LMFDB - Embedded newform 351.2.ba.a.98.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(71,351)] 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("351.71"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.ba (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			98.8
Character	$\chi$	$=$	351.98
Dual form			351.2.ba.a.197.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.754009 - 0.754009i) q^{2} +0.862941i q^{4} +(-0.595426 - 2.22216i) q^{5} +(-1.34030 - 5.00206i) q^{7} +(2.15868 + 2.15868i) q^{8} +(-2.12448 - 1.22657i) q^{10} +(-1.93671 - 1.93671i) q^{11} +(3.42168 + 1.13671i) q^{13} +(-4.78220 - 2.76100i) q^{14} +1.52945 q^{16} +(-0.0716242 - 0.124057i) q^{17} +(0.552200 - 2.06084i) q^{19} +(1.91759 - 0.513817i) q^{20} -2.92060 q^{22} +(-0.421808 - 0.730594i) q^{23} +(-0.253329 + 0.146260i) q^{25} +(3.43707 - 1.72289i) q^{26} +(4.31649 - 1.15660i) q^{28} +0.605036i q^{29} +(3.38018 - 0.905716i) q^{31} +(-3.16415 + 3.16415i) q^{32} +(-0.147545 - 0.0395346i) q^{34} +(-10.3173 + 5.95671i) q^{35} +(0.973046 + 3.63146i) q^{37} +(-1.13753 - 1.97025i) q^{38} +(3.51160 - 6.08227i) q^{40} +(7.55452 + 2.02423i) q^{41} +(0.187567 + 0.108292i) q^{43} +(1.67127 - 1.67127i) q^{44} +(-0.868921 - 0.232827i) q^{46} +(-2.72952 + 10.1867i) q^{47} +(-17.1621 + 9.90853i) q^{49} +(-0.0807314 + 0.301294i) q^{50} +(-0.980914 + 2.95271i) q^{52} +8.00631i q^{53} +(-3.15052 + 5.45686i) q^{55} +(7.90459 - 13.6912i) q^{56} +(0.456203 + 0.456203i) q^{58} +(-5.26532 - 5.26532i) q^{59} +(0.675442 - 1.16990i) q^{61} +(1.86577 - 3.23160i) q^{62} +7.83049i q^{64} +(0.488596 - 8.28034i) q^{65} +(1.98346 - 7.40238i) q^{67} +(0.107054 - 0.0618075i) q^{68} +(-3.28794 + 12.2708i) q^{70} +(7.04646 + 1.88809i) q^{71} +(-3.76736 + 3.76736i) q^{73} +(3.47184 + 2.00447i) q^{74} +(1.77838 + 0.476516i) q^{76} +(-7.09179 + 12.2833i) q^{77} +(1.62641 + 2.81703i) q^{79} +(-0.910674 - 3.39868i) q^{80} +(7.22246 - 4.16989i) q^{82} +(14.7099 + 3.94150i) q^{83} +(-0.233027 + 0.233027i) q^{85} +(0.223081 - 0.0597743i) q^{86} -8.36151i q^{88} +(14.2431 - 3.81643i) q^{89} +(1.09983 - 18.6390i) q^{91} +(0.630459 - 0.363996i) q^{92} +(5.62279 + 9.73895i) q^{94} -4.90830 q^{95} +(0.525725 - 0.140868i) q^{97} +(-5.46924 + 20.4115i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{2} + 6 q^{5} - 4 q^{7} - 30 q^{8} - 12 q^{10} + 6 q^{11} - 2 q^{13} + 12 q^{14} - 28 q^{16} - 4 q^{19} + 18 q^{20} - 4 q^{22} + 6 q^{23} + 48 q^{26} - 18 q^{31} - 54 q^{32} + 6 q^{34} - 6 q^{35}+ \cdots - 36 q^{98}+O(q^{100}) $ 48 * q + 6 * q^2 + 6 * q^5 - 4 * q^7 - 30 * q^8 - 12 * q^10 + 6 * q^11 - 2 * q^13 + 12 * q^14 - 28 * q^16 - 4 * q^19 + 18 * q^20 - 4 * q^22 + 6 * q^23 + 48 * q^26 - 18 * q^31 - 54 * q^32 + 6 * q^34 - 6 * q^35 - 6 * q^37 - 36 * q^38 - 12 * q^40 - 18 * q^41 - 30 * q^43 - 12 * q^44 - 12 * q^46 + 36 * q^47 - 6 * q^49 + 60 * q^50 + 56 * q^52 - 4 * q^55 + 6 * q^56 + 50 * q^58 + 6 * q^59 + 2 * q^61 - 18 * q^62 - 72 * q^65 + 26 * q^67 - 42 * q^68 - 16 * q^70 + 48 * q^71 - 22 * q^73 - 30 * q^74 + 6 * q^76 - 72 * q^77 + 8 * q^79 + 54 * q^80 - 12 * q^82 - 54 * q^83 - 24 * q^85 + 54 * q^86 - 16 * q^91 - 120 * q^92 + 26 * q^94 + 12 * q^95 - 24 * q^97 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.754009	−	0.754009i	0.533165	−	0.533165i	−0.388348	−	0.921513i	$-0.626954\pi$
$2$	0.754009	−	0.754009i	0.533165	−	0.533165i	0.921513	+	0.388348i	$0.126954\pi$
$3$		0			0
$3$		0			0
$4$			0.862941i			0.431471i
$5$	−0.595426	−	2.22216i	−0.266282	−	0.993779i	−0.961461	−	0.274942i	$-0.911341\pi$
$5$	−0.595426	−	2.22216i	−0.266282	−	0.993779i	0.695178	−	0.718837i	$-0.255325\pi$
$6$		0			0
$7$	−1.34030	−	5.00206i	−0.506585	−	1.89060i	−0.451832	−	0.892103i	$-0.649229\pi$
$7$	−1.34030	−	5.00206i	−0.506585	−	1.89060i	−0.0547531	−	0.998500i	$-0.517437\pi$
$8$	2.15868	+	2.15868i	0.763210	+	0.763210i
$9$		0			0
$10$	−2.12448	−	1.22657i	−0.671821	−	0.387876i
$11$	−1.93671	−	1.93671i	−0.583941	−	0.583941i	0.352043	−	0.935984i	$-0.385487\pi$
$11$	−1.93671	−	1.93671i	−0.583941	−	0.583941i	−0.935984	+	0.352043i	$0.885487\pi$
$12$		0			0
$13$	3.42168	+	1.13671i	0.949003	+	0.315267i
$13$	3.42168	+	1.13671i	0.949003	+	0.315267i
$14$	−4.78220	−	2.76100i	−1.27810	−	0.737909i
$15$		0			0
$16$	1.52945			0.382363
$17$	−0.0716242	−	0.124057i	−0.0173714	−	0.0300882i	0.857209	−	0.514969i	$-0.172196\pi$
$17$	−0.0716242	−	0.124057i	−0.0173714	−	0.0300882i	−0.874580	+	0.484880i	$0.838863\pi$
$18$		0			0
$19$	0.552200	−	2.06084i	0.126683	−	0.472789i	−0.873211	−	0.487343i	$-0.837966\pi$
$19$	0.552200	−	2.06084i	0.126683	−	0.472789i	0.999894	+	0.0145541i	$0.00463288\pi$
$20$	1.91759	−	0.513817i	0.428787	−	0.114893i
$21$		0			0
$22$	−2.92060			−0.622674
$23$	−0.421808	−	0.730594i	−0.0879531	−	0.152339i	0.818693	−	0.574232i	$-0.194699\pi$
$23$	−0.421808	−	0.730594i	−0.0879531	−	0.152339i	−0.906646	+	0.421893i	$0.861366\pi$
$24$		0			0
$25$	−0.253329	+	0.146260i	−0.0506658	+	0.0292519i
$26$	3.43707	−	1.72289i	0.674064	−	0.337886i
$27$		0			0
$28$	4.31649	−	1.15660i	0.815739	−	0.218577i
$29$			0.605036i			0.112352i	0.998421	+	0.0561762i	$0.0178909\pi$
$29$			0.605036i			0.112352i	−0.998421	+	0.0561762i	$0.982109\pi$
$30$		0			0
$31$	3.38018	−	0.905716i	0.607098	−	0.162671i	0.0578423	−	0.998326i	$-0.481578\pi$
$31$	3.38018	−	0.905716i	0.607098	−	0.162671i	0.549256	+	0.835654i	$0.314911\pi$
$32$	−3.16415	+	3.16415i	−0.559347	+	0.559347i
$33$		0			0
$34$	−0.147545	−	0.0395346i	−0.0253038	−	0.00678013i
$35$	−10.3173	+	5.95671i	−1.74395	+	1.00687i
$36$		0			0
$37$	0.973046	+	3.63146i	0.159968	+	0.597008i	0.998629	+	0.0523539i	$0.0166724\pi$
$37$	0.973046	+	3.63146i	0.159968	+	0.597008i	−0.838661	+	0.544654i	$0.816661\pi$
$38$	−1.13753	−	1.97025i	−0.184531	−	0.319617i
$39$		0			0
$40$	3.51160	−	6.08227i	0.555233	−	0.961691i
$41$	7.55452	+	2.02423i	1.17982	+	0.316131i	0.794854	−	0.606801i	$-0.207547\pi$
$41$	7.55452	+	2.02423i	1.17982	+	0.316131i	0.384963	+	0.922932i	$0.374214\pi$
$42$		0			0
$43$	0.187567	+	0.108292i	0.0286038	+	0.0165144i	0.514234	−	0.857650i	$-0.328076\pi$
$43$	0.187567	+	0.108292i	0.0286038	+	0.0165144i	−0.485630	+	0.874164i	$0.661410\pi$
$44$	1.67127	−	1.67127i	0.251953	−	0.251953i
$45$		0			0
$46$	−0.868921	−	0.232827i	−0.128115	−	0.0343284i
$47$	−2.72952	+	10.1867i	−0.398141	+	1.48588i	0.418222	+	0.908345i	$0.362653\pi$
$47$	−2.72952	+	10.1867i	−0.398141	+	1.48588i	−0.816363	+	0.577539i	$0.804013\pi$
$48$		0			0
$49$	−17.1621	+	9.90853i	−2.45172	+	1.41550i
$50$	−0.0807314	+	0.301294i	−0.0114171	+	0.0426093i
$51$		0			0
$52$	−0.980914	+	2.95271i	−0.136028	+	0.409467i
$53$			8.00631i			1.09975i	0.835246	+	0.549876i	$0.185325\pi$
$53$			8.00631i			1.09975i	−0.835246	+	0.549876i	$0.814675\pi$
$54$		0			0
$55$	−3.15052	+	5.45686i	−0.424816	+	0.735802i
$56$	7.90459	−	13.6912i	1.05630	−	1.82956i
$57$		0			0
$58$	0.456203	+	0.456203i	0.0599024	+	0.0599024i
$59$	−5.26532	−	5.26532i	−0.685487	−	0.685487i	0.275744	−	0.961231i	$-0.411076\pi$
$59$	−5.26532	−	5.26532i	−0.685487	−	0.685487i	−0.961231	+	0.275744i	$0.911076\pi$
$60$		0			0
$61$	0.675442	−	1.16990i	0.0864815	−	0.149790i	−0.819540	−	0.573022i	$-0.805771\pi$
$61$	0.675442	−	1.16990i	0.0864815	−	0.149790i	0.906022	+	0.423232i	$0.139104\pi$
$62$	1.86577	−	3.23160i	0.236953	−	0.410414i
$63$		0			0
$64$			7.83049i			0.978811i
$65$	0.488596	−	8.28034i	0.0606028	−	1.02705i
$66$		0			0
$67$	1.98346	−	7.40238i	0.242318	−	0.904345i	−0.732394	−	0.680881i	$-0.761597\pi$
$67$	1.98346	−	7.40238i	0.242318	−	0.904345i	0.974712	−	0.223464i	$-0.0717364\pi$
$68$	0.107054	−	0.0618075i	0.0129822	−	0.00749526i
$69$		0			0
$70$	−3.28794	+	12.2708i	−0.392985	+	1.46664i
$71$	7.04646	+	1.88809i	0.836261	+	0.224075i	0.651443	−	0.758697i	$-0.274164\pi$
$71$	7.04646	+	1.88809i	0.836261	+	0.224075i	0.184818	+	0.982773i	$0.440831\pi$
$72$		0			0
$73$	−3.76736	+	3.76736i	−0.440936	+	0.440936i	−0.892326	−	0.451391i	$-0.850928\pi$
$73$	−3.76736	+	3.76736i	−0.440936	+	0.440936i	0.451391	+	0.892326i	$0.350928\pi$
$74$	3.47184	+	2.00447i	0.403593	+	0.233014i
$75$		0			0
$76$	1.77838	+	0.476516i	0.203994	+	0.0546601i
$77$	−7.09179	+	12.2833i	−0.808185	+	1.39982i
$78$		0			0
$79$	1.62641	+	2.81703i	0.182986	+	0.316941i	0.942896	−	0.333087i	$-0.108090\pi$
$79$	1.62641	+	2.81703i	0.182986	+	0.316941i	−0.759910	+	0.650028i	$0.774757\pi$
$80$	−0.910674	−	3.39868i	−0.101816	−	0.379984i
$81$		0			0
$82$	7.22246	−	4.16989i	0.797587	−	0.460487i
$83$	14.7099	+	3.94150i	1.61462	+	0.432636i	0.949415	−	0.314025i	$-0.101677\pi$
$83$	14.7099	+	3.94150i	1.61462	+	0.432636i	0.665205	+	0.746661i	$0.268344\pi$
$84$		0			0
$85$	−0.233027	+	0.233027i	−0.0252753	+	0.0252753i
$86$	0.223081	−	0.0597743i	0.0240554	−	0.00644563i
$87$		0			0
$88$		−	8.36151i		−	0.891340i
$89$	14.2431	−	3.81643i	1.50977	−	0.404541i	0.593409	−	0.804901i	$-0.297782\pi$
$89$	14.2431	−	3.81643i	1.50977	−	0.404541i	0.916358	+	0.400361i	$0.131115\pi$
$90$		0			0
$91$	1.09983	−	18.6390i	0.115293	−	1.95390i
$92$	0.630459	−	0.363996i	0.0657299	−	0.0379492i
$93$		0			0
$94$	5.62279	+	9.73895i	0.579946	+	1.00450i
$95$	−4.90830			−0.503581
$96$		0			0
$97$	0.525725	−	0.140868i	0.0533793	−	0.0143029i	−0.232031	−	0.972708i	$-0.574537\pi$
$97$	0.525725	−	0.140868i	0.0533793	−	0.0143029i	0.285410	+	0.958406i	$0.407870\pi$
$98$	−5.46924	+	20.4115i	−0.552476	+	2.06187i
$99$		0			0
$100$	−0.126213	−	0.218608i	−0.0126213	−	0.0218608i
$101$	−3.51090			−0.349347			−0.174674	−	0.984626i	$-0.555887\pi$
$101$	−3.51090			−0.349347			−0.174674	+	0.984626i	$0.555887\pi$
$102$		0			0
$103$	0.661851	+	0.382120i	0.0652141	+	0.0376514i	0.532253	−	0.846586i	$-0.321346\pi$
$103$	0.661851	+	0.382120i	0.0652141	+	0.0376514i	−0.467038	+	0.884237i	$0.654679\pi$
$104$	4.93252	+	9.84012i	0.483674	+	0.964903i
$105$		0			0
$106$	6.03683	+	6.03683i	0.586349	+	0.586349i
$107$	−5.29840	−	3.05903i	−0.512216	−	0.295728i	0.221528	−	0.975154i	$-0.428896\pi$
$107$	−5.29840	−	3.05903i	−0.512216	−	0.295728i	−0.733744	+	0.679426i	$0.762229\pi$
$108$		0			0
$109$	−3.64352	−	3.64352i	−0.348986	−	0.348986i	0.510746	−	0.859732i	$-0.329369\pi$
$109$	−3.64352	−	3.64352i	−0.348986	−	0.348986i	−0.859732	+	0.510746i	$0.829369\pi$
$110$	1.73900	+	6.49004i	0.165807	+	0.618801i
$111$		0			0
$112$	−2.04992	−	7.65041i	−0.193699	−	0.722896i
$113$		−	9.31035i		−	0.875844i	−0.899013	−	0.437922i	$-0.855715\pi$
$113$		−	9.31035i		−	0.875844i	0.899013	−	0.437922i	$-0.144285\pi$
$114$		0			0
$115$	−1.37234	+	1.37234i	−0.127971	+	0.127971i
$116$	−0.522111			−0.0484768
$117$		0			0
$118$	−7.94020			−0.730955
$119$	−0.524542	+	0.524542i	−0.0480847	+	0.0480847i
$120$		0			0
$121$		−	3.49827i		−	0.318025i
$122$	−0.372826	−	1.39140i	−0.0337541	−	0.125972i
$123$		0			0
$124$	0.781580	+	2.91690i	0.0701879	+	0.261945i
$125$	−7.65781	−	7.65781i	−0.684936	−	0.684936i
$126$		0			0
$127$	0.310458	+	0.179243i	0.0275487	+	0.0159052i	0.513711	−	0.857963i	$-0.328270\pi$
$127$	0.310458	+	0.179243i	0.0275487	+	0.0159052i	−0.486162	+	0.873868i	$0.661604\pi$
$128$	−0.424033	−	0.424033i	−0.0374796	−	0.0374796i
$129$		0			0
$130$	−5.87504	−	6.61186i	−0.515276	−	0.579898i
$131$	10.1169	+	5.84101i	0.883920	+	0.510331i	0.871949	−	0.489597i	$-0.162856\pi$
$131$	10.1169	+	5.84101i	0.883920	+	0.510331i	0.0119710	+	0.999928i	$0.496189\pi$
$132$		0			0
$133$	−11.0486			−0.958032
$134$	−4.08591	−	7.07701i	−0.352969	−	0.611361i
$135$		0			0
$136$	0.113185	−	0.422413i	0.00970556	−	0.0362216i
$137$	−15.1873	+	4.06943i	−1.29754	+	0.347675i	−0.840520	−	0.541781i	$-0.817750\pi$
$137$	−15.1873	+	4.06943i	−1.29754	+	0.347675i	−0.457021	+	0.889456i	$0.651084\pi$
$138$		0			0
$139$	13.7650			1.16753			0.583767	−	0.811922i	$-0.301578\pi$
$139$	13.7650			1.16753			0.583767	+	0.811922i	$0.301578\pi$
$140$	−5.14029	−	8.90325i	−0.434434	−	0.752462i
$141$		0			0
$142$	6.73673	−	3.88945i	0.565334	−	0.326396i
$143$	−4.42533	−	8.82830i	−0.370065	−	0.738260i
$144$		0			0
$145$	1.34449	−	0.360254i	0.111654	−	0.0299175i
$146$			5.68124i			0.470183i
$147$		0			0
$148$	−3.13373	+	0.839681i	−0.257591	+	0.0690214i
$149$	9.35362	−	9.35362i	0.766278	−	0.766278i	−0.211171	−	0.977449i	$-0.567728\pi$
$149$	9.35362	−	9.35362i	0.766278	−	0.766278i	0.977449	+	0.211171i	$0.0677277\pi$
$150$		0			0
$151$	−11.1072	−	2.97615i	−0.903888	−	0.242196i	−0.223203	−	0.974772i	$-0.571651\pi$
$151$	−11.1072	−	2.97615i	−0.903888	−	0.242196i	−0.680685	+	0.732576i	$0.738318\pi$
$152$	5.64072	−	3.25667i	0.457523	−	0.264151i
$153$		0			0
$154$	3.91448	+	14.6090i	0.315438	+	1.17723i
$155$	−4.02529	−	6.97201i	−0.323319	−	0.560005i
$156$		0			0
$157$	−4.68972	+	8.12283i	−0.374280	+	0.648272i	−0.990219	−	0.139522i	$-0.955443\pi$
$157$	−4.68972	+	8.12283i	−0.374280	+	0.648272i	0.615939	+	0.787794i	$0.288777\pi$
$158$	3.35040	+	0.897737i	0.266543	+	0.0714201i
$159$		0			0
$160$	8.91525	+	5.14722i	0.704812	+	0.406924i
$161$	−3.08913	+	3.08913i	−0.243457	+	0.243457i
$162$		0			0
$163$	−14.3617	−	3.84819i	−1.12489	−	0.301414i	−0.352030	−	0.935989i	$-0.614508\pi$
$163$	−14.3617	−	3.84819i	−1.12489	−	0.301414i	−0.772861	+	0.634575i	$0.781175\pi$
$164$	−1.74679	+	6.51910i	−0.136401	+	0.509056i
$165$		0			0
$166$	14.0633	−	8.11946i	1.09152	−	0.630192i
$167$	0.558665	−	2.08497i	0.0432308	−	0.161339i	−0.940936	−	0.338585i	$-0.890052\pi$
$167$	0.558665	−	2.08497i	0.0432308	−	0.161339i	0.984167	+	0.177245i	$0.0567185\pi$
$168$		0			0
$169$	10.4158	+	7.77892i	0.801214	+	0.598378i
$170$			0.351409i			0.0269518i
$171$		0			0
$172$	−0.0934497	+	0.161860i	−0.00712547	+	0.0123417i
$173$	−6.04205	+	10.4651i	−0.459369	+	0.795650i	−0.998928	−	0.0462976i	$-0.985258\pi$
$173$	−6.04205	+	10.4651i	−0.459369	+	0.795650i	0.539559	+	0.841948i	$0.318591\pi$
$174$		0			0
$175$	1.07114	+	1.07114i	0.0809704	+	0.0809704i
$176$	−2.96211	−	2.96211i	−0.223277	−	0.223277i
$177$		0			0
$178$	7.86181	−	13.6171i	0.589267	−	1.02064i
$179$	1.54606	−	2.67786i	0.115558	−	0.200152i	−0.802445	−	0.596727i	$-0.796468\pi$
$179$	1.54606	−	2.67786i	0.115558	−	0.200152i	0.918003	+	0.396574i	$0.129801\pi$
$180$		0			0
$181$			20.3888i			1.51549i	0.652550	+	0.757745i	$0.273699\pi$
$181$			20.3888i			1.51549i	−0.652550	+	0.757745i	$0.726301\pi$
$182$	−13.2247	−	14.8832i	−0.980279	−	1.10322i
$183$		0			0
$184$	0.666569	−	2.48767i	0.0491401	−	0.183394i
$185$	7.49030	−	4.32453i	0.550698	−	0.317945i
$186$		0			0
$187$	−0.101547	+	0.378978i	−0.00742584	+	0.0277136i
$188$	−8.79053	−	2.35541i	−0.641115	−	0.171786i
$189$		0			0
$190$	−3.70090	+	3.70090i	−0.268492	+	0.268492i
$191$	−8.18928	−	4.72808i	−0.592555	−	0.342112i	0.173552	−	0.984825i	$-0.444476\pi$
$191$	−8.18928	−	4.72808i	−0.592555	−	0.342112i	−0.766107	+	0.642713i	$0.777809\pi$
$192$		0			0
$193$	0.383474	+	0.102752i	0.0276031	+	0.00739622i	0.272594	−	0.962129i	$-0.412118\pi$
$193$	0.383474	+	0.102752i	0.0276031	+	0.00739622i	−0.244991	+	0.969525i	$0.578785\pi$
$194$	0.290186	−	0.502617i	0.0208341	−	0.0360858i
$195$		0			0
$196$	−8.55047	−	14.8099i	−0.610748	−	1.05785i
$197$	−0.713601	−	2.66320i	−0.0508420	−	0.189745i	0.935834	−	0.352440i	$-0.114648\pi$
$197$	−0.713601	−	2.66320i	−0.0508420	−	0.189745i	−0.986676	+	0.162695i	$0.947981\pi$
$198$		0			0
$199$	13.4785	−	7.78181i	0.955465	−	0.551638i	0.0606908	−	0.998157i	$-0.480670\pi$
$199$	13.4785	−	7.78181i	0.955465	−	0.551638i	0.894774	+	0.446519i	$0.147336\pi$
$200$	−0.862586	−	0.231129i	−0.0609940	−	0.0163433i
$201$		0			0
$202$	−2.64725	+	2.64725i	−0.186260	+	0.186260i
$203$	3.02643	−	0.810930i	0.212414	−	0.0569161i
$204$		0			0
$205$		−	17.9926i		−	1.25666i
$206$	0.787163	−	0.210920i	0.0548443	−	0.0146955i
$207$		0			0
$208$	5.23329	+	1.73854i	0.362863	+	0.120546i
$209$	−5.06071	+	2.92180i	−0.350057	+	0.202105i
$210$		0			0
$211$	−4.61191	−	7.98807i	−0.317497	−	0.549921i	0.662468	−	0.749090i	$-0.269509\pi$
$211$	−4.61191	−	7.98807i	−0.317497	−	0.549921i	−0.979965	+	0.199169i	$0.936176\pi$
$212$	−6.90898			−0.474510
$213$		0			0
$214$	−6.30158	+	1.68850i	−0.430767	+	0.115424i
$215$	0.128960	−	0.481284i	0.00879498	−	0.0328233i
$216$		0			0
$217$	−9.06090	−	15.6939i	−0.615094	−	1.06537i
$218$	−5.49449			−0.372134
$219$		0			0
$220$	−4.70894	−	2.71871i	−0.317477	−	0.183295i
$221$	−0.104058	−	0.505898i	−0.00699973	−	0.0340304i
$222$		0			0
$223$	1.36740	+	1.36740i	0.0915676	+	0.0915676i	0.751407	−	0.659839i	$-0.229376\pi$
$223$	1.36740	+	1.36740i	0.0915676	+	0.0915676i	−0.659839	+	0.751407i	$0.729376\pi$
$224$	20.0682	+	11.5864i	1.34086	+	0.774146i
$225$		0			0
$226$	−7.02009	−	7.02009i	−0.466969	−	0.466969i
$227$	−4.96201	−	18.5185i	−0.329340	−	1.22912i	−0.909876	−	0.414880i	$-0.863823\pi$
$227$	−4.96201	−	18.5185i	−0.329340	−	1.22912i	0.580536	−	0.814235i	$-0.302843\pi$
$228$		0			0
$229$	4.89219	+	18.2579i	0.323285	+	1.20652i	0.916025	+	0.401122i	$0.131380\pi$
$229$	4.89219	+	18.2579i	0.323285	+	1.20652i	−0.592739	+	0.805394i	$0.701954\pi$
$230$			2.06951i			0.136460i
$231$		0			0
$232$	−1.30608	+	1.30608i	−0.0857485	+	0.0857485i
$233$	15.0092			0.983286			0.491643	−	0.870797i	$-0.336397\pi$
$233$	15.0092			0.983286			0.491643	+	0.870797i	$0.336397\pi$
$234$		0			0
$235$	24.2617			1.58266
$236$	4.54366	−	4.54366i	0.295767	−	0.295767i
$237$		0			0
$238$			0.791019i			0.0512741i
$239$	−1.78174	−	6.64956i	−0.115251	−	0.430124i	0.884054	−	0.467384i	$-0.154804\pi$
$239$	−1.78174	−	6.64956i	−0.115251	−	0.430124i	−0.999306	+	0.0372603i	$0.988137\pi$
$240$		0			0
$241$	0.264008	+	0.985292i	0.0170063	+	0.0634683i	0.973908	−	0.226945i	$-0.0728738\pi$
$241$	0.264008	+	0.985292i	0.0170063	+	0.0634683i	−0.956901	+	0.290413i	$0.906207\pi$
$242$	−2.63773	−	2.63773i	−0.169560	−	0.169560i
$243$		0			0
$244$	1.00956	+	0.582867i	0.0646301	+	0.0373142i
$245$	32.2371	+	32.2371i	2.05955	+	2.05955i
$246$		0			0
$247$	4.23203	−	6.42384i	0.269277	−	0.408739i
$248$	9.25189	+	5.34158i	0.587496	+	0.339191i
$249$		0			0
$250$	−11.5481			−0.730367
$251$	−14.6482	−	25.3714i	−0.924586	−	1.60143i	−0.792226	−	0.610228i	$-0.791078\pi$
$251$	−14.6482	−	25.3714i	−0.924586	−	1.60143i	−0.132359	−	0.991202i	$-0.542255\pi$
$252$		0			0
$253$	−0.598029	+	2.23187i	−0.0375977	+	0.140317i
$254$	0.369239	−	0.0989372i	0.0231681	−	0.00620787i
$255$		0			0
$256$	−16.3004			−1.01878
$257$	9.09224	+	15.7482i	0.567159	+	0.982347i	0.996845	+	0.0793694i	$0.0252907\pi$
$257$	9.09224	+	15.7482i	0.567159	+	0.982347i	−0.429687	+	0.902978i	$0.641376\pi$
$258$		0			0
$259$	16.8606	−	9.73448i	1.04767	−	0.604871i
$260$	7.14545	+	0.421629i	0.443142	+	0.0261483i
$261$		0			0
$262$	12.0324	−	3.22408i	0.743366	−	0.199184i
$263$			19.5534i			1.20572i	0.797848	+	0.602858i	$0.205971\pi$
$263$			19.5534i			1.20572i	−0.797848	+	0.602858i	$0.794029\pi$
$264$		0			0
$265$	17.7913	−	4.76716i	1.09291	−	0.292845i
$266$	−8.33071	+	8.33071i	−0.510789	+	0.510789i
$267$		0			0
$268$	6.38782	+	1.71161i	0.390198	+	0.104553i
$269$	−23.9955	+	13.8538i	−1.46303	+	0.844683i	−0.999150	−	0.0412138i	$-0.986878\pi$
$269$	−23.9955	+	13.8538i	−1.46303	+	0.844683i	−0.463883	+	0.885896i	$0.653544\pi$
$270$		0			0
$271$	2.16310	+	8.07278i	0.131399	+	0.490387i	0.999987	−	0.00514827i	$-0.00163875\pi$
$271$	2.16310	+	8.07278i	0.131399	+	0.490387i	−0.868588	+	0.495535i	$0.834972\pi$
$272$	−0.109546	−	0.189739i	−0.00664218	−	0.0115046i
$273$		0			0
$274$	−8.38299	+	14.5198i	−0.506435	+	0.877171i
$275$	0.773889	+	0.207363i	0.0466673	+	0.0125045i
$276$		0			0
$277$	13.6565	+	7.88460i	0.820541	+	0.473740i	0.850603	−	0.525808i	$-0.176237\pi$
$277$	13.6565	+	7.88460i	0.820541	+	0.473740i	−0.0300620	+	0.999548i	$0.509570\pi$
$278$	10.3789	−	10.3789i	0.622488	−	0.622488i
$279$		0			0
$280$	−35.1305	−	9.41319i	−2.09945	−	0.562546i
$281$	−3.53952	+	13.2097i	−0.211150	+	0.788022i	0.776337	+	0.630319i	$0.217076\pi$
$281$	−3.53952	+	13.2097i	−0.211150	+	0.788022i	−0.987486	+	0.157704i	$0.949591\pi$
$282$		0			0
$283$	−11.6559	+	6.72951i	−0.692869	+	0.400028i	−0.804686	−	0.593701i	$-0.797666\pi$
$283$	−11.6559	+	6.72951i	−0.692869	+	0.400028i	0.111817	+	0.993729i	$0.464333\pi$
$284$	−1.62931	+	6.08068i	−0.0966820	+	0.360822i
$285$		0			0
$286$	−9.99336	−	3.31988i	−0.590920	−	0.196308i
$287$		−	40.5013i		−	2.39071i
$288$		0			0
$289$	8.48974	−	14.7047i	0.499396	−	0.864980i
$290$	0.742120	−	1.28539i	0.0435788	−	0.0754807i
$291$		0			0
$292$	−3.25101	−	3.25101i	−0.190251	−	0.190251i
$293$	−5.04007	−	5.04007i	−0.294444	−	0.294444i	0.544389	−	0.838833i	$-0.316762\pi$
$293$	−5.04007	−	5.04007i	−0.294444	−	0.294444i	−0.838833	+	0.544389i	$0.816762\pi$
$294$		0			0
$295$	−8.56527	+	14.8355i	−0.498689	+	0.863756i
$296$	−5.73867	+	9.93966i	−0.333553	+	0.577731i
$297$		0			0
$298$		−	14.1054i		−	0.817105i
$299$	−0.612820	−	2.97933i	−0.0354403	−	0.172299i
$300$		0			0
$301$	0.290288	−	1.08337i	0.0167319	−	0.0624443i
$302$	−10.6189	+	6.13085i	−0.611051	+	0.352791i
$303$		0			0
$304$	0.844562	−	3.15195i	0.0484390	−	0.180777i
$305$	−3.00188	−	0.804351i	−0.171887	−	0.0460570i
$306$		0			0
$307$	−8.37481	+	8.37481i	−0.477976	+	0.477976i	−0.904484	−	0.426508i	$-0.859744\pi$
$307$	−8.37481	+	8.37481i	−0.477976	+	0.477976i	0.426508	+	0.904484i	$0.359744\pi$
$308$	−10.5998	−	6.11980i	−0.603980	−	0.348708i
$309$		0			0
$310$	−8.29206	−	2.22185i	−0.470957	−	0.126193i
$311$	−1.34766	+	2.33421i	−0.0764186	+	0.132361i	−0.901702	−	0.432357i	$-0.857682\pi$
$311$	−1.34766	+	2.33421i	−0.0764186	+	0.132361i	0.825284	+	0.564718i	$0.191015\pi$
$312$		0			0
$313$	1.67357	+	2.89871i	0.0945958	+	0.163845i	0.909440	−	0.415836i	$-0.136511\pi$
$313$	1.67357	+	2.89871i	0.0945958	+	0.163845i	−0.814844	+	0.579680i	$0.803177\pi$
$314$	2.58860	+	9.66077i	0.146083	+	0.545189i
$315$		0			0
$316$	−2.43093	+	1.40350i	−0.136751	+	0.0789530i
$317$	3.08107	+	0.825569i	0.173050	+	0.0463686i	0.344304	−	0.938858i	$-0.388115\pi$
$317$	3.08107	+	0.825569i	0.173050	+	0.0463686i	−0.171254	+	0.985227i	$0.554782\pi$
$318$		0			0
$319$	1.17178	−	1.17178i	0.0656072	−	0.0656072i
$320$	17.4006	−	4.66247i	0.972723	−	0.260640i
$321$		0			0
$322$			4.65846i			0.259606i
$323$	−0.295212	+	0.0791017i	−0.0164260	+	0.00440134i
$324$		0			0
$325$	−1.03307	+	0.212492i	−0.0573042	+	0.0117869i
$326$	−13.7304	+	7.92724i	−0.760456	+	0.439049i
$327$		0			0
$328$	11.9381	+	20.6775i	0.659174	+	1.14172i
$329$	54.6129			3.01091
$330$		0			0
$331$	−29.7907	+	7.98241i	−1.63745	+	0.438753i	−0.956060	−	0.293170i	$-0.905290\pi$
$331$	−29.7907	+	7.98241i	−1.63745	+	0.438753i	−0.681387	+	0.731923i	$0.738623\pi$
$332$	−3.40128	+	12.6938i	−0.186670	+	0.696661i
$333$		0			0
$334$	−1.15084	−	1.99332i	−0.0629714	−	0.109070i
$335$	−17.6303			−0.963244
$336$		0			0
$337$	−4.37979	−	2.52867i	−0.238582	−	0.137745i	0.375943	−	0.926643i	$-0.377319\pi$
$337$	−4.37979	−	2.52867i	−0.238582	−	0.137745i	−0.614525	+	0.788897i	$0.710652\pi$
$338$	13.7190	−	1.98822i	0.746213	−	0.108145i
$339$		0			0
$340$	−0.201088	−	0.201088i	−0.0109056	−	0.0109056i
$341$	−8.30056	−	4.79233i	−0.449500	−	0.259519i
$342$		0			0
$343$	46.9330	+	46.9330i	2.53415	+	2.53415i
$344$	0.171130	+	0.638667i	0.00922672	+	0.0344346i
$345$		0			0
$346$	3.33505	+	12.4466i	0.179293	+	0.669132i
$347$			9.93186i			0.533170i	0.963811	+	0.266585i	$0.0858954\pi$
$347$			9.93186i			0.533170i	−0.963811	+	0.266585i	$0.914105\pi$
$348$		0			0
$349$	−16.7774	+	16.7774i	−0.898073	+	0.898073i	−0.995266	−	0.0971927i	$-0.969014\pi$
$349$	−16.7774	+	16.7774i	−0.898073	+	0.898073i	0.0971927	+	0.995266i	$0.469014\pi$
$350$	1.61529			0.0863411
$351$		0			0
$352$	12.2561			0.653252
$353$	14.8488	−	14.8488i	0.790322	−	0.790322i	−0.191225	−	0.981546i	$-0.561246\pi$
$353$	14.8488	−	14.8488i	0.790322	−	0.790322i	0.981546	+	0.191225i	$0.0612459\pi$
$354$		0			0
$355$		−	16.7826i		−	0.890726i
$356$	3.29335	+	12.2910i	0.174547	+	0.651420i
$357$		0			0
$358$	−0.853384	−	3.18487i	−0.0451027	−	0.168326i
$359$	8.32119	+	8.32119i	0.439175	+	0.439175i	0.891734	−	0.452559i	$-0.149489\pi$
$359$	8.32119	+	8.32119i	0.439175	+	0.439175i	−0.452559	+	0.891734i	$0.649489\pi$
$360$		0			0
$361$	12.5124	+	7.22401i	0.658545	+	0.380211i
$362$	15.3734	+	15.3734i	0.808006	+	0.808006i
$363$		0			0
$364$	16.0844	+	0.949085i	0.843049	+	0.0497456i
$365$	10.6148	+	6.12849i	0.555607	+	0.320780i
$366$		0			0
$367$	−5.67060			−0.296003			−0.148001	−	0.988987i	$-0.547284\pi$
$367$	−5.67060			−0.296003			−0.148001	+	0.988987i	$0.547284\pi$
$368$	−0.645135	−	1.11741i	−0.0336300	−	0.0582489i
$369$		0			0
$370$	2.38702	−	8.90848i	0.124095	−	0.463130i
$371$	40.0481	−	10.7309i	2.07919	−	0.557118i
$372$		0			0
$373$	−26.9106			−1.39338			−0.696690	−	0.717373i	$-0.745345\pi$
$373$	−26.9106			−1.39338			−0.696690	+	0.717373i	$0.745345\pi$
$374$	0.209186	+	0.362320i	0.0108167	+	0.0187351i
$375$		0			0
$376$	−27.8820	+	16.0977i	−1.43791	+	0.830176i
$377$	−0.687751	+	2.07024i	−0.0354210	+	0.106623i
$378$		0			0
$379$	−26.3773	+	7.06778i	−1.35491	+	0.363047i	−0.861945	−	0.507001i	$-0.830754\pi$
$379$	−26.3773	+	7.06778i	−1.35491	+	0.363047i	−0.492966	+	0.870049i	$0.664087\pi$
$380$		−	4.23558i		−	0.217280i
$381$		0			0
$382$	−9.73981	+	2.60977i	−0.498332	+	0.133528i
$383$	−11.8575	+	11.8575i	−0.605891	+	0.605891i	−0.941870	−	0.335978i	$-0.890933\pi$
$383$	−11.8575	+	11.8575i	−0.605891	+	0.605891i	0.335978	+	0.941870i	$0.390933\pi$
$384$		0			0
$385$	31.5182	+	8.44527i	1.60632	+	0.430411i
$386$	0.366619	−	0.211667i	0.0186604	−	0.0107736i
$387$		0			0
$388$	0.121560	+	0.453670i	0.00617130	+	0.0230316i
$389$	−0.566623	−	0.981420i	−0.0287289	−	0.0497600i	0.851303	−	0.524674i	$-0.175813\pi$
$389$	−0.566623	−	0.981420i	−0.0287289	−	0.0497600i	−0.880032	+	0.474914i	$0.842479\pi$
$390$		0			0
$391$	−0.0604234	+	0.104656i	−0.00305574	+	0.00529270i
$392$	−58.4368	−	15.6581i	−2.95151	−	0.790854i
$393$		0			0
$394$	−2.54613	−	1.47001i	−0.128272	−	0.0740581i
$395$	5.29148	−	5.29148i	0.266243	−	0.266243i
$396$		0			0
$397$	17.9346	+	4.80557i	0.900114	+	0.241185i	0.679065	−	0.734078i	$-0.262385\pi$
$397$	17.9346	+	4.80557i	0.900114	+	0.241185i	0.221049	+	0.975263i	$0.429052\pi$
$398$	4.29535	−	16.0305i	0.215306	−	0.803534i
$399$		0			0
$400$	−0.387454	+	0.223697i	−0.0193727	+	0.0111848i
$401$	4.50864	−	16.8265i	0.225151	−	0.840274i	−0.757193	−	0.653191i	$-0.773430\pi$
$401$	4.50864	−	16.8265i	0.225151	−	0.840274i	0.982344	−	0.187083i	$-0.0599035\pi$
$402$		0			0
$403$	12.5954	+	0.743215i	0.627423	+	0.0370222i
$404$		−	3.02970i		−	0.150733i
$405$		0			0
$406$	1.67051	−	2.89340i	0.0829059	−	0.143597i
$407$	5.14858	−	8.91761i	0.255206	−	0.442029i
$408$		0			0
$409$	21.9023	+	21.9023i	1.08300	+	1.08300i	0.996228	+	0.0867723i	$0.0276553\pi$
$409$	21.9023	+	21.9023i	1.08300	+	1.08300i	0.0867723	+	0.996228i	$0.472345\pi$
$410$	−13.5666	−	13.5666i	−0.670006	−	0.670006i
$411$		0			0
$412$	−0.329747	+	0.571138i	−0.0162455	+	0.0281380i
$413$	−19.2804	+	33.3946i	−0.948725	+	1.64324i
$414$		0			0
$415$		−	35.0346i		−	1.71978i
$416$	−14.4234	+	7.22998i	−0.707166	+	0.354479i
$417$		0			0
$418$	−1.61276	+	6.01888i	−0.0788824	+	0.294393i
$419$	−18.5952	+	10.7360i	−0.908436	+	0.524486i	−0.879928	−	0.475108i	$-0.842409\pi$
$419$	−18.5952	+	10.7360i	−0.908436	+	0.524486i	−0.0285086	+	0.999594i	$0.509076\pi$
$420$		0			0
$421$	6.14101	−	22.9186i	0.299295	−	1.11698i	−0.638452	−	0.769662i	$-0.720425\pi$
$421$	6.14101	−	22.9186i	0.299295	−	1.11698i	0.937746	−	0.347321i	$-0.112908\pi$
$422$	−9.50050	−	2.54565i	−0.462477	−	0.123920i
$423$		0			0
$424$	−17.2831	+	17.2831i	−0.839341	+	0.839341i
$425$	0.0362890	+	0.0209515i	0.00176027	+	0.00101630i
$426$		0			0
$427$	−6.75721	−	1.81059i	−0.327004	−	0.0876206i
$428$	2.63977	−	4.57221i	0.127598	−	0.221006i
$429$		0			0
$430$	−0.265656	−	0.460129i	−0.0128111	−	0.0221894i
$431$	6.05706	+	22.6052i	0.291758	+	1.08886i	0.943758	+	0.330637i	$0.107264\pi$
$431$	6.05706	+	22.6052i	0.291758	+	1.08886i	−0.652000	+	0.758219i	$0.726070\pi$
$432$		0			0
$433$	−23.0080	+	13.2837i	−1.10569	+	0.638372i	−0.937710	−	0.347418i	$-0.887058\pi$
$433$	−23.0080	+	13.2837i	−1.10569	+	0.638372i	−0.167982	+	0.985790i	$0.553725\pi$
$434$	−18.6654	−	5.00137i	−0.895967	−	0.240074i
$435$		0			0
$436$	3.14414	−	3.14414i	0.150577	−	0.150577i
$437$	−1.73856	+	0.465845i	−0.0831665	+	0.0222844i
$438$		0			0
$439$			0.426976i			0.0203784i	0.999948	+	0.0101892i	$0.00324338\pi$
$439$			0.426976i			0.0203784i	−0.999948	+	0.0101892i	$0.996757\pi$
$440$	−18.5806	+	4.97865i	−0.885795	+	0.237348i
$441$		0			0
$442$	−0.459913	−	0.302991i	−0.0218758	−	0.0144118i
$443$	−9.92611	+	5.73084i	−0.471604	+	0.272281i	−0.716911	−	0.697165i	$-0.754445\pi$
$443$	−9.92611	+	5.73084i	−0.471604	+	0.272281i	0.245307	+	0.969445i	$0.421111\pi$
$444$		0			0
$445$	−16.9614	−	29.3780i	−0.804048	−	1.39265i
$446$	2.06206			0.0976412
$447$		0			0
$448$	39.1686	−	10.4952i	1.85054	−	0.495852i
$449$	−1.66954	+	6.23079i	−0.0787903	+	0.294049i	−0.994066	−	0.108779i	$-0.965306\pi$
$449$	−1.66954	+	6.23079i	−0.0787903	+	0.294049i	0.915276	+	0.402828i	$0.131973\pi$
$450$		0			0
$451$	−10.7106	−	18.5513i	−0.504342	−	0.873546i
$452$	8.03428			0.377901
$453$		0			0
$454$	−17.7045	−	10.2217i	−0.830914	−	0.479728i
$455$	−42.0737	+	8.65415i	−1.97244	+	0.405713i
$456$		0			0
$457$	7.68615	+	7.68615i	0.359543	+	0.359543i	0.863644	−	0.504101i	$-0.168176\pi$
$457$	7.68615	+	7.68615i	0.359543	+	0.359543i	−0.504101	+	0.863644i	$0.668176\pi$
$458$	17.4554	+	10.0779i	0.815636	+	0.470908i
$459$		0			0
$460$	−1.18425	−	1.18425i	−0.0552158	−	0.0552158i
$461$	4.40054	+	16.4230i	0.204953	+	0.764896i	0.989464	+	0.144781i	$0.0462477\pi$
$461$	4.40054	+	16.4230i	0.204953	+	0.764896i	−0.784510	+	0.620116i	$0.787086\pi$
$462$		0			0
$463$	−10.0407	−	37.4724i	−0.466630	−	1.74149i	−0.651427	−	0.758712i	$-0.725829\pi$
$463$	−10.0407	−	37.4724i	−0.466630	−	1.74149i	0.184796	−	0.982777i	$-0.440838\pi$
$464$			0.925373i			0.0429594i
$465$		0			0
$466$	11.3171	−	11.3171i	0.524253	−	0.524253i
$467$	37.7239			1.74566			0.872828	−	0.488028i	$-0.162284\pi$
$467$	37.7239			1.74566			0.872828	+	0.488028i	$0.162284\pi$
$468$		0			0
$469$	−39.6856			−1.83251
$470$	18.2935	−	18.2935i	0.843818	−	0.843818i
$471$		0			0
$472$		−	22.7323i		−	1.04634i
$473$	−0.153534	−	0.572995i	−0.00705948	−	0.0263463i
$474$		0			0
$475$	0.161529	+	0.602835i	0.00741147	+	0.0276600i
$476$	−0.452649	−	0.452649i	−0.0207471	−	0.0207471i
$477$		0			0
$478$	−6.35728	−	3.67037i	−0.290775	−	0.167879i
$479$	−14.7645	−	14.7645i	−0.674607	−	0.674607i	0.284167	−	0.958775i	$-0.408283\pi$
$479$	−14.7645	−	14.7645i	−0.674607	−	0.674607i	−0.958775	+	0.284167i	$0.908283\pi$
$480$		0			0
$481$	−0.798464	+	13.5318i	−0.0364068	+	0.616995i
$482$	0.941984	+	0.543855i	0.0429062	+	0.0247719i
$483$		0			0
$484$	3.01880			0.137218
$485$	−0.626060	−	1.08437i	−0.0284279	−	0.0492386i
$486$		0			0
$487$	4.59917	−	17.1643i	0.208408	−	0.777791i	−0.779975	−	0.625811i	$-0.784768\pi$
$487$	4.59917	−	17.1643i	0.208408	−	0.777791i	0.988384	−	0.151980i	$-0.0485650\pi$
$488$	3.98351	−	1.06738i	0.180325	−	0.0483180i
$489$		0			0
$490$	48.6141			2.19616
$491$	−7.29594	−	12.6369i	−0.329261	−	0.570297i	0.653104	−	0.757268i	$-0.273466\pi$
$491$	−7.29594	−	12.6369i	−0.329261	−	0.570297i	−0.982365	+	0.186971i	$0.940133\pi$
$492$		0			0
$493$	0.0750588	−	0.0433352i	0.00338048	−	0.00195172i
$494$	−1.65264	−	8.03462i	−0.0743559	−	0.361494i
$495$		0			0
$496$	5.16982	−	1.38525i	0.232132	−	0.0621995i
$497$		−	37.7775i		−	1.69455i
$498$		0			0
$499$	11.5561	−	3.09645i	0.517323	−	0.138616i	0.00929473	−	0.999957i	$-0.497041\pi$
$499$	11.5561	−	3.09645i	0.517323	−	0.138616i	0.508028	+	0.861341i	$0.330375\pi$
$500$	6.60824	−	6.60824i	0.295530	−	0.295530i
$501$		0			0
$502$	−30.1751	−	8.08540i	−1.34678	−	0.360869i
$503$	24.4849	−	14.1364i	1.09173	−	0.630310i	0.157693	−	0.987488i	$-0.449594\pi$
$503$	24.4849	−	14.1364i	1.09173	−	0.630310i	0.934036	+	0.357178i	$0.116261\pi$
$504$		0			0
$505$	2.09048	+	7.80177i	0.0930250	+	0.347174i
$506$	1.23193	+	2.13377i	0.0547661	+	0.0948577i
$507$		0			0
$508$	−0.154676	+	0.267907i	−0.00686264	+	0.0118864i
$509$	−8.79489	−	2.35658i	−0.389827	−	0.104454i	0.0585816	−	0.998283i	$-0.481342\pi$
$509$	−8.79489	−	2.35658i	−0.389827	−	0.104454i	−0.448408	+	0.893829i	$0.648009\pi$
$510$		0			0
$511$	23.8940	+	13.7952i	1.05701	+	0.610263i
$512$	−11.4426	+	11.4426i	−0.505696	+	0.505696i
$513$		0			0
$514$	18.7299	+	5.01867i	0.826142	+	0.221364i
$515$	0.455048	−	1.69826i	0.0200518	−	0.0748344i
$516$		0			0
$517$	25.0150	−	14.4424i	1.10016	−	0.635178i
$518$	5.37317	−	20.0529i	0.236083	−	0.881075i
$519$		0			0
$520$	18.9294	−	16.8199i	0.830107	−	0.737602i
$521$		−	10.8148i		−	0.473806i	−0.971533	−	0.236903i	$-0.923868\pi$
$521$		−	10.8148i		−	0.473806i	0.971533	−	0.236903i	$-0.0761324\pi$
$522$		0			0
$523$	−16.8346	+	29.1584i	−0.736125	+	1.27501i	0.218103	+	0.975926i	$0.430013\pi$
$523$	−16.8346	+	29.1584i	−0.736125	+	1.27501i	−0.954228	+	0.299080i	$0.903320\pi$
$524$	−5.04045	+	8.73031i	−0.220193	+	0.381385i
$525$		0			0
$526$	14.7435	+	14.7435i	0.642845	+	0.642845i
$527$	−0.354463	−	0.354463i	−0.0154406	−	0.0154406i
$528$		0			0
$529$	11.1442	−	19.3022i	0.484528	−	0.839228i
$530$	9.82031	−	17.0093i	0.426567	−	0.738836i
$531$		0			0
$532$		−	9.53425i		−	0.413362i
$533$	23.5482	+	15.5136i	1.01998	+	0.671967i
$534$		0			0
$535$	−3.64285	+	13.5953i	−0.157494	+	0.587777i
$536$	20.2611	−	11.6977i	0.875145	−	0.505265i
$537$		0			0
$538$	−7.64694	+	28.5388i	−0.329683	+	1.23039i
$539$	52.4280	+	14.0480i	2.25823	+	0.605092i
$540$		0			0
$541$	19.2044	−	19.2044i	0.825663	−	0.825663i	−0.161250	−	0.986914i	$-0.551553\pi$
$541$	19.2044	−	19.2044i	0.825663	−	0.825663i	0.986914	+	0.161250i	$0.0515526\pi$
$542$	7.71794	+	4.45596i	0.331514	+	0.191400i
$543$		0			0
$544$	0.619163	+	0.165904i	0.0265464	+	0.00711309i
$545$	−5.92703	+	10.2659i	−0.253886	+	0.439744i
$546$		0			0
$547$	−12.0347	−	20.8447i	−0.514565	−	0.891253i	−0.999857	−	0.0169009i	$-0.994620\pi$
$547$	−12.0347	−	20.8447i	−0.514565	−	0.891253i	0.485292	−	0.874352i	$-0.338713\pi$
$548$	−3.51168	−	13.1058i	−0.150011	−	0.559850i
$549$		0			0
$550$	0.739873	−	0.427166i	0.0315483	−	0.0182144i
$551$	1.24688	+	0.334101i	0.0531190	+	0.0142332i
$552$		0			0
$553$	11.9111	−	11.9111i	0.506511	−	0.506511i
$554$	16.2422	−	4.35208i	0.690065	−	0.184902i
$555$		0			0
$556$			11.8784i			0.503756i
$557$	−25.0352	+	6.70816i	−1.06078	+	0.284234i	−0.746698	−	0.665163i	$-0.768362\pi$
$557$	−25.0352	+	6.70816i	−1.06078	+	0.284234i	−0.314078	+	0.949397i	$0.601695\pi$
$558$		0			0
$559$	0.518699	+	0.583750i	0.0219386	+	0.0246900i
$560$	−15.7798	+	9.11050i	−0.666820	+	0.384989i
$561$		0			0
$562$	7.29137	+	12.6290i	0.307568	+	0.532723i
$563$	−16.4516			−0.693352			−0.346676	−	0.937985i	$-0.612690\pi$
$563$	−16.4516			−0.693352			−0.346676	+	0.937985i	$0.612690\pi$
$564$		0			0
$565$	−20.6891	+	5.54362i	−0.870396	+	0.233222i
$566$	−3.71451	+	13.8627i	−0.156132	+	0.582694i
$567$		0			0
$568$	11.1353	+	19.2869i	0.467226	+	0.809259i
$569$	−14.2291			−0.596516			−0.298258	−	0.954485i	$-0.596406\pi$
$569$	−14.2291			−0.596516			−0.298258	+	0.954485i	$0.596406\pi$
$570$		0			0
$571$	18.0451	+	10.4184i	0.755164	+	0.435994i	0.827557	−	0.561382i	$-0.189730\pi$
$571$	18.0451	+	10.4184i	0.755164	+	0.435994i	−0.0723925	+	0.997376i	$0.523063\pi$
$572$	7.61830	−	3.81880i	0.318537	−	0.159672i
$573$		0			0
$574$	−30.5383	−	30.5383i	−1.27464	−	1.27464i
$575$	0.213713	+	0.123387i	0.00891244	+	0.00514560i
$576$		0			0
$577$	−32.0720	−	32.0720i	−1.33517	−	1.33517i	−0.900670	−	0.434505i	$-0.856924\pi$
$577$	−32.0720	−	32.0720i	−1.33517	−	1.33517i	−0.434505	−	0.900670i	$-0.643076\pi$
$578$	−4.68611	−	17.4888i	−0.194916	−	0.727438i
$579$		0			0
$580$	0.310878	+	1.16021i	0.0129085	+	0.0481752i
$581$		−	78.8626i		−	3.27177i
$582$		0			0
$583$	15.5059	−	15.5059i	0.642191	−	0.642191i
$584$	−16.2651			−0.673053
$585$		0			0
$586$	−7.60051			−0.313974
$587$	−11.1721	+	11.1721i	−0.461121	+	0.461121i	−0.899023	−	0.437902i	$-0.855722\pi$
$587$	−11.1721	+	11.1721i	−0.461121	+	0.461121i	0.437902	+	0.899023i	$0.355722\pi$
$588$		0			0
$589$		−	7.46614i		−	0.307637i
$590$	4.72780	+	17.6444i	0.194640	+	0.726408i
$591$		0			0
$592$	1.48823	+	5.55414i	0.0611657	+	0.228274i
$593$	−25.1695	−	25.1695i	−1.03359	−	1.03359i	−0.999416	−	0.0341707i	$-0.989121\pi$
$593$	−25.1695	−	25.1695i	−1.03359	−	1.03359i	−0.0341707	−	0.999416i	$-0.510879\pi$
$594$		0			0
$595$	1.47794	+	0.853290i	0.0605897	+	0.0349815i
$596$	8.07162	+	8.07162i	0.330626	+	0.330626i
$597$		0			0
$598$	−2.70851	−	1.78437i	−0.110759	−	0.0729683i
$599$	1.33423	+	0.770320i	0.0545153	+	0.0314744i	0.527010	−	0.849859i	$-0.323313\pi$
$599$	1.33423	+	0.770320i	0.0545153	+	0.0314744i	−0.472495	+	0.881334i	$0.656646\pi$
$600$		0			0
$601$	29.3874			1.19874			0.599369	−	0.800473i	$-0.295418\pi$
$601$	29.3874			1.19874			0.599369	+	0.800473i	$0.295418\pi$
$602$	−0.597990	−	1.03575i	−0.0243722	−	0.0422140i
$603$		0			0
$604$	2.56825	−	9.58482i	0.104500	−	0.390001i
$605$	−7.77372	+	2.08296i	−0.316047	+	0.0846844i
$606$		0			0
$607$	−20.8526			−0.846382			−0.423191	−	0.906041i	$-0.639090\pi$
$607$	−20.8526			−0.846382			−0.423191	+	0.906041i	$0.639090\pi$
$608$	4.77355	+	8.26804i	0.193593	+	0.335313i
$609$		0			0
$610$	−2.86993	+	1.65696i	−0.116200	+	0.0670882i
$611$	−20.9189	+	31.7530i	−0.846287	+	1.28459i
$612$		0			0
$613$	−21.4484	+	5.74708i	−0.866292	+	0.232122i	−0.664484	−	0.747303i	$-0.731349\pi$
$613$	−21.4484	+	5.74708i	−0.866292	+	0.232122i	−0.201809	+	0.979425i	$0.564682\pi$
$614$			12.6294i			0.509680i
$615$		0			0
$616$	−41.8248	+	11.2069i	−1.68517	+	0.451540i
$617$	−8.58385	+	8.58385i	−0.345573	+	0.345573i	−0.858457	−	0.512885i	$-0.828577\pi$
$617$	−8.58385	+	8.58385i	−0.345573	+	0.345573i	0.512885	+	0.858457i	$0.328577\pi$
$618$		0			0
$619$	−5.57125	−	1.49281i	−0.223928	−	0.0600012i	0.145111	−	0.989415i	$-0.453646\pi$
$619$	−5.57125	−	1.49281i	−0.223928	−	0.0600012i	−0.369038	+	0.929414i	$0.620313\pi$
$620$	6.01643	−	3.47359i	0.241626	−	0.139503i
$621$		0			0
$622$	0.743870	+	2.77616i	0.0298265	+	0.111314i
$623$	−38.1800	−	66.1298i	−1.52965	−	2.64943i
$624$		0			0
$625$	−13.1885	+	22.8432i	−0.527541	+	0.913727i
$626$	3.44754	+	0.923765i	0.137791	+	0.0369211i
$627$		0			0
$628$	−7.00952	−	4.04695i	−0.279710	−	0.161491i
$629$	0.380813	−	0.380813i	0.0151840	−	0.0151840i
$630$		0			0
$631$	−0.701230	−	0.187894i	−0.0279155	−	0.00747994i	0.244834	−	0.969565i	$-0.421266\pi$
$631$	−0.701230	−	0.187894i	−0.0279155	−	0.00747994i	−0.272750	+	0.962085i	$0.587933\pi$
$632$	−2.57017	+	9.59200i	−0.102236	+	0.381549i
$633$		0			0
$634$	2.94564	−	1.70066i	0.116986	−	0.0675420i
$635$	0.213452	−	0.796612i	0.00847057	−	0.0316126i
$636$		0			0
$637$	−69.9862	+	14.3955i	−2.77296	+	0.570370i
$638$		−	1.76707i		−	0.0699589i
$639$		0			0
$640$	−0.689789	+	1.19475i	−0.0272663	+	0.0472266i
$641$	0.968362	−	1.67725i	0.0382480	−	0.0662475i	−0.846268	−	0.532758i	$-0.821156\pi$
$641$	0.968362	−	1.67725i	0.0382480	−	0.0662475i	0.884516	+	0.466510i	$0.154489\pi$
$642$		0			0
$643$	3.83575	+	3.83575i	0.151267	+	0.151267i	0.778684	−	0.627417i	$-0.215888\pi$
$643$	3.83575	+	3.83575i	0.151267	+	0.151267i	−0.627417	+	0.778684i	$0.715888\pi$
$644$	−2.66573	−	2.66573i	−0.105045	−	0.105045i
$645$		0			0
$646$	−0.162949	+	0.282236i	−0.00641114	+	0.0111044i
$647$	5.52455	−	9.56880i	0.217192	−	0.376188i	−0.736756	−	0.676159i	$-0.763643\pi$
$647$	5.52455	−	9.56880i	0.217192	−	0.376188i	0.953949	+	0.299970i	$0.0969767\pi$
$648$		0			0
$649$			20.3949i			0.800568i
$650$	−0.618720	+	0.939162i	−0.0242682	+	0.0368370i
$651$		0			0
$652$	3.32076	−	12.3933i	0.130051	−	0.485357i
$653$	−22.9231	+	13.2346i	−0.897049	+	0.517912i	−0.876242	−	0.481872i	$-0.839957\pi$
$653$	−22.9231	+	13.2346i	−0.897049	+	0.517912i	−0.0208076	+	0.999783i	$0.506624\pi$
$654$		0			0
$655$	6.95577	−	25.9593i	0.271784	−	1.01431i
$656$	11.5543	+	3.09595i	0.451118	+	0.120877i
$657$		0			0
$658$	41.1786	−	41.1786i	1.60531	−	1.60531i
$659$	38.2912	+	22.1074i	1.49161	+	0.861184i	0.999954	−	0.00960334i	$-0.00305688\pi$
$659$	38.2912	+	22.1074i	1.49161	+	0.861184i	0.491660	+	0.870787i	$0.336390\pi$
$660$		0			0
$661$	30.5589	+	8.18823i	1.18860	+	0.318485i	0.798334	−	0.602215i	$-0.205715\pi$
$661$	30.5589	+	8.18823i	1.18860	+	0.318485i	0.390270	+	0.920701i	$0.372382\pi$
$662$	−16.4437	+	28.4813i	−0.639102	+	1.10696i
$663$		0			0
$664$	23.2455	+	40.2624i	0.902102	+	1.56249i
$665$	6.57859	+	24.5516i	0.255107	+	0.952072i
$666$		0			0
$667$	0.442036	−	0.255209i	0.0171157	−	0.00988175i
$668$	1.79920	+	0.482095i	0.0696132	+	0.0186528i
$669$		0			0
$670$	−13.2934	+	13.2934i	−0.513568	+	0.513568i
$671$	−3.57390	+	0.957624i	−0.137969	+	0.0369687i
$672$		0			0
$673$			18.3367i			0.706829i	0.935467	+	0.353414i	$0.114979\pi$
$673$			18.3367i			0.706829i	−0.935467	+	0.353414i	$0.885021\pi$
$674$	−5.20904	+	1.39576i	−0.200645	+	0.0537626i
$675$		0			0
$676$	−6.71275	+	8.98820i	−0.258183	+	0.345700i
$677$	−16.0817	+	9.28475i	−0.618068	+	0.356842i	−0.776116	−	0.630590i	$-0.782813\pi$
$677$	−16.0817	+	9.28475i	−0.618068	+	0.356842i	0.158048	+	0.987431i	$0.449480\pi$
$678$		0			0
$679$	−1.40926	−	2.44091i	−0.0540824	−	0.0936734i
$680$	−1.00606			−0.0385807
$681$		0			0
$682$	−9.87215	+	2.64524i	−0.378024	+	0.101291i
$683$	−6.10105	+	22.7694i	−0.233450	+	0.871249i	0.745391	+	0.666628i	$0.232263\pi$
$683$	−6.10105	+	22.7694i	−0.233450	+	0.871249i	−0.978841	+	0.204621i	$0.934404\pi$
$684$		0			0
$685$	18.0858	+	31.3256i	0.691024	+	1.19689i
$686$	70.7759			2.70224
$687$		0			0
$688$	0.286875	+	0.165627i	0.0109370	+	0.00631448i
$689$	−9.10086	+	27.3950i	−0.346715	+	1.04367i
$690$		0			0
$691$	30.5011	+	30.5011i	1.16032	+	1.16032i	0.984406	+	0.175910i	$0.0562867\pi$
$691$	30.5011	+	30.5011i	1.16032	+	1.16032i	0.175910	+	0.984406i	$0.443713\pi$
$692$	−9.03080	−	5.21394i	−0.343300	−	0.198204i
$693$		0			0
$694$	7.48871	+	7.48871i	0.284268	+	0.284268i
$695$	−8.19604	−	30.5880i	−0.310893	−	1.16027i
$696$		0			0
$697$	−0.289967	−	1.08217i	−0.0109833	−	0.0409902i
$698$			25.3006i			0.957642i
$699$		0			0
$700$	−0.924328	+	0.924328i	−0.0349363	+	0.0349363i
$701$	16.2764			0.614753			0.307376	−	0.951588i	$-0.400549\pi$
$701$	16.2764			0.614753			0.307376	+	0.951588i	$0.400549\pi$
$702$		0			0
$703$	8.02116			0.302524
$704$	15.1654	−	15.1654i	0.571568	−	0.571568i
$705$		0			0
$706$		−	22.3923i		−	0.842744i
$707$	4.70565	+	17.5617i	0.176974	+	0.660477i
$708$		0			0
$709$	−1.26752	−	4.73044i	−0.0476026	−	0.177655i	0.938032	−	0.346550i	$-0.112647\pi$
$709$	−1.26752	−	4.73044i	−0.0476026	−	0.177655i	−0.985634	+	0.168895i	$0.945980\pi$
$710$	−12.6542	−	12.6542i	−0.474904	−	0.474904i
$711$		0			0
$712$	38.9848	+	22.5079i	1.46102	+	0.843519i
$713$	−2.08750	−	2.08750i	−0.0781774	−	0.0781774i
$714$		0			0
$715$	−16.9829	+	15.0904i	−0.635125	+	0.564348i
$716$	2.31083	+	1.33416i	0.0863599	+	0.0498599i
$717$		0			0
$718$	12.5485			0.468306
$719$	17.2570	+	29.8900i	0.643577	+	1.11471i	0.984628	+	0.174663i	$0.0558836\pi$
$719$	17.2570	+	29.8900i	0.643577	+	1.11471i	−0.341052	+	0.940045i	$0.610783\pi$
$720$		0			0
$721$	1.02431	−	3.82278i	0.0381473	−	0.142368i
$722$	14.8814	−	3.98746i	0.553828	−	0.148398i
$723$		0			0
$724$	−17.5944			−0.653890
$725$	−0.0884924	−	0.153273i	−0.00328653	−	0.00569243i
$726$		0			0
$727$	6.05240	−	3.49435i	0.224471	−	0.129598i	−0.383548	−	0.923521i	$-0.625298\pi$
$727$	6.05240	−	3.49435i	0.224471	−	0.129598i	0.608019	+	0.793923i	$0.291965\pi$
$728$	42.6099	−	37.8615i	1.57923	−	1.40324i
$729$		0			0
$730$	12.6246	−	3.38276i	0.467258	−	0.125201i
$731$		−	0.0310253i		−	0.00114751i
$732$		0			0
$733$	−22.0147	+	5.89883i	−0.813133	+	0.217878i	−0.641342	−	0.767255i	$-0.721622\pi$
$733$	−22.0147	+	5.89883i	−0.813133	+	0.217878i	−0.171791	+	0.985133i	$0.554955\pi$
$734$	−4.27568	+	4.27568i	−0.157818	+	0.157818i
$735$		0			0
$736$	3.64637	+	0.977042i	0.134407	+	0.0360142i
$737$	−18.1777	+	10.4949i	−0.669584	+	0.386585i
$738$		0			0
$739$	−3.70607	−	13.8313i	−0.136330	−	0.508791i	−0.999989	−	0.00471409i	$-0.998499\pi$
$739$	−3.70607	−	13.8313i	−0.136330	−	0.508791i	0.863659	−	0.504077i	$-0.168167\pi$
$740$	3.73181	+	6.46368i	0.137184	+	0.237610i
$741$		0			0
$742$	22.1055	−	38.2878i	0.811517	−	1.40559i
$743$	6.00805	+	1.60985i	0.220414	+	0.0590598i	0.367336	−	0.930088i	$-0.380270\pi$
$743$	6.00805	+	1.60985i	0.220414	+	0.0590598i	−0.146922	+	0.989148i	$0.546937\pi$
$744$		0			0
$745$	−26.3546	−	15.2158i	−0.965558	−	0.557465i
$746$	−20.2909	+	20.2909i	−0.742901	+	0.742901i
$747$		0			0
$748$	−0.327036	−	0.0876290i	−0.0119576	−	0.00320403i
$749$	−8.20004	+	30.6030i	−0.299623	+	1.11821i
$750$		0			0
$751$	−37.8087	+	21.8289i	−1.37966	+	0.796547i	−0.992118	−	0.125304i	$-0.960009\pi$
$751$	−37.8087	+	21.8289i	−1.37966	+	0.796547i	−0.387542	+	0.921852i	$0.626676\pi$
$752$	−4.17467	+	15.5801i	−0.152234	+	0.568146i
$753$		0			0
$754$	1.04241	+	2.07955i	0.0379623	+	0.0757328i
$755$			26.4539i			0.962757i
$756$		0			0
$757$	9.84349	−	17.0494i	0.357768	−	0.619672i	−0.629820	−	0.776741i	$-0.716871\pi$
$757$	9.84349	−	17.0494i	0.357768	−	0.619672i	0.987588	+	0.157069i	$0.0502046\pi$
$758$	−14.5596	+	25.2179i	−0.528827	+	0.915955i
$759$		0			0
$760$	−10.5955	−	10.5955i	−0.384338	−	0.384338i
$761$	−6.11282	−	6.11282i	−0.221590	−	0.221590i	0.587578	−	0.809168i	$-0.300082\pi$
$761$	−6.11282	−	6.11282i	−0.221590	−	0.221590i	−0.809168	+	0.587578i	$0.800082\pi$
$762$		0			0
$763$	−13.3417	+	23.1085i	−0.483002	+	0.836585i
$764$	4.08006	−	7.06686i	0.147611	−	0.255670i
$765$		0			0
$766$			17.8814i			0.646080i
$767$	−12.0311	−	24.0014i	−0.434418	−	0.866640i
$768$		0			0
$769$	−2.26984	+	8.47115i	−0.0818524	+	0.305477i	−0.994700	−	0.102824i	$-0.967212\pi$
$769$	−2.26984	+	8.47115i	−0.0818524	+	0.305477i	0.912847	+	0.408301i	$0.133879\pi$
$770$	30.1328	−	17.3972i	1.08591	−	0.626951i
$771$		0			0
$772$	−0.0886686	+	0.330916i	−0.00319125	+	0.0119099i
$773$	−3.74962	−	1.00471i	−0.134865	−	0.0361368i	0.190755	−	0.981638i	$-0.438906\pi$
$773$	−3.74962	−	1.00471i	−0.134865	−	0.0361368i	−0.325620	+	0.945501i	$0.605573\pi$
$774$		0			0
$775$	−0.723828	+	0.723828i	−0.0260007	+	0.0260007i
$776$	1.43896	+	0.830785i	0.0516558	+	0.0298235i
$777$		0			0
$778$	−1.16724	−	0.312761i	−0.0418475	−	0.0112130i
$779$	8.34321	−	14.4509i	0.298926	−	0.517756i
$780$		0			0
$781$	−9.99028	−	17.3037i	−0.357480	−	0.619174i
$782$	0.0333521	+	0.124472i	0.00119267	+	0.00445109i
$783$		0			0
$784$	−26.2485	+	15.1546i	−0.937448	+	0.541236i
$785$	20.8426	+	5.58475i	0.743904	+	0.199328i
$786$		0			0
$787$	3.03191	−	3.03191i	0.108076	−	0.108076i	−0.651001	−	0.759077i	$-0.725651\pi$
$787$	3.03191	−	3.03191i	0.108076	−	0.108076i	0.759077	+	0.651001i	$0.225651\pi$
$788$	2.29818	−	0.615796i	0.0818693	−	0.0219368i
$789$		0			0
$790$		−	7.97965i		−	0.283903i
$791$	−46.5710	+	12.4787i	−1.65587	+	0.443690i
$792$		0			0
$793$	3.64099	−	3.23524i	0.129295	−	0.114887i
$794$	17.1463	−	9.89944i	0.608501	−	0.351318i
$795$		0			0
$796$	6.71525	+	11.6311i	0.238016	+	0.412255i
$797$	−10.9142			−0.386603			−0.193301	−	0.981139i	$-0.561919\pi$
$797$	−10.9142			−0.386603			−0.193301	+	0.981139i	$0.561919\pi$
$798$		0			0
$799$	1.45923	−	0.390999i	0.0516238	−	0.0138326i
$800$	0.338784	−	1.26436i	0.0119778	−	0.0447018i
$801$		0			0
$802$	−9.28776	−	16.0869i	−0.327962	−	0.568047i
$803$	14.5926			0.514962
$804$		0			0
$805$	8.70387	+	5.02518i	0.306771	+	0.177114i
$806$	10.0575	−	8.93667i	0.354259	−	0.314781i
$807$		0			0
$808$	−7.57891	−	7.57891i	−0.266625	−	0.266625i
$809$	−24.7010	−	14.2611i	−0.868439	−	0.501394i	−0.00160994	−	0.999999i	$-0.500512\pi$
$809$	−24.7010	−	14.2611i	−0.868439	−	0.501394i	−0.866829	+	0.498605i	$0.833846\pi$
$810$		0			0
$811$	−14.4345	−	14.4345i	−0.506862	−	0.506862i	0.406700	−	0.913562i	$-0.366680\pi$
$811$	−14.4345	−	14.4345i	−0.506862	−	0.506862i	−0.913562	+	0.406700i	$0.866680\pi$
$812$	0.699785	+	2.61163i	0.0245576	+	0.0916503i
$813$		0			0
$814$	−2.84188	−	10.6060i	−0.0996078	−	0.371741i
$815$			34.2052i			1.19815i
$816$		0			0
$817$	0.326747	−	0.326747i	0.0114314	−	0.0114314i
$818$	33.0291			1.15484
$819$		0			0
$820$	15.5266			0.542211
$821$	−15.7089	+	15.7089i	−0.548243	+	0.548243i	−0.925932	−	0.377689i	$-0.876719\pi$
$821$	−15.7089	+	15.7089i	−0.548243	+	0.548243i	0.377689	+	0.925932i	$0.376719\pi$
$822$		0			0
$823$			56.1423i			1.95700i	0.206255	+	0.978498i	$0.433872\pi$
$823$			56.1423i			1.95700i	−0.206255	+	0.978498i	$0.566128\pi$
$824$	0.603851	+	2.25360i	0.0210361	+	0.0785080i
$825$		0			0
$826$	10.6422	+	39.7174i	0.370291	+	1.38195i
$827$	7.73555	+	7.73555i	0.268991	+	0.268991i	0.828694	−	0.559702i	$-0.189085\pi$
$827$	7.73555	+	7.73555i	0.268991	+	0.268991i	−0.559702	+	0.828694i	$0.689085\pi$
$828$		0			0
$829$	−22.3717	−	12.9163i	−0.777001	−	0.448602i	0.0583652	−	0.998295i	$-0.481411\pi$
$829$	−22.3717	−	12.9163i	−0.777001	−	0.448602i	−0.835366	+	0.549693i	$0.814745\pi$
$830$	−26.4164	−	26.4164i	−0.916926	−	0.916926i
$831$		0			0
$832$	−8.90100	+	26.7934i	−0.308587	+	0.928895i
$833$	2.45844	+	1.41938i	0.0851799	+	0.0491786i
$834$		0			0
$835$	−4.96577			−0.171847
$836$	−2.52134	−	4.36709i	−0.0872024	−	0.151039i
$837$		0			0
$838$	−5.92596	+	22.1160i	−0.204709	+	0.763984i
$839$	34.3643	−	9.20790i	1.18639	−	0.317892i	0.388931	−	0.921267i	$-0.372844\pi$
$839$	34.3643	−	9.20790i	1.18639	−	0.317892i	0.797458	+	0.603375i	$0.206178\pi$
$840$		0			0
$841$	28.6339			0.987377
$842$	−12.6504	−	21.9112i	−0.435962	−	0.755109i
$843$		0			0
$844$	6.89323	−	3.97981i	0.237275	−	0.136991i
$845$	11.0842	−	27.7773i	0.381307	−	0.955567i
$846$		0			0
$847$	−17.4986	+	4.68873i	−0.601259	+	0.161107i
$848$			12.2453i			0.420504i
$849$		0			0
$850$	0.0431598	−	0.0115646i	0.00148037	−	0.000396664i
$851$	2.24268	−	2.24268i	0.0768781	−	0.0768781i
$852$		0			0
$853$	−11.9527	−	3.20271i	−0.409252	−	0.109659i	0.0483186	−	0.998832i	$-0.484614\pi$
$853$	−11.9527	−	3.20271i	−0.409252	−	0.109659i	−0.457571	+	0.889173i	$0.651280\pi$
$854$	−6.46020	+	3.72980i	−0.221063	+	0.127631i
$855$		0			0
$856$	−4.83409	−	18.0411i	−0.165226	−	0.616630i
$857$	1.46053	+	2.52971i	0.0498907	+	0.0864132i	0.889892	−	0.456171i	$-0.150779\pi$
$857$	1.46053	+	2.52971i	0.0498907	+	0.0864132i	−0.840002	+	0.542584i	$0.817446\pi$
$858$		0			0
$859$	14.1298	−	24.4734i	0.482101	−	0.835023i	−0.517688	−	0.855569i	$-0.673207\pi$
$859$	14.1298	−	24.4734i	0.482101	−	0.835023i	0.999789	+	0.0205462i	$0.00654052\pi$
$860$	0.415320	+	0.111285i	0.0141623	+	0.00379477i
$861$		0			0
$862$	21.6116	+	12.4775i	0.736095	+	0.424985i
$863$	32.6894	−	32.6894i	1.11276	−	1.11276i	0.119986	−	0.992776i	$-0.461715\pi$
$863$	32.6894	−	32.6894i	1.11276	−	1.11276i	0.992776	−	0.119986i	$-0.0382850\pi$
$864$		0			0
$865$	26.8528	+	7.19519i	0.913023	+	0.244644i
$866$	−7.33222	+	27.3642i	−0.249159	+	0.929874i
$867$		0			0
$868$	13.5429	−	7.81903i	0.459678	−	0.265395i
$869$	2.30589	−	8.60569i	0.0782219	−	0.291928i
$870$		0			0
$871$	15.2011	−	23.0740i	0.515071	−	0.781831i
$872$		−	15.7304i		−	0.532699i
$873$		0			0
$874$	−0.959637	+	1.66214i	−0.0324602	+	0.0562227i
$875$	−28.0411	+	48.5686i	−0.947963	+	1.64192i
$876$		0			0
$877$	−39.9952	−	39.9952i	−1.35054	−	1.35054i	−0.885055	−	0.465486i	$-0.845880\pi$
$877$	−39.9952	−	39.9952i	−1.35054	−	1.35054i	−0.465486	−	0.885055i	$-0.654120\pi$
$878$	0.321943	+	0.321943i	0.0108651	+	0.0108651i
$879$		0			0
$880$	−4.81856	+	8.34599i	−0.162434	+	0.281343i
$881$	14.1084	−	24.4364i	0.475323	−	0.823284i	−0.524278	−	0.851547i	$-0.675665\pi$
$881$	14.1084	−	24.4364i	0.475323	−	0.823284i	0.999600	+	0.0282639i	$0.00899789\pi$
$882$		0			0
$883$			7.20265i			0.242388i	0.992629	+	0.121194i	$0.0386724\pi$
$883$			7.20265i			0.242388i	−0.992629	+	0.121194i	$0.961328\pi$
$884$	0.436560	−	0.0897963i	0.0146831	−	0.00302018i
$885$		0			0
$886$	−3.16327	+	11.8055i	−0.106272	+	0.396613i
$887$	27.3550	−	15.7934i	0.918490	−	0.530291i	0.0353373	−	0.999375i	$-0.488749\pi$
$887$	27.3550	−	15.7934i	0.918490	−	0.530291i	0.883153	+	0.469085i	$0.155416\pi$
$888$		0			0
$889$	0.480478	−	1.79317i	0.0161147	−	0.0601410i
$890$	−34.9404	−	9.36224i	−1.17120	−	0.313823i
$891$		0			0
$892$	−1.17998	+	1.17998i	−0.0395087	+	0.0395087i
$893$	19.4859	+	11.2502i	0.652071	+	0.376473i
$894$		0			0
$895$	−6.87119	−	1.84113i	−0.229678	−	0.0615421i
$896$	−1.55271	+	2.68937i	−0.0518724	+	0.0898456i
$897$		0			0
$898$	3.43923	+	5.95692i	0.114769	+	0.198785i
$899$	0.547991	+	2.04513i	0.0182765	+	0.0682090i
$900$		0			0
$901$	0.993237	−	0.573446i	0.0330895	−	0.0191042i
$902$	−22.0637	−	5.91196i	−0.734642	−	0.196847i
$903$		0			0
$904$	20.0981	−	20.0981i	0.668453	−	0.668453i
$905$	45.3072	−	12.1400i	1.50606	−	0.403549i
$906$		0			0
$907$		−	22.6161i		−	0.750954i	−0.926832	−	0.375477i	$-0.877479\pi$
$907$		−	22.6161i		−	0.750954i	0.926832	−	0.375477i	$-0.122521\pi$
$908$	15.9804	−	4.28192i	0.530327	−	0.142101i
$909$		0			0
$910$	−25.1986	+	38.2492i	−0.835326	+	1.26795i
$911$	20.2816	−	11.7096i	0.671958	−	0.387955i	−0.124860	−	0.992174i	$-0.539848\pi$
$911$	20.2816	−	11.7096i	0.671958	−	0.387955i	0.796818	+	0.604219i	$0.206515\pi$
$912$		0			0
$913$	−20.8553	−	36.1224i	−0.690209	−	1.19548i
$914$	11.5909			0.383391
$915$		0			0
$916$	−15.7555	+	4.22167i	−0.520576	+	0.139488i
$917$	15.6574	−	58.4342i	0.517053	−	1.92967i
$918$		0			0
$919$	13.0969	+	22.6845i	0.432027	+	0.748293i	0.997048	−	0.0767835i	$-0.0244650\pi$
$919$	13.0969	+	22.6845i	0.432027	+	0.748293i	−0.565020	+	0.825077i	$0.691132\pi$
$920$	−5.92489			−0.195338
$921$		0			0
$922$	15.7012	+	9.06506i	0.517090	+	0.298542i
$923$	21.9645	+	14.4702i	0.722971	+	0.476294i
$924$		0			0
$925$	−0.777637	−	0.777637i	−0.0255685	−	0.0255685i
$926$	−35.8253	−	20.6837i	−1.17729	−	0.679710i
$927$		0			0
$928$	−1.91442	−	1.91442i	−0.0628440	−	0.0628440i
$929$	−2.52294	−	9.41573i	−0.0827749	−	0.308920i	0.912109	−	0.409949i	$-0.134453\pi$
$929$	−2.52294	−	9.41573i	−0.0827749	−	0.308920i	−0.994884	+	0.101028i	$0.967787\pi$
$930$		0			0
$931$	10.9430	+	40.8397i	0.358642	+	1.33847i
$932$			12.9521i			0.424259i
$933$		0			0
$934$	28.4442	−	28.4442i	0.930722	−	0.930722i
$935$	0.902613			0.0295186
$936$		0			0
$937$	38.7284			1.26520			0.632601	−	0.774478i	$-0.281987\pi$
$937$	38.7284			1.26520			0.632601	+	0.774478i	$0.281987\pi$
$938$	−29.9233	+	29.9233i	−0.977031	+	0.977031i
$939$		0			0
$940$			20.9364i			0.682871i
$941$	−13.5986	−	50.7507i	−0.443302	−	1.65442i	−0.720382	−	0.693578i	$-0.756033\pi$
$941$	−13.5986	−	50.7507i	−0.443302	−	1.65442i	0.277080	−	0.960847i	$-0.410633\pi$
$942$		0			0
$943$	−1.70767	−	6.37312i	−0.0556094	−	0.207537i
$944$	−8.05305	−	8.05305i	−0.262104	−	0.262104i
$945$		0			0
$946$	−0.547809	−	0.316278i	−0.0178108	−	0.0102831i
$947$	−33.3193	−	33.3193i	−1.08273	−	1.08273i	−0.996254	−	0.0864783i	$-0.972439\pi$
$947$	−33.3193	−	33.3193i	−1.08273	−	1.08273i	−0.0864783	−	0.996254i	$-0.527561\pi$
$948$		0			0
$949$	−17.1731	+	8.60830i	−0.557462	+	0.279437i
$950$	0.576337	+	0.332749i	0.0186989	+	0.0107958i
$951$		0			0
$952$	−2.26464			−0.0733974
$953$	24.8010	+	42.9566i	0.803383	+	1.39150i	0.917377	+	0.398019i	$0.130302\pi$
$953$	24.8010	+	42.9566i	0.803383	+	1.39150i	−0.113994	+	0.993481i	$0.536364\pi$
$954$		0			0
$955$	−5.63044	+	21.0131i	−0.182197	+	0.679968i
$956$	5.73818	−	1.53754i	0.185586	−	0.0497276i
$957$		0			0
$958$	−22.2651			−0.719354
$959$	40.7111	+	70.5137i	1.31463	+	2.27701i
$960$		0			0
$961$	−16.2415	+	9.37703i	−0.523919	+	0.302485i
$962$	9.60101	+	10.8051i	0.309549	+	0.348371i
$963$		0			0
$964$	−0.850249	+	0.227824i	−0.0273847	+	0.00733770i
$965$		−	0.913321i		−	0.0294009i
$966$		0			0
$967$	57.2307	−	15.3349i	1.84042	−	0.493138i	0.841525	−	0.540218i	$-0.181658\pi$
$967$	57.2307	−	15.3349i	1.84042	−	0.493138i	0.998891	+	0.0470805i	$0.0149917\pi$
$968$	7.55166	−	7.55166i	0.242720	−	0.242720i
$969$		0			0
$970$	−1.28968	−	0.345568i	−0.0414091	−	0.0110955i
$971$	−19.4119	+	11.2075i	−0.622957	+	0.359665i	−0.778019	−	0.628240i	$-0.783776\pi$
$971$	−19.4119	+	11.2075i	−0.622957	+	0.359665i	0.155062	+	0.987905i	$0.450442\pi$
$972$		0			0
$973$	−18.4492	−	68.8535i	−0.591455	−	2.20734i
$974$	−9.47425	−	16.4099i	−0.303575	−	0.525807i
$975$		0			0
$976$	1.03306	−	1.78931i	0.0330673	−	0.0572743i
$977$	14.9916	+	4.01699i	0.479624	+	0.128515i	0.490528	−	0.871426i	$-0.336804\pi$
$977$	14.9916	+	4.01699i	0.479624	+	0.128515i	−0.0109035	+	0.999941i	$0.503471\pi$
$978$		0			0
$979$	−34.9762	−	20.1935i	−1.11784	−	0.645387i
$980$	−27.8187	+	27.8187i	−0.888635	+	0.888635i
$981$		0			0
$982$	−15.0296	−	4.02716i	−0.479613	−	0.128512i
$983$	−0.650655	+	2.42828i	−0.0207527	+	0.0774500i	−0.975526	−	0.219886i	$-0.929431\pi$
$983$	−0.650655	+	2.42828i	−0.0207527	+	0.0774500i	0.954773	+	0.297336i	$0.0960981\pi$
$984$		0			0
$985$	−5.49315	+	3.17147i	−0.175026	+	0.101051i
$986$	0.0239199	−	0.0892702i	0.000761764	−	0.00284294i
$987$		0			0
$988$	5.54339	+	3.65199i	0.176359	+	0.116185i
$989$		−	0.182714i		−	0.00580997i
$990$		0			0
$991$	15.2437	−	26.4028i	0.484231	−	0.838713i	−0.515605	−	0.856826i	$-0.672433\pi$
$991$	15.2437	−	26.4028i	0.484231	−	0.838713i	0.999836	+	0.0181139i	$0.00576614\pi$
$992$	−7.82956	+	13.5612i	−0.248589	+	0.430569i
$993$		0			0
$994$	−28.4845	−	28.4845i	−0.903475	−	0.903475i
$995$	−25.3179	−	25.3179i	−0.802630	−	0.802630i
$996$		0			0
$997$	3.99304	−	6.91615i	0.126461	−	0.219037i	−0.795842	−	0.605504i	$-0.792972\pi$
$997$	3.99304	−	6.91615i	0.126461	−	0.219037i	0.922303	+	0.386467i	$0.126305\pi$
$998$	6.37866	−	11.0482i	0.201913	−	0.349723i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.ba.a.98.8		48
3.2	odd	2		117.2.x.a.59.5	yes	48
9.2	odd	6		351.2.bf.a.332.8		48
9.7	even	3		117.2.bc.a.20.5	yes	48
13.2	odd	12		351.2.bf.a.314.8		48
39.2	even	12		117.2.bc.a.41.5	yes	48
117.2	even	12	inner	351.2.ba.a.197.8		48
117.106	odd	12		117.2.x.a.2.5	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.2.5	✓	48	117.106	odd	12
117.2.x.a.59.5	yes	48	3.2	odd	2
117.2.bc.a.20.5	yes	48	9.7	even	3
117.2.bc.a.41.5	yes	48	39.2	even	12
351.2.ba.a.98.8		48	1.1	even	1	trivial
351.2.ba.a.197.8		48	117.2	even	12	inner
351.2.bf.a.314.8		48	13.2	odd	12
351.2.bf.a.332.8		48	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.ba (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.754009 - 0.754009i) q^{2} +0.862941i q^{4} +(-0.595426 - 2.22216i) q^{5} +(-1.34030 - 5.00206i) q^{7} +(2.15868 + 2.15868i) q^{8} +(-2.12448 - 1.22657i) q^{10} +(-1.93671 - 1.93671i) q^{11} +(3.42168 + 1.13671i) q^{13} +(-4.78220 - 2.76100i) q^{14} +1.52945 q^{16} +(-0.0716242 - 0.124057i) q^{17} +(0.552200 - 2.06084i) q^{19} +(1.91759 - 0.513817i) q^{20} -2.92060 q^{22} +(-0.421808 - 0.730594i) q^{23} +(-0.253329 + 0.146260i) q^{25} +(3.43707 - 1.72289i) q^{26} +(4.31649 - 1.15660i) q^{28} +0.605036i q^{29} +(3.38018 - 0.905716i) q^{31} +(-3.16415 + 3.16415i) q^{32} +(-0.147545 - 0.0395346i) q^{34} +(-10.3173 + 5.95671i) q^{35} +(0.973046 + 3.63146i) q^{37} +(-1.13753 - 1.97025i) q^{38} +(3.51160 - 6.08227i) q^{40} +(7.55452 + 2.02423i) q^{41} +(0.187567 + 0.108292i) q^{43} +(1.67127 - 1.67127i) q^{44} +(-0.868921 - 0.232827i) q^{46} +(-2.72952 + 10.1867i) q^{47} +(-17.1621 + 9.90853i) q^{49} +(-0.0807314 + 0.301294i) q^{50} +(-0.980914 + 2.95271i) q^{52} +8.00631i q^{53} +(-3.15052 + 5.45686i) q^{55} +(7.90459 - 13.6912i) q^{56} +(0.456203 + 0.456203i) q^{58} +(-5.26532 - 5.26532i) q^{59} +(0.675442 - 1.16990i) q^{61} +(1.86577 - 3.23160i) q^{62} +7.83049i q^{64} +(0.488596 - 8.28034i) q^{65} +(1.98346 - 7.40238i) q^{67} +(0.107054 - 0.0618075i) q^{68} +(-3.28794 + 12.2708i) q^{70} +(7.04646 + 1.88809i) q^{71} +(-3.76736 + 3.76736i) q^{73} +(3.47184 + 2.00447i) q^{74} +(1.77838 + 0.476516i) q^{76} +(-7.09179 + 12.2833i) q^{77} +(1.62641 + 2.81703i) q^{79} +(-0.910674 - 3.39868i) q^{80} +(7.22246 - 4.16989i) q^{82} +(14.7099 + 3.94150i) q^{83} +(-0.233027 + 0.233027i) q^{85} +(0.223081 - 0.0597743i) q^{86} -8.36151i q^{88} +(14.2431 - 3.81643i) q^{89} +(1.09983 - 18.6390i) q^{91} +(0.630459 - 0.363996i) q^{92} +(5.62279 + 9.73895i) q^{94} -4.90830 q^{95} +(0.525725 - 0.140868i) q^{97} +(-5.46924 + 20.4115i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{2} + 6 q^{5} - 4 q^{7} - 30 q^{8} - 12 q^{10} + 6 q^{11} - 2 q^{13} + 12 q^{14} - 28 q^{16} - 4 q^{19} + 18 q^{20} - 4 q^{22} + 6 q^{23} + 48 q^{26} - 18 q^{31} - 54 q^{32} + 6 q^{34} - 6 q^{35}+ \cdots - 36 q^{98}+O(q^{100}) \) 48 * q + 6 * q^2 + 6 * q^5 - 4 * q^7 - 30 * q^8 - 12 * q^10 + 6 * q^11 - 2 * q^13 + 12 * q^14 - 28 * q^16 - 4 * q^19 + 18 * q^20 - 4 * q^22 + 6 * q^23 + 48 * q^26 - 18 * q^31 - 54 * q^32 + 6 * q^34 - 6 * q^35 - 6 * q^37 - 36 * q^38 - 12 * q^40 - 18 * q^41 - 30 * q^43 - 12 * q^44 - 12 * q^46 + 36 * q^47 - 6 * q^49 + 60 * q^50 + 56 * q^52 - 4 * q^55 + 6 * q^56 + 50 * q^58 + 6 * q^59 + 2 * q^61 - 18 * q^62 - 72 * q^65 + 26 * q^67 - 42 * q^68 - 16 * q^70 + 48 * q^71 - 22 * q^73 - 30 * q^74 + 6 * q^76 - 72 * q^77 + 8 * q^79 + 54 * q^80 - 12 * q^82 - 54 * q^83 - 24 * q^85 + 54 * q^86 - 16 * q^91 - 120 * q^92 + 26 * q^94 + 12 * q^95 - 24 * q^97 - 36 * q^98

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