LMFDB - Embedded newform 171.2.u.c.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(28,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("171.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.u (of order $9$, degree $6$, 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:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			73.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	171.73
Dual form			171.2.u.c.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93969 + 1.62760i) q^{2} +(0.766044 + 4.34445i) q^{4} +(0.233956 - 1.32683i) q^{5} +(-0.766044 - 1.32683i) q^{7} +(-3.05303 + 5.28801i) q^{8} +O(q^{10})$	\(q+(1.93969 + 1.62760i) q^{2} +(0.766044 + 4.34445i) q^{4} +(0.233956 - 1.32683i) q^{5} +(-0.766044 - 1.32683i) q^{7} +(-3.05303 + 5.28801i) q^{8} +(2.61334 - 2.19285i) q^{10} +(-0.592396 + 1.02606i) q^{11} +(-2.55303 - 0.929228i) q^{13} +(0.673648 - 3.82045i) q^{14} +(-6.23783 + 2.27038i) q^{16} +(-2.97178 - 2.49362i) q^{17} +(0.819078 - 4.28125i) q^{19} +5.94356 q^{20} +(-2.81908 + 1.02606i) q^{22} +(0.879385 + 4.98724i) q^{23} +(2.99273 + 1.08926i) q^{25} +(-3.43969 - 5.95772i) q^{26} +(5.17752 - 4.34445i) q^{28} +(3.56418 - 2.99070i) q^{29} +(1.91875 + 3.32337i) q^{31} +(-4.31908 - 1.57202i) q^{32} +(-1.70574 - 9.67372i) q^{34} +(-1.93969 + 0.705990i) q^{35} -4.10607 q^{37} +(8.55690 - 6.97118i) q^{38} +(6.30200 + 5.28801i) q^{40} +(-9.38326 + 3.41523i) q^{41} +(-1.51114 + 8.57013i) q^{43} +(-4.91147 - 1.78763i) q^{44} +(-6.41147 + 11.1050i) q^{46} +(-0.439693 + 0.368946i) q^{47} +(2.32635 - 4.02936i) q^{49} +(4.03209 + 6.98378i) q^{50} +(2.08125 - 11.8034i) q^{52} +(-0.511144 - 2.89884i) q^{53} +(1.22281 + 1.02606i) q^{55} +9.35504 q^{56} +11.7811 q^{58} +(3.01501 + 2.52990i) q^{59} +(-0.784463 - 4.44891i) q^{61} +(-1.68732 + 9.56926i) q^{62} +(0.819078 + 1.41868i) q^{64} +(-1.83022 + 3.17004i) q^{65} +(-2.97771 + 2.49860i) q^{67} +(8.55690 - 14.8210i) q^{68} +(-4.91147 - 1.78763i) q^{70} +(1.20439 - 6.83045i) q^{71} +(-5.75877 + 2.09602i) q^{73} +(-7.96451 - 6.68302i) q^{74} +(19.2271 + 0.278817i) q^{76} +1.81521 q^{77} +(-9.21688 + 3.35467i) q^{79} +(1.55303 + 8.80769i) q^{80} +(-23.7592 - 8.64766i) q^{82} +(6.15910 + 10.6679i) q^{83} +(-4.00387 + 3.35965i) q^{85} +(-16.8799 + 14.1639i) q^{86} +(-3.61721 - 6.26519i) q^{88} +(-2.27972 - 0.829748i) q^{89} +(0.722811 + 4.09927i) q^{91} +(-20.9932 + 7.64090i) q^{92} -1.45336 q^{94} +(-5.48886 - 2.08840i) q^{95} +(5.64543 + 4.73708i) q^{97} +(11.0706 - 4.02936i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{5} - 6 q^{8}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^5 - 6 * q^8	$ 6 q + 6 q^{2} + 6 q^{5} - 6 q^{8} + 9 q^{10} - 3 q^{13} + 3 q^{14} - 18 q^{16} - 3 q^{17} - 12 q^{19} + 6 q^{20} - 6 q^{23} - 15 q^{26} + 6 q^{28} + 3 q^{29} + 9 q^{31} - 9 q^{32} - 6 q^{35} + 15 q^{38} - 21 q^{41} - 3 q^{43} - 9 q^{44} - 18 q^{46} + 3 q^{47} + 15 q^{49} + 15 q^{50} + 15 q^{52} + 3 q^{53} + 18 q^{55} + 6 q^{56} + 36 q^{58} - 12 q^{59} - 12 q^{61} + 12 q^{62} - 12 q^{64} + 12 q^{65} - 30 q^{67} + 15 q^{68} - 9 q^{70} + 6 q^{71} - 12 q^{73} - 15 q^{74} + 36 q^{76} + 18 q^{77} - 39 q^{79} - 3 q^{80} - 54 q^{82} - 24 q^{86} + 9 q^{88} + 12 q^{89} + 15 q^{91} - 42 q^{92} + 18 q^{94} - 39 q^{95} + 18 q^{97} + 9 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^5 - 6 * q^8 + 9 * q^10 - 3 * q^13 + 3 * q^14 - 18 * q^16 - 3 * q^17 - 12 * q^19 + 6 * q^20 - 6 * q^23 - 15 * q^26 + 6 * q^28 + 3 * q^29 + 9 * q^31 - 9 * q^32 - 6 * q^35 + 15 * q^38 - 21 * q^41 - 3 * q^43 - 9 * q^44 - 18 * q^46 + 3 * q^47 + 15 * q^49 + 15 * q^50 + 15 * q^52 + 3 * q^53 + 18 * q^55 + 6 * q^56 + 36 * q^58 - 12 * q^59 - 12 * q^61 + 12 * q^62 - 12 * q^64 + 12 * q^65 - 30 * q^67 + 15 * q^68 - 9 * q^70 + 6 * q^71 - 12 * q^73 - 15 * q^74 + 36 * q^76 + 18 * q^77 - 39 * q^79 - 3 * q^80 - 54 * q^82 - 24 * q^86 + 9 * q^88 + 12 * q^89 + 15 * q^91 - 42 * q^92 + 18 * q^94 - 39 * q^95 + 18 * q^97 + 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	1.93969	+	1.62760i	1.37157	+	1.15088i	0.972216	+	0.234087i	$0.0752101\pi$
$2$	1.93969	+	1.62760i	1.37157	+	1.15088i	0.399354	+	0.916797i	$0.369234\pi$
$3$		0			0
$3$		0			0
$4$	0.766044	+	4.34445i	0.383022	+	2.17223i
$5$	0.233956	−	1.32683i	0.104628	−	0.593375i	−0.886740	−	0.462268i	$-0.847036\pi$
$5$	0.233956	−	1.32683i	0.104628	−	0.593375i	0.991368	−	0.131107i	$-0.0418532\pi$
$6$		0			0
$7$	−0.766044	−	1.32683i	−0.289538	−	0.501494i	0.684162	−	0.729330i	$-0.260168\pi$
$7$	−0.766044	−	1.32683i	−0.289538	−	0.501494i	−0.973699	+	0.227836i	$0.926835\pi$
$8$	−3.05303	+	5.28801i	−1.07941	+	1.86959i
$9$		0			0
$10$	2.61334	−	2.19285i	0.826411	−	0.693441i
$11$	−0.592396	+	1.02606i	−0.178614	+	0.309369i	−0.941406	−	0.337275i	$-0.890495\pi$
$11$	−0.592396	+	1.02606i	−0.178614	+	0.309369i	0.762792	+	0.646644i	$0.223828\pi$
$12$		0			0
$13$	−2.55303	−	0.929228i	−0.708084	−	0.257722i	−0.0372256	−	0.999307i	$-0.511852\pi$
$13$	−2.55303	−	0.929228i	−0.708084	−	0.257722i	−0.670859	+	0.741585i	$0.734074\pi$
$14$	0.673648	−	3.82045i	0.180040	−	1.02106i
$15$		0			0
$16$	−6.23783	+	2.27038i	−1.55946	+	0.567596i
$17$	−2.97178	−	2.49362i	−0.720763	−	0.604792i	0.206833	−	0.978376i	$-0.433684\pi$
$17$	−2.97178	−	2.49362i	−0.720763	−	0.604792i	−0.927596	+	0.373584i	$0.878129\pi$
$18$		0			0
$19$	0.819078	−	4.28125i	0.187909	−	0.982186i
$19$	0.819078	−	4.28125i	0.187909	−	0.982186i
$20$	5.94356			1.32902
$21$		0			0
$22$	−2.81908	+	1.02606i	−0.601029	+	0.218757i
$23$	0.879385	+	4.98724i	0.183364	+	1.03991i	0.928039	+	0.372484i	$0.121494\pi$
$23$	0.879385	+	4.98724i	0.183364	+	1.03991i	−0.744674	+	0.667428i	$0.767395\pi$
$24$		0			0
$25$	2.99273	+	1.08926i	0.598545	+	0.217853i
$26$	−3.43969	−	5.95772i	−0.674579	−	1.16841i
$27$		0			0
$28$	5.17752	−	4.34445i	0.978459	−	0.821025i
$29$	3.56418	−	2.99070i	0.661851	−	0.555359i	−0.248790	−	0.968557i	$-0.580033\pi$
$29$	3.56418	−	2.99070i	0.661851	−	0.555359i	0.910641	+	0.413198i	$0.135588\pi$
$30$		0			0
$31$	1.91875	+	3.32337i	0.344617	+	0.596895i	0.985284	−	0.170924i	$-0.0546753\pi$
$31$	1.91875	+	3.32337i	0.344617	+	0.596895i	−0.640667	+	0.767819i	$0.721342\pi$
$32$	−4.31908	−	1.57202i	−0.763512	−	0.277896i
$33$		0			0
$34$	−1.70574	−	9.67372i	−0.292531	−	1.65903i
$35$	−1.93969	+	0.705990i	−0.327868	+	0.119334i
$36$		0			0
$37$	−4.10607			−0.675033			−0.337517	−	0.941320i	$-0.609587\pi$
$37$	−4.10607			−0.675033			−0.337517	+	0.941320i	$0.609587\pi$
$38$	8.55690	−	6.97118i	1.38811	−	1.13088i
$39$		0			0
$40$	6.30200	+	5.28801i	0.996434	+	0.836108i
$41$	−9.38326	+	3.41523i	−1.46542	+	0.533369i	−0.946852	−	0.321669i	$-0.895756\pi$
$41$	−9.38326	+	3.41523i	−1.46542	+	0.533369i	−0.518566	+	0.855038i	$0.673534\pi$
$42$		0			0
$43$	−1.51114	+	8.57013i	−0.230447	+	1.30693i	0.621545	+	0.783378i	$0.286505\pi$
$43$	−1.51114	+	8.57013i	−0.230447	+	1.30693i	−0.851993	+	0.523554i	$0.824606\pi$
$44$	−4.91147	−	1.78763i	−0.740433	−	0.269495i
$45$		0			0
$46$	−6.41147	+	11.1050i	−0.945320	+	1.63734i
$47$	−0.439693	+	0.368946i	−0.0641358	+	0.0538163i	−0.674292	−	0.738465i	$-0.735551\pi$
$47$	−0.439693	+	0.368946i	−0.0641358	+	0.0538163i	0.610156	+	0.792281i	$0.291107\pi$
$48$		0			0
$49$	2.32635	−	4.02936i	0.332336	−	0.575623i
$50$	4.03209	+	6.98378i	0.570223	+	0.987656i
$51$		0			0
$52$	2.08125	−	11.8034i	0.288618	−	1.63683i
$53$	−0.511144	−	2.89884i	−0.0702111	−	0.398187i	−0.999579	−	0.0290308i	$-0.990758\pi$
$53$	−0.511144	−	2.89884i	−0.0702111	−	0.398187i	0.929367	−	0.369156i	$-0.120353\pi$
$54$		0			0
$55$	1.22281	+	1.02606i	0.164884	+	0.138354i
$56$	9.35504			1.25012
$57$		0			0
$58$	11.7811			1.54693
$59$	3.01501	+	2.52990i	0.392521	+	0.329365i	0.817595	−	0.575794i	$-0.195307\pi$
$59$	3.01501	+	2.52990i	0.392521	+	0.329365i	−0.425073	+	0.905159i	$0.639752\pi$
$60$		0			0
$61$	−0.784463	−	4.44891i	−0.100440	−	0.569624i	−0.992944	−	0.118585i	$-0.962164\pi$
$61$	−0.784463	−	4.44891i	−0.100440	−	0.569624i	0.892504	−	0.451040i	$-0.148947\pi$
$62$	−1.68732	+	9.56926i	−0.214290	+	1.21530i
$63$		0			0
$64$	0.819078	+	1.41868i	0.102385	+	0.177336i
$65$	−1.83022	+	3.17004i	−0.227011	+	0.393195i
$66$		0			0
$67$	−2.97771	+	2.49860i	−0.363785	+	0.305252i	−0.806297	−	0.591510i	$-0.798532\pi$
$67$	−2.97771	+	2.49860i	−0.363785	+	0.305252i	0.442512	+	0.896763i	$0.354087\pi$
$68$	8.55690	−	14.8210i	1.03768	−	1.79731i
$69$		0			0
$70$	−4.91147	−	1.78763i	−0.587033	−	0.213663i
$71$	1.20439	−	6.83045i	0.142935	−	0.810625i	−0.826067	−	0.563572i	$-0.809427\pi$
$71$	1.20439	−	6.83045i	0.142935	−	0.810625i	0.969002	−	0.247053i	$-0.0794622\pi$
$72$		0			0
$73$	−5.75877	+	2.09602i	−0.674013	+	0.245321i	−0.656275	−	0.754522i	$-0.727869\pi$
$73$	−5.75877	+	2.09602i	−0.674013	+	0.245321i	−0.0177383	+	0.999843i	$0.505647\pi$
$74$	−7.96451	−	6.68302i	−0.925855	−	0.776885i
$75$		0			0
$76$	19.2271	+	0.278817i	2.20551	+	0.0319825i
$77$	1.81521			0.206862
$78$		0			0
$79$	−9.21688	+	3.35467i	−1.03698	+	0.377430i	−0.803735	−	0.594988i	$-0.797157\pi$
$79$	−9.21688	+	3.35467i	−1.03698	+	0.377430i	−0.233246	+	0.972418i	$0.574935\pi$
$80$	1.55303	+	8.80769i	0.173634	+	0.984730i
$81$		0			0
$82$	−23.7592	−	8.64766i	−2.62377	−	0.954974i
$83$	6.15910	+	10.6679i	0.676049	+	1.17095i	0.976161	+	0.217047i	$0.0696426\pi$
$83$	6.15910	+	10.6679i	0.676049	+	1.17095i	−0.300112	+	0.953904i	$0.597024\pi$
$84$		0			0
$85$	−4.00387	+	3.35965i	−0.434281	+	0.364405i
$86$	−16.8799	+	14.1639i	−1.82020	+	1.52733i
$87$		0			0
$88$	−3.61721	−	6.26519i	−0.385596	−	0.667872i
$89$	−2.27972	−	0.829748i	−0.241649	−	0.0879532i	0.218356	−	0.975869i	$-0.429930\pi$
$89$	−2.27972	−	0.829748i	−0.241649	−	0.0879532i	−0.460006	+	0.887916i	$0.652153\pi$
$90$		0			0
$91$	0.722811	+	4.09927i	0.0757712	+	0.429720i
$92$	−20.9932	+	7.64090i	−2.18869	+	0.796619i
$93$		0			0
$94$	−1.45336			−0.149903
$95$	−5.48886	−	2.08840i	−0.563145	−	0.214265i
$96$		0			0
$97$	5.64543	+	4.73708i	0.573207	+	0.480977i	0.882708	−	0.469922i	$-0.155718\pi$
$97$	5.64543	+	4.73708i	0.573207	+	0.480977i	−0.309502	+	0.950899i	$0.600162\pi$
$98$	11.0706	−	4.02936i	1.11830	−	0.407027i
$99$		0			0
$100$	−2.43969	+	13.8362i	−0.243969	+	1.38362i
$101$	2.03936	+	0.742267i	0.202924	+	0.0738584i	0.441483	−	0.897270i	$-0.354453\pi$
$101$	2.03936	+	0.742267i	0.202924	+	0.0738584i	−0.238559	+	0.971128i	$0.576675\pi$
$102$		0			0
$103$	6.23783	−	10.8042i	0.614631	−	1.06457i	−0.375818	−	0.926694i	$-0.622638\pi$
$103$	6.23783	−	10.8042i	0.614631	−	1.06457i	0.990449	−	0.137879i	$-0.0440285\pi$
$104$	12.7083	−	10.6635i	1.24615	−	1.04564i
$105$		0			0
$106$	3.72668	−	6.45480i	0.361967	−	0.626946i
$107$	−3.34002	−	5.78509i	−0.322892	−	0.559266i	0.658191	−	0.752851i	$-0.271322\pi$
$107$	−3.34002	−	5.78509i	−0.322892	−	0.559266i	−0.981083	+	0.193585i	$0.937988\pi$
$108$		0			0
$109$	1.64156	−	9.30975i	0.157233	−	0.891712i	−0.799483	−	0.600689i	$-0.794893\pi$
$109$	1.64156	−	9.30975i	0.157233	−	0.891712i	0.956716	−	0.291023i	$-0.0939957\pi$
$110$	0.701867	+	3.98048i	0.0669204	+	0.379524i
$111$		0			0
$112$	7.79086	+	6.53731i	0.736167	+	0.617717i
$113$	−1.31046			−0.123278			−0.0616388	−	0.998099i	$-0.519633\pi$
$113$	−1.31046			−0.123278			−0.0616388	+	0.998099i	$0.519633\pi$
$114$		0			0
$115$	6.82295			0.636243
$116$	15.7233	+	13.1934i	1.45987	+	1.22498i
$117$		0			0
$118$	1.73055	+	9.81445i	0.159310	+	0.903493i
$119$	−1.03209	+	5.85327i	−0.0946114	+	0.536568i
$120$		0			0
$121$	4.79813	+	8.31061i	0.436194	+	0.755510i
$122$	5.71941	−	9.90630i	0.517811	−	0.896875i
$123$		0			0
$124$	−12.9684	+	10.8818i	−1.16459	+	0.977211i
$125$	5.51367	−	9.54996i	0.493158	−	0.854174i
$126$		0			0
$127$	13.6284	+	4.96032i	1.20932	+	0.440157i	0.866468	−	0.499232i	$-0.166385\pi$
$127$	13.6284	+	4.96032i	1.20932	+	0.440157i	0.342853	+	0.939389i	$0.388607\pi$
$128$	−2.31655	+	13.1378i	−0.204756	+	1.16123i
$129$		0			0
$130$	−8.70961	+	3.17004i	−0.763883	+	0.278031i
$131$	15.1741	+	12.7326i	1.32577	+	1.11245i	0.985047	+	0.172288i	$0.0551159\pi$
$131$	15.1741	+	12.7326i	1.32577	+	1.11245i	0.340722	+	0.940164i	$0.389329\pi$
$132$		0			0
$133$	−6.30793	+	2.19285i	−0.546967	+	0.190144i
$134$	−9.84255			−0.850267
$135$		0			0
$136$	22.2592	−	8.10170i	1.90871	−	0.694715i
$137$	−1.77197	−	10.0494i	−0.151390	−	0.858575i	−0.962012	−	0.273006i	$-0.911982\pi$
$137$	−1.77197	−	10.0494i	−0.151390	−	0.858575i	0.810622	−	0.585569i	$-0.199129\pi$
$138$		0			0
$139$	1.56031	+	0.567905i	0.132344	+	0.0481691i	0.407343	−	0.913275i	$-0.366455\pi$
$139$	1.56031	+	0.567905i	0.132344	+	0.0481691i	−0.274999	+	0.961444i	$0.588678\pi$
$140$	−4.55303	−	7.88609i	−0.384802	−	0.666496i
$141$		0			0
$142$	13.4534	−	11.2887i	1.12898	−	0.947328i
$143$	2.46585	−	2.06910i	0.206205	−	0.173026i
$144$		0			0
$145$	−3.13429	−	5.42874i	−0.260288	−	0.450832i
$146$	−14.5817	−	5.30731i	−1.20679	−	0.439236i
$147$		0			0
$148$	−3.14543	−	17.8386i	−0.258553	−	1.46633i
$149$	10.5312	−	3.83305i	0.862750	−	0.314015i	0.127523	−	0.991836i	$-0.459297\pi$
$149$	10.5312	−	3.83305i	0.862750	−	0.314015i	0.735228	+	0.677820i	$0.237075\pi$
$150$		0			0
$151$	−11.0419			−0.898576			−0.449288	−	0.893387i	$-0.648322\pi$
$151$	−11.0419			−0.898576			−0.449288	+	0.893387i	$0.648322\pi$
$152$	20.1386	+	17.4021i	1.63346	+	1.41150i
$153$		0			0
$154$	3.52094	+	2.95442i	0.283726	+	0.238074i
$155$	4.85844	−	1.76833i	0.390239	−	0.142036i
$156$		0			0
$157$	1.90895	−	10.8262i	0.152351	−	0.864023i	−0.808817	−	0.588060i	$-0.799892\pi$
$157$	1.90895	−	10.8262i	0.152351	−	0.864023i	0.961168	−	0.275964i	$-0.0889969\pi$
$158$	−23.3380	−	8.49432i	−1.85667	−	0.675772i
$159$		0			0
$160$	−3.09627	+	5.36289i	−0.244781	+	0.423974i
$161$	5.94356	−	4.98724i	0.468418	−	0.393050i
$162$		0			0
$163$	3.16637	−	5.48432i	0.248010	−	0.429565i	−0.714964	−	0.699161i	$-0.753557\pi$
$163$	3.16637	−	5.48432i	0.248010	−	0.429565i	0.962973	+	0.269596i	$0.0868902\pi$
$164$	−22.0253	−	38.1489i	−1.71989	−	2.97893i
$165$		0			0
$166$	−5.41622	+	30.7169i	−0.420380	+	2.38410i
$167$	2.39259	+	13.5690i	0.185144	+	1.05000i	0.925770	+	0.378087i	$0.123418\pi$
$167$	2.39259	+	13.5690i	0.185144	+	1.05000i	−0.740626	+	0.671917i	$0.765471\pi$
$168$		0			0
$169$	−4.30406	−	3.61154i	−0.331082	−	0.277811i
$170$	−13.2344			−1.01503
$171$		0			0
$172$	−38.3901			−2.92722
$173$	−19.3405	−	16.2286i	−1.47043	−	1.23384i	−0.915734	−	0.401784i	$-0.868390\pi$
$173$	−19.3405	−	16.2286i	−1.47043	−	1.23384i	−0.554696	−	0.832053i	$-0.687165\pi$
$174$		0			0
$175$	−0.847296	−	4.80526i	−0.0640496	−	0.363243i
$176$	1.36571	−	7.74535i	0.102945	−	0.583828i
$177$		0			0
$178$	−3.07145	−	5.31991i	−0.230215	−	0.398744i
$179$	2.91534	−	5.04952i	0.217903	−	0.377419i	−0.736264	−	0.676695i	$-0.763412\pi$
$179$	2.91534	−	5.04952i	0.217903	−	0.377419i	0.954167	+	0.299276i	$0.0967450\pi$
$180$		0			0
$181$	10.3892	−	8.71756i	0.772222	−	0.647971i	−0.169055	−	0.985607i	$-0.554072\pi$
$181$	10.3892	−	8.71756i	0.772222	−	0.647971i	0.941277	+	0.337635i	$0.109627\pi$
$182$	−5.26991	+	9.12776i	−0.390632	+	0.676595i
$183$		0			0
$184$	−29.0574	−	10.5760i	−2.14214	−	0.779674i
$185$	−0.960637	+	5.44804i	−0.0706274	+	0.400548i
$186$		0			0
$187$	4.31908	−	1.57202i	0.315842	−	0.114957i
$188$	−1.93969	−	1.62760i	−0.141467	−	0.118705i
$189$		0			0
$190$	−7.24763	−	12.9845i	−0.525798	−	0.941994i
$191$	10.2841			0.744128			0.372064	−	0.928207i	$-0.378650\pi$
$191$	10.2841			0.744128			0.372064	+	0.928207i	$0.378650\pi$
$192$		0			0
$193$	−12.9684	+	4.72010i	−0.933484	+	0.339760i	−0.763590	−	0.645702i	$-0.776565\pi$
$193$	−12.9684	+	4.72010i	−0.933484	+	0.339760i	−0.169895	+	0.985462i	$0.554343\pi$
$194$	3.24035	+	18.3770i	0.232644	+	1.31939i
$195$		0			0
$196$	19.2875	+	7.02006i	1.37768	+	0.501433i
$197$	−3.97044	−	6.87700i	−0.282882	−	0.489966i	0.689211	−	0.724560i	$-0.257957\pi$
$197$	−3.97044	−	6.87700i	−0.282882	−	0.489966i	−0.972093	+	0.234594i	$0.924624\pi$
$198$		0			0
$199$	20.7101	−	17.3778i	1.46810	−	1.23188i	0.550219	−	0.835020i	$-0.314544\pi$
$199$	20.7101	−	17.3778i	1.46810	−	1.23188i	0.917879	−	0.396861i	$-0.129900\pi$
$200$	−14.8969	+	12.5000i	−1.05337	+	0.883884i
$201$		0			0
$202$	2.74763	+	4.75903i	0.193322	+	0.334844i
$203$	−6.69846	−	2.43804i	−0.470140	−	0.171117i
$204$		0			0
$205$	2.33615	+	13.2490i	0.163164	+	0.925349i
$206$	29.6844	−	10.8042i	2.06821	−	0.752766i
$207$		0			0
$208$	18.0351			1.25051
$209$	3.90760	+	3.37662i	0.270295	+	0.233566i
$210$		0			0
$211$	−6.18345	−	5.18853i	−0.425686	−	0.357193i	0.404635	−	0.914478i	$-0.367399\pi$
$211$	−6.18345	−	5.18853i	−0.425686	−	0.357193i	−0.830321	+	0.557285i	$0.811843\pi$
$212$	12.2023	−	4.44129i	0.838060	−	0.305029i
$213$		0			0
$214$	2.93717	−	16.6575i	0.200781	−	1.13868i
$215$	11.0175	+	4.01006i	0.751390	+	0.273484i
$216$		0			0
$217$	2.93969	−	5.09170i	0.199559	−	0.345647i
$218$	18.3366	−	15.3863i	1.24191	−	1.04209i
$219$		0			0
$220$	−3.52094	+	6.09845i	−0.237382	+	0.411158i
$221$	5.26991	+	9.12776i	0.354493	+	0.614000i
$222$		0			0
$223$	−2.68732	+	15.2405i	−0.179956	+	1.02058i	0.752310	+	0.658809i	$0.228940\pi$
$223$	−2.68732	+	15.2405i	−0.179956	+	1.02058i	−0.932266	+	0.361773i	$0.882172\pi$
$224$	1.22281	+	6.93491i	0.0817025	+	0.463358i
$225$		0			0
$226$	−2.54189	−	2.13290i	−0.169084	−	0.141878i
$227$	−9.87258			−0.655266			−0.327633	−	0.944805i	$-0.606251\pi$
$227$	−9.87258			−0.655266			−0.327633	+	0.944805i	$0.606251\pi$
$228$		0			0
$229$	20.1189			1.32949			0.664746	−	0.747070i	$-0.268540\pi$
$229$	20.1189			1.32949			0.664746	+	0.747070i	$0.268540\pi$
$230$	13.2344	+	11.1050i	0.872652	+	0.732242i
$231$		0			0
$232$	4.93330	+	27.9781i	0.323887	+	1.83685i
$233$	−0.613808	+	3.48108i	−0.0402119	+	0.228053i	−0.998290	−	0.0584538i	$-0.981383\pi$
$233$	−0.613808	+	3.48108i	−0.0402119	+	0.228053i	0.958078	+	0.286507i	$0.0924941\pi$
$234$		0			0
$235$	0.386659	+	0.669713i	0.0252229	+	0.0436873i
$236$	−8.68139	+	15.0366i	−0.565110	+	0.978800i
$237$		0			0
$238$	−11.5287	+	9.67372i	−0.747294	+	0.627054i
$239$	5.98680	−	10.3694i	0.387254	−	0.670743i	−0.604825	−	0.796358i	$-0.706757\pi$
$239$	5.98680	−	10.3694i	0.387254	−	0.670743i	0.992079	+	0.125615i	$0.0400904\pi$
$240$		0			0
$241$	−12.1236	−	4.41263i	−0.780950	−	0.284243i	−0.0793814	−	0.996844i	$-0.525294\pi$
$241$	−12.1236	−	4.41263i	−0.780950	−	0.284243i	−0.701569	+	0.712602i	$0.747517\pi$
$242$	−4.21941	+	23.9294i	−0.271234	+	1.53824i
$243$		0			0
$244$	18.7271	−	6.81612i	1.19888	−	0.436358i
$245$	−4.80200	−	4.02936i	−0.306789	−	0.257426i
$246$		0			0
$247$	−6.06939	+	10.1691i	−0.386186	+	0.647042i
$248$	−23.4320			−1.48793
$249$		0			0
$250$	26.2383	−	9.54996i	1.65946	−	0.603992i
$251$	−2.49407	−	14.1446i	−0.157424	−	0.892798i	−0.956536	−	0.291615i	$-0.905807\pi$
$251$	−2.49407	−	14.1446i	−0.157424	−	0.892798i	0.799112	−	0.601183i	$-0.205304\pi$
$252$		0			0
$253$	−5.63816	−	2.05212i	−0.354468	−	0.129016i
$254$	18.3614	+	31.8029i	1.15210	+	1.99549i
$255$		0			0
$256$	−23.3666	+	19.6069i	−1.46042	+	1.22543i
$257$	−3.81315	+	3.19961i	−0.237858	+	0.199586i	−0.753923	−	0.656963i	$-0.771841\pi$
$257$	−3.81315	+	3.19961i	−0.237858	+	0.199586i	0.516065	+	0.856549i	$0.327396\pi$
$258$		0			0
$259$	3.14543	+	5.44804i	0.195447	+	0.338525i
$260$	−15.1741	−	5.52293i	−0.941059	−	0.342517i
$261$		0			0
$262$	8.70961	+	49.3946i	0.538081	+	3.05161i
$263$	−22.5929	+	8.22313i	−1.39314	+	0.507060i	−0.926133	−	0.377196i	$-0.876888\pi$
$263$	−22.5929	+	8.22313i	−1.39314	+	0.507060i	−0.467002	+	0.884256i	$0.654666\pi$
$264$		0			0
$265$	−3.96585			−0.243620
$266$	−15.8045	−	6.01330i	−0.969038	−	0.368699i
$267$		0			0
$268$	−13.1361	−	11.0225i	−0.802415	−	0.673306i
$269$	−12.3204	+	4.48427i	−0.751189	+	0.273411i	−0.689106	−	0.724660i	$-0.741997\pi$
$269$	−12.3204	+	4.48427i	−0.751189	+	0.273411i	−0.0620832	+	0.998071i	$0.519774\pi$
$270$		0			0
$271$	−4.61381	+	26.1662i	−0.280269	+	1.58948i	0.441443	+	0.897290i	$0.354467\pi$
$271$	−4.61381	+	26.1662i	−0.280269	+	1.58948i	−0.721711	+	0.692194i	$0.756644\pi$
$272$	24.1989	+	8.80769i	1.46728	+	0.534045i
$273$		0			0
$274$	12.9192	−	22.3767i	0.780478	−	1.35183i
$275$	−2.89053	+	2.42544i	−0.174305	+	0.146260i
$276$		0			0
$277$	8.25537	−	14.2987i	0.496017	−	0.859127i	−0.503973	−	0.863720i	$-0.668129\pi$
$277$	8.25537	−	14.2987i	0.496017	−	0.859127i	0.999989	+	0.00459317i	$0.00146206\pi$
$278$	2.10220	+	3.64111i	0.126081	+	0.218379i
$279$		0			0
$280$	2.18866	−	12.4125i	0.130798	−	0.741790i
$281$	3.36706	+	19.0955i	0.200862	+	1.13914i	0.903820	+	0.427913i	$0.140751\pi$
$281$	3.36706	+	19.0955i	0.200862	+	1.13914i	−0.702958	+	0.711231i	$0.748138\pi$
$282$		0			0
$283$	−8.66431	−	7.27022i	−0.515040	−	0.432170i	0.347859	−	0.937547i	$-0.386909\pi$
$283$	−8.66431	−	7.27022i	−0.515040	−	0.432170i	−0.862899	+	0.505377i	$0.831353\pi$
$284$	30.5972			1.81561
$285$		0			0
$286$	8.15064			0.481958
$287$	11.7194	+	9.83375i	0.691775	+	0.580468i
$288$		0			0
$289$	−0.338678	−	1.92074i	−0.0199222	−	0.112985i
$290$	2.75624	−	15.6314i	0.161852	−	0.917910i
$291$		0			0
$292$	−13.5175	−	23.4131i	−0.791054	−	1.37015i
$293$	1.94949	−	3.37662i	0.113891	−	0.197264i	−0.803445	−	0.595379i	$-0.797002\pi$
$293$	1.94949	−	3.37662i	0.113891	−	0.197264i	0.917336	+	0.398115i	$0.130335\pi$
$294$		0			0
$295$	4.06212	−	3.40852i	0.236506	−	0.198452i
$296$	12.5360	−	21.7129i	0.728638	−	1.26204i
$297$		0			0
$298$	26.6660	+	9.70562i	1.54472	+	0.562231i
$299$	2.38919	−	13.5497i	0.138170	−	0.783602i
$300$		0			0
$301$	12.5287	−	4.56007i	0.722141	−	0.262838i
$302$	−21.4179	−	17.9717i	−1.23246	−	1.03416i
$303$		0			0
$304$	4.61081	+	28.5653i	0.264448	+	1.63833i
$305$	−6.08647			−0.348510
$306$		0			0
$307$	−21.7777	+	7.92642i	−1.24292	+	0.452385i	−0.878002	−	0.478657i	$-0.841124\pi$
$307$	−21.7777	+	7.92642i	−1.24292	+	0.452385i	−0.364914	+	0.931041i	$0.618902\pi$
$308$	1.39053	+	7.88609i	0.0792328	+	0.449351i
$309$		0			0
$310$	12.3020	+	4.47756i	0.698707	+	0.254308i
$311$	−1.73055	−	2.99740i	−0.0981306	−	0.169967i	0.812780	−	0.582570i	$-0.197953\pi$
$311$	−1.73055	−	2.99740i	−0.0981306	−	0.169967i	−0.910911	+	0.412603i	$0.864620\pi$
$312$		0			0
$313$	−17.5346	+	14.7133i	−0.991115	+	0.831644i	−0.985729	−	0.168341i	$-0.946159\pi$
$313$	−17.5346	+	14.7133i	−0.991115	+	0.831644i	−0.00538626	+	0.999985i	$0.501715\pi$
$314$	21.3234	−	17.8925i	1.20335	−	1.00973i
$315$		0			0
$316$	−21.6348	−	37.4725i	−1.21705	−	2.10799i
$317$	24.5453	+	8.93378i	1.37860	+	0.501771i	0.921755	−	0.387773i	$-0.126756\pi$
$317$	24.5453	+	8.93378i	1.37860	+	0.501771i	0.456849	+	0.889544i	$0.348978\pi$
$318$		0			0
$319$	0.957234	+	5.42874i	0.0535948	+	0.303951i
$320$	2.07398	−	0.754866i	0.115939	−	0.0421983i
$321$		0			0
$322$	19.6459			1.09482
$323$	−13.1099	+	10.6805i	−0.729456	+	0.594277i
$324$		0			0
$325$	−6.62836	−	5.56185i	−0.367675	−	0.308516i
$326$	15.0680	−	5.48432i	0.834542	−	0.303748i
$327$		0			0
$328$	10.5876	−	60.0455i	0.584605	−	3.31546i
$329$	0.826352	+	0.300767i	0.0455583	+	0.0165818i
$330$		0			0
$331$	−9.52229	+	16.4931i	−0.523392	+	0.906542i	0.476237	+	0.879317i	$0.342000\pi$
$331$	−9.52229	+	16.4931i	−0.523392	+	0.906542i	−0.999629	+	0.0272251i	$0.991333\pi$
$332$	−41.6279	+	34.9300i	−2.28463	+	1.91703i
$333$		0			0
$334$	−17.4440	+	30.2139i	−0.954495	+	1.65323i
$335$	2.61856	+	4.53547i	0.143067	+	0.247799i
$336$		0			0
$337$	0.295445	−	1.67555i	0.0160939	−	0.0912731i	−0.975703	−	0.219098i	$-0.929688\pi$
$337$	0.295445	−	1.67555i	0.0160939	−	0.0912731i	0.991797	+	0.127825i	$0.0407996\pi$
$338$	−2.47044	−	14.0105i	−0.134374	−	0.762073i
$339$		0			0
$340$	−17.6630	−	14.8210i	−0.957909	−	0.803781i
$341$	−4.54664			−0.246214
$342$		0			0
$343$	−17.8530			−0.963970
$344$	−40.7053	−	34.1558i	−2.19468	−	1.84156i
$345$		0			0
$346$	−11.1010	−	62.9570i	−0.596794	−	3.38459i
$347$	0.851167	−	4.82721i	0.0456930	−	0.259138i	−0.953400	−	0.301708i	$-0.902443\pi$
$347$	0.851167	−	4.82721i	0.0456930	−	0.259138i	0.999094	+	0.0425697i	$0.0135544\pi$
$348$		0			0
$349$	14.0646	+	24.3607i	0.752863	+	1.30400i	0.946430	+	0.322910i	$0.104661\pi$
$349$	14.0646	+	24.3607i	0.752863	+	1.30400i	−0.193566	+	0.981087i	$0.562006\pi$
$350$	6.17752	−	10.6998i	0.330202	−	0.571927i
$351$		0			0
$352$	4.17159	−	3.50038i	0.222346	−	0.186571i
$353$	−4.15998	+	7.20529i	−0.221413	+	0.383499i	−0.955237	−	0.295841i	$-0.904400\pi$
$353$	−4.15998	+	7.20529i	−0.221413	+	0.383499i	0.733824	+	0.679340i	$0.237734\pi$
$354$		0			0
$355$	−8.78106	−	3.19604i	−0.466050	−	0.169628i
$356$	1.85844	−	10.5397i	0.0984972	−	0.558605i
$357$		0			0
$358$	13.8735	−	5.04952i	0.733235	−	0.266876i
$359$	−19.0967	−	16.0241i	−1.00789	−	0.845718i	−0.0198296	−	0.999803i	$-0.506312\pi$
$359$	−19.0967	−	16.0241i	−1.00789	−	0.845718i	−0.988057	+	0.154086i	$0.950757\pi$
$360$		0			0
$361$	−17.6582	−	7.01336i	−0.929380	−	0.369124i
$362$	34.3405			1.80490
$363$		0			0
$364$	−17.2554	+	6.28044i	−0.904427	+	0.329184i
$365$	1.43376	+	8.13127i	0.0750466	+	0.425610i
$366$		0			0
$367$	2.42989	+	0.884409i	0.126839	+	0.0461657i	0.404660	−	0.914467i	$-0.367390\pi$
$367$	2.42989	+	0.884409i	0.126839	+	0.0461657i	−0.277821	+	0.960633i	$0.589612\pi$
$368$	−16.8084	−	29.1130i	−0.876198	−	1.51762i
$369$		0			0
$370$	−10.7306	+	9.00400i	−0.557855	+	0.468096i
$371$	−3.45471	+	2.89884i	−0.179359	+	0.150500i
$372$		0			0
$373$	11.6917	+	20.2505i	0.605371	+	1.04853i	0.991993	+	0.126295i	$0.0403086\pi$
$373$	11.6917	+	20.2505i	0.605371	+	1.04853i	−0.386622	+	0.922238i	$0.626358\pi$
$374$	10.9363	+	3.98048i	0.565502	+	0.205826i
$375$		0			0
$376$	−0.608593	−	3.45150i	−0.0313858	−	0.177998i
$377$	−11.8785	+	4.32342i	−0.611774	+	0.222668i
$378$		0			0
$379$	25.4388			1.30670			0.653352	−	0.757054i	$-0.273362\pi$
$379$	25.4388			1.30670			0.653352	+	0.757054i	$0.273362\pi$
$380$	4.86824	−	25.4459i	0.249735	−	1.30535i
$381$		0			0
$382$	19.9479	+	16.7383i	1.02062	+	0.856405i
$383$	−25.8234	+	9.39895i	−1.31951	+	0.480264i	−0.903303	−	0.429003i	$-0.858865\pi$
$383$	−25.8234	+	9.39895i	−1.31951	+	0.480264i	−0.416212	+	0.909268i	$0.636643\pi$
$384$		0			0
$385$	0.424678	−	2.40847i	0.0216436	−	0.122747i
$386$	−32.8371	−	11.9517i	−1.67136	−	0.608327i
$387$		0			0
$388$	−16.2554	+	28.1551i	−0.825241	+	1.42936i
$389$	2.56031	−	2.14835i	0.129813	−	0.108926i	−0.575570	−	0.817753i	$-0.695220\pi$
$389$	2.56031	−	2.14835i	0.129813	−	0.108926i	0.705383	+	0.708827i	$0.250775\pi$
$390$		0			0
$391$	9.82295	−	17.0138i	0.496768	−	0.860427i
$392$	14.2049	+	24.6035i	0.717454	+	1.24267i
$393$		0			0
$394$	3.49154	−	19.8015i	0.175901	−	0.997587i
$395$	2.29473	+	13.0141i	0.115460	+	0.654808i
$396$		0			0
$397$	−10.0530	−	8.43550i	−0.504547	−	0.423365i	0.354658	−	0.934996i	$-0.384597\pi$
$397$	−10.0530	−	8.43550i	−0.504547	−	0.423365i	−0.859206	+	0.511631i	$0.829042\pi$
$398$	68.4552			3.43135
$399$		0			0
$400$	−21.1411			−1.05706
$401$	−13.1099	−	11.0005i	−0.654679	−	0.549341i	0.253808	−	0.967255i	$-0.418317\pi$
$401$	−13.1099	−	11.0005i	−0.654679	−	0.549341i	−0.908487	+	0.417914i	$0.862761\pi$
$402$		0			0
$403$	−1.81046	−	10.2676i	−0.0901854	−	0.511467i
$404$	−1.66250	+	9.42853i	−0.0827127	+	0.469087i
$405$		0			0
$406$	−9.02481	−	15.6314i	−0.447894	−	0.775775i
$407$	2.43242	−	4.21307i	0.120571	−	0.208834i
$408$		0			0
$409$	−6.73964	+	5.65523i	−0.333254	+	0.279633i	−0.794024	−	0.607886i	$-0.792018\pi$
$409$	−6.73964	+	5.65523i	−0.333254	+	0.279633i	0.460770	+	0.887519i	$0.347573\pi$
$410$	−17.0326	+	29.5013i	−0.841178	+	1.45696i
$411$		0			0
$412$	51.7169	+	18.8234i	2.54791	+	0.927364i
$413$	1.04710	−	5.93842i	0.0515246	−	0.292211i
$414$		0			0
$415$	15.5954	−	5.67626i	0.765548	−	0.278637i
$416$	9.56599	+	8.02682i	0.469011	+	0.393547i
$417$		0			0
$418$	2.08378	+	12.9096i	0.101921	+	0.631429i
$419$	−6.84018			−0.334165			−0.167082	−	0.985943i	$-0.553435\pi$
$419$	−6.84018			−0.334165			−0.167082	+	0.985943i	$0.553435\pi$
$420$		0			0
$421$	4.53209	−	1.64955i	0.220880	−	0.0803939i	−0.229210	−	0.973377i	$-0.573614\pi$
$421$	4.53209	−	1.64955i	0.220880	−	0.0803939i	0.450090	+	0.892983i	$0.351392\pi$
$422$	−3.54916	−	20.1283i	−0.172771	−	0.979830i
$423$		0			0
$424$	16.8897	+	6.14733i	0.820234	+	0.298541i
$425$	−6.17752	−	10.6998i	−0.299654	−	0.519015i
$426$		0			0
$427$	−5.30200	+	4.44891i	−0.256582	+	0.215298i
$428$	22.5744	−	18.9422i	1.09118	−	0.915606i
$429$		0			0
$430$	14.8439	+	25.7104i	0.715836	+	1.23986i
$431$	1.22503	+	0.445875i	0.0590077	+	0.0214771i	0.371355	−	0.928491i	$-0.378893\pi$
$431$	1.22503	+	0.445875i	0.0590077	+	0.0214771i	−0.312348	+	0.949968i	$0.601115\pi$
$432$		0			0
$433$	3.44238	+	19.5227i	0.165430	+	0.938202i	0.948620	+	0.316419i	$0.102480\pi$
$433$	3.44238	+	19.5227i	0.165430	+	0.938202i	−0.783189	+	0.621783i	$0.786409\pi$
$434$	13.9893	−	5.09170i	0.671509	−	0.244409i
$435$		0			0
$436$	41.7033			1.99722
$437$	22.0719	+	0.320070i	1.05584	+	0.0153110i
$438$		0			0
$439$	−26.4800	−	22.2193i	−1.26382	−	1.06047i	−0.995264	−	0.0972078i	$-0.969009\pi$
$439$	−26.4800	−	22.2193i	−1.26382	−	1.06047i	−0.268557	−	0.963264i	$-0.586547\pi$
$440$	−9.15910	+	3.33364i	−0.436643	+	0.158925i
$441$		0			0
$442$	−4.63429	+	26.2823i	−0.220430	+	1.25012i
$443$	15.9843	+	5.81780i	0.759436	+	0.276412i	0.692571	−	0.721350i	$-0.256478\pi$
$443$	15.9843	+	5.81780i	0.759436	+	0.276412i	0.0668650	+	0.997762i	$0.478700\pi$
$444$		0			0
$445$	−1.63429	+	2.83067i	−0.0774726	+	0.134186i
$446$	−30.0180	+	25.1881i	−1.42139	+	1.19269i
$447$		0			0
$448$	1.25490	−	2.17355i	0.0592885	−	0.102691i
$449$	18.7049	+	32.3978i	0.882737	+	1.52895i	0.848286	+	0.529539i	$0.177635\pi$
$449$	18.7049	+	32.3978i	0.882737	+	1.52895i	0.0344512	+	0.999406i	$0.489032\pi$
$450$		0			0
$451$	2.05438	−	11.6510i	0.0967369	−	0.548622i
$452$	−1.00387	−	5.69323i	−0.0472181	−	0.267787i
$453$		0			0
$454$	−19.1498	−	16.0686i	−0.898743	−	0.754135i
$455$	5.60813			0.262913
$456$		0			0
$457$	9.11112			0.426200			0.213100	−	0.977030i	$-0.431644\pi$
$457$	9.11112			0.426200			0.213100	+	0.977030i	$0.431644\pi$
$458$	39.0244	+	32.7454i	1.82349	+	1.53009i
$459$		0			0
$460$	5.22668	+	29.6420i	0.243695	+	1.38206i
$461$	4.24540	−	24.0769i	0.197728	−	1.12137i	−0.710751	−	0.703443i	$-0.751645\pi$
$461$	4.24540	−	24.0769i	0.197728	−	1.12137i	0.908480	−	0.417929i	$-0.137244\pi$
$462$		0			0
$463$	0.125362	+	0.217134i	0.00582609	+	0.0100911i	0.868924	−	0.494946i	$-0.164812\pi$
$463$	0.125362	+	0.217134i	0.00582609	+	0.0100911i	−0.863098	+	0.505037i	$0.831479\pi$
$464$	−15.4427	+	26.7475i	−0.716909	+	1.24172i
$465$		0			0
$466$	−6.85638	+	5.75319i	−0.317616	+	0.266511i
$467$	7.68092	−	13.3037i	0.355431	−	0.615624i	−0.631761	−	0.775163i	$-0.717668\pi$
$467$	7.68092	−	13.3037i	0.355431	−	0.615624i	0.987192	+	0.159539i	$0.0510009\pi$
$468$		0			0
$469$	5.59627	+	2.03687i	0.258412	+	0.0940541i
$470$	−0.340022	+	1.92836i	−0.0156841	+	0.0889487i
$471$		0			0
$472$	−22.5831	+	8.21956i	−1.03947	+	0.378336i
$473$	−7.89827	−	6.62744i	−0.363163	−	0.304730i
$474$		0			0
$475$	7.11468	−	11.9204i	0.326444	−	0.546946i
$476$	−26.2199			−1.20179
$477$		0			0
$478$	28.4898	−	10.3694i	1.30309	−	0.474287i
$479$	0.124896	+	0.708319i	0.00570663	+	0.0323639i	0.987528	−	0.157443i	$-0.0503250\pi$
$479$	0.124896	+	0.708319i	0.00570663	+	0.0323639i	−0.981821	+	0.189807i	$0.939214\pi$
$480$		0			0
$481$	10.4829	+	3.81547i	0.477980	+	0.173971i
$482$	−16.3341	−	28.2915i	−0.743998	−	1.28864i
$483$		0			0
$484$	−32.4295	+	27.2116i	−1.47407	+	1.23689i
$485$	7.60607	−	6.38225i	0.345374	−	0.289803i
$486$		0			0
$487$	−5.87346	−	10.1731i	−0.266152	−	0.460988i	0.701713	−	0.712460i	$-0.252419\pi$
$487$	−5.87346	−	10.1731i	−0.266152	−	0.460988i	−0.967865	+	0.251471i	$0.919086\pi$
$488$	25.9209	+	9.43442i	1.17338	+	0.427076i
$489$		0			0
$490$	−2.75624	−	15.6314i	−0.124514	−	0.706156i
$491$	0.0834734	−	0.0303818i	0.00376710	−	0.00137111i	−0.340136	−	0.940376i	$-0.610473\pi$
$491$	0.0834734	−	0.0303818i	0.00376710	−	0.00137111i	0.343903	+	0.939005i	$0.388251\pi$
$492$		0			0
$493$	−18.0496			−0.812914
$494$	−28.3239	+	9.84635i	−1.27435	+	0.443008i
$495$		0			0
$496$	−19.5141	−	16.3743i	−0.876211	−	0.735228i
$497$	−9.98545	+	3.63441i	−0.447909	+	0.163025i
$498$		0			0
$499$	2.55097	−	14.4673i	0.114197	−	0.647645i	−0.872947	−	0.487815i	$-0.837794\pi$
$499$	2.55097	−	14.4673i	0.114197	−	0.647645i	0.987145	−	0.159830i	$-0.0510947\pi$
$500$	45.7131	+	16.6382i	2.04435	+	0.744083i
$501$		0			0
$502$	18.1839	−	31.4955i	0.811588	−	1.40571i
$503$	3.75671	−	3.15225i	0.167503	−	0.140552i	−0.555183	−	0.831728i	$-0.687352\pi$
$503$	3.75671	−	3.15225i	0.167503	−	0.140552i	0.722686	+	0.691176i	$0.242907\pi$
$504$		0			0
$505$	1.46198	−	2.53223i	0.0650573	−	0.112683i
$506$	−7.59627	−	13.1571i	−0.337695	−	0.584905i
$507$		0			0
$508$	−11.1099	+	63.0076i	−0.492924	+	2.79551i
$509$	−1.11375	−	6.31640i	−0.0493662	−	0.279969i	0.950125	−	0.311870i	$-0.100955\pi$
$509$	−1.11375	−	6.31640i	−0.0493662	−	0.279969i	−0.999491	+	0.0319002i	$0.989844\pi$
$510$		0			0
$511$	7.19253	+	6.03525i	0.318179	+	0.266984i
$512$	−50.5553			−2.23425
$513$		0			0
$514$	−12.6040			−0.555939
$515$	−12.8760	−	10.8042i	−0.567384	−	0.476091i
$516$		0			0
$517$	−0.118089	−	0.669713i	−0.00519353	−	0.0294540i
$518$	−2.76604	+	15.6870i	−0.121533	+	0.689248i
$519$		0			0
$520$	−11.1755	−	19.3565i	−0.490076	−	0.848837i
$521$	−17.9067	+	31.0154i	−0.784508	+	1.35881i	0.144785	+	0.989463i	$0.453751\pi$
$521$	−17.9067	+	31.0154i	−0.784508	+	1.35881i	−0.929293	+	0.369344i	$0.879582\pi$
$522$		0			0
$523$	29.7015	−	24.9225i	1.29875	−	1.08978i	0.308395	−	0.951258i	$-0.400208\pi$
$523$	29.7015	−	24.9225i	1.29875	−	1.08978i	0.990359	−	0.138526i	$-0.0442363\pi$
$524$	−43.6921	+	75.6770i	−1.90870	+	3.30596i
$525$		0			0
$526$	−57.2071	−	20.8217i	−2.49435	−	0.907869i
$527$	2.58512	−	14.6610i	0.112610	−	0.638641i
$528$		0			0
$529$	−2.48633	+	0.904950i	−0.108101	+	0.0393456i
$530$	−7.69253	−	6.45480i	−0.334142	−	0.280379i
$531$		0			0
$532$	−14.3589	−	25.7247i	−0.622538	−	1.11531i
$533$	27.1293			1.17510
$534$		0			0
$535$	−8.45723	+	3.07818i	−0.365638	+	0.133081i
$536$	−4.12155	−	23.3745i	−0.178024	−	1.00962i
$537$		0			0
$538$	−31.1964	−	11.3546i	−1.34497	−	0.489530i
$539$	2.75624	+	4.77396i	0.118720	+	0.205629i
$540$		0			0
$541$	7.26991	−	6.10018i	0.312558	−	0.262267i	−0.472990	−	0.881068i	$-0.656825\pi$
$541$	7.26991	−	6.10018i	0.312558	−	0.262267i	0.785548	+	0.618800i	$0.212381\pi$
$542$	−51.5374	+	43.2450i	−2.21372	+	1.85753i
$543$		0			0
$544$	8.91534	+	15.4418i	0.382242	+	0.662063i
$545$	−11.9684	−	4.35613i	−0.512669	−	0.186596i
$546$		0			0
$547$	2.46791	+	13.9962i	0.105520	+	0.598435i	0.991011	+	0.133779i	$0.0427111\pi$
$547$	2.46791	+	13.9962i	0.105520	+	0.598435i	−0.885491	+	0.464657i	$0.846178\pi$
$548$	42.3016	−	15.3965i	1.80703	−	0.657707i
$549$		0			0
$550$	−9.55438			−0.407400
$551$	−9.88460	−	17.7088i	−0.421098	−	0.754418i
$552$		0			0
$553$	11.5116	+	9.65939i	0.489524	+	0.410759i
$554$	39.2854	−	14.2987i	1.66908	−	0.607494i
$555$		0			0
$556$	−1.27197	+	7.21372i	−0.0539437	+	0.305930i
$557$	21.1805	+	7.70908i	0.897447	+	0.326644i	0.749229	−	0.662311i	$-0.230424\pi$
$557$	21.1805	+	7.70908i	0.897447	+	0.326644i	0.148218	+	0.988955i	$0.452646\pi$
$558$		0			0
$559$	11.8216	−	20.4756i	0.500001	−	0.866026i
$560$	10.4966	−	8.80769i	0.443562	−	0.372193i
$561$		0			0
$562$	−24.5488	+	42.5197i	−1.03553	+	1.79358i
$563$	−21.4859	−	37.2147i	−0.905524	−	1.56841i	−0.820213	−	0.572058i	$-0.806145\pi$
$563$	−21.4859	−	37.2147i	−0.905524	−	1.56841i	−0.0853106	−	0.996354i	$-0.527188\pi$
$564$		0			0
$565$	−0.306589	+	1.73875i	−0.0128983	+	0.0731500i
$566$	−4.97313	−	28.2040i	−0.209036	−	1.18550i
$567$		0			0
$568$	32.4424	+	27.2224i	1.36125	+	1.14223i
$569$	−7.42696			−0.311354			−0.155677	−	0.987808i	$-0.549756\pi$
$569$	−7.42696			−0.311354			−0.155677	+	0.987808i	$0.549756\pi$
$570$		0			0
$571$	4.04458			0.169260			0.0846301	−	0.996412i	$-0.473029\pi$
$571$	4.04458			0.169260			0.0846301	+	0.996412i	$0.473029\pi$
$572$	10.8780	+	9.12776i	0.454834	+	0.381651i
$573$		0			0
$574$	6.72668	+	38.1489i	0.280766	+	1.59230i
$575$	−2.80066	+	15.8833i	−0.116796	+	0.662381i
$576$		0			0
$577$	−1.61721	−	2.80109i	−0.0673254	−	0.116611i	0.830398	−	0.557171i	$-0.188113\pi$
$577$	−1.61721	−	2.80109i	−0.0673254	−	0.116611i	−0.897723	+	0.440560i	$0.854780\pi$
$578$	2.46926	−	4.27688i	0.102707	−	0.177895i
$579$		0			0
$580$	21.1839	−	17.7754i	0.879614	−	0.738084i
$581$	9.43629	−	16.3441i	0.391483	−	0.678069i
$582$		0			0
$583$	3.27719	+	1.19280i	0.135727	+	0.0494007i
$584$	6.49794	−	36.8517i	0.268887	−	1.52493i
$585$		0			0
$586$	9.27719	−	3.37662i	0.383237	−	0.139487i
$587$	31.2610	+	26.2311i	1.29028	+	1.08267i	0.991738	+	0.128279i	$0.0409452\pi$
$587$	31.2610	+	26.2311i	1.29028	+	1.08267i	0.298543	+	0.954396i	$0.403499\pi$
$588$		0			0
$589$	15.7998	−	5.49254i	0.651019	−	0.226316i
$590$	13.4270			0.552779
$591$		0			0
$592$	25.6129	−	9.32234i	1.05268	−	0.383146i
$593$	1.92127	+	10.8961i	0.0788973	+	0.447449i	0.998507	+	0.0546164i	$0.0173936\pi$
$593$	1.92127	+	10.8961i	0.0788973	+	0.447449i	−0.919610	+	0.392832i	$0.871495\pi$
$594$		0			0
$595$	7.52481	+	2.73881i	0.308487	+	0.112280i
$596$	24.7199	+	42.8161i	1.01257	+	1.75381i
$597$		0			0
$598$	26.6878	−	22.3937i	1.09134	−	0.915747i
$599$	34.1332	−	28.6411i	1.39464	−	1.17024i	0.431224	−	0.902245i	$-0.358082\pi$
$599$	34.1332	−	28.6411i	1.39464	−	1.17024i	0.963419	−	0.268000i	$-0.0863626\pi$
$600$		0			0
$601$	2.49953	+	4.32932i	0.101958	+	0.176597i	0.912491	−	0.409096i	$-0.134156\pi$
$601$	2.49953	+	4.32932i	0.101958	+	0.176597i	−0.810533	+	0.585693i	$0.800823\pi$
$602$	31.7237	+	11.5465i	1.29296	+	0.470600i
$603$		0			0
$604$	−8.45858	−	47.9710i	−0.344175	−	1.95191i
$605$	12.1493	−	4.42198i	0.493939	−	0.179779i
$606$		0			0
$607$	−31.1881			−1.26589			−0.632943	−	0.774199i	$-0.718153\pi$
$607$	−31.1881			−1.26589			−0.632943	+	0.774199i	$0.718153\pi$
$608$	−10.2679	+	17.2035i	−0.416417	+	0.697692i
$609$		0			0
$610$	−11.8059	−	9.90630i	−0.478006	−	0.401095i
$611$	1.46538	−	0.533356i	0.0592831	−	0.0215773i
$612$		0			0
$613$	2.84255	−	16.1209i	0.114809	−	0.651117i	−0.872035	−	0.489444i	$-0.837200\pi$
$613$	2.84255	−	16.1209i	0.114809	−	0.651117i	0.986844	−	0.161673i	$-0.0516890\pi$
$614$	−55.1430	−	20.0704i	−2.22539	−	0.809975i
$615$		0			0
$616$	−5.54189	+	9.59883i	−0.223289	+	0.386748i
$617$	−12.3014	+	10.3221i	−0.495235	+	0.415551i	−0.855898	−	0.517145i	$-0.826995\pi$
$617$	−12.3014	+	10.3221i	−0.495235	+	0.415551i	0.360663	+	0.932696i	$0.382550\pi$
$618$		0			0
$619$	−11.9213	+	20.6483i	−0.479156	+	0.829923i	−0.999714	−	0.0239031i	$-0.992391\pi$
$619$	−11.9213	+	20.6483i	−0.479156	+	0.829923i	0.520558	+	0.853826i	$0.325724\pi$
$620$	11.4042	+	19.7527i	0.458004	+	0.793286i
$621$		0			0
$622$	1.52182	−	8.63068i	0.0610195	−	0.346059i
$623$	0.645430	+	3.66041i	0.0258586	+	0.146651i
$624$		0			0
$625$	0.817267	+	0.685768i	0.0326907	+	0.0274307i
$626$	−57.9590			−2.31651
$627$		0			0
$628$	48.4962			1.93521
$629$	12.2023	+	10.2390i	0.486539	+	0.408255i
$630$		0			0
$631$	3.72874	+	21.1467i	0.148439	+	0.841838i	0.964541	+	0.263931i	$0.0850193\pi$
$631$	3.72874	+	21.1467i	0.148439	+	0.841838i	−0.816103	+	0.577907i	$0.803870\pi$
$632$	10.3999	−	58.9809i	0.413687	−	2.34613i
$633$		0			0
$634$	33.0699	+	57.2787i	1.31337	+	2.27483i
$635$	9.76991	−	16.9220i	0.387707	−	0.671529i
$636$		0			0
$637$	−9.68345	+	8.12538i	−0.383672	+	0.321939i
$638$	−6.97906	+	12.0881i	−0.276303	+	0.478572i
$639$		0			0
$640$	16.8897	+	6.14733i	0.667622	+	0.242995i
$641$	−2.21466	+	12.5600i	−0.0874738	+	0.496089i	0.909322	+	0.416094i	$0.136601\pi$
$641$	−2.21466	+	12.5600i	−0.0874738	+	0.496089i	−0.996795	+	0.0799944i	$0.974510\pi$
$642$		0			0
$643$	−26.8828	+	9.78456i	−1.06016	+	0.385865i	−0.812487	−	0.582979i	$-0.801887\pi$
$643$	−26.8828	+	9.78456i	−1.06016	+	0.385865i	−0.247669	+	0.968845i	$0.579665\pi$
$644$	26.2199	+	22.0011i	1.03321	+	0.866964i
$645$		0			0
$646$	−42.8127	−	0.620838i	−1.68444	−	0.0244265i
$647$	−16.7128			−0.657046			−0.328523	−	0.944496i	$-0.606551\pi$
$647$	−16.7128			−0.657046			−0.328523	+	0.944496i	$0.606551\pi$
$648$		0			0
$649$	−4.38191	+	1.59489i	−0.172005	+	0.0626047i
$650$	−3.80453	−	21.5766i	−0.149226	−	0.846302i
$651$		0			0
$652$	26.2520	+	9.55493i	1.02811	+	0.374200i
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	0.999456	+	0.0329874i	$0.0105021\pi$
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	−0.471160	+	0.882048i	$0.656165\pi$
$654$		0			0
$655$	20.4440	−	17.1546i	0.798814	−	0.670285i
$656$	50.7772	−	42.6072i	1.98252	−	1.66353i
$657$		0			0
$658$	1.11334	+	1.92836i	0.0434025	+	0.0751754i
$659$	−41.2533	−	15.0150i	−1.60700	−	0.584900i	−0.626157	−	0.779697i	$-0.715373\pi$
$659$	−41.2533	−	15.0150i	−1.60700	−	0.584900i	−0.980844	+	0.194797i	$0.937595\pi$
$660$		0			0
$661$	−1.86777	−	10.5927i	−0.0726480	−	0.412007i	−0.999345	−	0.0361971i	$-0.988476\pi$
$661$	−1.86777	−	10.5927i	−0.0726480	−	0.412007i	0.926697	−	0.375810i	$-0.122636\pi$
$662$	−45.3144	+	16.4931i	−1.76119	+	0.641022i
$663$		0			0
$664$	−75.2158			−2.91894
$665$	1.43376	+	8.88257i	0.0555989	+	0.344451i
$666$		0			0
$667$	18.0496	+	15.1454i	0.698884	+	0.586434i
$668$	−57.1173	+	20.7890i	−2.20993	+	0.804350i
$669$		0			0
$670$	−2.30272	+	13.0594i	−0.0889618	+	0.504527i
$671$	5.02956	+	1.83061i	0.194164	+	0.0706700i
$672$		0			0
$673$	−2.32888	+	4.03374i	−0.0897717	+	0.155489i	−0.907415	−	0.420237i	$-0.861947\pi$
$673$	−2.32888	+	4.03374i	−0.0897717	+	0.155489i	0.817643	+	0.575726i	$0.195280\pi$
$674$	3.30019	−	2.76919i	0.127119	−	0.106665i
$675$		0			0
$676$	12.3931	−	21.4654i	0.476656	−	0.825592i
$677$	1.63429	+	2.83067i	0.0628107	+	0.108791i	0.895721	−	0.444617i	$-0.146660\pi$
$677$	1.63429	+	2.83067i	0.0628107	+	0.108791i	−0.832910	+	0.553408i	$0.813327\pi$
$678$		0			0
$679$	1.96064	−	11.1193i	0.0752423	−	0.426721i
$680$	−5.54189	−	31.4296i	−0.212522	−	1.20527i
$681$		0			0
$682$	−8.81908	−	7.40008i	−0.337700	−	0.283364i
$683$	−6.21894			−0.237961			−0.118981	−	0.992897i	$-0.537963\pi$
$683$	−6.21894			−0.237961			−0.118981	+	0.992897i	$0.537963\pi$
$684$		0			0
$685$	−13.7483			−0.525297
$686$	−34.6293	−	29.0574i	−1.32215	−	1.10942i
$687$		0			0
$688$	−10.0312	−	56.8898i	−0.382436	−	2.16890i
$689$	−1.38872	+	7.87581i	−0.0529060	+	0.300045i
$690$		0			0
$691$	−11.1088	−	19.2409i	−0.422597	−	0.731959i	0.573596	−	0.819139i	$-0.305548\pi$
$691$	−11.1088	−	19.2409i	−0.422597	−	0.731959i	−0.996193	+	0.0871792i	$0.972215\pi$
$692$	55.6887	−	96.4557i	2.11697	−	3.66670i
$693$		0			0
$694$	9.50774	−	7.97794i	0.360909	−	0.302839i
$695$	1.11856	−	1.93739i	0.0424292	−	0.0734896i
$696$		0			0
$697$	36.4013	+	13.2490i	1.37880	+	0.501841i
$698$	−12.3682	+	70.1438i	−0.468145	+	2.65498i
$699$		0			0
$700$	20.2271	−	7.36208i	0.764514	−	0.278260i
$701$	21.2750	+	17.8518i	0.803544	+	0.674254i	0.949058	−	0.315102i	$-0.102039\pi$
$701$	21.2750	+	17.8518i	0.803544	+	0.674254i	−0.145513	+	0.989356i	$0.546483\pi$
$702$		0			0
$703$	−3.36319	+	17.5791i	−0.126845	+	0.663008i
$704$	−1.94087			−0.0731495
$705$		0			0
$706$	−19.7964	+	7.20529i	−0.745047	+	0.271175i
$707$	−0.577382	−	3.27449i	−0.0217147	−	0.123150i
$708$		0			0
$709$	5.73947	+	2.08900i	0.215551	+	0.0784540i	0.447538	−	0.894265i	$-0.352301\pi$
$709$	5.73947	+	2.08900i	0.215551	+	0.0784540i	−0.231988	+	0.972719i	$0.574523\pi$
$710$	−11.8307	−	20.4914i	−0.443998	−	0.769027i
$711$		0			0
$712$	11.3478	−	9.52190i	0.425275	−	0.356848i
$713$	−14.8871	+	12.4918i	−0.557527	+	0.467821i
$714$		0			0
$715$	−2.16843	−	3.75584i	−0.0810948	−	0.140460i
$716$	24.1707	+	8.79742i	0.903302	+	0.328775i
$717$		0			0
$718$	−10.9611	−	62.1635i	−0.409065	−	2.31992i
$719$	36.3885	−	13.2443i	1.35706	−	0.493930i	0.441917	−	0.897056i	$-0.354299\pi$
$719$	36.3885	−	13.2443i	1.35706	−	0.493930i	0.915144	+	0.403126i	$0.132076\pi$
$720$		0			0
$721$	−19.1138			−0.711835
$722$	−22.8366	−	42.3442i	−0.849891	−	1.57589i
$723$		0			0
$724$	45.8316	+	38.4573i	1.70332	+	1.42925i
$725$	13.9243	−	5.06802i	0.517134	−	0.188221i
$726$		0			0
$727$	−1.92366	+	10.9096i	−0.0713445	+	0.404615i	0.928132	+	0.372252i	$0.121414\pi$
$727$	−1.92366	+	10.9096i	−0.0713445	+	0.404615i	−0.999476	+	0.0323628i	$0.989697\pi$
$728$	−23.8837	−	8.69296i	−0.885190	−	0.322183i
$729$		0			0
$730$	−10.4534	+	18.1058i	−0.386896	+	0.670124i
$731$	25.8614	−	21.7003i	0.956520	−	0.802615i
$732$		0			0
$733$	7.90373	−	13.6897i	0.291931	−	0.505639i	−0.682335	−	0.731039i	$-0.739036\pi$
$733$	7.90373	−	13.6897i	0.291931	−	0.505639i	0.974266	+	0.225400i	$0.0723689\pi$
$734$	3.27379	+	5.67036i	0.120838	+	0.209297i
$735$		0			0
$736$	4.04189	−	22.9227i	0.148986	−	0.844942i
$737$	−0.799726	−	4.53547i	−0.0294583	−	0.167066i
$738$		0			0
$739$	1.18685	+	0.995887i	0.0436591	+	0.0366343i	0.664356	−	0.747416i	$-0.268706\pi$
$739$	1.18685	+	0.995887i	0.0436591	+	0.0366343i	−0.620697	+	0.784050i	$0.713150\pi$
$740$	−24.4047			−0.897133
$741$		0			0
$742$	−11.4192			−0.419213
$743$	−29.2349	−	24.5310i	−1.07252	−	0.899955i	−0.0772453	−	0.997012i	$-0.524612\pi$
$743$	−29.2349	−	24.5310i	−1.07252	−	0.899955i	−0.995279	+	0.0970576i	$0.969057\pi$
$744$		0			0
$745$	−2.62196	−	14.8699i	−0.0960611	−	0.544790i
$746$	−10.2815	+	58.3091i	−0.376431	+	2.13485i
$747$		0			0
$748$	10.1382	+	17.5598i	0.370688	+	0.642050i
$749$	−5.11721	+	8.86327i	−0.186979	+	0.323857i
$750$		0			0
$751$	−19.4179	+	16.2935i	−0.708568	+	0.594559i	−0.924197	−	0.381916i	$-0.875264\pi$
$751$	−19.4179	+	16.2935i	−0.708568	+	0.594559i	0.215629	+	0.976475i	$0.430820\pi$
$752$	1.90508	−	3.29969i	0.0694710	−	0.120327i
$753$		0			0
$754$	−30.0774	−	10.9473i	−1.09536	−	0.398677i
$755$	−2.58331	+	14.6507i	−0.0940163	+	0.533193i
$756$		0			0
$757$	−39.8153	+	14.4916i	−1.44711	+	0.526705i	−0.941783	−	0.336222i	$-0.890851\pi$
$757$	−39.8153	+	14.4916i	−1.44711	+	0.526705i	−0.505328	+	0.862927i	$0.668628\pi$
$758$	49.3435	+	41.4041i	1.79224	+	1.50386i
$759$		0			0
$760$	27.8011	−	22.6492i	1.00845	−	0.821572i
$761$	2.85710			0.103570			0.0517848	−	0.998658i	$-0.483509\pi$
$761$	2.85710			0.103570			0.0517848	+	0.998658i	$0.483509\pi$
$762$		0			0
$763$	−13.6099	+	4.95361i	−0.492713	+	0.179333i
$764$	7.87804	+	44.6786i	0.285018	+	1.61641i
$765$		0			0
$766$	−65.3872	−	23.7990i	−2.36253	−	0.859892i
$767$	−5.34658	−	9.26055i	−0.193054	−	0.334379i
$768$		0			0
$769$	14.6472	−	12.2905i	0.528193	−	0.443207i	−0.339284	−	0.940684i	$-0.610185\pi$
$769$	14.6472	−	12.2905i	0.528193	−	0.443207i	0.867477	+	0.497477i	$0.165740\pi$
$770$	4.74376	−	3.98048i	0.170953	−	0.143447i
$771$		0			0
$772$	−30.4406	−	52.7247i	−1.09558	−	1.89760i
$773$	2.36319	+	0.860130i	0.0849980	+	0.0309367i	0.384169	−	0.923263i	$-0.374488\pi$
$773$	2.36319	+	0.860130i	0.0849980	+	0.0309367i	−0.299171	+	0.954199i	$0.596710\pi$
$774$		0			0
$775$	2.12226	+	12.0360i	0.0762340	+	0.432344i
$776$	−42.2854	+	15.3906i	−1.51796	+	0.552491i
$777$		0			0
$778$	8.46286			0.303408
$779$	6.93582	+	42.9694i	0.248502	+	1.53954i
$780$		0			0
$781$	6.29498	+	5.28211i	0.225252	+	0.189009i
$782$	46.7452	−	17.0138i	1.67160	−	0.608414i
$783$		0			0
$784$	−5.36319	+	30.4162i	−0.191542	+	1.08629i
$785$	−13.9179	−	5.06569i	−0.496750	−	0.180802i
$786$		0			0
$787$	−1.36303	+	2.36083i	−0.0485866	+	0.0841545i	−0.889296	−	0.457332i	$-0.848805\pi$
$787$	−1.36303	+	2.36083i	−0.0485866	+	0.0841545i	0.840709	+	0.541487i	$0.182138\pi$
$788$	26.8353	−	22.5175i	0.955967	−	0.802152i
$789$		0			0
$790$	−16.7306	+	28.9782i	−0.595246	+	1.03100i
$791$	1.00387	+	1.73875i	0.0356935	+	0.0618230i
$792$		0			0
$793$	−2.13129	+	12.0872i	−0.0756844	+	0.429228i
$794$	−5.77022	−	32.7245i	−0.204777	−	1.16135i
$795$		0			0
$796$	91.3620	+	76.6618i	3.23824	+	2.71720i
$797$	−22.0327			−0.780439			−0.390219	−	0.920722i	$-0.627601\pi$
$797$	−22.0327			−0.780439			−0.390219	+	0.920722i	$0.627601\pi$
$798$		0			0
$799$	2.22668			0.0787743
$800$	−11.2135	−	9.40923i	−0.396456	−	0.332666i
$801$		0			0
$802$	−7.52481	−	42.6753i	−0.265710	−	1.50692i
$803$	1.26083	−	7.15052i	0.0444937	−	0.252336i
$804$		0			0
$805$	−5.22668	−	9.05288i	−0.184216	−	0.319072i
$806$	13.1998	−	22.8627i	0.464943	−	0.805306i
$807$		0			0
$808$	−10.1514	+	8.51800i	−0.357124	+	0.299662i
$809$	27.3603	−	47.3893i	0.961935	−	1.66612i	0.244302	−	0.969699i	$-0.421441\pi$
$809$	27.3603	−	47.3893i	0.961935	−	1.66612i	0.717633	−	0.696422i	$-0.245226\pi$
$810$		0			0
$811$	2.17112	+	0.790224i	0.0762384	+	0.0277485i	0.379858	−	0.925045i	$-0.375973\pi$
$811$	2.17112	+	0.790224i	0.0762384	+	0.0277485i	−0.303619	+	0.952793i	$0.598195\pi$
$812$	5.46064	−	30.9688i	0.191631	−	1.08679i
$813$		0			0
$814$	11.5753	−	4.21307i	0.405715	−	0.147668i
$815$	−6.53596	−	5.48432i	−0.228945	−	0.192107i
$816$		0			0
$817$	35.4531	+	13.4892i	1.24035	+	0.471927i
$818$	−22.2772			−0.778906
$819$		0			0
$820$	−55.7700	+	20.2986i	−1.94757	+	0.708858i
$821$	−0.192944	−	1.09424i	−0.00673379	−	0.0381892i	0.981256	−	0.192710i	$-0.0617277\pi$
$821$	−0.192944	−	1.09424i	−0.00673379	−	0.0381892i	−0.987990	+	0.154521i	$0.950617\pi$
$822$		0			0
$823$	−19.4024	−	7.06191i	−0.676327	−	0.246163i	−0.0190572	−	0.999818i	$-0.506066\pi$
$823$	−19.4024	−	7.06191i	−0.676327	−	0.246163i	−0.657270	+	0.753656i	$0.728289\pi$
$824$	38.0886	+	65.9714i	1.32688	+	2.29822i
$825$		0			0
$826$	11.6964	−	9.81445i	0.406970	−	0.341488i
$827$	−27.8116	+	23.3367i	−0.967103	+	0.811495i	−0.982094	−	0.188392i	$-0.939672\pi$
$827$	−27.8116	+	23.3367i	−0.967103	+	0.811495i	0.0149913	+	0.999888i	$0.495228\pi$
$828$		0			0
$829$	3.57486	+	6.19183i	0.124160	+	0.215051i	0.921404	−	0.388606i	$-0.127043\pi$
$829$	3.57486	+	6.19183i	0.124160	+	0.215051i	−0.797244	+	0.603657i	$0.793710\pi$
$830$	39.4889	+	14.3728i	1.37068	+	0.498887i
$831$		0			0
$832$	−0.772852	−	4.38306i	−0.0267938	−	0.151955i
$833$	−16.9611	+	6.17334i	−0.587667	+	0.213893i
$834$		0			0
$835$	18.5635			0.642418
$836$	−11.6762	+	19.5630i	−0.403829	+	0.676602i
$837$		0			0
$838$	−13.2679	−	11.1331i	−0.458330	−	0.384585i
$839$	−32.5197	+	11.8362i	−1.12270	+	0.408631i	−0.835638	−	0.549280i	$-0.814902\pi$
$839$	−32.5197	+	11.8362i	−1.12270	+	0.408631i	−0.287065	+	0.957911i	$0.592680\pi$
$840$		0			0
$841$	−1.27672	+	7.24065i	−0.0440249	+	0.249678i
$842$	11.4757	+	4.17680i	0.395477	+	0.143942i
$843$		0			0
$844$	17.8045	−	30.8384i	0.612857	−	1.06150i
$845$	−5.79885	+	4.86581i	−0.199486	+	0.167389i
$846$		0			0
$847$	7.35117	−	12.7326i	0.252589	−	0.437497i
$848$	9.76991	+	16.9220i	0.335500	+	0.581103i
$849$		0			0
$850$	5.43242	−	30.8088i	0.186330	−	1.05673i
$851$	−3.61081	−	20.4779i	−0.123777	−	0.701975i
$852$		0			0
$853$	25.4716	+	21.3732i	0.872132	+	0.731805i	0.964546	−	0.263915i	$-0.0850139\pi$
$853$	25.4716	+	21.3732i	0.872132	+	0.731805i	−0.0924142	+	0.995721i	$0.529458\pi$
$854$	−17.5253			−0.599703
$855$		0			0
$856$	40.7888			1.39413
$857$	2.97700	+	2.49800i	0.101692	+	0.0853299i	0.692216	−	0.721690i	$-0.256634\pi$
$857$	2.97700	+	2.49800i	0.101692	+	0.0853299i	−0.590524	+	0.807020i	$0.701079\pi$
$858$		0			0
$859$	0.287866	+	1.63257i	0.00982187	+	0.0557026i	0.989325	−	0.145727i	$-0.0465522\pi$
$859$	0.287866	+	1.63257i	0.00982187	+	0.0557026i	−0.979503	+	0.201430i	$0.935441\pi$
$860$	−8.98158	+	50.9371i	−0.306269	+	1.73694i
$861$		0			0
$862$	1.65048	+	2.85872i	0.0562156	+	0.0973684i
$863$	−26.3594	+	45.6558i	−0.897284	+	1.55414i	−0.0663308	+	0.997798i	$0.521129\pi$
$863$	−26.3594	+	45.6558i	−0.897284	+	1.55414i	−0.830953	+	0.556343i	$0.812204\pi$
$864$		0			0
$865$	−26.0574	+	21.8647i	−0.885977	+	0.743423i
$866$	−25.0979	+	43.4709i	−0.852862	+	1.47720i
$867$		0			0
$868$	24.3726	+	8.87089i	0.827259	+	0.301098i
$869$	2.01795	−	11.4444i	0.0684543	−	0.388224i
$870$		0			0
$871$	9.92396	−	3.61203i	0.336261	−	0.122389i
$872$	44.2183	+	37.1035i	1.49742	+	1.25648i
$873$		0			0
$874$	42.2918	+	36.5450i	1.43054	+	1.23615i
$875$	−16.8949			−0.571151
$876$		0			0
$877$	19.9119	−	7.24735i	0.672378	−	0.244726i	0.0168069	−	0.999859i	$-0.494650\pi$
$877$	19.9119	−	7.24735i	0.672378	−	0.244726i	0.655572	+	0.755133i	$0.272428\pi$
$878$	−15.1989	−	86.1974i	−0.512939	−	2.90902i
$879$		0			0
$880$	−9.95723	−	3.62414i	−0.335658	−	0.122170i
$881$	16.0505	+	27.8003i	0.540755	+	0.936616i	0.998861	+	0.0477179i	$0.0151948\pi$
$881$	16.0505	+	27.8003i	0.540755	+	0.936616i	−0.458106	+	0.888898i	$0.651472\pi$
$882$		0			0
$883$	−36.2315	+	30.4018i	−1.21929	+	1.02310i	−0.220425	+	0.975404i	$0.570744\pi$
$883$	−36.2315	+	30.4018i	−1.21929	+	1.02310i	−0.998862	+	0.0476989i	$0.984811\pi$
$884$	−35.6181	+	29.8872i	−1.19797	+	1.00521i
$885$		0			0
$886$	21.5355	+	37.3007i	0.723501	+	1.25314i
$887$	9.92602	+	3.61278i	0.333283	+	0.121305i	0.503241	−	0.864146i	$-0.332141\pi$
$887$	9.92602	+	3.61278i	0.333283	+	0.121305i	−0.169958	+	0.985451i	$0.554363\pi$
$888$		0			0
$889$	−3.85844	−	21.8823i	−0.129408	−	0.733909i
$890$	−7.77719	+	2.83067i	−0.260692	+	0.0948841i
$891$		0			0
$892$	−68.2704			−2.28586
$893$	1.21941	+	2.18463i	0.0408059	+	0.0731059i
$894$		0			0
$895$	−6.01779	−	5.04952i	−0.201153	−	0.168787i
$896$	19.2062	−	6.99049i	0.641634	−	0.233536i
$897$		0			0
$898$	−16.4488	+	93.2857i	−0.548903	+	3.11298i
$899$	16.7780	+	6.10668i	0.559576	+	0.203669i
$900$		0			0
$901$	−5.70961	+	9.88933i	−0.190215	+	0.329461i
$902$	22.9479	−	19.2556i	0.764081	−	0.641141i
$903$		0			0
$904$	4.00088	−	6.92972i	0.133067	−	0.230479i
$905$	−9.13610	−	15.8242i	−0.303694	−	0.526014i
$906$		0			0
$907$	7.45306	−	42.2684i	0.247475	−	1.40350i	−0.567200	−	0.823580i	$-0.691973\pi$
$907$	7.45306	−	42.2684i	0.247475	−	1.40350i	0.814674	−	0.579919i	$-0.196916\pi$
$908$	−7.56283	−	42.8910i	−0.250981	−	1.42339i
$909$		0			0
$910$	10.8780	+	9.12776i	0.360604	+	0.302582i
$911$	55.1411			1.82691			0.913454	−	0.406942i	$-0.133405\pi$
$911$	55.1411			1.82691			0.913454	+	0.406942i	$0.133405\pi$
$912$		0			0
$913$	−14.5945			−0.483008
$914$	17.6728	+	14.8292i	0.584563	+	0.490507i
$915$		0			0
$916$	15.4119	+	87.4055i	0.509225	+	2.88796i
$917$	5.26991	−	29.8872i	0.174028	−	0.986961i
$918$		0			0
$919$	12.2788	+	21.2676i	0.405041	+	0.701552i	0.994326	−	0.106373i	$-0.0339237\pi$
$919$	12.2788	+	21.2676i	0.405041	+	0.701552i	−0.589285	+	0.807925i	$0.700590\pi$
$920$	−20.8307	+	36.0798i	−0.686767	+	1.18952i
$921$		0			0
$922$	47.4222	−	39.7920i	1.56177	−	1.31048i
$923$	−9.42190	+	16.3192i	−0.310126	+	0.537154i
$924$		0			0
$925$	−12.2883	−	4.47259i	−0.404038	−	0.147058i
$926$	−0.110242	+	0.625213i	−0.00362277	+	0.0205458i
$927$		0			0
$928$	−20.0954	+	7.31412i	−0.659663	+	0.240098i
$929$	17.0654	+	14.3195i	0.559896	+	0.469809i	0.878276	−	0.478155i	$-0.158694\pi$
$929$	17.0654	+	14.3195i	0.559896	+	0.469809i	−0.318379	+	0.947963i	$0.603139\pi$
$930$		0			0
$931$	−15.3452	−	13.2601i	−0.502920	−	0.434581i
$932$	−15.5936			−0.510785
$933$		0			0
$934$	36.5517	−	13.3037i	1.19601	−	0.435312i
$935$	−1.07532	−	6.09845i	−0.0351668	−	0.199441i
$936$		0			0
$937$	8.97565	+	3.26687i	0.293222	+	0.106724i	0.484443	−	0.874823i	$-0.339022\pi$
$937$	8.97565	+	3.26687i	0.293222	+	0.106724i	−0.191221	+	0.981547i	$0.561245\pi$
$938$	7.53983	+	13.0594i	0.246184	+	0.426403i
$939$		0			0
$940$	−2.61334	+	2.19285i	−0.0852378	+	0.0715230i
$941$	42.6883	−	35.8197i	1.39160	−	1.16769i	0.426909	−	0.904295i	$-0.359602\pi$
$941$	42.6883	−	35.8197i	1.39160	−	1.16769i	0.964688	−	0.263394i	$-0.0848420\pi$
$942$		0			0
$943$	−25.2841	−	43.7933i	−0.823362	−	1.42610i
$944$	−24.5510	−	8.93582i	−0.799066	−	0.290836i
$945$		0			0
$946$	−4.53343	−	25.7104i	−0.147395	−	0.835916i
$947$	−25.4119	+	9.24919i	−0.825777	+	0.300558i	−0.720125	−	0.693845i	$-0.755915\pi$
$947$	−25.4119	+	9.24919i	−0.825777	+	0.300558i	−0.105653	+	0.994403i	$0.533693\pi$
$948$		0			0
$949$	16.6500			0.540482
$950$	33.2019	−	11.5421i	1.07721	−	0.374476i
$951$		0			0
$952$	−27.8011	−	23.3279i	−0.901040	−	0.756062i
$953$	21.7361	−	7.91128i	0.704100	−	0.256272i	0.0349398	−	0.999389i	$-0.488876\pi$
$953$	21.7361	−	7.91128i	0.704100	−	0.256272i	0.669161	+	0.743118i	$0.266654\pi$
$954$		0			0
$955$	2.40601	−	13.6452i	0.0778567	−	0.441547i
$956$	49.6357	+	18.0659i	1.60533	+	0.584293i
$957$		0			0
$958$	−0.910597	+	1.57720i	−0.0294200	+	0.0509570i
$959$	−11.9764	+	10.0494i	−0.386737	+	0.324511i
$960$		0			0
$961$	8.13681	−	14.0934i	0.262478	−	0.454625i
$962$	14.1236	+	24.4628i	0.455363	+	0.788713i
$963$		0			0
$964$	9.88326	−	56.0507i	0.318318	−	1.80527i
$965$	3.22874	+	18.3111i	0.103937	+	0.589455i
$966$		0			0
$967$	29.9026	+	25.0913i	0.961603	+	0.806881i	0.981213	−	0.192927i	$-0.0617980\pi$
$967$	29.9026	+	25.0913i	0.961603	+	0.806881i	−0.0196101	+	0.999808i	$0.506242\pi$
$968$	−58.5954			−1.88333
$969$		0			0
$970$	25.1411			0.807234
$971$	31.5631	+	26.4845i	1.01291	+	0.849930i	0.988720	−	0.149778i	$-0.0478559\pi$
$971$	31.5631	+	26.4845i	1.01291	+	0.849930i	0.0241869	+	0.999707i	$0.492300\pi$
$972$		0			0
$973$	−0.441752	−	2.50530i	−0.0141619	−	0.0803162i
$974$	5.16503	−	29.2923i	0.165498	−	0.938587i
$975$		0			0
$976$	14.9941	+	25.9705i	0.479948	+	0.831295i
$977$	11.2469	−	19.4802i	0.359821	−	0.623227i	−0.628110	−	0.778125i	$-0.716171\pi$
$977$	11.2469	−	19.4802i	0.359821	−	0.623227i	0.987931	+	0.154897i	$0.0495046\pi$
$978$		0			0
$979$	2.20187	−	1.84759i	0.0703720	−	0.0590491i
$980$	13.8268	−	23.9488i	0.441682	−	0.765015i
$981$		0			0
$982$	0.211362	+	0.0769295i	0.00674484	+	0.00245492i
$983$	7.73536	−	43.8694i	0.246720	−	1.39922i	−0.569746	−	0.821821i	$-0.692958\pi$
$983$	7.73536	−	43.8694i	0.246720	−	1.39922i	0.816465	−	0.577395i	$-0.195931\pi$
$984$		0			0
$985$	−10.0535	+	3.65917i	−0.320331	+	0.116591i
$986$	−35.0107	−	29.3775i	−1.11497	−	0.935570i
$987$		0			0
$988$	−48.8285	−	18.5782i	−1.55344	−	0.591052i
$989$	−44.0702			−1.40135
$990$		0			0
$991$	42.5959	−	15.5036i	1.35310	−	0.492489i	0.439187	−	0.898395i	$-0.355266\pi$
$991$	42.5959	−	15.5036i	1.35310	−	0.492489i	0.913915	+	0.405907i	$0.133044\pi$
$992$	−3.06283	−	17.3702i	−0.0972451	−	0.551504i
$993$		0			0
$994$	−25.2841	−	9.20264i	−0.801961	−	0.291890i
$995$	−18.2121	−	31.5443i	−0.577363	−	1.00002i
$996$		0			0
$997$	−8.03667	+	6.74357i	−0.254524	+	0.213571i	−0.761117	−	0.648614i	$-0.775349\pi$
$997$	−8.03667	+	6.74357i	−0.254524	+	0.213571i	0.506593	+	0.862185i	$0.330905\pi$
$998$	28.4950	−	23.9101i	0.901994	−	0.756862i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.u.c.73.1		6
3.2	odd	2		19.2.e.a.16.1	yes	6
12.11	even	2		304.2.u.b.225.1		6
15.2	even	4		475.2.u.a.149.2		12
15.8	even	4		475.2.u.a.149.1		12
15.14	odd	2		475.2.l.a.301.1		6
19.5	even	9		3249.2.a.z.1.3		3
19.6	even	9	inner	171.2.u.c.82.1		6
19.14	odd	18		3249.2.a.s.1.1		3
21.2	odd	6		931.2.v.b.263.1		6
21.5	even	6		931.2.v.a.263.1		6
21.11	odd	6		931.2.x.a.814.1		6
21.17	even	6		931.2.x.b.814.1		6
21.20	even	2		931.2.w.a.491.1		6
57.2	even	18		361.2.c.h.292.1		6
57.5	odd	18		361.2.a.g.1.1		3
57.8	even	6		361.2.e.b.245.1		6
57.11	odd	6		361.2.e.f.245.1		6
57.14	even	18		361.2.a.h.1.3		3
57.17	odd	18		361.2.c.i.292.3		6
57.23	odd	18		361.2.e.f.28.1		6
57.26	odd	6		361.2.e.g.62.1		6
57.29	even	18		361.2.e.a.99.1		6
57.32	even	18		361.2.e.h.234.1		6
57.35	odd	18		361.2.c.i.68.3		6
57.41	even	18		361.2.c.h.68.1		6
57.44	odd	18		19.2.e.a.6.1	✓	6
57.47	odd	18		361.2.e.g.99.1		6
57.50	even	6		361.2.e.a.62.1		6
57.53	even	18		361.2.e.b.28.1		6
57.56	even	2		361.2.e.h.54.1		6
228.71	odd	18		5776.2.a.bi.1.2		3
228.119	even	18		5776.2.a.br.1.2		3
228.215	even	18		304.2.u.b.177.1		6
285.14	even	18		9025.2.a.x.1.1		3
285.44	odd	18		475.2.l.a.101.1		6
285.119	odd	18		9025.2.a.bd.1.3		3
285.158	even	36		475.2.u.a.424.2		12
285.272	even	36		475.2.u.a.424.1		12
399.44	odd	18		931.2.x.a.557.1		6
399.101	even	18		931.2.v.a.177.1		6
399.158	odd	18		931.2.v.b.177.1		6
399.215	even	18		931.2.x.b.557.1		6
399.272	even	18		931.2.w.a.785.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.6.1	✓	6	57.44	odd	18
19.2.e.a.16.1	yes	6	3.2	odd	2
171.2.u.c.73.1		6	1.1	even	1	trivial
171.2.u.c.82.1		6	19.6	even	9	inner
304.2.u.b.177.1		6	228.215	even	18
304.2.u.b.225.1		6	12.11	even	2
361.2.a.g.1.1		3	57.5	odd	18
361.2.a.h.1.3		3	57.14	even	18
361.2.c.h.68.1		6	57.41	even	18
361.2.c.h.292.1		6	57.2	even	18
361.2.c.i.68.3		6	57.35	odd	18
361.2.c.i.292.3		6	57.17	odd	18
361.2.e.a.62.1		6	57.50	even	6
361.2.e.a.99.1		6	57.29	even	18
361.2.e.b.28.1		6	57.53	even	18
361.2.e.b.245.1		6	57.8	even	6
361.2.e.f.28.1		6	57.23	odd	18
361.2.e.f.245.1		6	57.11	odd	6
361.2.e.g.62.1		6	57.26	odd	6
361.2.e.g.99.1		6	57.47	odd	18
361.2.e.h.54.1		6	57.56	even	2
361.2.e.h.234.1		6	57.32	even	18
475.2.l.a.101.1		6	285.44	odd	18
475.2.l.a.301.1		6	15.14	odd	2
475.2.u.a.149.1		12	15.8	even	4
475.2.u.a.149.2		12	15.2	even	4
475.2.u.a.424.1		12	285.272	even	36
475.2.u.a.424.2		12	285.158	even	36
931.2.v.a.177.1		6	399.101	even	18
931.2.v.a.263.1		6	21.5	even	6
931.2.v.b.177.1		6	399.158	odd	18
931.2.v.b.263.1		6	21.2	odd	6
931.2.w.a.491.1		6	21.20	even	2
931.2.w.a.785.1		6	399.272	even	18
931.2.x.a.557.1		6	399.44	odd	18
931.2.x.a.814.1		6	21.11	odd	6
931.2.x.b.557.1		6	399.215	even	18
931.2.x.b.814.1		6	21.17	even	6
3249.2.a.s.1.1		3	19.14	odd	18
3249.2.a.z.1.3		3	19.5	even	9
5776.2.a.bi.1.2		3	228.71	odd	18
5776.2.a.br.1.2		3	228.119	even	18
9025.2.a.x.1.1		3	285.14	even	18
9025.2.a.bd.1.3		3	285.119	odd	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.93969 + 1.62760i) q^{2} +(0.766044 + 4.34445i) q^{4} +(0.233956 - 1.32683i) q^{5} +(-0.766044 - 1.32683i) q^{7} +(-3.05303 + 5.28801i) q^{8} +O(q^{10})\)	\(q+(1.93969 + 1.62760i) q^{2} +(0.766044 + 4.34445i) q^{4} +(0.233956 - 1.32683i) q^{5} +(-0.766044 - 1.32683i) q^{7} +(-3.05303 + 5.28801i) q^{8} +(2.61334 - 2.19285i) q^{10} +(-0.592396 + 1.02606i) q^{11} +(-2.55303 - 0.929228i) q^{13} +(0.673648 - 3.82045i) q^{14} +(-6.23783 + 2.27038i) q^{16} +(-2.97178 - 2.49362i) q^{17} +(0.819078 - 4.28125i) q^{19} +5.94356 q^{20} +(-2.81908 + 1.02606i) q^{22} +(0.879385 + 4.98724i) q^{23} +(2.99273 + 1.08926i) q^{25} +(-3.43969 - 5.95772i) q^{26} +(5.17752 - 4.34445i) q^{28} +(3.56418 - 2.99070i) q^{29} +(1.91875 + 3.32337i) q^{31} +(-4.31908 - 1.57202i) q^{32} +(-1.70574 - 9.67372i) q^{34} +(-1.93969 + 0.705990i) q^{35} -4.10607 q^{37} +(8.55690 - 6.97118i) q^{38} +(6.30200 + 5.28801i) q^{40} +(-9.38326 + 3.41523i) q^{41} +(-1.51114 + 8.57013i) q^{43} +(-4.91147 - 1.78763i) q^{44} +(-6.41147 + 11.1050i) q^{46} +(-0.439693 + 0.368946i) q^{47} +(2.32635 - 4.02936i) q^{49} +(4.03209 + 6.98378i) q^{50} +(2.08125 - 11.8034i) q^{52} +(-0.511144 - 2.89884i) q^{53} +(1.22281 + 1.02606i) q^{55} +9.35504 q^{56} +11.7811 q^{58} +(3.01501 + 2.52990i) q^{59} +(-0.784463 - 4.44891i) q^{61} +(-1.68732 + 9.56926i) q^{62} +(0.819078 + 1.41868i) q^{64} +(-1.83022 + 3.17004i) q^{65} +(-2.97771 + 2.49860i) q^{67} +(8.55690 - 14.8210i) q^{68} +(-4.91147 - 1.78763i) q^{70} +(1.20439 - 6.83045i) q^{71} +(-5.75877 + 2.09602i) q^{73} +(-7.96451 - 6.68302i) q^{74} +(19.2271 + 0.278817i) q^{76} +1.81521 q^{77} +(-9.21688 + 3.35467i) q^{79} +(1.55303 + 8.80769i) q^{80} +(-23.7592 - 8.64766i) q^{82} +(6.15910 + 10.6679i) q^{83} +(-4.00387 + 3.35965i) q^{85} +(-16.8799 + 14.1639i) q^{86} +(-3.61721 - 6.26519i) q^{88} +(-2.27972 - 0.829748i) q^{89} +(0.722811 + 4.09927i) q^{91} +(-20.9932 + 7.64090i) q^{92} -1.45336 q^{94} +(-5.48886 - 2.08840i) q^{95} +(5.64543 + 4.73708i) q^{97} +(11.0706 - 4.02936i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{5} - 6 q^{8}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^5 - 6 * q^8	\( 6 q + 6 q^{2} + 6 q^{5} - 6 q^{8} + 9 q^{10} - 3 q^{13} + 3 q^{14} - 18 q^{16} - 3 q^{17} - 12 q^{19} + 6 q^{20} - 6 q^{23} - 15 q^{26} + 6 q^{28} + 3 q^{29} + 9 q^{31} - 9 q^{32} - 6 q^{35} + 15 q^{38} - 21 q^{41} - 3 q^{43} - 9 q^{44} - 18 q^{46} + 3 q^{47} + 15 q^{49} + 15 q^{50} + 15 q^{52} + 3 q^{53} + 18 q^{55} + 6 q^{56} + 36 q^{58} - 12 q^{59} - 12 q^{61} + 12 q^{62} - 12 q^{64} + 12 q^{65} - 30 q^{67} + 15 q^{68} - 9 q^{70} + 6 q^{71} - 12 q^{73} - 15 q^{74} + 36 q^{76} + 18 q^{77} - 39 q^{79} - 3 q^{80} - 54 q^{82} - 24 q^{86} + 9 q^{88} + 12 q^{89} + 15 q^{91} - 42 q^{92} + 18 q^{94} - 39 q^{95} + 18 q^{97} + 9 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^5 - 6 * q^8 + 9 * q^10 - 3 * q^13 + 3 * q^14 - 18 * q^16 - 3 * q^17 - 12 * q^19 + 6 * q^20 - 6 * q^23 - 15 * q^26 + 6 * q^28 + 3 * q^29 + 9 * q^31 - 9 * q^32 - 6 * q^35 + 15 * q^38 - 21 * q^41 - 3 * q^43 - 9 * q^44 - 18 * q^46 + 3 * q^47 + 15 * q^49 + 15 * q^50 + 15 * q^52 + 3 * q^53 + 18 * q^55 + 6 * q^56 + 36 * q^58 - 12 * q^59 - 12 * q^61 + 12 * q^62 - 12 * q^64 + 12 * q^65 - 30 * q^67 + 15 * q^68 - 9 * q^70 + 6 * q^71 - 12 * q^73 - 15 * q^74 + 36 * q^76 + 18 * q^77 - 39 * q^79 - 3 * q^80 - 54 * q^82 - 24 * q^86 + 9 * q^88 + 12 * q^89 + 15 * q^91 - 42 * q^92 + 18 * q^94 - 39 * q^95 + 18 * q^97 + 9 * q^98

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