LMFDB - Embedded newform 594.2.f.a.163.1

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			163.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	594.163
Dual form			594.2.f.a.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.381966 - 1.17557i) q^{5} +(-2.30902 - 1.67760i) q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.381966 - 1.17557i) q^{5} +(-2.30902 - 1.67760i) q^{7} +(-0.809017 + 0.587785i) q^{8} -1.23607 q^{10} +(-3.23607 + 0.726543i) q^{11} +(-1.92705 + 5.93085i) q^{13} +(-2.30902 + 1.67760i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-1.92705 - 5.93085i) q^{17} +(-4.04508 + 2.93893i) q^{19} +(-0.381966 + 1.17557i) q^{20} +(-0.309017 + 3.30220i) q^{22} +7.61803 q^{23} +(2.80902 - 2.04087i) q^{25} +(5.04508 + 3.66547i) q^{26} +(0.881966 + 2.71441i) q^{28} +(-5.73607 - 4.16750i) q^{29} +(-2.16312 + 6.65740i) q^{31} +1.00000 q^{32} -6.23607 q^{34} +(-1.09017 + 3.35520i) q^{35} +(-7.28115 - 5.29007i) q^{37} +(1.54508 + 4.75528i) q^{38} +(1.00000 + 0.726543i) q^{40} +(-2.73607 + 1.98787i) q^{41} -0.708204 q^{43} +(3.04508 + 1.31433i) q^{44} +(2.35410 - 7.24518i) q^{46} +(-1.42705 + 1.03681i) q^{47} +(0.354102 + 1.08981i) q^{49} +(-1.07295 - 3.30220i) q^{50} +(5.04508 - 3.66547i) q^{52} +(3.11803 - 9.59632i) q^{53} +(2.09017 + 3.52671i) q^{55} +2.85410 q^{56} +(-5.73607 + 4.16750i) q^{58} +(-7.54508 - 5.48183i) q^{59} +(1.07295 + 3.30220i) q^{61} +(5.66312 + 4.11450i) q^{62} +(0.309017 - 0.951057i) q^{64} +7.70820 q^{65} -6.09017 q^{67} +(-1.92705 + 5.93085i) q^{68} +(2.85410 + 2.07363i) q^{70} +(1.39919 + 4.30625i) q^{71} +(3.42705 + 2.48990i) q^{73} +(-7.28115 + 5.29007i) q^{74} +5.00000 q^{76} +(8.69098 + 3.75123i) q^{77} +(4.63525 - 14.2658i) q^{79} +(1.00000 - 0.726543i) q^{80} +(1.04508 + 3.21644i) q^{82} +(-1.16312 - 3.57971i) q^{83} +(-6.23607 + 4.53077i) q^{85} +(-0.218847 + 0.673542i) q^{86} +(2.19098 - 2.48990i) q^{88} +4.23607 q^{89} +(14.3992 - 10.4616i) q^{91} +(-6.16312 - 4.47777i) q^{92} +(0.545085 + 1.67760i) q^{94} +(5.00000 + 3.63271i) q^{95} +(1.85410 - 5.70634i) q^{97} +1.14590 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{4} - 6 q^{5} - 7 q^{7} - q^{8}+O(q^{10}) $ 4 * q - q^2 - q^4 - 6 * q^5 - 7 * q^7 - q^8	$ 4 q - q^{2} - q^{4} - 6 q^{5} - 7 q^{7} - q^{8} + 4 q^{10} - 4 q^{11} - q^{13} - 7 q^{14} - q^{16} - q^{17} - 5 q^{19} - 6 q^{20} + q^{22} + 26 q^{23} + 9 q^{25} + 9 q^{26} + 8 q^{28} - 14 q^{29} + 7 q^{31} + 4 q^{32} - 16 q^{34} + 18 q^{35} - 9 q^{37} - 5 q^{38} + 4 q^{40} - 2 q^{41} + 24 q^{43} + q^{44} - 4 q^{46} + q^{47} - 12 q^{49} - 11 q^{50} + 9 q^{52} + 8 q^{53} - 14 q^{55} - 2 q^{56} - 14 q^{58} - 19 q^{59} + 11 q^{61} + 7 q^{62} - q^{64} + 4 q^{65} - 2 q^{67} - q^{68} - 2 q^{70} - 19 q^{71} + 7 q^{73} - 9 q^{74} + 20 q^{76} + 37 q^{77} - 15 q^{79} + 4 q^{80} - 7 q^{82} + 11 q^{83} - 16 q^{85} - 21 q^{86} + 11 q^{88} + 8 q^{89} + 33 q^{91} - 9 q^{92} - 9 q^{94} + 20 q^{95} - 6 q^{97} + 18 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^4 - 6 * q^5 - 7 * q^7 - q^8 + 4 * q^10 - 4 * q^11 - q^13 - 7 * q^14 - q^16 - q^17 - 5 * q^19 - 6 * q^20 + q^22 + 26 * q^23 + 9 * q^25 + 9 * q^26 + 8 * q^28 - 14 * q^29 + 7 * q^31 + 4 * q^32 - 16 * q^34 + 18 * q^35 - 9 * q^37 - 5 * q^38 + 4 * q^40 - 2 * q^41 + 24 * q^43 + q^44 - 4 * q^46 + q^47 - 12 * q^49 - 11 * q^50 + 9 * q^52 + 8 * q^53 - 14 * q^55 - 2 * q^56 - 14 * q^58 - 19 * q^59 + 11 * q^61 + 7 * q^62 - q^64 + 4 * q^65 - 2 * q^67 - q^68 - 2 * q^70 - 19 * q^71 + 7 * q^73 - 9 * q^74 + 20 * q^76 + 37 * q^77 - 15 * q^79 + 4 * q^80 - 7 * q^82 + 11 * q^83 - 16 * q^85 - 21 * q^86 + 11 * q^88 + 8 * q^89 + 33 * q^91 - 9 * q^92 - 9 * q^94 + 20 * q^95 - 6 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$353$	$541$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.309017	−	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
$5$	−0.381966	−	1.17557i	−0.170820	−	0.525731i	0.828598	−	0.559845i	$-0.189139\pi$
$5$	−0.381966	−	1.17557i	−0.170820	−	0.525731i	−0.999418	+	0.0341136i	$0.989139\pi$
$6$		0			0
$7$	−2.30902	−	1.67760i	−0.872726	−	0.634073i	0.0585908	−	0.998282i	$-0.481339\pi$
$7$	−2.30902	−	1.67760i	−0.872726	−	0.634073i	−0.931317	+	0.364209i	$0.881339\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$		0			0
$10$	−1.23607			−0.390879
$11$	−3.23607	+	0.726543i	−0.975711	+	0.219061i
$11$	−3.23607	+	0.726543i	−0.975711	+	0.219061i
$12$		0			0
$13$	−1.92705	+	5.93085i	−0.534468	+	1.64492i	0.210329	+	0.977631i	$0.432547\pi$
$13$	−1.92705	+	5.93085i	−0.534468	+	1.64492i	−0.744796	+	0.667292i	$0.767453\pi$
$14$	−2.30902	+	1.67760i	−0.617111	+	0.448357i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−1.92705	−	5.93085i	−0.467379	−	1.43844i	−0.855966	−	0.517031i	$-0.827037\pi$
$17$	−1.92705	−	5.93085i	−0.467379	−	1.43844i	0.388588	−	0.921412i	$-0.372963\pi$
$18$		0			0
$19$	−4.04508	+	2.93893i	−0.928006	+	0.674236i	−0.945504	−	0.325611i	$-0.894430\pi$
$19$	−4.04508	+	2.93893i	−0.928006	+	0.674236i	0.0174977	+	0.999847i	$0.494430\pi$
$20$	−0.381966	+	1.17557i	−0.0854102	+	0.262866i
$21$		0			0
$22$	−0.309017	+	3.30220i	−0.0658826	+	0.704031i
$23$	7.61803			1.58847			0.794235	−	0.607611i	$-0.207872\pi$
$23$	7.61803			1.58847			0.794235	+	0.607611i	$0.207872\pi$
$24$		0			0
$25$	2.80902	−	2.04087i	0.561803	−	0.408174i
$26$	5.04508	+	3.66547i	0.989423	+	0.718858i
$27$		0			0
$28$	0.881966	+	2.71441i	0.166676	+	0.512976i
$29$	−5.73607	−	4.16750i	−1.06516	−	0.773885i	−0.0901248	−	0.995930i	$-0.528727\pi$
$29$	−5.73607	−	4.16750i	−1.06516	−	0.773885i	−0.975036	+	0.222046i	$0.928727\pi$
$30$		0			0
$31$	−2.16312	+	6.65740i	−0.388508	+	1.19570i	0.545396	+	0.838179i	$0.316379\pi$
$31$	−2.16312	+	6.65740i	−0.388508	+	1.19570i	−0.933904	+	0.357525i	$0.883621\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−6.23607			−1.06948
$35$	−1.09017	+	3.35520i	−0.184272	+	0.567132i
$36$		0			0
$37$	−7.28115	−	5.29007i	−1.19701	−	0.869682i	−0.203026	−	0.979173i	$-0.565078\pi$
$37$	−7.28115	−	5.29007i	−1.19701	−	0.869682i	−0.993988	+	0.109492i	$0.965078\pi$
$38$	1.54508	+	4.75528i	0.250646	+	0.771409i
$39$		0			0
$40$	1.00000	+	0.726543i	0.158114	+	0.114876i
$41$	−2.73607	+	1.98787i	−0.427302	+	0.310453i	−0.780569	−	0.625069i	$-0.785071\pi$
$41$	−2.73607	+	1.98787i	−0.427302	+	0.310453i	0.353267	+	0.935522i	$0.385071\pi$
$42$		0			0
$43$	−0.708204			−0.108000			−0.0540000	−	0.998541i	$-0.517197\pi$
$43$	−0.708204			−0.108000			−0.0540000	+	0.998541i	$0.517197\pi$
$44$	3.04508	+	1.31433i	0.459064	+	0.198142i
$45$		0			0
$46$	2.35410	−	7.24518i	0.347093	−	1.06824i
$47$	−1.42705	+	1.03681i	−0.208157	+	0.151235i	−0.686979	−	0.726677i	$-0.741064\pi$
$47$	−1.42705	+	1.03681i	−0.208157	+	0.151235i	0.478823	+	0.877912i	$0.341064\pi$
$48$		0			0
$49$	0.354102	+	1.08981i	0.0505860	+	0.155688i
$50$	−1.07295	−	3.30220i	−0.151738	−	0.467001i
$51$		0			0
$52$	5.04508	−	3.66547i	0.699627	−	0.508309i
$53$	3.11803	−	9.59632i	0.428295	−	1.31816i	−0.471509	−	0.881861i	$-0.656290\pi$
$53$	3.11803	−	9.59632i	0.428295	−	1.31816i	0.899804	−	0.436295i	$-0.143710\pi$
$54$		0			0
$55$	2.09017	+	3.52671i	0.281838	+	0.475542i
$56$	2.85410			0.381395
$57$		0			0
$58$	−5.73607	+	4.16750i	−0.753183	+	0.547219i
$59$	−7.54508	−	5.48183i	−0.982286	−	0.713673i	−0.0240680	−	0.999710i	$-0.507662\pi$
$59$	−7.54508	−	5.48183i	−0.982286	−	0.713673i	−0.958218	+	0.286037i	$0.907662\pi$
$60$		0			0
$61$	1.07295	+	3.30220i	0.137377	+	0.422803i	0.995952	−	0.0898847i	$-0.0286499\pi$
$61$	1.07295	+	3.30220i	0.137377	+	0.422803i	−0.858575	+	0.512688i	$0.828650\pi$
$62$	5.66312	+	4.11450i	0.719217	+	0.522542i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	7.70820			0.956085
$66$		0			0
$67$	−6.09017			−0.744033			−0.372016	−	0.928226i	$-0.621333\pi$
$67$	−6.09017			−0.744033			−0.372016	+	0.928226i	$0.621333\pi$
$68$	−1.92705	+	5.93085i	−0.233689	+	0.719222i
$69$		0			0
$70$	2.85410	+	2.07363i	0.341130	+	0.247846i
$71$	1.39919	+	4.30625i	0.166053	+	0.511058i	0.999112	−	0.0421251i	$-0.0134128\pi$
$71$	1.39919	+	4.30625i	0.166053	+	0.511058i	−0.833059	+	0.553184i	$0.813413\pi$
$72$		0			0
$73$	3.42705	+	2.48990i	0.401106	+	0.291421i	0.769991	−	0.638054i	$-0.220261\pi$
$73$	3.42705	+	2.48990i	0.401106	+	0.291421i	−0.368885	+	0.929475i	$0.620261\pi$
$74$	−7.28115	+	5.29007i	−0.846417	+	0.614958i
$75$		0			0
$76$	5.00000			0.573539
$77$	8.69098	+	3.75123i	0.990429	+	0.427492i
$78$		0			0
$79$	4.63525	−	14.2658i	0.521507	−	1.60503i	−0.249615	−	0.968345i	$-0.580304\pi$
$79$	4.63525	−	14.2658i	0.521507	−	1.60503i	0.771122	−	0.636688i	$-0.219696\pi$
$80$	1.00000	−	0.726543i	0.111803	−	0.0812299i
$81$		0			0
$82$	1.04508	+	3.21644i	0.115410	+	0.355196i
$83$	−1.16312	−	3.57971i	−0.127669	−	0.392924i	0.866709	−	0.498814i	$-0.166231\pi$
$83$	−1.16312	−	3.57971i	−0.127669	−	0.392924i	−0.994378	+	0.105890i	$0.966231\pi$
$84$		0			0
$85$	−6.23607	+	4.53077i	−0.676397	+	0.491431i
$86$	−0.218847	+	0.673542i	−0.0235989	+	0.0726299i
$87$		0			0
$88$	2.19098	−	2.48990i	0.233560	−	0.265424i
$89$	4.23607			0.449022			0.224511	−	0.974472i	$-0.427921\pi$
$89$	4.23607			0.449022			0.224511	+	0.974472i	$0.427921\pi$
$90$		0			0
$91$	14.3992	−	10.4616i	1.50944	−	1.09668i
$92$	−6.16312	−	4.47777i	−0.642550	−	0.466840i
$93$		0			0
$94$	0.545085	+	1.67760i	0.0562212	+	0.173031i
$95$	5.00000	+	3.63271i	0.512989	+	0.372708i
$96$		0			0
$97$	1.85410	−	5.70634i	0.188256	−	0.579391i	−0.811734	−	0.584028i	$-0.801476\pi$
$97$	1.85410	−	5.70634i	0.188256	−	0.579391i	0.999989	+	0.00463676i	$0.00147593\pi$
$98$	1.14590			0.115753
$99$		0			0
$100$	−3.47214			−0.347214
$101$	5.26393	−	16.2007i	0.523781	−	1.61203i	−0.242933	−	0.970043i	$-0.578110\pi$
$101$	5.26393	−	16.2007i	0.523781	−	1.61203i	0.766714	−	0.641989i	$-0.221890\pi$
$102$		0			0
$103$	4.50000	+	3.26944i	0.443398	+	0.322148i	0.786984	−	0.616974i	$-0.211642\pi$
$103$	4.50000	+	3.26944i	0.443398	+	0.322148i	−0.343586	+	0.939121i	$0.611642\pi$
$104$	−1.92705	−	5.93085i	−0.188963	−	0.581568i
$105$		0			0
$106$	−8.16312	−	5.93085i	−0.792872	−	0.576055i
$107$	−14.7812	+	10.7391i	−1.42895	+	1.03819i	−0.438737	+	0.898616i	$0.644574\pi$
$107$	−14.7812	+	10.7391i	−1.42895	+	1.03819i	−0.990211	+	0.139576i	$0.955426\pi$
$108$		0			0
$109$	4.32624			0.414378			0.207189	−	0.978301i	$-0.433568\pi$
$109$	4.32624			0.414378			0.207189	+	0.978301i	$0.433568\pi$
$110$	4.00000	−	0.898056i	0.381385	−	0.0856263i
$111$		0			0
$112$	0.881966	−	2.71441i	0.0833380	−	0.256488i
$113$	2.07295	−	1.50609i	0.195007	−	0.141681i	−0.485997	−	0.873960i	$-0.661544\pi$
$113$	2.07295	−	1.50609i	0.195007	−	0.141681i	0.681004	+	0.732280i	$0.261544\pi$
$114$		0			0
$115$	−2.90983	−	8.95554i	−0.271343	−	0.835108i
$116$	2.19098	+	6.74315i	0.203428	+	0.626086i
$117$		0			0
$118$	−7.54508	+	5.48183i	−0.694581	+	0.504643i
$119$	−5.50000	+	16.9273i	−0.504184	+	1.55172i
$120$		0			0
$121$	9.94427	−	4.70228i	0.904025	−	0.427480i
$122$	3.47214			0.314352
$123$		0			0
$124$	5.66312	−	4.11450i	0.508563	−	0.369493i
$125$	−8.47214	−	6.15537i	−0.757771	−	0.550553i
$126$		0			0
$127$	−1.07295	−	3.30220i	−0.0952088	−	0.293023i	0.892099	−	0.451840i	$-0.149232\pi$
$127$	−1.07295	−	3.30220i	−0.0952088	−	0.293023i	−0.987308	+	0.158817i	$0.949232\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$		0			0
$130$	2.38197	−	7.33094i	0.208912	−	0.642966i
$131$	−6.94427			−0.606724			−0.303362	−	0.952875i	$-0.598109\pi$
$131$	−6.94427			−0.606724			−0.303362	+	0.952875i	$0.598109\pi$
$132$		0			0
$133$	14.2705			1.23741
$134$	−1.88197	+	5.79210i	−0.162577	+	0.500361i
$135$		0			0
$136$	5.04508	+	3.66547i	0.432612	+	0.314311i
$137$	4.38197	+	13.4863i	0.374377	+	1.15221i	0.943898	+	0.330236i	$0.107128\pi$
$137$	4.38197	+	13.4863i	0.374377	+	1.15221i	−0.569522	+	0.821976i	$0.692872\pi$
$138$		0			0
$139$	6.92705	+	5.03280i	0.587545	+	0.426876i	0.841436	−	0.540356i	$-0.181711\pi$
$139$	6.92705	+	5.03280i	0.587545	+	0.426876i	−0.253891	+	0.967233i	$0.581711\pi$
$140$	2.85410	−	2.07363i	0.241216	−	0.175253i
$141$		0			0
$142$	4.52786			0.379970
$143$	1.92705	−	20.5927i	0.161148	−	1.72205i
$144$		0			0
$145$	−2.70820	+	8.33499i	−0.224904	+	0.692184i
$146$	3.42705	−	2.48990i	0.283625	−	0.206065i
$147$		0			0
$148$	2.78115	+	8.55951i	0.228609	+	0.703587i
$149$	−2.36475	−	7.27794i	−0.193727	−	0.596232i	−0.999989	−	0.00467270i	$-0.998513\pi$
$149$	−2.36475	−	7.27794i	−0.193727	−	0.596232i	0.806262	−	0.591559i	$-0.201487\pi$
$150$		0			0
$151$	3.11803	−	2.26538i	0.253742	−	0.184354i	−0.453642	−	0.891184i	$-0.649875\pi$
$151$	3.11803	−	2.26538i	0.253742	−	0.184354i	0.707384	+	0.706830i	$0.249875\pi$
$152$	1.54508	−	4.75528i	0.125323	−	0.385704i
$153$		0			0
$154$	6.25329	−	7.10642i	0.503904	−	0.572652i
$155$	8.65248			0.694984
$156$		0			0
$157$	6.00000	−	4.35926i	0.478852	−	0.347906i	−0.322029	−	0.946730i	$-0.604365\pi$
$157$	6.00000	−	4.35926i	0.478852	−	0.347906i	0.800881	+	0.598823i	$0.204365\pi$
$158$	−12.1353	−	8.81678i	−0.965429	−	0.701425i
$159$		0			0
$160$	−0.381966	−	1.17557i	−0.0301971	−	0.0929370i
$161$	−17.5902	−	12.7800i	−1.38630	−	1.00721i
$162$		0			0
$163$	−0.545085	+	1.67760i	−0.0426944	+	0.131400i	−0.970132	−	0.242579i	$-0.922007\pi$
$163$	−0.545085	+	1.67760i	−0.0426944	+	0.131400i	0.927437	+	0.373979i	$0.122007\pi$
$164$	3.38197			0.264087
$165$		0			0
$166$	−3.76393			−0.292138
$167$	−1.66312	+	5.11855i	−0.128696	+	0.396086i	−0.994556	−	0.104200i	$-0.966772\pi$
$167$	−1.66312	+	5.11855i	−0.128696	+	0.396086i	0.865860	+	0.500286i	$0.166772\pi$
$168$		0			0
$169$	−20.9443	−	15.2169i	−1.61110	−	1.17053i
$170$	2.38197	+	7.33094i	0.182688	+	0.562257i
$171$		0			0
$172$	0.572949	+	0.416272i	0.0436870	+	0.0317404i
$173$	−3.19098	+	2.31838i	−0.242606	+	0.176264i	−0.702443	−	0.711740i	$-0.747908\pi$
$173$	−3.19098	+	2.31838i	−0.242606	+	0.176264i	0.459838	+	0.888003i	$0.347908\pi$
$174$		0			0
$175$	−9.90983			−0.749113
$176$	−1.69098	−	2.85317i	−0.127463	−	0.215066i
$177$		0			0
$178$	1.30902	−	4.02874i	0.0981150	−	0.301967i
$179$	1.45492	−	1.05706i	0.108745	−	0.0790082i	−0.532084	−	0.846692i	$-0.678591\pi$
$179$	1.45492	−	1.05706i	0.108745	−	0.0790082i	0.640829	+	0.767684i	$0.278591\pi$
$180$		0			0
$181$	−3.51722	−	10.8249i	−0.261433	−	0.804608i	−0.992494	−	0.122296i	$-0.960974\pi$
$181$	−3.51722	−	10.8249i	−0.261433	−	0.804608i	0.731061	−	0.682312i	$-0.239026\pi$
$182$	−5.50000	−	16.9273i	−0.407687	−	1.25473i
$183$		0			0
$184$	−6.16312	+	4.47777i	−0.454351	+	0.330105i
$185$	−3.43769	+	10.5801i	−0.252744	+	0.777867i
$186$		0			0
$187$	10.5451	+	17.7926i	0.771133	+	1.30112i
$188$	1.76393			0.128648
$189$		0			0
$190$	5.00000	−	3.63271i	0.362738	−	0.263545i
$191$	−2.97214	−	2.15938i	−0.215056	−	0.156247i	0.475042	−	0.879963i	$-0.342433\pi$
$191$	−2.97214	−	2.15938i	−0.215056	−	0.156247i	−0.690098	+	0.723716i	$0.742433\pi$
$192$		0			0
$193$	5.38197	+	16.5640i	0.387402	+	1.19230i	0.934722	+	0.355379i	$0.115648\pi$
$193$	5.38197	+	16.5640i	0.387402	+	1.19230i	−0.547320	+	0.836923i	$0.684352\pi$
$194$	−4.85410	−	3.52671i	−0.348504	−	0.253203i
$195$		0			0
$196$	0.354102	−	1.08981i	0.0252930	−	0.0778438i
$197$	−12.3262			−0.878208			−0.439104	−	0.898436i	$-0.644704\pi$
$197$	−12.3262			−0.878208			−0.439104	+	0.898436i	$0.644704\pi$
$198$		0			0
$199$	1.94427			0.137826			0.0689129	−	0.997623i	$-0.478047\pi$
$199$	1.94427			0.137826			0.0689129	+	0.997623i	$0.478047\pi$
$200$	−1.07295	+	3.30220i	−0.0758690	+	0.233501i
$201$		0			0
$202$	−13.7812	−	10.0126i	−0.969639	−	0.704484i
$203$	6.25329	+	19.2456i	0.438895	+	1.35078i
$204$		0			0
$205$	3.38197	+	2.45714i	0.236207	+	0.171614i
$206$	4.50000	−	3.26944i	0.313530	−	0.227793i
$207$		0			0
$208$	−6.23607			−0.432394
$209$	10.9549	−	12.4495i	0.757767	−	0.861149i
$210$		0			0
$211$	−3.50000	+	10.7719i	−0.240950	+	0.741568i	0.755326	+	0.655349i	$0.227478\pi$
$211$	−3.50000	+	10.7719i	−0.240950	+	0.741568i	−0.996276	+	0.0862187i	$0.972522\pi$
$212$	−8.16312	+	5.93085i	−0.560645	+	0.407333i
$213$		0			0
$214$	5.64590	+	17.3763i	0.385946	+	1.18782i
$215$	0.270510	+	0.832544i	0.0184486	+	0.0567790i
$216$		0			0
$217$	16.1631	−	11.7432i	1.09722	−	0.797180i
$218$	1.33688	−	4.11450i	0.0905450	−	0.278669i
$219$		0			0
$220$	0.381966	−	4.08174i	0.0257521	−	0.275191i
$221$	38.8885			2.61593
$222$		0			0
$223$	−6.80902	+	4.94704i	−0.455966	+	0.331278i	−0.791947	−	0.610590i	$-0.790932\pi$
$223$	−6.80902	+	4.94704i	−0.455966	+	0.331278i	0.335981	+	0.941869i	$0.390932\pi$
$224$	−2.30902	−	1.67760i	−0.154278	−	0.112089i
$225$		0			0
$226$	−0.791796	−	2.43690i	−0.0526695	−	0.162100i
$227$	13.5902	+	9.87384i	0.902011	+	0.655350i	0.938982	−	0.343967i	$-0.111771\pi$
$227$	13.5902	+	9.87384i	0.902011	+	0.655350i	−0.0369705	+	0.999316i	$0.511771\pi$
$228$		0			0
$229$	6.88197	−	21.1805i	0.454773	−	1.39965i	−0.416628	−	0.909077i	$-0.636788\pi$
$229$	6.88197	−	21.1805i	0.454773	−	1.39965i	0.871401	−	0.490571i	$-0.163212\pi$
$230$	−9.41641			−0.620900
$231$		0			0
$232$	7.09017			0.465492
$233$	−6.07295	+	18.6906i	−0.397852	+	1.22446i	0.528866	+	0.848705i	$0.322617\pi$
$233$	−6.07295	+	18.6906i	−0.397852	+	1.22446i	−0.926718	+	0.375758i	$0.877383\pi$
$234$		0			0
$235$	1.76393	+	1.28157i	0.115066	+	0.0836005i
$236$	2.88197	+	8.86978i	0.187600	+	0.577373i
$237$		0			0
$238$	14.3992	+	10.4616i	0.933361	+	0.678126i
$239$	2.07295	−	1.50609i	0.134088	−	0.0974206i	−0.518719	−	0.854945i	$-0.673591\pi$
$239$	2.07295	−	1.50609i	0.134088	−	0.0974206i	0.652807	+	0.757524i	$0.273591\pi$
$240$		0			0
$241$	−20.0344			−1.29053			−0.645266	−	0.763958i	$-0.723253\pi$
$241$	−20.0344			−1.29053			−0.645266	+	0.763958i	$0.723253\pi$
$242$	−1.39919	−	10.9106i	−0.0899431	−	0.701363i
$243$		0			0
$244$	1.07295	−	3.30220i	0.0686885	−	0.211402i
$245$	1.14590	−	0.832544i	0.0732087	−	0.0531893i
$246$		0			0
$247$	−9.63525	−	29.6543i	−0.613077	−	1.88686i
$248$	−2.16312	−	6.65740i	−0.137358	−	0.422745i
$249$		0			0
$250$	−8.47214	+	6.15537i	−0.535825	+	0.389300i
$251$	−8.10739	+	24.9520i	−0.511734	+	1.57496i	0.277413	+	0.960751i	$0.410523\pi$
$251$	−8.10739	+	24.9520i	−0.511734	+	1.57496i	−0.789147	+	0.614204i	$0.789477\pi$
$252$		0			0
$253$	−24.6525	+	5.53483i	−1.54989	+	0.347972i
$254$	−3.47214			−0.217861
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−6.04508	−	4.39201i	−0.377082	−	0.273966i	0.383059	−	0.923724i	$-0.374870\pi$
$257$	−6.04508	−	4.39201i	−0.377082	−	0.273966i	−0.760142	+	0.649758i	$0.774870\pi$
$258$		0			0
$259$	7.93769	+	24.4297i	0.493224	+	1.51799i
$260$	−6.23607	−	4.53077i	−0.386745	−	0.280986i
$261$		0			0
$262$	−2.14590	+	6.60440i	−0.132574	+	0.408021i
$263$	17.9443			1.10649			0.553246	−	0.833018i	$-0.313389\pi$
$263$	17.9443			1.10649			0.553246	+	0.833018i	$0.313389\pi$
$264$		0			0
$265$	−12.4721			−0.766157
$266$	4.40983	−	13.5721i	0.270384	−	0.832156i
$267$		0			0
$268$	4.92705	+	3.57971i	0.300968	+	0.218666i
$269$	3.07295	+	9.45756i	0.187361	+	0.576638i	0.999981	−	0.00615595i	$-0.00195951\pi$
$269$	3.07295	+	9.45756i	0.187361	+	0.576638i	−0.812620	+	0.582794i	$0.801960\pi$
$270$		0			0
$271$	−9.11803	−	6.62464i	−0.553881	−	0.402418i	0.275333	−	0.961349i	$-0.411212\pi$
$271$	−9.11803	−	6.62464i	−0.553881	−	0.402418i	−0.829214	+	0.558931i	$0.811212\pi$
$272$	5.04508	−	3.66547i	0.305903	−	0.222252i
$273$		0			0
$274$	14.1803			0.856666
$275$	−7.60739	+	8.64527i	−0.458743	+	0.521329i
$276$		0			0
$277$	−0.0450850	+	0.138757i	−0.00270889	+	0.00833712i	−0.952402	−	0.304845i	$-0.901395\pi$
$277$	−0.0450850	+	0.138757i	−0.00270889	+	0.00833712i	0.949693	+	0.313183i	$0.101395\pi$
$278$	6.92705	−	5.03280i	0.415457	−	0.301847i
$279$		0			0
$280$	−1.09017	−	3.35520i	−0.0651501	−	0.200511i
$281$	−6.23607	−	19.1926i	−0.372013	−	1.14494i	−0.945472	−	0.325703i	$-0.894399\pi$
$281$	−6.23607	−	19.1926i	−0.372013	−	1.14494i	0.573459	−	0.819234i	$-0.305601\pi$
$282$		0			0
$283$	−5.42705	+	3.94298i	−0.322605	+	0.234386i	−0.737286	−	0.675581i	$-0.763893\pi$
$283$	−5.42705	+	3.94298i	−0.322605	+	0.234386i	0.414681	+	0.909967i	$0.363893\pi$
$284$	1.39919	−	4.30625i	0.0830265	−	0.255529i
$285$		0			0
$286$	−18.9894	−	8.19624i	−1.12286	−	0.484654i
$287$	9.65248			0.569768
$288$		0			0
$289$	−17.7082	+	12.8658i	−1.04166	+	0.756810i
$290$	7.09017	+	5.15131i	0.416349	+	0.302495i
$291$		0			0
$292$	−1.30902	−	4.02874i	−0.0766044	−	0.235764i
$293$	17.6074	+	12.7925i	1.02863	+	0.747347i	0.968035	−	0.250815i	$-0.0806987\pi$
$293$	17.6074	+	12.7925i	1.02863	+	0.747347i	0.0605998	+	0.998162i	$0.480699\pi$
$294$		0			0
$295$	−3.56231	+	10.9637i	−0.207405	+	0.638328i
$296$	9.00000			0.523114
$297$		0			0
$298$	−7.65248			−0.443296
$299$	−14.6803	+	45.1814i	−0.848986	+	2.61291i
$300$		0			0
$301$	1.63525	+	1.18808i	0.0942545	+	0.0684799i
$302$	−1.19098	−	3.66547i	−0.0685334	−	0.210924i
$303$		0			0
$304$	−4.04508	−	2.93893i	−0.232002	−	0.168559i
$305$	3.47214	−	2.52265i	0.198814	−	0.144447i
$306$		0			0
$307$	−5.09017			−0.290511			−0.145256	−	0.989394i	$-0.546400\pi$
$307$	−5.09017			−0.290511			−0.145256	+	0.989394i	$0.546400\pi$
$308$	−4.82624	−	8.14324i	−0.275000	−	0.464004i
$309$		0			0
$310$	2.67376	−	8.22899i	0.151859	−	0.467375i
$311$	−10.8992	+	7.91872i	−0.618036	+	0.449030i	−0.852235	−	0.523159i	$-0.824753\pi$
$311$	−10.8992	+	7.91872i	−0.618036	+	0.449030i	0.234199	+	0.972189i	$0.424753\pi$
$312$		0			0
$313$	10.2188	+	31.4504i	0.577603	+	1.77768i	0.627138	+	0.778908i	$0.284226\pi$
$313$	10.2188	+	31.4504i	0.577603	+	1.77768i	−0.0495348	+	0.998772i	$0.515774\pi$
$314$	−2.29180	−	7.05342i	−0.129334	−	0.398048i
$315$		0			0
$316$	−12.1353	+	8.81678i	−0.682661	+	0.495983i
$317$	4.98936	−	15.3557i	0.280230	−	0.862460i	−0.707558	−	0.706656i	$-0.750203\pi$
$317$	4.98936	−	15.3557i	0.280230	−	0.862460i	0.987788	−	0.155804i	$-0.0497969\pi$
$318$		0			0
$319$	21.5902	+	9.31881i	1.20882	+	0.521753i
$320$	−1.23607			−0.0690983
$321$		0			0
$322$	−17.5902	+	12.7800i	−0.980262	+	0.712202i
$323$	25.2254	+	18.3273i	1.40358	+	1.01976i
$324$		0			0
$325$	6.69098	+	20.5927i	0.371149	+	1.14228i
$326$	1.42705	+	1.03681i	0.0790370	+	0.0574238i
$327$		0			0
$328$	1.04508	−	3.21644i	0.0577052	−	0.177598i
$329$	5.03444			0.277558
$330$		0			0
$331$	−8.29180			−0.455758			−0.227879	−	0.973689i	$-0.573179\pi$
$331$	−8.29180			−0.455758			−0.227879	+	0.973689i	$0.573179\pi$
$332$	−1.16312	+	3.57971i	−0.0638344	+	0.196462i
$333$		0			0
$334$	4.35410	+	3.16344i	0.238246	+	0.173096i
$335$	2.32624	+	7.15942i	0.127096	+	0.391161i
$336$		0			0
$337$	−1.92705	−	1.40008i	−0.104973	−	0.0762675i	0.534060	−	0.845446i	$-0.320665\pi$
$337$	−1.92705	−	1.40008i	−0.104973	−	0.0762675i	−0.639034	+	0.769179i	$0.720665\pi$
$338$	−20.9443	+	15.2169i	−1.13922	+	0.827690i
$339$		0			0
$340$	7.70820			0.418036
$341$	2.16312	−	23.1154i	0.117139	−	1.25177i
$342$		0			0
$343$	−5.16312	+	15.8904i	−0.278782	+	0.858003i
$344$	0.572949	−	0.416272i	0.0308913	−	0.0224439i
$345$		0			0
$346$	1.21885	+	3.75123i	0.0655256	+	0.201667i
$347$	−9.68034	−	29.7930i	−0.519668	−	1.59937i	−0.774625	−	0.632421i	$-0.782061\pi$
$347$	−9.68034	−	29.7930i	−0.519668	−	1.59937i	0.254957	−	0.966952i	$-0.417939\pi$
$348$		0			0
$349$	−14.0172	+	10.1841i	−0.750325	+	0.545143i	−0.895927	−	0.444200i	$-0.853488\pi$
$349$	−14.0172	+	10.1841i	−0.750325	+	0.545143i	0.145603	+	0.989343i	$0.453488\pi$
$350$	−3.06231	+	9.42481i	−0.163687	+	0.503777i
$351$		0			0
$352$	−3.23607	+	0.726543i	−0.172483	+	0.0387248i
$353$	−9.32624			−0.496386			−0.248193	−	0.968711i	$-0.579837\pi$
$353$	−9.32624			−0.496386			−0.248193	+	0.968711i	$0.579837\pi$
$354$		0			0
$355$	4.52786	−	3.28969i	0.240314	−	0.174598i
$356$	−3.42705	−	2.48990i	−0.181633	−	0.131964i
$357$		0			0
$358$	−0.555728	−	1.71036i	−0.0293711	−	0.0903951i
$359$	−25.9894	−	18.8824i	−1.37167	−	0.996574i	−0.997605	−	0.0691694i	$-0.977965\pi$
$359$	−25.9894	−	18.8824i	−1.37167	−	0.996574i	−0.374061	−	0.927404i	$-0.622035\pi$
$360$		0			0
$361$	1.85410	−	5.70634i	0.0975843	−	0.300334i
$362$	−11.3820			−0.598223
$363$		0			0
$364$	−17.7984			−0.932888
$365$	1.61803	−	4.97980i	0.0846918	−	0.260654i
$366$		0			0
$367$	10.3992	+	7.55545i	0.542833	+	0.394391i	0.825136	−	0.564934i	$-0.191098\pi$
$367$	10.3992	+	7.55545i	0.542833	+	0.394391i	−0.282303	+	0.959325i	$0.591098\pi$
$368$	2.35410	+	7.24518i	0.122716	+	0.377681i
$369$		0			0
$370$	9.00000	+	6.53888i	0.467888	+	0.339940i
$371$	−23.2984	+	16.9273i	−1.20959	+	0.878820i
$372$		0			0
$373$	−23.7082			−1.22756			−0.613782	−	0.789475i	$-0.710353\pi$
$373$	−23.7082			−1.22756			−0.613782	+	0.789475i	$0.710353\pi$
$374$	20.1803	−	4.53077i	1.04350	−	0.234280i
$375$		0			0
$376$	0.545085	−	1.67760i	0.0281106	−	0.0865156i
$377$	35.7705	−	25.9888i	1.84227	−	1.33849i
$378$		0			0
$379$	4.54508	+	13.9883i	0.233465	+	0.718532i	0.997321	+	0.0731456i	$0.0233038\pi$
$379$	4.54508	+	13.9883i	0.233465	+	0.718532i	−0.763856	+	0.645387i	$0.776696\pi$
$380$	−1.90983	−	5.87785i	−0.0979722	−	0.301527i
$381$		0			0
$382$	−2.97214	+	2.15938i	−0.152068	+	0.110484i
$383$	5.76393	−	17.7396i	0.294523	−	0.906449i	−0.688858	−	0.724896i	$-0.741888\pi$
$383$	5.76393	−	17.7396i	0.294523	−	0.906449i	0.983381	−	0.181553i	$-0.0581123\pi$
$384$		0			0
$385$	1.09017	−	11.6497i	0.0555602	−	0.593724i
$386$	17.4164			0.886472
$387$		0			0
$388$	−4.85410	+	3.52671i	−0.246430	+	0.179042i
$389$	−24.2082	−	17.5883i	−1.22740	−	0.891762i	−0.230712	−	0.973022i	$-0.574105\pi$
$389$	−24.2082	−	17.5883i	−1.22740	−	0.891762i	−0.996693	+	0.0812605i	$0.974105\pi$
$390$		0			0
$391$	−14.6803	−	45.1814i	−0.742417	−	2.28492i
$392$	−0.927051	−	0.673542i	−0.0468231	−	0.0340190i
$393$		0			0
$394$	−3.80902	+	11.7229i	−0.191896	+	0.590594i
$395$	−18.5410			−0.932900
$396$		0			0
$397$	24.2705			1.21810			0.609051	−	0.793131i	$-0.291550\pi$
$397$	24.2705			1.21810			0.609051	+	0.793131i	$0.291550\pi$
$398$	0.600813	−	1.84911i	0.0301160	−	0.0926876i
$399$		0			0
$400$	2.80902	+	2.04087i	0.140451	+	0.102044i
$401$	6.07953	+	18.7109i	0.303597	+	0.934376i	0.980197	+	0.198025i	$0.0634527\pi$
$401$	6.07953	+	18.7109i	0.303597	+	0.934376i	−0.676600	+	0.736351i	$0.736547\pi$
$402$		0			0
$403$	−35.3156	−	25.6583i	−1.75920	−	1.27813i
$404$	−13.7812	+	10.0126i	−0.685638	+	0.498145i
$405$		0			0
$406$	20.2361			1.00430
$407$	27.4058	+	11.8290i	1.35845	+	0.586339i
$408$		0			0
$409$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$409$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$410$	3.38197	−	2.45714i	0.167023	−	0.121350i
$411$		0			0
$412$	−1.71885	−	5.29007i	−0.0846815	−	0.260623i
$413$	8.22542	+	25.3153i	0.404747	+	1.24568i
$414$		0			0
$415$	−3.76393	+	2.73466i	−0.184764	+	0.134239i
$416$	−1.92705	+	5.93085i	−0.0944814	+	0.290784i
$417$		0			0
$418$	−8.45492	−	14.2658i	−0.413543	−	0.697765i
$419$	4.14590			0.202540			0.101270	−	0.994859i	$-0.467709\pi$
$419$	4.14590			0.202540			0.101270	+	0.994859i	$0.467709\pi$
$420$		0			0
$421$	27.8435	−	20.2295i	1.35701	−	0.985923i	0.358378	−	0.933576i	$-0.383330\pi$
$421$	27.8435	−	20.2295i	1.35701	−	0.985923i	0.998629	−	0.0523469i	$-0.0166702\pi$
$422$	9.16312	+	6.65740i	0.446054	+	0.324077i
$423$		0			0
$424$	3.11803	+	9.59632i	0.151425	+	0.466039i
$425$	−17.5172	−	12.7270i	−0.849710	−	0.617350i
$426$		0			0
$427$	3.06231	−	9.42481i	0.148195	−	0.456098i
$428$	18.2705			0.883138
$429$		0			0
$430$	0.875388			0.0422150
$431$	−0.854102	+	2.62866i	−0.0411406	+	0.126618i	−0.969517	−	0.245023i	$-0.921205\pi$
$431$	−0.854102	+	2.62866i	−0.0411406	+	0.126618i	0.928377	+	0.371641i	$0.121205\pi$
$432$		0			0
$433$	−0.427051	−	0.310271i	−0.0205228	−	0.0149107i	0.577477	−	0.816407i	$-0.304037\pi$
$433$	−0.427051	−	0.310271i	−0.0205228	−	0.0149107i	−0.597999	+	0.801497i	$0.704037\pi$
$434$	−6.17376	−	19.0009i	−0.296350	−	0.912072i
$435$		0			0
$436$	−3.50000	−	2.54290i	−0.167620	−	0.121783i
$437$	−30.8156	+	22.3888i	−1.47411	+	1.07100i
$438$		0			0
$439$	−5.27051			−0.251548			−0.125774	−	0.992059i	$-0.540141\pi$
$439$	−5.27051			−0.251548			−0.125774	+	0.992059i	$0.540141\pi$
$440$	−3.76393	−	1.62460i	−0.179438	−	0.0774497i
$441$		0			0
$442$	12.0172	−	36.9852i	0.571601	−	1.75921i
$443$	−2.42705	+	1.76336i	−0.115313	+	0.0837796i	−0.643947	−	0.765070i	$-0.722704\pi$
$443$	−2.42705	+	1.76336i	−0.115313	+	0.0837796i	0.528634	+	0.848850i	$0.322704\pi$
$444$		0			0
$445$	−1.61803	−	4.97980i	−0.0767022	−	0.236065i
$446$	2.60081	+	8.00448i	0.123152	+	0.379023i
$447$		0			0
$448$	−2.30902	+	1.67760i	−0.109091	+	0.0792591i
$449$	7.85410	−	24.1724i	0.370658	−	1.14077i	−0.575704	−	0.817658i	$-0.695272\pi$
$449$	7.85410	−	24.1724i	0.370658	−	1.14077i	0.946362	−	0.323110i	$-0.104728\pi$
$450$		0			0
$451$	7.40983	−	8.42075i	0.348915	−	0.396518i
$452$	−2.56231			−0.120521
$453$		0			0
$454$	13.5902	−	9.87384i	0.637818	−	0.463402i
$455$	−17.7984	−	12.9313i	−0.834401	−	0.606228i
$456$		0			0
$457$	1.85410	+	5.70634i	0.0867312	+	0.266931i	0.985011	−	0.172493i	$-0.0551823\pi$
$457$	1.85410	+	5.70634i	0.0867312	+	0.266931i	−0.898279	+	0.439425i	$0.855182\pi$
$458$	−18.0172	−	13.0903i	−0.841889	−	0.611668i
$459$		0			0
$460$	−2.90983	+	8.95554i	−0.135672	+	0.417554i
$461$	−5.03444			−0.234477			−0.117239	−	0.993104i	$-0.537404\pi$
$461$	−5.03444			−0.234477			−0.117239	+	0.993104i	$0.537404\pi$
$462$		0			0
$463$	35.1246			1.63238			0.816190	−	0.577784i	$-0.196082\pi$
$463$	35.1246			1.63238			0.816190	+	0.577784i	$0.196082\pi$
$464$	2.19098	−	6.74315i	0.101714	−	0.313043i
$465$		0			0
$466$	15.8992	+	11.5514i	0.736516	+	0.535110i
$467$	7.33688	+	22.5806i	0.339510	+	1.04491i	0.964457	+	0.264238i	$0.0851205\pi$
$467$	7.33688	+	22.5806i	0.339510	+	1.04491i	−0.624947	+	0.780667i	$0.714879\pi$
$468$		0			0
$469$	14.0623	+	10.2169i	0.649337	+	0.471771i
$470$	1.76393	−	1.28157i	0.0813641	−	0.0591145i
$471$		0			0
$472$	9.32624			0.429275
$473$	2.29180	−	0.514540i	0.105377	−	0.0236586i
$474$		0			0
$475$	−5.36475	+	16.5110i	−0.246151	+	0.757576i
$476$	14.3992	−	10.4616i	0.659986	−	0.479508i
$477$		0			0
$478$	−0.791796	−	2.43690i	−0.0362159	−	0.111461i
$479$	−1.12868	−	3.47371i	−0.0515706	−	0.158718i	0.921954	−	0.387298i	$-0.126592\pi$
$479$	−1.12868	−	3.47371i	−0.0515706	−	0.158718i	−0.973525	+	0.228580i	$0.926592\pi$
$480$		0			0
$481$	45.4058	−	32.9892i	2.07032	−	1.50418i
$482$	−6.19098	+	19.0539i	−0.281992	+	0.867881i
$483$		0			0
$484$	−10.8090	−	2.04087i	−0.491319	−	0.0927668i
$485$	−7.41641			−0.336762
$486$		0			0
$487$	−13.2082	+	9.59632i	−0.598521	+	0.434851i	−0.845354	−	0.534207i	$-0.820610\pi$
$487$	−13.2082	+	9.59632i	−0.598521	+	0.434851i	0.246833	+	0.969058i	$0.420610\pi$
$488$	−2.80902	−	2.04087i	−0.127158	−	0.0923859i
$489$		0			0
$490$	−0.437694	−	1.34708i	−0.0197730	−	0.0608550i
$491$	−24.8435	−	18.0498i	−1.12117	−	0.814577i	−0.136784	−	0.990601i	$-0.543677\pi$
$491$	−24.8435	−	18.0498i	−1.12117	−	0.814577i	−0.984386	+	0.176024i	$0.943677\pi$
$492$		0			0
$493$	−13.6631	+	42.0508i	−0.615356	+	1.89387i
$494$	−31.1803			−1.40287
$495$		0			0
$496$	−7.00000			−0.314309
$497$	3.99342	−	12.2905i	0.179129	−	0.551304i
$498$		0			0
$499$	−14.7984	−	10.7516i	−0.662466	−	0.481310i	0.205029	−	0.978756i	$-0.434271\pi$
$499$	−14.7984	−	10.7516i	−0.662466	−	0.481310i	−0.867495	+	0.497446i	$0.834271\pi$
$500$	3.23607	+	9.95959i	0.144721	+	0.445407i
$501$		0			0
$502$	21.2254	+	15.4212i	0.947337	+	0.688281i
$503$	−1.00000	+	0.726543i	−0.0445878	+	0.0323949i	−0.609856	−	0.792512i	$-0.708773\pi$
$503$	−1.00000	+	0.726543i	−0.0445878	+	0.0323949i	0.565268	+	0.824907i	$0.308773\pi$
$504$		0			0
$505$	−21.0557			−0.936968
$506$	−2.35410	+	25.1563i	−0.104653	+	1.11833i
$507$		0			0
$508$	−1.07295	+	3.30220i	−0.0476044	+	0.146511i
$509$	−19.8541	+	14.4248i	−0.880018	+	0.639370i	−0.933256	−	0.359212i	$-0.883046\pi$
$509$	−19.8541	+	14.4248i	−0.880018	+	0.639370i	0.0532385	+	0.998582i	$0.483046\pi$
$510$		0			0
$511$	−3.73607	−	11.4984i	−0.165274	−	0.508661i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$		0			0
$514$	−6.04508	+	4.39201i	−0.266637	+	0.193723i
$515$	2.12461	−	6.53888i	0.0936216	−	0.288138i
$516$		0			0
$517$	3.86475	−	4.39201i	0.169971	−	0.193160i
$518$	25.6869			1.12862
$519$		0			0
$520$	−6.23607	+	4.53077i	−0.273470	+	0.198687i
$521$	0.190983	+	0.138757i	0.00836712	+	0.00607907i	0.591961	−	0.805967i	$-0.298354\pi$
$521$	0.190983	+	0.138757i	0.00836712	+	0.00607907i	−0.583594	+	0.812046i	$0.698354\pi$
$522$		0			0
$523$	−8.61803	−	26.5236i	−0.376840	−	1.15980i	−0.942229	−	0.334970i	$-0.891274\pi$
$523$	−8.61803	−	26.5236i	−0.376840	−	1.15980i	0.565388	−	0.824825i	$-0.308726\pi$
$524$	5.61803	+	4.08174i	0.245425	+	0.178312i
$525$		0			0
$526$	5.54508	−	17.0660i	0.241777	−	0.744114i
$527$	43.6525			1.90153
$528$		0			0
$529$	35.0344			1.52324
$530$	−3.85410	+	11.8617i	−0.167411	+	0.515240i
$531$		0			0
$532$	−11.5451	−	8.38800i	−0.500543	−	0.363666i
$533$	−6.51722	−	20.0579i	−0.282292	−	0.868806i
$534$		0			0
$535$	18.2705	+	13.2743i	0.789903	+	0.573898i
$536$	4.92705	−	3.57971i	0.212816	−	0.154620i
$537$		0			0
$538$	9.94427			0.428728
$539$	−1.93769	−	3.26944i	−0.0834624	−	0.140825i
$540$		0			0
$541$	−1.10081	+	3.38795i	−0.0473277	+	0.145660i	−0.971928	−	0.235280i	$-0.924399\pi$
$541$	−1.10081	+	3.38795i	−0.0473277	+	0.145660i	0.924600	+	0.380939i	$0.124399\pi$
$542$	−9.11803	+	6.62464i	−0.391653	+	0.284553i
$543$		0			0
$544$	−1.92705	−	5.93085i	−0.0826216	−	0.254283i
$545$	−1.65248	−	5.08580i	−0.0707843	−	0.217852i
$546$		0			0
$547$	21.4164	−	15.5599i	0.915699	−	0.665295i	−0.0267504	−	0.999642i	$-0.508516\pi$
$547$	21.4164	−	15.5599i	0.915699	−	0.665295i	0.942450	+	0.334348i	$0.108516\pi$
$548$	4.38197	−	13.4863i	0.187188	−	0.576106i
$549$		0			0
$550$	5.87132	+	9.90659i	0.250354	+	0.422419i
$551$	35.4508			1.51026
$552$		0			0
$553$	−34.6353	+	25.1640i	−1.47284	+	1.07008i
$554$	0.118034	+	0.0857567i	0.00501478	+	0.00364345i
$555$		0			0
$556$	−2.64590	−	8.14324i	−0.112211	−	0.345350i
$557$	12.7984	+	9.29856i	0.542285	+	0.393993i	0.824933	−	0.565231i	$-0.191213\pi$
$557$	12.7984	+	9.29856i	0.542285	+	0.393993i	−0.282648	+	0.959224i	$0.591213\pi$
$558$		0			0
$559$	1.36475	−	4.20025i	0.0577226	−	0.177652i
$560$	−3.52786			−0.149079
$561$		0			0
$562$	−20.1803			−0.851256
$563$	12.8090	−	39.4221i	0.539836	−	1.66144i	−0.193126	−	0.981174i	$-0.561863\pi$
$563$	12.8090	−	39.4221i	0.539836	−	1.66144i	0.732962	−	0.680270i	$-0.238137\pi$
$564$		0			0
$565$	−2.56231	−	1.86162i	−0.107797	−	0.0783191i
$566$	2.07295	+	6.37988i	0.0871325	+	0.268166i
$567$		0			0
$568$	−3.66312	−	2.66141i	−0.153701	−	0.111670i
$569$	−11.5902	+	8.42075i	−0.485885	+	0.353016i	−0.803600	−	0.595170i	$-0.797085\pi$
$569$	−11.5902	+	8.42075i	−0.485885	+	0.353016i	0.317714	+	0.948186i	$0.397085\pi$
$570$		0			0
$571$	31.4508			1.31618			0.658089	−	0.752941i	$-0.271365\pi$
$571$	31.4508			1.31618			0.658089	+	0.752941i	$0.271365\pi$
$572$	−13.6631	+	15.5272i	−0.571284	+	0.649224i
$573$		0			0
$574$	2.98278	−	9.18005i	0.124499	−	0.383168i
$575$	21.3992	−	15.5474i	0.892408	−	0.648372i
$576$		0			0
$577$	−9.93769	−	30.5851i	−0.413712	−	1.27327i	−0.913398	−	0.407067i	$-0.866551\pi$
$577$	−9.93769	−	30.5851i	−0.413712	−	1.27327i	0.499687	−	0.866206i	$-0.333449\pi$
$578$	6.76393	+	20.8172i	0.281342	+	0.865883i
$579$		0			0
$580$	7.09017	−	5.15131i	0.294403	−	0.213897i
$581$	−3.31966	+	10.2169i	−0.137723	+	0.423867i
$582$		0			0
$583$	−3.11803	+	33.3197i	−0.129136	+	1.37996i
$584$	−4.23607			−0.175290
$585$		0			0
$586$	17.6074	−	12.7925i	0.727355	−	0.528454i
$587$	−2.42705	−	1.76336i	−0.100175	−	0.0727815i	0.536570	−	0.843856i	$-0.319720\pi$
$587$	−2.42705	−	1.76336i	−0.100175	−	0.0727815i	−0.636745	+	0.771074i	$0.719720\pi$
$588$		0			0
$589$	−10.8156	−	33.2870i	−0.445649	−	1.37157i
$590$	9.32624	+	6.77591i	0.383955	+	0.278960i
$591$		0			0
$592$	2.78115	−	8.55951i	0.114305	−	0.351794i
$593$	22.1459			0.909423			0.454712	−	0.890639i	$-0.349742\pi$
$593$	22.1459			0.909423			0.454712	+	0.890639i	$0.349742\pi$
$594$		0			0
$595$	22.0000			0.901912
$596$	−2.36475	+	7.27794i	−0.0968637	+	0.298116i
$597$		0			0
$598$	38.4336	+	27.9237i	1.57167	+	1.14188i
$599$	−9.43769	−	29.0462i	−0.385614	−	1.18680i	−0.936034	−	0.351909i	$-0.885533\pi$
$599$	−9.43769	−	29.0462i	−0.385614	−	1.18680i	0.550420	−	0.834888i	$-0.314467\pi$
$600$		0			0
$601$	−7.38197	−	5.36331i	−0.301117	−	0.218774i	0.426959	−	0.904271i	$-0.359585\pi$
$601$	−7.38197	−	5.36331i	−0.301117	−	0.218774i	−0.728075	+	0.685497i	$0.759585\pi$
$602$	1.63525	−	1.18808i	0.0666480	−	0.0484226i
$603$		0			0
$604$	−3.85410			−0.156821
$605$	−9.32624	−	9.89408i	−0.379165	−	0.402252i
$606$		0			0
$607$	−7.14590	+	21.9928i	−0.290043	+	0.892661i	0.694799	+	0.719204i	$0.255494\pi$
$607$	−7.14590	+	21.9928i	−0.290043	+	0.892661i	−0.984842	+	0.173456i	$0.944506\pi$
$608$	−4.04508	+	2.93893i	−0.164050	+	0.119189i
$609$		0			0
$610$	−1.32624	−	4.08174i	−0.0536978	−	0.165265i
$611$	−3.39919	−	10.4616i	−0.137516	−	0.423232i
$612$		0			0
$613$	35.9336	−	26.1073i	1.45135	−	1.05446i	0.465831	−	0.884874i	$-0.345755\pi$
$613$	35.9336	−	26.1073i	1.45135	−	1.05446i	0.985515	−	0.169591i	$-0.0542445\pi$
$614$	−1.57295	+	4.84104i	−0.0634791	+	0.195368i
$615$		0			0
$616$	−9.23607	+	2.07363i	−0.372132	+	0.0835488i
$617$	−22.4721			−0.904694			−0.452347	−	0.891842i	$-0.649413\pi$
$617$	−22.4721			−0.904694			−0.452347	+	0.891842i	$0.649413\pi$
$618$		0			0
$619$	22.4443	−	16.3067i	0.902111	−	0.655422i	−0.0368960	−	0.999319i	$-0.511747\pi$
$619$	22.4443	−	16.3067i	0.902111	−	0.655422i	0.939007	+	0.343897i	$0.111747\pi$
$620$	−7.00000	−	5.08580i	−0.281127	−	0.204251i
$621$		0			0
$622$	4.16312	+	12.8128i	0.166926	+	0.513745i
$623$	−9.78115	−	7.10642i	−0.391874	−	0.284713i
$624$		0			0
$625$	1.36475	−	4.20025i	0.0545898	−	0.168010i
$626$	33.0689			1.32170
$627$		0			0
$628$	−7.41641			−0.295947
$629$	−17.3435	+	53.3777i	−0.691529	+	2.12831i
$630$		0			0
$631$	−0.690983	−	0.502029i	−0.0275076	−	0.0199854i	0.573947	−	0.818893i	$-0.305412\pi$
$631$	−0.690983	−	0.502029i	−0.0275076	−	0.0199854i	−0.601454	+	0.798907i	$0.705412\pi$
$632$	4.63525	+	14.2658i	0.184381	+	0.567465i
$633$		0			0
$634$	−13.0623	−	9.49032i	−0.518770	−	0.376909i
$635$	−3.47214	+	2.52265i	−0.137788	+	0.100108i
$636$		0			0
$637$	−7.14590			−0.283131
$638$	15.5344	−	17.6538i	0.615014	−	0.698921i
$639$		0			0
$640$	−0.381966	+	1.17557i	−0.0150985	+	0.0464685i
$641$	−2.45492	+	1.78360i	−0.0969633	+	0.0704480i	−0.635211	−	0.772339i	$-0.719087\pi$
$641$	−2.45492	+	1.78360i	−0.0969633	+	0.0704480i	0.538247	+	0.842787i	$0.319087\pi$
$642$		0			0
$643$	0.270510	+	0.832544i	0.0106679	+	0.0328323i	0.956249	−	0.292555i	$-0.0945054\pi$
$643$	0.270510	+	0.832544i	0.0106679	+	0.0328323i	−0.945581	+	0.325387i	$0.894505\pi$
$644$	6.71885	+	20.6785i	0.264760	+	0.814846i
$645$		0			0
$646$	25.2254	−	18.3273i	0.992481	−	0.721080i
$647$	7.88197	−	24.2582i	0.309872	−	0.953688i	−0.667942	−	0.744213i	$-0.732825\pi$
$647$	7.88197	−	24.2582i	0.309872	−	0.953688i	0.977814	−	0.209475i	$-0.0671754\pi$
$648$		0			0
$649$	28.3992	+	12.2577i	1.11477	+	0.481158i
$650$	21.6525			0.849280
$651$		0			0
$652$	1.42705	−	1.03681i	0.0558876	−	0.0406047i
$653$	7.69098	+	5.58783i	0.300971	+	0.218669i	0.728013	−	0.685564i	$-0.240444\pi$
$653$	7.69098	+	5.58783i	0.300971	+	0.218669i	−0.427041	+	0.904232i	$0.640444\pi$
$654$		0			0
$655$	2.65248	+	8.16348i	0.103641	+	0.318974i
$656$	−2.73607	−	1.98787i	−0.106826	−	0.0776133i
$657$		0			0
$658$	1.55573	−	4.78804i	0.0606486	−	0.186657i
$659$	−26.7771			−1.04309			−0.521544	−	0.853225i	$-0.674644\pi$
$659$	−26.7771			−1.04309			−0.521544	+	0.853225i	$0.674644\pi$
$660$		0			0
$661$	−7.61803			−0.296307			−0.148154	−	0.988964i	$-0.547333\pi$
$661$	−7.61803			−0.296307			−0.148154	+	0.988964i	$0.547333\pi$
$662$	−2.56231	+	7.88597i	−0.0995868	+	0.306497i
$663$		0			0
$664$	3.04508	+	2.21238i	0.118172	+	0.0858571i
$665$	−5.45085	−	16.7760i	−0.211375	−	0.650545i
$666$		0			0
$667$	−43.6976	−	31.7481i	−1.69198	−	1.22929i
$668$	4.35410	−	3.16344i	0.168465	−	0.122397i
$669$		0			0
$670$	7.52786			0.290827
$671$	−5.87132	−	9.90659i	−0.226660	−	0.382440i
$672$		0			0
$673$	−3.09017	+	9.51057i	−0.119117	+	0.366605i	−0.992784	−	0.119920i	$-0.961736\pi$
$673$	−3.09017	+	9.51057i	−0.119117	+	0.366605i	0.873666	+	0.486526i	$0.161736\pi$
$674$	−1.92705	+	1.40008i	−0.0742272	+	0.0539292i
$675$		0			0
$676$	8.00000	+	24.6215i	0.307692	+	0.946980i
$677$	−5.04508	−	15.5272i	−0.193898	−	0.596758i	−0.999988	−	0.00496391i	$-0.998420\pi$
$677$	−5.04508	−	15.5272i	−0.193898	−	0.596758i	0.806089	−	0.591794i	$-0.201580\pi$
$678$		0			0
$679$	−13.8541	+	10.0656i	−0.531672	+	0.386282i
$680$	2.38197	−	7.33094i	0.0913442	−	0.281129i
$681$		0			0
$682$	−21.3156	−	9.20029i	−0.816216	−	0.352297i
$683$	−33.8885			−1.29671			−0.648355	−	0.761339i	$-0.724543\pi$
$683$	−33.8885			−1.29671			−0.648355	+	0.761339i	$0.724543\pi$
$684$		0			0
$685$	14.1803	−	10.3026i	0.541803	−	0.393643i
$686$	13.5172	+	9.82084i	0.516090	+	0.374961i
$687$		0			0
$688$	−0.218847	−	0.673542i	−0.00834347	−	0.0256785i
$689$	50.9058	+	36.9852i	1.93936	+	1.40902i
$690$		0			0
$691$	10.2705	−	31.6094i	0.390709	−	1.20248i	−0.541545	−	0.840672i	$-0.682160\pi$
$691$	10.2705	−	31.6094i	0.390709	−	1.20248i	0.932254	−	0.361806i	$-0.117840\pi$
$692$	3.94427			0.149939
$693$		0			0
$694$	−31.3262			−1.18913
$695$	3.27051	−	10.0656i	0.124058	−	0.381810i
$696$		0			0
$697$	17.0623	+	12.3965i	0.646281	+	0.469551i
$698$	5.35410	+	16.4782i	0.202656	+	0.623710i
$699$		0			0
$700$	8.01722	+	5.82485i	0.303022	+	0.220159i
$701$	5.78115	−	4.20025i	0.218351	−	0.158641i	−0.473233	−	0.880937i	$-0.656913\pi$
$701$	5.78115	−	4.20025i	0.218351	−	0.158641i	0.691584	+	0.722296i	$0.256913\pi$
$702$		0			0
$703$	45.0000			1.69721
$704$	−0.309017	+	3.30220i	−0.0116465	+	0.124456i
$705$		0			0
$706$	−2.88197	+	8.86978i	−0.108464	+	0.333819i
$707$	−39.3328	+	28.5770i	−1.47926	+	1.07475i
$708$		0			0
$709$	−14.1287	−	43.4836i	−0.530614	−	1.63306i	−0.752941	−	0.658089i	$-0.771365\pi$
$709$	−14.1287	−	43.4836i	−0.530614	−	1.63306i	0.222327	−	0.974972i	$-0.428635\pi$
$710$	−1.72949	−	5.32282i	−0.0649066	−	0.199762i
$711$		0			0
$712$	−3.42705	+	2.48990i	−0.128434	+	0.0933129i
$713$	−16.4787	+	50.7163i	−0.617133	+	1.89934i
$714$		0			0
$715$	−24.9443	+	5.60034i	−0.932863	+	0.209441i
$716$	−1.79837			−0.0672084
$717$		0			0
$718$	−25.9894	+	18.8824i	−0.969914	+	0.704684i
$719$	39.4058	+	28.6300i	1.46959	+	1.06772i	0.980733	+	0.195352i	$0.0625849\pi$
$719$	39.4058	+	28.6300i	1.46959	+	1.06772i	0.488854	+	0.872366i	$0.337415\pi$
$720$		0			0
$721$	−4.90576	−	15.0984i	−0.182700	−	0.562293i
$722$	−4.85410	−	3.52671i	−0.180651	−	0.131251i
$723$		0			0
$724$	−3.51722	+	10.8249i	−0.130716	+	0.402304i
$725$	−24.6180			−0.914291
$726$		0			0
$727$	−5.14590			−0.190851			−0.0954254	−	0.995437i	$-0.530421\pi$
$727$	−5.14590			−0.190851			−0.0954254	+	0.995437i	$0.530421\pi$
$728$	−5.50000	+	16.9273i	−0.203844	+	0.627366i
$729$		0			0
$730$	−4.23607	−	3.07768i	−0.156784	−	0.113910i
$731$	1.36475	+	4.20025i	0.0504769	+	0.155352i
$732$		0			0
$733$	28.8885	+	20.9888i	1.06702	+	0.775237i	0.975375	−	0.220554i	$-0.0707866\pi$
$733$	28.8885	+	20.9888i	1.06702	+	0.775237i	0.0916480	+	0.995791i	$0.470787\pi$
$734$	10.3992	−	7.55545i	0.383841	−	0.278877i
$735$		0			0
$736$	7.61803			0.280804
$737$	19.7082	−	4.42477i	0.725961	−	0.162988i
$738$		0			0
$739$	−12.4828	+	38.4180i	−0.459186	+	1.41323i	0.406963	+	0.913445i	$0.366588\pi$
$739$	−12.4828	+	38.4180i	−0.459186	+	1.41323i	−0.866149	+	0.499786i	$0.833412\pi$
$740$	9.00000	−	6.53888i	0.330847	−	0.240374i
$741$		0			0
$742$	8.89919	+	27.3889i	0.326699	+	1.00548i
$743$	−14.2877	−	43.9731i	−0.524166	−	1.61322i	−0.765959	−	0.642889i	$-0.777736\pi$
$743$	−14.2877	−	43.9731i	−0.524166	−	1.61322i	0.241793	−	0.970328i	$-0.422264\pi$
$744$		0			0
$745$	−7.65248	+	5.55985i	−0.280365	+	0.203697i
$746$	−7.32624	+	22.5478i	−0.268233	+	0.825535i
$747$		0			0
$748$	1.92705	−	20.5927i	0.0704600	−	0.752945i
$749$	52.1459			1.90537
$750$		0			0
$751$	−13.4894	+	9.80059i	−0.492234	+	0.357629i	−0.806043	−	0.591857i	$-0.798395\pi$
$751$	−13.4894	+	9.80059i	−0.492234	+	0.357629i	0.313809	+	0.949486i	$0.398395\pi$
$752$	−1.42705	−	1.03681i	−0.0520392	−	0.0378087i
$753$		0			0
$754$	−13.6631	−	42.0508i	−0.497581	−	1.53140i
$755$	−3.85410	−	2.80017i	−0.140265	−	0.101909i
$756$		0			0
$757$	−11.1353	+	34.2708i	−0.404718	+	1.24559i	0.516413	+	0.856340i	$0.327267\pi$
$757$	−11.1353	+	34.2708i	−0.404718	+	1.24559i	−0.921131	+	0.389253i	$0.872733\pi$
$758$	14.7082			0.534226
$759$		0			0
$760$	−6.18034			−0.224184
$761$	13.8885	−	42.7445i	0.503459	−	1.54949i	−0.299886	−	0.953975i	$-0.596949\pi$
$761$	13.8885	−	42.7445i	0.503459	−	1.54949i	0.803345	−	0.595513i	$-0.203051\pi$
$762$		0			0
$763$	−9.98936	−	7.25769i	−0.361639	−	0.262746i
$764$	1.13525	+	3.49396i	0.0410721	+	0.126407i
$765$		0			0
$766$	−15.0902	−	10.9637i	−0.545230	−	0.396133i
$767$	47.0517	−	34.1850i	1.69894	−	1.23435i
$768$		0			0
$769$	−22.8541			−0.824140			−0.412070	−	0.911152i	$-0.635194\pi$
$769$	−22.8541			−0.824140			−0.412070	+	0.911152i	$0.635194\pi$
$770$	−10.7426	−	4.63677i	−0.387138	−	0.167098i
$771$		0			0
$772$	5.38197	−	16.5640i	0.193701	−	0.596151i
$773$	3.89919	−	2.83293i	0.140244	−	0.101893i	−0.515451	−	0.856919i	$-0.672376\pi$
$773$	3.89919	−	2.83293i	0.140244	−	0.101893i	0.655695	+	0.755026i	$0.272376\pi$
$774$		0			0
$775$	7.51064	+	23.1154i	0.269790	+	0.830329i
$776$	1.85410	+	5.70634i	0.0665584	+	0.204846i
$777$		0			0
$778$	−24.2082	+	17.5883i	−0.867906	+	0.630571i
$779$	5.22542	−	16.0822i	0.187220	−	0.576205i
$780$		0			0
$781$	−7.65654	−	12.9188i	−0.273973	−	0.462270i
$782$	−47.5066			−1.69883
$783$		0			0
$784$	−0.927051	+	0.673542i	−0.0331090	+	0.0240551i
$785$	−7.41641	−	5.38834i	−0.264703	−	0.192318i
$786$		0			0
$787$	2.92705	+	9.00854i	0.104338	+	0.321120i	0.989575	−	0.144022i	$-0.0460035\pi$
$787$	2.92705	+	9.00854i	0.104338	+	0.321120i	−0.885236	+	0.465141i	$0.846004\pi$
$788$	9.97214	+	7.24518i	0.355243	+	0.258099i
$789$		0			0
$790$	−5.72949	+	17.6336i	−0.203846	+	0.627374i
$791$	−7.31308			−0.260023
$792$		0			0
$793$	−21.6525			−0.768902
$794$	7.50000	−	23.0826i	0.266165	−	0.819172i
$795$		0			0
$796$	−1.57295	−	1.14281i	−0.0557517	−	0.0405060i
$797$	−3.33688	−	10.2699i	−0.118198	−	0.363777i	0.874402	−	0.485202i	$-0.161254\pi$
$797$	−3.33688	−	10.2699i	−0.118198	−	0.363777i	−0.992601	+	0.121424i	$0.961254\pi$
$798$		0			0
$799$	8.89919	+	6.46564i	0.314831	+	0.228738i
$800$	2.80902	−	2.04087i	0.0993137	−	0.0721557i
$801$		0			0
$802$	19.6738			0.694705
$803$	−12.8992	−	5.56758i	−0.455202	−	0.196476i
$804$		0			0
$805$	−8.30495	+	25.5600i	−0.292711	+	0.900872i
$806$	−35.3156	+	25.6583i	−1.24394	+	0.903774i
$807$		0			0
$808$	5.26393	+	16.2007i	0.185184	+	0.569939i
$809$	−0.319660	−	0.983813i	−0.0112387	−	0.0345890i	0.945280	−	0.326260i	$-0.105789\pi$
$809$	−0.319660	−	0.983813i	−0.0112387	−	0.0345890i	−0.956519	+	0.291671i	$0.905789\pi$
$810$		0			0
$811$	−3.38197	+	2.45714i	−0.118757	+	0.0862819i	−0.645578	−	0.763694i	$-0.723384\pi$
$811$	−3.38197	+	2.45714i	−0.118757	+	0.0862819i	0.526821	+	0.849976i	$0.323384\pi$
$812$	6.25329	−	19.2456i	0.219447	−	0.675390i
$813$		0			0
$814$	19.7188	−	22.4091i	0.691145	−	0.785438i
$815$	2.18034			0.0763740
$816$		0			0
$817$	2.86475	−	2.08136i	0.100225	−	0.0728175i
$818$		0			0
$819$		0			0
$820$	−1.29180	−	3.97574i	−0.0451115	−	0.138839i
$821$	4.71885	+	3.42844i	0.164689	+	0.119653i	0.667077	−	0.744989i	$-0.267545\pi$
$821$	4.71885	+	3.42844i	0.164689	+	0.119653i	−0.502388	+	0.864642i	$0.667545\pi$
$822$		0			0
$823$	−7.16970	+	22.0661i	−0.249920	+	0.769174i	0.744868	+	0.667212i	$0.232512\pi$
$823$	−7.16970	+	22.0661i	−0.249920	+	0.769174i	−0.994788	+	0.101963i	$0.967488\pi$
$824$	−5.56231			−0.193772
$825$		0			0
$826$	26.6180			0.926160
$827$	−10.8369	+	33.3525i	−0.376835	+	1.15978i	0.565397	+	0.824819i	$0.308723\pi$
$827$	−10.8369	+	33.3525i	−0.376835	+	1.15978i	−0.942232	+	0.334961i	$0.891277\pi$
$828$		0			0
$829$	9.87132	+	7.17194i	0.342845	+	0.249092i	0.745861	−	0.666101i	$-0.232038\pi$
$829$	9.87132	+	7.17194i	0.342845	+	0.249092i	−0.403016	+	0.915193i	$0.632038\pi$
$830$	1.43769	+	4.42477i	0.0499031	+	0.153586i
$831$		0			0
$832$	5.04508	+	3.66547i	0.174907	+	0.127077i
$833$	5.78115	−	4.20025i	0.200305	−	0.145530i
$834$		0			0
$835$	6.65248			0.230218
$836$	−16.1803	+	3.63271i	−0.559609	+	0.125640i
$837$		0			0
$838$	1.28115	−	3.94298i	0.0442567	−	0.136208i
$839$	−22.8992	+	16.6372i	−0.790568	+	0.574381i	−0.908132	−	0.418684i	$-0.862491\pi$
$839$	−22.8992	+	16.6372i	−0.790568	+	0.574381i	0.117564	+	0.993065i	$0.462491\pi$
$840$		0			0
$841$	6.57295	+	20.2295i	0.226653	+	0.697567i
$842$	−10.6353	−	32.7319i	−0.366515	−	1.12802i
$843$		0			0
$844$	9.16312	−	6.65740i	0.315408	−	0.229157i
$845$	−9.88854	+	30.4338i	−0.340176	+	1.04695i
$846$		0			0
$847$	−30.8500	−	5.82485i	−1.06002	−	0.200144i
$848$	10.0902			0.346498
$849$		0			0
$850$	−17.5172	+	12.7270i	−0.600836	+	0.436533i
$851$	−55.4681	−	40.2999i	−1.90142	−	1.38146i
$852$		0			0
$853$	0.0557281	+	0.171513i	0.00190809	+	0.00587251i	0.952006	−	0.306079i	$-0.0990173\pi$
$853$	0.0557281	+	0.171513i	0.00190809	+	0.00587251i	−0.950098	+	0.311952i	$0.899017\pi$
$854$	−8.01722	−	5.82485i	−0.274344	−	0.199322i
$855$		0			0
$856$	5.64590	−	17.3763i	0.192973	−	0.593909i
$857$	−9.11146			−0.311241			−0.155621	−	0.987817i	$-0.549738\pi$
$857$	−9.11146			−0.311241			−0.155621	+	0.987817i	$0.549738\pi$
$858$		0			0
$859$	−6.50658			−0.222002			−0.111001	−	0.993820i	$-0.535406\pi$
$859$	−6.50658			−0.222002			−0.111001	+	0.993820i	$0.535406\pi$
$860$	0.270510	−	0.832544i	0.00922431	−	0.0283895i
$861$		0			0
$862$	2.23607	+	1.62460i	0.0761608	+	0.0553340i
$863$	−3.32624	−	10.2371i	−0.113226	−	0.348475i	0.878347	−	0.478024i	$-0.158647\pi$
$863$	−3.32624	−	10.2371i	−0.113226	−	0.348475i	−0.991573	+	0.129549i	$0.958647\pi$
$864$		0			0
$865$	3.94427	+	2.86568i	0.134109	+	0.0974361i
$866$	−0.427051	+	0.310271i	−0.0145118	+	0.0105434i
$867$		0			0
$868$	−19.9787			−0.678122
$869$	−4.63525	+	49.5330i	−0.157240	+	1.68029i
$870$		0			0
$871$	11.7361	−	36.1199i	0.397661	−	1.22388i
$872$	−3.50000	+	2.54290i	−0.118525	+	0.0861134i
$873$		0			0
$874$	11.7705	+	36.2259i	0.398143	+	1.22536i
$875$	9.23607	+	28.4257i	0.312236	+	0.960964i
$876$		0			0
$877$	−6.14590	+	4.46526i	−0.207532	+	0.150781i	−0.686696	−	0.726944i	$-0.740940\pi$
$877$	−6.14590	+	4.46526i	−0.207532	+	0.150781i	0.479164	+	0.877725i	$0.340940\pi$
$878$	−1.62868	+	5.01255i	−0.0549652	+	0.169165i
$879$		0			0
$880$	−2.70820	+	3.07768i	−0.0912935	+	0.103749i
$881$	−50.3262			−1.69553			−0.847767	−	0.530369i	$-0.822053\pi$
$881$	−50.3262			−1.69553			−0.847767	+	0.530369i	$0.822053\pi$
$882$		0			0
$883$	−20.4271	+	14.8411i	−0.687425	+	0.499443i	−0.875813	−	0.482651i	$-0.839674\pi$
$883$	−20.4271	+	14.8411i	−0.687425	+	0.499443i	0.188388	+	0.982095i	$0.439674\pi$
$884$	−31.4615	−	22.8581i	−1.05816	−	0.768802i
$885$		0			0
$886$	0.927051	+	2.85317i	0.0311449	+	0.0958541i
$887$	35.9443	+	26.1150i	1.20689	+	0.876857i	0.994945	−	0.100424i	$-0.0320200\pi$
$887$	35.9443	+	26.1150i	1.20689	+	0.876857i	0.211946	+	0.977281i	$0.432020\pi$
$888$		0			0
$889$	−3.06231	+	9.42481i	−0.102706	+	0.316098i
$890$	−5.23607			−0.175513
$891$		0			0
$892$	8.41641			0.281802
$893$	2.72542	−	8.38800i	0.0912029	−	0.280694i
$894$		0			0
$895$	−1.79837	−	1.30660i	−0.0601130	−	0.0436747i
$896$	0.881966	+	2.71441i	0.0294644	+	0.0906821i
$897$		0			0
$898$	−20.5623	−	14.9394i	−0.686173	−	0.498534i
$899$	40.1525	−	29.1725i	1.33916	−	0.972957i
$900$		0			0
$901$	−62.9230			−2.09627
$902$	−5.71885	−	9.64932i	−0.190417	−	0.321287i
$903$		0			0
$904$	−0.791796	+	2.43690i	−0.0263347	+	0.0810500i
$905$	−11.3820	+	8.26948i	−0.378349	+	0.274887i
$906$		0			0
$907$	−1.81559	−	5.58783i	−0.0602858	−	0.185541i	0.916378	−	0.400314i	$-0.131099\pi$
$907$	−1.81559	−	5.58783i	−0.0602858	−	0.185541i	−0.976664	+	0.214773i	$0.931099\pi$
$908$	−5.19098	−	15.9762i	−0.172269	−	0.530189i
$909$		0			0
$910$	−17.7984	+	12.9313i	−0.590010	+	0.428668i
$911$	9.34346	−	28.7562i	0.309563	−	0.952736i	−0.668372	−	0.743827i	$-0.733009\pi$
$911$	9.34346	−	28.7562i	0.309563	−	0.952736i	0.977935	−	0.208909i	$-0.0669912\pi$
$912$		0			0
$913$	6.36475	+	10.7391i	0.210642	+	0.355414i
$914$	6.00000			0.198462
$915$		0			0
$916$	−18.0172	+	13.0903i	−0.595306	+	0.432515i
$917$	16.0344	+	11.6497i	0.529504	+	0.384707i
$918$		0			0
$919$	−10.3647	−	31.8994i	−0.341901	−	1.05226i	−0.963222	−	0.268708i	$-0.913403\pi$
$919$	−10.3647	−	31.8994i	−0.341901	−	1.05226i	0.621320	−	0.783557i	$-0.286597\pi$
$920$	7.61803	+	5.53483i	0.251159	+	0.182478i
$921$		0			0
$922$	−1.55573	+	4.78804i	−0.0512352	+	0.157686i
$923$	−28.2361			−0.929401
$924$		0			0
$925$	−31.2492			−1.02747
$926$	10.8541	−	33.4055i	0.356688	−	1.09777i
$927$		0			0
$928$	−5.73607	−	4.16750i	−0.188296	−	0.136805i
$929$	−6.31966	−	19.4499i	−0.207341	−	0.638131i	−0.999609	−	0.0279574i	$-0.991100\pi$
$929$	−6.31966	−	19.4499i	−0.207341	−	0.638131i	0.792268	−	0.610174i	$-0.208900\pi$
$930$		0			0
$931$	−4.63525	−	3.36771i	−0.151914	−	0.110372i
$932$	15.8992	−	11.5514i	0.520795	−	0.378380i
$933$		0			0
$934$	23.7426			0.776883
$935$	16.8885	−	19.1926i	0.552314	−	0.627667i
$936$		0			0
$937$	−3.00000	+	9.23305i	−0.0980057	+	0.301631i	−0.988025	−	0.154292i	$-0.950690\pi$
$937$	−3.00000	+	9.23305i	−0.0980057	+	0.301631i	0.890020	+	0.455922i	$0.150690\pi$
$938$	14.0623	−	10.2169i	0.459151	−	0.333592i
$939$		0			0
$940$	−0.673762	−	2.07363i	−0.0219757	−	0.0676342i
$941$	8.41641	+	25.9030i	0.274367	+	0.844415i	0.989386	+	0.145310i	$0.0464180\pi$
$941$	8.41641	+	25.9030i	0.274367	+	0.844415i	−0.715019	+	0.699105i	$0.753582\pi$
$942$		0			0
$943$	−20.8435	+	15.1437i	−0.678756	+	0.493145i
$944$	2.88197	−	8.86978i	0.0938000	−	0.288687i
$945$		0			0
$946$	0.218847	−	2.33863i	0.00711533	−	0.0760354i
$947$	−30.5967			−0.994261			−0.497130	−	0.867676i	$-0.665613\pi$
$947$	−30.5967			−0.994261			−0.497130	+	0.867676i	$0.665613\pi$
$948$		0			0
$949$	−21.3713	+	15.5272i	−0.693742	+	0.504033i
$950$	14.0451	+	10.2044i	0.455683	+	0.331073i
$951$		0			0
$952$	−5.50000	−	16.9273i	−0.178256	−	0.548616i
$953$	−30.6353	−	22.2578i	−0.992373	−	0.721001i	−0.0319337	−	0.999490i	$-0.510167\pi$
$953$	−30.6353	−	22.2578i	−0.992373	−	0.721001i	−0.960440	+	0.278489i	$0.910167\pi$
$954$		0			0
$955$	−1.40325	+	4.31877i	−0.0454082	+	0.139752i
$956$	−2.56231			−0.0828709
$957$		0			0
$958$	−3.65248			−0.118006
$959$	12.5066	−	38.4913i	0.403858	−	1.24295i
$960$		0			0
$961$	−14.5623	−	10.5801i	−0.469752	−	0.341295i
$962$	−17.3435	−	53.3777i	−0.559176	−	1.72097i
$963$		0			0
$964$	16.2082	+	11.7759i	0.522031	+	0.379278i
$965$	17.4164	−	12.6538i	0.560654	−	0.407339i
$966$		0			0
$967$	−6.29180			−0.202331			−0.101165	−	0.994870i	$-0.532257\pi$
$967$	−6.29180			−0.202331			−0.101165	+	0.994870i	$0.532257\pi$
$968$	−5.28115	+	9.64932i	−0.169743	+	0.310141i
$969$		0			0
$970$	−2.29180	+	7.05342i	−0.0735851	+	0.226472i
$971$	22.5623	−	16.3925i	0.724059	−	0.526060i	−0.163620	−	0.986524i	$-0.552317\pi$
$971$	22.5623	−	16.3925i	0.724059	−	0.526060i	0.887678	+	0.460464i	$0.152317\pi$
$972$		0			0
$973$	−7.55166	−	23.2416i	−0.242095	−	0.745092i
$974$	5.04508	+	15.5272i	0.161655	+	0.497523i
$975$		0			0
$976$	−2.80902	+	2.04087i	−0.0899144	+	0.0653267i
$977$	−10.3992	+	32.0054i	−0.332699	+	1.02394i	0.635145	+	0.772393i	$0.280940\pi$
$977$	−10.3992	+	32.0054i	−0.332699	+	1.02394i	−0.967844	+	0.251551i	$0.919060\pi$
$978$		0			0
$979$	−13.7082	+	3.07768i	−0.438116	+	0.0983632i
$980$	−1.41641			−0.0452455
$981$		0			0
$982$	−24.8435	+	18.0498i	−0.792787	+	0.575993i
$983$	13.0623	+	9.49032i	0.416623	+	0.302694i	0.776278	−	0.630391i	$-0.217106\pi$
$983$	13.0623	+	9.49032i	0.416623	+	0.302694i	−0.359655	+	0.933085i	$0.617106\pi$
$984$		0			0
$985$	4.70820	+	14.4904i	0.150016	+	0.461701i
$986$	35.7705	+	25.9888i	1.13917	+	0.827652i
$987$		0			0
$988$	−9.63525	+	29.6543i	−0.306538	+	0.943428i
$989$	−5.39512			−0.171555
$990$		0			0
$991$	39.7082			1.26137			0.630686	−	0.776038i	$-0.282773\pi$
$991$	39.7082			1.26137			0.630686	+	0.776038i	$0.282773\pi$
$992$	−2.16312	+	6.65740i	−0.0686791	+	0.211373i
$993$		0			0
$994$	−10.4549	−	7.59594i	−0.331610	−	0.240929i
$995$	−0.742646	−	2.28563i	−0.0235435	−	0.0724593i
$996$		0			0
$997$	37.1697	+	27.0054i	1.17718	+	0.855269i	0.991850	−	0.127409i	$-0.0406660\pi$
$997$	37.1697	+	27.0054i	1.17718	+	0.855269i	0.185326	+	0.982677i	$0.440666\pi$
$998$	−14.7984	+	10.7516i	−0.468434	+	0.340337i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	594.2.f.a.163.1	✓	4
3.2	odd	2		594.2.f.j.163.1	yes	4
11.4	even	5		6534.2.a.cm.1.1		2
11.5	even	5	inner	594.2.f.a.379.1	yes	4
11.7	odd	10		6534.2.a.bv.1.1		2
33.5	odd	10		594.2.f.j.379.1	yes	4
33.26	odd	10		6534.2.a.bf.1.2		2
33.29	even	10		6534.2.a.cb.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
594.2.f.a.163.1	✓	4	1.1	even	1	trivial
594.2.f.a.379.1	yes	4	11.5	even	5	inner
594.2.f.j.163.1	yes	4	3.2	odd	2
594.2.f.j.379.1	yes	4	33.5	odd	10
6534.2.a.bf.1.2		2	33.26	odd	10
6534.2.a.bv.1.1		2	11.7	odd	10
6534.2.a.cb.1.2		2	33.29	even	10
6534.2.a.cm.1.1		2	11.4	even	5

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)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.381966 - 1.17557i) q^{5} +(-2.30902 - 1.67760i) q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.381966 - 1.17557i) q^{5} +(-2.30902 - 1.67760i) q^{7} +(-0.809017 + 0.587785i) q^{8} -1.23607 q^{10} +(-3.23607 + 0.726543i) q^{11} +(-1.92705 + 5.93085i) q^{13} +(-2.30902 + 1.67760i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-1.92705 - 5.93085i) q^{17} +(-4.04508 + 2.93893i) q^{19} +(-0.381966 + 1.17557i) q^{20} +(-0.309017 + 3.30220i) q^{22} +7.61803 q^{23} +(2.80902 - 2.04087i) q^{25} +(5.04508 + 3.66547i) q^{26} +(0.881966 + 2.71441i) q^{28} +(-5.73607 - 4.16750i) q^{29} +(-2.16312 + 6.65740i) q^{31} +1.00000 q^{32} -6.23607 q^{34} +(-1.09017 + 3.35520i) q^{35} +(-7.28115 - 5.29007i) q^{37} +(1.54508 + 4.75528i) q^{38} +(1.00000 + 0.726543i) q^{40} +(-2.73607 + 1.98787i) q^{41} -0.708204 q^{43} +(3.04508 + 1.31433i) q^{44} +(2.35410 - 7.24518i) q^{46} +(-1.42705 + 1.03681i) q^{47} +(0.354102 + 1.08981i) q^{49} +(-1.07295 - 3.30220i) q^{50} +(5.04508 - 3.66547i) q^{52} +(3.11803 - 9.59632i) q^{53} +(2.09017 + 3.52671i) q^{55} +2.85410 q^{56} +(-5.73607 + 4.16750i) q^{58} +(-7.54508 - 5.48183i) q^{59} +(1.07295 + 3.30220i) q^{61} +(5.66312 + 4.11450i) q^{62} +(0.309017 - 0.951057i) q^{64} +7.70820 q^{65} -6.09017 q^{67} +(-1.92705 + 5.93085i) q^{68} +(2.85410 + 2.07363i) q^{70} +(1.39919 + 4.30625i) q^{71} +(3.42705 + 2.48990i) q^{73} +(-7.28115 + 5.29007i) q^{74} +5.00000 q^{76} +(8.69098 + 3.75123i) q^{77} +(4.63525 - 14.2658i) q^{79} +(1.00000 - 0.726543i) q^{80} +(1.04508 + 3.21644i) q^{82} +(-1.16312 - 3.57971i) q^{83} +(-6.23607 + 4.53077i) q^{85} +(-0.218847 + 0.673542i) q^{86} +(2.19098 - 2.48990i) q^{88} +4.23607 q^{89} +(14.3992 - 10.4616i) q^{91} +(-6.16312 - 4.47777i) q^{92} +(0.545085 + 1.67760i) q^{94} +(5.00000 + 3.63271i) q^{95} +(1.85410 - 5.70634i) q^{97} +1.14590 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{4} - 6 q^{5} - 7 q^{7} - q^{8}+O(q^{10}) \) 4 * q - q^2 - q^4 - 6 * q^5 - 7 * q^7 - q^8	\( 4 q - q^{2} - q^{4} - 6 q^{5} - 7 q^{7} - q^{8} + 4 q^{10} - 4 q^{11} - q^{13} - 7 q^{14} - q^{16} - q^{17} - 5 q^{19} - 6 q^{20} + q^{22} + 26 q^{23} + 9 q^{25} + 9 q^{26} + 8 q^{28} - 14 q^{29} + 7 q^{31} + 4 q^{32} - 16 q^{34} + 18 q^{35} - 9 q^{37} - 5 q^{38} + 4 q^{40} - 2 q^{41} + 24 q^{43} + q^{44} - 4 q^{46} + q^{47} - 12 q^{49} - 11 q^{50} + 9 q^{52} + 8 q^{53} - 14 q^{55} - 2 q^{56} - 14 q^{58} - 19 q^{59} + 11 q^{61} + 7 q^{62} - q^{64} + 4 q^{65} - 2 q^{67} - q^{68} - 2 q^{70} - 19 q^{71} + 7 q^{73} - 9 q^{74} + 20 q^{76} + 37 q^{77} - 15 q^{79} + 4 q^{80} - 7 q^{82} + 11 q^{83} - 16 q^{85} - 21 q^{86} + 11 q^{88} + 8 q^{89} + 33 q^{91} - 9 q^{92} - 9 q^{94} + 20 q^{95} - 6 q^{97} + 18 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^4 - 6 * q^5 - 7 * q^7 - q^8 + 4 * q^10 - 4 * q^11 - q^13 - 7 * q^14 - q^16 - q^17 - 5 * q^19 - 6 * q^20 + q^22 + 26 * q^23 + 9 * q^25 + 9 * q^26 + 8 * q^28 - 14 * q^29 + 7 * q^31 + 4 * q^32 - 16 * q^34 + 18 * q^35 - 9 * q^37 - 5 * q^38 + 4 * q^40 - 2 * q^41 + 24 * q^43 + q^44 - 4 * q^46 + q^47 - 12 * q^49 - 11 * q^50 + 9 * q^52 + 8 * q^53 - 14 * q^55 - 2 * q^56 - 14 * q^58 - 19 * q^59 + 11 * q^61 + 7 * q^62 - q^64 + 4 * q^65 - 2 * q^67 - q^68 - 2 * q^70 - 19 * q^71 + 7 * q^73 - 9 * q^74 + 20 * q^76 + 37 * q^77 - 15 * q^79 + 4 * q^80 - 7 * q^82 + 11 * q^83 - 16 * q^85 - 21 * q^86 + 11 * q^88 + 8 * q^89 + 33 * q^91 - 9 * q^92 - 9 * q^94 + 20 * q^95 - 6 * q^97 + 18 * q^98

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