LMFDB - Embedded newform 1170.2.bj.c.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(199,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1170.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 $ x^12 - 2x^11 - 8x^10 + 34x^9 + 8x^8 - 134x^7 + 98x^6 + 154x^5 + 104x^4 + 190x^3 - 1196x^2 - 338*x + 2197
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.1
Root			$-2.39378 - 0.0429626i$ of defining polynomial
Character	$\chi$	$=$	1170.199
Dual form			1170.2.bj.c.829.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.10012 - 0.767774i) q^{5} +(0.823063 + 1.42559i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.10012 - 0.767774i) q^{5} +(0.823063 + 1.42559i) q^{7} +1.00000 q^{8} +(1.71497 - 1.43487i) q^{10} +(-2.08305 - 1.20265i) q^{11} +(-3.59643 + 0.256262i) q^{13} -1.64613 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.210702 + 0.121649i) q^{17} +(3.82681 - 2.20941i) q^{19} +(0.385150 + 2.20265i) q^{20} +(2.08305 - 1.20265i) q^{22} +(7.46758 + 4.31141i) q^{23} +(3.82105 + 3.22484i) q^{25} +(1.57629 - 3.24273i) q^{26} +(0.823063 - 1.42559i) q^{28} +(-0.0221633 + 0.0383880i) q^{29} -4.24458i q^{31} +(-0.500000 - 0.866025i) q^{32} -0.243297i q^{34} +(-0.634006 - 3.62584i) q^{35} +(4.47415 - 7.74945i) q^{37} +4.41882i q^{38} +(-2.10012 - 0.767774i) q^{40} +(-0.210702 - 0.121649i) q^{41} +(-5.82728 + 3.36438i) q^{43} +2.40530i q^{44} +(-7.46758 + 4.31141i) q^{46} +7.29560 q^{47} +(2.14514 - 3.71548i) q^{49} +(-4.70332 + 1.69670i) q^{50} +(2.02015 + 2.98647i) q^{52} -2.44613i q^{53} +(3.45130 + 4.12502i) q^{55} +(0.823063 + 1.42559i) q^{56} +(-0.0221633 - 0.0383880i) q^{58} +(8.35669 - 4.82474i) q^{59} +(1.31630 + 2.27990i) q^{61} +(3.67591 + 2.12229i) q^{62} +1.00000 q^{64} +(7.74971 + 2.22307i) q^{65} +(0.937098 - 1.62310i) q^{67} +(0.210702 + 0.121649i) q^{68} +(3.45707 + 1.26385i) q^{70} +(6.53035 - 3.77030i) q^{71} +1.70370 q^{73} +(4.47415 + 7.74945i) q^{74} +(-3.82681 - 2.20941i) q^{76} -3.95942i q^{77} +6.79707 q^{79} +(1.71497 - 1.43487i) q^{80} +(0.210702 - 0.121649i) q^{82} +17.4986 q^{83} +(0.535898 - 0.0937060i) q^{85} -6.72876i q^{86} +(-2.08305 - 1.20265i) q^{88} +(8.69772 + 5.02163i) q^{89} +(-3.32541 - 4.91611i) q^{91} -8.62281i q^{92} +(-3.64780 + 6.31817i) q^{94} +(-9.73310 + 1.70191i) q^{95} +(8.25647 + 14.3006i) q^{97} +(2.14514 + 3.71548i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	$ 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 4 q^{10} - 6 q^{11} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} - 2 q^{20} + 6 q^{22} + 6 q^{23} - 10 q^{25} + 2 q^{26} + 2 q^{28} - 14 q^{29} - 6 q^{32} + 22 q^{35} + 12 q^{37} - 2 q^{40} + 18 q^{41} + 36 q^{43} - 6 q^{46} + 16 q^{47} + 8 q^{49} + 20 q^{50} - 10 q^{52} + 8 q^{55} + 2 q^{56} - 14 q^{58} + 36 q^{59} + 10 q^{61} + 6 q^{62} + 12 q^{64} + 44 q^{65} - 4 q^{67} - 18 q^{68} + 4 q^{70} + 12 q^{71} - 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 4 q^{80} - 18 q^{82} + 72 q^{83} + 48 q^{85} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} - 18 q^{95} + 48 q^{97} + 8 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 4 * q^10 - 6 * q^11 + 8 * q^13 - 4 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 - 2 * q^20 + 6 * q^22 + 6 * q^23 - 10 * q^25 + 2 * q^26 + 2 * q^28 - 14 * q^29 - 6 * q^32 + 22 * q^35 + 12 * q^37 - 2 * q^40 + 18 * q^41 + 36 * q^43 - 6 * q^46 + 16 * q^47 + 8 * q^49 + 20 * q^50 - 10 * q^52 + 8 * q^55 + 2 * q^56 - 14 * q^58 + 36 * q^59 + 10 * q^61 + 6 * q^62 + 12 * q^64 + 44 * q^65 - 4 * q^67 - 18 * q^68 + 4 * q^70 + 12 * q^71 - 28 * q^73 + 12 * q^74 + 6 * q^76 + 4 * q^79 + 4 * q^80 - 18 * q^82 + 72 * q^83 + 48 * q^85 - 6 * q^88 - 18 * q^89 + 2 * q^91 - 8 * q^94 - 18 * q^95 + 48 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.500000	+	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
$5$	−2.10012	−	0.767774i	−0.939204	−	0.343359i
$5$	−2.10012	−	0.767774i	−0.939204	−	0.343359i
$6$		0			0
$7$	0.823063	+	1.42559i	0.311088	+	0.538821i	0.978598	−	0.205780i	$-0.0659731\pi$
$7$	0.823063	+	1.42559i	0.311088	+	0.538821i	−0.667510	+	0.744601i	$0.732640\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	1.71497	−	1.43487i	0.542322	−	0.453747i
$11$	−2.08305	−	1.20265i	−0.628063	−	0.362612i	0.151939	−	0.988390i	$-0.451448\pi$
$11$	−2.08305	−	1.20265i	−0.628063	−	0.362612i	−0.780001	+	0.625778i	$0.784782\pi$
$12$		0			0
$13$	−3.59643	+	0.256262i	−0.997471	+	0.0710744i
$13$	−3.59643	+	0.256262i	−0.997471	+	0.0710744i
$14$	−1.64613			−0.439946
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.210702	+	0.121649i	−0.0511027	+	0.0295041i	−0.525334	−	0.850896i	$-0.676059\pi$
$17$	−0.210702	+	0.121649i	−0.0511027	+	0.0295041i	0.474231	+	0.880400i	$0.342726\pi$
$18$		0			0
$19$	3.82681	−	2.20941i	0.877930	−	0.506873i	0.00795483	−	0.999968i	$-0.497468\pi$
$19$	3.82681	−	2.20941i	0.877930	−	0.506873i	0.869975	+	0.493095i	$0.164135\pi$
$20$	0.385150	+	2.20265i	0.0861222	+	0.492527i
$21$		0			0
$22$	2.08305	−	1.20265i	0.444107	−	0.256405i
$23$	7.46758	+	4.31141i	1.55710	+	0.898991i	0.997533	+	0.0702038i	$0.0223650\pi$
$23$	7.46758	+	4.31141i	1.55710	+	0.898991i	0.559565	+	0.828787i	$0.310968\pi$
$24$		0			0
$25$	3.82105	+	3.22484i	0.764209	+	0.644969i
$26$	1.57629	−	3.24273i	0.309135	−	0.635952i
$27$		0			0
$28$	0.823063	−	1.42559i	0.155544	−	0.269411i
$29$	−0.0221633	+	0.0383880i	−0.00411562	+	0.00712846i	−0.868076	−	0.496432i	$-0.834643\pi$
$29$	−0.0221633	+	0.0383880i	−0.00411562	+	0.00712846i	0.863960	+	0.503560i	$0.167977\pi$
$30$		0			0
$31$		−	4.24458i		−	0.762348i	−0.924503	−	0.381174i	$-0.875520\pi$
$31$		−	4.24458i		−	0.762348i	0.924503	−	0.381174i	$-0.124480\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$		−	0.243297i		−	0.0417251i
$35$	−0.634006	−	3.62584i	−0.107167	−	0.612878i
$36$		0			0
$37$	4.47415	−	7.74945i	0.735545	−	1.27400i	−0.218939	−	0.975739i	$-0.570260\pi$
$37$	4.47415	−	7.74945i	0.735545	−	1.27400i	0.954484	−	0.298263i	$-0.0964071\pi$
$38$			4.41882i			0.716827i
$39$		0			0
$40$	−2.10012	−	0.767774i	−0.332059	−	0.121396i
$41$	−0.210702	−	0.121649i	−0.0329061	−	0.0189983i	0.483457	−	0.875368i	$-0.339381\pi$
$41$	−0.210702	−	0.121649i	−0.0329061	−	0.0189983i	−0.516363	+	0.856370i	$0.672714\pi$
$42$		0			0
$43$	−5.82728	+	3.36438i	−0.888652	+	0.513063i	−0.873501	−	0.486822i	$-0.838156\pi$
$43$	−5.82728	+	3.36438i	−0.888652	+	0.513063i	−0.0151507	+	0.999885i	$0.504823\pi$
$44$			2.40530i			0.362612i
$45$		0			0
$46$	−7.46758	+	4.31141i	−1.10103	+	0.635682i
$47$	7.29560			1.06417			0.532086	−	0.846690i	$-0.321408\pi$
$47$	7.29560			1.06417			0.532086	+	0.846690i	$0.321408\pi$
$48$		0			0
$49$	2.14514	−	3.71548i	0.306448	−	0.530783i
$50$	−4.70332	+	1.69670i	−0.665150	+	0.239950i
$51$		0			0
$52$	2.02015	+	2.98647i	0.280144	+	0.414149i
$53$		−	2.44613i		−	0.336002i	−0.985787	−	0.168001i	$-0.946269\pi$
$53$		−	2.44613i		−	0.336002i	0.985787	−	0.168001i	$-0.0537312\pi$
$54$		0			0
$55$	3.45130	+	4.12502i	0.465373	+	0.556218i
$56$	0.823063	+	1.42559i	0.109986	+	0.190502i
$57$		0			0
$58$	−0.0221633	−	0.0383880i	−0.00291018	−	0.00504059i
$59$	8.35669	−	4.82474i	1.08795	−	0.628127i	0.154919	−	0.987927i	$-0.450488\pi$
$59$	8.35669	−	4.82474i	1.08795	−	0.628127i	0.933029	+	0.359800i	$0.117155\pi$
$60$		0			0
$61$	1.31630	+	2.27990i	0.168535	+	0.291911i	0.937905	−	0.346892i	$-0.112763\pi$
$61$	1.31630	+	2.27990i	0.168535	+	0.291911i	−0.769370	+	0.638804i	$0.779430\pi$
$62$	3.67591	+	2.12229i	0.466841	+	0.269531i
$63$		0			0
$64$	1.00000			0.125000
$65$	7.74971	+	2.22307i	0.961233	+	0.275737i
$66$		0			0
$67$	0.937098	−	1.62310i	0.114485	−	0.198293i	−0.803089	−	0.595859i	$-0.796812\pi$
$67$	0.937098	−	1.62310i	0.114485	−	0.198293i	0.917574	+	0.397566i	$0.130145\pi$
$68$	0.210702	+	0.121649i	0.0255513	+	0.0147521i
$69$		0			0
$70$	3.45707	+	1.26385i	0.413199	+	0.151059i
$71$	6.53035	−	3.77030i	0.775010	−	0.447452i	−0.0596488	−	0.998219i	$-0.518998\pi$
$71$	6.53035	−	3.77030i	0.775010	−	0.447452i	0.834659	+	0.550767i	$0.185665\pi$
$72$		0			0
$73$	1.70370			0.199403			0.0997015	−	0.995017i	$-0.468211\pi$
$73$	1.70370			0.199403			0.0997015	+	0.995017i	$0.468211\pi$
$74$	4.47415	+	7.74945i	0.520109	+	0.900855i
$75$		0			0
$76$	−3.82681	−	2.20941i	−0.438965	−	0.253437i
$77$		−	3.95942i		−	0.451218i
$78$		0			0
$79$	6.79707			0.764730			0.382365	−	0.924011i	$-0.375110\pi$
$79$	6.79707			0.764730			0.382365	+	0.924011i	$0.375110\pi$
$80$	1.71497	−	1.43487i	0.191740	−	0.160424i
$81$		0			0
$82$	0.210702	−	0.121649i	0.0232681	−	0.0134338i
$83$	17.4986			1.92073			0.960363	−	0.278754i	$-0.0899214\pi$
$83$	17.4986			1.92073			0.960363	+	0.278754i	$0.0899214\pi$
$84$		0			0
$85$	0.535898	−	0.0937060i	0.0581263	−	0.0101638i
$86$		−	6.72876i		−	0.725581i
$87$		0			0
$88$	−2.08305	−	1.20265i	−0.222054	−	0.128203i
$89$	8.69772	+	5.02163i	0.921956	+	0.532292i	0.884259	−	0.466997i	$-0.154664\pi$
$89$	8.69772	+	5.02163i	0.921956	+	0.532292i	0.0376977	+	0.999289i	$0.487998\pi$
$90$		0			0
$91$	−3.32541	−	4.91611i	−0.348598	−	0.515348i
$92$		−	8.62281i		−	0.898991i
$93$		0			0
$94$	−3.64780	+	6.31817i	−0.376242	+	0.651670i
$95$	−9.73310	+	1.70191i	−0.998595	+	0.174612i
$96$		0			0
$97$	8.25647	+	14.3006i	0.838317	+	1.45201i	0.891301	+	0.453413i	$0.149794\pi$
$97$	8.25647	+	14.3006i	0.838317	+	1.45201i	−0.0529831	+	0.998595i	$0.516873\pi$
$98$	2.14514	+	3.71548i	0.216691	+	0.375321i
$99$		0			0
$100$	0.882273	−	4.92154i	0.0882273	−	0.492154i
$101$	−5.66777	+	9.81687i	−0.563964	+	0.976815i	0.433181	+	0.901307i	$0.357391\pi$
$101$	−5.66777	+	9.81687i	−0.563964	+	0.976815i	−0.997145	+	0.0755077i	$0.975942\pi$
$102$		0			0
$103$			5.98168i			0.589392i	0.955591	+	0.294696i	$0.0952184\pi$
$103$			5.98168i			0.589392i	−0.955591	+	0.294696i	$0.904782\pi$
$104$	−3.59643	+	0.256262i	−0.352659	+	0.0251286i
$105$		0			0
$106$	2.11841	+	1.22307i	0.205758	+	0.118795i
$107$	−9.24559	−	5.33795i	−0.893805	−	0.516039i	−0.0186200	−	0.999827i	$-0.505927\pi$
$107$	−9.24559	−	5.33795i	−0.893805	−	0.516039i	−0.875185	+	0.483788i	$0.839261\pi$
$108$		0			0
$109$			9.50683i			0.910589i	0.890341	+	0.455295i	$0.150466\pi$
$109$			9.50683i			0.910589i	−0.890341	+	0.455295i	$0.849534\pi$
$110$	−5.29802	+	0.926401i	−0.505147	+	0.0883288i
$111$		0			0
$112$	−1.64613			−0.155544
$113$	3.11433	−	1.79806i	0.292972	−	0.169147i	−0.346310	−	0.938120i	$-0.612565\pi$
$113$	3.11433	−	1.79806i	0.292972	−	0.169147i	0.639281	+	0.768973i	$0.279232\pi$
$114$		0			0
$115$	−12.3727	−	14.7879i	−1.15376	−	1.37898i
$116$	0.0443266			0.00411562
$117$		0			0
$118$			9.64947i			0.888306i
$119$	−0.346841	−	0.200249i	−0.0317949	−	0.0183568i
$120$		0			0
$121$	−2.60727	−	4.51593i	−0.237025	−	0.410539i
$122$	−2.63260			−0.238345
$123$		0			0
$124$	−3.67591	+	2.12229i	−0.330106	+	0.190587i
$125$	−5.54872	−	9.70627i	−0.496293	−	0.868155i
$126$		0			0
$127$	−15.0230	−	8.67351i	−1.33307	−	0.769650i	−0.347303	−	0.937753i	$-0.612902\pi$
$127$	−15.0230	−	8.67351i	−1.33307	−	0.769650i	−0.985769	+	0.168103i	$0.946236\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−5.80009	+	5.59991i	−0.508701	+	0.491145i
$131$	−14.1654			−1.23764			−0.618818	−	0.785534i	$-0.712388\pi$
$131$	−14.1654			−1.23764			−0.618818	+	0.785534i	$0.712388\pi$
$132$		0			0
$133$	6.29941	+	3.63697i	0.546228	+	0.315365i
$134$	0.937098	+	1.62310i	0.0809530	+	0.140215i
$135$		0			0
$136$	−0.210702	+	0.121649i	−0.0180675	+	0.0104313i
$137$	−3.66709	−	6.35158i	−0.313300	−	0.542652i	0.665774	−	0.746153i	$-0.268101\pi$
$137$	−3.66709	−	6.35158i	−0.313300	−	0.542652i	−0.979075	+	0.203501i	$0.934768\pi$
$138$		0			0
$139$	7.10185	+	12.3008i	0.602371	+	1.04334i	0.992461	+	0.122561i	$0.0391107\pi$
$139$	7.10185	+	12.3008i	0.602371	+	1.04334i	−0.390090	+	0.920777i	$0.627556\pi$
$140$	−2.82306	+	2.36198i	−0.238592	+	0.199624i
$141$		0			0
$142$			7.54060i			0.632793i
$143$	7.79974	+	3.79144i	0.652247	+	0.317056i
$144$		0			0
$145$	0.0760190	−	0.0636031i	0.00631303	−	0.00528195i
$146$	−0.851850	+	1.47545i	−0.0704996	+	0.122109i
$147$		0			0
$148$	−8.94829			−0.735545
$149$	9.61623	−	5.55193i	0.787792	−	0.454832i	−0.0513926	−	0.998679i	$-0.516366\pi$
$149$	9.61623	−	5.55193i	0.787792	−	0.454832i	0.839185	+	0.543847i	$0.183033\pi$
$150$		0			0
$151$			0.874663i			0.0711791i	0.999366	+	0.0355895i	$0.0113309\pi$
$151$			0.874663i			0.0711791i	−0.999366	+	0.0355895i	$0.988669\pi$
$152$	3.82681	−	2.20941i	0.310395	−	0.179207i
$153$		0			0
$154$	3.42896	+	1.97971i	0.276313	+	0.159530i
$155$	−3.25888	+	8.91414i	−0.261759	+	0.716001i
$156$		0			0
$157$		−	15.5085i		−	1.23771i	−0.785504	−	0.618856i	$-0.787596\pi$
$157$		−	15.5085i		−	1.23771i	0.785504	−	0.618856i	$-0.212404\pi$
$158$	−3.39854	+	5.88644i	−0.270373	+	0.468300i
$159$		0			0
$160$	0.385150	+	2.20265i	0.0304488	+	0.174135i
$161$			14.1942i			1.11866i
$162$		0			0
$163$	−10.9464	−	18.9597i	−0.857388	−	1.48504i	−0.874411	−	0.485185i	$-0.838752\pi$
$163$	−10.9464	−	18.9597i	−0.857388	−	1.48504i	0.0170229	−	0.999855i	$-0.494581\pi$
$164$			0.243297i			0.0189983i
$165$		0			0
$166$	−8.74932	+	15.1543i	−0.679079	+	1.17620i
$167$	−2.64815	+	4.58673i	−0.204920	+	0.354932i	−0.950107	−	0.311923i	$-0.899027\pi$
$167$	−2.64815	+	4.58673i	−0.204920	+	0.354932i	0.745187	+	0.666855i	$0.232360\pi$
$168$		0			0
$169$	12.8687	−	1.84326i	0.989897	−	0.141789i
$170$	−0.186797	+	0.510955i	−0.0143267	+	0.0391884i
$171$		0			0
$172$	5.82728	+	3.36438i	0.444326	+	0.256532i
$173$	−14.9469	+	8.62958i	−1.13639	+	0.656095i	−0.945534	−	0.325523i	$-0.894460\pi$
$173$	−14.9469	+	8.62958i	−1.13639	+	0.656095i	−0.190856	+	0.981618i	$0.561126\pi$
$174$		0			0
$175$	−1.45233	+	8.10148i	−0.109786	+	0.612414i
$176$	2.08305	−	1.20265i	0.157016	−	0.0906530i
$177$		0			0
$178$	−8.69772	+	5.02163i	−0.651922	+	0.376387i
$179$	4.17781	−	7.23617i	0.312264	−	0.540857i	−0.666588	−	0.745426i	$-0.732246\pi$
$179$	4.17781	−	7.23617i	0.312264	−	0.540857i	0.978852	+	0.204569i	$0.0655794\pi$
$180$		0			0
$181$	12.7335			0.946476			0.473238	−	0.880935i	$-0.343085\pi$
$181$	12.7335			0.946476			0.473238	+	0.880935i	$0.343085\pi$
$182$	5.92018	−	0.421840i	0.438833	−	0.0312689i
$183$		0			0
$184$	7.46758	+	4.31141i	0.550517	+	0.317841i
$185$	−15.3461	+	12.8397i	−1.12827	+	0.943991i
$186$		0			0
$187$	0.585202			0.0427942
$188$	−3.64780	−	6.31817i	−0.266043	−	0.460800i
$189$		0			0
$190$	3.39265	−	9.28007i	0.246129	−	0.673247i
$191$	0.207632	+	0.359629i	0.0150237	+	0.0260219i	0.873440	−	0.486933i	$-0.161884\pi$
$191$	0.207632	+	0.359629i	0.0150237	+	0.0260219i	−0.858416	+	0.512955i	$0.828551\pi$
$192$		0			0
$193$	12.9918	−	22.5025i	0.935173	−	1.61977i	0.160849	−	0.986979i	$-0.448577\pi$
$193$	12.9918	−	22.5025i	0.935173	−	1.61977i	0.774324	−	0.632789i	$-0.218090\pi$
$194$	−16.5129			−1.18556
$195$		0			0
$196$	−4.29027			−0.306448
$197$	−7.72121	+	13.3735i	−0.550113	+	0.952824i	0.448152	+	0.893957i	$0.352082\pi$
$197$	−7.72121	+	13.3735i	−0.550113	+	0.952824i	−0.998266	+	0.0588672i	$0.981251\pi$
$198$		0			0
$199$	6.85286	+	11.8695i	0.485787	+	0.841407i	0.999867	−	0.0163352i	$-0.00519988\pi$
$199$	6.85286	+	11.8695i	0.485787	+	0.841407i	−0.514080	+	0.857742i	$0.671867\pi$
$200$	3.82105	+	3.22484i	0.270189	+	0.228031i
$201$		0			0
$202$	−5.66777	−	9.81687i	−0.398783	−	0.690712i
$203$	−0.0729671			−0.00512129
$204$		0			0
$205$	0.349101	+	0.417249i	0.0243823	+	0.0291419i
$206$	−5.18029	−	2.99084i	−0.360928	−	0.208382i
$207$		0			0
$208$	1.57629	−	3.24273i	0.109296	−	0.224843i
$209$	−10.6286			−0.735193
$210$		0			0
$211$	8.05616	−	13.9537i	0.554609	−	0.960611i	−0.443325	−	0.896361i	$-0.646201\pi$
$211$	8.05616	−	13.9537i	0.554609	−	0.960611i	0.997934	−	0.0642497i	$-0.0204654\pi$
$212$	−2.11841	+	1.22307i	−0.145493	+	0.0840005i
$213$		0			0
$214$	9.24559	−	5.33795i	0.632016	−	0.364894i
$215$	14.8211	−	2.59159i	1.01079	−	0.176745i
$216$		0			0
$217$	6.05101	−	3.49355i	0.410769	−	0.237158i
$218$	−8.23316	−	4.75342i	−0.557620	−	0.321942i
$219$		0			0
$220$	1.84672	−	5.05142i	0.124506	−	0.340567i
$221$	0.726600	−	0.491496i	0.0488764	−	0.0330616i
$222$		0			0
$223$	−5.55886	+	9.62823i	−0.372249	+	0.644754i	−0.989911	−	0.141690i	$-0.954747\pi$
$223$	−5.55886	+	9.62823i	−0.372249	+	0.644754i	0.617662	+	0.786443i	$0.288080\pi$
$224$	0.823063	−	1.42559i	0.0549932	−	0.0952510i
$225$		0			0
$226$			3.59612i			0.239210i
$227$	−11.0399	−	19.1217i	−0.732747	−	1.26915i	−0.955705	−	0.294327i	$-0.904905\pi$
$227$	−11.0399	−	19.1217i	−0.732747	−	1.26915i	0.222958	−	0.974828i	$-0.428429\pi$
$228$		0			0
$229$			10.3397i			0.683266i	0.939834	+	0.341633i	$0.110980\pi$
$229$			10.3397i			0.683266i	−0.939834	+	0.341633i	$0.889020\pi$
$230$	18.9930	−	3.32108i	1.25236	−	0.218985i
$231$		0			0
$232$	−0.0221633	+	0.0383880i	−0.00145509	+	0.00252029i
$233$		−	21.8928i		−	1.43425i	−0.696947	−	0.717123i	$-0.745459\pi$
$233$		−	21.8928i		−	1.43425i	0.696947	−	0.717123i	$-0.254541\pi$
$234$		0			0
$235$	−15.3217	−	5.60137i	−0.999475	−	0.365393i
$236$	−8.35669	−	4.82474i	−0.543974	−	0.314064i
$237$		0			0
$238$	0.346841	−	0.200249i	0.0224824	−	0.0129802i
$239$			26.2510i			1.69804i	0.528362	+	0.849019i	$0.322806\pi$
$239$			26.2510i			1.69804i	−0.528362	+	0.849019i	$0.677194\pi$
$240$		0			0
$241$	22.5952	−	13.0454i	1.45549	−	0.840326i	0.456703	−	0.889619i	$-0.349030\pi$
$241$	22.5952	−	13.0454i	1.45549	−	0.840326i	0.998784	+	0.0492931i	$0.0156968\pi$
$242$	5.21455			0.335204
$243$		0			0
$244$	1.31630	−	2.27990i	0.0842676	−	0.145956i
$245$	−7.35770	+	6.15600i	−0.470066	+	0.393292i
$246$		0			0
$247$	−13.1967	+	8.92666i	−0.839684	+	0.567990i
$248$		−	4.24458i		−	0.269531i
$249$		0			0
$250$	11.1802	+	0.0478026i	0.707100	+	0.00302330i
$251$	0.312397	+	0.541088i	0.0197183	+	0.0341532i	0.875716	−	0.482826i	$-0.160390\pi$
$251$	0.312397	+	0.541088i	0.0197183	+	0.0341532i	−0.855998	+	0.516979i	$0.827056\pi$
$252$		0			0
$253$	−10.3702	−	17.9617i	−0.651970	−	1.12924i
$254$	15.0230	−	8.67351i	0.942624	−	0.544224i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−12.0758	−	6.97195i	−0.753266	−	0.434898i	0.0736066	−	0.997287i	$-0.476549\pi$
$257$	−12.0758	−	6.97195i	−0.753266	−	0.434898i	−0.826873	+	0.562389i	$0.809882\pi$
$258$		0			0
$259$	14.7300			0.915278
$260$	−1.94962	−	7.82298i	−0.120910	−	0.485160i
$261$		0			0
$262$	7.08270	−	12.2676i	0.437571	−	0.757894i
$263$	−16.8325	−	9.71828i	−1.03794	−	0.599255i	−0.118690	−	0.992931i	$-0.537870\pi$
$263$	−16.8325	−	9.71828i	−1.03794	−	0.599255i	−0.919249	+	0.393677i	$0.871203\pi$
$264$		0			0
$265$	−1.87808	+	5.13718i	−0.115369	+	0.315574i
$266$	−6.29941	+	3.63697i	−0.386242	+	0.222997i
$267$		0			0
$268$	−1.87420			−0.114485
$269$	1.50069	+	2.59928i	0.0914989	+	0.158481i	0.908142	−	0.418662i	$-0.137501\pi$
$269$	1.50069	+	2.59928i	0.0914989	+	0.158481i	−0.816643	+	0.577143i	$0.804168\pi$
$270$		0			0
$271$	−24.6538	−	14.2339i	−1.49761	−	0.864645i	−0.497613	−	0.867399i	$-0.665790\pi$
$271$	−24.6538	−	14.2339i	−1.49761	−	0.864645i	−0.999996	+	0.00275396i	$0.999123\pi$
$272$		−	0.243297i		−	0.0147521i
$273$		0			0
$274$	7.33417			0.443074
$275$	−4.08107	−	11.3129i	−0.246098	−	0.682192i
$276$		0			0
$277$	0.738423	−	0.426329i	0.0443676	−	0.0256156i	−0.477652	−	0.878549i	$-0.658512\pi$
$277$	0.738423	−	0.426329i	0.0443676	−	0.0256156i	0.522020	+	0.852933i	$0.325179\pi$
$278$	−14.2037			−0.851882
$279$		0			0
$280$	−0.634006	−	3.62584i	−0.0378891	−	0.216685i
$281$		−	15.6851i		−	0.935697i	−0.883809	−	0.467848i	$-0.845029\pi$
$281$		−	15.6851i		−	0.935697i	0.883809	−	0.467848i	$-0.154971\pi$
$282$		0			0
$283$	7.00390	+	4.04370i	0.416339	+	0.240373i	0.693510	−	0.720447i	$-0.256063\pi$
$283$	7.00390	+	4.04370i	0.416339	+	0.240373i	−0.277171	+	0.960821i	$0.589397\pi$
$284$	−6.53035	−	3.77030i	−0.387505	−	0.223726i
$285$		0			0
$286$	−7.18335	+	4.85905i	−0.424760	+	0.287322i
$287$		−	0.400498i		−	0.0236406i
$288$		0			0
$289$	−8.47040	+	14.6712i	−0.498259	+	0.863010i
$290$	0.0170724	+	0.0976359i	0.00100253	+	0.00573338i
$291$		0			0
$292$	−0.851850	−	1.47545i	−0.0498508	−	0.0863440i
$293$	0.967192	+	1.67523i	0.0565040	+	0.0978677i	0.892894	−	0.450267i	$-0.148671\pi$
$293$	0.967192	+	1.67523i	0.0565040	+	0.0978677i	−0.836390	+	0.548135i	$0.815338\pi$
$294$		0			0
$295$	−21.2544	+	3.71650i	−1.23748	+	0.216383i
$296$	4.47415	−	7.74945i	0.260054	−	0.450427i
$297$		0			0
$298$			11.1039i			0.643229i
$299$	−27.9615	−	13.5920i	−1.61705	−	0.786047i
$300$		0			0
$301$	−9.59244	−	5.53820i	−0.552899	−	0.319216i
$302$	−0.757480	−	0.437332i	−0.0435881	−	0.0251656i
$303$		0			0
$304$			4.41882i			0.253437i
$305$	−1.01395	−	5.79870i	−0.0580585	−	0.332033i
$306$		0			0
$307$	−12.4384			−0.709894			−0.354947	−	0.934886i	$-0.615501\pi$
$307$	−12.4384			−0.709894			−0.354947	+	0.934886i	$0.615501\pi$
$308$	−3.42896	+	1.97971i	−0.195383	+	0.112804i
$309$		0			0
$310$	−6.09043	−	7.27934i	−0.345913	−	0.413439i
$311$	18.3700			1.04167			0.520835	−	0.853657i	$-0.325621\pi$
$311$	18.3700			1.04167			0.520835	+	0.853657i	$0.325621\pi$
$312$		0			0
$313$			31.9445i			1.80561i	0.430051	+	0.902804i	$0.358496\pi$
$313$			31.9445i			1.80561i	−0.430051	+	0.902804i	$0.641504\pi$
$314$	13.4307	+	7.75425i	0.757941	+	0.437597i
$315$		0			0
$316$	−3.39854	−	5.88644i	−0.191183	−	0.331138i
$317$	23.3625			1.31217			0.656083	−	0.754689i	$-0.272212\pi$
$317$	23.3625			1.31217			0.656083	+	0.754689i	$0.272212\pi$
$318$		0			0
$319$	0.0923344	−	0.0533093i	0.00516973	−	0.00298475i
$320$	−2.10012	−	0.767774i	−0.117401	−	0.0429199i
$321$		0			0
$322$	−12.2926	−	7.09712i	−0.685038	−	0.395507i
$323$	−0.537543	+	0.931052i	−0.0299097	+	0.0518051i
$324$		0			0
$325$	−14.5685	−	10.6187i	−0.808117	−	0.589022i
$326$	21.8928			1.21253
$327$		0			0
$328$	−0.210702	−	0.121649i	−0.0116341	−	0.00671692i
$329$	6.00474	+	10.4005i	0.331052	+	0.573399i
$330$		0			0
$331$	−18.5879	+	10.7317i	−1.02168	+	0.589868i	−0.914590	−	0.404382i	$-0.867487\pi$
$331$	−18.5879	+	10.7317i	−1.02168	+	0.589868i	−0.107090	+	0.994249i	$0.534153\pi$
$332$	−8.74932	−	15.1543i	−0.480181	−	0.831698i
$333$		0			0
$334$	−2.64815	−	4.58673i	−0.144900	−	0.250975i
$335$	−3.21420	+	2.68924i	−0.175610	+	0.146929i
$336$		0			0
$337$			14.3561i			0.782026i	0.920385	+	0.391013i	$0.127875\pi$
$337$			14.3561i			0.782026i	−0.920385	+	0.391013i	$0.872125\pi$
$338$	−4.83802	+	12.0662i	−0.263154	+	0.656316i
$339$		0			0
$340$	−0.349101	−	0.417249i	−0.0189327	−	0.0226285i
$341$	−5.10473	+	8.84165i	−0.276437	+	0.478802i
$342$		0			0
$343$	18.5852			1.00351
$344$	−5.82728	+	3.36438i	−0.314186	+	0.181395i
$345$		0			0
$346$		−	17.2592i		−	0.927858i
$347$	0.576005	−	0.332557i	0.0309216	−	0.0178526i	−0.484460	−	0.874814i	$-0.660984\pi$
$347$	0.576005	−	0.332557i	0.0309216	−	0.0178526i	0.515381	+	0.856961i	$0.327650\pi$
$348$		0			0
$349$	3.25007	+	1.87643i	0.173972	+	0.100443i	0.584458	−	0.811424i	$-0.301307\pi$
$349$	3.25007	+	1.87643i	0.173972	+	0.100443i	−0.410485	+	0.911867i	$0.634641\pi$
$350$	−6.28992	−	5.30850i	−0.336210	−	0.283751i
$351$		0			0
$352$			2.40530i			0.128203i
$353$	2.28180	−	3.95219i	0.121448	−	0.210354i	−0.798891	−	0.601476i	$-0.794580\pi$
$353$	2.28180	−	3.95219i	0.121448	−	0.210354i	0.920339	+	0.391122i	$0.127913\pi$
$354$		0			0
$355$	−16.6093	+	2.90426i	−0.881530	+	0.154142i
$356$		−	10.0433i		−	0.532292i
$357$		0			0
$358$	4.17781	+	7.23617i	0.220804	+	0.382444i
$359$			4.75785i			0.251110i	0.992087	+	0.125555i	$0.0400711\pi$
$359$			4.75785i			0.251110i	−0.992087	+	0.125555i	$0.959929\pi$
$360$		0			0
$361$	0.262979	−	0.455494i	0.0138410	−	0.0239733i
$362$	−6.36677	+	11.0276i	−0.334630	+	0.579596i
$363$		0			0
$364$	−2.59477	+	5.33795i	−0.136003	+	0.279784i
$365$	−3.57798	−	1.30806i	−0.187280	−	0.0684668i
$366$		0			0
$367$	1.29432	+	0.747277i	0.0675630	+	0.0390075i	0.533401	−	0.845863i	$-0.320914\pi$
$367$	1.29432	+	0.747277i	0.0675630	+	0.0390075i	−0.465838	+	0.884870i	$0.654247\pi$
$368$	−7.46758	+	4.31141i	−0.389274	+	0.224748i
$369$		0			0
$370$	−3.44644	−	19.7099i	−0.179172	−	1.02467i
$371$	3.48717	−	2.01332i	0.181045	−	0.104526i
$372$		0			0
$373$	17.8323	−	10.2955i	0.923323	−	0.533081i	0.0386291	−	0.999254i	$-0.487701\pi$
$373$	17.8323	−	10.2955i	0.923323	−	0.533081i	0.884694	+	0.466173i	$0.154368\pi$
$374$	−0.292601	+	0.506800i	−0.0151300	+	0.0262060i
$375$		0			0
$376$	7.29560			0.376242
$377$	0.0698714	−	0.143739i	0.00359856	−	0.00740295i
$378$		0			0
$379$	−18.4173	−	10.6332i	−0.946032	−	0.546192i	−0.0541858	−	0.998531i	$-0.517256\pi$
$379$	−18.4173	−	10.6332i	−0.946032	−	0.546192i	−0.891846	+	0.452339i	$0.850590\pi$
$380$	6.34045	+	7.57816i	0.325258	+	0.388751i
$381$		0			0
$382$	−0.415264			−0.0212468
$383$	−5.31095	−	9.19884i	−0.271377	−	0.470039i	0.697838	−	0.716256i	$-0.254146\pi$
$383$	−5.31095	−	9.19884i	−0.271377	−	0.470039i	−0.969215	+	0.246217i	$0.920812\pi$
$384$		0			0
$385$	−3.03994	+	8.31527i	−0.154930	+	0.423786i
$386$	12.9918	+	22.5025i	0.661267	+	1.14535i
$387$		0			0
$388$	8.25647	−	14.3006i	0.419159	−	0.726004i
$389$	37.0443			1.87822			0.939111	−	0.343613i	$-0.111651\pi$
$389$	37.0443			1.87822			0.939111	+	0.343613i	$0.111651\pi$
$390$		0			0
$391$	−2.09791			−0.106096
$392$	2.14514	−	3.71548i	0.108346	−	0.187660i
$393$		0			0
$394$	−7.72121	−	13.3735i	−0.388989	−	0.673749i
$395$	−14.2747	−	5.21862i	−0.718238	−	0.262577i
$396$		0			0
$397$	−0.843593	−	1.46115i	−0.0423387	−	0.0733328i	0.844079	−	0.536218i	$-0.180148\pi$
$397$	−0.843593	−	1.46115i	−0.0423387	−	0.0733328i	−0.886418	+	0.462885i	$0.846814\pi$
$398$	−13.7057			−0.687006
$399$		0			0
$400$	−4.70332	+	1.69670i	−0.235166	+	0.0848351i
$401$	−17.2949	−	9.98524i	−0.863668	−	0.498639i	0.00157101	−	0.999999i	$-0.499500\pi$
$401$	−17.2949	−	9.98524i	−0.863668	−	0.498639i	−0.865239	+	0.501360i	$0.832833\pi$
$402$		0			0
$403$	1.08772	+	15.2653i	0.0541834	+	0.760420i
$404$	11.3355			0.563964
$405$		0			0
$406$	0.0364836	−	0.0631914i	0.00181065	−	0.00313614i
$407$	−18.6397	+	10.7616i	−0.923936	+	0.533435i
$408$		0			0
$409$	10.6603	−	6.15471i	0.527117	−	0.304331i	−0.212725	−	0.977112i	$-0.568234\pi$
$409$	10.6603	−	6.15471i	0.527117	−	0.304331i	0.739842	+	0.672781i	$0.234900\pi$
$410$	−0.535898	+	0.0937060i	−0.0264661	+	0.00462781i
$411$		0			0
$412$	5.18029	−	2.99084i	0.255214	−	0.147348i
$413$	13.7562	+	7.94212i	0.676896	+	0.390806i
$414$		0			0
$415$	−36.7493	−	13.4350i	−1.80395	−	0.659498i
$416$	2.02015	+	2.98647i	0.0990458	+	0.146424i
$417$		0			0
$418$	5.31428	−	9.20461i	0.259930	−	0.450212i
$419$	−11.0411	+	19.1238i	−0.539393	+	0.934256i	0.459544	+	0.888155i	$0.348013\pi$
$419$	−11.0411	+	19.1238i	−0.539393	+	0.934256i	−0.998937	+	0.0461011i	$0.985320\pi$
$420$		0			0
$421$			8.98036i			0.437676i	0.975761	+	0.218838i	$0.0702266\pi$
$421$			8.98036i			0.437676i	−0.975761	+	0.218838i	$0.929773\pi$
$422$	8.05616	+	13.9537i	0.392168	+	0.679254i
$423$		0			0
$424$		−	2.44613i		−	0.118795i
$425$	−1.19740	−	0.214655i	−0.0580824	−	0.0104123i
$426$		0			0
$427$	−2.16680	+	3.75300i	−0.104859	+	0.181621i
$428$			10.6759i			0.516039i
$429$		0			0
$430$	−5.16617	+	14.1312i	−0.249135	+	0.681469i
$431$	−7.16090	−	4.13435i	−0.344928	−	0.199145i	0.317521	−	0.948251i	$-0.397150\pi$
$431$	−7.16090	−	4.13435i	−0.344928	−	0.199145i	−0.662449	+	0.749107i	$0.730483\pi$
$432$		0			0
$433$	17.1825	−	9.92035i	0.825740	−	0.476741i	−0.0266515	−	0.999645i	$-0.508484\pi$
$433$	17.1825	−	9.92035i	0.825740	−	0.476741i	0.852392	+	0.522903i	$0.175151\pi$
$434$			6.98710i			0.335392i
$435$		0			0
$436$	8.23316	−	4.75342i	0.394297	−	0.227647i
$437$	38.1027			1.82270
$438$		0			0
$439$	−14.4415	+	25.0134i	−0.689255	+	1.19382i	0.282824	+	0.959172i	$0.408729\pi$
$439$	−14.4415	+	25.0134i	−0.689255	+	1.19382i	−0.972079	+	0.234653i	$0.924605\pi$
$440$	3.45130	+	4.12502i	0.164534	+	0.196653i
$441$		0			0
$442$	0.0623479	+	0.875002i	0.00296559	+	0.0416196i
$443$		−	5.76986i		−	0.274134i	−0.990562	−	0.137067i	$-0.956232\pi$
$443$		−	5.76986i		−	0.274134i	0.990562	−	0.137067i	$-0.0437676\pi$
$444$		0			0
$445$	−14.4108	−	17.2239i	−0.683138	−	0.816493i
$446$	−5.55886	−	9.62823i	−0.263220	−	0.455910i
$447$		0			0
$448$	0.823063	+	1.42559i	0.0388861	+	0.0673526i
$449$	33.9034	−	19.5741i	1.60000	−	0.923760i	0.608514	−	0.793543i	$-0.291766\pi$
$449$	33.9034	−	19.5741i	1.60000	−	0.923760i	0.991486	−	0.130217i	$-0.0415674\pi$
$450$		0			0
$451$	0.292601	+	0.506800i	0.0137780	+	0.0238643i
$452$	−3.11433	−	1.79806i	−0.146486	−	0.0845736i
$453$		0			0
$454$	22.0799			1.03626
$455$	3.20932	+	12.8776i	0.150455	+	0.603711i
$456$		0			0
$457$	−12.2403	+	21.2008i	−0.572575	+	0.991730i	0.423725	+	0.905791i	$0.360722\pi$
$457$	−12.2403	+	21.2008i	−0.572575	+	0.991730i	−0.996300	+	0.0859387i	$0.972611\pi$
$458$	−8.95443	−	5.16984i	−0.418413	−	0.241571i
$459$		0			0
$460$	−6.62037	+	18.1090i	−0.308677	+	0.844336i
$461$	−3.02923	+	1.74893i	−0.141085	+	0.0814557i	−0.568881	−	0.822420i	$-0.692624\pi$
$461$	−3.02923	+	1.74893i	−0.141085	+	0.0814557i	0.427796	+	0.903875i	$0.359290\pi$
$462$		0			0
$463$	18.3063			0.850767			0.425384	−	0.905013i	$-0.360139\pi$
$463$	18.3063			0.850767			0.425384	+	0.905013i	$0.360139\pi$
$464$	−0.0221633	−	0.0383880i	−0.00102891	−	0.00178212i
$465$		0			0
$466$	18.9597	+	10.9464i	0.878292	+	0.507082i
$467$		−	6.46019i		−	0.298942i	−0.988766	−	0.149471i	$-0.952243\pi$
$467$		−	6.46019i		−	0.298942i	0.988766	−	0.149471i	$-0.0477571\pi$
$468$		0			0
$469$	3.08516			0.142460
$470$	12.5118	−	10.4683i	0.577125	−	0.482865i
$471$		0			0
$472$	8.35669	−	4.82474i	0.384648	−	0.222077i
$473$	16.1847			0.744172
$474$		0			0
$475$	21.7474	+	3.89860i	0.997840	+	0.178880i
$476$			0.400498i			0.0183568i
$477$		0			0
$478$	−22.7341	−	13.1255i	−1.03983	−	0.600347i
$479$	−26.5980	−	15.3564i	−1.21529	−	0.701651i	−0.251387	−	0.967887i	$-0.580887\pi$
$479$	−26.5980	−	15.3564i	−1.21529	−	0.701651i	−0.963908	+	0.266236i	$0.914220\pi$
$480$		0			0
$481$	−14.1051	+	29.0169i	−0.643136	+	1.32306i
$482$			26.0907i			1.18840i
$483$		0			0
$484$	−2.60727	+	4.51593i	−0.118512	+	0.205270i
$485$	−6.35996	−	36.3722i	−0.288791	−	1.65158i
$486$		0			0
$487$	6.23335	+	10.7965i	0.282460	+	0.489235i	0.971990	−	0.235022i	$-0.0755162\pi$
$487$	6.23335	+	10.7965i	0.282460	+	0.489235i	−0.689530	+	0.724257i	$0.742183\pi$
$488$	1.31630	+	2.27990i	0.0595862	+	0.103206i
$489$		0			0
$490$	−1.65240	−	9.44996i	−0.0746478	−	0.426906i
$491$	−1.29120	+	2.23642i	−0.0582710	+	0.100928i	−0.893689	−	0.448686i	$-0.851892\pi$
$491$	−1.29120	+	2.23642i	−0.0582710	+	0.100928i	0.835418	+	0.549615i	$0.185225\pi$
$492$		0			0
$493$		−	0.0107845i		−	0.000485711i
$494$	−1.13238	−	15.8920i	−0.0509480	−	0.715014i
$495$		0			0
$496$	3.67591	+	2.12229i	0.165053	+	0.0952935i
$497$	10.7498	+	6.20639i	0.482194	+	0.278395i
$498$		0			0
$499$		−	20.2443i		−	0.906261i	−0.891444	−	0.453130i	$-0.850307\pi$
$499$		−	20.2443i		−	0.906261i	0.891444	−	0.453130i	$-0.149693\pi$
$500$	−5.63152	+	9.65847i	−0.251849	+	0.431940i
$501$		0			0
$502$	−0.624794			−0.0278859
$503$	7.33148	−	4.23283i	0.326894	−	0.188733i	−0.327567	−	0.944828i	$-0.606229\pi$
$503$	7.33148	−	4.23283i	0.326894	−	0.188733i	0.654461	+	0.756095i	$0.272895\pi$
$504$		0			0
$505$	19.4402	−	16.2651i	0.865076	−	0.723786i
$506$	20.7404			0.922024
$507$		0			0
$508$			17.3470i			0.769650i
$509$	33.4172	+	19.2935i	1.48119	+	0.855167i	0.999773	−	0.0213225i	$-0.00678766\pi$
$509$	33.4172	+	19.2935i	1.48119	+	0.855167i	0.481421	+	0.876490i	$0.340121\pi$
$510$		0			0
$511$	1.40225	+	2.42877i	0.0620320	+	0.107443i
$512$	1.00000			0.0441942
$513$		0			0
$514$	12.0758	−	6.97195i	0.532640	−	0.307520i
$515$	4.59258	−	12.5623i	0.202373	−	0.553560i
$516$		0			0
$517$	−15.1971	−	8.77404i	−0.668367	−	0.385882i
$518$	−7.36500	+	12.7566i	−0.323600	+	0.560491i
$519$		0			0
$520$	7.74971	+	2.22307i	0.339847	+	0.0974879i
$521$	−12.5345			−0.549148			−0.274574	−	0.961566i	$-0.588537\pi$
$521$	−12.5345			−0.549148			−0.274574	+	0.961566i	$0.588537\pi$
$522$		0			0
$523$	11.0846	+	6.39970i	0.484696	+	0.279839i	0.722371	−	0.691505i	$-0.243052\pi$
$523$	11.0846	+	6.39970i	0.484696	+	0.279839i	−0.237676	+	0.971345i	$0.576386\pi$
$524$	7.08270	+	12.2676i	0.309409	+	0.535912i
$525$		0			0
$526$	16.8325	−	9.71828i	0.733934	−	0.423737i
$527$	0.516347	+	0.894339i	0.0224924	+	0.0389580i
$528$		0			0
$529$	25.6765	+	44.4729i	1.11637	+	1.93361i
$530$	−3.50989	−	4.19505i	−0.152460	−	0.182221i
$531$		0			0
$532$		−	7.27393i		−	0.315365i
$533$	0.788948	+	0.383506i	0.0341731	+	0.0166115i
$534$		0			0
$535$	15.3186	+	18.3089i	0.662279	+	0.791562i
$536$	0.937098	−	1.62310i	0.0404765	−	0.0701073i
$537$		0			0
$538$	−3.00139			−0.129399
$539$	−8.93684	+	5.15969i	−0.384937	+	0.222243i
$540$		0			0
$541$			24.9605i			1.07314i	0.843857	+	0.536568i	$0.180280\pi$
$541$			24.9605i			1.07314i	−0.843857	+	0.536568i	$0.819720\pi$
$542$	24.6538	−	14.2339i	1.05897	−	0.611396i
$543$		0			0
$544$	0.210702	+	0.121649i	0.00903376	+	0.00521564i
$545$	7.29910	−	19.9655i	0.312659	−	0.855229i
$546$		0			0
$547$		−	10.4152i		−	0.445321i	−0.974896	−	0.222660i	$-0.928526\pi$
$547$		−	10.4152i		−	0.445321i	0.974896	−	0.222660i	$-0.0714741\pi$
$548$	−3.66709	+	6.35158i	−0.156650	+	0.271326i
$549$		0			0
$550$	11.8378	+	2.12213i	0.504764	+	0.0904878i
$551$			0.195871i			0.00834439i
$552$		0			0
$553$	5.59442	+	9.68981i	0.237899	+	0.412053i
$554$			0.852658i			0.0362260i
$555$		0			0
$556$	7.10185	−	12.3008i	0.301186	−	0.521669i
$557$	−0.697392	+	1.20792i	−0.0295495	+	0.0511812i	−0.880422	−	0.474191i	$-0.842741\pi$
$557$	−0.697392	+	1.20792i	−0.0295495	+	0.0511812i	0.850872	+	0.525372i	$0.176074\pi$
$558$		0			0
$559$	20.0953	−	13.5931i	0.849939	−	0.574926i
$560$	3.45707	+	1.26385i	0.146088	+	0.0534075i
$561$		0			0
$562$	13.5837	+	7.84257i	0.572995	+	0.330819i
$563$	14.0404	−	8.10624i	0.591733	−	0.341637i	−0.174049	−	0.984737i	$-0.555685\pi$
$563$	14.0404	−	8.10624i	0.591733	−	0.341637i	0.765782	+	0.643100i	$0.222352\pi$
$564$		0			0
$565$	−7.92099	+	1.38505i	−0.333238	+	0.0582693i
$566$	−7.00390	+	4.04370i	−0.294396	+	0.169970i
$567$		0			0
$568$	6.53035	−	3.77030i	0.274007	−	0.158198i
$569$	−19.6198	+	33.9825i	−0.822505	+	1.42462i	0.0813055	+	0.996689i	$0.474091\pi$
$569$	−19.6198	+	33.9825i	−0.822505	+	1.42462i	−0.903811	+	0.427932i	$0.859242\pi$
$570$		0			0
$571$	−16.0498			−0.671662			−0.335831	−	0.941922i	$-0.609017\pi$
$571$	−16.0498			−0.671662			−0.335831	+	0.941922i	$0.609017\pi$
$572$	−0.616387	−	8.65049i	−0.0257724	−	0.361695i
$573$		0			0
$574$	0.346841	+	0.200249i	0.0144769	+	0.00835823i
$575$	14.6303	+	40.5558i	0.610127	+	1.69130i
$576$		0			0
$577$	28.5363			1.18798			0.593992	−	0.804471i	$-0.297551\pi$
$577$	28.5363			1.18798			0.593992	+	0.804471i	$0.297551\pi$
$578$	−8.47040	−	14.6712i	−0.352322	−	0.610240i
$579$		0			0
$580$	−0.0930914	−	0.0340328i	−0.00386541	−	0.00141314i
$581$	14.4025	+	24.9458i	0.597515	+	1.03493i
$582$		0			0
$583$	−2.94183	+	5.09541i	−0.121838	+	0.211030i
$584$	1.70370			0.0704996
$585$		0			0
$586$	−1.93438			−0.0799087
$587$	−22.5265	+	39.0171i	−0.929770	+	1.61041i	−0.146066	+	0.989275i	$0.546661\pi$
$587$	−22.5265	+	39.0171i	−0.929770	+	1.61041i	−0.783704	+	0.621134i	$0.786672\pi$
$588$		0			0
$589$	−9.37800	−	16.2432i	−0.386414	−	0.669289i
$590$	7.40862	−	20.2651i	0.305008	−	0.834301i
$591$		0			0
$592$	4.47415	+	7.74945i	0.183886	+	0.318500i
$593$	−37.0634			−1.52201			−0.761005	−	0.648746i	$-0.775294\pi$
$593$	−37.0634			−1.52201			−0.761005	+	0.648746i	$0.775294\pi$
$594$		0			0
$595$	0.574664	+	0.686844i	0.0235589	+	0.0281578i
$596$	−9.61623	−	5.55193i	−0.393896	−	0.227416i
$597$		0			0
$598$	25.7518	−	17.4193i	1.05307	−	0.712330i
$599$	−18.6309			−0.761238			−0.380619	−	0.924732i	$-0.624289\pi$
$599$	−18.6309			−0.761238			−0.380619	+	0.924732i	$0.624289\pi$
$600$		0			0
$601$	9.69008	−	16.7837i	0.395266	−	0.684622i	−0.597869	−	0.801594i	$-0.703986\pi$
$601$	9.69008	−	16.7837i	0.395266	−	0.684622i	0.993135	+	0.116972i	$0.0373189\pi$
$602$	9.59244	−	5.53820i	0.390958	−	0.225720i
$603$		0			0
$604$	0.757480	−	0.437332i	0.0308214	−	0.0177948i
$605$	2.00839	+	11.4858i	0.0816525	+	0.466965i
$606$		0			0
$607$	30.2066	−	17.4398i	1.22605	−	0.707858i	0.259846	−	0.965650i	$-0.416328\pi$
$607$	30.2066	−	17.4398i	1.22605	−	0.707858i	0.966200	+	0.257792i	$0.0829949\pi$
$608$	−3.82681	−	2.20941i	−0.155198	−	0.0896034i
$609$		0			0
$610$	5.52879	+	2.02124i	0.223854	+	0.0818378i
$611$	−26.2381	+	1.86959i	−1.06148	+	0.0756354i
$612$		0			0
$613$	−4.07179	+	7.05254i	−0.164458	+	0.284849i	−0.936463	−	0.350767i	$-0.885921\pi$
$613$	−4.07179	+	7.05254i	−0.164458	+	0.284849i	0.772005	+	0.635617i	$0.219254\pi$
$614$	6.21918	−	10.7719i	0.250986	−	0.434720i
$615$		0			0
$616$		−	3.95942i		−	0.159530i
$617$	16.7288	+	28.9752i	0.673477	+	1.16650i	0.976912	+	0.213644i	$0.0685332\pi$
$617$	16.7288	+	28.9752i	0.673477	+	1.16650i	−0.303435	+	0.952852i	$0.598133\pi$
$618$		0			0
$619$		−	41.1780i		−	1.65508i	−0.561404	−	0.827542i	$-0.689739\pi$
$619$		−	41.1780i		−	1.65508i	0.561404	−	0.827542i	$-0.310261\pi$
$620$	9.34931	−	1.63480i	0.375477	−	0.0656551i
$621$		0			0
$622$	−9.18502	+	15.9089i	−0.368286	+	0.637890i
$623$			16.5325i			0.662359i
$624$		0			0
$625$	4.20078	+	24.6445i	0.168031	+	0.985782i
$626$	−27.6647	−	15.9722i	−1.10571	−	0.638379i
$627$		0			0
$628$	−13.4307	+	7.75425i	−0.535945	+	0.309428i
$629$			2.17709i			0.0868065i
$630$		0			0
$631$	12.6839	−	7.32307i	0.504939	−	0.291527i	−0.225812	−	0.974171i	$-0.572503\pi$
$631$	12.6839	−	7.32307i	0.504939	−	0.291527i	0.730751	+	0.682644i	$0.239170\pi$
$632$	6.79707			0.270373
$633$		0			0
$634$	−11.6812	+	20.2325i	−0.463921	+	0.803535i
$635$	24.8908	+	29.7497i	0.987761	+	1.18058i
$636$		0			0
$637$	−6.76270	+	13.9122i	−0.267948	+	0.551222i
$638$			0.106619i			0.00422107i
$639$		0			0
$640$	1.71497	−	1.43487i	0.0677903	−	0.0567184i
$641$	−23.9793	−	41.5334i	−0.947125	−	1.64047i	−0.751439	−	0.659803i	$-0.770640\pi$
$641$	−23.9793	−	41.5334i	−0.947125	−	1.64047i	−0.195686	−	0.980667i	$-0.562693\pi$
$642$		0			0
$643$	−1.99884	−	3.46209i	−0.0788265	−	0.136531i	0.823917	−	0.566710i	$-0.191784\pi$
$643$	−1.99884	−	3.46209i	−0.0788265	−	0.136531i	−0.902744	+	0.430178i	$0.858451\pi$
$644$	12.2926	−	7.09712i	0.484395	−	0.279666i
$645$		0			0
$646$	−0.537543	−	0.931052i	−0.0211494	−	0.0366318i
$647$	20.4521	+	11.8080i	0.804053	+	0.464220i	0.844886	−	0.534946i	$-0.179668\pi$
$647$	20.4521	+	11.8080i	0.804053	+	0.464220i	−0.0408333	+	0.999166i	$0.513001\pi$
$648$		0			0
$649$	−23.2098			−0.911066
$650$	16.4804	−	7.30736i	0.646413	−	0.286618i
$651$		0			0
$652$	−10.9464	+	18.9597i	−0.428694	+	0.742520i
$653$	30.5411	+	17.6329i	1.19516	+	0.690029i	0.959473	−	0.281799i	$-0.0909312\pi$
$653$	30.5411	+	17.6329i	1.19516	+	0.690029i	0.235692	+	0.971828i	$0.424265\pi$
$654$		0			0
$655$	29.7491	+	10.8758i	1.16239	+	0.424954i
$656$	0.210702	−	0.121649i	0.00822652	−	0.00474958i
$657$		0			0
$658$	−12.0095			−0.468178
$659$	−12.6686	−	21.9427i	−0.493499	−	0.854765i	0.506473	−	0.862256i	$-0.330949\pi$
$659$	−12.6686	−	21.9427i	−0.493499	−	0.854765i	−0.999972	+	0.00749088i	$0.997616\pi$
$660$		0			0
$661$	4.21373	+	2.43280i	0.163895	+	0.0946248i	0.579704	−	0.814827i	$-0.303168\pi$
$661$	4.21373	+	2.43280i	0.163895	+	0.0946248i	−0.415809	+	0.909452i	$0.636502\pi$
$662$		−	21.4634i		−	0.834199i
$663$		0			0
$664$	17.4986			0.679079
$665$	−10.4372	−	12.4746i	−0.404736	−	0.483744i
$666$		0			0
$667$	−0.331012	+	0.191110i	−0.0128168	+	0.00739981i
$668$	5.29630			0.204920
$669$		0			0
$670$	−0.721847	−	4.12820i	−0.0278874	−	0.159486i
$671$		−	6.33219i		−	0.244452i
$672$		0			0
$673$	6.48493	+	3.74408i	0.249976	+	0.144324i	0.619753	−	0.784797i	$-0.287233\pi$
$673$	6.48493	+	3.74408i	0.249976	+	0.144324i	−0.369777	+	0.929120i	$0.620566\pi$
$674$	−12.4327	−	7.17805i	−0.478891	−	0.276488i
$675$		0			0
$676$	−8.03064	−	10.2230i	−0.308871	−	0.393191i
$677$			37.4181i			1.43810i	0.694961	+	0.719048i	$0.255422\pi$
$677$			37.4181i			1.43810i	−0.694961	+	0.719048i	$0.744578\pi$
$678$		0			0
$679$	−13.5912	+	23.5406i	−0.521582	+	0.903406i
$680$	0.535898	−	0.0937060i	0.0205508	−	0.00359346i
$681$		0			0
$682$	−5.10473	−	8.84165i	−0.195470	−	0.338564i
$683$	3.13940	+	5.43761i	0.120126	+	0.208064i	0.919817	−	0.392347i	$-0.128337\pi$
$683$	3.13940	+	5.43761i	0.120126	+	0.208064i	−0.799691	+	0.600411i	$0.795003\pi$
$684$		0			0
$685$	2.82476	+	16.1546i	0.107928	+	0.617236i
$686$	−9.29260	+	16.0953i	−0.354793	+	0.614520i
$687$		0			0
$688$		−	6.72876i		−	0.256532i
$689$	0.626851	+	8.79735i	0.0238811	+	0.335152i
$690$		0			0
$691$	−9.17461	−	5.29696i	−0.349019	−	0.201506i	0.315234	−	0.949014i	$-0.397917\pi$
$691$	−9.17461	−	5.29696i	−0.349019	−	0.201506i	−0.664253	+	0.747508i	$0.731250\pi$
$692$	14.9469	+	8.62958i	0.568195	+	0.328047i
$693$		0			0
$694$			0.665114i			0.0252474i
$695$	−5.47056	−	31.2858i	−0.207510	−	1.18674i
$696$		0			0
$697$	0.0591936			0.00224212
$698$	−3.25007	+	1.87643i	−0.123017	+	0.0710239i
$699$		0			0
$700$	7.74225	−	2.79298i	0.292630	−	0.105565i
$701$	29.6773			1.12090			0.560449	−	0.828189i	$-0.310629\pi$
$701$	29.6773			1.12090			0.560449	+	0.828189i	$0.310629\pi$
$702$		0			0
$703$		−	39.5409i		−	1.49131i
$704$	−2.08305	−	1.20265i	−0.0785078	−	0.0453265i
$705$		0			0
$706$	2.28180	+	3.95219i	0.0858766	+	0.148743i
$707$	−18.6597			−0.701771
$708$		0			0
$709$	0.563901	−	0.325568i	0.0211777	−	0.0122270i	−0.489374	−	0.872074i	$-0.662775\pi$
$709$	0.563901	−	0.325568i	0.0211777	−	0.0122270i	0.510551	+	0.859847i	$0.329441\pi$
$710$	5.78948	−	15.8362i	0.217275	−	0.594322i
$711$		0			0
$712$	8.69772	+	5.02163i	0.325961	+	0.188194i
$713$	18.3001	−	31.6967i	0.685344	−	1.18705i
$714$		0			0
$715$	−13.4694	−	13.9509i	−0.503729	−	0.521735i
$716$	−8.35561			−0.312264
$717$		0			0
$718$	−4.12042	−	2.37892i	−0.153773	−	0.0887807i
$719$	3.21203	+	5.56340i	0.119789	+	0.207480i	0.919684	−	0.392660i	$-0.128445\pi$
$719$	3.21203	+	5.56340i	0.119789	+	0.207480i	−0.799895	+	0.600140i	$0.795112\pi$
$720$		0			0
$721$	−8.52740	+	4.92330i	−0.317577	+	0.183353i
$722$	0.262979	+	0.455494i	0.00978708	+	0.0169517i
$723$		0			0
$724$	−6.36677	−	11.0276i	−0.236619	−	0.409836i
$725$	−0.208482	+	0.0752090i	−0.00774283	+	0.00279319i
$726$		0			0
$727$			16.3170i			0.605165i	0.953123	+	0.302583i	$0.0978488\pi$
$727$			16.3170i			0.605165i	−0.953123	+	0.302583i	$0.902151\pi$
$728$	−3.32541	−	4.91611i	−0.123248	−	0.182203i
$729$		0			0
$730$	2.92180	−	2.44459i	0.108141	−	0.0904785i
$731$	0.818545	−	1.41776i	0.0302750	−	0.0524378i
$732$		0			0
$733$	24.4136			0.901735			0.450868	−	0.892591i	$-0.351115\pi$
$733$	24.4136			0.901735			0.450868	+	0.892591i	$0.351115\pi$
$734$	−1.29432	+	0.747277i	−0.0477743	+	0.0275825i
$735$		0			0
$736$		−	8.62281i		−	0.317841i
$737$	−3.90404	+	2.25400i	−0.143807	+	0.0830271i
$738$		0			0
$739$	4.75775	+	2.74689i	0.175017	+	0.101046i	0.584949	−	0.811070i	$-0.301114\pi$
$739$	4.75775	+	2.74689i	0.175017	+	0.101046i	−0.409932	+	0.912116i	$0.634448\pi$
$740$	18.7925	+	6.87027i	0.690827	+	0.252556i
$741$		0			0
$742$			4.02664i			0.147823i
$743$	10.6512	−	18.4484i	0.390753	−	0.676804i	−0.601796	−	0.798650i	$-0.705548\pi$
$743$	10.6512	−	18.4484i	0.390753	−	0.676804i	0.992549	+	0.121845i	$0.0388812\pi$
$744$		0			0
$745$	−24.4579	+	4.27666i	−0.896068	+	0.156685i
$746$			20.5910i			0.753890i
$747$		0			0
$748$	−0.292601	−	0.506800i	−0.0106986	−	0.0185304i
$749$		−	17.5739i		−	0.642135i
$750$		0			0
$751$	−15.4023	+	26.6776i	−0.562040	+	0.973481i	0.435279	+	0.900296i	$0.356650\pi$
$751$	−15.4023	+	26.6776i	−0.562040	+	0.973481i	−0.997318	+	0.0731853i	$0.976684\pi$
$752$	−3.64780	+	6.31817i	−0.133022	+	0.230400i
$753$		0			0
$754$	0.0895462	+	0.132380i	0.00326108	+	0.00482100i
$755$	0.671544	−	1.83690i	0.0244400	−	0.0668517i
$756$		0			0
$757$	−30.4180	−	17.5618i	−1.10556	−	0.638296i	−0.167885	−	0.985807i	$-0.553694\pi$
$757$	−30.4180	−	17.5618i	−1.10556	−	0.638296i	−0.937676	+	0.347511i	$0.887027\pi$
$758$	18.4173	−	10.6332i	0.668946	−	0.386216i
$759$		0			0
$760$	−9.73310	+	1.70191i	−0.353057	+	0.0617347i
$761$	25.0686	−	14.4734i	0.908737	−	0.524659i	0.0287122	−	0.999588i	$-0.490859\pi$
$761$	25.0686	−	14.4734i	0.908737	−	0.524659i	0.880024	+	0.474928i	$0.157526\pi$
$762$		0			0
$763$	−13.5528	+	7.82472i	−0.490645	+	0.283274i
$764$	0.207632	−	0.359629i	0.00751187	−	0.0130109i
$765$		0			0
$766$	10.6219			0.383785
$767$	−28.8179	+	19.4933i	−1.04055	+	0.703864i
$768$		0			0
$769$	−34.3740	−	19.8459i	−1.23956	−	0.715660i	−0.270555	−	0.962704i	$-0.587207\pi$
$769$	−34.3740	−	19.8459i	−1.23956	−	0.715660i	−0.969004	+	0.247045i	$0.920541\pi$
$770$	−5.68127	−	6.79030i	−0.204739	−	0.244706i
$771$		0			0
$772$	−25.9837			−0.935173
$773$	7.16938	+	12.4177i	0.257865	+	0.446635i	0.965670	−	0.259773i	$-0.0836478\pi$
$773$	7.16938	+	12.4177i	0.257865	+	0.446635i	−0.707805	+	0.706408i	$0.750314\pi$
$774$		0			0
$775$	13.6881	−	16.2187i	0.491691	−	0.582594i
$776$	8.25647	+	14.3006i	0.296390	+	0.513363i
$777$		0			0
$778$	−18.5222	+	32.0813i	−0.664052	+	1.15017i
$779$	−1.07509			−0.0385190
$780$		0			0
$781$	−18.1374			−0.649007
$782$	1.04895	−	1.81684i	0.0375105	−	0.0649701i
$783$		0			0
$784$	2.14514	+	3.71548i	0.0766120	+	0.132696i
$785$	−11.9070	+	32.5698i	−0.424980	+	1.16246i
$786$		0			0
$787$	5.52776	+	9.57437i	0.197043	+	0.341289i	0.947568	−	0.319553i	$-0.103533\pi$
$787$	5.52776	+	9.57437i	0.197043	+	0.341289i	−0.750525	+	0.660842i	$0.770199\pi$
$788$	15.4424			0.550113
$789$		0			0
$790$	11.6568	−	9.75294i	0.414730	−	0.346994i
$791$	5.12658	+	2.95983i	0.182280	+	0.105240i
$792$		0			0
$793$	−5.31824	−	7.86219i	−0.188856	−	0.279195i
$794$	1.68719			0.0598760
$795$		0			0
$796$	6.85286	−	11.8695i	0.242893	−	0.420704i
$797$	−0.453218	+	0.261666i	−0.0160538	+	0.00926867i	−0.508005	−	0.861354i	$-0.669617\pi$
$797$	−0.453218	+	0.261666i	−0.0160538	+	0.00926867i	0.491952	+	0.870623i	$0.336284\pi$
$798$		0			0
$799$	−1.53719	+	0.887500i	−0.0543820	+	0.0313975i
$800$	0.882273	−	4.92154i	0.0311931	−	0.174003i
$801$		0			0
$802$	17.2949	−	9.98524i	0.610705	−	0.352591i
$803$	−3.54889	−	2.04895i	−0.125238	−	0.0723059i
$804$		0			0
$805$	10.8980	−	29.8097i	0.384103	−	1.05065i
$806$	−13.7640	−	6.69067i	−0.484817	−	0.235669i
$807$		0			0
$808$	−5.66777	+	9.81687i	−0.199391	+	0.345356i
$809$	24.5608	−	42.5405i	0.863511	−	1.49564i	−0.00500771	−	0.999987i	$-0.501594\pi$
$809$	24.5608	−	42.5405i	0.863511	−	1.49564i	0.868518	−	0.495657i	$-0.165073\pi$
$810$		0			0
$811$		−	31.5157i		−	1.10667i	−0.832960	−	0.553333i	$-0.813356\pi$
$811$		−	31.5157i		−	1.10667i	0.832960	−	0.553333i	$-0.186644\pi$
$812$	0.0364836	+	0.0631914i	0.00128032	+	0.00221758i
$813$		0			0
$814$		−	21.5233i		−	0.754391i
$815$	8.43202	+	48.2222i	0.295361	+	1.68915i
$816$		0			0
$817$	−14.8666	+	25.7497i	−0.520116	+	0.900868i
$818$			12.3094i			0.430389i
$819$		0			0
$820$	0.186797	−	0.510955i	0.00652325	−	0.0178433i
$821$	13.8449	+	7.99335i	0.483190	+	0.278970i	0.721745	−	0.692159i	$-0.243340\pi$
$821$	13.8449	+	7.99335i	0.483190	+	0.278970i	−0.238555	+	0.971129i	$0.576674\pi$
$822$		0			0
$823$	21.8287	−	12.6028i	0.760900	−	0.439306i	−0.0687187	−	0.997636i	$-0.521891\pi$
$823$	21.8287	−	12.6028i	0.760900	−	0.439306i	0.829619	+	0.558330i	$0.188558\pi$
$824$			5.98168i			0.208382i
$825$		0			0
$826$	−13.7562	+	7.94212i	−0.478638	+	0.276342i
$827$	−22.0889			−0.768106			−0.384053	−	0.923311i	$-0.625472\pi$
$827$	−22.0889			−0.768106			−0.384053	+	0.923311i	$0.625472\pi$
$828$		0			0
$829$	−4.72499	+	8.18393i	−0.164106	+	0.284240i	−0.936337	−	0.351102i	$-0.885807\pi$
$829$	−4.72499	+	8.18393i	−0.164106	+	0.284240i	0.772232	+	0.635341i	$0.219141\pi$
$830$	30.0097	−	25.1083i	1.04165	−	0.871523i
$831$		0			0
$832$	−3.59643	+	0.256262i	−0.124684	+	0.00888430i
$833$			1.04381i			0.0361659i
$834$		0			0
$835$	9.08302	−	7.59952i	0.314331	−	0.262992i
$836$	5.31428	+	9.20461i	0.183798	+	0.318348i
$837$		0			0
$838$	−11.0411	−	19.1238i	−0.381409	−	0.660619i
$839$	10.8542	−	6.26667i	0.374728	−	0.216350i	−0.300794	−	0.953689i	$-0.597252\pi$
$839$	10.8542	−	6.26667i	0.374728	−	0.216350i	0.675522	+	0.737340i	$0.263918\pi$
$840$		0			0
$841$	14.4990	+	25.1130i	0.499966	+	0.865967i
$842$	−7.77722	−	4.49018i	−0.268021	−	0.154742i
$843$		0			0
$844$	−16.1123			−0.554609
$845$	−28.4410	−	6.00915i	−0.978400	−	0.206721i
$846$		0			0
$847$	4.29190	−	7.43379i	0.147471	−	0.255428i
$848$	2.11841	+	1.22307i	0.0727465	+	0.0420002i
$849$		0			0
$850$	0.784596	−	0.929650i	0.0269114	−	0.0318867i
$851$	66.8220	−	38.5797i	2.29063	−	1.32250i
$852$		0			0
$853$	−54.5472			−1.86766			−0.933830	−	0.357718i	$-0.883555\pi$
$853$	−54.5472			−1.86766			−0.933830	+	0.357718i	$0.883555\pi$
$854$	−2.16680	−	3.75300i	−0.0741463	−	0.128425i
$855$		0			0
$856$	−9.24559	−	5.33795i	−0.316008	−	0.182447i
$857$			16.1596i			0.552000i	0.961158	+	0.276000i	$0.0890091\pi$
$857$			16.1596i			0.552000i	−0.961158	+	0.276000i	$0.910991\pi$
$858$		0			0
$859$	8.02338			0.273754			0.136877	−	0.990588i	$-0.456293\pi$
$859$	8.02338			0.273754			0.136877	+	0.990588i	$0.456293\pi$
$860$	−9.65493	−	11.5397i	−0.329230	−	0.393499i
$861$		0			0
$862$	7.16090	−	4.13435i	0.243901	−	0.140816i
$863$	28.2909			0.963033			0.481517	−	0.876437i	$-0.340086\pi$
$863$	28.2909			0.963033			0.481517	+	0.876437i	$0.340086\pi$
$864$		0			0
$865$	38.0159	−	6.64737i	1.29258	−	0.226017i
$866$			19.8407i			0.674214i
$867$		0			0
$868$	−6.05101	−	3.49355i	−0.205385	−	0.118579i
$869$	−14.1586	−	8.17449i	−0.480298	−	0.277300i
$870$		0			0
$871$	−2.95427	+	6.07752i	−0.100102	+	0.205929i
$872$			9.50683i			0.321942i
$873$		0			0
$874$	−19.0513	+	32.9979i	−0.644421	+	1.11617i
$875$	9.27018	−	15.8991i	0.313389	−	0.537486i
$876$		0			0
$877$	11.3031	+	19.5775i	0.381678	+	0.661085i	0.991302	−	0.131605i	$-0.0420131\pi$
$877$	11.3031	+	19.5775i	0.381678	+	0.661085i	−0.609625	+	0.792690i	$0.708680\pi$
$878$	−14.4415	−	25.0134i	−0.487377	−	0.844161i
$879$		0			0
$880$	−5.29802	+	0.926401i	−0.178596	+	0.0312290i
$881$	−22.1679	+	38.3959i	−0.746854	+	1.29359i	0.202470	+	0.979289i	$0.435103\pi$
$881$	−22.1679	+	38.3959i	−0.746854	+	1.29359i	−0.949324	+	0.314301i	$0.898230\pi$
$882$		0			0
$883$			3.93200i			0.132322i	0.997809	+	0.0661612i	$0.0210752\pi$
$883$			3.93200i			0.132322i	−0.997809	+	0.0661612i	$0.978925\pi$
$884$	−0.788948	−	0.383506i	−0.0265352	−	0.0128987i
$885$		0			0
$886$	4.99684	+	2.88493i	0.167872	+	0.0969211i
$887$	−25.2382	−	14.5713i	−0.847416	−	0.489256i	0.0123622	−	0.999924i	$-0.496065\pi$
$887$	−25.2382	−	14.5713i	−0.847416	−	0.489256i	−0.859778	+	0.510668i	$0.829398\pi$
$888$		0			0
$889$		−	28.5554i		−	0.957717i
$890$	22.1218	−	3.86817i	0.741523	−	0.129661i
$891$		0			0
$892$	11.1177			0.372249
$893$	27.9189	−	16.1190i	0.934269	−	0.539401i
$894$		0			0
$895$	−14.3297	+	11.9893i	−0.478988	+	0.400756i
$896$	−1.64613			−0.0549932
$897$		0			0
$898$			39.1483i			1.30639i
$899$	0.162941	+	0.0940738i	0.00543437	+	0.00313754i
$900$		0			0
$901$	0.297569	+	0.515404i	0.00991344	+	0.0171706i
$902$	−0.585202			−0.0194851
$903$		0			0
$904$	3.11433	−	1.79806i	0.103581	−	0.0598026i
$905$	−26.7420	−	9.77648i	−0.888934	−	0.324981i
$906$		0			0
$907$	31.2795	+	18.0592i	1.03862	+	0.599647i	0.919442	−	0.393226i	$-0.128641\pi$
$907$	31.2795	+	18.0592i	1.03862	+	0.599647i	0.119177	+	0.992873i	$0.461974\pi$
$908$	−11.0399	+	19.1217i	−0.366373	+	0.634577i
$909$		0			0
$910$	−12.7570	−	3.65944i	−0.422890	−	0.121309i
$911$	16.1738			0.535863			0.267931	−	0.963438i	$-0.413660\pi$
$911$	16.1738			0.535863			0.267931	+	0.963438i	$0.413660\pi$
$912$		0			0
$913$	−36.4505	−	21.0447i	−1.20634	−	0.696478i
$914$	−12.2403	−	21.2008i	−0.404872	−	0.701259i
$915$		0			0
$916$	8.95443	−	5.16984i	0.295863	−	0.170816i
$917$	−11.6590	−	20.1940i	−0.385014	−	0.666865i
$918$		0			0
$919$	−1.12534	−	1.94914i	−0.0371214	−	0.0642962i	0.846868	−	0.531803i	$-0.178486\pi$
$919$	−1.12534	−	1.94914i	−0.0371214	−	0.0642962i	−0.883989	+	0.467507i	$0.845152\pi$
$920$	−12.3727	−	14.7879i	−0.407914	−	0.487543i
$921$		0			0
$922$		−	3.49785i		−	0.115196i
$923$	−22.5198	+	15.2331i	−0.741248	+	0.501404i
$924$		0			0
$925$	42.0867	−	15.1826i	1.38380	−	0.499200i
$926$	−9.15317	+	15.8537i	−0.300792	+	0.520987i
$927$		0			0
$928$	0.0443266			0.00145509
$929$	−23.2193	+	13.4057i	−0.761801	+	0.439826i	−0.829942	−	0.557850i	$-0.811626\pi$
$929$	−23.2193	+	13.4057i	−0.761801	+	0.439826i	0.0681412	+	0.997676i	$0.478293\pi$
$930$		0			0
$931$		−	18.9579i		−	0.621321i
$932$	−18.9597	+	10.9464i	−0.621046	+	0.358561i
$933$		0			0
$934$	5.59469	+	3.23010i	0.183064	+	0.105692i
$935$	−1.22900	−	0.449303i	−0.0401925	−	0.0146938i
$936$		0			0
$937$		−	44.1333i		−	1.44177i	−0.693053	−	0.720887i	$-0.743735\pi$
$937$		−	44.1333i		−	1.44177i	0.693053	−	0.720887i	$-0.256265\pi$
$938$	−1.54258	+	2.67183i	−0.0503671	+	0.0872383i
$939$		0			0
$940$	2.80990	+	16.0696i	0.0916489	+	0.524134i
$941$		−	28.3857i		−	0.925348i	−0.886528	−	0.462674i	$-0.846890\pi$
$941$		−	28.3857i		−	0.925348i	0.886528	−	0.462674i	$-0.153110\pi$
$942$		0			0
$943$	−1.04895	−	1.81684i	−0.0341586	−	0.0591645i
$944$			9.64947i			0.314064i
$945$		0			0
$946$	−8.09234	+	14.0163i	−0.263105	+	0.455710i
$947$	24.6676	−	42.7256i	0.801590	−	1.38839i	−0.116979	−	0.993134i	$-0.537321\pi$
$947$	24.6676	−	42.7256i	0.801590	−	1.38839i	0.918569	−	0.395260i	$-0.129346\pi$
$948$		0			0
$949$	−6.12724	+	0.436594i	−0.198899	+	0.0141724i
$950$	−14.2500	+	16.8845i	−0.462331	+	0.547806i
$951$		0			0
$952$	−0.346841	−	0.200249i	−0.0112412	−	0.00649011i
$953$	9.62904	−	5.55933i	0.311915	−	0.180084i	−0.335868	−	0.941909i	$-0.609030\pi$
$953$	9.62904	−	5.55933i	0.311915	−	0.180084i	0.647783	+	0.761825i	$0.275696\pi$
$954$		0			0
$955$	−0.159939	−	0.914681i	−0.00517551	−	0.0295984i
$956$	22.7341	−	13.1255i	0.735272	−	0.424510i
$957$		0			0
$958$	26.5980	−	15.3564i	0.859343	−	0.496142i
$959$	6.03648	−	10.4555i	0.194928	−	0.337626i
$960$		0			0
$961$	12.9836			0.418825
$962$	−18.0769	−	26.7238i	−0.582821	−	0.861610i
$963$		0			0
$964$	−22.5952	−	13.0454i	−0.727744	−	0.420163i
$965$	−44.5614	+	37.2833i	−1.43448	+	1.20019i
$966$		0			0
$967$	−55.3514			−1.77998			−0.889990	−	0.455980i	$-0.849289\pi$
$967$	−55.3514			−1.77998			−0.889990	+	0.455980i	$0.849289\pi$
$968$	−2.60727	−	4.51593i	−0.0838010	−	0.145148i
$969$		0			0
$970$	34.6792	+	12.6782i	1.11348	+	0.407073i
$971$	26.8248	+	46.4619i	0.860848	+	1.49103i	0.871112	+	0.491085i	$0.163399\pi$
$971$	26.8248	+	46.4619i	0.860848	+	1.49103i	−0.0102641	+	0.999947i	$0.503267\pi$
$972$		0			0
$973$	−11.6905	+	20.2486i	−0.374782	+	0.649141i
$974$	−12.4667			−0.399459
$975$		0			0
$976$	−2.63260			−0.0842676
$977$	6.23411	−	10.7978i	0.199447	−	0.345452i	−0.748902	−	0.662680i	$-0.769419\pi$
$977$	6.23411	−	10.7978i	0.199447	−	0.345452i	0.948349	+	0.317228i	$0.102752\pi$
$978$		0			0
$979$	−12.0785	−	20.9206i	−0.386031	−	0.668625i
$980$	9.01010	+	3.29396i	0.287817	+	0.105222i
$981$		0			0
$982$	−1.29120	−	2.23642i	−0.0412038	−	0.0713671i
$983$	−19.1972			−0.612296			−0.306148	−	0.951984i	$-0.599040\pi$
$983$	−19.1972			−0.612296			−0.306148	+	0.951984i	$0.599040\pi$
$984$		0			0
$985$	26.4833	−	22.1579i	0.843830	−	0.706010i
$986$	0.00933969	+	0.00539227i	0.000297436	+	0.000171725i
$987$		0			0
$988$	14.3291	+	6.96533i	0.455868	+	0.221597i
$989$	−58.0209			−1.84496
$990$		0			0
$991$	−27.4152	+	47.4845i	−0.870872	+	1.50840i	−0.00977694	+	0.999952i	$0.503112\pi$
$991$	−27.4152	+	47.4845i	−0.870872	+	1.50840i	−0.861096	+	0.508443i	$0.830221\pi$
$992$	−3.67591	+	2.12229i	−0.116710	+	0.0673827i
$993$		0			0
$994$	−10.7498	+	6.20639i	−0.340962	+	0.196855i
$995$	−5.27876	−	30.1889i	−0.167348	−	0.957052i
$996$		0			0
$997$	35.4227	−	20.4513i	1.12185	−	0.647700i	0.179977	−	0.983671i	$-0.442398\pi$
$997$	35.4227	−	20.4513i	1.12185	−	0.647700i	0.941872	+	0.335971i	$0.109064\pi$
$998$	17.5321	+	10.1222i	0.554969	+	0.320412i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bj.c.199.1		12
3.2	odd	2		390.2.x.b.199.6	yes	12
5.4	even	2		1170.2.bj.d.199.6		12
13.10	even	6		1170.2.bj.d.829.6		12
15.2	even	4		1950.2.bc.j.901.5		12
15.8	even	4		1950.2.bc.i.901.2		12
15.14	odd	2		390.2.x.a.199.1	yes	12
39.23	odd	6		390.2.x.a.49.1	✓	12
65.49	even	6	inner	1170.2.bj.c.829.1		12
195.23	even	12		1950.2.bc.i.751.2		12
195.62	even	12		1950.2.bc.j.751.5		12
195.179	odd	6		390.2.x.b.49.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.1	✓	12	39.23	odd	6
390.2.x.a.199.1	yes	12	15.14	odd	2
390.2.x.b.49.6	yes	12	195.179	odd	6
390.2.x.b.199.6	yes	12	3.2	odd	2
1170.2.bj.c.199.1		12	1.1	even	1	trivial
1170.2.bj.c.829.1		12	65.49	even	6	inner
1170.2.bj.d.199.6		12	5.4	even	2
1170.2.bj.d.829.6		12	13.10	even	6
1950.2.bc.i.751.2		12	195.23	even	12
1950.2.bc.i.901.2		12	15.8	even	4
1950.2.bc.j.751.5		12	195.62	even	12
1950.2.bc.j.901.5		12	15.2	even	4

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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.10012 - 0.767774i) q^{5} +(0.823063 + 1.42559i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.10012 - 0.767774i) q^{5} +(0.823063 + 1.42559i) q^{7} +1.00000 q^{8} +(1.71497 - 1.43487i) q^{10} +(-2.08305 - 1.20265i) q^{11} +(-3.59643 + 0.256262i) q^{13} -1.64613 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.210702 + 0.121649i) q^{17} +(3.82681 - 2.20941i) q^{19} +(0.385150 + 2.20265i) q^{20} +(2.08305 - 1.20265i) q^{22} +(7.46758 + 4.31141i) q^{23} +(3.82105 + 3.22484i) q^{25} +(1.57629 - 3.24273i) q^{26} +(0.823063 - 1.42559i) q^{28} +(-0.0221633 + 0.0383880i) q^{29} -4.24458i q^{31} +(-0.500000 - 0.866025i) q^{32} -0.243297i q^{34} +(-0.634006 - 3.62584i) q^{35} +(4.47415 - 7.74945i) q^{37} +4.41882i q^{38} +(-2.10012 - 0.767774i) q^{40} +(-0.210702 - 0.121649i) q^{41} +(-5.82728 + 3.36438i) q^{43} +2.40530i q^{44} +(-7.46758 + 4.31141i) q^{46} +7.29560 q^{47} +(2.14514 - 3.71548i) q^{49} +(-4.70332 + 1.69670i) q^{50} +(2.02015 + 2.98647i) q^{52} -2.44613i q^{53} +(3.45130 + 4.12502i) q^{55} +(0.823063 + 1.42559i) q^{56} +(-0.0221633 - 0.0383880i) q^{58} +(8.35669 - 4.82474i) q^{59} +(1.31630 + 2.27990i) q^{61} +(3.67591 + 2.12229i) q^{62} +1.00000 q^{64} +(7.74971 + 2.22307i) q^{65} +(0.937098 - 1.62310i) q^{67} +(0.210702 + 0.121649i) q^{68} +(3.45707 + 1.26385i) q^{70} +(6.53035 - 3.77030i) q^{71} +1.70370 q^{73} +(4.47415 + 7.74945i) q^{74} +(-3.82681 - 2.20941i) q^{76} -3.95942i q^{77} +6.79707 q^{79} +(1.71497 - 1.43487i) q^{80} +(0.210702 - 0.121649i) q^{82} +17.4986 q^{83} +(0.535898 - 0.0937060i) q^{85} -6.72876i q^{86} +(-2.08305 - 1.20265i) q^{88} +(8.69772 + 5.02163i) q^{89} +(-3.32541 - 4.91611i) q^{91} -8.62281i q^{92} +(-3.64780 + 6.31817i) q^{94} +(-9.73310 + 1.70191i) q^{95} +(8.25647 + 14.3006i) q^{97} +(2.14514 + 3.71548i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	\( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 4 q^{10} - 6 q^{11} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} - 2 q^{20} + 6 q^{22} + 6 q^{23} - 10 q^{25} + 2 q^{26} + 2 q^{28} - 14 q^{29} - 6 q^{32} + 22 q^{35} + 12 q^{37} - 2 q^{40} + 18 q^{41} + 36 q^{43} - 6 q^{46} + 16 q^{47} + 8 q^{49} + 20 q^{50} - 10 q^{52} + 8 q^{55} + 2 q^{56} - 14 q^{58} + 36 q^{59} + 10 q^{61} + 6 q^{62} + 12 q^{64} + 44 q^{65} - 4 q^{67} - 18 q^{68} + 4 q^{70} + 12 q^{71} - 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 4 q^{80} - 18 q^{82} + 72 q^{83} + 48 q^{85} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} - 18 q^{95} + 48 q^{97} + 8 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 4 * q^10 - 6 * q^11 + 8 * q^13 - 4 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 - 2 * q^20 + 6 * q^22 + 6 * q^23 - 10 * q^25 + 2 * q^26 + 2 * q^28 - 14 * q^29 - 6 * q^32 + 22 * q^35 + 12 * q^37 - 2 * q^40 + 18 * q^41 + 36 * q^43 - 6 * q^46 + 16 * q^47 + 8 * q^49 + 20 * q^50 - 10 * q^52 + 8 * q^55 + 2 * q^56 - 14 * q^58 + 36 * q^59 + 10 * q^61 + 6 * q^62 + 12 * q^64 + 44 * q^65 - 4 * q^67 - 18 * q^68 + 4 * q^70 + 12 * q^71 - 28 * q^73 + 12 * q^74 + 6 * q^76 + 4 * q^79 + 4 * q^80 - 18 * q^82 + 72 * q^83 + 48 * q^85 - 6 * q^88 - 18 * q^89 + 2 * q^91 - 8 * q^94 - 18 * q^95 + 48 * q^97 + 8 * q^98

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