LMFDB - Embedded newform 594.2.f.h.433.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [594,2,Mod(163,594)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(594, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("594.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 594 = 2 \cdot 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	594.f (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:	$4.74311388006$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			433.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	594.433
Dual form			594.2.f.h.487.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.30902 + 4.02874i) q^{7} +(-0.309017 + 0.951057i) q^{8} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.30902 + 4.02874i) q^{7} +(-0.309017 + 0.951057i) q^{8} +1.00000 q^{10} +(-2.19098 + 2.48990i) q^{11} +(-1.92705 - 1.40008i) q^{13} +(-1.30902 + 4.02874i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(3.73607 - 2.71441i) q^{17} +(-1.11803 + 3.44095i) q^{19} +(0.809017 + 0.587785i) q^{20} +(-3.23607 + 0.726543i) q^{22} +5.47214 q^{23} +(-1.23607 + 3.80423i) q^{25} +(-0.736068 - 2.26538i) q^{26} +(-3.42705 + 2.48990i) q^{28} +(-2.19098 - 6.74315i) q^{29} +(1.19098 + 0.865300i) q^{31} -1.00000 q^{32} +4.61803 q^{34} +(3.42705 + 2.48990i) q^{35} +(0.809017 + 2.48990i) q^{37} +(-2.92705 + 2.12663i) q^{38} +(0.309017 + 0.951057i) q^{40} +(0.763932 - 2.35114i) q^{41} +9.09017 q^{43} +(-3.04508 - 1.31433i) q^{44} +(4.42705 + 3.21644i) q^{46} +(-1.92705 + 5.93085i) q^{47} +(-8.85410 + 6.43288i) q^{49} +(-3.23607 + 2.35114i) q^{50} +(0.736068 - 2.26538i) q^{52} +(2.30902 + 1.67760i) q^{53} +(-0.309017 + 3.30220i) q^{55} -4.23607 q^{56} +(2.19098 - 6.74315i) q^{58} +(-4.59017 - 14.1271i) q^{59} +(8.73607 - 6.34712i) q^{61} +(0.454915 + 1.40008i) q^{62} +(-0.809017 - 0.587785i) q^{64} -2.38197 q^{65} -14.7082 q^{67} +(3.73607 + 2.71441i) q^{68} +(1.30902 + 4.02874i) q^{70} +(4.35410 - 3.16344i) q^{71} +(-1.30902 - 4.02874i) q^{73} +(-0.809017 + 2.48990i) q^{74} -3.61803 q^{76} +(-12.8992 - 5.56758i) q^{77} +(-3.61803 - 2.62866i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(2.00000 - 1.45309i) q^{82} +(11.8541 - 8.61251i) q^{83} +(1.42705 - 4.39201i) q^{85} +(7.35410 + 5.34307i) q^{86} +(-1.69098 - 2.85317i) q^{88} -0.291796 q^{89} +(3.11803 - 9.59632i) q^{91} +(1.69098 + 5.20431i) q^{92} +(-5.04508 + 3.66547i) q^{94} +(1.11803 + 3.44095i) q^{95} +(10.2082 + 7.41669i) q^{97} -10.9443 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{4} + q^{5} + 3 q^{7} + q^{8}+O(q^{10}) $ 4 * q + q^2 - q^4 + q^5 + 3 * q^7 + q^8	$ 4 q + q^{2} - q^{4} + q^{5} + 3 q^{7} + q^{8} + 4 q^{10} - 11 q^{11} - q^{13} - 3 q^{14} - q^{16} + 6 q^{17} + q^{20} - 4 q^{22} + 4 q^{23} + 4 q^{25} + 6 q^{26} - 7 q^{28} - 11 q^{29} + 7 q^{31} - 4 q^{32} + 14 q^{34} + 7 q^{35} + q^{37} - 5 q^{38} - q^{40} + 12 q^{41} + 14 q^{43} - q^{44} + 11 q^{46} - q^{47} - 22 q^{49} - 4 q^{50} - 6 q^{52} + 7 q^{53} + q^{55} - 8 q^{56} + 11 q^{58} + 4 q^{59} + 26 q^{61} + 13 q^{62} - q^{64} - 14 q^{65} - 32 q^{67} + 6 q^{68} + 3 q^{70} + 4 q^{71} - 3 q^{73} - q^{74} - 10 q^{76} - 27 q^{77} - 10 q^{79} + q^{80} + 8 q^{82} + 34 q^{83} - q^{85} + 16 q^{86} - 9 q^{88} - 28 q^{89} + 8 q^{91} + 9 q^{92} - 9 q^{94} + 14 q^{97} - 8 q^{98}+O(q^{100}) $ 4 * q + q^2 - q^4 + q^5 + 3 * q^7 + q^8 + 4 * q^10 - 11 * q^11 - q^13 - 3 * q^14 - q^16 + 6 * q^17 + q^20 - 4 * q^22 + 4 * q^23 + 4 * q^25 + 6 * q^26 - 7 * q^28 - 11 * q^29 + 7 * q^31 - 4 * q^32 + 14 * q^34 + 7 * q^35 + q^37 - 5 * q^38 - q^40 + 12 * q^41 + 14 * q^43 - q^44 + 11 * q^46 - q^47 - 22 * q^49 - 4 * q^50 - 6 * q^52 + 7 * q^53 + q^55 - 8 * q^56 + 11 * q^58 + 4 * q^59 + 26 * q^61 + 13 * q^62 - q^64 - 14 * q^65 - 32 * q^67 + 6 * q^68 + 3 * q^70 + 4 * q^71 - 3 * q^73 - q^74 - 10 * q^76 - 27 * q^77 - 10 * q^79 + q^80 + 8 * q^82 + 34 * q^83 - q^85 + 16 * q^86 - 9 * q^88 - 28 * q^89 + 8 * q^91 + 9 * q^92 - 9 * q^94 + 14 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/594\mathbb{Z}\right)^\times$.

$n$	$353$	$541$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i	−0.392000	−	0.919965i	$-0.628217\pi$
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i	0.753804	+	0.657099i	$0.228217\pi$
$6$		0			0
$7$	1.30902	+	4.02874i	0.494762	+	1.52272i	0.817327	+	0.576173i	$0.195455\pi$
$7$	1.30902	+	4.02874i	0.494762	+	1.52272i	−0.322566	+	0.946547i	$0.604545\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$		0			0
$10$	1.00000			0.316228
$11$	−2.19098	+	2.48990i	−0.660606	+	0.750733i
$11$	−2.19098	+	2.48990i	−0.660606	+	0.750733i
$12$		0			0
$13$	−1.92705	−	1.40008i	−0.534468	−	0.388314i	0.287559	−	0.957763i	$-0.407156\pi$
$13$	−1.92705	−	1.40008i	−0.534468	−	0.388314i	−0.822026	+	0.569449i	$0.807156\pi$
$14$	−1.30902	+	4.02874i	−0.349850	+	1.07673i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	3.73607	−	2.71441i	0.906130	−	0.658342i	−0.0339034	−	0.999425i	$-0.510794\pi$
$17$	3.73607	−	2.71441i	0.906130	−	0.658342i	0.940033	+	0.341083i	$0.110794\pi$
$18$		0			0
$19$	−1.11803	+	3.44095i	−0.256495	+	0.789409i	0.737037	+	0.675852i	$0.236224\pi$
$19$	−1.11803	+	3.44095i	−0.256495	+	0.789409i	−0.993532	+	0.113557i	$0.963776\pi$
$20$	0.809017	+	0.587785i	0.180902	+	0.131433i
$21$		0			0
$22$	−3.23607	+	0.726543i	−0.689932	+	0.154899i
$23$	5.47214			1.14102			0.570510	−	0.821291i	$-0.306746\pi$
$23$	5.47214			1.14102			0.570510	+	0.821291i	$0.306746\pi$
$24$		0			0
$25$	−1.23607	+	3.80423i	−0.247214	+	0.760845i
$26$	−0.736068	−	2.26538i	−0.144355	−	0.444278i
$27$		0			0
$28$	−3.42705	+	2.48990i	−0.647652	+	0.470547i
$29$	−2.19098	−	6.74315i	−0.406855	−	1.25217i	−0.919336	−	0.393473i	$-0.871273\pi$
$29$	−2.19098	−	6.74315i	−0.406855	−	1.25217i	0.512481	−	0.858699i	$-0.328727\pi$
$30$		0			0
$31$	1.19098	+	0.865300i	0.213907	+	0.155412i	0.689580	−	0.724210i	$-0.257795\pi$
$31$	1.19098	+	0.865300i	0.213907	+	0.155412i	−0.475673	+	0.879622i	$0.657795\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	4.61803			0.791986
$35$	3.42705	+	2.48990i	0.579277	+	0.420870i
$36$		0			0
$37$	0.809017	+	2.48990i	0.133002	+	0.409337i	0.995274	−	0.0971083i	$-0.0309593\pi$
$37$	0.809017	+	2.48990i	0.133002	+	0.409337i	−0.862272	+	0.506445i	$0.830959\pi$
$38$	−2.92705	+	2.12663i	−0.474830	+	0.344984i
$39$		0			0
$40$	0.309017	+	0.951057i	0.0488599	+	0.150375i
$41$	0.763932	−	2.35114i	0.119306	−	0.367187i	−0.873515	−	0.486798i	$-0.838165\pi$
$41$	0.763932	−	2.35114i	0.119306	−	0.367187i	0.992821	+	0.119611i	$0.0381648\pi$
$42$		0			0
$43$	9.09017			1.38624			0.693119	−	0.720823i	$-0.256236\pi$
$43$	9.09017			1.38624			0.693119	+	0.720823i	$0.256236\pi$
$44$	−3.04508	−	1.31433i	−0.459064	−	0.198142i
$45$		0			0
$46$	4.42705	+	3.21644i	0.652733	+	0.474238i
$47$	−1.92705	+	5.93085i	−0.281089	+	0.865104i	0.706454	+	0.707759i	$0.250294\pi$
$47$	−1.92705	+	5.93085i	−0.281089	+	0.865104i	−0.987544	+	0.157345i	$0.949706\pi$
$48$		0			0
$49$	−8.85410	+	6.43288i	−1.26487	+	0.918983i
$50$	−3.23607	+	2.35114i	−0.457649	+	0.332502i
$51$		0			0
$52$	0.736068	−	2.26538i	0.102074	−	0.314152i
$53$	2.30902	+	1.67760i	0.317168	+	0.230436i	0.734966	−	0.678104i	$-0.237198\pi$
$53$	2.30902	+	1.67760i	0.317168	+	0.230436i	−0.417798	+	0.908540i	$0.637198\pi$
$54$		0			0
$55$	−0.309017	+	3.30220i	−0.0416678	+	0.445268i
$56$	−4.23607			−0.566068
$57$		0			0
$58$	2.19098	−	6.74315i	0.287690	−	0.885419i
$59$	−4.59017	−	14.1271i	−0.597589	−	1.83919i	−0.541391	−	0.840771i	$-0.682102\pi$
$59$	−4.59017	−	14.1271i	−0.597589	−	1.83919i	−0.0561981	−	0.998420i	$-0.517898\pi$
$60$		0			0
$61$	8.73607	−	6.34712i	1.11854	−	0.812666i	0.134552	−	0.990907i	$-0.457040\pi$
$61$	8.73607	−	6.34712i	1.11854	−	0.812666i	0.983987	+	0.178240i	$0.0570405\pi$
$62$	0.454915	+	1.40008i	0.0577743	+	0.177811i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−2.38197			−0.295447
$66$		0			0
$67$	−14.7082			−1.79689			−0.898447	−	0.439083i	$-0.855303\pi$
$67$	−14.7082			−1.79689			−0.898447	+	0.439083i	$0.855303\pi$
$68$	3.73607	+	2.71441i	0.453065	+	0.329171i
$69$		0			0
$70$	1.30902	+	4.02874i	0.156457	+	0.481527i
$71$	4.35410	−	3.16344i	0.516737	−	0.375431i	−0.298636	−	0.954367i	$-0.596532\pi$
$71$	4.35410	−	3.16344i	0.516737	−	0.375431i	0.815373	+	0.578936i	$0.196532\pi$
$72$		0			0
$73$	−1.30902	−	4.02874i	−0.153209	−	0.471528i	0.844766	−	0.535136i	$-0.179739\pi$
$73$	−1.30902	−	4.02874i	−0.153209	−	0.471528i	−0.997975	+	0.0636073i	$0.979739\pi$
$74$	−0.809017	+	2.48990i	−0.0940463	+	0.289445i
$75$		0			0
$76$	−3.61803			−0.415017
$77$	−12.8992	−	5.56758i	−1.47000	−	0.634485i
$78$		0			0
$79$	−3.61803	−	2.62866i	−0.407061	−	0.295747i	0.365350	−	0.930870i	$-0.380949\pi$
$79$	−3.61803	−	2.62866i	−0.407061	−	0.295747i	−0.772411	+	0.635123i	$0.780949\pi$
$80$	−0.309017	+	0.951057i	−0.0345492	+	0.106331i
$81$		0			0
$82$	2.00000	−	1.45309i	0.220863	−	0.160466i
$83$	11.8541	−	8.61251i	1.30116	−	0.945346i	0.301191	−	0.953564i	$-0.402616\pi$
$83$	11.8541	−	8.61251i	1.30116	−	0.945346i	0.999966	+	0.00821829i	$0.00261599\pi$
$84$		0			0
$85$	1.42705	−	4.39201i	0.154785	−	0.476381i
$86$	7.35410	+	5.34307i	0.793013	+	0.576158i
$87$		0			0
$88$	−1.69098	−	2.85317i	−0.180259	−	0.304149i
$89$	−0.291796			−0.0309303			−0.0154652	−	0.999880i	$-0.504923\pi$
$89$	−0.291796			−0.0309303			−0.0154652	+	0.999880i	$0.504923\pi$
$90$		0			0
$91$	3.11803	−	9.59632i	0.326859	−	1.00597i
$92$	1.69098	+	5.20431i	0.176297	+	0.542587i
$93$		0			0
$94$	−5.04508	+	3.66547i	−0.520361	+	0.378064i
$95$	1.11803	+	3.44095i	0.114708	+	0.353035i
$96$		0			0
$97$	10.2082	+	7.41669i	1.03649	+	0.753051i	0.969597	−	0.244709i	$-0.0786925\pi$
$97$	10.2082	+	7.41669i	1.03649	+	0.753051i	0.0668895	+	0.997760i	$0.478692\pi$
$98$	−10.9443			−1.10554
$99$		0			0
$100$	−4.00000			−0.400000
$101$	−15.7533	−	11.4454i	−1.56751	−	1.13886i	−0.929492	−	0.368843i	$-0.879754\pi$
$101$	−15.7533	−	11.4454i	−1.56751	−	1.13886i	−0.638019	−	0.770021i	$-0.720246\pi$
$102$		0			0
$103$	−2.83688	−	8.73102i	−0.279526	−	0.860293i	−0.987986	−	0.154542i	$-0.950610\pi$
$103$	−2.83688	−	8.73102i	−0.279526	−	0.860293i	0.708460	−	0.705751i	$-0.249390\pi$
$104$	1.92705	−	1.40008i	0.188963	−	0.137290i
$105$		0			0
$106$	0.881966	+	2.71441i	0.0856641	+	0.263647i
$107$	1.00000	−	3.07768i	0.0966736	−	0.297531i	−0.891013	−	0.453979i	$-0.850004\pi$
$107$	1.00000	−	3.07768i	0.0966736	−	0.297531i	0.987686	+	0.156448i	$0.0500043\pi$
$108$		0			0
$109$	6.56231			0.628555			0.314277	−	0.949331i	$-0.398238\pi$
$109$	6.56231			0.628555			0.314277	+	0.949331i	$0.398238\pi$
$110$	−2.19098	+	2.48990i	−0.208902	+	0.237402i
$111$		0			0
$112$	−3.42705	−	2.48990i	−0.323826	−	0.235273i
$113$	−2.39919	+	7.38394i	−0.225697	+	0.694622i	0.772524	+	0.634986i	$0.218994\pi$
$113$	−2.39919	+	7.38394i	−0.225697	+	0.694622i	−0.998220	+	0.0596365i	$0.981006\pi$
$114$		0			0
$115$	4.42705	−	3.21644i	0.412825	−	0.299935i
$116$	5.73607	−	4.16750i	0.532581	−	0.386942i
$117$		0			0
$118$	4.59017	−	14.1271i	0.422559	−	1.30050i
$119$	15.8262	+	11.4984i	1.45079	+	1.05406i
$120$		0			0
$121$	−1.39919	−	10.9106i	−0.127199	−	0.991877i
$122$	10.7984			0.977639
$123$		0			0
$124$	−0.454915	+	1.40008i	−0.0408526	+	0.125731i
$125$	2.78115	+	8.55951i	0.248754	+	0.765586i
$126$		0			0
$127$	9.35410	−	6.79615i	0.830042	−	0.603061i	−0.0895290	−	0.995984i	$-0.528536\pi$
$127$	9.35410	−	6.79615i	0.830042	−	0.603061i	0.919571	+	0.392923i	$0.128536\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$		0			0
$130$	−1.92705	−	1.40008i	−0.169014	−	0.122796i
$131$	9.70820			0.848210			0.424105	−	0.905613i	$-0.360589\pi$
$131$	9.70820			0.848210			0.424105	+	0.905613i	$0.360589\pi$
$132$		0			0
$133$	−15.3262			−1.32895
$134$	−11.8992	−	8.64527i	−1.02793	−	0.746837i
$135$		0			0
$136$	1.42705	+	4.39201i	0.122369	+	0.376612i
$137$	5.78115	−	4.20025i	0.493917	−	0.358852i	−0.312772	−	0.949828i	$-0.601257\pi$
$137$	5.78115	−	4.20025i	0.493917	−	0.358852i	0.806689	+	0.590977i	$0.201257\pi$
$138$		0			0
$139$	1.07295	+	3.30220i	0.0910063	+	0.280089i	0.986192	−	0.165604i	$-0.0529574\pi$
$139$	1.07295	+	3.30220i	0.0910063	+	0.280089i	−0.895186	+	0.445693i	$0.852957\pi$
$140$	−1.30902	+	4.02874i	−0.110632	+	0.340491i
$141$		0			0
$142$	5.38197			0.451645
$143$	7.70820	−	1.73060i	0.644592	−	0.144720i
$144$		0			0
$145$	−5.73607	−	4.16750i	−0.476355	−	0.346092i
$146$	1.30902	−	4.02874i	0.108335	−	0.333421i
$147$		0			0
$148$	−2.11803	+	1.53884i	−0.174101	+	0.126492i
$149$	−15.5623	+	11.3067i	−1.27491	+	0.926279i	−0.999387	−	0.0350143i	$-0.988852\pi$
$149$	−15.5623	+	11.3067i	−1.27491	+	0.926279i	−0.275527	+	0.961293i	$0.588852\pi$
$150$		0			0
$151$	2.32624	−	7.15942i	0.189307	−	0.582626i	−0.810689	−	0.585476i	$-0.800907\pi$
$151$	2.32624	−	7.15942i	0.189307	−	0.582626i	0.999996	+	0.00285082i	$0.000907447\pi$
$152$	−2.92705	−	2.12663i	−0.237415	−	0.172492i
$153$		0			0
$154$	−7.16312	−	12.0862i	−0.577221	−	0.973935i
$155$	1.47214			0.118245
$156$		0			0
$157$	2.54508	−	7.83297i	0.203120	−	0.625139i	−0.796665	−	0.604421i	$-0.793405\pi$
$157$	2.54508	−	7.83297i	0.203120	−	0.625139i	0.999785	−	0.0207182i	$-0.00659530\pi$
$158$	−1.38197	−	4.25325i	−0.109943	−	0.338371i
$159$		0			0
$160$	−0.809017	+	0.587785i	−0.0639584	+	0.0464685i
$161$	7.16312	+	22.0458i	0.564533	+	1.73745i
$162$		0			0
$163$	−4.85410	−	3.52671i	−0.380203	−	0.276233i	0.381226	−	0.924482i	$-0.375502\pi$
$163$	−4.85410	−	3.52671i	−0.380203	−	0.276233i	−0.761429	+	0.648248i	$0.775502\pi$
$164$	2.47214			0.193041
$165$		0			0
$166$	14.6525			1.13725
$167$	−10.4721	−	7.60845i	−0.810358	−	0.588760i	0.103576	−	0.994622i	$-0.466971\pi$
$167$	−10.4721	−	7.60845i	−0.810358	−	0.588760i	−0.913934	+	0.405862i	$0.866971\pi$
$168$		0			0
$169$	−2.26393	−	6.96767i	−0.174149	−	0.535974i
$170$	3.73607	−	2.71441i	0.286543	−	0.208186i
$171$		0			0
$172$	2.80902	+	8.64527i	0.214186	+	0.659195i
$173$	0.791796	−	2.43690i	0.0601991	−	0.185274i	−0.916435	−	0.400185i	$-0.868946\pi$
$173$	0.791796	−	2.43690i	0.0601991	−	0.185274i	0.976634	+	0.214911i	$0.0689460\pi$
$174$		0			0
$175$	−16.9443			−1.28087
$176$	0.309017	−	3.30220i	0.0232930	−	0.248913i
$177$		0			0
$178$	−0.236068	−	0.171513i	−0.0176940	−	0.0128555i
$179$	−7.83688	+	24.1194i	−0.585756	+	1.80277i	0.0104571	+	0.999945i	$0.496671\pi$
$179$	−7.83688	+	24.1194i	−0.585756	+	1.80277i	−0.596213	+	0.802826i	$0.703329\pi$
$180$		0			0
$181$	−6.97214	+	5.06555i	−0.518235	+	0.376520i	−0.815939	−	0.578139i	$-0.803779\pi$
$181$	−6.97214	+	5.06555i	−0.518235	+	0.376520i	0.297704	+	0.954658i	$0.403779\pi$
$182$	8.16312	−	5.93085i	0.605091	−	0.439624i
$183$		0			0
$184$	−1.69098	+	5.20431i	−0.124661	+	0.383667i
$185$	2.11803	+	1.53884i	0.155721	+	0.113138i
$186$		0			0
$187$	−1.42705	+	15.2497i	−0.104356	+	1.11517i
$188$	−6.23607			−0.454812
$189$		0			0
$190$	−1.11803	+	3.44095i	−0.0811107	+	0.249633i
$191$	6.10081	+	18.7764i	0.441439	+	1.35861i	0.886342	+	0.463032i	$0.153238\pi$
$191$	6.10081	+	18.7764i	0.441439	+	1.35861i	−0.444902	+	0.895579i	$0.646762\pi$
$192$		0			0
$193$	3.04508	−	2.21238i	0.219190	−	0.159251i	−0.472772	−	0.881185i	$-0.656747\pi$
$193$	3.04508	−	2.21238i	0.219190	−	0.159251i	0.691962	+	0.721934i	$0.256747\pi$
$194$	3.89919	+	12.0005i	0.279945	+	0.861583i
$195$		0			0
$196$	−8.85410	−	6.43288i	−0.632436	−	0.459492i
$197$	−19.1803			−1.36654			−0.683271	−	0.730165i	$-0.739443\pi$
$197$	−19.1803			−1.36654			−0.683271	+	0.730165i	$0.739443\pi$
$198$		0			0
$199$	3.00000			0.212664			0.106332	−	0.994331i	$-0.466089\pi$
$199$	3.00000			0.212664			0.106332	+	0.994331i	$0.466089\pi$
$200$	−3.23607	−	2.35114i	−0.228825	−	0.166251i
$201$		0			0
$202$	−6.01722	−	18.5191i	−0.423370	−	1.30300i
$203$	24.2984	−	17.6538i	1.70541	−	1.23905i
$204$		0			0
$205$	−0.763932	−	2.35114i	−0.0533553	−	0.164211i
$206$	2.83688	−	8.73102i	0.197655	−	0.608319i
$207$		0			0
$208$	2.38197			0.165160
$209$	−6.11803	−	10.3229i	−0.423193	−	0.714047i
$210$		0			0
$211$	11.1353	+	8.09024i	0.766583	+	0.556955i	0.900922	−	0.433981i	$-0.142891\pi$
$211$	11.1353	+	8.09024i	0.766583	+	0.556955i	−0.134340	+	0.990935i	$0.542891\pi$
$212$	−0.881966	+	2.71441i	−0.0605737	+	0.186427i
$213$		0			0
$214$	2.61803	−	1.90211i	0.178965	−	0.130026i
$215$	7.35410	−	5.34307i	0.501546	−	0.364394i
$216$		0			0
$217$	−1.92705	+	5.93085i	−0.130817	+	0.402613i
$218$	5.30902	+	3.85723i	0.359572	+	0.261244i
$219$		0			0
$220$	−3.23607	+	0.726543i	−0.218176	+	0.0489835i
$221$	−11.0000			−0.739940
$222$		0			0
$223$	4.24671	−	13.0700i	0.284381	−	0.875234i	−0.702203	−	0.711977i	$-0.747800\pi$
$223$	4.24671	−	13.0700i	0.284381	−	0.875234i	0.986584	−	0.163257i	$-0.0522000\pi$
$224$	−1.30902	−	4.02874i	−0.0874624	−	0.269182i
$225$		0			0
$226$	−6.28115	+	4.56352i	−0.417816	+	0.303561i
$227$	−0.135255	−	0.416272i	−0.00897718	−	0.0276289i	0.946468	−	0.322799i	$-0.104624\pi$
$227$	−0.135255	−	0.416272i	−0.00897718	−	0.0276289i	−0.955445	+	0.295170i	$0.904624\pi$
$228$		0			0
$229$	12.8992	+	9.37181i	0.852402	+	0.619306i	0.925807	−	0.377996i	$-0.123387\pi$
$229$	12.8992	+	9.37181i	0.852402	+	0.619306i	−0.0734051	+	0.997302i	$0.523387\pi$
$230$	5.47214			0.360822
$231$		0			0
$232$	7.09017			0.465492
$233$	−17.6074	−	12.7925i	−1.15350	−	0.838066i	−0.164556	−	0.986368i	$-0.552619\pi$
$233$	−17.6074	−	12.7925i	−1.15350	−	0.838066i	−0.988942	+	0.148302i	$0.952619\pi$
$234$		0			0
$235$	1.92705	+	5.93085i	0.125707	+	0.386886i
$236$	12.0172	−	8.73102i	0.782254	−	0.568341i
$237$		0			0
$238$	6.04508	+	18.6049i	0.391845	+	1.20597i
$239$	−3.94427	+	12.1392i	−0.255134	+	0.785221i	0.738670	+	0.674068i	$0.235454\pi$
$239$	−3.94427	+	12.1392i	−0.255134	+	0.785221i	−0.993803	+	0.111153i	$0.964546\pi$
$240$		0			0
$241$	20.4164			1.31514			0.657568	−	0.753395i	$-0.271585\pi$
$241$	20.4164			1.31514			0.657568	+	0.753395i	$0.271585\pi$
$242$	5.28115	−	9.64932i	0.339485	−	0.620282i
$243$		0			0
$244$	8.73607	+	6.34712i	0.559269	+	0.406333i
$245$	−3.38197	+	10.4086i	−0.216066	+	0.664982i
$246$		0			0
$247$	6.97214	−	5.06555i	0.443626	−	0.322313i
$248$	−1.19098	+	0.865300i	−0.0756275	+	0.0549466i
$249$		0			0
$250$	−2.78115	+	8.55951i	−0.175896	+	0.541351i
$251$	−3.76393	−	2.73466i	−0.237577	−	0.172610i	0.462626	−	0.886554i	$-0.346907\pi$
$251$	−3.76393	−	2.73466i	−0.237577	−	0.172610i	−0.700203	+	0.713944i	$0.746907\pi$
$252$		0			0
$253$	−11.9894	+	13.6251i	−0.753764	+	0.856600i
$254$	11.5623			0.725484
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−0.298374	−	0.918300i	−0.0186121	−	0.0572820i	0.941319	−	0.337518i	$-0.109587\pi$
$257$	−0.298374	−	0.918300i	−0.0186121	−	0.0572820i	−0.959931	+	0.280236i	$0.909587\pi$
$258$		0			0
$259$	−8.97214	+	6.51864i	−0.557501	+	0.405048i
$260$	−0.736068	−	2.26538i	−0.0456490	−	0.140493i
$261$		0			0
$262$	7.85410	+	5.70634i	0.485228	+	0.352539i
$263$	−17.4164			−1.07394			−0.536971	−	0.843601i	$-0.680431\pi$
$263$	−17.4164			−1.07394			−0.536971	+	0.843601i	$0.680431\pi$
$264$		0			0
$265$	2.85410			0.175326
$266$	−12.3992	−	9.00854i	−0.760243	−	0.552349i
$267$		0			0
$268$	−4.54508	−	13.9883i	−0.277635	−	0.854473i
$269$	−4.19098	+	3.04493i	−0.255529	+	0.185652i	−0.708174	−	0.706038i	$-0.750481\pi$
$269$	−4.19098	+	3.04493i	−0.255529	+	0.185652i	0.452645	+	0.891691i	$0.350481\pi$
$270$		0			0
$271$	8.87132	+	27.3031i	0.538894	+	1.65855i	0.735080	+	0.677980i	$0.237144\pi$
$271$	8.87132	+	27.3031i	0.538894	+	1.65855i	−0.196186	+	0.980567i	$0.562856\pi$
$272$	−1.42705	+	4.39201i	−0.0865277	+	0.266305i
$273$		0			0
$274$	7.14590			0.431699
$275$	−6.76393	−	11.4127i	−0.407880	−	0.688210i
$276$		0			0
$277$	−1.85410	−	1.34708i	−0.111402	−	0.0809384i	0.530689	−	0.847566i	$-0.321933\pi$
$277$	−1.85410	−	1.34708i	−0.111402	−	0.0809384i	−0.642092	+	0.766628i	$0.721933\pi$
$278$	−1.07295	+	3.30220i	−0.0643512	+	0.198053i
$279$		0			0
$280$	−3.42705	+	2.48990i	−0.204805	+	0.148800i
$281$	6.92705	−	5.03280i	0.413233	−	0.300232i	−0.361676	−	0.932304i	$-0.617795\pi$
$281$	6.92705	−	5.03280i	0.413233	−	0.300232i	0.774909	+	0.632072i	$0.217795\pi$
$282$		0			0
$283$	−1.97214	+	6.06961i	−0.117231	+	0.360801i	−0.992406	−	0.123006i	$-0.960746\pi$
$283$	−1.97214	+	6.06961i	−0.117231	+	0.360801i	0.875175	+	0.483807i	$0.160746\pi$
$284$	4.35410	+	3.16344i	0.258368	+	0.187716i
$285$		0			0
$286$	7.25329	+	3.13068i	0.428896	+	0.185121i
$287$	10.4721			0.618151
$288$		0			0
$289$	1.33688	−	4.11450i	0.0786401	−	0.242029i
$290$	−2.19098	−	6.74315i	−0.128659	−	0.395972i
$291$		0			0
$292$	3.42705	−	2.48990i	0.200553	−	0.145710i
$293$	−1.59017	−	4.89404i	−0.0928987	−	0.285913i	0.893802	−	0.448463i	$-0.148028\pi$
$293$	−1.59017	−	4.89404i	−0.0928987	−	0.285913i	−0.986700	+	0.162550i	$0.948028\pi$
$294$		0			0
$295$	−12.0172	−	8.73102i	−0.699670	−	0.508340i
$296$	−2.61803			−0.152170
$297$		0			0
$298$	−19.2361			−1.11432
$299$	−10.5451	−	7.66145i	−0.609838	−	0.443073i
$300$		0			0
$301$	11.8992	+	36.6219i	0.685858	+	2.11085i
$302$	6.09017	−	4.42477i	0.350450	−	0.254617i
$303$		0			0
$304$	−1.11803	−	3.44095i	−0.0641236	−	0.197352i
$305$	3.33688	−	10.2699i	0.191069	−	0.588051i
$306$		0			0
$307$	−24.8885			−1.42046			−0.710232	−	0.703968i	$-0.751410\pi$
$307$	−24.8885			−1.42046			−0.710232	+	0.703968i	$0.751410\pi$
$308$	1.30902	−	13.9883i	0.0745882	−	0.797059i
$309$		0			0
$310$	1.19098	+	0.865300i	0.0676433	+	0.0491457i
$311$	−5.44427	+	16.7557i	−0.308716	+	0.950131i	0.669548	+	0.742769i	$0.266488\pi$
$311$	−5.44427	+	16.7557i	−0.308716	+	0.950131i	−0.978264	+	0.207362i	$0.933512\pi$
$312$		0			0
$313$	−20.8992	+	15.1841i	−1.18129	+	0.858259i	−0.992317	−	0.123723i	$-0.960517\pi$
$313$	−20.8992	+	15.1841i	−1.18129	+	0.858259i	−0.188975	+	0.981982i	$0.560517\pi$
$314$	6.66312	−	4.84104i	0.376022	−	0.273196i
$315$		0			0
$316$	1.38197	−	4.25325i	0.0777417	−	0.239264i
$317$	8.00000	+	5.81234i	0.449325	+	0.326454i	0.789329	−	0.613970i	$-0.210429\pi$
$317$	8.00000	+	5.81234i	0.449325	+	0.326454i	−0.340004	+	0.940424i	$0.610429\pi$
$318$		0			0
$319$	21.5902	+	9.31881i	1.20882	+	0.521753i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	−7.16312	+	22.0458i	−0.399185	+	1.22857i
$323$	5.16312	+	15.8904i	0.287284	+	0.884168i
$324$		0			0
$325$	7.70820	−	5.60034i	0.427574	−	0.310651i
$326$	−1.85410	−	5.70634i	−0.102689	−	0.316045i
$327$		0			0
$328$	2.00000	+	1.45309i	0.110432	+	0.0802332i
$329$	−26.4164			−1.45638
$330$		0			0
$331$	−29.0689			−1.59777			−0.798885	−	0.601484i	$-0.794577\pi$
$331$	−29.0689			−1.59777			−0.798885	+	0.601484i	$0.794577\pi$
$332$	11.8541	+	8.61251i	0.650578	+	0.472673i
$333$		0			0
$334$	−4.00000	−	12.3107i	−0.218870	−	0.673613i
$335$	−11.8992	+	8.64527i	−0.650122	+	0.472341i
$336$		0			0
$337$	−4.22542	−	13.0045i	−0.230174	−	0.708401i	−0.997725	−	0.0674141i	$-0.978525\pi$
$337$	−4.22542	−	13.0045i	−0.230174	−	0.708401i	0.767552	−	0.640987i	$-0.221475\pi$
$338$	2.26393	−	6.96767i	0.123142	−	0.378991i
$339$		0			0
$340$	4.61803			0.250448
$341$	−4.76393	+	1.06957i	−0.257981	+	0.0579204i
$342$		0			0
$343$	−13.5172	−	9.82084i	−0.729861	−	0.530275i
$344$	−2.80902	+	8.64527i	−0.151452	+	0.466121i
$345$		0			0
$346$	2.07295	−	1.50609i	0.111442	−	0.0809677i
$347$	19.5172	−	14.1801i	1.04774	−	0.761227i	0.0759581	−	0.997111i	$-0.475798\pi$
$347$	19.5172	−	14.1801i	1.04774	−	0.761227i	0.971781	+	0.235884i	$0.0757985\pi$
$348$		0			0
$349$	2.36475	−	7.27794i	0.126582	−	0.389579i	−0.867604	−	0.497256i	$-0.834341\pi$
$349$	2.36475	−	7.27794i	0.126582	−	0.389579i	0.994186	+	0.107677i	$0.0343411\pi$
$350$	−13.7082	−	9.95959i	−0.732734	−	0.532363i
$351$		0			0
$352$	2.19098	−	2.48990i	0.116780	−	0.132712i
$353$	2.94427			0.156708			0.0783539	−	0.996926i	$-0.475034\pi$
$353$	2.94427			0.156708			0.0783539	+	0.996926i	$0.475034\pi$
$354$		0			0
$355$	1.66312	−	5.11855i	0.0882692	−	0.271665i
$356$	−0.0901699	−	0.277515i	−0.00477900	−	0.0147082i
$357$		0			0
$358$	−20.5172	+	14.9066i	−1.08437	+	0.787840i
$359$	10.6008	+	32.6259i	0.559490	+	1.72193i	0.683782	+	0.729686i	$0.260334\pi$
$359$	10.6008	+	32.6259i	0.559490	+	1.72193i	−0.124293	+	0.992246i	$0.539666\pi$
$360$		0			0
$361$	4.78115	+	3.47371i	0.251640	+	0.182827i
$362$	−8.61803			−0.452954
$363$		0			0
$364$	10.0902			0.528869
$365$	−3.42705	−	2.48990i	−0.179380	−	0.130327i
$366$		0			0
$367$	11.4164	+	35.1361i	0.595932	+	1.83409i	0.550033	+	0.835143i	$0.314615\pi$
$367$	11.4164	+	35.1361i	0.595932	+	1.83409i	0.0458986	+	0.998946i	$0.485385\pi$
$368$	−4.42705	+	3.21644i	−0.230776	+	0.167669i
$369$		0			0
$370$	0.809017	+	2.48990i	0.0420588	+	0.129444i
$371$	−3.73607	+	11.4984i	−0.193967	+	0.596969i
$372$		0			0
$373$	−21.4721			−1.11179			−0.555893	−	0.831254i	$-0.687623\pi$
$373$	−21.4721			−1.11179			−0.555893	+	0.831254i	$0.687623\pi$
$374$	−10.1180	+	11.4984i	−0.523191	+	0.594570i
$375$		0			0
$376$	−5.04508	−	3.66547i	−0.260180	−	0.189032i
$377$	−5.21885	+	16.0620i	−0.268784	+	0.827233i
$378$		0			0
$379$	27.2705	−	19.8132i	1.40079	−	1.01773i	0.406210	−	0.913780i	$-0.366850\pi$
$379$	27.2705	−	19.8132i	1.40079	−	1.01773i	0.994582	−	0.103955i	$-0.0331499\pi$
$380$	−2.92705	+	2.12663i	−0.150155	+	0.109094i
$381$		0			0
$382$	−6.10081	+	18.7764i	−0.312145	+	0.960683i
$383$	26.3713	+	19.1599i	1.34751	+	0.979025i	0.999131	+	0.0416712i	$0.0132682\pi$
$383$	26.3713	+	19.1599i	1.34751	+	0.979025i	0.348380	+	0.937353i	$0.386732\pi$
$384$		0			0
$385$	−13.7082	+	3.07768i	−0.698635	+	0.156853i
$386$	3.76393			0.191579
$387$		0			0
$388$	−3.89919	+	12.0005i	−0.197951	+	0.609231i
$389$	−8.88197	−	27.3359i	−0.450334	−	1.38598i	−0.876527	−	0.481352i	$-0.840146\pi$
$389$	−8.88197	−	27.3359i	−0.450334	−	1.38598i	0.426194	−	0.904632i	$-0.359854\pi$
$390$		0			0
$391$	20.4443	−	14.8536i	1.03391	−	0.751181i
$392$	−3.38197	−	10.4086i	−0.170815	−	0.525715i
$393$		0			0
$394$	−15.5172	−	11.2739i	−0.781746	−	0.567972i
$395$	−4.47214			−0.225018
$396$		0			0
$397$	16.3820			0.822187			0.411094	−	0.911593i	$-0.365147\pi$
$397$	16.3820			0.822187			0.411094	+	0.911593i	$0.365147\pi$
$398$	2.42705	+	1.76336i	0.121657	+	0.0883890i
$399$		0			0
$400$	−1.23607	−	3.80423i	−0.0618034	−	0.190211i
$401$	4.04508	−	2.93893i	0.202002	−	0.146763i	−0.482186	−	0.876069i	$-0.660157\pi$
$401$	4.04508	−	2.93893i	0.202002	−	0.146763i	0.684188	+	0.729306i	$0.260157\pi$
$402$		0			0
$403$	−1.08359	−	3.33495i	−0.0539776	−	0.166126i
$404$	6.01722	−	18.5191i	0.299368	−	0.921360i
$405$		0			0
$406$	30.0344			1.49058
$407$	−7.97214	−	3.44095i	−0.395164	−	0.170562i
$408$		0			0
$409$	26.5066	+	19.2582i	1.31067	+	0.952255i	0.999998	+	0.00173586i	$0.000552540\pi$
$409$	26.5066	+	19.2582i	1.31067	+	0.952255i	0.310667	+	0.950519i	$0.399447\pi$
$410$	0.763932	−	2.35114i	0.0377279	−	0.116115i
$411$		0			0
$412$	7.42705	−	5.39607i	0.365905	−	0.265845i
$413$	50.9058	−	36.9852i	2.50491	−	1.81992i
$414$		0			0
$415$	4.52786	−	13.9353i	0.222264	−	0.684059i
$416$	1.92705	+	1.40008i	0.0944814	+	0.0686448i
$417$		0			0
$418$	1.11803	−	11.9475i	0.0546848	−	0.584370i
$419$	16.8328			0.822337			0.411168	−	0.911559i	$-0.365121\pi$
$419$	16.8328			0.822337			0.411168	+	0.911559i	$0.365121\pi$
$420$		0			0
$421$	−5.20820	+	16.0292i	−0.253832	+	0.781216i	0.740225	+	0.672359i	$0.234719\pi$
$421$	−5.20820	+	16.0292i	−0.253832	+	0.781216i	−0.994057	+	0.108856i	$0.965281\pi$
$422$	4.25329	+	13.0903i	0.207047	+	0.637225i
$423$		0			0
$424$	−2.30902	+	1.67760i	−0.112136	+	0.0814714i
$425$	5.70820	+	17.5680i	0.276889	+	0.852175i
$426$		0			0
$427$	37.0066	+	26.8869i	1.79087	+	1.30115i
$428$	3.23607			0.156421
$429$		0			0
$430$	9.09017			0.438367
$431$	10.6910	+	7.76745i	0.514967	+	0.374145i	0.814704	−	0.579877i	$-0.196899\pi$
$431$	10.6910	+	7.76745i	0.514967	+	0.374145i	−0.299738	+	0.954022i	$0.596899\pi$
$432$		0			0
$433$	1.97214	+	6.06961i	0.0947748	+	0.291687i	0.987195	−	0.159519i	$-0.0509942\pi$
$433$	1.97214	+	6.06961i	0.0947748	+	0.291687i	−0.892420	+	0.451205i	$0.850994\pi$
$434$	−5.04508	+	3.66547i	−0.242172	+	0.175948i
$435$		0			0
$436$	2.02786	+	6.24112i	0.0971171	+	0.298896i
$437$	−6.11803	+	18.8294i	−0.292665	+	0.900731i
$438$		0			0
$439$	−21.3262			−1.01785			−0.508923	−	0.860812i	$-0.669956\pi$
$439$	−21.3262			−1.01785			−0.508923	+	0.860812i	$0.669956\pi$
$440$	−3.04508	−	1.31433i	−0.145169	−	0.0626581i
$441$		0			0
$442$	−8.89919	−	6.46564i	−0.423291	−	0.307539i
$443$	−0.864745	+	2.66141i	−0.0410853	+	0.126447i	−0.969495	−	0.245110i	$-0.921176\pi$
$443$	−0.864745	+	2.66141i	−0.0410853	+	0.126447i	0.928410	+	0.371557i	$0.121176\pi$
$444$		0			0
$445$	−0.236068	+	0.171513i	−0.0111907	+	0.00813052i
$446$	11.1180	−	8.07772i	0.526454	−	0.382491i
$447$		0			0
$448$	1.30902	−	4.02874i	0.0618452	−	0.190340i
$449$	−32.3885	−	23.5317i	−1.52851	−	1.11053i	−0.957060	−	0.289891i	$-0.906381\pi$
$449$	−32.3885	−	23.5317i	−1.52851	−	1.11053i	−0.571450	−	0.820637i	$-0.693619\pi$
$450$		0			0
$451$	4.18034	+	7.05342i	0.196845	+	0.332133i
$452$	−7.76393			−0.365185
$453$		0			0
$454$	0.135255	−	0.416272i	0.00634783	−	0.0195366i
$455$	−3.11803	−	9.59632i	−0.146176	−	0.449883i
$456$		0			0
$457$	20.2082	−	14.6821i	0.945300	−	0.686801i	−0.00439065	−	0.999990i	$-0.501398\pi$
$457$	20.2082	−	14.6821i	0.945300	−	0.686801i	0.949691	+	0.313190i	$0.101398\pi$
$458$	4.92705	+	15.1639i	0.230226	+	0.708563i
$459$		0			0
$460$	4.42705	+	3.21644i	0.206412	+	0.149967i
$461$	28.9787			1.34967			0.674837	−	0.737967i	$-0.264214\pi$
$461$	28.9787			1.34967			0.674837	+	0.737967i	$0.264214\pi$
$462$		0			0
$463$	−13.0902			−0.608352			−0.304176	−	0.952616i	$-0.598381\pi$
$463$	−13.0902			−0.608352			−0.304176	+	0.952616i	$0.598381\pi$
$464$	5.73607	+	4.16750i	0.266290	+	0.193471i
$465$		0			0
$466$	−6.72542	−	20.6987i	−0.311549	−	0.958850i
$467$	−10.1631	+	7.38394i	−0.470293	+	0.341688i	−0.797555	−	0.603246i	$-0.793874\pi$
$467$	−10.1631	+	7.38394i	−0.470293	+	0.341688i	0.327262	+	0.944933i	$0.393874\pi$
$468$		0			0
$469$	−19.2533	−	59.2555i	−0.889034	−	2.73617i
$470$	−1.92705	+	5.93085i	−0.0888882	+	0.273570i
$471$		0			0
$472$	14.8541			0.683715
$473$	−19.9164	+	22.6336i	−0.915757	+	1.04069i
$474$		0			0
$475$	−11.7082	−	8.50651i	−0.537209	−	0.390305i
$476$	−6.04508	+	18.6049i	−0.277076	+	0.852752i
$477$		0			0
$478$	−10.3262	+	7.50245i	−0.472311	+	0.343154i
$479$	−24.2984	+	17.6538i	−1.11022	+	0.806623i	−0.982698	−	0.185213i	$-0.940703\pi$
$479$	−24.2984	+	17.6538i	−1.11022	+	0.806623i	−0.127523	+	0.991836i	$0.540703\pi$
$480$		0			0
$481$	1.92705	−	5.93085i	0.0878660	−	0.270424i
$482$	16.5172	+	12.0005i	0.752339	+	0.546606i
$483$		0			0
$484$	9.94427	−	4.70228i	0.452012	−	0.213740i
$485$	12.6180			0.572955
$486$		0			0
$487$	−6.43769	+	19.8132i	−0.291720	+	0.897821i	0.692584	+	0.721337i	$0.256472\pi$
$487$	−6.43769	+	19.8132i	−0.291720	+	0.897821i	−0.984304	+	0.176484i	$0.943528\pi$
$488$	3.33688	+	10.2699i	0.151054	+	0.464895i
$489$		0			0
$490$	−8.85410	+	6.43288i	−0.399988	+	0.290608i
$491$	−12.1287	−	37.3282i	−0.547360	−	1.68460i	−0.715313	−	0.698804i	$-0.753716\pi$
$491$	−12.1287	−	37.3282i	−0.547360	−	1.68460i	0.167953	−	0.985795i	$-0.446284\pi$
$492$		0			0
$493$	−26.4894	−	19.2456i	−1.19302	−	0.866780i
$494$	8.61803			0.387744
$495$		0			0
$496$	−1.47214			−0.0661009
$497$	18.4443	+	13.4005i	0.827339	+	0.601097i
$498$		0			0
$499$	−7.19756	−	22.1518i	−0.322207	−	0.991651i	−0.972686	−	0.232127i	$-0.925432\pi$
$499$	−7.19756	−	22.1518i	−0.322207	−	0.991651i	0.650478	−	0.759525i	$-0.274568\pi$
$500$	−7.28115	+	5.29007i	−0.325623	+	0.236579i
$501$		0			0
$502$	−1.43769	−	4.42477i	−0.0641674	−	0.197487i
$503$	10.8369	−	33.3525i	0.483193	−	1.48711i	−0.351389	−	0.936230i	$-0.614290\pi$
$503$	10.8369	−	33.3525i	0.483193	−	1.48711i	0.834582	−	0.550884i	$-0.185710\pi$
$504$		0			0
$505$	−19.4721			−0.866499
$506$	−17.7082	+	3.97574i	−0.787226	+	0.176743i
$507$		0			0
$508$	9.35410	+	6.79615i	0.415021	+	0.301531i
$509$	−3.29837	+	10.1514i	−0.146198	+	0.449951i	−0.997163	−	0.0752713i	$-0.976018\pi$
$509$	−3.29837	+	10.1514i	−0.146198	+	0.449951i	0.850965	+	0.525222i	$0.176018\pi$
$510$		0			0
$511$	14.5172	−	10.5474i	0.642204	−	0.466589i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$		0			0
$514$	0.298374	−	0.918300i	0.0131607	−	0.0405045i
$515$	−7.42705	−	5.39607i	−0.327275	−	0.237779i
$516$		0			0
$517$	−10.5451	−	17.7926i	−0.463772	−	0.782516i
$518$	−11.0902			−0.487274
$519$		0			0
$520$	0.736068	−	2.26538i	0.0322787	−	0.0993437i
$521$	−7.36475	−	22.6664i	−0.322655	−	0.993031i	−0.972488	−	0.232954i	$-0.925161\pi$
$521$	−7.36475	−	22.6664i	−0.322655	−	0.993031i	0.649833	−	0.760077i	$-0.274839\pi$
$522$		0			0
$523$	−20.7533	+	15.0781i	−0.907478	+	0.659321i	−0.940376	−	0.340137i	$-0.889526\pi$
$523$	−20.7533	+	15.0781i	−0.907478	+	0.659321i	0.0328978	+	0.999459i	$0.489526\pi$
$524$	3.00000	+	9.23305i	0.131056	+	0.403348i
$525$		0			0
$526$	−14.0902	−	10.2371i	−0.614361	−	0.446359i
$527$	6.79837			0.296142
$528$		0			0
$529$	6.94427			0.301925
$530$	2.30902	+	1.67760i	0.100297	+	0.0728702i
$531$		0			0
$532$	−4.73607	−	14.5761i	−0.205335	−	0.631955i
$533$	−4.76393	+	3.46120i	−0.206349	+	0.149921i
$534$		0			0
$535$	−1.00000	−	3.07768i	−0.0432338	−	0.133060i
$536$	4.54508	−	13.9883i	0.196318	−	0.604204i
$537$		0			0
$538$	−5.18034			−0.223340
$539$	3.38197	−	36.1401i	0.145672	−	1.55667i
$540$		0			0
$541$	7.94427	+	5.77185i	0.341551	+	0.248151i	0.745316	−	0.666711i	$-0.232299\pi$
$541$	7.94427	+	5.77185i	0.341551	+	0.248151i	−0.403765	+	0.914863i	$0.632299\pi$
$542$	−8.87132	+	27.3031i	−0.381056	+	1.17277i
$543$		0			0
$544$	−3.73607	+	2.71441i	−0.160183	+	0.116379i
$545$	5.30902	−	3.85723i	0.227413	−	0.165225i
$546$		0			0
$547$	10.1353	−	31.1931i	0.433352	−	1.33372i	−0.461414	−	0.887185i	$-0.652658\pi$
$547$	10.1353	−	31.1931i	0.433352	−	1.33372i	0.894766	−	0.446536i	$-0.147342\pi$
$548$	5.78115	+	4.20025i	0.246959	+	0.179426i
$549$		0			0
$550$	1.23607	−	13.2088i	0.0527061	−	0.563225i
$551$	25.6525			1.09283
$552$		0			0
$553$	5.85410	−	18.0171i	0.248942	−	0.766164i
$554$	−0.708204	−	2.17963i	−0.0300887	−	0.0926035i
$555$		0			0
$556$	−2.80902	+	2.04087i	−0.119129	+	0.0865522i
$557$	−0.461493	−	1.42033i	−0.0195541	−	0.0601813i	0.940803	−	0.338953i	$-0.110073\pi$
$557$	−0.461493	−	1.42033i	−0.0195541	−	0.0601813i	−0.960357	+	0.278772i	$0.910073\pi$
$558$		0			0
$559$	−17.5172	−	12.7270i	−0.740900	−	0.538295i
$560$	−4.23607			−0.179007
$561$		0			0
$562$	8.56231			0.361179
$563$	−10.0451	−	7.29818i	−0.423350	−	0.307582i	0.355634	−	0.934625i	$-0.384265\pi$
$563$	−10.0451	−	7.29818i	−0.423350	−	0.307582i	−0.778984	+	0.627043i	$0.784265\pi$
$564$		0			0
$565$	2.39919	+	7.38394i	0.100935	+	0.310645i
$566$	−5.16312	+	3.75123i	−0.217022	+	0.157676i
$567$		0			0
$568$	1.66312	+	5.11855i	0.0697829	+	0.214770i
$569$	10.1074	−	31.1074i	0.423724	−	1.30409i	−0.480487	−	0.877002i	$-0.659540\pi$
$569$	10.1074	−	31.1074i	0.423724	−	1.30409i	0.904211	−	0.427086i	$-0.140460\pi$
$570$		0			0
$571$	6.65248			0.278397			0.139199	−	0.990264i	$-0.455547\pi$
$571$	6.65248			0.278397			0.139199	+	0.990264i	$0.455547\pi$
$572$	4.02786	+	6.79615i	0.168413	+	0.284161i
$573$		0			0
$574$	8.47214	+	6.15537i	0.353620	+	0.256920i
$575$	−6.76393	+	20.8172i	−0.282075	+	0.868139i
$576$		0			0
$577$	−9.04508	+	6.57164i	−0.376552	+	0.273581i	−0.759923	−	0.650014i	$-0.774763\pi$
$577$	−9.04508	+	6.57164i	−0.376552	+	0.273581i	0.383371	+	0.923595i	$0.374763\pi$
$578$	3.50000	−	2.54290i	0.145581	−	0.105771i
$579$		0			0
$580$	2.19098	−	6.74315i	0.0909756	−	0.279994i
$581$	50.2148	+	36.4832i	2.08326	+	1.51358i
$582$		0			0
$583$	−9.23607	+	2.07363i	−0.382519	+	0.0858808i
$584$	4.23607			0.175290
$585$		0			0
$586$	1.59017	−	4.89404i	0.0656893	−	0.202171i
$587$	−8.06231	−	24.8132i	−0.332767	−	1.02415i	−0.967812	−	0.251676i	$-0.919018\pi$
$587$	−8.06231	−	24.8132i	−0.332767	−	1.02415i	0.635045	−	0.772475i	$-0.280982\pi$
$588$		0			0
$589$	−4.30902	+	3.13068i	−0.177550	+	0.128998i
$590$	−4.59017	−	14.1271i	−0.188974	−	0.581603i
$591$		0			0
$592$	−2.11803	−	1.53884i	−0.0870507	−	0.0632460i
$593$	−26.2148			−1.07651			−0.538256	−	0.842781i	$-0.680917\pi$
$593$	−26.2148			−1.07651			−0.538256	+	0.842781i	$0.680917\pi$
$594$		0			0
$595$	19.5623			0.801976
$596$	−15.5623	−	11.3067i	−0.637457	−	0.463140i
$597$		0			0
$598$	−4.02786	−	12.3965i	−0.164712	−	0.506930i
$599$	17.4894	−	12.7068i	0.714596	−	0.519184i	−0.170057	−	0.985434i	$-0.554395\pi$
$599$	17.4894	−	12.7068i	0.714596	−	0.519184i	0.884653	+	0.466250i	$0.154395\pi$
$600$		0			0
$601$	−6.91641	−	21.2865i	−0.282126	−	0.868295i	−0.987245	−	0.159206i	$-0.949107\pi$
$601$	−6.91641	−	21.2865i	−0.282126	−	0.868295i	0.705119	−	0.709089i	$-0.250893\pi$
$602$	−11.8992	+	36.6219i	−0.484975	+	1.49260i
$603$		0			0
$604$	7.52786			0.306304
$605$	−7.54508	−	8.00448i	−0.306751	−	0.325428i
$606$		0			0
$607$	−22.8992	−	16.6372i	−0.929449	−	0.675284i	0.0164086	−	0.999865i	$-0.494777\pi$
$607$	−22.8992	−	16.6372i	−0.929449	−	0.675284i	−0.945858	+	0.324581i	$0.894777\pi$
$608$	1.11803	−	3.44095i	0.0453423	−	0.139549i
$609$		0			0
$610$	8.73607	−	6.34712i	0.353713	−	0.256988i
$611$	12.0172	−	8.73102i	0.486165	−	0.353219i
$612$		0			0
$613$	−9.05166	+	27.8582i	−0.365593	+	1.12518i	0.584016	+	0.811742i	$0.301481\pi$
$613$	−9.05166	+	27.8582i	−0.365593	+	1.12518i	−0.949609	+	0.313438i	$0.898519\pi$
$614$	−20.1353	−	14.6291i	−0.812593	−	0.590383i
$615$		0			0
$616$	9.28115	−	10.5474i	0.373948	−	0.424966i
$617$	−27.8541			−1.12136			−0.560682	−	0.828031i	$-0.689461\pi$
$617$	−27.8541			−1.12136			−0.560682	+	0.828031i	$0.689461\pi$
$618$		0			0
$619$	7.87132	−	24.2254i	0.316375	−	0.973703i	−0.658810	−	0.752310i	$-0.728940\pi$
$619$	7.87132	−	24.2254i	0.316375	−	0.973703i	0.975185	−	0.221393i	$-0.0710603\pi$
$620$	0.454915	+	1.40008i	0.0182698	+	0.0562287i
$621$		0			0
$622$	−14.2533	+	10.3556i	−0.571505	+	0.415223i
$623$	−0.381966	−	1.17557i	−0.0153031	−	0.0470982i
$624$		0			0
$625$	−8.89919	−	6.46564i	−0.355967	−	0.258626i
$626$	−25.8328			−1.03249
$627$		0			0
$628$	8.23607			0.328655
$629$	9.78115	+	7.10642i	0.390000	+	0.283352i
$630$		0			0
$631$	3.92047	+	12.0660i	0.156072	+	0.480339i	0.998268	−	0.0588321i	$-0.0187377\pi$
$631$	3.92047	+	12.0660i	0.156072	+	0.480339i	−0.842196	+	0.539171i	$0.818738\pi$
$632$	3.61803	−	2.62866i	0.143918	−	0.104562i
$633$		0			0
$634$	3.05573	+	9.40456i	0.121358	+	0.373503i
$635$	3.57295	−	10.9964i	0.141788	−	0.436379i
$636$		0			0
$637$	26.0689			1.03289
$638$	11.9894	+	20.2295i	0.474663	+	0.800892i
$639$		0			0
$640$	−0.809017	−	0.587785i	−0.0319792	−	0.0232343i
$641$	1.01064	−	3.11044i	0.0399180	−	0.122855i	−0.929112	−	0.369799i	$-0.879426\pi$
$641$	1.01064	−	3.11044i	0.0399180	−	0.122855i	0.969030	+	0.246944i	$0.0794265\pi$
$642$		0			0
$643$	9.68034	−	7.03318i	0.381755	−	0.277361i	−0.380313	−	0.924858i	$-0.624184\pi$
$643$	9.68034	−	7.03318i	0.381755	−	0.277361i	0.762069	+	0.647496i	$0.224184\pi$
$644$	−18.7533	+	13.6251i	−0.738983	+	0.536903i
$645$		0			0
$646$	−5.16312	+	15.8904i	−0.203140	+	0.625201i
$647$	−21.0344	−	15.2824i	−0.826949	−	0.600814i	0.0917453	−	0.995783i	$-0.470755\pi$
$647$	−21.0344	−	15.2824i	−0.826949	−	0.600814i	−0.918695	+	0.394969i	$0.870755\pi$
$648$		0			0
$649$	45.2320	+	19.5232i	1.77551	+	0.766351i
$650$	9.52786			0.373714
$651$		0			0
$652$	1.85410	−	5.70634i	0.0726122	−	0.223477i
$653$	6.12868	+	18.8621i	0.239834	+	0.738132i	0.996443	+	0.0842653i	$0.0268543\pi$
$653$	6.12868	+	18.8621i	0.239834	+	0.738132i	−0.756610	+	0.653867i	$0.773146\pi$
$654$		0			0
$655$	7.85410	−	5.70634i	0.306885	−	0.222965i
$656$	0.763932	+	2.35114i	0.0298265	+	0.0917966i
$657$		0			0
$658$	−21.3713	−	15.5272i	−0.833141	−	0.605312i
$659$	−22.4164			−0.873219			−0.436610	−	0.899651i	$-0.643821\pi$
$659$	−22.4164			−0.873219			−0.436610	+	0.899651i	$0.643821\pi$
$660$		0			0
$661$	28.8885			1.12363			0.561817	−	0.827261i	$-0.310102\pi$
$661$	28.8885			1.12363			0.561817	+	0.827261i	$0.310102\pi$
$662$	−23.5172	−	17.0863i	−0.914023	−	0.664076i
$663$		0			0
$664$	4.52786	+	13.9353i	0.175715	+	0.540796i
$665$	−12.3992	+	9.00854i	−0.480820	+	0.349336i
$666$		0			0
$667$	−11.9894	−	36.8994i	−0.464230	−	1.42875i
$668$	4.00000	−	12.3107i	0.154765	−	0.476317i
$669$		0			0
$670$	−14.7082			−0.568227
$671$	−3.33688	+	35.6584i	−0.128819	+	1.37658i
$672$		0			0
$673$	−32.8885	−	23.8949i	−1.26776	−	0.921082i	−0.268649	−	0.963238i	$-0.586577\pi$
$673$	−32.8885	−	23.8949i	−1.26776	−	0.921082i	−0.999111	+	0.0421564i	$0.986577\pi$
$674$	4.22542	−	13.0045i	0.162757	−	0.500915i
$675$		0			0
$676$	5.92705	−	4.30625i	0.227963	−	0.165625i
$677$	−9.16312	+	6.65740i	−0.352167	+	0.255864i	−0.749778	−	0.661690i	$-0.769840\pi$
$677$	−9.16312	+	6.65740i	−0.352167	+	0.255864i	0.397610	+	0.917554i	$0.369840\pi$
$678$		0			0
$679$	−16.5172	+	50.8348i	−0.633873	+	1.95086i
$680$	3.73607	+	2.71441i	0.143272	+	0.104093i
$681$		0			0
$682$	−4.48278	−	1.93487i	−0.171654	−	0.0740900i
$683$	−14.6525			−0.560661			−0.280331	−	0.959903i	$-0.590444\pi$
$683$	−14.6525			−0.560661			−0.280331	+	0.959903i	$0.590444\pi$
$684$		0			0
$685$	2.20820	−	6.79615i	0.0843711	−	0.259668i
$686$	−5.16312	−	15.8904i	−0.197129	−	0.606700i
$687$		0			0
$688$	−7.35410	+	5.34307i	−0.280373	+	0.203703i
$689$	−2.10081	−	6.46564i	−0.0800346	−	0.246321i
$690$		0			0
$691$	40.4336	+	29.3768i	1.53817	+	1.11754i	0.951471	+	0.307737i	$0.0995718\pi$
$691$	40.4336	+	29.3768i	1.53817	+	1.11754i	0.586696	+	0.809807i	$0.300428\pi$
$692$	2.56231			0.0974043
$693$		0			0
$694$	24.1246			0.915758
$695$	2.80902	+	2.04087i	0.106552	+	0.0774146i
$696$		0			0
$697$	−3.52786	−	10.8576i	−0.133627	−	0.411263i
$698$	6.19098	−	4.49801i	0.234332	−	0.170252i
$699$		0			0
$700$	−5.23607	−	16.1150i	−0.197905	−	0.609088i
$701$	−0.291796	+	0.898056i	−0.0110210	+	0.0339191i	−0.956416	−	0.292008i	$-0.905677\pi$
$701$	−0.291796	+	0.898056i	−0.0110210	+	0.0339191i	0.945395	+	0.325927i	$0.105677\pi$
$702$		0			0
$703$	−9.47214			−0.357248
$704$	3.23607	−	0.726543i	0.121964	−	0.0273826i
$705$		0			0
$706$	2.38197	+	1.73060i	0.0896465	+	0.0651320i
$707$	25.4894	−	78.4482i	0.958626	−	2.95035i
$708$		0			0
$709$	−10.3713	+	7.53521i	−0.389503	+	0.282991i	−0.765252	−	0.643731i	$-0.777386\pi$
$709$	−10.3713	+	7.53521i	−0.389503	+	0.282991i	0.375749	+	0.926722i	$0.377386\pi$
$710$	4.35410	−	3.16344i	0.163407	−	0.118722i
$711$		0			0
$712$	0.0901699	−	0.277515i	0.00337926	−	0.0104003i
$713$	6.51722	+	4.73504i	0.244072	+	0.177329i
$714$		0			0
$715$	5.21885	−	5.93085i	0.195174	−	0.221801i
$716$	−25.3607			−0.947773
$717$		0			0
$718$	−10.6008	+	32.6259i	−0.395619	+	1.21759i
$719$	6.20820	+	19.1069i	0.231527	+	0.712567i	0.997563	+	0.0697692i	$0.0222263\pi$
$719$	6.20820	+	19.1069i	0.231527	+	0.712567i	−0.766036	+	0.642797i	$0.777774\pi$
$720$		0			0
$721$	31.4615	−	22.8581i	1.17169	−	0.851281i
$722$	1.82624	+	5.62058i	0.0679655	+	0.209176i
$723$		0			0
$724$	−6.97214	−	5.06555i	−0.259117	−	0.188260i
$725$	28.3607			1.05329
$726$		0			0
$727$	4.72949			0.175407			0.0877035	−	0.996147i	$-0.472047\pi$
$727$	4.72949			0.175407			0.0877035	+	0.996147i	$0.472047\pi$
$728$	8.16312	+	5.93085i	0.302545	+	0.219812i
$729$		0			0
$730$	−1.30902	−	4.02874i	−0.0484489	−	0.149110i
$731$	33.9615	−	24.6745i	1.25611	−	0.912618i
$732$		0			0
$733$	−4.10081	−	12.6210i	−0.151467	−	0.466167i	0.846319	−	0.532677i	$-0.178814\pi$
$733$	−4.10081	−	12.6210i	−0.151467	−	0.466167i	−0.997786	+	0.0665092i	$0.978814\pi$
$734$	−11.4164	+	35.1361i	−0.421387	+	1.29690i
$735$		0			0
$736$	−5.47214			−0.201706
$737$	32.2254	−	36.6219i	1.18704	−	1.34899i
$738$		0			0
$739$	−7.80902	−	5.67358i	−0.287259	−	0.208706i	0.434818	−	0.900518i	$-0.356813\pi$
$739$	−7.80902	−	5.67358i	−0.287259	−	0.208706i	−0.722078	+	0.691812i	$0.756813\pi$
$740$	−0.809017	+	2.48990i	−0.0297401	+	0.0915305i
$741$		0			0
$742$	−9.78115	+	7.10642i	−0.359077	+	0.260885i
$743$	−6.95492	+	5.05304i	−0.255151	+	0.185378i	−0.708007	−	0.706206i	$-0.750405\pi$
$743$	−6.95492	+	5.05304i	−0.255151	+	0.185378i	0.452856	+	0.891584i	$0.350405\pi$
$744$		0			0
$745$	−5.94427	+	18.2946i	−0.217781	+	0.670262i
$746$	−17.3713	−	12.6210i	−0.636009	−	0.462088i
$747$		0			0
$748$	−14.9443	+	3.35520i	−0.546417	+	0.122678i
$749$	13.7082			0.500887
$750$		0			0
$751$	0.0278640	−	0.0857567i	0.00101677	−	0.00312931i	−0.950547	−	0.310581i	$-0.899476\pi$
$751$	0.0278640	−	0.0857567i	0.00101677	−	0.00312931i	0.951564	+	0.307452i	$0.0994763\pi$
$752$	−1.92705	−	5.93085i	−0.0702723	−	0.216276i
$753$		0			0
$754$	−13.6631	+	9.92684i	−0.497581	+	0.361514i
$755$	−2.32624	−	7.15942i	−0.0846605	−	0.260558i
$756$		0			0
$757$	7.28115	+	5.29007i	0.264638	+	0.192271i	0.712189	−	0.701988i	$-0.247704\pi$
$757$	7.28115	+	5.29007i	0.264638	+	0.192271i	−0.447551	+	0.894258i	$0.647704\pi$
$758$	33.7082			1.22434
$759$		0			0
$760$	−3.61803			−0.131240
$761$	4.75329	+	3.45347i	0.172307	+	0.125188i	0.670596	−	0.741823i	$-0.266038\pi$
$761$	4.75329	+	3.45347i	0.172307	+	0.125188i	−0.498290	+	0.867011i	$0.666038\pi$
$762$		0			0
$763$	8.59017	+	26.4378i	0.310985	+	0.957114i
$764$	−15.9721	+	11.6044i	−0.577852	+	0.419834i
$765$		0			0
$766$	10.0729	+	31.0013i	0.363950	+	1.12012i
$767$	−10.9336	+	33.6502i	−0.394790	+	1.21504i
$768$		0			0
$769$	−51.3951			−1.85336			−0.926678	−	0.375857i	$-0.877348\pi$
$769$	−51.3951			−1.85336			−0.926678	+	0.375857i	$0.877348\pi$
$770$	−12.8992	−	5.56758i	−0.464854	−	0.200642i
$771$		0			0
$772$	3.04508	+	2.21238i	0.109595	+	0.0796254i
$773$	5.86068	−	18.0373i	0.210794	−	0.648757i	−0.788632	−	0.614866i	$-0.789210\pi$
$773$	5.86068	−	18.0373i	0.210794	−	0.648757i	0.999426	−	0.0338911i	$-0.0107899\pi$
$774$		0			0
$775$	−4.76393	+	3.46120i	−0.171125	+	0.124330i
$776$	−10.2082	+	7.41669i	−0.366453	+	0.266244i
$777$		0			0
$778$	8.88197	−	27.3359i	0.318434	−	0.980039i
$779$	7.23607	+	5.25731i	0.259259	+	0.188363i
$780$		0			0
$781$	−1.66312	+	17.7723i	−0.0595111	+	0.635943i
$782$	25.2705			0.903672
$783$		0			0
$784$	3.38197	−	10.4086i	0.120785	−	0.371736i
$785$	−2.54508	−	7.83297i	−0.0908380	−	0.279571i
$786$		0			0
$787$	2.13525	−	1.55135i	0.0761136	−	0.0552998i	−0.549078	−	0.835771i	$-0.685021\pi$
$787$	2.13525	−	1.55135i	0.0761136	−	0.0552998i	0.625191	+	0.780471i	$0.285021\pi$
$788$	−5.92705	−	18.2416i	−0.211142	−	0.649830i
$789$		0			0
$790$	−3.61803	−	2.62866i	−0.128724	−	0.0935234i
$791$	−32.8885			−1.16938
$792$		0			0
$793$	−25.7214			−0.913392
$794$	13.2533	+	9.62908i	0.470342	+	0.341723i
$795$		0			0
$796$	0.927051	+	2.85317i	0.0328585	+	0.101128i
$797$	11.0000	−	7.99197i	0.389640	−	0.283090i	−0.375668	−	0.926754i	$-0.622587\pi$
$797$	11.0000	−	7.99197i	0.389640	−	0.283090i	0.765308	+	0.643664i	$0.222587\pi$
$798$		0			0
$799$	8.89919	+	27.3889i	0.314831	+	0.968949i
$800$	1.23607	−	3.80423i	0.0437016	−	0.134500i
$801$		0			0
$802$	5.00000			0.176556
$803$	12.8992	+	5.56758i	0.455202	+	0.196476i
$804$		0			0
$805$	18.7533	+	13.6251i	0.660967	+	0.480220i
$806$	1.08359	−	3.33495i	0.0381679	−	0.117469i
$807$		0			0
$808$	15.7533	−	11.4454i	0.554199	−	0.402649i
$809$	−24.9443	+	18.1231i	−0.876994	+	0.637173i	−0.932454	−	0.361288i	$-0.882337\pi$
$809$	−24.9443	+	18.1231i	−0.876994	+	0.637173i	0.0554606	+	0.998461i	$0.482337\pi$
$810$		0			0
$811$	−9.07295	+	27.9237i	−0.318594	+	0.980533i	0.655655	+	0.755060i	$0.272392\pi$
$811$	−9.07295	+	27.9237i	−0.318594	+	0.980533i	−0.974250	+	0.225472i	$0.927608\pi$
$812$	24.2984	+	17.6538i	0.852706	+	0.619527i
$813$		0			0
$814$	−4.42705	−	7.46969i	−0.155168	−	0.261813i
$815$	−6.00000			−0.210171
$816$		0			0
$817$	−10.1631	+	31.2789i	−0.355563	+	1.09431i
$818$	10.1246	+	31.1604i	0.353999	+	1.08950i
$819$		0			0
$820$	2.00000	−	1.45309i	0.0698430	−	0.0507439i
$821$	−3.80244	−	11.7027i	−0.132706	−	0.408427i	0.862520	−	0.506023i	$-0.168885\pi$
$821$	−3.80244	−	11.7027i	−0.132706	−	0.408427i	−0.995226	+	0.0975956i	$0.968885\pi$
$822$		0			0
$823$	−21.5795	−	15.6784i	−0.752215	−	0.546516i	0.144298	−	0.989534i	$-0.453908\pi$
$823$	−21.5795	−	15.6784i	−0.752215	−	0.546516i	−0.896513	+	0.443018i	$0.853908\pi$
$824$	9.18034			0.319812
$825$		0			0
$826$	62.9230			2.18937
$827$	−38.6976	−	28.1154i	−1.34565	−	0.977669i	−0.999216	−	0.0395933i	$-0.987394\pi$
$827$	−38.6976	−	28.1154i	−1.34565	−	0.977669i	−0.346430	−	0.938076i	$-0.612606\pi$
$828$		0			0
$829$	0.826238	+	2.54290i	0.0286964	+	0.0883185i	0.964379	−	0.264524i	$-0.0852150\pi$
$829$	0.826238	+	2.54290i	0.0286964	+	0.0883185i	−0.935683	+	0.352843i	$0.885215\pi$
$830$	11.8541	−	8.61251i	0.411462	−	0.298945i
$831$		0			0
$832$	0.736068	+	2.26538i	0.0255186	+	0.0785381i
$833$	−15.6180	+	48.0674i	−0.541133	+	1.66544i
$834$		0			0
$835$	−12.9443			−0.447955
$836$	7.92705	−	9.00854i	0.274163	−	0.311567i
$837$		0			0
$838$	13.6180	+	9.89408i	0.470427	+	0.341785i
$839$	−6.53444	+	20.1109i	−0.225594	+	0.694307i	0.772637	+	0.634848i	$0.218937\pi$
$839$	−6.53444	+	20.1109i	−0.225594	+	0.694307i	−0.998231	+	0.0594586i	$0.981063\pi$
$840$		0			0
$841$	−17.2082	+	12.5025i	−0.593386	+	0.431120i
$842$	−13.6353	+	9.90659i	−0.469902	+	0.341404i
$843$		0			0
$844$	−4.25329	+	13.0903i	−0.146404	+	0.450586i
$845$	−5.92705	−	4.30625i	−0.203897	−	0.148140i
$846$		0			0
$847$	42.1246	−	19.9192i	1.44742	−	0.684431i
$848$	−2.85410			−0.0980103
$849$		0			0
$850$	−5.70820	+	17.5680i	−0.195790	+	0.602579i
$851$	4.42705	+	13.6251i	0.151757	+	0.467061i
$852$		0			0
$853$	28.1074	−	20.4212i	0.962379	−	0.699209i	0.00867675	−	0.999962i	$-0.497238\pi$
$853$	28.1074	−	20.4212i	0.962379	−	0.699209i	0.953702	+	0.300753i	$0.0972381\pi$
$854$	14.1353	+	43.5038i	0.483698	+	1.48867i
$855$		0			0
$856$	2.61803	+	1.90211i	0.0894826	+	0.0650129i
$857$	50.7426			1.73334			0.866668	−	0.498886i	$-0.166257\pi$
$857$	50.7426			1.73334			0.866668	+	0.498886i	$0.166257\pi$
$858$		0			0
$859$	−39.0689			−1.33301			−0.666507	−	0.745499i	$-0.732211\pi$
$859$	−39.0689			−1.33301			−0.666507	+	0.745499i	$0.732211\pi$
$860$	7.35410	+	5.34307i	0.250773	+	0.182197i
$861$		0			0
$862$	4.08359	+	12.5680i	0.139088	+	0.428068i
$863$	−24.9894	+	18.1558i	−0.850648	+	0.618032i	−0.925325	−	0.379176i	$-0.876207\pi$
$863$	−24.9894	+	18.1558i	−0.850648	+	0.618032i	0.0746769	+	0.997208i	$0.476207\pi$
$864$		0			0
$865$	−0.791796	−	2.43690i	−0.0269219	−	0.0828570i
$866$	−1.97214	+	6.06961i	−0.0670159	+	0.206254i
$867$		0			0
$868$	−6.23607			−0.211666
$869$	14.4721	−	3.24920i	0.490934	−	0.110221i
$870$		0			0
$871$	28.3435	+	20.5927i	0.960381	+	0.697758i
$872$	−2.02786	+	6.24112i	−0.0686721	+	0.211351i
$873$		0			0
$874$	−16.0172	+	11.6372i	−0.541791	+	0.393634i
$875$	−30.8435	+	22.4091i	−1.04270	+	0.757565i
$876$		0			0
$877$	−2.97871	+	9.16754i	−0.100584	+	0.309566i	−0.988669	−	0.150114i	$-0.952036\pi$
$877$	−2.97871	+	9.16754i	−0.100584	+	0.309566i	0.888085	+	0.459680i	$0.152036\pi$
$878$	−17.2533	−	12.5352i	−0.582270	−	0.423044i
$879$		0			0
$880$	−1.69098	−	2.85317i	−0.0570030	−	0.0961803i
$881$	3.29180			0.110903			0.0554517	−	0.998461i	$-0.482340\pi$
$881$	3.29180			0.110903			0.0554517	+	0.998461i	$0.482340\pi$
$882$		0			0
$883$	−14.1074	+	43.4181i	−0.474752	+	1.46113i	0.371541	+	0.928417i	$0.378829\pi$
$883$	−14.1074	+	43.4181i	−0.474752	+	1.46113i	−0.846293	+	0.532718i	$0.821171\pi$
$884$	−3.39919	−	10.4616i	−0.114327	−	0.351862i
$885$		0			0
$886$	−2.26393	+	1.64484i	−0.0760583	+	0.0552596i
$887$	−5.55573	−	17.0988i	−0.186543	−	0.574121i	0.813428	−	0.581665i	$-0.197599\pi$
$887$	−5.55573	−	17.0988i	−0.186543	−	0.574121i	−0.999972	+	0.00754438i	$0.997599\pi$
$888$		0			0
$889$	39.6246	+	28.7890i	1.32897	+	0.965551i
$890$	−0.291796			−0.00978103
$891$		0			0
$892$	13.7426			0.460138
$893$	−18.2533	−	13.2618i	−0.610823	−	0.443789i
$894$		0			0
$895$	7.83688	+	24.1194i	0.261958	+	0.806224i
$896$	3.42705	−	2.48990i	0.114490	−	0.0831817i
$897$		0			0
$898$	−12.3713	−	38.0750i	−0.412836	−	1.27058i
$899$	3.22542	−	9.92684i	0.107574	−	0.331079i
$900$		0			0
$901$	13.1803			0.439101
$902$	−0.763932	+	8.16348i	−0.0254362	+	0.271814i
$903$		0			0
$904$	−6.28115	−	4.56352i	−0.208908	−	0.151781i
$905$	−2.66312	+	8.19624i	−0.0885251	+	0.272452i
$906$		0			0
$907$	24.2254	−	17.6008i	0.804392	−	0.584425i	−0.107807	−	0.994172i	$-0.534383\pi$
$907$	24.2254	−	17.6008i	0.804392	−	0.584425i	0.912199	+	0.409747i	$0.134383\pi$
$908$	0.354102	−	0.257270i	0.0117513	−	0.00853781i
$909$		0			0
$910$	3.11803	−	9.59632i	0.103362	−	0.318115i
$911$	9.23607	+	6.71040i	0.306005	+	0.222325i	0.730180	−	0.683255i	$-0.239436\pi$
$911$	9.23607	+	6.71040i	0.306005	+	0.222325i	−0.424176	+	0.905580i	$0.639436\pi$
$912$		0			0
$913$	−4.52786	+	48.3854i	−0.149850	+	1.60132i
$914$	24.9787			0.826222
$915$		0			0
$916$	−4.92705	+	15.1639i	−0.162794	+	0.501029i
$917$	12.7082	+	39.1118i	0.419662	+	1.29159i
$918$		0			0
$919$	−4.83688	+	3.51420i	−0.159554	+	0.115923i	−0.664697	−	0.747113i	$-0.731440\pi$
$919$	−4.83688	+	3.51420i	−0.159554	+	0.115923i	0.505144	+	0.863035i	$0.331440\pi$
$920$	1.69098	+	5.20431i	0.0557501	+	0.171581i
$921$		0			0
$922$	23.4443	+	17.0333i	0.772096	+	0.560961i
$923$	−12.8197			−0.421964
$924$		0			0
$925$	−10.4721			−0.344322
$926$	−10.5902	−	7.69421i	−0.348015	−	0.252847i
$927$		0			0
$928$	2.19098	+	6.74315i	0.0719225	+	0.221355i
$929$	43.4164	−	31.5439i	1.42445	−	1.03492i	0.433429	−	0.901188i	$-0.357304\pi$
$929$	43.4164	−	31.5439i	1.42445	−	1.03492i	0.991017	−	0.133733i	$-0.0426964\pi$
$930$		0			0
$931$	−12.2361	−	37.6587i	−0.401021	−	1.23422i
$932$	6.72542	−	20.6987i	0.220299	−	0.678009i
$933$		0			0
$934$	−12.5623			−0.411051
$935$	7.80902	+	13.1760i	0.255382	+	0.430902i
$936$		0			0
$937$	20.1525	+	14.6416i	0.658353	+	0.478321i	0.866106	−	0.499860i	$-0.166615\pi$
$937$	20.1525	+	14.6416i	0.658353	+	0.478321i	−0.207754	+	0.978181i	$0.566615\pi$
$938$	19.2533	−	59.2555i	0.628642	−	1.93476i
$939$		0			0
$940$	−5.04508	+	3.66547i	−0.164553	+	0.119554i
$941$	−24.2705	+	17.6336i	−0.791196	+	0.574838i	−0.908318	−	0.418280i	$-0.862633\pi$
$941$	−24.2705	+	17.6336i	−0.791196	+	0.574838i	0.117122	+	0.993118i	$0.462633\pi$
$942$		0			0
$943$	4.18034	−	12.8658i	0.136131	−	0.418967i
$944$	12.0172	+	8.73102i	0.391127	+	0.284171i
$945$		0			0
$946$	−29.4164	+	6.60440i	−0.956410	+	0.214727i
$947$	−53.9230			−1.75226			−0.876131	−	0.482073i	$-0.839884\pi$
$947$	−53.9230			−1.75226			−0.876131	+	0.482073i	$0.839884\pi$
$948$		0			0
$949$	−3.11803	+	9.59632i	−0.101216	+	0.311510i
$950$	−4.47214	−	13.7638i	−0.145095	−	0.446557i
$951$		0			0
$952$	−15.8262	+	11.4984i	−0.512931	+	0.372666i
$953$	9.22949	+	28.4054i	0.298973	+	0.920143i	0.981858	+	0.189617i	$0.0607248\pi$
$953$	9.22949	+	28.4054i	0.298973	+	0.920143i	−0.682886	+	0.730525i	$0.739275\pi$
$954$		0			0
$955$	15.9721	+	11.6044i	0.516846	+	0.375511i
$956$	−12.7639			−0.412815
$957$		0			0
$958$	−30.0344			−0.970369
$959$	24.4894	+	17.7926i	0.790803	+	0.574552i
$960$		0			0
$961$	−8.90983	−	27.4216i	−0.287414	−	0.884569i
$962$	5.04508	−	3.66547i	0.162660	−	0.118179i
$963$		0			0
$964$	6.30902	+	19.4172i	0.203200	+	0.625385i
$965$	1.16312	−	3.57971i	0.0374421	−	0.115235i
$966$		0			0
$967$	1.14590			0.0368496			0.0184248	−	0.999830i	$-0.494135\pi$
$967$	1.14590			0.0368496			0.0184248	+	0.999830i	$0.494135\pi$
$968$	10.8090	+	2.04087i	0.347415	+	0.0655961i
$969$		0			0
$970$	10.2082	+	7.41669i	0.327766	+	0.238136i
$971$	6.87132	−	21.1478i	0.220511	−	0.678664i	−0.778205	−	0.628010i	$-0.783870\pi$
$971$	6.87132	−	21.1478i	0.220511	−	0.678664i	0.998716	−	0.0506535i	$-0.0161304\pi$
$972$		0			0
$973$	−11.8992	+	8.64527i	−0.381470	+	0.277154i
$974$	−16.8541	+	12.2452i	−0.540040	+	0.392362i
$975$		0			0
$976$	−3.33688	+	10.2699i	−0.106811	+	0.328730i
$977$	36.3156	+	26.3848i	1.16184	+	0.844125i	0.990009	−	0.141001i	$-0.0450322\pi$
$977$	36.3156	+	26.3848i	1.16184	+	0.844125i	0.171829	+	0.985127i	$0.445032\pi$
$978$		0			0
$979$	0.639320	−	0.726543i	0.0204328	−	0.0232204i
$980$	−10.9443			−0.349602
$981$		0			0
$982$	12.1287	−	37.3282i	0.387042	−	1.19119i
$983$	6.79837	+	20.9232i	0.216834	+	0.667348i	0.999018	+	0.0443001i	$0.0141058\pi$
$983$	6.79837	+	20.9232i	0.216834	+	0.667348i	−0.782184	+	0.623048i	$0.785894\pi$
$984$		0			0
$985$	−15.5172	+	11.2739i	−0.494420	+	0.359217i
$986$	−10.1180	−	31.1401i	−0.322224	−	0.991703i
$987$		0			0
$988$	6.97214	+	5.06555i	0.221813	+	0.161157i
$989$	49.7426			1.58172
$990$		0			0
$991$	−30.4164			−0.966209			−0.483105	−	0.875563i	$-0.660491\pi$
$991$	−30.4164			−0.966209			−0.483105	+	0.875563i	$0.660491\pi$
$992$	−1.19098	−	0.865300i	−0.0378137	−	0.0274733i
$993$		0			0
$994$	7.04508	+	21.6825i	0.223457	+	0.687728i
$995$	2.42705	−	1.76336i	0.0769427	−	0.0559021i
$996$		0			0
$997$	13.3262	+	41.0139i	0.422046	+	1.29892i	0.905794	+	0.423717i	$0.139275\pi$
$997$	13.3262	+	41.0139i	0.422046	+	1.29892i	−0.483748	+	0.875207i	$0.660725\pi$
$998$	7.19756	−	22.1518i	0.227835	−	0.701203i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	594.2.f.h.433.1	yes	4
3.2	odd	2		594.2.f.c.433.1	✓	4
11.3	even	5	inner	594.2.f.h.487.1	yes	4
11.5	even	5		6534.2.a.bg.1.2		2
11.6	odd	10		6534.2.a.bz.1.1		2
33.5	odd	10		6534.2.a.cn.1.2		2
33.14	odd	10		594.2.f.c.487.1	yes	4
33.17	even	10		6534.2.a.bt.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
594.2.f.c.433.1	✓	4	3.2	odd	2
594.2.f.c.487.1	yes	4	33.14	odd	10
594.2.f.h.433.1	yes	4	1.1	even	1	trivial
594.2.f.h.487.1	yes	4	11.3	even	5	inner
6534.2.a.bg.1.2		2	11.5	even	5
6534.2.a.bt.1.1		2	33.17	even	10
6534.2.a.bz.1.1		2	11.6	odd	10
6534.2.a.cn.1.2		2	33.5	odd	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:	\( N \)	\(=\)	\( 594 = 2 \cdot 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	594.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.30902 + 4.02874i) q^{7} +(-0.309017 + 0.951057i) q^{8} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.30902 + 4.02874i) q^{7} +(-0.309017 + 0.951057i) q^{8} +1.00000 q^{10} +(-2.19098 + 2.48990i) q^{11} +(-1.92705 - 1.40008i) q^{13} +(-1.30902 + 4.02874i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(3.73607 - 2.71441i) q^{17} +(-1.11803 + 3.44095i) q^{19} +(0.809017 + 0.587785i) q^{20} +(-3.23607 + 0.726543i) q^{22} +5.47214 q^{23} +(-1.23607 + 3.80423i) q^{25} +(-0.736068 - 2.26538i) q^{26} +(-3.42705 + 2.48990i) q^{28} +(-2.19098 - 6.74315i) q^{29} +(1.19098 + 0.865300i) q^{31} -1.00000 q^{32} +4.61803 q^{34} +(3.42705 + 2.48990i) q^{35} +(0.809017 + 2.48990i) q^{37} +(-2.92705 + 2.12663i) q^{38} +(0.309017 + 0.951057i) q^{40} +(0.763932 - 2.35114i) q^{41} +9.09017 q^{43} +(-3.04508 - 1.31433i) q^{44} +(4.42705 + 3.21644i) q^{46} +(-1.92705 + 5.93085i) q^{47} +(-8.85410 + 6.43288i) q^{49} +(-3.23607 + 2.35114i) q^{50} +(0.736068 - 2.26538i) q^{52} +(2.30902 + 1.67760i) q^{53} +(-0.309017 + 3.30220i) q^{55} -4.23607 q^{56} +(2.19098 - 6.74315i) q^{58} +(-4.59017 - 14.1271i) q^{59} +(8.73607 - 6.34712i) q^{61} +(0.454915 + 1.40008i) q^{62} +(-0.809017 - 0.587785i) q^{64} -2.38197 q^{65} -14.7082 q^{67} +(3.73607 + 2.71441i) q^{68} +(1.30902 + 4.02874i) q^{70} +(4.35410 - 3.16344i) q^{71} +(-1.30902 - 4.02874i) q^{73} +(-0.809017 + 2.48990i) q^{74} -3.61803 q^{76} +(-12.8992 - 5.56758i) q^{77} +(-3.61803 - 2.62866i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(2.00000 - 1.45309i) q^{82} +(11.8541 - 8.61251i) q^{83} +(1.42705 - 4.39201i) q^{85} +(7.35410 + 5.34307i) q^{86} +(-1.69098 - 2.85317i) q^{88} -0.291796 q^{89} +(3.11803 - 9.59632i) q^{91} +(1.69098 + 5.20431i) q^{92} +(-5.04508 + 3.66547i) q^{94} +(1.11803 + 3.44095i) q^{95} +(10.2082 + 7.41669i) q^{97} -10.9443 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{4} + q^{5} + 3 q^{7} + q^{8}+O(q^{10}) \) 4 * q + q^2 - q^4 + q^5 + 3 * q^7 + q^8	\( 4 q + q^{2} - q^{4} + q^{5} + 3 q^{7} + q^{8} + 4 q^{10} - 11 q^{11} - q^{13} - 3 q^{14} - q^{16} + 6 q^{17} + q^{20} - 4 q^{22} + 4 q^{23} + 4 q^{25} + 6 q^{26} - 7 q^{28} - 11 q^{29} + 7 q^{31} - 4 q^{32} + 14 q^{34} + 7 q^{35} + q^{37} - 5 q^{38} - q^{40} + 12 q^{41} + 14 q^{43} - q^{44} + 11 q^{46} - q^{47} - 22 q^{49} - 4 q^{50} - 6 q^{52} + 7 q^{53} + q^{55} - 8 q^{56} + 11 q^{58} + 4 q^{59} + 26 q^{61} + 13 q^{62} - q^{64} - 14 q^{65} - 32 q^{67} + 6 q^{68} + 3 q^{70} + 4 q^{71} - 3 q^{73} - q^{74} - 10 q^{76} - 27 q^{77} - 10 q^{79} + q^{80} + 8 q^{82} + 34 q^{83} - q^{85} + 16 q^{86} - 9 q^{88} - 28 q^{89} + 8 q^{91} + 9 q^{92} - 9 q^{94} + 14 q^{97} - 8 q^{98}+O(q^{100}) \) 4 * q + q^2 - q^4 + q^5 + 3 * q^7 + q^8 + 4 * q^10 - 11 * q^11 - q^13 - 3 * q^14 - q^16 + 6 * q^17 + q^20 - 4 * q^22 + 4 * q^23 + 4 * q^25 + 6 * q^26 - 7 * q^28 - 11 * q^29 + 7 * q^31 - 4 * q^32 + 14 * q^34 + 7 * q^35 + q^37 - 5 * q^38 - q^40 + 12 * q^41 + 14 * q^43 - q^44 + 11 * q^46 - q^47 - 22 * q^49 - 4 * q^50 - 6 * q^52 + 7 * q^53 + q^55 - 8 * q^56 + 11 * q^58 + 4 * q^59 + 26 * q^61 + 13 * q^62 - q^64 - 14 * q^65 - 32 * q^67 + 6 * q^68 + 3 * q^70 + 4 * q^71 - 3 * q^73 - q^74 - 10 * q^76 - 27 * q^77 - 10 * q^79 + q^80 + 8 * q^82 + 34 * q^83 - q^85 + 16 * q^86 - 9 * q^88 - 28 * q^89 + 8 * q^91 + 9 * q^92 - 9 * q^94 + 14 * q^97 - 8 * q^98

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