−12.8961			−1.18718
$119$	0.248440	+	9.87572i	0.0227745	+	0.905305i
$120$		0			0
$121$	−1.15272	+	1.99658i	−0.104793	+	0.181507i
$122$	−6.04163	−	10.4644i	−0.546984	−	0.947403i
$123$		0			0
$124$	0.257295	−	0.445647i	0.0231057	−	0.0400203i
$125$	4.50739			0.403153
$126$		0			0
$127$	8.80992			0.781754			0.390877	−	0.920443i	$-0.372172\pi$
$127$	8.80992			0.781754			0.390877	+	0.920443i	$0.372172\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−0.336285	−	0.582462i	−0.0294941	−	0.0510853i
$131$	−10.5687	+	18.3055i	−0.923389	+	1.59936i	−0.129258	+	0.991611i	$0.541260\pi$
$131$	−10.5687	+	18.3055i	−0.923389	+	1.59936i	−0.794131	+	0.607746i	$0.792074\pi$
$132$		0			0
$133$	9.15126	−	5.59496i	0.793515	−	0.485145i
$134$	−2.32023			−0.200438
$135$		0			0
$136$	−1.86693	−	3.23361i	−0.160088	−	0.277280i
$137$	2.20321	+	3.81607i	0.188233	+	0.326029i	0.944661	−	0.328048i	$-0.106391\pi$
$137$	2.20321	+	3.81607i	0.188233	+	0.326029i	−0.756428	+	0.654077i	$0.773057\pi$
$138$		0			0
$139$	2.02491			0.171750			0.0858751	−	0.996306i	$-0.472631\pi$
$139$	2.02491			0.171750			0.0858751	+	0.996306i	$0.472631\pi$
$140$	1.07014	+	0.582462i	0.0904430	+	0.0492271i
$141$		0			0
$142$	−0.839883	+	1.45472i	−0.0704815	+	0.122077i
$143$	−2.66372	−	4.61369i	−0.222751	−	0.385816i
$144$		0			0
$145$	2.06654	−	3.57935i	0.171617	−	0.297249i
$146$	13.2412			1.09585
$147$		0			0
$148$	9.10817			0.748687
$149$	4.58113	−	7.93474i	0.375300	−	0.650040i	−0.615071	−	0.788471i	$-0.710873\pi$
$149$	4.58113	−	7.93474i	0.375300	−	0.650040i	0.990372	+	0.138432i	$0.0442062\pi$
$150$		0			0
$151$	0.0519482	+	0.0899768i	0.00422748	+	0.00732221i	0.868131	−	0.496334i	$-0.165321\pi$
$151$	0.0519482	+	0.0899768i	0.00422748	+	0.00732221i	−0.863904	+	0.503657i	$0.831988\pi$
$152$	−2.02704	+	3.51094i	−0.164415	+	0.284775i
$153$		0			0
$154$	8.47656	+	4.61369i	0.683060	+	0.371782i
$155$	0.236971			0.0190340
$156$		0			0
$157$	−10.4911	−	18.1712i	−0.837285	−	1.45022i	−0.892157	−	0.451726i	$-0.850808\pi$
$157$	−10.4911	−	18.1712i	−0.837285	−	1.45022i	0.0548721	−	0.998493i	$-0.482525\pi$
$158$	2.50360	+	4.33636i	0.199176	+	0.344982i
$159$		0			0
$160$	−0.460505			−0.0364061
$161$	2.55768	−	1.56373i	0.201574	−	0.123239i
$162$		0			0
$163$	−11.5182	+	19.9501i	−0.902174	+	1.56261i	−0.0775078	+	0.996992i	$0.524696\pi$
$163$	−11.5182	+	19.9501i	−0.902174	+	1.56261i	−0.824666	+	0.565620i	$0.808637\pi$
$164$	−0.472958	−	0.819187i	−0.0369318	−	0.0639678i
$165$		0			0
$166$	3.32383	−	5.75705i	0.257979	−	0.446833i
$167$	10.6300			0.822571			0.411285	−	0.911507i	$-0.365080\pi$
$167$	10.6300			0.822571			0.411285	+	0.911507i	$0.365080\pi$
$168$		0			0
$169$	−10.8669			−0.835917
$170$	0.859728	−	1.48909i	0.0659382	−	0.114208i
$171$		0			0
$172$	4.66372	+	8.07779i	0.355605	+	0.615926i
$173$	−1.46936	+	2.54500i	−0.111713	+	0.193493i	−0.916461	−	0.400124i	$-0.868967\pi$
$173$	−1.46936	+	2.54500i	−0.111713	+	0.193493i	0.804748	+	0.593617i	$0.202301\pi$
$174$		0			0
$175$	−0.318576	−	12.6637i	−0.0240821	−	0.957284i
$176$	−3.64766			−0.274953
$177$		0			0
$178$	−1.36333	−	2.36135i	−0.102186	−	0.176991i
$179$	−4.58113	−	7.93474i	−0.342409	−	0.593071i	0.642470	−	0.766311i	$-0.277910\pi$
$179$	−4.58113	−	7.93474i	−0.342409	−	0.593071i	−0.984880	+	0.173240i	$0.944576\pi$
$180$		0			0
$181$	22.4284			1.66709			0.833545	−	0.552452i	$-0.186308\pi$
$181$	22.4284			1.66709			0.833545	+	0.552452i	$0.186308\pi$
$182$	−3.29679	+	2.01561i	−0.244374	+	0.149407i
$183$		0			0
$184$	−0.566537	+	0.981271i	−0.0417657	+	0.0723403i
$185$	2.09718	+	3.63242i	0.154188	+	0.267061i
$186$		0			0
$187$	6.80992	−	11.7951i	0.497990	−	0.862545i
$188$	2.32743			0.169745
$189$		0			0
$190$	−1.86693			−0.135441
$191$	−1.24484	+	2.15613i	−0.0900736	+	0.156012i	−0.907542	−	0.419962i	$-0.862044\pi$
$191$	−1.24484	+	2.15613i	−0.0900736	+	0.156012i	0.817468	+	0.575974i	$0.195377\pi$
$192$		0			0
$193$	−2.24484	−	3.88818i	−0.161587	−	0.279877i	0.773851	−	0.633368i	$-0.218328\pi$
$193$	−2.24484	−	3.88818i	−0.161587	−	0.279877i	−0.935438	+	0.353491i	$0.884995\pi$
$194$	−5.59358	+	9.68836i	−0.401596	+	0.695584i
$195$		0			0
$196$	3.19076	−	6.23049i	0.227911	−	0.445035i
$197$	12.7339			0.907249			0.453625	−	0.891193i	$-0.350131\pi$
$197$	12.7339			0.907249			0.453625	+	0.891193i	$0.350131\pi$
$198$		0			0
$199$	−1.47296	−	2.55124i	−0.104415	−	0.180852i	0.809084	−	0.587693i	$-0.199964\pi$
$199$	−1.47296	−	2.55124i	−0.104415	−	0.180852i	−0.913499	+	0.406841i	$0.866630\pi$
$200$	2.39397	+	4.14647i	0.169279	+	0.293200i
$201$		0			0
$202$	13.7558			0.967857
$203$	−20.8566	−	11.3520i	−1.46385	−	0.796755i
$204$		0			0
$205$	0.217799	−	0.377240i	0.0152118	−	0.0263476i
$206$	−5.58113	−	9.66679i	−0.388855	−	0.673517i
$207$		0			0
$208$	0.730252	−	1.26483i	0.0506339	−	0.0877005i
$209$	−14.7879			−1.02290
$210$		0			0
$211$	1.21634			0.0837361			0.0418680	−	0.999123i	$-0.486669\pi$
$211$	1.21634			0.0837361			0.0418680	+	0.999123i	$0.486669\pi$
$212$	6.21780	−	10.7695i	0.427040	−	0.739655i
$213$		0			0
$214$	−3.89037	−	6.73832i	−0.265940	−	0.460622i
$215$	−2.14766	+	3.71986i	−0.146469	+	0.253693i
$216$		0			0
$217$	−0.0342393	−	1.36104i	−0.00232432	−	0.0923937i
$218$	7.51459			0.508952
$219$		0			0
$220$	−0.839883	−	1.45472i	−0.0566249	−	0.0980773i
$221$	2.72665	+	4.72270i	0.183415	+	0.317683i
$222$		0			0
$223$	0.891832			0.0597215			0.0298607	−	0.999554i	$-0.490494\pi$
$223$	0.891832			0.0597215			0.0298607	+	0.999554i	$0.490494\pi$
$224$	0.0665372	+	2.64491i	0.00444571	+	0.176721i
$225$		0			0
$226$	3.03064	−	5.24922i	0.201595	−	0.349173i
$227$	7.32597	+	12.6889i	0.486242	+	0.842195i	0.999875	−	0.0158147i	$-0.00503418\pi$
$227$	7.32597	+	12.6889i	0.486242	+	0.842195i	−0.513633	+	0.858010i	$0.671701\pi$
$228$		0			0
$229$	4.78794	−	8.29295i	0.316396	−	0.548013i	−0.663338	−	0.748320i	$-0.730861\pi$
$229$	4.78794	−	8.29295i	0.316396	−	0.548013i	0.979733	+	0.200307i	$0.0641939\pi$
$230$	−0.521786			−0.0344056
$231$		0			0
$232$	8.97509			0.589244
$233$	7.21420	−	12.4954i	0.472618	−	0.818598i	−0.526891	−	0.849933i	$-0.676642\pi$
$233$	7.21420	−	12.4954i	0.472618	−	0.818598i	0.999509	+	0.0313345i	$0.00997571\pi$
$234$		0			0
$235$	0.535897	+	0.928200i	0.0349580	+	0.0605491i
$236$	6.44805	−	11.1684i	0.419732	−	0.726998i
$237$		0			0
$238$	−8.67684	−	4.72270i	−0.562436	−	0.306127i
$239$	18.3097			1.18436			0.592179	−	0.805807i	$-0.298268\pi$
$239$	18.3097			1.18436			0.592179	+	0.805807i	$0.298268\pi$
$240$		0			0
$241$	−0.0466924	−	0.0808735i	−0.00300772	−	0.00520952i	0.864518	−	0.502602i	$-0.167624\pi$
$241$	−0.0466924	−	0.0808735i	−0.00300772	−	0.00520952i	−0.867525	+	0.497393i	$0.834291\pi$
$242$	−1.15272	−	1.99658i	−0.0741000	−	0.128345i
$243$		0			0
$244$	12.0833			0.773552
$245$	3.21946	−	0.162084i	0.205684	−	0.0103552i
$246$		0			0
$247$	2.96050	−	5.12774i	0.188372	−	0.326271i
$248$	0.257295	+	0.445647i	0.0163382	+	0.0282986i
$249$		0			0
$250$	−2.25370	+	3.90352i	−0.142536	+	0.246880i
$251$	−18.2733			−1.15340			−0.576702	−	0.816955i	$-0.695661\pi$
$251$	−18.2733			−1.15340			−0.576702	+	0.816955i	$0.695661\pi$
$252$		0			0
$253$	−4.13307			−0.259844
$254$	−4.40496	+	7.62961i	−0.276392	+	0.478724i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.5256	−	18.2308i	0.656568	−	1.13721i	−0.324931	−	0.945738i	$-0.605341\pi$
$257$	10.5256	−	18.2308i	0.656568	−	1.13721i	0.981498	−	0.191471i	$-0.0613257\pi$
$258$		0			0
$259$	20.5598	−	12.5700i	1.27752	−	0.781062i
$260$	0.672570			0.0417110
$261$		0			0
$262$	−10.5687	−	18.3055i	−0.652935	−	1.13092i
$263$	2.58259	+	4.47318i	0.159249	+	0.275828i	0.934598	−	0.355705i	$-0.115759\pi$
$263$	2.58259	+	4.47318i	0.159249	+	0.275828i	−0.775349	+	0.631533i	$0.782426\pi$
$264$		0			0
$265$	5.72665			0.351786
$266$	0.269748	+	10.7227i	0.0165393	+	0.657451i
$267$		0			0
$268$	1.16012	−	2.00938i	0.0708654	−	0.122742i
$269$	8.42840	+	14.5984i	0.513889	+	0.890081i	0.999870	+	0.0161123i	$0.00512891\pi$
$269$	8.42840	+	14.5984i	0.513889	+	0.890081i	−0.485981	+	0.873969i	$0.661538\pi$
$270$		0			0
$271$	12.5562	−	21.7480i	0.762736	−	1.32110i	−0.178699	−	0.983904i	$-0.557189\pi$
$271$	12.5562	−	21.7480i	0.762736	−	1.32110i	0.941435	−	0.337194i	$-0.109478\pi$
$272$	3.73385			0.226398
$273$		0			0
$274$	−4.40642			−0.266202
$275$	−8.73239	+	15.1249i	−0.526583	+	0.912068i
$276$		0			0
$277$	−1.69076	−	2.92848i	−0.101588	−	0.175955i	0.810751	−	0.585391i	$-0.199059\pi$
$277$	−1.69076	−	2.92848i	−0.101588	−	0.175955i	−0.912339	+	0.409436i	$0.865726\pi$
$278$	−1.01245	+	1.75362i	−0.0607229	+	0.105175i
$279$		0			0
$280$	−1.03950	+	0.635534i	−0.0621217	+	0.0379804i
$281$	20.2776			1.20966			0.604831	−	0.796354i	$-0.293241\pi$
$281$	20.2776			1.20966			0.604831	+	0.796354i	$0.293241\pi$
$282$		0			0
$283$	−8.67471	−	15.0250i	−0.515658	−	0.893145i	−0.999835	−	0.0181754i	$-0.994214\pi$
$283$	−8.67471	−	15.0250i	−0.515658	−	0.893145i	0.484177	−	0.874970i	$-0.339119\pi$
$284$	−0.839883	−	1.45472i	−0.0498379	−	0.0863218i
$285$		0			0
$286$	5.32743			0.315018
$287$	−2.19815	−	1.19643i	−0.129753	−	0.0706228i
$288$		0			0
$289$	1.52918	−	2.64861i	0.0899517	−	0.155801i
$290$	2.06654	+	3.57935i	0.121351	+	0.210187i
$291$		0			0
$292$	−6.62062	+	11.4673i	−0.387443	+	0.671070i
$293$	9.87120			0.576682			0.288341	−	0.957528i	$-0.406896\pi$
$293$	9.87120			0.576682			0.288341	+	0.957528i	$0.406896\pi$
$294$		0			0
$295$	5.93872			0.345766
$296$	−4.55408	+	7.88791i	−0.264701	+	0.458475i
$297$		0			0
$298$	4.58113	+	7.93474i	0.265378	+	0.459647i
$299$	0.827430	−	1.43315i	0.0478515	−	0.0828813i
$300$		0			0
$301$	21.6754	+	11.7977i	1.24935	+	0.680005i
$302$	−0.103896			−0.00597856
$303$		0			0
$304$	−2.02704	−	3.51094i	−0.116259	−	0.201366i
$305$	2.78220	+	4.81891i	0.159308	+	0.275930i
$306$		0			0
$307$	7.78794			0.444481			0.222240	−	0.974992i	$-0.428663\pi$
$307$	7.78794			0.444481			0.222240	+	0.974992i	$0.428663\pi$
$308$	−8.23385	+	5.03407i	−0.469167	+	0.286843i
$309$		0			0
$310$	−0.118485	+	0.205223i	−0.00672952	+	0.0116559i
$311$	−7.70535	−	13.3461i	−0.436930	−	0.756785i	0.560521	−	0.828140i	$-0.310601\pi$
$311$	−7.70535	−	13.3461i	−0.436930	−	0.756785i	−0.997451	+	0.0713552i	$0.977268\pi$
$312$		0			0
$313$	−4.24844	+	7.35851i	−0.240136	+	0.415928i	−0.960753	−	0.277406i	$-0.910525\pi$
$313$	−4.24844	+	7.35851i	−0.240136	+	0.415928i	0.720617	+	0.693334i	$0.243859\pi$
$314$	20.9823			1.18410
$315$		0			0
$316$	−5.00720			−0.281677
$317$	7.05262	−	12.2155i	0.396115	−	0.686091i	−0.597128	−	0.802146i	$-0.703692\pi$
$317$	7.05262	−	12.2155i	0.396115	−	0.686091i	0.993243	+	0.116055i	$0.0370249\pi$
$318$		0			0
$319$	16.3691	+	28.3520i	0.916491	+	1.58741i
$320$	0.230252	−	0.398809i	0.0128715	−	0.0222941i
$321$		0			0
$322$	0.0753916	+	2.99689i	0.00420141	+	0.167010i
$323$	15.1373			0.842264
$324$		0			0
$325$	−3.49640	−	6.05594i	−0.193945	−	0.335923i
$326$	−11.5182	−	19.9501i	−0.637933	−	1.10493i
$327$		0			0
$328$	0.945916			0.0522295
$329$	5.25370	−	3.21204i	0.289646	−	0.177086i
$330$		0			0
$331$	−13.7719	+	23.8536i	−0.756971	+	1.31111i	0.187417	+	0.982280i	$0.439988\pi$
$331$	−13.7719	+	23.8536i	−0.756971	+	1.31111i	−0.944388	+	0.328832i	$0.893345\pi$
$332$	3.32383	+	5.75705i	0.182419	+	0.315959i
$333$		0			0
$334$	−5.31498	+	9.20581i	−0.290823	+	0.503720i
$335$	1.06848			0.0583772
$336$		0			0
$337$	−1.49688			−0.0815403			−0.0407701	−	0.999169i	$-0.512981\pi$
$337$	−1.49688			−0.0815403			−0.0407701	+	0.999169i	$0.512981\pi$
$338$	5.43346	−	9.41103i	0.295541	−	0.511893i
$339$		0			0
$340$	0.859728	+	1.48909i	0.0466253	+	0.0807574i
$341$	−0.938524	+	1.62557i	−0.0508239	+	0.0880296i
$342$		0			0
$343$	−1.39610	−	18.4676i	−0.0753825	−	0.997155i
$344$	−9.32743			−0.502901
$345$		0			0
$346$	−1.46936	−	2.54500i	−0.0789932	−	0.136820i
$347$	9.14406	+	15.8380i	0.490879	+	0.850228i	0.999945	−	0.0105001i	$-0.00334233\pi$
$347$	9.14406	+	15.8380i	0.490879	+	0.850228i	−0.509066	+	0.860728i	$0.670009\pi$
$348$		0			0
$349$	7.80272			0.417670			0.208835	−	0.977951i	$-0.433033\pi$
$349$	7.80272			0.417670			0.208835	+	0.977951i	$0.433033\pi$
$350$	11.1264	+	6.05594i	0.594729	+	0.323704i
$351$		0			0
$352$	1.82383	−	3.15897i	0.0972106	−	0.168374i
$353$	−13.4626	−	23.3180i	−0.716544	−	1.24109i	−0.962361	−	0.271774i	$-0.912390\pi$
$353$	−13.4626	−	23.3180i	−0.716544	−	1.24109i	0.245817	−	0.969316i	$-0.420944\pi$
$354$		0			0
$355$	0.386770	−	0.669906i	0.0205276	−	0.0355549i
$356$	2.72665			0.144512
$357$		0			0
$358$	9.16225			0.484240
$359$	−3.13161	+	5.42411i	−0.165280	+	0.286274i	−0.936755	−	0.349987i	$-0.886186\pi$
$359$	−3.13161	+	5.42411i	−0.165280	+	0.286274i	0.771475	+	0.636260i	$0.219519\pi$
$360$		0			0
$361$	1.28220	+	2.22084i	0.0674842	+	0.116886i
$362$	−11.2142	+	19.4236i	−0.589405	+	1.02088i
$363$		0			0
$364$	−0.0971780	−	3.86291i	−0.00509351	−	0.202472i
$365$	−6.09766			−0.319166
$366$		0			0
$367$	−14.6367	−	25.3515i	−0.764028	−	1.32334i	−0.940759	−	0.339076i	$-0.889886\pi$
$367$	−14.6367	−	25.3515i	−0.764028	−	1.32334i	0.176731	−	0.984259i	$-0.443448\pi$
$368$	−0.566537	−	0.981271i	−0.0295328	−	0.0511523i
$369$		0			0
$370$	−4.19436			−0.218054
$371$	−0.827430	−	32.8911i	−0.0429580	−	1.70762i
$372$		0			0
$373$	−8.92986	+	15.4670i	−0.462371	+	0.800850i	−0.999079	−	0.0429184i	$-0.986334\pi$
$373$	−8.92986	+	15.4670i	−0.462371	+	0.800850i	0.536708	+	0.843768i	$0.319668\pi$
$374$	6.80992	+	11.7951i	0.352132	+	0.609911i
$375$		0			0
$376$	−1.16372	+	2.01561i	−0.0600140	+	0.103947i
$377$	−13.1082			−0.675105
$378$		0			0
$379$	−22.4255			−1.15192			−0.575960	−	0.817478i	$-0.695371\pi$
$379$	−22.4255			−1.15192			−0.575960	+	0.817478i	$0.695371\pi$
$380$	0.933463	−	1.61680i	0.0478856	−	0.0829403i
$381$		0			0
$382$	−1.24484	−	2.15613i	−0.0636916	−	0.110317i
$383$	7.07014	−	12.2458i	0.361267	−	0.625733i	−0.626903	−	0.779098i	$-0.715678\pi$
$383$	7.07014	−	12.2458i	0.361267	−	0.625733i	0.988170	+	0.153365i	$0.0490109\pi$
$384$		0			0
$385$	−3.90350	−	2.12463i	−0.198941	−	0.108281i
$386$	4.48968			0.228519
$387$		0			0
$388$	−5.59358	−	9.68836i	−0.283971	−	0.491852i
$389$	11.5651	+	20.0313i	0.586373	+	1.01563i	0.994703	+	0.102793i	$0.0327779\pi$
$389$	11.5651	+	20.0313i	0.586373	+	1.01563i	−0.408330	+	0.912834i	$0.633889\pi$
$390$		0			0
$391$	4.23073			0.213957
$392$	3.80039	+	5.87852i	0.191949	+	0.296910i
$393$		0			0
$394$	−6.36693	+	11.0278i	−0.320761	+	0.555574i
$395$	−1.15292	−	1.99691i	−0.0580097	−	0.100476i
$396$		0			0
$397$	−5.13307	+	8.89075i	−0.257622	+	0.446214i	−0.965604	−	0.260016i	$-0.916272\pi$
$397$	−5.13307	+	8.89075i	−0.257622	+	0.446214i	0.707983	+	0.706230i	$0.249605\pi$
$398$	2.94592			0.147665
$399$		0			0
$400$	−4.78794			−0.239397
$401$	−17.0167	+	29.4738i	−0.849775	+	1.47185i	0.0316345	+	0.999500i	$0.489929\pi$
$401$	−17.0167	+	29.4738i	−0.849775	+	1.47185i	−0.881409	+	0.472353i	$0.843405\pi$
$402$		0			0
$403$	−0.375780	−	0.650870i	−0.0187189	−	0.0324221i
$404$	−6.87792	+	11.9129i	−0.342189	+	0.592689i
$405$		0			0
$406$	20.2594	−	12.3863i	1.00546	−	0.614724i
$407$	−33.2235			−1.64683
$408$		0			0
$409$	1.74484	+	3.02215i	0.0862769	+	0.149436i	0.905935	−	0.423418i	$-0.139170\pi$
$409$	1.74484	+	3.02215i	0.0862769	+	0.149436i	−0.819658	+	0.572854i	$0.805836\pi$
$410$	0.217799	+	0.377240i	0.0107563	+	0.0186305i
$411$		0			0
$412$	11.1623			0.549925
$413$	−0.858071	−	34.1091i	−0.0422229	−	1.67840i
$414$		0			0
$415$	−1.53064	+	2.65115i	−0.0751362	+	0.130140i
$416$	0.730252	+	1.26483i	0.0358036	+	0.0620136i
$417$		0			0
$418$	7.39397	−	12.8067i	0.361651	−	0.626398i
$419$	−28.9794			−1.41573			−0.707867	−	0.706345i	$-0.750343\pi$
$419$	−28.9794			−1.41573			−0.707867	+	0.706345i	$0.750343\pi$
$420$		0			0
$421$	2.12256			0.103447			0.0517237	−	0.998661i	$-0.483528\pi$
$421$	2.12256			0.103447			0.0517237	+	0.998661i	$0.483528\pi$
$422$	−0.608168	+	1.05338i	−0.0296052	+	0.0512777i
$423$		0			0
$424$	6.21780	+	10.7695i	0.301963	+	0.523015i
$425$	8.93872	−	15.4823i	0.433592	−	0.751003i
$426$		0			0
$427$	27.2755	−	16.6759i	1.31995	−	0.807002i
$428$	7.78074			0.376096
$429$		0			0
$430$	−2.14766	−	3.71986i	−0.103570	−	0.179388i
$431$	10.9356	+	18.9410i	0.526749	+	0.912356i	0.999514	+	0.0311679i	$0.00992265\pi$
$431$	10.9356	+	18.9410i	0.526749	+	0.912356i	−0.472765	+	0.881189i	$0.656744\pi$
$432$		0			0
$433$	−13.0512			−0.627199			−0.313599	−	0.949555i	$-0.601535\pi$
$433$	−13.0512			−0.627199			−0.313599	+	0.949555i	$0.601535\pi$
$434$	1.19582	+	0.650870i	0.0574011	+	0.0312428i
$435$		0			0
$436$	−3.75729	+	6.50783i	−0.179942	+	0.311668i
$437$	−2.29679	−	3.97816i	−0.109870	−	0.190301i
$438$		0			0
$439$	−2.43200	+	4.21235i	−0.116073	+	0.201044i	−0.918208	−	0.396098i	$-0.870364\pi$
$439$	−2.43200	+	4.21235i	−0.116073	+	0.201044i	0.802135	+	0.597143i	$0.203697\pi$
$440$	1.67977			0.0800797
$441$		0			0
$442$	−5.45331			−0.259387
$443$	5.76975	−	9.99350i	0.274129	−	0.474805i	−0.695786	−	0.718249i	$-0.744944\pi$
$443$	5.76975	−	9.99350i	0.274129	−	0.474805i	0.969915	+	0.243444i	$0.0782771\pi$
$444$		0			0
$445$	0.627819	+	1.08741i	0.0297615	+	0.0515484i
$446$	−0.445916	+	0.772349i	−0.0211147	+	0.0365718i
$447$		0			0
$448$	−2.32383	−	1.26483i	−0.109791	−	0.0597578i
$449$	−26.4251			−1.24708			−0.623538	−	0.781793i	$-0.714306\pi$
$449$	−26.4251			−1.24708			−0.623538	+	0.781793i	$0.714306\pi$
$450$		0			0
$451$	1.72519	+	2.98812i	0.0812361	+	0.140705i
$452$	3.03064	+	5.24922i	0.142549	+	0.246903i
$453$		0			0
$454$	−14.6519			−0.687649
$455$	1.51819	−	0.928200i	0.0711737	−	0.0435147i
$456$		0			0
$457$	1.86906	−	3.23731i	0.0874310	−	0.151435i	−0.818994	−	0.573803i	$-0.805468\pi$
$457$	1.86906	−	3.23731i	0.0874310	−	0.151435i	0.906425	+	0.422368i	$0.138801\pi$
$458$	4.78794	+	8.29295i	0.223726	+	0.387504i
$459$		0			0
$460$	0.260893	−	0.451880i	0.0121642	−	0.0210690i
$461$	15.8099			0.736341			0.368171	−	0.929758i	$-0.379984\pi$
$461$	15.8099			0.736341			0.368171	+	0.929758i	$0.379984\pi$
$462$		0			0
$463$	−38.3930			−1.78427			−0.892137	−	0.451766i	$-0.850794\pi$
$463$	−38.3930			−1.78427			−0.892137	+	0.451766i	$0.850794\pi$
$464$	−4.48755	+	7.77266i	−0.208329	+	0.360837i
$465$		0			0
$466$	7.21420	+	12.4954i	0.334191	+	0.578836i
$467$	3.15652	−	5.46725i	0.146066	−	0.252994i	−0.783704	−	0.621134i	$-0.786672\pi$
$467$	3.15652	−	5.46725i	0.146066	−	0.252994i	0.929770	+	0.368140i	$0.120005\pi$
$468$		0			0
$469$	−0.154382	−	6.13682i	−0.00712869	−	0.283372i
$470$	−1.07179			−0.0494381
$471$		0			0
$472$	6.44805	+	11.1684i	0.296796	+	0.514065i
$473$	−17.0117	−	29.4651i	−0.782197	−	1.35481i
$474$		0			0
$475$	−19.4107			−0.890624
$476$	8.42840	−	5.15301i	0.386315	−	0.236188i
$477$		0			0
$478$	−9.15486	+	15.8567i	−0.418734	+	0.725268i
$479$	10.2068	+	17.6787i	0.466361	+	0.807761i	0.999262	−	0.0384168i	$-0.0122314\pi$
$479$	10.2068	+	17.6787i	0.466361	+	0.807761i	−0.532901	+	0.846178i	$0.678898\pi$
$480$		0			0
$481$	6.65126	−	11.5203i	0.303271	−	0.525282i
$482$	0.0933847			0.00425356
$483$		0			0
$484$	2.30545			0.104793
$485$	2.57587	−	4.46154i	0.116964	−	0.202588i
$486$		0			0
$487$	6.18190	+	10.7074i	0.280129	+	0.485197i	0.971416	−	0.237383i	$-0.0762895\pi$
$487$	6.18190	+	10.7074i	0.280129	+	0.485197i	−0.691287	+	0.722580i	$0.742956\pi$
$488$	−6.04163	+	10.4644i	−0.273492	+	0.473702i
$489$		0			0
$490$	−1.46936	+	2.86917i	−0.0663789	+	0.129616i
$491$	−0.414007			−0.0186839			−0.00934194	−	0.999956i	$-0.502974\pi$
$491$	−0.414007			−0.0186839			−0.00934194	+	0.999956i	$0.502974\pi$
$492$		0			0
$493$	−16.7558	−	29.0220i	−0.754645	−	1.30708i
$494$	2.96050	+	5.12774i	0.133199	+	0.230708i
$495$		0			0
$496$	−0.514589			−0.0231057
$497$	−3.90350	−	2.12463i	−0.175096	−	0.0953025i
$498$		0			0
$499$	0.461967	−	0.800151i	0.0206805	−	0.0358197i	−0.855500	−	0.517803i	$-0.826750\pi$
$499$	0.461967	−	0.800151i	0.0206805	−	0.0358197i	0.876180	+	0.481983i	$0.160083\pi$
$500$	−2.25370	−	3.90352i	−0.100788	−	0.174571i
$501$		0			0
$502$	9.13667	−	15.8252i	0.407790	−	0.706312i
$503$	−23.8142			−1.06182			−0.530911	−	0.847428i	$-0.678150\pi$
$503$	−23.8142			−1.06182			−0.530911	+	0.847428i	$0.678150\pi$
$504$		0			0
$505$	−6.33463			−0.281887
$506$	2.06654	−	3.57935i	0.0918688	−	0.159121i
$507$		0			0
$508$	−4.40496	−	7.62961i	−0.195438	−	0.338509i
$509$	15.3171	−	26.5300i	0.678919	−	1.17592i	−0.296388	−	0.955068i	$-0.595782\pi$
$509$	15.3171	−	26.5300i	0.678919	−	1.17592i	0.975307	−	0.220855i	$-0.0708846\pi$
$510$		0			0
$511$	0.881036	+	35.0220i	0.0389747	+	1.54928i
$512$	1.00000			0.0441942
$513$		0			0
$514$	10.5256	+	18.2308i	0.464263	+	0.804128i
$515$	2.57014	+	4.45161i	0.113254	+	0.196161i
$516$		0			0
$517$	−8.48968			−0.373376
$518$	0.606032	+	24.0903i	0.0266275	+	1.05847i
$519$		0			0
$520$	−0.336285	+	0.582462i	−0.0147471	+	0.0255427i
$521$	−13.4518	−	23.2993i	−0.589336	−	1.02076i	−0.994320	−	0.106436i	$-0.966056\pi$
$521$	−13.4518	−	23.2993i	−0.589336	−	1.02076i	0.404984	−	0.914324i	$-0.367277\pi$
$522$		0			0
$523$	−7.85301	+	13.6018i	−0.343388	+	0.594766i	−0.985060	−	0.172214i	$-0.944908\pi$
$523$	−7.85301	+	13.6018i	−0.343388	+	0.594766i	0.641671	+	0.766980i	$0.278241\pi$
$524$	21.1373			0.923389
$525$		0			0
$526$	−5.16518			−0.225212
$527$	0.960699	−	1.66398i	0.0418487	−	0.0724841i
$528$		0			0
$529$	10.8581	+	18.8067i	0.472090	+	0.817684i
$530$	−2.86333	+	4.95943i	−0.124375	+	0.215424i
$531$		0			0
$532$	−9.42101	−	5.12774i	−0.408453	−	0.222316i
$533$	−1.38151			−0.0598400
$534$		0			0
$535$	1.79153	+	3.10303i	0.0774548	+	0.134156i
$536$	1.16012	+	2.00938i	0.0501094	+	0.0867920i
$537$		0			0
$538$	−16.8568			−0.726748
$539$	−11.6388	+	22.7267i	−0.501319	+	0.978910i
$540$		0			0
$541$	−2.05934	+	3.56688i	−0.0885379	+	0.153352i	−0.906893	−	0.421360i	$-0.861553\pi$
$541$	−2.05934	+	3.56688i	−0.0885379	+	0.153352i	0.818355	+	0.574713i	$0.194886\pi$
$542$	12.5562	+	21.7480i	0.539336	+	0.934157i
$543$		0			0
$544$	−1.86693	+	3.23361i	−0.0800438	+	0.138640i
$545$	−3.46050			−0.148232
$546$		0			0
$547$	23.7204			1.01421			0.507106	−	0.861884i	$-0.330715\pi$
$547$	23.7204			1.01421			0.507106	+	0.861884i	$0.330715\pi$
$548$	2.20321	−	3.81607i	0.0941165	−	0.163015i
$549$		0			0
$550$	−8.73239	−	15.1249i	−0.372350	−	0.644930i
$551$	−18.1929	+	31.5110i	−0.775043	+	1.34241i
$552$		0			0
$553$	−11.3027	+	6.91033i	−0.480641	+	0.293857i
$554$	3.38151			0.143667
$555$		0			0
$556$	−1.01245	−	1.75362i	−0.0429376	−	0.0743701i
$557$	−21.0313	−	36.4273i	−0.891125	−	1.54347i	−0.838528	−	0.544859i	$-0.816583\pi$
$557$	−21.0313	−	36.4273i	−0.891125	−	1.54347i	−0.0525975	−	0.998616i	$-0.516750\pi$
$558$		0			0
$559$	13.6228			0.576181
$560$	−0.0306407	−	1.21800i	−0.00129481	−	0.0514697i
$561$		0			0
$562$	−10.1388	+	17.5609i	−0.427680	+	0.740763i
$563$	−5.91216	−	10.2402i	−0.249168	−	0.431571i	0.714127	−	0.700016i	$-0.246824\pi$
$563$	−5.91216	−	10.2402i	−0.249168	−	0.431571i	−0.963295	+	0.268445i	$0.913490\pi$
$564$		0			0
$565$	−1.39562	+	2.41729i	−0.0587144	+	0.101696i
$566$	17.3494			0.729250
$567$		0			0
$568$	1.67977			0.0704815
$569$	−7.10078	+	12.2989i	−0.297680	+	0.515597i	−0.975605	−	0.219534i	$-0.929546\pi$
$569$	−7.10078	+	12.2989i	−0.297680	+	0.515597i	0.677925	+	0.735131i	$0.262880\pi$
$570$		0			0
$571$	−5.97869	−	10.3554i	−0.250200	−	0.433360i	0.713380	−	0.700777i	$-0.247163\pi$
$571$	−5.97869	−	10.3554i	−0.250200	−	0.433360i	−0.963581	+	0.267417i	$0.913830\pi$
$572$	−2.66372	+	4.61369i	−0.111376	+	0.192908i
$573$		0			0
$574$	2.13521	−	1.30544i	0.0891220	−	0.0544880i
$575$	−5.42509			−0.226242
$576$		0			0
$577$	21.3135	+	36.9161i	0.887293	+	1.53684i	0.843062	+	0.537816i	$0.180750\pi$
$577$	21.3135	+	36.9161i	0.887293	+	1.53684i	0.0442307	+	0.999021i	$0.485916\pi$
$578$	1.52918	+	2.64861i	0.0636054	+	0.110168i
$579$		0			0
$580$	−4.13307			−0.171617
$581$	15.4481	+	8.40819i	0.640893	+	0.348831i
$582$		0			0
$583$	−22.6804	+	39.2837i	−0.939328	+	1.62696i
$584$	−6.62062	−	11.4673i	−0.273963	−	0.474518i
$585$		0			0
$586$	−4.93560	+	8.54871i	−0.203888	+	0.353144i
$587$	−41.0656			−1.69496			−0.847478	−	0.530830i	$-0.821880\pi$
$587$	−41.0656			−1.69496			−0.847478	+	0.530830i	$0.821880\pi$
$588$		0			0
$589$	−2.08619			−0.0859599
$590$	−2.96936	+	5.14308i	−0.122247	+	0.211737i
$591$		0			0
$592$	−4.55408	−	7.88791i	−0.187172	−	0.324191i
$593$	16.1008	−	27.8874i	0.661180	−	1.14520i	−0.319126	−	0.947712i	$-0.603389\pi$
$593$	16.1008	−	27.8874i	0.661180	−	1.14520i	0.980306	−	0.197485i	$-0.0632772\pi$
$594$		0			0
$595$	3.99573	+	2.17483i	0.163809	+	0.0891592i
$596$	−9.16225			−0.375300
$597$		0			0
$598$	0.827430	+	1.43315i	0.0338361	+	0.0586059i
$599$	−9.53590	−	16.5167i	−0.389626	−	0.674852i	0.602773	−	0.797913i	$-0.294062\pi$
$599$	−9.53590	−	16.5167i	−0.389626	−	0.674852i	−0.992399	+	0.123060i	$0.960729\pi$
$600$		0			0
$601$	−8.54377			−0.348508			−0.174254	−	0.984701i	$-0.555751\pi$
$601$	−8.54377			−0.348508			−0.174254	+	0.984701i	$0.555751\pi$
$602$	−21.0548	+	12.8726i	−0.858128	+	0.524648i
$603$		0			0
$604$	0.0519482	−	0.0899768i	0.00211374	−	0.00366111i
$605$	0.530835	+	0.919434i	0.0215815	+	0.0373803i
$606$		0			0
$607$	−19.0057	+	32.9189i	−0.771419	+	1.33614i	0.165366	+	0.986232i	$0.447119\pi$
$607$	−19.0057	+	32.9189i	−0.771419	+	1.33614i	−0.936785	+	0.349905i	$0.886214\pi$
$608$	4.05408			0.164415
$609$		0			0
$610$	−5.56440			−0.225296
$611$	1.69961	−	2.94381i	0.0687589	−	0.119094i
$612$		0			0
$613$	11.3296	+	19.6234i	0.457597	+	0.792581i	0.998833	−	0.0482894i	$-0.0153770\pi$
$613$	11.3296	+	19.6234i	0.457597	+	0.792581i	−0.541237	+	0.840870i	$0.682044\pi$
$614$	−3.89397	+	6.74455i	−0.157148	+	0.272188i
$615$		0			0
$616$	−0.242705	−	9.64776i	−0.00977888	−	0.388719i
$617$	20.2776			0.816346			0.408173	−	0.912905i	$-0.366166\pi$
$617$	20.2776			0.816346			0.408173	+	0.912905i	$0.366166\pi$
$618$		0			0
$619$	−1.03064	−	1.78512i	−0.0414249	−	0.0717501i	0.844570	−	0.535446i	$-0.179856\pi$
$619$	−1.03064	−	1.78512i	−0.0414249	−	0.0717501i	−0.885994	+	0.463696i	$0.846523\pi$
$620$	−0.118485	−	0.205223i	−0.00475849	−	0.00824194i
$621$		0			0
$622$	15.4107			0.617912
$623$	6.15486	−	3.76300i	0.246589	−	0.150761i
$624$		0			0
$625$	−10.9320	+	18.9348i	−0.437280	+	0.757391i
$626$	−4.24844	−	7.35851i	−0.169802	−	0.294105i
$627$		0			0
$628$	−10.4911	+	18.1712i	−0.418642	+	0.725110i
$629$	34.0085			1.35601
$630$		0			0
$631$	1.63715			0.0651740			0.0325870	−	0.999469i	$-0.489625\pi$
$631$	1.63715			0.0651740			0.0325870	+	0.999469i	$0.489625\pi$
$632$	2.50360	−	4.33636i	0.0995878	−	0.172491i
$633$		0			0
$634$	7.05262	+	12.2155i	0.280095	+	0.485139i
$635$	2.02850	−	3.51347i	0.0804988	−	0.139428i
$636$		0			0
$637$	−5.55049	−	8.58561i	−0.219918	−	0.340174i
$638$	−32.7381			−1.29611
$639$		0			0
$640$	0.230252	+	0.398809i	0.00910153	+	0.0157643i
$641$	−10.9662	−	18.9941i	−0.433140	−	0.750221i	0.564001	−	0.825774i	$-0.309261\pi$
$641$	−10.9662	−	18.9941i	−0.433140	−	0.750221i	−0.997142	+	0.0755526i	$0.975928\pi$
$642$		0			0
$643$	28.3638			1.11856			0.559280	−	0.828979i	$-0.311078\pi$
$643$	28.3638			1.11856			0.559280	+	0.828979i	$0.311078\pi$
$644$	−2.63307	−	1.43315i	−0.103758	−	0.0564741i
$645$		0			0
$646$	−7.56867	+	13.1093i	−0.297785	+	0.515780i
$647$	17.3904	+	30.1210i	0.683686	+	1.18418i	0.973848	+	0.227201i	$0.0729575\pi$
$647$	17.3904	+	30.1210i	0.683686	+	1.18418i	−0.290162	+	0.956978i	$0.593709\pi$
$648$		0			0
$649$	−23.5203	+	40.7384i	−0.923253	+	1.59912i
$650$	6.99280			0.274280
$651$		0			0
$652$	23.0364			0.902174
$653$	1.59931	−	2.77009i	0.0625860	−	0.108402i	−0.833035	−	0.553221i	$-0.813399\pi$
$653$	1.59931	−	2.77009i	0.0625860	−	0.108402i	0.895621	+	0.444819i	$0.146732\pi$
$654$		0			0
$655$	4.86693	+	8.42976i	0.190167	+	0.329378i
$656$	−0.472958	+	0.819187i	−0.0184659	+	0.0319839i
$657$		0			0
$658$	0.154861	+	6.15585i	0.00603710	+	0.239980i
$659$	−10.6084			−0.413243			−0.206622	−	0.978421i	$-0.566247\pi$
$659$	−10.6084			−0.413243			−0.206622	+	0.978421i	$0.566247\pi$
$660$		0			0
$661$	−5.06507	−	8.77297i	−0.197009	−	0.341229i	0.750549	−	0.660815i	$-0.229789\pi$
$661$	−5.06507	−	8.77297i	−0.197009	−	0.341229i	−0.947557	+	0.319586i	$0.896456\pi$
$662$	−13.7719	−	23.8536i	−0.535259	−	0.927097i
$663$		0			0
$664$	−6.64766			−0.257979
$665$	−0.124220	−	4.93786i	−0.00481705	−	0.191482i
$666$		0			0
$667$	−5.08472	+	8.80700i	−0.196881	+	0.341008i
$668$	−5.31498	−	9.20581i	−0.205643	−	0.356184i
$669$		0			0
$670$	−0.534239	+	0.925330i	−0.0206395	+	0.0357486i
$671$	−44.0757			−1.70152
$672$		0			0
$673$	−3.21634			−0.123981			−0.0619903	−	0.998077i	$-0.519745\pi$
$673$	−3.21634			−0.123981			−0.0619903	+	0.998077i	$0.519745\pi$
$674$	0.748440	−	1.29634i	0.0288288	−	0.0499330i
$675$		0			0
$676$	5.43346	+	9.41103i	0.208979	+	0.361963i
$677$	14.6819	−	25.4298i	0.564271	−	0.977347i	−0.432846	−	0.901468i	$-0.642491\pi$
$677$	14.6819	−	25.4298i	0.564271	−	0.977347i	0.997117	−	0.0758786i	$-0.0241762\pi$
$678$		0			0
$679$	−25.9971	−	14.1499i	−0.997676	−	0.543023i
$680$	−1.71946			−0.0659382
$681$		0			0
$682$	−0.938524	−	1.62557i	−0.0359379	−	0.0622463i
$683$	12.6278	+	21.8720i	0.483190	+	0.836910i	0.999814	−	0.0193029i	$-0.00614468\pi$
$683$	12.6278	+	21.8720i	0.483190	+	0.836910i	−0.516624	+	0.856213i	$0.672811\pi$
$684$		0			0
$685$	2.02918			0.0775309
$686$	16.6914	+	8.02472i	0.637282	+	0.306385i
$687$		0			0
$688$	4.66372	−	8.07779i	0.177802	−	0.307963i
$689$	−9.08113	−	15.7290i	−0.345963	−	0.599226i
$690$		0			0
$691$	7.68190	−	13.3054i	0.292233	−	0.506163i	−0.682104	−	0.731255i	$-0.738935\pi$
$691$	7.68190	−	13.3054i	0.292233	−	0.506163i	0.974338	+	0.225092i	$0.0722683\pi$
$692$	2.93872			0.111713
$693$		0			0
$694$	−18.2881			−0.694208
$695$	0.466240	−	0.807551i	0.0176855	−	0.0306321i
$696$		0			0
$697$	−1.76595	−	3.05872i	−0.0668903	−	0.115857i
$698$	−3.90136	+	6.75735i	−0.147669	+	0.255770i
$699$		0			0
$700$	−10.8078	+	6.60773i	−0.408496	+	0.249749i
$701$	−13.3700			−0.504980			−0.252490	−	0.967600i	$-0.581249\pi$
$701$	−13.3700			−0.504980			−0.252490	+	0.967600i	$0.581249\pi$
$702$		0			0
$703$	−18.4626	−	31.9782i	−0.696332	−	1.20608i
$704$	1.82383	+	3.15897i	0.0687382	+	0.119058i
$705$		0			0
$706$	26.9253			1.01335
$707$	0.915275	+	36.3830i	0.0344225	+	1.36832i
$708$		0			0
$709$	0.562939	−	0.975038i	0.0211416	−	0.0366183i	−0.855261	−	0.518197i	$-0.826603\pi$
$709$	0.562939	−	0.975038i	0.0211416	−	0.0366183i	0.876403	+	0.481579i	$0.159937\pi$
$710$	0.386770	+	0.669906i	0.0145152	+	0.0251411i
$711$		0			0
$712$	−1.36333	+	2.36135i	−0.0510928	+	0.0884954i
$713$	−0.583068			−0.0218361
$714$		0			0
$715$	−2.45331			−0.0917485
$716$	−4.58113	+	7.93474i	−0.171205	+	0.296535i
$717$		0			0
$718$	−3.13161	−	5.42411i	−0.116871	−	0.202426i
$719$	9.13667	−	15.8252i	0.340740	−	0.590180i	−0.643830	−	0.765169i	$-0.722656\pi$
$719$	9.13667	−	15.8252i	0.340740	−	0.590180i	0.984570	+	0.174989i	$0.0559889\pi$
$720$		0			0
$721$	25.1965	−	15.4048i	0.938366	−	0.573705i
$722$	−2.56440			−0.0954371
$723$		0			0
$724$	−11.2142	−	19.4236i	−0.416772	−	0.721871i
$725$	21.4861	+	37.2150i	0.797973	+	1.38213i
$726$		0			0
$727$	29.6955			1.10135			0.550673	−	0.834721i	$-0.314371\pi$
$727$	29.6955			1.10135			0.550673	+	0.834721i	$0.314371\pi$
$728$	3.39397	+	1.84730i	0.125789	+	0.0684654i
$729$		0			0
$730$	3.04883	−	5.28073i	0.112842	−	0.195448i
$731$	17.4136	+	30.1613i	0.644066	+	1.11555i
$732$		0			0
$733$	−9.61390	+	16.6518i	−0.355098	+	0.615047i	−0.987135	−	0.159891i	$-0.948886\pi$
$733$	−9.61390	+	16.6518i	−0.355098	+	0.615047i	0.632037	+	0.774938i	$0.282219\pi$
$734$	29.2733			1.08050
$735$		0			0
$736$	1.13307			0.0417657
$737$	−4.23171	+	7.32955i	−0.155877	+	0.269987i
$738$		0			0
$739$	−15.1336	−	26.2121i	−0.556697	−	0.964227i	−0.997769	−	0.0667556i	$-0.978735\pi$
$739$	−15.1336	−	26.2121i	−0.556697	−	0.964227i	0.441073	−	0.897471i	$-0.354598\pi$
$740$	2.09718	−	3.63242i	0.0770938	−	0.133530i
$741$		0			0
$742$	28.8982	+	15.7290i	1.06089	+	0.577429i
$743$	23.7630			0.871781			0.435890	−	0.900000i	$-0.356433\pi$
$743$	23.7630			0.871781			0.435890	+	0.900000i	$0.356433\pi$
$744$		0			0
$745$	−2.10963	−	3.65399i	−0.0772909	−	0.133872i
$746$	−8.92986	−	15.4670i	−0.326946	−	0.566286i
$747$		0			0
$748$	−13.6198			−0.497990
$749$	17.5634	−	10.7380i	0.641753	−	0.392360i
$750$		0			0
$751$	−6.33415	+	10.9711i	−0.231136	+	0.400340i	−0.958143	−	0.286291i	$-0.907578\pi$
$751$	−6.33415	+	10.9711i	−0.231136	+	0.400340i	0.727006	+	0.686631i	$0.240911\pi$
$752$	−1.16372	−	2.01561i	−0.0424363	−	0.0735019i
$753$		0			0
$754$	6.55408	−	11.3520i	0.238686	−	0.413416i
$755$	0.0478448			0.00174125
$756$		0			0
$757$	−29.0799			−1.05693			−0.528464	−	0.848955i	$-0.677232\pi$
$757$	−29.0799			−1.05693			−0.528464	+	0.848955i	$0.677232\pi$
$758$	11.2127	−	19.4210i	0.407265	−	0.705404i
$759$		0			0
$760$	0.933463	+	1.61680i	0.0338603	+	0.0586477i
$761$	−14.6015	+	25.2905i	−0.529302	+	0.916778i	0.470114	+	0.882606i	$0.344213\pi$
$761$	−14.6015	+	25.2905i	−0.529302	+	0.916778i	−0.999416	+	0.0341724i	$0.989120\pi$
$762$		0			0
$763$	0.500000	+	19.8754i	0.0181012	+	0.719539i
$764$	2.48968			0.0900736
$765$		0			0
$766$	7.07014	+	12.2458i	0.255454	+	0.442460i
$767$	−9.41741	−	16.3114i	−0.340043	−	0.588972i
$768$		0			0
$769$	−25.1737			−0.907788			−0.453894	−	0.891056i	$-0.649965\pi$
$769$	−25.1737			−0.907788			−0.453894	+	0.891056i	$0.649965\pi$
$770$	3.79173	−	2.31821i	0.136644	−	0.0835426i
$771$		0			0
$772$	−2.24484	+	3.88818i	−0.0807936	+	0.139939i
$773$	−0.752039	−	1.30257i	−0.0270490	−	0.0468502i	0.852184	−	0.523242i	$-0.175278\pi$
$773$	−0.752039	−	1.30257i	−0.0270490	−	0.0468502i	−0.879233	+	0.476392i	$0.841944\pi$
$774$		0			0
$775$	−1.23191	+	2.13373i	−0.0442515	+	0.0766458i
$776$	11.1872			0.401596
$777$		0			0
$778$	−23.1301			−0.829256
$779$	−1.91741	+	3.32105i	−0.0686984	+	0.118989i
$780$		0			0
$781$	3.06361	+	5.30633i	0.109625	+	0.189875i
$782$	−2.11537	+	3.66392i	−0.0756453	+	0.131022i
$783$		0			0
$784$	−6.99115	+	0.351971i	−0.249684	+	0.0125704i
$785$	−9.66245			−0.344868
$786$		0			0
$787$	7.47656	+	12.9498i	0.266510	+	0.461610i	0.967958	−	0.251111i	$-0.0807960\pi$
$787$	7.47656	+	12.9498i	0.266510	+	0.461610i	−0.701448	+	0.712721i	$0.747463\pi$
$788$	−6.36693	−	11.0278i	−0.226812	−	0.392850i
$789$		0			0
$790$	2.30584			0.0820381
$791$	14.0854	+	7.66652i	0.500819	+	0.272590i
$792$		0			0
$793$	8.82383	−	15.2833i	0.313343	−	0.542727i
$794$	−5.13307	−	8.89075i	−0.182166	−	0.315521i
$795$		0			0
$796$	−1.47296	+	2.55124i	−0.0522076	+	0.0904262i
$797$	9.12588			0.323255			0.161628	−	0.986852i	$-0.448326\pi$
$797$	9.12588			0.323255			0.161628	+	0.986852i	$0.448326\pi$
$798$		0			0
$799$	8.69028			0.307440
$800$	2.39397	−	4.14647i	0.0846395	−	0.146600i
$801$		0			0
$802$	−17.0167	−	29.4738i	−0.600881	−	1.04076i
$803$	24.1498	−	41.8287i	0.852228	−	1.47610i
$804$		0			0
$805$	−0.0347182	−	1.38008i	−0.00122366	−	0.0486414i
$806$	0.751560			0.0264726
$807$		0			0
$808$	−6.87792	−	11.9129i	−0.241964	−	0.419094i
$809$	17.7755	+	30.7880i	0.624953	+	1.08245i	0.988550	+	0.150894i	$0.0482151\pi$
$809$	17.7755	+	30.7880i	0.624953	+	1.08245i	−0.363597	+	0.931556i	$0.618452\pi$
$810$		0			0
$811$	−13.5070			−0.474295			−0.237148	−	0.971474i	$-0.576212\pi$
$811$	−13.5070			−0.474295			−0.237148	+	0.971474i	$0.576212\pi$
$812$	0.597178	+	23.7384i	0.0209568	+	0.833053i
$813$		0			0
$814$	16.6118	−	28.7724i	0.582242	−	1.00847i
$815$	5.30418	+	9.18711i	0.185797	+	0.321810i
$816$		0			0
$817$	18.9071	−	32.7480i	0.661475	−	1.14571i
$818$	−3.48968			−0.122014
$819$		0			0
$820$	−0.435599			−0.0152118
$821$	−10.8114	+	18.7259i	−0.377320	+	0.653537i	−0.990671	−	0.136273i	$-0.956488\pi$
$821$	−10.8114	+	18.7259i	−0.377320	+	0.653537i	0.613352	+	0.789810i	$0.289821\pi$
$822$		0			0
$823$	0.753501	+	1.30510i	0.0262654	+	0.0454930i	0.878859	−	0.477081i	$-0.158305\pi$
$823$	0.753501	+	1.30510i	0.0262654	+	0.0454930i	−0.852594	+	0.522574i	$0.824972\pi$
$824$	−5.58113	+	9.66679i	−0.194428	+	0.336759i
$825$		0			0
$826$	29.9684	+	16.3114i	1.04273	+	0.567547i
$827$	23.3786			0.812953			0.406477	−	0.913661i	$-0.366757\pi$
$827$	23.3786			0.812953			0.406477	+	0.913661i	$0.366757\pi$
$828$		0			0
$829$	−11.0095	−	19.0691i	−0.382377	−	0.662296i	0.609025	−	0.793151i	$-0.291561\pi$
$829$	−11.0095	−	19.0691i	−0.382377	−	0.662296i	−0.991401	+	0.130855i	$0.958228\pi$
$830$	−1.53064	−	2.65115i	−0.0531293	−	0.0920227i
$831$		0			0
$832$	−1.46050			−0.0506339
$833$	11.9138	−	23.2637i	0.412789	−	0.806041i
$834$		0			0
$835$	2.44757	−	4.23932i	0.0847018	−	0.146708i
$836$	7.39397	+	12.8067i	0.255726	+	0.442930i
$837$		0			0
$838$	14.4897	−	25.0969i	0.500538	−	0.866957i
$839$	2.13015			0.0735409			0.0367705	−	0.999324i	$-0.488293\pi$
$839$	2.13015			0.0735409			0.0367705	+	0.999324i	$0.488293\pi$
$840$		0			0
$841$	51.5523			1.77767
$842$	−1.06128	+	1.83819i	−0.0365742	+	0.0633483i
$843$		0			0
$844$	−0.608168	−	1.05338i	−0.0209340	−	0.0362588i
$845$	−2.50214	+	4.33383i	−0.0860761	+	0.149088i
$846$		0			0
$847$	5.20408	−	3.18171i	0.178814	−	0.109325i
$848$	−12.4356			−0.427040
$849$		0			0
$850$	8.93872	+	15.4823i	0.306596	+	0.531039i
$851$	−5.16012	−	8.93758i	−0.176887	−	0.306376i
$852$		0			0
$853$	7.00293			0.239776			0.119888	−	0.992787i	$-0.461747\pi$
$853$	7.00293			0.239776			0.119888	+	0.992787i	$0.461747\pi$
$854$	0.803987	+	31.9592i	0.0275119	+	1.09362i
$855$		0			0
$856$	−3.89037	+	6.73832i	−0.132970	+	0.230311i
$857$	−5.46410	−	9.46410i	−0.186650	−	0.323288i	0.757481	−	0.652857i	$-0.226430\pi$
$857$	−5.46410	−	9.46410i	−0.186650	−	0.323288i	−0.944131	+	0.329569i	$0.893096\pi$
$858$		0			0
$859$	6.95379	−	12.0443i	0.237260	−	0.410947i	−0.722667	−	0.691196i	$-0.757084\pi$
$859$	6.95379	−	12.0443i	0.237260	−	0.410947i	0.959927	+	0.280250i	$0.0904173\pi$
$860$	4.29533			0.146469
$861$		0			0
$862$	−21.8712			−0.744936
$863$	−18.4231	+	31.9098i	−0.627131	+	1.08622i	0.360993	+	0.932568i	$0.382438\pi$
$863$	−18.4231	+	31.9098i	−0.627131	+	1.08622i	−0.988125	+	0.153655i	$0.950896\pi$
$864$		0			0
$865$	0.676647	+	1.17199i	0.0230067	+	0.0398488i
$866$	6.52558	−	11.3026i	0.221748	−	0.384079i
$867$		0			0
$868$	−1.16158	+	0.710174i	−0.0394266	+	0.0241049i
$869$	18.2646			0.619583
$870$		0			0
$871$	−1.69436	−	2.93471i	−0.0574111	−	0.0994389i
$872$	−3.75729	−	6.50783i	−0.127238	−	0.220383i
$873$		0			0
$874$	4.59358			0.155380
$875$	−10.4744	−	5.70110i	−0.354100	−	0.192732i
$876$		0			0
$877$	5.17977	−	8.97162i	0.174908	−	0.302950i	−0.765221	−	0.643767i	$-0.777370\pi$
$877$	5.17977	−	8.97162i	0.174908	−	0.302950i	0.940130	+	0.340817i	$0.110704\pi$
$878$	−2.43200	−	4.21235i	−0.0820760	−	0.142160i
$879$		0			0
$880$	−0.839883	+	1.45472i	−0.0283125	+	0.0490386i
$881$	9.34806			0.314944			0.157472	−	0.987523i	$-0.449666\pi$
$881$	9.34806			0.314944			0.157472	+	0.987523i	$0.449666\pi$
$882$		0			0
$883$	2.29494			0.0772308			0.0386154	−	0.999254i	$-0.487705\pi$
$883$	2.29494			0.0772308			0.0386154	+	0.999254i	$0.487705\pi$
$884$	2.72665	−	4.72270i	0.0917073	−	0.158842i
$885$		0			0
$886$	5.76975	+	9.99350i	0.193838	+	0.335738i
$887$	13.8363	−	23.9651i	0.464577	−	0.804671i	−0.534605	−	0.845102i	$-0.679540\pi$
$887$	13.8363	−	23.9651i	0.464577	−	0.804671i	0.999182	+	0.0404309i	$0.0128731\pi$
$888$		0			0
$889$	−20.4728	−	11.1431i	−0.686634	−	0.373727i
$890$	−1.25564			−0.0420891
$891$		0			0
$892$	−0.445916	−	0.772349i	−0.0149304	−	0.0258602i
$893$	−4.71780	−	8.17147i	−0.157875	−	0.273448i
$894$		0			0
$895$	−4.21926			−0.141034
$896$	2.25729	−	1.38008i	0.0754109	−	0.0461052i
$897$		0			0
$898$	13.2125	−	22.8848i	0.440908	−	0.763676i
$899$	2.30924	+	3.99973i	0.0770176	+	0.133398i
$900$		0			0
$901$	23.2163	−	40.2119i	0.773448	−	1.33965i
$902$	−3.45038			−0.114885
$903$		0			0
$904$	−6.06128			−0.201595
$905$	5.16419	−	8.94465i	0.171664	−	0.297330i
$906$		0			0
$907$	1.46576	+	2.53877i	0.0486698	+	0.0842985i	0.889334	−	0.457258i	$-0.151168\pi$
$907$	1.46576	+	2.53877i	0.0486698	+	0.0842985i	−0.840664	+	0.541557i	$0.817835\pi$
$908$	7.32597	−	12.6889i	0.243121	−	0.421098i
$909$		0			0
$910$	0.0447509	+	1.77889i	0.00148348	+	0.0589696i
$911$	−30.6342			−1.01496			−0.507479	−	0.861664i	$-0.669422\pi$
$911$	−30.6342			−1.01496			−0.507479	+	0.861664i	$0.669422\pi$
$912$		0			0
$913$	−12.1242	−	20.9998i	−0.401253	−	0.694991i
$914$	1.86906	+	3.23731i	0.0618231	+	0.107081i
$915$		0			0
$916$	−9.57587			−0.316396
$917$	47.7132	−	29.1712i	1.57563	−	0.963319i
$918$		0			0
$919$	13.1857	−	22.8383i	0.434956	−	0.753366i	−0.562336	−	0.826909i	$-0.690097\pi$
$919$	13.1857	−	22.8383i	0.434956	−	0.753366i	0.997292	+	0.0735429i	$0.0234306\pi$
$920$	0.260893	+	0.451880i	0.00860139	+	0.0148980i
$921$		0			0
$922$	−7.90496	+	13.6918i	−0.260336	+	0.450915i
$923$	−2.45331			−0.0807516
$924$		0			0
$925$	−43.6093			−1.43387
$926$	19.1965	−	33.2493i	0.630836	−	1.09264i
$927$		0			0
$928$	−4.48755	−	7.77266i	−0.147311	−	0.255150i
$929$	−8.93706	+	15.4794i	−0.293215	+	0.507864i	−0.974568	−	0.224091i	$-0.928059\pi$
$929$	−8.93706	+	15.4794i	−0.293215	+	0.507864i	0.681353	+	0.731955i	$0.261392\pi$
$930$		0			0
$931$	−28.3427	+	1.42692i	−0.928894	+	0.0467654i
$932$	−14.4284			−0.472618
$933$		0			0
$934$	3.15652	+	5.46725i	0.103284	+	0.178894i
$935$	−3.13600	−	5.43171i	−0.102558	−	0.177636i
$936$		0			0
$937$	15.9134			0.519869			0.259934	−	0.965626i	$-0.416299\pi$
$937$	15.9134			0.519869			0.259934	+	0.965626i	$0.416299\pi$
$938$	5.39183	+	2.93471i	0.176050	+	0.0958217i
$939$		0			0
$940$	0.535897	−	0.928200i	0.0174790	−	0.0302745i
$941$	8.14027	+	14.0994i	0.265365	+	0.459626i	0.967659	−	0.252261i	$-0.0811741\pi$
$941$	8.14027	+	14.0994i	0.265365	+	0.459626i	−0.702294	+	0.711887i	$0.747841\pi$
$942$		0			0
$943$	−0.535897	+	0.928200i	−0.0174512	+	0.0302264i
$944$	−12.8961			−0.419732
$945$		0			0
$946$	34.0233			1.10619
$947$	14.2951	−	24.7599i	0.464529	−	0.804589i	−0.534651	−	0.845073i	$-0.679557\pi$
$947$	14.2951	−	24.7599i	0.464529	−	0.804589i	0.999180	+	0.0404846i	$0.0128902\pi$
$948$		0			0
$949$	9.66945	+	16.7480i	0.313884	+	0.543662i
$950$	9.70535	−	16.8102i	0.314883	−	0.545393i
$951$		0			0
$952$	0.248440	+	9.87572i	0.00805199	+	0.320074i
$953$	−29.3537			−0.950859			−0.475430	−	0.879754i	$-0.657707\pi$
$953$	−29.3537			−0.950859			−0.475430	+	0.879754i	$0.657707\pi$
$954$		0			0
$955$	0.573256	+	0.992908i	0.0185501	+	0.0321297i
$956$	−9.15486	−	15.8567i	−0.296089	−	0.512842i
$957$		0			0
$958$	−20.4136			−0.659534
$959$	−0.293191	−	11.6546i	−0.00946763	−	0.376347i
$960$		0			0
$961$	15.3676	−	26.6175i	0.495729	−	0.858628i
$962$	6.65126	+	11.5203i	0.214445	+	0.371430i
$963$		0			0
$964$	−0.0466924	+	0.0808735i	−0.00150386	+	0.00260476i
$965$	−2.06752			−0.0665559
$966$		0			0
$967$	9.39630			0.302165			0.151082	−	0.988521i	$-0.451724\pi$
$967$	9.39630			0.302165			0.151082	+	0.988521i	$0.451724\pi$
$968$	−1.15272	+	1.99658i	−0.0370500	+	0.0641724i
$969$		0			0
$970$	2.57587	+	4.46154i	0.0827062	+	0.143251i
$971$	7.77335	−	13.4638i	0.249459	−	0.432075i	−0.713917	−	0.700230i	$-0.753081\pi$
$971$	7.77335	−	13.4638i	0.249459	−	0.432075i	0.963376	+	0.268155i	$0.0864140\pi$
$972$		0			0
$973$	−4.70554	−	2.56117i	−0.150853	−	0.0821074i
$974$	−12.3638			−0.396162
$975$		0			0
$976$	−6.04163	−	10.4644i	−0.193388	−	0.334958i
$977$	4.79893	+	8.31198i	0.153531	+	0.265924i	0.932523	−	0.361110i	$-0.117602\pi$
$977$	4.79893	+	8.31198i	0.153531	+	0.265924i	−0.778992	+	0.627034i	$0.784269\pi$
$978$		0			0
$979$	−9.94592			−0.317873
$980$	−1.75010	−	2.70709i	−0.0559048	−	0.0864748i
$981$		0			0
$982$	0.207004	−	0.358541i	0.00660575	−	0.0114415i
$983$	23.4267	+	40.5763i	0.747197	+	1.29418i	0.949161	+	0.314790i	$0.101934\pi$
$983$	23.4267	+	40.5763i	0.747197	+	1.29418i	−0.201964	+	0.979393i	$0.564732\pi$
$984$		0			0
$985$	2.93200	−	5.07837i	0.0934213	−	0.161810i
$986$	33.5117			1.06723
$987$		0			0
$988$	−5.92101			−0.188372
$989$	5.28434	−	9.15274i	0.168032	−	0.291040i
$990$		0			0
$991$	10.8260	+	18.7511i	0.343898	+	0.595649i	0.985153	−	0.171679i	$-0.0549192\pi$
$991$	10.8260	+	18.7511i	0.343898	+	0.595649i	−0.641255	+	0.767328i	$0.721586\pi$
$992$	0.257295	−	0.445647i	0.00816911	−	0.0141493i
$993$		0			0
$994$	3.79173	−	2.31821i	0.120266	−	0.0735292i
$995$	−1.35661			−0.0430074
$996$		0			0
$997$	28.6190	+	49.5695i	0.906372	+	1.56988i	0.819065	+	0.573700i	$0.194493\pi$
$997$	28.6190	+	49.5695i	0.906372	+	1.56988i	0.0873064	+	0.996182i	$0.472174\pi$
$998$	0.461967	+	0.800151i	0.0146233	+	0.0253283i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.g.k.163.3		6
3.2	odd	2		1134.2.g.n.163.1		6
7.2	even	3		7938.2.a.cb.1.1		3
7.4	even	3	inner	1134.2.g.k.487.3		6
7.5	odd	6		7938.2.a.by.1.3		3
9.2	odd	6		378.2.e.c.37.1		6
9.4	even	3		126.2.h.c.79.3	yes	6
9.5	odd	6		378.2.h.d.289.3		6
9.7	even	3		126.2.e.d.121.2	yes	6
21.2	odd	6		7938.2.a.bu.1.3		3
21.5	even	6		7938.2.a.bx.1.1		3
21.11	odd	6		1134.2.g.n.487.1		6
36.7	odd	6		1008.2.q.h.625.2		6
36.11	even	6		3024.2.q.h.2305.1		6
36.23	even	6		3024.2.t.g.289.3		6
36.31	odd	6		1008.2.t.g.961.1		6
63.2	odd	6		2646.2.f.o.1765.1		6
63.4	even	3		126.2.e.d.25.2	✓	6
63.5	even	6		2646.2.f.n.883.3		6
63.11	odd	6		378.2.h.d.361.3		6
63.13	odd	6		882.2.h.o.79.1		6
63.16	even	3		882.2.f.l.589.2		6
63.20	even	6		2646.2.e.o.1549.3		6
63.23	odd	6		2646.2.f.o.883.1		6
63.25	even	3		126.2.h.c.67.3	yes	6
63.31	odd	6		882.2.e.p.655.2		6
63.32	odd	6		378.2.e.c.235.1		6
63.34	odd	6		882.2.e.p.373.2		6
63.38	even	6		2646.2.h.p.361.1		6
63.40	odd	6		882.2.f.m.295.2		6
63.41	even	6		2646.2.h.p.667.1		6
63.47	even	6		2646.2.f.n.1765.3		6
63.52	odd	6		882.2.h.o.67.1		6
63.58	even	3		882.2.f.l.295.2		6
63.59	even	6		2646.2.e.o.2125.3		6
63.61	odd	6		882.2.f.m.589.2		6
252.11	even	6		3024.2.t.g.1873.3		6
252.67	odd	6		1008.2.q.h.529.2		6
252.95	even	6		3024.2.q.h.2881.1		6
252.151	odd	6		1008.2.t.g.193.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.2	✓	6	63.4	even	3
126.2.e.d.121.2	yes	6	9.7	even	3
126.2.h.c.67.3	yes	6	63.25	even	3
126.2.h.c.79.3	yes	6	9.4	even	3
378.2.e.c.37.1		6	9.2	odd	6
378.2.e.c.235.1		6	63.32	odd	6
378.2.h.d.289.3		6	9.5	odd	6
378.2.h.d.361.3		6	63.11	odd	6
882.2.e.p.373.2		6	63.34	odd	6
882.2.e.p.655.2		6	63.31	odd	6
882.2.f.l.295.2		6	63.58	even	3
882.2.f.l.589.2		6	63.16	even	3
882.2.f.m.295.2		6	63.40	odd	6
882.2.f.m.589.2		6	63.61	odd	6
882.2.h.o.67.1		6	63.52	odd	6
882.2.h.o.79.1		6	63.13	odd	6
1008.2.q.h.529.2		6	252.67	odd	6
1008.2.q.h.625.2		6	36.7	odd	6
1008.2.t.g.193.1		6	252.151	odd	6
1008.2.t.g.961.1		6	36.31	odd	6
1134.2.g.k.163.3		6	1.1	even	1	trivial
1134.2.g.k.487.3		6	7.4	even	3	inner
1134.2.g.n.163.1		6	3.2	odd	2
1134.2.g.n.487.1		6	21.11	odd	6
2646.2.e.o.1549.3		6	63.20	even	6
2646.2.e.o.2125.3		6	63.59	even	6
2646.2.f.n.883.3		6	63.5	even	6
2646.2.f.n.1765.3		6	63.47	even	6
2646.2.f.o.883.1		6	63.23	odd	6
2646.2.f.o.1765.1		6	63.2	odd	6
2646.2.h.p.361.1		6	63.38	even	6
2646.2.h.p.667.1		6	63.41	even	6
3024.2.q.h.2305.1		6	36.11	even	6
3024.2.q.h.2881.1		6	252.95	even	6
3024.2.t.g.289.3		6	36.23	even	6
3024.2.t.g.1873.3		6	252.11	even	6
7938.2.a.bu.1.3		3	21.2	odd	6
7938.2.a.bx.1.1		3	21.5	even	6
7938.2.a.by.1.3		3	7.5	odd	6
7938.2.a.cb.1.1		3	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.230252 - 0.398809i) q^{5} +(-2.32383 - 1.26483i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.230252 - 0.398809i) q^{5} +(-2.32383 - 1.26483i) q^{7} +1.00000 q^{8} +(0.230252 + 0.398809i) q^{10} +(1.82383 + 3.15897i) q^{11} -1.46050 q^{13} +(2.25729 - 1.38008i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.86693 - 3.23361i) q^{17} +(-2.02704 + 3.51094i) q^{19} -0.460505 q^{20} -3.64766 q^{22} +(-0.566537 + 0.981271i) q^{23} +(2.39397 + 4.14647i) q^{25} +(0.730252 - 1.26483i) q^{26} +(0.0665372 + 2.64491i) q^{28} +8.97509 q^{29} +(0.257295 + 0.445647i) q^{31} +(-0.500000 - 0.866025i) q^{32} +3.73385 q^{34} +(-1.03950 + 0.635534i) q^{35} +(-4.55408 + 7.88791i) q^{37} +(-2.02704 - 3.51094i) q^{38} +(0.230252 - 0.398809i) q^{40} +0.945916 q^{41} -9.32743 q^{43} +(1.82383 - 3.15897i) q^{44} +(-0.566537 - 0.981271i) q^{46} +(-1.16372 + 2.01561i) q^{47} +(3.80039 + 5.87852i) q^{49} -4.78794 q^{50} +(0.730252 + 1.26483i) q^{52} +(6.21780 + 10.7695i) q^{53} +1.67977 q^{55} +(-2.32383 - 1.26483i) q^{56} +(-4.48755 + 7.77266i) q^{58} +(6.44805 + 11.1684i) q^{59} +(-6.04163 + 10.4644i) q^{61} -0.514589 q^{62} +1.00000 q^{64} +(-0.336285 + 0.582462i) q^{65} +(1.16012 + 2.00938i) q^{67} +(-1.86693 + 3.23361i) q^{68} +(-0.0306407 - 1.21800i) q^{70} +1.67977 q^{71} +(-6.62062 - 11.4673i) q^{73} +(-4.55408 - 7.88791i) q^{74} +4.05408 q^{76} +(-0.242705 - 9.64776i) q^{77} +(2.50360 - 4.33636i) q^{79} +(0.230252 + 0.398809i) q^{80} +(-0.472958 + 0.819187i) q^{82} -6.64766 q^{83} -1.71946 q^{85} +(4.66372 - 8.07779i) q^{86} +(1.82383 + 3.15897i) q^{88} +(-1.36333 + 2.36135i) q^{89} +(3.39397 + 1.84730i) q^{91} +1.13307 q^{92} +(-1.16372 - 2.01561i) q^{94} +(0.933463 + 1.61680i) q^{95} +11.1872 q^{97} +(-6.99115 + 0.351971i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} - 5 q^{5} - 2 q^{7} + 6 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 - 5 * q^5 - 2 * q^7 + 6 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} - 5 q^{5} - 2 q^{7} + 6 q^{8} - 5 q^{10} - q^{11} + 4 q^{13} - 2 q^{14} - 3 q^{16} - 4 q^{17} - 3 q^{19} + 10 q^{20} + 2 q^{22} - 7 q^{23} - 2 q^{25} - 2 q^{26} + 4 q^{28} + 10 q^{29} - 14 q^{31} - 3 q^{32} + 8 q^{34} - 19 q^{35} - 9 q^{37} - 3 q^{38} - 5 q^{40} + 24 q^{41} - 36 q^{43} - q^{44} - 7 q^{46} + 3 q^{47} + 12 q^{49} + 4 q^{50} - 2 q^{52} + 9 q^{53} + 14 q^{55} - 2 q^{56} - 5 q^{58} + 4 q^{59} + 4 q^{61} + 28 q^{62} + 6 q^{64} - 12 q^{65} + 5 q^{67} - 4 q^{68} + 17 q^{70} + 14 q^{71} - 25 q^{73} - 9 q^{74} + 6 q^{76} - 17 q^{77} + 7 q^{79} - 5 q^{80} - 12 q^{82} - 16 q^{83} - 28 q^{85} + 18 q^{86} - q^{88} - 9 q^{89} + 4 q^{91} + 14 q^{92} + 3 q^{94} + 2 q^{95} + 56 q^{97} - 12 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 - 5 * q^5 - 2 * q^7 + 6 * q^8 - 5 * q^10 - q^11 + 4 * q^13 - 2 * q^14 - 3 * q^16 - 4 * q^17 - 3 * q^19 + 10 * q^20 + 2 * q^22 - 7 * q^23 - 2 * q^25 - 2 * q^26 + 4 * q^28 + 10 * q^29 - 14 * q^31 - 3 * q^32 + 8 * q^34 - 19 * q^35 - 9 * q^37 - 3 * q^38 - 5 * q^40 + 24 * q^41 - 36 * q^43 - q^44 - 7 * q^46 + 3 * q^47 + 12 * q^49 + 4 * q^50 - 2 * q^52 + 9 * q^53 + 14 * q^55 - 2 * q^56 - 5 * q^58 + 4 * q^59 + 4 * q^61 + 28 * q^62 + 6 * q^64 - 12 * q^65 + 5 * q^67 - 4 * q^68 + 17 * q^70 + 14 * q^71 - 25 * q^73 - 9 * q^74 + 6 * q^76 - 17 * q^77 + 7 * q^79 - 5 * q^80 - 12 * q^82 - 16 * q^83 - 28 * q^85 + 18 * q^86 - q^88 - 9 * q^89 + 4 * q^91 + 14 * q^92 + 3 * q^94 + 2 * q^95 + 56 * q^97 - 12 * q^98

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