LMFDB - Embedded newform 1323.2.h.e.802.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(226,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

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

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

chi := DirichletCharacter("1323.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.h (of order $3$, degree $2$, 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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			802.3
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	1323.802
Dual form			1323.2.h.e.226.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.46050 q^{2} +4.05408 q^{4} +(1.29679 - 2.24611i) q^{5} +5.05408 q^{8} +O(q^{10})$	\(q+2.46050 q^{2} +4.05408 q^{4} +(1.29679 - 2.24611i) q^{5} +5.05408 q^{8} +(3.19076 - 5.52655i) q^{10} +(2.25729 + 3.90975i) q^{11} +(0.500000 + 0.866025i) q^{13} +4.32743 q^{16} +(0.472958 - 0.819187i) q^{17} +(-2.02704 - 3.51094i) q^{19} +(5.25729 - 9.10590i) q^{20} +(5.55408 + 9.61996i) q^{22} +(-0.136673 + 0.236725i) q^{23} +(-0.863327 - 1.49533i) q^{25} +(1.23025 + 2.13086i) q^{26} +(1.23025 - 2.13086i) q^{29} -2.32743 q^{31} +0.539495 q^{32} +(1.16372 - 2.01561i) q^{34} +(-0.890369 - 1.54216i) q^{37} +(-4.98755 - 8.63868i) q^{38} +(6.55408 - 11.3520i) q^{40} +(3.20321 + 5.54812i) q^{41} +(5.21780 - 9.03749i) q^{43} +(9.15126 + 15.8505i) q^{44} +(-0.336285 + 0.582462i) q^{46} -12.1623 q^{47} +(-2.12422 - 3.67926i) q^{50} +(2.02704 + 3.51094i) q^{52} +(-3.13667 + 5.43288i) q^{53} +11.7089 q^{55} +(3.02704 - 5.24299i) q^{58} -2.72665 q^{59} +2.27335 q^{61} -5.72665 q^{62} -7.32743 q^{64} +2.59358 q^{65} -15.8171 q^{67} +(1.91741 - 3.32105i) q^{68} -3.27335 q^{71} +(-0.753696 + 1.30544i) q^{73} +(-2.19076 - 3.79450i) q^{74} +(-8.21780 - 14.2336i) q^{76} +14.7089 q^{79} +(5.61177 - 9.71987i) q^{80} +(7.88151 + 13.6512i) q^{82} +(0.472958 - 0.819187i) q^{83} +(-1.22665 - 2.12463i) q^{85} +(12.8384 - 22.2368i) q^{86} +(11.4086 + 19.7602i) q^{88} +(7.17830 + 12.4332i) q^{89} +(-0.554084 + 0.959702i) q^{92} -29.9253 q^{94} -10.5146 q^{95} +(-5.74484 + 9.95036i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 6 q^{4} + 5 q^{5} + 12 q^{8}+O(q^{10}) $ 6 * q + 2 * q^2 + 6 * q^4 + 5 * q^5 + 12 * q^8	$ 6 q + 2 q^{2} + 6 q^{4} + 5 q^{5} + 12 q^{8} - 2 q^{11} + 3 q^{13} + 6 q^{16} + 12 q^{17} - 3 q^{19} + 16 q^{20} + 15 q^{22} - 6 q^{25} + q^{26} + q^{29} + 6 q^{31} + 16 q^{32} - 3 q^{34} + 3 q^{37} - 8 q^{38} + 21 q^{40} + 22 q^{41} + 3 q^{43} + 23 q^{44} - 12 q^{46} - 18 q^{47} + 10 q^{50} + 3 q^{52} - 18 q^{53} + 12 q^{55} + 9 q^{58} - 18 q^{59} + 12 q^{61} - 36 q^{62} - 24 q^{64} + 10 q^{65} - 6 q^{68} - 18 q^{71} + 3 q^{73} + 6 q^{74} - 21 q^{76} + 30 q^{79} - 11 q^{80} + 9 q^{82} + 12 q^{83} - 9 q^{85} + 34 q^{86} + 21 q^{88} + 2 q^{89} + 15 q^{92} - 48 q^{94} - 32 q^{95} + 3 q^{97}+O(q^{100}) $ 6 * q + 2 * q^2 + 6 * q^4 + 5 * q^5 + 12 * q^8 - 2 * q^11 + 3 * q^13 + 6 * q^16 + 12 * q^17 - 3 * q^19 + 16 * q^20 + 15 * q^22 - 6 * q^25 + q^26 + q^29 + 6 * q^31 + 16 * q^32 - 3 * q^34 + 3 * q^37 - 8 * q^38 + 21 * q^40 + 22 * q^41 + 3 * q^43 + 23 * q^44 - 12 * q^46 - 18 * q^47 + 10 * q^50 + 3 * q^52 - 18 * q^53 + 12 * q^55 + 9 * q^58 - 18 * q^59 + 12 * q^61 - 36 * q^62 - 24 * q^64 + 10 * q^65 - 6 * q^68 - 18 * q^71 + 3 * q^73 + 6 * q^74 - 21 * q^76 + 30 * q^79 - 11 * q^80 + 9 * q^82 + 12 * q^83 - 9 * q^85 + 34 * q^86 + 21 * q^88 + 2 * q^89 + 15 * q^92 - 48 * q^94 - 32 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.46050			1.73984			0.869920	−	0.493193i	$-0.164170\pi$
$2$	2.46050			1.73984			0.869920	+	0.493193i	$0.164170\pi$
$3$		0			0
$3$		0			0
$4$	4.05408			2.02704
$5$	1.29679	−	2.24611i	0.579942	−	1.00449i	−0.415543	−	0.909573i	$-0.636409\pi$
$5$	1.29679	−	2.24611i	0.579942	−	1.00449i	0.995485	−	0.0949156i	$-0.0302581\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	5.05408			1.78689
$9$		0			0
$10$	3.19076	−	5.52655i	1.00901	−	1.74765i
$11$	2.25729	+	3.90975i	0.680600	+	1.17883i	0.974798	+	0.223089i	$0.0716141\pi$
$11$	2.25729	+	3.90975i	0.680600	+	1.17883i	−0.294198	+	0.955744i	$0.595053\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	0.926995	−	0.375073i	$-0.122382\pi$
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	−0.788320	+	0.615265i	$0.789049\pi$
$14$		0			0
$15$		0			0
$16$	4.32743			1.08186
$17$	0.472958	−	0.819187i	0.114709	−	0.198682i	−0.802954	−	0.596041i	$-0.796740\pi$
$17$	0.472958	−	0.819187i	0.114709	−	0.198682i	0.917663	+	0.397359i	$0.130073\pi$
$18$		0			0
$19$	−2.02704	−	3.51094i	−0.465035	−	0.805465i	0.534168	−	0.845378i	$-0.320625\pi$
$19$	−2.02704	−	3.51094i	−0.465035	−	0.805465i	−0.999203	+	0.0399136i	$0.987292\pi$
$20$	5.25729	−	9.10590i	1.17557	−	2.03614i
$21$		0			0
$22$	5.55408	+	9.61996i	1.18413	+	2.05098i
$23$	−0.136673	+	0.236725i	−0.0284983	+	0.0493605i	−0.879923	−	0.475117i	$-0.842406\pi$
$23$	−0.136673	+	0.236725i	−0.0284983	+	0.0493605i	0.851425	+	0.524477i	$0.175739\pi$
$24$		0			0
$25$	−0.863327	−	1.49533i	−0.172665	−	0.299065i
$26$	1.23025	+	2.13086i	0.241272	+	0.417896i
$27$		0			0
$28$		0			0
$29$	1.23025	−	2.13086i	0.228452	−	0.395691i	−0.728897	−	0.684623i	$-0.759967\pi$
$29$	1.23025	−	2.13086i	0.228452	−	0.395691i	0.957350	+	0.288932i	$0.0933002\pi$
$30$		0			0
$31$	−2.32743			−0.418019			−0.209009	−	0.977914i	$-0.567024\pi$
$31$	−2.32743			−0.418019			−0.209009	+	0.977914i	$0.567024\pi$
$32$	0.539495			0.0953702
$33$		0			0
$34$	1.16372	−	2.01561i	0.199576	−	0.345675i
$35$		0			0
$36$		0			0
$37$	−0.890369	−	1.54216i	−0.146376	−	0.253530i	0.783510	−	0.621380i	$-0.213428\pi$
$37$	−0.890369	−	1.54216i	−0.146376	−	0.253530i	−0.929885	+	0.367849i	$0.880094\pi$
$38$	−4.98755	−	8.63868i	−0.809087	−	1.40138i
$39$		0			0
$40$	6.55408	−	11.3520i	1.03629	−	1.79491i
$41$	3.20321	+	5.54812i	0.500257	+	0.866471i	1.00000		0.000297253i	$9.46187e-5\pi$
$41$	3.20321	+	5.54812i	0.500257	+	0.866471i	−0.499743	+	0.866174i	$0.666572\pi$
$42$		0			0
$43$	5.21780	−	9.03749i	0.795707	−	1.37820i	−0.126682	−	0.991943i	$-0.540433\pi$
$43$	5.21780	−	9.03749i	0.795707	−	1.37820i	0.922389	−	0.386262i	$-0.126234\pi$
$44$	9.15126	+	15.8505i	1.37960	+	2.38955i
$45$		0			0
$46$	−0.336285	+	0.582462i	−0.0495825	+	0.0858794i
$47$	−12.1623			−1.77405			−0.887023	−	0.461724i	$-0.847231\pi$
$47$	−12.1623			−1.77405			−0.887023	+	0.461724i	$0.847231\pi$
$48$		0			0
$49$		0			0
$50$	−2.12422	−	3.67926i	−0.300410	−	0.520326i
$51$		0			0
$52$	2.02704	+	3.51094i	0.281100	+	0.486880i
$53$	−3.13667	+	5.43288i	−0.430855	+	0.746263i	−0.996947	−	0.0780790i	$-0.975121\pi$
$53$	−3.13667	+	5.43288i	−0.430855	+	0.746263i	0.566092	+	0.824342i	$0.308455\pi$
$54$		0			0
$55$	11.7089			1.57883
$56$		0			0
$57$		0			0
$58$	3.02704	−	5.24299i	0.397470	−	0.688438i
$59$	−2.72665			−0.354980			−0.177490	−	0.984123i	$-0.556798\pi$
$59$	−2.72665			−0.354980			−0.177490	+	0.984123i	$0.556798\pi$
$60$		0			0
$61$	2.27335			0.291072			0.145536	−	0.989353i	$-0.453509\pi$
$61$	2.27335			0.291072			0.145536	+	0.989353i	$0.453509\pi$
$62$	−5.72665			−0.727286
$63$		0			0
$64$	−7.32743			−0.915929
$65$	2.59358			0.321694
$66$		0			0
$67$	−15.8171			−1.93237			−0.966184	−	0.257854i	$-0.916985\pi$
$67$	−15.8171			−1.93237			−0.966184	+	0.257854i	$0.916985\pi$
$68$	1.91741	−	3.32105i	0.232520	−	0.402737i
$69$		0			0
$70$		0			0
$71$	−3.27335			−0.388475			−0.194237	−	0.980955i	$-0.562223\pi$
$71$	−3.27335			−0.388475			−0.194237	+	0.980955i	$0.562223\pi$
$72$		0			0
$73$	−0.753696	+	1.30544i	−0.0882134	+	0.152790i	−0.906756	−	0.421656i	$-0.861449\pi$
$73$	−0.753696	+	1.30544i	−0.0882134	+	0.152790i	0.818543	+	0.574446i	$0.194782\pi$
$74$	−2.19076	−	3.79450i	−0.254670	−	0.441102i
$75$		0			0
$76$	−8.21780	−	14.2336i	−0.942646	−	1.63271i
$77$		0			0
$78$		0			0
$79$	14.7089			1.65489			0.827443	−	0.561550i	$-0.189795\pi$
$79$	14.7089			1.65489			0.827443	+	0.561550i	$0.189795\pi$
$80$	5.61177	−	9.71987i	0.627415	−	1.08671i
$81$		0			0
$82$	7.88151	+	13.6512i	0.870368	+	1.50752i
$83$	0.472958	−	0.819187i	0.0519139	−	0.0899175i	−0.838901	−	0.544285i	$-0.816801\pi$
$83$	0.472958	−	0.819187i	0.0519139	−	0.0899175i	0.890815	+	0.454367i	$0.150135\pi$
$84$		0			0
$85$	−1.22665	−	2.12463i	−0.133049	−	0.230448i
$86$	12.8384	−	22.2368i	1.38440	−	2.39786i
$87$		0			0
$88$	11.4086	+	19.7602i	1.21616	+	2.10644i
$89$	7.17830	+	12.4332i	0.760899	+	1.31792i	0.942388	+	0.334522i	$0.108575\pi$
$89$	7.17830	+	12.4332i	0.760899	+	1.31792i	−0.181489	+	0.983393i	$0.558092\pi$
$90$		0			0
$91$		0			0
$92$	−0.554084	+	0.959702i	−0.0577673	+	0.100056i
$93$		0			0
$94$	−29.9253			−3.08656
$95$	−10.5146			−1.07877
$96$		0			0
$97$	−5.74484	+	9.95036i	−0.583300	+	1.01031i	0.411785	+	0.911281i	$0.364906\pi$
$97$	−5.74484	+	9.95036i	−0.583300	+	1.01031i	−0.995085	+	0.0990246i	$0.968428\pi$
$98$		0			0
$99$		0			0
$100$	−3.50000	−	6.06218i	−0.350000	−	0.606218i
$101$	1.83988	+	3.18677i	0.183075	+	0.317096i	0.942926	−	0.333002i	$-0.108061\pi$
$101$	1.83988	+	3.18677i	0.183075	+	0.317096i	−0.759851	+	0.650097i	$0.774728\pi$
$102$		0			0
$103$	−4.86333	+	8.42353i	−0.479198	+	0.829995i	−0.999715	−	0.0238560i	$-0.992406\pi$
$103$	−4.86333	+	8.42353i	−0.479198	+	0.829995i	0.520518	+	0.853851i	$0.325739\pi$
$104$	2.52704	+	4.37697i	0.247797	+	0.429197i
$105$		0			0
$106$	−7.71780	+	13.3676i	−0.749619	+	1.29838i
$107$	−0.687159	−	1.19019i	−0.0664301	−	0.115060i	0.830897	−	0.556426i	$-0.187828\pi$
$107$	−0.687159	−	1.19019i	−0.0664301	−	0.115060i	−0.897327	+	0.441365i	$0.854494\pi$
$108$		0			0
$109$	1.69961	−	2.94381i	0.162793	−	0.281966i	−0.773076	−	0.634313i	$-0.781283\pi$
$109$	1.69961	−	2.94381i	0.162793	−	0.281966i	0.935869	+	0.352347i	$0.114616\pi$
$110$	28.8099			2.74692
$111$		0			0
$112$		0			0
$113$	5.19436	+	8.99689i	0.488644	+	0.846356i	0.999915	−	0.0130636i	$-0.00415840\pi$
$113$	5.19436	+	8.99689i	0.488644	+	0.846356i	−0.511271	+	0.859420i	$0.670825\pi$
$114$		0			0
$115$	0.354473	+	0.613964i	0.0330547	+	0.0572525i
$116$	4.98755	−	8.63868i	0.463082	−	0.802082i
$117$		0			0
$118$	−6.70895			−0.617608
$119$		0			0
$120$		0			0
$121$	−4.69076	+	8.12463i	−0.426432	+	0.738603i
$122$	5.59358			0.506419
$123$		0			0
$124$	−9.43560			−0.847342
$125$	8.48968			0.759340
$126$		0			0
$127$	0.672570			0.0596809			0.0298405	−	0.999555i	$-0.490500\pi$
$127$	0.672570			0.0596809			0.0298405	+	0.999555i	$0.490500\pi$
$128$	−19.1082			−1.68894
$129$		0			0
$130$	6.38151			0.559696
$131$	−3.95691	+	6.85356i	−0.345717	+	0.598799i	−0.985484	−	0.169770i	$-0.945697\pi$
$131$	−3.95691	+	6.85356i	−0.345717	+	0.598799i	0.639767	+	0.768569i	$0.279031\pi$
$132$		0			0
$133$		0			0
$134$	−38.9181			−3.36201
$135$		0			0
$136$	2.39037	−	4.14024i	0.204972	−	0.355023i
$137$	−1.83628	−	3.18054i	−0.156884	−	0.271732i	0.776859	−	0.629674i	$-0.216812\pi$
$137$	−1.83628	−	3.18054i	−0.156884	−	0.271732i	−0.933744	+	0.357943i	$0.883478\pi$
$138$		0			0
$139$	−1.02704	−	1.77889i	−0.0871126	−	0.150883i	0.819177	−	0.573541i	$-0.194431\pi$
$139$	−1.02704	−	1.77889i	−0.0871126	−	0.150883i	−0.906289	+	0.422658i	$0.861097\pi$
$140$		0			0
$141$		0			0
$142$	−8.05408			−0.675884
$143$	−2.25729	+	3.90975i	−0.188764	+	0.326950i
$144$		0			0
$145$	−3.19076	−	5.52655i	−0.264978	−	0.458955i
$146$	−1.85447	+	3.21204i	−0.153477	+	0.265830i
$147$		0			0
$148$	−3.60963	−	6.25206i	−0.296710	−	0.513917i
$149$	−6.77188	+	11.7292i	−0.554774	+	0.960897i	0.443147	+	0.896449i	$0.353862\pi$
$149$	−6.77188	+	11.7292i	−0.554774	+	0.960897i	−0.997921	+	0.0644482i	$0.979471\pi$
$150$		0			0
$151$	−4.96410	−	8.59808i	−0.403973	−	0.699702i	0.590228	−	0.807236i	$-0.299038\pi$
$151$	−4.96410	−	8.59808i	−0.403973	−	0.699702i	−0.994201	+	0.107535i	$0.965704\pi$
$152$	−10.2448	−	17.7446i	−0.830966	−	1.43928i
$153$		0			0
$154$		0			0
$155$	−3.01819	+	5.22765i	−0.242427	+	0.419895i
$156$		0			0
$157$	−6.05408			−0.483169			−0.241584	−	0.970380i	$-0.577667\pi$
$157$	−6.05408			−0.483169			−0.241584	+	0.970380i	$0.577667\pi$
$158$	36.1914			2.87924
$159$		0			0
$160$	0.699612	−	1.21176i	0.0553092	−	0.0957983i
$161$		0			0
$162$		0			0
$163$	−8.90856	−	15.4301i	−0.697772	−	1.20858i	−0.969237	−	0.246128i	$-0.920842\pi$
$163$	−8.90856	−	15.4301i	−0.697772	−	1.20858i	0.271465	−	0.962448i	$-0.412492\pi$
$164$	12.9861	+	22.4926i	1.01404	+	1.75637i
$165$		0			0
$166$	1.16372	−	2.01561i	0.0903218	−	0.156442i
$167$	4.23385	+	7.33325i	0.327625	+	0.567464i	0.982040	−	0.188672i	$-0.0604183\pi$
$167$	4.23385	+	7.33325i	0.327625	+	0.567464i	−0.654415	+	0.756136i	$0.727085\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	−3.01819	−	5.22765i	−0.231484	−	0.400943i
$171$		0			0
$172$	21.1534	−	36.6388i	1.61293	−	2.79368i
$173$	17.3566			1.31960			0.659799	−	0.751442i	$-0.270641\pi$
$173$	17.3566			1.31960			0.659799	+	0.751442i	$0.270641\pi$
$174$		0			0
$175$		0			0
$176$	9.76829	+	16.9192i	0.736312	+	1.27533i
$177$		0			0
$178$	17.6623	+	30.5919i	1.32384	+	2.29296i
$179$	−5.67471	+	9.82888i	−0.424147	+	0.734645i	−0.996340	−	0.0854741i	$-0.972759\pi$
$179$	−5.67471	+	9.82888i	−0.424147	+	0.734645i	0.572193	+	0.820119i	$0.306093\pi$
$180$		0			0
$181$	−21.8889			−1.62699			−0.813495	−	0.581572i	$-0.802438\pi$
$181$	−21.8889			−1.62699			−0.813495	+	0.581572i	$0.802438\pi$
$182$		0			0
$183$		0			0
$184$	−0.690757	+	1.19643i	−0.0509233	+	0.0882018i
$185$	−4.61849			−0.339558
$186$		0			0
$187$	4.27042			0.312284
$188$	−49.3068			−3.59607
$189$		0			0
$190$	−25.8712			−1.87689
$191$	0.701748			0.0507767			0.0253883	−	0.999678i	$-0.491918\pi$
$191$	0.701748			0.0507767			0.0253883	+	0.999678i	$0.491918\pi$
$192$		0			0
$193$	12.1445			0.874183			0.437092	−	0.899417i	$-0.356009\pi$
$193$	12.1445			0.874183			0.437092	+	0.899417i	$0.356009\pi$
$194$	−14.1352	+	24.4829i	−1.01485	+	1.75777i
$195$		0			0
$196$		0			0
$197$	16.4107			1.16921			0.584607	−	0.811317i	$-0.301249\pi$
$197$	16.4107			1.16921			0.584607	+	0.811317i	$0.301249\pi$
$198$		0			0
$199$	11.3530	−	19.6640i	0.804794	−	1.39394i	−0.111637	−	0.993749i	$-0.535609\pi$
$199$	11.3530	−	19.6640i	0.804794	−	1.39394i	0.916430	−	0.400194i	$-0.131057\pi$
$200$	−4.36333	−	7.55750i	−0.308534	−	0.534396i
$201$		0			0
$202$	4.52704	+	7.84107i	0.318522	+	0.551696i
$203$		0			0
$204$		0			0
$205$	16.6156			1.16048
$206$	−11.9662	+	20.7261i	−0.833727	+	1.44406i
$207$		0			0
$208$	2.16372	+	3.74766i	0.150027	+	0.259854i
$209$	9.15126	−	15.8505i	0.633006	−	1.09640i
$210$		0			0
$211$	−2.28074	−	3.95035i	−0.157012	−	0.271954i	0.776778	−	0.629775i	$-0.216853\pi$
$211$	−2.28074	−	3.95035i	−0.157012	−	0.271954i	−0.933790	+	0.357822i	$0.883520\pi$
$212$	−12.7163	+	22.0253i	−0.873362	+	1.51271i
$213$		0			0
$214$	−1.69076	−	2.92848i	−0.115578	−	0.200187i
$215$	−13.5328	−	23.4395i	−0.922928	−	1.59856i
$216$		0			0
$217$		0			0
$218$	4.18190	−	7.24327i	0.283234	−	0.490576i
$219$		0			0
$220$	47.4690			3.20036
$221$	0.945916			0.0636292
$222$		0			0
$223$	6.66225	−	11.5394i	0.446137	−	0.772733i	−0.551993	−	0.833849i	$-0.686133\pi$
$223$	6.66225	−	11.5394i	0.446137	−	0.772733i	0.998131	+	0.0611159i	$0.0194659\pi$
$224$		0			0
$225$		0			0
$226$	12.7807	+	22.1369i	0.850162	+	1.47252i
$227$	−0.690757	−	1.19643i	−0.0458472	−	0.0794096i	0.842191	−	0.539179i	$-0.181265\pi$
$227$	−0.690757	−	1.19643i	−0.0458472	−	0.0794096i	−0.888038	+	0.459769i	$0.847932\pi$
$228$		0			0
$229$	−8.98968	+	15.5706i	−0.594055	+	1.02893i	0.399625	+	0.916679i	$0.369141\pi$
$229$	−8.98968	+	15.5706i	−0.594055	+	1.02893i	−0.993679	+	0.112254i	$0.964193\pi$
$230$	0.872181	+	1.51066i	0.0575099	+	0.0996101i
$231$		0			0
$232$	6.21780	−	10.7695i	0.408219	−	0.707055i
$233$	−9.49115	−	16.4391i	−0.621786	−	1.07696i	−0.989153	−	0.146888i	$-0.953074\pi$
$233$	−9.49115	−	16.4391i	−0.621786	−	1.07696i	0.367367	−	0.930076i	$-0.380259\pi$
$234$		0			0
$235$	−15.7719	+	27.3177i	−1.02884	+	1.78201i
$236$	−11.0541			−0.719560
$237$		0			0
$238$		0			0
$239$	2.44592	+	4.23645i	0.158213	+	0.274033i	0.934224	−	0.356686i	$-0.116093\pi$
$239$	2.44592	+	4.23645i	0.158213	+	0.274033i	−0.776011	+	0.630719i	$0.782760\pi$
$240$		0			0
$241$	−13.0797	−	22.6546i	−0.842535	−	1.45931i	−0.887745	−	0.460336i	$-0.847729\pi$
$241$	−13.0797	−	22.6546i	−0.842535	−	1.45931i	0.0452094	−	0.998978i	$-0.485604\pi$
$242$	−11.5416	+	19.9907i	−0.741924	+	1.28505i
$243$		0			0
$244$	9.21634			0.590016
$245$		0			0
$246$		0			0
$247$	2.02704	−	3.51094i	0.128978	−	0.223396i
$248$	−11.7630			−0.746953
$249$		0			0
$250$	20.8889			1.32113
$251$	18.4576			1.16503			0.582516	−	0.812819i	$-0.302068\pi$
$251$	18.4576			1.16503			0.582516	+	0.812819i	$0.302068\pi$
$252$		0			0
$253$	−1.23405			−0.0775838
$254$	1.65486			0.103835
$255$		0			0
$256$	−32.3609			−2.02256
$257$	5.86693	−	10.1618i	0.365969	−	0.633876i	−0.622962	−	0.782252i	$-0.714071\pi$
$257$	5.86693	−	10.1618i	0.365969	−	0.633876i	0.988931	+	0.148375i	$0.0474044\pi$
$258$		0			0
$259$		0			0
$260$	10.5146			0.652087
$261$		0			0
$262$	−9.73599	+	16.8632i	−0.601491	+	1.04181i
$263$	−3.76089	−	6.51406i	−0.231907	−	0.401674i	0.726463	−	0.687206i	$-0.241163\pi$
$263$	−3.76089	−	6.51406i	−0.231907	−	0.401674i	−0.958369	+	0.285532i	$0.907830\pi$
$264$		0			0
$265$	8.13521	+	14.0906i	0.499742	+	0.865579i
$266$		0			0
$267$		0			0
$268$	−64.1239			−3.91699
$269$	9.41741	−	16.3114i	0.574190	−	0.994526i	−0.421939	−	0.906624i	$-0.638651\pi$
$269$	9.41741	−	16.3114i	0.574190	−	0.994526i	0.996129	−	0.0879017i	$-0.0280161\pi$
$270$		0			0
$271$	−11.9911	−	20.7693i	−0.728410	−	1.26164i	−0.957555	−	0.288251i	$-0.906926\pi$
$271$	−11.9911	−	20.7693i	−0.728410	−	1.26164i	0.229145	−	0.973392i	$-0.426407\pi$
$272$	2.04669	−	3.54498i	0.124099	−	0.214946i
$273$		0			0
$274$	−4.51819	−	7.82573i	−0.272954	−	0.472770i
$275$	3.89757	−	6.75078i	0.235032	−	0.407088i
$276$		0			0
$277$	−3.58113	−	6.20269i	−0.215169	−	0.372684i	0.738156	−	0.674630i	$-0.235697\pi$
$277$	−3.58113	−	6.20269i	−0.215169	−	0.372684i	−0.953325	+	0.301947i	$0.902364\pi$
$278$	−2.52704	−	4.37697i	−0.151562	−	0.262513i
$279$		0			0
$280$		0			0
$281$	7.44085	−	12.8879i	0.443884	−	0.768830i	−0.554090	−	0.832457i	$-0.686933\pi$
$281$	7.44085	−	12.8879i	0.443884	−	0.768830i	0.997974	+	0.0636271i	$0.0202668\pi$
$282$		0			0
$283$	−19.9971			−1.18870			−0.594351	−	0.804205i	$-0.702591\pi$
$283$	−19.9971			−1.18870			−0.594351	+	0.804205i	$0.702591\pi$
$284$	−13.2704			−0.787455
$285$		0			0
$286$	−5.55408	+	9.61996i	−0.328420	+	0.568840i
$287$		0			0
$288$		0			0
$289$	8.05262	+	13.9475i	0.473684	+	0.820444i
$290$	−7.85087	−	13.5981i	−0.461019	−	0.798509i
$291$		0			0
$292$	−3.05555	+	5.29236i	−0.178812	+	0.309712i
$293$	−7.53278	−	13.0472i	−0.440070	−	0.762223i	0.557625	−	0.830093i	$-0.311713\pi$
$293$	−7.53278	−	13.0472i	−0.440070	−	0.762223i	−0.997694	+	0.0678705i	$0.978380\pi$
$294$		0			0
$295$	−3.53590	+	6.12435i	−0.205868	+	0.356574i
$296$	−4.50000	−	7.79423i	−0.261557	−	0.453030i
$297$		0			0
$298$	−16.6623	+	28.8599i	−0.965218	+	1.67181i
$299$	−0.273346			−0.0158080
$300$		0			0
$301$		0			0
$302$	−12.2142	−	21.1556i	−0.702848	−	1.21737i
$303$		0			0
$304$	−8.77188	−	15.1933i	−0.503102	−	0.871398i
$305$	2.94805	−	5.10618i	0.168805	−	0.292379i
$306$		0			0
$307$	27.2704			1.55641			0.778203	−	0.628013i	$-0.216132\pi$
$307$	27.2704			1.55641			0.778203	+	0.628013i	$0.216132\pi$
$308$		0			0
$309$		0			0
$310$	−7.42627	+	12.8627i	−0.421784	+	0.730551i
$311$	−15.9823			−0.906273			−0.453136	−	0.891441i	$-0.649695\pi$
$311$	−15.9823			−0.906273			−0.453136	+	0.891441i	$0.649695\pi$
$312$		0			0
$313$	−11.5979			−0.655549			−0.327775	−	0.944756i	$-0.606299\pi$
$313$	−11.5979			−0.655549			−0.327775	+	0.944756i	$0.606299\pi$
$314$	−14.8961			−0.840636
$315$		0			0
$316$	59.6313			3.35452
$317$	2.01771			0.113326			0.0566629	−	0.998393i	$-0.481954\pi$
$317$	2.01771			0.113326			0.0566629	+	0.998393i	$0.481954\pi$
$318$		0			0
$319$	11.1082			0.621938
$320$	−9.50214	+	16.4582i	−0.531186	+	0.920040i
$321$		0			0
$322$		0			0
$323$	−3.83482			−0.213375
$324$		0			0
$325$	0.863327	−	1.49533i	0.0478888	−	0.0829458i
$326$	−21.9195	−	37.9658i	−1.21401	−	2.10273i
$327$		0			0
$328$	16.1893	+	28.0407i	0.893904	+	1.54829i
$329$		0			0
$330$		0			0
$331$	−19.7089			−1.08330			−0.541651	−	0.840604i	$-0.682200\pi$
$331$	−19.7089			−1.08330			−0.541651	+	0.840604i	$0.682200\pi$
$332$	1.91741	−	3.32105i	0.105232	−	0.182266i
$333$		0			0
$334$	10.4174	+	18.0435i	0.570015	+	0.987296i
$335$	−20.5115	+	35.5269i	−1.12066	+	1.94104i
$336$		0			0
$337$	14.5256	+	25.1590i	0.791259	+	1.37050i	0.925188	+	0.379509i	$0.123907\pi$
$337$	14.5256	+	25.1590i	0.791259	+	1.37050i	−0.133929	+	0.990991i	$0.542759\pi$
$338$	14.7630	−	25.5703i	0.803003	−	1.39084i
$339$		0			0
$340$	−4.97296	−	8.61342i	−0.269697	−	0.467128i
$341$	−5.25370	−	9.09967i	−0.284504	−	0.492775i
$342$		0			0
$343$		0			0
$344$	26.3712	−	45.6763i	1.42184	−	2.46270i
$345$		0			0
$346$	42.7060			2.29589
$347$	−29.0833			−1.56127			−0.780636	−	0.624986i	$-0.785105\pi$
$347$	−29.0833			−1.56127			−0.780636	+	0.624986i	$0.785105\pi$
$348$		0			0
$349$	12.3815	−	21.4454i	0.662767	−	1.14795i	−0.317118	−	0.948386i	$-0.602715\pi$
$349$	12.3815	−	21.4454i	0.662767	−	1.14795i	0.979885	−	0.199561i	$-0.0639515\pi$
$350$		0			0
$351$		0			0
$352$	1.21780	+	2.10929i	0.0649089	+	0.112426i
$353$	16.6513	+	28.8408i	0.886257	+	1.53504i	0.844266	+	0.535925i	$0.180037\pi$
$353$	16.6513	+	28.8408i	0.886257	+	1.53504i	0.0419914	+	0.999118i	$0.486630\pi$
$354$		0			0
$355$	−4.24484	+	7.35228i	−0.225293	+	0.390219i
$356$	29.1015	+	50.4052i	1.54237	+	2.67147i
$357$		0			0
$358$	−13.9626	+	24.1840i	−0.737949	+	1.27816i
$359$	12.7683	+	22.1153i	0.673884	+	1.16720i	0.976794	+	0.214182i	$0.0687087\pi$
$359$	12.7683	+	22.1153i	0.673884	+	1.16720i	−0.302909	+	0.953019i	$0.597958\pi$
$360$		0			0
$361$	1.28220	−	2.22084i	0.0674842	−	0.116886i
$362$	−53.8578			−2.83070
$363$		0			0
$364$		0			0
$365$	1.95477	+	3.38576i	0.102317	+	0.177219i
$366$		0			0
$367$	13.7252	+	23.7727i	0.716449	+	1.24093i	0.962398	+	0.271644i	$0.0875672\pi$
$367$	13.7252	+	23.7727i	0.716449	+	1.24093i	−0.245949	+	0.969283i	$0.579100\pi$
$368$	−0.591443	+	1.02441i	−0.0308311	+	0.0534011i
$369$		0			0
$370$	−11.3638			−0.590776
$371$		0			0
$372$		0			0
$373$	−8.16372	+	14.1400i	−0.422701	+	0.732140i	−0.996203	−	0.0870646i	$-0.972251\pi$
$373$	−8.16372	+	14.1400i	−0.422701	+	0.732140i	0.573502	+	0.819204i	$0.305585\pi$
$374$	10.5074			0.543324
$375$		0			0
$376$	−61.4690			−3.17002
$377$	2.46050			0.126722
$378$		0			0
$379$	12.0364			0.618267			0.309134	−	0.951019i	$-0.399961\pi$
$379$	12.0364			0.618267			0.309134	+	0.951019i	$0.399961\pi$
$380$	−42.6270			−2.18672
$381$		0			0
$382$	1.72665			0.0883433
$383$	6.21780	−	10.7695i	0.317715	−	0.550298i	−0.662296	−	0.749242i	$-0.730418\pi$
$383$	6.21780	−	10.7695i	0.317715	−	0.550298i	0.980011	+	0.198944i	$0.0637512\pi$
$384$		0			0
$385$		0			0
$386$	29.8817			1.52094
$387$		0			0
$388$	−23.2901	+	40.3396i	−1.18237	+	2.04793i
$389$	10.3004	+	17.8408i	0.522250	+	0.904564i	0.999665	+	0.0258860i	$0.00824070\pi$
$389$	10.3004	+	17.8408i	0.522250	+	0.904564i	−0.477414	+	0.878678i	$0.658426\pi$
$390$		0			0
$391$	0.129281	+	0.223922i	0.00653803	+	0.0113242i
$392$		0			0
$393$		0			0
$394$	40.3786			2.03424
$395$	19.0744	−	33.0378i	0.959738	−	1.66231i
$396$		0			0
$397$	−11.8186	−	20.4704i	−0.593157	−	1.02738i	−0.993804	−	0.111146i	$-0.964548\pi$
$397$	−11.8186	−	20.4704i	−0.593157	−	1.02738i	0.400647	−	0.916233i	$-0.368785\pi$
$398$	27.9341	−	48.3833i	1.40021	−	2.42524i
$399$		0			0
$400$	−3.73599	−	6.47092i	−0.186799	−	0.323546i
$401$	−1.28220	+	2.22084i	−0.0640300	+	0.110903i	−0.896263	−	0.443522i	$-0.853729\pi$
$401$	−1.28220	+	2.22084i	−0.0640300	+	0.110903i	0.832233	+	0.554426i	$0.187062\pi$
$402$		0			0
$403$	−1.16372	−	2.01561i	−0.0579688	−	0.100405i
$404$	7.45904	+	12.9194i	0.371101	+	0.642766i
$405$		0			0
$406$		0			0
$407$	4.01965	−	6.96224i	0.199247	−	0.345105i
$408$		0			0
$409$	34.3245			1.69724			0.848619	−	0.529005i	$-0.177435\pi$
$409$	34.3245			1.69724			0.848619	+	0.529005i	$0.177435\pi$
$410$	40.8827			2.01905
$411$		0			0
$412$	−19.7163	+	34.1497i	−0.971354	+	1.68243i
$413$		0			0
$414$		0			0
$415$	−1.22665	−	2.12463i	−0.0602141	−	0.104294i
$416$	0.269748	+	0.467216i	0.0132255	+	0.0229072i
$417$		0			0
$418$	22.5167	−	39.0001i	1.10133	−	1.90756i
$419$	−2.02850	−	3.51347i	−0.0990989	−	0.171644i	0.812213	−	0.583361i	$-0.198263\pi$
$419$	−2.02850	−	3.51347i	−0.0990989	−	0.171644i	−0.911312	+	0.411717i	$0.864929\pi$
$420$		0			0
$421$	10.5344	−	18.2462i	0.513417	−	0.889264i	−0.486462	−	0.873702i	$-0.661713\pi$
$421$	10.5344	−	18.2462i	0.513417	−	0.889264i	0.999879	−	0.0155624i	$-0.00495387\pi$
$422$	−5.61177	−	9.71987i	−0.273177	−	0.473156i
$423$		0			0
$424$	−15.8530	+	27.4582i	−0.769890	+	1.33349i
$425$	−1.63327			−0.0792252
$426$		0			0
$427$		0			0
$428$	−2.78580	−	4.82515i	−0.134657	−	0.233232i
$429$		0			0
$430$	−33.2975	−	57.6729i	−1.60575	−	2.78123i
$431$	11.3092	−	19.5882i	0.544747	−	0.943530i	−0.453876	−	0.891065i	$-0.649959\pi$
$431$	11.3092	−	19.5882i	0.544747	−	0.943530i	0.998623	−	0.0524646i	$-0.0167077\pi$
$432$		0			0
$433$	−2.41789			−0.116196			−0.0580982	−	0.998311i	$-0.518504\pi$
$433$	−2.41789			−0.116196			−0.0580982	+	0.998311i	$0.518504\pi$
$434$		0			0
$435$		0			0
$436$	6.89037	−	11.9345i	0.329989	−	0.571557i
$437$	1.10817			0.0530109
$438$		0			0
$439$	23.4897			1.12110			0.560551	−	0.828120i	$-0.310589\pi$
$439$	23.4897			1.12110			0.560551	+	0.828120i	$0.310589\pi$
$440$	59.1780			2.82120
$441$		0			0
$442$	2.32743			0.110705
$443$	13.4179			0.637503			0.318752	−	0.947838i	$-0.396736\pi$
$443$	13.4179			0.637503			0.318752	+	0.947838i	$0.396736\pi$
$444$		0			0
$445$	37.2350			1.76511
$446$	16.3925	−	28.3927i	0.776208	−	1.34443i
$447$		0			0
$448$		0			0
$449$	9.16225			0.432393			0.216197	−	0.976350i	$-0.430635\pi$
$449$	9.16225			0.432393			0.216197	+	0.976350i	$0.430635\pi$
$450$		0			0
$451$	−14.4612	+	25.0475i	−0.680950	+	1.17944i
$452$	21.0584	+	36.4741i	0.990502	+	1.71560i
$453$		0			0
$454$	−1.69961	−	2.94381i	−0.0797667	−	0.138160i
$455$		0			0
$456$		0			0
$457$	8.81711			0.412447			0.206224	−	0.978505i	$-0.433883\pi$
$457$	8.81711			0.412447			0.206224	+	0.978505i	$0.433883\pi$
$458$	−22.1192	+	38.3115i	−1.03356	+	1.79018i
$459$		0			0
$460$	1.43706	+	2.48906i	0.0670033	+	0.116053i
$461$	2.82957	−	4.90095i	0.131786	−	0.228260i	−0.792579	−	0.609769i	$-0.791262\pi$
$461$	2.82957	−	4.90095i	0.131786	−	0.228260i	0.924365	+	0.381509i	$0.124595\pi$
$462$		0			0
$463$	−7.86333	−	13.6197i	−0.365440	−	0.632960i	0.623407	−	0.781898i	$-0.285748\pi$
$463$	−7.86333	−	13.6197i	−0.365440	−	0.632960i	−0.988847	+	0.148937i	$0.952415\pi$
$464$	5.32383	−	9.22115i	0.247153	−	0.428081i
$465$		0			0
$466$	−23.3530	−	40.4486i	−1.08181	−	1.87375i
$467$	10.9985	+	19.0500i	0.508952	+	0.881530i	0.999946	+	0.0103675i	$0.00330013\pi$
$467$	10.9985	+	19.0500i	0.508952	+	0.881530i	−0.490995	+	0.871163i	$0.663367\pi$
$468$		0			0
$469$		0			0
$470$	−38.8068	+	67.2153i	−1.79002	+	3.10041i
$471$		0			0
$472$	−13.7807			−0.634310
$473$	47.1124			2.16623
$474$		0			0
$475$	−3.50000	+	6.06218i	−0.160591	+	0.278152i
$476$		0			0
$477$		0			0
$478$	6.01819	+	10.4238i	0.275265	+	0.476774i
$479$	−12.4875	−	21.6291i	−0.570571	−	0.988257i	−0.996507	−	0.0835043i	$-0.973389\pi$
$479$	−12.4875	−	21.6291i	−0.570571	−	0.988257i	0.425937	−	0.904753i	$-0.359945\pi$
$480$		0			0
$481$	0.890369	−	1.54216i	0.0405973	−	0.0703166i
$482$	−32.1826	−	55.7419i	−1.46588	−	2.53897i
$483$		0			0
$484$	−19.0167	+	32.9379i	−0.864397	+	1.49718i
$485$	14.8997	+	25.8070i	0.676561	+	1.17184i
$486$		0			0
$487$	8.79893	−	15.2402i	0.398717	−	0.690599i	−0.594851	−	0.803836i	$-0.702789\pi$
$487$	8.79893	−	15.2402i	0.398717	−	0.690599i	0.993568	+	0.113238i	$0.0361221\pi$
$488$	11.4897			0.520114
$489$		0			0
$490$		0			0
$491$	6.89757	+	11.9469i	0.311283	+	0.539158i	0.978640	−	0.205580i	$-0.0659080\pi$
$491$	6.89757	+	11.9469i	0.311283	+	0.539158i	−0.667358	+	0.744737i	$0.732575\pi$
$492$		0			0
$493$	−1.16372	−	2.01561i	−0.0524111	−	0.0907787i
$494$	4.98755	−	8.63868i	0.224400	−	0.388673i
$495$		0			0
$496$	−10.0718			−0.452237
$497$		0			0
$498$		0			0
$499$	−6.54377	+	11.3341i	−0.292939	+	0.507386i	−0.974503	−	0.224373i	$-0.927967\pi$
$499$	−6.54377	+	11.3341i	−0.292939	+	0.507386i	0.681564	+	0.731758i	$0.261300\pi$
$500$	34.4179			1.53921
$501$		0			0
$502$	45.4150			2.02697
$503$	−22.3068			−0.994611			−0.497305	−	0.867576i	$-0.665677\pi$
$503$	−22.3068			−0.994611			−0.497305	+	0.867576i	$0.665677\pi$
$504$		0			0
$505$	9.54377			0.424692
$506$	−3.03638			−0.134983
$507$		0			0
$508$	2.72665			0.120976
$509$	7.94659	−	13.7639i	0.352226	−	0.610074i	−0.634413	−	0.772994i	$-0.718758\pi$
$509$	7.94659	−	13.7639i	0.352226	−	0.610074i	0.986639	+	0.162920i	$0.0520914\pi$
$510$		0			0
$511$		0			0
$512$	−41.4078			−1.82998
$513$		0			0
$514$	14.4356	−	25.0032i	0.636727	−	1.10284i
$515$	12.6134	+	21.8471i	0.555814	+	0.962698i
$516$		0			0
$517$	−27.4538	−	47.5514i	−1.20742	−	2.09131i
$518$		0			0
$519$		0			0
$520$	13.1082			0.574831
$521$	−2.20895	+	3.82600i	−0.0967756	+	0.167620i	−0.910348	−	0.413843i	$-0.864186\pi$
$521$	−2.20895	+	3.82600i	−0.0967756	+	0.167620i	0.813573	+	0.581463i	$0.197520\pi$
$522$		0			0
$523$	12.6367	+	21.8874i	0.552563	+	0.957067i	0.998089	+	0.0617982i	$0.0196835\pi$
$523$	12.6367	+	21.8874i	0.552563	+	0.957067i	−0.445526	+	0.895269i	$0.646983\pi$
$524$	−16.0416	+	27.7849i	−0.700782	+	1.21379i
$525$		0			0
$526$	−9.25370	−	16.0279i	−0.403480	−	0.698848i
$527$	−1.10078	+	1.90660i	−0.0479506	+	0.0830528i
$528$		0			0
$529$	11.4626	+	19.8539i	0.498376	+	0.863212i
$530$	20.0167	+	34.6700i	0.869471	+	1.50597i
$531$		0			0
$532$		0			0
$533$	−3.20321	+	5.54812i	−0.138746	+	0.240316i
$534$		0			0
$535$	−3.56440			−0.154103
$536$	−79.9410			−3.45293
$537$		0			0
$538$	23.1716	−	40.1344i	0.998998	−	1.73032i
$539$		0			0
$540$		0			0
$541$	1.71926	+	2.97785i	0.0739168	+	0.128028i	0.900615	−	0.434618i	$-0.143117\pi$
$541$	1.71926	+	2.97785i	0.0739168	+	0.128028i	−0.826698	+	0.562646i	$0.809783\pi$
$542$	−29.5043	−	51.1029i	−1.26732	−	2.19506i
$543$		0			0
$544$	0.255158	−	0.441947i	0.0109398	−	0.0189483i
$545$	−4.40808	−	7.63501i	−0.188821	−	0.327048i
$546$		0			0
$547$	3.46410	−	6.00000i	0.148114	−	0.256542i	−0.782416	−	0.622756i	$-0.786013\pi$
$547$	3.46410	−	6.00000i	0.148114	−	0.256542i	0.930531	+	0.366214i	$0.119346\pi$
$548$	−7.44445	−	12.8942i	−0.318011	−	0.550812i
$549$		0			0
$550$	9.58998	−	16.6103i	0.408918	−	0.708267i
$551$	−9.97509			−0.424953
$552$		0			0
$553$		0			0
$554$	−8.81138	−	15.2618i	−0.374360	−	0.648410i
$555$		0			0
$556$	−4.16372	−	7.21177i	−0.176581	−	0.305847i
$557$	16.7917	−	29.0841i	0.711488	−	1.23233i	−0.252810	−	0.967516i	$-0.581355\pi$
$557$	16.7917	−	29.0841i	0.711488	−	1.23233i	0.964298	−	0.264818i	$-0.0853119\pi$
$558$		0			0
$559$	10.4356			0.441379
$560$		0			0
$561$		0			0
$562$	18.3083	−	31.7108i	0.772287	−	1.33764i
$563$	42.4792			1.79028			0.895142	−	0.445781i	$-0.147074\pi$
$563$	42.4792			1.79028			0.895142	+	0.445781i	$0.147074\pi$
$564$		0			0
$565$	26.9439			1.13354
$566$	−49.2029			−2.06815
$567$		0			0
$568$	−16.5438			−0.694161
$569$	−10.4035			−0.436137			−0.218069	−	0.975933i	$-0.569976\pi$
$569$	−10.4035			−0.436137			−0.218069	+	0.975933i	$0.569976\pi$
$570$		0			0
$571$	17.8496			0.746983			0.373491	−	0.927634i	$-0.378161\pi$
$571$	17.8496			0.746983			0.373491	+	0.927634i	$0.378161\pi$
$572$	−9.15126	+	15.8505i	−0.382633	+	0.662741i
$573$		0			0
$574$		0			0
$575$	0.471974			0.0196827
$576$		0			0
$577$	5.97150	−	10.3429i	0.248597	−	0.430582i	−0.714540	−	0.699595i	$-0.753364\pi$
$577$	5.97150	−	10.3429i	0.248597	−	0.430582i	0.963137	+	0.269013i	$0.0866973\pi$
$578$	19.8135	+	34.3180i	0.824134	+	1.42744i
$579$		0			0
$580$	−12.9356	−	22.4051i	−0.537122	−	0.930322i
$581$		0			0
$582$		0			0
$583$	−28.3216			−1.17296
$584$	−3.80924	+	6.59780i	−0.157628	+	0.273019i
$585$		0			0
$586$	−18.5344	−	32.1026i	−0.765650	−	1.32615i
$587$	−11.9299	+	20.6631i	−0.492398	+	0.852859i	−0.999962	−	0.00875568i	$-0.997213\pi$
$587$	−11.9299	+	20.6631i	−0.492398	+	0.852859i	0.507563	+	0.861614i	$0.330546\pi$
$588$		0			0
$589$	4.71780	+	8.17147i	0.194394	+	0.336699i
$590$	−8.70009	+	15.0690i	−0.358177	+	0.620381i
$591$		0			0
$592$	−3.85301	−	6.67361i	−0.158358	−	0.274284i
$593$	−9.79007	−	16.9569i	−0.402030	−	0.696336i	0.591941	−	0.805981i	$-0.298362\pi$
$593$	−9.79007	−	16.9569i	−0.402030	−	0.696336i	−0.993971	+	0.109645i	$0.965029\pi$
$594$		0			0
$595$		0			0
$596$	−27.4538	+	47.5514i	−1.12455	+	1.94778i
$597$		0			0
$598$	−0.672570			−0.0275034
$599$	−18.5467			−0.757797			−0.378899	−	0.925438i	$-0.623697\pi$
$599$	−18.5467			−0.757797			−0.378899	+	0.925438i	$0.623697\pi$
$600$		0			0
$601$	−9.09931	+	15.7605i	−0.371169	+	0.642883i	−0.989746	−	0.142841i	$-0.954376\pi$
$601$	−9.09931	+	15.7605i	−0.371169	+	0.642883i	0.618577	+	0.785724i	$0.287710\pi$
$602$		0			0
$603$		0			0
$604$	−20.1249	−	34.8573i	−0.818870	−	1.41832i
$605$	12.1659	+	21.0719i	0.494612	+	0.856693i
$606$		0			0
$607$	−11.1549	+	19.3208i	−0.452762	+	0.784206i	−0.998556	−	0.0537125i	$-0.982895\pi$
$607$	−11.1549	+	19.3208i	−0.452762	+	0.784206i	0.545795	+	0.837919i	$0.316228\pi$
$608$	−1.09358	−	1.89413i	−0.0443505	−	0.0768173i
$609$		0			0
$610$	7.25370	−	12.5638i	0.293694	−	0.508692i
$611$	−6.08113	−	10.5328i	−0.246016	−	0.426112i
$612$		0			0
$613$	−5.11849	+	8.86548i	−0.206734	+	0.358073i	−0.950684	−	0.310162i	$-0.899617\pi$
$613$	−5.11849	+	8.86548i	−0.206734	+	0.358073i	0.743950	+	0.668235i	$0.232950\pi$
$614$	67.0990			2.70790
$615$		0			0
$616$		0			0
$617$	−5.66372	−	9.80984i	−0.228013	−	0.394929i	0.729206	−	0.684294i	$-0.239889\pi$
$617$	−5.66372	−	9.80984i	−0.228013	−	0.394929i	−0.957219	+	0.289364i	$0.906556\pi$
$618$		0			0
$619$	4.31663	+	7.47663i	0.173500	+	0.300511i	0.939641	−	0.342161i	$-0.111159\pi$
$619$	4.31663	+	7.47663i	0.173500	+	0.300511i	−0.766141	+	0.642672i	$0.777826\pi$
$620$	−12.2360	+	21.1934i	−0.491409	+	0.851145i
$621$		0			0
$622$	−39.3245			−1.57677
$623$		0			0
$624$		0			0
$625$	15.3260	−	26.5454i	0.613039	−	1.06181i
$626$	−28.5366			−1.14055
$627$		0			0
$628$	−24.5438			−0.979403
$629$	−1.68443			−0.0671626
$630$		0			0
$631$	−14.8535			−0.591308			−0.295654	−	0.955295i	$-0.595538\pi$
$631$	−14.8535			−0.591308			−0.295654	+	0.955295i	$0.595538\pi$
$632$	74.3402			2.95710
$633$		0			0
$634$	4.96458			0.197169
$635$	0.872181	−	1.51066i	0.0346115	−	0.0599488i
$636$		0			0
$637$		0			0
$638$	27.3317			1.08207
$639$		0			0
$640$	−24.7793	+	42.9190i	−0.979487	+	1.69652i
$641$	−17.0797	−	29.5828i	−0.674606	−	1.16845i	−0.976584	−	0.215137i	$-0.930980\pi$
$641$	−17.0797	−	29.5828i	−0.674606	−	1.16845i	0.301978	−	0.953315i	$-0.402353\pi$
$642$		0			0
$643$	−5.41741	−	9.38323i	−0.213642	−	0.370039i	0.739210	−	0.673475i	$-0.235199\pi$
$643$	−5.41741	−	9.38323i	−0.213642	−	0.370039i	−0.952852	+	0.303437i	$0.901866\pi$
$644$		0			0
$645$		0			0
$646$	−9.43560			−0.371239
$647$	−16.4846	+	28.5522i	−0.648077	+	1.12250i	0.335504	+	0.942039i	$0.391093\pi$
$647$	−16.4846	+	28.5522i	−0.648077	+	1.12250i	−0.983582	+	0.180464i	$0.942240\pi$
$648$		0			0
$649$	−6.15486	−	10.6605i	−0.241599	−	0.418462i
$650$	2.12422	−	3.67926i	0.0833188	−	0.144312i
$651$		0			0
$652$	−36.1160	−	62.5548i	−1.41441	−	2.44984i
$653$	−1.96557	+	3.40446i	−0.0769185	+	0.133227i	−0.901919	−	0.431905i	$-0.857841\pi$
$653$	−1.96557	+	3.40446i	−0.0769185	+	0.133227i	0.825000	+	0.565132i	$0.191175\pi$
$654$		0			0
$655$	10.2626	+	17.7753i	0.400991	+	0.694537i
$656$	13.8617	+	24.0091i	0.541207	+	0.937399i
$657$		0			0
$658$		0			0
$659$	8.40856	−	14.5640i	0.327551	−	0.567335i	−0.654474	−	0.756084i	$-0.727110\pi$
$659$	8.40856	−	14.5640i	0.327551	−	0.567335i	0.982025	+	0.188749i	$0.0604434\pi$
$660$		0			0
$661$	17.0216			0.662063			0.331032	−	0.943620i	$-0.392603\pi$
$661$	17.0216			0.662063			0.331032	+	0.943620i	$0.392603\pi$
$662$	−48.4940			−1.88477
$663$		0			0
$664$	2.39037	−	4.14024i	0.0927643	−	0.160672i
$665$		0			0
$666$		0			0
$667$	0.336285	+	0.582462i	0.0130210	+	0.0225530i
$668$	17.1644	+	29.7296i	0.664110	+	1.15027i
$669$		0			0
$670$	−50.4686	+	87.4141i	−1.94977	+	3.37710i
$671$	5.13161	+	8.88821i	0.198104	+	0.343126i
$672$		0			0
$673$	−14.3727	+	24.8942i	−0.554025	+	0.959600i	0.443953	+	0.896050i	$0.353576\pi$
$673$	−14.3727	+	24.8942i	−0.554025	+	0.959600i	−0.997979	+	0.0635501i	$0.979758\pi$
$674$	35.7403	+	61.9039i	1.37666	+	2.38445i
$675$		0			0
$676$	24.3245	−	42.1313i	0.935558	−	1.62043i
$677$	−6.03638			−0.231997			−0.115998	−	0.993249i	$-0.537007\pi$
$677$	−6.03638			−0.231997			−0.115998	+	0.993249i	$0.537007\pi$
$678$		0			0
$679$		0			0
$680$	−6.19961	−	10.7380i	−0.237744	−	0.411785i
$681$		0			0
$682$	−12.9267	−	22.3898i	−0.494991	−	0.857349i
$683$	10.2556	−	17.7633i	0.392421	−	0.679693i	−0.600347	−	0.799739i	$-0.704971\pi$
$683$	10.2556	−	17.7633i	0.392421	−	0.679693i	0.992768	+	0.120046i	$0.0383043\pi$
$684$		0			0
$685$	−9.52510			−0.363935
$686$		0			0
$687$		0			0
$688$	22.5797	−	39.1091i	0.860842	−	1.49102i
$689$	−6.27335			−0.238995
$690$		0			0
$691$	15.0029			0.570738			0.285369	−	0.958418i	$-0.407884\pi$
$691$	15.0029			0.570738			0.285369	+	0.958418i	$0.407884\pi$
$692$	70.3652			2.67488
$693$		0			0
$694$	−71.5595			−2.71636
$695$	−5.32743			−0.202081
$696$		0			0
$697$	6.05993			0.229536
$698$	30.4648	−	52.7665i	1.15311	−	1.99724i
$699$		0			0
$700$		0			0
$701$	−38.5113			−1.45455			−0.727275	−	0.686346i	$-0.759214\pi$
$701$	−38.5113			−1.45455			−0.727275	+	0.686346i	$0.759214\pi$
$702$		0			0
$703$	−3.60963	+	6.25206i	−0.136140	+	0.235801i
$704$	−16.5402	−	28.6484i	−0.623381	−	1.07973i
$705$		0			0
$706$	40.9705	+	70.9630i	1.54195	+	2.67073i
$707$		0			0
$708$		0			0
$709$	7.64008			0.286929			0.143465	−	0.989655i	$-0.454176\pi$
$709$	7.64008			0.286929			0.143465	+	0.989655i	$0.454176\pi$
$710$	−10.4445	+	18.0903i	−0.391973	+	0.678918i
$711$		0			0
$712$	36.2798	+	62.8384i	1.35964	+	2.35497i
$713$	0.318097	−	0.550960i	0.0119128	−	0.0206336i
$714$		0			0
$715$	5.85447	+	10.1402i	0.218945	+	0.379224i
$716$	−23.0057	+	39.8471i	−0.859765	+	1.48916i
$717$		0			0
$718$	31.4164	+	54.4148i	1.17245	+	2.03074i
$719$	15.0182	+	26.0123i	0.560084	+	0.970094i	0.997488	+	0.0708289i	$0.0225644\pi$
$719$	15.0182	+	26.0123i	0.560084	+	0.970094i	−0.437405	+	0.899265i	$0.644102\pi$
$720$		0			0
$721$		0			0
$722$	3.15486	−	5.46438i	0.117412	−	0.203363i
$723$		0			0
$724$	−88.7395			−3.29798
$725$	−4.24844			−0.157783
$726$		0			0
$727$	1.72812	−	2.99319i	0.0640923	−	0.111011i	−0.832199	−	0.554478i	$-0.812918\pi$
$727$	1.72812	−	2.99319i	0.0640923	−	0.111011i	0.896291	+	0.443466i	$0.146251\pi$
$728$		0			0
$729$		0			0
$730$	4.80972	+	8.33068i	0.178016	+	0.308332i
$731$	−4.93560	−	8.54871i	−0.182550	−	0.316185i
$732$		0			0
$733$	19.2630	−	33.3645i	0.711496	−	1.23235i	−0.252799	−	0.967519i	$-0.581351\pi$
$733$	19.2630	−	33.3645i	0.711496	−	1.23235i	0.964295	−	0.264829i	$-0.0853155\pi$
$734$	33.7709	+	58.4929i	1.24651	+	2.15901i
$735$		0			0
$736$	−0.0737345	+	0.127712i	−0.00271789	+	0.00470752i
$737$	−35.7039	−	61.8409i	−1.31517	−	2.27794i
$738$		0			0
$739$	−22.5620	+	39.0785i	−0.829955	+	1.43752i	0.0681179	+	0.997677i	$0.478301\pi$
$739$	−22.5620	+	39.0785i	−0.829955	+	1.43752i	−0.898073	+	0.439847i	$0.855033\pi$
$740$	−18.7237			−0.688298
$741$		0			0
$742$		0			0
$743$	4.74338	+	8.21577i	0.174018	+	0.301407i	0.939821	−	0.341668i	$-0.110992\pi$
$743$	4.74338	+	8.21577i	0.174018	+	0.301407i	−0.765803	+	0.643075i	$0.777658\pi$
$744$		0			0
$745$	17.5634	+	30.4207i	0.643474	+	1.11453i
$746$	−20.0869	+	34.7915i	−0.735432	+	1.27381i
$747$		0			0
$748$	17.3126			0.633013
$749$		0			0
$750$		0			0
$751$	4.91595	−	8.51467i	0.179386	−	0.310705i	−0.762285	−	0.647242i	$-0.775922\pi$
$751$	4.91595	−	8.51467i	0.179386	−	0.310705i	0.941670	+	0.336537i	$0.109256\pi$
$752$	−52.6313			−1.91927
$753$		0			0
$754$	6.05408			0.220477
$755$	−25.7496			−0.937124
$756$		0			0
$757$	−41.8171			−1.51987			−0.759934	−	0.650000i	$-0.774769\pi$
$757$	−41.8171			−1.51987			−0.759934	+	0.650000i	$0.774769\pi$
$758$	29.6156			1.07569
$759$		0			0
$760$	−53.1416			−1.92765
$761$	−11.4897	+	19.9007i	−0.416501	+	0.721400i	−0.995585	−	0.0938675i	$-0.970077\pi$
$761$	−11.4897	+	19.9007i	−0.416501	+	0.721400i	0.579084	+	0.815268i	$0.303410\pi$
$762$		0			0
$763$		0			0
$764$	2.84494			0.102926
$765$		0			0
$766$	15.2989	−	26.4985i	0.552773	−	0.957430i
$767$	−1.36333	−	2.36135i	−0.0492269	−	0.0852635i
$768$		0			0
$769$	3.04329	+	5.27113i	0.109744	+	0.190082i	0.915666	−	0.401939i	$-0.131664\pi$
$769$	3.04329	+	5.27113i	0.109744	+	0.190082i	−0.805923	+	0.592021i	$0.798330\pi$
$770$		0			0
$771$		0			0
$772$	49.2350			1.77201
$773$	20.9107	−	36.2184i	0.752105	−	1.30268i	−0.194695	−	0.980864i	$-0.562372\pi$
$773$	20.9107	−	36.2184i	0.752105	−	1.30268i	0.946801	−	0.321821i	$-0.104295\pi$
$774$		0			0
$775$	2.00933	+	3.48027i	0.0721774	+	0.125015i
$776$	−29.0349	+	50.2899i	−1.04229	+	1.80530i
$777$		0			0
$778$	25.3442	+	43.8974i	0.908632	+	1.57380i
$779$	12.9861	−	22.4926i	0.465275	−	0.805880i
$780$		0			0
$781$	−7.38891	−	12.7980i	−0.264396	−	0.457947i
$782$	0.318097	+	0.550960i	0.0113751	+	0.0197023i
$783$		0			0
$784$		0			0
$785$	−7.85087	+	13.5981i	−0.280210	+	0.485337i
$786$		0			0
$787$	−32.2920			−1.15109			−0.575543	−	0.817772i	$-0.695209\pi$
$787$	−32.2920			−1.15109			−0.575543	+	0.817772i	$0.695209\pi$
$788$	66.5303			2.37004
$789$		0			0
$790$	46.9327	−	81.2898i	1.66979	−	2.89216i
$791$		0			0
$792$		0			0
$793$	1.13667	+	1.96878i	0.0403644	+	0.0699133i
$794$	−29.0797	−	50.3675i	−1.03200	−	1.78747i
$795$		0			0
$796$	46.0261	−	79.7195i	1.63135	−	2.82558i
$797$	−23.2829	−	40.3271i	−0.824722	−	1.42846i	−0.902132	−	0.431461i	$-0.857998\pi$
$797$	−23.2829	−	40.3271i	−0.824722	−	1.42846i	0.0774101	−	0.996999i	$-0.475335\pi$
$798$		0			0
$799$	−5.75223	+	9.96316i	−0.203499	+	0.352471i
$800$	−0.465761	−	0.806721i	−0.0164671	−	0.0285219i
$801$		0			0
$802$	−3.15486	+	5.46438i	−0.111402	+	0.192954i
$803$	−6.80525			−0.240152
$804$		0			0
$805$		0			0
$806$	−2.86333	−	4.95943i	−0.100856	−	0.174688i
$807$		0			0
$808$	9.29893	+	16.1062i	0.327135	+	0.566615i
$809$	−5.40116	+	9.35509i	−0.189895	+	0.328908i	−0.945215	−	0.326448i	$-0.894148\pi$
$809$	−5.40116	+	9.35509i	−0.189895	+	0.328908i	0.755320	+	0.655356i	$0.227481\pi$
$810$		0			0
$811$	−5.58307			−0.196048			−0.0980240	−	0.995184i	$-0.531252\pi$
$811$	−5.58307			−0.196048			−0.0980240	+	0.995184i	$0.531252\pi$
$812$		0			0
$813$		0			0
$814$	9.89037	−	17.1306i	0.346657	−	0.600428i
$815$	−46.2101			−1.61867
$816$		0			0
$817$	−42.3068			−1.48013
$818$	84.4556			2.95292
$819$		0			0
$820$	67.3609			2.35234
$821$	31.7879			1.10941			0.554703	−	0.832048i	$-0.312832\pi$
$821$	31.7879			1.10941			0.554703	+	0.832048i	$0.312832\pi$
$822$		0			0
$823$	−36.0000			−1.25488			−0.627441	−	0.778664i	$-0.715897\pi$
$823$	−36.0000			−1.25488			−0.627441	+	0.778664i	$0.715897\pi$
$824$	−24.5797	+	42.5732i	−0.856273	+	1.48311i
$825$		0			0
$826$		0			0
$827$	−15.9224			−0.553675			−0.276837	−	0.960917i	$-0.589286\pi$
$827$	−15.9224			−0.553675			−0.276837	+	0.960917i	$0.589286\pi$
$828$		0			0
$829$	17.7360	−	30.7196i	0.615996	−	1.06694i	−0.374213	−	0.927343i	$-0.622087\pi$
$829$	17.7360	−	30.7196i	0.615996	−	1.06694i	0.990209	−	0.139594i	$-0.0445797\pi$
$830$	−3.01819	−	5.22765i	−0.104763	−	0.181455i
$831$		0			0
$832$	−3.66372	−	6.34574i	−0.127016	−	0.219999i
$833$		0			0
$834$		0			0
$835$	21.9617			0.760014
$836$	37.1000	−	64.2591i	1.28313	−	2.22245i
$837$		0			0
$838$	−4.99115	−	8.64492i	−0.172416	−	0.298634i
$839$	27.3391	−	47.3527i	0.943850	−	1.63480i	0.185814	−	0.982585i	$-0.440508\pi$
$839$	27.3391	−	47.3527i	0.943850	−	1.63480i	0.758037	−	0.652212i	$-0.226159\pi$
$840$		0			0
$841$	11.4730	+	19.8717i	0.395619	+	0.685233i
$842$	25.9200	−	44.8948i	0.893263	−	1.54718i
$843$		0			0
$844$	−9.24630	−	16.0151i	−0.318271	−	0.551261i
$845$	−15.5615	−	26.9533i	−0.535331	−	0.927221i
$846$		0			0
$847$		0			0
$848$	−13.5737	+	23.5104i	−0.466124	+	0.807350i
$849$		0			0
$850$	−4.01867			−0.137839
$851$	0.486758			0.0166858
$852$		0			0
$853$	−1.09884	+	1.90324i	−0.0376234	+	0.0651656i	−0.884224	−	0.467063i	$-0.845312\pi$
$853$	−1.09884	+	1.90324i	−0.0376234	+	0.0651656i	0.846601	+	0.532229i	$0.178645\pi$
$854$		0			0
$855$		0			0
$856$	−3.47296	−	6.01534i	−0.118703	−	0.205600i
$857$	7.88823	+	13.6628i	0.269457	+	0.466713i	0.968722	−	0.248150i	$-0.0798225\pi$
$857$	7.88823	+	13.6628i	0.269457	+	0.466713i	−0.699265	+	0.714863i	$0.746489\pi$
$858$		0			0
$859$	2.78813	−	4.82918i	0.0951298	−	0.164770i	−0.814533	−	0.580117i	$-0.803007\pi$
$859$	2.78813	−	4.82918i	0.0951298	−	0.164770i	0.909663	+	0.415348i	$0.136340\pi$
$860$	−54.8630	−	95.0255i	−1.87081	−	3.24034i
$861$		0			0
$862$	27.8264	−	48.1968i	0.947773	−	1.64159i
$863$	11.5634	+	20.0284i	0.393623	+	0.681776i	0.992924	−	0.118748i	$-0.0378881\pi$
$863$	11.5634	+	20.0284i	0.393623	+	0.681776i	−0.599301	+	0.800524i	$0.704555\pi$
$864$		0			0
$865$	22.5079	−	38.9848i	0.765291	−	1.32552i
$866$	−5.94923			−0.202163
$867$		0			0
$868$		0			0
$869$	33.2024	+	57.5083i	1.12631	+	1.95083i
$870$		0			0
$871$	−7.90856	−	13.6980i	−0.267971	−	0.464140i
$872$	8.58998	−	14.8783i	0.290893	−	0.503842i
$873$		0			0
$874$	2.72665			0.0922304
$875$		0			0
$876$		0			0
$877$	−1.96264	+	3.39939i	−0.0662737	+	0.114789i	−0.897258	−	0.441506i	$-0.854444\pi$
$877$	−1.96264	+	3.39939i	−0.0662737	+	0.114789i	0.830985	+	0.556295i	$0.187778\pi$
$878$	57.7965			1.95054
$879$		0			0
$880$	50.6696			1.70807
$881$	27.1986			0.916345			0.458173	−	0.888863i	$-0.348504\pi$
$881$	27.1986			0.916345			0.458173	+	0.888863i	$0.348504\pi$
$882$		0			0
$883$	8.21341			0.276403			0.138202	−	0.990404i	$-0.455868\pi$
$883$	8.21341			0.276403			0.138202	+	0.990404i	$0.455868\pi$
$884$	3.83482			0.128979
$885$		0			0
$886$	33.0148			1.10915
$887$	3.24057	−	5.61283i	0.108808	−	0.188460i	−0.806480	−	0.591262i	$-0.798630\pi$
$887$	3.24057	−	5.61283i	0.108808	−	0.188460i	0.915287	+	0.402801i	$0.131963\pi$
$888$		0			0
$889$		0			0
$890$	91.6169			3.07101
$891$		0			0
$892$	27.0093	−	46.7815i	0.904339	−	1.56636i
$893$	24.6534	+	42.7009i	0.824995	+	1.42893i
$894$		0			0
$895$	14.7178	+	25.4920i	0.491962	+	0.852103i
$896$		0			0
$897$		0			0
$898$	22.5438			0.752295
$899$	−2.86333	+	4.95943i	−0.0954973	+	0.165406i
$900$		0			0
$901$	2.96703	+	5.13904i	0.0988461	+	0.171206i
$902$	−35.5818	+	61.6295i	−1.18474	+	2.05204i
$903$		0			0
$904$	26.2527	+	45.4710i	0.873152	+	1.51234i
$905$	−28.3853	+	49.1648i	−0.943560	+	1.63429i
$906$		0			0
$907$	−5.06440	−	8.77180i	−0.168161	−	0.291263i	0.769613	−	0.638511i	$-0.220449\pi$
$907$	−5.06440	−	8.77180i	−0.168161	−	0.291263i	−0.937773	+	0.347248i	$0.887116\pi$
$908$	−2.80039	−	4.85041i	−0.0929341	−	0.160967i
$909$		0			0
$910$		0			0
$911$	22.9612	−	39.7699i	0.760738	−	1.31764i	−0.181733	−	0.983348i	$-0.558171\pi$
$911$	22.9612	−	39.7699i	0.760738	−	1.31764i	0.942471	−	0.334289i	$-0.108496\pi$
$912$		0			0
$913$	4.27042			0.141330
$914$	21.6946			0.717592
$915$		0			0
$916$	−36.4449	+	63.1245i	−1.20417	+	2.08569i
$917$		0			0
$918$		0			0
$919$	2.46216	+	4.26459i	0.0812192	+	0.140676i	0.903774	−	0.428010i	$-0.140785\pi$
$919$	2.46216	+	4.26459i	0.0812192	+	0.140676i	−0.822555	+	0.568686i	$0.807452\pi$
$920$	1.79153	+	3.10303i	0.0590651	+	0.102304i
$921$		0			0
$922$	6.96216	−	12.0588i	0.229287	−	0.397136i
$923$	−1.63667	−	2.83480i	−0.0538718	−	0.0933086i
$924$		0			0
$925$	−1.53736	+	2.66278i	−0.0505481	+	0.0875518i
$926$	−19.3478	−	33.5113i	−0.635807	−	1.10125i
$927$		0			0
$928$	0.663715	−	1.14959i	0.0217875	−	0.0377371i
$929$	0.00758649			0.000248905			0.000124452	−	1.00000i	$-0.499960\pi$
$929$	0.00758649			0.000248905			0.000124452		1.00000i	$0.499960\pi$
$930$		0			0
$931$		0			0
$932$	−38.4779	−	66.6457i	−1.26039	−	2.18305i
$933$		0			0
$934$	27.0620	+	46.8727i	0.885494	+	1.53372i
$935$	5.53784	−	9.59182i	0.181107	−	0.313686i
$936$		0			0
$937$	−21.1623			−0.691341			−0.345670	−	0.938356i	$-0.612348\pi$
$937$	−21.1623			−0.691341			−0.345670	+	0.938356i	$0.612348\pi$
$938$		0			0
$939$		0			0
$940$	−63.9405	+	110.748i	−2.08551	+	3.61221i
$941$	4.55816			0.148592			0.0742959	−	0.997236i	$-0.476329\pi$
$941$	4.55816			0.148592			0.0742959	+	0.997236i	$0.476329\pi$
$942$		0			0
$943$	−1.75117			−0.0570260
$944$	−11.7994			−0.384038
$945$		0			0
$946$	115.920			3.76890
$947$	−13.7352			−0.446334			−0.223167	−	0.974780i	$-0.571640\pi$
$947$	−13.7352			−0.446334			−0.223167	+	0.974780i	$0.571640\pi$
$948$		0			0
$949$	−1.50739			−0.0489320
$950$	−8.61177	+	14.9160i	−0.279403	+	0.483940i
$951$		0			0
$952$		0			0
$953$	−8.80699			−0.285286			−0.142643	−	0.989774i	$-0.545560\pi$
$953$	−8.80699			−0.285286			−0.142643	+	0.989774i	$0.545560\pi$
$954$		0			0
$955$	0.910019	−	1.57620i	0.0294475	−	0.0510046i
$956$	9.91595	+	17.1749i	0.320705	+	0.555477i
$957$		0			0
$958$	−30.7257	−	53.2184i	−0.992701	−	1.71941i
$959$		0			0
$960$		0			0
$961$	−25.5831			−0.825260
$962$	2.19076	−	3.79450i	0.0706329	−	0.122340i
$963$		0			0
$964$	−53.0261	−	91.8438i	−1.70785	−	2.95809i
$965$	15.7489	−	27.2779i	0.506976	−	0.878108i
$966$		0			0
$967$	−19.1642	−	33.1934i	−0.616279	−	1.06743i	−0.990159	−	0.139949i	$-0.955306\pi$
$967$	−19.1642	−	33.1934i	−0.616279	−	1.06743i	0.373880	−	0.927477i	$-0.378027\pi$
$968$	−23.7075	+	41.0626i	−0.761987	+	1.31980i
$969$		0			0
$970$	36.6608	+	63.4984i	1.17711	+	2.03881i
$971$	15.5093	+	26.8630i	0.497718	+	0.862073i	0.999997	−	0.00263281i	$-0.000838049\pi$
$971$	15.5093	+	26.8630i	0.497718	+	0.862073i	−0.502278	+	0.864706i	$0.667505\pi$
$972$		0			0
$973$		0			0
$974$	21.6498	−	37.4986i	0.693704	−	1.20153i
$975$		0			0
$976$	9.83775			0.314899
$977$	52.7424			1.68738			0.843689	−	0.536832i	$-0.180379\pi$
$977$	52.7424			1.68738			0.843689	+	0.536832i	$0.180379\pi$
$978$		0			0
$979$	−32.4071	+	56.1307i	−1.03574	+	1.79395i
$980$		0			0
$981$		0			0
$982$	16.9715	+	29.3955i	0.541582	+	0.938048i
$983$	9.15146	+	15.8508i	0.291886	+	0.505562i	0.974256	−	0.225446i	$-0.0723838\pi$
$983$	9.15146	+	15.8508i	0.291886	+	0.505562i	−0.682370	+	0.731007i	$0.739050\pi$
$984$		0			0
$985$	21.2812	−	36.8601i	0.678076	−	1.17446i
$986$	−2.86333	−	4.95943i	−0.0911869	−	0.157940i
$987$		0			0
$988$	8.21780	−	14.2336i	0.261443	−	0.452833i
$989$	1.42627	+	2.47036i	0.0453526	+	0.0785530i
$990$		0			0
$991$	6.30039	−	10.9126i	0.200138	−	0.346650i	−0.748434	−	0.663209i	$-0.769194\pi$
$991$	6.30039	−	10.9126i	0.200138	−	0.346650i	0.948573	+	0.316559i	$0.102527\pi$
$992$	−1.25564			−0.0398665
$993$		0			0
$994$		0			0
$995$	−29.4449	−	51.0001i	−0.933467	−	1.61681i
$996$		0			0
$997$	5.87120	+	10.1692i	0.185943	+	0.322062i	0.943894	−	0.330249i	$-0.107133\pi$
$997$	5.87120	+	10.1692i	0.185943	+	0.322062i	−0.757951	+	0.652311i	$0.773799\pi$
$998$	−16.1010	+	27.8877i	−0.509667	+	0.882770i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.h.e.802.3		6
3.2	odd	2		441.2.h.b.214.1		6
7.2	even	3		1323.2.g.b.667.1		6
7.3	odd	6		189.2.f.a.127.1		6
7.4	even	3		1323.2.f.c.883.1		6
7.5	odd	6		1323.2.g.c.667.1		6
7.6	odd	2		1323.2.h.d.802.3		6
9.4	even	3		1323.2.g.b.361.1		6
9.5	odd	6		441.2.g.d.67.3		6
21.2	odd	6		441.2.g.d.79.3		6
21.5	even	6		441.2.g.e.79.3		6
21.11	odd	6		441.2.f.d.295.3		6
21.17	even	6		63.2.f.b.43.3	yes	6
21.20	even	2		441.2.h.c.214.1		6
28.3	even	6		3024.2.r.g.2017.2		6
63.4	even	3		1323.2.f.c.442.1		6
63.5	even	6		441.2.h.c.373.1		6
63.11	odd	6		3969.2.a.m.1.1		3
63.13	odd	6		1323.2.g.c.361.1		6
63.23	odd	6		441.2.h.b.373.1		6
63.25	even	3		3969.2.a.p.1.3		3
63.31	odd	6		189.2.f.a.64.1		6
63.32	odd	6		441.2.f.d.148.3		6
63.38	even	6		567.2.a.d.1.1		3
63.40	odd	6		1323.2.h.d.226.3		6
63.41	even	6		441.2.g.e.67.3		6
63.52	odd	6		567.2.a.g.1.3		3
63.58	even	3	inner	1323.2.h.e.226.3		6
63.59	even	6		63.2.f.b.22.3	✓	6
84.59	odd	6		1008.2.r.k.673.3		6
252.31	even	6		3024.2.r.g.1009.2		6
252.59	odd	6		1008.2.r.k.337.3		6
252.115	even	6		9072.2.a.cd.1.2		3
252.227	odd	6		9072.2.a.bq.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.3	✓	6	63.59	even	6
63.2.f.b.43.3	yes	6	21.17	even	6
189.2.f.a.64.1		6	63.31	odd	6
189.2.f.a.127.1		6	7.3	odd	6
441.2.f.d.148.3		6	63.32	odd	6
441.2.f.d.295.3		6	21.11	odd	6
441.2.g.d.67.3		6	9.5	odd	6
441.2.g.d.79.3		6	21.2	odd	6
441.2.g.e.67.3		6	63.41	even	6
441.2.g.e.79.3		6	21.5	even	6
441.2.h.b.214.1		6	3.2	odd	2
441.2.h.b.373.1		6	63.23	odd	6
441.2.h.c.214.1		6	21.20	even	2
441.2.h.c.373.1		6	63.5	even	6
567.2.a.d.1.1		3	63.38	even	6
567.2.a.g.1.3		3	63.52	odd	6
1008.2.r.k.337.3		6	252.59	odd	6
1008.2.r.k.673.3		6	84.59	odd	6
1323.2.f.c.442.1		6	63.4	even	3
1323.2.f.c.883.1		6	7.4	even	3
1323.2.g.b.361.1		6	9.4	even	3
1323.2.g.b.667.1		6	7.2	even	3
1323.2.g.c.361.1		6	63.13	odd	6
1323.2.g.c.667.1		6	7.5	odd	6
1323.2.h.d.226.3		6	63.40	odd	6
1323.2.h.d.802.3		6	7.6	odd	2
1323.2.h.e.226.3		6	63.58	even	3	inner
1323.2.h.e.802.3		6	1.1	even	1	trivial
3024.2.r.g.1009.2		6	252.31	even	6
3024.2.r.g.2017.2		6	28.3	even	6
3969.2.a.m.1.1		3	63.11	odd	6
3969.2.a.p.1.3		3	63.25	even	3
9072.2.a.bq.1.2		3	252.227	odd	6
9072.2.a.cd.1.2		3	252.115	even	6

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.46050 q^{2} +4.05408 q^{4} +(1.29679 - 2.24611i) q^{5} +5.05408 q^{8} +O(q^{10})\)	\(q+2.46050 q^{2} +4.05408 q^{4} +(1.29679 - 2.24611i) q^{5} +5.05408 q^{8} +(3.19076 - 5.52655i) q^{10} +(2.25729 + 3.90975i) q^{11} +(0.500000 + 0.866025i) q^{13} +4.32743 q^{16} +(0.472958 - 0.819187i) q^{17} +(-2.02704 - 3.51094i) q^{19} +(5.25729 - 9.10590i) q^{20} +(5.55408 + 9.61996i) q^{22} +(-0.136673 + 0.236725i) q^{23} +(-0.863327 - 1.49533i) q^{25} +(1.23025 + 2.13086i) q^{26} +(1.23025 - 2.13086i) q^{29} -2.32743 q^{31} +0.539495 q^{32} +(1.16372 - 2.01561i) q^{34} +(-0.890369 - 1.54216i) q^{37} +(-4.98755 - 8.63868i) q^{38} +(6.55408 - 11.3520i) q^{40} +(3.20321 + 5.54812i) q^{41} +(5.21780 - 9.03749i) q^{43} +(9.15126 + 15.8505i) q^{44} +(-0.336285 + 0.582462i) q^{46} -12.1623 q^{47} +(-2.12422 - 3.67926i) q^{50} +(2.02704 + 3.51094i) q^{52} +(-3.13667 + 5.43288i) q^{53} +11.7089 q^{55} +(3.02704 - 5.24299i) q^{58} -2.72665 q^{59} +2.27335 q^{61} -5.72665 q^{62} -7.32743 q^{64} +2.59358 q^{65} -15.8171 q^{67} +(1.91741 - 3.32105i) q^{68} -3.27335 q^{71} +(-0.753696 + 1.30544i) q^{73} +(-2.19076 - 3.79450i) q^{74} +(-8.21780 - 14.2336i) q^{76} +14.7089 q^{79} +(5.61177 - 9.71987i) q^{80} +(7.88151 + 13.6512i) q^{82} +(0.472958 - 0.819187i) q^{83} +(-1.22665 - 2.12463i) q^{85} +(12.8384 - 22.2368i) q^{86} +(11.4086 + 19.7602i) q^{88} +(7.17830 + 12.4332i) q^{89} +(-0.554084 + 0.959702i) q^{92} -29.9253 q^{94} -10.5146 q^{95} +(-5.74484 + 9.95036i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 6 q^{4} + 5 q^{5} + 12 q^{8}+O(q^{10}) \) 6 * q + 2 * q^2 + 6 * q^4 + 5 * q^5 + 12 * q^8	\( 6 q + 2 q^{2} + 6 q^{4} + 5 q^{5} + 12 q^{8} - 2 q^{11} + 3 q^{13} + 6 q^{16} + 12 q^{17} - 3 q^{19} + 16 q^{20} + 15 q^{22} - 6 q^{25} + q^{26} + q^{29} + 6 q^{31} + 16 q^{32} - 3 q^{34} + 3 q^{37} - 8 q^{38} + 21 q^{40} + 22 q^{41} + 3 q^{43} + 23 q^{44} - 12 q^{46} - 18 q^{47} + 10 q^{50} + 3 q^{52} - 18 q^{53} + 12 q^{55} + 9 q^{58} - 18 q^{59} + 12 q^{61} - 36 q^{62} - 24 q^{64} + 10 q^{65} - 6 q^{68} - 18 q^{71} + 3 q^{73} + 6 q^{74} - 21 q^{76} + 30 q^{79} - 11 q^{80} + 9 q^{82} + 12 q^{83} - 9 q^{85} + 34 q^{86} + 21 q^{88} + 2 q^{89} + 15 q^{92} - 48 q^{94} - 32 q^{95} + 3 q^{97}+O(q^{100}) \) 6 * q + 2 * q^2 + 6 * q^4 + 5 * q^5 + 12 * q^8 - 2 * q^11 + 3 * q^13 + 6 * q^16 + 12 * q^17 - 3 * q^19 + 16 * q^20 + 15 * q^22 - 6 * q^25 + q^26 + q^29 + 6 * q^31 + 16 * q^32 - 3 * q^34 + 3 * q^37 - 8 * q^38 + 21 * q^40 + 22 * q^41 + 3 * q^43 + 23 * q^44 - 12 * q^46 - 18 * q^47 + 10 * q^50 + 3 * q^52 - 18 * q^53 + 12 * q^55 + 9 * q^58 - 18 * q^59 + 12 * q^61 - 36 * q^62 - 24 * q^64 + 10 * q^65 - 6 * q^68 - 18 * q^71 + 3 * q^73 + 6 * q^74 - 21 * q^76 + 30 * q^79 - 11 * q^80 + 9 * q^82 + 12 * q^83 - 9 * q^85 + 34 * q^86 + 21 * q^88 + 2 * q^89 + 15 * q^92 - 48 * q^94 - 32 * q^95 + 3 * q^97

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