LMFDB - Embedded newform 819.2.s.e.802.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(289,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("819.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.s (of order $3$, degree $2$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			802.2
Root			$-1.02737 - 1.77946i$ of defining polynomial
Character	$\chi$	$=$	819.802
Dual form			819.2.s.e.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.05474 q^{2} +2.22196 q^{4} +(0.274662 + 0.475728i) q^{5} +(2.59269 + 0.527227i) q^{7} -0.456078 q^{8} +(-0.564359 - 0.977499i) q^{10} +(2.34912 + 4.06880i) q^{11} +(-0.663964 + 3.54389i) q^{13} +(-5.32730 - 1.08331i) q^{14} -3.50680 q^{16} +0.603612 q^{17} +(-0.280555 + 0.485935i) q^{19} +(0.610289 + 1.05705i) q^{20} +(-4.82684 - 8.36033i) q^{22} -0.376699 q^{23} +(2.34912 - 4.06880i) q^{25} +(1.36427 - 7.28178i) q^{26} +(5.76086 + 1.17148i) q^{28} +(-2.09200 + 3.62344i) q^{29} +(-0.577330 + 0.999965i) q^{31} +8.11773 q^{32} -1.24027 q^{34} +(0.461296 + 1.37822i) q^{35} -8.80232 q^{37} +(0.576468 - 0.998472i) q^{38} +(-0.125267 - 0.216969i) q^{40} +(3.96001 - 6.85894i) q^{41} +(-0.747200 - 1.29419i) q^{43} +(5.21966 + 9.04072i) q^{44} +0.774020 q^{46} +(1.09885 + 1.90326i) q^{47} +(6.44406 + 2.73387i) q^{49} +(-4.82684 + 8.36033i) q^{50} +(-1.47530 + 7.87439i) q^{52} +(-4.52338 + 7.83473i) q^{53} +(-1.29043 + 2.23509i) q^{55} +(-1.18247 - 0.240457i) q^{56} +(4.29851 - 7.44524i) q^{58} -8.53654 q^{59} +(-3.71212 + 6.42958i) q^{61} +(1.18626 - 2.05467i) q^{62} -9.66624 q^{64} +(-1.86829 + 0.657505i) q^{65} +(4.79936 + 8.31274i) q^{67} +1.34120 q^{68} +(-0.947844 - 2.83190i) q^{70} +(-2.88877 - 5.00350i) q^{71} +(7.24668 - 12.5516i) q^{73} +18.0865 q^{74} +(-0.623383 + 1.07973i) q^{76} +(3.94536 + 11.7876i) q^{77} +(7.31102 + 12.6631i) q^{79} +(-0.963186 - 1.66829i) q^{80} +(-8.13680 + 14.0934i) q^{82} +14.8750 q^{83} +(0.165789 + 0.287155i) q^{85} +(1.53530 + 2.65922i) q^{86} +(-1.07138 - 1.85569i) q^{88} -9.18353 q^{89} +(-3.58988 + 8.83814i) q^{91} -0.837013 q^{92} +(-2.25784 - 3.91070i) q^{94} -0.308231 q^{95} +(3.15034 + 5.45655i) q^{97} +(-13.2409 - 5.61740i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} + q^{7} - 12 q^{8} - 4 q^{10} + 2 q^{11} + 5 q^{13} + 7 q^{14} + 12 q^{16} - 4 q^{17} - 11 q^{19} + 20 q^{20} + 7 q^{22} + 8 q^{23} + 2 q^{25} - 33 q^{26} - q^{28} - 15 q^{29} + 3 q^{31}+ \cdots - 18 q^{98}+O(q^{100}) $ 16 * q + 12 * q^4 + q^7 - 12 * q^8 - 4 * q^10 + 2 * q^11 + 5 * q^13 + 7 * q^14 + 12 * q^16 - 4 * q^17 - 11 * q^19 + 20 * q^20 + 7 * q^22 + 8 * q^23 + 2 * q^25 - 33 * q^26 - q^28 - 15 * q^29 + 3 * q^31 + 6 * q^32 - 68 * q^34 - 8 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 - 4 * q^46 - 5 * q^47 + 7 * q^49 + 7 * q^50 - 18 * q^52 - 36 * q^53 - 15 * q^55 + 51 * q^56 + 20 * q^58 - 34 * q^59 - 22 * q^61 + 6 * q^62 - 20 * q^64 + 24 * q^65 + 26 * q^67 + 10 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 + 30 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 + 28 * q^80 - q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 + 24 * q^88 + 40 * q^89 - 10 * q^91 + 94 * q^92 - 20 * q^94 + 7 * q^97 - 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.05474			−1.45292			−0.726461	−	0.687208i	$-0.758836\pi$
$2$	−2.05474			−1.45292			−0.726461	+	0.687208i	$0.758836\pi$
$3$		0			0
$3$		0			0
$4$	2.22196			1.11098
$5$	0.274662	+	0.475728i	0.122833	+	0.212752i	0.920884	−	0.389838i	$-0.127469\pi$
$5$	0.274662	+	0.475728i	0.122833	+	0.212752i	−0.798051	+	0.602590i	$0.794136\pi$
$6$		0			0
$7$	2.59269	+	0.527227i	0.979944	+	0.199273i
$7$	2.59269	+	0.527227i	0.979944	+	0.199273i
$8$	−0.456078			−0.161248
$9$		0			0
$10$	−0.564359	−	0.977499i	−0.178466	−	0.309112i
$11$	2.34912	+	4.06880i	0.708287	+	1.22679i	0.965492	+	0.260432i	$0.0838650\pi$
$11$	2.34912	+	4.06880i	0.708287	+	1.22679i	−0.257205	+	0.966357i	$0.582802\pi$
$12$		0			0
$13$	−0.663964	+	3.54389i	−0.184150	+	0.982898i
$13$	−0.663964	+	3.54389i	−0.184150	+	0.982898i
$14$	−5.32730	−	1.08331i	−1.42378	−	0.289528i
$15$		0			0
$16$	−3.50680			−0.876701
$17$	0.603612			0.146397			0.0731987	−	0.997317i	$-0.476679\pi$
$17$	0.603612			0.146397			0.0731987	+	0.997317i	$0.476679\pi$
$18$		0			0
$19$	−0.280555	+	0.485935i	−0.0643637	+	0.111481i	−0.896412	−	0.443223i	$-0.853835\pi$
$19$	−0.280555	+	0.485935i	−0.0643637	+	0.111481i	0.832048	+	0.554704i	$0.187168\pi$
$20$	0.610289	+	1.05705i	0.136465	+	0.236364i
$21$		0			0
$22$	−4.82684	−	8.36033i	−1.02909	−	1.78243i
$23$	−0.376699			−0.0785473			−0.0392736	−	0.999228i	$-0.512504\pi$
$23$	−0.376699			−0.0785473			−0.0392736	+	0.999228i	$0.512504\pi$
$24$		0			0
$25$	2.34912	−	4.06880i	0.469824	−	0.813760i
$26$	1.36427	−	7.28178i	0.267556	−	1.42807i
$27$		0			0
$28$	5.76086	+	1.17148i	1.08870	+	0.221389i
$29$	−2.09200	+	3.62344i	−0.388474	+	0.672856i	−0.992244	−	0.124302i	$-0.960331\pi$
$29$	−2.09200	+	3.62344i	−0.388474	+	0.672856i	0.603771	+	0.797158i	$0.293664\pi$
$30$		0			0
$31$	−0.577330	+	0.999965i	−0.103691	+	0.179599i	−0.913203	−	0.407505i	$-0.866399\pi$
$31$	−0.577330	+	0.999965i	−0.103691	+	0.179599i	0.809511	+	0.587104i	$0.199732\pi$
$32$	8.11773			1.43503
$33$		0			0
$34$	−1.24027			−0.212704
$35$	0.461296	+	1.37822i	0.0779732	+	0.232962i
$36$		0			0
$37$	−8.80232			−1.44709			−0.723547	−	0.690276i	$-0.757489\pi$
$37$	−8.80232			−1.44709			−0.723547	+	0.690276i	$0.757489\pi$
$38$	0.576468	−	0.998472i	0.0935154	−	0.161973i
$39$		0			0
$40$	−0.125267	−	0.216969i	−0.0198065	−	0.0343059i
$41$	3.96001	−	6.85894i	0.618450	−	1.07119i	−0.371319	−	0.928506i	$-0.621094\pi$
$41$	3.96001	−	6.85894i	0.618450	−	1.07119i	0.989769	−	0.142681i	$-0.0455724\pi$
$42$		0			0
$43$	−0.747200	−	1.29419i	−0.113947	−	0.197362i	0.803411	−	0.595424i	$-0.203016\pi$
$43$	−0.747200	−	1.29419i	−0.113947	−	0.197362i	−0.917358	+	0.398062i	$0.869683\pi$
$44$	5.21966	+	9.04072i	0.786894	+	1.36294i
$45$		0			0
$46$	0.774020			0.114123
$47$	1.09885	+	1.90326i	0.160283	+	0.277619i	0.934970	−	0.354726i	$-0.115426\pi$
$47$	1.09885	+	1.90326i	0.160283	+	0.277619i	−0.774687	+	0.632345i	$0.782093\pi$
$48$		0			0
$49$	6.44406	+	2.73387i	0.920581	+	0.390553i
$50$	−4.82684	+	8.36033i	−0.682618	+	1.18233i
$51$		0			0
$52$	−1.47530	+	7.87439i	−0.204588	+	1.09198i
$53$	−4.52338	+	7.83473i	−0.621334	+	1.07618i	0.367903	+	0.929864i	$0.380076\pi$
$53$	−4.52338	+	7.83473i	−0.621334	+	1.07618i	−0.989238	+	0.146318i	$0.953258\pi$
$54$		0			0
$55$	−1.29043	+	2.23509i	−0.174001	+	0.301379i
$56$	−1.18247	−	0.240457i	−0.158014	−	0.0321324i
$57$		0			0
$58$	4.29851	−	7.44524i	0.564422	−	0.977608i
$59$	−8.53654			−1.11136			−0.555681	−	0.831395i	$-0.687543\pi$
$59$	−8.53654			−1.11136			−0.555681	+	0.831395i	$0.687543\pi$
$60$		0			0
$61$	−3.71212	+	6.42958i	−0.475288	+	0.823223i	−0.999599	−	0.0283034i	$-0.990990\pi$
$61$	−3.71212	+	6.42958i	−0.475288	+	0.823223i	0.524311	+	0.851527i	$0.324323\pi$
$62$	1.18626	−	2.05467i	0.150656	−	0.260943i
$63$		0			0
$64$	−9.66624			−1.20828
$65$	−1.86829	+	0.657505i	−0.231733	+	0.0815535i
$66$		0			0
$67$	4.79936	+	8.31274i	0.586336	+	1.01556i	0.994707	+	0.102747i	$0.0327634\pi$
$67$	4.79936	+	8.31274i	0.586336	+	1.01556i	−0.408372	+	0.912816i	$0.633903\pi$
$68$	1.34120			0.162645
$69$		0			0
$70$	−0.947844	−	2.83190i	−0.113289	−	0.338476i
$71$	−2.88877	−	5.00350i	−0.342834	−	0.593806i	0.642124	−	0.766601i	$-0.278053\pi$
$71$	−2.88877	−	5.00350i	−0.342834	−	0.593806i	−0.984958	+	0.172795i	$0.944720\pi$
$72$		0			0
$73$	7.24668	−	12.5516i	0.848160	−	1.46906i	−0.0346892	−	0.999398i	$-0.511044\pi$
$73$	7.24668	−	12.5516i	0.848160	−	1.46906i	0.882849	−	0.469657i	$-0.155623\pi$
$74$	18.0865			2.10251
$75$		0			0
$76$	−0.623383	+	1.07973i	−0.0715069	+	0.123854i
$77$	3.94536	+	11.7876i	0.449616	+	1.34333i
$78$		0			0
$79$	7.31102	+	12.6631i	0.822554	+	1.42471i	0.903774	+	0.428009i	$0.140785\pi$
$79$	7.31102	+	12.6631i	0.822554	+	1.42471i	−0.0812206	+	0.996696i	$0.525882\pi$
$80$	−0.963186	−	1.66829i	−0.107687	−	0.186520i
$81$		0			0
$82$	−8.13680	+	14.0934i	−0.898560	+	1.55635i
$83$	14.8750			1.63274			0.816371	−	0.577528i	$-0.195983\pi$
$83$	14.8750			1.63274			0.816371	+	0.577528i	$0.195983\pi$
$84$		0			0
$85$	0.165789	+	0.287155i	0.0179824	+	0.0311464i
$86$	1.53530	+	2.65922i	0.165556	+	0.286751i
$87$		0			0
$88$	−1.07138	−	1.85569i	−0.114210	−	0.197817i
$89$	−9.18353			−0.973452			−0.486726	−	0.873555i	$-0.661809\pi$
$89$	−9.18353			−0.973452			−0.486726	+	0.873555i	$0.661809\pi$
$90$		0			0
$91$	−3.58988	+	8.83814i	−0.376322	+	0.926489i
$92$	−0.837013			−0.0872646
$93$		0			0
$94$	−2.25784	−	3.91070i	−0.232879	−	0.403358i
$95$	−0.308231			−0.0316238
$96$		0			0
$97$	3.15034	+	5.45655i	0.319869	+	0.554029i	0.980460	−	0.196717i	$-0.0630279\pi$
$97$	3.15034	+	5.45655i	0.319869	+	0.554029i	−0.660592	+	0.750745i	$0.729695\pi$
$98$	−13.2409	−	5.61740i	−1.33753	−	0.567443i
$99$		0			0
$100$	5.21966	−	9.04072i	0.521966	−	0.904072i
$101$	2.22194	+	3.84851i	0.221091	+	0.382941i	0.955140	−	0.296156i	$-0.0957049\pi$
$101$	2.22194	+	3.84851i	0.221091	+	0.382941i	−0.734049	+	0.679097i	$0.762372\pi$
$102$		0			0
$103$	8.31431	+	14.4008i	0.819234	+	1.41895i	0.906248	+	0.422747i	$0.138934\pi$
$103$	8.31431	+	14.4008i	0.819234	+	1.41895i	−0.0870141	+	0.996207i	$0.527733\pi$
$104$	0.302820	−	1.61629i	0.0296939	−	0.158490i
$105$		0			0
$106$	9.29438	−	16.0983i	0.902750	−	1.56361i
$107$	−17.8721			−1.72776			−0.863881	−	0.503696i	$-0.831973\pi$
$107$	−17.8721			−1.72776			−0.863881	+	0.503696i	$0.831973\pi$
$108$		0			0
$109$	−5.07774	+	8.79490i	−0.486359	+	0.842399i	−0.999877	−	0.0156799i	$-0.995009\pi$
$109$	−5.07774	+	8.79490i	−0.486359	+	0.842399i	0.513518	+	0.858079i	$0.328342\pi$
$110$	2.65150	−	4.59253i	0.252810	−	0.437880i
$111$		0			0
$112$	−9.09205	−	1.84888i	−0.859118	−	0.174703i
$113$	3.74505	+	6.48662i	0.352305	+	0.610210i	0.986653	−	0.162838i	$-0.0520647\pi$
$113$	3.74505	+	6.48662i	0.352305	+	0.610210i	−0.634348	+	0.773048i	$0.718731\pi$
$114$		0			0
$115$	−0.103465	−	0.179207i	−0.00964816	−	0.0167111i
$116$	−4.64834	+	8.05116i	−0.431587	+	0.747531i
$117$		0			0
$118$	17.5404			1.61472
$119$	1.56498	+	0.318240i	0.143461	+	0.0291730i
$120$		0			0
$121$	−5.53675	+	9.58992i	−0.503340	+	0.871811i
$122$	7.62745	−	13.2111i	0.690557	−	1.19608i
$123$		0			0
$124$	−1.28281	+	2.22189i	−0.115199	+	0.199531i
$125$	5.32748			0.476504
$126$		0			0
$127$	2.36612	−	4.09824i	0.209959	−	0.363660i	−0.741742	−	0.670685i	$-0.766000\pi$
$127$	2.36612	−	4.09824i	0.209959	−	0.363660i	0.951702	+	0.307025i	$0.0993335\pi$
$128$	3.62616			0.320510
$129$		0			0
$130$	3.83886	−	1.35100i	0.336691	−	0.118491i
$131$	1.78705	+	3.09527i	0.156136	+	0.270435i	0.933472	−	0.358650i	$-0.116763\pi$
$131$	1.78705	+	3.09527i	0.156136	+	0.270435i	−0.777336	+	0.629085i	$0.783430\pi$
$132$		0			0
$133$	−0.983589	+	1.11196i	−0.0852880	+	0.0964194i
$134$	−9.86145	−	17.0805i	−0.851900	−	1.47553i
$135$		0			0
$136$	−0.275294			−0.0236063
$137$	19.2576			1.64529			0.822644	−	0.568557i	$-0.192498\pi$
$137$	19.2576			1.64529			0.822644	+	0.568557i	$0.192498\pi$
$138$		0			0
$139$	−4.83155	−	8.36849i	−0.409807	−	0.709806i	0.585061	−	0.810989i	$-0.301070\pi$
$139$	−4.83155	−	8.36849i	−0.409807	−	0.709806i	−0.994868	+	0.101183i	$0.967737\pi$
$140$	1.02498	+	3.06236i	0.0866269	+	0.258817i
$141$		0			0
$142$	5.93568	+	10.2809i	0.498111	+	0.862753i
$143$	−15.9791	+	5.62349i	−1.33624	+	0.470260i
$144$		0			0
$145$	−2.29837			−0.190869
$146$	−14.8901	+	25.7903i	−1.23231	+	2.13442i
$147$		0			0
$148$	−19.5584			−1.60769
$149$	3.56248	−	6.17039i	0.291850	−	0.505498i	−0.682398	−	0.730981i	$-0.739063\pi$
$149$	3.56248	−	6.17039i	0.291850	−	0.505498i	0.974247	+	0.225483i	$0.0723960\pi$
$150$		0			0
$151$	9.82744	−	17.0216i	0.799746	−	1.38520i	−0.120036	−	0.992770i	$-0.538301\pi$
$151$	9.82744	−	17.0216i	0.799746	−	1.38520i	0.919781	−	0.392431i	$-0.128366\pi$
$152$	0.127955	−	0.221625i	0.0103785	−	0.0179761i
$153$		0			0
$154$	−8.10670	−	24.2206i	−0.653256	−	1.95175i
$155$	−0.634282			−0.0509468
$156$		0			0
$157$	2.60509	−	4.51215i	0.207909	−	0.360109i	−0.743147	−	0.669129i	$-0.766668\pi$
$157$	2.60509	−	4.51215i	0.207909	−	0.360109i	0.951056	+	0.309020i	$0.100001\pi$
$158$	−15.0223	−	26.0193i	−1.19511	−	2.06999i
$159$		0			0
$160$	2.22963	+	3.86184i	0.176268	+	0.305305i
$161$	−0.976664	−	0.198606i	−0.0769719	−	0.0156523i
$162$		0			0
$163$	2.08690	−	3.61461i	0.163458	−	0.283118i	−0.772648	−	0.634834i	$-0.781068\pi$
$163$	2.08690	−	3.61461i	0.163458	−	0.283118i	0.936107	+	0.351716i	$0.114402\pi$
$164$	8.79901	−	15.2403i	0.687087	−	1.19007i
$165$		0			0
$166$	−30.5642			−2.37225
$167$	2.52335	−	4.37058i	0.195263	−	0.338205i	−0.751724	−	0.659478i	$-0.770777\pi$
$167$	2.52335	−	4.37058i	0.195263	−	0.338205i	0.946987	+	0.321273i	$0.104111\pi$
$168$		0			0
$169$	−12.1183	−	4.70603i	−0.932177	−	0.362002i
$170$	−0.340654	−	0.590030i	−0.0261270	−	0.0452532i
$171$		0			0
$172$	−1.66025	−	2.87564i	−0.126593	−	0.219265i
$173$	1.36949	−	2.37202i	0.104120	−	0.180341i	−0.809258	−	0.587453i	$-0.800131\pi$
$173$	1.36949	−	2.37202i	0.104120	−	0.180341i	0.913378	+	0.407112i	$0.133464\pi$
$174$		0			0
$175$	8.23572	−	9.31060i	0.622562	−	0.703816i
$176$	−8.23791	−	14.2685i	−0.620956	−	1.07553i
$177$		0			0
$178$	18.8698			1.41435
$179$	−6.34782	−	10.9948i	−0.474459	−	0.821787i	0.525114	−	0.851032i	$-0.324023\pi$
$179$	−6.34782	−	10.9948i	−0.474459	−	0.821787i	−0.999572	+	0.0292456i	$0.990690\pi$
$180$		0			0
$181$	7.95691			0.591432			0.295716	−	0.955276i	$-0.404442\pi$
$181$	7.95691			0.591432			0.295716	+	0.955276i	$0.404442\pi$
$182$	7.37629	−	18.1601i	0.546767	−	1.34612i
$183$		0			0
$184$	0.171805			0.0126656
$185$	−2.41766	−	4.18752i	−0.177750	−	0.307872i
$186$		0			0
$187$	1.41796	+	2.45597i	0.103691	+	0.179599i
$188$	2.44160	+	4.22897i	0.178072	+	0.308429i
$189$		0			0
$190$	0.633335			0.0459469
$191$	1.53989	−	2.66717i	0.111423	−	0.192990i	−0.804921	−	0.593382i	$-0.797793\pi$
$191$	1.53989	−	2.66717i	0.111423	−	0.192990i	0.916344	+	0.400392i	$0.131126\pi$
$192$		0			0
$193$	1.69587	+	2.93734i	0.122072	+	0.211434i	0.920584	−	0.390543i	$-0.127713\pi$
$193$	1.69587	+	2.93734i	0.122072	+	0.211434i	−0.798513	+	0.601978i	$0.794380\pi$
$194$	−6.47314	−	11.2118i	−0.464744	−	0.804961i
$195$		0			0
$196$	14.3185	+	6.07456i	1.02275	+	0.433897i
$197$	−2.06163	+	3.57085i	−0.146885	+	0.254413i	−0.930075	−	0.367370i	$-0.880258\pi$
$197$	−2.06163	+	3.57085i	−0.146885	+	0.254413i	0.783189	+	0.621783i	$0.213591\pi$
$198$		0			0
$199$	−1.14828			−0.0813997			−0.0406998	−	0.999171i	$-0.512959\pi$
$199$	−1.14828			−0.0813997			−0.0406998	+	0.999171i	$0.512959\pi$
$200$	−1.07138	+	1.85569i	−0.0757583	+	0.131217i
$201$		0			0
$202$	−4.56551	−	7.90769i	−0.321228	−	0.556383i
$203$	−7.33427	+	8.29150i	−0.514765	+	0.581949i
$204$		0			0
$205$	4.35066			0.303863
$206$	−17.0838	−	29.5900i	−1.19028	−	2.06163i
$207$		0			0
$208$	2.32839	−	12.4277i	0.161445	−	0.861708i
$209$	−2.63623			−0.182352
$210$		0			0
$211$	−2.28300	+	3.95427i	−0.157168	+	0.272223i	−0.933846	−	0.357674i	$-0.883570\pi$
$211$	−2.28300	+	3.95427i	−0.157168	+	0.272223i	0.776678	+	0.629898i	$0.216903\pi$
$212$	−10.0508	+	17.4085i	−0.690291	+	1.19562i
$213$		0			0
$214$	36.7226			2.51030
$215$	0.410455	−	0.710929i	0.0279928	−	0.0484849i
$216$		0			0
$217$	−2.02404	+	2.28821i	−0.137401	+	0.155334i
$218$	10.4334	−	18.0713i	0.706642	−	1.22394i
$219$		0			0
$220$	−2.86729	+	4.96628i	−0.193312	+	0.334827i
$221$	−0.400776	+	2.13913i	−0.0269591	+	0.143894i
$222$		0			0
$223$	8.42312	−	14.5893i	0.564054	−	0.976970i	−0.433083	−	0.901354i	$-0.642574\pi$
$223$	8.42312	−	14.5893i	0.564054	−	0.976970i	0.997137	−	0.0756163i	$-0.0240924\pi$
$224$	21.0468	+	4.27989i	1.40625	+	0.285962i
$225$		0			0
$226$	−7.69512	−	13.3283i	−0.511872	−	0.886588i
$227$	28.4730			1.88982			0.944909	−	0.327333i	$-0.106150\pi$
$227$	28.4730			1.88982			0.944909	+	0.327333i	$0.106150\pi$
$228$		0			0
$229$	−13.1373	−	22.7545i	−0.868137	−	1.50366i	−0.863899	−	0.503666i	$-0.831984\pi$
$229$	−13.1373	−	22.7545i	−0.868137	−	1.50366i	−0.00423787	−	0.999991i	$-0.501349\pi$
$230$	0.212594	+	0.368223i	0.0140180	+	0.0242799i
$231$		0			0
$232$	0.954114	−	1.65257i	0.0626406	−	0.108497i
$233$	11.0974	+	19.2212i	0.727014	+	1.25922i	0.958140	+	0.286301i	$0.0924257\pi$
$233$	11.0974	+	19.2212i	0.727014	+	1.25922i	−0.231126	+	0.972924i	$0.574241\pi$
$234$		0			0
$235$	−0.603622	+	1.04550i	−0.0393760	+	0.0682012i
$236$	−18.9679			−1.23470
$237$		0			0
$238$	−3.21562	−	0.653902i	−0.208438	−	0.0423862i
$239$	−27.3213			−1.76727			−0.883633	−	0.468180i	$-0.844910\pi$
$239$	−27.3213			−1.76727			−0.883633	+	0.468180i	$0.844910\pi$
$240$		0			0
$241$	−23.7831			−1.53200			−0.766001	−	0.642839i	$-0.777756\pi$
$241$	−23.7831			−1.53200			−0.766001	+	0.642839i	$0.777756\pi$
$242$	11.3766	−	19.7048i	0.731314	−	1.26667i
$243$		0			0
$244$	−8.24820	+	14.2863i	−0.528037	+	0.914586i
$245$	0.469360	+	3.81651i	0.0299863	+	0.243828i
$246$		0			0
$247$	−1.53582	−	1.31690i	−0.0977221	−	0.0837923i
$248$	0.263308	−	0.456062i	0.0167201	−	0.0289600i
$249$		0			0
$250$	−10.9466			−0.692323
$251$	−4.16795	−	7.21910i	−0.263079	−	0.455666i	0.703980	−	0.710220i	$-0.251405\pi$
$251$	−4.16795	−	7.21910i	−0.263079	−	0.455666i	−0.967058	+	0.254554i	$0.918071\pi$
$252$		0			0
$253$	−0.884913	−	1.53271i	−0.0556340	−	0.0963609i
$254$	−4.86177	+	8.42084i	−0.305055	+	0.528370i
$255$		0			0
$256$	11.8817			0.742604
$257$	13.7742			0.859214			0.429607	−	0.903016i	$-0.358652\pi$
$257$	13.7742			0.859214			0.429607	+	0.903016i	$0.358652\pi$
$258$		0			0
$259$	−22.8217	−	4.64082i	−1.41807	−	0.288367i
$260$	−4.15128	+	1.46095i	−0.257452	+	0.0906044i
$261$		0			0
$262$	−3.67193	−	6.35998i	−0.226853	−	0.392921i
$263$	−4.52282	−	7.83375i	−0.278889	−	0.483050i	0.692220	−	0.721687i	$-0.256633\pi$
$263$	−4.52282	−	7.83375i	−0.278889	−	0.483050i	−0.971109	+	0.238637i	$0.923299\pi$
$264$		0			0
$265$	−4.96960			−0.305280
$266$	2.02102	−	2.28480i	0.123917	−	0.140090i
$267$		0			0
$268$	10.6640	+	18.4706i	0.651408	+	1.12827i
$269$	−2.28856			−0.139536			−0.0697681	−	0.997563i	$-0.522226\pi$
$269$	−2.28856			−0.139536			−0.0697681	+	0.997563i	$0.522226\pi$
$270$		0			0
$271$	3.98115			0.241838			0.120919	−	0.992662i	$-0.461416\pi$
$271$	3.98115			0.241838			0.120919	+	0.992662i	$0.461416\pi$
$272$	−2.11675			−0.128347
$273$		0			0
$274$	−39.5694			−2.39047
$275$	22.0735			1.33108
$276$		0			0
$277$	−8.39999			−0.504706			−0.252353	−	0.967635i	$-0.581204\pi$
$277$	−8.39999			−0.504706			−0.252353	+	0.967635i	$0.581204\pi$
$278$	9.92758	+	17.1951i	0.595417	+	1.03129i
$279$		0			0
$280$	−0.210387	−	0.628579i	−0.0125730	−	0.0375648i
$281$	12.9559			0.772884			0.386442	−	0.922314i	$-0.373704\pi$
$281$	12.9559			0.772884			0.386442	+	0.922314i	$0.373704\pi$
$282$		0			0
$283$	−12.8026	−	22.1747i	−0.761033	−	1.31815i	−0.942319	−	0.334717i	$-0.891359\pi$
$283$	−12.8026	−	22.1747i	−0.761033	−	1.31815i	0.181286	−	0.983431i	$-0.441974\pi$
$284$	−6.41874	−	11.1176i	−0.380882	−	0.659707i
$285$		0			0
$286$	32.8329	−	11.5548i	1.94145	−	0.683251i
$287$	13.8833	−	15.6953i	0.819505	−	0.926463i
$288$		0			0
$289$	−16.6357			−0.978568
$290$	4.72255			0.277318
$291$		0			0
$292$	16.1019	−	27.8892i	0.942290	−	1.63209i
$293$	12.3943	+	21.4675i	0.724081	+	1.25415i	0.959351	+	0.282215i	$0.0910692\pi$
$293$	12.3943	+	21.4675i	0.724081	+	1.25415i	−0.235270	+	0.971930i	$0.575597\pi$
$294$		0			0
$295$	−2.34466	−	4.06107i	−0.136511	−	0.236445i
$296$	4.01455			0.233341
$297$		0			0
$298$	−7.31997	+	12.6786i	−0.424035	+	0.734450i
$299$	0.250115	−	1.33498i	0.0144645	−	0.0772040i
$300$		0			0
$301$	−1.25493	−	3.74937i	−0.0723327	−	0.216110i
$302$	−20.1929	+	34.9751i	−1.16197	+	2.01259i
$303$		0			0
$304$	0.983851	−	1.70408i	0.0564277	−	0.0977357i
$305$	−4.07831			−0.233523
$306$		0			0
$307$	−25.2086			−1.43873			−0.719365	−	0.694632i	$-0.755567\pi$
$307$	−25.2086			−1.43873			−0.719365	+	0.694632i	$0.755567\pi$
$308$	8.76645	+	26.1917i	0.499515	+	1.49241i
$309$		0			0
$310$	1.30329			0.0740217
$311$	2.06640	−	3.57911i	0.117175	−	0.202953i	−0.801472	−	0.598032i	$-0.795950\pi$
$311$	2.06640	−	3.57911i	0.117175	−	0.202953i	0.918647	+	0.395079i	$0.129283\pi$
$312$		0			0
$313$	15.0691	+	26.1005i	0.851758	+	1.47529i	0.879620	+	0.475676i	$0.157797\pi$
$313$	15.0691	+	26.1005i	0.851758	+	1.47529i	−0.0278626	+	0.999612i	$0.508870\pi$
$314$	−5.35279	+	9.27131i	−0.302076	+	0.523210i
$315$		0			0
$316$	16.2448	+	28.1369i	0.913843	+	1.58282i
$317$	5.76330	+	9.98233i	0.323699	+	0.560663i	0.981248	−	0.192748i	$-0.0617401\pi$
$317$	5.76330	+	9.98233i	0.323699	+	0.560663i	−0.657549	+	0.753412i	$0.728407\pi$
$318$		0			0
$319$	−19.6574			−1.10060
$320$	−2.65495	−	4.59850i	−0.148416	−	0.257064i
$321$		0			0
$322$	2.00679	+	0.408084i	0.111834	+	0.0227416i
$323$	−0.169346	+	0.293316i	−0.00942268	+	0.0163206i
$324$		0			0
$325$	12.8596	+	11.0266i	0.713324	+	0.611644i
$326$	−4.28803	+	7.42709i	−0.237492	+	0.411348i
$327$		0			0
$328$	−1.80608	+	3.12822i	−0.0997239	+	0.172727i
$329$	1.84552	+	5.51389i	0.101747	+	0.303991i
$330$		0			0
$331$	0.567695	−	0.983277i	0.0312033	−	0.0540458i	−0.850002	−	0.526779i	$-0.823399\pi$
$331$	0.567695	−	0.983277i	0.0312033	−	0.0540458i	0.881205	+	0.472734i	$0.156733\pi$
$332$	33.0517			1.81395
$333$		0			0
$334$	−5.18484	+	8.98041i	−0.283702	+	0.491386i
$335$	−2.63640	+	4.56639i	−0.144042	+	0.249488i
$336$		0			0
$337$	23.3181			1.27022			0.635110	−	0.772421i	$-0.280955\pi$
$337$	23.3181			1.27022			0.635110	+	0.772421i	$0.280955\pi$
$338$	24.9000	+	9.66967i	1.35438	+	0.525961i
$339$		0			0
$340$	0.368378	+	0.638049i	0.0199781	+	0.0346030i
$341$	−5.42487			−0.293773
$342$		0			0
$343$	15.2661	+	10.4856i	0.824291	+	0.566167i
$344$	0.340782	+	0.590252i	0.0183737	+	0.0318242i
$345$		0			0
$346$	−2.81394	+	4.87389i	−0.151279	+	0.262022i
$347$	−2.53822			−0.136259			−0.0681294	−	0.997676i	$-0.521703\pi$
$347$	−2.53822			−0.136259			−0.0681294	+	0.997676i	$0.521703\pi$
$348$		0			0
$349$	−5.34353	+	9.25527i	−0.286033	+	0.495423i	−0.972859	−	0.231398i	$-0.925670\pi$
$349$	−5.34353	+	9.25527i	−0.286033	+	0.495423i	0.686826	+	0.726822i	$0.259003\pi$
$350$	−16.9223	+	19.1309i	−0.904534	+	1.02259i
$351$		0			0
$352$	19.0695	+	33.0294i	1.01641	+	1.76047i
$353$	11.1203	+	19.2610i	0.591875	+	1.02516i	0.993980	+	0.109564i	$0.0349455\pi$
$353$	11.1203	+	19.2610i	0.591875	+	1.02516i	−0.402105	+	0.915594i	$0.631721\pi$
$354$		0			0
$355$	1.58687	−	2.74854i	0.0842223	−	0.145877i
$356$	−20.4055			−1.08149
$357$		0			0
$358$	13.0431	+	22.5914i	0.689351	+	1.19399i
$359$	−8.38142	−	14.5170i	−0.442354	−	0.766180i	0.555509	−	0.831510i	$-0.312523\pi$
$359$	−8.38142	−	14.5170i	−0.442354	−	0.766180i	−0.997864	+	0.0653300i	$0.979190\pi$
$360$		0			0
$361$	9.34258	+	16.1818i	0.491715	+	0.851675i
$362$	−16.3494			−0.859305
$363$		0			0
$364$	−7.97659	+	19.6380i	−0.418087	+	1.02931i
$365$	7.96155			0.416726
$366$		0			0
$367$	2.34097	+	4.05468i	0.122198	+	0.211653i	0.920634	−	0.390427i	$-0.127672\pi$
$367$	2.34097	+	4.05468i	0.122198	+	0.211653i	−0.798436	+	0.602079i	$0.794339\pi$
$368$	1.32101			0.0688625
$369$		0			0
$370$	4.96767	+	8.60426i	0.258257	+	0.447314i
$371$	−15.8584	+	17.9282i	−0.823327	+	0.930783i
$372$		0			0
$373$	3.38086	−	5.85582i	0.175054	−	0.303203i	−0.765126	−	0.643881i	$-0.777323\pi$
$373$	3.38086	−	5.85582i	0.175054	−	0.303203i	0.940180	+	0.340678i	$0.110657\pi$
$374$	−2.91354	−	5.04639i	−0.150655	−	0.260943i
$375$		0			0
$376$	−0.501160	−	0.868034i	−0.0258453	−	0.0447655i
$377$	−11.4521	−	9.81963i	−0.589811	−	0.505737i
$378$		0			0
$379$	9.62497	−	16.6709i	0.494402	−	0.856329i	−0.505578	−	0.862781i	$-0.668721\pi$
$379$	9.62497	−	16.6709i	0.494402	−	0.856329i	0.999979	+	0.00645256i	$0.00205393\pi$
$380$	−0.684878			−0.0351335
$381$		0			0
$382$	−3.16408	+	5.48036i	−0.161889	+	0.280399i
$383$	6.74254	−	11.6784i	0.344528	−	0.596740i	−0.640740	−	0.767758i	$-0.721372\pi$
$383$	6.74254	−	11.6784i	0.344528	−	0.596740i	0.985268	+	0.171018i	$0.0547057\pi$
$384$		0			0
$385$	−4.52408	+	5.11454i	−0.230568	+	0.260661i
$386$	−3.48458	−	6.03547i	−0.177361	−	0.307198i
$387$		0			0
$388$	6.99994	+	12.1243i	0.355368	+	0.615516i
$389$	−16.4229	+	28.4453i	−0.832675	+	1.44224i	0.0632336	+	0.997999i	$0.479859\pi$
$389$	−16.4229	+	28.4453i	−0.832675	+	1.44224i	−0.895909	+	0.444238i	$0.853475\pi$
$390$		0			0
$391$	−0.227380			−0.0114991
$392$	−2.93900	−	1.24686i	−0.148442	−	0.0629759i
$393$		0			0
$394$	4.23612	−	7.33718i	0.213413	−	0.369642i
$395$	−4.01612	+	6.95612i	−0.202073	+	0.350000i
$396$		0			0
$397$	13.3054	−	23.0457i	0.667781	−	1.15663i	−0.310743	−	0.950494i	$-0.600578\pi$
$397$	13.3054	−	23.0457i	0.667781	−	1.15663i	0.978523	−	0.206136i	$-0.0660889\pi$
$398$	2.35943			0.118267
$399$		0			0
$400$	−8.23791	+	14.2685i	−0.411895	+	0.713424i
$401$	23.1117			1.15414			0.577071	−	0.816694i	$-0.304195\pi$
$401$	23.1117			1.15414			0.577071	+	0.816694i	$0.304195\pi$
$402$		0			0
$403$	−3.16044	−	2.70993i	−0.157433	−	0.134991i
$404$	4.93706	+	8.55124i	0.245628	+	0.425440i
$405$		0			0
$406$	15.0700	−	17.0369i	0.747913	−	0.845527i
$407$	−20.6777	−	35.8149i	−1.02496	−	1.77528i
$408$		0			0
$409$	−7.24147			−0.358067			−0.179034	−	0.983843i	$-0.557297\pi$
$409$	−7.24147			−0.358067			−0.179034	+	0.983843i	$0.557297\pi$
$410$	−8.93948			−0.441489
$411$		0			0
$412$	18.4741	+	31.9981i	0.910154	+	1.57643i
$413$	−22.1326	−	4.50069i	−1.08907	−	0.221465i
$414$		0			0
$415$	4.08559	+	7.07645i	0.200554	+	0.347369i
$416$	−5.38988	+	28.7684i	−0.264261	+	1.41048i
$417$		0			0
$418$	5.41677			0.264943
$419$	17.5550	−	30.4062i	0.857618	−	1.48544i	−0.0165759	−	0.999863i	$-0.505277\pi$
$419$	17.5550	−	30.4062i	0.857618	−	1.48544i	0.874194	−	0.485576i	$-0.161390\pi$
$420$		0			0
$421$	25.2731			1.23174			0.615868	−	0.787849i	$-0.288805\pi$
$421$	25.2731			1.23174			0.615868	+	0.787849i	$0.288805\pi$
$422$	4.69098	−	8.12501i	0.228353	−	0.395519i
$423$		0			0
$424$	2.06302	−	3.57325i	0.100189	−	0.173532i
$425$	1.41796	−	2.45597i	0.0687810	−	0.119132i
$426$		0			0
$427$	−13.0142	+	14.7128i	−0.629802	+	0.712001i
$428$	−39.7112			−1.91951
$429$		0			0
$430$	−0.843379	+	1.46077i	−0.0406713	+	0.0704448i
$431$	8.78466	+	15.2155i	0.423142	+	0.732904i	0.996245	−	0.0865796i	$-0.0275937\pi$
$431$	8.78466	+	15.2155i	0.423142	+	0.732904i	−0.573103	+	0.819484i	$0.694260\pi$
$432$		0			0
$433$	−3.02011	−	5.23098i	−0.145137	−	0.251385i	0.784287	−	0.620398i	$-0.213029\pi$
$433$	−3.02011	−	5.23098i	−0.145137	−	0.251385i	−0.929424	+	0.369013i	$0.879696\pi$
$434$	4.15889	−	4.70169i	0.199633	−	0.225688i
$435$		0			0
$436$	−11.2826	+	19.5420i	−0.540336	+	0.935890i
$437$	0.105685	−	0.183052i	0.00505559	−	0.00875654i
$438$		0			0
$439$	24.8563			1.18633			0.593164	−	0.805081i	$-0.297878\pi$
$439$	24.8563			1.18633			0.593164	+	0.805081i	$0.297878\pi$
$440$	0.588537	−	1.01938i	0.0280574	−	0.0485968i
$441$		0			0
$442$	0.823492	−	4.39537i	0.0391695	−	0.209066i
$443$	−15.8094	−	27.3826i	−0.751126	−	1.30099i	−0.947278	−	0.320414i	$-0.896178\pi$
$443$	−15.8094	−	27.3826i	−0.751126	−	1.30099i	0.196152	−	0.980574i	$-0.437155\pi$
$444$		0			0
$445$	−2.52237	−	4.36887i	−0.119572	−	0.207104i
$446$	−17.3073	+	29.9772i	−0.819527	+	1.41946i
$447$		0			0
$448$	−25.0615	−	5.09630i	−1.18405	−	0.240778i
$449$	2.63384	+	4.56194i	0.124298	+	0.215291i	0.921459	−	0.388477i	$-0.126999\pi$
$449$	2.63384	+	4.56194i	0.124298	+	0.215291i	−0.797160	+	0.603768i	$0.793665\pi$
$450$		0			0
$451$	37.2102			1.75216
$452$	8.32137	+	14.4130i	0.391404	+	0.677932i
$453$		0			0
$454$	−58.5046			−2.74576
$455$	−5.19056	+	0.719691i	−0.243337	+	0.0337396i
$456$		0			0
$457$	−18.4895			−0.864902			−0.432451	−	0.901658i	$-0.642351\pi$
$457$	−18.4895			−0.864902			−0.432451	+	0.901658i	$0.642351\pi$
$458$	26.9937	+	46.7545i	1.26133	+	2.18470i
$459$		0			0
$460$	−0.229895	−	0.398191i	−0.0107189	−	0.0185657i
$461$	−4.79101	−	8.29827i	−0.223140	−	0.386489i	0.732620	−	0.680638i	$-0.238297\pi$
$461$	−4.79101	−	8.29827i	−0.223140	−	0.386489i	−0.955760	+	0.294149i	$0.904964\pi$
$462$		0			0
$463$	2.22178			0.103255			0.0516275	−	0.998666i	$-0.483559\pi$
$463$	2.22178			0.103255			0.0516275	+	0.998666i	$0.483559\pi$
$464$	7.33622	−	12.7067i	0.340575	−	0.589894i
$465$		0			0
$466$	−22.8023	−	39.4947i	−1.05629	−	1.82956i
$467$	−6.76331	−	11.7144i	−0.312969	−	0.542078i	0.666035	−	0.745921i	$-0.267990\pi$
$467$	−6.76331	−	11.7144i	−0.312969	−	0.542078i	−0.979004	+	0.203843i	$0.934657\pi$
$468$		0			0
$469$	8.06055	+	24.0827i	0.372202	+	1.11204i
$470$	1.24029	−	2.14824i	0.0572102	−	0.0990910i
$471$		0			0
$472$	3.89333			0.179205
$473$	3.51053	−	6.08041i	0.161414	−	0.279578i
$474$		0			0
$475$	1.31812	+	2.28304i	0.0604793	+	0.104753i
$476$	3.47732	+	0.707119i	0.159383	+	0.0324107i
$477$		0			0
$478$	56.1382			2.56770
$479$	−7.29355	−	12.6328i	−0.333251	−	0.577207i	0.649897	−	0.760023i	$-0.274812\pi$
$479$	−7.29355	−	12.6328i	−0.333251	−	0.577207i	−0.983147	+	0.182816i	$0.941479\pi$
$480$		0			0
$481$	5.84442	−	31.1945i	0.266483	−	1.42235i
$482$	48.8681			2.22588
$483$		0			0
$484$	−12.3024	+	21.3085i	−0.559202	+	0.968567i
$485$	−1.73056	+	2.99741i	−0.0785806	+	0.136106i
$486$		0			0
$487$	−1.50126			−0.0680284			−0.0340142	−	0.999421i	$-0.510829\pi$
$487$	−1.50126			−0.0680284			−0.0340142	+	0.999421i	$0.510829\pi$
$488$	1.69302	−	2.93239i	0.0766393	−	0.132743i
$489$		0			0
$490$	−0.964413	−	7.84195i	−0.0435677	−	0.354263i
$491$	−14.1980	+	24.5917i	−0.640748	+	1.10981i	0.344518	+	0.938780i	$0.388042\pi$
$491$	−14.1980	+	24.5917i	−0.640748	+	1.10981i	−0.985266	+	0.171028i	$0.945291\pi$
$492$		0			0
$493$	−1.26275	+	2.18715i	−0.0568715	+	0.0985044i
$494$	3.15572	+	2.70589i	0.141983	+	0.121744i
$495$		0			0
$496$	2.02458	−	3.50668i	0.0909064	−	0.157455i
$497$	−4.85170	−	14.4955i	−0.217629	−	0.650214i
$498$		0			0
$499$	−10.5569	−	18.2851i	−0.472593	−	0.818554i	0.526915	−	0.849918i	$-0.323348\pi$
$499$	−10.5569	−	18.2851i	−0.472593	−	0.818554i	−0.999508	+	0.0313633i	$0.990015\pi$
$500$	11.8375			0.529387
$501$		0			0
$502$	8.56406	+	14.8334i	0.382233	+	0.662046i
$503$	−14.2618	−	24.7022i	−0.635903	−	1.10142i	−0.986323	−	0.164824i	$-0.947294\pi$
$503$	−14.2618	−	24.7022i	−0.635903	−	1.10142i	0.350420	−	0.936593i	$-0.386039\pi$
$504$		0			0
$505$	−1.22056	+	2.11408i	−0.0543143	+	0.0940752i
$506$	1.81827	+	3.14933i	0.0808318	+	0.140005i
$507$		0			0
$508$	5.25744	−	9.10615i	0.233261	−	0.404020i
$509$	−34.2589			−1.51850			−0.759250	−	0.650800i	$-0.774434\pi$
$509$	−34.2589			−1.51850			−0.759250	+	0.650800i	$0.774434\pi$
$510$		0			0
$511$	25.4059	−	28.7218i	1.12389	−	1.27058i
$512$	−31.6661			−1.39946
$513$		0			0
$514$	−28.3025			−1.24837
$515$	−4.56725	+	7.91071i	−0.201257	+	0.348587i
$516$		0			0
$517$	−5.16264	+	8.94196i	−0.227053	+	0.393267i
$518$	46.8927	+	9.53569i	2.06035	+	0.418974i
$519$		0			0
$520$	0.852089	−	0.299874i	0.0373666	−	0.0131503i
$521$	17.2434	−	29.8665i	0.755448	−	1.30847i	−0.189703	−	0.981841i	$-0.560753\pi$
$521$	17.2434	−	29.8665i	0.755448	−	1.30847i	0.945151	−	0.326633i	$-0.105914\pi$
$522$		0			0
$523$	31.3896			1.37257			0.686285	−	0.727332i	$-0.259240\pi$
$523$	31.3896			1.37257			0.686285	+	0.727332i	$0.259240\pi$
$524$	3.97077	+	6.87757i	0.173464	+	0.300448i
$525$		0			0
$526$	9.29323	+	16.0963i	0.405204	+	0.701834i
$527$	−0.348483	+	0.603590i	−0.0151802	+	0.0262928i
$528$		0			0
$529$	−22.8581			−0.993830
$530$	10.2112			0.443548
$531$		0			0
$532$	−2.18550	+	2.47074i	−0.0947534	+	0.107120i
$533$	21.6780	+	18.5879i	0.938980	+	0.805133i
$534$		0			0
$535$	−4.90879	−	8.50227i	−0.212225	−	0.367585i
$536$	−2.18889	−	3.79126i	−0.0945455	−	0.163758i
$537$		0			0
$538$	4.70241			0.202735
$539$	4.01433	+	32.6418i	0.172909	+	1.40598i
$540$		0			0
$541$	−4.55013	−	7.88106i	−0.195626	−	0.338833i	0.751480	−	0.659756i	$-0.229340\pi$
$541$	−4.55013	−	7.88106i	−0.195626	−	0.338833i	−0.947105	+	0.320923i	$0.896007\pi$
$542$	−8.18023			−0.351371
$543$		0			0
$544$	4.89996			0.210084
$545$	−5.57865			−0.238963
$546$		0			0
$547$	−35.9950			−1.53903			−0.769517	−	0.638626i	$-0.779503\pi$
$547$	−35.9950			−1.53903			−0.769517	+	0.638626i	$0.779503\pi$
$548$	42.7897			1.82789
$549$		0			0
$550$	−45.3553			−1.93396
$551$	−1.17384	−	2.03315i	−0.0500072	−	0.0866150i
$552$		0			0
$553$	12.2789	+	36.6859i	0.522151	+	1.56004i
$554$	17.2598			0.733299
$555$		0			0
$556$	−10.7355	−	18.5945i	−0.455288	−	0.788581i
$557$	−7.95708	−	13.7821i	−0.337152	−	0.583965i	0.646744	−	0.762707i	$-0.276130\pi$
$557$	−7.95708	−	13.7821i	−0.337152	−	0.583965i	−0.983896	+	0.178743i	$0.942797\pi$
$558$		0			0
$559$	5.08257	−	1.78870i	0.214970	−	0.0756540i
$560$	−1.61767	−	4.83316i	−0.0683592	−	0.204238i
$561$		0			0
$562$	−26.6210			−1.12294
$563$	25.2247			1.06310			0.531548	−	0.847028i	$-0.321610\pi$
$563$	25.2247			1.06310			0.531548	+	0.847028i	$0.321610\pi$
$564$		0			0
$565$	−2.05725	+	3.56326i	−0.0865490	+	0.149907i
$566$	26.3059	+	45.5632i	1.10572	+	1.91517i
$567$		0			0
$568$	1.31751	+	2.28199i	0.0552813	+	0.0957501i
$569$	−34.1685			−1.43242			−0.716208	−	0.697886i	$-0.754124\pi$
$569$	−34.1685			−1.43242			−0.716208	+	0.697886i	$0.754124\pi$
$570$		0			0
$571$	−7.15867	+	12.3992i	−0.299581	+	0.518889i	−0.976040	−	0.217591i	$-0.930180\pi$
$571$	−7.15867	+	12.3992i	−0.299581	+	0.518889i	0.676459	+	0.736480i	$0.263514\pi$
$572$	−35.5050	+	12.4952i	−1.48454	+	0.522450i
$573$		0			0
$574$	−28.5266	+	32.2497i	−1.19068	+	1.34608i
$575$	−0.884913	+	1.53271i	−0.0369034	+	0.0639186i
$576$		0			0
$577$	5.34662	−	9.26061i	0.222583	−	0.385524i	−0.733009	−	0.680219i	$-0.761885\pi$
$577$	5.34662	−	9.26061i	0.222583	−	0.385524i	0.955591	+	0.294695i	$0.0952180\pi$
$578$	34.1820			1.42178
$579$		0			0
$580$	−5.10688			−0.212052
$581$	38.5662	+	7.84249i	1.59999	+	0.325361i
$582$		0			0
$583$	−42.5039			−1.76033
$584$	−3.30505	+	5.72452i	−0.136764	+	0.236882i
$585$		0			0
$586$	−25.4670	−	44.1102i	−1.05203	−	1.82217i
$587$	21.3592	−	36.9951i	0.881587	−	1.52695i	0.0320103	−	0.999488i	$-0.489809\pi$
$587$	21.3592	−	36.9951i	0.881587	−	1.52695i	0.849576	−	0.527465i	$-0.176858\pi$
$588$		0			0
$589$	−0.323945	−	0.561090i	−0.0133479	−	0.0231193i
$590$	4.81767	+	8.34446i	0.198341	+	0.343536i
$591$		0			0
$592$	30.8680			1.26867
$593$	−14.0922	−	24.4084i	−0.578697	−	1.00233i	−0.995629	−	0.0933948i	$-0.970228\pi$
$593$	−14.0922	−	24.4084i	−0.578697	−	1.00233i	0.416932	−	0.908938i	$-0.363105\pi$
$594$		0			0
$595$	0.278444	+	0.831913i	0.0114151	+	0.0341051i
$596$	7.91570	−	13.7104i	0.324240	−	0.561599i
$597$		0			0
$598$	−0.513921	+	2.74304i	−0.0210158	+	0.112171i
$599$	−15.7857	+	27.3417i	−0.644987	+	1.11715i	0.339317	+	0.940672i	$0.389804\pi$
$599$	−15.7857	+	27.3417i	−0.644987	+	1.11715i	−0.984304	+	0.176479i	$0.943529\pi$
$600$		0			0
$601$	16.0445	−	27.7899i	0.654469	−	1.13357i	−0.327558	−	0.944831i	$-0.606226\pi$
$601$	16.0445	−	27.7899i	0.654469	−	1.13357i	0.982027	−	0.188742i	$-0.0604409\pi$
$602$	2.57855	+	7.70399i	0.105094	+	0.313991i
$603$		0			0
$604$	21.8362	−	37.8214i	0.888503	−	1.53893i
$605$	−6.08293			−0.247306
$606$		0			0
$607$	9.33324	−	16.1657i	0.378825	−	0.656144i	−0.612067	−	0.790806i	$-0.709662\pi$
$607$	9.33324	−	16.1657i	0.378825	−	0.656144i	0.990892	+	0.134662i	$0.0429950\pi$
$608$	−2.27747	+	3.94469i	−0.0923636	+	0.159978i
$609$		0			0
$610$	8.37988			0.339291
$611$	−7.47452	+	2.63049i	−0.302387	+	0.106418i
$612$		0			0
$613$	−8.96569	−	15.5290i	−0.362121	−	0.627211i	0.626189	−	0.779671i	$-0.284614\pi$
$613$	−8.96569	−	15.5290i	−0.362121	−	0.627211i	−0.988310	+	0.152460i	$0.951281\pi$
$614$	51.7971			2.09036
$615$		0			0
$616$	−1.79939	−	5.37609i	−0.0724997	−	0.216609i
$617$	15.8059	+	27.3765i	0.636320	+	1.10214i	0.986234	+	0.165356i	$0.0528774\pi$
$617$	15.8059	+	27.3765i	0.636320	+	1.10214i	−0.349914	+	0.936782i	$0.613789\pi$
$618$		0			0
$619$	16.3184	−	28.2644i	0.655894	−	1.13604i	−0.325775	−	0.945447i	$-0.605625\pi$
$619$	16.3184	−	28.2644i	0.655894	−	1.13604i	0.981669	−	0.190594i	$-0.0610413\pi$
$620$	−1.40935			−0.0566009
$621$		0			0
$622$	−4.24592	+	7.35415i	−0.170246	+	0.294875i
$623$	−23.8100	−	4.84180i	−0.953929	−	0.193983i
$624$		0			0
$625$	−10.2824	−	17.8096i	−0.411294	−	0.712382i
$626$	−30.9632	−	53.6298i	−1.23754	−	2.14348i
$627$		0			0
$628$	5.78842	−	10.0258i	0.230983	−	0.400075i
$629$	−5.31319			−0.211851
$630$		0			0
$631$	12.7985	+	22.1676i	0.509500	+	0.882480i	0.999939	+	0.0110045i	$0.00350290\pi$
$631$	12.7985	+	22.1676i	0.509500	+	0.882480i	−0.490440	+	0.871475i	$0.663164\pi$
$632$	−3.33440	−	5.77535i	−0.132635	−	0.229731i
$633$		0			0
$634$	−11.8421	−	20.5111i	−0.470310	−	0.814600i
$635$	2.59954			0.103159
$636$		0			0
$637$	−13.9672	+	21.0219i	−0.553399	+	0.832916i
$638$	40.3909			1.59909
$639$		0			0
$640$	0.995967	+	1.72507i	0.0393691	+	0.0681892i
$641$	−43.2415			−1.70794			−0.853969	−	0.520324i	$-0.825811\pi$
$641$	−43.2415			−1.70794			−0.853969	+	0.520324i	$0.825811\pi$
$642$		0			0
$643$	2.25709	+	3.90939i	0.0890108	+	0.154171i	0.907093	−	0.420930i	$-0.138296\pi$
$643$	2.25709	+	3.90939i	0.0890108	+	0.154171i	−0.818082	+	0.575101i	$0.804963\pi$
$644$	−2.17011	−	0.441295i	−0.0855144	−	0.0173895i
$645$		0			0
$646$	0.347963	−	0.602689i	0.0136904	−	0.0237125i
$647$	−5.72020	−	9.90769i	−0.224884	−	0.389511i	0.731400	−	0.681948i	$-0.238867\pi$
$647$	−5.72020	−	9.90769i	−0.224884	−	0.389511i	−0.956285	+	0.292437i	$0.905534\pi$
$648$		0			0
$649$	−20.0534	−	34.7334i	−0.787163	−	1.36341i
$650$	−26.4232	−	22.6567i	−1.03640	−	0.888670i
$651$		0			0
$652$	4.63701	−	8.03153i	0.181599	−	0.314539i
$653$	21.7515			0.851201			0.425600	−	0.904911i	$-0.360063\pi$
$653$	21.7515			0.851201			0.425600	+	0.904911i	$0.360063\pi$
$654$		0			0
$655$	−0.981671	+	1.70030i	−0.0383571	+	0.0664364i
$656$	−13.8870	+	24.0530i	−0.542196	+	0.939111i
$657$		0			0
$658$	−3.79206	−	11.3296i	−0.147830	−	0.441675i
$659$	−3.28320	−	5.68668i	−0.127895	−	0.221521i	0.794966	−	0.606655i	$-0.207489\pi$
$659$	−3.28320	−	5.68668i	−0.127895	−	0.221521i	−0.922861	+	0.385133i	$0.874156\pi$
$660$		0			0
$661$	23.0777	+	39.9718i	0.897619	+	1.55472i	0.830529	+	0.556975i	$0.188038\pi$
$661$	23.0777	+	39.9718i	0.897619	+	1.55472i	0.0670899	+	0.997747i	$0.478629\pi$
$662$	−1.16647	+	2.02038i	−0.0453360	+	0.0785243i
$663$		0			0
$664$	−6.78416			−0.263276
$665$	−0.799147	−	0.162508i	−0.0309896	−	0.00630177i
$666$		0			0
$667$	0.788053	−	1.36495i	0.0305135	−	0.0528510i
$668$	5.60680	−	9.71127i	0.216934	−	0.375740i
$669$		0			0
$670$	5.41713	−	9.38275i	0.209282	−	0.362487i
$671$	−34.8809			−1.34656
$672$		0			0
$673$	−5.50174	+	9.52930i	−0.212077	+	0.367327i	−0.952364	−	0.304963i	$-0.901356\pi$
$673$	−5.50174	+	9.52930i	−0.212077	+	0.367327i	0.740288	+	0.672290i	$0.234689\pi$
$674$	−47.9128			−1.84553
$675$		0			0
$676$	−26.9264	−	10.4566i	−1.03563	−	0.402178i
$677$	11.0575	+	19.1522i	0.424976	+	0.736080i	0.996418	−	0.0845623i	$-0.0269492\pi$
$677$	11.0575	+	19.1522i	0.424976	+	0.736080i	−0.571442	+	0.820642i	$0.693616\pi$
$678$		0			0
$679$	5.29101	+	15.8081i	0.203050	+	0.606658i
$680$	−0.0756129	−	0.130965i	−0.00289962	−	0.00502229i
$681$		0			0
$682$	11.1467			0.426830
$683$	8.47618			0.324332			0.162166	−	0.986763i	$-0.448152\pi$
$683$	8.47618			0.324332			0.162166	+	0.986763i	$0.448152\pi$
$684$		0			0
$685$	5.28933	+	9.16139i	0.202095	+	0.350039i
$686$	−31.3678	−	21.5451i	−1.19763	−	0.822596i
$687$		0			0
$688$	2.62028	+	4.53847i	0.0998974	+	0.173027i
$689$	−24.7620	−	21.2323i	−0.943359	−	0.808888i
$690$		0			0
$691$	1.91943			0.0730185			0.0365092	−	0.999333i	$-0.488376\pi$
$691$	1.91943			0.0730185			0.0365092	+	0.999333i	$0.488376\pi$
$692$	3.04295	−	5.27055i	0.115676	−	0.200356i
$693$		0			0
$694$	5.21539			0.197973
$695$	2.65408	−	4.59701i	0.100675	−	0.174374i
$696$		0			0
$697$	2.39031	−	4.14014i	0.0905395	−	0.156819i
$698$	10.9796	−	19.0172i	0.415583	−	0.719811i
$699$		0			0
$700$	18.2995	−	20.6878i	0.691655	−	0.781926i
$701$	18.1080			0.683929			0.341965	−	0.939713i	$-0.388908\pi$
$701$	18.1080			0.683929			0.341965	+	0.939713i	$0.388908\pi$
$702$		0			0
$703$	2.46953	−	4.27736i	0.0931403	−	0.161324i
$704$	−22.7072	−	39.3300i	−0.855809	−	1.48230i
$705$		0			0
$706$	−22.8494	−	39.5763i	−0.859948	−	1.48947i
$707$	3.73175	+	11.1494i	0.140347	+	0.419318i
$708$		0			0
$709$	14.1884	−	24.5751i	0.532857	−	0.922936i	−0.466407	−	0.884570i	$-0.654452\pi$
$709$	14.1884	−	24.5751i	0.532857	−	0.922936i	0.999264	−	0.0383652i	$-0.0122150\pi$
$710$	−3.26061	+	5.64754i	−0.122368	+	0.211948i
$711$		0			0
$712$	4.18841			0.156967
$713$	0.217480	−	0.376686i	0.00814468	−	0.0141070i
$714$		0			0
$715$	−7.06411	−	6.05715i	−0.264183	−	0.226525i
$716$	−14.1046	−	24.4299i	−0.527115	−	0.912990i
$717$		0			0
$718$	17.2217	+	29.8288i	0.642706	+	1.11320i
$719$	22.1741	−	38.4067i	0.826955	−	1.43233i	−0.0734616	−	0.997298i	$-0.523405\pi$
$719$	22.1741	−	38.4067i	0.826955	−	1.43233i	0.900416	−	0.435029i	$-0.143262\pi$
$720$		0			0
$721$	13.9639	+	41.7203i	0.520044	+	1.55375i
$722$	−19.1966	−	33.2495i	−0.714423	−	1.23742i
$723$		0			0
$724$	17.6800			0.657071
$725$	9.82870	+	17.0238i	0.365029	+	0.632248i
$726$		0			0
$727$	24.1298			0.894924			0.447462	−	0.894303i	$-0.352328\pi$
$727$	24.1298			0.894924			0.447462	+	0.894303i	$0.352328\pi$
$728$	1.63727	−	4.03089i	0.0606812	−	0.149395i
$729$		0			0
$730$	−16.3589			−0.605471
$731$	−0.451019	−	0.781187i	−0.0166815	−	0.0288933i
$732$		0			0
$733$	16.7734	+	29.0524i	0.619540	+	1.07308i	0.989570	+	0.144055i	$0.0460143\pi$
$733$	16.7734	+	29.0524i	0.619540	+	1.07308i	−0.370029	+	0.929020i	$0.620652\pi$
$734$	−4.81009	−	8.33132i	−0.177544	−	0.307515i
$735$		0			0
$736$	−3.05795			−0.112717
$737$	−22.5486	+	39.0553i	−0.830588	+	1.43862i
$738$		0			0
$739$	8.41105	+	14.5684i	0.309405	+	0.535906i	0.978232	−	0.207512i	$-0.0665367\pi$
$739$	8.41105	+	14.5684i	0.309405	+	0.535906i	−0.668827	+	0.743418i	$0.733203\pi$
$740$	−5.37196	−	9.30451i	−0.197477	−	0.342041i
$741$		0			0
$742$	32.5849	−	36.8377i	1.19623	−	1.35236i
$743$	16.5645	−	28.6906i	0.607694	−	1.05256i	−0.383926	−	0.923364i	$-0.625428\pi$
$743$	16.5645	−	28.6906i	0.607694	−	1.05256i	0.991620	−	0.129192i	$-0.0412385\pi$
$744$		0			0
$745$	3.91391			0.143394
$746$	−6.94680	+	12.0322i	−0.254340	+	0.440530i
$747$		0			0
$748$	3.15065	+	5.45709i	0.115199	+	0.199531i
$749$	−46.3368	−	9.42265i	−1.69311	−	0.344296i
$750$		0			0
$751$	−29.7949			−1.08723			−0.543616	−	0.839334i	$-0.682945\pi$
$751$	−29.7949			−1.08723			−0.543616	+	0.839334i	$0.682945\pi$
$752$	−3.85344	−	6.67435i	−0.140520	−	0.243388i
$753$		0			0
$754$	23.5310	+	20.1768i	0.856950	+	0.734796i
$755$	10.7969			0.392939
$756$		0			0
$757$	−11.0742	+	19.1810i	−0.402498	+	0.697147i	−0.994027	−	0.109137i	$-0.965191\pi$
$757$	−11.0742	+	19.1810i	−0.402498	+	0.697147i	0.591529	+	0.806284i	$0.298525\pi$
$758$	−19.7768	+	34.2545i	−0.718327	+	1.24418i
$759$		0			0
$760$	0.140577			0.00509928
$761$	21.4467	−	37.1468i	0.777443	−	1.34657i	−0.155969	−	0.987762i	$-0.549850\pi$
$761$	21.4467	−	37.1468i	0.777443	−	1.34657i	0.933411	−	0.358808i	$-0.116817\pi$
$762$		0			0
$763$	−17.8019	+	20.1253i	−0.644472	+	0.728586i
$764$	3.42159	−	5.92637i	0.123789	−	0.214408i
$765$		0			0
$766$	−13.8542	+	23.9961i	−0.500572	+	0.867016i
$767$	5.66795	−	30.2525i	0.204658	−	1.09236i
$768$		0			0
$769$	25.5865	−	44.3171i	0.922671	−	1.59811i	0.127407	−	0.991850i	$-0.459334\pi$
$769$	25.5865	−	44.3171i	0.922671	−	1.59811i	0.795264	−	0.606263i	$-0.207332\pi$
$770$	9.29581	−	10.5091i	0.334998	−	0.378720i
$771$		0			0
$772$	3.76817	+	6.52666i	0.135619	+	0.234900i
$773$	36.3249			1.30652			0.653259	−	0.757135i	$-0.273401\pi$
$773$	36.3249			1.30652			0.653259	+	0.757135i	$0.273401\pi$
$774$		0			0
$775$	2.71244	+	4.69808i	0.0974336	+	0.168760i
$776$	−1.43680	−	2.48862i	−0.0515782	−	0.0893361i
$777$		0			0
$778$	33.7449	−	58.4478i	1.20981	−	2.09546i
$779$	2.22200	+	3.84862i	0.0796115	+	0.137891i
$780$		0			0
$781$	13.5721	−	23.5076i	0.485650	−	0.841170i
$782$	0.467208			0.0167073
$783$		0			0
$784$	−22.5981	−	9.58715i	−0.807074	−	0.342398i
$785$	2.86208			0.102152
$786$		0			0
$787$	−54.3948			−1.93896			−0.969482	−	0.245162i	$-0.921159\pi$
$787$	−54.3948			−1.93896			−0.969482	+	0.245162i	$0.921159\pi$
$788$	−4.58087	+	7.93431i	−0.163187	+	0.282648i
$789$		0			0
$790$	8.25208	−	14.2930i	0.293596	−	0.508523i
$791$	6.28983	+	18.7923i	0.223641	+	0.668177i
$792$		0			0
$793$	−20.3210	−	17.4243i	−0.721620	−	0.618757i
$794$	−27.3392	+	47.3529i	−0.970233	+	1.68049i
$795$		0			0
$796$	−2.55145			−0.0904336
$797$	−15.9900	−	27.6955i	−0.566396	−	0.981026i	−0.996918	−	0.0784465i	$-0.975004\pi$
$797$	−15.9900	−	27.6955i	−0.566396	−	0.981026i	0.430522	−	0.902580i	$-0.358329\pi$
$798$		0			0
$799$	0.663276	+	1.14883i	0.0234650	+	0.0406426i
$800$	19.0695	−	33.0294i	0.674210	−	1.16777i
$801$		0			0
$802$	−47.4886			−1.67688
$803$	68.0933			2.40296
$804$		0			0
$805$	−0.173770	−	0.519176i	−0.00612458	−	0.0182986i
$806$	6.49388	+	5.56821i	0.228737	+	0.196132i
$807$		0			0
$808$	−1.01338	−	1.75522i	−0.0356505	−	0.0617485i
$809$	−0.0423933	−	0.0734274i	−0.00149047	−	0.00258157i	0.865279	−	0.501290i	$-0.167141\pi$
$809$	−0.0423933	−	0.0734274i	−0.00149047	−	0.00258157i	−0.866770	+	0.498709i	$0.833808\pi$
$810$		0			0
$811$	2.81654			0.0989019			0.0494510	−	0.998777i	$-0.484253\pi$
$811$	2.81654			0.0989019			0.0494510	+	0.998777i	$0.484253\pi$
$812$	−16.2965	+	18.4234i	−0.571894	+	0.646535i
$813$		0			0
$814$	42.4874	+	73.5903i	1.48918	+	2.57934i
$815$	2.29276			0.0803120
$816$		0			0
$817$	0.838522			0.0293362
$818$	14.8793			0.520244
$819$		0			0
$820$	9.66701			0.337586
$821$	−16.7031			−0.582943			−0.291471	−	0.956580i	$-0.594145\pi$
$821$	−16.7031			−0.582943			−0.291471	+	0.956580i	$0.594145\pi$
$822$		0			0
$823$	−26.3739			−0.919336			−0.459668	−	0.888091i	$-0.652032\pi$
$823$	−26.3739			−0.919336			−0.459668	+	0.888091i	$0.652032\pi$
$824$	−3.79198	−	6.56790i	−0.132100	−	0.228804i
$825$		0			0
$826$	45.4767	+	9.24776i	1.58234	+	0.321771i
$827$	36.8372			1.28095			0.640477	−	0.767977i	$-0.278737\pi$
$827$	36.8372			1.28095			0.640477	+	0.767977i	$0.278737\pi$
$828$		0			0
$829$	−12.4027	−	21.4822i	−0.430765	−	0.746107i	0.566174	−	0.824286i	$-0.308423\pi$
$829$	−12.4027	−	21.4822i	−0.430765	−	0.746107i	−0.996939	+	0.0781784i	$0.975090\pi$
$830$	−8.39483	−	14.5403i	−0.291389	−	0.504700i
$831$		0			0
$832$	6.41803	−	34.2561i	0.222505	−	1.18762i
$833$	3.88971	+	1.65020i	0.134771	+	0.0571759i
$834$		0			0
$835$	2.77228			0.0959386
$836$	−5.85761			−0.202590
$837$		0			0
$838$	−36.0710	+	62.4768i	−1.24605	+	2.15823i
$839$	11.4460	+	19.8250i	0.395159	+	0.684435i	0.993121	−	0.117089i	$-0.0373562\pi$
$839$	11.4460	+	19.8250i	0.395159	+	0.684435i	−0.597963	+	0.801524i	$0.704023\pi$
$840$		0			0
$841$	5.74711	+	9.95429i	0.198176	+	0.343251i
$842$	−51.9297			−1.78962
$843$		0			0
$844$	−5.07274	+	8.78625i	−0.174611	+	0.302435i
$845$	−1.08965	−	7.05759i	−0.0374849	−	0.242788i
$846$		0			0
$847$	−19.4111	+	21.9446i	−0.666974	+	0.754024i
$848$	15.8626	−	27.4749i	0.544724	−	0.943490i
$849$		0			0
$850$	−2.91354	+	5.04639i	−0.0999335	+	0.173090i
$851$	3.31583			0.113665
$852$		0			0
$853$	0.727097			0.0248953			0.0124477	−	0.999923i	$-0.496038\pi$
$853$	0.727097			0.0248953			0.0124477	+	0.999923i	$0.496038\pi$
$854$	26.7409	−	30.2309i	0.915053	−	1.03448i
$855$		0			0
$856$	8.15108			0.278598
$857$	−6.16106	+	10.6713i	−0.210458	+	0.364524i	−0.951858	−	0.306540i	$-0.900829\pi$
$857$	−6.16106	+	10.6713i	−0.210458	+	0.364524i	0.741400	+	0.671063i	$0.234162\pi$
$858$		0			0
$859$	−17.1581	−	29.7187i	−0.585427	−	1.01399i	−0.994822	−	0.101632i	$-0.967594\pi$
$859$	−17.1581	−	29.7187i	−0.585427	−	1.01399i	0.409395	−	0.912357i	$-0.365740\pi$
$860$	0.912016	−	1.57966i	0.0310995	−	0.0538659i
$861$		0			0
$862$	−18.0502	−	31.2639i	−0.614793	−	1.06485i
$863$	−17.8997	−	31.0032i	−0.609313	−	1.05536i	−0.991354	−	0.131216i	$-0.958112\pi$
$863$	−17.8997	−	31.0032i	−0.609313	−	1.05536i	0.382041	−	0.924146i	$-0.375221\pi$
$864$		0			0
$865$	1.50458			0.0511574
$866$	6.20554	+	10.7483i	0.210873	+	0.365242i
$867$		0			0
$868$	−4.49735	+	5.08433i	−0.152650	+	0.172573i
$869$	−34.3489	+	59.4941i	−1.16521	+	2.01820i
$870$		0			0
$871$	−32.6460	+	11.4891i	−1.10617	+	0.389292i
$872$	2.31585	−	4.01117i	0.0784245	−	0.135835i
$873$		0			0
$874$	−0.217155	+	0.376124i	−0.00734538	+	0.0127226i
$875$	13.8125	+	2.80879i	0.466947	+	0.0949544i
$876$		0			0
$877$	−14.9040	+	25.8145i	−0.503272	+	0.871693i	0.496721	+	0.867910i	$0.334537\pi$
$877$	−14.9040	+	25.8145i	−0.503272	+	0.871693i	−0.999993	+	0.00378256i	$0.998796\pi$
$878$	−51.0734			−1.72364
$879$		0			0
$880$	4.52528	−	7.83801i	0.152547	−	0.264219i
$881$	−11.3524	+	19.6629i	−0.382470	+	0.662458i	−0.991415	−	0.130755i	$-0.958260\pi$
$881$	−11.3524	+	19.6629i	−0.382470	+	0.662458i	0.608944	+	0.793213i	$0.291593\pi$
$882$		0			0
$883$	51.4418			1.73115			0.865577	−	0.500776i	$-0.166952\pi$
$883$	51.4418			1.73115			0.865577	+	0.500776i	$0.166952\pi$
$884$	−0.890511	+	4.75308i	−0.0299511	+	0.159863i
$885$		0			0
$886$	32.4842	+	56.2642i	1.09133	+	1.89023i
$887$	−14.8077			−0.497194			−0.248597	−	0.968607i	$-0.579969\pi$
$887$	−14.8077			−0.497194			−0.248597	+	0.968607i	$0.579969\pi$
$888$		0			0
$889$	8.29532	−	9.37799i	0.278216	−	0.314528i
$890$	5.18281	+	8.97689i	0.173728	+	0.300906i
$891$		0			0
$892$	18.7159	−	32.4169i	0.626654	−	1.08540i
$893$	−1.23315			−0.0412657
$894$		0			0
$895$	3.48701	−	6.03968i	0.116558	−	0.201884i
$896$	9.40150	+	1.91181i	0.314082	+	0.0638690i
$897$		0			0
$898$	−5.41186	−	9.37361i	−0.180596	−	0.312801i
$899$	−2.41554	−	4.18384i	−0.0805628	−	0.139539i
$900$		0			0
$901$	−2.73037	+	4.72913i	−0.0909617	+	0.157550i
$902$	−76.4574			−2.54575
$903$		0			0
$904$	−1.70804	−	2.95841i	−0.0568085	−	0.0983952i
$905$	2.18546	+	3.78533i	0.0726471	+	0.125829i
$906$		0			0
$907$	1.11175	+	1.92561i	0.0369151	+	0.0639389i	0.883893	−	0.467690i	$-0.154914\pi$
$907$	1.11175	+	1.92561i	0.0369151	+	0.0639389i	−0.846978	+	0.531629i	$0.821580\pi$
$908$	63.2659			2.09955
$909$		0			0
$910$	10.6653	−	1.47878i	0.353550	−	0.0490210i
$911$	29.3786			0.973355			0.486678	−	0.873582i	$-0.338209\pi$
$911$	29.3786			0.973355			0.486678	+	0.873582i	$0.338209\pi$
$912$		0			0
$913$	34.9431	+	60.5233i	1.15645	+	2.00303i
$914$	37.9911			1.25663
$915$		0			0
$916$	−29.1906	−	50.5596i	−0.964484	−	1.67054i
$917$	3.00137	+	8.96725i	0.0991138	+	0.296125i
$918$		0			0
$919$	10.8455	−	18.7850i	0.357761	−	0.619661i	−0.629825	−	0.776737i	$-0.716874\pi$
$919$	10.8455	−	18.7850i	0.357761	−	0.619661i	0.987586	+	0.157076i	$0.0502069\pi$
$920$	0.0471882	+	0.0817323i	0.00155575	+	0.00269463i
$921$		0			0
$922$	9.84429	+	17.0508i	0.324204	+	0.561538i
$923$	19.6499	−	6.91534i	0.646784	−	0.227621i
$924$		0			0
$925$	−20.6777	+	35.8149i	−0.679880	+	1.17759i
$926$	−4.56519			−0.150021
$927$		0			0
$928$	−16.9823	+	29.4141i	−0.557470	+	0.965566i
$929$	−15.5615	+	26.9534i	−0.510557	+	0.884311i	0.489368	+	0.872077i	$0.337227\pi$
$929$	−15.5615	+	26.9534i	−0.510557	+	0.884311i	−0.999925	+	0.0122336i	$0.996106\pi$
$930$		0			0
$931$	−3.13640	+	2.36440i	−0.102791	+	0.0774900i
$932$	24.6580	+	42.7089i	0.807699	+	1.39898i
$933$		0			0
$934$	13.8969	+	24.0701i	0.454719	+	0.787597i
$935$	−0.778918	+	1.34913i	−0.0254733	+	0.0441211i
$936$		0			0
$937$	13.1250			0.428777			0.214388	−	0.976749i	$-0.431224\pi$
$937$	13.1250			0.428777			0.214388	+	0.976749i	$0.431224\pi$
$938$	−16.5624	−	49.4837i	−0.540780	−	1.61570i
$939$		0			0
$940$	−1.34123	+	2.32307i	−0.0437460	+	0.0757703i
$941$	23.5806	−	40.8428i	0.768705	−	1.33144i	−0.169560	−	0.985520i	$-0.554235\pi$
$941$	23.5806	−	40.8428i	0.768705	−	1.33144i	0.938265	−	0.345917i	$-0.112432\pi$
$942$		0			0
$943$	−1.49173	+	2.58376i	−0.0485776	+	0.0841388i
$944$	29.9360			0.974333
$945$		0			0
$946$	−7.21323	+	12.4937i	−0.234522	+	0.406204i
$947$	−4.31484			−0.140214			−0.0701068	−	0.997539i	$-0.522334\pi$
$947$	−4.31484			−0.140214			−0.0701068	+	0.997539i	$0.522334\pi$
$948$		0			0
$949$	39.6700	+	34.0152i	1.28774	+	1.10418i
$950$	−2.70839	−	4.69106i	−0.0878716	−	0.152198i
$951$		0			0
$952$	−0.713752	−	0.145143i	−0.0231328	−	0.00470410i
$953$	5.09812	+	8.83020i	0.165144	+	0.286038i	0.936707	−	0.350116i	$-0.113858\pi$
$953$	5.09812	+	8.83020i	0.165144	+	0.286038i	−0.771562	+	0.636154i	$0.780524\pi$
$954$		0			0
$955$	1.69180			0.0547454
$956$	−60.7069			−1.96340
$957$		0			0
$958$	14.9864	+	25.9571i	0.484187	+	0.838637i
$959$	49.9290	+	10.1531i	1.61229	+	0.327861i
$960$		0			0
$961$	14.8334	+	25.6922i	0.478496	+	0.828780i
$962$	−12.0088	+	64.0966i	−0.387179	+	2.06656i
$963$		0			0
$964$	−52.8451			−1.70203
$965$	−0.931584	+	1.61355i	−0.0299887	+	0.0519420i
$966$		0			0
$967$	14.3246			0.460649			0.230324	−	0.973114i	$-0.426021\pi$
$967$	14.3246			0.460649			0.230324	+	0.973114i	$0.426021\pi$
$968$	2.52519	−	4.37376i	0.0811627	−	0.140578i
$969$		0			0
$970$	3.55585	−	6.15891i	0.114171	−	0.197751i
$971$	−8.54294	+	14.7968i	−0.274156	+	0.474852i	−0.969922	−	0.243416i	$-0.921732\pi$
$971$	−8.54294	+	14.7968i	−0.274156	+	0.474852i	0.695766	+	0.718269i	$0.255065\pi$
$972$		0			0
$973$	−8.11461	−	24.2442i	−0.260142	−	0.777233i
$974$	3.08469			0.0988400
$975$		0			0
$976$	13.0177	−	22.5473i	0.416686	−	0.721721i
$977$	−25.0285	−	43.3507i	−0.800733	−	1.38691i	−0.919134	−	0.393945i	$-0.871110\pi$
$977$	−25.0285	−	43.3507i	−0.800733	−	1.38691i	0.118401	−	0.992966i	$-0.462223\pi$
$978$		0			0
$979$	−21.5732	−	37.3659i	−0.689484	−	1.19422i
$980$	1.04290	+	8.48016i	0.0333142	+	0.270889i
$981$		0			0
$982$	29.1733	−	50.5296i	0.930956	−	1.61246i
$983$	−20.6067	+	35.6919i	−0.657252	+	1.13839i	0.324072	+	0.946032i	$0.394948\pi$
$983$	−20.6067	+	35.6919i	−0.657252	+	1.13839i	−0.981324	+	0.192362i	$0.938385\pi$
$984$		0			0
$985$	−2.26501			−0.0721692
$986$	2.59463	−	4.49403i	0.0826299	−	0.143119i
$987$		0			0
$988$	−3.41254	−	2.92610i	−0.108567	−	0.0930917i
$989$	0.281470	+	0.487520i	0.00895022	+	0.0155022i
$990$		0			0
$991$	−5.01241	−	8.68175i	−0.159225	−	0.275785i	0.775365	−	0.631514i	$-0.217566\pi$
$991$	−5.01241	−	8.68175i	−0.159225	−	0.275785i	−0.934589	+	0.355729i	$0.884233\pi$
$992$	−4.68661	+	8.11745i	−0.148800	+	0.257729i
$993$		0			0
$994$	9.96900	+	29.7846i	0.316197	+	0.944710i
$995$	−0.315390	−	0.546271i	−0.00999853	−	0.0173180i
$996$		0			0
$997$	−43.8518			−1.38880			−0.694401	−	0.719588i	$-0.744330\pi$
$997$	−43.8518			−1.38880			−0.694401	+	0.719588i	$0.744330\pi$
$998$	21.6917	+	37.5712i	0.686640	+	1.18930i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.e.802.2		16
3.2	odd	2		273.2.l.b.256.7	yes	16
7.2	even	3		819.2.n.e.100.7		16
13.3	even	3		819.2.n.e.172.7		16
21.2	odd	6		273.2.j.b.100.2	✓	16
39.29	odd	6		273.2.j.b.172.2	yes	16
91.16	even	3	inner	819.2.s.e.289.2		16
273.107	odd	6		273.2.l.b.16.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.2	✓	16	21.2	odd	6
273.2.j.b.172.2	yes	16	39.29	odd	6
273.2.l.b.16.7	yes	16	273.107	odd	6
273.2.l.b.256.7	yes	16	3.2	odd	2
819.2.n.e.100.7		16	7.2	even	3
819.2.n.e.172.7		16	13.3	even	3
819.2.s.e.289.2		16	91.16	even	3	inner
819.2.s.e.802.2		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.05474 q^{2} +2.22196 q^{4} +(0.274662 + 0.475728i) q^{5} +(2.59269 + 0.527227i) q^{7} -0.456078 q^{8} +(-0.564359 - 0.977499i) q^{10} +(2.34912 + 4.06880i) q^{11} +(-0.663964 + 3.54389i) q^{13} +(-5.32730 - 1.08331i) q^{14} -3.50680 q^{16} +0.603612 q^{17} +(-0.280555 + 0.485935i) q^{19} +(0.610289 + 1.05705i) q^{20} +(-4.82684 - 8.36033i) q^{22} -0.376699 q^{23} +(2.34912 - 4.06880i) q^{25} +(1.36427 - 7.28178i) q^{26} +(5.76086 + 1.17148i) q^{28} +(-2.09200 + 3.62344i) q^{29} +(-0.577330 + 0.999965i) q^{31} +8.11773 q^{32} -1.24027 q^{34} +(0.461296 + 1.37822i) q^{35} -8.80232 q^{37} +(0.576468 - 0.998472i) q^{38} +(-0.125267 - 0.216969i) q^{40} +(3.96001 - 6.85894i) q^{41} +(-0.747200 - 1.29419i) q^{43} +(5.21966 + 9.04072i) q^{44} +0.774020 q^{46} +(1.09885 + 1.90326i) q^{47} +(6.44406 + 2.73387i) q^{49} +(-4.82684 + 8.36033i) q^{50} +(-1.47530 + 7.87439i) q^{52} +(-4.52338 + 7.83473i) q^{53} +(-1.29043 + 2.23509i) q^{55} +(-1.18247 - 0.240457i) q^{56} +(4.29851 - 7.44524i) q^{58} -8.53654 q^{59} +(-3.71212 + 6.42958i) q^{61} +(1.18626 - 2.05467i) q^{62} -9.66624 q^{64} +(-1.86829 + 0.657505i) q^{65} +(4.79936 + 8.31274i) q^{67} +1.34120 q^{68} +(-0.947844 - 2.83190i) q^{70} +(-2.88877 - 5.00350i) q^{71} +(7.24668 - 12.5516i) q^{73} +18.0865 q^{74} +(-0.623383 + 1.07973i) q^{76} +(3.94536 + 11.7876i) q^{77} +(7.31102 + 12.6631i) q^{79} +(-0.963186 - 1.66829i) q^{80} +(-8.13680 + 14.0934i) q^{82} +14.8750 q^{83} +(0.165789 + 0.287155i) q^{85} +(1.53530 + 2.65922i) q^{86} +(-1.07138 - 1.85569i) q^{88} -9.18353 q^{89} +(-3.58988 + 8.83814i) q^{91} -0.837013 q^{92} +(-2.25784 - 3.91070i) q^{94} -0.308231 q^{95} +(3.15034 + 5.45655i) q^{97} +(-13.2409 - 5.61740i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} + q^{7} - 12 q^{8} - 4 q^{10} + 2 q^{11} + 5 q^{13} + 7 q^{14} + 12 q^{16} - 4 q^{17} - 11 q^{19} + 20 q^{20} + 7 q^{22} + 8 q^{23} + 2 q^{25} - 33 q^{26} - q^{28} - 15 q^{29} + 3 q^{31}+ \cdots - 18 q^{98}+O(q^{100}) \) 16 * q + 12 * q^4 + q^7 - 12 * q^8 - 4 * q^10 + 2 * q^11 + 5 * q^13 + 7 * q^14 + 12 * q^16 - 4 * q^17 - 11 * q^19 + 20 * q^20 + 7 * q^22 + 8 * q^23 + 2 * q^25 - 33 * q^26 - q^28 - 15 * q^29 + 3 * q^31 + 6 * q^32 - 68 * q^34 - 8 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 - 4 * q^46 - 5 * q^47 + 7 * q^49 + 7 * q^50 - 18 * q^52 - 36 * q^53 - 15 * q^55 + 51 * q^56 + 20 * q^58 - 34 * q^59 - 22 * q^61 + 6 * q^62 - 20 * q^64 + 24 * q^65 + 26 * q^67 + 10 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 + 30 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 + 28 * q^80 - q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 + 24 * q^88 + 40 * q^89 - 10 * q^91 + 94 * q^92 - 20 * q^94 + 7 * q^97 - 18 * q^98

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