LMFDB - Embedded newform 845.2.o.f.357.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(258,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.258"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.o (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,4,-2,-6,6,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			357.3
Root			$-0.493902i$ of defining polynomial
Character	$\chi$	$=$	845.357
Dual form			845.2.o.f.258.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.246951 - 0.427732i) q^{2} +(-0.243392 - 0.908353i) q^{3} +(0.878030 + 1.52079i) q^{4} +(2.21791 - 0.284413i) q^{5} +(-0.448637 - 0.120212i) q^{6} +(3.18307 - 1.83775i) q^{7} +1.85513 q^{8} +(1.83221 - 1.05783i) q^{9} +(0.426062 - 1.01890i) q^{10} +(-0.664257 + 0.177987i) q^{11} +(1.16771 - 1.16771i) q^{12} -1.81533i q^{14} +(-0.798168 - 1.94542i) q^{15} +(-1.29794 + 2.24809i) q^{16} +(-2.29359 - 0.614565i) q^{17} -1.04493i q^{18} +(-1.41763 + 5.29067i) q^{19} +(2.37992 + 3.12325i) q^{20} +(-2.44406 - 2.44406i) q^{21} +(-0.0879082 + 0.328078i) q^{22} +(-1.30811 + 0.350507i) q^{23} +(-0.451523 - 1.68511i) q^{24} +(4.83822 - 1.26160i) q^{25} +(-3.40171 - 3.40171i) q^{27} +(5.58966 + 3.22719i) q^{28} +(-8.24134 - 4.75814i) q^{29} +(-1.02922 - 0.139021i) q^{30} +(-4.81595 + 4.81595i) q^{31} +(2.49618 + 4.32351i) q^{32} +(0.323350 + 0.560059i) q^{33} +(-0.829273 + 0.829273i) q^{34} +(6.53707 - 4.98125i) q^{35} +(3.21748 + 1.85761i) q^{36} +(1.58936 + 0.917615i) q^{37} +(1.91290 + 1.91290i) q^{38} +(4.11449 - 0.527621i) q^{40} +(-0.143350 - 0.534988i) q^{41} +(-1.64896 + 0.441838i) q^{42} +(0.560778 - 2.09285i) q^{43} +(-0.853919 - 0.853919i) q^{44} +(3.76281 - 2.86727i) q^{45} +(-0.173116 + 0.646078i) q^{46} +3.80918i q^{47} +(2.35797 + 0.631815i) q^{48} +(3.25462 - 5.63717i) q^{49} +(0.655176 - 2.38101i) q^{50} +2.23297i q^{51} +(-2.47293 + 2.47293i) q^{53} +(-2.29507 + 0.614963i) q^{54} +(-1.42264 + 0.583682i) q^{55} +(5.90499 - 3.40925i) q^{56} +5.15084 q^{57} +(-4.07041 + 2.35005i) q^{58} +(10.0508 + 2.69310i) q^{59} +(2.25776 - 2.92199i) q^{60} +(-3.09904 - 5.36770i) q^{61} +(0.870630 + 3.24924i) q^{62} +(3.88804 - 6.73428i) q^{63} -2.72601 q^{64} +0.319406 q^{66} +(6.12371 - 10.6066i) q^{67} +(-1.07921 - 4.02768i) q^{68} +(0.636768 + 1.10291i) q^{69} +(-0.516303 - 4.02624i) q^{70} +(-6.47512 - 1.73500i) q^{71} +(3.39898 - 1.96240i) q^{72} -3.37642 q^{73} +(0.784986 - 0.453212i) q^{74} +(-2.32356 - 4.08774i) q^{75} +(-9.29074 + 2.48945i) q^{76} +(-1.78728 + 1.78728i) q^{77} +3.12149i q^{79} +(-2.23932 + 5.35521i) q^{80} +(0.911483 - 1.57873i) q^{81} +(-0.264231 - 0.0708006i) q^{82} +2.13918i q^{83} +(1.57095 - 5.86286i) q^{84} +(-5.26175 - 0.710723i) q^{85} +(-0.756694 - 0.756694i) q^{86} +(-2.31619 + 8.64414i) q^{87} +(-1.23228 + 0.330188i) q^{88} +(-0.874198 - 3.26255i) q^{89} +(-0.297190 - 2.31755i) q^{90} +(-1.68161 - 1.68161i) q^{92} +(5.54675 + 3.20242i) q^{93} +(1.62931 + 0.940681i) q^{94} +(-1.63944 + 12.1374i) q^{95} +(3.31972 - 3.31972i) q^{96} +(3.53688 + 6.12606i) q^{97} +(-1.60746 - 2.78421i) q^{98} +(-1.02878 + 1.02878i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{5} - 4 q^{6} - 6 q^{7} - 12 q^{8} + 12 q^{9} + 2 q^{10} - 8 q^{11} + 24 q^{12} - 12 q^{15} - 2 q^{16} - 4 q^{17} + 16 q^{19} - 8 q^{20} - 4 q^{21} + 16 q^{22} + 10 q^{23}+ \cdots + 60 q^{99}+O(q^{100}) $ 20 * q + 4 * q^2 - 2 * q^3 - 6 * q^4 + 6 * q^5 - 4 * q^6 - 6 * q^7 - 12 * q^8 + 12 * q^9 + 2 * q^10 - 8 * q^11 + 24 * q^12 - 12 * q^15 - 2 * q^16 - 4 * q^17 + 16 * q^19 - 8 * q^20 - 4 * q^21 + 16 * q^22 + 10 * q^23 - 28 * q^24 - 18 * q^25 + 4 * q^27 + 6 * q^28 + 26 * q^30 + 6 * q^32 + 18 * q^33 + 2 * q^34 + 40 * q^35 - 36 * q^36 + 42 * q^37 + 8 * q^38 - 16 * q^40 - 28 * q^41 + 40 * q^42 - 10 * q^43 - 36 * q^44 + 32 * q^45 + 8 * q^46 - 56 * q^48 - 18 * q^49 - 8 * q^50 - 10 * q^53 + 12 * q^54 - 10 * q^55 + 12 * q^57 - 90 * q^58 + 8 * q^59 + 92 * q^60 - 16 * q^61 + 44 * q^62 + 32 * q^63 - 20 * q^64 - 32 * q^66 + 58 * q^67 + 22 * q^68 + 16 * q^69 - 32 * q^70 - 56 * q^71 - 66 * q^72 - 72 * q^73 + 18 * q^74 + 38 * q^75 - 80 * q^76 + 28 * q^77 - 68 * q^80 - 14 * q^81 - 56 * q^82 + 32 * q^84 - 6 * q^85 - 60 * q^86 - 34 * q^87 - 82 * q^88 - 6 * q^89 - 46 * q^90 - 8 * q^92 + 48 * q^93 - 48 * q^94 + 26 * q^95 - 56 * q^96 + 22 * q^97 - 4 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.246951	−	0.427732i	0.174621	−	0.302452i	−0.765409	−	0.643544i	$-0.777463\pi$
$2$	0.246951	−	0.427732i	0.174621	−	0.302452i	0.940030	+	0.341092i	$0.110797\pi$
$3$	−0.243392	−	0.908353i	−0.140523	−	0.524438i	−0.999914	−	0.0131191i	$-0.995824\pi$
$3$	−0.243392	−	0.908353i	−0.140523	−	0.524438i	0.859391	−	0.511318i	$-0.170843\pi$
$4$	0.878030	+	1.52079i	0.439015	+	0.760397i
$5$	2.21791	−	0.284413i	0.991878	−	0.127193i
$5$	2.21791	−	0.284413i	0.991878	−	0.127193i
$6$	−0.448637	−	0.120212i	−0.183155	−	0.0490763i
$7$	3.18307	−	1.83775i	1.20309	−	0.694603i	0.241847	−	0.970314i	$-0.422247\pi$
$7$	3.18307	−	1.83775i	1.20309	−	0.694603i	0.961240	+	0.275712i	$0.0889135\pi$
$8$	1.85513			0.655886
$9$	1.83221	−	1.05783i	0.610737	−	0.352609i
$10$	0.426062	−	1.01890i	0.134733	−	0.322206i
$11$	−0.664257	+	0.177987i	−0.200281	+	0.0536651i	−0.357565	−	0.933888i	$-0.616393\pi$
$11$	−0.664257	+	0.177987i	−0.200281	+	0.0536651i	0.157284	+	0.987553i	$0.449726\pi$
$12$	1.16771	−	1.16771i	0.337089	−	0.337089i
$13$		0			0
$13$		0			0
$14$		−	1.81533i		−	0.485168i
$15$	−0.798168	−	1.94542i	−0.206086	−	0.502305i
$16$	−1.29794	+	2.24809i	−0.324484	+	0.562023i
$17$	−2.29359	−	0.614565i	−0.556277	−	0.149054i	−0.0302815	−	0.999541i	$-0.509640\pi$
$17$	−2.29359	−	0.614565i	−0.556277	−	0.149054i	−0.525995	+	0.850487i	$0.676307\pi$
$18$		−	1.04493i		−	0.246291i
$19$	−1.41763	+	5.29067i	−0.325227	+	1.21376i	0.588857	+	0.808238i	$0.299578\pi$
$19$	−1.41763	+	5.29067i	−0.325227	+	1.21376i	−0.914084	+	0.405526i	$0.867088\pi$
$20$	2.37992	+	3.12325i	0.532167	+	0.698381i
$21$	−2.44406	−	2.44406i	−0.533337	−	0.533337i
$22$	−0.0879082	+	0.328078i	−0.0187421	+	0.0699464i
$23$	−1.30811	+	0.350507i	−0.272760	+	0.0730858i	−0.392606	−	0.919707i	$-0.628426\pi$
$23$	−1.30811	+	0.350507i	−0.272760	+	0.0730858i	0.119846	+	0.992792i	$0.461760\pi$
$24$	−0.451523	−	1.68511i	−0.0921668	−	0.343971i
$25$	4.83822	−	1.26160i	0.967644	−	0.252320i
$26$		0			0
$27$	−3.40171	−	3.40171i	−0.654659	−	0.654659i
$28$	5.58966	+	3.22719i	1.05635	+	0.609882i
$29$	−8.24134	−	4.75814i	−1.53038	−	0.883564i	−0.999344	−	0.0362142i	$-0.988470\pi$
$29$	−8.24134	−	4.75814i	−1.53038	−	0.883564i	−0.531034	−	0.847350i	$-0.678197\pi$
$30$	−1.02922	−	0.139021i	−0.187910	−	0.0253816i
$31$	−4.81595	+	4.81595i	−0.864970	+	0.864970i	−0.991910	−	0.126940i	$-0.959484\pi$
$31$	−4.81595	+	4.81595i	−0.864970	+	0.864970i	0.126940	+	0.991910i	$0.459484\pi$
$32$	2.49618	+	4.32351i	0.441266	+	0.764295i
$33$	0.323350	+	0.560059i	0.0562880	+	0.0974937i
$34$	−0.829273	+	0.829273i	−0.142219	+	0.142219i
$35$	6.53707	−	4.98125i	1.10497	−	0.841986i
$36$	3.21748	+	1.85761i	0.536246	+	0.309602i
$37$	1.58936	+	0.917615i	0.261289	+	0.150855i	0.624922	−	0.780687i	$-0.285131\pi$
$37$	1.58936	+	0.917615i	0.261289	+	0.150855i	−0.363634	+	0.931542i	$0.618464\pi$
$38$	1.91290	+	1.91290i	0.310314	+	0.310314i
$39$		0			0
$40$	4.11449	−	0.527621i	0.650559	−	0.0834242i
$41$	−0.143350	−	0.534988i	−0.0223874	−	0.0835510i	0.953828	−	0.300352i	$-0.0971043\pi$
$41$	−0.143350	−	0.534988i	−0.0223874	−	0.0835510i	−0.976216	+	0.216801i	$0.930438\pi$
$42$	−1.64896	+	0.441838i	−0.254440	+	0.0681771i
$43$	0.560778	−	2.09285i	0.0855178	−	0.319157i	−0.909894	−	0.414841i	$-0.863837\pi$
$43$	0.560778	−	2.09285i	0.0855178	−	0.319157i	0.995412	+	0.0956841i	$0.0305039\pi$
$44$	−0.853919	−	0.853919i	−0.128733	−	0.128733i
$45$	3.76281	−	2.86727i	0.560927	−	0.427427i
$46$	−0.173116	+	0.646078i	−0.0255246	+	0.0952590i
$47$			3.80918i			0.555626i	0.960635	+	0.277813i	$0.0896096\pi$
$47$			3.80918i			0.555626i	−0.960635	+	0.277813i	$0.910390\pi$
$48$	2.35797	+	0.631815i	0.340343	+	0.0911947i
$49$	3.25462	−	5.63717i	0.464946	−	0.805310i
$50$	0.655176	−	2.38101i	0.0926559	−	0.336726i
$51$			2.23297i			0.312678i
$52$		0			0
$53$	−2.47293	+	2.47293i	−0.339683	+	0.339683i	−0.856248	−	0.516565i	$-0.827211\pi$
$53$	−2.47293	+	2.47293i	−0.339683	+	0.339683i	0.516565	+	0.856248i	$0.327211\pi$
$54$	−2.29507	+	0.614963i	−0.312320	+	0.0836858i
$55$	−1.42264	+	0.583682i	−0.191828	+	0.0787036i
$56$	5.90499	−	3.40925i	0.789088	−	0.455580i
$57$	5.15084			0.682245
$58$	−4.07041	+	2.35005i	−0.534471	+	0.308577i
$59$	10.0508	+	2.69310i	1.30850	+	0.350612i	0.844659	−	0.535305i	$-0.179803\pi$
$59$	10.0508	+	2.69310i	1.30850	+	0.350612i	0.463844	+	0.885917i	$0.346470\pi$
$60$	2.25776	−	2.92199i	0.291476	−	0.377227i
$61$	−3.09904	−	5.36770i	−0.396792	−	0.687263i	0.596536	−	0.802586i	$-0.296543\pi$
$61$	−3.09904	−	5.36770i	−0.396792	−	0.687263i	−0.993328	+	0.115323i	$0.963210\pi$
$62$	0.870630	+	3.24924i	0.110570	+	0.412653i
$63$	3.88804	−	6.73428i	0.489847	−	0.848439i
$64$	−2.72601			−0.340751
$65$		0			0
$66$	0.319406			0.0393162
$67$	6.12371	−	10.6066i	0.748130	−	1.29580i	−0.200588	−	0.979676i	$-0.564285\pi$
$67$	6.12371	−	10.6066i	0.748130	−	1.29580i	0.948718	−	0.316124i	$-0.102381\pi$
$68$	−1.07921	−	4.02768i	−0.130874	−	0.488428i
$69$	0.636768	+	1.10291i	0.0766579	+	0.132775i
$70$	−0.516303	−	4.02624i	−0.0617101	−	0.481227i
$71$	−6.47512	−	1.73500i	−0.768456	−	0.205907i	−0.146767	−	0.989171i	$-0.546887\pi$
$71$	−6.47512	−	1.73500i	−0.768456	−	0.205907i	−0.621689	+	0.783264i	$0.713553\pi$
$72$	3.39898	−	1.96240i	0.400574	−	0.231271i
$73$	−3.37642			−0.395180			−0.197590	−	0.980285i	$-0.563312\pi$
$73$	−3.37642			−0.395180			−0.197590	+	0.980285i	$0.563312\pi$
$74$	0.784986	−	0.453212i	0.0912528	−	0.0526848i
$75$	−2.32356	−	4.08774i	−0.268302	−	0.472012i
$76$	−9.29074	+	2.48945i	−1.06572	+	0.285559i
$77$	−1.78728	+	1.78728i	−0.203680	+	0.203680i
$78$		0			0
$79$			3.12149i			0.351195i	0.984462	+	0.175598i	$0.0561857\pi$
$79$			3.12149i			0.351195i	−0.984462	+	0.175598i	$0.943814\pi$
$80$	−2.23932	+	5.35521i	−0.250363	+	0.598730i
$81$	0.911483	−	1.57873i	0.101276	−	0.175415i
$82$	−0.264231	−	0.0708006i	−0.0291795	−	0.00781862i
$83$			2.13918i			0.234805i	0.993084	+	0.117403i	$0.0374568\pi$
$83$			2.13918i			0.234805i	−0.993084	+	0.117403i	$0.962543\pi$
$84$	1.57095	−	5.86286i	0.171405	−	0.639691i
$85$	−5.26175	−	0.710723i	−0.570717	−	0.0770887i
$86$	−0.756694	−	0.756694i	−0.0815964	−	0.0815964i
$87$	−2.31619	+	8.64414i	−0.248322	+	0.926749i
$88$	−1.23228	+	0.330188i	−0.131361	+	0.0351982i
$89$	−0.874198	−	3.26255i	−0.0926648	−	0.345830i	0.903990	−	0.427553i	$-0.140624\pi$
$89$	−0.874198	−	3.26255i	−0.0926648	−	0.345830i	−0.996655	+	0.0817233i	$0.973958\pi$
$90$	−0.297190	−	2.31755i	−0.0313266	−	0.244291i
$91$		0			0
$92$	−1.68161	−	1.68161i	−0.175320	−	0.175320i
$93$	5.54675	+	3.20242i	0.575171	+	0.332075i
$94$	1.62931	+	0.940681i	0.168050	+	0.0970238i
$95$	−1.63944	+	12.1374i	−0.168203	+	1.24527i
$96$	3.31972	−	3.31972i	0.338817	−	0.338817i
$97$	3.53688	+	6.12606i	0.359116	+	0.622007i	0.987813	−	0.155643i	$-0.0497449\pi$
$97$	3.53688	+	6.12606i	0.359116	+	0.622007i	−0.628697	+	0.777650i	$0.716412\pi$
$98$	−1.60746	−	2.78421i	−0.162378	−	0.281248i
$99$	−1.02878	+	1.02878i	−0.103396	+	0.103396i
$100$	6.16674	+	6.25021i	0.616674	+	0.625021i
$101$	−12.9641	−	7.48483i	−1.28998	−	0.744769i	−0.311327	−	0.950303i	$-0.600774\pi$
$101$	−12.9641	−	7.48483i	−1.28998	−	0.744769i	−0.978650	+	0.205534i	$0.934107\pi$
$102$	0.955111	+	0.551433i	0.0945700	+	0.0546000i
$103$	3.17851	+	3.17851i	0.313188	+	0.313188i	0.846143	−	0.532956i	$-0.178919\pi$
$103$	3.17851	+	3.17851i	0.313188	+	0.313188i	−0.532956	+	0.846143i	$0.678919\pi$
$104$		0			0
$105$	−6.11581	−	4.72557i	−0.596842	−	0.461168i
$106$	0.447058	+	1.66844i	0.0434221	+	0.162054i
$107$	14.7329	−	3.94767i	1.42428	−	0.381635i	0.537282	−	0.843403i	$-0.319451\pi$
$107$	14.7329	−	3.94767i	1.42428	−	0.381635i	0.887001	+	0.461767i	$0.152784\pi$
$108$	2.18649	−	8.16010i	0.210395	−	0.785206i
$109$	2.25902	+	2.25902i	0.216375	+	0.216375i	0.806969	−	0.590594i	$-0.201107\pi$
$109$	2.25902	+	2.25902i	0.216375	+	0.216375i	−0.590594	+	0.806969i	$0.701107\pi$
$110$	−0.101663	+	0.752648i	−0.00969315	+	0.0717622i
$111$	0.446681	−	1.66704i	0.0423971	−	0.158228i
$112$			9.54111i			0.901550i
$113$	−16.0061	−	4.28882i	−1.50573	−	0.403458i	−0.590713	−	0.806881i	$-0.701154\pi$
$113$	−16.0061	−	4.28882i	−1.50573	−	0.403458i	−0.915014	+	0.403423i	$0.867820\pi$
$114$	1.27200	−	2.20318i	0.119134	−	0.206346i
$115$	−2.80158	+	1.14944i	−0.261248	+	0.107185i
$116$		−	16.7112i		−	1.55159i
$117$		0			0
$118$	3.63398	−	3.63398i	0.334535	−	0.334535i
$119$	−8.43007	+	2.25883i	−0.772783	+	0.207067i
$120$	−1.48070	−	3.60899i	−0.135169	−	0.329455i
$121$	−9.11672	+	5.26354i	−0.828793	+	0.478504i
$122$	−3.06124			−0.277152
$123$	−0.451067	+	0.260424i	−0.0406714	+	0.0234816i
$124$	−11.5526	−	3.09551i	−1.03746	−	0.277985i
$125$	10.3719	−	4.17416i	0.927691	−	0.373349i
$126$	−1.92031	−	3.32607i	−0.171075	−	0.296310i
$127$	2.14812	+	8.01688i	0.190614	+	0.711383i	0.993359	+	0.115059i	$0.0367058\pi$
$127$	2.14812	+	8.01688i	0.190614	+	0.711383i	−0.802744	+	0.596324i	$0.796628\pi$
$128$	−5.66555	+	9.81302i	−0.500768	+	0.867356i
$129$	−2.03754			−0.179395
$130$		0			0
$131$	1.37409			0.120054			0.0600272	−	0.998197i	$-0.480881\pi$
$131$	1.37409			0.120054			0.0600272	+	0.998197i	$0.480881\pi$
$132$	−0.567822	+	0.983497i	−0.0494226	+	0.0856025i
$133$	5.21049	+	19.4458i	0.451807	+	1.68617i
$134$	−3.02451	−	5.23861i	−0.261278	−	0.452547i
$135$	−8.51216	−	6.57718i	−0.732610	−	0.566074i
$136$	−4.25489	−	1.14010i	−0.364854	−	0.0977624i
$137$	−10.6760	+	6.16380i	−0.912114	+	0.526609i	−0.881111	−	0.472910i	$-0.843203\pi$
$137$	−10.6760	+	6.16380i	−0.912114	+	0.526609i	−0.0310029	+	0.999519i	$0.509870\pi$
$138$	0.629002			0.0535442
$139$	5.54392	−	3.20078i	0.470229	−	0.271487i	−0.246107	−	0.969243i	$-0.579151\pi$
$139$	5.54392	−	3.20078i	0.470229	−	0.271487i	0.716336	+	0.697756i	$0.245818\pi$
$140$	13.3152	+	5.56784i	1.12534	+	0.470569i
$141$	3.46008	−	0.927126i	0.291391	−	0.0780781i
$142$	−2.34115	+	2.34115i	−0.196465	+	0.196465i
$143$		0			0
$144$			5.49197i			0.457664i
$145$	−19.6318	−	8.20917i	−1.63033	−	0.681734i
$146$	−0.833811	+	1.44420i	−0.0690067	+	0.119523i
$147$	−5.91269	−	1.58430i	−0.487670	−	0.130671i
$148$			3.22278i			0.264911i
$149$	4.34882	−	16.2300i	0.356269	−	1.32961i	−0.522611	−	0.852571i	$-0.675042\pi$
$149$	4.34882	−	16.2300i	0.356269	−	1.32961i	0.878880	−	0.477043i	$-0.158291\pi$
$150$	−2.32226	−	0.0156106i	−0.189612	−	0.00127460i
$151$	3.31542	+	3.31542i	0.269805	+	0.269805i	0.829022	−	0.559217i	$-0.188898\pi$
$151$	3.31542	+	3.31542i	0.269805	+	0.269805i	−0.559217	+	0.829022i	$0.688898\pi$
$152$	−2.62988	+	9.81486i	−0.213312	+	0.796090i
$153$	−4.85244	+	1.30021i	−0.392297	+	0.105116i
$154$	0.323106	+	1.20585i	0.0260366	+	0.0971699i
$155$	−9.31161	+	12.0510i	−0.747926	+	0.967963i
$156$		0			0
$157$	9.87941	+	9.87941i	0.788463	+	0.788463i	0.981242	−	0.192779i	$-0.0617501\pi$
$157$	9.87941	+	9.87941i	0.788463	+	0.788463i	−0.192779	+	0.981242i	$0.561750\pi$
$158$	1.33516	+	0.770855i	0.106220	+	0.0613259i
$159$	2.84819	+	1.64440i	0.225876	+	0.130410i
$160$	6.76595	+	8.87919i	0.534895	+	0.701962i
$161$	−3.51966	+	3.51966i	−0.277388	+	0.277388i
$162$	−0.450183	−	0.779740i	−0.0353697	−	0.0612622i
$163$	0.0659848	+	0.114289i	0.00516833	+	0.00895180i	0.868598	−	0.495517i	$-0.165022\pi$
$163$	0.0659848	+	0.114289i	0.00516833	+	0.00895180i	−0.863430	+	0.504469i	$0.831688\pi$
$164$	0.687741	−	0.687741i	0.0537035	−	0.0537035i
$165$	0.876448	+	1.15019i	0.0682314	+	0.0895424i
$166$	0.914995	+	0.528272i	0.0710174	+	0.0410019i
$167$	18.7380	+	10.8184i	1.44999	+	0.837152i	0.998480	−	0.0551149i	$-0.0175525\pi$
$167$	18.7380	+	10.8184i	1.44999	+	0.837152i	0.451509	+	0.892267i	$0.350886\pi$
$168$	−4.53403	−	4.53403i	−0.349808	−	0.349808i
$169$		0			0
$170$	−1.60339	+	2.07510i	−0.122975	+	0.159153i
$171$	2.99922	+	11.1932i	0.229356	+	0.855969i
$172$	3.67518	−	0.984760i	0.280230	−	0.0750873i
$173$	2.00162	−	7.47013i	0.152180	−	0.567943i	−0.847150	−	0.531353i	$-0.821684\pi$
$173$	2.00162	−	7.47013i	0.152180	−	0.567943i	0.999330	−	0.0365902i	$-0.0116496\pi$
$174$	3.12539	+	3.12539i	0.236935	+	0.236935i
$175$	13.0819	−	12.9072i	0.988898	−	0.975691i
$176$	0.462032	−	1.72433i	0.0348270	−	0.129976i
$177$		−	9.78515i		−	0.735497i
$178$	−1.61138	−	0.431768i	−0.120778	−	0.0323624i
$179$	−8.17681	+	14.1627i	−0.611164	+	1.05857i	0.379881	+	0.925035i	$0.375965\pi$
$179$	−8.17681	+	14.1627i	−0.611164	+	1.05857i	−0.991045	+	0.133531i	$0.957368\pi$
$180$	7.66439	+	3.20492i	0.571270	+	0.238880i
$181$			18.0387i			1.34081i	0.741997	+	0.670403i	$0.233879\pi$
$181$			18.0387i			1.34081i	−0.741997	+	0.670403i	$0.766121\pi$
$182$		0			0
$183$	−4.12148	+	4.12148i	−0.304668	+	0.304668i
$184$	−2.42671	+	0.650235i	−0.178899	+	0.0479359i
$185$	3.78603	+	1.58315i	0.278354	+	0.116396i
$186$	2.73955	−	1.58168i	0.200873	−	0.115974i
$187$	1.63292			0.119411
$188$	−5.79298	+	3.34458i	−0.422496	+	0.243928i
$189$	−17.0793	−	4.57640i	−1.24234	−	0.332884i
$190$	4.78669	+	3.69858i	0.347263	+	0.268324i
$191$	−2.59552	−	4.49557i	−0.187805	−	0.325288i	0.756713	−	0.653747i	$-0.226804\pi$
$191$	−2.59552	−	4.49557i	−0.187805	−	0.325288i	−0.944518	+	0.328459i	$0.893471\pi$
$192$	0.663490	+	2.47618i	0.0478833	+	0.178703i
$193$	−5.05073	+	8.74813i	−0.363560	+	0.629704i	−0.988544	−	0.150934i	$-0.951772\pi$
$193$	−5.05073	+	8.74813i	−0.363560	+	0.629704i	0.624984	+	0.780637i	$0.285105\pi$
$194$	3.49375			0.250836
$195$		0			0
$196$	11.4306			0.816473
$197$	6.53197	−	11.3137i	0.465384	−	0.806068i	−0.533835	−	0.845589i	$-0.679250\pi$
$197$	6.53197	−	11.3137i	0.465384	−	0.806068i	0.999219	+	0.0395205i	$0.0125831\pi$
$198$	0.185983	+	0.694099i	0.0132173	+	0.0493275i
$199$	3.92506	+	6.79840i	0.278240	+	0.481926i	0.970947	−	0.239293i	$-0.0769156\pi$
$199$	3.92506	+	6.79840i	0.278240	+	0.481926i	−0.692707	+	0.721219i	$0.743582\pi$
$200$	8.97550	−	2.34043i	0.634664	−	0.165493i
$201$	−11.1250	−	2.98093i	−0.784695	−	0.210258i
$202$	−6.40300	+	3.69677i	−0.450513	+	0.260104i
$203$	−34.9770			−2.45491
$204$	−3.39588	+	1.96061i	−0.237759	+	0.137270i
$205$	−0.470093	−	1.14578i	−0.0328327	−	0.0800249i
$206$	2.14448	−	0.574613i	0.149413	−	0.0400352i
$207$	−2.02596	+	2.02596i	−0.140814	+	0.140814i
$208$		0			0
$209$		−	3.76669i		−	0.260547i
$210$	−3.53158	+	1.44894i	−0.243702	+	0.0999864i
$211$	−6.21205	+	10.7596i	−0.427655	+	0.740720i	−0.996664	−	0.0816108i	$-0.973994\pi$
$211$	−6.21205	+	10.7596i	−0.427655	+	0.740720i	0.569009	+	0.822331i	$0.307327\pi$
$212$	−5.93213	−	1.58951i	−0.407420	−	0.109168i
$213$			6.30398i			0.431942i
$214$	1.94976	−	7.27661i	0.133283	−	0.497419i
$215$	0.648520	−	4.80124i	0.0442287	−	0.327442i
$216$	−6.31059	−	6.31059i	−0.429382	−	0.429382i
$217$	−6.47901	+	24.1800i	−0.439824	+	1.64145i
$218$	1.52412	−	0.408387i	0.103226	−	0.0276594i
$219$	0.821796	+	3.06698i	0.0555318	+	0.207248i
$220$	−2.13678	−	1.65105i	−0.144062	−	0.111314i
$221$		0			0
$222$	−0.602736	−	0.602736i	−0.0404530	−	0.0404530i
$223$	−8.61258	−	4.97247i	−0.576741	−	0.332981i	0.183096	−	0.983095i	$-0.441388\pi$
$223$	−8.61258	−	4.97247i	−0.576741	−	0.332981i	−0.759837	+	0.650114i	$0.774721\pi$
$224$	15.8910	+	9.17468i	1.06176	+	0.613009i
$225$	7.53008	−	7.42952i	0.502006	−	0.495302i
$226$	−5.78718	+	5.78718i	−0.384958	+	0.384958i
$227$	7.30290	+	12.6490i	0.484710	+	0.839543i	0.999846	−	0.0175659i	$-0.00559170\pi$
$227$	7.30290	+	12.6490i	0.484710	+	0.839543i	−0.515135	+	0.857109i	$0.672258\pi$
$228$	4.52259	+	7.83336i	0.299516	+	0.518777i
$229$	15.6183	−	15.6183i	1.03209	−	1.03209i	0.0326207	−	0.999468i	$-0.489615\pi$
$229$	15.6183	−	15.6183i	1.03209	−	1.03209i	0.999468	−	0.0326207i	$-0.0103853\pi$
$230$	−0.200203	+	1.48218i	−0.0132010	+	0.0977319i
$231$	2.05849	+	1.18847i	0.135439	+	0.0781956i
$232$	−15.2887	−	8.82695i	−1.00375	−	0.579517i
$233$	−16.5625	−	16.5625i	−1.08505	−	1.08505i	−0.996030	−	0.0890148i	$-0.971628\pi$
$233$	−16.5625	−	16.5625i	−1.08505	−	1.08505i	−0.0890148	−	0.996030i	$-0.528372\pi$
$234$		0			0
$235$	1.08338	+	8.44841i	0.0706719	+	0.551113i
$236$	4.72926	+	17.6498i	0.307848	+	1.14891i
$237$	2.83541	−	0.759747i	0.184180	−	0.0493509i
$238$	−1.11564	+	4.16362i	−0.0723162	+	0.269888i
$239$	−14.6022	−	14.6022i	−0.944535	−	0.944535i	0.0540053	−	0.998541i	$-0.482801\pi$
$239$	−14.6022	−	14.6022i	−0.944535	−	0.944535i	−0.998541	+	0.0540053i	$0.982801\pi$
$240$	5.40945	+	0.730672i	0.349178	+	0.0471647i
$241$	0.802065	−	2.99335i	0.0516656	−	0.192818i	−0.935270	−	0.353936i	$-0.884843\pi$
$241$	0.802065	−	2.99335i	0.0516656	−	0.192818i	0.986935	+	0.161117i	$0.0515098\pi$
$242$			5.19935i			0.334227i
$243$	−15.5964	−	4.17903i	−1.00051	−	0.268085i
$244$	5.44211	−	9.42600i	0.348395	−	0.603438i
$245$	5.61516	−	13.4284i	0.358740	−	0.857907i
$246$			0.257248i			0.0164015i
$247$		0			0
$248$	−8.93419	+	8.93419i	−0.567322	+	0.567322i
$249$	1.94313	−	0.520660i	0.123141	−	0.0329955i
$250$	0.775929	−	5.46720i	0.0490741	−	0.345776i
$251$	25.5728	−	14.7645i	1.61414	−	0.931925i	0.625745	−	0.780028i	$-0.284795\pi$
$251$	25.5728	−	14.7645i	1.61414	−	0.931925i	0.988396	−	0.151897i	$-0.0485382\pi$
$252$	13.6553			0.860201
$253$	0.806536	−	0.465654i	0.0507065	−	0.0292754i
$254$	3.95955	+	1.06096i	0.248444	+	0.0665704i
$255$	0.635084	+	4.95251i	0.0397705	+	0.310138i
$256$	0.0722145	+	0.125079i	0.00451341	+	0.00781745i
$257$	1.85447	+	6.92097i	0.115679	+	0.431718i	0.999337	−	0.0364143i	$-0.0115936\pi$
$257$	1.85447	+	6.92097i	0.115679	+	0.431718i	−0.883658	+	0.468133i	$0.844927\pi$
$258$	−0.503172	+	0.871519i	−0.0313261	+	0.0542584i
$259$	6.74538			0.419137
$260$		0			0
$261$	−20.1332			−1.24621
$262$	0.339332	−	0.587740i	0.0209640	−	0.0363107i
$263$	−3.48511	−	13.0066i	−0.214901	−	0.802023i	−0.986201	−	0.165551i	$-0.947060\pi$
$263$	−3.48511	−	13.0066i	−0.214901	−	0.802023i	0.771300	−	0.636472i	$-0.219607\pi$
$264$	0.599855	+	1.03898i	0.0369185	+	0.0639448i
$265$	−4.78140	+	6.18807i	−0.293719	+	0.380130i
$266$	9.60433	+	2.57347i	0.588879	+	0.157790i
$267$	−2.75077	+	1.58816i	−0.168345	+	0.0971938i
$268$	21.5072			1.31376
$269$	−7.01806	+	4.05188i	−0.427899	+	0.247047i	−0.698451	−	0.715658i	$-0.746127\pi$
$269$	−7.01806	+	4.05188i	−0.427899	+	0.247047i	0.270552	+	0.962705i	$0.412794\pi$
$270$	−4.91535	+	2.01668i	−0.299139	+	0.122731i
$271$	−8.88325	+	2.38026i	−0.539619	+	0.144590i	−0.518326	−	0.855183i	$-0.673445\pi$
$271$	−8.88325	+	2.38026i	−0.539619	+	0.144590i	−0.0212923	+	0.999773i	$0.506778\pi$
$272$	4.35853	−	4.35853i	0.264275	−	0.264275i
$273$		0			0
$274$			6.08862i			0.367827i
$275$	−2.98927	+	1.69917i	−0.180260	+	0.102464i
$276$	−1.11820	+	1.93679i	−0.0673080	+	0.116581i
$277$	−24.9641	−	6.68911i	−1.49995	−	0.401910i	−0.586865	−	0.809685i	$-0.699638\pi$
$277$	−24.9641	−	6.68911i	−1.49995	−	0.401910i	−0.913082	+	0.407775i	$0.866305\pi$
$278$		−	3.16174i		−	0.189629i
$279$	−3.72939	+	13.9183i	−0.223273	+	0.833266i
$280$	12.1271	−	9.24085i	0.724732	−	0.552246i
$281$	−5.41928	−	5.41928i	−0.323287	−	0.323287i	0.526740	−	0.850027i	$-0.323414\pi$
$281$	−5.41928	−	5.41928i	−0.323287	−	0.323287i	−0.850027	+	0.526740i	$0.823414\pi$
$282$	0.457909	−	1.70894i	0.0272681	−	0.101766i
$283$	−8.48623	+	2.27388i	−0.504454	+	0.135168i	−0.502066	−	0.864829i	$-0.667427\pi$
$283$	−8.48623	+	2.27388i	−0.504454	+	0.135168i	−0.00238762	+	0.999997i	$0.500760\pi$
$284$	−3.04677	−	11.3707i	−0.180793	−	0.674728i
$285$	11.4241	−	1.46496i	0.676704	−	0.0867769i
$286$		0			0
$287$	−1.43946	−	1.43946i	−0.0849688	−	0.0849688i
$288$	9.14705	+	5.28105i	0.538995	+	0.311189i
$289$	−9.83958	−	5.68088i	−0.578799	−	0.334170i
$290$	−8.35941	+	6.36988i	−0.490882	+	0.374052i
$291$	4.70377	−	4.70377i	0.275740	−	0.275740i
$292$	−2.96460	−	5.13484i	−0.173490	−	0.300494i
$293$	−6.61798	−	11.4627i	−0.386626	−	0.669657i	0.605367	−	0.795947i	$-0.293026\pi$
$293$	−6.61798	−	11.4627i	−0.386626	−	0.669657i	−0.991993	+	0.126290i	$0.959693\pi$
$294$	−2.13780	+	2.13780i	−0.124679	+	0.124679i
$295$	23.0577	+	3.11448i	1.34247	+	0.181332i
$296$	2.94846	+	1.70229i	0.171375	+	0.0989437i
$297$	2.86507	+	1.65415i	0.166248	+	0.0959834i
$298$	−5.86814	−	5.86814i	−0.339932	−	0.339932i
$299$		0			0
$300$	4.17646	−	7.12283i	0.241128	−	0.411237i
$301$	−2.06114	−	7.69226i	−0.118802	−	0.443375i
$302$	2.23685	−	0.599363i	0.128716	−	0.0344895i
$303$	−3.64350	+	13.5977i	−0.209314	+	0.781169i
$304$	−10.0539	−	10.0539i	−0.576632	−	0.576632i
$305$	−8.40003	−	11.0236i	−0.480984	−	0.631212i
$306$	−0.642175	+	2.39663i	−0.0367107	+	0.137006i
$307$			15.4782i			0.883389i	0.897165	+	0.441695i	$0.145623\pi$
$307$			15.4782i			0.883389i	−0.897165	+	0.441695i	$0.854377\pi$
$308$	−4.28737	−	1.14880i	−0.244296	−	0.0654588i
$309$	2.11358	−	3.66083i	0.120237	−	0.208257i
$310$	2.85510	+	6.95889i	0.162159	+	0.395238i
$311$			5.34922i			0.303326i	0.988432	+	0.151663i	$0.0484629\pi$
$311$			5.34922i			0.303326i	−0.988432	+	0.151663i	$0.951537\pi$
$312$		0			0
$313$	24.3923	−	24.3923i	1.37873	−	1.37873i	0.531967	−	0.846765i	$-0.321453\pi$
$313$	24.3923	−	24.3923i	1.37873	−	1.37873i	0.846765	−	0.531967i	$-0.178547\pi$
$314$	6.66547	−	1.78601i	0.376154	−	0.100790i
$315$	6.70799	−	16.0418i	0.377952	−	0.903854i
$316$	−4.74714	+	2.74076i	−0.267048	+	0.154180i
$317$	18.9851			1.06631			0.533156	−	0.846017i	$-0.321006\pi$
$317$	18.9851			1.06631			0.533156	+	0.846017i	$0.321006\pi$
$318$	1.40673	−	0.812173i	0.0788852	−	0.0455444i
$319$	6.32125	+	1.69378i	0.353922	+	0.0948332i
$320$	−6.04604	+	0.775312i	−0.337984	+	0.0433412i
$321$	−7.17175	−	12.4218i	−0.400288	−	0.693319i
$322$	0.636287	+	2.37466i	0.0354589	+	0.132334i
$323$	6.50293	−	11.2634i	0.361832	−	0.626712i
$324$	3.20124			0.177847
$325$		0			0
$326$	0.0651800			0.00360999
$327$	1.50216	−	2.60181i	0.0830695	−	0.143881i
$328$	−0.265931	−	0.992469i	−0.0146836	−	0.0548000i
$329$	7.00031	+	12.1249i	0.385940	+	0.668467i
$330$	0.708414	−	0.0908432i	0.0389969	−	0.00500075i
$331$	−6.77766	−	1.81607i	−0.372534	−	0.0998202i	0.0676941	−	0.997706i	$-0.478436\pi$
$331$	−6.77766	−	1.81607i	−0.372534	−	0.0998202i	−0.440228	+	0.897886i	$0.645102\pi$
$332$	−3.25325	+	1.87826i	−0.178545	+	0.103083i
$333$	3.88272			0.212772
$334$	9.25473	−	5.34322i	0.506396	−	0.292368i
$335$	10.5652	−	25.2661i	0.577237	−	1.38043i
$336$	8.66669	−	2.32223i	0.472807	−	0.126688i
$337$	1.10195	−	1.10195i	0.0600271	−	0.0600271i	−0.676456	−	0.736483i	$-0.736485\pi$
$337$	1.10195	−	1.10195i	0.0600271	−	0.0600271i	0.736483	+	0.676456i	$0.236485\pi$
$338$		0			0
$339$			15.5830i			0.846355i
$340$	−3.53912	−	8.62608i	−0.191936	−	0.467815i
$341$	2.34185	−	4.05620i	0.126818	−	0.219656i
$342$	5.52836	+	1.48132i	0.298940	+	0.0801006i
$343$			1.80378i			0.0973947i
$344$	1.04031	−	3.88250i	0.0560899	−	0.209331i
$345$	1.72598	+	2.26506i	0.0929234	+	0.121947i
$346$	−2.70091	−	2.70091i	−0.145202	−	0.145202i
$347$	6.68561	−	24.9510i	0.358902	−	1.33944i	−0.516600	−	0.856227i	$-0.672803\pi$
$347$	6.68561	−	24.9510i	0.358902	−	1.33944i	0.875502	−	0.483214i	$-0.160531\pi$
$348$	−15.1796	+	4.06737i	−0.813714	+	0.218034i
$349$	2.43287	+	9.07958i	0.130228	+	0.486019i	0.999972	−	0.00748510i	$-0.00238260\pi$
$349$	2.43287	+	9.07958i	0.130228	+	0.486019i	−0.869744	+	0.493504i	$0.835716\pi$
$350$	−2.29023	−	8.78298i	−0.122418	−	0.469470i
$351$		0			0
$352$	−2.42763	−	2.42763i	−0.129393	−	0.129393i
$353$	2.82798	+	1.63274i	0.150518	+	0.0869017i	0.573368	−	0.819298i	$-0.305637\pi$
$353$	2.82798	+	1.63274i	0.150518	+	0.0869017i	−0.422849	+	0.906200i	$0.638970\pi$
$354$	−4.18542	−	2.41645i	−0.222452	−	0.128433i
$355$	−14.8547	−	2.00647i	−0.788404	−	0.106492i
$356$	4.19410	−	4.19410i	0.222287	−	0.222287i
$357$	4.10363	+	7.10769i	0.217187	+	0.376179i
$358$	4.03854	+	6.99496i	0.213444	+	0.369695i
$359$	3.12090	−	3.12090i	0.164715	−	0.164715i	−0.619937	−	0.784652i	$-0.712842\pi$
$359$	3.12090	−	3.12090i	0.164715	−	0.164715i	0.784652	+	0.619937i	$0.212842\pi$
$360$	6.98049	−	5.31914i	0.367904	−	0.280343i
$361$	−9.52706	−	5.50045i	−0.501424	−	0.289497i
$362$	7.71573	+	4.45468i	0.405530	+	0.234133i
$363$	7.00009	+	7.00009i	0.367410	+	0.367410i
$364$		0			0
$365$	−7.48859	+	0.960297i	−0.391971	+	0.0502643i
$366$	0.745084	+	2.78069i	0.0389461	+	0.145349i
$367$	−24.2349	+	6.49371i	−1.26505	+	0.338969i	−0.828132	−	0.560533i	$-0.810596\pi$
$367$	−24.2349	+	6.49371i	−1.26505	+	0.338969i	−0.436917	+	0.899502i	$0.643930\pi$
$368$	0.909872	−	3.39569i	0.0474303	−	0.177012i
$369$	−0.828572	−	0.828572i	−0.0431337	−	0.0431337i
$370$	1.61213	−	1.22844i	0.0838105	−	0.0638636i
$371$	−3.32690	+	12.4161i	−0.172724	+	0.644614i
$372$			11.2473i			0.583144i
$373$	11.0372	+	2.95740i	0.571483	+	0.153128i	0.532976	−	0.846130i	$-0.321073\pi$
$373$	11.0372	+	2.95740i	0.571483	+	0.153128i	0.0385061	+	0.999258i	$0.487740\pi$
$374$	0.403250	−	0.698450i	0.0208516	−	0.0361160i
$375$	−6.31605	−	8.40538i	−0.326160	−	0.434052i
$376$			7.06651i			0.364427i
$377$		0			0
$378$	−6.17523	+	6.17523i	−0.317620	+	0.317620i
$379$	−1.94107	+	0.520109i	−0.0997062	+	0.0267162i	−0.308327	−	0.951280i	$-0.599769\pi$
$379$	−1.94107	+	0.520109i	−0.0997062	+	0.0267162i	0.208621	+	0.977997i	$0.433102\pi$
$380$	−19.8980	+	8.16377i	−1.02074	+	0.418792i
$381$	6.75932	−	3.90249i	0.346290	−	0.199931i
$382$	−2.56386			−0.131179
$383$	−22.9077	+	13.2258i	−1.17053	+	0.675806i	−0.953805	−	0.300427i	$-0.902871\pi$
$383$	−22.9077	+	13.2258i	−1.17053	+	0.675806i	−0.216725	+	0.976233i	$0.569538\pi$
$384$	10.2926	+	2.75790i	0.525244	+	0.140739i
$385$	−3.45570	+	4.47235i	−0.176119	+	0.227932i
$386$	2.49457	+	4.32072i	0.126970	+	0.219919i
$387$	−1.18641	−	4.42775i	−0.0603088	−	0.225075i
$388$	−6.21098	+	10.7577i	−0.315315	+	0.546141i
$389$	0.650094			0.0329611			0.0164805	−	0.999864i	$-0.494754\pi$
$389$	0.650094			0.0329611			0.0164805	+	0.999864i	$0.494754\pi$
$390$		0			0
$391$	3.21568			0.162624
$392$	6.03773	−	10.4577i	0.304951	−	0.528191i
$393$	−0.334442	−	1.24815i	−0.0168704	−	0.0629610i
$394$	−3.22615	−	5.58786i	−0.162531	−	0.281512i
$395$	0.887791	+	6.92317i	0.0446696	+	0.348343i
$396$	−2.46786	−	0.661261i	−0.124015	−	0.0332296i
$397$	23.3897	−	13.5041i	1.17390	−	0.677750i	0.219303	−	0.975657i	$-0.429622\pi$
$397$	23.3897	−	13.5041i	1.17390	−	0.677750i	0.954595	+	0.297907i	$0.0962884\pi$
$398$	3.87719			0.194346
$399$	16.3955	−	9.46593i	0.820800	−	0.473889i
$400$	−3.44350	+	12.5142i	−0.172175	+	0.625712i
$401$	−4.78969	+	1.28339i	−0.239186	+	0.0640896i	−0.376421	−	0.926449i	$-0.622845\pi$
$401$	−4.78969	+	1.28339i	−0.239186	+	0.0640896i	0.137235	+	0.990539i	$0.456179\pi$
$402$	−4.02236	+	4.02236i	−0.200617	+	0.200617i
$403$		0			0
$404$		−	26.2876i		−	1.30786i
$405$	1.57257	−	3.76072i	0.0781417	−	0.186872i
$406$	−8.63761	+	14.9608i	−0.428677	+	0.742491i
$407$	−1.21906	−	0.326647i	−0.0604268	−	0.0161913i
$408$			4.14243i			0.205081i
$409$	−1.56473	+	5.83965i	−0.0773708	+	0.288752i	−0.993760	−	0.111536i	$-0.964423\pi$
$409$	−1.56473	+	5.83965i	−0.0773708	+	0.288752i	0.916390	+	0.400288i	$0.131090\pi$
$410$	−0.606177	−	0.0818784i	−0.0299370	−	0.00404368i
$411$	8.19736	+	8.19736i	0.404346	+	0.404346i
$412$	−2.04303	+	7.62468i	−0.100653	+	0.375641i
$413$	36.9416	−	9.89848i	1.81778	−	0.487073i
$414$	0.366254	+	1.36688i	0.0180004	+	0.0671784i
$415$	0.608410	+	4.74450i	0.0298657	+	0.232898i
$416$		0			0
$417$	−4.25679	−	4.25679i	−0.208456	−	0.208456i
$418$	−1.61113	−	0.930187i	−0.0788030	−	0.0454969i
$419$	4.65114	+	2.68534i	0.227223	+	0.131187i	0.609290	−	0.792947i	$-0.291454\pi$
$419$	4.65114	+	2.68534i	0.227223	+	0.131187i	−0.382067	+	0.924135i	$0.624788\pi$
$420$	1.81675	−	13.4501i	0.0886481	−	0.656296i
$421$	−14.1377	+	14.1377i	−0.689029	+	0.689029i	−0.962017	−	0.272988i	$-0.911988\pi$
$421$	−14.1377	+	14.1377i	−0.689029	+	0.689029i	0.272988	+	0.962017i	$0.411988\pi$
$422$	3.06814	+	5.31418i	0.149355	+	0.258690i
$423$	4.02946	+	6.97923i	0.195919	+	0.339342i
$424$	−4.58760	+	4.58760i	−0.222794	+	0.222794i
$425$	−11.8722	−	0.0798070i	−0.575887	−	0.00387121i
$426$	2.69641	+	1.55677i	0.130642	+	0.0754260i
$427$	−19.7289	−	11.3905i	−0.954750	−	0.551225i
$428$	18.9395	+	18.9395i	0.915476	+	0.915476i
$429$		0			0
$430$	−1.89349	−	1.46306i	−0.0913122	−	0.0705552i
$431$	4.31985	+	16.1219i	0.208080	+	0.776564i	0.988489	+	0.151295i	$0.0483443\pi$
$431$	4.31985	+	16.1219i	0.208080	+	0.776564i	−0.780409	+	0.625269i	$0.784989\pi$
$432$	12.0625	−	3.23215i	0.580360	−	0.155507i
$433$	1.96538	−	7.33490i	0.0944502	−	0.352493i	−0.902485	−	0.430721i	$-0.858259\pi$
$433$	1.96538	−	7.33490i	0.0944502	−	0.352493i	0.996936	+	0.0782277i	$0.0249261\pi$
$434$	8.74255	+	8.74255i	0.419656	+	0.419656i
$435$	−2.67859	+	19.8306i	−0.128429	+	0.950807i
$436$	−1.45201	+	5.41899i	−0.0695388	+	0.259522i
$437$		−	7.41767i		−	0.354835i
$438$	1.51479	+	0.405886i	0.0723794	+	0.0193940i
$439$	−6.84536	+	11.8565i	−0.326711	+	0.565880i	−0.981857	−	0.189622i	$-0.939274\pi$
$439$	−6.84536	+	11.8565i	−0.326711	+	0.565880i	0.655146	+	0.755502i	$0.272607\pi$
$440$	−2.63917	+	1.08280i	−0.125818	+	0.0516206i
$441$		−	13.7713i		−	0.655777i
$442$		0			0
$443$	6.46290	−	6.46290i	0.307062	−	0.307062i	−0.536707	−	0.843769i	$-0.680332\pi$
$443$	6.46290	−	6.46290i	0.307062	−	0.307062i	0.843769	+	0.536707i	$0.180332\pi$
$444$	2.92742	−	0.784399i	0.138929	−	0.0372259i
$445$	−2.86680	−	6.98740i	−0.135899	−	0.331235i
$446$	−4.25377	+	2.45591i	−0.201422	+	0.116291i
$447$	−15.8010			−0.747364
$448$	−8.67708	+	5.00971i	−0.409953	+	0.236687i
$449$	24.8352	+	6.65458i	1.17205	+	0.314049i	0.791768	−	0.610822i	$-0.209161\pi$
$449$	24.8352	+	6.65458i	1.17205	+	0.314049i	0.380280	+	0.924872i	$0.375828\pi$
$450$	−1.31828	−	5.05558i	−0.0621443	−	0.238322i
$451$	0.190442	+	0.329855i	0.00896755	+	0.0155323i
$452$	−7.53143	−	28.1077i	−0.354249	−	1.32207i
$453$	2.20462	−	3.81852i	0.103582	−	0.179409i
$454$	7.21383			0.338562
$455$		0			0
$456$	9.55545			0.447475
$457$	0.413767	−	0.716665i	0.0193552	−	0.0335242i	−0.856186	−	0.516668i	$-0.827172\pi$
$457$	0.413767	−	0.716665i	0.0193552	−	0.0335242i	0.875541	+	0.483144i	$0.160505\pi$
$458$	−2.82349	−	10.5374i	−0.131933	−	0.492381i
$459$	5.71155	+	9.89269i	0.266592	+	0.461751i
$460$	−4.20792	−	3.25138i	−0.196195	−	0.151596i
$461$	23.2589	+	6.23219i	1.08327	+	0.290262i	0.755936	−	0.654646i	$-0.227182\pi$
$461$	23.2589	+	6.23219i	1.08327	+	0.290262i	0.327337	+	0.944908i	$0.393849\pi$
$462$	1.01669	−	0.586988i	0.0473008	−	0.0273091i
$463$	−6.35566			−0.295373			−0.147686	−	0.989034i	$-0.547183\pi$
$463$	−6.35566			−0.295373			−0.147686	+	0.989034i	$0.547183\pi$
$464$	21.3935	−	12.3515i	0.993167	−	0.573405i
$465$	13.2130	+	5.52509i	0.612737	+	0.256220i
$466$	−11.1744	+	2.99418i	−0.517645	+	0.138703i
$467$	15.6194	−	15.6194i	0.722781	−	0.722781i	−0.246390	−	0.969171i	$-0.579244\pi$
$467$	15.6194	−	15.6194i	0.722781	−	0.722781i	0.969171	+	0.246390i	$0.0792443\pi$
$468$		0			0
$469$		−	45.0153i		−	2.07861i
$470$	3.88119	+	1.62295i	0.179026	+	0.0748610i
$471$	6.56942	−	11.3786i	0.302703	−	0.524297i
$472$	18.6455	+	4.99605i	0.858229	+	0.229962i
$473$			1.49000i			0.0685104i
$474$	0.375240	−	1.40042i	0.0172354	−	0.0643232i
$475$	−0.184093	+	27.3859i	−0.00844675	+	1.25655i
$476$	−10.8371	−	10.8371i	−0.496716	−	0.496716i
$477$	−1.91500	+	7.14687i	−0.0876818	+	0.327233i
$478$	−9.85182	+	2.63979i	−0.450612	+	0.120741i
$479$	−2.44935	−	9.14111i	−0.111914	−	0.417668i	0.887124	−	0.461532i	$-0.152700\pi$
$479$	−2.44935	−	9.14111i	−0.111914	−	0.417668i	−0.999038	+	0.0438638i	$0.986033\pi$
$480$	6.41866	−	8.30700i	0.292970	−	0.379161i
$481$		0			0
$482$	−1.08228	−	1.08228i	−0.0492964	−	0.0492964i
$483$	4.05375	+	2.34044i	0.184452	+	0.106494i
$484$	−16.0095	−	9.24310i	−0.727705	−	0.420141i
$485$	9.58681	+	12.5811i	0.435314	+	0.571278i
$486$	−5.63904	+	5.63904i	−0.255792	+	0.255792i
$487$	3.07948	+	5.33382i	0.139545	+	0.241698i	0.927324	−	0.374259i	$-0.122103\pi$
$487$	3.07948	+	5.33382i	0.139545	+	0.241698i	−0.787780	+	0.615957i	$0.788769\pi$
$488$	−5.74911	−	9.95775i	−0.260250	−	0.450766i
$489$	0.0877545	−	0.0877545i	0.00396840	−	0.00396840i
$490$	−4.35707	−	5.71793i	−0.196832	−	0.258310i
$491$	−12.8290	−	7.40681i	−0.578964	−	0.334265i	0.181758	−	0.983343i	$-0.441821\pi$
$491$	−12.8290	−	7.40681i	−0.578964	−	0.334265i	−0.760721	+	0.649078i	$0.775155\pi$
$492$	−0.792102	−	0.457320i	−0.0357107	−	0.0206176i
$493$	15.9781	+	15.9781i	0.719615	+	0.719615i
$494$		0			0
$495$	−1.98914	+	2.57433i	−0.0894051	+	0.115708i
$496$	−4.57590	−	17.0775i	−0.205464	−	0.766802i
$497$	−23.7993	+	6.37699i	−1.06754	+	0.286047i
$498$	0.257155	−	0.959715i	0.0115234	−	0.0430059i
$499$	21.0529	+	21.0529i	0.942459	+	0.942459i	0.998432	−	0.0559733i	$-0.0178262\pi$
$499$	21.0529	+	21.0529i	0.942459	+	0.942459i	−0.0559733	+	0.998432i	$0.517826\pi$
$500$	15.4549	+	12.1085i	0.691164	+	0.541508i
$501$	5.26622	−	19.6538i	0.235278	−	0.878068i
$502$		−	14.5844i		−	0.650933i
$503$	37.4393	+	10.0318i	1.66934	+	0.447297i	0.964932	−	0.262502i	$-0.0845476\pi$
$503$	37.4393	+	10.0318i	1.66934	+	0.447297i	0.704404	+	0.709799i	$0.251214\pi$
$504$	7.21280	−	12.4929i	0.321284	−	0.556479i
$505$	−30.8820	−	12.9135i	−1.37423	−	0.574643i
$506$		−	0.459974i		−	0.0204484i
$507$		0			0
$508$	−10.3059	+	10.3059i	−0.457250	+	0.457250i
$509$	5.36291	−	1.43699i	0.237707	−	0.0636933i	−0.137999	−	0.990432i	$-0.544067\pi$
$509$	5.36291	−	1.43699i	0.237707	−	0.0636933i	0.375706	+	0.926739i	$0.377400\pi$
$510$	2.27518	+	0.951382i	0.100747	+	0.0421279i
$511$	−10.7474	+	6.20501i	−0.475437	+	0.274493i
$512$	−22.5909			−0.998384
$513$	22.8197	−	13.1750i	1.00751	−	0.581688i
$514$	3.41828	+	0.915926i	0.150774	+	0.0403997i
$515$	7.95364	+	6.14563i	0.350479	+	0.270809i
$516$	−1.78902	−	3.09867i	−0.0787572	−	0.136411i
$517$	−0.677985	−	2.53028i	−0.0298178	−	0.111281i
$518$	1.66578	−	2.88521i	0.0731900	−	0.126769i
$519$	−7.27269			−0.319236
$520$		0			0
$521$	−13.8692			−0.607619			−0.303809	−	0.952733i	$-0.598259\pi$
$521$	−13.8692			−0.607619			−0.303809	+	0.952733i	$0.598259\pi$
$522$	−4.97191	+	8.61159i	−0.217614	+	0.376919i
$523$	8.10818	+	30.2601i	0.354546	+	1.32318i	0.881055	+	0.473014i	$0.156834\pi$
$523$	8.10818	+	30.2601i	0.354546	+	1.32318i	−0.526509	+	0.850170i	$0.676499\pi$
$524$	1.20649	+	2.08970i	0.0527057	+	0.0912890i
$525$	−14.9083	−	8.74146i	−0.650652	−	0.381508i
$526$	−6.42400	−	1.72130i	−0.280100	−	0.0750524i
$527$	14.0055	−	8.08609i	0.610090	−	0.352236i
$528$	−1.67875			−0.0730583
$529$	−18.3303	+	10.5830i	−0.796969	+	0.460130i
$530$	1.46606	+	3.57331i	0.0636816	+	0.155214i
$531$	21.2640	−	5.69768i	0.922781	−	0.247258i
$532$	−24.9981	+	24.9981i	−1.08381	+	1.08381i
$533$		0			0
$534$			1.56879i			0.0678882i
$535$	31.5534	−	12.9458i	1.36417	−	0.559695i
$536$	11.3602	−	19.6765i	0.490688	−	0.849897i
$537$	14.8549	+	3.98035i	0.641035	+	0.171765i
$538$			4.00246i			0.172558i
$539$	−1.15856	+	4.32381i	−0.0499028	+	0.186240i
$540$	2.52860	−	18.7202i	0.108814	−	0.805589i
$541$	10.7732	+	10.7732i	0.463175	+	0.463175i	0.899695	−	0.436520i	$-0.143789\pi$
$541$	10.7732	+	10.7732i	0.463175	+	0.463175i	−0.436520	+	0.899695i	$0.643789\pi$
$542$	−1.17561	+	4.38745i	−0.0504969	+	0.188457i
$543$	16.3855	−	4.39048i	0.703170	−	0.188414i
$544$	−3.06813	−	11.4504i	−0.131545	−	0.490932i
$545$	5.65278	+	4.36780i	0.242139	+	0.187096i
$546$		0			0
$547$	14.2704	+	14.2704i	0.610159	+	0.610159i	0.942987	−	0.332828i	$-0.108003\pi$
$547$	14.2704	+	14.2704i	0.610159	+	0.610159i	−0.332828	+	0.942987i	$0.608003\pi$
$548$	−18.7477	−	10.8240i	−0.800863	−	0.462379i
$549$	−11.3562	−	6.55650i	−0.484671	−	0.279825i
$550$	−0.0114157	+	1.69822i	−0.000486767	+	0.0724122i
$551$	36.8569	−	36.8569i	1.57016	−	1.57016i
$552$	1.18128	+	2.04605i	0.0502788	+	0.0870855i
$553$	5.73651	+	9.93592i	0.243941	+	0.422518i
$554$	−9.02605	+	9.02605i	−0.383480	+	0.383480i
$555$	0.516571	−	3.82437i	0.0219272	−	0.162336i
$556$	9.73546	+	5.62077i	0.412875	+	0.238374i
$557$	14.4727	+	8.35584i	0.613229	+	0.354048i	0.774228	−	0.632906i	$-0.218138\pi$
$557$	14.4727	+	8.35584i	0.613229	+	0.354048i	−0.160999	+	0.986955i	$0.551472\pi$
$558$	5.03231	+	5.03231i	0.213035	+	0.213035i
$559$		0			0
$560$	2.71361	+	21.1613i	0.114671	+	0.894227i
$561$	−0.397439	−	1.48326i	−0.0167799	−	0.0626234i
$562$	−3.65629	+	0.979701i	−0.154231	+	0.0413262i
$563$	5.84179	−	21.8019i	0.246202	−	0.918839i	−0.726573	−	0.687089i	$-0.758888\pi$
$563$	5.84179	−	21.8019i	0.246202	−	0.918839i	0.972775	−	0.231750i	$-0.0744452\pi$
$564$	4.44802	+	4.44802i	0.187296	+	0.187296i
$565$	−36.7198	−	4.95987i	−1.54481	−	0.208663i
$566$	−1.12307	+	4.19136i	−0.0472063	+	0.176176i
$567$		−	6.70030i		−	0.281386i
$568$	−12.0122	−	3.21865i	−0.504019	−	0.135052i
$569$	−2.86843	+	4.96826i	−0.120251	+	0.208280i	−0.919866	−	0.392232i	$-0.871703\pi$
$569$	−2.86843	+	4.96826i	−0.120251	+	0.208280i	0.799616	+	0.600512i	$0.205037\pi$
$570$	2.19458	−	5.24821i	0.0919206	−	0.219823i
$571$		−	46.5634i		−	1.94862i	−0.225214	−	0.974309i	$-0.572308\pi$
$571$		−	46.5634i		−	1.94862i	0.225214	−	0.974309i	$-0.427692\pi$
$572$		0			0
$573$	−3.45183	+	3.45183i	−0.144202	+	0.144202i
$574$	−0.971181	+	0.260227i	−0.0405363	+	0.0108617i
$575$	−5.88672	+	3.34614i	−0.245493	+	0.139544i
$576$	−4.99463	+	2.88365i	−0.208109	+	0.120152i
$577$	28.9429			1.20491			0.602455	−	0.798153i	$-0.294189\pi$
$577$	28.9429			1.20491			0.602455	+	0.798153i	$0.294189\pi$
$578$	−4.85978	+	2.80580i	−0.202140	+	0.116706i
$579$	9.17569	+	2.45862i	0.381329	+	0.102177i
$580$	−4.75287	−	37.0638i	−0.197352	−	1.53899i
$581$	3.93127	+	6.80916i	0.163097	+	0.282491i
$582$	−0.850351	−	3.17355i	−0.0352482	−	0.131548i
$583$	1.20251	−	2.08281i	0.0498030	−	0.0862613i
$584$	−6.26369			−0.259193
$585$		0			0
$586$	−6.53726			−0.270052
$587$	−9.84577	+	17.0534i	−0.406379	+	0.703868i	−0.994481	−	0.104918i	$-0.966542\pi$
$587$	−9.84577	+	17.0534i	−0.406379	+	0.703868i	0.588102	+	0.808787i	$0.299875\pi$
$588$	−2.78213	−	10.3830i	−0.114733	−	0.428189i
$589$	−18.6524	−	32.3069i	−0.768558	−	1.33118i
$590$	7.02628	−	9.09338i	0.289267	−	0.374368i
$591$	−11.8667	−	3.17966i	−0.488129	−	0.130794i
$592$	−4.12577	+	2.38201i	−0.169568	+	0.0979001i
$593$	21.8216			0.896106			0.448053	−	0.894007i	$-0.352118\pi$
$593$	21.8216			0.896106			0.448053	+	0.894007i	$0.352118\pi$
$594$	1.41506	−	0.816987i	0.0580607	−	0.0335214i
$595$	−18.0547	+	7.40749i	−0.740169	+	0.303677i
$596$	28.5009	−	7.63679i	1.16744	−	0.312815i
$597$	5.22002	−	5.22002i	0.213641	−	0.213641i
$598$		0			0
$599$			37.6041i			1.53646i	0.640172	+	0.768232i	$0.278863\pi$
$599$			37.6041i			1.53646i	−0.640172	+	0.768232i	$0.721137\pi$
$600$	−4.31050	−	7.58328i	−0.175976	−	0.309586i
$601$	10.1487	−	17.5781i	0.413976	−	0.717027i	−0.581344	−	0.813658i	$-0.697473\pi$
$601$	10.1487	−	17.5781i	0.413976	−	0.717027i	0.995320	+	0.0966302i	$0.0308064\pi$
$602$	−3.79922	−	1.01800i	−0.154845	−	0.0414905i
$603$		−	25.9113i		−	1.05519i
$604$	−2.13103	+	7.95310i	−0.0867103	+	0.323607i
$605$	−18.7230	+	14.2670i	−0.761199	+	0.580034i
$606$	4.91641	+	4.91641i	0.199716	+	0.199716i
$607$	8.91757	−	33.2808i	0.361953	−	1.35083i	−0.509552	−	0.860440i	$-0.670189\pi$
$607$	8.91757	−	33.2808i	0.361953	−	1.35083i	0.871505	−	0.490387i	$-0.163144\pi$
$608$	−26.4129	+	7.07732i	−1.07119	+	0.287023i
$609$	8.51314	+	31.7715i	0.344970	+	1.28744i
$610$	−6.78955	+	0.870657i	−0.274901	+	0.0352519i
$611$		0			0
$612$	−6.23794	−	6.23794i	−0.252154	−	0.252154i
$613$	21.5350	+	12.4332i	0.869790	+	0.502173i	0.867278	−	0.497824i	$-0.165867\pi$
$613$	21.5350	+	12.4332i	0.869790	+	0.502173i	0.00251133	+	0.999997i	$0.499201\pi$
$614$	6.62053	+	3.82236i	0.267183	+	0.154258i
$615$	−0.926357	+	0.705885i	−0.0373543	+	0.0284640i
$616$	−3.31563	+	3.31563i	−0.133591	+	0.133591i
$617$	−13.9081	−	24.0895i	−0.559917	−	0.969805i	−0.997503	−	0.0706286i	$-0.977499\pi$
$617$	−13.9081	−	24.0895i	−0.559917	−	0.969805i	0.437585	−	0.899177i	$-0.355834\pi$
$618$	−1.04390	−	1.80809i	−0.0419919	−	0.0727321i
$619$	−19.5593	+	19.5593i	−0.786156	+	0.786156i	−0.980862	−	0.194705i	$-0.937625\pi$
$619$	−19.5593	+	19.5593i	−0.786156	+	0.786156i	0.194705	+	0.980862i	$0.437625\pi$
$620$	−26.5030	−	3.57985i	−1.06439	−	0.143770i
$621$	5.64213	+	3.25749i	0.226411	+	0.130718i
$622$	2.28803	+	1.32099i	0.0917416	+	0.0529671i
$623$	−8.77838	−	8.77838i	−0.351698	−	0.351698i
$624$		0			0
$625$	21.8167	−	12.2078i	0.872669	−	0.488312i
$626$	−4.40965	−	16.4570i	−0.176245	−	0.657755i
$627$	−3.42148	+	0.916783i	−0.136641	+	0.0366128i
$628$	−6.35012	+	23.6990i	−0.253397	+	0.945692i
$629$	−3.08139	−	3.08139i	−0.122863	−	0.122863i
$630$	−5.20504	−	6.83076i	−0.207374	−	0.272144i
$631$	3.38116	−	12.6187i	0.134602	−	0.502341i	−0.865397	−	0.501086i	$-0.832934\pi$
$631$	3.38116	−	12.6187i	0.134602	−	0.502341i	0.999999	−	0.00125496i	$-0.000399466\pi$
$632$			5.79076i			0.230344i
$633$	11.2855	+	3.02393i	0.448557	+	0.120190i
$634$	4.68840	−	8.12054i	0.186200	−	0.322508i
$635$	7.04442	+	17.1697i	0.279549	+	0.681360i
$636$			5.77534i			0.229007i
$637$		0			0
$638$	2.28552	−	2.28552i	0.0904846	−	0.0904846i
$639$	−13.6991	+	3.67067i	−0.541929	+	0.145210i
$640$	−9.77471	+	23.3757i	−0.386379	+	0.924006i
$641$	−23.7092	+	13.6885i	−0.936456	+	0.540663i	−0.888848	−	0.458203i	$-0.848493\pi$
$641$	−23.7092	+	13.6885i	−0.936456	+	0.540663i	−0.0476083	+	0.998866i	$0.515160\pi$
$642$	−7.08428			−0.279594
$643$	27.2816	−	15.7510i	1.07588	−	0.621161i	0.146099	−	0.989270i	$-0.453328\pi$
$643$	27.2816	−	15.7510i	1.07588	−	0.621161i	0.929783	+	0.368109i	$0.119995\pi$
$644$	−8.44305	−	2.26231i	−0.332703	−	0.0891475i
$645$	−4.51907	+	0.579501i	−0.177938	+	0.0228178i
$646$	−3.21181	−	5.56301i	−0.126367	−	0.218874i
$647$	10.8106	+	40.3457i	0.425008	+	1.58615i	0.763905	+	0.645329i	$0.223280\pi$
$647$	10.8106	+	40.3457i	0.425008	+	1.58615i	−0.338896	+	0.940824i	$0.610054\pi$
$648$	1.69092	−	2.92875i	0.0664254	−	0.115052i
$649$	−7.15565			−0.280884
$650$		0			0
$651$	23.5409			0.922641
$652$	−0.115873	+	0.200698i	−0.00453795	+	0.00785996i
$653$	−3.93069	−	14.6695i	−0.153820	−	0.574064i	−0.999204	−	0.0399041i	$-0.987295\pi$
$653$	−3.93069	−	14.6695i	−0.153820	−	0.574064i	0.845384	−	0.534160i	$-0.179372\pi$
$654$	−0.741918	−	1.28504i	−0.0290113	−	0.0502490i
$655$	3.04759	−	0.390807i	0.119079	−	0.0152701i
$656$	1.38876	+	0.372117i	0.0542220	+	0.0145287i
$657$	−6.18632	+	3.57167i	−0.241351	+	0.139344i
$658$	6.91493			0.269572
$659$	−24.6914	+	14.2556i	−0.961840	+	0.555319i	−0.896739	−	0.442560i	$-0.854070\pi$
$659$	−24.6914	+	14.2556i	−0.961840	+	0.555319i	−0.0651015	+	0.997879i	$0.520737\pi$
$660$	−0.979658	+	2.34280i	−0.0381331	+	0.0911934i
$661$	−6.08664	+	1.63091i	−0.236743	+	0.0634351i	−0.375240	−	0.926928i	$-0.622440\pi$
$661$	−6.08664	+	1.63091i	−0.236743	+	0.0634351i	0.138497	+	0.990363i	$0.455773\pi$
$662$	−2.45054	+	2.45054i	−0.0952430	+	0.0952430i
$663$		0			0
$664$			3.96845i			0.154006i
$665$	17.0870	+	41.6471i	0.662606	+	1.61501i
$666$	0.958840	−	1.66076i	0.0371543	−	0.0643531i
$667$	12.4483	+	3.33552i	0.482002	+	0.129152i
$668$			37.9955i			1.47009i
$669$	−2.42052	+	9.03352i	−0.0935829	+	0.349256i
$670$	−8.19801	−	10.7585i	−0.316717	−	0.415638i
$671$	3.01394	+	3.01394i	0.116352	+	0.116352i
$672$	4.46610	−	16.6677i	0.172283	−	0.642970i
$673$	22.1285	−	5.92931i	0.852991	−	0.228558i	0.194272	−	0.980948i	$-0.437765\pi$
$673$	22.1285	−	5.92931i	0.852991	−	0.228558i	0.658719	+	0.752389i	$0.271099\pi$
$674$	−0.199212	−	0.743468i	−0.00767334	−	0.0286373i
$675$	−20.7498	−	12.1666i	−0.798660	−	0.468293i
$676$		0			0
$677$	−16.1247	−	16.1247i	−0.619724	−	0.619724i	0.325736	−	0.945461i	$-0.394388\pi$
$677$	−16.1247	−	16.1247i	−0.619724	−	0.619724i	−0.945461	+	0.325736i	$0.894388\pi$
$678$	6.66536	+	3.84825i	0.255982	+	0.147791i
$679$	22.5163	+	12.9998i	0.864096	+	0.498886i
$680$	−9.76121	−	1.31848i	−0.374325	−	0.0505614i
$681$	9.71227	−	9.71227i	0.372175	−	0.372175i
$682$	−1.15664	−	2.00337i	−0.0442902	−	0.0767129i
$683$	−16.0240	−	27.7544i	−0.613142	−	1.06199i	−0.990707	−	0.136010i	$-0.956572\pi$
$683$	−16.0240	−	27.7544i	−0.613142	−	1.06199i	0.377565	−	0.925983i	$-0.376761\pi$
$684$	−14.3892	+	14.3892i	−0.550185	+	0.550185i
$685$	−21.9253	+	16.7071i	−0.837724	+	0.638346i
$686$	0.771532	+	0.445444i	0.0294572	+	0.0170071i
$687$	−17.9883	−	10.3856i	−0.686298	−	0.396234i
$688$	3.97707	+	3.97707i	0.151624	+	0.151624i
$689$		0			0
$690$	1.39507	−	0.178896i	0.0531093	−	0.00681046i
$691$	−0.142620	−	0.532264i	−0.00542551	−	0.0202483i	0.963160	−	0.268929i	$-0.0866697\pi$
$691$	−0.142620	−	0.532264i	−0.00542551	−	0.0202483i	−0.968586	+	0.248681i	$0.920003\pi$
$692$	13.1180	−	3.51496i	0.498672	−	0.133619i
$693$	−1.38404	+	5.16531i	−0.0525754	+	0.196214i
$694$	−9.02132	−	9.02132i	−0.342445	−	0.342445i
$695$	11.3855	−	8.67580i	0.431878	−	0.329092i
$696$	−4.29682	+	16.0360i	−0.162871	+	0.607842i
$697$			1.31514i			0.0498144i
$698$	4.48442	+	1.20160i	0.169738	+	0.0454811i
$699$	−11.0134	+	19.0758i	−0.416565	+	0.721512i
$700$	31.1155	+	8.56194i	1.17605	+	0.323611i
$701$			9.52279i			0.359671i	0.983697	+	0.179835i	$0.0575565\pi$
$701$			9.52279i			0.359671i	−0.983697	+	0.179835i	$0.942443\pi$
$702$		0			0
$703$	−7.10792	+	7.10792i	−0.268080	+	0.268080i
$704$	1.81077	−	0.485195i	0.0682460	−	0.0182865i
$705$	7.41045	−	3.04037i	0.279094	−	0.114507i
$706$	1.39674	−	0.806411i	0.0525672	−	0.0303497i
$707$	−55.0209			−2.06927
$708$	14.8812	−	8.59166i	0.559270	−	0.322894i
$709$	−31.3471	−	8.39944i	−1.17727	−	0.315448i	−0.383425	−	0.923572i	$-0.625255\pi$
$709$	−31.3471	−	8.39944i	−1.17727	−	0.315448i	−0.793842	+	0.608124i	$0.791922\pi$
$710$	−4.52661	+	5.85831i	−0.169881	+	0.219859i
$711$	3.30200	+	5.71923i	0.123835	+	0.214488i
$712$	−1.62175	−	6.05244i	−0.0607776	−	0.226825i
$713$	4.61177	−	7.98782i	0.172712	−	0.299146i
$714$	4.05358			0.151701
$715$		0			0
$716$	−28.7180			−1.07324
$717$	−9.70986	+	16.8180i	−0.362621	+	0.628079i
$718$	−0.564197	−	2.10561i	−0.0210557	−	0.0785808i
$719$	−4.21240	−	7.29608i	−0.157096	−	0.272098i	0.776724	−	0.629841i	$-0.216880\pi$
$719$	−4.21240	−	7.29608i	−0.157096	−	0.272098i	−0.933820	+	0.357743i	$0.883546\pi$
$720$	1.56199	+	12.1807i	0.0582118	+	0.453947i
$721$	15.9587	+	4.27612i	0.594333	+	0.159251i
$722$	−4.70543	+	2.71668i	−0.175118	+	0.101104i
$723$	−2.91423			−0.108381
$724$	−27.4332	+	15.8385i	−1.01955	+	0.588635i
$725$	−45.8763	−	12.6236i	−1.70380	−	0.468830i
$726$	4.72284	−	1.26548i	0.175281	−	0.0469664i
$727$	8.33682	−	8.33682i	0.309195	−	0.309195i	−0.535402	−	0.844597i	$-0.679840\pi$
$727$	8.33682	−	8.33682i	0.309195	−	0.309195i	0.844597	+	0.535402i	$0.179840\pi$
$728$		0			0
$729$			9.71523i			0.359824i
$730$	−1.43857	+	3.44025i	−0.0532437	+	0.127329i
$731$	−2.57239	+	4.45551i	−0.0951432	+	0.164793i
$732$	−9.88670	−	2.64913i	−0.365423	−	0.0979148i
$733$		−	18.6238i		−	0.687887i	−0.938990	−	0.343944i	$-0.888237\pi$
$733$		−	18.6238i		−	0.687887i	0.938990	−	0.343944i	$-0.111763\pi$
$734$	−3.20725	+	11.9696i	−0.118382	+	0.441807i
$735$	−13.5644	−	1.83219i	−0.500330	−	0.0675812i
$736$	−4.78070	−	4.78070i	−0.176219	−	0.176219i
$737$	−2.17988	+	8.13543i	−0.0802970	+	0.299672i
$738$	−0.559023	+	0.149790i	−0.0205779	+	0.00551383i
$739$	8.54061	+	31.8740i	0.314171	+	1.17250i	0.924758	+	0.380555i	$0.124267\pi$
$739$	8.54061	+	31.8740i	0.314171	+	1.17250i	−0.610587	+	0.791949i	$0.709066\pi$
$740$	0.916598	+	7.14782i	0.0336948	+	0.262759i
$741$		0			0
$742$	4.48920	+	4.48920i	0.164804	+	0.164804i
$743$	−32.5366	−	18.7850i	−1.19365	−	0.689155i	−0.234518	−	0.972112i	$-0.575351\pi$
$743$	−32.5366	−	18.7850i	−1.19365	−	0.689155i	−0.959133	+	0.282957i	$0.908685\pi$
$744$	10.2899	+	5.94088i	0.377246	+	0.217803i
$745$	5.02925	−	37.2335i	0.184258	−	1.36413i
$746$	3.99061	−	3.99061i	0.146107	−	0.146107i
$747$	2.26288	+	3.91943i	0.0827946	+	0.143404i
$748$	1.43375	+	2.48333i	0.0524231	+	0.0907995i
$749$	39.6410	−	39.6410i	1.44845	−	1.44845i
$750$	−5.15500	+	0.625858i	−0.188234	+	0.0228531i
$751$	29.1051	+	16.8038i	1.06206	+	0.613181i	0.926001	−	0.377520i	$-0.123223\pi$
$751$	29.1051	+	16.8038i	1.06206	+	0.613181i	0.136059	+	0.990701i	$0.456556\pi$
$752$	−8.56339	−	4.94407i	−0.312275	−	0.180292i
$753$	−19.6356	−	19.6356i	−0.715560	−	0.715560i
$754$		0			0
$755$	8.29623	+	6.41034i	0.301931	+	0.233296i
$756$	−8.03643	−	29.9924i	−0.292282	−	1.09081i
$757$	15.5871	−	4.17654i	0.566521	−	0.151799i	0.0358205	−	0.999358i	$-0.488596\pi$
$757$	15.5871	−	4.17654i	0.566521	−	0.151799i	0.530701	+	0.847559i	$0.321929\pi$
$758$	−0.256883	+	0.958699i	−0.00933040	+	0.0348215i
$759$	−0.619282	−	0.619282i	−0.0224785	−	0.0224785i
$760$	−3.04137	+	22.5164i	−0.110322	+	0.816756i
$761$	−4.05514	+	15.1340i	−0.146999	+	0.548606i	0.852660	+	0.522467i	$0.174988\pi$
$761$	−4.05514	+	15.1340i	−0.146999	+	0.548606i	−0.999658	+	0.0261397i	$0.991679\pi$
$762$		−	3.85490i		−	0.139648i
$763$	11.3421	+	3.03911i	0.410612	+	0.110023i
$764$	4.55789	−	7.89449i	0.164899	−	0.285613i
$765$	−10.3925	+	4.26384i	−0.375741	+	0.154159i
$766$			13.0645i			0.472039i
$767$		0			0
$768$	0.0960396	−	0.0960396i	0.00346553	−	0.00346553i
$769$	−31.4959	+	8.43930i	−1.13577	+	0.304329i	−0.777249	−	0.629193i	$-0.783386\pi$
$769$	−31.4959	+	8.43930i	−1.13577	+	0.304329i	−0.358521	+	0.933522i	$0.616719\pi$
$770$	1.05958	+	2.58256i	0.0381845	+	0.0930690i
$771$	5.83532	−	3.36902i	0.210154	−	0.121332i
$772$	−17.7388			−0.638433
$773$	20.7033	−	11.9531i	0.744646	−	0.429921i	−0.0791103	−	0.996866i	$-0.525208\pi$
$773$	20.7033	−	11.9531i	0.744646	−	0.429921i	0.823756	+	0.566944i	$0.191875\pi$
$774$	−2.18688	−	0.585972i	−0.0786056	−	0.0210623i
$775$	−17.2248	+	29.3764i	−0.618733	+	1.05523i
$776$	6.56136	+	11.3646i	0.235539	+	0.407966i
$777$	−1.64177	−	6.12718i	−0.0588983	−	0.219811i
$778$	0.160541	−	0.278066i	0.00575569	−	0.00996914i
$779$	3.03366			0.108692
$780$		0			0
$781$	4.60995			0.164957
$782$	0.794114	−	1.37545i	0.0283975	−	0.0491858i
$783$	11.8488	+	44.2204i	0.423443	+	1.58031i
$784$	8.44858	+	14.6334i	0.301735	+	0.522620i
$785$	24.7214	+	19.1018i	0.882346	+	0.681772i
$786$	−0.616466	−	0.165181i	−0.0219886	−	0.00589183i
$787$	−13.6065	+	7.85572i	−0.485020	+	0.280026i	−0.722506	−	0.691365i	$-0.757010\pi$
$787$	−13.6065	+	7.85572i	−0.485020	+	0.280026i	0.237486	+	0.971391i	$0.423676\pi$
$788$	22.9411			0.817242
$789$	−10.9664	+	6.33143i	−0.390412	+	0.225405i
$790$	3.18050	+	1.32995i	0.113157	+	0.0473174i
$791$	−58.8303	+	15.7635i	−2.09176	+	0.560487i
$792$	−1.90851	+	1.90851i	−0.0678161	+	0.0678161i
$793$		0			0
$794$		−	13.3394i		−	0.473397i
$795$	6.78470	+	2.83707i	0.240629	+	0.100621i
$796$	−6.89264	+	11.9384i	−0.244303	+	0.423146i
$797$	30.1666	+	8.08312i	1.06856	+	0.286319i	0.749900	−	0.661552i	$-0.230102\pi$
$797$	30.1666	+	8.08312i	1.06856	+	0.286319i	0.318656	+	0.947870i	$0.396768\pi$
$798$		−	9.35048i		−	0.331003i
$799$	2.34099	−	8.73669i	0.0828183	−	0.309082i
$800$	17.5316	+	17.7689i	0.619836	+	0.628225i
$801$	−5.05293	−	5.05293i	−0.178537	−	0.178537i
$802$	−0.633871	+	2.36564i	−0.0223827	+	0.0835336i
$803$	2.24281	−	0.600960i	0.0791471	−	0.0212074i
$804$	−5.23469	−	19.5361i	−0.184613	−	0.688986i
$805$	−6.80525	+	8.80732i	−0.239853	+	0.310417i
$806$		0			0
$807$	5.38868	+	5.38868i	0.189690	+	0.189690i
$808$	−24.0500	−	13.8853i	−0.846078	−	0.488483i
$809$	11.4546	+	6.61331i	0.402722	+	0.232512i	0.687658	−	0.726035i	$-0.258639\pi$
$809$	11.4546	+	6.61331i	0.402722	+	0.232512i	−0.284936	+	0.958547i	$0.591972\pi$
$810$	−1.22023	−	1.60135i	−0.0428746	−	0.0562658i
$811$	−22.0736	+	22.0736i	−0.775109	+	0.775109i	−0.978995	−	0.203886i	$-0.934643\pi$
$811$	−22.0736	+	22.0736i	−0.775109	+	0.775109i	0.203886	+	0.978995i	$0.434643\pi$
$812$	−30.7109	−	53.1928i	−1.07774	−	1.86670i
$813$	4.32423	+	7.48978i	0.151657	+	0.262678i
$814$	−0.440767	+	0.440767i	−0.0154489	+	0.0154489i
$815$	0.178853	+	0.234715i	0.00626496	+	0.00822172i
$816$	−5.01991	−	2.89825i	−0.175732	−	0.101459i
$817$	10.2776	+	5.93379i	0.359568	+	0.207597i
$818$	2.11139	+	2.11139i	0.0738230	+	0.0738230i
$819$		0			0
$820$	1.32974	−	1.72095i	0.0464366	−	0.0600981i
$821$	−2.34418	−	8.74860i	−0.0818124	−	0.305328i	0.912879	−	0.408230i	$-0.133854\pi$
$821$	−2.34418	−	8.74860i	−0.0818124	−	0.305328i	−0.994692	+	0.102902i	$0.967187\pi$
$822$	5.53062	−	1.48192i	0.192902	−	0.0516881i
$823$	−10.8551	+	40.5117i	−0.378384	+	1.41215i	0.469953	+	0.882691i	$0.344271\pi$
$823$	−10.8551	+	40.5117i	−0.378384	+	1.41215i	−0.848337	+	0.529457i	$0.822396\pi$
$824$	5.89653	+	5.89653i	0.205415	+	0.205415i
$825$	2.27101	+	2.30175i	0.0790664	+	0.0801366i
$826$	4.88888	−	18.2455i	0.170106	−	0.634844i
$827$		−	38.2009i		−	1.32838i	−0.747566	−	0.664188i	$-0.768778\pi$
$827$		−	38.2009i		−	1.32838i	0.747566	−	0.664188i	$-0.231222\pi$
$828$	−4.85992	−	1.30221i	−0.168894	−	0.0452550i
$829$	14.6750	−	25.4178i	0.509682	−	0.882796i	−0.490255	−	0.871579i	$-0.663096\pi$
$829$	14.6750	−	25.4178i	0.509682	−	0.882796i	0.999937	−	0.0112165i	$-0.00357041\pi$
$830$	2.17962	+	0.911423i	0.0756557	+	0.0316359i
$831$			24.3043i			0.843106i
$832$		0			0
$833$	−10.9292	+	10.9292i	−0.378673	+	0.378673i
$834$	−2.87198	+	0.769545i	−0.0994485	+	0.0266471i
$835$	44.6360	+	18.6648i	1.54469	+	0.645923i
$836$	5.72835	−	3.30726i	0.198119	−	0.114384i
$837$	32.7649			1.13252
$838$	2.29721	−	1.32629i	0.0793557	−	0.0458161i
$839$	−34.0331	−	9.11914i	−1.17495	−	0.314828i	−0.382030	−	0.924150i	$-0.624775\pi$
$839$	−34.0331	−	9.11914i	−1.17495	−	0.314828i	−0.792923	+	0.609322i	$0.791442\pi$
$840$	−11.3456	−	8.76652i	−0.391460	−	0.302474i
$841$	30.7798	+	53.3122i	1.06137	+	1.83835i
$842$	2.55582	+	9.53846i	0.0880795	+	0.328717i
$843$	−3.60361	+	6.24163i	−0.124115	+	0.214973i
$844$	−21.8175			−0.750988
$845$		0			0
$846$	3.98031			0.136846
$847$	−19.3461	+	33.5084i	−0.664740	+	1.15136i
$848$	−2.34967	−	8.76909i	−0.0806880	−	0.301132i
$849$	4.13097	+	7.15504i	0.141774	+	0.245560i
$850$	−2.96599	+	5.05841i	−0.101733	+	0.173502i
$851$	−2.40068	−	0.643261i	−0.0822944	−	0.0220507i
$852$	−9.58705	+	5.53509i	−0.328447	+	0.189629i
$853$	−17.6392			−0.603954			−0.301977	−	0.953315i	$-0.597647\pi$
$853$	−17.6392			−0.603954			−0.301977	+	0.953315i	$0.597647\pi$
$854$	−9.74415	+	5.62579i	−0.333438	+	0.192511i
$855$	9.83549	+	23.9725i	0.336367	+	0.819844i
$856$	27.3314	−	7.32342i	0.934167	−	0.250309i
$857$	−6.30427	+	6.30427i	−0.215350	+	0.215350i	−0.806535	−	0.591186i	$-0.798660\pi$
$857$	−6.30427	+	6.30427i	−0.215350	+	0.215350i	0.591186	+	0.806535i	$0.298660\pi$
$858$		0			0
$859$			29.2307i			0.997338i	0.866793	+	0.498669i	$0.166178\pi$
$859$			29.2307i			0.997338i	−0.866793	+	0.498669i	$0.833822\pi$
$860$	7.87112	−	3.22937i	0.268403	−	0.110121i
$861$	−0.957186	+	1.65789i	−0.0326208	+	0.0565009i
$862$	7.96263	+	2.13358i	0.271208	+	0.0726701i
$863$		−	15.7688i		−	0.536775i	−0.963311	−	0.268387i	$-0.913509\pi$
$863$		−	15.7688i		−	0.536775i	0.963311	−	0.268387i	$-0.0864907\pi$
$864$	6.21604	−	23.1986i	0.211474	−	0.789232i
$865$	2.31480	−	17.1373i	0.0787054	−	0.582687i
$866$	−2.65202	−	2.65202i	−0.0901192	−	0.0901192i
$867$	−2.76537	+	10.3205i	−0.0939168	+	0.350502i
$868$	−42.4615	+	11.3775i	−1.44124	+	0.386179i
$869$	−0.555585	−	2.07347i	−0.0188469	−	0.0703377i
$870$	7.82071	+	6.04291i	0.265147	+	0.204874i
$871$		0			0
$872$	4.19076	+	4.19076i	0.141917	+	0.141917i
$873$	12.9606	+	7.48283i	0.438651	+	0.253255i
$874$	−3.17277	−	1.83180i	−0.107321	−	0.0619616i
$875$	25.3434	−	32.3476i	0.856764	−	1.09355i
$876$	−3.94269	+	3.94269i	−0.133211	+	0.133211i
$877$	−22.3613	−	38.7309i	−0.755088	−	1.30785i	−0.945331	−	0.326114i	$-0.894261\pi$
$877$	−22.3613	−	38.7309i	−0.755088	−	1.30785i	0.190242	−	0.981737i	$-0.439073\pi$
$878$	3.38094	+	5.85595i	0.114101	+	0.197629i
$879$	−8.80139	+	8.80139i	−0.296863	+	0.296863i
$880$	0.534323	−	3.95580i	0.0180120	−	0.133350i
$881$	18.0323	+	10.4110i	0.607525	+	0.350755i	0.771996	−	0.635627i	$-0.219258\pi$
$881$	18.0323	+	10.4110i	0.607525	+	0.350755i	−0.164471	+	0.986382i	$0.552592\pi$
$882$	−5.89043	−	3.40084i	−0.198341	−	0.114512i
$883$	−5.33747	−	5.33747i	−0.179620	−	0.179620i	0.611570	−	0.791190i	$-0.290538\pi$
$883$	−5.33747	−	5.33747i	−0.179620	−	0.179620i	−0.791190	+	0.611570i	$0.790538\pi$
$884$		0			0
$885$	−2.78302	−	21.7026i	−0.0935502	−	0.729523i
$886$	−1.16837	−	4.36041i	−0.0392521	−	0.146491i
$887$	25.8911	−	6.93749i	0.869337	−	0.232938i	0.203536	−	0.979067i	$-0.434757\pi$
$887$	25.8911	−	6.93749i	0.869337	−	0.232938i	0.665801	+	0.746129i	$0.268090\pi$
$888$	0.828649	−	3.09256i	0.0278077	−	0.103780i
$889$	21.5706	+	21.5706i	0.723454	+	0.723454i
$890$	−3.69669	−	0.499324i	−0.123913	−	0.0167374i
$891$	−0.324464	+	1.21092i	−0.0108700	+	0.0405673i
$892$		−	17.4639i		−	0.584736i
$893$	−20.1531	−	5.40002i	−0.674399	−	0.180705i
$894$	−3.90208	+	6.75861i	−0.130505	+	0.226042i
$895$	−14.1074	+	33.7370i	−0.471557	+	1.12770i
$896$			41.6474i			1.39134i
$897$		0			0
$898$	8.97946	−	8.97946i	0.299648	−	0.299648i
$899$	62.6048	−	16.7749i	2.08799	−	0.559475i
$900$	17.9104	+	4.92835i	0.597014	+	0.164278i
$901$	7.19167	−	4.15211i	0.239589	−	0.138327i
$902$	0.188119			0.00626368
$903$	−6.48562	+	3.74447i	−0.215828	+	0.124608i
$904$	−29.6933	−	7.95630i	−0.987585	−	0.264623i
$905$	5.13044	+	40.0082i	0.170542	+	1.32992i
$906$	−1.08887	−	1.88597i	−0.0361752	−	0.0626572i
$907$	−10.4931	−	39.1608i	−0.348418	−	1.30031i	−0.888568	−	0.458744i	$-0.848299\pi$
$907$	−10.4931	−	39.1608i	−0.348418	−	1.30031i	0.540151	−	0.841568i	$-0.318367\pi$
$908$	−12.8243	+	22.2124i	−0.425590	+	0.737144i
$909$	−31.6707			−1.05045
$910$		0			0
$911$	8.00072			0.265076			0.132538	−	0.991178i	$-0.457687\pi$
$911$	8.00072			0.265076			0.132538	+	0.991178i	$0.457687\pi$
$912$	−6.68546	+	11.5796i	−0.221378	+	0.383437i
$913$	−0.380746	−	1.42096i	−0.0126009	−	0.0470271i
$914$	−0.204360	−	0.353962i	−0.00675963	−	0.0117080i
$915$	−7.96885	+	10.3133i	−0.263442	+	0.340946i
$916$	37.4656	+	10.0389i	1.23790	+	0.331694i
$917$	4.37381	−	2.52522i	0.144436	−	0.0833901i
$918$	5.64189			0.186210
$919$	−1.84237	+	1.06369i	−0.0607741	+	0.0350879i	−0.530079	−	0.847948i	$-0.677838\pi$
$919$	−1.84237	+	1.06369i	−0.0607741	+	0.0350879i	0.469305	+	0.883036i	$0.344504\pi$
$920$	−5.19728	+	2.13235i	−0.171349	+	0.0703014i
$921$	14.0597	−	3.76728i	0.463283	−	0.124136i
$922$	8.40950	−	8.40950i	0.276952	−	0.276952i
$923$		0			0
$924$			4.17405i			0.137316i
$925$	8.84732	+	2.43449i	0.290898	+	0.0800455i
$926$	−1.56954	+	2.71852i	−0.0515782	+	0.0893360i
$927$	9.18601	+	2.46138i	0.301708	+	0.0808425i
$928$		−	47.5087i		−	1.55955i
$929$	−5.15841	+	19.2515i	−0.169242	+	0.631620i	0.828219	+	0.560405i	$0.189354\pi$
$929$	−5.15841	+	19.2515i	−0.169242	+	0.631620i	−0.997461	+	0.0712153i	$0.977312\pi$
$930$	5.62621	−	4.28718i	0.184491	−	0.140582i
$931$	25.2106	+	25.2106i	0.826243	+	0.826243i
$932$	10.6458	−	39.7305i	0.348713	−	1.30142i
$933$	4.85898	−	1.30196i	0.159076	−	0.0426242i
$934$	−2.82369	−	10.5382i	−0.0923940	−	0.344819i
$935$	3.62166	−	0.464422i	0.118441	−	0.0151882i
$936$		0			0
$937$	17.2774	+	17.2774i	0.564427	+	0.564427i	0.930562	−	0.366135i	$-0.119319\pi$
$937$	17.2774	+	17.2774i	0.564427	+	0.564427i	−0.366135	+	0.930562i	$0.619319\pi$
$938$	−19.2545	−	11.1166i	−0.628680	−	0.362969i
$939$	−28.0937	−	16.2199i	−0.916802	−	0.529316i
$940$	−11.8970	+	9.06556i	−0.388039	+	0.295686i
$941$	−24.2129	+	24.2129i	−0.789319	+	0.789319i	−0.981383	−	0.192063i	$-0.938482\pi$
$941$	−24.2129	+	24.2129i	−0.789319	+	0.789319i	0.192063	+	0.981383i	$0.438482\pi$
$942$	−3.24465	−	5.61989i	−0.105716	−	0.183106i
$943$	0.375034	+	0.649578i	0.0122128	+	0.0211532i
$944$	−19.0996	+	19.0996i	−0.621640	+	0.621640i
$945$	−39.1820	−	5.29244i	−1.27459	−	0.172163i
$946$	0.637321	+	0.367957i	0.0207211	+	0.0119633i
$947$	−7.18880	−	4.15045i	−0.233605	−	0.134872i	0.378629	−	0.925548i	$-0.376396\pi$
$947$	−7.18880	−	4.15045i	−0.233605	−	0.134872i	−0.612234	+	0.790677i	$0.709729\pi$
$948$	3.64500	+	3.64500i	0.118384	+	0.118384i
$949$		0			0
$950$	11.6684	+	6.84172i	0.378572	+	0.221975i
$951$	−4.62084	−	17.2452i	−0.149841	−	0.559214i
$952$	−15.6388	+	4.19041i	−0.506857	+	0.135812i
$953$	−1.23858	+	4.62244i	−0.0401215	+	0.149736i	−0.983081	−	0.183173i	$-0.941363\pi$
$953$	−1.23858	+	4.62244i	−0.0401215	+	0.149736i	0.942959	+	0.332908i	$0.108030\pi$
$954$	2.58403	+	2.58403i	0.0836611	+	0.0836611i
$955$	−7.03521	−	9.23255i	−0.227654	−	0.298758i
$956$	9.38573	−	35.0280i	0.303556	−	1.13289i
$957$		−	6.15418i		−	0.198936i
$958$	−4.51481	−	1.20974i	−0.145867	−	0.0390849i
$959$	−22.6550	+	39.2396i	−0.731568	+	1.26711i
$960$	2.17582	+	5.30323i	0.0702241	+	0.171161i
$961$		−	15.3867i		−	0.496346i
$962$		0			0
$963$	22.8178	−	22.8178i	0.735294	−	0.735294i
$964$	5.25650	−	1.40848i	0.169301	−	0.0453639i
$965$	−8.71398	+	20.8390i	−0.280513	+	0.670832i
$966$	2.00216	−	1.15595i	0.0644183	−	0.0371919i
$967$	−8.78782			−0.282597			−0.141299	−	0.989967i	$-0.545128\pi$
$967$	−8.78782			−0.282597			−0.141299	+	0.989967i	$0.545128\pi$
$968$	−16.9127	+	9.76453i	−0.543594	+	0.313844i
$969$	−11.8139	−	3.16552i	−0.379517	−	0.101691i
$970$	7.74880	−	0.993666i	0.248799	−	0.0319047i
$971$	2.71693	+	4.70586i	0.0871905	+	0.151018i	0.906323	−	0.422587i	$-0.138878\pi$
$971$	2.71693	+	4.70586i	0.0871905	+	0.151018i	−0.819132	+	0.573605i	$0.805544\pi$
$972$	−7.33863	−	27.3881i	−0.235387	−	0.878475i
$973$	11.7645	−	20.3766i	0.377151	−	0.653245i
$974$	3.04192			0.0974695
$975$		0			0
$976$	16.0894			0.515010
$977$	−9.33626	+	16.1709i	−0.298693	+	0.517352i	−0.975837	−	0.218499i	$-0.929884\pi$
$977$	−9.33626	+	16.1709i	−0.298693	+	0.517352i	0.677144	+	0.735851i	$0.263217\pi$
$978$	−0.0158643	−	0.0592064i	−0.000507285	−	0.00189321i
$979$	1.16138	+	2.01158i	0.0371180	+	0.0642903i
$980$	25.3521	−	3.25101i	0.809842	−	0.103850i
$981$	6.52865	+	1.74935i	0.208444	+	0.0558524i
$982$	−6.33626	+	3.65824i	−0.202198	+	0.116739i
$983$	−6.62470			−0.211295			−0.105648	−	0.994404i	$-0.533692\pi$
$983$	−6.62470			−0.211295			−0.105648	+	0.994404i	$0.533692\pi$
$984$	−0.836786	+	0.483119i	−0.0266758	+	0.0154013i
$985$	11.2695	−	26.9505i	0.359077	−	0.858715i
$986$	10.7801	−	2.88852i	0.343309	−	0.0919893i
$987$	9.30986	−	9.30986i	0.296336	−	0.296336i
$988$		0			0
$989$			2.93424i			0.0933033i
$990$	0.609904	+	1.48655i	0.0193840	+	0.0472457i
$991$	21.6135	−	37.4357i	0.686576	−	1.18919i	−0.286362	−	0.958121i	$-0.592446\pi$
$991$	21.6135	−	37.4357i	0.686576	−	1.18919i	0.972939	−	0.231064i	$-0.0742206\pi$
$992$	−32.8433	−	8.80033i	−1.04277	−	0.279411i
$993$			6.59853i			0.209398i
$994$	−3.14961	+	11.7545i	−0.0998995	+	0.372830i
$995$	10.6390	+	13.9619i	0.337278	+	0.442621i
$996$	2.49794	+	2.49794i	0.0791504	+	0.0791504i
$997$	11.7001	−	43.6654i	0.370547	−	1.38290i	−0.489197	−	0.872173i	$-0.662710\pi$
$997$	11.7001	−	43.6654i	0.370547	−	1.38290i	0.859744	−	0.510725i	$-0.170623\pi$
$998$	14.2040	−	3.80596i	0.449621	−	0.120476i
$999$	−2.28507	−	8.52799i	−0.0722963	−	0.269814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.o.f.357.3		20
5.3	odd	4		845.2.t.e.188.3		20
13.2	odd	12		845.2.t.f.427.3		20
13.3	even	3		845.2.o.g.587.3		20
13.4	even	6		845.2.k.e.577.6		20
13.5	odd	4		65.2.t.a.7.3	yes	20
13.6	odd	12		845.2.f.e.437.6		20
13.7	odd	12		845.2.f.d.437.5		20
13.8	odd	4		845.2.t.g.657.3		20
13.9	even	3		845.2.k.d.577.5		20
13.10	even	6		65.2.o.a.2.3	✓	20
13.11	odd	12		845.2.t.e.427.3		20
13.12	even	2		845.2.o.e.357.3		20
39.5	even	4		585.2.dp.a.397.3		20
39.23	odd	6		585.2.cf.a.262.3		20
65.3	odd	12		845.2.t.g.418.3		20
65.8	even	4		845.2.o.g.488.3		20
65.18	even	4		65.2.o.a.33.3	yes	20
65.23	odd	12		65.2.t.a.28.3	yes	20
65.28	even	12		845.2.o.e.258.3		20
65.33	even	12		845.2.k.d.268.5		20
65.38	odd	4		845.2.t.f.188.3		20
65.43	odd	12		845.2.f.e.408.5		20
65.44	odd	4		325.2.x.b.7.3		20
65.48	odd	12		845.2.f.d.408.6		20
65.49	even	6		325.2.s.b.132.3		20
65.57	even	4		325.2.s.b.293.3		20
65.58	even	12		845.2.k.e.268.6		20
65.62	odd	12		325.2.x.b.93.3		20
65.63	even	12	inner	845.2.o.f.258.3		20
195.23	even	12		585.2.dp.a.28.3		20
195.83	odd	4		585.2.cf.a.163.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.3	✓	20	13.10	even	6
65.2.o.a.33.3	yes	20	65.18	even	4
65.2.t.a.7.3	yes	20	13.5	odd	4
65.2.t.a.28.3	yes	20	65.23	odd	12
325.2.s.b.132.3		20	65.49	even	6
325.2.s.b.293.3		20	65.57	even	4
325.2.x.b.7.3		20	65.44	odd	4
325.2.x.b.93.3		20	65.62	odd	12
585.2.cf.a.163.3		20	195.83	odd	4
585.2.cf.a.262.3		20	39.23	odd	6
585.2.dp.a.28.3		20	195.23	even	12
585.2.dp.a.397.3		20	39.5	even	4
845.2.f.d.408.6		20	65.48	odd	12
845.2.f.d.437.5		20	13.7	odd	12
845.2.f.e.408.5		20	65.43	odd	12
845.2.f.e.437.6		20	13.6	odd	12
845.2.k.d.268.5		20	65.33	even	12
845.2.k.d.577.5		20	13.9	even	3
845.2.k.e.268.6		20	65.58	even	12
845.2.k.e.577.6		20	13.4	even	6
845.2.o.e.258.3		20	65.28	even	12
845.2.o.e.357.3		20	13.12	even	2
845.2.o.f.258.3		20	65.63	even	12	inner
845.2.o.f.357.3		20	1.1	even	1	trivial
845.2.o.g.488.3		20	65.8	even	4
845.2.o.g.587.3		20	13.3	even	3
845.2.t.e.188.3		20	5.3	odd	4
845.2.t.e.427.3		20	13.11	odd	12
845.2.t.f.188.3		20	65.38	odd	4
845.2.t.f.427.3		20	13.2	odd	12
845.2.t.g.418.3		20	65.3	odd	12
845.2.t.g.657.3		20	13.8	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.o (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.246951 - 0.427732i) q^{2} +(-0.243392 - 0.908353i) q^{3} +(0.878030 + 1.52079i) q^{4} +(2.21791 - 0.284413i) q^{5} +(-0.448637 - 0.120212i) q^{6} +(3.18307 - 1.83775i) q^{7} +1.85513 q^{8} +(1.83221 - 1.05783i) q^{9} +(0.426062 - 1.01890i) q^{10} +(-0.664257 + 0.177987i) q^{11} +(1.16771 - 1.16771i) q^{12} -1.81533i q^{14} +(-0.798168 - 1.94542i) q^{15} +(-1.29794 + 2.24809i) q^{16} +(-2.29359 - 0.614565i) q^{17} -1.04493i q^{18} +(-1.41763 + 5.29067i) q^{19} +(2.37992 + 3.12325i) q^{20} +(-2.44406 - 2.44406i) q^{21} +(-0.0879082 + 0.328078i) q^{22} +(-1.30811 + 0.350507i) q^{23} +(-0.451523 - 1.68511i) q^{24} +(4.83822 - 1.26160i) q^{25} +(-3.40171 - 3.40171i) q^{27} +(5.58966 + 3.22719i) q^{28} +(-8.24134 - 4.75814i) q^{29} +(-1.02922 - 0.139021i) q^{30} +(-4.81595 + 4.81595i) q^{31} +(2.49618 + 4.32351i) q^{32} +(0.323350 + 0.560059i) q^{33} +(-0.829273 + 0.829273i) q^{34} +(6.53707 - 4.98125i) q^{35} +(3.21748 + 1.85761i) q^{36} +(1.58936 + 0.917615i) q^{37} +(1.91290 + 1.91290i) q^{38} +(4.11449 - 0.527621i) q^{40} +(-0.143350 - 0.534988i) q^{41} +(-1.64896 + 0.441838i) q^{42} +(0.560778 - 2.09285i) q^{43} +(-0.853919 - 0.853919i) q^{44} +(3.76281 - 2.86727i) q^{45} +(-0.173116 + 0.646078i) q^{46} +3.80918i q^{47} +(2.35797 + 0.631815i) q^{48} +(3.25462 - 5.63717i) q^{49} +(0.655176 - 2.38101i) q^{50} +2.23297i q^{51} +(-2.47293 + 2.47293i) q^{53} +(-2.29507 + 0.614963i) q^{54} +(-1.42264 + 0.583682i) q^{55} +(5.90499 - 3.40925i) q^{56} +5.15084 q^{57} +(-4.07041 + 2.35005i) q^{58} +(10.0508 + 2.69310i) q^{59} +(2.25776 - 2.92199i) q^{60} +(-3.09904 - 5.36770i) q^{61} +(0.870630 + 3.24924i) q^{62} +(3.88804 - 6.73428i) q^{63} -2.72601 q^{64} +0.319406 q^{66} +(6.12371 - 10.6066i) q^{67} +(-1.07921 - 4.02768i) q^{68} +(0.636768 + 1.10291i) q^{69} +(-0.516303 - 4.02624i) q^{70} +(-6.47512 - 1.73500i) q^{71} +(3.39898 - 1.96240i) q^{72} -3.37642 q^{73} +(0.784986 - 0.453212i) q^{74} +(-2.32356 - 4.08774i) q^{75} +(-9.29074 + 2.48945i) q^{76} +(-1.78728 + 1.78728i) q^{77} +3.12149i q^{79} +(-2.23932 + 5.35521i) q^{80} +(0.911483 - 1.57873i) q^{81} +(-0.264231 - 0.0708006i) q^{82} +2.13918i q^{83} +(1.57095 - 5.86286i) q^{84} +(-5.26175 - 0.710723i) q^{85} +(-0.756694 - 0.756694i) q^{86} +(-2.31619 + 8.64414i) q^{87} +(-1.23228 + 0.330188i) q^{88} +(-0.874198 - 3.26255i) q^{89} +(-0.297190 - 2.31755i) q^{90} +(-1.68161 - 1.68161i) q^{92} +(5.54675 + 3.20242i) q^{93} +(1.62931 + 0.940681i) q^{94} +(-1.63944 + 12.1374i) q^{95} +(3.31972 - 3.31972i) q^{96} +(3.53688 + 6.12606i) q^{97} +(-1.60746 - 2.78421i) q^{98} +(-1.02878 + 1.02878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{5} - 4 q^{6} - 6 q^{7} - 12 q^{8} + 12 q^{9} + 2 q^{10} - 8 q^{11} + 24 q^{12} - 12 q^{15} - 2 q^{16} - 4 q^{17} + 16 q^{19} - 8 q^{20} - 4 q^{21} + 16 q^{22} + 10 q^{23}+ \cdots + 60 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 - 2 * q^3 - 6 * q^4 + 6 * q^5 - 4 * q^6 - 6 * q^7 - 12 * q^8 + 12 * q^9 + 2 * q^10 - 8 * q^11 + 24 * q^12 - 12 * q^15 - 2 * q^16 - 4 * q^17 + 16 * q^19 - 8 * q^20 - 4 * q^21 + 16 * q^22 + 10 * q^23 - 28 * q^24 - 18 * q^25 + 4 * q^27 + 6 * q^28 + 26 * q^30 + 6 * q^32 + 18 * q^33 + 2 * q^34 + 40 * q^35 - 36 * q^36 + 42 * q^37 + 8 * q^38 - 16 * q^40 - 28 * q^41 + 40 * q^42 - 10 * q^43 - 36 * q^44 + 32 * q^45 + 8 * q^46 - 56 * q^48 - 18 * q^49 - 8 * q^50 - 10 * q^53 + 12 * q^54 - 10 * q^55 + 12 * q^57 - 90 * q^58 + 8 * q^59 + 92 * q^60 - 16 * q^61 + 44 * q^62 + 32 * q^63 - 20 * q^64 - 32 * q^66 + 58 * q^67 + 22 * q^68 + 16 * q^69 - 32 * q^70 - 56 * q^71 - 66 * q^72 - 72 * q^73 + 18 * q^74 + 38 * q^75 - 80 * q^76 + 28 * q^77 - 68 * q^80 - 14 * q^81 - 56 * q^82 + 32 * q^84 - 6 * q^85 - 60 * q^86 - 34 * q^87 - 82 * q^88 - 6 * q^89 - 46 * q^90 - 8 * q^92 + 48 * q^93 - 48 * q^94 + 26 * q^95 - 56 * q^96 + 22 * q^97 - 4 * q^98 + 60 * q^99

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