LMFDB - Embedded newform 845.2.o.g.587.3

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,-6,6,8] 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			587.3
Root			$0.493902i$ of defining polynomial
Character	$\chi$	$=$	845.587
Dual form			845.2.o.g.488.3

$q$-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} +(0.908353 + 0.243392i) q^{3} +(0.878030 - 1.52079i) q^{4} +(2.21791 - 0.284413i) q^{5} +(0.120212 + 0.448637i) q^{6} +(-3.18307 - 1.83775i) q^{7} +1.85513 q^{8} +(-1.83221 - 1.05783i) q^{9} +(0.669366 + 0.878433i) q^{10} +(0.177987 - 0.664257i) q^{11} +(1.16771 - 1.16771i) q^{12} -1.81533i q^{14} +(2.08387 + 0.281475i) q^{15} +(-1.29794 - 2.24809i) q^{16} +(0.614565 + 2.29359i) q^{17} -1.04493i q^{18} +(5.29067 - 1.41763i) q^{19} +(1.51486 - 3.62270i) q^{20} +(-2.44406 - 2.44406i) q^{21} +(0.328078 - 0.0879082i) q^{22} +(0.350507 - 1.30811i) q^{23} +(1.68511 + 0.451523i) 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} +(0.394217 + 0.960845i) 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} +(-7.58243 - 3.17064i) 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} +(0.534988 + 0.143350i) q^{41} +(0.441838 - 1.64896i) q^{42} +(-2.09285 + 0.560778i) q^{43} +(-0.853919 - 0.853919i) q^{44} +(-4.36453 - 1.82506i) q^{45} +(0.646078 - 0.173116i) q^{46} +3.80918i q^{47} +(-0.631815 - 2.35797i) q^{48} +(3.25462 + 5.63717i) q^{49} +(1.73443 + 1.75791i) q^{50} +2.23297i q^{51} +(-2.47293 + 2.47293i) q^{53} +(0.614963 - 2.29507i) q^{54} +(0.205836 - 1.52388i) q^{55} +(-5.90499 - 3.40925i) q^{56} +5.15084 q^{57} +(4.07041 + 2.35005i) q^{58} +(-2.69310 - 10.0508i) q^{59} +(2.25776 - 2.92199i) q^{60} +(-3.09904 + 5.36770i) q^{61} +(-3.24924 - 0.870630i) q^{62} +(3.88804 + 6.73428i) q^{63} -2.72601 q^{64} +0.319406 q^{66} +(6.12371 + 10.6066i) q^{67} +(4.02768 + 1.07921i) q^{68} +(0.636768 - 1.10291i) q^{69} +(-0.516303 - 4.02624i) q^{70} +(1.73500 + 6.47512i) q^{71} +(-3.39898 - 1.96240i) q^{72} -3.37642 q^{73} +(-0.784986 - 0.453212i) q^{74} +(4.70187 + 0.0316067i) q^{75} +(2.48945 - 9.29074i) q^{76} +(-1.78728 + 1.78728i) q^{77} +3.12149i q^{79} +(-3.51809 - 4.61691i) q^{80} +(0.911483 + 1.57873i) q^{81} +(0.0708006 + 0.264231i) q^{82} +2.13918i q^{83} +(-5.86286 + 1.57095i) q^{84} +(2.01537 + 4.91217i) q^{85} +(-0.756694 - 0.756694i) q^{86} +(8.64414 - 2.31619i) q^{87} +(0.330188 - 1.23228i) q^{88} +(3.26255 + 0.874198i) 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} +(11.3310 - 4.64891i) 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} + 8 q^{6} + 6 q^{7} - 12 q^{8} - 12 q^{9} - 10 q^{10} + 16 q^{11} + 24 q^{12} - 12 q^{15} - 2 q^{16} - 10 q^{17} - 20 q^{19} - 14 q^{20} - 4 q^{21} + 16 q^{22}+ \cdots + 60 q^{99}+O(q^{100}) $ 20 * q + 4 * q^2 - 2 * q^3 - 6 * q^4 + 6 * q^5 + 8 * q^6 + 6 * q^7 - 12 * q^8 - 12 * q^9 - 10 * q^10 + 16 * q^11 + 24 * q^12 - 12 * q^15 - 2 * q^16 - 10 * q^17 - 20 * q^19 - 14 * q^20 - 4 * q^21 + 16 * q^22 - 2 * q^23 + 32 * q^24 - 18 * q^25 + 4 * q^27 - 6 * q^28 + 14 * q^30 + 6 * q^32 + 18 * q^33 + 2 * q^34 - 20 * q^35 + 36 * q^36 - 42 * q^37 + 8 * q^38 - 16 * q^40 - 10 * q^41 - 56 * q^42 - 22 * q^43 - 36 * q^44 - 52 * q^45 - 4 * q^46 + 28 * q^48 - 18 * q^49 - 44 * q^50 - 10 * q^53 - 48 * q^54 + 26 * q^55 + 12 * q^57 + 90 * q^58 - 16 * q^59 + 92 * q^60 - 16 * q^61 - 40 * q^62 + 32 * q^63 - 20 * q^64 - 32 * q^66 + 58 * q^67 + 28 * q^68 + 16 * q^69 - 32 * q^70 + 16 * q^71 + 66 * q^72 - 72 * q^73 - 18 * q^74 - 34 * q^75 + 64 * q^76 + 28 * q^77 + 34 * q^80 - 14 * q^81 + 22 * q^82 - 40 * q^84 + 6 * q^85 - 60 * q^86 + 62 * q^87 + 50 * q^88 - 6 * q^89 - 46 * q^90 - 8 * q^92 - 48 * q^93 + 48 * q^94 + 14 * 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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

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

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	0.940030	−	0.341092i	$-0.110797\pi$
$2$	0.246951	+	0.427732i	0.174621	+	0.302452i	−0.765409	+	0.643544i	$0.777463\pi$
$3$	0.908353	+	0.243392i	0.524438	+	0.140523i	0.511318	−	0.859391i	$-0.329157\pi$
$3$	0.908353	+	0.243392i	0.524438	+	0.140523i	0.0131191	+	0.999914i	$0.495824\pi$
$4$	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
$6$	0.120212	+	0.448637i	0.0490763	+	0.183155i
$7$	−3.18307	−	1.83775i	−1.20309	−	0.694603i	−0.241847	−	0.970314i	$-0.577753\pi$
$7$	−3.18307	−	1.83775i	−1.20309	−	0.694603i	−0.961240	+	0.275712i	$0.911086\pi$
$8$	1.85513			0.655886
$9$	−1.83221	−	1.05783i	−0.610737	−	0.352609i
$10$	0.669366	+	0.878433i	0.211672	+	0.277785i
$11$	0.177987	−	0.664257i	0.0536651	−	0.200281i	−0.933888	−	0.357565i	$-0.883607\pi$
$11$	0.177987	−	0.664257i	0.0536651	−	0.200281i	0.987553	+	0.157284i	$0.0502738\pi$
$12$	1.16771	−	1.16771i	0.337089	−	0.337089i
$13$		0			0
$13$		0			0
$14$		−	1.81533i		−	0.485168i
$15$	2.08387	+	0.281475i	0.538052	+	0.0726764i
$16$	−1.29794	−	2.24809i	−0.324484	−	0.562023i
$17$	0.614565	+	2.29359i	0.149054	+	0.556277i	0.999541	+	0.0302815i	$0.00964039\pi$
$17$	0.614565	+	2.29359i	0.149054	+	0.556277i	−0.850487	+	0.525995i	$0.823693\pi$
$18$		−	1.04493i		−	0.246291i
$19$	5.29067	−	1.41763i	1.21376	−	0.325227i	0.405526	−	0.914084i	$-0.367088\pi$
$19$	5.29067	−	1.41763i	1.21376	−	0.325227i	0.808238	+	0.588857i	$0.200422\pi$
$20$	1.51486	−	3.62270i	0.338732	−	0.810060i
$21$	−2.44406	−	2.44406i	−0.533337	−	0.533337i
$22$	0.328078	−	0.0879082i	0.0699464	−	0.0187421i
$23$	0.350507	−	1.30811i	0.0730858	−	0.272760i	−0.919707	−	0.392606i	$-0.871574\pi$
$23$	0.350507	−	1.30811i	0.0730858	−	0.272760i	0.992792	+	0.119846i	$0.0382402\pi$
$24$	1.68511	+	0.451523i	0.343971	+	0.0921668i
$25$	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	0.531034	−	0.847350i	$-0.321803\pi$
$29$	8.24134	−	4.75814i	1.53038	−	0.883564i	0.999344	−	0.0362142i	$-0.0115299\pi$
$30$	0.394217	+	0.960845i	0.0719738	+	0.175426i
$31$	−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
$35$	−7.58243	−	3.17064i	−1.28166	−	0.535937i
$36$	−3.21748	+	1.85761i	−0.536246	+	0.309602i
$37$	−1.58936	+	0.917615i	−0.261289	+	0.150855i	−0.624922	−	0.780687i	$-0.714869\pi$
$37$	−1.58936	+	0.917615i	−0.261289	+	0.150855i	0.363634	+	0.931542i	$0.381536\pi$
$38$	1.91290	+	1.91290i	0.310314	+	0.310314i
$39$		0			0
$40$	4.11449	−	0.527621i	0.650559	−	0.0834242i
$41$	0.534988	+	0.143350i	0.0835510	+	0.0223874i	0.300352	−	0.953828i	$-0.402896\pi$
$41$	0.534988	+	0.143350i	0.0835510	+	0.0223874i	−0.216801	+	0.976216i	$0.569562\pi$
$42$	0.441838	−	1.64896i	0.0681771	−	0.254440i
$43$	−2.09285	+	0.560778i	−0.319157	+	0.0855178i	−0.414841	−	0.909894i	$-0.636163\pi$
$43$	−2.09285	+	0.560778i	−0.319157	+	0.0855178i	0.0956841	+	0.995412i	$0.469496\pi$
$44$	−0.853919	−	0.853919i	−0.128733	−	0.128733i
$45$	−4.36453	−	1.82506i	−0.650626	−	0.272064i
$46$	0.646078	−	0.173116i	0.0952590	−	0.0255246i
$47$			3.80918i			0.555626i	0.960635	+	0.277813i	$0.0896096\pi$
$47$			3.80918i			0.555626i	−0.960635	+	0.277813i	$0.910390\pi$
$48$	−0.631815	−	2.35797i	−0.0911947	−	0.340343i
$49$	3.25462	+	5.63717i	0.464946	+	0.805310i
$50$	1.73443	+	1.75791i	0.245285	+	0.248605i
$51$			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	$0.327211\pi$
$54$	0.614963	−	2.29507i	0.0836858	−	0.312320i
$55$	0.205836	−	1.52388i	0.0277549	−	0.205480i
$56$	−5.90499	−	3.40925i	−0.789088	−	0.455580i
$57$	5.15084			0.682245
$58$	4.07041	+	2.35005i	0.534471	+	0.308577i
$59$	−2.69310	−	10.0508i	−0.350612	−	1.30850i	−0.885917	−	0.463844i	$-0.846470\pi$
$59$	−2.69310	−	10.0508i	−0.350612	−	1.30850i	0.535305	−	0.844659i	$-0.320197\pi$
$60$	2.25776	−	2.92199i	0.291476	−	0.377227i
$61$	−3.09904	+	5.36770i	−0.396792	+	0.687263i	−0.993328	−	0.115323i	$-0.963210\pi$
$61$	−3.09904	+	5.36770i	−0.396792	+	0.687263i	0.596536	+	0.802586i	$0.296543\pi$
$62$	−3.24924	−	0.870630i	−0.412653	−	0.110570i
$63$	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	0.948718	+	0.316124i	$0.102381\pi$
$67$	6.12371	+	10.6066i	0.748130	+	1.29580i	−0.200588	+	0.979676i	$0.564285\pi$
$68$	4.02768	+	1.07921i	0.488428	+	0.130874i
$69$	0.636768	−	1.10291i	0.0766579	−	0.132775i
$70$	−0.516303	−	4.02624i	−0.0617101	−	0.481227i
$71$	1.73500	+	6.47512i	0.205907	+	0.768456i	0.989171	+	0.146767i	$0.0468866\pi$
$71$	1.73500	+	6.47512i	0.205907	+	0.768456i	−0.783264	+	0.621689i	$0.786447\pi$
$72$	−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
$75$	4.70187	+	0.0316067i	0.542926	+	0.00364963i
$76$	2.48945	−	9.29074i	0.285559	−	1.06572i
$77$	−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	$0.943814\pi$
$80$	−3.51809	−	4.61691i	−0.393334	−	0.516186i
$81$	0.911483	+	1.57873i	0.101276	+	0.175415i
$82$	0.0708006	+	0.264231i	0.00781862	+	0.0291795i
$83$			2.13918i			0.234805i	0.993084	+	0.117403i	$0.0374568\pi$
$83$			2.13918i			0.234805i	−0.993084	+	0.117403i	$0.962543\pi$
$84$	−5.86286	+	1.57095i	−0.639691	+	0.171405i
$85$	2.01537	+	4.91217i	0.218598	+	0.532800i
$86$	−0.756694	−	0.756694i	−0.0815964	−	0.0815964i
$87$	8.64414	−	2.31619i	0.926749	−	0.248322i
$88$	0.330188	−	1.23228i	0.0351982	−	0.131361i
$89$	3.26255	+	0.874198i	0.345830	+	0.0926648i	0.427553	−	0.903990i	$-0.359376\pi$
$89$	3.26255	+	0.874198i	0.345830	+	0.0926648i	−0.0817233	+	0.996655i	$0.526042\pi$
$90$	−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
$95$	11.3310	−	4.64891i	1.16254	−	0.476968i
$96$	3.31972	−	3.31972i	0.338817	−	0.338817i
$97$	3.53688	−	6.12606i	0.359116	−	0.622007i	−0.628697	−	0.777650i	$-0.716412\pi$
$97$	3.53688	−	6.12606i	0.359116	−	0.622007i	0.987813	+	0.155643i	$0.0497449\pi$
$98$	−1.60746	+	2.78421i	−0.162378	+	0.281248i
$99$	−1.02878	+	1.02878i	−0.103396	+	0.103396i
$100$	2.32947	−	8.46566i	0.232947	−	0.846566i
$101$	12.9641	−	7.48483i	1.28998	−	0.744769i	0.311327	−	0.950303i	$-0.399226\pi$
$101$	12.9641	−	7.48483i	1.28998	−	0.744769i	0.978650	+	0.205534i	$0.0658932\pi$
$102$	−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
$106$	−1.66844	−	0.447058i	−0.162054	−	0.0434221i
$107$	−3.94767	+	14.7329i	−0.381635	+	1.42428i	0.461767	+	0.887001i	$0.347216\pi$
$107$	−3.94767	+	14.7329i	−0.381635	+	1.42428i	−0.843403	+	0.537282i	$0.819451\pi$
$108$	−8.16010	+	2.18649i	−0.785206	+	0.210395i
$109$	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	$0.701107\pi$
$110$	0.702643	−	0.288282i	0.0669944	−	0.0274866i
$111$	−1.66704	+	0.446681i	−0.158228	+	0.0423971i
$112$			9.54111i			0.901550i
$113$	4.28882	+	16.0061i	0.403458	+	1.50573i	0.806881	+	0.590713i	$0.201154\pi$
$113$	4.28882	+	16.0061i	0.403458	+	1.50573i	−0.403423	+	0.915014i	$0.632180\pi$
$114$	1.27200	+	2.20318i	0.119134	+	0.206346i
$115$	0.405349	−	3.00096i	0.0377990	−	0.279841i
$116$		−	16.7112i		−	1.55159i
$117$		0			0
$118$	3.63398	−	3.63398i	0.334535	−	0.334535i
$119$	2.25883	−	8.43007i	0.207067	−	0.772783i
$120$	3.86583	+	0.522171i	0.352900	+	0.0476674i
$121$	9.11672	+	5.26354i	0.828793	+	0.478504i
$122$	−3.06124			−0.277152
$123$	0.451067	+	0.260424i	0.0406714	+	0.0234816i
$124$	3.09551	+	11.5526i	0.277985	+	1.03746i
$125$	10.3719	−	4.17416i	0.927691	−	0.373349i
$126$	−1.92031	+	3.32607i	−0.171075	+	0.296310i
$127$	−8.01688	−	2.14812i	−0.711383	−	0.190614i	−0.115059	−	0.993359i	$-0.536706\pi$
$127$	−8.01688	−	2.14812i	−0.711383	−	0.190614i	−0.596324	+	0.802744i	$0.703372\pi$
$128$	−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
$133$	−19.4458	−	5.21049i	−1.68617	−	0.451807i
$134$	−3.02451	+	5.23861i	−0.261278	+	0.452547i
$135$	−8.51216	−	6.57718i	−0.732610	−	0.566074i
$136$	1.14010	+	4.25489i	0.0977624	+	0.364854i
$137$	10.6760	+	6.16380i	0.912114	+	0.526609i	0.881111	−	0.472910i	$-0.156797\pi$
$137$	10.6760	+	6.16380i	0.912114	+	0.526609i	0.0310029	+	0.999519i	$0.490130\pi$
$138$	0.629002			0.0535442
$139$	−5.54392	−	3.20078i	−0.470229	−	0.271487i	0.246107	−	0.969243i	$-0.420849\pi$
$139$	−5.54392	−	3.20078i	−0.470229	−	0.271487i	−0.716336	+	0.697756i	$0.754182\pi$
$140$	−11.4795	+	8.74739i	−0.970195	+	0.739289i
$141$	−0.927126	+	3.46008i	−0.0780781	+	0.291391i
$142$	−2.34115	+	2.34115i	−0.196465	+	0.196465i
$143$		0			0
$144$			5.49197i			0.457664i
$145$	16.9252	−	12.8971i	1.40557	−	1.07104i
$146$	−0.833811	−	1.44420i	−0.0690067	−	0.119523i
$147$	1.58430	+	5.91269i	0.130671	+	0.487670i
$148$			3.22278i			0.264911i
$149$	−16.2300	+	4.34882i	−1.32961	+	0.356269i	−0.852571	−	0.522611i	$-0.824958\pi$
$149$	−16.2300	+	4.34882i	−1.32961	+	0.356269i	−0.477043	+	0.878880i	$0.658291\pi$
$150$	1.14761	+	2.01894i	0.0937022	+	0.164846i
$151$	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	$0.688898\pi$
$152$	9.81486	−	2.62988i	0.796090	−	0.213312i
$153$	1.30021	−	4.85244i	0.105116	−	0.392297i
$154$	−1.20585	−	0.323106i	−0.0971699	−	0.0260366i
$155$	−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
$160$	4.30663	−	10.2991i	0.340469	−	0.814214i
$161$	−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	−0.863430	−	0.504469i	$-0.831688\pi$
$163$	0.0659848	−	0.114289i	0.00516833	−	0.00895180i	0.868598	+	0.495517i	$0.165022\pi$
$164$	0.687741	−	0.687741i	0.0537035	−	0.0537035i
$165$	0.557872	−	1.33412i	0.0434303	−	0.103861i
$166$	−0.914995	+	0.528272i	−0.0710174	+	0.0410019i
$167$	−18.7380	+	10.8184i	−1.44999	+	0.837152i	−0.998480	−	0.0551149i	$-0.982447\pi$
$167$	−18.7380	+	10.8184i	−1.44999	+	0.837152i	−0.451509	+	0.892267i	$0.649114\pi$
$168$	−4.53403	−	4.53403i	−0.349808	−	0.349808i
$169$		0			0
$170$	−1.60339	+	2.07510i	−0.122975	+	0.159153i
$171$	−11.1932	−	2.99922i	−0.855969	−	0.229356i
$172$	−0.984760	+	3.67518i	−0.0750873	+	0.280230i
$173$	−7.47013	+	2.00162i	−0.567943	+	0.152180i	−0.531353	−	0.847150i	$-0.678316\pi$
$173$	−7.47013	+	2.00162i	−0.567943	+	0.152180i	−0.0365902	+	0.999330i	$0.511650\pi$
$174$	3.12539	+	3.12539i	0.236935	+	0.236935i
$175$	−17.7189	−	4.87565i	−1.33942	−	0.368565i
$176$	−1.72433	+	0.462032i	−0.129976	+	0.0348270i
$177$		−	9.78515i		−	0.735497i
$178$	0.431768	+	1.61138i	0.0323624	+	0.120778i
$179$	−8.17681	−	14.1627i	−0.611164	−	1.05857i	−0.991045	−	0.133531i	$-0.957368\pi$
$179$	−8.17681	−	14.1627i	−0.611164	−	1.05857i	0.379881	−	0.925035i	$-0.375965\pi$
$180$	−6.60773	+	5.03510i	−0.492511	+	0.375294i
$181$			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
$184$	0.650235	−	2.42671i	0.0479359	−	0.178899i
$185$	−3.26406	+	2.48722i	−0.239979	+	0.182864i
$186$	−2.73955	−	1.58168i	−0.200873	−	0.115974i
$187$	1.63292			0.119411
$188$	5.79298	+	3.34458i	0.422496	+	0.243928i
$189$	4.57640	+	17.0793i	0.332884	+	1.24234i
$190$	4.78669	+	3.69858i	0.347263	+	0.268324i
$191$	−2.59552	+	4.49557i	−0.187805	+	0.325288i	−0.944518	−	0.328459i	$-0.893471\pi$
$191$	−2.59552	+	4.49557i	−0.187805	+	0.325288i	0.756713	+	0.653747i	$0.226804\pi$
$192$	−2.47618	−	0.663490i	−0.178703	−	0.0478833i
$193$	−5.05073	−	8.74813i	−0.363560	−	0.629704i	0.624984	−	0.780637i	$-0.285105\pi$
$193$	−5.05073	−	8.74813i	−0.363560	−	0.629704i	−0.988544	+	0.150934i	$0.951772\pi$
$194$	3.49375			0.250836
$195$		0			0
$196$	11.4306			0.816473
$197$	6.53197	+	11.3137i	0.465384	+	0.806068i	0.999219	−	0.0395205i	$-0.0125831\pi$
$197$	6.53197	+	11.3137i	0.465384	+	0.806068i	−0.533835	+	0.845589i	$0.679250\pi$
$198$	−0.694099	−	0.185983i	−0.0493275	−	0.0132173i
$199$	3.92506	−	6.79840i	0.278240	−	0.481926i	−0.692707	−	0.721219i	$-0.743582\pi$
$199$	3.92506	−	6.79840i	0.278240	−	0.481926i	0.970947	+	0.239293i	$0.0769156\pi$
$200$	8.97550	−	2.34043i	0.634664	−	0.165493i
$201$	2.98093	+	11.1250i	0.210258	+	0.784695i
$202$	6.40300	+	3.69677i	0.450513	+	0.260104i
$203$	−34.9770			−2.45491
$204$	3.39588	+	1.96061i	0.237759	+	0.137270i
$205$	1.22732	+	0.165779i	0.0857200	+	0.0115785i
$206$	−0.574613	+	2.14448i	−0.0400352	+	0.149413i
$207$	−2.02596	+	2.02596i	−0.140814	+	0.140814i
$208$		0			0
$209$		−	3.76669i		−	0.260547i
$210$	0.510970	−	3.78291i	0.0352603	−	0.261045i
$211$	−6.21205	−	10.7596i	−0.427655	−	0.740720i	0.569009	−	0.822331i	$-0.307327\pi$
$211$	−6.21205	−	10.7596i	−0.427655	−	0.740720i	−0.996664	+	0.0816108i	$0.973994\pi$
$212$	1.58951	+	5.93213i	0.109168	+	0.407420i
$213$			6.30398i			0.431942i
$214$	−7.27661	+	1.94976i	−0.497419	+	0.133283i
$215$	−4.48226	+	1.83899i	−0.305687	+	0.125418i
$216$	−6.31059	−	6.31059i	−0.429382	−	0.429382i
$217$	24.1800	−	6.47901i	1.64145	−	0.439824i
$218$	−0.408387	+	1.52412i	−0.0276594	+	0.103226i
$219$	−3.06698	−	0.821796i	−0.207248	−	0.0555318i
$220$	−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	$-0.558612\pi$
$223$	8.61258	−	4.97247i	0.576741	−	0.332981i	0.759837	+	0.650114i	$0.225279\pi$
$224$	−15.8910	+	9.17468i	−1.06176	+	0.613009i
$225$	−10.1992	−	2.80648i	−0.679946	−	0.187099i
$226$	−5.78718	+	5.78718i	−0.384958	+	0.384958i
$227$	7.30290	−	12.6490i	0.484710	−	0.839543i	−0.515135	−	0.857109i	$-0.672258\pi$
$227$	7.30290	−	12.6490i	0.484710	−	0.839543i	0.999846	+	0.0175659i	$0.00559170\pi$
$228$	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	$-0.0103853\pi$
$230$	1.38370	−	0.567708i	0.0912388	−	0.0374336i
$231$	−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
$236$	−17.6498	−	4.72926i	−1.14891	−	0.307848i
$237$	−0.759747	+	2.83541i	−0.0493509	+	0.184180i
$238$	4.16362	−	1.11564i	0.269888	−	0.0723162i
$239$	−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	$0.982801\pi$
$240$	−2.07194	−	5.05005i	−0.133743	−	0.325980i
$241$	−2.99335	+	0.802065i	−0.192818	+	0.0516656i	−0.353936	−	0.935270i	$-0.615157\pi$
$241$	−2.99335	+	0.802065i	−0.192818	+	0.0516656i	0.161117	+	0.986935i	$0.448490\pi$
$242$			5.19935i			0.334227i
$243$	4.17903	+	15.5964i	0.268085	+	1.00051i
$244$	5.44211	+	9.42600i	0.348395	+	0.603438i
$245$	8.82173	+	11.5771i	0.563600	+	0.739631i
$246$			0.257248i			0.0164015i
$247$		0			0
$248$	−8.93419	+	8.93419i	−0.567322	+	0.567322i
$249$	−0.520660	+	1.94313i	−0.0329955	+	0.123141i
$250$	4.34677	+	3.40558i	0.274914	+	0.215388i
$251$	−25.5728	−	14.7645i	−1.61414	−	0.931925i	−0.988396	−	0.151897i	$-0.951462\pi$
$251$	−25.5728	−	14.7645i	−1.61414	−	0.931925i	−0.625745	−	0.780028i	$-0.715205\pi$
$252$	13.6553			0.860201
$253$	−0.806536	−	0.465654i	−0.0507065	−	0.0292754i
$254$	−1.06096	−	3.95955i	−0.0665704	−	0.248444i
$255$	0.635084	+	4.95251i	0.0397705	+	0.310138i
$256$	0.0722145	−	0.125079i	0.00451341	−	0.00781745i
$257$	−6.92097	−	1.85447i	−0.431718	−	0.115679i	0.0364143	−	0.999337i	$-0.488406\pi$
$257$	−6.92097	−	1.85447i	−0.431718	−	0.115679i	−0.468133	+	0.883658i	$0.655073\pi$
$258$	−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
$263$	13.0066	+	3.48511i	0.802023	+	0.214901i	0.636472	−	0.771300i	$-0.280393\pi$
$263$	13.0066	+	3.48511i	0.802023	+	0.214901i	0.165551	+	0.986201i	$0.447060\pi$
$264$	0.599855	−	1.03898i	0.0369185	−	0.0639448i
$265$	−4.78140	+	6.18807i	−0.293719	+	0.380130i
$266$	−2.57347	−	9.60433i	−0.157790	−	0.588879i
$267$	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	$-0.253873\pi$
$269$	7.01806	+	4.05188i	0.427899	+	0.247047i	−0.270552	+	0.962705i	$0.587206\pi$
$270$	0.711183	−	5.26516i	0.0432812	−	0.320427i
$271$	2.38026	−	8.88325i	0.144590	−	0.539619i	−0.855183	−	0.518326i	$-0.826555\pi$
$271$	2.38026	−	8.88325i	0.144590	−	0.539619i	0.999773	−	0.0212923i	$-0.00677808\pi$
$272$	4.35853	−	4.35853i	0.264275	−	0.264275i
$273$		0			0
$274$			6.08862i			0.367827i
$275$	0.0231133	−	3.43837i	0.00139378	−	0.207341i
$276$	−1.11820	−	1.93679i	−0.0673080	−	0.116581i
$277$	6.68911	+	24.9641i	0.401910	+	1.49995i	0.809685	+	0.586865i	$0.199638\pi$
$277$	6.68911	+	24.9641i	0.401910	+	1.49995i	−0.407775	+	0.913082i	$0.633695\pi$
$278$		−	3.16174i		−	0.189629i
$279$	13.9183	−	3.72939i	0.833266	−	0.223273i
$280$	−14.0664	−	5.88194i	−0.840626	−	0.351513i
$281$	−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	$0.823414\pi$
$282$	−1.70894	+	0.457909i	−0.101766	+	0.0272681i
$283$	2.27388	−	8.48623i	0.135168	−	0.504454i	−0.864829	−	0.502066i	$-0.832573\pi$
$283$	2.27388	−	8.48623i	0.135168	−	0.504454i	0.999997	−	0.00238762i	$-0.000760005\pi$
$284$	11.3707	+	3.04677i	0.674728	+	0.180793i
$285$	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
$290$	9.69618	+	4.05452i	0.569379	+	0.238090i
$291$	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	−0.991993	−	0.126290i	$-0.959693\pi$
$293$	−6.61798	+	11.4627i	−0.386626	+	0.669657i	0.605367	+	0.795947i	$0.293026\pi$
$294$	−2.13780	+	2.13780i	−0.124679	+	0.124679i
$295$	−8.83163	−	21.5258i	−0.514197	−	1.25328i
$296$	−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
$301$	7.69226	+	2.06114i	0.443375	+	0.118802i
$302$	−0.599363	+	2.23685i	−0.0344895	+	0.128716i
$303$	13.5977	−	3.64350i	0.781169	−	0.209314i
$304$	−10.0539	−	10.0539i	−0.576632	−	0.576632i
$305$	−5.34674	+	12.7865i	−0.306154	+	0.732150i
$306$	2.39663	−	0.642175i	0.137006	−	0.0367107i
$307$			15.4782i			0.883389i	0.897165	+	0.441695i	$0.145623\pi$
$307$			15.4782i			0.883389i	−0.897165	+	0.441695i	$0.854377\pi$
$308$	1.14880	+	4.28737i	0.0654588	+	0.244296i
$309$	2.11358	+	3.66083i	0.120237	+	0.208257i
$310$	−7.45412	−	1.00685i	−0.423366	−	0.0571854i
$311$			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	$-0.178547\pi$
$314$	−1.78601	+	6.66547i	−0.100790	+	0.376154i
$315$	10.5386	+	13.8302i	0.593784	+	0.779243i
$316$	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
$319$	−1.69378	−	6.32125i	−0.0948332	−	0.353922i
$320$	−6.04604	+	0.775312i	−0.337984	+	0.0433412i
$321$	−7.17175	+	12.4218i	−0.400288	+	0.693319i
$322$	−2.37466	−	0.636287i	−0.132334	−	0.0354589i
$323$	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
$328$	0.992469	+	0.265931i	0.0548000	+	0.0146836i
$329$	7.00031	−	12.1249i	0.385940	−	0.668467i
$330$	0.708414	−	0.0908432i	0.0389969	−	0.00500075i
$331$	1.81607	+	6.77766i	0.0998202	+	0.372534i	0.997706	−	0.0676941i	$-0.0215642\pi$
$331$	1.81607	+	6.77766i	0.0998202	+	0.372534i	−0.897886	+	0.440228i	$0.854898\pi$
$332$	3.25325	+	1.87826i	0.178545	+	0.103083i
$333$	3.88272			0.212772
$334$	−9.25473	−	5.34322i	−0.506396	−	0.292368i
$335$	16.5985	+	21.7827i	0.906871	+	1.19012i
$336$	−2.32223	+	8.66669i	−0.126688	+	0.472807i
$337$	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
$340$	9.23996	+	1.24807i	0.501107	+	0.0676862i
$341$	2.34185	+	4.05620i	0.126818	+	0.219656i
$342$	−1.48132	−	5.52836i	−0.0801006	−	0.298940i
$343$			1.80378i			0.0973947i
$344$	−3.88250	+	1.04031i	−0.209331	+	0.0560899i
$345$	1.09861	−	2.62727i	0.0591471	−	0.141447i
$346$	−2.70091	−	2.70091i	−0.145202	−	0.145202i
$347$	−24.9510	+	6.68561i	−1.33944	+	0.358902i	−0.856227	−	0.516600i	$-0.827197\pi$
$347$	−24.9510	+	6.68561i	−1.33944	+	0.358902i	−0.483214	+	0.875502i	$0.660531\pi$
$348$	4.06737	−	15.1796i	0.218034	−	0.813714i
$349$	−9.07958	−	2.43287i	−0.486019	−	0.130228i	0.00748510	−	0.999972i	$-0.497617\pi$
$349$	−9.07958	−	2.43287i	−0.486019	−	0.130228i	−0.493504	+	0.869744i	$0.664284\pi$
$350$	−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	$-0.694363\pi$
$353$	−2.82798	+	1.63274i	−0.150518	+	0.0869017i	0.422849	+	0.906200i	$0.361030\pi$
$354$	4.18542	−	2.41645i	0.222452	−	0.128433i
$355$	5.68968	+	13.8678i	0.301977	+	0.736024i
$356$	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	$0.212842\pi$
$360$	−8.09676	−	3.38571i	−0.426737	−	0.178443i
$361$	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
$366$	−2.78069	−	0.745084i	−0.145349	−	0.0389461i
$367$	6.49371	−	24.2349i	0.338969	−	1.26505i	−0.560533	−	0.828132i	$-0.689404\pi$
$367$	6.49371	−	24.2349i	0.338969	−	1.26505i	0.899502	−	0.436917i	$-0.143930\pi$
$368$	−3.39569	+	0.909872i	−0.177012	+	0.0474303i
$369$	−0.828572	−	0.828572i	−0.0431337	−	0.0431337i
$370$	−1.86992	−	0.781922i	−0.0972128	−	0.0406502i
$371$	12.4161	−	3.32690i	0.644614	−	0.172724i
$372$			11.2473i			0.583144i
$373$	−2.95740	−	11.0372i	−0.153128	−	0.571483i	−0.999258	−	0.0385061i	$-0.987740\pi$
$373$	−2.95740	−	11.0372i	−0.153128	−	0.571483i	0.846130	−	0.532976i	$-0.178927\pi$
$374$	0.403250	+	0.698450i	0.0208516	+	0.0361160i
$375$	10.4373	−	1.26717i	0.538980	−	0.0654364i
$376$			7.06651i			0.364427i
$377$		0			0
$378$	−6.17523	+	6.17523i	−0.317620	+	0.317620i
$379$	0.520109	−	1.94107i	0.0267162	−	0.0997062i	−0.951280	−	0.308327i	$-0.900231\pi$
$379$	0.520109	−	1.94107i	0.0267162	−	0.0997062i	0.977997	+	0.208621i	$0.0668975\pi$
$380$	2.87896	−	21.3140i	0.147687	−	1.09339i
$381$	−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	$-0.0971291\pi$
$383$	22.9077	+	13.2258i	1.17053	+	0.675806i	0.216725	+	0.976233i	$0.430462\pi$
$384$	−2.75790	−	10.2926i	−0.140739	−	0.525244i
$385$	−3.45570	+	4.47235i	−0.176119	+	0.227932i
$386$	2.49457	−	4.32072i	0.126970	−	0.219919i
$387$	4.42775	+	1.18641i	0.225075	+	0.0603088i
$388$	−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
$393$	1.24815	+	0.334442i	0.0629610	+	0.0168704i
$394$	−3.22615	+	5.58786i	−0.162531	+	0.281512i
$395$	0.887791	+	6.92317i	0.0446696	+	0.348343i
$396$	0.661261	+	2.46786i	0.0332296	+	0.124015i
$397$	−23.3897	−	13.5041i	−1.17390	−	0.677750i	−0.219303	−	0.975657i	$-0.570378\pi$
$397$	−23.3897	−	13.5041i	−1.17390	−	0.677750i	−0.954595	+	0.297907i	$0.903712\pi$
$398$	3.87719			0.194346
$399$	−16.3955	−	9.46593i	−0.820800	−	0.473889i
$400$	−9.11589	−	9.23928i	−0.455795	−	0.461964i
$401$	1.28339	−	4.78969i	0.0640896	−	0.239186i	−0.926449	−	0.376421i	$-0.877155\pi$
$401$	1.28339	−	4.78969i	0.0640896	−	0.239186i	0.990539	+	0.137235i	$0.0438215\pi$
$402$	−4.02236	+	4.02236i	−0.200617	+	0.200617i
$403$		0			0
$404$		−	26.2876i		−	1.30786i
$405$	2.47060	+	3.24225i	0.122765	+	0.161109i
$406$	−8.63761	−	14.9608i	−0.428677	−	0.742491i
$407$	0.326647	+	1.21906i	0.0161913	+	0.0604268i
$408$			4.14243i			0.205081i
$409$	5.83965	−	1.56473i	0.288752	−	0.0773708i	−0.111536	−	0.993760i	$-0.535577\pi$
$409$	5.83965	−	1.56473i	0.288752	−	0.0773708i	0.400288	+	0.916390i	$0.368910\pi$
$410$	0.232180	+	0.565904i	0.0114665	+	0.0279480i
$411$	8.19736	+	8.19736i	0.404346	+	0.404346i
$412$	7.62468	−	2.04303i	0.375641	−	0.100653i
$413$	−9.89848	+	36.9416i	−0.487073	+	1.81778i
$414$	−1.36688	−	0.366254i	−0.0671784	−	0.0180004i
$415$	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	$-0.708546\pi$
$419$	−4.65114	+	2.68534i	−0.227223	+	0.131187i	0.382067	+	0.924135i	$0.375212\pi$
$420$	−12.5565	+	5.15169i	−0.612693	+	0.251377i
$421$	−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
$425$	5.86699	+	10.3215i	0.284591	+	0.500668i
$426$	−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
$431$	−16.1219	−	4.31985i	−0.776564	−	0.208080i	−0.151295	−	0.988489i	$-0.548344\pi$
$431$	−16.1219	−	4.31985i	−0.776564	−	0.208080i	−0.625269	+	0.780409i	$0.715011\pi$
$432$	−3.23215	+	12.0625i	−0.155507	+	0.580360i
$433$	−7.33490	+	1.96538i	−0.352493	+	0.0944502i	−0.430721	−	0.902485i	$-0.641741\pi$
$433$	−7.33490	+	1.96538i	−0.352493	+	0.0944502i	0.0782277	+	0.996936i	$0.475074\pi$
$434$	8.74255	+	8.74255i	0.419656	+	0.419656i
$435$	18.5131	−	7.59559i	0.887637	−	0.364181i
$436$	5.41899	−	1.45201i	0.259522	−	0.0695388i
$437$		−	7.41767i		−	0.354835i
$438$	−0.405886	−	1.51479i	−0.0193940	−	0.0723794i
$439$	−6.84536	−	11.8565i	−0.326711	−	0.565880i	0.655146	−	0.755502i	$-0.272607\pi$
$439$	−6.84536	−	11.8565i	−0.326711	−	0.565880i	−0.981857	+	0.189622i	$0.939274\pi$
$440$	0.381851	−	2.82699i	0.0182040	−	0.134772i
$441$		−	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	$0.180332\pi$
$444$	−0.784399	+	2.92742i	−0.0372259	+	0.138929i
$445$	7.48467	+	1.01098i	0.354807	+	0.0479250i
$446$	4.25377	+	2.45591i	0.201422	+	0.116291i
$447$	−15.8010			−0.747364
$448$	8.67708	+	5.00971i	0.409953	+	0.236687i
$449$	−6.65458	−	24.8352i	−0.314049	−	1.17205i	−0.924872	−	0.380280i	$-0.875828\pi$
$449$	−6.65458	−	24.8352i	−0.314049	−	1.17205i	0.610822	−	0.791768i	$-0.290839\pi$
$450$	−1.31828	−	5.05558i	−0.0621443	−	0.238322i
$451$	0.190442	−	0.329855i	0.00896755	−	0.0155323i
$452$	28.1077	+	7.53143i	1.32207	+	0.354249i
$453$	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	0.875541	−	0.483144i	$-0.160505\pi$
$457$	0.413767	+	0.716665i	0.0193552	+	0.0335242i	−0.856186	+	0.516668i	$0.827172\pi$
$458$	10.5374	+	2.82349i	0.492381	+	0.131933i
$459$	5.71155	−	9.89269i	0.266592	−	0.461751i
$460$	−4.20792	−	3.25138i	−0.196195	−	0.151596i
$461$	−6.23219	−	23.2589i	−0.290262	−	1.08327i	−0.944908	−	0.327337i	$-0.893849\pi$
$461$	−6.23219	−	23.2589i	−0.290262	−	1.08327i	0.654646	−	0.755936i	$-0.272818\pi$
$462$	−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
$465$	−11.3914	+	8.68022i	−0.528262	+	0.402536i
$466$	2.99418	−	11.1744i	0.138703	−	0.517645i
$467$	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
$470$	−3.34611	+	2.54974i	−0.154345	+	0.117611i
$471$	6.56942	+	11.3786i	0.302703	+	0.524297i
$472$	−4.99605	−	18.6455i	−0.229962	−	0.858229i
$473$			1.49000i			0.0685104i
$474$	−1.40042	+	0.375240i	−0.0643232	+	0.0172354i
$475$	23.8089	−	13.5335i	1.09243	−	0.620961i
$476$	−10.8371	−	10.8371i	−0.496716	−	0.496716i
$477$	7.14687	−	1.91500i	0.327233	−	0.0876818i
$478$	2.63979	−	9.85182i	0.120741	−	0.450612i
$479$	9.14111	+	2.44935i	0.417668	+	0.111914i	0.461532	−	0.887124i	$-0.347300\pi$
$479$	9.14111	+	2.44935i	0.417668	+	0.111914i	−0.0438638	+	0.999038i	$0.513967\pi$
$480$	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
$485$	6.10215	−	14.5930i	0.277084	−	0.662633i
$486$	−5.63904	+	5.63904i	−0.255792	+	0.255792i
$487$	3.07948	−	5.33382i	0.139545	−	0.241698i	−0.787780	−	0.615957i	$-0.788769\pi$
$487$	3.07948	−	5.33382i	0.139545	−	0.241698i	0.927324	+	0.374259i	$0.122103\pi$
$488$	−5.74911	+	9.95775i	−0.260250	+	0.450766i
$489$	0.0877545	−	0.0877545i	0.00396840	−	0.00396840i
$490$	−2.77334	+	6.63230i	−0.125287	+	0.299617i
$491$	12.8290	−	7.40681i	0.578964	−	0.334265i	−0.181758	−	0.983343i	$-0.558179\pi$
$491$	12.8290	−	7.40681i	0.578964	−	0.334265i	0.760721	+	0.649078i	$0.224845\pi$
$492$	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
$496$	17.0775	+	4.57590i	0.766802	+	0.205464i
$497$	6.37699	−	23.7993i	0.286047	−	1.06754i
$498$	−0.959715	+	0.257155i	−0.0430059	+	0.0115234i
$499$	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	$0.517826\pi$
$500$	2.75881	−	19.4386i	0.123378	−	0.869319i
$501$	−19.6538	+	5.26622i	−0.878068	+	0.235278i
$502$		−	14.5844i		−	0.650933i
$503$	−10.0318	−	37.4393i	−0.447297	−	1.66934i	−0.709799	−	0.704404i	$-0.751214\pi$
$503$	−10.0318	−	37.4393i	−0.447297	−	1.66934i	0.262502	−	0.964932i	$-0.415452\pi$
$504$	7.21280	+	12.4929i	0.321284	+	0.556479i
$505$	26.6244	−	20.2878i	1.18477	−	0.902796i
$506$		−	0.459974i		−	0.0204484i
$507$		0			0
$508$	−10.3059	+	10.3059i	−0.457250	+	0.457250i
$509$	−1.43699	+	5.36291i	−0.0636933	+	0.237707i	−0.990432	−	0.137999i	$-0.955933\pi$
$509$	−1.43699	+	5.36291i	−0.0636933	+	0.237707i	0.926739	+	0.375706i	$0.122600\pi$
$510$	−1.96151	+	1.49467i	−0.0868572	+	0.0661852i
$511$	10.7474	+	6.20501i	0.475437	+	0.274493i
$512$	−22.5909			−0.998384
$513$	−22.8197	−	13.1750i	−1.00751	−	0.581688i
$514$	−0.915926	−	3.41828i	−0.0403997	−	0.150774i
$515$	7.95364	+	6.14563i	0.350479	+	0.270809i
$516$	−1.78902	+	3.09867i	−0.0787572	+	0.136411i
$517$	2.53028	+	0.677985i	0.111281	+	0.0298178i
$518$	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
$523$	−30.2601	−	8.10818i	−1.32318	−	0.354546i	−0.473014	−	0.881055i	$-0.656834\pi$
$523$	−30.2601	−	8.10818i	−1.32318	−	0.354546i	−0.850170	+	0.526509i	$0.823501\pi$
$524$	1.20649	−	2.08970i	0.0527057	−	0.0912890i
$525$	−14.9083	−	8.74146i	−0.650652	−	0.381508i
$526$	1.72130	+	6.42400i	0.0750524	+	0.280100i
$527$	−14.0055	−	8.08609i	−0.610090	−	0.352236i
$528$	−1.67875			−0.0730583
$529$	18.3303	+	10.5830i	0.796969	+	0.460130i
$530$	−3.82760	−	0.517007i	−0.166260	−	0.0224574i
$531$	−5.69768	+	21.2640i	−0.247258	+	0.922781i
$532$	−24.9981	+	24.9981i	−1.08381	+	1.08381i
$533$		0			0
$534$			1.56879i			0.0678882i
$535$	−4.56534	+	33.7990i	−0.197377	+	1.46126i
$536$	11.3602	+	19.6765i	0.490688	+	0.849897i
$537$	−3.98035	−	14.8549i	−0.171765	−	0.641035i
$538$			4.00246i			0.172558i
$539$	4.32381	−	1.15856i	0.186240	−	0.0499028i
$540$	−17.4765	+	7.17027i	−0.752067	+	0.308559i
$541$	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	$0.643789\pi$
$542$	4.38745	−	1.17561i	0.188457	−	0.0504969i
$543$	−4.39048	+	16.3855i	−0.188414	+	0.703170i
$544$	11.4504	+	3.06813i	0.490932	+	0.131545i
$545$	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
$550$	1.47641	−	0.839222i	0.0629542	−	0.0357846i
$551$	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
$555$	−3.57029	+	1.46482i	−0.151550	+	0.0621783i
$556$	−9.73546	+	5.62077i	−0.412875	+	0.238374i
$557$	−14.4727	+	8.35584i	−0.613229	+	0.354048i	−0.774228	−	0.632906i	$-0.781862\pi$
$557$	−14.4727	+	8.35584i	−0.613229	+	0.354048i	0.160999	+	0.986955i	$0.448528\pi$
$558$	5.03231	+	5.03231i	0.213035	+	0.213035i
$559$		0			0
$560$	2.71361	+	21.1613i	0.114671	+	0.894227i
$561$	1.48326	+	0.397439i	0.0626234	+	0.0167799i
$562$	0.979701	−	3.65629i	0.0413262	−	0.154231i
$563$	−21.8019	+	5.84179i	−0.918839	+	0.246202i	−0.687089	−	0.726573i	$-0.741112\pi$
$563$	−21.8019	+	5.84179i	−0.918839	+	0.246202i	−0.231750	+	0.972775i	$0.574445\pi$
$564$	4.44802	+	4.44802i	0.187296	+	0.187296i
$565$	14.0645	+	34.2802i	0.591700	+	1.44218i
$566$	4.19136	−	1.12307i	0.176176	−	0.0472063i
$567$		−	6.70030i		−	0.281386i
$568$	3.21865	+	12.0122i	0.135052	+	0.504019i
$569$	−2.86843	−	4.96826i	−0.120251	−	0.208280i	0.799616	−	0.600512i	$-0.205037\pi$
$569$	−2.86843	−	4.96826i	−0.120251	−	0.208280i	−0.919866	+	0.392232i	$0.871703\pi$
$570$	3.44780	+	4.52466i	0.144412	+	0.189517i
$571$		−	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
$574$	0.260227	−	0.971181i	0.0108617	−	0.0405363i
$575$	0.0455166	−	6.77112i	0.00189817	−	0.282375i
$576$	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
$579$	−2.45862	−	9.17569i	−0.102177	−	0.381329i
$580$	−4.75287	−	37.0638i	−0.197352	−	1.53899i
$581$	3.93127	−	6.80916i	0.163097	−	0.282491i
$582$	3.17355	+	0.850351i	0.131548	+	0.0352482i
$583$	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	0.588102	−	0.808787i	$-0.299875\pi$
$587$	−9.84577	−	17.0534i	−0.406379	−	0.703868i	−0.994481	+	0.104918i	$0.966542\pi$
$588$	10.3830	+	2.78213i	0.428189	+	0.114733i
$589$	−18.6524	+	32.3069i	−0.768558	+	1.33118i
$590$	7.02628	−	9.09338i	0.289267	−	0.374368i
$591$	3.17966	+	11.8667i	0.130794	+	0.488129i
$592$	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
$595$	2.61226	−	19.3395i	0.107092	−	0.792844i
$596$	−7.63679	+	28.5009i	−0.312815	+	1.16744i
$597$	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	$0.721137\pi$
$600$	8.72256	+	0.0586345i	0.356097	+	0.00239374i
$601$	10.1487	+	17.5781i	0.413976	+	0.717027i	0.995320	−	0.0966302i	$-0.0308064\pi$
$601$	10.1487	+	17.5781i	0.413976	+	0.717027i	−0.581344	+	0.813658i	$0.697473\pi$
$602$	1.01800	+	3.79922i	0.0414905	+	0.154845i
$603$		−	25.9113i		−	1.05519i
$604$	7.95310	−	2.13103i	0.323607	−	0.0867103i
$605$	21.7171	+	9.08113i	0.882924	+	0.369201i
$606$	4.91641	+	4.91641i	0.199716	+	0.199716i
$607$	−33.2808	+	8.91757i	−1.35083	+	0.361953i	−0.860440	−	0.509552i	$-0.829811\pi$
$607$	−33.2808	+	8.91757i	−1.35083	+	0.361953i	−0.490387	+	0.871505i	$0.663144\pi$
$608$	7.07732	−	26.4129i	0.287023	−	1.07119i
$609$	−31.7715	−	8.51314i	−1.28744	−	0.344970i
$610$	−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	$-0.834133\pi$
$613$	−21.5350	+	12.4332i	−0.869790	+	0.502173i	−0.00251133	+	0.999997i	$0.500799\pi$
$614$	−6.62053	+	3.82236i	−0.267183	+	0.154258i
$615$	1.07449	+	0.449307i	0.0433277	+	0.0181178i
$616$	−3.31563	+	3.31563i	−0.133591	+	0.133591i
$617$	−13.9081	+	24.0895i	−0.559917	+	0.969805i	0.437585	+	0.899177i	$0.355834\pi$
$617$	−13.9081	+	24.0895i	−0.559917	+	0.969805i	−0.997503	+	0.0706286i	$0.977499\pi$
$618$	−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	$0.437625\pi$
$620$	10.1513	+	24.7422i	0.407685	+	0.993671i
$621$	−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
$626$	16.4570	+	4.40965i	0.657755	+	0.176245i
$627$	0.916783	−	3.42148i	0.0366128	−	0.136641i
$628$	23.6990	−	6.35012i	0.945692	−	0.253397i
$629$	−3.08139	−	3.08139i	−0.122863	−	0.122863i
$630$	−3.31309	+	7.92308i	−0.131997	+	0.315663i
$631$	−12.6187	+	3.38116i	−0.502341	+	0.134602i	−0.501086	−	0.865397i	$-0.667066\pi$
$631$	−12.6187	+	3.38116i	−0.502341	+	0.134602i	−0.00125496	+	0.999999i	$0.500399\pi$
$632$			5.79076i			0.230344i
$633$	−3.02393	−	11.2855i	−0.120190	−	0.448557i
$634$	4.68840	+	8.12054i	0.186200	+	0.322508i
$635$	−18.3916	−	2.48422i	−0.729850	−	0.0985832i
$636$			5.77534i			0.229007i
$637$		0			0
$638$	2.28552	−	2.28552i	0.0904846	−	0.0904846i
$639$	3.67067	−	13.6991i	0.145210	−	0.541929i
$640$	−15.3566	−	20.1530i	−0.607023	−	0.796617i
$641$	23.7092	+	13.6885i	0.936456	+	0.540663i	0.888848	−	0.458203i	$-0.151507\pi$
$641$	23.7092	+	13.6885i	0.936456	+	0.540663i	0.0476083	+	0.998866i	$0.484840\pi$
$642$	−7.08428			−0.279594
$643$	−27.2816	−	15.7510i	−1.07588	−	0.621161i	−0.146099	−	0.989270i	$-0.546672\pi$
$643$	−27.2816	−	15.7510i	−1.07588	−	0.621161i	−0.929783	+	0.368109i	$0.880005\pi$
$644$	2.26231	+	8.44305i	0.0891475	+	0.332703i
$645$	−4.51907	+	0.579501i	−0.177938	+	0.0228178i
$646$	−3.21181	+	5.56301i	−0.126367	+	0.218874i
$647$	−40.3457	−	10.8106i	−1.58615	−	0.425008i	−0.645329	−	0.763905i	$-0.723280\pi$
$647$	−40.3457	−	10.8106i	−1.58615	−	0.425008i	−0.940824	+	0.338896i	$0.889946\pi$
$648$	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
$653$	14.6695	+	3.93069i	0.574064	+	0.153820i	0.534160	−	0.845384i	$-0.320628\pi$
$653$	14.6695	+	3.93069i	0.574064	+	0.153820i	0.0399041	+	0.999204i	$0.487295\pi$
$654$	−0.741918	+	1.28504i	−0.0290113	+	0.0502490i
$655$	3.04759	−	0.390807i	0.119079	−	0.0152701i
$656$	−0.372117	−	1.38876i	−0.0145287	−	0.0542220i
$657$	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	$-0.145930\pi$
$659$	24.6914	+	14.2556i	0.961840	+	0.555319i	0.0651015	+	0.997879i	$0.479263\pi$
$660$	−1.53910	−	2.01981i	−0.0599092	−	0.0786210i
$661$	1.63091	−	6.08664i	0.0634351	−	0.236743i	−0.926928	−	0.375240i	$-0.877560\pi$
$661$	1.63091	−	6.08664i	0.0634351	−	0.236743i	0.990363	+	0.138497i	$0.0442271\pi$
$662$	−2.45054	+	2.45054i	−0.0952430	+	0.0952430i
$663$		0			0
$664$			3.96845i			0.154006i
$665$	−44.6110	−	6.02575i	−1.72994	−	0.233669i
$666$	0.958840	+	1.66076i	0.0371543	+	0.0643531i
$667$	−3.33552	−	12.4483i	−0.129152	−	0.482002i
$668$			37.9955i			1.47009i
$669$	9.03352	−	2.42052i	0.349256	−	0.0935829i
$670$	−5.21816	+	12.4790i	−0.201595	+	0.482104i
$671$	3.01394	+	3.01394i	0.116352	+	0.116352i
$672$	−16.6677	+	4.46610i	−0.642970	+	0.172283i
$673$	−5.92931	+	22.1285i	−0.228558	+	0.852991i	0.752389	+	0.658719i	$0.228901\pi$
$673$	−5.92931	+	22.1285i	−0.228558	+	0.852991i	−0.980948	+	0.194272i	$0.937765\pi$
$674$	0.743468	+	0.199212i	0.0286373	+	0.00767334i
$675$	−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
$680$	3.73877	+	9.11270i	0.143375	+	0.349456i
$681$	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	0.377565	+	0.925983i	$0.376761\pi$
$683$	−16.0240	+	27.7544i	−0.613142	+	1.06199i	−0.990707	+	0.136010i	$0.956572\pi$
$684$	−14.3892	+	14.3892i	−0.550185	+	0.550185i
$685$	25.4315	+	10.6343i	0.971686	+	0.406317i
$686$	−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
$691$	0.532264	+	0.142620i	0.0202483	+	0.00542551i	0.268929	−	0.963160i	$-0.413330\pi$
$691$	0.532264	+	0.142620i	0.0202483	+	0.00542551i	−0.248681	+	0.968586i	$0.579997\pi$
$692$	−3.51496	+	13.1180i	−0.133619	+	0.498672i
$693$	5.16531	−	1.38404i	0.196214	−	0.0525754i
$694$	−9.02132	−	9.02132i	−0.342445	−	0.342445i
$695$	−13.2062	−	5.52228i	−0.500941	−	0.209472i
$696$	16.0360	−	4.29682i	0.607842	−	0.162871i
$697$			1.31514i			0.0498144i
$698$	−1.20160	−	4.48442i	−0.0454811	−	0.169738i
$699$	−11.0134	−	19.0758i	−0.416565	−	0.721512i
$700$	−22.9726	+	22.6658i	−0.868282	+	0.856687i
$701$			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
$704$	−0.485195	+	1.81077i	−0.0182865	+	0.0682460i
$705$	−1.07219	+	7.93782i	−0.0403809	+	0.298956i
$706$	−1.39674	−	0.806411i	−0.0525672	−	0.0303497i
$707$	−55.0209			−2.06927
$708$	−14.8812	−	8.59166i	−0.559270	−	0.322894i
$709$	8.39944	+	31.3471i	0.315448	+	1.17727i	0.923572	+	0.383425i	$0.125255\pi$
$709$	8.39944	+	31.3471i	0.315448	+	1.17727i	−0.608124	+	0.793842i	$0.708078\pi$
$710$	−4.52661	+	5.85831i	−0.169881	+	0.219859i
$711$	3.30200	−	5.71923i	0.123835	−	0.214488i
$712$	6.05244	+	1.62175i	0.226825	+	0.0607776i
$713$	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
$718$	2.10561	+	0.564197i	0.0785808	+	0.0210557i
$719$	−4.21240	+	7.29608i	−0.157096	+	0.272098i	−0.933820	−	0.357743i	$-0.883546\pi$
$719$	−4.21240	+	7.29608i	−0.157096	+	0.272098i	0.776724	+	0.629841i	$0.216880\pi$
$720$	1.56199	+	12.1807i	0.0582118	+	0.453947i
$721$	−4.27612	−	15.9587i	−0.159251	−	0.594333i
$722$	4.70543	+	2.71668i	0.175118	+	0.101104i
$723$	−2.91423			−0.108381
$724$	27.4332	+	15.8385i	1.01955	+	0.588635i
$725$	33.8705	−	33.4182i	1.25792	−	1.24112i
$726$	−1.26548	+	4.72284i	−0.0469664	+	0.175281i
$727$	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
$730$	−2.26006	−	2.96596i	−0.0836487	−	0.109775i
$731$	−2.57239	−	4.45551i	−0.0951432	−	0.164793i
$732$	2.64913	+	9.88670i	0.0979148	+	0.365423i
$733$		−	18.6238i		−	0.687887i	−0.938990	−	0.343944i	$-0.888237\pi$
$733$		−	18.6238i		−	0.687887i	0.938990	−	0.343944i	$-0.111763\pi$
$734$	11.9696	−	3.20725i	0.441807	−	0.118382i
$735$	5.19547	+	12.6632i	0.191638	+	0.467089i
$736$	−4.78070	−	4.78070i	−0.176219	−	0.176219i
$737$	8.13543	−	2.17988i	0.299672	−	0.0802970i
$738$	0.149790	−	0.559023i	0.00551383	−	0.0205779i
$739$	−31.8740	−	8.54061i	−1.17250	−	0.314171i	−0.380555	−	0.924758i	$-0.624267\pi$
$739$	−31.8740	−	8.54061i	−1.17250	−	0.314171i	−0.791949	+	0.610587i	$0.790934\pi$
$740$	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	$-0.424649\pi$
$743$	32.5366	−	18.7850i	1.19365	−	0.689155i	0.959133	+	0.282957i	$0.0913154\pi$
$744$	−10.2899	+	5.94088i	−0.377246	+	0.217803i
$745$	−34.7598	+	14.2613i	−1.27350	+	0.522493i
$746$	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
$750$	3.11951	+	4.15144i	0.113908	+	0.151589i
$751$	−29.1051	+	16.8038i	−1.06206	+	0.613181i	−0.926001	−	0.377520i	$-0.876777\pi$
$751$	−29.1051	+	16.8038i	−1.06206	+	0.613181i	−0.136059	+	0.990701i	$0.543444\pi$
$752$	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
$756$	29.9924	+	8.03643i	1.09081	+	0.292282i
$757$	−4.17654	+	15.5871i	−0.151799	+	0.566521i	0.847559	+	0.530701i	$0.178071\pi$
$757$	−4.17654	+	15.5871i	−0.151799	+	0.566521i	−0.999358	+	0.0358205i	$0.988596\pi$
$758$	0.958699	−	0.256883i	0.0348215	−	0.00933040i
$759$	−0.619282	−	0.619282i	−0.0224785	−	0.0224785i
$760$	21.0205	−	8.62431i	0.762493	−	0.312837i
$761$	15.1340	−	4.05514i	0.548606	−	0.146999i	0.0261397	−	0.999658i	$-0.491679\pi$
$761$	15.1340	−	4.05514i	0.548606	−	0.146999i	0.522467	+	0.852660i	$0.325012\pi$
$762$		−	3.85490i		−	0.139648i
$763$	−3.03911	−	11.3421i	−0.110023	−	0.410612i
$764$	4.55789	+	7.89449i	0.164899	+	0.285613i
$765$	1.50364	−	11.1321i	0.0543644	−	0.402480i
$766$			13.0645i			0.472039i
$767$		0			0
$768$	0.0960396	−	0.0960396i	0.00346553	−	0.00346553i
$769$	8.43930	−	31.4959i	0.304329	−	1.13577i	−0.629193	−	0.777249i	$-0.716614\pi$
$769$	8.43930	−	31.4959i	0.304329	−	1.13577i	0.933522	−	0.358521i	$-0.116719\pi$
$770$	−2.76635	−	0.373660i	−0.0996924	−	0.0134658i
$771$	−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	$-0.474792\pi$
$773$	−20.7033	−	11.9531i	−0.744646	−	0.429921i	−0.823756	+	0.566944i	$0.808125\pi$
$774$	0.585972	+	2.18688i	0.0210623	+	0.0786056i
$775$	−17.2248	+	29.3764i	−0.618733	+	1.05523i
$776$	6.56136	−	11.3646i	0.235539	−	0.407966i
$777$	6.12718	+	1.64177i	0.219811	+	0.0588983i
$778$	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
$783$	−44.2204	−	11.8488i	−1.58031	−	0.423443i
$784$	8.44858	−	14.6334i	0.301735	−	0.522620i
$785$	24.7214	+	19.1018i	0.882346	+	0.681772i
$786$	0.165181	+	0.616466i	0.00589183	+	0.0219886i
$787$	13.6065	+	7.85572i	0.485020	+	0.280026i	0.722506	−	0.691365i	$-0.242990\pi$
$787$	13.6065	+	7.85572i	0.485020	+	0.280026i	−0.237486	+	0.971391i	$0.576324\pi$
$788$	22.9411			0.817242
$789$	10.9664	+	6.33143i	0.390412	+	0.225405i
$790$	−2.74202	+	2.08942i	−0.0975566	+	0.0743382i
$791$	15.7635	−	58.8303i	0.560487	−	2.09176i
$792$	−1.90851	+	1.90851i	−0.0678161	+	0.0678161i
$793$		0			0
$794$		−	13.3394i		−	0.473397i
$795$	−5.84933	+	4.45719i	−0.207454	+	0.158080i
$796$	−6.89264	−	11.9384i	−0.244303	−	0.423146i
$797$	−8.08312	−	30.1666i	−0.286319	−	1.06856i	−0.947870	−	0.318656i	$-0.896768\pi$
$797$	−8.08312	−	30.1666i	−0.286319	−	1.06856i	0.661552	−	0.749900i	$-0.269898\pi$
$798$		−	9.35048i		−	0.331003i
$799$	−8.73669	+	2.34099i	−0.309082	+	0.0828183i
$800$	6.62252	−	24.0673i	0.234141	−	0.850906i
$801$	−5.05293	−	5.05293i	−0.178537	−	0.178537i
$802$	2.36564	−	0.633871i	0.0835336	−	0.0223827i
$803$	−0.600960	+	2.24281i	−0.0212074	+	0.0791471i
$804$	19.5361	+	5.23469i	0.688986	+	0.184613i
$805$	−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	$-0.741361\pi$
$809$	−11.4546	+	6.61331i	−0.402722	+	0.232512i	0.284936	+	0.958547i	$0.408028\pi$
$810$	−0.776696	+	1.85743i	−0.0272903	+	0.0652634i
$811$	−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
$815$	0.113843	−	0.272249i	0.00398774	−	0.00953647i
$816$	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
$821$	8.74860	+	2.34418i	0.305328	+	0.0818124i	0.408230	−	0.912879i	$-0.366146\pi$
$821$	8.74860	+	2.34418i	0.305328	+	0.0818124i	−0.102902	+	0.994692i	$0.532813\pi$
$822$	−1.48192	+	5.53062i	−0.0516881	+	0.192902i
$823$	40.5117	−	10.8551i	1.41215	−	0.378384i	0.529457	−	0.848337i	$-0.322396\pi$
$823$	40.5117	−	10.8551i	1.41215	−	0.378384i	0.882691	+	0.469953i	$0.155729\pi$
$824$	5.89653	+	5.89653i	0.205415	+	0.205415i
$825$	0.857868	−	3.11763i	0.0298671	−	0.108542i
$826$	−18.2455	+	4.88888i	−0.634844	+	0.170106i
$827$		−	38.2009i		−	1.32838i	−0.747566	−	0.664188i	$-0.768778\pi$
$827$		−	38.2009i		−	1.32838i	0.747566	−	0.664188i	$-0.231222\pi$
$828$	1.30221	+	4.85992i	0.0452550	+	0.168894i
$829$	14.6750	+	25.4178i	0.509682	+	0.882796i	0.999937	+	0.0112165i	$0.00357041\pi$
$829$	14.6750	+	25.4178i	0.509682	+	0.882796i	−0.490255	+	0.871579i	$0.663096\pi$
$830$	−1.87913	+	1.43189i	−0.0652254	+	0.0497018i
$831$			24.3043i			0.843106i
$832$		0			0
$833$	−10.9292	+	10.9292i	−0.378673	+	0.378673i
$834$	0.769545	−	2.87198i	0.0266471	−	0.0994485i
$835$	−38.4822	+	29.3235i	−1.33173	+	1.01478i
$836$	−5.72835	−	3.30726i	−0.198119	−	0.114384i
$837$	32.7649			1.13252
$838$	−2.29721	−	1.32629i	−0.0793557	−	0.0458161i
$839$	9.11914	+	34.0331i	0.314828	+	1.17495i	0.924150	+	0.382030i	$0.124775\pi$
$839$	9.11914	+	34.0331i	0.314828	+	1.17495i	−0.609322	+	0.792923i	$0.708558\pi$
$840$	−11.3456	−	8.76652i	−0.391460	−	0.302474i
$841$	30.7798	−	53.3122i	1.06137	−	1.83835i
$842$	−9.53846	−	2.55582i	−0.328717	−	0.0880795i
$843$	−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
$848$	8.76909	+	2.34967i	0.301132	+	0.0806880i
$849$	4.13097	−	7.15504i	0.141774	−	0.245560i
$850$	−2.96599	+	5.05841i	−0.101733	+	0.173502i
$851$	0.643261	+	2.40068i	0.0220507	+	0.0822944i
$852$	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
$855$	−25.6786	−	3.46849i	−0.878189	−	0.118620i
$856$	−7.32342	+	27.3314i	−0.250309	+	0.934167i
$857$	−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	$0.833822\pi$
$860$	−1.13884	+	8.43127i	−0.0388341	+	0.287504i
$861$	−0.957186	−	1.65789i	−0.0326208	−	0.0565009i
$862$	−2.13358	−	7.96263i	−0.0726701	−	0.271208i
$863$		−	15.7688i		−	0.536775i	−0.963311	−	0.268387i	$-0.913509\pi$
$863$		−	15.7688i		−	0.536775i	0.963311	−	0.268387i	$-0.0864907\pi$
$864$	−23.1986	+	6.21604i	−0.789232	+	0.211474i
$865$	−15.9988	+	6.56400i	−0.543974	+	0.223183i
$866$	−2.65202	−	2.65202i	−0.0901192	−	0.0901192i
$867$	10.3205	−	2.76537i	0.350502	−	0.0939168i
$868$	11.3775	−	42.4615i	0.386179	−	1.44124i
$869$	2.07347	+	0.555585i	0.0703377	+	0.0188469i
$870$	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
$875$	−40.6855	−	5.77427i	−1.37542	−	0.195206i
$876$	−3.94269	+	3.94269i	−0.133211	+	0.133211i
$877$	−22.3613	+	38.7309i	−0.755088	+	1.30785i	0.190242	+	0.981737i	$0.439073\pi$
$877$	−22.3613	+	38.7309i	−0.755088	+	1.30785i	−0.945331	+	0.326114i	$0.894261\pi$
$878$	3.38094	−	5.85595i	0.114101	−	0.197629i
$879$	−8.80139	+	8.80139i	−0.296863	+	0.296863i
$880$	−3.69299	+	1.51516i	−0.124491	+	0.0510761i
$881$	−18.0323	+	10.4110i	−0.607525	+	0.350755i	−0.771996	−	0.635627i	$-0.780742\pi$
$881$	−18.0323	+	10.4110i	−0.607525	+	0.350755i	0.164471	+	0.986382i	$0.447408\pi$
$882$	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
$886$	4.36041	+	1.16837i	0.146491	+	0.0392521i
$887$	−6.93749	+	25.8911i	−0.232938	+	0.869337i	0.746129	+	0.665801i	$0.231910\pi$
$887$	−6.93749	+	25.8911i	−0.232938	+	0.869337i	−0.979067	+	0.203536i	$0.934757\pi$
$888$	−3.09256	+	0.828649i	−0.103780	+	0.0278077i
$889$	21.5706	+	21.5706i	0.723454	+	0.723454i
$890$	1.41592	+	3.45109i	0.0474617	+	0.115681i
$891$	1.21092	−	0.324464i	0.0405673	−	0.0108700i
$892$		−	17.4639i		−	0.584736i
$893$	5.40002	+	20.1531i	0.180705	+	0.674399i
$894$	−3.90208	−	6.75861i	−0.130505	−	0.226042i
$895$	−22.1635	−	29.0859i	−0.740842	−	0.972233i
$896$			41.6474i			1.39134i
$897$		0			0
$898$	8.97946	−	8.97946i	0.299648	−	0.299648i
$899$	−16.7749	+	62.6048i	−0.559475	+	2.08799i
$900$	−13.2233	+	13.0467i	−0.440776	+	0.434890i
$901$	−7.19167	−	4.15211i	−0.239589	−	0.138327i
$902$	0.188119			0.00626368
$903$	6.48562	+	3.74447i	0.215828	+	0.124608i
$904$	7.95630	+	29.6933i	0.264623	+	0.987585i
$905$	5.13044	+	40.0082i	0.170542	+	1.32992i
$906$	−1.08887	+	1.88597i	−0.0361752	+	0.0626572i
$907$	39.1608	+	10.4931i	1.30031	+	0.348418i	0.841568	−	0.540151i	$-0.181633\pi$
$907$	39.1608	+	10.4931i	1.30031	+	0.348418i	0.458744	+	0.888568i	$0.348299\pi$
$908$	−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
$913$	1.42096	+	0.380746i	0.0470271	+	0.0126009i
$914$	−0.204360	+	0.353962i	−0.00675963	+	0.0117080i
$915$	−7.96885	+	10.3133i	−0.263442	+	0.340946i
$916$	−10.0389	−	37.4656i	−0.331694	−	1.23790i
$917$	−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	$-0.322162\pi$
$919$	1.84237	+	1.06369i	0.0607741	+	0.0350879i	−0.469305	+	0.883036i	$0.655496\pi$
$920$	0.751973	−	5.56715i	0.0247918	−	0.183543i
$921$	−3.76728	+	14.0597i	−0.124136	+	0.463283i
$922$	8.40950	−	8.40950i	0.276952	−	0.276952i
$923$		0			0
$924$			4.17405i			0.137316i
$925$	−6.53199	+	6.44476i	−0.214770	+	0.211902i
$926$	−1.56954	−	2.71852i	−0.0515782	−	0.0893360i
$927$	−2.46138	−	9.18601i	−0.0808425	−	0.301708i
$928$		−	47.5087i		−	1.55955i
$929$	19.2515	−	5.15841i	0.631620	−	0.169242i	0.0712153	−	0.997461i	$-0.477312\pi$
$929$	19.2515	−	5.15841i	0.631620	−	0.169242i	0.560405	+	0.828219i	$0.310646\pi$
$930$	−6.52591	−	2.72885i	−0.213993	−	0.0894826i
$931$	25.2106	+	25.2106i	0.826243	+	0.826243i
$932$	−39.7305	+	10.6458i	−1.30142	+	0.348713i
$933$	−1.30196	+	4.85898i	−0.0426242	+	0.159076i
$934$	10.5382	+	2.82369i	0.344819	+	0.0923940i
$935$	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
$940$	13.7995	+	5.77037i	0.450091	+	0.188209i
$941$	−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
$945$	15.0076	+	36.5788i	0.488197	+	1.18991i
$946$	−0.637321	+	0.367957i	−0.0207211	+	0.0119633i
$947$	7.18880	−	4.15045i	0.233605	−	0.134872i	−0.378629	−	0.925548i	$-0.623604\pi$
$947$	7.18880	−	4.15045i	0.233605	−	0.134872i	0.612234	+	0.790677i	$0.290271\pi$
$948$	3.64500	+	3.64500i	0.118384	+	0.118384i
$949$		0			0
$950$	11.6684	+	6.84172i	0.378572	+	0.221975i
$951$	17.2452	+	4.62084i	0.559214	+	0.149841i
$952$	4.19041	−	15.6388i	0.135812	−	0.506857i
$953$	4.62244	−	1.23858i	0.149736	−	0.0401215i	−0.183173	−	0.983081i	$-0.558637\pi$
$953$	4.62244	−	1.23858i	0.149736	−	0.0401215i	0.332908	+	0.942959i	$0.391970\pi$
$954$	2.58403	+	2.58403i	0.0836611	+	0.0836611i
$955$	−4.47802	+	10.7089i	−0.144905	+	0.346533i
$956$	−35.0280	+	9.38573i	−1.13289	+	0.303556i
$957$		−	6.15418i		−	0.198936i
$958$	1.20974	+	4.51481i	0.0390849	+	0.145867i
$959$	−22.6550	−	39.2396i	−0.731568	−	1.26711i
$960$	−5.68064	−	0.767302i	−0.183342	−	0.0247646i
$961$		−	15.3867i		−	0.496346i
$962$		0			0
$963$	22.8178	−	22.8178i	0.735294	−	0.735294i
$964$	−1.40848	+	5.25650i	−0.0453639	+	0.169301i
$965$	−13.6901	−	17.9660i	−0.440701	−	0.578347i
$966$	−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
$969$	3.16552	+	11.8139i	0.101691	+	0.379517i
$970$	7.74880	−	0.993666i	0.248799	−	0.0319047i
$971$	2.71693	−	4.70586i	0.0871905	−	0.151018i	−0.819132	−	0.573605i	$-0.805544\pi$
$971$	2.71693	−	4.70586i	0.0871905	−	0.151018i	0.906323	+	0.422587i	$0.138878\pi$
$972$	27.3881	+	7.33863i	0.878475	+	0.235387i
$973$	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	0.677144	−	0.735851i	$-0.263217\pi$
$977$	−9.33626	−	16.1709i	−0.298693	−	0.517352i	−0.975837	+	0.218499i	$0.929884\pi$
$978$	0.0592064	+	0.0158643i	0.00189321	+	0.000507285i
$979$	1.16138	−	2.01158i	0.0371180	−	0.0642903i
$980$	25.3521	−	3.25101i	0.809842	−	0.103850i
$981$	−1.74935	−	6.52865i	−0.0558524	−	0.208444i
$982$	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
$985$	17.7051	+	23.2350i	0.564130	+	0.740327i
$986$	−2.88852	+	10.7801i	−0.0919893	+	0.343309i
$987$	9.30986	−	9.30986i	0.296336	−	0.296336i
$988$		0			0
$989$			2.93424i			0.0933033i
$990$	−1.59234	−	0.215083i	−0.0506080	−	0.00683579i
$991$	21.6135	+	37.4357i	0.686576	+	1.18919i	0.972939	+	0.231064i	$0.0742206\pi$
$991$	21.6135	+	37.4357i	0.686576	+	1.18919i	−0.286362	+	0.958121i	$0.592446\pi$
$992$	8.80033	+	32.8433i	0.279411	+	1.04277i
$993$			6.59853i			0.209398i
$994$	11.7545	−	3.14961i	0.372830	−	0.0998995i
$995$	6.77186	−	16.1946i	0.214682	−	0.513402i
$996$	2.49794	+	2.49794i	0.0791504	+	0.0791504i
$997$	−43.6654	+	11.7001i	−1.38290	+	0.370547i	−0.872173	−	0.489197i	$-0.837290\pi$
$997$	−43.6654	+	11.7001i	−1.38290	+	0.370547i	−0.510725	+	0.859744i	$0.670623\pi$
$998$	−3.80596	+	14.2040i	−0.120476	+	0.449621i
$999$	8.52799	+	2.28507i	0.269814	+	0.0722963i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.3	✓	20	13.12	even	2
65.2.o.a.33.3	yes	20	65.58	even	12
65.2.t.a.7.3	yes	20	13.6	odd	12
65.2.t.a.28.3	yes	20	65.38	odd	4
325.2.s.b.132.3		20	65.64	even	2
325.2.s.b.293.3		20	65.32	even	12
325.2.x.b.7.3		20	65.19	odd	12
325.2.x.b.93.3		20	65.12	odd	4
585.2.cf.a.163.3		20	195.188	odd	12
585.2.cf.a.262.3		20	39.38	odd	2
585.2.dp.a.28.3		20	195.38	even	4
585.2.dp.a.397.3		20	39.32	even	12
845.2.f.d.408.6		20	65.3	odd	12
845.2.f.d.437.5		20	13.11	odd	12
845.2.f.e.408.5		20	65.23	odd	12
845.2.f.e.437.6		20	13.2	odd	12
845.2.k.d.268.5		20	65.63	even	12
845.2.k.d.577.5		20	13.3	even	3
845.2.k.e.268.6		20	65.28	even	12
845.2.k.e.577.6		20	13.10	even	6
845.2.o.e.258.3		20	65.18	even	4
845.2.o.e.357.3		20	13.4	even	6
845.2.o.f.258.3		20	65.8	even	4
845.2.o.f.357.3		20	13.9	even	3
845.2.o.g.488.3		20	65.33	even	12	inner
845.2.o.g.587.3		20	1.1	even	1	trivial
845.2.t.e.188.3		20	65.48	odd	12
845.2.t.e.427.3		20	13.8	odd	4
845.2.t.f.188.3		20	65.43	odd	12
845.2.t.f.427.3		20	13.5	odd	4
845.2.t.g.418.3		20	5.3	odd	4
845.2.t.g.657.3		20	13.7	odd	12

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} +(0.908353 + 0.243392i) q^{3} +(0.878030 - 1.52079i) q^{4} +(2.21791 - 0.284413i) q^{5} +(0.120212 + 0.448637i) q^{6} +(-3.18307 - 1.83775i) q^{7} +1.85513 q^{8} +(-1.83221 - 1.05783i) q^{9} +(0.669366 + 0.878433i) q^{10} +(0.177987 - 0.664257i) q^{11} +(1.16771 - 1.16771i) q^{12} -1.81533i q^{14} +(2.08387 + 0.281475i) q^{15} +(-1.29794 - 2.24809i) q^{16} +(0.614565 + 2.29359i) q^{17} -1.04493i q^{18} +(5.29067 - 1.41763i) q^{19} +(1.51486 - 3.62270i) q^{20} +(-2.44406 - 2.44406i) q^{21} +(0.328078 - 0.0879082i) q^{22} +(0.350507 - 1.30811i) q^{23} +(1.68511 + 0.451523i) 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} +(0.394217 + 0.960845i) 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} +(-7.58243 - 3.17064i) 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} +(0.534988 + 0.143350i) q^{41} +(0.441838 - 1.64896i) q^{42} +(-2.09285 + 0.560778i) q^{43} +(-0.853919 - 0.853919i) q^{44} +(-4.36453 - 1.82506i) q^{45} +(0.646078 - 0.173116i) q^{46} +3.80918i q^{47} +(-0.631815 - 2.35797i) q^{48} +(3.25462 + 5.63717i) q^{49} +(1.73443 + 1.75791i) q^{50} +2.23297i q^{51} +(-2.47293 + 2.47293i) q^{53} +(0.614963 - 2.29507i) q^{54} +(0.205836 - 1.52388i) q^{55} +(-5.90499 - 3.40925i) q^{56} +5.15084 q^{57} +(4.07041 + 2.35005i) q^{58} +(-2.69310 - 10.0508i) q^{59} +(2.25776 - 2.92199i) q^{60} +(-3.09904 + 5.36770i) q^{61} +(-3.24924 - 0.870630i) q^{62} +(3.88804 + 6.73428i) q^{63} -2.72601 q^{64} +0.319406 q^{66} +(6.12371 + 10.6066i) q^{67} +(4.02768 + 1.07921i) q^{68} +(0.636768 - 1.10291i) q^{69} +(-0.516303 - 4.02624i) q^{70} +(1.73500 + 6.47512i) q^{71} +(-3.39898 - 1.96240i) q^{72} -3.37642 q^{73} +(-0.784986 - 0.453212i) q^{74} +(4.70187 + 0.0316067i) q^{75} +(2.48945 - 9.29074i) q^{76} +(-1.78728 + 1.78728i) q^{77} +3.12149i q^{79} +(-3.51809 - 4.61691i) q^{80} +(0.911483 + 1.57873i) q^{81} +(0.0708006 + 0.264231i) q^{82} +2.13918i q^{83} +(-5.86286 + 1.57095i) q^{84} +(2.01537 + 4.91217i) q^{85} +(-0.756694 - 0.756694i) q^{86} +(8.64414 - 2.31619i) q^{87} +(0.330188 - 1.23228i) q^{88} +(3.26255 + 0.874198i) 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} +(11.3310 - 4.64891i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{5} + 8 q^{6} + 6 q^{7} - 12 q^{8} - 12 q^{9} - 10 q^{10} + 16 q^{11} + 24 q^{12} - 12 q^{15} - 2 q^{16} - 10 q^{17} - 20 q^{19} - 14 q^{20} - 4 q^{21} + 16 q^{22}+ \cdots + 60 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 - 2 * q^3 - 6 * q^4 + 6 * q^5 + 8 * q^6 + 6 * q^7 - 12 * q^8 - 12 * q^9 - 10 * q^10 + 16 * q^11 + 24 * q^12 - 12 * q^15 - 2 * q^16 - 10 * q^17 - 20 * q^19 - 14 * q^20 - 4 * q^21 + 16 * q^22 - 2 * q^23 + 32 * q^24 - 18 * q^25 + 4 * q^27 - 6 * q^28 + 14 * q^30 + 6 * q^32 + 18 * q^33 + 2 * q^34 - 20 * q^35 + 36 * q^36 - 42 * q^37 + 8 * q^38 - 16 * q^40 - 10 * q^41 - 56 * q^42 - 22 * q^43 - 36 * q^44 - 52 * q^45 - 4 * q^46 + 28 * q^48 - 18 * q^49 - 44 * q^50 - 10 * q^53 - 48 * q^54 + 26 * q^55 + 12 * q^57 + 90 * q^58 - 16 * q^59 + 92 * q^60 - 16 * q^61 - 40 * q^62 + 32 * q^63 - 20 * q^64 - 32 * q^66 + 58 * q^67 + 28 * q^68 + 16 * q^69 - 32 * q^70 + 16 * q^71 + 66 * q^72 - 72 * q^73 - 18 * q^74 - 34 * q^75 + 64 * q^76 + 28 * q^77 + 34 * q^80 - 14 * q^81 + 22 * q^82 - 40 * q^84 + 6 * q^85 - 60 * q^86 + 62 * q^87 + 50 * q^88 - 6 * q^89 - 46 * q^90 - 8 * q^92 - 48 * q^93 + 48 * q^94 + 14 * q^95 - 56 * q^96 + 22 * q^97 - 4 * q^98 + 60 * q^99

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