LMFDB - Embedded newform 891.2.bb.a.557.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(8,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([5, 27]))

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

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

chi := DirichletCharacter("891.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.bb (of order $90$, degree $24$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$816$
Relative dimension:	$34$ over $\Q(\zeta_{90})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			557.1
Character	$\chi$	$=$	891.557
Dual form			891.2.bb.a.8.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16150 + 2.38143i) q^{2} +(-3.09081 - 3.95605i) q^{4} +(0.0429102 - 0.613644i) q^{5} +(-1.71414 - 0.0598591i) q^{7} +(7.82768 - 1.66383i) q^{8} +O(q^{10})$	\(q+(-1.16150 + 2.38143i) q^{2} +(-3.09081 - 3.95605i) q^{4} +(0.0429102 - 0.613644i) q^{5} +(-1.71414 - 0.0598591i) q^{7} +(7.82768 - 1.66383i) q^{8} +(1.41151 + 0.814937i) q^{10} +(2.23807 + 2.44766i) q^{11} +(-0.903460 - 0.935560i) q^{13} +(2.13353 - 4.01258i) q^{14} +(-2.70054 + 10.8313i) q^{16} +(0.0482878 + 0.459428i) q^{17} +(0.141343 + 0.664968i) q^{19} +(-2.56024 + 1.72690i) q^{20} +(-8.42846 + 2.48687i) q^{22} +(1.57794 + 4.33534i) q^{23} +(4.57662 + 0.643202i) q^{25} +(3.27734 - 1.06487i) q^{26} +(5.06127 + 6.96624i) q^{28} +(-9.02279 + 4.79750i) q^{29} +(-4.59403 - 1.31732i) q^{31} +(-10.3966 - 8.72380i) q^{32} +(-1.15018 - 0.418632i) q^{34} +(-0.110286 + 1.04930i) q^{35} +(-7.04556 - 1.49758i) q^{37} +(-1.74775 - 0.435762i) q^{38} +(-0.685109 - 4.87481i) q^{40} +(8.34437 + 4.43678i) q^{41} +(-3.76508 - 4.48705i) q^{43} +(2.76560 - 16.4192i) q^{44} +(-12.1571 - 1.27776i) q^{46} +(-6.13622 - 4.79414i) q^{47} +(-4.04826 - 0.283082i) q^{49} +(-6.84750 + 10.1518i) q^{50} +(-0.908705 + 6.46577i) q^{52} +(-3.92774 + 5.40607i) q^{53} +(1.59803 - 1.26835i) q^{55} +(-13.5173 + 2.38347i) q^{56} +(-0.944938 - 27.0595i) q^{58} +(-11.0077 - 4.44742i) q^{59} +(1.57199 + 5.48217i) q^{61} +(8.47308 - 9.41031i) q^{62} +(12.4553 - 5.54545i) q^{64} +(-0.612868 + 0.514258i) q^{65} +(0.459764 - 2.60745i) q^{67} +(1.66827 - 1.61103i) q^{68} +(-2.37075 - 1.48141i) q^{70} +(-11.1758 + 1.17462i) q^{71} +(11.9371 + 10.7482i) q^{73} +(11.7498 - 15.0391i) q^{74} +(2.19378 - 2.61445i) q^{76} +(-3.68986 - 4.32959i) q^{77} +(-1.05828 - 0.516157i) q^{79} +(6.53066 + 2.12194i) q^{80} +(-20.2579 + 14.7182i) q^{82} +(11.5025 + 11.1078i) q^{83} +(0.283997 - 0.00991741i) q^{85} +(15.0588 - 3.75457i) q^{86} +(21.5914 + 15.4357i) q^{88} +(-11.2798 + 6.51241i) q^{89} +(1.49265 + 1.65776i) q^{91} +(12.2738 - 19.6421i) q^{92} +(18.5442 - 9.04459i) q^{94} +(0.414119 - 0.0582006i) q^{95} +(7.82613 - 0.547257i) q^{97} +(5.37620 - 9.31185i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 816 q + 30 q^{2} - 18 q^{4} + 21 q^{5} - 30 q^{7} + 45 q^{8}+O(q^{10}) $ 816 * q + 30 * q^2 - 18 * q^4 + 21 * q^5 - 30 * q^7 + 45 * q^8	$ 816 q + 30 q^{2} - 18 q^{4} + 21 q^{5} - 30 q^{7} + 45 q^{8} + 33 q^{11} - 30 q^{13} + 18 q^{14} - 30 q^{16} + 45 q^{17} - 15 q^{19} + 60 q^{20} - 15 q^{22} + 84 q^{23} - 27 q^{25} - 60 q^{28} - 60 q^{29} - 9 q^{31} - 42 q^{34} + 45 q^{35} - 9 q^{37} + 18 q^{38} - 90 q^{40} + 30 q^{41} + 108 q^{44} - 15 q^{46} + 6 q^{47} - 18 q^{49} + 105 q^{50} - 30 q^{52} - 48 q^{55} - 54 q^{56} - 18 q^{58} - 81 q^{59} - 30 q^{61} + 45 q^{62} + 51 q^{64} + 6 q^{67} + 225 q^{68} - 93 q^{70} + 27 q^{71} - 15 q^{73} + 30 q^{74} + 141 q^{77} - 30 q^{79} - 36 q^{82} - 15 q^{83} - 30 q^{85} - 93 q^{86} - 108 q^{88} - 54 q^{89} - 9 q^{91} - 276 q^{92} - 30 q^{94} - 90 q^{95} - 81 q^{97}+O(q^{100}) $ 816 * q + 30 * q^2 - 18 * q^4 + 21 * q^5 - 30 * q^7 + 45 * q^8 + 33 * q^11 - 30 * q^13 + 18 * q^14 - 30 * q^16 + 45 * q^17 - 15 * q^19 + 60 * q^20 - 15 * q^22 + 84 * q^23 - 27 * q^25 - 60 * q^28 - 60 * q^29 - 9 * q^31 - 42 * q^34 + 45 * q^35 - 9 * q^37 + 18 * q^38 - 90 * q^40 + 30 * q^41 + 108 * q^44 - 15 * q^46 + 6 * q^47 - 18 * q^49 + 105 * q^50 - 30 * q^52 - 48 * q^55 - 54 * q^56 - 18 * q^58 - 81 * q^59 - 30 * q^61 + 45 * q^62 + 51 * q^64 + 6 * q^67 + 225 * q^68 - 93 * q^70 + 27 * q^71 - 15 * q^73 + 30 * q^74 + 141 * q^77 - 30 * q^79 - 36 * q^82 - 15 * q^83 - 30 * q^85 - 93 * q^86 - 108 * q^88 - 54 * q^89 - 9 * q^91 - 276 * q^92 - 30 * q^94 - 90 * q^95 - 81 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−1.16150	+	2.38143i	−0.821306	+	1.68393i	−0.0961241	+	0.995369i	$0.530645\pi$
$2$	−1.16150	+	2.38143i	−0.821306	+	1.68393i	−0.725182	+	0.688557i	$0.758244\pi$
$3$		0			0
$3$		0			0
$4$	−3.09081	−	3.95605i	−1.54540	−	1.97803i
$5$	0.0429102	−	0.613644i	0.0191900	−	0.274430i	−0.978487	−	0.206308i	$-0.933855\pi$
$5$	0.0429102	−	0.613644i	0.0191900	−	0.274430i	0.997677	−	0.0681216i	$-0.0217006\pi$
$6$		0			0
$7$	−1.71414	−	0.0598591i	−0.647884	−	0.0226246i	−0.290927	−	0.956745i	$-0.593964\pi$
$7$	−1.71414	−	0.0598591i	−0.647884	−	0.0226246i	−0.356957	+	0.934121i	$0.616186\pi$
$8$	7.82768	−	1.66383i	2.76750	−	0.588251i
$9$		0			0
$10$	1.41151	+	0.814937i	0.446359	+	0.257706i
$11$	2.23807	+	2.44766i	0.674805	+	0.737996i
$11$	2.23807	+	2.44766i	0.674805	+	0.737996i
$12$		0			0
$13$	−0.903460	−	0.935560i	−0.250575	−	0.259478i	0.582256	−	0.813005i	$-0.302170\pi$
$13$	−0.903460	−	0.935560i	−0.250575	−	0.259478i	−0.832831	+	0.553528i	$0.813281\pi$
$14$	2.13353	−	4.01258i	0.570209	−	1.07241i
$15$		0			0
$16$	−2.70054	+	10.8313i	−0.675135	+	2.70782i
$17$	0.0482878	+	0.459428i	0.0117115	+	0.111428i	0.998816	−	0.0486505i	$-0.0154920\pi$
$17$	0.0482878	+	0.459428i	0.0117115	+	0.111428i	−0.987104	+	0.160078i	$0.948825\pi$
$18$		0			0
$19$	0.141343	+	0.664968i	0.0324264	+	0.152554i	0.991382	−	0.131002i	$-0.0418193\pi$
$19$	0.141343	+	0.664968i	0.0324264	+	0.152554i	−0.958956	+	0.283556i	$0.908486\pi$
$20$	−2.56024	+	1.72690i	−0.572486	+	0.386147i
$21$		0			0
$22$	−8.42846	+	2.48687i	−1.79695	+	0.530202i
$23$	1.57794	+	4.33534i	0.329022	+	0.903982i	0.988360	+	0.152134i	$0.0486147\pi$
$23$	1.57794	+	4.33534i	0.329022	+	0.903982i	−0.659337	+	0.751847i	$0.729163\pi$
$24$		0			0
$25$	4.57662	+	0.643202i	0.915325	+	0.128640i
$26$	3.27734	−	1.06487i	0.642740	−	0.208839i
$27$		0			0
$28$	5.06127	+	6.96624i	0.956491	+	1.31650i
$29$	−9.02279	+	4.79750i	−1.67549	+	0.890874i	−0.689457	+	0.724327i	$0.742151\pi$
$29$	−9.02279	+	4.79750i	−1.67549	+	0.890874i	−0.986033	+	0.166547i	$0.946738\pi$
$30$		0			0
$31$	−4.59403	−	1.31732i	−0.825112	−	0.236597i	−0.163596	−	0.986527i	$-0.552309\pi$
$31$	−4.59403	−	1.31732i	−0.825112	−	0.236597i	−0.661517	+	0.749930i	$0.730087\pi$
$32$	−10.3966	−	8.72380i	−1.83788	−	1.54216i
$33$		0			0
$34$	−1.15018	−	0.418632i	−0.197255	−	0.0717949i
$35$	−0.110286	+	1.04930i	−0.0186418	+	0.177365i
$36$		0			0
$37$	−7.04556	−	1.49758i	−1.15828	−	0.246201i	−0.411590	−	0.911369i	$-0.635026\pi$
$37$	−7.04556	−	1.49758i	−1.15828	−	0.246201i	−0.746693	+	0.665168i	$0.768360\pi$
$38$	−1.74775	−	0.435762i	−0.283522	−	0.0706899i
$39$		0			0
$40$	−0.685109	−	4.87481i	−0.108325	−	0.770775i
$41$	8.34437	+	4.43678i	1.30317	+	0.692909i	0.968403	−	0.249392i	$-0.0802306\pi$
$41$	8.34437	+	4.43678i	1.30317	+	0.692909i	0.334769	+	0.942300i	$0.391342\pi$
$42$		0			0
$43$	−3.76508	−	4.48705i	−0.574170	−	0.684269i	0.398311	−	0.917250i	$-0.369596\pi$
$43$	−3.76508	−	4.48705i	−0.574170	−	0.684269i	−0.972481	+	0.232981i	$0.925152\pi$
$44$	2.76560	−	16.4192i	0.416930	−	2.47528i
$45$		0			0
$46$	−12.1571	−	1.27776i	−1.79247	−	0.188396i
$47$	−6.13622	−	4.79414i	−0.895060	−	0.699297i	0.0592096	−	0.998246i	$-0.481142\pi$
$47$	−6.13622	−	4.79414i	−0.895060	−	0.699297i	−0.954269	+	0.298948i	$0.903364\pi$
$48$		0			0
$49$	−4.04826	−	0.283082i	−0.578322	−	0.0404402i
$50$	−6.84750	+	10.1518i	−0.968383	+	1.43569i
$51$		0			0
$52$	−0.908705	+	6.46577i	−0.126015	+	0.896641i
$53$	−3.92774	+	5.40607i	−0.539517	+	0.742581i	−0.988543	−	0.150938i	$-0.951771\pi$
$53$	−3.92774	+	5.40607i	−0.539517	+	0.742581i	0.449027	+	0.893518i	$0.351771\pi$
$54$		0			0
$55$	1.59803	−	1.26835i	0.215478	−	0.171025i
$56$	−13.5173	+	2.38347i	−1.80633	+	0.318505i
$57$		0			0
$58$	−0.944938	−	27.0595i	−0.124076	−	3.55308i
$59$	−11.0077	−	4.44742i	−1.43309	−	0.579004i	−0.478807	−	0.877920i	$-0.658931\pi$
$59$	−11.0077	−	4.44742i	−1.43309	−	0.579004i	−0.954279	+	0.298916i	$0.903375\pi$
$60$		0			0
$61$	1.57199	+	5.48217i	0.201272	+	0.701920i	0.995539	+	0.0943506i	$0.0300775\pi$
$61$	1.57199	+	5.48217i	0.201272	+	0.701920i	−0.794267	+	0.607569i	$0.792145\pi$
$62$	8.47308	−	9.41031i	1.07608	−	1.19511i
$63$		0			0
$64$	12.4553	−	5.54545i	1.55691	−	0.693181i
$65$	−0.612868	+	0.514258i	−0.0760170	+	0.0637858i
$66$		0			0
$67$	0.459764	−	2.60745i	0.0561691	−	0.318551i	−0.943758	−	0.330637i	$-0.892736\pi$
$67$	0.459764	−	2.60745i	0.0561691	−	0.318551i	0.999927	+	0.0120867i	$0.00384742\pi$
$68$	1.66827	−	1.61103i	0.202308	−	0.195366i
$69$		0			0
$70$	−2.37075	−	1.48141i	−0.283358	−	0.177062i
$71$	−11.1758	+	1.17462i	−1.32632	+	0.139402i	−0.741058	−	0.671441i	$-0.765676\pi$
$71$	−11.1758	+	1.17462i	−1.32632	+	0.139402i	−0.585264	+	0.810843i	$0.699009\pi$
$72$		0			0
$73$	11.9371	+	10.7482i	1.39713	+	1.25799i	0.926830	+	0.375482i	$0.122523\pi$
$73$	11.9371	+	10.7482i	1.39713	+	1.25799i	0.470305	+	0.882504i	$0.344144\pi$
$74$	11.7498	−	15.0391i	1.36589	−	1.74826i
$75$		0			0
$76$	2.19378	−	2.61445i	0.251644	−	0.299898i
$77$	−3.68986	−	4.32959i	−0.420498	−	0.493403i
$78$		0			0
$79$	−1.05828	−	0.516157i	−0.119066	−	0.0580722i	0.377876	−	0.925856i	$-0.376655\pi$
$79$	−1.05828	−	0.516157i	−0.119066	−	0.0580722i	−0.496941	+	0.867784i	$0.665544\pi$
$80$	6.53066	+	2.12194i	0.730151	+	0.237240i
$81$		0			0
$82$	−20.2579	+	14.7182i	−2.23711	+	1.62536i
$83$	11.5025	+	11.1078i	1.26256	+	1.21924i	0.964316	+	0.264755i	$0.0852911\pi$
$83$	11.5025	+	11.1078i	1.26256	+	1.21924i	0.298248	+	0.954488i	$0.403598\pi$
$84$		0			0
$85$	0.283997	−	0.00991741i	0.0308038	−	0.00107569i
$86$	15.0588	−	3.75457i	1.62383	−	0.404866i
$87$		0			0
$88$	21.5914	+	15.4357i	2.30165	+	1.64545i
$89$	−11.2798	+	6.51241i	−1.19566	+	0.690314i	−0.959584	−	0.281422i	$-0.909194\pi$
$89$	−11.2798	+	6.51241i	−1.19566	+	0.690314i	−0.236074	+	0.971735i	$0.575861\pi$
$90$		0			0
$91$	1.49265	+	1.65776i	0.156473	+	0.173781i
$92$	12.2738	−	19.6421i	1.27963	−	2.04783i
$93$		0			0
$94$	18.5442	−	9.04459i	1.91268	−	0.932878i
$95$	0.414119	−	0.0582006i	0.0424877	−	0.00597125i
$96$		0			0
$97$	7.82613	−	0.547257i	0.794623	−	0.0555655i	0.333327	−	0.942811i	$-0.391829\pi$
$97$	7.82613	−	0.547257i	0.794623	−	0.0555655i	0.461297	+	0.887246i	$0.347384\pi$
$98$	5.37620	−	9.31185i	0.543078	−	0.940639i
$99$		0			0
$100$	−11.6009	−	20.0934i	−1.16009	−	2.00934i
$101$	−0.804559	−	1.19281i	−0.0800566	−	0.118689i	0.786883	−	0.617103i	$-0.211694\pi$
$101$	−0.804559	−	1.19281i	−0.0800566	−	0.118689i	−0.866939	+	0.498414i	$0.833916\pi$
$102$		0			0
$103$	−2.17721	+	5.38878i	−0.214527	+	0.530972i	−0.995625	−	0.0934357i	$-0.970215\pi$
$103$	−2.17721	+	5.38878i	−0.214527	+	0.530972i	0.781099	+	0.624407i	$0.214660\pi$
$104$	−8.62860	−	5.82007i	−0.846104	−	0.570705i
$105$		0			0
$106$	−8.31211	−	15.6328i	−0.807344	−	1.51839i
$107$	−3.36033	+	10.3420i	−0.324856	+	0.999803i	0.646650	+	0.762787i	$0.276169\pi$
$107$	−3.36033	+	10.3420i	−0.324856	+	0.999803i	−0.971506	+	0.237016i	$0.923831\pi$
$108$		0			0
$109$		−	8.12587i		−	0.778318i	−0.921171	−	0.389159i	$-0.872766\pi$
$109$		−	8.12587i		−	0.778318i	0.921171	−	0.389159i	$-0.127234\pi$
$110$	1.16438	+	5.27878i	0.111020	+	0.503312i
$111$		0			0
$112$	5.27745	−	18.4047i	0.498672	−	1.73908i
$113$	2.93048	+	4.68975i	0.275676	+	0.441174i	0.956695	−	0.291091i	$-0.0940184\pi$
$113$	2.93048	+	4.68975i	0.275676	+	0.441174i	−0.681019	+	0.732266i	$0.738463\pi$
$114$		0			0
$115$	2.72807	−	0.782261i	0.254394	−	0.0729462i
$116$	46.8669	+	20.8665i	4.35148	+	1.93741i
$117$		0			0
$118$	23.3767	−	21.0485i	2.15200	−	1.93767i
$119$	−0.0552712	−	0.790414i	−0.00506670	−	0.0724572i
$120$		0			0
$121$	−0.982042	+	10.9561i	−0.0892765	+	0.996007i
$122$	−14.8813	−	2.62397i	−1.34729	−	0.237563i
$123$		0			0
$124$	8.98789	+	22.2458i	0.807137	+	1.99773i
$125$	1.23056	−	5.78932i	0.110064	−	0.517812i
$126$		0			0
$127$	−5.80393	+	13.0358i	−0.515016	+	1.15674i	0.449635	+	0.893212i	$0.351554\pi$
$127$	−5.80393	+	13.0358i	−0.515016	+	1.15674i	−0.964651	+	0.263532i	$0.915113\pi$
$128$	−0.313426	+	8.97535i	−0.0277032	+	0.793317i
$129$		0			0
$130$	−0.512822	−	2.05682i	−0.0449774	−	0.180395i
$131$	−14.2204	+	5.17580i	−1.24244	+	0.452211i	−0.877841	−	0.478953i	$-0.841016\pi$
$131$	−14.2204	+	5.17580i	−1.24244	+	0.452211i	−0.364600	+	0.931164i	$0.618794\pi$
$132$		0			0
$133$	−0.202478	−	1.14831i	−0.0175570	−	0.0995710i
$134$	5.67545	+	4.12345i	0.490284	+	0.356212i
$135$		0			0
$136$	1.14239	+	3.51591i	0.0979591	+	0.301487i
$137$	14.3100	−	14.8184i	1.22258	−	1.26602i	0.269610	−	0.962970i	$-0.413105\pi$
$137$	14.3100	−	14.8184i	1.22258	−	1.26602i	0.952974	−	0.303053i	$-0.0980058\pi$
$138$		0			0
$139$	−0.0165610	+	0.0129389i	−0.00140468	+	0.00109746i	−0.616364	−	0.787462i	$-0.711395\pi$
$139$	−0.0165610	+	0.0129389i	−0.00140468	+	0.00109746i	0.614959	+	0.788559i	$0.289173\pi$
$140$	4.49197	−	2.80690i	0.379641	−	0.237226i
$141$		0			0
$142$	10.1834	−	27.9787i	0.854574	−	2.34792i
$143$	0.267919	−	4.30521i	0.0224045	−	0.360020i
$144$		0			0
$145$	2.55679	+	5.74265i	0.212330	+	0.476901i
$146$	−39.4612	+	15.9434i	−3.26583	+	1.31948i
$147$		0			0
$148$	15.8520	+	32.5014i	1.30302	+	2.67160i
$149$	−4.26774	−	8.75017i	−0.349627	−	0.716841i	0.649423	−	0.760428i	$-0.275011\pi$
$149$	−4.26774	−	8.75017i	−0.349627	−	0.716841i	−0.999050	+	0.0435861i	$0.986122\pi$
$150$		0			0
$151$	0.230911	−	0.0932943i	0.0187913	−	0.00759218i	−0.365192	−	0.930932i	$-0.618997\pi$
$151$	0.230911	−	0.0932943i	0.0187913	−	0.00759218i	0.383983	+	0.923340i	$0.374552\pi$
$152$	2.21278	+	4.96999i	0.179480	+	0.403119i
$153$		0			0
$154$	14.5964	−	3.75832i	1.17621	−	0.302854i
$155$	−1.00549	+	2.76257i	−0.0807633	+	0.221895i
$156$		0			0
$157$	3.70800	−	2.31702i	0.295931	−	0.184918i	−0.373825	−	0.927499i	$-0.621954\pi$
$157$	3.70800	−	2.31702i	0.295931	−	0.184918i	0.669756	+	0.742581i	$0.266399\pi$
$158$	2.45838	−	1.92070i	0.195579	−	0.152803i
$159$		0			0
$160$	−5.79943	+	6.00549i	−0.458485	+	0.474775i
$161$	−2.44529	−	7.52584i	−0.192716	−	0.593119i
$162$		0			0
$163$	0.657814	+	0.477930i	0.0515240	+	0.0374343i	0.613249	−	0.789890i	$-0.289862\pi$
$163$	0.657814	+	0.477930i	0.0515240	+	0.0374343i	−0.561725	+	0.827324i	$0.689862\pi$
$164$	−8.23871	−	46.7240i	−0.643335	−	3.64853i
$165$		0			0
$166$	−39.8127	+	14.4907i	−3.09007	+	1.12469i
$167$	1.86802	+	7.49220i	0.144551	+	0.579764i	0.998257	+	0.0590088i	$0.0187940\pi$
$167$	1.86802	+	7.49220i	0.144551	+	0.579764i	−0.853706	+	0.520755i	$0.825650\pi$
$168$		0			0
$169$	0.394661	−	11.3016i	0.0303585	−	0.869354i
$170$	−0.306246	+	0.687839i	−0.0234880	+	0.0527549i
$171$		0			0
$172$	−6.11387	+	28.7635i	−0.466178	+	2.19320i
$173$	−0.816902	−	2.02190i	−0.0621079	−	0.153722i	0.892939	−	0.450178i	$-0.148640\pi$
$173$	−0.816902	−	2.02190i	−0.0621079	−	0.153722i	−0.955047	+	0.296456i	$0.904195\pi$
$174$		0			0
$175$	−7.80647	−	1.37649i	−0.590114	−	0.104053i
$176$	−32.5552	+	17.6312i	−2.45394	+	1.32900i
$177$		0			0
$178$	−2.40732	−	34.4263i	−0.180436	−	2.58036i
$179$	−1.52670	+	1.37465i	−0.114111	+	0.102746i	−0.724211	−	0.689578i	$-0.757796\pi$
$179$	−1.52670	+	1.37465i	−0.114111	+	0.102746i	0.610100	+	0.792324i	$0.291129\pi$
$180$		0			0
$181$	−0.885886	−	0.394422i	−0.0658474	−	0.0293171i	0.373549	−	0.927611i	$-0.378141\pi$
$181$	−0.885886	−	0.394422i	−0.0658474	−	0.0293171i	−0.439396	+	0.898293i	$0.644808\pi$
$182$	−5.68157	+	1.62916i	−0.421146	+	0.120762i
$183$		0			0
$184$	19.5648	+	31.3103i	1.44234	+	2.30823i
$185$	−1.22131	+	4.25921i	−0.0897924	+	0.313143i
$186$		0			0
$187$	−1.01645	+	1.14643i	−0.0743302	+	0.0838350i
$188$			39.0930i			2.85115i
$189$		0			0
$190$	−0.342399	+	1.05380i	−0.0248402	+	0.0764503i
$191$	−3.76263	−	7.07647i	−0.272254	−	0.512036i	0.708888	−	0.705321i	$-0.249197\pi$
$191$	−3.76263	−	7.07647i	−0.272254	−	0.512036i	−0.981143	+	0.193285i	$0.938086\pi$
$192$		0			0
$193$	−7.45071	−	5.02557i	−0.536314	−	0.361748i	0.260976	−	0.965345i	$-0.415956\pi$
$193$	−7.45071	−	5.02557i	−0.536314	−	0.361748i	−0.797290	+	0.603597i	$0.793734\pi$
$194$	−7.78682	+	19.2730i	−0.559061	+	1.38372i
$195$		0			0
$196$	11.3925	+	16.8901i	0.813750	+	1.20643i
$197$	9.22560	+	15.9792i	0.657297	+	1.13847i	0.981313	+	0.192420i	$0.0616335\pi$
$197$	9.22560	+	15.9792i	0.657297	+	1.13847i	−0.324016	+	0.946052i	$0.605033\pi$
$198$		0			0
$199$	0.564555	−	0.977838i	0.0400202	−	0.0693171i	−0.845321	−	0.534258i	$-0.820591\pi$
$199$	0.564555	−	0.977838i	0.0400202	−	0.0693171i	0.885342	+	0.464941i	$0.153924\pi$
$200$	36.8945	−	2.57992i	2.60884	−	0.182428i
$201$		0			0
$202$	3.77509	−	0.530554i	0.265614	−	0.0373296i
$203$	15.7535	−	7.68350i	1.10568	−	0.539276i
$204$		0			0
$205$	3.08066	−	4.93009i	0.215163	−	0.344332i
$206$	−10.3042	−	11.4439i	−0.717926	−	0.797337i
$207$		0			0
$208$	12.5731	−	7.25910i	0.871790	−	0.503328i
$209$	−1.31128	+	1.83421i	−0.0907028	+	0.126875i
$210$		0			0
$211$	−11.4729	+	2.86052i	−0.789828	+	0.196926i	−0.615892	−	0.787831i	$-0.711204\pi$
$211$	−11.4729	+	2.86052i	−0.789828	+	0.196926i	−0.173936	+	0.984757i	$0.555649\pi$
$212$	33.5266	−	1.17077i	2.30262	−	0.0804091i
$213$		0			0
$214$	−20.7258	−	20.0147i	−1.41679	−	1.36818i
$215$	−2.91501	+	2.11788i	−0.198802	+	0.144438i
$216$		0			0
$217$	7.79596	+	2.53306i	0.529224	+	0.171955i
$218$	19.3512	+	9.43822i	1.31063	+	0.639237i
$219$		0			0
$220$	−9.95686	−	2.40164i	−0.671292	−	0.161919i
$221$	0.386196	−	0.460251i	0.0259784	−	0.0309598i
$222$		0			0
$223$	−16.6479	+	21.3083i	−1.11483	+	1.42691i	−0.222836	+	0.974856i	$0.571532\pi$
$223$	−16.6479	+	21.3083i	−1.11483	+	1.42691i	−0.891990	+	0.452056i	$0.850691\pi$
$224$	17.2991	+	15.5761i	1.15584	+	1.04073i
$225$		0			0
$226$	−14.5721	+	1.53159i	−0.969320	+	0.101880i
$227$	10.5251	+	6.57679i	0.698573	+	0.436517i	0.832171	−	0.554519i	$-0.187098\pi$
$227$	10.5251	+	6.57679i	0.698573	+	0.436517i	−0.133598	+	0.991036i	$0.542653\pi$
$228$		0			0
$229$	−13.7313	+	13.2601i	−0.907388	+	0.876254i	−0.992762	−	0.120095i	$-0.961680\pi$
$229$	−13.7313	+	13.2601i	−0.907388	+	0.876254i	0.0853746	+	0.996349i	$0.472791\pi$
$230$	−1.30576	+	7.40531i	−0.0860989	+	0.488291i
$231$		0			0
$232$	−62.6453	+	52.5657i	−4.11287	+	3.45111i
$233$	−5.09708	+	2.26936i	−0.333921	+	0.148671i	−0.566846	−	0.823823i	$-0.691837\pi$
$233$	−5.09708	+	2.26936i	−0.333921	+	0.148671i	0.232926	+	0.972494i	$0.425170\pi$
$234$		0			0
$235$	−3.20520	+	3.55974i	−0.209084	+	0.232212i
$236$	16.4286	+	57.2934i	1.06941	+	3.72948i
$237$		0			0
$238$	1.94652	+	0.786443i	0.126174	+	0.0509775i
$239$	0.220192	+	6.30547i	0.0142430	+	0.407867i	0.985484	+	0.169768i	$0.0543019\pi$
$239$	0.220192	+	6.30547i	0.0142430	+	0.407867i	−0.971241	+	0.238099i	$0.923476\pi$
$240$		0			0
$241$	−4.00179	+	0.705624i	−0.257778	+	0.0454532i	−0.301044	−	0.953610i	$-0.597335\pi$
$241$	−4.00179	+	0.705624i	−0.257778	+	0.0454532i	0.0432656	+	0.999064i	$0.486224\pi$
$242$	−24.9505	−	15.0642i	−1.60388	−	0.968361i
$243$		0			0
$244$	16.8290	−	23.1632i	1.07737	−	1.48287i
$245$	−0.347423	+	2.47204i	−0.0221960	+	0.157933i
$246$		0			0
$247$	0.494419	−	0.733006i	0.0314591	−	0.0466401i
$248$	−38.1524	−	2.66788i	−2.42268	−	0.169410i
$249$		0			0
$250$	12.3576	+	9.65479i	0.781562	+	0.610623i
$251$	−19.4501	−	2.04429i	−1.22768	−	0.129034i	−0.531597	−	0.846997i	$-0.678408\pi$
$251$	−19.4501	−	2.04429i	−1.22768	−	0.129034i	−0.696081	+	0.717963i	$0.745075\pi$
$252$		0			0
$253$	−7.07989	+	13.5651i	−0.445109	+	0.852829i
$254$	−24.3027	−	28.9628i	−1.52489	−	1.81729i
$255$		0			0
$256$	3.06608	+	1.63026i	0.191630	+	0.101892i
$257$	0.0244987	+	0.174317i	0.00152819	+	0.0108736i	0.991017	−	0.133734i	$-0.0426968\pi$
$257$	0.0244987	+	0.174317i	0.00152819	+	0.0108736i	−0.989489	+	0.144608i	$0.953808\pi$
$258$		0			0
$259$	11.9874	+	2.98880i	0.744863	+	0.185715i
$260$	3.92869	+	0.835069i	0.243647	+	0.0517888i
$261$		0			0
$262$	4.19120	−	39.8766i	0.258933	−	2.46358i
$263$	14.6793	+	5.34285i	0.905167	+	0.329454i	0.752322	−	0.658796i	$-0.228934\pi$
$263$	14.6793	+	5.34285i	0.905167	+	0.329454i	0.152846	+	0.988250i	$0.451156\pi$
$264$		0			0
$265$	3.14886	+	2.64221i	0.193433	+	0.162310i
$266$	2.96980	+	0.851575i	0.182090	+	0.0522134i
$267$		0			0
$268$	−11.7363	+	6.24028i	−0.716906	+	0.381186i
$269$	3.43294	+	4.72504i	0.209310	+	0.288091i	0.900745	−	0.434348i	$-0.143021\pi$
$269$	3.43294	+	4.72504i	0.209310	+	0.288091i	−0.691435	+	0.722439i	$0.743021\pi$
$270$		0			0
$271$	−0.0396553	+	0.0128848i	−0.00240889	+	0.000782695i	−0.310221	−	0.950664i	$-0.600403\pi$
$271$	−0.0396553	+	0.0128848i	−0.00240889	+	0.000782695i	0.307812	+	0.951447i	$0.400403\pi$
$272$	−5.10659	−	0.717685i	−0.309633	−	0.0435160i
$273$		0			0
$274$	18.6680	+	51.2898i	1.12777	+	3.09853i
$275$	8.66849	+	12.6415i	0.522729	+	0.762313i
$276$		0			0
$277$	5.64882	−	3.81017i	0.339404	−	0.228931i	−0.377650	−	0.925948i	$-0.623268\pi$
$277$	5.64882	−	3.81017i	0.339404	−	0.228931i	0.717054	+	0.697017i	$0.245490\pi$
$278$	−0.0115774	−	0.0544674i	−0.000694366	−	0.00326674i
$279$		0			0
$280$	0.882572	+	8.39711i	0.0527438	+	0.501823i
$281$	6.45631	−	25.8948i	0.385151	−	1.54476i	−0.394712	−	0.918805i	$-0.629155\pi$
$281$	6.45631	−	25.8948i	0.385151	−	1.54476i	0.779862	−	0.625951i	$-0.215289\pi$
$282$		0			0
$283$	9.12847	−	17.1681i	0.542631	−	1.02054i	−0.449254	−	0.893404i	$-0.648310\pi$
$283$	9.12847	−	17.1681i	0.542631	−	1.02054i	0.991885	−	0.127137i	$-0.0405786\pi$
$284$	39.1891	+	40.5815i	2.32545	+	2.40807i
$285$		0			0
$286$	9.94138	+	5.63854i	0.587846	+	0.333414i
$287$	−14.0378	−	8.10475i	−0.828627	−	0.478408i
$288$		0			0
$289$	16.4198	−	3.49013i	0.965869	−	0.205302i
$290$	−16.6454	−	0.581271i	−0.977454	−	0.0341334i
$291$		0			0
$292$	5.62524	−	80.4447i	0.329192	−	4.70767i
$293$	11.7668	+	15.0608i	0.687424	+	0.879862i	0.997487	−	0.0708537i	$-0.0225723\pi$
$293$	11.7668	+	15.0608i	0.687424	+	0.879862i	−0.310063	+	0.950716i	$0.600350\pi$
$294$		0			0
$295$	−3.20148	+	6.56400i	−0.186397	+	0.382171i
$296$	−57.6422			−3.35038
$297$		0			0
$298$	25.7949			1.49426
$299$	2.63037	−	5.39306i	0.152118	−	0.311889i
$300$		0			0
$301$	6.18529	+	7.91681i	0.356514	+	0.456317i
$302$	−0.0460301	+	0.658261i	−0.00264874	+	0.0378787i
$303$		0			0
$304$	−7.58415	−	0.264844i	−0.434981	−	0.0151899i
$305$	3.43155	−	0.729399i	0.196490	−	0.0417653i
$306$		0			0
$307$	−0.669905	−	0.386770i	−0.0382335	−	0.0220741i	0.480761	−	0.876851i	$-0.340360\pi$
$307$	−0.669905	−	0.386770i	−0.0382335	−	0.0220741i	−0.518995	+	0.854777i	$0.673694\pi$
$308$	−5.72346	+	27.9792i	−0.326125	+	1.59426i
$309$		0			0
$310$	−5.41100	−	5.60325i	−0.307324	−	0.318243i
$311$	7.61699	−	14.3255i	0.431920	−	0.812324i	−0.568023	−	0.823013i	$-0.692291\pi$
$311$	7.61699	−	14.3255i	0.431920	−	0.812324i	0.999943	+	0.0106893i	$0.00340257\pi$
$312$		0			0
$313$	3.47635	−	13.9429i	0.196495	−	0.788099i	−0.788431	−	0.615123i	$-0.789106\pi$
$313$	3.47635	−	13.9429i	0.196495	−	0.788099i	0.984926	−	0.172976i	$-0.0553382\pi$
$314$	1.21097	+	11.5216i	0.0683388	+	0.650200i
$315$		0			0
$316$	1.22899	+	5.78195i	0.0691361	+	0.325260i
$317$	18.1355	−	12.2325i	1.01859	−	0.687047i	0.0680598	−	0.997681i	$-0.478319\pi$
$317$	18.1355	−	12.2325i	1.01859	−	0.687047i	0.950530	+	0.310634i	$0.100541\pi$
$318$		0			0
$319$	−31.9363	−	11.3475i	−1.78809	−	0.635339i
$320$	−2.86847	−	7.88107i	−0.160353	−	0.440565i
$321$		0			0
$322$	20.7625	+	2.91798i	1.15705	+	0.162613i
$323$	−0.298680	+	0.0970469i	−0.0166190	+	0.00539983i
$324$		0			0
$325$	−3.53304	−	4.86281i	−0.195978	−	0.269740i
$326$	−1.90221	+	1.01142i	−0.105354	+	0.0560175i
$327$		0			0
$328$	72.6991	+	20.8461i	4.01414	+	1.15104i
$329$	10.2314	+	8.58514i	0.564074	+	0.473314i
$330$		0			0
$331$	8.23558	+	2.99751i	0.452668	+	0.164758i	0.558285	−	0.829649i	$-0.311459\pi$
$331$	8.23558	+	2.99751i	0.452668	+	0.164758i	−0.105617	+	0.994407i	$0.533682\pi$
$332$	8.39118	−	79.8367i	0.460526	−	4.38161i
$333$		0			0
$334$	−20.0119	−	4.25365i	−1.09500	−	0.232750i
$335$	−1.58032	−	0.394017i	−0.0863420	−	0.0215275i
$336$		0			0
$337$	−4.41711	−	31.4293i	−0.240615	−	1.71207i	−0.618141	−	0.786067i	$-0.712114\pi$
$337$	−4.41711	−	31.4293i	−0.240615	−	1.71207i	0.377526	−	0.925999i	$-0.376775\pi$
$338$	26.4556	+	14.0667i	1.43899	+	0.765127i
$339$		0			0
$340$	−0.917015	−	1.09286i	−0.0497321	−	0.0592684i
$341$	−7.05745	−	14.1929i	−0.382182	−	0.768587i
$342$		0			0
$343$	18.8629	+	1.98257i	1.01850	+	0.107048i
$344$	−36.9376	−	28.8588i	−1.99154	−	1.55596i
$345$		0			0
$346$	5.76386	+	0.403048i	0.309867	+	0.0216680i
$347$	−1.51013	+	2.23885i	−0.0810678	+	0.120188i	−0.867391	−	0.497628i	$-0.834205\pi$
$347$	−1.51013	+	2.23885i	−0.0810678	+	0.120188i	0.786323	+	0.617816i	$0.211982\pi$
$348$		0			0
$349$	2.45334	−	17.4564i	0.131324	−	0.934421i	−0.807462	−	0.589920i	$-0.799159\pi$
$349$	2.45334	−	17.4564i	0.131324	−	0.934421i	0.938786	−	0.344501i	$-0.111952\pi$
$350$	12.3453	−	16.9918i	0.659881	−	0.908249i
$351$		0			0
$352$	−1.91555	−	44.9719i	−0.102099	−	2.39701i
$353$	−7.87364	+	1.38833i	−0.419071	+	0.0738936i	−0.379208	−	0.925312i	$-0.623803\pi$
$353$	−7.87364	+	1.38833i	−0.419071	+	0.0738936i	−0.0398636	+	0.999205i	$0.512692\pi$
$354$		0			0
$355$	0.241245	+	6.90836i	0.0128040	+	0.366658i
$356$	60.6272	+	24.4950i	3.21323	+	1.29823i
$357$		0			0
$358$	−1.50036	−	5.23239i	−0.0792966	−	0.276540i
$359$	−21.2953	+	23.6509i	−1.12393	+	1.24825i	−0.158558	+	0.987350i	$0.550685\pi$
$359$	−21.2953	+	23.6509i	−1.12393	+	1.24825i	−0.965367	+	0.260896i	$0.915982\pi$
$360$		0			0
$361$	16.9352	−	7.54002i	0.891324	−	0.396843i
$362$	1.96825	−	1.65156i	0.103449	−	0.0868038i
$363$		0			0
$364$	1.94468	−	11.0288i	0.101929	−	0.578068i
$365$	7.10782	−	6.86394i	0.372040	−	0.359275i
$366$		0			0
$367$	11.2294	+	7.01691i	0.586170	+	0.366280i	0.790352	−	0.612653i	$-0.209898\pi$
$367$	11.2294	+	7.01691i	0.586170	+	0.366280i	−0.204182	+	0.978933i	$0.565453\pi$
$368$	−51.2186	+	5.38329i	−2.66995	+	0.280623i
$369$		0			0
$370$	−8.72446	−	7.85554i	−0.453563	−	0.408390i
$371$	7.05630	−	9.03165i	0.366345	−	0.468900i
$372$		0			0
$373$	20.1696	−	24.0372i	1.04434	−	1.24460i	0.0754405	−	0.997150i	$-0.475964\pi$
$373$	20.1696	−	24.0372i	1.04434	−	1.24460i	0.968901	−	0.247448i	$-0.0795918\pi$
$374$	−1.54953	−	3.75218i	−0.0801242	−	0.194021i
$375$		0			0
$376$	−56.0090	−	27.3174i	−2.88844	−	1.40879i
$377$	12.6401	+	4.10701i	0.650997	+	0.211522i
$378$		0			0
$379$	14.3649	−	10.4367i	0.737874	−	0.536097i	−0.154170	−	0.988044i	$-0.549270\pi$
$379$	14.3649	−	10.4367i	0.737874	−	0.536097i	0.892045	+	0.451947i	$0.149270\pi$
$380$	−1.51021	−	1.45839i	−0.0774719	−	0.0748138i
$381$		0			0
$382$	21.2224	−	0.741104i	1.08583	−	0.0379182i
$383$	3.56203	−	0.888113i	0.182011	−	0.0453805i	−0.149850	−	0.988709i	$-0.547879\pi$
$383$	3.56203	−	0.888113i	0.182011	−	0.0453805i	0.331861	+	0.943328i	$0.392323\pi$
$384$		0			0
$385$	−2.81516	+	2.07848i	−0.143474	+	0.105929i
$386$	20.6221	−	11.9062i	1.04964	−	0.606007i
$387$		0			0
$388$	−26.3541	−	29.2691i	−1.33792	−	1.48592i
$389$	1.39217	−	2.22793i	0.0705856	−	0.112961i	−0.810872	−	0.585223i	$-0.801007\pi$
$389$	1.39217	−	2.22793i	0.0705856	−	0.112961i	0.881458	+	0.472262i	$0.156563\pi$
$390$		0			0
$391$	−1.91558	+	0.934292i	−0.0968752	+	0.0472492i
$392$	−32.1595	+	4.51972i	−1.62430	+	0.228280i
$393$		0			0
$394$	−48.7689	+	3.41026i	−2.45694	+	0.171806i
$395$	−0.362147	+	0.627258i	−0.0182216	+	0.0315608i
$396$		0			0
$397$	10.4449	+	18.0911i	0.524215	+	0.907968i	0.999603	+	0.0281909i	$0.00897464\pi$
$397$	10.4449	+	18.0911i	0.524215	+	0.907968i	−0.475387	+	0.879777i	$0.657692\pi$
$398$	1.67292	+	2.48021i	0.0838560	+	0.124322i
$399$		0			0
$400$	−19.3260	+	47.8336i	−0.966302	+	2.39168i
$401$	−21.0885	−	14.2244i	−1.05311	−	0.710330i	−0.0946346	−	0.995512i	$-0.530168\pi$
$401$	−21.0885	−	14.2244i	−1.05311	−	0.710330i	−0.958473	+	0.285182i	$0.907946\pi$
$402$		0			0
$403$	2.91809	+	5.48813i	0.145361	+	0.273383i
$404$	−2.23207	+	6.86962i	−0.111050	+	0.341776i
$405$		0			0
$406$			46.4403i			2.30479i
$407$	−12.1029	−	20.5968i	−0.599920	−	1.02095i
$408$		0			0
$409$	−7.92108	+	27.6241i	−0.391672	+	1.36592i	0.480616	+	0.876931i	$0.340413\pi$
$409$	−7.92108	+	27.6241i	−0.391672	+	1.36592i	−0.872288	+	0.488992i	$0.837365\pi$
$410$	8.16248	+	13.0627i	0.403116	+	0.645121i
$411$		0			0
$412$	28.0476	−	8.04253i	1.38181	−	0.396227i
$413$	18.6026	+	8.28241i	0.915374	+	0.407551i
$414$		0			0
$415$	7.30983	−	6.58180i	0.358826	−	0.323088i
$416$	1.23129	+	17.6083i	0.0603689	+	0.863316i
$417$		0			0
$418$	−2.84499	−	5.25315i	−0.139153	−	0.256940i
$419$	16.4329	+	2.89757i	0.802802	+	0.141556i	0.559970	−	0.828513i	$-0.310813\pi$
$419$	16.4329	+	2.89757i	0.802802	+	0.141556i	0.242832	+	0.970068i	$0.421924\pi$
$420$		0			0
$421$	12.1380	+	30.0427i	0.591572	+	1.46419i	0.864737	+	0.502225i	$0.167485\pi$
$421$	12.1380	+	30.0427i	0.591572	+	1.46419i	−0.273165	+	0.961967i	$0.588071\pi$
$422$	6.51368	−	30.6445i	0.317081	−	1.49175i
$423$		0			0
$424$	−21.7503	+	48.8521i	−1.05629	+	2.37247i
$425$	−0.0745100	+	2.13369i	−0.00361427	+	0.103499i
$426$		0			0
$427$	−2.36645	−	9.49130i	−0.114520	−	0.459316i
$428$	51.2998	−	18.6716i	2.47967	−	0.902526i
$429$		0			0
$430$	−1.65780	−	9.40183i	−0.0799460	−	0.453396i
$431$	7.69080	+	5.58769i	0.370453	+	0.269150i	0.757399	−	0.652953i	$-0.226470\pi$
$431$	7.69080	+	5.58769i	0.370453	+	0.269150i	−0.386946	+	0.922102i	$0.626470\pi$
$432$		0			0
$433$	−7.09353	−	21.8317i	−0.340894	−	1.04916i	−0.963746	−	0.266823i	$-0.914026\pi$
$433$	−7.09353	−	21.8317i	−0.340894	−	1.04916i	0.622852	−	0.782340i	$-0.285974\pi$
$434$	−15.0873	+	15.6234i	−0.724215	+	0.749947i
$435$		0			0
$436$	−32.1464	+	25.1155i	−1.53953	+	1.20282i
$437$	−2.65983	+	1.66205i	−0.127237	+	0.0795065i
$438$		0			0
$439$	−1.91262	+	5.25489i	−0.0912845	+	0.250802i	−0.976930	−	0.213560i	$-0.931494\pi$
$439$	−1.91262	+	5.25489i	−0.0912845	+	0.250802i	0.885645	+	0.464362i	$0.153716\pi$
$440$	10.3985	−	12.5871i	0.495730	−	0.600066i
$441$		0			0
$442$	0.647488	+	1.45428i	0.0307979	+	0.0691732i
$443$	−10.5824	+	4.27557i	−0.502786	+	0.203139i	−0.611967	−	0.790883i	$-0.709622\pi$
$443$	−10.5824	+	4.27557i	−0.502786	+	0.203139i	0.109181	+	0.994022i	$0.465177\pi$
$444$		0			0
$445$	3.51228	+	7.20124i	0.166498	+	0.341372i
$446$	−31.4078	−	64.3955i	−1.48720	−	3.04922i
$447$		0			0
$448$	−21.6820	+	8.76012i	−1.02438	+	0.413877i
$449$	5.47523	+	12.2976i	0.258392	+	0.580358i	0.995430	−	0.0954934i	$-0.0304429\pi$
$449$	5.47523	+	12.2976i	0.258392	+	0.580358i	−0.737038	+	0.675851i	$0.763776\pi$
$450$		0			0
$451$	7.81561	+	30.3540i	0.368023	+	1.42931i
$452$	9.49535	−	26.0883i	0.446624	−	1.22709i
$453$		0			0
$454$	−27.8871	+	17.4258i	−1.30880	+	0.817832i
$455$	1.08133	−	0.844824i	0.0506933	−	0.0396060i
$456$		0			0
$457$	−1.72165	+	1.78282i	−0.0805353	+	0.0833967i	−0.758398	−	0.651792i	$-0.774018\pi$
$457$	−1.72165	+	1.78282i	−0.0805353	+	0.0833967i	0.677863	+	0.735189i	$0.262906\pi$
$458$	−15.6292	−	48.1018i	−0.730305	−	2.24765i
$459$		0			0
$460$	−11.5266	−	8.37457i	−0.537431	−	0.390466i
$461$	2.24987	+	12.7596i	0.104787	+	0.594275i	0.991305	+	0.131582i	$0.0420057\pi$
$461$	2.24987	+	12.7596i	0.104787	+	0.594275i	−0.886519	+	0.462693i	$0.846883\pi$
$462$		0			0
$463$	9.89023	−	3.59975i	0.459638	−	0.167294i	−0.101815	−	0.994803i	$-0.532465\pi$
$463$	9.89023	−	3.59975i	0.459638	−	0.167294i	0.561453	+	0.827509i	$0.310243\pi$
$464$	−27.5967	−	110.684i	−1.28114	−	5.13838i
$465$		0			0
$466$	0.515927	−	14.7742i	0.0238998	−	0.684402i
$467$	5.59457	−	12.5656i	0.258886	−	0.581467i	−0.736605	−	0.676323i	$-0.763572\pi$
$467$	5.59457	−	12.5656i	0.258886	−	0.581467i	0.995491	+	0.0948559i	$0.0302390\pi$
$468$		0			0
$469$	−0.944179	+	4.44201i	−0.0435981	+	0.205113i
$470$	−4.75443	−	11.7676i	−0.219305	−	0.542800i
$471$		0			0
$472$	−93.5649	−	16.4980i	−4.30667	−	0.759382i
$473$	2.55622	−	19.2580i	0.117535	−	0.885483i
$474$		0			0
$475$	0.219166	+	3.13422i	0.0100560	+	0.143808i
$476$	−2.95609	+	2.66168i	−0.135492	+	0.121998i
$477$		0			0
$478$	−15.2718	−	6.79944i	−0.698516	−	0.310999i
$479$	−5.01079	+	1.43682i	−0.228949	+	0.0656500i	−0.388150	−	0.921596i	$-0.626886\pi$
$479$	−5.01079	+	1.43682i	−0.228949	+	0.0656500i	0.159201	+	0.987246i	$0.449108\pi$
$480$		0			0
$481$	4.96431	+	7.94455i	0.226353	+	0.362240i
$482$	2.96769	−	10.3496i	0.135175	−	0.471410i
$483$		0			0
$484$	46.3781	−	29.9781i	2.10810	−	1.36264i
$485$		−	4.82594i		−	0.219135i
$486$		0			0
$487$	−6.05340	+	18.6304i	−0.274306	+	0.844226i	0.715097	+	0.699025i	$0.246383\pi$
$487$	−6.05340	+	18.6304i	−0.274306	+	0.844226i	−0.989402	+	0.145200i	$0.953617\pi$
$488$	21.4264	+	40.2972i	0.969927	+	1.82417i
$489$		0			0
$490$	−5.48347	−	3.69864i	−0.247718	−	0.167088i
$491$	1.21113	−	2.99765i	0.0546574	−	0.135282i	−0.897385	−	0.441249i	$-0.854535\pi$
$491$	1.21113	−	2.99765i	0.0546574	−	0.135282i	0.952042	+	0.305967i	$0.0989799\pi$
$492$		0			0
$493$	−2.63980	−	3.91366i	−0.118891	−	0.176262i
$494$	1.17134	+	2.02881i	0.0527009	+	0.0912807i
$495$		0			0
$496$	26.6746	−	46.2017i	1.19772	−	2.07452i
$497$	19.2272	−	1.34450i	0.862457	−	0.0603089i
$498$		0			0
$499$	−25.4225	+	3.57290i	−1.13807	+	0.159945i	−0.682935	−	0.730480i	$-0.739297\pi$
$499$	−25.4225	+	3.57290i	−1.13807	+	0.159945i	−0.455131	+	0.890424i	$0.650408\pi$
$500$	−26.7063	+	13.0255i	−1.19434	+	0.582519i
$501$		0			0
$502$	27.4596	−	43.9446i	1.22558	−	1.96134i
$503$	1.88123	+	2.08931i	0.0838797	+	0.0931579i	0.783624	−	0.621236i	$-0.213369\pi$
$503$	1.88123	+	2.08931i	0.0838797	+	0.0931579i	−0.699744	+	0.714394i	$0.746703\pi$
$504$		0			0
$505$	−0.766483	+	0.442529i	−0.0341081	+	0.0196923i
$506$	−24.0810	−	32.6161i	−1.07053	−	1.44996i
$507$		0			0
$508$	69.5094	−	17.3306i	3.08398	−	0.768923i
$509$	−5.99218	+	0.209251i	−0.265599	+	0.00927490i	−0.167389	−	0.985891i	$-0.553534\pi$
$509$	−5.99218	+	0.209251i	−0.265599	+	0.00927490i	−0.0982092	+	0.995166i	$0.531311\pi$
$510$		0			0
$511$	−19.8185	−	19.1385i	−0.876720	−	0.846638i
$512$	−21.9749	+	15.9657i	−0.971163	+	0.705591i
$513$		0			0
$514$	−0.443580	−	0.144128i	−0.0195655	−	0.00635720i
$515$	3.21337	+	1.56726i	0.141598	+	0.0690619i
$516$		0			0
$517$	−1.99891	−	25.7490i	−0.0879121	−	1.13244i
$518$	−21.0411	+	25.0758i	−0.924491	+	1.10177i
$519$		0			0
$520$	−3.94170	+	5.04515i	−0.172855	+	0.221245i
$521$	−4.20469	−	3.78592i	−0.184211	−	0.165864i	0.571866	−	0.820347i	$-0.306220\pi$
$521$	−4.20469	−	3.78592i	−0.184211	−	0.165864i	−0.756077	+	0.654483i	$0.772886\pi$
$522$		0			0
$523$	36.1307	−	3.79748i	1.57988	−	0.166052i	0.726437	−	0.687233i	$-0.241175\pi$
$523$	36.1307	−	3.79748i	1.57988	−	0.166052i	0.853446	+	0.521181i	$0.174508\pi$
$524$	64.4282	+	40.2592i	2.81456	+	1.75873i
$525$		0			0
$526$	−29.7737	+	28.7521i	−1.29820	+	1.25365i
$527$	0.383377	−	2.17424i	0.0167001	−	0.0947112i
$528$		0			0
$529$	1.31370	−	1.10232i	0.0571173	−	0.0479271i
$530$	−9.94965	+	4.42987i	−0.432185	+	0.192421i
$531$		0			0
$532$	−3.91695	+	4.35021i	−0.169821	+	0.188606i
$533$	−3.38793	−	11.8151i	−0.146747	−	0.511769i
$534$		0			0
$535$	6.20214	+	2.50583i	0.268142	+	0.108336i
$536$	−0.739456	−	21.1753i	−0.0319396	−	0.914632i
$537$		0			0
$538$	−15.2397	+	2.68717i	−0.657031	+	0.115852i
$539$	−8.36741	−	10.5423i	−0.360410	−	0.454089i
$540$		0			0
$541$	−1.17931	+	1.62318i	−0.0507024	+	0.0697858i	−0.833615	−	0.552345i	$-0.813733\pi$
$541$	−1.17931	+	1.62318i	−0.0507024	+	0.0697858i	0.782913	+	0.622131i	$0.213733\pi$
$542$	0.0153755	−	0.109402i	0.000660433	−	0.00469922i
$543$		0			0
$544$	3.50593	−	5.19775i	0.150315	−	0.222852i
$545$	−4.98640	−	0.348683i	−0.213594	−	0.0149359i
$546$		0			0
$547$	−15.6652	−	12.2390i	−0.669797	−	0.523303i	0.222396	−	0.974956i	$-0.428612\pi$
$547$	−15.6652	−	12.2390i	−0.669797	−	0.523303i	−0.892193	+	0.451654i	$0.850834\pi$
$548$	−102.852	−	10.8102i	−4.39361	−	0.461787i
$549$		0			0
$550$	−40.1734	+	5.96024i	−1.71300	+	0.254146i
$551$	−4.46550	−	5.32177i	−0.190236	−	0.226715i
$552$		0			0
$553$	1.78314	+	0.948112i	0.0758268	+	0.0403178i
$554$	2.51256	+	17.8778i	0.106748	+	0.759555i
$555$		0			0
$556$	0.102374	+	0.0255246i	0.00434161	+	0.00108249i
$557$	−3.37720	−	0.717846i	−0.143096	−	0.0304161i	0.135807	−	0.990735i	$-0.456637\pi$
$557$	−3.37720	−	0.717846i	−0.143096	−	0.0304161i	−0.278903	+	0.960319i	$0.589971\pi$
$558$		0			0
$559$	−0.796304	+	7.57633i	−0.0336801	+	0.320445i
$560$	−11.0675	−	4.02822i	−0.467685	−	0.170224i
$561$		0			0
$562$	54.1678	+	45.4521i	2.28493	+	1.91728i
$563$	−42.8798	−	12.2956i	−1.80717	−	0.518197i	−0.809542	−	0.587062i	$-0.800285\pi$
$563$	−42.8798	−	12.2956i	−1.80717	−	0.518197i	−0.997626	+	0.0688645i	$0.978062\pi$
$564$		0			0
$565$	3.00358	−	1.59703i	0.126362	−	0.0671877i
$566$	30.2820	+	41.6797i	1.27285	+	1.75193i
$567$		0			0
$568$	−85.5262	+	27.7891i	−3.58860	+	1.16601i
$569$	−1.97756	−	0.277927i	−0.0829035	−	0.0116513i	0.0975994	−	0.995226i	$-0.468884\pi$
$569$	−1.97756	−	0.277927i	−0.0829035	−	0.0116513i	−0.180503	+	0.983574i	$0.557773\pi$
$570$		0			0
$571$	1.41619	+	3.89096i	0.0592658	+	0.162832i	0.965792	−	0.259318i	$-0.0834978\pi$
$571$	1.41619	+	3.89096i	0.0592658	+	0.162832i	−0.906526	+	0.422150i	$0.861276\pi$
$572$	−17.8597	+	12.2467i	−0.746753	+	0.512060i
$573$		0			0
$574$	35.6059	−	24.0165i	1.48616	−	1.00243i
$575$	4.43311	+	20.8562i	0.184874	+	0.869762i
$576$		0			0
$577$	3.52513	+	33.5394i	0.146753	+	1.39626i	0.781675	+	0.623687i	$0.214366\pi$
$577$	3.52513	+	33.5394i	0.146753	+	1.39626i	−0.634921	+	0.772577i	$0.718968\pi$
$578$	−10.7601	+	43.1564i	−0.447561	+	1.79507i
$579$		0			0
$580$	14.8157	−	27.8642i	0.615187	−	1.15700i
$581$	−19.0520	−	19.7289i	−0.790410	−	0.818493i
$582$		0			0
$583$	−22.0228	+	2.48543i	−0.912090	+	0.102936i
$584$	111.323	+	64.2725i	4.60659	+	2.65961i
$585$		0			0
$586$	−49.5335	+	10.5287i	−2.04621	+	0.434935i
$587$	−20.9856	−	0.732832i	−0.866167	−	0.0302472i	−0.401631	−	0.915801i	$-0.631557\pi$
$587$	−20.9856	−	0.732832i	−0.866167	−	0.0302472i	−0.464536	+	0.885554i	$0.653779\pi$
$588$		0			0
$589$	0.226638	−	3.24108i	0.00933846	−	0.133546i
$590$	−11.9132	−	15.2482i	−0.490458	−	0.627758i
$591$		0			0
$592$	35.2475	−	72.2681i	1.44866	−	2.97020i
$593$	6.44646			0.264724			0.132362	−	0.991201i	$-0.457744\pi$
$593$	6.44646			0.264724			0.132362	+	0.991201i	$0.457744\pi$
$594$		0			0
$595$	−0.487405			−0.0199816
$596$	−21.4254	+	43.9285i	−0.877617	+	1.79938i
$597$		0			0
$598$	9.78803	+	12.5281i	0.400262	+	0.512312i
$599$	2.75006	−	39.3277i	0.112365	−	1.60689i	−0.535098	−	0.844790i	$-0.679725\pi$
$599$	2.75006	−	39.3277i	0.112365	−	1.60689i	0.647462	−	0.762098i	$-0.275830\pi$
$600$		0			0
$601$	3.79706	+	0.132596i	0.154885	+	0.00540872i	0.112237	−	0.993681i	$-0.464198\pi$
$601$	3.79706	+	0.132596i	0.154885	+	0.00540872i	0.0426482	+	0.999090i	$0.486421\pi$
$602$	−26.0376	+	5.53446i	−1.06121	+	0.225568i
$603$		0			0
$604$	−1.08278	−	0.625144i	−0.0440577	−	0.0254367i
$605$	6.68099	+	1.07275i	0.271621	+	0.0436135i
$606$		0			0
$607$	22.8286	+	23.6397i	0.926585	+	0.959507i	0.999284	−	0.0378470i	$-0.0120499\pi$
$607$	22.8286	+	23.6397i	0.926585	+	0.959507i	−0.0726984	+	0.997354i	$0.523161\pi$
$608$	4.33155	−	8.14647i	0.175668	−	0.330383i
$609$		0			0
$610$	−2.24874	+	9.01921i	−0.0910489	+	0.365177i
$611$	1.05862	+	10.0721i	0.0428273	+	0.407474i
$612$		0			0
$613$	−6.72557	−	31.6413i	−0.271643	−	1.27798i	−0.876405	−	0.481575i	$-0.840065\pi$
$613$	−6.72557	−	31.6413i	−0.271643	−	1.27798i	0.604762	−	0.796407i	$-0.293268\pi$
$614$	1.69916	−	1.14610i	0.0685726	−	0.0462528i
$615$		0			0
$616$	−36.0867	−	27.7514i	−1.45398	−	1.11814i
$617$	−1.50850	−	4.14458i	−0.0607301	−	0.166855i	0.905617	−	0.424097i	$-0.139408\pi$
$617$	−1.50850	−	4.14458i	−0.0607301	−	0.166855i	−0.966347	+	0.257242i	$0.917186\pi$
$618$		0			0
$619$	35.7108	+	5.01882i	1.43534	+	0.201724i	0.813565	−	0.581474i	$-0.197524\pi$
$619$	35.7108	+	5.01882i	1.43534	+	0.201724i	0.621773	+	0.783198i	$0.286413\pi$
$620$	14.0367	−	4.56080i	0.563727	−	0.183166i
$621$		0			0
$622$	25.2680	+	34.7784i	1.01315	+	1.39449i
$623$	19.7250	−	10.4880i	0.790266	−	0.420192i
$624$		0			0
$625$	18.7131	+	5.36588i	0.748522	+	0.214635i
$626$	29.1663	+	24.4734i	1.16572	+	0.978154i
$627$		0			0
$628$	−20.6270	−	7.50761i	−0.823106	−	0.299586i
$629$	0.347816	−	3.30924i	0.0138683	−	0.131948i
$630$		0			0
$631$	8.30642	+	1.76558i	0.330673	+	0.0702868i	0.370257	−	0.928929i	$-0.379270\pi$
$631$	8.30642	+	1.76558i	0.330673	+	0.0702868i	−0.0395834	+	0.999216i	$0.512603\pi$
$632$	−9.14266	−	2.27952i	−0.363675	−	0.0906745i
$633$		0			0
$634$	8.06655	+	57.3965i	0.320364	+	2.27951i
$635$	7.75032	+	4.12092i	0.307562	+	0.163534i
$636$		0			0
$637$	3.39260	+	4.04314i	0.134420	+	0.160195i
$638$	64.1175	−	62.8740i	2.53843	−	2.48921i
$639$		0			0
$640$	5.49422	+	0.577466i	0.217178	+	0.0228264i
$641$	19.5614	+	15.2830i	0.772628	+	0.603643i	0.922917	−	0.384999i	$-0.125798\pi$
$641$	19.5614	+	15.2830i	0.772628	+	0.603643i	−0.150289	+	0.988642i	$0.548020\pi$
$642$		0			0
$643$	2.59631	+	0.181552i	0.102388	+	0.00715969i	0.120859	−	0.992670i	$-0.461435\pi$
$643$	2.59631	+	0.181552i	0.102388	+	0.00715969i	−0.0184704	+	0.999829i	$0.505880\pi$
$644$	−22.2147	+	32.9346i	−0.875382	+	1.29781i
$645$		0			0
$646$	0.115806	−	0.824005i	0.00455634	−	0.0324201i
$647$	17.8579	−	24.5794i	0.702068	−	0.966314i	−0.297863	−	0.954609i	$-0.596274\pi$
$647$	17.8579	−	24.5794i	0.702068	−	0.966314i	0.999931	−	0.0117056i	$-0.00372610\pi$
$648$		0			0
$649$	−13.7504	−	36.8968i	−0.539751	−	1.44833i
$650$	15.6841	−	2.76553i	0.615181	−	0.108473i
$651$		0			0
$652$	−0.142461	−	4.07954i	−0.00557919	−	0.159767i
$653$	28.1383	+	11.3686i	1.10114	+	0.444888i	0.851980	−	0.523575i	$-0.175402\pi$
$653$	28.1383	+	11.3686i	1.10114	+	0.444888i	0.249157	+	0.968463i	$0.419846\pi$
$654$		0			0
$655$	2.56590	+	8.94835i	0.100258	+	0.349641i
$656$	−70.5903	+	78.3984i	−2.75609	+	3.06094i
$657$		0			0
$658$	−32.3287	+	14.3937i	−1.26030	+	0.561123i
$659$	−4.92089	+	4.12912i	−0.191691	+	0.160848i	−0.733582	−	0.679601i	$-0.762153\pi$
$659$	−4.92089	+	4.12912i	−0.191691	+	0.160848i	0.541891	+	0.840449i	$0.317708\pi$
$660$		0			0
$661$	7.94027	−	45.0315i	0.308841	−	1.75152i	−0.296012	−	0.955184i	$-0.595657\pi$
$661$	7.94027	−	45.0315i	0.308841	−	1.75152i	0.604853	−	0.796338i	$-0.293232\pi$
$662$	−16.7040	+	16.1309i	−0.649219	+	0.626944i
$663$		0			0
$664$	108.519	+	67.8105i	4.21137	+	2.63156i
$665$	−0.713341	+	0.0749752i	−0.0276622	+	0.00290741i
$666$		0			0
$667$	−35.0362	−	31.5468i	−1.35661	−	1.22150i
$668$	23.8659	−	30.5469i	0.923399	−	1.18190i
$669$		0			0
$670$	2.77387	−	3.30577i	0.107164	−	0.127713i
$671$	−9.90024	+	16.1172i	−0.382195	+	0.622197i
$672$		0			0
$673$	28.8329	+	14.0627i	1.11143	+	0.542078i	0.900252	−	0.435370i	$-0.143382\pi$
$673$	28.8329	+	14.0627i	1.11143	+	0.542078i	0.211174	+	0.977449i	$0.432271\pi$
$674$	79.9773	+	25.9862i	3.08061	+	1.00095i
$675$		0			0
$676$	−45.9296	+	33.3698i	−1.76652	+	1.28345i
$677$	16.0542	+	15.5034i	0.617013	+	0.595843i	0.936036	−	0.351904i	$-0.114466\pi$
$677$	16.0542	+	15.5034i	0.617013	+	0.595843i	−0.319023	+	0.947747i	$0.603355\pi$
$678$		0			0
$679$	−13.4478	+	0.469609i	−0.516081	+	0.0180219i
$680$	2.20654	−	0.550152i	0.0846170	−	0.0210974i
$681$		0			0
$682$	41.9966	−	0.321789i	1.60813	−	0.0123219i
$683$	0.999916	−	0.577302i	0.0382607	−	0.0220898i	−0.480748	−	0.876859i	$-0.659635\pi$
$683$	0.999916	−	0.577302i	0.0382607	−	0.0220898i	0.519008	+	0.854769i	$0.326301\pi$
$684$		0			0
$685$	−8.47919	−	9.41709i	−0.323973	−	0.359809i
$686$	−26.6306	+	42.6178i	−1.01676	+	1.62716i
$687$		0			0
$688$	58.7682	−	28.6632i	2.24052	−	1.09277i
$689$	8.60626	−	1.20953i	0.327872	−	0.0460794i
$690$		0			0
$691$	−3.32814	+	0.232726i	−0.126608	+	0.00885333i	−0.132920	−	0.991127i	$-0.542435\pi$
$691$	−3.32814	+	0.232726i	−0.126608	+	0.00885333i	0.00631165	+	0.999980i	$0.497991\pi$
$692$	−5.47387	+	9.48103i	−0.208085	+	0.360415i
$693$		0			0
$694$	−3.57766	−	6.19669i	−0.135806	−	0.235223i
$695$	0.00722922	+	0.0107178i	0.000274220	+	0.000406548i
$696$		0			0
$697$	−1.63545	+	4.04788i	−0.0619471	+	0.153324i
$698$	38.7217	+	26.1181i	1.46564	+	0.988586i
$699$		0			0
$700$	18.6828	+	35.1373i	0.706145	+	1.32806i
$701$	−5.28920	+	16.2785i	−0.199770	+	0.614829i	0.800118	+	0.599843i	$0.204770\pi$
$701$	−5.28920	+	16.2785i	−0.199770	+	0.614829i	−0.999888	+	0.0149862i	$0.995230\pi$
$702$		0			0
$703$		−	4.89674i		−	0.184684i
$704$	41.4492	+	18.0751i	1.56218	+	0.681232i
$705$		0			0
$706$	5.83902	−	20.3631i	0.219754	−	0.766375i
$707$	1.30773	+	2.09280i	0.0491821	+	0.0787078i
$708$		0			0
$709$	−15.7050	+	4.50333i	−0.589812	+	0.169126i	−0.557251	−	0.830344i	$-0.688144\pi$
$709$	−15.7050	+	4.50333i	−0.589812	+	0.169126i	−0.0325609	+	0.999470i	$0.510366\pi$
$710$	−16.7320	−	7.44957i	−0.627941	−	0.279577i
$711$		0			0
$712$	−77.4593	+	69.7447i	−2.90291	+	2.61379i
$713$	−1.53806	−	21.9953i	−0.0576010	−	0.823732i
$714$		0			0
$715$	−2.63037	−	0.349144i	−0.0983703	−	0.0130572i
$716$	10.1569	+	1.79094i	0.379582	+	0.0669305i
$717$		0			0
$718$	−31.5884	−	78.1839i	−1.17887	−	2.91780i
$719$	4.90386	−	23.0709i	0.182883	−	0.860398i	−0.787024	−	0.616923i	$-0.788379\pi$
$719$	4.90386	−	23.0709i	0.182883	−	0.860398i	0.969907	−	0.243475i	$-0.0782875\pi$
$720$		0			0
$721$	4.05460	−	9.10679i	0.151001	−	0.339155i
$722$	−1.71418	+	49.0877i	−0.0637952	+	1.82685i
$723$		0			0
$724$	1.17775	+	4.72370i	0.0437707	+	0.175555i
$725$	−44.3797	+	16.1529i	−1.64822	+	0.599903i
$726$		0			0
$727$	5.17861	+	29.3693i	0.192064	+	1.08925i	0.916538	+	0.399947i	$0.130971\pi$
$727$	5.17861	+	29.3693i	0.192064	+	1.08925i	−0.724474	+	0.689302i	$0.757917\pi$
$728$	14.4423	+	10.4929i	0.535265	+	0.388893i
$729$		0			0
$730$	8.09026	+	24.8993i	0.299434	+	0.921563i
$731$	1.87967	−	1.94645i	0.0695221	−	0.0719922i
$732$		0			0
$733$	−21.2340	+	16.5898i	−0.784294	+	0.612758i	−0.926161	−	0.377128i	$-0.876912\pi$
$733$	−21.2340	+	16.5898i	−0.784294	+	0.612758i	0.141867	+	0.989886i	$0.454689\pi$
$734$	−29.7533	+	18.5919i	−1.09821	+	0.686240i
$735$		0			0
$736$	21.4155	−	58.8385i	0.789385	−	2.16882i
$737$	7.41112	−	4.71032i	0.272992	−	0.173507i
$738$		0			0
$739$	−3.53467	−	7.93899i	−0.130025	−	0.292040i	0.836788	−	0.547527i	$-0.184431\pi$
$739$	−3.53467	−	7.93899i	−0.130025	−	0.292040i	−0.966812	+	0.255487i	$0.917764\pi$
$740$	20.6245	−	8.33283i	0.758171	−	0.306321i
$741$		0			0
$742$	13.3124	+	27.2944i	0.488712	+	1.00201i
$743$	−3.14790	−	6.45414i	−0.115485	−	0.236780i	0.833220	−	0.552941i	$-0.186495\pi$
$743$	−3.14790	−	6.45414i	−0.115485	−	0.236780i	−0.948705	+	0.316162i	$0.897606\pi$
$744$		0			0
$745$	−5.55262	+	2.24340i	−0.203432	+	0.0821919i
$746$	33.8159	+	75.9517i	1.23809	+	2.78079i
$747$		0			0
$748$	7.67698	+	0.477748i	0.280698	+	0.0174682i
$749$	6.37914	−	17.5266i	0.233089	−	0.640406i
$750$		0			0
$751$	4.01958	−	2.51171i	0.146676	−	0.0916536i	−0.454596	−	0.890698i	$-0.650216\pi$
$751$	4.01958	−	2.51171i	0.146676	−	0.0916536i	0.601272	+	0.799044i	$0.294661\pi$
$752$	68.4977	−	53.5163i	2.49786	−	1.95154i
$753$		0			0
$754$	−24.4620	+	25.3312i	−0.890855	+	0.922508i
$755$	−0.0473410	−	0.145701i	−0.00172292	−	0.00530259i
$756$		0			0
$757$	−8.61542	−	6.25947i	−0.313133	−	0.227504i	0.420107	−	0.907475i	$-0.361993\pi$
$757$	−8.61542	−	6.25947i	−0.313133	−	0.227504i	−0.733240	+	0.679970i	$0.761993\pi$
$758$	8.16944	+	46.3312i	0.296728	+	1.68283i
$759$		0			0
$760$	3.14475	−	1.14460i	0.114072	−	0.0415189i
$761$	8.79388	+	35.2703i	0.318778	+	1.27855i	0.889322	+	0.457282i	$0.151177\pi$
$761$	8.79388	+	35.2703i	0.318778	+	1.27855i	−0.570544	+	0.821267i	$0.693268\pi$
$762$		0			0
$763$	−0.486407	+	13.9289i	−0.0176091	+	0.504260i
$764$	−16.3654	+	36.7572i	−0.592078	+	1.32983i
$765$		0			0
$766$	−2.02232	+	9.51427i	−0.0730694	+	0.343765i
$767$	5.78423	+	14.3165i	0.208856	+	0.516938i
$768$		0			0
$769$	−21.4421	−	3.78082i	−0.773221	−	0.136340i	−0.226903	−	0.973917i	$-0.572860\pi$
$769$	−21.4421	−	3.78082i	−0.773221	−	0.136340i	−0.546318	+	0.837578i	$0.683971\pi$
$770$	−1.67993	−	9.11827i	−0.0605406	−	0.328600i
$771$		0			0
$772$	3.14730	+	45.0085i	0.113274	+	1.61989i
$773$	−38.6493	+	34.8000i	−1.39012	+	1.25167i	−0.458273	+	0.888811i	$0.651532\pi$
$773$	−38.6493	+	34.8000i	−1.39012	+	1.25167i	−0.931845	+	0.362857i	$0.881801\pi$
$774$		0			0
$775$	−20.1778	−	8.98376i	−0.724810	−	0.322706i
$776$	60.3500	−	17.3051i	2.16644	−	0.621216i
$777$		0			0
$778$	3.68866	+	5.90310i	0.132245	+	0.211636i
$779$	−1.77089	+	6.17584i	−0.0634489	+	0.221273i
$780$		0			0
$781$	−27.8873	−	24.7256i	−0.997887	−	0.884752i
$782$		−	5.64701i		−	0.201937i
$783$		0			0
$784$	13.9986	−	43.0833i	0.499950	−	1.53869i
$785$	−1.26271	−	2.37482i	−0.0450682	−	0.0847609i
$786$		0			0
$787$	−27.8041	−	18.7541i	−0.991108	−	0.668511i	−0.0472574	−	0.998883i	$-0.515048\pi$
$787$	−27.8041	−	18.7541i	−0.991108	−	0.668511i	−0.943851	+	0.330372i	$0.892826\pi$
$788$	34.7001	−	85.8856i	1.23614	−	3.05955i
$789$		0			0
$790$	−1.07314	−	1.59099i	−0.0381805	−	0.0566049i
$791$	−4.74253	−	8.21430i	−0.168625	−	0.292067i
$792$		0			0
$793$	3.70867	−	6.42361i	0.131699	−	0.228109i
$794$	−55.2146	+	3.86098i	−1.95949	+	0.137021i
$795$		0			0
$796$	−5.61331	+	0.788899i	−0.198959	+	0.0279618i
$797$	35.0878	−	17.1134i	1.24287	−	0.606189i	0.304730	−	0.952439i	$-0.401434\pi$
$797$	35.0878	−	17.1134i	1.24287	−	0.606189i	0.938142	+	0.346250i	$0.112545\pi$
$798$		0			0
$799$	1.90626	−	3.05065i	0.0674386	−	0.107924i
$800$	−41.9702	−	46.6127i	−1.48387	−	1.64801i
$801$		0			0
$802$	58.3686	−	33.6991i	2.06107	−	1.18996i
$803$	0.408194	+	53.2733i	0.0144049	+	1.87997i
$804$		0			0
$805$	−4.72312	+	1.17760i	−0.166468	+	0.0415051i
$806$	−16.4590	+	0.574761i	−0.579743	+	0.0202451i
$807$		0			0
$808$	−8.28246	−	7.99828i	−0.291376	−	0.281378i
$809$	−2.83436	+	2.05928i	−0.0996507	+	0.0724004i	−0.636495	−	0.771281i	$-0.719616\pi$
$809$	−2.83436	+	2.05928i	−0.0996507	+	0.0724004i	0.536844	+	0.843681i	$0.319616\pi$
$810$		0			0
$811$	9.72074	+	3.15846i	0.341342	+	0.110909i	0.474671	−	0.880163i	$-0.342567\pi$
$811$	9.72074	+	3.15846i	0.341342	+	0.110909i	−0.133330	+	0.991072i	$0.542567\pi$
$812$	−79.0874	−	38.5735i	−2.77542	−	1.35366i
$813$		0			0
$814$	63.1075	−	4.89908i	2.21192	−	0.171713i
$815$	0.321506	−	0.383156i	0.0112619	−	0.0134214i
$816$		0			0
$817$	2.45158	−	3.13787i	0.0857698	−	0.109780i
$818$	−56.5845	−	50.9489i	−1.97843	−	1.78139i
$819$		0			0
$820$	−29.0254	+	3.05070i	−1.01361	+	0.106535i
$821$	−8.02414	−	5.01404i	−0.280045	−	0.174991i	0.382624	−	0.923904i	$-0.375021\pi$
$821$	−8.02414	−	5.01404i	−0.280045	−	0.174991i	−0.662668	+	0.748913i	$0.730576\pi$
$822$		0			0
$823$	−11.5290	+	11.1335i	−0.401877	+	0.388088i	−0.867945	−	0.496661i	$-0.834559\pi$
$823$	−11.5290	+	11.1335i	−0.401877	+	0.388088i	0.466068	+	0.884749i	$0.345670\pi$
$824$	−8.07650	+	45.8041i	−0.281358	+	1.59566i
$825$		0			0
$826$	−41.3309	+	34.6808i	−1.43809	+	1.20670i
$827$	−20.6736	+	9.20447i	−0.718890	+	0.320071i	−0.733375	−	0.679824i	$-0.762056\pi$
$827$	−20.6736	+	9.20447i	−0.718890	+	0.320071i	0.0144845	+	0.999895i	$0.495389\pi$
$828$		0			0
$829$	−9.49949	+	10.5503i	−0.329931	+	0.366426i	−0.885172	−	0.465264i	$-0.845959\pi$
$829$	−9.49949	+	10.5503i	−0.329931	+	0.366426i	0.555241	+	0.831690i	$0.312626\pi$
$830$	7.18373	+	25.0527i	0.249351	+	0.869590i
$831$		0			0
$832$	−16.4409	−	6.64257i	−0.569987	−	0.230290i
$833$	−0.0654259	−	1.87355i	−0.00226687	−	0.0649147i
$834$		0			0
$835$	4.67770	−	0.824805i	0.161879	−	0.0285436i
$836$	11.3091	−	0.481706i	0.391134	−	0.0166601i
$837$		0			0
$838$	−25.9873	+	35.7684i	−0.897716	+	1.23560i
$839$	−0.192329	+	1.36849i	−0.00663994	+	0.0472456i	−0.993306	−	0.115511i	$-0.963150\pi$
$839$	−0.192329	+	1.36849i	−0.00663994	+	0.0472456i	0.986666	+	0.162756i	$0.0520384\pi$
$840$		0			0
$841$	42.1781	−	62.5317i	1.45442	−	2.15626i
$842$	−85.6430	−	5.98874i	−2.95145	−	0.206386i
$843$		0			0
$844$	46.7769	+	36.5462i	1.61013	+	1.25797i
$845$	−6.91823	−	0.727135i	−0.237994	−	0.0250142i
$846$		0			0
$847$	2.33918	−	18.7215i	0.0803751	−	0.643277i
$848$	−47.9476	−	57.1417i	−1.64653	−	1.96225i
$849$		0			0
$850$	−4.99469	−	2.65572i	−0.171316	−	0.0910905i
$851$	−4.62492	−	32.9080i	−0.158540	−	1.12807i
$852$		0			0
$853$	−25.9349	−	6.46631i	−0.887995	−	0.221402i	−0.228890	−	0.973452i	$-0.573510\pi$
$853$	−25.9349	−	6.46631i	−0.887995	−	0.221402i	−0.659106	+	0.752050i	$0.729065\pi$
$854$	25.3515	+	5.38863i	0.867511	+	0.184395i
$855$		0			0
$856$	−9.09627	+	86.5452i	−0.310904	+	2.95805i
$857$	−15.8178	−	5.75720i	−0.540325	−	0.196662i	0.0574176	−	0.998350i	$-0.481713\pi$
$857$	−15.8178	−	5.75720i	−0.540325	−	0.196662i	−0.597743	+	0.801688i	$0.703936\pi$
$858$		0			0
$859$	−14.7210	−	12.3524i	−0.502275	−	0.421459i	0.356126	−	0.934438i	$-0.384097\pi$
$859$	−14.7210	−	12.3524i	−0.502275	−	0.421459i	−0.858401	+	0.512979i	$0.828542\pi$
$860$	17.3882	+	4.98599i	0.592933	+	0.170021i
$861$		0			0
$862$	−22.2396	+	11.8250i	−0.757484	+	0.402761i
$863$	−27.5578	−	37.9300i	−0.938078	−	1.29115i	−0.956624	−	0.291325i	$-0.905904\pi$
$863$	−27.5578	−	37.9300i	−0.938078	−	1.29115i	0.0185466	−	0.999828i	$-0.494096\pi$
$864$		0			0
$865$	−1.27578	+	0.414527i	−0.0433779	+	0.0140943i
$866$	60.2298	+	8.46474i	2.04669	+	0.287644i
$867$		0			0
$868$	−14.0749	−	38.6704i	−0.477733	−	1.31256i
$869$	−1.10513	−	3.74550i	−0.0374890	−	0.127057i
$870$		0			0
$871$	−2.85480	+	1.92559i	−0.0967313	+	0.0652461i
$872$	−13.5200	−	63.6068i	−0.457846	−	2.15400i
$873$		0			0
$874$	−0.868653	−	8.26468i	−0.0293826	−	0.279557i
$875$	−2.45589	+	9.85004i	−0.0830243	+	0.332992i
$876$		0			0
$877$	−0.876208	+	1.64791i	−0.0295875	+	0.0556459i	−0.897303	−	0.441415i	$-0.854477\pi$
$877$	−0.876208	+	1.64791i	−0.0295875	+	0.0556459i	0.867715	+	0.497061i	$0.165588\pi$
$878$	−10.2926	−	10.6583i	−0.347360	−	0.359702i
$879$		0			0
$880$	9.42233	+	20.7339i	0.317627	+	0.698939i
$881$	44.4271	+	25.6500i	1.49679	+	0.864171i	0.999993	−	0.00369717i	$-0.00117685\pi$
$881$	44.4271	+	25.6500i	1.49679	+	0.864171i	0.496795	+	0.867868i	$0.334510\pi$
$882$		0			0
$883$	9.86183	−	2.09620i	0.331877	−	0.0705427i	−0.0389595	−	0.999241i	$-0.512404\pi$
$883$	9.86183	−	2.09620i	0.331877	−	0.0705427i	0.370837	+	0.928698i	$0.379071\pi$
$884$	−3.01444	−	0.105266i	−0.101386	−	0.00354049i
$885$		0			0
$886$	2.10951	−	30.1674i	0.0708704	−	1.01349i
$887$	−32.1134	−	41.1033i	−1.07826	−	1.38011i	−0.919634	−	0.392776i	$-0.871515\pi$
$887$	−32.1134	−	41.1033i	−1.07826	−	1.38011i	−0.158629	−	0.987338i	$-0.550708\pi$
$888$		0			0
$889$	10.7291	−	21.9978i	0.359841	−	0.737784i
$890$	−21.2288			−0.711591
$891$		0			0
$892$	135.752			4.54533
$893$	2.32064	−	4.75801i	0.0776571	−	0.159221i
$894$		0			0
$895$	0.778033	+	0.995836i	0.0260068	+	0.0332871i
$896$	1.07451	−	15.3662i	0.0358970	−	0.513350i
$897$		0			0
$898$	−35.6453	−	1.24476i	−1.18950	−	0.0415382i
$899$	47.7708	−	10.1540i	1.59325	−	0.338655i
$900$		0			0
$901$	−2.67336	−	1.54347i	−0.0890626	−	0.0514203i
$902$	−81.3638	−	16.6439i	−2.70912	−	0.554180i
$903$		0			0
$904$	30.7418	+	31.8341i	1.02246	+	1.05878i
$905$	−0.280048	+	0.526694i	−0.00930911	+	0.0175079i
$906$		0			0
$907$	3.78945	−	15.1986i	0.125826	−	0.504662i	−0.873998	−	0.485929i	$-0.838481\pi$
$907$	3.78945	−	15.1986i	0.125826	−	0.504662i	0.999825	−	0.0187330i	$-0.00596325\pi$
$908$	−6.51282	−	61.9653i	−0.216135	−	2.05639i
$909$		0			0
$910$	0.755929	+	3.55637i	0.0250588	+	0.117892i
$911$	−32.7721	+	22.1051i	−1.08579	+	0.732374i	−0.965510	−	0.260366i	$-0.916157\pi$
$911$	−32.7721	+	22.1051i	−1.08579	+	0.732374i	−0.120280	+	0.992740i	$0.538379\pi$
$912$		0			0
$913$	−1.44471	+	53.0143i	−0.0478128	+	1.75452i
$914$	−2.24596	−	6.17073i	−0.0742899	−	0.204110i
$915$		0			0
$916$	94.8985	+	13.3371i	3.13554	+	0.440671i
$917$	24.6855	−	8.02082i	0.815188	−	0.264871i
$918$		0			0
$919$	−12.2576	−	16.8711i	−0.404340	−	0.556527i	0.557486	−	0.830186i	$-0.311766\pi$
$919$	−12.2576	−	16.8711i	−0.404340	−	0.556527i	−0.961827	+	0.273659i	$0.911766\pi$
$920$	20.0529	−	10.6623i	0.661125	−	0.351526i
$921$		0			0
$922$	−32.9994	−	9.46243i	−1.08678	−	0.311628i
$923$	11.1958	+	9.39440i	0.368514	+	0.309220i
$924$		0			0
$925$	−31.2816	−	11.3856i	−1.02853	−	0.374356i
$926$	−2.91496	+	27.7340i	−0.0957916	+	0.911396i
$927$		0			0
$928$	135.659	+	28.8352i	4.45323	+	0.946562i
$929$	50.7865	+	12.6625i	1.66625	+	0.415443i	0.957134	−	0.289646i	$-0.0935376\pi$
$929$	50.7865	+	12.6625i	1.66625	+	0.415443i	0.709118	+	0.705089i	$0.249093\pi$
$930$		0			0
$931$	−0.383953	−	2.73197i	−0.0125836	−	0.0895367i
$932$	24.7318	+	13.1501i	0.810118	+	0.430747i
$933$		0			0
$934$	23.4260	+	27.9181i	0.766524	+	0.913507i
$935$	0.659882	+	0.672932i	0.0215804	+	0.0220072i
$936$		0			0
$937$	−39.6658	−	4.16905i	−1.29583	−	0.136197i	−0.568611	−	0.822606i	$-0.692519\pi$
$937$	−39.6658	−	4.16905i	−1.29583	−	0.136197i	−0.727215	+	0.686409i	$0.759186\pi$
$938$	−9.48168	−	7.40790i	−0.309588	−	0.241877i
$939$		0			0
$940$	23.9892	+	1.67749i	0.782441	+	0.0547136i
$941$	23.5683	−	34.9415i	0.768306	−	1.13906i	−0.218291	−	0.975884i	$-0.570048\pi$
$941$	23.5683	−	34.9415i	0.768306	−	1.13906i	0.986597	−	0.163176i	$-0.0521739\pi$
$942$		0			0
$943$	−6.06809	+	43.1767i	−0.197604	+	1.40603i
$944$	77.8980	−	107.217i	2.53536	−	3.48963i
$945$		0			0
$946$	42.8925	+	28.4557i	1.39456	+	0.925173i
$947$	−32.7602	+	5.77651i	−1.06456	+	0.187711i	−0.678381	−	0.734711i	$-0.737318\pi$
$947$	−32.7602	+	5.77651i	−1.06456	+	0.187711i	−0.386183	+	0.922422i	$0.626207\pi$
$948$		0			0
$949$	−0.729093	−	20.8785i	−0.0236674	−	0.677744i
$950$	−7.71849	−	3.11847i	−0.250421	−	0.101177i
$951$		0			0
$952$	−1.74776	−	6.09515i	−0.0566451	−	0.197545i
$953$	−16.3034	+	18.1067i	−0.528119	+	0.586535i	−0.946890	−	0.321556i	$-0.895794\pi$
$953$	−16.3034	+	18.1067i	−0.528119	+	0.586535i	0.418772	+	0.908091i	$0.362461\pi$
$954$		0			0
$955$	−4.50389	+	2.00526i	−0.145743	+	0.0648887i
$956$	24.2642	−	20.3601i	0.784760	−	0.658492i
$957$		0			0
$958$	2.39835	−	13.6017i	0.0774872	−	0.439452i
$959$	−25.4163	+	24.5442i	−0.820736	+	0.792575i
$960$		0			0
$961$	−6.91969	−	4.32391i	−0.223216	−	0.139481i
$962$	−24.6855	+	2.59455i	−0.795891	+	0.0836515i
$963$		0			0
$964$	15.1603	+	13.6504i	0.488279	+	0.439648i
$965$	−3.40362	+	4.35644i	−0.109566	+	0.140239i
$966$		0			0
$967$	−27.4619	+	32.7278i	−0.883115	+	1.05246i	0.115136	+	0.993350i	$0.463269\pi$
$967$	−27.4619	+	32.7278i	−0.883115	+	1.05246i	−0.998252	+	0.0591061i	$0.981175\pi$
$968$	10.5419	+	87.3946i	0.338829	+	2.80897i
$969$		0			0
$970$	11.4927	+	5.60534i	0.369007	+	0.179977i
$971$	−30.4399	−	9.89052i	−0.976863	−	0.317402i	−0.223280	−	0.974754i	$-0.571676\pi$
$971$	−30.4399	−	9.89052i	−0.976863	−	0.317402i	−0.753583	+	0.657352i	$0.771676\pi$
$972$		0			0
$973$	0.0291624	−	0.0211877i	0.000934902	−	0.000679246i
$974$	−37.3361	−	36.0550i	−1.19633	−	1.15528i
$975$		0			0
$976$	−63.6241	+	2.22180i	−2.03656	+	0.0711181i
$977$	−32.9925	+	8.22596i	−1.05552	+	0.263172i	−0.730768	−	0.682626i	$-0.760838\pi$
$977$	−32.9925	+	8.22596i	−1.05552	+	0.263172i	−0.324756	+	0.945798i	$0.605282\pi$
$978$		0			0
$979$	−41.1852	−	13.0339i	−1.31628	−	0.416564i
$980$	10.8533	−	6.26618i	0.346697	−	0.200166i
$981$		0			0
$982$	5.73196	+	6.36599i	0.182914	+	0.203147i
$983$	−18.8007	+	30.0874i	−0.599650	+	0.959640i	0.399431	+	0.916763i	$0.369208\pi$
$983$	−18.8007	+	30.0874i	−0.599650	+	0.959640i	−0.999080	+	0.0428768i	$0.986348\pi$
$984$		0			0
$985$	10.2014	−	4.97556i	0.325044	−	0.158535i
$986$	12.3863	−	1.74077i	0.394459	−	0.0554375i
$987$		0			0
$988$	−4.42797	+	0.309634i	−0.140872	+	0.00985076i
$989$	13.5119	−	23.4032i	0.429652	−	0.744179i
$990$		0			0
$991$	24.1598	+	41.8460i	0.767461	+	1.32928i	0.938936	+	0.344093i	$0.111813\pi$
$991$	24.1598	+	41.8460i	0.767461	+	1.32928i	−0.171475	+	0.985189i	$0.554853\pi$
$992$	36.2704	+	53.7731i	1.15159	+	1.70730i
$993$		0			0
$994$	−19.1306	+	47.3499i	−0.606785	+	1.50185i
$995$	−0.575819	−	0.388395i	−0.0182547	−	0.0123129i
$996$		0			0
$997$	3.77724	+	7.10395i	0.119626	+	0.224984i	0.935565	−	0.353154i	$-0.114891\pi$
$997$	3.77724	+	7.10395i	0.119626	+	0.224984i	−0.815939	+	0.578138i	$0.803780\pi$
$998$	21.0196	−	64.6918i	0.665365	−	2.04778i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.bb.a.557.1		816
3.2	odd	2		297.2.x.a.95.34	yes	816
11.8	odd	10	inner	891.2.bb.a.800.1		816
27.2	odd	18	inner	891.2.bb.a.656.1		816
27.25	even	9		297.2.x.a.29.34	✓	816
33.8	even	10		297.2.x.a.41.34	yes	816
297.52	odd	90		297.2.x.a.272.34	yes	816
297.272	even	90	inner	891.2.bb.a.8.1		816

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.x.a.29.34	✓	816	27.25	even	9
297.2.x.a.41.34	yes	816	33.8	even	10
297.2.x.a.95.34	yes	816	3.2	odd	2
297.2.x.a.272.34	yes	816	297.52	odd	90
891.2.bb.a.8.1		816	297.272	even	90	inner
891.2.bb.a.557.1		816	1.1	even	1	trivial
891.2.bb.a.656.1		816	27.2	odd	18	inner
891.2.bb.a.800.1		816	11.8	odd	10	inner

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.bb (of order \(90\), degree \(24\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.16150 + 2.38143i) q^{2} +(-3.09081 - 3.95605i) q^{4} +(0.0429102 - 0.613644i) q^{5} +(-1.71414 - 0.0598591i) q^{7} +(7.82768 - 1.66383i) q^{8} +O(q^{10})\)	\(q+(-1.16150 + 2.38143i) q^{2} +(-3.09081 - 3.95605i) q^{4} +(0.0429102 - 0.613644i) q^{5} +(-1.71414 - 0.0598591i) q^{7} +(7.82768 - 1.66383i) q^{8} +(1.41151 + 0.814937i) q^{10} +(2.23807 + 2.44766i) q^{11} +(-0.903460 - 0.935560i) q^{13} +(2.13353 - 4.01258i) q^{14} +(-2.70054 + 10.8313i) q^{16} +(0.0482878 + 0.459428i) q^{17} +(0.141343 + 0.664968i) q^{19} +(-2.56024 + 1.72690i) q^{20} +(-8.42846 + 2.48687i) q^{22} +(1.57794 + 4.33534i) q^{23} +(4.57662 + 0.643202i) q^{25} +(3.27734 - 1.06487i) q^{26} +(5.06127 + 6.96624i) q^{28} +(-9.02279 + 4.79750i) q^{29} +(-4.59403 - 1.31732i) q^{31} +(-10.3966 - 8.72380i) q^{32} +(-1.15018 - 0.418632i) q^{34} +(-0.110286 + 1.04930i) q^{35} +(-7.04556 - 1.49758i) q^{37} +(-1.74775 - 0.435762i) q^{38} +(-0.685109 - 4.87481i) q^{40} +(8.34437 + 4.43678i) q^{41} +(-3.76508 - 4.48705i) q^{43} +(2.76560 - 16.4192i) q^{44} +(-12.1571 - 1.27776i) q^{46} +(-6.13622 - 4.79414i) q^{47} +(-4.04826 - 0.283082i) q^{49} +(-6.84750 + 10.1518i) q^{50} +(-0.908705 + 6.46577i) q^{52} +(-3.92774 + 5.40607i) q^{53} +(1.59803 - 1.26835i) q^{55} +(-13.5173 + 2.38347i) q^{56} +(-0.944938 - 27.0595i) q^{58} +(-11.0077 - 4.44742i) q^{59} +(1.57199 + 5.48217i) q^{61} +(8.47308 - 9.41031i) q^{62} +(12.4553 - 5.54545i) q^{64} +(-0.612868 + 0.514258i) q^{65} +(0.459764 - 2.60745i) q^{67} +(1.66827 - 1.61103i) q^{68} +(-2.37075 - 1.48141i) q^{70} +(-11.1758 + 1.17462i) q^{71} +(11.9371 + 10.7482i) q^{73} +(11.7498 - 15.0391i) q^{74} +(2.19378 - 2.61445i) q^{76} +(-3.68986 - 4.32959i) q^{77} +(-1.05828 - 0.516157i) q^{79} +(6.53066 + 2.12194i) q^{80} +(-20.2579 + 14.7182i) q^{82} +(11.5025 + 11.1078i) q^{83} +(0.283997 - 0.00991741i) q^{85} +(15.0588 - 3.75457i) q^{86} +(21.5914 + 15.4357i) q^{88} +(-11.2798 + 6.51241i) q^{89} +(1.49265 + 1.65776i) q^{91} +(12.2738 - 19.6421i) q^{92} +(18.5442 - 9.04459i) q^{94} +(0.414119 - 0.0582006i) q^{95} +(7.82613 - 0.547257i) q^{97} +(5.37620 - 9.31185i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 816 q + 30 q^{2} - 18 q^{4} + 21 q^{5} - 30 q^{7} + 45 q^{8}+O(q^{10}) \) 816 * q + 30 * q^2 - 18 * q^4 + 21 * q^5 - 30 * q^7 + 45 * q^8	\( 816 q + 30 q^{2} - 18 q^{4} + 21 q^{5} - 30 q^{7} + 45 q^{8} + 33 q^{11} - 30 q^{13} + 18 q^{14} - 30 q^{16} + 45 q^{17} - 15 q^{19} + 60 q^{20} - 15 q^{22} + 84 q^{23} - 27 q^{25} - 60 q^{28} - 60 q^{29} - 9 q^{31} - 42 q^{34} + 45 q^{35} - 9 q^{37} + 18 q^{38} - 90 q^{40} + 30 q^{41} + 108 q^{44} - 15 q^{46} + 6 q^{47} - 18 q^{49} + 105 q^{50} - 30 q^{52} - 48 q^{55} - 54 q^{56} - 18 q^{58} - 81 q^{59} - 30 q^{61} + 45 q^{62} + 51 q^{64} + 6 q^{67} + 225 q^{68} - 93 q^{70} + 27 q^{71} - 15 q^{73} + 30 q^{74} + 141 q^{77} - 30 q^{79} - 36 q^{82} - 15 q^{83} - 30 q^{85} - 93 q^{86} - 108 q^{88} - 54 q^{89} - 9 q^{91} - 276 q^{92} - 30 q^{94} - 90 q^{95} - 81 q^{97}+O(q^{100}) \) 816 * q + 30 * q^2 - 18 * q^4 + 21 * q^5 - 30 * q^7 + 45 * q^8 + 33 * q^11 - 30 * q^13 + 18 * q^14 - 30 * q^16 + 45 * q^17 - 15 * q^19 + 60 * q^20 - 15 * q^22 + 84 * q^23 - 27 * q^25 - 60 * q^28 - 60 * q^29 - 9 * q^31 - 42 * q^34 + 45 * q^35 - 9 * q^37 + 18 * q^38 - 90 * q^40 + 30 * q^41 + 108 * q^44 - 15 * q^46 + 6 * q^47 - 18 * q^49 + 105 * q^50 - 30 * q^52 - 48 * q^55 - 54 * q^56 - 18 * q^58 - 81 * q^59 - 30 * q^61 + 45 * q^62 + 51 * q^64 + 6 * q^67 + 225 * q^68 - 93 * q^70 + 27 * q^71 - 15 * q^73 + 30 * q^74 + 141 * q^77 - 30 * q^79 - 36 * q^82 - 15 * q^83 - 30 * q^85 - 93 * q^86 - 108 * q^88 - 54 * q^89 - 9 * q^91 - 276 * q^92 - 30 * q^94 - 90 * q^95 - 81 * q^97

Introduction

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