LMFDB - Embedded newform 845.2.t.f.188.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(188,845)] 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("845.188"); 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, 5])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [20,6,-2,6,0,4] 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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			188.3
Root			$0.493902i$ of defining polynomial
Character	$\chi$	$=$	845.188
Dual form			845.2.t.f.427.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.427732 + 0.246951i) q^{2} +(0.908353 - 0.243392i) q^{3} +(-0.878030 - 1.52079i) q^{4} +(-0.284413 + 2.21791i) q^{5} +(0.448637 + 0.120212i) q^{6} +(1.83775 + 3.18307i) q^{7} -1.85513i q^{8} +(-1.83221 + 1.05783i) q^{9} +(-0.669366 + 0.878433i) q^{10} +(0.664257 - 0.177987i) q^{11} +(-1.16771 - 1.16771i) q^{12} +1.81533i q^{14} +(0.281475 + 2.08387i) q^{15} +(-1.29794 + 2.24809i) q^{16} +(-0.614565 + 2.29359i) q^{17} -1.04493 q^{18} +(-1.41763 + 5.29067i) q^{19} +(3.62270 - 1.51486i) q^{20} +(2.44406 + 2.44406i) q^{21} +(0.328078 + 0.0879082i) q^{22} +(-0.350507 - 1.30811i) q^{23} +(-0.451523 - 1.68511i) q^{24} +(-4.83822 - 1.26160i) q^{25} +(-3.40171 + 3.40171i) q^{27} +(3.22719 - 5.58966i) q^{28} +(8.24134 + 4.75814i) q^{29} +(-0.394217 + 0.960845i) q^{30} +(4.81595 - 4.81595i) q^{31} +(-4.32351 + 2.49618i) q^{32} +(0.560059 - 0.323350i) q^{33} +(-0.829273 + 0.829273i) q^{34} +(-7.58243 + 3.17064i) q^{35} +(3.21748 + 1.85761i) q^{36} +(-0.917615 + 1.58936i) q^{37} +(-1.91290 + 1.91290i) q^{38} +(4.11449 + 0.527621i) q^{40} +(0.143350 + 0.534988i) q^{41} +(0.441838 + 1.64896i) q^{42} +(2.09285 + 0.560778i) q^{43} +(-0.853919 - 0.853919i) q^{44} +(-1.82506 - 4.36453i) q^{45} +(0.173116 - 0.646078i) q^{46} -3.80918 q^{47} +(-0.631815 + 2.35797i) q^{48} +(-3.25462 + 5.63717i) q^{49} +(-1.75791 - 1.73443i) q^{50} +2.23297i q^{51} +(-2.47293 - 2.47293i) q^{53} +(-2.29507 + 0.614963i) q^{54} +(0.205836 + 1.52388i) q^{55} +(5.90499 - 3.40925i) q^{56} +5.15084i q^{57} +(2.35005 + 4.07041i) q^{58} +(10.0508 + 2.69310i) q^{59} +(2.92199 - 2.25776i) q^{60} +(-3.09904 - 5.36770i) q^{61} +(3.24924 - 0.870630i) q^{62} +(-6.73428 - 3.88804i) q^{63} +2.72601 q^{64} +0.319406 q^{66} +(10.6066 + 6.12371i) q^{67} +(4.02768 - 1.07921i) q^{68} +(-0.636768 - 1.10291i) q^{69} +(-4.02624 - 0.516303i) q^{70} +(6.47512 + 1.73500i) q^{71} +(1.96240 + 3.39898i) q^{72} +3.37642i q^{73} +(-0.784986 + 0.453212i) q^{74} +(-4.70187 + 0.0316067i) q^{75} +(9.29074 - 2.48945i) q^{76} +(1.78728 + 1.78728i) q^{77} -3.12149i q^{79} +(-4.61691 - 3.51809i) q^{80} +(0.911483 - 1.57873i) q^{81} +(-0.0708006 + 0.264231i) q^{82} +2.13918 q^{83} +(1.57095 - 5.86286i) q^{84} +(-4.91217 - 2.01537i) q^{85} +(0.756694 + 0.756694i) q^{86} +(8.64414 + 2.31619i) q^{87} +(-0.330188 - 1.23228i) q^{88} +(-0.874198 - 3.26255i) q^{89} +(0.297190 - 2.31755i) q^{90} +(-1.68161 + 1.68161i) q^{92} +(3.20242 - 5.54675i) q^{93} +(-1.62931 - 0.940681i) q^{94} +(-11.3310 - 4.64891i) q^{95} +(-3.31972 + 3.31972i) q^{96} +(-6.12606 + 3.53688i) q^{97} +(-2.78421 + 1.60746i) q^{98} +(-1.02878 + 1.02878i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 4 q^{6} - 2 q^{7} - 12 q^{9} + 10 q^{10} + 8 q^{11} - 24 q^{12} - 8 q^{15} - 2 q^{16} + 10 q^{17} + 16 q^{19} + 12 q^{20} + 4 q^{21} + 16 q^{22} + 2 q^{23} - 28 q^{24}+ \cdots + 60 q^{99}+O(q^{100}) $ 20 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 4 * q^6 - 2 * q^7 - 12 * q^9 + 10 * q^10 + 8 * q^11 - 24 * q^12 - 8 * q^15 - 2 * q^16 + 10 * q^17 + 16 * q^19 + 12 * q^20 + 4 * q^21 + 16 * q^22 + 2 * q^23 - 28 * q^24 + 18 * q^25 + 4 * q^27 + 18 * q^28 - 14 * q^30 - 48 * q^32 - 18 * q^33 + 2 * q^34 - 20 * q^35 - 36 * q^36 - 4 * q^37 - 8 * q^38 - 16 * q^40 + 28 * q^41 - 56 * q^42 + 22 * q^43 - 36 * q^44 + 6 * q^45 - 8 * q^46 - 40 * q^47 + 28 * q^48 + 18 * q^49 - 78 * q^50 - 10 * q^53 + 12 * q^54 + 26 * q^55 + 8 * q^59 + 28 * q^60 - 16 * q^61 + 40 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 + 28 * q^68 - 16 * q^69 - 12 * q^70 + 56 * q^71 + 4 * q^72 - 18 * q^74 + 34 * q^75 + 80 * q^76 - 28 * q^77 - 110 * q^80 - 14 * q^81 - 22 * q^82 + 48 * q^83 + 32 * q^84 + 28 * q^85 + 60 * q^86 + 62 * q^87 - 50 * q^88 - 6 * q^89 + 46 * q^90 - 8 * q^92 + 32 * q^93 + 48 * q^94 - 14 * q^95 + 56 * q^96 - 66 * q^97 + 30 * q^98 + 60 * q^99

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.427732	+	0.246951i	0.302452	+	0.174621i	0.643544	−	0.765409i	$-0.277463\pi$
$2$	0.427732	+	0.246951i	0.302452	+	0.174621i	−0.341092	+	0.940030i	$0.610797\pi$
$3$	0.908353	−	0.243392i	0.524438	−	0.140523i	0.0131191	−	0.999914i	$-0.495824\pi$
$3$	0.908353	−	0.243392i	0.524438	−	0.140523i	0.511318	+	0.859391i	$0.329157\pi$
$4$	−0.878030	−	1.52079i	−0.439015	−	0.760397i
$5$	−0.284413	+	2.21791i	−0.127193	+	0.991878i
$5$	−0.284413	+	2.21791i	−0.127193	+	0.991878i
$6$	0.448637	+	0.120212i	0.183155	+	0.0490763i
$7$	1.83775	+	3.18307i	0.694603	+	1.20309i	0.970314	+	0.241847i	$0.0777532\pi$
$7$	1.83775	+	3.18307i	0.694603	+	1.20309i	−0.275712	+	0.961240i	$0.588914\pi$
$8$		−	1.85513i		−	0.655886i
$9$	−1.83221	+	1.05783i	−0.610737	+	0.352609i
$10$	−0.669366	+	0.878433i	−0.211672	+	0.277785i
$11$	0.664257	−	0.177987i	0.200281	−	0.0536651i	−0.157284	−	0.987553i	$-0.550274\pi$
$11$	0.664257	−	0.177987i	0.200281	−	0.0536651i	0.357565	+	0.933888i	$0.383607\pi$
$12$	−1.16771	−	1.16771i	−0.337089	−	0.337089i
$13$		0			0
$13$		0			0
$14$			1.81533i			0.485168i
$15$	0.281475	+	2.08387i	0.0726764	+	0.538052i
$16$	−1.29794	+	2.24809i	−0.324484	+	0.562023i
$17$	−0.614565	+	2.29359i	−0.149054	+	0.556277i	0.850487	+	0.525995i	$0.176307\pi$
$17$	−0.614565	+	2.29359i	−0.149054	+	0.556277i	−0.999541	+	0.0302815i	$0.990360\pi$
$18$	−1.04493			−0.246291
$19$	−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	$0.867088\pi$
$20$	3.62270	−	1.51486i	0.810060	−	0.338732i
$21$	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	$-0.128426\pi$
$23$	−0.350507	−	1.30811i	−0.0730858	−	0.272760i	−0.992792	+	0.119846i	$0.961760\pi$
$24$	−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
$28$	3.22719	−	5.58966i	0.609882	−	1.05635i
$29$	8.24134	+	4.75814i	1.53038	+	0.883564i	0.999344	+	0.0362142i	$0.0115299\pi$
$29$	8.24134	+	4.75814i	1.53038	+	0.883564i	0.531034	+	0.847350i	$0.321803\pi$
$30$	−0.394217	+	0.960845i	−0.0719738	+	0.175426i
$31$	4.81595	−	4.81595i	0.864970	−	0.864970i	−0.126940	−	0.991910i	$-0.540516\pi$
$31$	4.81595	−	4.81595i	0.864970	−	0.864970i	0.991910	+	0.126940i	$0.0405157\pi$
$32$	−4.32351	+	2.49618i	−0.764295	+	0.441266i
$33$	0.560059	−	0.323350i	0.0974937	−	0.0562880i
$34$	−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
$37$	−0.917615	+	1.58936i	−0.150855	+	0.261289i	−0.931542	−	0.363634i	$-0.881536\pi$
$37$	−0.917615	+	1.58936i	−0.150855	+	0.261289i	0.780687	+	0.624922i	$0.214869\pi$
$38$	−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	0.976216	−	0.216801i	$-0.0695624\pi$
$41$	0.143350	+	0.534988i	0.0223874	+	0.0835510i	−0.953828	+	0.300352i	$0.902896\pi$
$42$	0.441838	+	1.64896i	0.0681771	+	0.254440i
$43$	2.09285	+	0.560778i	0.319157	+	0.0855178i	0.414841	−	0.909894i	$-0.363837\pi$
$43$	2.09285	+	0.560778i	0.319157	+	0.0855178i	−0.0956841	+	0.995412i	$0.530504\pi$
$44$	−0.853919	−	0.853919i	−0.128733	−	0.128733i
$45$	−1.82506	−	4.36453i	−0.272064	−	0.650626i
$46$	0.173116	−	0.646078i	0.0255246	−	0.0952590i
$47$	−3.80918			−0.555626			−0.277813	−	0.960635i	$-0.589610\pi$
$47$	−3.80918			−0.555626			−0.277813	+	0.960635i	$0.589610\pi$
$48$	−0.631815	+	2.35797i	−0.0911947	+	0.340343i
$49$	−3.25462	+	5.63717i	−0.464946	+	0.805310i
$50$	−1.75791	−	1.73443i	−0.248605	−	0.245285i
$51$			2.23297i			0.312678i
$52$		0			0
$53$	−2.47293	−	2.47293i	−0.339683	−	0.339683i	0.516565	−	0.856248i	$-0.327211\pi$
$53$	−2.47293	−	2.47293i	−0.339683	−	0.339683i	−0.856248	+	0.516565i	$0.827211\pi$
$54$	−2.29507	+	0.614963i	−0.312320	+	0.0836858i
$55$	0.205836	+	1.52388i	0.0277549	+	0.205480i
$56$	5.90499	−	3.40925i	0.789088	−	0.455580i
$57$			5.15084i			0.682245i
$58$	2.35005	+	4.07041i	0.308577	+	0.534471i
$59$	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	$0.346470\pi$
$60$	2.92199	−	2.25776i	0.377227	−	0.291476i
$61$	−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	$0.963210\pi$
$62$	3.24924	−	0.870630i	0.412653	−	0.110570i
$63$	−6.73428	−	3.88804i	−0.848439	−	0.489847i
$64$	2.72601			0.340751
$65$		0			0
$66$	0.319406			0.0393162
$67$	10.6066	+	6.12371i	1.29580	+	0.748130i	0.979676	−	0.200588i	$-0.0642852\pi$
$67$	10.6066	+	6.12371i	1.29580	+	0.748130i	0.316124	+	0.948718i	$0.397619\pi$
$68$	4.02768	−	1.07921i	0.488428	−	0.130874i
$69$	−0.636768	−	1.10291i	−0.0766579	−	0.132775i
$70$	−4.02624	−	0.516303i	−0.481227	−	0.0617101i
$71$	6.47512	+	1.73500i	0.768456	+	0.205907i	0.621689	−	0.783264i	$-0.286447\pi$
$71$	6.47512	+	1.73500i	0.768456	+	0.205907i	0.146767	+	0.989171i	$0.453113\pi$
$72$	1.96240	+	3.39898i	0.231271	+	0.400574i
$73$			3.37642i			0.395180i	0.980285	+	0.197590i	$0.0633115\pi$
$73$			3.37642i			0.395180i	−0.980285	+	0.197590i	$0.936688\pi$
$74$	−0.784986	+	0.453212i	−0.0912528	+	0.0526848i
$75$	−4.70187	+	0.0316067i	−0.542926	+	0.00364963i
$76$	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	$-0.943814\pi$
$79$		−	3.12149i		−	0.351195i	0.984462	−	0.175598i	$-0.0561857\pi$
$80$	−4.61691	−	3.51809i	−0.516186	−	0.393334i
$81$	0.911483	−	1.57873i	0.101276	−	0.175415i
$82$	−0.0708006	+	0.264231i	−0.00781862	+	0.0291795i
$83$	2.13918			0.234805			0.117403	−	0.993084i	$-0.462543\pi$
$83$	2.13918			0.234805			0.117403	+	0.993084i	$0.462543\pi$
$84$	1.57095	−	5.86286i	0.171405	−	0.639691i
$85$	−4.91217	−	2.01537i	−0.532800	−	0.218598i
$86$	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
$89$	−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
$93$	3.20242	−	5.54675i	0.332075	−	0.575171i
$94$	−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
$97$	−6.12606	+	3.53688i	−0.622007	+	0.359116i	−0.777650	−	0.628697i	$-0.783588\pi$
$97$	−6.12606	+	3.53688i	−0.622007	+	0.359116i	0.155643	+	0.987813i	$0.450255\pi$
$98$	−2.78421	+	1.60746i	−0.281248	+	0.162378i
$99$	−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	$-0.600774\pi$
$101$	−12.9641	−	7.48483i	−1.28998	−	0.744769i	−0.978650	+	0.205534i	$0.934107\pi$
$102$	−0.551433	+	0.955111i	−0.0546000	+	0.0945700i
$103$	−3.17851	+	3.17851i	−0.313188	+	0.313188i	−0.846143	−	0.532956i	$-0.821081\pi$
$103$	−3.17851	+	3.17851i	−0.313188	+	0.313188i	0.532956	+	0.846143i	$0.321081\pi$
$104$		0			0
$105$	−6.11581	+	4.72557i	−0.596842	+	0.461168i
$106$	−0.447058	−	1.66844i	−0.0434221	−	0.162054i
$107$	−3.94767	−	14.7329i	−0.381635	−	1.42428i	−0.843403	−	0.537282i	$-0.819451\pi$
$107$	−3.94767	−	14.7329i	−0.381635	−	1.42428i	0.461767	−	0.887001i	$-0.347216\pi$
$108$	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	$0.701107\pi$
$110$	−0.288282	+	0.702643i	−0.0274866	+	0.0669944i
$111$	−0.446681	+	1.66704i	−0.0423971	+	0.158228i
$112$	−9.54111			−0.901550
$113$	4.28882	−	16.0061i	0.403458	−	1.50573i	−0.403423	−	0.915014i	$-0.632180\pi$
$113$	4.28882	−	16.0061i	0.403458	−	1.50573i	0.806881	−	0.590713i	$-0.201154\pi$
$114$	−1.27200	+	2.20318i	−0.119134	+	0.206346i
$115$	3.00096	−	0.405349i	0.279841	−	0.0377990i
$116$		−	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
$120$	3.86583	−	0.522171i	0.352900	−	0.0476674i
$121$	−9.11672	+	5.26354i	−0.828793	+	0.478504i
$122$		−	3.06124i		−	0.277152i
$123$	0.260424	+	0.451067i	0.0234816	+	0.0406714i
$124$	−11.5526	−	3.09551i	−1.03746	−	0.277985i
$125$	4.17416	−	10.3719i	0.373349	−	0.927691i
$126$	−1.92031	−	3.32607i	−0.171075	−	0.296310i
$127$	8.01688	−	2.14812i	0.711383	−	0.190614i	0.115059	−	0.993359i	$-0.463294\pi$
$127$	8.01688	−	2.14812i	0.711383	−	0.190614i	0.596324	+	0.802744i	$0.296628\pi$
$128$	9.81302	+	5.66555i	0.867356	+	0.500768i
$129$	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	$0.480881\pi$
$132$	−0.983497	−	0.567822i	−0.0856025	−	0.0494226i
$133$	−19.4458	+	5.21049i	−1.68617	+	0.451807i
$134$	3.02451	+	5.23861i	0.261278	+	0.452547i
$135$	−6.57718	−	8.51216i	−0.566074	−	0.732610i
$136$	4.25489	+	1.14010i	0.364854	+	0.0977624i
$137$	−6.16380	−	10.6760i	−0.526609	−	0.912114i	−0.999519	−	0.0310029i	$-0.990130\pi$
$137$	−6.16380	−	10.6760i	−0.526609	−	0.912114i	0.472910	−	0.881111i	$-0.343203\pi$
$138$		−	0.629002i		−	0.0535442i
$139$	−5.54392	+	3.20078i	−0.470229	+	0.271487i	−0.716336	−	0.697756i	$-0.754182\pi$
$139$	−5.54392	+	3.20078i	−0.470229	+	0.271487i	0.246107	+	0.969243i	$0.420849\pi$
$140$	11.4795	+	8.74739i	0.970195	+	0.739289i
$141$	−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
$145$	−12.8971	+	16.9252i	−1.07104	+	1.40557i
$146$	−0.833811	+	1.44420i	−0.0690067	+	0.119523i
$147$	−1.58430	+	5.91269i	−0.130671	+	0.487670i
$148$	3.22278			0.264911
$149$	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	$-0.158291\pi$
$150$	−2.01894	−	1.14761i	−0.164846	−	0.0937022i
$151$	−3.31542	−	3.31542i	−0.269805	−	0.269805i	0.559217	−	0.829022i	$-0.311102\pi$
$151$	−3.31542	−	3.31542i	−0.269805	−	0.269805i	−0.829022	+	0.559217i	$0.811102\pi$
$152$	9.81486	+	2.62988i	0.796090	+	0.213312i
$153$	−1.30021	−	4.85244i	−0.105116	−	0.392297i
$154$	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	−0.192779	−	0.981242i	$-0.561750\pi$
$157$	9.87941	−	9.87941i	0.788463	−	0.788463i	0.981242	+	0.192779i	$0.0617501\pi$
$158$	0.770855	−	1.33516i	0.0613259	−	0.106220i
$159$	−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
$162$	0.779740	−	0.450183i	0.0612622	−	0.0353697i
$163$	0.114289	−	0.0659848i	0.00895180	−	0.00516833i	−0.495517	−	0.868598i	$-0.665022\pi$
$163$	0.114289	−	0.0659848i	0.00895180	−	0.00516833i	0.504469	+	0.863430i	$0.331688\pi$
$164$	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
$167$	−10.8184	+	18.7380i	−0.837152	+	1.44999i	0.0551149	+	0.998480i	$0.482447\pi$
$167$	−10.8184	+	18.7380i	−0.837152	+	1.44999i	−0.892267	+	0.451509i	$0.850886\pi$
$168$	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
$172$	−0.984760	−	3.67518i	−0.0750873	−	0.280230i
$173$	7.47013	+	2.00162i	0.567943	+	0.152180i	0.531353	−	0.847150i	$-0.321684\pi$
$173$	7.47013	+	2.00162i	0.567943	+	0.152180i	0.0365902	+	0.999330i	$0.488350\pi$
$174$	3.12539	+	3.12539i	0.236935	+	0.236935i
$175$	−4.87565	−	17.7189i	−0.368565	−	1.33942i
$176$	−0.462032	+	1.72433i	−0.0348270	+	0.129976i
$177$	9.78515			0.735497
$178$	0.431768	−	1.61138i	0.0323624	−	0.120778i
$179$	8.17681	−	14.1627i	0.611164	−	1.05857i	−0.379881	−	0.925035i	$-0.624035\pi$
$179$	8.17681	−	14.1627i	0.611164	−	1.05857i	0.991045	−	0.133531i	$-0.0426317\pi$
$180$	−5.03510	+	6.60773i	−0.375294	+	0.492511i
$181$			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
$185$	−3.26406	−	2.48722i	−0.239979	−	0.182864i
$186$	2.73955	−	1.58168i	0.200873	−	0.115974i
$187$			1.63292i			0.119411i
$188$	3.34458	+	5.79298i	0.243928	+	0.422496i
$189$	−17.0793	−	4.57640i	−1.24234	−	0.332884i
$190$	−3.69858	−	4.78669i	−0.268324	−	0.347263i
$191$	−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	$0.893471\pi$
$192$	2.47618	−	0.663490i	0.178703	−	0.0478833i
$193$	8.74813	+	5.05073i	0.629704	+	0.363560i	0.780637	−	0.624984i	$-0.214895\pi$
$193$	8.74813	+	5.05073i	0.629704	+	0.363560i	−0.150934	+	0.988544i	$0.548228\pi$
$194$	−3.49375			−0.250836
$195$		0			0
$196$	11.4306			0.816473
$197$	11.3137	+	6.53197i	0.806068	+	0.465384i	0.845589	−	0.533835i	$-0.179250\pi$
$197$	11.3137	+	6.53197i	0.806068	+	0.465384i	−0.0395205	+	0.999219i	$0.512583\pi$
$198$	−0.694099	+	0.185983i	−0.0493275	+	0.0132173i
$199$	−3.92506	−	6.79840i	−0.278240	−	0.481926i	0.692707	−	0.721219i	$-0.256418\pi$
$199$	−3.92506	−	6.79840i	−0.278240	−	0.481926i	−0.970947	+	0.239293i	$0.923084\pi$
$200$	−2.34043	+	8.97550i	−0.165493	+	0.634664i
$201$	11.1250	+	2.98093i	0.784695	+	0.210258i
$202$	−3.69677	−	6.40300i	−0.260104	−	0.450513i
$203$			34.9770i			2.45491i
$204$	3.39588	−	1.96061i	0.237759	−	0.137270i
$205$	−1.22732	+	0.165779i	−0.0857200	+	0.0115785i
$206$	−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
$210$	−3.78291	+	0.510970i	−0.261045	+	0.0352603i
$211$	−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	$0.307327\pi$
$212$	−1.58951	+	5.93213i	−0.109168	+	0.407420i
$213$	6.30398			0.431942
$214$	1.94976	−	7.27661i	0.133283	−	0.497419i
$215$	−1.83899	+	4.48226i	−0.125418	+	0.305687i
$216$	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
$219$	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
$223$	−4.97247	+	8.61258i	−0.332981	+	0.576741i	−0.983095	−	0.183096i	$-0.941388\pi$
$223$	−4.97247	+	8.61258i	−0.332981	+	0.576741i	0.650114	+	0.759837i	$0.274721\pi$
$224$	−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
$227$	−12.6490	+	7.30290i	−0.839543	+	0.484710i	−0.857109	−	0.515135i	$-0.827742\pi$
$227$	−12.6490	+	7.30290i	−0.839543	+	0.484710i	0.0175659	+	0.999846i	$0.494408\pi$
$228$	7.83336	−	4.52259i	0.518777	−	0.299516i
$229$	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
$232$	8.82695	−	15.2887i	0.579517	−	1.00375i
$233$	16.5625	−	16.5625i	1.08505	−	1.08505i	0.0890148	−	0.996030i	$-0.471628\pi$
$233$	16.5625	−	16.5625i	1.08505	−	1.08505i	0.996030	−	0.0890148i	$-0.0283719\pi$
$234$		0			0
$235$	1.08338	−	8.44841i	0.0706719	−	0.551113i
$236$	−4.72926	−	17.6498i	−0.307848	−	1.14891i
$237$	−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	$0.982801\pi$
$240$	−5.05005	−	2.07194i	−0.325980	−	0.133743i
$241$	−0.802065	+	2.99335i	−0.0516656	+	0.192818i	−0.986935	−	0.161117i	$-0.948490\pi$
$241$	−0.802065	+	2.99335i	−0.0516656	+	0.192818i	0.935270	+	0.353936i	$0.115157\pi$
$242$	−5.19935			−0.334227
$243$	4.17903	−	15.5964i	0.268085	−	1.00051i
$244$	−5.44211	+	9.42600i	−0.348395	+	0.603438i
$245$	−11.5771	−	8.82173i	−0.739631	−	0.563600i
$246$			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
$250$	4.34677	−	3.40558i	0.274914	−	0.215388i
$251$	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	$-0.0485382\pi$
$252$			13.6553i			0.860201i
$253$	−0.465654	−	0.806536i	−0.0292754	−	0.0507065i
$254$	3.95955	+	1.06096i	0.248444	+	0.0665704i
$255$	−4.95251	−	0.635084i	−0.310138	−	0.0397705i
$256$	0.0722145	+	0.125079i	0.00451341	+	0.00781745i
$257$	6.92097	−	1.85447i	0.431718	−	0.115679i	−0.0364143	−	0.999337i	$-0.511594\pi$
$257$	6.92097	−	1.85447i	0.431718	−	0.115679i	0.468133	+	0.883658i	$0.344927\pi$
$258$	0.871519	+	0.503172i	0.0542584	+	0.0313261i
$259$	−6.74538			−0.419137
$260$		0			0
$261$	−20.1332			−1.24621
$262$	0.587740	+	0.339332i	0.0363107	+	0.0209640i
$263$	13.0066	−	3.48511i	0.802023	−	0.214901i	0.165551	−	0.986201i	$-0.447060\pi$
$263$	13.0066	−	3.48511i	0.802023	−	0.214901i	0.636472	+	0.771300i	$0.280393\pi$
$264$	−0.599855	−	1.03898i	−0.0369185	−	0.0639448i
$265$	6.18807	−	4.78140i	0.380130	−	0.293719i
$266$	−9.60433	−	2.57347i	−0.588879	−	0.157790i
$267$	−1.58816	−	2.75077i	−0.0971938	−	0.168345i
$268$		−	21.5072i		−	1.31376i
$269$	7.01806	−	4.05188i	0.427899	−	0.247047i	−0.270552	−	0.962705i	$-0.587206\pi$
$269$	7.01806	−	4.05188i	0.427899	−	0.247047i	0.698451	+	0.715658i	$0.253873\pi$
$270$	−0.711183	−	5.26516i	−0.0432812	−	0.320427i
$271$	8.88325	−	2.38026i	0.539619	−	0.144590i	0.0212923	−	0.999773i	$-0.493222\pi$
$271$	8.88325	−	2.38026i	0.539619	−	0.144590i	0.518326	+	0.855183i	$0.326555\pi$
$272$	−4.35853	−	4.35853i	−0.264275	−	0.264275i
$273$		0			0
$274$		−	6.08862i		−	0.367827i
$275$	−3.43837	+	0.0231133i	−0.207341	+	0.00139378i
$276$	−1.11820	+	1.93679i	−0.0673080	+	0.116581i
$277$	−6.68911	+	24.9641i	−0.401910	+	1.49995i	0.407775	+	0.913082i	$0.366305\pi$
$277$	−6.68911	+	24.9641i	−0.401910	+	1.49995i	−0.809685	+	0.586865i	$0.800362\pi$
$278$	−3.16174			−0.189629
$279$	−3.72939	+	13.9183i	−0.223273	+	0.833266i
$280$	5.88194	+	14.0664i	0.351513	+	0.840626i
$281$	5.41928	+	5.41928i	0.323287	+	0.323287i	0.850027	−	0.526740i	$-0.176586\pi$
$281$	5.41928	+	5.41928i	0.323287	+	0.323287i	−0.526740	+	0.850027i	$0.676586\pi$
$282$	−1.70894	−	0.457909i	−0.101766	−	0.0272681i
$283$	−2.27388	−	8.48623i	−0.135168	−	0.504454i	−0.999997	−	0.00238762i	$-0.999240\pi$
$283$	−2.27388	−	8.48623i	−0.135168	−	0.504454i	0.864829	−	0.502066i	$-0.167427\pi$
$284$	−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
$288$	5.28105	−	9.14705i	0.311189	−	0.538995i
$289$	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
$292$	5.13484	−	2.96460i	0.300494	−	0.173490i
$293$	−11.4627	+	6.61798i	−0.669657	+	0.386626i	−0.795947	−	0.605367i	$-0.793026\pi$
$293$	−11.4627	+	6.61798i	−0.669657	+	0.386626i	0.126290	+	0.991993i	$0.459693\pi$
$294$	−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
$297$	−1.65415	+	2.86507i	−0.0959834	+	0.166248i
$298$	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
$302$	−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
$305$	12.7865	−	5.34674i	0.732150	−	0.306154i
$306$	0.642175	−	2.39663i	0.0367107	−	0.137006i
$307$	−15.4782			−0.883389			−0.441695	−	0.897165i	$-0.645623\pi$
$307$	−15.4782			−0.883389			−0.441695	+	0.897165i	$0.645623\pi$
$308$	1.14880	−	4.28737i	0.0654588	−	0.244296i
$309$	−2.11358	+	3.66083i	−0.120237	+	0.208257i
$310$	1.00685	+	7.45412i	0.0571854	+	0.423366i
$311$			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	0.846765	+	0.531967i	$0.178547\pi$
$313$	24.3923	+	24.3923i	1.37873	+	1.37873i	0.531967	+	0.846765i	$0.321453\pi$
$314$	6.66547	−	1.78601i	0.376154	−	0.100790i
$315$	10.5386	−	13.8302i	0.593784	−	0.779243i
$316$	−4.74714	+	2.74076i	−0.267048	+	0.154180i
$317$			18.9851i			1.06631i	0.846017	+	0.533156i	$0.178994\pi$
$317$			18.9851i			1.06631i	−0.846017	+	0.533156i	$0.821006\pi$
$318$	−0.812173	−	1.40673i	−0.0455444	−	0.0788852i
$319$	6.32125	+	1.69378i	0.353922	+	0.0948332i
$320$	−0.775312	+	6.04604i	−0.0433412	+	0.337984i
$321$	−7.17175	−	12.4218i	−0.400288	−	0.693319i
$322$	2.37466	−	0.636287i	0.132334	−	0.0354589i
$323$	−11.2634	−	6.50293i	−0.626712	−	0.361832i
$324$	−3.20124			−0.177847
$325$		0			0
$326$	0.0651800			0.00360999
$327$	2.60181	+	1.50216i	0.143881	+	0.0830695i
$328$	0.992469	−	0.265931i	0.0548000	−	0.0146836i
$329$	−7.00031	−	12.1249i	−0.385940	−	0.668467i
$330$	−0.0908432	+	0.708414i	−0.00500075	+	0.0389969i
$331$	6.77766	+	1.81607i	0.372534	+	0.0998202i	0.440228	−	0.897886i	$-0.354898\pi$
$331$	6.77766	+	1.81607i	0.372534	+	0.0998202i	−0.0676941	+	0.997706i	$0.521564\pi$
$332$	−1.87826	−	3.25325i	−0.103083	−	0.178545i
$333$		−	3.88272i		−	0.212772i
$334$	−9.25473	+	5.34322i	−0.506396	+	0.292368i
$335$	−16.5985	+	21.7827i	−0.906871	+	1.19012i
$336$	−8.66669	+	2.32223i	−0.472807	+	0.126688i
$337$	−1.10195	−	1.10195i	−0.0600271	−	0.0600271i	0.676456	−	0.736483i	$-0.263515\pi$
$337$	−1.10195	−	1.10195i	−0.0600271	−	0.0600271i	−0.736483	+	0.676456i	$0.763515\pi$
$338$		0			0
$339$		−	15.5830i		−	0.846355i
$340$	1.24807	+	9.23996i	0.0676862	+	0.501107i
$341$	2.34185	−	4.05620i	0.126818	−	0.219656i
$342$	1.48132	−	5.52836i	0.0801006	−	0.298940i
$343$	1.80378			0.0973947
$344$	1.04031	−	3.88250i	0.0560899	−	0.209331i
$345$	2.62727	−	1.09861i	0.141447	−	0.0591471i
$346$	2.70091	+	2.70091i	0.145202	+	0.145202i
$347$	−24.9510	−	6.68561i	−1.33944	−	0.358902i	−0.483214	−	0.875502i	$-0.660531\pi$
$347$	−24.9510	−	6.68561i	−1.33944	−	0.358902i	−0.856227	+	0.516600i	$0.827197\pi$
$348$	−4.06737	−	15.1796i	−0.218034	−	0.813714i
$349$	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
$353$	1.63274	−	2.82798i	0.0869017	−	0.150518i	−0.819298	−	0.573368i	$-0.805637\pi$
$353$	1.63274	−	2.82798i	0.0869017	−	0.150518i	0.906200	+	0.422849i	$0.138970\pi$
$354$	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
$357$	−7.10769	+	4.10363i	−0.376179	+	0.217187i
$358$	6.99496	−	4.03854i	0.369695	−	0.213444i
$359$	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
$362$	−4.45468	+	7.71573i	−0.234133	+	0.405530i
$363$	−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
$367$	6.49371	+	24.2349i	0.338969	+	1.26505i	0.899502	+	0.436917i	$0.143930\pi$
$367$	6.49371	+	24.2349i	0.338969	+	1.26505i	−0.560533	+	0.828132i	$0.689404\pi$
$368$	3.39569	+	0.909872i	0.177012	+	0.0474303i
$369$	−0.828572	−	0.828572i	−0.0431337	−	0.0431337i
$370$	−0.781922	−	1.86992i	−0.0406502	−	0.0972128i
$371$	3.32690	−	12.4161i	0.172724	−	0.644614i
$372$	−11.2473			−0.583144
$373$	−2.95740	+	11.0372i	−0.153128	+	0.571483i	0.846130	+	0.532976i	$0.178927\pi$
$373$	−2.95740	+	11.0372i	−0.153128	+	0.571483i	−0.999258	+	0.0385061i	$0.987740\pi$
$374$	−0.403250	+	0.698450i	−0.0208516	+	0.0361160i
$375$	1.26717	−	10.4373i	0.0654364	−	0.538980i
$376$			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	$0.433102\pi$
$380$	2.87896	+	21.3140i	0.147687	+	1.09339i
$381$	6.75932	−	3.90249i	0.346290	−	0.199931i
$382$		−	2.56386i		−	0.131179i
$383$	13.2258	+	22.9077i	0.675806	+	1.17053i	0.976233	+	0.216725i	$0.0695376\pi$
$383$	13.2258	+	22.9077i	0.675806	+	1.17053i	−0.300427	+	0.953805i	$0.597129\pi$
$384$	10.2926	+	2.75790i	0.525244	+	0.140739i
$385$	−4.47235	+	3.45570i	−0.227932	+	0.176119i
$386$	2.49457	+	4.32072i	0.126970	+	0.219919i
$387$	−4.42775	+	1.18641i	−0.225075	+	0.0603088i
$388$	10.7577	+	6.21098i	0.546141	+	0.315315i
$389$	−0.650094			−0.0329611			−0.0164805	−	0.999864i	$-0.505246\pi$
$389$	−0.650094			−0.0329611			−0.0164805	+	0.999864i	$0.505246\pi$
$390$		0			0
$391$	3.21568			0.162624
$392$	10.4577	+	6.03773i	0.528191	+	0.304951i
$393$	1.24815	−	0.334442i	0.0629610	−	0.0168704i
$394$	3.22615	+	5.58786i	0.162531	+	0.281512i
$395$	6.92317	+	0.887791i	0.348343	+	0.0446696i
$396$	2.46786	+	0.661261i	0.124015	+	0.0332296i
$397$	13.5041	+	23.3897i	0.677750	+	1.17390i	0.975657	+	0.219303i	$0.0703782\pi$
$397$	13.5041	+	23.3897i	0.677750	+	1.17390i	−0.297907	+	0.954595i	$0.596288\pi$
$398$		−	3.87719i		−	0.194346i
$399$	−16.3955	+	9.46593i	−0.820800	+	0.473889i
$400$	9.11589	−	9.23928i	0.455795	−	0.461964i
$401$	4.78969	−	1.28339i	0.239186	−	0.0640896i	−0.137235	−	0.990539i	$-0.543821\pi$
$401$	4.78969	−	1.28339i	0.239186	−	0.0640896i	0.376421	+	0.926449i	$0.377155\pi$
$402$	4.02236	+	4.02236i	0.200617	+	0.200617i
$403$		0			0
$404$			26.2876i			1.30786i
$405$	3.24225	+	2.47060i	0.161109	+	0.122765i
$406$	−8.63761	+	14.9608i	−0.428677	+	0.742491i
$407$	−0.326647	+	1.21906i	−0.0161913	+	0.0604268i
$408$	4.14243			0.205081
$409$	−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	$0.131090\pi$
$410$	−0.565904	−	0.232180i	−0.0279480	−	0.0114665i
$411$	−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
$414$	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
$418$	−0.930187	+	1.61113i	−0.0454969	+	0.0788030i
$419$	−4.65114	−	2.68534i	−0.227223	−	0.131187i	0.382067	−	0.924135i	$-0.375212\pi$
$419$	−4.65114	−	2.68534i	−0.227223	−	0.131187i	−0.609290	+	0.792947i	$0.708546\pi$
$420$	12.5565	+	5.15169i	0.612693	+	0.251377i
$421$	14.1377	−	14.1377i	0.689029	−	0.689029i	−0.272988	−	0.962017i	$-0.588012\pi$
$421$	14.1377	−	14.1377i	0.689029	−	0.689029i	0.962017	+	0.272988i	$0.0880119\pi$
$422$	−5.31418	+	3.06814i	−0.258690	+	0.149355i
$423$	6.97923	−	4.02946i	0.339342	−	0.195919i
$424$	−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
$427$	11.3905	−	19.7289i	0.551225	−	0.954750i
$428$	−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	$-0.951656\pi$
$431$	−4.31985	−	16.1219i	−0.208080	−	0.776564i	0.780409	−	0.625269i	$-0.215011\pi$
$432$	−3.23215	−	12.0625i	−0.155507	−	0.580360i
$433$	7.33490	+	1.96538i	0.352493	+	0.0944502i	0.430721	−	0.902485i	$-0.358259\pi$
$433$	7.33490	+	1.96538i	0.352493	+	0.0944502i	−0.0782277	+	0.996936i	$0.524926\pi$
$434$	8.74255	+	8.74255i	0.419656	+	0.419656i
$435$	−7.59559	+	18.5131i	−0.364181	+	0.887637i
$436$	1.45201	−	5.41899i	0.0695388	−	0.259522i
$437$	7.41767			0.354835
$438$	−0.405886	+	1.51479i	−0.0193940	+	0.0723794i
$439$	6.84536	−	11.8565i	0.326711	−	0.565880i	−0.655146	−	0.755502i	$-0.727393\pi$
$439$	6.84536	−	11.8565i	0.326711	−	0.565880i	0.981857	+	0.189622i	$0.0607262\pi$
$440$	2.82699	−	0.381851i	0.134772	−	0.0182040i
$441$		−	13.7713i		−	0.655777i
$442$		0			0
$443$	6.46290	+	6.46290i	0.307062	+	0.307062i	0.843769	−	0.536707i	$-0.180332\pi$
$443$	6.46290	+	6.46290i	0.307062	+	0.307062i	−0.536707	+	0.843769i	$0.680332\pi$
$444$	2.92742	−	0.784399i	0.138929	−	0.0372259i
$445$	7.48467	−	1.01098i	0.354807	−	0.0479250i
$446$	−4.25377	+	2.45591i	−0.201422	+	0.116291i
$447$		−	15.8010i		−	0.747364i
$448$	5.00971	+	8.67708i	0.236687	+	0.409953i
$449$	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	$0.375828\pi$
$450$	5.05558	+	1.31828i	0.238322	+	0.0621443i
$451$	0.190442	+	0.329855i	0.00896755	+	0.0155323i
$452$	−28.1077	+	7.53143i	−1.32207	+	0.354249i
$453$	−3.81852	−	2.20462i	−0.179409	−	0.103582i
$454$	−7.21383			−0.338562
$455$		0			0
$456$	9.55545			0.447475
$457$	0.716665	+	0.413767i	0.0335242	+	0.0193552i	0.516668	−	0.856186i	$-0.327172\pi$
$457$	0.716665	+	0.413767i	0.0335242	+	0.0193552i	−0.483144	+	0.875541i	$0.660505\pi$
$458$	10.5374	−	2.82349i	0.492381	−	0.131933i
$459$	−5.71155	−	9.89269i	−0.266592	−	0.461751i
$460$	−3.25138	−	4.20792i	−0.151596	−	0.196195i
$461$	−23.2589	−	6.23219i	−1.08327	−	0.290262i	−0.327337	−	0.944908i	$-0.606151\pi$
$461$	−23.2589	−	6.23219i	−1.08327	−	0.290262i	−0.755936	+	0.654646i	$0.772818\pi$
$462$	0.586988	+	1.01669i	0.0273091	+	0.0473008i
$463$			6.35566i			0.295373i	0.989034	+	0.147686i	$0.0471826\pi$
$463$			6.35566i			0.295373i	−0.989034	+	0.147686i	$0.952817\pi$
$464$	−21.3935	+	12.3515i	−0.993167	+	0.573405i
$465$	11.3914	+	8.68022i	0.528262	+	0.402536i
$466$	11.1744	−	2.99418i	0.517645	−	0.138703i
$467$	−15.6194	−	15.6194i	−0.722781	−	0.722781i	0.246390	−	0.969171i	$-0.420756\pi$
$467$	−15.6194	−	15.6194i	−0.722781	−	0.722781i	−0.969171	+	0.246390i	$0.920756\pi$
$468$		0			0
$469$			45.0153i			2.07861i
$470$	2.54974	−	3.34611i	0.117611	−	0.154345i
$471$	6.56942	−	11.3786i	0.302703	−	0.524297i
$472$	4.99605	−	18.6455i	0.229962	−	0.858229i
$473$	1.49000			0.0685104
$474$	0.375240	−	1.40042i	0.0172354	−	0.0643232i
$475$	13.5335	−	23.8089i	0.620961	−	1.09243i
$476$	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
$479$	−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
$483$	2.34044	−	4.05375i	0.106494	−	0.184452i
$484$	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
$487$	−5.33382	+	3.07948i	−0.241698	+	0.139545i	−0.615957	−	0.787780i	$-0.711231\pi$
$487$	−5.33382	+	3.07948i	−0.241698	+	0.139545i	0.374259	+	0.927324i	$0.377897\pi$
$488$	−9.95775	+	5.74911i	−0.450766	+	0.260250i
$489$	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	$-0.441821\pi$
$491$	−12.8290	−	7.40681i	−0.578964	−	0.334265i	−0.760721	+	0.649078i	$0.775155\pi$
$492$	0.457320	−	0.792102i	0.0206176	−	0.0357107i
$493$	−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
$497$	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	$0.517826\pi$
$500$	−19.4386	+	2.75881i	−0.869319	+	0.123378i
$501$	−5.26622	+	19.6538i	−0.235278	+	0.878068i
$502$	14.5844			0.650933
$503$	−10.0318	+	37.4393i	−0.447297	+	1.66934i	0.262502	+	0.964932i	$0.415452\pi$
$503$	−10.0318	+	37.4393i	−0.447297	+	1.66934i	−0.709799	+	0.704404i	$0.751214\pi$
$504$	−7.21280	+	12.4929i	−0.321284	+	0.556479i
$505$	20.2878	−	26.6244i	0.902796	−	1.18477i
$506$		−	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	$0.377400\pi$
$510$	−1.96151	−	1.49467i	−0.0868572	−	0.0661852i
$511$	−10.7474	+	6.20501i	−0.475437	+	0.274493i
$512$		−	22.5909i		−	0.998384i
$513$	−13.1750	−	22.8197i	−0.581688	−	1.00751i
$514$	3.41828	+	0.915926i	0.150774	+	0.0403997i
$515$	−6.14563	−	7.95364i	−0.270809	−	0.350479i
$516$	−1.78902	−	3.09867i	−0.0787572	−	0.136411i
$517$	−2.53028	+	0.677985i	−0.111281	+	0.0298178i
$518$	−2.88521	−	1.66578i	−0.126769	−	0.0731900i
$519$	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	$0.598259\pi$
$522$	−8.61159	−	4.97191i	−0.376919	−	0.217614i
$523$	−30.2601	+	8.10818i	−1.32318	+	0.354546i	−0.850170	−	0.526509i	$-0.823501\pi$
$523$	−30.2601	+	8.10818i	−1.32318	+	0.354546i	−0.473014	+	0.881055i	$0.656834\pi$
$524$	−1.20649	−	2.08970i	−0.0527057	−	0.0912890i
$525$	−8.74146	−	14.9083i	−0.381508	−	0.650652i
$526$	6.42400	+	1.72130i	0.280100	+	0.0750524i
$527$	8.08609	+	14.0055i	0.352236	+	0.610090i
$528$			1.67875i			0.0730583i
$529$	18.3303	−	10.5830i	0.796969	−	0.460130i
$530$	3.82760	−	0.517007i	0.166260	−	0.0224574i
$531$	−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
$535$	33.7990	−	4.56534i	1.46126	−	0.197377i
$536$	11.3602	−	19.6765i	0.490688	−	0.849897i
$537$	3.98035	−	14.8549i	0.171765	−	0.641035i
$538$	4.00246			0.172558
$539$	−1.15856	+	4.32381i	−0.0499028	+	0.186240i
$540$	−7.17027	+	17.4765i	−0.308559	+	0.752067i
$541$	−10.7732	−	10.7732i	−0.463175	−	0.463175i	0.436520	−	0.899695i	$-0.356211\pi$
$541$	−10.7732	−	10.7732i	−0.463175	−	0.463175i	−0.899695	+	0.436520i	$0.856211\pi$
$542$	4.38745	+	1.17561i	0.188457	+	0.0504969i
$543$	4.39048	+	16.3855i	0.188414	+	0.703170i
$544$	−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	−0.332828	−	0.942987i	$-0.608003\pi$
$547$	14.2704	−	14.2704i	0.610159	−	0.610159i	0.942987	+	0.332828i	$0.108003\pi$
$548$	−10.8240	+	18.7477i	−0.462379	+	0.800863i
$549$	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
$552$	−2.04605	+	1.18128i	−0.0870855	+	0.0502788i
$553$	9.93592	−	5.73651i	0.422518	−	0.243941i
$554$	−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
$557$	−8.35584	+	14.4727i	−0.354048	+	0.613229i	−0.986955	−	0.160999i	$-0.948528\pi$
$557$	−8.35584	+	14.4727i	−0.354048	+	0.613229i	0.632906	+	0.774228i	$0.281862\pi$
$558$	−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
$562$	0.979701	+	3.65629i	0.0413262	+	0.154231i
$563$	21.8019	+	5.84179i	0.918839	+	0.246202i	0.687089	−	0.726573i	$-0.258888\pi$
$563$	21.8019	+	5.84179i	0.918839	+	0.246202i	0.231750	+	0.972775i	$0.425555\pi$
$564$	4.44802	+	4.44802i	0.187296	+	0.187296i
$565$	34.2802	+	14.0645i	1.44218	+	0.591700i
$566$	1.12307	−	4.19136i	0.0472063	−	0.176176i
$567$	6.70030			0.281386
$568$	3.21865	−	12.0122i	0.135052	−	0.504019i
$569$	2.86843	−	4.96826i	0.120251	−	0.208280i	−0.799616	−	0.600512i	$-0.794963\pi$
$569$	2.86843	−	4.96826i	0.120251	−	0.208280i	0.919866	+	0.392232i	$0.128297\pi$
$570$	−4.52466	−	3.44780i	−0.189517	−	0.144412i
$571$		−	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
$575$	0.0455166	+	6.77112i	0.00189817	+	0.282375i
$576$	−4.99463	+	2.88365i	−0.208109	+	0.120152i
$577$			28.9429i			1.20491i	0.798153	+	0.602455i	$0.205811\pi$
$577$			28.9429i			1.20491i	−0.798153	+	0.602455i	$0.794189\pi$
$578$	2.80580	+	4.85978i	0.116706	+	0.202140i
$579$	9.17569	+	2.45862i	0.381329	+	0.102177i
$580$	37.0638	+	4.75287i	1.53899	+	0.197352i
$581$	3.93127	+	6.80916i	0.163097	+	0.282491i
$582$	−3.17355	+	0.850351i	−0.131548	+	0.0352482i
$583$	−2.08281	−	1.20251i	−0.0862613	−	0.0498030i
$584$	6.26369			0.259193
$585$		0			0
$586$	−6.53726			−0.270052
$587$	−17.0534	−	9.84577i	−0.703868	−	0.406379i	0.104918	−	0.994481i	$-0.466542\pi$
$587$	−17.0534	−	9.84577i	−0.703868	−	0.406379i	−0.808787	+	0.588102i	$0.799875\pi$
$588$	10.3830	−	2.78213i	0.428189	−	0.114733i
$589$	18.6524	+	32.3069i	0.768558	+	1.33118i
$590$	−9.09338	+	7.02628i	−0.374368	+	0.289267i
$591$	11.8667	+	3.17966i	0.488129	+	0.130794i
$592$	−2.38201	−	4.12577i	−0.0979001	−	0.169568i
$593$		−	21.8216i		−	0.896106i	−0.894007	−	0.448053i	$-0.852118\pi$
$593$		−	21.8216i		−	0.896106i	0.894007	−	0.448053i	$-0.147882\pi$
$594$	−1.41506	+	0.816987i	−0.0580607	+	0.0335214i
$595$	−2.61226	−	19.3395i	−0.107092	−	0.792844i
$596$	−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	$-0.721137\pi$
$599$		−	37.6041i		−	1.53646i	0.640172	−	0.768232i	$-0.278863\pi$
$600$	0.0586345	+	8.72256i	0.00239374	+	0.356097i
$601$	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	$0.0308064\pi$
$602$	−1.01800	+	3.79922i	−0.0414905	+	0.154845i
$603$	−25.9113			−1.05519
$604$	−2.13103	+	7.95310i	−0.0867103	+	0.323607i
$605$	−9.08113	−	21.7171i	−0.369201	−	0.882924i
$606$	−4.91641	−	4.91641i	−0.199716	−	0.199716i
$607$	−33.2808	−	8.91757i	−1.35083	−	0.361953i	−0.490387	−	0.871505i	$-0.663144\pi$
$607$	−33.2808	−	8.91757i	−1.35083	−	0.361953i	−0.860440	+	0.509552i	$0.829811\pi$
$608$	−7.07732	−	26.4129i	−0.287023	−	1.07119i
$609$	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
$613$	12.4332	−	21.5350i	0.502173	−	0.869790i	−0.497824	−	0.867278i	$-0.665867\pi$
$613$	12.4332	−	21.5350i	0.502173	−	0.869790i	0.999997	−	0.00251133i	$-0.000799381\pi$
$614$	−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
$617$	24.0895	−	13.9081i	0.969805	−	0.559917i	0.0706286	−	0.997503i	$-0.477499\pi$
$617$	24.0895	−	13.9081i	0.969805	−	0.559917i	0.899177	+	0.437585i	$0.144166\pi$
$618$	−1.80809	+	1.04390i	−0.0727321	+	0.0419919i
$619$	−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
$622$	−1.32099	+	2.28803i	−0.0529671	+	0.0917416i
$623$	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
$627$	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
$630$	7.92308	−	3.31309i	0.315663	−	0.131997i
$631$	−3.38116	+	12.6187i	−0.134602	+	0.502341i	0.865397	+	0.501086i	$0.167066\pi$
$631$	−3.38116	+	12.6187i	−0.134602	+	0.502341i	−0.999999	+	0.00125496i	$0.999601\pi$
$632$	−5.79076			−0.230344
$633$	−3.02393	+	11.2855i	−0.120190	+	0.448557i
$634$	−4.68840	+	8.12054i	−0.186200	+	0.322508i
$635$	2.48422	+	18.3916i	0.0985832	+	0.729850i
$636$			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
$640$	−15.3566	+	20.1530i	−0.607023	+	0.796617i
$641$	−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	$0.515160\pi$
$642$		−	7.08428i		−	0.279594i
$643$	−15.7510	−	27.2816i	−0.621161	−	1.07588i	−0.989270	−	0.146099i	$-0.953328\pi$
$643$	−15.7510	−	27.2816i	−0.621161	−	1.07588i	0.368109	−	0.929783i	$-0.380005\pi$
$644$	−8.44305	−	2.26231i	−0.332703	−	0.0891475i
$645$	−0.579501	+	4.51907i	−0.0228178	+	0.177938i
$646$	−3.21181	−	5.56301i	−0.126367	−	0.218874i
$647$	40.3457	−	10.8106i	1.58615	−	0.425008i	0.645329	−	0.763905i	$-0.276720\pi$
$647$	40.3457	−	10.8106i	1.58615	−	0.425008i	0.940824	+	0.338896i	$0.110054\pi$
$648$	−2.92875	−	1.69092i	−0.115052	−	0.0664254i
$649$	7.15565			0.280884
$650$		0			0
$651$	23.5409			0.922641
$652$	−0.200698	−	0.115873i	−0.00785996	−	0.00453795i
$653$	14.6695	−	3.93069i	0.574064	−	0.153820i	0.0399041	−	0.999204i	$-0.487295\pi$
$653$	14.6695	−	3.93069i	0.574064	−	0.153820i	0.534160	+	0.845384i	$0.320628\pi$
$654$	0.741918	+	1.28504i	0.0290113	+	0.0502490i
$655$	−0.390807	+	3.04759i	−0.0152701	+	0.119079i
$656$	−1.38876	−	0.372117i	−0.0542220	−	0.0145287i
$657$	−3.57167	−	6.18632i	−0.139344	−	0.241351i
$658$		−	6.91493i		−	0.269572i
$659$	24.6914	−	14.2556i	0.961840	−	0.555319i	0.0651015	−	0.997879i	$-0.479263\pi$
$659$	24.6914	−	14.2556i	0.961840	−	0.555319i	0.896739	+	0.442560i	$0.145930\pi$
$660$	1.53910	−	2.01981i	0.0599092	−	0.0786210i
$661$	6.08664	−	1.63091i	0.236743	−	0.0634351i	−0.138497	−	0.990363i	$-0.544227\pi$
$661$	6.08664	−	1.63091i	0.236743	−	0.0634351i	0.375240	+	0.926928i	$0.377560\pi$
$662$	2.45054	+	2.45054i	0.0952430	+	0.0952430i
$663$		0			0
$664$		−	3.96845i		−	0.154006i
$665$	−6.02575	−	44.6110i	−0.233669	−	1.72994i
$666$	0.958840	−	1.66076i	0.0371543	−	0.0643531i
$667$	3.33552	−	12.4483i	0.129152	−	0.482002i
$668$	37.9955			1.47009
$669$	−2.42052	+	9.03352i	−0.0935829	+	0.349256i
$670$	−12.4790	+	5.21816i	−0.482104	+	0.201595i
$671$	−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	0.980948	+	0.194272i	$0.0622345\pi$
$673$	5.92931	+	22.1285i	0.228558	+	0.852991i	−0.752389	+	0.658719i	$0.771099\pi$
$674$	−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	−0.945461	−	0.325736i	$-0.894388\pi$
$677$	−16.1247	+	16.1247i	−0.619724	+	0.619724i	0.325736	+	0.945461i	$0.394388\pi$
$678$	3.84825	−	6.66536i	0.147791	−	0.255982i
$679$	−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
$682$	2.00337	−	1.15664i	0.0767129	−	0.0442902i
$683$	−27.7544	+	16.0240i	−1.06199	+	0.613142i	−0.925983	−	0.377565i	$-0.876761\pi$
$683$	−27.7544	+	16.0240i	−1.06199	+	0.613142i	−0.136010	+	0.990707i	$0.543428\pi$
$684$	−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
$687$	10.3856	−	17.9883i	0.396234	−	0.686298i
$688$	−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	0.968586	−	0.248681i	$-0.0799970\pi$
$691$	0.142620	+	0.532264i	0.00542551	+	0.0202483i	−0.963160	+	0.268929i	$0.913330\pi$
$692$	−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
$695$	−5.52228	−	13.2062i	−0.209472	−	0.500941i
$696$	4.29682	−	16.0360i	0.162871	−	0.607842i
$697$	−1.31514			−0.0498144
$698$	−1.20160	+	4.48442i	−0.0454811	+	0.169738i
$699$	11.0134	−	19.0758i	0.416565	−	0.721512i
$700$	−22.6658	+	22.9726i	−0.856687	+	0.868282i
$701$			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
$705$	−1.07219	−	7.93782i	−0.0403809	−	0.298956i
$706$	1.39674	−	0.806411i	0.0525672	−	0.0303497i
$707$		−	55.0209i		−	2.06927i
$708$	−8.59166	−	14.8812i	−0.322894	−	0.559270i
$709$	−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	$0.791922\pi$
$710$	−5.85831	+	4.52661i	−0.219859	+	0.169881i
$711$	3.30200	+	5.71923i	0.123835	+	0.214488i
$712$	−6.05244	+	1.62175i	−0.226825	+	0.0607776i
$713$	−7.98782	−	4.61177i	−0.299146	−	0.172712i
$714$	−4.05358			−0.151701
$715$		0			0
$716$	−28.7180			−1.07324
$717$	−16.8180	−	9.70986i	−0.628079	−	0.362621i
$718$	2.10561	−	0.564197i	0.0785808	−	0.0210557i
$719$	4.21240	+	7.29608i	0.157096	+	0.272098i	0.933820	−	0.357743i	$-0.116454\pi$
$719$	4.21240	+	7.29608i	0.157096	+	0.272098i	−0.776724	+	0.629841i	$0.783120\pi$
$720$	12.1807	+	1.56199i	0.453947	+	0.0582118i
$721$	−15.9587	−	4.27612i	−0.594333	−	0.159251i
$722$	−2.71668	−	4.70543i	−0.101104	−	0.175118i
$723$			2.91423i			0.108381i
$724$	27.4332	−	15.8385i	1.01955	−	0.588635i
$725$	−33.8705	−	33.4182i	−1.25792	−	1.24112i
$726$	−4.72284	+	1.26548i	−0.175281	+	0.0469664i
$727$	−8.33682	−	8.33682i	−0.309195	−	0.309195i	0.535402	−	0.844597i	$-0.320160\pi$
$727$	−8.33682	−	8.33682i	−0.309195	−	0.309195i	−0.844597	+	0.535402i	$0.820160\pi$
$728$		0			0
$729$		−	9.71523i		−	0.359824i
$730$	−2.96596	−	2.26006i	−0.109775	−	0.0836487i
$731$	−2.57239	+	4.45551i	−0.0951432	+	0.164793i
$732$	−2.64913	+	9.88670i	−0.0979148	+	0.365423i
$733$	−18.6238			−0.687887			−0.343944	−	0.938990i	$-0.611763\pi$
$733$	−18.6238			−0.687887			−0.343944	+	0.938990i	$0.611763\pi$
$734$	−3.20725	+	11.9696i	−0.118382	+	0.441807i
$735$	−12.6632	−	5.19547i	−0.467089	−	0.191638i
$736$	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
$739$	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
$743$	−18.7850	+	32.5366i	−0.689155	+	1.19365i	0.282957	+	0.959133i	$0.408685\pi$
$743$	−18.7850	+	32.5366i	−0.689155	+	1.19365i	−0.972112	+	0.234518i	$0.924649\pi$
$744$	−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
$747$	−3.91943	+	2.26288i	−0.143404	+	0.0827946i
$748$	2.48333	−	1.43375i	0.0907995	−	0.0524231i
$749$	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	$-0.123223\pi$
$751$	29.1051	+	16.8038i	1.06206	+	0.613181i	0.136059	+	0.990701i	$0.456556\pi$
$752$	4.94407	−	8.56339i	0.180292	−	0.312275i
$753$	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
$757$	−4.17654	−	15.5871i	−0.151799	−	0.566521i	−0.999358	−	0.0358205i	$-0.988596\pi$
$757$	−4.17654	−	15.5871i	−0.151799	−	0.566521i	0.847559	−	0.530701i	$-0.178071\pi$
$758$	−0.958699	−	0.256883i	−0.0348215	−	0.00933040i
$759$	−0.619282	−	0.619282i	−0.0224785	−	0.0224785i
$760$	−8.62431	+	21.0205i	−0.312837	+	0.762493i
$761$	4.05514	−	15.1340i	0.146999	−	0.548606i	−0.852660	−	0.522467i	$-0.825012\pi$
$761$	4.05514	−	15.1340i	0.146999	−	0.548606i	0.999658	−	0.0261397i	$-0.00832146\pi$
$762$	3.85490			0.139648
$763$	−3.03911	+	11.3421i	−0.110023	+	0.410612i
$764$	−4.55789	+	7.89449i	−0.164899	+	0.285613i
$765$	11.1321	−	1.50364i	0.402480	−	0.0543644i
$766$			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	$0.616719\pi$
$770$	−2.76635	+	0.373660i	−0.0996924	+	0.0134658i
$771$	5.83532	−	3.36902i	0.210154	−	0.121332i
$772$		−	17.7388i		−	0.638433i
$773$	−11.9531	−	20.7033i	−0.429921	−	0.744646i	0.566944	−	0.823756i	$-0.308125\pi$
$773$	−11.9531	−	20.7033i	−0.429921	−	0.744646i	−0.996866	+	0.0791103i	$0.974792\pi$
$774$	−2.18688	−	0.585972i	−0.0786056	−	0.0210623i
$775$	−29.3764	+	17.2248i	−1.05523	+	0.618733i
$776$	6.56136	+	11.3646i	0.235539	+	0.407966i
$777$	−6.12718	+	1.64177i	−0.219811	+	0.0588983i
$778$	−0.278066	−	0.160541i	−0.00996914	−	0.00575569i
$779$	−3.03366			−0.108692
$780$		0			0
$781$	4.60995			0.164957
$782$	1.37545	+	0.794114i	0.0491858	+	0.0283975i
$783$	−44.2204	+	11.8488i	−1.58031	+	0.423443i
$784$	−8.44858	−	14.6334i	−0.301735	−	0.522620i
$785$	19.1018	+	24.7214i	0.681772	+	0.882346i
$786$	0.616466	+	0.165181i	0.0219886	+	0.00589183i
$787$	−7.85572	−	13.6065i	−0.280026	−	0.485020i	0.691365	−	0.722506i	$-0.257010\pi$
$787$	−7.85572	−	13.6065i	−0.280026	−	0.485020i	−0.971391	+	0.237486i	$0.923676\pi$
$788$		−	22.9411i		−	0.817242i
$789$	10.9664	−	6.33143i	0.390412	−	0.225405i
$790$	2.74202	+	2.08942i	0.0975566	+	0.0743382i
$791$	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
$795$	4.45719	−	5.84933i	0.158080	−	0.207454i
$796$	−6.89264	+	11.9384i	−0.244303	+	0.423146i
$797$	8.08312	−	30.1666i	0.286319	−	1.06856i	−0.661552	−	0.749900i	$-0.730102\pi$
$797$	8.08312	−	30.1666i	0.286319	−	1.06856i	0.947870	−	0.318656i	$-0.103232\pi$
$798$	−9.35048			−0.331003
$799$	2.34099	−	8.73669i	0.0828183	−	0.309082i
$800$	24.0673	−	6.62252i	0.850906	−	0.234141i
$801$	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
$804$	−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
$808$	−13.8853	+	24.0500i	−0.488483	+	0.846078i
$809$	−11.4546	−	6.61331i	−0.402722	−	0.232512i	0.284936	−	0.958547i	$-0.408028\pi$
$809$	−11.4546	−	6.61331i	−0.402722	−	0.232512i	−0.687658	+	0.726035i	$0.741361\pi$
$810$	0.776696	+	1.85743i	0.0272903	+	0.0652634i
$811$	22.0736	−	22.0736i	0.775109	−	0.775109i	−0.203886	−	0.978995i	$-0.565357\pi$
$811$	22.0736	−	22.0736i	0.775109	−	0.775109i	0.978995	+	0.203886i	$0.0653572\pi$
$812$	53.1928	−	30.7109i	1.86670	−	1.07774i
$813$	7.48978	−	4.32423i	0.262678	−	0.151657i
$814$	−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
$817$	−5.93379	+	10.2776i	−0.207597	+	0.359568i
$818$	−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	0.994692	−	0.102902i	$-0.0328128\pi$
$821$	2.34418	+	8.74860i	0.0818124	+	0.305328i	−0.912879	+	0.408230i	$0.866146\pi$
$822$	−1.48192	−	5.53062i	−0.0516881	−	0.192902i
$823$	−40.5117	−	10.8551i	−1.41215	−	0.378384i	−0.529457	−	0.848337i	$-0.677604\pi$
$823$	−40.5117	−	10.8551i	−1.41215	−	0.378384i	−0.882691	+	0.469953i	$0.844271\pi$
$824$	5.89653	+	5.89653i	0.205415	+	0.205415i
$825$	−3.11763	+	0.857868i	−0.108542	+	0.0298671i
$826$	−4.88888	+	18.2455i	−0.170106	+	0.634844i
$827$	38.2009			1.32838			0.664188	−	0.747566i	$-0.268778\pi$
$827$	38.2009			1.32838			0.664188	+	0.747566i	$0.268778\pi$
$828$	1.30221	−	4.85992i	0.0452550	−	0.168894i
$829$	−14.6750	+	25.4178i	−0.509682	+	0.882796i	0.490255	+	0.871579i	$0.336904\pi$
$829$	−14.6750	+	25.4178i	−0.509682	+	0.882796i	−0.999937	+	0.0112165i	$0.996430\pi$
$830$	−1.43189	+	1.87913i	−0.0497018	+	0.0652254i
$831$			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
$835$	−38.4822	−	29.3235i	−1.33173	−	1.01478i
$836$	5.72835	−	3.30726i	0.198119	−	0.114384i
$837$			32.7649i			1.13252i
$838$	−1.32629	−	2.29721i	−0.0458161	−	0.0793557i
$839$	−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	$0.791442\pi$
$840$	8.76652	+	11.3456i	0.302474	+	0.391460i
$841$	30.7798	+	53.3122i	1.06137	+	1.83835i
$842$	9.53846	−	2.55582i	0.328717	−	0.0880795i
$843$	6.24163	+	3.60361i	0.214973	+	0.124115i
$844$	21.8175			0.750988
$845$		0			0
$846$	3.98031			0.136846
$847$	−33.5084	−	19.3461i	−1.15136	−	0.664740i
$848$	8.76909	−	2.34967i	0.301132	−	0.0806880i
$849$	−4.13097	−	7.15504i	−0.141774	−	0.245560i
$850$	5.05841	−	2.96599i	0.173502	−	0.101733i
$851$	2.40068	+	0.643261i	0.0822944	+	0.0220507i
$852$	−5.53509	−	9.58705i	−0.189629	−	0.328447i
$853$			17.6392i			0.603954i	0.953315	+	0.301977i	$0.0976465\pi$
$853$			17.6392i			0.603954i	−0.953315	+	0.301977i	$0.902353\pi$
$854$	9.74415	−	5.62579i	0.333438	−	0.192511i
$855$	25.6786	−	3.46849i	0.878189	−	0.118620i
$856$	−27.3314	+	7.32342i	−0.934167	+	0.250309i
$857$	6.30427	+	6.30427i	0.215350	+	0.215350i	0.806535	−	0.591186i	$-0.201340\pi$
$857$	6.30427	+	6.30427i	0.215350	+	0.215350i	−0.591186	+	0.806535i	$0.701340\pi$
$858$		0			0
$859$		−	29.2307i		−	0.997338i	−0.866793	−	0.498669i	$-0.833822\pi$
$859$		−	29.2307i		−	0.997338i	0.866793	−	0.498669i	$-0.166178\pi$
$860$	8.43127	−	1.13884i	0.287504	−	0.0388341i
$861$	−0.957186	+	1.65789i	−0.0326208	+	0.0565009i
$862$	2.13358	−	7.96263i	0.0726701	−	0.271208i
$863$	−15.7688			−0.536775			−0.268387	−	0.963311i	$-0.586491\pi$
$863$	−15.7688			−0.536775			−0.268387	+	0.963311i	$0.586491\pi$
$864$	6.21604	−	23.1986i	0.211474	−	0.789232i
$865$	−6.56400	+	15.9988i	−0.223183	+	0.543974i
$866$	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
$869$	−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
$873$	7.48283	−	12.9606i	0.253255	−	0.438651i
$874$	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
$877$	38.7309	−	22.3613i	1.30785	−	0.755088i	0.326114	−	0.945331i	$-0.394261\pi$
$877$	38.7309	−	22.3613i	1.30785	−	0.755088i	0.981737	+	0.190242i	$0.0609274\pi$
$878$	5.85595	−	3.38094i	0.197629	−	0.114101i
$879$	−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	$-0.219258\pi$
$881$	18.0323	+	10.4110i	0.607525	+	0.350755i	−0.164471	+	0.986382i	$0.552592\pi$
$882$	3.40084	−	5.89043i	0.114512	−	0.198341i
$883$	5.33747	−	5.33747i	0.179620	−	0.179620i	−0.611570	−	0.791190i	$-0.709462\pi$
$883$	5.33747	−	5.33747i	0.179620	−	0.179620i	0.791190	+	0.611570i	$0.209462\pi$
$884$		0			0
$885$	−2.78302	+	21.7026i	−0.0935502	+	0.729523i
$886$	1.16837	+	4.36041i	0.0392521	+	0.146491i
$887$	−6.93749	−	25.8911i	−0.232938	−	0.869337i	−0.979067	−	0.203536i	$-0.934757\pi$
$887$	−6.93749	−	25.8911i	−0.232938	−	0.869337i	0.746129	−	0.665801i	$-0.231910\pi$
$888$	3.09256	+	0.828649i	0.103780	+	0.0278077i
$889$	21.5706	+	21.5706i	0.723454	+	0.723454i
$890$	3.45109	+	1.41592i	0.115681	+	0.0474617i
$891$	0.324464	−	1.21092i	0.0108700	−	0.0405673i
$892$	17.4639			0.584736
$893$	5.40002	−	20.1531i	0.180705	−	0.674399i
$894$	3.90208	−	6.75861i	0.130505	−	0.226042i
$895$	29.0859	+	22.1635i	0.972233	+	0.740842i
$896$			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
$900$	−13.2233	−	13.0467i	−0.440776	−	0.434890i
$901$	7.19167	−	4.15211i	0.239589	−	0.138327i
$902$			0.188119i			0.00626368i
$903$	3.74447	+	6.48562i	0.124608	+	0.215828i
$904$	−29.6933	−	7.95630i	−0.987585	−	0.264623i
$905$	−40.0082	−	5.13044i	−1.32992	−	0.170542i
$906$	−1.08887	−	1.88597i	−0.0361752	−	0.0626572i
$907$	−39.1608	+	10.4931i	−1.30031	+	0.348418i	−0.841568	−	0.540151i	$-0.818367\pi$
$907$	−39.1608	+	10.4931i	−1.30031	+	0.348418i	−0.458744	+	0.888568i	$0.651701\pi$
$908$	22.2124	+	12.8243i	0.737144	+	0.425590i
$909$	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	$0.457687\pi$
$912$	−11.5796	−	6.68546i	−0.383437	−	0.221378i
$913$	1.42096	−	0.380746i	0.0470271	−	0.0126009i
$914$	0.204360	+	0.353962i	0.00675963	+	0.0117080i
$915$	10.3133	−	7.96885i	0.340946	−	0.263442i
$916$	−37.4656	−	10.0389i	−1.23790	−	0.331694i
$917$	2.52522	+	4.37381i	0.0833901	+	0.144436i
$918$		−	5.64189i		−	0.186210i
$919$	1.84237	−	1.06369i	0.0607741	−	0.0350879i	−0.469305	−	0.883036i	$-0.655496\pi$
$919$	1.84237	−	1.06369i	0.0607741	−	0.0350879i	0.530079	+	0.847948i	$0.322162\pi$
$920$	−0.751973	−	5.56715i	−0.0247918	−	0.183543i
$921$	−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
$925$	6.44476	−	6.53199i	0.211902	−	0.214770i
$926$	−1.56954	+	2.71852i	−0.0515782	+	0.0893360i
$927$	2.46138	−	9.18601i	0.0808425	−	0.301708i
$928$	−47.5087			−1.55955
$929$	−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	$0.977312\pi$
$930$	2.72885	+	6.52591i	0.0894826	+	0.213993i
$931$	−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
$934$	−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	−0.366135	−	0.930562i	$-0.619319\pi$
$937$	17.2774	−	17.2774i	0.564427	−	0.564427i	0.930562	+	0.366135i	$0.119319\pi$
$938$	−11.1166	+	19.2545i	−0.362969	+	0.628680i
$939$	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	−0.192063	−	0.981383i	$-0.561518\pi$
$941$	24.2129	−	24.2129i	0.789319	−	0.789319i	0.981383	+	0.192063i	$0.0615179\pi$
$942$	5.61989	−	3.24465i	0.183106	−	0.105716i
$943$	0.649578	−	0.375034i	0.0211532	−	0.0122128i
$944$	−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
$947$	4.15045	−	7.18880i	0.134872	−	0.233605i	−0.790677	−	0.612234i	$-0.790271\pi$
$947$	4.15045	−	7.18880i	0.134872	−	0.233605i	0.925548	+	0.378629i	$0.123604\pi$
$948$	−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
$952$	4.19041	+	15.6388i	0.135812	+	0.506857i
$953$	−4.62244	−	1.23858i	−0.149736	−	0.0401215i	0.183173	−	0.983081i	$-0.441363\pi$
$953$	−4.62244	−	1.23858i	−0.149736	−	0.0401215i	−0.332908	+	0.942959i	$0.608030\pi$
$954$	2.58403	+	2.58403i	0.0836611	+	0.0836611i
$955$	10.7089	−	4.47802i	0.346533	−	0.144905i
$956$	−9.38573	+	35.0280i	−0.303556	+	1.13289i
$957$	6.15418			0.198936
$958$	1.20974	−	4.51481i	0.0390849	−	0.145867i
$959$	22.6550	−	39.2396i	0.731568	−	1.26711i
$960$	0.767302	+	5.68064i	0.0247646	+	0.183342i
$961$		−	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
$965$	−13.6901	+	17.9660i	−0.440701	+	0.578347i
$966$	2.00216	−	1.15595i	0.0644183	−	0.0371919i
$967$		−	8.78782i		−	0.282597i	−0.989967	−	0.141299i	$-0.954872\pi$
$967$		−	8.78782i		−	0.282597i	0.989967	−	0.141299i	$-0.0451278\pi$
$968$	9.76453	+	16.9127i	0.313844	+	0.543594i
$969$	−11.8139	−	3.16552i	−0.379517	−	0.101691i
$970$	0.993666	−	7.74880i	0.0319047	−	0.248799i
$971$	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	$0.805544\pi$
$972$	−27.3881	+	7.33863i	−0.878475	+	0.235387i
$973$	−20.3766	−	11.7645i	−0.653245	−	0.377151i
$974$	−3.04192			−0.0974695
$975$		0			0
$976$	16.0894			0.515010
$977$	−16.1709	−	9.33626i	−0.517352	−	0.298693i	0.218499	−	0.975837i	$-0.429884\pi$
$977$	−16.1709	−	9.33626i	−0.517352	−	0.298693i	−0.735851	+	0.677144i	$0.763217\pi$
$978$	0.0592064	−	0.0158643i	0.00189321	−	0.000507285i
$979$	−1.16138	−	2.01158i	−0.0371180	−	0.0642903i
$980$	−3.25101	+	25.3521i	−0.103850	+	0.809842i
$981$	−6.52865	−	1.74935i	−0.208444	−	0.0558524i
$982$	−3.65824	−	6.33626i	−0.116739	−	0.202198i
$983$			6.62470i			0.211295i	0.994404	+	0.105648i	$0.0336915\pi$
$983$			6.62470i			0.211295i	−0.994404	+	0.105648i	$0.966308\pi$
$984$	0.836786	−	0.483119i	0.0266758	−	0.0154013i
$985$	−17.7051	+	23.2350i	−0.564130	+	0.740327i
$986$	−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
$990$	−0.215083	−	1.59234i	−0.00683579	−	0.0506080i
$991$	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	$-0.0742206\pi$
$992$	−8.80033	+	32.8433i	−0.279411	+	1.04277i
$993$	6.59853			0.209398
$994$	−3.14961	+	11.7545i	−0.0998995	+	0.372830i
$995$	16.1946	−	6.77186i	0.513402	−	0.214682i
$996$	−2.49794	−	2.49794i	−0.0791504	−	0.0791504i
$997$	−43.6654	−	11.7001i	−1.38290	−	0.370547i	−0.510725	−	0.859744i	$-0.670623\pi$
$997$	−43.6654	−	11.7001i	−1.38290	−	0.370547i	−0.872173	+	0.489197i	$0.837290\pi$
$998$	3.80596	+	14.2040i	0.120476	+	0.449621i
$999$	−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.t.f.188.3		20
5.2	odd	4		845.2.o.e.357.3		20
13.2	odd	12		845.2.o.f.258.3		20
13.3	even	3		65.2.t.a.28.3	yes	20
13.4	even	6		845.2.f.d.408.6		20
13.5	odd	4		845.2.o.g.488.3		20
13.6	odd	12		845.2.k.d.268.5		20
13.7	odd	12		845.2.k.e.268.6		20
13.8	odd	4		65.2.o.a.33.3	yes	20
13.9	even	3		845.2.f.e.408.5		20
13.10	even	6		845.2.t.g.418.3		20
13.11	odd	12		845.2.o.e.258.3		20
13.12	even	2		845.2.t.e.188.3		20
39.8	even	4		585.2.cf.a.163.3		20
39.29	odd	6		585.2.dp.a.28.3		20
65.2	even	12		845.2.t.e.427.3		20
65.3	odd	12		325.2.s.b.132.3		20
65.7	even	12		845.2.f.e.437.6		20
65.8	even	4		325.2.x.b.7.3		20
65.12	odd	4		845.2.o.f.357.3		20
65.17	odd	12		845.2.k.d.577.5		20
65.22	odd	12		845.2.k.e.577.6		20
65.29	even	6		325.2.x.b.93.3		20
65.32	even	12		845.2.f.d.437.5		20
65.34	odd	4		325.2.s.b.293.3		20
65.37	even	12	inner	845.2.t.f.427.3		20
65.42	odd	12		65.2.o.a.2.3	✓	20
65.47	even	4		65.2.t.a.7.3	yes	20
65.57	even	4		845.2.t.g.657.3		20
65.62	odd	12		845.2.o.g.587.3		20
195.47	odd	4		585.2.dp.a.397.3		20
195.107	even	12		585.2.cf.a.262.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.3	✓	20	65.42	odd	12
65.2.o.a.33.3	yes	20	13.8	odd	4
65.2.t.a.7.3	yes	20	65.47	even	4
65.2.t.a.28.3	yes	20	13.3	even	3
325.2.s.b.132.3		20	65.3	odd	12
325.2.s.b.293.3		20	65.34	odd	4
325.2.x.b.7.3		20	65.8	even	4
325.2.x.b.93.3		20	65.29	even	6
585.2.cf.a.163.3		20	39.8	even	4
585.2.cf.a.262.3		20	195.107	even	12
585.2.dp.a.28.3		20	39.29	odd	6
585.2.dp.a.397.3		20	195.47	odd	4
845.2.f.d.408.6		20	13.4	even	6
845.2.f.d.437.5		20	65.32	even	12
845.2.f.e.408.5		20	13.9	even	3
845.2.f.e.437.6		20	65.7	even	12
845.2.k.d.268.5		20	13.6	odd	12
845.2.k.d.577.5		20	65.17	odd	12
845.2.k.e.268.6		20	13.7	odd	12
845.2.k.e.577.6		20	65.22	odd	12
845.2.o.e.258.3		20	13.11	odd	12
845.2.o.e.357.3		20	5.2	odd	4
845.2.o.f.258.3		20	13.2	odd	12
845.2.o.f.357.3		20	65.12	odd	4
845.2.o.g.488.3		20	13.5	odd	4
845.2.o.g.587.3		20	65.62	odd	12
845.2.t.e.188.3		20	13.12	even	2
845.2.t.e.427.3		20	65.2	even	12
845.2.t.f.188.3		20	1.1	even	1	trivial
845.2.t.f.427.3		20	65.37	even	12	inner
845.2.t.g.418.3		20	13.10	even	6
845.2.t.g.657.3		20	65.57	even	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.t (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.427732 + 0.246951i) q^{2} +(0.908353 - 0.243392i) q^{3} +(-0.878030 - 1.52079i) q^{4} +(-0.284413 + 2.21791i) q^{5} +(0.448637 + 0.120212i) q^{6} +(1.83775 + 3.18307i) q^{7} -1.85513i q^{8} +(-1.83221 + 1.05783i) q^{9} +(-0.669366 + 0.878433i) q^{10} +(0.664257 - 0.177987i) q^{11} +(-1.16771 - 1.16771i) q^{12} +1.81533i q^{14} +(0.281475 + 2.08387i) q^{15} +(-1.29794 + 2.24809i) q^{16} +(-0.614565 + 2.29359i) q^{17} -1.04493 q^{18} +(-1.41763 + 5.29067i) q^{19} +(3.62270 - 1.51486i) q^{20} +(2.44406 + 2.44406i) q^{21} +(0.328078 + 0.0879082i) q^{22} +(-0.350507 - 1.30811i) q^{23} +(-0.451523 - 1.68511i) q^{24} +(-4.83822 - 1.26160i) q^{25} +(-3.40171 + 3.40171i) q^{27} +(3.22719 - 5.58966i) q^{28} +(8.24134 + 4.75814i) q^{29} +(-0.394217 + 0.960845i) q^{30} +(4.81595 - 4.81595i) q^{31} +(-4.32351 + 2.49618i) q^{32} +(0.560059 - 0.323350i) q^{33} +(-0.829273 + 0.829273i) q^{34} +(-7.58243 + 3.17064i) q^{35} +(3.21748 + 1.85761i) q^{36} +(-0.917615 + 1.58936i) q^{37} +(-1.91290 + 1.91290i) q^{38} +(4.11449 + 0.527621i) q^{40} +(0.143350 + 0.534988i) q^{41} +(0.441838 + 1.64896i) q^{42} +(2.09285 + 0.560778i) q^{43} +(-0.853919 - 0.853919i) q^{44} +(-1.82506 - 4.36453i) q^{45} +(0.173116 - 0.646078i) q^{46} -3.80918 q^{47} +(-0.631815 + 2.35797i) q^{48} +(-3.25462 + 5.63717i) q^{49} +(-1.75791 - 1.73443i) q^{50} +2.23297i q^{51} +(-2.47293 - 2.47293i) q^{53} +(-2.29507 + 0.614963i) q^{54} +(0.205836 + 1.52388i) q^{55} +(5.90499 - 3.40925i) q^{56} +5.15084i q^{57} +(2.35005 + 4.07041i) q^{58} +(10.0508 + 2.69310i) q^{59} +(2.92199 - 2.25776i) q^{60} +(-3.09904 - 5.36770i) q^{61} +(3.24924 - 0.870630i) q^{62} +(-6.73428 - 3.88804i) q^{63} +2.72601 q^{64} +0.319406 q^{66} +(10.6066 + 6.12371i) q^{67} +(4.02768 - 1.07921i) q^{68} +(-0.636768 - 1.10291i) q^{69} +(-4.02624 - 0.516303i) q^{70} +(6.47512 + 1.73500i) q^{71} +(1.96240 + 3.39898i) q^{72} +3.37642i q^{73} +(-0.784986 + 0.453212i) q^{74} +(-4.70187 + 0.0316067i) q^{75} +(9.29074 - 2.48945i) q^{76} +(1.78728 + 1.78728i) q^{77} -3.12149i q^{79} +(-4.61691 - 3.51809i) q^{80} +(0.911483 - 1.57873i) q^{81} +(-0.0708006 + 0.264231i) q^{82} +2.13918 q^{83} +(1.57095 - 5.86286i) q^{84} +(-4.91217 - 2.01537i) q^{85} +(0.756694 + 0.756694i) q^{86} +(8.64414 + 2.31619i) q^{87} +(-0.330188 - 1.23228i) q^{88} +(-0.874198 - 3.26255i) q^{89} +(0.297190 - 2.31755i) q^{90} +(-1.68161 + 1.68161i) q^{92} +(3.20242 - 5.54675i) q^{93} +(-1.62931 - 0.940681i) q^{94} +(-11.3310 - 4.64891i) q^{95} +(-3.31972 + 3.31972i) q^{96} +(-6.12606 + 3.53688i) q^{97} +(-2.78421 + 1.60746i) q^{98} +(-1.02878 + 1.02878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 4 q^{6} - 2 q^{7} - 12 q^{9} + 10 q^{10} + 8 q^{11} - 24 q^{12} - 8 q^{15} - 2 q^{16} + 10 q^{17} + 16 q^{19} + 12 q^{20} + 4 q^{21} + 16 q^{22} + 2 q^{23} - 28 q^{24}+ \cdots + 60 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 4 * q^6 - 2 * q^7 - 12 * q^9 + 10 * q^10 + 8 * q^11 - 24 * q^12 - 8 * q^15 - 2 * q^16 + 10 * q^17 + 16 * q^19 + 12 * q^20 + 4 * q^21 + 16 * q^22 + 2 * q^23 - 28 * q^24 + 18 * q^25 + 4 * q^27 + 18 * q^28 - 14 * q^30 - 48 * q^32 - 18 * q^33 + 2 * q^34 - 20 * q^35 - 36 * q^36 - 4 * q^37 - 8 * q^38 - 16 * q^40 + 28 * q^41 - 56 * q^42 + 22 * q^43 - 36 * q^44 + 6 * q^45 - 8 * q^46 - 40 * q^47 + 28 * q^48 + 18 * q^49 - 78 * q^50 - 10 * q^53 + 12 * q^54 + 26 * q^55 + 8 * q^59 + 28 * q^60 - 16 * q^61 + 40 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 + 28 * q^68 - 16 * q^69 - 12 * q^70 + 56 * q^71 + 4 * q^72 - 18 * q^74 + 34 * q^75 + 80 * q^76 - 28 * q^77 - 110 * q^80 - 14 * q^81 - 22 * q^82 + 48 * q^83 + 32 * q^84 + 28 * q^85 + 60 * q^86 + 62 * q^87 - 50 * q^88 - 6 * q^89 + 46 * q^90 - 8 * q^92 + 32 * q^93 + 48 * q^94 - 14 * q^95 + 56 * q^96 - 66 * q^97 + 30 * q^98 + 60 * q^99

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