LMFDB - Embedded newform 990.2.n.i.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [990,2,Mod(91,990)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(990, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("990.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.n (of order $5$, degree $4$, 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:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.2769390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 5x^{5} + 21x^{4} + 75x^{3} - 198x^{2} - 87x + 841 $ x^8 - x^7 - 2x^6 + 5x^5 + 21x^4 + 75x^3 - 198x^2 - 87x + 841
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 330)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.2
Root			$-2.08774 - 0.152618i$ of defining polynomial
Character	$\chi$	$=$	990.361
Dual form			990.2.n.i.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(2.58774 + 1.88011i) q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(2.58774 + 1.88011i) q^{7} +(-0.809017 + 0.587785i) q^{8} +1.00000 q^{10} +(-3.26001 + 0.610212i) q^{11} +(-2.08774 + 6.42541i) q^{13} +(2.58774 - 1.88011i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.172263 - 0.530170i) q^{17} +(-5.18706 + 3.76862i) q^{19} +(0.309017 - 0.951057i) q^{20} +(-0.427051 + 3.28902i) q^{22} -2.59489 q^{23} +(-0.809017 + 0.587785i) q^{25} +(5.46578 + 3.97112i) q^{26} +(-0.988430 - 3.04208i) q^{28} +(-3.95734 - 2.87518i) q^{29} +(0.747638 - 2.30099i) q^{31} +1.00000 q^{32} -0.557453 q^{34} +(-0.988430 + 3.04208i) q^{35} +(4.63805 + 3.36974i) q^{37} +(1.98128 + 6.09775i) q^{38} +(-0.809017 - 0.587785i) q^{40} +(1.06773 - 0.775752i) q^{41} -1.32139 q^{43} +(2.99607 + 1.42251i) q^{44} +(-0.801866 + 2.46789i) q^{46} +(-4.84775 + 3.52210i) q^{47} +(0.998501 + 3.07307i) q^{49} +(0.309017 + 0.951057i) q^{50} +(5.46578 - 3.97112i) q^{52} +(0.752362 - 2.31553i) q^{53} +(-1.58774 - 2.91188i) q^{55} -3.19863 q^{56} +(-3.95734 + 2.87518i) q^{58} +(8.35410 + 6.06961i) q^{59} +(1.21293 + 3.73301i) q^{61} +(-1.95734 - 1.42209i) q^{62} +(0.309017 - 0.951057i) q^{64} -6.75608 q^{65} +15.1676 q^{67} +(-0.172263 + 0.530170i) q^{68} +(2.58774 + 1.88011i) q^{70} +(1.96256 + 6.04014i) q^{71} +(5.61803 + 4.08174i) q^{73} +(4.63805 - 3.36974i) q^{74} +6.41156 q^{76} +(-9.58332 - 4.55008i) q^{77} +(3.60696 - 11.1011i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-0.407837 - 1.25519i) q^{82} +(2.47214 + 7.60845i) q^{83} +(0.450989 - 0.327663i) q^{85} +(-0.408331 + 1.25671i) q^{86} +(2.27873 - 2.40986i) q^{88} +13.0775 q^{89} +(-17.4830 + 12.7021i) q^{91} +(2.09931 + 1.52524i) q^{92} +(1.85168 + 5.69887i) q^{94} +(-5.18706 - 3.76862i) q^{95} +(2.35883 - 7.25972i) q^{97} +3.23122 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 3 q^{7} - 2 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 3 * q^7 - 2 * q^8	$ 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 3 q^{7} - 2 q^{8} + 8 q^{10} - 10 q^{11} + q^{13} + 3 q^{14} - 2 q^{16} - 3 q^{17} - 12 q^{19} - 2 q^{20} + 10 q^{22} - 2 q^{25} + q^{26} - 2 q^{28} - 27 q^{29} - 6 q^{31} + 8 q^{32} + 22 q^{34} - 2 q^{35} - 4 q^{37} + 13 q^{38} - 2 q^{40} + 23 q^{41} - 2 q^{43} - 10 q^{44} - 5 q^{46} - 5 q^{47} - 53 q^{49} - 2 q^{50} + q^{52} + 18 q^{53} + 5 q^{55} - 2 q^{56} - 27 q^{58} + 40 q^{59} - 20 q^{61} - 11 q^{62} - 2 q^{64} - 4 q^{65} + 18 q^{67} - 3 q^{68} + 3 q^{70} + 10 q^{71} + 36 q^{73} - 4 q^{74} - 2 q^{76} - 50 q^{77} - 11 q^{79} - 2 q^{80} - 12 q^{82} - 16 q^{83} - 8 q^{85} + 13 q^{86} + 5 q^{88} + 46 q^{89} - 39 q^{91} + 5 q^{92} + 15 q^{94} - 12 q^{95} + 16 q^{97} + 62 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 3 * q^7 - 2 * q^8 + 8 * q^10 - 10 * q^11 + q^13 + 3 * q^14 - 2 * q^16 - 3 * q^17 - 12 * q^19 - 2 * q^20 + 10 * q^22 - 2 * q^25 + q^26 - 2 * q^28 - 27 * q^29 - 6 * q^31 + 8 * q^32 + 22 * q^34 - 2 * q^35 - 4 * q^37 + 13 * q^38 - 2 * q^40 + 23 * q^41 - 2 * q^43 - 10 * q^44 - 5 * q^46 - 5 * q^47 - 53 * q^49 - 2 * q^50 + q^52 + 18 * q^53 + 5 * q^55 - 2 * q^56 - 27 * q^58 + 40 * q^59 - 20 * q^61 - 11 * q^62 - 2 * q^64 - 4 * q^65 + 18 * q^67 - 3 * q^68 + 3 * q^70 + 10 * q^71 + 36 * q^73 - 4 * q^74 - 2 * q^76 - 50 * q^77 - 11 * q^79 - 2 * q^80 - 12 * q^82 - 16 * q^83 - 8 * q^85 + 13 * q^86 + 5 * q^88 + 46 * q^89 - 39 * q^91 + 5 * q^92 + 15 * q^94 - 12 * q^95 + 16 * q^97 + 62 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$6$		0			0
$7$	2.58774	+	1.88011i	0.978075	+	0.710613i	0.957278	−	0.289170i	$-0.0933794\pi$
$7$	2.58774	+	1.88011i	0.978075	+	0.710613i	0.0207976	+	0.999784i	$0.493379\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$		0			0
$10$	1.00000			0.316228
$11$	−3.26001	+	0.610212i	−0.982929	+	0.183986i
$11$	−3.26001	+	0.610212i	−0.982929	+	0.183986i
$12$		0			0
$13$	−2.08774	+	6.42541i	−0.579036	+	1.78209i	0.0429695	+	0.999076i	$0.486318\pi$
$13$	−2.08774	+	6.42541i	−0.579036	+	1.78209i	−0.622005	+	0.783013i	$0.713682\pi$
$14$	2.58774	−	1.88011i	0.691604	−	0.502479i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.172263	−	0.530170i	−0.0417798	−	0.128585i	0.927991	−	0.372603i	$-0.121535\pi$
$17$	−0.172263	−	0.530170i	−0.0417798	−	0.128585i	−0.969771	+	0.244018i	$0.921535\pi$
$18$		0			0
$19$	−5.18706	+	3.76862i	−1.18999	+	0.864580i	−0.993263	−	0.115878i	$-0.963032\pi$
$19$	−5.18706	+	3.76862i	−1.18999	+	0.864580i	−0.196729	+	0.980458i	$0.563032\pi$
$20$	0.309017	−	0.951057i	0.0690983	−	0.212663i
$21$		0			0
$22$	−0.427051	+	3.28902i	−0.0910476	+	0.701221i
$23$	−2.59489			−0.541073			−0.270536	−	0.962710i	$-0.587201\pi$
$23$	−2.59489			−0.541073			−0.270536	+	0.962710i	$0.587201\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	5.46578	+	3.97112i	1.07193	+	0.778802i
$27$		0			0
$28$	−0.988430	−	3.04208i	−0.186796	−	0.574898i
$29$	−3.95734	−	2.87518i	−0.734860	−	0.533907i	0.156237	−	0.987720i	$-0.450064\pi$
$29$	−3.95734	−	2.87518i	−0.734860	−	0.533907i	−0.891097	+	0.453813i	$0.850064\pi$
$30$		0			0
$31$	0.747638	−	2.30099i	0.134280	−	0.413270i	−0.861198	−	0.508270i	$-0.830285\pi$
$31$	0.747638	−	2.30099i	0.134280	−	0.413270i	0.995477	+	0.0949999i	$0.0302851\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−0.557453			−0.0956025
$35$	−0.988430	+	3.04208i	−0.167075	+	0.514205i
$36$		0			0
$37$	4.63805	+	3.36974i	0.762490	+	0.553982i	0.899673	−	0.436564i	$-0.143805\pi$
$37$	4.63805	+	3.36974i	0.762490	+	0.553982i	−0.137183	+	0.990546i	$0.543805\pi$
$38$	1.98128	+	6.09775i	0.321406	+	0.989186i
$39$		0			0
$40$	−0.809017	−	0.587785i	−0.127917	−	0.0929370i
$41$	1.06773	−	0.775752i	0.166752	−	0.121152i	−0.501280	−	0.865285i	$-0.667137\pi$
$41$	1.06773	−	0.775752i	0.166752	−	0.121152i	0.668031	+	0.744133i	$0.267137\pi$
$42$		0			0
$43$	−1.32139			−0.201509			−0.100755	−	0.994911i	$-0.532126\pi$
$43$	−1.32139			−0.201509			−0.100755	+	0.994911i	$0.532126\pi$
$44$	2.99607	+	1.42251i	0.451675	+	0.214452i
$45$		0			0
$46$	−0.801866	+	2.46789i	−0.118229	+	0.363871i
$47$	−4.84775	+	3.52210i	−0.707117	+	0.513751i	−0.882242	−	0.470796i	$-0.843967\pi$
$47$	−4.84775	+	3.52210i	−0.707117	+	0.513751i	0.175125	+	0.984546i	$0.443967\pi$
$48$		0			0
$49$	0.998501	+	3.07307i	0.142643	+	0.439010i
$50$	0.309017	+	0.951057i	0.0437016	+	0.134500i
$51$		0			0
$52$	5.46578	−	3.97112i	0.757968	−	0.550696i
$53$	0.752362	−	2.31553i	0.103345	−	0.318063i	−0.885994	−	0.463698i	$-0.846522\pi$
$53$	0.752362	−	2.31553i	0.103345	−	0.318063i	0.989338	+	0.145635i	$0.0465224\pi$
$54$		0			0
$55$	−1.58774	−	2.91188i	−0.214091	−	0.392638i
$56$	−3.19863			−0.427435
$57$		0			0
$58$	−3.95734	+	2.87518i	−0.519624	+	0.377529i
$59$	8.35410	+	6.06961i	1.08761	+	0.790196i	0.978994	−	0.203888i	$-0.0653577\pi$
$59$	8.35410	+	6.06961i	1.08761	+	0.790196i	0.108617	+	0.994084i	$0.465358\pi$
$60$		0			0
$61$	1.21293	+	3.73301i	0.155300	+	0.477963i	0.998191	−	0.0601206i	$-0.0191485\pi$
$61$	1.21293	+	3.73301i	0.155300	+	0.477963i	−0.842892	+	0.538083i	$0.819149\pi$
$62$	−1.95734	−	1.42209i	−0.248583	−	0.180606i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−6.75608			−0.837989
$66$		0			0
$67$	15.1676			1.85302			0.926511	−	0.376268i	$-0.122793\pi$
$67$	15.1676			1.85302			0.926511	+	0.376268i	$0.122793\pi$
$68$	−0.172263	+	0.530170i	−0.0208899	+	0.0642925i
$69$		0			0
$70$	2.58774	+	1.88011i	0.309295	+	0.224716i
$71$	1.96256	+	6.04014i	0.232913	+	0.716832i	0.997391	+	0.0721830i	$0.0229966\pi$
$71$	1.96256	+	6.04014i	0.232913	+	0.716832i	−0.764478	+	0.644649i	$0.777003\pi$
$72$		0			0
$73$	5.61803	+	4.08174i	0.657541	+	0.477732i	0.865832	−	0.500335i	$-0.166790\pi$
$73$	5.61803	+	4.08174i	0.657541	+	0.477732i	−0.208291	+	0.978067i	$0.566790\pi$
$74$	4.63805	−	3.36974i	0.539162	−	0.391724i
$75$		0			0
$76$	6.41156			0.735456
$77$	−9.58332	−	4.55008i	−1.09212	−	0.518530i
$78$		0			0
$79$	3.60696	−	11.1011i	0.405814	−	1.24897i	−0.514399	−	0.857551i	$-0.671985\pi$
$79$	3.60696	−	11.1011i	0.405814	−	1.24897i	0.920213	−	0.391417i	$-0.128015\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$		0			0
$82$	−0.407837	−	1.25519i	−0.0450381	−	0.138613i
$83$	2.47214	+	7.60845i	0.271352	+	0.835136i	0.990162	+	0.139929i	$0.0446874\pi$
$83$	2.47214	+	7.60845i	0.271352	+	0.835136i	−0.718809	+	0.695207i	$0.755313\pi$
$84$		0			0
$85$	0.450989	−	0.327663i	0.0489167	−	0.0355400i
$86$	−0.408331	+	1.25671i	−0.0440314	+	0.135515i
$87$		0			0
$88$	2.27873	−	2.40986i	0.242913	−	0.256891i
$89$	13.0775			1.38621			0.693104	−	0.720837i	$-0.256243\pi$
$89$	13.0775			1.38621			0.693104	+	0.720837i	$0.256243\pi$
$90$		0			0
$91$	−17.4830	+	12.7021i	−1.83272	+	1.33155i
$92$	2.09931	+	1.52524i	0.218869	+	0.159017i
$93$		0			0
$94$	1.85168	+	5.69887i	0.190986	+	0.587794i
$95$	−5.18706	−	3.76862i	−0.532181	−	0.386652i
$96$		0			0
$97$	2.35883	−	7.25972i	0.239503	−	0.737113i	−0.756990	−	0.653427i	$-0.773331\pi$
$97$	2.35883	−	7.25972i	0.239503	−	0.737113i	0.996492	−	0.0836861i	$-0.0266693\pi$
$98$	3.23122			0.326402
$99$		0			0
$100$	1.00000			0.100000
$101$	−4.93619	+	15.1920i	−0.491170	+	1.51166i	0.331672	+	0.943395i	$0.392387\pi$
$101$	−4.93619	+	15.1920i	−0.491170	+	1.51166i	−0.822842	+	0.568270i	$0.807613\pi$
$102$		0			0
$103$	−14.7972	−	10.7508i	−1.45802	−	1.05931i	−0.983874	−	0.178861i	$-0.942759\pi$
$103$	−14.7972	−	10.7508i	−1.45802	−	1.05931i	−0.474141	−	0.880449i	$-0.657241\pi$
$104$	−2.08774	−	6.42541i	−0.204720	−	0.630064i
$105$		0			0
$106$	−1.96971	−	1.43108i	−0.191315	−	0.138999i
$107$	13.8463	−	10.0599i	1.33857	−	0.972526i	0.339072	−	0.940760i	$-0.389887\pi$
$107$	13.8463	−	10.0599i	1.33857	−	0.972526i	0.999495	−	0.0317659i	$-0.0101131\pi$
$108$		0			0
$109$	8.94427			0.856706			0.428353	−	0.903612i	$-0.359094\pi$
$109$	8.94427			0.856706			0.428353	+	0.903612i	$0.359094\pi$
$110$	−3.26001	+	0.610212i	−0.310829	+	0.0581815i
$111$		0			0
$112$	−0.988430	+	3.04208i	−0.0933979	+	0.287449i
$113$	3.89676	−	2.83116i	0.366576	−	0.266333i	−0.389213	−	0.921148i	$-0.627253\pi$
$113$	3.89676	−	2.83116i	0.366576	−	0.266333i	0.755790	+	0.654814i	$0.227253\pi$
$114$		0			0
$115$	−0.801866	−	2.46789i	−0.0747744	−	0.230132i
$116$	1.51157	+	4.65213i	0.140346	+	0.431940i
$117$		0			0
$118$	8.35410	−	6.06961i	0.769057	−	0.558753i
$119$	0.551004	−	1.69582i	0.0505104	−	0.155455i
$120$		0			0
$121$	10.2553	−	3.97859i	0.932298	−	0.361690i
$122$	3.92512			0.355364
$123$		0			0
$124$	−1.95734	+	1.42209i	−0.175774	+	0.127708i
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$		0			0
$127$	−5.01087	−	15.4219i	−0.444643	−	1.36847i	−0.882875	−	0.469608i	$-0.844395\pi$
$127$	−5.01087	−	15.4219i	−0.444643	−	1.36847i	0.438232	−	0.898862i	$-0.355605\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$		0			0
$130$	−2.08774	+	6.42541i	−0.183107	+	0.563546i
$131$	−17.2888			−1.51053			−0.755265	−	0.655420i	$-0.772492\pi$
$131$	−17.2888			−1.51053			−0.755265	+	0.655420i	$0.772492\pi$
$132$		0			0
$133$	−20.5082			−1.77828
$134$	4.68706	−	14.4253i	0.404900	−	1.24615i
$135$		0			0
$136$	0.450989	+	0.327663i	0.0386720	+	0.0280969i
$137$	−2.45099	−	7.54337i	−0.209402	−	0.644474i	−0.999504	−	0.0314977i	$-0.989972\pi$
$137$	−2.45099	−	7.54337i	−0.209402	−	0.644474i	0.790102	−	0.612976i	$-0.210028\pi$
$138$		0			0
$139$	6.64832	+	4.83029i	0.563904	+	0.409700i	0.832886	−	0.553445i	$-0.186687\pi$
$139$	6.64832	+	4.83029i	0.563904	+	0.409700i	−0.268982	+	0.963145i	$0.586687\pi$
$140$	2.58774	−	1.88011i	0.218704	−	0.158898i
$141$		0			0
$142$	6.35097			0.532962
$143$	2.88519	−	22.2209i	0.241272	−	1.85820i
$144$		0			0
$145$	1.51157	−	4.65213i	0.125529	−	0.386339i
$146$	5.61803	−	4.08174i	0.464952	−	0.337807i
$147$		0			0
$148$	−1.77158	−	5.45235i	−0.145623	−	0.448180i
$149$	1.88047	+	5.78748i	0.154054	+	0.474129i	0.998064	−	0.0621986i	$-0.0198112\pi$
$149$	1.88047	+	5.78748i	0.154054	+	0.474129i	−0.844010	+	0.536327i	$0.819811\pi$
$150$		0			0
$151$	−14.7857	+	10.7424i	−1.20324	+	0.874206i	−0.994600	−	0.103787i	$-0.966904\pi$
$151$	−14.7857	+	10.7424i	−1.20324	+	0.874206i	−0.208641	+	0.977992i	$0.566904\pi$
$152$	1.98128	−	6.09775i	0.160703	−	0.494593i
$153$		0			0
$154$	−7.28880	+	7.70823i	−0.587348	+	0.621147i
$155$	2.41941			0.194331
$156$		0			0
$157$	−14.9566	+	10.8666i	−1.19367	+	0.867252i	−0.993647	−	0.112539i	$-0.964102\pi$
$157$	−14.9566	+	10.8666i	−1.19367	+	0.867252i	−0.200023	+	0.979791i	$0.564102\pi$
$158$	−9.44314	−	6.86084i	−0.751256	−	0.545819i
$159$		0			0
$160$	0.309017	+	0.951057i	0.0244299	+	0.0751876i
$161$	−6.71492	−	4.87868i	−0.529210	−	0.384494i
$162$		0			0
$163$	3.56853	−	10.9828i	0.279509	−	0.860240i	−0.708482	−	0.705729i	$-0.750620\pi$
$163$	3.56853	−	10.9828i	0.279509	−	0.860240i	0.987991	−	0.154511i	$-0.0493802\pi$
$164$	−1.31979			−0.103058
$165$		0			0
$166$	8.00000			0.620920
$167$	−0.912256	+	2.80764i	−0.0705925	+	0.217261i	−0.980128	−	0.198364i	$-0.936437\pi$
$167$	−0.912256	+	2.80764i	−0.0705925	+	0.217261i	0.909536	+	0.415625i	$0.136437\pi$
$168$		0			0
$169$	−26.4101	−	19.1880i	−2.03154	−	1.47600i
$170$	−0.172263	−	0.530170i	−0.0132119	−	0.0406622i
$171$		0			0
$172$	1.06902	+	0.776691i	0.0815123	+	0.0592221i
$173$	1.48972	−	1.08235i	0.113261	−	0.0822893i	−0.529713	−	0.848177i	$-0.677700\pi$
$173$	1.48972	−	1.08235i	0.113261	−	0.0822893i	0.642974	+	0.765888i	$0.277700\pi$
$174$		0			0
$175$	−3.19863			−0.241793
$176$	−1.58774	−	2.91188i	−0.119681	−	0.219492i
$177$		0			0
$178$	4.04116	−	12.4374i	0.302898	−	0.932223i
$179$	−15.0172	+	10.9106i	−1.12244	+	0.815500i	−0.984577	−	0.174951i	$-0.944023\pi$
$179$	−15.0172	+	10.9106i	−1.12244	+	0.815500i	−0.137863	+	0.990451i	$0.544023\pi$
$180$		0			0
$181$	2.94427	+	9.06154i	0.218846	+	0.673539i	0.998858	+	0.0477744i	$0.0152128\pi$
$181$	2.94427	+	9.06154i	0.218846	+	0.673539i	−0.780012	+	0.625764i	$0.784787\pi$
$182$	6.67791	+	20.5525i	0.495000	+	1.52345i
$183$		0			0
$184$	2.09931	−	1.52524i	0.154763	−	0.112442i
$185$	−1.77158	+	5.45235i	−0.130249	+	0.400865i
$186$		0			0
$187$	0.885093	+	1.62324i	0.0647244	+	0.118703i
$188$	5.99215			0.437022
$189$		0			0
$190$	−5.18706	+	3.76862i	−0.376309	+	0.273404i
$191$	0.739195	+	0.537057i	0.0534863	+	0.0388601i	0.614207	−	0.789145i	$-0.289476\pi$
$191$	0.739195	+	0.537057i	0.0534863	+	0.0388601i	−0.560721	+	0.828005i	$0.689476\pi$
$192$		0			0
$193$	7.19863	+	22.1551i	0.518169	+	1.59476i	0.777442	+	0.628955i	$0.216517\pi$
$193$	7.19863	+	22.1551i	0.518169	+	1.59476i	−0.259273	+	0.965804i	$0.583483\pi$
$194$	−6.17549	−	4.48675i	−0.443374	−	0.322130i
$195$		0			0
$196$	0.998501	−	3.07307i	0.0713215	−	0.219505i
$197$	24.5896			1.75194			0.875969	−	0.482367i	$-0.160223\pi$
$197$	24.5896			1.75194			0.875969	+	0.482367i	$0.160223\pi$
$198$		0			0
$199$	10.5112			0.745117			0.372559	−	0.928009i	$-0.378481\pi$
$199$	10.5112			0.745117			0.372559	+	0.928009i	$0.378481\pi$
$200$	0.309017	−	0.951057i	0.0218508	−	0.0672499i
$201$		0			0
$202$	12.9231	+	9.38920i	0.909268	+	0.660622i
$203$	−4.83495	−	14.8804i	−0.339347	−	1.04440i
$204$		0			0
$205$	1.06773	+	0.775752i	0.0745736	+	0.0541809i
$206$	−14.7972	+	10.7508i	−1.03097	+	0.749045i
$207$		0			0
$208$	−6.75608			−0.468450
$209$	14.6102	−	15.4509i	1.01061	−	1.06876i
$210$		0			0
$211$	−2.18433	+	6.72266i	−0.150375	+	0.462807i	−0.997663	−	0.0683268i	$-0.978234\pi$
$211$	−2.18433	+	6.72266i	−0.150375	+	0.462807i	0.847288	+	0.531134i	$0.178234\pi$
$212$	−1.96971	+	1.43108i	−0.135280	+	0.0982868i
$213$		0			0
$214$	−5.28880	−	16.2772i	−0.361535	−	1.11269i
$215$	−0.408331	−	1.25671i	−0.0278479	−	0.0857071i
$216$		0			0
$217$	6.26080	−	4.54874i	0.425011	−	0.308789i
$218$	2.76393	−	8.50651i	0.187197	−	0.576133i
$219$		0			0
$220$	−0.427051	+	3.28902i	−0.0287918	+	0.221745i
$221$	3.76620			0.253342
$222$		0			0
$223$	−0.648324	+	0.471035i	−0.0434150	+	0.0315428i	−0.609281	−	0.792954i	$-0.708542\pi$
$223$	−0.648324	+	0.471035i	−0.0434150	+	0.0315428i	0.565866	+	0.824497i	$0.308542\pi$
$224$	2.58774	+	1.88011i	0.172901	+	0.125620i
$225$		0			0
$226$	−1.48843	−	4.58092i	−0.0990089	−	0.304718i
$227$	−3.93942	−	2.86216i	−0.261468	−	0.189968i	0.449326	−	0.893368i	$-0.351664\pi$
$227$	−3.93942	−	2.86216i	−0.261468	−	0.189968i	−0.710794	+	0.703400i	$0.751664\pi$
$228$		0			0
$229$	−0.358826	+	1.10435i	−0.0237119	+	0.0729778i	−0.962212	−	0.272301i	$-0.912215\pi$
$229$	−0.358826	+	1.10435i	−0.0237119	+	0.0729778i	0.938500	+	0.345278i	$0.112215\pi$
$230$	−2.59489			−0.171102
$231$		0			0
$232$	4.89154			0.321146
$233$	−3.72450	+	11.4628i	−0.244000	+	0.750955i	0.751799	+	0.659392i	$0.229186\pi$
$233$	−3.72450	+	11.4628i	−0.244000	+	0.750955i	−0.995799	+	0.0915628i	$0.970814\pi$
$234$		0			0
$235$	−4.84775	−	3.52210i	−0.316232	−	0.229756i
$236$	−3.19098	−	9.82084i	−0.207715	−	0.639282i
$237$		0			0
$238$	−1.44255	−	1.04807i	−0.0935064	−	0.0679364i
$239$	−22.8631	+	16.6110i	−1.47889	+	1.07448i	−0.500982	+	0.865458i	$0.667028\pi$
$239$	−22.8631	+	16.6110i	−1.47889	+	1.07448i	−0.977911	+	0.209021i	$0.932972\pi$
$240$		0			0
$241$	24.7857			1.59659			0.798293	−	0.602270i	$-0.205737\pi$
$241$	24.7857			1.59659			0.798293	+	0.602270i	$0.205737\pi$
$242$	−0.614809	−	10.9828i	−0.0395214	−	0.706001i
$243$		0			0
$244$	1.21293	−	3.73301i	0.0776498	−	0.238981i
$245$	−2.61411	+	1.89926i	−0.167009	+	0.121339i
$246$		0			0
$247$	−13.3857	−	41.1969i	−0.851711	−	2.62130i
$248$	0.747638	+	2.30099i	0.0474751	+	0.146113i
$249$		0			0
$250$	−0.809017	+	0.587785i	−0.0511667	+	0.0371748i
$251$	5.51952	−	16.9873i	0.348389	−	1.07223i	−0.611355	−	0.791356i	$-0.709375\pi$
$251$	5.51952	−	16.9873i	0.348389	−	1.07223i	0.959744	−	0.280875i	$-0.0906246\pi$
$252$		0			0
$253$	8.45937	−	1.58344i	0.531836	−	0.0995498i
$254$	−16.2155			−1.01745
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	3.49687	+	2.54063i	0.218129	+	0.158480i	0.691484	−	0.722392i	$-0.256957\pi$
$257$	3.49687	+	2.54063i	0.218129	+	0.158480i	−0.473355	+	0.880872i	$0.656957\pi$
$258$		0			0
$259$	5.66661	+	17.4400i	0.352106	+	1.08367i
$260$	5.46578	+	3.97112i	0.338974	+	0.246279i
$261$		0			0
$262$	−5.34253	+	16.4426i	−0.330063	+	1.01583i
$263$	−23.0282			−1.41998			−0.709989	−	0.704212i	$-0.751300\pi$
$263$	−23.0282			−1.41998			−0.709989	+	0.704212i	$0.751300\pi$
$264$		0			0
$265$	2.43470			0.149562
$266$	−6.33737	+	19.5044i	−0.388569	+	1.19589i
$267$		0			0
$268$	−12.2709	−	8.91531i	−0.749563	−	0.544589i
$269$	3.66392	+	11.2764i	0.223393	+	0.687533i	0.998451	+	0.0556425i	$0.0177207\pi$
$269$	3.66392	+	11.2764i	0.223393	+	0.687533i	−0.775058	+	0.631890i	$0.782279\pi$
$270$		0			0
$271$	−9.24451	−	6.71653i	−0.561564	−	0.408000i	0.270467	−	0.962729i	$-0.412822\pi$
$271$	−9.24451	−	6.71653i	−0.561564	−	0.408000i	−0.832031	+	0.554729i	$0.812822\pi$
$272$	0.450989	−	0.327663i	0.0273452	−	0.0198675i
$273$		0			0
$274$	−7.93157			−0.479164
$275$	2.27873	−	2.40986i	0.137412	−	0.145320i
$276$		0			0
$277$	4.64713	−	14.3024i	0.279219	−	0.859348i	−0.708853	−	0.705356i	$-0.750787\pi$
$277$	4.64713	−	14.3024i	0.279219	−	0.859348i	0.988072	−	0.153992i	$-0.0492129\pi$
$278$	6.64832	−	4.83029i	0.398740	−	0.289702i
$279$		0			0
$280$	−0.988430	−	3.04208i	−0.0590700	−	0.181799i
$281$	4.09962	+	12.6173i	0.244563	+	0.752687i	0.995708	+	0.0925498i	$0.0295017\pi$
$281$	4.09962	+	12.6173i	0.244563	+	0.752687i	−0.751145	+	0.660137i	$0.770498\pi$
$282$		0			0
$283$	12.2334	−	8.88811i	0.727202	−	0.528343i	−0.161475	−	0.986877i	$-0.551625\pi$
$283$	12.2334	−	8.88811i	0.727202	−	0.528343i	0.888677	+	0.458533i	$0.151625\pi$
$284$	1.96256	−	6.04014i	0.116456	−	0.358416i
$285$		0			0
$286$	−20.2417	−	9.61060i	−1.19692	−	0.568287i
$287$	4.22151			0.249188
$288$		0			0
$289$	13.5019	−	9.80969i	0.794228	−	0.577041i
$290$	−3.95734	−	2.87518i	−0.232383	−	0.168836i
$291$		0			0
$292$	−2.14590	−	6.60440i	−0.125579	−	0.386493i
$293$	11.2585	+	8.17978i	0.657729	+	0.477868i	0.865895	−	0.500225i	$-0.166750\pi$
$293$	11.2585	+	8.17978i	0.657729	+	0.477868i	−0.208166	+	0.978093i	$0.566750\pi$
$294$		0			0
$295$	−3.19098	+	9.82084i	−0.185786	+	0.571791i
$296$	−5.73294			−0.333220
$297$		0			0
$298$	6.08532			0.352513
$299$	5.41747	−	16.6733i	0.313301	−	0.964240i
$300$		0			0
$301$	−3.41941	−	2.48434i	−0.197091	−	0.143195i
$302$	5.64762	+	17.3816i	0.324984	+	1.00020i
$303$		0			0
$304$	−5.18706	−	3.76862i	−0.297498	−	0.216145i
$305$	−3.17549	+	2.30713i	−0.181828	+	0.132106i
$306$		0			0
$307$	−24.0813			−1.37439			−0.687197	−	0.726471i	$-0.741159\pi$
$307$	−24.0813			−1.37439			−0.687197	+	0.726471i	$0.741159\pi$
$308$	5.07860	+	9.31403i	0.289380	+	0.530716i
$309$		0			0
$310$	0.747638	−	2.30099i	0.0424630	−	0.130688i
$311$	−24.5792	+	17.8578i	−1.39376	+	1.01262i	−0.398317	+	0.917248i	$0.630406\pi$
$311$	−24.5792	+	17.8578i	−1.39376	+	1.01262i	−0.995441	+	0.0953766i	$0.969594\pi$
$312$		0			0
$313$	5.00645	+	15.4083i	0.282981	+	0.870927i	0.986996	+	0.160742i	$0.0513887\pi$
$313$	5.00645	+	15.4083i	0.282981	+	0.870927i	−0.704015	+	0.710185i	$0.748611\pi$
$314$	5.71293	+	17.5826i	0.322399	+	0.992243i
$315$		0			0
$316$	−9.44314	+	6.86084i	−0.531218	+	0.385952i
$317$	10.2173	−	31.4458i	0.573863	−	1.76617i	−0.0661538	−	0.997809i	$-0.521073\pi$
$317$	10.2173	−	31.4458i	0.573863	−	1.76617i	0.640017	−	0.768361i	$-0.278927\pi$
$318$		0			0
$319$	14.6554	+	6.95828i	0.820546	+	0.389589i
$320$	1.00000			0.0559017
$321$		0			0
$322$	−6.71492	+	4.87868i	−0.374208	+	0.271878i
$323$	2.89154	+	2.10083i	0.160890	+	0.116893i
$324$		0			0
$325$	−2.08774	−	6.42541i	−0.115807	−	0.356418i
$326$	−9.34253	−	6.78775i	−0.517435	−	0.375939i
$327$		0			0
$328$	−0.407837	+	1.25519i	−0.0225190	+	0.0693065i
$329$	−19.1666			−1.05669
$330$		0			0
$331$	−0.733928			−0.0403403			−0.0201702	−	0.999797i	$-0.506421\pi$
$331$	−0.733928			−0.0403403			−0.0201702	+	0.999797i	$0.506421\pi$
$332$	2.47214	−	7.60845i	0.135676	−	0.417568i
$333$		0			0
$334$	2.38832	+	1.73521i	0.130683	+	0.0949467i
$335$	4.68706	+	14.4253i	0.256081	+	0.788137i
$336$		0			0
$337$	−13.2530	−	9.62883i	−0.721934	−	0.524516i	0.165067	−	0.986282i	$-0.447216\pi$
$337$	−13.2530	−	9.62883i	−0.721934	−	0.524516i	−0.887002	+	0.461766i	$0.847216\pi$
$338$	−26.4101	+	19.1880i	−1.43652	+	1.04369i
$339$		0			0
$340$	−0.557453			−0.0302322
$341$	−1.03321	+	7.95747i	−0.0559515	+	0.430921i
$342$		0			0
$343$	3.72518	−	11.4649i	0.201141	−	0.619048i
$344$	1.06902	−	0.776691i	0.0576379	−	0.0418764i
$345$		0			0
$346$	−0.569023	−	1.75127i	−0.0305909	−	0.0941491i
$347$	−5.00645	−	15.4083i	−0.268760	−	0.827159i	−0.990803	−	0.135311i	$-0.956797\pi$
$347$	−5.00645	−	15.4083i	−0.268760	−	0.827159i	0.722043	−	0.691848i	$-0.243203\pi$
$348$		0			0
$349$	3.39467	−	2.46637i	0.181713	−	0.132022i	−0.493211	−	0.869910i	$-0.664177\pi$
$349$	3.39467	−	2.46637i	0.181713	−	0.132022i	0.674923	+	0.737888i	$0.264177\pi$
$350$	−0.988430	+	3.04208i	−0.0528338	+	0.162606i
$351$		0			0
$352$	−3.26001	+	0.610212i	−0.173759	+	0.0325244i
$353$	−3.32139			−0.176780			−0.0883898	−	0.996086i	$-0.528172\pi$
$353$	−3.32139			−0.176780			−0.0883898	+	0.996086i	$0.528172\pi$
$354$		0			0
$355$	−5.13805	+	3.73301i	−0.272699	+	0.198128i
$356$	−10.5799	−	7.68674i	−0.560733	−	0.407396i
$357$		0			0
$358$	5.73607	+	17.6538i	0.303161	+	0.933032i
$359$	17.9443	+	13.0373i	0.947062	+	0.688081i	0.950110	−	0.311914i	$-0.100970\pi$
$359$	17.9443	+	13.0373i	0.947062	+	0.688081i	−0.00304782	+	0.999995i	$0.500970\pi$
$360$		0			0
$361$	6.83176	−	21.0260i	0.359566	−	1.10663i
$362$	9.52786			0.500773
$363$		0			0
$364$	21.6102			1.13268
$365$	−2.14590	+	6.60440i	−0.112321	+	0.345690i
$366$		0			0
$367$	13.7935	+	10.0216i	0.720016	+	0.523122i	0.886389	−	0.462941i	$-0.153206\pi$
$367$	13.7935	+	10.0216i	0.720016	+	0.523122i	−0.166373	+	0.986063i	$0.553206\pi$
$368$	−0.801866	−	2.46789i	−0.0418002	−	0.128648i
$369$		0			0
$370$	4.63805	+	3.36974i	0.241121	+	0.175184i
$371$	6.30037	−	4.57748i	0.327099	−	0.237651i
$372$		0			0
$373$	0.231215			0.0119719			0.00598594	−	0.999982i	$-0.498095\pi$
$373$	0.231215			0.0119719			0.00598594	+	0.999982i	$0.498095\pi$
$374$	1.81730	−	0.340165i	0.0939704	−	0.0175895i
$375$		0			0
$376$	1.85168	−	5.69887i	0.0954929	−	0.293897i
$377$	26.7361	−	19.4249i	1.37698	−	1.00043i
$378$		0			0
$379$	−3.69963	−	11.3863i	−0.190037	−	0.584875i	0.809961	−	0.586483i	$-0.199488\pi$
$379$	−3.69963	−	11.3863i	−0.190037	−	0.584875i	−0.999999	+	0.00160836i	$0.999488\pi$
$380$	1.98128	+	6.09775i	0.101637	+	0.312808i
$381$		0			0
$382$	0.739195	−	0.537057i	0.0378205	−	0.0274782i
$383$	−0.948996	+	2.92071i	−0.0484914	+	0.149241i	−0.972370	−	0.233444i	$-0.925001\pi$
$383$	−0.948996	+	2.92071i	−0.0484914	+	0.149241i	0.923879	+	0.382685i	$0.125001\pi$
$384$		0			0
$385$	1.36598	−	10.5203i	0.0696166	−	0.536166i
$386$	23.2952			1.18570
$387$		0			0
$388$	−6.17549	+	4.48675i	−0.313513	+	0.227780i
$389$	15.9837	+	11.6128i	0.810406	+	0.588794i	0.913948	−	0.405831i	$-0.133018\pi$
$389$	15.9837	+	11.6128i	0.810406	+	0.588794i	−0.103542	+	0.994625i	$0.533018\pi$
$390$		0			0
$391$	0.447003	+	1.37573i	0.0226059	+	0.0695739i
$392$	−2.61411	−	1.89926i	−0.132032	−	0.0959272i
$393$		0			0
$394$	7.59861	−	23.3861i	0.382813	−	1.17818i
$395$	11.6724			0.587300
$396$		0			0
$397$	−11.4546			−0.574889			−0.287444	−	0.957797i	$-0.592806\pi$
$397$	−11.4546			−0.574889			−0.287444	+	0.957797i	$0.592806\pi$
$398$	3.24813	−	9.99672i	0.162814	−	0.501090i
$399$		0			0
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	−6.89111	−	21.2087i	−0.344126	−	1.05911i	−0.962050	−	0.272872i	$-0.912026\pi$
$401$	−6.89111	−	21.2087i	−0.344126	−	1.05911i	0.617925	−	0.786237i	$-0.287974\pi$
$402$		0			0
$403$	13.2240	+	9.60777i	0.658732	+	0.478597i
$404$	12.9231	−	9.38920i	0.642950	−	0.467130i
$405$		0			0
$406$	−15.6462			−0.776509
$407$	−17.1763	−	8.15517i	−0.851398	−	0.404237i
$408$		0			0
$409$	−11.2115	+	34.5054i	−0.554372	+	1.70618i	0.143222	+	0.989691i	$0.454254\pi$
$409$	−11.2115	+	34.5054i	−0.554372	+	1.70618i	−0.697595	+	0.716492i	$0.745746\pi$
$410$	1.06773	−	0.775752i	0.0527315	−	0.0383117i
$411$		0			0
$412$	5.65204	+	17.3952i	0.278456	+	0.857000i
$413$	10.2068	+	31.4132i	0.502242	+	1.54574i
$414$		0			0
$415$	−6.47214	+	4.70228i	−0.317705	+	0.230826i
$416$	−2.08774	+	6.42541i	−0.102360	+	0.315032i
$417$		0			0
$418$	−10.1799	−	18.6697i	−0.497916	−	0.913165i
$419$	−9.06157			−0.442687			−0.221343	−	0.975196i	$-0.571044\pi$
$419$	−9.06157			−0.442687			−0.221343	+	0.975196i	$0.571044\pi$
$420$		0			0
$421$	1.96256	−	1.42588i	0.0956493	−	0.0694933i	−0.538933	−	0.842349i	$-0.681172\pi$
$421$	1.96256	−	1.42588i	0.0956493	−	0.0694933i	0.634582	+	0.772856i	$0.281172\pi$
$422$	5.71864	+	4.15483i	0.278379	+	0.202254i
$423$		0			0
$424$	0.752362	+	2.31553i	0.0365379	+	0.112452i
$425$	0.450989	+	0.327663i	0.0218762	+	0.0158940i
$426$		0			0
$427$	−3.87971	+	11.9405i	−0.187752	+	0.577842i
$428$	−17.1149			−0.827280
$429$		0			0
$430$	−1.32139			−0.0637229
$431$	−0.821514	+	2.52836i	−0.0395709	+	0.121787i	−0.968891	−	0.247490i	$-0.920394\pi$
$431$	−0.821514	+	2.52836i	−0.0395709	+	0.121787i	0.929320	+	0.369276i	$0.120394\pi$
$432$		0			0
$433$	15.5265	+	11.2806i	0.746154	+	0.542113i	0.894632	−	0.446803i	$-0.147437\pi$
$433$	15.5265	+	11.2806i	0.746154	+	0.542113i	−0.148478	+	0.988916i	$0.547437\pi$
$434$	−2.39141	−	7.36002i	−0.114792	−	0.353292i
$435$		0			0
$436$	−7.23607	−	5.25731i	−0.346545	−	0.251780i
$437$	13.4599	−	9.77916i	0.643873	−	0.467801i
$438$		0			0
$439$	12.6955			0.605923			0.302962	−	0.953003i	$-0.402025\pi$
$439$	12.6955			0.605923			0.302962	+	0.953003i	$0.402025\pi$
$440$	2.99607	+	1.42251i	0.142832	+	0.0678156i
$441$		0			0
$442$	1.16382	−	3.58187i	0.0553573	−	0.170372i
$443$	13.6876	−	9.94466i	0.650320	−	0.472485i	−0.213060	−	0.977039i	$-0.568343\pi$
$443$	13.6876	−	9.94466i	0.650320	−	0.472485i	0.863380	+	0.504554i	$0.168343\pi$
$444$		0			0
$445$	4.04116	+	12.4374i	0.191569	+	0.589590i
$446$	0.247638	+	0.762151i	0.0117260	+	0.0360889i
$447$		0			0
$448$	2.58774	−	1.88011i	0.122259	−	0.0888267i
$449$	5.95814	−	18.3373i	0.281182	−	0.865389i	−0.706335	−	0.707878i	$-0.749653\pi$
$449$	5.95814	−	18.3373i	0.281182	−	0.865389i	0.987517	−	0.157512i	$-0.0503472\pi$
$450$		0			0
$451$	−3.00744	+	3.18050i	−0.141615	+	0.149764i
$452$	−4.81666			−0.226557
$453$		0			0
$454$	−3.93942	+	2.86216i	−0.184886	+	0.134328i
$455$	−17.4830	−	12.7021i	−0.819616	−	0.595486i
$456$		0			0
$457$	12.2129	+	37.5875i	0.571297	+	1.75827i	0.648457	+	0.761252i	$0.275415\pi$
$457$	12.2129	+	37.5875i	0.571297	+	1.75827i	−0.0771599	+	0.997019i	$0.524585\pi$
$458$	0.939419	+	0.682528i	0.0438962	+	0.0318924i
$459$		0			0
$460$	−0.801866	+	2.46789i	−0.0373872	+	0.115066i
$461$	−13.8398			−0.644584			−0.322292	−	0.946640i	$-0.604453\pi$
$461$	−13.8398			−0.644584			−0.322292	+	0.946640i	$0.604453\pi$
$462$		0			0
$463$	12.5919			0.585195			0.292598	−	0.956236i	$-0.405480\pi$
$463$	12.5919			0.585195			0.292598	+	0.956236i	$0.405480\pi$
$464$	1.51157	−	4.65213i	0.0701729	−	0.215970i
$465$		0			0
$466$	9.75086	+	7.08442i	0.451700	+	0.328179i
$467$	3.62687	+	11.1624i	0.167832	+	0.516533i	0.999234	−	0.0391385i	$-0.0124614\pi$
$467$	3.62687	+	11.1624i	0.167832	+	0.516533i	−0.831402	+	0.555671i	$0.812461\pi$
$468$		0			0
$469$	39.2500	+	28.5168i	1.81239	+	1.31678i
$470$	−4.84775	+	3.52210i	−0.223610	+	0.162462i
$471$		0			0
$472$	−10.3262			−0.475304
$473$	4.30772	−	0.806326i	0.198069	−	0.0370749i
$474$		0			0
$475$	1.98128	−	6.09775i	0.0909073	−	0.279784i
$476$	−1.44255	+	1.04807i	−0.0661190	+	0.0480383i
$477$		0			0
$478$	8.73294	+	26.8772i	0.399435	+	1.22934i
$479$	−6.61318	−	20.3533i	−0.302164	−	0.929965i	−0.980720	−	0.195417i	$-0.937394\pi$
$479$	−6.61318	−	20.3533i	−0.302164	−	0.929965i	0.678556	−	0.734548i	$-0.262606\pi$
$480$		0			0
$481$	−31.3350	+	22.7662i	−1.42875	+	1.03805i
$482$	7.65919	−	23.5726i	0.348867	−	1.07370i
$483$		0			0
$484$	−10.6353	−	2.80916i	−0.483421	−	0.127689i
$485$	7.63332			0.346611
$486$		0			0
$487$	12.8231	−	9.31654i	0.581071	−	0.422173i	−0.258039	−	0.966134i	$-0.583076\pi$
$487$	12.8231	−	9.31654i	0.581071	−	0.422173i	0.839110	+	0.543962i	$0.183076\pi$
$488$	−3.17549	−	2.30713i	−0.143748	−	0.104439i
$489$		0			0
$490$	0.998501	+	3.07307i	0.0451077	+	0.138827i
$491$	22.3853	+	16.2639i	1.01024	+	0.733979i	0.964258	−	0.264964i	$-0.0853599\pi$
$491$	22.3853	+	16.2639i	1.01024	+	0.733979i	0.0459769	+	0.998943i	$0.485360\pi$
$492$		0			0
$493$	−0.842630	+	2.59335i	−0.0379501	+	0.116799i
$494$	−43.3170			−1.94892
$495$		0			0
$496$	2.41941			0.108635
$497$	−6.27749	+	19.3201i	−0.281584	+	0.866627i
$498$		0			0
$499$	5.71309	+	4.15080i	0.255753	+	0.185815i	0.708273	−	0.705939i	$-0.249475\pi$
$499$	5.71309	+	4.15080i	0.255753	+	0.185815i	−0.452520	+	0.891754i	$0.649475\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$		0			0
$502$	−14.4503	−	10.4987i	−0.644948	−	0.468582i
$503$	0.933067	−	0.677913i	0.0416034	−	0.0302267i	−0.566789	−	0.823863i	$-0.691815\pi$
$503$	0.933067	−	0.677913i	0.0416034	−	0.0302267i	0.608393	+	0.793636i	$0.291815\pi$
$504$		0			0
$505$	−15.9739			−0.710827
$506$	1.10815	−	8.53465i	0.0492634	−	0.379411i
$507$		0			0
$508$	−5.01087	+	15.4219i	−0.222321	+	0.684235i
$509$	−6.85674	+	4.98171i	−0.303919	+	0.220810i	−0.729283	−	0.684212i	$-0.760146\pi$
$509$	−6.85674	+	4.98171i	−0.303919	+	0.220810i	0.425364	+	0.905023i	$0.360146\pi$
$510$		0			0
$511$	6.86393	+	21.1250i	0.303642	+	0.934515i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$		0			0
$514$	3.49687	−	2.54063i	0.154240	−	0.112062i
$515$	5.65204	−	17.3952i	0.249059	−	0.766524i
$516$		0			0
$517$	13.6545	−	14.4402i	0.600523	−	0.635080i
$518$	18.3375			0.805705
$519$		0			0
$520$	5.46578	−	3.97112i	0.239690	−	0.174145i
$521$	25.1295	+	18.2576i	1.10094	+	0.799882i	0.981214	−	0.192925i	$-0.0617973\pi$
$521$	25.1295	+	18.2576i	1.10094	+	0.799882i	0.119730	+	0.992807i	$0.461797\pi$
$522$		0			0
$523$	6.12860	+	18.8619i	0.267985	+	0.824773i	0.990991	+	0.133931i	$0.0427600\pi$
$523$	6.12860	+	18.8619i	0.267985	+	0.824773i	−0.723006	+	0.690842i	$0.757240\pi$
$524$	13.9869	+	10.1621i	0.611022	+	0.443933i
$525$		0			0
$526$	−7.11610	+	21.9011i	−0.310277	+	0.954934i
$527$	−1.34871			−0.0587506
$528$		0			0
$529$	−16.2665			−0.707240
$530$	0.752362	−	2.31553i	0.0326805	−	0.100580i
$531$		0			0
$532$	16.5915	+	12.0544i	0.719331	+	0.522625i
$533$	2.75538	+	8.48019i	0.119349	+	0.367318i
$534$		0			0
$535$	13.8463	+	10.0599i	0.598626	+	0.434927i
$536$	−12.2709	+	8.91531i	−0.530021	+	0.385083i
$537$		0			0
$538$	11.8567			0.511178
$539$	−5.13034	−	9.40893i	−0.220979	−	0.405271i
$540$		0			0
$541$	7.79751	−	23.9983i	0.335241	−	1.03177i	−0.631362	−	0.775488i	$-0.717504\pi$
$541$	7.79751	−	23.9983i	0.335241	−	1.03177i	0.966603	−	0.256278i	$-0.0824962\pi$
$542$	−9.24451	+	6.71653i	−0.397086	+	0.288500i
$543$		0			0
$544$	−0.172263	−	0.530170i	−0.00738570	−	0.0227308i
$545$	2.76393	+	8.50651i	0.118394	+	0.364379i
$546$		0			0
$547$	−10.9136	+	7.92923i	−0.466634	+	0.339029i	−0.796128	−	0.605128i	$-0.793122\pi$
$547$	−10.9136	+	7.92923i	−0.466634	+	0.339029i	0.329494	+	0.944158i	$0.393122\pi$
$548$	−2.45099	+	7.54337i	−0.104701	+	0.322237i
$549$		0			0
$550$	−1.58774	−	2.91188i	−0.0677016	−	0.124163i
$551$	31.3624			1.33608
$552$		0			0
$553$	30.2051	−	21.9453i	1.28445	−	0.933208i
$554$	−12.1663	−	8.83937i	−0.516898	−	0.375549i
$555$		0			0
$556$	−2.53943	−	7.81557i	−0.107696	−	0.331454i
$557$	31.1108	+	22.6033i	1.31821	+	0.957733i	0.999953	+	0.00972678i	$0.00309618\pi$
$557$	31.1108	+	22.6033i	1.31821	+	0.957733i	0.318253	+	0.948006i	$0.396904\pi$
$558$		0			0
$559$	2.75871	−	8.49045i	0.116681	−	0.359108i
$560$	−3.19863			−0.135167
$561$		0			0
$562$	13.2666			0.559620
$563$	8.60373	−	26.4796i	0.362604	−	1.11598i	−0.588864	−	0.808232i	$-0.700425\pi$
$563$	8.60373	−	26.4796i	0.362604	−	1.11598i	0.951468	−	0.307748i	$-0.0995755\pi$
$564$		0			0
$565$	3.89676	+	2.83116i	0.163938	+	0.119108i
$566$	−4.67276	−	14.3813i	−0.196411	−	0.604490i
$567$		0			0
$568$	−5.13805	−	3.73301i	−0.215588	−	0.156634i
$569$	−6.68417	+	4.85633i	−0.280215	+	0.203588i	−0.719011	−	0.694999i	$-0.755405\pi$
$569$	−6.68417	+	4.85633i	−0.280215	+	0.203588i	0.438796	+	0.898587i	$0.355405\pi$
$570$		0			0
$571$	−6.71079			−0.280838			−0.140419	−	0.990092i	$-0.544845\pi$
$571$	−6.71079			−0.280838			−0.140419	+	0.990092i	$0.544845\pi$
$572$	−15.3953	+	16.2812i	−0.643708	+	0.680750i
$573$		0			0
$574$	1.30452	−	4.01490i	0.0544496	−	0.167578i
$575$	2.09931	−	1.52524i	0.0875474	−	0.0636069i
$576$		0			0
$577$	−12.3031	−	37.8650i	−0.512185	−	1.57634i	−0.788347	−	0.615231i	$-0.789063\pi$
$577$	−12.3031	−	37.8650i	−0.512185	−	1.57634i	0.276162	−	0.961111i	$-0.410937\pi$
$578$	−5.15726	−	15.8724i	−0.214514	−	0.660205i
$579$		0			0
$580$	−3.95734	+	2.87518i	−0.164320	+	0.119385i
$581$	−7.90744	+	24.3366i	−0.328056	+	1.00965i
$582$		0			0
$583$	−1.03974	+	8.00775i	−0.0430616	+	0.331647i
$584$	−6.94427			−0.287356
$585$		0			0
$586$	11.2585	−	8.17978i	0.465085	−	0.337904i
$587$	−8.13805	−	5.91264i	−0.335893	−	0.244041i	0.407034	−	0.913413i	$-0.366563\pi$
$587$	−8.13805	−	5.91264i	−0.335893	−	0.244041i	−0.742927	+	0.669372i	$0.766563\pi$
$588$		0			0
$589$	4.79352	+	14.7529i	0.197514	+	0.607884i
$590$	8.35410	+	6.06961i	0.343933	+	0.249882i
$591$		0			0
$592$	−1.77158	+	5.45235i	−0.0728113	+	0.224090i
$593$	23.6430			0.970900			0.485450	−	0.874264i	$-0.338656\pi$
$593$	23.6430			0.970900			0.485450	+	0.874264i	$0.338656\pi$
$594$		0			0
$595$	1.78309			0.0730994
$596$	1.88047	−	5.78748i	0.0770269	−	0.237064i
$597$		0			0
$598$	−14.1831	−	10.3046i	−0.579991	−	0.421388i
$599$	−9.70335	−	29.8638i	−0.396468	−	1.22020i	−0.927812	−	0.373048i	$-0.878313\pi$
$599$	−9.70335	−	29.8638i	−0.396468	−	1.22020i	0.531344	−	0.847156i	$-0.321687\pi$
$600$		0			0
$601$	−13.8721	−	10.0787i	−0.565856	−	0.411118i	0.267742	−	0.963491i	$-0.413723\pi$
$601$	−13.8721	−	10.0787i	−0.565856	−	0.411118i	−0.833597	+	0.552373i	$0.813723\pi$
$602$	−3.41941	+	2.48434i	−0.139365	+	0.101254i
$603$		0			0
$604$	18.2761			0.743644
$605$	6.95292	+	8.52390i	0.282676	+	0.346546i
$606$		0			0
$607$	−0.433098	+	1.33294i	−0.0175789	+	0.0541023i	−0.959461	−	0.281841i	$-0.909055\pi$
$607$	−0.433098	+	1.33294i	−0.0175789	+	0.0541023i	0.941882	+	0.335943i	$0.109055\pi$
$608$	−5.18706	+	3.76862i	−0.210363	+	0.152838i
$609$		0			0
$610$	1.21293	+	3.73301i	0.0491100	+	0.151145i
$611$	−12.5101	−	38.5020i	−0.506103	−	1.55763i
$612$		0			0
$613$	−9.73920	+	7.07594i	−0.393362	+	0.285795i	−0.766832	−	0.641848i	$-0.778168\pi$
$613$	−9.73920	+	7.07594i	−0.393362	+	0.285795i	0.373470	+	0.927642i	$0.378168\pi$
$614$	−7.44154	+	22.9027i	−0.300316	+	0.924278i
$615$		0			0
$616$	10.4275	−	1.95184i	0.420138	−	0.0786419i
$617$	5.25177			0.211428			0.105714	−	0.994397i	$-0.466287\pi$
$617$	5.25177			0.211428			0.105714	+	0.994397i	$0.466287\pi$
$618$		0			0
$619$	−34.0049	+	24.7060i	−1.36677	+	0.993018i	−0.368791	+	0.929512i	$0.620228\pi$
$619$	−34.0049	+	24.7060i	−1.36677	+	0.993018i	−0.997981	+	0.0635059i	$0.979772\pi$
$620$	−1.95734	−	1.42209i	−0.0786087	−	0.0571126i
$621$		0			0
$622$	9.38842	+	28.8946i	0.376441	+	1.15857i
$623$	33.8411	+	24.5870i	1.35582	+	0.985058i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	16.2012			0.647531
$627$		0			0
$628$	18.4874			0.737729
$629$	0.987571	−	3.03943i	0.0393770	−	0.121190i
$630$		0			0
$631$	13.7493	+	9.98943i	0.547350	+	0.397673i	0.826807	−	0.562485i	$-0.190155\pi$
$631$	13.7493	+	9.98943i	0.547350	+	0.397673i	−0.279458	+	0.960158i	$0.590155\pi$
$632$	3.60696	+	11.1011i	0.143477	+	0.441577i
$633$		0			0
$634$	−26.7494	−	19.4345i	−1.06235	−	0.771845i
$635$	13.1186	−	9.53124i	0.520597	−	0.378236i
$636$		0			0
$637$	−21.8304			−0.864950
$638$	11.1465	−	11.7879i	0.441294	−	0.466688i
$639$		0			0
$640$	0.309017	−	0.951057i	0.0122150	−	0.0375938i
$641$	−40.3764	+	29.3352i	−1.59477	+	1.15867i	−0.698078	+	0.716022i	$0.745961\pi$
$641$	−40.3764	+	29.3352i	−1.59477	+	1.15867i	−0.896695	+	0.442649i	$0.854039\pi$
$642$		0			0
$643$	−8.26864	−	25.4482i	−0.326083	−	1.00358i	−0.970949	−	0.239285i	$-0.923087\pi$
$643$	−8.26864	−	25.4482i	−0.326083	−	1.00358i	0.644866	−	0.764296i	$-0.276913\pi$
$644$	2.56487	+	7.89386i	0.101070	+	0.311062i
$645$		0			0
$646$	2.89154	−	2.10083i	0.113766	−	0.0826560i
$647$	2.42748	−	7.47103i	0.0954343	−	0.293716i	−0.891932	−	0.452169i	$-0.850650\pi$
$647$	2.42748	−	7.47103i	0.0954343	−	0.293716i	0.987367	+	0.158452i	$0.0506504\pi$
$648$		0			0
$649$	−30.9382	−	14.6892i	−1.21443	−	0.576601i
$650$	−6.75608			−0.264995
$651$		0			0
$652$	−9.34253	+	6.78775i	−0.365882	+	0.265829i
$653$	0.234934	+	0.170689i	0.00919367	+	0.00667959i	0.592373	−	0.805664i	$-0.298191\pi$
$653$	0.234934	+	0.170689i	0.00919367	+	0.00667959i	−0.583179	+	0.812344i	$0.698191\pi$
$654$		0			0
$655$	−5.34253	−	16.4426i	−0.208750	−	0.642466i
$656$	1.06773	+	0.775752i	0.0416879	+	0.0302880i
$657$		0			0
$658$	−5.92282	+	18.2286i	−0.230896	+	0.710623i
$659$	17.7202			0.690282			0.345141	−	0.938551i	$-0.387831\pi$
$659$	17.7202			0.690282			0.345141	+	0.938551i	$0.387831\pi$
$660$		0			0
$661$	22.9494			0.892630			0.446315	−	0.894876i	$-0.352736\pi$
$661$	22.9494			0.892630			0.446315	+	0.894876i	$0.352736\pi$
$662$	−0.226796	+	0.698007i	−0.00881468	+	0.0271288i
$663$		0			0
$664$	−6.47214	−	4.70228i	−0.251168	−	0.182484i
$665$	−6.33737	−	19.5044i	−0.245753	−	0.756349i
$666$		0			0
$667$	10.2689	+	7.46078i	0.397613	+	0.288883i
$668$	2.38832	−	1.73521i	0.0924068	−	0.0671375i
$669$		0			0
$670$	15.1676			0.585977
$671$	−6.23208	−	11.4295i	−0.240587	−	0.441231i
$672$		0			0
$673$	−10.9108	+	33.5800i	−0.420581	+	1.29442i	0.486581	+	0.873635i	$0.338244\pi$
$673$	−10.9108	+	33.5800i	−0.420581	+	1.29442i	−0.907163	+	0.420780i	$0.861756\pi$
$674$	−13.2530	+	9.62883i	−0.510485	+	0.370889i
$675$		0			0
$676$	10.0877	+	31.0469i	0.387990	+	1.19411i
$677$	13.0479	+	40.1572i	0.501471	+	1.54337i	0.806624	+	0.591065i	$0.201292\pi$
$677$	13.0479	+	40.1572i	0.501471	+	1.54337i	−0.305153	+	0.952303i	$0.598708\pi$
$678$		0			0
$679$	19.7531	−	14.3515i	0.758054	−	0.550758i
$680$	−0.172263	+	0.530170i	−0.00660597	+	0.0203311i
$681$		0			0
$682$	7.24872	+	3.44163i	0.277568	+	0.131787i
$683$	−34.7325			−1.32900			−0.664502	−	0.747287i	$-0.731356\pi$
$683$	−34.7325			−1.32900			−0.664502	+	0.747287i	$0.731356\pi$
$684$		0			0
$685$	6.41677	−	4.66206i	0.245172	−	0.178128i
$686$	−9.75265	−	7.08571i	−0.372358	−	0.270534i
$687$		0			0
$688$	−0.408331	−	1.25671i	−0.0155675	−	0.0479117i
$689$	13.3075	+	9.66848i	0.506976	+	0.368340i
$690$		0			0
$691$	5.16631	−	15.9003i	0.196536	−	0.604874i	−0.803420	−	0.595413i	$-0.796988\pi$
$691$	5.16631	−	15.9003i	0.196536	−	0.604874i	0.999955	−	0.00946111i	$-0.00301161\pi$
$692$	−1.84140			−0.0699994
$693$		0			0
$694$	−16.2012			−0.614990
$695$	−2.53943	+	7.81557i	−0.0963262	+	0.296462i
$696$		0			0
$697$	−0.595210	−	0.432446i	−0.0225452	−	0.0163800i
$698$	−1.29665	−	3.99067i	−0.0490789	−	0.151049i
$699$		0			0
$700$	2.58774	+	1.88011i	0.0978075	+	0.0710613i
$701$	−0.517428	+	0.375934i	−0.0195430	+	0.0141988i	−0.597514	−	0.801859i	$-0.703845\pi$
$701$	−0.517428	+	0.375934i	−0.0195430	+	0.0141988i	0.577971	+	0.816057i	$0.303845\pi$
$702$		0			0
$703$	−36.7571			−1.38632
$704$	−0.427051	+	3.28902i	−0.0160951	+	0.123959i
$705$		0			0
$706$	−1.02636	+	3.15883i	−0.0386277	+	0.118884i
$707$	−41.3363	+	30.0326i	−1.55461	+	1.12949i
$708$		0			0
$709$	3.90584	+	12.0210i	0.146687	+	0.451456i	0.997224	−	0.0744588i	$-0.0237229\pi$
$709$	3.90584	+	12.0210i	0.146687	+	0.451456i	−0.850537	+	0.525915i	$0.823723\pi$
$710$	1.96256	+	6.04014i	0.0736535	+	0.226682i
$711$		0			0
$712$	−10.5799	+	7.68674i	−0.396498	+	0.288073i
$713$	−1.94004	+	5.97083i	−0.0726551	+	0.223609i
$714$		0			0
$715$	22.0249	−	4.12264i	0.823683	−	0.154178i
$716$	18.5623			0.693706
$717$		0			0
$718$	17.9443	−	13.0373i	0.669674	−	0.486547i
$719$	33.2474	+	24.1556i	1.23992	+	0.900853i	0.997593	−	0.0693423i	$-0.0220901\pi$
$719$	33.2474	+	24.1556i	1.23992	+	0.900853i	0.242325	+	0.970195i	$0.422090\pi$
$720$		0			0
$721$	−18.0788	−	55.6408i	−0.673289	−	2.07217i
$722$	−17.8858	−	12.9948i	−0.665640	−	0.483616i
$723$		0			0
$724$	2.94427	−	9.06154i	0.109423	−	0.336769i
$725$	4.89154			0.181667
$726$		0			0
$727$	−15.8668			−0.588467			−0.294234	−	0.955734i	$-0.595064\pi$
$727$	−15.8668			−0.588467			−0.294234	+	0.955734i	$0.595064\pi$
$728$	6.67791	−	20.5525i	0.247500	−	0.761727i
$729$		0			0
$730$	5.61803	+	4.08174i	0.207933	+	0.151072i
$731$	0.227625	+	0.700559i	0.00841902	+	0.0259111i
$732$		0			0
$733$	−16.8173	−	12.2184i	−0.621159	−	0.451299i	0.232167	−	0.972676i	$-0.425418\pi$
$733$	−16.8173	−	12.2184i	−0.621159	−	0.451299i	−0.853326	+	0.521377i	$0.825418\pi$
$734$	13.7935	−	10.0216i	0.509128	−	0.369903i
$735$		0			0
$736$	−2.59489			−0.0956491
$737$	−49.4466	+	9.25548i	−1.82139	+	0.340930i
$738$		0			0
$739$	−10.6966	+	32.9209i	−0.393482	+	1.21101i	0.536655	+	0.843802i	$0.319688\pi$
$739$	−10.6966	+	32.9209i	−0.393482	+	1.21101i	−0.930137	+	0.367212i	$0.880312\pi$
$740$	4.63805	−	3.36974i	0.170498	−	0.123874i
$741$		0			0
$742$	−2.40653	−	7.40653i	−0.0883463	−	0.271902i
$743$	12.7455	+	39.2267i	0.467588	+	1.43909i	0.855699	+	0.517474i	$0.173128\pi$
$743$	12.7455	+	39.2267i	0.467588	+	1.43909i	−0.388111	+	0.921613i	$0.626872\pi$
$744$		0			0
$745$	−4.92313	+	3.57686i	−0.180369	+	0.131046i
$746$	0.0714495	−	0.219899i	0.00261595	−	0.00805107i
$747$		0			0
$748$	0.238061	−	1.83347i	0.00870437	−	0.0670384i
$749$	54.7442			2.00031
$750$		0			0
$751$	−2.71665	+	1.97376i	−0.0991318	+	0.0720235i	−0.636247	−	0.771485i	$-0.719514\pi$
$751$	−2.71665	+	1.97376i	−0.0991318	+	0.0720235i	0.537115	+	0.843509i	$0.319514\pi$
$752$	−4.84775	−	3.52210i	−0.176779	−	0.128438i
$753$		0			0
$754$	−10.2123	−	31.4302i	−0.371910	−	1.14462i
$755$	−14.7857	−	10.7424i	−0.538106	−	0.390957i
$756$		0			0
$757$	4.55017	−	14.0040i	0.165379	−	0.508984i	−0.833685	−	0.552240i	$-0.813773\pi$
$757$	4.55017	−	14.0040i	0.165379	−	0.508984i	0.999064	+	0.0432562i	$0.0137732\pi$
$758$	−11.9723			−0.434852
$759$		0			0
$760$	6.41156			0.232572
$761$	0.0710163	−	0.218566i	0.00257434	−	0.00792300i	−0.949761	−	0.312976i	$-0.898674\pi$
$761$	0.0710163	−	0.218566i	0.00257434	−	0.00792300i	0.952335	+	0.305053i	$0.0986741\pi$
$762$		0			0
$763$	23.1455	+	16.8162i	0.837923	+	0.608787i
$764$	−0.282347	−	0.868976i	−0.0102150	−	0.0314384i
$765$		0			0
$766$	2.48450	+	1.80510i	0.0897688	+	0.0652208i
$767$	−56.4410	+	41.0068i	−2.03797	+	1.48067i
$768$		0			0
$769$	26.3568			0.950451			0.475226	−	0.879864i	$-0.342366\pi$
$769$	26.3568			0.950451			0.475226	+	0.879864i	$0.342366\pi$
$770$	−9.58332	−	4.55008i	−0.345359	−	0.163974i
$771$		0			0
$772$	7.19863	−	22.1551i	0.259084	−	0.797379i
$773$	−44.2997	+	32.1856i	−1.59335	+	1.15764i	−0.694396	+	0.719593i	$0.744329\pi$
$773$	−44.2997	+	32.1856i	−1.59335	+	1.15764i	−0.898954	+	0.438044i	$0.855671\pi$
$774$		0			0
$775$	0.747638	+	2.30099i	0.0268559	+	0.0826541i
$776$	2.35883	+	7.25972i	0.0846769	+	0.260609i
$777$		0			0
$778$	15.9837	−	11.6128i	0.573044	−	0.416341i
$779$	−2.61487	+	8.04774i	−0.0936874	+	0.288340i
$780$		0			0
$781$	−10.0837	−	18.4933i	−0.360824	−	0.661742i
$782$	1.44653			0.0517279
$783$		0			0
$784$	−2.61411	+	1.89926i	−0.0933610	+	0.0678307i
$785$	−14.9566	−	10.8666i	−0.533825	−	0.387847i
$786$		0			0
$787$	−2.30473	−	7.09322i	−0.0821546	−	0.252846i	0.901539	−	0.432698i	$-0.142438\pi$
$787$	−2.30473	−	7.09322i	−0.0821546	−	0.252846i	−0.983694	+	0.179852i	$0.942438\pi$
$788$	−19.8934	−	14.4534i	−0.708674	−	0.514882i
$789$		0			0
$790$	3.60696	−	11.1011i	0.128330	−	0.394958i
$791$	15.4067			0.547799
$792$		0			0
$793$	−26.5184			−0.941697
$794$	−3.53966	+	10.8940i	−0.125618	+	0.386612i
$795$		0			0
$796$	−8.50372	−	6.17831i	−0.301406	−	0.218985i
$797$	−10.8448	−	33.3770i	−0.384144	−	1.18227i	−0.937100	−	0.349062i	$-0.886500\pi$
$797$	−10.8448	−	33.3770i	−0.384144	−	1.18227i	0.552956	−	0.833210i	$-0.313500\pi$
$798$		0			0
$799$	2.70239	+	1.96340i	0.0956039	+	0.0694603i
$800$	−0.809017	+	0.587785i	−0.0286031	+	0.0207813i
$801$		0			0
$802$	−22.3001			−0.787444
$803$	−20.8056	−	9.87831i	−0.734212	−	0.348598i
$804$		0			0
$805$	2.56487	−	7.89386i	0.0903998	−	0.278222i
$806$	13.2240	−	9.60777i	0.465794	−	0.338419i
$807$		0			0
$808$	−4.93619	−	15.1920i	−0.173655	−	0.534454i
$809$	−7.03401	−	21.6485i	−0.247303	−	0.761119i	−0.995249	−	0.0973602i	$-0.968960\pi$
$809$	−7.03401	−	21.6485i	−0.247303	−	0.761119i	0.747947	−	0.663759i	$-0.231040\pi$
$810$		0			0
$811$	17.6095	−	12.7940i	0.618353	−	0.449259i	−0.233993	−	0.972238i	$-0.575179\pi$
$811$	17.6095	−	12.7940i	0.618353	−	0.449259i	0.852346	+	0.522979i	$0.175179\pi$
$812$	−4.83495	+	14.8804i	−0.169673	+	0.522201i
$813$		0			0
$814$	−13.0638	+	13.8156i	−0.457886	+	0.484235i
$815$	11.5480			0.404509
$816$		0			0
$817$	6.85410	−	4.97980i	0.239795	−	0.174221i
$818$	29.3521	+	21.3255i	1.02627	+	0.745629i
$819$		0			0
$820$	−0.407837	−	1.25519i	−0.0142423	−	0.0438332i
$821$	−28.7404	−	20.8811i	−1.00305	−	0.728756i	−0.0403069	−	0.999187i	$-0.512834\pi$
$821$	−28.7404	−	20.8811i	−1.00305	−	0.728756i	−0.962739	+	0.270432i	$0.912834\pi$
$822$		0			0
$823$	12.2469	−	37.6922i	0.426901	−	1.31387i	−0.474260	−	0.880385i	$-0.657284\pi$
$823$	12.2469	−	37.6922i	0.426901	−	1.31387i	0.901162	−	0.433483i	$-0.142716\pi$
$824$	18.2904			0.637176
$825$		0			0
$826$	33.0298			1.14925
$827$	5.44600	−	16.7611i	0.189376	−	0.582839i	−0.810620	−	0.585572i	$-0.800870\pi$
$827$	5.44600	−	16.7611i	0.189376	−	0.582839i	0.999996	+	0.00273299i	$0.000869940\pi$
$828$		0			0
$829$	−5.70335	−	4.14373i	−0.198086	−	0.143918i	0.484321	−	0.874890i	$-0.339067\pi$
$829$	−5.70335	−	4.14373i	−0.198086	−	0.143918i	−0.682407	+	0.730973i	$0.739067\pi$
$830$	2.47214	+	7.60845i	0.0858091	+	0.264093i
$831$		0			0
$832$	5.46578	+	3.97112i	0.189492	+	0.137674i
$833$	1.45724	−	1.05875i	0.0504905	−	0.0366835i
$834$		0			0
$835$	−2.95212			−0.102162
$836$	−20.9017	+	3.91241i	−0.722901	+	0.135314i
$837$		0			0
$838$	−2.80018	+	8.61806i	−0.0967306	+	0.297706i
$839$	−18.2514	+	13.2604i	−0.630107	+	0.457799i	−0.856437	−	0.516251i	$-0.827327\pi$
$839$	−18.2514	+	13.2604i	−0.630107	+	0.457799i	0.226330	+	0.974051i	$0.427327\pi$
$840$		0			0
$841$	−1.56758	−	4.82453i	−0.0540546	−	0.166363i
$842$	−0.749631	−	2.30713i	−0.0258340	−	0.0795088i
$843$		0			0
$844$	5.71864	−	4.15483i	0.196844	−	0.143015i
$845$	10.0877	−	31.0469i	0.347029	−	1.06805i
$846$		0			0
$847$	34.0182	+	8.98544i	1.16888	+	0.308743i
$848$	2.43470			0.0836078
$849$		0			0
$850$	0.450989	−	0.327663i	0.0154688	−	0.0112387i
$851$	−12.0352	−	8.74411i	−0.412563	−	0.299744i
$852$		0			0
$853$	5.68233	+	17.4884i	0.194559	+	0.598792i	0.999981	+	0.00609051i	$0.00193868\pi$
$853$	5.68233	+	17.4884i	0.194559	+	0.598792i	−0.805422	+	0.592702i	$0.798061\pi$
$854$	10.1572	+	7.37964i	0.347572	+	0.252526i
$855$		0			0
$856$	−5.28880	+	16.2772i	−0.180767	+	0.556345i
$857$	−21.9179			−0.748700			−0.374350	−	0.927287i	$-0.622134\pi$
$857$	−21.9179			−0.748700			−0.374350	+	0.927287i	$0.622134\pi$
$858$		0			0
$859$	−32.0841			−1.09470			−0.547348	−	0.836905i	$-0.684363\pi$
$859$	−32.0841			−1.09470			−0.547348	+	0.836905i	$0.684363\pi$
$860$	−0.408331	+	1.25671i	−0.0139240	+	0.0428535i
$861$		0			0
$862$	2.15075	+	1.56261i	0.0732549	+	0.0532228i
$863$	−0.125550	−	0.386403i	−0.00427377	−	0.0131533i	0.948897	−	0.315586i	$-0.102201\pi$
$863$	−0.125550	−	0.386403i	−0.00427377	−	0.0131533i	−0.953171	+	0.302433i	$0.902201\pi$
$864$		0			0
$865$	1.48972	+	1.08235i	0.0506521	+	0.0368009i
$866$	15.5265	−	11.2806i	0.527611	−	0.383332i
$867$		0			0
$868$	−7.73878			−0.262671
$869$	−4.98469	+	38.3906i	−0.169094	+	1.30231i
$870$		0			0
$871$	−31.6661	+	97.4583i	−1.07297	+	3.30225i
$872$	−7.23607	+	5.25731i	−0.245044	+	0.178035i
$873$		0			0
$874$	−5.14121	−	15.8230i	−0.173904	−	0.535222i
$875$	−0.988430	−	3.04208i	−0.0334150	−	0.102841i
$876$		0			0
$877$	5.16591	−	3.75325i	0.174440	−	0.126738i	−0.497139	−	0.867671i	$-0.665616\pi$
$877$	5.16591	−	3.75325i	0.174440	−	0.126738i	0.671580	+	0.740932i	$0.265616\pi$
$878$	3.92313	−	12.0741i	0.132399	−	0.407482i
$879$		0			0
$880$	2.27873	−	2.40986i	0.0768159	−	0.0812362i
$881$	39.6551			1.33601			0.668006	−	0.744155i	$-0.267148\pi$
$881$	39.6551			1.33601			0.668006	+	0.744155i	$0.267148\pi$
$882$		0			0
$883$	3.96842	−	2.88322i	0.133548	−	0.0970282i	−0.519006	−	0.854771i	$-0.673698\pi$
$883$	3.96842	−	2.88322i	0.133548	−	0.0970282i	0.652554	+	0.757743i	$0.273698\pi$
$884$	−3.04692	−	2.21372i	−0.102479	−	0.0744554i
$885$		0			0
$886$	−5.22822	−	16.0908i	−0.175645	−	0.540581i
$887$	−6.16248	−	4.47730i	−0.206916	−	0.150333i	0.479501	−	0.877541i	$-0.340818\pi$
$887$	−6.16248	−	4.47730i	−0.206916	−	0.150333i	−0.686417	+	0.727208i	$0.740818\pi$
$888$		0			0
$889$	16.0279	−	49.3288i	0.537559	−	1.65444i
$890$	13.0775			0.438358
$891$		0			0
$892$	0.801373			0.0268319
$893$	11.8721	−	36.5386i	0.397285	−	1.22272i
$894$		0			0
$895$	−15.0172	−	10.9106i	−0.501970	−	0.364703i
$896$	−0.988430	−	3.04208i	−0.0330211	−	0.101629i
$897$		0			0
$898$	−15.5986	−	11.3331i	−0.520532	−	0.378189i
$899$	−9.57442	+	6.95622i	−0.319325	+	0.232003i
$900$		0			0
$901$	−1.35723			−0.0452159
$902$	2.09549	+	3.84307i	0.0697720	+	0.127960i
$903$		0			0
$904$	−1.48843	+	4.58092i	−0.0495045	+	0.152359i
$905$	−7.70820	+	5.60034i	−0.256229	+	0.186162i
$906$		0			0
$907$	−15.9819	−	49.1873i	−0.530672	−	1.63324i	−0.752820	−	0.658226i	$-0.771307\pi$
$907$	−15.9819	−	49.1873i	−0.530672	−	1.63324i	0.222149	−	0.975013i	$-0.428693\pi$
$908$	1.50472	+	4.63107i	0.0499360	+	0.153687i
$909$		0			0
$910$	−17.4830	+	12.7021i	−0.579556	+	0.421072i
$911$	9.95072	−	30.6252i	0.329682	−	1.01466i	−0.639600	−	0.768708i	$-0.720900\pi$
$911$	9.95072	−	30.6252i	0.329682	−	1.01466i	0.969283	−	0.245950i	$-0.0790998\pi$
$912$		0			0
$913$	−12.7019	−	23.2951i	−0.420373	−	0.770954i
$914$	39.5219			1.30727
$915$		0			0
$916$	0.939419	−	0.682528i	0.0310393	−	0.0225514i
$917$	−44.7390	−	32.5048i	−1.47741	−	1.07340i
$918$		0			0
$919$	−9.74986	−	30.0070i	−0.321618	−	0.989839i	−0.972944	−	0.231041i	$-0.925787\pi$
$919$	−9.74986	−	30.0070i	−0.321618	−	0.989839i	0.651326	−	0.758798i	$-0.274213\pi$
$920$	2.09931	+	1.52524i	0.0692123	+	0.0502857i
$921$		0			0
$922$	−4.27673	+	13.1624i	−0.140847	+	0.433482i
$923$	−42.9077			−1.41232
$924$		0			0
$925$	−5.73294			−0.188498
$926$	3.89111	−	11.9756i	0.127870	−	0.393543i
$927$		0			0
$928$	−3.95734	−	2.87518i	−0.129906	−	0.0943823i
$929$	−8.27723	−	25.4747i	−0.271567	−	0.835797i	−0.990107	−	0.140312i	$-0.955189\pi$
$929$	−8.27723	−	25.4747i	−0.271567	−	0.835797i	0.718540	−	0.695485i	$-0.244811\pi$
$930$		0			0
$931$	−16.7605	−	12.1772i	−0.549303	−	0.399092i
$932$	9.75086	−	7.08442i	0.319400	−	0.232058i
$933$		0			0
$934$	11.7368			0.384040
$935$	−1.27028	+	1.34338i	−0.0415427	+	0.0439333i
$936$		0			0
$937$	6.59975	−	20.3119i	0.215604	−	0.663562i	−0.783506	−	0.621384i	$-0.786571\pi$
$937$	6.59975	−	20.3119i	0.215604	−	0.663562i	0.999110	−	0.0421774i	$-0.0134295\pi$
$938$	39.2500	−	28.5168i	1.28156	−	0.931105i
$939$		0			0
$940$	1.85168	+	5.69887i	0.0603950	+	0.185877i
$941$	−12.8482	−	39.5428i	−0.418841	−	1.28906i	−0.908770	−	0.417297i	$-0.862977\pi$
$941$	−12.8482	−	39.5428i	−0.418841	−	1.28906i	0.489929	−	0.871762i	$-0.337023\pi$
$942$		0			0
$943$	−2.77065	+	2.01299i	−0.0902248	+	0.0655521i
$944$	−3.19098	+	9.82084i	−0.103858	+	0.319641i
$945$		0			0
$946$	0.564299	−	4.34606i	0.0183469	−	0.141303i
$947$	−8.59847			−0.279413			−0.139706	−	0.990193i	$-0.544616\pi$
$947$	−8.59847			−0.279413			−0.139706	+	0.990193i	$0.544616\pi$
$948$		0			0
$949$	−37.9559	+	27.5766i	−1.23210	+	0.895173i
$950$	−5.18706	−	3.76862i	−0.168290	−	0.122270i
$951$		0			0
$952$	0.551004	+	1.69582i	0.0178581	+	0.0549617i
$953$	−4.74138	−	3.44482i	−0.153588	−	0.111589i	0.508337	−	0.861158i	$-0.330260\pi$
$953$	−4.74138	−	3.44482i	−0.153588	−	0.111589i	−0.661925	+	0.749570i	$0.730260\pi$
$954$		0			0
$955$	−0.282347	+	0.868976i	−0.00913655	+	0.0281194i
$956$	28.2604			0.914006
$957$		0			0
$958$	−21.4007			−0.691425
$959$	7.83980	−	24.1284i	0.253160	−	0.779148i
$960$		0			0
$961$	20.3439	+	14.7807i	0.656256	+	0.476798i
$962$	11.9689	+	36.8365i	0.385893	+	1.18766i
$963$		0			0
$964$	−20.0520	−	14.5687i	−0.645832	−	0.469225i
$965$	−18.8463	+	13.6926i	−0.606682	+	0.440780i
$966$		0			0
$967$	−24.7496			−0.795894			−0.397947	−	0.917408i	$-0.630277\pi$
$967$	−24.7496			−0.795894			−0.397947	+	0.917408i	$0.630277\pi$
$968$	−5.95814	+	9.24665i	−0.191502	+	0.297199i
$969$		0			0
$970$	2.35883	−	7.25972i	0.0757373	−	0.233096i
$971$	34.9025	−	25.3581i	1.12007	−	0.813781i	0.135853	−	0.990729i	$-0.456622\pi$
$971$	34.9025	−	25.3581i	1.12007	−	0.813781i	0.984220	+	0.176948i	$0.0566225\pi$
$972$		0			0
$973$	8.12270	+	24.9991i	0.260402	+	0.801435i
$974$	−4.89799	−	15.0745i	−0.156942	−	0.483017i
$975$		0			0
$976$	−3.17549	+	2.30713i	−0.101645	+	0.0738493i
$977$	13.1493	−	40.4695i	0.420685	−	1.29474i	−0.486381	−	0.873747i	$-0.661683\pi$
$977$	13.1493	−	40.4695i	0.420685	−	1.29474i	0.907066	−	0.420988i	$-0.138317\pi$
$978$		0			0
$979$	−42.6326	+	7.98003i	−1.36254	+	0.255043i
$980$	3.23122			0.103217
$981$		0			0
$982$	22.3853	−	16.2639i	0.714344	−	0.519001i
$983$	14.8433	+	10.7843i	0.473427	+	0.343965i	0.798775	−	0.601629i	$-0.205482\pi$
$983$	14.8433	+	10.7843i	0.473427	+	0.343965i	−0.325348	+	0.945594i	$0.605482\pi$
$984$		0			0
$985$	7.59861	+	23.3861i	0.242112	+	0.745144i
$986$	2.20603	+	1.60278i	0.0702544	+	0.0510428i
$987$		0			0
$988$	−13.3857	+	41.1969i	−0.425855	+	1.31065i
$989$	3.42886			0.109031
$990$		0			0
$991$	1.48883			0.0472941			0.0236471	−	0.999720i	$-0.492472\pi$
$991$	1.48883			0.0472941			0.0236471	+	0.999720i	$0.492472\pi$
$992$	0.747638	−	2.30099i	0.0237375	−	0.0730566i
$993$		0			0
$994$	16.4347	+	11.9405i	0.521277	+	0.378730i
$995$	3.24813	+	9.99672i	0.102973	+	0.316917i
$996$		0			0
$997$	45.2568	+	32.8810i	1.43330	+	1.04135i	0.989391	+	0.145278i	$0.0464077\pi$
$997$	45.2568	+	32.8810i	1.43330	+	1.04135i	0.443906	+	0.896073i	$0.353592\pi$
$998$	5.71309	−	4.15080i	0.180845	−	0.131391i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.n.i.361.2		8
3.2	odd	2		330.2.m.f.31.2	✓	8
11.5	even	5	inner	990.2.n.i.181.2		8
33.5	odd	10		330.2.m.f.181.2	yes	8
33.26	odd	10		3630.2.a.bq.1.2		4
33.29	even	10		3630.2.a.bs.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.f.31.2	✓	8	3.2	odd	2
330.2.m.f.181.2	yes	8	33.5	odd	10
990.2.n.i.181.2		8	11.5	even	5	inner
990.2.n.i.361.2		8	1.1	even	1	trivial
3630.2.a.bq.1.2		4	33.26	odd	10
3630.2.a.bs.1.3		4	33.29	even	10

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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(2.58774 + 1.88011i) q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(2.58774 + 1.88011i) q^{7} +(-0.809017 + 0.587785i) q^{8} +1.00000 q^{10} +(-3.26001 + 0.610212i) q^{11} +(-2.08774 + 6.42541i) q^{13} +(2.58774 - 1.88011i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.172263 - 0.530170i) q^{17} +(-5.18706 + 3.76862i) q^{19} +(0.309017 - 0.951057i) q^{20} +(-0.427051 + 3.28902i) q^{22} -2.59489 q^{23} +(-0.809017 + 0.587785i) q^{25} +(5.46578 + 3.97112i) q^{26} +(-0.988430 - 3.04208i) q^{28} +(-3.95734 - 2.87518i) q^{29} +(0.747638 - 2.30099i) q^{31} +1.00000 q^{32} -0.557453 q^{34} +(-0.988430 + 3.04208i) q^{35} +(4.63805 + 3.36974i) q^{37} +(1.98128 + 6.09775i) q^{38} +(-0.809017 - 0.587785i) q^{40} +(1.06773 - 0.775752i) q^{41} -1.32139 q^{43} +(2.99607 + 1.42251i) q^{44} +(-0.801866 + 2.46789i) q^{46} +(-4.84775 + 3.52210i) q^{47} +(0.998501 + 3.07307i) q^{49} +(0.309017 + 0.951057i) q^{50} +(5.46578 - 3.97112i) q^{52} +(0.752362 - 2.31553i) q^{53} +(-1.58774 - 2.91188i) q^{55} -3.19863 q^{56} +(-3.95734 + 2.87518i) q^{58} +(8.35410 + 6.06961i) q^{59} +(1.21293 + 3.73301i) q^{61} +(-1.95734 - 1.42209i) q^{62} +(0.309017 - 0.951057i) q^{64} -6.75608 q^{65} +15.1676 q^{67} +(-0.172263 + 0.530170i) q^{68} +(2.58774 + 1.88011i) q^{70} +(1.96256 + 6.04014i) q^{71} +(5.61803 + 4.08174i) q^{73} +(4.63805 - 3.36974i) q^{74} +6.41156 q^{76} +(-9.58332 - 4.55008i) q^{77} +(3.60696 - 11.1011i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-0.407837 - 1.25519i) q^{82} +(2.47214 + 7.60845i) q^{83} +(0.450989 - 0.327663i) q^{85} +(-0.408331 + 1.25671i) q^{86} +(2.27873 - 2.40986i) q^{88} +13.0775 q^{89} +(-17.4830 + 12.7021i) q^{91} +(2.09931 + 1.52524i) q^{92} +(1.85168 + 5.69887i) q^{94} +(-5.18706 - 3.76862i) q^{95} +(2.35883 - 7.25972i) q^{97} +3.23122 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 3 q^{7} - 2 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 3 * q^7 - 2 * q^8	\( 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 3 q^{7} - 2 q^{8} + 8 q^{10} - 10 q^{11} + q^{13} + 3 q^{14} - 2 q^{16} - 3 q^{17} - 12 q^{19} - 2 q^{20} + 10 q^{22} - 2 q^{25} + q^{26} - 2 q^{28} - 27 q^{29} - 6 q^{31} + 8 q^{32} + 22 q^{34} - 2 q^{35} - 4 q^{37} + 13 q^{38} - 2 q^{40} + 23 q^{41} - 2 q^{43} - 10 q^{44} - 5 q^{46} - 5 q^{47} - 53 q^{49} - 2 q^{50} + q^{52} + 18 q^{53} + 5 q^{55} - 2 q^{56} - 27 q^{58} + 40 q^{59} - 20 q^{61} - 11 q^{62} - 2 q^{64} - 4 q^{65} + 18 q^{67} - 3 q^{68} + 3 q^{70} + 10 q^{71} + 36 q^{73} - 4 q^{74} - 2 q^{76} - 50 q^{77} - 11 q^{79} - 2 q^{80} - 12 q^{82} - 16 q^{83} - 8 q^{85} + 13 q^{86} + 5 q^{88} + 46 q^{89} - 39 q^{91} + 5 q^{92} + 15 q^{94} - 12 q^{95} + 16 q^{97} + 62 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 3 * q^7 - 2 * q^8 + 8 * q^10 - 10 * q^11 + q^13 + 3 * q^14 - 2 * q^16 - 3 * q^17 - 12 * q^19 - 2 * q^20 + 10 * q^22 - 2 * q^25 + q^26 - 2 * q^28 - 27 * q^29 - 6 * q^31 + 8 * q^32 + 22 * q^34 - 2 * q^35 - 4 * q^37 + 13 * q^38 - 2 * q^40 + 23 * q^41 - 2 * q^43 - 10 * q^44 - 5 * q^46 - 5 * q^47 - 53 * q^49 - 2 * q^50 + q^52 + 18 * q^53 + 5 * q^55 - 2 * q^56 - 27 * q^58 + 40 * q^59 - 20 * q^61 - 11 * q^62 - 2 * q^64 - 4 * q^65 + 18 * q^67 - 3 * q^68 + 3 * q^70 + 10 * q^71 + 36 * q^73 - 4 * q^74 - 2 * q^76 - 50 * q^77 - 11 * q^79 - 2 * q^80 - 12 * q^82 - 16 * q^83 - 8 * q^85 + 13 * q^86 + 5 * q^88 + 46 * q^89 - 39 * q^91 + 5 * q^92 + 15 * q^94 - 12 * q^95 + 16 * q^97 + 62 * q^98

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